diff --git a/-gRXU-O1FY4.txt b/-gRXU-O1FY4.txt new file mode 100644 index 0000000000000000000000000000000000000000..14ace8784c6b24e109c8e5485b937303d210024f --- /dev/null +++ b/-gRXU-O1FY4.txt @@ -0,0 +1,2398 @@ +Before I begin today, +I thought I would take the + +first five minutes and show you +some fun stuff I have been + +hacking on for the past three +years. + +This has to do with 6.002 and +circuits and all that stuff, + +but this is completely +optional, this is for fun, + +this is to go build your +intuition, this is to check your + +answers, whatever you want. +This is not a required part of + +the course. +Just for fun. + +There is this URL out here that +I put down here. + +I have been hacking on this +system for the past three years, + +and for the first time this +year and very tentatively and + +gingerly introducing it to +students. + +The idea here is that it is a, +that is kind of defocused. + +Any chance of focusing that a +little bit better? + +The idea of this is that it is +a Web-based interactive + +simulation package that I have +pulled together. + +And what you can do is you can +pull up a bunch of circuits. + +Notice that the URL is up here. +It is + +euryale.lcs.mit.edu/websim. +And there is the pointer to it. + +So you have a bunch of fun +things you can play with. + +And we have gone through all of +these things in lecture. + +Let's pick the MOSFET +amplifier. + +You come to this page. +This is something you have seen + +in class. +And let's play with this little + +circuit. +And you see the mouse? + +Good. +You can set up a bunch of + +parameters. +You can set up the MOSFET + +parameters VT and K. +You can set up the value of R + +for your resistor, +you can establish a bias + +voltage, and you can have an +input voltage vIN. + +So you can apply a bunch of +input voltages. + +You can apply a zero input, +unit in pulse, + +unit step, sine wave, +square waves. + +Or this was the part that took +me the longest to get right. + +You can also input a bunch of +music. + +And so far I just have two +clips, so you are going to get + +bored listening to them. +Good. + +So you can also input music. +And what you can do is you can + +watch the waveforms, +you can listen to the output + +and do a bunch of fun stuff. +One experiment I would love for + +you guys to try out. +Again, remember, + +this is completely optional. +Just for fun. + +You can apply some input. +Step input, for example, + +to an RLC circuit and spend 30 +seconds thinking about what + +should the output look like. +I divine that the output should + +look like this and then do this +and see if what you thought was + +correct. +And it's fun to kind of play + +around with it. +Let me start with, + +just as an example, +let's say I input classical + +music. +And let us say I would like to + +listen to the output here that +is the voltage at the drain + +terminal of the MOSFET. +For listening it sets up a + +default timeframe to listen to, +so you go ahead and do it. + +This shows you the time domain +waveform of a clip of the music + +and then you can listen to it. +Lot's of distortion, + +right? +As you can see, + +there is a bunch of distortion. +And that is as you expect + +because the peak-to-peak voltage +is 1 volt, the bias is 2.5, + +and so this is clipping at the +lower end, plus the MOSFET is + +nonlinear. +You can play around with a + +bunch of things and you can have +a lot of fun. + +And the reason I created this +is that MIT is putting a bunch + +of its courses on the Web. +And one of the hottest things + +about courses like this is the +lab component. + +If you are beaming a course to, +say, a Third World country or + +something, how do you get people +to set up the massive lab + +infrastructure? +I know you hate your + +oscilloscopes, +I know you hate your wires, + +I know you hate the clips, +but the fact is you have them. + +I know a lot of places those +are way too expensive to pull + +together, which is why I have +been creating this Web-based + +kind of interactive laboratory +so that people can learn this + +stuff over the Web. +Let's go do another example + +very quickly. +Let's say you learned about, + +well, let's do RC circuits. +Here is the parallel RC + +circuit. +And you can set up capacitor + +values, resistor values, +you can set up input. + +Here, let me look at the time +domain waveform for the voltage + +across the capacitor. +And this time around let me + +play a unit step. +And let's see what the output + +is going to look like. +You can think in your minds + +what should the output look +like, and then you can go and + +plot it. +There you go. + +That's what the output looks +like. + +So you can play around with it +and have fun. + +That's all the good news. +The bad news is that so far I + +just have one Pentium III +machine behind us. + +It is a Linux box, +so don't all of you try it at + +once. +However, what I have also done, + +and that took me another six +months of hacking in the small + +amount of time professors have +to hack on stuff, + +I've hacked an incredibly +elaborate cashing system so that + +once anyone in class tries out +some combination of parameters + +it goes and squirrels away all +the outputs. + +If anybody else types in the +same sets of parameters it will + +just get all the output and play +it back to you. + +So if enough of you play with +over time, we may end up cashing + +all the important waveforms and +music clips and all of that + +stuff. +I have allocated a few + +gigabytes of storage, +so I am hoping that it may + +work. +Go forth. + +Play with it. +And this is completely my + +fault, so if there are any bugs +or anything simply email them to + +me. +This is the first time this is + +coming alive so bear with it. +Now let me switch back to the + +scheduled presentation for +today. + +All right, hope and pray that +this works. + +Yes. +Good. + +I am going to do today's +lecture using view graphs. + +And the reason I am going to do +that and not do my usual + +blackboard presentation which I +way, way, way prefer to a view + +graph presentation. +The only reason I am going to + +do this for today, +and maybe one more lecture, + +is that there is just a huge +amount of math grunge in this + +lecture. +What I want to do is kind of + +blast through that, +but you will have it all in the + +notes that you have, +so that you don't waste time in + +class as you watch me stumbling +over twiddles and tildes and all + +that stuff. +The key thing here is that the + +insight is actually very simple. +The beginning and the end are + +connected very tightly and very +simple. + +There is a bunch of math grunge +in the middle that we are going + +to work through and, +again, follows a complete old + +established pattern. +So, in that sense, + +there is really nothing +dramatically new in there. + +Let me spend the next five +minutes reviewing for you how we + +got here, what have we covered +so far and set up the + +presentation. +The first ten view graphs I am + +going to blast through and just +tell you where we are in terms + +of LC and RLC circuits. +I began by showing you this + +little demo, two inverters, +one driving. + +I can model the inductance here +with a little inductor, + +the capacitor of the gate here. +And recall that when I wanted + +to speed this up by introducing +a 50 ohm smaller resistance, + +I got some really strange +behavior. + +Just to remind you, +for Tuesday's lecture it would + +help if you quickly reviewed the +appendix on complex algebra in + +the course notes. +Remember all the real and + +imaginary j and omega stuff? +It would be good to very + +quickly skim through that. +It is a couple of pages. + +Remember this demo? +And the relevant circuit that + +is of interest to us is this one +here. + +It is the resistor, +there is the inductor and there + +is a capacitor. +This is Page 3. + +I am just going to blast +through the first ten view + +graphs. +It is all old stuff. + +Then we observed the following +output. + +We applied this input at VA and +we got this output, + +a very slowly rising waveform +because of the RC transient. + +And because of that you saw a +delay. + +Notice that this delay was +because of the slowly rising + +transient. +This waveform took some time to + +hit the threshold of the +neighboring transistor. + +So we say ah-ha, +let's try to speed this sucker + +up by reducing the resistance in +the collector of the first + +inverter. +And so I had this input. + +Now, to my surprise, +instead of seeing a nice little + +much higher and much faster +transitioning circuit, + +well, I did see a much faster +transitioning circuit but I got + +all this strange behavior on the +output that I was interested in. + +And because of that, +if these excursions were low + +enough, I could actually trigger +the output and get a whole bunch + +of false ones here because of +these negative excursions which + +should not really be there. +That was kind of strange. + +In the last lecture we said +let's take this one step at a + +time. +Let's not jump into an RLC + +circuit. +Let's go step by step. + +Let's start with an LC, +understand the behavior. + +We started off with an LC +circuit of this sort, + +and using the node equation we +showed that this was the + +equation that governed the +behavior of the circuit. + +And then we said that for a +step input and for zero initial + +conditions, that is the zero +state response, + +let's find out what the output, +the voltage across the + +capacitor looks like. +And so we obtained the total + +solution to be this. +And there was a sinusoidal term + +in there. +And the omega nought which was + +one by square root of LC. +And this was the circuit. + +And so for this step input +notice that the output looked + +like this. +So far an input step I had an + +output that went like this. +Notice that it is indeed + +possible for the output voltage +to actually go above the input + +value VI. +This is kind of non-intuitive + +but this can happen. +So this waveform jumps up and + +down. +But the steady state value, + +on average if you will, +is VI. + +On the other hand, +it does have sinusoidal + +excursions and this kind of goes +on because there is nothing to + +dissipate the energy inside that +circuit. + +By the way, the fact that the +capacitor voltage shoots above + +the input voltage is actually a +very important property. + +We won't dwell on it in 6.002, +but just squirrel that away in + +your brain somewhere. +I promise you that some time in + +your life you will have to +create a little design somewhere + +that will need a higher voltage +than your DC input. + +And you can use this primitive +fact to actually produce a DC + +voltage higher than you are +given, and then use that + +somehow. +In fact, there is a whole + +research area of what are called +DC to DC converters, + +voltage converters. +Let's say you have 1.5 volt + +battery, a AA battery, +but let's say a circuit needs + +1.8 volts. +The Pentium IIIs, + +for example, +needed 1.8 volts. + +And the strong arm is another +chip that required 1.8 volts a + +few years ago, +but the AA cell was 1.5 volts. + +How do get 1.8 from 1.5? +Well, you have to step it up + +somehow. +And this basic principle where + +the voltage can jump up above +the input is actually used, + +of course with additional +circuitry, to kind of get higher + +voltages. +It is a really key point that + +you can squirrel away. +This was pretty much where we + +got to in the last lecture. +This starts off the material + +for today. +What we are going to do is take + +that same circuit, +but instead we are going to put + +in this little resistor here. +This is what we set out to + +analyze. +And for details you can read + +the course notes Section 13.6. +The green curve here was the + +behavior of the LC circuit. +And what we are going to show + +today is that the moment we +introduce R this sinusoid here + +gets damp. +It kind of loses energy. + +And I am going to show you that +the behavior is going to look + +like this. +By introducing R this guy + +doesn't keep oscillating +forever. + +Rather it begins to oscillate +and then kind of loses energy + +and kind of gets tired and +settles down at VI. + +And remember the demo. +This is exactly what you saw in + +the demo. +You had a step input and you + +had this funny behavior. +And for the RLC that is exactly + +what it was. +So today's lecture will close + +the loop on what you saw in the +demo and the weird behavior, + +and I am going to show you the +mathematics foundations for that + +today. +Let's go ahead and analyze the + +RLC circuit. +I purposely created the entire + +presentation to follow as +closely as possible both the + +discussion of the RC networks +and the LC networks so that the + +math is all the same. +Exactly the same steps in the + +mathematics are in the +exposition of the analysis. + +What's different are the +results because the circuit is + +different. +So don't get bogged down or + +whatever in the mathematics. +Just remember it is the same + +set of steps that you are going +to be applying. + +We start by writing down the +element rules for our elements. + +Nothing new here. +For the inductor V is Ldi/dt. + +The integral form which is +simply 1/L integral vLdt=i. + +We saw this the last time. +And for the capacitor, + +the current through the +capacitor is simply Cdv/dt. + +Those are the two element rules +for the capacitor and inductor. + +The element rule for the +resistor, of course, + +is V=iR. +You know that. + +And for the voltage source we +know that, too, + +the voltage is a constant. +Just follow the same + +established pattern. +By the way, just so you are + +aware, I have booby trapped the +presentation a little bit to + +prevent you from falling asleep. +You see the dash lines here? + +Whenever you see a dash line, +that stuff needs to be copied + +down. +Don't trip over that. + +Don't say I didn't warn you. +We start by using the usual + +node method. +And I have two nodes in this + +case. +Unlike the LC circuits, + +I have two unknown nodes. +One is this node here with the + +node voltage vA and the second +node is the node with voltage + +vT. +Let me start with vA and write + +the node equation for that. +It is simply 1/L, + +the node equation for this is +the current going in this + +direction with is vI-vA integral +and that equals the current + +going this way which is vA-v/R, +node equation. + +I then write the node equation +for the node v, + +for this node here, +and that is simply + +(vA-v)/R=Cdvdt. +And that is what I have here, + +two node equations. +Let me summarize the results + +for you and then show you a view +graph where I grind through the + +math as to how I got the result. +Here is the result I am going + +to get. +If I take these two node + +equations and I massage some of +the mathematics, + +I am going to get this result. +And I will show you that in a + +second. +By grinding through some math + +and solving these two equations +and expressing this in terms of + +v, I get a second order +differential equation, + +d^2v blah, blah, +blah. + +Notice that this is different +from the LC in this term. + +Every step of the way you can +check to see if I am lying or I + +am correct. +I will indulge you, + +indulge myself rather with a +little story here. + +Richard Fineman was a known +smart guy. + +And one of the reasons that he +was that was in the middle of + +talks he was known to get up and +ask some of the darndest, + +hardest questions and say +ah-ha, you have a bug in this + +proof here or a bug in this +equation that is not right. + +And usually he would be +correct. + +So his trick in doing this and +which is one reason how he + +became a known smart guy. +What he would do is, + +as the speaker went on talking +he would kind of follow along + +and think of a simple initial +primitive case. + +In this case, +I have an RLC circuit. + +So think of a simpler case of +this. + +A simpler case of this is R=0. +Whenever you set R to be zero, + +you should get exactly what we +got in the last lecture, + +correct? +That is what Fineman would do. + +He would boil this down to a +simpler case, + +make some assumptions and just +follow along. + +And whenever he found a +discrepancy between the math + +here and his simple case he +would say oh, + +there is a bug there. +If you want you can catch me + +that way. +Here, what Fineman would do is + +replace R being zero, +and notice then this equation + +here is exactly what we got the +last time with R being zero. + +Just remember that Fineman +trick. + +This is the equation we get, +the second-order differential + +equation with an R term in +there. + +And let me just grind through +the math and show you how I got + +this from this. +So the two node equations + +again. +And what I do is I start by + +taking these two equations and +differentiating this with + +respect to t and this is what I +get. + +And, at the same time, +I have replaced (vA-v)/R here + +by this term. +I replace this with this and + +differentiate. +Then I simply divide the whole + +thing by C. +Then I take this expression + +here and write down vA is equal +to this stuff here. + +Next I am going to substitute +this back for vA and eliminate + +vA. +So I take this vA, + +stick the sucker in here, +and thereby eliminate vA and + +get this. +And then I simplify it and here + +is what I get. +That is what I get. + +I just grind through the two +equations and get that result. + +So like a stuck record I will +repeat our mantra here, + +which is here is how we solve +the equations that we run across + +in this course, +the same three steps. + +Find the particular solution. +Find the homogenous solution. + +Find the total solution and +then find the constants using + +the initial conditions. +Same steps. + +You could recite this in your +sleep. + +And the homogenous solution is +obtained using a further four + +steps. +Let's just go through and apply + +this method to our equation and +get the results. + +vP is a particular solution and +vH is the homogenous solution. + +With a particular solution, +oh. + +Before I go on to do that, +let me set up my inputs and my + +state variables. +My input is going to be a step. + +Remember, I am trying to take +you to the point where the demo + +left off. +The demo had a step input, + +so I am going to use a step +input rising to vI. + +And I am going to with the +initial conditions being all + +zeros. +So the capacitor voltage is + +zero, inductor current, +another state variable is also + +zero, and therefore this is also +fondly called the ZSR or the + +zero state response because +there is only an input but zero + +state. +Again, remember the dashed + +lines here. +Don't say I didn't warn you. + +Let's start with a particular +solution. + +This is as simple as it gets. +I simply write down the + +particular equation and stick my +specific input. + +And remember the solution to +the particular equation is any + +old solution, +it doesn't have to be a general + +solution, any old solution that +satisfies it. + +And I am going to find a simple +solution here. + +And V particular is a constant +VI. + +It works. +Because remember this has been + +working all along. +And I am going to keep pushing + +this and see if this works until +the end of the course. + +Guess what? +It will. + +So this is a solution. +I'm done. + +That is my particular solution. +Simple. + +Second, I go and do my +homogenous solution. + +And the homogenous equation, +remember, is the same old + +differential equation with the +drive set to zero. + +Remember that sometimes this +equation with the drive set to + +zero is the entire equation you +have to deal with in situations + +where you have zero input, +for example. + +Or in other situations in which +you have an impulse at the + +input. +And the impulse simply sets up + +the initial conditions like a +charge in the capacitor or + +something like that. +So we are going to blast + +through this four-step method. +The method simply says that + +four steps, I am going to assume +a solution of the form Ae^st. + +And if you think you've seen +that before, yes, + +you have seen it many times +before. + +And you will see it again, +again and again. + +And we need to find A and s. +We want to form the + +characteristic equation, +find the roots of the equation + +and then write down the general +solution to the homogenous + +equation as this. +Same old same old. + +Let me just walk through the +steps here. + +Step A, assume a solution to +the form Ae^st. + +And so I substitute Ae^st as my +tentative solution to the + +equation. +Again, let me remind you that + +the differential equations that +we solve here are really easy + +because the way you solve them +is you begin by assuming you + +know the solution and stick it +in and find out what makes it + +work. +I am going to stick Ae^st into + +this differential equation, +and A comes out here. + +Differentiate this d squared, +I get s squared down here, + +A s here and this simply gets +stuck down here with the 1/LC + +coefficient. +The next step I begin + +eliminating what I can, +so I eliminate the A's, + +then eliminate the e^st's, +and I end up with this equation + +here. +I end up with this equation. + +This is my characteristic +equation. + +It is an equation in s. +Do people remember the + +characteristic equation we got +for the LC circuit? + +Remember the Fineman trick? +That's right, + +LC. +S^2+1/LC=0. + +This thing wasn't there. +All you do is simply follow the + +R. +Just follow the R. + +Just imagine this is a dollar +sign and kind of follow it. + +And you will see what the +differences are between the LC + +and the RLC. +So this is the characteristic + +equation. +What I am going to do, + +iss much as I wrote the +characteristic equation for the + +LC circuit, by substituting +omega nought squared for 1/LC. + +Let me do the same thing here +but introduce something for R + +and L as well. +What I will do is let me give + +you this canonic form. +The very first second-order + +equation I learned about when I +was a kid was this one, + +S^2+2AS+B^2 or something like +that. + +Let me write it in that form +where I get 2 alpha s plus omega + +nought squared. +Again, remember the alpha comes + +about because of R. +So omega nought squared is 1/LC + +and alpha is RL/2. +Omega nought squared is 1/LC + +and R/L is equal to two alpha. +I am just writing this in a + +simpler form so that from now on +going forward I am just going to + +deal with alphas and omega +noughts. + +Once I get to this +characteristic equation, + +after that I can give you one +generic way of solving it. + +And depending on the kind of +circuit you have, + +a series RLC, +which is what we have, + +or a parallel RLC we will +simply get different + +coefficients for the alpha term. +This is going to stay the same + +but this term will look +different, alpha is going to + +look different. +There is a real pattern here. + +And what I am doing is simply +focusing on what is important, + +what the differences are +between the pattern. + +You learned the LC situation +and the RLC situation. + +Given this I can now write +down, I am just simply replacing + +this as my characteristic +equation in dealing with alphas + +and omegas. +I will give you a physical + +significance of alpha in a +little bit. + +Do you remember the physical +significance of omega nought? + +That was the oscillation +frequency. + +In other words, +given an inductor and + +capacitor, you put some charge +on the capacitor and you watch + +it, it will oscillate. +And its oscillation frequency + +will be one by a square root of +LC. + +The magnitude of the initial +conditions will determine how + +high are the oscillations or +what the phase is in terms of + +when it starts, +but the frequency is going to + +be the same. +Step three, to solve the + +homogenous equation, +is find the roots of the + +equation, s1 and s2, +and here are my roots. + +Good old roots for a +second-order, + +little s squared equation here. +Finally, given that I have the + +roots, I can write down the +general homogenous solution. + +So general solution is simply +A1e^s1t, A2e^s2t. + +That's it. +That's the solution. + +This looks big and corny, +but we are going to make some + +simplifications as we go along +and show that it ends up boiling + +down to something cos omega t. +The math is kind of involved + +but we get down to something +very simple, a cosine. + +Hold this general solution. +From that, as a step three of + +the differential equation +solution, I write the total + +solution down. +And my total solution is the + +sum of the particular and the +homogenous, so therefore I get + +this. +VI was my particular and this + +term here is my homogenous +solution. + +Now, if I wasn't doing circuits +and simply trying to solve this + +mathematically here is what I +would do. + +I would find the unknown from +the initial conditions, + +so I know that v(0)=0. +And so therefore if I + +substitute zero for V(0) I get +this. + +If I substitute zero here, +t is 0, t is 0, + +so I simply get V1+A1+A2. +And let me just blast through + +because I am going to redo this +differently. + +i=Cdv/dt. +And so that's what I get. + +I substitute zero and this is +what I would get. + +I hurried through this. +Don't worry. + +I'm going to do it again. +If you just do it + +mathematically, +you can solve this equation + +here and these two simultaneous +equations in a1 and a2 and get + +the coefficients and you are +done. + +But it doesn't give us a whole +lot of insight into the behavior + +of these terms here. +What I am going to do for now + +is kind of ignore that. +Ignore I did that and instead + +try to go down a path that is a +little bit more intuitive. + +Let's stare at this expression +we got for the total solution. + +That is the expression we got. +All I did is, + +I had alpha in there, +I simply pulled out the alpha + +outside. +So this is my total solution, + +V1-A1e^(-alpha t) something +else and something else. + +Three cases to consider +depending on the relative values + +of alpha and omega nought. +If alpha is greater than omega + +nought then I get a real +quantity here. + +The square root of a positive +number, I get a real number, + +and that number will add up to +the minus alpha and I am going + +to get a solution that will look +like, oh, I'm sorry. + +Let me just do it a little +differently. + +There are three situations +here. + +One is alpha greater than omega +nought. + +Alpha equal to omega nought. +Alpha less than omega nought. + +Alpha is greater, +alpha is less, + +alpha is equal to this term +inside the square root sign. + +For reasons you will understand +shortly, we call this + +"overdamped" case, +the "underdamped" case and the + +"critically damped" case. +When alpha is greater than + +omega nought this term gives me +a real number, + +and I get something as simple +as this. + +Remember, for the series RLC +circuit, alpha was R/2L. + +So if R is big, +in other words, + +if in my RLC circuit R is huge +then I am going to get this + +situation. +My output voltage on the + +capacitor is going to look like +this, the sum of two + +exponentials. +And if I were to plot it very + +quickly for you, +for a VI step, + +V would look like this. +So v would simply look like + +this because it is the sum of a +couple of exponentials. + +All right. +Now, alpha is positive here. + +Remember alpha1 and alpha2 are +both positive. + +These two added up, +because of this constant VI, + +give rise to something that +increases in the following + +manner. +Let's look at the situation + +where alpha is less than omega +nought, where the term inside + +the square root sign is +negative. + +What I can do is pull the +negative sign out and express it + +this way. +What I am going to do is since + +alpha is less than omega nought, +I am going to reverse these two + +and pull out square root of +minus one to the outside. + +This is what I get. +I am just playing around with + +this so that whatever is under +the square root sign ends up + +giving me a positive real +number. + +So I pull the j outside and +this is what I get. + +Now, let me blast through a +bunch of math and end up with + +something very, +very simple for this + +underdamped case. +Let me define a few other + +terms. +I am going to call omega nought + +minus alpha squared the square +root of that. + +I am going to call it omega d. +And here is what I get. + +So I have defined three things +for you now, alpha, + +omega nought and omega d. +And I get this equation in + +terms of alpha and omega d. +And then, remember from your + +good-old Euler relationship? +e to the j omega d is simply + +cosine plus a j sine. +I am just going to blast + +through a bunch of math rather +quickly. + +Once I replace this in terms of +a cosine and sine, + +cosine and a j sine and then +collect all the coefficients + +together, I get an equation of +the form VI plus some constant e + +to the minus alpha t, +cosine, the sum of the constant + +e to the minus alpha t, +sine. + +Remember the sines and cosines +are coming out, + +but because of my R I am +getting this funny alpha here, + +e to the minus alpha here. +So I am getting sums of sine + +and cosine. +And K1 and K2 are some + +constants which I will need to +determine for my initial + +conditions. +I am going to continue on with + +this and keep on simplifying it +because, as I promised you, + +I want to get to something that +is just a cosine. + +I want to go down this path. +I am not going to cover this + +case, the critically damped +case. + +And I will touch upon it later +but not dwell on it. + +Let me continue down the path +of the underdamped case, + +and this is what we have. +Continuing with the math, + +let's start with the initial +conditions, v nought equals + +zero, and that gives me K1 is +simply -VI. + +So at v(0)=0 t is zero, +so this terms goes away, + +the cosine becomes a 1, +e^(alpha t) goes away, + +and K1=-VI. +Then I know that i(0) and i is + +simply Cdv/dt. +And I get this nasty + +expression. +I substitute t=0 and I get + +something that looks like this. +I know what K1 is, + +and so therefore K2 is simply +-V1alpha divided by omega + +nought. +I have taken this expression + +where the unknowns K1 and K2 are +to be found. + +I set the initial conditions +down at t=0 and I get K1 and K2 + +as follows, which gives me the +following solution. + +This is the solution I get +where I do not have any unknowns + +anymore. +Remember that omega d and alpha + +are directly related to circuit +parameters. + +Alpha was R/2L and omega d was +square root of alpha squared + +minus omega nought squared. +** omega d = sqrt(alpha^2 - + +omega_0^2) ** +And omega nought squared was 1 + +by square root of LC. +So I know it all now. + +I still have sines and cosines +here, so I am going to simplify + +this a little further. +Oh, before I go on to do that, + +let's do the Fineman trick +again and notice if I am still + +true to the LC circuit I did the +last time. + +Remember when R goes to zero +alpha goes to zero. + +Because alpha is R divided by +2L. + +If alpha was zero what happens? +If alpha was zero, + +this guy goes to one, +this whole term goes to zero + +and omega dt now ends up +becoming omega nought, + +and I get this term here. +I get VI-VIcosine(omega t), + +which is exactly what I +expected in my equation. + +This is the same as the LC case +that I got. + +Let's go back to this situation +and simply if further. + +If you look at Appendix B.7 in +your course notes, + +Appendix B.7 is a quick +tutorial on trig. + +And in that trig tutorial you +will see that, + +and you have probably seen this +before, too, multiple times, + +the scaled sum of sines are +also sines. + +This is an incredibly cool fact +of sinusoids. + +If you take two sinusoids of +the same frequency and you scale + +them up in any which way and add +them up you also end up with a + +sinusoid. +It is hard to believe but it is + +true. +It is an incredible property of + +sinusoids. +Take any two sinusoids, + +scale them in any way you like, +same frequency, + +add them up, +you will get a sinusoid. + +What that is saying is that, +look, here is a sinusoid, + +here is a sinusoidal function, +and I am scaling them up in + +some manner. +So I should be able to add them + +up and be able to express that +as single sine. + +And to be sure you can, +look at the Appendix, + +and there is an expression for +a1 sinX plus a2 cosX is equal to + +a cosine of blah, +blah, blah. + +This is what you get. +No magic here. + +Just math. +From here I directly get this. + +And look at what I have. +It is absolutely unbelievable. + +v(t) is simply VI, +there is a constant here, + +this an e to the minus alpha +term and there is a cosine. + +Again, to pull the Fineman +trick, if this alpha were to go + +to zero here then you would end +up with the expression you had + +for the LC situation. +Let's stare at this a little + +while longer. +There is a constant plus a + +minus, a cosine term, +so there is a sinusoid at the + +output, and there is an e to the +minus alpha which ends up giving + +you the decay you have seen +before. + +In other words, +to a step input, + +the LC circuit would give you a +sinusoid. + +That is what the LC circuit +would do if alpha was zero. + +But because of this alpha term +here, e to the minus alpha t, + +that gives rise to a damping +effect, so this causes this + +thing to become smaller and +smaller as time goes by until + +this term goes to zero at t +equals infinity. + +This guy damps down and so +therefore you end up getting the + +curve that you saw like this. +Twenty minutes of juggling math + +solving a second-order +differential equation, + +but what ends up is the same +sinusoid but it is damped in the + +following manner such that the +frequency, rather the amplitude + +keeps decaying until it starts +off at zero and then settles + +down at vI. +This is exactly what you saw in + +the demo that we showed you +earlier. + +The critically damped case, +I am not going to do it here. + +I am going to point you to the +following insight. + +The underdamped case looked +like this. + +It was a sinusoid that kind of +decayed out. + +That is the underdamped case. +And then I showed you the + +overdamped case. +The overdamped case looked like + +this. +And, as you might expect, + +the critically damped case is +kind of in the middle and looks + +like this. +So the overdamped case would + +look like this, +underdamped like this, + +and the critically damped case +kind of goes up and kind of + +settles down almost immediately. +This is when alpha equals omega + +nought. +I won't do that case here, + +but I will simply point you to +Section 13.2.3. + +Just to tie things together, +recall this demo here that we + +showed you in class yesterday. +This is exactly the kind of + +form of the sinusoid you saw +because of that input step. + +If you want to see a complete +analysis of inverter pairs and + +look at the delays and so on +because of that, + +you can look at Page 170 and +example 898. + +In the next five or six +minutes, what I would like to do + +is stare at the RLC circuit. +And much like I showed you some + +intuitive methods to get the RC +response, what we are going to + +do is do the same thing for the +RLC. + +In the RLC situation, +much like the RC situation, + +experts don't go around writing +15 pages of differential + +equations and solving them each +time they see an RLC circuit. + +They stare at it and boom, +the response pops out, + +the sketch pops out. +This one is going to be another + +one like our Bend it Like +Beckham series here. + +And this one is in honor of +Leslie Kolodziejski. + +And I call it "Konquer it like +Kolodziejski". + +Again, as I said, +experts don't go around solving + +long differential equations and +spending ten pages of notes + +trying to get a sinusoid. +They look at a circuit and + +sketch response. +I am going to show you how to + +do that, too. +And what you can do is, + +to practice, +go to Websim and try out + +various combinations of inputs +and initial conditions and + +sketch it, time yourself, +give yourself 30 seconds or a + +minute if you like, +and sketch it and check it + +against the Websim response. +If it doesn't match either you + +are wrong or there is a bug in +Websim. + +What I am going to do is, +the response to the critically + +damped and underdamped case was +very easy to sketch out. + +You started with an initial +condition, you settled at VI and + +just kind of drew it like that. +The interesting case is the + +underdamped case, +and that is what I am going to + +dwell on. +Before we go on and I show you + +the intuitive method, +as a first step I would like to + +build some intuition. +Let's stare at this response + +here and try to understand what +is going on. + +This is the response that we +saw. + +And this fact that you see an +oscillation happening is also + +called "ringing". +You say that your circuit is + +ringing. +All right. + +You see some interesting facts. +You see that frequency of the + +ringing is given by omega d. +This cosine omega d, + +so that is the frequency omega +d. + +So the time is 2 pi divided by +omega d. + +The oscillation frequency is +omega d, but omega d is simply + +omega nought squared minus alpha +squared. + +Once you have a big value of R +alpha becomes very small and + +omega d is very commonly equal +to, very close to omega nought. + +So omega d and omega nought +very commonly are very close + +together. +And when that happens this + +frequency is directly omega +nought. + +Alpha governs how quickly your +sinusoid decays. + +e to the alpha t here is the +envelope that governs how + +quickly my sinusoid decays. +And notice that each of these + +terms, alpha and omega nought, +comes directly from my + +characteristic equation. +Which means that once you get + +your characteristic equation you +really don't have to do much + +else. +And up until now you still have + +to write the differential +equation to get the + +characteristic equation, +so you still have to do some + +differential equation stuff, +but in two lectures I am going + +to show you a way that you can +even write down the + +characteristic equation by +inspection. + +Look at your circuit and boom, +in 15 seconds or less write + +down the characteristic +equation. + +It is absolutely unbelievable. +What are the other factors that + +are interesting here? +Of course I need to find out + +initial values. +I start off at zero. + +This is my capacitor voltage. +If I don't have an infinite + +spike or an impulse my capacitor +voltage tries to stay where it + +is and starts off at zero. +And the final value is given by + +VI, the capacitor is a long-term +open so therefore VI appears + +across the capacitor. +In the long-term my final value + +is going to be VI. +There is one other interesting + +parameter, which I will simply +define today but dwell on about + +a week from today, +and that is called the Q. + +Some of you may have heard the +term oh, that's a high Q + +circuit. +Q is an indication of how ringy + +the circuit is. +And Q is defined as omega + +nought by 2 alpha. +It is called the "quality + +factor". +And it turns out that Q is + +approximately the number of +cycles of ringing. + +So if you have a high Q you +ring for a long time and if you + +have a low Q you ring for a very +short time. + +That is called the quality +factor defined by omega nought + +by 2 alpha. +Notice that Q, + +omega nought, +alpha, omega d, + +all of these come from the +terms in the characteristic + +equation. +We will spend more time on Q + +later. +With this insight here is how I + +can go about very quickly +sketching out the form of the + +response. +Here is my circuit. + +I want to sketch the form of +the response for a step input at + +vI. +Zero to vI step input here, + +I want to find out what happens +at this point. + +This is described to you in a +lot more detail in Section 13.8 + +in your course notes. +Let's go through the steps. + +Let's do the really simple +situation first. + +Let's also assume for fun that +you are given that v(0) starts + +out being some positive value. +Some v(0) which is a positive + +number. +And, to make it harder on + +ourselves, let's say i(0) starts +out being some negative number. + +So i(0) is some negative +current. + +The first thing I know is v(0), +the capacitor voltage starts + +out here, which can change +suddenly. + +And I also know that in the +long-term this is an open + +circuit. +So that this voltage vI will + +appear directly across the +capacitor in the long-term. + +So I get starting out at v(0), +ending at vI, + +I am also half the way there. +I know the initial and ending + +point of the curve. +And then I know that somewhere + +in here there must be some funny +gyrations here, + +because remember I am dealing +with the underdamped case. + +And you can determine that from +alpha and omega nought. + +If alpha is less than omega +nought, you know that you are in + +the underdamped case and this is +what you get. + +Let's compute and write the +characteristic equation down. + +A week from today you will +write it by inspection, + +but for now you will do it by +writing down a differential + +equation. +And from the characteristic + +equation you will get omega d, +you will get alpha, + +omega nought and Q. +So omega d gives you the + +frequency of oscillations. +My frequency of oscillation is + +now known. +From Q I know how long it + +rings, because I know it rings +for about Q cycles. + +I know that ringing stops +approximately here. + +And then I know that between +that the start and end point my + +curve kind of looks like this, +something like this. + +Right there we are 95% of the +way there. + +The only question is I do not +know if it goes like this or it + +goes like this. +I am not quite sure yet if it + +starts off going high or starts +off going low. + +Not quite clear. +I also do not know what the + +maximum amplitude is. +It turns out this is rather + +complicated to determine so we +won't deal with that. + +Just simply so you can draw a +rough sketch. + +The questions is which way does +it start? + +I could leave it for you to +think about. + +Yeah, let me do that. +It is given on this page so + +don't look at it. +Think about it, + +and think about how you can +determine whether it goes up or + +down. +It turns out that in this case + +it is going to down and then +ring. + +See if you can figure it out +for yourselves and then we will + +talk about it next week. \ No newline at end of file diff --git a/0UYCJ0cjG9k.txt b/0UYCJ0cjG9k.txt new file mode 100644 index 0000000000000000000000000000000000000000..aaad02108cc17da22d8539903348af23d5ab0e54 --- /dev/null +++ b/0UYCJ0cjG9k.txt @@ -0,0 +1,13131 @@ +align:start position:0% + +Okay. Uh so hi everyone. I'm Pablo. I'm + + align:start position:0% +Okay. Uh so hi everyone. I'm Pablo. I'm + + + align:start position:0% +Okay. Uh so hi everyone. I'm Pablo. I'm +uh teaching Lar's lecture this week. I + + align:start position:0% +uh teaching Lar's lecture this week. I + + + align:start position:0% +uh teaching Lar's lecture this week. I +hope we are all here to learn about + + align:start position:0% +hope we are all here to learn about + + + align:start position:0% +hope we are all here to learn about +projection theory. And the plan for this + + align:start position:0% +projection theory. And the plan for this + + + align:start position:0% +projection theory. And the plan for this +week is to talk about Bugans projection + + align:start position:0% +week is to talk about Bugans projection + + + align:start position:0% +week is to talk about Bugans projection +theorem uh which is an extremely + + align:start position:0% +theorem uh which is an extremely + + + align:start position:0% +theorem uh which is an extremely +important theorem with applications uh + + align:start position:0% +important theorem with applications uh + + + align:start position:0% +important theorem with applications uh +in many areas of mathematics including + + align:start position:0% +in many areas of mathematics including + + + align:start position:0% +in many areas of mathematics including +some pretty striking recent ones and + + align:start position:0% +some pretty striking recent ones and + + + align:start position:0% +some pretty striking recent ones and +okay I think Larry has told you at least + + align:start position:0% +okay I think Larry has told you at least + + + align:start position:0% +okay I think Larry has told you at least +a bit about it and well uh we won't be + + align:start position:0% +a bit about it and well uh we won't be + + + align:start position:0% +a bit about it and well uh we won't be +able to do a full proof because it would + + align:start position:0% +able to do a full proof because it would + + + align:start position:0% +able to do a full proof because it would +take way too long but what I'm going to + + align:start position:0% +take way too long but what I'm going to + + + align:start position:0% +take way too long but what I'm going to +do is explain um okay so you've seen the + + align:start position:0% +do is explain um okay so you've seen the + + + align:start position:0% +do is explain um okay so you've seen the +analog of this theorem in the final + + align:start position:0% +analog of this theorem in the final + + + align:start position:0% +analog of this theorem in the final +field setting and I'm going to state it + + align:start position:0% +field setting and I'm going to state it + + + align:start position:0% +field setting and I'm going to state it +uh to so as our starting point and then + + align:start position:0% +uh to so as our starting point and then + + + align:start position:0% +uh to so as our starting point and then +the plan is to go through the steps in + + align:start position:0% +the plan is to go through the steps in + + + align:start position:0% +the plan is to go through the steps in +the strategy in the final field setting + + align:start position:0% +the strategy in the final field setting + + + align:start position:0% +the strategy in the final field setting +and see what goes wrong and what are the + + align:start position:0% +and see what goes wrong and what are the + + + align:start position:0% +and see what goes wrong and what are the +ideas that one uses to overcome what + + align:start position:0% +ideas that one uses to overcome what + + + align:start position:0% +ideas that one uses to overcome what +goes wrong. Okay. So recall uh how this + + align:start position:0% +goes wrong. Okay. So recall uh how this + + + align:start position:0% +goes wrong. Okay. So recall uh how this +theorem looks like in the finite field + + align:start position:0% +theorem looks like in the finite field + + + align:start position:0% +theorem looks like in the finite field +setting and by finite field I mean prime + + align:start position:0% +setting and by finite field I mean prime + + + align:start position:0% +setting and by finite field I mean prime +prime finite field prime order because + + align:start position:0% +prime finite field prime order because + + + align:start position:0% +prime finite field prime order because +otherwise it's not true. + + align:start position:0% +otherwise it's not true. + + + align:start position:0% +otherwise it's not true. +Okay. And the statement was hopefully + + align:start position:0% +Okay. And the statement was hopefully + + + align:start position:0% +Okay. And the statement was hopefully +something like this. um given + + align:start position:0% + + + + align:start position:0% + +t between 0 and two and s between 0 and + + align:start position:0% +t between 0 and two and s between 0 and + + + align:start position:0% +t between 0 and two and s between 0 and +one t I want it to be neither zero nor + + align:start position:0% +one t I want it to be neither zero nor + + + align:start position:0% +one t I want it to be neither zero nor +two because there wouldn't be anything + + align:start position:0% +two because there wouldn't be anything + + + align:start position:0% +two because there wouldn't be anything +to say s has to be positive could be one + + align:start position:0% +to say s has to be positive could be one + + + align:start position:0% +to say s has to be positive could be one +uh there exists + + align:start position:0% +uh there exists + + + align:start position:0% +uh there exists +some epsilon that depends on these two + + align:start position:0% +some epsilon that depends on these two + + + align:start position:0% +some epsilon that depends on these two +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +and is positive + + align:start position:0% + + + + align:start position:0% + +with the following properties. If X + + align:start position:0% +with the following properties. If X + + + align:start position:0% +with the following properties. If X +is in FP squared + + align:start position:0% +is in FP squared + + + align:start position:0% +is in FP squared +and has size P to the S. So sort of S + + align:start position:0% +and has size P to the S. So sort of S + + + align:start position:0% +and has size P to the S. So sort of S +dimension an S S dimensional set in some + + align:start position:0% +dimension an S S dimensional set in some + + + align:start position:0% +dimension an S S dimensional set in some +sense. And D is a set of directions. + + align:start position:0% +sense. And D is a set of directions. + + + align:start position:0% +sense. And D is a set of directions. +Let's say a subset of FP and it has size + + align:start position:0% +Let's say a subset of FP and it has size + + + align:start position:0% +Let's say a subset of FP and it has size +P to the T. So sort of dimension T. + + align:start position:0% +P to the T. So sort of dimension T. + + + align:start position:0% +P to the T. So sort of dimension T. +uh then + + align:start position:0% + + + + align:start position:0% + +so I use the notation + + align:start position:0% +so I use the notation + + + align:start position:0% +so I use the notation +pi theta of x uh to be the projection + + align:start position:0% +pi theta of x uh to be the projection + + + align:start position:0% +pi theta of x uh to be the projection +and we can write the projection in this + + align:start position:0% +and we can write the projection in this + + + align:start position:0% +and we can write the projection in this +way I guess just x1 plus theta x2 + + align:start position:0% +way I guess just x1 plus theta x2 + + + align:start position:0% +way I guess just x1 plus theta x2 +so from fp² to fp + + align:start position:0% +so from fp² to fp + + + align:start position:0% +so from fp² to fp +then um + + align:start position:0% +then um + + + align:start position:0% +then um +we can find uh sorry I missed messed up + + align:start position:0% +we can find uh sorry I missed messed up + + + align:start position:0% +we can find uh sorry I missed messed up +the parameters already So the size of x + + align:start position:0% +the parameters already So the size of x + + + align:start position:0% +the parameters already So the size of x +is between p to the zero and p^2 and t + + align:start position:0% +is between p to the zero and p^2 and t + + + align:start position:0% +is between p to the zero and p^2 and t +is between zero and two. So this should + + align:start position:0% +is between zero and two. So this should + + + align:start position:0% +is between zero and two. So this should +be t this should be s. Okay. Uh then + + align:start position:0% +be t this should be s. Okay. Uh then + + + align:start position:0% +be t this should be s. Okay. Uh then +there is a large pro large between + + align:start position:0% +there is a large pro large between + + + align:start position:0% +there is a large pro large between +quotes projection. Uh then the maximum + + align:start position:0% +quotes projection. Uh then the maximum + + + align:start position:0% +quotes projection. Uh then the maximum +over theta in d of the size of the + + align:start position:0% +over theta in d of the size of the + + + align:start position:0% +over theta in d of the size of the +projection of x is at least + + align:start position:0% +projection of x is at least + + + align:start position:0% +projection of x is at least +p to the t / 2 plus epsilon. So we gain + + align:start position:0% +p to the t / 2 plus epsilon. So we gain + + + align:start position:0% +p to the t / 2 plus epsilon. So we gain +an epsilon over t / two and t p to the t + + align:start position:0% +an epsilon over t / two and t p to the t + + + align:start position:0% +an epsilon over t / two and t p to the t +over two is sort of the obvious lower + + align:start position:0% +over two is sort of the obvious lower + + + align:start position:0% +over two is sort of the obvious lower +bound and I'm going to come back to this + + align:start position:0% +bound and I'm going to come back to this + + + align:start position:0% +bound and I'm going to come back to this +obvious lower bound uh in a minute. + + align:start position:0% +obvious lower bound uh in a minute. + + + align:start position:0% +obvious lower bound uh in a minute. +In fact uh there is a stronger version. + + align:start position:0% +In fact uh there is a stronger version. + + + align:start position:0% +In fact uh there is a stronger version. +I think you proved this in detail and uh + + align:start position:0% +I think you proved this in detail and uh + + + align:start position:0% +I think you proved this in detail and uh +you discussed the stronger version. + + align:start position:0% +you discussed the stronger version. + + + align:start position:0% +you discussed the stronger version. +So let me state the stronger version + + align:start position:0% +So let me state the stronger version + + + align:start position:0% +So let me state the stronger version +because well first of all it's important + + align:start position:0% +because well first of all it's important + + + align:start position:0% +because well first of all it's important +in itself for applications of the final + + align:start position:0% +in itself for applications of the final + + + align:start position:0% +in itself for applications of the final +field result. But I would say it's even + + align:start position:0% +field result. But I would say it's even + + + align:start position:0% +field result. But I would say it's even +more important in the uklidian case. + + align:start position:0% + + + + align:start position:0% + +Not only we can find so at this size we + + align:start position:0% +Not only we can find so at this size we + + + align:start position:0% +Not only we can find so at this size we +can find the direction so that the + + align:start position:0% +can find the direction so that the + + + align:start position:0% +can find the direction so that the +projection is large the projection of + + align:start position:0% +projection is large the projection of + + + align:start position:0% +projection is large the projection of +the whole set but moreover we can find + + align:start position:0% +the whole set but moreover we can find + + + align:start position:0% +the whole set but moreover we can find +the direction so that if we project any + + align:start position:0% +the direction so that if we project any + + + align:start position:0% +the direction so that if we project any +dense subset of x the projection is + + align:start position:0% +dense subset of x the projection is + + + align:start position:0% +dense subset of x the projection is +still large. So if we take the maximum + + align:start position:0% +still large. So if we take the maximum + + + align:start position:0% +still large. So if we take the maximum +over now the minimum so we look at the + + align:start position:0% +over now the minimum so we look at the + + + align:start position:0% +over now the minimum so we look at the +worst possible subset which is dense. So + + align:start position:0% +worst possible subset which is dense. So + + + align:start position:0% +worst possible subset which is dense. So +we take the minimum over subsets of X + + align:start position:0% +we take the minimum over subsets of X + + + align:start position:0% +we take the minimum over subsets of X +which are dense in the sense that they + + align:start position:0% +which are dense in the sense that they + + + align:start position:0% +which are dense in the sense that they +have relative density + + align:start position:0% +have relative density + + + align:start position:0% +have relative density +uh P to the minus epsilon + + align:start position:0% + + + + align:start position:0% + +and then we look at the projection of Y. + + align:start position:0% +and then we look at the projection of Y. + + + align:start position:0% +and then we look at the projection of Y. +So we try to make the projection of a + + align:start position:0% +So we try to make the projection of a + + + align:start position:0% +So we try to make the projection of a +dens set of X as small as possible but + + align:start position:0% +dens set of X as small as possible but + + + align:start position:0% +dens set of X as small as possible but +we can't even if we have this additional + + align:start position:0% +we can't even if we have this additional + + + align:start position:0% +we can't even if we have this additional +robustness of going looking at all + + align:start position:0% +robustness of going looking at all + + + align:start position:0% +robustness of going looking at all +subsets of Y we still have a gain over T + + align:start position:0% +subsets of Y we still have a gain over T + + + align:start position:0% +subsets of Y we still have a gain over T +/2. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is Bans protection theorem + + align:start position:0% +Okay. So this is Bans protection theorem + + + align:start position:0% +Okay. So this is Bans protection theorem +in the finite field setting + + align:start position:0% + + + + align:start position:0% + +and you have proved at least this + + align:start position:0% +and you have proved at least this + + + align:start position:0% +and you have proved at least this +version and I think discussed this + + align:start position:0% +version and I think discussed this + + + align:start position:0% +version and I think discussed this +version. If anything I say is not + + align:start position:0% +version. If anything I say is not + + + align:start position:0% +version. If anything I say is not +correct or if I say something that you + + align:start position:0% +correct or if I say something that you + + + align:start position:0% +correct or if I say something that you +are not familiar with or you don't + + align:start position:0% +are not familiar with or you don't + + + align:start position:0% +are not familiar with or you don't +understand anything please just ask. + + align:start position:0% +understand anything please just ask. + + + align:start position:0% +understand anything please just ask. +Okay. So now we want to uh Okay. So + + align:start position:0% +Okay. So now we want to uh Okay. So + + + align:start position:0% +Okay. So now we want to uh Okay. So +before moving to the uklidian case uh + + align:start position:0% +before moving to the uklidian case uh + + + align:start position:0% +before moving to the uklidian case uh +let me make this remark + + align:start position:0% +let me make this remark + + + align:start position:0% +let me make this remark +on the trivial bound. + + align:start position:0% +on the trivial bound. + + + align:start position:0% +on the trivial bound. +So the trivial bound is p to the t /2 + + align:start position:0% +So the trivial bound is p to the t /2 + + + align:start position:0% +So the trivial bound is p to the t /2 +without the just without the epsilon for + + align:start position:0% +without the just without the epsilon for + + + align:start position:0% +without the just without the epsilon for +this. So this theorem is not true if uh + + align:start position:0% +this. So this theorem is not true if uh + + + align:start position:0% +this. So this theorem is not true if uh +p is p square. If we replace P by P + + align:start position:0% +p is p square. If we replace P by P + + + align:start position:0% +p is p square. If we replace P by P +square or anything which is not a prime + + align:start position:0% +square or anything which is not a prime + + + align:start position:0% +square or anything which is not a prime +because if you look at FP square for + + align:start position:0% +because if you look at FP square for + + + align:start position:0% +because if you look at FP square for +example then FP sitting there and um + + align:start position:0% +example then FP sitting there and um + + + align:start position:0% +example then FP sitting there and um +if we take F to be XP and D to be FP + + align:start position:0% +if we take F to be XP and D to be FP + + + align:start position:0% +if we take F to be XP and D to be FP +sitting in FP squared we don't escape FP + + align:start position:0% +sitting in FP squared we don't escape FP + + + align:start position:0% +sitting in FP squared we don't escape FP +because FP is a sub + + align:start position:0% +because FP is a sub + + + align:start position:0% +because FP is a sub +uh so this is not true + + align:start position:0% +uh so this is not true + + + align:start position:0% +uh so this is not true +but without the epsilon is true in any + + align:start position:0% +but without the epsilon is true in any + + + align:start position:0% +but without the epsilon is true in any +field and the argument is trivial so uh + + align:start position:0% +field and the argument is trivial so uh + + + align:start position:0% +field and the argument is trivial so uh +okay so one should never use the word + + align:start position:0% +okay so one should never use the word + + + align:start position:0% +okay so one should never use the word +trivial but I will use it in this case. + + align:start position:0% + + + + align:start position:0% + +So everything is trivial once you've + + align:start position:0% +So everything is trivial once you've + + + align:start position:0% +So everything is trivial once you've +understood it and nothing is trivial + + align:start position:0% +understood it and nothing is trivial + + + align:start position:0% +understood it and nothing is trivial +before you've understood it but uh I + + align:start position:0% +before you've understood it but uh I + + + align:start position:0% +before you've understood it but uh I +will still use the word trivial here. Um + + align:start position:0% +will still use the word trivial here. Um + + + align:start position:0% +will still use the word trivial here. Um +so if D has at least two elements so + + align:start position:0% +so if D has at least two elements so + + + align:start position:0% +so if D has at least two elements so +same setting as above so if D has more + + align:start position:0% +same setting as above so if D has more + + + align:start position:0% +same setting as above so if D has more +than one element so let's allow P to the + + align:start position:0% +than one element so let's allow P to the + + + align:start position:0% +than one element so let's allow P to the +S where S is positive just two elements + + align:start position:0% +S where S is positive just two elements + + + align:start position:0% +S where S is positive just two elements +then the maximum + + align:start position:0% +then the maximum + + + align:start position:0% +then the maximum +over theta in B + + align:start position:0% +over theta in B + + + align:start position:0% +over theta in B +of the projection + + align:start position:0% +of the projection + + + align:start position:0% +of the projection +of X is at least + + align:start position:0% + + + + align:start position:0% + +the size of X to the 1/2. So if the size + + align:start position:0% +the size of X to the 1/2. So if the size + + + align:start position:0% +the size of X to the 1/2. So if the size +of x is p to the u t would be at least p + + align:start position:0% +of x is p to the u t would be at least p + + + align:start position:0% +of x is p to the u t would be at least p +to the t /2 and again we will see that + + align:start position:0% +to the t /2 and again we will see that + + + align:start position:0% +to the t /2 and again we will see that +this doesn't use the fact that p is + + align:start position:0% +this doesn't use the fact that p is + + + align:start position:0% +this doesn't use the fact that p is +prime. + + align:start position:0% +prime. + + + align:start position:0% +prime. +So it's much more general. Okay. And and + + align:start position:0% +So it's much more general. Okay. And and + + + align:start position:0% +So it's much more general. Okay. And and +this is trivial because just take two + + align:start position:0% +this is trivial because just take two + + + align:start position:0% +this is trivial because just take two +elements. Okay. Again trivial. I will + + align:start position:0% +elements. Okay. Again trivial. I will + + + align:start position:0% +elements. Okay. Again trivial. I will +explain it and then once you've + + align:start position:0% +explain it and then once you've + + + align:start position:0% +explain it and then once you've +understood it you will see that you will + + align:start position:0% +understood it you will see that you will + + + align:start position:0% +understood it you will see that you will +agree that it's trivial. Um okay so know + + align:start position:0% +agree that it's trivial. Um okay so know + + + align:start position:0% +agree that it's trivial. Um okay so know +that. So just take two elements. So D + + align:start position:0% +that. So just take two elements. So D + + + align:start position:0% +that. So just take two elements. So D +has at least two elements by so let's + + align:start position:0% +has at least two elements by so let's + + + align:start position:0% +has at least two elements by so let's +just take two elements theta and theta + + align:start position:0% +just take two elements theta and theta + + + align:start position:0% +just take two elements theta and theta +prime in D and then uh so the + + align:start position:0% +prime in D and then uh so the + + + align:start position:0% +prime in D and then uh so the +observation that makes this trivial is + + align:start position:0% +observation that makes this trivial is + + + align:start position:0% +observation that makes this trivial is +that uh if you map X + + align:start position:0% + + + + align:start position:0% + +to the projection in direction theta + + align:start position:0% +to the projection in direction theta + + + align:start position:0% +to the projection in direction theta +comma the projection in direction theta + + align:start position:0% +comma the projection in direction theta + + + align:start position:0% +comma the projection in direction theta +prime. So this is small x an element of + + align:start position:0% +prime. So this is small x an element of + + + align:start position:0% +prime. So this is small x an element of +xp squ. + + align:start position:0% + + + + align:start position:0% + +Uh this is injective. + + align:start position:0% +Uh this is injective. + + + align:start position:0% +Uh this is injective. +So we can recover a vector from two + + align:start position:0% +So we can recover a vector from two + + + align:start position:0% +So we can recover a vector from two +projections + + align:start position:0% +projections + + + align:start position:0% +projections +by linear algebra. + + align:start position:0% + + + + align:start position:0% + +So this means that the image of X under + + align:start position:0% +So this means that the image of X under + + + align:start position:0% +So this means that the image of X under +this map has size at least + + align:start position:0% +this map has size at least + + + align:start position:0% +this map has size at least +the domain because if you have an + + align:start position:0% +the domain because if you have an + + + align:start position:0% +the domain because if you have an +injective M map the image has the size + + align:start position:0% +injective M map the image has the size + + + align:start position:0% +injective M map the image has the size +of the domain. Okay. So this implies + + align:start position:0% +of the domain. Okay. So this implies + + + align:start position:0% +of the domain. Okay. So this implies +that the size of x is at least the size + + align:start position:0% +that the size of x is at least the size + + + align:start position:0% +that the size of x is at least the size +of the projection in direction theta of + + align:start position:0% +of the projection in direction theta of + + + align:start position:0% +of the projection in direction theta of +x times + + align:start position:0% +x times + + + align:start position:0% +x times +the size uh of the projection in + + align:start position:0% +the size uh of the projection in + + + align:start position:0% +the size uh of the projection in +direction of theta prime. So at least + + align:start position:0% +direction of theta prime. So at least + + + align:start position:0% +direction of theta prime. So at least +one of these two has to be at least + + align:start position:0% +one of these two has to be at least + + + align:start position:0% +one of these two has to be at least +square root of x square root of the size + + align:start position:0% +square root of x square root of the size + + + align:start position:0% +square root of x square root of the size +of x. + + align:start position:0% +of x. + + + align:start position:0% +of x. +Okay. Uh so this is the proof of the + + align:start position:0% +Okay. Uh so this is the proof of the + + + align:start position:0% +Okay. Uh so this is the proof of the +trivial bound and I hope you will agree + + align:start position:0% +trivial bound and I hope you will agree + + + align:start position:0% +trivial bound and I hope you will agree +that it's very easy and it uses + + align:start position:0% +that it's very easy and it uses + + + align:start position:0% +that it's very easy and it uses +literally nothing. Well uh it uses that + + align:start position:0% +literally nothing. Well uh it uses that + + + align:start position:0% +literally nothing. Well uh it uses that +this map is injected but this is a very + + align:start position:0% +this map is injected but this is a very + + + align:start position:0% +this map is injected but this is a very +general fact + + align:start position:0% + + + + align:start position:0% + +in particular this is true on any finite + + align:start position:0% +in particular this is true on any finite + + + align:start position:0% +in particular this is true on any finite +field it doesn't have to be prime but + + align:start position:0% +field it doesn't have to be prime but + + + align:start position:0% +field it doesn't have to be prime but +for this we need it to be prime okay so + + align:start position:0% +for this we need it to be prime okay so + + + align:start position:0% +for this we need it to be prime okay so +now we want to uh have a uklidian + + align:start position:0% +now we want to uh have a uklidian + + + align:start position:0% +now we want to uh have a uklidian +version of + + align:start position:0% +version of + + + align:start position:0% +version of +this statement and we will see that okay + + align:start position:0% +this statement and we will see that okay + + + align:start position:0% +this statement and we will see that okay +so maybe let's discuss the uklidian + + align:start position:0% +so maybe let's discuss the uklidian + + + align:start position:0% +so maybe let's discuss the uklidian +setting so I will start with the setting + + align:start position:0% +setting so I will start with the setting + + + align:start position:0% +setting so I will start with the setting +uh which is the way in which nucleidian + + align:start position:0% +uh which is the way in which nucleidian + + + align:start position:0% +uh which is the way in which nucleidian +setting has appeared in this course + + align:start position:0% +setting has appeared in this course + + + align:start position:0% +setting has appeared in this course +before but then I will rescale things uh + + align:start position:0% +before but then I will rescale things uh + + + align:start position:0% +before but then I will rescale things uh +to a setting that I like better but + + align:start position:0% +to a setting that I like better but + + + align:start position:0% +to a setting that I like better but +let's start uh with the following so we + + align:start position:0% +let's start uh with the following so we + + + align:start position:0% +let's start uh with the following so we +have a parameter r which is the scale or + + align:start position:0% +have a parameter r which is the scale or + + + align:start position:0% +have a parameter r which is the scale or +maybe one / r is the scale + + align:start position:0% +maybe one / r is the scale + + + align:start position:0% +maybe one / r is the scale +and then we have our set x is contained + + align:start position:0% +and then we have our set x is contained + + + align:start position:0% +and then we have our set x is contained +in the ball of radius r let's say center + + align:start position:0% +in the ball of radius r let's say center + + + align:start position:0% +in the ball of radius r let's say center +at the origin or really any any ball of + + align:start position:0% +at the origin or really any any ball of + + + align:start position:0% +at the origin or really any any ball of +radius r it doesn't make any + + align:start position:0% +radius r it doesn't make any + + + align:start position:0% +radius r it doesn't make any +And let's suppose that X is a union + + align:start position:0% +And let's suppose that X is a union + + + align:start position:0% +And let's suppose that X is a union +of unit balls + + align:start position:0% + + + + align:start position:0% + +and D let's say in 01 + + align:start position:0% +and D let's say in 01 + + + align:start position:0% +and D let's say in 01 +maybe one two would be slightly more + + align:start position:0% +maybe one two would be slightly more + + + align:start position:0% +maybe one two would be slightly more +natural but it doesn't really matter + + align:start position:0% +natural but it doesn't really matter + + + align:start position:0% +natural but it doesn't really matter +much is a one / r separated set. + + align:start position:0% + + + + align:start position:0% + +Okay, so G is a finite set of + + align:start position:0% +Okay, so G is a finite set of + + + align:start position:0% +Okay, so G is a finite set of +directions. They are separated by the + + align:start position:0% +directions. They are separated by the + + + align:start position:0% +directions. They are separated by the +scale one / R + + align:start position:0% +scale one / R + + + align:start position:0% +scale one / R +and X is a unit of unit balls MBR. So we + + align:start position:0% +and X is a unit of unit balls MBR. So we + + + align:start position:0% +and X is a unit of unit balls MBR. So we +measure X by le measure. We measure it + + align:start position:0% +measure X by le measure. We measure it + + + align:start position:0% +measure X by le measure. We measure it +by cardinality and use bars in both + + align:start position:0% +by cardinality and use bars in both + + + align:start position:0% +by cardinality and use bars in both +cases. I think this is the convention + + align:start position:0% +cases. I think this is the convention + + + align:start position:0% +cases. I think this is the convention +you've been using in this course + + align:start position:0% +you've been using in this course + + + align:start position:0% +you've been using in this course +and well we would like the following + + align:start position:0% +and well we would like the following + + + align:start position:0% +and well we would like the following +well we would like that right. So uh + + align:start position:0% +well we would like that right. So uh + + + align:start position:0% +well we would like that right. So uh +except that now x is not in fp square + + align:start position:0% +except that now x is not in fp square + + + align:start position:0% +except that now x is not in fp square +but in br and d is no longer in fp but + + align:start position:0% +but in br and d is no longer in fp but + + + align:start position:0% +but in br and d is no longer in fp but +in 01. So pi theta is still the same. So + + align:start position:0% +in 01. So pi theta is still the same. So + + + align:start position:0% +in 01. So pi theta is still the same. So +pi theta of x1 x2 + + align:start position:0% +pi theta of x1 x2 + + + align:start position:0% +pi theta of x1 x2 +is x1 plus theta x2. + + align:start position:0% +is x1 plus theta x2. + + + align:start position:0% +is x1 plus theta x2. +We could look at orthogonal projections + + align:start position:0% +We could look at orthogonal projections + + + align:start position:0% +We could look at orthogonal projections +but up to a parameterization + + align:start position:0% +but up to a parameterization + + + align:start position:0% +but up to a parameterization +uh is this is actually easier to work + + align:start position:0% +uh is this is actually easier to work + + + align:start position:0% +uh is this is actually easier to work +with. It's not important. Okay. So we + + align:start position:0% +with. It's not important. Okay. So we + + + align:start position:0% +with. It's not important. Okay. So we +can ask does the same happen? + + align:start position:0% + + + + align:start position:0% + +So just all the bars mean different + + align:start position:0% +So just all the bars mean different + + + align:start position:0% +So just all the bars mean different +things now. So when we project X we are + + align:start position:0% +things now. So when we project X we are + + + align:start position:0% +things now. So when we project X we are +looking at the measure measure one + + align:start position:0% +looking at the measure measure one + + + align:start position:0% +looking at the measure measure one +dimensional measure of the image and so + + align:start position:0% +dimensional measure of the image and so + + + align:start position:0% +dimensional measure of the image and so +on. So do we have any hope of proving + + align:start position:0% +on. So do we have any hope of proving + + + align:start position:0% +on. So do we have any hope of proving +the same theorem in this generality? + + align:start position:0% +the same theorem in this generality? + + + align:start position:0% +the same theorem in this generality? +So does anyone want to guess could this + + align:start position:0% +So does anyone want to guess could this + + + align:start position:0% +So does anyone want to guess could this +theorem be true in this setting? It's + + align:start position:0% +theorem be true in this setting? It's + + + align:start position:0% +theorem be true in this setting? It's +not true because the and the balls are + + align:start position:0% +not true because the and the balls are + + + align:start position:0% +not true because the and the balls are +closely packed into kind of a kind of a + + align:start position:0% +closely packed into kind of a kind of a + + + align:start position:0% +closely packed into kind of a kind of a +ball radius root r. Okay, great. That's + + align:start position:0% +ball radius root r. Okay, great. That's + + + align:start position:0% +ball radius root r. Okay, great. That's +a great example. But that great example + + align:start position:0% +a great example. But that great example + + + align:start position:0% +a great example. But that great example +and I will come back to this still + + align:start position:0% +and I will come back to this still + + + align:start position:0% +and I will come back to this still +satisfies the trivial bound. So can the + + align:start position:0% +satisfies the trivial bound. So can the + + + align:start position:0% +satisfies the trivial bound. So can the +trivial bound happen in this setting as + + align:start position:0% +trivial bound happen in this setting as + + + align:start position:0% +trivial bound happen in this setting as +written? + + align:start position:0% +written? + + + align:start position:0% +written? +Because yeah, yeah, if you have + + align:start position:0% +Because yeah, yeah, if you have + + + align:start position:0% +Because yeah, yeah, if you have +everything is is packed into a smaller + + align:start position:0% +everything is is packed into a smaller + + + align:start position:0% +everything is is packed into a smaller +ball, if you project, you still have an + + align:start position:0% +ball, if you project, you still have an + + + align:start position:0% +ball, if you project, you still have an +interval of size the square root. So + + align:start position:0% +interval of size the square root. So + + + align:start position:0% +interval of size the square root. So +you're right, that fails. I'm going to + + align:start position:0% +you're right, that fails. I'm going to + + + align:start position:0% +you're right, that fails. I'm going to +come back to your example. That fails, + + align:start position:0% +come back to your example. That fails, + + + align:start position:0% +come back to your example. That fails, +but this still holds. Can the trivial + + align:start position:0% +but this still holds. Can the trivial + + + align:start position:0% +but this still holds. Can the trivial +bound be true in this setting without + + align:start position:0% +bound be true in this setting without + + + align:start position:0% +bound be true in this setting without +assuming anything else? + + align:start position:0% + + + + align:start position:0% + +There are only two directions. + + align:start position:0% +There are only two directions. + + + align:start position:0% +There are only two directions. +Okay. Uh yeah, two directions. Maybe + + align:start position:0% +Okay. Uh yeah, two directions. Maybe + + + align:start position:0% +Okay. Uh yeah, two directions. Maybe +it's asking too much. Let's say there + + align:start position:0% +it's asking too much. Let's say there + + + align:start position:0% +it's asking too much. Let's say there +are Okay. What is P to the T and what is + + align:start position:0% +are Okay. What is P to the T and what is + + + align:start position:0% +are Okay. What is P to the T and what is +P to the S? It would be row to the T and + + align:start position:0% +P to the S? It would be row to the T and + + + align:start position:0% +P to the S? It would be row to the T and +row to the S. Uh not not row R. R to the + + align:start position:0% +row to the S. Uh not not row R. R to the + + + align:start position:0% +row to the S. Uh not not row R. R to the +T, R to the S. Let's say there are R to + + align:start position:0% +T, R to the S. Let's say there are R to + + + align:start position:0% +T, R to the S. Let's say there are R to +the S directions. Let's make it a little + + align:start position:0% +the S directions. Let's make it a little + + + align:start position:0% +the S directions. Let's make it a little +bit more. Yeah. With two directions. Uh + + align:start position:0% +bit more. Yeah. With two directions. Uh + + + align:start position:0% +bit more. Yeah. With two directions. Uh +maybe. Okay, let's say there are r to + + align:start position:0% +maybe. Okay, let's say there are r to + + + align:start position:0% +maybe. Okay, let's say there are r to +the s directions which are 1 / r + + align:start position:0% +the s directions which are 1 / r + + + align:start position:0% +the s directions which are 1 / r +separated. Can the trivial bound hold? + + align:start position:0% + + + + align:start position:0% + +Okay, what is an example of a set that + + align:start position:0% +Okay, what is an example of a set that + + + align:start position:0% +Okay, what is an example of a set that +has one very small projection? + + align:start position:0% + + + + align:start position:0% + +So what is a set in the plane that has + + align:start position:0% +So what is a set in the plane that has + + + align:start position:0% +So what is a set in the plane that has +one very small projection? + + align:start position:0% +one very small projection? + + + align:start position:0% +one very small projection? +>> All of the balls in a line. + + align:start position:0% +>> All of the balls in a line. + + + align:start position:0% +>> All of the balls in a line. +>> A line. Okay, it cannot literally be a + + align:start position:0% +>> A line. Okay, it cannot literally be a + + + align:start position:0% +>> A line. Okay, it cannot literally be a +line because it's a union of balls. But + + align:start position:0% +line because it's a union of balls. But + + + align:start position:0% +line because it's a union of balls. But +we put the balls in a in a long segment. + + align:start position:0% +we put the balls in a in a long segment. + + + align:start position:0% +we put the balls in a in a long segment. +So uh so an example that should make us + + align:start position:0% +So uh so an example that should make us + + + align:start position:0% +So uh so an example that should make us +kind of scared is + + align:start position:0% +kind of scared is + + + align:start position:0% +kind of scared is +a 1* r rectangle. So packed with balls + + align:start position:0% +a 1* r rectangle. So packed with balls + + + align:start position:0% +a 1* r rectangle. So packed with balls +in this way as someone suggested. + + align:start position:0% +in this way as someone suggested. + + + align:start position:0% +in this way as someone suggested. +Then if we project literally down we get + + align:start position:0% +Then if we project literally down we get + + + align:start position:0% +Then if we project literally down we get +something of of size one which is much + + align:start position:0% +something of of size one which is much + + + align:start position:0% +something of of size one which is much +much much less than square root of r. + + align:start position:0% +much much less than square root of r. + + + align:start position:0% +much much less than square root of r. +But if we perturve the vertical + + align:start position:0% +But if we perturve the vertical + + + align:start position:0% +But if we perturve the vertical +projection by r to the s the projection + + align:start position:0% +projection by r to the s the projection + + + align:start position:0% +projection by r to the s the projection +will have size r to the s and if s is + + align:start position:0% +will have size r to the s and if s is + + + align:start position:0% +will have size r to the s and if s is +less than 12 it will be less than square + + align:start position:0% +less than 12 it will be less than square + + + align:start position:0% +less than 12 it will be less than square +root of r. So, + + align:start position:0% +root of r. So, + + + align:start position:0% +root of r. So, +so instead of projecting in this + + align:start position:0% +so instead of projecting in this + + + align:start position:0% +so instead of projecting in this +direction, if we project in a nearby + + align:start position:0% +direction, if we project in a nearby + + + align:start position:0% +direction, if we project in a nearby +direction, uh this is still bad. So, + + align:start position:0% +direction, uh this is still bad. So, + + + align:start position:0% +direction, uh this is still bad. So, +so if this is x + + align:start position:0% +so if this is x + + + align:start position:0% +so if this is x +and + + align:start position:0% + + + + align:start position:0% + +okay, so I think actually I chose a bad + + align:start position:0% +okay, so I think actually I chose a bad + + + align:start position:0% +okay, so I think actually I chose a bad +so this projection cannot be written in + + align:start position:0% +so this projection cannot be written in + + + align:start position:0% +so this projection cannot be written in +this way. Oh yes, it can be written in + + align:start position:0% +this way. Oh yes, it can be written in + + + align:start position:0% +this way. Oh yes, it can be written in +this way. Just theta is zero. It can be + + align:start position:0% +this way. Just theta is zero. It can be + + + align:start position:0% +this way. Just theta is zero. It can be +very well written in this way. Uh okay. + + align:start position:0% +very well written in this way. Uh okay. + + + align:start position:0% +very well written in this way. Uh okay. +So and if theta is let's say uh minus r + + align:start position:0% +So and if theta is let's say uh minus r + + + align:start position:0% +So and if theta is let's say uh minus r +to the s r to the s + + align:start position:0% +to the s r to the s + + + align:start position:0% +to the s r to the s +then the projection of x will have size + + align:start position:0% +then the projection of x will have size + + + align:start position:0% +then the projection of x will have size +of the order of r to the s + + align:start position:0% +of the order of r to the s + + + align:start position:0% +of the order of r to the s +and well s could be positive but less + + align:start position:0% +and well s could be positive but less + + + align:start position:0% +and well s could be positive but less +than 1/2. + + align:start position:0% +than 1/2. + + + align:start position:0% +than 1/2. +So this this is very bad. Okay. Uh so we + + align:start position:0% +So this this is very bad. Okay. Uh so we + + + align:start position:0% +So this this is very bad. Okay. Uh so we +don't want okay this is not theta this + + align:start position:0% +don't want okay this is not theta this + + + align:start position:0% +don't want okay this is not theta this +is d + + align:start position:0% +is d + + + align:start position:0% +is d +so this is very bad so we don't want d + + align:start position:0% +so this is very bad so we don't want d + + + align:start position:0% +so this is very bad so we don't want d +to look like an interval or to be very + + align:start position:0% +to look like an interval or to be very + + + align:start position:0% +to look like an interval or to be very +concentrated in an interval or something + + align:start position:0% +concentrated in an interval or something + + + align:start position:0% +concentrated in an interval or something +like this so we want to avoid such such + + align:start position:0% +like this so we want to avoid such such + + + align:start position:0% +like this so we want to avoid such such +a situation okay so this is bad it makes + + align:start position:0% +a situation okay so this is bad it makes + + + align:start position:0% +a situation okay so this is bad it makes +even the trivial estimate hopeless + + align:start position:0% +even the trivial estimate hopeless + + + align:start position:0% +even the trivial estimate hopeless +so maybe we'll come back to this if + + align:start position:0% +so maybe we'll come back to this if + + + align:start position:0% +so maybe we'll come back to this if +there is time maybe not but maybe as an + + align:start position:0% +there is time maybe not but maybe as an + + + align:start position:0% +there is time maybe not but maybe as an +exercise for to uh not exercise for + + align:start position:0% +exercise for to uh not exercise for + + + align:start position:0% +exercise for to uh not exercise for +marks or anything but you can think at + + align:start position:0% +marks or anything but you can think at + + + align:start position:0% +marks or anything but you can think at +not now now pay attention but you can + + align:start position:0% +not now now pay attention but you can + + + align:start position:0% +not now now pay attention but you can +think later what goes wrong with this + + align:start position:0% +think later what goes wrong with this + + + align:start position:0% +think later what goes wrong with this +argument because in R2 it's still true + + align:start position:0% +argument because in R2 it's still true + + + align:start position:0% +argument because in R2 it's still true +that two projections even if the angles + + align:start position:0% +that two projections even if the angles + + + align:start position:0% +that two projections even if the angles +are very close determine + + align:start position:0% +are very close determine + + + align:start position:0% +are very close determine +the the original vector so why why so + + align:start position:0% +the the original vector so why why so + + + align:start position:0% +the the original vector so why why so +how is this compatible so you can think + + align:start position:0% +how is this compatible so you can think + + + align:start position:0% +how is this compatible so you can think +about this and then you will understand + + align:start position:0% +about this and then you will understand + + + align:start position:0% +about this and then you will understand +many of their well not many one of one + + align:start position:0% +many of their well not many one of one + + + align:start position:0% +many of their well not many one of one +of the important reasons why things are + + align:start position:0% +of the important reasons why things are + + + align:start position:0% +of the important reasons why things are +much more complicated in this ukidian + + align:start position:0% +much more complicated in this ukidian + + + align:start position:0% +much more complicated in this ukidian +warp. + + align:start position:0% +warp. + + + align:start position:0% +warp. +Okay. So now suppose that uh we avoid + + align:start position:0% +Okay. So now suppose that uh we avoid + + + align:start position:0% +Okay. So now suppose that uh we avoid +this in some way. Uh can we have a hope + + align:start position:0% +this in some way. Uh can we have a hope + + + align:start position:0% +this in some way. Uh can we have a hope +of having the theorem and the answer as + + align:start position:0% +of having the theorem and the answer as + + + align:start position:0% +of having the theorem and the answer as +you said is still no. So this is one + + align:start position:0% +you said is still no. So this is one + + + align:start position:0% +you said is still no. So this is one +example we should be worried about. Uh + + align:start position:0% +example we should be worried about. Uh + + + align:start position:0% +example we should be worried about. Uh +here is another example we should be + + align:start position:0% +here is another example we should be + + + align:start position:0% +here is another example we should be +worried about + + align:start position:0% + + + + align:start position:0% + +where x is essentially let's say a ball + + align:start position:0% +where x is essentially let's say a ball + + + align:start position:0% +where x is essentially let's say a ball +of radius square root of r. It can be + + align:start position:0% +of radius square root of r. It can be + + + align:start position:0% +of radius square root of r. It can be +really any radius between zero and one + + align:start position:0% +really any radius between zero and one + + + align:start position:0% +really any radius between zero and one +but just two. Okay. So x should be a + + align:start position:0% +but just two. Okay. So x should be a + + + align:start position:0% +but just two. Okay. So x should be a +union of this joint unit ball. So we + + align:start position:0% +union of this joint unit ball. So we + + + align:start position:0% +union of this joint unit ball. So we +just pack + + align:start position:0% +just pack + + + align:start position:0% +just pack +in a very dense way unit balls in a bowl + + align:start position:0% +in a very dense way unit balls in a bowl + + + align:start position:0% +in a very dense way unit balls in a bowl +of radius r to the 12. + + align:start position:0% +of radius r to the 12. + + + align:start position:0% +of radius r to the 12. +So the volume of X the area of X is + + align:start position:0% +So the volume of X the area of X is + + + align:start position:0% +So the volume of X the area of X is +roughly R. + + align:start position:0% + + + + align:start position:0% + +But if we project it in any direction. + + align:start position:0% +But if we project it in any direction. + + + align:start position:0% +But if we project it in any direction. +Okay. So we have to get rid of bad sets + + align:start position:0% +Okay. So we have to get rid of bad sets + + + align:start position:0% +Okay. So we have to get rid of bad sets +like this. But let's get rid of bad sets + + align:start position:0% +like this. But let's get rid of bad sets + + + align:start position:0% +like this. But let's get rid of bad sets +like this in the strongest possible way. + + align:start position:0% +like this in the strongest possible way. + + + align:start position:0% +like this in the strongest possible way. +Let's suppose that G is everything. + + align:start position:0% +Let's suppose that G is everything. + + + align:start position:0% +Let's suppose that G is everything. +So here we can so we are we are focusing + + align:start position:0% +So here we can so we are we are focusing + + + align:start position:0% +So here we can so we are we are focusing +on what can go wrong with X. So let D be + + align:start position:0% +on what can go wrong with X. So let D be + + + align:start position:0% +on what can go wrong with X. So let D be +absolutely everything. + + align:start position:0% +absolutely everything. + + + align:start position:0% +absolutely everything. +Well, here every projection + + align:start position:0% +Well, here every projection + + + align:start position:0% +Well, here every projection +is going to be a segment of length + + align:start position:0% +is going to be a segment of length + + + align:start position:0% +is going to be a segment of length +roughly r to the 1/2. + + align:start position:0% +roughly r to the 1/2. + + + align:start position:0% +roughly r to the 1/2. +So if you look at the projection of x, + + align:start position:0% +So if you look at the projection of x, + + + align:start position:0% +So if you look at the projection of x, +this has size roughly square root of the + + align:start position:0% +this has size roughly square root of the + + + align:start position:0% +this has size roughly square root of the +size of x + + align:start position:0% +size of x + + + align:start position:0% +size of x +and this is for every theta. + + align:start position:0% + + + + align:start position:0% + +So in fact if you avoid this in a + + align:start position:0% +So in fact if you avoid this in a + + + align:start position:0% +So in fact if you avoid this in a +suitable way we recover the trivial + + align:start position:0% +suitable way we recover the trivial + + + align:start position:0% +suitable way we recover the trivial +bound but it is no longer trivial. Uh + + align:start position:0% +bound but it is no longer trivial. Uh + + + align:start position:0% +bound but it is no longer trivial. Uh +maybe we'll come back to this on + + align:start position:0% +maybe we'll come back to this on + + + align:start position:0% +maybe we'll come back to this on +Thursday depending on how we are doing + + align:start position:0% +Thursday depending on how we are doing + + + align:start position:0% +Thursday depending on how we are doing +with time. So the trivial bound is no + + align:start position:0% +with time. So the trivial bound is no + + + align:start position:0% +with time. So the trivial bound is no +longer trivial even in the best case. + + align:start position:0% +longer trivial even in the best case. + + + align:start position:0% +longer trivial even in the best case. +But if we want to go beyond the trivial + + align:start position:0% +But if we want to go beyond the trivial + + + align:start position:0% +But if we want to go beyond the trivial +bound uh we also need to assume + + align:start position:0% +bound uh we also need to assume + + + align:start position:0% +bound uh we also need to assume +something about x. So we need to avoid + + align:start position:0% +something about x. So we need to avoid + + + align:start position:0% +something about x. So we need to avoid +this and we need to avoid this. And you + + align:start position:0% +this and we need to avoid this. And you + + + align:start position:0% +this and we need to avoid this. And you +see that in both cases uh what's going + + align:start position:0% +see that in both cases uh what's going + + + align:start position:0% +see that in both cases uh what's going +on? So the geometric + + align:start position:0% +on? So the geometric + + + align:start position:0% +on? So the geometric +picture is different but in both cases D + + align:start position:0% +picture is different but in both cases D + + + align:start position:0% +picture is different but in both cases D +is + + align:start position:0% +is + + + align:start position:0% +is +an interval X is a ball. So we want to + + align:start position:0% +an interval X is a ball. So we want to + + + align:start position:0% +an interval X is a ball. So we want to +avoid X D looking like an interval or X + + align:start position:0% +avoid X D looking like an interval or X + + + align:start position:0% +avoid X D looking like an interval or X +looking like a box. And if we do that in + + align:start position:0% +looking like a box. And if we do that in + + + align:start position:0% +looking like a box. And if we do that in +a suitable way then we can indeed get + + align:start position:0% +a suitable way then we can indeed get + + + align:start position:0% +a suitable way then we can indeed get +a similar statement. So let me actually + + align:start position:0% +a similar statement. So let me actually + + + align:start position:0% +a similar statement. So let me actually +state it. + + align:start position:0% +state it. + + + align:start position:0% +state it. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay, let me say that Bugan didn't state + + align:start position:0% +Okay, let me say that Bugan didn't state + + + align:start position:0% +Okay, let me say that Bugan didn't state +it in this way but + + align:start position:0% + + + + align:start position:0% + +okay this follows from what he proved. + + align:start position:0% +okay this follows from what he proved. + + + align:start position:0% +okay this follows from what he proved. +Okay. Um suppose that + + align:start position:0% +Okay. Um suppose that + + + align:start position:0% +Okay. Um suppose that +same same setting as before. So, + + align:start position:0% + + + + align:start position:0% + +so we are still assuming this + + align:start position:0% + + + + align:start position:0% + +would have been faster to just write + + align:start position:0% +would have been faster to just write + + + align:start position:0% +would have been faster to just write +everything down again. But okay, but we + + align:start position:0% +everything down again. But okay, but we + + + align:start position:0% +everything down again. But okay, but we +need to have some assumptions uh to + + align:start position:0% +need to have some assumptions uh to + + + align:start position:0% +need to have some assumptions uh to +avoid these web examples. + + align:start position:0% +avoid these web examples. + + + align:start position:0% +avoid these web examples. +So uh okay, so first of all we need some + + align:start position:0% +So uh okay, so first of all we need some + + + align:start position:0% +So uh okay, so first of all we need some +quantifier. So given + + align:start position:0% +quantifier. So given + + + align:start position:0% +quantifier. So given +zero t uh so t is strictly between zero + + align:start position:0% +zero t uh so t is strictly between zero + + + align:start position:0% +zero t uh so t is strictly between zero +and two and s + + align:start position:0% +and two and s + + + align:start position:0% +and two and s +larger than zero there exist now two + + align:start position:0% +larger than zero there exist now two + + + align:start position:0% +larger than zero there exist now two +parameters so I could do with one + + align:start position:0% +parameters so I could do with one + + + align:start position:0% +parameters so I could do with one +parameter so you see that even here I'm + + align:start position:0% +parameter so you see that even here I'm + + + align:start position:0% +parameter so you see that even here I'm +using epsilon for two different things + + align:start position:0% +using epsilon for two different things + + + align:start position:0% +using epsilon for two different things +for the growth and for the robustness in + + align:start position:0% +for the growth and for the robustness in + + + align:start position:0% +for the growth and for the robustness in +passing to subsets here I'm going to use + + align:start position:0% +passing to subsets here I'm going to use + + + align:start position:0% +passing to subsets here I'm going to use +two different letters because they + + align:start position:0% +two different letters because they + + + align:start position:0% +two different letters because they +denote different + + align:start position:0% +denote different + + + align:start position:0% +denote different +thinks + + align:start position:0% +thinks + + + align:start position:0% +thinks +so there exist epsilon + + align:start position:0% +so there exist epsilon + + + align:start position:0% +so there exist epsilon +and ita both depending on s and t and + + align:start position:0% +and ita both depending on s and t and + + + align:start position:0% +and ita both depending on s and t and +both positive such that the following + + align:start position:0% +both positive such that the following + + + align:start position:0% +both positive such that the following +holds + + align:start position:0% +holds + + + align:start position:0% +holds +okay so suppose that we have x union of + + align:start position:0% +okay so suppose that we have x union of + + + align:start position:0% +okay so suppose that we have x union of +unit balls in the r + + align:start position:0% +unit balls in the r + + + align:start position:0% +unit balls in the r +uh 1 / r separated set of directions + + align:start position:0% + + + + align:start position:0% + +uh okay and then we need to assume + + align:start position:0% +uh okay and then we need to assume + + + align:start position:0% +uh okay and then we need to assume +something because otherwise it's not + + align:start position:0% +something because otherwise it's not + + + align:start position:0% +something because otherwise it's not +true so we need to assume that x and d + + align:start position:0% +true so we need to assume that x and d + + + align:start position:0% +true so we need to assume that x and d +are not very concentrated in small balls + + align:start position:0% +are not very concentrated in small balls + + + align:start position:0% +are not very concentrated in small balls +or small intervals. So this is what we + + align:start position:0% +or small intervals. So this is what we + + + align:start position:0% +or small intervals. So this is what we +are going to assume. + + align:start position:0% +are going to assume. + + + align:start position:0% +are going to assume. +If we intercept x with any ball of + + align:start position:0% +If we intercept x with any ball of + + + align:start position:0% +If we intercept x with any ball of +radius r + + align:start position:0% +radius r + + + align:start position:0% +radius r +we see only a small piece of x and the + + align:start position:0% +we see only a small piece of x and the + + + align:start position:0% +we see only a small piece of x and the +smaller the r the smaller the piece and + + align:start position:0% +smaller the r the smaller the piece and + + + align:start position:0% +smaller the r the smaller the piece and +the range of this little r is between + + align:start position:0% +the range of this little r is between + + + align:start position:0% +the range of this little r is between +one and big r because x is a unit of + + align:start position:0% +one and big r because x is a unit of + + + align:start position:0% +one and big r because x is a unit of +unit balls and it's a subset of the r + + align:start position:0% +unit balls and it's a subset of the r + + + align:start position:0% +unit balls and it's a subset of the r +ball. Okay so this should be less or + + align:start position:0% +ball. Okay so this should be less or + + + align:start position:0% +ball. Okay so this should be less or +equal than what? Well, on the one hand, + + align:start position:0% +equal than what? Well, on the one hand, + + + align:start position:0% +equal than what? Well, on the one hand, +we want to compare this to the natural + + align:start position:0% +we want to compare this to the natural + + + align:start position:0% +we want to compare this to the natural +scale, which is R. So, this tells us how + + align:start position:0% +scale, which is R. So, this tells us how + + + align:start position:0% +scale, which is R. So, this tells us how +much smaller the reference scale is + + align:start position:0% +much smaller the reference scale is + + + align:start position:0% +much smaller the reference scale is +compared to the global scale. And let's + + align:start position:0% +compared to the global scale. And let's + + + align:start position:0% +compared to the global scale. And let's +put the T here, which is motivated by + + align:start position:0% +put the T here, which is motivated by + + + align:start position:0% +put the T here, which is motivated by +the fact that okay uh + + align:start position:0% +the fact that okay uh + + + align:start position:0% +the fact that okay uh +okay, so X has area R to the T and D has + + align:start position:0% +okay, so X has area R to the T and D has + + + align:start position:0% +okay, so X has area R to the T and D has +cardinality R to the S. + + align:start position:0% +cardinality R to the S. + + + align:start position:0% +cardinality R to the S. +Okay, so this T matches this T + + align:start position:0% + + + + align:start position:0% + +and then I have the size of X. So this + + align:start position:0% +and then I have the size of X. So this + + + align:start position:0% +and then I have the size of X. So this +is saying if R is much smaller than big + + align:start position:0% +is saying if R is much smaller than big + + + align:start position:0% +is saying if R is much smaller than big +R. So if if R is big R, we have all of + + align:start position:0% +R. So if if R is big R, we have all of + + + align:start position:0% +R. So if if R is big R, we have all of +X. So we can we cannot get any gain + + align:start position:0% +X. So we can we cannot get any gain + + + align:start position:0% +X. So we can we cannot get any gain +because X is contained in the ball of + + align:start position:0% +because X is contained in the ball of + + + align:start position:0% +because X is contained in the ball of +radius R. But if we are intersecting X + + align:start position:0% +radius R. But if we are intersecting X + + + align:start position:0% +radius R. But if we are intersecting X +with a smaller ball, + + align:start position:0% +with a smaller ball, + + + align:start position:0% +with a smaller ball, +we have + + align:start position:0% +we have + + + align:start position:0% +we have +a big decay sort of power decay with + + align:start position:0% +a big decay sort of power decay with + + + align:start position:0% +a big decay sort of power decay with +respect to so + + align:start position:0% +respect to so + + + align:start position:0% +respect to so +only a very small part of X can be in a + + align:start position:0% +only a very small part of X can be in a + + + align:start position:0% +only a very small part of X can be in a +small ball compared to the whole of X. + + align:start position:0% +small ball compared to the whole of X. + + + align:start position:0% +small ball compared to the whole of X. +Okay. And it turns out that it's very + + align:start position:0% +Okay. And it turns out that it's very + + + align:start position:0% +Okay. And it turns out that it's very +important for applications to have some + + align:start position:0% +important for applications to have some + + + align:start position:0% +important for applications to have some +leeway here. And this leeway is given by + + align:start position:0% +leeway here. And this leeway is given by + + + align:start position:0% +leeway here. And this leeway is given by +this parameter EA. + + align:start position:0% +this parameter EA. + + + align:start position:0% +this parameter EA. +So this leeway says that actually + + align:start position:0% +So this leeway says that actually + + + align:start position:0% +So this leeway says that actually +we don't need to assume anything if R is + + align:start position:0% +we don't need to assume anything if R is + + + align:start position:0% +we don't need to assume anything if R is +very close little R is very close to big + + align:start position:0% +very close little R is very close to big + + + align:start position:0% +very close little R is very close to big +R because if R is very close to big R + + align:start position:0% +R because if R is very close to big R + + + align:start position:0% +R because if R is very close to big R +this will still be bigger than one and + + align:start position:0% +this will still be bigger than one and + + + align:start position:0% +this will still be bigger than one and +then we have a trivial trivial + + align:start position:0% +then we have a trivial trivial + + + align:start position:0% +then we have a trivial trivial +inequality. So this is saying the global + + align:start position:0% +inequality. So this is saying the global + + + align:start position:0% +inequality. So this is saying the global +scales don't matter. Okay and a very + + align:start position:0% +scales don't matter. Okay and a very + + + align:start position:0% +scales don't matter. Okay and a very +similar story with D. + + align:start position:0% +similar story with D. + + + align:start position:0% +similar story with D. +If we intersect D okay balls here are + + align:start position:0% +If we intersect D okay balls here are + + + align:start position:0% +If we intersect D okay balls here are +intervals but I'm going to + + align:start position:0% + + + + align:start position:0% + +still the notation for balls this is at + + align:start position:0% +still the notation for balls this is at + + + align:start position:0% +still the notation for balls this is at +most again we have our ley r to the + + align:start position:0% +most again we have our ley r to the + + + align:start position:0% +most again we have our ley r to the +epsilon + + align:start position:0% +epsilon + + + align:start position:0% +epsilon +and then row is between zero and one so + + align:start position:0% +and then row is between zero and one so + + + align:start position:0% +and then row is between zero and one so +here the right thing to write is row to + + align:start position:0% +here the right thing to write is row to + + + align:start position:0% +here the right thing to write is row to +the s + + align:start position:0% +the s + + + align:start position:0% +the s +times + + align:start position:0% +times + + + align:start position:0% +times +okay so the size of x is actually r to + + align:start position:0% +okay so the size of x is actually r to + + + align:start position:0% +okay so the size of x is actually r to +the t but still I want to write it in + + align:start position:0% +the t but still I want to write it in + + + align:start position:0% +the t but still I want to write it in +this way so it's clear that when we + + align:start position:0% +this way so it's clear that when we + + + align:start position:0% +this way so it's clear that when we +intersect with the ball we are seeing + + align:start position:0% +intersect with the ball we are seeing + + + align:start position:0% +intersect with the ball we are seeing +only a small piece of X + + align:start position:0% +only a small piece of X + + + align:start position:0% +only a small piece of X +and same thing here. + + align:start position:0% +and same thing here. + + + align:start position:0% +and same thing here. +Okay, so these are the conditions that + + align:start position:0% +Okay, so these are the conditions that + + + align:start position:0% +Okay, so these are the conditions that +we impose to avoid these bad control + + align:start position:0% +we impose to avoid these bad control + + + align:start position:0% +we impose to avoid these bad control +examples and you could say that they are + + align:start position:0% +examples and you could say that they are + + + align:start position:0% +examples and you could say that they are +overkill and we are avoiding not only + + align:start position:0% +overkill and we are avoiding not only + + + align:start position:0% +overkill and we are avoiding not only +this but okay put it in a different way + + align:start position:0% +this but okay put it in a different way + + + align:start position:0% +this but okay put it in a different way +there is a whole universe between this + + align:start position:0% +there is a whole universe between this + + + align:start position:0% +there is a whole universe between this +and this and yeah this is true and in + + align:start position:0% +and this and yeah this is true and in + + + align:start position:0% +and this and yeah this is true and in +fact these conditions can be weakened + + align:start position:0% +fact these conditions can be weakened + + + align:start position:0% +fact these conditions can be weakened +maybe I will make some remark about this + + align:start position:0% +maybe I will make some remark about this + + + align:start position:0% +maybe I will make some remark about this +but anyway so these are the assumptions + + align:start position:0% +but anyway so these are the assumptions + + + align:start position:0% +but anyway so these are the assumptions +then + + align:start position:0% +then + + + align:start position:0% +then +there exist one direction and once there + + align:start position:0% +there exist one direction and once there + + + align:start position:0% +there exist one direction and once there +is one direction there are many ctions + + align:start position:0% +is one direction there are many ctions + + + align:start position:0% +is one direction there are many ctions +are such that we have the same uh + + align:start position:0% +are such that we have the same uh + + + align:start position:0% +are such that we have the same uh +conclusion. + + align:start position:0% + + + + align:start position:0% + +So if we look at the infyom + + align:start position:0% +So if we look at the infyom + + + align:start position:0% +So if we look at the infyom +over all dense subsets and dense means + + align:start position:0% +over all dense subsets and dense means + + + align:start position:0% +over all dense subsets and dense means +with respect to this so this parameter + + align:start position:0% +with respect to this so this parameter + + + align:start position:0% +with respect to this so this parameter +it so it is like a tolerance parameter + + align:start position:0% +it so it is like a tolerance parameter + + + align:start position:0% +it so it is like a tolerance parameter +it gives us some leeway at different + + align:start position:0% +it gives us some leeway at different + + + align:start position:0% +it gives us some leeway at different +places to play with. + + align:start position:0% + + + + align:start position:0% + +So y sorry yeah y is a dense subset of x + + align:start position:0% +So y sorry yeah y is a dense subset of x + + + align:start position:0% +So y sorry yeah y is a dense subset of x +with this leeway r to the minus epsilon + + align:start position:0% +with this leeway r to the minus epsilon + + + align:start position:0% +with this leeway r to the minus epsilon +then we project this subset and we get + + align:start position:0% +then we project this subset and we get + + + align:start position:0% +then we project this subset and we get +the gain. + + align:start position:0% +the gain. + + + align:start position:0% +the gain. +So the trivial now is no longer trivial + + align:start position:0% +So the trivial now is no longer trivial + + + align:start position:0% +So the trivial now is no longer trivial +but sort of natural lower bound is t + + align:start position:0% +but sort of natural lower bound is t + + + align:start position:0% +but sort of natural lower bound is t +over two and we beat it by epsilon. + + align:start position:0% + + + + align:start position:0% + +>> Yes. Does Y also have to be a union of + + align:start position:0% +>> Yes. Does Y also have to be a union of + + + align:start position:0% +>> Yes. Does Y also have to be a union of +univolves? + + align:start position:0% +univolves? + + + align:start position:0% +univolves? +>> Uh, that's a very good question. + + align:start position:0% + + + + align:start position:0% + +>> I don't think so. But yeah, just in + + align:start position:0% +>> I don't think so. But yeah, just in + + + align:start position:0% +>> I don't think so. But yeah, just in +case. Yes. Just in case I'm too tired. + + align:start position:0% +case. Yes. Just in case I'm too tired. + + + align:start position:0% +case. Yes. Just in case I'm too tired. +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +Yeah. Let's say yes. Let's say yes. + + align:start position:0% +Yeah. Let's say yes. Let's say yes. + + + align:start position:0% +Yeah. Let's say yes. Let's say yes. +Yeah. So, we're going to restate this in + + align:start position:0% +Yeah. So, we're going to restate this in + + + align:start position:0% +Yeah. So, we're going to restate this in +a different language soon. Uh, where we + + align:start position:0% +a different language soon. Uh, where we + + + align:start position:0% +a different language soon. Uh, where we +will get rid of balls. Yeah, let's say y + + align:start position:0% +will get rid of balls. Yeah, let's say y + + + align:start position:0% +will get rid of balls. Yeah, let's say y +is also unit balls. + + align:start position:0% +is also unit balls. + + + align:start position:0% +is also unit balls. +Okay, so you see that there are lots of + + align:start position:0% +Okay, so you see that there are lots of + + + align:start position:0% +Okay, so you see that there are lots of +parameters. It's kind of a technical + + align:start position:0% +parameters. It's kind of a technical + + + align:start position:0% +parameters. It's kind of a technical +statement. The assumption looks a bit + + align:start position:0% +statement. The assumption looks a bit + + + align:start position:0% +statement. The assumption looks a bit +strange if you have never seen this + + align:start position:0% +strange if you have never seen this + + + align:start position:0% +strange if you have never seen this +before, but nevertheless is again an + + align:start position:0% +before, but nevertheless is again an + + + align:start position:0% +before, but nevertheless is again an +extremely important theorem with an + + align:start position:0% +extremely important theorem with an + + + align:start position:0% +extremely important theorem with an +unbelievably range of applications and + + align:start position:0% +unbelievably range of applications and + + + align:start position:0% +unbelievably range of applications and +we keep discovering applications and + + align:start position:0% +we keep discovering applications and + + + align:start position:0% +we keep discovering applications and +something which is also important to + + align:start position:0% +something which is also important to + + + align:start position:0% +something which is also important to +remark is that all the applications + + align:start position:0% +remark is that all the applications + + + align:start position:0% +remark is that all the applications +really use the statement as a black box. + + align:start position:0% +really use the statement as a black box. + + + align:start position:0% +really use the statement as a black box. +they don't okay it's sometimes people + + align:start position:0% +they don't okay it's sometimes people + + + align:start position:0% +they don't okay it's sometimes people +also get inspired by the proof but it's + + align:start position:0% +also get inspired by the proof but it's + + + align:start position:0% +also get inspired by the proof but it's +not a situation where the proof gets + + align:start position:0% +not a situation where the proof gets + + + align:start position:0% +not a situation where the proof gets +used really the statement gets used so + + align:start position:0% +used really the statement gets used so + + + align:start position:0% +used really the statement gets used so +it's a very very powerful statement and + + align:start position:0% +it's a very very powerful statement and + + + align:start position:0% +it's a very very powerful statement and +I guess in the rest of the course with + + align:start position:0% +I guess in the rest of the course with + + + align:start position:0% +I guess in the rest of the course with +Larry you will see some some of the ways + + align:start position:0% +Larry you will see some some of the ways + + + align:start position:0% +Larry you will see some some of the ways +in which it is very powerful okay so how + + align:start position:0% +in which it is very powerful okay so how + + + align:start position:0% +in which it is very powerful okay so how +does one prove this and by the way I'm + + align:start position:0% +does one prove this and by the way I'm + + + align:start position:0% +does one prove this and by the way I'm +going to sort of as I say sketch the + + align:start position:0% +going to sort of as I say sketch the + + + align:start position:0% +going to sort of as I say sketch the +proof skipping pretty much all details + + align:start position:0% +proof skipping pretty much all details + + + align:start position:0% +proof skipping pretty much all details +but the proof I'm going to sketch is not + + align:start position:0% +but the proof I'm going to sketch is not + + + align:start position:0% +but the proof I'm going to sketch is not +Bans proof + + align:start position:0% +Bans proof + + + align:start position:0% +Bans proof +It's it's a + + align:start position:0% +It's it's a + + + align:start position:0% +It's it's a +uh yeah maybe a new proof that I'm + + align:start position:0% +uh yeah maybe a new proof that I'm + + + align:start position:0% +uh yeah maybe a new proof that I'm +writing together with Hong Wang that + + align:start position:0% +writing together with Hong Wang that + + + align:start position:0% +writing together with Hong Wang that +takes ideas from different places. U + + align:start position:0% +takes ideas from different places. U + + + align:start position:0% +takes ideas from different places. U +so it's is not Bhan's original proof. + + align:start position:0% +so it's is not Bhan's original proof. + + + align:start position:0% +so it's is not Bhan's original proof. +Okay. So um the general scheme will + + align:start position:0% +Okay. So um the general scheme will + + + align:start position:0% +Okay. So um the general scheme will +follow the steps that you've seen in the + + align:start position:0% +follow the steps that you've seen in the + + + align:start position:0% +follow the steps that you've seen in the +final field setting but there are very + + align:start position:0% +final field setting but there are very + + + align:start position:0% +final field setting but there are very +significant challenges. So what I'm + + align:start position:0% +significant challenges. So what I'm + + + align:start position:0% +significant challenges. So what I'm +going to do is go over each of the steps + + align:start position:0% +going to do is go over each of the steps + + + align:start position:0% +going to do is go over each of the steps +and explain what the challenges are and + + align:start position:0% +and explain what the challenges are and + + + align:start position:0% +and explain what the challenges are and +what can one do to fix them and then you + + align:start position:0% +what can one do to fix them and then you + + + align:start position:0% +what can one do to fix them and then you +will have to trust me that indeed they + + align:start position:0% +will have to trust me that indeed they + + + align:start position:0% +will have to trust me that indeed they +they can be fixed. So I won't go into + + align:start position:0% +they can be fixed. So I won't go into + + + align:start position:0% +they can be fixed. So I won't go into +the details. So + + align:start position:0% +the details. So + + + align:start position:0% +the details. So +before doing so, so uh + + align:start position:0% +before doing so, so uh + + + align:start position:0% +before doing so, so uh +you saw that if we want to go from + + align:start position:0% +you saw that if we want to go from + + + align:start position:0% +you saw that if we want to go from +finite field to + + align:start position:0% +finite field to + + + align:start position:0% +finite field to +uklidian settings, + + align:start position:0% +uklidian settings, + + + align:start position:0% +uklidian settings, +uh sometimes you have to add more + + align:start position:0% +uh sometimes you have to add more + + + align:start position:0% +uh sometimes you have to add more +assumptions otherwise things fail + + align:start position:0% +assumptions otherwise things fail + + + align:start position:0% +assumptions otherwise things fail +because of some easy examples. But this + + align:start position:0% +because of some easy examples. But this + + + align:start position:0% +because of some easy examples. But this +is not always the case. So there are + + align:start position:0% +is not always the case. So there are + + + align:start position:0% +is not always the case. So there are +some some statements in the finite + + align:start position:0% +some some statements in the finite + + + align:start position:0% +some some statements in the finite +setting that extend pretty in a pretty + + align:start position:0% +setting that extend pretty in a pretty + + + align:start position:0% +setting that extend pretty in a pretty +straightforward way to this uklidian + + align:start position:0% +straightforward way to this uklidian + + + align:start position:0% +straightforward way to this uklidian +setting. So + + align:start position:0% +setting. So + + + align:start position:0% +setting. So +um so in order to do this uh I'm going + + align:start position:0% +um so in order to do this uh I'm going + + + align:start position:0% +um so in order to do this uh I'm going +to sort of change the language a little + + align:start position:0% +to sort of change the language a little + + + align:start position:0% +to sort of change the language a little +bit and + + align:start position:0% +bit and + + + align:start position:0% +bit and +uh maybe rescale this. So instead of + + align:start position:0% +uh maybe rescale this. So instead of + + + align:start position:0% +uh maybe rescale this. So instead of +looking at union of unions of unit balls + + align:start position:0% +looking at union of unions of unit balls + + + align:start position:0% +looking at union of unions of unit balls +in the R ball, I'm going to look at so + + align:start position:0% +in the R ball, I'm going to look at so + + + align:start position:0% +in the R ball, I'm going to look at so +basically I need to rescale the set down + + align:start position:0% +basically I need to rescale the set down + + + align:start position:0% +basically I need to rescale the set down +by one over R. So X is going to live in + + align:start position:0% +by one over R. So X is going to live in + + + align:start position:0% +by one over R. So X is going to live in +the unit ball and then it will be a + + align:start position:0% +the unit ball and then it will be a + + + align:start position:0% +the unit ball and then it will be a +union of one over R balls and of course + + align:start position:0% +union of one over R balls and of course + + + align:start position:0% +union of one over R balls and of course +you have to rescale if you rescale you + + align:start position:0% +you have to rescale if you rescale you + + + align:start position:0% +you have to rescale if you rescale you +have to rescale everywhere else in the + + align:start position:0% +have to rescale everywhere else in the + + + align:start position:0% +have to rescale everywhere else in the +statement. But instead of looking at the + + align:start position:0% +statement. But instead of looking at the + + + align:start position:0% +statement. But instead of looking at the +volume of uh the set X, I'm going to use + + align:start position:0% +volume of uh the set X, I'm going to use + + + align:start position:0% +volume of uh the set X, I'm going to use +the delta covering number. And for the + + align:start position:0% +the delta covering number. And for the + + + align:start position:0% +the delta covering number. And for the +directions, instead of assuming that + + align:start position:0% +directions, instead of assuming that + + + align:start position:0% +directions, instead of assuming that +they are disjoint, I'm also going to use + + align:start position:0% +they are disjoint, I'm also going to use + + + align:start position:0% +they are disjoint, I'm also going to use +the delta covering number. So I bring + + align:start position:0% +the delta covering number. So I bring + + + align:start position:0% +the delta covering number. So I bring +both. So basically X and D, I want to + + align:start position:0% +both. So basically X and D, I want to + + + align:start position:0% +both. So basically X and D, I want to +use the same language and same scale to + + align:start position:0% +use the same language and same scale to + + + align:start position:0% +use the same language and same scale to +make things more homogeneous. + + align:start position:0% +make things more homogeneous. + + + align:start position:0% +make things more homogeneous. +So let me spend a couple of minutes + + align:start position:0% + + + + align:start position:0% + +uh talking about the data covering + + align:start position:0% +uh talking about the data covering + + + align:start position:0% +uh talking about the data covering +number. Suppose that X is a subset of + + align:start position:0% +number. Suppose that X is a subset of + + + align:start position:0% +number. Suppose that X is a subset of +really any metric space but let's say RD + + align:start position:0% + + + + align:start position:0% + +then uh okay so this is I guess + + align:start position:0% +then uh okay so this is I guess + + + align:start position:0% +then uh okay so this is I guess +definition or notation + + align:start position:0% +definition or notation + + + align:start position:0% +definition or notation +XAR delta so bar with your subscript + + align:start position:0% +XAR delta so bar with your subscript + + + align:start position:0% +XAR delta so bar with your subscript +delta + + align:start position:0% +delta + + + align:start position:0% +delta +is the smallest + + align:start position:0% +is the smallest + + + align:start position:0% +is the smallest +number of delta balls + + align:start position:0% + + + + align:start position:0% + +needed to cover + + align:start position:0% + + + + align:start position:0% + +could be infinite but we only so in all + + align:start position:0% +could be infinite but we only so in all + + + align:start position:0% +could be infinite but we only so in all +this business we are only looking at + + align:start position:0% +this business we are only looking at + + + align:start position:0% +this business we are only looking at +bounded sets in which case this is + + align:start position:0% +bounded sets in which case this is + + + align:start position:0% +bounded sets in which case this is +finite. So everything we are going to + + align:start position:0% +finite. So everything we are going to + + + align:start position:0% +finite. So everything we are going to +see is going to be a finite number. + + align:start position:0% +see is going to be a finite number. + + + align:start position:0% +see is going to be a finite number. +Okay. So this is a basically uh our + + align:start position:0% +Okay. So this is a basically uh our + + + align:start position:0% +Okay. So this is a basically uh our +measuring resolution is delta. We cannot + + align:start position:0% +measuring resolution is delta. We cannot + + + align:start position:0% +measuring resolution is delta. We cannot +distinguish anything that happens under + + align:start position:0% +distinguish anything that happens under + + + align:start position:0% +distinguish anything that happens under +scale delta. So this is a natural way of + + align:start position:0% +scale delta. So this is a natural way of + + + align:start position:0% +scale delta. So this is a natural way of +measuring the size of the set. + + align:start position:0% +measuring the size of the set. + + + align:start position:0% +measuring the size of the set. +Okay. So, some just just a definition + + align:start position:0% +Okay. So, some just just a definition + + + align:start position:0% +Okay. So, some just just a definition +but some observations. + + align:start position:0% + + + + align:start position:0% + +Well, uh the first one I think I should + + align:start position:0% +Well, uh the first one I think I should + + + align:start position:0% +Well, uh the first one I think I should +never use the words the word trivial but + + align:start position:0% +never use the words the word trivial but + + + align:start position:0% +never use the words the word trivial but +I hope I'm justify justifying saying + + align:start position:0% +I hope I'm justify justifying saying + + + align:start position:0% +I hope I'm justify justifying saying +that this is trivial. If x + + align:start position:0% + + + + align:start position:0% + +is to make it really trivial two delta + + align:start position:0% +is to make it really trivial two delta + + + align:start position:0% +is to make it really trivial two delta +separated + + align:start position:0% + + + + align:start position:0% + +then the delta covering number is just + + align:start position:0% +then the delta covering number is just + + + align:start position:0% +then the delta covering number is just +the cardality + + align:start position:0% +the cardality + + + align:start position:0% +the cardality +because for each point in the set we + + align:start position:0% +because for each point in the set we + + + align:start position:0% +because for each point in the set we +need a different ball. + + align:start position:0% + + + + align:start position:0% + +Okay. So this will be the case for d. D + + align:start position:0% +Okay. So this will be the case for d. D + + + align:start position:0% +Okay. So this will be the case for d. D +is delta separated but delta separated + + align:start position:0% +is delta separated but delta separated + + + align:start position:0% +is delta separated but delta separated +to delta separated doesn't make a big + + align:start position:0% +to delta separated doesn't make a big + + + align:start position:0% +to delta separated doesn't make a big +difference. So if the set is delta + + align:start position:0% +difference. So if the set is delta + + + align:start position:0% +difference. So if the set is delta +separated is morally just the + + align:start position:0% +separated is morally just the + + + align:start position:0% +separated is morally just the +cardinality. + + align:start position:0% +cardinality. + + + align:start position:0% +cardinality. +Okay. If X is a union + + align:start position:0% + + + + align:start position:0% + +of delta balls + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the delta covering number is well you + + align:start position:0% +the delta covering number is well you + + + align:start position:0% +the delta covering number is well you +use the balls to cover the set and okay + + align:start position:0% +use the balls to cover the set and okay + + + align:start position:0% +use the balls to cover the set and okay +you need to normalize to pass between + + align:start position:0% +you need to normalize to pass between + + + align:start position:0% +you need to normalize to pass between +measure and counting how many balls + + align:start position:0% +measure and counting how many balls + + + align:start position:0% +measure and counting how many balls +there are. So + + align:start position:0% +there are. So + + + align:start position:0% +there are. So +I think this should be delta to the + + align:start position:0% +I think this should be delta to the + + + align:start position:0% +I think this should be delta to the +minus D. So this is the ambient + + align:start position:0% +minus D. So this is the ambient + + + align:start position:0% +minus D. So this is the ambient +dimension where x lives times the le + + align:start position:0% +dimension where x lives times the le + + + align:start position:0% +dimension where x lives times the le +measure of x. + + align:start position:0% +measure of x. + + + align:start position:0% +measure of x. +Did I get this right? And it's not + + align:start position:0% +Did I get this right? And it's not + + + align:start position:0% +Did I get this right? And it's not +actually equal. It's comparable. + + align:start position:0% + + + + align:start position:0% + +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +>> Or does x have to be a disjoint union of + + align:start position:0% +>> Or does x have to be a disjoint union of + + + align:start position:0% +>> Or does x have to be a disjoint union of +delta balls? + + align:start position:0% +delta balls? + + + align:start position:0% +delta balls? +>> Yeah, that's a very good question. No. + + align:start position:0% +>> Yeah, that's a very good question. No. + + + align:start position:0% +>> Yeah, that's a very good question. No. +uh is easier to believe if it if it is a + + align:start position:0% +uh is easier to believe if it if it is a + + + align:start position:0% +uh is easier to believe if it if it is a +disjoint union of delta balls and it is + + align:start position:0% +disjoint union of delta balls and it is + + + align:start position:0% +disjoint union of delta balls and it is +also true if it's a non- disjoint unit + + align:start position:0% +also true if it's a non- disjoint unit + + + align:start position:0% +also true if it's a non- disjoint unit +of delta balls and the reason is that if + + align:start position:0% +of delta balls and the reason is that if + + + align:start position:0% +of delta balls and the reason is that if +you have a non- disjoint unit of delta + + align:start position:0% +you have a non- disjoint unit of delta + + + align:start position:0% +you have a non- disjoint unit of delta +balls you can cover it by finitely + + align:start position:0% +balls you can cover it by finitely + + + align:start position:0% +balls you can cover it by finitely +overlapping okay if the if you have a + + align:start position:0% +overlapping okay if the if you have a + + + align:start position:0% +overlapping okay if the if you have a +disjoint unit of delta balls I hope this + + align:start position:0% +disjoint unit of delta balls I hope this + + + align:start position:0% +disjoint unit of delta balls I hope this +is clear because the best way to cover + + align:start position:0% +is clear because the best way to cover + + + align:start position:0% +is clear because the best way to cover +it by using those those balls + + align:start position:0% +it by using those those balls + + + align:start position:0% +it by using those those balls +if you have a finitely overlapping + + align:start position:0% +if you have a finitely overlapping + + + align:start position:0% +if you have a finitely overlapping +collection of delta balls then well you + + align:start position:0% +collection of delta balls then well you + + + align:start position:0% +collection of delta balls then well you +just cover by the finally overlapping + + align:start position:0% +just cover by the finally overlapping + + + align:start position:0% +just cover by the finally overlapping +family and you lose and any any union of + + align:start position:0% +family and you lose and any any union of + + + align:start position:0% +family and you lose and any any union of +balls you can cover by a finite + + align:start position:0% +balls you can cover by a finite + + + align:start position:0% +balls you can cover by a finite +overlapping. So I guess you need some + + align:start position:0% +overlapping. So I guess you need some + + + align:start position:0% +overlapping. So I guess you need some +covering theorem to make it precise. + + align:start position:0% +covering theorem to make it precise. + + + align:start position:0% +covering theorem to make it precise. +Anyway, it's true and we are not going + + align:start position:0% +Anyway, it's true and we are not going + + + align:start position:0% +Anyway, it's true and we are not going +to use it. But you can convince yourself + + align:start position:0% +to use it. But you can convince yourself + + + align:start position:0% +to use it. But you can convince yourself +that it's true. Again, easier to believe + + align:start position:0% +that it's true. Again, easier to believe + + + align:start position:0% +that it's true. Again, easier to believe +if the balls are disjoint, but also + + align:start position:0% +if the balls are disjoint, but also + + + align:start position:0% +if the balls are disjoint, but also +true. If balls are disjoint is equal if + + align:start position:0% +true. If balls are disjoint is equal if + + + align:start position:0% +true. If balls are disjoint is equal if +the PS are not disjoint, there is a + + align:start position:0% +the PS are not disjoint, there is a + + + align:start position:0% +the PS are not disjoint, there is a +wiggle. In fact, the wiggle I guess that + + align:start position:0% +wiggle. In fact, the wiggle I guess that + + + align:start position:0% +wiggle. In fact, the wiggle I guess that +maybe depends on the ambient dimension + + align:start position:0% +maybe depends on the ambient dimension + + + align:start position:0% +maybe depends on the ambient dimension +D. + + align:start position:0% +D. + + + align:start position:0% +D. +Okay. So I'm just making these remarks + + align:start position:0% +Okay. So I'm just making these remarks + + + align:start position:0% +Okay. So I'm just making these remarks +to say that to to sort of explain how + + align:start position:0% +to say that to to sort of explain how + + + align:start position:0% +to say that to to sort of explain how +this relates to our previous setting + + align:start position:0% +this relates to our previous setting + + + align:start position:0% +this relates to our previous setting +because now from now on we are going to + + align:start position:0% +because now from now on we are going to + + + align:start position:0% +because now from now on we are going to +measure everything by the delta covering + + align:start position:0% +measure everything by the delta covering + + + align:start position:0% +measure everything by the delta covering +number and the point I want to make is + + align:start position:0% +number and the point I want to make is + + + align:start position:0% +number and the point I want to make is +that this recovers the volume and the + + align:start position:0% +that this recovers the volume and the + + + align:start position:0% +that this recovers the volume and the +cardality when the sets are delta + + align:start position:0% +cardality when the sets are delta + + + align:start position:0% +cardality when the sets are delta +separated or unit of delta balls. + + align:start position:0% + + + + align:start position:0% + +Okay. So another way of thinking about + + align:start position:0% +Okay. So another way of thinking about + + + align:start position:0% +Okay. So another way of thinking about +the delta covering number is as a box + + align:start position:0% +the delta covering number is as a box + + + align:start position:0% +the delta covering number is as a box +counting number. So let d delta + + align:start position:0% +counting number. So let d delta + + + align:start position:0% +counting number. So let d delta +uh be the covering of our d by delta + + align:start position:0% +uh be the covering of our d by delta + + + align:start position:0% +uh be the covering of our d by delta +cubes. + + align:start position:0% +cubes. + + + align:start position:0% +cubes. +So + + align:start position:0% +So + + + align:start position:0% +So +so this is delta k + + align:start position:0% +so this is delta k + + + align:start position:0% +so this is delta k +plus z delta + + align:start position:0% +plus z delta + + + align:start position:0% +plus z delta +maybe let's make it half open so that + + align:start position:0% +maybe let's make it half open so that + + + align:start position:0% +maybe let's make it half open so that +this is a partition to the d + + align:start position:0% +this is a partition to the d + + + align:start position:0% +this is a partition to the d +where k is in z to the d. + + align:start position:0% +where k is in z to the d. + + + align:start position:0% +where k is in z to the d. +So I'm I'm just doing like a diadic + + align:start position:0% +So I'm I'm just doing like a diadic + + + align:start position:0% +So I'm I'm just doing like a diadic +covering. Delta doesn't have to be + + align:start position:0% +covering. Delta doesn't have to be + + + align:start position:0% +covering. Delta doesn't have to be +diatic, but I'm So this is this is a + + align:start position:0% +diatic, but I'm So this is this is a + + + align:start position:0% +diatic, but I'm So this is this is a +how do you say the tiling of RD by cubes + + align:start position:0% +how do you say the tiling of RD by cubes + + + align:start position:0% +how do you say the tiling of RD by cubes +of size delta. + + align:start position:0% +of size delta. + + + align:start position:0% +of size delta. +I make them half open so they are + + align:start position:0% +I make them half open so they are + + + align:start position:0% +I make them half open so they are +disjoint but it's not really important. + + align:start position:0% +disjoint but it's not really important. + + + align:start position:0% +disjoint but it's not really important. +Okay. So uh + + align:start position:0% +Okay. So uh + + + align:start position:0% +Okay. So uh +the delta covering number + + align:start position:0% + + + + align:start position:0% + +is up to a multibility constant the + + align:start position:0% +is up to a multibility constant the + + + align:start position:0% +is up to a multibility constant the +number of cubes in the delta that are + + align:start position:0% +number of cubes in the delta that are + + + align:start position:0% +number of cubes in the delta that are +hit by the set. + + align:start position:0% +hit by the set. + + + align:start position:0% +hit by the set. +So the cardinality + + align:start position:0% +So the cardinality + + + align:start position:0% +So the cardinality +of the cubes in the delta + + align:start position:0% +of the cubes in the delta + + + align:start position:0% +of the cubes in the delta +which intersect the set. + + align:start position:0% +which intersect the set. + + + align:start position:0% +which intersect the set. +So this is why this is called box + + align:start position:0% +So this is why this is called box + + + align:start position:0% +So this is why this is called box +counting number as well. + + align:start position:0% + + + + align:start position:0% + +Okay, why is this true is because if you + + align:start position:0% +Okay, why is this true is because if you + + + align:start position:0% +Okay, why is this true is because if you +cover by cubes in an efficient way, so + + align:start position:0% +cover by cubes in an efficient way, so + + + align:start position:0% +cover by cubes in an efficient way, so +if you know how many cubes you're + + align:start position:0% +if you know how many cubes you're + + + align:start position:0% +if you know how many cubes you're +hitting, well, you can cover each cube + + align:start position:0% +hitting, well, you can cover each cube + + + align:start position:0% +hitting, well, you can cover each cube +by a a finite number of balls of radius + + align:start position:0% +by a a finite number of balls of radius + + + align:start position:0% +by a a finite number of balls of radius +delta. + + align:start position:0% +delta. + + + align:start position:0% +delta. +Again, this wiggle may depend on D. So D + + align:start position:0% +Again, this wiggle may depend on D. So D + + + align:start position:0% +Again, this wiggle may depend on D. So D +is a fixed parameter. It will be one or + + align:start position:0% +is a fixed parameter. It will be one or + + + align:start position:0% +is a fixed parameter. It will be one or +two for Bansuction theorem. So I + + align:start position:0% +two for Bansuction theorem. So I + + + align:start position:0% +two for Bansuction theorem. So I +consider it as a constant. So you can + + align:start position:0% +consider it as a constant. So you can + + + align:start position:0% +consider it as a constant. So you can +cover each each of these cubes by a + + align:start position:0% +cover each each of these cubes by a + + + align:start position:0% +cover each each of these cubes by a +finite number of delta balls and vice + + align:start position:0% +finite number of delta balls and vice + + + align:start position:0% +finite number of delta balls and vice +versa. If you have a delta ball, you can + + align:start position:0% +versa. If you have a delta ball, you can + + + align:start position:0% +versa. If you have a delta ball, you can +cover it by a finite number of cubes. + + align:start position:0% +cover it by a finite number of cubes. + + + align:start position:0% +cover it by a finite number of cubes. +So that's that's the proof proof by + + align:start position:0% +So that's that's the proof proof by + + + align:start position:0% +So that's that's the proof proof by +picture. Okay. And one nice consequence + + align:start position:0% +picture. Okay. And one nice consequence + + + align:start position:0% +picture. Okay. And one nice consequence +of this is that this allows us to snap + + align:start position:0% +of this is that this allows us to snap + + + align:start position:0% +of this is that this allows us to snap +any set to a grid and then this allows + + align:start position:0% +any set to a grid and then this allows + + + align:start position:0% +any set to a grid and then this allows +us to apply uc non- ucleian uh integer + + align:start position:0% +us to apply uc non- ucleian uh integer + + + align:start position:0% +us to apply uc non- ucleian uh integer +results discrete results. So + + align:start position:0% +results discrete results. So + + + align:start position:0% +results discrete results. So +let's define + + align:start position:0% + + + + align:start position:0% + +so what is x supperscript bracket delta + + align:start position:0% +so what is x supperscript bracket delta + + + align:start position:0% +so what is x supperscript bracket delta +is the set that is obtained by snapping + + align:start position:0% +is the set that is obtained by snapping + + + align:start position:0% +is the set that is obtained by snapping +points to the grid. So if uh x + + align:start position:0% +points to the grid. So if uh x + + + align:start position:0% +points to the grid. So if uh x +intersects this this cube then this + + align:start position:0% +intersects this this cube then this + + + align:start position:0% +intersects this this cube then this +point will be an ex in x delta. + + align:start position:0% +point will be an ex in x delta. + + + align:start position:0% +point will be an ex in x delta. +In this way I I snap it to the latis. + + align:start position:0% +In this way I I snap it to the latis. + + + align:start position:0% +In this way I I snap it to the latis. +Okay. Formally this is all the case + + align:start position:0% +Okay. Formally this is all the case + + + align:start position:0% +Okay. Formally this is all the case +such that the cube delta k plus 0 delta + + align:start position:0% +such that the cube delta k plus 0 delta + + + align:start position:0% +such that the cube delta k plus 0 delta +to the d intersects x. + + align:start position:0% + + + + align:start position:0% + +Okay. So anytime there we see something + + align:start position:0% +Okay. So anytime there we see something + + + align:start position:0% +Okay. So anytime there we see something +here we look at this point. Okay. And + + align:start position:0% +here we look at this point. Okay. And + + + align:start position:0% +here we look at this point. Okay. And +then uh because of this + + align:start position:0% + + + + align:start position:0% + +the delta covering number is roughly up + + align:start position:0% +the delta covering number is roughly up + + + align:start position:0% +the delta covering number is roughly up +to a multiplicative constant the same as + + align:start position:0% +to a multiplicative constant the same as + + + align:start position:0% +to a multiplicative constant the same as +the cardinality. This is now a finite + + align:start position:0% +the cardinality. This is now a finite + + + align:start position:0% +the cardinality. This is now a finite +set and it's a finite set in a latis. So + + align:start position:0% +set and it's a finite set in a latis. So + + + align:start position:0% +set and it's a finite set in a latis. So +it's just the not just not just a latis + + align:start position:0% +it's just the not just not just a latis + + + align:start position:0% +it's just the not just not just a latis +it's just the integer latis scaled down + + align:start position:0% +it's just the integer latis scaled down + + + align:start position:0% +it's just the integer latis scaled down +by delta but it's just the integer + + align:start position:0% +by delta but it's just the integer + + + align:start position:0% +by delta but it's just the integer +latis. + + align:start position:0% +latis. + + + align:start position:0% +latis. +Okay. And by using this uh one can + + align:start position:0% +Okay. And by using this uh one can + + + align:start position:0% +Okay. And by using this uh one can +extend many results that are true um in + + align:start position:0% +extend many results that are true um in + + + align:start position:0% +extend many results that are true um in +ZD to delta covering numbers. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So using this + + align:start position:0% + + + + align:start position:0% + +in particular the following three things + + align:start position:0% +in particular the following three things + + + align:start position:0% +in particular the following three things +which are three very important tools in + + align:start position:0% +which are three very important tools in + + + align:start position:0% +which are three very important tools in +the proof of the finite field case of + + align:start position:0% +the proof of the finite field case of + + + align:start position:0% +the proof of the finite field case of +bans projection theorem and also in the + + align:start position:0% +bans projection theorem and also in the + + + align:start position:0% +bans projection theorem and also in the +uklidian case uh the rua triangle + + align:start position:0% +uklidian case uh the rua triangle + + + align:start position:0% +uklidian case uh the rua triangle +inequality + + align:start position:0% + + + + align:start position:0% + +the punic rou are + + align:start position:0% + + + + align:start position:0% + +inequalities + + align:start position:0% + + + + align:start position:0% + +and the valuic theorem. + + align:start position:0% + + + + align:start position:0% + +They all hold for delta covering numbers + + align:start position:0% +They all hold for delta covering numbers + + + align:start position:0% +They all hold for delta covering numbers +by putting bar delt. So when you see bar + + align:start position:0% +by putting bar delt. So when you see bar + + + align:start position:0% +by putting bar delt. So when you see bar +you put delta. Okay. And you lose + + align:start position:0% +you put delta. Okay. And you lose + + + align:start position:0% +you put delta. Okay. And you lose +multiligative constants because of this. + + align:start position:0% +multiligative constants because of this. + + + align:start position:0% +multiligative constants because of this. +So where you have equality you no longer + + align:start position:0% +So where you have equality you no longer + + + align:start position:0% +So where you have equality you no longer +have equality. But this is very + + align:start position:0% +have equality. But this is very + + + align:start position:0% +have equality. But this is very +harmless. + + align:start position:0% + + + + align:start position:0% + +Okay. For example, I'm going to state + + align:start position:0% +Okay. For example, I'm going to state + + + align:start position:0% +Okay. For example, I'm going to state +the RA triangle inequality as a model + + align:start position:0% +the RA triangle inequality as a model + + + align:start position:0% +the RA triangle inequality as a model +and then you can imagine how the other + + align:start position:0% +and then you can imagine how the other + + + align:start position:0% +and then you can imagine how the other +two behave. + + align:start position:0% +two behave. + + + align:start position:0% +two behave. +Um, so we have okay so we have three + + align:start position:0% +Um, so we have okay so we have three + + + align:start position:0% +Um, so we have okay so we have three +sets + + align:start position:0% +sets + + + align:start position:0% +sets +in the same RD. + + align:start position:0% +in the same RD. + + + align:start position:0% +in the same RD. +Let's say bounded to make sure that the + + align:start position:0% +Let's say bounded to make sure that the + + + align:start position:0% +Let's say bounded to make sure that the +delta governing number is finite. Then + + align:start position:0% +delta governing number is finite. Then + + + align:start position:0% +delta governing number is finite. Then +let's see if I get this right. If not, + + align:start position:0% +let's see if I get this right. If not, + + + align:start position:0% +let's see if I get this right. If not, +you just let me know. Okay. in in the + + align:start position:0% +you just let me know. Okay. in in the + + + align:start position:0% +you just let me know. Okay. in in the +original. So in the discrete triangular + + align:start position:0% +original. So in the discrete triangular + + + align:start position:0% +original. So in the discrete triangular +inequality here we have inequality here + + align:start position:0% +inequality here we have inequality here + + + align:start position:0% +inequality here we have inequality here +we have inequality up to a constant. So + + align:start position:0% +we have inequality up to a constant. So + + + align:start position:0% +we have inequality up to a constant. So +this is the only thing we have to + + align:start position:0% +this is the only thing we have to + + + align:start position:0% +this is the only thing we have to +change. + + align:start position:0% + + + + align:start position:0% + +Okay. Did I get this right? Is this the + + align:start position:0% +Okay. Did I get this right? Is this the + + + align:start position:0% +Okay. Did I get this right? Is this the +correct statement? Okay. So this is an + + align:start position:0% +correct statement? Okay. So this is an + + + align:start position:0% +correct statement? Okay. So this is an +example. Just put delta delta delta + + align:start position:0% +example. Just put delta delta delta + + + align:start position:0% +example. Just put delta delta delta +delta and take equality by equality up + + align:start position:0% +delta and take equality by equality up + + + align:start position:0% +delta and take equality by equality up +to a constant. And how do you prove + + align:start position:0% +to a constant. And how do you prove + + + align:start position:0% +to a constant. And how do you prove +this? Well, you + + align:start position:0% +this? Well, you + + + align:start position:0% +this? Well, you +you snap it to the grid. You have to be + + align:start position:0% +you snap it to the grid. You have to be + + + align:start position:0% +you snap it to the grid. You have to be +a very like a little bit careful because + + align:start position:0% +a very like a little bit careful because + + + align:start position:0% +a very like a little bit careful because +you can snap A to the grid. You can snap + + align:start position:0% +you can snap A to the grid. You can snap + + + align:start position:0% +you can snap A to the grid. You can snap +B to the grid and then you can take A + + align:start position:0% +B to the grid and then you can take A + + + align:start position:0% +B to the grid and then you can take A +minus B for the snapped versions and + + align:start position:0% +minus B for the snapped versions and + + + align:start position:0% +minus B for the snapped versions and +that's not going to be exactly the same + + align:start position:0% +that's not going to be exactly the same + + + align:start position:0% +that's not going to be exactly the same +as snapping A minus B to the grid. So + + align:start position:0% +as snapping A minus B to the grid. So + + + align:start position:0% +as snapping A minus B to the grid. So +there is something that doesn't exactly + + align:start position:0% +there is something that doesn't exactly + + + align:start position:0% +there is something that doesn't exactly +commute + + align:start position:0% +commute + + + align:start position:0% +commute +but it almost commutes. So almost + + align:start position:0% +but it almost commutes. So almost + + + align:start position:0% +but it almost commutes. So almost +commutes. So I'm not going to another + + align:start position:0% +commutes. So I'm not going to another + + + align:start position:0% +commutes. So I'm not going to another +exercise is for you to convince yourself + + align:start position:0% +exercise is for you to convince yourself + + + align:start position:0% +exercise is for you to convince yourself +that this is true. So okay. So you see + + align:start position:0% +that this is true. So okay. So you see + + + align:start position:0% +that this is true. So okay. So you see +that for the projection theorem + + align:start position:0% +that for the projection theorem + + + align:start position:0% +that for the projection theorem +we really need to impose assumptions if + + align:start position:0% +we really need to impose assumptions if + + + align:start position:0% +we really need to impose assumptions if +we wanted to hold in the nuclean + + align:start position:0% +we wanted to hold in the nuclean + + + align:start position:0% +we wanted to hold in the nuclean +setting. But this is not always true. + + align:start position:0% +setting. But this is not always true. + + + align:start position:0% +setting. But this is not always true. +Here we have three very important tools + + align:start position:0% +Here we have three very important tools + + + align:start position:0% +Here we have three very important tools +and they basically work in the same way. + + align:start position:0% +and they basically work in the same way. + + + align:start position:0% +and they basically work in the same way. +Okay. So now we can start going over + + align:start position:0% + + + + align:start position:0% + +the steps in the proof of the theorem in + + align:start position:0% +the steps in the proof of the theorem in + + + align:start position:0% +the steps in the proof of the theorem in +the final field setting and seeing what + + align:start position:0% +the final field setting and seeing what + + + align:start position:0% +the final field setting and seeing what +the obstacles are and what one can do to + + align:start position:0% +the obstacles are and what one can do to + + + align:start position:0% +the obstacles are and what one can do to +overcome the obstacles if one wants to + + align:start position:0% +overcome the obstacles if one wants to + + + align:start position:0% +overcome the obstacles if one wants to +follow the same scheme of proof in the + + align:start position:0% +follow the same scheme of proof in the + + + align:start position:0% +follow the same scheme of proof in the +uklidian setting. Any questions so far? + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. So in the finite field setting + + align:start position:0% + + + + align:start position:0% + +what was the first step in the proof? It + + align:start position:0% +what was the first step in the proof? It + + + align:start position:0% +what was the first step in the proof? It +was to prove expansion + + align:start position:0% +was to prove expansion + + + align:start position:0% +was to prove expansion +using a polomial for just one set. So + + align:start position:0% +using a polomial for just one set. So + + + align:start position:0% +using a polomial for just one set. So +let's recall what uh this was. So if we + + align:start position:0% +let's recall what uh this was. So if we + + + align:start position:0% +let's recall what uh this was. So if we +have a and fp okay I guess let's state + + align:start position:0% +have a and fp okay I guess let's state + + + align:start position:0% +have a and fp okay I guess let's state +the quantifiers first. So given s + + align:start position:0% + + + + align:start position:0% + +01 there exists an epsilon + + align:start position:0% + + + + align:start position:0% + +such that the following holds uh if + + align:start position:0% +such that the following holds uh if + + + align:start position:0% +such that the following holds uh if +we have a subset of our of our prime + + align:start position:0% +we have a subset of our of our prime + + + align:start position:0% +we have a subset of our of our prime +field so here it has to be a prime field + + align:start position:0% +field so here it has to be a prime field + + + align:start position:0% +field so here it has to be a prime field +this already fails if it's not the prime + + align:start position:0% +this already fails if it's not the prime + + + align:start position:0% +this already fails if it's not the prime +field and well I'm going to come back to + + align:start position:0% +field and well I'm going to come back to + + + align:start position:0% +field and well I'm going to come back to +this point several times okay and + + align:start position:0% +this point several times okay and + + + align:start position:0% +this point several times okay and +suppose that it has size p to the s + + align:start position:0% +suppose that it has size p to the s + + + align:start position:0% +suppose that it has size p to the s +then uh There exist a polomial + + align:start position:0% +then uh There exist a polomial + + + align:start position:0% +then uh There exist a polomial +actually uh + + align:start position:0% +actually uh + + + align:start position:0% +actually uh +there exist a polomial which is fixed + + align:start position:0% +there exist a polomial which is fixed + + + align:start position:0% +there exist a polomial which is fixed +for all s for all epsilon and for all a + + align:start position:0% +for all s for all epsilon and for all a + + + align:start position:0% +for all s for all epsilon and for all a +and it can be x1 x2 x3 - x4 x5 x6 so + + align:start position:0% +and it can be x1 x2 x3 - x4 x5 x6 so + + + align:start position:0% +and it can be x1 x2 x3 - x4 x5 x6 so +that polinomial works but it doesn't + + align:start position:0% +that polinomial works but it doesn't + + + align:start position:0% +that polinomial works but it doesn't +really matter which polinomial it is so + + align:start position:0% +really matter which polinomial it is so + + + align:start position:0% +really matter which polinomial it is so +let's call it q + + align:start position:0% +let's call it q + + + align:start position:0% +let's call it q +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +if we apply q to a we get expansion + + align:start position:0% + + + + align:start position:0% + +Okay. So I think what you did with Larry + + align:start position:0% +Okay. So I think what you did with Larry + + + align:start position:0% +Okay. So I think what you did with Larry +gave the following polinomial. + + align:start position:0% +gave the following polinomial. + + + align:start position:0% +gave the following polinomial. +I think it was clear from what you did + + align:start position:0% +I think it was clear from what you did + + + align:start position:0% +I think it was clear from what you did +with Larry that really doesn't matter + + align:start position:0% +with Larry that really doesn't matter + + + align:start position:0% +with Larry that really doesn't matter +which polinomial it is as long as you + + align:start position:0% +which polinomial it is as long as you + + + align:start position:0% +which polinomial it is as long as you +have some polomial because at the later + + align:start position:0% +have some polomial because at the later + + + align:start position:0% +have some polomial because at the later +stage one is going to apply pura to + + align:start position:0% +stage one is going to apply pura to + + + align:start position:0% +stage one is going to apply pura to +bring down the polomial to the simplest + + align:start position:0% +bring down the polomial to the simplest + + + align:start position:0% +bring down the polomial to the simplest +possible polomial. + + align:start position:0% +possible polomial. + + + align:start position:0% +possible polomial. +Uh so that was a later step at this step + + align:start position:0% +Uh so that was a later step at this step + + + align:start position:0% +Uh so that was a later step at this step +any polomial works. + + align:start position:0% +any polomial works. + + + align:start position:0% +any polomial works. +Okay so this one works but it's not too + + align:start position:0% +Okay so this one works but it's not too + + + align:start position:0% +Okay so this one works but it's not too +important which one it is. Okay how how + + align:start position:0% +important which one it is. Okay how how + + + align:start position:0% +important which one it is. Okay how how +did you prove this? So we can see to + + align:start position:0% +did you prove this? So we can see to + + + align:start position:0% +did you prove this? So we can see to +what extent things go wrong in the + + align:start position:0% +what extent things go wrong in the + + + align:start position:0% +what extent things go wrong in the +in the uklidian setting and to what + + align:start position:0% +in the uklidian setting and to what + + + align:start position:0% +in the uklidian setting and to what +extent we can recycle some of the ideas. + + align:start position:0% +extent we can recycle some of the ideas. + + + align:start position:0% +extent we can recycle some of the ideas. +So idea of proof + + align:start position:0% + + + + align:start position:0% + +if I claim that you saw something with + + align:start position:0% +if I claim that you saw something with + + + align:start position:0% +if I claim that you saw something with +Larry and you didn't please let me know. + + align:start position:0% +Larry and you didn't please let me know. + + + align:start position:0% +Larry and you didn't please let me know. +Uh he told me and showed me notes but I + + align:start position:0% +Uh he told me and showed me notes but I + + + align:start position:0% +Uh he told me and showed me notes but I +could still be wrong about something. + + align:start position:0% +could still be wrong about something. + + + align:start position:0% +could still be wrong about something. +Okay. What was the idea of proof behind + + align:start position:0% +Okay. What was the idea of proof behind + + + align:start position:0% +Okay. What was the idea of proof behind +this? Uh so one looks at + + align:start position:0% +this? Uh so one looks at + + + align:start position:0% +this? Uh so one looks at +maybe let's call it x a minus a over a + + align:start position:0% +maybe let's call it x a minus a over a + + + align:start position:0% +maybe let's call it x a minus a over a +minus a and here uh we skip zero we + + align:start position:0% +minus a and here uh we skip zero we + + + align:start position:0% +minus a and here uh we skip zero we +don't want to divide by zero and then + + align:start position:0% +don't want to divide by zero and then + + + align:start position:0% +don't want to divide by zero and then +there are two possibilities either x is + + align:start position:0% +there are two possibilities either x is + + + align:start position:0% +there are two possibilities either x is +everything + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% + + + + align:start position:0% + +one can conclude in some way I'm not + + align:start position:0% +one can conclude in some way I'm not + + + align:start position:0% +one can conclude in some way I'm not +this is not I'm not going to recall how + + align:start position:0% +this is not I'm not going to recall how + + + align:start position:0% +this is not I'm not going to recall how +to do it and the other possibible ility + + align:start position:0% +to do it and the other possibible ility + + + align:start position:0% +to do it and the other possibible ility +is that X is not everything. + + align:start position:0% +is that X is not everything. + + + align:start position:0% +is that X is not everything. +And if it's not everything, + + align:start position:0% +And if it's not everything, + + + align:start position:0% +And if it's not everything, +there exists some uh little X in X + + align:start position:0% +there exists some uh little X in X + + + align:start position:0% +there exists some uh little X in X +such that X + one is not in X + + align:start position:0% + + + + align:start position:0% + +because it's not everything and then one + + align:start position:0% +because it's not everything and then one + + + align:start position:0% +because it's not everything and then one +can also conclude. So in both case this + + align:start position:0% +can also conclude. So in both case this + + + align:start position:0% +can also conclude. So in both case this +one has to work. I'm not saying it's + + align:start position:0% +one has to work. I'm not saying it's + + + align:start position:0% +one has to work. I'm not saying it's +trivial, but this was the structure of + + align:start position:0% +trivial, but this was the structure of + + + align:start position:0% +trivial, but this was the structure of +the proof. And this extremely innocent + + align:start position:0% +the proof. And this extremely innocent + + + align:start position:0% +the proof. And this extremely innocent +step is what distinguishes + + align:start position:0% +step is what distinguishes + + + align:start position:0% +step is what distinguishes +FP from FP square. If we were working in + + align:start position:0% +FP from FP square. If we were working in + + + align:start position:0% +FP from FP square. If we were working in +FP square, we would not be able to do + + align:start position:0% +FP square, we would not be able to do + + + align:start position:0% +FP square, we would not be able to do +this because FP square + + align:start position:0% +this because FP square + + + align:start position:0% +this because FP square +has a + + align:start position:0% +has a + + + align:start position:0% +has a +subgroup which is FP. So you cannot + + align:start position:0% +subgroup which is FP. So you cannot + + + align:start position:0% +subgroup which is FP. So you cannot +escape FP by adding one. + + align:start position:0% +escape FP by adding one. + + + align:start position:0% +escape FP by adding one. +So this extremely innocent adding plus + + align:start position:0% +So this extremely innocent adding plus + + + align:start position:0% +So this extremely innocent adding plus +one uh distinguishes okay so + + align:start position:0% +one uh distinguishes okay so + + + align:start position:0% +one uh distinguishes okay so +distinguishes + + align:start position:0% + + + + align:start position:0% + +FP and FP square let's say + + align:start position:0% +FP and FP square let's say + + + align:start position:0% +FP and FP square let's say +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +we want to do something similar + + align:start position:0% +we want to do something similar + + + align:start position:0% +we want to do something similar +and so let's say uh we have an A. + + align:start position:0% +and so let's say uh we have an A. + + + align:start position:0% +and so let's say uh we have an A. +Well, first of all, + + align:start position:0% +Well, first of all, + + + align:start position:0% +Well, first of all, +it's very likely that we will need to + + align:start position:0% +it's very likely that we will need to + + + align:start position:0% +it's very likely that we will need to +assume something about A. In fact, we + + align:start position:0% +assume something about A. In fact, we + + + align:start position:0% +assume something about A. In fact, we +need to assume something about A in the + + align:start position:0% +need to assume something about A in the + + + align:start position:0% +need to assume something about A in the +UK setting because if A is a is a + + align:start position:0% +UK setting because if A is a is a + + + align:start position:0% +UK setting because if A is a is a +segment, + + align:start position:0% +segment, + + + align:start position:0% +segment, +it does like any polinomial check, it + + align:start position:0% +it does like any polinomial check, it + + + align:start position:0% +it does like any polinomial check, it +doesn't grow. So, if X is + + align:start position:0% +doesn't grow. So, if X is + + + align:start position:0% +doesn't grow. So, if X is +1 1 + R 1 1 + + + align:start position:0% +1 1 + R 1 1 + + + + align:start position:0% +1 1 + R 1 1 + +delta to the + + align:start position:0% +delta to the + + + align:start position:0% +delta to the +1 - t something like this, just just a + + align:start position:0% +1 - t something like this, just just a + + + align:start position:0% +1 - t something like this, just just a +small small segment. If you add it to + + align:start position:0% +small small segment. If you add it to + + + align:start position:0% +small small segment. If you add it to +itself, multiply by itself, you get + + align:start position:0% +itself, multiply by itself, you get + + + align:start position:0% +itself, multiply by itself, you get +slightly longer segments. There is no + + align:start position:0% +slightly longer segments. There is no + + + align:start position:0% +slightly longer segments. There is no +real growth is exactly the same issue uh + + align:start position:0% +real growth is exactly the same issue uh + + + align:start position:0% +real growth is exactly the same issue uh +as we had when we were projecting uh an + + align:start position:0% +as we had when we were projecting uh an + + + align:start position:0% +as we had when we were projecting uh an +X which was too concentrated in a large + + align:start position:0% +X which was too concentrated in a large + + + align:start position:0% +X which was too concentrated in a large +ball. Okay, but now we sort of know how + + align:start position:0% +ball. Okay, but now we sort of know how + + + align:start position:0% +ball. Okay, but now we sort of know how +to get rid of that. We need to assume + + align:start position:0% +to get rid of that. We need to assume + + + align:start position:0% +to get rid of that. We need to assume +that A is not too concentrated inside + + align:start position:0% +that A is not too concentrated inside + + + align:start position:0% +that A is not too concentrated inside +any segment. Okay, but even assuming + + align:start position:0% +any segment. Okay, but even assuming + + + align:start position:0% +any segment. Okay, but even assuming +that we do that, uh we see that we have + + align:start position:0% +that we do that, uh we see that we have + + + align:start position:0% +that we do that, uh we see that we have +lots of problems if we try to do + + align:start position:0% +lots of problems if we try to do + + + align:start position:0% +lots of problems if we try to do +something like this. + + align:start position:0% +something like this. + + + align:start position:0% +something like this. +What are the problems? So can you tell + + align:start position:0% +What are the problems? So can you tell + + + align:start position:0% +What are the problems? So can you tell +me some problems? Why? So some + + align:start position:0% +me some problems? Why? So some + + + align:start position:0% +me some problems? Why? So some +challenges in + + align:start position:0% +challenges in + + + align:start position:0% +challenges in +trying to do something like this. If now + + align:start position:0% +trying to do something like this. If now + + + align:start position:0% +trying to do something like this. If now +a is a subset of let's say 01 or one two + + align:start position:0% +a is a subset of let's say 01 or one two + + + align:start position:0% +a is a subset of let's say 01 or one two +let's say 01 it doesn't matter. + + align:start position:0% +let's say 01 it doesn't matter. + + + align:start position:0% +let's say 01 it doesn't matter. +So what things you should be worried + + align:start position:0% +So what things you should be worried + + + align:start position:0% +So what things you should be worried +about? + + align:start position:0% +about? + + + align:start position:0% +about? +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +>> Uh x could be unbounded. + + align:start position:0% +>> Uh x could be unbounded. + + + align:start position:0% +>> Uh x could be unbounded. +>> X could be unbounded. Yes. So a so in + + align:start position:0% +>> X could be unbounded. Yes. So a so in + + + align:start position:0% +>> X could be unbounded. Yes. So a so in +the final field we need to avoid zero in + + align:start position:0% +the final field we need to avoid zero in + + + align:start position:0% +the final field we need to avoid zero in +the denominator but in the ukidian case + + align:start position:0% +the denominator but in the ukidian case + + + align:start position:0% +the denominator but in the ukidian case +we don't only need to assume zero. We + + align:start position:0% +we don't only need to assume zero. We + + + align:start position:0% +we don't only need to assume zero. We +should be very worried about small + + align:start position:0% +should be very worried about small + + + align:start position:0% +should be very worried about small +denominators not just zero but small + + align:start position:0% +denominators not just zero but small + + + align:start position:0% +denominators not just zero but small +denominators because this is going to + + align:start position:0% +denominators because this is going to + + + align:start position:0% +denominators because this is going to +blow up and yeah this is certainly an + + align:start position:0% +blow up and yeah this is certainly an + + + align:start position:0% +blow up and yeah this is certainly an +issue. + + align:start position:0% +issue. + + + align:start position:0% +issue. +Are there any other issues one should + + align:start position:0% +Are there any other issues one should + + + align:start position:0% +Are there any other issues one should +worry about? + + align:start position:0% + + + + align:start position:0% + +What does it mean to equal FP? + + align:start position:0% + + + + align:start position:0% + +>> That's right. Well, I mean, okay. Yeah, + + align:start position:0% +>> That's right. Well, I mean, okay. Yeah, + + + align:start position:0% +>> That's right. Well, I mean, okay. Yeah, +that's Yeah, what does it mean to equal + + align:start position:0% +that's Yeah, what does it mean to equal + + + align:start position:0% +that's Yeah, what does it mean to equal +FP is not clear. And I would say what is + + align:start position:0% +FP is not clear. And I would say what is + + + align:start position:0% +FP is not clear. And I would say what is +even much less clear is what does it + + align:start position:0% +even much less clear is what does it + + + align:start position:0% +even much less clear is what does it +mean to add one + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +I don't know R is certainly not I mean R + + align:start position:0% +I don't know R is certainly not I mean R + + + align:start position:0% +I don't know R is certainly not I mean R +is invariant and they're adding one and + + align:start position:0% +is invariant and they're adding one and + + + align:start position:0% +is invariant and they're adding one and +it's not I mean this doesn't live in 01 + + align:start position:0% +it's not I mean this doesn't live in 01 + + + align:start position:0% +it's not I mean this doesn't live in 01 +anymore. If we force it to live in 01 by + + align:start position:0% +anymore. If we force it to live in 01 by + + + align:start position:0% +anymore. If we force it to live in 01 by +intersecting with 01, there could still + + align:start position:0% +intersecting with 01, there could still + + + align:start position:0% +intersecting with 01, there could still +be something. I mean, if we add one, we + + align:start position:0% +be something. I mean, if we add one, we + + + align:start position:0% +be something. I mean, if we add one, we +could still land here. So adding one + + align:start position:0% +could still land here. So adding one + + + align:start position:0% +could still land here. So adding one +doesn't seem like a good idea. And from + + align:start position:0% +doesn't seem like a good idea. And from + + + align:start position:0% +doesn't seem like a good idea. And from +a conceptual point of view, there is + + align:start position:0% +a conceptual point of view, there is + + + align:start position:0% +a conceptual point of view, there is +something that is even more worrying, + + align:start position:0% +something that is even more worrying, + + + align:start position:0% +something that is even more worrying, +which is here it is crucial that FP + + align:start position:0% +which is here it is crucial that FP + + + align:start position:0% +which is here it is crucial that FP +doesn't have any sub additive subgroup. + + align:start position:0% +doesn't have any sub additive subgroup. + + + align:start position:0% +doesn't have any sub additive subgroup. +So it's a simple group. It doesn't have + + align:start position:0% +So it's a simple group. It doesn't have + + + align:start position:0% +So it's a simple group. It doesn't have +any non-trivial subgroups because if it + + align:start position:0% +any non-trivial subgroups because if it + + + align:start position:0% +any non-trivial subgroups because if it +had a subgroup, this wouldn't be true. + + align:start position:0% + + + + align:start position:0% + +Now does R have any subfields or + + align:start position:0% +Now does R have any subfields or + + + align:start position:0% +Now does R have any subfields or +subgroups + + align:start position:0% +subgroups + + + align:start position:0% +subgroups +or sub rings? + + align:start position:0% +or sub rings? + + + align:start position:0% +or sub rings? +Well, first of all, it does have + + align:start position:0% +Well, first of all, it does have + + + align:start position:0% +Well, first of all, it does have +subgroups, additive subgroups. + + align:start position:0% +subgroups, additive subgroups. + + + align:start position:0% +subgroups, additive subgroups. +It does + + align:start position:0% +It does + + + align:start position:0% +It does +of any dimension. Okay, so of course it + + align:start position:0% +of any dimension. Okay, so of course it + + + align:start position:0% +of any dimension. Okay, so of course it +does. All of our rational numbers, + + align:start position:0% +does. All of our rational numbers, + + + align:start position:0% +does. All of our rational numbers, +number fields, but okay, number fields + + align:start position:0% +number fields, but okay, number fields + + + align:start position:0% +number fields, but okay, number fields +are countable. So we are interested in + + align:start position:0% +are countable. So we are interested in + + + align:start position:0% +are countable. So we are interested in +larger things, but it does have + + align:start position:0% +larger things, but it does have + + + align:start position:0% +larger things, but it does have +subgroups of intermediate size. It does + + align:start position:0% +subgroups of intermediate size. It does + + + align:start position:0% +subgroups of intermediate size. It does +not have sub rings of intermediate size. + + align:start position:0% +not have sub rings of intermediate size. + + + align:start position:0% +not have sub rings of intermediate size. +But this is a difficult theorem and in + + align:start position:0% +But this is a difficult theorem and in + + + align:start position:0% +But this is a difficult theorem and in +fact it's a consequence of bhans + + align:start position:0% +fact it's a consequence of bhans + + + align:start position:0% +fact it's a consequence of bhans +protection theorem. So we cannot really + + align:start position:0% +protection theorem. So we cannot really + + + align:start position:0% +protection theorem. So we cannot really +use it. So here we are escaping because + + align:start position:0% +use it. So here we are escaping because + + + align:start position:0% +use it. So here we are escaping because +x is not a sub ring. But it's not so + + align:start position:0% +x is not a sub ring. But it's not so + + + align:start position:0% +x is not a sub ring. But it's not so +clear if there is a subring type + + align:start position:0% +clear if there is a subring type + + + align:start position:0% +clear if there is a subring type +structure here in R. Okay. All of these + + align:start position:0% +structure here in R. Okay. All of these + + + align:start position:0% +structure here in R. Okay. All of these +things should make it very scary and a + + align:start position:0% +things should make it very scary and a + + + align:start position:0% +things should make it very scary and a +normal person would give up at this + + align:start position:0% +normal person would give up at this + + + align:start position:0% +normal person would give up at this +stage. uh but there is a paper by Larry + + align:start position:0% +stage. uh but there is a paper by Larry + + + align:start position:0% +stage. uh but there is a paper by Larry +Guth and uh George Zal my colleague at + + align:start position:0% +Guth and uh George Zal my colleague at + + + align:start position:0% +Guth and uh George Zal my colleague at +UBC and Netscats where they managed to + + align:start position:0% +UBC and Netscats where they managed to + + + align:start position:0% +UBC and Netscats where they managed to +extend this idea to the uklidian setting + + align:start position:0% +extend this idea to the uklidian setting + + + align:start position:0% +extend this idea to the uklidian setting +not to prove transportation theorem to + + align:start position:0% +not to prove transportation theorem to + + + align:start position:0% +not to prove transportation theorem to +prove some different related theorem. So + + align:start position:0% +prove some different related theorem. So + + + align:start position:0% +prove some different related theorem. So +let me tell you what they did to + + align:start position:0% +let me tell you what they did to + + + align:start position:0% +let me tell you what they did to +overcome + + align:start position:0% +overcome + + + align:start position:0% +overcome +these obstacles. uh but first of all uh + + align:start position:0% +these obstacles. uh but first of all uh + + + align:start position:0% +these obstacles. uh but first of all uh +I should define something that I should + + align:start position:0% +I should define something that I should + + + align:start position:0% +I should define something that I should +have defined before. + + align:start position:0% +have defined before. + + + align:start position:0% +have defined before. +So we have these non-conentration + + align:start position:0% +So we have these non-conentration + + + align:start position:0% +So we have these non-conentration +conditions. So we call this + + align:start position:0% +conditions. So we call this + + + align:start position:0% +conditions. So we call this +non-conentration conditions because it + + align:start position:0% +non-conentration conditions because it + + + align:start position:0% +non-conentration conditions because it +tells us that X and D are not + + align:start position:0% +tells us that X and D are not + + + align:start position:0% +tells us that X and D are not +concentrated in both. So + + align:start position:0% +concentrated in both. So + + + align:start position:0% +concentrated in both. So +non-conentration conditions. So looking + + align:start position:0% +non-conentration conditions. So looking + + + align:start position:0% +non-conentration conditions. So looking +at this uh we are going to write a + + align:start position:0% +at this uh we are going to write a + + + align:start position:0% +at this uh we are going to write a +definition + + align:start position:0% +definition + + + align:start position:0% +definition +which is inspired by this so that we + + align:start position:0% +which is inspired by this so that we + + + align:start position:0% +which is inspired by this so that we +don't have to repeat these sort of + + align:start position:0% +don't have to repeat these sort of + + + align:start position:0% +don't have to repeat these sort of +conditions every time. + + align:start position:0% + + + + align:start position:0% + +By the way, even in in in the final + + align:start position:0% +By the way, even in in in the final + + + align:start position:0% +By the way, even in in in the final +field setting, uh what Bangatan Tower + + align:start position:0% +field setting, uh what Bangatan Tower + + + align:start position:0% +field setting, uh what Bangatan Tower +did was also not this. So this this idea + + align:start position:0% +did was also not this. So this this idea + + + align:start position:0% +did was also not this. So this this idea +came later. Uh so it's originated from + + align:start position:0% +came later. Uh so it's originated from + + + align:start position:0% +came later. Uh so it's originated from +GV which is after Bangkawo proved + + align:start position:0% +GV which is after Bangkawo proved + + + align:start position:0% +GV which is after Bangkawo proved +something like this. So Bangas did + + align:start position:0% +something like this. So Bangas did + + + align:start position:0% +something like this. So Bangas did +something much much more complicated. + + align:start position:0% +something much much more complicated. + + + align:start position:0% +something much much more complicated. +Okay. Um definition + + align:start position:0% + + + + align:start position:0% + +the subset of the unit ball in RD. + + align:start position:0% +the subset of the unit ball in RD. + + + align:start position:0% +the subset of the unit ball in RD. +We just want to fix some region of + + align:start position:0% +We just want to fix some region of + + + align:start position:0% +We just want to fix some region of +space. So why not fix the unit ball uh + + align:start position:0% +space. So why not fix the unit ball uh + + + align:start position:0% +space. So why not fix the unit ball uh +is a and okay let delta be uh between + + align:start position:0% +is a and okay let delta be uh between + + + align:start position:0% +is a and okay let delta be uh between +zero and one not zero and maybe also not + + align:start position:0% +zero and one not zero and maybe also not + + + align:start position:0% +zero and one not zero and maybe also not +one. Uh so we say that this is a delta. + + align:start position:0% +one. Uh so we say that this is a delta. + + + align:start position:0% +one. Uh so we say that this is a delta. +Okay. And then we have a parameter t + + align:start position:0% +Okay. And then we have a parameter t + + + align:start position:0% +Okay. And then we have a parameter t +which is between zero and d. And then we + + align:start position:0% +which is between zero and d. And then we + + + align:start position:0% +which is between zero and d. And then we +have a constant which is positive. + + align:start position:0% +have a constant which is positive. + + + align:start position:0% +have a constant which is positive. +Let's say at least one. Okay. So we say + + align:start position:0% +Let's say at least one. Okay. So we say + + + align:start position:0% +Let's say at least one. Okay. So we say +that x is a delta s c d. So this d tells + + align:start position:0% +that x is a delta s c d. So this d tells + + + align:start position:0% +that x is a delta s c d. So this d tells +us the ambient dimension. And I will + + align:start position:0% +us the ambient dimension. And I will + + + align:start position:0% +us the ambient dimension. And I will +probably forget to write it down or it + + align:start position:0% +probably forget to write it down or it + + + align:start position:0% +probably forget to write it down or it +will be clear from context. Set + + align:start position:0% +will be clear from context. Set + + + align:start position:0% +will be clear from context. Set +if the following holds + + align:start position:0% +if the following holds + + + align:start position:0% +if the following holds +if we interet x. So note I'm not + + align:start position:0% +if we interet x. So note I'm not + + + align:start position:0% +if we interet x. So note I'm not +assuming X is a union of all. I'm not + + align:start position:0% +assuming X is a union of all. I'm not + + + align:start position:0% +assuming X is a union of all. I'm not +assuming X is delta separated. I'm not + + align:start position:0% +assuming X is delta separated. I'm not + + + align:start position:0% +assuming X is delta separated. I'm not +assuming anything and I'm not assuming + + align:start position:0% +assuming anything and I'm not assuming + + + align:start position:0% +assuming anything and I'm not assuming +anything because I'm using to use the + + align:start position:0% +anything because I'm using to use the + + + align:start position:0% +anything because I'm using to use the +delta covering number to measure things. + + align:start position:0% +delta covering number to measure things. + + + align:start position:0% +delta covering number to measure things. +So this is nothing about the delta + + align:start position:0% +So this is nothing about the delta + + + align:start position:0% +So this is nothing about the delta +covering number. You don't need to + + align:start position:0% +covering number. You don't need to + + + align:start position:0% +covering number. You don't need to +assume anything as long as you remember + + align:start position:0% +assume anything as long as you remember + + + align:start position:0% +assume anything as long as you remember +to write the bar delta. Okay. So uh if I + + align:start position:0% +to write the bar delta. Okay. So uh if I + + + align:start position:0% +to write the bar delta. Okay. So uh if I +intersect X with a ball + + align:start position:0% +intersect X with a ball + + + align:start position:0% +intersect X with a ball +and measure it by the delta covering + + align:start position:0% +and measure it by the delta covering + + + align:start position:0% +and measure it by the delta covering +number, this is at most C. So C is the + + align:start position:0% +number, this is at most C. So C is the + + + align:start position:0% +number, this is at most C. So C is the +tolerance the leeway that I have times R + + align:start position:0% +tolerance the leeway that I have times R + + + align:start position:0% +tolerance the leeway that I have times R +to the S. So S measures the degree of + + align:start position:0% +to the S. So S measures the degree of + + + align:start position:0% +to the S. So S measures the degree of +concentration of non concentration the + + align:start position:0% +concentration of non concentration the + + + align:start position:0% +concentration of non concentration the +degree of non concentration. So the + + align:start position:0% +degree of non concentration. So the + + + align:start position:0% +degree of non concentration. So the +larger the S, so R is going to be + + align:start position:0% +larger the S, so R is going to be + + + align:start position:0% +larger the S, so R is going to be +between zero and one or between delta + + align:start position:0% +between zero and one or between delta + + + align:start position:0% +between zero and one or between delta +and one. So the larger S, the smaller + + align:start position:0% +and one. So the larger S, the smaller + + + align:start position:0% +and one. So the larger S, the smaller +this is and the stronger this condition + + align:start position:0% +this is and the stronger this condition + + + align:start position:0% +this is and the stronger this condition +becomes times the size of X. + + align:start position:0% +becomes times the size of X. + + + align:start position:0% +becomes times the size of X. +So again this says that a ball cannot + + align:start position:0% +So again this says that a ball cannot + + + align:start position:0% +So again this says that a ball cannot +contain too much of x and this is for + + align:start position:0% +contain too much of x and this is for + + + align:start position:0% +contain too much of x and this is for +every well but for every center and for + + align:start position:0% +every well but for every center and for + + + align:start position:0% +every well but for every center and for +every + + align:start position:0% +every + + + align:start position:0% +every +radius between delta and one. + + align:start position:0% +radius between delta and one. + + + align:start position:0% +radius between delta and one. +Yes s + + align:start position:0% +Yes s + + + align:start position:0% +Yes s +>> sorry. Yes. + + align:start position:0% +>> sorry. Yes. + + + align:start position:0% +>> sorry. Yes. +Well it could be s or t but one has to + + align:start position:0% +Well it could be s or t but one has to + + + align:start position:0% +Well it could be s or t but one has to +fix one. Yeah. S. Thank you. + + align:start position:0% + + + + align:start position:0% + +Okay. So I hope you agree that in the + + align:start position:0% +Okay. So I hope you agree that in the + + + align:start position:0% +Okay. So I hope you agree that in the +statement of regress projection theorem + + align:start position:0% +statement of regress projection theorem + + + align:start position:0% +statement of regress projection theorem +this is the condition we have on X and + + align:start position:0% +this is the condition we have on X and + + + align:start position:0% +this is the condition we have on X and +on D. On X we had a T and on G we had an + + align:start position:0% +on D. On X we had a T and on G we had an + + + align:start position:0% +on D. On X we had a T and on G we had an +S. But this is the condition that we had + + align:start position:0% +S. But this is the condition that we had + + + align:start position:0% +S. But this is the condition that we had +and so we can bring them both under the + + align:start position:0% +and so we can bring them both under the + + + align:start position:0% +and so we can bring them both under the +same umbrella using the delta covering + + align:start position:0% +same umbrella using the delta covering + + + align:start position:0% +same umbrella using the delta covering +number. + + align:start position:0% + + + + align:start position:0% + +Okay. This is saying X is not too + + align:start position:0% +Okay. This is saying X is not too + + + align:start position:0% +Okay. This is saying X is not too +concentrated inside small balls and the + + align:start position:0% +concentrated inside small balls and the + + + align:start position:0% +concentrated inside small balls and the +strength of the concentration is given + + align:start position:0% +strength of the concentration is given + + + align:start position:0% +strength of the concentration is given +by S and there is a tolerance given by + + align:start position:0% +by S and there is a tolerance given by + + + align:start position:0% +by S and there is a tolerance given by +C. C could depend on delta. So C is + + align:start position:0% +C. C could depend on delta. So C is + + + align:start position:0% +C. C could depend on delta. So C is +anything in particular it could depend + + align:start position:0% +anything in particular it could depend + + + align:start position:0% +anything in particular it could depend +on delta and in the statement of BAN + + align:start position:0% +on delta and in the statement of BAN + + + align:start position:0% +on delta and in the statement of BAN +projection theorem. So in ban projection + + align:start position:0% +projection theorem. So in ban projection + + + align:start position:0% +projection theorem. So in ban projection +theorem this in fact is going to be + + align:start position:0% +theorem this in fact is going to be + + + align:start position:0% +theorem this in fact is going to be +delta to the minus EA. So you have a + + align:start position:0% +delta to the minus EA. So you have a + + + align:start position:0% +delta to the minus EA. So you have a +leeway that increases as a power with + + align:start position:0% +leeway that increases as a power with + + + align:start position:0% +leeway that increases as a power with +delta very small power but nevertheless + + align:start position:0% +delta very small power but nevertheless + + + align:start position:0% +delta very small power but nevertheless +a power. Okay. Uh so now we can state uh + + align:start position:0% +a power. Okay. Uh so now we can state uh + + + align:start position:0% +a power. Okay. Uh so now we can state uh +something + + align:start position:0% +something + + + align:start position:0% +something +I don't know + + align:start position:0% +I don't know + + + align:start position:0% +I don't know +uh + + align:start position:0% + + + + align:start position:0% + +lema. So it is the analog of the first + + align:start position:0% +lema. So it is the analog of the first + + + align:start position:0% +lema. So it is the analog of the first +step in the proof. So it's the analog of + + align:start position:0% +step in the proof. So it's the analog of + + + align:start position:0% +step in the proof. So it's the analog of +this + + align:start position:0% + + + + align:start position:0% + +Given an s between zero and one + + align:start position:0% +Given an s between zero and one + + + align:start position:0% +Given an s between zero and one +there exists an epsilon + + align:start position:0% +there exists an epsilon + + + align:start position:0% +there exists an epsilon +and all these epsilons can be taken to + + align:start position:0% +and all these epsilons can be taken to + + + align:start position:0% +and all these epsilons can be taken to +depend continue they depend continuously + + align:start position:0% +depend continue they depend continuously + + + align:start position:0% +depend continue they depend continuously +on s. So this is important in the so + + align:start position:0% +on s. So this is important in the so + + + align:start position:0% +on s. So this is important in the so +okay uh well I started saying the + + align:start position:0% +okay uh well I started saying the + + + align:start position:0% +okay uh well I started saying the +sentence I'm going to finish. So in the + + align:start position:0% +sentence I'm going to finish. So in the + + + align:start position:0% +sentence I'm going to finish. So in the +final setting one does this and then + + align:start position:0% +final setting one does this and then + + + align:start position:0% +final setting one does this and then +what is the next step? one iterates this + + align:start position:0% +what is the next step? one iterates this + + + align:start position:0% +what is the next step? one iterates this +and then one keeps growing. In order to + + align:start position:0% +and then one keeps growing. In order to + + + align:start position:0% +and then one keeps growing. In order to +know that you keep growing, you need to + + align:start position:0% +know that you keep growing, you need to + + + align:start position:0% +know that you keep growing, you need to +know that this epsilon + + align:start position:0% +know that this epsilon + + + align:start position:0% +know that this epsilon +remains bounded away from zero as long + + align:start position:0% +remains bounded away from zero as long + + + align:start position:0% +remains bounded away from zero as long +as the exponent remains bounded away + + align:start position:0% +as the exponent remains bounded away + + + align:start position:0% +as the exponent remains bounded away +from one. Okay, so the same is going to + + align:start position:0% +from one. Okay, so the same is going to + + + align:start position:0% +from one. Okay, so the same is going to +be true here although as we will see + + align:start position:0% +be true here although as we will see + + + align:start position:0% +be true here although as we will see +next time I think next time uh it's much + + align:start position:0% +next time I think next time uh it's much + + + align:start position:0% +next time I think next time uh it's much +more much much more complicated to + + align:start position:0% +more much much more complicated to + + + align:start position:0% +more much much more complicated to +iterate in this case but okay let's + + align:start position:0% +iterate in this case but okay let's + + + align:start position:0% +iterate in this case but okay let's +focus on this uh for today. Okay, given + + align:start position:0% +focus on this uh for today. Okay, given + + + align:start position:0% +focus on this uh for today. Okay, given +S there is an epsilon + + align:start position:0% +S there is an epsilon + + + align:start position:0% +S there is an epsilon +such that the following holds. + + align:start position:0% +such that the following holds. + + + align:start position:0% +such that the following holds. +Suppose A is in 01. + + align:start position:0% +Suppose A is in 01. + + + align:start position:0% +Suppose A is in 01. +The delta covering number is delta to + + align:start position:0% +The delta covering number is delta to + + + align:start position:0% +The delta covering number is delta to +the minus s + + align:start position:0% +the minus s + + + align:start position:0% +the minus s +and a is a + + align:start position:0% +and a is a + + + align:start position:0% +and a is a +delta + + align:start position:0% +delta + + + align:start position:0% +delta +s + + align:start position:0% +s + + + align:start position:0% +s +delta to the epsilon minus epsilon set. + + align:start position:0% + + + + align:start position:0% + +So it's is very nonconentrated because s + + align:start position:0% +So it's is very nonconentrated because s + + + align:start position:0% +So it's is very nonconentrated because s +matches the size. But on the other hand + + align:start position:0% +matches the size. But on the other hand + + + align:start position:0% +matches the size. But on the other hand +there is quite a bit of leeway in this + + align:start position:0% +there is quite a bit of leeway in this + + + align:start position:0% +there is quite a bit of leeway in this +delta to the minus epsilon. + + align:start position:0% +delta to the minus epsilon. + + + align:start position:0% +delta to the minus epsilon. +Then + + align:start position:0% +Then + + + align:start position:0% +Then +oh okay so there exist a polomial + + align:start position:0% + + + + align:start position:0% + +Q + + align:start position:0% +Q + + + align:start position:0% +Q +it could be the same Q. So that that Q + + align:start position:0% +it could be the same Q. So that that Q + + + align:start position:0% +it could be the same Q. So that that Q +if you want + + align:start position:0% + + + + align:start position:0% + +any polomial so really it doesn't matter + + align:start position:0% +any polomial so really it doesn't matter + + + align:start position:0% +any polomial so really it doesn't matter +because you can always apply polic but + + align:start position:0% +because you can always apply polic but + + + align:start position:0% +because you can always apply polic but +let's say that polinomial but any + + align:start position:0% +let's say that polinomial but any + + + align:start position:0% +let's say that polinomial but any +polinomial will do then + + align:start position:0% + + + + align:start position:0% + +we have we have growth I'm just putting + + align:start position:0% +we have we have growth I'm just putting + + + align:start position:0% +we have we have growth I'm just putting +delta governing number everywhere and we + + align:start position:0% +delta governing number everywhere and we + + + align:start position:0% +delta governing number everywhere and we +get growth + + align:start position:0% +get growth + + + align:start position:0% +get growth +so we get minus delta minus s which was + + align:start position:0% +so we get minus delta minus s which was + + + align:start position:0% +so we get minus delta minus s which was +the size of a but + + align:start position:0% +the size of a but + + + align:start position:0% +the size of a but +We get a delta to the minus epsilon grow + + align:start position:0% +We get a delta to the minus epsilon grow + + + align:start position:0% +We get a delta to the minus epsilon grow +over that. + + align:start position:0% + + + + align:start position:0% + +Okay. So it looks very very similar uh + + align:start position:0% +Okay. So it looks very very similar uh + + + align:start position:0% +Okay. So it looks very very similar uh +to that to what to this except that we + + align:start position:0% +to that to what to this except that we + + + align:start position:0% +to that to what to this except that we +need to add this non concentration + + align:start position:0% +need to add this non concentration + + + align:start position:0% +need to add this non concentration +assumption. We certainly need to add + + align:start position:0% +assumption. We certainly need to add + + + align:start position:0% +assumption. We certainly need to add +something because otherwise if a is just + + align:start position:0% +something because otherwise if a is just + + + align:start position:0% +something because otherwise if a is just +an interval is not true. It's not clear + + align:start position:0% +an interval is not true. It's not clear + + + align:start position:0% +an interval is not true. It's not clear +between interval and this what happens + + align:start position:0% +between interval and this what happens + + + align:start position:0% +between interval and this what happens +but okay with this assumption it is + + align:start position:0% +but okay with this assumption it is + + + align:start position:0% +but okay with this assumption it is +true. + + align:start position:0% +true. + + + align:start position:0% +true. +Okay. So how can one prove that? Uh so + + align:start position:0% +Okay. So how can one prove that? Uh so + + + align:start position:0% +Okay. So how can one prove that? Uh so +we want to use this strategy but we saw + + align:start position:0% +we want to use this strategy but we saw + + + align:start position:0% +we want to use this strategy but we saw +that there are many problems. So I'm not + + align:start position:0% +that there are many problems. So I'm not + + + align:start position:0% +that there are many problems. So I'm not +going to do the whole proof, but I'm + + align:start position:0% +going to do the whole proof, but I'm + + + align:start position:0% +going to do the whole proof, but I'm +going to tell you how to solve + + align:start position:0% + + + + align:start position:0% + +okay two of the problems or to some + + align:start position:0% +okay two of the problems or to some + + + align:start position:0% +okay two of the problems or to some +degree I will tell you how to solve two + + align:start position:0% +degree I will tell you how to solve two + + + align:start position:0% +degree I will tell you how to solve two +of the problems. + + align:start position:0% + + + + align:start position:0% + +Okay, one is really cheating but okay so + + align:start position:0% +Okay, one is really cheating but okay so + + + align:start position:0% +Okay, one is really cheating but okay so +I guess what I'm going to tell you is + + align:start position:0% +I guess what I'm going to tell you is + + + align:start position:0% +I guess what I'm going to tell you is +that cheating doesn't always work but it + + align:start position:0% +that cheating doesn't always work but it + + + align:start position:0% +that cheating doesn't always work but it +does work in this case in this + + align:start position:0% +does work in this case in this + + + align:start position:0% +does work in this case in this +particular case. + + align:start position:0% + + + + align:start position:0% + +I should finish at 225. Is that right? + + align:start position:0% +I should finish at 225. Is that right? + + + align:start position:0% +I should finish at 225. Is that right? +Okay. Plenty of time. + + align:start position:0% +Okay. Plenty of time. + + + align:start position:0% +Okay. Plenty of time. +Okay. So, idea of proof. I'm not going + + align:start position:0% +Okay. So, idea of proof. I'm not going + + + align:start position:0% +Okay. So, idea of proof. I'm not going +to prove it but + + align:start position:0% + + + + align:start position:0% + +okay. So + + align:start position:0% +okay. So + + + align:start position:0% +okay. So +uh with in the final field setting this + + align:start position:0% +uh with in the final field setting this + + + align:start position:0% +uh with in the final field setting this +works here we have the problem that uh + + align:start position:0% +works here we have the problem that uh + + + align:start position:0% +works here we have the problem that uh +the denominators can be very small and + + align:start position:0% +the denominators can be very small and + + + align:start position:0% +the denominators can be very small and +then this could be huge. So well we are + + align:start position:0% +then this could be huge. So well we are + + + align:start position:0% +then this could be huge. So well we are +going to do two things at twice to try + + align:start position:0% +going to do two things at twice to try + + + align:start position:0% +going to do two things at twice to try +to at least uh reduce the issue. So + + align:start position:0% +to at least uh reduce the issue. So + + + align:start position:0% +to at least uh reduce the issue. So +we're going to define b in the following + + align:start position:0% +we're going to define b in the following + + + align:start position:0% +we're going to define b in the following +way. + + align:start position:0% + + + + align:start position:0% + +It is essentially a over a a minus a + + align:start position:0% +It is essentially a over a a minus a + + + align:start position:0% +It is essentially a over a a minus a +over a minus a. + + align:start position:0% +over a minus a. + + + align:start position:0% +over a minus a. +Okay. So we pick some gamma and the + + align:start position:0% +Okay. So we pick some gamma and the + + + align:start position:0% +Okay. So we pick some gamma and the +gamma in the proof has to be picked + + align:start position:0% +gamma in the proof has to be picked + + + align:start position:0% +gamma in the proof has to be picked +carefully so that things work out and + + align:start position:0% +carefully so that things work out and + + + align:start position:0% +carefully so that things work out and +I'm going to go into the proof but you + + align:start position:0% +I'm going to go into the proof but you + + + align:start position:0% +I'm going to go into the proof but you +we have to pretend that there is a gamma + + align:start position:0% +we have to pretend that there is a gamma + + + align:start position:0% +we have to pretend that there is a gamma +so that will work. Okay. So first of all + + align:start position:0% +so that will work. Okay. So first of all + + + align:start position:0% +so that will work. Okay. So first of all +I restrict the denominators + + align:start position:0% +I restrict the denominators + + + align:start position:0% +I restrict the denominators +to being larger than delta 2 the gamma. + + align:start position:0% +to being larger than delta 2 the gamma. + + + align:start position:0% +to being larger than delta 2 the gamma. +So in this way + + align:start position:0% +So in this way + + + align:start position:0% +So in this way +well I got rid of the worst possible + + align:start position:0% +well I got rid of the worst possible + + + align:start position:0% +well I got rid of the worst possible +case where the expansion is too much. + + align:start position:0% +case where the expansion is too much. + + + align:start position:0% +case where the expansion is too much. +But even then this could escape the + + align:start position:0% +But even then this could escape the + + + align:start position:0% +But even then this could escape the +interval 01 and I don't want to escape + + align:start position:0% +interval 01 and I don't want to escape + + + align:start position:0% +interval 01 and I don't want to escape +the interval 01. + + align:start position:0% + + + + align:start position:0% + +So I intersect it with the interval 01. + + align:start position:0% + + + + align:start position:0% + +So this B is going to play the role of + + align:start position:0% +So this B is going to play the role of + + + align:start position:0% +So this B is going to play the role of +X. + + align:start position:0% +X. + + + align:start position:0% +X. +And by doing this I'm avoiding again I'm + + align:start position:0% +And by doing this I'm avoiding again I'm + + + align:start position:0% +And by doing this I'm avoiding again I'm +avoiding two related but not exactly the + + align:start position:0% +avoiding two related but not exactly the + + + align:start position:0% +avoiding two related but not exactly the +same issues. One is that this could + + align:start position:0% +same issues. One is that this could + + + align:start position:0% +same issues. One is that this could +escape our sort of reference interval + + align:start position:0% +escape our sort of reference interval + + + align:start position:0% +escape our sort of reference interval +and the other is that the denominators + + align:start position:0% +and the other is that the denominators + + + align:start position:0% +and the other is that the denominators +could be too small. They can still be + + align:start position:0% +could be too small. They can still be + + + align:start position:0% +could be too small. They can still be +quite small because so gamma is not + + align:start position:0% +quite small because so gamma is not + + + align:start position:0% +quite small because so gamma is not +zero. So this can still be small but + + align:start position:0% +zero. So this can still be small but + + + align:start position:0% +zero. So this can still be small but +so there is a trade-off. + + align:start position:0% +so there is a trade-off. + + + align:start position:0% +so there is a trade-off. +If we allow too small denominator things + + align:start position:0% +If we allow too small denominator things + + + align:start position:0% +If we allow too small denominator things +blow up too much but we still have to + + align:start position:0% +blow up too much but we still have to + + + align:start position:0% +blow up too much but we still have to +allow small denominators otherwise we + + align:start position:0% +allow small denominators otherwise we + + + align:start position:0% +allow small denominators otherwise we +are missing too much of a minus a over a + + align:start position:0% +are missing too much of a minus a over a + + + align:start position:0% +are missing too much of a minus a over a +minus a. So this gamma is gives us the + + align:start position:0% +minus a. So this gamma is gives us the + + + align:start position:0% +minus a. So this gamma is gives us the +tradeoff. + + align:start position:0% +tradeoff. + + + align:start position:0% +tradeoff. +Okay so that's one thing we do uh but + + align:start position:0% +Okay so that's one thing we do uh but + + + align:start position:0% +Okay so that's one thing we do uh but +the most important thing to understand + + align:start position:0% +the most important thing to understand + + + align:start position:0% +the most important thing to understand +is + + align:start position:0% +is + + + align:start position:0% +is +what do we do instead of this? So really + + align:start position:0% +what do we do instead of this? So really + + + align:start position:0% +what do we do instead of this? So really +adding one doesn't really make sense in + + align:start position:0% +adding one doesn't really make sense in + + + align:start position:0% +adding one doesn't really make sense in +this setting. So what do we do? And here + + align:start position:0% +this setting. So what do we do? And here + + + align:start position:0% +this setting. So what do we do? And here +comes a very easy but absolutely + + align:start position:0% +comes a very easy but absolutely + + + align:start position:0% +comes a very easy but absolutely +critical lema. + + align:start position:0% +critical lema. + + + align:start position:0% +critical lema. +So in the same way that + + align:start position:0% +So in the same way that + + + align:start position:0% +So in the same way that +the method in FP doesn't work in FP + + align:start position:0% +the method in FP doesn't work in FP + + + align:start position:0% +the method in FP doesn't work in FP +squared + + align:start position:0% +squared + + + align:start position:0% +squared +what works in R. Okay, this is a remark + + align:start position:0% +what works in R. Okay, this is a remark + + + align:start position:0% +what works in R. Okay, this is a remark +I should have made earlier but uh I + + align:start position:0% +I should have made earlier but uh I + + + align:start position:0% +I should have made earlier but uh I +don't think we have the statement + + align:start position:0% +don't think we have the statement + + + align:start position:0% +don't think we have the statement +anymore. Yeah, we don't have the + + align:start position:0% +anymore. Yeah, we don't have the + + + align:start position:0% +anymore. Yeah, we don't have the +statement of bug prediction theorem + + align:start position:0% +statement of bug prediction theorem + + + align:start position:0% +statement of bug prediction theorem +anymore. But bug prediction theorem is + + align:start position:0% +anymore. But bug prediction theorem is + + + align:start position:0% +anymore. But bug prediction theorem is +not true over C because over C you could + + align:start position:0% +not true over C because over C you could + + + align:start position:0% +not true over C because over C you could +you could take X to be essentially R + + align:start position:0% +you could take X to be essentially R + + + align:start position:0% +you could take X to be essentially R +squared living in C square and you could + + align:start position:0% +squared living in C square and you could + + + align:start position:0% +squared living in C square and you could +take D to be a piece of R living in C + + align:start position:0% +take D to be a piece of R living in C + + + align:start position:0% +take D to be a piece of R living in C +and because R is a subring of C you + + align:start position:0% +and because R is a subring of C you + + + align:start position:0% +and because R is a subring of C you +don't escape. So there is no growth. So + + align:start position:0% +don't escape. So there is no growth. So + + + align:start position:0% +don't escape. So there is no growth. So +it's exactly the same reason why it + + align:start position:0% +it's exactly the same reason why it + + + align:start position:0% +it's exactly the same reason why it +doesn't work in FP square because FP + + align:start position:0% +doesn't work in FP square because FP + + + align:start position:0% +doesn't work in FP square because FP +square has an intermediate algebraic + + align:start position:0% +square has an intermediate algebraic + + + align:start position:0% +square has an intermediate algebraic +structure. C has an intermediate + + align:start position:0% +structure. C has an intermediate + + + align:start position:0% +structure. C has an intermediate +algebraic structure which is R and + + align:start position:0% +algebraic structure which is R and + + + align:start position:0% +algebraic structure which is R and +because of this it doesn't work + + align:start position:0% +because of this it doesn't work + + + align:start position:0% +because of this it doesn't work +and + + align:start position:0% +and + + + align:start position:0% +and +here we use that FP doesn't have an + + align:start position:0% +here we use that FP doesn't have an + + + align:start position:0% +here we use that FP doesn't have an +intermediate algebraic structure. So + + align:start position:0% +intermediate algebraic structure. So + + + align:start position:0% +intermediate algebraic structure. So +actually this lema is very crucial in + + align:start position:0% +actually this lema is very crucial in + + + align:start position:0% +actually this lema is very crucial in +the sense that it is what distinguishes + + align:start position:0% +the sense that it is what distinguishes + + + align:start position:0% +the sense that it is what distinguishes +R from C or for many or okay from many + + align:start position:0% +R from C or for many or okay from many + + + align:start position:0% +R from C or for many or okay from many +other things but in particular from C. + + align:start position:0% +other things but in particular from C. + + + align:start position:0% +other things but in particular from C. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So there are many ways in which R is + + align:start position:0% +So there are many ways in which R is + + + align:start position:0% +So there are many ways in which R is +different from C and we will see that it + + align:start position:0% +different from C and we will see that it + + + align:start position:0% +different from C and we will see that it +is the order structure uh what + + align:start position:0% +is the order structure uh what + + + align:start position:0% +is the order structure uh what +distinguishes R from C in the lema in + + align:start position:0% +distinguishes R from C in the lema in + + + align:start position:0% +distinguishes R from C in the lema in +the proof of dilemma. Actually dilemma + + align:start position:0% +the proof of dilemma. Actually dilemma + + + align:start position:0% +the proof of dilemma. Actually dilemma +can be proved in many ways and some of + + align:start position:0% +can be proved in many ways and some of + + + align:start position:0% +can be proved in many ways and some of +them do not use the order structure but + + align:start position:0% +them do not use the order structure but + + + align:start position:0% +them do not use the order structure but +in my proof I will use the order + + align:start position:0% +in my proof I will use the order + + + align:start position:0% +in my proof I will use the order +structure. Okay. So here is the lema. Uh + + align:start position:0% +structure. Okay. So here is the lema. Uh + + + align:start position:0% +structure. Okay. So here is the lema. Uh +suppose that B + + align:start position:0% +suppose that B + + + align:start position:0% +suppose that B +eventually we are going to apply to this + + align:start position:0% +eventually we are going to apply to this + + + align:start position:0% +eventually we are going to apply to this +B that's why I call it B. But a priority + + align:start position:0% +B that's why I call it B. But a priority + + + align:start position:0% +B that's why I call it B. But a priority +is any B it's contained in 01 and + + align:start position:0% +is any B it's contained in 01 and + + + align:start position:0% +is any B it's contained in 01 and +suppose that zero is in B zero is in + + align:start position:0% +suppose that zero is in B zero is in + + + align:start position:0% +suppose that zero is in B zero is in +this B because A1 could be equal to A2 + + align:start position:0% +this B because A1 could be equal to A2 + + + align:start position:0% +this B because A1 could be equal to A2 +okay and then uh + + align:start position:0% +okay and then uh + + + align:start position:0% +okay and then uh +let row + + align:start position:0% +let row + + + align:start position:0% +let row +be the largest gap + + align:start position:0% + + + + align:start position:0% + +in B. + + align:start position:0% +in B. + + + align:start position:0% +in B. +Okay, what is the largest gap? So a gap + + align:start position:0% +Okay, what is the largest gap? So a gap + + + align:start position:0% +Okay, what is the largest gap? So a gap +is a + + align:start position:0% +is a + + + align:start position:0% +is a +is a connected component of the + + align:start position:0% +is a connected component of the + + + align:start position:0% +is a connected component of the +complement. So we are in R. So connected + + align:start position:0% +complement. So we are in R. So connected + + + align:start position:0% +complement. So we are in R. So connected +components are segments. + + align:start position:0% +components are segments. + + + align:start position:0% +components are segments. +So the complement is a union of + + align:start position:0% +So the complement is a union of + + + align:start position:0% +So the complement is a union of +segments. Well could be points. I mean B + + align:start position:0% +segments. Well could be points. I mean B + + + align:start position:0% +segments. Well could be points. I mean B +could be dense but let's imagine B is + + align:start position:0% +could be dense but let's imagine B is + + + align:start position:0% +could be dense but let's imagine B is +closed. I think it doesn't have to be + + align:start position:0% +closed. I think it doesn't have to be + + + align:start position:0% +closed. I think it doesn't have to be +closed. Maybe let's say closed. + + align:start position:0% +closed. Maybe let's say closed. + + + align:start position:0% +closed. Maybe let's say closed. +It's not really important. + + align:start position:0% +It's not really important. + + + align:start position:0% +It's not really important. +Okay. If it's closed and the complement + + align:start position:0% +Okay. If it's closed and the complement + + + align:start position:0% +Okay. If it's closed and the complement +is a finite or contraable union of open + + align:start position:0% +is a finite or contraable union of open + + + align:start position:0% +is a finite or contraable union of open +intervals. Each of them has a length and + + align:start position:0% +intervals. Each of them has a length and + + + align:start position:0% +intervals. Each of them has a length and +we take the supreum maybe + + align:start position:0% +we take the supreum maybe + + + align:start position:0% +we take the supreum maybe +okay everything is going to be fi like + + align:start position:0% +okay everything is going to be fi like + + + align:start position:0% +okay everything is going to be fi like +finiteary because in our application but + + align:start position:0% +finiteary because in our application but + + + align:start position:0% +finiteary because in our application but +let's say the largest in the sense of + + align:start position:0% +let's say the largest in the sense of + + + align:start position:0% +let's say the largest in the sense of +the supreum of the length of the gaps in + + align:start position:0% +the supreum of the length of the gaps in + + + align:start position:0% +the supreum of the length of the gaps in +B so is it clear what this is we just + + align:start position:0% +B so is it clear what this is we just + + + align:start position:0% +B so is it clear what this is we just +look at the complimentary intervals and + + align:start position:0% +look at the complimentary intervals and + + + align:start position:0% +look at the complimentary intervals and +we look at the largest one then + + align:start position:0% + + + + align:start position:0% + +there exist B in B + + align:start position:0% +there exist B in B + + + align:start position:0% +there exist B in B +such that either + + align:start position:0% + + + + align:start position:0% + +The distance from B / 2 to B is at least + + align:start position:0% +The distance from B / 2 to B is at least + + + align:start position:0% +The distance from B / 2 to B is at least +row over four + + align:start position:0% +row over four + + + align:start position:0% +row over four +or + + align:start position:0% +or + + + align:start position:0% +or +the distance from B + 1 / two + + align:start position:0% +the distance from B + 1 / two + + + align:start position:0% +the distance from B + 1 / two +to B is at least row over 4. + + align:start position:0% + + + + align:start position:0% + +Okay. So proof, + + align:start position:0% +Okay. So proof, + + + align:start position:0% +Okay. So proof, +let B prime be B / 2 union B + 1 / two. + + align:start position:0% +let B prime be B / 2 union B + 1 / two. + + + align:start position:0% +let B prime be B / 2 union B + 1 / two. +And this means what you expect it to + + align:start position:0% +And this means what you expect it to + + + align:start position:0% +And this means what you expect it to +mean. So you take little B in B divided + + align:start position:0% +mean. So you take little B in B divided + + + align:start position:0% +mean. So you take little B in B divided +by two and you do that for every little + + align:start position:0% +by two and you do that for every little + + + align:start position:0% +by two and you do that for every little +B in B. And then you take little B plus + + align:start position:0% +B in B. And then you take little B plus + + + align:start position:0% +B in B. And then you take little B plus +one over two for every little B in B. So + + align:start position:0% +one over two for every little B in B. So + + + align:start position:0% +one over two for every little B in B. So +I hope it's clear what this is. + + align:start position:0% +I hope it's clear what this is. + + + align:start position:0% +I hope it's clear what this is. +Okay. So this is contained in 01 as well + + align:start position:0% +Okay. So this is contained in 01 as well + + + align:start position:0% +Okay. So this is contained in 01 as well +because B is contained in 01. So this is + + align:start position:0% +because B is contained in 01. So this is + + + align:start position:0% +because B is contained in 01. So this is +contained in 0 1/2. This is contained in + + align:start position:0% +contained in 0 1/2. This is contained in + + + align:start position:0% +contained in 0 1/2. This is contained in +one half one. + + align:start position:0% +one half one. + + + align:start position:0% +one half one. +So we have zero, we have one, we have + + align:start position:0% +So we have zero, we have one, we have + + + align:start position:0% +So we have zero, we have one, we have +1/2 and 1/2 is in B prime because zero + + align:start position:0% +1/2 and 1/2 is in B prime because zero + + + align:start position:0% +1/2 and 1/2 is in B prime because zero +is in B. + + align:start position:0% + + + + align:start position:0% + +You will see that this is important. So + + align:start position:0% +You will see that this is important. So + + + align:start position:0% +You will see that this is important. So +zero is in B. So one half is in B prime. + + align:start position:0% +zero is in B. So one half is in B prime. + + + align:start position:0% +zero is in B. So one half is in B prime. +Now what is the largest gap in B prime? + + align:start position:0% +Now what is the largest gap in B prime? + + + align:start position:0% +Now what is the largest gap in B prime? +So by definition the largest gap in B is + + align:start position:0% +So by definition the largest gap in B is + + + align:start position:0% +So by definition the largest gap in B is +row. So that's the definition of row. So + + align:start position:0% +row. So that's the definition of row. So + + + align:start position:0% +row. So that's the definition of row. So +what is the largest gap in B prime? + + align:start position:0% +what is the largest gap in B prime? + + + align:start position:0% +what is the largest gap in B prime? +>> Row over two. + + align:start position:0% +>> Row over two. + + + align:start position:0% +>> Row over two. +Here the largest gap is row over two + + align:start position:0% +Here the largest gap is row over two + + + align:start position:0% +Here the largest gap is row over two +because I'm scaling down by a factor of + + align:start position:0% +because I'm scaling down by a factor of + + + align:start position:0% +because I'm scaling down by a factor of +two. And here the largest gap is row + + align:start position:0% +two. And here the largest gap is row + + + align:start position:0% +two. And here the largest gap is row +over two because I'm translating and + + align:start position:0% +over two because I'm translating and + + + align:start position:0% +over two because I'm translating and +scaling down by Yes. + + align:start position:0% +scaling down by Yes. + + + align:start position:0% +scaling down by Yes. +>> Could actually there be a gap of size + + align:start position:0% +>> Could actually there be a gap of size + + + align:start position:0% +>> Could actually there be a gap of size +row if B has a big gap at the ends of + + align:start position:0% +row if B has a big gap at the ends of + + + align:start position:0% +row if B has a big gap at the ends of +the intervals? + + align:start position:0% +the intervals? + + + align:start position:0% +the intervals? +Okay. So I guess uh + + align:start position:0% +Okay. So I guess uh + + + align:start position:0% +Okay. So I guess uh +maybe let's assume that one is also in B + + align:start position:0% +maybe let's assume that one is also in B + + + align:start position:0% +maybe let's assume that one is also in B +or something like this. So I mean there + + align:start position:0% +or something like this. So I mean there + + + align:start position:0% +or something like this. So I mean there +could be an infinite gap. + + align:start position:0% +could be an infinite gap. + + + align:start position:0% +could be an infinite gap. +Is is that what you're worried about? + + align:start position:0% +Is is that what you're worried about? + + + align:start position:0% +Is is that what you're worried about? +>> That yeah there's a gap from like one + + align:start position:0% +>> That yeah there's a gap from like one + + + align:start position:0% +>> That yeah there's a gap from like one +minus row to one or something. But if + + align:start position:0% +minus row to one or something. But if + + + align:start position:0% +minus row to one or something. But if +one is in in B then uh + + align:start position:0% +one is in in B then uh + + + align:start position:0% +one is in in B then uh +>> let's say zero and one are in B. So one + + align:start position:0% +>> let's say zero and one are in B. So one + + + align:start position:0% +>> let's say zero and one are in B. So one +is also here because you could take A3 + + align:start position:0% +is also here because you could take A3 + + + align:start position:0% +is also here because you could take A3 +and A4 to be A1 and A2. + + align:start position:0% +and A4 to be A1 and A2. + + + align:start position:0% +and A4 to be A1 and A2. +So one is in B. + + align:start position:0% +So one is in B. + + + align:start position:0% +So one is in B. +Uh if you define the gap in a way that + + align:start position:0% +Uh if you define the gap in a way that + + + align:start position:0% +Uh if you define the gap in a way that +avoids this issue, you don't need one to + + align:start position:0% +avoids this issue, you don't need one to + + + align:start position:0% +avoids this issue, you don't need one to +be in B. But let's it's not important. + + align:start position:0% +be in B. But let's it's not important. + + + align:start position:0% +be in B. But let's it's not important. +Okay. Why is it important that one half + + align:start position:0% +Okay. Why is it important that one half + + + align:start position:0% +Okay. Why is it important that one half +is in B? Because here the largest gap is + + align:start position:0% +is in B? Because here the largest gap is + + + align:start position:0% +is in B? Because here the largest gap is +has size row over two. Here the largest + + align:start position:0% +has size row over two. Here the largest + + + align:start position:0% +has size row over two. Here the largest +gap has size row over two. But if one + + align:start position:0% +gap has size row over two. But if one + + + align:start position:0% +gap has size row over two. But if one +half wasn't here, there they could be + + align:start position:0% +half wasn't here, there they could be + + + align:start position:0% +half wasn't here, there they could be +combined to form a larger gap going + + align:start position:0% +combined to form a larger gap going + + + align:start position:0% +combined to form a larger gap going +across. But it cannot go across because + + align:start position:0% +across. But it cannot go across because + + + align:start position:0% +across. But it cannot go across because +there is one half is there. Okay. So now + + align:start position:0% +there is one half is there. Okay. So now + + + align:start position:0% +there is one half is there. Okay. So now +um + + align:start position:0% + + + + align:start position:0% + +now let's draw the largest gap or the + + align:start position:0% +now let's draw the largest gap or the + + + align:start position:0% +now let's draw the largest gap or the +gap that approximates the largest gap. + + align:start position:0% +gap that approximates the largest gap. + + + align:start position:0% +gap that approximates the largest gap. +So this one has size let's say row minus + + align:start position:0% +So this one has size let's say row minus + + + align:start position:0% +So this one has size let's say row minus +epsilon + + align:start position:0% + + + + align:start position:0% + +and okay so this is the center of the + + align:start position:0% +and okay so this is the center of the + + + align:start position:0% +and okay so this is the center of the +gap. So this is the gap in B not in B + + align:start position:0% +gap. So this is the gap in B not in B + + + align:start position:0% +gap. So this is the gap in B not in B +prime in B. And now let's write let's + + align:start position:0% +prime in B. And now let's write let's + + + align:start position:0% +prime in B. And now let's write let's +draw + + align:start position:0% +draw + + + align:start position:0% +draw +an interval in the middle of length row + + align:start position:0% +an interval in the middle of length row + + + align:start position:0% +an interval in the middle of length row +over two. + + align:start position:0% + + + + align:start position:0% + +Maybe a closed interval. + + align:start position:0% +Maybe a closed interval. + + + align:start position:0% +Maybe a closed interval. +This closed interval contains an element + + align:start position:0% +This closed interval contains an element + + + align:start position:0% +This closed interval contains an element +of B prime because the largest gap of B + + align:start position:0% +of B prime because the largest gap of B + + + align:start position:0% +of B prime because the largest gap of B +prime is row over two. That means that + + align:start position:0% +prime is row over two. That means that + + + align:start position:0% +prime is row over two. That means that +any interval of length row over two + + align:start position:0% +any interval of length row over two + + + align:start position:0% +any interval of length row over two +contains a point in B prime. Okay. So + + align:start position:0% +contains a point in B prime. Okay. So + + + align:start position:0% +contains a point in B prime. Okay. So +maybe let's write this down. So largest + + align:start position:0% +maybe let's write this down. So largest + + + align:start position:0% +maybe let's write this down. So largest +gap. + + align:start position:0% + + + + align:start position:0% + +So this interval contains a point in B + + align:start position:0% +So this interval contains a point in B + + + align:start position:0% +So this interval contains a point in B +prime. + + align:start position:0% +prime. + + + align:start position:0% +prime. +But this point is a distance at least + + align:start position:0% +But this point is a distance at least + + + align:start position:0% +But this point is a distance at least +row over four from B + + align:start position:0% +row over four from B + + + align:start position:0% +row over four from B +because this gap is double the size. So + + align:start position:0% +because this gap is double the size. So + + + align:start position:0% +because this gap is double the size. So +even if the point was at one of the end + + align:start position:0% +even if the point was at one of the end + + + align:start position:0% +even if the point was at one of the end +points, so the point could be here. But + + align:start position:0% +points, so the point could be here. But + + + align:start position:0% +points, so the point could be here. But +even if it was at one of the end points, + + align:start position:0% +even if it was at one of the end points, + + + align:start position:0% +even if it was at one of the end points, +this is row over four. This is row over + + align:start position:0% +this is row over four. This is row over + + + align:start position:0% +this is row over four. This is row over +four. + + align:start position:0% + + + + align:start position:0% + +Okay. So maybe let's do a larger + + align:start position:0% +Okay. So maybe let's do a larger + + + align:start position:0% +Okay. So maybe let's do a larger +picture. So this is row minus epsilon + + align:start position:0% +picture. So this is row minus epsilon + + + align:start position:0% +picture. So this is row minus epsilon +gap in b. + + align:start position:0% + + + + align:start position:0% + +Okay. And this is a row interval. + + align:start position:0% + + + + align:start position:0% + +So it contains + + align:start position:0% + + + + align:start position:0% + +some point in b prime because the + + align:start position:0% +some point in b prime because the + + + align:start position:0% +some point in b prime because the +largest gap in b prime is row. And this + + align:start position:0% +largest gap in b prime is row. And this + + + align:start position:0% +largest gap in b prime is row. And this +interval has length row. So it cannot be + + align:start position:0% +interval has length row. So it cannot be + + + align:start position:0% +interval has length row. So it cannot be +completely empty otherwise it would be a + + align:start position:0% +completely empty otherwise it would be a + + + align:start position:0% +completely empty otherwise it would be a +larger gap. Okay. Whichever point is in + + align:start position:0% +larger gap. Okay. Whichever point is in + + + align:start position:0% +larger gap. Okay. Whichever point is in +this interval is at large distance from + + align:start position:0% +this interval is at large distance from + + + align:start position:0% +this interval is at large distance from +B because there is nothing in B here. + + align:start position:0% +B because there is nothing in B here. + + + align:start position:0% +B because there is nothing in B here. +So that's the proof. So you do the + + align:start position:0% +So that's the proof. So you do the + + + align:start position:0% +So that's the proof. So you do the +calculation is at least row over four. + + align:start position:0% +calculation is at least row over four. + + + align:start position:0% +calculation is at least row over four. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +maybe row over five because you need to + + align:start position:0% +maybe row over five because you need to + + + align:start position:0% +maybe row over five because you need to +take into account this epsilon. Maybe + + align:start position:0% +take into account this epsilon. Maybe + + + align:start position:0% +take into account this epsilon. Maybe +row over five just in case + + align:start position:0% +row over five just in case + + + align:start position:0% +row over five just in case +it's not it's not important. + + align:start position:0% + + + + align:start position:0% + +So you see that this is a simple + + align:start position:0% +So you see that this is a simple + + + align:start position:0% +So you see that this is a simple +geometric argument but it very very + + align:start position:0% +geometric argument but it very very + + + align:start position:0% +geometric argument but it very very +strongly uses the order structure of R. + + align:start position:0% +strongly uses the order structure of R. + + + align:start position:0% +strongly uses the order structure of R. +So this argument doesn't work in C + + align:start position:0% +So this argument doesn't work in C + + + align:start position:0% +So this argument doesn't work in C +because there is no order and in fact it + + align:start position:0% +because there is no order and in fact it + + + align:start position:0% +because there is no order and in fact it +cannot work because what we are going to + + align:start position:0% +cannot work because what we are going to + + + align:start position:0% +cannot work because what we are going to +prove using this is not true over C. + + align:start position:0% +prove using this is not true over C. + + + align:start position:0% +prove using this is not true over C. +Any questions about this? + + align:start position:0% + + + + align:start position:0% + +Okay you can prove this lema in other + + align:start position:0% +Okay you can prove this lema in other + + + align:start position:0% +Okay you can prove this lema in other +ways. So Guat and Zal in their paper I + + align:start position:0% +ways. So Guat and Zal in their paper I + + + align:start position:0% +ways. So Guat and Zal in their paper I +think they don't do this proof but I + + align:start position:0% +think they don't do this proof but I + + + align:start position:0% +think they don't do this proof but I +think this proof is easier and shows how + + align:start position:0% +think this proof is easier and shows how + + + align:start position:0% +think this proof is easier and shows how +the order structure is fundamental. + + align:start position:0% +the order structure is fundamental. + + + align:start position:0% +the order structure is fundamental. +Okay. So + + align:start position:0% + + + + align:start position:0% + +hopefully I have proved the lema. + + align:start position:0% +hopefully I have proved the lema. + + + align:start position:0% +hopefully I have proved the lema. +Okay. So of course a point in B prime + + align:start position:0% +Okay. So of course a point in B prime + + + align:start position:0% +Okay. So of course a point in B prime +has either this form or this form + + align:start position:0% +has either this form or this form + + + align:start position:0% +has either this form or this form +because that's the definition of B + + align:start position:0% +because that's the definition of B + + + align:start position:0% +because that's the definition of B +prime. Okay. So here we have a B prime + + align:start position:0% +prime. Okay. So here we have a B prime + + + align:start position:0% +prime. Okay. So here we have a B prime +in B prime which is far from B. that B + + align:start position:0% +in B prime which is far from B. that B + + + align:start position:0% +in B prime which is far from B. that B +prime is either this or this because + + align:start position:0% +prime is either this or this because + + + align:start position:0% +prime is either this or this because +that's the definition of B prime. So + + align:start position:0% +that's the definition of B prime. So + + + align:start position:0% +that's the definition of B prime. So +that's how one concludes the proof. + + align:start position:0% +that's how one concludes the proof. + + + align:start position:0% +that's how one concludes the proof. +Any questions again? + + align:start position:0% + + + + align:start position:0% + +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +now what the idea is to use B over two + + align:start position:0% +now what the idea is to use B over two + + + align:start position:0% +now what the idea is to use B over two +or B+ over two instead of + + align:start position:0% +or B+ over two instead of + + + align:start position:0% +or B+ over two instead of +B+ one. + + align:start position:0% +B+ one. + + + align:start position:0% +B+ one. +So why does B+1 work? So what is + + align:start position:0% +So why does B+1 work? So what is + + + align:start position:0% +So why does B+1 work? So what is +important about b+ or x + one? So what + + align:start position:0% +important about b+ or x + one? So what + + + align:start position:0% +important about b+ or x + one? So what +is important is that + + align:start position:0% +is important is that + + + align:start position:0% +is important is that +again it's a polomial in this case is a + + align:start position:0% +again it's a polomial in this case is a + + + align:start position:0% +again it's a polomial in this case is a +linear polomial but + + align:start position:0% +linear polomial but + + + align:start position:0% +linear polomial but +that that takes something in x and lands + + align:start position:0% +that that takes something in x and lands + + + align:start position:0% +that that takes something in x and lands +it not in x. Well the same is true for b + + align:start position:0% +it not in x. Well the same is true for b + + + align:start position:0% +it not in x. Well the same is true for b +over two and b plus one over two. + + align:start position:0% + + + + align:start position:0% + +you take something in B and it lands far + + align:start position:0% +you take something in B and it lands far + + + align:start position:0% +you take something in B and it lands far +from B. + + align:start position:0% + + + + align:start position:0% + +Okay. So, uh + + align:start position:0% +Okay. So, uh + + + align:start position:0% +Okay. So, uh +let's say first step of proof. So, I'm + + align:start position:0% +let's say first step of proof. So, I'm + + + align:start position:0% +let's say first step of proof. So, I'm +not going to prove but + + align:start position:0% + + + + align:start position:0% + +well, we have to pick a row in 01 + + align:start position:0% +well, we have to pick a row in 01 + + + align:start position:0% +well, we have to pick a row in 01 +carefully. + + align:start position:0% + + + + align:start position:0% + +In fact, it's going to be a power of + + align:start position:0% +In fact, it's going to be a power of + + + align:start position:0% +In fact, it's going to be a power of +delta as usual. Some power don't + + align:start position:0% +delta as usual. Some power don't + + + align:start position:0% +delta as usual. Some power don't +remember which power. One has to choose + + align:start position:0% +remember which power. One has to choose + + + align:start position:0% +remember which power. One has to choose +this power carefully. And then there are + + align:start position:0% +this power carefully. And then there are + + + align:start position:0% +this power carefully. And then there are +two cases that sort of morally + + align:start position:0% +two cases that sort of morally + + + align:start position:0% +two cases that sort of morally +correspond to those two cases. + + align:start position:0% + + + + align:start position:0% + +B now is that B that B up up there. Not + + align:start position:0% +B now is that B that B up up there. Not + + + align:start position:0% +B now is that B that B up up there. Not +an arbitrary B. that be is row dense. + + align:start position:0% + + + + align:start position:0% + +Row dense means that the largest gap is + + align:start position:0% +Row dense means that the largest gap is + + + align:start position:0% +Row dense means that the largest gap is +at most row + + align:start position:0% +at most row + + + align:start position:0% +at most row +or if you take the row neighborhood you + + align:start position:0% +or if you take the row neighborhood you + + + align:start position:0% +or if you take the row neighborhood you +cover everything everything is 01. + + align:start position:0% +cover everything everything is 01. + + + align:start position:0% +cover everything everything is 01. +So any questions about what row dense + + align:start position:0% +So any questions about what row dense + + + align:start position:0% +So any questions about what row dense +means? + + align:start position:0% + + + + align:start position:0% + +Okay. And here we use an argument which + + align:start position:0% +Okay. And here we use an argument which + + + align:start position:0% +Okay. And here we use an argument which +is similar + + align:start position:0% +is similar + + + align:start position:0% +is similar +to the case x - x /x sorry uh it's not x + + align:start position:0% +to the case x - x /x sorry uh it's not x + + + align:start position:0% +to the case x - x /x sorry uh it's not x +it's a minus a + + align:start position:0% +it's a minus a + + + align:start position:0% +it's a minus a +over a minus a equals fp + + align:start position:0% +over a minus a equals fp + + + align:start position:0% +over a minus a equals fp +to get growth + + align:start position:0% +to get growth + + + align:start position:0% +to get growth +which I'm not going to show + + align:start position:0% +which I'm not going to show + + + align:start position:0% +which I'm not going to show +this is the sort of easier case + + align:start position:0% +this is the sort of easier case + + + align:start position:0% +this is the sort of easier case +I here was also the easier case. + + align:start position:0% +I here was also the easier case. + + + align:start position:0% +I here was also the easier case. +Okay. And the other possibility is that + + align:start position:0% +Okay. And the other possibility is that + + + align:start position:0% +Okay. And the other possibility is that +there exist a B in B such that either + + align:start position:0% + + + + align:start position:0% + +B / 2 is far from B + + align:start position:0% +B / 2 is far from B + + + align:start position:0% +B / 2 is far from B +or + + align:start position:0% +or + + + align:start position:0% +or +B + 1 / two + + align:start position:0% +B + 1 / two + + + align:start position:0% +B + 1 / two +is far from B. + + align:start position:0% + + + + align:start position:0% + +in this sense. + + align:start position:0% +in this sense. + + + align:start position:0% +in this sense. +So there are two cases by dilemma. + + align:start position:0% + + + + align:start position:0% + +Okay. And then we use B over two or B + + align:start position:0% +Okay. And then we use B over two or B + + + align:start position:0% +Okay. And then we use B over two or B +plus one over two in a similar way to X + + align:start position:0% +plus one over two in a similar way to X + + + align:start position:0% +plus one over two in a similar way to X +the way that X + one was used in the + + align:start position:0% +the way that X + one was used in the + + + align:start position:0% +the way that X + one was used in the +final field setting + + align:start position:0% + + + + align:start position:0% + +to get expansion. + + align:start position:0% +to get expansion. + + + align:start position:0% +to get expansion. +And it works. is much more complicated. + + align:start position:0% +And it works. is much more complicated. + + + align:start position:0% +And it works. is much more complicated. +So the the actual details are much more + + align:start position:0% +So the the actual details are much more + + + align:start position:0% +So the the actual details are much more +complicated than in the final field + + align:start position:0% +complicated than in the final field + + + align:start position:0% +complicated than in the final field +setting + + align:start position:0% + + + + align:start position:0% + +but it works and + + align:start position:0% +but it works and + + + align:start position:0% +but it works and +I would say the overall idea is very + + align:start position:0% +I would say the overall idea is very + + + align:start position:0% +I would say the overall idea is very +similar but the details are much more + + align:start position:0% +similar but the details are much more + + + align:start position:0% +similar but the details are much more +complicated. + + align:start position:0% + + + + align:start position:0% + +Okay. So, so far so good module, lots of + + align:start position:0% +Okay. So, so far so good module, lots of + + + align:start position:0% +Okay. So, so far so good module, lots of +details, but uh this was the first step + + align:start position:0% +details, but uh this was the first step + + + align:start position:0% +details, but uh this was the first step +in the final field setting and we can + + align:start position:0% +in the final field setting and we can + + + align:start position:0% +in the final field setting and we can +replicate it. So, it seems that things + + align:start position:0% +replicate it. So, it seems that things + + + align:start position:0% +replicate it. So, it seems that things +are going well. But now we have a much + + align:start position:0% +are going well. But now we have a much + + + align:start position:0% +are going well. But now we have a much +bigger issue. + + align:start position:0% + + + + align:start position:0% + +Maybe I'm going to explain the much + + align:start position:0% +Maybe I'm going to explain the much + + + align:start position:0% +Maybe I'm going to explain the much +bigger issue and talk about how to + + align:start position:0% +bigger issue and talk about how to + + + align:start position:0% +bigger issue and talk about how to +overcome it next time because this is + + align:start position:0% +overcome it next time because this is + + + align:start position:0% +overcome it next time because this is +maybe the biggest issue, the biggest + + align:start position:0% +maybe the biggest issue, the biggest + + + align:start position:0% +maybe the biggest issue, the biggest +difference. Okay, you can see that this + + align:start position:0% +difference. Okay, you can see that this + + + align:start position:0% +difference. Okay, you can see that this +was already a big issue and a big + + align:start position:0% +was already a big issue and a big + + + align:start position:0% +was already a big issue and a big +difference in the proof. But now comes I + + align:start position:0% +difference in the proof. But now comes I + + + align:start position:0% +difference in the proof. But now comes I +would say a bigger issue. + + align:start position:0% +would say a bigger issue. + + + align:start position:0% +would say a bigger issue. +This was the first step in the final + + align:start position:0% +This was the first step in the final + + + align:start position:0% +This was the first step in the final +field setting. What is the second step + + align:start position:0% +field setting. What is the second step + + + align:start position:0% +field setting. What is the second step +in the final field setting? Iterate in + + align:start position:0% +in the final field setting? Iterate in + + + align:start position:0% +in the final field setting? Iterate in +the first step and you just iterate. + + align:start position:0% +the first step and you just iterate. + + + align:start position:0% +the first step and you just iterate. +Nobody's preventing you from iterating. + + align:start position:0% +Nobody's preventing you from iterating. + + + align:start position:0% +Nobody's preventing you from iterating. +So you get that Q of A growth. So you + + align:start position:0% +So you get that Q of A growth. So you + + + align:start position:0% +So you get that Q of A growth. So you +can do Q of Q of A. + + align:start position:0% +can do Q of Q of A. + + + align:start position:0% +can do Q of Q of A. +So here + + align:start position:0% +So here + + + align:start position:0% +So here +maybe let's call it the second step. + + align:start position:0% +maybe let's call it the second step. + + + align:start position:0% +maybe let's call it the second step. +You look at Q of Q of Q of Q of A + + align:start position:0% +You look at Q of Q of Q of Q of A + + + align:start position:0% +You look at Q of Q of Q of Q of A +and this is very large. + + align:start position:0% +and this is very large. + + + align:start position:0% +and this is very large. +So uh you can make it as close to P as + + align:start position:0% +So uh you can make it as close to P as + + + align:start position:0% +So uh you can make it as close to P as +you want + + align:start position:0% +you want + + + align:start position:0% +you want +in terms of powers. + + align:start position:0% +in terms of powers. + + + align:start position:0% +in terms of powers. +I don't know + + align:start position:0% +I don't know + + + align:start position:0% +I don't know +I don't know it. So for any ita if we + + align:start position:0% +I don't know it. So for any ita if we + + + align:start position:0% +I don't know it. So for any ita if we +iterate enough times we keep growing and + + align:start position:0% +iterate enough times we keep growing and + + + align:start position:0% +iterate enough times we keep growing and +we can reach any power we want. In fact, + + align:start position:0% +we can reach any power we want. In fact, + + + align:start position:0% +we can reach any power we want. In fact, +we actually eventually in the fin + + align:start position:0% +we actually eventually in the fin + + + align:start position:0% +we actually eventually in the fin +setting we get all of all of the finite + + align:start position:0% +setting we get all of all of the finite + + + align:start position:0% +setting we get all of all of the finite +field after iterating finite finitely + + align:start position:0% +field after iterating finite finitely + + + align:start position:0% +field after iterating finite finitely +many times. I don't know if you saw this + + align:start position:0% +many times. I don't know if you saw this + + + align:start position:0% +many times. I don't know if you saw this +but anyway so this is clear because we + + align:start position:0% +but anyway so this is clear because we + + + align:start position:0% +but anyway so this is clear because we +just keep iterating. + + align:start position:0% +just keep iterating. + + + align:start position:0% +just keep iterating. +Okay. So now let's go back to + + align:start position:0% + + + + align:start position:0% + +sorry did I ever state + + align:start position:0% +sorry did I ever state + + + align:start position:0% +sorry did I ever state +uh + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +oh here it is okay so here is the lema + + align:start position:0% +oh here it is okay so here is the lema + + + align:start position:0% +oh here it is okay so here is the lema +that + + align:start position:0% +that + + + align:start position:0% +that +I told you we can prove using this idea. + + align:start position:0% +I told you we can prove using this idea. + + + align:start position:0% +I told you we can prove using this idea. +So then this is the lema. So we have a + + align:start position:0% +So then this is the lema. So we have a + + + align:start position:0% +So then this is the lema. So we have a +delta s delta to the minus epsilon set + + align:start position:0% +delta s delta to the minus epsilon set + + + align:start position:0% +delta s delta to the minus epsilon set +of size delta t to the minus s. Then we + + align:start position:0% +of size delta t to the minus s. Then we + + + align:start position:0% +of size delta t to the minus s. Then we +apply q and the size grows. + + align:start position:0% +apply q and the size grows. + + + align:start position:0% +apply q and the size grows. +Okay. So what's the problem? + + align:start position:0% +Okay. So what's the problem? + + + align:start position:0% +Okay. So what's the problem? +We would like to iterate but we cannot. + + align:start position:0% +We would like to iterate but we cannot. + + + align:start position:0% +We would like to iterate but we cannot. +So why can we not iterate? Well, + + align:start position:0% +So why can we not iterate? Well, + + + align:start position:0% +So why can we not iterate? Well, +apparently we cannot. I'm not saying in + + align:start position:0% +apparently we cannot. I'm not saying in + + + align:start position:0% +apparently we cannot. I'm not saying in +the end we will iterate but why why is + + align:start position:0% +the end we will iterate but why why is + + + align:start position:0% +the end we will iterate but why why is +it completely unclear whether we can + + align:start position:0% +it completely unclear whether we can + + + align:start position:0% +it completely unclear whether we can +iterate? + + align:start position:0% +iterate? + + + align:start position:0% +iterate? +There's no guarantee that Q of A will + + align:start position:0% +There's no guarantee that Q of A will + + + align:start position:0% +There's no guarantee that Q of A will +satisfy the spacing condition. + + align:start position:0% +satisfy the spacing condition. + + + align:start position:0% +satisfy the spacing condition. +>> Exactly. That's the issue and it is a + + align:start position:0% +>> Exactly. That's the issue and it is a + + + align:start position:0% +>> Exactly. That's the issue and it is a +big issue. So we know that the size of Q + + align:start position:0% +big issue. So we know that the size of Q + + + align:start position:0% +big issue. So we know that the size of Q +of A grows. + + align:start position:0% +of A grows. + + + align:start position:0% +of A grows. +But here we have this additional + + align:start position:0% +But here we have this additional + + + align:start position:0% +But here we have this additional +assumption and we need it or we need + + align:start position:0% +assumption and we need it or we need + + + align:start position:0% +assumption and we need it or we need +some assumption. We need the assumption + + align:start position:0% +some assumption. We need the assumption + + + align:start position:0% +some assumption. We need the assumption +that A is a delta S delta to the minus + + align:start position:0% +that A is a delta S delta to the minus + + + align:start position:0% +that A is a delta S delta to the minus +epsilon set. So in order to iterate we + + align:start position:0% +epsilon set. So in order to iterate we + + + align:start position:0% +epsilon set. So in order to iterate we +would need to know that not only Q of A + + align:start position:0% +would need to know that not only Q of A + + + align:start position:0% +would need to know that not only Q of A +has grown in size but we would need to + + align:start position:0% +has grown in size but we would need to + + + align:start position:0% +has grown in size but we would need to +know that Q of A is a delta S plus + + align:start position:0% +know that Q of A is a delta S plus + + + align:start position:0% +know that Q of A is a delta S plus +epsilon delta to the minus epsilon set + + align:start position:0% +epsilon delta to the minus epsilon set + + + align:start position:0% +epsilon delta to the minus epsilon set +and we don't know that a priori if we go + + align:start position:0% +and we don't know that a priori if we go + + + align:start position:0% +and we don't know that a priori if we go +over the proof the proof doesn't show + + align:start position:0% +over the proof the proof doesn't show + + + align:start position:0% +over the proof the proof doesn't show +that so when we okay so I haven't given + + align:start position:0% +that so when we okay so I haven't given + + + align:start position:0% +that so when we okay so I haven't given +the proof of the lema only gave a very + + align:start position:0% +the proof of the lema only gave a very + + + align:start position:0% +the proof of the lema only gave a very +rough sketch but you have to trust me + + align:start position:0% +rough sketch but you have to trust me + + + align:start position:0% +rough sketch but you have to trust me +that if you go through the proof we do + + align:start position:0% +that if you go through the proof we do + + + align:start position:0% +that if you go through the proof we do +not get any non concentration for Q of A + + align:start position:0% +not get any non concentration for Q of A + + + align:start position:0% +not get any non concentration for Q of A +we literally only get get growth at + + align:start position:0% +we literally only get get growth at + + + align:start position:0% +we literally only get get growth at +scale delta. + + align:start position:0% +scale delta. + + + align:start position:0% +scale delta. +Okay, so let me write this somewhere. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Big issue + + align:start position:0% + + + + align:start position:0% + +We know + + align:start position:0% +We know + + + align:start position:0% +We know +Q of A grows + + align:start position:0% + + + + align:start position:0% + +in delta covering number. + + align:start position:0% +in delta covering number. + + + align:start position:0% +in delta covering number. +But + + align:start position:0% + + + + align:start position:0% + +the proof + + align:start position:0% + + + + align:start position:0% + +does not show + + align:start position:0% + + + + align:start position:0% + +that Q of A + + align:start position:0% +that Q of A + + + align:start position:0% +that Q of A +is a delta S plus epsilon could be a + + align:start position:0% +is a delta S plus epsilon could be a + + + align:start position:0% +is a delta S plus epsilon could be a +different epsilon that's we did the same + + align:start position:0% +different epsilon that's we did the same + + + align:start position:0% +different epsilon that's we did the same +epsilon but we need some epsilon if we + + align:start position:0% +epsilon but we need some epsilon if we + + + align:start position:0% +epsilon but we need some epsilon if we +want to iterate here + + align:start position:0% + + + + align:start position:0% + +Okay. So we are going to talk about some + + align:start position:0% +Okay. So we are going to talk about some + + + align:start position:0% +Okay. So we are going to talk about some +of the things we do to overcome this uh + + align:start position:0% +of the things we do to overcome this uh + + + align:start position:0% +of the things we do to overcome this uh +in the next lecture. But let me say that + + align:start position:0% +in the next lecture. But let me say that + + + align:start position:0% +in the next lecture. But let me say that +I think in fact it is not true that Q of + + align:start position:0% +I think in fact it is not true that Q of + + + align:start position:0% +I think in fact it is not true that Q of +A has to be a delta S plus epsilon delta + + align:start position:0% +A has to be a delta S plus epsilon delta + + + align:start position:0% +A has to be a delta S plus epsilon delta +2 minus epsilon set. + + align:start position:0% +2 minus epsilon set. + + + align:start position:0% +2 minus epsilon set. +It is not even true. But what is true is + + align:start position:0% +It is not even true. But what is true is + + + align:start position:0% +It is not even true. But what is true is +that Q of A contains a delta S plus + + align:start position:0% +that Q of A contains a delta S plus + + + align:start position:0% +that Q of A contains a delta S plus +epsilon delta to the minus epsilon set. + + align:start position:0% + + + + align:start position:0% + +Okay. And this is good enough because we + + align:start position:0% +Okay. And this is good enough because we + + + align:start position:0% +Okay. And this is good enough because we +just just take that subset and use that + + align:start position:0% +just just take that subset and use that + + + align:start position:0% +just just take that subset and use that +to iterate and then we then we can + + align:start position:0% +to iterate and then we then we can + + + align:start position:0% +to iterate and then we then we can +iterate and the second step will work in + + align:start position:0% +iterate and the second step will work in + + + align:start position:0% +iterate and the second step will work in +the same way. But this is a big issue + + align:start position:0% +the same way. But this is a big issue + + + align:start position:0% +the same way. But this is a big issue +and somehow we have to go through the + + align:start position:0% +and somehow we have to go through the + + + align:start position:0% +and somehow we have to go through the +whole steps of the proof in the finite + + align:start position:0% +whole steps of the proof in the finite + + + align:start position:0% +whole steps of the proof in the finite +field setting + + align:start position:0% +field setting + + + align:start position:0% +field setting +just to get this and then we have to + + align:start position:0% +just to get this and then we have to + + + align:start position:0% +just to get this and then we have to +sort of do the full so one has to sort + + align:start position:0% +sort of do the full so one has to sort + + + align:start position:0% +sort of do the full so one has to sort +of cycle through all the steps twice in + + align:start position:0% +of cycle through all the steps twice in + + + align:start position:0% +of cycle through all the steps twice in +this proof. The first cycle is to solve + + align:start position:0% +this proof. The first cycle is to solve + + + align:start position:0% +this proof. The first cycle is to solve +this issue. So we have to use valuedic + + align:start position:0% +this issue. So we have to use valuedic + + + align:start position:0% +this issue. So we have to use valuedic +hours for example to solve this issue + + align:start position:0% +hours for example to solve this issue + + + align:start position:0% +hours for example to solve this issue +that comes much later in the proof in + + align:start position:0% +that comes much later in the proof in + + + align:start position:0% +that comes much later in the proof in +the finite field setting and then we + + align:start position:0% +the finite field setting and then we + + + align:start position:0% +the finite field setting and then we +have to use it again once we have + + align:start position:0% +have to use it again once we have + + + align:start position:0% +have to use it again once we have +expanded + + align:start position:0% +expanded + + + align:start position:0% +expanded +a lot uh by iterating okay so I'll + + align:start position:0% +a lot uh by iterating okay so I'll + + + align:start position:0% +a lot uh by iterating okay so I'll +explain uh the ideas behind this on + + align:start position:0% +explain uh the ideas behind this on + + + align:start position:0% +explain uh the ideas behind this on +Thursday yes for showing that QA + + align:start position:0% +Thursday yes for showing that QA + + + align:start position:0% +Thursday yes for showing that QA +contains the delta s plus epus epsilon + + align:start position:0% +contains the delta s plus epus epsilon + + + align:start position:0% +contains the delta s plus epus epsilon +set does that set have to be kind of + + align:start position:0% +set does that set have to be kind of + + + align:start position:0% +set does that set have to be kind of +very close to the size of a and like an + + align:start position:0% +very close to the size of a and like an + + + align:start position:0% +very close to the size of a and like an +s plus epsilon or delta spacing level. + + align:start position:0% + + + + align:start position:0% + +>> Well, it needs to be much okay. Uh + + align:start position:0% +>> Well, it needs to be much okay. Uh + + + align:start position:0% +>> Well, it needs to be much okay. Uh +something maybe I should have say but I + + align:start position:0% +something maybe I should have say but I + + + align:start position:0% +something maybe I should have say but I +didn't say is that a delta t c ignore + + align:start position:0% +didn't say is that a delta t c ignore + + + align:start position:0% +didn't say is that a delta t c ignore +this for a moment. So a delta t cz set + + align:start position:0% +this for a moment. So a delta t cz set + + + align:start position:0% +this for a moment. So a delta t cz set +has size at least delta to the minus t + + align:start position:0% +has size at least delta to the minus t + + + align:start position:0% +has size at least delta to the minus t +because you apply the definition of + + align:start position:0% +because you apply the definition of + + + align:start position:0% +because you apply the definition of +delta t cz set at scale delta. This is + + align:start position:0% +delta t cz set at scale delta. This is + + + align:start position:0% +delta t cz set at scale delta. This is +something I should have mentioned. I + + align:start position:0% +something I should have mentioned. I + + + align:start position:0% +something I should have mentioned. I +will try to remember to mention it next + + align:start position:0% +will try to remember to mention it next + + + align:start position:0% +will try to remember to mention it next +time. So this set that is contained + + align:start position:0% +time. So this set that is contained + + + align:start position:0% +time. So this set that is contained +actually has already size bigger than + + align:start position:0% +actually has already size bigger than + + + align:start position:0% +actually has already size bigger than +the size of a but in addition to having + + align:start position:0% +the size of a but in addition to having + + + align:start position:0% +the size of a but in addition to having +larger size it has good spacing. + + align:start position:0% +larger size it has good spacing. + + + align:start position:0% +larger size it has good spacing. +But yeah one question is that I'm going + + align:start position:0% +But yeah one question is that I'm going + + + align:start position:0% +But yeah one question is that I'm going +to answer next time is how how come that + + align:start position:0% +to answer next time is how how come that + + + align:start position:0% +to answer next time is how how come that +something contains so this notion of + + align:start position:0% +something contains so this notion of + + + align:start position:0% +something contains so this notion of +delta s set is bad in the sense that it + + align:start position:0% +delta s set is bad in the sense that it + + + align:start position:0% +delta s set is bad in the sense that it +is not monotone. So you can so if you + + align:start position:0% +is not monotone. So you can so if you + + + align:start position:0% +is not monotone. So you can so if you +take a set which has this non spacing + + align:start position:0% +take a set which has this non spacing + + + align:start position:0% +take a set which has this non spacing +condition or non concentration condition + + align:start position:0% +condition or non concentration condition + + + align:start position:0% +condition or non concentration condition +and make it larger you may lose + + align:start position:0% +and make it larger you may lose + + + align:start position:0% +and make it larger you may lose +the non concentration condition and + + align:start position:0% +the non concentration condition and + + + align:start position:0% +the non concentration condition and +that's kind of bad. So we'll see how to + + align:start position:0% +that's kind of bad. So we'll see how to + + + align:start position:0% +that's kind of bad. So we'll see how to +get around this next time. + + align:start position:0% + + + + align:start position:0% + +Any other questions? + + align:start position:0% +Any other questions? + + + align:start position:0% +Any other questions? +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +>> I wonder like in the two cases you wrote + + align:start position:0% +>> I wonder like in the two cases you wrote + + + align:start position:0% +>> I wonder like in the two cases you wrote +so in the first case you said the set is + + align:start position:0% +so in the first case you said the set is + + + align:start position:0% +so in the first case you said the set is +dense. So somehow it is large but in the + + align:start position:0% +dense. So somehow it is large but in the + + + align:start position:0% +dense. So somehow it is large but in the +second case what's the intuition behind + + align:start position:0% +second case what's the intuition behind + + + align:start position:0% +second case what's the intuition behind +okay I have one element that is far away + + align:start position:0% +okay I have one element that is far away + + + align:start position:0% +okay I have one element that is far away +from the set and then we can get the + + align:start position:0% +from the set and then we can get the + + + align:start position:0% +from the set and then we can get the +set. is really very similar to what you + + align:start position:0% +set. is really very similar to what you + + + align:start position:0% +set. is really very similar to what you +did in the final field setting. In the + + align:start position:0% +did in the final field setting. In the + + + align:start position:0% +did in the final field setting. In the +case when x is in a minus a over a minus + + align:start position:0% +case when x is in a minus a over a minus + + + align:start position:0% +case when x is in a minus a over a minus +a and x plus one is not. You use that to + + align:start position:0% +a and x plus one is not. You use that to + + + align:start position:0% +a and x plus one is not. You use that to +show that some projection of the + + align:start position:0% +show that some projection of the + + + align:start position:0% +show that some projection of the +original set is large. + + align:start position:0% +original set is large. + + + align:start position:0% +original set is large. +>> Okay? + + align:start position:0% +>> Okay? + + + align:start position:0% +>> Okay? +>> It's it's a very similar idea except + + align:start position:0% +>> It's it's a very similar idea except + + + align:start position:0% +>> It's it's a very similar idea except +that you have to fight with small + + align:start position:0% +that you have to fight with small + + + align:start position:0% +that you have to fight with small +denominators and but but morally it's a + + align:start position:0% +denominators and but but morally it's a + + + align:start position:0% +denominators and but but morally it's a +very similar idea. Okay. \ No newline at end of file diff --git a/1Ed3U4rmyXU.txt b/1Ed3U4rmyXU.txt new file mode 100644 index 0000000000000000000000000000000000000000..0739b67482263118683cd2ff1eb752c70d152e9f --- /dev/null +++ b/1Ed3U4rmyXU.txt @@ -0,0 +1,1851 @@ +align:start position:0% + +hi everyone my name is Morgan Bingley + + align:start position:0% +hi everyone my name is Morgan Bingley + + + align:start position:0% +hi everyone my name is Morgan Bingley +I'm a first year masters student at EPFL + + align:start position:0% +I'm a first year masters student at EPFL + + + align:start position:0% +I'm a first year masters student at EPFL +in + + align:start position:0% +in + + + align:start position:0% +in +science in engineering and I'm gonna + + align:start position:0% +science in engineering and I'm gonna + + + align:start position:0% +science in engineering and I'm gonna +present you this video about it transfer + + align:start position:0% +present you this video about it transfer + + + align:start position:0% +present you this video about it transfer +in a materiality this video will start + + align:start position:0% +in a materiality this video will start + + + align:start position:0% +in a materiality this video will start +with a little introduction where I will + + align:start position:0% +with a little introduction where I will + + + align:start position:0% +with a little introduction where I will +give you some definitions which will be + + align:start position:0% +give you some definitions which will be + + + align:start position:0% +give you some definitions which will be +useful for it transfer and where I will + + align:start position:0% +useful for it transfer and where I will + + + align:start position:0% +useful for it transfer and where I will +talk a bit about int equations then I'm + + align:start position:0% +talk a bit about int equations then I'm + + + align:start position:0% +talk a bit about int equations then I'm +gonna present you some concrete example + + align:start position:0% +gonna present you some concrete example + + + align:start position:0% +gonna present you some concrete example +that you can meet in your everyday life + + align:start position:0% +that you can meet in your everyday life + + + align:start position:0% +that you can meet in your everyday life +in order to be able to see the next + + align:start position:0% +in order to be able to see the next + + + align:start position:0% +in order to be able to see the next +example in a proper way we need to give + + align:start position:0% +example in a proper way we need to give + + + align:start position:0% +example in a proper way we need to give +some definitions in this video we do not + + align:start position:0% +some definitions in this video we do not + + + align:start position:0% +some definitions in this video we do not +say that it is a form of energy the + + align:start position:0% +say that it is a form of energy the + + + align:start position:0% +say that it is a form of energy the +temperature is a measurable + + align:start position:0% +temperature is a measurable + + + align:start position:0% +temperature is a measurable +manifestation of the stored heat if two + + align:start position:0% +manifestation of the stored heat if two + + + align:start position:0% +manifestation of the stored heat if two +values which have different temperatures + + align:start position:0% +values which have different temperatures + + + align:start position:0% +values which have different temperatures +are in contact late transfer occurs + + align:start position:0% +are in contact late transfer occurs + + + align:start position:0% +are in contact late transfer occurs +transferring the ridge from the warmer + + align:start position:0% +transferring the ridge from the warmer + + + align:start position:0% +transferring the ridge from the warmer +to the colder body several it transfer + + align:start position:0% +to the colder body several it transfer + + + align:start position:0% +to the colder body several it transfer +modes exists the Witkin diction which + + align:start position:0% +modes exists the Witkin diction which + + + align:start position:0% +modes exists the Witkin diction which +correspond to the heat exchange between + + align:start position:0% +correspond to the heat exchange between + + + align:start position:0% +correspond to the heat exchange between +two points of a motionless and a packed + + align:start position:0% +two points of a motionless and a packed + + + align:start position:0% +two points of a motionless and a packed +solid liquid or gas the convention which + + align:start position:0% +solid liquid or gas the convention which + + + align:start position:0% +solid liquid or gas the convention which +correspond to a heat exchange between a + + align:start position:0% +correspond to a heat exchange between a + + + align:start position:0% +correspond to a heat exchange between a +wall and a freed with a heat transfer + + align:start position:0% +wall and a freed with a heat transfer + + + align:start position:0% +wall and a freed with a heat transfer +done by the moving fluid finally the + + align:start position:0% +done by the moving fluid finally the + + + align:start position:0% +done by the moving fluid finally the +radiation corresponds to a heat exchange + + align:start position:0% +radiation corresponds to a heat exchange + + + align:start position:0% +radiation corresponds to a heat exchange +between two walls separated by a + + align:start position:0% +between two walls separated by a + + + align:start position:0% +between two walls separated by a +transparent environment as we gonna talk + + align:start position:0% +transparent environment as we gonna talk + + + align:start position:0% +transparent environment as we gonna talk +about speed transfer in this video it's + + align:start position:0% +about speed transfer in this video it's + + + align:start position:0% +about speed transfer in this video it's +important to understand hours into + + align:start position:0% +important to understand hours into + + + align:start position:0% +important to understand hours into +equations in this kind of phenomena + + align:start position:0% +equations in this kind of phenomena + + + align:start position:0% +equations in this kind of phenomena +first the in condition law which defines + + align:start position:0% +first the in condition law which defines + + + align:start position:0% +first the in condition law which defines +the diffusive thermal flux in function + + align:start position:0% +the diffusive thermal flux in function + + + align:start position:0% +the diffusive thermal flux in function +of the temperature gradient and this + + align:start position:0% +of the temperature gradient and this + + + align:start position:0% +of the temperature gradient and this +relation alline is linearly governed by + + align:start position:0% +relation alline is linearly governed by + + + align:start position:0% +relation alline is linearly governed by +the terminal connection coefficient k + + align:start position:0% +the terminal connection coefficient k + + + align:start position:0% +the terminal connection coefficient k +here then the heat equation which has a + + align:start position:0% +here then the heat equation which has a + + + align:start position:0% +here then the heat equation which has a +time dependent term a speed dependent + + align:start position:0% +time dependent term a speed dependent + + + align:start position:0% +time dependent term a speed dependent +channel which correspond to the + + align:start position:0% +channel which correspond to the + + + align:start position:0% +channel which correspond to the +advection phenomena a divergence term + + align:start position:0% +advection phenomena a divergence term + + + align:start position:0% +advection phenomena a divergence term +here of the diffusive thermal flex and + + align:start position:0% +here of the diffusive thermal flex and + + + align:start position:0% +here of the diffusive thermal flex and +finally a heat source term which + + align:start position:0% +finally a heat source term which + + + align:start position:0% +finally a heat source term which +corrects from often to chemical reaction + + align:start position:0% +corrects from often to chemical reaction + + + align:start position:0% +corrects from often to chemical reaction +which are either exothermic or + + align:start position:0% +which are either exothermic or + + + align:start position:0% +which are either exothermic or +endothermic + + align:start position:0% +endothermic + + + align:start position:0% +endothermic +combining both equations we get this + + align:start position:0% +combining both equations we get this + + + align:start position:0% +combining both equations we get this +final relation which + + align:start position:0% +final relation which + + + align:start position:0% +final relation which +fans heat transfer and heat phenomena we + + align:start position:0% +fans heat transfer and heat phenomena we + + + align:start position:0% +fans heat transfer and heat phenomena we +now gonna apply it to see relations to + + align:start position:0% +now gonna apply it to see relations to + + + align:start position:0% +now gonna apply it to see relations to +some concrete's example as first example + + align:start position:0% +some concrete's example as first example + + + align:start position:0% +some concrete's example as first example +a simple wall of a house with thickness + + align:start position:0% +a simple wall of a house with thickness + + + align:start position:0% +a simple wall of a house with thickness +e is chosen it's thermal state is stable + + align:start position:0% +e is chosen it's thermal state is stable + + + align:start position:0% +e is chosen it's thermal state is stable +and there is no coyote power a thin wall + + align:start position:0% +and there is no coyote power a thin wall + + + align:start position:0% +and there is no coyote power a thin wall +is considered with an M directional heat + + align:start position:0% +is considered with an M directional heat + + + align:start position:0% +is considered with an M directional heat +flux along x axis the temperatures on + + align:start position:0% +flux along x axis the temperatures on + + + align:start position:0% +flux along x axis the temperatures on +both side of the wall are different t1 + + align:start position:0% +both side of the wall are different t1 + + + align:start position:0% +both side of the wall are different t1 +here is lower than t2 here the + + align:start position:0% +here is lower than t2 here the + + + align:start position:0% +here is lower than t2 here the +temperature profile in the wall is + + align:start position:0% +temperature profile in the wall is + + + align:start position:0% +temperature profile in the wall is +research softest problem it is adapt to + + align:start position:0% +research softest problem it is adapt to + + + align:start position:0% +research softest problem it is adapt to +use Cartesian system the temperature + + align:start position:0% +use Cartesian system the temperature + + + align:start position:0% +use Cartesian system the temperature +only change along x axis and an am a + + align:start position:0% +only change along x axis and an am a + + + align:start position:0% +only change along x axis and an am a +genius distribution of the temperature + + align:start position:0% +genius distribution of the temperature + + + align:start position:0% +genius distribution of the temperature +is weighted in the other directions the + + align:start position:0% +is weighted in the other directions the + + + align:start position:0% +is weighted in the other directions the +conditions of this problem allowed to + + align:start position:0% +conditions of this problem allowed to + + + align:start position:0% +conditions of this problem allowed to +simplify the heat equations present and + + align:start position:0% +simplify the heat equations present and + + + align:start position:0% +simplify the heat equations present and +before which becomes such an equation as + + align:start position:0% +before which becomes such an equation as + + + align:start position:0% +before which becomes such an equation as +pandering conditions we define the + + align:start position:0% +pandering conditions we define the + + + align:start position:0% +pandering conditions we define the +temperature in x equals 0 to t1 here and + + align:start position:0% +temperature in x equals 0 to t1 here and + + + align:start position:0% +temperature in x equals 0 to t1 here and +in X again e32 here we then define the + + align:start position:0% +in X again e32 here we then define the + + + align:start position:0% +in X again e32 here we then define the +system and try to solve it you can see + + align:start position:0% +system and try to solve it you can see + + + align:start position:0% +system and try to solve it you can see +here that this solution is dependent of + + align:start position:0% +here that this solution is dependent of + + + align:start position:0% +here that this solution is dependent of +a the thickness to be able to have a + + align:start position:0% +a the thickness to be able to have a + + + align:start position:0% +a the thickness to be able to have a +general solution non-dependent of this + + align:start position:0% +general solution non-dependent of this + + + align:start position:0% +general solution non-dependent of this +thickness a violent change down the + + align:start position:0% +thickness a violent change down the + + + align:start position:0% +thickness a violent change down the +temperatures is not in function of x + + align:start position:0% +temperatures is not in function of x + + + align:start position:0% +temperatures is not in function of x +anymore as it is here but in function of + + align:start position:0% +anymore as it is here but in function of + + + align:start position:0% +anymore as it is here but in function of +the ratio x over e which vary between 0 + + align:start position:0% +the ratio x over e which vary between 0 + + + align:start position:0% +the ratio x over e which vary between 0 +and 1 the differential system of + + align:start position:0% +and 1 the differential system of + + + align:start position:0% +and 1 the differential system of +equation and the solution are as + + align:start position:0% +equation and the solution are as + + + align:start position:0% +equation and the solution are as +following here we define the system and + + align:start position:0% +following here we define the system and + + + align:start position:0% +following here we define the system and +here we try to solve it the solutions + + align:start position:0% +here we try to solve it the solutions + + + align:start position:0% +here we try to solve it the solutions +look like this changing the disposition + + align:start position:0% +look like this changing the disposition + + + align:start position:0% +look like this changing the disposition +of the of the equation it's possible to + + align:start position:0% +of the of the equation it's possible to + + + align:start position:0% +of the of the equation it's possible to +get t scan of solution + + align:start position:0% +get t scan of solution + + + align:start position:0% +get t scan of solution +it's then possible to generalize this + + align:start position:0% +it's then possible to generalize this + + + align:start position:0% +it's then possible to generalize this +equation to every k is doing the + + align:start position:0% +equation to every k is doing the + + + align:start position:0% +equation to every k is doing the +following transformation here + + align:start position:0% +following transformation here + + + align:start position:0% +following transformation here +so we can now say that our solution only + + align:start position:0% +so we can now say that our solution only + + + align:start position:0% +so we can now say that our solution only +depend of X Y Z value thus it's possible + + align:start position:0% +depend of X Y Z value thus it's possible + + + align:start position:0% +depend of X Y Z value thus it's possible +to plot the temperature profile for this + + align:start position:0% +to plot the temperature profile for this + + + align:start position:0% +to plot the temperature profile for this +case it's look like this so we have a + + align:start position:0% +case it's look like this so we have a + + + align:start position:0% +case it's look like this so we have a +linearly behavior between day 1 hit T 1 + + align:start position:0% +linearly behavior between day 1 hit T 1 + + + align:start position:0% +linearly behavior between day 1 hit T 1 +here and T 2 here over the x-axis it + + align:start position:0% +here and T 2 here over the x-axis it + + + align:start position:0% +here and T 2 here over the x-axis it +will maybe be easier to see the + + align:start position:0% +will maybe be easier to see the + + + align:start position:0% +will maybe be easier to see the +temperature distribution in the world + + align:start position:0% +temperature distribution in the world + + + align:start position:0% +temperature distribution in the world +here we can clearly see that if it's our + + align:start position:0% +here we can clearly see that if it's our + + + align:start position:0% +here we can clearly see that if it's our +world we have a linear gradient of the + + align:start position:0% +world we have a linear gradient of the + + + align:start position:0% +world we have a linear gradient of the +temperature we with here our minimum at + + align:start position:0% +temperature we with here our minimum at + + + align:start position:0% +temperature we with here our minimum at +T 1 and here our maximum at T 2 that's + + align:start position:0% +T 1 and here our maximum at T 2 that's + + + align:start position:0% +T 1 and here our maximum at T 2 that's +all for this first example as a second + + align:start position:0% +all for this first example as a second + + + align:start position:0% +all for this first example as a second +example a concrete wall with a thickness + + align:start position:0% +example a concrete wall with a thickness + + + align:start position:0% +example a concrete wall with a thickness +e is chosen this concrete wall is + + align:start position:0% +e is chosen this concrete wall is + + + align:start position:0% +e is chosen this concrete wall is +hardening due to an exothermic chemical + + align:start position:0% +hardening due to an exothermic chemical + + + align:start position:0% +hardening due to an exothermic chemical +reaction like iteration for the concrete + + align:start position:0% +reaction like iteration for the concrete + + + align:start position:0% +reaction like iteration for the concrete +the temperature is the same at both side + + align:start position:0% +the temperature is the same at both side + + + align:start position:0% +the temperature is the same at both side +of the wall and is equal to TW this case + + align:start position:0% +of the wall and is equal to TW this case + + + align:start position:0% +of the wall and is equal to TW this case +is assumed as a stable and muncha less + + align:start position:0% +is assumed as a stable and muncha less + + + align:start position:0% +is assumed as a stable and muncha less +case to solve this problem + + align:start position:0% +case to solve this problem + + + align:start position:0% +case to solve this problem +it is adapt to use Cartesian system the + + align:start position:0% +it is adapt to use Cartesian system the + + + align:start position:0% +it is adapt to use Cartesian system the +temperature Allen change along x axis + + align:start position:0% +temperature Allen change along x axis + + + align:start position:0% +temperature Allen change along x axis +and an imagined us distribution of the + + align:start position:0% +and an imagined us distribution of the + + + align:start position:0% +and an imagined us distribution of the +temperature is weighted in the other + + align:start position:0% +temperature is weighted in the other + + + align:start position:0% +temperature is weighted in the other +directions the condition of this problem + + align:start position:0% +directions the condition of this problem + + + align:start position:0% +directions the condition of this problem +a let's simplify the heat equation + + align:start position:0% +a let's simplify the heat equation + + + align:start position:0% +a let's simplify the heat equation +presented before which becomes this kind + + align:start position:0% +presented before which becomes this kind + + + align:start position:0% +presented before which becomes this kind +of equation ad boundary conditions we + + align:start position:0% +of equation ad boundary conditions we + + + align:start position:0% +of equation ad boundary conditions we +have the temperature defined in x equals + + align:start position:0% +have the temperature defined in x equals + + + align:start position:0% +have the temperature defined in x equals +0 and x equal to e as TW again we define + + align:start position:0% +0 and x equal to e as TW again we define + + + align:start position:0% +0 and x equal to e as TW again we define +the differential equation system and its + + align:start position:0% +the differential equation system and its + + + align:start position:0% +the differential equation system and its +boundary conditions and try to solve it + + align:start position:0% +boundary conditions and try to solve it + + + align:start position:0% +boundary conditions and try to solve it +to get a general solution usable for + + align:start position:0% +to get a general solution usable for + + + align:start position:0% +to get a general solution usable for +ledge amount of cases it look like to be + + align:start position:0% +ledge amount of cases it look like to be + + + align:start position:0% +ledge amount of cases it look like to be +easier to a dimensionalities result just + + align:start position:0% +easier to a dimensionalities result just + + + align:start position:0% +easier to a dimensionalities result just +a very odd Oh change is done the + + align:start position:0% +a very odd Oh change is done the + + + align:start position:0% +a very odd Oh change is done the +temperature is not in function of X + + align:start position:0% +temperature is not in function of X + + + align:start position:0% +temperature is not in function of X +anymore as before but in function of the + + align:start position:0% +anymore as before but in function of the + + + align:start position:0% +anymore as before but in function of the +ratio is over e which vary between 0 and + + align:start position:0% +ratio is over e which vary between 0 and + + + align:start position:0% +ratio is over e which vary between 0 and +1 what as it was explained before the + + align:start position:0% +1 what as it was explained before the + + + align:start position:0% +1 what as it was explained before the +differential system of equation and the + + align:start position:0% +differential system of equation and the + + + align:start position:0% +differential system of equation and the +solution are as following + + align:start position:0% +solution are as following + + + align:start position:0% +solution are as following +so the different shout system of + + align:start position:0% +so the different shout system of + + + align:start position:0% +so the different shout system of +equations is this one and it's solution + + align:start position:0% +equations is this one and it's solution + + + align:start position:0% +equations is this one and it's solution +looks like this furthermore all terms + + align:start position:0% +looks like this furthermore all terms + + + align:start position:0% +looks like this furthermore all terms +that are independent of x / ue are + + align:start position:0% +that are independent of x / ue are + + + align:start position:0% +that are independent of x / ue are +placed to the left side of the equal + + align:start position:0% +placed to the left side of the equal + + + align:start position:0% +placed to the left side of the equal +sign + + align:start position:0% +sign + + + align:start position:0% +sign +thus the temperature profile looks like + + align:start position:0% +thus the temperature profile looks like + + + align:start position:0% +thus the temperature profile looks like +this we can clearly see our symmetrical + + align:start position:0% +this we can clearly see our symmetrical + + + align:start position:0% +this we can clearly see our symmetrical +behavior in distillation with a maximum + + align:start position:0% +behavior in distillation with a maximum + + + align:start position:0% +behavior in distillation with a maximum +in the center of the piece where the + + align:start position:0% +in the center of the piece where the + + + align:start position:0% +in the center of the piece where the +temperature is the higher due to the + + align:start position:0% +temperature is the higher due to the + + + align:start position:0% +temperature is the higher due to the +exothermic phenomena the minimum are at + + align:start position:0% +exothermic phenomena the minimum are at + + + align:start position:0% +exothermic phenomena the minimum are at +the phases where the temperature is + + align:start position:0% +the phases where the temperature is + + + align:start position:0% +the phases where the temperature is +equal to TW we can also see the + + align:start position:0% +equal to TW we can also see the + + + align:start position:0% +equal to TW we can also see the +temperature distribution in the world as + + align:start position:0% +temperature distribution in the world as + + + align:start position:0% +temperature distribution in the world as +following we can clearly see this + + align:start position:0% +following we can clearly see this + + + align:start position:0% +following we can clearly see this +maximum in the center of the piece and + + align:start position:0% +maximum in the center of the piece and + + + align:start position:0% +maximum in the center of the piece and +the minima at the side of the world as + + align:start position:0% +the minima at the side of the world as + + + align:start position:0% +the minima at the side of the world as +the last example a thin steel bar is + + align:start position:0% +the last example a thin steel bar is + + + align:start position:0% +the last example a thin steel bar is +considered during a continuous still not + + align:start position:0% +considered during a continuous still not + + + align:start position:0% +considered during a continuous still not +treatment process the bar is extracted + + align:start position:0% +treatment process the bar is extracted + + + align:start position:0% +treatment process the bar is extracted +from an oven heated at temperature of T + + align:start position:0% +from an oven heated at temperature of T + + + align:start position:0% +from an oven heated at temperature of T +0 and then quenched after a distance in + + align:start position:0% +0 and then quenched after a distance in + + + align:start position:0% +0 and then quenched after a distance in +a water bath which at which he is at a + + align:start position:0% +a water bath which at which he is at a + + + align:start position:0% +a water bath which at which he is at a +TL temperature the temperature profile + + align:start position:0% +TL temperature the temperature profile + + + align:start position:0% +TL temperature the temperature profile +of the bar between the exit of the oven + + align:start position:0% +of the bar between the exit of the oven + + + align:start position:0% +of the bar between the exit of the oven +and the entrance of the water brass is + + align:start position:0% +and the entrance of the water brass is + + + align:start position:0% +and the entrance of the water brass is +researched when the steady state is + + align:start position:0% +researched when the steady state is + + + align:start position:0% +researched when the steady state is +established to solve this problem it is + + align:start position:0% +established to solve this problem it is + + + align:start position:0% +established to solve this problem it is +adapt to use Cartesian system as the bar + + align:start position:0% +adapt to use Cartesian system as the bar + + + align:start position:0% +adapt to use Cartesian system as the bar +is still a uniform temperature is + + align:start position:0% +is still a uniform temperature is + + + align:start position:0% +is still a uniform temperature is +assumed in its transversal section which + + align:start position:0% +assumed in its transversal section which + + + align:start position:0% +assumed in its transversal section which +means the temperature field only depend + + align:start position:0% +means the temperature field only depend + + + align:start position:0% +means the temperature field only depend +on the x position the conditions of this + + align:start position:0% +on the x position the conditions of this + + + align:start position:0% +on the x position the conditions of this +problem allowed to simplify the heat + + align:start position:0% +problem allowed to simplify the heat + + + align:start position:0% +problem allowed to simplify the heat +equation presented before which becomes + + align:start position:0% +equation presented before which becomes + + + align:start position:0% +equation presented before which becomes +this equation as boundary conditions we + + align:start position:0% +this equation as boundary conditions we + + + align:start position:0% +this equation as boundary conditions we +have that the temperature in x equals 0 + + align:start position:0% +have that the temperature in x equals 0 + + + align:start position:0% +have that the temperature in x equals 0 +here is equal to t0 and the temperature + + align:start position:0% +here is equal to t0 and the temperature + + + align:start position:0% +here is equal to t0 and the temperature +in X ax kal-el it is equal to TL the + + align:start position:0% +in X ax kal-el it is equal to TL the + + + align:start position:0% +in X ax kal-el it is equal to TL the +differential equation system is the + + align:start position:0% +differential equation system is the + + + align:start position:0% +differential equation system is the +following and its solution is as follows + + align:start position:0% +following and its solution is as follows + + + align:start position:0% +following and its solution is as follows +this looks like quite complicated but we + + align:start position:0% +this looks like quite complicated but we + + + align:start position:0% +this looks like quite complicated but we +can simplify a bit knowing the factor + + align:start position:0% +can simplify a bit knowing the factor + + + align:start position:0% +can simplify a bit knowing the factor +Rho times CP / K + + align:start position:0% +Rho times CP / K + + + align:start position:0% +Rho times CP / K +it's one over alpha where alpha is the + + align:start position:0% +it's one over alpha where alpha is the + + + align:start position:0% +it's one over alpha where alpha is the +thermal diffusivity coefficient of the + + align:start position:0% +thermal diffusivity coefficient of the + + + align:start position:0% +thermal diffusivity coefficient of the +material we still have this solution + + align:start position:0% +material we still have this solution + + + align:start position:0% +material we still have this solution +this solution also looks like + + align:start position:0% +this solution also looks like + + + align:start position:0% +this solution also looks like +complicated however it's appear simply + + align:start position:0% +complicated however it's appear simply + + + align:start position:0% +complicated however it's appear simply +our rewriting in the following way as + + align:start position:0% +our rewriting in the following way as + + + align:start position:0% +our rewriting in the following way as +for the previous example a general + + align:start position:0% +for the previous example a general + + + align:start position:0% +for the previous example a general +solution is researched in this case this + + align:start position:0% +solution is researched in this case this + + + align:start position:0% +solution is researched in this case this +solution looks like this you can only + + align:start position:0% +solution looks like this you can only + + + align:start position:0% +solution looks like this you can only +add that we still have this solution + + align:start position:0% +add that we still have this solution + + + align:start position:0% +add that we still have this solution +here and knowing the ratio VL our alpha + + align:start position:0% +here and knowing the ratio VL our alpha + + + align:start position:0% +here and knowing the ratio VL our alpha +response to the a dimensional page + + align:start position:0% +response to the a dimensional page + + + align:start position:0% +response to the a dimensional page +remember which defends the ratio between + + align:start position:0% +remember which defends the ratio between + + + align:start position:0% +remember which defends the ratio between +advection and diffusion phenomena of + + align:start position:0% +advection and diffusion phenomena of + + + align:start position:0% +advection and diffusion phenomena of +process it's possible to simplify a bit + + align:start position:0% +process it's possible to simplify a bit + + + align:start position:0% +process it's possible to simplify a bit +here the peclet number is put at the + + align:start position:0% +here the peclet number is put at the + + + align:start position:0% +here the peclet number is put at the +denominator and here at the numerator + + align:start position:0% + + + + align:start position:0% + +finally in the same way as the previous + + align:start position:0% +finally in the same way as the previous + + + align:start position:0% +finally in the same way as the previous +cases a viable chain is done when + + align:start position:0% +cases a viable chain is done when + + + align:start position:0% +cases a viable chain is done when +placing x over l by the viable excel + + align:start position:0% + + + + align:start position:0% + +it's possible to try to understand how + + align:start position:0% +it's possible to try to understand how + + + align:start position:0% +it's possible to try to understand how +the peclet number works bearing the + + align:start position:0% +the peclet number works bearing the + + + align:start position:0% +the peclet number works bearing the +temperature profile in function of it + + align:start position:0% +temperature profile in function of it + + + align:start position:0% +temperature profile in function of it +here we have the temperature profile + + align:start position:0% +here we have the temperature profile + + + align:start position:0% +here we have the temperature profile +with a low back a number we see that + + align:start position:0% +with a low back a number we see that + + + align:start position:0% +with a low back a number we see that +it's almost a linear behavior as we add + + align:start position:0% +it's almost a linear behavior as we add + + + align:start position:0% +it's almost a linear behavior as we add +for the first example however when we + + align:start position:0% +for the first example however when we + + + align:start position:0% +for the first example however when we +increase the peclet number we see that + + align:start position:0% +increase the peclet number we see that + + + align:start position:0% +increase the peclet number we see that +it's increased the curvature of a curve + + align:start position:0% +it's increased the curvature of a curve + + + align:start position:0% +it's increased the curvature of a curve +and when we are ever at big picture + + align:start position:0% +and when we are ever at big picture + + + align:start position:0% +and when we are ever at big picture +number we we almost have a vertical line + + align:start position:0% +number we we almost have a vertical line + + + align:start position:0% +number we we almost have a vertical line +here that's due to the speed of the bar + + align:start position:0% +here that's due to the speed of the bar + + + align:start position:0% +here that's due to the speed of the bar +it's possible to show this result on the + + align:start position:0% +it's possible to show this result on the + + + align:start position:0% +it's possible to show this result on the +graph with the graphical solution of the + + align:start position:0% +graph with the graphical solution of the + + + align:start position:0% +graph with the graphical solution of the +true temperature profile for different + + align:start position:0% +true temperature profile for different + + + align:start position:0% +true temperature profile for different +pixel number we define your a list of + + align:start position:0% +pixel number we define your a list of + + + align:start position:0% +pixel number we define your a list of +spectral number applied to the solution + + align:start position:0% +spectral number applied to the solution + + + align:start position:0% +spectral number applied to the solution +on it the graphical solutions look like + + align:start position:0% +on it the graphical solutions look like + + + align:start position:0% +on it the graphical solutions look like +this we can see that + + align:start position:0% +this we can see that + + + align:start position:0% +this we can see that +solution for the low pixel number are + + align:start position:0% +solution for the low pixel number are + + + align:start position:0% +solution for the low pixel number are +quite linear and that's it's bigger more + + align:start position:0% +quite linear and that's it's bigger more + + + align:start position:0% +quite linear and that's it's bigger more +in mercury as the Beca number increase + + align:start position:0% +in mercury as the Beca number increase + + + align:start position:0% +in mercury as the Beca number increase +till the number of and well here finally + + align:start position:0% +till the number of and well here finally + + + align:start position:0% +till the number of and well here finally +it's also possible to present a solution + + align:start position:0% +it's also possible to present a solution + + + align:start position:0% +it's also possible to present a solution +in a wall allowing a viable peclet + + align:start position:0% +in a wall allowing a viable peclet + + + align:start position:0% +in a wall allowing a viable peclet +number here we can clearly see that the + + align:start position:0% +number here we can clearly see that the + + + align:start position:0% +number here we can clearly see that the +gradient is linear when the peclet + + align:start position:0% +gradient is linear when the peclet + + + align:start position:0% +gradient is linear when the peclet +number is low but if we increase it we + + align:start position:0% +number is low but if we increase it we + + + align:start position:0% +number is low but if we increase it we +saw that the differential of the + + align:start position:0% +saw that the differential of the + + + align:start position:0% +saw that the differential of the +temperature is almost on T style of the + + align:start position:0% +temperature is almost on T style of the + + + align:start position:0% +temperature is almost on T style of the +ball so that's all for this video about + + align:start position:0% +ball so that's all for this video about + + + align:start position:0% +ball so that's all for this video about +it transferring material here are my + + align:start position:0% +it transferring material here are my + + + align:start position:0% +it transferring material here are my +references thank you for watching \ No newline at end of file diff --git a/1cejTnuMo1Y.txt b/1cejTnuMo1Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..1f2f58f2b95bbcd3253091f2e8fe97387e380337 --- /dev/null +++ b/1cejTnuMo1Y.txt @@ -0,0 +1,2683 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I want us to practice uh doing + + align:start position:0% +I want us to practice uh doing + + + align:start position:0% +I want us to practice uh doing +integration again and so what we're + + align:start position:0% +integration again and so what we're + + + align:start position:0% +integration again and so what we're +going to do is two problems one is a + + align:start position:0% +going to do is two problems one is a + + + align:start position:0% +going to do is two problems one is a +definite integral one is indefinite so + + align:start position:0% +definite integral one is indefinite so + + + align:start position:0% +definite integral one is indefinite so +this this integral we're going to have + + align:start position:0% +this this integral we're going to have + + + align:start position:0% +this this integral we're going to have +uh find the value of the integral from + + align:start position:0% +uh find the value of the integral from + + + align:start position:0% +uh find the value of the integral from +minus pi over 4 to pi over 4 of secant + + align:start position:0% +minus pi over 4 to pi over 4 of secant + + + align:start position:0% +minus pi over 4 to pi over 4 of secant +cubed U du and then this one I just want + + align:start position:0% +cubed U du and then this one I just want + + + align:start position:0% +cubed U du and then this one I just want +you to actually just find an + + align:start position:0% +you to actually just find an + + + align:start position:0% +you to actually just find an +anti-derivative then for one over two + + align:start position:0% +anti-derivative then for one over two + + + align:start position:0% +anti-derivative then for one over two +sin U cosine U so why don't you take a + + align:start position:0% +sin U cosine U so why don't you take a + + + align:start position:0% +sin U cosine U so why don't you take a +while to work on this pause the video + + align:start position:0% +while to work on this pause the video + + + align:start position:0% +while to work on this pause the video +and then when you're ready uh restart + + align:start position:0% +and then when you're ready uh restart + + + align:start position:0% +and then when you're ready uh restart +the video and I will come back and show + + align:start position:0% +the video and I will come back and show + + + align:start position:0% +the video and I will come back and show +you how I did + + align:start position:0% + + + + align:start position:0% + +it okay welcome back so again we're + + align:start position:0% +it okay welcome back so again we're + + + align:start position:0% +it okay welcome back so again we're +going to work on on finding in this one + + align:start position:0% +going to work on on finding in this one + + + align:start position:0% +going to work on on finding in this one +a specific number and in this one an + + align:start position:0% +a specific number and in this one an + + + align:start position:0% +a specific number and in this one an +anti-derivative so we'll start off with + + align:start position:0% +anti-derivative so we'll start off with + + + align:start position:0% +anti-derivative so we'll start off with +the integral fromus piun 4 to piun 4 of + + align:start position:0% +the integral fromus piun 4 to piun 4 of + + + align:start position:0% +the integral fromus piun 4 to piun 4 of +secant cubed U and the first thing I'm + + align:start position:0% +secant cubed U and the first thing I'm + + + align:start position:0% +secant cubed U and the first thing I'm +going to do is I'm going to drop the + + align:start position:0% +going to do is I'm going to drop the + + + align:start position:0% +going to do is I'm going to drop the +bounds and just find find uh the + + align:start position:0% +bounds and just find find uh the + + + align:start position:0% +bounds and just find find uh the +function I need and then I'll bring the + + align:start position:0% +function I need and then I'll bring the + + + align:start position:0% +function I need and then I'll bring the +bounds back in I don't want to write the + + align:start position:0% +bounds back in I don't want to write the + + + align:start position:0% +bounds back in I don't want to write the +bounds down at every step um I'm not + + align:start position:0% +bounds down at every step um I'm not + + + align:start position:0% +bounds down at every step um I'm not +doing any any substitution I don't think + + align:start position:0% +doing any any substitution I don't think + + + align:start position:0% +doing any any substitution I don't think +so I don't need to worry about if I'm + + align:start position:0% +so I don't need to worry about if I'm + + + align:start position:0% +so I don't need to worry about if I'm +changing the bounds or not so I'll keep + + align:start position:0% +changing the bounds or not so I'll keep + + + align:start position:0% +changing the bounds or not so I'll keep +the bounds the same but I won't write + + align:start position:0% +the bounds the same but I won't write + + + align:start position:0% +the bounds the same but I won't write +them down again until near the end all + + align:start position:0% +them down again until near the end all + + + align:start position:0% +them down again until near the end all +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +let's look at this integral so the + + align:start position:0% +let's look at this integral so the + + + align:start position:0% +let's look at this integral so the +easiest way I think to start an integral + + align:start position:0% +easiest way I think to start an integral + + + align:start position:0% +easiest way I think to start an integral +like this is to split it up into secant + + align:start position:0% +like this is to split it up into secant + + + align:start position:0% +like this is to split it up into secant +U and then secant squar U maybe there + + align:start position:0% +U and then secant squar U maybe there + + + align:start position:0% +U and then secant squar U maybe there +are some other ways you did it but when + + align:start position:0% +are some other ways you did it but when + + + align:start position:0% +are some other ways you did it but when +I was looking at this problem the way I + + align:start position:0% +I was looking at this problem the way I + + + align:start position:0% +I was looking at this problem the way I +saw was to start off and write this as + + align:start position:0% +saw was to start off and write this as + + + align:start position:0% +saw was to start off and write this as +secant U Time 1 oops let me make sure + + align:start position:0% +secant U Time 1 oops let me make sure + + + align:start position:0% +secant U Time 1 oops let me make sure +yeah Time 1 + tan^ 2 + + align:start position:0% +yeah Time 1 + tan^ 2 + + + align:start position:0% +yeah Time 1 + tan^ 2 +U D + + align:start position:0% +U D + + + align:start position:0% +U D +U because secant s u is equal to 1 plus + + align:start position:0% +U because secant s u is equal to 1 plus + + + align:start position:0% +U because secant s u is equal to 1 plus +tangent s u and what does this do for us + + align:start position:0% +tangent s u and what does this do for us + + + align:start position:0% +tangent s u and what does this do for us +well it partially answers the question + + align:start position:0% +well it partially answers the question + + + align:start position:0% +well it partially answers the question +but not completely we'll see so what it + + align:start position:0% +but not completely we'll see so what it + + + align:start position:0% +but not completely we'll see so what it +does first is it gives us something we + + align:start position:0% +does first is it gives us something we + + + align:start position:0% +does first is it gives us something we +can + + align:start position:0% +can + + + align:start position:0% +can +find pretty easily the first one we just + + align:start position:0% +find pretty easily the first one we just + + + align:start position:0% +find pretty easily the first one we just +get the integral of secant U we know + + align:start position:0% +get the integral of secant U we know + + + align:start position:0% +get the integral of secant U we know +that one the second one is a little + + align:start position:0% +that one the second one is a little + + + align:start position:0% +that one the second one is a little +harder because we get the integral of + + align:start position:0% +harder because we get the integral of + + + align:start position:0% +harder because we get the integral of +secant U tangent s u + + align:start position:0% +secant U tangent s u + + + align:start position:0% +secant U tangent s u +du and this has promise but it's not not + + align:start position:0% +du and this has promise but it's not not + + + align:start position:0% +du and this has promise but it's not not +uh going to work for us right away + + align:start position:0% +uh going to work for us right away + + + align:start position:0% +uh going to work for us right away +because you know the derivative of + + align:start position:0% +because you know the derivative of + + + align:start position:0% +because you know the derivative of +tangent is secant squared and the + + align:start position:0% +tangent is secant squared and the + + + align:start position:0% +tangent is secant squared and the +derivative of secant is secant tangent + + align:start position:0% +derivative of secant is secant tangent + + + align:start position:0% +derivative of secant is secant tangent +so a a substitution won't work in this + + align:start position:0% +so a a substitution won't work in this + + + align:start position:0% +so a a substitution won't work in this +case because neither one of these + + align:start position:0% +case because neither one of these + + + align:start position:0% +case because neither one of these +functions is a derivative of the other + + align:start position:0% +functions is a derivative of the other + + + align:start position:0% +functions is a derivative of the other +one if I move even move off a tangent + + align:start position:0% +one if I move even move off a tangent + + + align:start position:0% +one if I move even move off a tangent +and I have I have secant tangent times + + align:start position:0% +and I have I have secant tangent times + + + align:start position:0% +and I have I have secant tangent times +another tangent it's not the right + + align:start position:0% +another tangent it's not the right + + + align:start position:0% +another tangent it's not the right +derivative of tangent derivative is + + align:start position:0% +derivative of tangent derivative is + + + align:start position:0% +derivative of tangent derivative is +secant squar so my main point here is + + align:start position:0% +secant squar so my main point here is + + + align:start position:0% +secant squar so my main point here is +that U substitution doesn't work or the + + align:start position:0% +that U substitution doesn't work or the + + + align:start position:0% +that U substitution doesn't work or the +substitution strategy doesn't work so + + align:start position:0% +substitution strategy doesn't work so + + + align:start position:0% +substitution strategy doesn't work so +what we're going to do is we're actually + + align:start position:0% +what we're going to do is we're actually + + + align:start position:0% +what we're going to do is we're actually +going to make take this part and make it + + align:start position:0% +going to make take this part and make it + + + align:start position:0% +going to make take this part and make it +into an integration by parts problem so + + align:start position:0% +into an integration by parts problem so + + + align:start position:0% +into an integration by parts problem so +this is going to be I'm going to not + + align:start position:0% +this is going to be I'm going to not + + + align:start position:0% +this is going to be I'm going to not +stop writing equal signs I'm going to + + align:start position:0% +stop writing equal signs I'm going to + + + align:start position:0% +stop writing equal signs I'm going to +figure out the integral of this one so + + align:start position:0% +figure out the integral of this one so + + + align:start position:0% +figure out the integral of this one so +this is a little + + align:start position:0% +this is a little + + + align:start position:0% +this is a little +sidebar and I'm going to look at the + + align:start position:0% +sidebar and I'm going to look at the + + + align:start position:0% +sidebar and I'm going to look at the +integral of secant U uh tangent squ + + align:start position:0% + + + + align:start position:0% + +U and the way I'm going to write that is + + align:start position:0% +U and the way I'm going to write that is + + + align:start position:0% +U and the way I'm going to write that is +I'm going to write that as secant U + + align:start position:0% +I'm going to write that as secant U + + + align:start position:0% +I'm going to write that as secant U +tangent U will be one function I + + align:start position:0% +tangent U will be one function I + + + align:start position:0% +tangent U will be one function I +want we'll call that um + + align:start position:0% +want we'll call that um + + + align:start position:0% +want we'll call that um +W I guess V Prime is we can use V + + align:start position:0% +W I guess V Prime is we can use V + + + align:start position:0% +W I guess V Prime is we can use V +Prime and then what the usual thing we + + align:start position:0% +Prime and then what the usual thing we + + + align:start position:0% +Prime and then what the usual thing we +call U we'll call W so tangent U we'll + + align:start position:0% +call U we'll call W so tangent U we'll + + + align:start position:0% +call U we'll call W so tangent U we'll +call + + align:start position:0% +call + + + align:start position:0% +call +W and I want to write down I want to + + align:start position:0% +W and I want to write down I want to + + + align:start position:0% +W and I want to write down I want to +explain to you why I'm picking these and + + align:start position:0% +explain to you why I'm picking these and + + + align:start position:0% +explain to you why I'm picking these and +sort of where this is going to get us so + + align:start position:0% +sort of where this is going to get us so + + + align:start position:0% +sort of where this is going to get us so +this is an easy thing to take an + + align:start position:0% +this is an easy thing to take an + + + align:start position:0% +this is an easy thing to take an +anti-derivative of right I can take this + + align:start position:0% +anti-derivative of right I can take this + + + align:start position:0% +anti-derivative of right I can take this +I know I know V is going to be secant U + + align:start position:0% +I know I know V is going to be secant U + + + align:start position:0% +I know I know V is going to be secant U +because the derivative of secant U is + + align:start position:0% +because the derivative of secant U is + + + align:start position:0% +because the derivative of secant U is +secant U tangent U and then W is tangent + + align:start position:0% +secant U tangent U and then W is tangent + + + align:start position:0% +secant U tangent U and then W is tangent +u w Prime is secant squ U so if you + + align:start position:0% +u w Prime is secant squ U so if you + + + align:start position:0% +u w Prime is secant squ U so if you +think about what does an integration by + + align:start position:0% +think about what does an integration by + + + align:start position:0% +think about what does an integration by +parts have it has it's going to have VW + + align:start position:0% +parts have it has it's going to have VW + + + align:start position:0% +parts have it has it's going to have VW +minus the integral of VW Prime that's a + + align:start position:0% +minus the integral of VW Prime that's a + + + align:start position:0% +minus the integral of VW Prime that's a +lot to take in but the point is that + + align:start position:0% +lot to take in but the point is that + + + align:start position:0% +lot to take in but the point is that +that integral is going to have the the + + align:start position:0% +that integral is going to have the the + + + align:start position:0% +that integral is going to have the the +anti-derivative of this which is secant + + align:start position:0% +anti-derivative of this which is secant + + + align:start position:0% +anti-derivative of this which is secant +and the derivative of this which is + + align:start position:0% +and the derivative of this which is + + + align:start position:0% +and the derivative of this which is +secant squ so it's going to have a + + align:start position:0% +secant squ so it's going to have a + + + align:start position:0% +secant squ so it's going to have a +secant cubed which might seem weird + + align:start position:0% +secant cubed which might seem weird + + + align:start position:0% +secant cubed which might seem weird +because now we're getting back to what + + align:start position:0% +because now we're getting back to what + + + align:start position:0% +because now we're getting back to what +we started with but the sign on the + + align:start position:0% +we started with but the sign on the + + + align:start position:0% +we started with but the sign on the +secant cubed is going to be opposite + + align:start position:0% +secant cubed is going to be opposite + + + align:start position:0% +secant cubed is going to be opposite +again this is a lot of talking but let's + + align:start position:0% +again this is a lot of talking but let's + + + align:start position:0% +again this is a lot of talking but let's +figure out now I just want to see show + + align:start position:0% +figure out now I just want to see show + + + align:start position:0% +figure out now I just want to see show +you where uh where we're headed with + + align:start position:0% +you where uh where we're headed with + + + align:start position:0% +you where uh where we're headed with +this why I picked the things I did so as + + align:start position:0% +this why I picked the things I did so as + + + align:start position:0% +this why I picked the things I did so as +I mentioned let me just write these down + + align:start position:0% +I mentioned let me just write these down + + + align:start position:0% +I mentioned let me just write these down +uh secant U is equal to V and secant squ + + align:start position:0% +uh secant U is equal to V and secant squ + + + align:start position:0% +uh secant U is equal to V and secant squ +U + + align:start position:0% +U + + + align:start position:0% +U +is equal to W Prime sorry that looks a + + align:start position:0% +is equal to W Prime sorry that looks a + + + align:start position:0% +is equal to W Prime sorry that looks a +little weird but that's a u okay so now + + align:start position:0% +little weird but that's a u okay so now + + + align:start position:0% +little weird but that's a u okay so now +let's write this with an integration by + + align:start position:0% +let's write this with an integration by + + + align:start position:0% +let's write this with an integration by +parts I get VW which is uh secant U + + align:start position:0% +parts I get VW which is uh secant U + + + align:start position:0% +parts I get VW which is uh secant U +tangent + + align:start position:0% +tangent + + + align:start position:0% +tangent +U minus the integral of VDW which is + + align:start position:0% +U minus the integral of VDW which is + + + align:start position:0% +U minus the integral of VDW which is +secant Cub U + + align:start position:0% + + + + align:start position:0% + +du so this is what I was trying to show + + align:start position:0% +du so this is what I was trying to show + + + align:start position:0% +du so this is what I was trying to show +you we were anticipating so when I put + + align:start position:0% +you we were anticipating so when I put + + + align:start position:0% +you we were anticipating so when I put +this all together I replace this + + align:start position:0% +this all together I replace this + + + align:start position:0% +this all together I replace this +integral by these two things and what's + + align:start position:0% +integral by these two things and what's + + + align:start position:0% +integral by these two things and what's +the point there notice what I have if I + + align:start position:0% +the point there notice what I have if I + + + align:start position:0% +the point there notice what I have if I +actually look at the pieces I have up + + align:start position:0% +actually look at the pieces I have up + + + align:start position:0% +actually look at the pieces I have up +here I have a secant cubed U it's going + + align:start position:0% +here I have a secant cubed U it's going + + + align:start position:0% +here I have a secant cubed U it's going +to equal secant U plus this I have to + + align:start position:0% +to equal secant U plus this I have to + + + align:start position:0% +to equal secant U plus this I have to +evaluate that at the bounds minus + + align:start position:0% +evaluate that at the bounds minus + + + align:start position:0% +evaluate that at the bounds minus +this so I have the same thing on this + + align:start position:0% +this so I have the same thing on this + + + align:start position:0% +this so I have the same thing on this +side that I had on the other side but + + align:start position:0% +side that I had on the other side but + + + align:start position:0% +side that I had on the other side but +with a minus sign so if I add it to the + + align:start position:0% +with a minus sign so if I add it to the + + + align:start position:0% +with a minus sign so if I add it to the +other side I'm going to get two of them + + align:start position:0% +other side I'm going to get two of them + + + align:start position:0% +other side I'm going to get two of them +so this was sort of where we're where + + align:start position:0% +so this was sort of where we're where + + + align:start position:0% +so this was sort of where we're where +we're headed now let's let's um let's + + align:start position:0% +we're headed now let's let's um let's + + + align:start position:0% +we're headed now let's let's um let's +put it all together let's take it take + + align:start position:0% +put it all together let's take it take + + + align:start position:0% +put it all together let's take it take +it back so this stuff here is that right + + align:start position:0% +it back so this stuff here is that right + + + align:start position:0% +it back so this stuff here is that right +that's what we did I'm going to + + align:start position:0% +that's what we did I'm going to + + + align:start position:0% +that's what we did I'm going to +write just the uh the important stuff + + align:start position:0% +write just the uh the important stuff + + + align:start position:0% +write just the uh the important stuff +right here I've got the integral of + + align:start position:0% +right here I've got the integral of + + + align:start position:0% +right here I've got the integral of +secant cubed + + align:start position:0% +secant cubed + + + align:start position:0% +secant cubed +U du is equal + + align:start position:0% +U du is equal + + + align:start position:0% +U du is equal +to secant U tangent + + align:start position:0% +to secant U tangent + + + align:start position:0% +to secant U tangent +U uh + + align:start position:0% +U uh + + + align:start position:0% +U uh +plus that secant I I forgot to put that + + align:start position:0% +plus that secant I I forgot to put that + + + align:start position:0% +plus that secant I I forgot to put that +one in so let me write in that one plus + + align:start position:0% +one in so let me write in that one plus + + + align:start position:0% +one in so let me write in that one plus +the integral of secant + + align:start position:0% + + + + align:start position:0% + +U uh du minus secant Cub u d the + + align:start position:0% +U uh du minus secant Cub u d the + + + align:start position:0% +U uh du minus secant Cub u d the +integral of secant Cub U + + align:start position:0% + + + + align:start position:0% + +du okay and now I'm going to work some + + align:start position:0% +du okay and now I'm going to work some + + + align:start position:0% +du okay and now I'm going to work some +magic I'm actually going to erase + + align:start position:0% +magic I'm actually going to erase + + + align:start position:0% +magic I'm actually going to erase +something and move it to the other side + + align:start position:0% +something and move it to the other side + + + align:start position:0% +something and move it to the other side +so let me sneak an eraser off screen I'm + + align:start position:0% +so let me sneak an eraser off screen I'm + + + align:start position:0% +so let me sneak an eraser off screen I'm +going to add this to the other side + + align:start position:0% +going to add this to the other side + + + align:start position:0% +going to add this to the other side +what's going to + + align:start position:0% + + + + align:start position:0% + +happen I come over here and I get two of + + align:start position:0% +happen I come over here and I get two of + + + align:start position:0% +happen I come over here and I get two of +them right there was one on this side + + align:start position:0% +them right there was one on this side + + + align:start position:0% +them right there was one on this side +with a minus sign I added it and now I + + align:start position:0% +with a minus sign I added it and now I + + + align:start position:0% +with a minus sign I added it and now I +have two of them and now what's the + + align:start position:0% +have two of them and now what's the + + + align:start position:0% +have two of them and now what's the +magic well I just divide everything by + + align:start position:0% +magic well I just divide everything by + + + align:start position:0% +magic well I just divide everything by +two and so this is going to be over two + + align:start position:0% +two and so this is going to be over two + + + align:start position:0% +two and so this is going to be over two +and this is going to be over + + align:start position:0% +and this is going to be over + + + align:start position:0% +and this is going to be over +two and now I know what an + + align:start position:0% +two and now I know what an + + + align:start position:0% +two and now I know what an +anti-derivative is notice I haven't put + + align:start position:0% +anti-derivative is notice I haven't put + + + align:start position:0% +anti-derivative is notice I haven't put +in the plus C because I'm about to put + + align:start position:0% +in the plus C because I'm about to put + + + align:start position:0% +in the plus C because I'm about to put +in some bounds all right and by the way + + align:start position:0% +in some bounds all right and by the way + + + align:start position:0% +in some bounds all right and by the way +I know I know anti derivative of secant + + align:start position:0% +I know I know anti derivative of secant + + + align:start position:0% +I know I know anti derivative of secant +U so we'll get to that in one second but + + align:start position:0% +U so we'll get to that in one second but + + + align:start position:0% +U so we'll get to that in one second but +hopefully everyone follows I had an + + align:start position:0% +hopefully everyone follows I had an + + + align:start position:0% +hopefully everyone follows I had an +integral of secant cubed U on this side + + align:start position:0% +integral of secant cubed U on this side + + + align:start position:0% +integral of secant cubed U on this side +I had an minus integral of secant cubed + + align:start position:0% +I had an minus integral of secant cubed + + + align:start position:0% +I had an minus integral of secant cubed +U over here I added it to the other side + + align:start position:0% +U over here I added it to the other side + + + align:start position:0% +U over here I added it to the other side +it gave me two of them so then I just + + align:start position:0% +it gave me two of them so then I just + + + align:start position:0% +it gave me two of them so then I just +divided by two all right and now let me + + align:start position:0% +divided by two all right and now let me + + + align:start position:0% +divided by two all right and now let me +just uh explicitly write down the last + + align:start position:0% +just uh explicitly write down the last + + + align:start position:0% +just uh explicitly write down the last +thing we + + align:start position:0% + + + + align:start position:0% + +need we still need this one and this is + + align:start position:0% +need we still need this one and this is + + + align:start position:0% +need we still need this one and this is +going to be 1 12 natural log absolute + + align:start position:0% +going to be 1 12 natural log absolute + + + align:start position:0% +going to be 1 12 natural log absolute +value + + align:start position:0% +value + + + align:start position:0% +value +secant U plus tangent + + align:start position:0% +secant U plus tangent + + + align:start position:0% +secant U plus tangent +U okay so now we just have to evaluate + + align:start position:0% +U okay so now we just have to evaluate + + + align:start position:0% +U okay so now we just have to evaluate +everywhere and we're done so now we have + + align:start position:0% +everywhere and we're done so now we have + + + align:start position:0% +everywhere and we're done so now we have +to evaluate all of this remember I said + + align:start position:0% +to evaluate all of this remember I said + + + align:start position:0% +to evaluate all of this remember I said +I left out the bounds the bounds are pi + + align:start position:0% +I left out the bounds the bounds are pi + + + align:start position:0% +I left out the bounds the bounds are pi +over 4 minus Pi + + align:start position:0% +over 4 minus Pi + + + align:start position:0% +over 4 minus Pi +over4 pi over + + align:start position:0% +over4 pi over + + + align:start position:0% +over4 pi over +4 minus pi over + + align:start position:0% +4 minus pi over + + + align:start position:0% +4 minus pi over +4 all right so I'm going to give myself + + align:start position:0% +4 all right so I'm going to give myself + + + align:start position:0% +4 all right so I'm going to give myself +a little cheat sheet up here and then + + align:start position:0% +a little cheat sheet up here and then + + + align:start position:0% +a little cheat sheet up here and then +I'm going to I'm going to write down the + + align:start position:0% +I'm going to I'm going to write down the + + + align:start position:0% +I'm going to I'm going to write down the +numbers I get here so my cheat sheet is + + align:start position:0% +numbers I get here so my cheat sheet is + + + align:start position:0% +numbers I get here so my cheat sheet is +to remind myself that secant of plus or + + align:start position:0% +to remind myself that secant of plus or + + + align:start position:0% +to remind myself that secant of plus or +minus pi over 4 is equal to < tk2 let me + + align:start position:0% +minus pi over 4 is equal to < tk2 let me + + + align:start position:0% +minus pi over 4 is equal to < tk2 let me +just make sure that's right cosine pi + + align:start position:0% +just make sure that's right cosine pi + + + align:start position:0% +just make sure that's right cosine pi +over 4 is 1 over < tk2 cosine is even so + + align:start position:0% +over 4 is 1 over < tk2 cosine is even so + + + align:start position:0% +over 4 is 1 over < tk2 cosine is even so +plus or minus Pi over4 will be the same + + align:start position:0% +plus or minus Pi over4 will be the same + + + align:start position:0% +plus or minus Pi over4 will be the same +secant is one over that so I'm + + align:start position:0% +secant is one over that so I'm + + + align:start position:0% +secant is one over that so I'm +good tangent of pi over + + align:start position:0% +good tangent of pi over + + + align:start position:0% +good tangent of pi over +4 well tangent odd so I should say plus + + align:start position:0% +4 well tangent odd so I should say plus + + + align:start position:0% +4 well tangent odd so I should say plus +or minus here tangent odd so it's going + + align:start position:0% +or minus here tangent odd so it's going + + + align:start position:0% +or minus here tangent odd so it's going +to be they're gonna have two different + + align:start position:0% +to be they're gonna have two different + + + align:start position:0% +to be they're gonna have two different +signs tangent pi over 4 is s pi over4 + + align:start position:0% +signs tangent pi over 4 is s pi over4 + + + align:start position:0% +signs tangent pi over 4 is s pi over4 +over cosine Pi over4 they have the same + + align:start position:0% +over cosine Pi over4 they have the same + + + align:start position:0% +over cosine Pi over4 they have the same +value there so it's one so tangent plus + + align:start position:0% +value there so it's one so tangent plus + + + align:start position:0% +value there so it's one so tangent plus +orus pi4 is plus orus one so that's what + + align:start position:0% +orus pi4 is plus orus one so that's what + + + align:start position:0% +orus pi4 is plus orus one so that's what +we're working with so now let's start + + align:start position:0% +we're working with so now let's start + + + align:start position:0% +we're working with so now let's start +plugging + + align:start position:0% +plugging + + + align:start position:0% +plugging +in secant pi over 4 tangent pi over 4 + + align:start position:0% +in secant pi over 4 tangent pi over 4 + + + align:start position:0% +in secant pi over 4 tangent pi over 4 +gives me < tk2 * 1 over 2 so I get < tk2 + + align:start position:0% +gives me < tk2 * 1 over 2 so I get < tk2 + + + align:start position:0% +gives me < tk2 * 1 over 2 so I get < tk2 +over two as the first thing so I have to + + align:start position:0% +over two as the first thing so I have to + + + align:start position:0% +over two as the first thing so I have to +write this equals is from here uh so I + + align:start position:0% +write this equals is from here uh so I + + + align:start position:0% +write this equals is from here uh so I +have < tk2 over two + + align:start position:0% +have < tk2 over two + + + align:start position:0% +have < tk2 over two +and then secant Pius Pi 4 is again < tk2 + + align:start position:0% +and then secant Pius Pi 4 is again < tk2 + + + align:start position:0% +and then secant Pius Pi 4 is again < tk2 +tangent minus Pi 4 is minus one so I + + align:start position:0% +tangent minus Pi 4 is minus one so I + + + align:start position:0% +tangent minus Pi 4 is minus one so I +have minus a I have a a negative here + + align:start position:0% +have minus a I have a a negative here + + + align:start position:0% +have minus a I have a a negative here +and then I have a one here or aun2 here + + align:start position:0% +and then I have a one here or aun2 here + + + align:start position:0% +and then I have a one here or aun2 here +negative 1 over two so I get another + + align:start position:0% +negative 1 over two so I get another + + + align:start position:0% +negative 1 over two so I get another +negative so I have a + + align:start position:0% +negative so I have a + + + align:start position:0% +negative so I have a +plus so one negative came from I was + + align:start position:0% +plus so one negative came from I was + + + align:start position:0% +plus so one negative came from I was +using the lower bound and one negative + + align:start position:0% +using the lower bound and one negative + + + align:start position:0% +using the lower bound and one negative +came from the tangent that gave me a + + align:start position:0% +came from the tangent that gave me a + + + align:start position:0% +came from the tangent that gave me a +plus and then I have plus 12 well again + + align:start position:0% +plus and then I have plus 12 well again + + + align:start position:0% +plus and then I have plus 12 well again +natural log of secant pi over 4 is going + + align:start position:0% +natural log of secant pi over 4 is going + + + align:start position:0% +natural log of secant pi over 4 is going +to be so I'm going to have natural log + + align:start position:0% +to be so I'm going to have natural log + + + align:start position:0% +to be so I'm going to have natural log +of < tk2 + 1 and then I'm going to have + + align:start position:0% +of < tk2 + 1 and then I'm going to have + + + align:start position:0% +of < tk2 + 1 and then I'm going to have +a natural log of < tk2 minus one and I'm + + align:start position:0% +a natural log of < tk2 minus one and I'm + + + align:start position:0% +a natural log of < tk2 minus one and I'm +going to have a negative in between them + + align:start position:0% +going to have a negative in between them + + + align:start position:0% +going to have a negative in between them +so I'm going to work a little magic here + + align:start position:0% +so I'm going to work a little magic here + + + align:start position:0% +so I'm going to work a little magic here +it's going to be natural log of < tk2 + + + align:start position:0% +it's going to be natural log of < tk2 + + + + align:start position:0% +it's going to be natural log of < tk2 + +1 over < tk2 minus one now just to point + + align:start position:0% +1 over < tk2 minus one now just to point + + + align:start position:0% +1 over < tk2 minus one now just to point +out where did that come from that came + + align:start position:0% +out where did that come from that came + + + align:start position:0% +out where did that come from that came +from putting in root2 for both of the + + align:start position:0% +from putting in root2 for both of the + + + align:start position:0% +from putting in root2 for both of the +the pi 4 andus piun over 4 tangent piun + + align:start position:0% +the pi 4 andus piun over 4 tangent piun + + + align:start position:0% +the pi 4 andus piun over 4 tangent piun +4 was the plus + + align:start position:0% +4 was the plus + + + align:start position:0% +4 was the plus +one uh tangent of piun 4 was the minus + + align:start position:0% +one uh tangent of piun 4 was the minus + + + align:start position:0% +one uh tangent of piun 4 was the minus +one how do I get this Division I had + + align:start position:0% +one how do I get this Division I had + + + align:start position:0% +one how do I get this Division I had +natural log of something minus natural + + align:start position:0% +natural log of something minus natural + + + align:start position:0% +natural log of something minus natural +log of something else so in the end I + + align:start position:0% +log of something else so in the end I + + + align:start position:0% +log of something else so in the end I +get < tk2 plus a half natural log + + align:start position:0% +get < tk2 plus a half natural log + + + align:start position:0% +get < tk2 plus a half natural log +absolute < tk2 + 1 over < tk2 minus + + align:start position:0% +absolute < tk2 + 1 over < tk2 minus + + + align:start position:0% +absolute < tk2 + 1 over < tk2 minus +1 all + + align:start position:0% +1 all + + + align:start position:0% +1 all +right that is part a + + align:start position:0% +right that is part a + + + align:start position:0% +right that is part a +so part A let me just remind you what + + align:start position:0% +so part A let me just remind you what + + + align:start position:0% +so part A let me just remind you what +did we do we had secant cubed U we did a + + align:start position:0% +did we do we had secant cubed U we did a + + + align:start position:0% +did we do we had secant cubed U we did a +substitution for one of the SEC for + + align:start position:0% +substitution for one of the SEC for + + + align:start position:0% +substitution for one of the SEC for +secant squared we got something we could + + align:start position:0% +secant squared we got something we could + + + align:start position:0% +secant squared we got something we could +deal with and something that didn't look + + align:start position:0% +deal with and something that didn't look + + + align:start position:0% +deal with and something that didn't look +so promising but once we did an + + align:start position:0% +so promising but once we did an + + + align:start position:0% +so promising but once we did an +integration by parts we were back to + + align:start position:0% +integration by parts we were back to + + + align:start position:0% +integration by parts we were back to +what we started with with a with a + + align:start position:0% +what we started with with a with a + + + align:start position:0% +what we started with with a with a +different sign so we moved it to the + + align:start position:0% +different sign so we moved it to the + + + align:start position:0% +different sign so we moved it to the +other side we were basically able to + + align:start position:0% +other side we were basically able to + + + align:start position:0% +other side we were basically able to +solve for secant cubed U so we got all + + align:start position:0% +solve for secant cubed U so we got all + + + align:start position:0% +solve for secant cubed U so we got all +the way through and then we just had to + + align:start position:0% +the way through and then we just had to + + + align:start position:0% +the way through and then we just had to +evaluate so the big step was once you + + align:start position:0% +evaluate so the big step was once you + + + align:start position:0% +evaluate so the big step was once you +were here here knowing an integration by + + align:start position:0% +were here here knowing an integration by + + + align:start position:0% +were here here knowing an integration by +parts actually would save you that's + + align:start position:0% +parts actually would save you that's + + + align:start position:0% +parts actually would save you that's +sort of the hard thing to see takes a + + align:start position:0% +sort of the hard thing to see takes a + + + align:start position:0% +sort of the hard thing to see takes a +little while to see that one maybe all + + align:start position:0% +little while to see that one maybe all + + + align:start position:0% +little while to see that one maybe all +right so now the next one if we come + + align:start position:0% +right so now the next one if we come + + + align:start position:0% +right so now the next one if we come +back here we're trying to find an + + align:start position:0% +back here we're trying to find an + + + align:start position:0% +back here we're trying to find an +anti-derivative of 1 over two sin U + + align:start position:0% +anti-derivative of 1 over two sin U + + + align:start position:0% +anti-derivative of 1 over two sin U +cosine U and um there there may be some + + align:start position:0% +cosine U and um there there may be some + + + align:start position:0% +cosine U and um there there may be some +other ways to do this but actually this + + align:start position:0% +other ways to do this but actually this + + + align:start position:0% +other ways to do this but actually this +problem part of the reason I wanted to + + align:start position:0% +problem part of the reason I wanted to + + + align:start position:0% +problem part of the reason I wanted to +do this problem was I wanted to remind + + align:start position:0% +do this problem was I wanted to remind + + + align:start position:0% +do this problem was I wanted to remind +you that it's good to know some of the + + align:start position:0% +you that it's good to know some of the + + + align:start position:0% +you that it's good to know some of the +basic trigonometric identities because + + align:start position:0% +basic trigonometric identities because + + + align:start position:0% +basic trigonometric identities because +it'll make your life a lot easier so + + align:start position:0% +it'll make your life a lot easier so + + + align:start position:0% +it'll make your life a lot easier so +this integral uh is actually the same as + + align:start position:0% +this integral uh is actually the same as + + + align:start position:0% +this integral uh is actually the same as +is the integral of du over sin 2 U and + + align:start position:0% +is the integral of du over sin 2 U and + + + align:start position:0% +is the integral of du over sin 2 U and +the reason is there's a trigonometric + + align:start position:0% +the reason is there's a trigonometric + + + align:start position:0% +the reason is there's a trigonometric +identity that says 2 sin U cosine U is + + align:start position:0% +identity that says 2 sin U cosine U is + + + align:start position:0% +identity that says 2 sin U cosine U is +equal to sin 2 U so I want to wanted to + + align:start position:0% +equal to sin 2 U so I want to wanted to + + + align:start position:0% +equal to sin 2 U so I want to wanted to +give you a reason for why we know those + + align:start position:0% +give you a reason for why we know those + + + align:start position:0% +give you a reason for why we know those +why we know some of those identities and + + align:start position:0% +why we know some of those identities and + + + align:start position:0% +why we know some of those identities and +you end up in these situations there + + align:start position:0% +you end up in these situations there + + + align:start position:0% +you end up in these situations there +might be other ways to handle this one + + align:start position:0% +might be other ways to handle this one + + + align:start position:0% +might be other ways to handle this one +but the easiest most direct way is if + + align:start position:0% +but the easiest most direct way is if + + + align:start position:0% +but the easiest most direct way is if +you do this you change it so that b is + + align:start position:0% +you do this you change it so that b is + + + align:start position:0% +you do this you change it so that b is +it's actually the same thing as integral + + align:start position:0% +it's actually the same thing as integral + + + align:start position:0% +it's actually the same thing as integral +of du over sin 2u so it's just a + + align:start position:0% +of du over sin 2u so it's just a + + + align:start position:0% +of du over sin 2u so it's just a +straight up uh double angle formula you + + align:start position:0% +straight up uh double angle formula you + + + align:start position:0% +straight up uh double angle formula you +can you can call it if you need if you + + align:start position:0% +can you can call it if you need if you + + + align:start position:0% +can you can call it if you need if you +need a fancy name and now what is this + + align:start position:0% +need a fancy name and now what is this + + + align:start position:0% +need a fancy name and now what is this +well this is equal to the integral of uh + + align:start position:0% +well this is equal to the integral of uh + + + align:start position:0% +well this is equal to the integral of uh +what's one over sign is going to be + + align:start position:0% +what's one over sign is going to be + + + align:start position:0% +what's one over sign is going to be +cosecant cosecant to + + align:start position:0% +cosecant cosecant to + + + align:start position:0% +cosecant cosecant to +U and we know the anti-derivative to + + align:start position:0% +U and we know the anti-derivative to + + + align:start position:0% +U and we know the anti-derivative to +cosecant U we know that that's going to + + align:start position:0% +cosecant U we know that that's going to + + + align:start position:0% +cosecant U we know that that's going to +be negative natural log of cosecant U + + align:start position:0% +be negative natural log of cosecant U + + + align:start position:0% +be negative natural log of cosecant U +plus cotangent U but the problem is uh + + align:start position:0% +plus cotangent U but the problem is uh + + + align:start position:0% +plus cotangent U but the problem is uh +when there's a two there what do we do + + align:start position:0% +when there's a two there what do we do + + + align:start position:0% +when there's a two there what do we do +well just think about it is if you had + + align:start position:0% +well just think about it is if you had + + + align:start position:0% +well just think about it is if you had +the anti-derivative you know by the + + align:start position:0% +the anti-derivative you know by the + + + align:start position:0% +the anti-derivative you know by the +chain rule if you just if you just put + + align:start position:0% +chain rule if you just if you just put + + + align:start position:0% +chain rule if you just if you just put +in two U's everywhere there was a u when + + align:start position:0% +in two U's everywhere there was a u when + + + align:start position:0% +in two U's everywhere there was a u when +you took the derivative you would end up + + align:start position:0% +you took the derivative you would end up + + + align:start position:0% +you took the derivative you would end up +with an extra two in front so you have + + align:start position:0% +with an extra two in front so you have + + + align:start position:0% +with an extra two in front so you have +to basically you have to just put in a + + align:start position:0% +to basically you have to just put in a + + + align:start position:0% +to basically you have to just put in a +one half in front um you could do a a + + align:start position:0% +one half in front um you could do a a + + + align:start position:0% +one half in front um you could do a a +substitution to check this but it's + + align:start position:0% +substitution to check this but it's + + + align:start position:0% +substitution to check this but it's +really straight forward to say this + + align:start position:0% +really straight forward to say this + + + align:start position:0% +really straight forward to say this +anti-derivative is equal to + + align:start position:0% +anti-derivative is equal to + + + align:start position:0% +anti-derivative is equal to +ne2 half natural log + + align:start position:0% +ne2 half natural log + + + align:start position:0% +ne2 half natural log +absolute cose 2 U plus Cent 2 + + align:start position:0% +absolute cose 2 U plus Cent 2 + + + align:start position:0% +absolute cose 2 U plus Cent 2 +U now that I have that written out I'll + + align:start position:0% +U now that I have that written out I'll + + + align:start position:0% +U now that I have that written out I'll +just point out again if there was no two + + align:start position:0% +just point out again if there was no two + + + align:start position:0% +just point out again if there was no two +here the 1/2 wouldn't be here and we' + + align:start position:0% +here the 1/2 wouldn't be here and we' + + + align:start position:0% +here the 1/2 wouldn't be here and we' +just have cant U cotangent U inside here + + align:start position:0% +just have cant U cotangent U inside here + + + align:start position:0% +just have cant U cotangent U inside here +but once we once we have to have the two + + align:start position:0% +but once we once we have to have the two + + + align:start position:0% +but once we once we have to have the two +to get a cosecant to U in the in the end + + align:start position:0% +to get a cosecant to U in the in the end + + + align:start position:0% +to get a cosecant to U in the in the end +we also need to divide by two to kill it + + align:start position:0% +we also need to divide by two to kill it + + + align:start position:0% +we also need to divide by two to kill it +off when we take a derivative the chain + + align:start position:0% +off when we take a derivative the chain + + + align:start position:0% +off when we take a derivative the chain +rule would give us a two in front so + + align:start position:0% +rule would give us a two in front so + + + align:start position:0% +rule would give us a two in front so +the2 kills it off so we don't end up + + align:start position:0% +the2 kills it off so we don't end up + + + align:start position:0% +the2 kills it off so we don't end up +with you know with this not here the + + align:start position:0% +with you know with this not here the + + + align:start position:0% +with you know with this not here the +derivative of this is 2 cose 2 U so we + + align:start position:0% +derivative of this is 2 cose 2 U so we + + + align:start position:0% +derivative of this is 2 cose 2 U so we +divide by two then we get it we get the + + align:start position:0% +divide by two then we get it we get the + + + align:start position:0% +divide by two then we get it we get the +right answer so this one I you know I'm + + align:start position:0% +right answer so this one I you know I'm + + + align:start position:0% +right answer so this one I you know I'm +not intentionally trying to trick you I + + align:start position:0% +not intentionally trying to trick you I + + + align:start position:0% +not intentionally trying to trick you I +just want to point out that uh that it's + + align:start position:0% +just want to point out that uh that it's + + + align:start position:0% +just want to point out that uh that it's +good to know some of these trigonometric + + align:start position:0% +good to know some of these trigonometric + + + align:start position:0% +good to know some of these trigonometric +identities and make solving these + + align:start position:0% +identities and make solving these + + + align:start position:0% +identities and make solving these +problems a lot easier to deal with so + + align:start position:0% +problems a lot easier to deal with so + + + align:start position:0% +problems a lot easier to deal with so +the main point of this one was actually + + align:start position:0% +the main point of this one was actually + + + align:start position:0% +the main point of this one was actually +knowing the identity in my mind maybe + + align:start position:0% +knowing the identity in my mind maybe + + + align:start position:0% +knowing the identity in my mind maybe +you found another way to do it um + + align:start position:0% +you found another way to do it um + + + align:start position:0% +you found another way to do it um +probably it didn't take two lines though + + align:start position:0% +probably it didn't take two lines though + + + align:start position:0% +probably it didn't take two lines though +so if you found another way to do it + + align:start position:0% +so if you found another way to do it + + + align:start position:0% +so if you found another way to do it +actually it's good it's creative and I + + align:start position:0% +actually it's good it's creative and I + + + align:start position:0% +actually it's good it's creative and I +like that but uh I was I was hoping to + + align:start position:0% +like that but uh I was I was hoping to + + + align:start position:0% +like that but uh I was I was hoping to +convince you that sometimes it's simple + + align:start position:0% +convince you that sometimes it's simple + + + align:start position:0% +convince you that sometimes it's simple +to know a few of these + + align:start position:0% +to know a few of these + + + align:start position:0% +to know a few of these +identities and that is where I will stop \ No newline at end of file diff --git a/1towIPbNi8g.txt b/1towIPbNi8g.txt new file mode 100644 index 0000000000000000000000000000000000000000..df1964b726dcc27ca970dbcc3abafa8cc2955987 --- /dev/null +++ b/1towIPbNi8g.txt @@ -0,0 +1,12451 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu you have a handout here of + + align:start position:0% +ocw.mit.edu you have a handout here of + + + align:start position:0% +ocw.mit.edu you have a handout here of +16th century vocal music and + + align:start position:0% +16th century vocal music and + + + align:start position:0% +16th century vocal music and +instrumental music that's um the onepage + + align:start position:0% +instrumental music that's um the onepage + + + align:start position:0% +instrumental music that's um the onepage +outline the rest is for next class class + + align:start position:0% +outline the rest is for next class class + + + align:start position:0% +outline the rest is for next class class +uh have out the thing that says begins + + align:start position:0% +uh have out the thing that says begins + + + align:start position:0% +uh have out the thing that says begins +uh Hinrich eak This was + + align:start position:0% +uh Hinrich eak This was + + + align:start position:0% +uh Hinrich eak This was +um um and then we'll open it to the + + align:start position:0% +um um and then we'll open it to the + + + align:start position:0% +um um and then we'll open it to the +Martin Luther piece after that have the + + align:start position:0% +Martin Luther piece after that have the + + + align:start position:0% +Martin Luther piece after that have the +office of sexed out we will do that + + align:start position:0% +office of sexed out we will do that + + + align:start position:0% +office of sexed out we will do that +about 15 minutes into the 10 minutes + + align:start position:0% +about 15 minutes into the 10 minutes + + + align:start position:0% +about 15 minutes into the 10 minutes +into the class or so and then um the + + align:start position:0% +into the class or so and then um the + + + align:start position:0% +into the class or so and then um the +third packet you'll need is one that + + align:start position:0% + + + + align:start position:0% + +begins okay so the this is uh class 16 + + align:start position:0% +begins okay so the this is uh class 16 + + + align:start position:0% +begins okay so the this is uh class 16 +we left off last class looking at um a + + align:start position:0% +we left off last class looking at um a + + + align:start position:0% +we left off last class looking at um a +little bit on + + align:start position:0% +little bit on + + + align:start position:0% +little bit on +the SE secular music of Germany and we + + align:start position:0% +the SE secular music of Germany and we + + + align:start position:0% +the SE secular music of Germany and we +began with um Hinrich eo's piece um + + align:start position:0% +began with um Hinrich eo's piece um + + + align:start position:0% +began with um Hinrich eo's piece um +inbrook glassen right and what were some + + align:start position:0% +inbrook glassen right and what were some + + + align:start position:0% +inbrook glassen right and what were some +of the characteristics of this piece you + + align:start position:0% +of the characteristics of this piece you + + + align:start position:0% +of the characteristics of this piece you +remember looking at + + align:start position:0% + + + + align:start position:0% + +that was r twice once with tenor Melody + + align:start position:0% +that was r twice once with tenor Melody + + + align:start position:0% +that was r twice once with tenor Melody +and once with yeah yeah so so what what + + align:start position:0% +and once with yeah yeah so so what what + + + align:start position:0% +and once with yeah yeah so so what what +were some of the main differences um if + + align:start position:0% +were some of the main differences um if + + + align:start position:0% +were some of the main differences um if +we look at the the range again + + align:start position:0% + + + + align:start position:0% + +that have my coffee + + align:start position:0% +that have my coffee + + + align:start position:0% +that have my coffee +here especially we we talked a bit about + + align:start position:0% +here especially we we talked a bit about + + + align:start position:0% +here especially we we talked a bit about +where the melody was looking what did + + align:start position:0% +where the melody was looking what did + + + align:start position:0% +where the melody was looking what did +the other voices do in the first version + + align:start position:0% +the other voices do in the first version + + + align:start position:0% +the other voices do in the first version +which what do we call what do we call + + align:start position:0% +which what do we call what do we call + + + align:start position:0% +which what do we call what do we call +that when the Melody's in the tenor + + align:start position:0% +that when the Melody's in the tenor + + + align:start position:0% +that when the Melody's in the tenor +which is a German + + align:start position:0% +which is a German + + + align:start position:0% +which is a German +word tenor lead yeah yeah so just lead + + align:start position:0% +word tenor lead yeah yeah so just lead + + + align:start position:0% +word tenor lead yeah yeah so just lead +like like you might have seen with + + align:start position:0% +like like you might have seen with + + + align:start position:0% +like like you might have seen with +Schubert leads leader and stuff like + + align:start position:0% +Schubert leads leader and stuff like + + + align:start position:0% +Schubert leads leader and stuff like +that what what's the alto do in the + + align:start position:0% +that what what's the alto do in the + + + align:start position:0% +that what what's the alto do in the +tenor Lead + + align:start position:0% +tenor Lead + + + align:start position:0% +tenor Lead +version Echo yeah it's an echo + + align:start position:0% +version Echo yeah it's an echo + + + align:start position:0% +version Echo yeah it's an echo +imitation um then notice one of the + + align:start position:0% +imitation um then notice one of the + + + align:start position:0% +imitation um then notice one of the +things is that all look at the cffs of + + align:start position:0% +things is that all look at the cffs of + + + align:start position:0% +things is that all look at the cffs of +the top three voices this this is kind + + align:start position:0% +the top three voices this this is kind + + + align:start position:0% +the top three voices this this is kind +of something to really pay attention to + + align:start position:0% +of something to really pay attention to + + + align:start position:0% +of something to really pay attention to +they're all they're all sort of Lish CS + + align:start position:0% +they're all they're all sort of Lish CS + + + align:start position:0% +they're all they're all sort of Lish CS +so this is sort of + + align:start position:0% +so this is sort of + + + align:start position:0% +so this is sort of +yeah yeah that's that top treble cluff + + align:start position:0% +yeah yeah that's that top treble cluff + + + align:start position:0% +yeah yeah that's that top treble cluff +is actually treble HGB so we're not + + align:start position:0% +is actually treble HGB so we're not + + + align:start position:0% +is actually treble HGB so we're not +we're not talking this huge um Melody + + align:start position:0% +we're not talking this huge um Melody + + + align:start position:0% +we're not talking this huge um Melody +contrast that from sets from 1510 to the + + align:start position:0% +contrast that from sets from 1510 to the + + + align:start position:0% +contrast that from sets from 1510 to the +next piece the next Arrangement as Lisa + + align:start position:0% +next piece the next Arrangement as Lisa + + + align:start position:0% +next piece the next Arrangement as Lisa +said we have two different arrangements + + align:start position:0% +said we have two different arrangements + + + align:start position:0% +said we have two different arrangements +and + + align:start position:0% +and + + + align:start position:0% +and +here we we have something a lot closer + + align:start position:0% +here we we have something a lot closer + + + align:start position:0% +here we we have something a lot closer +to the modern satb so soprano Alto tener + + align:start position:0% +to the modern satb so soprano Alto tener + + + align:start position:0% +to the modern satb so soprano Alto tener +base so we have the um the top voice + + align:start position:0% +base so we have the um the top voice + + + align:start position:0% +base so we have the um the top voice +rarely + + align:start position:0% +rarely + + + align:start position:0% +rarely +crosses with the in fact does it ever + + align:start position:0% +crosses with the in fact does it ever + + + align:start position:0% +crosses with the in fact does it ever +cross with the + + align:start position:0% +cross with the + + + align:start position:0% +cross with the +alto yeah oh yeah yeah we we mentioned + + align:start position:0% +alto yeah oh yeah yeah we we mentioned + + + align:start position:0% +alto yeah oh yeah yeah we we mentioned +that in class + + align:start position:0% +that in class + + + align:start position:0% +that in class +yeah bin yeah that one place where it + + align:start position:0% +yeah bin yeah that one place where it + + + align:start position:0% +yeah bin yeah that one place where it +confuses the melody uh also note the the + + align:start position:0% +confuses the melody uh also note the the + + + align:start position:0% +confuses the melody uh also note the the +alto is a little bit lower than we + + align:start position:0% +alto is a little bit lower than we + + + align:start position:0% +alto is a little bit lower than we +usually um usually go isn't it I mean + + align:start position:0% +usually um usually go isn't it I mean + + + align:start position:0% +usually um usually go isn't it I mean +especially in + + align:start position:0% + + + + align:start position:0% + +the yeah it's a only barely better than + + align:start position:0% +the yeah it's a only barely better than + + + align:start position:0% +the yeah it's a only barely better than +the last one though it's only + + align:start position:0% +the last one though it's only + + + align:start position:0% +the last one though it's only +better last goes to e down there this + + align:start position:0% +better last goes to e down there this + + + align:start position:0% +better last goes to e down there this +one goes to like + + align:start position:0% +one goes to like + + + align:start position:0% +one goes to like +yeah would certainly not like to but + + align:start position:0% +yeah would certainly not like to but + + + align:start position:0% +yeah would certainly not like to but +remember we're still in the period where + + align:start position:0% +remember we're still in the period where + + + align:start position:0% +remember we're still in the period where +we don't know exactly what you know I + + align:start position:0% +we don't know exactly what you know I + + + align:start position:0% +we don't know exactly what you know I +mean yeah maybe this is a maybe that was + + align:start position:0% +mean yeah maybe this is a maybe that was + + + align:start position:0% +mean yeah maybe this is a maybe that was +a maybe that if um let's see what that + + align:start position:0% +a maybe that if um let's see what that + + + align:start position:0% +a maybe that if um let's see what that +that makes things better right yeah yeah + + align:start position:0% +that makes things better right yeah yeah + + + align:start position:0% +that makes things better right yeah yeah +so if this was if this was a then Al we + + align:start position:0% +so if this was if this was a then Al we + + + align:start position:0% +so if this was if this was a then Al we +also we're in the period where we don't + + align:start position:0% +also we're in the period where we don't + + + align:start position:0% +also we're in the period where we don't +know for any given piece whether um we + + align:start position:0% +know for any given piece whether um we + + + align:start position:0% +know for any given piece whether um we +have women singing or we have boys or we + + align:start position:0% +have women singing or we have boys or we + + + align:start position:0% +have women singing or we have boys or we +have uh adult men who have trained to + + align:start position:0% +have uh adult men who have trained to + + + align:start position:0% +have uh adult men who have trained to +sing high um so there's a lot of lot of + + align:start position:0% +sing high um so there's a lot of lot of + + + align:start position:0% +sing high um so there's a lot of lot of +unknown questions for the performance of + + align:start position:0% +unknown questions for the performance of + + + align:start position:0% +unknown questions for the performance of +any individual piece we saw uh when we + + align:start position:0% +any individual piece we saw uh when we + + + align:start position:0% +any individual piece we saw uh when we +looked at remember the piece that we + + align:start position:0% +looked at remember the piece that we + + + align:start position:0% +looked at remember the piece that we +looked at with the French piece we + + align:start position:0% +looked at with the French piece we + + + align:start position:0% +looked at with the French piece we +looked at the original prints and we + + align:start position:0% +looked at the original prints and we + + + align:start position:0% +looked at the original prints and we +looked at some of the Performing + + align:start position:0% +looked at some of the Performing + + + align:start position:0% +looked at some of the Performing +ensembles for that + + align:start position:0% +ensembles for that + + + align:start position:0% +ensembles for that +piece yeah what was + + align:start position:0% +piece yeah what was + + + align:start position:0% +piece yeah what was +it what was the question the the the + + align:start position:0% +it what was the question the the the + + + align:start position:0% +it what was the question the the the +French piece that we looked at with + + align:start position:0% +French piece that we looked at with + + + align:start position:0% +French piece that we looked at with +where we saw some of the uh Arrangements + + align:start position:0% +where we saw some of the uh Arrangements + + + align:start position:0% +where we saw some of the uh Arrangements +in performing ensembles and we saw that + + align:start position:0% +in performing ensembles and we saw that + + + align:start position:0% +in performing ensembles and we saw that +women played important part in the + + align:start position:0% +women played important part in the + + + align:start position:0% +women played important part in the +performance of those of some of + + align:start position:0% +performance of those of some of + + + align:start position:0% +performance of those of some of +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +them okay we haven't all been doing our + + align:start position:0% +them okay we haven't all been doing our + + + align:start position:0% +them okay we haven't all been doing our +reviews that's why I just sort of you + + align:start position:0% +reviews that's why I just sort of you + + + align:start position:0% +reviews that's why I just sort of you +stimulate there there's a brain cell + + align:start position:0% +stimulate there there's a brain cell + + + align:start position:0% +stimulate there there's a brain cell +back there that's holding that's holding + + align:start position:0% +back there that's holding that's holding + + + align:start position:0% +back there that's holding that's holding +this important piece of data and you + + align:start position:0% +this important piece of data and you + + + align:start position:0% +this important piece of data and you +it'll come back out + + align:start position:0% +it'll come back out + + + align:start position:0% +it'll come back out +ton yeah well we take take a little bit + + align:start position:0% +ton yeah well we take take a little bit + + + align:start position:0% +ton yeah well we take take a little bit +of time these these next couple weeks as + + align:start position:0% +of time these these next couple weeks as + + + align:start position:0% +of time these these next couple weeks as +as there's one class per week for most + + align:start position:0% +as there's one class per week for most + + + align:start position:0% +as there's one class per week for most +of the weeks and just you know go back + + align:start position:0% +of the weeks and just you know go back + + + align:start position:0% +of the weeks and just you know go back +and just just play through these pieces + + align:start position:0% +and just just play through these pieces + + + align:start position:0% +and just just play through these pieces +and be like right right right you know + + align:start position:0% +and be like right right right you know + + + align:start position:0% +and be like right right right you know +that that's that's good to have in your + + align:start position:0% +that that's that's good to have in your + + + align:start position:0% +that that's that's good to have in your +head all semester and not just when we + + align:start position:0% +head all semester and not just when we + + + align:start position:0% +head all semester and not just when we +do it and at the at the exam it's great + + align:start position:0% +do it and at the at the exam it's great + + + align:start position:0% +do it and at the at the exam it's great +so so we've gone back and we've looked a + + align:start position:0% +so so we've gone back and we've looked a + + + align:start position:0% +so so we've gone back and we've looked a +little bit at at Sak + + align:start position:0% +little bit at at Sak + + + align:start position:0% +little bit at at Sak +now go on and continue to the next next + + align:start position:0% +now go on and continue to the next next + + + align:start position:0% +now go on and continue to the next next +piece in the packet and we'll um look at + + align:start position:0% +piece in the packet and we'll um look at + + + align:start position:0% +piece in the packet and we'll um look at +this + + align:start position:0% +this + + + align:start position:0% +this +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um composer perhaps in quotation marks + + align:start position:0% +um composer perhaps in quotation marks + + + align:start position:0% +um composer perhaps in quotation marks +uh Martin + + align:start position:0% +uh Martin + + + align:start position:0% +uh Martin +Luther and Martin Luther's Protestant + + align:start position:0% +Luther and Martin Luther's Protestant + + + align:start position:0% +Luther and Martin Luther's Protestant +Reformation um you guys basically all + + align:start position:0% +Reformation um you guys basically all + + + align:start position:0% +Reformation um you guys basically all +all know something about you know + + align:start position:0% +all know something about you know + + + align:start position:0% +all know something about you know +nailing thesis to a wall of a church and + + align:start position:0% +nailing thesis to a wall of a church and + + + align:start position:0% +nailing thesis to a wall of a church and +saying that you know you shouldn't be + + align:start position:0% +saying that you know you shouldn't be + + + align:start position:0% +saying that you know you shouldn't be +able to pay your way out of out of hell + + align:start position:0% +able to pay your way out of out of hell + + + align:start position:0% +able to pay your way out of out of hell +and Purgatory you should you know and + + align:start position:0% +and Purgatory you should you know and + + + align:start position:0% +and Purgatory you should you know and +things things like this and and for him + + align:start position:0% +things things like this and and for him + + + align:start position:0% +things things like this and and for him +you know I should be able to marry this + + align:start position:0% +you know I should be able to marry this + + + align:start position:0% +you know I should be able to marry this +cute nun that uh that I've been + + align:start position:0% +cute nun that uh that I've been + + + align:start position:0% +cute nun that uh that I've been +attracted to which eventually does you + + align:start position:0% +attracted to which eventually does you + + + align:start position:0% +attracted to which eventually does you +know all these things that that H that + + align:start position:0% +know all these things that that H that + + + align:start position:0% +know all these things that that H that +go into uh the Protestant Reformation + + align:start position:0% +go into uh the Protestant Reformation + + + align:start position:0% +go into uh the Protestant Reformation +but one of the main things that for us + + align:start position:0% +but one of the main things that for us + + + align:start position:0% +but one of the main things that for us +that's important is uh change to a + + align:start position:0% +that's important is uh change to a + + + align:start position:0% +that's important is uh change to a +simpler vocal style and a and a musical + + align:start position:0% +simpler vocal style and a and a musical + + + align:start position:0% +simpler vocal style and a and a musical +style that takes some of the Simplicity + + align:start position:0% +style that takes some of the Simplicity + + + align:start position:0% +style that takes some of the Simplicity +of the music of iach for instance that + + align:start position:0% +of the music of iach for instance that + + + align:start position:0% +of the music of iach for instance that +we were looking at um and so we can hear + + align:start position:0% +we were looking at um and so we can hear + + + align:start position:0% +we were looking at um and so we can hear +some of the Simplicity in a coral that a + + align:start position:0% +some of the Simplicity in a coral that a + + + align:start position:0% +some of the Simplicity in a coral that a +cral Melody a simple Melody for people + + align:start position:0% +cral Melody a simple Melody for people + + + align:start position:0% +cral Melody a simple Melody for people +to sing as a group that uh that he's + + align:start position:0% +to sing as a group that uh that he's + + + align:start position:0% +to sing as a group that uh that he's +arranged that he's put together that + + align:start position:0% +arranged that he's put together that + + + align:start position:0% +arranged that he's put together that +he's written words to and um perhaps + + align:start position:0% +he's written words to and um perhaps + + + align:start position:0% +he's written words to and um perhaps +he's written the music to + + align:start position:0% +he's written the music to + + + align:start position:0% +he's written the music to +not entirely sure um Fest is A Mighty + + align:start position:0% +not entirely sure um Fest is A Mighty + + + align:start position:0% +not entirely sure um Fest is A Mighty +Fortress Is Our God there's um there's a + + align:start position:0% +Fortress Is Our God there's um there's a + + + align:start position:0% +Fortress Is Our God there's um there's a +famous story of Martin Luther composing + + align:start position:0% +famous story of Martin Luther composing + + + align:start position:0% +famous story of Martin Luther composing +this um or arranging this piece by + + align:start position:0% +this um or arranging this piece by + + + align:start position:0% +this um or arranging this piece by +taking um a drinking song and writing + + align:start position:0% +taking um a drinking song and writing + + + align:start position:0% +taking um a drinking song and writing +new words to it where um where he said + + align:start position:0% +new words to it where um where he said + + + align:start position:0% +new words to it where um where he said +something + + align:start position:0% + + + + align:start position:0% + +like uh leader hobin why should the + + align:start position:0% +like uh leader hobin why should the + + + align:start position:0% +like uh leader hobin why should the +devil have all the good songs and taking + + align:start position:0% +devil have all the good songs and taking + + + align:start position:0% +devil have all the good songs and taking +it back unfortunately this is something + + align:start position:0% +it back unfortunately this is something + + + align:start position:0% +it back unfortunately this is something +I learned in my music history class and + + align:start position:0% +I learned in my music history class and + + + align:start position:0% +I learned in my music history class and +uh apparently there's no truth to this + + align:start position:0% +uh apparently there's no truth to this + + + align:start position:0% +uh apparently there's no truth to this +or or there's nobody's been able to + + align:start position:0% +or or there's nobody's been able to + + + align:start position:0% +or or there's nobody's been able to +document that this used to be a drinking + + align:start position:0% +document that this used to be a drinking + + + align:start position:0% +document that this used to be a drinking +song but let's listen to the first + + align:start position:0% +song but let's listen to the first + + + align:start position:0% +song but let's listen to the first +version um here it is in Luther's + + align:start position:0% +version um here it is in Luther's + + + align:start position:0% +version um here it is in Luther's +edition of of Psalms and hymns and um + + align:start position:0% +edition of of Psalms and hymns and um + + + align:start position:0% +edition of of Psalms and hymns and um +things like that and you'll see um he's + + align:start position:0% +things like that and you'll see um he's + + + align:start position:0% +things like that and you'll see um he's +written it in slightly different it's a + + align:start position:0% +written it in slightly different it's a + + + align:start position:0% +written it in slightly different it's a +slightly different version from what you + + align:start position:0% +slightly different version from what you + + + align:start position:0% +slightly different version from what you +have here but it's very similar and it's + + align:start position:0% +have here but it's very similar and it's + + + align:start position:0% +have here but it's very similar and it's +this um single impression actually this + + align:start position:0% +this um single impression actually this + + + align:start position:0% +this um single impression actually this +is a rather nice um music print lot lot + + align:start position:0% +is a rather nice um music print lot lot + + + align:start position:0% +is a rather nice um music print lot lot +less jaggedy than some of the other ones + + align:start position:0% +less jaggedy than some of the other ones + + + align:start position:0% +less jaggedy than some of the other ones +we've looked at but um you see single + + align:start position:0% +we've looked at but um you see single + + + align:start position:0% +we've looked at but um you see single +Melody going across and let's you can + + align:start position:0% +Melody going across and let's you can + + + align:start position:0% +Melody going across and let's you can +either follow along here and see what + + align:start position:0% +either follow along here and see what + + + align:start position:0% +either follow along here and see what +the difference is between this and your + + align:start position:0% +the difference is between this and your + + + align:start position:0% +the difference is between this and your +version or follow along in the score for + + align:start position:0% +version or follow along in the score for + + + align:start position:0% +version or follow along in the score for +a + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +second + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so compare um that setting to a slightly + + align:start position:0% +so compare um that setting to a slightly + + + align:start position:0% +so compare um that setting to a slightly +probably a slightly later setting though + + align:start position:0% +probably a slightly later setting though + + + align:start position:0% +probably a slightly later setting though +published at the same time in 1529 by + + align:start position:0% +published at the same time in 1529 by + + + align:start position:0% +published at the same time in 1529 by +Johan valter another composer + + align:start position:0% +Johan valter another composer + + + align:start position:0% +Johan valter another composer +professional composer who going to take + + align:start position:0% +professional composer who going to take + + + align:start position:0% +professional composer who going to take +this melody and um put it into um well + + align:start position:0% +this melody and um put it into um well + + + align:start position:0% +this melody and um put it into um well +into a more tenor lead fashion so go + + align:start position:0% +into a more tenor lead fashion so go + + + align:start position:0% +into a more tenor lead fashion so go +ahead and look at your score and find + + align:start position:0% +ahead and look at your score and find + + + align:start position:0% +ahead and look at your score and find +the melody in the + + align:start position:0% + + + + align:start position:0% + +tenor and um let's listen to about that + + align:start position:0% +tenor and um let's listen to about that + + + align:start position:0% +tenor and um let's listen to about that +much of the four part + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +version + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so you can hear it's not completely + + align:start position:0% +so you can hear it's not completely + + + align:start position:0% +so you can hear it's not completely +unelaborated they still have that uh + + align:start position:0% +unelaborated they still have that uh + + + align:start position:0% +unelaborated they still have that uh +soprano Those runs and things but it's a + + align:start position:0% +soprano Those runs and things but it's a + + + align:start position:0% +soprano Those runs and things but it's a +little little less ornamented than some + + align:start position:0% +little little less ornamented than some + + + align:start position:0% +little little less ornamented than some +of the um well certainly it doesn't have + + align:start position:0% +of the um well certainly it doesn't have + + + align:start position:0% +of the um well certainly it doesn't have +any the intellectual sophistry of like + + align:start position:0% +any the intellectual sophistry of like + + + align:start position:0% +any the intellectual sophistry of like +the missa of johanes aim with four + + align:start position:0% +the missa of johanes aim with four + + + align:start position:0% +the missa of johanes aim with four +different time signatures going at the + + align:start position:0% +different time signatures going at the + + + align:start position:0% +different time signatures going at the +same time and things like that + + align:start position:0% +same time and things like that + + + align:start position:0% +same time and things like that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um and in fact some of the other + + align:start position:0% +um and in fact some of the other + + + align:start position:0% +um and in fact some of the other +Protestant groups that were to arise + + align:start position:0% +Protestant groups that were to arise + + + align:start position:0% +Protestant groups that were to arise +soon the Calvinists and went further on + + align:start position:0% +soon the Calvinists and went further on + + + align:start position:0% +soon the Calvinists and went further on +the austerity + + align:start position:0% + + + + align:start position:0% + +side + + align:start position:0% +side + + + align:start position:0% +side +but there's always you know when when + + align:start position:0% +but there's always you know when when + + + align:start position:0% +but there's always you know when when +one new group arises with a new idea of + + align:start position:0% +one new group arises with a new idea of + + + align:start position:0% +one new group arises with a new idea of +music there's always yeah as Jester + + align:start position:0% +music there's always yeah as Jester + + + align:start position:0% +music there's always yeah as Jester +shows there's there's always has to be a + + align:start position:0% +shows there's there's always has to be a + + + align:start position:0% +shows there's there's always has to be a +counter reaction and basically um you + + align:start position:0% +counter reaction and basically um you + + + align:start position:0% +counter reaction and basically um you +know like uh I don't know if if Stanford + + align:start position:0% +know like uh I don't know if if Stanford + + + align:start position:0% +know like uh I don't know if if Stanford +started offering a you know $200,000 + + align:start position:0% +started offering a you know $200,000 + + + align:start position:0% +started offering a you know $200,000 +free scholarship to every student + + align:start position:0% +free scholarship to every student + + + align:start position:0% +free scholarship to every student +they're going to start attracting new + + align:start position:0% +they're going to start attracting new + + + align:start position:0% +they're going to start attracting new +people and and Luther is offering some + + align:start position:0% +people and and Luther is offering some + + + align:start position:0% +people and and Luther is offering some +really great things I mean you don't + + align:start position:0% +really great things I mean you don't + + + align:start position:0% +really great things I mean you don't +have to pay to get out of purgatory + + align:start position:0% +have to pay to get out of purgatory + + + align:start position:0% +have to pay to get out of purgatory +anymore fantastic you can you can be a + + align:start position:0% +anymore fantastic you can you can be a + + + align:start position:0% +anymore fantastic you can you can be a +priest and you can marry that's even + + align:start position:0% +priest and you can marry that's even + + + align:start position:0% +priest and you can marry that's even +better um all all these good things and + + align:start position:0% +better um all all these good things and + + + align:start position:0% +better um all all these good things and +so the Catholic Church begins to lose um + + align:start position:0% +so the Catholic Church begins to lose um + + + align:start position:0% +so the Catholic Church begins to lose um +some of their um some of their followers + + align:start position:0% +some of their um some of their followers + + + align:start position:0% +some of their um some of their followers +some of people so um what are some of + + align:start position:0% +some of people so um what are some of + + + align:start position:0% +some of people so um what are some of +the things that they can do well one of + + align:start position:0% +the things that they can do well one of + + + align:start position:0% +the things that they can do well one of +the things musically that we care about + + align:start position:0% +the things musically that we care about + + + align:start position:0% +the things musically that we care about +is there can be a renewed emphasis on + + align:start position:0% +is there can be a renewed emphasis on + + + align:start position:0% +is there can be a renewed emphasis on +the simple on things that that that have + + align:start position:0% +the simple on things that that that have + + + align:start position:0% +the simple on things that that that have +always worked and not not the new weird + + align:start position:0% +always worked and not not the new weird + + + align:start position:0% +always worked and not not the new weird +stuff that's going on so it's a renewed + + align:start position:0% +stuff that's going on so it's a renewed + + + align:start position:0% +stuff that's going on so it's a renewed +emphasis on Plain chant in the Catholic + + align:start position:0% +emphasis on Plain chant in the Catholic + + + align:start position:0% +emphasis on Plain chant in the Catholic +Counter Reformation of the 16th century + + align:start position:0% +Counter Reformation of the 16th century + + + align:start position:0% +Counter Reformation of the 16th century +so that's why we're delaying a little + + align:start position:0% +so that's why we're delaying a little + + + align:start position:0% +so that's why we're delaying a little +bit singing uh sex until now let's + + align:start position:0% +bit singing uh sex until now let's + + + align:start position:0% +bit singing uh sex until now let's +remember that that um chant is the most + + align:start position:0% +remember that that um chant is the most + + + align:start position:0% +remember that that um chant is the most +important Musical form still going on by + + align:start position:0% +important Musical form still going on by + + + align:start position:0% +important Musical form still going on by +by singing it and um so we're going to + + align:start position:0% +by singing it and um so we're going to + + + align:start position:0% +by singing it and um so we're going to +sing the office of sex for for Tuesday + + align:start position:0% +sing the office of sex for for Tuesday + + + align:start position:0% +sing the office of sex for for Tuesday +which is pretty appropriate since it's + + align:start position:0% +which is pretty appropriate since it's + + + align:start position:0% +which is pretty appropriate since it's +uh almost noon and uh and Tuesday and + + align:start position:0% +uh almost noon and uh and Tuesday and + + + align:start position:0% +uh almost noon and uh and Tuesday and +who's um who's our Abbott or abbis today + + align:start position:0% +who's um who's our Abbott or abbis today + + + align:start position:0% +who's um who's our Abbott or abbis today +Lisa I think I'm the great great and uh + + align:start position:0% +Lisa I think I'm the great great and uh + + + align:start position:0% +Lisa I think I'm the great great and uh +caner okay this will make C is that + + align:start position:0% +caner okay this will make C is that + + + align:start position:0% +caner okay this will make C is that +pretty good for C + + align:start position:0% +pretty good for C + + + align:start position:0% +pretty good for C +today yeah go + + align:start position:0% +today yeah go + + + align:start position:0% +today yeah go +ahead + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +glor + + align:start position:0% +glor + + + align:start position:0% +glor +amen + + align:start position:0% + + + + align:start position:0% + +let's keep the temple + + align:start position:0% + + + + align:start position:0% + +up + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +spe + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +no come on come on we this one always + + align:start position:0% +no come on come on we this one always + + + align:start position:0% +no come on come on we this one always +grabs us into + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +know + + align:start position:0% + + + + align:start position:0% + +illumin + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +glor and right back to the Anton after + + align:start position:0% +glor and right back to the Anton after + + + align:start position:0% +glor and right back to the Anton after +this + + align:start position:0% + + + + align:start position:0% + +de + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +local + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +long + + align:start position:0% +long + + + align:start position:0% +long +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +usen + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +amen good wow we really getting getting + + align:start position:0% +amen good wow we really getting getting + + + align:start position:0% +amen good wow we really getting getting +that down very + + align:start position:0% +that down very + + + align:start position:0% +that down very +nice so yeah one of the things you can + + align:start position:0% +nice so yeah one of the things you can + + + align:start position:0% +nice so yeah one of the things you can +do is you can emphasize that um you know + + align:start position:0% +do is you can emphasize that um you know + + + align:start position:0% +do is you can emphasize that um you know +that that that chant will become a + + align:start position:0% +that that that chant will become a + + + align:start position:0% +that that that chant will become a +bigger part of the musical service you + + align:start position:0% +bigger part of the musical service you + + + align:start position:0% +bigger part of the musical service you +can also emphasize that the priests + + align:start position:0% +can also emphasize that the priests + + + align:start position:0% +can also emphasize that the priests +should know exactly how to do chant and + + align:start position:0% +should know exactly how to do chant and + + + align:start position:0% +should know exactly how to do chant and +how to do how to run a mass and how to + + align:start position:0% +how to do how to run a mass and how to + + + align:start position:0% +how to do how to run a mass and how to +run an office and so we begin to get + + align:start position:0% +run an office and so we begin to get + + + align:start position:0% +run an office and so we begin to get +these um publications of more books that + + align:start position:0% +these um publications of more books that + + + align:start position:0% +these um publications of more books that +are telling you exactly how you should + + align:start position:0% +are telling you exactly how you should + + + align:start position:0% +are telling you exactly how you should +um how you should conduct your your + + align:start position:0% +um how you should conduct your your + + + align:start position:0% +um how you should conduct your your +services for specifically for priests + + align:start position:0% +services for specifically for priests + + + align:start position:0% +services for specifically for priests +and we own two of them here at MIT which + + align:start position:0% +and we own two of them here at MIT which + + + align:start position:0% +and we own two of them here at MIT which +is how we can get these photos and + + align:start position:0% +is how we can get these photos and + + + align:start position:0% +is how we can get these photos and +things like that and which Julie is + + align:start position:0% +things like that and which Julie is + + + align:start position:0% +things like that and which Julie is +working on right now for her paper so + + align:start position:0% +working on right now for her paper so + + + align:start position:0% +working on right now for her paper so +it's great well um because I don't know + + align:start position:0% +it's great well um because I don't know + + + align:start position:0% +it's great well um because I don't know +everything that's in this book except + + align:start position:0% +everything that's in this book except + + + align:start position:0% +everything that's in this book except +that there wormholes and things like + + align:start position:0% +that there wormholes and things like + + + align:start position:0% +that there wormholes and things like +that um but um but you can see a couple + + align:start position:0% +that um but um but you can see a couple + + + align:start position:0% +that um but um but you can see a couple +things here one it's published in + + align:start position:0% +things here one it's published in + + + align:start position:0% +things here one it's published in +md5 50 + + align:start position:0% +md5 50 + + + align:start position:0% +md5 50 +6076 in Venice + + align:start position:0% +6076 in Venice + + + align:start position:0% +6076 in Venice +venettis and we can see here um this is + + align:start position:0% +venettis and we can see here um this is + + + align:start position:0% +venettis and we can see here um this is +the suer + + align:start position:0% +the suer + + + align:start position:0% +the suer +K Santi triti Kili + + align:start position:0% +K Santi triti Kili + + + align:start position:0% +K Santi triti Kili +after the the way of doing things after + + align:start position:0% +after the the way of doing things after + + + align:start position:0% +after the the way of doing things after +the Council of Trent after this big + + align:start position:0% +the Council of Trent after this big + + + align:start position:0% +the Council of Trent after this big +Council that comes up to try to make + + align:start position:0% +Council that comes up to try to make + + + align:start position:0% +Council that comes up to try to make +sure that the Catholic church is + + align:start position:0% +sure that the Catholic church is + + + align:start position:0% +sure that the Catholic church is +responding properly to the um to the to + + align:start position:0% +responding properly to the um to the to + + + align:start position:0% +responding properly to the um to the to +the sort of the the what you say the + + align:start position:0% +the sort of the the what you say the + + + align:start position:0% +the sort of the the what you say the +the opportunities you say the the + + align:start position:0% +the opportunities you say the the + + + align:start position:0% +the opportunities you say the the +problems presented by the Protestant + + align:start position:0% +problems presented by the Protestant + + + align:start position:0% +problems presented by the Protestant +Reformation and if we look through we + + align:start position:0% +Reformation and if we look through we + + + align:start position:0% +Reformation and if we look through we +can see things U like little things like + + align:start position:0% +can see things U like little things like + + + align:start position:0% +can see things U like little things like +how you should sing the re esant in + + align:start position:0% +how you should sing the re esant in + + + align:start position:0% +how you should sing the re esant in +Pache properly and we don't always do + + align:start position:0% +Pache properly and we don't always do + + + align:start position:0% +Pache properly and we don't always do +that right and how in + + align:start position:0% +that right and how in + + + align:start position:0% +that right and how in +amen I mean you can kind of imagine that + + align:start position:0% +amen I mean you can kind of imagine that + + + align:start position:0% +amen I mean you can kind of imagine that +if a priest needs to be taught how to + + align:start position:0% +if a priest needs to be taught how to + + + align:start position:0% +if a priest needs to be taught how to +sing amen there was probably some pretty + + align:start position:0% +sing amen there was probably some pretty + + + align:start position:0% +sing amen there was probably some pretty +bad singing going on in various places + + align:start position:0% +bad singing going on in various places + + + align:start position:0% +bad singing going on in various places +um let's see we can we can see various + + align:start position:0% +um let's see we can we can see various + + + align:start position:0% +um let's see we can we can see various +things that um that maybe we should + + align:start position:0% +things that um that maybe we should + + + align:start position:0% +things that um that maybe we should +maybe I don't know in future years I + + align:start position:0% +maybe I don't know in future years I + + + align:start position:0% +maybe I don't know in future years I +should I should consult this and try to + + align:start position:0% +should I should consult this and try to + + + align:start position:0% +should I should consult this and try to +do more we should try to do not only the + + align:start position:0% +do more we should try to do not only the + + + align:start position:0% +do more we should try to do not only the +office of sex but the office of sex as + + align:start position:0% +office of sex but the office of sex as + + + align:start position:0% +office of sex but the office of sex as +it would have been done in Venice during + + align:start position:0% +it would have been done in Venice during + + + align:start position:0% +it would have been done in Venice during +The Counter Reformation because there + + align:start position:0% +The Counter Reformation because there + + + align:start position:0% +The Counter Reformation because there +are all kinds of things in these red + + align:start position:0% +are all kinds of things in these red + + + align:start position:0% +are all kinds of things in these red +marks that tell you exactly what a + + align:start position:0% +marks that tell you exactly what a + + + align:start position:0% +marks that tell you exactly what a +priest should be doing during it for + + align:start position:0% +priest should be doing during it for + + + align:start position:0% +priest should be doing during it for +instance we see + + align:start position:0% +instance we see + + + align:start position:0% +instance we see +Ando SOS Al and finally the the the + + align:start position:0% +Ando SOS Al and finally the the the + + + align:start position:0% +Ando SOS Al and finally the the the +priest says in and the problem with Alta + + align:start position:0% +priest says in and the problem with Alta + + + align:start position:0% +priest says in and the problem with Alta +is it either means loud or high and we + + align:start position:0% +is it either means loud or high and we + + + align:start position:0% +is it either means loud or high and we +don't really know probably loud you + + align:start position:0% +don't really know probably loud you + + + align:start position:0% +don't really know probably loud you +probably don't want says potterer we + + align:start position:0% +probably don't want says potterer we + + + align:start position:0% +probably don't want says potterer we +probably don't want the priest going + + align:start position:0% +probably don't want the priest going + + + align:start position:0% +probably don't want the priest going +poter but really + + align:start position:0% +poter but really + + + align:start position:0% +poter but really +poter um and things like that as are + + align:start position:0% +poter um and things like that as are + + + align:start position:0% +poter um and things like that as are +going through and we can see that + + align:start position:0% +going through and we can see that + + + align:start position:0% +going through and we can see that +there's even um tells you when to do Dom + + align:start position:0% +there's even um tells you when to do Dom + + + align:start position:0% +there's even um tells you when to do Dom +v v they're at least at least well + + align:start position:0% +v v they're at least at least well + + + align:start position:0% +v v they're at least at least well +educated enough to know what goes after + + align:start position:0% +educated enough to know what goes after + + + align:start position:0% +educated enough to know what goes after +vo at Kump so so we can learn a lot by + + align:start position:0% +vo at Kump so so we can learn a lot by + + + align:start position:0% +vo at Kump so so we can learn a lot by +looking at uh what we have + + align:start position:0% +looking at uh what we have + + + align:start position:0% +looking at uh what we have +here the other the people who are are + + align:start position:0% +here the other the people who are are + + + align:start position:0% +here the other the people who are are +the first people who are threatened by + + align:start position:0% +the first people who are threatened by + + + align:start position:0% +the first people who are threatened by +the Protestant Reformation are obviously + + align:start position:0% +the Protestant Reformation are obviously + + + align:start position:0% +the Protestant Reformation are obviously +the + + align:start position:0% +the + + + align:start position:0% +the +Catholics who then is threatened by The + + align:start position:0% +Catholics who then is threatened by The + + + align:start position:0% +Catholics who then is threatened by The +Counter Reformation well a lot of people + + align:start position:0% +Counter Reformation well a lot of people + + + align:start position:0% +Counter Reformation well a lot of people +but for our purposes it's important to + + align:start position:0% +but for our purposes it's important to + + + align:start position:0% +but for our purposes it's important to +think about the people who are writing + + align:start position:0% +think about the people who are writing + + + align:start position:0% +think about the people who are writing +that really complex music that is now + + align:start position:0% +that really complex music that is now + + + align:start position:0% +that really complex music that is now +sort of out of style and that's the + + align:start position:0% +sort of out of style and that's the + + + align:start position:0% +sort of out of style and that's the +ponic composers um let's let's step back + + align:start position:0% +ponic composers um let's let's step back + + + align:start position:0% +ponic composers um let's let's step back +a bit and review and think about some of + + align:start position:0% +a bit and review and think about some of + + + align:start position:0% +a bit and review and think about some of +the the music that we've looked at so + + align:start position:0% +the the music that we've looked at so + + + align:start position:0% +the the music that we've looked at so +far in this class how many voices at a + + align:start position:0% +far in this class how many voices at a + + + align:start position:0% +far in this class how many voices at a +time how many different parts are in Say + + align:start position:0% +time how many different parts are in Say + + + align:start position:0% +time how many different parts are in Say +nonante by yakap deblon maybe two yeah + + align:start position:0% +nonante by yakap deblon maybe two yeah + + + align:start position:0% +nonante by yakap deblon maybe two yeah +that particular one was two and go to + + align:start position:0% +that particular one was two and go to + + + align:start position:0% +that particular one was two and go to +forign yeah so so then if we look at DUI + + align:start position:0% +forign yeah so so then if we look at DUI + + + align:start position:0% +forign yeah so so then if we look at DUI +we were getting four like in ner rosar + + align:start position:0% +we were getting four like in ner rosar + + + align:start position:0% +we were getting four like in ner rosar +and Flores we had the two higher voices + + align:start position:0% +and Flores we had the two higher voices + + + align:start position:0% +and Flores we had the two higher voices +and the two paired bottom voices + + align:start position:0% +and the two paired bottom voices + + + align:start position:0% +and the two paired bottom voices +actually stayed at four for a lot of + + align:start position:0% +actually stayed at four for a lot of + + + align:start position:0% +actually stayed at four for a lot of +what we were looking at we've we've sort + + align:start position:0% +what we were looking at we've we've sort + + + align:start position:0% +what we were looking at we've we've sort +of in this class um not done that that + + align:start position:0% +of in this class um not done that that + + + align:start position:0% +of in this class um not done that that +much any bigger pieces but basically we + + align:start position:0% +much any bigger pieces but basically we + + + align:start position:0% +much any bigger pieces but basically we +start getting more and more six voice + + align:start position:0% +start getting more and more six voice + + + align:start position:0% +start getting more and more six voice +pieces and then eight voice pieces even + + align:start position:0% +pieces and then eight voice pieces even + + + align:start position:0% +pieces and then eight voice pieces even +12 um no actually in when when we were + + align:start position:0% +12 um no actually in when when we were + + + align:start position:0% +12 um no actually in when when we were +counting the four voices in The 14th + + align:start position:0% +counting the four voices in The 14th + + + align:start position:0% +counting the four voices in The 14th +Century some of them were optional or + + align:start position:0% +Century some of them were optional or + + + align:start position:0% +Century some of them were optional or +some of them not optional you can choose + + align:start position:0% +some of them not optional you can choose + + + align:start position:0% +some of them not optional you can choose +one or the other part but when we get to + + align:start position:0% +one or the other part but when we get to + + + align:start position:0% +one or the other part but when we get to +um into the 16th century we start seeing + + align:start position:0% +um into the 16th century we start seeing + + + align:start position:0% +um into the 16th century we start seeing +some Mass pieces some motets with 8 12 + + align:start position:0% +some Mass pieces some motets with 8 12 + + + align:start position:0% +some Mass pieces some motets with 8 12 +voices and where we get uh just the text + + align:start position:0% +voices and where we get uh just the text + + + align:start position:0% +voices and where we get uh just the text +is everywhere and so the story goes this + + align:start position:0% +is everywhere and so the story goes this + + + align:start position:0% +is everywhere and so the story goes this +guy giovan palestrina who um is really + + align:start position:0% +guy giovan palestrina who um is really + + + align:start position:0% +guy giovan palestrina who um is really +unusual for all the people that we've + + align:start position:0% +unusual for all the people that we've + + + align:start position:0% +unusual for all the people that we've +studied who um who worked in Italy in + + align:start position:0% +studied who um who worked in Italy in + + + align:start position:0% +studied who um who worked in Italy in +that he was Italian um and not not + + align:start position:0% +that he was Italian um and not not + + + align:start position:0% +that he was Italian um and not not +somebody who came not an igree + + align:start position:0% +somebody who came not an igree + + + align:start position:0% +somebody who came not an igree +um he was in some ways according to + + align:start position:0% +um he was in some ways according to + + + align:start position:0% +um he was in some ways according to +another one of these legends that we're + + align:start position:0% +another one of these legends that we're + + + align:start position:0% +another one of these legends that we're +not sure if it's really true or not uh + + align:start position:0% +not sure if it's really true or not uh + + + align:start position:0% +not sure if it's really true or not uh +was sort of got wind that the Catholic + + align:start position:0% +was sort of got wind that the Catholic + + + align:start position:0% +was sort of got wind that the Catholic +church was going to ban all poliany + + align:start position:0% +church was going to ban all poliany + + + align:start position:0% +church was going to ban all poliany +because as part of The Counter + + align:start position:0% +because as part of The Counter + + + align:start position:0% +because as part of The Counter +Reformation and according to Legend + + align:start position:0% +Reformation and according to Legend + + + align:start position:0% +Reformation and according to Legend +again he creates a mass the missa papa + + align:start position:0% +again he creates a mass the missa papa + + + align:start position:0% +again he creates a mass the missa papa +maelis for Pope marelius uh that is that + + align:start position:0% +maelis for Pope marelius uh that is that + + + align:start position:0% +maelis for Pope marelius uh that is that +was so clear even though it had so many + + align:start position:0% +was so clear even though it had so many + + + align:start position:0% +was so clear even though it had so many +voices and that you could understand the + + align:start position:0% +voices and that you could understand the + + + align:start position:0% +voices and that you could understand the +text that you could really be sure that + + align:start position:0% +text that you could really be sure that + + + align:start position:0% +text that you could really be sure that +were still singing to God even though it + + align:start position:0% +were still singing to God even though it + + + align:start position:0% +were still singing to God even though it +was such uh such a complex piece so + + align:start position:0% +was such uh such a complex piece so + + + align:start position:0% +was such uh such a complex piece so +we're going pretty quickly to get um + + align:start position:0% +we're going pretty quickly to get um + + + align:start position:0% +we're going pretty quickly to get um +through through a lot of music today but + + align:start position:0% +through through a lot of music today but + + + align:start position:0% +through through a lot of music today but +we can we can look at what The Counter + + align:start position:0% +we can we can look at what The Counter + + + align:start position:0% +we can we can look at what The Counter +Reformation response to what's happening + + align:start position:0% +Reformation response to what's happening + + + align:start position:0% +Reformation response to what's happening +is through one of his pieces we won't + + align:start position:0% +is through one of his pieces we won't + + + align:start position:0% +is through one of his pieces we won't +look at the missa machell we'll instead + + align:start position:0% +look at the missa machell we'll instead + + + align:start position:0% +look at the missa machell we'll instead +look at um another one of his pieces uh + + align:start position:0% +look at um another one of his pieces uh + + + align:start position:0% +look at um another one of his pieces uh +we'll actually look at two pieces first + + align:start position:0% +we'll actually look at two pieces first + + + align:start position:0% +we'll actually look at two pieces first +a motet by him called the miss the motet + + align:start position:0% +a motet by him called the miss the motet + + + align:start position:0% +a motet by him called the miss the motet +to us Petrus and so go ahead and turn to + + align:start position:0% +to us Petrus and so go ahead and turn to + + + align:start position:0% +to us Petrus and so go ahead and turn to +that from + + align:start position:0% +that from + + + align:start position:0% +that from +1573 and then a mass based on this motet + + align:start position:0% +1573 and then a mass based on this motet + + + align:start position:0% +1573 and then a mass based on this motet +so it's after tore Tremor which we'll + + align:start position:0% +so it's after tore Tremor which we'll + + + align:start position:0% +so it's after tore Tremor which we'll +get back to um when we do some really + + align:start position:0% +get back to um when we do some really + + + align:start position:0% +get back to um when we do some really +cool chromatic stuff in about four + + align:start position:0% +cool chromatic stuff in about four + + + align:start position:0% +cool chromatic stuff in about four +classes + + align:start position:0% + + + + align:start position:0% + +um now let's just listen to the opening + + align:start position:0% +um now let's just listen to the opening + + + align:start position:0% +um now let's just listen to the opening +of TS pet roots and get this back in our + + align:start position:0% +of TS pet roots and get this back in our + + + align:start position:0% +of TS pet roots and get this back in our +heads actually have to + + align:start position:0% +heads actually have to + + + align:start position:0% +heads actually have to +plug + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in heart + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so let's just listen to that much um I + + align:start position:0% +so let's just listen to that much um I + + + align:start position:0% +so let's just listen to that much um I +don't know I always think that if you're + + align:start position:0% +don't know I always think that if you're + + + align:start position:0% +don't know I always think that if you're +trying to convince some people that that + + align:start position:0% +trying to convince some people that that + + + align:start position:0% +trying to convince some people that that +no really six voice uh pany can be very + + align:start position:0% +no really six voice uh pany can be very + + + align:start position:0% +no really six voice uh pany can be very +clear and easy and and you expect them + + align:start position:0% +clear and easy and and you expect them + + + align:start position:0% +clear and easy and and you expect them +to have an attention span of a fly what + + align:start position:0% +to have an attention span of a fly what + + + align:start position:0% +to have an attention span of a fly what +might you do at the beginning that he + + align:start position:0% +might you do at the beginning that he + + + align:start position:0% +might you do at the beginning that he +does here put them all in together yeah + + align:start position:0% +does here put them all in together yeah + + + align:start position:0% +does here put them all in together yeah +yeah exactly three voices here the three + + align:start position:0% +yeah exactly three voices here the three + + + align:start position:0% +yeah exactly three voices here the three +highest voices than the three lowest + + align:start position:0% +highest voices than the three lowest + + + align:start position:0% +highest voices than the three lowest +voices coming in + + align:start position:0% +voices coming in + + + align:start position:0% +voices coming in +here what um and just let's uh wait + + align:start position:0% +here what um and just let's uh wait + + + align:start position:0% +here what um and just let's uh wait +don't shout it out just wait till we all + + align:start position:0% +don't shout it out just wait till we all + + + align:start position:0% +don't shout it out just wait till we all +have the answer ahead what what do we + + align:start position:0% +have the answer ahead what what do we + + + align:start position:0% +have the answer ahead what what do we +call what we call the texture the how + + align:start position:0% +call what we call the texture the how + + + align:start position:0% +call what we call the texture the how +the the words are set in this um in this + + align:start position:0% +the the words are set in this um in this + + + align:start position:0% +the the words are set in this um in this +section so just when you have it + + align:start position:0% +section so just when you have it + + + align:start position:0% +section so just when you have it +how is it contrapuntal or + + align:start position:0% + + + + align:start position:0% + +what so do the syllables line up with + + align:start position:0% +what so do the syllables line up with + + + align:start position:0% +what so do the syllables line up with +each other or are they separate so what + + align:start position:0% +each other or are they separate so what + + + align:start position:0% +each other or are they separate so what +do we call that anybody now roughly + + align:start position:0% +do we call that anybody now roughly + + + align:start position:0% +do we call that anybody now roughly +homophonic homophonic phic homophony + + align:start position:0% +homophonic homophonic phic homophony + + + align:start position:0% +homophonic homophonic phic homophony +where you have not monophonic not one + + align:start position:0% +where you have not monophonic not one + + + align:start position:0% +where you have not monophonic not one +part but as it's roughly homophonic I + + align:start position:0% +part but as it's roughly homophonic I + + + align:start position:0% +part but as it's roughly homophonic I +mean there are things like that super + + align:start position:0% +mean there are things like that super + + + align:start position:0% +mean there are things like that super +honk honk that you know that that aren't + + align:start position:0% +honk honk that you know that that aren't + + + align:start position:0% +honk honk that you know that that aren't +exactly like that but it's roughly there + + align:start position:0% +exactly like that but it's roughly there + + + align:start position:0% +exactly like that but it's roughly there +the text for this piece T Petrus you are + + align:start position:0% +the text for this piece T Petrus you are + + + align:start position:0% +the text for this piece T Petrus you are +Peter at Super hunk Petr and on this + + align:start position:0% +Peter at Super hunk Petr and on this + + + align:start position:0% +Peter at Super hunk Petr and on this +rock uh what is it edifico uh ecclesium + + align:start position:0% +rock uh what is it edifico uh ecclesium + + + align:start position:0% +rock uh what is it edifico uh ecclesium +yeah ma'am uh I will build my church + + align:start position:0% +yeah ma'am uh I will build my church + + + align:start position:0% +yeah ma'am uh I will build my church +this is um kind of a pond that Jesus + + align:start position:0% +this is um kind of a pond that Jesus + + + align:start position:0% +this is um kind of a pond that Jesus +gives to to uh Peter um naming him Peter + + align:start position:0% +gives to to uh Peter um naming him Peter + + + align:start position:0% +gives to to uh Peter um naming him Peter +and saying that he's going to build + + align:start position:0% +and saying that he's going to build + + + align:start position:0% +and saying that he's going to build +because he's the rock on which the + + align:start position:0% +because he's the rock on which the + + + align:start position:0% +because he's the rock on which the +church will be built if we go to the + + align:start position:0% +church will be built if we go to the + + + align:start position:0% +church will be built if we go to the +interior of St Peter's Basilica is in + + align:start position:0% +interior of St Peter's Basilica is in + + + align:start position:0% +interior of St Peter's Basilica is in +the Vatican St Peter's Basilica um we + + align:start position:0% +the Vatican St Peter's Basilica um we + + + align:start position:0% +the Vatican St Peter's Basilica um we +see at the very top um + + align:start position:0% +see at the very top um + + + align:start position:0% +see at the very top um +here inscribed TS Petrus so it's one of + + align:start position:0% +here inscribed TS Petrus so it's one of + + + align:start position:0% +here inscribed TS Petrus so it's one of +the most important um texts in uh here's + + align:start position:0% +the most important um texts in uh here's + + + align:start position:0% +the most important um texts in uh here's +where the um + + align:start position:0% +where the um + + + align:start position:0% +where the um +this wonderfully ugly grotesque altar + + align:start position:0% +this wonderfully ugly grotesque altar + + + align:start position:0% +this wonderfully ugly grotesque altar +where the pope can preach and things + + align:start position:0% +where the pope can preach and things + + + align:start position:0% +where the pope can preach and things +like that and it's right there and the + + align:start position:0% +like that and it's right there and the + + + align:start position:0% +like that and it's right there and the +the idea of who is Peter um in the + + align:start position:0% +the idea of who is Peter um in the + + + align:start position:0% +the idea of who is Peter um in the +Catholic Church anybody who's follows + + align:start position:0% +Catholic Church anybody who's follows + + + align:start position:0% +Catholic Church anybody who's follows +this to the Pope the pope yeah + + align:start position:0% +this to the Pope the pope yeah + + + align:start position:0% +this to the Pope the pope yeah +because according to tradition Jesus + + align:start position:0% +because according to tradition Jesus + + + align:start position:0% +because according to tradition Jesus +gives the keys to heaven to Peter who + + align:start position:0% +gives the keys to heaven to Peter who + + + align:start position:0% +gives the keys to heaven to Peter who +gives it to the second pope who's that + + align:start position:0% +gives it to the second pope who's that + + + align:start position:0% +gives it to the second pope who's that +lenus or something like that who gives + + align:start position:0% +lenus or something like that who gives + + + align:start position:0% +lenus or something like that who gives +it third Pope and it's handed all the + + align:start position:0% +it third Pope and it's handed all the + + + align:start position:0% +it third Pope and it's handed all the +way down and that's why there's the keys + + align:start position:0% +way down and that's why there's the keys + + + align:start position:0% +way down and that's why there's the keys +in the miter of the um symbol of the + + align:start position:0% +in the miter of the um symbol of the + + + align:start position:0% +in the miter of the um symbol of the +Pope because uh Pope is Peter who has + + align:start position:0% +Pope because uh Pope is Peter who has + + + align:start position:0% +Pope because uh Pope is Peter who has +the key to + + align:start position:0% +the key to + + + align:start position:0% +the key to +um so that's that sort of gives + + align:start position:0% +um so that's that sort of gives + + + align:start position:0% +um so that's that sort of gives +something about what the um how this how + + align:start position:0% +something about what the um how this how + + + align:start position:0% +something about what the um how this how +this piece is text or where it comes + + align:start position:0% +this piece is text or where it comes + + + align:start position:0% +this piece is text or where it comes +from but let's listen um let's just + + align:start position:0% +from but let's listen um let's just + + + align:start position:0% +from but let's listen um let's just +listen a little bit more to how the + + align:start position:0% +listen a little bit more to how the + + + align:start position:0% +listen a little bit more to how the +four-part style goes in here and we'll + + align:start position:0% +four-part style goes in here and we'll + + + align:start position:0% +four-part style goes in here and we'll +hear what what's the technique that we + + align:start position:0% +hear what what's the technique that we + + + align:start position:0% +hear what what's the technique that we +heard um we heard a lot of homophony in + + align:start position:0% +heard um we heard a lot of homophony in + + + align:start position:0% +heard um we heard a lot of homophony in +Josan right so these homophonic sections + + align:start position:0% +Josan right so these homophonic sections + + + align:start position:0% +Josan right so these homophonic sections +we've heard earlier what's the other + + align:start position:0% +we've heard earlier what's the other + + + align:start position:0% +we've heard earlier what's the other +thing that Josan does a lot of just + + align:start position:0% +thing that Josan does a lot of just + + + align:start position:0% +thing that Josan does a lot of just +um in terms of how how he brings variety + + align:start position:0% +um in terms of how how he brings variety + + + align:start position:0% +um in terms of how how he brings variety +into a longer piece longer motet like + + align:start position:0% +into a longer piece longer motet like + + + align:start position:0% +into a longer piece longer motet like +the a Maria Faro Serena that we looked + + align:start position:0% +the a Maria Faro Serena that we looked + + + align:start position:0% +the a Maria Faro Serena that we looked +at yeah go like imitation yeah imitation + + align:start position:0% +at yeah go like imitation yeah imitation + + + align:start position:0% +at yeah go like imitation yeah imitation +now how long was it imitation was it + + align:start position:0% +now how long was it imitation was it + + + align:start position:0% +now how long was it imitation was it +like a Kia did it go all the way through + + align:start position:0% +like a Kia did it go all the way through + + + align:start position:0% +like a Kia did it go all the way through +no it yeah we call these things little + + align:start position:0% +no it yeah we call these things little + + + align:start position:0% +no it yeah we call these things little +points of imitation see if there see if + + align:start position:0% +points of imitation see if there see if + + + align:start position:0% +points of imitation see if there see if +you can hear any of these things going + + align:start position:0% +you can hear any of these things going + + + align:start position:0% +you can hear any of these things going +on here there it's not not a huge huge + + align:start position:0% +on here there it's not not a huge huge + + + align:start position:0% +on here there it's not not a huge huge +number because that would be a little + + align:start position:0% +number because that would be a little + + + align:start position:0% +number because that would be a little +Maybe considered too intellectual but + + align:start position:0% +Maybe considered too intellectual but + + + align:start position:0% +Maybe considered too intellectual but +let's let's keep listening for a little + + align:start position:0% +let's let's keep listening for a little + + + align:start position:0% +let's let's keep listening for a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +more measure 20 + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +case + + align:start position:0% +case + + + align:start position:0% +case +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +God + + align:start position:0% +God + + + align:start position:0% +God +[Music] + + align:start position:0% + + + + align:start position:0% + +s do you hear that + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +imitation and again there's that that + + align:start position:0% +imitation and again there's that that + + + align:start position:0% +imitation and again there's that that +cheap form of imitation that we talked + + align:start position:0% +cheap form of imitation that we talked + + + align:start position:0% +cheap form of imitation that we talked +about with jasan where it sounds like + + align:start position:0% +about with jasan where it sounds like + + + align:start position:0% +about with jasan where it sounds like +it's imitation d + + align:start position:0% + + + + align:start position:0% + +da but in fact your other voice has + + align:start position:0% +da but in fact your other voice has + + + align:start position:0% +da but in fact your other voice has +stopped singing by the time you do it so + + align:start position:0% +stopped singing by the time you do it so + + + align:start position:0% +stopped singing by the time you do it so +you don't actually have to write + + align:start position:0% +you don't actually have to write + + + align:start position:0% +you don't actually have to write +Counterpoint against it this is not at + + align:start position:0% +Counterpoint against it this is not at + + + align:start position:0% +Counterpoint against it this is not at +all to say that palestrina or jasan + + align:start position:0% +all to say that palestrina or jasan + + + align:start position:0% +all to say that palestrina or jasan +couldn't have written Counterpoint + + align:start position:0% +couldn't have written Counterpoint + + + align:start position:0% +couldn't have written Counterpoint +against um something that they had just + + align:start position:0% +against um something that they had just + + + align:start position:0% +against um something that they had just +written as a point of invitation but + + align:start position:0% +written as a point of invitation but + + + align:start position:0% +written as a point of invitation but +that this is a way of thinning out the + + align:start position:0% +that this is a way of thinning out the + + + align:start position:0% +that this is a way of thinning out the +texture and making it a little bit + + align:start position:0% +texture and making it a little bit + + + align:start position:0% +texture and making it a little bit +clearer so we'll stop uh listening there + + align:start position:0% +clearer so we'll stop uh listening there + + + align:start position:0% +clearer so we'll stop uh listening there +please listen to the the whole motet or + + align:start position:0% +please listen to the the whole motet or + + + align:start position:0% +please listen to the the whole motet or +the whole first part of the motet that's + + align:start position:0% +the whole first part of the motet that's + + + align:start position:0% +the whole first part of the motet that's +given it's really really beautiful piece + + align:start position:0% +given it's really really beautiful piece + + + align:start position:0% +given it's really really beautiful piece +uh with + + align:start position:0% +uh with + + + align:start position:0% +uh with +palestrina compare this to um maybe to + + align:start position:0% +palestrina compare this to um maybe to + + + align:start position:0% +palestrina compare this to um maybe to +to the tenor lead but especially to + + align:start position:0% +to the tenor lead but especially to + + + align:start position:0% +to the tenor lead but especially to +Tonka VI where we remember we with Tonka + + align:start position:0% +Tonka VI where we remember we with Tonka + + + align:start position:0% +Tonka VI where we remember we with Tonka +VI didn't have the piece in your head + + align:start position:0% +VI didn't have the piece in your head + + + align:start position:0% +VI didn't have the piece in your head +but maybe remember the exercise where we + + align:start position:0% +but maybe remember the exercise where we + + + align:start position:0% +but maybe remember the exercise where we +sang through one of the parts the + + align:start position:0% +sang through one of the parts the + + + align:start position:0% +sang through one of the parts the +soprano and it was very melodic we sang + + align:start position:0% +soprano and it was very melodic we sang + + + align:start position:0% +soprano and it was very melodic we sang +through the tenor it was pretty melodic + + align:start position:0% +through the tenor it was pretty melodic + + + align:start position:0% +through the tenor it was pretty melodic +sang through the alto a little less + + align:start position:0% +sang through the alto a little less + + + align:start position:0% +sang through the alto a little less +melodic and then we sing the bass + + align:start position:0% + + + + align:start position:0% + +right something like that look here how + + align:start position:0% +right something like that look here how + + + align:start position:0% +right something like that look here how +is there differentiation in the voices + + align:start position:0% +is there differentiation in the voices + + + align:start position:0% +is there differentiation in the voices +or actually sorry of course it's a + + align:start position:0% +or actually sorry of course it's a + + + align:start position:0% +or actually sorry of course it's a +contrast of of course a rhetorical + + align:start position:0% +contrast of of course a rhetorical + + + align:start position:0% +contrast of of course a rhetorical +question I hate when I do that no there + + align:start position:0% +question I hate when I do that no there + + + align:start position:0% +question I hate when I do that no there +isn't uh but but let's look specifically + + align:start position:0% +isn't uh but but let's look specifically + + + align:start position:0% +isn't uh but but let's look specifically +at how little differentiation there is I + + align:start position:0% +at how little differentiation there is I + + + align:start position:0% +at how little differentiation there is I +mean if we were to let's let's choose a + + align:start position:0% +mean if we were to let's let's choose a + + + align:start position:0% +mean if we were to let's let's choose a +passage sort of at random and sing sort + + align:start position:0% +passage sort of at random and sing sort + + + align:start position:0% +passage sort of at random and sing sort +of each part of it maybe + + align:start position:0% +of each part of it maybe + + + align:start position:0% +of each part of it maybe +um uh well let's just compare like + + align:start position:0% +um uh well let's just compare like + + + align:start position:0% +um uh well let's just compare like +measure 15 we'll sing the top part um + + align:start position:0% +measure 15 we'll sing the top part um + + + align:start position:0% +measure 15 we'll sing the top part um +we'll sing it on pitch a little bit um + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +probably want to sing that low here + + align:start position:0% +probably want to sing that low here + + + align:start position:0% +probably want to sing that low here +unless you have that high G so + + align:start position:0% + + + + align:start position:0% + +men women up here if anybody wants to go + + align:start position:0% +men women up here if anybody wants to go + + + align:start position:0% +men women up here if anybody wants to go +up here go ahead but ready and um we're + + align:start position:0% +up here go ahead but ready and um we're + + + align:start position:0% +up here go ahead but ready and um we're +starting the final syllable is the traum + + align:start position:0% +starting the final syllable is the traum + + + align:start position:0% +starting the final syllable is the traum +of petrum okay ready + + align:start position:0% + + + + align:start position:0% + +TR + + align:start position:0% + + + + align:start position:0% + +yeah so we have that that + + align:start position:0% + + + + align:start position:0% + +leap kind of a bass like motion but we + + align:start position:0% +leap kind of a bass like motion but we + + + align:start position:0% +leap kind of a bass like motion but we +still have the melodic y now let's look + + align:start position:0% +still have the melodic y now let's look + + + align:start position:0% +still have the melodic y now let's look +at let's do the third part there what + + align:start position:0% +at let's do the third part there what + + + align:start position:0% +at let's do the third part there what +labeled alus and then we'll we'll sing + + align:start position:0% +labeled alus and then we'll we'll sing + + + align:start position:0% +labeled alus and then we'll we'll sing +[Music] + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +yeah so a little uh actually less + + align:start position:0% +yeah so a little uh actually less + + + align:start position:0% +yeah so a little uh actually less +melodic interest maybe but not not huge + + align:start position:0% +melodic interest maybe but not not huge + + + align:start position:0% +melodic interest maybe but not not huge +but you know as after the repeated G's + + align:start position:0% +but you know as after the repeated G's + + + align:start position:0% +but you know as after the repeated G's +then a little bit of motion and let's do + + align:start position:0% +then a little bit of motion and let's do + + + align:start position:0% +then a little bit of motion and let's do +uh let's do the base part um so in base + + align:start position:0% +uh let's do the base part um so in base + + + align:start position:0% +uh let's do the base part um so in base +cluff + + align:start position:0% + + + + align:start position:0% + +everybody actually well actually this + + align:start position:0% +everybody actually well actually this + + + align:start position:0% +everybody actually well actually this +this is also good to biit because due to + + align:start position:0% +this is also good to biit because due to + + + align:start position:0% +this is also good to biit because due to +our Cho choice of octaves most of us + + align:start position:0% +our Cho choice of octaves most of us + + + align:start position:0% +our Cho choice of octaves most of us +will sing the base part above the + + align:start position:0% +will sing the base part above the + + + align:start position:0% +will sing the base part above the +soprano but that's okay he + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +a yeah so maybe I don't know what do you + + align:start position:0% +a yeah so maybe I don't know what do you + + + align:start position:0% +a yeah so maybe I don't know what do you +what what do you think is there any + + align:start position:0% +what what do you think is there any + + + align:start position:0% +what what do you think is there any +differentiation voices is a little lot a + + align:start position:0% +differentiation voices is a little lot a + + + align:start position:0% +differentiation voices is a little lot a +little a little and it's not going to be + + align:start position:0% +little a little and it's not going to be + + + align:start position:0% +little a little and it's not going to be +much ornamentation in the two those + + align:start position:0% +much ornamentation in the two those + + + align:start position:0% +much ornamentation in the two those +parts um yeah let's let's check that + + align:start position:0% +parts um yeah let's let's check that + + + align:start position:0% +parts um yeah let's let's check that +runs the runs happen I think happen + + align:start position:0% +runs the runs happen I think happen + + + align:start position:0% +runs the runs happen I think happen +quite as much yeah boy don't some of us + + align:start position:0% +quite as much yeah boy don't some of us + + + align:start position:0% +quite as much yeah boy don't some of us +wish we were doing a statistical paper + + align:start position:0% +wish we were doing a statistical paper + + + align:start position:0% +wish we were doing a statistical paper +on where the runs happens we actually + + align:start position:0% +on where the runs happens we actually + + + align:start position:0% +on where the runs happens we actually +have as a data set of palestinia writes + + align:start position:0% +have as a data set of palestinia writes + + + align:start position:0% +have as a data set of palestinia writes +104 masses 104 masses and they're all + + align:start position:0% +104 masses 104 masses and they're all + + + align:start position:0% +104 masses 104 masses and they're all +encoded into a computer now so we'd be + + align:start position:0% +encoded into a computer now so we'd be + + + align:start position:0% +encoded into a computer now so we'd be +able to check that but let's let's check + + align:start position:0% +able to check that but let's let's check + + + align:start position:0% +able to check that but let's let's check +let's just compare the number of runs in + + align:start position:0% +let's just compare the number of runs in + + + align:start position:0% +let's just compare the number of runs in +the top um the top part to the base and + + align:start position:0% +the top um the top part to the base and + + + align:start position:0% +the top um the top part to the base and +um so let's let's quickly scan through + + align:start position:0% +um so let's let's quickly scan through + + + align:start position:0% +um so let's let's quickly scan through +that well let's this is a great hypo is + + align:start position:0% +that well let's this is a great hypo is + + + align:start position:0% +that well let's this is a great hypo is +I've never actually thought of this and + + align:start position:0% +I've never actually thought of this and + + + align:start position:0% +I've never actually thought of this and +you you scared me for a second cuz I'm + + align:start position:0% +you you scared me for a second cuz I'm + + + align:start position:0% +you you scared me for a second cuz I'm +like oh shoot but but let's let's figure + + align:start position:0% +like oh shoot but but let's let's figure + + + align:start position:0% +like oh shoot but but let's let's figure +it out so um top actually we'll do this + + align:start position:0% +it out so um top actually we'll do this + + + align:start position:0% +it out so um top actually we'll do this +we'll we'll go in parallel um this side + + align:start position:0% +we'll we'll go in parallel um this side + + + align:start position:0% +we'll we'll go in parallel um this side +of the room count the number of runs in + + align:start position:0% +of the room count the number of runs in + + + align:start position:0% +of the room count the number of runs in +Kus one and we and this side count and + + align:start position:0% +Kus one and we and this side count and + + + align:start position:0% +Kus one and we and this side count and +do the on the base and we'll all come up + + align:start position:0% +do the on the base and we'll all come up + + + align:start position:0% +do the on the base and we'll all come up +with slightly different answers because + + align:start position:0% +with slightly different answers because + + + align:start position:0% +with slightly different answers because +some of us will consider some things a + + align:start position:0% +some of us will consider some things a + + + align:start position:0% +some of us will consider some things a +run and some things not but um when you + + align:start position:0% +run and some things not but um when you + + + align:start position:0% +run and some things not but um when you +have it just jot it down on a piece of + + align:start position:0% +have it just jot it down on a piece of + + + align:start position:0% +have it just jot it down on a piece of +paper and then we'll get the numbers um + + align:start position:0% +paper and then we'll get the numbers um + + + align:start position:0% +paper and then we'll get the numbers um +I like this kind of Hands-On + + align:start position:0% +I like this kind of Hands-On + + + align:start position:0% +I like this kind of Hands-On +[Applause] + + align:start position:0% + + + + align:start position:0% + +thing + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +do we got it something like that how how + + align:start position:0% +do we got it something like that how how + + + align:start position:0% +do we got it something like that how how +many do you have for the top part I have + + align:start position:0% +many do you have for the top part I have + + + align:start position:0% +many do you have for the top part I have +seven how many do you have eight nine + + align:start position:0% +seven how many do you have eight nine + + + align:start position:0% +seven how many do you have eight nine +nine I got nine but I I think we might + + align:start position:0% +nine I got nine but I I think we might + + + align:start position:0% +nine I got nine but I I think we might +be very generous in what we consider a + + align:start position:0% +be very generous in what we consider a + + + align:start position:0% +be very generous in what we consider a +rod uh go ahead um I was a little + + align:start position:0% +rod uh go ahead um I was a little + + + align:start position:0% +rod uh go ahead um I was a little +conservative but I got three three three + + align:start position:0% +conservative but I got three three three + + + align:start position:0% +conservative but I got three three three +yeah that's that's like yeah so there + + align:start position:0% +yeah that's that's like yeah so there + + + align:start position:0% +yeah that's that's like yeah so there +eight also in the second voice too okay + + align:start position:0% +eight also in the second voice too okay + + + align:start position:0% +eight also in the second voice too okay +well yeah so so we can um + + align:start position:0% +well yeah so so we can um + + + align:start position:0% +well yeah so so we can um +yeah and we could probably go through + + align:start position:0% +yeah and we could probably go through + + + align:start position:0% +yeah and we could probably go through +all them but it looks like uh looks like + + align:start position:0% +all them but it looks like uh looks like + + + align:start position:0% +all them but it looks like uh looks like +Dave's at least our very small + + align:start position:0% +Dave's at least our very small + + + align:start position:0% +Dave's at least our very small +unscientific survey of One Piece uh + + align:start position:0% +unscientific survey of One Piece uh + + + align:start position:0% +unscientific survey of One Piece uh +there's there's something to that + + align:start position:0% +there's there's something to that + + + align:start position:0% +there's there's something to that +intuition that there are still runs so + + align:start position:0% +intuition that there are still runs so + + + align:start position:0% +intuition that there are still runs so +so that in the bottom part um but there + + align:start position:0% +so that in the bottom part um but there + + + align:start position:0% +so that in the bottom part um but there +there is some differentiation of voices + + align:start position:0% +there is some differentiation of voices + + + align:start position:0% +there is some differentiation of voices +maybe not a huge huge slot let's let's + + align:start position:0% +maybe not a huge huge slot let's let's + + + align:start position:0% +maybe not a huge huge slot let's let's +turn our attention to a completely + + align:start position:0% +turn our attention to a completely + + + align:start position:0% +turn our attention to a completely +different piece that has no relation to + + align:start position:0% +different piece that has no relation to + + + align:start position:0% +different piece that has no relation to +what we just heard maybe or maybe not + + align:start position:0% +what we just heard maybe or maybe not + + + align:start position:0% +what we just heard maybe or maybe not +and listen to the cirer of the strangely + + align:start position:0% +and listen to the cirer of the strangely + + + align:start position:0% +and listen to the cirer of the strangely +named missa 2s petus so go ahead + + align:start position:0% +named missa 2s petus so go ahead + + + align:start position:0% +named missa 2s petus so go ahead +continue ahead this is um written or + + align:start position:0% +continue ahead this is um written or + + + align:start position:0% +continue ahead this is um written or +published about about 15 years later + + align:start position:0% +published about about 15 years later + + + align:start position:0% +published about about 15 years later +here we + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% +go + + + align:start position:0% +go +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay the Fade's not really working today + + align:start position:0% +okay the Fade's not really working today + + + align:start position:0% +okay the Fade's not really working today +but + + align:start position:0% +but + + + align:start position:0% +but +um let me say a little bit do you hear a + + align:start position:0% +um let me say a little bit do you hear a + + + align:start position:0% +um let me say a little bit do you hear a +relation besides the relation of of + + align:start position:0% +relation besides the relation of of + + + align:start position:0% +relation besides the relation of of +singing slower in one to yeah um let me + + align:start position:0% +singing slower in one to yeah um let me + + + align:start position:0% +singing slower in one to yeah um let me +say a little bit about about some of the + + align:start position:0% +say a little bit about about some of the + + + align:start position:0% +say a little bit about about some of the +things so what what do we do how do we + + align:start position:0% +things so what what do we do how do we + + + align:start position:0% +things so what what do we do how do we +take uh aonic motet and make the opening + + align:start position:0% +take uh aonic motet and make the opening + + + align:start position:0% +take uh aonic motet and make the opening +of a curier one thing you might um see + + align:start position:0% +of a curier one thing you might um see + + + align:start position:0% +of a curier one thing you might um see +is what do we do we take these top three + + align:start position:0% +is what do we do we take these top three + + + align:start position:0% +is what do we do we take these top three +voices at the beginning we have this + + align:start position:0% +voices at the beginning we have this + + + align:start position:0% +voices at the beginning we have this +High clear section and we move this + + align:start position:0% +High clear section and we move this + + + align:start position:0% +High clear section and we move this +voice the third voice here down to the + + align:start position:0% +voice the third voice here down to the + + + align:start position:0% +voice the third voice here down to the +bottom + + align:start position:0% +bottom + + + align:start position:0% +bottom +part and what else do we do we swap + + align:start position:0% +part and what else do we do we swap + + + align:start position:0% +part and what else do we do we swap +these two voices here and that's that's + + align:start position:0% +these two voices here and that's that's + + + align:start position:0% +these two voices here and that's that's +kind of an interesting reason what uh uh + + align:start position:0% +kind of an interesting reason what uh uh + + + align:start position:0% +kind of an interesting reason what uh uh +just one just one second on this um we + + align:start position:0% +just one just one second on this um we + + + align:start position:0% +just one just one second on this um we +swap them + + align:start position:0% + + + + align:start position:0% + +and then we also obviously because + + align:start position:0% +and then we also obviously because + + + align:start position:0% +and then we also obviously because +there's kir has a different accent + + align:start position:0% +there's kir has a different accent + + + align:start position:0% +there's kir has a different accent +structure than two ESP Petrus you're + + align:start position:0% +structure than two ESP Petrus you're + + + align:start position:0% +structure than two ESP Petrus you're +going to break up some of the notes + + align:start position:0% +going to break up some of the notes + + + align:start position:0% +going to break up some of the notes +there's also um perhaps responding to + + align:start position:0% +there's also um perhaps responding to + + + align:start position:0% +there's also um perhaps responding to +criticism that there wasn't W enough + + align:start position:0% +criticism that there wasn't W enough + + + align:start position:0% +criticism that there wasn't W enough +runs in the base uh we have things like + + align:start position:0% +runs in the base uh we have things like + + + align:start position:0% +runs in the base uh we have things like +the pet Truse gets filled in as as a + + align:start position:0% +the pet Truse gets filled in as as a + + + align:start position:0% +the pet Truse gets filled in as as a +runwood who knows why why these things + + align:start position:0% +runwood who knows why why these things + + + align:start position:0% +runwood who knows why why these things +happen um wouldn't it be great to know + + align:start position:0% +happen um wouldn't it be great to know + + + align:start position:0% +happen um wouldn't it be great to know +to look through like all I mean we've + + align:start position:0% +to look through like all I mean we've + + + align:start position:0% +to look through like all I mean we've +encoded 104 I haven't uh somebody has + + align:start position:0% +encoded 104 I haven't uh somebody has + + + align:start position:0% +encoded 104 I haven't uh somebody has +encoded a 104 palestin masses to start + + align:start position:0% +encoded a 104 palestin masses to start + + + align:start position:0% +encoded a 104 palestin masses to start +encoding the motets and then be able to + + align:start position:0% +encoding the motets and then be able to + + + align:start position:0% +encoding the motets and then be able to +figure out how in each case that there's + + align:start position:0% +figure out how in each case that there's + + + align:start position:0% +figure out how in each case that there's +a a a borrowing and maybe there are even + + align:start position:0% +a a a borrowing and maybe there are even + + + align:start position:0% +a a a borrowing and maybe there are even +ones that we don't know about yet so so + + align:start position:0% +ones that we don't know about yet so so + + + align:start position:0% +ones that we don't know about yet so so +there's a lot of work so we done Davey + + align:start position:0% +there's a lot of work so we done Davey + + + align:start position:0% +there's a lot of work so we done Davey +um the in when the lowest three parts + + align:start position:0% +um the in when the lowest three parts + + + align:start position:0% +um the in when the lowest three parts +come in in the mad they come in in the + + align:start position:0% +come in in the mad they come in in the + + + align:start position:0% +come in in the mad they come in in the +same uh they are imitating the top three + + align:start position:0% +same uh they are imitating the top three + + + align:start position:0% +same uh they are imitating the top three +parts and they have the same um relation + + align:start position:0% +parts and they have the same um relation + + + align:start position:0% +parts and they have the same um relation +to the top three parts as they do in the + + align:start position:0% +to the top three parts as they do in the + + + align:start position:0% +to the top three parts as they do in the +mass so it's basically exactly imitating + + align:start position:0% +mass so it's basically exactly imitating + + + align:start position:0% +mass so it's basically exactly imitating +the motet from measure seven on from + + align:start position:0% +the motet from measure seven on from + + + align:start position:0% +the motet from measure seven on from +measure seven on measure seven on if you + + align:start position:0% +measure seven on measure seven on if you + + + align:start position:0% +measure seven on measure seven on if you +look at measure seven it's just filled + + align:start position:0% +look at measure seven it's just filled + + + align:start position:0% +look at measure seven it's just filled +in + + align:start position:0% +in + + + align:start position:0% +in +Things 2 three four five six seven for + + align:start position:0% +Things 2 three four five six seven for + + + align:start position:0% +Things 2 three four five six seven for +measure seven on it's utting what part + + align:start position:0% +measure seven on it's utting what part + + + align:start position:0% +measure seven on it's utting what part +of the of the mot let's just make sure + + align:start position:0% +of the of the mot let's just make sure + + + align:start position:0% +of the of the mot let's just make sure +we all have there only three parts in + + align:start position:0% +we all have there only three parts in + + + align:start position:0% +we all have there only three parts in +that part of the Mot three in the you + + align:start position:0% +that part of the Mot three in the you + + + align:start position:0% +that part of the Mot three in the you +have three topes and then you have they + + align:start position:0% +have three topes and then you have they + + + align:start position:0% +have three topes and then you have they +come in for six measures and you have + + align:start position:0% +come in for six measures and you have + + + align:start position:0% +come in for six measures and you have +the bottes and they come in for six me + + align:start position:0% +the bottes and they come in for six me + + + align:start position:0% +the bottes and they come in for six me +can you say a little bit more slowly for + + align:start position:0% +can you say a little bit more slowly for + + + align:start position:0% +can you say a little bit more slowly for +everybody because I've uh from measures + + align:start position:0% +everybody because I've uh from measures + + + align:start position:0% +everybody because I've uh from measures +seven of the Cur of the mass of the + + align:start position:0% +seven of the Cur of the mass of the + + + align:start position:0% +seven of the Cur of the mass of the +seven of the mve 1 2 3 4 5 6 7even uhhuh + + align:start position:0% +seven of the mve 1 2 3 4 5 6 7even uhhuh + + + align:start position:0% +seven of the mve 1 2 3 4 5 6 7even uhhuh +um uh so the second system to um uh + + align:start position:0% +um uh so the second system to um uh + + + align:start position:0% +um uh so the second system to um uh +measure 12 it's roughly imitating um the + + align:start position:0% +measure 12 it's roughly imitating um the + + + align:start position:0% +measure 12 it's roughly imitating um the +opening of the mass is roughly IM those + + align:start position:0% +opening of the mass is roughly IM those + + + align:start position:0% +opening of the mass is roughly IM those +that sequence of measures so there's + + align:start position:0% +that sequence of measures so there's + + + align:start position:0% +that sequence of measures so there's +another way we can look at that as + + align:start position:0% +another way we can look at that as + + + align:start position:0% +another way we can look at that as +missing the first six measures of the + + align:start position:0% +missing the first six measures of the + + + align:start position:0% +missing the first six measures of the +piece and starting on measure seven yeah + + align:start position:0% +piece and starting on measure seven yeah + + + align:start position:0% +piece and starting on measure seven yeah +because it's basically the same the the + + align:start position:0% +because it's basically the same the the + + + align:start position:0% +because it's basically the same the the +second six measure is the same as the + + align:start position:0% +second six measure is the same as the + + + align:start position:0% +second six measure is the same as the +first six measure only the Shuff right + + align:start position:0% +first six measure only the Shuff right + + + align:start position:0% +first six measure only the Shuff right +but what happens in the what happens in + + align:start position:0% +but what happens in the what happens in + + + align:start position:0% +but what happens in the what happens in +the um in the mass in measure three here + + align:start position:0% +the um in the mass in measure three here + + + align:start position:0% +the um in the mass in measure three here +just + + align:start position:0% +just + + + align:start position:0% +just +as uh you get the the first three + + align:start position:0% +as uh you get the the first three + + + align:start position:0% +as uh you get the the first three +measures only in fact in fact this is a + + align:start position:0% +measures only in fact in fact this is a + + + align:start position:0% +measures only in fact in fact this is a +bad uh example cuz it doesn't it makes + + align:start position:0% +bad uh example cuz it doesn't it makes + + + align:start position:0% +bad uh example cuz it doesn't it makes +it look like nothing happens like + + align:start position:0% +it look like nothing happens like + + + align:start position:0% +it look like nothing happens like +nothing enters in measure um measure + + align:start position:0% +nothing enters in measure um measure + + + align:start position:0% +nothing enters in measure um measure +four confuse that yeah so what what do + + align:start position:0% +four confuse that yeah so what what do + + + align:start position:0% +four confuse that yeah so what what do +we have there that's exact + + align:start position:0% +we have there that's exact + + + align:start position:0% +we have there that's exact +Canon not exact not exactly + + align:start position:0% +Canon not exact not exactly + + + align:start position:0% +Canon not exact not exactly +well the first two measures it's + + align:start position:0% + + + + align:start position:0% + +exact so we have this the opening of the + + align:start position:0% +exact so we have this the opening of the + + + align:start position:0% +exact so we have this the opening of the +the lower three Parts becomes the + + align:start position:0% +the lower three Parts becomes the + + + align:start position:0% +the lower three Parts becomes the +section of the top three parts right + + align:start position:0% +section of the top three parts right + + + align:start position:0% +section of the top three parts right +becomes top three parts he still + + align:start position:0% +becomes top three parts he still + + + align:start position:0% +becomes top three parts he still +cheating sort of because pet out well + + align:start position:0% +cheating sort of because pet out well + + + align:start position:0% +cheating sort of because pet out well +right + + align:start position:0% +right + + + align:start position:0% +right +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +but okay okay let's recover recover + + align:start position:0% +but okay okay let's recover recover + + + align:start position:0% +but okay okay let's recover recover +recover we got to move on um yeah but + + align:start position:0% +recover we got to move on um yeah but + + + align:start position:0% +recover we got to move on um yeah but +one of the things that's interesting + + align:start position:0% +one of the things that's interesting + + + align:start position:0% +one of the things that's interesting +about that does this texture occur in + + align:start position:0% +about that does this texture occur in + + + align:start position:0% +about that does this texture occur in +the mot composed first and the fact that + + align:start position:0% +the mot composed first and the fact that + + + align:start position:0% +the mot composed first and the fact that +he's able to do this have the the three + + align:start position:0% +he's able to do this have the the three + + + align:start position:0% +he's able to do this have the the three +parts work against + + align:start position:0% +parts work against + + + align:start position:0% +parts work against +themselves that is to say sound at the + + align:start position:0% +themselves that is to say sound at the + + + align:start position:0% +themselves that is to say sound at the +same time as their opening even if he + + align:start position:0% +same time as their opening even if he + + + align:start position:0% +same time as their opening even if he +has to let it Peter out after a little + + align:start position:0% +has to let it Peter out after a little + + + align:start position:0% +has to let it Peter out after a little +bit that's still um that still says + + align:start position:0% +bit that's still um that still says + + + align:start position:0% +bit that's still um that still says +something about I don't know the kind of + + align:start position:0% +something about I don't know the kind of + + + align:start position:0% +something about I don't know the kind of +contrapuntal thinking that's going on + + align:start position:0% +contrapuntal thinking that's going on + + + align:start position:0% +contrapuntal thinking that's going on +here um + + align:start position:0% +here um + + + align:start position:0% +here um +palestrina's contrapuntal writing the + + align:start position:0% +palestrina's contrapuntal writing the + + + align:start position:0% +palestrina's contrapuntal writing the +way that he structures voices against + + align:start position:0% +way that he structures voices against + + + align:start position:0% +way that he structures voices against +each other became sort of the norm of um + + align:start position:0% +each other became sort of the norm of um + + + align:start position:0% +each other became sort of the norm of um +music pedagogy later that is to say that + + align:start position:0% +music pedagogy later that is to say that + + + align:start position:0% +music pedagogy later that is to say that +this was considered such the perfect way + + align:start position:0% +this was considered such the perfect way + + + align:start position:0% +this was considered such the perfect way +to write Counterpoint that if you've + + align:start position:0% +to write Counterpoint that if you've + + + align:start position:0% +to write Counterpoint that if you've +taken um species Counterpoint um + + align:start position:0% +taken um species Counterpoint um + + + align:start position:0% +taken um species Counterpoint um +Sometimes some of you in the 301 in the + + align:start position:0% +Sometimes some of you in the 301 in the + + + align:start position:0% +Sometimes some of you in the 301 in the +first year um Theory class do a little + + align:start position:0% +first year um Theory class do a little + + + align:start position:0% +first year um Theory class do a little +bit of this this is a musical style + + align:start position:0% +bit of this this is a musical style + + + align:start position:0% +bit of this this is a musical style +derived from not exactly but a lot of + + align:start position:0% +derived from not exactly but a lot of + + + align:start position:0% +derived from not exactly but a lot of +the the um the music of palestrina and + + align:start position:0% +the the um the music of palestrina and + + + align:start position:0% +the the um the music of palestrina and +so he sort of considered this pure music + + align:start position:0% +so he sort of considered this pure music + + + align:start position:0% +so he sort of considered this pure music +ideal um later we would call what + + align:start position:0% +ideal um later we would call what + + + align:start position:0% +ideal um later we would call what +palestrina the style that palestrina + + align:start position:0% +palestrina the style that palestrina + + + align:start position:0% +palestrina the style that palestrina +poses in uh the Prima practica the first + + align:start position:0% +poses in uh the Prima practica the first + + + align:start position:0% +poses in uh the Prima practica the first +practice of music as um obviously he + + align:start position:0% +practice of music as um obviously he + + + align:start position:0% +practice of music as um obviously he +didn't call it that because he didn't + + align:start position:0% +didn't call it that because he didn't + + + align:start position:0% +didn't call it that because he didn't +realize that there would later be a + + align:start position:0% +realize that there would later be a + + + align:start position:0% +realize that there would later be a +secunda practica a second practice that + + align:start position:0% +secunda practica a second practice that + + + align:start position:0% +secunda practica a second practice that +we'll get to toward the end of the + + align:start position:0% +we'll get to toward the end of the + + + align:start position:0% +we'll get to toward the end of the +semester but these are terms that you'll + + align:start position:0% +semester but these are terms that you'll + + + align:start position:0% +semester but these are terms that you'll +see come up um often with with + + align:start position:0% +see come up um often with with + + + align:start position:0% +see come up um often with with +palestrina you'll also hear sometimes + + align:start position:0% +palestrina you'll also hear sometimes + + + align:start position:0% +palestrina you'll also hear sometimes +the term stil Antico the ancient style + + align:start position:0% +the term stil Antico the ancient style + + + align:start position:0% +the term stil Antico the ancient style +which of course he didn't consider + + align:start position:0% +which of course he didn't consider + + + align:start position:0% +which of course he didn't consider +himself the stano anymore than the + + align:start position:0% +himself the stano anymore than the + + + align:start position:0% +himself the stano anymore than the +arantia consider themselves the ARs + + align:start position:0% +arantia consider themselves the ARs + + + align:start position:0% +arantia consider themselves the ARs +Antigua compared to the ARs Nova right + + align:start position:0% +Antigua compared to the ARs Nova right + + + align:start position:0% +Antigua compared to the ARs Nova right +so all these terms anytime you hear a + + align:start position:0% +so all these terms anytime you hear a + + + align:start position:0% +so all these terms anytime you hear a +term that says somebody is old they + + align:start position:0% +term that says somebody is old they + + + align:start position:0% +term that says somebody is old they +probably thought of themselves as pretty + + align:start position:0% +probably thought of themselves as pretty + + + align:start position:0% +probably thought of themselves as pretty +new at the + + align:start position:0% +new at the + + + align:start position:0% +new at the +time questions about what we're doing + + align:start position:0% +time questions about what we're doing + + + align:start position:0% +time questions about what we're doing +with + + align:start position:0% + + + + align:start position:0% + +this okay we're actually making pretty + + align:start position:0% +this okay we're actually making pretty + + + align:start position:0% +this okay we're actually making pretty +good time I think we might actually get + + align:start position:0% +good time I think we might actually get + + + align:start position:0% +good time I think we might actually get +to um most of the things on the syllabus + + align:start position:0% +to um most of the things on the syllabus + + + align:start position:0% +to um most of the things on the syllabus +that say um if time maybe + + align:start position:0% + + + + align:start position:0% + +we've just listened to a really a purely + + align:start position:0% +we've just listened to a really a purely + + + align:start position:0% +we've just listened to a really a purely +vocal style I mean something that's very + + align:start position:0% +vocal style I mean something that's very + + + align:start position:0% +vocal style I mean something that's very +much designed for voice but um we've + + align:start position:0% +much designed for voice but um we've + + + align:start position:0% +much designed for voice but um we've +talked only a little bit in this class + + align:start position:0% +talked only a little bit in this class + + + align:start position:0% +talked only a little bit in this class +about some of the things that were + + align:start position:0% +about some of the things that were + + + align:start position:0% +about some of the things that were +happening in um in instruments and + + align:start position:0% +happening in um in instruments and + + + align:start position:0% +happening in um in instruments and +things and so I want to say a little bit + + align:start position:0% +things and so I want to say a little bit + + + align:start position:0% +things and so I want to say a little bit +about instrumental music in general at + + align:start position:0% +about instrumental music in general at + + + align:start position:0% +about instrumental music in general at +the um as before getting and looking at + + align:start position:0% +the um as before getting and looking at + + + align:start position:0% +the um as before getting and looking at +certain specific instrumental Pieces by + + align:start position:0% +certain specific instrumental Pieces by + + + align:start position:0% +certain specific instrumental Pieces by +Michael pretorius uh what we have have + + align:start position:0% +Michael pretorius uh what we have have + + + align:start position:0% +Michael pretorius uh what we have have +here is uh a very beautiful book uh + + align:start position:0% +here is uh a very beautiful book uh + + + align:start position:0% +here is uh a very beautiful book uh +which I'll pass around fact simil of + + align:start position:0% +which I'll pass around fact simil of + + + align:start position:0% +which I'll pass around fact simil of +here it's a collection of + + align:start position:0% +here it's a collection of + + + align:start position:0% +here it's a collection of +dances and uh this particular collection + + align:start position:0% +dances and uh this particular collection + + + align:start position:0% +dances and uh this particular collection +was G to be given as a gift to margarit + + align:start position:0% +was G to be given as a gift to margarit + + + align:start position:0% +was G to be given as a gift to margarit +of Austria but um she was currently in + + align:start position:0% +of Austria but um she was currently in + + + align:start position:0% +of Austria but um she was currently in +morning and so it was considered + + align:start position:0% +morning and so it was considered + + + align:start position:0% +morning and so it was considered +inappropriate to give a book of dances + + align:start position:0% +inappropriate to give a book of dances + + + align:start position:0% +inappropriate to give a book of dances +to somebody in morning unless you dyed + + align:start position:0% +to somebody in morning unless you dyed + + + align:start position:0% +to somebody in morning unless you dyed +all the paper uh black and then wrote + + align:start position:0% +all the paper uh black and then wrote + + + align:start position:0% +all the paper uh black and then wrote +instead in gold and silver um to put in + + align:start position:0% +instead in gold and silver um to put in + + + align:start position:0% +instead in gold and silver um to put in +all the notes it's a really beautiful + + align:start position:0% +all the notes it's a really beautiful + + + align:start position:0% +all the notes it's a really beautiful +book I'll pass it around in a second um + + align:start position:0% +book I'll pass it around in a second um + + + align:start position:0% +book I'll pass it around in a second um +but to say that doesn't really look like + + align:start position:0% +but to say that doesn't really look like + + + align:start position:0% +but to say that doesn't really look like +a great Melody you'd want to sing from + + align:start position:0% +a great Melody you'd want to sing from + + + align:start position:0% +a great Melody you'd want to sing from +does it I mean you can just hear if + + align:start position:0% +does it I mean you can just hear if + + + align:start position:0% +does it I mean you can just hear if +that's C what's the first note + + align:start position:0% +that's C what's the first note + + + align:start position:0% +that's C what's the first note +there f f so something like + + align:start position:0% +there f f so something like + + + align:start position:0% +there f f so something like +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +f it's not exact the greatest Melody + + align:start position:0% +f it's not exact the greatest Melody + + + align:start position:0% +f it's not exact the greatest Melody +ever instead um what we get from this + + align:start position:0% +ever instead um what we get from this + + + align:start position:0% +ever instead um what we get from this +term boss dances these + + align:start position:0% +term boss dances these + + + align:start position:0% +term boss dances these +were these were interesting what we + + align:start position:0% +were these were interesting what we + + + align:start position:0% +were these were interesting what we +might call still from the class teners + + align:start position:0% +might call still from the class teners + + + align:start position:0% +might call still from the class teners +these were interesting lower parts to be + + align:start position:0% +these were interesting lower parts to be + + + align:start position:0% +these were interesting lower parts to be +um to be performed and above it + + align:start position:0% +um to be performed and above it + + + align:start position:0% +um to be performed and above it +instrumentalists would improvise we've + + align:start position:0% +instrumentalists would improvise we've + + + align:start position:0% +instrumentalists would improvise we've +seen a number of times in this class + + align:start position:0% +seen a number of times in this class + + + align:start position:0% +seen a number of times in this class +pictures of people playing instruments + + align:start position:0% +pictures of people playing instruments + + + align:start position:0% +pictures of people playing instruments +and the one thing that they generally + + align:start position:0% +and the one thing that they generally + + + align:start position:0% +and the one thing that they generally +have in common is they're not saying + + align:start position:0% +have in common is they're not saying + + + align:start position:0% +have in common is they're not saying +they're looking at music oops + + align:start position:0% +they're looking at music oops + + + align:start position:0% +they're looking at music oops +we'll look for viruses later + + align:start position:0% +we'll look for viruses later + + + align:start position:0% +we'll look for viruses later +um and this this book tends to say + + align:start position:0% +um and this this book tends to say + + + align:start position:0% +um and this this book tends to say +things like um well in this case um what + + align:start position:0% +things like um well in this case um what + + + align:start position:0% +things like um well in this case um what +is this uh + + align:start position:0% +is this uh + + + align:start position:0% +is this uh +Venice name of a dance in LV i i i in uh + + align:start position:0% +Venice name of a dance in LV i i i in uh + + + align:start position:0% +Venice name of a dance in LV i i i in uh +55 58 notes and six measures um + + align:start position:0% +55 58 notes and six measures um + + + align:start position:0% +55 58 notes and six measures um +everything perfect as you can see and so + + align:start position:0% +everything perfect as you can see and so + + + align:start position:0% +everything perfect as you can see and so +always for some reason always always + + align:start position:0% +always for some reason always always + + + align:start position:0% +always for some reason always always +says you know the the beautiful saying + + align:start position:0% +says you know the the beautiful saying + + + align:start position:0% +says you know the the beautiful saying +in the number of notes and the number of + + align:start position:0% +in the number of notes and the number of + + + align:start position:0% +in the number of notes and the number of +measures as you can see so that might + + align:start position:0% +measures as you can see so that might + + + align:start position:0% +measures as you can see so that might +give you some idea of you know trying to + + align:start position:0% +give you some idea of you know trying to + + + align:start position:0% +give you some idea of you know trying to +plan this the extent of a dance + + align:start position:0% +plan this the extent of a dance + + + align:start position:0% +plan this the extent of a dance +something like that and then below it + + align:start position:0% +something like that and then below it + + + align:start position:0% +something like that and then below it +there are all these things here there's + + align:start position:0% +there are all these things here there's + + + align:start position:0% +there are all these things here there's +a um I think that's a r b SS D D D D D + + align:start position:0% +a um I think that's a r b SS D D D D D + + + align:start position:0% +a um I think that's a r b SS D D D D D +SS r r r r and I used to know what all + + align:start position:0% +SS r r r r and I used to know what all + + + align:start position:0% +SS r r r r and I used to know what all +these things were but these were the + + align:start position:0% +these things were but these were the + + + align:start position:0% +these things were but these were the +particular dance steps that um that you + + align:start position:0% +particular dance steps that um that you + + + align:start position:0% +particular dance steps that um that you +would do at the time so you'd always + + align:start position:0% +would do at the time so you'd always + + + align:start position:0% +would do at the time so you'd always +begin with a bow and then it would tell + + align:start position:0% +begin with a bow and then it would tell + + + align:start position:0% +begin with a bow and then it would tell +you to do some kind of movement forward + + align:start position:0% +you to do some kind of movement forward + + + align:start position:0% +you to do some kind of movement forward +and movement forward and then double + + align:start position:0% +and movement forward and then double + + + align:start position:0% +and movement forward and then double +backwards and stuff and you can kind of + + align:start position:0% +backwards and stuff and you can kind of + + + align:start position:0% +backwards and stuff and you can kind of +figure out what the movements are based + + align:start position:0% +figure out what the movements are based + + + align:start position:0% +figure out what the movements are based +on which one of them is always accur in + + align:start position:0% +on which one of them is always accur in + + + align:start position:0% +on which one of them is always accur in +pairs or you know which ones occur in + + align:start position:0% +pairs or you know which ones occur in + + + align:start position:0% +pairs or you know which ones occur in +triplets things like that it's a really + + align:start position:0% +triplets things like that it's a really + + + align:start position:0% +triplets things like that it's a really +really interesting collection and we + + align:start position:0% +really interesting collection and we + + + align:start position:0% +really interesting collection and we +have um we have also dance treates + + align:start position:0% +have um we have also dance treates + + + align:start position:0% +have um we have also dance treates +people who study dance history can can + + align:start position:0% +people who study dance history can can + + + align:start position:0% +people who study dance history can can +work with you if you're ever interested + + align:start position:0% +work with you if you're ever interested + + + align:start position:0% +work with you if you're ever interested +in sort of having your own Renaissance + + align:start position:0% +in sort of having your own Renaissance + + + align:start position:0% +in sort of having your own Renaissance +dance party and you can you can + + align:start position:0% +dance party and you can you can + + + align:start position:0% +dance party and you can you can +basically um you can look at some of the + + align:start position:0% +basically um you can look at some of the + + + align:start position:0% +basically um you can look at some of the +um the the things that we're going to be + + align:start position:0% +um the the things that we're going to be + + + align:start position:0% +um the the things that we're going to be +looking at with the pretorius which is + + align:start position:0% +looking at with the pretorius which is + + + align:start position:0% +looking at with the pretorius which is +and um and other sort of Music at the + + align:start position:0% +and um and other sort of Music at the + + + align:start position:0% +and um and other sort of Music at the +time to try to figure out what you might + + align:start position:0% +time to try to figure out what you might + + + align:start position:0% +time to try to figure out what you might +improvise above these but I'll pass this + + align:start position:0% +improvise above these but I'll pass this + + + align:start position:0% +improvise above these but I'll pass this +around for now this is some idea of + + align:start position:0% +around for now this is some idea of + + + align:start position:0% +around for now this is some idea of +instrumental music what other pieces for + + align:start position:0% +instrumental music what other pieces for + + + align:start position:0% +instrumental music what other pieces for +instruments that we looked at we looked + + align:start position:0% +instruments that we looked at we looked + + + align:start position:0% +instruments that we looked at we looked +at the Tonia Viv because that originally + + align:start position:0% +at the Tonia Viv because that originally + + + align:start position:0% +at the Tonia Viv because that originally +started off as a purely vocal piece four + + align:start position:0% +started off as a purely vocal piece four + + + align:start position:0% +started off as a purely vocal piece four +four voices and then we saw it we heard + + align:start position:0% +four voices and then we saw it we heard + + + align:start position:0% +four voices and then we saw it we heard +it for four voices and loot but we + + align:start position:0% +it for four voices and loot but we + + + align:start position:0% +it for four voices and loot but we +didn't really study that we heard it for + + align:start position:0% +didn't really study that we heard it for + + + align:start position:0% +didn't really study that we heard it for +a solo voice and a solo Loot and then we + + align:start position:0% +a solo voice and a solo Loot and then we + + + align:start position:0% +a solo voice and a solo Loot and then we +saw it for keyboard yeah for solo + + align:start position:0% +saw it for keyboard yeah for solo + + + align:start position:0% +saw it for keyboard yeah for solo +keyboard instrument so um remember with + + align:start position:0% +keyboard instrument so um remember with + + + align:start position:0% +keyboard instrument so um remember with +the keyboard music and stuff like that + + align:start position:0% +the keyboard music and stuff like that + + + align:start position:0% +the keyboard music and stuff like that +there was it was written out with a lot + + align:start position:0% +there was it was written out with a lot + + + align:start position:0% +there was it was written out with a lot +of um ornamentation a lot of of things + + align:start position:0% +of um ornamentation a lot of of things + + + align:start position:0% +of um ornamentation a lot of of things +like like that a lot of um ways of + + align:start position:0% +like like that a lot of um ways of + + + align:start position:0% +like like that a lot of um ways of +decorating the + + align:start position:0% +decorating the + + + align:start position:0% +decorating the +music um so let's but let's look at + + align:start position:0% +music um so let's but let's look at + + + align:start position:0% +music um so let's but let's look at +another collection of music and I think + + align:start position:0% +another collection of music and I think + + + align:start position:0% +another collection of music and I think +of instrumental music I find it really + + align:start position:0% +of instrumental music I find it really + + + align:start position:0% +of instrumental music I find it really +interesting this is Michael pretorius + + align:start position:0% +interesting this is Michael pretorius + + + align:start position:0% +interesting this is Michael pretorius +who would probably possibly uh run and + + align:start position:0% +who would probably possibly uh run and + + + align:start position:0% +who would probably possibly uh run and +hide his head in shame if he knew that + + align:start position:0% +hide his head in shame if he knew that + + + align:start position:0% +hide his head in shame if he knew that +we were studying him entirely for this + + align:start position:0% +we were studying him entirely for this + + + align:start position:0% +we were studying him entirely for this +one little throwaway thing he did uh + + align:start position:0% +one little throwaway thing he did uh + + + align:start position:0% +one little throwaway thing he did uh +toward the end of his life called turp + + align:start position:0% +toward the end of his life called turp + + + align:start position:0% +toward the end of his life called turp +sicker his only collection of + + align:start position:0% +sicker his only collection of + + + align:start position:0% +sicker his only collection of +instrumental music but it stands as one + + align:start position:0% +instrumental music but it stands as one + + + align:start position:0% +instrumental music but it stands as one +of the very few collections of + + align:start position:0% +of the very few collections of + + + align:start position:0% +of the very few collections of +instrumental music in general of this + + align:start position:0% +instrumental music in general of this + + + align:start position:0% +instrumental music in general of this +period um so go ahead and grab that out + + align:start position:0% +period um so go ahead and grab that out + + + align:start position:0% +period um so go ahead and grab that out +while I see where I threw + + align:start position:0% +while I see where I threw + + + align:start position:0% +while I see where I threw +it my copy ah here we + + align:start position:0% +it my copy ah here we + + + align:start position:0% +it my copy ah here we +are and it begins um it's after some of + + align:start position:0% +are and it begins um it's after some of + + + align:start position:0% +are and it begins um it's after some of +the magical here the first thing we see + + align:start position:0% + + + + align:start position:0% + +is well in your packet is this title + + align:start position:0% +is well in your packet is this title + + + align:start position:0% +is well in your packet is this title +page right do you see if you can grab + + align:start position:0% +page right do you see if you can grab + + + align:start position:0% +page right do you see if you can grab +that it's this thing that begins with + + align:start position:0% +that it's this thing that begins with + + + align:start position:0% +that it's this thing that begins with +uhan Chino at the + + align:start position:0% + + + + align:start position:0% + +front a little bit before + + align:start position:0% +front a little bit before + + + align:start position:0% +front a little bit before +that s yeah it's it's before the the + + align:start position:0% +that s yeah it's it's before the the + + + align:start position:0% +that s yeah it's it's before the the +pictures of the pretty musical + + align:start position:0% + + + + align:start position:0% + +instruments yeah yep and um so pretorius + + align:start position:0% +instruments yeah yep and um so pretorius + + + align:start position:0% +instruments yeah yep and um so pretorius +is + + align:start position:0% +is + + + align:start position:0% +is +um he's in Germany but he's writing what + + align:start position:0% +um he's in Germany but he's writing what + + + align:start position:0% +um he's in Germany but he's writing what +we can see from this well first off he + + align:start position:0% +we can see from this well first off he + + + align:start position:0% +we can see from this well first off he +uses this uh calls it TP sicker anybody + + align:start position:0% +uses this uh calls it TP sicker anybody + + + align:start position:0% +uses this uh calls it TP sicker anybody +know who turp sicker + + align:start position:0% +know who turp sicker + + + align:start position:0% +know who turp sicker +is dance the mus of dance yeah and so + + align:start position:0% +is dance the mus of dance yeah and so + + + align:start position:0% +is dance the mus of dance yeah and so +that that says something we can see from + + align:start position:0% +that that says something we can see from + + + align:start position:0% +that that says something we can see from +the title page here um that this large + + align:start position:0% +the title page here um that this large + + + align:start position:0% +the title page here um that this large +thing one of the things that's + + align:start position:0% +thing one of the things that's + + + align:start position:0% +thing one of the things that's +interesting is they they change fonts + + align:start position:0% +interesting is they they change fonts + + + align:start position:0% +interesting is they they change fonts +depending on the language so here in + + align:start position:0% +depending on the language so here in + + + align:start position:0% +depending on the language so here in +German they write that there's some some + + align:start position:0% +German they write that there's some some + + + align:start position:0% +German they write that there's some some +frisha that there's these are French + + align:start position:0% +frisha that there's these are French + + + align:start position:0% +frisha that there's these are French +dances and leader danen un leader on + + align:start position:0% +dances and leader danen un leader on + + + align:start position:0% +dances and leader danen un leader on +here so think he's kind of trying to + + align:start position:0% +here so think he's kind of trying to + + + align:start position:0% +here so think he's kind of trying to +pass these off bit as French and and + + align:start position:0% +pass these off bit as French and and + + + align:start position:0% +pass these off bit as French and and +we'll see that some of them U may + + align:start position:0% +we'll see that some of them U may + + + align:start position:0% +we'll see that some of them U may +actually be uh let's let's listen to his + + align:start position:0% +actually be uh let's let's listen to his + + + align:start position:0% +actually be uh let's let's listen to his +first piece the bronzo um the bronzo + + align:start position:0% +first piece the bronzo um the bronzo + + + align:start position:0% +first piece the bronzo um the bronzo +sampler so this is the first uh + + align:start position:0% +sampler so this is the first uh + + + align:start position:0% +sampler so this is the first uh +what is it 200 and um 200 plus odd + + align:start position:0% +what is it 200 and um 200 plus odd + + + align:start position:0% +what is it 200 and um 200 plus odd +dances that has published in 1612 let's + + align:start position:0% +dances that has published in 1612 let's + + + align:start position:0% +dances that has published in 1612 let's +listen to the + + align:start position:0% + + + + align:start position:0% + +bronz + + align:start position:0% +bronz + + + align:start position:0% +bronz +oops + + align:start position:0% +oops + + + align:start position:0% +oops +um we're renaming the + + align:start position:0% + + + + align:start position:0% + +Bron obviously as always percussion + + align:start position:0% +Bron obviously as always percussion + + + align:start position:0% +Bron obviously as always percussion +Parts not + + align:start position:0% +Parts not + + + align:start position:0% +Parts not +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +notated + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and so let's sorry about that uh but got + + align:start position:0% +and so let's sorry about that uh but got + + + align:start position:0% +and so let's sorry about that uh but got +to have a lot of music get through I + + align:start position:0% +to have a lot of music get through I + + + align:start position:0% +to have a lot of music get through I +kind of want to get still to the magical + + align:start position:0% +kind of want to get still to the magical + + + align:start position:0% +kind of want to get still to the magical +I'm I'm so excited that we might + + align:start position:0% +I'm I'm so excited that we might + + + align:start position:0% +I'm I'm so excited that we might +actually make it to the second probably + + align:start position:0% +actually make it to the second probably + + + align:start position:0% +actually make it to the second probably +not have time um topic today + + align:start position:0% +not have time um topic today + + + align:start position:0% +not have time um topic today +um + + align:start position:0% +um + + + align:start position:0% +um +so keep this out for a second well I + + align:start position:0% +so keep this out for a second well I + + + align:start position:0% +so keep this out for a second well I +play this is from 16 published in + + align:start position:0% +play this is from 16 published in + + + align:start position:0% +play this is from 16 published in +1612 and um pretorius um attributes this + + align:start position:0% +1612 and um pretorius um attributes this + + + align:start position:0% +1612 and um pretorius um attributes this +to some fris Carbell that he's just sort + + align:start position:0% +to some fris Carbell that he's just sort + + + align:start position:0% +to some fris Carbell that he's just sort +of arranged stuff but go keep this out + + align:start position:0% +of arranged stuff but go keep this out + + + align:start position:0% +of arranged stuff but go keep this out +while I play a little French popular + + align:start position:0% +while I play a little French popular + + + align:start position:0% +while I play a little French popular +song from the 1530s about the same time + + align:start position:0% +song from the 1530s about the same time + + + align:start position:0% +song from the 1530s about the same time +as ton + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +V + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +now let's let's go back to the pr torus + + align:start position:0% +now let's let's go back to the pr torus + + + align:start position:0% +now let's let's go back to the pr torus +and listen + + align:start position:0% +and listen + + + align:start position:0% +and listen +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +again + + align:start position:0% +again + + + align:start position:0% +again +[Music] + + align:start position:0% + + + + align:start position:0% + +so let's just spread around because + + align:start position:0% +so let's just spread around because + + + align:start position:0% +so let's just spread around because +youve you've spoken a bit Let's uh what + + align:start position:0% +youve you've spoken a bit Let's uh what + + + align:start position:0% +youve you've spoken a bit Let's uh what +are some of the connections between the + + align:start position:0% +are some of the connections between the + + + align:start position:0% +are some of the connections between the +song and the um and the Dan so what are + + align:start position:0% +song and the um and the Dan so what are + + + align:start position:0% +song and the um and the Dan so what are +some + + align:start position:0% +some + + + align:start position:0% +some +differences the tempo sounds really + + align:start position:0% +differences the tempo sounds really + + + align:start position:0% +differences the tempo sounds really +different the tempo sounds really + + align:start position:0% +different the tempo sounds really + + + align:start position:0% +different the tempo sounds really +different right now do you think uh + + align:start position:0% +different right now do you think uh + + + align:start position:0% +different right now do you think uh +where where does that discrepancy come + + align:start position:0% +where where does that discrepancy come + + + align:start position:0% +where where does that discrepancy come +from probably well they probably the + + align:start position:0% +from probably well they probably the + + + align:start position:0% +from probably well they probably the +tempo wasn't really notated + + align:start position:0% +tempo wasn't really notated + + + align:start position:0% +tempo wasn't really notated +notated yeah so the tempo wasn't notated + + align:start position:0% +notated yeah so the tempo wasn't notated + + + align:start position:0% +notated yeah so the tempo wasn't notated +um does that mean that they had to be + + align:start position:0% +um does that mean that they had to be + + + align:start position:0% +um does that mean that they had to be +done in the same tempo no but doesn't I + + align:start position:0% +done in the same tempo no but doesn't I + + + align:start position:0% +done in the same tempo no but doesn't I +mean in fact quite likely in 70 or 80 + + align:start position:0% +mean in fact quite likely in 70 or 80 + + + align:start position:0% +mean in fact quite likely in 70 or 80 +years maybe the tempo that this piece + + align:start position:0% +years maybe the tempo that this piece + + + align:start position:0% +years maybe the tempo that this piece +would be cons performed in W would + + align:start position:0% +would be cons performed in W would + + + align:start position:0% +would be cons performed in W would +change but yeah definitely dance at + + align:start position:0% +change but yeah definitely dance at + + + align:start position:0% +change but yeah definitely dance at +really high speed pretty difficult to + + align:start position:0% +really high speed pretty difficult to + + + align:start position:0% +really high speed pretty difficult to +dce at pretty high speed but people + + align:start position:0% +dce at pretty high speed but people + + + align:start position:0% +dce at pretty high speed but people +would say it's pretty difficult to sing + + align:start position:0% +would say it's pretty difficult to sing + + + align:start position:0% +would say it's pretty difficult to sing +at pretty high speeds too so so not + + align:start position:0% +at pretty high speeds too so so not + + + align:start position:0% +at pretty high speeds too so so not +exactly sure other differences or + + align:start position:0% +exactly sure other differences or + + + align:start position:0% +exactly sure other differences or +similarities phrases are different the + + align:start position:0% +similarities phrases are different the + + + align:start position:0% +similarities phrases are different the +phrases are of different lengths let's + + align:start position:0% +phrases are of different lengths let's + + + align:start position:0% +phrases are of different lengths let's +let's um look at the the opening phrase + + align:start position:0% +let's um look at the the opening phrase + + + align:start position:0% +let's um look at the the opening phrase +of the of the Bron and how what do we + + align:start position:0% +of the of the Bron and how what do we + + + align:start position:0% +of the of the Bron and how what do we +want to call the the phrase do we want + + align:start position:0% +want to call the the phrase do we want + + + align:start position:0% +want to call the the phrase do we want +to say or what do we want to count + + align:start position:0% +to say or what do we want to count + + + align:start position:0% +to say or what do we want to count +measures quarter notes half notes what + + align:start position:0% +measures quarter notes half notes what + + + align:start position:0% +measures quarter notes half notes what +what what do you feel like is is the + + align:start position:0% +what what do you feel like is is the + + + align:start position:0% +what what do you feel like is is the +determining + + align:start position:0% + + + + align:start position:0% + +thing measures are pretty simple to me + + align:start position:0% +thing measures are pretty simple to me + + + align:start position:0% +thing measures are pretty simple to me +uh you might might call might say half + + align:start position:0% +uh you might might call might say half + + + align:start position:0% +uh you might might call might say half +notes but but yeah I mean what do you + + align:start position:0% +notes but but yeah I mean what do you + + + align:start position:0% +notes but but yeah I mean what do you +what do you think you're going to be + + align:start position:0% +what do you think you're going to be + + + align:start position:0% +what do you think you're going to be +stepping to cuz you want to want to + + align:start position:0% +stepping to cuz you want to want to + + + align:start position:0% +stepping to cuz you want to want to +count numbers of left steps and right + + align:start position:0% +count numbers of left steps and right + + + align:start position:0% +count numbers of left steps and right +steps and when you get back to your left + + align:start position:0% +steps and when you get back to your left + + + align:start position:0% +steps and when you get back to your left +foot call that some sort of unit um + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% +you + + + align:start position:0% +you +or + + align:start position:0% +or + + + align:start position:0% +or +probably steing on the yeah yeah so we + + align:start position:0% +probably steing on the yeah yeah so we + + + align:start position:0% +probably steing on the yeah yeah so we +should keep these things in mind it + + align:start position:0% +should keep these things in mind it + + + align:start position:0% +should keep these things in mind it +doesn't really for the purposes of this + + align:start position:0% +doesn't really for the purposes of this + + + align:start position:0% +doesn't really for the purposes of this +exercise it doesn't matter too much what + + align:start position:0% +exercise it doesn't matter too much what + + + align:start position:0% +exercise it doesn't matter too much what +we count but but think about how um you + + align:start position:0% +we count but but think about how um you + + + align:start position:0% +we count but but think about how um you +know for instance if we count U measures + + align:start position:0% +know for instance if we count U measures + + + align:start position:0% +know for instance if we count U measures +what happens in the second phrase that + + align:start position:0% +what happens in the second phrase that + + + align:start position:0% +what happens in the second phrase that +might be um little odd to people who + + align:start position:0% +might be um little odd to people who + + + align:start position:0% +might be um little odd to people who +like + + align:start position:0% + + + + align:start position:0% + +dances what's what's the second phrase + + align:start position:0% +dances what's what's the second phrase + + + align:start position:0% +dances what's what's the second phrase +what's the property it has that dances + + align:start position:0% +what's the property it has that dances + + + align:start position:0% +what's the property it has that dances +tend not to + + align:start position:0% +tend not to + + + align:start position:0% +tend not to +have it's not yeah it's an odd number of + + align:start position:0% +have it's not yeah it's an odd number of + + + align:start position:0% +have it's not yeah it's an odd number of +odd number of measures so so maybe + + align:start position:0% +odd number of measures so so maybe + + + align:start position:0% +odd number of measures so so maybe +measures might not be the best but who I + + align:start position:0% +measures might not be the best but who I + + + align:start position:0% +measures might not be the best but who I +I'm not a dance historian we you know we + + align:start position:0% +I'm not a dance historian we you know we + + + align:start position:0% +I'm not a dance historian we you know we +should bring one in and and uh know that + + align:start position:0% +should bring one in and and uh know that + + + align:start position:0% +should bring one in and and uh know that +speaking of that uh parentheses you know + + align:start position:0% +speaking of that uh parentheses you know + + + align:start position:0% +speaking of that uh parentheses you know +there's no class this Thursday uh + + align:start position:0% +there's no class this Thursday uh + + + align:start position:0% +there's no class this Thursday uh +because of Veterans Day um many of you + + align:start position:0% +because of Veterans Day um many of you + + + align:start position:0% +because of Veterans Day um many of you +will take advantage of the um the + + align:start position:0% +will take advantage of the um the + + + align:start position:0% +will take advantage of the um the +extension on the paper granted to people + + align:start position:0% +extension on the paper granted to people + + + align:start position:0% +extension on the paper granted to people +who want to turn in Thursday or Friday + + align:start position:0% +who want to turn in Thursday or Friday + + + align:start position:0% +who want to turn in Thursday or Friday +uh to do that on Monday again we at 5: + + align:start position:0% +uh to do that on Monday again we at 5: + + + align:start position:0% +uh to do that on Monday again we at 5: +the connection is we do have a visitor + + align:start position:0% +the connection is we do have a visitor + + + align:start position:0% +the connection is we do have a visitor +coming and that is Jane Alden speaking + + align:start position:0% +coming and that is Jane Alden speaking + + + align:start position:0% +coming and that is Jane Alden speaking +about uh expensive fact sili and whether + + align:start position:0% +about uh expensive fact sili and whether + + + align:start position:0% +about uh expensive fact sili and whether +they're worth um the money just for the + + align:start position:0% +they're worth um the money just for the + + + align:start position:0% +they're worth um the money just for the +off factor and us especially shanier and + + align:start position:0% +off factor and us especially shanier and + + + align:start position:0% +off factor and us especially shanier and +we'll bring in some ones that we don't + + align:start position:0% +we'll bring in some ones that we don't + + + align:start position:0% +we'll bring in some ones that we don't +currently own that um are far far beyond + + align:start position:0% +currently own that um are far far beyond + + + align:start position:0% +currently own that um are far far beyond +the price range of anything we've seen + + align:start position:0% +the price range of anything we've seen + + + align:start position:0% +the price range of anything we've seen +in the class and and talk about them + + align:start position:0% +in the class and and talk about them + + + align:start position:0% +in the class and and talk about them +um just a remk this is basically in my + + align:start position:0% +um just a remk this is basically in my + + + align:start position:0% +um just a remk this is basically in my +great so we've moved back to the music + + align:start position:0% +great so we've moved back to the music + + + align:start position:0% +great so we've moved back to the music +fantastic thank you thank you I was like + + align:start position:0% +fantastic thank you thank you I was like + + + align:start position:0% +fantastic thank you thank you I was like +I was SE in mind have we seen things in + + align:start position:0% +I was SE in mind have we seen things in + + + align:start position:0% +I was SE in mind have we seen things in +minor like with a raised + + align:start position:0% +minor like with a raised + + + align:start position:0% +minor like with a raised +seven yeah consistently raised seven + + align:start position:0% +seven yeah consistently raised seven + + + align:start position:0% +seven yeah consistently raised seven +have we seen things in + + align:start position:0% +have we seen things in + + + align:start position:0% +have we seen things in +minor well we + + align:start position:0% +minor well we + + + align:start position:0% +minor well we +haven't the sound like mine yeah exactly + + align:start position:0% +haven't the sound like mine yeah exactly + + + align:start position:0% +haven't the sound like mine yeah exactly +so we we've we've only first we only + + align:start position:0% +so we we've we've only first we only + + + align:start position:0% +so we we've we've only first we only +started getting to Pieces where it + + align:start position:0% +started getting to Pieces where it + + + align:start position:0% +started getting to Pieces where it +seemed appropriate to even talk about + + align:start position:0% +seemed appropriate to even talk about + + + align:start position:0% +seemed appropriate to even talk about +these terms but the one the first piece + + align:start position:0% +these terms but the one the first piece + + + align:start position:0% +these terms but the one the first piece +that we felt it was appropriate was the + + align:start position:0% +that we felt it was appropriate was the + + + align:start position:0% +that we felt it was appropriate was the +um the um HRI glassbook glass and um + + align:start position:0% +um the um HRI glassbook glass and um + + + align:start position:0% +um the um HRI glassbook glass and um +yeah yeah and we talked about that as + + align:start position:0% +yeah yeah and we talked about that as + + + align:start position:0% +yeah yeah and we talked about that as +being sort of it felt like F major even + + align:start position:0% +being sort of it felt like F major even + + + align:start position:0% +being sort of it felt like F major even +though there were some things that + + align:start position:0% +though there were some things that + + + align:start position:0% +though there were some things that +different yeah let's keep this in mind + + align:start position:0% +different yeah let's keep this in mind + + + align:start position:0% +different yeah let's keep this in mind +um I + + align:start position:0% +um I + + + align:start position:0% +um I +thinkal + + align:start position:0% +thinkal + + + align:start position:0% +thinkal +of it even has a p thir at the end yeah + + align:start position:0% +of it even has a p thir at the end yeah + + + align:start position:0% +of it even has a p thir at the end yeah +so the picky third this raised major um + + align:start position:0% +so the picky third this raised major um + + + align:start position:0% +so the picky third this raised major um +chord at the end of saying minor yeah + + align:start position:0% +chord at the end of saying minor yeah + + + align:start position:0% +chord at the end of saying minor yeah +well let's do you mind if we table that + + align:start position:0% +well let's do you mind if we table that + + + align:start position:0% +well let's do you mind if we table that +discussion for just a little bit because + + align:start position:0% +discussion for just a little bit because + + + align:start position:0% +discussion for just a little bit because +um because we can we can look at whether + + align:start position:0% +um because we can we can look at whether + + + align:start position:0% +um because we can we can look at whether +or not um when we look at for instance + + align:start position:0% +or not um when we look at for instance + + + align:start position:0% +or not um when we look at for instance +the uh the song that's based on we can + + align:start position:0% +the uh the song that's based on we can + + + align:start position:0% +the uh the song that's based on we can +see that it has a lot of the same + + align:start position:0% +see that it has a lot of the same + + + align:start position:0% +see that it has a lot of the same +characteristics but all those + + align:start position:0% +characteristics but all those + + + align:start position:0% +characteristics but all those +Sharps all the fs are written above the + + align:start position:0% +Sharps all the fs are written above the + + + align:start position:0% +Sharps all the fs are written above the +staff and what does that + + align:start position:0% +staff and what does that + + + align:start position:0% +staff and what does that +mean suggested by the editor they're + + align:start position:0% +mean suggested by the editor they're + + + align:start position:0% +mean suggested by the editor they're +suggested by the editor so if a person + + align:start position:0% +suggested by the editor so if a person + + + align:start position:0% +suggested by the editor so if a person +wanted to make a real case that well + + align:start position:0% +wanted to make a real case that well + + + align:start position:0% +wanted to make a real case that well +this doesn't have the picky thirds this + + align:start position:0% +this doesn't have the picky thirds this + + + align:start position:0% +this doesn't have the picky thirds this +doesn't have the um uh you know this + + align:start position:0% +doesn't have the um uh you know this + + + align:start position:0% +doesn't have the um uh you know this +doesn't have those raised leading tones + + align:start position:0% +doesn't have those raised leading tones + + + align:start position:0% +doesn't have those raised leading tones +um you know be here but on the other + + align:start position:0% +um you know be here but on the other + + + align:start position:0% +um you know be here but on the other +hand let's this is this kind of a neat + + align:start position:0% +hand let's this is this kind of a neat + + + align:start position:0% +hand let's this is this kind of a neat +exercise when we when we are doing our + + align:start position:0% +exercise when we when we are doing our + + + align:start position:0% +exercise when we when we are doing our +own + + align:start position:0% +own + + + align:start position:0% +own +um additions of the mus of fcta we you + + align:start position:0% +um additions of the mus of fcta we you + + + align:start position:0% +um additions of the mus of fcta we you +know trying to figure out who would have + + align:start position:0% +know trying to figure out who would have + + + align:start position:0% +know trying to figure out who would have +thought this what sorts of evidence do + + align:start position:0% +thought this what sorts of evidence do + + + align:start position:0% +thought this what sorts of evidence do +we have that those f shs um might + + align:start position:0% +we have that those f shs um might + + + align:start position:0% +we have that those f shs um might +actually exist and one of the pieces of + + align:start position:0% +actually exist and one of the pieces of + + + align:start position:0% +actually exist and one of the pieces of +evidence we do have is that somebody + + align:start position:0% +evidence we do have is that somebody + + + align:start position:0% +evidence we do have is that somebody +only only 80 years later well but you + + align:start position:0% +only only 80 years later well but you + + + align:start position:0% +only only 80 years later well but you +know it's not that bad compared to only + + align:start position:0% +know it's not that bad compared to only + + + align:start position:0% +know it's not that bad compared to only +uh 500 years later only 80 years later + + align:start position:0% +uh 500 years later only 80 years later + + + align:start position:0% +uh 500 years later only 80 years later +had written in the FPS in his own + + align:start position:0% +had written in the FPS in his own + + + align:start position:0% +had written in the FPS in his own +rangement in the ptus one right so when + + align:start position:0% +rangement in the ptus one right so when + + + align:start position:0% +rangement in the ptus one right so when +you look at it there the sharps are in + + align:start position:0% +you look at it there the sharps are in + + + align:start position:0% +you look at it there the sharps are in +the are in the print are in the + + align:start position:0% +the are in the print are in the + + + align:start position:0% +the are in the print are in the +original we're jumping around a lot + + align:start position:0% +original we're jumping around a lot + + + align:start position:0% +original we're jumping around a lot +today but I think it's I think it's kind + + align:start position:0% +today but I think it's I think it's kind + + + align:start position:0% +today but I think it's I think it's kind +of good even more than usual but um good + + align:start position:0% +of good even more than usual but um good + + + align:start position:0% +of good even more than usual but um good +what other other other differences so so + + align:start position:0% +what other other other differences so so + + + align:start position:0% +what other other other differences so so +you looked at actually a similarity + + align:start position:0% +you looked at actually a similarity + + + align:start position:0% +you looked at actually a similarity +between the two they both have similar + + align:start position:0% +between the two they both have similar + + + align:start position:0% +between the two they both have similar +modality there's there's one that I um I + + align:start position:0% +modality there's there's one that I um I + + + align:start position:0% +modality there's there's one that I um I +like to notice because of um what I did + + align:start position:0% +like to notice because of um what I did + + + align:start position:0% +like to notice because of um what I did +with the arrows in TS + + align:start position:0% + + + + align:start position:0% + +Petrus let spread out around the + + align:start position:0% +Petrus let spread out around the + + + align:start position:0% +Petrus let spread out around the +contributions um the tenor of the song + + align:start position:0% +contributions um the tenor of the song + + + align:start position:0% +contributions um the tenor of the song +mov into the soprano the tenor of the + + align:start position:0% +mov into the soprano the tenor of the + + + align:start position:0% +mov into the soprano the tenor of the +song moves into the soprano yeah does + + align:start position:0% +song moves into the soprano yeah does + + + align:start position:0% +song moves into the soprano yeah does +the soprano move + + align:start position:0% + + + + align:start position:0% + +anywhere I don't see it I don't see it I + + align:start position:0% +anywhere I don't see it I don't see it I + + + align:start position:0% +anywhere I don't see it I don't see it I +don't see + + align:start position:0% +don't see + + + align:start position:0% +don't see +okay and there there's some there's a + + align:start position:0% +okay and there there's some there's a + + + align:start position:0% +okay and there there's some there's a +few things a little oh go ahead go ahead + + align:start position:0% +few things a little oh go ahead go ahead + + + align:start position:0% +few things a little oh go ahead go ahead +see oh sorry I thought you how for a + + align:start position:0% +see oh sorry I thought you how for a + + + align:start position:0% +see oh sorry I thought you how for a +second what about um is it even possible + + align:start position:0% +second what about um is it even possible + + + align:start position:0% +second what about um is it even possible +to have a one toone correspondence of + + align:start position:0% +to have a one toone correspondence of + + + align:start position:0% +to have a one toone correspondence of +the voices from one to the other there + + align:start position:0% +the voices from one to the other there + + + align:start position:0% +the voices from one to the other there +more voes there's no more voices so even + + align:start position:0% +more voes there's no more voices so even + + + align:start position:0% +more voes there's no more voices so even +if you had yeah well you have two here + + align:start position:0% +if you had yeah well you have two here + + + align:start position:0% +if you had yeah well you have two here +in the the DS it looks sort of like you + + align:start position:0% +in the the DS it looks sort of like you + + + align:start position:0% +in the the DS it looks sort of like you +actually have three voices it's just + + align:start position:0% +actually have three voices it's just + + + align:start position:0% +actually have three voices it's just +that two you have you have sort of two + + align:start position:0% +that two you have you have sort of two + + + align:start position:0% +that two you have you have sort of two +pairs of voices which are moving in + + align:start position:0% +pairs of voices which are moving in + + + align:start position:0% +pairs of voices which are moving in +thirds at in the beginning and then you + + align:start position:0% +thirds at in the beginning and then you + + + align:start position:0% +thirds at in the beginning and then you +have one the middle voice right two + + align:start position:0% +have one the middle voice right two + + + align:start position:0% +have one the middle voice right two +pairs of voices moving in thirds at the + + align:start position:0% +pairs of voices moving in thirds at the + + + align:start position:0% +pairs of voices moving in thirds at the +beginning yeah you although only for the + + align:start position:0% +beginning yeah you although only for the + + + align:start position:0% +beginning yeah you although only for the +first measure for the lowest two parts + + align:start position:0% +first measure for the lowest two parts + + + align:start position:0% +first measure for the lowest two parts +so maybe maybe maybe not uh it's um yeah + + align:start position:0% +so maybe maybe maybe not uh it's um yeah + + + align:start position:0% +so maybe maybe maybe not uh it's um yeah +cuz we do have but what what look at the + + align:start position:0% +cuz we do have but what what look at the + + + align:start position:0% +cuz we do have but what what look at the +base part is it exactly the + + align:start position:0% +base part is it exactly the + + + align:start position:0% +base part is it exactly the +same between both + + align:start position:0% + + + + align:start position:0% + +parts No No in fact so we have quite a + + align:start position:0% +parts No No in fact so we have quite a + + + align:start position:0% +parts No No in fact so we have quite a +bit of differences let me say something + + align:start position:0% +bit of differences let me say something + + + align:start position:0% +bit of differences let me say something +about this this particular piece it's a + + align:start position:0% +about this this particular piece it's a + + + align:start position:0% +about this this particular piece it's a +it's a body piece like um you know like + + align:start position:0% +it's a body piece like um you know like + + + align:start position:0% +it's a body piece like um you know like +like so many of the pieces we have here + + align:start position:0% +like so many of the pieces we have here + + + align:start position:0% +like so many of the pieces we have here +the text uh la la + + align:start position:0% +the text uh la la + + + align:start position:0% +the text uh la la +la la la la a fake syllable just to fill + + align:start position:0% +la la la la a fake syllable just to fill + + + align:start position:0% +la la la la a fake syllable just to fill +things I won't tell I won I will never + + align:start position:0% +things I won't tell I won I will never + + + align:start position:0% +things I won't tell I won I will never +tell um sorry sorry I I will + + align:start position:0% +tell um sorry sorry I I will + + + align:start position:0% +tell um sorry sorry I I will +tell I will tell you I will tell you the + + align:start position:0% +tell I will tell you I will tell you the + + + align:start position:0% +tell I will tell you I will tell you the +story + + align:start position:0% +story + + + align:start position:0% +story +um there is a man in our in our town + + align:start position:0% +um there is a man in our in our town + + + align:start position:0% +um there is a man in our in our town +uh who is jealous of his wife in + + align:start position:0% +uh who is jealous of his wife in + + + align:start position:0% +uh who is jealous of his wife in +he's not jealous without cause may but + + align:start position:0% +he's not jealous without cause may but + + + align:start position:0% +he's not jealous without cause may but +he's completely cuckolded that is to say + + align:start position:0% +he's completely cuckolded that is to say + + + align:start position:0% +he's completely cuckolded that is to say +he's jealous but but he hasn't figured + + align:start position:0% +he's jealous but but he hasn't figured + + + align:start position:0% +he's jealous but but he hasn't figured +out that actually she's you know got + + align:start position:0% +out that actually she's you know got + + + align:start position:0% +out that actually she's you know got +something on the side stuff and so um + + align:start position:0% +something on the side stuff and so um + + + align:start position:0% +something on the side stuff and so um +and so this this is the type of song + + align:start position:0% +and so this this is the type of song + + + align:start position:0% +and so this this is the type of song +that people like to do and like to laugh + + align:start position:0% +that people like to do and like to laugh + + + align:start position:0% +that people like to do and like to laugh +at a lot and so it becomes a a little + + align:start position:0% +at a lot and so it becomes a a little + + + align:start position:0% +at a lot and so it becomes a a little +dance here and we we looked at the + + align:start position:0% +dance here and we we looked at the + + + align:start position:0% +dance here and we we looked at the +differences in phrase length and we + + align:start position:0% +differences in phrase length and we + + + align:start position:0% +differences in phrase length and we +looked at um you know all these these + + align:start position:0% +looked at um you know all these these + + + align:start position:0% +looked at um you know all these these +other things and what's what's + + align:start position:0% +other things and what's what's + + + align:start position:0% +other things and what's what's +interesting is is that again many many + + align:start position:0% +interesting is is that again many many + + + align:start position:0% +interesting is is that again many many +opportunities for research nobody as far + + align:start position:0% +opportunities for research nobody as far + + + align:start position:0% +opportunities for research nobody as far +as I know has systematically gone + + align:start position:0% +as I know has systematically gone + + + align:start position:0% +as I know has systematically gone +through the dances of um of uh torius + + align:start position:0% +through the dances of um of uh torius + + + align:start position:0% +through the dances of um of uh torius +and found whether or not there's + + align:start position:0% +and found whether or not there's + + + align:start position:0% +and found whether or not there's +actually orig more original French songs + + align:start position:0% +actually orig more original French songs + + + align:start position:0% +actually orig more original French songs +in that um behind them there there + + align:start position:0% +in that um behind them there there + + + align:start position:0% +in that um behind them there there +others have been found but there's not + + align:start position:0% +others have been found but there's not + + + align:start position:0% +others have been found but there's not +there's not that systematic work which + + align:start position:0% +there's not that systematic work which + + + align:start position:0% +there's not that systematic work which +is interesting because um a lot of these + + align:start position:0% +is interesting because um a lot of these + + + align:start position:0% +is interesting because um a lot of these +dances and similar dances later became + + align:start position:0% +dances and similar dances later became + + + align:start position:0% +dances and similar dances later became +um considered Icelandic folk music and + + align:start position:0% +um considered Icelandic folk music and + + + align:start position:0% +um considered Icelandic folk music and +uh all the way until the 19th and 20th + + align:start position:0% +uh all the way until the 19th and 20th + + + align:start position:0% +uh all the way until the 19th and 20th +Century and only now there's an + + align:start position:0% +Century and only now there's an + + + align:start position:0% +Century and only now there's an +Icelandic scholar named Arie ingleson + + align:start position:0% +Icelandic scholar named Arie ingleson + + + align:start position:0% +Icelandic scholar named Arie ingleson +who's probably the most hated man in + + align:start position:0% +who's probably the most hated man in + + + align:start position:0% +who's probably the most hated man in +Iceland because he's found out that all + + align:start position:0% +Iceland because he's found out that all + + + align:start position:0% +Iceland because he's found out that all +these things that for for generations + + align:start position:0% +these things that for for generations + + + align:start position:0% +these things that for for generations +and generations were considered uh their + + align:start position:0% +and generations were considered uh their + + + align:start position:0% +and generations were considered uh their +Icelandic music was actually maybe the + + align:start position:0% +Icelandic music was actually maybe the + + + align:start position:0% +Icelandic music was actually maybe the +fourth voice of of um of a French song + + align:start position:0% +fourth voice of of um of a French song + + + align:start position:0% +fourth voice of of um of a French song +of the 15th century or maybe the third + + align:start position:0% +of the 15th century or maybe the third + + + align:start position:0% +of the 15th century or maybe the third +voice of of aorus dance or so so a lot + + align:start position:0% +voice of of aorus dance or so so a lot + + + align:start position:0% +voice of of aorus dance or so so a lot +of these uh these connections that we + + align:start position:0% +of these uh these connections that we + + + align:start position:0% +of these uh these connections that we +can still make and we can still + + align:start position:0% +can still make and we can still + + + align:start position:0% +can still make and we can still +find when looking at pretorius um always + + align:start position:0% +find when looking at pretorius um always + + + align:start position:0% +find when looking at pretorius um always +comes up the question + + align:start position:0% +comes up the question + + + align:start position:0% +comes up the question +of what instruments we get to play this + + align:start position:0% +of what instruments we get to play this + + + align:start position:0% +of what instruments we get to play this +right and things and so um and and even + + align:start position:0% +right and things and so um and and even + + + align:start position:0% +right and things and so um and and even +if we knew you know that this should be + + align:start position:0% +if we knew you know that this should be + + + align:start position:0% +if we knew you know that this should be +played on on a sack butt or on a on a a + + align:start position:0% +played on on a sack butt or on a on a a + + + align:start position:0% +played on on a sack butt or on a on a a +sham you know what exactly what types + + align:start position:0% +sham you know what exactly what types + + + align:start position:0% +sham you know what exactly what types +unfortunately um one of the reasons + + align:start position:0% +unfortunately um one of the reasons + + + align:start position:0% +unfortunately um one of the reasons +there's not that much instrumental music + + align:start position:0% +there's not that much instrumental music + + + align:start position:0% +there's not that much instrumental music +out there but one of the reasons why of + + align:start position:0% +out there but one of the reasons why of + + + align:start position:0% +out there but one of the reasons why of +the music music that instrumental music + + align:start position:0% +the music music that instrumental music + + + align:start position:0% +the music music that instrumental music +that is written down pror has performed + + align:start position:0% +that is written down pror has performed + + + align:start position:0% +that is written down pror has performed +a lot is because he was also um in his + + align:start position:0% +a lot is because he was also um in his + + + align:start position:0% +a lot is because he was also um in his +large sort of collection and description + + align:start position:0% +large sort of collection and description + + + align:start position:0% +large sort of collection and description +of everything about music in the world + + align:start position:0% +of everything about music in the world + + + align:start position:0% +of everything about music in the world +he produced these um these images of + + align:start position:0% +he produced these um these images of + + + align:start position:0% +he produced these um these images of +instruments from the time so this is + + align:start position:0% +instruments from the time so this is + + + align:start position:0% +instruments from the time so this is +from his day organography about + + align:start position:0% +from his day organography about + + + align:start position:0% +from his day organography about +instruments from his cinama mus of 1619 + + align:start position:0% +instruments from his cinama mus of 1619 + + + align:start position:0% +instruments from his cinama mus of 1619 +so um about seven years later and so we + + align:start position:0% +so um about seven years later and so we + + + align:start position:0% +so um about seven years later and so we +see in the first page at the bottom + + align:start position:0% +see in the first page at the bottom + + + align:start position:0% +see in the first page at the bottom +there's um there's all these things + + align:start position:0% +there's um there's all these things + + + align:start position:0% +there's um there's all these things +about um what the instruments are um + + align:start position:0% +about um what the instruments are um + + + align:start position:0% +about um what the instruments are um +trombones he calls them here the same as + + align:start position:0% +trombones he calls them here the same as + + + align:start position:0% +trombones he calls them here the same as +the modern German um term and you can + + align:start position:0% +the modern German um term and you can + + + align:start position:0% +the modern German um term and you can +see that some of the trombones are quite + + align:start position:0% +see that some of the trombones are quite + + + align:start position:0% +see that some of the trombones are quite +are quite intricate um continue to this + + align:start position:0% +are quite intricate um continue to this + + + align:start position:0% +are quite intricate um continue to this +next page we have a lot of depictions + + align:start position:0% +next page we have a lot of depictions + + + align:start position:0% +next page we have a lot of depictions +of double read instruments in the top + + align:start position:0% +of double read instruments in the top + + + align:start position:0% +of double read instruments in the top +right corner and bag pipes I think these + + align:start position:0% +right corner and bag pipes I think these + + + align:start position:0% +right corner and bag pipes I think these +are um really interesting and showing + + align:start position:0% +are um really interesting and showing + + + align:start position:0% +are um really interesting and showing +exactly where each of the individual + + align:start position:0% +exactly where each of the individual + + + align:start position:0% +exactly where each of the individual +keys are on them continuing on uh we + + align:start position:0% +keys are on them continuing on uh we + + + align:start position:0% +keys are on them continuing on uh we +have a set of crumb horns on the next + + align:start position:0% +have a set of crumb horns on the next + + + align:start position:0% +have a set of crumb horns on the next +page and uh why are they Crum horns do + + align:start position:0% +page and uh why are they Crum horns do + + + align:start position:0% +page and uh why are they Crum horns do +they have these hooks why do they have + + align:start position:0% +they have these hooks why do they have + + + align:start position:0% +they have these hooks why do they have +these hooks because otherwise they + + align:start position:0% +these hooks because otherwise they + + + align:start position:0% +these hooks because otherwise they +wouldn't be crumb horns it's kind of a + + align:start position:0% +wouldn't be crumb horns it's kind of a + + + align:start position:0% +wouldn't be crumb horns it's kind of a +self-fulfilling prophecy the crumb horn + + align:start position:0% +self-fulfilling prophecy the crumb horn + + + align:start position:0% +self-fulfilling prophecy the crumb horn +and you can see um from the pictures + + align:start position:0% +and you can see um from the pictures + + + align:start position:0% +and you can see um from the pictures +especially the one on the left here that + + align:start position:0% +especially the one on the left here that + + + align:start position:0% +especially the one on the left here that +the crumb Horn's basically uh OBO or + + align:start position:0% +the crumb Horn's basically uh OBO or + + + align:start position:0% +the crumb Horn's basically uh OBO or +sham that then you put a cap over the um + + align:start position:0% +sham that then you put a cap over the um + + + align:start position:0% +sham that then you put a cap over the um +the mouthpiece this makes it easier to + + align:start position:0% +the mouthpiece this makes it easier to + + + align:start position:0% +the mouthpiece this makes it easier to +be say a Wandering Minstrel or somebody + + align:start position:0% +be say a Wandering Minstrel or somebody + + + align:start position:0% +be say a Wandering Minstrel or somebody +playing while while moving because you + + align:start position:0% +playing while while moving because you + + + align:start position:0% +playing while while moving because you +don't have to worry about damaging your + + align:start position:0% +don't have to worry about damaging your + + + align:start position:0% +don't have to worry about damaging your +read so much um it keeps the read um + + align:start position:0% +read so much um it keeps the read um + + + align:start position:0% +read so much um it keeps the read um +about the same U sort of moisture + + align:start position:0% +about the same U sort of moisture + + + align:start position:0% +about the same U sort of moisture +whether it's being played or not it does + + align:start position:0% +whether it's being played or not it does + + + align:start position:0% +whether it's being played or not it does +make it incredibly hard to play in tune + + align:start position:0% +make it incredibly hard to play in tune + + + align:start position:0% +make it incredibly hard to play in tune +the crumb horn may be the most difficult + + align:start position:0% +the crumb horn may be the most difficult + + + align:start position:0% +the crumb horn may be the most difficult +uh instrument to play in tune MIT has + + align:start position:0% +uh instrument to play in tune MIT has + + + align:start position:0% +uh instrument to play in tune MIT has +four of them if we ever want to get + + align:start position:0% +four of them if we ever want to get + + + align:start position:0% +four of them if we ever want to get +together and and sound uh try to see + + align:start position:0% +together and and sound uh try to see + + + align:start position:0% +together and and sound uh try to see +what the the most uh ugly sound we could + + align:start position:0% +what the the most uh ugly sound we could + + + align:start position:0% +what the the most uh ugly sound we could +possibly make we could play it on the + + align:start position:0% +possibly make we could play it on the + + + align:start position:0% +possibly make we could play it on the +other hand when played well the Crum + + align:start position:0% +other hand when played well the Crum + + + align:start position:0% +other hand when played well the Crum +horn is one of the most beautiful + + align:start position:0% +horn is one of the most beautiful + + + align:start position:0% +horn is one of the most beautiful +instruments there um let's continue on + + align:start position:0% +instruments there um let's continue on + + + align:start position:0% +instruments there um let's continue on +some nice pictures we're going to be + + align:start position:0% +some nice pictures we're going to be + + + align:start position:0% +some nice pictures we're going to be +joined in um two classes I believe or + + align:start position:0% +joined in um two classes I believe or + + + align:start position:0% +joined in um two classes I believe or +three classes that's uh two weeks from + + align:start position:0% +three classes that's uh two weeks from + + + align:start position:0% +three classes that's uh two weeks from +today by um a master loot player Doug + + align:start position:0% +today by um a master loot player Doug + + + align:start position:0% +today by um a master loot player Doug +flick so we'll talk more about loots and + + align:start position:0% +flick so we'll talk more about loots and + + + align:start position:0% +flick so we'll talk more about loots and +similar instruments then you all will um + + align:start position:0% +similar instruments then you all will um + + + align:start position:0% +similar instruments then you all will um +be given a piece for the loot written in + + align:start position:0% +be given a piece for the loot written in + + + align:start position:0% +be given a piece for the loot written in +this obscure notation that only + + align:start position:0% +this obscure notation that only + + + align:start position:0% +this obscure notation that only +lutenists read and um you guys will join + + align:start position:0% +lutenists read and um you guys will join + + + align:start position:0% +lutenists read and um you guys will join +that ranks and try to figure out how to + + align:start position:0% +that ranks and try to figure out how to + + + align:start position:0% +that ranks and try to figure out how to +figure out how to play music for the + + align:start position:0% +figure out how to play music for the + + + align:start position:0% +figure out how to play music for the +loot um you can also see here that a lot + + align:start position:0% +loot um you can also see here that a lot + + + align:start position:0% +loot um you can also see here that a lot +of Fred instruments at the time of many + + align:start position:0% +of Fred instruments at the time of many + + + align:start position:0% +of Fred instruments at the time of many +many strings we'll get to specific + + align:start position:0% +many strings we'll get to specific + + + align:start position:0% +many strings we'll get to specific +instruments in a bit um on the page that + + align:start position:0% +instruments in a bit um on the page that + + + align:start position:0% +instruments in a bit um on the page that +says 22 at the top left corner there's + + align:start position:0% +says 22 at the top left corner there's + + + align:start position:0% +says 22 at the top left corner there's +that instrument that we've um we've + + align:start position:0% +that instrument that we've um we've + + + align:start position:0% +that instrument that we've um we've +talked about a number of times in class + + align:start position:0% +talked about a number of times in class + + + align:start position:0% +talked about a number of times in class +the hery gery which is sort of a crank + + align:start position:0% +the hery gery which is sort of a crank + + + align:start position:0% +the hery gery which is sort of a crank +violin that's played um with a keyboard + + align:start position:0% +violin that's played um with a keyboard + + + align:start position:0% +violin that's played um with a keyboard +yeah this come up a couple times but I + + align:start position:0% +yeah this come up a couple times but I + + + align:start position:0% +yeah this come up a couple times but I +really want to get uh to some of these + + align:start position:0% +really want to get uh to some of these + + + align:start position:0% +really want to get uh to some of these +other instruments where he shows uh + + align:start position:0% +other instruments where he shows uh + + + align:start position:0% +other instruments where he shows uh +exactly how organs are um to be pumped + + align:start position:0% +exactly how organs are um to be pumped + + + align:start position:0% +exactly how organs are um to be pumped +at the + + align:start position:0% +at the + + + align:start position:0% +at the +time and then the next page of your + + align:start position:0% +time and then the next page of your + + + align:start position:0% +time and then the next page of your +handout um one of my favorite favorite + + align:start position:0% +handout um one of my favorite favorite + + + align:start position:0% +handout um one of my favorite favorite +pages in the entire book where he just + + align:start position:0% +pages in the entire book where he just + + + align:start position:0% +pages in the entire book where he just +has a picture of a ruler and if you go + + align:start position:0% +has a picture of a ruler and if you go + + + align:start position:0% +has a picture of a ruler and if you go +back and flip back to the other Pages + + align:start position:0% +back and flip back to the other Pages + + + align:start position:0% +back and flip back to the other Pages +second you'll see that there's rulers at + + align:start position:0% +second you'll see that there's rulers at + + + align:start position:0% +second you'll see that there's rulers at +the bottom about anything this is + + align:start position:0% +the bottom about anything this is + + + align:start position:0% +the bottom about anything this is +beginning of the first really + + align:start position:0% +beginning of the first really + + + align:start position:0% +beginning of the first really +scientifically accurate um depictions of + + align:start position:0% +scientifically accurate um depictions of + + + align:start position:0% +scientifically accurate um depictions of +instruments and he talks about on this + + align:start position:0% +instruments and he talks about on this + + + align:start position:0% +instruments and he talks about on this +page about the importance of drawing + + align:start position:0% +page about the importance of drawing + + + align:start position:0% +page about the importance of drawing +things to scale and having instruments + + align:start position:0% +things to scale and having instruments + + + align:start position:0% +things to scale and having instruments +to scale and and that that the ruler at + + align:start position:0% +to scale and and that that the ruler at + + + align:start position:0% +to scale and and that that the ruler at +the bottom of each page changes in size + + align:start position:0% +the bottom of each page changes in size + + + align:start position:0% +the bottom of each page changes in size +to show the particular instruments on + + align:start position:0% +to show the particular instruments on + + + align:start position:0% +to show the particular instruments on +that page so this is um compared to what + + align:start position:0% +that page so this is um compared to what + + + align:start position:0% +that page so this is um compared to what +we saw um in the Middle Ages in the + + align:start position:0% +we saw um in the Middle Ages in the + + + align:start position:0% +we saw um in the Middle Ages in the +early Renaissance uh much more + + align:start position:0% +early Renaissance uh much more + + + align:start position:0% +early Renaissance uh much more +scientific view of music of the time but + + align:start position:0% +scientific view of music of the time but + + + align:start position:0% +scientific view of music of the time but +however turn to the last page uh I've + + align:start position:0% +however turn to the last page uh I've + + + align:start position:0% +however turn to the last page uh I've +lost mine where is it and I'll get it + + align:start position:0% +lost mine where is it and I'll get it + + + align:start position:0% +lost mine where is it and I'll get it +back and just look at those instruments + + align:start position:0% +back and just look at those instruments + + + align:start position:0% +back and just look at those instruments +the + + align:start position:0% +the + + + align:start position:0% +the +um this is the opposite of the + + align:start position:0% +um this is the opposite of the + + + align:start position:0% +um this is the opposite of the +scientific view of the time this is a a + + align:start position:0% +scientific view of the time this is a a + + + align:start position:0% +scientific view of the time this is a a +a view of scholarship that we don't + + align:start position:0% +a view of scholarship that we don't + + + align:start position:0% +a view of scholarship that we don't +really take that um sort of that that + + align:start position:0% +really take that um sort of that that + + + align:start position:0% +really take that um sort of that that +good uh view of anymore and that is + + align:start position:0% +good uh view of anymore and that is + + + align:start position:0% +good uh view of anymore and that is +there are all these instruments depicted + + align:start position:0% +there are all these instruments depicted + + + align:start position:0% +there are all these instruments depicted +in the Bible that we have no idea what + + align:start position:0% +in the Bible that we have no idea what + + + align:start position:0% +in the Bible that we have no idea what +they um actually looked like or sounded + + align:start position:0% +they um actually looked like or sounded + + + align:start position:0% +they um actually looked like or sounded +like so we should draw them anyhow and + + align:start position:0% +like so we should draw them anyhow and + + + align:start position:0% +like so we should draw them anyhow and +just sort of make them up and so you'll + + align:start position:0% +just sort of make them up and so you'll + + + align:start position:0% +just sort of make them up and so you'll +see that there's there's hearts that + + align:start position:0% +see that there's there's hearts that + + + align:start position:0% +see that there's there's hearts that +that would never actually work cuz they + + align:start position:0% +that would never actually work cuz they + + + align:start position:0% +that would never actually work cuz they +have no sounding boards that that work + + align:start position:0% +have no sounding boards that that work + + + align:start position:0% +have no sounding boards that that work +properly we have these these instruments + + align:start position:0% +properly we have these these instruments + + + align:start position:0% +properly we have these these instruments +that seem to have three mouthpieces and + + align:start position:0% +that seem to have three mouthpieces and + + + align:start position:0% +that seem to have three mouthpieces and +four um tone holes at the b or four uh + + align:start position:0% +four um tone holes at the b or four uh + + + align:start position:0% +four um tone holes at the b or four uh +Bells at the bottom so um so like eer + + align:start position:0% +Bells at the bottom so um so like eer + + + align:start position:0% +Bells at the bottom so um so like eer +yeah it's it's a lot it's a lot like eer + + align:start position:0% +yeah it's it's a lot it's a lot like eer + + + align:start position:0% +yeah it's it's a lot it's a lot like eer +drawing so plan um great uh let's listen + + align:start position:0% +drawing so plan um great uh let's listen + + + align:start position:0% +drawing so plan um great uh let's listen +to a little bit of how uh some of these + + align:start position:0% +to a little bit of how uh some of these + + + align:start position:0% +to a little bit of how uh some of these +instruments may have sounded in common + + align:start position:0% +instruments may have sounded in common + + + align:start position:0% +instruments may have sounded in common +and listen listen to them uh by listen + + align:start position:0% +and listen listen to them uh by listen + + + align:start position:0% +and listen listen to them uh by listen +to these set of volas on your own and um + + align:start position:0% +to these set of volas on your own and um + + + align:start position:0% +to these set of volas on your own and um +probably if we have a little bit of time + + align:start position:0% +probably if we have a little bit of time + + + align:start position:0% +probably if we have a little bit of time +next class we'll go through the + + align:start position:0% +next class we'll go through the + + + align:start position:0% +next class we'll go through the +instruments in general that are here but + + align:start position:0% +instruments in general that are here but + + + align:start position:0% +instruments in general that are here but +we'll just listen for a little bit to + + align:start position:0% +we'll just listen for a little bit to + + + align:start position:0% +we'll just listen for a little bit to +get some of these ear instruments our + + align:start position:0% +get some of these ear instruments our + + + align:start position:0% +get some of these ear instruments our +ear + + align:start position:0% +ear + + + align:start position:0% +ear +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +recorders what's low instruments + + align:start position:0% + + + + align:start position:0% + +there s kind of like Aon yeah do you + + align:start position:0% +there s kind of like Aon yeah do you + + + align:start position:0% +there s kind of like Aon yeah do you +remember um so we have some of these um + + align:start position:0% +remember um so we have some of these um + + + align:start position:0% +remember um so we have some of these um +dosier which kind of early bassoons I + + align:start position:0% +dosier which kind of early bassoons I + + + align:start position:0% +dosier which kind of early bassoons I +think think that might be going on + + align:start position:0% +think think that might be going on + + + align:start position:0% +think think that might be going on +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +here this is a particular 20th century + + align:start position:0% +here this is a particular 20th century + + + align:start position:0% +here this is a particular 20th century +21st century recording ideal I think + + align:start position:0% +21st century recording ideal I think + + + align:start position:0% +21st century recording ideal I think +that you'll hear we'll listen to one + + align:start position:0% +that you'll hear we'll listen to one + + + align:start position:0% +that you'll hear we'll listen to one +whole P one whole dance takes about 45 + + align:start position:0% +whole P one whole dance takes about 45 + + + align:start position:0% +whole P one whole dance takes about 45 +seconds and then you'll hear it segues + + align:start position:0% +seconds and then you'll hear it segues + + + align:start position:0% +seconds and then you'll hear it segues +really nicely into another dance but + + align:start position:0% +really nicely into another dance but + + + align:start position:0% +really nicely into another dance but +listen to the + + align:start position:0% +listen to the + + + align:start position:0% +listen to the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +instrumentation + + align:start position:0% +instrumentation + + + align:start position:0% +instrumentation +well maybe we'll skip forward a bit + + align:start position:0% + + + + align:start position:0% + +but forgot there was one extra repeat in + + align:start position:0% +but forgot there was one extra repeat in + + + align:start position:0% +but forgot there was one extra repeat in +this + + align:start position:0% +this + + + align:start position:0% +this +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +version + + align:start position:0% +version + + + align:start position:0% +version +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +actually let we'll skip ahead bit so you + + align:start position:0% +actually let we'll skip ahead bit so you + + + align:start position:0% +actually let we'll skip ahead bit so you +can + + align:start position:0% +can + + + align:start position:0% +can +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +hear so as they switch to each Dance The + + align:start position:0% +hear so as they switch to each Dance The + + + align:start position:0% +hear so as they switch to each Dance The +Ensemble transforms + + align:start position:0% +Ensemble transforms + + + align:start position:0% +Ensemble transforms +dramatically the likelihood that this is + + align:start position:0% +dramatically the likelihood that this is + + + align:start position:0% +dramatically the likelihood that this is +actual performance practice is is + + align:start position:0% +actual performance practice is is + + + align:start position:0% +actual performance practice is is +probably quite low um it's not really + + align:start position:0% +probably quite low um it's not really + + + align:start position:0% +probably quite low um it's not really +something you didn't have the wulfen + + align:start position:0% +something you didn't have the wulfen + + + align:start position:0% +something you didn't have the wulfen +build will fil harmonic always at your + + align:start position:0% +build will fil harmonic always at your + + + align:start position:0% +build will fil harmonic always at your +disposal anytime you wanted to have a + + align:start position:0% +disposal anytime you wanted to have a + + + align:start position:0% +disposal anytime you wanted to have a +dance you can hear um some of the + + align:start position:0% +dance you can hear um some of the + + + align:start position:0% +dance you can hear um some of the +different textures and Different + + align:start position:0% +different textures and Different + + + align:start position:0% +different textures and Different +instrumental + + align:start position:0% +instrumental + + + align:start position:0% +instrumental +combinations that this performance uh + + align:start position:0% +combinations that this performance uh + + + align:start position:0% +combinations that this performance uh +chooses to + + align:start position:0% +chooses to + + + align:start position:0% +chooses to +[Music] + + align:start position:0% + + + + align:start position:0% + +do so here we have their little brass + + align:start position:0% +do so here we have their little brass + + + align:start position:0% +do so here we have their little brass +section the the one rule that we hear + + align:start position:0% +section the the one rule that we hear + + + align:start position:0% +section the the one rule that we hear +about a lot in um instrumental music is + + align:start position:0% +about a lot in um instrumental music is + + + align:start position:0% +about a lot in um instrumental music is +that you don't mix loud and soft + + align:start position:0% +that you don't mix loud and soft + + + align:start position:0% +that you don't mix loud and soft +instruments and Loud instruments tended + + align:start position:0% +instruments and Loud instruments tended + + + align:start position:0% +instruments and Loud instruments tended +to include a lot of things we wouldn't + + align:start position:0% +to include a lot of things we wouldn't + + + align:start position:0% +to include a lot of things we wouldn't +think of as loud today Shams which are + + align:start position:0% +think of as loud today Shams which are + + + align:start position:0% +think of as loud today Shams which are +which are obos but they have much + + align:start position:0% +which are obos but they have much + + + align:start position:0% +which are obos but they have much +greater + + align:start position:0% +greater + + + align:start position:0% +greater +force but again like so many + + align:start position:0% +force but again like so many + + + align:start position:0% +force but again like so many +prohibitions if it keeps getting + + align:start position:0% +prohibitions if it keeps getting + + + align:start position:0% +prohibitions if it keeps getting +repeated probably it was happening from + + align:start position:0% +repeated probably it was happening from + + + align:start position:0% +repeated probably it was happening from +time to + + align:start position:0% +time to + + + align:start position:0% +time to +time so you can hear a loud instrument + + align:start position:0% + + + + align:start position:0% + +section + + align:start position:0% +section + + + align:start position:0% +section +so that gives you some sense of what's + + align:start position:0% +so that gives you some sense of what's + + + align:start position:0% +so that gives you some sense of what's +happening + + align:start position:0% +happening + + + align:start position:0% +happening +there let's we have about 5 minutes left + + align:start position:0% +there let's we have about 5 minutes left + + + align:start position:0% +there let's we have about 5 minutes left +let's let me tell you a little bit about + + align:start position:0% +let's let me tell you a little bit about + + + align:start position:0% +let's let me tell you a little bit about +the next uh class's assignment and we'll + + align:start position:0% +the next uh class's assignment and we'll + + + align:start position:0% +the next uh class's assignment and we'll +start um just get this tiniest Taste of + + align:start position:0% +start um just get this tiniest Taste of + + + align:start position:0% +start um just get this tiniest Taste of +the one one major genre of 16th century + + align:start position:0% +the one one major genre of 16th century + + + align:start position:0% +the one one major genre of 16th century +music that we didn't we haven't gotten + + align:start position:0% +music that we didn't we haven't gotten + + + align:start position:0% +music that we didn't we haven't gotten +to so far especially of vocal music and + + align:start position:0% +to so far especially of vocal music and + + + align:start position:0% +to so far especially of vocal music and +that's the magical so next class uh the + + align:start position:0% +that's the magical so next class uh the + + + align:start position:0% +that's the magical so next class uh the +readings are just two chapters of about + + align:start position:0% +readings are just two chapters of about + + + align:start position:0% +readings are just two chapters of about +12 pages from the right textbook this + + align:start position:0% +12 pages from the right textbook this + + + align:start position:0% +12 pages from the right textbook this +will give you an overview of just sort + + align:start position:0% +will give you an overview of just sort + + + align:start position:0% +will give you an overview of just sort +of English music at at the sort of the + + align:start position:0% +of English music at at the sort of the + + + align:start position:0% +of English music at at the sort of the +the lightest level um you know just not + + align:start position:0% +the lightest level um you know just not + + + align:start position:0% +the lightest level um you know just not +not that hugely deep but we're going to + + align:start position:0% +not that hugely deep but we're going to + + + align:start position:0% +not that hugely deep but we're going to +spend four classes on England so the + + align:start position:0% +spend four classes on England so the + + + align:start position:0% +spend four classes on England so the +following class will give take a little + + align:start position:0% +following class will give take a little + + + align:start position:0% +following class will give take a little +bit deeper reading of certain aspects so + + align:start position:0% +bit deeper reading of certain aspects so + + + align:start position:0% +bit deeper reading of certain aspects so +be a little prepared for that um skim + + align:start position:0% +be a little prepared for that um skim + + + align:start position:0% +be a little prepared for that um skim +this early uh six this early uh piece in + + align:start position:0% +this early uh six this early uh piece in + + + align:start position:0% +this early uh six this early uh piece in +sort of English music um King Henry VI's + + align:start position:0% +sort of English music um King Henry VI's + + + align:start position:0% +sort of English music um King Henry VI's +Pastime with good company uh just so you + + align:start position:0% +Pastime with good company uh just so you + + + align:start position:0% +Pastime with good company uh just so you +can sort of hear what's happened to + + align:start position:0% +can sort of hear what's happened to + + + align:start position:0% +can sort of hear what's happened to +English music since the last time we + + align:start position:0% +English music since the last time we + + + align:start position:0% +English music since the last time we +talked about England which was when we + + align:start position:0% +talked about England which was when we + + + align:start position:0% +talked about England which was when we +talked about the countenance angas the + + align:start position:0% +talked about the countenance angas the + + + align:start position:0% +talked about the countenance angas the +idea that English music was somehow + + align:start position:0% +idea that English music was somehow + + + align:start position:0% +idea that English music was somehow +influencing the continent so you can + + align:start position:0% +influencing the continent so you can + + + align:start position:0% +influencing the continent so you can +hear a little bit what was happening + + align:start position:0% +hear a little bit what was happening + + + align:start position:0% +hear a little bit what was happening +then but basically we're going to focus + + align:start position:0% +then but basically we're going to focus + + + align:start position:0% +then but basically we're going to focus +on English music at the end of the 16th + + align:start position:0% +on English music at the end of the 16th + + + align:start position:0% +on English music at the end of the 16th +and early 17th century which will sound + + align:start position:0% +and early 17th century which will sound + + + align:start position:0% +and early 17th century which will sound +a lot like Italian music in the middle + + align:start position:0% +a lot like Italian music in the middle + + + align:start position:0% +a lot like Italian music in the middle +of the 16th century so we'll I'll put up + + align:start position:0% +of the 16th century so we'll I'll put up + + + align:start position:0% +of the 16th century so we'll I'll put up +this timeline U very soon so you can see + + align:start position:0% +this timeline U very soon so you can see + + + align:start position:0% +this timeline U very soon so you can see +sort of how these um the time relates uh + + align:start position:0% +sort of how these um the time relates uh + + + align:start position:0% +sort of how these um the time relates uh +but we'll listen to a piece from 1601 + + align:start position:0% +but we'll listen to a piece from 1601 + + + align:start position:0% +but we'll listen to a piece from 1601 +Thomas wils as vesto was from lmos Hill + + align:start position:0% +Thomas wils as vesto was from lmos Hill + + + align:start position:0% +Thomas wils as vesto was from lmos Hill +descending which is an English magical + + align:start position:0% +descending which is an English magical + + + align:start position:0% +descending which is an English magical +in the four or five minutes we have left + + align:start position:0% +in the four or five minutes we have left + + + align:start position:0% +in the four or five minutes we have left +let me just say a little bit about the + + align:start position:0% +let me just say a little bit about the + + + align:start position:0% +let me just say a little bit about the +magical since you've listened to it go + + align:start position:0% +magical since you've listened to it go + + + align:start position:0% +magical since you've listened to it go +ahead and grab the packet that says IL + + align:start position:0% +ahead and grab the packet that says IL + + + align:start position:0% +ahead and grab the packet that says IL +biano do Chino on the front + + align:start position:0% + + + + align:start position:0% + +by jacqu aradel another one of these + + align:start position:0% +by jacqu aradel another one of these + + + align:start position:0% +by jacqu aradel another one of these +people who Masters the um the Italian + + align:start position:0% +people who Masters the um the Italian + + + align:start position:0% +people who Masters the um the Italian +style without really being + + align:start position:0% +style without really being + + + align:start position:0% +style without really being +Italian let's listen go ahead and turn + + align:start position:0% +Italian let's listen go ahead and turn + + + align:start position:0% +Italian let's listen go ahead and turn +to um turn to the opening of it and + + align:start position:0% +to um turn to the opening of it and + + + align:start position:0% +to um turn to the opening of it and +let's just + + align:start position:0% +let's just + + + align:start position:0% +let's just +um we'll just listen to a little bit of + + align:start position:0% +um we'll just listen to a little bit of + + + align:start position:0% +um we'll just listen to a little bit of +what's Happening Here a little bit of + + align:start position:0% +what's Happening Here a little bit of + + + align:start position:0% +what's Happening Here a little bit of +the music and then I'll talk a bit about + + align:start position:0% +the music and then I'll talk a bit about + + + align:start position:0% +the music and then I'll talk a bit about +the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +magical + + align:start position:0% +magical + + + align:start position:0% +magical +[Music] + + align:start position:0% + + + + align:start position:0% + +so let me say something about um about + + align:start position:0% +so let me say something about um about + + + align:start position:0% +so let me say something about um about +the text of what we have so far + + align:start position:0% +the text of what we have so far + + + align:start position:0% +the text of what we have so far +the verse is a very typical style of + + align:start position:0% +the verse is a very typical style of + + + align:start position:0% +the verse is a very typical style of +Italian verse that um and that is the we + + align:start position:0% +Italian verse that um and that is the we + + + align:start position:0% +Italian verse that um and that is the we +can tend to count Accents in our uh in + + align:start position:0% +can tend to count Accents in our uh in + + + align:start position:0% +can tend to count Accents in our uh in +in English verse right you've heard of I + + align:start position:0% +in English verse right you've heard of I + + + align:start position:0% +in English verse right you've heard of I +Amic pentamer there's five accents that + + align:start position:0% +Amic pentamer there's five accents that + + + align:start position:0% +Amic pentamer there's five accents that +go y y y y y y y Etc the Italians always + + align:start position:0% +go y y y y y y y Etc the Italians always + + + align:start position:0% +go y y y y y y y Etc the Italians always +tend to count syllables and here uh it's + + align:start position:0% +tend to count syllables and here uh it's + + + align:start position:0% +tend to count syllables and here uh it's +s and 11 are the two syllables that are + + align:start position:0% +s and 11 are the two syllables that are + + + align:start position:0% +s and 11 are the two syllables that are +all over Italian poetry and this will + + align:start position:0% +all over Italian poetry and this will + + + align:start position:0% +all over Italian poetry and this will +become important and a little bit as we + + align:start position:0% +become important and a little bit as we + + + align:start position:0% +become important and a little bit as we +see Italian madal Styles will sweep + + align:start position:0% +see Italian madal Styles will sweep + + + align:start position:0% +see Italian madal Styles will sweep +England and all of a sudden we'll start + + align:start position:0% +England and all of a sudden we'll start + + + align:start position:0% +England and all of a sudden we'll start +writing English um English poetry in + + align:start position:0% +writing English um English poetry in + + + align:start position:0% +writing English um English poetry in +these Italian forms that just doesn't + + align:start position:0% +these Italian forms that just doesn't + + + align:start position:0% +these Italian forms that just doesn't +work for English but they're quite quite + + align:start position:0% +work for English but they're quite quite + + + align:start position:0% +work for English but they're quite quite +fun so the Italians do everything in + + align:start position:0% +fun so the Italians do everything in + + + align:start position:0% +fun so the Italians do everything in +seven and 11 syllable lines and here we + + align:start position:0% +seven and 11 syllable lines and here we + + + align:start position:0% +seven and 11 syllable lines and here we +have 7711 if you look at the second line + + align:start position:0% +have 7711 if you look at the second line + + + align:start position:0% +have 7711 if you look at the second line +of the uh poetry kando Mo + + align:start position:0% +of the uh poetry kando Mo + + + align:start position:0% +of the uh poetry kando Mo +Edo um that's pretty simple 1 2 3 4 5 6 + + align:start position:0% +Edo um that's pretty simple 1 2 3 4 5 6 + + + align:start position:0% +Edo um that's pretty simple 1 2 3 4 5 6 +7 the first line you have to learn how + + align:start position:0% +7 the first line you have to learn how + + + align:start position:0% +7 the first line you have to learn how +to count like Italians and maybe uh the + + align:start position:0% +to count like Italians and maybe uh the + + + align:start position:0% +to count like Italians and maybe uh the +way the Italians count uh were on camera + + align:start position:0% +way the Italians count uh were on camera + + + align:start position:0% +way the Italians count uh were on camera +I was going to make a quip about the + + align:start position:0% +I was going to make a quip about the + + + align:start position:0% +I was going to make a quip about the +economy or something there being + + align:start position:0% +economy or something there being + + + align:start position:0% +economy or something there being +influenced by inability to count + + align:start position:0% +influenced by inability to count + + + align:start position:0% +influenced by inability to count +syllables but whatever now I have anyhow + + align:start position:0% +syllables but whatever now I have anyhow + + + align:start position:0% +syllables but whatever now I have anyhow +um because you want to count not IL + + align:start position:0% +um because you want to count not IL + + + align:start position:0% +um because you want to count not IL +ilano do Chino which would get you to + + align:start position:0% +ilano do Chino which would get you to + + + align:start position:0% +ilano do Chino which would get you to +eight but you want to in the beautiful + + align:start position:0% +eight but you want to in the beautiful + + + align:start position:0% +eight but you want to in the beautiful +Italian manner alide as many vowels as + + align:start position:0% +Italian manner alide as many vowels as + + + align:start position:0% +Italian manner alide as many vowels as +you can + + align:start position:0% + + + + align:start position:0% + +Soo get to seven or in the last + + align:start position:0% +Soo get to seven or in the last + + + align:start position:0% +Soo get to seven or in the last +line J + + align:start position:0% + + + + align:start position:0% + +Al um and even though there should + + align:start position:0% +Al um and even though there should + + + align:start position:0% +Al um and even though there should +there's there syllables are being left + + align:start position:0% +there's there syllables are being left + + + align:start position:0% +there's there syllables are being left +out in order to make it have um 11 + + align:start position:0% +out in order to make it have um 11 + + + align:start position:0% +out in order to make it have um 11 +syllable lines so that's the Poetry + + align:start position:0% + + + + align:start position:0% + +here but look at how um aradel sets this + + align:start position:0% +here but look at how um aradel sets this + + + align:start position:0% +here but look at how um aradel sets this +and um and this is a really clear um + + align:start position:0% +and um and this is a really clear um + + + align:start position:0% +and um and this is a really clear um +making making music sort of be the + + align:start position:0% +making making music sort of be the + + + align:start position:0% +making making music sort of be the +servant of the meaning of the + + align:start position:0% +servant of the meaning of the + + + align:start position:0% +servant of the meaning of the +text sorry I'm doing all this without + + align:start position:0% +text sorry I'm doing all this without + + + align:start position:0% +text sorry I'm doing all this without +giving you a translation the sweet uh + + align:start position:0% +giving you a translation the sweet uh + + + align:start position:0% +giving you a translation the sweet uh +the white sweet Swan sings while dying + + align:start position:0% +the white sweet Swan sings while dying + + + align:start position:0% +the white sweet Swan sings while dying +and I crying move to the end of my life + + align:start position:0% +and I crying move to the end of my life + + + align:start position:0% +and I crying move to the end of my life +approach the end of my life so he sets + + align:start position:0% +approach the end of my life so he sets + + + align:start position:0% +approach the end of my life so he sets +not the white and sweet + + align:start position:0% +not the white and sweet + + + align:start position:0% +not the white and sweet +Swan sings while dying and I crying move + + align:start position:0% +Swan sings while dying and I crying move + + + align:start position:0% +Swan sings while dying and I crying move +to the end of my life but as we would + + align:start position:0% +to the end of my life but as we would + + + align:start position:0% +to the end of my life but as we would +expect given the syntax the white sweet + + align:start position:0% +expect given the syntax the white sweet + + + align:start position:0% +expect given the syntax the white sweet +Swan uh sings dying and I crying move to + + align:start position:0% +Swan uh sings dying and I crying move to + + + align:start position:0% +Swan uh sings dying and I crying move to +the end of my + + align:start position:0% +the end of my + + + align:start position:0% +the end of my +life the early Italian magical is an + + align:start position:0% +life the early Italian magical is an + + + align:start position:0% +life the early Italian magical is an +attempt to bring um two Traditions + + align:start position:0% +attempt to bring um two Traditions + + + align:start position:0% +attempt to bring um two Traditions +together one is this tradition of easy + + align:start position:0% +together one is this tradition of easy + + + align:start position:0% +together one is this tradition of easy +to hear homophonic off um transparent + + align:start position:0% +to hear homophonic off um transparent + + + align:start position:0% +to hear homophonic off um transparent +text settings that um that we that we' + + align:start position:0% +text settings that um that we that we' + + + align:start position:0% +text settings that um that we that we' +saw in the French songs like ton V that + + align:start position:0% +saw in the French songs like ton V that + + + align:start position:0% +saw in the French songs like ton V that +we saw in frula like ELO of jasan Elo + + align:start position:0% +we saw in frula like ELO of jasan Elo + + + align:start position:0% +we saw in frula like ELO of jasan Elo +Elo B Bor that one with all the + + align:start position:0% +Elo B Bor that one with all the + + + align:start position:0% +Elo B Bor that one with all the +patter um Dal b guo k uh to bring that + + align:start position:0% +patter um Dal b guo k uh to bring that + + + align:start position:0% +patter um Dal b guo k uh to bring that +together with um with sophisticated + + align:start position:0% +together with um with sophisticated + + + align:start position:0% +together with um with sophisticated +texts and so we're kind of merging a + + align:start position:0% +texts and so we're kind of merging a + + + align:start position:0% +texts and so we're kind of merging a +musical forms that used to be considered + + align:start position:0% +musical forms that used to be considered + + + align:start position:0% +musical forms that used to be considered +lighter with uh very high-minded texts + + align:start position:0% +lighter with uh very high-minded texts + + + align:start position:0% +lighter with uh very high-minded texts +and so the text might come from uh + + align:start position:0% +and so the text might come from uh + + + align:start position:0% +and so the text might come from uh +petrarch um who set the text to nonante + + align:start position:0% +petrarch um who set the text to nonante + + + align:start position:0% +petrarch um who set the text to nonante +uh they might come from any number of + + align:start position:0% +uh they might come from any number of + + + align:start position:0% +uh they might come from any number of +very important Italian um poets and when + + align:start position:0% +very important Italian um poets and when + + + align:start position:0% +very important Italian um poets and when +you listen to this so we're going to end + + align:start position:0% +you listen to this so we're going to end + + + align:start position:0% +you listen to this so we're going to end +now but when you listen to this on your + + align:start position:0% +now but when you listen to this on your + + + align:start position:0% +now but when you listen to this on your +own try to hear how he tries to bring + + align:start position:0% +own try to hear how he tries to bring + + + align:start position:0% +own try to hear how he tries to bring +out individual words in particular how + + align:start position:0% +out individual words in particular how + + + align:start position:0% +out individual words in particular how +does at the end and a thousand deaths I + + align:start position:0% +does at the end and a thousand deaths I + + + align:start position:0% +does at the end and a thousand deaths I +would die a thousand deaths how is that + + align:start position:0% +would die a thousand deaths how is that + + + align:start position:0% +would die a thousand deaths how is that +set and this it's great that we're going + + align:start position:0% +set and this it's great that we're going + + + align:start position:0% +set and this it's great that we're going +to divide the class here so that you can + + align:start position:0% +to divide the class here so that you can + + + align:start position:0% +to divide the class here so that you can +really put one like one database one + + align:start position:0% +really put one like one database one + + + align:start position:0% +really put one like one database one +mental storage unit for the idea that + + align:start position:0% +mental storage unit for the idea that + + + align:start position:0% +mental storage unit for the idea that +the magical began as an attempt to bring + + align:start position:0% +the magical began as an attempt to bring + + + align:start position:0% +the magical began as an attempt to bring +very sophisticated texts and treat them + + align:start position:0% +very sophisticated texts and treat them + + + align:start position:0% +very sophisticated texts and treat them +very seriously in music this magical is + + align:start position:0% +very seriously in music this magical is + + + align:start position:0% +very seriously in music this magical is +written about 1538 so we've jumped we've + + align:start position:0% +written about 1538 so we've jumped we've + + + align:start position:0% +written about 1538 so we've jumped we've +been jumping forward and backward + + align:start position:0% +been jumping forward and backward + + + align:start position:0% +been jumping forward and backward +throughout the 16th century today but we + + align:start position:0% +throughout the 16th century today but we + + + align:start position:0% +throughout the 16th century today but we +jumped backwards to do the magical + + align:start position:0% +jumped backwards to do the magical + + + align:start position:0% +jumped backwards to do the magical +because keep that brain cell keep that + + align:start position:0% +because keep that brain cell keep that + + + align:start position:0% +because keep that brain cell keep that +area really separate from when you + + align:start position:0% +area really separate from when you + + + align:start position:0% +area really separate from when you +listen to the other setting of Bianco + + align:start position:0% +listen to the other setting of Bianco + + + align:start position:0% +listen to the other setting of Bianco +doino written at the end of the century + + align:start position:0% +doino written at the end of the century + + + align:start position:0% +doino written at the end of the century +when the madal becomes a place to do the + + align:start position:0% +when the madal becomes a place to do the + + + align:start position:0% +when the madal becomes a place to do the +silliest things possible with texts and + + align:start position:0% +silliest things possible with texts and + + + align:start position:0% +silliest things possible with texts and +not respect the text and to and later to + + align:start position:0% +not respect the text and to and later to + + + align:start position:0% +not respect the text and to and later to +get very very bad texts that let you do + + align:start position:0% +get very very bad texts that let you do + + + align:start position:0% +get very very bad texts that let you do +whatever you want musically so we're + + align:start position:0% +whatever you want musically so we're + + + align:start position:0% +whatever you want musically so we're +going to go in two classes from the + + align:start position:0% +going to go in two classes from the + + + align:start position:0% +going to go in two classes from the +magical being a very serious + + align:start position:0% +magical being a very serious + + + align:start position:0% +magical being a very serious +sophisticated genre to the magical being + + align:start position:0% +sophisticated genre to the magical being + + + align:start position:0% +sophisticated genre to the magical being +a lot of fun and that's what will + + align:start position:0% +a lot of fun and that's what will + + + align:start position:0% +a lot of fun and that's what will +continue next Tuesday um feel free to + + align:start position:0% +continue next Tuesday um feel free to + + + align:start position:0% +continue next Tuesday um feel free to +keep emailing me with questions about + + align:start position:0% +keep emailing me with questions about + + + align:start position:0% +keep emailing me with questions about +papers drafts things um and I look + + align:start position:0% +papers drafts things um and I look + + + align:start position:0% +papers drafts things um and I look +forward to reading them thank + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/2IBWxERRjvM.txt b/2IBWxERRjvM.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7b28b1b3372a290b2dd7e64ab71d5adce787cfc --- /dev/null +++ b/2IBWxERRjvM.txt @@ -0,0 +1,2184 @@ +align:start position:0% + +So today we're going to take a look at + + align:start position:0% +So today we're going to take a look at + + + align:start position:0% +So today we're going to take a look at +sidal functions and specifically we're + + align:start position:0% +sidal functions and specifically we're + + + align:start position:0% +sidal functions and specifically we're +going to use complex numbers uh to get a + + align:start position:0% +going to use complex numbers uh to get a + + + align:start position:0% +going to use complex numbers uh to get a +handle on sinusoidal functions the + + align:start position:0% +handle on sinusoidal functions the + + + align:start position:0% +handle on sinusoidal functions the +reason is complex numbers provide a + + align:start position:0% +reason is complex numbers provide a + + + align:start position:0% +reason is complex numbers provide a +robust way of analyzing sinodal + + align:start position:0% +robust way of analyzing sinodal + + + align:start position:0% +robust way of analyzing sinodal +functions so specifically we're + + align:start position:0% +functions so specifically we're + + + align:start position:0% +functions so specifically we're +interested in this function e to the I + + align:start position:0% +interested in this function e to the I + + + align:start position:0% +interested in this function e to the I +Omega T / 2 + 3 I and we're asked to + + align:start position:0% +Omega T / 2 + 3 I and we're asked to + + + align:start position:0% +Omega T / 2 + 3 I and we're asked to +write the real part of this function uh + + align:start position:0% +write the real part of this function uh + + + align:start position:0% +write the real part of this function uh +using Polar form and then rectangular + + align:start position:0% +using Polar form and then rectangular + + + align:start position:0% +using Polar form and then rectangular +form and then secondly we're asked + + align:start position:0% +form and then secondly we're asked + + + align:start position:0% +form and then secondly we're asked +several properties of this uh function + + align:start position:0% +several properties of this uh function + + + align:start position:0% +several properties of this uh function +the real part of this function what's + + align:start position:0% +the real part of this function what's + + + align:start position:0% +the real part of this function what's +the circular frequency what's the + + align:start position:0% +the circular frequency what's the + + + align:start position:0% +the circular frequency what's the +amplitude and what's the phase leg and + + align:start position:0% +amplitude and what's the phase leg and + + + align:start position:0% +amplitude and what's the phase leg and +then lastly we're asked to sketch the + + align:start position:0% +then lastly we're asked to sketch the + + + align:start position:0% +then lastly we're asked to sketch the +real part of this function versus time + + align:start position:0% +real part of this function versus time + + + align:start position:0% +real part of this function versus time +so I'll let you take a look at this and + + align:start position:0% +so I'll let you take a look at this and + + + align:start position:0% +so I'll let you take a look at this and +try it for yourself and I'll come back + + align:start position:0% +try it for yourself and I'll come back + + + align:start position:0% +try it for yourself and I'll come back +in a + + align:start position:0% + + + + align:start position:0% + +moment + + align:start position:0% + + + + align:start position:0% + +hi everyone welcome back okay so let's + + align:start position:0% +hi everyone welcome back okay so let's + + + align:start position:0% +hi everyone welcome back okay so let's +take a look at this problem so we're + + align:start position:0% +take a look at this problem so we're + + + align:start position:0% +take a look at this problem so we're +asked to write e to the I Omega + + align:start position:0% +asked to write e to the I Omega + + + align:start position:0% +asked to write e to the I Omega +T ID 2 + 3 I uh but we're asked to write + + align:start position:0% +T ID 2 + 3 I uh but we're asked to write + + + align:start position:0% +T ID 2 + 3 I uh but we're asked to write +the real part of this function using + + align:start position:0% +the real part of this function using + + + align:start position:0% +the real part of this function using +Polar form and then also rectangular + + align:start position:0% +Polar form and then also rectangular + + + align:start position:0% +Polar form and then also rectangular +form so I'll first start off with Polar + + align:start position:0% +form so I'll first start off with Polar + + + align:start position:0% +form so I'll first start off with Polar +form + + align:start position:0% + + + + align:start position:0% + +and if we take a look at this function + + align:start position:0% +and if we take a look at this function + + + align:start position:0% +and if we take a look at this function +we see that the um the + + align:start position:0% +we see that the um the + + + align:start position:0% +we see that the um the +numerator is already written in polar + + align:start position:0% +numerator is already written in polar + + + align:start position:0% +numerator is already written in polar +form so just recall that Polar form is + + align:start position:0% +form so just recall that Polar form is + + + align:start position:0% +form so just recall that Polar form is +of the form + + align:start position:0% +of the form + + + align:start position:0% +of the form +r e to the I + + align:start position:0% + + + + align:start position:0% + +Theta uh meanwhile the denominator is + + align:start position:0% +Theta uh meanwhile the denominator is + + + align:start position:0% +Theta uh meanwhile the denominator is +written in cartisian form or rectangular + + align:start position:0% +written in cartisian form or rectangular + + + align:start position:0% +written in cartisian form or rectangular +form so we need to convert this into + + align:start position:0% +form so we need to convert this into + + + align:start position:0% +form so we need to convert this into +Polar + + align:start position:0% +Polar + + + align:start position:0% +Polar +form so what we can do is we can write 2 + + align:start position:0% +form so what we can do is we can write 2 + + + align:start position:0% +form so what we can do is we can write 2 ++ 3 + + align:start position:0% ++ 3 + + + align:start position:0% ++ 3 +I we can combine these two into a + + align:start position:0% +I we can combine these two into a + + + align:start position:0% +I we can combine these two into a +modulus and the modulus is going to be + + align:start position:0% +modulus and the modulus is going to be + + + align:start position:0% +modulus and the modulus is going to be +the square root of 2^ + + align:start position:0% +the square root of 2^ + + + align:start position:0% +the square root of 2^ +2 + 3^ + + align:start position:0% +2 + 3^ + + + align:start position:0% +2 + 3^ +2 so this is the the complex modulus or + + align:start position:0% +2 so this is the the complex modulus or + + + align:start position:0% +2 so this is the the complex modulus or +the uh the modulus of the complex + + align:start position:0% +the uh the modulus of the complex + + + align:start position:0% +the uh the modulus of the complex +number and then we have e to the I + + align:start position:0% +number and then we have e to the I + + + align:start position:0% +number and then we have e to the I +fi and the angle + + align:start position:0% +fi and the angle + + + align:start position:0% +fi and the angle +fi we can d used + + align:start position:0% +fi we can d used + + + align:start position:0% +fi we can d used +by writing a + + align:start position:0% +by writing a + + + align:start position:0% +by writing a +triangle which is is over to the right + + align:start position:0% +triangle which is is over to the right + + + align:start position:0% +triangle which is is over to the right +by two uh units and then it's up two + + align:start position:0% +by two uh units and then it's up two + + + align:start position:0% +by two uh units and then it's up two +units and this is the angle + + align:start position:0% +units and this is the angle + + + align:start position:0% +units and this is the angle +F so we see from the + + align:start position:0% +F so we see from the + + + align:start position:0% +F so we see from the +triangle that the arc + + align:start position:0% +triangle that the arc + + + align:start position:0% +triangle that the arc +tangent of or sorry the tangent of fi is + + align:start position:0% +tangent of or sorry the tangent of fi is + + + align:start position:0% +tangent of or sorry the tangent of fi is +equal to 3 + + align:start position:0% + + + + align:start position:0% + +over2 okay so putting the pieces + + align:start position:0% +over2 okay so putting the pieces + + + align:start position:0% +over2 okay so putting the pieces +together we + + align:start position:0% +together we + + + align:start position:0% +together we +have e to the I Omega + + align:start position:0% +have e to the I Omega + + + align:start position:0% +have e to the I Omega +T /un + + align:start position:0% +T /un + + + align:start position:0% +T /un +13 e to the + + align:start position:0% + + + + align:start position:0% + +II and the beautiful thing about polar + + align:start position:0% +II and the beautiful thing about polar + + + align:start position:0% +II and the beautiful thing about polar +form is that when we divide and + + align:start position:0% +form is that when we divide and + + + align:start position:0% +form is that when we divide and +multiply uh these complex exponentials + + align:start position:0% +multiply uh these complex exponentials + + + align:start position:0% +multiply uh these complex exponentials +it just turns into a simple addition or + + align:start position:0% +it just turns into a simple addition or + + + align:start position:0% +it just turns into a simple addition or +subtraction of the + + align:start position:0% +subtraction of the + + + align:start position:0% +subtraction of the +phases + + align:start position:0% + + + + align:start position:0% + +so we have 1/ < + + align:start position:0% +so we have 1/ < + + + align:start position:0% +so we have 1/ < +tk3 e to the I Omega T minus + + align:start position:0% +tk3 e to the I Omega T minus + + + align:start position:0% +tk3 e to the I Omega T minus +5 so we've successfully combined all the + + align:start position:0% +5 so we've successfully combined all the + + + align:start position:0% +5 so we've successfully combined all the +terms into one polar + + align:start position:0% +terms into one polar + + + align:start position:0% +terms into one polar +term and then now we're asked to uh + + align:start position:0% +term and then now we're asked to uh + + + align:start position:0% +term and then now we're asked to uh +compute the real part and here we use + + align:start position:0% +compute the real part and here we use + + + align:start position:0% +compute the real part and here we use +Oilers formula + + align:start position:0% +Oilers formula + + + align:start position:0% +Oilers formula +so just to recall Oilers + + align:start position:0% +so just to recall Oilers + + + align:start position:0% +so just to recall Oilers +formula we have e to the + + align:start position:0% +formula we have e to the + + + align:start position:0% +formula we have e to the +I + + align:start position:0% +I + + + align:start position:0% +I +Theta then this is equal to cosine + + align:start position:0% +Theta then this is equal to cosine + + + align:start position:0% +Theta then this is equal to cosine +theta plus I sin + + align:start position:0% + + + + align:start position:0% + +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +okay so at the end of the day we're + + align:start position:0% +okay so at the end of the day we're + + + align:start position:0% +okay so at the end of the day we're +interested in the real part and I'm + + align:start position:0% +interested in the real part and I'm + + + align:start position:0% +interested in the real part and I'm +going to use this notation re with a + + align:start position:0% +going to use this notation re with a + + + align:start position:0% +going to use this notation re with a +curly bracket to denote the real part of + + align:start position:0% +curly bracket to denote the real part of + + + align:start position:0% +curly bracket to denote the real part of +1 < + + align:start position:0% +1 < + + + align:start position:0% +1 < +tk3 and I'll use Oilers formula on E to + + align:start position:0% +tk3 and I'll use Oilers formula on E to + + + align:start position:0% +tk3 and I'll use Oilers formula on E to +I Omega T minus 5 so we have + + align:start position:0% +I Omega T minus 5 so we have + + + align:start position:0% +I Omega T minus 5 so we have +cosine Omega T minus + + align:start position:0% + + + + align:start position:0% + +5 plus + + align:start position:0% +5 plus + + + align:start position:0% +5 plus +I + + align:start position:0% +I + + + align:start position:0% +I +S Omega T minus + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +sorry 1 overun 13 is multiplying both + + align:start position:0% +sorry 1 overun 13 is multiplying both + + + align:start position:0% +sorry 1 overun 13 is multiplying both +the sign and the cosine + + align:start position:0% + + + + align:start position:0% + +and we see that the second term is + + align:start position:0% +and we see that the second term is + + + align:start position:0% +and we see that the second term is +purely imaginary so when we take the + + align:start position:0% +purely imaginary so when we take the + + + align:start position:0% +purely imaginary so when we take the +real part of a real number plus an + + align:start position:0% +real part of a real number plus an + + + align:start position:0% +real part of a real number plus an +imaginary number we just are left at the + + align:start position:0% +imaginary number we just are left at the + + + align:start position:0% +imaginary number we just are left at the +real number at the end of the + + align:start position:0% + + + + align:start position:0% + +day so the answer we're looking + + align:start position:0% + + + + align:start position:0% + +for is 1 overun 13 cosine Omega T minus + + align:start position:0% +for is 1 overun 13 cosine Omega T minus + + + align:start position:0% +for is 1 overun 13 cosine Omega T minus +5 where + + align:start position:0% + + + + align:start position:0% + +from before fi + + align:start position:0% +from before fi + + + align:start position:0% +from before fi +is the arct tangent of 3 + + align:start position:0% + + + + align:start position:0% + +over2 and F can also be thought of uh + + align:start position:0% +over2 and F can also be thought of uh + + + align:start position:0% +over2 and F can also be thought of uh +the angle uh being between Z and pi over + + align:start position:0% +the angle uh being between Z and pi over + + + align:start position:0% +the angle uh being between Z and pi over +2 okay so this is uh this concludes the + + align:start position:0% +2 okay so this is uh this concludes the + + + align:start position:0% +2 okay so this is uh this concludes the +polar form computation uh secondly we + + align:start position:0% +polar form computation uh secondly we + + + align:start position:0% +polar form computation uh secondly we +also have to compute this using re uh + + align:start position:0% +also have to compute this using re uh + + + align:start position:0% +also have to compute this using re uh +using a rectangular form calculation + + align:start position:0% +using a rectangular form calculation + + + align:start position:0% +using a rectangular form calculation +so let's use let's do the + + align:start position:0% + + + + align:start position:0% + +calculation in rectangular + + align:start position:0% +calculation in rectangular + + + align:start position:0% +calculation in rectangular +form and for this I'm going to use + + align:start position:0% +form and for this I'm going to use + + + align:start position:0% +form and for this I'm going to use +Oilers formula to expand out the + + align:start position:0% + + + + align:start position:0% + +numerator so + + align:start position:0% +numerator so + + + align:start position:0% +numerator so +first we want to take the real part + + align:start position:0% +first we want to take the real part + + + align:start position:0% +first we want to take the real part +of the numerator is cosine Omega t + + align:start position:0% +of the numerator is cosine Omega t + + + align:start position:0% +of the numerator is cosine Omega t +plus I sin Omega + + align:start position:0% + + + + align:start position:0% + +T the denominator was 2 + I 3 + + align:start position:0% + + + + align:start position:0% + +I and uh typically what we want to do is + + align:start position:0% +I and uh typically what we want to do is + + + align:start position:0% +I and uh typically what we want to do is +we want to uh turn the denominator into + + align:start position:0% +we want to uh turn the denominator into + + + align:start position:0% +we want to uh turn the denominator into +an entirely real number so what we do is + + align:start position:0% +an entirely real number so what we do is + + + align:start position:0% +an entirely real number so what we do is +we multiply the top and bottom by the + + align:start position:0% +we multiply the top and bottom by the + + + align:start position:0% +we multiply the top and bottom by the +complex + + align:start position:0% + + + + align:start position:0% + +conjugate of the denominator so for + + align:start position:0% +conjugate of the denominator so for + + + align:start position:0% +conjugate of the denominator so for +example I have 2 + 3 I so I'm going to + + align:start position:0% +example I have 2 + 3 I so I'm going to + + + align:start position:0% +example I have 2 + 3 I so I'm going to +multiply the top and bottom by 2 - 3 + + align:start position:0% + + + + align:start position:0% + +I okay and when I do this you'll note + + align:start position:0% +I okay and when I do this you'll note + + + align:start position:0% +I okay and when I do this you'll note +that when we multiply out 2 + 3 I and 2 + + align:start position:0% +that when we multiply out 2 + 3 I and 2 + + + align:start position:0% +that when we multiply out 2 + 3 I and 2 +- 3 I we have a difference of + + align:start position:0% +- 3 I we have a difference of + + + align:start position:0% +- 3 I we have a difference of +squares so we're left with 2 * 2 is + + align:start position:0% +squares so we're left with 2 * 2 is + + + align:start position:0% +squares so we're left with 2 * 2 is +4 the cross terms cancel and then we + + align:start position:0% +4 the cross terms cancel and then we + + + align:start position:0% +4 the cross terms cancel and then we +have 3 I * -3 I that's going to give us + + align:start position:0% +have 3 I * -3 I that's going to give us + + + align:start position:0% +have 3 I * -3 I that's going to give us +9 i^ 2 which is + + + align:start position:0% + + + + align:start position:0% + +9 so the denominator is going to be 4 + + + align:start position:0% + + + + align:start position:0% + +9 and then the numerator I'll write at + + align:start position:0% +9 and then the numerator I'll write at + + + align:start position:0% +9 and then the numerator I'll write at +all the terms just for completeness but + + align:start position:0% +all the terms just for completeness but + + + align:start position:0% +all the terms just for completeness but +it'll be two 2 * cosine Omega + + align:start position:0% + + + + align:start position:0% + +t plus + + align:start position:0% +t plus + + + align:start position:0% +t plus +three + + align:start position:0% +three + + + align:start position:0% +three +sin Omega + + align:start position:0% + + + + align:start position:0% + +T and then now we have some imaginary + + align:start position:0% +T and then now we have some imaginary + + + align:start position:0% +T and then now we have some imaginary +terms which are ne3 cosine Omega + + align:start position:0% + + + + align:start position:0% + +T and plus + + align:start position:0% +T and plus + + + align:start position:0% +T and plus +2 sin Omega + + align:start position:0% + + + + align:start position:0% + +T + + align:start position:0% +T + + + align:start position:0% +T +okay but + + align:start position:0% + + + + align:start position:0% + +then but now we're going to take the + + align:start position:0% +then but now we're going to take the + + + align:start position:0% +then but now we're going to take the +real part of this complex + + align:start position:0% +real part of this complex + + + align:start position:0% +real part of this complex +function and if we take a look at it + + align:start position:0% +function and if we take a look at it + + + align:start position:0% +function and if we take a look at it +this first term is entirely real the + + align:start position:0% +this first term is entirely real the + + + align:start position:0% +this first term is entirely real the +second term is entirely complex because + + align:start position:0% +second term is entirely complex because + + + align:start position:0% +second term is entirely complex because +we're multiplying by an I so when we + + align:start position:0% +we're multiplying by an I so when we + + + align:start position:0% +we're multiplying by an I so when we +take the real part at the end of the day + + align:start position:0% +take the real part at the end of the day + + + align:start position:0% +take the real part at the end of the day +the second term is is going to drop + + align:start position:0% + + + + align:start position:0% + +out so so when the dust + + align:start position:0% +out so so when the dust + + + align:start position:0% +out so so when the dust +settles we have 1 over + + align:start position:0% +settles we have 1 over + + + align:start position:0% +settles we have 1 over +13 2 * cosine Omega + + align:start position:0% +13 2 * cosine Omega + + + align:start position:0% +13 2 * cosine Omega +t+ 3 sin Omega + + align:start position:0% + + + + align:start position:0% + +t Okay so this concludes part + + align:start position:0% + + + + align:start position:0% + +A for Part B we're asked several uh + + align:start position:0% +A for Part B we're asked several uh + + + align:start position:0% +A for Part B we're asked several uh +questions about this complex sinusoidal + + align:start position:0% +questions about this complex sinusoidal + + + align:start position:0% +questions about this complex sinusoidal +function or sorry this uh sinusoidal + + align:start position:0% +function or sorry this uh sinusoidal + + + align:start position:0% +function or sorry this uh sinusoidal +function when written um in uh its real + + align:start position:0% +function when written um in uh its real + + + align:start position:0% +function when written um in uh its real +form specifically uh what's the circular + + align:start position:0% + + + + align:start position:0% + +frequency and the circular frequency is + + align:start position:0% +frequency and the circular frequency is + + + align:start position:0% +frequency and the circular frequency is +just the frequency uh that this function + + align:start position:0% +just the frequency uh that this function + + + align:start position:0% +just the frequency uh that this function +oscillates at and we can we can get this + + align:start position:0% +oscillates at and we can we can get this + + + align:start position:0% +oscillates at and we can we can get this +from looking at the rectangular form or + + align:start position:0% +from looking at the rectangular form or + + + align:start position:0% +from looking at the rectangular form or +or the polar + + align:start position:0% +or the polar + + + align:start position:0% +or the polar +form and it's simply just going to be + + align:start position:0% +form and it's simply just going to be + + + align:start position:0% +form and it's simply just going to be +Omega so note how this this function + + align:start position:0% +Omega so note how this this function + + + align:start position:0% +Omega so note how this this function +oscillates with frequency + + align:start position:0% + + + + align:start position:0% + +Omega uh + + align:start position:0% +Omega uh + + + align:start position:0% +Omega uh +secondly we're asked about the + + align:start position:0% + + + + align:start position:0% + +amplitude and if we take a look at it + + align:start position:0% +amplitude and if we take a look at it + + + align:start position:0% +amplitude and if we take a look at it +the amplitude is a little tricky to get + + align:start position:0% +the amplitude is a little tricky to get + + + align:start position:0% +the amplitude is a little tricky to get +from the rectangular form but it's + + align:start position:0% +from the rectangular form but it's + + + align:start position:0% +from the rectangular form but it's +completely Apparent from The Polar form + + align:start position:0% +completely Apparent from The Polar form + + + align:start position:0% +completely Apparent from The Polar form +so if we take a look at the polar form + + align:start position:0% +so if we take a look at the polar form + + + align:start position:0% +so if we take a look at the polar form +we have 1 overun 13 cosine Omega T minus + + align:start position:0% +we have 1 overun 13 cosine Omega T minus + + + align:start position:0% +we have 1 overun 13 cosine Omega T minus +5 and F oscillates between plus one and + + align:start position:0% +5 and F oscillates between plus one and + + + align:start position:0% +5 and F oscillates between plus one and +sorry cosine oscillates between + one + + align:start position:0% +sorry cosine oscillates between + one + + + align:start position:0% +sorry cosine oscillates between + one +and minus one so this function takes on + + align:start position:0% +and minus one so this function takes on + + + align:start position:0% +and minus one so this function takes on +a maximum value of + 1 overun 13 and a + + align:start position:0% +a maximum value of + 1 overun 13 and a + + + align:start position:0% +a maximum value of + 1 overun 13 and a +maximum negative value of negative 1 + + align:start position:0% +maximum negative value of negative 1 + + + align:start position:0% +maximum negative value of negative 1 +overun 13 so the amplitude of this + + align:start position:0% +overun 13 so the amplitude of this + + + align:start position:0% +overun 13 so the amplitude of this +function is just going to + + align:start position:0% +function is just going to + + + align:start position:0% +function is just going to +be 1un + + align:start position:0% + + + + align:start position:0% + +13 and then lastly the phase + + align:start position:0% +13 and then lastly the phase + + + align:start position:0% +13 and then lastly the phase +lag + + align:start position:0% + + + + align:start position:0% + +this is the angle that the cosine is + + align:start position:0% +this is the angle that the cosine is + + + align:start position:0% +this is the angle that the cosine is +picked up and shifted + + align:start position:0% + + + + align:start position:0% + +over so again we can we can get this uh + + align:start position:0% +over so again we can we can get this uh + + + align:start position:0% +over so again we can we can get this uh +directly from The Polar form or Sor yeah + + align:start position:0% +directly from The Polar form or Sor yeah + + + align:start position:0% +directly from The Polar form or Sor yeah +sorry from The Polar + + align:start position:0% +sorry from The Polar + + + align:start position:0% +sorry from The Polar +form meanwhile it's a little less + + align:start position:0% +form meanwhile it's a little less + + + align:start position:0% +form meanwhile it's a little less +obvious what this angle is when we take + + align:start position:0% +obvious what this angle is when we take + + + align:start position:0% +obvious what this angle is when we take +a look at the rectangular + + align:start position:0% +a look at the rectangular + + + align:start position:0% +a look at the rectangular +form so in our + + align:start position:0% +form so in our + + + align:start position:0% +form so in our +case the phase like is just going to be + + align:start position:0% + + + + align:start position:0% + +five which is tan inverse 3 + + align:start position:0% + + + + align:start position:0% + +over2 okay so this concludes Part + + align:start position:0% +over2 okay so this concludes Part + + + align:start position:0% +over2 okay so this concludes Part +B and then lastly for part C we're just + + align:start position:0% +B and then lastly for part C we're just + + + align:start position:0% +B and then lastly for part C we're just +asked to sketch sketch this + + align:start position:0% + + + + align:start position:0% + +diagram and again this function is going + + align:start position:0% +diagram and again this function is going + + + align:start position:0% +diagram and again this function is going +to + + align:start position:0% + + + + align:start position:0% + +be uh or the most the most direct way at + + align:start position:0% +be uh or the most the most direct way at + + + align:start position:0% +be uh or the most the most direct way at +sketching this function is through the + + align:start position:0% +sketching this function is through the + + + align:start position:0% +sketching this function is through the +Polar form so I'll write time on this + + align:start position:0% + + + + align:start position:0% + +axis and if we just + + align:start position:0% +axis and if we just + + + align:start position:0% +axis and if we just +recall that a + + align:start position:0% +recall that a + + + align:start position:0% +recall that a +cosine might look something like + + align:start position:0% + + + + align:start position:0% + +this so this is a cosine + + align:start position:0% +this so this is a cosine + + + align:start position:0% +this so this is a cosine +function and in our case we're looking + + align:start position:0% +function and in our case we're looking + + + align:start position:0% +function and in our case we're looking +at plotting 1/ < TK 13 cosine Omega TUS + + align:start position:0% +at plotting 1/ < TK 13 cosine Omega TUS + + + align:start position:0% +at plotting 1/ < TK 13 cosine Omega TUS +5 so we're interested in a cosine which + + align:start position:0% +5 so we're interested in a cosine which + + + align:start position:0% +5 so we're interested in a cosine which +has an + + align:start position:0% +has an + + + align:start position:0% +has an +amplitude of 1un + + align:start position:0% +amplitude of 1un + + + align:start position:0% +amplitude of 1un +13 and a maximum negative value of minus + + align:start position:0% +13 and a maximum negative value of minus + + + align:start position:0% +13 and a maximum negative value of minus +one overun + + align:start position:0% + + + + align:start position:0% + +13 whose + + align:start position:0% +13 whose + + + align:start position:0% +13 whose +frequency is + + align:start position:0% +frequency is + + + align:start position:0% +frequency is +Omega so there's a there's a quick way + + align:start position:0% +Omega so there's a there's a quick way + + + align:start position:0% +Omega so there's a there's a quick way +on finding uh the + + align:start position:0% +on finding uh the + + + align:start position:0% +on finding uh the +zeros so if the zero of a regular cosine + + align:start position:0% +zeros so if the zero of a regular cosine + + + align:start position:0% +zeros so if the zero of a regular cosine +is at Pi / 2 + + align:start position:0% +is at Pi / 2 + + + align:start position:0% +is at Pi / 2 +then uh if we have an angular frequency + + align:start position:0% +then uh if we have an angular frequency + + + align:start position:0% +then uh if we have an angular frequency +of Omega the zero here is going to be Pi + + align:start position:0% +of Omega the zero here is going to be Pi + + + align:start position:0% +of Omega the zero here is going to be Pi +/ 2 + + align:start position:0% +/ 2 + + + align:start position:0% +/ 2 +Omega and this zero is going to be at 3 + + align:start position:0% +Omega and this zero is going to be at 3 + + + align:start position:0% +Omega and this zero is going to be at 3 +pi over 2 + + align:start position:0% + + + + align:start position:0% + +Omega and lastly this is not the co this + + align:start position:0% +Omega and lastly this is not the co this + + + align:start position:0% +Omega and lastly this is not the co this +is not necessarily the cosine of our + + align:start position:0% +is not necessarily the cosine of our + + + align:start position:0% +is not necessarily the cosine of our +function our function is this cosine + + align:start position:0% +function our function is this cosine + + + align:start position:0% +function our function is this cosine +however it must be picked up and shifted + + align:start position:0% +however it must be picked up and shifted + + + align:start position:0% +however it must be picked up and shifted +over by some phase leg fi so in our case + + align:start position:0% +over by some phase leg fi so in our case + + + align:start position:0% +over by some phase leg fi so in our case +the function we're actually looking for + + align:start position:0% +the function we're actually looking for + + + align:start position:0% +the function we're actually looking for +is some shifted cosine which looks like + + align:start position:0% + + + + align:start position:0% + +this and this distance here is + + align:start position:0% + + + + align:start position:0% + +five five over Omega + + align:start position:0% + + + + align:start position:0% + +s okay so this just gives us a quick + + align:start position:0% +s okay so this just gives us a quick + + + align:start position:0% +s okay so this just gives us a quick +sketch of this + + align:start position:0% +sketch of this + + + align:start position:0% +sketch of this +function and again we note that + + align:start position:0% +function and again we note that + + + align:start position:0% +function and again we note that +uh we were able to plot this using the + + align:start position:0% +uh we were able to plot this using the + + + align:start position:0% +uh we were able to plot this using the +polar form uh very quickly and the + + align:start position:0% +polar form uh very quickly and the + + + align:start position:0% +polar form uh very quickly and the +reason is because the polar form gives + + align:start position:0% +reason is because the polar form gives + + + align:start position:0% +reason is because the polar form gives +us the amplitude the circular frequency + + align:start position:0% +us the amplitude the circular frequency + + + align:start position:0% +us the amplitude the circular frequency +and the phase leg whereas if we were to + + align:start position:0% +and the phase leg whereas if we were to + + + align:start position:0% +and the phase leg whereas if we were to +take a look at the equivalent + + align:start position:0% +take a look at the equivalent + + + align:start position:0% +take a look at the equivalent +rectangular form it's a little less + + align:start position:0% +rectangular form it's a little less + + + align:start position:0% +rectangular form it's a little less +obvious the rectangular form is actually + + align:start position:0% +obvious the rectangular form is actually + + + align:start position:0% +obvious the rectangular form is actually +the sum of a sign and a cosine and + + align:start position:0% +the sum of a sign and a cosine and + + + align:start position:0% +the sum of a sign and a cosine and +unless you can just add signs and + + align:start position:0% +unless you can just add signs and + + + align:start position:0% +unless you can just add signs and +cosines in your head very quickly it's a + + align:start position:0% +cosines in your head very quickly it's a + + + align:start position:0% +cosines in your head very quickly it's a +little less obvious on how to come up + + align:start position:0% +little less obvious on how to come up + + + align:start position:0% +little less obvious on how to come up +with this + + align:start position:0% +with this + + + align:start position:0% +with this +picture Okay so just to summarize we've + + align:start position:0% +picture Okay so just to summarize we've + + + align:start position:0% +picture Okay so just to summarize we've +kind of used we've used complex + + align:start position:0% +kind of used we've used complex + + + align:start position:0% +kind of used we've used complex +functions uh to analyze sinodal + + align:start position:0% +functions uh to analyze sinodal + + + align:start position:0% +functions uh to analyze sinodal +functions and uh we've used uh polar + + align:start position:0% +functions and uh we've used uh polar + + + align:start position:0% +functions and uh we've used uh polar +form and rectangular form to get a + + align:start position:0% +form and rectangular form to get a + + + align:start position:0% +form and rectangular form to get a +handle on uh the complex functions and + + align:start position:0% +handle on uh the complex functions and + + + align:start position:0% +handle on uh the complex functions and +specifically complex functions are a + + align:start position:0% +specifically complex functions are a + + + align:start position:0% +specifically complex functions are a +very good way to uh represent sinusoidal + + align:start position:0% +very good way to uh represent sinusoidal + + + align:start position:0% +very good way to uh represent sinusoidal +functions and uh just to reiterate the + + align:start position:0% +functions and uh just to reiterate the + + + align:start position:0% +functions and uh just to reiterate the +reason is that they contain a lot of + + align:start position:0% +reason is that they contain a lot of + + + align:start position:0% +reason is that they contain a lot of +information that we can uh graphically + + align:start position:0% +information that we can uh graphically + + + align:start position:0% +information that we can uh graphically +uh handle and turn into a sketch so I'll + + align:start position:0% +uh handle and turn into a sketch so I'll + + + align:start position:0% +uh handle and turn into a sketch so I'll +just conclude there and I'll see you + + align:start position:0% +just conclude there and I'll see you + + + align:start position:0% +just conclude there and I'll see you +next time \ No newline at end of file diff --git a/2g9OSRKJuzM.txt b/2g9OSRKJuzM.txt new file mode 100644 index 0000000000000000000000000000000000000000..a1d8e695528324da43e347235e5c03f9eb4a96f4 --- /dev/null +++ b/2g9OSRKJuzM.txt @@ -0,0 +1,3646 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +SRINIVAS DEVADAS: All right. + +Good morning, everyone. + +And let's get started. + +Today's lecture is about a +randomized data structure + +called the skip list. + +And it's a data structure +that, obviously because it's + +randomized, we'd have to do +a probabilistic analysis for. + +And we're going to sort of raise +the stakes here a little bit + +with respect to +our expectation-- + +the pun intended of this +data structure-- in the sense + +that we're not going to be happy +with just doing an expected + +value analysis or to get +what the expectation is + +of the search complexity +in a skip list. + +We're going to introduce this +notion with high probability, + +which is a stronger notion than +just giving you the expected + +value or the expectation for +the complexity of a search + +algorithm. + +And we're going to prove +that under this notion, + +that search has a +particular complexity + +with high probability. + +So we'll get to the with high +probability part a little bit + +later in the lecture, +but we're just + +going to start off doing some +cool data structure design, + +I guess, [INAUDIBLE] +pointing to the skip list. + +The skip list is a relatively +young data structure + +invented by a guy called +Bill Pugh in 1989, + +so not much older than you guys. + +It's relatively easy to +implement as you'll see. + +I won't really claim +that, but hopefully you'll + +be convinced by the time you're +done describing the structure. + +Especially in comparison +to balanced trees. + +And we can do a comparison after +we do our analysis of the data + +structure as to what the +complexity comparisons are + +for search and insert +when you take a skip list + +and compare it to an +AVL tree, for example, + +or a red black tree, et cetera. + +In general, when we +have a data structure, + +we want it to be dynamic. + +The skip list maintains +a dynamic set. + +What that means +is not only do you + +want to search on +it-- obviously it's + +uninteresting to have a static +data structure and do a search. + +You want to be able to +change it, want to be + +able to insert values into it. + +There's a complexity of +insert to worry about. + +You want to be able +to delete values. + +And the richness of +the data structure + +comes from the operations +and the augmentations + +you can do on it, and the skip +lists are no exception to that. + +So if you want to maintain +a dynamic set of n elements, + +and you obviously know a ton +of data structures to do this, + +each of which has +different characteristics. + +And this is, if you +ignore hash tables, + +this is your first real +randomized data structure, + +if you're just taking +6006 and this class + +might have seen randomized +structures in other classes. + +So we're going to try and +do this in order log n time. + +As you know with +balanced binary trees, + +you can do things in order +log n time, a ton of things, + +pretty much everything +that is interesting. + +And this, given that +it's randomized, + +it's a relatively +easy analysis to show + +that the expectation or the +expected value of a search + +would be order log +n expected time. + +But we're going to, as I +said, raise the stakes, + +and we're going to +spend a ton of time + +the second half of this showing +the with high probability + +result. And that's +a stronger result + +than just saying that search +takes expected order log n + +time. + +All right, so +that's the context. + +You can think of a +skip list as beginning + +with a simple linked list. + +So if we have one link list +and that link list-- let's + +first think of this +as being unsorted. + +So suppose I have a link +list which is unsorted + +and I want to search for a +particular value in this link + +list. + +And we can assume that this +is a doubly-linked list, + +so the arrows go both ways. + +You have a pointer, let's say, +just to the first element. + +So if you have a +list that's unsorted + +and you want to +search for an element, + +you would want to do +a membership query. + +If there's n elements, +the complexity is? + +AUDIENCE: Order n. + +SRINIVAS DEVADAS: Order n. + +So a linked list, the search +takes the order n time. + +Now let's go ahead and say +that we are sorting this list, + +so it's a sorted linked list. + +So your values here, +14, 23, 34, 42, 50, 59. + +They're sorted in +ascending order. + +You still only have a pointer +to the front of the list + +and it's a +doubly-linked list, what + +is the complexity of search +in the sorted link list? + +AUDIENCE: Log n. + +SRINIVAS DEVADAS: Log n. + +Oh, I wanted to hear that. + +Because it is? + +AUDIENCE: Order n. + +SRINIVAS DEVADAS: It's order n. + +log n is-- yeah, that +was a trick question. + +Because I liked that answer, +the person who said log n + +gets a Frisbee. + +This person won't admit. + +[LAUGHTER] + +Oh, it was you. + +OK, all right. + +There you go. + +All right. + +So log n would imply that +you have random access. + +If you have an array that's +sorted and you can go + +[? AFi, ?] and you can go +[? AFi ?] divided by 2, + +or [? AF2i ?] and you can +go directly to that element, + +then you can do binary search +and you can get a log n, + +order log in. + +But here, the sorting +actually doesn't help you + +with respect to the +search simply because you + +have to start from +the beginning, + +from the front of the list, +and you've got to keep walking. + +The only place that it helps you +is that if you know it's sorted + +and you're looking +for 37, you can + +stop after you see 42, right? + +That's pretty much the only +place that it helps you. + +But it's still +order n because that + +could happen-- on +average is going + +to happen halfway through the +list for a given membership + +query. + +So it's still order n +for a sorted link list. + +But now let's say that we +had two sorted link lists. + +And how are these two +link lists structured? + +Well, they're structured +in a certain way, + +and let me draw our canonical +example for skip list + +that I'm going to +keep coming back to. + +So I won't erase this, but I'll +draw one out-- 1, 2, 3, 4, 5, + +6, 7, 8, 9-- 9 elements. + +So that's my first +list which is sorted, + +and so I have 14, 23, 34, +42, 50, 59, 66, 72, and 79. + +What I'm going to have +now is another list sort + +of on top of this. + +I can move from top +to bottom, et cetera. + +But I'm not going +to have elements + +on top of each bottom element. + +By convention, I'm +going to have elements + +on top of the first +element, regardless + +of how many lists I have. + +We only have two at this point. + +And so I see a 14, which +is exactly the same element + +duplicated up on the top list. + +And that list is +also sorted, but I + +won't have all of the +elements in the top list. + +I'm just picking a couple here. + +So I've got 34, 42-- +they're adjacent here-- + +and then I go all +the way up to 72, + +and I duplicate it, et cetera. + +Now, this looks kind of random. + +Anybody recognize these numbers? + +No one from the great +City of New York? + +No? + +Yup, yup. + +AUDIENCE: On the subway stops? + +SRINIVAS DEVADAS: Yeah, subway +stops on the Seventh Avenue + +Express Line. + +So this is exactly the notion +of a skip list, the fact + +that you have-- +could you stand up? + +Great. + +All right. + +So the notion here +is that you don't + +have to make a lot of stops if +you know you have to go far. + +So if you want to go from +14th Street to 72nd Street, + +you just take the express line. + +But if you want to go to 66th +Street, what would you do? + +AUDIENCE: Go to 72nd +and then go back. + +SRINIVAS DEVADAS: +Well, that's one way. + +That's one way. + +That's not the way I wanted. + +The way we're going +to do this is we're + +not going to overshoot. + +So we want to minimize +distance, let's say. + +So our secondary +thing is going to be + +minimizing distance travel. + +And so you're going to pop +up the express line, go + +all the way to 42nd +Street, and you're + +going to say if I go to the +next stop on the Express Line, + +I'm going too far. + +And so you're going to pop +down to the local line. + +So you can think of this as +being link list L0 and link + +list L1. + +You're going to pop +down, and then you're + +going to go to 66th Street. + +So search 66 will be +going from 14 to 42 + +on L1, and then from 42, +let's just say that's walking. + +42 to 42, L1 to L0. + +And then 42 to 66 on L0. + +So that's the basic +notion of a skip list. + +So you can see that it's +really pretty simple. + +What we're going to do +now is do two things. + +I want to think about this +double-sorted list as a data + +structure in its own right +before I dive into skip lists + +in general. + +And I want to analyze at some +level, the best case situation + +for worst case complexity. + +And by that I mean I want to +structure the express stops + +in the best manner possible. + +These stops are very +structured for passengers + +because they figured fancy +stops on 42nd Avenue, whatever-- + +fancy stores. + +Everybody wants to go there +and so on and so forth. + +So you have 34 pretty close +to 42 because they're both + +popular destinations. + +But let's say that +things where I + +guess more egalitarian and +randomized, if you will. + +And what I want to do +is I want to structure + +this double-sorted list so +I get the best worst case + +complexity for search. + +And so let's do that. + +And before I do that, let me +write out the search algorithm, + +which is going to be important. + +I want you to assimilate +this, keep it in your head + +because we're going +to analyze search + +pretty much for the rest +of the morning here. + +And so I'll write this down. + +You've got a sense of what it +is based on what I just did here + +with this example of 66, +but worth writing down. + +We're going to walk right +in the top linked list, + +so this is simply +for two linked lists, + +and we'll generalize +at some point. + +So we want to walk right +in the top linked list, L1, + +until going right +would go too far. + +Now, there was this answer with +72, which I kind of dismissed. + +But there's no reason +why you can't overshoot + +one stop and go backwards. + +It would just be a +different search algorithm. + +It's not something we're +going to analyze here. + +It turns out in analyzing that +with high probability would + +be even more painful +than the painful analysis + +we're going to do. + +So we won't go there. + +And then we walk down +to the bottom list. + +And the bottom +list we'll call L0. + +And walk right in L0 until +the element is found or not. + +And you know that +if you've overshot. + +So if you're looking here for +route 67, when you get to 72 + +here-- you've seen +66 and you get to 72 + +and you're looking +for 67, search fails. + +It stops and fails. + +Doesn't succeed in this case. + +So that's what we +got for search. + +And that's our two +linked list argument. + +Now, our analysis essentially +says what I have is + +I'm walking right at +the bottom list here, + +and my top list is L1, +so I start with L1. + +And my search cost +is going to be + +approximately the length of L1. + +The worst case analysis, +I could go all the way + +on the top list-- it's possible. + +But for a given value, I'm +going to be looking at only + +a portion of the bottom list. + +I'm not going to go all the +way on the bottom list ever. + +I'm only going to be +looking at a portion of it. + +So it's going to be +L0 divided by L1, + +if I have interspersed my +express stops in a uniform way. + +So there's no reason-- +if I have 100 elements + +in the bottom list, +and if I had five, + +just for argument sake, +five in the top list, + +then I'd put them at, let's +say, the 0 position, 20, 40, 60, + +et cetera. + +So I want to have +roughly equal spacings. + +But we need to make that +a little more concrete, + +and a little more precise. + +And what I'm saying +here simply is + +that this is the cost of +traversal in the top list, + +and this is the cost of +traversal in the bottom list, + +because I'm not going to go +all the way in the bottom list. + +I'm only going to go a +portion on the bottom list. + +Everybody gets that? + +Yup? + +All right, good. + +So if I want to minimize +this cost, which + +is going to tell +me how to scatter + +these elements in the top list, +how to choose my express stops, + +if you will-- I want to +scatter these in a uniform way, + +then this is minimized +when terms are equal. + +You could go off and +differentiate and do that. + +It's fairly standard. + +And what you end up getting +is you want to get L1 square + +equals L0 equals n. + +So all of the elements are +down at the bottom list, + +and so the cardinality +of the bottom list is n. + +And roughly speaking, you're +going to end up optimizing, + +if you have this satisfied, +which means that L1 is + +going to be square root of n. + +OK? + +So what you've done here is +you've said a bunch of things, + +actually. + +You've decided how +many elements are + +going to be in your top list. + +If there's n elements +in the bottom list, + +you want to have the square root +of n elements in the top list. + +And not only that, +in order to make sure + +that this works properly, and +that you don't get a worse case + +cost that is not +optimal, you do have + +to intersperse the +square root of n elements + +at regular intervals in +relation to the bottom list + +on the top list. + +OK, so pictorially +what this means is it's + +not what you have here. + +What you really +want is something + +that, let's say, looks like +this where this part here + +is square root of n elements +up until that point, + +and then let's say we +go from here to here + +or square root of n +elements, and maybe I'll + +have a 66 here because +that's exactly where I + +want my square root of n. + +Basically, three +elements in between. + +So I got 66 here, et cetera. + +I mean I chose n to be +a particular value here, + +but you get the picture. + +So the search now, as you can +see if you just add those up + +you get square root +of n here, and you + +got n divided by +square root of n here. + +So that's square +root of n as well. + +So the search cost is +order square root of n. + +And so that's it. + +That's the first +generalization, and really + +the most important +one, that comes + +from going from a +single sorted list + +to an approximation +of a skip list. + +So what do you do if you +want to make things better? + +So we want to make +things better? + +Are we happy with +square root of n? + +AUDIENCE: No. + +SRINIVAS DEVADAS: No. + +Well, what's our target? + +AUDIENCE: Log n. + +SRINIVAS DEVADAS: +Log n, obviously. + +Well, I guess you can +argue that our target may + +be order 1 at some point, +but for today's lecture + +it is order log n +with high probability. + +We'll leave it at that. + +And so what do you do if +you want to go this way + +and generalize? + +You simply add more lists. + +I mean it seems to be pretty +much the only thing we + +could do here. + +So let's go ahead +and add a third list. + +So if you have two +sorted lists, that + +implies I have 2 +square root of n. + +If I want to be explicit +about the constant in terms + +of the search cost, +assuming things + +are interspersed exactly right. + +Keep that in mind because +that is going to go away + +when we go and randomize. + +We're going to be flipping +coins and things like that. + +But so far, things +are very structured. + +What do you think-- we won't +do this analysis-- the cost is + +going to be if I +intersperse optimally, what + +is the cost going +to be for a search + +when I have three sorted lists? + +AUDIENCE: Cube root. + +SRINIVAS DEVADAS: Cube root. + +Great guess. + +Who said cube root? + +AUDIENCE: [INAUDIBLE]. + +SRINIVAS DEVADAS: You +already have a Frisbee. + +Give it to a friend. + +I need to get rid of these. + +So it's going to be cube +root, and the constant + +in front of that is going to be? + +AUDIENCE: 3. + +SRINIVAS DEVADAS: 3. + +So you have-- right? + +So let's just keep going. + +You have k sorted lists. + +You're going to have k +times the k-th root of n. + +That's what you got. + +And I'm not going to +bother drawing this, + +but essentially +what happens is you + +are making the same number +of moves which corresponds + +to the root of n, the +corresponding root of n, + +at every level. + +And the last thing we have to do +to get a sense for what happens + +here is we have log n sorted +lists, so the number of levels + +here is log n. + +So this is starting to look kind +of familiar because it borrows + +from other data structures. + +And what this is I'm just going +to substitute log n for k, + +and I got this kind +of scary looking-- + +I was scared the +first time I saw this. + +Oh, this is n. + +It's the log n-th root of n, OK? + +And so it's kind +of scary looking. + +But what is the log n-th +root of n-- and we can assume + +that n is a power of two? + +AUDIENCE: 2. + +SRINIVAS DEVADAS: 2, exactly. + +It's not that scary +looking, and that's + +because I'm not a mathematician. + +That's why I was scared. + +So 2 log n. + +All right. + +So that's it. + +So you get a sense of how +this works now, right? + +We haven't talked about +randomized structures yet, + +but I've given you +the template that's + +associated with the skip list, +which essentially says what I'm + +going to have are-- if it was +static data items and n was + +a power of two, then +essentially what + +I'm saying is I'm going to +have a bunch of items, n items, + +at the bottom. + +I'm going to have n over +2 items at the list that's + +just immediately above. + +And each of them are +going to be alternating. + +You're going to have +an item in between. + +And then on the top I'm +going to see n over 4 items, + +and so on and so forth. + +What does that look like? + +Kind of looks like +a tree, right? + +I mean it doesn't +have the structure + +of a tree in the sense +of the edges of a tree. + +It's quite different +because you're + +connecting things differently. + +You have all the +leaves connected down + +at the bottom of +this so-called tree + +with this doubly linked +list, but it has the triangle + +structure of a tree. + +And that's where the +log n comes from. + +So this is would +all be wonderful + +if this were a static set. + +And n doesn't have to be a +power of 2-- you could pad it, + +and so on and so forth. + +But the big thing here +is that we haven't quite + +accomplished what +we set out to do, + +even though we seem to have +this log n cost for search. + +But it's all based on a static +set which doesn't change. + +And the problem, of course, is +that you could have deletions. + +You want to take away 42. + +For some reason you +can't go to 42nd Avenue, + +or I guess art-- you +can't go to [INAUDIBLE] + +would be a better example. + +So stuff breaks, right? + +And so you take stuff out +and you insert things in. + +Suppose I wanted to insert +60, 61, 62, 63, and 64 + +into that list that I have? + +What would happen? + +Yeah, you're shaking your head. + +I mean that log n would go +away, so it would be a problem. + +But what we have +to do now is move + +to the probabilistic domain. + +We have to think +about what happens + +when we insert elements. + +We need an algorithm for insert. + +So then we can start with the +null list and build it up. + +And then you start +with a null list + +and you have a randomized +algorithm for insert, + +it ain't going to +look that pretty. + +It's going to look random. + +But you have to have a +certain amount of structure + +so you can still get +your order log n. + +So you have to do the +insertion appropriately. + +So that's what we +have to do next. + +But any questions +about that complexity + +that I have up there? + +All right, good. + +I want a canonical +example of a list here, + +and I kind of ran out +of room over there, + +so bear with me as I draw you +a more sophisticated skip list + +that has a few more levels. + +And the reason for this is +it's only interesting when + +you have three or more levels. + +The search algorithm +is kind of the same. + +You go up top and when +you overshoot you pop down + +one level, and then you do +the same thing over and over. + +But we are going +to have to bound + +the number of levels in the skip +list in a probabilistic way. + +We have to actually discover +the expected number of levels + +because we're going to be doing +inserts in a randomized way. + +And so it's worthwhile +having a picture that's + +a little more interesting than +the picture of the two linked + +lists that I had up there. + +So I'm going to leave this on +for the rest of the lecture. + +So that's our bottom, +and that hasn't changed + +from our previous examples. + +I'm not going to bother drawing +the horizontal connections. + +When you see things adjacent +horizontally at the same level, + +assume that they're all +connected-- all of them. + +And so I have four levels here. + +And you can think of this +as being the entire list + +or part of it. + +Just to delineate +things nicely, we'll + +assume that 79, which +is the last element, + +is all the way up +at the top as well. + +Sort of the terminus, +termini, corresponding + +to our analogy of subways. + +And so that's our +top-most level. + +And then I might have +50 here at this level, + +or so that looks like. + +I will have 50, so +the invariant here, + +and that's another reason +I want to draw this out, + +is that if you have a station +at highest level, then + +you will have-- it's got +to be sitting on something. + +So if you've got a 79 at +level four, or level three + +here if this is L0, then you +will see 79 at L2, L1, and L0. + +And if you see 50 here, +it's not in L3 so that's OK, + +but it's in L2, so it's +got to be at L1 as well. + +Of course you know that +everything is down at L1, + +so this is interesting from a +standpoint of the relationship + +between Li and Li plus 1 where +i is greater than or equal to 1. + +So the implication is that if +you see it at at Li plus 1, + +it's going to be at +Li and Li minus 1 + +if that happens to +exist, et cetera. + +And so one last thing +here just to finish it up. + +I got 34 here, which is +an additional thing which + +ends there. + +So the highest level is +this second level or L1. + +This is 66. + +And then that's it. + +So that's our skip list. + +So if you wanted to search +for 72, you would start here, + +and then you'd go to 79, +or you'd look and say, + +oh, 79 is too far, so I'm +going to pop down a level. + +And then you'd say 50, oh, good. + +I can get to 50. + +79 is too far, so I'm +going to pop down a level. + +And then you go to 66-- +79 is too far-- and at 66, + +you pop down a level and +then you go 66 to 72. + +So same as what we had before. + +Hopefully it's not +too complicated. + +So that's our skip list. + +It's still looking +pretty structured, + +looking pretty regular. + +But if I start +taking that and start + +inserting things +and deleting things, + +it could become quite irregular. + +I could take away +23, for example. + +And there's nothing +that's stopping me + +from taking away 34 or 79. + +You've got to delete +an element, you've + +got to delete an element. + +I mean the fact that +it's in four levels + +shouldn't make a difference. + +And so that's something +to keep in mind. + +So this could get pretty messy. + +So let's talk about +insert, and I've + +spent a bunch of time skirting +around the issue of what + +exactly happens when +you insert an element. + +Turns out delete is pretty easy. + +Insert is more interesting. + +Let's do insert. + +To insert an element +x into a skip list, + +the first thing +we're going to do + +is search to figure out where +x fits into the bottom list. + +So you do a search just like +you would if you were just + +doing a search. + +You always insert into +the appropriate position. + +So if there's a +single sorted list, + +that would pretty much be it. + +And so that part is easy. + +If you want to insert 67, you +do all of the search operations + +that I just went +over, and then you + +insert 67 between 66 and 72. + +So do your pointer +manipulations, what have you, + +and you're good. + +But you're not done yet, because +you want this to be a skip list + +and you want this to +have expected search + +over any random query as +the list grows and shrinks + +of order log n, expectation, +and also with high probability. + +So what you're going to have to +do is when you start inserting, + +you're going to have +to decide if you're + +going to what is called +promote these elements or not. + +And the notion of a +promotion is that you + +are going up and duplicating +this inserted element + +some number of levels up. + +So if you just look +at how this works, + +it's really pretty +straightforward. + +What is going to happen is +simply that let's say I have 67 + +and I'm going to insert +it between 66 and 72. + +That much is a given. + +That is deterministic. + +Then I'm going to flip a +coin or spin a Frisbee. + +I like this better. + +I'm not sure if this +is biased or not. + +It's probably seriously biased. + +[LAUGHTER] + +Would it ever go the +other way is the question. + +Would it ever? + +No. + +All right. + +So we've got a problem here. + +I think we might have to +do something like that. + +[LAUGHTER] + +I'm procrastinating. + +I don't want to teach the +rest of this material. + +[LAUGHTER] + +All right. + +Let's go, let's go. + +So I'd like to insert +into some of the lists, + +and the big question +is which ones? + +It's going to be really cool. + +I'm just going to flip +coins, fair coins, + +and decide how much to +promote these elements. + +So flip fair coin. + +If heads, promote x to the +next level up, and repeat. + +Else, if you ever get +a tails, you stop. + +And this next level up +may be newly created. + +So what might happen with the +67 is that you stick it in here, + +and it might happen that +the first time you flip you + +get a tails, in which +case, 67 is going + +to just be at the bottom list. + +But if you get one heads, +then you're not only + +going to put 67 in +here, you're going + +to put 67 up here as well. + +And you're going to flip again. + +And if you get a heads again, +you're going to put 67 up here. + +And if you get a +heads again, you're + +going to create a +new list up there, + +and at this point when +you create the new list, + +it's only going +to be 67 up there. + +And that's going to be +the front of your list, + +because that's the one element +that you're duplicating. + +So you're going to keep +going until you get a tails. + +Now, that's why this +coin had better be fair. + +So you're going to +keep going and you're + +going to keep adding. + +Every time you insert +there's a potential + +for increasing the number +of levels in this list. + +Now, the number +of levels is going + +to be bounded in expectation +with a high probability + +of regular +expectation, but I want + +to make it clear that +every time you insert, + +if you get a chain +of heads, you're + +going to be adding levels. + +And so the first time you +get a tails, you just stop. + +You just stop. + +So you can see that this can +get pretty messy pretty quick. + +And especially if you were +starting from ground zero + +and adding 14, 23-- +all of those things, + +the bottom is going +to look exactly + +like it looks now because +you're going to put it in there. + +It's deterministic. + +But the very next level after +that looked pretty messy. + +You could have all of +them chunked up here, + +and a big gap, et +cetera, et cetera. + +So it's all about +randomized search cost. + +The worse case cost here +is going to be order n. + +Worst case cost is +going to be order n, + +because you have no idea +where these things are + +going to end up. + +But the randomized cost +is what's cool about this. + +Any questions about +insert or anything I said? + +Yeah, go ahead. + +AUDIENCE: Is worse +case really order n? + +What if you had a really +long, like a lot of lists + +on top of each other, and +you start at the top of that + +and you had to walk all +the way [INAUDIBLE]? + +SRINIVAS DEVADAS: Well, you go +n down and n this way, right? + +You would be checking +so it would be order n. + +AUDIENCE: So it's +[? bounded ?] by n? + +SRINIVAS DEVADAS: +Yeah, the worst case. + +AUDIENCE: Worse +case is infinity. + +SRINIVAS DEVADAS: +Worse case is infinity. + +Oh, in that sense, yeah. + +OK. + +Well, n elements, Eric is right. + +So what is happening +here is that you + +have a small probability +that you will + +keep flipping heads forever. + +So at some level, if you +somehow take that away and use + +Frisbees instead +or you truncate it. + +Let's say at some point you +ended up saying that you only + +have n levels total. + +So it's not a-- I +should have gone there. + +The question has to +be posed a little more + +precisely for the +answer to be order n. + +You have to have some more +limitations to avoid the case + +that Eric just mentioned, which +is in the randomized situation + +you will have the +possibility of getting + +an infinite number of heads. + +Yeah, question back there. + +AUDIENCE: [INAUDIBLE]. + +SRINIVAS DEVADAS: Yes, you +can certainly do capping + +and you can do a +bunch of other things. + +It ends up becoming +something which is not + +as clean as what you have here. + +The analysis is messy. + +And it's sort of in between +a randomized data structure, + +a purely randomized +data structure, + +and a deterministic one. + +I think the important +thing to bring out here + +is the worst case is much +worse than order log n, OK? + +Cool. + +Good. + +Thanks for those questions. + +And so what we have here now is +an insert algorithm that could + +make things look pretty messy. + +I'm going to leave the insert +up here, and that, of course, + +is part of that. + +Now, for the rest +of the lecture we're + +going to talk about why +skip lists are good. + +And we're going to justify +this randomized data structure + +and show lots of nice +results with respect + +to the expectation on the +number of levels, expectation + +on the number of +moves in a search, + +regardless of what items +you're inserting and deleting. + +One last thing. + +To delete an item, +you just delete it. + +You find it, search, and +delete at all levels. + +So you can't leave it +in any of the levels. + +So you find it, and you have +to have the pointers set up + +properly-- move the +previous pointer over + +to the next one, et +cetera, et cetera. + +We won't get into +that here, but you + +have to do the delete +at every level. + +Yeah, question. + +AUDIENCE: So what happens +if you inserted 10s + +and you flip off a tail? + +So that's like your +first element is not + +going to go up all the way, +and then have you do search. + +SRINIVAS DEVADAS: +So typically what + +happens is you need to +have a minus infinity here. + +And that's a good point. + +It's a corner case. + +You have to have a +minus infinity that + +goes up all the way. + +Good question. + +So the question was what happens +if I had something less than 14 + +and I inserted it? + +Well, that doesn't +happen because nothing + +is less than minus infinity, +and that goes up all the way. + +But thanks for bringing it up. + +And so we're going to do +a little warm-up Lemma. + +I don't know if +you've ever heard + +these two terms in juxtaposition +like this-- warm up and Lemma. + +But here you go, your +first warm-up Lemma. + +I guess you'd never +have a warm-up theorem. + +It's a warm-up Lemma for +this theorem, which is + +going to take a while to prove. + +This comes down to trying to +get a sense of how many levels + +you're going to have from +a probabilistic standpoint. + +The number of levels in +an n element skip list + +is order log n. + +And I'm going to now define +the term with high probability. + +So what does this mean exactly? + +Well, what this +means is order log n + +is something like c +log n plus a constant. + +Let's ignore the constant +and let's stick with c log n. + +And with high probability +is a probability + +that is really a +function of n and alpha. + +And you have this inverse +polynomial relationship + +in the sense that +obviously as n grows here, + +an alpha-- we'll assume that +alpha is greater than the 1-- + +you are going to get a +decrease in this quantity. + +So this is going to get closer +and closer to 1 as n grows. + +So that's the difference +between with high probability + +and just sort of giving you +an expectation number where + +you have no such guarantees. + +What is interesting about +this is that as n grows, + +you're going to get a higher +and higher probability. + +And this constant c is going +to be related to alpha. + +That's the other thing that's +interesting about this. + +So it's like saying-- and +you can kind of say this + +for using Chernoff bounds that +we'll get to in a few minutes, + +even for expectation as well. + +But what this says is that +if, for example, c doubled, + +then you are saying that +your number of levels + +is order 4 log n. + +I mean I understand that that +doesn't make too much sense, + +but it's less than or equal +to 4 log n plus a constant. + +And that 4 is going to get +reflected in the alpha here. + +When the 4 goes from 4 to +8, the alpha increases. + +So the more room that you have +with respect to this constant, + +the higher the probability. + +It becomes an +overwhelming probability + +that you're going to be +within those number of levels. + +So maybe there's +an 80% probability + +that you're within 2 log n. + +But there's a +99.99999% probability + +that you're within 4 log +n, and so on and so forth. + +So that's the kind of thing +that with the high probability + +analysis tells you explicitly. + +And so you can do that, +you can do this analysis + +fairly straightforwardly. + +And let me do that +on a different board. + +Let me go ahead and +do that over here. + +Actually, I don't +really need this. + +So let's do that over here. + +And so this is our first with +high probability analysis. + +And I want to prove +that warm-up Lemma. + +So usually what you +do here is you look + +at the failure probability. + +So with high +probability is typically + +something that +looks like 1 minus 1 + +divided by n raised to alpha. + +And this part here is +the failure probability. + +And that's typically +what you analyze + +and what we're +going to do today. + +So the failure probability +is that it's not less + +than c log n levels, is the +complement of what we just + +looked at, which is the +probability that it's strictly + +greater than c log n levels. + +And that's the probability +that some element gets promoted + +greater than c log n times. + +So why would you have +more than c log n levels? + +It's essentially because +you inserted something + +and that element got promoted +strictly greater than c + +log n times, which +obviously implies that you + +had the sequence +of heads, and we'll + +get to that in just a second. + +But before we go to that +step of figuring out + +exactly what's going on here +as to why this got promoted + +and what the probability +of each promotion + +is, what I have here is I +have a sequence of inserts + +potentially that +I have to analyze. + +And in general, when I +have an n element list, + +I'm going to assume that +each of these elements + +got inserted into the +list at some point. + +So I've had n inserts. + +And we just look at the case +where you have n inserts, + +you could have deletes, and so +you could have more inserts, + +but it won't really +change anything. + +You have n inserts corresponding +to each of these elements, + +and one of those n elements got +promoted in this failure case + +greater than c log n times. + +That's essentially +what's happened here. + +And so you don't know which +one, but you can typically + +do this in with high +probability analysis + +because the probabilities +are so small + +and they're inverse +polynomials, polynomials like n + +raised to alpha. + +You can use what's +called the union bound + +that I'm sure you've used before +in some context or the other. + +And you essentially +say that this + +is less than or equal +to the probability + +that a particular element x. + +So you just pick an element, +arbitrary element x, + +but you pick one. + +Gets promoted greater +than c log n times. + +So you have a small probability. + +You have no idea whether these +events are independent or not. + +The union bound +doesn't care about it. + +It's like saying you've got +a 0.001 probability that any + +of these elements could get +promoted greater than c log n + +times, and there's +10 of those elements. + +You don't know whether they're +independent events or not, + +but you can certainly +use the union + +bound that says the overall +failure probability is going + +to be less than or equal to +n equals 10, in my example, + +times that 0.001. + +That's basically it. + +Now you can go off +and say, what does it + +mean for an element +to get promoted? + +What actually has to happen +for an element to get promoted? + +And you have n times 1 +over 2, because you're + +flipping a fair +coin, and you are + +getting a c log n heads here. + +You flip and you +get one promotion. + +There's two levels +associated with a promotion, + +the level you came from +and the level you went to. + +And so a promotion +is a move, so you're + +going to have one more level. + +If you count levels, then you +have the number of promotions, + +right? + +That's just simply +corresponds to taking this 1/2 + +and raising it to c log n, +because that's essentially + +the number of +promotions you have. + +And you got n 1/2 c log n, +and what does that turn into? + +What is n times 1/2 c log n? + +1 over 2 raised to +log n would give you? + +2 raised to log ns? + +Is n, right? + +So you got n divided +by n raised to c, which + +is 1 divided by n +raised to c minus 1, + +which is 1 divided by n +raised to alpha where alpha + +is c minus 1. + +So that's it. + +That's our first with +high probability analysis. + +Not too hard. + +What I've done is done +exactly what I just told you + +that the notion of with +high probability is. + +You have a failure +probability that is related. + +Inverse polynomial and the +degree of the polynomial alpha + +is related to c. + +And so that's what +I have out there, + +but c equals-- what did it have? + +Alpha equals c minus 1 +or c equals alpha plus 1. + +So what I've done here +is done an analysis + +that tells you with high +probability how many levels + +I'm going to have given +my insert algorithm. + +So this is the first part +of what we'd like to show. + +This just tells us +how big this skip list + +is going to grow vertically. + +It doesn't tell us anything +about the structure of the list + +internally as to whether +the randomization is going + +to cause that pretty +structure that you see up + +here to be completely messed up +to the point where we don't get + +order log n search complexity, +because we are spending way too + +much time let's say on the +bottom list or the list + +just above the bottom +list, et cetera. + +So we need to get a sense of +how the structure corresponding + +to the skip list, whether it's +going to look somewhat uniform + +or not. + +We have to categorize +that, and the only way + +we're going to +characterize that is + +by analyzing search and +counting the number of moves + +that a search makes. + +And the reason it's +more complicated + +than what you see up there +is that in a search, as you + +can see, you're going to be +moving at different levels. + +You're going to be +moving at the top level. + +Maybe at relatively +small number of moves, + +you're going to pop down one, +move a few moves at that level, + +pop down, et cetera, et cetera. + +So there's a lot of things +going on in search which + +happen at different +levels, and the total cost + +is going to have to +be all of the moves. + +So we're going to think +about all of the moves-- + +up moves, down moves, +and add them all up. + +They all have to be order +log n with high probability. + +There's no getting around that +because each of them costs you. + +So that's the thing that we'll +spend the next 20 minutes on. + +And the theorem that we +like to prove for search + +is that-- this is +what I just said-- + +any search in an n element skip +list costs order log n w.h.p. + +So it doesn't matter how +this skip list looks. + +There's n elements, +they got inserted + +using the insert +algorithm-- that's + +important to know if you're +going to have to use that. + +And when I do a search for an +element, it may be in there, + +it may not be in there. + +Doesn't really matter. + +We'll assume a +successful search. + +That is going to cost me order +log n with high probability. + +And the cool idea here in +terms of analyzing the search + +in order to figure out +how we're going to add up + +all of these moves is +we're going to analyze + +the search backwards. + +So that's a cool idea. + +So what does that mean exactly? + +Well, what that +means is that we're + +going to think +about this b search, + +which think of it as the +backward search, starts-- + +it actually ends, so that's what +I'm writing in brackets here, + +at the node in the bottom list. + +So we're assuming a successful +search, as I mentioned before. + +Otherwise, the point would +just be in between two members. + +You know that it's not in there +because you're looking for 67 + +and you see 66 to your +left and 72 to your right. + +So either way it +works, but keep in mind + +that it's a successful +search because it just makes + +things a little bit easier. + +Now, at each node that we +visit, what we're going to do + +is we're going to say that +if the node was not promoted + +higher, then what +actually happened here + +was that when you inserted +that particular element, + +you got a tails. + +Because otherwise you +would have gotten a heads, + +that element would have +been promoted higher. + +Then you go-- and +that really means + +that you came from the left-hand +side, so you make a left move. + +Now, search of course makes +down moves and right moves, + +but this is a backward search +so it's going to make left moves + +and up moves. + +What else do I have here? + +Running out of room, so let +me-- let's continue with that. + +All right. + +And now the case is if +the node was promoted + +higher, that means +we got heads here + +in that particular insertion. + +Then we go, and that means +that during the search + +we came from upstairs. + +And then lastly, we +stop, which means + +we start when we reach the top +level or minus infinity if we + +go all the way back. + +So that's it. + +A lot of writing here, but +this should make things clear. + +So let's say that +we're searching for 66. + +I want to trace through what +the backwards path would + +look like, and keep that +code in mind as I do this. + +So I'm searching for +66, and obviously, we + +know how to find it. + +We've done that. + +But let's go backwards +as to what exactly + +happened when we look for 66. + +When we look for 66, right at +this point when you see 66, + +where would you have come from? + +AUDIENCE: [INAUDIBLE] + +SRINIVAS DEVADAS: You'd +have come from the top. + +And so if you go look +at what happens here, + +the node when it got inserted +was promoted one level. + +So that means that you would go +up top in the backward search + +first. + +Your first move would +be going up like that. + +Now, if there's a 66 up there, +you would go up one more. + +But there's not, so you go left. + +You go to 50. + +And when you have a 50 up here, +would you stay on this level? + +AUDIENCE: No. + +SRINIVAS DEVADAS: No. + +You'd go up to 50 +because the first chance + +you get you want to get +up to the higher levels. + +And again, this 50 was +promoted so you go up there, + +and you go to 14, and pretty +much that's the end of that. + +So this would look like you go +like that, you have an up move, + +then you have a left move-- +different colors here + +would be good-- then +you have an up move, + +and a left, and then an up. + +So that's our backward search. + +And it's not that +complicated, hopefully. + +If you're looking for +66 or 59, you do that. + +So it's much more natural, +and you just need to flip it. + +Why am I doing all this? + +Well, the reason +I'm doing all this + +is that I have to do some +bounding of the moves, + +and I know that the moves that +correspond to the up moves + +are probabilistic in the sense +that the reason I'm making them + +is because I flipped +heads at some point. + +So all of this is going +to turn into counting + +how many coin flips +come out heads + +in a long stream of coin flips. + +So that's what this +backward search + +is going to allow us to do. + +And that crucial thing is +what we'll look at next. + +So the analysis itself +is a bit painful, + +but there's a bunch of algebra. + +But what I want to +do is to make sure + +that you get the high +level picture, number one, + +and the insights as to why +the expected value or the with + +high probability value is +going to be order log n. + +But the key is the strategy. + +So we're going to +go off and we're + +going to prove this theorem. + +Our backward search makes +up moves and left moves. + +We know that. + +Each with probability 1/2. + +And the reason for +that is when you go up + +is because you got +a heads, and if you + +didn't get a heads in you got a +tails, that meant you go left. + +Because of the previous +element, every time you're + +passing these elements +that are inserted, + +and they were inserted +by flipping coins. + +So that's key point number one. + +All of that, if you look +at what happens here + +when I drew this out, +you got heads here + +and you got tails there. + +So each of those +things for a fair coin + +is happening with +probability 1/2. + +And it's all about +coin flips here. + +Now, the number +of moves going up + +is less than the number of +levels-- the number of levels + +is one more than that. + +And we've shown that that's +c log n with high probability + +by the warm-up Lemma. + +That's what this just did. + +The number of up moves-- I mean +you can't go off the list here. + +This list is now you're +not inserting anymore, + +you're doing a search. + +So it's not like you're +going to be adding + +levels or anything like that. + +So the number of up moves +we've taken care of. + +So this last thing here which +I'm going to write out here + +is the key observation, +which is going to make + +the whole analysis possible. + +And so this last thing it +says that the total number + +of moves-- so now the total +number of moves has to include, + +obviously, the up +moves and the left + +moves, and there's +no other kind. + +The total number +of moves is going + +to correspond to +the number of moves + +till you get c log n up moves. + +So what does that mean? + +There's some sequence +of heads and tails + +that I'm getting, each of +them with probability 1/2. + +Every time that I got a +heads, I moved up a level. + +The fact of the matter is that +I can't get more than c log n + +heads because I'm going +to run out of levels. + +That's it. + +I'm going to run out of room +vertically if I keep popping up + +and keep doing up moves. + +So at that point I'm +forced to go left. + +Maybe I'm going +left in the middle + +there when I still +had a chance to go up. + +That corresponds to getting a +tails as opposed to a heads. + +But I can limit the +total number of moves + +from a probabilistic +standpoint by saying + +during that sequence +of coin flips I only + +have a certain number +of heads that I + +could have possibly gotten. + +Because if I got more heads +than that, I would be up top. + +I'd be out of the skip +list, and that doesn't work. + +So the total number of +moves is the number of moves + +till you get c log n up moves, +which essentially corresponds + +to-- now, forget about +skip lists for a second. + +Our claim is the +total number of moves + +is the number of coin flips, +so these are the same, + +because every move +corresponds to a coin flip. + +Until-- it's a fair +coin, probability 1/2-- + +until c log n heads +have been obtained. + +So the number of +coin flips until c + +log n heads is the +total number of moves. + +This equals that. + +And what we now want to show, if +you believe that, and hopefully + +you do because the +argument is simply + +that you run out of levels, +that this is order log n w.h.p. + +That's why it's a claim. + +So the observation is +that the number of coin + +flips, as you flip a +fair coin, until you + +get c log n heads will give +you the number of moves + +in your search, total number +of moves in your search. + +It includes the up moves +as well as the left moves. + +And now what we have +to show is that that + +is going to be order log +n with high probability. + +OK? + +And then once you do that +you've done two things. + +You've bounded the number +of levels in the skip list + +to be order log n +with high probability. + +And you've said the number +of moves in the search + +is order log n with high +probability assuming + +that the number of levels +is c log n, obviously. + +So it's not that the bottom +one subsumes the top one. + +It's the last thing to +keep in mind as we get all + +of these items out of the way. + +This assumes that there are +less than or equal to c log n + +levels. + +That's the only reason why +I could make an argument + +that I've run out of levels. + +So if I have this event A +here-- if I call this event A, + +and I have this event +B, what I really want + +is-- I've shown you that event +A happens with high probability. + +That's the warm-up Lemma. + +I need to show you that event B +happens with high probability. + +And then I have to show you +that event A and event B + +happen with high probability, +because I need both. + +Any questions? + +We're stopping a minute here. + +The rest of the analysis, +a bunch of algebra, + +we'll get through it, you +can look at the notes. + +This is the key point. + +If you got this, you got it. + +Yeah. + +AUDIENCE: Can you just say +that because the probability + +of drawing an up move +instead of a left move + +is 1/2, that the expected +number of left moves + +should be equal to the number +of up moves, [INAUDIBLE] + +bound the up moves? + +SRINIVAS DEVADAS: +So the argument + +is that since you +have 1/2, can you + +simply say that the expected +number of left moves + +is going to be the same as +the same as the up moves? + +You can make arguments +about expectation. + +You can say that at any level, +the number of left moves + +that you're going to have is +going to be two in expectation. + +It's not going to give you your +with high probability proof. + +It's not going to relate +that to the 1 divided + +by n raised to alpha. + +But I will tell you that if you +just wanted to show expectation + +for search is order +log n, you won't + +have to jump through +all of these hoops. + +At some level you'll be +making the assumptions + +that I've made explicit +here through my observations + +when you do that expectation. + +So if you really want to write +a precise proof of expected + +value for search +complexity, you would + +have to do a lot of the +things that I'm doing here. + +I'm not saying you +waved your hands. + +You did not. + +But it needed more to +than what you just said. + +OK? + +So this is pretty much +what the analysis is. + +With high probability analysis +we bounded the vertical, + +we bounded the number of moves. + +Assuming the +vertical was bounded, + +we got the result for +the number of moves. + +So both of those happen +with high probability. + +You got your result, +which is the theorem + +that we have somewhere. + +Woah, did I erase the theorem? + +AUDIENCE: [INAUDIBLE]. + +SRINIVAS DEVADAS: +It's somewhere. + +All right. + +Good. + +So let's do what +we can with respect + +to showing this theorem. + +There's a couple ways +that you could prove this. + +There's a way that you +could use a Chernoff bound. + +And this is kind +of a cool result + +that I think is worth knowing. + +I don't know if +you've seen this, + +but this is a seminal +theorem by Chernoff + +that says if you have a +random variable representing + +the total number of +tails, let's say-- + +it could be heads as +well-- in a series of m-- + +not n, m-- independent coin +flips where each flip has + +a probability p of +coming up heads, + +then for all r greater +than 0, we have + +this beautiful result that +says the probability that y, + +which is a random variable-- +a particular instance + +when you evaluate +it-- that it is larger + +than the expectation +by r is bounded. + +So just a beautiful +result that says here's + +a random variable that +corresponds to flipping a coin. + +I'm going to flip +this a bunch of times, + +and I know what +the expectation is. + +If it's a fair coin +of 1/2, then I'm + +going to get m over 2-- +expected number of heads + +is going to be m over 2. + +Expected number of tails +is going to be m over 2. + +If it's p, then obviously +it's a little bit + +different-- p times m. + +But what I have here is if you +tell me what the probability is + +that I'm 10 away +from the expectation + +and that would imply that r is +10, then that is bounded by e + +raised to minus 2 times +10 square divided by m. + +So that's Chernoff's bound. + +And you can see how this relates +to our with high probability + +analysis. + +Because our with +high probability + +analysis is exactly this. + +This is the hammer that you can +use to do with high probability + +analysis. + +Because this tells you as you +get further and further away + +from the average or you get +further and further away + +from the expectation, what +the probability is that you're + +going to be so far away. + +What is the probability that in +100 coin flips that are fair, + +you get 50 heads? + +It's a reasonably large number +because the expected value + +corresponds to 50. + +So r is 0. + +So that just says +this is a-- well, + +it doesn't tell you much +because this says it's less than + +or equal to 1. + +That's all it's says. + +But if you had 75, what are +the probability that you + +get 75 heads when you +flip a coin 100 times? + +Then e of y for a fair coin +would be 50, r would be 25, + +and you'd go off and you +could do the math for that. + +So it's a beautiful +relationship that tells you + +how the probabilities change as +your random variable value is + +further and further away +from the expectation. + +And you can imagine +that this is going + +to be very useful in showing our +with high probability result. + +And I think what I +have time for is just + +to give you a sense of how +this result works out-- I'm not + +going to do the algebra. + +I don't think it's worth it to +write all of this on the board + +when you can read +it in the notes. + +But the bottom +line is we're going + +to show this little Lemma +that says for any c, + +invoking this Chernoff +bound, there's a constant d, + +such that with high +probability, the number of heads + +in flipping d log n. + +So I have a new constant here. + +d log n fair coins, +or a single fair coin, + +d log n times, +assuming independence, + +is at least c log n. + +So what does this say? + +A lot of words. + +It just says, hey, you +want an order log n + +bound here eventually. + +The beauty of order log n +is that there's a constant + +in there that you control. + +That constant is d. + +So you tell me +that c log n is 50. + +So c log n is 50. + +Then what I'm going to do is +I'm going to say something like, + +well, if I flip a +coin 1,000 times, then + +I'm going to have an +overwhelming probability + +that I'm going to get 50 heads. + +And that's it. + +That's what the Lemma says. + +It says tell me what c log n is. + +Give me that value. + +And I will find you a d, such +that by invoking Chernoff, + +I'm going to show you an +overwhelming probability that + +for that d you're going to +get at least c log n heads. + +So everybody buy that? + +Make sense from what +you see up there? + +Yup? + +So this essentially +can be shown-- + +it turns out that +what you have to do + +is-- and you don't +have to choose 8, + +but you can choose d equals 8c. + +Just choose d +equals 8c and you'll + +see the algebra in the +notes corresponding to what + +each of these values are. + +So e of y, just to tell +you, would be m over 2. + +You're flipping m coins, fair +coin with probability 1/2. + +So you got m over 2. + +And then the last +thing that I'll + +tell you is that what you want +in terms of invoking that, + +you want r-- remember we were +talking about tails here-- so r + +is going to be d +log n minus c log n. + +So you just invoke Chernoff +with e of y equals m over 2. + +And what you're saying here +is you want c log n heads. + +You want to make sure you +get c log n heads, which + +means that the number +of tails is going + +to be d log n minus c log n. + +And typically we analyze +failure probability, + +so what this is is this is +going to be a tiny number. + +So the failure is when you +get fewer than c log n heads. + +And so that means that you're +getting more than d log + +n minus c log n tails as +you're flipping this coin. + +Fewer than c log n heads means +you're getting at least d log + +n minus c log n tails. + +So that's why this +is your r here. + +And then when your +r gets that large, + +and you can play around +with the d and the c + +and choose d equals +8c, you realize + +that this is going to be +a minuscule probability. + +And you can turn that +around to a polynomial-- + +again, a little bit of algebra. + +But you can show +this result on here + +that says that +the number of coin + +flips until c log n +heads is order log + +n with high probability +by appropriately + +choosing the constant d to +be some time/number over c. + +So I'll let you do that algebra. + +But this one last thing +that-- we're not quite done. + +So you thought we were done, +but we're not quite done. + +And why is it that +we're not quite done? + +Real quick question +worth five Frisbees. + +Why is it that we're +not quite done? + +What did I say? + +I have done event A +and event B, right? + +AUDIENCE: [INAUDIBLE]. + +SRINIVAS DEVADAS: I haven't +done the last thing which + +is to show that probability +of event A-- this + +is with high +probability happens-- + +and I need to show +that probability + +of event A and event +B happens-- or this + +is with high probability. + +Or I should just say +event A and event + +B happen with high probability. + +And you can see that. + +It turns out it's +pretty straightforward, + +but you got the gist of it. + +Thanks for being so patient. + +And there you go guys. + +Woah. \ No newline at end of file diff --git a/4GiPsGjGVVM.txt b/4GiPsGjGVVM.txt new file mode 100644 index 0000000000000000000000000000000000000000..af116795f4f5cb36ab2670acdf18dcd20a40d070 --- /dev/null +++ b/4GiPsGjGVVM.txt @@ -0,0 +1,3675 @@ +align:start position:0% + +today on Chalk radio we're expanding our + + align:start position:0% +today on Chalk radio we're expanding our + + + align:start position:0% +today on Chalk radio we're expanding our +traditional understanding of economics + + align:start position:0% +traditional understanding of economics + + + align:start position:0% +traditional understanding of economics +at the end of the day what economists + + align:start position:0% +at the end of the day what economists + + + align:start position:0% +at the end of the day what economists +should be trying to do or economics + + align:start position:0% +should be trying to do or economics + + + align:start position:0% +should be trying to do or economics +should try to do is maximize people's + + align:start position:0% +should try to do is maximize people's + + + align:start position:0% +should try to do is maximize people's +well-being + + align:start position:0% +well-being + + + align:start position:0% +well-being +I'm your host Sarah Hansen today we're + + align:start position:0% +I'm your host Sarah Hansen today we're + + + align:start position:0% +I'm your host Sarah Hansen today we're +talking about economics and well-being + + align:start position:0% +talking about economics and well-being + + + align:start position:0% +talking about economics and well-being +from exploring the impact of Trends in + + align:start position:0% +from exploring the impact of Trends in + + + align:start position:0% +from exploring the impact of Trends in +decision making to dissecting why + + align:start position:0% +decision making to dissecting why + + + align:start position:0% +decision making to dissecting why +students procrastinate Dr Frank shilbach + + align:start position:0% +students procrastinate Dr Frank shilbach + + + align:start position:0% +students procrastinate Dr Frank shilbach +is working to understand how our + + align:start position:0% +is working to understand how our + + + align:start position:0% +is working to understand how our +psychological well-being impacts our + + align:start position:0% +psychological well-being impacts our + + + align:start position:0% +psychological well-being impacts our +economic behaviors and vice versa + + align:start position:0% +economic behaviors and vice versa + + + align:start position:0% +economic behaviors and vice versa +my name is Frank schilbach I'm an + + align:start position:0% +my name is Frank schilbach I'm an + + + align:start position:0% +my name is Frank schilbach I'm an +associate professor at MIT in the + + align:start position:0% +associate professor at MIT in the + + + align:start position:0% +associate professor at MIT in the +economics Department I study mostly + + align:start position:0% +economics Department I study mostly + + + align:start position:0% +economics Department I study mostly +issues related to Poverty studying + + align:start position:0% +issues related to Poverty studying + + + align:start position:0% +issues related to Poverty studying +development economics with developing + + align:start position:0% +development economics with developing + + + align:start position:0% +development economics with developing +countries and I'm specifically + + align:start position:0% +countries and I'm specifically + + + align:start position:0% +countries and I'm specifically +interested in issues that + + align:start position:0% +interested in issues that + + + align:start position:0% +interested in issues that +disproportionately affect the poor that + + align:start position:0% +disproportionately affect the poor that + + + align:start position:0% +disproportionately affect the poor that +are in one way or the other + + align:start position:0% +are in one way or the other + + + align:start position:0% +are in one way or the other +psychological or have psychological + + align:start position:0% +psychological or have psychological + + + align:start position:0% +psychological or have psychological +effects these include sleep deprivation + + align:start position:0% +effects these include sleep deprivation + + + align:start position:0% +effects these include sleep deprivation +physical pain loneliness mental distress + + align:start position:0% +physical pain loneliness mental distress + + + align:start position:0% +physical pain loneliness mental distress +or mental health issues such as + + align:start position:0% +or mental health issues such as + + + align:start position:0% +or mental health issues such as +depression or anxiety or just worries + + align:start position:0% +depression or anxiety or just worries + + + align:start position:0% +depression or anxiety or just worries +about money and all of these factors + + align:start position:0% +about money and all of these factors + + + align:start position:0% +about money and all of these factors +might affect people's psychological + + align:start position:0% +might affect people's psychological + + + align:start position:0% +might affect people's psychological +well-being they might also have impacts + + align:start position:0% +well-being they might also have impacts + + + align:start position:0% +well-being they might also have impacts +on people's decision making such as how + + align:start position:0% +on people's decision making such as how + + + align:start position:0% +on people's decision making such as how +much money to save whether to purchase + + align:start position:0% +much money to save whether to purchase + + + align:start position:0% +much money to save whether to purchase +insurance or what food to eat or + + align:start position:0% +insurance or what food to eat or + + + align:start position:0% +insurance or what food to eat or +purchase as well as people's work + + align:start position:0% +purchase as well as people's work + + + align:start position:0% +purchase as well as people's work +decisions so how productive people are + + align:start position:0% +decisions so how productive people are + + + align:start position:0% +decisions so how productive people are +at work how many hours they work how + + align:start position:0% +at work how many hours they work how + + + align:start position:0% +at work how many hours they work how +much do they earn and all together these + + align:start position:0% +much do they earn and all together these + + + align:start position:0% +much do they earn and all together these +might affect people's ability to escape + + align:start position:0% +might affect people's ability to escape + + + align:start position:0% +might affect people's ability to escape +poverty or become richer in the future + + align:start position:0% +poverty or become richer in the future + + + align:start position:0% +poverty or become richer in the future +and thus as a whole perhaps lead to what + + align:start position:0% +and thus as a whole perhaps lead to what + + + align:start position:0% +and thus as a whole perhaps lead to what +people might call a psychological + + align:start position:0% +people might call a psychological + + + align:start position:0% +people might call a psychological +poverty trap app because they have to + + align:start position:0% +poverty trap app because they have to + + + align:start position:0% +poverty trap app because they have to +struggle with so many issues associated + + align:start position:0% +struggle with so many issues associated + + + align:start position:0% +struggle with so many issues associated +with poverty their sleeping conditions + + align:start position:0% +with poverty their sleeping conditions + + + align:start position:0% +with poverty their sleeping conditions +are bad + + align:start position:0% +are bad + + + align:start position:0% +are bad +struggled with mental distress Etc + + align:start position:0% +struggled with mental distress Etc + + + align:start position:0% +struggled with mental distress Etc +[Music] + + align:start position:0% + + + + align:start position:0% + +actors in his work Frank's model of + + align:start position:0% +actors in his work Frank's model of + + + align:start position:0% +actors in his work Frank's model of +Economics diverges from many traditional + + align:start position:0% +Economics diverges from many traditional + + + align:start position:0% +Economics diverges from many traditional +models + + align:start position:0% +models + + + align:start position:0% +models +our lab is really the world + + align:start position:0% +our lab is really the world + + + align:start position:0% +our lab is really the world +we can look around and talk to people + + align:start position:0% +we can look around and talk to people + + + align:start position:0% +we can look around and talk to people +every day and experience things try to + + align:start position:0% +every day and experience things try to + + + align:start position:0% +every day and experience things try to +introspect how we make decisions + + align:start position:0% +introspect how we make decisions + + + align:start position:0% +introspect how we make decisions +ourselves but also talk to people and + + align:start position:0% +ourselves but also talk to people and + + + align:start position:0% +ourselves but also talk to people and +try to understand and you can take a cab + + align:start position:0% +try to understand and you can take a cab + + + align:start position:0% +try to understand and you can take a cab +or an Uber and just ask your Uber driver + + align:start position:0% +or an Uber and just ask your Uber driver + + + align:start position:0% +or an Uber and just ask your Uber driver +how they're making choices on whether or + + align:start position:0% +how they're making choices on whether or + + + align:start position:0% +how they're making choices on whether or +not to stop working or how much to work + + align:start position:0% +not to stop working or how much to work + + + align:start position:0% +not to stop working or how much to work +you can ask anybody on your friends and + + align:start position:0% +you can ask anybody on your friends and + + + align:start position:0% +you can ask anybody on your friends and +so on try to understand how they make + + align:start position:0% +so on try to understand how they make + + + align:start position:0% +so on try to understand how they make +choices in their lives and what factors + + align:start position:0% +choices in their lives and what factors + + + align:start position:0% +choices in their lives and what factors +seem important + + align:start position:0% +seem important + + + align:start position:0% +seem important +some of the research I've been doing on + + align:start position:0% +some of the research I've been doing on + + + align:start position:0% +some of the research I've been doing on +sleep but also on alcohol consumption on + + align:start position:0% +sleep but also on alcohol consumption on + + + align:start position:0% +sleep but also on alcohol consumption on +mental health comes very much from this + + align:start position:0% +mental health comes very much from this + + + align:start position:0% +mental health comes very much from this +type of approach I spent some time in + + align:start position:0% +type of approach I spent some time in + + + align:start position:0% +type of approach I spent some time in +India trying to work on some research + + align:start position:0% +India trying to work on some research + + + align:start position:0% +India trying to work on some research +projects and while working on these + + align:start position:0% +projects and while working on these + + + align:start position:0% +projects and while working on these +research projects to spend a lot of time + + align:start position:0% +research projects to spend a lot of time + + + align:start position:0% +research projects to spend a lot of time +talking to people so would have lots of + + align:start position:0% +talking to people so would have lots of + + + align:start position:0% +talking to people so would have lots of +conversations with people asking them + + align:start position:0% +conversations with people asking them + + + align:start position:0% +conversations with people asking them +their basic things about what are things + + align:start position:0% +their basic things about what are things + + + align:start position:0% +their basic things about what are things +that make you happy what are things that + + align:start position:0% +that make you happy what are things that + + + align:start position:0% +that make you happy what are things that +are difficult in your life what are + + align:start position:0% +are difficult in your life what are + + + align:start position:0% +are difficult in your life what are +things that you think that could be + + align:start position:0% +things that you think that could be + + + align:start position:0% +things that you think that could be +improved or if you could improve one + + align:start position:0% +improved or if you could improve one + + + align:start position:0% +improved or if you could improve one +thing in your life what would you do and + + align:start position:0% +thing in your life what would you do and + + + align:start position:0% +thing in your life what would you do and +so on and a lot of the things that I'm + + align:start position:0% +so on and a lot of the things that I'm + + + align:start position:0% +so on and a lot of the things that I'm +now studying are precisely issues that + + align:start position:0% +now studying are precisely issues that + + + align:start position:0% +now studying are precisely issues that +are in some ways overlooked by or have + + align:start position:0% +are in some ways overlooked by or have + + + align:start position:0% +are in some ways overlooked by or have +until recently at least not received a + + align:start position:0% +until recently at least not received a + + + align:start position:0% +until recently at least not received a +lot of attention in economics so far for + + align:start position:0% +lot of attention in economics so far for + + + align:start position:0% +lot of attention in economics so far for +example say sleep deprivation + + align:start position:0% +example say sleep deprivation + + + align:start position:0% +example say sleep deprivation +yet they seemed really important in part + + align:start position:0% +yet they seemed really important in part + + + align:start position:0% +yet they seemed really important in part +because if you just look at people's + + align:start position:0% +because if you just look at people's + + + align:start position:0% +because if you just look at people's +sleeping conditions they are replete + + align:start position:0% +sleeping conditions they are replete + + + align:start position:0% +sleeping conditions they are replete +with all sorts of factors that are + + align:start position:0% +with all sorts of factors that are + + + align:start position:0% +with all sorts of factors that are +terrible for people's sleep and this is + + align:start position:0% +terrible for people's sleep and this is + + + align:start position:0% +terrible for people's sleep and this is +where the introspection comes in if you + + align:start position:0% +where the introspection comes in if you + + + align:start position:0% +where the introspection comes in if you +then think about how do you function on + + align:start position:0% +then think about how do you function on + + + align:start position:0% +then think about how do you function on +a really bad night of sleep you know + + align:start position:0% +a really bad night of sleep you know + + + align:start position:0% +a really bad night of sleep you know +that's very difficult at least for me so + + align:start position:0% +that's very difficult at least for me so + + + align:start position:0% +that's very difficult at least for me so +if I sleep badly I'm very sensitive to + + align:start position:0% +if I sleep badly I'm very sensitive to + + + align:start position:0% +if I sleep badly I'm very sensitive to +sleep I I don't function particularly + + align:start position:0% +sleep I I don't function particularly + + + align:start position:0% +sleep I I don't function particularly +well and putting these things together + + align:start position:0% +well and putting these things together + + + align:start position:0% +well and putting these things together +has then gotten me interested in + + align:start position:0% +has then gotten me interested in + + + align:start position:0% +has then gotten me interested in +understanding and researching the impact + + align:start position:0% +understanding and researching the impact + + + align:start position:0% +understanding and researching the impact +of improving sleep on people's lives + + align:start position:0% +of improving sleep on people's lives + + + align:start position:0% +of improving sleep on people's lives +intuitively I know sleep deprivation is + + align:start position:0% +intuitively I know sleep deprivation is + + + align:start position:0% +intuitively I know sleep deprivation is +bad I feel grumpy and impatient and get + + align:start position:0% +bad I feel grumpy and impatient and get + + + align:start position:0% +bad I feel grumpy and impatient and get +frustrated more easily when I don't get + + align:start position:0% +frustrated more easily when I don't get + + + align:start position:0% +frustrated more easily when I don't get +enough sleep but I had no idea it might + + align:start position:0% +enough sleep but I had no idea it might + + + align:start position:0% +enough sleep but I had no idea it might +affect how much money I make and how + + align:start position:0% +affect how much money I make and how + + + align:start position:0% +affect how much money I make and how +much money I save + + align:start position:0% +much money I save + + + align:start position:0% +much money I save +D so what we did in one of our studies + + align:start position:0% +D so what we did in one of our studies + + + align:start position:0% +D so what we did in one of our studies +we tried to provide people with + + align:start position:0% +we tried to provide people with + + + align:start position:0% +we tried to provide people with +different interventions to improve their + + align:start position:0% +different interventions to improve their + + + align:start position:0% +different interventions to improve their +sleep including eye shades earplugs + + align:start position:0% +sleep including eye shades earplugs + + + align:start position:0% +sleep including eye shades earplugs +mattress table fan and so on so these + + align:start position:0% +mattress table fan and so on so these + + + align:start position:0% +mattress table fan and so on so these +are all kind of interventions to improve + + align:start position:0% +are all kind of interventions to improve + + + align:start position:0% +are all kind of interventions to improve +your sleep environment we also gave + + align:start position:0% +your sleep environment we also gave + + + align:start position:0% +your sleep environment we also gave +people some information about doctors + + align:start position:0% +people some information about doctors + + + align:start position:0% +people some information about doctors +say you know sleep is important for your + + align:start position:0% +say you know sleep is important for your + + + align:start position:0% +say you know sleep is important for your +health and other people were given + + align:start position:0% +health and other people were given + + + align:start position:0% +health and other people were given +incentives to sleep more so they're + + align:start position:0% +incentives to sleep more so they're + + + align:start position:0% +incentives to sleep more so they're +actually paid by the number of hours + + align:start position:0% +actually paid by the number of hours + + + align:start position:0% +actually paid by the number of hours +that they slept and the more they slept + + align:start position:0% +that they slept and the more they slept + + + align:start position:0% +that they slept and the more they slept +the more they were paid + + align:start position:0% +the more they were paid + + + align:start position:0% +the more they were paid +and all of these interventions were in + + align:start position:0% +and all of these interventions were in + + + align:start position:0% +and all of these interventions were in +fact quite successful in increasing + + align:start position:0% +fact quite successful in increasing + + + align:start position:0% +fact quite successful in increasing +people's sleep and what we were then + + align:start position:0% +people's sleep and what we were then + + + align:start position:0% +people's sleep and what we were then +interested in is now if you increase + + align:start position:0% +interested in is now if you increase + + + align:start position:0% +interested in is now if you increase +your sleep does it improve different + + align:start position:0% +your sleep does it improve different + + + align:start position:0% +your sleep does it improve different +aspects so if you're live ranging from + + align:start position:0% +aspects so if you're live ranging from + + + align:start position:0% +aspects so if you're live ranging from +cognition so these are just measures of + + align:start position:0% +cognition so these are just measures of + + + align:start position:0% +cognition so these are just measures of +attention work productivity so we hired + + align:start position:0% +attention work productivity so we hired + + + align:start position:0% +attention work productivity so we hired +people for a month to work as data entry + + align:start position:0% +people for a month to work as data entry + + + align:start position:0% +people for a month to work as data entry +workers so then we looked at people's + + align:start position:0% +workers so then we looked at people's + + + align:start position:0% +workers so then we looked at people's +labor Supply how many hours did people + + align:start position:0% +labor Supply how many hours did people + + + align:start position:0% +labor Supply how many hours did people +work how productive were they how fast + + align:start position:0% +work how productive were they how fast + + + align:start position:0% +work how productive were they how fast +did they work how many mistakes did they + + align:start position:0% +did they work how many mistakes did they + + + align:start position:0% +did they work how many mistakes did they +make and so on how much money did they + + align:start position:0% +make and so on how much money did they + + + align:start position:0% +make and so on how much money did they +earn overall and so is it the case that + + align:start position:0% +earn overall and so is it the case that + + + align:start position:0% +earn overall and so is it the case that +if you sleep more now do you make more + + align:start position:0% +if you sleep more now do you make more + + + align:start position:0% +if you sleep more now do you make more +money at work on an everyday basis and + + align:start position:0% +money at work on an everyday basis and + + + align:start position:0% +money at work on an everyday basis and +then we looked at other things such as + + align:start position:0% +then we looked at other things such as + + + align:start position:0% +then we looked at other things such as +savings we gave people an attractive + + align:start position:0% +savings we gave people an attractive + + + align:start position:0% +savings we gave people an attractive +savings opportunities you look at do + + align:start position:0% +savings opportunities you look at do + + + align:start position:0% +savings opportunities you look at do +people save more when they sleep more as + + align:start position:0% +people save more when they sleep more as + + + align:start position:0% +people save more when they sleep more as +well as the economists would call + + align:start position:0% +well as the economists would call + + + align:start position:0% +well as the economists would call +preferences which is time risk and + + align:start position:0% +preferences which is time risk and + + + align:start position:0% +preferences which is time risk and +social preferences so how do you make + + align:start position:0% +social preferences so how do you make + + + align:start position:0% +social preferences so how do you make +decisions over time how pro-social are + + align:start position:0% +decisions over time how pro-social are + + + align:start position:0% +decisions over time how pro-social are +you when you decide between your own + + align:start position:0% +you when you decide between your own + + + align:start position:0% +you when you decide between your own +outcomes versus others how how nice are + + align:start position:0% +outcomes versus others how how nice are + + + align:start position:0% +outcomes versus others how how nice are +you to others and how do you make + + align:start position:0% +you to others and how do you make + + + align:start position:0% +you to others and how do you make +decisions in the face of risk and the + + align:start position:0% +decisions in the face of risk and the + + + align:start position:0% +decisions in the face of risk and the +idea here would be that if you found + + align:start position:0% +idea here would be that if you found + + + align:start position:0% +idea here would be that if you found +effects people might for example be more + + align:start position:0% +effects people might for example be more + + + align:start position:0% +effects people might for example be more +patient if they have slept more so they + + align:start position:0% +patient if they have slept more so they + + + align:start position:0% +patient if they have slept more so they +might be willing to save more for the + + align:start position:0% +might be willing to save more for the + + + align:start position:0% +might be willing to save more for the +future which could have high returns in + + align:start position:0% +future which could have high returns in + + + align:start position:0% +future which could have high returns in +the future + + align:start position:0% +the future + + + align:start position:0% +the future +at MIT Frank's work in behavioral + + align:start position:0% +at MIT Frank's work in behavioral + + + align:start position:0% +at MIT Frank's work in behavioral +economics seeks to enhance current + + align:start position:0% +economics seeks to enhance current + + + align:start position:0% +economics seeks to enhance current +economic models with insights from + + align:start position:0% +economic models with insights from + + + align:start position:0% +economic models with insights from +anthropology and sociology in order to + + align:start position:0% +anthropology and sociology in order to + + + align:start position:0% +anthropology and sociology in order to +make the field of Economics reflect what + + align:start position:0% +make the field of Economics reflect what + + + align:start position:0% +make the field of Economics reflect what +actually goes on in people's lives I + + align:start position:0% +actually goes on in people's lives I + + + align:start position:0% +actually goes on in people's lives I +asked Frank to explain a bit more about + + align:start position:0% +asked Frank to explain a bit more about + + + align:start position:0% +asked Frank to explain a bit more about +how his work Builds on traditional + + align:start position:0% +how his work Builds on traditional + + + align:start position:0% +how his work Builds on traditional +economic models + + align:start position:0% +economic models + + + align:start position:0% +economic models +economics makes a lot of very Stark + + align:start position:0% +economics makes a lot of very Stark + + + align:start position:0% +economics makes a lot of very Stark +assumptions on people's behavior so + + align:start position:0% +assumptions on people's behavior so + + + align:start position:0% +assumptions on people's behavior so +economics usually your standard + + align:start position:0% +economics usually your standard + + + align:start position:0% +economics usually your standard +economics usually assumes that people + + align:start position:0% +economics usually assumes that people + + + align:start position:0% +economics usually assumes that people +are very rational they're very willful + + align:start position:0% +are very rational they're very willful + + + align:start position:0% +are very rational they're very willful +they're also very well informed and very + + align:start position:0% +they're also very well informed and very + + + align:start position:0% +they're also very well informed and very +attentive + + align:start position:0% +attentive + + + align:start position:0% +attentive +so you can think of this and this is + + align:start position:0% +so you can think of this and this is + + + align:start position:0% +so you can think of this and this is +usually called homoeconomic because this + + align:start position:0% +usually called homoeconomic because this + + + align:start position:0% +usually called homoeconomic because this +is a person sort of the ideal human who + + align:start position:0% +is a person sort of the ideal human who + + + align:start position:0% +is a person sort of the ideal human who +doesn't make any mistakes who makes + + align:start position:0% +doesn't make any mistakes who makes + + + align:start position:0% +doesn't make any mistakes who makes +perfect decisions + + align:start position:0% +perfect decisions + + + align:start position:0% +perfect decisions +and is always right in what they do and + + align:start position:0% +and is always right in what they do and + + + align:start position:0% +and is always right in what they do and +they perfectly optimize at any point in + + align:start position:0% +they perfectly optimize at any point in + + + align:start position:0% +they perfectly optimize at any point in +time + + align:start position:0% +time + + + align:start position:0% +time +Frank explained that although standard + + align:start position:0% +Frank explained that although standard + + + align:start position:0% +Frank explained that although standard +economics Frameworks do help explain a + + align:start position:0% +economics Frameworks do help explain a + + + align:start position:0% +economics Frameworks do help explain a +lot of important behaviors + + align:start position:0% +lot of important behaviors + + + align:start position:0% +lot of important behaviors +their assumptions often miss some + + align:start position:0% +their assumptions often miss some + + + align:start position:0% +their assumptions often miss some +important parts of people's choices + + align:start position:0% +important parts of people's choices + + + align:start position:0% +important parts of people's choices +looking through a psychological lens can + + align:start position:0% +looking through a psychological lens can + + + align:start position:0% +looking through a psychological lens can +help round out the picture + + align:start position:0% +help round out the picture + + + align:start position:0% +help round out the picture +there are a number of examples in which + + align:start position:0% +there are a number of examples in which + + + align:start position:0% +there are a number of examples in which +psychological insights have been quite + + align:start position:0% +psychological insights have been quite + + + align:start position:0% +psychological insights have been quite +important in informing models one very + + align:start position:0% +important in informing models one very + + + align:start position:0% +important in informing models one very +successful area is the area of + + align:start position:0% +successful area is the area of + + + align:start position:0% +successful area is the area of +self-control or decision making over + + align:start position:0% +self-control or decision making over + + + align:start position:0% +self-control or decision making over +time this is the question on when we + + align:start position:0% +time this is the question on when we + + + align:start position:0% +time this is the question on when we +have unpleasant tasks that we might not + + align:start position:0% +have unpleasant tasks that we might not + + + align:start position:0% +have unpleasant tasks that we might not +want to do for example when we choose + + align:start position:0% +want to do for example when we choose + + + align:start position:0% +want to do for example when we choose +when to do certain things or when to + + align:start position:0% +when to do certain things or when to + + + align:start position:0% +when to do certain things or when to +consume earlier versus later when there + + align:start position:0% +consume earlier versus later when there + + + align:start position:0% +consume earlier versus later when there +are Temptations on when people try to + + align:start position:0% +are Temptations on when people try to + + + align:start position:0% +are Temptations on when people try to +procrastinate people tend to have + + align:start position:0% +procrastinate people tend to have + + + align:start position:0% +procrastinate people tend to have +imperfect self-control so we don't + + align:start position:0% +imperfect self-control so we don't + + + align:start position:0% +imperfect self-control so we don't +always do the things we plan to do we + + align:start position:0% +always do the things we plan to do we + + + align:start position:0% +always do the things we plan to do we +don't always plan to do the things we + + align:start position:0% +don't always plan to do the things we + + + align:start position:0% +don't always plan to do the things we +want to do on time students + + align:start position:0% +want to do on time students + + + align:start position:0% +want to do on time students +procrastinate their problem sets faculty + + align:start position:0% +procrastinate their problem sets faculty + + + align:start position:0% +procrastinate their problem sets faculty +procrastinate writing their problem sets + + align:start position:0% +procrastinate writing their problem sets + + + align:start position:0% +procrastinate writing their problem sets +people consume too early people overeat + + align:start position:0% +people consume too early people overeat + + + align:start position:0% +people consume too early people overeat +people over indulge in things they are + + align:start position:0% +people over indulge in things they are + + + align:start position:0% +people over indulge in things they are +joyful in the moment but have perhaps + + align:start position:0% +joyful in the moment but have perhaps + + + align:start position:0% +joyful in the moment but have perhaps +long-run consequences and people under + + align:start position:0% +long-run consequences and people under + + + align:start position:0% +long-run consequences and people under +invest in things that are painful in the + + align:start position:0% +invest in things that are painful in the + + + align:start position:0% +invest in things that are painful in the +Moment Like say going to the gym or + + align:start position:0% +Moment Like say going to the gym or + + + align:start position:0% +Moment Like say going to the gym or +going to the doctor or making good + + align:start position:0% +going to the doctor or making good + + + align:start position:0% +going to the doctor or making good +health choices that are in fact then + + align:start position:0% +health choices that are in fact then + + + align:start position:0% +health choices that are in fact then +costly in the future + + align:start position:0% +costly in the future + + + align:start position:0% +costly in the future +and so behavioral economics has then + + align:start position:0% +and so behavioral economics has then + + + align:start position:0% +and so behavioral economics has then +tried to model or try to understand + + align:start position:0% +tried to model or try to understand + + + align:start position:0% +tried to model or try to understand +self-control problems or what people + + align:start position:0% +self-control problems or what people + + + align:start position:0% +self-control problems or what people +call present Focus which is people + + align:start position:0% +call present Focus which is people + + + align:start position:0% +call present Focus which is people +excessively focus on the present they've + + align:start position:0% +excessively focus on the present they've + + + align:start position:0% +excessively focus on the present they've +put lots of weight on what they + + align:start position:0% +put lots of weight on what they + + + align:start position:0% +put lots of weight on what they +experience right now if you have a donut + + align:start position:0% +experience right now if you have a donut + + + align:start position:0% +experience right now if you have a donut +in front of you it's hard to resist + + align:start position:0% +in front of you it's hard to resist + + + align:start position:0% +in front of you it's hard to resist +or if you're in bed in the morning and + + align:start position:0% +or if you're in bed in the morning and + + + align:start position:0% +or if you're in bed in the morning and +think about you to exercise early or + + align:start position:0% +think about you to exercise early or + + + align:start position:0% +think about you to exercise early or +should I sleep for another hour it might + + align:start position:0% +should I sleep for another hour it might + + + align:start position:0% +should I sleep for another hour it might +be very tempting to say well I'd rather + + align:start position:0% +be very tempting to say well I'd rather + + + align:start position:0% +be very tempting to say well I'd rather +sleep another hour even though your plan + + align:start position:0% +sleep another hour even though your plan + + + align:start position:0% +sleep another hour even though your plan +was very much to get up early and + + align:start position:0% +was very much to get up early and + + + align:start position:0% +was very much to get up early and +exercise and be virtuous and so on and + + align:start position:0% +exercise and be virtuous and so on and + + + align:start position:0% +exercise and be virtuous and so on and +so now behavioral economics has helped + + align:start position:0% +so now behavioral economics has helped + + + align:start position:0% +so now behavioral economics has helped +us understand such issues and potential + + align:start position:0% +us understand such issues and potential + + + align:start position:0% +us understand such issues and potential +ways to overcome them through what + + align:start position:0% +ways to overcome them through what + + + align:start position:0% +ways to overcome them through what +people call commitment devices for + + align:start position:0% +people call commitment devices for + + + align:start position:0% +people call commitment devices for +example which are essentially contracts + + align:start position:0% +example which are essentially contracts + + + align:start position:0% +example which are essentially contracts +or type of policies that might help + + align:start position:0% +or type of policies that might help + + + align:start position:0% +or type of policies that might help +people overcome self-control issues + + align:start position:0% +people overcome self-control issues + + + align:start position:0% +people overcome self-control issues +that's interesting I also think + + align:start position:0% +that's interesting I also think + + + align:start position:0% +that's interesting I also think +especially what you say about using + + align:start position:0% +especially what you say about using + + + align:start position:0% +especially what you say about using +insights from anthropology to inform + + align:start position:0% +insights from anthropology to inform + + + align:start position:0% +insights from anthropology to inform +standard models like insights from + + align:start position:0% +standard models like insights from + + + align:start position:0% +standard models like insights from +community members and anthropologists + + align:start position:0% +community members and anthropologists + + + align:start position:0% +community members and anthropologists +working with community members it might + + align:start position:0% +working with community members it might + + + align:start position:0% +working with community members it might +look like someone is not making an + + align:start position:0% +look like someone is not making an + + + align:start position:0% +look like someone is not making an +informed decision once you start looking + + align:start position:0% +informed decision once you start looking + + + align:start position:0% +informed decision once you start looking +into the Community Network a decision + + align:start position:0% +into the Community Network a decision + + + align:start position:0% +into the Community Network a decision +that might not seem rational might + + align:start position:0% +that might not seem rational might + + + align:start position:0% +that might not seem rational might +actually be very rational in that + + align:start position:0% +actually be very rational in that + + + align:start position:0% +actually be very rational in that +particular context like they might be + + align:start position:0% +particular context like they might be + + + align:start position:0% +particular context like they might be +making decisions based on ties to other + + align:start position:0% +making decisions based on ties to other + + + align:start position:0% +making decisions based on ties to other +community members or reciprocity or you + + align:start position:0% +community members or reciprocity or you + + + align:start position:0% +community members or reciprocity or you +know things that would benefit them in + + align:start position:0% +know things that would benefit them in + + + align:start position:0% +know things that would benefit them in +other ways that these standardized + + align:start position:0% +other ways that these standardized + + + align:start position:0% +other ways that these standardized +models might miss and I think it might + + align:start position:0% +models might miss and I think it might + + + align:start position:0% +models might miss and I think it might +be a way to make economics more + + align:start position:0% +be a way to make economics more + + + align:start position:0% +be a way to make economics more +culturally relevant or informed + + align:start position:0% +culturally relevant or informed + + + align:start position:0% +culturally relevant or informed +that's exactly right so in a way you + + align:start position:0% +that's exactly right so in a way you + + + align:start position:0% +that's exactly right so in a way you +might see people's choices and think + + align:start position:0% +might see people's choices and think + + + align:start position:0% +might see people's choices and think +that they're making irrational choices + + align:start position:0% +that they're making irrational choices + + + align:start position:0% +that they're making irrational choices +one way or the other + + align:start position:0% +one way or the other + + + align:start position:0% +one way or the other +but in fact it's that our models are + + align:start position:0% +but in fact it's that our models are + + + align:start position:0% +but in fact it's that our models are +mispecified so typically our definition + + align:start position:0% +mispecified so typically our definition + + + align:start position:0% +mispecified so typically our definition +of rationality is to say we can have a + + align:start position:0% +of rationality is to say we can have a + + + align:start position:0% +of rationality is to say we can have a +set of choices or preferences we can + + align:start position:0% +set of choices or preferences we can + + + align:start position:0% +set of choices or preferences we can +have some model of your behavior that + + align:start position:0% +have some model of your behavior that + + + align:start position:0% +have some model of your behavior that +explains what you're doing overall and + + align:start position:0% +explains what you're doing overall and + + + align:start position:0% +explains what you're doing overall and +if you can have such a model then we can + + align:start position:0% +if you can have such a model then we can + + + align:start position:0% +if you can have such a model then we can +rationalize your behavior in some ways + + align:start position:0% +rationalize your behavior in some ways + + + align:start position:0% +rationalize your behavior in some ways +and we say certain choices are rational + + align:start position:0% +and we say certain choices are rational + + + align:start position:0% +and we say certain choices are rational +now if you make certain choices where + + align:start position:0% +now if you make certain choices where + + + align:start position:0% +now if you make certain choices where +our existing models say this does not + + align:start position:0% +our existing models say this does not + + + align:start position:0% +our existing models say this does not +compute this does not add up it doesn't + + align:start position:0% +compute this does not add up it doesn't + + + align:start position:0% +compute this does not add up it doesn't +seem right + + align:start position:0% +seem right + + + align:start position:0% +seem right +one might be tempted to say while these + + align:start position:0% +one might be tempted to say while these + + + align:start position:0% +one might be tempted to say while these +choices appear irrational + + align:start position:0% +choices appear irrational + + + align:start position:0% +choices appear irrational +but in fact they're not irrational it's + + align:start position:0% +but in fact they're not irrational it's + + + align:start position:0% +but in fact they're not irrational it's +just we have mispecified the model we + + align:start position:0% +just we have mispecified the model we + + + align:start position:0% +just we have mispecified the model we +have misunderstood we have forgotten or + + align:start position:0% +have misunderstood we have forgotten or + + + align:start position:0% +have misunderstood we have forgotten or +or omitted certain factors that seem + + align:start position:0% +or omitted certain factors that seem + + + align:start position:0% +or omitted certain factors that seem +important and those could be exactly as + + align:start position:0% +important and those could be exactly as + + + align:start position:0% +important and those could be exactly as +you say like social or cultural factors + + align:start position:0% +you say like social or cultural factors + + + align:start position:0% +you say like social or cultural factors +how people care about others or how + + align:start position:0% +how people care about others or how + + + align:start position:0% +how people care about others or how +people care about others influences + + align:start position:0% +people care about others influences + + + align:start position:0% +people care about others influences +potentially and that could be really + + align:start position:0% +potentially and that could be really + + + align:start position:0% +potentially and that could be really +important + + align:start position:0% +important + + + align:start position:0% +important +[Music] + + align:start position:0% + + + + align:start position:0% + +before we get back to our interview with + + align:start position:0% +before we get back to our interview with + + + align:start position:0% +before we get back to our interview with +Frank we wanted to take a moment to + + align:start position:0% +Frank we wanted to take a moment to + + + align:start position:0% +Frank we wanted to take a moment to +thank all of our listeners who have + + align:start position:0% +thank all of our listeners who have + + + align:start position:0% +thank all of our listeners who have +written to us with appreciation feedback + + align:start position:0% +written to us with appreciation feedback + + + align:start position:0% +written to us with appreciation feedback +and questions for our guests + + align:start position:0% +and questions for our guests + + + align:start position:0% +and questions for our guests +we also wanted to thank those of you + + align:start position:0% +we also wanted to thank those of you + + + align:start position:0% +we also wanted to thank those of you +who've left us ratings and reviews on + + align:start position:0% +who've left us ratings and reviews on + + + align:start position:0% +who've left us ratings and reviews on +Apple podcasts hearing how much you're + + align:start position:0% +Apple podcasts hearing how much you're + + + align:start position:0% +Apple podcasts hearing how much you're +enjoying the show means a lot to us + + align:start position:0% +enjoying the show means a lot to us + + + align:start position:0% +enjoying the show means a lot to us +so we thought it might be a good idea to + + align:start position:0% +so we thought it might be a good idea to + + + align:start position:0% +so we thought it might be a good idea to +share some of these reviews from time to + + align:start position:0% +share some of these reviews from time to + + + align:start position:0% +share some of these reviews from time to +time on the show starting with this one + + align:start position:0% +time on the show starting with this one + + + align:start position:0% +time on the show starting with this one +which also happens to include a + + align:start position:0% +which also happens to include a + + + align:start position:0% +which also happens to include a +suggestion it says + + align:start position:0% +suggestion it says + + + align:start position:0% +suggestion it says +I am very thankful that this podcast + + align:start position:0% +I am very thankful that this podcast + + + align:start position:0% +I am very thankful that this podcast +exists as mentioned in the trailer it is + + align:start position:0% +exists as mentioned in the trailer it is + + + align:start position:0% +exists as mentioned in the trailer it is +close to being able to have a quick + + align:start position:0% +close to being able to have a quick + + + align:start position:0% +close to being able to have a quick +conversation with these great professors + + align:start position:0% +conversation with these great professors + + + align:start position:0% +conversation with these great professors +about their interesting courses I love + + align:start position:0% +about their interesting courses I love + + + align:start position:0% +about their interesting courses I love +the episode with Gilbert Strang and look + + align:start position:0% +the episode with Gilbert Strang and look + + + align:start position:0% +the episode with Gilbert Strang and look +forward to listening to subjects that I + + align:start position:0% +forward to listening to subjects that I + + + align:start position:0% +forward to listening to subjects that I +would not normally be exposed to + + align:start position:0% +would not normally be exposed to + + + align:start position:0% +would not normally be exposed to +suggestion please do an episode on 6001 + + align:start position:0% +suggestion please do an episode on 6001 + + + align:start position:0% +suggestion please do an episode on 6001 +with Dr Annabelle Professor Eric crimson + + align:start position:0% +with Dr Annabelle Professor Eric crimson + + + align:start position:0% +with Dr Annabelle Professor Eric crimson +and professor John gutake + + align:start position:0% +and professor John gutake + + + align:start position:0% +and professor John gutake +wow what a great review thank you so + + align:start position:0% +wow what a great review thank you so + + + align:start position:0% +wow what a great review thank you so +much so interestingly Eric Grimson was + + align:start position:0% +much so interestingly Eric Grimson was + + + align:start position:0% +much so interestingly Eric Grimson was +recently named interim vice president + + align:start position:0% +recently named interim vice president + + + align:start position:0% +recently named interim vice president +for open learning which technically + + align:start position:0% +for open learning which technically + + + align:start position:0% +for open learning which technically +means he's my colleague now and you know + + align:start position:0% +means he's my colleague now and you know + + + align:start position:0% +means he's my colleague now and you know +I think he'd probably be into the idea + + align:start position:0% +I think he'd probably be into the idea + + + align:start position:0% +I think he'd probably be into the idea +of appearing on Chalk radio so why don't + + align:start position:0% +of appearing on Chalk radio so why don't + + + align:start position:0% +of appearing on Chalk radio so why don't +I give him a call right now + + align:start position:0% +I give him a call right now + + + align:start position:0% +I give him a call right now +foreign + + align:start position:0% + + + + align:start position:0% + +hi Eric this is Sarah from chalk radio + + align:start position:0% +hi Eric this is Sarah from chalk radio + + + align:start position:0% +hi Eric this is Sarah from chalk radio +hi Sarah how are you doing + + align:start position:0% +hi Sarah how are you doing + + + align:start position:0% +hi Sarah how are you doing +I'm doing great hey um we got a request + + align:start position:0% +I'm doing great hey um we got a request + + + align:start position:0% +I'm doing great hey um we got a request +to have you on the show + + align:start position:0% +to have you on the show + + + align:start position:0% +to have you on the show +um to talk about computer programming + + align:start position:0% +um to talk about computer programming + + + align:start position:0% +um to talk about computer programming +and I'm wondering if you'd be up for + + align:start position:0% +and I'm wondering if you'd be up for + + + align:start position:0% +and I'm wondering if you'd be up for +that I'd love to it'd be great right + + align:start position:0% +that I'd love to it'd be great right + + + align:start position:0% +that I'd love to it'd be great right +just let me know when and where I'll be + + align:start position:0% +just let me know when and where I'll be + + + align:start position:0% +just let me know when and where I'll be +there great we'll be in touch and we'll + + align:start position:0% +there great we'll be in touch and we'll + + + align:start position:0% +there great we'll be in touch and we'll +talk soon + + align:start position:0% +talk soon + + + align:start position:0% +talk soon +well there you have it you can look + + align:start position:0% +well there you have it you can look + + + align:start position:0% +well there you have it you can look +forward to an interview with Eric + + align:start position:0% +forward to an interview with Eric + + + align:start position:0% +forward to an interview with Eric +Crimson later this season on Chalk radio + + align:start position:0% +Crimson later this season on Chalk radio + + + align:start position:0% +Crimson later this season on Chalk radio +and if you have a suggestion for a guest + + align:start position:0% +and if you have a suggestion for a guest + + + align:start position:0% +and if you have a suggestion for a guest +you'd like to hear on Chalk radio you + + align:start position:0% +you'd like to hear on Chalk radio you + + + align:start position:0% +you'd like to hear on Chalk radio you +can let us know in a review on Apple + + align:start position:0% +can let us know in a review on Apple + + + align:start position:0% +can let us know in a review on Apple +podcasts or Spotify or you can email us + + align:start position:0% +podcasts or Spotify or you can email us + + + align:start position:0% +podcasts or Spotify or you can email us +directly at chalkradio mit.edu + + align:start position:0% +directly at chalkradio mit.edu + + + align:start position:0% +directly at chalkradio mit.edu +okay now back to our interview with + + align:start position:0% +okay now back to our interview with + + + align:start position:0% +okay now back to our interview with +Frank schilbach + + align:start position:0% +Frank schilbach + + + align:start position:0% +Frank schilbach +it's clear students mental health is an + + align:start position:0% +it's clear students mental health is an + + + align:start position:0% +it's clear students mental health is an +important factor for Frank and he takes + + align:start position:0% +important factor for Frank and he takes + + + align:start position:0% +important factor for Frank and he takes +that into account in the way he + + align:start position:0% +that into account in the way he + + + align:start position:0% +that into account in the way he +structures his course + + align:start position:0% +structures his course + + + align:start position:0% +structures his course +when I started my problem since we do at + + align:start position:0% +when I started my problem since we do at + + + align:start position:0% +when I started my problem since we do at +9am or whenever in class essentially at + + align:start position:0% +9am or whenever in class essentially at + + + align:start position:0% +9am or whenever in class essentially at +the beginning of class and that's very + + align:start position:0% +the beginning of class and that's very + + + align:start position:0% +the beginning of class and that's very +standard in many classes at MIT + + align:start position:0% +standard in many classes at MIT + + + align:start position:0% +standard in many classes at MIT +but of course what that leads to is + + align:start position:0% +but of course what that leads to is + + + align:start position:0% +but of course what that leads to is +students like pulling all-nighters or + + align:start position:0% +students like pulling all-nighters or + + + align:start position:0% +students like pulling all-nighters or +doing the problem sets in the middle of + + align:start position:0% +doing the problem sets in the middle of + + + align:start position:0% +doing the problem sets in the middle of +the night which you know arguably is not + + align:start position:0% +the night which you know arguably is not + + + align:start position:0% +the night which you know arguably is not +good for them or good for their health + + align:start position:0% +good for them or good for their health + + + align:start position:0% +good for them or good for their health +or their mental health for that matter + + align:start position:0% +or their mental health for that matter + + + align:start position:0% +or their mental health for that matter +and so now I shifted to to having + + align:start position:0% +and so now I shifted to to having + + + align:start position:0% +and so now I shifted to to having +problems that do at 6 PM or 8 PM in fact + + align:start position:0% +problems that do at 6 PM or 8 PM in fact + + + align:start position:0% +problems that do at 6 PM or 8 PM in fact +on Fridays in part because I want + + align:start position:0% +on Fridays in part because I want + + + align:start position:0% +on Fridays in part because I want +students to to have some weekends and + + align:start position:0% +students to to have some weekends and + + + align:start position:0% +students to to have some weekends and +again not work in the middle of the + + align:start position:0% +again not work in the middle of the + + + align:start position:0% +again not work in the middle of the +night so very small choices that I like + + align:start position:0% +night so very small choices that I like + + + align:start position:0% +night so very small choices that I like +to think are well informed by at least + + align:start position:0% +to think are well informed by at least + + + align:start position:0% +to think are well informed by at least +some behavioral economics or + + align:start position:0% +some behavioral economics or + + + align:start position:0% +some behavioral economics or +psychological considerations yeah it + + align:start position:0% +psychological considerations yeah it + + + align:start position:0% +psychological considerations yeah it +also pushes Mental Health and Wellness + + align:start position:0% +also pushes Mental Health and Wellness + + + align:start position:0% +also pushes Mental Health and Wellness +out of this cordoned off area that like + + align:start position:0% +out of this cordoned off area that like + + + align:start position:0% +out of this cordoned off area that like +oh yeah it's important to think about + + align:start position:0% +oh yeah it's important to think about + + + align:start position:0% +oh yeah it's important to think about +but we're gonna like consider all these + + align:start position:0% +but we're gonna like consider all these + + + align:start position:0% +but we're gonna like consider all these +other things first you're really pulling + + align:start position:0% +other things first you're really pulling + + + align:start position:0% +other things first you're really pulling +it into the center of what you're doing + + align:start position:0% +it into the center of what you're doing + + + align:start position:0% +it into the center of what you're doing +which is I think a pretty unique + + align:start position:0% +which is I think a pretty unique + + + align:start position:0% +which is I think a pretty unique +approach to teaching + + align:start position:0% +approach to teaching + + + align:start position:0% +approach to teaching +yeah I think that's right I think it's + + align:start position:0% +yeah I think that's right I think it's + + + align:start position:0% +yeah I think that's right I think it's +also in economics more broadly mental + + align:start position:0% +also in economics more broadly mental + + + align:start position:0% +also in economics more broadly mental +health at least until recently has not + + align:start position:0% +health at least until recently has not + + + align:start position:0% +health at least until recently has not +received a lot of attention so in some + + align:start position:0% +received a lot of attention so in some + + + align:start position:0% +received a lot of attention so in some +of the research that I have been doing + + align:start position:0% +of the research that I have been doing + + + align:start position:0% +of the research that I have been doing +it's still viewed as in some ways + + align:start position:0% +it's still viewed as in some ways + + + align:start position:0% +it's still viewed as in some ways +instrumental in the sense that you say + + align:start position:0% +instrumental in the sense that you say + + + align:start position:0% +instrumental in the sense that you say +well if you can improve people's mental + + align:start position:0% +well if you can improve people's mental + + + align:start position:0% +well if you can improve people's mental +health we can improve people's + + align:start position:0% +health we can improve people's + + + align:start position:0% +health we can improve people's +productivity or their decision making or + + align:start position:0% +productivity or their decision making or + + + align:start position:0% +productivity or their decision making or +other types of outcomes + + align:start position:0% +other types of outcomes + + + align:start position:0% +other types of outcomes +what I increasingly think is is in fact + + align:start position:0% +what I increasingly think is is in fact + + + align:start position:0% +what I increasingly think is is in fact +more important is just mental health by + + align:start position:0% +more important is just mental health by + + + align:start position:0% +more important is just mental health by +itself as an outcome is what we should + + align:start position:0% +itself as an outcome is what we should + + + align:start position:0% +itself as an outcome is what we should +strive for + + align:start position:0% +strive for + + + align:start position:0% +strive for +of course that's very hard to measure in + + align:start position:0% +of course that's very hard to measure in + + + align:start position:0% +of course that's very hard to measure in +some ways in the sense that economists + + align:start position:0% +some ways in the sense that economists + + + align:start position:0% +some ways in the sense that economists +believe in choices and hard outcomes + + align:start position:0% +believe in choices and hard outcomes + + + align:start position:0% +believe in choices and hard outcomes +such as productivity or earnings or the + + align:start position:0% +such as productivity or earnings or the + + + align:start position:0% +such as productivity or earnings or the +like that are easier to measure and + + align:start position:0% +like that are easier to measure and + + + align:start position:0% +like that are easier to measure and +mental health is much more difficult to + + align:start position:0% +mental health is much more difficult to + + + align:start position:0% +mental health is much more difficult to +measure in some ways + + align:start position:0% +measure in some ways + + + align:start position:0% +measure in some ways +but at the end of the day what + + align:start position:0% +but at the end of the day what + + + align:start position:0% +but at the end of the day what +economists should be trying to do or + + align:start position:0% +economists should be trying to do or + + + align:start position:0% +economists should be trying to do or +economics should try to do is maximize + + align:start position:0% +economics should try to do is maximize + + + align:start position:0% +economics should try to do is maximize +people's well-being + + align:start position:0% + + + + align:start position:0% + +all right my last question + + align:start position:0% +all right my last question + + + align:start position:0% +all right my last question +so on your ocw website page there's an + + align:start position:0% +so on your ocw website page there's an + + + align:start position:0% +so on your ocw website page there's an +image of a credit card frozen in ice in + + align:start position:0% +image of a credit card frozen in ice in + + + align:start position:0% +image of a credit card frozen in ice in +a glass + + align:start position:0% +a glass + + + align:start position:0% +a glass +so 30 second answer should we all be + + align:start position:0% +so 30 second answer should we all be + + + align:start position:0% +so 30 second answer should we all be +freezing our credit cards + + align:start position:0% +freezing our credit cards + + + align:start position:0% +freezing our credit cards +at some point I was showing my wife this + + align:start position:0% +at some point I was showing my wife this + + + align:start position:0% +at some point I was showing my wife this +exact slide with this exact example + + align:start position:0% +exact slide with this exact example + + + align:start position:0% +exact slide with this exact example +and she was done just telling me well + + align:start position:0% +and she was done just telling me well + + + align:start position:0% +and she was done just telling me well +haven't you seen Confessions of a + + align:start position:0% +haven't you seen Confessions of a + + + align:start position:0% +haven't you seen Confessions of a +Shopaholic which in fact is this movie + + align:start position:0% +Shopaholic which in fact is this movie + + + align:start position:0% +Shopaholic which in fact is this movie +where somebody exactly has this approach + + align:start position:0% +where somebody exactly has this approach + + + align:start position:0% +where somebody exactly has this approach +and the bottom line from that movie is + + align:start position:0% +and the bottom line from that movie is + + + align:start position:0% +and the bottom line from that movie is +well there's a person who really likes + + align:start position:0% +well there's a person who really likes + + + align:start position:0% +well there's a person who really likes +to shop and she has in fact Frozen her + + align:start position:0% +to shop and she has in fact Frozen her + + + align:start position:0% +to shop and she has in fact Frozen her +credit card + + align:start position:0% +credit card + + + align:start position:0% +credit card +and then once the shop gets the credit + + align:start position:0% +and then once the shop gets the credit + + + align:start position:0% +and then once the shop gets the credit +card out of the freezer but then just + + align:start position:0% +card out of the freezer but then just + + + align:start position:0% +card out of the freezer but then just +spends a lot of time with trying to + + align:start position:0% +spends a lot of time with trying to + + + align:start position:0% +spends a lot of time with trying to +unfreeze their credit card and then + + align:start position:0% +unfreeze their credit card and then + + + align:start position:0% +unfreeze their credit card and then +shops anyway so you want to be kind of + + align:start position:0% +shops anyway so you want to be kind of + + + align:start position:0% +shops anyway so you want to be kind of +careful with these types of policies are + + align:start position:0% +careful with these types of policies are + + + align:start position:0% +careful with these types of policies are +they really achieving the behavior that + + align:start position:0% +they really achieving the behavior that + + + align:start position:0% +they really achieving the behavior that +you want to achieve as in like does it + + align:start position:0% +you want to achieve as in like does it + + + align:start position:0% +you want to achieve as in like does it +really make you shop less if you would + + align:start position:0% +really make you shop less if you would + + + align:start position:0% +really make you shop less if you would +like to do so or does it just make + + align:start position:0% +like to do so or does it just make + + + align:start position:0% +like to do so or does it just make +things more convenient and you're kind + + align:start position:0% +things more convenient and you're kind + + + align:start position:0% +things more convenient and you're kind +of circumventing these types of policies + + align:start position:0% +of circumventing these types of policies + + + align:start position:0% +of circumventing these types of policies +or these types of things that you set + + align:start position:0% +or these types of things that you set + + + align:start position:0% +or these types of things that you set +out to do in the first place so if it's + + align:start position:0% +out to do in the first place so if it's + + + align:start position:0% +out to do in the first place so if it's +just then you put your credit card into + + align:start position:0% +just then you put your credit card into + + + align:start position:0% +just then you put your credit card into +the freezer then you unfreeze it by + + align:start position:0% +the freezer then you unfreeze it by + + + align:start position:0% +the freezer then you unfreeze it by +putting it into the bathtub or the lake + + align:start position:0% +putting it into the bathtub or the lake + + + align:start position:0% +putting it into the bathtub or the lake +then you just put in a lot of effort and + + align:start position:0% +then you just put in a lot of effort and + + + align:start position:0% +then you just put in a lot of effort and +Shop anyway and so you might as well + + align:start position:0% +Shop anyway and so you might as well + + + align:start position:0% +Shop anyway and so you might as well +have just shopped in the first place if + + align:start position:0% +have just shopped in the first place if + + + align:start position:0% +have just shopped in the first place if +that makes you happy + + align:start position:0% +that makes you happy + + + align:start position:0% +that makes you happy +Frank's approach of including societal + + align:start position:0% +Frank's approach of including societal + + + align:start position:0% +Frank's approach of including societal +factors such as mental health and + + align:start position:0% +factors such as mental health and + + + align:start position:0% +factors such as mental health and +economic models is what makes his work + + align:start position:0% +economic models is what makes his work + + + align:start position:0% +economic models is what makes his work +so important and what makes economics + + align:start position:0% +so important and what makes economics + + + align:start position:0% +so important and what makes economics +feel so human and accessible if you are + + align:start position:0% +feel so human and accessible if you are + + + align:start position:0% +feel so human and accessible if you are +ready to dive into teaching or learning + + align:start position:0% +ready to dive into teaching or learning + + + align:start position:0% +ready to dive into teaching or learning +with his materials you can find them on + + align:start position:0% +with his materials you can find them on + + + align:start position:0% +with his materials you can find them on +our MIT open courseware website + + align:start position:0% +our MIT open courseware website + + + align:start position:0% +our MIT open courseware website +there you'll find his 23 video lectures + + align:start position:0% +there you'll find his 23 video lectures + + + align:start position:0% +there you'll find his 23 video lectures +lecture slides recitation notes problem + + align:start position:0% +lecture slides recitation notes problem + + + align:start position:0% +lecture slides recitation notes problem +sets with Solutions and quizzes with + + align:start position:0% +sets with Solutions and quizzes with + + + align:start position:0% +sets with Solutions and quizzes with +Solutions all available for reuse and + + align:start position:0% +Solutions all available for reuse and + + + align:start position:0% +Solutions all available for reuse and +remixing and all for free you can help + + align:start position:0% +remixing and all for free you can help + + + align:start position:0% +remixing and all for free you can help +others find the materials too by + + align:start position:0% +others find the materials too by + + + align:start position:0% +others find the materials too by +subscribing to this podcast and leaving + + align:start position:0% +subscribing to this podcast and leaving + + + align:start position:0% +subscribing to this podcast and leaving +us a rating and review + + align:start position:0% +us a rating and review + + + align:start position:0% +us a rating and review +thank you so much for listening until + + align:start position:0% +thank you so much for listening until + + + align:start position:0% +thank you so much for listening until +next time signing off from Cambridge + + align:start position:0% +next time signing off from Cambridge + + + align:start position:0% +next time signing off from Cambridge +Massachusetts I'm your host Sarah Hansen + + align:start position:0% +Massachusetts I'm your host Sarah Hansen + + + align:start position:0% +Massachusetts I'm your host Sarah Hansen +from MIT open courseware + + align:start position:0% +from MIT open courseware + + + align:start position:0% +from MIT open courseware +MIT chalk radio's producers include + + align:start position:0% +MIT chalk radio's producers include + + + align:start position:0% +MIT chalk radio's producers include +myself Brett Pache and Dave leshansky + + align:start position:0% +myself Brett Pache and Dave leshansky + + + align:start position:0% +myself Brett Pache and Dave leshansky +our scriptwriter is nidhi shastri + + align:start position:0% +our scriptwriter is nidhi shastri + + + align:start position:0% +our scriptwriter is nidhi shastri +show notes for this episode were written + + align:start position:0% +show notes for this episode were written + + + align:start position:0% +show notes for this episode were written +by Peter Chipman Frank Showbox ocw + + align:start position:0% +by Peter Chipman Frank Showbox ocw + + + align:start position:0% +by Peter Chipman Frank Showbox ocw +coresight was built by Cheryl Siegel + + align:start position:0% +coresight was built by Cheryl Siegel + + + align:start position:0% +coresight was built by Cheryl Siegel +we're funded by MIT open learning and + + align:start position:0% +we're funded by MIT open learning and + + + align:start position:0% +we're funded by MIT open learning and +supporters like you \ No newline at end of file diff --git a/4d3RQs2JnKg.txt b/4d3RQs2JnKg.txt new file mode 100644 index 0000000000000000000000000000000000000000..7e080e965026786db1c40b24e3cf8badfed236eb --- /dev/null +++ b/4d3RQs2JnKg.txt @@ -0,0 +1,326 @@ +PROFESSOR: So +typically in the course + +we start off talking +about the structure + +of these cellular materials. + +We do some modeling of honeycomb +and foam type materials, + +and that takes not +quite half the term, + +but most of the first +part of the term anyway. + +And I give them +more problem sets + +at the beginning of the +term, and they don't really + +start on the projects +at the beginning. + +So I give them some background +information to get them going. + +And I assign the project at +the beginning of the course, + +and I think there's +three kind of deadlines. + +One is they have to +give me a proposal. + +I think that's typically +about a month into the course, + +and that can be +fairly brief, but I + +want to at least know +they've got a team. + +They've got an idea. + +They've got some idea +of how they're going + +to carry out their project. + +Then in about another +month they have + +to send me a sort of update on +the project, and by that point, + +I would have expected them, +if they're doing a literature + +review, to start +reading some papers + +and be able to tell me +something about the background + +to their project. + +If they're doing +experiments, I would + +have expected them to at +least gone into the lab + +and maybe made some materials, +or bought some materials, + +and done some preliminary tests. + +And I give them +feedback at that point. + +And at the end of the term, +they hand in the final project. + +And I see them twice +a week in class, + +and I don't really have a formal +recitation, but what I do do + +is every week that a problem +set is due I have office hours. + +And in fact, I don't actually +have it in my office. + +I book a room, and we +do a little tutorial. + +So there's times +throughout the term + +they can see me and come +and ask me questions + +about the project as well. + +So the question is what kind of +feedback do I give the students + +and how do they interact +with me on the projects, + +and typically there's about 20 +students that take the course. + +So if they do it in pairs, +there's roughly 10 projects. + +Some of the projects students +just do literature searches, + +and I don't really get +that involved with those. + +They're perfectly capable +of going to the library + +and doing a literature search. + +And some of the students +who are taking it + +are graduate students, and +they often do finite element + +numerical calculations. + +And again, I give them some +advice about how to set it up, + +but often they have +experience doing this, + +and it's sort of applying +what they already + +know to something new, but +they kind of know what to do. + +The way I get the most +involved is if students + +do experimental projects. + +So for instance, in this +elephant skull project, + +I had this connection at the +Museum of Comparatives Zoology, + +and I took the student up there. + +They had this idea +about 3D printing it, + +and we have a 3D printer +in the department. + +And one of the technical +staff, Mike Tarkanian, + +is very, very good +with the students + +and very helpful in getting +them set up on the 3D printer, + +so he helps with that. + +And I give them sort +of general advice. + +When they said now +we want to measure + +some sort of +acoustical response, + +I suggested maybe +you could suspend it + +from a wire, or +thread, or something + +and then put an accelerometer +and measure the vibrations. + +So I try to give them some +general advice like that, + +but they then carry the +experiment out themselves. + +They have to figure out how to +actually put it into practice + +and how to do it. + +And I think they get a +big kick out of that. + +MIT students enjoy that kind +of thing so that's kind of fun, + +and obviously I was +very delighted too + +with this elephant +skull project. + +So there's different +things I try + +to help with-- mostly giving +general advice about how + +they can do their +experimental projects. + +So what are some +of the challenges + +that students encounter +in their projects. + +So I think one thing is +students sometimes are + +little over ambitious in +what's possible to accomplish, + +because typically we have to +cover some material before they + +can even start the project. + +So typically they +don't start the project + +until a month or six +weeks into the term, + +and the term is only three +months long more or less. + +And so they really have a fairly +limited amount of time-- maybe + +six weeks or eight +weeks, something + +like that-- to actually +do the project. + +So if they want +to make materials, + +if they want to do some sort +of processing to make a foam, + +for example, they don't +really have a lot of time, + +because often it takes +some trial and error + +to be able to do that. + +So the projects have +to be fairly focused + +so that they can actually get +something interesting out of it + +in a fairly short +amount of time. + +And sometimes +students might want + +to do something where they +would have to order materials, + +and it may take a few weeks +for the materials to come in. + +So again, I try +to discourage them + +from doing projects where +there's going to be a long lead + +time on getting some +critical thing that they + +need for the project. + +So there are some limitations, +partly because of just the time + +we have for them +to actually do it. + +And they're not just +taking my course. + +They're taking other +courses, so there's + +sort of a limited amount of +time they can spend on it, too. \ No newline at end of file diff --git a/5AjzlkahiL0.txt b/5AjzlkahiL0.txt new file mode 100644 index 0000000000000000000000000000000000000000..0e4ba10372ae142b127bfe833c66606a87d300e4 --- /dev/null +++ b/5AjzlkahiL0.txt @@ -0,0 +1,2395 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay so lesson number + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +PA try to repeat with + + align:start position:0% + + + + align:start position:0% + +me and then you say your name instead of + + align:start position:0% +me and then you say your name instead of + + + align:start position:0% +me and then you say your name instead of +my + + align:start position:0% +my + + + align:start position:0% +my +name actually you canot say + + align:start position:0% +name actually you canot say + + + align:start position:0% +name actually you canot say +PA as you see literally it means hello I + + align:start position:0% +PA as you see literally it means hello I + + + align:start position:0% +PA as you see literally it means hello I +call myself paa my name is or I'm called + + align:start position:0% +call myself paa my name is or I'm called + + + align:start position:0% +call myself paa my name is or I'm called +something like this and typically we do + + align:start position:0% +something like this and typically we do + + + align:start position:0% +something like this and typically we do +not put the + + align:start position:0% +not put the + + + align:start position:0% +not put the +subject + + align:start position:0% +subject + + + align:start position:0% +subject +yeah yeah you can + + align:start position:0% +yeah yeah you can + + + align:start position:0% +yeah yeah you can +say but typically you don't want to do + + align:start position:0% +say but typically you don't want to do + + + align:start position:0% +say but typically you don't want to do +it unless you want to emphasize who you + + align:start position:0% + + + + align:start position:0% + +are okay now let's do this I say m PA + + align:start position:0% +are okay now let's do this I say m PA + + + align:start position:0% +are okay now let's do this I say m PA +and then I ask + + align:start position:0% +and then I ask + + + align:start position:0% +and then I ask +you you stand up you + + align:start position:0% +you you stand up you + + + align:start position:0% +you you stand up you +say then you ask somebody else + + align:start position:0% + + + + align:start position:0% + +okay wa a second I know many of you + + align:start position:0% +okay wa a second I know many of you + + + align:start position:0% +okay wa a second I know many of you +speak Spanish so you tend to + + align:start position:0% + + + + align:start position:0% + +say yeah let's try all + + align:start position:0% +say yeah let's try all + + + align:start position:0% +say yeah let's try all +together yes + + align:start position:0% +together yes + + + align:start position:0% +together yes +good + + align:start position:0% + + + + align:start position:0% + +that literally means pleasure nice to + + align:start position:0% +that literally means pleasure nice to + + + align:start position:0% +that literally means pleasure nice to +meet you so let's repeat + + align:start position:0% + + + + align:start position:0% + +okay good perfect so as you might have + + align:start position:0% +okay good perfect so as you might have + + + align:start position:0% +okay good perfect so as you might have +noticed we pronounce letters differently + + align:start position:0% +noticed we pronounce letters differently + + + align:start position:0% +noticed we pronounce letters differently +from English let's start first of all to + + align:start position:0% +from English let's start first of all to + + + align:start position:0% +from English let's start first of all to +see how we pronounce the vowels so we + + align:start position:0% +see how we pronounce the vowels so we + + + align:start position:0% +see how we pronounce the vowels so we +have + + align:start position:0% +have + + + align:start position:0% +have +a open your mouth as much as you + + align:start position:0% + + + + align:start position:0% + +can + + align:start position:0% +can + + + align:start position:0% +can +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +e e + + align:start position:0% +e e + + + align:start position:0% +e e +e + + align:start position:0% +e + + + align:start position:0% +e +or + + align:start position:0% +or + + + align:start position:0% +or +and + + align:start position:0% +and + + + align:start position:0% +and +O so forget saying U + + align:start position:0% +O so forget saying U + + + align:start position:0% +O so forget saying U +no o a a a e o o yes excellent Bim now + + align:start position:0% +no o a a a e o o yes excellent Bim now + + + align:start position:0% +no o a a a e o o yes excellent Bim now +this seems + + align:start position:0% +this seems + + + align:start position:0% +this seems +simple it's a little bit more tricky we + + align:start position:0% +simple it's a little bit more tricky we + + + align:start position:0% +simple it's a little bit more tricky we +also use + + align:start position:0% +also use + + + align:start position:0% +also use +accents so we have two kinds of accents + + align:start position:0% +accents so we have two kinds of accents + + + align:start position:0% +accents so we have two kinds of accents +we + + align:start position:0% +we + + + align:start position:0% +we +have a gray accent in Italian is GRA so + + align:start position:0% +have a gray accent in Italian is GRA so + + + align:start position:0% +have a gray accent in Italian is GRA so +you spell it the same way but you + + align:start position:0% +you spell it the same way but you + + + align:start position:0% +you spell it the same way but you +pronounce it differently aent gra and + + align:start position:0% +pronounce it differently aent gra and + + + align:start position:0% +pronounce it differently aent gra and +it's an accent in this direction from + + align:start position:0% +it's an accent in this direction from + + + align:start position:0% +it's an accent in this direction from +the top to the bottom and then we have a + + align:start position:0% + + + + align:start position:0% + +cute + + align:start position:0% +cute + + + align:start position:0% +cute +ACC + + align:start position:0% +ACC + + + align:start position:0% +ACC +a + + align:start position:0% + + + + align:start position:0% + +so what's the difference well for + + align:start position:0% +so what's the difference well for + + + align:start position:0% +so what's the difference well for +example if I + + align:start position:0% +example if I + + + align:start position:0% +example if I +write + + align:start position:0% +write + + + align:start position:0% +write +Cafe and I put a gr accent I pronounce + + align:start position:0% +Cafe and I put a gr accent I pronounce + + + align:start position:0% +Cafe and I put a gr accent I pronounce +it as C it's open right that's + + align:start position:0% + + + + align:start position:0% + +try if I + + align:start position:0% +try if I + + + align:start position:0% +try if I +say + + align:start position:0% +say + + + align:start position:0% +say +y it's + + align:start position:0% + + + + align:start position:0% + +it's close you see the difference can + + align:start position:0% +it's close you see the difference can + + + align:start position:0% +it's close you see the difference can +you can you hear that yeah + + align:start position:0% +you can you hear that yeah + + + align:start position:0% +you can you hear that yeah +[Music] + + align:start position:0% + + + + align:start position:0% + +so yes now most of the words actually + + align:start position:0% +so yes now most of the words actually + + + align:start position:0% +so yes now most of the words actually +have great + + align:start position:0% +have great + + + align:start position:0% +have great +accents and even the words that have + + align:start position:0% +accents and even the words that have + + + align:start position:0% +accents and even the words that have +acute accents most of the times are + + align:start position:0% +acute accents most of the times are + + + align:start position:0% +acute accents most of the times are +pronounced by Italians as if the accent + + align:start position:0% +pronounced by Italians as if the accent + + + align:start position:0% +pronounced by Italians as if the accent +was bra was open so when I say the okay + + align:start position:0% +was bra was open so when I say the okay + + + align:start position:0% +was bra was open so when I say the okay +I will say the C nobody will complain + + align:start position:0% +I will say the C nobody will complain + + + align:start position:0% +I will say the C nobody will complain +everybody understands the only people + + align:start position:0% +everybody understands the only people + + + align:start position:0% +everybody understands the only people +who would complain are the people from + + align:start position:0% +who would complain are the people from + + + align:start position:0% +who would complain are the people from +the Academia de la Kusa so Academia de + + align:start position:0% +the Academia de la Kusa so Academia de + + + align:start position:0% +the Academia de la Kusa so Academia de +lausa means the Academy of the brand + + align:start position:0% +lausa means the Academy of the brand + + + align:start position:0% +lausa means the Academy of the brand +it's kind of a weird name and it was + + align:start position:0% +it's kind of a weird name and it was + + + align:start position:0% +it's kind of a weird name and it was +founded founded in the 16th century by a + + align:start position:0% +founded founded in the 16th century by a + + + align:start position:0% +founded founded in the 16th century by a +group of Scholars of linguists who + + align:start position:0% +group of Scholars of linguists who + + + align:start position:0% +group of Scholars of linguists who +wanted to develop the pure Italian you + + align:start position:0% +wanted to develop the pure Italian you + + + align:start position:0% +wanted to develop the pure Italian you +know Italian + + align:start position:0% +know Italian + + + align:start position:0% +know Italian +comes from Latin and then there was + + align:start position:0% +comes from Latin and then there was + + + align:start position:0% +comes from Latin and then there was +there were a lot of regional + + align:start position:0% +there were a lot of regional + + + align:start position:0% +there were a lot of regional +dialects then the scholars in in Tuscan + + align:start position:0% +dialects then the scholars in in Tuscan + + + align:start position:0% +dialects then the scholars in in Tuscan +in Florence in pente they decided no we + + align:start position:0% +in Florence in pente they decided no we + + + align:start position:0% +in Florence in pente they decided no we +want to decide what is the real pure + + align:start position:0% +want to decide what is the real pure + + + align:start position:0% +want to decide what is the real pure +Italian this group are called the + + align:start position:0% +Italian this group are called the + + + align:start position:0% +Italian this group are called the +Academia de lausa The Academy of brand + + align:start position:0% +Academia de lausa The Academy of brand + + + align:start position:0% +Academia de lausa The Academy of brand +and the name comes from the fact that + + align:start position:0% +and the name comes from the fact that + + + align:start position:0% +and the name comes from the fact that +when you + + align:start position:0% +when you + + + align:start position:0% +when you +sift um you you know you want to divide + + align:start position:0% +sift um you you know you want to divide + + + align:start position:0% +sift um you you know you want to divide +the flour good flour from the low + + align:start position:0% +the flour good flour from the low + + + align:start position:0% +the flour good flour from the low +quality + + align:start position:0% +quality + + + align:start position:0% +quality +R you do this process of of dividing of + + align:start position:0% +R you do this process of of dividing of + + + align:start position:0% +R you do this process of of dividing of +sifting so they wanted to divide the bad + + align:start position:0% +sifting so they wanted to divide the bad + + + align:start position:0% +sifting so they wanted to divide the bad +Italian from the good high quality + + align:start position:0% +Italian from the good high quality + + + align:start position:0% +Italian from the good high quality +Italian so back to our + + align:start position:0% + + + + align:start position:0% + +absence here we have again bowels is + + align:start position:0% +absence here we have again bowels is + + + align:start position:0% +absence here we have again bowels is +this time instead of just saying a a e + + align:start position:0% +this time instead of just saying a a e + + + align:start position:0% +this time instead of just saying a a e +or U we will go from a to e and then + + align:start position:0% +or U we will go from a to e and then + + + align:start position:0% +or U we will go from a to e and then +from a to U and you will see why cuz if + + align:start position:0% +from a to U and you will see why cuz if + + + align:start position:0% +from a to U and you will see why cuz if +I say ah my mouth is completely open + + align:start position:0% +I say ah my mouth is completely open + + + align:start position:0% +I say ah my mouth is completely open +ah now I have the + + align:start position:0% +ah now I have the + + + align:start position:0% +ah now I have the +letter but there is the great accent so + + align:start position:0% +letter but there is the great accent so + + + align:start position:0% +letter but there is the great accent so +it's + + align:start position:0% +it's + + + align:start position:0% +it's +a and then I close my mouth a little bit + + align:start position:0% +a and then I close my mouth a little bit + + + align:start position:0% +a and then I close my mouth a little bit +more + + align:start position:0% +more + + + align:start position:0% +more +e and then the last one is e and my + + align:start position:0% +e and then the last one is e and my + + + align:start position:0% +e and then the last one is e and my +mouth is + + align:start position:0% +mouth is + + + align:start position:0% +mouth is +e right so it goes from very open + + align:start position:0% +e right so it goes from very open + + + align:start position:0% +e right so it goes from very open +[Music] + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +e + + align:start position:0% +e + + + align:start position:0% +e +e same goes from a to + + align:start position:0% +e same goes from a to + + + align:start position:0% +e same goes from a to +O together + + align:start position:0% + + + + align:start position:0% + +a okay let's try again all together I + + align:start position:0% +a okay let's try again all together I + + + align:start position:0% +a okay let's try again all together I +didn't hear all the + + align:start position:0% +didn't hear all the + + + align:start position:0% +didn't hear all the +voices a a a oh + + align:start position:0% +voices a a a oh + + + align:start position:0% +voices a a a oh +o o + + align:start position:0% +o o + + + align:start position:0% +o o +o now accents are really really + + align:start position:0% +o now accents are really really + + + align:start position:0% +o now accents are really really +important especially at the end of the + + align:start position:0% +important especially at the end of the + + + align:start position:0% +important especially at the end of the +word that's where we put them oh another + + align:start position:0% +word that's where we put them oh another + + + align:start position:0% +word that's where we put them oh another +small thing I told you that there is a + + align:start position:0% +small thing I told you that there is a + + + align:start position:0% +small thing I told you that there is a +grave and an acute accent but again most + + align:start position:0% +grave and an acute accent but again most + + + align:start position:0% +grave and an acute accent but again most +Italians they will write Cafe with + + align:start position:0% +Italians they will write Cafe with + + + align:start position:0% +Italians they will write Cafe with +something that's like this + + align:start position:0% +something that's like this + + + align:start position:0% +something that's like this +although it should + + align:start position:0% +although it should + + + align:start position:0% +although it should +be with a great accent but well with a + + align:start position:0% +be with a great accent but well with a + + + align:start position:0% +be with a great accent but well with a +handwriting we don't really pay too much + + align:start position:0% +handwriting we don't really pay too much + + + align:start position:0% +handwriting we don't really pay too much +attention Okay so you don't have to + + align:start position:0% +attention Okay so you don't have to + + + align:start position:0% +attention Okay so you don't have to +worry that much as long as you pronounce + + align:start position:0% +worry that much as long as you pronounce + + + align:start position:0% +worry that much as long as you pronounce +it correctly you don't say Cafe what is + + align:start position:0% +it correctly you don't say Cafe what is + + + align:start position:0% +it correctly you don't say Cafe what is +Cafe doesn't exist + + align:start position:0% +Cafe doesn't exist + + + align:start position:0% +Cafe doesn't exist +Cafe so for + + align:start position:0% +Cafe so for + + + align:start position:0% +Cafe so for +example if you + + align:start position:0% +example if you + + + align:start position:0% +example if you +say papa without an accent it means the + + align:start position:0% +say papa without an accent it means the + + + align:start position:0% +say papa without an accent it means the +PO okay if you write Papa that means + + align:start position:0% +PO okay if you write Papa that means + + + align:start position:0% +PO okay if you write Papa that means +dead so there is a huge difference + + align:start position:0% +dead so there is a huge difference + + + align:start position:0% +dead so there is a huge difference +between the PO and your + + align:start position:0% +between the PO and your + + + align:start position:0% +between the PO and your +dead + + align:start position:0% +dead + + + align:start position:0% +dead +right or if you say + + align:start position:0% +right or if you say + + + align:start position:0% +right or if you say +per well per is a a pair + + align:start position:0% +per well per is a a pair + + + align:start position:0% +per well per is a a pair +tree it's a tree if you + + align:start position:0% +tree it's a tree if you + + + align:start position:0% +tree it's a tree if you +say p well is a conjugation it means but + + align:start position:0% +say p well is a conjugation it means but + + + align:start position:0% +say p well is a conjugation it means but +or however so let's try to read these + + align:start position:0% + + + + align:start position:0% + +words so we put the accent since there + + align:start position:0% +words so we put the accent since there + + + align:start position:0% +words so we put the accent since there +is no accent here we put the accent on + + align:start position:0% +is no accent here we put the accent on + + + align:start position:0% +is no accent here we put the accent on +the first syllable + + align:start position:0% +the first syllable + + + align:start position:0% +the first syllable +Papa yeah you can also do like this just + + align:start position:0% +Papa yeah you can also do like this just + + + align:start position:0% +Papa yeah you can also do like this just +to remind yourself + + align:start position:0% +to remind yourself + + + align:start position:0% +to remind yourself +Pap + + align:start position:0% +Pap + + + align:start position:0% +Pap +yeah + + align:start position:0% + + + + align:start position:0% + +Pap yes let's try to introduce the + + align:start position:0% +Pap yes let's try to introduce the + + + align:start position:0% +Pap yes let's try to introduce the +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +you probably noticed that we try tend to + + align:start position:0% +you probably noticed that we try tend to + + + align:start position:0% +you probably noticed that we try tend to +move a lot and move our hands a lot and + + align:start position:0% +move a lot and move our hands a lot and + + + align:start position:0% +move a lot and move our hands a lot and +in Italy when we count we count in a + + align:start position:0% +in Italy when we count we count in a + + + align:start position:0% +in Italy when we count we count in a +different way so we start with Uno and + + align:start position:0% +different way so we start with Uno and + + + align:start position:0% +different way so we start with Uno and +this is one + + align:start position:0% + + + + align:start position:0% + +Uno in the US I think you do this is two + + align:start position:0% +Uno in the US I think you do this is two + + + align:start position:0% +Uno in the US I think you do this is two +right nobody understand me when I say + + align:start position:0% +right nobody understand me when I say + + + align:start position:0% +right nobody understand me when I say +this is + + align:start position:0% +this is + + + align:start position:0% +this is +Du so let's write this down + + align:start position:0% + + + + align:start position:0% + +and now we have something very + + align:start position:0% +and now we have something very + + + align:start position:0% +and now we have something very +interesting + + align:start position:0% + + + + align:start position:0% + +qu so you see we have a + + align:start position:0% +qu so you see we have a + + + align:start position:0% +qu so you see we have a +double + + align:start position:0% +double + + + align:start position:0% +double +consonant and it's extremely + + align:start position:0% +consonant and it's extremely + + + align:start position:0% +consonant and it's extremely +important this is like one one of the + + align:start position:0% +important this is like one one of the + + + align:start position:0% +important this is like one one of the +biggest and most common errors of + + align:start position:0% +biggest and most common errors of + + + align:start position:0% +biggest and most common errors of +foreigners who try to speak Italian is + + align:start position:0% +foreigners who try to speak Italian is + + + align:start position:0% +foreigners who try to speak Italian is +to forget that we have double consonants + + align:start position:0% +to forget that we have double consonants + + + align:start position:0% +to forget that we have double consonants +and if you change from single consonant + + align:start position:0% +and if you change from single consonant + + + align:start position:0% +and if you change from single consonant +to a double consonant you change + + align:start position:0% +to a double consonant you change + + + align:start position:0% +to a double consonant you change +completely the meaning of what you're + + align:start position:0% +completely the meaning of what you're + + + align:start position:0% +completely the meaning of what you're +saying so let's say + + align:start position:0% +saying so let's say + + + align:start position:0% +saying so let's say +again yeah so you spend a little bit + + align:start position:0% +again yeah so you spend a little bit + + + align:start position:0% +again yeah so you spend a little bit +more time on the + + align:start position:0% + + + + align:start position:0% + +T + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +chin qu so here for those of you who + + align:start position:0% +chin qu so here for those of you who + + + align:start position:0% +chin qu so here for those of you who +speak Spanish you turn probably to + + align:start position:0% +speak Spanish you turn probably to + + + align:start position:0% +speak Spanish you turn probably to +read while we + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +pronounce + + align:start position:0% + + + + align:start position:0% + +qu qu just remember + + align:start position:0% + + + + align:start position:0% + +say we have another + + align:start position:0% + + + + align:start position:0% + +double yeah for example if I say set + + align:start position:0% +double yeah for example if I say set + + + align:start position:0% +double yeah for example if I say set +without the Double T it means that it + + align:start position:0% +without the Double T it means that it + + + align:start position:0% +without the Double T it means that it +means + + align:start position:0% +means + + + align:start position:0% +means +thirst o means I'm + + align:start position:0% +thirst o means I'm + + + align:start position:0% +thirst o means I'm +thirsty okay so this is + + align:start position:0% + + + + align:start position:0% + +very different + + align:start position:0% + + + + align:start position:0% + +from and now we have another + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +good so doubles are extremely important + + align:start position:0% +good so doubles are extremely important + + + align:start position:0% +good so doubles are extremely important +again if you + + align:start position:0% + + + + align:start position:0% + +say + + align:start position:0% +say + + + align:start position:0% +say +papa that's the pope we are a very + + align:start position:0% +papa that's the pope we are a very + + + align:start position:0% +papa that's the pope we are a very +Catholic country so keep using the papa + + align:start position:0% +Catholic country so keep using the papa + + + align:start position:0% +Catholic country so keep using the papa +as an example + + align:start position:0% +as an example + + + align:start position:0% +as an example +if you put the + + align:start position:0% +if you put the + + + align:start position:0% +if you put the +double it's + + align:start position:0% +double it's + + + align:start position:0% +double it's +p and p means food in a cute cute way + + align:start position:0% +p and p means food in a cute cute way + + + align:start position:0% +p and p means food in a cute cute way +like you're talking to a little baby and + + align:start position:0% +like you're talking to a little baby and + + + align:start position:0% +like you're talking to a little baby and +you say it do it this + + align:start position:0% +you say it do it this + + + align:start position:0% +you say it do it this +Papa or sometimes you want want to use + + align:start position:0% +Papa or sometimes you want want to use + + + align:start position:0% +Papa or sometimes you want want to use +it if um if something looks like baby + + align:start position:0% +it if um if something looks like baby + + + align:start position:0% +it if um if something looks like baby +food like if you read food and it + + align:start position:0% +food like if you read food and it + + + align:start position:0% +food like if you read food and it +doesn't look very tasty then you say + + align:start position:0% +doesn't look very tasty then you say + + + align:start position:0% +doesn't look very tasty then you say +what's this + + align:start position:0% +what's this + + + align:start position:0% +what's this +Papa + + align:start position:0% + + + + align:start position:0% + +is difference + + align:start position:0% + + + + align:start position:0% + +for that means ninth the ninth syon for + + align:start position:0% +for that means ninth the ninth syon for + + + align:start position:0% +for that means ninth the ninth syon for +example + + align:start position:0% +example + + + align:start position:0% +example +open + + align:start position:0% +open + + + align:start position:0% +open +well n and n is + + align:start position:0% + + + + align:start position:0% + +Grandma y so + + align:start position:0% +Grandma y so + + + align:start position:0% +Grandma y so +n n + + align:start position:0% +n n + + + align:start position:0% +n n +y very good now we will soon start to + + align:start position:0% +y very good now we will soon start to + + + align:start position:0% +y very good now we will soon start to +cook I + + align:start position:0% +cook I + + + align:start position:0% +cook I +promise but before we do that let's try + + align:start position:0% +promise but before we do that let's try + + + align:start position:0% +promise but before we do that let's try +to + + align:start position:0% + + + + align:start position:0% + +learn to cook so we start with the + + align:start position:0% +learn to cook so we start with the + + + align:start position:0% +learn to cook so we start with the +indicativo present that's the + + align:start position:0% +indicativo present that's the + + + align:start position:0% +indicativo present that's the +tense uh indicative present of the + + align:start position:0% + + + + align:start position:0% + +verb + + align:start position:0% +verb + + + align:start position:0% +verb +so like + + align:start position:0% +so like + + + align:start position:0% +so like +ch + + align:start position:0% +ch + + + align:start position:0% +ch +[Music] + + align:start position:0% + + + + align:start position:0% + +right in Italian we have + + align:start position:0% +right in Italian we have + + + align:start position:0% +right in Italian we have +verbs that end with different + + align:start position:0% +verbs that end with different + + + align:start position:0% +verbs that end with different +combinations so we have the verbs + + align:start position:0% + + + + align:start position:0% + +like that end + + align:start position:0% + + + + align:start position:0% + +in we have verbs + + align:start position:0% +in we have verbs + + + align:start position:0% +in we have verbs +like + + align:start position:0% +like + + + align:start position:0% +like +be to drink it end the end with + + align:start position:0% +be to drink it end the end with + + + align:start position:0% +be to drink it end the end with +in and then we have verbs + + align:start position:0% +in and then we have verbs + + + align:start position:0% +in and then we have verbs +like to + + align:start position:0% + + + + align:start position:0% + +sleep the end with e + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so verbs that + + align:start position:0% +so verbs that + + + align:start position:0% +so verbs that +end with they will conjugate like the + + align:start position:0% +end with they will conjugate like the + + + align:start position:0% +end with they will conjugate like the +verb verbs that end + + align:start position:0% +verb verbs that end + + + align:start position:0% +verb verbs that end +with they conjugate like ver verbs that + + align:start position:0% +with they conjugate like ver verbs that + + + align:start position:0% +with they conjugate like ver verbs that +end in this is the + + align:start position:0% + + + + align:start position:0% + +infinitive so they will conjugate like + + align:start position:0% +infinitive so they will conjugate like + + + align:start position:0% +infinitive so they will conjugate like +the verb d + + align:start position:0% +the verb d + + + align:start position:0% +the verb d +then we have a lot of exceptions you + + align:start position:0% +then we have a lot of exceptions you + + + align:start position:0% +then we have a lot of exceptions you +will hate exceptions but you don't have + + align:start position:0% +will hate exceptions but you don't have + + + align:start position:0% +will hate exceptions but you don't have +to worry we learn all the way but we + + align:start position:0% +to worry we learn all the way but we + + + align:start position:0% +to worry we learn all the way but we +want to know first how the regular and + + align:start position:0% +want to know first how the regular and + + + align:start position:0% +want to know first how the regular and +good verbs behave so let's go back to + + align:start position:0% +good verbs behave so let's go back to + + + align:start position:0% +good verbs behave so let's go back to +our verb because then we we have + + align:start position:0% +our verb because then we we have + + + align:start position:0% +our verb because then we we have +to we have + + align:start position:0% +to we have + + + align:start position:0% +to we have +to as I told you usually we just neglect + + align:start position:0% +to as I told you usually we just neglect + + + align:start position:0% +to as I told you usually we just neglect +the subject so I wrote it in parenthesis + + align:start position:0% +the subject so I wrote it in parenthesis + + + align:start position:0% +the subject so I wrote it in parenthesis +but typically I will not say you Cino I + + align:start position:0% +but typically I will not say you Cino I + + + align:start position:0% +but typically I will not say you Cino I +just say + + align:start position:0% +just say + + + align:start position:0% +just say +Cino okay + + align:start position:0% +Cino okay + + + align:start position:0% +Cino okay +and in order to remember when the accent + + align:start position:0% +and in order to remember when the accent + + + align:start position:0% +and in order to remember when the accent +you can clap your hands okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +okay stand + + align:start position:0% + + + + align:start position:0% + +up you can move + + align:start position:0% + + + + align:start position:0% + +okay so you see they all have the same + + align:start position:0% +okay so you see they all have the same + + + align:start position:0% +okay so you see they all have the same +beginning and then we change the end + + align:start position:0% +beginning and then we change the end + + + align:start position:0% +beginning and then we change the end +based on the subject so in English you + + align:start position:0% +based on the subject so in English you + + + align:start position:0% +based on the subject so in English you +say I cook you cook she cooks you just + + align:start position:0% +say I cook you cook she cooks you just + + + align:start position:0% +say I cook you cook she cooks you just +add One S easy and then what's there we + + align:start position:0% +add One S easy and then what's there we + + + align:start position:0% +add One S easy and then what's there we +cook again you cook it's the same and + + align:start position:0% +cook again you cook it's the same and + + + align:start position:0% +cook again you cook it's the same and +they cook that's that's boring so no we + + align:start position:0% +they cook that's that's boring so no we + + + align:start position:0% +they cook that's that's boring so no we +like to change the end for every + + align:start position:0% +like to change the end for every + + + align:start position:0% +like to change the end for every +subject + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so Lou or Le so Lou is masculine and Le + + align:start position:0% +so Lou or Le so Lou is masculine and Le + + + align:start position:0% +so Lou or Le so Lou is masculine and Le +feminine okay now it's a little bit + + align:start position:0% + + + + align:start position:0% + +different + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah a very common error is to + + align:start position:0% +yeah a very common error is to + + + align:start position:0% +yeah a very common error is to +say no you can't say + + align:start position:0% + + + + align:start position:0% + +that okay so how about we can go around + + align:start position:0% +that okay so how about we can go around + + + align:start position:0% +that okay so how about we can go around +you don't have to be don't worry like + + align:start position:0% +you don't have to be don't worry like + + + align:start position:0% +you don't have to be don't worry like +you don't pronounce it correctly + + align:start position:0% +you don't pronounce it correctly + + + align:start position:0% +you don't pronounce it correctly +whatever it's like the first half an + + align:start position:0% +whatever it's like the first half an + + + align:start position:0% +whatever it's like the first half an +hour of Italian in your + + align:start position:0% +hour of Italian in your + + + align:start position:0% +hour of Italian in your +life um so we can just go around and and + + align:start position:0% +life um so we can just go around and and + + + align:start position:0% +life um so we can just go around and and +read through + + align:start position:0% +read through + + + align:start position:0% +read through +so Anita you can start + + align:start position:0% +so Anita you can start + + + align:start position:0% +so Anita you can start +[Music] + + align:start position:0% + + + + align:start position:0% + +with yeah this is the first one that's + + align:start position:0% +with yeah this is the first one that's + + + align:start position:0% +with yeah this is the first one that's +different + + align:start position:0% + + + + align:start position:0% + +is it's right because the the others + + align:start position:0% +is it's right because the the others + + + align:start position:0% +is it's right because the the others +they you clap you have the accent on the + + align:start position:0% +they you clap you have the accent on the + + + align:start position:0% +they you clap you have the accent on the +I on the + + align:start position:0% + + + + align:start position:0% + +E and now it + + align:start position:0% + + + + align:start position:0% + +changes + + align:start position:0% + + + + align:start position:0% + +yes here is the game on + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +e \ No newline at end of file diff --git a/6ILIA7h7B8I.txt b/6ILIA7h7B8I.txt new file mode 100644 index 0000000000000000000000000000000000000000..f0d36d6d6743bafad580222cd04e7956302974da --- /dev/null +++ b/6ILIA7h7B8I.txt @@ -0,0 +1,14667 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu the first problem set is is + + align:start position:0% +ocw.mit.edu the first problem set is is + + + align:start position:0% +ocw.mit.edu the first problem set is is +out and I should let you know that uh + + align:start position:0% +out and I should let you know that uh + + + align:start position:0% +out and I should let you know that uh +Hayden is watching out for + + align:start position:0% +Hayden is watching out for + + + align:start position:0% +Hayden is watching out for +you because we actually trimmed off one + + align:start position:0% +you because we actually trimmed off one + + + align:start position:0% +you because we actually trimmed off one +problem from past problem sets so this + + align:start position:0% +problem from past problem sets so this + + + align:start position:0% +problem from past problem sets so this +is uh a little bit of a revamp from from + + align:start position:0% +is uh a little bit of a revamp from from + + + align:start position:0% +is uh a little bit of a revamp from from +the past and and slightly shorter so so + + align:start position:0% +the past and and slightly shorter so so + + + align:start position:0% +the past and and slightly shorter so so +uh sort of the trade-off is maybe asking + + align:start position:0% +uh sort of the trade-off is maybe asking + + + align:start position:0% +uh sort of the trade-off is maybe asking +slightly fewer questions but then + + align:start position:0% +slightly fewer questions but then + + + align:start position:0% +slightly fewer questions but then +emphasizing a little bit more the + + align:start position:0% +emphasizing a little bit more the + + + align:start position:0% +emphasizing a little bit more the +discussive uh responses from you uh on + + align:start position:0% +discussive uh responses from you uh on + + + align:start position:0% +discussive uh responses from you uh on +on the problem Set uh as we talked about + + align:start position:0% +on the problem Set uh as we talked about + + + align:start position:0% +on the problem Set uh as we talked about +last time we'd really like uh a little + + align:start position:0% +last time we'd really like uh a little + + + align:start position:0% +last time we'd really like uh a little +bit of textual description from you uh + + align:start position:0% +bit of textual description from you uh + + + align:start position:0% +bit of textual description from you uh +about about the problem and your thought + + align:start position:0% +about about the problem and your thought + + + align:start position:0% +about about the problem and your thought +processes on + + align:start position:0% +processes on + + + align:start position:0% +processes on +those okay good so let's uh start with + + align:start position:0% +those okay good so let's uh start with + + + align:start position:0% +those okay good so let's uh start with +today if you recall yes uh Tuesday was + + align:start position:0% +today if you recall yes uh Tuesday was + + + align:start position:0% +today if you recall yes uh Tuesday was +kind of the broad overview a little bit + + align:start position:0% +kind of the broad overview a little bit + + + align:start position:0% +kind of the broad overview a little bit +of the outline of what we're going to be + + align:start position:0% +of the outline of what we're going to be + + + align:start position:0% +of the outline of what we're going to be +seeing uh throughout the course of the + + align:start position:0% +seeing uh throughout the course of the + + + align:start position:0% +seeing uh throughout the course of the +semester today I'm going to focus in a + + align:start position:0% +semester today I'm going to focus in a + + + align:start position:0% +semester today I'm going to focus in a +little bit ON Semiconductor uh process + + align:start position:0% +little bit ON Semiconductor uh process + + + align:start position:0% +little bit ON Semiconductor uh process +technology but with a real emphasis on + + align:start position:0% +technology but with a real emphasis on + + + align:start position:0% +technology but with a real emphasis on +variation in semiconductor processes and + + align:start position:0% +variation in semiconductor processes and + + + align:start position:0% +variation in semiconductor processes and +the basic agenda here is give you a very + + align:start position:0% +the basic agenda here is give you a very + + + align:start position:0% +the basic agenda here is give you a very +quick I think it's a four slide process + + align:start position:0% +quick I think it's a four slide process + + + align:start position:0% +quick I think it's a four slide process +uh summary of a typical process sequence + + align:start position:0% +uh summary of a typical process sequence + + + align:start position:0% +uh summary of a typical process sequence +it's going to be a bit + + align:start position:0% +it's going to be a bit + + + align:start position:0% +it's going to be a bit +stylized + + align:start position:0% +stylized + + + align:start position:0% +stylized +um another reading assignment that is + + align:start position:0% +um another reading assignment that is + + + align:start position:0% +um another reading assignment that is +coming but I have not quite issued yet + + align:start position:0% +coming but I have not quite issued yet + + + align:start position:0% +coming but I have not quite issued yet +uh in order to give you some room to + + align:start position:0% +uh in order to give you some room to + + + align:start position:0% +uh in order to give you some room to +work on problem set one will be chapter + + align:start position:0% +work on problem set one will be chapter + + + align:start position:0% +work on problem set one will be chapter +two of uh May and Spanos which is a + + align:start position:0% +two of uh May and Spanos which is a + + + align:start position:0% +two of uh May and Spanos which is a +fairly nice condensed but good enough + + align:start position:0% +fairly nice condensed but good enough + + + align:start position:0% +fairly nice condensed but good enough +depth and detail uh description of + + align:start position:0% +depth and detail uh description of + + + align:start position:0% +depth and detail uh description of +semiconductor process technology so it + + align:start position:0% +semiconductor process technology so it + + + align:start position:0% +semiconductor process technology so it +is an + + align:start position:0% +is an + + + align:start position:0% +is an +excellent uh sort of 50 page 30 to well + + align:start position:0% +excellent uh sort of 50 page 30 to well + + + align:start position:0% +excellent uh sort of 50 page 30 to well +I guess chapter 2 is about uh something + + align:start position:0% +I guess chapter 2 is about uh something + + + align:start position:0% +I guess chapter 2 is about uh something +like 50 pages + + align:start position:0% +like 50 pages + + + align:start position:0% +like 50 pages +uh a nice introduction to uh in and some + + align:start position:0% +uh a nice introduction to uh in and some + + + align:start position:0% +uh a nice introduction to uh in and some +details on semic conductor processing + + align:start position:0% +details on semic conductor processing + + + align:start position:0% +details on semic conductor processing +but what I want to do is set a little + + align:start position:0% +but what I want to do is set a little + + + align:start position:0% +but what I want to do is set a little +bit of a baseline to make sure everybody + + align:start position:0% +bit of a baseline to make sure everybody + + + align:start position:0% +bit of a baseline to make sure everybody +has a a course picture of what is + + align:start position:0% +has a a course picture of what is + + + align:start position:0% +has a a course picture of what is +involved in making integrated circuits + + align:start position:0% +involved in making integrated circuits + + + align:start position:0% +involved in making integrated circuits +since that is going to be one of the + + align:start position:0% +since that is going to be one of the + + + align:start position:0% +since that is going to be one of the +processes that we use to illustrate lots + + align:start position:0% +processes that we use to illustrate lots + + + align:start position:0% +processes that we use to illustrate lots +of things and so what I'm going to talk + + align:start position:0% +of things and so what I'm going to talk + + + align:start position:0% +of things and so what I'm going to talk +a little bit about after going flying + + align:start position:0% +a little bit about after going flying + + + align:start position:0% +a little bit about after going flying +through the whole process sequence is + + align:start position:0% +through the whole process sequence is + + + align:start position:0% +through the whole process sequence is +some of the types of variation that + + align:start position:0% +some of the types of variation that + + + align:start position:0% +some of the types of variation that +arise in microfabrication and it with + + align:start position:0% +arise in microfabrication and it with + + + align:start position:0% +arise in microfabrication and it with +emphasis on parametric variation and + + align:start position:0% +emphasis on parametric variation and + + + align:start position:0% +emphasis on parametric variation and +then we'll talk a little bit about + + align:start position:0% +then we'll talk a little bit about + + + align:start position:0% +then we'll talk a little bit about +temporal variation sort of run to- run + + align:start position:0% +temporal variation sort of run to- run + + + align:start position:0% +temporal variation sort of run to- run +uh uh wafer to wafer if you will and + + align:start position:0% +uh uh wafer to wafer if you will and + + + align:start position:0% +uh uh wafer to wafer if you will and +then spatial variations and + + align:start position:0% +then spatial variations and + + + align:start position:0% +then spatial variations and +semiconductor processing is an + + align:start position:0% +semiconductor processing is an + + + align:start position:0% +semiconductor processing is an +interesting one because there are + + align:start position:0% +interesting one because there are + + + align:start position:0% +interesting one because there are +nesting of replication of the products + + align:start position:0% +nesting of replication of the products + + + align:start position:0% +nesting of replication of the products +uh within additional geometric + + align:start position:0% +uh within additional geometric + + + align:start position:0% +uh within additional geometric +structures so we'll talk about that a + + align:start position:0% +structures so we'll talk about that a + + + align:start position:0% +structures so we'll talk about that a +little bit and then what we'll be doing + + align:start position:0% +little bit and then what we'll be doing + + + align:start position:0% +little bit and then what we'll be doing +sort of mixed in with the discussion uh + + align:start position:0% +sort of mixed in with the discussion uh + + + align:start position:0% +sort of mixed in with the discussion uh +of these types of variation is trying to + + align:start position:0% +of these types of variation is trying to + + + align:start position:0% +of these types of variation is trying to +give you a little bit of a preview some + + align:start position:0% +give you a little bit of a preview some + + + align:start position:0% +give you a little bit of a preview some +examples drawn from uh uh both the + + align:start position:0% +examples drawn from uh uh both the + + + align:start position:0% +examples drawn from uh uh both the +literature and and some of the research + + align:start position:0% +literature and and some of the research + + + align:start position:0% +literature and and some of the research +that my group has been doing over the + + align:start position:0% +that my group has been doing over the + + + align:start position:0% +that my group has been doing over the +last 10 years or so we'll try to give + + align:start position:0% +last 10 years or so we'll try to give + + + align:start position:0% +last 10 years or so we'll try to give +you a preview of some of the kinds of + + align:start position:0% +you a preview of some of the kinds of + + + align:start position:0% +you a preview of some of the kinds of +manufacturing control techniques that + + align:start position:0% +manufacturing control techniques that + + + align:start position:0% +manufacturing control techniques that +we'll be diving in much more detail + + align:start position:0% +we'll be diving in much more detail + + + align:start position:0% +we'll be diving in much more detail +throughout the term so we'll see a + + align:start position:0% +throughout the term so we'll see a + + + align:start position:0% +throughout the term so we'll see a +little bit uh early on about basic + + align:start position:0% +little bit uh early on about basic + + + align:start position:0% +little bit uh early on about basic +statistical analysis trying to decide is + + align:start position:0% +statistical analysis trying to decide is + + + align:start position:0% +statistical analysis trying to decide is +there something varying here or not uh + + align:start position:0% +there something varying here or not uh + + + align:start position:0% +there something varying here or not uh +basic detection and Analysis of that and + + align:start position:0% +basic detection and Analysis of that and + + + align:start position:0% +basic detection and Analysis of that and +we'll talk a little bit about process + + align:start position:0% +we'll talk a little bit about process + + + align:start position:0% +we'll talk a little bit about process +modeling especially from an empirical + + align:start position:0% +modeling especially from an empirical + + + align:start position:0% +modeling especially from an empirical +point of view and sort of a little bit + + align:start position:0% +point of view and sort of a little bit + + + align:start position:0% +point of view and sort of a little bit +of the boundary between physical + + align:start position:0% +of the boundary between physical + + + align:start position:0% +of the boundary between physical +modeling and and empirical modeling I'll + + align:start position:0% +modeling and and empirical modeling I'll + + + align:start position:0% +modeling and and empirical modeling I'll +give you a little example of that then + + align:start position:0% +give you a little example of that then + + + align:start position:0% +give you a little example of that then +we'll talk about using those kinds of + + align:start position:0% +we'll talk about using those kinds of + + + align:start position:0% +we'll talk about using those kinds of +models for uh process optimization and + + align:start position:0% +models for uh process optimization and + + + align:start position:0% +models for uh process optimization and +some of the kinds of strategies that + + align:start position:0% +some of the kinds of strategies that + + + align:start position:0% +some of the kinds of strategies that +arise to have robust designs and then + + align:start position:0% +arise to have robust designs and then + + + align:start position:0% +arise to have robust designs and then +lastly a very simple example of feedback + + align:start position:0% +lastly a very simple example of feedback + + + align:start position:0% +lastly a very simple example of feedback +control in a unit process in + + align:start position:0% +control in a unit process in + + + align:start position:0% +control in a unit process in +semiconductor + + align:start position:0% + + + + align:start position:0% + +fabrication + + align:start position:0% +fabrication + + + align:start position:0% +fabrication +so the following is from a a book it's a + + align:start position:0% +so the following is from a a book it's a + + + align:start position:0% +so the following is from a a book it's a +little bit dated it's about 10 years old + + align:start position:0% +little bit dated it's about 10 years old + + + align:start position:0% +little bit dated it's about 10 years old +uh it's actually an interesting book + + align:start position:0% +uh it's actually an interesting book + + + align:start position:0% +uh it's actually an interesting book +because it's about statistical case + + align:start position:0% +because it's about statistical case + + + align:start position:0% +because it's about statistical case +studies in industrial process + + align:start position:0% +studies in industrial process + + + align:start position:0% +studies in industrial process +Improvement where almost all of the all + + align:start position:0% +Improvement where almost all of the all + + + align:start position:0% +Improvement where almost all of the all +of the cases are really drawn from the + + align:start position:0% +of the cases are really drawn from the + + + align:start position:0% +of the cases are really drawn from the +semiconductor industry um so before they + + align:start position:0% +semiconductor industry um so before they + + + align:start position:0% +semiconductor industry um so before they +dive into those statistical methods they + + align:start position:0% +dive into those statistical methods they + + + align:start position:0% +dive into those statistical methods they +themselves give a very quick uh overview + + align:start position:0% +themselves give a very quick uh overview + + + align:start position:0% +themselves give a very quick uh overview +of the semiconductor fabrication process + + align:start position:0% +of the semiconductor fabrication process + + + align:start position:0% +of the semiconductor fabrication process +so I like this example or this I think + + align:start position:0% +so I like this example or this I think + + + align:start position:0% +so I like this example or this I think +there's three or four uh slides that are + + align:start position:0% +there's three or four uh slides that are + + + align:start position:0% +there's three or four uh slides that are +uh have have a sequence a little bit + + align:start position:0% +uh have have a sequence a little bit + + + align:start position:0% +uh have have a sequence a little bit +because it's uh uh fairly simplified and + + align:start position:0% +because it's uh uh fairly simplified and + + + align:start position:0% +because it's uh uh fairly simplified and +abstracted so we can go through it + + align:start position:0% +abstracted so we can go through it + + + align:start position:0% +abstracted so we can go through it +quickly but the real reason I love this + + align:start position:0% +quickly but the real reason I love this + + + align:start position:0% +quickly but the real reason I love this +is there are mistakes in it there are + + align:start position:0% +is there are mistakes in it there are + + + align:start position:0% +is there are mistakes in it there are +errors things that don't necessarily + + align:start position:0% +errors things that don't necessarily + + + align:start position:0% +errors things that don't necessarily +make physical sense or uh don't quite + + align:start position:0% +make physical sense or uh don't quite + + + align:start position:0% +make physical sense or uh don't quite +well a lot of this is of course simplif + + align:start position:0% +well a lot of this is of course simplif + + + align:start position:0% +well a lot of this is of course simplif +simplification of the process to get it + + align:start position:0% +simplification of the process to get it + + + align:start position:0% +simplification of the process to get it +down to something easy but even in that + + align:start position:0% +down to something easy but even in that + + + align:start position:0% +down to something easy but even in that +with that caveat there's things that are + + align:start position:0% +with that caveat there's things that are + + + align:start position:0% +with that caveat there's things that are +just don't quite line up so your + + align:start position:0% +just don't quite line up so your + + + align:start position:0% +just don't quite line up so your +challenge is to try to point out to + + align:start position:0% +challenge is to try to point out to + + + align:start position:0% +challenge is to try to point out to +me uh as we go through it what can't be + + align:start position:0% +me uh as we go through it what can't be + + + align:start position:0% +me uh as we go through it what can't be +right okay now even if you don't have a + + align:start position:0% +right okay now even if you don't have a + + + align:start position:0% +right okay now even if you don't have a +lot of semiconductor background so see + + align:start position:0% +lot of semiconductor background so see + + + align:start position:0% +lot of semiconductor background so see +if you can catch + + align:start position:0% +if you can catch + + + align:start position:0% +if you can catch +these so + + align:start position:0% +these so + + + align:start position:0% +these so +actually let's see if I can skip ahead + + align:start position:0% + + + + align:start position:0% + +briefly what we're I I'm skipping to the + + align:start position:0% +briefly what we're I I'm skipping to the + + + align:start position:0% +briefly what we're I I'm skipping to the +end of the sequence this is Step 25 what + + align:start position:0% +end of the sequence this is Step 25 what + + + align:start position:0% +end of the sequence this is Step 25 what +we're showing here is the fabrication + + align:start position:0% +we're showing here is the fabrication + + + align:start position:0% +we're showing here is the fabrication +sequence of building up thin films on + + align:start position:0% +sequence of building up thin films on + + + align:start position:0% +sequence of building up thin films on +the surface of the wafer as well as + + align:start position:0% +the surface of the wafer as well as + + + align:start position:0% +the surface of the wafer as well as +changing the material properties of + + align:start position:0% +changing the material properties of + + + align:start position:0% +changing the material properties of +parts of the surface of the wafer scoped + + align:start position:0% +parts of the surface of the wafer scoped + + + align:start position:0% +parts of the surface of the wafer scoped +in or zoomed in to trying to build a + + align:start position:0% +in or zoomed in to trying to build a + + + align:start position:0% +in or zoomed in to trying to build a +single + + align:start position:0% +single + + + align:start position:0% +single +transistor now there are people that + + align:start position:0% +transistor now there are people that + + + align:start position:0% +transistor now there are people that +build and sell single transistors but + + align:start position:0% +build and sell single transistors but + + + align:start position:0% +build and sell single transistors but +really we're talking integrated circuits + + align:start position:0% +really we're talking integrated circuits + + + align:start position:0% +really we're talking integrated circuits +at the isscc conference earlier this + + align:start position:0% +at the isscc conference earlier this + + + align:start position:0% +at the isscc conference earlier this +week uh Intel announced their two + + align:start position:0% +week uh Intel announced their two + + + align:start position:0% +week uh Intel announced their two +billion + + align:start position:0% +billion + + + align:start position:0% +billion +transistor + + align:start position:0% +transistor + + + align:start position:0% +transistor +microprocessor so that's the level of + + align:start position:0% +microprocessor so that's the level of + + + align:start position:0% +microprocessor so that's the level of +integration that's out there now we're + + align:start position:0% +integration that's out there now we're + + + align:start position:0% +integration that's out there now we're +going to focus on one clearly and we + + align:start position:0% +going to focus on one clearly and we + + + align:start position:0% +going to focus on one clearly and we +talk a little bit later part of the + + align:start position:0% +talk a little bit later part of the + + + align:start position:0% +talk a little bit later part of the +challenge is to build a product with two + + align:start position:0% +challenge is to build a product with two + + + align:start position:0% +challenge is to build a product with two +billion of these things and have them + + align:start position:0% +billion of these things and have them + + + align:start position:0% +billion of these things and have them +all work okay so this is a + + align:start position:0% +all work okay so this is a + + + align:start position:0% +all work okay so this is a +wonderful industry in terms of Exquisite + + align:start position:0% +wonderful industry in terms of Exquisite + + + align:start position:0% +wonderful industry in terms of Exquisite +manufacturing control required to have + + align:start position:0% +manufacturing control required to have + + + align:start position:0% +manufacturing control required to have +all two billion things work uh on on + + align:start position:0% +all two billion things work uh on on + + + align:start position:0% +all two billion things work uh on on +your circuit but to get a picture of + + align:start position:0% +your circuit but to get a picture of + + + align:start position:0% +your circuit but to get a picture of +what's really going on we're going to + + align:start position:0% +what's really going on we're going to + + + align:start position:0% +what's really going on we're going to +focus in on a single transistor and + + align:start position:0% +focus in on a single transistor and + + + align:start position:0% +focus in on a single transistor and +there there's a picture of it uh uh + + align:start position:0% +there there's a picture of it uh uh + + + align:start position:0% +there there's a picture of it uh uh +geometrically and over on the right here + + align:start position:0% +geometrically and over on the right here + + + align:start position:0% +geometrically and over on the right here +is a a very abstracted picture of the + + align:start position:0% +is a a very abstracted picture of the + + + align:start position:0% +is a a very abstracted picture of the +function of of a single mosfet + + align:start position:0% +function of of a single mosfet + + + align:start position:0% +function of of a single mosfet +transistor and the basic idea is that + + align:start position:0% +transistor and the basic idea is that + + + align:start position:0% +transistor and the basic idea is that +this can act as a an electronic switch + + align:start position:0% +this can act as a an electronic switch + + + align:start position:0% +this can act as a an electronic switch +under uh the application of different + + align:start position:0% +under uh the application of different + + + align:start position:0% +under uh the application of different +voltage uh conditions so that one can + + align:start position:0% +voltage uh conditions so that one can + + + align:start position:0% +voltage uh conditions so that one can +control the flow of + + align:start position:0% +control the flow of + + + align:start position:0% +control the flow of +current uh in an onoff kind of kind of + + align:start position:0% +current uh in an onoff kind of kind of + + + align:start position:0% +current uh in an onoff kind of kind of +fashion and therefore perform uh certain + + align:start position:0% +fashion and therefore perform uh certain + + + align:start position:0% +fashion and therefore perform uh certain +logic functions depending on the + + align:start position:0% +logic functions depending on the + + + align:start position:0% +logic functions depending on the +presence or absence of voltage on + + align:start position:0% +presence or absence of voltage on + + + align:start position:0% +presence or absence of voltage on +components of the structure the basic + + align:start position:0% +components of the structure the basic + + + align:start position:0% +components of the structure the basic +elements here + + align:start position:0% +elements here + + + align:start position:0% +elements here +are well the real action is right down + + align:start position:0% +are well the real action is right down + + + align:start position:0% +are well the real action is right down +here in the in the center of the the + + align:start position:0% +here in the in the center of the the + + + align:start position:0% +here in the in the center of the the +device in the center of the transistor + + align:start position:0% +device in the center of the transistor + + + align:start position:0% +device in the center of the transistor +you essentially have a a source in a + + align:start position:0% +you essentially have a a source in a + + + align:start position:0% +you essentially have a a source in a +drain these are electrically conductive + + align:start position:0% +drain these are electrically conductive + + + align:start position:0% +drain these are electrically conductive +and these little blue things are in this + + align:start position:0% +and these little blue things are in this + + + align:start position:0% +and these little blue things are in this +picture aluminum pads or metal pads + + align:start position:0% +picture aluminum pads or metal pads + + + align:start position:0% +picture aluminum pads or metal pads +metal connections uh if you will that + + align:start position:0% +metal connections uh if you will that + + + align:start position:0% +metal connections uh if you will that +make uh contact to the semiconductor the + + align:start position:0% +make uh contact to the semiconductor the + + + align:start position:0% +make uh contact to the semiconductor the +Silicon uh semiconductor layer uh + + align:start position:0% +Silicon uh semiconductor layer uh + + + align:start position:0% +Silicon uh semiconductor layer uh +underneath these red regions have been + + align:start position:0% +underneath these red regions have been + + + align:start position:0% +underneath these red regions have been +very highly doped and we'll see the + + align:start position:0% +very highly doped and we'll see the + + + align:start position:0% +very highly doped and we'll see the +process for for doing that that make + + align:start position:0% +process for for doing that that make + + + align:start position:0% +process for for doing that that make +them also uh much more metallic in + + align:start position:0% +them also uh much more metallic in + + + align:start position:0% +them also uh much more metallic in +nature they are highly conductive so + + align:start position:0% +nature they are highly conductive so + + + align:start position:0% +nature they are highly conductive so +this is how we get uh electrical access + + align:start position:0% +this is how we get uh electrical access + + + align:start position:0% +this is how we get uh electrical access +down to the semiconductor the + + align:start position:0% +down to the semiconductor the + + + align:start position:0% +down to the semiconductor the +interesting part is is the silicon that + + align:start position:0% +interesting part is is the silicon that + + + align:start position:0% +interesting part is is the silicon that +has been only lightly doped and that's + + align:start position:0% +has been only lightly doped and that's + + + align:start position:0% +has been only lightly doped and that's +what I think these little dots are meant + + align:start position:0% +what I think these little dots are meant + + + align:start position:0% +what I think these little dots are meant +to indicate to + + align:start position:0% +to indicate to + + + align:start position:0% +to indicate to +control uh the degree at which it will + + align:start position:0% +control uh the degree at which it will + + + align:start position:0% +control uh the degree at which it will +conduct under different amounts of uh + + align:start position:0% +conduct under different amounts of uh + + + align:start position:0% +conduct under different amounts of uh +potential applied to it from the control + + align:start position:0% +potential applied to it from the control + + + align:start position:0% +potential applied to it from the control +of a gate this blue I guess it's green + + align:start position:0% +of a gate this blue I guess it's green + + + align:start position:0% +of a gate this blue I guess it's green +on this picture uh this is the the gate + + align:start position:0% +on this picture uh this is the the gate + + + align:start position:0% +on this picture uh this is the the gate +electrode and eventually it it's + + align:start position:0% +electrode and eventually it it's + + + align:start position:0% +electrode and eventually it it's +typically made out of polysilicon and + + align:start position:0% +typically made out of polysilicon and + + + align:start position:0% +typically made out of polysilicon and +eventually contacted also by by metal so + + align:start position:0% +eventually contacted also by by metal so + + + align:start position:0% +eventually contacted also by by metal so +that we can uh + + align:start position:0% +that we can uh + + + align:start position:0% +that we can uh +apply positive or negative voltage to + + align:start position:0% +apply positive or negative voltage to + + + align:start position:0% +apply positive or negative voltage to +the gate and if we apply in a typical + + align:start position:0% +the gate and if we apply in a typical + + + align:start position:0% +the gate and if we apply in a typical +nmos transistor enough of a positive + + align:start position:0% +nmos transistor enough of a positive + + + align:start position:0% +nmos transistor enough of a positive +voltage what we do is we attract lots + + align:start position:0% +voltage what we do is we attract lots + + + align:start position:0% +voltage what we do is we attract lots +and lots of negative charges to uh uh + + align:start position:0% +and lots of negative charges to uh uh + + + align:start position:0% +and lots of negative charges to uh uh +sort of counteract the positive charges + + align:start position:0% +sort of counteract the positive charges + + + align:start position:0% +sort of counteract the positive charges +were're we're creating on the surface of + + align:start position:0% +were're we're creating on the surface of + + + align:start position:0% +were're we're creating on the surface of +the gate we we create lots of uh or or + + align:start position:0% +the gate we we create lots of uh or or + + + align:start position:0% +the gate we we create lots of uh or or +attract or uh uh generate an inversion + + align:start position:0% +attract or uh uh generate an inversion + + + align:start position:0% +attract or uh uh generate an inversion +uh with lots and lots of electrons + + align:start position:0% +uh with lots and lots of electrons + + + align:start position:0% +uh with lots and lots of electrons +negative charge down here in this very + + align:start position:0% +negative charge down here in this very + + + align:start position:0% +negative charge down here in this very +very thin surface layer of the Silicon + + align:start position:0% +very thin surface layer of the Silicon + + + align:start position:0% +very thin surface layer of the Silicon +so the semiconducting Silicon can be + + align:start position:0% +so the semiconducting Silicon can be + + + align:start position:0% +so the semiconducting Silicon can be +made to conduct under certain voltage or + + align:start position:0% +made to conduct under certain voltage or + + + align:start position:0% +made to conduct under certain voltage or +bias conditions and now current can flow + + align:start position:0% +bias conditions and now current can flow + + + align:start position:0% +bias conditions and now current can flow +from the d uh from the gate or + + align:start position:0% +from the d uh from the gate or + + + align:start position:0% +from the d uh from the gate or +underneath the gate from the source to + + align:start position:0% +underneath the gate from the source to + + + align:start position:0% +underneath the gate from the source to +the drain so if we apply a positive + + align:start position:0% +the drain so if we apply a positive + + + align:start position:0% +the drain so if we apply a positive +voltage we turn the thing on and um uh + + align:start position:0% +voltage we turn the thing on and um uh + + + align:start position:0% +voltage we turn the thing on and um uh +current can flow alternatively if we uh + + align:start position:0% +current can flow alternatively if we uh + + + align:start position:0% +current can flow alternatively if we uh +apply either an opposite voltage or no + + align:start position:0% +apply either an opposite voltage or no + + + align:start position:0% +apply either an opposite voltage or no +voltage in a typical uh uh mosfet for + + align:start position:0% +voltage in a typical uh uh mosfet for + + + align:start position:0% +voltage in a typical uh uh mosfet for +logic + + align:start position:0% +logic + + + align:start position:0% +logic +operations uh the conductivity of the + + align:start position:0% +operations uh the conductivity of the + + + align:start position:0% +operations uh the conductivity of the +Silicon layer will be so low that uh + + align:start position:0% +Silicon layer will be so low that uh + + + align:start position:0% +Silicon layer will be so low that uh +current is blocked and the thing is off + + align:start position:0% +current is blocked and the thing is off + + + align:start position:0% +current is blocked and the thing is off +so the basic idea here is we need to + + align:start position:0% +so the basic idea here is we need to + + + align:start position:0% +so the basic idea here is we need to +control carefully the conditions + + align:start position:0% +control carefully the conditions + + + align:start position:0% +control carefully the conditions +uh and properties of the Silicon layer + + align:start position:0% +uh and properties of the Silicon layer + + + align:start position:0% +uh and properties of the Silicon layer +and then we need to set up the rest of + + align:start position:0% +and then we need to set up the rest of + + + align:start position:0% +and then we need to set up the rest of +the geometry to be able to have access + + align:start position:0% +the geometry to be able to have access + + + align:start position:0% +the geometry to be able to have access +to the and and form the structures for + + align:start position:0% +to the and and form the structures for + + + align:start position:0% +to the and and form the structures for +the source drain and and the + + align:start position:0% +the source drain and and the + + + align:start position:0% +the source drain and and the +gate so what we're going to see in this + + align:start position:0% +gate so what we're going to see in this + + + align:start position:0% +gate so what we're going to see in this +sequence is how we start from some raw + + align:start position:0% +sequence is how we start from some raw + + + align:start position:0% +sequence is how we start from some raw +material build up the thin film layers + + align:start position:0% +material build up the thin film layers + + + align:start position:0% +material build up the thin film layers +uh and and differentiate both the + + align:start position:0% +uh and and differentiate both the + + + align:start position:0% +uh and and differentiate both the +geometry and change those properties so + + align:start position:0% +geometry and change those properties so + + + align:start position:0% +geometry and change those properties so +in this picture we're starting out here + + align:start position:0% +in this picture we're starting out here + + + align:start position:0% +in this picture we're starting out here +with uh the + + align:start position:0% +with uh the + + + align:start position:0% +with uh the +in white + + align:start position:0% +in white + + + align:start position:0% +in white +we add or create a thin layer of silicon + + align:start position:0% +we add or create a thin layer of silicon + + + align:start position:0% +we add or create a thin layer of silicon +dioxide uh in this in this picture now + + align:start position:0% +dioxide uh in this in this picture now + + + align:start position:0% +dioxide uh in this in this picture now +there's lots of different processes and + + align:start position:0% +there's lots of different processes and + + + align:start position:0% +there's lots of different processes and +some many of these are discussed in more + + align:start position:0% +some many of these are discussed in more + + + align:start position:0% +some many of these are discussed in more +detail in May Spanos for creating um uh + + align:start position:0% +detail in May Spanos for creating um uh + + + align:start position:0% +detail in May Spanos for creating um uh +silicon dioxide one is deposit on the + + align:start position:0% +silicon dioxide one is deposit on the + + + align:start position:0% +silicon dioxide one is deposit on the +surface the other is to actually quote + + align:start position:0% +surface the other is to actually quote + + + align:start position:0% +surface the other is to actually quote +grow a silicon dioxide layer that is we + + align:start position:0% +grow a silicon dioxide layer that is we + + + align:start position:0% +grow a silicon dioxide layer that is we +essentially uh subject the wafer to an + + align:start position:0% +essentially uh subject the wafer to an + + + align:start position:0% +essentially uh subject the wafer to an +oxygen carrying ambient either O2 or or + + align:start position:0% +oxygen carrying ambient either O2 or or + + + align:start position:0% +oxygen carrying ambient either O2 or or +a an H2O uh Vapor kind of uh ambient and + + align:start position:0% +a an H2O uh Vapor kind of uh ambient and + + + align:start position:0% +a an H2O uh Vapor kind of uh ambient and +the oxygen will react with the Silicon + + align:start position:0% +the oxygen will react with the Silicon + + + align:start position:0% +the oxygen will react with the Silicon +forming + + align:start position:0% +forming + + + align:start position:0% +forming +sio2 and we have a very nice stable + + align:start position:0% +sio2 and we have a very nice stable + + + align:start position:0% +sio2 and we have a very nice stable +silicon dioxide + + align:start position:0% +silicon dioxide + + + align:start position:0% +silicon dioxide +layer it turns + + align:start position:0% +layer it turns + + + align:start position:0% +layer it turns +out that that simple process of being + + align:start position:0% +out that that simple process of being + + + align:start position:0% +out that that simple process of being +able to + + align:start position:0% +able to + + + align:start position:0% +able to +grow a very high quality silicon dioxide + + align:start position:0% +grow a very high quality silicon dioxide + + + align:start position:0% +grow a very high quality silicon dioxide +layer was kind of the Crux process that + + align:start position:0% +layer was kind of the Crux process that + + + align:start position:0% +layer was kind of the Crux process that +enabled integrated circuits in some + + align:start position:0% +enabled integrated circuits in some + + + align:start position:0% +enabled integrated circuits in some +fashion um and we we'll talk about it a + + align:start position:0% +fashion um and we we'll talk about it a + + + align:start position:0% +fashion um and we we'll talk about it a +little bit later but basically we get + + align:start position:0% +little bit later but basically we get + + + align:start position:0% +little bit later but basically we get +we're going to need insulating layers + + align:start position:0% +we're going to need insulating layers + + + align:start position:0% +we're going to need insulating layers +between conducting layers one conducting + + align:start position:0% +between conducting layers one conducting + + + align:start position:0% +between conducting layers one conducting +layer being the Silicon itself the + + align:start position:0% +layer being the Silicon itself the + + + align:start position:0% +layer being the Silicon itself the +others when we build multiple levels of + + align:start position:0% +others when we build multiple levels of + + + align:start position:0% +others when we build multiple levels of +of of wiring we need insulators between + + align:start position:0% +of of wiring we need insulators between + + + align:start position:0% +of of wiring we need insulators between +them but in particular for the formation + + align:start position:0% +them but in particular for the formation + + + align:start position:0% +them but in particular for the formation +of that transistor the creation of a + + align:start position:0% +of that transistor the creation of a + + + align:start position:0% +of that transistor the creation of a +very good highquality very stable + + align:start position:0% +very good highquality very stable + + + align:start position:0% +very good highquality very stable +well-controlled oxide insulating layer + + align:start position:0% +well-controlled oxide insulating layer + + + align:start position:0% +well-controlled oxide insulating layer +between the gate electrode and the + + align:start position:0% +between the gate electrode and the + + + align:start position:0% +between the gate electrode and the +Silicon electrode was crucial that forms + + align:start position:0% +Silicon electrode was crucial that forms + + + align:start position:0% +Silicon electrode was crucial that forms +basically a metal gate oxide + + align:start position:0% +basically a metal gate oxide + + + align:start position:0% +basically a metal gate oxide +semiconductor or MOS transistor + + align:start position:0% +semiconductor or MOS transistor + + + align:start position:0% +semiconductor or MOS transistor +structure and that the ability to uh uh + + align:start position:0% +structure and that the ability to uh uh + + + align:start position:0% +structure and that the ability to uh uh +create a mod capacitor and then contact + + align:start position:0% +create a mod capacitor and then contact + + + align:start position:0% +create a mod capacitor and then contact +it on the sides where you can invert the + + align:start position:0% +it on the sides where you can invert the + + + align:start position:0% +it on the sides where you can invert the +the the Silicon layer was a big + + align:start position:0% +the the Silicon layer was a big + + + align:start position:0% +the the Silicon layer was a big +challenge the first transistors were in + + align:start position:0% +challenge the first transistors were in + + + align:start position:0% +challenge the first transistors were in +fact bipolar + + align:start position:0% +fact bipolar + + + align:start position:0% +fact bipolar +transistors uh shortly after the + + align:start position:0% +transistors uh shortly after the + + + align:start position:0% +transistors uh shortly after the +invention of the bipolar transistor uh + + align:start position:0% +invention of the bipolar transistor uh + + + align:start position:0% +invention of the bipolar transistor uh +Shockley went off on his own and also + + align:start position:0% +Shockley went off on his own and also + + + align:start position:0% +Shockley went off on his own and also +invented the Moss + + align:start position:0% +invented the Moss + + + align:start position:0% +invented the Moss +transistor um in the very early versions + + align:start position:0% +transistor um in the very early versions + + + align:start position:0% +transistor um in the very early versions +a + + align:start position:0% +a + + + align:start position:0% +a +different uh semiconductor material was + + align:start position:0% +different uh semiconductor material was + + + align:start position:0% +different uh semiconductor material was +used different element than silicon + + align:start position:0% +used different element than silicon + + + align:start position:0% +used different element than silicon +anybody + + align:start position:0% +anybody + + + align:start position:0% +anybody +know what were the first transistors + + align:start position:0% +know what were the first transistors + + + align:start position:0% +know what were the first transistors +built out of geranium + + align:start position:0% +built out of geranium + + + align:start position:0% +built out of geranium +geranium why aren't all of our + + align:start position:0% +geranium why aren't all of our + + + align:start position:0% +geranium why aren't all of our +transistors built out of germanium now + + align:start position:0% +transistors built out of germanium now + + + align:start position:0% +transistors built out of germanium now +we'll come back to that some of them are + + align:start position:0% +we'll come back to that some of them are + + + align:start position:0% +we'll come back to that some of them are +starting to be + + align:start position:0% +starting to be + + + align:start position:0% +starting to be +again the problem is if you if you uh + + align:start position:0% +again the problem is if you if you uh + + + align:start position:0% +again the problem is if you if you uh +oxidize germanium you get an insulating + + align:start position:0% +oxidize germanium you get an insulating + + + align:start position:0% +oxidize germanium you get an insulating +layer + + align:start position:0% +layer + + + align:start position:0% +layer +the problem is it's extremely soft and + + align:start position:0% +the problem is it's extremely soft and + + + align:start position:0% +the problem is it's extremely soft and +unstable and in fact if you if you + + align:start position:0% +unstable and in fact if you if you + + + align:start position:0% +unstable and in fact if you if you +oxidize the surface of of geranium you + + align:start position:0% +oxidize the surface of of geranium you + + + align:start position:0% +oxidize the surface of of geranium you +can wipe + + align:start position:0% +can wipe + + + align:start position:0% +can wipe +away uh the oxide it is not stable and + + align:start position:0% +away uh the oxide it is not stable and + + + align:start position:0% +away uh the oxide it is not stable and +manufacturable and so it was really uh + + align:start position:0% +manufacturable and so it was really uh + + + align:start position:0% +manufacturable and so it was really uh +this ability right here to be able to + + align:start position:0% +this ability right here to be able to + + + align:start position:0% +this ability right here to be able to +grow a very hard um high quality uh + + align:start position:0% +grow a very hard um high quality uh + + + align:start position:0% +grow a very hard um high quality uh +silicon dioxide that that that was + + align:start position:0% +silicon dioxide that that that was + + + align:start position:0% +silicon dioxide that that that was +crucial for being able to build up for + + align:start position:0% +crucial for being able to build up for + + + align:start position:0% +crucial for being able to build up for +both the conversion over to to silicon + + align:start position:0% +both the conversion over to to silicon + + + align:start position:0% +both the conversion over to to silicon +and for being able to build up complex + + align:start position:0% +and for being able to build up complex + + + align:start position:0% +and for being able to build up complex +structures Okay so we've got this uh + + align:start position:0% +structures Okay so we've got this uh + + + align:start position:0% +structures Okay so we've got this uh +thin thin silicon dioxide layer here uh + + align:start position:0% +thin thin silicon dioxide layer here uh + + + align:start position:0% +thin thin silicon dioxide layer here uh +that has been grown now what we want to + + align:start position:0% +that has been grown now what we want to + + + align:start position:0% +that has been grown now what we want to +do is start building the region where + + align:start position:0% +do is start building the region where + + + align:start position:0% +do is start building the region where +we're actually going to have the active + + align:start position:0% +we're actually going to have the active + + + align:start position:0% +we're actually going to have the active +device uh so we're going to go through a + + align:start position:0% +device uh so we're going to go through a + + + align:start position:0% +device uh so we're going to go through a +sequence here uh that gets repeated + + align:start position:0% +sequence here uh that gets repeated + + + align:start position:0% +sequence here uh that gets repeated +again and again this is referred to as + + align:start position:0% +again and again this is referred to as + + + align:start position:0% +again and again this is referred to as +the photolithographic sequence and so + + align:start position:0% +the photolithographic sequence and so + + + align:start position:0% +the photolithographic sequence and so +what we start with is depositing a thin + + align:start position:0% +what we start with is depositing a thin + + + align:start position:0% +what we start with is depositing a thin +layer of photo resist shown in red here + + align:start position:0% +layer of photo resist shown in red here + + + align:start position:0% +layer of photo resist shown in red here +this is typically spun on so this is a + + align:start position:0% +this is typically spun on so this is a + + + align:start position:0% +this is typically spun on so this is a +uh a polymer type of material uh it's in + + align:start position:0% +uh a polymer type of material uh it's in + + + align:start position:0% +uh a polymer type of material uh it's in +a solvent so that one can sort of drop + + align:start position:0% +a solvent so that one can sort of drop + + + align:start position:0% +a solvent so that one can sort of drop +uh the uh material on and then spin the + + align:start position:0% +uh the uh material on and then spin the + + + align:start position:0% +uh the uh material on and then spin the +wafer very rapidly in order to get the + + align:start position:0% +wafer very rapidly in order to get the + + + align:start position:0% +wafer very rapidly in order to get the +controlled film thickness that one wants + + align:start position:0% +controlled film thickness that one wants + + + align:start position:0% +controlled film thickness that one wants +for the the photo resist and this is uh + + align:start position:0% +for the the photo resist and this is uh + + + align:start position:0% +for the the photo resist and this is uh +uh uh interacts with with uh light in + + align:start position:0% +uh uh interacts with with uh light in + + + align:start position:0% +uh uh interacts with with uh light in +one of two different ways you can have + + align:start position:0% +one of two different ways you can have + + + align:start position:0% +one of two different ways you can have +positive or negative photo resist what's + + align:start position:0% +positive or negative photo resist what's + + + align:start position:0% +positive or negative photo resist what's +shown in this in the next picture is a a + + align:start position:0% +shown in this in the next picture is a a + + + align:start position:0% +shown in this in the next picture is a a +typical uh uh let's see is this one + + align:start position:0% +typical uh uh let's see is this one + + + align:start position:0% +typical uh uh let's see is this one +positive or negative this one's a + + align:start position:0% +positive or negative this one's a + + + align:start position:0% +positive or negative this one's a +positive photo resist because we're + + align:start position:0% +positive photo resist because we're + + + align:start position:0% +positive photo resist because we're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +uh basically transform or implant or um + + align:start position:0% +uh basically transform or implant or um + + + align:start position:0% +uh basically transform or implant or um +um imprint if you will the The Mask + + align:start position:0% +um imprint if you will the The Mask + + + align:start position:0% +um imprint if you will the The Mask +layer here in the same fashion with the + + align:start position:0% +layer here in the same fashion with the + + + align:start position:0% +layer here in the same fashion with the +uh underlying photo resist the basic + + align:start position:0% +uh underlying photo resist the basic + + + align:start position:0% +uh underlying photo resist the basic +idea of the photo resist is it contains + + align:start position:0% +idea of the photo resist is it contains + + + align:start position:0% +idea of the photo resist is it contains +photoactive compounds that under + + align:start position:0% +photoactive compounds that under + + + align:start position:0% +photoactive compounds that under +exposure to light will change the + + align:start position:0% +exposure to light will change the + + + align:start position:0% +exposure to light will change the +polymer linking of of the photo resist + + align:start position:0% +polymer linking of of the photo resist + + + align:start position:0% +polymer linking of of the photo resist +Yeah + + align:start position:0% +Yeah + + + align:start position:0% +Yeah +question + + align:start position:0% +question + + + align:start position:0% +question +I yes understand the as the chromium the + + align:start position:0% +I yes understand the as the chromium the + + + align:start position:0% +I yes understand the as the chromium the +black part right light sh + + align:start position:0% + + + + align:start position:0% + +that's exactly right that's that's right + + align:start position:0% +that's exactly right that's that's right + + + align:start position:0% +that's exactly right that's that's right +so what we have is the goal is to take + + align:start position:0% +so what we have is the goal is to take + + + align:start position:0% +so what we have is the goal is to take +some + + align:start position:0% +some + + + align:start position:0% +some +design from some CAD system or whatever + + align:start position:0% +design from some CAD system or whatever + + + align:start position:0% +design from some CAD system or whatever +that enables us to differentiate the + + align:start position:0% +that enables us to differentiate the + + + align:start position:0% +that enables us to differentiate the +surface the design is used to make a + + align:start position:0% +surface the design is used to make a + + + align:start position:0% +surface the design is used to make a +physical well in most cases a physical + + align:start position:0% +physical well in most cases a physical + + + align:start position:0% +physical well in most cases a physical +glass plate if you will that has metal + + align:start position:0% +glass plate if you will that has metal + + + align:start position:0% +glass plate if you will that has metal +blocking areas the chromium that are + + align:start position:0% +blocking areas the chromium that are + + + align:start position:0% +blocking areas the chromium that are +intended to block the transmission of + + align:start position:0% +intended to block the transmission of + + + align:start position:0% +intended to block the transmission of +the light source in some regions and + + align:start position:0% +the light source in some regions and + + + align:start position:0% +the light source in some regions and +allow it in others so that's exactly + + align:start position:0% +allow it in others so that's exactly + + + align:start position:0% +allow it in others so that's exactly +right the side are not + + align:start position:0% +right the side are not + + + align:start position:0% +right the side are not +exposed yeah so so this is actually a + + align:start position:0% +exposed yeah so so this is actually a + + + align:start position:0% +exposed yeah so so this is actually a +cutaway I mean this this is going on for + + align:start position:0% +cutaway I mean this this is going on for + + + align:start position:0% +cutaway I mean this this is going on for +if this is only a couple of + + align:start position:0% +if this is only a couple of + + + align:start position:0% +if this is only a couple of +microns wide the entire wafer or the + + align:start position:0% +microns wide the entire wafer or the + + + align:start position:0% +microns wide the entire wafer or the +entire chip depending on on how the + + align:start position:0% +entire chip depending on on how the + + + align:start position:0% +entire chip depending on on how the +photolithography it goes on forever so + + align:start position:0% +photolithography it goes on forever so + + + align:start position:0% +photolithography it goes on forever so +so this is just a cutaway no but I mean + + align:start position:0% +so this is just a cutaway no but I mean + + + align:start position:0% +so this is just a cutaway no but I mean +like the middle is exposed yes yes okay + + align:start position:0% +like the middle is exposed yes yes okay + + + align:start position:0% +like the middle is exposed yes yes okay +so we can wash away the exposed part + + align:start position:0% +so we can wash away the exposed part + + + align:start position:0% +so we can wash away the exposed part +right it's not like + + align:start position:0% +right it's not like + + + align:start position:0% +right it's not like +solidifying the no so in this case Okay + + align:start position:0% +solidifying the no so in this case Okay + + + align:start position:0% +solidifying the no so in this case Okay +so so so that's the the the two types of + + align:start position:0% +so so so that's the the the two types of + + + align:start position:0% +so so so that's the the the two types of +photo resist U uh activity so in this + + align:start position:0% +photo resist U uh activity so in this + + + align:start position:0% +photo resist U uh activity so in this +case with a positive photo resist what + + align:start position:0% +case with a positive photo resist what + + + align:start position:0% +case with a positive photo resist what +happens is the the uh light energy from + + align:start position:0% +happens is the the uh light energy from + + + align:start position:0% +happens is the the uh light energy from +the uh the exposure system will break + + align:start position:0% +the uh the exposure system will break + + + align:start position:0% +the uh the exposure system will break +down some of the polymer chains uh in + + align:start position:0% +down some of the polymer chains uh in + + + align:start position:0% +down some of the polymer chains uh in +the in these photoactive polymer chains + + align:start position:0% +the in these photoactive polymer chains + + + align:start position:0% +the in these photoactive polymer chains +in the photo resist weakening them we + + align:start position:0% +in the photo resist weakening them we + + + align:start position:0% +in the photo resist weakening them we +then go in and do a u develop + + align:start position:0% +then go in and do a u develop + + + align:start position:0% +then go in and do a u develop +process uh where a chemical solvent is + + align:start position:0% +process uh where a chemical solvent is + + + align:start position:0% +process uh where a chemical solvent is +used that attacks the weakened polymer + + align:start position:0% +used that attacks the weakened polymer + + + align:start position:0% +used that attacks the weakened polymer +chains and rinses it away so we have the + + align:start position:0% +chains and rinses it away so we have the + + + align:start position:0% +chains and rinses it away so we have the +spin-on resist we do the exposure to + + align:start position:0% +spin-on resist we do the exposure to + + + align:start position:0% +spin-on resist we do the exposure to +light through the mask then we do a + + align:start position:0% +light through the mask then we do a + + + align:start position:0% +light through the mask then we do a +develop rinsing away the resist and and + + align:start position:0% +develop rinsing away the resist and and + + + align:start position:0% +develop rinsing away the resist and and +in the positive case the the pattern on + + align:start position:0% +in the positive case the the pattern on + + + align:start position:0% +in the positive case the the pattern on +the mask is + + align:start position:0% +the mask is + + + align:start position:0% +the mask is +transferred directly if you if you will + + align:start position:0% +transferred directly if you if you will + + + align:start position:0% +transferred directly if you if you will +into the pattern of the photo resist + + align:start position:0% +into the pattern of the photo resist + + + align:start position:0% +into the pattern of the photo resist +there is also in fact more commonly used + + align:start position:0% +there is also in fact more commonly used + + + align:start position:0% +there is also in fact more commonly used +a negative photor resist that actually + + align:start position:0% +a negative photor resist that actually + + + align:start position:0% +a negative photor resist that actually +works in the opposite way which is + + align:start position:0% +works in the opposite way which is + + + align:start position:0% +works in the opposite way which is +anywhere where the light exposes it + + align:start position:0% +anywhere where the light exposes it + + + align:start position:0% +anywhere where the light exposes it +actually strengthens the the chemical + + align:start position:0% +actually strengthens the the chemical + + + align:start position:0% +actually strengthens the the chemical +bonding of the photoactive compound in + + align:start position:0% +bonding of the photoactive compound in + + + align:start position:0% +bonding of the photoactive compound in +the polymer + + align:start position:0% +the polymer + + + align:start position:0% +the polymer +and makes it more resistant to + + align:start position:0% +and makes it more resistant to + + + align:start position:0% +and makes it more resistant to +dissolution in the developer in which + + align:start position:0% +dissolution in the developer in which + + + align:start position:0% +dissolution in the developer in which +case I would rinse away everything that + + align:start position:0% +case I would rinse away everything that + + + align:start position:0% +case I would rinse away everything that +did not get exposed and leave the + + align:start position:0% +did not get exposed and leave the + + + align:start position:0% +did not get exposed and leave the +pattern which did get + + align:start position:0% +pattern which did get + + + align:start position:0% +pattern which did get +exposed okay so actually there's some + + align:start position:0% +exposed okay so actually there's some + + + align:start position:0% +exposed okay so actually there's some +degree + + align:start position:0% +degree + + + align:start position:0% +degree +of design choice and picking positive + + align:start position:0% +of design choice and picking positive + + + align:start position:0% +of design choice and picking positive +and negative uh photo resist depending + + align:start position:0% +and negative uh photo resist depending + + + align:start position:0% +and negative uh photo resist depending +on uh some manufacturing control issues + + align:start position:0% +on uh some manufacturing control issues + + + align:start position:0% +on uh some manufacturing control issues +it turns out uh uh + + align:start position:0% +it turns out uh uh + + + align:start position:0% +it turns out uh uh +if you're if you're developing away + + align:start position:0% +if you're if you're developing away + + + align:start position:0% +if you're if you're developing away +material you might in one case or the + + align:start position:0% +material you might in one case or the + + + align:start position:0% +material you might in one case or the +other be able to actually over develop + + align:start position:0% +other be able to actually over develop + + + align:start position:0% +other be able to actually over develop +or overexpose slightly and control + + align:start position:0% +or overexpose slightly and control + + + align:start position:0% +or overexpose slightly and control +slightly the the line widths of these + + align:start position:0% +slightly the the line widths of these + + + align:start position:0% +slightly the the line widths of these +features a little bit better in one + + align:start position:0% +features a little bit better in one + + + align:start position:0% +features a little bit better in one +photo resist case than the other + + align:start position:0% +photo resist case than the other + + + align:start position:0% +photo resist case than the other +depending on what you want to do + + align:start position:0% +depending on what you want to do + + + align:start position:0% +depending on what you want to do +okay okay so so far this sequence of + + align:start position:0% +okay okay so so far this sequence of + + + align:start position:0% +okay okay so so far this sequence of +three steps has simply transferred the + + align:start position:0% +three steps has simply transferred the + + + align:start position:0% +three steps has simply transferred the +mask p pattern into a photo resist + + align:start position:0% +mask p pattern into a photo resist + + + align:start position:0% +mask p pattern into a photo resist +pattern but the photo resist is itself + + align:start position:0% +pattern but the photo resist is itself + + + align:start position:0% +pattern but the photo resist is itself +only temporary its purpose is to act as + + align:start position:0% +only temporary its purpose is to act as + + + align:start position:0% +only temporary its purpose is to act as +a mask to allow us to differentiate more + + align:start position:0% +a mask to allow us to differentiate more + + + align:start position:0% +a mask to allow us to differentiate more +aggressive physical uh transformations + + align:start position:0% +aggressive physical uh transformations + + + align:start position:0% +aggressive physical uh transformations +of the remaining wafer and in particular + + align:start position:0% +of the remaining wafer and in particular + + + align:start position:0% +of the remaining wafer and in particular +in the following case as shown here in + + align:start position:0% +in the following case as shown here in + + + align:start position:0% +in the following case as shown here in +in step five this is saying what we want + + align:start position:0% +in step five this is saying what we want + + + align:start position:0% +in step five this is saying what we want +to do now is do a another etch of the + + align:start position:0% +to do now is do a another etch of the + + + align:start position:0% +to do now is do a another etch of the +silicon dioxide + + align:start position:0% +silicon dioxide + + + align:start position:0% +silicon dioxide +layer uh in this case using a plasma a + + align:start position:0% +layer uh in this case using a plasma a + + + align:start position:0% +layer uh in this case using a plasma a +gas plasma etch I guess that's what the + + align:start position:0% +gas plasma etch I guess that's what the + + + align:start position:0% +gas plasma etch I guess that's what the +little lightning uh storm here is so + + align:start position:0% +little lightning uh storm here is so + + + align:start position:0% +little lightning uh storm here is so +um this is typically done in a in + + align:start position:0% +um this is typically done in a in + + + align:start position:0% +um this is typically done in a in +a u very low press vacuum uh equipment + + align:start position:0% +a u very low press vacuum uh equipment + + + align:start position:0% +a u very low press vacuum uh equipment +where we have some feed gas we apply uh + + align:start position:0% +where we have some feed gas we apply uh + + + align:start position:0% +where we have some feed gas we apply uh +RF energy to dissociate the the species + + align:start position:0% +RF energy to dissociate the the species + + + align:start position:0% +RF energy to dissociate the the species +in the gas many of those species then + + align:start position:0% +in the gas many of those species then + + + align:start position:0% +in the gas many of those species then +become very highly chemically reactive + + align:start position:0% +become very highly chemically reactive + + + align:start position:0% +become very highly chemically reactive +and interact with the surface of the + + align:start position:0% +and interact with the surface of the + + + align:start position:0% +and interact with the surface of the +wafer and etch away uh particular + + align:start position:0% +wafer and etch away uh particular + + + align:start position:0% +wafer and etch away uh particular +species so one would design the plasma + + align:start position:0% +species so one would design the plasma + + + align:start position:0% +species so one would design the plasma +process to + + align:start position:0% +process to + + + align:start position:0% +process to +preferentially etch away the silicon + + align:start position:0% +preferentially etch away the silicon + + + align:start position:0% +preferentially etch away the silicon +dioxide while not attacking or only very + + align:start position:0% +dioxide while not attacking or only very + + + align:start position:0% +dioxide while not attacking or only very +very slowly attacking the protective + + align:start position:0% +very slowly attacking the protective + + + align:start position:0% +very slowly attacking the protective +photo resist layer so what this is + + align:start position:0% +photo resist layer so what this is + + + align:start position:0% +photo resist layer so what this is +allowing us to do is essentially + + align:start position:0% +allowing us to do is essentially + + + align:start position:0% +allowing us to do is essentially +vertically etch down into the silicon + + align:start position:0% +vertically etch down into the silicon + + + align:start position:0% +vertically etch down into the silicon +dioxide + + align:start position:0% +dioxide + + + align:start position:0% +dioxide +layer now in this picture what they're + + align:start position:0% +layer now in this picture what they're + + + align:start position:0% +layer now in this picture what they're +trying to do here is show that we are + + align:start position:0% +trying to do here is show that we are + + + align:start position:0% +trying to do here is show that we are +partially etching some silicon dioxide + + align:start position:0% +partially etching some silicon dioxide + + + align:start position:0% +partially etching some silicon dioxide +layer + + align:start position:0% +layer + + + align:start position:0% +layer +away apparently leaving a small + + align:start position:0% +away apparently leaving a small + + + align:start position:0% +away apparently leaving a small +remaining level or layer of silicon + + align:start position:0% +remaining level or layer of silicon + + + align:start position:0% +remaining level or layer of silicon +dioxide so you can sort of see that + + align:start position:0% +dioxide so you can sort of see that + + + align:start position:0% +dioxide so you can sort of see that +shadow down in there what what they're + + align:start position:0% +shadow down in there what what they're + + + align:start position:0% +shadow down in there what what they're +trying to show in this case is they're + + align:start position:0% +trying to show in this case is they're + + + align:start position:0% +trying to show in this case is they're +leaving this thin silicon dioxide layer + + align:start position:0% +leaving this thin silicon dioxide layer + + + align:start position:0% +leaving this thin silicon dioxide layer +that is going to be that insulator + + align:start position:0% +that is going to be that insulator + + + align:start position:0% +that is going to be that insulator +between the gate electrode and the and + + align:start position:0% +between the gate electrode and the and + + + align:start position:0% +between the gate electrode and the and +the Silicon that that we talked about in + + align:start position:0% +the Silicon that that we talked about in + + + align:start position:0% +the Silicon that that we talked about in +the final + + align:start position:0% +the final + + + align:start position:0% +the final +structure so typically this might be oh + + align:start position:0% +structure so typically this might be oh + + + align:start position:0% +structure so typically this might be oh +what what you might have is close to + + align:start position:0% +what what you might have is close to + + + align:start position:0% +what what you might have is close to +modern technology you might have a half + + align:start position:0% +modern technology you might have a half + + + align:start position:0% +modern technology you might have a half +a micron in the of of silicon dioxide + + align:start position:0% +a micron in the of of silicon dioxide + + + align:start position:0% +a micron in the of of silicon dioxide +that you want fairly thick silicon + + align:start position:0% +that you want fairly thick silicon + + + align:start position:0% +that you want fairly thick silicon +dioxide out here to act as a a very very + + align:start position:0% +dioxide out here to act as a a very very + + + align:start position:0% +dioxide out here to act as a a very very +big insulating layer separ separating + + align:start position:0% +big insulating layer separ separating + + + align:start position:0% +big insulating layer separ separating +your metal electrodes from other uh + + align:start position:0% +your metal electrodes from other uh + + + align:start position:0% +your metal electrodes from other uh +other components but this silicon + + align:start position:0% +other components but this silicon + + + align:start position:0% +other components but this silicon +dioxide layer that's used uh between the + + align:start position:0% +dioxide layer that's used uh between the + + + align:start position:0% +dioxide layer that's used uh between the +gate and the semiconductor needs to be + + align:start position:0% +gate and the semiconductor needs to be + + + align:start position:0% +gate and the semiconductor needs to be +extremely + + align:start position:0% +extremely + + + align:start position:0% +extremely +thin and the reason is the closer I can + + align:start position:0% +thin and the reason is the closer I can + + + align:start position:0% +thin and the reason is the closer I can +get my two plates of that capacitor the + + align:start position:0% +get my two plates of that capacitor the + + + align:start position:0% +get my two plates of that capacitor the +more control I well the more capacitance + + align:start position:0% +more control I well the more capacitance + + + align:start position:0% +more control I well the more capacitance +I have but the more control I have of of + + align:start position:0% +I have but the more control I have of of + + + align:start position:0% +I have but the more control I have of of +the uh of the Silicon + + align:start position:0% +the uh of the Silicon + + + align:start position:0% +the uh of the Silicon +surface okay so the harder I can turn + + align:start position:0% +surface okay so the harder I can turn + + + align:start position:0% +surface okay so the harder I can turn +the device on the more more current I + + align:start position:0% +the device on the more more current I + + + align:start position:0% +the device on the more more current I +can flow per unit area and so on okay so + + align:start position:0% +can flow per unit area and so on okay so + + + align:start position:0% +can flow per unit area and so on okay so +in this process apparently we're etching + + align:start position:0% +in this process apparently we're etching + + + align:start position:0% +in this process apparently we're etching +from about uh you know a half Micron + + align:start position:0% +from about uh you know a half Micron + + + align:start position:0% +from about uh you know a half Micron +5,000 angstroms down + + align:start position:0% +5,000 angstroms down + + + align:start position:0% +5,000 angstroms down +to we might be at 100 angstrom or or + + align:start position:0% +to we might be at 100 angstrom or or + + + align:start position:0% +to we might be at 100 angstrom or or +below remaining gate oxide layer is is + + align:start position:0% +below remaining gate oxide layer is is + + + align:start position:0% +below remaining gate oxide layer is is +in in a in a modern process really what + + align:start position:0% +in in a in a modern process really what + + + align:start position:0% +in in a in a modern process really what +you + + align:start position:0% + + + + align:start position:0% + +want everybody happy with + + align:start position:0% +want everybody happy with + + + align:start position:0% +want everybody happy with +that so what is the + + align:start position:0% + + + + align:start position:0% + +tolerance + + align:start position:0% +tolerance + + + align:start position:0% +tolerance +hooray how would you do that yeah what + + align:start position:0% +hooray how would you do that yeah what + + + align:start position:0% +hooray how would you do that yeah what +is the tolerance well first off to + + align:start position:0% +is the tolerance well first off to + + + align:start position:0% +is the tolerance well first off to +answer your question you want that to be + + align:start position:0% +answer your question you want that to be + + + align:start position:0% +answer your question you want that to be +100 angstroms plus or + + align:start position:0% +100 angstroms plus or + + + align:start position:0% +100 angstroms plus or +minus well in fact some of the kinds of + + align:start position:0% +minus well in fact some of the kinds of + + + align:start position:0% +minus well in fact some of the kinds of +control that they quote are Plus or + + align:start position:0% +control that they quote are Plus or + + + align:start position:0% +control that they quote are Plus or +minus5 + + align:start position:0% +minus5 + + + align:start position:0% +minus5 +angstroms which is you know less than an + + align:start position:0% +angstroms which is you know less than an + + + align:start position:0% +angstroms which is you know less than an +atomic layer in some cases right + + align:start position:0% +atomic layer in some cases right + + + align:start position:0% +atomic layer in some cases right +um what they actually mean is on average + + align:start position:0% +um what they actually mean is on average + + + align:start position:0% +um what they actually mean is on average +uh over over certain kinds of areas but + + align:start position:0% +uh over over certain kinds of areas but + + + align:start position:0% +uh over over certain kinds of areas but +how would + + align:start position:0% +how would + + + align:start position:0% +how would +you actually achieve that with the + + align:start position:0% +you actually achieve that with the + + + align:start position:0% +you actually achieve that with the +manufacturing + + align:start position:0% +manufacturing + + + align:start position:0% +manufacturing +process how are you going to etch + + align:start position:0% +process how are you going to etch + + + align:start position:0% +process how are you going to etch +down through 5,000 + + align:start position:0% +down through 5,000 + + + align:start position:0% +down through 5,000 +angstroms and stop a th000 angstroms or + + align:start position:0% +angstroms and stop a th000 angstroms or + + + align:start position:0% +angstroms and stop a th000 angstroms or +100 angstroms before you hit the + + align:start position:0% + + + + align:start position:0% + +Silicon there's very carefully no the + + align:start position:0% +Silicon there's very carefully no the + + + align:start position:0% +Silicon there's very carefully no the +answer is you're + + align:start position:0% +answer is you're + + + align:start position:0% +answer is you're +not you're + + align:start position:0% + + + + align:start position:0% + +not at at present at least uh and there + + align:start position:0% +not at at present at least uh and there + + + align:start position:0% +not at at present at least uh and there +are some additional reasons uh why one + + align:start position:0% +are some additional reasons uh why one + + + align:start position:0% +are some additional reasons uh why one +wouldn't wouldn't want to do it but at + + align:start position:0% +wouldn't wouldn't want to do it but at + + + align:start position:0% +wouldn't wouldn't want to do it but at +present we don't have the observability + + align:start position:0% +present we don't have the observability + + + align:start position:0% +present we don't have the observability +to be able to know when we're within 100 + + align:start position:0% +to be able to know when we're within 100 + + + align:start position:0% +to be able to know when we're within 100 +angstroms uh second there's no way you + + align:start position:0% +angstroms uh second there's no way you + + + align:start position:0% +angstroms uh second there's no way you +could be that uniform across the whole + + align:start position:0% +could be that uniform across the whole + + + align:start position:0% +could be that uniform across the whole +wafer I mean what if on one part of the + + align:start position:0% +wafer I mean what if on one part of the + + + align:start position:0% +wafer I mean what if on one part of the +wafer for instead of 5,000 angstroms it + + align:start position:0% +wafer for instead of 5,000 angstroms it + + + align:start position:0% +wafer for instead of 5,000 angstroms it +was 50001 angstroms by the time I get + + align:start position:0% +was 50001 angstroms by the time I get + + + align:start position:0% +was 50001 angstroms by the time I get +down to you know etching 4900 angstroms + + align:start position:0% +down to you know etching 4900 angstroms + + + align:start position:0% +down to you know etching 4900 angstroms +everywhere that little one out of 5,000 + + align:start position:0% +everywhere that little one out of 5,000 + + + align:start position:0% +everywhere that little one out of 5,000 +controlability has been trans uh or + + align:start position:0% +controlability has been trans uh or + + + align:start position:0% +controlability has been trans uh or +variability which is not bad that'd be + + align:start position:0% +variability which is not bad that'd be + + + align:start position:0% +variability which is not bad that'd be +great if I got you + + align:start position:0% +great if I got you + + + align:start position:0% +great if I got you +know you know whatever that percentage + + align:start position:0% +know you know whatever that percentage + + + align:start position:0% +know you know whatever that percentage +is 05 or .2% or whatever I mean that's + + align:start position:0% +is 05 or .2% or whatever I mean that's + + + align:start position:0% +is 05 or .2% or whatever I mean that's +amazing but but it would magnify by the + + align:start position:0% +amazing but but it would magnify by the + + + align:start position:0% +amazing but but it would magnify by the +time I I add down even if I could atch + + align:start position:0% +time I I add down even if I could atch + + + align:start position:0% +time I I add down even if I could atch +uniformly there's just no way most + + align:start position:0% +uniformly there's just no way most + + + align:start position:0% +uniformly there's just no way most +importantly to be able to know when + + align:start position:0% +importantly to be able to know when + + + align:start position:0% +importantly to be able to know when +you're within 100 angstroms and be able + + align:start position:0% +you're within 100 angstroms and be able + + + align:start position:0% +you're within 100 angstroms and be able +to stop controllably at that + + align:start position:0% +to stop controllably at that + + + align:start position:0% +to stop controllably at that +level so what do you think they really + + align:start position:0% +level so what do you think they really + + + align:start position:0% +level so what do you think they really +do etch all the way through then row + + align:start position:0% +do etch all the way through then row + + + align:start position:0% +do etch all the way through then row +another layer that's exactly right we + + align:start position:0% +another layer that's exactly right we + + + align:start position:0% +another layer that's exactly right we +can controllably etch all the way + + align:start position:0% +can controllably etch all the way + + + align:start position:0% +can controllably etch all the way +through using ideas of uh etch + + align:start position:0% +through using ideas of uh etch + + + align:start position:0% +through using ideas of uh etch +selectivity the same idea I mentioned of + + align:start position:0% +selectivity the same idea I mentioned of + + + align:start position:0% +selectivity the same idea I mentioned of +we can we can form the uh or or choose + + align:start position:0% +we can we can form the uh or or choose + + + align:start position:0% +we can we can form the uh or or choose +an etch chemistry that allows us to uh + + align:start position:0% +an etch chemistry that allows us to uh + + + align:start position:0% +an etch chemistry that allows us to uh +etch silicon dioxide and not etch photo + + align:start position:0% +etch silicon dioxide and not etch photo + + + align:start position:0% +etch silicon dioxide and not etch photo +resist we can also use to etch silicon + + align:start position:0% +resist we can also use to etch silicon + + + align:start position:0% +resist we can also use to etch silicon +dioxide but not etch silicon you can + + align:start position:0% +dioxide but not etch silicon you can + + + align:start position:0% +dioxide but not etch silicon you can +have uh very good selectivity so that + + align:start position:0% +have uh very good selectivity so that + + + align:start position:0% +have uh very good selectivity so that +one can stop controllably on the surface + + align:start position:0% +one can stop controllably on the surface + + + align:start position:0% +one can stop controllably on the surface +of the Silicon now you everybody knows + + align:start position:0% +of the Silicon now you everybody knows + + + align:start position:0% +of the Silicon now you everybody knows +exactly where they are across every + + align:start position:0% +exactly where they are across every + + + align:start position:0% +exactly where they are across every +place in the wafer one can even over + + align:start position:0% +place in the wafer one can even over + + + align:start position:0% +place in the wafer one can even over +atch a little bit right you don't even + + align:start position:0% +atch a little bit right you don't even + + + align:start position:0% +atch a little bit right you don't even +have to try to set up a timed etch if I + + align:start position:0% +have to try to set up a timed etch if I + + + align:start position:0% +have to try to set up a timed etch if I +was etching at a thousand angstroms a + + align:start position:0% +was etching at a thousand angstroms a + + + align:start position:0% +was etching at a thousand angstroms a +minute and I started with 5,000 anrs I + + align:start position:0% +minute and I started with 5,000 anrs I + + + align:start position:0% +minute and I started with 5,000 anrs I +might etch for you know five minutes but + + align:start position:0% +might etch for you know five minutes but + + + align:start position:0% +might etch for you know five minutes but +to be sure that I've got the same degree + + align:start position:0% +to be sure that I've got the same degree + + + align:start position:0% +to be sure that I've got the same degree +of uniformity everywhere I might at for + + align:start position:0% +of uniformity everywhere I might at for + + + align:start position:0% +of uniformity everywhere I might at for +an extra 10 seconds that way I'm sure + + align:start position:0% +an extra 10 seconds that way I'm sure + + + align:start position:0% +an extra 10 seconds that way I'm sure +that I'm clearing everywhere across the + + align:start position:0% +that I'm clearing everywhere across the + + + align:start position:0% +that I'm clearing everywhere across the +wafer even if there's spatial + + align:start position:0% +wafer even if there's spatial + + + align:start position:0% +wafer even if there's spatial +non-uniformity in my etch or today's + + align:start position:0% +non-uniformity in my etch or today's + + + align:start position:0% +non-uniformity in my etch or today's +etch is etching slightly slower than + + align:start position:0% +etch is etching slightly slower than + + + align:start position:0% +etch is etching slightly slower than +yesterday's + + align:start position:0% +yesterday's + + + align:start position:0% +yesterday's +then I can go back in and with different + + align:start position:0% +then I can go back in and with different + + + align:start position:0% +then I can go back in and with different +process + + align:start position:0% +process + + + align:start position:0% +process +conditions lower lower temperatures more + + align:start position:0% +conditions lower lower temperatures more + + + align:start position:0% +conditions lower lower temperatures more +pure chemicals um or or or slightly + + align:start position:0% +pure chemicals um or or or slightly + + + align:start position:0% +pure chemicals um or or or slightly +different primarily uh different + + align:start position:0% +different primarily uh different + + + align:start position:0% +different primarily uh different +temperature or even using alternative + + align:start position:0% +temperature or even using alternative + + + align:start position:0% +temperature or even using alternative +process + + align:start position:0% +process + + + align:start position:0% +process +Technologies + + align:start position:0% +Technologies + + + align:start position:0% +Technologies +um that involve very very + + align:start position:0% +um that involve very very + + + align:start position:0% +um that involve very very +shorttime uh oxidations rapid thermal uh + + align:start position:0% +shorttime uh oxidations rapid thermal uh + + + align:start position:0% +shorttime uh oxidations rapid thermal uh +oxidations I can now controllably grow + + align:start position:0% +oxidations I can now controllably grow + + + align:start position:0% +oxidations I can now controllably grow +up a th000 anrs or 100 angstroms or + + align:start position:0% +up a th000 anrs or 100 angstroms or + + + align:start position:0% +up a th000 anrs or 100 angstroms or +whatever I need okay so so that's that's + + align:start position:0% +whatever I need okay so so that's that's + + + align:start position:0% +whatever I need okay so so that's that's +the first mistake I remember that one I + + align:start position:0% +the first mistake I remember that one I + + + align:start position:0% +the first mistake I remember that one I +think there's another one someplace + + align:start position:0% +think there's another one someplace + + + align:start position:0% +think there's another one someplace +but + + align:start position:0% +but + + + align:start position:0% +but +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so uh still sort of taking this at face + + align:start position:0% +so uh still sort of taking this at face + + + align:start position:0% +so uh still sort of taking this at face +value we had the photolithographic + + align:start position:0% +value we had the photolithographic + + + align:start position:0% +value we had the photolithographic +sequence that imprinted onto the uh + + align:start position:0% +sequence that imprinted onto the uh + + + align:start position:0% +sequence that imprinted onto the uh +photo resist we used that then to + + align:start position:0% +photo resist we used that then to + + + align:start position:0% +photo resist we used that then to +controllably uh change the of the + + align:start position:0% +controllably uh change the of the + + + align:start position:0% +controllably uh change the of the +permanent structure the silicon dioxide + + align:start position:0% +permanent structure the silicon dioxide + + + align:start position:0% +permanent structure the silicon dioxide +and then we remove using another + + align:start position:0% +and then we remove using another + + + align:start position:0% +and then we remove using another +chemical solvent or in in many cases + + align:start position:0% +chemical solvent or in in many cases + + + align:start position:0% +chemical solvent or in in many cases +another plasma ET a plasma Ash that + + align:start position:0% +another plasma ET a plasma Ash that + + + align:start position:0% +another plasma ET a plasma Ash that +removes the the the temporary uh photo + + align:start position:0% +removes the the the temporary uh photo + + + align:start position:0% +removes the the the temporary uh photo +resist okay then we go on we've done + + align:start position:0% +resist okay then we go on we've done + + + align:start position:0% +resist okay then we go on we've done +that sequence we've now deposited or + + align:start position:0% +that sequence we've now deposited or + + + align:start position:0% +that sequence we've now deposited or +grown and then spatially differentiated + + align:start position:0% +grown and then spatially differentiated + + + align:start position:0% +grown and then spatially differentiated +to be able to create one level of the + + align:start position:0% +to be able to create one level of the + + + align:start position:0% +to be able to create one level of the +the structure and now we're going to + + align:start position:0% +the structure and now we're going to + + + align:start position:0% +the structure and now we're going to +repeat that that kind of idea multiple + + align:start position:0% +repeat that that kind of idea multiple + + + align:start position:0% +repeat that that kind of idea multiple +times and then mix in a few additional + + align:start position:0% +times and then mix in a few additional + + + align:start position:0% +times and then mix in a few additional +transformation steps Next Step here is + + align:start position:0% +transformation steps Next Step here is + + + align:start position:0% +transformation steps Next Step here is +we're depositing a our our + + align:start position:0% +we're depositing a our our + + + align:start position:0% +we're depositing a our our +polysilicon uh layer uh again this will + + align:start position:0% +polysilicon uh layer uh again this will + + + align:start position:0% +polysilicon uh layer uh again this will +be fairly highly doped in uh either uh + + align:start position:0% +be fairly highly doped in uh either uh + + + align:start position:0% +be fairly highly doped in uh either uh +subsequent to the deposition or during + + align:start position:0% +subsequent to the deposition or during + + + align:start position:0% +subsequent to the deposition or during +the deposition it is a semiconducting + + align:start position:0% +the deposition it is a semiconducting + + + align:start position:0% +the deposition it is a semiconducting +layer but if one dopes it that is adds + + align:start position:0% +layer but if one dopes it that is adds + + + align:start position:0% +layer but if one dopes it that is adds +uh Elemental impurities of a particular + + align:start position:0% +uh Elemental impurities of a particular + + + align:start position:0% +uh Elemental impurities of a particular +type to play with the band structure uh + + align:start position:0% +type to play with the band structure uh + + + align:start position:0% +type to play with the band structure uh +of the Silicon one can make that behave + + align:start position:0% +of the Silicon one can make that behave + + + align:start position:0% +of the Silicon one can make that behave +in a fairly metallic fashion and in the + + align:start position:0% +in a fairly metallic fashion and in the + + + align:start position:0% +in a fairly metallic fashion and in the +MOs transistor that poly silicon is very + + align:start position:0% +MOs transistor that poly silicon is very + + + align:start position:0% +MOs transistor that poly silicon is very +highly doped and is a conductor under + + align:start position:0% +highly doped and is a conductor under + + + align:start position:0% +highly doped and is a conductor under +all all all conditions uh so we've + + align:start position:0% +all all all conditions uh so we've + + + align:start position:0% +all all all conditions uh so we've +deposited that recall what are we what + + align:start position:0% +deposited that recall what are we what + + + align:start position:0% +deposited that recall what are we what +what geometry do we want we want this + + align:start position:0% +what geometry do we want we want this + + + align:start position:0% +what geometry do we want we want this +thin gate electrode so we're going to do + + align:start position:0% +thin gate electrode so we're going to do + + + align:start position:0% +thin gate electrode so we're going to do +a photo resist or photolithographic step + + align:start position:0% +a photo resist or photolithographic step + + + align:start position:0% +a photo resist or photolithographic step +again to do that deposit photo resist uh + + align:start position:0% +again to do that deposit photo resist uh + + + align:start position:0% +again to do that deposit photo resist uh +expose in this case uh here again + + align:start position:0% +expose in this case uh here again + + + align:start position:0% +expose in this case uh here again +another positive photo resist case so + + align:start position:0% +another positive photo resist case so + + + align:start position:0% +another positive photo resist case so +we're blocking this structure we uh + + align:start position:0% +we're blocking this structure we uh + + + align:start position:0% +we're blocking this structure we uh +develop and and dissolve + + align:start position:0% +develop and and dissolve + + + align:start position:0% +develop and and dissolve +away uh uh the exposed photo resist and + + align:start position:0% +away uh uh the exposed photo resist and + + + align:start position:0% +away uh uh the exposed photo resist and +then we're doing a plasma Edge again to + + align:start position:0% +then we're doing a plasma Edge again to + + + align:start position:0% +then we're doing a plasma Edge again to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh plasma to to form the gate electrode + + align:start position:0% +uh plasma to to form the gate electrode + + + align:start position:0% +uh plasma to to form the gate electrode +and then uh remove or Ash away the the + + align:start position:0% +and then uh remove or Ash away the the + + + align:start position:0% +and then uh remove or Ash away the the +photo resist now this structure right + + align:start position:0% +photo resist now this structure right + + + align:start position:0% +photo resist now this structure right +here is very very critical this is the + + align:start position:0% +here is very very critical this is the + + + align:start position:0% +here is very very critical this is the +gate + + align:start position:0% +gate + + + align:start position:0% +gate +electrode the again the current is going + + align:start position:0% +electrode the again the current is going + + + align:start position:0% +electrode the again the current is going +to flow in this direction along this + + align:start position:0% +to flow in this direction along this + + + align:start position:0% +to flow in this direction along this +length underneath that gate electrode in + + align:start position:0% +length underneath that gate electrode in + + + align:start position:0% +length underneath that gate electrode in +the silicon and this is referred to as + + align:start position:0% +the silicon and this is referred to as + + + align:start position:0% +the silicon and this is referred to as +the channel length so the channel is the + + align:start position:0% +the channel length so the channel is the + + + align:start position:0% +the channel length so the channel is the +structure that we're going to create + + align:start position:0% +structure that we're going to create + + + align:start position:0% +structure that we're going to create +underneath the silicon and the length of + + align:start position:0% +underneath the silicon and the length of + + + align:start position:0% +underneath the silicon and the length of +that physical electron Ro is very very + + align:start position:0% +that physical electron Ro is very very + + + align:start position:0% +that physical electron Ro is very very +very critical in + + align:start position:0% +very critical in + + + align:start position:0% +very critical in +determining many of the most important + + align:start position:0% +determining many of the most important + + + align:start position:0% +determining many of the most important +characteristics of the + + align:start position:0% +characteristics of the + + + align:start position:0% +characteristics of the +transistor you can sort of think of it + + align:start position:0% +transistor you can sort of think of it + + + align:start position:0% +transistor you can sort of think of it +as uh and we're actually getting closer + + align:start position:0% +as uh and we're actually getting closer + + + align:start position:0% +as uh and we're actually getting closer +in in in the dimensions that we're + + align:start position:0% +in in in the dimensions that we're + + + align:start position:0% +in in in the dimensions that we're +talking about now that the time of + + align:start position:0% +talking about now that the time of + + + align:start position:0% +talking about now that the time of +flight of an electron underneath that + + align:start position:0% +flight of an electron underneath that + + + align:start position:0% +flight of an electron underneath that +electrode will depend on the width or or + + align:start position:0% +electrode will depend on the width or or + + + align:start position:0% +electrode will depend on the width or or +the length that it it it needs to + + align:start position:0% +the length that it it it needs to + + + align:start position:0% +the length that it it it needs to +Transit we're getting close to these uh + + align:start position:0% +Transit we're getting close to these uh + + + align:start position:0% +Transit we're getting close to these uh +velocity limited uh transport regimes + + align:start position:0% +velocity limited uh transport regimes + + + align:start position:0% +velocity limited uh transport regimes +and so uh from one one point of view the + + align:start position:0% +and so uh from one one point of view the + + + align:start position:0% +and so uh from one one point of view the +ability or the speed of the transistor + + align:start position:0% +ability or the speed of the transistor + + + align:start position:0% +ability or the speed of the transistor +is critically dependent on variations in + + align:start position:0% +is critically dependent on variations in + + + align:start position:0% +is critically dependent on variations in +that channel length this is often + + align:start position:0% +that channel length this is often + + + align:start position:0% +that channel length this is often +referred to as the CD of the or one of + + align:start position:0% +referred to as the CD of the or one of + + + align:start position:0% +referred to as the CD of the or one of +the CDs of the process critical + + align:start position:0% +the CDs of the process critical + + + align:start position:0% +the CDs of the process critical +dimensions of the + + align:start position:0% +dimensions of the + + + align:start position:0% +dimensions of the +process and uh uh in modern technology + + align:start position:0% +process and uh uh in modern technology + + + align:start position:0% +process and uh uh in modern technology +in fact that that is perhaps the + + align:start position:0% +in fact that that is perhaps the + + + align:start position:0% +in fact that that is perhaps the +smallest lateral Dimension that is uh + + align:start position:0% +smallest lateral Dimension that is uh + + + align:start position:0% +smallest lateral Dimension that is uh +determinative of the generation of the + + align:start position:0% +determinative of the generation of the + + + align:start position:0% +determinative of the generation of the +technology and the performance and + + align:start position:0% +technology and the performance and + + + align:start position:0% +technology and the performance and +charact uh characteristics of the + + align:start position:0% +charact uh characteristics of the + + + align:start position:0% +charact uh characteristics of the +technology so if we talk about a 65 + + align:start position:0% +technology so if we talk about a 65 + + + align:start position:0% +technology so if we talk about a 65 +nanometer technology they're talking + + align:start position:0% +nanometer technology they're talking + + + align:start position:0% +nanometer technology they're talking +typically about that channel length that + + align:start position:0% +typically about that channel length that + + + align:start position:0% +typically about that channel length that +minimum feature size being 65 + + align:start position:0% +minimum feature size being 65 + + + align:start position:0% +minimum feature size being 65 +nanometers okay in fact often uh tricks + + align:start position:0% +nanometers okay in fact often uh tricks + + + align:start position:0% +nanometers okay in fact often uh tricks +are played when where + + align:start position:0% +are played when where + + + align:start position:0% +are played when where +photolithographically using using the + + align:start position:0% +photolithographically using using the + + + align:start position:0% +photolithographically using using the +exposure that's the dimension that they + + align:start position:0% +exposure that's the dimension that they + + + align:start position:0% +exposure that's the dimension that they +can they can form but you might actually + + align:start position:0% +can they can form but you might actually + + + align:start position:0% +can they can form but you might actually +over etch and Shrink that get that to + + align:start position:0% +over etch and Shrink that get that to + + + align:start position:0% +over etch and Shrink that get that to +even a smaller Dimension than you could + + align:start position:0% +even a smaller Dimension than you could + + + align:start position:0% +even a smaller Dimension than you could +photolithographically Define in order to + + align:start position:0% +photolithographically Define in order to + + + align:start position:0% +photolithographically Define in order to +sort of boost uh the speed and the + + align:start position:0% +sort of boost uh the speed and the + + + align:start position:0% +sort of boost uh the speed and the +controllability of the of the + + align:start position:0% +controllability of the of the + + + align:start position:0% +controllability of the of the +device so this is very critical very + + align:start position:0% +device so this is very critical very + + + align:start position:0% +device so this is very critical very +critical uh lithography step and + + align:start position:0% +critical uh lithography step and + + + align:start position:0% +critical uh lithography step and +sequence uh going on the next thing we + + align:start position:0% +sequence uh going on the next thing we + + + align:start position:0% +sequence uh going on the next thing we +need to do is start to form these source + + align:start position:0% +need to do is start to form these source + + + align:start position:0% +need to do is start to form these source +and drain regions uh we need to + + align:start position:0% +and drain regions uh we need to + + + align:start position:0% +and drain regions uh we need to +differentiate the Silicon underneath and + + align:start position:0% +differentiate the Silicon underneath and + + + align:start position:0% +differentiate the Silicon underneath and +what we're going to do here is using + + align:start position:0% +what we're going to do here is using + + + align:start position:0% +what we're going to do here is using +another uh process an ion implantation + + align:start position:0% +another uh process an ion implantation + + + align:start position:0% +another uh process an ion implantation +process I believe in + + align:start position:0% +process I believe in + + + align:start position:0% +process I believe in +this yes I think that's what their + + align:start position:0% +this yes I think that's what their + + + align:start position:0% +this yes I think that's what their +little picture there is um where where + + align:start position:0% +little picture there is um where where + + + align:start position:0% +little picture there is um where where +we actually implant those dopen atoms we + + align:start position:0% +we actually implant those dopen atoms we + + + align:start position:0% +we actually implant those dopen atoms we +shoot them with a uh uh essentially a + + align:start position:0% +shoot them with a uh uh essentially a + + + align:start position:0% +shoot them with a uh uh essentially a +high energy electron gun or um ion gun + + align:start position:0% +high energy electron gun or um ion gun + + + align:start position:0% +high energy electron gun or um ion gun +into into the Silicon in a very + + align:start position:0% +into into the Silicon in a very + + + align:start position:0% +into into the Silicon in a very +controlled fashion the guys who are + + align:start position:0% +controlled fashion the guys who are + + + align:start position:0% +controlled fashion the guys who are +going to Varan here in semi in uh in + + align:start position:0% +going to Varan here in semi in uh in + + + align:start position:0% +going to Varan here in semi in uh in +Gloucester Massachusetts uh Varian sells + + align:start position:0% +Gloucester Massachusetts uh Varian sells + + + align:start position:0% +Gloucester Massachusetts uh Varian sells +ion implanters that's their business + + align:start position:0% +ion implanters that's their business + + + align:start position:0% +ion implanters that's their business +they're I don't know 75% or something of + + align:start position:0% +they're I don't know 75% or something of + + + align:start position:0% +they're I don't know 75% or something of +the market now they're they're they're + + align:start position:0% +the market now they're they're they're + + + align:start position:0% +the market now they're they're they're +dominant and they sell the equipment for + + align:start position:0% +dominant and they sell the equipment for + + + align:start position:0% +dominant and they sell the equipment for +uh ion implantation and + + align:start position:0% +uh ion implantation and + + + align:start position:0% +uh ion implantation and +some there's also other competing ion + + align:start position:0% +some there's also other competing ion + + + align:start position:0% +some there's also other competing ion +implant companies but most of them are + + align:start position:0% +implant companies but most of them are + + + align:start position:0% +implant companies but most of them are +also in Massachusetts so Massachusetts + + align:start position:0% +also in Massachusetts so Massachusetts + + + align:start position:0% +also in Massachusetts so Massachusetts +is the ion implant capital of the + + align:start position:0% +is the ion implant capital of the + + + align:start position:0% +is the ion implant capital of the +world the basic idea there again is + + align:start position:0% +world the basic idea there again is + + + align:start position:0% +world the basic idea there again is +we're highly doping uh in a controllable + + align:start position:0% +we're highly doping uh in a controllable + + + align:start position:0% +we're highly doping uh in a controllable +fashion just these regions uh those th + + align:start position:0% +fashion just these regions uh those th + + + align:start position:0% +fashion just these regions uh those th +those regions we don't want to dope + + align:start position:0% +those regions we don't want to dope + + + align:start position:0% +those regions we don't want to dope +underneath the channel we want to keep + + align:start position:0% +underneath the channel we want to keep + + + align:start position:0% +underneath the channel we want to keep +that fairly lightly doped so that we can + + align:start position:0% +that fairly lightly doped so that we can + + + align:start position:0% +that fairly lightly doped so that we can +invert it for electrical action and in + + align:start position:0% +invert it for electrical action and in + + + align:start position:0% +invert it for electrical action and in +this case we're we're getting something + + align:start position:0% +this case we're we're getting something + + + align:start position:0% +this case we're we're getting something +often referred to as a self aligned + + align:start position:0% +often referred to as a self aligned + + + align:start position:0% +often referred to as a self aligned +process + + align:start position:0% +process + + + align:start position:0% +process +whereby we don't have to selectively + + align:start position:0% +whereby we don't have to selectively + + + align:start position:0% +whereby we don't have to selectively +shoot the ions just in here we can + + align:start position:0% +shoot the ions just in here we can + + + align:start position:0% +shoot the ions just in here we can +blanket the whole wafer and use these + + align:start position:0% +blanket the whole wafer and use these + + + align:start position:0% +blanket the whole wafer and use these +thick oxide and use the polysilicon as + + align:start position:0% +thick oxide and use the polysilicon as + + + align:start position:0% +thick oxide and use the polysilicon as +the mask itself to prevent the ions from + + align:start position:0% +the mask itself to prevent the ions from + + + align:start position:0% +the mask itself to prevent the ions from +reaching the under underlying uh silicon + + align:start position:0% +reaching the under underlying uh silicon + + + align:start position:0% +reaching the under underlying uh silicon +regions so instead of having to you know + + align:start position:0% +regions so instead of having to you know + + + align:start position:0% +regions so instead of having to you know +put down another photo resist layer and + + align:start position:0% +put down another photo resist layer and + + + align:start position:0% +put down another photo resist layer and +try to open up just exactly those + + align:start position:0% +try to open up just exactly those + + + align:start position:0% +try to open up just exactly those +regions and and worry about aligning of + + align:start position:0% +regions and and worry about aligning of + + + align:start position:0% +regions and and worry about aligning of +the physical mask to match up exactly + + align:start position:0% +the physical mask to match up exactly + + + align:start position:0% +the physical mask to match up exactly +with the existing structures on the + + align:start position:0% +with the existing structures on the + + + align:start position:0% +with the existing structures on the +wafer we can we can take advantage of of + + align:start position:0% +wafer we can we can take advantage of of + + + align:start position:0% +wafer we can we can take advantage of of +the underlying structures to achieve + + align:start position:0% +the underlying structures to achieve + + + align:start position:0% +the underlying structures to achieve +that that uh spatial uh alignment yeah + + align:start position:0% +that that uh spatial uh alignment yeah + + + align:start position:0% +that that uh spatial uh alignment yeah +can you elaborate a little bit upon the + + align:start position:0% +can you elaborate a little bit upon the + + + align:start position:0% +can you elaborate a little bit upon the +the process of placing this photo resist + + align:start position:0% +the process of placing this photo resist + + + align:start position:0% +the process of placing this photo resist +seems like you're going to have one + + align:start position:0% +seems like you're going to have one + + + align:start position:0% +seems like you're going to have one +you're going to off and put another I + + align:start position:0% +you're going to off and put another I + + + align:start position:0% +you're going to off and put another I +mean how do you make sure everything + + align:start position:0% +mean how do you make sure everything + + + align:start position:0% +mean how do you make sure everything +lines up the way you needed to this is a + + align:start position:0% +lines up the way you needed to this is a + + + align:start position:0% +lines up the way you needed to this is a +a wonderful manufacturing control + + align:start position:0% +a wonderful manufacturing control + + + align:start position:0% +a wonderful manufacturing control +challenge um overlay and Alignment are + + align:start position:0% +challenge um overlay and Alignment are + + + align:start position:0% +challenge um overlay and Alignment are +uh almost more so than the the physical + + align:start position:0% +uh almost more so than the the physical + + + align:start position:0% +uh almost more so than the the physical +Dimension that can be imaged are the + + align:start position:0% +Dimension that can be imaged are the + + + align:start position:0% +Dimension that can be imaged are the +manufacturing control problems there's + + align:start position:0% +manufacturing control problems there's + + + align:start position:0% +manufacturing control problems there's +more description in in in man's Manos + + align:start position:0% +more description in in in man's Manos + + + align:start position:0% +more description in in in man's Manos +but but essentially uh over time the + + align:start position:0% +but but essentially uh over time the + + + align:start position:0% +but but essentially uh over time the +ability to optically line up the + + align:start position:0% +ability to optically line up the + + + align:start position:0% +ability to optically line up the +existing structures + + align:start position:0% +existing structures + + + align:start position:0% +existing structures +typically you might actually use + + align:start position:0% +typically you might actually use + + + align:start position:0% +typically you might actually use +alignment marks that you build up in + + align:start position:0% +alignment marks that you build up in + + + align:start position:0% +alignment marks that you build up in +parallel to these transistors to Aid in + + align:start position:0% +parallel to these transistors to Aid in + + + align:start position:0% +parallel to these transistors to Aid in +the optical uh automatic Optical + + align:start position:0% +the optical uh automatic Optical + + + align:start position:0% +the optical uh automatic Optical +recognition of spatial locations on the + + align:start position:0% +recognition of spatial locations on the + + + align:start position:0% +recognition of spatial locations on the +wafer uh it's it's a huge challenge to + + align:start position:0% +wafer uh it's it's a huge challenge to + + + align:start position:0% +wafer uh it's it's a huge challenge to +then line that up with the physical mask + + align:start position:0% +then line that up with the physical mask + + + align:start position:0% +then line that up with the physical mask +plate uh such that you minimize minimize + + align:start position:0% +plate uh such that you minimize minimize + + + align:start position:0% +plate uh such that you minimize minimize +offsets there's also Exquisite + + align:start position:0% +offsets there's also Exquisite + + + align:start position:0% +offsets there's also Exquisite +Environmental al control in the + + align:start position:0% +Environmental al control in the + + + align:start position:0% +Environmental al control in the +equipment that's used for this imagine + + align:start position:0% +equipment that's used for this imagine + + + align:start position:0% +equipment that's used for this imagine +that I don't need to line up just for + + align:start position:0% +that I don't need to line up just for + + + align:start position:0% +that I don't need to line up just for +one transistor I got to make sure + + align:start position:0% +one transistor I got to make sure + + + align:start position:0% +one transistor I got to make sure +across maybe a 1 cm squared or 2 cm + + align:start position:0% +across maybe a 1 cm squared or 2 cm + + + align:start position:0% +across maybe a 1 cm squared or 2 cm +squared chip that all of my transistors + + align:start position:0% +squared chip that all of my transistors + + + align:start position:0% +squared chip that all of my transistors +are lining up and in fact in older + + align:start position:0% +are lining up and in fact in older + + + align:start position:0% +are lining up and in fact in older +Technologies I had to make sure the + + align:start position:0% +Technologies I had to make sure the + + + align:start position:0% +Technologies I had to make sure the +whole wafer was lined up because I had a + + align:start position:0% +whole wafer was lined up because I had a + + + align:start position:0% +whole wafer was lined up because I had a +big glass plate that I was using in + + align:start position:0% +big glass plate that I was using in + + + align:start position:0% +big glass plate that I was using in +almost a one for one transformation so + + align:start position:0% +almost a one for one transformation so + + + align:start position:0% +almost a one for one transformation so +everything across a whole wafer had to + + align:start position:0% +everything across a whole wafer had to + + + align:start position:0% +everything across a whole wafer had to +be lined up and if the temperature of + + align:start position:0% +be lined up and if the temperature of + + + align:start position:0% +be lined up and if the temperature of +the glass plate and that of the wafer + + align:start position:0% +the glass plate and that of the wafer + + + align:start position:0% +the glass plate and that of the wafer +were off by a + + align:start position:0% +were off by a + + + align:start position:0% +were off by a +degree the thermal expansion would upset + + align:start position:0% +degree the thermal expansion would upset + + + align:start position:0% +degree the thermal expansion would upset +the alignment for example so over time + + align:start position:0% +the alignment for example so over time + + + align:start position:0% +the alignment for example so over time +you've seen uh both to achieve smaller + + align:start position:0% +you've seen uh both to achieve smaller + + + align:start position:0% +you've seen uh both to achieve smaller +Dimension but also to achieve better + + align:start position:0% +Dimension but also to achieve better + + + align:start position:0% +Dimension but also to achieve better +control a number of that as the driver + + align:start position:0% +control a number of that as the driver + + + align:start position:0% +control a number of that as the driver +for the evolution photoi lithographic + + align:start position:0% +for the evolution photoi lithographic + + + align:start position:0% +for the evolution photoi lithographic +equipment uh one step was uh + + align:start position:0% +equipment uh one step was uh + + + align:start position:0% +equipment uh one step was uh +photolithographic reduction from say a + + align:start position:0% +photolithographic reduction from say a + + + align:start position:0% +photolithographic reduction from say a +10: one or a + + align:start position:0% +10: one or a + + + align:start position:0% +10: one or a +5:1 uh glass plate down to a smaller + + align:start position:0% +5:1 uh glass plate down to a smaller + + + align:start position:0% +5:1 uh glass plate down to a smaller +chip or smaller smaller wafer the second + + align:start position:0% +chip or smaller smaller wafer the second + + + align:start position:0% +chip or smaller smaller wafer the second +was chipto Chip stepping so in fact the + + align:start position:0% +was chipto Chip stepping so in fact the + + + align:start position:0% +was chipto Chip stepping so in fact the +photo lith lithography equipment is + + align:start position:0% +photo lith lithography equipment is + + + align:start position:0% +photo lith lithography equipment is +typically called now a stepper because + + align:start position:0% +typically called now a stepper because + + + align:start position:0% +typically called now a stepper because +it's Imaging one + + align:start position:0% +it's Imaging one + + + align:start position:0% +it's Imaging one +field maybe one chip there may be more + + align:start position:0% +field maybe one chip there may be more + + + align:start position:0% +field maybe one chip there may be more +than one chip in each field field but + + align:start position:0% +than one chip in each field field but + + + align:start position:0% +than one chip in each field field but +I'm I'm stepping through in order to get + + align:start position:0% +I'm I'm stepping through in order to get + + + align:start position:0% +I'm I'm stepping through in order to get +the control and be able to achieve the + + align:start position:0% +the control and be able to achieve the + + + align:start position:0% +the control and be able to achieve the +alignment on on one chip at a time and + + align:start position:0% +alignment on on one chip at a time and + + + align:start position:0% +alignment on on one chip at a time and +in the most modern equipment in fact + + align:start position:0% +in the most modern equipment in fact + + + align:start position:0% +in the most modern equipment in fact +they don't even image the whole chip at + + align:start position:0% +they don't even image the whole chip at + + + align:start position:0% +they don't even image the whole chip at +one time they're SL they're Imaging + + align:start position:0% +one time they're SL they're Imaging + + + align:start position:0% +one time they're SL they're Imaging +slices of that so that they can do all + + align:start position:0% +slices of that so that they can do all + + + align:start position:0% +slices of that so that they can do all +kinds of other on the-fly alignment + + align:start position:0% +kinds of other on the-fly alignment + + + align:start position:0% +kinds of other on the-fly alignment +control as well as leveling because uh + + align:start position:0% +control as well as leveling because uh + + + align:start position:0% +control as well as leveling because uh +turns out the depth of focus is a big + + align:start position:0% +turns out the depth of focus is a big + + + align:start position:0% +turns out the depth of focus is a big +constraint and if if I have a focal + + align:start position:0% +constraint and if if I have a focal + + + align:start position:0% +constraint and if if I have a focal +plane + + align:start position:0% +plane + + + align:start position:0% +plane +um + + align:start position:0% +um + + + align:start position:0% +um +uh mismatch where I'm in focus on the + + align:start position:0% +uh mismatch where I'm in focus on the + + + align:start position:0% +uh mismatch where I'm in focus on the +left side of the Chip and not on the + + align:start position:0% +left side of the Chip and not on the + + + align:start position:0% +left side of the Chip and not on the +right then I don't get the dimensional + + align:start position:0% +right then I don't get the dimensional + + + align:start position:0% +right then I don't get the dimensional +control I need so so it's it's really uh + + align:start position:0% +control I need so so it's it's really uh + + + align:start position:0% +control I need so so it's it's really uh +amazing innovations that are exactly + + align:start position:0% +amazing innovations that are exactly + + + align:start position:0% +amazing innovations that are exactly +driven by the manufacturing control + + align:start position:0% +driven by the manufacturing control + + + align:start position:0% +driven by the manufacturing control +necessary so there's a little bit more + + align:start position:0% +necessary so there's a little bit more + + + align:start position:0% +necessary so there's a little bit more +description in here uh uh uh talking + + align:start position:0% +description in here uh uh uh talking + + + align:start position:0% +description in here uh uh uh talking +about some of some of that equipment as + + align:start position:0% +about some of some of that equipment as + + + align:start position:0% +about some of some of that equipment as +well and in this in fact I'm not really + + align:start position:0% +well and in this in fact I'm not really + + + align:start position:0% +well and in this in fact I'm not really +talking here much about uh uh the + + align:start position:0% +talking here much about uh uh the + + + align:start position:0% +talking here much about uh uh the +processing equipment I'm trying to get + + align:start position:0% +processing equipment I'm trying to get + + + align:start position:0% +processing equipment I'm trying to get +us through uh uh at least the process + + align:start position:0% +us through uh uh at least the process + + + align:start position:0% +us through uh uh at least the process +sequence but the equipment itself is + + align:start position:0% +sequence but the equipment itself is + + + align:start position:0% +sequence but the equipment itself is +fascinating is really + + align:start position:0% +fascinating is really + + + align:start position:0% +fascinating is really +fascinating okay we're almost there with + + align:start position:0% +fascinating okay we're almost there with + + + align:start position:0% +fascinating okay we're almost there with +this this device because now we're + + align:start position:0% +this this device because now we're + + + align:start position:0% +this this device because now we're +primarily just repeating these same + + align:start position:0% +primarily just repeating these same + + + align:start position:0% +primarily just repeating these same +kinds of same kinds of structures um + + align:start position:0% +kinds of same kinds of structures um + + + align:start position:0% +kinds of same kinds of structures um +what we're going to do now is another + + align:start position:0% +what we're going to do now is another + + + align:start position:0% +what we're going to do now is another +photolithography step here essentially + + align:start position:0% +photolithography step here essentially + + + align:start position:0% +photolithography step here essentially +uh what we want to do with this yellow + + align:start position:0% +uh what we want to do with this yellow + + + align:start position:0% +uh what we want to do with this yellow +layer is uh build up an insulating layer + + align:start position:0% +layer is uh build up an insulating layer + + + align:start position:0% +layer is uh build up an insulating layer +so I think uh a new layer of silicon + + align:start position:0% +so I think uh a new layer of silicon + + + align:start position:0% +so I think uh a new layer of silicon +dioxide is deposited in this case it's + + align:start position:0% +dioxide is deposited in this case it's + + + align:start position:0% +dioxide is deposited in this case it's +not thermally grown through that + + align:start position:0% +not thermally grown through that + + + align:start position:0% +not thermally grown through that +chemical reaction of oxide and and + + align:start position:0% +chemical reaction of oxide and and + + + align:start position:0% +chemical reaction of oxide and and +silicon because I've already got + + align:start position:0% +silicon because I've already got + + + align:start position:0% +silicon because I've already got +polysilicon I've got uh uh well I guess + + align:start position:0% +polysilicon I've got uh uh well I guess + + + align:start position:0% +polysilicon I've got uh uh well I guess +it actually might work in this case I've + + align:start position:0% +it actually might work in this case I've + + + align:start position:0% +it actually might work in this case I've +already got a very thick layer of of + + align:start position:0% +already got a very thick layer of of + + + align:start position:0% +already got a very thick layer of of +silicon in this case we use typically a + + align:start position:0% +silicon in this case we use typically a + + + align:start position:0% +silicon in this case we use typically a +chemical vapor deposition process again + + align:start position:0% +chemical vapor deposition process again + + + align:start position:0% +chemical vapor deposition process again +in vacuum equipment but we + + align:start position:0% +in vacuum equipment but we + + + align:start position:0% +in vacuum equipment but we +decompose uh uh silicon dioxide carrying + + align:start position:0% +decompose uh uh silicon dioxide carrying + + + align:start position:0% +decompose uh uh silicon dioxide carrying +molecules in a gas + + align:start position:0% +molecules in a gas + + + align:start position:0% +molecules in a gas +plasma so there'll be a more complex + + align:start position:0% +plasma so there'll be a more complex + + + align:start position:0% +plasma so there'll be a more complex +molecule typically coming in and we + + align:start position:0% +molecule typically coming in and we + + + align:start position:0% +molecule typically coming in and we +decompose that and basically it snows if + + align:start position:0% +decompose that and basically it snows if + + + align:start position:0% +decompose that and basically it snows if +on the surface of the wafer and builds + + align:start position:0% +on the surface of the wafer and builds + + + align:start position:0% +on the surface of the wafer and builds +up a silicon dioxide um layer so we + + align:start position:0% +up a silicon dioxide um layer so we + + + align:start position:0% +up a silicon dioxide um layer so we +deposit that silicon dioxide and what + + align:start position:0% +deposit that silicon dioxide and what + + + align:start position:0% +deposit that silicon dioxide and what +we're going to do is now open up holes + + align:start position:0% +we're going to do is now open up holes + + + align:start position:0% +we're going to do is now open up holes +within that using photolithography step + + align:start position:0% +within that using photolithography step + + + align:start position:0% +within that using photolithography step +you can see here's the mask where we + + align:start position:0% +you can see here's the mask where we + + + align:start position:0% +you can see here's the mask where we +want to open up a hole down where we'll + + align:start position:0% +want to open up a hole down where we'll + + + align:start position:0% +want to open up a hole down where we'll +be able to make contact to the gate and + + align:start position:0% +be able to make contact to the gate and + + + align:start position:0% +be able to make contact to the gate and +make contact to the source and + + align:start position:0% +make contact to the source and + + + align:start position:0% +make contact to the source and +drain so we go through again photo photo + + align:start position:0% +drain so we go through again photo photo + + + align:start position:0% +drain so we go through again photo photo +lithography put our resist uh + + align:start position:0% +lithography put our resist uh + + + align:start position:0% +lithography put our resist uh +uh down expose it develop it plasma + + align:start position:0% +uh down expose it develop it plasma + + + align:start position:0% +uh down expose it develop it plasma +etch again controllably etching through + + align:start position:0% +etch again controllably etching through + + + align:start position:0% +etch again controllably etching through +the oxide stopping on the Silicon layer + + align:start position:0% +the oxide stopping on the Silicon layer + + + align:start position:0% +the oxide stopping on the Silicon layer +uh remove the photo resist and now we + + align:start position:0% +uh remove the photo resist and now we + + + align:start position:0% +uh remove the photo resist and now we +put down a metal layer now typically + + align:start position:0% +put down a metal layer now typically + + + align:start position:0% +put down a metal layer now typically +what's done for metal layers is some + + align:start position:0% +what's done for metal layers is some + + + align:start position:0% +what's done for metal layers is some +form of a physical vapor + + align:start position:0% +form of a physical vapor + + + align:start position:0% +form of a physical vapor +deposition where + + align:start position:0% +deposition where + + + align:start position:0% +deposition where +um + + align:start position:0% +um + + + align:start position:0% +um +uh one example is a metal evaporator + + align:start position:0% +uh one example is a metal evaporator + + + align:start position:0% +uh one example is a metal evaporator +where the the wafer will be positioned + + align:start position:0% +where the the wafer will be positioned + + + align:start position:0% +where the the wafer will be positioned +some distance away from a metal Source + + align:start position:0% +some distance away from a metal Source + + + align:start position:0% +some distance away from a metal Source +the metal source aluminum or or or or + + align:start position:0% +the metal source aluminum or or or or + + + align:start position:0% +the metal source aluminum or or or or +other materials will be uh uh heated + + align:start position:0% +other materials will be uh uh heated + + + align:start position:0% +other materials will be uh uh heated +up either directly electrically or under + + align:start position:0% +up either directly electrically or under + + + align:start position:0% +up either directly electrically or under +uh sputtering kinds of kind kinds of + + align:start position:0% +uh sputtering kinds of kind kinds of + + + align:start position:0% +uh sputtering kinds of kind kinds of +activity such that uh either individual + + align:start position:0% +activity such that uh either individual + + + align:start position:0% +activity such that uh either individual +molecules or small uh agglomerations of + + align:start position:0% +molecules or small uh agglomerations of + + + align:start position:0% +molecules or small uh agglomerations of +molecules become very excited + + align:start position:0% +molecules become very excited + + + align:start position:0% +molecules become very excited +and + + align:start position:0% +and + + + align:start position:0% +and +uh uh traj through the uh through the + + align:start position:0% +uh uh traj through the uh through the + + + align:start position:0% +uh uh traj through the uh through the +vacuum uh and build up the uh layer on + + align:start position:0% +vacuum uh and build up the uh layer on + + + align:start position:0% +vacuum uh and build up the uh layer on +the surface of the of the wafer so in + + align:start position:0% +the surface of the of the wafer so in + + + align:start position:0% +the surface of the of the wafer so in +this case is an older technology they're + + align:start position:0% +this case is an older technology they're + + + align:start position:0% +this case is an older technology they're +talking about this being aluminum I'll + + align:start position:0% +talking about this being aluminum I'll + + + align:start position:0% +talking about this being aluminum I'll +show you a little bit later that most of + + align:start position:0% +show you a little bit later that most of + + + align:start position:0% +show you a little bit later that most of +the uh most advanced chips are now using + + align:start position:0% +the uh most advanced chips are now using + + + align:start position:0% +the uh most advanced chips are now using +a copper interconnect which has which + + align:start position:0% +a copper interconnect which has which + + + align:start position:0% +a copper interconnect which has which +has other challenges so the basic idea + + align:start position:0% +has other challenges so the basic idea + + + align:start position:0% +has other challenges so the basic idea +is now again we've covered the whole + + align:start position:0% +is now again we've covered the whole + + + align:start position:0% +is now again we've covered the whole +surface of the + + align:start position:0% +surface of the + + + align:start position:0% +surface of the +wafer and we selectively go in with a + + align:start position:0% +wafer and we selectively go in with a + + + align:start position:0% +wafer and we selectively go in with a +photolithography step and remove where + + align:start position:0% +photolithography step and remove where + + + align:start position:0% +photolithography step and remove where +we don't want the metal lines I've + + align:start position:0% +we don't want the metal lines I've + + + align:start position:0% +we don't want the metal lines I've +protected uh where I'm not going to want + + align:start position:0% +protected uh where I'm not going to want + + + align:start position:0% +protected uh where I'm not going to want +to etch so I'm protecting parts of the + + align:start position:0% +to etch so I'm protecting parts of the + + + align:start position:0% +to etch so I'm protecting parts of the +aluminum and then I do a plasma etch or + + align:start position:0% +aluminum and then I do a plasma etch or + + + align:start position:0% +aluminum and then I do a plasma etch or +a chemical etch uh in order to + + align:start position:0% +a chemical etch uh in order to + + + align:start position:0% +a chemical etch uh in order to +remove uh the aluminum and then I I + + align:start position:0% +remove uh the aluminum and then I I + + + align:start position:0% +remove uh the aluminum and then I I +remove strip away the the photo resist + + align:start position:0% +remove strip away the the photo resist + + + align:start position:0% +remove strip away the the photo resist +leaving uh my structure now this is a + + align:start position:0% +leaving uh my structure now this is a + + + align:start position:0% +leaving uh my structure now this is a +single level metal very simple + + align:start position:0% +single level metal very simple + + + align:start position:0% +single level metal very simple +transistor uh in + + align:start position:0% +transistor uh in + + + align:start position:0% +transistor uh in +and building up a several billion uh + + align:start position:0% +and building up a several billion uh + + + align:start position:0% +and building up a several billion uh +transistor chip or even 100 transistor + + align:start position:0% +transistor chip or even 100 transistor + + + align:start position:0% +transistor chip or even 100 transistor +chip we now need to also electrically + + align:start position:0% +chip we now need to also electrically + + + align:start position:0% +chip we now need to also electrically +interconnect all of those devices and + + align:start position:0% +interconnect all of those devices and + + + align:start position:0% +interconnect all of those devices and +there's a whole additional sequence of + + align:start position:0% +there's a whole additional sequence of + + + align:start position:0% +there's a whole additional sequence of +process steps that are used to build + + align:start position:0% +process steps that are used to build + + + align:start position:0% +process steps that are used to build +multiple levels of metal + + align:start position:0% +multiple levels of metal + + + align:start position:0% +multiple levels of metal +contact but conceptually they're very + + align:start position:0% +contact but conceptually they're very + + + align:start position:0% +contact but conceptually they're very +similar to those that we've seen uh so + + align:start position:0% +similar to those that we've seen uh so + + + align:start position:0% +similar to those that we've seen uh so +far here I've got access to this + + align:start position:0% +far here I've got access to this + + + align:start position:0% +far here I've got access to this +individual transistor clearly laterally + + align:start position:0% +individual transistor clearly laterally + + + align:start position:0% +individual transistor clearly laterally +I can have uh you know neighboring + + align:start position:0% +I can have uh you know neighboring + + + align:start position:0% +I can have uh you know neighboring +transistors that I've wired together + + align:start position:0% +transistors that I've wired together + + + align:start position:0% +transistors that I've wired together +with the patterned + + align:start position:0% +with the patterned + + + align:start position:0% +with the patterned +aluminum when you get a certain number + + align:start position:0% +aluminum when you get a certain number + + + align:start position:0% +aluminum when you get a certain number +of transistors it becomes very hard to + + align:start position:0% +of transistors it becomes very hard to + + + align:start position:0% +of transistors it becomes very hard to +have just one level of wiring you need + + align:start position:0% +have just one level of wiring you need + + + align:start position:0% +have just one level of wiring you need +to be able to have a wire that goes over + + align:start position:0% +to be able to have a wire that goes over + + + align:start position:0% +to be able to have a wire that goes over +another wire and that's where we get to + + align:start position:0% +another wire and that's where we get to + + + align:start position:0% +another wire and that's where we get to +multiple level interconnect structures + + align:start position:0% +multiple level interconnect structures + + + align:start position:0% +multiple level interconnect structures +where one would deposit another layer of + + align:start position:0% +where one would deposit another layer of + + + align:start position:0% +where one would deposit another layer of +silicon dioxide or other insulator and + + align:start position:0% +silicon dioxide or other insulator and + + + align:start position:0% +silicon dioxide or other insulator and +then build vertical Vias down from one + + align:start position:0% +then build vertical Vias down from one + + + align:start position:0% +then build vertical Vias down from one +level to the next to contact multiple + + align:start position:0% +level to the next to contact multiple + + + align:start position:0% +level to the next to contact multiple +streets on level two with streets on + + align:start position:0% +streets on level two with streets on + + + align:start position:0% +streets on level two with streets on +level one and so on up to uh six eight + + align:start position:0% +level one and so on up to uh six eight + + + align:start position:0% +level one and so on up to uh six eight +or even 10 levels of metal in modern uh + + align:start position:0% +or even 10 levels of metal in modern uh + + + align:start position:0% +or even 10 levels of metal in modern uh +structures so when I buy a chip in a + + align:start position:0% +structures so when I buy a chip in a + + + align:start position:0% +structures so when I buy a chip in a +computer um are there several um + + align:start position:0% +computer um are there several um + + + align:start position:0% +computer um are there several um +transistors above each other or are just + + align:start position:0% +transistors above each other or are just + + + align:start position:0% +transistors above each other or are just +connectors yeah good good question + + align:start position:0% +connectors yeah good good question + + + align:start position:0% +connectors yeah good good question +almost all existing uh semiconductor + + align:start position:0% +almost all existing uh semiconductor + + + align:start position:0% +almost all existing uh semiconductor +chips are planer processes meaning all + + align:start position:0% +chips are planer processes meaning all + + + align:start position:0% +chips are planer processes meaning all +of the transistors are in just one plane + + align:start position:0% +of the transistors are in just one plane + + + align:start position:0% +of the transistors are in just one plane +just at the surface of the Silicon in + + align:start position:0% +just at the surface of the Silicon in + + + align:start position:0% +just at the surface of the Silicon in +fact let me hand this around this is + + align:start position:0% +fact let me hand this around this is + + + align:start position:0% +fact let me hand this around this is +this just has a copper interconnect test + + align:start position:0% +this just has a copper interconnect test + + + align:start position:0% +this just has a copper interconnect test +pattern on it so but this is an um an 8 + + align:start position:0% +pattern on it so but this is an um an 8 + + + align:start position:0% +pattern on it so but this is an um an 8 +in wafer and the basic idea is we can + + align:start position:0% +in wafer and the basic idea is we can + + + align:start position:0% +in wafer and the basic idea is we can +get that very nicely grown silicon layer + + align:start position:0% +get that very nicely grown silicon layer + + + align:start position:0% +get that very nicely grown silicon layer +and control of the surface of the + + align:start position:0% +and control of the surface of the + + + align:start position:0% +and control of the surface of the +Silicon layer it's actually quite + + align:start position:0% +Silicon layer it's actually quite + + + align:start position:0% +Silicon layer it's actually quite +difficult to build up multiple levels of + + align:start position:0% +difficult to build up multiple levels of + + + align:start position:0% +difficult to build up multiple levels of +independent and high quality silicon + + align:start position:0% +independent and high quality silicon + + + align:start position:0% +independent and high quality silicon +layers on on the wafer there's an awful + + align:start position:0% +layers on on the wafer there's an awful + + + align:start position:0% +layers on on the wafer there's an awful +lot of research pass that around + + align:start position:0% +lot of research pass that around + + + align:start position:0% +lot of research pass that around +um + + align:start position:0% +um + + + align:start position:0% +um +uh for 3D integrated circuits where one + + align:start position:0% +uh for 3D integrated circuits where one + + + align:start position:0% +uh for 3D integrated circuits where one +would in fact build multiple strata or + + align:start position:0% +would in fact build multiple strata or + + + align:start position:0% +would in fact build multiple strata or +multiple layers of transistors and then + + align:start position:0% +multiple layers of transistors and then + + + align:start position:0% +multiple layers of transistors and then +Bond the Wafers together to be able to + + align:start position:0% +Bond the Wafers together to be able to + + + align:start position:0% +Bond the Wafers together to be able to +have in a very compact form factor + + align:start position:0% +have in a very compact form factor + + + align:start position:0% +have in a very compact form factor +multiple uh uh devices in the third + + align:start position:0% +multiple uh uh devices in the third + + + align:start position:0% +multiple uh uh devices in the third +dimension you get lots of benefits of + + align:start position:0% +dimension you get lots of benefits of + + + align:start position:0% +dimension you get lots of benefits of +smaller footprint um at that coarse + + align:start position:0% +smaller footprint um at that coarse + + + align:start position:0% +smaller footprint um at that coarse +level of 3D uh I would say many several + + align:start position:0% +level of 3D uh I would say many several + + + align:start position:0% +level of 3D uh I would say many several +uh memory chip makers are already doing + + align:start position:0% +uh memory chip makers are already doing + + + align:start position:0% +uh memory chip makers are already doing +sort of Chip stacking within one package + + align:start position:0% +sort of Chip stacking within one package + + + align:start position:0% +sort of Chip stacking within one package +so in some of the memory chips if you + + align:start position:0% +so in some of the memory chips if you + + + align:start position:0% +so in some of the memory chips if you +were to you know etch away that sort of + + align:start position:0% +were to you know etch away that sort of + + + align:start position:0% +were to you know etch away that sort of +the black packaging and casing uh around + + align:start position:0% +the black packaging and casing uh around + + + align:start position:0% +the black packaging and casing uh around +one of those chips you might find a + + align:start position:0% +one of those chips you might find a + + + align:start position:0% +one of those chips you might find a +stacking + + align:start position:0% +stacking + + + align:start position:0% +stacking +uh but they are not heavily electrically + + align:start position:0% +uh but they are not heavily electrically + + + align:start position:0% +uh but they are not heavily electrically +interconnected it's not sort of like a + + align:start position:0% +interconnected it's not sort of like a + + + align:start position:0% +interconnected it's not sort of like a +fully integrated structure in fact at + + align:start position:0% +fully integrated structure in fact at + + + align:start position:0% +fully integrated structure in fact at +the end of the day they typically have + + align:start position:0% +the end of the day they typically have + + + align:start position:0% +the end of the day they typically have +Bond + + align:start position:0% +Bond + + + align:start position:0% +Bond +wires uh sort of big macroscopic wires + + align:start position:0% +wires uh sort of big macroscopic wires + + + align:start position:0% +wires uh sort of big macroscopic wires +coming in the sides of the chip + + align:start position:0% +coming in the sides of the chip + + + align:start position:0% +coming in the sides of the chip +separately at each of the uh of the + + align:start position:0% +separately at each of the uh of the + + + align:start position:0% +separately at each of the uh of the +stacking now there's other variants so + + align:start position:0% +stacking now there's other variants so + + + align:start position:0% +stacking now there's other variants so +for example um many of the uh thin film + + align:start position:0% +for example um many of the uh thin film + + + align:start position:0% +for example um many of the uh thin film +transistor + + align:start position:0% +transistor + + + align:start position:0% +transistor +TFT displays will actually have a layer + + align:start position:0% +TFT displays will actually have a layer + + + align:start position:0% +TFT displays will actually have a layer +of transistors that are a deposited + + align:start position:0% +of transistors that are a deposited + + + align:start position:0% +of transistors that are a deposited +layer of poly + + align:start position:0% +layer of poly + + + align:start position:0% +layer of poly +silicon not not quite the same pure + + align:start position:0% +silicon not not quite the same pure + + + align:start position:0% +silicon not not quite the same pure +crystallin layer and sometimes those + + align:start position:0% +crystallin layer and sometimes those + + + align:start position:0% +crystallin layer and sometimes those +include stacked transistors so there + + align:start position:0% +include stacked transistors so there + + + align:start position:0% +include stacked transistors so there +there are some technologies they're just + + align:start position:0% +there are some technologies they're just + + + align:start position:0% +there are some technologies they're just +not quite the same quality or the same + + align:start position:0% +not quite the same quality or the same + + + align:start position:0% +not quite the same quality or the same +high-speed + + align:start position:0% + + + + align:start position:0% + +nature okay anybody uh detect any + + align:start position:0% +nature okay anybody uh detect any + + + align:start position:0% +nature okay anybody uh detect any +other obvious mistakes or errors in + + align:start position:0% +other obvious mistakes or errors in + + + align:start position:0% +other obvious mistakes or errors in +their in their + + align:start position:0% +their in their + + + align:start position:0% +their in their +pictures maybe it was just that one that + + align:start position:0% +pictures maybe it was just that one that + + + align:start position:0% +pictures maybe it was just that one that +one uh inability to controllably etch + + align:start position:0% +one uh inability to controllably etch + + + align:start position:0% +one uh inability to controllably etch +down to a 100 + + align:start position:0% +down to a 100 + + + align:start position:0% +down to a 100 +angstrom now there's lots of other + + align:start position:0% +angstrom now there's lots of other + + + align:start position:0% +angstrom now there's lots of other +abstractions in here and one of the + + align:start position:0% +abstractions in here and one of the + + + align:start position:0% +abstractions in here and one of the +other neat things in this picture is + + align:start position:0% +other neat things in this picture is + + + align:start position:0% +other neat things in this picture is +it's showing you're building up a fairly + + align:start position:0% +it's showing you're building up a fairly + + + align:start position:0% +it's showing you're building up a fairly +complicated geometry using controllable + + align:start position:0% +complicated geometry using controllable + + + align:start position:0% +complicated geometry using controllable +processes one of the most important + + align:start position:0% +processes one of the most important + + + align:start position:0% +processes one of the most important +things that you have for control of this + + align:start position:0% +things that you have for control of this + + + align:start position:0% +things that you have for control of this +Lal differentiation is + + align:start position:0% +Lal differentiation is + + + align:start position:0% +Lal differentiation is +photolithography notice we were never + + align:start position:0% +photolithography notice we were never + + + align:start position:0% +photolithography notice we were never +just depositing directly aluminum where + + align:start position:0% +just depositing directly aluminum where + + + align:start position:0% +just depositing directly aluminum where +we wanted it it's always a deposit + + align:start position:0% +we wanted it it's always a deposit + + + align:start position:0% +we wanted it it's always a deposit +everywhere because you can do that + + align:start position:0% +everywhere because you can do that + + + align:start position:0% +everywhere because you can do that +across in parallel across the whole + + align:start position:0% +across in parallel across the whole + + + align:start position:0% +across in parallel across the whole +surface of the wafer and then have to go + + align:start position:0% +surface of the wafer and then have to go + + + align:start position:0% +surface of the wafer and then have to go +back into a subtractive process to to + + align:start position:0% +back into a subtractive process to to + + + align:start position:0% +back into a subtractive process to to +typically remove what you want there are + + align:start position:0% +typically remove what you want there are + + + align:start position:0% +typically remove what you want there are +very very few steps where you can + + align:start position:0% +very very few steps where you can + + + align:start position:0% +very very few steps where you can +selectively grow or selectively add + + align:start position:0% +selectively grow or selectively add + + + align:start position:0% +selectively grow or selectively add +material only where you want it + + align:start position:0% +material only where you want it + + + align:start position:0% +material only where you want it +okay so that's an example of a of a of a + + align:start position:0% +okay so that's an example of a of a of a + + + align:start position:0% +okay so that's an example of a of a of a +huge constraint in semiconductor + + align:start position:0% +huge constraint in semiconductor + + + align:start position:0% +huge constraint in semiconductor +processing so what I want to do now with + + align:start position:0% +processing so what I want to do now with + + + align:start position:0% +processing so what I want to do now with +that as the kind of the overview of the + + align:start position:0% +that as the kind of the overview of the + + + align:start position:0% +that as the kind of the overview of the +unit process and how they all stack up + + align:start position:0% +unit process and how they all stack up + + + align:start position:0% +unit process and how they all stack up +to build a more complicated structure I + + align:start position:0% +to build a more complicated structure I + + + align:start position:0% +to build a more complicated structure I +want to talk a little bit about sort of + + align:start position:0% +want to talk a little bit about sort of + + + align:start position:0% +want to talk a little bit about sort of +the input output kind of picture of of + + align:start position:0% +the input output kind of picture of of + + + align:start position:0% +the input output kind of picture of of +semiconductor processing this is very + + align:start position:0% +semiconductor processing this is very + + + align:start position:0% +semiconductor processing this is very +similar to uh our generic picture that + + align:start position:0% +similar to uh our generic picture that + + + align:start position:0% +similar to uh our generic picture that +hopefully you guys haveed started + + align:start position:0% +hopefully you guys haveed started + + + align:start position:0% +hopefully you guys haveed started +reading that process control overview + + align:start position:0% +reading that process control overview + + + align:start position:0% +reading that process control overview +where we've got different uh inputs to + + align:start position:0% +where we've got different uh inputs to + + + align:start position:0% +where we've got different uh inputs to +the unit process including the raw + + align:start position:0% +the unit process including the raw + + + align:start position:0% +the unit process including the raw +material the wafer we've got inputs in + + align:start position:0% +material the wafer we've got inputs in + + + align:start position:0% +material the wafer we've got inputs in +terms of the environment that we create + + align:start position:0% +terms of the environment that we create + + + align:start position:0% +terms of the environment that we create +around the wafer that vacuum process the + + align:start position:0% +around the wafer that vacuum process the + + + align:start position:0% +around the wafer that vacuum process the +chemical etchants the gas uh ambient uh + + align:start position:0% +chemical etchants the gas uh ambient uh + + + align:start position:0% +chemical etchants the gas uh ambient uh +used in plasma plasma etching and then + + align:start position:0% +used in plasma plasma etching and then + + + align:start position:0% +used in plasma plasma etching and then +other control factors on the machine or + + align:start position:0% +other control factors on the machine or + + + align:start position:0% +other control factors on the machine or +the facility things like thermal control + + align:start position:0% +the facility things like thermal control + + + align:start position:0% +the facility things like thermal control +in in photolithography to be able to + + align:start position:0% +in in photolithography to be able to + + + align:start position:0% +in in photolithography to be able to +ensure that there's not thermal + + align:start position:0% +ensure that there's not thermal + + + align:start position:0% +ensure that there's not thermal +expansion of the components and then we + + align:start position:0% +expansion of the components and then we + + + align:start position:0% +expansion of the components and then we +get changes in many of these Wafers uh + + align:start position:0% +get changes in many of these Wafers uh + + + align:start position:0% +get changes in many of these Wafers uh +many of these states many of these are + + align:start position:0% +many of these states many of these are + + + align:start position:0% +many of these states many of these are +desirable we saw the change in the wafer + + align:start position:0% +desirable we saw the change in the wafer + + + align:start position:0% +desirable we saw the change in the wafer +State terms of the geometry as well as + + align:start position:0% +State terms of the geometry as well as + + + align:start position:0% +State terms of the geometry as well as +things like doping processes that that + + align:start position:0% +things like doping processes that that + + + align:start position:0% +things like doping processes that that +change the conductivity of the Silicon + + align:start position:0% +change the conductivity of the Silicon + + + align:start position:0% +change the conductivity of the Silicon +layers but we also often have a side + + align:start position:0% +layers but we also often have a side + + + align:start position:0% +layers but we also often have a side +effects changes in the state of the + + align:start position:0% +effects changes in the state of the + + + align:start position:0% +effects changes in the state of the +equipment and this turns out to be a big + + align:start position:0% +equipment and this turns out to be a big + + + align:start position:0% +equipment and this turns out to be a big +deal in in much of semiconductor control + + align:start position:0% +deal in in much of semiconductor control + + + align:start position:0% +deal in in much of semiconductor control +so for example every one of those + + align:start position:0% +so for example every one of those + + + align:start position:0% +so for example every one of those +coating processes occurs in some kind of + + align:start position:0% +coating processes occurs in some kind of + + + align:start position:0% +coating processes occurs in some kind of +a chamber I coat up a film I coat + + align:start position:0% +a chamber I coat up a film I coat + + + align:start position:0% +a chamber I coat up a film I coat +aluminum on the surface of the wafer + + align:start position:0% +aluminum on the surface of the wafer + + + align:start position:0% +aluminum on the surface of the wafer +what do you think happens to the rest of + + align:start position:0% +what do you think happens to the rest of + + + align:start position:0% +what do you think happens to the rest of +the + + align:start position:0% +the + + + align:start position:0% +the +chamber it gets coated too so over time + + align:start position:0% +chamber it gets coated too so over time + + + align:start position:0% +chamber it gets coated too so over time +you will often get buildup of material + + align:start position:0% +you will often get buildup of material + + + align:start position:0% +you will often get buildup of material +in the rest of the equipment and there + + align:start position:0% +in the rest of the equipment and there + + + align:start position:0% +in the rest of the equipment and there +will need to be other steps to go in and + + align:start position:0% +will need to be other steps to go in and + + + align:start position:0% +will need to be other steps to go in and +clean or reset the equipment state so + + align:start position:0% +clean or reset the equipment state so + + + align:start position:0% +clean or reset the equipment state so +actually we often are worried not not + + align:start position:0% +actually we often are worried not not + + + align:start position:0% +actually we often are worried not not +only about the product and what's + + align:start position:0% +only about the product and what's + + + align:start position:0% +only about the product and what's +happening with the product but in + + align:start position:0% +happening with the product but in + + + align:start position:0% +happening with the product but in +manufacturing control we're also very + + align:start position:0% +manufacturing control we're also very + + + align:start position:0% +manufacturing control we're also very +worried about what's happening with the + + align:start position:0% +worried about what's happening with the + + + align:start position:0% +worried about what's happening with the +equipment so what we often don't have + + align:start position:0% +equipment so what we often don't have + + + align:start position:0% +equipment so what we often don't have +control over are all these disturbances + + align:start position:0% +control over are all these disturbances + + + align:start position:0% +control over are all these disturbances +there may be + + align:start position:0% +there may be + + + align:start position:0% +there may be +variations in the process coming from + + align:start position:0% +variations in the process coming from + + + align:start position:0% +variations in the process coming from +lots of different + + align:start position:0% +lots of different + + + align:start position:0% +lots of different +sources some might be the incoming + + align:start position:0% +sources some might be the incoming + + + align:start position:0% +sources some might be the incoming +material in this case if there's + + align:start position:0% +material in this case if there's + + + align:start position:0% +material in this case if there's +variability in the starting wafer or the + + align:start position:0% +variability in the starting wafer or the + + + align:start position:0% +variability in the starting wafer or the +wafer as processed up to some step that + + align:start position:0% +wafer as processed up to some step that + + + align:start position:0% +wafer as processed up to some step that +might interact with the step that we're + + align:start position:0% +might interact with the step that we're + + + align:start position:0% +might interact with the step that we're +now performing uh and and limit our + + align:start position:0% +now performing uh and and limit our + + + align:start position:0% +now performing uh and and limit our +ability to control and then similarly + + align:start position:0% +ability to control and then similarly + + + align:start position:0% +ability to control and then similarly +there may be influences A variation + + align:start position:0% +there may be influences A variation + + + align:start position:0% +there may be influences A variation +coming from uh the machine or the + + align:start position:0% +coming from uh the machine or the + + + align:start position:0% +coming from uh the machine or the +facility uh or the wafer environment so + + align:start position:0% +facility uh or the wafer environment so + + + align:start position:0% +facility uh or the wafer environment so +what I want to do is talk a little bit + + align:start position:0% +what I want to do is talk a little bit + + + align:start position:0% +what I want to do is talk a little bit +about some of those different kinds of + + align:start position:0% +about some of those different kinds of + + + align:start position:0% +about some of those different kinds of +kinds of variations uh and build on what + + align:start position:0% +kinds of variations uh and build on what + + + align:start position:0% +kinds of variations uh and build on what +we've seen here now I mentioned this a + + align:start position:0% +we've seen here now I mentioned this a + + + align:start position:0% +we've seen here now I mentioned this a +little + + align:start position:0% +little + + + align:start position:0% +little +bit uh last time it used to be 10 years + + align:start position:0% +bit uh last time it used to be 10 years + + + align:start position:0% +bit uh last time it used to be 10 years +ago 15 years ago if we talked about + + align:start position:0% +ago 15 years ago if we talked about + + + align:start position:0% +ago 15 years ago if we talked about +yield + + align:start position:0% +yield + + + align:start position:0% +yield +the percentage of functioning devices + + align:start position:0% +the percentage of functioning devices + + + align:start position:0% +the percentage of functioning devices +that came out of a semiconductor Fab the + + align:start position:0% +that came out of a semiconductor Fab the + + + align:start position:0% +that came out of a semiconductor Fab the +main worry limiting yield were was + + align:start position:0% +main worry limiting yield were was + + + align:start position:0% +main worry limiting yield were was +particle defects and you can imagine + + align:start position:0% +particle defects and you can imagine + + + align:start position:0% +particle defects and you can imagine +we're talking about very very small + + align:start position:0% +we're talking about very very small + + + align:start position:0% +we're talking about very very small +features here and if pieces of + + align:start position:0% +features here and if pieces of + + + align:start position:0% +features here and if pieces of +extraneous matter were to fall between + + align:start position:0% +extraneous matter were to fall between + + + align:start position:0% +extraneous matter were to fall between +say two metal lines that would cause an + + align:start position:0% +say two metal lines that would cause an + + + align:start position:0% +say two metal lines that would cause an +electrical short or could cause an + + align:start position:0% +electrical short or could cause an + + + align:start position:0% +electrical short or could cause an +electrical short and now the device does + + align:start position:0% +electrical short and now the device does + + + align:start position:0% +electrical short and now the device does +not function it does not function + + align:start position:0% +not function it does not function + + + align:start position:0% +not function it does not function +correctly uh in other cases the particle + + align:start position:0% +correctly uh in other cases the particle + + + align:start position:0% +correctly uh in other cases the particle +if it happened to appear uh in the photo + + align:start position:0% +if it happened to appear uh in the photo + + + align:start position:0% +if it happened to appear uh in the photo +resist it might cause an open in one of + + align:start position:0% +resist it might cause an open in one of + + + align:start position:0% +resist it might cause an open in one of +these lines it + + align:start position:0% +these lines it + + + align:start position:0% +these lines it +might um uh prevent or or cause uh me to + + align:start position:0% +might um uh prevent or or cause uh me to + + + align:start position:0% +might um uh prevent or or cause uh me to +etch away regions where I didn't want to + + align:start position:0% +etch away regions where I didn't want to + + + align:start position:0% +etch away regions where I didn't want to +so not only can I have shorts I might + + align:start position:0% +so not only can I have shorts I might + + + align:start position:0% +so not only can I have shorts I might +have opens between lines and this defect + + align:start position:0% +have opens between lines and this defect + + + align:start position:0% +have opens between lines and this defect +control was the primary source of yield + + align:start position:0% +control was the primary source of yield + + + align:start position:0% +control was the primary source of yield +loss in the fat and so there's been ex + + align:start position:0% +loss in the fat and so there's been ex + + + align:start position:0% +loss in the fat and so there's been ex +that's why if you go into an IC Fab it's + + align:start position:0% +that's why if you go into an IC Fab it's + + + align:start position:0% +that's why if you go into an IC Fab it's +a clean room everybody's wearing clean + + align:start position:0% +a clean room everybody's wearing clean + + + align:start position:0% +a clean room everybody's wearing clean +room garments there's incredible amounts + + align:start position:0% +room garments there's incredible amounts + + + align:start position:0% +room garments there's incredible amounts +of air flow to filter out and remove uh + + align:start position:0% +of air flow to filter out and remove uh + + + align:start position:0% +of air flow to filter out and remove uh +all kinds of dust particles or other + + align:start position:0% +all kinds of dust particles or other + + + align:start position:0% +all kinds of dust particles or other +extraneous matter down to very very tiny + + align:start position:0% +extraneous matter down to very very tiny + + + align:start position:0% +extraneous matter down to very very tiny +Dimensions uh that's really the measures + + align:start position:0% +Dimensions uh that's really the measures + + + align:start position:0% +Dimensions uh that's really the measures +that have been taken in order to get the + + align:start position:0% +that have been taken in order to get the + + + align:start position:0% +that have been taken in order to get the +cleanliness you need in order + + align:start position:0% +cleanliness you need in order + + + align:start position:0% +cleanliness you need in order +to not eliminate but get those particles + + align:start position:0% +to not eliminate but get those particles + + + align:start position:0% +to not eliminate but get those particles +down to a a particle density and down to + + align:start position:0% +down to a a particle density and down to + + + align:start position:0% +down to a a particle density and down to +a presence of size that are small enough + + align:start position:0% +a presence of size that are small enough + + + align:start position:0% +a presence of size that are small enough +not to have too big of a yield impact + + align:start position:0% +not to have too big of a yield impact + + + align:start position:0% +not to have too big of a yield impact +what I mean by size is imagine that uh + + align:start position:0% +what I mean by size is imagine that uh + + + align:start position:0% +what I mean by size is imagine that uh +that little dust particle is only a + + align:start position:0% +that little dust particle is only a + + + align:start position:0% +that little dust particle is only a +quarter of the width of any of the + + align:start position:0% +quarter of the width of any of the + + + align:start position:0% +quarter of the width of any of the +minimum feature size on your structure + + align:start position:0% +minimum feature size on your structure + + + align:start position:0% +minimum feature size on your structure +well that might mean I I lose a quarter + + align:start position:0% +well that might mean I I lose a quarter + + + align:start position:0% +well that might mean I I lose a quarter +of the width of one of those metal lines + + align:start position:0% +of the width of one of those metal lines + + + align:start position:0% +of the width of one of those metal lines +but at least it still conducts it might + + align:start position:0% +but at least it still conducts it might + + + align:start position:0% +but at least it still conducts it might +have a slightly higher resistance than I + + align:start position:0% +have a slightly higher resistance than I + + + align:start position:0% +have a slightly higher resistance than I +expect but functionally I'm still okay + + align:start position:0% +expect but functionally I'm still okay + + + align:start position:0% +expect but functionally I'm still okay +similarly if if it's too small of a + + align:start position:0% +similarly if if it's too small of a + + + align:start position:0% +similarly if if it's too small of a +particle to bridge between lines I'm not + + align:start position:0% +particle to bridge between lines I'm not + + + align:start position:0% +particle to bridge between lines I'm not +going to have a short so the the idea is + + align:start position:0% +going to have a short so the the idea is + + + align:start position:0% +going to have a short so the the idea is +to control the particles down to a + + align:start position:0% +to control the particles down to a + + + align:start position:0% +to control the particles down to a +certain feature now there are some very + + align:start position:0% +certain feature now there are some very + + + align:start position:0% +certain feature now there are some very +interesting manufacturing control + + align:start position:0% +interesting manufacturing control + + + align:start position:0% +interesting manufacturing control +Technologies that are used to uh + + align:start position:0% +Technologies that are used to uh + + + align:start position:0% +Technologies that are used to uh +characterize the presence and density of + + align:start position:0% +characterize the presence and density of + + + align:start position:0% +characterize the presence and density of +these kinds of + + align:start position:0% +these kinds of + + + align:start position:0% +these kinds of +particles and I what I've pictured here + + align:start position:0% +particles and I what I've pictured here + + + align:start position:0% +particles and I what I've pictured here +is a a metal layout a metal pattern + + align:start position:0% +is a a metal layout a metal pattern + + + align:start position:0% +is a a metal layout a metal pattern +structure referred to as a nest + + align:start position:0% +structure referred to as a nest + + + align:start position:0% +structure referred to as a nest +structure that allows one to uh build a + + align:start position:0% +structure that allows one to uh build a + + + align:start position:0% +structure that allows one to uh build a +large number of these these sort of + + align:start position:0% +large number of these these sort of + + + align:start position:0% +large number of these these sort of +snaking lines and electrically connect + + align:start position:0% +snaking lines and electrically connect + + + align:start position:0% +snaking lines and electrically connect +between these different lines in order + + align:start position:0% +between these different lines in order + + + align:start position:0% +between these different lines in order +to test if there is a bridging defect + + align:start position:0% +to test if there is a bridging defect + + + align:start position:0% +to test if there is a bridging defect +between lines and count the number of + + align:start position:0% +between lines and count the number of + + + align:start position:0% +between lines and count the number of +those events so you build this structure + + align:start position:0% +those events so you build this structure + + + align:start position:0% +those events so you build this structure +to sort of spatially sample as large an + + align:start position:0% +to sort of spatially sample as large an + + + align:start position:0% +to sort of spatially sample as large an +area as you can to try to capture some + + align:start position:0% +area as you can to try to capture some + + + align:start position:0% +area as you can to try to capture some +number of these defects and you can also + + align:start position:0% +number of these defects and you can also + + + align:start position:0% +number of these defects and you can also +use this structure to characterize the + + align:start position:0% +use this structure to characterize the + + + align:start position:0% +use this structure to characterize the +size of these defects especially if + + align:start position:0% +size of these defects especially if + + + align:start position:0% +size of these defects especially if +they're relatively large so for example + + align:start position:0% +they're relatively large so for example + + + align:start position:0% +they're relatively large so for example +if I had a a big particle that bridged + + align:start position:0% +if I had a a big particle that bridged + + + align:start position:0% +if I had a a big particle that bridged +three of these lines I know within + + align:start position:0% +three of these lines I know within + + + align:start position:0% +three of these lines I know within +certain uh bounds that I've got a a a a + + align:start position:0% +certain uh bounds that I've got a a a a + + + align:start position:0% +certain uh bounds that I've got a a a a +a particle between some uh size interval + + align:start position:0% +a particle between some uh size interval + + + align:start position:0% +a particle between some uh size interval +and so that's what's shown over here is + + align:start position:0% +and so that's what's shown over here is + + + align:start position:0% +and so that's what's shown over here is +kind of a defect count as a function of + + align:start position:0% +kind of a defect count as a function of + + + align:start position:0% +kind of a defect count as a function of +the size in microns of of different + + align:start position:0% +the size in microns of of different + + + align:start position:0% +the size in microns of of different +different particles for these large area + + align:start position:0% +different particles for these large area + + + align:start position:0% +different particles for these large area +sampling structures now this turns out + + align:start position:0% +sampling structures now this turns out + + + align:start position:0% +sampling structures now this turns out +to be still a uh an important part of + + align:start position:0% +to be still a uh an important part of + + + align:start position:0% +to be still a uh an important part of +semiconductor fabrication is + + align:start position:0% +semiconductor fabrication is + + + align:start position:0% +semiconductor fabrication is +understanding your defect densities + + align:start position:0% +understanding your defect densities + + + align:start position:0% +understanding your defect densities +defect counts uh + + align:start position:0% +defect counts uh + + + align:start position:0% +defect counts uh +understanding uh what the typical sizes + + align:start position:0% +understanding uh what the typical sizes + + + align:start position:0% +understanding uh what the typical sizes +are what levels of the process they come + + align:start position:0% +are what levels of the process they come + + + align:start position:0% +are what levels of the process they come +in uh you know are you mostly getting + + align:start position:0% +in uh you know are you mostly getting + + + align:start position:0% +in uh you know are you mostly getting +these in aluminum deposition are you + + align:start position:0% +these in aluminum deposition are you + + + align:start position:0% +these in aluminum deposition are you +mostly getting these in in other etge + + align:start position:0% +mostly getting these in in other etge + + + align:start position:0% +mostly getting these in in other etge +processes and actually then feeding that + + align:start position:0% +processes and actually then feeding that + + + align:start position:0% +processes and actually then feeding that +information to design for design for + + align:start position:0% +information to design for design for + + + align:start position:0% +information to design for design for +manufacturability to optimize the layout + + align:start position:0% +manufacturability to optimize the layout + + + align:start position:0% +manufacturability to optimize the layout +of the circuit to minimize the + + align:start position:0% +of the circuit to minimize the + + + align:start position:0% +of the circuit to minimize the +likelihood of a particle falling in a + + align:start position:0% +likelihood of a particle falling in a + + + align:start position:0% +likelihood of a particle falling in a +bad + + align:start position:0% +bad + + + align:start position:0% +bad +location okay and we'll talk about that + + align:start position:0% +location okay and we'll talk about that + + + align:start position:0% +location okay and we'll talk about that +I think somewhere near the midpoint or + + align:start position:0% +I think somewhere near the midpoint or + + + align:start position:0% +I think somewhere near the midpoint or +second uh last third of the of the + + align:start position:0% +second uh last third of the of the + + + align:start position:0% +second uh last third of the of the +course we'll talk about yield modeling + + align:start position:0% +course we'll talk about yield modeling + + + align:start position:0% +course we'll talk about yield modeling +and some of the technologies that are + + align:start position:0% +and some of the technologies that are + + + align:start position:0% +and some of the technologies that are +used for + + align:start position:0% +used for + + + align:start position:0% +used for +characterizing uh statistically the uh + + align:start position:0% +characterizing uh statistically the uh + + + align:start position:0% +characterizing uh statistically the uh +uh Point defects particle defects and + + align:start position:0% +uh Point defects particle defects and + + + align:start position:0% +uh Point defects particle defects and +some of the strategies used for for + + align:start position:0% +some of the strategies used for for + + + align:start position:0% +some of the strategies used for for +optimizing uh or minimize the impact on + + align:start position:0% +optimizing uh or minimize the impact on + + + align:start position:0% +optimizing uh or minimize the impact on +circuits but what is becoming much more + + align:start position:0% +circuits but what is becoming much more + + + align:start position:0% +circuits but what is becoming much more +important and we mentioned this uh on + + align:start position:0% +important and we mentioned this uh on + + + align:start position:0% +important and we mentioned this uh on +Tuesday as well is parametric control + + align:start position:0% +Tuesday as well is parametric control + + + align:start position:0% +Tuesday as well is parametric control +and in some cases even these defect + + align:start position:0% +and in some cases even these defect + + + align:start position:0% +and in some cases even these defect +controls turn into parametric control + + align:start position:0% +controls turn into parametric control + + + align:start position:0% +controls turn into parametric control +problems if what I'm worried about is + + align:start position:0% +problems if what I'm worried about is + + + align:start position:0% +problems if what I'm worried about is +not so much yes no functionality but + + align:start position:0% +not so much yes no functionality but + + + align:start position:0% +not so much yes no functionality but +changes in the resistance of + + align:start position:0% +changes in the resistance of + + + align:start position:0% +changes in the resistance of +lines because of the presence of defects + + align:start position:0% +lines because of the presence of defects + + + align:start position:0% +lines because of the presence of defects +and + + align:start position:0% +and + + + align:start position:0% +and +so much more broadly than defects we're + + align:start position:0% +so much more broadly than defects we're + + + align:start position:0% +so much more broadly than defects we're +much more concerned with uh Contin + + align:start position:0% +much more concerned with uh Contin + + + align:start position:0% +much more concerned with uh Contin +continuous parameter control of geometry + + align:start position:0% +continuous parameter control of geometry + + + align:start position:0% +continuous parameter control of geometry +as well as some of these other + + align:start position:0% +as well as some of these other + + + align:start position:0% +as well as some of these other +properties that we saw in the sequence + + align:start position:0% +properties that we saw in the sequence + + + align:start position:0% +properties that we saw in the sequence +so for example that critical Dimension + + align:start position:0% +so for example that critical Dimension + + + align:start position:0% +so for example that critical Dimension +control might + + align:start position:0% +control might + + + align:start position:0% +control might +be the channel length of transistors on + + align:start position:0% +be the channel length of transistors on + + + align:start position:0% +be the channel length of transistors on +my device and inherently you're going to + + align:start position:0% +my device and inherently you're going to + + + align:start position:0% +my device and inherently you're going to +have some statistical Distribution on + + align:start position:0% +have some statistical Distribution on + + + align:start position:0% +have some statistical Distribution on +channel length call that L okay so for + + align:start position:0% +channel length call that L okay so for + + + align:start position:0% +channel length call that L okay so for +example if I were let me start down here + + align:start position:0% +example if I were let me start down here + + + align:start position:0% +example if I were let me start down here +if I were to to + + align:start position:0% +if I were to to + + + align:start position:0% +if I were to to +sample uh many nominally identical + + align:start position:0% +sample uh many nominally identical + + + align:start position:0% +sample uh many nominally identical +transistors that were laid out exactly + + align:start position:0% +transistors that were laid out exactly + + + align:start position:0% +transistors that were laid out exactly +the same or assumed to behave exactly + + align:start position:0% +the same or assumed to behave exactly + + + align:start position:0% +the same or assumed to behave exactly +the same and I measured some electrical + + align:start position:0% +the same and I measured some electrical + + + align:start position:0% +the same and I measured some electrical +characteristic or some geometric + + align:start position:0% +characteristic or some geometric + + + align:start position:0% +characteristic or some geometric +characteristic I might get a + + align:start position:0% +characteristic I might get a + + + align:start position:0% +characteristic I might get a +distribution drawn here as a gaussian + + align:start position:0% +distribution drawn here as a gaussian + + + align:start position:0% +distribution drawn here as a gaussian +it's not always but but very often + + align:start position:0% +it's not always but but very often + + + align:start position:0% +it's not always but but very often +that's a great model and I might have + + align:start position:0% +that's a great model and I might have + + + align:start position:0% +that's a great model and I might have +some distribution of that across the + + align:start position:0% +some distribution of that across the + + + align:start position:0% +some distribution of that across the +Chip And that very often there are + + align:start position:0% +Chip And that very often there are + + + align:start position:0% +Chip And that very often there are +inherent physical limitations in the + + align:start position:0% +inherent physical limitations in the + + + align:start position:0% +inherent physical limitations in the +process that that give rise to those + + align:start position:0% +process that that give rise to those + + + align:start position:0% +process that that give rise to those +sources of + + align:start position:0% +sources of + + + align:start position:0% +sources of +variation um some of which will come + + align:start position:0% +variation um some of which will come + + + align:start position:0% +variation um some of which will come +back to might be systematic or might be + + align:start position:0% +back to might be systematic or might be + + + align:start position:0% +back to might be systematic or might be +random now what's interesting is in we + + align:start position:0% +random now what's interesting is in we + + + align:start position:0% +random now what's interesting is in we +have a physical nesting on the wafer we + + align:start position:0% +have a physical nesting on the wafer we + + + align:start position:0% +have a physical nesting on the wafer we +have many chips now if I were to take + + align:start position:0% +have many chips now if I were to take + + + align:start position:0% +have many chips now if I were to take +and measure the same transistor on each + + align:start position:0% +and measure the same transistor on each + + + align:start position:0% +and measure the same transistor on each +chip I would also get a distribution I + + align:start position:0% +chip I would also get a distribution I + + + align:start position:0% +chip I would also get a distribution I +have chipto chip variability in + + align:start position:0% +have chipto chip variability in + + + align:start position:0% +have chipto chip variability in +parameters and often that will come + + align:start position:0% +parameters and often that will come + + + align:start position:0% +parameters and often that will come +because of of different physical causes + + align:start position:0% +because of of different physical causes + + + align:start position:0% +because of of different physical causes +it may be we're doing that + + align:start position:0% +it may be we're doing that + + + align:start position:0% +it may be we're doing that +photolithographic stepping and every + + align:start position:0% +photolithographic stepping and every + + + align:start position:0% +photolithographic stepping and every +time I have a little bit different + + align:start position:0% +time I have a little bit different + + + align:start position:0% +time I have a little bit different +overlay control or offset control so the + + align:start position:0% +overlay control or offset control so the + + + align:start position:0% +overlay control or offset control so the +source of this may be uh this + + align:start position:0% +source of this may be uh this + + + align:start position:0% +source of this may be uh this +distribution may be because of a wafer + + align:start position:0% +distribution may be because of a wafer + + + align:start position:0% +distribution may be because of a wafer +level or AC cross wafer sources of + + align:start position:0% +level or AC cross wafer sources of + + + align:start position:0% +level or AC cross wafer sources of +variation that are very different than + + align:start position:0% +variation that are very different than + + + align:start position:0% +variation that are very different than +the sources of physical variation of + + align:start position:0% +the sources of physical variation of + + + align:start position:0% +the sources of physical variation of +replication of transistors within the + + align:start position:0% +replication of transistors within the + + + align:start position:0% +replication of transistors within the +chip now we also can have wafer to wafer + + align:start position:0% +chip now we also can have wafer to wafer + + + align:start position:0% +chip now we also can have wafer to wafer +variations again if I were to either + + align:start position:0% +variations again if I were to either + + + align:start position:0% +variations again if I were to either +calculate the average over one wafer or + + align:start position:0% +calculate the average over one wafer or + + + align:start position:0% +calculate the average over one wafer or +maybe just sample exactly the same + + align:start position:0% +maybe just sample exactly the same + + + align:start position:0% +maybe just sample exactly the same +location on every wafer and stack that + + align:start position:0% +location on every wafer and stack that + + + align:start position:0% +location on every wafer and stack that +up + + align:start position:0% +up + + + align:start position:0% +up +across 20 24 Wafers or large numbers of + + align:start position:0% +across 20 24 Wafers or large numbers of + + + align:start position:0% +across 20 24 Wafers or large numbers of +of Wafers that might be in one + + align:start position:0% +of Wafers that might be in one + + + align:start position:0% +of Wafers that might be in one +lot processed even relatively close in + + align:start position:0% +lot processed even relatively close in + + + align:start position:0% +lot processed even relatively close in +time to each other there's also going to + + align:start position:0% +time to each other there's also going to + + + align:start position:0% +time to each other there's also going to +be a deviation and that might arise + + align:start position:0% +be a deviation and that might arise + + + align:start position:0% +be a deviation and that might arise +because of changes in the equipment + + align:start position:0% +because of changes in the equipment + + + align:start position:0% +because of changes in the equipment +state from one run to the next right the + + align:start position:0% +state from one run to the next right the + + + align:start position:0% +state from one run to the next right the +first wafer it may have a + + align:start position:0% +first wafer it may have a + + + align:start position:0% +first wafer it may have a +pristine uh equipment with no buildup on + + align:start position:0% +pristine uh equipment with no buildup on + + + align:start position:0% +pristine uh equipment with no buildup on +the on the of material on the wafer wall + + align:start position:0% +the on the of material on the wafer wall + + + align:start position:0% +the on the of material on the wafer wall +the next wafer might see a slightly + + align:start position:0% +the next wafer might see a slightly + + + align:start position:0% +the next wafer might see a slightly +different process unintentionally than + + align:start position:0% +different process unintentionally than + + + align:start position:0% +different process unintentionally than +the previous one because of changes or + + align:start position:0% +the previous one because of changes or + + + align:start position:0% +the previous one because of changes or +degradation in the W in the equipment + + align:start position:0% +degradation in the W in the equipment + + + align:start position:0% +degradation in the W in the equipment +State over time affecting that wafer + + align:start position:0% +State over time affecting that wafer + + + align:start position:0% +State over time affecting that wafer +state that might be an example and then + + align:start position:0% +state that might be an example and then + + + align:start position:0% +state that might be an example and then +finally in semiconductor Fab we + + align:start position:0% +finally in semiconductor Fab we + + + align:start position:0% +finally in semiconductor Fab we +typically are are processing a lot of + + align:start position:0% +typically are are processing a lot of + + + align:start position:0% +typically are are processing a lot of +Wafers that may be 24 Wafers at a time + + align:start position:0% +Wafers that may be 24 Wafers at a time + + + align:start position:0% +Wafers that may be 24 Wafers at a time +and from one lot to the next these might + + align:start position:0% +and from one lot to the next these might + + + align:start position:0% +and from one lot to the next these might +be processed uh at substantially + + align:start position:0% +be processed uh at substantially + + + align:start position:0% +be processed uh at substantially +different points in time and there may + + align:start position:0% +different points in time and there may + + + align:start position:0% +different points in time and there may +be another distribution associated with + + align:start position:0% +be another distribution associated with + + + align:start position:0% +be another distribution associated with +that and physical sources or causes of + + align:start position:0% +that and physical sources or causes of + + + align:start position:0% +that and physical sources or causes of +that variation that are different than + + align:start position:0% +that variation that are different than + + + align:start position:0% +that variation that are different than +these other spatial or temporal + + align:start position:0% +these other spatial or temporal + + + align:start position:0% +these other spatial or temporal +sources some companies there's not a lot + + align:start position:0% +sources some companies there's not a lot + + + align:start position:0% +sources some companies there's not a lot +of them uh these days have multiple Fabs + + align:start position:0% +of them uh these days have multiple Fabs + + + align:start position:0% +of them uh these days have multiple Fabs +so I could continue this up um Intel in + + align:start position:0% +so I could continue this up um Intel in + + + align:start position:0% +so I could continue this up um Intel in +particular is very famous for making the + + align:start position:0% +particular is very famous for making the + + + align:start position:0% +particular is very famous for making the +same product in multiple Fabs in + + align:start position:0% +same product in multiple Fabs in + + + align:start position:0% +same product in multiple Fabs in +multiple States and in fact multiple + + align:start position:0% +multiple States and in fact multiple + + + align:start position:0% +multiple States and in fact multiple +countries uh around the world and they + + align:start position:0% +countries uh around the world and they + + + align:start position:0% +countries uh around the world and they +work very very hard to have matching + + align:start position:0% +work very very hard to have matching + + + align:start position:0% +work very very hard to have matching +from one Fab to the other in terms of + + align:start position:0% +from one Fab to the other in terms of + + + align:start position:0% +from one Fab to the other in terms of +the equipment and so on to minimize Fab + + align:start position:0% +the equipment and so on to minimize Fab + + + align:start position:0% +the equipment and so on to minimize Fab +Toof Fab deviations or differences in + + align:start position:0% +Toof Fab deviations or differences in + + + align:start position:0% +Toof Fab deviations or differences in +their chips they really don't want + + align:start position:0% +their chips they really don't want + + + align:start position:0% +their chips they really don't want +people saying I'm only going to buy you + + align:start position:0% +people saying I'm only going to buy you + + + align:start position:0% +people saying I'm only going to buy you +know my my Pentium or or what iium chip + + align:start position:0% +know my my Pentium or or what iium chip + + + align:start position:0% +know my my Pentium or or what iium chip +from the Albuquerque Fab because it's + + align:start position:0% +from the Albuquerque Fab because it's + + + align:start position:0% +from the Albuquerque Fab because it's +better than the one + + align:start position:0% +better than the one + + + align:start position:0% +better than the one +from Portland or whatever they they + + align:start position:0% +from Portland or whatever they they + + + align:start position:0% +from Portland or whatever they they +really want to minimize that so so + + align:start position:0% +really want to minimize that so so + + + align:start position:0% +really want to minimize that so so +you've got you know extensions up the up + + align:start position:0% +you've got you know extensions up the up + + + align:start position:0% +you've got you know extensions up the up +the hierarchy as + + align:start position:0% +the hierarchy as + + + align:start position:0% +the hierarchy as +well now if we were to actually zoom in + + align:start position:0% +well now if we were to actually zoom in + + + align:start position:0% +well now if we were to actually zoom in +on one of those distributions what's + + align:start position:0% +on one of those distributions what's + + + align:start position:0% +on one of those distributions what's +also going to be very interesting is + + align:start position:0% +also going to be very interesting is + + + align:start position:0% +also going to be very interesting is +trying to understand what the sources of + + align:start position:0% +trying to understand what the sources of + + + align:start position:0% +trying to understand what the sources of +variation are at each of the spatial + + align:start position:0% +variation are at each of the spatial + + + align:start position:0% +variation are at each of the spatial +scale + + align:start position:0% +scale + + + align:start position:0% +scale +and you might have a fairly complex + + align:start position:0% +and you might have a fairly complex + + + align:start position:0% +and you might have a fairly complex +distribution say over Channel length and + + align:start position:0% +distribution say over Channel length and + + + align:start position:0% +distribution say over Channel length and +what's often very the very very much the + + align:start position:0% +what's often very the very very much the + + + align:start position:0% +what's often very the very very much the +case and very interesting is that Total + + align:start position:0% +case and very interesting is that Total + + + align:start position:0% +case and very interesting is that Total +distribution is the compounded effect of + + align:start position:0% +distribution is the compounded effect of + + + align:start position:0% +distribution is the compounded effect of +multiple additional sources that are + + align:start position:0% +multiple additional sources that are + + + align:start position:0% +multiple additional sources that are +sort of convolved together and a lot of + + align:start position:0% +sort of convolved together and a lot of + + + align:start position:0% +sort of convolved together and a lot of +work will be done in designing test + + align:start position:0% +work will be done in designing test + + + align:start position:0% +work will be done in designing test +procedures uh designing process control + + align:start position:0% +procedures uh designing process control + + + align:start position:0% +procedures uh designing process control +charts and whatnot to be able to track + + align:start position:0% +charts and whatnot to be able to track + + + align:start position:0% +charts and whatnot to be able to track +IND individual contributors and separate + + align:start position:0% +IND individual contributors and separate + + + align:start position:0% +IND individual contributors and separate +them out into the component sources of + + align:start position:0% +them out into the component sources of + + + align:start position:0% +them out into the component sources of +variation why do you want to do + + align:start position:0% +variation why do you want to do + + + align:start position:0% +variation why do you want to do +this if you can identify individual + + align:start position:0% +this if you can identify individual + + + align:start position:0% +this if you can identify individual +sources that's crucial to being able to + + align:start position:0% +sources that's crucial to being able to + + + align:start position:0% +sources that's crucial to being able to +go and squeeze them down right you got + + align:start position:0% +go and squeeze them down right you got + + + align:start position:0% +go and squeeze them down right you got +to know what the source is in in order + + align:start position:0% +to know what the source is in in order + + + align:start position:0% +to know what the source is in in order +to remove it what else is the case often + + align:start position:0% +to remove it what else is the case often + + + align:start position:0% +to remove it what else is the case often +is that some of these are not completely + + align:start position:0% +is that some of these are not completely + + + align:start position:0% +is that some of these are not completely +random many of the sources of variation + + align:start position:0% +random many of the sources of variation + + + align:start position:0% +random many of the sources of variation +have a systematic physical cause and + + align:start position:0% +have a systematic physical cause and + + + align:start position:0% +have a systematic physical cause and +if we understand what is systematic or + + align:start position:0% +if we understand what is systematic or + + + align:start position:0% +if we understand what is systematic or +repeatable every every time you you run + + align:start position:0% +repeatable every every time you you run + + + align:start position:0% +repeatable every every time you you run +this you might actually find that the + + align:start position:0% +this you might actually find that the + + + align:start position:0% +this you might actually find that the +transistor in the upper right corner of + + align:start position:0% +transistor in the upper right corner of + + + align:start position:0% +transistor in the upper right corner of +the chip is a little bit too wide you + + align:start position:0% +the chip is a little bit too wide you + + + align:start position:0% +the chip is a little bit too wide you +might then track that back to the photo + + align:start position:0% +might then track that back to the photo + + + align:start position:0% +might then track that back to the photo +lithographic imperfection that's causing + + align:start position:0% +lithographic imperfection that's causing + + + align:start position:0% +lithographic imperfection that's causing +that once you know that you can + + align:start position:0% +that once you know that you can + + + align:start position:0% +that once you know that you can +compensate can counteract that source of + + align:start position:0% +compensate can counteract that source of + + + align:start position:0% +compensate can counteract that source of +variation so that's a lot of the work is + + align:start position:0% +variation so that's a lot of the work is + + + align:start position:0% +variation so that's a lot of the work is +trying to um break these down so let me + + align:start position:0% +trying to um break these down so let me + + + align:start position:0% +trying to um break these down so let me +give you a little bit more example of + + align:start position:0% +give you a little bit more example of + + + align:start position:0% +give you a little bit more example of +some of these uh sources of + + align:start position:0% +some of these uh sources of + + + align:start position:0% +some of these uh sources of +variation and the tools and techniques + + align:start position:0% +variation and the tools and techniques + + + align:start position:0% +variation and the tools and techniques +that are evolving to handle + + align:start position:0% + + + + align:start position:0% + +them let me zoom into one unit process + + align:start position:0% +them let me zoom into one unit process + + + align:start position:0% +them let me zoom into one unit process +uh we've done actually a lot of research + + align:start position:0% +uh we've done actually a lot of research + + + align:start position:0% +uh we've done actually a lot of research +on chemical mechanical polishing in + + align:start position:0% +on chemical mechanical polishing in + + + align:start position:0% +on chemical mechanical polishing in +semiconductor Fab and the basic process + + align:start position:0% +semiconductor Fab and the basic process + + + align:start position:0% +semiconductor Fab and the basic process +is you take that + + align:start position:0% +is you take that + + + align:start position:0% +is you take that +wafer you press it or you hold it in a + + align:start position:0% +wafer you press it or you hold it in a + + + align:start position:0% +wafer you press it or you hold it in a +wafer carrier and press it face down + + align:start position:0% +wafer carrier and press it face down + + + align:start position:0% +wafer carrier and press it face down +onto a rotating table or platin to which + + align:start position:0% +onto a rotating table or platin to which + + + align:start position:0% +onto a rotating table or platin to which +is a fixed an abrasive pad you also drip + + align:start position:0% +is a fixed an abrasive pad you also drip + + + align:start position:0% +is a fixed an abrasive pad you also drip +a a wet abrasive slurry so it's a uh + + align:start position:0% +a a wet abrasive slurry so it's a uh + + + align:start position:0% +a a wet abrasive slurry so it's a uh +very very fine particle grit uh in a + + align:start position:0% +very very fine particle grit uh in a + + + align:start position:0% +very very fine particle grit uh in a +chemically active slurry and then you + + align:start position:0% +chemically active slurry and then you + + + align:start position:0% +chemically active slurry and then you +rotate both the the wafer + + align:start position:0% +rotate both the the wafer + + + align:start position:0% +rotate both the the wafer +and and the pad or the or the table and + + align:start position:0% +and and the pad or the or the table and + + + align:start position:0% +and and the pad or the or the table and +the basic goal of this is to flatten the + + align:start position:0% +the basic goal of this is to flatten the + + + align:start position:0% +the basic goal of this is to flatten the +surface of the wafer if you go back + + align:start position:0% +surface of the wafer if you go back + + + align:start position:0% +surface of the wafer if you go back +to this picture with even one level of + + align:start position:0% +to this picture with even one level of + + + align:start position:0% +to this picture with even one level of +metal look at all of the + + align:start position:0% +metal look at all of the + + + align:start position:0% +metal look at all of the +topography the differences in Heights + + align:start position:0% +topography the differences in Heights + + + align:start position:0% +topography the differences in Heights +that are generated because we're etching + + align:start position:0% +that are generated because we're etching + + + align:start position:0% +that are generated because we're etching +down filling in and so on if one were to + + align:start position:0% +down filling in and so on if one were to + + + align:start position:0% +down filling in and so on if one were to +try to build multiple levels of metal + + align:start position:0% +try to build multiple levels of metal + + + align:start position:0% +try to build multiple levels of metal +you have a real problem here you keep + + align:start position:0% +you have a real problem here you keep + + + align:start position:0% +you have a real problem here you keep +building up in some regions where you + + align:start position:0% +building up in some regions where you + + + align:start position:0% +building up in some regions where you +have more metal and in those regions + + align:start position:0% +have more metal and in those regions + + + align:start position:0% +have more metal and in those regions +where you don't you get thinner and + + align:start position:0% +where you don't you get thinner and + + + align:start position:0% +where you don't you get thinner and +thinner by + + align:start position:0% +thinner by + + + align:start position:0% +thinner by +comparison that becomes a huge challenge + + align:start position:0% +comparison that becomes a huge challenge + + + align:start position:0% +comparison that becomes a huge challenge +in terms of uh other processes like + + align:start position:0% +in terms of uh other processes like + + + align:start position:0% +in terms of uh other processes like +photolithography talked about that depth + + align:start position:0% +photolithography talked about that depth + + + align:start position:0% +photolithography talked about that depth +of focus now I want a pattern or image + + align:start position:0% +of focus now I want a pattern or image + + + align:start position:0% +of focus now I want a pattern or image +at the top of one of these levels and + + align:start position:0% +at the top of one of these levels and + + + align:start position:0% +at the top of one of these levels and +I've got also these recessed regions + + align:start position:0% +I've got also these recessed regions + + + align:start position:0% +I've got also these recessed regions +becomes very difficult to image say a + + align:start position:0% +becomes very difficult to image say a + + + align:start position:0% +becomes very difficult to image say a +metal for layer and so + + align:start position:0% +metal for layer and so + + + align:start position:0% +metal for layer and so +CMP has + + align:start position:0% +CMP has + + + align:start position:0% +CMP has +been created to basically braid away the + + align:start position:0% +been created to basically braid away the + + + align:start position:0% +been created to basically braid away the +raised + + align:start position:0% +raised + + + align:start position:0% +raised +surfaces and get it down to a planer a + + align:start position:0% +surfaces and get it down to a planer a + + + align:start position:0% +surfaces and get it down to a planer a +planer + + align:start position:0% +planer + + + align:start position:0% +planer +surface now one of the big problems in + + align:start position:0% +surface now one of the big problems in + + + align:start position:0% +surface now one of the big problems in +CMP is the process itself is often not + + align:start position:0% +CMP is the process itself is often not + + + align:start position:0% +CMP is the process itself is often not +all that + + align:start position:0% +all that + + + align:start position:0% +all that +stable that polishing path that abrasive + + align:start position:0% +stable that polishing path that abrasive + + + align:start position:0% +stable that polishing path that abrasive +pad what happens if you use sandpaper + + align:start position:0% +pad what happens if you use sandpaper + + + align:start position:0% +pad what happens if you use sandpaper +for a while on a piece of wood well you + + align:start position:0% +for a while on a piece of wood well you + + + align:start position:0% +for a while on a piece of wood well you +smooth out you know the grain or + + align:start position:0% +smooth out you know the grain or + + + align:start position:0% +smooth out you know the grain or +whatever in the piece of wood what + + align:start position:0% +whatever in the piece of wood what + + + align:start position:0% +whatever in the piece of wood what +happens to your + + align:start position:0% +happens to your + + + align:start position:0% +happens to your +sandpaper it also wears right fills in + + align:start position:0% +sandpaper it also wears right fills in + + + align:start position:0% +sandpaper it also wears right fills in +it gets cookie but it basically it + + align:start position:0% +it gets cookie but it basically it + + + align:start position:0% +it gets cookie but it basically it +changes its state the process and the + + align:start position:0% +changes its state the process and the + + + align:start position:0% +changes its state the process and the +equipment changes its state over + + align:start position:0% +equipment changes its state over + + + align:start position:0% +equipment changes its state over +fabrication as well and if you looked at + + align:start position:0% +fabrication as well and if you looked at + + + align:start position:0% +fabrication as well and if you looked at +the normalized removal rate for uh 300 + + align:start position:0% +the normalized removal rate for uh 300 + + + align:start position:0% +the normalized removal rate for uh 300 +50 wafer + + align:start position:0% +50 wafer + + + align:start position:0% +50 wafer +sequence you will often find drift in + + align:start position:0% +sequence you will often find drift in + + + align:start position:0% +sequence you will often find drift in +the removal rate you might start out + + align:start position:0% +the removal rate you might start out + + + align:start position:0% +the removal rate you might start out +with a fairly High removal rate and over + + align:start position:0% +with a fairly High removal rate and over + + + align:start position:0% +with a fairly High removal rate and over +time it drifts down and this is + + align:start position:0% +time it drifts down and this is + + + align:start position:0% +time it drifts down and this is +something like uh you know a 20 or 40% + + align:start position:0% +something like uh you know a 20 or 40% + + + align:start position:0% +something like uh you know a 20 or 40% +kind of kind of drift similarly if you + + align:start position:0% +kind of kind of drift similarly if you + + + align:start position:0% +kind of kind of drift similarly if you +looked at the wafer measured some some + + align:start position:0% +looked at the wafer measured some some + + + align:start position:0% +looked at the wafer measured some some +pattern some eight sample point and + + align:start position:0% +pattern some eight sample point and + + + align:start position:0% +pattern some eight sample point and +calculated a non-uniformity metric maybe + + align:start position:0% +calculated a non-uniformity metric maybe + + + align:start position:0% +calculated a non-uniformity metric maybe +at standard deviation of of those points + + align:start position:0% +at standard deviation of of those points + + + align:start position:0% +at standard deviation of of those points +uh one would find uh maybe you can see + + align:start position:0% +uh one would find uh maybe you can see + + + align:start position:0% +uh one would find uh maybe you can see +it looks like there's a slight increase + + align:start position:0% +it looks like there's a slight increase + + + align:start position:0% +it looks like there's a slight increase +in that non-uniformity over time the the + + align:start position:0% +in that non-uniformity over time the the + + + align:start position:0% +in that non-uniformity over time the the +pad is not quite as uniform as well so + + align:start position:0% +pad is not quite as uniform as well so + + + align:start position:0% +pad is not quite as uniform as well so +this is the kind of temporal wafer to + + align:start position:0% +this is the kind of temporal wafer to + + + align:start position:0% +this is the kind of temporal wafer to +wafer variation that you don't want + + align:start position:0% +wafer variation that you don't want + + + align:start position:0% +wafer variation that you don't want +and would like to understand it if + + align:start position:0% +and would like to understand it if + + + align:start position:0% +and would like to understand it if +there's a systematic Trend then maybe + + align:start position:0% +there's a systematic Trend then maybe + + + align:start position:0% +there's a systematic Trend then maybe +there are control approaches that can be + + align:start position:0% +there are control approaches that can be + + + align:start position:0% +there are control approaches that can be +used to compensate or correct for that + + align:start position:0% +used to compensate or correct for that + + + align:start position:0% +used to compensate or correct for that +yeah poling seems be + + align:start position:0% +yeah poling seems be + + + align:start position:0% +yeah poling seems be +IDE way to + + align:start position:0% + + + + align:start position:0% + +get yeah so sort of the semiconductor + + align:start position:0% +get yeah so sort of the semiconductor + + + align:start position:0% +get yeah so sort of the semiconductor +industry really got it start about + + align:start position:0% +industry really got it start about + + + align:start position:0% +industry really got it start about +1960 and for 30 years it was all about + + align:start position:0% +1960 and for 30 years it was all about + + + align:start position:0% +1960 and for 30 years it was all about +defects those + + align:start position:0% +defects those + + + align:start position:0% +defects those +particles keep them away from the wafer + + align:start position:0% +particles keep them away from the wafer + + + align:start position:0% +particles keep them away from the wafer +at whatever cost and then uh primarily + + align:start position:0% +at whatever cost and then uh primarily + + + align:start position:0% +at whatever cost and then uh primarily +folks from IBM around 1990 said yeah + + align:start position:0% +folks from IBM around 1990 said yeah + + + align:start position:0% +folks from IBM around 1990 said yeah +we're going to pour slurries with uh uh + + align:start position:0% +we're going to pour slurries with uh uh + + + align:start position:0% +we're going to pour slurries with uh uh +100 nanometer particles on it and then + + align:start position:0% +100 nanometer particles on it and then + + + align:start position:0% +100 nanometer particles on it and then +we're going to rub the heck out of the + + align:start position:0% +we're going to rub the heck out of the + + + align:start position:0% +we're going to rub the heck out of the +surface of your of your wafer and + + align:start position:0% +surface of your of your wafer and + + + align:start position:0% +surface of your of your wafer and +everybody thought they were crazy but it + + align:start position:0% +everybody thought they were crazy but it + + + align:start position:0% +everybody thought they were crazy but it +turns + + align:start position:0% +turns + + + align:start position:0% +turns +out that + + align:start position:0% +out that + + + align:start position:0% +out that +uh first off the control of the process + + align:start position:0% +uh first off the control of the process + + + align:start position:0% +uh first off the control of the process +can be very good in terms of not a very + + align:start position:0% +can be very good in terms of not a very + + + align:start position:0% +can be very good in terms of not a very +very fine AB braiding of the surface so + + align:start position:0% +very fine AB braiding of the surface so + + + align:start position:0% +very fine AB braiding of the surface so +you're not like gouging out you're + + align:start position:0% +you're not like gouging out you're + + + align:start position:0% +you're not like gouging out you're +really doing almost nanometer by + + align:start position:0% +really doing almost nanometer by + + + align:start position:0% +really doing almost nanometer by +nanometer scale abrasion but then you + + align:start position:0% +nanometer scale abrasion but then you + + + align:start position:0% +nanometer scale abrasion but then you +still have all those particles so a lot + + align:start position:0% +still have all those particles so a lot + + + align:start position:0% +still have all those particles so a lot +of the work was very very effective post + + align:start position:0% +of the work was very very effective post + + + align:start position:0% +of the work was very very effective post +poolish cleaning processes that involve + + align:start position:0% +poolish cleaning processes that involve + + + align:start position:0% +poolish cleaning processes that involve +chemical baths that involve brush + + align:start position:0% +chemical baths that involve brush + + + align:start position:0% +chemical baths that involve brush +cleaning in fact uh that involve + + align:start position:0% +cleaning in fact uh that involve + + + align:start position:0% +cleaning in fact uh that involve +hydronic agitation to sort of levitate + + align:start position:0% +hydronic agitation to sort of levitate + + + align:start position:0% +hydronic agitation to sort of levitate +the particles uh off of the surface of + + align:start position:0% +the particles uh off of the surface of + + + align:start position:0% +the particles uh off of the surface of +the wafer in a clean bath that they uh + + align:start position:0% +the wafer in a clean bath that they uh + + + align:start position:0% +the wafer in a clean bath that they uh +actually + + align:start position:0% +actually + + + align:start position:0% +actually +found + + align:start position:0% +found + + + align:start position:0% +found +no + + align:start position:0% +no + + + align:start position:0% +no +appreciable defect oriented yield loss + + align:start position:0% +appreciable defect oriented yield loss + + + align:start position:0% +appreciable defect oriented yield loss +once you did those those Extreme + + align:start position:0% +once you did those those Extreme + + + align:start position:0% +once you did those those Extreme +Measures to clean up the wafer and in + + align:start position:0% +Measures to clean up the wafer and in + + + align:start position:0% +Measures to clean up the wafer and in +fact the irony ended up being + + align:start position:0% +fact the irony ended up being + + + align:start position:0% +fact the irony ended up being +that the uh CMP process by planarizing + + align:start position:0% +that the uh CMP process by planarizing + + + align:start position:0% +that the uh CMP process by planarizing +actually improved the + + align:start position:0% +actually improved the + + + align:start position:0% +actually improved the +defectivity because many of these + + align:start position:0% +defectivity because many of these + + + align:start position:0% +defectivity because many of these +particles might be uh present in layer + + align:start position:0% +particles might be uh present in layer + + + align:start position:0% +particles might be uh present in layer +three you've got a lump but didn't + + align:start position:0% +three you've got a lump but didn't + + + align:start position:0% +three you've got a lump but didn't +destroy the the action of level three + + align:start position:0% +destroy the the action of level three + + + align:start position:0% +destroy the the action of level three +but if it's sticking up by the time you + + align:start position:0% +but if it's sticking up by the time you + + + align:start position:0% +but if it's sticking up by the time you +go into level four and you do a + + align:start position:0% +go into level four and you do a + + + align:start position:0% +go into level four and you do a +metalization over that well now you've + + align:start position:0% +metalization over that well now you've + + + align:start position:0% +metalization over that well now you've +got a problem and the CMP process which + + align:start position:0% +got a problem and the CMP process which + + + align:start position:0% +got a problem and the CMP process which +would go in and and flatten or planarize + + align:start position:0% +would go in and and flatten or planarize + + + align:start position:0% +would go in and and flatten or planarize +between levels would actually you know + + align:start position:0% +between levels would actually you know + + + align:start position:0% +between levels would actually you know +chop the heads off of these defects and + + align:start position:0% +chop the heads off of these defects and + + + align:start position:0% +chop the heads off of these defects and +reduce their impact for for subsequent + + align:start position:0% +reduce their impact for for subsequent + + + align:start position:0% +reduce their impact for for subsequent +levels so it actually ended up being it + + align:start position:0% +levels so it actually ended up being it + + + align:start position:0% +levels so it actually ended up being it +but but it it is a fascinating story of + + align:start position:0% +but but it it is a fascinating story of + + + align:start position:0% +but but it it is a fascinating story of +the uh adoption of CMP because + + align:start position:0% +the uh adoption of CMP because + + + align:start position:0% +the uh adoption of CMP because +um it was so counterintuitive of a + + align:start position:0% +um it was so counterintuitive of a + + + align:start position:0% +um it was so counterintuitive of a +process exactly as you said so we'll + + align:start position:0% +process exactly as you said so we'll + + + align:start position:0% +process exactly as you said so we'll +come back at the end uh uh or or or + + align:start position:0% +come back at the end uh uh or or or + + + align:start position:0% +come back at the end uh uh or or or +later to uh control strategies for + + align:start position:0% +later to uh control strategies for + + + align:start position:0% +later to uh control strategies for +dealing with this uh of the course I + + align:start position:0% +dealing with this uh of the course I + + + align:start position:0% +dealing with this uh of the course I +mean basically this kind of a drift you + + align:start position:0% +mean basically this kind of a drift you + + + align:start position:0% +mean basically this kind of a drift you +could start to think well I can measure + + align:start position:0% +could start to think well I can measure + + + align:start position:0% +could start to think well I can measure +this and maybe what I would like to do + + align:start position:0% +this and maybe what I would like to do + + + align:start position:0% +this and maybe what I would like to do +on subsequent runs if my removal rate + + align:start position:0% +on subsequent runs if my removal rate + + + align:start position:0% +on subsequent runs if my removal rate +has drifted down I'd like a strategy + + align:start position:0% +has drifted down I'd like a strategy + + + align:start position:0% +has drifted down I'd like a strategy +where I polish a little bit longer or I + + align:start position:0% +where I polish a little bit longer or I + + + align:start position:0% +where I polish a little bit longer or I +press a little bit harder these sorts of + + align:start position:0% +press a little bit harder these sorts of + + + align:start position:0% +press a little bit harder these sorts of +things um so you only do this polishing + + align:start position:0% +things um so you only do this polishing + + + align:start position:0% +things um so you only do this polishing +at the very end no you do it at each + + align:start position:0% +at the very end no you do it at each + + + align:start position:0% +at the very end no you do it at each +level at each level each each metal + + align:start position:0% +level at each level each each metal + + + align:start position:0% +level at each level each each metal +level okay as well as in some other + + align:start position:0% +level okay as well as in some other + + + align:start position:0% +level okay as well as in some other +places but yeah yeah so it's actually + + align:start position:0% +places but yeah yeah so it's actually + + + align:start position:0% +places but yeah yeah so it's actually +used repeatedly in multi-level + + align:start position:0% +used repeatedly in multi-level + + + align:start position:0% +used repeatedly in multi-level +interconnect + + align:start position:0% +interconnect + + + align:start position:0% +interconnect +okay what here's an example of a little + + align:start position:0% +okay what here's an example of a little + + + align:start position:0% +okay what here's an example of a little +test chip to try to characterize some of + + align:start position:0% +test chip to try to characterize some of + + + align:start position:0% +test chip to try to characterize some of +those spatial variations and decompose + + align:start position:0% +those spatial variations and decompose + + + align:start position:0% +those spatial variations and decompose +them that we talked about + + align:start position:0% +them that we talked about + + + align:start position:0% +them that we talked about +this is a a chip design that + + align:start position:0% +this is a a chip design that + + + align:start position:0% +this is a a chip design that +has uh a few thousand ring oscillators a + + align:start position:0% +has uh a few thousand ring oscillators a + + + align:start position:0% +has uh a few thousand ring oscillators a +ring oscillator is a chain of an odd + + align:start position:0% +ring oscillator is a chain of an odd + + + align:start position:0% +ring oscillator is a chain of an odd +number of inverters Each of which does a + + align:start position:0% +number of inverters Each of which does a + + + align:start position:0% +number of inverters Each of which does a +logic 0o to one or 1 to zero uh + + align:start position:0% +logic 0o to one or 1 to zero uh + + + align:start position:0% +logic 0o to one or 1 to zero uh +computation and if you organize those in + + align:start position:0% +computation and if you organize those in + + + align:start position:0% +computation and if you organize those in +a ring fashion it oscillates at some + + align:start position:0% +a ring fashion it oscillates at some + + + align:start position:0% +a ring fashion it oscillates at some +high frequency that indicates the speed + + align:start position:0% +high frequency that indicates the speed + + + align:start position:0% +high frequency that indicates the speed +of the individual transistors in that + + align:start position:0% +of the individual transistors in that + + + align:start position:0% +of the individual transistors in that +structure so a ring oscillator is a + + align:start position:0% +structure so a ring oscillator is a + + + align:start position:0% +structure so a ring oscillator is a +wonderful stand in electric electronic + + align:start position:0% +wonderful stand in electric electronic + + + align:start position:0% +wonderful stand in electric electronic +circuit telling you a lot about the + + align:start position:0% +circuit telling you a lot about the + + + align:start position:0% +circuit telling you a lot about the +speed of your technology what we did is + + align:start position:0% +speed of your technology what we did is + + + align:start position:0% +speed of your technology what we did is +uh built a tiled architecture where + + align:start position:0% +uh built a tiled architecture where + + + align:start position:0% +uh built a tiled architecture where +we've got thousands of these structures + + align:start position:0% +we've got thousands of these structures + + + align:start position:0% +we've got thousands of these structures +replicated spatially so now we can + + align:start position:0% +replicated spatially so now we can + + + align:start position:0% +replicated spatially so now we can +measure multiple instances and see if + + align:start position:0% +measure multiple instances and see if + + + align:start position:0% +measure multiple instances and see if +there's a spatial pattern as well as we + + align:start position:0% +there's a spatial pattern as well as we + + + align:start position:0% +there's a spatial pattern as well as we +can also play with some of the design + + align:start position:0% +can also play with some of the design + + + align:start position:0% +can also play with some of the design +parameters of each of those ring + + align:start position:0% +parameters of each of those ring + + + align:start position:0% +parameters of each of those ring +oscillators in particular we can do + + align:start position:0% +oscillators in particular we can do + + + align:start position:0% +oscillators in particular we can do +things like take that Pol po silicon + + align:start position:0% +things like take that Pol po silicon + + + align:start position:0% +things like take that Pol po silicon +gate electrode and split it into three + + align:start position:0% +gate electrode and split it into three + + + align:start position:0% +gate electrode and split it into three +of them we can play with the spacing + + align:start position:0% +of them we can play with the spacing + + + align:start position:0% +of them we can play with the spacing +between those electrodes we can Orient + + align:start position:0% +between those electrodes we can Orient + + + align:start position:0% +between those electrodes we can Orient +uh those poly fingers vertically or + + align:start position:0% +uh those poly fingers vertically or + + + align:start position:0% +uh those poly fingers vertically or +horizontally on the on on the layout we + + align:start position:0% +horizontally on the on on the layout we + + + align:start position:0% +horizontally on the on on the layout we +can also look at the effect of nearby + + align:start position:0% +can also look at the effect of nearby + + + align:start position:0% +can also look at the effect of nearby +structures for example how dense per + + align:start position:0% +structures for example how dense per + + + align:start position:0% +structures for example how dense per +unit area do you have transistors or or + + align:start position:0% +unit area do you have transistors or or + + + align:start position:0% +unit area do you have transistors or or +polysilicon uh uh gate electrodes would + + align:start position:0% +polysilicon uh uh gate electrodes would + + + align:start position:0% +polysilicon uh uh gate electrodes would +that have an effect on the ring + + align:start position:0% +that have an effect on the ring + + + align:start position:0% +that have an effect on the ring +oscillator + + align:start position:0% +oscillator + + + align:start position:0% +oscillator +and now if you go out and build this + + align:start position:0% +and now if you go out and build this + + + align:start position:0% +and now if you go out and build this +this is a wonderful kind of data where + + align:start position:0% +this is a wonderful kind of data where + + + align:start position:0% +this is a wonderful kind of data where +you can aggregate or map out the data at + + align:start position:0% +you can aggregate or map out the data at + + + align:start position:0% +you can aggregate or map out the data at +these different spatial scales to look + + align:start position:0% +these different spatial scales to look + + + align:start position:0% +these different spatial scales to look +for Trends so for example if we look at + + align:start position:0% +for Trends so for example if we look at + + + align:start position:0% +for Trends so for example if we look at +the wafer scale variation in the ring + + align:start position:0% +the wafer scale variation in the ring + + + align:start position:0% +the wafer scale variation in the ring +oscillator speed got something like 30 + + align:start position:0% +oscillator speed got something like 30 + + + align:start position:0% +oscillator speed got something like 30 +chips in the upper half of one of these + + align:start position:0% +chips in the upper half of one of these + + + align:start position:0% +chips in the upper half of one of these +Wafers and mapped out here in the color + + align:start position:0% +Wafers and mapped out here in the color + + + align:start position:0% +Wafers and mapped out here in the color +is the average ring oscillator speed + + align:start position:0% +is the average ring oscillator speed + + + align:start position:0% +is the average ring oscillator speed +from high to low low and you can sort of + + align:start position:0% +from high to low low and you can sort of + + + align:start position:0% +from high to low low and you can sort of +see a spatial + + align:start position:0% +see a spatial + + + align:start position:0% +see a spatial +trend from one side of the wafer to the + + align:start position:0% +trend from one side of the wafer to the + + + align:start position:0% +trend from one side of the wafer to the +other this is telling us there is a + + align:start position:0% +other this is telling us there is a + + + align:start position:0% +other this is telling us there is a +wafer level non-uniformity and in fact + + align:start position:0% +wafer level non-uniformity and in fact + + + align:start position:0% +wafer level non-uniformity and in fact +that across wafer variation is about 9% + + align:start position:0% +that across wafer variation is about 9% + + + align:start position:0% +that across wafer variation is about 9% +in speed of these + + align:start position:0% +in speed of these + + + align:start position:0% +in speed of these +devices you can also then start to look + + align:start position:0% +devices you can also then start to look + + + align:start position:0% +devices you can also then start to look +I guess that's the same thing you can + + align:start position:0% +I guess that's the same thing you can + + + align:start position:0% +I guess that's the same thing you can +also start to look and say depending on + + align:start position:0% +also start to look and say depending on + + + align:start position:0% +also start to look and say depending on +how you designed the uh transistor what + + align:start position:0% +how you designed the uh transistor what + + + align:start position:0% +how you designed the uh transistor what +kind of offsets do you get in the in the + + align:start position:0% +kind of offsets do you get in the in the + + + align:start position:0% +kind of offsets do you get in the in the +frequency and what kind of variation do + + align:start position:0% +frequency and what kind of variation do + + + align:start position:0% +frequency and what kind of variation do +you get + + align:start position:0% +you get + + + align:start position:0% +you get +in the speed of the devices and what's + + align:start position:0% +in the speed of the devices and what's + + + align:start position:0% +in the speed of the devices and what's +interesting uh here is that many of + + align:start position:0% +interesting uh here is that many of + + + align:start position:0% +interesting uh here is that many of +these ring oscillator designs are from + + align:start position:0% +these ring oscillator designs are from + + + align:start position:0% +these ring oscillator designs are from +the circuit designer perspective they + + align:start position:0% +the circuit designer perspective they + + + align:start position:0% +the circuit designer perspective they +think of them as + + align:start position:0% +think of them as + + + align:start position:0% +think of them as +identical but in fabrication because of + + align:start position:0% +identical but in fabrication because of + + + align:start position:0% +identical but in fabrication because of +neighborhood or nearby structures in + + align:start position:0% +neighborhood or nearby structures in + + + align:start position:0% +neighborhood or nearby structures in +fact there are slight deviations so + + align:start position:0% +fact there are slight deviations so + + + align:start position:0% +fact there are slight deviations so +phenomenally identical transistors May + + align:start position:0% +phenomenally identical transistors May + + + align:start position:0% +phenomenally identical transistors May +in fact have substantial systematic + + align:start position:0% +in fact have substantial systematic + + + align:start position:0% +in fact have substantial systematic +highly repeatable effects and if the + + align:start position:0% +highly repeatable effects and if the + + + align:start position:0% +highly repeatable effects and if the +manufacturing line can capture and + + align:start position:0% +manufacturing line can capture and + + + align:start position:0% +manufacturing line can capture and +characterize those and send that + + align:start position:0% +characterize those and send that + + + align:start position:0% +characterize those and send that +information to + + align:start position:0% +information to + + + align:start position:0% +information to +design design can compensate right so + + align:start position:0% +design design can compensate right so + + + align:start position:0% +design design can compensate right so +this is another theme this design and + + align:start position:0% +this is another theme this design and + + + align:start position:0% +this is another theme this design and +Manufacturing link can be very important + + align:start position:0% +Manufacturing link can be very important + + + align:start position:0% +Manufacturing link can be very important +we can also map out identical + + align:start position:0% +we can also map out identical + + + align:start position:0% +we can also map out identical +transistors + + align:start position:0% +transistors + + + align:start position:0% +transistors +within one of these chips and here again + + align:start position:0% +within one of these chips and here again + + + align:start position:0% +within one of these chips and here again +you can see a top to bottom variation in + + align:start position:0% +you can see a top to bottom variation in + + + align:start position:0% +you can see a top to bottom variation in +the ring oscillator speed and in this + + align:start position:0% +the ring oscillator speed and in this + + + align:start position:0% +the ring oscillator speed and in this +case that within each individual chip is + + align:start position:0% +case that within each individual chip is + + + align:start position:0% +case that within each individual chip is +about 4% in this in this particular case + + align:start position:0% +about 4% in this in this particular case + + + align:start position:0% +about 4% in this in this particular case +which is quite interesting notice we + + align:start position:0% +which is quite interesting notice we + + + align:start position:0% +which is quite interesting notice we +said there's 9% across the whole wafer I + + align:start position:0% +said there's 9% across the whole wafer I + + + align:start position:0% +said there's 9% across the whole wafer I +might have 10 chips lined up sort of in + + align:start position:0% +might have 10 chips lined up sort of in + + + align:start position:0% +might have 10 chips lined up sort of in +a line across the wafer if I were to say + + align:start position:0% +a line across the wafer if I were to say + + + align:start position:0% +a line across the wafer if I were to say +from Center to Edge I have a systematic + + align:start position:0% +from Center to Edge I have a systematic + + + align:start position:0% +from Center to Edge I have a systematic +Trend or from one edge of the wafer to + + align:start position:0% +Trend or from one edge of the wafer to + + + align:start position:0% +Trend or from one edge of the wafer to +the other a + + align:start position:0% +the other a + + + align:start position:0% +the other a +systematic trend of about + + align:start position:0% +systematic trend of about + + + align:start position:0% +systematic trend of about +10% and I MA that down to + + align:start position:0% +10% and I MA that down to + + + align:start position:0% +10% and I MA that down to +one10 you know because I've got 10 chips + + align:start position:0% +one10 you know because I've got 10 chips + + + align:start position:0% +one10 you know because I've got 10 chips +that would be about a 1% variation you + + align:start position:0% +that would be about a 1% variation you + + + align:start position:0% +that would be about a 1% variation you +might expect because of wafer level + + align:start position:0% +might expect because of wafer level + + + align:start position:0% +might expect because of wafer level +sources on each chip but what we find is + + align:start position:0% +sources on each chip but what we find is + + + align:start position:0% +sources on each chip but what we find is +something like + + align:start position:0% +something like + + + align:start position:0% +something like +4% that's telling us there's a different + + align:start position:0% +4% that's telling us there's a different + + + align:start position:0% +4% that's telling us there's a different +source of physical variation at work + + align:start position:0% +source of physical variation at work + + + align:start position:0% +source of physical variation at work +within each of the chips + + align:start position:0% +within each of the chips + + + align:start position:0% +within each of the chips +and then you can also look for other + + align:start position:0% +and then you can also look for other + + + align:start position:0% +and then you can also look for other +systematic effects things like um the + + align:start position:0% +systematic effects things like um the + + + align:start position:0% +systematic effects things like um the +proximity of one poly finger to another + + align:start position:0% +proximity of one poly finger to another + + + align:start position:0% +proximity of one poly finger to another +can have photolithographic effects uh + + align:start position:0% +can have photolithographic effects uh + + + align:start position:0% +can have photolithographic effects uh +and in particular that can result in an + + align:start position:0% +and in particular that can result in an + + + align:start position:0% +and in particular that can result in an +offset depending on whether I have one + + align:start position:0% +offset depending on whether I have one + + + align:start position:0% +offset depending on whether I have one +micron or two Micron or 2x or 3x spacing + + align:start position:0% +micron or two Micron or 2x or 3x spacing + + + align:start position:0% +micron or two Micron or 2x or 3x spacing +between the devices but in this case the + + align:start position:0% +between the devices but in this case the + + + align:start position:0% +between the devices but in this case the +variation across many many replicates of + + align:start position:0% +variation across many many replicates of + + + align:start position:0% +variation across many many replicates of +each of those is about the same an + + align:start position:0% +each of those is about the same an + + + align:start position:0% +each of those is about the same an +interesting effect is if we take that + + align:start position:0% +interesting effect is if we take that + + + align:start position:0% +interesting effect is if we take that +same poly that single gate electrode and + + align:start position:0% +same poly that single gate electrode and + + + align:start position:0% +same poly that single gate electrode and +split it up into two or split it up up + + align:start position:0% +split it up into two or split it up up + + + align:start position:0% +split it up into two or split it up up +into three and then look at the effect + + align:start position:0% +into three and then look at the effect + + + align:start position:0% +into three and then look at the effect +on ring oscillator speed offset and + + align:start position:0% +on ring oscillator speed offset and + + + align:start position:0% +on ring oscillator speed offset and +variance what do you think we're going + + align:start position:0% +variance what do you think we're going + + + align:start position:0% +variance what do you think we're going +to + + align:start position:0% +to + + + align:start position:0% +to +see we didn't know so you may not know + + align:start position:0% + + + + align:start position:0% + +but edges right you have more edges and + + align:start position:0% +but edges right you have more edges and + + + align:start position:0% +but edges right you have more edges and +that's exactly right if we look at the + + align:start position:0% +that's exactly right if we look at the + + + align:start position:0% +that's exactly right if we look at the +sigma with one finger two finger or four + + align:start position:0% +sigma with one finger two finger or four + + + align:start position:0% +sigma with one finger two finger or four +finger we found a proportional increase + + align:start position:0% +finger we found a proportional increase + + + align:start position:0% +finger we found a proportional increase +in in the variance with more + + align:start position:0% +in in the variance with more + + + align:start position:0% +in in the variance with more +opportunities for variation by by the + + align:start position:0% +opportunities for variation by by the + + + align:start position:0% +opportunities for variation by by the +fingering so that's a that was a an + + align:start position:0% +fingering so that's a that was a an + + + align:start position:0% +fingering so that's a that was a an +interesting implication for some design + + align:start position:0% +interesting implication for some design + + + align:start position:0% +interesting implication for some design +uh Kinds of Kinds of + + align:start position:0% +uh Kinds of Kinds of + + + align:start position:0% +uh Kinds of Kinds of +effects okay so that's an example where + + align:start position:0% +effects okay so that's an example where + + + align:start position:0% +effects okay so that's an example where +design of experiments could be used to + + align:start position:0% +design of experiments could be used to + + + align:start position:0% +design of experiments could be used to +come up with test structures and + + align:start position:0% +come up with test structures and + + + align:start position:0% +come up with test structures and +characterize and split out some of these + + align:start position:0% +characterize and split out some of these + + + align:start position:0% +characterize and split out some of these +sources of + + align:start position:0% +sources of + + + align:start position:0% +sources of +variation + + align:start position:0% +variation + + + align:start position:0% +variation +now I'm not going to go into the full + + align:start position:0% +now I'm not going to go into the full + + + align:start position:0% +now I'm not going to go into the full +detail on these slides I I I put more + + align:start position:0% +detail on these slides I I I put more + + + align:start position:0% +detail on these slides I I I put more +slides in here than I needed because + + align:start position:0% +slides in here than I needed because + + + align:start position:0% +slides in here than I needed because +this is a current area of my research + + align:start position:0% +this is a current area of my research + + + align:start position:0% +this is a current area of my research +and I get real excited about it but uh + + align:start position:0% +and I get real excited about it but uh + + + align:start position:0% +and I get real excited about it but uh +it helps explain a little bit this + + align:start position:0% +it helps explain a little bit this + + + align:start position:0% +it helps explain a little bit this +multi-level + + align:start position:0% +multi-level + + + align:start position:0% +multi-level +interconnect and the I I'll I'll cover + + align:start position:0% +interconnect and the I I'll I'll cover + + + align:start position:0% +interconnect and the I I'll I'll cover +the first one very briefly there's two + + align:start position:0% +the first one very briefly there's two + + + align:start position:0% +the first one very briefly there's two +sequences that I didn't talk about in + + align:start position:0% +sequences that I didn't talk about in + + + align:start position:0% +sequences that I didn't talk about in +the + + align:start position:0% +the + + + align:start position:0% +the +earlier flow because it's a 10year old + + align:start position:0% +earlier flow because it's a 10year old + + + align:start position:0% +earlier flow because it's a 10year old +process modern uh integrated circuits + + align:start position:0% +process modern uh integrated circuits + + + align:start position:0% +process modern uh integrated circuits +especially for microprocess or logic and + + align:start position:0% +especially for microprocess or logic and + + + align:start position:0% +especially for microprocess or logic and +now even memory are using copper + + align:start position:0% +now even memory are using copper + + + align:start position:0% +now even memory are using copper +interconnect copper conducts better than + + align:start position:0% +interconnect copper conducts better than + + + align:start position:0% +interconnect copper conducts better than +aluminum you get speed improvements you + + align:start position:0% +aluminum you get speed improvements you + + + align:start position:0% +aluminum you get speed improvements you +get reliability improvements it's a big + + align:start position:0% +get reliability improvements it's a big + + + align:start position:0% +get reliability improvements it's a big +drive to move to Copper but it's a + + align:start position:0% +drive to move to Copper but it's a + + + align:start position:0% +drive to move to Copper but it's a +little bit more complicated of a process + + align:start position:0% +little bit more complicated of a process + + + align:start position:0% +little bit more complicated of a process +the basic process + + align:start position:0% +the basic process + + + align:start position:0% +the basic process +is different than in aluminum because we + + align:start position:0% +is different than in aluminum because we + + + align:start position:0% +is different than in aluminum because we +do not have an effective plasma etch + + align:start position:0% +do not have an effective plasma etch + + + align:start position:0% +do not have an effective plasma etch +process for the removal selective + + align:start position:0% +process for the removal selective + + + align:start position:0% +process for the removal selective +removal of copper it's just a bad + + align:start position:0% +removal of copper it's just a bad + + + align:start position:0% +removal of copper it's just a bad +process in that way so instead what we + + align:start position:0% +process in that way so instead what we + + + align:start position:0% +process in that way so instead what we +have to do is go through the following + + align:start position:0% +have to do is go through the following + + + align:start position:0% +have to do is go through the following +sequence we photolithog graphically ET + + align:start position:0% +sequence we photolithog graphically ET + + + align:start position:0% +sequence we photolithog graphically ET +in our insulating + + align:start position:0% +in our insulating + + + align:start position:0% +in our insulating +layer where we want ultimately the + + align:start position:0% +layer where we want ultimately the + + + align:start position:0% +layer where we want ultimately the +copper line to reside then we fill in + + align:start position:0% +copper line to reside then we fill in + + + align:start position:0% +copper line to reside then we fill in +Copper everywhere we happen to do that + + align:start position:0% +Copper everywhere we happen to do that + + + align:start position:0% +Copper everywhere we happen to do that +using an electroplating process and that + + align:start position:0% +using an electroplating process and that + + + align:start position:0% +using an electroplating process and that +electroplating process results in nice + + align:start position:0% +electroplating process results in nice + + + align:start position:0% +electroplating process results in nice +filling of features of different sizes + + align:start position:0% +filling of features of different sizes + + + align:start position:0% +filling of features of different sizes +but it also overfills and even more + + align:start position:0% +but it also overfills and even more + + + align:start position:0% +but it also overfills and even more +problematic is it overfills to different + + align:start position:0% +problematic is it overfills to different + + + align:start position:0% +problematic is it overfills to different +amounts or different thicknesses + + align:start position:0% +amounts or different thicknesses + + + align:start position:0% +amounts or different thicknesses +depending on the feature size that we + + align:start position:0% +depending on the feature size that we + + + align:start position:0% +depending on the feature size that we +filled up so you get this very + + align:start position:0% +filled up so you get this very + + + align:start position:0% +filled up so you get this very +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +topography now I described CMP as + + align:start position:0% +topography now I described CMP as + + + align:start position:0% +topography now I described CMP as +wonderful for flattening and removing + + align:start position:0% +wonderful for flattening and removing + + + align:start position:0% +wonderful for flattening and removing +and ab braiding away topography so the + + align:start position:0% +and ab braiding away topography so the + + + align:start position:0% +and ab braiding away topography so the +second step is using CMP to remove all + + align:start position:0% +second step is using CMP to remove all + + + align:start position:0% +second step is using CMP to remove all +this excess copper and it will polish + + align:start position:0% +this excess copper and it will polish + + + align:start position:0% +this excess copper and it will polish +away and ideally you would like to stop + + align:start position:0% +away and ideally you would like to stop + + + align:start position:0% +away and ideally you would like to stop +exactly on the surface of the oxide and + + align:start position:0% +exactly on the surface of the oxide and + + + align:start position:0% +exactly on the surface of the oxide and +have your nice remaining copper lines + + align:start position:0% +have your nice remaining copper lines + + + align:start position:0% +have your nice remaining copper lines +where you where you wanted them but it + + align:start position:0% +where you where you wanted them but it + + + align:start position:0% +where you where you wanted them but it +also has a geometric + + align:start position:0% +also has a geometric + + + align:start position:0% +also has a geometric +imperfection arising from overp polish + + align:start position:0% +imperfection arising from overp polish + + + align:start position:0% +imperfection arising from overp polish +where uh big fat wide lines the + + align:start position:0% +where uh big fat wide lines the + + + align:start position:0% +where uh big fat wide lines the +polishing pad that polyurethane pad + + align:start position:0% +polishing pad that polyurethane pad + + + align:start position:0% +polishing pad that polyurethane pad +actually digs down in and uh overp + + align:start position:0% +actually digs down in and uh overp + + + align:start position:0% +actually digs down in and uh overp +polishes certain features and in regions + + align:start position:0% +polishes certain features and in regions + + + align:start position:0% +polishes certain features and in regions +where you've got a lot of copper and + + align:start position:0% +where you've got a lot of copper and + + + align:start position:0% +where you've got a lot of copper and +very little hard supporting oxide it + + align:start position:0% +very little hard supporting oxide it + + + align:start position:0% +very little hard supporting oxide it +actually erodes down in + + align:start position:0% +actually erodes down in + + + align:start position:0% +actually erodes down in +appreciably so these are some systematic + + align:start position:0% +appreciably so these are some systematic + + + align:start position:0% +appreciably so these are some systematic +effects they are manufacturing + + align:start position:0% +effects they are manufacturing + + + align:start position:0% +effects they are manufacturing +limitations and one would like to uh + + align:start position:0% +limitations and one would like to uh + + + align:start position:0% +limitations and one would like to uh +model and characterize those and in fact + + align:start position:0% +model and characterize those and in fact + + + align:start position:0% +model and characterize those and in fact +that's what this wafer was for what we + + align:start position:0% +that's what this wafer was for what we + + + align:start position:0% +that's what this wafer was for what we +came up with was a test structure + + align:start position:0% +came up with was a test structure + + + align:start position:0% +came up with was a test structure +methodology where you would put lots of + + align:start position:0% +methodology where you would put lots of + + + align:start position:0% +methodology where you would put lots of +features of different sizes on a wafer + + align:start position:0% +features of different sizes on a wafer + + + align:start position:0% +features of different sizes on a wafer +run it through the process measure the + + align:start position:0% +run it through the process measure the + + + align:start position:0% +run it through the process measure the +results so this is a measurement of the + + align:start position:0% +results so this is a measurement of the + + + align:start position:0% +results so this is a measurement of the +electrol electroplated profile for + + align:start position:0% +electrol electroplated profile for + + + align:start position:0% +electrol electroplated profile for +different feature sizes like those + + align:start position:0% +different feature sizes like those + + + align:start position:0% +different feature sizes like those +little lines and spaces between the + + align:start position:0% +little lines and spaces between the + + + align:start position:0% +little lines and spaces between the +lines of quarter Micron quarter Micron + + align:start position:0% +lines of quarter Micron quarter Micron + + + align:start position:0% +lines of quarter Micron quarter Micron +versus say 100 Micron and 100 Micron + + align:start position:0% +versus say 100 Micron and 100 Micron + + + align:start position:0% +versus say 100 Micron and 100 Micron +lines and then you could measure the + + align:start position:0% +lines and then you could measure the + + + align:start position:0% +lines and then you could measure the +surface topography and see how much over + + align:start position:0% +surface topography and see how much over + + + align:start position:0% +surface topography and see how much over +plating or how much uh underfill you + + align:start position:0% +plating or how much uh underfill you + + + align:start position:0% +plating or how much uh underfill you +might have in each of those + + align:start position:0% +might have in each of those + + + align:start position:0% +might have in each of those +regions now this is kind of a neat + + align:start position:0% +regions now this is kind of a neat + + + align:start position:0% +regions now this is kind of a neat +example + + align:start position:0% +example + + + align:start position:0% +example +for something that we'll be learning + + align:start position:0% +for something that we'll be learning + + + align:start position:0% +for something that we'll be learning +about uh later in the term which is + + align:start position:0% +about uh later in the term which is + + + align:start position:0% +about uh later in the term which is +empirical modeling this is an empirical + + align:start position:0% +empirical modeling this is an empirical + + + align:start position:0% +empirical modeling this is an empirical +process where we run the wafer through + + align:start position:0% +process where we run the wafer through + + + align:start position:0% +process where we run the wafer through +we take measurements and then we + + align:start position:0% +we take measurements and then we + + + align:start position:0% +we take measurements and then we +developed in our first first level model + + align:start position:0% +developed in our first first level model + + + align:start position:0% +developed in our first first level model +response surface models that are + + align:start position:0% +response surface models that are + + + align:start position:0% +response surface models that are +basically uh Power models as a function + + align:start position:0% +basically uh Power models as a function + + + align:start position:0% +basically uh Power models as a function +of line width and line space so you can + + align:start position:0% +of line width and line space so you can + + + align:start position:0% +of line width and line space so you can +empirically fit a model that describes + + align:start position:0% +empirically fit a model that describes + + + align:start position:0% +empirically fit a model that describes +how much over plating height or what the + + align:start position:0% +how much over plating height or what the + + + align:start position:0% +how much over plating height or what the +step height might be and then one can + + align:start position:0% +step height might be and then one can + + + align:start position:0% +step height might be and then one can +use that to characterize uh step height + + align:start position:0% +use that to characterize uh step height + + + align:start position:0% +use that to characterize uh step height +or the amount of Bulge as a function of + + align:start position:0% +or the amount of Bulge as a function of + + + align:start position:0% +or the amount of Bulge as a function of +line width and line space and give some + + align:start position:0% +line width and line space and give some + + + align:start position:0% +line width and line space and give some +feedback to the designer saying hey if + + align:start position:0% +feedback to the designer saying hey if + + + align:start position:0% +feedback to the designer saying hey if +you design in these ranges this is + + align:start position:0% +you design in these ranges this is + + + align:start position:0% +you design in these ranges this is +what's actually going to happen as + + align:start position:0% +what's actually going to happen as + + + align:start position:0% +what's actually going to happen as +opposed to what you thought was going to + + align:start position:0% +opposed to what you thought was going to + + + align:start position:0% +opposed to what you thought was going to +happen and so so that's a a little + + align:start position:0% +happen and so so that's a a little + + + align:start position:0% +happen and so so that's a a little +response surface model kind of example + + align:start position:0% +response surface model kind of example + + + align:start position:0% +response surface model kind of example +then one can also build those perhaps + + align:start position:0% +then one can also build those perhaps + + + align:start position:0% +then one can also build those perhaps +into design tools that could predict for + + align:start position:0% +into design tools that could predict for + + + align:start position:0% +into design tools that could predict for +a whole chip maybe a product chip what + + align:start position:0% +a whole chip maybe a product chip what + + + align:start position:0% +a whole chip maybe a product chip what +the uh electroplated process thickness + + align:start position:0% +the uh electroplated process thickness + + + align:start position:0% +the uh electroplated process thickness +would be or what the CMP process would + + align:start position:0% +would be or what the CMP process would + + + align:start position:0% +would be or what the CMP process would +be I'm going to skip these this is + + align:start position:0% +be I'm going to skip these this is + + + align:start position:0% +be I'm going to skip these this is +essentially doing the same thing for CMP + + align:start position:0% +essentially doing the same thing for CMP + + + align:start position:0% +essentially doing the same thing for CMP +but the idea here is this linkage again + + align:start position:0% +but the idea here is this linkage again + + + align:start position:0% +but the idea here is this linkage again +between design and manufacturer where + + align:start position:0% +between design and manufacturer where + + + align:start position:0% +between design and manufacturer where +the + + align:start position:0% +the + + + align:start position:0% +the +manufacturing Fab can characterize what + + align:start position:0% +manufacturing Fab can characterize what + + + align:start position:0% +manufacturing Fab can characterize what +the actual amount of dishing or erosion + + align:start position:0% +the actual amount of dishing or erosion + + + align:start position:0% +the actual amount of dishing or erosion +is going to be for very complicated + + align:start position:0% +is going to be for very complicated + + + align:start position:0% +is going to be for very complicated +product chips and that information could + + align:start position:0% +product chips and that information could + + + align:start position:0% +product chips and that information could +get fed back to to the designer so that + + align:start position:0% +get fed back to to the designer so that + + + align:start position:0% +get fed back to to the designer so that +they actually know in this location my + + align:start position:0% +they actually know in this location my + + + align:start position:0% +they actually know in this location my +final copper wire is going to + + align:start position:0% +final copper wire is going to + + + align:start position:0% +final copper wire is going to +be this thick not this thick and that + + align:start position:0% +be this thick not this thick and that + + + align:start position:0% +be this thick not this thick and that +could be very important because the + + align:start position:0% +could be very important because the + + + align:start position:0% +could be very important because the +thickness of a copper wire determines + + align:start position:0% +thickness of a copper wire determines + + + align:start position:0% +thickness of a copper wire determines +its electrical resistance it even affect + + align:start position:0% +its electrical resistance it even affect + + + align:start position:0% +its electrical resistance it even affect +the coupling capacitance between two + + align:start position:0% +the coupling capacitance between two + + + align:start position:0% +the coupling capacitance between two +neighbor wires so those key electrical + + align:start position:0% +neighbor wires so those key electrical + + + align:start position:0% +neighbor wires so those key electrical +parameters resistance capacitance that + + align:start position:0% +parameters resistance capacitance that + + + align:start position:0% +parameters resistance capacitance that +determine interconnect speed depend on + + align:start position:0% +determine interconnect speed depend on + + + align:start position:0% +determine interconnect speed depend on +that + + align:start position:0% +that + + + align:start position:0% +that +critically so so that linkage uh with + + align:start position:0% +critically so so that linkage uh with + + + align:start position:0% +critically so so that linkage uh with +robust design can be very important one + + align:start position:0% +robust design can be very important one + + + align:start position:0% +robust design can be very important one +can also use those kinds of models to + + align:start position:0% +can also use those kinds of models to + + + align:start position:0% +can also use those kinds of models to +play with process parameters and + + align:start position:0% +play with process parameters and + + + align:start position:0% +play with process parameters and +empirically as a function of the process + + align:start position:0% +empirically as a function of the process + + + align:start position:0% +empirically as a function of the process +conditions minimize these systematic + + align:start position:0% +conditions minimize these systematic + + + align:start position:0% +conditions minimize these systematic +sources of variation and one approach + + align:start position:0% +sources of variation and one approach + + + align:start position:0% +sources of variation and one approach +that + + align:start position:0% +that + + + align:start position:0% +that +is dominant in a number of Industries is + + align:start position:0% +is dominant in a number of Industries is + + + align:start position:0% +is dominant in a number of Industries is +a capturing of these dependencies on + + align:start position:0% +a capturing of these dependencies on + + + align:start position:0% +a capturing of these dependencies on +design features like line width or line + + align:start position:0% +design features like line width or line + + + align:start position:0% +design features like line width or line +space and what is a good region to be + + align:start position:0% +space and what is a good region to be + + + align:start position:0% +space and what is a good region to be +operating in in these ideas of design + + align:start position:0% +operating in in these ideas of design + + + align:start position:0% +operating in in these ideas of design +roles and so in fact this is some work + + align:start position:0% +roles and so in fact this is some work + + + align:start position:0% +roles and so in fact this is some work +from LSI logic uh looking at the Copper + + align:start position:0% +from LSI logic uh looking at the Copper + + + align:start position:0% +from LSI logic uh looking at the Copper +interconnect space and saying okay what + + align:start position:0% +interconnect space and saying okay what + + + align:start position:0% +interconnect space and saying okay what +region what limits what combinations of + + align:start position:0% +region what limits what combinations of + + + align:start position:0% +region what limits what combinations of +line width and line space can you have + + align:start position:0% +line width and line space can you have + + + align:start position:0% +line width and line space can you have +and where are the boundaries because of + + align:start position:0% +and where are the boundaries because of + + + align:start position:0% +and where are the boundaries because of +some of these different physical effects + + align:start position:0% +some of these different physical effects + + + align:start position:0% +some of these different physical effects +so for example photolithography says I + + align:start position:0% +so for example photolithography says I + + + align:start position:0% +so for example photolithography says I +can't pattern smaller than certain + + align:start position:0% +can't pattern smaller than certain + + + align:start position:0% +can't pattern smaller than certain +Dimensions uh dishing limits that + + align:start position:0% +Dimensions uh dishing limits that + + + align:start position:0% +Dimensions uh dishing limits that +dishing down into wide features says I + + align:start position:0% +dishing down into wide features says I + + + align:start position:0% +dishing down into wide features says I +can't have features wider than 10 + + align:start position:0% +can't have features wider than 10 + + + align:start position:0% +can't have features wider than 10 +microns I'll dish them too much so this + + align:start position:0% +microns I'll dish them too much so this + + + align:start position:0% +microns I'll dish them too much so this +is another way of coupling between + + align:start position:0% +is another way of coupling between + + + align:start position:0% +is another way of coupling between +design and + + align:start position:0% +design and + + + align:start position:0% +design and +manufacturer and then the last thing + + align:start position:0% +manufacturer and then the last thing + + + align:start position:0% +manufacturer and then the last thing +I've already alluded to but coming going + + align:start position:0% +I've already alluded to but coming going + + + align:start position:0% +I've already alluded to but coming going +back to the CMP + + align:start position:0% +back to the CMP + + + align:start position:0% +back to the CMP +problem we also can develop and we'll + + align:start position:0% +problem we also can develop and we'll + + + align:start position:0% +problem we also can develop and we'll +talk about uh response surface or + + align:start position:0% +talk about uh response surface or + + + align:start position:0% +talk about uh response surface or +empirical models that say okay here's + + align:start position:0% +empirical models that say okay here's + + + align:start position:0% +empirical models that say okay here's +what the removal rate is or the + + align:start position:0% +what the removal rate is or the + + + align:start position:0% +what the removal rate is or the +non-uniformity is as a function of some + + align:start position:0% +non-uniformity is as a function of some + + + align:start position:0% +non-uniformity is as a function of some +of the process conditions like the speed + + align:start position:0% +of the process conditions like the speed + + + align:start position:0% +of the process conditions like the speed +of rotation or the pressure or downforce + + align:start position:0% +of rotation or the pressure or downforce + + + align:start position:0% +of rotation or the pressure or downforce +of rotation and once you have a basic + + align:start position:0% +of rotation and once you have a basic + + + align:start position:0% +of rotation and once you have a basic +control + + align:start position:0% +control + + + align:start position:0% +control +model for example the normalized removal + + align:start position:0% +model for example the normalized removal + + + align:start position:0% +model for example the normalized removal +rate is a function of downforce and + + align:start position:0% +rate is a function of downforce and + + + align:start position:0% +rate is a function of downforce and +speed I've got some input output + + align:start position:0% +speed I've got some input output + + + align:start position:0% +speed I've got some input output +empirical relationship between these I + + align:start position:0% +empirical relationship between these I + + + align:start position:0% +empirical relationship between these I +can now use this in a runby run control + + align:start position:0% +can now use this in a runby run control + + + align:start position:0% +can now use this in a runby run control +kind of feedback situation where i' make + + align:start position:0% +kind of feedback situation where i' make + + + align:start position:0% +kind of feedback situation where i' make +a measurement on every wafer that comes + + align:start position:0% +a measurement on every wafer that comes + + + align:start position:0% +a measurement on every wafer that comes +out what the average removal rate was + + align:start position:0% +out what the average removal rate was + + + align:start position:0% +out what the average removal rate was +use that together with this empirical + + align:start position:0% +use that together with this empirical + + + align:start position:0% +use that together with this empirical +model perhaps do a model update to track + + align:start position:0% +model perhaps do a model update to track + + + align:start position:0% +model perhaps do a model update to track +The Changing State of the equipment and + + align:start position:0% +The Changing State of the equipment and + + + align:start position:0% +The Changing State of the equipment and +PAD as it also gets perturbed from run + + align:start position:0% +PAD as it also gets perturbed from run + + + align:start position:0% +PAD as it also gets perturbed from run +to run use that new model to say for the + + align:start position:0% +to run use that new model to say for the + + + align:start position:0% +to run use that new model to say for the +next wafer change the recipe slightly + + align:start position:0% +next wafer change the recipe slightly + + + align:start position:0% +next wafer change the recipe slightly +polish a little bit longer or press a + + align:start position:0% +polish a little bit longer or press a + + + align:start position:0% +polish a little bit longer or press a +little bit harder to compensate for that + + align:start position:0% +little bit harder to compensate for that + + + align:start position:0% +little bit harder to compensate for that +known characterized variation source and + + align:start position:0% +known characterized variation source and + + + align:start position:0% +known characterized variation source and +so this is just an example you can + + align:start position:0% +so this is just an example you can + + + align:start position:0% +so this is just an example you can +imagine that using these simplified + + align:start position:0% +imagine that using these simplified + + + align:start position:0% +imagine that using these simplified +models one can have some compensation + + align:start position:0% +models one can have some compensation + + + align:start position:0% +models one can have some compensation +strategy that brings the removal rate + + align:start position:0% +strategy that brings the removal rate + + + align:start position:0% +strategy that brings the removal rate +back up back up to Target and so we'll + + align:start position:0% +back up back up to Target and so we'll + + + align:start position:0% +back up back up to Target and so we'll +talk about that in the latter part of + + align:start position:0% +talk about that in the latter part of + + + align:start position:0% +talk about that in the latter part of +the term as well these are just examples + + align:start position:0% +the term as well these are just examples + + + align:start position:0% +the term as well these are just examples +showing for different numbers of Wafers + + align:start position:0% +showing for different numbers of Wafers + + + align:start position:0% +showing for different numbers of Wafers +you have to actually change the speed or + + align:start position:0% +you have to actually change the speed or + + + align:start position:0% +you have to actually change the speed or +the pressure uh down Force but you can + + align:start position:0% +the pressure uh down Force but you can + + + align:start position:0% +the pressure uh down Force but you can +get very good control of the + + align:start position:0% +get very good control of the + + + align:start position:0% +get very good control of the +output so to wrap up for today this was + + align:start position:0% +output so to wrap up for today this was + + + align:start position:0% +output so to wrap up for today this was +a a whirlwind tour through the + + align:start position:0% +a a whirlwind tour through the + + + align:start position:0% +a a whirlwind tour through the +semiconductor fabrication process and I + + align:start position:0% +semiconductor fabrication process and I + + + align:start position:0% +semiconductor fabrication process and I +hope you have a feel for the Myriad + + align:start position:0% +hope you have a feel for the Myriad + + + align:start position:0% +hope you have a feel for the Myriad +different kinds of variations that are + + align:start position:0% +different kinds of variations that are + + + align:start position:0% +different kinds of variations that are +out there and a glimpse forward uh to to + + align:start position:0% +out there and a glimpse forward uh to to + + + align:start position:0% +out there and a glimpse forward uh to to +some of the techniques that we're going + + align:start position:0% +some of the techniques that we're going + + + align:start position:0% +some of the techniques that we're going +to be developing through the term uh to + + align:start position:0% +to be developing through the term uh to + + + align:start position:0% +to be developing through the term uh to +deal with this so we'll see you on + + align:start position:0% +deal with this so we'll see you on + + + align:start position:0% +deal with this so we'll see you on +Tuesday uh Dave will be giving uh that + + align:start position:0% +Tuesday uh Dave will be giving uh that + + + align:start position:0% +Tuesday uh Dave will be giving uh that +lecture and talking about uh the rest of + + align:start position:0% +lecture and talking about uh the rest of + + + align:start position:0% +lecture and talking about uh the rest of +the processes out there in the world + + align:start position:0% +the processes out there in the world + + + align:start position:0% +the processes out there in the world +besides semiconductor fabrication and + + align:start position:0% +besides semiconductor fabrication and + + + align:start position:0% +besides semiconductor fabrication and +building up some intuition that we'll + + align:start position:0% +building up some intuition that we'll + + + align:start position:0% +building up some intuition that we'll +use uh uh in those + + align:start position:0% +use uh uh in those + + + align:start position:0% +use uh uh in those +processes so get started on the problem + + align:start position:0% +processes so get started on the problem + + + align:start position:0% +processes so get started on the problem +set as well \ No newline at end of file diff --git a/739SB34oEyo.txt b/739SB34oEyo.txt new file mode 100644 index 0000000000000000000000000000000000000000..99a3a0f8ecdb4ce5f9f4597eb654319290dd3fcb --- /dev/null +++ b/739SB34oEyo.txt @@ -0,0 +1,859 @@ +align:start position:0% + +I of course want my students to be as + + align:start position:0% +I of course want my students to be as + + + align:start position:0% +I of course want my students to be as +excited about chemistry as I am and you + + align:start position:0% +excited about chemistry as I am and you + + + align:start position:0% +excited about chemistry as I am and you +know I I feel like MIT is you know a + + align:start position:0% +know I I feel like MIT is you know a + + + align:start position:0% +know I I feel like MIT is you know a +relatively serious place um but the MIT + + align:start position:0% +relatively serious place um but the MIT + + + align:start position:0% +relatively serious place um but the MIT +students are really fun people and + + align:start position:0% +students are really fun people and + + + align:start position:0% +students are really fun people and +they're willing to make fun of + + align:start position:0% +they're willing to make fun of + + + align:start position:0% +they're willing to make fun of +themselves and be a little geeky and I + + align:start position:0% +themselves and be a little geeky and I + + + align:start position:0% +themselves and be a little geeky and I +love that and so whenever I can kind of + + align:start position:0% +love that and so whenever I can kind of + + + align:start position:0% +love that and so whenever I can kind of +encourage something like that in class I + + align:start position:0% +encourage something like that in class I + + + align:start position:0% +encourage something like that in class I +always try to take advantage of it and + + align:start position:0% +always try to take advantage of it and + + + align:start position:0% +always try to take advantage of it and +uh you know one of the things I like to + + align:start position:0% +uh you know one of the things I like to + + + align:start position:0% +uh you know one of the things I like to +ask them is sort of you know if you're + + align:start position:0% +ask them is sort of you know if you're + + + align:start position:0% +ask them is sort of you know if you're +going to if one geek is going to propose + + align:start position:0% +going to if one geek is going to propose + + + align:start position:0% +going to if one geek is going to propose +marriage to another geek um you know do + + align:start position:0% +marriage to another geek um you know do + + + align:start position:0% +marriage to another geek um you know do +you really give them a diamond or maybe + + align:start position:0% +you really give them a diamond or maybe + + + align:start position:0% +you really give them a diamond or maybe +graphite because you know one is more + + align:start position:0% +graphite because you know one is more + + + align:start position:0% +graphite because you know one is more +kinetically uh stable and one is more + + align:start position:0% +kinetically uh stable and one is more + + + align:start position:0% +kinetically uh stable and one is more +thermodynamically stable and what's the + + align:start position:0% +thermodynamically stable and what's the + + + align:start position:0% +thermodynamically stable and what's the +best gift and that often then you know + + align:start position:0% +best gift and that often then you know + + + align:start position:0% +best gift and that often then you know +they they can discuss which they think + + align:start position:0% +they they can discuss which they think + + + align:start position:0% +they they can discuss which they think +and then I'm like actually neither + + align:start position:0% +and then I'm like actually neither + + + align:start position:0% +and then I'm like actually neither +because what you should give them is the + + align:start position:0% +because what you should give them is the + + + align:start position:0% +because what you should give them is the +Green Lantern ring and then someone gets + + align:start position:0% +Green Lantern ring and then someone gets + + + align:start position:0% +Green Lantern ring and then someone gets +say what about Lord of the Rings ring + + align:start position:0% +say what about Lord of the Rings ring + + + align:start position:0% +say what about Lord of the Rings ring +you know and so you have you can sort of + + align:start position:0% +you know and so you have you can sort of + + + align:start position:0% +you know and so you have you can sort of +Bring In These funds but you know your + + align:start position:0% +Bring In These funds but you know your + + + align:start position:0% +Bring In These funds but you know your +arguments are kind of based on chemical + + align:start position:0% +arguments are kind of based on chemical + + + align:start position:0% +arguments are kind of based on chemical +principles rather than other things so + + align:start position:0% +principles rather than other things so + + + align:start position:0% +principles rather than other things so +you know if you can really bring in sort + + align:start position:0% +you know if you can really bring in sort + + + align:start position:0% +you know if you can really bring in sort +of the fun humor um that MIT students + + align:start position:0% +of the fun humor um that MIT students + + + align:start position:0% +of the fun humor um that MIT students +enjoy and they're always with me on that + + align:start position:0% +enjoy and they're always with me on that + + + align:start position:0% +enjoy and they're always with me on that +and I I I love that part um so we we I + + align:start position:0% +and I I I love that part um so we we I + + + align:start position:0% +and I I I love that part um so we we I +I'm always looking for ways to kind of + + align:start position:0% +I'm always looking for ways to kind of + + + align:start position:0% +I'm always looking for ways to kind of +uh have something be a little bit more + + align:start position:0% +uh have something be a little bit more + + + align:start position:0% +uh have something be a little bit more +fun especially in some of uh in some of + + align:start position:0% +fun especially in some of uh in some of + + + align:start position:0% +fun especially in some of uh in some of +the units I feel really lend themselves + + align:start position:0% +the units I feel really lend themselves + + + align:start position:0% +the units I feel really lend themselves +to these fun examples and other ones um + + align:start position:0% +to these fun examples and other ones um + + + align:start position:0% +to these fun examples and other ones um +are a bit more challenging but I want to + + align:start position:0% +are a bit more challenging but I want to + + + align:start position:0% +are a bit more challenging but I want to +make sure that everyone has something in + + align:start position:0% +make sure that everyone has something in + + + align:start position:0% +make sure that everyone has something in +and if I find something online or + + align:start position:0% +and if I find something online or + + + align:start position:0% +and if I find something online or +whatever I really try to use that in my + + align:start position:0% +whatever I really try to use that in my + + + align:start position:0% +whatever I really try to use that in my +class and I found um these videos of + + align:start position:0% +class and I found um these videos of + + + align:start position:0% +class and I found um these videos of +dogs teaching chemistry um which this at + + align:start position:0% +dogs teaching chemistry um which this at + + + align:start position:0% +dogs teaching chemistry um which this at +least some of the students love there's + + align:start position:0% +least some of the students love there's + + + align:start position:0% +least some of the students love there's +always a few MIT students that are like + + align:start position:0% +always a few MIT students that are like + + + align:start position:0% +always a few MIT students that are like +I wish you would just stick to the facts + + align:start position:0% +I wish you would just stick to the facts + + + align:start position:0% +I wish you would just stick to the facts +and straight derivations but uh for the + + align:start position:0% +and straight derivations but uh for the + + + align:start position:0% +and straight derivations but uh for the +most part I think uh attendance would + + align:start position:0% +most part I think uh attendance would + + + align:start position:0% +most part I think uh attendance would +suggest that students come and that + + align:start position:0% +suggest that students come and that + + + align:start position:0% +suggest that students come and that +they're engaged and that they're they're + + align:start position:0% +they're engaged and that they're they're + + + align:start position:0% +they're engaged and that they're they're +seeing these little things and and I've + + align:start position:0% +seeing these little things and and I've + + + align:start position:0% +seeing these little things and and I've +discovered that it really helps people + + align:start position:0% +discovered that it really helps people + + + align:start position:0% +discovered that it really helps people +remember when you do something a little + + align:start position:0% +remember when you do something a little + + + align:start position:0% +remember when you do something a little +bit different uh one of my favorite + + align:start position:0% +bit different uh one of my favorite + + + align:start position:0% +bit different uh one of my favorite +things to do is uh when I teach about + + align:start position:0% +things to do is uh when I teach about + + + align:start position:0% +things to do is uh when I teach about +buffers I don't know why so many + + align:start position:0% +buffers I don't know why so many + + + align:start position:0% +buffers I don't know why so many +students have trouble with with the + + align:start position:0% +students have trouble with with the + + + align:start position:0% +students have trouble with with the +concept of buffering acid-based + + align:start position:0% +concept of buffering acid-based + + + align:start position:0% +concept of buffering acid-based +titrations it's just really hard for a + + align:start position:0% +titrations it's just really hard for a + + + align:start position:0% +titrations it's just really hard for a +number of people so I thought over the + + align:start position:0% +number of people so I thought over the + + + align:start position:0% +number of people so I thought over the +years of ways that I can really get them + + align:start position:0% +years of ways that I can really get them + + + align:start position:0% +years of ways that I can really get them +to remember certain things and some of + + align:start position:0% +to remember certain things and some of + + + align:start position:0% +to remember certain things and some of +it I can make fun others is I have to + + align:start position:0% +it I can make fun others is I have to + + + align:start position:0% +it I can make fun others is I have to +figure out how to just make them + + align:start position:0% +figure out how to just make them + + + align:start position:0% +figure out how to just make them +memorize certain things um and really + + align:start position:0% +memorize certain things um and really + + + align:start position:0% +memorize certain things um and really +just get them there where they can just + + align:start position:0% +just get them there where they can just + + + align:start position:0% +just get them there where they can just +kind of do this off the top of their + + align:start position:0% +kind of do this off the top of their + + + align:start position:0% +kind of do this off the top of their +head and so when I talk about a buffer I + + align:start position:0% +head and so when I talk about a buffer I + + + align:start position:0% +head and so when I talk about a buffer I +always want to make the point that you + + align:start position:0% +always want to make the point that you + + + align:start position:0% +always want to make the point that you +need in your two buffer you need + + align:start position:0% +need in your two buffer you need + + + align:start position:0% +need in your two buffer you need +something that's a weak acid and and the + + align:start position:0% +something that's a weak acid and and the + + + align:start position:0% +something that's a weak acid and and the +conjugate of that is a conjugate weak + + align:start position:0% +conjugate of that is a conjugate weak + + + align:start position:0% +conjugate of that is a conjugate weak +base and you can't just have an acid or + + align:start position:0% +base and you can't just have an acid or + + + align:start position:0% +base and you can't just have an acid or +just have a base that won't buffer + + align:start position:0% +just have a base that won't buffer + + + align:start position:0% +just have a base that won't buffer +because you need the something if you + + align:start position:0% +because you need the something if you + + + align:start position:0% +because you need the something if you +add acid you need something that will + + align:start position:0% +add acid you need something that will + + + align:start position:0% +add acid you need something that will +buffer it to change that keep the pH + + align:start position:0% +buffer it to change that keep the pH + + + align:start position:0% +buffer it to change that keep the pH +constant you have if you add base you + + align:start position:0% +constant you have if you add base you + + + align:start position:0% +constant you have if you add base you +need something that will um so it has to + + align:start position:0% +need something that will um so it has to + + + align:start position:0% +need something that will um so it has to +go both ways so I like to dress up and I + + align:start position:0% +go both ways so I like to dress up and I + + + align:start position:0% +go both ways so I like to dress up and I +have the abbreviation for a weak acid um + + align:start position:0% +have the abbreviation for a weak acid um + + + align:start position:0% +have the abbreviation for a weak acid um +taped on the front of my shirt and the + + align:start position:0% +taped on the front of my shirt and the + + + align:start position:0% +taped on the front of my shirt and the +abbreviation for the weak base taped on + + align:start position:0% +abbreviation for the weak base taped on + + + align:start position:0% +abbreviation for the weak base taped on +the back of my shirt and I said I am a + + align:start position:0% +the back of my shirt and I said I am a + + + align:start position:0% +the back of my shirt and I said I am a +buffer and I'm an acid and then I turn + + align:start position:0% +buffer and I'm an acid and then I turn + + + align:start position:0% +buffer and I'm an acid and then I turn +around I'm a base and I turn around + + align:start position:0% +around I'm a base and I turn around + + + align:start position:0% +around I'm a base and I turn around +again I'm an acid and I just twirl + + align:start position:0% +again I'm an acid and I just twirl + + + align:start position:0% +again I'm an acid and I just twirl +around the classroom and I said um I + + align:start position:0% +around the classroom and I said um I + + + align:start position:0% +around the classroom and I said um I +want this engraved in your brain that a + + align:start position:0% +want this engraved in your brain that a + + + align:start position:0% +want this engraved in your brain that a +buffer has to have both a weak acid and + + align:start position:0% +buffer has to have both a weak acid and + + + align:start position:0% +buffer has to have both a weak acid and +a weak base and if I keep twirling like + + align:start position:0% +a weak base and if I keep twirling like + + + align:start position:0% +a weak base and if I keep twirling like +this you will try to purge this memory + + align:start position:0% +this you will try to purge this memory + + + align:start position:0% +this you will try to purge this memory +from your brain of Professor drenin + + align:start position:0% +from your brain of Professor drenin + + + align:start position:0% +from your brain of Professor drenin +twirling around the classroom as an acid + + align:start position:0% +twirling around the classroom as an acid + + + align:start position:0% +twirling around the classroom as an acid +and a base but you won't be able to + + align:start position:0% +and a base but you won't be able to + + + align:start position:0% +and a base but you won't be able to +it'll be with you for the rest of your + + align:start position:0% +it'll be with you for the rest of your + + + align:start position:0% +it'll be with you for the rest of your +life you'll be on your deathbed going + + align:start position:0% +life you'll be on your deathbed going + + + align:start position:0% +life you'll be on your deathbed going +please can the image of Professor drenan + + align:start position:0% +please can the image of Professor drenan + + + align:start position:0% +please can the image of Professor drenan +twirling around in that silly t-shirt + + align:start position:0% +twirling around in that silly t-shirt + + + align:start position:0% +twirling around in that silly t-shirt +that she made with lab tape please can + + align:start position:0% +that she made with lab tape please can + + + align:start position:0% +that she made with lab tape please can +it leave my brain now but no no it will + + align:start position:0% +it leave my brain now but no no it will + + + align:start position:0% +it leave my brain now but no no it will +be with you forever and when I do that + + align:start position:0% +be with you forever and when I do that + + + align:start position:0% +be with you forever and when I do that +the students do better on the acidbase + + align:start position:0% +the students do better on the acidbase + + + align:start position:0% +the students do better on the acidbase +problems so I am okay with really + + align:start position:0% +problems so I am okay with really + + + align:start position:0% +problems so I am okay with really +embarrassing myself whatever it takes I + + align:start position:0% +embarrassing myself whatever it takes I + + + align:start position:0% +embarrassing myself whatever it takes I +go that extra distance um because I want + + align:start position:0% +go that extra distance um because I want + + + align:start position:0% +go that extra distance um because I want +them to remember + + align:start position:0% + + + + align:start position:0% + +that \ No newline at end of file diff --git a/7iIkKOSlWoI.txt b/7iIkKOSlWoI.txt new file mode 100644 index 0000000000000000000000000000000000000000..b449dc3a20e84496df9b0d2ba627eda105908b71 --- /dev/null +++ b/7iIkKOSlWoI.txt @@ -0,0 +1,8411 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu we were talking last time + + align:start position:0% +ocw.mit.edu we were talking last time + + + align:start position:0% +ocw.mit.edu we were talking last time +and I I didn't quite get to that + + align:start position:0% +and I I didn't quite get to that + + + align:start position:0% +and I I didn't quite get to that +tremendously important chapter chapter + + align:start position:0% +tremendously important chapter chapter + + + align:start position:0% +tremendously important chapter chapter +six difficulties on + + align:start position:0% +six difficulties on + + + align:start position:0% +six difficulties on +Theory um and we were just sort of uh + + align:start position:0% +Theory um and we were just sort of uh + + + align:start position:0% +Theory um and we were just sort of uh +finishing up I think with the tree + + align:start position:0% +finishing up I think with the tree + + + align:start position:0% +finishing up I think with the tree +metaphor and I I couldn't resist adding + + align:start position:0% +metaphor and I I couldn't resist adding + + + align:start position:0% +metaphor and I I couldn't resist adding +this to your packet because um the tree + + align:start position:0% +this to your packet because um the tree + + + align:start position:0% +this to your packet because um the tree +metaphor has floated in and out in many + + align:start position:0% +metaphor has floated in and out in many + + + align:start position:0% +metaphor has floated in and out in many +different places and Darwin picks up on + + align:start position:0% +different places and Darwin picks up on + + + align:start position:0% +different places and Darwin picks up on +it and uh he gives a a whole + + align:start position:0% +it and uh he gives a a whole + + + align:start position:0% +it and uh he gives a a whole +uh passage in uh toward the end of + + align:start position:0% +uh passage in uh toward the end of + + + align:start position:0% +uh passage in uh toward the end of +chapter + + align:start position:0% +chapter + + + align:start position:0% +chapter +4 uh where he discusses uh the tree as a + + align:start position:0% +4 uh where he discusses uh the tree as a + + + align:start position:0% +4 uh where he discusses uh the tree as a +as a metaphor for the way in which uh + + align:start position:0% +as a metaphor for the way in which uh + + + align:start position:0% +as a metaphor for the way in which uh +organisms have flourished and some of + + align:start position:0% +organisms have flourished and some of + + + align:start position:0% +organisms have flourished and some of +them have uh overtopped and expanded + + align:start position:0% +them have uh overtopped and expanded + + + align:start position:0% +them have uh overtopped and expanded +above others and certain lines have + + align:start position:0% +above others and certain lines have + + + align:start position:0% +above others and certain lines have +become big Trunks and others have kind + + align:start position:0% +become big Trunks and others have kind + + + align:start position:0% +become big Trunks and others have kind +of diminished and so forth and the tree + + align:start position:0% +of diminished and so forth and the tree + + + align:start position:0% +of diminished and so forth and the tree +is an nice kind of three-dimensional and + + align:start position:0% +is an nice kind of three-dimensional and + + + align:start position:0% +is an nice kind of three-dimensional and +somebody was talking in last class + + align:start position:0% +somebody was talking in last class + + + align:start position:0% +somebody was talking in last class +Darwin's uh one illustration is sort of + + align:start position:0% +Darwin's uh one illustration is sort of + + + align:start position:0% +Darwin's uh one illustration is sort of +a little bit more two-dimensional than + + align:start position:0% +a little bit more two-dimensional than + + + align:start position:0% +a little bit more two-dimensional than +we would like it to be because if you + + align:start position:0% +we would like it to be because if you + + + align:start position:0% +we would like it to be because if you +can sort of think of it as uh working in + + align:start position:0% +can sort of think of it as uh working in + + + align:start position:0% +can sort of think of it as uh working in +all Dimensions you get a much more uh + + align:start position:0% +all Dimensions you get a much more uh + + + align:start position:0% +all Dimensions you get a much more uh +robust sense of you know how this how + + align:start position:0% +robust sense of you know how this how + + + align:start position:0% +robust sense of you know how this how +these different U + + align:start position:0% +these different U + + + align:start position:0% +these different U +forms + + align:start position:0% +forms + + + align:start position:0% +forms +so you know you you you get a better + + align:start position:0% +so you know you you you get a better + + + align:start position:0% +so you know you you you get a better +sense of how these forms are uh emerging + + align:start position:0% +sense of how these forms are uh emerging + + + align:start position:0% +sense of how these forms are uh emerging +and and and replacing each other over + + align:start position:0% +and and and replacing each other over + + + align:start position:0% +and and and replacing each other over +time but as we were saying we're saying + + align:start position:0% +time but as we were saying we're saying + + + align:start position:0% +time but as we were saying we're saying +a number of things this this chart + + align:start position:0% +a number of things this this chart + + + align:start position:0% +a number of things this this chart +actually which appears at the end of the + + align:start position:0% +actually which appears at the end of the + + + align:start position:0% +actually which appears at the end of the +book so Darwin's visual strategy in the + + align:start position:0% +book so Darwin's visual strategy in the + + + align:start position:0% +book so Darwin's visual strategy in the +origin is uh + + align:start position:0% +origin is uh + + + align:start position:0% +origin is uh +pretty uh minimalist you might say it's + + align:start position:0% +pretty uh minimalist you might say it's + + + align:start position:0% +pretty uh minimalist you might say it's +got one graphic maybe that was wise + + align:start position:0% +got one graphic maybe that was wise + + + align:start position:0% +got one graphic maybe that was wise +because uh the whole thing is + + align:start position:0% +because uh the whole thing is + + + align:start position:0% +because uh the whole thing is +um verbally described um + + align:start position:0% +um verbally described um + + + align:start position:0% +um verbally described um +so it + + align:start position:0% +so it + + + align:start position:0% +so it +uh you know it's probably as I was + + align:start position:0% +uh you know it's probably as I was + + + align:start position:0% +uh you know it's probably as I was +saying just as well that he used just + + align:start position:0% +saying just as well that he used just + + + align:start position:0% +saying just as well that he used just +one chart but this chart is the one and + + align:start position:0% +one chart but this chart is the one and + + + align:start position:0% +one chart but this chart is the one and +it sort of nailed down a whole variety + + align:start position:0% +it sort of nailed down a whole variety + + + align:start position:0% +it sort of nailed down a whole variety +of ways in which you can think about + + align:start position:0% +of ways in which you can think about + + + align:start position:0% +of ways in which you can think about +Darwin thought you could think about + + align:start position:0% +Darwin thought you could think about + + + align:start position:0% +Darwin thought you could think about +Evolution and these uh different layers + + align:start position:0% +Evolution and these uh different layers + + + align:start position:0% +Evolution and these uh different layers +um represent uh vast amounts of time and + + align:start position:0% +um represent uh vast amounts of time and + + + align:start position:0% +um represent uh vast amounts of time and +so this this concept of the emergence of + + align:start position:0% +so this this concept of the emergence of + + + align:start position:0% +so this this concept of the emergence of +species but as you can see in the chart + + align:start position:0% +species but as you can see in the chart + + + align:start position:0% +species but as you can see in the chart +most species that have ever existed are + + align:start position:0% +most species that have ever existed are + + + align:start position:0% +most species that have ever existed are +long + + align:start position:0% +long + + + align:start position:0% +long +gone so you know the the vast proportion + + align:start position:0% +gone so you know the the vast proportion + + + align:start position:0% +gone so you know the the vast proportion +of species that have existed in time + + align:start position:0% +of species that have existed in time + + + align:start position:0% +of species that have existed in time +have been + + align:start position:0% +have been + + + align:start position:0% +have been +replaced and there are certain patterns + + align:start position:0% +replaced and there are certain patterns + + + align:start position:0% +replaced and there are certain patterns +of replacement that he meant to capture + + align:start position:0% +of replacement that he meant to capture + + + align:start position:0% +of replacement that he meant to capture +in this um in in this + + align:start position:0% +in this um in in this + + + align:start position:0% +in this um in in this +graphic and as you can see uh a has done + + align:start position:0% +graphic and as you can see uh a has done + + + align:start position:0% +graphic and as you can see uh a has done +very well for itself and in in some + + align:start position:0% +very well for itself and in in some + + + align:start position:0% +very well for itself and in in some +sense uh success leads to Greater + + align:start position:0% +sense uh success leads to Greater + + + align:start position:0% +sense uh success leads to Greater +success in evolutionary + + align:start position:0% +success in evolutionary + + + align:start position:0% +success in evolutionary +terms um that is uh organisms that have + + align:start position:0% +terms um that is uh organisms that have + + + align:start position:0% +terms um that is uh organisms that have +been very very + + align:start position:0% +been very very + + + align:start position:0% +been very very +successful tend to Branch out and as + + align:start position:0% +successful tend to Branch out and as + + + align:start position:0% +successful tend to Branch out and as +they Branch out more of them + + align:start position:0% +they Branch out more of them + + + align:start position:0% +they Branch out more of them +diversify into the uh into the places uh + + align:start position:0% +diversify into the uh into the places uh + + + align:start position:0% +diversify into the uh into the places uh +in nature and they tend to Crow out + + align:start position:0% +in nature and they tend to Crow out + + + align:start position:0% +in nature and they tend to Crow out +other + + align:start position:0% +other + + + align:start position:0% +other +forms so that that uh this whole process + + align:start position:0% +forms so that that uh this whole process + + + align:start position:0% +forms so that that uh this whole process +is uh leads to uh certain kinds of has a + + align:start position:0% +is uh leads to uh certain kinds of has a + + + align:start position:0% +is uh leads to uh certain kinds of has a +certain kind of + + align:start position:0% +certain kind of + + + align:start position:0% +certain kind of +directionality in in uh the direction of + + align:start position:0% +directionality in in uh the direction of + + + align:start position:0% +directionality in in uh the direction of +uh successful + + align:start position:0% +uh successful + + + align:start position:0% +uh successful +forms um there are some hold outs as you + + align:start position:0% +forms um there are some hold outs as you + + + align:start position:0% +forms um there are some hold outs as you +can see in + + align:start position:0% +can see in + + + align:start position:0% +can see in +f um ceoc cans or horseshoe crabs or + + align:start position:0% +f um ceoc cans or horseshoe crabs or + + + align:start position:0% +f um ceoc cans or horseshoe crabs or +whatever that simply uh exist in very + + align:start position:0% +whatever that simply uh exist in very + + + align:start position:0% +whatever that simply uh exist in very +very stable + + align:start position:0% +very stable + + + align:start position:0% +very stable +environments and have sort sort of uh + + align:start position:0% +environments and have sort sort of uh + + + align:start position:0% +environments and have sort sort of uh +been able to exploit + + align:start position:0% +been able to exploit + + + align:start position:0% +been able to exploit +the space the place what we would Now + + align:start position:0% +the space the place what we would Now + + + align:start position:0% +the space the place what we would Now +call the + + align:start position:0% +call the + + + align:start position:0% +call the +niche and flourish there and nothing + + align:start position:0% +niche and flourish there and nothing + + + align:start position:0% +niche and flourish there and nothing +really emerges + + align:start position:0% +really emerges + + + align:start position:0% +really emerges +to uh displace + + align:start position:0% +to uh displace + + + align:start position:0% +to uh displace +them um so um and then you know there + + align:start position:0% +them um so um and then you know there + + + align:start position:0% +them um so um and then you know there +are other forms that have also been very + + align:start position:0% +are other forms that have also been very + + + align:start position:0% +are other forms that have also been very +successful I don't know maybe one of + + align:start position:0% +successful I don't know maybe one of + + + align:start position:0% +successful I don't know maybe one of +these is arthopods or insect insects or + + align:start position:0% +these is arthopods or insect insects or + + + align:start position:0% +these is arthopods or insect insects or +something like that and another one + + align:start position:0% +something like that and another one + + + align:start position:0% +something like that and another one +maybe mammals and I don't know he + + align:start position:0% +maybe mammals and I don't know he + + + align:start position:0% +maybe mammals and I don't know he +doesn't put names to each one of these + + align:start position:0% +doesn't put names to each one of these + + + align:start position:0% +doesn't put names to each one of these +but the pattern is what he's interested + + align:start position:0% +but the pattern is what he's interested + + + align:start position:0% +but the pattern is what he's interested +in so then uh he ends up in this chapter + + align:start position:0% +in so then uh he ends up in this chapter + + + align:start position:0% +in so then uh he ends up in this chapter +of saying you know the affinities of all + + align:start position:0% +of saying you know the affinities of all + + + align:start position:0% +of saying you know the affinities of all +the beings of the same class have + + align:start position:0% +the beings of the same class have + + + align:start position:0% +the beings of the same class have +sometimes been + + align:start position:0% +sometimes been + + + align:start position:0% +sometimes been +represented he's talking about a class + + align:start position:0% +represented he's talking about a class + + + align:start position:0% +represented he's talking about a class +now uh by a great tree I believe this + + align:start position:0% +now uh by a great tree I believe this + + + align:start position:0% +now uh by a great tree I believe this +simile largely speaks the truth the + + align:start position:0% +simile largely speaks the truth the + + + align:start position:0% +simile largely speaks the truth the +green and budding Twigs may represent + + align:start position:0% +green and budding Twigs may represent + + + align:start position:0% +green and budding Twigs may represent +existing species and those produced + + align:start position:0% +existing species and those produced + + + align:start position:0% +existing species and those produced +during each former Year may represent + + align:start position:0% +during each former Year may represent + + + align:start position:0% +during each former Year may represent +the long succession of extinct species + + align:start position:0% +the long succession of extinct species + + + align:start position:0% +the long succession of extinct species +at each period of growth all the growing + + align:start position:0% +at each period of growth all the growing + + + align:start position:0% +at each period of growth all the growing +Twigs have tried to Branch out on all um + + align:start position:0% +Twigs have tried to Branch out on all um + + + align:start position:0% +Twigs have tried to Branch out on all um +sides and to overtop and kill the + + align:start position:0% +sides and to overtop and kill the + + + align:start position:0% +sides and to overtop and kill the +surrounding twigs and branches out + + align:start position:0% +surrounding twigs and branches out + + + align:start position:0% +surrounding twigs and branches out +compete + + align:start position:0% +compete + + + align:start position:0% +compete +them he sees this as a uh a accurate + + align:start position:0% +them he sees this as a uh a accurate + + + align:start position:0% +them he sees this as a uh a accurate +simile for the way in which uh organic + + align:start position:0% +simile for the way in which uh organic + + + align:start position:0% +simile for the way in which uh organic +Life Works sort of constantly trying to + + align:start position:0% +Life Works sort of constantly trying to + + + align:start position:0% +Life Works sort of constantly trying to +make the best use of available + + align:start position:0% +make the best use of available + + + align:start position:0% +make the best use of available +resources + + align:start position:0% +resources + + + align:start position:0% +resources +um well I won't read the whole thing but + + align:start position:0% +um well I won't read the whole thing but + + + align:start position:0% +um well I won't read the whole thing but +uh as you see this is um a very powerful + + align:start position:0% +uh as you see this is um a very powerful + + + align:start position:0% +uh as you see this is um a very powerful +metaphor and it it always makes me think + + align:start position:0% +metaphor and it it always makes me think + + + align:start position:0% +metaphor and it it always makes me think +a little bit of uh filo's uh vegetative + + align:start position:0% +a little bit of uh filo's uh vegetative + + + align:start position:0% +a little bit of uh filo's uh vegetative +principle the idea that you know the + + align:start position:0% +principle the idea that you know the + + + align:start position:0% +principle the idea that you know the +world is emerged through some kind of + + align:start position:0% +world is emerged through some kind of + + + align:start position:0% +world is emerged through some kind of +process that is + + align:start position:0% +process that is + + + align:start position:0% +process that is +best + + align:start position:0% +best + + + align:start position:0% +best +uh compared to + + align:start position:0% +uh compared to + + + align:start position:0% +uh compared to +growth rather than + + align:start position:0% +growth rather than + + + align:start position:0% +growth rather than +fabrication fabrication is something + + align:start position:0% +fabrication fabrication is something + + + align:start position:0% +fabrication fabrication is something +that we purposefully create and + + align:start position:0% +that we purposefully create and + + + align:start position:0% +that we purposefully create and +make + + align:start position:0% +make + + + align:start position:0% +make +growth has an innate uh force that + + align:start position:0% +growth has an innate uh force that + + + align:start position:0% +growth has an innate uh force that +drives + + align:start position:0% +drives + + + align:start position:0% +drives +it as Dylan Thomas would have said the + + align:start position:0% +it as Dylan Thomas would have said the + + + align:start position:0% +it as Dylan Thomas would have said the +force that drives the + + align:start position:0% +force that drives the + + + align:start position:0% +force that drives the +green uh Leaf the green but or the green + + align:start position:0% +green uh Leaf the green but or the green + + + align:start position:0% +green uh Leaf the green but or the green +leaf through the fuse + + align:start position:0% +leaf through the fuse + + + align:start position:0% +leaf through the fuse +um the so this this sort of organic + + align:start position:0% +um the so this this sort of organic + + + align:start position:0% +um the so this this sort of organic +metaphor is what dominates uh Darwin's + + align:start position:0% +metaphor is what dominates uh Darwin's + + + align:start position:0% +metaphor is what dominates uh Darwin's +book this sort of sense of growth + + align:start position:0% +book this sort of sense of growth + + + align:start position:0% +book this sort of sense of growth +constantly growing uh everything + + align:start position:0% +constantly growing uh everything + + + align:start position:0% +constantly growing uh everything +massively uh making a massive effort to + + align:start position:0% +massively uh making a massive effort to + + + align:start position:0% +massively uh making a massive effort to +reproduce so it's Tak malus and or it's + + align:start position:0% +reproduce so it's Tak malus and or it's + + + align:start position:0% +reproduce so it's Tak malus and or it's +it's an expansion of the malthusian idea + + align:start position:0% +it's an expansion of the malthusian idea + + + align:start position:0% +it's an expansion of the malthusian idea +of production into u a fundamental force + + align:start position:0% +of production into u a fundamental force + + + align:start position:0% +of production into u a fundamental force +of + + align:start position:0% +of + + + align:start position:0% +of +nature um and so as I said I think last + + align:start position:0% +nature um and so as I said I think last + + + align:start position:0% +nature um and so as I said I think last +class too uh you know Darwin's view is + + align:start position:0% +class too uh you know Darwin's view is + + + align:start position:0% +class too uh you know Darwin's view is +it's a scientific it's a very material + + align:start position:0% +it's a scientific it's a very material + + + align:start position:0% +it's a scientific it's a very material +scientific view I mean he's not trying + + align:start position:0% +scientific view I mean he's not trying + + + align:start position:0% +scientific view I mean he's not trying +to talk about theology or something like + + align:start position:0% +to talk about theology or something like + + + align:start position:0% +to talk about theology or something like +that that's that's not really even in + + align:start position:0% +that that's that's not really even in + + + align:start position:0% +that that's that's not really even in +the book and so it's I mean he mentions + + align:start position:0% +the book and so it's I mean he mentions + + + align:start position:0% +the book and so it's I mean he mentions +something at the end but uh it's really + + align:start position:0% +something at the end but uh it's really + + + align:start position:0% +something at the end but uh it's really +a scientific view it's just trying to + + align:start position:0% +a scientific view it's just trying to + + + align:start position:0% +a scientific view it's just trying to +put together from a scientific point of + + align:start position:0% +put together from a scientific point of + + + align:start position:0% +put together from a scientific point of +view how organic life uh is + + align:start position:0% +view how organic life uh is + + + align:start position:0% +view how organic life uh is +organized and it has really in some + + align:start position:0% +organized and it has really in some + + + align:start position:0% +organized and it has really in some +sense that's the limit of its purpose so + + align:start position:0% +sense that's the limit of its purpose so + + + align:start position:0% +sense that's the limit of its purpose so +to take it as some great track that is + + align:start position:0% +to take it as some great track that is + + + align:start position:0% +to take it as some great track that is +against this or that religious View and + + align:start position:0% +against this or that religious View and + + + align:start position:0% +against this or that religious View and +so forth is just to misunderstand what + + align:start position:0% +so forth is just to misunderstand what + + + align:start position:0% +so forth is just to misunderstand what +Dar is trying to do in the book + + align:start position:0% +Dar is trying to do in the book + + + align:start position:0% +Dar is trying to do in the book +it's it's about + + align:start position:0% + + + + align:start position:0% + +science okay well being a good scientist + + align:start position:0% +science okay well being a good scientist + + + align:start position:0% +science okay well being a good scientist +Darwin is one of the first + + align:start position:0% +Darwin is one of the first + + + align:start position:0% +Darwin is one of the first +to suggest where the weaknesses of his + + align:start position:0% +to suggest where the weaknesses of his + + + align:start position:0% +to suggest where the weaknesses of his +theory are and it turns out that his + + align:start position:0% +theory are and it turns out that his + + + align:start position:0% +theory are and it turns out that his +weaknesses are what people over the ages + + align:start position:0% +weaknesses are what people over the ages + + + align:start position:0% +weaknesses are what people over the ages +have used you know to uh uh to uh oppose + + align:start position:0% +have used you know to uh uh to uh oppose + + + align:start position:0% +have used you know to uh uh to uh oppose +his his General view that is Darwin was + + align:start position:0% +his his General view that is Darwin was + + + align:start position:0% +his his General view that is Darwin was +the first out and he said yes there are + + align:start position:0% +the first out and he said yes there are + + + align:start position:0% +the first out and he said yes there are +many many things in my work here uh that + + align:start position:0% +many many things in my work here uh that + + + align:start position:0% +many many things in my work here uh that +would be that are + + align:start position:0% +would be that are + + + align:start position:0% +would be that are +challenging and that present tremendous + + align:start position:0% +challenging and that present tremendous + + + align:start position:0% +challenging and that present tremendous +difficulties and he's sort of the first + + align:start position:0% +difficulties and he's sort of the first + + + align:start position:0% +difficulties and he's sort of the first +to say this um and so what he does in + + align:start position:0% +to say this um and so what he does in + + + align:start position:0% +to say this um and so what he does in +this chapter is he mentions these + + align:start position:0% +this chapter is he mentions these + + + align:start position:0% +this chapter is he mentions these +difficulties it's uh chapter six it's a + + align:start position:0% +difficulties it's uh chapter six it's a + + + align:start position:0% +difficulties it's uh chapter six it's a +it's a beautiful chapter it's a + + align:start position:0% +it's a beautiful chapter it's a + + + align:start position:0% +it's a beautiful chapter it's a +excellent piece of sort of + + align:start position:0% +excellent piece of sort of + + + align:start position:0% +excellent piece of sort of +um framing uh it's an excellent + + align:start position:0% +um framing uh it's an excellent + + + align:start position:0% +um framing uh it's an excellent +framework in which to think about you + + align:start position:0% +framework in which to think about you + + + align:start position:0% +framework in which to think about you +know the limits of his views too and he + + align:start position:0% +know the limits of his views too and he + + + align:start position:0% +know the limits of his views too and he +recognizes them and the first of course + + align:start position:0% +recognizes them and the first of course + + + align:start position:0% +recognizes them and the first of course +is uh what he says um the absence of + + align:start position:0% +is uh what he says um the absence of + + + align:start position:0% +is uh what he says um the absence of +transitional + + align:start position:0% +transitional + + + align:start position:0% +transitional +varieties so what does he mean by this + + align:start position:0% +varieties so what does he mean by this + + + align:start position:0% +varieties so what does he mean by this +absence of + + align:start position:0% +absence of + + + align:start position:0% +absence of +transitional varieties + + align:start position:0% + + + + align:start position:0% + +forms yeah Charles if you were to say + + align:start position:0% +forms yeah Charles if you were to say + + + align:start position:0% +forms yeah Charles if you were to say +that one I guess if like one thing came + + align:start position:0% +that one I guess if like one thing came + + + align:start position:0% +that one I guess if like one thing came +from something else a long time ago you + + align:start position:0% +from something else a long time ago you + + + align:start position:0% +from something else a long time ago you +can't really see the transition like + + align:start position:0% +can't really see the transition like + + + align:start position:0% +can't really see the transition like +there like you don't see it happening + + align:start position:0% +there like you don't see it happening + + + align:start position:0% +there like you don't see it happening +and there's like there's that Gap okay + + align:start position:0% +and there's like there's that Gap okay + + + align:start position:0% +and there's like there's that Gap okay +all right so there are many many uh + + align:start position:0% +all right so there are many many uh + + + align:start position:0% +all right so there are many many uh +there are many existing forms but where + + align:start position:0% +there are many existing forms but where + + + align:start position:0% +there are many existing forms but where +are the where are the links the + + align:start position:0% +are the where are the links the + + + align:start position:0% +are the where are the links the +so-called missing links you know if if + + align:start position:0% +so-called missing links you know if if + + + align:start position:0% +so-called missing links you know if if +reptiles and birds are in some sense uh + + align:start position:0% +reptiles and birds are in some sense uh + + + align:start position:0% +reptiles and birds are in some sense uh +descending from a common + + align:start position:0% +descending from a common + + + align:start position:0% +descending from a common +ancestor where is the thing that looks + + align:start position:0% +ancestor where is the thing that looks + + + align:start position:0% +ancestor where is the thing that looks +like a bird reptile or where is a thing + + align:start position:0% +like a bird reptile or where is a thing + + + align:start position:0% +like a bird reptile or where is a thing +that looks like uh a I don't know a uh a + + align:start position:0% +that looks like uh a I don't know a uh a + + + align:start position:0% +that looks like uh a I don't know a uh a +dog and a horse or you know I mean you + + align:start position:0% +dog and a horse or you know I mean you + + + align:start position:0% +dog and a horse or you know I mean you +can you can + + align:start position:0% +can you can + + + align:start position:0% +can you can +constantly ask this question of where + + align:start position:0% +constantly ask this question of where + + + align:start position:0% +constantly ask this question of where +are the intermediate + + align:start position:0% +are the intermediate + + + align:start position:0% +are the intermediate +forms and um you know it's it's true + + align:start position:0% +forms and um you know it's it's true + + + align:start position:0% +forms and um you know it's it's true +there if you go back + + align:start position:0% +there if you go back + + + align:start position:0% +there if you go back +here these forms down here in the bottom + + align:start position:0% +here these forms down here in the bottom + + + align:start position:0% +here these forms down here in the bottom +of the chart there where are they well + + align:start position:0% +of the chart there where are they well + + + align:start position:0% +of the chart there where are they well +if they're if they're these vast numbers + + align:start position:0% +if they're if they're these vast numbers + + + align:start position:0% +if they're if they're these vast numbers +and of course uh this is this is a + + align:start position:0% +and of course uh this is this is a + + + align:start position:0% +and of course uh this is this is a +problem uh this notion of uh transition + + align:start position:0% +problem uh this notion of uh transition + + + align:start position:0% +problem uh this notion of uh transition +is uh incredibly important to Darwin's + + align:start position:0% +is uh incredibly important to Darwin's + + + align:start position:0% +is uh incredibly important to Darwin's +theory he says uh Natura nonn facet uh + + align:start position:0% +theory he says uh Natura nonn facet uh + + + align:start position:0% +theory he says uh Natura nonn facet uh +salum nature does not U develop through + + align:start position:0% +salum nature does not U develop through + + + align:start position:0% +salum nature does not U develop through +jumps it's a very + + align:start position:0% +jumps it's a very + + + align:start position:0% +jumps it's a very +graduated incremental process so then + + align:start position:0% +graduated incremental process so then + + + align:start position:0% +graduated incremental process so then +the question is okay if it's so + + align:start position:0% +the question is okay if it's so + + + align:start position:0% +the question is okay if it's so +incremental where are all those + + align:start position:0% +incremental where are all those + + + align:start position:0% +incremental where are all those +incremental + + align:start position:0% +incremental + + + align:start position:0% +incremental +forms so uh the first the that that + + align:start position:0% +forms so uh the first the that that + + + align:start position:0% +forms so uh the first the that that +first point is they they have been + + align:start position:0% +first point is they they have been + + + align:start position:0% +first point is they they have been +supplanted by more successful uh + + align:start position:0% +supplanted by more successful uh + + + align:start position:0% +supplanted by more successful uh +descendants species and therefore do not + + align:start position:0% +descendants species and therefore do not + + + align:start position:0% +descendants species and therefore do not +cannot compete successfully for the same + + align:start position:0% +cannot compete successfully for the same + + + align:start position:0% +cannot compete successfully for the same +places in + + align:start position:0% +places in + + + align:start position:0% +places in +nature uh and then of + + align:start position:0% +nature uh and then of + + + align:start position:0% +nature uh and then of +course they're not around anymore and + + align:start position:0% +course they're not around anymore and + + + align:start position:0% +course they're not around anymore and +haven't been around for many thousands + + align:start position:0% +haven't been around for many thousands + + + align:start position:0% +haven't been around for many thousands +of + + align:start position:0% +of + + + align:start position:0% +of +years and the + + align:start position:0% +years and the + + + align:start position:0% +years and the +remains organic life does not preserve + + align:start position:0% +remains organic life does not preserve + + + align:start position:0% +remains organic life does not preserve +that well in + + align:start position:0% +that well in + + + align:start position:0% +that well in +time I mean what we know about organic + + align:start position:0% +time I mean what we know about organic + + + align:start position:0% +time I mean what we know about organic +life is primarily through fossilized + + align:start position:0% +life is primarily through fossilized + + + align:start position:0% +life is primarily through fossilized +form + + align:start position:0% +form + + + align:start position:0% +form +and what is the what is the probability + + align:start position:0% +and what is the what is the probability + + + align:start position:0% +and what is the what is the probability +of an single form getting + + align:start position:0% +of an single form getting + + + align:start position:0% +of an single form getting +fossilized pretty rare set of conditions + + align:start position:0% +fossilized pretty rare set of conditions + + + align:start position:0% +fossilized pretty rare set of conditions +have to exist in order to capture a form + + align:start position:0% +have to exist in order to capture a form + + + align:start position:0% +have to exist in order to capture a form +that said it's amazing how much does how + + align:start position:0% +that said it's amazing how much does how + + + align:start position:0% +that said it's amazing how much does how +many remnants there are but you know + + align:start position:0% +many remnants there are but you know + + + align:start position:0% +many remnants there are but you know +these these ancient forms as they get + + align:start position:0% +these these ancient forms as they get + + + align:start position:0% +these these ancient forms as they get +supplanted die off and generation so + + align:start position:0% +supplanted die off and generation so + + + align:start position:0% +supplanted die off and generation so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +uh they'll simply get reabsorbed into + + align:start position:0% +uh they'll simply get reabsorbed into + + + align:start position:0% +uh they'll simply get reabsorbed into +the system + + align:start position:0% +the system + + + align:start position:0% +the system +as you know the stuff of which they are + + align:start position:0% +as you know the stuff of which they are + + + align:start position:0% +as you know the stuff of which they are +made as they as as the Bible says uh + + align:start position:0% +made as they as as the Bible says uh + + + align:start position:0% +made as they as as the Bible says uh +dust to + + align:start position:0% +dust to + + + align:start position:0% +dust to +dust uh so yeah dust doesn't preserve + + align:start position:0% +dust uh so yeah dust doesn't preserve + + + align:start position:0% +dust uh so yeah dust doesn't preserve +very + + align:start position:0% +very + + + align:start position:0% +very +well uh there are certain forms that + + align:start position:0% +well uh there are certain forms that + + + align:start position:0% +well uh there are certain forms that +have uh that have calcium or some kind + + align:start position:0% +have uh that have calcium or some kind + + + align:start position:0% +have uh that have calcium or some kind +of compound in them that uh can + + align:start position:0% +of compound in them that uh can + + + align:start position:0% +of compound in them that uh can +withstand + + align:start position:0% +withstand + + + align:start position:0% +withstand +time uh reasonably well some of the + + align:start position:0% +time uh reasonably well some of the + + + align:start position:0% +time uh reasonably well some of the +those forms actually turn out to be U + + align:start position:0% +those forms actually turn out to be U + + + align:start position:0% +those forms actually turn out to be U +that you know they do withstand time + + align:start position:0% +that you know they do withstand time + + + align:start position:0% +that you know they do withstand time +that of course if you recall when we + + align:start position:0% +that of course if you recall when we + + + align:start position:0% +that of course if you recall when we +were talking about Charles LEL he had + + align:start position:0% +were talking about Charles LEL he had + + + align:start position:0% +were talking about Charles LEL he had +all these index + + align:start position:0% +all these index + + + align:start position:0% +all these index +fossils uh of of of various snails and + + align:start position:0% +fossils uh of of of various snails and + + + align:start position:0% +fossils uh of of of various snails and +uh um and he was able to use those to + + align:start position:0% +uh um and he was able to use those to + + + align:start position:0% +uh um and he was able to use those to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +identify the age of the stratum or at + + align:start position:0% +identify the age of the stratum or at + + + align:start position:0% +identify the age of the stratum or at +least to place it more or less in in a + + align:start position:0% +least to place it more or less in in a + + + align:start position:0% +least to place it more or less in in a +in a area in a period so yeah there's + + align:start position:0% +in a area in a period so yeah there's + + + align:start position:0% +in a area in a period so yeah there's +there's not a whole lot + + align:start position:0% +there's not a whole lot + + + align:start position:0% +there's not a whole lot +left so absence of traditional uh + + align:start position:0% +left so absence of traditional uh + + + align:start position:0% +left so absence of traditional uh +transitional varieties um I gave you + + align:start position:0% +transitional varieties um I gave you + + + align:start position:0% +transitional varieties um I gave you +this little I don't know if you had time + + align:start position:0% +this little I don't know if you had time + + + align:start position:0% +this little I don't know if you had time +to look at it but if you click on this + + align:start position:0% +to look at it but if you click on this + + + align:start position:0% +to look at it but if you click on this +whale ancestral form this was a a quite + + align:start position:0% +whale ancestral form this was a a quite + + + align:start position:0% +whale ancestral form this was a a quite +a fascinating article came out on these + + align:start position:0% +a fascinating article came out on these + + + align:start position:0% +a fascinating article came out on these +um remains + + align:start position:0% +um remains + + + align:start position:0% +um remains +discovered in um uh + + align:start position:0% +discovered in um uh + + + align:start position:0% +discovered in um uh +uh in Asia of um ancestral wolflike + + align:start position:0% +uh in Asia of um ancestral wolflike + + + align:start position:0% +uh in Asia of um ancestral wolflike +organisms that it is believed + + align:start position:0% +organisms that it is believed + + + align:start position:0% +organisms that it is believed +ultimately uh transitioned + + align:start position:0% +ultimately uh transitioned + + + align:start position:0% +ultimately uh transitioned +into uh large + + align:start position:0% +into uh large + + + align:start position:0% +into uh large +whik uh forms and you know there's the + + align:start position:0% +whik uh forms and you know there's the + + + align:start position:0% +whik uh forms and you know there's the +article I mean I I recommend you read + + align:start position:0% +article I mean I I recommend you read + + + align:start position:0% +article I mean I I recommend you read +the article but it's it's it's quite + + align:start position:0% +the article but it's it's it's quite + + + align:start position:0% +the article but it's it's it's quite +interesting it it uh suggests that these + + align:start position:0% +interesting it it uh suggests that these + + + align:start position:0% +interesting it it uh suggests that these +mammals + + align:start position:0% +mammals + + + align:start position:0% +mammals +the whale is descended from a land + + align:start position:0% +the whale is descended from a land + + + align:start position:0% +the whale is descended from a land +animal land mammal and that the + + align:start position:0% +animal land mammal and that the + + + align:start position:0% +animal land mammal and that the +likelihood is that this uh mammal was + + align:start position:0% +likelihood is that this uh mammal was + + + align:start position:0% +likelihood is that this uh mammal was +able to discover a food source a stable + + align:start position:0% +able to discover a food source a stable + + + align:start position:0% +able to discover a food source a stable +food source that lasted over long + + align:start position:0% +food source that lasted over long + + + align:start position:0% +food source that lasted over long +periods of time thousands and thousands + + align:start position:0% +periods of time thousands and thousands + + + align:start position:0% +periods of time thousands and thousands +of years and it adapted to Aquatic + + align:start position:0% +of years and it adapted to Aquatic + + + align:start position:0% +of years and it adapted to Aquatic +habits and they've identified a whole + + align:start position:0% +habits and they've identified a whole + + + align:start position:0% +habits and they've identified a whole +series of uh bone remains fossils and + + align:start position:0% +series of uh bone remains fossils and + + + align:start position:0% +series of uh bone remains fossils and +things of that that that they've + + align:start position:0% +things of that that that they've + + + align:start position:0% +things of that that that they've +organized into these whole periods I'm + + align:start position:0% +organized into these whole periods I'm + + + align:start position:0% +organized into these whole periods I'm +told that this is you know a + + align:start position:0% +told that this is you know a + + + align:start position:0% +told that this is you know a +controversial Theory but that um um a + + align:start position:0% +controversial Theory but that um um a + + + align:start position:0% +controversial Theory but that um um a +lot of the uh a lot of the fossil + + align:start position:0% +lot of the uh a lot of the fossil + + + align:start position:0% +lot of the uh a lot of the fossil +science is is in place + + align:start position:0% +science is is in place + + + align:start position:0% +science is is in place +and um and that that uh recalls the + + align:start position:0% +and um and that that uh recalls the + + + align:start position:0% +and um and that that uh recalls the +U this whole U be whale Darin has this + + align:start position:0% +U this whole U be whale Darin has this + + + align:start position:0% +U this whole U be whale Darin has this +be whale passage where he says uh and it + + align:start position:0% +be whale passage where he says uh and it + + + align:start position:0% +be whale passage where he says uh and it +sounds kind of humorous and I think it + + align:start position:0% +sounds kind of humorous and I think it + + + align:start position:0% +sounds kind of humorous and I think it +was thought a little to be a little + + align:start position:0% +was thought a little to be a little + + + align:start position:0% +was thought a little to be a little +humorous by many it was contemporaries + + align:start position:0% +humorous by many it was contemporaries + + + align:start position:0% +humorous by many it was contemporaries +but he says um it's on page + + align:start position:0% +but he says um it's on page + + + align:start position:0% +but he says um it's on page +184 uh in North America the black bear + + align:start position:0% +184 uh in North America the black bear + + + align:start position:0% +184 uh in North America the black bear +was seen by + + align:start position:0% +was seen by + + + align:start position:0% +was seen by +Hearn uh a naturalist swimming for hours + + align:start position:0% +Hearn uh a naturalist swimming for hours + + + align:start position:0% +Hearn uh a naturalist swimming for hours +with widely open mouth thus catching + + align:start position:0% +with widely open mouth thus catching + + + align:start position:0% +with widely open mouth thus catching +like a whale insects in the water even + + align:start position:0% +like a whale insects in the water even + + + align:start position:0% +like a whale insects in the water even +in so extreme a case as this if the + + align:start position:0% +in so extreme a case as this if the + + + align:start position:0% +in so extreme a case as this if the +supply of insects were constant and if + + align:start position:0% +supply of insects were constant and if + + + align:start position:0% +supply of insects were constant and if +better adapted competitors did not + + align:start position:0% +better adapted competitors did not + + + align:start position:0% +better adapted competitors did not +already exist in the country I can see + + align:start position:0% +already exist in the country I can see + + + align:start position:0% +already exist in the country I can see +no difficulty in a race of bears being + + align:start position:0% +no difficulty in a race of bears being + + + align:start position:0% +no difficulty in a race of bears being +rendered by natural selection more and + + align:start position:0% +rendered by natural selection more and + + + align:start position:0% +rendered by natural selection more and +more aquatic in their structure and + + align:start position:0% +more aquatic in their structure and + + + align:start position:0% +more aquatic in their structure and +habits with larger and larger mouths + + align:start position:0% +habits with larger and larger mouths + + + align:start position:0% +habits with larger and larger mouths +till a creature was produced as + + align:start position:0% +till a creature was produced as + + + align:start position:0% +till a creature was produced as +monstrous as a + + align:start position:0% +monstrous as a + + + align:start position:0% +monstrous as a +whale uh this was a pretty wild argument + + align:start position:0% +whale uh this was a pretty wild argument + + + align:start position:0% +whale uh this was a pretty wild argument +at the time but here we have uh + + align:start position:0% +at the time but here we have uh + + + align:start position:0% +at the time but here we have uh +modern uh modern science uh confirming + + align:start position:0% +modern uh modern science uh confirming + + + align:start position:0% +modern uh modern science uh confirming +something like that happening in this + + align:start position:0% +something like that happening in this + + + align:start position:0% +something like that happening in this +this whole series collection of fossils + + align:start position:0% +this whole series collection of fossils + + + align:start position:0% +this whole series collection of fossils +okay + + align:start position:0% + + + + align:start position:0% + +okay uh the other organ the + + align:start position:0% +okay uh the other organ the + + + align:start position:0% +okay uh the other organ the +other difficulty that Darwin mentions is + + align:start position:0% +other difficulty that Darwin mentions is + + + align:start position:0% +other difficulty that Darwin mentions is +uh difficulty of explaining organs of + + align:start position:0% +uh difficulty of explaining organs of + + + align:start position:0% +uh difficulty of explaining organs of +extreme Perfection what he calls extreme + + align:start position:0% +extreme Perfection what he calls extreme + + + align:start position:0% +extreme Perfection what he calls extreme +Perfection + + align:start position:0% +Perfection + + + align:start position:0% +Perfection +um and this is U I think this is still + + align:start position:0% + + + + align:start position:0% + +working so this is something I uh + + align:start position:0% +working so this is something I uh + + + align:start position:0% +working so this is something I uh +uh included as a little inset uh again + + align:start position:0% +uh included as a little inset uh again + + + align:start position:0% +uh included as a little inset uh again +it's for your own exploration but uh + + align:start position:0% +it's for your own exploration but uh + + + align:start position:0% +it's for your own exploration but uh +it's a very interesting account of the + + align:start position:0% +it's a very interesting account of the + + + align:start position:0% +it's a very interesting account of the +selection process that might be required + + align:start position:0% +selection process that might be required + + + align:start position:0% +selection process that might be required +to produce an + + align:start position:0% +to produce an + + + align:start position:0% +to produce an +eye and um you know it argues that you + + align:start position:0% +eye and um you know it argues that you + + + align:start position:0% +eye and um you know it argues that you +know it's actually happened more than + + align:start position:0% +know it's actually happened more than + + + align:start position:0% +know it's actually happened more than +once uh and so why why is this such a + + align:start position:0% +once uh and so why why is this such a + + + align:start position:0% +once uh and so why why is this such a +problem for darh + + align:start position:0% +problem for darh + + + align:start position:0% +problem for darh +what is what is the basis of the problem + + align:start position:0% +what is what is the basis of the problem + + + align:start position:0% +what is what is the basis of the problem +of organs of extreme Perfection why why + + align:start position:0% +of organs of extreme Perfection why why + + + align:start position:0% +of organs of extreme Perfection why why +is this a difficulty for Darwin's + + align:start position:0% + + + + align:start position:0% + +theory yeah D put Darwin up against uh + + align:start position:0% +theory yeah D put Darwin up against uh + + + align:start position:0% +theory yeah D put Darwin up against uh +Haley it was just um how organs are so + + align:start position:0% +Haley it was just um how organs are so + + + align:start position:0% +Haley it was just um how organs are so +perfected that there must be some some + + align:start position:0% +perfected that there must be some some + + + align:start position:0% +perfected that there must be some some +design behind it um but like you said I + + align:start position:0% +design behind it um but like you said I + + + align:start position:0% +design behind it um but like you said I +think Darwin kept pressing the idea that + + align:start position:0% +think Darwin kept pressing the idea that + + + align:start position:0% +think Darwin kept pressing the idea that +you know natural + + align:start position:0% +you know natural + + + align:start position:0% +you know natural +selection was the driving force for this + + align:start position:0% +selection was the driving force for this + + + align:start position:0% +selection was the driving force for this +um in incremental steps and there's a + + align:start position:0% +um in incremental steps and there's a + + + align:start position:0% +um in incremental steps and there's a +quotation how he + + align:start position:0% +quotation how he + + + align:start position:0% +quotation how he +says um reason ought to conquer + + align:start position:0% +says um reason ought to conquer + + + align:start position:0% +says um reason ought to conquer +imagination uhuh um which I thought was + + align:start position:0% +imagination uhuh um which I thought was + + + align:start position:0% +imagination uhuh um which I thought was +sort + + align:start position:0% +sort + + + align:start position:0% +sort +of like the Darwin vers + + align:start position:0% +of like the Darwin vers + + + align:start position:0% +of like the Darwin vers +py um argument and Darwin also says have + + align:start position:0% +py um argument and Darwin also says have + + + align:start position:0% +py um argument and Darwin also says have +we any right to assume that the Creator + + align:start position:0% +we any right to assume that the Creator + + + align:start position:0% +we any right to assume that the Creator +works by intellectual powers like those + + align:start position:0% +works by intellectual powers like those + + + align:start position:0% +works by intellectual powers like those +of man um when he talks about how the + + align:start position:0% +of man um when he talks about how the + + + align:start position:0% +of man um when he talks about how the +eye can be like a + + align:start position:0% +eye can be like a + + + align:start position:0% +eye can be like a +telescope so that's sort of he's trying + + align:start position:0% +telescope so that's sort of he's trying + + + align:start position:0% +telescope so that's sort of he's trying +to disprove P's Theory and sort of push + + align:start position:0% +to disprove P's Theory and sort of push + + + align:start position:0% +to disprove P's Theory and sort of push +on his own okay um but at the same time + + align:start position:0% +on his own okay um but at the same time + + + align:start position:0% +on his own okay um but at the same time +I I wonder if like he's saying he's + + align:start position:0% +I I wonder if like he's saying he's + + + align:start position:0% +I I wonder if like he's saying he's +citing crustations in these different + + align:start position:0% +citing crustations in these different + + + align:start position:0% +citing crustations in these different +like Optical nerves and stuff and + + align:start position:0% +like Optical nerves and stuff and + + + align:start position:0% +like Optical nerves and stuff and +whether those are actually connected or + + align:start position:0% +whether those are actually connected or + + + align:start position:0% +whether those are actually connected or +whether he's just putting them together + + align:start position:0% +whether he's just putting them together + + + align:start position:0% +whether he's just putting them together +to sort of say Natural + + align:start position:0% +to sort of say Natural + + + align:start position:0% +to sort of say Natural +Selections so yes there there are + + align:start position:0% +Selections so yes there there are + + + align:start position:0% +Selections so yes there there are +various types of eyes and eyes have + + align:start position:0% +various types of eyes and eyes have + + + align:start position:0% +various types of eyes and eyes have +emerged in these forms and under + + align:start position:0% +emerged in these forms and under + + + align:start position:0% +emerged in these forms and under +Darwin's theory the um the + + align:start position:0% +Darwin's theory the um the + + + align:start position:0% +Darwin's theory the um the +characteristics of the eye have been + + align:start position:0% +characteristics of the eye have been + + + align:start position:0% +characteristics of the eye have been +passed down + + align:start position:0% +passed down + + + align:start position:0% +passed down +through generations and over time + + align:start position:0% +through generations and over time + + + align:start position:0% +through generations and over time +through U stages in different species + + align:start position:0% +through U stages in different species + + + align:start position:0% +through U stages in different species +and so uh part of the problem of the + + align:start position:0% +and so uh part of the problem of the + + + align:start position:0% +and so uh part of the problem of the +argument is as you say it's it's sort of + + align:start position:0% +argument is as you say it's it's sort of + + + align:start position:0% +argument is as you say it's it's sort of +paley's already uh captured you know his + + align:start position:0% +paley's already uh captured you know his + + + align:start position:0% +paley's already uh captured you know his +made his argument about the eye as the + + align:start position:0% +made his argument about the eye as the + + + align:start position:0% +made his argument about the eye as the +greatest uh illustration possible of the + + align:start position:0% +greatest uh illustration possible of the + + + align:start position:0% +greatest uh illustration possible of the +necessity of + + align:start position:0% +necessity of + + + align:start position:0% +necessity of +a Divine Force how else could something + + align:start position:0% +a Divine Force how else could something + + + align:start position:0% +a Divine Force how else could something +like this be produced in any kind of + + align:start position:0% +like this be produced in any kind of + + + align:start position:0% +like this be produced in any kind of +natural way and Darwin is kind of + + align:start position:0% +natural way and Darwin is kind of + + + align:start position:0% +natural way and Darwin is kind of +admitting this is this is a problem + + align:start position:0% +admitting this is this is a problem + + + align:start position:0% +admitting this is this is a problem +but uh and part of the problem is goes + + align:start position:0% +but uh and part of the problem is goes + + + align:start position:0% +but uh and part of the problem is goes +back goes to his so-called um doctrine + + align:start position:0% +back goes to his so-called um doctrine + + + align:start position:0% +back goes to his so-called um doctrine +of + + align:start position:0% +of + + + align:start position:0% +of +utility anybody figure out what this + + align:start position:0% +utility anybody figure out what this + + + align:start position:0% +utility anybody figure out what this +utility argument why is + + align:start position:0% +utility argument why is + + + align:start position:0% +utility argument why is +utility over these graduated stages such + + align:start position:0% +utility over these graduated stages such + + + align:start position:0% +utility over these graduated stages such +a big + + align:start position:0% + + + + align:start position:0% + +deal yeah + + align:start position:0% +deal yeah + + + align:start position:0% +deal yeah +Jake because the evolution is involving + + align:start position:0% +Jake because the evolution is involving + + + align:start position:0% +Jake because the evolution is involving +things so that they fit they're as best + + align:start position:0% +things so that they fit they're as best + + + align:start position:0% +things so that they fit they're as best +adapted as they can to what they have + + align:start position:0% +adapted as they can to what they have + + + align:start position:0% +adapted as they can to what they have +available and work their + + align:start position:0% +available and work their + + + align:start position:0% +available and work their +niches and adapting something that isn't + + align:start position:0% +niches and adapting something that isn't + + + align:start position:0% +niches and adapting something that isn't +useful yeah is going to be just the + + align:start position:0% +useful yeah is going to be just the + + + align:start position:0% +useful yeah is going to be just the +waste of res the already scarce + + align:start position:0% +waste of res the already scarce + + + align:start position:0% +waste of res the already scarce +resources that we trying to maximize so + + align:start position:0% +resources that we trying to maximize so + + + align:start position:0% +resources that we trying to maximize so +it's it theoretically shouldn't happen + + align:start position:0% +it's it theoretically shouldn't happen + + + align:start position:0% +it's it theoretically shouldn't happen +because it's absolutely pointless and + + align:start position:0% +because it's absolutely pointless and + + + align:start position:0% +because it's absolutely pointless and +actually negative overall us resources + + align:start position:0% +actually negative overall us resources + + + align:start position:0% +actually negative overall us resources +get but it still happens so he can't + + align:start position:0% +get but it still happens so he can't + + + align:start position:0% +get but it still happens so he can't +explain why that's yeah weak this is a + + align:start position:0% +explain why that's yeah weak this is a + + + align:start position:0% +explain why that's yeah weak this is a +this is a challenge yeah so what are the + + align:start position:0% +this is a challenge yeah so what are the + + + align:start position:0% +this is a challenge yeah so what are the +intermediate forms of uh the + + align:start position:0% +intermediate forms of uh the + + + align:start position:0% +intermediate forms of uh the +eye or the tail of the giraffe + + align:start position:0% +eye or the tail of the giraffe + + + align:start position:0% +eye or the tail of the giraffe +or the flagellum of the bacterium um you + + align:start position:0% +or the flagellum of the bacterium um you + + + align:start position:0% +or the flagellum of the bacterium um you +know what are the intermediate forms and + + align:start position:0% +know what are the intermediate forms and + + + align:start position:0% +know what are the intermediate forms and +how did those benefit the organism what + + align:start position:0% +how did those benefit the organism what + + + align:start position:0% +how did those benefit the organism what +were the utility of those intermediate + + align:start position:0% +were the utility of those intermediate + + + align:start position:0% +were the utility of those intermediate +forms and you can see a lot of different + + align:start position:0% +forms and you can see a lot of different + + + align:start position:0% +forms and you can see a lot of different +uh uh problems in this and that is um + + align:start position:0% +uh uh problems in this and that is um + + + align:start position:0% +uh uh problems in this and that is um +you you can see how an eye is really + + align:start position:0% +you you can see how an eye is really + + + align:start position:0% +you you can see how an eye is really +useful to an + + align:start position:0% +useful to an + + + align:start position:0% +useful to an +organism but what is a half eye or what + + align:start position:0% +organism but what is a half eye or what + + + align:start position:0% +organism but what is a half eye or what +is a quarter eye or you know and and if + + align:start position:0% +is a quarter eye or you know and and if + + + align:start position:0% +is a quarter eye or you know and and if +this thing is developed over a period + + align:start position:0% +this thing is developed over a period + + + align:start position:0% +this thing is developed over a period +dysfunctionality has developed over a + + align:start position:0% +dysfunctionality has developed over a + + + align:start position:0% +dysfunctionality has developed over a +period of millions of years what were + + align:start position:0% +period of millions of years what were + + + align:start position:0% +period of millions of years what were +all those incremental + + align:start position:0% +all those incremental + + + align:start position:0% +all those incremental +forms U doing + + align:start position:0% +forms U doing + + + align:start position:0% +forms U doing +for the organisms that they were part of + + align:start position:0% +for the organisms that they were part of + + + align:start position:0% +for the organisms that they were part of +so this utilitarian this this utility + + align:start position:0% +so this utilitarian this this utility + + + align:start position:0% +so this utilitarian this this utility +question is I mean according to dar's + + align:start position:0% +question is I mean according to dar's + + + align:start position:0% +question is I mean according to dar's +Theory every single one of those slight + + align:start position:0% +Theory every single one of those slight + + + align:start position:0% +Theory every single one of those slight +gradations must have been + + align:start position:0% +gradations must have been + + + align:start position:0% +gradations must have been +beneficial and some people would argue + + align:start position:0% +beneficial and some people would argue + + + align:start position:0% +beneficial and some people would argue +that you + + align:start position:0% +that you + + + align:start position:0% +that you +know that this is highly + + align:start position:0% +know that this is highly + + + align:start position:0% +know that this is highly +unlikely that you know this form is in + + align:start position:0% +unlikely that you know this form is in + + + align:start position:0% +unlikely that you know this form is in +its its full expression is incredibly + + align:start position:0% +its its full expression is incredibly + + + align:start position:0% +its its full expression is incredibly +useful but the transitional uh stages uh + + align:start position:0% +useful but the transitional uh stages uh + + + align:start position:0% +useful but the transitional uh stages uh +are harder to + + align:start position:0% +are harder to + + + align:start position:0% +are harder to +argue the benefit for so this comes back + + align:start position:0% +argue the benefit for so this comes back + + + align:start position:0% +argue the benefit for so this comes back +to um uh the whole question of uh + + align:start position:0% +to um uh the whole question of uh + + + align:start position:0% +to um uh the whole question of uh +utility so and of course Evolution works + + align:start position:0% +utility so and of course Evolution works + + + align:start position:0% +utility so and of course Evolution works +with the evolutionary process is + + align:start position:0% +with the evolutionary process is + + + align:start position:0% +with the evolutionary process is +simply possible with whatever exists + + align:start position:0% +simply possible with whatever exists + + + align:start position:0% +simply possible with whatever exists +evolution is not you know it doesn't + + align:start position:0% +evolution is not you know it doesn't + + + align:start position:0% +evolution is not you know it doesn't +work the way somebody in a workshop + + align:start position:0% +work the way somebody in a workshop + + + align:start position:0% +work the way somebody in a workshop +works and says well I need Birch for + + align:start position:0% +works and says well I need Birch for + + + align:start position:0% +works and says well I need Birch for +this type of thing and maybe I'll use + + align:start position:0% +this type of thing and maybe I'll use + + + align:start position:0% +this type of thing and maybe I'll use +pine for that or you know Evolution just + + align:start position:0% +pine for that or you know Evolution just + + + align:start position:0% +pine for that or you know Evolution just +has a material that is part of the + + align:start position:0% +has a material that is part of the + + + align:start position:0% +has a material that is part of the +organism to work + + align:start position:0% +organism to work + + + align:start position:0% +organism to work +with as those materials + + align:start position:0% +with as those materials + + + align:start position:0% +with as those materials +change that's all that's it so that's + + align:start position:0% +change that's all that's it so that's + + + align:start position:0% +change that's all that's it so that's +that's that's the subject matter of + + align:start position:0% +that's that's the subject matter of + + + align:start position:0% +that's that's the subject matter of +evolution those are the opportunities + + align:start position:0% +evolution those are the opportunities + + + align:start position:0% +evolution those are the opportunities +so um it's a in some ways it's a very + + align:start position:0% +so um it's a in some ways it's a very + + + align:start position:0% +so um it's a in some ways it's a very +constrained + + align:start position:0% +constrained + + + align:start position:0% +constrained +Theory and um it it it follows the + + align:start position:0% +Theory and um it it it follows the + + + align:start position:0% +Theory and um it it it follows the +general uh philosophy and spirit of + + align:start position:0% +general uh philosophy and spirit of + + + align:start position:0% +general uh philosophy and spirit of +parsimony that you know it just works + + align:start position:0% +parsimony that you know it just works + + + align:start position:0% +parsimony that you know it just works +with whatever is + + align:start position:0% +with whatever is + + + align:start position:0% +with whatever is +available and + + align:start position:0% +available and + + + align:start position:0% +available and +uh it's it's pretty amazing what it's + + align:start position:0% +uh it's it's pretty amazing what it's + + + align:start position:0% +uh it's it's pretty amazing what it's +what has been produced over millions of + + align:start position:0% +what has been produced over millions of + + + align:start position:0% +what has been produced over millions of +years when you think of the diversity of + + align:start position:0% +years when you think of the diversity of + + + align:start position:0% +years when you think of the diversity of +life but + + align:start position:0% +life but + + + align:start position:0% +life but +um + + align:start position:0% +um + + + align:start position:0% +um +okay so then he uh I mean there there + + align:start position:0% +okay so then he uh I mean there there + + + align:start position:0% +okay so then he uh I mean there there +there are a lot of other things in here + + align:start position:0% +there are a lot of other things in here + + + align:start position:0% +there are a lot of other things in here +and he does mention instincts as one of + + align:start position:0% +and he does mention instincts as one of + + + align:start position:0% +and he does mention instincts as one of +the problems and he devotes a whole + + align:start position:0% +the problems and he devotes a whole + + + align:start position:0% +the problems and he devotes a whole +chapter to Instinct he just feels that + + align:start position:0% +chapter to Instinct he just feels that + + + align:start position:0% +chapter to Instinct he just feels that +he you know really needs to go into this + + align:start position:0% +he you know really needs to go into this + + + align:start position:0% +he you know really needs to go into this +very smart way to divide up some of + + align:start position:0% +very smart way to divide up some of + + + align:start position:0% +very smart way to divide up some of +these uh issues this his his chapter on + + align:start position:0% +these uh issues this his his chapter on + + + align:start position:0% +these uh issues this his his chapter on +instinct is uh quite quite + + align:start position:0% +instinct is uh quite quite + + + align:start position:0% +instinct is uh quite quite +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +extraordinary okay so he says over and + + align:start position:0% +extraordinary okay so he says over and + + + align:start position:0% +extraordinary okay so he says over and +over again + + align:start position:0% +over again + + + align:start position:0% +over again +um um for example on page 194 he says + + align:start position:0% +um um for example on page 194 he says + + + align:start position:0% +um um for example on page 194 he says +I've I've been astonished although in + + align:start position:0% +I've I've been astonished although in + + + align:start position:0% +I've I've been astonished although in +many cases is most difficult to + + align:start position:0% +many cases is most difficult to + + + align:start position:0% +many cases is most difficult to +conjecture by what transitions an organ + + align:start position:0% +conjecture by what transitions an organ + + + align:start position:0% +conjecture by what transitions an organ +could have arrived at its present + + align:start position:0% +could have arrived at its present + + + align:start position:0% +could have arrived at its present +state yet considering that the + + align:start position:0% +state yet considering that the + + + align:start position:0% +state yet considering that the +proportion of living in know forms to + + align:start position:0% +proportion of living in know forms to + + + align:start position:0% +proportion of living in know forms to +the extinct and unknown is very + + align:start position:0% +the extinct and unknown is very + + + align:start position:0% +the extinct and unknown is very +small I've been astonished how rarely an + + align:start position:0% +small I've been astonished how rarely an + + + align:start position:0% +small I've been astonished how rarely an +organ can be named towards which no + + align:start position:0% +organ can be named towards which no + + + align:start position:0% +organ can be named towards which no +transitional grade is known to + + align:start position:0% +transitional grade is known to + + + align:start position:0% +transitional grade is known to +lead the truth of this remark is indeed + + align:start position:0% +lead the truth of this remark is indeed + + + align:start position:0% +lead the truth of this remark is indeed +shown by that old canon in natural + + align:start position:0% +shown by that old canon in natural + + + align:start position:0% +shown by that old canon in natural +history of Natura known facet + + align:start position:0% +history of Natura known facet + + + align:start position:0% +history of Natura known facet +salum um we meet with this ad um + + align:start position:0% +salum um we meet with this ad um + + + align:start position:0% +salum um we meet with this ad um +admission in the writings of uh almost + + align:start position:0% +admission in the writings of uh almost + + + align:start position:0% +admission in the writings of uh almost +every experienced + + align:start position:0% +every experienced + + + align:start position:0% +every experienced +naturalist um okay + + align:start position:0% +naturalist um okay + + + align:start position:0% +naturalist um okay +so this is his uh his answer and you + + align:start position:0% +so this is his uh his answer and you + + + align:start position:0% +so this is his uh his answer and you +know some people would say well it's not + + align:start position:0% +know some people would say well it's not + + + align:start position:0% +know some people would say well it's not +a great answer it doesn't really on the + + align:start position:0% +a great answer it doesn't really on the + + + align:start position:0% +a great answer it doesn't really on the +other hand um transitional forms are the + + align:start position:0% +other hand um transitional forms are the + + + align:start position:0% +other hand um transitional forms are the +subject of huge fields of study and + + align:start position:0% +subject of huge fields of study and + + + align:start position:0% +subject of huge fields of study and +Darwin can't produce everything in this + + align:start position:0% +Darwin can't produce everything in this + + + align:start position:0% +Darwin can't produce everything in this +single book if you want the gradiation + + align:start position:0% +single book if you want the gradiation + + + align:start position:0% +single book if you want the gradiation +of forms and so forth you go to a + + align:start position:0% +of forms and so forth you go to a + + + align:start position:0% +of forms and so forth you go to a +comparative anatomist and you know look + + align:start position:0% +comparative anatomist and you know look + + + align:start position:0% +comparative anatomist and you know look +and see what the all these gradiation of + + align:start position:0% +and see what the all these gradiation of + + + align:start position:0% +and see what the all these gradiation of +structures and you can see them uh the + + align:start position:0% +structures and you can see them uh the + + + align:start position:0% +structures and you can see them uh the +the two chambered three chambered four + + align:start position:0% +the two chambered three chambered four + + + align:start position:0% +the two chambered three chambered four +chambered heart and you know you can + + align:start position:0% +chambered heart and you know you can + + + align:start position:0% +chambered heart and you know you can +sort of see how things emerge over these + + align:start position:0% +sort of see how things emerge over these + + + align:start position:0% +sort of see how things emerge over these +different expressions of different + + align:start position:0% +different expressions of different + + + align:start position:0% +different expressions of different +organisms um but he can't do that here + + align:start position:0% +organisms um but he can't do that here + + + align:start position:0% +organisms um but he can't do that here +he can only cite + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +okay he does say a couple of things um + + align:start position:0% +okay he does say a couple of things um + + + align:start position:0% +okay he does say a couple of things um +he says he holds that any any change in + + align:start position:0% +he says he holds that any any change in + + + align:start position:0% +he says he holds that any any change in +an organism beneficial to another + + align:start position:0% +an organism beneficial to another + + + align:start position:0% +an organism beneficial to another +organism would destroy his + + align:start position:0% +organism would destroy his + + + align:start position:0% +organism would destroy his +theory organisms only only change to can + + align:start position:0% +theory organisms only only change to can + + + align:start position:0% +theory organisms only only change to can +only change for the benefit of + + align:start position:0% +only change for the benefit of + + + align:start position:0% +only change for the benefit of +themselves and then he also says + + align:start position:0% +themselves and then he also says + + + align:start position:0% +themselves and then he also says +um um the foregoing remarks this on page + + align:start position:0% +um um the foregoing remarks this on page + + + align:start position:0% +um um the foregoing remarks this on page +199 the foregoing remarks lead me to say + + align:start position:0% +199 the foregoing remarks lead me to say + + + align:start position:0% +199 the foregoing remarks lead me to say +a few words on on the protest lately + + align:start position:0% +a few words on on the protest lately + + + align:start position:0% +a few words on on the protest lately +made by some naturalists against the + + align:start position:0% +made by some naturalists against the + + + align:start position:0% +made by some naturalists against the +utilitarian doctrine that every detail + + align:start position:0% +utilitarian doctrine that every detail + + + align:start position:0% +utilitarian doctrine that every detail +of structure has been produced for the + + align:start position:0% +of structure has been produced for the + + + align:start position:0% +of structure has been produced for the +good of its + + align:start position:0% +good of its + + + align:start position:0% +good of its +possessor they believe that very many + + align:start position:0% +possessor they believe that very many + + + align:start position:0% +possessor they believe that very many +structures have been created for beauty + + align:start position:0% +structures have been created for beauty + + + align:start position:0% +structures have been created for beauty +in the eyes of + + align:start position:0% +in the eyes of + + + align:start position:0% +in the eyes of +man and he adds or for mere variety this + + align:start position:0% +man and he adds or for mere variety this + + + align:start position:0% +man and he adds or for mere variety this +Doctrine if true would be absolutely + + align:start position:0% +Doctrine if true would be absolutely + + + align:start position:0% +Doctrine if true would be absolutely +fatal to my + + align:start position:0% +fatal to my + + + align:start position:0% +fatal to my +theory + + align:start position:0% + + + + align:start position:0% + +oh it's yeah it's a big admission isn't + + align:start position:0% +oh it's yeah it's a big admission isn't + + + align:start position:0% +oh it's yeah it's a big admission isn't +it if you can show me one + + align:start position:0% +it if you can show me one + + + align:start position:0% +it if you can show me one +example and my theory Falls so that's + + align:start position:0% +example and my theory Falls so that's + + + align:start position:0% +example and my theory Falls so that's +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +maybe I don't know it it who knows + + align:start position:0% +maybe I don't know it it who knows + + + align:start position:0% +maybe I don't know it it who knows +exactly what he's talking about here he + + align:start position:0% +exactly what he's talking about here he + + + align:start position:0% +exactly what he's talking about here he +is talking about some naturalists he's + + align:start position:0% +is talking about some naturalists he's + + + align:start position:0% +is talking about some naturalists he's +he's aware of who are arguing that you + + align:start position:0% +he's aware of who are arguing that you + + + align:start position:0% +he's aware of who are arguing that you +know there that beauty is one of the one + + align:start position:0% +know there that beauty is one of the one + + + align:start position:0% +know there that beauty is one of the one +of the purposes in nature that there's a + + align:start position:0% +of the purposes in nature that there's a + + + align:start position:0% +of the purposes in nature that there's a +purposeful U uh rationale or basis for + + align:start position:0% +purposeful U uh rationale or basis for + + + align:start position:0% +purposeful U uh rationale or basis for +many structures why else would some of + + align:start position:0% +many structures why else would some of + + + align:start position:0% +many structures why else would some of +these things so Beauty uh these + + align:start position:0% +these things so Beauty uh these + + + align:start position:0% +these things so Beauty uh these +beautious forms that Wordsworth speaks + + align:start position:0% +beautious forms that Wordsworth speaks + + + align:start position:0% +beautious forms that Wordsworth speaks +of why else would they be there except + + align:start position:0% +of why else would they be there except + + + align:start position:0% +of why else would they be there except +for incredible beauty that they express + + align:start position:0% +for incredible beauty that they express + + + align:start position:0% +for incredible beauty that they express +but um In Darwin's view there's some + + align:start position:0% +but um In Darwin's view there's some + + + align:start position:0% +but um In Darwin's view there's some +functionality someplace down there and + + align:start position:0% +functionality someplace down there and + + + align:start position:0% +functionality someplace down there and +whatever the beauty is is it's + + align:start position:0% +whatever the beauty is is it's + + + align:start position:0% +whatever the beauty is is it's +probably a uh human interpretation of + + align:start position:0% +probably a uh human interpretation of + + + align:start position:0% +probably a uh human interpretation of +something that has a very hard + + align:start position:0% +something that has a very hard + + + align:start position:0% +something that has a very hard +utilitarian explanation at the base like + + align:start position:0% +utilitarian explanation at the base like + + + align:start position:0% +utilitarian explanation at the base like +I don't know s the songs of a song bird + + align:start position:0% +I don't know s the songs of a song bird + + + align:start position:0% +I don't know s the songs of a song bird +or something like that you know are they + + align:start position:0% +or something like that you know are they + + + align:start position:0% +or something like that you know are they +really there for me to wake up in the + + align:start position:0% +really there for me to wake up in the + + + align:start position:0% +really there for me to wake up in the +morning and hear this delightful uh + + align:start position:0% +morning and hear this delightful uh + + + align:start position:0% +morning and hear this delightful uh +chorus or are these birds somehow + + align:start position:0% +chorus or are these birds somehow + + + align:start position:0% +chorus or are these birds somehow +dominating their territory through you + + align:start position:0% +dominating their territory through you + + + align:start position:0% +dominating their territory through you +know various I don't know there are many + + align:start position:0% +know various I don't know there are many + + + align:start position:0% +know various I don't know there are many +many ways in which you can explain + + align:start position:0% +many ways in which you can explain + + + align:start position:0% +many ways in which you can explain +things there's a kind of brutal + + align:start position:0% +things there's a kind of brutal + + + align:start position:0% +things there's a kind of brutal +Simplicity to Darwin is there + + align:start position:0% +Simplicity to Darwin is there + + + align:start position:0% +Simplicity to Darwin is there +not I mean it's elegant but it's + + align:start position:0% +not I mean it's elegant but it's + + + align:start position:0% +not I mean it's elegant but it's +also + + align:start position:0% +also + + + align:start position:0% +also +massive it's it's + + align:start position:0% +massive it's it's + + + align:start position:0% +massive it's it's +uh uh I + + align:start position:0% +uh uh I + + + align:start position:0% +uh uh I +mean organic existence is so complicated + + align:start position:0% +mean organic existence is so complicated + + + align:start position:0% +mean organic existence is so complicated +and so complex and to see it sort of + + align:start position:0% +and so complex and to see it sort of + + + align:start position:0% +and so complex and to see it sort of +boil down into these principles is uh is + + align:start position:0% +boil down into these principles is uh is + + + align:start position:0% +boil down into these principles is uh is +sort of breathtaking + + align:start position:0% +sort of breathtaking + + + align:start position:0% +sort of breathtaking +really + + align:start position:0% +really + + + align:start position:0% +really +uh + + align:start position:0% + + + + align:start position:0% + +okay all right I'm going to have a look + + align:start position:0% + + + + align:start position:0% + +at + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% + + + + align:start position:0% + +uh all right there's a lot more to this + + align:start position:0% +uh all right there's a lot more to this + + + align:start position:0% +uh all right there's a lot more to this +book of course uh and + + align:start position:0% +book of course uh and + + + align:start position:0% +book of course uh and +um it as I've been saying over and over + + align:start position:0% +um it as I've been saying over and over + + + align:start position:0% +um it as I've been saying over and over +again it's it's pulling together + + align:start position:0% +again it's it's pulling together + + + align:start position:0% +again it's it's pulling together +the the knowledge of the day from many + + align:start position:0% +the the knowledge of the day from many + + + align:start position:0% +the the knowledge of the day from many +many different + + align:start position:0% +many different + + + align:start position:0% +many different +fields and uh that's of course its uh + + align:start position:0% +fields and uh that's of course its uh + + + align:start position:0% +fields and uh that's of course its uh +its strength in many ways is it's just + + align:start position:0% +its strength in many ways is it's just + + + align:start position:0% +its strength in many ways is it's just +it's a it's it's a kind of a grand + + align:start position:0% +it's a it's it's a kind of a grand + + + align:start position:0% +it's a it's it's a kind of a grand +unification Theory you could call it + + align:start position:0% +unification Theory you could call it + + + align:start position:0% +unification Theory you could call it +that of the biology and the earth + + align:start position:0% +that of the biology and the earth + + + align:start position:0% +that of the biology and the earth +science and related Allied Sciences of + + align:start position:0% +science and related Allied Sciences of + + + align:start position:0% +science and related Allied Sciences of +Darwin's + + align:start position:0% +Darwin's + + + align:start position:0% +Darwin's +day and uh the fact that he could unify + + align:start position:0% +day and uh the fact that he could unify + + + align:start position:0% +day and uh the fact that he could unify +so many of these different fields many + + align:start position:0% +so many of these different fields many + + + align:start position:0% +so many of these different fields many +of them which had been the the life work + + align:start position:0% +of them which had been the the life work + + + align:start position:0% +of them which had been the the life work +of uh naturalists working through them + + align:start position:0% +of uh naturalists working through them + + + align:start position:0% +of uh naturalists working through them +for + + align:start position:0% +for + + + align:start position:0% +for +generations and the fact that Darwin + + align:start position:0% +generations and the fact that Darwin + + + align:start position:0% +generations and the fact that Darwin +could pull these all together under + + align:start position:0% +could pull these all together under + + + align:start position:0% +could pull these all together under +these + + align:start position:0% +these + + + align:start position:0% +these +fundamentally uh this core of + + align:start position:0% +fundamentally uh this core of + + + align:start position:0% +fundamentally uh this core of +fundamental principles is very very + + align:start position:0% +fundamental principles is very very + + + align:start position:0% +fundamental principles is very very +impressive it shows the vast extent of + + align:start position:0% +impressive it shows the vast extent of + + + align:start position:0% +impressive it shows the vast extent of +his + + align:start position:0% +his + + + align:start position:0% +his +learning okay so these are some of the + + align:start position:0% +learning okay so these are some of the + + + align:start position:0% +learning okay so these are some of the +fields that uh Darwin worked in uh + + align:start position:0% +fields that uh Darwin worked in uh + + + align:start position:0% +fields that uh Darwin worked in uh +geology Natural History + + align:start position:0% +geology Natural History + + + align:start position:0% +geology Natural History +paleontology whole chapter on + + align:start position:0% +paleontology whole chapter on + + + align:start position:0% +paleontology whole chapter on +Instinct understanding + + align:start position:0% +Instinct understanding + + + align:start position:0% +Instinct understanding +hybridization uh geological + + align:start position:0% +hybridization uh geological + + + align:start position:0% +hybridization uh geological +distribution embryology which was uh + + align:start position:0% +distribution embryology which was uh + + + align:start position:0% +distribution embryology which was uh +emerging as a uh a very large field + + align:start position:0% +emerging as a uh a very large field + + + align:start position:0% +emerging as a uh a very large field +German um the natural system of + + align:start position:0% +German um the natural system of + + + align:start position:0% +German um the natural system of +classification that is uh u i mean + + align:start position:0% +classification that is uh u i mean + + + align:start position:0% +classification that is uh u i mean +taxonomy was a huge huge area of of + + align:start position:0% +taxonomy was a huge huge area of of + + + align:start position:0% +taxonomy was a huge huge area of of +endeavor all since the time of Lenas and + + align:start position:0% +endeavor all since the time of Lenas and + + + align:start position:0% +endeavor all since the time of Lenas and +before + + align:start position:0% +before + + + align:start position:0% +before +indeed and it still is + + align:start position:0% +indeed and it still is + + + align:start position:0% +indeed and it still is +actually uh because + + align:start position:0% +actually uh because + + + align:start position:0% +actually uh because +classification allows us to think kind + + align:start position:0% +classification allows us to think kind + + + align:start position:0% +classification allows us to think kind +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +abstractly about how + + align:start position:0% +abstractly about how + + + align:start position:0% +abstractly about how +organisms the patterns of or organic + + align:start position:0% +organisms the patterns of or organic + + + align:start position:0% +organisms the patterns of or organic +life how they're organized and so we + + align:start position:0% +life how they're organized and so we + + + align:start position:0% +life how they're organized and so we +have you know system after system + + align:start position:0% +have you know system after system + + + align:start position:0% +have you know system after system +developing but it was a very big fear + + align:start position:0% +developing but it was a very big fear + + + align:start position:0% +developing but it was a very big fear +um Lenas had produced massive massive + + align:start position:0% +um Lenas had produced massive massive + + + align:start position:0% +um Lenas had produced massive massive +collections of work just on you know uh + + align:start position:0% +collections of work just on you know uh + + + align:start position:0% +collections of work just on you know uh +organizing life forms according to genus + + align:start position:0% +organizing life forms according to genus + + + align:start position:0% +organizing life forms according to genus +species families so on and uh published + + align:start position:0% +species families so on and uh published + + + align:start position:0% +species families so on and uh published +whole books that basically sort of look + + align:start position:0% +whole books that basically sort of look + + + align:start position:0% +whole books that basically sort of look +like telephone books you they just kind + + align:start position:0% +like telephone books you they just kind + + + align:start position:0% +like telephone books you they just kind +of I mean obviously there were + + align:start position:0% +of I mean obviously there were + + + align:start position:0% +of I mean obviously there were +tremendous more than that but you know + + align:start position:0% +tremendous more than that but you know + + + align:start position:0% +tremendous more than that but you know +you look at them and it's just a whole + + align:start position:0% +you look at them and it's just a whole + + + align:start position:0% +you look at them and it's just a whole +set of charts of relations and so forth + + align:start position:0% +set of charts of relations and so forth + + + align:start position:0% +set of charts of relations and so forth +but it's a massive effort to create a + + align:start position:0% +but it's a massive effort to create a + + + align:start position:0% +but it's a massive effort to create a +unified system for thinking about plant + + align:start position:0% +unified system for thinking about plant + + + align:start position:0% +unified system for thinking about plant +species plantarum as uh he he published + + align:start position:0% +species plantarum as uh he he published + + + align:start position:0% +species plantarum as uh he he published +these books and it was a way of sort of + + align:start position:0% +these books and it was a way of sort of + + + align:start position:0% +these books and it was a way of sort of +thinking about all these different forms + + align:start position:0% +thinking about all these different forms + + + align:start position:0% +thinking about all these different forms +and putting them all into some kind of + + align:start position:0% +and putting them all into some kind of + + + align:start position:0% +and putting them all into some kind of +order only lenaeus wasn't doing it to + + align:start position:0% +order only lenaeus wasn't doing it to + + + align:start position:0% +order only lenaeus wasn't doing it to +argue while they're all related and this + + align:start position:0% +argue while they're all related and this + + + align:start position:0% +argue while they're all related and this +and Darwin took that that was that was + + align:start position:0% +and Darwin took that that was that was + + + align:start position:0% +and Darwin took that that was that was +uh very exciting to Darwin because he + + align:start position:0% +uh very exciting to Darwin because he + + + align:start position:0% +uh very exciting to Darwin because he +could take that and he say hey what he's + + align:start position:0% +could take that and he say hey what he's + + + align:start position:0% +could take that and he say hey what he's +really talking about is the unity of + + align:start position:0% +really talking about is the unity of + + + align:start position:0% +really talking about is the unity of +descent um and in in in the various uh + + align:start position:0% +descent um and in in in the various uh + + + align:start position:0% +descent um and in in in the various uh +relations of all these + + align:start position:0% +relations of all these + + + align:start position:0% +relations of all these +organisms so tremendous amount of work + + align:start position:0% +organisms so tremendous amount of work + + + align:start position:0% +organisms so tremendous amount of work +had already been done for in this sector + + align:start position:0% +had already been done for in this sector + + + align:start position:0% +had already been done for in this sector +by lenaeus and and people who followed + + align:start position:0% +by lenaeus and and people who followed + + + align:start position:0% +by lenaeus and and people who followed +him + + align:start position:0% +him + + + align:start position:0% +him +so and uh morphology of course which is + + align:start position:0% +so and uh morphology of course which is + + + align:start position:0% +so and uh morphology of course which is +part of U the basis for the natural + + align:start position:0% +part of U the basis for the natural + + + align:start position:0% +part of U the basis for the natural +system + + align:start position:0% +system + + + align:start position:0% +system +okay so at the end of uh that chapter on + + align:start position:0% +okay so at the end of uh that chapter on + + + align:start position:0% +okay so at the end of uh that chapter on +difficulties on theory he mentions the + + align:start position:0% +difficulties on theory he mentions the + + + align:start position:0% +difficulties on theory he mentions the +two great laws Unity of type and + + align:start position:0% +two great laws Unity of type and + + + align:start position:0% +two great laws Unity of type and +conditions of + + align:start position:0% +conditions of + + + align:start position:0% +conditions of +existence and we can see uh what he's + + align:start position:0% +existence and we can see uh what he's + + + align:start position:0% +existence and we can see uh what he's +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +here um let me just read this because + + align:start position:0% +here um let me just read this because + + + align:start position:0% +here um let me just read this because +it's a crucial part of this it is + + align:start position:0% +it's a crucial part of this it is + + + align:start position:0% +it's a crucial part of this it is +generally acknowledged that all organic + + align:start position:0% +generally acknowledged that all organic + + + align:start position:0% +generally acknowledged that all organic +beings have been formed on two great + + align:start position:0% +beings have been formed on two great + + + align:start position:0% +beings have been formed on two great +laws Unity of type and the conditions of + + align:start position:0% +laws Unity of type and the conditions of + + + align:start position:0% +laws Unity of type and the conditions of +existence by unity of type is meant that + + align:start position:0% +existence by unity of type is meant that + + + align:start position:0% +existence by unity of type is meant that +fundamental agreement in structure which + + align:start position:0% +fundamental agreement in structure which + + + align:start position:0% +fundamental agreement in structure which +we see in organic beings of the same + + align:start position:0% +we see in organic beings of the same + + + align:start position:0% +we see in organic beings of the same +class and which is quite independent of + + align:start position:0% +class and which is quite independent of + + + align:start position:0% +class and which is quite independent of +their habits of Life on my theory Unity + + align:start position:0% +their habits of Life on my theory Unity + + + align:start position:0% +their habits of Life on my theory Unity +of type is explained by unity of + + align:start position:0% +of type is explained by unity of + + + align:start position:0% +of type is explained by unity of +descent okay so you see these different + + align:start position:0% +descent okay so you see these different + + + align:start position:0% +descent okay so you see these different +uh uh brain forms uh of + + align:start position:0% +uh uh brain forms uh of + + + align:start position:0% +uh uh brain forms uh of +vertebrates and uh you know the the + + align:start position:0% +vertebrates and uh you know the the + + + align:start position:0% +vertebrates and uh you know the the +shifts and changes but you see the the + + align:start position:0% +shifts and changes but you see the the + + + align:start position:0% +shifts and changes but you see the the +fundament Al patterns the fundamental + + align:start position:0% +fundament Al patterns the fundamental + + + align:start position:0% +fundament Al patterns the fundamental +types of of uh these + + align:start position:0% +types of of uh these + + + align:start position:0% +types of of uh these +organisms and you know this is a vast + + align:start position:0% +organisms and you know this is a vast + + + align:start position:0% +organisms and you know this is a vast +field you can go + + align:start position:0% +field you can go + + + align:start position:0% +field you can go +into various classes of animals + + align:start position:0% +into various classes of animals + + + align:start position:0% +into various classes of animals +organisms plants and so forth and you + + align:start position:0% +organisms plants and so forth and you + + + align:start position:0% +organisms plants and so forth and you +can do this kind of study of just you + + align:start position:0% +can do this kind of study of just you + + + align:start position:0% +can do this kind of study of just you +know the various morphological forms and + + align:start position:0% +know the various morphological forms and + + + align:start position:0% +know the various morphological forms and +Trace the + + align:start position:0% +Trace the + + + align:start position:0% +Trace the +graduation how they're + + align:start position:0% +graduation how they're + + + align:start position:0% +graduation how they're +related okay so then he he mentioned s + + align:start position:0% +related okay so then he he mentioned s + + + align:start position:0% +related okay so then he he mentioned s +that um the other great law of exist + + align:start position:0% +that um the other great law of exist + + + align:start position:0% +that um the other great law of exist +uh of organic development is conditions + + align:start position:0% +uh of organic development is conditions + + + align:start position:0% +uh of organic development is conditions +of + + align:start position:0% +of + + + align:start position:0% +of +existence + + align:start position:0% +existence + + + align:start position:0% +existence +why why does he make conditions of + + align:start position:0% +why why does he make conditions of + + + align:start position:0% +why why does he make conditions of +existence so + + align:start position:0% +existence so + + + align:start position:0% +existence so +crucial he says in fact the law of + + align:start position:0% +crucial he says in fact the law of + + + align:start position:0% +crucial he says in fact the law of +conditions of existence is the higher + + align:start position:0% +conditions of existence is the higher + + + align:start position:0% +conditions of existence is the higher +law as it includes through the + + align:start position:0% +law as it includes through the + + + align:start position:0% +law as it includes through the +inheritance of former adaptations that + + align:start position:0% +inheritance of former adaptations that + + + align:start position:0% +inheritance of former adaptations that +of unity of + + align:start position:0% +of unity of + + + align:start position:0% +of unity of +type why is condition of existence such + + align:start position:0% + + + + align:start position:0% + +a profound principle in this + + align:start position:0% +a profound principle in this + + + align:start position:0% +a profound principle in this +work yeah Chris just some historical + + align:start position:0% +work yeah Chris just some historical + + + align:start position:0% +work yeah Chris just some historical +background uh before uh Darwin published + + align:start position:0% +background uh before uh Darwin published + + + align:start position:0% +background uh before uh Darwin published +the Origin of Species there was a debate + + align:start position:0% +the Origin of Species there was a debate + + + align:start position:0% +the Origin of Species there was a debate +between kuier + + align:start position:0% +between kuier + + + align:start position:0% +between kuier +andair who yeah who who both supported + + align:start position:0% +andair who yeah who who both supported + + + align:start position:0% +andair who yeah who who both supported +uh the unity of um the unity of type and + + align:start position:0% +uh the unity of um the unity of type and + + + align:start position:0% +uh the unity of um the unity of type and +conditions of + + align:start position:0% +conditions of + + + align:start position:0% +conditions of +existence and and that those were the + + align:start position:0% +existence and and that those were the + + + align:start position:0% +existence and and that those were the +two prevailing paradigms of the time + + align:start position:0% +two prevailing paradigms of the time + + + align:start position:0% +two prevailing paradigms of the time +they were competing and so Darwin sought + + align:start position:0% +they were competing and so Darwin sought + + + align:start position:0% +they were competing and so Darwin sought +to integrate both of them MH uh he found + + align:start position:0% +to integrate both of them MH uh he found + + + align:start position:0% +to integrate both of them MH uh he found +that the conditions of + + align:start position:0% +that the conditions of + + + align:start position:0% +that the conditions of +existence encompassed Unity of type and + + align:start position:0% +existence encompassed Unity of type and + + + align:start position:0% +existence encompassed Unity of type and +so tried to integrate it based upon + + align:start position:0% +so tried to integrate it based upon + + + align:start position:0% +so tried to integrate it based upon +conditions of exist good nice yeah so + + align:start position:0% +conditions of exist good nice yeah so + + + align:start position:0% +conditions of exist good nice yeah so +why would these two things be so so + + align:start position:0% +why would these two things be so so + + + align:start position:0% +why would these two things be so so +profoundly + + align:start position:0% + + + + align:start position:0% + +interconnected it could both be + + align:start position:0% +interconnected it could both be + + + align:start position:0% +interconnected it could both be +explained by natural selection by Darwin + + align:start position:0% +explained by natural selection by Darwin + + + align:start position:0% +explained by natural selection by Darwin +they could both be cast in the light of + + align:start position:0% +they could both be cast in the light of + + + align:start position:0% +they could both be cast in the light of +M derwin's natural selection scheme + + align:start position:0% +M derwin's natural selection scheme + + + align:start position:0% +M derwin's natural selection scheme +absolutely and and and the type these + + align:start position:0% +absolutely and and and the type these + + + align:start position:0% +absolutely and and and the type these +types and + + align:start position:0% +types and + + + align:start position:0% +types and +forms are really the functioning forms + + align:start position:0% +forms are really the functioning forms + + + align:start position:0% +forms are really the functioning forms +that can exist within the conditions of + + align:start position:0% +that can exist within the conditions of + + + align:start position:0% +that can exist within the conditions of +existence so these features are really + + align:start position:0% +existence so these features are really + + + align:start position:0% +existence so these features are really +the stuff of + + align:start position:0% +the stuff of + + + align:start position:0% +the stuff of +survival these forms have emerged + + align:start position:0% +survival these forms have emerged + + + align:start position:0% +survival these forms have emerged +through the competition for + + align:start position:0% +through the competition for + + + align:start position:0% +through the competition for +survival and survival means ability + + align:start position:0% +survival and survival means ability + + + align:start position:0% +survival and survival means ability +to flourish under conditions of + + align:start position:0% +to flourish under conditions of + + + align:start position:0% +to flourish under conditions of +existence so in some sense conditions of + + align:start position:0% +existence so in some sense conditions of + + + align:start position:0% +existence so in some sense conditions of +existence + + align:start position:0% +existence + + + align:start position:0% +existence +and type are + + align:start position:0% +and type are + + + align:start position:0% +and type are +constantly in + + align:start position:0% +constantly in + + + align:start position:0% +constantly in +flux so what about conditions of + + align:start position:0% +flux so what about conditions of + + + align:start position:0% +flux so what about conditions of +existence how do conditions of existence + + align:start position:0% + + + + align:start position:0% + +fluctuate geographical change + + align:start position:0% +fluctuate geographical change + + + align:start position:0% +fluctuate geographical change +yeah yeah absolutely geographical change + + align:start position:0% +yeah yeah absolutely geographical change + + + align:start position:0% +yeah yeah absolutely geographical change +um what are some of the + + align:start position:0% + + + + align:start position:0% + +others um + + align:start position:0% +others um + + + align:start position:0% +others um +relationships between + + align:start position:0% +relationships between + + + align:start position:0% +relationships between +organisms relationships between + + align:start position:0% +organisms relationships between + + + align:start position:0% +organisms relationships between +organisms + + align:start position:0% +organisms + + + align:start position:0% +organisms +absolutely as new organisms develop + + align:start position:0% +absolutely as new organisms develop + + + align:start position:0% +absolutely as new organisms develop +other + + align:start position:0% +other + + + align:start position:0% +other +organisms are kind of in competition for + + align:start position:0% +organisms are kind of in competition for + + + align:start position:0% +organisms are kind of in competition for +similar things tremendous what else + + align:start position:0% +similar things tremendous what else + + + align:start position:0% +similar things tremendous what else +fces food sources food sources + + align:start position:0% +fces food sources food sources + + + align:start position:0% +fces food sources food sources +absolutely and food sources are very uh + + align:start position:0% +absolutely and food sources are very uh + + + align:start position:0% +absolutely and food sources are very uh +closely connected to + + align:start position:0% + + + + align:start position:0% + +uh climate and the Earth conditions of + + align:start position:0% +uh climate and the Earth conditions of + + + align:start position:0% +uh climate and the Earth conditions of +uh I mean there were ice ages and things + + align:start position:0% +uh I mean there were ice ages and things + + + align:start position:0% +uh I mean there were ice ages and things +of that sort things either managed to + + align:start position:0% +of that sort things either managed to + + + align:start position:0% +of that sort things either managed to +adapt to them or they + + align:start position:0% +adapt to them or they + + + align:start position:0% +adapt to them or they +didn't um I mean this was well known in + + align:start position:0% +didn't um I mean this was well known in + + + align:start position:0% +didn't um I mean this was well known in +dar's time Louie ausy was a great + + align:start position:0% +dar's time Louie ausy was a great + + + align:start position:0% +dar's time Louie ausy was a great +uh uh student of uh the ice ages and + + align:start position:0% +uh uh student of uh the ice ages and + + + align:start position:0% +uh uh student of uh the ice ages and +Daren knew his work very well but uh it + + align:start position:0% +Daren knew his work very well but uh it + + + align:start position:0% +Daren knew his work very well but uh it +was quite + + align:start position:0% +was quite + + + align:start position:0% +was quite +clear that the geological changes that + + align:start position:0% +clear that the geological changes that + + + align:start position:0% +clear that the geological changes that +Charles LEL and other geologists had uh + + align:start position:0% +Charles LEL and other geologists had uh + + + align:start position:0% +Charles LEL and other geologists had uh +charted were the Earth was in constant + + align:start position:0% +charted were the Earth was in constant + + + align:start position:0% +charted were the Earth was in constant +flux maybe not in the lifetime of an + + align:start position:0% +flux maybe not in the lifetime of an + + + align:start position:0% +flux maybe not in the lifetime of an +individual so you'd think oh this is + + align:start position:0% +individual so you'd think oh this is + + + align:start position:0% +individual so you'd think oh this is +very nice it's all so stable when in + + align:start position:0% +very nice it's all so stable when in + + + align:start position:0% +very nice it's all so stable when in +fact it's changing constantly in in + + align:start position:0% +fact it's changing constantly in in + + + align:start position:0% +fact it's changing constantly in in +chapter 7 on on page uh + + align:start position:0% +chapter 7 on on page uh + + + align:start position:0% +chapter 7 on on page uh +209 he says + + align:start position:0% +209 he says + + + align:start position:0% +209 he says +um it is thus I it will be universally + + align:start position:0% +um it is thus I it will be universally + + + align:start position:0% +um it is thus I it will be universally +admitted that instincts are as important + + align:start position:0% +admitted that instincts are as important + + + align:start position:0% +admitted that instincts are as important +as corporeal structure physical + + align:start position:0% +as corporeal structure physical + + + align:start position:0% +as corporeal structure physical +structure for the welfare of each + + align:start position:0% +structure for the welfare of each + + + align:start position:0% +structure for the welfare of each +species under its present conditions of + + align:start position:0% +species under its present conditions of + + + align:start position:0% +species under its present conditions of +Life under changed conditions of life it + + align:start position:0% +Life under changed conditions of life it + + + align:start position:0% +Life under changed conditions of life it +is at least possible that slight + + align:start position:0% +is at least possible that slight + + + align:start position:0% +is at least possible that slight +modifications of instinct might be + + align:start position:0% +modifications of instinct might be + + + align:start position:0% +modifications of instinct might be +profitable to a + + align:start position:0% +profitable to a + + + align:start position:0% +profitable to a +species it can be shown that instincts + + align:start position:0% +species it can be shown that instincts + + + align:start position:0% +species it can be shown that instincts +do vary ever so little if it can be + + align:start position:0% +do vary ever so little if it can be + + + align:start position:0% +do vary ever so little if it can be +shown in if it can be shown that + + align:start position:0% +shown in if it can be shown that + + + align:start position:0% +shown in if it can be shown that +instincts do vary ever so little then I + + align:start position:0% +instincts do vary ever so little then I + + + align:start position:0% +instincts do vary ever so little then I +can see no difficulty in natural + + align:start position:0% +can see no difficulty in natural + + + align:start position:0% +can see no difficulty in natural +selection preserving and continually + + align:start position:0% +selection preserving and continually + + + align:start position:0% +selection preserving and continually +accumulating variations of instinct to + + align:start position:0% +accumulating variations of instinct to + + + align:start position:0% +accumulating variations of instinct to +any extent that may be profitable it is + + align:start position:0% +any extent that may be profitable it is + + + align:start position:0% +any extent that may be profitable it is +thus as I believe that all the most + + align:start position:0% +thus as I believe that all the most + + + align:start position:0% +thus as I believe that all the most +complex and wonderful instincts have + + align:start position:0% +complex and wonderful instincts have + + + align:start position:0% +complex and wonderful instincts have +originated as modifications of corporeal + + align:start position:0% +originated as modifications of corporeal + + + align:start position:0% +originated as modifications of corporeal +structure arise from and are increased + + align:start position:0% +structure arise from and are increased + + + align:start position:0% +structure arise from and are increased +by use are habit and are diminished or + + align:start position:0% +by use are habit and are diminished or + + + align:start position:0% +by use are habit and are diminished or +lost by disuse so I do not doubt it has + + align:start position:0% +lost by disuse so I do not doubt it has + + + align:start position:0% +lost by disuse so I do not doubt it has +been within + + align:start position:0% +been within + + + align:start position:0% +been within +instincts but I believe that the effects + + align:start position:0% +instincts but I believe that the effects + + + align:start position:0% +instincts but I believe that the effects +of habit are of quite subordinate + + align:start position:0% +of habit are of quite subordinate + + + align:start position:0% +of habit are of quite subordinate +importance so he distinguishes between + + align:start position:0% +importance so he distinguishes between + + + align:start position:0% +importance so he distinguishes between +habit and Instinct I mean they both have + + align:start position:0% +habit and Instinct I mean they both have + + + align:start position:0% +habit and Instinct I mean they both have +you know certain similar goals that is + + align:start position:0% +you know certain similar goals that is + + + align:start position:0% +you know certain similar goals that is +they're repetitious they tend + + align:start position:0% +they're repetitious they tend + + + align:start position:0% +they're repetitious they tend +to uh require uh a very low threshold of + + align:start position:0% +to uh require uh a very low threshold of + + + align:start position:0% +to uh require uh a very low threshold of +rational or no threshold of + + align:start position:0% +rational or no threshold of + + + align:start position:0% +rational or no threshold of +rational um + + align:start position:0% +rational um + + + align:start position:0% +rational um +consideration uh before their invoked as + + align:start position:0% +consideration uh before their invoked as + + + align:start position:0% +consideration uh before their invoked as +sources of + + align:start position:0% +sources of + + + align:start position:0% +sources of +Behavior Uh but the one is + + align:start position:0% +Behavior Uh but the one is + + + align:start position:0% +Behavior Uh but the one is +learned and the other according to + + align:start position:0% +learned and the other according to + + + align:start position:0% +learned and the other according to +Darwin is + + align:start position:0% +Darwin is + + + align:start position:0% +Darwin is +inherited and if it is + + align:start position:0% +inherited and if it is + + + align:start position:0% +inherited and if it is +inherited there's got to be a physical + + align:start position:0% +inherited there's got to be a physical + + + align:start position:0% +inherited there's got to be a physical +basis for it and as we were talking last + + align:start position:0% +basis for it and as we were talking last + + + align:start position:0% +basis for it and as we were talking last +time it's a little hard to get your head + + align:start position:0% +time it's a little hard to get your head + + + align:start position:0% +time it's a little hard to get your head +around that at first because instinct is + + align:start position:0% +around that at first because instinct is + + + align:start position:0% +around that at first because instinct is +a kind of a it's a mental processing + + align:start position:0% +a kind of a it's a mental processing + + + align:start position:0% +a kind of a it's a mental processing +it's it's it's a it's not like an + + align:start position:0% +it's it's it's a it's not like an + + + align:start position:0% +it's it's it's a it's not like an +object I mean we you know when we talk + + align:start position:0% +object I mean we you know when we talk + + + align:start position:0% +object I mean we you know when we talk +about uh the heart or we talk about uh + + align:start position:0% +about uh the heart or we talk about uh + + + align:start position:0% +about uh the heart or we talk about uh +you know some physical we know what it + + align:start position:0% +you know some physical we know what it + + + align:start position:0% +you know some physical we know what it +looks like we don't know what Instinct + + align:start position:0% +looks like we don't know what Instinct + + + align:start position:0% +looks like we don't know what Instinct +looks like so it's + + align:start position:0% +looks like so it's + + + align:start position:0% +looks like so it's +mental so it's it's a it's a challenge + + align:start position:0% +mental so it's it's a it's a challenge + + + align:start position:0% +mental so it's it's a it's a challenge +but uh this was a very very great + + align:start position:0% +but uh this was a very very great + + + align:start position:0% +but uh this was a very very great +challenge for Darin and his solution was + + align:start position:0% +challenge for Darin and his solution was + + + align:start position:0% +challenge for Darin and his solution was +to align it with the physiology of + + align:start position:0% +to align it with the physiology of + + + align:start position:0% +to align it with the physiology of +organisms and to say it basically + + align:start position:0% +organisms and to say it basically + + + align:start position:0% +organisms and to say it basically +behaves the same way it's it's it has + + align:start position:0% +behaves the same way it's it's it has + + + align:start position:0% +behaves the same way it's it's it has +the same Expressions the same uh basis + + align:start position:0% +the same Expressions the same uh basis + + + align:start position:0% +the same Expressions the same uh basis +as physical + + align:start position:0% + + + + align:start position:0% + +organisms and + + align:start position:0% +organisms and + + + align:start position:0% +organisms and +therefore it is tremendously + + align:start position:0% + + + + align:start position:0% + +stable and it + + align:start position:0% +stable and it + + + align:start position:0% +stable and it +basically + + align:start position:0% +basically + + + align:start position:0% +basically +changes it's subject to a gradual change + + align:start position:0% +changes it's subject to a gradual change + + + align:start position:0% +changes it's subject to a gradual change +an improvement or uh maybe improvements + + align:start position:0% +an improvement or uh maybe improvements + + + align:start position:0% +an improvement or uh maybe improvements +wrong gradual change in + + align:start position:0% + + + + align:start position:0% + +time and he uses as his great + + align:start position:0% +time and he uses as his great + + + align:start position:0% +time and he uses as his great +illustration beehives uh the the + + align:start position:0% +illustration beehives uh the the + + + align:start position:0% +illustration beehives uh the the +behavior of ants of + + align:start position:0% +behavior of ants of + + + align:start position:0% +behavior of ants of +bees and he talks about the + + align:start position:0% +bees and he talks about the + + + align:start position:0% +bees and he talks about the +graduation in the + + align:start position:0% +graduation in the + + + align:start position:0% +graduation in the +structure uh and the in the comb + + align:start position:0% +structure uh and the in the comb + + + align:start position:0% +structure uh and the in the comb +precision and therefore + + align:start position:0% +precision and therefore + + + align:start position:0% +precision and therefore +the the um success and functionality of + + align:start position:0% +the the um success and functionality of + + + align:start position:0% +the the um success and functionality of +the comb from uh The Humble bee it's big + + align:start position:0% +the comb from uh The Humble bee it's big + + + align:start position:0% +the comb from uh The Humble bee it's big +bee to the Mexican bee uh to The Hive be + + align:start position:0% +bee to the Mexican bee uh to The Hive be + + + align:start position:0% +bee to the Mexican bee uh to The Hive be +and he can he argues that this sort of + + align:start position:0% +and he can he argues that this sort of + + + align:start position:0% +and he can he argues that this sort of +change in these different honeycomb + + align:start position:0% +change in these different honeycomb + + + align:start position:0% +change in these different honeycomb +structures reflects a + + align:start position:0% +structures reflects a + + + align:start position:0% +structures reflects a +graduation + + align:start position:0% +graduation + + + align:start position:0% +graduation +in + + align:start position:0% +in + + + align:start position:0% +in +uh functionality improve + + align:start position:0% +uh functionality improve + + + align:start position:0% +uh functionality improve +functionality and that this is U reflex + + align:start position:0% +functionality and that this is U reflex + + + align:start position:0% +functionality and that this is U reflex +it's a refle reflection of natural + + align:start position:0% +it's a refle reflection of natural + + + align:start position:0% +it's a refle reflection of natural +selection so the hives themselves become + + align:start position:0% +selection so the hives themselves become + + + align:start position:0% +selection so the hives themselves become +the the reflection of it's like the + + align:start position:0% +the the reflection of it's like the + + + align:start position:0% +the the reflection of it's like the +Instinct it's almost like he's taken the + + align:start position:0% +Instinct it's almost like he's taken the + + + align:start position:0% +Instinct it's almost like he's taken the +organ out of the body here and put it in + + align:start position:0% +organ out of the body here and put it in + + + align:start position:0% +organ out of the body here and put it in +these hives and there it is you you look + + align:start position:0% +these hives and there it is you you look + + + align:start position:0% +these hives and there it is you you look +at this + + align:start position:0% +at this + + + align:start position:0% +at this +graduated uh beehives and you see + + align:start position:0% +graduated uh beehives and you see + + + align:start position:0% +graduated uh beehives and you see +increase and the type of functionality + + align:start position:0% +increase and the type of functionality + + + align:start position:0% +increase and the type of functionality +he's talking about is the ability to + + align:start position:0% +he's talking about is the ability to + + + align:start position:0% +he's talking about is the ability to +store + + align:start position:0% + + + + align:start position:0% + +honey and you know the the amount of + + align:start position:0% +honey and you know the the amount of + + + align:start position:0% +honey and you know the the amount of +work and the amount of honey that can be + + align:start position:0% +work and the amount of honey that can be + + + align:start position:0% +work and the amount of honey that can be +St or for units of work + + align:start position:0% +St or for units of work + + + align:start position:0% +St or for units of work +time and the argument behind that why + + align:start position:0% +time and the argument behind that why + + + align:start position:0% +time and the argument behind that why +would that be + + align:start position:0% + + + + align:start position:0% + +adaptive + + align:start position:0% +adaptive + + + align:start position:0% +adaptive +well bees that have access to more uh + + align:start position:0% +well bees that have access to more uh + + + align:start position:0% +well bees that have access to more uh +more + + align:start position:0% +more + + + align:start position:0% +more +honey and can build a honey uh + + align:start position:0% +honey and can build a honey uh + + + align:start position:0% +honey and can build a honey uh +containers and so forth with less + + align:start position:0% +containers and so forth with less + + + align:start position:0% +containers and so forth with less +effort have a + + align:start position:0% + + + + align:start position:0% + +advantage as he says here U the bees of + + align:start position:0% +advantage as he says here U the bees of + + + align:start position:0% +advantage as he says here U the bees of +course are no more knowing that they + + align:start position:0% +course are no more knowing that they + + + align:start position:0% +course are no more knowing that they +swept their spheres at one particular + + align:start position:0% +swept their spheres at one particular + + + align:start position:0% +swept their spheres at one particular +distance from each other then they know + + align:start position:0% +distance from each other then they know + + + align:start position:0% +distance from each other then they know +what are the several angles of the + + align:start position:0% +what are the several angles of the + + + align:start position:0% +what are the several angles of the +hexagonal prisms and of the basil romic + + align:start position:0% +hexagonal prisms and of the basil romic + + + align:start position:0% +hexagonal prisms and of the basil romic +plates he's actually done a whole study + + align:start position:0% +plates he's actually done a whole study + + + align:start position:0% +plates he's actually done a whole study +he's basing this on the work of uh Huber + + align:start position:0% +he's basing this on the work of uh Huber + + + align:start position:0% +he's basing this on the work of uh Huber +uh a naturalist um a Swiss naturalist + + align:start position:0% +uh a naturalist um a Swiss naturalist + + + align:start position:0% +uh a naturalist um a Swiss naturalist +who actually did a huge study of + + align:start position:0% +who actually did a huge study of + + + align:start position:0% +who actually did a huge study of +honeybees so he's he hasn't done this + + align:start position:0% +honeybees so he's he hasn't done this + + + align:start position:0% +honeybees so he's he hasn't done this +all he's he's studied Huber and other + + align:start position:0% +all he's he's studied Huber and other + + + align:start position:0% +all he's he's studied Huber and other +other work too but um so he says the + + align:start position:0% +other work too but um so he says the + + + align:start position:0% +other work too but um so he says the +Motive Power of the process of natural + + align:start position:0% +Motive Power of the process of natural + + + align:start position:0% +Motive Power of the process of natural +selection has been economy of wax that + + align:start position:0% +selection has been economy of wax that + + + align:start position:0% +selection has been economy of wax that +individual swarm which wasted least + + align:start position:0% +individual swarm which wasted least + + + align:start position:0% +individual swarm which wasted least +honey in the secretion of wax having + + align:start position:0% +honey in the secretion of wax having + + + align:start position:0% +honey in the secretion of wax having +succeeded best and having transmitted by + + align:start position:0% +succeeded best and having transmitted by + + + align:start position:0% +succeeded best and having transmitted by +inheritance its newly acquired + + align:start position:0% +inheritance its newly acquired + + + align:start position:0% +inheritance its newly acquired +economical Instinct uh to new swarms + + align:start position:0% +economical Instinct uh to new swarms + + + align:start position:0% +economical Instinct uh to new swarms +will have had the best chance of + + align:start position:0% +will have had the best chance of + + + align:start position:0% +will have had the best chance of +succeeding in the struggle for + + align:start position:0% +succeeding in the struggle for + + + align:start position:0% +succeeding in the struggle for +existence so this is his great kind of + + align:start position:0% +existence so this is his great kind of + + + align:start position:0% +existence so this is his great kind of +illustration of U the power of + + align:start position:0% +illustration of U the power of + + + align:start position:0% +illustration of U the power of +instinct I want to skip to his section + + align:start position:0% +instinct I want to skip to his section + + + align:start position:0% +instinct I want to skip to his section +on + + align:start position:0% +on + + + align:start position:0% +on +embryology so why is embryology so + + align:start position:0% +embryology so why is embryology so + + + align:start position:0% +embryology so why is embryology so +important to + + align:start position:0% +important to + + + align:start position:0% +important to +Darin what how does he put what what is + + align:start position:0% +Darin what how does he put what what is + + + align:start position:0% +Darin what how does he put what what is +embryology first what are we talking + + align:start position:0% +embryology first what are we talking + + + align:start position:0% +embryology first what are we talking +about what kind of a field is embryology + + align:start position:0% +about what kind of a field is embryology + + + align:start position:0% +about what kind of a field is embryology +Claire it's almost like metaphorical for + + align:start position:0% +Claire it's almost like metaphorical for + + + align:start position:0% +Claire it's almost like metaphorical for +the development of species throughout + + align:start position:0% +the development of species throughout + + + align:start position:0% +the development of species throughout +time they start out being so similar the + + align:start position:0% +time they start out being so similar the + + + align:start position:0% +time they start out being so similar the +embryological form like you can't tell + + align:start position:0% +embryological form like you can't tell + + + align:start position:0% +embryological form like you can't tell +the difference between a pig and a human + + align:start position:0% +the difference between a pig and a human + + + align:start position:0% +the difference between a pig and a human +or like a frog well yeah and then as + + align:start position:0% +or like a frog well yeah and then as + + + align:start position:0% +or like a frog well yeah and then as +time goes on they become more and more + + align:start position:0% +time goes on they become more and more + + + align:start position:0% +time goes on they become more and more +like different they D from one another + + align:start position:0% +like different they D from one another + + + align:start position:0% +like different they D from one another +so it kind of shows his theory in a very + + align:start position:0% +so it kind of shows his theory in a very + + + align:start position:0% +so it kind of shows his theory in a very +fast forwarded kind of way like how we + + align:start position:0% +fast forwarded kind of way like how we + + + align:start position:0% +fast forwarded kind of way like how we +all came from a common ancestor okay so + + align:start position:0% +all came from a common ancestor okay so + + + align:start position:0% +all came from a common ancestor okay so +yes um so embryology is the study of + + align:start position:0% +yes um so embryology is the study of + + + align:start position:0% +yes um so embryology is the study of +embryos and the processes of development + + align:start position:0% +embryos and the processes of development + + + align:start position:0% +embryos and the processes of development +in the embryo + + align:start position:0% +in the embryo + + + align:start position:0% +in the embryo +and it's uh it's a whole scientific + + align:start position:0% +and it's uh it's a whole scientific + + + align:start position:0% +and it's uh it's a whole scientific +field and it's in its in its own on its + + align:start position:0% +field and it's in its in its own on its + + + align:start position:0% +field and it's in its in its own on its +own and it had developed in Darwin's + + align:start position:0% +own and it had developed in Darwin's + + + align:start position:0% +own and it had developed in Darwin's +time it was a result of uh a lot of work + + align:start position:0% +time it was a result of uh a lot of work + + + align:start position:0% +time it was a result of uh a lot of work +in Germany that was brought over to + + align:start position:0% +in Germany that was brought over to + + + align:start position:0% +in Germany that was brought over to +England and darn was quite familiar with + + align:start position:0% +England and darn was quite familiar with + + + align:start position:0% +England and darn was quite familiar with +it and he saw in + + align:start position:0% +it and he saw in + + + align:start position:0% +it and he saw in +embryological development and theories + + align:start position:0% +embryological development and theories + + + align:start position:0% +embryological development and theories +some interesting support for his concept + + align:start position:0% +some interesting support for his concept + + + align:start position:0% +some interesting support for his concept +so as Claire said uh it was it was um + + align:start position:0% +so as Claire said uh it was it was um + + + align:start position:0% +so as Claire said uh it was it was um +hard to distinguish between many of + + align:start position:0% +hard to distinguish between many of + + + align:start position:0% +hard to distinguish between many of +these embryos at various stages so why + + align:start position:0% +these embryos at various stages so why + + + align:start position:0% +these embryos at various stages so why +is that so important to + + align:start position:0% +is that so important to + + + align:start position:0% +is that so important to +D Chris it mirrors his + + align:start position:0% +D Chris it mirrors his + + + align:start position:0% +D Chris it mirrors his +uh the the framework he set up where + + align:start position:0% +uh the the framework he set up where + + + align:start position:0% +uh the the framework he set up where +various species that were that seemed + + align:start position:0% +various species that were that seemed + + + align:start position:0% +various species that were that seemed +very different emerged from + + align:start position:0% +very different emerged from + + + align:start position:0% +very different emerged from +similar early species + + align:start position:0% +similar early species + + + align:start position:0% +similar early species +and he states that two different species + + align:start position:0% +and he states that two different species + + + align:start position:0% +and he states that two different species +could have the same could have embryos + + align:start position:0% +could have the same could have embryos + + + align:start position:0% +could have the same could have embryos +that look very similar but after a while + + align:start position:0% +that look very similar but after a while + + + align:start position:0% +that look very similar but after a while +they take different shapes okay they + + align:start position:0% +they take different shapes okay they + + + align:start position:0% +they take different shapes okay they +take different shapes but in the + + align:start position:0% +take different shapes but in the + + + align:start position:0% +take different shapes but in the +similarity what do they + + align:start position:0% +similarity what do they + + + align:start position:0% +similarity what do they +illustrate in Darwin je common ancestor + + align:start position:0% +illustrate in Darwin je common ancestor + + + align:start position:0% +illustrate in Darwin je common ancestor +a common ancestor the fact that these + + align:start position:0% +a common ancestor the fact that these + + + align:start position:0% +a common ancestor the fact that these +forms it's it's another example of + + align:start position:0% +forms it's it's another example of + + + align:start position:0% +forms it's it's another example of +parsimony in some sense it just shows + + align:start position:0% +parsimony in some sense it just shows + + + align:start position:0% +parsimony in some sense it just shows +developmental uh life life forms + + align:start position:0% +developmental uh life life forms + + + align:start position:0% +developmental uh life life forms +developmentally have kind of passed + + align:start position:0% +developmentally have kind of passed + + + align:start position:0% +developmentally have kind of passed +through uh a uh similar set of processes + + align:start position:0% +through uh a uh similar set of processes + + + align:start position:0% +through uh a uh similar set of processes +that argues or at least supports the + + align:start position:0% +that argues or at least supports the + + + align:start position:0% +that argues or at least supports the +argument or fits with the argument that + + align:start position:0% +argument or fits with the argument that + + + align:start position:0% +argument or fits with the argument that +they come from common ancestral + + align:start position:0% +they come from common ancestral + + + align:start position:0% +they come from common ancestral +forms and you can go you can track these + + align:start position:0% +forms and you can go you can track these + + + align:start position:0% +forms and you can go you can track these +across many many different forms that + + align:start position:0% +across many many different forms that + + + align:start position:0% +across many many different forms that +exist in quite unrelated adult forms and + + align:start position:0% +exist in quite unrelated adult forms and + + + align:start position:0% +exist in quite unrelated adult forms and +entirely in entirely different + + align:start position:0% + + + + align:start position:0% + +classes there are stages this + + align:start position:0% +classes there are stages this + + + align:start position:0% +classes there are stages this +development so he says for the + + align:start position:0% +development so he says for the + + + align:start position:0% +development so he says for the +development is the animal in its less + + align:start position:0% +development is the animal in its less + + + align:start position:0% +development is the animal in its less +modified State and in so far it reveals + + align:start position:0% +modified State and in so far it reveals + + + align:start position:0% +modified State and in so far it reveals +the structure of its + + align:start position:0% +the structure of its + + + align:start position:0% +the structure of its +progenitor well this may not be quite + + align:start position:0% +progenitor well this may not be quite + + + align:start position:0% +progenitor well this may not be quite +true but but it it gives you some of the + + align:start position:0% +true but but it it gives you some of the + + + align:start position:0% +true but but it it gives you some of the +uh some of the + + align:start position:0% +uh some of the + + + align:start position:0% +uh some of the +characteristics in two groups of animal + + align:start position:0% +characteristics in two groups of animal + + + align:start position:0% +characteristics in two groups of animal +however much they may at present differ + + align:start position:0% +however much they may at present differ + + + align:start position:0% +however much they may at present differ +from each other in structure and habits + + align:start position:0% +from each other in structure and habits + + + align:start position:0% +from each other in structure and habits +if they pass through the same or similar + + align:start position:0% +if they pass through the same or similar + + + align:start position:0% +if they pass through the same or similar +embryonic stages we may feel assured + + align:start position:0% +embryonic stages we may feel assured + + + align:start position:0% +embryonic stages we may feel assured +that they have both descended from the + + align:start position:0% +that they have both descended from the + + + align:start position:0% +that they have both descended from the +same or nearly similar + + align:start position:0% +same or nearly similar + + + align:start position:0% +same or nearly similar +parents that's the fundamental + + align:start position:0% +parents that's the fundamental + + + align:start position:0% +parents that's the fundamental +principle + + align:start position:0% +principle + + + align:start position:0% +principle +um thus community in embryonic structure + + align:start position:0% +um thus community in embryonic structure + + + align:start position:0% +um thus community in embryonic structure +reveals community of + + align:start position:0% +reveals community of + + + align:start position:0% +reveals community of +descent so again he's putting yet + + align:start position:0% +descent so again he's putting yet + + + align:start position:0% +descent so again he's putting yet +another field of science into the + + align:start position:0% +another field of science into the + + + align:start position:0% +another field of science into the +framework of his theory and you see + + align:start position:0% +framework of his theory and you see + + + align:start position:0% +framework of his theory and you see +again the illustration of Darwin the + + align:start position:0% +again the illustration of Darwin the + + + align:start position:0% +again the illustration of Darwin the +great synthesizer he's pulling this work + + align:start position:0% +great synthesizer he's pulling this work + + + align:start position:0% +great synthesizer he's pulling this work +together and it's it fits uh you can + + align:start position:0% +together and it's it fits uh you can + + + align:start position:0% +together and it's it fits uh you can +argue + + align:start position:0% +argue + + + align:start position:0% +argue +but you know it's it's pretty + + align:start position:0% +but you know it's it's pretty + + + align:start position:0% +but you know it's it's pretty +ingenious so this is a lot of material + + align:start position:0% +ingenious so this is a lot of material + + + align:start position:0% +ingenious so this is a lot of material +and you know it's kind of overwhelming + + align:start position:0% +and you know it's kind of overwhelming + + + align:start position:0% +and you know it's kind of overwhelming +but uhu um I did want to kind of explore + + align:start position:0% +but uhu um I did want to kind of explore + + + align:start position:0% +but uhu um I did want to kind of explore +some of these key Core Concepts of + + align:start position:0% +some of these key Core Concepts of + + + align:start position:0% +some of these key Core Concepts of +Darwin um because they're so fundamental + + align:start position:0% +Darwin um because they're so fundamental + + + align:start position:0% +Darwin um because they're so fundamental +to the way we think + + align:start position:0% +to the way we think + + + align:start position:0% +to the way we think +today and we think in these terms today + + align:start position:0% +today and we think in these terms today + + + align:start position:0% +today and we think in these terms today +almost without you know uh too much + + align:start position:0% +almost without you know uh too much + + + align:start position:0% +almost without you know uh too much +reflection on it simply because it seems + + align:start position:0% +reflection on it simply because it seems + + + align:start position:0% +reflection on it simply because it seems +pretty much the way uh at least in + + align:start position:0% +pretty much the way uh at least in + + + align:start position:0% +pretty much the way uh at least in +certain fields that we + + align:start position:0% +certain fields that we + + + align:start position:0% +certain fields that we +study um it's just sort of acceptive + + align:start position:0% +study um it's just sort of acceptive + + + align:start position:0% +study um it's just sort of acceptive +acceptive system but um you know here's + + align:start position:0% +acceptive system but um you know here's + + + align:start position:0% +acceptive system but um you know here's +here's where it was being + + align:start position:0% +here's where it was being + + + align:start position:0% +here's where it was being +assembled this is this is a work that + + align:start position:0% +assembled this is this is a work that + + + align:start position:0% +assembled this is this is a work that +assembled it but having said that I I I + + align:start position:0% +assembled it but having said that I I I + + + align:start position:0% +assembled it but having said that I I I +do want + + align:start position:0% +do want + + + align:start position:0% +do want +to um end on Darwin's note here is he + + align:start position:0% +to um end on Darwin's note here is he + + + align:start position:0% +to um end on Darwin's note here is he +says U you know he steps back at the end + + align:start position:0% +says U you know he steps back at the end + + + align:start position:0% +says U you know he steps back at the end +of his chapter and you know he he he + + align:start position:0% +of his chapter and you know he he he + + + align:start position:0% +of his chapter and you know he he he +admits that there are a lot of things + + align:start position:0% +admits that there are a lot of things + + + align:start position:0% +admits that there are a lot of things +that U could be uh disagreed with + + align:start position:0% +that U could be uh disagreed with + + + align:start position:0% +that U could be uh disagreed with +however the system stand the the big + + align:start position:0% +however the system stand the the big + + + align:start position:0% +however the system stand the the big +picture of the system works works + + align:start position:0% +picture of the system works works + + + align:start position:0% +picture of the system works works +beautifully and um you know uh it will + + align:start position:0% +beautifully and um you know uh it will + + + align:start position:0% +beautifully and um you know uh it will +be disturbing he understood to some + + align:start position:0% +be disturbing he understood to some + + + align:start position:0% +be disturbing he understood to some +people but as he said it is interesting + + align:start position:0% +people but as he said it is interesting + + + align:start position:0% +people but as he said it is interesting +this is a very famous passage to + + align:start position:0% +this is a very famous passage to + + + align:start position:0% +this is a very famous passage to +contemplate an entangled Bank clothed + + align:start position:0% +contemplate an entangled Bank clothed + + + align:start position:0% +contemplate an entangled Bank clothed +with many plants of many kinds with + + align:start position:0% +with many plants of many kinds with + + + align:start position:0% +with many plants of many kinds with +birds singing on the bushes and with + + align:start position:0% +birds singing on the bushes and with + + + align:start position:0% +birds singing on the bushes and with +various insects flitting about this is + + align:start position:0% +various insects flitting about this is + + + align:start position:0% +various insects flitting about this is +what he encountered when he went to + + align:start position:0% +what he encountered when he went to + + + align:start position:0% +what he encountered when he went to +South America as a young man and with + + align:start position:0% +South America as a young man and with + + + align:start position:0% +South America as a young man and with +worms crawling through the damp Earth + + align:start position:0% +worms crawling through the damp Earth + + + align:start position:0% +worms crawling through the damp Earth +and to reflect that these elaborately + + align:start position:0% +and to reflect that these elaborately + + + align:start position:0% +and to reflect that these elaborately +constructed forms so different from each + + align:start position:0% +constructed forms so different from each + + + align:start position:0% +constructed forms so different from each +other and dependent on each other in so + + align:start position:0% +other and dependent on each other in so + + + align:start position:0% +other and dependent on each other in so +complex a manner have all been produced + + align:start position:0% +complex a manner have all been produced + + + align:start position:0% +complex a manner have all been produced +by laws acting around + + align:start position:0% +by laws acting around + + + align:start position:0% +by laws acting around +us the key message of the book this is + + align:start position:0% +us the key message of the book this is + + + align:start position:0% +us the key message of the book this is +this is basically happening through the + + align:start position:0% +this is basically happening through the + + + align:start position:0% +this is basically happening through the +laws of that we can can + + align:start position:0% +laws of that we can can + + + align:start position:0% +laws of that we can can +observe and we don't need any + + align:start position:0% +observe and we don't need any + + + align:start position:0% +observe and we don't need any +explanation beyond that for these + + align:start position:0% +explanation beyond that for these + + + align:start position:0% +explanation beyond that for these +forms um and that's in some sense the + + align:start position:0% +forms um and that's in some sense the + + + align:start position:0% +forms um and that's in some sense the +quintessential naturalist + + align:start position:0% + + + + align:start position:0% + +argument \ No newline at end of file diff --git a/802a1jvk5Ck.txt b/802a1jvk5Ck.txt new file mode 100644 index 0000000000000000000000000000000000000000..165cb1f4ccf730c657c5c1c36b1581201b4dde2c --- /dev/null +++ b/802a1jvk5Ck.txt @@ -0,0 +1,6155 @@ +align:start position:0% + +all right folks Tina's going to tell you + + align:start position:0% +all right folks Tina's going to tell you + + + align:start position:0% +all right folks Tina's going to tell you +more we had a little bit of weight and + + align:start position:0% +more we had a little bit of weight and + + + align:start position:0% +more we had a little bit of weight and +balance before that fight planning the + + align:start position:0% +balance before that fight planning the + + + align:start position:0% +balance before that fight planning the +sample but Tina is now going to give you + + align:start position:0% +sample but Tina is now going to give you + + + align:start position:0% +sample but Tina is now going to give you +the the real story so you guys all ready + + align:start position:0% +the the real story so you guys all ready + + + align:start position:0% +the the real story so you guys all ready +to go out and get your drones license + + align:start position:0% +to go out and get your drones license + + + align:start position:0% +to go out and get your drones license +good I'm really glad all right we in + + align:start position:0% +good I'm really glad all right we in + + + align:start position:0% +good I'm really glad all right we in +balance so we talked a little bit we've + + align:start position:0% +balance so we talked a little bit we've + + + align:start position:0% +balance so we talked a little bit we've +actually had quite a few discussions + + align:start position:0% +actually had quite a few discussions + + + align:start position:0% +actually had quite a few discussions +throughout about stability about where + + align:start position:0% +throughout about stability about where + + + align:start position:0% +throughout about stability about where +the center of G is how that affects your + + align:start position:0% +the center of G is how that affects your + + + align:start position:0% +the center of G is how that affects your +controllability of the aircraft so + + align:start position:0% +controllability of the aircraft so + + + align:start position:0% +controllability of the aircraft so +weight and balances and not only an + + align:start position:0% +weight and balances and not only an + + + align:start position:0% +weight and balances and not only an +important thing to know but it's a + + align:start position:0% +important thing to know but it's a + + + align:start position:0% +important thing to know but it's a +required thing that you have to do + + align:start position:0% +required thing that you have to do + + + align:start position:0% +required thing that you have to do +before you go flying each time and one + + align:start position:0% +before you go flying each time and one + + + align:start position:0% +before you go flying each time and one +thing that's also relevant is to + + align:start position:0% +thing that's also relevant is to + + + align:start position:0% +thing that's also relevant is to +understand the center of gravity and you + + align:start position:0% +understand the center of gravity and you + + + align:start position:0% +understand the center of gravity and you +want to make sure that center of gravity + + align:start position:0% +want to make sure that center of gravity + + + align:start position:0% +want to make sure that center of gravity +is within the limits for your given + + align:start position:0% +is within the limits for your given + + + align:start position:0% +is within the limits for your given +aircraft so we talked about yesterday + + align:start position:0% +aircraft so we talked about yesterday + + + align:start position:0% +aircraft so we talked about yesterday +when we were talking about aerodynamic + + align:start position:0% +when we were talking about aerodynamic + + + align:start position:0% +when we were talking about aerodynamic +flight that certain aircraft have to be + + align:start position:0% +flight that certain aircraft have to be + + + align:start position:0% +flight that certain aircraft have to be +reinforced to do certain operations so + + align:start position:0% +reinforced to do certain operations so + + + align:start position:0% +reinforced to do certain operations so +again it really has to do with that and + + align:start position:0% +again it really has to do with that and + + + align:start position:0% +again it really has to do with that and +and by the way from yesterday mark left + + align:start position:0% +and by the way from yesterday mark left + + + align:start position:0% +and by the way from yesterday mark left +behind some of his aerodynamic procedure + + align:start position:0% +behind some of his aerodynamic procedure + + + align:start position:0% +behind some of his aerodynamic procedure +diagrams if you want to take a look at + + align:start position:0% +diagrams if you want to take a look at + + + align:start position:0% +diagrams if you want to take a look at +that those are up front well one thing + + align:start position:0% +that those are up front well one thing + + + align:start position:0% +that those are up front well one thing +that really you have to keep in mind in + + align:start position:0% +that really you have to keep in mind in + + + align:start position:0% +that really you have to keep in mind in +terms of what the aircraft can handle is + + align:start position:0% +terms of what the aircraft can handle is + + + align:start position:0% +terms of what the aircraft can handle is +just what is the max gross weight so + + align:start position:0% +just what is the max gross weight so + + + align:start position:0% +just what is the max gross weight so +what are what can this airframe sustain + + align:start position:0% +what are what can this airframe sustain + + + align:start position:0% +what are what can this airframe sustain +in terms of stresses on its body we also + + align:start position:0% +in terms of stresses on its body we also + + + align:start position:0% +in terms of stresses on its body we also +talked this morning about performance + + align:start position:0% +talked this morning about performance + + + align:start position:0% +talked this morning about performance +and discuss you know certain things like + + align:start position:0% +and discuss you know certain things like + + + align:start position:0% +and discuss you know certain things like +the distance the length of the runway + + align:start position:0% +the distance the length of the runway + + + align:start position:0% +the distance the length of the runway +and the distance you need to take off + + align:start position:0% +and the distance you need to take off + + + align:start position:0% +and the distance you need to take off +are affected by how the airplane is + + align:start position:0% +are affected by how the airplane is + + + align:start position:0% +are affected by how the airplane is +weighted so we're going to talk about + + align:start position:0% +weighted so we're going to talk about + + + align:start position:0% +weighted so we're going to talk about +those things specifically and then one + + align:start position:0% +those things specifically and then one + + + align:start position:0% +those things specifically and then one +thing I have on here is if you go over + + align:start position:0% +thing I have on here is if you go over + + + align:start position:0% +thing I have on here is if you go over +your gross weight then you get into test + + align:start position:0% +your gross weight then you get into test + + + align:start position:0% +your gross weight then you get into test +pilot territory and right after this + + align:start position:0% +pilot territory and right after this + + + align:start position:0% +pilot territory and right after this +after we'll grab lunch and come back + + align:start position:0% +after we'll grab lunch and come back + + + align:start position:0% +after we'll grab lunch and come back +we'll hear from Joe Joe a test pilot + + align:start position:0% +we'll hear from Joe Joe a test pilot + + + align:start position:0% +we'll hear from Joe Joe a test pilot +he's going to tell you some really cool + + align:start position:0% +he's going to tell you some really cool + + + align:start position:0% +he's going to tell you some really cool +things as well all right so it's just + + align:start position:0% +things as well all right so it's just + + + align:start position:0% +things as well all right so it's just +some basic terms to get started off so + + align:start position:0% +some basic terms to get started off so + + + align:start position:0% +some basic terms to get started off so +when you're thinking about an aircraft + + align:start position:0% +when you're thinking about an aircraft + + + align:start position:0% +when you're thinking about an aircraft +one piece of information is its standard + + align:start position:0% +one piece of information is its standard + + + align:start position:0% +one piece of information is its standard +empty weight so that's the weight of the + + align:start position:0% +empty weight so that's the weight of the + + + align:start position:0% +empty weight so that's the weight of the +airplane and there's also some fuel in + + align:start position:0% +airplane and there's also some fuel in + + + align:start position:0% +airplane and there's also some fuel in +the tank that sometimes it's hard to to + + align:start position:0% +the tank that sometimes it's hard to to + + + align:start position:0% +the tank that sometimes it's hard to to +drain and when you when you refill that + + align:start position:0% +drain and when you when you refill that + + + align:start position:0% +drain and when you when you refill that +fuel kind of sits at the bottom and + + align:start position:0% +fuel kind of sits at the bottom and + + + align:start position:0% +fuel kind of sits at the bottom and +can't be used by the aircraft so that's + + align:start position:0% +can't be used by the aircraft so that's + + + align:start position:0% +can't be used by the aircraft so that's +the unusable fuel and then there's some + + align:start position:0% +the unusable fuel and then there's some + + + align:start position:0% +the unusable fuel and then there's some +different fluids and fuel oil inside the + + align:start position:0% +different fluids and fuel oil inside the + + + align:start position:0% +different fluids and fuel oil inside the +aircraft so all those count in the + + align:start position:0% +aircraft so all those count in the + + + align:start position:0% +aircraft so all those count in the +calculation of the standard empty weight + + align:start position:0% +calculation of the standard empty weight + + + align:start position:0% +calculation of the standard empty weight +there's also the basic empty weight + + align:start position:0% +there's also the basic empty weight + + + align:start position:0% +there's also the basic empty weight +where you have some optional equipment + + align:start position:0% +where you have some optional equipment + + + align:start position:0% +where you have some optional equipment +inside and we'll go to a aircraft's Poh + + align:start position:0% +inside and we'll go to a aircraft's Poh + + + align:start position:0% +inside and we'll go to a aircraft's Poh +to look into what it actually reports + + align:start position:0% +to look into what it actually reports + + + align:start position:0% +to look into what it actually reports +about what it contains there's also a + + align:start position:0% +about what it contains there's also a + + + align:start position:0% +about what it contains there's also a +good rule of thumb to know about what + + align:start position:0% +good rule of thumb to know about what + + + align:start position:0% +good rule of thumb to know about what +weight you're going to associate with + + align:start position:0% +weight you're going to associate with + + + align:start position:0% +weight you're going to associate with +the per gallon of fuel so it's generally + + align:start position:0% +the per gallon of fuel so it's generally + + + align:start position:0% +the per gallon of fuel so it's generally +good number is six pounds for the fuel + + align:start position:0% +good number is six pounds for the fuel + + + align:start position:0% +good number is six pounds for the fuel +that you'll be using it's slightly more + + align:start position:0% +that you'll be using it's slightly more + + + align:start position:0% +that you'll be using it's slightly more +for different types of fuel so right at + + align:start position:0% +for different types of fuel so right at + + + align:start position:0% +for different types of fuel so right at +the beginning of the class we talked + + align:start position:0% +the beginning of the class we talked + + + align:start position:0% +the beginning of the class we talked +about weight which was the force pulling + + align:start position:0% +about weight which was the force pulling + + + align:start position:0% +about weight which was the force pulling +the aircraft down which has to oppose + + align:start position:0% +the aircraft down which has to oppose + + + align:start position:0% +the aircraft down which has to oppose +the lift pulling it up so the weight + + align:start position:0% +the lift pulling it up so the weight + + + align:start position:0% +the lift pulling it up so the weight +actually you know becomes less as you + + align:start position:0% +actually you know becomes less as you + + + align:start position:0% +actually you know becomes less as you +burn fuel so when you take off you have + + align:start position:0% +burn fuel so when you take off you have + + + align:start position:0% +burn fuel so when you take off you have +all the fuel on the airport craft as + + align:start position:0% +all the fuel on the airport craft as + + + align:start position:0% +all the fuel on the airport craft as +you've been flying for a while that fuel + + align:start position:0% +you've been flying for a while that fuel + + + align:start position:0% +you've been flying for a while that fuel +is used and the aircraft has less weight + + align:start position:0% +is used and the aircraft has less weight + + + align:start position:0% +is used and the aircraft has less weight +so there's a fully loaded aircraft has + + align:start position:0% +so there's a fully loaded aircraft has + + + align:start position:0% +so there's a fully loaded aircraft has +something called the maximum ramp weight + + align:start position:0% +something called the maximum ramp weight + + + align:start position:0% +something called the maximum ramp weight +so that has fuel that will be expended + + align:start position:0% +so that has fuel that will be expended + + + align:start position:0% +so that has fuel that will be expended +even when it's just taxiing over to the + + align:start position:0% +even when it's just taxiing over to the + + + align:start position:0% +even when it's just taxiing over to the +runway and so you make certain + + align:start position:0% +runway and so you make certain + + + align:start position:0% +runway and so you make certain +assumptions about how much fuel you'll + + align:start position:0% +assumptions about how much fuel you'll + + + align:start position:0% +assumptions about how much fuel you'll +actually burn off just taxiing up to the + + align:start position:0% +actually burn off just taxiing up to the + + + align:start position:0% +actually burn off just taxiing up to the +runway and then before you take off and + + align:start position:0% +runway and then before you take off and + + + align:start position:0% +runway and then before you take off and +so when you're calculating the weight of + + align:start position:0% +so when you're calculating the weight of + + + align:start position:0% +so when you're calculating the weight of +the airplane when it takes off it'll be + + align:start position:0% +the airplane when it takes off it'll be + + + align:start position:0% +the airplane when it takes off it'll be +slightly different than how you fueled + + align:start position:0% +slightly different than how you fueled + + + align:start position:0% +slightly different than how you fueled +it when it was sitting parking on the + + align:start position:0% +it when it was sitting parking on the + + + align:start position:0% +it when it was sitting parking on the +ramp okay some of the biggest things + + align:start position:0% +ramp okay some of the biggest things + + + align:start position:0% +ramp okay some of the biggest things +that you would keep in mind that you + + align:start position:0% +that you would keep in mind that you + + + align:start position:0% +that you would keep in mind that you +change every time you get into the + + align:start position:0% +change every time you get into the + + + align:start position:0% +change every time you get into the +airplane so there's the weight of the + + align:start position:0% +airplane so there's the weight of the + + + align:start position:0% +airplane so there's the weight of the +passengers the baggage you take with you + + align:start position:0% +passengers the baggage you take with you + + + align:start position:0% +passengers the baggage you take with you +and then how much fuel you fill the + + align:start position:0% +and then how much fuel you fill the + + + align:start position:0% +and then how much fuel you fill the +plane with before you take off so the + + align:start position:0% +plane with before you take off so the + + + align:start position:0% +plane with before you take off so the +a load in this case is the passengers + + align:start position:0% +a load in this case is the passengers + + + align:start position:0% +a load in this case is the passengers +and the cargo so whatever baggage and + + align:start position:0% +and the cargo so whatever baggage and + + + align:start position:0% +and the cargo so whatever baggage and +the weight of those bags that you take + + align:start position:0% +the weight of those bags that you take + + + align:start position:0% +the weight of those bags that you take +with you so one thing to keep in mind in + + align:start position:0% +with you so one thing to keep in mind in + + + align:start position:0% +with you so one thing to keep in mind in +addition to just the weight we have to + + align:start position:0% +addition to just the weight we have to + + + align:start position:0% +addition to just the weight we have to +figure out where that vector that force + + align:start position:0% +figure out where that vector that force + + + align:start position:0% +figure out where that vector that force +vector acts on the aircraft if all of + + align:start position:0% +vector acts on the aircraft if all of + + + align:start position:0% +vector acts on the aircraft if all of +the weight is really at the front you + + align:start position:0% +the weight is really at the front you + + + align:start position:0% +the weight is really at the front you +might have a center of gravity at the + + align:start position:0% +might have a center of gravity at the + + + align:start position:0% +might have a center of gravity at the +front which will create a moment on the + + align:start position:0% +front which will create a moment on the + + + align:start position:0% +front which will create a moment on the +airplane so it'll cause it to bend in a + + align:start position:0% +airplane so it'll cause it to bend in a + + + align:start position:0% +airplane so it'll cause it to bend in a +particular direction and if all that + + align:start position:0% +particular direction and if all that + + + align:start position:0% +particular direction and if all that +weight was acting at the back of the + + align:start position:0% +weight was acting at the back of the + + + align:start position:0% +weight was acting at the back of the +plane you had a lot of really heavy + + align:start position:0% +plane you had a lot of really heavy + + + align:start position:0% +plane you had a lot of really heavy +bricks at your tail which is not a good + + align:start position:0% +bricks at your tail which is not a good + + + align:start position:0% +bricks at your tail which is not a good +idea it would cause that force vector to + + align:start position:0% +idea it would cause that force vector to + + + align:start position:0% +idea it would cause that force vector to +act over here and create a moment so + + align:start position:0% +act over here and create a moment so + + + align:start position:0% +act over here and create a moment so +that's all related to torque which we + + align:start position:0% +that's all related to torque which we + + + align:start position:0% +that's all related to torque which we +talked about before so it's also + + align:start position:0% +talked about before so it's also + + + align:start position:0% +talked about before so it's also +important not just to calculate what the + + align:start position:0% +important not just to calculate what the + + + align:start position:0% +important not just to calculate what the +weight is of the airplane wants + + align:start position:0% +weight is of the airplane wants + + + align:start position:0% +weight is of the airplane wants +everybody and everything is inside but + + align:start position:0% +everybody and everything is inside but + + + align:start position:0% +everybody and everything is inside but +also where how that weight is + + align:start position:0% +also where how that weight is + + + align:start position:0% +also where how that weight is +distributed in the airplane and how it + + align:start position:0% +distributed in the airplane and how it + + + align:start position:0% +distributed in the airplane and how it +affects the airplane the center of + + align:start position:0% +affects the airplane the center of + + + align:start position:0% +affects the airplane the center of +gravity all right so I think that many + + align:start position:0% +gravity all right so I think that many + + + align:start position:0% +gravity all right so I think that many +of you have already it looks like most + + align:start position:0% +of you have already it looks like most + + + align:start position:0% +of you have already it looks like most +most folks in the rooms were either MIT + + align:start position:0% +most folks in the rooms were either MIT + + + align:start position:0% +most folks in the rooms were either MIT +undergrad or grad student which means + + align:start position:0% +undergrad or grad student which means + + + align:start position:0% +undergrad or grad student which means +you already understand some of these + + align:start position:0% +you already understand some of these + + + align:start position:0% +you already understand some of these +basic physics terms about torque and + + align:start position:0% +basic physics terms about torque and + + + align:start position:0% +basic physics terms about torque and +moment so we'll just cover them very + + align:start position:0% +moment so we'll just cover them very + + + align:start position:0% +moment so we'll just cover them very +briefly the moment is the weight times + + align:start position:0% +briefly the moment is the weight times + + + align:start position:0% +briefly the moment is the weight times +the arm so basically where the weight is + + align:start position:0% +the arm so basically where the weight is + + + align:start position:0% +the arm so basically where the weight is +times how far away it is from a + + align:start position:0% +times how far away it is from a + + + align:start position:0% +times how far away it is from a +particular location that you're + + align:start position:0% +particular location that you're + + + align:start position:0% +particular location that you're +calculating it from so we're gonna do a + + align:start position:0% +calculating it from so we're gonna do a + + + align:start position:0% +calculating it from so we're gonna do a +couple basic examples so we have a + + align:start position:0% +couple basic examples so we have a + + + align:start position:0% +couple basic examples so we have a +seesaw here so in this case whenever + + align:start position:0% +seesaw here so in this case whenever + + + align:start position:0% +seesaw here so in this case whenever +you're calculating your moment you have + + align:start position:0% +you're calculating your moment you have + + + align:start position:0% +you're calculating your moment you have +to pick a reference point and make sure + + align:start position:0% +to pick a reference point and make sure + + + align:start position:0% +to pick a reference point and make sure +you're consistent as you use it so in + + align:start position:0% +you're consistent as you use it so in + + + align:start position:0% +you're consistent as you use it so in +this case they have a their data point + + align:start position:0% +this case they have a their data point + + + align:start position:0% +this case they have a their data point +is at that triangle at that fulcrum in + + align:start position:0% +is at that triangle at that fulcrum in + + + align:start position:0% +is at that triangle at that fulcrum in +the middle and so they have a moment on + + align:start position:0% +the middle and so they have a moment on + + + align:start position:0% +the middle and so they have a moment on +the right and a moment on the left so + + align:start position:0% +the right and a moment on the left so + + + align:start position:0% +the right and a moment on the left so +you see various rectangles that + + align:start position:0% +you see various rectangles that + + + align:start position:0% +you see various rectangles that +represent different objects or different + + align:start position:0% +represent different objects or different + + + align:start position:0% +represent different objects or different +weight and then they calculate it so + + align:start position:0% +weight and then they calculate it so + + + align:start position:0% +weight and then they calculate it so +that blue box that's five pounds is ten + + align:start position:0% +that blue box that's five pounds is ten + + + align:start position:0% +that blue box that's five pounds is ten +inches away so to figure out what the + + align:start position:0% +inches away so to figure out what the + + + align:start position:0% +inches away so to figure out what the +moment is that it applies you just + + align:start position:0% +moment is that it applies you just + + + align:start position:0% +moment is that it applies you just +calculate the weight times how far away + + align:start position:0% +calculate the weight times how far away + + + align:start position:0% +calculate the weight times how far away +it is + + align:start position:0% +it is + + + align:start position:0% +it is +okay so in order to figure out what the + + align:start position:0% +okay so in order to figure out what the + + + align:start position:0% +okay so in order to figure out what the +center of gravity is you might want to + + align:start position:0% +center of gravity is you might want to + + + align:start position:0% +center of gravity is you might want to +consider where you're doing that + + align:start position:0% +consider where you're doing that + + + align:start position:0% +consider where you're doing that +reference point so rather than doing the + + align:start position:0% +reference point so rather than doing the + + + align:start position:0% +reference point so rather than doing the +reference point from right in the middle + + align:start position:0% +reference point from right in the middle + + + align:start position:0% +reference point from right in the middle +of the aircraft in this case they're + + align:start position:0% +of the aircraft in this case they're + + + align:start position:0% +of the aircraft in this case they're +starting at the end so where that yellow + + align:start position:0% +starting at the end so where that yellow + + + align:start position:0% +starting at the end so where that yellow +line is where it says datum is where + + align:start position:0% +line is where it says datum is where + + + align:start position:0% +line is where it says datum is where +they're starting and then they're there + + align:start position:0% +they're starting and then they're there + + + align:start position:0% +they're starting and then they're there +using the lengths from that same + + align:start position:0% +using the lengths from that same + + + align:start position:0% +using the lengths from that same +reference point so now you have a purple + + align:start position:0% +reference point so now you have a purple + + + align:start position:0% +reference point so now you have a purple +box of five pounds that's ten inches + + align:start position:0% +box of five pounds that's ten inches + + + align:start position:0% +box of five pounds that's ten inches +from that datum and then three pounds + + align:start position:0% +from that datum and then three pounds + + + align:start position:0% +from that datum and then three pounds +and a green weight that's farther and + + align:start position:0% +and a green weight that's farther and + + + align:start position:0% +and a green weight that's farther and +the red box that's the farthest away so + + align:start position:0% +the red box that's the farthest away so + + + align:start position:0% +the red box that's the farthest away so +here they've listed all those different + + align:start position:0% +here they've listed all those different + + + align:start position:0% +here they've listed all those different +boxes and the the weight of each of + + align:start position:0% +boxes and the the weight of each of + + + align:start position:0% +boxes and the the weight of each of +those boxes times how far it is you + + align:start position:0% +those boxes times how far it is you + + + align:start position:0% +those boxes times how far it is you +multiply that to get the moment that it + + align:start position:0% +multiply that to get the moment that it + + + align:start position:0% +multiply that to get the moment that it +applies and use that to calculate the + + align:start position:0% +applies and use that to calculate the + + + align:start position:0% +applies and use that to calculate the +location of the center of gravity and + + align:start position:0% +location of the center of gravity and + + + align:start position:0% +location of the center of gravity and +just in terms of if you've if you've + + align:start position:0% +just in terms of if you've if you've + + + align:start position:0% +just in terms of if you've if you've +been on a seesaw before who has been on + + align:start position:0% +been on a seesaw before who has been on + + + align:start position:0% +been on a seesaw before who has been on +a seesaw before all right good I'm glad + + align:start position:0% +a seesaw before all right good I'm glad + + + align:start position:0% +a seesaw before all right good I'm glad +so as you know that that fulcrum or + + align:start position:0% +so as you know that that fulcrum or + + + align:start position:0% +so as you know that that fulcrum or +where that triangle is if you put that + + align:start position:0% +where that triangle is if you put that + + + align:start position:0% +where that triangle is if you put that +triangle at the center of gravity so all + + align:start position:0% +triangle at the center of gravity so all + + + align:start position:0% +triangle at the center of gravity so all +the the kids sitting on one side of the + + align:start position:0% +the the kids sitting on one side of the + + + align:start position:0% +the the kids sitting on one side of the +seesaw weigh the same as the kids + + align:start position:0% +seesaw weigh the same as the kids + + + align:start position:0% +seesaw weigh the same as the kids +sitting on the other side of the seesaw + + align:start position:0% +sitting on the other side of the seesaw + + + align:start position:0% +sitting on the other side of the seesaw +at the appropriate lens away so they're + + align:start position:0% +at the appropriate lens away so they're + + + align:start position:0% +at the appropriate lens away so they're +applying the same moment than the the + + align:start position:0% +applying the same moment than the the + + + align:start position:0% +applying the same moment than the the +fulcrum balances so if we determined + + align:start position:0% +fulcrum balances so if we determined + + + align:start position:0% +fulcrum balances so if we determined +what the center of gravity of this + + align:start position:0% +what the center of gravity of this + + + align:start position:0% +what the center of gravity of this +airplane was and I put my finger there + + align:start position:0% +airplane was and I put my finger there + + + align:start position:0% +airplane was and I put my finger there +then it would balance and it wouldn't + + align:start position:0% +then it would balance and it wouldn't + + + align:start position:0% +then it would balance and it wouldn't +tilt one way or the other that's the + + align:start position:0% +tilt one way or the other that's the + + + align:start position:0% +tilt one way or the other that's the +whole idea so for for a given aircraft + + align:start position:0% +whole idea so for for a given aircraft + + + align:start position:0% +whole idea so for for a given aircraft +there is not only the center of gravity + + align:start position:0% +there is not only the center of gravity + + + align:start position:0% +there is not only the center of gravity +but in the testing process they could + + align:start position:0% +but in the testing process they could + + + align:start position:0% +but in the testing process they could +they understand what is that approved + + align:start position:0% +they understand what is that approved + + + align:start position:0% +they understand what is that approved +range of where that center of gravity + + align:start position:0% +range of where that center of gravity + + + align:start position:0% +range of where that center of gravity +can be such that the aircraft is still + + align:start position:0% +can be such that the aircraft is still + + + align:start position:0% +can be such that the aircraft is still +stable + + align:start position:0% +stable + + + align:start position:0% +stable +so if it if you're thinking about + + align:start position:0% +so if it if you're thinking about + + + align:start position:0% +so if it if you're thinking about +putting a lot of weight at the front of + + align:start position:0% +putting a lot of weight at the front of + + + align:start position:0% +putting a lot of weight at the front of +the aircraft then and less weight at the + + align:start position:0% +the aircraft then and less weight at the + + + align:start position:0% +the aircraft then and less weight at the +back of the aircraft that in the center + + align:start position:0% +back of the aircraft that in the center + + + align:start position:0% +back of the aircraft that in the center +of gravity moves forward and there's a + + align:start position:0% +of gravity moves forward and there's a + + + align:start position:0% +of gravity moves forward and there's a +limit to how far forward that center of + + align:start position:0% +limit to how far forward that center of + + + align:start position:0% +limit to how far forward that center of +gravity can be that allows the plane + + align:start position:0% +gravity can be that allows the plane + + + align:start position:0% +gravity can be that allows the plane +still to be stable so that's the forward + + align:start position:0% +still to be stable so that's the forward + + + align:start position:0% +still to be stable so that's the forward +CG limit and then you see the same thing + + align:start position:0% +CG limit and then you see the same thing + + + align:start position:0% +CG limit and then you see the same thing +at the back aft just means back so how + + align:start position:0% +at the back aft just means back so how + + + align:start position:0% +at the back aft just means back so how +far back the center of gravity can be + + align:start position:0% +far back the center of gravity can be + + + align:start position:0% +far back the center of gravity can be +all right so we've already discussed + + align:start position:0% +all right so we've already discussed + + + align:start position:0% +all right so we've already discussed +some of the performance things but just + + align:start position:0% +some of the performance things but just + + + align:start position:0% +some of the performance things but just +to just to remind you you know what are + + align:start position:0% +to just to remind you you know what are + + + align:start position:0% +to just to remind you you know what are +some of the things that can happen if + + align:start position:0% +some of the things that can happen if + + + align:start position:0% +some of the things that can happen if +your airplane is is overloaded you want + + align:start position:0% +your airplane is is overloaded you want + + + align:start position:0% +your airplane is is overloaded you want +to just shout out some things that you + + align:start position:0% +to just shout out some things that you + + + align:start position:0% +to just shout out some things that you +would experience if you have a very very + + align:start position:0% +would experience if you have a very very + + + align:start position:0% +would experience if you have a very very +heavy airplane yes very good just to + + align:start position:0% +heavy airplane yes very good just to + + + align:start position:0% +heavy airplane yes very good just to +repeat it longer to takeoff so we have + + align:start position:0% +repeat it longer to takeoff so we have + + + align:start position:0% +repeat it longer to takeoff so we have +takeoff and landing distances increase + + align:start position:0% +takeoff and landing distances increase + + + align:start position:0% +takeoff and landing distances increase +so if you have a very heavy airplane you + + align:start position:0% +so if you have a very heavy airplane you + + + align:start position:0% +so if you have a very heavy airplane you +may not be able to take off from a short + + align:start position:0% +may not be able to take off from a short + + + align:start position:0% +may not be able to take off from a short +field runway and then of course it's + + align:start position:0% +field runway and then of course it's + + + align:start position:0% +field runway and then of course it's +talking about if your aircraft gets + + align:start position:0% +talking about if your aircraft gets + + + align:start position:0% +talking about if your aircraft gets +outside the approved envelope it'll talk + + align:start position:0% +outside the approved envelope it'll talk + + + align:start position:0% +outside the approved envelope it'll talk +about what we mean by envelope then it + + align:start position:0% +about what we mean by envelope then it + + + align:start position:0% +about what we mean by envelope then it +then it hasn't been tested to be stable + + align:start position:0% +then it hasn't been tested to be stable + + + align:start position:0% +then it hasn't been tested to be stable +at those areas and so now you've become + + align:start position:0% +at those areas and so now you've become + + + align:start position:0% +at those areas and so now you've become +a test pilot which you may not want to + + align:start position:0% +a test pilot which you may not want to + + + align:start position:0% +a test pilot which you may not want to +do again we're gonna hear from a test + + align:start position:0% +do again we're gonna hear from a test + + + align:start position:0% +do again we're gonna hear from a test +pilot very soon okay so what happens if + + align:start position:0% +pilot very soon okay so what happens if + + + align:start position:0% +pilot very soon okay so what happens if +not just that it's overloaded maybe it's + + align:start position:0% +not just that it's overloaded maybe it's + + + align:start position:0% +not just that it's overloaded maybe it's +still within the envelope for the total + + align:start position:0% +still within the envelope for the total + + + align:start position:0% +still within the envelope for the total +amount of weight but what if the center + + align:start position:0% +amount of weight but what if the center + + + align:start position:0% +amount of weight but what if the center +of gravity has moved too far forward and + + align:start position:0% +of gravity has moved too far forward and + + + align:start position:0% +of gravity has moved too far forward and +passed that forward CG limit so your + + align:start position:0% +passed that forward CG limit so your + + + align:start position:0% +passed that forward CG limit so your +plane naturally wants to be nose-down so + + align:start position:0% +plane naturally wants to be nose-down so + + + align:start position:0% +plane naturally wants to be nose-down so +what is the impact of that well it'll be + + align:start position:0% +what is the impact of that well it'll be + + + align:start position:0% +what is the impact of that well it'll be +harder to climb right it's harder to + + align:start position:0% +harder to climb right it's harder to + + + align:start position:0% +harder to climb right it's harder to +climb because your nose keeps that keeps + + align:start position:0% +climb because your nose keeps that keeps + + + align:start position:0% +climb because your nose keeps that keeps +pulling it down for example what does it + + align:start position:0% +pulling it down for example what does it + + + align:start position:0% +pulling it down for example what does it +mean to have a stall speed increased is + + align:start position:0% +mean to have a stall speed increased is + + + align:start position:0% +mean to have a stall speed increased is +that a good thing + + align:start position:0% +that a good thing + + + align:start position:0% +that a good thing +and why not why is it not a good thing + + align:start position:0% + + + + align:start position:0% + +yes basically if your stall speed has + + align:start position:0% +yes basically if your stall speed has + + + align:start position:0% +yes basically if your stall speed has +increased that means you're likely to + + align:start position:0% +increased that means you're likely to + + + align:start position:0% +increased that means you're likely to +stall at a higher speed so if you you + + align:start position:0% +stall at a higher speed so if you you + + + align:start position:0% +stall at a higher speed so if you you +know traditionally can can fly at 60 + + align:start position:0% +know traditionally can can fly at 60 + + + align:start position:0% +know traditionally can can fly at 60 +knots without stalling but that stall + + align:start position:0% +knots without stalling but that stall + + + align:start position:0% +knots without stalling but that stall +speed has increased from say 40 knots up + + align:start position:0% +speed has increased from say 40 knots up + + + align:start position:0% +speed has increased from say 40 knots up +to 60 knots and that means that when you + + align:start position:0% +to 60 knots and that means that when you + + + align:start position:0% +to 60 knots and that means that when you +traditionally have been able to fly + + align:start position:0% +traditionally have been able to fly + + + align:start position:0% +traditionally have been able to fly +safely at 60 knots you could actually + + align:start position:0% +safely at 60 knots you could actually + + + align:start position:0% +safely at 60 knots you could actually +stall at 60 knots so an increased stall + + align:start position:0% +stall at 60 knots so an increased stall + + + align:start position:0% +stall at 60 knots so an increased stall +speed is bad what about an aft CG having + + align:start position:0% +speed is bad what about an aft CG having + + + align:start position:0% +speed is bad what about an aft CG having +the the weight too far to the back what + + align:start position:0% +the the weight too far to the back what + + + align:start position:0% +the the weight too far to the back what +is the impact there you tend to pitch up + + align:start position:0% +is the impact there you tend to pitch up + + + align:start position:0% +is the impact there you tend to pitch up +right and so one thing that they are + + align:start position:0% +right and so one thing that they are + + + align:start position:0% +right and so one thing that they are +talking about here is Flair so this is + + align:start position:0% +talking about here is Flair so this is + + + align:start position:0% +talking about here is Flair so this is +when you're you're coming into land + + align:start position:0% +when you're you're coming into land + + + align:start position:0% +when you're you're coming into land +you kind of go down but then you sort of + + align:start position:0% +you kind of go down but then you sort of + + + align:start position:0% +you kind of go down but then you sort of +flare up and it could actually over over + + align:start position:0% +flare up and it could actually over over + + + align:start position:0% +flare up and it could actually over over +flare and that can cause some really + + align:start position:0% +flare and that can cause some really + + + align:start position:0% +flare and that can cause some really +strange things when you're trying to + + align:start position:0% +strange things when you're trying to + + + align:start position:0% +strange things when you're trying to +land such as bouncing and you definitely + + align:start position:0% +land such as bouncing and you definitely + + + align:start position:0% +land such as bouncing and you definitely +don't want to do that but all these + + align:start position:0% +don't want to do that but all these + + + align:start position:0% +don't want to do that but all these +things you might actually just notice + + align:start position:0% +things you might actually just notice + + + align:start position:0% +things you might actually just notice +when you're feeling the airplane it acts + + align:start position:0% +when you're feeling the airplane it acts + + + align:start position:0% +when you're feeling the airplane it acts +differently than you want it want it to + + align:start position:0% +differently than you want it want it to + + + align:start position:0% +differently than you want it want it to +act so here's just a basically a + + align:start position:0% +act so here's just a basically a + + + align:start position:0% +act so here's just a basically a +cross-section if you took off the the + + align:start position:0% +cross-section if you took off the the + + + align:start position:0% +cross-section if you took off the the +wings and the top of the fuselage and + + align:start position:0% +wings and the top of the fuselage and + + + align:start position:0% +wings and the top of the fuselage and +you're looking at the plane it shows you + + align:start position:0% +you're looking at the plane it shows you + + + align:start position:0% +you're looking at the plane it shows you +know the pilot sitting in the left seat + + align:start position:0% +know the pilot sitting in the left seat + + + align:start position:0% +know the pilot sitting in the left seat +a passenger and the right seat two + + align:start position:0% +a passenger and the right seat two + + + align:start position:0% +a passenger and the right seat two +passengers in the back this one actually + + align:start position:0% +passengers in the back this one actually + + + align:start position:0% +passengers in the back this one actually +has a third row of passengers and then + + align:start position:0% +has a third row of passengers and then + + + align:start position:0% +has a third row of passengers and then +two baggage compartments so this is just + + align:start position:0% +two baggage compartments so this is just + + + align:start position:0% +two baggage compartments so this is just +showing you know traditionally when + + align:start position:0% +showing you know traditionally when + + + align:start position:0% +showing you know traditionally when +you're loading up an airplane that + + align:start position:0% +you're loading up an airplane that + + + align:start position:0% +you're loading up an airplane that +payload again is your passengers in your + + align:start position:0% +payload again is your passengers in your + + + align:start position:0% +payload again is your passengers in your +baggage where do they sit so now I'm + + align:start position:0% +baggage where do they sit so now I'm + + + align:start position:0% +baggage where do they sit so now I'm +going to go over to this document viewer + + align:start position:0% +going to go over to this document viewer + + + align:start position:0% +going to go over to this document viewer +and talk about specific airplane the + + align:start position:0% +and talk about specific airplane the + + + align:start position:0% +and talk about specific airplane the +plane I like to fly a Cessna 172 okay so + + align:start position:0% +plane I like to fly a Cessna 172 okay so + + + align:start position:0% +plane I like to fly a Cessna 172 okay so +this this book is talking about a + + align:start position:0% +this this book is talking about a + + + align:start position:0% +this this book is talking about a +particular aircraft as Skyhawk so it's a + + align:start position:0% +particular aircraft as Skyhawk so it's a + + + align:start position:0% +particular aircraft as Skyhawk so it's a +Cessna 172 this is a plane that many of + + align:start position:0% +Cessna 172 this is a plane that many of + + + align:start position:0% +Cessna 172 this is a plane that many of +you guys might use as a flying aircraft + + align:start position:0% +you guys might use as a flying aircraft + + + align:start position:0% +you guys might use as a flying aircraft +we've also talked about for example a + + align:start position:0% +we've also talked about for example a + + + align:start position:0% +we've also talked about for example a +piper we just + + align:start position:0% +piper we just + + + align:start position:0% +piper we just +lowing airplane that you might use so + + align:start position:0% +lowing airplane that you might use so + + + align:start position:0% +lowing airplane that you might use so +this is what a Cessna looks like it has + + align:start position:0% +this is what a Cessna looks like it has + + + align:start position:0% +this is what a Cessna looks like it has +that tricycle gear at the bottom + + align:start position:0% +that tricycle gear at the bottom + + + align:start position:0% +that tricycle gear at the bottom +whatever plane you are using for + + align:start position:0% +whatever plane you are using for + + + align:start position:0% +whatever plane you are using for +training I would get very familiar with + + align:start position:0% +training I would get very familiar with + + + align:start position:0% +training I would get very familiar with +this book and in particular remember + + align:start position:0% +this book and in particular remember + + + align:start position:0% +this book and in particular remember +what the table of contents is because + + align:start position:0% +what the table of contents is because + + + align:start position:0% +what the table of contents is because +when you get your oral exam on your fa + + align:start position:0% +when you get your oral exam on your fa + + + align:start position:0% +when you get your oral exam on your fa +examination it's ok if you don't + + align:start position:0% +examination it's ok if you don't + + + align:start position:0% +examination it's ok if you don't +remember everything what's really great + + align:start position:0% +remember everything what's really great + + + align:start position:0% +remember everything what's really great +is if you know how to find information + + align:start position:0% +is if you know how to find information + + + align:start position:0% +is if you know how to find information +and you can say hey you know if I didn't + + align:start position:0% +and you can say hey you know if I didn't + + + align:start position:0% +and you can say hey you know if I didn't +remember this I would go look at my poh + + align:start position:0% +remember this I would go look at my poh + + + align:start position:0% +remember this I would go look at my poh +and I would go look at the weight and + + align:start position:0% +and I would go look at the weight and + + + align:start position:0% +and I would go look at the weight and +balance section section 6 of my book and + + align:start position:0% +balance section section 6 of my book and + + + align:start position:0% +balance section section 6 of my book and +I'd be able to flip and find this + + align:start position:0% +I'd be able to flip and find this + + + align:start position:0% +I'd be able to flip and find this +information very quickly so oftentimes + + align:start position:0% +information very quickly so oftentimes + + + align:start position:0% +information very quickly so oftentimes +you'll get questions in that oral exam + + align:start position:0% +you'll get questions in that oral exam + + + align:start position:0% +you'll get questions in that oral exam +where they would ask how you would go + + align:start position:0% +where they would ask how you would go + + + align:start position:0% +where they would ask how you would go +about finding information we discussed + + align:start position:0% +about finding information we discussed + + + align:start position:0% +about finding information we discussed +that a lot with regard to weather data + + align:start position:0% +that a lot with regard to weather data + + + align:start position:0% +that a lot with regard to weather data +what are the sources of weather data so + + align:start position:0% +what are the sources of weather data so + + + align:start position:0% +what are the sources of weather data so +with regard to weight and balance the + + align:start position:0% +with regard to weight and balance the + + + align:start position:0% +with regard to weight and balance the +information about your airplane as found + + align:start position:0% +information about your airplane as found + + + align:start position:0% +information about your airplane as found +with a book made about your particular + + align:start position:0% +with a book made about your particular + + + align:start position:0% +with a book made about your particular +airplane and if you're at a particular + + align:start position:0% +airplane and if you're at a particular + + + align:start position:0% +airplane and if you're at a particular +flight school and we'll show you that in + + align:start position:0% +flight school and we'll show you that in + + + align:start position:0% +flight school and we'll show you that in +an example they might have they most + + align:start position:0% +an example they might have they most + + + align:start position:0% +an example they might have they most +likely have all of this weight and + + align:start position:0% +likely have all of this weight and + + + align:start position:0% +likely have all of this weight and +balance information listed in a + + align:start position:0% +balance information listed in a + + + align:start position:0% +balance information listed in a +spreadsheet sometimes it's accessible + + align:start position:0% +spreadsheet sometimes it's accessible + + + align:start position:0% +spreadsheet sometimes it's accessible +online so you know for your exact + + align:start position:0% +online so you know for your exact + + + align:start position:0% +online so you know for your exact +airplane what its gross weight is so if + + align:start position:0% +airplane what its gross weight is so if + + + align:start position:0% +airplane what its gross weight is so if +we flip to that section 6 it has a fair + + align:start position:0% +we flip to that section 6 it has a fair + + + align:start position:0% +we flip to that section 6 it has a fair +amount of information including the + + align:start position:0% +amount of information including the + + + align:start position:0% +amount of information including the +picture we just showed you so it talks + + align:start position:0% +picture we just showed you so it talks + + + align:start position:0% +picture we just showed you so it talks +about in this case there are only two + + align:start position:0% +about in this case there are only two + + + align:start position:0% +about in this case there are only two +rows of seats so the pilot and passenger + + align:start position:0% +rows of seats so the pilot and passenger + + + align:start position:0% +rows of seats so the pilot and passenger +one row of seats so it seats four people + + align:start position:0% +one row of seats so it seats four people + + + align:start position:0% +one row of seats so it seats four people +and then it has a baggage area but + + align:start position:0% +and then it has a baggage area but + + + align:start position:0% +and then it has a baggage area but +what's really important to understand is + + align:start position:0% +what's really important to understand is + + + align:start position:0% +what's really important to understand is +that even though this Cessna can fit + + align:start position:0% +that even though this Cessna can fit + + + align:start position:0% +that even though this Cessna can fit +four people will show you that if you + + align:start position:0% +four people will show you that if you + + + align:start position:0% +four people will show you that if you +put you know four 200-pound people in + + align:start position:0% +put you know four 200-pound people in + + + align:start position:0% +put you know four 200-pound people in +there with a bunch of bags you'll + + align:start position:0% +there with a bunch of bags you'll + + + align:start position:0% +there with a bunch of bags you'll +actually exceed the allotment so just + + align:start position:0% +actually exceed the allotment so just + + + align:start position:0% +actually exceed the allotment so just +because there for seeds doesn't mean you + + align:start position:0% +because there for seeds doesn't mean you + + + align:start position:0% +because there for seeds doesn't mean you +can take four large people on a flight + + align:start position:0% +can take four large people on a flight + + + align:start position:0% +can take four large people on a flight +some of it is is something we'll keep in + + align:start position:0% +some of it is is something we'll keep in + + + align:start position:0% +some of it is is something we'll keep in +mind and maybe you can reduce bags and + + align:start position:0% +mind and maybe you can reduce bags and + + + align:start position:0% +mind and maybe you can reduce bags and +reduce fuel such that you can make that + + align:start position:0% +reduce fuel such that you can make that + + + align:start position:0% +reduce fuel such that you can make that +weight work out so we talked about + + align:start position:0% +weight work out so we talked about + + + align:start position:0% +weight work out so we talked about +envelopes + + align:start position:0% + + + + align:start position:0% + +so the envelope is basically a a line on + + align:start position:0% +so the envelope is basically a a line on + + + align:start position:0% +so the envelope is basically a a line on +this graph that shows where the center + + align:start position:0% +this graph that shows where the center + + + align:start position:0% +this graph that shows where the center +of gravity can be and the envelope is + + align:start position:0% +of gravity can be and the envelope is + + + align:start position:0% +of gravity can be and the envelope is +where is it safe to be so if you're + + align:start position:0% +where is it safe to be so if you're + + + align:start position:0% +where is it safe to be so if you're +inside the envelope so inside this line + + align:start position:0% +inside the envelope so inside this line + + + align:start position:0% +inside the envelope so inside this line +if your calculations result in the + + align:start position:0% +if your calculations result in the + + + align:start position:0% +if your calculations result in the +center of gravity inside then you're + + align:start position:0% +center of gravity inside then you're + + + align:start position:0% +center of gravity inside then you're +within the envelope if you're outside of + + align:start position:0% +within the envelope if you're outside of + + + align:start position:0% +within the envelope if you're outside of +it then you're not you can you can see a + + align:start position:0% +it then you're not you can you can see a + + + align:start position:0% +it then you're not you can you can see a +little pencil mark towards the top where + + align:start position:0% +little pencil mark towards the top where + + + align:start position:0% +little pencil mark towards the top where +I took a flight recently and I was + + align:start position:0% +I took a flight recently and I was + + + align:start position:0% +I took a flight recently and I was +trying to calculate whether or not I was + + align:start position:0% +trying to calculate whether or not I was + + + align:start position:0% +trying to calculate whether or not I was +inside and in fact I was and it's okay + + align:start position:0% +inside and in fact I was and it's okay + + + align:start position:0% +inside and in fact I was and it's okay +that I'm right at the edge of the + + align:start position:0% +that I'm right at the edge of the + + + align:start position:0% +that I'm right at the edge of the +envelope as long as you're inside you're + + align:start position:0% +envelope as long as you're inside you're + + + align:start position:0% +envelope as long as you're inside you're +still with inside the tested limits now + + align:start position:0% +still with inside the tested limits now + + + align:start position:0% +still with inside the tested limits now +there are two different categories are + + align:start position:0% +there are two different categories are + + + align:start position:0% +there are two different categories are +two different lines here there's a + + align:start position:0% +two different lines here there's a + + + align:start position:0% +two different lines here there's a +bigger line that says normal category + + align:start position:0% +bigger line that says normal category + + + align:start position:0% +bigger line that says normal category +and then there's a smaller line that + + align:start position:0% +and then there's a smaller line that + + + align:start position:0% +and then there's a smaller line that +smaller envelope that's talking about + + align:start position:0% +smaller envelope that's talking about + + + align:start position:0% +smaller envelope that's talking about +utility category does anyone know what + + align:start position:0% +utility category does anyone know what + + + align:start position:0% +utility category does anyone know what +the difference is between normal and + + align:start position:0% +the difference is between normal and + + + align:start position:0% +the difference is between normal and +utility G limits is that what you're + + align:start position:0% +utility G limits is that what you're + + + align:start position:0% +utility G limits is that what you're +going to say so there's different + + align:start position:0% +going to say so there's different + + + align:start position:0% +going to say so there's different +restrictions one question you might get + + align:start position:0% +restrictions one question you might get + + + align:start position:0% +restrictions one question you might get +asked is how do you find out where the + + align:start position:0% +asked is how do you find out where the + + + align:start position:0% +asked is how do you find out where the +answer is + + align:start position:0% + + + + align:start position:0% + +and it's right in here right where you + + align:start position:0% +and it's right in here right where you + + + align:start position:0% +and it's right in here right where you +would think it is and I'm actually going + + align:start position:0% +would think it is and I'm actually going + + + align:start position:0% +would think it is and I'm actually going +to show you a real example so we're + + align:start position:0% +to show you a real example so we're + + + align:start position:0% +to show you a real example so we're +going to go through an example of you + + align:start position:0% +going to go through an example of you + + + align:start position:0% +going to go through an example of you +know loading up an airplane don't want + + align:start position:0% +know loading up an airplane don't want + + + align:start position:0% +know loading up an airplane don't want +to embarrass anyone but we might ask + + align:start position:0% +to embarrass anyone but we might ask + + + align:start position:0% +to embarrass anyone but we might ask +some of you what your weight is so + + align:start position:0% +some of you what your weight is so + + + align:start position:0% +some of you what your weight is so +beware so every time you have to + + align:start position:0% +beware so every time you have to + + + align:start position:0% +beware so every time you have to +calculate your weight and balance you + + align:start position:0% +calculate your weight and balance you + + + align:start position:0% +calculate your weight and balance you +can do it by hand or you can use a + + align:start position:0% +can do it by hand or you can use a + + + align:start position:0% +can do it by hand or you can use a +computer to do it and I would just + + align:start position:0% +computer to do it and I would just + + + align:start position:0% +computer to do it and I would just +caution that you have to double check + + align:start position:0% +caution that you have to double check + + + align:start position:0% +caution that you have to double check +all the information so here's a great + + align:start position:0% +all the information so here's a great + + + align:start position:0% +all the information so here's a great +link that tells you for a particular + + align:start position:0% +link that tells you for a particular + + + align:start position:0% +link that tells you for a particular +Cessna 172 a weight and balance + + align:start position:0% +Cessna 172 a weight and balance + + + align:start position:0% +Cessna 172 a weight and balance +calculator so here you can actually type + + align:start position:0% +calculator so here you can actually type + + + align:start position:0% +calculator so here you can actually type +in the empty weight now there's a big + + align:start position:0% +in the empty weight now there's a big + + + align:start position:0% +in the empty weight now there's a big +warning here use your own AC data what + + align:start position:0% +warning here use your own AC data what + + + align:start position:0% +warning here use your own AC data what +is that saying what are the AC aircraft + + align:start position:0% +is that saying what are the AC aircraft + + + align:start position:0% +is that saying what are the AC aircraft +use your own aircrafts data so look at + + align:start position:0% +use your own aircrafts data so look at + + + align:start position:0% +use your own aircrafts data so look at +your actual information from your school + + align:start position:0% +your actual information from your school + + + align:start position:0% +your actual information from your school +to figure out for the plane that you're + + align:start position:0% +to figure out for the plane that you're + + + align:start position:0% +to figure out for the plane that you're +renting what that what those pieces of + + align:start position:0% +renting what that what those pieces of + + + align:start position:0% +renting what that what those pieces of +information are so here is a link from + + align:start position:0% +information are so here is a link from + + + align:start position:0% +information are so here is a link from +East Coast Aero Club just as an example + + align:start position:0% +East Coast Aero Club just as an example + + + align:start position:0% +East Coast Aero Club just as an example +and they have provided for every + + align:start position:0% +and they have provided for every + + + align:start position:0% +and they have provided for every +aircraft that they have a bunch of + + align:start position:0% +aircraft that they have a bunch of + + + align:start position:0% +aircraft that they have a bunch of +information so for each aircraft they + + align:start position:0% +information so for each aircraft they + + + align:start position:0% +information so for each aircraft they +have provided the empty weight and the + + align:start position:0% +have provided the empty weight and the + + + align:start position:0% +have provided the empty weight and the +CG the moment gross weight useful load + + align:start position:0% +CG the moment gross weight useful load + + + align:start position:0% +CG the moment gross weight useful load +and then they also talk about two + + align:start position:0% +and then they also talk about two + + + align:start position:0% +and then they also talk about two +different settings for fuel so there's + + align:start position:0% +different settings for fuel so there's + + + align:start position:0% +different settings for fuel so there's +you can have full fuel or fuel to tabs + + align:start position:0% +you can have full fuel or fuel to tabs + + + align:start position:0% +you can have full fuel or fuel to tabs +so that is something you'll hear pretty + + align:start position:0% +so that is something you'll hear pretty + + + align:start position:0% +so that is something you'll hear pretty +frequently you know fill the fuel two + + align:start position:0% +frequently you know fill the fuel two + + + align:start position:0% +frequently you know fill the fuel two +tabs so if you want to have extra mass + + align:start position:0% +tabs so if you want to have extra mass + + + align:start position:0% +tabs so if you want to have extra mass +extra extra weight in your plane you + + align:start position:0% +extra extra weight in your plane you + + + align:start position:0% +extra extra weight in your plane you +have some heavier folks flying with you + + align:start position:0% +have some heavier folks flying with you + + + align:start position:0% +have some heavier folks flying with you +you might only want the fuel two tabs + + align:start position:0% +you might only want the fuel two tabs + + + align:start position:0% +you might only want the fuel two tabs +but if it's just you or you and your + + align:start position:0% +but if it's just you or you and your + + + align:start position:0% +but if it's just you or you and your +instructor and you want to fly a + + align:start position:0% +instructor and you want to fly a + + + align:start position:0% +instructor and you want to fly a +cross-country flight you might want the + + align:start position:0% +cross-country flight you might want the + + + align:start position:0% +cross-country flight you might want the +fuel full so these are all things you + + align:start position:0% +fuel full so these are all things you + + + align:start position:0% +fuel full so these are all things you +can change this calculator has some + + align:start position:0% +can change this calculator has some + + + align:start position:0% +can change this calculator has some +restrictions which is that the kind of + + align:start position:0% +restrictions which is that the kind of + + + align:start position:0% +restrictions which is that the kind of +the weight is is identified here in + + align:start position:0% +the weight is is identified here in + + + align:start position:0% +the weight is is identified here in +terms of + + align:start position:0% +terms of + + + align:start position:0% +terms of +so they have the the oils you might want + + align:start position:0% +so they have the the oils you might want + + + align:start position:0% +so they have the the oils you might want +to check what is in the oil level inside + + align:start position:0% +to check what is in the oil level inside + + + align:start position:0% +to check what is in the oil level inside +your engine for a Cessna 172 six quarts + + align:start position:0% +your engine for a Cessna 172 six quarts + + + align:start position:0% +your engine for a Cessna 172 six quarts +is a really good number to have but you + + align:start position:0% +is a really good number to have but you + + + align:start position:0% +is a really good number to have but you +check it every time during our + + align:start position:0% +check it every time during our + + + align:start position:0% +check it every time during our +pre-flight it could be five quarts it + + align:start position:0% +pre-flight it could be five quarts it + + + align:start position:0% +pre-flight it could be five quarts it +could be seven quarts + + align:start position:0% +could be seven quarts + + + align:start position:0% +could be seven quarts +so you want to double-check that and of + + align:start position:0% +so you want to double-check that and of + + + align:start position:0% +so you want to double-check that and of +course if you see that it's low four + + align:start position:0% +course if you see that it's low four + + + align:start position:0% +course if you see that it's low four +quarts you really want to ask someone to + + align:start position:0% +quarts you really want to ask someone to + + + align:start position:0% +quarts you really want to ask someone to +fill that up before you go flying but + + align:start position:0% +fill that up before you go flying but + + + align:start position:0% +fill that up before you go flying but +the other thing here is you actually + + align:start position:0% +the other thing here is you actually + + + align:start position:0% +the other thing here is you actually +list the the weight of the people that + + align:start position:0% +list the the weight of the people that + + + align:start position:0% +list the the weight of the people that +are sitting in the front and the back so + + align:start position:0% +are sitting in the front and the back so + + + align:start position:0% +are sitting in the front and the back so +I talked about embarrassing folks but + + align:start position:0% +I talked about embarrassing folks but + + + align:start position:0% +I talked about embarrassing folks but +let's not let's not embarrass folks + + align:start position:0% +let's not let's not embarrass folks + + + align:start position:0% +let's not let's not embarrass folks +right now so let's say the pilot and + + align:start position:0% +right now so let's say the pilot and + + + align:start position:0% +right now so let's say the pilot and +let's say you're doing some great + + align:start position:0% +let's say you're doing some great + + + align:start position:0% +let's say you're doing some great +resource management you have another + + align:start position:0% +resource management you have another + + + align:start position:0% +resource management you have another +pilot sitting next to you is your + + align:start position:0% +pilot sitting next to you is your + + + align:start position:0% +pilot sitting next to you is your +copilot is there and you also have some + + align:start position:0% +copilot is there and you also have some + + + align:start position:0% +copilot is there and you also have some +some big folks sitting in the back both + + align:start position:0% +some big folks sitting in the back both + + + align:start position:0% +some big folks sitting in the back both +the left and the right side and you know + + align:start position:0% +the left and the right side and you know + + + align:start position:0% +the left and the right side and you know +you want to take a bunch of pictures and + + align:start position:0% +you want to take a bunch of pictures and + + + align:start position:0% +you want to take a bunch of pictures and +stuff but you you want to get as low as + + align:start position:0% +stuff but you you want to get as low as + + + align:start position:0% +stuff but you you want to get as low as +you want so you put in some bags so this + + align:start position:0% +you want so you put in some bags so this + + + align:start position:0% +you want so you put in some bags so this +it's actually hard to see because + + align:start position:0% +it's actually hard to see because + + + align:start position:0% +it's actually hard to see because +there's too much weight this this red + + align:start position:0% +there's too much weight this this red + + + align:start position:0% +there's too much weight this this red +little plus sign is showing where your + + align:start position:0% +little plus sign is showing where your + + + align:start position:0% +little plus sign is showing where your +center of gravity fell and whether it's + + align:start position:0% +center of gravity fell and whether it's + + + align:start position:0% +center of gravity fell and whether it's +within that utility or normal category + + align:start position:0% +within that utility or normal category + + + align:start position:0% +within that utility or normal category +so in this case we have three people + + align:start position:0% +so in this case we have three people + + + align:start position:0% +so in this case we have three people +front two or 200 pounds each one person + + align:start position:0% +front two or 200 pounds each one person + + + align:start position:0% +front two or 200 pounds each one person +in the rear with 200 and bags they're + + align:start position:0% +in the rear with 200 and bags they're + + + align:start position:0% +in the rear with 200 and bags they're +weighing about ten pounds does this is + + align:start position:0% +weighing about ten pounds does this is + + + align:start position:0% +weighing about ten pounds does this is +this safe to fly no so your little red + + align:start position:0% +this safe to fly no so your little red + + + align:start position:0% +this safe to fly no so your little red +dot went outside the limits and you have + + align:start position:0% +dot went outside the limits and you have + + + align:start position:0% +dot went outside the limits and you have +a much smaller person sitting in the + + align:start position:0% +a much smaller person sitting in the + + + align:start position:0% +a much smaller person sitting in the +back seat you cross over that line and + + align:start position:0% +back seat you cross over that line and + + + align:start position:0% +back seat you cross over that line and +now you're back into the normal category + + align:start position:0% +now you're back into the normal category + + + align:start position:0% +now you're back into the normal category +so you can fly again another thing you + + align:start position:0% +so you can fly again another thing you + + + align:start position:0% +so you can fly again another thing you +can alter is of course the fuel fill the + + align:start position:0% +can alter is of course the fuel fill the + + + align:start position:0% +can alter is of course the fuel fill the +fuel to tabs so this is also talking + + align:start position:0% +fuel to tabs so this is also talking + + + align:start position:0% +fuel to tabs so this is also talking +about so most of the time in the in the + + align:start position:0% +about so most of the time in the in the + + + align:start position:0% +about so most of the time in the in the +Poh book so the section six is about + + align:start position:0% +Poh book so the section six is about + + + align:start position:0% +Poh book so the section six is about +weight and balance so although the one + + align:start position:0% +weight and balance so although the one + + + align:start position:0% +weight and balance so although the one +example I just showed you was for a + + align:start position:0% +example I just showed you was for a + + + align:start position:0% +example I just showed you was for a +Cessna 172 the piper warrior also has + + align:start position:0% +Cessna 172 the piper warrior also has + + + align:start position:0% +Cessna 172 the piper warrior also has +that + + align:start position:0% +that + + + align:start position:0% +that +sistent so really recommend just + + align:start position:0% +sistent so really recommend just + + + align:start position:0% +sistent so really recommend just +memorizing the table of contents for + + align:start position:0% +memorizing the table of contents for + + + align:start position:0% +memorizing the table of contents for +your Poh so the way that you go about + + align:start position:0% +your Poh so the way that you go about + + + align:start position:0% +your Poh so the way that you go about +calculating it is the same way we + + align:start position:0% +calculating it is the same way we + + + align:start position:0% +calculating it is the same way we +entered it into their little calculators + + align:start position:0% +entered it into their little calculators + + + align:start position:0% +entered it into their little calculators +so first you have to determine the basic + + align:start position:0% +so first you have to determine the basic + + + align:start position:0% +so first you have to determine the basic +empty weight of the aircraft and then + + align:start position:0% +empty weight of the aircraft and then + + + align:start position:0% +empty weight of the aircraft and then +the moment section six almost always + + align:start position:0% +the moment section six almost always + + + align:start position:0% +the moment section six almost always +also has a place for you to do that + + align:start position:0% +also has a place for you to do that + + + align:start position:0% +also has a place for you to do that +calculation and so they have a place + + align:start position:0% +calculation and so they have a place + + + align:start position:0% +calculation and so they have a place +right there where you can you know enter + + align:start position:0% +right there where you can you know enter + + + align:start position:0% +right there where you can you know enter +in your airplane the moment and it does + + align:start position:0% +in your airplane the moment and it does + + + align:start position:0% +in your airplane the moment and it does +the same steps that we just saw on the + + align:start position:0% +the same steps that we just saw on the + + + align:start position:0% +the same steps that we just saw on the +slide so you start with that basic empty + + align:start position:0% +slide so you start with that basic empty + + + align:start position:0% +slide so you start with that basic empty +weight then you focus on the fuel and it + + align:start position:0% +weight then you focus on the fuel and it + + + align:start position:0% +weight then you focus on the fuel and it +gives you the six pounds per gallon as + + align:start position:0% +gives you the six pounds per gallon as + + + align:start position:0% +gives you the six pounds per gallon as +what you're going to most likely be + + align:start position:0% +what you're going to most likely be + + + align:start position:0% +what you're going to most likely be +using what is the max number of gallons + + align:start position:0% +using what is the max number of gallons + + + align:start position:0% +using what is the max number of gallons +what is you know the amount four tabs + + align:start position:0% +what is you know the amount four tabs + + + align:start position:0% +what is you know the amount four tabs +you want to actually look this up for + + align:start position:0% +you want to actually look this up for + + + align:start position:0% +you want to actually look this up for +your airplane the weight of the pilot + + align:start position:0% +your airplane the weight of the pilot + + + align:start position:0% +your airplane the weight of the pilot +and the front passenger the rear + + align:start position:0% +and the front passenger the rear + + + align:start position:0% +and the front passenger the rear +passengers and the baggage area and then + + align:start position:0% +passengers and the baggage area and then + + + align:start position:0% +passengers and the baggage area and then +you get this ramp weight and as I talked + + align:start position:0% +you get this ramp weight and as I talked + + + align:start position:0% +you get this ramp weight and as I talked +about you can actually have your plane + + align:start position:0% +about you can actually have your plane + + + align:start position:0% +about you can actually have your plane +be a little heavier than the envelope + + align:start position:0% +be a little heavier than the envelope + + + align:start position:0% +be a little heavier than the envelope +right when it's fueled on the ramp + + align:start position:0% +right when it's fueled on the ramp + + + align:start position:0% +right when it's fueled on the ramp +because there's some allowance for the + + align:start position:0% +because there's some allowance for the + + + align:start position:0% +because there's some allowance for the +fuel that your burn off during taxi and + + align:start position:0% +fuel that your burn off during taxi and + + + align:start position:0% +fuel that your burn off during taxi and +so that's right here so fuel allowance + + align:start position:0% +so that's right here so fuel allowance + + + align:start position:0% +so that's right here so fuel allowance +for engines start taxi and run up so + + align:start position:0% +for engines start taxi and run up so + + + align:start position:0% +for engines start taxi and run up so +they took off about eight pounds over + + align:start position:0% +they took off about eight pounds over + + + align:start position:0% +they took off about eight pounds over +there and then you can calculate it and + + align:start position:0% +there and then you can calculate it and + + + align:start position:0% +there and then you can calculate it and +once you locate the point then you go to + + align:start position:0% +once you locate the point then you go to + + + align:start position:0% +once you locate the point then you go to +that diagram right here so you you go to + + align:start position:0% +that diagram right here so you you go to + + + align:start position:0% +that diagram right here so you you go to +the weight and the moment and you figure + + align:start position:0% +the weight and the moment and you figure + + + align:start position:0% +the weight and the moment and you figure +out whether you're not whether or not + + align:start position:0% +out whether you're not whether or not + + + align:start position:0% +out whether you're not whether or not +you're in the safe whether you're not + + align:start position:0% +you're in the safe whether you're not + + + align:start position:0% +you're in the safe whether you're not +you're in the envelope for that normal + + align:start position:0% +you're in the envelope for that normal + + + align:start position:0% +you're in the envelope for that normal +category of aircraft so what we just + + align:start position:0% +category of aircraft so what we just + + + align:start position:0% +category of aircraft so what we just +went through is the same procedure + + align:start position:0% +went through is the same procedure + + + align:start position:0% +went through is the same procedure +that's listed right here and so here is + + align:start position:0% +that's listed right here and so here is + + + align:start position:0% +that's listed right here and so here is +it just doing that same example for a + + align:start position:0% +it just doing that same example for a + + + align:start position:0% +it just doing that same example for a +particular Piper warrior so they have + + align:start position:0% +particular Piper warrior so they have + + + align:start position:0% +particular Piper warrior so they have +the basic empty weight of the aircraft + + align:start position:0% +the basic empty weight of the aircraft + + + align:start position:0% +the basic empty weight of the aircraft +just as a hint if it's something round + + align:start position:0% +just as a hint if it's something round + + + align:start position:0% +just as a hint if it's something round +like 1500 then you probably didn't get + + align:start position:0% +like 1500 then you probably didn't get + + + align:start position:0% +like 1500 then you probably didn't get +the exact accurate amount so again if + + align:start position:0% +the exact accurate amount so again if + + + align:start position:0% +the exact accurate amount so again if +you look at the the real thing there + + align:start position:0% +you look at the the real thing there + + + align:start position:0% +you look at the the real thing there +you're getting it down to some very + + align:start position:0% +you're getting it down to some very + + + align:start position:0% +you're getting it down to some very +specific accurate numbers + + align:start position:0% +specific accurate numbers + + + align:start position:0% +specific accurate numbers +so like 1190 6.63 that means you got a + + align:start position:0% +so like 1190 6.63 that means you got a + + + align:start position:0% +so like 1190 6.63 that means you got a +real number here's our piper warrior and + + align:start position:0% +real number here's our piper warrior and + + + align:start position:0% +real number here's our piper warrior and +so they have the basic empty weight the + + align:start position:0% +so they have the basic empty weight the + + + align:start position:0% +so they have the basic empty weight the +passengers in the front and the rear + + align:start position:0% +passengers in the front and the rear + + + align:start position:0% +passengers in the front and the rear +they don't have any bags here right now + + align:start position:0% +they don't have any bags here right now + + + align:start position:0% +they don't have any bags here right now +and they they basically multiplied the + + align:start position:0% +and they they basically multiplied the + + + align:start position:0% +and they they basically multiplied the +weight times the arm the arm is really + + align:start position:0% +weight times the arm the arm is really + + + align:start position:0% +weight times the arm the arm is really +indicated in the in the book and in + + align:start position:0% +indicated in the in the book and in + + + align:start position:0% +indicated in the in the book and in +these calculators as to where where the + + align:start position:0% +these calculators as to where where the + + + align:start position:0% +these calculators as to where where the +location is of the chair now of course + + align:start position:0% +location is of the chair now of course + + + align:start position:0% +location is of the chair now of course +the seats slide forward and back but + + align:start position:0% +the seats slide forward and back but + + + align:start position:0% +the seats slide forward and back but +usually they don't they don't get into + + align:start position:0% +usually they don't they don't get into + + + align:start position:0% +usually they don't they don't get into +that many specifics and then you can + + align:start position:0% +that many specifics and then you can + + + align:start position:0% +that many specifics and then you can +calculate here the moment so next we do + + align:start position:0% +calculate here the moment so next we do + + + align:start position:0% +calculate here the moment so next we do +the ramp condition so ramp condition is + + align:start position:0% +the ramp condition so ramp condition is + + + align:start position:0% +the ramp condition so ramp condition is +basically what's the weight and loading + + align:start position:0% +basically what's the weight and loading + + + align:start position:0% +basically what's the weight and loading +of your airplane once it's fueled up and + + align:start position:0% +of your airplane once it's fueled up and + + + align:start position:0% +of your airplane once it's fueled up and +sitting on the ramp then you in this + + align:start position:0% +sitting on the ramp then you in this + + + align:start position:0% +sitting on the ramp then you in this +case they took off seven pounds for that + + align:start position:0% +case they took off seven pounds for that + + + align:start position:0% +case they took off seven pounds for that +taxi and run-up and then your takeoff + + align:start position:0% +taxi and run-up and then your takeoff + + + align:start position:0% +taxi and run-up and then your takeoff +condition in this case it's two thousand + + align:start position:0% +condition in this case it's two thousand + + + align:start position:0% +condition in this case it's two thousand +four hundred and forty pounds and it has + + align:start position:0% +four hundred and forty pounds and it has + + + align:start position:0% +four hundred and forty pounds and it has +a moment here as calculated so you + + align:start position:0% +a moment here as calculated so you + + + align:start position:0% +a moment here as calculated so you +basically do the same thing we just + + align:start position:0% +basically do the same thing we just + + + align:start position:0% +basically do the same thing we just +showed so you look at the the weight on + + align:start position:0% +showed so you look at the the weight on + + + align:start position:0% +showed so you look at the the weight on +the left and they'll CG location as the + + align:start position:0% +the left and they'll CG location as the + + + align:start position:0% +the left and they'll CG location as the +vertical line and you see where those + + align:start position:0% +vertical line and you see where those + + + align:start position:0% +vertical line and you see where those +two lines intersect and you see whether + + align:start position:0% +two lines intersect and you see whether + + + align:start position:0% +two lines intersect and you see whether +or not it's inside the envelope you can + + align:start position:0% +or not it's inside the envelope you can + + + align:start position:0% +or not it's inside the envelope you can +also check the landing condition in + + align:start position:0% +also check the landing condition in + + + align:start position:0% +also check the landing condition in +general you will have burned fuel during + + align:start position:0% +general you will have burned fuel during + + + align:start position:0% +general you will have burned fuel during +your flight and so your landing + + align:start position:0% +your flight and so your landing + + + align:start position:0% +your flight and so your landing +condition will be lower but you know you + + align:start position:0% +condition will be lower but you know you + + + align:start position:0% +condition will be lower but you know you +might have heard big big jets and you've + + align:start position:0% +might have heard big big jets and you've + + + align:start position:0% +might have heard big big jets and you've +heard that sometimes they have to do a + + align:start position:0% +heard that sometimes they have to do a + + + align:start position:0% +heard that sometimes they have to do a +fuel dump why do they have to do a fuel + + align:start position:0% +fuel dump why do they have to do a fuel + + + align:start position:0% +fuel dump why do they have to do a fuel +dump well maybe they calculated their + + align:start position:0% +dump well maybe they calculated their + + + align:start position:0% +dump well maybe they calculated their +landing based on having flown across the + + align:start position:0% +landing based on having flown across the + + + align:start position:0% +landing based on having flown across the +country but their flight across the + + align:start position:0% +country but their flight across the + + + align:start position:0% +country but their flight across the +country was canceled because if weather + + align:start position:0% +country was canceled because if weather + + + align:start position:0% +country was canceled because if weather +or whatever and so they had to dump + + align:start position:0% +or whatever and so they had to dump + + + align:start position:0% +or whatever and so they had to dump +their fuel in order to land which you + + align:start position:0% +their fuel in order to land which you + + + align:start position:0% +their fuel in order to land which you +don't like to here is once they've + + align:start position:0% +don't like to here is once they've + + + align:start position:0% +don't like to here is once they've +dumped their fuel then you have another + + align:start position:0% +dumped their fuel then you have another + + + align:start position:0% +dumped their fuel then you have another +delay in the air and you're like hey + + align:start position:0% +delay in the air and you're like hey + + + align:start position:0% +delay in the air and you're like hey +what happened I thought we dumped all of + + align:start position:0% +what happened I thought we dumped all of + + + align:start position:0% +what happened I thought we dumped all of +our fuel but of course as a small little + + align:start position:0% +our fuel but of course as a small little + + + align:start position:0% +our fuel but of course as a small little +airplane dumping fuel is not really a + + align:start position:0% +airplane dumping fuel is not really a + + + align:start position:0% +airplane dumping fuel is not really a +procedure you're gonna be doing so it + + align:start position:0% +procedure you're gonna be doing so it + + + align:start position:0% +procedure you're gonna be doing so it +might be a good idea to just calculate + + align:start position:0% +might be a good idea to just calculate + + + align:start position:0% +might be a good idea to just calculate +the landing and the runway lengths with + + align:start position:0% +the landing and the runway lengths with + + + align:start position:0% +the landing and the runway lengths with +the full fuel in case you know you have + + align:start position:0% +the full fuel in case you know you have + + + align:start position:0% +the full fuel in case you know you have +to + + align:start position:0% +to + + + align:start position:0% +to +landing right then and there before + + align:start position:0% +landing right then and there before + + + align:start position:0% +landing right then and there before +you've flown all the distance you + + align:start position:0% +you've flown all the distance you + + + align:start position:0% +you've flown all the distance you +thought you're going to get to fly so + + align:start position:0% +thought you're going to get to fly so + + + align:start position:0% +thought you're going to get to fly so +yeah in general as you can see that + + align:start position:0% +yeah in general as you can see that + + + align:start position:0% +yeah in general as you can see that +where we were beforehand was higher and + + align:start position:0% +where we were beforehand was higher and + + + align:start position:0% +where we were beforehand was higher and +the weight goes down so your landing + + align:start position:0% +the weight goes down so your landing + + + align:start position:0% +the weight goes down so your landing +condition is almost always going to stay + + align:start position:0% +condition is almost always going to stay + + + align:start position:0% +condition is almost always going to stay +within the envelope there's some some + + align:start position:0% +within the envelope there's some some + + + align:start position:0% +within the envelope there's some some +places where if you're CG is too far aft + + align:start position:0% +places where if you're CG is too far aft + + + align:start position:0% +places where if you're CG is too far aft +or too far forward where actually that + + align:start position:0% +or too far forward where actually that + + + align:start position:0% +or too far forward where actually that +reduction in weight could cause you to + + align:start position:0% +reduction in weight could cause you to + + + align:start position:0% +reduction in weight could cause you to +come outside the envelope alright so + + align:start position:0% +come outside the envelope alright so + + + align:start position:0% +come outside the envelope alright so +there also a lot of spreadsheets + + align:start position:0% +there also a lot of spreadsheets + + + align:start position:0% +there also a lot of spreadsheets +available you can make your own + + align:start position:0% +available you can make your own + + + align:start position:0% +available you can make your own +spreadsheet pretty quickly in Excel + + align:start position:0% +spreadsheet pretty quickly in Excel + + + align:start position:0% +spreadsheet pretty quickly in Excel +using the data from the particular + + align:start position:0% +using the data from the particular + + + align:start position:0% +using the data from the particular +aircraft that you're renting or buying + + align:start position:0% + + + + align:start position:0% + +alright and these are just some of + + align:start position:0% +alright and these are just some of + + + align:start position:0% +alright and these are just some of +snapshots from the the book that we just + + align:start position:0% +snapshots from the the book that we just + + + align:start position:0% +snapshots from the the book that we just +looked at and they show pictures of + + align:start position:0% +looked at and they show pictures of + + + align:start position:0% +looked at and they show pictures of +where the seats are in the airplane in + + align:start position:0% +where the seats are in the airplane in + + + align:start position:0% +where the seats are in the airplane in +order for you to calculate that you + + align:start position:0% +order for you to calculate that you + + + align:start position:0% +order for you to calculate that you +could also calculate the moment left to + + align:start position:0% +could also calculate the moment left to + + + align:start position:0% +could also calculate the moment left to +right it's pretty easy to think about + + align:start position:0% +right it's pretty easy to think about + + + align:start position:0% +right it's pretty easy to think about +though that in that tiny little airplane + + align:start position:0% +though that in that tiny little airplane + + + align:start position:0% +though that in that tiny little airplane +if if you're sitting on the front and + + align:start position:0% +if if you're sitting on the front and + + + align:start position:0% +if if you're sitting on the front and +the left and no one's sitting on your + + align:start position:0% +the left and no one's sitting on your + + + align:start position:0% +the left and no one's sitting on your +right and you have someone sitting in + + align:start position:0% +right and you have someone sitting in + + + align:start position:0% +right and you have someone sitting in +the back on the left you're gonna be + + align:start position:0% +the back on the left you're gonna be + + + align:start position:0% +the back on the left you're gonna be +tilted over it's very easy to fix that + + align:start position:0% +tilted over it's very easy to fix that + + + align:start position:0% +tilted over it's very easy to fix that +problem just make sure you have someone + + align:start position:0% +problem just make sure you have someone + + + align:start position:0% +problem just make sure you have someone +sitting on the other side I have noticed + + align:start position:0% +sitting on the other side I have noticed + + + align:start position:0% +sitting on the other side I have noticed +some of these effects before I'm a + + align:start position:0% +some of these effects before I'm a + + + align:start position:0% +some of these effects before I'm a +little bit of a smaller person and there + + align:start position:0% +little bit of a smaller person and there + + + align:start position:0% +little bit of a smaller person and there +was a very very large instructor sitting + + align:start position:0% +was a very very large instructor sitting + + + align:start position:0% +was a very very large instructor sitting +next to me and actually could tell as I + + align:start position:0% +next to me and actually could tell as I + + + align:start position:0% +next to me and actually could tell as I +was flying that it was a little bit + + align:start position:0% +was flying that it was a little bit + + + align:start position:0% +was flying that it was a little bit +tilted and so the the future flights we + + align:start position:0% +tilted and so the the future flights we + + + align:start position:0% +tilted and so the the future flights we +put some more bags on my side and it was + + align:start position:0% +put some more bags on my side and it was + + + align:start position:0% +put some more bags on my side and it was +a little bit more evened out usually you + + align:start position:0% +a little bit more evened out usually you + + + align:start position:0% +a little bit more evened out usually you +won't run into that too much as an issue + + align:start position:0% +won't run into that too much as an issue + + + align:start position:0% +won't run into that too much as an issue +in some of the the small like puddle + + align:start position:0% +in some of the the small like puddle + + + align:start position:0% +in some of the the small like puddle +jumper aircraft is so a commercial + + align:start position:0% +jumper aircraft is so a commercial + + + align:start position:0% +jumper aircraft is so a commercial +aircraft they have sometimes a situation + + align:start position:0% +aircraft they have sometimes a situation + + + align:start position:0% +aircraft they have sometimes a situation +where there's only one row of seats on + + align:start position:0% +where there's only one row of seats on + + + align:start position:0% +where there's only one row of seats on +one side and then there's the aisle and + + align:start position:0% +one side and then there's the aisle and + + + align:start position:0% +one side and then there's the aisle and +then two seats on the other side have + + align:start position:0% +then two seats on the other side have + + + align:start position:0% +then two seats on the other side have +you guys seen that configuration I'm + + align:start position:0% +you guys seen that configuration I'm + + + align:start position:0% +you guys seen that configuration I'm +getting a lot of head nods so in that + + align:start position:0% +getting a lot of head nods so in that + + + align:start position:0% +getting a lot of head nods so in that +situation they might enforce that you + + align:start position:0% +situation they might enforce that you + + + align:start position:0% +situation they might enforce that you +have to sit in the seat that was + + align:start position:0% +have to sit in the seat that was + + + align:start position:0% +have to sit in the seat that was +assigned to you and when people try to + + align:start position:0% +assigned to you and when people try to + + + align:start position:0% +assigned to you and when people try to +move you know from the the side that + + align:start position:0% +move you know from the the side that + + + align:start position:0% +move you know from the the side that +only had one seat in the row to the side + + align:start position:0% +only had one seat in the row to the side + + + align:start position:0% +only had one seat in the row to the side +that has two seats because they just + + align:start position:0% +that has two seats because they just + + + align:start position:0% +that has two seats because they just +want more space to spread out they + + align:start position:0% +want more space to spread out they + + + align:start position:0% +want more space to spread out they +might say hey for weight and balance + + align:start position:0% +might say hey for weight and balance + + + align:start position:0% +might say hey for weight and balance +reasons you have to sit in the seat that + + align:start position:0% +reasons you have to sit in the seat that + + + align:start position:0% +reasons you have to sit in the seat that +was assigned for takeoff and so that's + + align:start position:0% +was assigned for takeoff and so that's + + + align:start position:0% +was assigned for takeoff and so that's +what they're talking about there any + + align:start position:0% +what they're talking about there any + + + align:start position:0% +what they're talking about there any +questions about weight and balance + + align:start position:0% + + + + align:start position:0% + +do you guys think you could do weight + + align:start position:0% +do you guys think you could do weight + + + align:start position:0% +do you guys think you could do weight +and balance calculations yes okay I'm + + align:start position:0% +and balance calculations yes okay I'm + + + align:start position:0% +and balance calculations yes okay I'm +getting a lot of head nods so everyone + + align:start position:0% +getting a lot of head nods so everyone + + + align:start position:0% +getting a lot of head nods so everyone +took physics that's good good job yes + + align:start position:0% + + + + align:start position:0% + +hello laughter question I will actually + + align:start position:0% +hello laughter question I will actually + + + align:start position:0% +hello laughter question I will actually +defer to Philip who flies helicopters + + align:start position:0% +defer to Philip who flies helicopters + + + align:start position:0% +defer to Philip who flies helicopters +quite frequently so once he's back we'll + + align:start position:0% +quite frequently so once he's back we'll + + + align:start position:0% +quite frequently so once he's back we'll +ask him about helicopter cge limits good + + align:start position:0% +ask him about helicopter cge limits good + + + align:start position:0% +ask him about helicopter cge limits good +question + + align:start position:0% +question + + + align:start position:0% +question +anything else + + align:start position:0% + + + + align:start position:0% + +so the question is do when you're + + align:start position:0% +so the question is do when you're + + + align:start position:0% +so the question is do when you're +actually flying do you do this + + align:start position:0% +actually flying do you do this + + + align:start position:0% +actually flying do you do this +calculation every single time or do you + + align:start position:0% +calculation every single time or do you + + + align:start position:0% +calculation every single time or do you +mostly only do it when you're really + + align:start position:0% +mostly only do it when you're really + + + align:start position:0% +mostly only do it when you're really +loading the aircraft so it's actually + + align:start position:0% +loading the aircraft so it's actually + + + align:start position:0% +loading the aircraft so it's actually +required that you have the weight and + + align:start position:0% +required that you have the weight and + + + align:start position:0% +required that you have the weight and +balance done the reason you don't do it + + align:start position:0% +balance done the reason you don't do it + + + align:start position:0% +balance done the reason you don't do it +every single time though is you + + align:start position:0% +every single time though is you + + + align:start position:0% +every single time though is you +frequently fly in the same configuration + + align:start position:0% +frequently fly in the same configuration + + + align:start position:0% +frequently fly in the same configuration +so if you rent from a flight school you + + align:start position:0% +so if you rent from a flight school you + + + align:start position:0% +so if you rent from a flight school you +might frequently rent you know a couple + + align:start position:0% +might frequently rent you know a couple + + + align:start position:0% +might frequently rent you know a couple +aircraft and you might frequently you + + align:start position:0% +aircraft and you might frequently you + + + align:start position:0% +aircraft and you might frequently you +know fly just yourself doing a solo + + align:start position:0% +know fly just yourself doing a solo + + + align:start position:0% +know fly just yourself doing a solo +flight or fly with your instructor so + + align:start position:0% +flight or fly with your instructor so + + + align:start position:0% +flight or fly with your instructor so +you might just keep it stored that you + + align:start position:0% +you might just keep it stored that you + + + align:start position:0% +you might just keep it stored that you +have you know a couple pieces of paper + + align:start position:0% +have you know a couple pieces of paper + + + align:start position:0% +have you know a couple pieces of paper +in your flight bag that are the weight + + align:start position:0% +in your flight bag that are the weight + + + align:start position:0% +in your flight bag that are the weight +and balance calculations for what you + + align:start position:0% +and balance calculations for what you + + + align:start position:0% +and balance calculations for what you +almost always fly and is almost always + + align:start position:0% +almost always fly and is almost always + + + align:start position:0% +almost always fly and is almost always +within the normal category envelope but + + align:start position:0% +within the normal category envelope but + + + align:start position:0% +within the normal category envelope but +you definitely want to do those + + align:start position:0% +you definitely want to do those + + + align:start position:0% +you definitely want to do those +calculations if you're getting you know + + align:start position:0% +calculations if you're getting you know + + + align:start position:0% +calculations if you're getting you know +passengers in the back seat whenever we + + align:start position:0% +passengers in the back seat whenever we + + + align:start position:0% +passengers in the back seat whenever we +go on these MIT fly outs we actually ask + + align:start position:0% +go on these MIT fly outs we actually ask + + + align:start position:0% +go on these MIT fly outs we actually ask +people for their weights and and it's + + align:start position:0% +people for their weights and and it's + + + align:start position:0% +people for their weights and and it's +actually a big restriction too so when + + align:start position:0% +actually a big restriction too so when + + + align:start position:0% +actually a big restriction too so when +we're trying to get passengers to sit + + align:start position:0% +we're trying to get passengers to sit + + + align:start position:0% +we're trying to get passengers to sit +down just because I fly a Cessna with + + align:start position:0% +down just because I fly a Cessna with + + + align:start position:0% +down just because I fly a Cessna with +four seats as we just saw from the + + align:start position:0% +four seats as we just saw from the + + + align:start position:0% +four seats as we just saw from the +example I don't have four pass and you + + align:start position:0% +example I don't have four pass and you + + + align:start position:0% +example I don't have four pass and you +know I don't have three passengers to + + align:start position:0% +know I don't have three passengers to + + + align:start position:0% +know I don't have three passengers to +offer I often say you know I have 220 + + align:start position:0% +offer I often say you know I have 220 + + + align:start position:0% +offer I often say you know I have 220 +pounds available and so they then have + + align:start position:0% +pounds available and so they then have + + + align:start position:0% +pounds available and so they then have +to sort out Sebastian and his team as to + + align:start position:0% +to sort out Sebastian and his team as to + + + align:start position:0% +to sort out Sebastian and his team as to +who to assign to my plane versus another + + align:start position:0% +who to assign to my plane versus another + + + align:start position:0% +who to assign to my plane versus another +plane and also if people aren't being if + + align:start position:0% +plane and also if people aren't being if + + + align:start position:0% +plane and also if people aren't being if +you if you notice people aren't being + + align:start position:0% +you if you notice people aren't being + + + align:start position:0% +you if you notice people aren't being +overly forthcoming about their weight + + align:start position:0% +overly forthcoming about their weight + + + align:start position:0% +overly forthcoming about their weight +you might want to increase the amount + + align:start position:0% +you might want to increase the amount + + + align:start position:0% +you might want to increase the amount +that they gave you yeah I mean let me + + align:start position:0% +that they gave you yeah I mean let me + + + align:start position:0% +that they gave you yeah I mean let me +let me add that I obviously have a lot + + align:start position:0% +let me add that I obviously have a lot + + + align:start position:0% +let me add that I obviously have a lot +more experience being over overweight + + align:start position:0% +more experience being over overweight + + + align:start position:0% +more experience being over overweight +then Tina might have but also yeah + + align:start position:0% +then Tina might have but also yeah + + + align:start position:0% +then Tina might have but also yeah +actually these pants are a good example + + align:start position:0% +actually these pants are a good example + + + align:start position:0% +actually these pants are a good example +twenty years ago some friends and I we + + align:start position:0% +twenty years ago some friends and I we + + + align:start position:0% +twenty years ago some friends and I we +made a web front end to a Levi Strauss + + align:start position:0% +made a web front end to a Levi Strauss + + + align:start position:0% +made a web front end to a Levi Strauss +Factory that could make custom cut + + align:start position:0% +Factory that could make custom cut + + + align:start position:0% +Factory that could make custom cut +khakis so we asked people in the web + + align:start position:0% +khakis so we asked people in the web + + + align:start position:0% +khakis so we asked people in the web +form when they ordered + + align:start position:0% +form when they ordered + + + align:start position:0% +form when they ordered +what's your waist size what's your + + align:start position:0% +what's your waist size what's your + + + align:start position:0% +what's your waist size what's your +inseam what's your height and weight and + + align:start position:0% +inseam what's your height and weight and + + + align:start position:0% +inseam what's your height and weight and +from that we had software to try to + + align:start position:0% +from that we had software to try to + + + align:start position:0% +from that we had software to try to +infer their actual weight their actual + + align:start position:0% +infer their actual weight their actual + + + align:start position:0% +infer their actual weight their actual +waist size and then we make them you + + align:start position:0% +waist size and then we make them you + + + align:start position:0% +waist size and then we make them you +can't really see this but these pants + + align:start position:0% +can't really see this but these pants + + + align:start position:0% +can't really see this but these pants +just say pair number seven they don't + + align:start position:0% +just say pair number seven they don't + + + align:start position:0% +just say pair number seven they don't +say anything about what size it actually + + align:start position:0% +say anything about what size it actually + + + align:start position:0% +say anything about what size it actually +is they would get their pants this was + + align:start position:0% +is they would get their pants this was + + + align:start position:0% +is they would get their pants this was +in 1990 + + align:start position:0% +in 1990 + + + align:start position:0% +in 1990 +and they would get their pants if they + + align:start position:0% +and they would get their pants if they + + + align:start position:0% +and they would get their pants if they +didn't fit they'd say look it needs to + + align:start position:0% +didn't fit they'd say look it needs to + + + align:start position:0% +didn't fit they'd say look it needs to +be a little looser in the waist it needs + + align:start position:0% +be a little looser in the waist it needs + + + align:start position:0% +be a little looser in the waist it needs +to be a little shorter and then a + + align:start position:0% +to be a little shorter and then a + + + align:start position:0% +to be a little shorter and then a +revised pair would be made and sent to + + align:start position:0% +revised pair would be made and sent to + + + align:start position:0% +revised pair would be made and sent to +them but we never relied on their stated + + align:start position:0% +them but we never relied on their stated + + + align:start position:0% +them but we never relied on their stated +weight or their stated waist size + + align:start position:0% +weight or their stated waist size + + + align:start position:0% +weight or their stated waist size +exactly so there is a question for you + + align:start position:0% +exactly so there is a question for you + + + align:start position:0% +exactly so there is a question for you +that I wasn't able to answer about + + align:start position:0% +that I wasn't able to answer about + + + align:start position:0% +that I wasn't able to answer about +helicopter CGS and really thinking about + + align:start position:0% +helicopter CGS and really thinking about + + + align:start position:0% +helicopter CGS and really thinking about +was it the lateral CG what was your + + align:start position:0% +was it the lateral CG what was your + + + align:start position:0% +was it the lateral CG what was your +question + + align:start position:0% + + + + align:start position:0% + +it's very hard to get to the question is + + align:start position:0% +it's very hard to get to the question is + + + align:start position:0% +it's very hard to get to the question is +yeah it's very hard to get a helicopter + + align:start position:0% +yeah it's very hard to get a helicopter + + + align:start position:0% +yeah it's very hard to get a helicopter +out of lab as with an aircraft if you + + align:start position:0% +out of lab as with an aircraft if you + + + align:start position:0% +out of lab as with an aircraft if you +have you know two heavy people in the + + align:start position:0% +have you know two heavy people in the + + + align:start position:0% +have you know two heavy people in the +back and a light person in the front + + align:start position:0% +back and a light person in the front + + + align:start position:0% +back and a light person in the front +it's easy to get out of the front back + + align:start position:0% +it's easy to get out of the front back + + + align:start position:0% +it's easy to get out of the front back +CG longitudinal CGG but he's talking + + align:start position:0% +CG longitudinal CGG but he's talking + + + align:start position:0% +CG longitudinal CGG but he's talking +about what we just discussed you know + + align:start position:0% +about what we just discussed you know + + + align:start position:0% +about what we just discussed you know +it's frequently the case that you might + + align:start position:0% +it's frequently the case that you might + + + align:start position:0% +it's frequently the case that you might +have a forward CG or a nav CG but you + + align:start position:0% +have a forward CG or a nav CG but you + + + align:start position:0% +have a forward CG or a nav CG but you +but you don't usually have an issue with + + align:start position:0% +but you don't usually have an issue with + + + align:start position:0% +but you don't usually have an issue with +the CG on the left or the right + + align:start position:0% +the CG on the left or the right + + + align:start position:0% +the CG on the left or the right +unless I mean it's very visible and a + + align:start position:0% +unless I mean it's very visible and a + + + align:start position:0% +unless I mean it's very visible and a +four-seat aircraft it how to fix those + + align:start position:0% +four-seat aircraft it how to fix those + + + align:start position:0% +four-seat aircraft it how to fix those +types of problems one issue with the + + align:start position:0% +types of problems one issue with the + + + align:start position:0% +types of problems one issue with the +Robinson is they put the main fuel tank + + align:start position:0% +Robinson is they put the main fuel tank + + + align:start position:0% +Robinson is they put the main fuel tank +on the left so they're budgeting for in + + align:start position:0% +on the left so they're budgeting for in + + + align:start position:0% +on the left so they're budgeting for in +a solo situation a pilot of at least a + + align:start position:0% +a solo situation a pilot of at least a + + + align:start position:0% +a solo situation a pilot of at least a +certain minimum weight in the front + + align:start position:0% +certain minimum weight in the front + + + align:start position:0% +certain minimum weight in the front +right so very lightweight like sometimes + + align:start position:0% +right so very lightweight like sometimes + + + align:start position:0% +right so very lightweight like sometimes +when teenagers are learning to fly + + align:start position:0% +when teenagers are learning to fly + + + align:start position:0% +when teenagers are learning to fly +helicopters they have to add a little + + align:start position:0% +helicopters they have to add a little + + + align:start position:0% +helicopters they have to add a little +bit of ballast let's say like a big + + align:start position:0% +bit of ballast let's say like a big + + + align:start position:0% +bit of ballast let's say like a big +heavy you know Jim weight like a 50 + + align:start position:0% +heavy you know Jim weight like a 50 + + + align:start position:0% +heavy you know Jim weight like a 50 +pound Jim like Jim wait in the front + + align:start position:0% +pound Jim like Jim wait in the front + + + align:start position:0% +pound Jim like Jim wait in the front +left foot well or something the other + + align:start position:0% +left foot well or something the other + + + align:start position:0% +left foot well or something the other +the other thing that could go wrong is + + align:start position:0% +the other thing that could go wrong is + + + align:start position:0% +the other thing that could go wrong is +so when you do your pre-flight one of + + align:start position:0% +so when you do your pre-flight one of + + + align:start position:0% +so when you do your pre-flight one of +the things that you do is that if you're + + align:start position:0% +the things that you do is that if you're + + + align:start position:0% +the things that you do is that if you're +sitting and the pilot seat so on the + + align:start position:0% +sitting and the pilot seat so on the + + + align:start position:0% +sitting and the pilot seat so on the +left side so - you're right in the + + align:start position:0% +left side so - you're right in the + + + align:start position:0% +left side so - you're right in the +middle at the bottom there's a little + + align:start position:0% +middle at the bottom there's a little + + + align:start position:0% +middle at the bottom there's a little +knob where you can say whether you want + + align:start position:0% +knob where you can say whether you want + + + align:start position:0% +knob where you can say whether you want +the fuel to be coming from the left tank + + align:start position:0% +the fuel to be coming from the left tank + + + align:start position:0% +the fuel to be coming from the left tank +the right tank or the or both and pretty + + align:start position:0% +the right tank or the or both and pretty + + + align:start position:0% +the right tank or the or both and pretty +much all the time the checklist says + + align:start position:0% +much all the time the checklist says + + + align:start position:0% +much all the time the checklist says +that after you've parked the plane you + + align:start position:0% +that after you've parked the plane you + + + align:start position:0% +that after you've parked the plane you +want to twist it to the left or the + + align:start position:0% +want to twist it to the left or the + + + align:start position:0% +want to twist it to the left or the +right and the reason is you don't want + + align:start position:0% +right and the reason is you don't want + + + align:start position:0% +right and the reason is you don't want +while it's sitting there fuel to be + + align:start position:0% +while it's sitting there fuel to be + + + align:start position:0% +while it's sitting there fuel to be +sloshing across a plane and so you you + + align:start position:0% +sloshing across a plane and so you you + + + align:start position:0% +sloshing across a plane and so you you +set it to left for example now if you + + align:start position:0% +set it to left for example now if you + + + align:start position:0% +set it to left for example now if you +skip that step + + align:start position:0% +skip that step + + + align:start position:0% +skip that step +even though it comes up several times + + align:start position:0% +even though it comes up several times + + + align:start position:0% +even though it comes up several times +throughout your your pre-flight and then + + align:start position:0% +throughout your your pre-flight and then + + + align:start position:0% +throughout your your pre-flight and then +your + + align:start position:0% +your + + + align:start position:0% +your +run up check if you if you didn't put + + align:start position:0% +run up check if you if you didn't put + + + align:start position:0% +run up check if you if you didn't put +the fuel to draw from both tanks and + + align:start position:0% +the fuel to draw from both tanks and + + + align:start position:0% +the fuel to draw from both tanks and +it's only drawing from one tank then you + + align:start position:0% +it's only drawing from one tank then you + + + align:start position:0% +it's only drawing from one tank then you +might experience that that instability + + align:start position:0% +might experience that that instability + + + align:start position:0% +might experience that that instability +all right why don't we should we take a + + align:start position:0% +all right why don't we should we take a + + + align:start position:0% +all right why don't we should we take a +15-minute break so people can run out + + align:start position:0% +15-minute break so people can run out + + + align:start position:0% +15-minute break so people can run out +grab food bring it back and then we'll + + align:start position:0% +grab food bring it back and then we'll + + + align:start position:0% +grab food bring it back and then we'll +hear from dojo about the test-fire bill + + align:start position:0% +hear from dojo about the test-fire bill + + + align:start position:0% +hear from dojo about the test-fire bill +and life potentially outside of the + + align:start position:0% +and life potentially outside of the + + + align:start position:0% +and life potentially outside of the +limits + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/9_xG0AGRa-w.txt b/9_xG0AGRa-w.txt new file mode 100644 index 0000000000000000000000000000000000000000..03e1a7d3d1628b94fece6eb8907dd0afb3078599 --- /dev/null +++ b/9_xG0AGRa-w.txt @@ -0,0 +1,13968 @@ +align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +last time we spoke about uh + + align:start position:0% +last time we spoke about uh + + + align:start position:0% +last time we spoke about uh +we covered sets and induction + + align:start position:0% +we covered sets and induction + + + align:start position:0% +we covered sets and induction +this time i want to ask a question about + + align:start position:0% +this time i want to ask a question about + + + align:start position:0% +this time i want to ask a question about +sets + + align:start position:0% +sets + + + align:start position:0% +sets +um + + align:start position:0% +um + + + align:start position:0% +um +which turns out is is + + align:start position:0% +which turns out is is + + + align:start position:0% +which turns out is is +you know actually quite a deep question + + align:start position:0% +you know actually quite a deep question + + + align:start position:0% +you know actually quite a deep question +i mean i didn't come up with it + + align:start position:0% +i mean i didn't come up with it + + + align:start position:0% +i mean i didn't come up with it +myself this question is + + align:start position:0% + + + + align:start position:0% + +at least 150 years old probably + + align:start position:0% + + + + align:start position:0% + +so the question that i want to ask is + + align:start position:0% + + + + align:start position:0% + +if a and b are sets + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +let's phrase it this way at least a + + align:start position:0% +let's phrase it this way at least a + + + align:start position:0% +let's phrase it this way at least a +little more efficiently + + align:start position:0% + + + + align:start position:0% + +when do + + align:start position:0% + + + + align:start position:0% + +two sets + + align:start position:0% + + + + align:start position:0% + +a and b + + align:start position:0% + + + + align:start position:0% + +have the same size + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +this is especially interesting if these + + align:start position:0% +this is especially interesting if these + + + align:start position:0% +this is especially interesting if these +two sets are not finite meaning + + align:start position:0% +two sets are not finite meaning + + + align:start position:0% +two sets are not finite meaning +there's not five of them there's not + + align:start position:0% +there's not five of them there's not + + + align:start position:0% +there's not five of them there's not +eight of them + + align:start position:0% +eight of them + + + align:start position:0% +eight of them +um but there's + + align:start position:0% +um but there's + + + align:start position:0% +um but there's +infinitely many members whatever that + + align:start position:0% +infinitely many members whatever that + + + align:start position:0% +infinitely many members whatever that +means and i'll actually define what that + + align:start position:0% +means and i'll actually define what that + + + align:start position:0% +means and i'll actually define what that +means for example + + align:start position:0% +means for example + + + align:start position:0% +means for example +do the natural numbers and the integers + + align:start position:0% +do the natural numbers and the integers + + + align:start position:0% +do the natural numbers and the integers +have the same size + + align:start position:0% +have the same size + + + align:start position:0% +have the same size +do the natural numbers and the rational + + align:start position:0% +do the natural numbers and the rational + + + align:start position:0% +do the natural numbers and the rational +numbers have the same size + + align:start position:0% +numbers have the same size + + + align:start position:0% +numbers have the same size +what about the rational numbers and the + + align:start position:0% +what about the rational numbers and the + + + align:start position:0% +what about the rational numbers and the +real numbers even though we haven't + + align:start position:0% +real numbers even though we haven't + + + align:start position:0% +real numbers even though we haven't +defined that yet you can still + + align:start position:0% +defined that yet you can still + + + align:start position:0% +defined that yet you can still +um keep in mind + + align:start position:0% +um keep in mind + + + align:start position:0% +um keep in mind +you know your notion of the real numbers + + align:start position:0% +you know your notion of the real numbers + + + align:start position:0% +you know your notion of the real numbers +from + + align:start position:0% +from + + + align:start position:0% +from +calculus + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +this question is why is it deep + + align:start position:0% +this question is why is it deep + + + align:start position:0% +this question is why is it deep +because + + align:start position:0% +because + + + align:start position:0% +because +it depends on this word here + + align:start position:0% +it depends on this word here + + + align:start position:0% +it depends on this word here +size + + align:start position:0% +size + + + align:start position:0% +size +and + + align:start position:0% + + + + align:start position:0% + +what exactly that means so + + align:start position:0% + + + + align:start position:0% + +i'm not + + align:start position:0% + + + + align:start position:0% + +so kind of an answer + + align:start position:0% +so kind of an answer + + + align:start position:0% +so kind of an answer +this is due to george cantor + + align:start position:0% + + + + align:start position:0% + +he said that two sets so not an answer + + align:start position:0% +he said that two sets so not an answer + + + align:start position:0% +he said that two sets so not an answer +but a way of defining size a way of + + align:start position:0% +but a way of defining size a way of + + + align:start position:0% +but a way of defining size a way of +saying the two sets have the same size + + align:start position:0% +saying the two sets have the same size + + + align:start position:0% +saying the two sets have the same size +he said two sets have the same size when + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +of the two sets + + align:start position:0% +of the two sets + + + align:start position:0% +of the two sets +the elements of the two sets + + align:start position:0% + + + + align:start position:0% + +can be paired off + + align:start position:0% +can be paired off + + + align:start position:0% +can be paired off +okay meaning + + align:start position:0% +okay meaning + + + align:start position:0% +okay meaning +and i will make this much more precise + + align:start position:0% +and i will make this much more precise + + + align:start position:0% +and i will make this much more precise +in + + align:start position:0% +in + + + align:start position:0% +in +a minute or so + + align:start position:0% +a minute or so + + + align:start position:0% +a minute or so +what what + + align:start position:0% +what what + + + align:start position:0% +what what +does he mean or what do i mean for + + align:start position:0% +does he mean or what do i mean for + + + align:start position:0% +does he mean or what do i mean for +example the set a b and c + + align:start position:0% +example the set a b and c + + + align:start position:0% +example the set a b and c +and the set one two and three + + align:start position:0% +and the set one two and three + + + align:start position:0% +and the set one two and three +so this one consi this set consists of + + align:start position:0% +so this one consi this set consists of + + + align:start position:0% +so this one consi this set consists of +three letters a b and c this set + + align:start position:0% +three letters a b and c this set + + + align:start position:0% +three letters a b and c this set +consists of three integers one two and + + align:start position:0% +consists of three integers one two and + + + align:start position:0% +consists of three integers one two and +three they have the same size because i + + align:start position:0% +three they have the same size because i + + + align:start position:0% +three they have the same size because i +can essentially pair them off + + align:start position:0% +can essentially pair them off + + + align:start position:0% +can essentially pair them off +uh a + + align:start position:0% +uh a + + + align:start position:0% +uh a +so a and one go together + + align:start position:0% +so a and one go together + + + align:start position:0% +so a and one go together +b and two go together and c and three go + + align:start position:0% +b and two go together and c and three go + + + align:start position:0% +b and two go together and c and three go +together meaning each one of each member + + align:start position:0% +together meaning each one of each member + + + align:start position:0% +together meaning each one of each member +of this set gets paired off with + + align:start position:0% +of this set gets paired off with + + + align:start position:0% +of this set gets paired off with +an element of this set + + align:start position:0% +an element of this set + + + align:start position:0% +an element of this set +and every element of this set gets + + align:start position:0% +and every element of this set gets + + + align:start position:0% +and every element of this set gets +paired off with a unique element from + + align:start position:0% +paired off with a unique element from + + + align:start position:0% +paired off with a unique element from +this set + + align:start position:0% +this set + + + align:start position:0% +this set +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +to make + + align:start position:0% +to make + + + align:start position:0% +to make +and so this is uh + + align:start position:0% + + + + align:start position:0% + +goes under the name of the theory of + + align:start position:0% +goes under the name of the theory of + + + align:start position:0% +goes under the name of the theory of +cardinality or + + align:start position:0% + + + + align:start position:0% + +cardinal numbers if you like + + align:start position:0% +cardinal numbers if you like + + + align:start position:0% +cardinal numbers if you like +but we won't go too deeply into it + + align:start position:0% +but we won't go too deeply into it + + + align:start position:0% +but we won't go too deeply into it +so the way you make + + align:start position:0% +so the way you make + + + align:start position:0% +so the way you make +or the way + + align:start position:0% +or the way + + + align:start position:0% +or the way +one makes this + + align:start position:0% +one makes this + + + align:start position:0% +one makes this +pairing off business more precise + + align:start position:0% +pairing off business more precise + + + align:start position:0% +pairing off business more precise +is using the language of functions + + align:start position:0% +is using the language of functions + + + align:start position:0% +is using the language of functions +and you've been dealing with functions + + align:start position:0% +and you've been dealing with functions + + + align:start position:0% +and you've been dealing with functions +since you've been + + align:start position:0% +since you've been + + + align:start position:0% +since you've been +um + + align:start position:0% +um + + + align:start position:0% +um +doing calculus so + + align:start position:0% +doing calculus so + + + align:start position:0% +doing calculus so +i'm just gonna quickly um + + align:start position:0% +i'm just gonna quickly um + + + align:start position:0% +i'm just gonna quickly um +reintroduce or review some terminology + + align:start position:0% +reintroduce or review some terminology + + + align:start position:0% +reintroduce or review some terminology +that goes along with functions that + + align:start position:0% +that goes along with functions that + + + align:start position:0% +that goes along with functions that +you know will be the + + align:start position:0% +you know will be the + + + align:start position:0% +you know will be the +precise + + align:start position:0% +precise + + + align:start position:0% +precise +uh meaning of this pairing off business + + align:start position:0% +uh meaning of this pairing off business + + + align:start position:0% +uh meaning of this pairing off business +that i'm writing here so + + align:start position:0% +that i'm writing here so + + + align:start position:0% +that i'm writing here so +but just uh with an eye towards the + + align:start position:0% +but just uh with an eye towards the + + + align:start position:0% +but just uh with an eye towards the +future this is why i'm + + align:start position:0% +future this is why i'm + + + align:start position:0% +future this is why i'm +reviewing some of these + + align:start position:0% +reviewing some of these + + + align:start position:0% +reviewing some of these +some of this terminology related to + + align:start position:0% +some of this terminology related to + + + align:start position:0% +some of this terminology related to +functions so + + align:start position:0% + + + + align:start position:0% + +so brief review of some terminology for + + align:start position:0% +so brief review of some terminology for + + + align:start position:0% +so brief review of some terminology for +functions so let me just recall that + + align:start position:0% + + + + align:start position:0% + +if a and b are sets + + align:start position:0% +if a and b are sets + + + align:start position:0% +if a and b are sets +then + + align:start position:0% + + + + align:start position:0% + +function f + + align:start position:0% + + + + align:start position:0% + +a b so a function's usually written as f + + align:start position:0% +a b so a function's usually written as f + + + align:start position:0% +a b so a function's usually written as f +colon a arrow to b meaning it takes + + align:start position:0% +colon a arrow to b meaning it takes + + + align:start position:0% +colon a arrow to b meaning it takes +elements from a into elements from b + + align:start position:0% +elements from a into elements from b + + + align:start position:0% +elements from a into elements from b +this is + + align:start position:0% + + + + align:start position:0% + +a mapping that + + align:start position:0% + + + + align:start position:0% + +or if you like an assignment + + align:start position:0% + + + + align:start position:0% + +that assigns to each x + + align:start position:0% +that assigns to each x + + + align:start position:0% +that assigns to each x +in a + + align:start position:0% + + + + align:start position:0% + +a unique element + + align:start position:0% + + + + align:start position:0% + +which we denote f of x + + align:start position:0% +which we denote f of x + + + align:start position:0% +which we denote f of x +and b okay so one single input x + + align:start position:0% +and b okay so one single input x + + + align:start position:0% +and b okay so one single input x +gives me a single output + + align:start position:0% +gives me a single output + + + align:start position:0% +gives me a single output +um an input does not give me three + + align:start position:0% +um an input does not give me three + + + align:start position:0% +um an input does not give me three +outputs now this is what one would call + + align:start position:0% +outputs now this is what one would call + + + align:start position:0% +outputs now this is what one would call +a naive definition probably not + + align:start position:0% +a naive definition probably not + + + align:start position:0% +a naive definition probably not +necessarily completely unambiguous but + + align:start position:0% +necessarily completely unambiguous but + + + align:start position:0% +necessarily completely unambiguous but +for us this suffices in the textbook you + + align:start position:0% +for us this suffices in the textbook you + + + align:start position:0% +for us this suffices in the textbook you +can look up + + align:start position:0% +can look up + + + align:start position:0% +can look up +a function is + + align:start position:0% +a function is + + + align:start position:0% +a function is +unambiguously defined or + + align:start position:0% +unambiguously defined or + + + align:start position:0% +unambiguously defined or +as a subset of the cartesian product of + + align:start position:0% +as a subset of the cartesian product of + + + align:start position:0% +as a subset of the cartesian product of +a and b + + align:start position:0% +a and b + + + align:start position:0% +a and b +which you would recognize as essentially + + align:start position:0% +which you would recognize as essentially + + + align:start position:0% +which you would recognize as essentially +describing the graph of the function but + + align:start position:0% +describing the graph of the function but + + + align:start position:0% +describing the graph of the function but +then you never use that definition of + + align:start position:0% +then you never use that definition of + + + align:start position:0% +then you never use that definition of +again + + align:start position:0% +again + + + align:start position:0% +again +and you essentially use this definition + + align:start position:0% +and you essentially use this definition + + + align:start position:0% +and you essentially use this definition +uh when you think about functions + + align:start position:0% +uh when you think about functions + + + align:start position:0% +uh when you think about functions +and when you prove properties of + + align:start position:0% +and when you prove properties of + + + align:start position:0% +and when you prove properties of +functions so + + align:start position:0% +functions so + + + align:start position:0% +functions so +this we will just take as our definition + + align:start position:0% +this we will just take as our definition + + + align:start position:0% +this we will just take as our definition +and it will be unambiguous uh + + align:start position:0% +and it will be unambiguous uh + + + align:start position:0% +and it will be unambiguous uh +enough for us + + align:start position:0% +enough for us + + + align:start position:0% +enough for us +so + + align:start position:0% + + + + align:start position:0% + +let f be a function from a to b + + align:start position:0% + + + + align:start position:0% + +if c is a subset of a + + align:start position:0% + + + + align:start position:0% + +we define + + align:start position:0% +we define + + + align:start position:0% +we define +a set so this is f of capital c so c is + + align:start position:0% +a set so this is f of capital c so c is + + + align:start position:0% +a set so this is f of capital c so c is +not an element of a it's a subset of a + + align:start position:0% +not an element of a it's a subset of a + + + align:start position:0% +not an element of a it's a subset of a +this is a + + align:start position:0% +this is a + + + align:start position:0% +this is a +subset of b + + align:start position:0% +subset of b + + + align:start position:0% +subset of b +this is + + align:start position:0% + + + + align:start position:0% + +let me write it slightly differently + + align:start position:0% +let me write it slightly differently + + + align:start position:0% +let me write it slightly differently +here this is a set of all y and b such + + align:start position:0% +here this is a set of all y and b such + + + align:start position:0% +here this is a set of all y and b such +that + + align:start position:0% +that + + + align:start position:0% +that +there exists an x and c + + align:start position:0% + + + + align:start position:0% + +such that y equals to f of x + + align:start position:0% +such that y equals to f of x + + + align:start position:0% +such that y equals to f of x +and + + align:start position:0% +and + + + align:start position:0% +and +i could write this a little more + + align:start position:0% +i could write this a little more + + + align:start position:0% +i could write this a little more +efficiently as this is the set of all + + align:start position:0% +efficiently as this is the set of all + + + align:start position:0% +efficiently as this is the set of all +elements f of x + + align:start position:0% +elements f of x + + + align:start position:0% +elements f of x +as x + + align:start position:0% +as x + + + align:start position:0% +as x +ranges over the + + align:start position:0% + + + + align:start position:0% + +elements of this subset c + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +if d is a subset of b + + align:start position:0% + + + + align:start position:0% + +we define + + align:start position:0% +we define + + + align:start position:0% +we define +the sub the set f inverse of d + + align:start position:0% +the sub the set f inverse of d + + + align:start position:0% +the sub the set f inverse of d +this is the set of guys that get mapped + + align:start position:0% +this is the set of guys that get mapped + + + align:start position:0% +this is the set of guys that get mapped +into d so + + align:start position:0% +into d so + + + align:start position:0% +into d so +i should say this is the inverse image + + align:start position:0% +i should say this is the inverse image + + + align:start position:0% +i should say this is the inverse image +of d + + align:start position:0% +of d + + + align:start position:0% +of d +not a + + align:start position:0% +not a + + + align:start position:0% +not a +the inverse of this function f + + align:start position:0% +the inverse of this function f + + + align:start position:0% +the inverse of this function f +okay so you know the inverse + + align:start position:0% +okay so you know the inverse + + + align:start position:0% +okay so you know the inverse +whatever that means for now + + align:start position:0% +whatever that means for now + + + align:start position:0% +whatever that means for now +um + + align:start position:0% +um + + + align:start position:0% +um +does not necessarily always exist so + + align:start position:0% +does not necessarily always exist so + + + align:start position:0% +does not necessarily always exist so +this inverse image of the set d always + + align:start position:0% +this inverse image of the set d always + + + align:start position:0% +this inverse image of the set d always +exists + + align:start position:0% +exists + + + align:start position:0% +exists +this is the set of all elements in a + + align:start position:0% +this is the set of all elements in a + + + align:start position:0% +this is the set of all elements in a +such that + + align:start position:0% + + + + align:start position:0% + +f of x + + align:start position:0% +f of x + + + align:start position:0% +f of x +is in d + + align:start position:0% +is in d + + + align:start position:0% +is in d +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +for example + + align:start position:0% + + + + align:start position:0% + +let me + + align:start position:0% +let me + + + align:start position:0% +let me +uh + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +one two three four + + align:start position:0% +one two three four + + + align:start position:0% +one two three four +and + + align:start position:0% + + + + align:start position:0% + +a b + + align:start position:0% +a b + + + align:start position:0% +a b +c d + + align:start position:0% +c d + + + align:start position:0% +c d +and let's suppose + + align:start position:0% +and let's suppose + + + align:start position:0% +and let's suppose +1 goes to a + + align:start position:0% +1 goes to a + + + align:start position:0% +1 goes to a +2 goes to a + + align:start position:0% +2 goes to a + + + align:start position:0% +2 goes to a +3 goes to c + + align:start position:0% +3 goes to c + + + align:start position:0% +3 goes to c +4 goes to d + + align:start position:0% +4 goes to d + + + align:start position:0% +4 goes to d +ok + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +f of the set one two this is where what + + align:start position:0% +f of the set one two this is where what + + + align:start position:0% +f of the set one two this is where what +is the set that gets + + align:start position:0% +is the set that gets + + + align:start position:0% +is the set that gets +so this is the subset of so this should + + align:start position:0% +so this is the subset of so this should + + + align:start position:0% +so this is the subset of so this should +be you should think of as b + + align:start position:0% +be you should think of as b + + + align:start position:0% +be you should think of as b +a b and c uh and d and then one two and + + align:start position:0% +a b and c uh and d and then one two and + + + align:start position:0% +a b and c uh and d and then one two and +three this is a + + align:start position:0% +three this is a + + + align:start position:0% +three this is a +so f of + + align:start position:0% +so f of + + + align:start position:0% +so f of +the set of one two so one gets mapped to + + align:start position:0% +the set of one two so one gets mapped to + + + align:start position:0% +the set of one two so one gets mapped to +a two gets mapped to a so this is just + + align:start position:0% +a two gets mapped to a so this is just + + + align:start position:0% +a two gets mapped to a so this is just +the set + + align:start position:0% +the set + + + align:start position:0% +the set +two + + align:start position:0% +two + + + align:start position:0% +two +f of + + align:start position:0% +f of + + + align:start position:0% +f of +the set uh let's go with one + + align:start position:0% +the set uh let's go with one + + + align:start position:0% +the set uh let's go with one +and three + + align:start position:0% +and three + + + align:start position:0% +and three +one gets mapped to a + + align:start position:0% +one gets mapped to a + + + align:start position:0% +one gets mapped to a +so this should be + + align:start position:0% +so this should be + + + align:start position:0% +so this should be +a + + align:start position:0% +a + + + align:start position:0% +a +one gets mapped to a + + align:start position:0% +one gets mapped to a + + + align:start position:0% +one gets mapped to a +and three gets maps gets mapped to c + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so a couple of inverse images + + align:start position:0% +and so a couple of inverse images + + + align:start position:0% +and so a couple of inverse images +if i look at the inverse image of a + + align:start position:0% + + + + align:start position:0% + +this is equal to the set of all guys + + align:start position:0% +this is equal to the set of all guys + + + align:start position:0% +this is equal to the set of all guys +that map to a + + align:start position:0% +that map to a + + + align:start position:0% +that map to a +this is well one maps to a + + align:start position:0% +this is well one maps to a + + + align:start position:0% +this is well one maps to a +and two maps to a so this is one two + + align:start position:0% + + + + align:start position:0% + +now if i look at the inverse image of + + align:start position:0% +now if i look at the inverse image of + + + align:start position:0% +now if i look at the inverse image of +a + + align:start position:0% +a + + + align:start position:0% +a +c + + align:start position:0% +c + + + align:start position:0% +c +d + + align:start position:0% +d + + + align:start position:0% +d +what elements get mapped to a c and d + + align:start position:0% +what elements get mapped to a c and d + + + align:start position:0% +what elements get mapped to a c and d +well one and two get mapped to a + + align:start position:0% +well one and two get mapped to a + + + align:start position:0% +well one and two get mapped to a +three gets mapped to c four gets mapped + + align:start position:0% +three gets mapped to c four gets mapped + + + align:start position:0% +three gets mapped to c four gets mapped +to d so everything maps into a c and d + + align:start position:0% +to d so everything maps into a c and d + + + align:start position:0% +to d so everything maps into a c and d +so this is just the original set + + align:start position:0% +so this is just the original set + + + align:start position:0% +so this is just the original set +or the set a one two three four + + align:start position:0% +or the set a one two three four + + + align:start position:0% +or the set a one two three four +okay + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% + + + + align:start position:0% + +some more terminology + + align:start position:0% +some more terminology + + + align:start position:0% +some more terminology +and this is what we will mean by + + align:start position:0% +and this is what we will mean by + + + align:start position:0% +and this is what we will mean by +when two sets can be paired off + + align:start position:0% +when two sets can be paired off + + + align:start position:0% +when two sets can be paired off +or this makes that more precise + + align:start position:0% + + + + align:start position:0% + +let f be a function from a to b + + align:start position:0% + + + + align:start position:0% + +we say that f is + + align:start position:0% + + + + align:start position:0% + +injective + + align:start position:0% +injective + + + align:start position:0% +injective +or + + align:start position:0% +or + + + align:start position:0% +or +i'll write one to one should be + + align:start position:0% +i'll write one to one should be + + + align:start position:0% +i'll write one to one should be +read one to one + + align:start position:0% + + + + align:start position:0% + +if f satisfies the following property + + align:start position:0% + + + + align:start position:0% + +f of x one equals f of x two + + align:start position:0% + + + + align:start position:0% + +implies + + align:start position:0% +implies + + + align:start position:0% +implies +x one equals x2 + + align:start position:0% +x one equals x2 + + + align:start position:0% +x one equals x2 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so injective or one to one means if i + + align:start position:0% +so injective or one to one means if i + + + align:start position:0% +so injective or one to one means if i +take two different + + align:start position:0% +take two different + + + align:start position:0% +take two different +uh inputs i get two different outputs + + align:start position:0% +uh inputs i get two different outputs + + + align:start position:0% +uh inputs i get two different outputs +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's essentially what this means i + + align:start position:0% +that's essentially what this means i + + + align:start position:0% +that's essentially what this means i +mean taking the + + align:start position:0% + + + + align:start position:0% + +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +so equivalently + + align:start position:0% + + + + align:start position:0% + +from a logical standpoint + + align:start position:0% + + + + align:start position:0% + +this statement implying this statement + + align:start position:0% +this statement implying this statement + + + align:start position:0% +this statement implying this statement +is equivalent to the negation of this + + align:start position:0% +is equivalent to the negation of this + + + align:start position:0% +is equivalent to the negation of this +statement implying the negation of this + + align:start position:0% +statement implying the negation of this + + + align:start position:0% +statement implying the negation of this +statement so equivalently this means x + + align:start position:0% +statement so equivalently this means x + + + align:start position:0% +statement so equivalently this means x +not equal to x2 + + align:start position:0% +not equal to x2 + + + align:start position:0% +not equal to x2 +implies f of x1 + + align:start position:0% +implies f of x1 + + + align:start position:0% +implies f of x1 +not equal to f of x2 so maybe this is + + align:start position:0% +not equal to f of x2 so maybe this is + + + align:start position:0% +not equal to f of x2 so maybe this is +clear if i were to define f as injective + + align:start position:0% +clear if i were to define f as injective + + + align:start position:0% +clear if i were to define f as injective +if it satisfies this property + + align:start position:0% +if it satisfies this property + + + align:start position:0% +if it satisfies this property +um maybe that would have been clear that + + align:start position:0% +um maybe that would have been clear that + + + align:start position:0% +um maybe that would have been clear that +you know f takes two different + + align:start position:0% +you know f takes two different + + + align:start position:0% +you know f takes two different +elements to two different elements + + align:start position:0% + + + + align:start position:0% + +but this condition here is typically + + align:start position:0% +but this condition here is typically + + + align:start position:0% +but this condition here is typically +easier to verify or at least simpler to + + align:start position:0% +easier to verify or at least simpler to + + + align:start position:0% +easier to verify or at least simpler to +state and verify + + align:start position:0% + + + + align:start position:0% + +so f is surjective + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +onto + + align:start position:0% +onto + + + align:start position:0% +onto +if + + align:start position:0% + + + + align:start position:0% + +the image of a + + align:start position:0% +the image of a + + + align:start position:0% +the image of a +is b + + align:start position:0% +is b + + + align:start position:0% +is b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +let me write that statement out a little + + align:start position:0% +let me write that statement out a little + + + align:start position:0% +let me write that statement out a little +bit more everything in the set b + + align:start position:0% +bit more everything in the set b + + + align:start position:0% +bit more everything in the set b +gets mapped to by something from a + + align:start position:0% +gets mapped to by something from a + + + align:start position:0% +gets mapped to by something from a +so + + align:start position:0% + + + + align:start position:0% + +so equivalently this says that uh + + align:start position:0% +so equivalently this says that uh + + + align:start position:0% +so equivalently this says that uh +for all y and b + + align:start position:0% +for all y and b + + + align:start position:0% +for all y and b +there exists an x and a + + align:start position:0% +there exists an x and a + + + align:start position:0% +there exists an x and a +so that + + align:start position:0% + + + + align:start position:0% + +f of x equals y + + align:start position:0% +f of x equals y + + + align:start position:0% +f of x equals y +okay + + align:start position:0% + + + + align:start position:0% + +f is + + align:start position:0% + + + + align:start position:0% + +bijective + + align:start position:0% + + + + align:start position:0% + +if f is + + align:start position:0% +if f is + + + align:start position:0% +if f is +one to one and onto so + + align:start position:0% +one to one and onto so + + + align:start position:0% +one to one and onto so +it's f is bijective if it's both + + align:start position:0% +it's f is bijective if it's both + + + align:start position:0% +it's f is bijective if it's both +injective and surjective + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +for example this map that we just drew + + align:start position:0% +for example this map that we just drew + + + align:start position:0% +for example this map that we just drew +over here that sends 1 to a + + align:start position:0% +over here that sends 1 to a + + + align:start position:0% +over here that sends 1 to a +2 to b + + align:start position:0% +2 to b + + + align:start position:0% +2 to b +i mean 2 to a 3 to c 4 to d + + align:start position:0% +i mean 2 to a 3 to c 4 to d + + + align:start position:0% +i mean 2 to a 3 to c 4 to d +this is neither injective nor surjective + + align:start position:0% +this is neither injective nor surjective + + + align:start position:0% +this is neither injective nor surjective +it's not injective because it takes two + + align:start position:0% +it's not injective because it takes two + + + align:start position:0% +it's not injective because it takes two +different elements + + align:start position:0% +different elements + + + align:start position:0% +different elements +to + + align:start position:0% +to + + + align:start position:0% +to +image in b namely a so it takes one and + + align:start position:0% +image in b namely a so it takes one and + + + align:start position:0% +image in b namely a so it takes one and +two to a + + align:start position:0% +two to a + + + align:start position:0% +two to a +it's not surjective because nothing gets + + align:start position:0% +it's not surjective because nothing gets + + + align:start position:0% +it's not surjective because nothing gets +mapped to the element b + + align:start position:0% +mapped to the element b + + + align:start position:0% +mapped to the element b +uh + + align:start position:0% +uh + + + align:start position:0% +uh +here so + + align:start position:0% + + + + align:start position:0% + +so we've seen that's not subjective of + + align:start position:0% +so we've seen that's not subjective of + + + align:start position:0% +so we've seen that's not subjective of +course this map if i take + + align:start position:0% +course this map if i take + + + align:start position:0% +course this map if i take +again imagine this is one two three + + align:start position:0% + + + + align:start position:0% + +a b c d + + align:start position:0% +a b c d + + + align:start position:0% +a b c d +this map + + align:start position:0% +this map + + + align:start position:0% +this map +here + + align:start position:0% +here + + + align:start position:0% +here +this function here that takes 1 to a 2 + + align:start position:0% +this function here that takes 1 to a 2 + + + align:start position:0% +this function here that takes 1 to a 2 +to b 3 to c + + align:start position:0% +to b 3 to c + + + align:start position:0% +to b 3 to c +this is actually injective but not + + align:start position:0% +this is actually injective but not + + + align:start position:0% +this is actually injective but not +surjective + + align:start position:0% + + + + align:start position:0% + +and then of course we could change this + + align:start position:0% +and then of course we could change this + + + align:start position:0% +and then of course we could change this +slightly + + align:start position:0% +slightly + + + align:start position:0% +slightly +and + + align:start position:0% + + + + align:start position:0% + +one goes to a two goes to b and + + align:start position:0% +one goes to a two goes to b and + + + align:start position:0% +one goes to a two goes to b and +three goes to b + + align:start position:0% +three goes to b + + + align:start position:0% +three goes to b +then this is + + align:start position:0% +then this is + + + align:start position:0% +then this is +third objective but not + + align:start position:0% + + + + align:start position:0% + +injective + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +the map that sends + + align:start position:0% +the map that sends + + + align:start position:0% +the map that sends +um + + align:start position:0% + + + + align:start position:0% + +let's switch sides here + + align:start position:0% +let's switch sides here + + + align:start position:0% +let's switch sides here +a b and c + + align:start position:0% +a b and c + + + align:start position:0% +a b and c +one two three + + align:start position:0% +one two three + + + align:start position:0% +one two three +a to one b to two c to three this is + + align:start position:0% +a to one b to two c to three this is + + + align:start position:0% +a to one b to two c to three this is +a bijection + + align:start position:0% + + + + align:start position:0% + +biject div so if i say something's an + + align:start position:0% +biject div so if i say something's an + + + align:start position:0% +biject div so if i say something's an +injection or surjection or bijection + + align:start position:0% +injection or surjection or bijection + + + align:start position:0% +injection or surjection or bijection +that just means it's a map that is + + align:start position:0% +that just means it's a map that is + + + align:start position:0% +that just means it's a map that is +injected surjective or bijective + + align:start position:0% + + + + align:start position:0% + +respectively + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and now + + align:start position:0% + + + + align:start position:0% + +definition + + align:start position:0% +definition + + + align:start position:0% +definition +so this is really there's not much to + + align:start position:0% +so this is really there's not much to + + + align:start position:0% +so this is really there's not much to +this definition but just + + align:start position:0% +this definition but just + + + align:start position:0% +this definition but just +defining a couple of + + align:start position:0% + + + + align:start position:0% + +functions that are related to a given + + align:start position:0% +functions that are related to a given + + + align:start position:0% +functions that are related to a given +function + + align:start position:0% +function + + + align:start position:0% +function +if f goes from a to b + + align:start position:0% +if f goes from a to b + + + align:start position:0% +if f goes from a to b +g goes from + + align:start position:0% + + + + align:start position:0% + +b to c + + align:start position:0% + + + + align:start position:0% + +the composition g of f + + align:start position:0% +the composition g of f + + + align:start position:0% +the composition g of f +is the function which goes from a to c + + align:start position:0% + + + + align:start position:0% + +is defined + + align:start position:0% +is defined + + + align:start position:0% +is defined +by + + align:start position:0% +by + + + align:start position:0% +by +g of f + + align:start position:0% +g of f + + + align:start position:0% +g of f +of x equals g + + align:start position:0% +of x equals g + + + align:start position:0% +of x equals g +of + + align:start position:0% +of + + + align:start position:0% +of +f x + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +if f + + align:start position:0% + + + + align:start position:0% + +is bijective + + align:start position:0% + + + + align:start position:0% + +so this is the composition of two + + align:start position:0% +so this is the composition of two + + + align:start position:0% +so this is the composition of two +functions i didn't write the word + + align:start position:0% +functions i didn't write the word + + + align:start position:0% +functions i didn't write the word +composition but this is + + align:start position:0% +composition but this is + + + align:start position:0% +composition but this is +g of f means the composition or is + + align:start position:0% +g of f means the composition or is + + + align:start position:0% +g of f means the composition or is +referred to as a composition if f is + + align:start position:0% +referred to as a composition if f is + + + align:start position:0% +referred to as a composition if f is +bijective + + align:start position:0% + + + + align:start position:0% + +then we define + + align:start position:0% +then we define + + + align:start position:0% +then we define +the inverse function to f + + align:start position:0% + + + + align:start position:0% + +b + + align:start position:0% +b + + + align:start position:0% +b +to a + + align:start position:0% +to a + + + align:start position:0% +to a +by + + align:start position:0% +by + + + align:start position:0% +by +the following + + align:start position:0% + + + + align:start position:0% + +if y is in b + + align:start position:0% +if y is in b + + + align:start position:0% +if y is in b +then + + align:start position:0% +then + + + align:start position:0% +then +f inverse of y and a + + align:start position:0% +f inverse of y and a + + + align:start position:0% +f inverse of y and a +is the + + align:start position:0% + + + + align:start position:0% + +unique + + align:start position:0% + + + + align:start position:0% + +element in a + + align:start position:0% +element in a + + + align:start position:0% +element in a +such that + + align:start position:0% + + + + align:start position:0% + +if i take this element stick it into f i + + align:start position:0% +if i take this element stick it into f i + + + align:start position:0% +if i take this element stick it into f i +get back y + + align:start position:0% +get back y + + + align:start position:0% +get back y +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +inverse the inverse of a function only + + align:start position:0% +inverse the inverse of a function only + + + align:start position:0% +inverse the inverse of a function only +exists for bijective + + align:start position:0% +exists for bijective + + + align:start position:0% +exists for bijective +functions + + align:start position:0% +functions + + + align:start position:0% +functions +or at least is only defined for biject's + + align:start position:0% +or at least is only defined for biject's + + + align:start position:0% +or at least is only defined for biject's +bijective functions + + align:start position:0% +bijective functions + + + align:start position:0% +bijective functions +you know keep that in mind don't confuse + + align:start position:0% +you know keep that in mind don't confuse + + + align:start position:0% +you know keep that in mind don't confuse +that with the + + align:start position:0% +that with the + + + align:start position:0% +that with the +inverse image of sets okay + + align:start position:0% +inverse image of sets okay + + + align:start position:0% +inverse image of sets okay +although those two + + align:start position:0% +although those two + + + align:start position:0% +although those two +notations look the same you have an + + align:start position:0% +notations look the same you have an + + + align:start position:0% +notations look the same you have an +inverse f to the minus 1 + + align:start position:0% + + + + align:start position:0% + +after the minus 1 + + align:start position:0% +after the minus 1 + + + align:start position:0% +after the minus 1 +if it's a function that is the inverse + + align:start position:0% +if it's a function that is the inverse + + + align:start position:0% +if it's a function that is the inverse +function however if i'm taking f to the + + align:start position:0% +function however if i'm taking f to the + + + align:start position:0% +function however if i'm taking f to the +minus 1 of a set that means the inverse + + align:start position:0% +minus 1 of a set that means the inverse + + + align:start position:0% +minus 1 of a set that means the inverse +image of that set as defined over there + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +bijections meaning bijective functions + + align:start position:0% +bijections meaning bijective functions + + + align:start position:0% +bijections meaning bijective functions +will be + + align:start position:0% +will be + + + align:start position:0% +will be +what we mean when we say two sets can be + + align:start position:0% +what we mean when we say two sets can be + + + align:start position:0% +what we mean when we say two sets can be +paired off + + align:start position:0% +paired off + + + align:start position:0% +paired off +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it's what we mean when we + + align:start position:0% +it's what we mean when we + + + align:start position:0% +it's what we mean when we +or at least what + + align:start position:0% +or at least what + + + align:start position:0% +or at least what +cantor's + + align:start position:0% +cantor's + + + align:start position:0% +cantor's +and to answer to that original question + + align:start position:0% +and to answer to that original question + + + align:start position:0% +and to answer to that original question +was + + align:start position:0% +was + + + align:start position:0% +was +uh + + align:start position:0% +uh + + + align:start position:0% +uh +when do two sets have the same size so + + align:start position:0% + + + + align:start position:0% + +this is the notion of cardinality + + align:start position:0% +this is the notion of cardinality + + + align:start position:0% +this is the notion of cardinality +that i alluded to + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +two sets we say two sets a + + align:start position:0% +two sets we say two sets a + + + align:start position:0% +two sets we say two sets a +and b + + align:start position:0% + + + + align:start position:0% + +have the same + + align:start position:0% + + + + align:start position:0% + +cardinality + + align:start position:0% + + + + align:start position:0% + +if there exists a bijection + + align:start position:0% +if there exists a bijection + + + align:start position:0% +if there exists a bijection +or a bijective function + + align:start position:0% + + + + align:start position:0% + +f + + align:start position:0% +f + + + align:start position:0% +f +from a to b + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +uh + + align:start position:0% + + + + align:start position:0% + +so let me just + + align:start position:0% + + + + align:start position:0% + +make uh some notation here so this is + + align:start position:0% +make uh some notation here so this is + + + align:start position:0% +make uh some notation here so this is +not really + + align:start position:0% +not really + + + align:start position:0% +not really +um + + align:start position:0% +um + + + align:start position:0% +um +you know new objects i'm defining or + + align:start position:0% +you know new objects i'm defining or + + + align:start position:0% +you know new objects i'm defining or +operations this is just some notation so + + align:start position:0% +operations this is just some notation so + + + align:start position:0% +operations this is just some notation so +when two sets have the same cardinality + + align:start position:0% +when two sets have the same cardinality + + + align:start position:0% +when two sets have the same cardinality +uh we write + + align:start position:0% + + + + align:start position:0% + +so this is just a shorthand way of + + align:start position:0% +so this is just a shorthand way of + + + align:start position:0% +so this is just a shorthand way of +writing that two functions have the same + + align:start position:0% +writing that two functions have the same + + + align:start position:0% +writing that two functions have the same +cardinality you should not + + align:start position:0% +cardinality you should not + + + align:start position:0% +cardinality you should not +necessarily think this means taking the + + align:start position:0% +necessarily think this means taking the + + + align:start position:0% +necessarily think this means taking the +absolute value of a set okay that that + + align:start position:0% +absolute value of a set okay that that + + + align:start position:0% +absolute value of a set okay that that +doesn't mean anything + + align:start position:0% +doesn't mean anything + + + align:start position:0% +doesn't mean anything +all right this is just shorthand + + align:start position:0% +all right this is just shorthand + + + align:start position:0% +all right this is just shorthand +notation for saying two sets have the + + align:start position:0% +notation for saying two sets have the + + + align:start position:0% +notation for saying two sets have the +same cardinality + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +a has the same cardinality as + + align:start position:0% +a has the same cardinality as + + + align:start position:0% +a has the same cardinality as +the set one two three up to n + + align:start position:0% + + + + align:start position:0% + +we write + + align:start position:0% +we write + + + align:start position:0% +we write +a equals n + + align:start position:0% +a equals n + + + align:start position:0% +a equals n +okay that's just shorthand for saying + + align:start position:0% +okay that's just shorthand for saying + + + align:start position:0% +okay that's just shorthand for saying +that a set has the same cardinality as + + align:start position:0% +that a set has the same cardinality as + + + align:start position:0% +that a set has the same cardinality as +the natural numbers up to n + + align:start position:0% + + + + align:start position:0% + +we write a + + align:start position:0% +we write a + + + align:start position:0% +we write a +so if + + align:start position:0% + + + + align:start position:0% + +there exists an injective + + align:start position:0% +there exists an injective + + + align:start position:0% +there exists an injective +function or i will often say either + + align:start position:0% +function or i will often say either + + + align:start position:0% +function or i will often say either +function or map i did + + align:start position:0% +function or map i did + + + align:start position:0% +function or map i did +you know you should take those as uh + + align:start position:0% +you know you should take those as uh + + + align:start position:0% +you know you should take those as uh +synonymous + + align:start position:0% +synonymous + + + align:start position:0% +synonymous +there exists an inject injective + + align:start position:0% +there exists an inject injective + + + align:start position:0% +there exists an inject injective +function f + + align:start position:0% +function f + + + align:start position:0% +function f +if there exists an injective function f + + align:start position:0% +if there exists an injective function f + + + align:start position:0% +if there exists an injective function f +from a to b + + align:start position:0% + + + + align:start position:0% + +we write + + align:start position:0% + + + + align:start position:0% + +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +again do not read this as taking the + + align:start position:0% +again do not read this as taking the + + + align:start position:0% +again do not read this as taking the +absolute value of some set + + align:start position:0% +absolute value of some set + + + align:start position:0% +absolute value of some set +and that absolute value is less than or + + align:start position:0% +and that absolute value is less than or + + + align:start position:0% +and that absolute value is less than or +equal to the absolute value of the other + + align:start position:0% +equal to the absolute value of the other + + + align:start position:0% +equal to the absolute value of the other +set because that's meaningless we + + align:start position:0% +set because that's meaningless we + + + align:start position:0% +set because that's meaningless we +haven't + + align:start position:0% +haven't + + + align:start position:0% +haven't +said what that means even + + align:start position:0% + + + + align:start position:0% + +this is just shorthand notation + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +if a + + align:start position:0% +if a + + + align:start position:0% +if a +if there exists an injection from a to b + + align:start position:0% + + + + align:start position:0% + +but they don't have the same cardinality + + align:start position:0% + + + + align:start position:0% + +we write + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +okay so even though this notation of + + align:start position:0% +okay so even though this notation of + + + align:start position:0% +okay so even though this notation of +these absolute value things being on the + + align:start position:0% +these absolute value things being on the + + + align:start position:0% +these absolute value things being on the +outside of the set + + align:start position:0% +outside of the set + + + align:start position:0% +outside of the set +makes you think absolute value + + align:start position:0% + + + + align:start position:0% + +or shouldn't be interpreted as absolute + + align:start position:0% +or shouldn't be interpreted as absolute + + + align:start position:0% +or shouldn't be interpreted as absolute +value it's okay to kind of think as + + align:start position:0% +value it's okay to kind of think as + + + align:start position:0% +value it's okay to kind of think as +you know + + align:start position:0% +you know + + + align:start position:0% +you know +a certain ordering being there as one as + + align:start position:0% +a certain ordering being there as one as + + + align:start position:0% +a certain ordering being there as one as +sort of a having smaller size than b + + align:start position:0% +sort of a having smaller size than b + + + align:start position:0% +sort of a having smaller size than b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we write this because there being a + + align:start position:0% +we write this because there being a + + + align:start position:0% +we write this because there being a +injection from one set to the other + + align:start position:0% +injection from one set to the other + + + align:start position:0% +injection from one set to the other +kind of means i can pair off + + align:start position:0% +kind of means i can pair off + + + align:start position:0% +kind of means i can pair off +elements of a + + align:start position:0% +elements of a + + + align:start position:0% +elements of a +with some elements of b + + align:start position:0% +with some elements of b + + + align:start position:0% +with some elements of b +okay maybe i don't get all of the + + align:start position:0% +okay maybe i don't get all of the + + + align:start position:0% +okay maybe i don't get all of the +elements of b but i can pair off some of + + align:start position:0% +elements of b but i can pair off some of + + + align:start position:0% +elements of b but i can pair off some of +the elements of a with some of the + + align:start position:0% +the elements of a with some of the + + + align:start position:0% +the elements of a with some of the +elements of b for example that first map + + align:start position:0% +elements of b for example that first map + + + align:start position:0% +elements of b for example that first map +we wrote up there + + align:start position:0% +we wrote up there + + + align:start position:0% +we wrote up there +yeah that says that the set one two + + align:start position:0% +yeah that says that the set one two + + + align:start position:0% +yeah that says that the set one two +three + + align:start position:0% +three + + + align:start position:0% +three +uh in size is less than or equal to the + + align:start position:0% +uh in size is less than or equal to the + + + align:start position:0% +uh in size is less than or equal to the +size of abcd because we found an + + align:start position:0% +size of abcd because we found an + + + align:start position:0% +size of abcd because we found an +injection an injective map from the + + align:start position:0% +injection an injective map from the + + + align:start position:0% +injection an injective map from the +first set to the second + + align:start position:0% +first set to the second + + + align:start position:0% +first set to the second +set + + align:start position:0% +set + + + align:start position:0% +set +um this third map would say that + + align:start position:0% +um this third map would say that + + + align:start position:0% +um this third map would say that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the size of the set abc is equal to + + align:start position:0% +the size of the set abc is equal to + + + align:start position:0% +the size of the set abc is equal to +three written here + + align:start position:0% +three written here + + + align:start position:0% +three written here +or shorthand written here + + align:start position:0% +or shorthand written here + + + align:start position:0% +or shorthand written here +okay and in fact + + align:start position:0% + + + + align:start position:0% + +that first map that we wrote up there + + align:start position:0% +that first map that we wrote up there + + + align:start position:0% +that first map that we wrote up there +again + + align:start position:0% +again + + + align:start position:0% +again +uh is + + align:start position:0% +uh is + + + align:start position:0% +uh is +so from first map this says that the set + + align:start position:0% +so from first map this says that the set + + + align:start position:0% +so from first map this says that the set +of one two three + + align:start position:0% +of one two three + + + align:start position:0% +of one two three +uh in our shorthand notation absolute + + align:start position:0% +uh in our shorthand notation absolute + + + align:start position:0% +uh in our shorthand notation absolute +value has is less than the size of abcd + + align:start position:0% +value has is less than the size of abcd + + + align:start position:0% +value has is less than the size of abcd +okay so don't think of + + align:start position:0% +okay so don't think of + + + align:start position:0% +okay so don't think of +these as saying the absolute value it's + + align:start position:0% +these as saying the absolute value it's + + + align:start position:0% +these as saying the absolute value it's +best to maybe think of this as saying + + align:start position:0% +best to maybe think of this as saying + + + align:start position:0% +best to maybe think of this as saying +the size of okay + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +if there exists an injective injective + + align:start position:0% +if there exists an injective injective + + + align:start position:0% +if there exists an injective injective +map from our function from one set to + + align:start position:0% +map from our function from one set to + + + align:start position:0% +map from our function from one set to +another then the size of a is less than + + align:start position:0% +another then the size of a is less than + + + align:start position:0% +another then the size of a is less than +or equal to the size of b + + align:start position:0% +or equal to the size of b + + + align:start position:0% +or equal to the size of b +if the size of a is less than or equal + + align:start position:0% +if the size of a is less than or equal + + + align:start position:0% +if the size of a is less than or equal +to size of b but the size of a and b are + + align:start position:0% +to size of b but the size of a and b are + + + align:start position:0% +to size of b but the size of a and b are +not the same we write the size of a is + + align:start position:0% +not the same we write the size of a is + + + align:start position:0% +not the same we write the size of a is +less than the size of b + + align:start position:0% +less than the size of b + + + align:start position:0% +less than the size of b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so best to think of those + + align:start position:0% +so best to think of those + + + align:start position:0% +so best to think of those +um this absolute value looking thing as + + align:start position:0% +um this absolute value looking thing as + + + align:start position:0% +um this absolute value looking thing as +being shorthand for r for saying the + + align:start position:0% +being shorthand for r for saying the + + + align:start position:0% +being shorthand for r for saying the +words size of + + align:start position:0% +words size of + + + align:start position:0% +words size of +okay + + align:start position:0% + + + + align:start position:0% + +now i'm not going to prove this it goes + + align:start position:0% +now i'm not going to prove this it goes + + + align:start position:0% +now i'm not going to prove this it goes +a little bit beyond + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +scope of this class but let me just say + + align:start position:0% +scope of this class but let me just say + + + align:start position:0% +scope of this class but let me just say +that + + align:start position:0% +that + + + align:start position:0% +that +this uh ordering this inequality + + align:start position:0% +this uh ordering this inequality + + + align:start position:0% +this uh ordering this inequality +these symbols that we're writing + + align:start position:0% +these symbols that we're writing + + + align:start position:0% +these symbols that we're writing +does + + align:start position:0% +does + + + align:start position:0% +does +bear some sort of semblance to the + + align:start position:0% +bear some sort of semblance to the + + + align:start position:0% +bear some sort of semblance to the +ordering of real numbers in that if i + + align:start position:0% +ordering of real numbers in that if i + + + align:start position:0% +ordering of real numbers in that if i +have two real numbers + + align:start position:0% +have two real numbers + + + align:start position:0% +have two real numbers +one is less than or equal to the other + + align:start position:0% +one is less than or equal to the other + + + align:start position:0% +one is less than or equal to the other +and vice versa so a is less than or + + align:start position:0% +and vice versa so a is less than or + + + align:start position:0% +and vice versa so a is less than or +equal to b and b is less than or equal + + align:start position:0% +equal to b and b is less than or equal + + + align:start position:0% +equal to b and b is less than or equal +to a then a must equal b + + align:start position:0% +to a then a must equal b + + + align:start position:0% +to a then a must equal b +that is in fact true also for + + align:start position:0% +that is in fact true also for + + + align:start position:0% +that is in fact true also for +this elementary notion of size of sets + + align:start position:0% +this elementary notion of size of sets + + + align:start position:0% +this elementary notion of size of sets +and this is + + align:start position:0% + + + + align:start position:0% + +i mean you should it shouldn't surprise + + align:start position:0% +i mean you should it shouldn't surprise + + + align:start position:0% +i mean you should it shouldn't surprise +you for + + align:start position:0% +you for + + + align:start position:0% +you for +you know finite sets + + align:start position:0% +you know finite sets + + + align:start position:0% +you know finite sets +um + + align:start position:0% +um + + + align:start position:0% +um +necessarily if if i have + + align:start position:0% + + + + align:start position:0% + +a pairing of a + + align:start position:0% + + + + align:start position:0% + +if a is no bigger than + + align:start position:0% +if a is no bigger than + + + align:start position:0% +if a is no bigger than +uh n and n is no bigger than the size of + + align:start position:0% +uh n and n is no bigger than the size of + + + align:start position:0% +uh n and n is no bigger than the size of +a then a should have n elements + + align:start position:0% +a then a should have n elements + + + align:start position:0% +a then a should have n elements +um but it's + + align:start position:0% +um but it's + + + align:start position:0% +um but it's +takes a little bit more to prove for + + align:start position:0% +takes a little bit more to prove for + + + align:start position:0% +takes a little bit more to prove for +um + + align:start position:0% +um + + + align:start position:0% +um +sets which are not finite so i forgot to + + align:start position:0% +sets which are not finite so i forgot to + + + align:start position:0% +sets which are not finite so i forgot to +write this down we also say that a + + align:start position:0% +write this down we also say that a + + + align:start position:0% +write this down we also say that a +if + + align:start position:0% +if + + + align:start position:0% +if +the size of a is equal to the size of + + align:start position:0% +the size of a is equal to the size of + + + align:start position:0% +the size of a is equal to the size of +this finite set 1 through n we say a + + align:start position:0% + + + + align:start position:0% + +is finite + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this theorem that i'm stating here is + + align:start position:0% +so this theorem that i'm stating here is + + + align:start position:0% +so this theorem that i'm stating here is +the + + align:start position:0% +the + + + align:start position:0% +the +cantor schroeder + + align:start position:0% +cantor schroeder + + + align:start position:0% +cantor schroeder +bernstein + + align:start position:0% + + + + align:start position:0% + +theorem + + align:start position:0% + + + + align:start position:0% + +which states that + + align:start position:0% +which states that + + + align:start position:0% +which states that +if the size of a + + align:start position:0% +if the size of a + + + align:start position:0% +if the size of a +is less than or equal to the size of b + + align:start position:0% +is less than or equal to the size of b + + + align:start position:0% +is less than or equal to the size of b +and the size of b + + align:start position:0% +and the size of b + + + align:start position:0% +and the size of b +is less than or equal to the size of a + + align:start position:0% +is less than or equal to the size of a + + + align:start position:0% +is less than or equal to the size of a +then + + align:start position:0% + + + + align:start position:0% + +size of a equals size of b so + + align:start position:0% +size of a equals size of b so + + + align:start position:0% +size of a equals size of b so +again if you're thinking of these + + align:start position:0% +again if you're thinking of these + + + align:start position:0% +again if you're thinking of these +in the context of + + align:start position:0% +in the context of + + + align:start position:0% +in the context of +real numbers one being less than or + + align:start position:0% +real numbers one being less than or + + + align:start position:0% +real numbers one being less than or +equal to the other and vice versa + + align:start position:0% +equal to the other and vice versa + + + align:start position:0% +equal to the other and vice versa +of course that implies that those two + + align:start position:0% +of course that implies that those two + + + align:start position:0% +of course that implies that those two +real numbers are equal to each other but + + align:start position:0% +real numbers are equal to each other but + + + align:start position:0% +real numbers are equal to each other but +we're not talking about real numbers + + align:start position:0% +we're not talking about real numbers + + + align:start position:0% +we're not talking about real numbers +again this is just shorthand notation + + align:start position:0% +again this is just shorthand notation + + + align:start position:0% +again this is just shorthand notation +for saying there exists a bijective map + + align:start position:0% +for saying there exists a bijective map + + + align:start position:0% +for saying there exists a bijective map +from a to b + + align:start position:0% +from a to b + + + align:start position:0% +from a to b +this means there exists a bijective map + + align:start position:0% +this means there exists a bijective map + + + align:start position:0% +this means there exists a bijective map +from a to this set + + align:start position:0% +from a to this set + + + align:start position:0% +from a to this set +this means there exists an injective map + + align:start position:0% +this means there exists an injective map + + + align:start position:0% +this means there exists an injective map +from a into this from a to this set + + align:start position:0% +from a into this from a to this set + + + align:start position:0% +from a into this from a to this set +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is not a statement about real + + align:start position:0% +so this is not a statement about real + + + align:start position:0% +so this is not a statement about real +numbers this is a statement about + + align:start position:0% +numbers this is a statement about + + + align:start position:0% +numbers this is a statement about +cardinality + + align:start position:0% +cardinality + + + align:start position:0% +cardinality +all right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +you know + + align:start position:0% +you know + + + align:start position:0% +you know +finite sets are sets that you can count + + align:start position:0% +finite sets are sets that you can count + + + align:start position:0% +finite sets are sets that you can count +um if you had in fingers + + align:start position:0% +um if you had in fingers + + + align:start position:0% +um if you had in fingers +now + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% + + + + align:start position:0% + +we would like to be able to define what + + align:start position:0% +we would like to be able to define what + + + align:start position:0% +we would like to be able to define what +it means to be able to count a set + + align:start position:0% +it means to be able to count a set + + + align:start position:0% +it means to be able to count a set +so what i mean by count asset meaning if + + align:start position:0% +so what i mean by count asset meaning if + + + align:start position:0% +so what i mean by count asset meaning if +i had infinite time + + align:start position:0% +i had infinite time + + + align:start position:0% +i had infinite time +i could go + + align:start position:0% +i could go + + + align:start position:0% +i could go +through the set + + align:start position:0% +through the set + + + align:start position:0% +through the set +counting them one two three 4 5 6 7 8 9 + + align:start position:0% +counting them one two three 4 5 6 7 8 9 + + + align:start position:0% +counting them one two three 4 5 6 7 8 9 +10 and so on i don't need to go any more + + align:start position:0% +10 and so on i don't need to go any more + + + align:start position:0% +10 and so on i don't need to go any more +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +but what does that + + align:start position:0% +but what does that + + + align:start position:0% +but what does that +process of counting mean that means for + + align:start position:0% +process of counting mean that means for + + + align:start position:0% +process of counting mean that means for +each element of the set that i'm trying + + align:start position:0% +each element of the set that i'm trying + + + align:start position:0% +each element of the set that i'm trying +to count i can pair it off + + align:start position:0% +to count i can pair it off + + + align:start position:0% +to count i can pair it off +with + + align:start position:0% +with + + + align:start position:0% +with +a natural number one two three and so on + + align:start position:0% +a natural number one two three and so on + + + align:start position:0% +a natural number one two three and so on +so this is how we define + + align:start position:0% +so this is how we define + + + align:start position:0% +so this is how we define +uh countable sets + + align:start position:0% +uh countable sets + + + align:start position:0% +uh countable sets +so + + align:start position:0% + + + + align:start position:0% + +if a has the same size as the natural + + align:start position:0% +if a has the same size as the natural + + + align:start position:0% +if a has the same size as the natural +numbers meaning there exists a bijection + + align:start position:0% +numbers meaning there exists a bijection + + + align:start position:0% +numbers meaning there exists a bijection +from a to + + align:start position:0% +from a to + + + align:start position:0% +from a to +the natural numbers + + align:start position:0% + + + + align:start position:0% + +then we say a is + + align:start position:0% + + + + align:start position:0% + +countably infinite + + align:start position:0% + + + + align:start position:0% + +if a is finite + + align:start position:0% + + + + align:start position:0% + +or accountably + + align:start position:0% +or accountably + + + align:start position:0% +or accountably +i also use a lot of shorthand so + + align:start position:0% +i also use a lot of shorthand so + + + align:start position:0% +i also use a lot of shorthand so +but it's not clever shorthand so you + + align:start position:0% +but it's not clever shorthand so you + + + align:start position:0% +but it's not clever shorthand so you +should just be able to sound what + + align:start position:0% +should just be able to sound what + + + align:start position:0% +should just be able to sound what +like if you just sound that out you'll + + align:start position:0% +like if you just sound that out you'll + + + align:start position:0% +like if you just sound that out you'll +you'll get what word i mean countably uh + + align:start position:0% +you'll get what word i mean countably uh + + + align:start position:0% +you'll get what word i mean countably uh +accountably infinite infinite + + align:start position:0% + + + + align:start position:0% + +we say a is + + align:start position:0% + + + + align:start position:0% + +countable okay + + align:start position:0% +countable okay + + + align:start position:0% +countable okay +so + + align:start position:0% +so + + + align:start position:0% +so +countably infinite means i need all the + + align:start position:0% +countably infinite means i need all the + + + align:start position:0% +countably infinite means i need all the +natural numbers to be able to count off + + align:start position:0% +natural numbers to be able to count off + + + align:start position:0% +natural numbers to be able to count off +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the elements of the set a + + align:start position:0% +the elements of the set a + + + align:start position:0% +the elements of the set a +countable means maybe i stop after some + + align:start position:0% +countable means maybe i stop after some + + + align:start position:0% +countable means maybe i stop after some +point and i've counted all them + + align:start position:0% +point and i've counted all them + + + align:start position:0% +point and i've counted all them +so a is finite or it's countably + + align:start position:0% +so a is finite or it's countably + + + align:start position:0% +so a is finite or it's countably +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +otherwise if a set is not countable we + + align:start position:0% +otherwise if a set is not countable we + + + align:start position:0% +otherwise if a set is not countable we +say it's uncountable + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +let's uh take a look at a couple of + + align:start position:0% +let's uh take a look at a couple of + + + align:start position:0% +let's uh take a look at a couple of +accountable sets that maybe um + + align:start position:0% +accountable sets that maybe um + + + align:start position:0% +accountable sets that maybe um +don't come off as being + + align:start position:0% +don't come off as being + + + align:start position:0% +don't come off as being +accountable + + align:start position:0% +accountable + + + align:start position:0% +accountable +um + + align:start position:0% + + + + align:start position:0% + +set of + + align:start position:0% + + + + align:start position:0% + +actually that's a homework problem + + align:start position:0% +actually that's a homework problem + + + align:start position:0% +actually that's a homework problem +the set of even integers + + align:start position:0% + + + + align:start position:0% + +is countable + + align:start position:0% + + + + align:start position:0% + +the set of + + align:start position:0% + + + + align:start position:0% + +odd so i said integers a minute ago + + align:start position:0% +odd so i said integers a minute ago + + + align:start position:0% +odd so i said integers a minute ago +maybe i should just say natural numbers + + align:start position:0% +maybe i should just say natural numbers + + + align:start position:0% +maybe i should just say natural numbers +the set of odd natural numbers + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +countable + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +in fact + + align:start position:0% + + + + align:start position:0% + +so this is just a side + + align:start position:0% + + + + align:start position:0% + +so these are two + + align:start position:0% +so these are two + + + align:start position:0% +so these are two +disjoint subsets that make up + + align:start position:0% +disjoint subsets that make up + + + align:start position:0% +disjoint subsets that make up +the natural numbers the even and odd + + align:start position:0% +the natural numbers the even and odd + + + align:start position:0% +the natural numbers the even and odd +natural numbers + + align:start position:0% +natural numbers + + + align:start position:0% +natural numbers +and they both have the same size as the + + align:start position:0% +and they both have the same size as the + + + align:start position:0% +and they both have the same size as the +set that they make up + + align:start position:0% +set that they make up + + + align:start position:0% +set that they make up +so it + + align:start position:0% +so it + + + align:start position:0% +so it +you know it's + + align:start position:0% +you know it's + + + align:start position:0% +you know it's +almost like saying the cardinality of + + align:start position:0% +almost like saying the cardinality of + + + align:start position:0% +almost like saying the cardinality of +the natural numbers is twice the + + align:start position:0% +the natural numbers is twice the + + + align:start position:0% +the natural numbers is twice the +cardinality of the natural numbers since + + align:start position:0% +cardinality of the natural numbers since + + + align:start position:0% +cardinality of the natural numbers since +it's + + align:start position:0% +it's + + + align:start position:0% +it's +you would think that the size of n + + align:start position:0% +you would think that the size of n + + + align:start position:0% +you would think that the size of n +should be the size of this set plus the + + align:start position:0% +should be the size of this set plus the + + + align:start position:0% +should be the size of this set plus the +size of this set since they're + + align:start position:0% +size of this set since they're + + + align:start position:0% +size of this set since they're +destroying and they make up the set + + align:start position:0% +destroying and they make up the set + + + align:start position:0% +destroying and they make up the set +um + + align:start position:0% + + + + align:start position:0% + +but you know that that's not how + + align:start position:0% +but you know that that's not how + + + align:start position:0% +but you know that that's not how +cardinality works + + align:start position:0% +cardinality works + + + align:start position:0% +cardinality works +um + + align:start position:0% +um + + + align:start position:0% +um +you know you don't just add + + align:start position:0% +you know you don't just add + + + align:start position:0% +you know you don't just add +cardinalities to get the + + align:start position:0% +cardinalities to get the + + + align:start position:0% +cardinalities to get the +cardinalities but + + align:start position:0% +cardinalities but + + + align:start position:0% +cardinalities but +so this is kind of a subtle + + align:start position:0% + + + + align:start position:0% + +kind of interesting thing about + + align:start position:0% +kind of interesting thing about + + + align:start position:0% +kind of interesting thing about +cardinalities + + align:start position:0% +cardinalities + + + align:start position:0% +cardinalities +and feynman + + align:start position:0% +and feynman + + + align:start position:0% +and feynman +so richard feynman who won the nobel + + align:start position:0% +so richard feynman who won the nobel + + + align:start position:0% +so richard feynman who won the nobel +prize in the 60s for his work on qed + + align:start position:0% + + + + align:start position:0% + +described + + align:start position:0% +described + + + align:start position:0% +described +this as saying um + + align:start position:0% + + + + align:start position:0% + +there are + + align:start position:0% + + + + align:start position:0% + +twice as many numbers + + align:start position:0% + + + + align:start position:0% + +as numbers + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% + + + + align:start position:0% + +let's uh + + align:start position:0% +let's uh + + + align:start position:0% +let's uh +prove this + + align:start position:0% + + + + align:start position:0% + +so what does this mean that this means + + align:start position:0% +so what does this mean that this means + + + align:start position:0% +so what does this mean that this means +we have to be able to find a + + align:start position:0% +we have to be able to find a + + + align:start position:0% +we have to be able to find a +bijective function from this set + + align:start position:0% +bijective function from this set + + + align:start position:0% +bijective function from this set +to this set + + align:start position:0% +to this set + + + align:start position:0% +to this set +okay or + + align:start position:0% +okay or + + + align:start position:0% +okay or +from this set to this set okay one or + + align:start position:0% +from this set to this set okay one or + + + align:start position:0% +from this set to this set okay one or +the other um + + align:start position:0% +the other um + + + align:start position:0% +the other um +and + + align:start position:0% +and + + + align:start position:0% +and +so in fact + + align:start position:0% +so in fact + + + align:start position:0% +so in fact +um + + align:start position:0% + + + + align:start position:0% + +maybe i should well i'll say something + + align:start position:0% +maybe i should well i'll say something + + + align:start position:0% +maybe i should well i'll say something +about uh about that in a minute um + + align:start position:0% + + + + align:start position:0% + +well let me let me pause let me pause + + align:start position:0% +well let me let me pause let me pause + + + align:start position:0% +well let me let me pause let me pause +this just for a minute + + align:start position:0% + + + + align:start position:0% + +and let me make a few comments + + align:start position:0% +and let me make a few comments + + + align:start position:0% +and let me make a few comments +about cardinality + + align:start position:0% +about cardinality + + + align:start position:0% +about cardinality +which maybe i should have + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +this you can think of is a little + + align:start position:0% +this you can think of is a little + + + align:start position:0% +this you can think of is a little +theorem + + align:start position:0% + + + + align:start position:0% + +if i have two sets + + align:start position:0% +if i have two sets + + + align:start position:0% +if i have two sets +a has the same size as b + + align:start position:0% + + + + align:start position:0% + +then b has the same size as a + + align:start position:0% +then b has the same size as a + + + align:start position:0% +then b has the same size as a +so remember this i mean what i just said + + align:start position:0% +so remember this i mean what i just said + + + align:start position:0% +so remember this i mean what i just said +in english + + align:start position:0% +in english + + + align:start position:0% +in english +is not exactly what those symbols mean + + align:start position:0% +is not exactly what those symbols mean + + + align:start position:0% +is not exactly what those symbols mean +remember this means there exists a + + align:start position:0% +remember this means there exists a + + + align:start position:0% +remember this means there exists a +bijection from a to b this means there + + align:start position:0% +bijection from a to b this means there + + + align:start position:0% +bijection from a to b this means there +exists a bijection from b to a + + align:start position:0% +exists a bijection from b to a + + + align:start position:0% +exists a bijection from b to a +so what is the proof of this + + align:start position:0% +so what is the proof of this + + + align:start position:0% +so what is the proof of this +statement + + align:start position:0% + + + + align:start position:0% + +so let's start off with the hypothesis + + align:start position:0% + + + + align:start position:0% + +suppose + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +there exists + + align:start position:0% + + + + align:start position:0% + +bijective map + + align:start position:0% +bijective map + + + align:start position:0% +bijective map +bijection bijective function + + align:start position:0% +bijection bijective function + + + align:start position:0% +bijection bijective function +f from + + align:start position:0% +f from + + + align:start position:0% +f from +a to b + + align:start position:0% +a to b + + + align:start position:0% +a to b +okay + + align:start position:0% + + + + align:start position:0% + +now if i have a bijection from a to b + + align:start position:0% +now if i have a bijection from a to b + + + align:start position:0% +now if i have a bijection from a to b +then what would be a bijection going + + align:start position:0% +then what would be a bijection going + + + align:start position:0% +then what would be a bijection going +from b to a that would just be the + + align:start position:0% +from b to a that would just be the + + + align:start position:0% +from b to a that would just be the +inverse + + align:start position:0% + + + + align:start position:0% + +so this is not the inverse image of sets + + align:start position:0% +so this is not the inverse image of sets + + + align:start position:0% +so this is not the inverse image of sets +like we described but the actual inverse + + align:start position:0% +like we described but the actual inverse + + + align:start position:0% +like we described but the actual inverse +which we defined over there + + align:start position:0% + + + + align:start position:0% + +is a bijection + + align:start position:0% + + + + align:start position:0% + +so b has the same size as a + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +one other statement so + + align:start position:0% + + + + align:start position:0% + +if a and b have the same size + + align:start position:0% + + + + align:start position:0% + +and b + + align:start position:0% +and b + + + align:start position:0% +and b +and c have the same size + + align:start position:0% +and c have the same size + + + align:start position:0% +and c have the same size +so again a b and c are sets i should + + align:start position:0% +so again a b and c are sets i should + + + align:start position:0% +so again a b and c are sets i should +have written that at the beginning + + align:start position:0% +have written that at the beginning + + + align:start position:0% +have written that at the beginning +but from this context you should + + align:start position:0% +but from this context you should + + + align:start position:0% +but from this context you should +understand that a b and c are sets then + + align:start position:0% + + + + align:start position:0% + +a and c have the same size + + align:start position:0% +a and c have the same size + + + align:start position:0% +a and c have the same size +okay + + align:start position:0% + + + + align:start position:0% + +so let's do a proof of that + + align:start position:0% +so let's do a proof of that + + + align:start position:0% +so let's do a proof of that +so + + align:start position:0% +so + + + align:start position:0% +so +let's start with the hypothesis meaning + + align:start position:0% +let's start with the hypothesis meaning + + + align:start position:0% +let's start with the hypothesis meaning +a has the same size as b and b has the + + align:start position:0% +a has the same size as b and b has the + + + align:start position:0% +a has the same size as b and b has the +same size as c + + align:start position:0% + + + + align:start position:0% + +so what do these two statements mean in + + align:start position:0% +so what do these two statements mean in + + + align:start position:0% +so what do these two statements mean in +terms of the definition that means there + + align:start position:0% +terms of the definition that means there + + + align:start position:0% +terms of the definition that means there +exists bijection from a to b + + align:start position:0% +exists bijection from a to b + + + align:start position:0% +exists bijection from a to b +and a bijection from b to c + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +this statement so + + align:start position:0% +this statement so + + + align:start position:0% +this statement so +let me finish this and then i'll say + + align:start position:0% +let me finish this and then i'll say + + + align:start position:0% +let me finish this and then i'll say +what i was going to say then there + + align:start position:0% +what i was going to say then there + + + align:start position:0% +what i was going to say then there +exists bijections f + + align:start position:0% +exists bijections f + + + align:start position:0% +exists bijections f +from a to b + + align:start position:0% + + + + align:start position:0% + +and g + + align:start position:0% +and g + + + align:start position:0% +and g +from b to c + + align:start position:0% +from b to c + + + align:start position:0% +from b to c +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so perhaps i should have said a few more + + align:start position:0% +so perhaps i should have said a few more + + + align:start position:0% +so perhaps i should have said a few more +words about why this is true + + align:start position:0% +words about why this is true + + + align:start position:0% +words about why this is true +so but i'm going to leave this as the + + align:start position:0% +so but i'm going to leave this as the + + + align:start position:0% +so but i'm going to leave this as the +exercise + + align:start position:0% +exercise + + + align:start position:0% +exercise +just to kind of pause the lecture and do + + align:start position:0% +just to kind of pause the lecture and do + + + align:start position:0% +just to kind of pause the lecture and do +it yourself and what i'll write + + align:start position:0% +it yourself and what i'll write + + + align:start position:0% +it yourself and what i'll write +uh + + align:start position:0% +uh + + + align:start position:0% +uh +shortly for this case i'll actually + + align:start position:0% +shortly for this case i'll actually + + + align:start position:0% +shortly for this case i'll actually +prove that the thing i'm going to define + + align:start position:0% +prove that the thing i'm going to define + + + align:start position:0% +prove that the thing i'm going to define +is a bijection that should help you + + align:start position:0% +is a bijection that should help you + + + align:start position:0% +is a bijection that should help you +so + + align:start position:0% +so + + + align:start position:0% +so +let me draw over here off to the side + + align:start position:0% +let me draw over here off to the side + + + align:start position:0% +let me draw over here off to the side +we have + + align:start position:0% +we have + + + align:start position:0% +we have +you know again 1 2 3 + + align:start position:0% +you know again 1 2 3 + + + align:start position:0% +you know again 1 2 3 +a b c + + align:start position:0% + + + + align:start position:0% + +so think of this as f + + align:start position:0% +so think of this as f + + + align:start position:0% +so think of this as f +this is my set a this is my set b + + align:start position:0% +this is my set a this is my set b + + + align:start position:0% +this is my set a this is my set b +and then i have + + align:start position:0% +and then i have + + + align:start position:0% +and then i have +alpha beta gamma + + align:start position:0% +alpha beta gamma + + + align:start position:0% +alpha beta gamma +and a gets mapped to alpha b gets mapped + + align:start position:0% +and a gets mapped to alpha b gets mapped + + + align:start position:0% +and a gets mapped to alpha b gets mapped +to beta c gets mapped to gamma + + align:start position:0% +to beta c gets mapped to gamma + + + align:start position:0% +to beta c gets mapped to gamma +so what would be the map going from a + + align:start position:0% +so what would be the map going from a + + + align:start position:0% +so what would be the map going from a +down to + + align:start position:0% +down to + + + align:start position:0% +down to +the set c + + align:start position:0% +the set c + + + align:start position:0% +the set c +well + + align:start position:0% +well + + + align:start position:0% +well +perhaps the composition one gets mapped + + align:start position:0% +perhaps the composition one gets mapped + + + align:start position:0% +perhaps the composition one gets mapped +to a which gets mapped to alpha so one + + align:start position:0% +to a which gets mapped to alpha so one + + + align:start position:0% +to a which gets mapped to alpha so one +gets mapped to alpha two gets mapped to + + align:start position:0% +gets mapped to alpha two gets mapped to + + + align:start position:0% +gets mapped to alpha two gets mapped to +beta + + align:start position:0% +beta + + + align:start position:0% +beta +3 gets mapped to gamma how do i build + + align:start position:0% +3 gets mapped to gamma how do i build + + + align:start position:0% +3 gets mapped to gamma how do i build +this function out of the things that i + + align:start position:0% +this function out of the things that i + + + align:start position:0% +this function out of the things that i +know namely this f in + + align:start position:0% +know namely this f in + + + align:start position:0% +know namely this f in +g + + align:start position:0% +g + + + align:start position:0% +g +well this function going from a to c is + + align:start position:0% +well this function going from a to c is + + + align:start position:0% +well this function going from a to c is +just the composition of these two + + align:start position:0% +just the composition of these two + + + align:start position:0% +just the composition of these two +functions so this is off to the side + + align:start position:0% +functions so this is off to the side + + + align:start position:0% +functions so this is off to the side +this is not a part of the proof + + align:start position:0% + + + + align:start position:0% + +let h go from + + align:start position:0% + + + + align:start position:0% + +a to c + + align:start position:0% + + + + align:start position:0% + +be the function + + align:start position:0% + + + + align:start position:0% + +g of f x + + align:start position:0% + + + + align:start position:0% + +okay so i claim that this function is a + + align:start position:0% +okay so i claim that this function is a + + + align:start position:0% +okay so i claim that this function is a +bijection + + align:start position:0% +bijection + + + align:start position:0% +bijection +so we want to prove + + align:start position:0% + + + + align:start position:0% + +okay that it's one to one and onto + + align:start position:0% +okay that it's one to one and onto + + + align:start position:0% +okay that it's one to one and onto +all right so let's do uh + + align:start position:0% +all right so let's do uh + + + align:start position:0% +all right so let's do uh +one to one first + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +suppose so we this is the part where i'm + + align:start position:0% +suppose so we this is the part where i'm + + + align:start position:0% +suppose so we this is the part where i'm +going to put this in parentheses meaning + + align:start position:0% +going to put this in parentheses meaning + + + align:start position:0% +going to put this in parentheses meaning +what we're doing now + + align:start position:0% +what we're doing now + + + align:start position:0% +what we're doing now +so + + align:start position:0% +so + + + align:start position:0% +so +we're going to prove that h is one to + + align:start position:0% +we're going to prove that h is one to + + + align:start position:0% +we're going to prove that h is one to +one + + align:start position:0% +one + + + align:start position:0% +one +so that means we have to verify + + align:start position:0% +so that means we have to verify + + + align:start position:0% +so that means we have to verify +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the definition that i've erased + + align:start position:0% +the definition that i've erased + + + align:start position:0% +the definition that i've erased +so remember the definition so + + align:start position:0% + + + + align:start position:0% + +let's write it all out + + align:start position:0% + + + + align:start position:0% + +we first show + + align:start position:0% + + + + align:start position:0% + +h is one to one and what this means + + align:start position:0% +h is one to one and what this means + + + align:start position:0% +h is one to one and what this means +according to the definition that i'm now + + align:start position:0% +according to the definition that i'm now + + + align:start position:0% +according to the definition that i'm now +writing over + + align:start position:0% + + + + align:start position:0% + +if h of x1 equals h of x2 + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +x1 equals x2 + + align:start position:0% +x1 equals x2 + + + align:start position:0% +x1 equals x2 +okay so this is what we want to prove + + align:start position:0% +okay so this is what we want to prove + + + align:start position:0% +okay so this is what we want to prove +this is the definition of + + align:start position:0% +this is the definition of + + + align:start position:0% +this is the definition of +h being one to one + + align:start position:0% +h being one to one + + + align:start position:0% +h being one to one +so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so let's start + + align:start position:0% + + + + align:start position:0% + +if h of x1 equals h of x2 + + align:start position:0% +if h of x1 equals h of x2 + + + align:start position:0% +if h of x1 equals h of x2 +then + + align:start position:0% +then + + + align:start position:0% +then +in terms of how we've defined h + + align:start position:0% +in terms of how we've defined h + + + align:start position:0% +in terms of how we've defined h +which is g of f of x so the composition + + align:start position:0% +which is g of f of x so the composition + + + align:start position:0% +which is g of f of x so the composition +and this means g + + align:start position:0% +and this means g + + + align:start position:0% +and this means g +of f of x1 + + align:start position:0% + + + + align:start position:0% + +equals g of f of x2 + + align:start position:0% +equals g of f of x2 + + + align:start position:0% +equals g of f of x2 +okay that's just what h is + + align:start position:0% +okay that's just what h is + + + align:start position:0% +okay that's just what h is +now + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +statement here + + align:start position:0% +statement here + + + align:start position:0% +statement here +now g we know is a bijection okay we + + align:start position:0% +now g we know is a bijection okay we + + + align:start position:0% +now g we know is a bijection okay we +know g is one to one + + align:start position:0% +know g is one to one + + + align:start position:0% +know g is one to one +and since g of something equals g of + + align:start position:0% +and since g of something equals g of + + + align:start position:0% +and since g of something equals g of +something else and g is one to one this + + align:start position:0% +something else and g is one to one this + + + align:start position:0% +something else and g is one to one this +implies that f of x one + + align:start position:0% +implies that f of x one + + + align:start position:0% +implies that f of x one +equals f of x two + + align:start position:0% + + + + align:start position:0% + +this is since + + align:start position:0% +this is since + + + align:start position:0% +this is since +g is one to one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so starting with this and the definition + + align:start position:0% +so starting with this and the definition + + + align:start position:0% +so starting with this and the definition +of h being the composition + + align:start position:0% +of h being the composition + + + align:start position:0% +of h being the composition +we conclude that f of x one has to equal + + align:start position:0% +we conclude that f of x one has to equal + + + align:start position:0% +we conclude that f of x one has to equal +f of x two because g is one to one + + align:start position:0% +f of x two because g is one to one + + + align:start position:0% +f of x two because g is one to one +now since f is also one to one right we + + align:start position:0% +now since f is also one to one right we + + + align:start position:0% +now since f is also one to one right we +are assuming that f and g are bijections + + align:start position:0% +are assuming that f and g are bijections + + + align:start position:0% +are assuming that f and g are bijections +since f is one to one this implies + + align:start position:0% +since f is one to one this implies + + + align:start position:0% +since f is one to one this implies +x one equals x2 + + align:start position:0% +x one equals x2 + + + align:start position:0% +x one equals x2 +since f + + align:start position:0% +since f + + + align:start position:0% +since f +is one to one + + align:start position:0% + + + + align:start position:0% + +and this is what we wanted to prove + + align:start position:0% +and this is what we wanted to prove + + + align:start position:0% +and this is what we wanted to prove +right we wanted to start with assuming h + + align:start position:0% +right we wanted to start with assuming h + + + align:start position:0% +right we wanted to start with assuming h +of x one equals h of x two and prove x + + align:start position:0% +of x one equals h of x two and prove x + + + align:start position:0% +of x one equals h of x two and prove x +one equals x two which is what we've + + align:start position:0% +one equals x two which is what we've + + + align:start position:0% +one equals x two which is what we've +done + + align:start position:0% +done + + + align:start position:0% +done +so thus + + align:start position:0% +so thus + + + align:start position:0% +so thus +we've proven that h is one to one + + align:start position:0% +we've proven that h is one to one + + + align:start position:0% +we've proven that h is one to one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now we have to show that it's surjective + + align:start position:0% +now we have to show that it's surjective + + + align:start position:0% +now we have to show that it's surjective +that it's onto + + align:start position:0% + + + + align:start position:0% + +hfa equals c + + align:start position:0% +hfa equals c + + + align:start position:0% +hfa equals c +and again i'll write out what this means + + align:start position:0% +and again i'll write out what this means + + + align:start position:0% +and again i'll write out what this means +this means for all + + align:start position:0% +this means for all + + + align:start position:0% +this means for all +y and c + + align:start position:0% +y and c + + + align:start position:0% +y and c +or let me call it z + + align:start position:0% +or let me call it z + + + align:start position:0% +or let me call it z +there exists an x in a + + align:start position:0% +there exists an x in a + + + align:start position:0% +there exists an x in a +such that + + align:start position:0% +such that + + + align:start position:0% +such that +h of x + + align:start position:0% +h of x + + + align:start position:0% +h of x +equals z + + align:start position:0% +equals z + + + align:start position:0% +equals z +okay + + align:start position:0% + + + + align:start position:0% + +now we use the fact that f and g were + + align:start position:0% +now we use the fact that f and g were + + + align:start position:0% +now we use the fact that f and g were +injective to conclude that the + + align:start position:0% +injective to conclude that the + + + align:start position:0% +injective to conclude that the +composition + + align:start position:0% +composition + + + align:start position:0% +composition +is injective so + + align:start position:0% +is injective so + + + align:start position:0% +is injective so +it stands to reason that we're going to + + align:start position:0% +it stands to reason that we're going to + + + align:start position:0% +it stands to reason that we're going to +use the fact that they're both + + align:start position:0% +use the fact that they're both + + + align:start position:0% +use the fact that they're both +surjective to prove that h is subjective + + align:start position:0% + + + + align:start position:0% + +so we need to prove that for all z and c + + align:start position:0% +so we need to prove that for all z and c + + + align:start position:0% +so we need to prove that for all z and c +there exists an x and a such that h of x + + align:start position:0% +there exists an x and a such that h of x + + + align:start position:0% +there exists an x and a such that h of x +equals z so + + align:start position:0% +equals z so + + + align:start position:0% +equals z so +let z be in c + + align:start position:0% +let z be in c + + + align:start position:0% +let z be in c +now we need to find some x and a that + + align:start position:0% +now we need to find some x and a that + + + align:start position:0% +now we need to find some x and a that +gets mapped to z + + align:start position:0% +gets mapped to z + + + align:start position:0% +gets mapped to z +we'll use that + + align:start position:0% +we'll use that + + + align:start position:0% +we'll use that +g and f are both surjective + + align:start position:0% +g and f are both surjective + + + align:start position:0% +g and f are both surjective +so + + align:start position:0% + + + + align:start position:0% + +and what's the picture that kind of goes + + align:start position:0% +and what's the picture that kind of goes + + + align:start position:0% +and what's the picture that kind of goes +along with this + + align:start position:0% + + + + align:start position:0% + +here's the set c + + align:start position:0% +here's the set c + + + align:start position:0% +here's the set c +b and a + + align:start position:0% +b and a + + + align:start position:0% +b and a +we have some element of z + + align:start position:0% +we have some element of z + + + align:start position:0% +we have some element of z +and + + align:start position:0% +and + + + align:start position:0% +and +we know that since g + + align:start position:0% +we know that since g + + + align:start position:0% +we know that since g +is surjective there's some + + align:start position:0% +is surjective there's some + + + align:start position:0% +is surjective there's some +element in b that gets mapped to z by g + + align:start position:0% +element in b that gets mapped to z by g + + + align:start position:0% +element in b that gets mapped to z by g +okay + + align:start position:0% + + + + align:start position:0% + +but now since f going from + + align:start position:0% +but now since f going from + + + align:start position:0% +but now since f going from +a to b is surjective there exists some x + + align:start position:0% +a to b is surjective there exists some x + + + align:start position:0% +a to b is surjective there exists some x +which maps to y + + align:start position:0% + + + + align:start position:0% + +okay and then that's the whole argument + + align:start position:0% +okay and then that's the whole argument + + + align:start position:0% +okay and then that's the whole argument +that's it + + align:start position:0% +that's it + + + align:start position:0% +that's it +all right i drew this picture but now i + + align:start position:0% +all right i drew this picture but now i + + + align:start position:0% +all right i drew this picture but now i +just need to + + align:start position:0% +just need to + + + align:start position:0% +just need to +turn it into english + + align:start position:0% +turn it into english + + + align:start position:0% +turn it into english +using + + align:start position:0% +using + + + align:start position:0% +using +the properties and assumptions that i + + align:start position:0% +the properties and assumptions that i + + + align:start position:0% +the properties and assumptions that i +have + + align:start position:0% + + + + align:start position:0% + +since g is + + align:start position:0% +since g is + + + align:start position:0% +since g is +surjective + + align:start position:0% +surjective + + + align:start position:0% +surjective +there exists a y and b + + align:start position:0% +there exists a y and b + + + align:start position:0% +there exists a y and b +such that + + align:start position:0% +such that + + + align:start position:0% +such that +g of y equals z + + align:start position:0% + + + + align:start position:0% + +since f is + + align:start position:0% + + + + align:start position:0% + +so objective + + align:start position:0% + + + + align:start position:0% + +there exists an x in a + + align:start position:0% +there exists an x in a + + + align:start position:0% +there exists an x in a +so that + + align:start position:0% +so that + + + align:start position:0% +so that +f of x equals y + + align:start position:0% + + + + align:start position:0% + +but then + + align:start position:0% +but then + + + align:start position:0% +but then +if i look at h of x this is equal to g + + align:start position:0% +if i look at h of x this is equal to g + + + align:start position:0% +if i look at h of x this is equal to g +of f of x which is equal to g of y which + + align:start position:0% +of f of x which is equal to g of y which + + + align:start position:0% +of f of x which is equal to g of y which +is equal to z + + align:start position:0% +is equal to z + + + align:start position:0% +is equal to z +by how we've defined y + + align:start position:0% +by how we've defined y + + + align:start position:0% +by how we've defined y +remember g of y equals z how we found y + + align:start position:0% +remember g of y equals z how we found y + + + align:start position:0% +remember g of y equals z how we found y +and how we found x remember f of x + + align:start position:0% +and how we found x remember f of x + + + align:start position:0% +and how we found x remember f of x +equals this y okay + + align:start position:0% + + + + align:start position:0% + +and therefore this map h is on 2 + + align:start position:0% +and therefore this map h is on 2 + + + align:start position:0% +and therefore this map h is on 2 +and therefore h is a bijection proving + + align:start position:0% +and therefore h is a bijection proving + + + align:start position:0% +and therefore h is a bijection proving +this theorem + + align:start position:0% +this theorem + + + align:start position:0% +this theorem +so that should help you + + align:start position:0% + + + + align:start position:0% + +in your mini exercise to to + + align:start position:0% + + + + align:start position:0% + +prove that the inverse of a bijection is + + align:start position:0% +prove that the inverse of a bijection is + + + align:start position:0% +prove that the inverse of a bijection is +a bijection + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +back to + + align:start position:0% +back to + + + align:start position:0% +back to +what we're doing to begin with + + align:start position:0% +what we're doing to begin with + + + align:start position:0% +what we're doing to begin with +we want to show + + align:start position:0% +we want to show + + + align:start position:0% +we want to show +the set of even natural numbers has the + + align:start position:0% +the set of even natural numbers has the + + + align:start position:0% +the set of even natural numbers has the +same + + align:start position:0% +same + + + align:start position:0% +same +size as the natural numbers has the same + + align:start position:0% +size as the natural numbers has the same + + + align:start position:0% +size as the natural numbers has the same +cardinality as the natural numbers and + + align:start position:0% +cardinality as the natural numbers and + + + align:start position:0% +cardinality as the natural numbers and +the same for the odd one so i'm just + + align:start position:0% +the same for the odd one so i'm just + + + align:start position:0% +the same for the odd one so i'm just +going to do the odd ones + + align:start position:0% +going to do the odd ones + + + align:start position:0% +going to do the odd ones +again this will be a small exercise for + + align:start position:0% +again this will be a small exercise for + + + align:start position:0% +again this will be a small exercise for +you to do + + align:start position:0% +you to do + + + align:start position:0% +you to do +to prove number two the statement for + + align:start position:0% +to prove number two the statement for + + + align:start position:0% +to prove number two the statement for +the + + align:start position:0% +the + + + align:start position:0% +the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +odd ones so i'm going to do the even one + + align:start position:0% +odd ones so i'm going to do the even one + + + align:start position:0% +odd ones so i'm going to do the even one +and you can do the odd ones + + align:start position:0% +and you can do the odd ones + + + align:start position:0% +and you can do the odd ones +you should if you plan on studying more + + align:start position:0% +you should if you plan on studying more + + + align:start position:0% +you should if you plan on studying more +math + + align:start position:0% +math + + + align:start position:0% +math +get used to + + align:start position:0% +get used to + + + align:start position:0% +get used to +the instructor + + align:start position:0% +the instructor + + + align:start position:0% +the instructor +professor + + align:start position:0% +professor + + + align:start position:0% +professor +research paper writer + + align:start position:0% +research paper writer + + + align:start position:0% +research paper writer +textbook author + + align:start position:0% +textbook author + + + align:start position:0% +textbook author +giving out little exercises to make sure + + align:start position:0% +giving out little exercises to make sure + + + align:start position:0% +giving out little exercises to make sure +that you're following along and that you + + align:start position:0% +that you're following along and that you + + + align:start position:0% +that you're following along and that you +can do + + align:start position:0% +can do + + + align:start position:0% +can do +some minor tasks + + align:start position:0% + + + + align:start position:0% + +at some point during + + align:start position:0% +at some point during + + + align:start position:0% +at some point during +the discussion + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +we're going to find + + align:start position:0% +we're going to find + + + align:start position:0% +we're going to find +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% + + + + align:start position:0% + +we want to show + + align:start position:0% + + + + align:start position:0% + +that the natural numbers has the same + + align:start position:0% +that the natural numbers has the same + + + align:start position:0% +that the natural numbers has the same +size as the even natural numbers which + + align:start position:0% +size as the even natural numbers which + + + align:start position:0% +size as the even natural numbers which +is the same as this statement by that + + align:start position:0% +is the same as this statement by that + + + align:start position:0% +is the same as this statement by that +first theorem i wrote up there + + align:start position:0% +first theorem i wrote up there + + + align:start position:0% +first theorem i wrote up there +um + + align:start position:0% +um + + + align:start position:0% +um +now + + align:start position:0% +now + + + align:start position:0% +now +we that means we need to find a + + align:start position:0% +we that means we need to find a + + + align:start position:0% +we that means we need to find a +bijection from the natural numbers + + align:start position:0% +bijection from the natural numbers + + + align:start position:0% +bijection from the natural numbers +to + + align:start position:0% +to + + + align:start position:0% +to +the set of even natural numbers + + align:start position:0% +the set of even natural numbers + + + align:start position:0% +the set of even natural numbers +um + + align:start position:0% +um + + + align:start position:0% +um +this should be + + align:start position:0% +this should be + + + align:start position:0% +this should be +not too bad + + align:start position:0% +not too bad + + + align:start position:0% +not too bad +i mean so again this is uh + + align:start position:0% +i mean so again this is uh + + + align:start position:0% +i mean so again this is uh +off to the side this is not part of the + + align:start position:0% +off to the side this is not part of the + + + align:start position:0% +off to the side this is not part of the +proof + + align:start position:0% + + + + align:start position:0% + +what would be the map going from + + align:start position:0% +what would be the map going from + + + align:start position:0% +what would be the map going from +these guys to these guys + + align:start position:0% +these guys to these guys + + + align:start position:0% +these guys to these guys +well + + align:start position:0% +well + + + align:start position:0% +well +i mean there's several you could choose + + align:start position:0% +i mean there's several you could choose + + + align:start position:0% +i mean there's several you could choose +but maybe the simplest is one gets + + align:start position:0% +but maybe the simplest is one gets + + + align:start position:0% +but maybe the simplest is one gets +mapped to two two gets mapped to four + + align:start position:0% +mapped to two two gets mapped to four + + + align:start position:0% +mapped to two two gets mapped to four +three gets mapped to six four gets + + align:start position:0% +three gets mapped to six four gets + + + align:start position:0% +three gets mapped to six four gets +mapped to eight five to ten six to + + align:start position:0% +mapped to eight five to ten six to + + + align:start position:0% +mapped to eight five to ten six to +twelve and so on and so on + + align:start position:0% +twelve and so on and so on + + + align:start position:0% +twelve and so on and so on +okay now what is that map + + align:start position:0% +okay now what is that map + + + align:start position:0% +okay now what is that map +and now i'll re + + align:start position:0% +and now i'll re + + + align:start position:0% +and now i'll re +uh i'll continue the proof + + align:start position:0% + + + + align:start position:0% + +let f be the function + + align:start position:0% + + + + align:start position:0% + +into the even + + align:start position:0% +into the even + + + align:start position:0% +into the even +natural numbers + + align:start position:0% +natural numbers + + + align:start position:0% +natural numbers +defined by + + align:start position:0% + + + + align:start position:0% + +f of n equals + + align:start position:0% +f of n equals + + + align:start position:0% +f of n equals +2 times n + + align:start position:0% +2 times n + + + align:start position:0% +2 times n +and so + + align:start position:0% + + + + align:start position:0% + +we're in a natural number okay so this + + align:start position:0% +we're in a natural number okay so this + + + align:start position:0% +we're in a natural number okay so this +is just formally writing the function + + align:start position:0% +is just formally writing the function + + + align:start position:0% +is just formally writing the function +that takes one to two two to four three + + align:start position:0% +that takes one to two two to four three + + + align:start position:0% +that takes one to two two to four three +to six four to eight and so on and so on + + align:start position:0% +to six four to eight and so on and so on + + + align:start position:0% +to six four to eight and so on and so on +um + + align:start position:0% +um + + + align:start position:0% +um +i claim f is uh bijection so i have to + + align:start position:0% +i claim f is uh bijection so i have to + + + align:start position:0% +i claim f is uh bijection so i have to +show that f is one to one and onto + + align:start position:0% + + + + align:start position:0% + +so we first show + + align:start position:0% + + + + align:start position:0% + +f is one to one + + align:start position:0% + + + + align:start position:0% + +so that means that i have to assume f of + + align:start position:0% +so that means that i have to assume f of + + + align:start position:0% +so that means that i have to assume f of +n one equals f of n two and conclude + + align:start position:0% +n one equals f of n two and conclude + + + align:start position:0% +n one equals f of n two and conclude +that n one equals m two + + align:start position:0% +that n one equals m two + + + align:start position:0% +that n one equals m two +so let me actually write out what this + + align:start position:0% +so let me actually write out what this + + + align:start position:0% +so let me actually write out what this +means again for you to say that f is one + + align:start position:0% +means again for you to say that f is one + + + align:start position:0% +means again for you to say that f is one +to one is one to one i e + + align:start position:0% +to one is one to one i e + + + align:start position:0% +to one is one to one i e +if + + align:start position:0% +if + + + align:start position:0% +if +f of n one equals f of + + align:start position:0% +f of n one equals f of + + + align:start position:0% +f of n one equals f of +n two + + align:start position:0% +n two + + + align:start position:0% +n two +then + + align:start position:0% + + + + align:start position:0% + +n one equals n2 but this is this is easy + + align:start position:0% +n one equals n2 but this is this is easy + + + align:start position:0% +n one equals n2 but this is this is easy +to verify for this function that we've + + align:start position:0% +to verify for this function that we've + + + align:start position:0% +to verify for this function that we've +written down + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +if f of n1 equals f of n2 so remember + + align:start position:0% +if f of n1 equals f of n2 so remember + + + align:start position:0% +if f of n1 equals f of n2 so remember +this is what we want to show all right + + align:start position:0% +this is what we want to show all right + + + align:start position:0% +this is what we want to show all right +so to show it i start with my + + align:start position:0% +so to show it i start with my + + + align:start position:0% +so to show it i start with my +assumption + + align:start position:0% +assumption + + + align:start position:0% +assumption +and i need to conclude n one equals n + + align:start position:0% +and i need to conclude n one equals n + + + align:start position:0% +and i need to conclude n one equals n +two + + align:start position:0% +two + + + align:start position:0% +two +so + + align:start position:0% + + + + align:start position:0% + +suppose f of n1 equals f of n2 my + + align:start position:0% +suppose f of n1 equals f of n2 my + + + align:start position:0% +suppose f of n1 equals f of n2 my +assumption my hypothesis i need to + + align:start position:0% +assumption my hypothesis i need to + + + align:start position:0% +assumption my hypothesis i need to +conclude n1 equals n2 + + align:start position:0% + + + + align:start position:0% + +then this implies by the definition of f + + align:start position:0% +then this implies by the definition of f + + + align:start position:0% +then this implies by the definition of f +2 times n1 equals 2 times n2 + + align:start position:0% +2 times n1 equals 2 times n2 + + + align:start position:0% +2 times n1 equals 2 times n2 +which by algebra of just eliminating the + + align:start position:0% +which by algebra of just eliminating the + + + align:start position:0% +which by algebra of just eliminating the +2's n1 equals n2 which is the conclusion + + align:start position:0% +2's n1 equals n2 which is the conclusion + + + align:start position:0% +2's n1 equals n2 which is the conclusion +that i want + + align:start position:0% +that i want + + + align:start position:0% +that i want +okay so i've proven the statement + + align:start position:0% +okay so i've proven the statement + + + align:start position:0% +okay so i've proven the statement +that if f of n1 equals f of n2 then n1 + + align:start position:0% +that if f of n1 equals f of n2 then n1 + + + align:start position:0% +that if f of n1 equals f of n2 then n1 +equals n2 therefore f is one to one + + align:start position:0% +equals n2 therefore f is one to one + + + align:start position:0% +equals n2 therefore f is one to one +so + + align:start position:0% + + + + align:start position:0% + +thus f is one to one + + align:start position:0% +thus f is one to one + + + align:start position:0% +thus f is one to one +so now we wanna show + + align:start position:0% + + + + align:start position:0% + +f is + + align:start position:0% +f is + + + align:start position:0% +f is +on to surjective + + align:start position:0% +on to surjective + + + align:start position:0% +on to surjective +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i'll write this out again ie + + align:start position:0% +i'll write this out again ie + + + align:start position:0% +i'll write this out again ie +for all + + align:start position:0% +for all + + + align:start position:0% +for all +elements that are in + + align:start position:0% + + + + align:start position:0% + +that are an even number + + align:start position:0% + + + + align:start position:0% + +there exists an n + + align:start position:0% +there exists an n + + + align:start position:0% +there exists an n +such that + + align:start position:0% +such that + + + align:start position:0% +such that +f of n equals m + + align:start position:0% +f of n equals m + + + align:start position:0% +f of n equals m +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +let m be an even integer + + align:start position:0% +let m be an even integer + + + align:start position:0% +let m be an even integer +and so not to confuse this let me write + + align:start position:0% +and so not to confuse this let me write + + + align:start position:0% +and so not to confuse this let me write +2 times + + align:start position:0% +2 times + + + align:start position:0% +2 times +k + + align:start position:0% +k + + + align:start position:0% +k +this is the same set + + align:start position:0% +this is the same set + + + align:start position:0% +this is the same set +just using a different dummy variable + + align:start position:0% +just using a different dummy variable + + + align:start position:0% +just using a different dummy variable +instead of n in my description of the + + align:start position:0% +instead of n in my description of the + + + align:start position:0% +instead of n in my description of the +even natural numbers + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +and let's do that here as well + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +again this is not changing anything this + + align:start position:0% +again this is not changing anything this + + + align:start position:0% +again this is not changing anything this +is just changing the letter i'm using to + + align:start position:0% +is just changing the letter i'm using to + + + align:start position:0% +is just changing the letter i'm using to +describe the set + + align:start position:0% +describe the set + + + align:start position:0% +describe the set +um which is inconsequential + + align:start position:0% + + + + align:start position:0% + +but i don't want you to get the false + + align:start position:0% +but i don't want you to get the false + + + align:start position:0% +but i don't want you to get the false +impression that + + align:start position:0% +impression that + + + align:start position:0% +impression that +somehow i'm not doing anything at all + + align:start position:0% + + + + align:start position:0% + +okay so suppose i have an even integer + + align:start position:0% +okay so suppose i have an even integer + + + align:start position:0% +okay so suppose i have an even integer +then there exists + + align:start position:0% +then there exists + + + align:start position:0% +then there exists +simply by the definition of this set + + align:start position:0% +simply by the definition of this set + + + align:start position:0% +simply by the definition of this set +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +an n + + align:start position:0% +an n + + + align:start position:0% +an n +natural number + + align:start position:0% +natural number + + + align:start position:0% +natural number +so that + + align:start position:0% +so that + + + align:start position:0% +so that +m equals 2 times n + + align:start position:0% + + + + align:start position:0% + +then f + + align:start position:0% +then f + + + align:start position:0% +then f +of this natural number which is 2 times + + align:start position:0% +of this natural number which is 2 times + + + align:start position:0% +of this natural number which is 2 times +n equals m and therefore + + align:start position:0% +n equals m and therefore + + + align:start position:0% +n equals m and therefore +i get something that maps to m + + align:start position:0% + + + + align:start position:0% + +therefore f is onto therefore f is a + + align:start position:0% +therefore f is onto therefore f is a + + + align:start position:0% +therefore f is onto therefore f is a +bijection + + align:start position:0% +bijection + + + align:start position:0% +bijection +and + + align:start position:0% +and + + + align:start position:0% +and +the two sets have the same cardinality + + align:start position:0% +the two sets have the same cardinality + + + align:start position:0% +the two sets have the same cardinality +okay + + align:start position:0% + + + + align:start position:0% + +all right um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let's + + align:start position:0% +let's + + + align:start position:0% +let's +where are we at where should i write + + align:start position:0% +where are we at where should i write + + + align:start position:0% +where are we at where should i write +it's right here + + align:start position:0% + + + + align:start position:0% + +maybe i'll leave that up because i don't + + align:start position:0% +maybe i'll leave that up because i don't + + + align:start position:0% +maybe i'll leave that up because i don't +want to + + align:start position:0% + + + + align:start position:0% + +now using this and i'll probably put + + align:start position:0% +now using this and i'll probably put + + + align:start position:0% +now using this and i'll probably put +this in the + + align:start position:0% +this in the + + + align:start position:0% +this in the +in the homework i mean + + align:start position:0% +in the homework i mean + + + align:start position:0% +in the homework i mean +one can um + + align:start position:0% +one can um + + + align:start position:0% +one can um +also + + align:start position:0% +also + + + align:start position:0% +also +show + + align:start position:0% +show + + + align:start position:0% +show +i should say using this but + + align:start position:0% +i should say using this but + + + align:start position:0% +i should say using this but +one can also show that + + align:start position:0% + + + + align:start position:0% + +the integers + + align:start position:0% +the integers + + + align:start position:0% +the integers +have the same size as the natural + + align:start position:0% +have the same size as the natural + + + align:start position:0% +have the same size as the natural +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +um which again is a little bit + + align:start position:0% +um which again is a little bit + + + align:start position:0% +um which again is a little bit +surprising since the natural numbers are + + align:start position:0% +surprising since the natural numbers are + + + align:start position:0% +surprising since the natural numbers are +a strict subset of z + + align:start position:0% +a strict subset of z + + + align:start position:0% +a strict subset of z +um + + align:start position:0% + + + + align:start position:0% + +so what's the proof uh so i'm gonna draw + + align:start position:0% +so what's the proof uh so i'm gonna draw + + + align:start position:0% +so what's the proof uh so i'm gonna draw +a picture + + align:start position:0% +a picture + + + align:start position:0% +a picture +then i'm gonna write down the function + + align:start position:0% +then i'm gonna write down the function + + + align:start position:0% +then i'm gonna write down the function +and then i'm gonna leave it as + + align:start position:0% +and then i'm gonna leave it as + + + align:start position:0% +and then i'm gonna leave it as +uh actually i'm gonna put in the + + align:start position:0% +uh actually i'm gonna put in the + + + align:start position:0% +uh actually i'm gonna put in the +homework that for you to verify that + + align:start position:0% +homework that for you to verify that + + + align:start position:0% +homework that for you to verify that +this function is one to one and onto + + align:start position:0% +this function is one to one and onto + + + align:start position:0% +this function is one to one and onto +so let's say + + align:start position:0% + + + + align:start position:0% + +there's as many + + align:start position:0% +there's as many + + + align:start position:0% +there's as many +natural numbers as i want to write + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +and as many integers as i want to write + + align:start position:0% +and as many integers as i want to write + + + align:start position:0% +and as many integers as i want to write +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +what would be a way of + + align:start position:0% +what would be a way of + + + align:start position:0% +what would be a way of +mapping the integers in a one-to-one and + + align:start position:0% +mapping the integers in a one-to-one and + + + align:start position:0% +mapping the integers in a one-to-one and +onto fashion + + align:start position:0% +onto fashion + + + align:start position:0% +onto fashion +onto the natural numbers + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +what we could do + + align:start position:0% +what we could do + + + align:start position:0% +what we could do +first off let's send zero to one + + align:start position:0% +first off let's send zero to one + + + align:start position:0% +first off let's send zero to one +just to get zero out of the way + + align:start position:0% +just to get zero out of the way + + + align:start position:0% +just to get zero out of the way +and + + align:start position:0% +and + + + align:start position:0% +and +from then on now we just need to find a + + align:start position:0% +from then on now we just need to find a + + + align:start position:0% +from then on now we just need to find a +way to map the positive integers and the + + align:start position:0% +way to map the positive integers and the + + + align:start position:0% +way to map the positive integers and the +negative integers + + align:start position:0% +negative integers + + + align:start position:0% +negative integers +onto the natural numbers bigger than 2. + + align:start position:0% +onto the natural numbers bigger than 2. + + + align:start position:0% +onto the natural numbers bigger than 2. +and in some way + + align:start position:0% +and in some way + + + align:start position:0% +and in some way +you know + + align:start position:0% + + + + align:start position:0% + +mentally we should feel like we can do + + align:start position:0% +mentally we should feel like we can do + + + align:start position:0% +mentally we should feel like we can do +this + + align:start position:0% + + + + align:start position:0% + +because we kind of did it over there but + + align:start position:0% +because we kind of did it over there but + + + align:start position:0% +because we kind of did it over there but +not not explicitly so + + align:start position:0% +not not explicitly so + + + align:start position:0% +not not explicitly so +um + + align:start position:0% +um + + + align:start position:0% +um +how about we take one + + align:start position:0% +how about we take one + + + align:start position:0% +how about we take one +to two + + align:start position:0% +to two + + + align:start position:0% +to two +two to four + + align:start position:0% +two to four + + + align:start position:0% +two to four +three + + align:start position:0% +three + + + align:start position:0% +three +to six + + align:start position:0% +to six + + + align:start position:0% +to six +okay four would then go to eight + + align:start position:0% + + + + align:start position:0% + +and we'll take + + align:start position:0% + + + + align:start position:0% + +one to three + + align:start position:0% +one to three + + + align:start position:0% +one to three +minus two to + + align:start position:0% +minus two to + + + align:start position:0% +minus two to +five + + align:start position:0% +five + + + align:start position:0% +five +they're getting crossed + + align:start position:0% +they're getting crossed + + + align:start position:0% +they're getting crossed +and then + + align:start position:0% +and then + + + align:start position:0% +and then +minus three + + align:start position:0% +minus three + + + align:start position:0% +minus three +would get sent to seven so you see that + + align:start position:0% +would get sent to seven so you see that + + + align:start position:0% +would get sent to seven so you see that +the positive integers gets mapped to the + + align:start position:0% +the positive integers gets mapped to the + + + align:start position:0% +the positive integers gets mapped to the +even natural numbers + + align:start position:0% +even natural numbers + + + align:start position:0% +even natural numbers +and the negative uh integers + + align:start position:0% +and the negative uh integers + + + align:start position:0% +and the negative uh integers +get mapped to + + align:start position:0% +get mapped to + + + align:start position:0% +get mapped to +the odd natural numbers bigger than one + + align:start position:0% +the odd natural numbers bigger than one + + + align:start position:0% +the odd natural numbers bigger than one +okay + + align:start position:0% + + + + align:start position:0% + +so i'm not even going to write the proof + + align:start position:0% +so i'm not even going to write the proof + + + align:start position:0% +so i'm not even going to write the proof +this will be um + + align:start position:0% +this will be um + + + align:start position:0% +this will be um +part of the homework + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% +you know + + + align:start position:0% +you know +it is a bit surprising that there are + + align:start position:0% +it is a bit surprising that there are + + + align:start position:0% +it is a bit surprising that there are +twice as many numbers as numbers + + align:start position:0% +twice as many numbers as numbers + + + align:start position:0% +twice as many numbers as numbers +uh not too surprising since you know + + align:start position:0% +uh not too surprising since you know + + + align:start position:0% +uh not too surprising since you know +kind of these subsets if you + + align:start position:0% +kind of these subsets if you + + + align:start position:0% +kind of these subsets if you +picture them as i've been doing as + + align:start position:0% +picture them as i've been doing as + + + align:start position:0% +picture them as i've been doing as +subsets of the + + align:start position:0% +subsets of the + + + align:start position:0% +subsets of the +real line you know they're kind of + + align:start position:0% +real line you know they're kind of + + + align:start position:0% +real line you know they're kind of +discreet so you should be able to count + + align:start position:0% +discreet so you should be able to count + + + align:start position:0% +discreet so you should be able to count +them + + align:start position:0% +them + + + align:start position:0% +them +um what is not what is more surprising + + align:start position:0% +um what is not what is more surprising + + + align:start position:0% +um what is not what is more surprising +are + + align:start position:0% +are + + + align:start position:0% +are +is whether or not you can count subsets + + align:start position:0% +is whether or not you can count subsets + + + align:start position:0% +is whether or not you can count subsets +that in some sense are not discrete for + + align:start position:0% +that in some sense are not discrete for + + + align:start position:0% +that in some sense are not discrete for +example what about + + align:start position:0% +example what about + + + align:start position:0% +example what about +uh the rational numbers + + align:start position:0% +uh the rational numbers + + + align:start position:0% +uh the rational numbers +so + + align:start position:0% +so + + + align:start position:0% +so +this is a theorem + + align:start position:0% + + + + align:start position:0% + +that and let me just look at those + + align:start position:0% +that and let me just look at those + + + align:start position:0% +that and let me just look at those +positive rational numbers in fact i + + align:start position:0% +positive rational numbers in fact i + + + align:start position:0% +positive rational numbers in fact i +could take all rational numbers but + + align:start position:0% +could take all rational numbers but + + + align:start position:0% +could take all rational numbers but +for the statement of this theorem + + align:start position:0% + + + + align:start position:0% + +if i look at those rational numbers + + align:start position:0% +if i look at those rational numbers + + + align:start position:0% +if i look at those rational numbers +with + + align:start position:0% +with + + + align:start position:0% +with +which are positive + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +this has the same size + + align:start position:0% +this has the same size + + + align:start position:0% +this has the same size +as + + align:start position:0% +as + + + align:start position:0% +as +the natural numbers you can count the + + align:start position:0% +the natural numbers you can count the + + + align:start position:0% +the natural numbers you can count the +positive rational numbers which is just + + align:start position:0% +positive rational numbers which is just + + + align:start position:0% +positive rational numbers which is just +you know + + align:start position:0% +you know + + + align:start position:0% +you know +a bit uh + + align:start position:0% +a bit uh + + + align:start position:0% +a bit uh +a bit crazy to me because + + align:start position:0% +a bit crazy to me because + + + align:start position:0% +a bit crazy to me because +you know here + + align:start position:0% +you know here + + + align:start position:0% +you know here +at least for let's say the integers + + align:start position:0% +at least for let's say the integers + + + align:start position:0% +at least for let's say the integers +once i'm at an integer + + align:start position:0% +once i'm at an integer + + + align:start position:0% +once i'm at an integer +i can move to a next biggest one and + + align:start position:0% +i can move to a next biggest one and + + + align:start position:0% +i can move to a next biggest one and +count that one in some way right + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +so that kind of makes it believable that + + align:start position:0% +so that kind of makes it believable that + + + align:start position:0% +so that kind of makes it believable that +i can count + + align:start position:0% +i can count + + + align:start position:0% +i can count +uh the integers the integers have the + + align:start position:0% +uh the integers the integers have the + + + align:start position:0% +uh the integers the integers have the +same size as the natural numbers even + + align:start position:0% +same size as the natural numbers even + + + align:start position:0% +same size as the natural numbers even +though that at first glance it looks + + align:start position:0% +though that at first glance it looks + + + align:start position:0% +though that at first glance it looks +like there's twice as many + + align:start position:0% +like there's twice as many + + + align:start position:0% +like there's twice as many +um + + align:start position:0% +um + + + align:start position:0% +um +but for rational numbers you know + + align:start position:0% +but for rational numbers you know + + + align:start position:0% +but for rational numbers you know +between any two rational numbers there's + + align:start position:0% +between any two rational numbers there's + + + align:start position:0% +between any two rational numbers there's +another rational number in between them + + align:start position:0% +another rational number in between them + + + align:start position:0% +another rational number in between them +right you just take uh + + align:start position:0% +right you just take uh + + + align:start position:0% +right you just take uh +take the average of those two rational + + align:start position:0% +take the average of those two rational + + + align:start position:0% +take the average of those two rational +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +so it's not cl so now this idea of + + align:start position:0% +so it's not cl so now this idea of + + + align:start position:0% +so it's not cl so now this idea of +being at a rational number and then sort + + align:start position:0% +being at a rational number and then sort + + + align:start position:0% +being at a rational number and then sort +of moving to the next big one + + align:start position:0% +of moving to the next big one + + + align:start position:0% +of moving to the next big one +that you can't do that now so now it's + + align:start position:0% +that you can't do that now so now it's + + + align:start position:0% +that you can't do that now so now it's +it's a little bit + + align:start position:0% +it's a little bit + + + align:start position:0% +it's a little bit +up in the air at least whether or not + + align:start position:0% +up in the air at least whether or not + + + align:start position:0% +up in the air at least whether or not +you can count the rational numbers + + align:start position:0% +you can count the rational numbers + + + align:start position:0% +you can count the rational numbers +and what i'm saying is + + align:start position:0% +and what i'm saying is + + + align:start position:0% +and what i'm saying is +that indeed you can and this will be + + align:start position:0% +that indeed you can and this will be + + + align:start position:0% +that indeed you can and this will be +part of the homework + + align:start position:0% + + + + align:start position:0% + +i will at least + + align:start position:0% + + + + align:start position:0% + +give you an idea of + + align:start position:0% +give you an idea of + + + align:start position:0% +give you an idea of +how the proof will go what we will + + align:start position:0% +how the proof will go what we will + + + align:start position:0% +how the proof will go what we will +actually be able to write down a map + + align:start position:0% +actually be able to write down a map + + + align:start position:0% +actually be able to write down a map +based on a simple fact + + align:start position:0% +based on a simple fact + + + align:start position:0% +based on a simple fact +so let me not write down proof but + + align:start position:0% +so let me not write down proof but + + + align:start position:0% +so let me not write down proof but +let me write down + + align:start position:0% +let me write down + + + align:start position:0% +let me write down +remark + + align:start position:0% +remark + + + align:start position:0% +remark +so we'll actually actually be able to + + align:start position:0% +so we'll actually actually be able to + + + align:start position:0% +so we'll actually actually be able to +write down a map based on one simple + + align:start position:0% +write down a map based on one simple + + + align:start position:0% +write down a map based on one simple +fact which is this fundamental theorem + + align:start position:0% +fact which is this fundamental theorem + + + align:start position:0% +fact which is this fundamental theorem +of arithmetic which says + + align:start position:0% +of arithmetic which says + + + align:start position:0% +of arithmetic which says +that so this is just discussion now you + + align:start position:0% +that so this is just discussion now you + + + align:start position:0% +that so this is just discussion now you +know + + align:start position:0% + + + + align:start position:0% + +more stuff will be written in the + + align:start position:0% +more stuff will be written in the + + + align:start position:0% +more stuff will be written in the +homework about this but so just try to + + align:start position:0% +homework about this but so just try to + + + align:start position:0% +homework about this but so just try to +follow along + + align:start position:0% +follow along + + + align:start position:0% +follow along +so the fundamental theorem of arithmetic + + align:start position:0% +so the fundamental theorem of arithmetic + + + align:start position:0% +so the fundamental theorem of arithmetic +says that if you have a positive natural + + align:start position:0% +says that if you have a positive natural + + + align:start position:0% +says that if you have a positive natural +number + + align:start position:0% +number + + + align:start position:0% +number +you can write it in a unique way as a + + align:start position:0% +you can write it in a unique way as a + + + align:start position:0% +you can write it in a unique way as a +product of prime numbers + + align:start position:0% +product of prime numbers + + + align:start position:0% +product of prime numbers +now for rational numbers + + align:start position:0% +now for rational numbers + + + align:start position:0% +now for rational numbers +using that + + align:start position:0% +using that + + + align:start position:0% +using that +that means you can write every rational + + align:start position:0% +that means you can write every rational + + + align:start position:0% +that means you can write every rational +number uniquely + + align:start position:0% +number uniquely + + + align:start position:0% +number uniquely +as a product of prime numbers + + align:start position:0% +as a product of prime numbers + + + align:start position:0% +as a product of prime numbers +divided by another product of prime + + align:start position:0% +divided by another product of prime + + + align:start position:0% +divided by another product of prime +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +where no two prime numbers uh + + align:start position:0% +where no two prime numbers uh + + + align:start position:0% +where no two prime numbers uh +where the where the prime numbers up top + + align:start position:0% +where the where the prime numbers up top + + + align:start position:0% +where the where the prime numbers up top +and the prime numbers at the bottom uh + + align:start position:0% +and the prime numbers at the bottom uh + + + align:start position:0% +and the prime numbers at the bottom uh +none are in common meaning you've + + align:start position:0% +none are in common meaning you've + + + align:start position:0% +none are in common meaning you've +uh simplified as much as possible so + + align:start position:0% +uh simplified as much as possible so + + + align:start position:0% +uh simplified as much as possible so +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +um + + align:start position:0% +um + + + align:start position:0% +um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +15 over 3 + + align:start position:0% +15 over 3 + + + align:start position:0% +15 over 3 +no that's not good + + align:start position:0% +no that's not good + + + align:start position:0% +no that's not good +let's say 15 over 30 + + align:start position:0% +let's say 15 over 30 + + + align:start position:0% +let's say 15 over 30 +you have one half okay + + align:start position:0% +you have one half okay + + + align:start position:0% +you have one half okay +so + + align:start position:0% +so + + + align:start position:0% +so +the map that i would take + + align:start position:0% +the map that i would take + + + align:start position:0% +the map that i would take +so what i'm saying here is that every + + align:start position:0% +so what i'm saying here is that every + + + align:start position:0% +so what i'm saying here is that every +rational number + + align:start position:0% + + + + align:start position:0% + +can be written as + + align:start position:0% + + + + align:start position:0% + +some + + align:start position:0% +some + + + align:start position:0% +some +product + + align:start position:0% +product + + + align:start position:0% +product +so let me not use that notation but some + + align:start position:0% +so let me not use that notation but some + + + align:start position:0% +so let me not use that notation but some +product p r one + + align:start position:0% +product p r one + + + align:start position:0% +product p r one +p n r n + + align:start position:0% + + + + align:start position:0% + +q one + + align:start position:0% +q one + + + align:start position:0% +q one +s one + + align:start position:0% + + + + align:start position:0% + +q m + + align:start position:0% +q m + + + align:start position:0% +q m +s n where + + align:start position:0% +s n where + + + align:start position:0% +s n where +p1 p1 p2 and pn these are all primes q1 + + align:start position:0% +p1 p1 p2 and pn these are all primes q1 + + + align:start position:0% +p1 p1 p2 and pn these are all primes q1 +up to qm they're all primes r1 or n + + align:start position:0% +up to qm they're all primes r1 or n + + + align:start position:0% +up to qm they're all primes r1 or n +these are all exponents positive + + align:start position:0% +these are all exponents positive + + + align:start position:0% +these are all exponents positive +natural numbers so + + align:start position:0% +natural numbers so + + + align:start position:0% +natural numbers so +rj + + align:start position:0% +rj + + + align:start position:0% +rj +s k these are natural numbers + + align:start position:0% +s k these are natural numbers + + + align:start position:0% +s k these are natural numbers +p 1 p n q 1 to q m are primes + + align:start position:0% +p 1 p n q 1 to q m are primes + + + align:start position:0% +p 1 p n q 1 to q m are primes +and + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +j k + + align:start position:0% +j k + + + align:start position:0% +j k +qj does not equal + + align:start position:0% +qj does not equal + + + align:start position:0% +qj does not equal +pk so there's no prime that appears both + + align:start position:0% +pk so there's no prime that appears both + + + align:start position:0% +pk so there's no prime that appears both +up here and down here we've already + + align:start position:0% +up here and down here we've already + + + align:start position:0% +up here and down here we've already +simplified that away + + align:start position:0% +simplified that away + + + align:start position:0% +simplified that away +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so then + + align:start position:0% + + + + align:start position:0% + +the map + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this uh + + align:start position:0% + + + + align:start position:0% + +so just so + + align:start position:0% +so just so + + + align:start position:0% +so just so +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you don't think i'm i'm + + align:start position:0% +you don't think i'm i'm + + + align:start position:0% +you don't think i'm i'm +fooling you + + align:start position:0% +fooling you + + + align:start position:0% +fooling you +you know nine halves + + align:start position:0% +you know nine halves + + + align:start position:0% +you know nine halves +which is a positive rational number this + + align:start position:0% +which is a positive rational number this + + + align:start position:0% +which is a positive rational number this +is three squared over two + + align:start position:0% +is three squared over two + + + align:start position:0% +is three squared over two +yeah + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know 20 i'm not going to do any more + + align:start position:0% +you know 20 i'm not going to do any more + + + align:start position:0% +you know 20 i'm not going to do any more +that's it + + align:start position:0% +that's it + + + align:start position:0% +that's it +you should + + align:start position:0% +you should + + + align:start position:0% +you should +so + + align:start position:0% + + + + align:start position:0% + +the map that we will take from this + + align:start position:0% +the map that we will take from this + + + align:start position:0% +the map that we will take from this +rational number to + + align:start position:0% +rational number to + + + align:start position:0% +rational number to +a natural number + + align:start position:0% +a natural number + + + align:start position:0% +a natural number +will be + + align:start position:0% +will be + + + align:start position:0% +will be +this gets mapped to + + align:start position:0% +this gets mapped to + + + align:start position:0% +this gets mapped to +the natural number p1 + + align:start position:0% +the natural number p1 + + + align:start position:0% +the natural number p1 +to r1 + + align:start position:0% +to r1 + + + align:start position:0% +to r1 +pn + + align:start position:0% + + + + align:start position:0% + +2rn + + align:start position:0% +2rn + + + align:start position:0% +2rn +times now + + align:start position:0% +times now + + + align:start position:0% +times now +q one two + + align:start position:0% +q one two + + + align:start position:0% +q one two +two s one minus one + + align:start position:0% + + + + align:start position:0% + +q m + + align:start position:0% +q m + + + align:start position:0% +q m +two s n minus one so basically i map it + + align:start position:0% +two s n minus one so basically i map it + + + align:start position:0% +two s n minus one so basically i map it +to the integer + + align:start position:0% +to the integer + + + align:start position:0% +to the integer +that has this exp has this expansion in + + align:start position:0% +that has this exp has this expansion in + + + align:start position:0% +that has this exp has this expansion in +terms of prime numbers + + align:start position:0% +terms of prime numbers + + + align:start position:0% +terms of prime numbers +where now the exponents of these prime + + align:start position:0% +where now the exponents of these prime + + + align:start position:0% +where now the exponents of these prime +numbers is even depending on these + + align:start position:0% +numbers is even depending on these + + + align:start position:0% +numbers is even depending on these +exponents on top and the exponents of + + align:start position:0% +exponents on top and the exponents of + + + align:start position:0% +exponents on top and the exponents of +this one + + align:start position:0% +this one + + + align:start position:0% +this one +are odd depending on this exponent on + + align:start position:0% +are odd depending on this exponent on + + + align:start position:0% +are odd depending on this exponent on +top + + align:start position:0% +top + + + align:start position:0% +top +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so for example 3 squared over 2 + + align:start position:0% +so for example 3 squared over 2 + + + align:start position:0% +so for example 3 squared over 2 +this would + + align:start position:0% +this would + + + align:start position:0% +this would +get mapped to a + + align:start position:0% +get mapped to a + + + align:start position:0% +get mapped to a +three to the fourth times + + align:start position:0% +three to the fourth times + + + align:start position:0% +three to the fourth times +two + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so what we'll do in the homework is show + + align:start position:0% +so what we'll do in the homework is show + + + align:start position:0% +so what we'll do in the homework is show +that this map is in fact a bijection + + align:start position:0% +that this map is in fact a bijection + + + align:start position:0% +that this map is in fact a bijection +so + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +those two theorems + + align:start position:0% +those two theorems + + + align:start position:0% +those two theorems +you will prove in the homework they + + align:start position:0% +you will prove in the homework they + + + align:start position:0% +you will prove in the homework they +won't be too + + align:start position:0% +won't be too + + + align:start position:0% +won't be too +too bad i will leave enough hints + + align:start position:0% +too bad i will leave enough hints + + + align:start position:0% +too bad i will leave enough hints +so + + align:start position:0% +so + + + align:start position:0% +so +uh dealt with z + + align:start position:0% +uh dealt with z + + + align:start position:0% +uh dealt with z +dealt with q essentially + + align:start position:0% + + + + align:start position:0% + +i mean so + + align:start position:0% +i mean so + + + align:start position:0% +i mean so +let me + + align:start position:0% + + + + align:start position:0% + +actually write down this is really a + + align:start position:0% +actually write down this is really a + + + align:start position:0% +actually write down this is really a +corollary of + + align:start position:0% +corollary of + + + align:start position:0% +corollary of +these two theorems here + + align:start position:0% +these two theorems here + + + align:start position:0% +these two theorems here +which i haven't proved but you will + + align:start position:0% +which i haven't proved but you will + + + align:start position:0% +which i haven't proved but you will +prove in the homework + + align:start position:0% +prove in the homework + + + align:start position:0% +prove in the homework +so + + align:start position:0% +so + + + align:start position:0% +so +it says that + + align:start position:0% + + + + align:start position:0% + +the rationals are countable all the + + align:start position:0% +the rationals are countable all the + + + align:start position:0% +the rationals are countable all the +rationals not just the positive ones + + align:start position:0% +rationals not just the positive ones + + + align:start position:0% +rationals not just the positive ones +and + + align:start position:0% +and + + + align:start position:0% +and +what's the proof + + align:start position:0% +what's the proof + + + align:start position:0% +what's the proof +so + + align:start position:0% + + + + align:start position:0% + +we know that + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +i'm going to give you kind of a sketch + + align:start position:0% +i'm going to give you kind of a sketch + + + align:start position:0% +i'm going to give you kind of a sketch +should i sketch it or should i write it + + align:start position:0% +should i sketch it or should i write it + + + align:start position:0% +should i sketch it or should i write it +all out i'm running a little bit at a + + align:start position:0% +all out i'm running a little bit at a + + + align:start position:0% +all out i'm running a little bit at a +time + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% + + + + align:start position:0% + +so maybe i will just + + align:start position:0% +so maybe i will just + + + align:start position:0% +so maybe i will just +tell you why this is true + + align:start position:0% +tell you why this is true + + + align:start position:0% +tell you why this is true +i mean all the details are essentially + + align:start position:0% +i mean all the details are essentially + + + align:start position:0% +i mean all the details are essentially +here i'm just not going to write it as + + align:start position:0% +here i'm just not going to write it as + + + align:start position:0% +here i'm just not going to write it as +carefully as i've been writing down the + + align:start position:0% +carefully as i've been writing down the + + + align:start position:0% +carefully as i've been writing down the +proofs before + + align:start position:0% +proofs before + + + align:start position:0% +proofs before +so + + align:start position:0% +so + + + align:start position:0% +so +let me write this as + + align:start position:0% +let me write this as + + + align:start position:0% +let me write this as +the proof sketch + + align:start position:0% + + + + align:start position:0% + +of course you can write these + + align:start position:0% +of course you can write these + + + align:start position:0% +of course you can write these +you can actually use the definitions and + + align:start position:0% +you can actually use the definitions and + + + align:start position:0% +you can actually use the definitions and +write this out but this is a the + + align:start position:0% +write this out but this is a the + + + align:start position:0% +write this out but this is a the +essential idea so + + align:start position:0% +essential idea so + + + align:start position:0% +essential idea so +um + + align:start position:0% + + + + align:start position:0% + +we have that the size of + + align:start position:0% +we have that the size of + + + align:start position:0% +we have that the size of +rational numbers + + align:start position:0% + + + + align:start position:0% + +so let me + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +this has the same size as + + align:start position:0% + + + + align:start position:0% + +the rational numbers + + align:start position:0% +the rational numbers + + + align:start position:0% +the rational numbers +which are negative + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and this how do we establish this + + align:start position:0% +and this how do we establish this + + + align:start position:0% +and this how do we establish this +or + + align:start position:0% +or + + + align:start position:0% +or +let me instead of using the same letter + + align:start position:0% +let me instead of using the same letter + + + align:start position:0% +let me instead of using the same letter +let's say r + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +f of q equals minus q + + align:start position:0% +f of q equals minus q + + + align:start position:0% +f of q equals minus q +is a + + align:start position:0% + + + + align:start position:0% + +bijection + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% +from + + + align:start position:0% +from +the first set to the second set + + align:start position:0% + + + + align:start position:0% + +if i just take a rational number + + align:start position:0% +if i just take a rational number + + + align:start position:0% +if i just take a rational number +positive one take its minus then i get + + align:start position:0% +positive one take its minus then i get + + + align:start position:0% +positive one take its minus then i get +an element of the second set and this + + align:start position:0% +an element of the second set and this + + + align:start position:0% +an element of the second set and this +is a bijection okay + + align:start position:0% +is a bijection okay + + + align:start position:0% +is a bijection okay +um okay so + + align:start position:0% + + + + align:start position:0% + +thus + + align:start position:0% + + + + align:start position:0% + +since this has the same size as the + + align:start position:0% +since this has the same size as the + + + align:start position:0% +since this has the same size as the +natural numbers + + align:start position:0% + + + + align:start position:0% + +and by that theorem we proved over there + + align:start position:0% +and by that theorem we proved over there + + + align:start position:0% +and by that theorem we proved over there +the size of this set is the same as the + + align:start position:0% +the size of this set is the same as the + + + align:start position:0% +the size of this set is the same as the +natural numbers so + + align:start position:0% +natural numbers so + + + align:start position:0% +natural numbers so +it is countable + + align:start position:0% +it is countable + + + align:start position:0% +it is countable +okay + + align:start position:0% + + + + align:start position:0% + +then there exists + + align:start position:0% + + + + align:start position:0% + +bijections + + align:start position:0% + + + + align:start position:0% + +f + + align:start position:0% +f + + + align:start position:0% +f +going from + + align:start position:0% +going from + + + align:start position:0% +going from +q so the positive rational numbers + + align:start position:0% + + + + align:start position:0% + +to the natural numbers + + align:start position:0% + + + + align:start position:0% + +and g going from the negative ones + + align:start position:0% + + + + align:start position:0% + +to the natural numbers + + align:start position:0% +to the natural numbers + + + align:start position:0% +to the natural numbers +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +picture here is + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +well let's not write draw the picture + + align:start position:0% +well let's not write draw the picture + + + align:start position:0% +well let's not write draw the picture +yet + + align:start position:0% +yet + + + align:start position:0% +yet +okay so i have these two bijections from + + align:start position:0% +okay so i have these two bijections from + + + align:start position:0% +okay so i have these two bijections from +the positive rationals to the integers + + align:start position:0% +the positive rationals to the integers + + + align:start position:0% +the positive rationals to the integers +this one from + + align:start position:0% +this one from + + + align:start position:0% +this one from +um + + align:start position:0% +um + + + align:start position:0% +um +the negative rationals to the + + align:start position:0% +the negative rationals to the + + + align:start position:0% +the negative rationals to the +natural numbers + + align:start position:0% +natural numbers + + + align:start position:0% +natural numbers +how do i get a map that goes from all of + + align:start position:0% +how do i get a map that goes from all of + + + align:start position:0% +how do i get a map that goes from all of +q + + align:start position:0% +q + + + align:start position:0% +q +now to the natural numbers well let's go + + align:start position:0% +now to the natural numbers well let's go + + + align:start position:0% +now to the natural numbers well let's go +in between and go to the integers + + align:start position:0% +in between and go to the integers + + + align:start position:0% +in between and go to the integers +then i define + + align:start position:0% + + + + align:start position:0% + +a function + + align:start position:0% +a function + + + align:start position:0% +a function +h + + align:start position:0% +h + + + align:start position:0% +h +which goes now from all of q + + align:start position:0% +which goes now from all of q + + + align:start position:0% +which goes now from all of q +to + + align:start position:0% +to + + + align:start position:0% +to +the integers + + align:start position:0% + + + + align:start position:0% + +by + + align:start position:0% +by + + + align:start position:0% +by +h of x + + align:start position:0% +h of x + + + align:start position:0% +h of x +equals + + align:start position:0% +equals + + + align:start position:0% +equals +0 if x equals 0 + + align:start position:0% +0 if x equals 0 + + + align:start position:0% +0 if x equals 0 +equals + + align:start position:0% +equals + + + align:start position:0% +equals +f of x if x is positive + + align:start position:0% +f of x if x is positive + + + align:start position:0% +f of x if x is positive +and negative + + align:start position:0% +and negative + + + align:start position:0% +and negative +g of x + + align:start position:0% +g of x + + + align:start position:0% +g of x +if x is negative + + align:start position:0% +if x is negative + + + align:start position:0% +if x is negative +okay + + align:start position:0% + + + + align:start position:0% + +and h is + + align:start position:0% + + + + align:start position:0% + +bijection + + align:start position:0% +bijection + + + align:start position:0% +bijection +so everything up into this point um + + align:start position:0% +so everything up into this point um + + + align:start position:0% +so everything up into this point um +has been + + align:start position:0% +has been + + + align:start position:0% +has been +completely fine with the exception of me + + align:start position:0% +completely fine with the exception of me + + + align:start position:0% +completely fine with the exception of me +verifying that this map is a bijection + + align:start position:0% +verifying that this map is a bijection + + + align:start position:0% +verifying that this map is a bijection +and this map is a bijection so that's + + align:start position:0% +and this map is a bijection so that's + + + align:start position:0% +and this map is a bijection so that's +kind of the only parts that i'm leaving + + align:start position:0% +kind of the only parts that i'm leaving + + + align:start position:0% +kind of the only parts that i'm leaving +out for you to verify + + align:start position:0% +out for you to verify + + + align:start position:0% +out for you to verify +then h is a bijection + + align:start position:0% +then h is a bijection + + + align:start position:0% +then h is a bijection +so + + align:start position:0% + + + + align:start position:0% + +q + + align:start position:0% +q + + + align:start position:0% +q +has the same + + align:start position:0% +has the same + + + align:start position:0% +has the same +cardinality as integers + + align:start position:0% +cardinality as integers + + + align:start position:0% +cardinality as integers +which we've shown has the same + + align:start position:0% +which we've shown has the same + + + align:start position:0% +which we've shown has the same +cardinality + + align:start position:0% +cardinality + + + align:start position:0% +cardinality +as the natural numbers + + align:start position:0% + + + + align:start position:0% + +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +rationals have the same cardinality + + align:start position:0% +rationals have the same cardinality + + + align:start position:0% +rationals have the same cardinality +as the natural numbers so they are + + align:start position:0% +as the natural numbers so they are + + + align:start position:0% +as the natural numbers so they are +accountably infinite + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +natural question is + + align:start position:0% +natural question is + + + align:start position:0% +natural question is +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +i mean is there anything bigger than the + + align:start position:0% +i mean is there anything bigger than the + + + align:start position:0% +i mean is there anything bigger than the +natural numbers because everything i've + + align:start position:0% +natural numbers because everything i've + + + align:start position:0% +natural numbers because everything i've +written down this has the size of the + + align:start position:0% +written down this has the size of the + + + align:start position:0% +written down this has the size of the +natural numbers + + align:start position:0% + + + + align:start position:0% + +we haven't really defined + + align:start position:0% +we haven't really defined + + + align:start position:0% +we haven't really defined +the real numbers well enough yet to + + align:start position:0% + + + + align:start position:0% + +make + + align:start position:0% +make + + + align:start position:0% +make +any sort of claim + + align:start position:0% +any sort of claim + + + align:start position:0% +any sort of claim +like that about the real numbers + + align:start position:0% +like that about the real numbers + + + align:start position:0% +like that about the real numbers +and now is there just any set + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +is bigger in size than the natural + + align:start position:0% +is bigger in size than the natural + + + align:start position:0% +is bigger in size than the natural +numbers the answer to that + + align:start position:0% + + + + align:start position:0% + +you know was unknown and it's + + align:start position:0% +you know was unknown and it's + + + align:start position:0% +you know was unknown and it's +pretty um + + align:start position:0% +pretty um + + + align:start position:0% +pretty um +pretty strikingly yes + + align:start position:0% +pretty strikingly yes + + + align:start position:0% +pretty strikingly yes +in fact + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let me phrase that question + + align:start position:0% + + + + align:start position:0% + +does there exist + + align:start position:0% +does there exist + + + align:start position:0% +does there exist +you set + + align:start position:0% + + + + align:start position:0% + +a such that + + align:start position:0% + + + + align:start position:0% + +a has strictly bigger cardinality than + + align:start position:0% +a has strictly bigger cardinality than + + + align:start position:0% +a has strictly bigger cardinality than +the natural numbers so a is uncountable + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so to answer this question astoundedly + + align:start position:0% +so to answer this question astoundedly + + + align:start position:0% +so to answer this question astoundedly +yes + + align:start position:0% +yes + + + align:start position:0% +yes +let me first define for a + + align:start position:0% +let me first define for a + + + align:start position:0% +let me first define for a +general object + + align:start position:0% + + + + align:start position:0% + +if a is a set + + align:start position:0% + + + + align:start position:0% + +we define + + align:start position:0% +we define + + + align:start position:0% +we define +script p of a + + align:start position:0% +script p of a + + + align:start position:0% +script p of a +this is the power set of a + + align:start position:0% + + + + align:start position:0% + +this is a set that consists of all + + align:start position:0% +this is a set that consists of all + + + align:start position:0% +this is a set that consists of all +subsets of a + + align:start position:0% +subsets of a + + + align:start position:0% +subsets of a +so this is the + + align:start position:0% +so this is the + + + align:start position:0% +so this is the +set of all sets b + + align:start position:0% +set of all sets b + + + align:start position:0% +set of all sets b +such that b is a subset + + align:start position:0% +such that b is a subset + + + align:start position:0% +such that b is a subset +of a + + align:start position:0% +of a + + + align:start position:0% +of a +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so for example + + align:start position:0% + + + + align:start position:0% + +uh if a is + + align:start position:0% +uh if a is + + + align:start position:0% +uh if a is +the empty set + + align:start position:0% + + + + align:start position:0% + +the power set + + align:start position:0% + + + + align:start position:0% + +so a is empty + + align:start position:0% +so a is empty + + + align:start position:0% +so a is empty +what + + align:start position:0% +what + + + align:start position:0% +what +are the subsets of the empty set well + + align:start position:0% +are the subsets of the empty set well + + + align:start position:0% +are the subsets of the empty set well +there's only one subset of the empty set + + align:start position:0% +there's only one subset of the empty set + + + align:start position:0% +there's only one subset of the empty set +the empty set + + align:start position:0% +the empty set + + + align:start position:0% +the empty set +so and even though the empty set has no + + align:start position:0% +so and even though the empty set has no + + + align:start position:0% +so and even though the empty set has no +members its power set has one member + + align:start position:0% + + + + align:start position:0% + +if a equals one + + align:start position:0% +if a equals one + + + align:start position:0% +if a equals one +then the power set of a the set of all + + align:start position:0% +then the power set of a the set of all + + + align:start position:0% +then the power set of a the set of all +subsets consists of the empty set + + align:start position:0% +subsets consists of the empty set + + + align:start position:0% +subsets consists of the empty set +and + + align:start position:0% +and + + + align:start position:0% +and +the set itself + + align:start position:0% +the set itself + + + align:start position:0% +the set itself +one + + align:start position:0% +one + + + align:start position:0% +one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and let's do one more + + align:start position:0% + + + + align:start position:0% + +if a is the set 1 2 + + align:start position:0% +if a is the set 1 2 + + + align:start position:0% +if a is the set 1 2 +then the power set + + align:start position:0% + + + + align:start position:0% + +of a + + align:start position:0% +of a + + + align:start position:0% +of a +this is the set + + align:start position:0% + + + + align:start position:0% + +which consists of the empty set because + + align:start position:0% +which consists of the empty set because + + + align:start position:0% +which consists of the empty set because +this is a subset of the set + + align:start position:0% +this is a subset of the set + + + align:start position:0% +this is a subset of the set +the set consisting of one because this + + align:start position:0% +the set consisting of one because this + + + align:start position:0% +the set consisting of one because this +is a subset of this set + + align:start position:0% +is a subset of this set + + + align:start position:0% +is a subset of this set +or two + + align:start position:0% + + + + align:start position:0% + +one two + + align:start position:0% +one two + + + align:start position:0% +one two +now notice something + + align:start position:0% +now notice something + + + align:start position:0% +now notice something +this set had cardinality uh strictly + + align:start position:0% +this set had cardinality uh strictly + + + align:start position:0% +this set had cardinality uh strictly +speaking + + align:start position:0% +speaking + + + align:start position:0% +speaking +i should have defined that as being + + align:start position:0% +i should have defined that as being + + + align:start position:0% +i should have defined that as being +having cardinality zero yet its power + + align:start position:0% +having cardinality zero yet its power + + + align:start position:0% +having cardinality zero yet its power +set has cardinality one + + align:start position:0% +set has cardinality one + + + align:start position:0% +set has cardinality one +a has size one because it's uh in one to + + align:start position:0% +a has size one because it's uh in one to + + + align:start position:0% +a has size one because it's uh in one to +one correspondence with just + + align:start position:0% +one correspondence with just + + + align:start position:0% +one correspondence with just +one + + align:start position:0% +one + + + align:start position:0% +one +and its power set has + + align:start position:0% +and its power set has + + + align:start position:0% +and its power set has +uh two elements so + + align:start position:0% +uh two elements so + + + align:start position:0% +uh two elements so +um + + align:start position:0% +um + + + align:start position:0% +um +has cardinality two i could count them + + align:start position:0% +has cardinality two i could count them + + + align:start position:0% +has cardinality two i could count them +off one two + + align:start position:0% +off one two + + + align:start position:0% +off one two +a has size two has two elements and the + + align:start position:0% +a has size two has two elements and the + + + align:start position:0% +a has size two has two elements and the +power set of a has size four it has four + + align:start position:0% +power set of a has size four it has four + + + align:start position:0% +power set of a has size four it has four +different elements that empty set one + + align:start position:0% +different elements that empty set one + + + align:start position:0% +different elements that empty set one +two + + align:start position:0% +two + + + align:start position:0% +two +one two + + align:start position:0% +one two + + + align:start position:0% +one two +so what one can prove in general + + align:start position:0% + + + + align:start position:0% + +and which will appear on the homework is + + align:start position:0% +and which will appear on the homework is + + + align:start position:0% +and which will appear on the homework is +if + + align:start position:0% +if + + + align:start position:0% +if +a + + align:start position:0% +a + + + align:start position:0% +a +has the same car has size n so it's a + + align:start position:0% +has the same car has size n so it's a + + + align:start position:0% +has the same car has size n so it's a +finite set of size n + + align:start position:0% +finite set of size n + + + align:start position:0% +finite set of size n +meaning it's in one to one + + align:start position:0% +meaning it's in one to one + + + align:start position:0% +meaning it's in one to one +correspondence with the + + align:start position:0% +correspondence with the + + + align:start position:0% +correspondence with the +numbers one up to n + + align:start position:0% +numbers one up to n + + + align:start position:0% +numbers one up to n +then + + align:start position:0% + + + + align:start position:0% + +its power set is also finite + + align:start position:0% + + + + align:start position:0% + +and has cardinality two to the n + + align:start position:0% +and has cardinality two to the n + + + align:start position:0% +and has cardinality two to the n +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +you can prove by induction if you like + + align:start position:0% +you can prove by induction if you like + + + align:start position:0% +you can prove by induction if you like +that two to the n is always bigger than + + align:start position:0% +that two to the n is always bigger than + + + align:start position:0% +that two to the n is always bigger than +n + + align:start position:0% +n + + + align:start position:0% +n +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% + + + + align:start position:0% + +so a theorem i'll prove next time + + align:start position:0% +so a theorem i'll prove next time + + + align:start position:0% +so a theorem i'll prove next time +which will finish our discussion of sets + + align:start position:0% +which will finish our discussion of sets + + + align:start position:0% +which will finish our discussion of sets +and uh cardinality + + align:start position:0% +and uh cardinality + + + align:start position:0% +and uh cardinality +um + + align:start position:0% +um + + + align:start position:0% +um +and then we'll move on to the real + + align:start position:0% +and then we'll move on to the real + + + align:start position:0% +and then we'll move on to the real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +is this theorem due to cantor + + align:start position:0% + + + + align:start position:0% + +uh which says that not just for + + align:start position:0% +uh which says that not just for + + + align:start position:0% +uh which says that not just for +you know finite sets do we have the + + align:start position:0% +you know finite sets do we have the + + + align:start position:0% +you know finite sets do we have the +power set being in some sense strictly + + align:start position:0% +power set being in some sense strictly + + + align:start position:0% +power set being in some sense strictly +bigger than the original set but for any + + align:start position:0% +bigger than the original set but for any + + + align:start position:0% +bigger than the original set but for any +set + + align:start position:0% +set + + + align:start position:0% +set +so + + align:start position:0% +so + + + align:start position:0% +so +this theorem due to cantor is if a + + align:start position:0% +this theorem due to cantor is if a + + + align:start position:0% +this theorem due to cantor is if a +is a set + + align:start position:0% +is a set + + + align:start position:0% +is a set +then + + align:start position:0% + + + + align:start position:0% + +the cardinality of a is strictly smaller + + align:start position:0% +the cardinality of a is strictly smaller + + + align:start position:0% +the cardinality of a is strictly smaller +than + + align:start position:0% +than + + + align:start position:0% +than +the cardinality of its power set + + align:start position:0% +the cardinality of its power set + + + align:start position:0% +the cardinality of its power set +so + + align:start position:0% +so + + + align:start position:0% +so +this definitely answers our question + + align:start position:0% +this definitely answers our question + + + align:start position:0% +this definitely answers our question +does there exist a set with cardinality + + align:start position:0% +does there exist a set with cardinality + + + align:start position:0% +does there exist a set with cardinality +bigger than the natural numbers + + align:start position:0% +bigger than the natural numbers + + + align:start position:0% +bigger than the natural numbers +so let me write this as a remark + + align:start position:0% + + + + align:start position:0% + +uh in fact + + align:start position:0% +uh in fact + + + align:start position:0% +uh in fact +maybe i'll state this as another theorem + + align:start position:0% +maybe i'll state this as another theorem + + + align:start position:0% +maybe i'll state this as another theorem +which just follows immediately from this + + align:start position:0% +which just follows immediately from this + + + align:start position:0% +which just follows immediately from this +kind of getting used over and over again + + align:start position:0% +kind of getting used over and over again + + + align:start position:0% +kind of getting used over and over again +is that + + align:start position:0% +is that + + + align:start position:0% +is that +the cardinality of the natural numbers + + align:start position:0% +the cardinality of the natural numbers + + + align:start position:0% +the cardinality of the natural numbers +this is less than the cardinality + + align:start position:0% +this is less than the cardinality + + + align:start position:0% +this is less than the cardinality +of the power set of the natural numbers + + align:start position:0% +of the power set of the natural numbers + + + align:start position:0% +of the power set of the natural numbers +which is less than the cardinality of + + align:start position:0% +which is less than the cardinality of + + + align:start position:0% +which is less than the cardinality of +the + + align:start position:0% +the + + + align:start position:0% +the +power set of the power set of the + + align:start position:0% +power set of the power set of the + + + align:start position:0% +power set of the power set of the +natural numbers + + align:start position:0% +natural numbers + + + align:start position:0% +natural numbers +right i can now take this as a set and + + align:start position:0% +right i can now take this as a set and + + + align:start position:0% +right i can now take this as a set and +take its power set and i get a new set + + align:start position:0% +take its power set and i get a new set + + + align:start position:0% +take its power set and i get a new set +with bigger size + + align:start position:0% +with bigger size + + + align:start position:0% +with bigger size +which is less than + + align:start position:0% +which is less than + + + align:start position:0% +which is less than +the power set of the power set where how + + align:start position:0% +the power set of the power set where how + + + align:start position:0% +the power set of the power set where how +many do we have now of the power set of + + align:start position:0% +many do we have now of the power set of + + + align:start position:0% +many do we have now of the power set of +natural numbers + + align:start position:0% +natural numbers + + + align:start position:0% +natural numbers +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +and formally this means they're + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +there's an infinity of infinitudes + + align:start position:0% +there's an infinity of infinitudes + + + align:start position:0% +there's an infinity of infinitudes +there's an infinite an infinite number + + align:start position:0% +there's an infinite an infinite number + + + align:start position:0% +there's an infinite an infinite number +of infinite sizes okay + + align:start position:0% +of infinite sizes okay + + + align:start position:0% +of infinite sizes okay +one getting strictly uh in some sense + + align:start position:0% +one getting strictly uh in some sense + + + align:start position:0% +one getting strictly uh in some sense +strictly bigger than the previous size + + align:start position:0% +strictly bigger than the previous size + + + align:start position:0% +strictly bigger than the previous size +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% + + + + align:start position:0% + +maybe you're wondering + + align:start position:0% +maybe you're wondering + + + align:start position:0% +maybe you're wondering +uh there's one more question that's kind + + align:start position:0% +uh there's one more question that's kind + + + align:start position:0% +uh there's one more question that's kind +of + + align:start position:0% + + + + align:start position:0% + +sandwiched in between here + + align:start position:0% +sandwiched in between here + + + align:start position:0% +sandwiched in between here +pun intended + + align:start position:0% +pun intended + + + align:start position:0% +pun intended +is + + align:start position:0% + + + + align:start position:0% + +let's look at this first + + align:start position:0% +let's look at this first + + + align:start position:0% +let's look at this first +guy + + align:start position:0% + + + + align:start position:0% + +does there exist + + align:start position:0% + + + + align:start position:0% + +set a + + align:start position:0% +set a + + + align:start position:0% +set a +such that + + align:start position:0% + + + + align:start position:0% + +it has size bigger than + + align:start position:0% +it has size bigger than + + + align:start position:0% +it has size bigger than +natural numbers so it's uncountable but + + align:start position:0% +natural numbers so it's uncountable but + + + align:start position:0% +natural numbers so it's uncountable but +has size strictly smaller than the power + + align:start position:0% +has size strictly smaller than the power + + + align:start position:0% +has size strictly smaller than the power +set of the natural numbers + + align:start position:0% +set of the natural numbers + + + align:start position:0% +set of the natural numbers +and this question is called the + + align:start position:0% + + + + align:start position:0% + +continuum hypothesis + + align:start position:0% + + + + align:start position:0% + +hypothesis because it is independent + + align:start position:0% +hypothesis because it is independent + + + align:start position:0% +hypothesis because it is independent +from one of the + + align:start position:0% +from one of the + + + align:start position:0% +from one of the +uh standard + + align:start position:0% +uh standard + + + align:start position:0% +uh standard +axiomatic treatments of set theory + + align:start position:0% +axiomatic treatments of set theory + + + align:start position:0% +axiomatic treatments of set theory +um + + align:start position:0% +um + + + align:start position:0% +um +but we will not touch this question this + + align:start position:0% +but we will not touch this question this + + + align:start position:0% +but we will not touch this question this +is beyond the scope of this class + + align:start position:0% +is beyond the scope of this class + + + align:start position:0% +is beyond the scope of this class +but it's an interesting question that's + + align:start position:0% +but it's an interesting question that's + + + align:start position:0% +but it's an interesting question that's +out there that you know people just + + align:start position:0% +out there that you know people just + + + align:start position:0% +out there that you know people just +don't know \ No newline at end of file diff --git a/AVn49LbYoB8.txt b/AVn49LbYoB8.txt new file mode 100644 index 0000000000000000000000000000000000000000..6c4cf354561b403e7de36dd3acf7a84a3c8e5079 --- /dev/null +++ b/AVn49LbYoB8.txt @@ -0,0 +1,1355 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop coreware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu in this demonstration we're + + align:start position:0% +ocw.mit.edu in this demonstration we're + + + align:start position:0% +ocw.mit.edu in this demonstration we're +going to show simple way of rotating the + + align:start position:0% +going to show simple way of rotating the + + + align:start position:0% +going to show simple way of rotating the +plane of polarization of laser light + + align:start position:0% +plane of polarization of laser light + + + align:start position:0% +plane of polarization of laser light +from 0° to anywhere to 90° using simple + + align:start position:0% +from 0° to anywhere to 90° using simple + + + align:start position:0% +from 0° to anywhere to 90° using simple +techniques for example by the use of + + align:start position:0% +techniques for example by the use of + + + align:start position:0% +techniques for example by the use of +polarizers the setup that we're going to + + align:start position:0% +polarizers the setup that we're going to + + + align:start position:0% +polarizers the setup that we're going to +use is + + align:start position:0% +use is + + + align:start position:0% +use is +here we have a laser helium neon laser + + align:start position:0% +here we have a laser helium neon laser + + + align:start position:0% +here we have a laser helium neon laser +and here is the the beam of the laser + + align:start position:0% +and here is the the beam of the laser + + + align:start position:0% +and here is the the beam of the laser +light we're going to reflect it of this + + align:start position:0% +light we're going to reflect it of this + + + align:start position:0% +light we're going to reflect it of this +mirror and then reflect it again of the + + align:start position:0% +mirror and then reflect it again of the + + + align:start position:0% +mirror and then reflect it again of the +second mirror and then we'll go through + + align:start position:0% +second mirror and then we'll go through + + + align:start position:0% +second mirror and then we'll go through +a polarizer + + align:start position:0% +a polarizer + + + align:start position:0% +a polarizer +and then the light coming out of the + + align:start position:0% +and then the light coming out of the + + + align:start position:0% +and then the light coming out of the +polarizer will go onto onto the + + align:start position:0% +polarizer will go onto onto the + + + align:start position:0% +polarizer will go onto onto the +screen the purpose of this polarizer is + + align:start position:0% +screen the purpose of this polarizer is + + + align:start position:0% +screen the purpose of this polarizer is +to establish the state of polarization + + align:start position:0% +to establish the state of polarization + + + align:start position:0% +to establish the state of polarization +of the light coming out of the polarizer + + align:start position:0% +of the light coming out of the polarizer + + + align:start position:0% +of the light coming out of the polarizer +if the polarizer is any good the state + + align:start position:0% +if the polarizer is any good the state + + + align:start position:0% +if the polarizer is any good the state +of polarization after the polarizer + + align:start position:0% +of polarization after the polarizer + + + align:start position:0% +of polarization after the polarizer +should be plain polarized now the little + + align:start position:0% +should be plain polarized now the little + + + align:start position:0% +should be plain polarized now the little +arrow here labels the transmission axis + + align:start position:0% +arrow here labels the transmission axis + + + align:start position:0% +arrow here labels the transmission axis +of the polarizer which means that the + + align:start position:0% +of the polarizer which means that the + + + align:start position:0% +of the polarizer which means that the +state of polariz ation of the light then + + align:start position:0% +state of polariz ation of the light then + + + align:start position:0% +state of polariz ation of the light then +is aligned with that Arrow now let us uh + + align:start position:0% +is aligned with that Arrow now let us uh + + + align:start position:0% +is aligned with that Arrow now let us uh +show indeed that the state of + + align:start position:0% +show indeed that the state of + + + align:start position:0% +show indeed that the state of +polarization of that polarizer is indeed + + align:start position:0% +polarization of that polarizer is indeed + + + align:start position:0% +polarization of that polarizer is indeed +as we said it was so we take another + + align:start position:0% +as we said it was so we take another + + + align:start position:0% +as we said it was so we take another +polarizer and we put it over here again + + align:start position:0% +polarizer and we put it over here again + + + align:start position:0% +polarizer and we put it over here again +the arrow labels the transmission axis + + align:start position:0% +the arrow labels the transmission axis + + + align:start position:0% +the arrow labels the transmission axis +of the second + + align:start position:0% +of the second + + + align:start position:0% +of the second +polarizer now when I have the arrow + + align:start position:0% +polarizer now when I have the arrow + + + align:start position:0% +polarizer now when I have the arrow +vertical the same as in this case the uh + + align:start position:0% +vertical the same as in this case the uh + + + align:start position:0% +vertical the same as in this case the uh +the light is around a Peak value it's + + align:start position:0% +the light is around a Peak value it's + + + align:start position:0% +the light is around a Peak value it's +very difficult for us to see what's + + align:start position:0% +very difficult for us to see what's + + + align:start position:0% +very difficult for us to see what's +happening around the peak value so it's + + align:start position:0% +happening around the peak value so it's + + + align:start position:0% +happening around the peak value so it's +nice to turn the the uh transmission + + align:start position:0% +nice to turn the the uh transmission + + + align:start position:0% +nice to turn the the uh transmission +axis of the of this polarizer until we + + align:start position:0% +axis of the of this polarizer until we + + + align:start position:0% +axis of the of this polarizer until we +extinguish the light which means that + + align:start position:0% +extinguish the light which means that + + + align:start position:0% +extinguish the light which means that +the transmission axis of this polarizer + + align:start position:0% +the transmission axis of this polarizer + + + align:start position:0% +the transmission axis of this polarizer +which is uh going to be referred to as + + align:start position:0% +which is uh going to be referred to as + + + align:start position:0% +which is uh going to be referred to as +the analyzer is orthogonal to the axis + + align:start position:0% +the analyzer is orthogonal to the axis + + + align:start position:0% +the analyzer is orthogonal to the axis +here and the fact as we look on the + + align:start position:0% +here and the fact as we look on the + + + align:start position:0% +here and the fact as we look on the +screen the fact that we can null the + + align:start position:0% +screen the fact that we can null the + + + align:start position:0% +screen the fact that we can null the +light means that the polarization here + + align:start position:0% +light means that the polarization here + + + align:start position:0% +light means that the polarization here +uh before entering this analyzer is + + align:start position:0% +uh before entering this analyzer is + + + align:start position:0% +uh before entering this analyzer is +indeed plain polarized and the direction + + align:start position:0% +indeed plain polarized and the direction + + + align:start position:0% +indeed plain polarized and the direction +of the arrow here uh which labels the uh + + align:start position:0% +of the arrow here uh which labels the uh + + + align:start position:0% +of the arrow here uh which labels the uh +the + + align:start position:0% +the + + + align:start position:0% +the +null uh intensity which means that that + + align:start position:0% +null uh intensity which means that that + + + align:start position:0% +null uh intensity which means that that +the transmission axis now of the + + align:start position:0% +the transmission axis now of the + + + align:start position:0% +the transmission axis now of the +polarizer is orthogonal to the + + align:start position:0% +polarizer is orthogonal to the + + + align:start position:0% +polarizer is orthogonal to the +polarization of the light um is then + + align:start position:0% +polarization of the light um is then + + + align:start position:0% +polarization of the light um is then +indicated by by direction of the arrow + + align:start position:0% +indicated by by direction of the arrow + + + align:start position:0% +indicated by by direction of the arrow +but we all know that the the the true + + align:start position:0% +but we all know that the the the true + + + align:start position:0% +but we all know that the the the true +polarization of the light is the + + align:start position:0% +polarization of the light is the + + + align:start position:0% +polarization of the light is the +vertical in the vertical Direction but + + align:start position:0% +vertical in the vertical Direction but + + + align:start position:0% +vertical in the vertical Direction but +it's much easier for us to label the uh + + align:start position:0% +it's much easier for us to label the uh + + + align:start position:0% +it's much easier for us to label the uh +the block axis the direction of the + + align:start position:0% +the block axis the direction of the + + + align:start position:0% +the block axis the direction of the +block axis so please keep in mind that + + align:start position:0% +block axis so please keep in mind that + + + align:start position:0% +block axis so please keep in mind that +the even though I might show you the + + align:start position:0% +the even though I might show you the + + + align:start position:0% +the even though I might show you the +null on the on the screen the actual + + align:start position:0% +null on the on the screen the actual + + + align:start position:0% +null on the on the screen the actual +polarization is 90° away from that now + + align:start position:0% +polarization is 90° away from that now + + + align:start position:0% +polarization is 90° away from that now +I'm going to demonstrate the rotation of + + align:start position:0% +I'm going to demonstrate the rotation of + + + align:start position:0% +I'm going to demonstrate the rotation of +the plane of + + align:start position:0% +the plane of + + + align:start position:0% +the plane of +polarization by means of a polarizer + + align:start position:0% +polarization by means of a polarizer + + + align:start position:0% +polarization by means of a polarizer +first what I'm going to do is set this + + align:start position:0% +first what I'm going to do is set this + + + align:start position:0% +first what I'm going to do is set this +analyzer back to where it was said the + + align:start position:0% +analyzer back to where it was said the + + + align:start position:0% +analyzer back to where it was said the +arrow vertical and then take uh another + + align:start position:0% +arrow vertical and then take uh another + + + align:start position:0% +arrow vertical and then take uh another +polarizer then to to rotate the plane of + + align:start position:0% +polarizer then to to rotate the plane of + + + align:start position:0% +polarizer then to to rotate the plane of +polarization + + align:start position:0% +polarization + + + align:start position:0% +polarization +now at the beginning I'm going to set + + align:start position:0% +now at the beginning I'm going to set + + + align:start position:0% +now at the beginning I'm going to set +this this polarizer Arrow which again + + align:start position:0% +this this polarizer Arrow which again + + + align:start position:0% +this this polarizer Arrow which again +labels the transmission axis of this + + align:start position:0% +labels the transmission axis of this + + + align:start position:0% +labels the transmission axis of this +polarizer in line with all the others + + align:start position:0% +polarizer in line with all the others + + + align:start position:0% +polarizer in line with all the others +the then I want to rotate the plane of + + align:start position:0% +the then I want to rotate the plane of + + + align:start position:0% +the then I want to rotate the plane of +polarization of the light by this + + align:start position:0% +polarization of the light by this + + + align:start position:0% +polarization of the light by this +polarizer let's say by + + align:start position:0% +polarizer let's say by + + + align:start position:0% +polarizer let's say by +45° well in order to check that indeed I + + align:start position:0% +45° well in order to check that indeed I + + + align:start position:0% +45° well in order to check that indeed I +have rotated by 45° again I'm going to + + align:start position:0% +have rotated by 45° again I'm going to + + + align:start position:0% +have rotated by 45° again I'm going to +track the null so now if we look on the + + align:start position:0% +track the null so now if we look on the + + + align:start position:0% +track the null so now if we look on the +screen and I rotate the analyzer let's + + align:start position:0% +screen and I rotate the analyzer let's + + + align:start position:0% +screen and I rotate the analyzer let's +see where null is this + + align:start position:0% +see where null is this + + + align:start position:0% +see where null is this +time and here it is we can see that null + + align:start position:0% +time and here it is we can see that null + + + align:start position:0% +time and here it is we can see that null +is when the arrow is is in this + + align:start position:0% +is when the arrow is is in this + + + align:start position:0% +is when the arrow is is in this +direction which is again 90° to the + + align:start position:0% +direction which is again 90° to the + + + align:start position:0% +direction which is again 90° to the +position + + align:start position:0% +position + + + align:start position:0% +position +in this direction which is uh about + + align:start position:0% +in this direction which is uh about + + + align:start position:0% +in this direction which is uh about +uh uh 50° or so from where it was before + + align:start position:0% +uh uh 50° or so from where it was before + + + align:start position:0% +uh uh 50° or so from where it was before +now let me go back to to the to aligning + + align:start position:0% +now let me go back to to the to aligning + + + align:start position:0% +now let me go back to to the to aligning +the analyzer with the with the peak + + align:start position:0% +the analyzer with the with the peak + + + align:start position:0% +the analyzer with the with the peak +transmission and you can see that the + + align:start position:0% +transmission and you can see that the + + + align:start position:0% +transmission and you can see that the +peak transmission it's not that + + align:start position:0% +peak transmission it's not that + + + align:start position:0% +peak transmission it's not that +difficult to see but you can see that uh + + align:start position:0% +difficult to see but you can see that uh + + + align:start position:0% +difficult to see but you can see that uh +it is about half about half or so about + + align:start position:0% +it is about half about half or so about + + + align:start position:0% +it is about half about half or so about +half the intensity of the peak + + align:start position:0% +half the intensity of the peak + + + align:start position:0% +half the intensity of the peak +transmission that I had when this + + align:start position:0% +transmission that I had when this + + + align:start position:0% +transmission that I had when this +polarizer was uh in the boat vertical uh + + align:start position:0% +polarizer was uh in the boat vertical uh + + + align:start position:0% +polarizer was uh in the boat vertical uh +Direction now the if I want to rotate + + align:start position:0% +Direction now the if I want to rotate + + + align:start position:0% +Direction now the if I want to rotate +the polarization some more uh let's say + + align:start position:0% +the polarization some more uh let's say + + + align:start position:0% +the polarization some more uh let's say +uh close to uh 90° again track the uh + + align:start position:0% +uh close to uh 90° again track the uh + + + align:start position:0% +uh close to uh 90° again track the uh +the direction of the null now as we + + align:start position:0% +the direction of the null now as we + + + align:start position:0% +the direction of the null now as we +watch on the screen here the position of + + align:start position:0% +watch on the screen here the position of + + + align:start position:0% +watch on the screen here the position of +null now is is over here and shows that + + align:start position:0% +null now is is over here and shows that + + + align:start position:0% +null now is is over here and shows that +the arrow is pretty close to Vertical + + align:start position:0% +the arrow is pretty close to Vertical + + + align:start position:0% +the arrow is pretty close to Vertical +which mean again we've rotated the plane + + align:start position:0% +which mean again we've rotated the plane + + + align:start position:0% +which mean again we've rotated the plane +of + + align:start position:0% +of + + + align:start position:0% +of +polarization uh uh some more now the + + align:start position:0% +polarization uh uh some more now the + + + align:start position:0% +polarization uh uh some more now the +interesting thing about going close to + + align:start position:0% +interesting thing about going close to + + + align:start position:0% +interesting thing about going close to +90 degrees is that the peak transmission + + align:start position:0% +90 degrees is that the peak transmission + + + align:start position:0% +90 degrees is that the peak transmission +the peak transmission of the light as + + align:start position:0% +the peak transmission of the light as + + + align:start position:0% +the peak transmission of the light as +you can see over here is not uh is not + + align:start position:0% +you can see over here is not uh is not + + + align:start position:0% +you can see over here is not uh is not +so big and in fact if I go even closer + + align:start position:0% +so big and in fact if I go even closer + + + align:start position:0% +so big and in fact if I go even closer +to uh + + align:start position:0% +to uh + + + align:start position:0% +to uh +90° closer to 90° I don't even get any + + align:start position:0% +90° closer to 90° I don't even get any + + + align:start position:0% +90° closer to 90° I don't even get any +light transmitted through through the uh + + align:start position:0% +light transmitted through through the uh + + + align:start position:0% +light transmitted through through the uh +through the polarizer so the conclusion + + align:start position:0% +through the polarizer so the conclusion + + + align:start position:0% +through the polarizer so the conclusion +then is that I can rotate the the pl of + + align:start position:0% +then is that I can rotate the the pl of + + + align:start position:0% +then is that I can rotate the the pl of +polarization of light using a simple + + align:start position:0% +polarization of light using a simple + + + align:start position:0% +polarization of light using a simple +polarizer but the penalty is that as I + + align:start position:0% +polarizer but the penalty is that as I + + + align:start position:0% +polarizer but the penalty is that as I +get close to 90° of rotation + + align:start position:0% +get close to 90° of rotation + + + align:start position:0% +get close to 90° of rotation +polarization rotation I get very little + + align:start position:0% +polarization rotation I get very little + + + align:start position:0% +polarization rotation I get very little +light uh transmitted so in order to + + align:start position:0% +light uh transmitted so in order to + + + align:start position:0% +light uh transmitted so in order to +overcome this problem we use a second + + align:start position:0% +overcome this problem we use a second + + + align:start position:0% +overcome this problem we use a second +polarizer and we place the second + + align:start position:0% +polarizer and we place the second + + + align:start position:0% +polarizer and we place the second +polarizer in this case I place it before + + align:start position:0% +polarizer in this case I place it before + + + align:start position:0% +polarizer in this case I place it before +the the first before this polarizer + + align:start position:0% +the the first before this polarizer + + + align:start position:0% +the the first before this polarizer +here and uh and remember even before I + + align:start position:0% +here and uh and remember even before I + + + align:start position:0% +here and uh and remember even before I +put it in that the polarization of the + + align:start position:0% +put it in that the polarization of the + + + align:start position:0% +put it in that the polarization of the +light now is along along this axis which + + align:start position:0% +light now is along along this axis which + + + align:start position:0% +light now is along along this axis which +is 90° with respect to this one and + + align:start position:0% +is 90° with respect to this one and + + + align:start position:0% +is 90° with respect to this one and +that's why we didn't get any light + + align:start position:0% +that's why we didn't get any light + + + align:start position:0% +that's why we didn't get any light +through the analyzer now I'm going to + + align:start position:0% +through the analyzer now I'm going to + + + align:start position:0% +through the analyzer now I'm going to +put this polarizer + + align:start position:0% +put this polarizer + + + align:start position:0% +put this polarizer +here and uh the this polariz this + + align:start position:0% +here and uh the this polariz this + + + align:start position:0% +here and uh the this polariz this +polarizer is still along this direction + + align:start position:0% +polarizer is still along this direction + + + align:start position:0% +polarizer is still along this direction +which is orthogonal to this one and + + align:start position:0% +which is orthogonal to this one and + + + align:start position:0% +which is orthogonal to this one and +before remember there was no light + + align:start position:0% +before remember there was no light + + + align:start position:0% +before remember there was no light +coming through and now and now you can + + align:start position:0% +coming through and now and now you can + + + align:start position:0% +coming through and now and now you can +see by adjusting the the axis of of this + + align:start position:0% +see by adjusting the the axis of of this + + + align:start position:0% +see by adjusting the the axis of of this +polarizer here I can get some light to + + align:start position:0% +polarizer here I can get some light to + + + align:start position:0% +polarizer here I can get some light to +come through with polarization that is + + align:start position:0% +come through with polarization that is + + + align:start position:0% +come through with polarization that is +orthogonal to the original one and again + + align:start position:0% +orthogonal to the original one and again + + + align:start position:0% +orthogonal to the original one and again +to go demonstrate that the null + + align:start position:0% + + + + align:start position:0% + +now is along the vertical Direction + + align:start position:0% +now is along the vertical Direction + + + align:start position:0% +now is along the vertical Direction +which means I have achieved 90° + + align:start position:0% +which means I have achieved 90° + + + align:start position:0% +which means I have achieved 90° +rotation using now two polarizers and + + align:start position:0% +rotation using now two polarizers and + + + align:start position:0% +rotation using now two polarizers and +still have light + + align:start position:0% +still have light + + + align:start position:0% +still have light +left the sad story is that you only get + + align:start position:0% +left the sad story is that you only get + + + align:start position:0% +left the sad story is that you only get +one qu of the light coming out when you + + align:start position:0% +one qu of the light coming out when you + + + align:start position:0% +one qu of the light coming out when you +rotate the polarization by 90° but + + align:start position:0% +rotate the polarization by 90° but + + + align:start position:0% +rotate the polarization by 90° but +quarter of the light at 90° rotation is + + align:start position:0% +quarter of the light at 90° rotation is + + + align:start position:0% +quarter of the light at 90° rotation is +better than no light at all so to + + align:start position:0% +better than no light at all so to + + + align:start position:0% +better than no light at all so to +summarize if you use only one polarizer + + align:start position:0% +summarize if you use only one polarizer + + + align:start position:0% +summarize if you use only one polarizer +you can rotate the state of polarization + + align:start position:0% +you can rotate the state of polarization + + + align:start position:0% +you can rotate the state of polarization +by let's say up to about 45° or so and + + align:start position:0% +by let's say up to about 45° or so and + + + align:start position:0% +by let's say up to about 45° or so and +only lose half the intensity if you want + + align:start position:0% +only lose half the intensity if you want + + + align:start position:0% +only lose half the intensity if you want +to go more then you pay uh penalty in + + align:start position:0% +to go more then you pay uh penalty in + + + align:start position:0% +to go more then you pay uh penalty in +intensity if you use two polarizers then + + align:start position:0% +intensity if you use two polarizers then + + + align:start position:0% +intensity if you use two polarizers then +you can rotate any way you want and the + + align:start position:0% +you can rotate any way you want and the + + + align:start position:0% +you can rotate any way you want and the +worst thing you can do at 90° rotation + + align:start position:0% +worst thing you can do at 90° rotation + + + align:start position:0% +worst thing you can do at 90° rotation +is that you get only quarter of the + + align:start position:0% +is that you get only quarter of the + + + align:start position:0% +is that you get only quarter of the +light coming through \ No newline at end of file diff --git a/Bd4Q4Dl4brc.txt b/Bd4Q4Dl4brc.txt new file mode 100644 index 0000000000000000000000000000000000000000..7710fdb8057e973aa0a3aea44917dbb0384c6b34 --- /dev/null +++ b/Bd4Q4Dl4brc.txt @@ -0,0 +1,1469 @@ +PROFESSOR: OK, why don't we +you get started again? + +I can understand why there is +an air of excitement in the + +room since tomorrow's +a holiday. + +But we still got two hours +before the day is over. + +Any questions on what we have +done up to this point? + +No, that's good. + +Let me erase some of this art +work then and ask why one + +would indulge in this rather +bizarre exercise of taking the + +elements of something that +represents a physical property + +and constructing a surface +out of them. + +Well, the name suggests that +maybe these surfaces, be they + +hyperboloids of one or two +sheets or imaginary + +ellipsoids, have something to +say about the property that + +the tensor that formed the +coefficient of these + +functions is doing. + +So let me take the case +of an ellipsoid. + +That would be the case +where all the + +coefficients are positive. + +And let's let this be +x1 and this x2. + +And let me ask a +first question. + +If this is to be a well deserved +function, does the + +surface transform in exactly +the same way + +as the tensor elements? + +In other words, if we take the +tensor in one coordinate + +system and then change the +coordinate system to a + +different coordinate system, are +the coefficients in front + +of x1, x2, and x3 still the +elements of the tensor in that + +new coordinate system? + +So let me show you that this +is, in fact, the case. + +Suppose our original relation, +sticking to conductivity, is + +that x sigma ij xi +xj equals 1. + +And then for some reason or +another, we change axes. + +So the new equation will be some +different coefficients. + +Because as we change axes, +they're going to wink on and + +off, still the same surface, but +now referred to different + +axes xi prime and xj prime +still equal to 1. + +And let me now use the reverse +transformation to put xi prime + +in the terms of xi. + +If we do that, we can say that +xi prime is cli x sub l prime. + +That's the reverse +transformation. + +So notice the inverted order +of the direction cosine + +subscripts. + +And then xj prime is going +to be equal to cmj + +times x sub ep prime. + +To find this, let's just +rearrange these terms in a + +trivial fashion. + +Then I will have cx sigma ij +cil cmj times xl prime xm + +prime equals 1. + +And what is this? + +This is a summation of direction +cosines where the + +first subscript goes with the +subscript on sigma prime. + +What did I do wrong? + +This is mj. + +Why is that not coming first? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Well, what I would +like to get this in the form + +of is a summation of sigma +ij prime over two dummy + +indices l and m. + +What did I do wrong? + +Ah, yes, right, right, right, +right, this is li. + +Thank you somebody said it. + +And my nose was right in it. + +And I didn't notice it. + +OK, this is a summation of all +the original elements sigma ij + +prime times dummy +indices l and m. + +And this actually +is sigma ijn. + +So it's the same set +of coefficients. + +And that is a technicality, +which probably you wouldn't + +want to worry about. + +So anyway, the elements of the +tensor transform in the same + +way that the equations for +the surfaces transform. + +So if you change coordinate +system, the coefficients that + +you should use should be the +elements that are in the + +transform tensor. + +OK, now I'm going to +ask a question. + +Suppose I define some direction +by a set of + +direction cosines li and I ask +the value of the radius of the + +surface in that direction. + +So this is some radius vector. + +The radius vector will have +components, R1, R2, R3 or Ri. + +And each of those components +will be equal to the magnitude + +of R times the direction +cosines li. + +Yes, sir? + +AUDIENCE: Could you briefly rego +over what you just stated + +before you erased +it [INAUDIBLE]? + +PROFESSOR: Oh, OK. + +I'm sorry. + +I said aij xi xj equals +1 is the original + +equation for the quadric. + +If we change the coordinate +system, we're going to have + +some new elements aij prime +times xi prime xj prime. + +Because we've got a new +coordinate system. + +And therefore, the coefficients +in front of the + +equation for the quadric +have to change. + +And now what I did was to +express xi prime and xj prime + +in terms of xi and xj using the +reverse transformation. + +And xi prime in terms of the +original x's will be c sub l + +sub i x sub l prime. + +Usually, we write it xl +equals cil x sub l. + +This is the reverse +transformation where the order + +of the subscripts is reversed. + +So this will give +me x of i prime. + +The expression for x sub j prime +will be given by cmj x + +sub j where m is +a dummy index. + +And that's equal to 1. + +And if I just rearrange this, +then I will have cli cmj times + +aij prime equals +1 times xl xj. + +And this is going +to be alx lxm. + +And this will be alm times xl +xm equals 1, which is the + +equation for the quadric in the + +original coordinate system. + +I think that was better when I +was standing in front of it so + +you couldn't see it. + +It's just that the surface +transforms formally to the + +surface that we would create +if we used the new tensor + +elements for the same change of +coordinates system, which + +you would probably will be +willing to take my word for. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: This is a direction +cosine for the-- + +AUDIENCE: [INAUDIBLE] +right below. + +PROFESSOR: Right below? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: cli cmj aij prime +xl xm, and then I collected + +the cli cmj times alm. + +And that is the transfer. + +Yes? + +AUDIENCE: In the previous +[INAUDIBLE], you defined the + +derivitave side as being +xi prime equals cil xl. + +[INAUDIBLE]? + +PROFESSOR: You can say that x +prime is cil times x sub l. + +And if we want to use the same +direction cosine scheme but do + +it in reverse, we would say that +x sub l is equal to c-- + +yeah, OK, x sub i is cli +times x sub i, right, + +no, times x sub l-- + +is that right-- x sub l prime. + +AUDIENCE: On the second line +to the third line, you say + +that xi prime equals +cli [INAUDIBLE]. + +It's either xi equals xcli xl +prime or xi prime equals cil. + +PROFESSOR: OK, you want to say +this. xi prime and cil becomes + +xl, yes, yeah. + +And then mj times x-- + +that's x sub m. + +OK, and then this says that cil +cjm times aij prime should + +be alm, right, OK, OK. + +So it's OK then. + +OK, that was supposed to be a +small point that everybody + +would accept. + +But now it's done correctly. + +OK, let's get back to +this, which is more + +hair raising and exciting. + +What is the radius of the +quadric in a given direction + +that we specify by three +direction cosines l1, l2, l3? + +So there's some radius from the +center of the quadric out + +to the surface in that +particular direction specified + +by three direction cosines. + +And we know what those three +components are, sub i, are + +going to be in terms of the +direction cosines, magnitude + +of R times li. + +And those points at the terminus +of the radius vector + +go to one point on the surface +of the quadric. + +So these values of R are +coordinates that satisfy the + +surface of the quadric. + +So we can say that just +substitute Ri for the + +different values xi in the +equation for the quadric. + +And this says that sigma ij +magnitude of R times li, that + +would correspond to x sub +i times magnitude of + +R times l sub j. + +That's the magnitude of xj. + +That should be equal to 1. + +And if I rearranged this +slightly, this says that the + +magnitude of R squared is going +to be equal to 1 over + +sigma ij times li lj. + +So the radius of the quadric +gives me not the value of the + +property in that direction. + +This is the value of the +property that will occur in + +the direction specified by +the direction cosines lj. + +The radius of the quadric is +going to be equal to 1 over + +the square root of +the value of the + +property in that direction. + +So this is why it's called the +representation quadric. + +If you construct the surface +from the tensor elements, you + +will have defined a quadratic +form, which has the property + +that, as you go in different +directions look at the + +distance out to the surface of +the quadric in that direction, + +that that distance squared is +going to be equal to 1 over + +the property in that direction +or, alternatively, the radius + +is going to be 1 over the square +root of the value of + +the property. + +There is an enormous +implication here. + +This says that the value of the +property, if the quadratic + +form is an ellipsoid, the value +of the property as we go + +around in different directions +in the crystal is going to be + +a smooth, uniformly +varying function. + +They're going to be no +lobes sticking out. + +They're going to be no +dimples, no lumps. + +It's going to be an almost +monotonous property, not very + +interesting. + +It's going to change +in a uniform way. + +And in fact, we could put the +two surfaces side by side. + +If this is the value of the +quadric as a function of + +direction, if we make a polar +plot of the property as a + +function of direction, it's +going to look sort of like the + +reciprocal of this. + +The minimum value of the +property will be in the + +direction of the maximum value +of the radius of the quadric. + +And the maximum value of the +property is going to go in the + +direction of the +minimum value. + +So the value of the property as +a function of direction is + +going to be a quasi-ellipsoidal +sort of + +variation but not really +an ellipsoid. + +It's going to go as this +inverse square of + +the radii in ellipsoid. + +But the thing is it's going to +be something that varies + +uniformly between extreme values +of the maximum and + +minimum value of the property. + +We are, I assure you, for higher +ranked tensor property + +going to look at some absolutely +wild surfaces with + +surfaces that do have lobes and +extreme values and very, + +very irregular variation of +properties with directions but + +not for second ranked +tensor properties. + +There will be a few variations +on this theme, which are also + +interesting to touch upon. + +In principle, we can get other +quadratic forms from the + +tensor if some of the elements +of the tensor are negative. + +And in particular, what +would we see-- + +and I'll draw this +relative to the + +principal axes of the surface-- + +what would we see for an +hyperboloid of one sheet? + +This is the sort of surface +that might result if one + +principal value of the tensor +had a negative value. + +Well, this is the quadric. + +And this is a radius in one +particular direction. + +What would this say about +the property? + +Well, let me, to make it clear, +look at one of these + +sections through the quadric +that our hyperbola. + +In directions like this, we +have a radius that is a + +minimum out to the surface. + +In other directions, +the radius gets + +progressively larger. + +And then if we plot the +reciprocal of the square root + +of that, that says that, in +this direction, we get the + +maximum value of the property. + +And as the direction approaches +the asymptote, the + +reciprocal will go down to 0. + +But how did I get +two y-axes here? + +OK, so the maximum will +be in the direction + +of the minimum radius. + +And then it will go down +to 0 for the asymptote. + +And that's going to be +symmetrical on either side of + +this principle axis. + +So what then are the radii in +directions outside of the + +asymptotes of this +hyperboloid? + +Within this range, the +radius is imaginary. + +But if you square it, you +get a negative number. + +So within these two lobes, +the value of + +the property is positive. + +As you go away from the +asymptotes, you'll get another + +lobe like this and another lobe +like this where the value + +of the property is negative. + +How in the world could +you get anything + +that looked like that? + +Well, a good example of a +property that has this + +behavior is thermal expansion. + +And let me give you +two examples. + +The structure of selenium +and tellurium + +is a hexagonal structure. + +And there are chain-like +molecules that are pairs of + +bonds that rise up around +a threefold screw axis. + +So this is two coordinated atoms +in the structure just + +spirals up in this triangular +spiral around the threefold + +screw axis. + +So this is a material in which +the bonding is very, very + +anisotropic. + +The bonding within these +covalently bonded spirals, + +which are like springs that you +might put on your screen + +door in the summertime, the +bonding is very strong. + +Between these individual +molecular chains, the bonding + +is very weak. + +So what happens when you +heat this stuff up? + +It expands like the dickens +in the direction + +of these weak bonds. + +But the spirals are, in part, +held in this extended form by + +repulsive interactions +in like chains. + +So when these spirals move apart +as a result of large + +thermal expansion in the plane +normal to the chain, the + +chains relax a little bit. + +So you have a large positive +thermal expansion here. + +But in one direction along the +normal to the hexagonal in the + +structure, the thermal expansion +is negative. + +And that gives you a variation +of property with direction + +that looks exactly like this. + +Negative value of the property, +that means the + +structure, contracts +in that direction, + +positive values this way. + +The structure expands. + +So there's a good +example of this. + +There's another example of a +material, which, again, has a + +negative thermal expansion +in one direction. + +And this is calcium carbonate, +which is a complicated + +hexagonal structure. + +But it looks very, very much +like the structure of rock + +salt in a distorted form. + +These are the calcium atoms. + +And calcite is CaCL3 And +the calciums are in a + +face-centered cubic +arrangement just + +like in rock salt. + +The carbonate groups are very +tightly bonded little + +triangles with the carbon +in the middle. + +And these things are arranged +on the edges of the cell. + +And this is going to +be very schematic. + +These triangles are +normal to the body + +diagonal of the cells. + +So you have one family of +triangles that are all + +parallel to one another. + +On the next edge, the triangles +are anti-parallel to + +this first orientation. + +So think of rock salt. + +Tip it up on its +body diagonal. + +Every place you have a chlorine +anion, place a + +triangle in an orientation that +is perpendicular to the + +body's diagonal of the +rock salt structure. + +Again, these tightly bonded +little triangles don't do much + +as you increase temperature. + +But the bonding between the +calcium and the triangles is + +rather weak. + +So again, you find that the +structure expands in one + +direction so strongly that +it contracts to the other + +direction so calcium +carbonate. + +The calcite form also has the +distinction of having a + +negative thermal expansion +coefficient. + +We'll talk quite a bit about +expansion coefficients as one + +example of a tensor property. + +Interestingly, and we'll say +more about this and I'll give + +you some references when we come +to this point, can you + +get a material that has a +negative thermal expansion + +coefficient in all directions? + +No, that seems as though it +would violate in a flagrant + +way some vast law of +thermodynamics that things + +have to increase their volume +when you increase temperature. + +There were, however, a few odd +ball materials that over a + +very, very limited temperature +range would contract but only + +by a tiny amount in +all directions. + +And then one of the very +interesting discoveries of + +recent years done primarily by +a crystal chemist named Art + +Slate, who's out at the +University of Oregon, he + +discovered a family of materials +that have large + +negative expansion coefficients +in all directions + +over a considerable range of + +temperatures, like 100 degrees. + +So these are materials, when +you heat them up, they + +contract amazing +as that seems. + +And there's a structural +reason for it. + +These are tetrahedral frameworks +in which one corner + +of a tetrahedron is dangling. + +And as you heat it up, this +tetrahedral corner can get + +closer to other tetrahedra, +which takes energy to do. + +But in so doing, you actually +are changing the net volume + +occupied by the solid +so very, very + +anomalous set of compounds. + +More of these have been found. + +There are probably a dozen +materials now that have + +negative thermal expansion +coefficients in all + +directions. + +So is the imaginary ellipsoid +a viable representation + +quadric for real materials? + +Yes, in the case of thermal +expansion coefficients. + +OK, so the representation +quadric then is a dandy device + +for seeing with one function +how a property + +will vary with direction. + +For an ellipsodial quadric, the +variation of the property + +itself with direction is not +really ellipsodial but + +quasi-ellipsodial in that +there's a small principal + +axis, a large principal axis. + +And the large value of the +property goes with the short + +axis of the quadric. + +So we have a nice device for +representing the value of the + +property as a function +of direction. + +It looks as though we've lost +all information about the + +direction of the resulting +vector, the generalized + +displacement. + +It looks as though that's +not in here at all. + +Well, there was an ad years +ago for a bottle spaghetti + +sauce, which offends many cooks +who are very fiercely + +proud of their own +spaghetti sauce. + +So here's a wife who's using +the canned stuff. + +And her husband comes home and +looks at it very, very + +skeptically and says, +where's the basil? + +And the housewife says, +it's in there. + +It's in there. + +And he sniffs again and says, +where is the basil? + +And she says finally, +it's in there. + +It's in there. + +Well, this is a similar +situation. + +Where is the direction of +the generalized force? + +And I say, it's in there. + +It's in there. + +Not obvious, but +it's in there. + +So let me now show you +where it is lurking. + +I think we have time to +carry this through. + +Let me describe how it's +embodied in the quadric and + +then prove to you that this +is indeed the case. + +And I'll use a general quadric +in the form of an ellipsoid. + +That looks more like an +egg than an ellipsoid. + +It has a pointed end. + +OK, this is something +that's called the + +radius normal property. + +And what it says, in words, is +that, if you pick a particular + +direction relative to the +quadric, we know that its + +length is going to be inversely +proportional to the + +square root of the value +of the property. + +If you want to know what the +direction of the resulting + +vector is, for example, in our +relation for conductivity now + +getting very warm, it says the +current flow is given by a + +linear combination of +every component of + +the electric field. + +The radius normal properties is +that, if you want to know + +where J is for this particular +direction, look at the point + +where the radius vector +intersects the surface of the + +quadric and, at that point, +construct a perpendicular to + +the surface, which, in general, +will not be parallel + +to R. And this will be the +direction of J. It won't give + +you the magnitude. + +But it'll give you the +direction of it. + +OK, let me now prove to you +that the quadric does have + +this property. + +In our conductivity relation, +the direction of J is going to + +be given by the tensor +relation. + +Namely that J sub i is equal +to sigma ij times E sub j, + +which can be written as sigma ij +times the direction cosines + +of E sub j times the +magnitude of E. + +I'm going to want to compare +this expression, with which + +you're very familiar term by +term, with the normal to the + +surface that we can +compute from its + +derivative at that point. + +So this will say that J1 is +equal to sigma 1, 1 l1 times + +the magnitude of E plus sigma +1, 2 times l2 times the + +magnitude of E plus sigma 1, 3 +times l3 times the magnitude + +of E. And I don't need +to write much more. + +J2 will be sigma 2, 1 times l1 +magnitude of E plus sigma 2, 2 + +l2 times the magnitude +of E and so on. + +What is going to be the normal +to the surface as a function + +of direction? + +OK, to do this I'm going to +say that the normal to the + +surface is going to be, if I +have some function of xyz, the + +normal to that function +is the gradient. + +Let me say that that's +G of xyz. + +And we can say then that the x1 +component of the normal is + +not going to be equal to but +proportional to the gradient + +of the equation for the quadric +with respect to x1, + +dx2, and dx3. + +So it's going to be proportional +to the + +differential of the function +that gives us the surface with + +respect to x1 times i plus the +differential of the function + +with respect to x2 times +j plus dF dx3 times k. + +So this is the normal +entirely. + +So if we split this into +components, N1 is going to be + +equal to dF dx1. + +And if I differentiate the +equation for the quadric, + +that's going to be 2 sigma +1, 1 times x1. + +Remember the equation for the +quadrant is sigma 1, 1 times + +x1 squared plus sigma +1, 2 times x1 x2. + +So if I differentiate-- +let me write it down. + +If I take those terms and +differentiate with respect to + +x1, I'm going to get 2 +sigma 1, 1 times x1. + +Here I'll get sigma +1, 2 times x2. + +But then down in this line where +I have a sigma 2, 1 x2 + +x1, if I differentiate with +respect to x1, I'll have + +another term sigma 2, 1. + +And if I differentiate with +respect to x3, I'll have sigma + +1, 3 plus sigma 3, 1 times x3. + +And a similar thing for the x2 +component of the normal, + +that's going to be proportional +to the gradient + +with respect to x2. + +And that's going to be equal to +sigma 1, 2 plus sigma 2, 1 + +times x1 plus 2 sigma 2, 2 times +x2 plus sigma 2, 3 plus + +sigma 3, 2 times x3 and +similarly for N3. + +OK, I've made my case if I +can demonstrate that each + +component of J, J sub i, is +proportional to each component + +of the gradient to the function + +that defines the quadric. + +If you look at them, they're +close but no cigar. + +The first term is OK. + +I've got a 2 out in front of +sigma 1, 1 for the x1 term. + +Here, though, I have the sum +of two off-diagonal terms. + +And for this expression, +I have just sigma 1, 2. + +And down here I've just the +single term sigma 2, 1. + +So the conclusion we're forced +to draw is that these two + +expressions would have +components of a vector that + +are parallel to one another +if sigma 1, 2 was + +equal to sigma 2, 1. + +Because if these were equal, +I could write just + +twice sigma 1, 2. + +And down here I could write +twice sigma 2, 1 and do that + +all the way through these +two expressions. + +And then this factor of 2 would +just be part of the + +proportionality constant. + +So the radius normal property +will be true or valid only for + +symmetric tensors. + +That is it's going to be true +only if sigma ij is + +equal to sigma ji. + +We mentioned when we first +started talking about second + +ranked tensors that a tensor +does not have to be symmetric. + +And showing that the tensor is +symmetric has nothing to do + +with symmetry. + +Because it's symmetric in an +algebraic sense not in the + +literal sense of geometrical +symmetry. + +And there are some properties, +the thermal electricity tensor + +is one notable example, where +the tensor is a second ranked + +tensor but it decidedly +is not symmetric. + +So this is OK for most +properties but not all. + +OK, so here are properties of +the representation surface + +that we can construct from the +representation quadric. + +And what I would like to do +following this and after the + +inevitable unpleasantness of +a quiz is to look at some + +specific properties that +illustrate second ranked + +tensor properties. + +And in particular, I would like +to look at some other + +sorts of second ranked tensor +properties that represent + +generalized forces, namely +stress and strain. + +You've seen these before in +other contexts perhaps not + +actually defined rigorously +in terms of tensors. + +Because, obviously, stress and +strain can be regarded as + +generalized forces. + +A stress is something that +you can apply to a solid. + +And that will cause various +things to happen. + +In addition to mechanical +behavior, different properties + +and effects can result. + +So that is going to involve a +generalized force, which is a + +second ranked tensor. + +And a thing that might happen +could be a vector. + +It could be another second +ranked tensor. + +And this is going to introduce +us to the nasty world of + +higher ranked tensor properties +and their + +representation surfaces. + +So this is a nice place to quit +and pause for a quiz. + +When we resume, we'll look at +stress and strain in terms of + +our tensor algebra. \ No newline at end of file diff --git a/CHhwJjR0mZA.txt b/CHhwJjR0mZA.txt new file mode 100644 index 0000000000000000000000000000000000000000..67394ef85f603bec4d863cea699e138ad7b40baf --- /dev/null +++ b/CHhwJjR0mZA.txt @@ -0,0 +1,9816 @@ +align:start position:0% + +good morning good + + align:start position:0% +good morning good + + + align:start position:0% +good morning good +morning welcome to double o six + + align:start position:0% +morning welcome to double o six + + + align:start position:0% +morning welcome to double o six +introduction to algorithms lecture two + + align:start position:0% +introduction to algorithms lecture two + + + align:start position:0% +introduction to algorithms lecture two +i am eric domain and i love algorithms + + align:start position:0% +i am eric domain and i love algorithms + + + align:start position:0% +i am eric domain and i love algorithms +are you with me yeah + + align:start position:0% +are you with me yeah + + + align:start position:0% +are you with me yeah +today we're not doing algorithms no + + align:start position:0% +today we're not doing algorithms no + + + align:start position:0% +today we're not doing algorithms no +we're doing data structures it's okay + + align:start position:0% +we're doing data structures it's okay + + + align:start position:0% +we're doing data structures it's okay +there's lots of algorithms in each data + + align:start position:0% +there's lots of algorithms in each data + + + align:start position:0% +there's lots of algorithms in each data +structure it's like multiple algorithms + + align:start position:0% +structure it's like multiple algorithms + + + align:start position:0% +structure it's like multiple algorithms +for free + + align:start position:0% +for free + + + align:start position:0% +for free +we're going to talk about sequences and + + align:start position:0% +we're going to talk about sequences and + + + align:start position:0% +we're going to talk about sequences and +sets and + + align:start position:0% +sets and + + + align:start position:0% +sets and +linked lists and dynamic arrays fairly + + align:start position:0% +linked lists and dynamic arrays fairly + + + align:start position:0% +linked lists and dynamic arrays fairly +simple data structures today this + + align:start position:0% +simple data structures today this + + + align:start position:0% +simple data structures today this +is the beginning of several data + + align:start position:0% +is the beginning of several data + + + align:start position:0% +is the beginning of several data +structures we'll be talking about the + + align:start position:0% +structures we'll be talking about the + + + align:start position:0% +structures we'll be talking about the +next few lectures + + align:start position:0% +next few lectures + + + align:start position:0% +next few lectures +uh but before we actually start with one + + align:start position:0% +uh but before we actually start with one + + + align:start position:0% +uh but before we actually start with one +let me tell you slash remind you + + align:start position:0% +let me tell you slash remind you + + + align:start position:0% +let me tell you slash remind you +of the idea the difference between an + + align:start position:0% +of the idea the difference between an + + + align:start position:0% +of the idea the difference between an +interface + + align:start position:0% +interface + + + align:start position:0% +interface +which you might call an api if you're a + + align:start position:0% +which you might call an api if you're a + + + align:start position:0% +which you might call an api if you're a +programmer or an adt if you're an + + align:start position:0% +programmer or an adt if you're an + + + align:start position:0% +programmer or an adt if you're an +ancient algorithms person like me + + align:start position:0% +ancient algorithms person like me + + + align:start position:0% +ancient algorithms person like me +versus a data structure + + align:start position:0% + + + + align:start position:0% + +these are useful distinctions uh the + + align:start position:0% +these are useful distinctions uh the + + + align:start position:0% +these are useful distinctions uh the +idea is that + + align:start position:0% +idea is that + + + align:start position:0% +idea is that +an interface says what you want to do a + + align:start position:0% +an interface says what you want to do a + + + align:start position:0% +an interface says what you want to do a +data structure says how you do it + + align:start position:0% +data structure says how you do it + + + align:start position:0% +data structure says how you do it +so you might call this a specification + + align:start position:0% + + + + align:start position:0% + +and in the context of data structures + + align:start position:0% +and in the context of data structures + + + align:start position:0% +and in the context of data structures +we're trying to store some data so the + + align:start position:0% +we're trying to store some data so the + + + align:start position:0% +we're trying to store some data so the +interface will specify + + align:start position:0% +interface will specify + + + align:start position:0% +interface will specify +what data you can store + + align:start position:0% + + + + align:start position:0% + +whereas the data structure will give you + + align:start position:0% +whereas the data structure will give you + + + align:start position:0% +whereas the data structure will give you +an actual representation + + align:start position:0% +an actual representation + + + align:start position:0% +an actual representation +and tell you how to store it + + align:start position:0% + + + + align:start position:0% + +this is pretty boring just storing data + + align:start position:0% +this is pretty boring just storing data + + + align:start position:0% +this is pretty boring just storing data +is really easy you just + + align:start position:0% +is really easy you just + + + align:start position:0% +is really easy you just +throw it in a file or something what + + align:start position:0% +throw it in a file or something what + + + align:start position:0% +throw it in a file or something what +makes it interesting + + align:start position:0% +makes it interesting + + + align:start position:0% +makes it interesting +is uh having operations on that data + + align:start position:0% +is uh having operations on that data + + + align:start position:0% +is uh having operations on that data +so in the interface you specify + + align:start position:0% +so in the interface you specify + + + align:start position:0% +so in the interface you specify +what the operations do what operations + + align:start position:0% +what the operations do what operations + + + align:start position:0% +what the operations do what operations +are supported + + align:start position:0% + + + + align:start position:0% + +and some sense what they mean + + align:start position:0% +and some sense what they mean + + + align:start position:0% +and some sense what they mean +and the data structure actually gives + + align:start position:0% +and the data structure actually gives + + + align:start position:0% +and the data structure actually gives +you algorithms + + align:start position:0% +you algorithms + + + align:start position:0% +you algorithms +this is where the algorithms come in for + + align:start position:0% +this is where the algorithms come in for + + + align:start position:0% +this is where the algorithms come in for +how to support those operations + + align:start position:0% + + + + align:start position:0% + +all right so um in this class we're + + align:start position:0% +all right so um in this class we're + + + align:start position:0% +all right so um in this class we're +going to focus on + + align:start position:0% +going to focus on + + + align:start position:0% +going to focus on +two main interfaces + + align:start position:0% +two main interfaces + + + align:start position:0% +two main interfaces +and various special cases of them + + align:start position:0% +and various special cases of them + + + align:start position:0% +and various special cases of them +so the idea is to separate what you want + + align:start position:0% +so the idea is to separate what you want + + + align:start position:0% +so the idea is to separate what you want +to do versus how to do it because + + align:start position:0% +to do versus how to do it because + + + align:start position:0% +to do versus how to do it because +for you can think of this as the problem + + align:start position:0% +for you can think of this as the problem + + + align:start position:0% +for you can think of this as the problem +statement + + align:start position:0% +statement + + + align:start position:0% +statement +so yesterday or last class jason talked + + align:start position:0% +so yesterday or last class jason talked + + + align:start position:0% +so yesterday or last class jason talked +about + + align:start position:0% +about + + + align:start position:0% +about +problems and defined what a problem was + + align:start position:0% +problems and defined what a problem was + + + align:start position:0% +problems and defined what a problem was +versus algorithmic solutions to the + + align:start position:0% +versus algorithmic solutions to the + + + align:start position:0% +versus algorithmic solutions to the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and this is the analogous notion for + + align:start position:0% +and this is the analogous notion for + + + align:start position:0% +and this is the analogous notion for +data structures where we want to + + align:start position:0% +data structures where we want to + + + align:start position:0% +data structures where we want to +maintain a data + + align:start position:0% +maintain a data + + + align:start position:0% +maintain a data +maintain some data according to various + + align:start position:0% +maintain some data according to various + + + align:start position:0% +maintain some data according to various +operations + + align:start position:0% +operations + + + align:start position:0% +operations +so the same problem can be solved by + + align:start position:0% +so the same problem can be solved by + + + align:start position:0% +so the same problem can be solved by +many different data structures and we're + + align:start position:0% +many different data structures and we're + + + align:start position:0% +many different data structures and we're +going to see that + + align:start position:0% +going to see that + + + align:start position:0% +going to see that +and different data structures are going + + align:start position:0% +and different data structures are going + + + align:start position:0% +and different data structures are going +to have different advantages they might + + align:start position:0% +to have different advantages they might + + + align:start position:0% +to have different advantages they might +support some operations faster than + + align:start position:0% +support some operations faster than + + + align:start position:0% +support some operations faster than +others + + align:start position:0% +others + + + align:start position:0% +others +and depending on what you actually use + + align:start position:0% +and depending on what you actually use + + + align:start position:0% +and depending on what you actually use +those data structures for you choose + + align:start position:0% +those data structures for you choose + + + align:start position:0% +those data structures for you choose +the right data structure but you can + + align:start position:0% +the right data structure but you can + + + align:start position:0% +the right data structure but you can +maintain the same interface + + align:start position:0% +maintain the same interface + + + align:start position:0% +maintain the same interface +we're going to think about two data + + align:start position:0% +we're going to think about two data + + + align:start position:0% +we're going to think about two data +structures one is called a set + + align:start position:0% +structures one is called a set + + + align:start position:0% +structures one is called a set +and one is called a sequence + + align:start position:0% +and one is called a sequence + + + align:start position:0% +and one is called a sequence +these are highly loaded terms set means + + align:start position:0% +these are highly loaded terms set means + + + align:start position:0% +these are highly loaded terms set means +something to a mathematician it means + + align:start position:0% +something to a mathematician it means + + + align:start position:0% +something to a mathematician it means +someone else something else to a python + + align:start position:0% +someone else something else to a python + + + align:start position:0% +someone else something else to a python +programmer + + align:start position:0% +programmer + + + align:start position:0% +programmer +sequence similarly i guess there's not a + + align:start position:0% +sequence similarly i guess there's not a + + + align:start position:0% +sequence similarly i guess there's not a +python sequence data type + + align:start position:0% +python sequence data type + + + align:start position:0% +python sequence data type +built in um the idea is we want to store + + align:start position:0% +built in um the idea is we want to store + + + align:start position:0% +built in um the idea is we want to store +n + + align:start position:0% +n + + + align:start position:0% +n +things the things will be fairly + + align:start position:0% +things the things will be fairly + + + align:start position:0% +things the things will be fairly +arbitrary + + align:start position:0% +arbitrary + + + align:start position:0% +arbitrary +think of them as integers or strings and + + align:start position:0% +think of them as integers or strings and + + + align:start position:0% +think of them as integers or strings and +on the one hand we care about their + + align:start position:0% +on the one hand we care about their + + + align:start position:0% +on the one hand we care about their +values + + align:start position:0% +values + + + align:start position:0% +values +and maybe we want to maintain them in + + align:start position:0% +and maybe we want to maintain them in + + + align:start position:0% +and maybe we want to maintain them in +sorted order and be able to search for a + + align:start position:0% +sorted order and be able to search for a + + + align:start position:0% +sorted order and be able to search for a +given value + + align:start position:0% +given value + + + align:start position:0% +given value +which we'll call a key and on the other + + align:start position:0% +which we'll call a key and on the other + + + align:start position:0% +which we'll call a key and on the other +hand we care about representing + + align:start position:0% +hand we care about representing + + + align:start position:0% +hand we care about representing +a particular sequence that we care about + + align:start position:0% +a particular sequence that we care about + + + align:start position:0% +a particular sequence that we care about +maybe we want to represent the numbers 5 + + align:start position:0% +maybe we want to represent the numbers 5 + + + align:start position:0% +maybe we want to represent the numbers 5 + + align:start position:0% + + + align:start position:0% +9 7 in that order and store that + + align:start position:0% +9 7 in that order and store that + + + align:start position:0% +9 7 in that order and store that +in python you could store that in a list + + align:start position:0% +in python you could store that in a list + + + align:start position:0% +in python you could store that in a list +for example + + align:start position:0% +for example + + + align:start position:0% +for example +and it will keep track of that order and + + align:start position:0% +and it will keep track of that order and + + + align:start position:0% +and it will keep track of that order and +this is the first item the second item + + align:start position:0% +this is the first item the second item + + + align:start position:0% +this is the first item the second item +the last item + + align:start position:0% +the last item + + + align:start position:0% +the last item +today we're going to be focusing on this + + align:start position:0% +today we're going to be focusing on this + + + align:start position:0% +today we're going to be focusing on this +sequence data structure although at the + + align:start position:0% +sequence data structure although at the + + + align:start position:0% +sequence data structure although at the +end i'll mention + + align:start position:0% +end i'll mention + + + align:start position:0% +end i'll mention +the interface for sets but we're going + + align:start position:0% +the interface for sets but we're going + + + align:start position:0% +the interface for sets but we're going +to be actually solving sequences today + + align:start position:0% +to be actually solving sequences today + + + align:start position:0% +to be actually solving sequences today +and in the next several lectures we'll + + align:start position:0% +and in the next several lectures we'll + + + align:start position:0% +and in the next several lectures we'll +be bouncing back and forth between these + + align:start position:0% +be bouncing back and forth between these + + + align:start position:0% +be bouncing back and forth between these +they're closely related + + align:start position:0% +they're closely related + + + align:start position:0% +they're closely related +pretty abstract at the moment on the + + align:start position:0% +pretty abstract at the moment on the + + + align:start position:0% +pretty abstract at the moment on the +other hand we're gonna have two + + align:start position:0% +other hand we're gonna have two + + + align:start position:0% +other hand we're gonna have two +main + + align:start position:0% + + + + align:start position:0% + +let's call them data structure + + align:start position:0% +let's call them data structure + + + align:start position:0% +let's call them data structure +tools or approaches + + align:start position:0% + + + + align:start position:0% + +one is arrays + + align:start position:0% +one is arrays + + + align:start position:0% +one is arrays +and the other is pointers pointer based + + align:start position:0% +and the other is pointers pointer based + + + align:start position:0% +and the other is pointers pointer based +or linked + + align:start position:0% +or linked + + + align:start position:0% +or linked +data structures you may have seen these + + align:start position:0% +data structures you may have seen these + + + align:start position:0% +data structures you may have seen these +they're used a lot in programming of + + align:start position:0% +they're used a lot in programming of + + + align:start position:0% +they're used a lot in programming of +course but we're going to see both of + + align:start position:0% +course but we're going to see both of + + + align:start position:0% +course but we're going to see both of +these today i'll come back to this + + align:start position:0% +these today i'll come back to this + + + align:start position:0% +these today i'll come back to this +sort of highlight in a moment let's jump + + align:start position:0% +sort of highlight in a moment let's jump + + + align:start position:0% +sort of highlight in a moment let's jump +into the sequence interface + + align:start position:0% +into the sequence interface + + + align:start position:0% +into the sequence interface +which i conveniently have part of here + + align:start position:0% +which i conveniently have part of here + + + align:start position:0% +which i conveniently have part of here +there's a few different levels of + + align:start position:0% +there's a few different levels of + + + align:start position:0% +there's a few different levels of +sequences that we might care about i'm + + align:start position:0% +sequences that we might care about i'm + + + align:start position:0% +sequences that we might care about i'm +going to start with the static + + align:start position:0% +going to start with the static + + + align:start position:0% +going to start with the static +sequence interface this is where the + + align:start position:0% +sequence interface this is where the + + + align:start position:0% +sequence interface this is where the +item the number of items doesn't change + + align:start position:0% +item the number of items doesn't change + + + align:start position:0% +item the number of items doesn't change +uh though the actual items might so here + + align:start position:0% +uh though the actual items might so here + + + align:start position:0% +uh though the actual items might so here +we have n + + align:start position:0% +we have n + + + align:start position:0% +we have n +items i'm going to label them x 0 to x n + + align:start position:0% +items i'm going to label them x 0 to x n + + + align:start position:0% +items i'm going to label them x 0 to x n +minus 1 as in python + + align:start position:0% +minus 1 as in python + + + align:start position:0% +minus 1 as in python +so the number of items is n and the + + align:start position:0% +so the number of items is n and the + + + align:start position:0% +so the number of items is n and the +operations i want to support are build + + align:start position:0% +operations i want to support are build + + + align:start position:0% +operations i want to support are build +length iteration get and set + + align:start position:0% +length iteration get and set + + + align:start position:0% +length iteration get and set +so what do these do build is how you get + + align:start position:0% +so what do these do build is how you get + + + align:start position:0% +so what do these do build is how you get +started to build + + align:start position:0% +started to build + + + align:start position:0% +started to build +a data structure in this interface you + + align:start position:0% +a data structure in this interface you + + + align:start position:0% +a data structure in this interface you +call build of + + align:start position:0% +call build of + + + align:start position:0% +call build of +x exactly how you specify x isn't too + + align:start position:0% +x exactly how you specify x isn't too + + + align:start position:0% +x exactly how you specify x isn't too +important but the idea is i give you + + align:start position:0% +important but the idea is i give you + + + align:start position:0% +important but the idea is i give you +some items in some order + + align:start position:0% +some items in some order + + + align:start position:0% +some items in some order +in python this would be an iterable i'm + + align:start position:0% +in python this would be an iterable i'm + + + align:start position:0% +in python this would be an iterable i'm +going to want to also know its length + + align:start position:0% +going to want to also know its length + + + align:start position:0% +going to want to also know its length +and i want to make a new data structure + + align:start position:0% +and i want to make a new data structure + + + align:start position:0% +and i want to make a new data structure +of size n a new static sequence of size + + align:start position:0% +of size n a new static sequence of size + + + align:start position:0% +of size n a new static sequence of size +n + + align:start position:0% +n + + + align:start position:0% +n +that has those items in that order so + + align:start position:0% +that has those items in that order so + + + align:start position:0% +that has those items in that order so +that's how you build one of these + + align:start position:0% +that's how you build one of these + + + align:start position:0% +that's how you build one of these +because somehow we have to specify n to + + align:start position:0% +because somehow we have to specify n to + + + align:start position:0% +because somehow we have to specify n to +this data structure because n is not + + align:start position:0% +this data structure because n is not + + + align:start position:0% +this data structure because n is not +going to + + align:start position:0% +going to + + + align:start position:0% +going to +be allowed to change i'm going to give + + align:start position:0% +be allowed to change i'm going to give + + + align:start position:0% +be allowed to change i'm going to give +you a length + + align:start position:0% +you a length + + + align:start position:0% +you a length +method um these are + + align:start position:0% +method um these are + + + align:start position:0% +method um these are +methods are the object-oriented way of + + align:start position:0% +methods are the object-oriented way of + + + align:start position:0% +methods are the object-oriented way of +thinking of operations + + align:start position:0% +thinking of operations + + + align:start position:0% +thinking of operations +that your interface supports + + align:start position:0% +that your interface supports + + + align:start position:0% +that your interface supports +so length will just return this fixed + + align:start position:0% +so length will just return this fixed + + + align:start position:0% +so length will just return this fixed +value and it or sequence this is the + + align:start position:0% +value and it or sequence this is the + + + align:start position:0% +value and it or sequence this is the +sense in which we want to maintain the + + align:start position:0% +sense in which we want to maintain the + + + align:start position:0% +sense in which we want to maintain the +order i want to be able to output x0 + + align:start position:0% +order i want to be able to output x0 + + + align:start position:0% +order i want to be able to output x0 +through xn minus 1 in the sequence order + + align:start position:0% +through xn minus 1 in the sequence order + + + align:start position:0% +through xn minus 1 in the sequence order +in that specified order that they were + + align:start position:0% +in that specified order that they were + + + align:start position:0% +in that specified order that they were +built in + + align:start position:0% +built in + + + align:start position:0% +built in +or that it was changed to so uh + + align:start position:0% +or that it was changed to so uh + + + align:start position:0% +or that it was changed to so uh +this is going to iterate through all the + + align:start position:0% +this is going to iterate through all the + + + align:start position:0% +this is going to iterate through all the +items + + align:start position:0% +items + + + align:start position:0% +items +so it's going to take at least linear + + align:start position:0% +so it's going to take at least linear + + + align:start position:0% +so it's going to take at least linear +time to output that but more interesting + + align:start position:0% +time to output that but more interesting + + + align:start position:0% +time to output that but more interesting +is we can + + align:start position:0% +is we can + + + align:start position:0% +is we can +dynamically access anywhere in the + + align:start position:0% +dynamically access anywhere in the + + + align:start position:0% +dynamically access anywhere in the +middle of the sequence + + align:start position:0% +middle of the sequence + + + align:start position:0% +middle of the sequence +we can get the item x i given the value + + align:start position:0% +we can get the item x i given the value + + + align:start position:0% +we can get the item x i given the value +i + + align:start position:0% +i + + + align:start position:0% +i +and we can change x i to a given new + + align:start position:0% +and we can change x i to a given new + + + align:start position:0% +and we can change x i to a given new +item + + align:start position:0% +item + + + align:start position:0% +item +okay so that's called get at and set at + + align:start position:0% +okay so that's called get at and set at + + + align:start position:0% +okay so that's called get at and set at +pretty straightforward + + align:start position:0% +pretty straightforward + + + align:start position:0% +pretty straightforward +this should remind you very closely of + + align:start position:0% +this should remind you very closely of + + + align:start position:0% +this should remind you very closely of +something a data structure so this is an + + align:start position:0% +something a data structure so this is an + + + align:start position:0% +something a data structure so this is an +interface this is + + align:start position:0% +interface this is + + + align:start position:0% +interface this is +something i might want to solve but what + + align:start position:0% +something i might want to solve but what + + + align:start position:0% +something i might want to solve but what +is the obvious data structure that + + align:start position:0% +is the obvious data structure that + + + align:start position:0% +is the obvious data structure that +solves + + align:start position:0% +solves + + + align:start position:0% +solves +this problem yeah a list in python it's + + align:start position:0% +this problem yeah a list in python it's + + + align:start position:0% +this problem yeah a list in python it's +called the list + + align:start position:0% +called the list + + + align:start position:0% +called the list +i prefer to call it an array but to each + + align:start position:0% +i prefer to call it an array but to each + + + align:start position:0% +i prefer to call it an array but to each +their own + + align:start position:0% +their own + + + align:start position:0% +their own +we're gonna use this this could mean + + align:start position:0% +we're gonna use this this could mean + + + align:start position:0% +we're gonna use this this could mean +many things um + + align:start position:0% +many things um + + + align:start position:0% +many things um +but the uh solution + + align:start position:0% + + + + align:start position:0% + +to this interface problem the + + align:start position:0% +to this interface problem the + + + align:start position:0% +to this interface problem the +natural solution + + align:start position:0% + + + + align:start position:0% + +is as what i'll call a static array + + align:start position:0% + + + + align:start position:0% + +jason mentioned these in + + align:start position:0% +jason mentioned these in + + + align:start position:0% +jason mentioned these in +uh in lecture one uh it's a little + + align:start position:0% +uh in lecture one uh it's a little + + + align:start position:0% +uh in lecture one uh it's a little +tricky because there are no static + + align:start position:0% +tricky because there are no static + + + align:start position:0% +tricky because there are no static +arrays in python there are only dynamic + + align:start position:0% +arrays in python there are only dynamic + + + align:start position:0% +arrays in python there are only dynamic +arrays which is something we will get to + + align:start position:0% +arrays which is something we will get to + + + align:start position:0% +arrays which is something we will get to +but uh i want to talk about what is a + + align:start position:0% +but uh i want to talk about what is a + + + align:start position:0% +but uh i want to talk about what is a +static array + + align:start position:0% +static array + + + align:start position:0% +static array +really and this relates to + + align:start position:0% +really and this relates to + + + align:start position:0% +really and this relates to +our notion of our model of computation + + align:start position:0% +our notion of our model of computation + + + align:start position:0% +our notion of our model of computation +which jason also talked about + + align:start position:0% +which jason also talked about + + + align:start position:0% +which jason also talked about +which we call the word ram + + align:start position:0% + + + + align:start position:0% + +remember + + align:start position:0% + + + + align:start position:0% + +so the idea in word ram is that your + + align:start position:0% +so the idea in word ram is that your + + + align:start position:0% +so the idea in word ram is that your +memory + + align:start position:0% +memory + + + align:start position:0% +memory +is an array + + align:start position:0% +is an array + + + align:start position:0% +is an array +of w bit words this is a bit circular + + align:start position:0% +of w bit words this is a bit circular + + + align:start position:0% +of w bit words this is a bit circular +i'm going to define + + align:start position:0% +i'm going to define + + + align:start position:0% +i'm going to define +an array in terms of the word ram which + + align:start position:0% +an array in terms of the word ram which + + + align:start position:0% +an array in terms of the word ram which +is defined in terms of arrays but + + align:start position:0% + + + + align:start position:0% + +i think you know the idea so we have + + align:start position:0% +i think you know the idea so we have + + + align:start position:0% +i think you know the idea so we have +a big memory which goes off to infinity + + align:start position:0% +a big memory which goes off to infinity + + + align:start position:0% +a big memory which goes off to infinity +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +it's divided into words + + align:start position:0% +it's divided into words + + + align:start position:0% +it's divided into words +each word here is w bits long + + align:start position:0% +each word here is w bits long + + + align:start position:0% +each word here is w bits long +this is word zero word one word two and + + align:start position:0% +this is word zero word one word two and + + + align:start position:0% +this is word zero word one word two and +you can + + align:start position:0% +you can + + + align:start position:0% +you can +access this array randomly random access + + align:start position:0% +access this array randomly random access + + + align:start position:0% +access this array randomly random access +memory so i can give you the number five + + align:start position:0% +memory so i can give you the number five + + + align:start position:0% +memory so i can give you the number five +and get zero one two three + + align:start position:0% +and get zero one two three + + + align:start position:0% +and get zero one two three +four five the fifth word in this + + align:start position:0% +four five the fifth word in this + + + align:start position:0% +four five the fifth word in this +round that's how actual memories work + + align:start position:0% +round that's how actual memories work + + + align:start position:0% +round that's how actual memories work +uh you can access any of them equally + + align:start position:0% +uh you can access any of them equally + + + align:start position:0% +uh you can access any of them equally +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +okay so that's memory + + align:start position:0% +okay so that's memory + + + align:start position:0% +okay so that's memory +and so what we want to do is when we say + + align:start position:0% +and so what we want to do is when we say + + + align:start position:0% +and so what we want to do is when we say +an array + + align:start position:0% + + + + align:start position:0% + +we want this to be a consecutive + + align:start position:0% + + + + align:start position:0% + +chunk of memory + + align:start position:0% + + + + align:start position:0% + +let me get a color + + align:start position:0% + + + + align:start position:0% + +so let's say i have an array of size + + align:start position:0% +so let's say i have an array of size + + + align:start position:0% +so let's say i have an array of size +four and it lives + + align:start position:0% +four and it lives + + + align:start position:0% +four and it lives +here + + align:start position:0% + + + + align:start position:0% + +jason can't spell but i can't count so i + + align:start position:0% +jason can't spell but i can't count so i + + + align:start position:0% +jason can't spell but i can't count so i +think that's four + + align:start position:0% +think that's four + + + align:start position:0% +think that's four +we've got uh so the array starts here + + align:start position:0% +we've got uh so the array starts here + + + align:start position:0% +we've got uh so the array starts here +and it ends over here it's of size four + + align:start position:0% +and it ends over here it's of size four + + + align:start position:0% +and it ends over here it's of size four +and it's consecutive which means if i + + align:start position:0% +and it's consecutive which means if i + + + align:start position:0% +and it's consecutive which means if i +want to + + align:start position:0% +want to + + + align:start position:0% +want to +access um + + align:start position:0% +access um + + + align:start position:0% +access um +the array at position + + align:start position:0% +the array at position + + + align:start position:0% +the array at position +at index i then + + align:start position:0% +at index i then + + + align:start position:0% +at index i then +this is the same thing as accessing my + + align:start position:0% +this is the same thing as accessing my + + + align:start position:0% +this is the same thing as accessing my +memory array + + align:start position:0% +memory array + + + align:start position:0% +memory array +at position wherever the array starts + + align:start position:0% +at position wherever the array starts + + + align:start position:0% +at position wherever the array starts +which i'll call the address of the array + + align:start position:0% + + + + align:start position:0% + +in python this is id of array + + align:start position:0% +in python this is id of array + + + align:start position:0% +in python this is id of array +plus i okay this is just simple offset + + align:start position:0% +plus i okay this is just simple offset + + + align:start position:0% +plus i okay this is just simple offset +arithmetic + + align:start position:0% +arithmetic + + + align:start position:0% +arithmetic +if i want to know the zeroth item of the + + align:start position:0% +if i want to know the zeroth item of the + + + align:start position:0% +if i want to know the zeroth item of the +array it's right here where it starts + + align:start position:0% +array it's right here where it starts + + + align:start position:0% +array it's right here where it starts +the first item is one after that the + + align:start position:0% +the first item is one after that the + + + align:start position:0% +the first item is one after that the +second item is one after that + + align:start position:0% +second item is one after that + + + align:start position:0% +second item is one after that +so as long as i store my array + + align:start position:0% +so as long as i store my array + + + align:start position:0% +so as long as i store my array +consecutively in memory + + align:start position:0% +consecutively in memory + + + align:start position:0% +consecutively in memory +i can access the array in constant time + + align:start position:0% +i can access the array in constant time + + + align:start position:0% +i can access the array in constant time +i can do get + + align:start position:0% +i can do get + + + align:start position:0% +i can do get +at and set at as quickly as i can + + align:start position:0% +at and set at as quickly as i can + + + align:start position:0% +at and set at as quickly as i can +randomly access the memory + + align:start position:0% +randomly access the memory + + + align:start position:0% +randomly access the memory +and get a value or set a value which + + align:start position:0% +and get a value or set a value which + + + align:start position:0% +and get a value or set a value which +we're assuming + + align:start position:0% +we're assuming + + + align:start position:0% +we're assuming +is constant time so + + align:start position:0% +is constant time so + + + align:start position:0% +is constant time so +[Music] + + align:start position:0% + + + + align:start position:0% + +array access is constant time + + align:start position:0% +array access is constant time + + + align:start position:0% +array access is constant time +okay this is what allows a static array + + align:start position:0% +okay this is what allows a static array + + + align:start position:0% +okay this is what allows a static array +to actually solve this problem + + align:start position:0% +to actually solve this problem + + + align:start position:0% +to actually solve this problem +in constant time per + + align:start position:0% + + + + align:start position:0% + +get at and set at operation so this may + + align:start position:0% +get at and set at operation so this may + + + align:start position:0% +get at and set at operation so this may +seem simple but we're really going to + + align:start position:0% +seem simple but we're really going to + + + align:start position:0% +seem simple but we're really going to +need this model and really rely on this + + align:start position:0% +need this model and really rely on this + + + align:start position:0% +need this model and really rely on this +model + + align:start position:0% +model + + + align:start position:0% +model +increasingly as we get to more + + align:start position:0% +increasingly as we get to more + + + align:start position:0% +increasingly as we get to more +interesting data structures this is the + + align:start position:0% +interesting data structures this is the + + + align:start position:0% +interesting data structures this is the +first time we're actually needing it + + align:start position:0% +first time we're actually needing it + + + align:start position:0% +first time we're actually needing it +uh let's see length is also constant + + align:start position:0% +uh let's see length is also constant + + + align:start position:0% +uh let's see length is also constant +time + + align:start position:0% +time + + + align:start position:0% +time +we're just going to store that number n + + align:start position:0% +we're just going to store that number n + + + align:start position:0% +we're just going to store that number n +along with its address + + align:start position:0% +along with its address + + + align:start position:0% +along with its address +and build is going to take linear time + + align:start position:0% +and build is going to take linear time + + + align:start position:0% +and build is going to take linear time +iteration will take + + align:start position:0% +iteration will take + + + align:start position:0% +iteration will take +linear time + + align:start position:0% + + + + align:start position:0% + +okay pretty straightforward i guess one + + align:start position:0% +okay pretty straightforward i guess one + + + align:start position:0% +okay pretty straightforward i guess one +thing here when defining build i need to + + align:start position:0% +thing here when defining build i need to + + + align:start position:0% +thing here when defining build i need to +introduce a little bit more of our model + + align:start position:0% +introduce a little bit more of our model + + + align:start position:0% +introduce a little bit more of our model +of computation which is + + align:start position:0% +of computation which is + + + align:start position:0% +of computation which is +how do you create an array in the + + align:start position:0% +how do you create an array in the + + + align:start position:0% +how do you create an array in the +beginning + + align:start position:0% +beginning + + + align:start position:0% +beginning +i claim i can do it in linear time and + + align:start position:0% +i claim i can do it in linear time and + + + align:start position:0% +i claim i can do it in linear time and +that's just part of the model + + align:start position:0% +that's just part of the model + + + align:start position:0% +that's just part of the model +so this is called the memory allocation + + align:start position:0% + + + + align:start position:0% + +model + + align:start position:0% + + + + align:start position:0% + +there are a few possible choices here + + align:start position:0% +there are a few possible choices here + + + align:start position:0% +there are a few possible choices here +but the cleanest one is just to assume + + align:start position:0% +but the cleanest one is just to assume + + + align:start position:0% +but the cleanest one is just to assume +that you can + + align:start position:0% +that you can + + + align:start position:0% +that you can +allocate an array + + align:start position:0% +allocate an array + + + align:start position:0% +allocate an array +of size n + + align:start position:0% + + + + align:start position:0% + +in theta n time + + align:start position:0% +in theta n time + + + align:start position:0% +in theta n time +so it takes linear time to make an array + + align:start position:0% +so it takes linear time to make an array + + + align:start position:0% +so it takes linear time to make an array +of size n + + align:start position:0% +of size n + + + align:start position:0% +of size n +you could imagine this being constant it + + align:start position:0% +you could imagine this being constant it + + + align:start position:0% +you could imagine this being constant it +doesn't really matter much but it does + + align:start position:0% +doesn't really matter much but it does + + + align:start position:0% +doesn't really matter much but it does +take work and in particular if you just + + align:start position:0% +take work and in particular if you just + + + align:start position:0% +take work and in particular if you just +allocate some chunk of memory you have + + align:start position:0% +allocate some chunk of memory you have + + + align:start position:0% +allocate some chunk of memory you have +no idea whether it's initialized so + + align:start position:0% +no idea whether it's initialized so + + + align:start position:0% +no idea whether it's initialized so +initializing that array to zeros + + align:start position:0% +initializing that array to zeros + + + align:start position:0% +initializing that array to zeros +will cost linear time it won't really + + align:start position:0% +will cost linear time it won't really + + + align:start position:0% +will cost linear time it won't really +matter constant versus linear but a nice + + align:start position:0% +matter constant versus linear but a nice + + + align:start position:0% +matter constant versus linear but a nice +side effect of this model + + align:start position:0% +side effect of this model + + + align:start position:0% +side effect of this model +is that space if you're just allocating + + align:start position:0% +is that space if you're just allocating + + + align:start position:0% +is that space if you're just allocating +arrays the amount of space you use is at + + align:start position:0% +arrays the amount of space you use is at + + + align:start position:0% +arrays the amount of space you use is at +most the amount of time you use + + align:start position:0% +most the amount of time you use + + + align:start position:0% +most the amount of time you use +or i guess big o of that + + align:start position:0% + + + + align:start position:0% + +so that's a nice feature it's pretty + + align:start position:0% +so that's a nice feature it's pretty + + + align:start position:0% +so that's a nice feature it's pretty +weird if you imagine + + align:start position:0% +weird if you imagine + + + align:start position:0% +weird if you imagine +it's unrealistic to imagine you can + + align:start position:0% +it's unrealistic to imagine you can + + + align:start position:0% +it's unrealistic to imagine you can +allocate an array that's + + align:start position:0% +allocate an array that's + + + align:start position:0% +allocate an array that's +infinite size and then just use a few + + align:start position:0% +infinite size and then just use a few + + + align:start position:0% +infinite size and then just use a few +items out of it that won't be + + align:start position:0% +items out of it that won't be + + + align:start position:0% +items out of it that won't be +give you a good data structure so we'll + + align:start position:0% +give you a good data structure so we'll + + + align:start position:0% +give you a good data structure so we'll +assume it costs + + align:start position:0% +assume it costs + + + align:start position:0% +assume it costs +to allocate memory and okay great we + + align:start position:0% +to allocate memory and okay great we + + + align:start position:0% +to allocate memory and okay great we +solved the static sequence problem + + align:start position:0% +solved the static sequence problem + + + align:start position:0% +solved the static sequence problem +very simple kind of boring these are + + align:start position:0% +very simple kind of boring these are + + + align:start position:0% +very simple kind of boring these are +optimal running times + + align:start position:0% +optimal running times + + + align:start position:0% +optimal running times +now let's make it interesting make sure + + align:start position:0% +now let's make it interesting make sure + + + align:start position:0% +now let's make it interesting make sure +i didn't miss anything + + align:start position:0% +i didn't miss anything + + + align:start position:0% +i didn't miss anything +and talk about + + align:start position:0% +and talk about + + + align:start position:0% +and talk about +oh there is one thing i wanted to talk + + align:start position:0% +oh there is one thing i wanted to talk + + + align:start position:0% +oh there is one thing i wanted to talk +about + + align:start position:0% +about + + + align:start position:0% +about +in the word ram a side effect + + align:start position:0% +in the word ram a side effect + + + align:start position:0% +in the word ram a side effect +of this assumption that array access + + align:start position:0% +of this assumption that array access + + + align:start position:0% +of this assumption that array access +should take constant time + + align:start position:0% +should take constant time + + + align:start position:0% +should take constant time +and that accessing these positions in my + + align:start position:0% +and that accessing these positions in my + + + align:start position:0% +and that accessing these positions in my +memory + + align:start position:0% +memory + + + align:start position:0% +memory +should take constant time is that + + align:start position:0% + + + + align:start position:0% + +we need to assume w + + align:start position:0% +we need to assume w + + + align:start position:0% +we need to assume w +is at least log n or so + + align:start position:0% +is at least log n or so + + + align:start position:0% +is at least log n or so +w remember is the machine word size in + + align:start position:0% +w remember is the machine word size in + + + align:start position:0% +w remember is the machine word size in +real computers this is currently 64. + + align:start position:0% +real computers this is currently 64. + + + align:start position:0% +real computers this is currently 64. +um or 256 and some + + align:start position:0% +um or 256 and some + + + align:start position:0% +um or 256 and some +bizarre instructions but uh we don't + + align:start position:0% +bizarre instructions but uh we don't + + + align:start position:0% +bizarre instructions but uh we don't +usually think of the machine as getting + + align:start position:0% +usually think of the machine as getting + + + align:start position:0% +usually think of the machine as getting +bigger over time + + align:start position:0% +bigger over time + + + align:start position:0% +bigger over time +but you should think of the machine as + + align:start position:0% +but you should think of the machine as + + + align:start position:0% +but you should think of the machine as +getting bigger over time this is a + + align:start position:0% +getting bigger over time this is a + + + align:start position:0% +getting bigger over time this is a +statement + + align:start position:0% +statement + + + align:start position:0% +statement +that says the word side has to grow with + + align:start position:0% +that says the word side has to grow with + + + align:start position:0% +that says the word side has to grow with +n + + align:start position:0% +n + + + align:start position:0% +n +it might grow faster than log n but it + + align:start position:0% +it might grow faster than log n but it + + + align:start position:0% +it might grow faster than log n but it +has to grow at least as fast as log n + + align:start position:0% +has to grow at least as fast as log n + + + align:start position:0% +has to grow at least as fast as log n +why do i say that because if i have n + + align:start position:0% +why do i say that because if i have n + + + align:start position:0% +why do i say that because if i have n +things that i'm dealing with and here's + + align:start position:0% +things that i'm dealing with and here's + + + align:start position:0% +things that i'm dealing with and here's +the problem size + + align:start position:0% +the problem size + + + align:start position:0% +the problem size +maybe it's the array i'm trying to store + + align:start position:0% +maybe it's the array i'm trying to store + + + align:start position:0% +maybe it's the array i'm trying to store +whatever if i'm having to + + align:start position:0% +whatever if i'm having to + + + align:start position:0% +whatever if i'm having to +deal with n things in my memory at the + + align:start position:0% +deal with n things in my memory at the + + + align:start position:0% +deal with n things in my memory at the +very least i need to be able to address + + align:start position:0% +very least i need to be able to address + + + align:start position:0% +very least i need to be able to address +them + + align:start position:0% +them + + + align:start position:0% +them +i should be able to say give me the ith + + align:start position:0% +i should be able to say give me the ith + + + align:start position:0% +i should be able to say give me the ith +one and represent that number i + + align:start position:0% +one and represent that number i + + + align:start position:0% +one and represent that number i +in a word otherwise because the machine + + align:start position:0% +in a word otherwise because the machine + + + align:start position:0% +in a word otherwise because the machine +is designed to only work with w bit + + align:start position:0% +is designed to only work with w bit + + + align:start position:0% +is designed to only work with w bit +words in constant time + + align:start position:0% +words in constant time + + + align:start position:0% +words in constant time +if i want to be able to access the ith + + align:start position:0% +if i want to be able to access the ith + + + align:start position:0% +if i want to be able to access the ith +word in constant time i need a word size + + align:start position:0% +word in constant time i need a word size + + + align:start position:0% +word in constant time i need a word size +that's at least log n just to address + + align:start position:0% +that's at least log n just to address + + + align:start position:0% +that's at least log n just to address +the n + + align:start position:0% +the n + + + align:start position:0% +the n +things in my input so this is a totally + + align:start position:0% +things in my input so this is a totally + + + align:start position:0% +things in my input so this is a totally +reasonable assumption it may seem weird + + align:start position:0% +reasonable assumption it may seem weird + + + align:start position:0% +reasonable assumption it may seem weird +because you think of a real machine as + + align:start position:0% +because you think of a real machine as + + + align:start position:0% +because you think of a real machine as +having constant size + + align:start position:0% +having constant size + + + align:start position:0% +having constant size +but you know real machine has constant + + align:start position:0% +but you know real machine has constant + + + align:start position:0% +but you know real machine has constant +size ram also + + align:start position:0% +size ram also + + + align:start position:0% +size ram also +my machine has 24 gigs of ram or + + align:start position:0% +my machine has 24 gigs of ram or + + + align:start position:0% +my machine has 24 gigs of ram or +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +that laptop has eight but uh you don't + + align:start position:0% +that laptop has eight but uh you don't + + + align:start position:0% +that laptop has eight but uh you don't +think of that as changing over time but + + align:start position:0% +think of that as changing over time but + + + align:start position:0% +think of that as changing over time but +of course if you wanted to process a + + align:start position:0% +of course if you wanted to process a + + + align:start position:0% +of course if you wanted to process a +larger input you would + + align:start position:0% +larger input you would + + + align:start position:0% +larger input you would +buy more ram so eventually + + align:start position:0% +buy more ram so eventually + + + align:start position:0% +buy more ram so eventually +when our ends get really really big + + align:start position:0% +when our ends get really really big + + + align:start position:0% +when our ends get really really big +we're going to have to increase w just + + align:start position:0% +we're going to have to increase w just + + + align:start position:0% +we're going to have to increase w just +so we can address that round + + align:start position:0% +so we can address that round + + + align:start position:0% +so we can address that round +that's the the intuition here but this + + align:start position:0% +that's the the intuition here but this + + + align:start position:0% +that's the the intuition here but this +is a way to bridge + + align:start position:0% +is a way to bridge + + + align:start position:0% +is a way to bridge +reality which are fixed machines with + + align:start position:0% +reality which are fixed machines with + + + align:start position:0% +reality which are fixed machines with +theory in + + align:start position:0% +theory in + + + align:start position:0% +theory in +in algorithms we care about scalability + + align:start position:0% +in algorithms we care about scalability + + + align:start position:0% +in algorithms we care about scalability +for very large n we want to know what + + align:start position:0% +for very large n we want to know what + + + align:start position:0% +for very large n we want to know what +that growth function is + + align:start position:0% +that growth function is + + + align:start position:0% +that growth function is +and ignore the lead constant factor + + align:start position:0% +and ignore the lead constant factor + + + align:start position:0% +and ignore the lead constant factor +that's what asymptotic notion notation + + align:start position:0% +that's what asymptotic notion notation + + + align:start position:0% +that's what asymptotic notion notation +is all about + + align:start position:0% +is all about + + + align:start position:0% +is all about +and for that we need a notion of word + + align:start position:0% +and for that we need a notion of word + + + align:start position:0% +and for that we need a notion of word +size also changing in this asymptotic + + align:start position:0% +size also changing in this asymptotic + + + align:start position:0% +size also changing in this asymptotic +way + + align:start position:0% +way + + + align:start position:0% +way +all right that's uh that will be more + + align:start position:0% +all right that's uh that will be more + + + align:start position:0% +all right that's uh that will be more +important + + align:start position:0% +important + + + align:start position:0% +important +next week when we talk about hashing and + + align:start position:0% +next week when we talk about hashing and + + + align:start position:0% +next week when we talk about hashing and +why hashing is a reasonable thing to do + + align:start position:0% +why hashing is a reasonable thing to do + + + align:start position:0% +why hashing is a reasonable thing to do +but let's move on to dynamic sequences + + align:start position:0% +but let's move on to dynamic sequences + + + align:start position:0% +but let's move on to dynamic sequences +which is where things get interesting + + align:start position:0% + + + + align:start position:0% + +so i have the update here so we start + + align:start position:0% +so i have the update here so we start + + + align:start position:0% +so i have the update here so we start +with + + align:start position:0% +with + + + align:start position:0% +with +static sequences so all of these + + align:start position:0% +static sequences so all of these + + + align:start position:0% +static sequences so all of these +operations + + align:start position:0% +operations + + + align:start position:0% +operations +are still something we want to support + + align:start position:0% +are still something we want to support + + + align:start position:0% +are still something we want to support +in a dynamic sequence but we add two + + align:start position:0% +in a dynamic sequence but we add two + + + align:start position:0% +in a dynamic sequence but we add two +dynamic operations + + align:start position:0% +dynamic operations + + + align:start position:0% +dynamic operations +somewhat controversial operations so + + align:start position:0% +somewhat controversial operations so + + + align:start position:0% +somewhat controversial operations so +exciting + + align:start position:0% +exciting + + + align:start position:0% +exciting +i want to be able to insert in the + + align:start position:0% +i want to be able to insert in the + + + align:start position:0% +i want to be able to insert in the +middle of my sequence + + align:start position:0% +middle of my sequence + + + align:start position:0% +middle of my sequence +and i want to be able to delete from the + + align:start position:0% +and i want to be able to delete from the + + + align:start position:0% +and i want to be able to delete from the +middle of my sequence so + + align:start position:0% +middle of my sequence so + + + align:start position:0% +middle of my sequence so +here's my sequence which i'm going to + + align:start position:0% +here's my sequence which i'm going to + + + align:start position:0% +here's my sequence which i'm going to +think of + + align:start position:0% +think of + + + align:start position:0% +think of +in a picture i'm going to draw it as an + + align:start position:0% +in a picture i'm going to draw it as an + + + align:start position:0% +in a picture i'm going to draw it as an +array but it's stored however it's + + align:start position:0% +array but it's stored however it's + + + align:start position:0% +array but it's stored however it's +stored we don't know + + align:start position:0% +stored we don't know + + + align:start position:0% +stored we don't know +this is an interface not an + + align:start position:0% +this is an interface not an + + + align:start position:0% +this is an interface not an +implementation so we have x0 + + align:start position:0% +implementation so we have x0 + + + align:start position:0% +implementation so we have x0 +x1 x2 x3 + + align:start position:0% + + + + align:start position:0% + +uh and let's say i insert at position + + align:start position:0% +uh and let's say i insert at position + + + align:start position:0% +uh and let's say i insert at position +2 so position 2 is here + + align:start position:0% +2 so position 2 is here + + + align:start position:0% +2 so position 2 is here +so i come in with my new x and i would + + align:start position:0% +so i come in with my new x and i would + + + align:start position:0% +so i come in with my new x and i would +like + + align:start position:0% +like + + + align:start position:0% +like +x to be the new x2 but i don't want to + + align:start position:0% +x to be the new x2 but i don't want to + + + align:start position:0% +x to be the new x2 but i don't want to +lose any information if i did set at 2 + + align:start position:0% +lose any information if i did set at 2 + + + align:start position:0% +lose any information if i did set at 2 +then i would erase this and replace it + + align:start position:0% +then i would erase this and replace it + + + align:start position:0% +then i would erase this and replace it +with x but i want to do insert at which + + align:start position:0% +with x but i want to do insert at which + + + align:start position:0% +with x but i want to do insert at which +means all of these guys conceptually are + + align:start position:0% +means all of these guys conceptually are + + + align:start position:0% +means all of these guys conceptually are +going to shift over by one in terms of + + align:start position:0% +going to shift over by one in terms of + + + align:start position:0% +going to shift over by one in terms of +their indices + + align:start position:0% +their indices + + + align:start position:0% +their indices +so then i would get this picture that's + + align:start position:0% +so then i would get this picture that's + + + align:start position:0% +so then i would get this picture that's +one bigger + + align:start position:0% + + + + align:start position:0% + +and now i've got the new x i've got what + + align:start position:0% +and now i've got the new x i've got what + + + align:start position:0% +and now i've got the new x i've got what +was the old x2 + + align:start position:0% +was the old x2 + + + align:start position:0% +was the old x2 +which i don't hesitate to call x2 + + align:start position:0% +which i don't hesitate to call x2 + + + align:start position:0% +which i don't hesitate to call x2 +because that's its old name not its new + + align:start position:0% +because that's its old name not its new + + + align:start position:0% +because that's its old name not its new +name i'm going to draw arrows to say + + align:start position:0% +name i'm going to draw arrows to say + + + align:start position:0% +name i'm going to draw arrows to say +these guys get copied over + + align:start position:0% +these guys get copied over + + + align:start position:0% +these guys get copied over +uh these ones are definitely unchanged + + align:start position:0% +uh these ones are definitely unchanged + + + align:start position:0% +uh these ones are definitely unchanged +our new x2 which i'll call x2 prime is x + + align:start position:0% +our new x2 which i'll call x2 prime is x + + + align:start position:0% +our new x2 which i'll call x2 prime is x +and this is x3 prime x4 prime + + align:start position:0% +and this is x3 prime x4 prime + + + align:start position:0% +and this is x3 prime x4 prime +and so on i i want to be careful here + + align:start position:0% +and so on i i want to be careful here + + + align:start position:0% +and so on i i want to be careful here +and of course the new n + + align:start position:0% +and of course the new n + + + align:start position:0% +and of course the new n +prime is n plus one + + align:start position:0% +prime is n plus one + + + align:start position:0% +prime is n plus one +uh i want to be careful about the + + align:start position:0% +uh i want to be careful about the + + + align:start position:0% +uh i want to be careful about the +labeling because the key + + align:start position:0% +labeling because the key + + + align:start position:0% +labeling because the key +what makes insert ad interesting is that + + align:start position:0% +what makes insert ad interesting is that + + + align:start position:0% +what makes insert ad interesting is that +later when i call get + + align:start position:0% +later when i call get + + + align:start position:0% +later when i call get +at it's with the new indexing so + + align:start position:0% +at it's with the new indexing so + + + align:start position:0% +at it's with the new indexing so +previously + + align:start position:0% +previously + + + align:start position:0% +previously +if i did get at 2 i would get this value + + align:start position:0% +if i did get at 2 i would get this value + + + align:start position:0% +if i did get at 2 i would get this value +and afterwards if i did get at it 2 i + + align:start position:0% +and afterwards if i did get at it 2 i + + + align:start position:0% +and afterwards if i did get at it 2 i +get the new value if i did get at it 3 + + align:start position:0% +get the new value if i did get at it 3 + + + align:start position:0% +get the new value if i did get at it 3 +down here i would get + + align:start position:0% +down here i would get + + + align:start position:0% +down here i would get +i get the value that used to be x2 okay + + align:start position:0% +i get the value that used to be x2 okay + + + align:start position:0% +i get the value that used to be x2 okay +that's maybe hard to track + + align:start position:0% +that's maybe hard to track + + + align:start position:0% +that's maybe hard to track +but this is a useful conceptually very + + align:start position:0% +but this is a useful conceptually very + + + align:start position:0% +but this is a useful conceptually very +useful thing to do + + align:start position:0% +useful thing to do + + + align:start position:0% +useful thing to do +especially when you're inserting or + + align:start position:0% +especially when you're inserting or + + + align:start position:0% +especially when you're inserting or +deleting at the ends + + align:start position:0% +deleting at the ends + + + align:start position:0% +deleting at the ends +so we're going to define in particular + + align:start position:0% +so we're going to define in particular + + + align:start position:0% +so we're going to define in particular +insert and delete + + align:start position:0% + + + + align:start position:0% + +uh first and last + + align:start position:0% + + + + align:start position:0% + +uh these are + + align:start position:0% +uh these are + + + align:start position:0% +uh these are +sometimes given if if you have an insert + + align:start position:0% +sometimes given if if you have an insert + + + align:start position:0% +sometimes given if if you have an insert +it has an x + + align:start position:0% +it has an x + + + align:start position:0% +it has an x +if you do a delete it has no argument + + align:start position:0% +if you do a delete it has no argument + + + align:start position:0% +if you do a delete it has no argument +so this means insert at the beginning of + + align:start position:0% +so this means insert at the beginning of + + + align:start position:0% +so this means insert at the beginning of +the array which would be like adding it + + align:start position:0% +the array which would be like adding it + + + align:start position:0% +the array which would be like adding it +here + + align:start position:0% +here + + + align:start position:0% +here +and insert last means adding it on here + + align:start position:0% +and insert last means adding it on here + + + align:start position:0% +and insert last means adding it on here +so insert last doesn't change the + + align:start position:0% +so insert last doesn't change the + + + align:start position:0% +so insert last doesn't change the +indices of any of the old items that's a + + align:start position:0% +indices of any of the old items that's a + + + align:start position:0% +indices of any of the old items that's a +nice feature of insert last insert first + + align:start position:0% +nice feature of insert last insert first + + + align:start position:0% +nice feature of insert last insert first +changes all of them they all get + + align:start position:0% +changes all of them they all get + + + align:start position:0% +changes all of them they all get +incremented by one + + align:start position:0% +incremented by one + + + align:start position:0% +incremented by one +and we're also interested in the similar + + align:start position:0% +and we're also interested in the similar + + + align:start position:0% +and we're also interested in the similar +things here we could do + + align:start position:0% +things here we could do + + + align:start position:0% +things here we could do +get first + + align:start position:0% +get first + + + align:start position:0% +get first +or last or + + align:start position:0% +or last or + + + align:start position:0% +or last or +set first or last + + align:start position:0% + + + + align:start position:0% + +okay which are the obvious special cases + + align:start position:0% +okay which are the obvious special cases + + + align:start position:0% +okay which are the obvious special cases +of get ad and set out now these special + + align:start position:0% +of get ad and set out now these special + + + align:start position:0% +of get ad and set out now these special +cases are particularly interesting + + align:start position:0% +cases are particularly interesting + + + align:start position:0% +cases are particularly interesting +in an algorithms context if you were a + + align:start position:0% +in an algorithms context if you were a + + + align:start position:0% +in an algorithms context if you were a +mathematician you would say well + + align:start position:0% +mathematician you would say well + + + align:start position:0% +mathematician you would say well +why do i even bother this this is just + + align:start position:0% +why do i even bother this this is just + + + align:start position:0% +why do i even bother this this is just +shorthand for + + align:start position:0% +shorthand for + + + align:start position:0% +shorthand for +a particular call to get or set but what + + align:start position:0% +a particular call to get or set but what + + + align:start position:0% +a particular call to get or set but what +makes it interesting + + align:start position:0% +makes it interesting + + + align:start position:0% +makes it interesting +from a data structure's perspective is + + align:start position:0% +from a data structure's perspective is + + + align:start position:0% +from a data structure's perspective is +that we care about algorithms for + + align:start position:0% +that we care about algorithms for + + + align:start position:0% +that we care about algorithms for +supporting these operations and maybe + + align:start position:0% +supporting these operations and maybe + + + align:start position:0% +supporting these operations and maybe +the algorithm for supporting get first + + align:start position:0% +the algorithm for supporting get first + + + align:start position:0% +the algorithm for supporting get first +or set first + + align:start position:0% +or set first + + + align:start position:0% +or set first +or in particular insert first or insert + + align:start position:0% +or in particular insert first or insert + + + align:start position:0% +or in particular insert first or insert +last + + align:start position:0% +last + + + align:start position:0% +last +might be more efficient maybe we can + + align:start position:0% +might be more efficient maybe we can + + + align:start position:0% +might be more efficient maybe we can +solve this problem better + + align:start position:0% +solve this problem better + + + align:start position:0% +solve this problem better +than we can solve insert at so while + + align:start position:0% +than we can solve insert at so while + + + align:start position:0% +than we can solve insert at so while +ideally we could solve the entire + + align:start position:0% +ideally we could solve the entire + + + align:start position:0% +ideally we could solve the entire +dynamics sequence interface + + align:start position:0% +dynamics sequence interface + + + align:start position:0% +dynamics sequence interface +constant time per operation that's not + + align:start position:0% +constant time per operation that's not + + + align:start position:0% +constant time per operation that's not +actually possible you can prove that + + align:start position:0% +actually possible you can prove that + + + align:start position:0% +actually possible you can prove that +but special cases of it where we're just + + align:start position:0% +but special cases of it where we're just + + + align:start position:0% +but special cases of it where we're just +inserting and deleting from the ends say + + align:start position:0% +inserting and deleting from the ends say + + + align:start position:0% +inserting and deleting from the ends say +we can do that so that's why it's + + align:start position:0% +we can do that so that's why it's + + + align:start position:0% +we can do that so that's why it's +interesting to introduce + + align:start position:0% +interesting to introduce + + + align:start position:0% +interesting to introduce +special cases that we care about + + align:start position:0% +special cases that we care about + + + align:start position:0% +special cases that we care about +cool that's the definition of the + + align:start position:0% +cool that's the definition of the + + + align:start position:0% +cool that's the definition of the +dynamic sequence interface + + align:start position:0% +dynamic sequence interface + + + align:start position:0% +dynamic sequence interface +now we're going to actually solve it + + align:start position:0% + + + + align:start position:0% + +so uh our first data structure for this + + align:start position:0% +so uh our first data structure for this + + + align:start position:0% +so uh our first data structure for this +is called + + align:start position:0% +is called + + + align:start position:0% +is called +linked bliss i've taken + + align:start position:0% + + + + align:start position:0% + +probably you've probably seen linked + + align:start position:0% +probably you've probably seen linked + + + align:start position:0% +probably you've probably seen linked +lists before at some point + + align:start position:0% +lists before at some point + + + align:start position:0% +lists before at some point +but the main new part here is we're + + align:start position:0% +but the main new part here is we're + + + align:start position:0% +but the main new part here is we're +going to actually analyze them + + align:start position:0% +going to actually analyze them + + + align:start position:0% +going to actually analyze them +and see how they how efficiently they + + align:start position:0% +and see how they how efficiently they + + + align:start position:0% +and see how they how efficiently they +implement all these operations we might + + align:start position:0% +implement all these operations we might + + + align:start position:0% +implement all these operations we might +care about + + align:start position:0% +care about + + + align:start position:0% +care about +so first review what is a linked list + + align:start position:0% +so first review what is a linked list + + + align:start position:0% +so first review what is a linked list +we store our items + + align:start position:0% +we store our items + + + align:start position:0% +we store our items +in a bunch of nodes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +each node has an item in it + + align:start position:0% +each node has an item in it + + + align:start position:0% +each node has an item in it +and a next field + + align:start position:0% + + + + align:start position:0% + +so you could think of these as class + + align:start position:0% +so you could think of these as class + + + align:start position:0% +so you could think of these as class +objects with two + + align:start position:0% +objects with two + + + align:start position:0% +objects with two +class variables the item and and a next + + align:start position:0% +class variables the item and and a next + + + align:start position:0% +class variables the item and and a next +pointer + + align:start position:0% +pointer + + + align:start position:0% +pointer +and we assemble those into this kind of + + align:start position:0% +and we assemble those into this kind of + + + align:start position:0% +and we assemble those into this kind of +structure where we + + align:start position:0% +structure where we + + + align:start position:0% +structure where we +store in the item fields we're going to + + align:start position:0% +store in the item fields we're going to + + + align:start position:0% +store in the item fields we're going to +store the actual values + + align:start position:0% +store the actual values + + + align:start position:0% +store the actual values +that we want to represent in our + + align:start position:0% +that we want to represent in our + + + align:start position:0% +that we want to represent in our +sequence x zero through x n minus 1 + + align:start position:0% +sequence x zero through x n minus 1 + + + align:start position:0% +sequence x zero through x n minus 1 +in order and then we're going to use the + + align:start position:0% +in order and then we're going to use the + + + align:start position:0% +in order and then we're going to use the +next pointers to link these all together + + align:start position:0% +next pointers to link these all together + + + align:start position:0% +next pointers to link these all together +in that order so the next pointers are + + align:start position:0% +in that order so the next pointers are + + + align:start position:0% +in that order so the next pointers are +what actually give us the order + + align:start position:0% +what actually give us the order + + + align:start position:0% +what actually give us the order +and in addition we're going to keep + + align:start position:0% +and in addition we're going to keep + + + align:start position:0% +and in addition we're going to keep +track of what's called the head of the + + align:start position:0% +track of what's called the head of the + + + align:start position:0% +track of what's called the head of the +list + + align:start position:0% +list + + + align:start position:0% +list +so the data structure is going to be + + align:start position:0% +so the data structure is going to be + + + align:start position:0% +so the data structure is going to be +represented by head + + align:start position:0% +represented by head + + + align:start position:0% +represented by head +if you wanted to you could also store + + align:start position:0% +if you wanted to you could also store + + + align:start position:0% +if you wanted to you could also store +length + + align:start position:0% +length + + + align:start position:0% +length +so this could be the data structure + + align:start position:0% +so this could be the data structure + + + align:start position:0% +so this could be the data structure +itself + + align:start position:0% + + + + align:start position:0% + +and it's pointing to all of these types + + align:start position:0% +and it's pointing to all of these types + + + align:start position:0% +and it's pointing to all of these types +of data structures notice we've just + + align:start position:0% +of data structures notice we've just + + + align:start position:0% +of data structures notice we've just +seen + + align:start position:0% +seen + + + align:start position:0% +seen +an array based data structure which is + + align:start position:0% +an array based data structure which is + + + align:start position:0% +an array based data structure which is +just a static + + align:start position:0% +just a static + + + align:start position:0% +just a static +array and we've seen a pointer-based + + align:start position:0% +array and we've seen a pointer-based + + + align:start position:0% +array and we've seen a pointer-based +data structure + + align:start position:0% + + + + align:start position:0% + +and we're relying on the fact that + + align:start position:0% +and we're relying on the fact that + + + align:start position:0% +and we're relying on the fact that +pointers + + align:start position:0% +pointers + + + align:start position:0% +pointers +can be stored in a single word which + + align:start position:0% +can be stored in a single word which + + + align:start position:0% +can be stored in a single word which +means we can de-reference them we can + + align:start position:0% +means we can de-reference them we can + + + align:start position:0% +means we can de-reference them we can +see what's on the other side of the + + align:start position:0% +see what's on the other side of the + + + align:start position:0% +see what's on the other side of the +pointer + + align:start position:0% +pointer + + + align:start position:0% +pointer +in constant time in our word ram model + + align:start position:0% +in constant time in our word ram model + + + align:start position:0% +in constant time in our word ram model +in reality each of these nodes is stored + + align:start position:0% +in reality each of these nodes is stored + + + align:start position:0% +in reality each of these nodes is stored +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +in the array of the computer + + align:start position:0% +in the array of the computer + + + align:start position:0% +in the array of the computer +so maybe each one is two words long so + + align:start position:0% +so maybe each one is two words long so + + + align:start position:0% +so maybe each one is two words long so +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +uh one node is the first node is here + + align:start position:0% +uh one node is the first node is here + + + align:start position:0% +uh one node is the first node is here +maybe the second node is here the third + + align:start position:0% +maybe the second node is here the third + + + align:start position:0% +maybe the second node is here the third +node is here + + align:start position:0% +node is here + + + align:start position:0% +node is here +they're in some arbitrary order we're + + align:start position:0% +they're in some arbitrary order we're + + + align:start position:0% +they're in some arbitrary order we're +using this fact + + align:start position:0% +using this fact + + + align:start position:0% +using this fact +that we can allocate a an array + + align:start position:0% +that we can allocate a an array + + + align:start position:0% +that we can allocate a an array +of size n in linear time in this case + + align:start position:0% +of size n in linear time in this case + + + align:start position:0% +of size n in linear time in this case +we're going to have a raise of size 2. + + align:start position:0% +we're going to have a raise of size 2. + + + align:start position:0% +we're going to have a raise of size 2. +we can just say oh please give me a new + + align:start position:0% +we can just say oh please give me a new + + + align:start position:0% +we can just say oh please give me a new +array of size 2. + + align:start position:0% +array of size 2. + + + align:start position:0% +array of size 2. +and that will give make us one of these + + align:start position:0% +and that will give make us one of these + + + align:start position:0% +and that will give make us one of these +nodes + + align:start position:0% +nodes + + + align:start position:0% +nodes +and then we're storing pointers pointers + + align:start position:0% +and then we're storing pointers pointers + + + align:start position:0% +and then we're storing pointers pointers +are just indices + + align:start position:0% +are just indices + + + align:start position:0% +are just indices +into the giant memory array they're just + + align:start position:0% +into the giant memory array they're just + + + align:start position:0% +into the giant memory array they're just +what is the address of this little array + + align:start position:0% +what is the address of this little array + + + align:start position:0% +what is the address of this little array +okay if you've ever wondered how + + align:start position:0% +okay if you've ever wondered how + + + align:start position:0% +okay if you've ever wondered how +pointers are implemented they're just + + align:start position:0% +pointers are implemented they're just + + + align:start position:0% +pointers are implemented they're just +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +that say where in memory is this thing + + align:start position:0% +that say where in memory is this thing + + + align:start position:0% +that say where in memory is this thing +over here and + + align:start position:0% +over here and + + + align:start position:0% +over here and +in memory they're an arbitrary order + + align:start position:0% +in memory they're an arbitrary order + + + align:start position:0% +in memory they're an arbitrary order +this is really nice because it's + + align:start position:0% +this is really nice because it's + + + align:start position:0% +this is really nice because it's +easy to manipulate the order of a linked + + align:start position:0% +easy to manipulate the order of a linked + + + align:start position:0% +easy to manipulate the order of a linked +list without actually physically moving + + align:start position:0% +list without actually physically moving + + + align:start position:0% +list without actually physically moving +nodes around whereas arrays + + align:start position:0% +nodes around whereas arrays + + + align:start position:0% +nodes around whereas arrays +are problematic maybe it's worth + + align:start position:0% +are problematic maybe it's worth + + + align:start position:0% +are problematic maybe it's worth +mentioning + + align:start position:0% +mentioning + + + align:start position:0% +mentioning +let's start analyzing things so we care + + align:start position:0% +let's start analyzing things so we care + + + align:start position:0% +let's start analyzing things so we care +about these dynamic sequence + + align:start position:0% +about these dynamic sequence + + + align:start position:0% +about these dynamic sequence +operations and we could try to apply it + + align:start position:0% +operations and we could try to apply it + + + align:start position:0% +operations and we could try to apply it +to the static array data structure or we + + align:start position:0% +to the static array data structure or we + + + align:start position:0% +to the static array data structure or we +could try + + align:start position:0% +could try + + + align:start position:0% +could try +to or sorry we could try to implement + + align:start position:0% +to or sorry we could try to implement + + + align:start position:0% +to or sorry we could try to implement +these operations in a static array + + align:start position:0% +these operations in a static array + + + align:start position:0% +these operations in a static array +it's possible just not going to be very + + align:start position:0% +it's possible just not going to be very + + + align:start position:0% +it's possible just not going to be very +good + + align:start position:0% +good + + + align:start position:0% +good +and we can try to implement it with + + align:start position:0% +and we can try to implement it with + + + align:start position:0% +and we can try to implement it with +linked lists and it's also + + align:start position:0% +linked lists and it's also + + + align:start position:0% +linked lists and it's also +not going to be that great let's + + align:start position:0% +not going to be that great let's + + + align:start position:0% +not going to be that great let's +go over here + + align:start position:0% + + + + align:start position:0% + +our goal is the next data structure + + align:start position:0% +our goal is the next data structure + + + align:start position:0% +our goal is the next data structure +which is dynamic arrays + + align:start position:0% +which is dynamic arrays + + + align:start position:0% +which is dynamic arrays +but linked lists and static arrays each + + align:start position:0% +but linked lists and static arrays each + + + align:start position:0% +but linked lists and static arrays each +have their advantages + + align:start position:0% + + + + align:start position:0% + +so let's first analyze dynamic + + align:start position:0% +so let's first analyze dynamic + + + align:start position:0% +so let's first analyze dynamic +sequence operations + + align:start position:0% + + + + align:start position:0% + +um first on a static array + + align:start position:0% + + + + align:start position:0% + +and then on a linked list + + align:start position:0% + + + + align:start position:0% + +so in a static array i think you all + + align:start position:0% +so in a static array i think you all + + + align:start position:0% +so in a static array i think you all +see if i try to insert at the beginning + + align:start position:0% +see if i try to insert at the beginning + + + align:start position:0% +see if i try to insert at the beginning +of the static array that's kind of the + + align:start position:0% +of the static array that's kind of the + + + align:start position:0% +of the static array that's kind of the +worst case + + align:start position:0% +worst case + + + align:start position:0% +worst case +if i insert first then everybody has to + + align:start position:0% +if i insert first then everybody has to + + + align:start position:0% +if i insert first then everybody has to +shift over + + align:start position:0% +shift over + + + align:start position:0% +shift over +if i'm going to maintain this invariant + + align:start position:0% +if i'm going to maintain this invariant + + + align:start position:0% +if i'm going to maintain this invariant +that the ith item in the array + + align:start position:0% +that the ith item in the array + + + align:start position:0% +that the ith item in the array +represents i guess i didn't write it + + align:start position:0% +represents i guess i didn't write it + + + align:start position:0% +represents i guess i didn't write it +anywhere here + + align:start position:0% +anywhere here + + + align:start position:0% +anywhere here +maybe here + + align:start position:0% + + + + align:start position:0% + +static array we're going to maintain + + align:start position:0% +static array we're going to maintain + + + align:start position:0% +static array we're going to maintain +this invariant that a of i + + align:start position:0% +this invariant that a of i + + + align:start position:0% +this invariant that a of i +represents x i + + align:start position:0% +represents x i + + + align:start position:0% +represents x i +okay if i want to maintain that at all + + align:start position:0% +okay if i want to maintain that at all + + + align:start position:0% +okay if i want to maintain that at all +times when i insert a new thing in the + + align:start position:0% +times when i insert a new thing in the + + + align:start position:0% +times when i insert a new thing in the +front because the indices of all the + + align:start position:0% +front because the indices of all the + + + align:start position:0% +front because the indices of all the +previous items change + + align:start position:0% +previous items change + + + align:start position:0% +previous items change +i have to spend time to copy those over + + align:start position:0% +i have to spend time to copy those over + + + align:start position:0% +i have to spend time to copy those over +you can do it in linear time + + align:start position:0% +you can do it in linear time + + + align:start position:0% +you can do it in linear time +but no better okay so + + align:start position:0% +but no better okay so + + + align:start position:0% +but no better okay so +static array + + align:start position:0% + + + + align:start position:0% + +insert and delete + + align:start position:0% + + + + align:start position:0% + +anywhere + + align:start position:0% + + + + align:start position:0% + +cost + + align:start position:0% +cost + + + align:start position:0% +cost +and time + + align:start position:0% + + + + align:start position:0% + +actually uh for two reasons uh reason + + align:start position:0% +actually uh for two reasons uh reason + + + align:start position:0% +actually uh for two reasons uh reason +number one + + align:start position:0% +number one + + + align:start position:0% +number one +is that uh if we're near the front + + align:start position:0% +is that uh if we're near the front + + + align:start position:0% +is that uh if we're near the front +then we have to do shifting + + align:start position:0% +then we have to do shifting + + + align:start position:0% +then we have to do shifting +okay what about insert or delete the + + align:start position:0% +okay what about insert or delete the + + + align:start position:0% +okay what about insert or delete the +last element of an array + + align:start position:0% +last element of an array + + + align:start position:0% +last element of an array +is that any easier because then if i + + align:start position:0% +is that any easier because then if i + + + align:start position:0% +is that any easier because then if i +insert the very last element + + align:start position:0% +insert the very last element + + + align:start position:0% +insert the very last element +none of the indices change i'm just + + align:start position:0% +none of the indices change i'm just + + + align:start position:0% +none of the indices change i'm just +adding a new element + + align:start position:0% + + + + align:start position:0% + +so i don't have to do shifting + + align:start position:0% + + + + align:start position:0% + +so can i do insert and delete last in + + align:start position:0% +so can i do insert and delete last in + + + align:start position:0% +so can i do insert and delete last in +constant time in a static array + + align:start position:0% + + + + align:start position:0% + +no because the size is constant so our + + align:start position:0% +no because the size is constant so our + + + align:start position:0% +no because the size is constant so our +model is that + + align:start position:0% +model is that + + + align:start position:0% +model is that +uh remember our allocation model is that + + align:start position:0% +uh remember our allocation model is that + + + align:start position:0% +uh remember our allocation model is that +we can allocate a static array + + align:start position:0% +we can allocate a static array + + + align:start position:0% +we can allocate a static array +of size n but it's just a size n i can't + + align:start position:0% +of size n but it's just a size n i can't + + + align:start position:0% +of size n but it's just a size n i can't +just say + + align:start position:0% +just say + + + align:start position:0% +just say +please make it bigger by one i need i + + align:start position:0% +please make it bigger by one i need i + + + align:start position:0% +please make it bigger by one i need i +need space to store this extra element + + align:start position:0% +need space to store this extra element + + + align:start position:0% +need space to store this extra element +and if you think about where things are + + align:start position:0% +and if you think about where things are + + + align:start position:0% +and if you think about where things are +in memory when you + + align:start position:0% +in memory when you + + + align:start position:0% +in memory when you +call to this memory allocator which is + + align:start position:0% +call to this memory allocator which is + + + align:start position:0% +call to this memory allocator which is +part of your operating system you say + + align:start position:0% +part of your operating system you say + + + align:start position:0% +part of your operating system you say +please give me + + align:start position:0% +please give me + + + align:start position:0% +please give me +some a chunk of memory it's going to + + align:start position:0% +some a chunk of memory it's going to + + + align:start position:0% +some a chunk of memory it's going to +place them in various places in memory + + align:start position:0% +place them in various places in memory + + + align:start position:0% +place them in various places in memory +and some of them might be next to each + + align:start position:0% +and some of them might be next to each + + + align:start position:0% +and some of them might be next to each +other + + align:start position:0% +other + + + align:start position:0% +other +so if i try to grow this array by one + + align:start position:0% +so if i try to grow this array by one + + + align:start position:0% +so if i try to grow this array by one +there might already be something + + align:start position:0% +there might already be something + + + align:start position:0% +there might already be something +there and that's not possible without + + align:start position:0% +there and that's not possible without + + + align:start position:0% +there and that's not possible without +first shifting so even though in the + + align:start position:0% +first shifting so even though in the + + + align:start position:0% +first shifting so even though in the +array i don't have to do any shifting in + + align:start position:0% +array i don't have to do any shifting in + + + align:start position:0% +array i don't have to do any shifting in +memory i might have to do shifting + + align:start position:0% +memory i might have to do shifting + + + align:start position:0% +memory i might have to do shifting +and that's outside the model so we're + + align:start position:0% +and that's outside the model so we're + + + align:start position:0% +and that's outside the model so we're +going to stick to this model of just + + align:start position:0% +going to stick to this model of just + + + align:start position:0% +going to stick to this model of just +you can allocate memory you can also + + align:start position:0% +you can allocate memory you can also + + + align:start position:0% +you can allocate memory you can also +de-allocate memory just to keep space + + align:start position:0% +de-allocate memory just to keep space + + + align:start position:0% +de-allocate memory just to keep space +usage small but the only way to get more + + align:start position:0% +usage small but the only way to get more + + + align:start position:0% +usage small but the only way to get more +space is to ask for a new array and that + + align:start position:0% +space is to ask for a new array and that + + + align:start position:0% +space is to ask for a new array and that +new array won't be contiguous to your + + align:start position:0% +new array won't be contiguous to your + + + align:start position:0% +new array won't be contiguous to your +old one + + align:start position:0% +old one + + + align:start position:0% +old one +so question + + align:start position:0% + + + + align:start position:0% + +uh what is a dynamic array will be the + + align:start position:0% +uh what is a dynamic array will be the + + + align:start position:0% +uh what is a dynamic array will be the +next topic so maybe we'll come back to + + align:start position:0% +next topic so maybe we'll come back to + + + align:start position:0% +next topic so maybe we'll come back to +that + + align:start position:0% +that + + + align:start position:0% +that +yeah okay so in a static array you're + + align:start position:0% +yeah okay so in a static array you're + + + align:start position:0% +yeah okay so in a static array you're +just not allowed to make it bigger + + align:start position:0% +just not allowed to make it bigger + + + align:start position:0% +just not allowed to make it bigger +and so you have to allocate a new array + + align:start position:0% +and so you have to allocate a new array + + + align:start position:0% +and so you have to allocate a new array +which we say takes linear time even if + + align:start position:0% +which we say takes linear time even if + + + align:start position:0% +which we say takes linear time even if +allocating the new array didn't take + + align:start position:0% +allocating the new array didn't take + + + align:start position:0% +allocating the new array didn't take +linear time + + align:start position:0% +linear time + + + align:start position:0% +linear time +you have to copy all the elements over + + align:start position:0% +you have to copy all the elements over + + + align:start position:0% +you have to copy all the elements over +from the old array to the new one then + + align:start position:0% +from the old array to the new one then + + + align:start position:0% +from the old array to the new one then +you can throw away the old one + + align:start position:0% +you can throw away the old one + + + align:start position:0% +you can throw away the old one +so just the copying from an array of + + align:start position:0% +so just the copying from an array of + + + align:start position:0% +so just the copying from an array of +size n to an array of size n plus one + + align:start position:0% +size n to an array of size n plus one + + + align:start position:0% +size n to an array of size n plus one +that will take linear time so static + + align:start position:0% +that will take linear time so static + + + align:start position:0% +that will take linear time so static +arrays are really bad for + + align:start position:0% +arrays are really bad for + + + align:start position:0% +arrays are really bad for +dynamic operations no surprise but you + + align:start position:0% +dynamic operations no surprise but you + + + align:start position:0% +dynamic operations no surprise but you +could do them + + align:start position:0% +could do them + + + align:start position:0% +could do them +okay that's static array now linked + + align:start position:0% +okay that's static array now linked + + + align:start position:0% +okay that's static array now linked +lists are going to be almost the + + align:start position:0% +lists are going to be almost the + + + align:start position:0% +lists are going to be almost the +opposite + + align:start position:0% +opposite + + + align:start position:0% +opposite +well almost so if we store + + align:start position:0% +well almost so if we store + + + align:start position:0% +well almost so if we store +the length okay we can compute the + + align:start position:0% +the length okay we can compute the + + + align:start position:0% +the length okay we can compute the +length of the array very quickly + + align:start position:0% +length of the array very quickly + + + align:start position:0% +length of the array very quickly +we can insert and delete at the front + + align:start position:0% +we can insert and delete at the front + + + align:start position:0% +we can insert and delete at the front +really efficiently if i want to add a + + align:start position:0% +really efficiently if i want to add a + + + align:start position:0% +really efficiently if i want to add a +new item + + align:start position:0% +new item + + + align:start position:0% +new item +at the begin as a new first item + + align:start position:0% +at the begin as a new first item + + + align:start position:0% +at the begin as a new first item +then what do i do i allocate a new node + + align:start position:0% +then what do i do i allocate a new node + + + align:start position:0% +then what do i do i allocate a new node +which i'll call x + + align:start position:0% +which i'll call x + + + align:start position:0% +which i'll call x +so this is insert + + align:start position:0% +so this is insert + + + align:start position:0% +so this is insert +first of x + + align:start position:0% +first of x + + + align:start position:0% +first of x +i'll allocate a new array size 2. i'm + + align:start position:0% +i'll allocate a new array size 2. i'm + + + align:start position:0% +i'll allocate a new array size 2. i'm +going to + + align:start position:0% +going to + + + align:start position:0% +going to +change let me do it in red + + align:start position:0% +change let me do it in red + + + align:start position:0% +change let me do it in red +i'm going to change this head pointer uh + + align:start position:0% +i'm going to change this head pointer uh + + + align:start position:0% +i'm going to change this head pointer uh +maybe i should do that + + align:start position:0% +maybe i should do that + + + align:start position:0% +maybe i should do that +later so i'm going to set the next + + align:start position:0% +later so i'm going to set the next + + + align:start position:0% +later so i'm going to set the next +pointer here to this one + + align:start position:0% +pointer here to this one + + + align:start position:0% +pointer here to this one +and then i'm going to change this head + + align:start position:0% +and then i'm going to change this head + + + align:start position:0% +and then i'm going to change this head +pointer to point to here + + align:start position:0% +pointer to point to here + + + align:start position:0% +pointer to point to here +and boom now i've got a linked list + + align:start position:0% +and boom now i've got a linked list + + + align:start position:0% +and boom now i've got a linked list +again we don't know anything about the + + align:start position:0% +again we don't know anything about the + + + align:start position:0% +again we don't know anything about the +order and memory of these + + align:start position:0% +order and memory of these + + + align:start position:0% +order and memory of these +these lists we just care about the order + + align:start position:0% +these lists we just care about the order + + + align:start position:0% +these lists we just care about the order +that's represented implicitly by + + align:start position:0% +that's represented implicitly by + + + align:start position:0% +that's represented implicitly by +following the next pointers repeatedly + + align:start position:0% +following the next pointers repeatedly + + + align:start position:0% +following the next pointers repeatedly +so now i've got a new list that has x in + + align:start position:0% +so now i've got a new list that has x in + + + align:start position:0% +so now i've got a new list that has x in +front and then x0 and then x1 + + align:start position:0% +front and then x0 and then x1 + + + align:start position:0% +front and then x0 and then x1 +and so on so insert and delete first at + + align:start position:0% +and so on so insert and delete first at + + + align:start position:0% +and so on so insert and delete first at +least are really efficient + + align:start position:0% +least are really efficient + + + align:start position:0% +least are really efficient +we won't get much more than that but a + + align:start position:0% +we won't get much more than that but a + + + align:start position:0% +we won't get much more than that but a +linked list + + align:start position:0% +linked list + + + align:start position:0% +linked list +insert and delete uh + + align:start position:0% + + + + align:start position:0% + +first our constant time + + align:start position:0% + + + + align:start position:0% + +so that's cool however everything else + + align:start position:0% +so that's cool however everything else + + + align:start position:0% +so that's cool however everything else +is going to be slow + + align:start position:0% +is going to be slow + + + align:start position:0% +is going to be slow +if i want to get the 10th item + + align:start position:0% +if i want to get the 10th item + + + align:start position:0% +if i want to get the 10th item +in a linked list i have to follow these + + align:start position:0% +in a linked list i have to follow these + + + align:start position:0% +in a linked list i have to follow these +pointers + + align:start position:0% +pointers + + + align:start position:0% +pointers +10 times i go 0 0 1 + + align:start position:0% +10 times i go 0 0 1 + + + align:start position:0% +10 times i go 0 0 1 +2 3 and it's on follow ten next pointers + + align:start position:0% +2 3 and it's on follow ten next pointers + + + align:start position:0% +2 3 and it's on follow ten next pointers +and i'll get the tenth item + + align:start position:0% +and i'll get the tenth item + + + align:start position:0% +and i'll get the tenth item +accessing the item is gonna take order i + + align:start position:0% +accessing the item is gonna take order i + + + align:start position:0% +accessing the item is gonna take order i +time + + align:start position:0% +time + + + align:start position:0% +time +so uh + + align:start position:0% + + + + align:start position:0% + +get and set at need + + align:start position:0% + + + + align:start position:0% + +i time which in the worst case is theta + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% + + + + align:start position:0% + +okay so we have sort of complementary + + align:start position:0% +okay so we have sort of complementary + + + align:start position:0% +okay so we have sort of complementary +data structures here on the one hand a + + align:start position:0% +data structures here on the one hand a + + + align:start position:0% +data structures here on the one hand a +static array + + align:start position:0% +static array + + + align:start position:0% +static array +can do constant time get at set at so + + align:start position:0% +can do constant time get at set at so + + + align:start position:0% +can do constant time get at set at so +it's very fast at the random access + + align:start position:0% +it's very fast at the random access + + + align:start position:0% +it's very fast at the random access +aspect because it's an array + + align:start position:0% +aspect because it's an array + + + align:start position:0% +aspect because it's an array +linked lists are very bad at random + + align:start position:0% +linked lists are very bad at random + + + align:start position:0% +linked lists are very bad at random +access but they're + + align:start position:0% +access but they're + + + align:start position:0% +access but they're +better at being dynamic we can insert + + align:start position:0% +better at being dynamic we can insert + + + align:start position:0% +better at being dynamic we can insert +and delete at the beginning at least + + align:start position:0% +and delete at the beginning at least + + + align:start position:0% +and delete at the beginning at least +in constant time now if we want to + + align:start position:0% +in constant time now if we want to + + + align:start position:0% +in constant time now if we want to +actually insert a delete + + align:start position:0% +actually insert a delete + + + align:start position:0% +actually insert a delete +at a particular position that's still + + align:start position:0% +at a particular position that's still + + + align:start position:0% +at a particular position that's still +hard because we have to walk to that + + align:start position:0% +hard because we have to walk to that + + + align:start position:0% +hard because we have to walk to that +position + + align:start position:0% +position + + + align:start position:0% +position +even inserting and deleting at the end + + align:start position:0% +even inserting and deleting at the end + + + align:start position:0% +even inserting and deleting at the end +of the list is hard + + align:start position:0% +of the list is hard + + + align:start position:0% +of the list is hard +although that's fixable + + align:start position:0% + + + + align:start position:0% + +and maybe i'll leave that for problem + + align:start position:0% +and maybe i'll leave that for problem + + + align:start position:0% +and maybe i'll leave that for problem +session or problem set + + align:start position:0% +session or problem set + + + align:start position:0% +session or problem set +but uh an easy so here's here's a small + + align:start position:0% +but uh an easy so here's here's a small + + + align:start position:0% +but uh an easy so here's here's a small +puzzle + + align:start position:0% +puzzle + + + align:start position:0% +puzzle +suppose you wanted to solve uh get + + align:start position:0% +suppose you wanted to solve uh get + + + align:start position:0% +suppose you wanted to solve uh get +last efficiently in a linked list + + align:start position:0% +last efficiently in a linked list + + + align:start position:0% +last efficiently in a linked list +how would you solve that in constant + + align:start position:0% +how would you solve that in constant + + + align:start position:0% +how would you solve that in constant +time + + align:start position:0% +time + + + align:start position:0% +time +yeah double a linked list is a good idea + + align:start position:0% +yeah double a linked list is a good idea + + + align:start position:0% +yeah double a linked list is a good idea +but actually not the right answer + + align:start position:0% +but actually not the right answer + + + align:start position:0% +but actually not the right answer +that's an answer to the next question i + + align:start position:0% +that's an answer to the next question i + + + align:start position:0% +that's an answer to the next question i +might ask yeah + + align:start position:0% +might ask yeah + + + align:start position:0% +might ask yeah +store pointer to the last element that's + + align:start position:0% +store pointer to the last element that's + + + align:start position:0% +store pointer to the last element that's +all we need here + + align:start position:0% +all we need here + + + align:start position:0% +all we need here +and often a doubly linked list has this + + align:start position:0% +and often a doubly linked list has this + + + align:start position:0% +and often a doubly linked list has this +i usually call this the tail + + align:start position:0% +i usually call this the tail + + + align:start position:0% +i usually call this the tail +head and tail and if you always just + + align:start position:0% +head and tail and if you always just + + + align:start position:0% +head and tail and if you always just +store a pointer + + align:start position:0% +store a pointer + + + align:start position:0% +store a pointer +to the last list this is what we call + + align:start position:0% +to the last list this is what we call + + + align:start position:0% +to the last list this is what we call +data structure augmentation where we add + + align:start position:0% +data structure augmentation where we add + + + align:start position:0% +data structure augmentation where we add +some extra information to the data + + align:start position:0% +some extra information to the data + + + align:start position:0% +some extra information to the data +structure and + + align:start position:0% +structure and + + + align:start position:0% +structure and +mean we have to keep it up to date all + + align:start position:0% +mean we have to keep it up to date all + + + align:start position:0% +mean we have to keep it up to date all +the time so if we do + + align:start position:0% +the time so if we do + + + align:start position:0% +the time so if we do +an insert last or something insert last + + align:start position:0% +an insert last or something insert last + + + align:start position:0% +an insert last or something insert last +also becomes easy because i can just + + align:start position:0% +also becomes easy because i can just + + + align:start position:0% +also becomes easy because i can just +add a new node here and update the + + align:start position:0% +add a new node here and update the + + + align:start position:0% +add a new node here and update the +pointer here delete last is trickier + + align:start position:0% +pointer here delete last is trickier + + + align:start position:0% +pointer here delete last is trickier +that's where you need a doubly linked + + align:start position:0% +that's where you need a doubly linked + + + align:start position:0% +that's where you need a doubly linked +list + + align:start position:0% +list + + + align:start position:0% +list +but whenever i add something to the end + + align:start position:0% +but whenever i add something to the end + + + align:start position:0% +but whenever i add something to the end +of this list i have to update the tail + + align:start position:0% +of this list i have to update the tail + + + align:start position:0% +of this list i have to update the tail +pointer also + + align:start position:0% +pointer also + + + align:start position:0% +pointer also +as long as i maintain this now suddenly + + align:start position:0% +as long as i maintain this now suddenly + + + align:start position:0% +as long as i maintain this now suddenly +get last as fast in constant time + + align:start position:0% +get last as fast in constant time + + + align:start position:0% +get last as fast in constant time +so link lists are great if you're + + align:start position:0% +so link lists are great if you're + + + align:start position:0% +so link lists are great if you're +working on the ends even dynamically + + align:start position:0% +working on the ends even dynamically + + + align:start position:0% +working on the ends even dynamically +arrays are great if you're doing random + + align:start position:0% +arrays are great if you're doing random + + + align:start position:0% +arrays are great if you're doing random +access and nothing dynamic nothing + + align:start position:0% +access and nothing dynamic nothing + + + align:start position:0% +access and nothing dynamic nothing +adding + + align:start position:0% +adding + + + align:start position:0% +adding +or deleting at the ends or in the middle + + align:start position:0% +or deleting at the ends or in the middle + + + align:start position:0% +or deleting at the ends or in the middle +okay so our final goal for today + + align:start position:0% +okay so our final goal for today + + + align:start position:0% +okay so our final goal for today +is to get sort of the best of both + + align:start position:0% +is to get sort of the best of both + + + align:start position:0% +is to get sort of the best of both +worlds with dynamic arrays we're going + + align:start position:0% +worlds with dynamic arrays we're going + + + align:start position:0% +worlds with dynamic arrays we're going +to try to get + + align:start position:0% +to try to get + + + align:start position:0% +to try to get +all the good running times of linked + + align:start position:0% +all the good running times of linked + + + align:start position:0% +all the good running times of linked +lists and all the good running times of + + align:start position:0% +lists and all the good running times of + + + align:start position:0% +lists and all the good running times of +static arrays + + align:start position:0% +static arrays + + + align:start position:0% +static arrays +we won't get quite all of them but most + + align:start position:0% +we won't get quite all of them but most + + + align:start position:0% +we won't get quite all of them but most +of them + + align:start position:0% +of them + + + align:start position:0% +of them +[Applause] + + align:start position:0% + + + + align:start position:0% + +and in some sense + + align:start position:0% +and in some sense + + + align:start position:0% +and in some sense +another way to describe what these + + align:start position:0% +another way to describe what these + + + align:start position:0% +another way to describe what these +introductory lectures are about is + + align:start position:0% +introductory lectures are about is + + + align:start position:0% +introductory lectures are about is +telling you about how python + + align:start position:0% +telling you about how python + + + align:start position:0% +telling you about how python +is implemented so what we're going to + + align:start position:0% +is implemented so what we're going to + + + align:start position:0% +is implemented so what we're going to +talk about next dynamic arrays + + align:start position:0% +talk about next dynamic arrays + + + align:start position:0% +talk about next dynamic arrays +i've alluded to many times but these are + + align:start position:0% + + + + align:start position:0% + +what python calls lists + + align:start position:0% + + + + align:start position:0% + +so you don't have to implement a dynamic + + align:start position:0% +so you don't have to implement a dynamic + + + align:start position:0% +so you don't have to implement a dynamic +array by hand because it's already built + + align:start position:0% +array by hand because it's already built + + + align:start position:0% +array by hand because it's already built +into many fancy new languages + + align:start position:0% +into many fancy new languages + + + align:start position:0% +into many fancy new languages +for free because they're so darn useful + + align:start position:0% +for free because they're so darn useful + + + align:start position:0% +for free because they're so darn useful +this lecture is about + + align:start position:0% +this lecture is about + + + align:start position:0% +this lecture is about +how these are actually implemented and + + align:start position:0% +how these are actually implemented and + + + align:start position:0% +how these are actually implemented and +why they're efficient + + align:start position:0% +why they're efficient + + + align:start position:0% +why they're efficient +and in recitation notes you'll see how + + align:start position:0% +and in recitation notes you'll see how + + + align:start position:0% +and in recitation notes you'll see how +to actually implement them if all you + + align:start position:0% +to actually implement them if all you + + + align:start position:0% +to actually implement them if all you +had were static arrays + + align:start position:0% +had were static arrays + + + align:start position:0% +had were static arrays +but luckily we have dynamic arrays so we + + align:start position:0% +but luckily we have dynamic arrays so we + + + align:start position:0% +but luckily we have dynamic arrays so we +don't have to + + align:start position:0% +don't have to + + + align:start position:0% +don't have to +actually implement them but in the in + + align:start position:0% +actually implement them but in the in + + + align:start position:0% +actually implement them but in the in +inside the python interpreter + + align:start position:0% +inside the python interpreter + + + align:start position:0% +inside the python interpreter +this is exactly what's happening okay so + + align:start position:0% +this is exactly what's happening okay so + + + align:start position:0% +this is exactly what's happening okay so +the idea is to + + align:start position:0% +the idea is to + + + align:start position:0% +the idea is to +relax the + + align:start position:0% +relax the + + + align:start position:0% +relax the +constraint or the invariant whatever + + align:start position:0% +constraint or the invariant whatever + + + align:start position:0% +constraint or the invariant whatever +that the size of the array we use + + align:start position:0% +that the size of the array we use + + + align:start position:0% +that the size of the array we use +equals n which is the number of + + align:start position:0% +equals n which is the number of + + + align:start position:0% +equals n which is the number of +items in the sequence + + align:start position:0% + + + + align:start position:0% + +okay remember in the sequence problem + + align:start position:0% +okay remember in the sequence problem + + + align:start position:0% +okay remember in the sequence problem +we're supposed to represent n items + + align:start position:0% +we're supposed to represent n items + + + align:start position:0% +we're supposed to represent n items +with a static array we allocated an + + align:start position:0% +with a static array we allocated an + + + align:start position:0% +with a static array we allocated an +array of size exactly n + + align:start position:0% +array of size exactly n + + + align:start position:0% +array of size exactly n +so let's relax that let's not make it + + align:start position:0% +so let's relax that let's not make it + + + align:start position:0% +so let's relax that let's not make it +exactly n let's make it + + align:start position:0% +exactly n let's make it + + + align:start position:0% +exactly n let's make it +roughly n how roughly you can think + + align:start position:0% +roughly n how roughly you can think + + + align:start position:0% +roughly n how roughly you can think +about for a while + + align:start position:0% +about for a while + + + align:start position:0% +about for a while +uh but the from an algorithm's + + align:start position:0% +uh but the from an algorithm's + + + align:start position:0% +uh but the from an algorithm's +perspective usually that when we say + + align:start position:0% +perspective usually that when we say + + + align:start position:0% +perspective usually that when we say +roughly + + align:start position:0% +roughly + + + align:start position:0% +roughly +we mean throw away constant factors and + + align:start position:0% +we mean throw away constant factors and + + + align:start position:0% +we mean throw away constant factors and +that turns out to be the right answer + + align:start position:0% +that turns out to be the right answer + + + align:start position:0% +that turns out to be the right answer +here it's not always the right answer + + align:start position:0% +here it's not always the right answer + + + align:start position:0% +here it's not always the right answer +but we're gonna uh enforce + + align:start position:0% +but we're gonna uh enforce + + + align:start position:0% +but we're gonna uh enforce +uh that the size of the array is + + align:start position:0% +uh that the size of the array is + + + align:start position:0% +uh that the size of the array is +theta m probably also greater than or + + align:start position:0% +theta m probably also greater than or + + + align:start position:0% +theta m probably also greater than or +equal to n + + align:start position:0% +equal to n + + + align:start position:0% +equal to n +0.5 n would not be very helpful so it's + + align:start position:0% +0.5 n would not be very helpful so it's + + + align:start position:0% +0.5 n would not be very helpful so it's +going to be at least + + align:start position:0% +going to be at least + + + align:start position:0% +going to be at least +n and it's going to be at most + + align:start position:0% +n and it's going to be at most + + + align:start position:0% +n and it's going to be at most +some constant times n 2n + + align:start position:0% +some constant times n 2n + + + align:start position:0% +some constant times n 2n +10n 1.1 times n any of these constants + + align:start position:0% +10n 1.1 times n any of these constants + + + align:start position:0% +10n 1.1 times n any of these constants +will work i'm going to use 2n + + align:start position:0% +will work i'm going to use 2n + + + align:start position:0% +will work i'm going to use 2n +here but there are lots of options + + align:start position:0% +here but there are lots of options + + + align:start position:0% +here but there are lots of options +uh and now things almost work + + align:start position:0% +uh and now things almost work + + + align:start position:0% +uh and now things almost work +for free there's going to be one + + align:start position:0% +for free there's going to be one + + + align:start position:0% +for free there's going to be one +subtlety here + + align:start position:0% +subtlety here + + + align:start position:0% +subtlety here +and i'm going to focus on we're still + + align:start position:0% +and i'm going to focus on we're still + + + align:start position:0% +and i'm going to focus on we're still +going to maintain + + align:start position:0% + + + + align:start position:0% + +that the item of the array is + + align:start position:0% +that the item of the array is + + + align:start position:0% +that the item of the array is +represents x i okay so this data + + align:start position:0% +represents x i okay so this data + + + align:start position:0% +represents x i okay so this data +structure + + align:start position:0% +structure + + + align:start position:0% +structure +let me draw a picture so we've got an + + align:start position:0% +let me draw a picture so we've got an + + + align:start position:0% +let me draw a picture so we've got an +array of some size + + align:start position:0% +array of some size + + + align:start position:0% +array of some size +the first few items + + align:start position:0% +the first few items + + + align:start position:0% +the first few items +are used to store + + align:start position:0% + + + + align:start position:0% + +the sequence but then there's going to + + align:start position:0% +the sequence but then there's going to + + + align:start position:0% +the sequence but then there's going to +be some blank ones at the end + + align:start position:0% +be some blank ones at the end + + + align:start position:0% +be some blank ones at the end +okay maybe we'll keep track of this so + + align:start position:0% +okay maybe we'll keep track of this so + + + align:start position:0% +okay maybe we'll keep track of this so +the data structure itself + + align:start position:0% +the data structure itself + + + align:start position:0% +the data structure itself +is going to have an array and it's going + + align:start position:0% +is going to have an array and it's going + + + align:start position:0% +is going to have an array and it's going +to have a length + + align:start position:0% +to have a length + + + align:start position:0% +to have a length +something like this so we're also going + + align:start position:0% +something like this so we're also going + + + align:start position:0% +something like this so we're also going +to keep track of the length so + + align:start position:0% +to keep track of the length so + + + align:start position:0% +to keep track of the length so +we know that the first length items are + + align:start position:0% +we know that the first length items are + + + align:start position:0% +we know that the first length items are +where their data is and the remainder + + align:start position:0% +where their data is and the remainder + + + align:start position:0% +where their data is and the remainder +are just are meaningless + + align:start position:0% +are just are meaningless + + + align:start position:0% +are just are meaningless +okay so now if i want to go and do an + + align:start position:0% +okay so now if i want to go and do an + + + align:start position:0% +okay so now if i want to go and do an +insert last + + align:start position:0% +insert last + + + align:start position:0% +insert last +what do i do i just go to + + align:start position:0% +what do i do i just go to + + + align:start position:0% +what do i do i just go to +a of length and set it to x + + align:start position:0% + + + + align:start position:0% + +and then i increment length + + align:start position:0% + + + + align:start position:0% + +boom easy constant time yeah + + align:start position:0% + + + + align:start position:0% + +how do you know you have enough room + + align:start position:0% +how do you know you have enough room + + + align:start position:0% +how do you know you have enough room +indeed i don't this was an incorrect + + align:start position:0% +indeed i don't this was an incorrect + + + align:start position:0% +indeed i don't this was an incorrect +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +but it's usually correct as long as i + + align:start position:0% +but it's usually correct as long as i + + + align:start position:0% +but it's usually correct as long as i +have extra space this is all i need to + + align:start position:0% +have extra space this is all i need to + + + align:start position:0% +have extra space this is all i need to +do + + align:start position:0% +do + + + align:start position:0% +do +for insert last but uh + + align:start position:0% +for insert last but uh + + + align:start position:0% +for insert last but uh +i'm also going to store the size + + align:start position:0% +i'm also going to store the size + + + align:start position:0% +i'm also going to store the size +of the array this is the actual this + + align:start position:0% +of the array this is the actual this + + + align:start position:0% +of the array this is the actual this +whole thing is size + + align:start position:0% +whole thing is size + + + align:start position:0% +whole thing is size +and this part is length + + align:start position:0% +and this part is length + + + align:start position:0% +and this part is length +so length is always going to be less + + align:start position:0% +so length is always going to be less + + + align:start position:0% +so length is always going to be less +than or equal to size + + align:start position:0% +than or equal to size + + + align:start position:0% +than or equal to size +and so there's a problem if length + + align:start position:0% +and so there's a problem if length + + + align:start position:0% +and so there's a problem if length +equals size + + align:start position:0% +equals size + + + align:start position:0% +equals size +then i don't have any space okay + + align:start position:0% + + + + align:start position:0% + +just add to the end + + align:start position:0% +just add to the end + + + align:start position:0% +just add to the end +unless + + align:start position:0% + + + + align:start position:0% + +n equals size i'm using n + + align:start position:0% +n equals size i'm using n + + + align:start position:0% +n equals size i'm using n +and length for the same thing uh so the + + align:start position:0% +and length for the same thing uh so the + + + align:start position:0% +and length for the same thing uh so the +length here + + align:start position:0% +length here + + + align:start position:0% +length here +is same as n that's our actual number of + + align:start position:0% +is same as n that's our actual number of + + + align:start position:0% +is same as n that's our actual number of +things we're trying to + + align:start position:0% +things we're trying to + + + align:start position:0% +things we're trying to +represent and size this is great this is + + align:start position:0% +represent and size this is great this is + + + align:start position:0% +represent and size this is great this is +the interface + + align:start position:0% +the interface + + + align:start position:0% +the interface +size this is what we're trying to + + align:start position:0% +size this is what we're trying to + + + align:start position:0% +size this is what we're trying to +represent and this + + align:start position:0% +represent and this + + + align:start position:0% +represent and this +is the representation size this is the + + align:start position:0% +is the representation size this is the + + + align:start position:0% +is the representation size this is the +size of my array + + align:start position:0% +size of my array + + + align:start position:0% +size of my array +these are the number of items i'm trying + + align:start position:0% +these are the number of items i'm trying + + + align:start position:0% +these are the number of items i'm trying +to store in that array okay this is the + + align:start position:0% +to store in that array okay this is the + + + align:start position:0% +to store in that array okay this is the +interface versus data structure + + align:start position:0% +interface versus data structure + + + align:start position:0% +interface versus data structure +here's the interface here's the data + + align:start position:0% +here's the interface here's the data + + + align:start position:0% +here's the interface here's the data +structure + + align:start position:0% +structure + + + align:start position:0% +structure +okay cool um + + align:start position:0% + + + + align:start position:0% + +what do i do in the case when n equals + + align:start position:0% +what do i do in the case when n equals + + + align:start position:0% +what do i do in the case when n equals +size + + align:start position:0% + + + + align:start position:0% + +i'm gonna have to make my array bigger + + align:start position:0% +i'm gonna have to make my array bigger + + + align:start position:0% +i'm gonna have to make my array bigger +okay this should + + align:start position:0% +okay this should + + + align:start position:0% +okay this should +sound just like static arrays + + align:start position:0% +sound just like static arrays + + + align:start position:0% +sound just like static arrays +with static arrays we made our array + + align:start position:0% +with static arrays we made our array + + + align:start position:0% +with static arrays we made our array +bigger every time we insert it + + align:start position:0% +bigger every time we insert it + + + align:start position:0% +bigger every time we insert it +and that was this linear cost of + + align:start position:0% +and that was this linear cost of + + + align:start position:0% +and that was this linear cost of +allocation + + align:start position:0% +allocation + + + align:start position:0% +allocation +we're going to do that sometimes with + + align:start position:0% +we're going to do that sometimes with + + + align:start position:0% +we're going to do that sometimes with +static rays we had to do it every single + + align:start position:0% +static rays we had to do it every single + + + align:start position:0% +static rays we had to do it every single +time because size + + align:start position:0% +time because size + + + align:start position:0% +time because size +equaled n now we have some flexibility + + align:start position:0% +equaled n now we have some flexibility + + + align:start position:0% +equaled n now we have some flexibility +we're only going to do it sometimes + + align:start position:0% +we're only going to do it sometimes + + + align:start position:0% +we're only going to do it sometimes +it's like uh cookies are a sometimes + + align:start position:0% +it's like uh cookies are a sometimes + + + align:start position:0% +it's like uh cookies are a sometimes +food apparently + + align:start position:0% +food apparently + + + align:start position:0% +food apparently +according to modern cookie monster um i + + align:start position:0% +according to modern cookie monster um i + + + align:start position:0% +according to modern cookie monster um i +don't understand + + align:start position:0% +don't understand + + + align:start position:0% +don't understand +but uh if n equals size + + align:start position:0% +but uh if n equals size + + + align:start position:0% +but uh if n equals size +we're going to uh + + align:start position:0% + + + + align:start position:0% + +uh allocate + + align:start position:0% + + + + align:start position:0% + +a new array + + align:start position:0% +a new array + + + align:start position:0% +a new array +of size + + align:start position:0% + + + + align:start position:0% + +any suggestions bigger i like it + + align:start position:0% +any suggestions bigger i like it + + + align:start position:0% +any suggestions bigger i like it +greater than size how much bigger + + align:start position:0% +greater than size how much bigger + + + align:start position:0% +greater than size how much bigger +twice five + + align:start position:0% +twice five + + + align:start position:0% +twice five +five things size plus five come on jason + + align:start position:0% +five things size plus five come on jason + + + align:start position:0% +five things size plus five come on jason +trolling me all right so there are a + + align:start position:0% +trolling me all right so there are a + + + align:start position:0% +trolling me all right so there are a +couple of natural + + align:start position:0% +couple of natural + + + align:start position:0% +couple of natural +choices here one is a constant factor + + align:start position:0% +choices here one is a constant factor + + + align:start position:0% +choices here one is a constant factor +larger you could use 1.1 or 1.01 + + align:start position:0% +larger you could use 1.1 or 1.01 + + + align:start position:0% +larger you could use 1.1 or 1.01 +or 2 or 5 or 10 they'll all work + + align:start position:0% +or 2 or 5 or 10 they'll all work + + + align:start position:0% +or 2 or 5 or 10 they'll all work +or you could use jason's trolling answer + + align:start position:0% +or you could use jason's trolling answer + + + align:start position:0% +or you could use jason's trolling answer +of size plus a constant like 5. + + align:start position:0% +of size plus a constant like 5. + + + align:start position:0% +of size plus a constant like 5. +why is this bad + + align:start position:0% + + + + align:start position:0% + +you'll have to do it again you'll have + + align:start position:0% +you'll have to do it again you'll have + + + align:start position:0% +you'll have to do it again you'll have +to resize frequently + + align:start position:0% +to resize frequently + + + align:start position:0% +to resize frequently +when five steps later so + + align:start position:0% +when five steps later so + + + align:start position:0% +when five steps later so +uh in the original static array we were + + align:start position:0% +uh in the original static array we were + + + align:start position:0% +uh in the original static array we were +reallocating every single time + + align:start position:0% +reallocating every single time + + + align:start position:0% +reallocating every single time +that's like n plus one if we do n plus + + align:start position:0% +that's like n plus one if we do n plus + + + align:start position:0% +that's like n plus one if we do n plus +five that really doesn't change things + + align:start position:0% +five that really doesn't change things + + + align:start position:0% +five that really doesn't change things +if we ignore constant + + align:start position:0% +if we ignore constant + + + align:start position:0% +if we ignore constant +factors now we'll have to spend linear + + align:start position:0% +factors now we'll have to spend linear + + + align:start position:0% +factors now we'll have to spend linear +time every five steps instead of linear + + align:start position:0% +time every five steps instead of linear + + + align:start position:0% +time every five steps instead of linear +time every one step + + align:start position:0% +time every one step + + + align:start position:0% +time every one step +that's still linear time per operation + + align:start position:0% +that's still linear time per operation + + + align:start position:0% +that's still linear time per operation +just we're changing the constant factor + + align:start position:0% +just we're changing the constant factor + + + align:start position:0% +just we're changing the constant factor +okay whereas two times size well now we + + align:start position:0% +okay whereas two times size well now we + + + align:start position:0% +okay whereas two times size well now we +have to think a little bit harder + + align:start position:0% +have to think a little bit harder + + + align:start position:0% +have to think a little bit harder +um let's just think about the case where + + align:start position:0% +um let's just think about the case where + + + align:start position:0% +um let's just think about the case where +we're + + align:start position:0% +we're + + + align:start position:0% +we're +inserting at the end of an array so + + align:start position:0% +inserting at the end of an array so + + + align:start position:0% +inserting at the end of an array so +let's say we do + + align:start position:0% +let's say we do + + + align:start position:0% +let's say we do +n uh insert + + align:start position:0% +n uh insert + + + align:start position:0% +n uh insert +last + + align:start position:0% + + + + align:start position:0% + +from an empty array + + align:start position:0% + + + + align:start position:0% + +when do we resize well at the beginning + + align:start position:0% +when do we resize well at the beginning + + + align:start position:0% +when do we resize well at the beginning +i guess i didn't say what we do for an + + align:start position:0% +i guess i didn't say what we do for an + + + align:start position:0% +i guess i didn't say what we do for an +empty array let's say size equals one + + align:start position:0% +empty array let's say size equals one + + + align:start position:0% +empty array let's say size equals one +so we can insert one item for free as + + align:start position:0% +so we can insert one item for free as + + + align:start position:0% +so we can insert one item for free as +soon as we insert the second item + + align:start position:0% +soon as we insert the second item + + + align:start position:0% +soon as we insert the second item +then we have to resize that seems bad + + align:start position:0% +then we have to resize that seems bad + + + align:start position:0% +then we have to resize that seems bad +immediately we have to resize + + align:start position:0% +immediately we have to resize + + + align:start position:0% +immediately we have to resize +then we insert the third item okay now + + align:start position:0% +then we insert the third item okay now + + + align:start position:0% +then we insert the third item okay now +let's draw a picture so we start with + + align:start position:0% +let's draw a picture so we start with + + + align:start position:0% +let's draw a picture so we start with +one item + + align:start position:0% +one item + + + align:start position:0% +one item +we fill it up uh then we + + align:start position:0% +we fill it up uh then we + + + align:start position:0% +we fill it up uh then we +grow to size two because that's twice + + align:start position:0% +grow to size two because that's twice + + + align:start position:0% +grow to size two because that's twice +one then we fill it up + + align:start position:0% +one then we fill it up + + + align:start position:0% +one then we fill it up +immediately we have to resize again but + + align:start position:0% +immediately we have to resize again but + + + align:start position:0% +immediately we have to resize again but +now we get start to get some benefit + + align:start position:0% +now we get start to get some benefit + + + align:start position:0% +now we get start to get some benefit +now we have size four and so we can + + align:start position:0% +now we have size four and so we can + + + align:start position:0% +now we have size four and so we can +insert two items before + + align:start position:0% +insert two items before + + + align:start position:0% +insert two items before +we have to resize and now we're size + + align:start position:0% +we have to resize and now we're size + + + align:start position:0% +we have to resize and now we're size +eight + + align:start position:0% +eight + + + align:start position:0% +eight +and we get to insert four items before + + align:start position:0% +and we get to insert four items before + + + align:start position:0% +and we get to insert four items before +we refill + + align:start position:0% +we refill + + + align:start position:0% +we refill +so uh this is going to resize and again + + align:start position:0% +so uh this is going to resize and again + + + align:start position:0% +so uh this is going to resize and again +resizes are + + align:start position:0% +resizes are + + + align:start position:0% +resizes are +expensive both because we have to pay to + + align:start position:0% +expensive both because we have to pay to + + + align:start position:0% +expensive both because we have to pay to +allocate the new array + + align:start position:0% +allocate the new array + + + align:start position:0% +allocate the new array +i drew it as just extending it but in + + align:start position:0% +i drew it as just extending it but in + + + align:start position:0% +i drew it as just extending it but in +fact we're creating a whole new + + align:start position:0% +fact we're creating a whole new + + + align:start position:0% +fact we're creating a whole new +array and then we have to copy all of + + align:start position:0% +array and then we have to copy all of + + + align:start position:0% +array and then we have to copy all of +the items over + + align:start position:0% +the items over + + + align:start position:0% +the items over +so there's the allocation cost and then + + align:start position:0% +so there's the allocation cost and then + + + align:start position:0% +so there's the allocation cost and then +the copying costs so it's linear either + + align:start position:0% +the copying costs so it's linear either + + + align:start position:0% +the copying costs so it's linear either +way + + align:start position:0% +way + + + align:start position:0% +way +but we're going to resize at n + + align:start position:0% +but we're going to resize at n + + + align:start position:0% +but we're going to resize at n +equals 1 2 4 8 + + align:start position:0% +equals 1 2 4 8 + + + align:start position:0% +equals 1 2 4 8 +16. you know this sequence all the + + align:start position:0% +16. you know this sequence all the + + + align:start position:0% +16. you know this sequence all the +powers of 2 + + align:start position:0% +powers of 2 + + + align:start position:0% +powers of 2 +because we're doubling that is exactly + + align:start position:0% +because we're doubling that is exactly + + + align:start position:0% +because we're doubling that is exactly +powers of 2. + + align:start position:0% +powers of 2. + + + align:start position:0% +powers of 2. +so we pay a linear cost + + align:start position:0% +so we pay a linear cost + + + align:start position:0% +so we pay a linear cost +so this resize cost the allocation + + align:start position:0% +so this resize cost the allocation + + + align:start position:0% +so this resize cost the allocation +and the copying is going to be it's + + align:start position:0% +and the copying is going to be it's + + + align:start position:0% +and the copying is going to be it's +linear each time + + align:start position:0% +linear each time + + + align:start position:0% +linear each time +so it's 1 plus 2 plus 4 plus + + align:start position:0% +so it's 1 plus 2 plus 4 plus + + + align:start position:0% +so it's 1 plus 2 plus 4 plus +8 plus 16. okay really i should write + + align:start position:0% +8 plus 16. okay really i should write + + + align:start position:0% +8 plus 16. okay really i should write +this as + + align:start position:0% +this as + + + align:start position:0% +this as +a sum from i equals 1 + + align:start position:0% +a sum from i equals 1 + + + align:start position:0% +a sum from i equals 1 +to roughly log n log base 2 of n is lg + + align:start position:0% +to roughly log n log base 2 of n is lg + + + align:start position:0% +to roughly log n log base 2 of n is lg +of 2 to the i + + align:start position:0% + + + + align:start position:0% + +okay if you want a terminus here it's + + align:start position:0% +okay if you want a terminus here it's + + + align:start position:0% +okay if you want a terminus here it's +roughly n + + align:start position:0% +roughly n + + + align:start position:0% +roughly n +it's actually the next the previous + + align:start position:0% +it's actually the next the previous + + + align:start position:0% +it's actually the next the previous +power of 2 of n or something + + align:start position:0% +power of 2 of n or something + + + align:start position:0% +power of 2 of n or something +okay but uh that won't matter that'll + + align:start position:0% +okay but uh that won't matter that'll + + + align:start position:0% +okay but uh that won't matter that'll +just affect things by a constant factor + + align:start position:0% +just affect things by a constant factor + + + align:start position:0% +just affect things by a constant factor +what is the sum of two to the i + + align:start position:0% +what is the sum of two to the i + + + align:start position:0% +what is the sum of two to the i +this is a geometric series anyone know + + align:start position:0% +this is a geometric series anyone know + + + align:start position:0% +this is a geometric series anyone know +the answer + + align:start position:0% + + + + align:start position:0% + +two to the uh top limit + + align:start position:0% +two to the uh top limit + + + align:start position:0% +two to the uh top limit +uh plus one minus one yeah so this is + + align:start position:0% +uh plus one minus one yeah so this is + + + align:start position:0% +uh plus one minus one yeah so this is +the identity + + align:start position:0% +the identity + + + align:start position:0% +the identity +sum of two to the i uh from i equals one + + align:start position:0% +sum of two to the i uh from i equals one + + + align:start position:0% +sum of two to the i uh from i equals one +to + + align:start position:0% +to + + + align:start position:0% +to +k is two to the k plus one + + align:start position:0% +k is two to the k plus one + + + align:start position:0% +k is two to the k plus one +plus one minus one so the plus one's + + align:start position:0% +plus one minus one so the plus one's + + + align:start position:0% +plus one minus one so the plus one's +upstairs + + align:start position:0% +upstairs + + + align:start position:0% +upstairs +minus one's downstairs an easy way to + + align:start position:0% +minus one's downstairs an easy way to + + + align:start position:0% +minus one's downstairs an easy way to +remember this is if you think in binary + + align:start position:0% +remember this is if you think in binary + + + align:start position:0% +remember this is if you think in binary +as we all should we're computer + + align:start position:0% +as we all should we're computer + + + align:start position:0% +as we all should we're computer +scientists uh two to the i + + align:start position:0% +scientists uh two to the i + + + align:start position:0% +scientists uh two to the i +is means you set the ith bit to one so + + align:start position:0% +is means you set the ith bit to one so + + + align:start position:0% +is means you set the ith bit to one so +here's + + align:start position:0% +here's + + + align:start position:0% +here's +uh here's a bit string this is the ith + + align:start position:0% +uh here's a bit string this is the ith + + + align:start position:0% +uh here's a bit string this is the ith +bit + + align:start position:0% +bit + + + align:start position:0% +bit +this is 2 to the i the zeros down here + + align:start position:0% +this is 2 to the i the zeros down here + + + align:start position:0% +this is 2 to the i the zeros down here +if i sum them all up + + align:start position:0% +if i sum them all up + + + align:start position:0% +if i sum them all up +what that means is i'm putting ones here + + align:start position:0% +what that means is i'm putting ones here + + + align:start position:0% +what that means is i'm putting ones here +okay uh and if you think about what this + + align:start position:0% +okay uh and if you think about what this + + + align:start position:0% +okay uh and if you think about what this +means this is up to k + + align:start position:0% +means this is up to k + + + align:start position:0% +means this is up to k +from zero sorry i should do zero to be + + align:start position:0% +from zero sorry i should do zero to be + + + align:start position:0% +from zero sorry i should do zero to be +proper + + align:start position:0% +proper + + + align:start position:0% +proper +if i write so that's the left hand side + + align:start position:0% +if i write so that's the left hand side + + + align:start position:0% +if i write so that's the left hand side +the right hand side is 2 to the k plus 1 + + align:start position:0% +the right hand side is 2 to the k plus 1 + + + align:start position:0% +the right hand side is 2 to the k plus 1 +which is a 1 here + + align:start position:0% +which is a 1 here + + + align:start position:0% +which is a 1 here +and the rest 0s so if you know your + + align:start position:0% +and the rest 0s so if you know your + + + align:start position:0% +and the rest 0s so if you know your +binary arithmetic you + + align:start position:0% +binary arithmetic you + + + align:start position:0% +binary arithmetic you +subtract if you add one to this you get + + align:start position:0% +subtract if you add one to this you get + + + align:start position:0% +subtract if you add one to this you get +this so if you subtract one from this + + align:start position:0% +this so if you subtract one from this + + + align:start position:0% +this so if you subtract one from this +you get this + + align:start position:0% +you get this + + + align:start position:0% +you get this +okay this is why this identity holds um + + align:start position:0% +okay this is why this identity holds um + + + align:start position:0% +okay this is why this identity holds um +or the higher level thing is to say oh + + align:start position:0% +or the higher level thing is to say oh + + + align:start position:0% +or the higher level thing is to say oh +this is a geometric series + + align:start position:0% +this is a geometric series + + + align:start position:0% +this is a geometric series +so i know i you should know this i'm + + align:start position:0% +so i know i you should know this i'm + + + align:start position:0% +so i know i you should know this i'm +telling you now + + align:start position:0% +telling you now + + + align:start position:0% +telling you now +geometric series are dominated by the + + align:start position:0% +geometric series are dominated by the + + + align:start position:0% +geometric series are dominated by the +last term + + align:start position:0% +last term + + + align:start position:0% +last term +the biggest term if you have any series + + align:start position:0% +the biggest term if you have any series + + + align:start position:0% +the biggest term if you have any series +you can identify as geometric which + + align:start position:0% +you can identify as geometric which + + + align:start position:0% +you can identify as geometric which +means it's growing at least + + align:start position:0% +means it's growing at least + + + align:start position:0% +means it's growing at least +exponentially + + align:start position:0% +exponentially + + + align:start position:0% +exponentially +then in terms of theta notation you can + + align:start position:0% +then in terms of theta notation you can + + + align:start position:0% +then in terms of theta notation you can +just look at the last + + align:start position:0% +just look at the last + + + align:start position:0% +just look at the last +term and put a theta around it and + + align:start position:0% +term and put a theta around it and + + + align:start position:0% +term and put a theta around it and +you're done so this is + + align:start position:0% +you're done so this is + + + align:start position:0% +you're done so this is +theta the last term like 2 to the log n + + align:start position:0% +theta the last term like 2 to the log n + + + align:start position:0% +theta the last term like 2 to the log n +which is theta n + + align:start position:0% + + + + align:start position:0% + +cool linear time linear time for + + align:start position:0% +cool linear time linear time for + + + align:start position:0% +cool linear time linear time for +all of my operations i'm doing n + + align:start position:0% +all of my operations i'm doing n + + + align:start position:0% +all of my operations i'm doing n +operations here + + align:start position:0% +operations here + + + align:start position:0% +operations here +and i spend linear total time to do all + + align:start position:0% +and i spend linear total time to do all + + + align:start position:0% +and i spend linear total time to do all +the resizing + + align:start position:0% +the resizing + + + align:start position:0% +the resizing +that's good that's like constant each + + align:start position:0% +that's good that's like constant each + + + align:start position:0% +that's good that's like constant each +kind of the kind of is an important + + align:start position:0% +kind of the kind of is an important + + + align:start position:0% +kind of the kind of is an important +notion + + align:start position:0% +notion + + + align:start position:0% +notion +which we call + + align:start position:0% + + + + align:start position:0% + +amortization + + align:start position:0% + + + + align:start position:0% + +so i want to say an operation + + align:start position:0% + + + + align:start position:0% + +takes + + align:start position:0% + + + + align:start position:0% + +t of n amortized time + + align:start position:0% + + + + align:start position:0% + +if um + + align:start position:0% +if um + + + align:start position:0% +if um +let's say any k of those operations + + align:start position:0% + + + + align:start position:0% + +take at most k + + align:start position:0% +take at most k + + + align:start position:0% +take at most k +times t of n time this is a little bit + + align:start position:0% +times t of n time this is a little bit + + + align:start position:0% +times t of n time this is a little bit +sloppy but + + align:start position:0% +sloppy but + + + align:start position:0% +sloppy but +be good enough so the idea is here if + + align:start position:0% +be good enough so the idea is here if + + + align:start position:0% +be good enough so the idea is here if +this works for n or k + + align:start position:0% +this works for n or k + + + align:start position:0% +this works for n or k +to do n operations from an empty array + + align:start position:0% +to do n operations from an empty array + + + align:start position:0% +to do n operations from an empty array +here + + align:start position:0% +here + + + align:start position:0% +here +takes linear time which means uh + + align:start position:0% +takes linear time which means uh + + + align:start position:0% +takes linear time which means uh +i would call this constant amortized + + align:start position:0% +i would call this constant amortized + + + align:start position:0% +i would call this constant amortized +amortized means a particular kind of + + align:start position:0% +amortized means a particular kind of + + + align:start position:0% +amortized means a particular kind of +averaging + + align:start position:0% + + + + align:start position:0% + +averaging over the sequence of + + align:start position:0% +averaging over the sequence of + + + align:start position:0% +averaging over the sequence of +operations so while individual + + align:start position:0% +operations so while individual + + + align:start position:0% +operations so while individual +operations will be expensive + + align:start position:0% +operations will be expensive + + + align:start position:0% +operations will be expensive +one near the end when i have to resize + + align:start position:0% +one near the end when i have to resize + + + align:start position:0% +one near the end when i have to resize +the array is going to take linear time + + align:start position:0% +the array is going to take linear time + + + align:start position:0% +the array is going to take linear time +just for that one operation + + align:start position:0% +just for that one operation + + + align:start position:0% +just for that one operation +but most of the operations are cheap + + align:start position:0% +but most of the operations are cheap + + + align:start position:0% +but most of the operations are cheap +most of them are constant + + align:start position:0% +most of them are constant + + + align:start position:0% +most of them are constant +so i can think of charging that high + + align:start position:0% +so i can think of charging that high + + + align:start position:0% +so i can think of charging that high +cost to all of the other operations that + + align:start position:0% +cost to all of the other operations that + + + align:start position:0% +cost to all of the other operations that +made it happen + + align:start position:0% +made it happen + + + align:start position:0% +made it happen +and so this is averaging + + align:start position:0% + + + + align:start position:0% + +over the operation sequence every insert + + align:start position:0% +over the operation sequence every insert + + + align:start position:0% +over the operation sequence every insert +last + + align:start position:0% +last + + + align:start position:0% +last +over there uh only takes constant time + + align:start position:0% +over there uh only takes constant time + + + align:start position:0% +over there uh only takes constant time +on average + + align:start position:0% +on average + + + align:start position:0% +on average +over the the sequence of operations that + + align:start position:0% +over the the sequence of operations that + + + align:start position:0% +over the the sequence of operations that +we do + + align:start position:0% +we do + + + align:start position:0% +we do +and so it's almost constant it's not + + align:start position:0% +and so it's almost constant it's not + + + align:start position:0% +and so it's almost constant it's not +quite as good as constant worst case + + align:start position:0% +quite as good as constant worst case + + + align:start position:0% +quite as good as constant worst case +but it's almost as good and it's as good + + align:start position:0% +but it's almost as good and it's as good + + + align:start position:0% +but it's almost as good and it's as good +as you could hope to do + + align:start position:0% +as you could hope to do + + + align:start position:0% +as you could hope to do +in this dynamic array allocation model + + align:start position:0% +in this dynamic array allocation model + + + align:start position:0% +in this dynamic array allocation model +let me put this into a table uh and + + align:start position:0% +let me put this into a table uh and + + + align:start position:0% +let me put this into a table uh and +you'll find these in the lecture notes + + align:start position:0% +you'll find these in the lecture notes + + + align:start position:0% +you'll find these in the lecture notes +also + + align:start position:0% +also + + + align:start position:0% +also +so we have on the top the main + + align:start position:0% +so we have on the top the main + + + align:start position:0% +so we have on the top the main +operations of the sequence interface + + align:start position:0% +operations of the sequence interface + + + align:start position:0% +operations of the sequence interface +which we will revisit in lecture seven + + align:start position:0% +which we will revisit in lecture seven + + + align:start position:0% +which we will revisit in lecture seven +we'll see some other data structures for + + align:start position:0% +we'll see some other data structures for + + + align:start position:0% +we'll see some other data structures for +this + + align:start position:0% +this + + + align:start position:0% +this +get ad and set ad in the first column + + align:start position:0% +get ad and set ad in the first column + + + align:start position:0% +get ad and set ad in the first column +insert and delete first insert and + + align:start position:0% +insert and delete first insert and + + + align:start position:0% +insert and delete first insert and +delete last + + align:start position:0% +delete last + + + align:start position:0% +delete last +insert and delete at an arbitrary + + align:start position:0% +insert and delete at an arbitrary + + + align:start position:0% +insert and delete at an arbitrary +position so + + align:start position:0% +position so + + + align:start position:0% +position so +we've seen three data structures now + + align:start position:0% +we've seen three data structures now + + + align:start position:0% +we've seen three data structures now +arrays + + align:start position:0% +arrays + + + align:start position:0% +arrays +were really good at get at set at they + + align:start position:0% +were really good at get at set at they + + + align:start position:0% +were really good at get at set at they +took constant time + + align:start position:0% +took constant time + + + align:start position:0% +took constant time +that's the blue one we're omitting the + + align:start position:0% +that's the blue one we're omitting the + + + align:start position:0% +that's the blue one we're omitting the +thetas here + + align:start position:0% +thetas here + + + align:start position:0% +thetas here +all the other operations took linear + + align:start position:0% +all the other operations took linear + + + align:start position:0% +all the other operations took linear +time no matter where they were + + align:start position:0% +time no matter where they were + + + align:start position:0% +time no matter where they were +linked lists were really good at insert + + align:start position:0% +linked lists were really good at insert + + + align:start position:0% +linked lists were really good at insert +and delete first they took constant time + + align:start position:0% +and delete first they took constant time + + + align:start position:0% +and delete first they took constant time +but everything else took linear time in + + align:start position:0% +but everything else took linear time in + + + align:start position:0% +but everything else took linear time in +the worst case + + align:start position:0% +the worst case + + + align:start position:0% +the worst case +these new dynamic arrays achieve + + align:start position:0% +these new dynamic arrays achieve + + + align:start position:0% +these new dynamic arrays achieve +get at and set out in constant time + + align:start position:0% +get at and set out in constant time + + + align:start position:0% +get at and set out in constant time +because they maintain this invariant + + align:start position:0% +because they maintain this invariant + + + align:start position:0% +because they maintain this invariant +uh here that a of i equals x + + align:start position:0% +uh here that a of i equals x + + + align:start position:0% +uh here that a of i equals x +i so we can still do gets and set at + + align:start position:0% +i so we can still do gets and set at + + + align:start position:0% +i so we can still do gets and set at +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +and we also just showed that insert last + + align:start position:0% +and we also just showed that insert last + + + align:start position:0% +and we also just showed that insert last +is constant amortized + + align:start position:0% +is constant amortized + + + align:start position:0% +is constant amortized +delete last uh + + align:start position:0% +delete last uh + + + align:start position:0% +delete last uh +you don't have to resize the array you + + align:start position:0% +you don't have to resize the array you + + + align:start position:0% +you don't have to resize the array you +could just decrease + + align:start position:0% +could just decrease + + + align:start position:0% +could just decrease +length and boom you've deleted the last + + align:start position:0% +length and boom you've deleted the last + + + align:start position:0% +length and boom you've deleted the last +item + + align:start position:0% +item + + + align:start position:0% +item +it's not so satisfying because if you + + align:start position:0% +it's not so satisfying because if you + + + align:start position:0% +it's not so satisfying because if you +insert n items and then delete n items + + align:start position:0% +insert n items and then delete n items + + + align:start position:0% +insert n items and then delete n items +you'll still have an array of size theta + + align:start position:0% +you'll still have an array of size theta + + + align:start position:0% +you'll still have an array of size theta +n even though your current value of n is + + align:start position:0% +n even though your current value of n is + + + align:start position:0% +n even though your current value of n is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +um you can get around that with a little + + align:start position:0% +um you can get around that with a little + + + align:start position:0% +um you can get around that with a little +bit more trickery which are described in + + align:start position:0% +bit more trickery which are described in + + + align:start position:0% +bit more trickery which are described in +the lecture notes but + + align:start position:0% +the lecture notes but + + + align:start position:0% +the lecture notes but +it's beyond the we're only going to do + + align:start position:0% +it's beyond the we're only going to do + + + align:start position:0% +it's beyond the we're only going to do +very simple amortized analysis in this + + align:start position:0% +very simple amortized analysis in this + + + align:start position:0% +very simple amortized analysis in this +class + + align:start position:0% +class + + + align:start position:0% +class +to prove that that algorithm is also + + align:start position:0% +to prove that that algorithm is also + + + align:start position:0% +to prove that that algorithm is also +constant amortized which it is + + align:start position:0% +constant amortized which it is + + + align:start position:0% +constant amortized which it is +uh you'll see in o46 or you can find it + + align:start position:0% +uh you'll see in o46 or you can find it + + + align:start position:0% +uh you'll see in o46 or you can find it +in the clrs book + + align:start position:0% +in the clrs book + + + align:start position:0% +in the clrs book +uh that's it for today \ No newline at end of file diff --git a/CbcJFO6VtsY.txt b/CbcJFO6VtsY.txt new file mode 100644 index 0000000000000000000000000000000000000000..c57d6fc7947c40c42363e8a560b9816891d1c911 --- /dev/null +++ b/CbcJFO6VtsY.txt @@ -0,0 +1,160 @@ +Let's follow along as the assembler processes +our source file. + +The assembler maintains a symbol table that +maps symbols names to their numeric values. + +Initially the symbol table is loaded with +mappings for all the register symbols. + +The assembler reads the source file line-by-line, +defining symbols and labels, expanding macros, + +or evaluating expressions to generate bytes +for the output array. + +Whenever the assembler encounters a use of +a symbol or label, it's replaced by the corresponding + +numeric value found in the symbol table. + +The first line, N = 12, defines the value +of the symbol N to be 12, so the appropriate + +entry is made in the symbol table. + +Advancing to the next line, the assembler +encounters an invocation of the ADDC macro + +with the arguments "r31", "N", and "r1". + +As we'll see in a couple of slides, this triggers +a series of nested macro expansions that eventually + +lead to generating a 32-bit binary value to +be placed in memory location 0. + +The 32-bit value is formatted here to show +the instruction fields and the destination + +address is shown in brackets. + +The next instruction is processed in the same +way, generating a second 32-bit word. + +On the fourth line, the label loop is defined +to have the value of the location in memory + +that's about to filled, in this case, location +8. + +So the appropriate entry is made in the symbol +table and the MUL macro is expanded into the + +32-bit word to be placed in location 8. + +The assembler processes the file line-by-line +until it reaches the end of the file. + +Actually the assembler makes two passes through +the file. + +On the first pass it loads the symbol table +with the values from all the symbol and label + +definitions. + +Then, on the second pass, it generates the +binary output. + +.152 The two-pass approach allows a statement +to refer to symbol or label that is defined + +later in the file, e.g., a forward branch +instruction could refer to the label for an + +instruction later in the program. + +As we saw in the previous slide, there's nothing +magic about the register symbols. + +They are just symbolic names for the values +0 through 31. + +So when processing ADDC(r31,N,r1), UASM replaces +the symbols with their values and actually + +expands ADDC(31,12,1). + +UASM is very simple. + +It simply replaces symbols with their values, +expands macros and evaluates expressions. + +So if you use a register symbol where a numeric +value is expected, the value of the symbol + +is used as the numeric constant. + +Probably not what the programmer intended. + +Similarly, if you use a symbol or expression +where a register number is expected, the low-order + +5 bits of the value is used as the register +number, in this example, as the Rb register + +number. + +Again probably not what the programmer intended. + +The moral of the story is that when writing +UASM assembly language programs, you have + +to keep your wits about you and recognize +that the interpretation of an operand is determined + +by the opcode macro, not by the way you wrote +the operand. + +Recall from Lecture 9 that branch instructions +use the 16-bit constant field of the instruction + +to encode the address of the branch target +as a word offset from the location of the + +branch instruction. + +Well, actually the offset is calculated from +the instruction immediately following the + +branch, so an offset of -1 would refer to +the branch itself. + +The calculation of the offset is a bit tedious +to do by hand and would, of course, change + +if we added or removed instructions between +the branch instruction and branch target. + +Happily macros for the branch instructions +incorporate the necessary formula to compute + +the offset from the address of the branch +and the address of the branch target. + +So we just specify the address of the branch +target, usually with a label, and let UASM + +do the heavy lifting. + +Here we see that BNE branches backwards by +three instructions (remember to count from + +the instruction following the branch) so the +offset is -3. + +The 16-bit two's complement representation +of -3 is the value placed in the constant + +field of the BNE instruction. \ No newline at end of file diff --git a/DyRLOmVRQDw.txt b/DyRLOmVRQDw.txt new file mode 100644 index 0000000000000000000000000000000000000000..a969b39757fe1aff341dd847495dce50ecd56043 --- /dev/null +++ b/DyRLOmVRQDw.txt @@ -0,0 +1,3375 @@ +PROFESSOR: The topic of this +chapter is finding trellis + +representations for block codes, +in particular linear + +block codes. + +We're looking only at binary +block codes, except one of the + +homework problems looks at MDS +codes over ground field of q. + +The principles are the same for +general Fq or in fact for + +group codes. + +We're looking for minimal +trellis representations. + +And so just to review our line +of thought, basically we + +proved a basic theorem called +the state space theorem that + +tells us that there is a vector +space over the ground + +field at any time which we can +identify with the state space. + +It has a certain dimension. + +And we got a little formula in +terms of subcodes for the + +dimension of the state space. + +We set up a little generator +matrix where we isolated the + +past part of the code with +respect to a certain cut time + +future part of the code, +generators for that. + +We subtract those +generators out. + +What's left? + +The number of generators is the +number of generators it + +takes to generate the state +space, in other words the + +dimension of the state space. + +So we got a theorem on the +dimension of the state space + +at any time. + +And then we found a nifty little +algorithm to find a -- + +to determine the dimensions of +the state spaces at all times, + +the minimal state spaces. + +And in fact we can use this +algorithm to construct a + +minimal trellis realization. + +The algorithm involves a + +trellis-oriented generator matrix. + +And the idea here turns +out to be very simple. + +All you do is you find any +generator matrix for your + +linear block code, and +you reduce it to + +trellis-oriented form. + +Trellis-oriented form means that +the generators have as + +short a span as possible. + +It's a minimum span +generator matrix. + +And we do that just in a greedy +fashion by any time we + +have an opportunity to add two +generators together such that + +either their starting position +cancels, or their end position + +cancels, we do it. + +And out of that we get a shorter +generator, and we can + +replace one of the two +generators in the + +combination by that. + +We can keep shortening +everything up. + +The algorithm must terminate at +the point where no further + +shortening is possible. + +And that is explicitly the +point at which all the + +starting times of the generators +are different, and + +all the ending times of all the +generators are different. + +For example, here's a + +trellis-oriented generator matrix. + +The starting times, +the spans of the + +generators, are like this. + +The active times, starting +times -- + +there's the starting time of +this one, and its ending time. + +Here's the starting time +of the next one, + +and its ending time. + +The starting time of the +next one, and its + +ending time is here. + +And the starting time +of this one, and its + +ending time is here. + +We're not always going to find +that the starting and ending + +times are disjoint. + +This happens, it turns +out, because this + +is a self-dual code. + +In a self-dual code, you will +always get this each time, + +either a starting time +or an ending time. + +But that's not a general +property. + +For instance, another example +that we've used is, say, the 8 + +7 2 single parity check code. + +What are its generators? + +Its generators look like +this, dot, dot, dot, + +down to 0, 0, 1, 1. + +That's a set of trellis-oriented +generators + +with starting time, ending +time, the first one here. + +Starting time, ending time +of the second one there. + +So in general for this one, +every time is a starting and + +ending time up to here, where +every intermediate time is + +both the starting and +an ending time. + +So it could happen that way, +or another example would be + +the 8 1 8 repetition code. + +What's a trellis-oriented +generator matrix for that? + +It only has one generator. + +It looks like that. + +It has a starting span +as the whole thing. + +The starting time is here. + +The ending time is here. + +So for general codes, the +starting times and ending + +times could be anywhere. + +There will always +be k of them. + +And otherwise, there's always +one at the beginning. + +If it's a nontrivial code, +there's always an ending time + +at the end, et cetera. + +But this particular behavior +is for self-dual codes. + +Anyway, having done that +we can now read off the + +dimensions of the state spaces +by simply looking for how many + +generators are active at +any particular time. + +For a state space, we're always +looking at the times + +between the symbols, +cut times. + +We could in fact draw a trivial +one there, but we're + +looking between here. + +How many are active +at this time? + +One. + +So dimension of the state +space at state + +time k is 1, 2, 3. + +This point, we come +back to 2 again. + +3, 2, 1, 0, 0 at the end. + +It's always zero at the ends +because at that point + +everything's in the future, or +everything is in the past. + +So these are trivial +state spaces. + +These are the nontrivial state +spaces in the trellis. + +And in fact, you remember +we had a little picture. + +We can draw this complete +trellis out with the state + +spaces of size 1 2 +4 8 4 8 4 2 1. + +So this is called the state +dimension profile, just this + +set, this ordered set. + +Or the state space size profile +is 2 to the dimension, + +of binary codes, whatever. + +And similarly down here, if we +look at state space sizes, we + +see the dimension is going +to be one at every time. + +So in this case, the dimension +of the state space is 0, 1, 1, + +1, 1, 1, 1, 1, 1, 0. + +And similarly down here, we +look at the cut time. + +It cuts one active generator +every time. + +So it's 0, 1, 1, 1, 1, 1, 0. + +So we get at least the state +space dimensions just by + +inspection of the + +trellis-oriented generator matrix. + +Question? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: We proved it +in several steps. + +First we have the state space +theorem, which I gave to you + +in the following form: the +dimension of the state space + +at time k is equal to the +dimension of the code minus + +the past subcode. + +Let me write that. + +The dimension of the past +subcode minus the dimension of + +the future subcode at time k +relative to this cut time. + +And we proved from the +trellis-oriented generator + +matrix that the past subcode +is generated by all the + +trellis-oriented generators that +have support on the past, + +and the future by all +the ones that have + +support on the future. + +So, it's simply we +take those out. + +And what do we have left? + +We have the ones that are active +at time k, the ones + +that are neither wholly +supported on the past nor on + +the future. + +They're supported both on +the past and future. + +And those, that's what +this difference is. + +So explicitly we have -- + +the code is generated +by all generators. + +That's all k generators. + +Cpk is generated by +trellis-oriented generators + +supported on the past. + +And Cfk is generated by the +trellis-oriented generators + +supported on the future. + +So the difference -- + +state code sk is generated +by the trellis-oriented + +generators not supported +on past or future, or + +active at time k. + +Probably good to write all +that out at least once. + +Yeah? + +AUDIENCE: [INAUDIBLE] + +self-dual codes all have such +properties that each time is + +starting and ending? + +PROFESSOR: Yes. + +AUDIENCE: Why is that? + +PROFESSOR: Why? + +It's a duality theorem, and +we're not doing many duality + +theorems in this course, so +I'll simply tell you. + +AUDIENCE: [INAUDIBLE] + +has this property, it +must be a self-dual. + +PROFESSOR: I don't think +that's true. + +It's possible that's true. + +Duality theorems are very +strong, but I don't think this + +is a sufficient property. + +For instance, suppose I just +changed one of the generators + +to look like that. + +It still has disjoint starting +and ending times, but now I + +don't think the code +is self-dual. + +So here's another code generated +by these four + +generators, and I don't +believe self-dual. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: I'm guessing +that it isn't. + +To prove it I would compute +the dual code, and I would + +find that it wasn't same +code, didn't have + +the same code words. + +But I'm guessing that if I just +make random changes in + +the interior here, I'm not going +to get a self-dual code, + +because that's a very strong +structural property. + +But I'm not going to take the +time in class to do that. + +But these are good questions. + +The whole subject of duality +is a wonderful and elegant + +topic that we just don't +have time to do + +much in this course. + +If I did it another time, +I could spend + +many lectures on duality. + +Some of the homework problems +have suggested what you might + +be able to do in orthogonal +codes, but -- + +well, one of the problems you'll +do on the homework -- + +I was going to talk about +it a little later. + +There's a dual state space +theorem that basically says + +the state space sizes, or +dimensions, are the same for + +the dual code as they are +for the primal code. + +Here's one example. + +Of course, dual is itself, so +it's trivial that the state + +space size is the same. + +But here's another less +trivial example. + +These two codes are orthogonal +to each other. + +And what is similar about +their trellises? + +Their trellises are both +two-state trellises. + +They don't look the same. + +This trellis looks like this, +because they're all zeroes up + +here, and all ones down here. + +That's the repetition code +trellis, whereas this trellis + +looks like this. + +It has crosses every time and +so forth, abstractly. + +So trellises are not the same. + +They have different branching +properties, but the state + +space sizes are the +same at all times. + +This is a general property of +dual codes which you will + +prove on the homework, if you +haven't done so already. + +Sorry, it's hard to know what to +tell you about and what to + +suppress, because I'm also +trying to cover more + +material this year. + +There's a lot of material that's +really nice that I have + +to skip over. + +Let's continue from this. + +Let's make a minimal +realization. + +So, a canonical minimal +trellis. + +I'm doing this in a little bit +different order than it's done + +in the notes, but I think you +will see this kind of argument + +very quickly. + +I've got this trellis-oriented +generator matrix, but suppose + +I didn't know what the +trellis looked like. + +I put it up the first +time last time. + +But all I have is this generator +matrix, and I want + +to generate a trellis now for +this code which has minimal + +state spaces. + +It's also going to turn out to +be minimal in every other way. + +Well, let's start off +by realizing the + +first generator here. + +The first generator generates a +little one-dimensional code. + +G1, the code generated by the +first generator, is simply the + +two code words 0, 0, 0, +0, 1, 1, 1, 1, 0, 0. + +So let me realize that little +one-dimensional code with a + +minimal trellis for that. + +What would it look like? + +If I go through this, I'll +see that it has -- + +my trellis-oriented generator +matrix for this code is simply + +1, 1, 1, 1, 0, 0, 0. + +I see from that that the +dimensions of the state spaces + +is 0, 1, 1, 1, 0, 0, 0, 0, 0. + +And you can easily see that what +the trellis, the minimal + +trellis, a minimal trellis looks +like is 0, 0, 0, 0, 1, + +1, 1, 1, 0, 0, 0, 0. + +So there is the minimal trellis +realization for that + +one-dimensional code. + +It has state spaces of +dimension 0, 1, 1, + +1, 0, 0, 0, 0, 0. + +Therefore the state spaces +are all minimal, + +as proved from this. + +It's all sort of elementary. + +Similarly, I can realize this +one by another little machine + +that looks like this. + +0, 0, 0, 0, 0, 0, 0. + +This is just the state +transition diagram of a linear + +time-varying finite +state machine. + +And it looks like that, and it +too is minimal by the same + +argument for the one-dimensional +code generated + +by this generator. + +What is this saying here? + +This is saying we really -- + +what we should imagine here +is we have a little memory + +element that's only active at +state times 1, 2, and 3. + +So to realize this, this is a + +one-dimensional memory element. + +Think of it as a little -- + +well, a memory for +an element of f2. + +It's active during the interval +1 through 3, during + +the time that this generator +is active. + +It's active at these three +times, not otherwise. + +So you can think of it +as just disappearing. + +It comes into existence +at time 1. + +It holds whatever the +input bit is. + +Think of -- + +we're trying to create the +code as the set of all -- + +sum of ui gi. + +And so what this memory element +really does is it + +holds ui during the time that +it's needed, which is at times + +1, 2, and 3. + +Whatever the coefficient is -- + +what could it be, 0 or 1? + +Element of the base field, f2. + +So the memory element holds, it +contains u1 in this case. + +Yeah? + +AUDIENCE: What if we look at +this matrix only for the + +second code. + +PROFESSOR: Yes. + +AUDIENCE: So that will give +0, 1, 0, 1, 1, 0, 1, 0. + +PROFESSOR: Correct. + +AUDIENCE: So some places it +will suggest that the + +dimension is -- + +PROFESSOR: The fact that +the values are -- + +there will always be 1 here at +the starting time and the + +ending time. + +Otherwise we wouldn't +draw a branch there. + +But they can be arbitrary +in between. + +So don't be thrown off by the +fact that there are some 0 + +values in here. + +What we're doing here is we're +realizing u2 times g2, where + +u2 can be either 0 or 1. + +And g2 can be arbitrary, except +that it has a starting + +time and an ending +time, so it's not + +arbitrary for this kind. + +AUDIENCE: What if we try +to find the state space + +[INAUDIBLE] + +PROFESSOR: For this, what I +need is a one-dimensional + +memory element containing u2 +which is active during a + +different interval, +2 through 6. + +So think of these as like +little stars that + +wink on or wink off. + +This thing comes into +existence for three + +consecutive times, and +then it disappears. + +This thing comes into existence +for five consecutive + +times, and then it disappears. + +Because those are the only +times when it's needed to + +contribute to the output. + +So altogether, we can think of +there as sort of being four + +memory elements which contain +u1, u2, u3, and u4. + +And we form the outputs g1k +times this, sort of like in + +the convolutional code. + +g2k g3k and g4k. + +The generators step along in +time, and we form the outputs. + +We sum this all together in a +summer, and this provides yk, + +the output, as we go from k +equals 1 through 8 as we go + +through the code word. + +But we only need this one +for -- it's only on from + +time 1, 2, and 3. + +And this is on from +time 2 through 6. + +And this is on from +time 3 through 5. + +And this is on from +time 4 through 7. + +Because we don't need +it any other time. + +So you can think of an input +coming in at time 1, at the + +starting time of the first +generator, being saved for as + +long as it's needed, then +it's discarded. + +And in fact we don't need that +memory element anymore. + +How many people are +getting this? + +Raise your hand if +you get this. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: It's a time -- + +what I'm trying to do is draw +a time-varying machine. + +So how do I do that? + +At time 1, it looks like this. + +Time 1, it just has u1, +and we multiply it by + +g11, which is 1. + +And that gives me the +output at time 1. + +There's nothing else +that contributes. + +At time 2, we've got now another +input, u1 and u2. + +And we've got to sum the +contributions from both of + +those, times their respective +coefficients. + +At time 3, we're up to +three of them, and + +we need all of them. + +We're going to form some linear +combination according + +to the generator matrix. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: It's time-varying, +yeah. + +So get used to it. + +For a block code it obviously +has to be time-varying. + +Obviously if we regard these as +impulse responses, this is + +the impulse response to u1. + +It only lasts in terms of symbol +times from time 0 1 2 + +3, for four time units +of symbol time. + +This is the impulse +response to u2. + +u2 you can think of as an input +that comes in at time 2, + +and whose output rings +for five more times. + +So you need to save u2 for five +more times, and then it + +disappears. + +We don't need to save +it anymore. + +We can let it drop off +the end of the shift + +register, if you like. + +u3 comes in at time 3, and this +is its impulse response. + +And u4 comes in at time 5, and +this is its impulse response. + +Does that help? + +How many people are not +getting it now? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: We don't need it +here, but we're going to need + +it again at time 4, so +we have to save it. + +What are you going to do +with it at time 3? + +You going to hide +it somewhere? + +So I still need to save it. + +This, again, is linear system +theory, except I guess you + +just don't get taught linear +system theory anymore. + +But this is what you have +to do if you -- + +before, for convolutional codes, +we did linear systems + +theory for linear time-invariant +systems. + +They have to be over a finite +field, but who cares? + +We did general linear +system theory. + +This is general linear system +theory for realizing + +time-varying systems. + +In fact, one comment that might +be good to make at this + +point is that -- + +now go back and remember +what we did with + +convolutional codes. + +We started out with a rate 1 +over n convolutional code c, + +and we found some generator +for it. + +Basically we can take any code +word in the code, and all of + +its shifts will generate +the code. + +Any non-zero code word, all of +its time shifts generate the + +convolutional code. + +So take any code word g of d in +a convolutional code, and g + +of d, dg of d, d squared +g of d and so forth + +generate the code. + +But then we converted it by +doing a little polynomial or + +Laurent series algebra. + +We took a rational one and we +converted it to a canonical + +one, g prime of d. + +Which if you remember, this is +the polynomial code word of + +minimum degree in the code. + +We call that degree nu. + +What were we doing there? + +The shifts of g prime of d +form a trellis-oriented + +generator matrix for this +convolutional code. + +For instance, for our canonical +example, g prime of + +d looked like this. + +Polynomial notation, it's 1 plus +d squared 1 plus d plus d + +squared is the generator +matrix. + +Let me write that out as 1, 1 +at time 0 or coefficient 0. + +0, 1, 1, 1, and then all +0's before that, and + +all 0's after that. + +Is somebody sleeping? + +Wake him up please, before +I turn around. + +What? + +Oh, all right. + +I'm very glad to hear that. + +So here is g prime of d +written out as bits. + +dg prime of d looks like what? + +It looks like the same thing +shifted over one. + +d squared g prime of d looks +like this and so forth. + +Is this trellis-oriented? + +In this case, each time interval +contains two symbols. + +Here are our divisions +between symbols. + +We've got a rate 1/2 code, so +we chose to take them two + +symbols at a time. + +Where are the starting +and ending times? + +This one starts here, +ends here. + +This one starts here, +ends here. + +Starts here, ends here. + +So all the starting times and +ending times are different. + +Ergo, this is a + +trellis-oriented generator matrix. + +Modulo some hand-waving about +infinite sequences. + +Ergo, we ought to be able to use +the state space theorem to + +say what are the state +space sizes. + +Any time I have a cut here, +what are the spans? + +The spans are like there, +there, there, so forth. + +So the state space dimension at +each time is going to be 2, + +2, 2, 2, 2. + +And if we go through this +construction procedure, what + +are we going to get? + +We're going to get something +that at time 0, we need to + +have in memory, we need +to remember u minus + +1 and u minus 2. + +At time 1, just doing what I did +up here, we need to have + +in memory u minus 1 and u0. + +At time 2, we need to have +in memory u0 and u1. + +And we achieve that just +by implementing this + +with a shift register. + +In the time-invariant case it's +very easy, and you all + +understand it. + +So exactly the same theory goes +through for rate 1 over n + +convolutional codes. + +I will tell you briefly that to +treat rate k over n, it's + +basically just the same thing, +except we need k generators + +starting at each time here. + +But in order to get a canonical +encoder, we just get + +a trellis-oriented generator +matrix again. + +And by the way, modulo this +hand-waving about infinite + +sequences, I've now proved what +I asserted, that this + +encoder is minimal among all +encoders for this code, that + +it has the minimum number +of memory elements. + +Because from this argument, +the minimal state space + +dimension at each time is 2 +once I've achieved this + +canonical trellis-oriented +generator matrix. + +By the way, this theory +is very general. + +It's really all you need to know +to do minimal realization + +theory of linear systems, +whether they're time-varying + +or time-invariant over any +field, or over groups. + +So that was a parenthetical +comment about convolutional + +codes just to tie it back +to what we did in + +the previous chapter. + +I haven't completed +what I wanted to + +say about block codes. + +How am I going to do this +without erasing something? + +Let's go back to block codes. + +And I guess I'll move over. + +The point that I was in the +process of making was that I + +can realize each one of these +generators individually by a + +little trellis diagram that's +one-dimensional during the + +time that the generator is +active, and zero-dimensional + +state space during the time +the generator is inactive. + +And think of this as just +one component here. + +To generate a code word, +a particular code + +word is just the sum. + +All I need to do is sum the +outputs of all these + +generators independently. + +How many different possibilities +are there? + +There are 2 to the k possible +code words. + +Each one of these generates +one of two + +possible code words. + +If I take the set of all +possible sums of these four + +code words, I'm going to have +16 possible code words. + +So that very quickly was what +I was doing when I said, + +here's a little machine that +generates the first code, c1. + +Here's a little machine that +generates the second code, c2. + +Only has two possible code words +according to the value + +of what's in storage. + +This generates the +third component. + +This generates the +fourth component. + +Sum it all together, +and you get -- + +sorry, I'm calling this y now. y +equals the sum of the ui gi. + +You see that? + +I hope I've beaten it into +the ground enough now. + +So it's a linear time-varying +machine. + +That is a realization of it, +if you've understood my + +description of it now. + +And now we can draw +the trellis of it. + +That what can happen at time +1, we can either have u1. + +Now I can label my states +here, at this time u1. + +u1 can be either 0 or 1. + +This is u1. + +At time 2, I have both u1 +and u2 in my state. + +So this can either be 0, 0 +or 0, 1, or 1, 0 or 1, 1. + +And obviously if I've already +determined u1 is 0 here, it's + +still going to be 0 at time 2. + +I label these with their +associated outputs. + +This is 1. + +This is also 1. + +This can turn it back to 0. + +And I just keep going. + +At the third time, I +have u1, u2, u3. + +I have eight states. + +At time 4, I come back. + +I only have u2, u3 at time +4, and so these merge. + +So I get something -- + +this doesn't merge like +that, though. + +It merges down here. + +0, 0, 0, 0, 0, 1. + +This merges to 0, 1 when +I drop the first one. + +It's probably worth doing +this more carefully + +than I'm doing it. + +0, 1 can go to 0, 1, +0, or 0, 1, 1. + +0, 1, 0 can either go to -- + +u2 equals 1. + +I guess these can't cross. + +u2 -- + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Excuse me? + +AUDIENCE: [INAUDIBLE] + +u3 and u4. + +PROFESSOR: No, this +is state time. + +State time 1, 2, 3. + +u4 hasn't started yet. + +So I'm sorry, this +is 5 through 7. + +Is that right? + +It only lasts for +three intervals. + +So I only have u2, u3. + +u1, u2 has to be 0, 0, 1, so +this would then go to 0, 1. + +0, 1. + +These seem to cross. + +Yes, they do cross. + +So let's see if I can actually +complete it. + +This could go to 1, +0, 0, or 1, 0, 1. + +And then this one goes up +to either 0, 0 or 0, 1. + +This one can go to 1, +1, 0 or 1, 1, 1. + +And that can go like this. + +So there's the trellis +for the first half. + +It's topologically the same, but +looks a little different + +from what I put up before. + +I interchanged these two with +these two, and this + +one with this one. + +But you can recover the trellis +that I had before. + +In any case, I claim when I've +labeled this with what the + +appropriate output is +at each time, I've + +got my minimal trellis. + +And now we can make more +comments about + +how the trellis works. + +You see that whenever a +generator starts, we have + +what's called a divergence in +the trellis, a branching + +process, a branching out, +whereas whenever a generator + +ends, we have a convergence +in. + +So a starting time -- + +if we have a generator starting, +then we get a branch + +that looks like this, like +here, and here, and here. + +When we have an ending time, +we have branches that look + +like this, like here. + +So this is a starting time, +starting time, starting time, + +and ending time. + +So this tells you when things +open and close in the trellis. + +Now again, as I've said for +these more general trellises, + +down here we can have starting +and ending at the same time. + +And in that case, +we get a cross. + +We get a starting and ending +at the same time, we get + +something that looks +like this. + +And if we get neither starting +nor ending, empty, then + +nothing happens. + +We just get -- + +the trellis segment looks like +that, like this one here. + +In this case we have a starting +time, an ending time + +in this trellis. + +Here we have nothing +happening. + +Here we have nothing +happening. + +So you just get an extension, +a parallel extension where + +nothing happens. + +So again, the starting and +ending times tell you what + +happens in the trellis. + +There's one other thing that you +can read from the trellis, + +which is the size of +branch spaces. + +And since as usual I'm running +a little later + +than I intend to -- + +let me just state without proof +that there is a similar + +theorem for branch spaces. + +What is a branch? + +When we look in a trellis, a +branch is one of these things. + +That's a branch. + +What do we need to +define a branch? + +We have a initial state, the +code output at time k. + +We're calling that y time +k in the next state. + +So it's that triple. + +Again, this is linear +system theory. + +State, output, next state. + +Those are the three things +that define a branch. + +This branch is state 1 0. + +Output whatever it is, y k, +and next state 1 0 0. + +And that differentiates it +from this down here. + +If we define the branch +as this triple, + +then we can add triples. + +States form a vector space +over the ground field. + +These are simply symbols +over the ground field. + +These are vectors over +the ground field. + +So we can add them. + +And we find that it's closed, +and the set of all branches is + +a vector space. + +It's fairly easy to show. + +Look at the notes, but it's +basically because these are + +all projected from code words +in the first place, and code + +words form a vector space, so +this is just a projection of + +the code words, a certain kind +of projection onto the state + +spaces and symbol spaces +and so forth. + +A projection of a vector space +is a vector space. + +Roughly the proof. + +And what is the dimension +of the branch space? + +Again, I'm just going to +give you the answer. + +Suppose we have a + +trellis-oriented generator matrix. + +Let's suppose we want to find +out the size of the branch + +space at this time. + +What doesn't enter into +the branch space? + +What doesn't make a difference +to the branches? + +All the pasts that arrive at the +same state at time k are + +equivalent. + +So this generator doesn't +enter in. + +All the futures that depart from +time k plus 1 don't enter + +in, so anything that's supported +by the future at + +time k plus 1 doesn't +enter in. + +And what's left is all of the +generators that are active at + +symbol time k. + +Notice the symbol times occur +between the state times. + +So certainly this +is an easy -- + +this is one of those results +that's easier to understand + +than to prove, and I'll refer +you to the notes to prove. + +The dimension of the branch +space is simply the number of + +generators that are active +at symbol time k. + +Because branches are +synchronized with the symbol + +times, not with the +state times. + +So how does that come +out over here? + +There's the dimension of the +branch space is 1 here. + +It's 2 here. + +It's 3 here. + +It's 4 here. + +I'm sorry, it's 3 again here. + +This one hasn't started yet. + +It's 3 again here. + +It's 3 again here, +2 here, 1 here. + +That means that the size of the +branch space is 2, 4, 8, + +8, 8, 8, 4, 2. + +Is that right? + +There are two branches here. + +There are four branches here. + +There are eight branches here. + +There are still eight +branches here. + +And it's symmetric on +the other side. + +So it looks like we got the +right answer there, and in + +fact it's a general rule. + +So that's great. + +That's another property of + +trellis-oriented generator matrix. + +We can again, by inspection, get +the dimensions of all the + +branch space sizes. + +Are the branch sizes +important? + +Yes. + +In fact, they're more important +from a complexity + +point of view than the +state space sizes. + +95% of the literature has +to do with state spaces. + +State space is a little bit more +elegant mathematically. + +For instance, you don't have the +same kind of dual branch + +space theorem as you have a +dual state space theorem. + +But actually, when you're asking +what's going on in the + +Viterbi algorithm, what +does the Viterbi + +algorithm have to do? + +At a minimum, it has to do one +thing for each branch. + +It has to perform a metric +extension, a metric addition + +computation at least once +for each branch. + +So the Viterbi algorithm +complexity is better estimated + +by the size of the branch space +than the size of the + +state space. + +To progress at this point, a +Viterbi algorithm has to do at + +least eight things. + +To progress again, it has to +do at least eight things. + +So it's more relevant from the +point of view of complexity. + +Furthermore, you can play games +with state space size. + +And you've seen me play games +with state space size. + +For instance, if I draw this +as a two-section trellis -- + +the first picture I put up was +only a four-state trellis, and + +it looked like this. + +I went immediately +to time 2, and I + +aggregated these two things. + +0, 0 and 1, 1 were up +here, and 0, 1 and + +1, 0 were down here. + +And then I had a nice -- + +I just drew these four +states over here. + +And if I do it like that, then +I get a much nicer picture. + +It looks like this. + +It looks only like a +four-state trellis. + +Now, is this still a +legitimate trellis? + +Yeah, it's still a legitimate +trellis. + +If I do a Viterbi algorithm +decoding of this trellis, is + +it any different from this? + +Well, in detail it is a +little bit different. + +You do the additions and the +comparisons and the selection. + +So you only do selections +every this often. + +And if you think about it, +it's really legitimate to + +think of this -- + +if you think exactly how the +Viterbi algorithm works, + +really what's it doing? + +It's not making any +selection here. + +It's just adding an increment +there, and then adding another + +increment, and it's not +making any selection + +until it gets here. + +So it's perfectly legitimate to +think of this as basically + +being a four-state algorithm. + +It really isn't doing any +work at this stage. + +All the work occurs at this +stage if you think about the + +operation of the Viterbi +algorithm. + +So this is a quite legitimate +representation. + +And so what are we +going to say? + +Is the state complexity of this +code, is it four states + +or is it eight states? + +Well, to some degree it's just +a matter of definition. + +How do you choose +to define it? + +If you want something more +fundamental, it's better to go + +to branch complexity. + +What's the branch complexity +here for the + +fully displayed trellis? + +It's eight. + +By branch complexity, I +mean the maximum size + +of any branch space. + +What's the branch +complexity here? + +It's eight. + +We've still got eight. + +Ultimately we've got to compare +these eight things and + +reduce them to four, whether +we do it here or here. + +I gave you another trellis which +was only a two-section + +trellis, where I just showed +the four central states. + +And we actually have two +branches going there, two + +branches going there, two +branches going there, and two + +branches going there. + +What's the branch complexity +of that trellis? + +Still eight. + +There are eight ways to get +from the origin to here. + +If you go back to how we do this +theorem, if you believe + +this theorem, what happens now +if we say arbitrarily, OK, + +we're going to define the state +spaces as we do in a + +rate 1/2 convolutional code. + +We're just going to define +the state times to + +be every two times. + +Then the dimension of the state +spaces, just at those + +times we've defined, +is 0, 2, 2, 2, 0. + +They don't change. + +We just have fewer of +them by our choice. + +What happens to the dimensions +of the branch spaces? + +Again, if the theorem is +correct, we should just count + +the number of active generators +at each now of + +these four bi-symbol times. + +So it's 2, 3, 3, 2. + +Is that right? + +That is the branch complexity +of this trellis down here. + +It's 4 in the initial interval, +and 8 over here. + +So again it's correct. + +Suppose we go to that so-called +two-section trellis. + +We just say there's a first +half and a second half. + +Now the states is going to +be 0 2 0, and the branch + +complexity is going to be -- + +there are three active +generators in the first half, + +and three active generators +in the second half. + +So by playing this kind of +game, which is called + +sectionalization, we can make +the state complexity sometimes + +appear simpler. + +There are limits to how much +simpler we can make it. + +Well, there actually aren't. + +Suppose we took the whole eight +symbols as one time. + +We'd have 0 dimensional state +space at the beginning, and 0 + +dimensional at the end. + +What does that trellis +look like? + +It looks like 16 parallel +transitions from + +beginning to end. + +That's a legitimate +trellis, right? + +We should have one state at the +beginning and one state at + +the end, and 16 transitions. + +Is that what we get if +we went through this? + +Yeah. + +We have 0 0. + +And what's the branch +complexity? + +It's 4. + +The dimension of the branch +space is 4 if we took the + +whole thing. + +So we can mask state complexity +by picking our + +state spaces at appropriate +times, but you can't ever mask + +branch complexity. + +And again, it's a very +intuitive proof here. + +Let's take this time here, where +there are three active + +generators. + +By expanding that time, can we +ever get fewer than three + +active generators? + +No, any interval that includes +this particular time is going + +to have three active +generators in it. + +So branch complexity cannot +be reduced by this kind of + +sectionalization game. + +State complexity can be +apparently reduced. + +It isn't really. + +But branch complexity cannot. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: And if you go too +far, it might increase. + +So at the very end of the +chapter, I talk about + +sectionalization. + +It's not a very important +issue. + +There's a very easy heuristic +for how you should + +sectionalize, which is basically +you should make the + +sections as big as you can +without increasing branch + +complexity. + +So in this case, the heuristic +says we know we're going to + +have to have branch +complexity of 3. + +But without increasing -- + +if I just make this one +partition at the center, I + +just take these two sections, +first half, second half. + +Then I have an increased +branch complexity. + +So that's a good +sectionalization. + +This will probably lead to the +simplest Viterbi algorithm and + +the simplest-looking trellis +representation of the code. + +So that's the character of the +sectionalization algorithm. + +You can read about it. + +It usually winds up with +a sensible time-varying + +sectionalization, and it's +worth five minutes of + +discussion. + +Yes. + +AUDIENCE: Is it like a monotonic +kind of thing, like + +if you make sections bigger, +then you'll only either + +increase or keep the same +branch complexity? + +PROFESSOR: Yeah, that was my +basic argument, that if I have + +any section that includes this +time, and I start making it + +bigger, the dimension +can only increase. + +So the algorithm is to keep +increasing it until I get to + +some place where I might have to +include another generator. + +For instance here, if I'm taking +this time, I don't want + +to push it out over here, +because then I'll get the + +fourth generator in there. + +So any section that includes +time 3 should not be extended + +in this direction, because we'll +get another generator. + +But no problem with extending +in this direction. + +So that's the basic heuristic. + +It's easy. + +And it's not very productive. + +It doesn't really change the +complexity of the Viterbi + +algorithm as a representation +of code. + +So these are just a couple +of arguments to say + +really we might -- + +the branch complexity +is more fundamental. + +We want to focus on branch +complexity a little bit more. + +But of course, if you have a +fully displayed trellis, the + +maximum state space dimension is +either going to be equal to + +the maximum branch space +dimension or one less than it. + +Because in these binary +trellises, we get at most a + +binary branch at each time. + +So any branch complexity is +at most twice that of the + +adjacent state space. + +So they're not going to +differ by very much. + +So state complexity is a good +proxy for branch complexity in + +a fully displayed or +unsectionalized trellis. + +While I'm on this subject, +there's another interesting + +direction we can go, which is +average dimension bounds. + +Again, think of our +realization here. + +What does it contribute? + +What does a single generator +contribute overall to state + +and branch space complexity? + +A single generator Gj of span +S, which of course has to be + +greater than or equal to +the minimum distance + +to the code, right? + +The span can't be less +of a generator. + +It can't be less than +the minimum nonzero + +weight of any code word. + +Span S contributes overall +to all the state space + +dimensions. + +It contributes S minus 1 state +space dimensions, because it's + +active for S minus +1 state times. + +And it contributes S branch +dimensions because it's active + +for S symbols. + +If I look at it spread out +across time, this generator of + +span 4, it contributed three +times to a state space + +dimension, and it +contributed four + +times to a branch dimension. + +So total state dimension has to +be greater than or equal to + +k times d minus 1. + +And the total branch dimension, +just summing up + +across the trellis, is greater +than or equal to k + +generators times d. + +Now how many different +nontrivial + +state spaces are there? + +There are n minus 1 nontrivial +state times. + +Excuse me. + +For instance, in this code +of length 8, there are 7 + +nontrivial state spaces. + +So the average state dimension +has to be greater than or + +equal to k d minus +1 over n minus 1. + +And the average branch dimension +has got to be + +greater than or equal to k d +over the n symbol times. + +So actually we might remember +that quantity. + +That's what we called the coding +gain of the code, the + +nominal coding gain on +the additive white + +Gaussian noise channel. + +Well, if the average dimension +is lower bounded by something, + +then certainly the maximum state +space dimension is lower + +bounded by that. + +Max has to be at least as +great as the average. + +So if these are what are called +the average dimension + +bounds on the maximum state +space size, and there are some + +interesting implications. + +Again, this expression for +branch dimension is nicer + +here, because it's +this k d over n + +nominal coding gain thing. + +It's in terms of the basic n +k d parameters of the code. + +And it says what? + +It says if you want a nominal +coding gain of 2, it implies + +that the max branch dimension is +greater than or equal to 2. + +Or the max size is greater than +or equal to 2 to the 2, + +or you need a branch space of at +least size 4, or dimension + +2 to get a 3 dB nominal +coding gain. + +Similarly, if you want +a 6 dB gain -- + +let's get right down to dB. + +It says you're going to need a +branch space size greater than + +or equal to 4, or at least +a 16-state trellis. + +So we know if we want a 6 dB +coding gain, we're going to + +need at least a 16-state +trellis, + +or a 16-branch trellis. + +It might be an eight-state +trellis. + +Well, these are not tight, but +they're quite indicative in + +fact of what we see in both the +tables for block codes and + +for convolutional codes. + +These same bounds hold for +convolutional codes, by the + +way, just average over +infinite time. + +But they're still +perfectly good. + +So they tell us that +in order to get -- + +if we want the nominal coding +gain to keep going up to 8, to + +16, to infinity, it says we're +going to need infinite trellis + +complexity to get infinite +coding gain. + +Let's do some little +asymptotics, be a little bit + +more refined about this. + +A sequence of codes Cn of length +n going to infinity is + +called good if both the rate k +over n is bounded away from 0 + +as n goes to infinity, and the +distance d over n is bounded + +away from 0. + +The rate and the relative +distance are both bounded away + +from 0 as n goes to infinity. + +Is that clear? + +In other words, we want the +dimension and the minimum + +distance both to increase +linearly with n in a good + +sequence of codes. + +This is a classical algebraic +definition, and it's easy to + +prove there exists good +sequences of codes. + +You just pick a code at random, +rate 1/2 of binary + +linear code. + +It on average will have +a relative minimum + +distance about 11%. + +This is just basic information +theory. + +So there certainly exists +sequences of good codes, and + +this is what most of coding +theory was occupied with + +constructing for a +very long time. + +What happens if you have a +good sequence of codes? + +We have this nominal coding +gain, which is equal to kd + +over n, which is equal to n +times k over n times d over n. + +If both of these are bounded +away from zero, then the + +nominal coding gain has to +increase linearly with n. + +That means that the average, +or the maximum branch + +dimension, in a minimal trellis +representation for + +your code has to increase at +least linearly with n, which + +means that the actual branch +complexity, the size of B, has + +to increase as -- + +it goes as 2 to the nominal +coding gain, which is in other + +words exponentially with n. + +So basically what this says is +that if your objective is to + +get a good sequence of codes, +if this is the way you think + +you're going to get to channel +capacity, then sure enough, + +your nominal coding gain +will go up to infinity + +linearly with n. + +But how are you going +to decode it? + +Our first method was simply +maximum likelihood decoding. + +The complexity of that, +computing the distance to + +every code word, that +certainly goes up + +exponentially with n, exhaustive +decoding, comparing + +with every code word. + +But now we have a new method +which is, we hope, simpler, + +which is trellis decoding. + +But we find out, unfortunately, +the complexity + +of trellis decoding +is going to go up + +exponentially with n as well. + +So the good news was that with +the Viterbi algorithm and a + +minimal trellis, we can get +a simpler optimum maximum + +likelihood decoding algorithm +for block code, simpler than + +exhaustive decoding. + +The bad news is that under +this assumption, the + +complexity of that algorithm +is still going to go up + +exponentially with n. + +Maybe just a lower exponent, +that's all. + +So we haven't really solved our +basic problem, which is + +exponential decoding complexity, +by going to + +trellis decoding. + +We have, however, another +way to go. + +Do we really need the coding +gain to go to infinity, the + +nominal coding gain +to go to infinity? + +If we go back and remember the +name of the game, the playing + +field that we're on, at least in +the additive white Gaussian + +noise channel, we found the +distance between uncoded and + +the Shannon limit was some +finite number, something like + +9 dB at a 10 to the minus 5 +error probability, larger at + +lower error probability. + +So that's the maximum +effective coding + +gain we can ever get. + +So maybe we only need a finite +nominal coding gain. + +In practice, this means maybe +we don't need a minimum + +distance that goes up +linearly with n. + +Maybe we can have a very +long code with + +a low minimum distance. + +And that would be another +way to crack + +the complexity problem. + +In fact, some of the +capacity-approaching codes + +that we're going to talk about, +specifically turbo + +codes, tend to have bad +minimum distances. + +You have a turbo code that's +thousands of bits long, and + +its minimum distance will be +something like 20 or 30. + +And yet it signals within 1 +dB of the Shannon limit. + +It gives you low error +probabilities within 1 dB of + +the Shannon limit. + +So maybe there's another way to +go, at least if we're only + +interested in a certain +error probability. + +Maybe it's 10 to the minus 5. + +Maybe it's 10 to the minus 10. + +But it's still only a finite +error probability. + +Maybe we don't need the minimum + +distance to go to infinity. + +Maybe we can get by sampling +codes which are lousy in + +classical terms, which have +poor minimum distance. + +Maybe they'd be lousy in +distance terms, or in nominal + +coding gain terms, but they'll +be very good from the point of + +view of complexity. + +Maybe there's some +trade-off here. + +We know the code is going to +have to be long, but maybe it + +doesn't have to have +large distance. + +Yeah. + +AUDIENCE: [INAUDIBLE] + +That's what you are +saying, isn't it? + +We try to maintain the -- + +PROFESSOR: We certainly want +to maintain a finite rate. + +This was the problem with +orthogonal and simplex codes + +and so forth, is that the rate +went to zero, and therefore + +the spectral efficiency +went to zero. + +In practically all cases, +that's unacceptable. + +So we need to maintain some +minimal rate or spectral + +efficiency on the additive +white Gaussian noise. + +So that we need, but this +maybe we don't need. + +So that's just a interesting +little bit of philosophy we + +can do at this point, is how +should you really design + +capacity-achieving codes? + +And this seems to be a clue to +the way to go that has in fact + +proved to be good. + +However, I should add that not +all capacity-approaching codes + +have this property. + +A random low-density parity +check code is going to have + +both low complexity and a very +good minimum distance as well. + +So this certainly isn't +the full story. + +There are just two more topics +in chapter 10, and maybe I'll + +discuss them both briefly +right now. + +One is I skipped over +projections. + +And how shall I introduce +this subject? + +I talked about the subcode of, +say, this code, which is + +pretty badly marked-up by now, +but let me keep using it. + +I talked about the subcode +that's supported, say, on the + +first half. + +In this case it's simply the +subcode that's generated by + +the first generator. + +Here's another code that we can +look at that's kind of a + +first half code. + +Suppose we just take the set +of all possible first + +four-tuples in this code. + +That's called the projection +onto the first half. + +In other words, what are +the set of all possible + +four-tuples? + +They're the set of code words +that are generated by 1, 1, 1, + +1, 0, 1, 0, 1, 0, 0, +1, 1, and this + +doesn't contribute anything. + +So it's a linear code. + +It's length 4. + +It has three generators, +dimension 3. + +And we can quickly convince +ourselves that it's the even + +weight, or zero sum, or +a single parity check + +code of length 4. + +So if we project this on +to the first half, we + +get a 4, 3, 2 code. + +So that's what I mean +by a projection. + +If I project on to here, +I get the 1 0 code. + +I'm sorry, I get the universe +code of length 1, all + +one-tuples. + +On here I get all two-tuples. + +On here I get all +three-tuples. + +But on here I don't get +all four-tuples. + +I get a single parity +check code. + +So those are my projections. + +Some things can be done nicely +in terms of projections. + +Projections are kind of +the dual to subcodes. + +In fact, you prove this on the +homework in the course of + +proving the dual state +space theorem. + +In other words, the dual of a +subcode of a code C is the + +projection of the dual code +of C, and vice versa. + +They're always tongue twisters, +the duality theorem. + +But that's what you will +prove along the way. + +Let me give you the relevance +of this to + +the state space theorem. + +So I had the state space +theorem right here. + +So let me leave it up. + +State space theorem +is based on -- + +in general, we divide the +generator matrix g prime into + +a part that is a generator +for the past subcode 0. + +0 generator for the +future subcode. + +And then some stuff down here, +which is generators of the + +state space code. + +By construction here, the +projections of any nonzero + +vector in the state space +code are nonzero. + +If they were zero, any nonzero +linear combination of these + +generators down here cannot +be zero on here. + +So the projection on to the +first half here, the dimension + +of the projection -- + +I'm making a slight skip here +-- is basically equal to the + +dimension of the past subspace +code plus the dimension of the + +state code. + +It's basically generated by +these generators and these + +generators projected +onto here. + +We can forget about +these generators. + +So let me write that down. + +The dimension of C projected +onto the past is equal to the + +dimension of the past subcode +plus the dimension of the + +state space code. + +Which leads to another version +of the state space theorem. + +I could simply write state space +theorem as dimension of + +the state space at time k is +simply the difference between + +the dimension of the projection, +C projected on the + +past, minus the dimension +of the subcode. + +It's all of these guys +minus these guys. + +And again, if we look back here, +we see we have the 4, 3 + +code is C projected on +p, 4, 3, 2, and C -- + +the subcode is 4, 1, 4. + +In fact, for this, these are +both Reed-Muller codes of half + +the length. + +This is not an accident, +as you will + +prove in the homework. + +The state space size is the +difference in the dimensions + +of these two codes. + +This is a very handy thing +to know, and you're + +going to need this. + +This, for instance, will give +you that in general for + +Reed-Muller codes, if you +divide them in half -- + +we had this general picture of +say the 8 4 code being made up + +by the new u plus +v construction. + +These two together make +the 8, 4, 4 code. + +If you have the u u plus v +construction, there you are, + +first half, second half. + +You will find that the +projection on the first half + +is always this guy, which +is the u code. + +And the subcode is v code, +which is the homework. + +And so you can quickly read +off from this what the + +dimension of the central +state space is + +for Reed-Muller codes. + +In this case it's 2. + +But for instance if we have the +32, 16, 8 code, then what + +is that made up of? + +That's made up from the +16, 11, 4 code and + +the 16, 5, 8 code. + +And so we can see the dimension +of the central state + +space here is going to be 6. + +We're going to get a 64-state +trellis for this code, at + +least just measuring the size +of the central state space. + +Now it turns out you +can keep having -- + +if you go down and you make +four cuts here, then the + +relevant codes are what you +get one more space back. + +At this space, we have the 2, +2, 1 as the projected code, + +and the 2, 0, infinity +as the subcode. + +And again, the difference in +dimensions here is going to be + +the same as the different +dimensions here. + +Minor miracle at first. + +It turns out to be just +from the construction. + +Here we go back to the 8, +7, 2 and the 8, 1, 8. + +And again we see the difference +here is 6. + +So that means that Reed-Muller +codes always have trellises, + +least if you put them +in four sections. + +They always look like +this abstractly. + +They look like what +we've already seen + +for the 8, 4, 4 code. + +And you'll do this on the +homework using projections. + +That's not very hard. + +It doesn't mean that -- + +so we know, for instance, for +the 32 16 8, we're going to do + +this, and there are going to be +64 states here, 64 states + +here, 64 states here. + +We don't know what it's going to +be in between, but you can + +figure that out too. + +In fact, we get a minimal +trellis for the whole thing. + +That's what you need +to do the homework. + +There are actually two more +topics that I want to do in + +Chapter 10. + +One is the Muder bound. + +And one -- + +I actually want to see how +good are these block code + +trellises vis-a-vis +convolutional code trellises. + +So I'll do both of those at the +beginning of next time. + +For homework problem set, let's +this week do only the + +first four problems. + +So for this Wednesday, +do problem set -- + +what are we up to? + +Seven, is it? + +One through four, and for +Wednesday, 4/20, we'll do + +problem set seven, five and six, +plus I'll probably have + +another one. + +But we have a holiday next +Monday also if you recall, + +Patriots' Day. + +So we only get one more +class on Wednesday. + +So I probably won't have much +more to add than this. + +Is that clear? + +Maybe Ashish you could +put out a email to + +the class to do that. + +So good. + +We'll come back and clean +up Chapter 10 quickly on + +Wednesday, and then +move on to 11. \ No newline at end of file diff --git a/FGxxnOLvSfg.txt b/FGxxnOLvSfg.txt new file mode 100644 index 0000000000000000000000000000000000000000..ea3d38be78b08dcc0aaa564b4e75f858083fd198 --- /dev/null +++ b/FGxxnOLvSfg.txt @@ -0,0 +1,11795 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +thanks everyone for coming today + + align:start position:0% +thanks everyone for coming today + + + align:start position:0% +thanks everyone for coming today +so + + align:start position:0% +so + + + align:start position:0% +so +first thing I wanted to do is just + + align:start position:0% +first thing I wanted to do is just + + + align:start position:0% +first thing I wanted to do is just +review where we are as usual in terms of + + align:start position:0% +review where we are as usual in terms of + + + align:start position:0% +review where we are as usual in terms of +the calendar + + align:start position:0% +the calendar + + + align:start position:0% +the calendar +so we did the first part of contracts + + align:start position:0% +so we did the first part of contracts + + + align:start position:0% +so we did the first part of contracts +and mechanism design as kind of an + + align:start position:0% +and mechanism design as kind of an + + + align:start position:0% +and mechanism design as kind of an +introduction class time and now we're + + align:start position:0% +introduction class time and now we're + + + align:start position:0% +introduction class time and now we're +going to do the second which is very + + align:start position:0% +going to do the second which is very + + + align:start position:0% +going to do the second which is very +explicit about another application + + align:start position:0% +explicit about another application + + + align:start position:0% +explicit about another application +Beyond medieval villages + + align:start position:0% +Beyond medieval villages + + + align:start position:0% +Beyond medieval villages +and we'll definitely have real live data + + align:start position:0% +and we'll definitely have real live data + + + align:start position:0% +and we'll definitely have real live data +and so on and then by Thursday + + align:start position:0% +and so on and then by Thursday + + + align:start position:0% +and so on and then by Thursday +uh we will get into General equilibrium + + align:start position:0% +uh we will get into General equilibrium + + + align:start position:0% +uh we will get into General equilibrium +again balrasian worlds and begin to look + + align:start position:0% +again balrasian worlds and begin to look + + + align:start position:0% +again balrasian worlds and begin to look +at trade applications both in emerging + + align:start position:0% +at trade applications both in emerging + + + align:start position:0% +at trade applications both in emerging +markets and and then later in the U.S + + align:start position:0% +markets and and then later in the U.S + + + align:start position:0% +markets and and then later in the U.S +say a little bit about the reading list + + align:start position:0% +say a little bit about the reading list + + + align:start position:0% +say a little bit about the reading list +especially since you might miss this the + + align:start position:0% +especially since you might miss this the + + + align:start position:0% +especially since you might miss this the +paper application that we're going to + + align:start position:0% +paper application that we're going to + + + align:start position:0% +paper application that we're going to +feature today is this paper uh with my + + align:start position:0% +feature today is this paper uh with my + + + align:start position:0% +feature today is this paper uh with my +co-authors on five Villages and uh we're + + align:start position:0% +co-authors on five Villages and uh we're + + + align:start position:0% +co-authors on five Villages and uh we're +going to both stress the application + + align:start position:0% +going to both stress the application + + + align:start position:0% +going to both stress the application +using the tools you've already learned + + align:start position:0% +using the tools you've already learned + + + align:start position:0% +using the tools you've already learned +in a different context + + align:start position:0% +in a different context + + + align:start position:0% +in a different context +but also some of the techniques remember + + align:start position:0% +but also some of the techniques remember + + + align:start position:0% +but also some of the techniques remember +the class is trying to balance both + + align:start position:0% +the class is trying to balance both + + + align:start position:0% +the class is trying to balance both +learning tools and how to use them as + + align:start position:0% +learning tools and how to use them as + + + align:start position:0% +learning tools and how to use them as +well as + + align:start position:0% +well as + + + align:start position:0% +well as +as the economics so please don't miss + + align:start position:0% +as the economics so please don't miss + + + align:start position:0% +as the economics so please don't miss +this scrivenov starred article + + align:start position:0% +this scrivenov starred article + + + align:start position:0% +this scrivenov starred article +on Computing moral hazard programs with + + align:start position:0% +on Computing moral hazard programs with + + + align:start position:0% +on Computing moral hazard programs with +lotteries because it and it I will say a + + align:start position:0% +lotteries because it and it I will say a + + + align:start position:0% +lotteries because it and it I will say a +lot about those techniques today but not + + align:start position:0% +lot about those techniques today but not + + + align:start position:0% +lot about those techniques today but not +enough so there's two starred articles + + align:start position:0% +enough so there's two starred articles + + + align:start position:0% +enough so there's two starred articles +I wanted to again I have earmarked a few + + align:start position:0% +I wanted to again I have earmarked a few + + + align:start position:0% +I wanted to again I have earmarked a few +of these from what we did last time + + align:start position:0% +of these from what we did last time + + + align:start position:0% +of these from what we did last time +for mechanism design we did a single + + align:start position:0% +for mechanism design we did a single + + + align:start position:0% +for mechanism design we did a single +period we worked through the so-called + + align:start position:0% +period we worked through the so-called + + + align:start position:0% +period we worked through the so-called +Revelation principle + + align:start position:0% +Revelation principle + + + align:start position:0% +Revelation principle +and finally we got to a two period + + align:start position:0% +and finally we got to a two period + + + align:start position:0% +and finally we got to a two period +problem and the question the review + + align:start position:0% +problem and the question the review + + + align:start position:0% +problem and the question the review +question is written here is now + + align:start position:0% +question is written here is now + + + align:start position:0% +question is written here is now +maintaining the lotteries write down the + + align:start position:0% +maintaining the lotteries write down the + + + align:start position:0% +maintaining the lotteries write down the +programming problem for the two periods + + align:start position:0% +programming problem for the two periods + + + align:start position:0% +programming problem for the two periods +dates one and two I'm not asking you to + + align:start position:0% +dates one and two I'm not asking you to + + + align:start position:0% +dates one and two I'm not asking you to +literally write it down but could + + align:start position:0% +literally write it down but could + + + align:start position:0% +literally write it down but could +someone volunteer to tell me about the + + align:start position:0% +someone volunteer to tell me about the + + + align:start position:0% +someone volunteer to tell me about the +truth-telling constraints at the final + + align:start position:0% +truth-telling constraints at the final + + + align:start position:0% +truth-telling constraints at the final +date two + + align:start position:0% +date two + + + align:start position:0% +date two +in words what they look like and then + + align:start position:0% +in words what they look like and then + + + align:start position:0% +in words what they look like and then +also in words what the truth only + + align:start position:0% +also in words what the truth only + + + align:start position:0% +also in words what the truth only +constrained at date one looks like + + align:start position:0% +constrained at date one looks like + + + align:start position:0% +constrained at date one looks like +I remember the true towering constraints + + align:start position:0% +I remember the true towering constraints + + + align:start position:0% +I remember the true towering constraints +at the final day or two is that no + + align:start position:0% +at the final day or two is that no + + + align:start position:0% +at the final day or two is that no +matter what you already announced at the + + align:start position:0% +matter what you already announced at the + + + align:start position:0% +matter what you already announced at the +data one + + align:start position:0% +data one + + + align:start position:0% +data one +um based on the FIFA went shoot how when + + align:start position:0% +um based on the FIFA went shoot how when + + + align:start position:0% +um based on the FIFA went shoot how when +you announced at the 801 you want to + + align:start position:0% +you announced at the 801 you want to + + + align:start position:0% +you announced at the 801 you want to +choose uh you the the true towering + + align:start position:0% +choose uh you the the true towering + + + align:start position:0% +choose uh you the the true towering +bring you the maximized utility + + align:start position:0% + + + + align:start position:0% + +function is like the utility at the data + + align:start position:0% +function is like the utility at the data + + + align:start position:0% +function is like the utility at the data +to + + align:start position:0% +to + + + align:start position:0% +to +is the + + align:start position:0% +is the + + + align:start position:0% +is the +you feed tattoo and feed her one tutor + + align:start position:0% +you feed tattoo and feed her one tutor + + + align:start position:0% +you feed tattoo and feed her one tutor +and what which modify the probability + + align:start position:0% +and what which modify the probability + + + align:start position:0% +and what which modify the probability +function the probability function was + + align:start position:0% +function the probability function was + + + align:start position:0% +function the probability function was +depending on whether you are + + align:start position:0% +depending on whether you are + + + align:start position:0% +depending on whether you are +announced in DP to one and then the + + align:start position:0% +announced in DP to one and then the + + + align:start position:0% +announced in DP to one and then the +whole function will be bigger than any + + align:start position:0% +whole function will be bigger than any + + + align:start position:0% +whole function will be bigger than any +announcement at the theater + + align:start position:0% +announcement at the theater + + + align:start position:0% +announcement at the theater +G yeah + + align:start position:0% +G yeah + + + align:start position:0% +G yeah +so okay + + align:start position:0% +so okay + + + align:start position:0% +so okay +uh and what about at date one he did a + + align:start position:0% +uh and what about at date one he did a + + + align:start position:0% +uh and what about at date one he did a +one is that you want to you do not only + + align:start position:0% +one is that you want to you do not only + + + align:start position:0% +one is that you want to you do not only +care about the + + align:start position:0% +care about the + + + align:start position:0% +care about the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the at this moment but you also care + + align:start position:0% +the at this moment but you also care + + + align:start position:0% +the at this moment but you also care +about the future I mean that uh for data + + align:start position:0% +about the future I mean that uh for data + + + align:start position:0% +about the future I mean that uh for data +one the maximize the utility of not + + align:start position:0% +one the maximize the utility of not + + + align:start position:0% +one the maximize the utility of not +mathematic the + + align:start position:0% +mathematic the + + + align:start position:0% +mathematic the +um you're telling the truth that bring + + align:start position:0% +um you're telling the truth that bring + + + align:start position:0% +um you're telling the truth that bring +you the utility which is larger than any + + align:start position:0% +you the utility which is larger than any + + + align:start position:0% +you the utility which is larger than any +feta one + + align:start position:0% +feta one + + + align:start position:0% +feta one +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +and what is it assuming about day two + + align:start position:0% +and what is it assuming about day two + + + align:start position:0% +and what is it assuming about day two +even though it's a date one constraint + + align:start position:0% + + + + align:start position:0% + +there's a few minutes that it + + align:start position:0% + + + + align:start position:0% + +the day two do not care about what yeah + + align:start position:0% + + + + align:start position:0% + +yeah you're very close so the point of + + align:start position:0% +yeah you're very close so the point of + + + align:start position:0% +yeah you're very close so the point of +working backwards at day two we get the + + align:start position:0% +working backwards at day two we get the + + + align:start position:0% +working backwards at day two we get the +truth telling constraint so the utility + + align:start position:0% +truth telling constraint so the utility + + + align:start position:0% +truth telling constraint so the utility +is greater for telling the truth than + + align:start position:0% +is greater for telling the truth than + + + align:start position:0% +is greater for telling the truth than +announcing something counterfactual + + align:start position:0% +announcing something counterfactual + + + align:start position:0% +announcing something counterfactual +that's now imposed as part of the + + align:start position:0% +that's now imposed as part of the + + + align:start position:0% +that's now imposed as part of the +solution as a constraint + + align:start position:0% +solution as a constraint + + + align:start position:0% +solution as a constraint +so working back to day one it assumes + + align:start position:0% +so working back to day one it assumes + + + align:start position:0% +so working back to day one it assumes +truth telling at day two + + align:start position:0% +truth telling at day two + + + align:start position:0% +truth telling at day two +so we we only have to worry about + + align:start position:0% +so we we only have to worry about + + + align:start position:0% +so we we only have to worry about +whether to be truthful at date one or + + align:start position:0% +whether to be truthful at date one or + + + align:start position:0% +whether to be truthful at date one or +or lie at day one + + align:start position:0% +or lie at day one + + + align:start position:0% +or lie at day one +um because whatever they do truth or lie + + align:start position:0% +um because whatever they do truth or lie + + + align:start position:0% +um because whatever they do truth or lie +at date one they will tell the truth at + + align:start position:0% +at date one they will tell the truth at + + + align:start position:0% +at date one they will tell the truth at +day two + + align:start position:0% +day two + + + align:start position:0% +day two +so related to all of this is the message + + align:start position:0% +so related to all of this is the message + + + align:start position:0% +so related to all of this is the message +the announcement at date one you said + + align:start position:0% +the announcement at date one you said + + + align:start position:0% +the announcement at date one you said +something not + + align:start position:0% +something not + + + align:start position:0% +something not +quite right but I may have heard it + + align:start position:0% +quite right but I may have heard it + + + align:start position:0% +quite right but I may have heard it +wrong there's a probability transition + + align:start position:0% +wrong there's a probability transition + + + align:start position:0% +wrong there's a probability transition +function + + align:start position:0% +function + + + align:start position:0% +function +that has to do with the probability of + + align:start position:0% +that has to do with the probability of + + + align:start position:0% +that has to do with the probability of +States at day two conditioned on dates + + align:start position:0% +States at day two conditioned on dates + + + align:start position:0% +States at day two conditioned on dates +at State one and that never changes + + align:start position:0% +at State one and that never changes + + + align:start position:0% +at State one and that never changes +that's just part of the environment + + align:start position:0% +that's just part of the environment + + + align:start position:0% +that's just part of the environment +what what changes the M tilde one that + + align:start position:0% +what what changes the M tilde one that + + + align:start position:0% +what what changes the M tilde one that +you mentioned + + align:start position:0% +you mentioned + + + align:start position:0% +you mentioned +is the message at date one depending on + + align:start position:0% +is the message at date one depending on + + + align:start position:0% +is the message at date one depending on +whether or not they told the truth + + align:start position:0% +whether or not they told the truth + + + align:start position:0% +whether or not they told the truth +uh so the last very last part of this + + align:start position:0% +uh so the last very last part of this + + + align:start position:0% +uh so the last very last part of this +review question + + align:start position:0% +review question + + + align:start position:0% +review question +asks uh + + align:start position:0% +asks uh + + + align:start position:0% +asks uh +to describe the way in which past + + align:start position:0% +to describe the way in which past + + + align:start position:0% +to describe the way in which past +history matters + + align:start position:0% +history matters + + + align:start position:0% +history matters +or contemporary outcomes + + align:start position:0% +or contemporary outcomes + + + align:start position:0% +or contemporary outcomes +the key is that + + align:start position:0% +the key is that + + + align:start position:0% +the key is that +is that a probability + + align:start position:0% +is that a probability + + + align:start position:0% +is that a probability +because if + + align:start position:0% +because if + + + align:start position:0% +because if +you're telling the whatever you tell at + + align:start position:0% +you're telling the whatever you tell at + + + align:start position:0% +you're telling the whatever you tell at +the data one that will that will decide + + align:start position:0% +the data one that will that will decide + + + align:start position:0% +the data one that will that will decide +the probability because the three + + align:start position:0% +the probability because the three + + + align:start position:0% +the probability because the three +probability was + + align:start position:0% +probability was + + + align:start position:0% +probability was +conditioning on what you are telling + + align:start position:0% +conditioning on what you are telling + + + align:start position:0% +conditioning on what you are telling +yeah what do you announce + + align:start position:0% +yeah what do you announce + + + align:start position:0% +yeah what do you announce +so no I don't think I have that lecture + + align:start position:0% +so no I don't think I have that lecture + + + align:start position:0% +so no I don't think I have that lecture +open anymore we'd have to go back and + + align:start position:0% +open anymore we'd have to go back and + + + align:start position:0% +open anymore we'd have to go back and +look at it uh + + align:start position:0% + + + + align:start position:0% + +no it's buried back deeper in them go + + align:start position:0% +no it's buried back deeper in them go + + + align:start position:0% +no it's buried back deeper in them go +back and look at the Markov process the + + align:start position:0% +back and look at the Markov process the + + + align:start position:0% +back and look at the Markov process the +probability P of theta 2 conditioned on + + align:start position:0% +probability P of theta 2 conditioned on + + + align:start position:0% +probability P of theta 2 conditioned on +Theta 1 there's never that part never + + align:start position:0% +Theta 1 there's never that part never + + + align:start position:0% +Theta 1 there's never that part never +changes oh + + align:start position:0% + + + + align:start position:0% + +okay okay yeah Lottery + + align:start position:0% +okay okay yeah Lottery + + + align:start position:0% +okay okay yeah Lottery +yeah they're both probabilities I + + align:start position:0% +yeah they're both probabilities I + + + align:start position:0% +yeah they're both probabilities I +understand yeah okay good thank you okay + + align:start position:0% +understand yeah okay good thank you okay + + + align:start position:0% +understand yeah okay good thank you okay +perfect okay and then relatedly there's + + align:start position:0% +perfect okay and then relatedly there's + + + align:start position:0% +perfect okay and then relatedly there's +this question right afterwards + + align:start position:0% +this question right afterwards + + + align:start position:0% +this question right afterwards +what does the solution to that + + align:start position:0% +what does the solution to that + + + align:start position:0% +what does the solution to that +two-period problem look like + + align:start position:0% +two-period problem look like + + + align:start position:0% +two-period problem look like +is it full insurance is it borrowing and + + align:start position:0% +is it full insurance is it borrowing and + + + align:start position:0% +is it full insurance is it borrowing and +lending + + align:start position:0% +lending + + + align:start position:0% +lending +and if it's not either one what what is + + align:start position:0% +and if it's not either one what what is + + + align:start position:0% +and if it's not either one what what is +the logic of why we know it can't be + + align:start position:0% +the logic of why we know it can't be + + + align:start position:0% +the logic of why we know it can't be +either + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +um take a step with this + + align:start position:0% + + + + align:start position:0% + +um but yeah so I remember that we said + + align:start position:0% +um but yeah so I remember that we said + + + align:start position:0% +um but yeah so I remember that we said +that the full insurance + + align:start position:0% +that the full insurance + + + align:start position:0% +that the full insurance +um wasn't optimal because if you had + + align:start position:0% +um wasn't optimal because if you had + + + align:start position:0% +um wasn't optimal because if you had +full insurance then it wouldn't be + + align:start position:0% +full insurance then it wouldn't be + + + align:start position:0% +full insurance then it wouldn't be +truth-telling + + align:start position:0% +truth-telling + + + align:start position:0% +truth-telling +um and so you would never be able to + + align:start position:0% +um and so you would never be able to + + + align:start position:0% +um and so you would never be able to +like reach like that optimal equilibrium + + align:start position:0% +like reach like that optimal equilibrium + + + align:start position:0% +like reach like that optimal equilibrium +there + + align:start position:0% +there + + + align:start position:0% +there +um for the borrowing and lending I + + align:start position:0% +um for the borrowing and lending I + + + align:start position:0% +um for the borrowing and lending I +remember we had some kind of argument + + align:start position:0% +remember we had some kind of argument + + + align:start position:0% +remember we had some kind of argument +where we said that the incentive + + align:start position:0% +where we said that the incentive + + + align:start position:0% +where we said that the incentive +constraints won't bind + + align:start position:0% +constraints won't bind + + + align:start position:0% +constraints won't bind +um and so because those didn't bind + + align:start position:0% +um and so because those didn't bind + + + align:start position:0% +um and so because those didn't bind +um it's equivalent to just not having + + align:start position:0% +um it's equivalent to just not having + + + align:start position:0% +um it's equivalent to just not having +the incentive constraints at all which + + align:start position:0% +the incentive constraints at all which + + + align:start position:0% +the incentive constraints at all which +means you might as well just do full + + align:start position:0% +means you might as well just do full + + + align:start position:0% +means you might as well just do full +risk sharing but we already showed that + + align:start position:0% +risk sharing but we already showed that + + + align:start position:0% +risk sharing but we already showed that +we couldn't do that but I don't think I + + align:start position:0% +we couldn't do that but I don't think I + + + align:start position:0% +we couldn't do that but I don't think I +quite Recall why the incentive + + align:start position:0% +quite Recall why the incentive + + + align:start position:0% +quite Recall why the incentive +constraints don't bind in the first + + align:start position:0% +constraints don't bind in the first + + + align:start position:0% +constraints don't bind in the first +place + + align:start position:0% +place + + + align:start position:0% +place +well it's a perfect answer thank you and + + align:start position:0% +well it's a perfect answer thank you and + + + align:start position:0% +well it's a perfect answer thank you and +to answer your question the presumption + + align:start position:0% +to answer your question the presumption + + + align:start position:0% +to answer your question the presumption +is somehow if your income is low you + + align:start position:0% +is somehow if your income is low you + + + align:start position:0% +is somehow if your income is low you +want to borrow and you strictly prefer + + align:start position:0% +want to borrow and you strictly prefer + + + align:start position:0% +want to borrow and you strictly prefer +that to Lending + + align:start position:0% +that to Lending + + + align:start position:0% +that to Lending +so that strict preference is a strict + + align:start position:0% +so that strict preference is a strict + + + align:start position:0% +so that strict preference is a strict +inequality in the constraint and hence + + align:start position:0% +inequality in the constraint and hence + + + align:start position:0% +inequality in the constraint and hence +not binding + + align:start position:0% +not binding + + + align:start position:0% +not binding +and likewise if your income is high you + + align:start position:0% +and likewise if your income is high you + + + align:start position:0% +and likewise if your income is high you +strictly prefer to lend rather than + + align:start position:0% +strictly prefer to lend rather than + + + align:start position:0% +strictly prefer to lend rather than +borrow + + align:start position:0% + + + + align:start position:0% + +it's okay yeah that makes sense thanks + + align:start position:0% +it's okay yeah that makes sense thanks + + + align:start position:0% +it's okay yeah that makes sense thanks +yep your answer was really good thank + + align:start position:0% +yep your answer was really good thank + + + align:start position:0% +yep your answer was really good thank +you + + align:start position:0% +you + + + align:start position:0% +you +okay so let's go to + + align:start position:0% +okay so let's go to + + + align:start position:0% +okay so let's go to +maybe one more thing here + + align:start position:0% +maybe one more thing here + + + align:start position:0% +maybe one more thing here +I did feel that I was rushing a bit + + align:start position:0% +I did feel that I was rushing a bit + + + align:start position:0% +I did feel that I was rushing a bit +toward the end of the lecture so I could + + align:start position:0% +toward the end of the lecture so I could + + + align:start position:0% +toward the end of the lecture so I could +I'm happy to take questions rather than + + align:start position:0% +I'm happy to take questions rather than + + + align:start position:0% +I'm happy to take questions rather than +going through these + + align:start position:0% +going through these + + + align:start position:0% +going through these +uh let's try a couple of them + + align:start position:0% +uh let's try a couple of them + + + align:start position:0% +uh let's try a couple of them +to get the conversation going I drew a + + align:start position:0% +to get the conversation going I drew a + + + align:start position:0% +to get the conversation going I drew a +distinction between encryption + + align:start position:0% +distinction between encryption + + + align:start position:0% +distinction between encryption +hashing and cryptographic puzzles does + + align:start position:0% +hashing and cryptographic puzzles does + + + align:start position:0% +hashing and cryptographic puzzles does +anyone remember yeah I think I think I + + align:start position:0% +anyone remember yeah I think I think I + + + align:start position:0% +anyone remember yeah I think I think I +know this one so encryption is where you + + align:start position:0% +know this one so encryption is where you + + + align:start position:0% +know this one so encryption is where you +have some specific secret key is shared + + align:start position:0% +have some specific secret key is shared + + + align:start position:0% +have some specific secret key is shared +between two parties and then you can use + + align:start position:0% +between two parties and then you can use + + + align:start position:0% +between two parties and then you can use +that key to encrypt a message and then + + align:start position:0% +that key to encrypt a message and then + + + align:start position:0% +that key to encrypt a message and then +decrypt it at the other end hashing is + + align:start position:0% +decrypt it at the other end hashing is + + + align:start position:0% +decrypt it at the other end hashing is +some sort of function that's hard that + + align:start position:0% +some sort of function that's hard that + + + align:start position:0% +some sort of function that's hard that +like it's changes pretty randomly + + align:start position:0% +like it's changes pretty randomly + + + align:start position:0% +like it's changes pretty randomly +depending on the input so it's a short + + align:start position:0% +depending on the input so it's a short + + + align:start position:0% +depending on the input so it's a short +it's a short thing that I encap that + + align:start position:0% +it's a short thing that I encap that + + + align:start position:0% +it's a short thing that I encap that +encapsulates the whole message and if + + align:start position:0% +encapsulates the whole message and if + + + align:start position:0% +encapsulates the whole message and if +you change the message + + align:start position:0% +you change the message + + + align:start position:0% +you change the message +um it was it's with you it's very hard + + align:start position:0% +um it was it's with you it's very hard + + + align:start position:0% +um it was it's with you it's very hard +to change a message to keep the same + + align:start position:0% +to change a message to keep the same + + + align:start position:0% +to change a message to keep the same +hash + + align:start position:0% +hash + + + align:start position:0% +hash +um a quick photographic puzzle I think + + align:start position:0% +um a quick photographic puzzle I think + + + align:start position:0% +um a quick photographic puzzle I think +some of you are just hard to do and like + + align:start position:0% +some of you are just hard to do and like + + + align:start position:0% +some of you are just hard to do and like +it's like known to be hard in some way + + align:start position:0% +it's like known to be hard in some way + + + align:start position:0% +it's like known to be hard in some way +and I think homomorphic cryption I think + + align:start position:0% +and I think homomorphic cryption I think + + + align:start position:0% +and I think homomorphic cryption I think +that's the one where you have to sort of + + align:start position:0% +that's the one where you have to sort of + + + align:start position:0% +that's the one where you have to sort of +basically what amounts of linear + + align:start position:0% +basically what amounts of linear + + + align:start position:0% +basically what amounts of linear +function so you're just like uh encrypt + + align:start position:0% +function so you're just like uh encrypt + + + align:start position:0% +function so you're just like uh encrypt +something + + align:start position:0% +something + + + align:start position:0% +something +um add together all the encrypted things + + align:start position:0% +um add together all the encrypted things + + + align:start position:0% +um add together all the encrypted things +so then you can decrypt the sum and then + + align:start position:0% +so then you can decrypt the sum and then + + + align:start position:0% +so then you can decrypt the sum and then +you can get the correct you can get the + + align:start position:0% +you can get the correct you can get the + + + align:start position:0% +you can get the correct you can get the +correct + + align:start position:0% +correct + + + align:start position:0% +correct +um decrypted sum without having to know + + align:start position:0% +um decrypted sum without having to know + + + align:start position:0% +um decrypted sum without having to know +any of the individual components or + + align:start position:0% +any of the individual components or + + + align:start position:0% +any of the individual components or +something like that very good excellent + + align:start position:0% +something like that very good excellent + + + align:start position:0% +something like that very good excellent +so I would just just a couple words of + + align:start position:0% +so I would just just a couple words of + + + align:start position:0% +so I would just just a couple words of +comment the encryption part it's private + + align:start position:0% +comment the encryption part it's private + + + align:start position:0% +comment the encryption part it's private +and public keys and the private keys are + + align:start position:0% +and public keys and the private keys are + + + align:start position:0% +and public keys and the private keys are +never shared it's the public key that's + + align:start position:0% +never shared it's the public key that's + + + align:start position:0% +never shared it's the public key that's +shared between the parties and it I + + align:start position:0% +shared between the parties and it I + + + align:start position:0% +shared between the parties and it I +think I'll talk about this I I just + + align:start position:0% +think I'll talk about this I I just + + + align:start position:0% +think I'll talk about this I I just +described symmetric encryption yeah I + + align:start position:0% +described symmetric encryption yeah I + + + align:start position:0% +described symmetric encryption yeah I +thought yeah but yeah it's also like + + align:start position:0% +thought yeah but yeah it's also like + + + align:start position:0% +thought yeah but yeah it's also like +private public + + align:start position:0% +private public + + + align:start position:0% +private public +okay you're you have the background for + + align:start position:0% +okay you're you have the background for + + + align:start position:0% +okay you're you have the background for +this okay excellent + + align:start position:0% +this okay excellent + + + align:start position:0% +this okay excellent +um + + align:start position:0% +um + + + align:start position:0% +um +yeah and hashing is what you said it's + + align:start position:0% +yeah and hashing is what you said it's + + + align:start position:0% +yeah and hashing is what you said it's +kind of a one-way function you know what + + align:start position:0% +kind of a one-way function you know what + + + align:start position:0% +kind of a one-way function you know what +goes in but you cannot interpret what + + align:start position:0% +goes in but you cannot interpret what + + + align:start position:0% +goes in but you cannot interpret what +goes out + + align:start position:0% +goes out + + + align:start position:0% +goes out +and the puzzles are fine + + align:start position:0% +and the puzzles are fine + + + align:start position:0% +and the puzzles are fine +and homomorphic encryption yeah is fine + + align:start position:0% +and homomorphic encryption yeah is fine + + + align:start position:0% +and homomorphic encryption yeah is fine +so thank you that's great + + align:start position:0% +so thank you that's great + + + align:start position:0% +so thank you that's great +um + + align:start position:0% +um + + + align:start position:0% +um +sounds like you might have known the + + align:start position:0% +sounds like you might have known the + + + align:start position:0% +sounds like you might have known the +answers to these things before the class + + align:start position:0% +answers to these things before the class + + + align:start position:0% +answers to these things before the class +but that's I mean from other work that + + align:start position:0% +but that's I mean from other work that + + + align:start position:0% +but that's I mean from other work that +you're doing but that's fine + + align:start position:0% +you're doing but that's fine + + + align:start position:0% +you're doing but that's fine +um + + align:start position:0% +um + + + align:start position:0% +um +let's see one last thing uh + + align:start position:0% +let's see one last thing uh + + + align:start position:0% +let's see one last thing uh +consensus protocol is a consensus + + align:start position:0% +consensus protocol is a consensus + + + align:start position:0% +consensus protocol is a consensus +protocol necessarily incentive + + align:start position:0% +protocol necessarily incentive + + + align:start position:0% +protocol necessarily incentive +compatible + + align:start position:0% +compatible + + + align:start position:0% +compatible +so this is like begging for a discussion + + align:start position:0% +so this is like begging for a discussion + + + align:start position:0% +so this is like begging for a discussion +of how computer science + + align:start position:0% +of how computer science + + + align:start position:0% +of how computer science +use the word trust and economics use the + + align:start position:0% +use the word trust and economics use the + + + align:start position:0% +use the word trust and economics use the +words Trust + + align:start position:0% +words Trust + + + align:start position:0% +words Trust +and again I'll just taking volunteers + + align:start position:0% +and again I'll just taking volunteers + + + align:start position:0% +and again I'll just taking volunteers +today + + align:start position:0% +today + + + align:start position:0% +today +yeah so that again + + align:start position:0% +yeah so that again + + + align:start position:0% +yeah so that again +lots of information on those slides this + + align:start position:0% +lots of information on those slides this + + + align:start position:0% +lots of information on those slides this +kind of appeared on one slide and I + + align:start position:0% +kind of appeared on one slide and I + + + align:start position:0% +kind of appeared on one slide and I +didn't belabor it + + align:start position:0% +didn't belabor it + + + align:start position:0% +didn't belabor it +the basic idea in computer science is + + align:start position:0% +the basic idea in computer science is + + + align:start position:0% +the basic idea in computer science is +that most nodes are trustworthy they're + + align:start position:0% +that most nodes are trustworthy they're + + + align:start position:0% +that most nodes are trustworthy they're +going to follow the protocol + + align:start position:0% +going to follow the protocol + + + align:start position:0% +going to follow the protocol +but a handful of nodes or actors are + + align:start position:0% +but a handful of nodes or actors are + + + align:start position:0% +but a handful of nodes or actors are +either faulty in the sense that the + + align:start position:0% +either faulty in the sense that the + + + align:start position:0% +either faulty in the sense that the +computer doesn't work well or nefarious + + align:start position:0% +computer doesn't work well or nefarious + + + align:start position:0% +computer doesn't work well or nefarious +in the sense that they're determined to + + align:start position:0% +in the sense that they're determined to + + + align:start position:0% +in the sense that they're determined to +undercut the system + + align:start position:0% +undercut the system + + + align:start position:0% +undercut the system +so the basic premise is most nodes are + + align:start position:0% +so the basic premise is most nodes are + + + align:start position:0% +so the basic premise is most nodes are +honest in the sense that they're going + + align:start position:0% +honest in the sense that they're going + + + align:start position:0% +honest in the sense that they're going +to follow the uh the excuse me the + + align:start position:0% +to follow the uh the excuse me the + + + align:start position:0% +to follow the uh the excuse me the +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +in economics you know it's a dismal + + align:start position:0% +in economics you know it's a dismal + + + align:start position:0% +in economics you know it's a dismal +science we don't trust anybody + + align:start position:0% +science we don't trust anybody + + + align:start position:0% +science we don't trust anybody +so uh everyone on the other hand can be + + align:start position:0% +so uh everyone on the other hand can be + + + align:start position:0% +so uh everyone on the other hand can be +given incentives so we assume maximizing + + align:start position:0% +given incentives so we assume maximizing + + + align:start position:0% +given incentives so we assume maximizing +utility or profit maximizing behavior + + align:start position:0% +utility or profit maximizing behavior + + + align:start position:0% +utility or profit maximizing behavior +and then we load things up in a way that + + align:start position:0% +and then we load things up in a way that + + + align:start position:0% +and then we load things up in a way that +even though there are secrets + + align:start position:0% +even though there are secrets + + + align:start position:0% +even though there are secrets +like preference shocks or unobserved + + align:start position:0% +like preference shocks or unobserved + + + align:start position:0% +like preference shocks or unobserved +states and so on the actors have an + + align:start position:0% +states and so on the actors have an + + + align:start position:0% +states and so on the actors have an +incentive to reveal + + align:start position:0% +incentive to reveal + + + align:start position:0% +incentive to reveal +what they what what those states are so + + align:start position:0% +what they what what those states are so + + + align:start position:0% +what they what what those states are so +the messages as in mechanism design + + align:start position:0% +the messages as in mechanism design + + + align:start position:0% +the messages as in mechanism design +that we did earlier in the lecture + + align:start position:0% +that we did earlier in the lecture + + + align:start position:0% +that we did earlier in the lecture +uh are are part of the contract and + + align:start position:0% +uh are are part of the contract and + + + align:start position:0% +uh are are part of the contract and +they're going to be sent honestly + + align:start position:0% +they're going to be sent honestly + + + align:start position:0% +they're going to be sent honestly +but it's due to the incentive + + align:start position:0% +but it's due to the incentive + + + align:start position:0% +but it's due to the incentive +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +and without the incentive constraints we + + align:start position:0% +and without the incentive constraints we + + + align:start position:0% +and without the incentive constraints we +kind of assume everyone's going to cheat + + align:start position:0% +kind of assume everyone's going to cheat + + + align:start position:0% +kind of assume everyone's going to cheat +so it is it is kind of a philosophical + + align:start position:0% +so it is it is kind of a philosophical + + + align:start position:0% +so it is it is kind of a philosophical +difference + + align:start position:0% +difference + + + align:start position:0% +difference +anyway that's why in the lecture I put + + align:start position:0% +anyway that's why in the lecture I put + + + align:start position:0% +anyway that's why in the lecture I put +uh the discussion of Bitcoin and other + + align:start position:0% +uh the discussion of Bitcoin and other + + + align:start position:0% +uh the discussion of Bitcoin and other +algorithms in the context of mechanism + + align:start position:0% +algorithms in the context of mechanism + + + align:start position:0% +algorithms in the context of mechanism +design to draw this contrast + + align:start position:0% + + + + align:start position:0% + +okay so that's + + align:start position:0% +okay so that's + + + align:start position:0% +okay so that's +the review sheet and + + align:start position:0% +the review sheet and + + + align:start position:0% +the review sheet and +let's get to + + align:start position:0% +let's get to + + + align:start position:0% +let's get to +a little lecture here + + align:start position:0% + + + + align:start position:0% + +okay so today part two + + align:start position:0% +okay so today part two + + + align:start position:0% +okay so today part two +more on contracts + + align:start position:0% +more on contracts + + + align:start position:0% +more on contracts +so the application is going to be + + align:start position:0% +so the application is going to be + + + align:start position:0% +so the application is going to be +financial markets and we're going to try + + align:start position:0% +financial markets and we're going to try + + + align:start position:0% +financial markets and we're going to try +to figure out what kind of contracts + + align:start position:0% +to figure out what kind of contracts + + + align:start position:0% +to figure out what kind of contracts +a small business would write with a + + align:start position:0% +a small business would write with a + + + align:start position:0% +a small business would write with a +lender in particular what the underlying + + align:start position:0% +lender in particular what the underlying + + + align:start position:0% +lender in particular what the underlying +obstacles to trade are we're going to + + align:start position:0% +obstacles to trade are we're going to + + + align:start position:0% +obstacles to trade are we're going to +want to identify from data using the + + align:start position:0% +want to identify from data using the + + + align:start position:0% +want to identify from data using the +theory what those obstacles are + + align:start position:0% +theory what those obstacles are + + + align:start position:0% +theory what those obstacles are +that limit the ability to go into + + align:start position:0% +that limit the ability to go into + + + align:start position:0% +that limit the ability to go into +business or limit the ability to finance + + align:start position:0% +business or limit the ability to finance + + + align:start position:0% +business or limit the ability to finance +the business once you're already in + + align:start position:0% +the business once you're already in + + + align:start position:0% +the business once you're already in +business + + align:start position:0% +business + + + align:start position:0% +business +so that's the economics part of it the + + align:start position:0% +so that's the economics part of it the + + + align:start position:0% +so that's the economics part of it the +technique part of it is we're going to + + align:start position:0% +technique part of it is we're going to + + + align:start position:0% +technique part of it is we're going to +do a structural estimation of the model + + align:start position:0% +do a structural estimation of the model + + + align:start position:0% +do a structural estimation of the model +but we will also look at some reduced + + align:start position:0% +but we will also look at some reduced + + + align:start position:0% +but we will also look at some reduced +form techniques that are data summaries + + align:start position:0% +form techniques that are data summaries + + + align:start position:0% +form techniques that are data summaries +that are consistent with the structural + + align:start position:0% +that are consistent with the structural + + + align:start position:0% +that are consistent with the structural +model essentially we use reuse form + + align:start position:0% +model essentially we use reuse form + + + align:start position:0% +model essentially we use reuse form +techniques to identify stylized facts + + align:start position:0% +techniques to identify stylized facts + + + align:start position:0% +techniques to identify stylized facts +different across different regions and + + align:start position:0% +different across different regions and + + + align:start position:0% +different across different regions and +then we use the theory to try to make + + align:start position:0% +then we use the theory to try to make + + + align:start position:0% +then we use the theory to try to make +sense of what we're seeing as kind of an + + align:start position:0% +sense of what we're seeing as kind of an + + + align:start position:0% +sense of what we're seeing as kind of an +experimental laboratory and they're + + align:start position:0% +experimental laboratory and they're + + + align:start position:0% +experimental laboratory and they're +going to be two sources of constraints + + align:start position:0% +going to be two sources of constraints + + + align:start position:0% +going to be two sources of constraints +so one is for sure a collateral + + align:start position:0% +so one is for sure a collateral + + + align:start position:0% +so one is for sure a collateral +constraint agents can borrow but + + align:start position:0% +constraint agents can borrow but + + + align:start position:0% +constraint agents can borrow but +potentially not much in order to borrow + + align:start position:0% +potentially not much in order to borrow + + + align:start position:0% +potentially not much in order to borrow +they have to post collateral so that the + + align:start position:0% +they have to post collateral so that the + + + align:start position:0% +they have to post collateral so that the +amount they can borrow is limited by + + align:start position:0% +amount they can borrow is limited by + + + align:start position:0% +amount they can borrow is limited by +their wealth + + align:start position:0% +their wealth + + + align:start position:0% +their wealth +that means low wealth households may not + + align:start position:0% +that means low wealth households may not + + + align:start position:0% +that means low wealth households may not +borrow very much and it may not make + + align:start position:0% +borrow very much and it may not make + + + align:start position:0% +borrow very much and it may not make +sense to go into a business at all + + align:start position:0% +sense to go into a business at all + + + align:start position:0% +sense to go into a business at all +because they can only operate it at a + + align:start position:0% +because they can only operate it at a + + + align:start position:0% +because they can only operate it at a +very small scale or if they do go into + + align:start position:0% +very small scale or if they do go into + + + align:start position:0% +very small scale or if they do go into +business because it's the best + + align:start position:0% +business because it's the best + + + align:start position:0% +business because it's the best +alternative notwithstanding they are not + + align:start position:0% +alternative notwithstanding they are not + + + align:start position:0% +alternative notwithstanding they are not +investing very much because of that + + align:start position:0% +investing very much because of that + + + align:start position:0% +investing very much because of that +collateral constraint now when there's a + + align:start position:0% +collateral constraint now when there's a + + + align:start position:0% +collateral constraint now when there's a +collateral constraint that's binding the + + align:start position:0% +collateral constraint that's binding the + + + align:start position:0% +collateral constraint that's binding the +borrowing is a proportion of wealth + + align:start position:0% +borrowing is a proportion of wealth + + + align:start position:0% +borrowing is a proportion of wealth +so if you're thinking about going across + + align:start position:0% +so if you're thinking about going across + + + align:start position:0% +so if you're thinking about going across +different firms in the cross section + + align:start position:0% +different firms in the cross section + + + align:start position:0% +different firms in the cross section +as net worth increases borrowing would + + align:start position:0% +as net worth increases borrowing would + + + align:start position:0% +as net worth increases borrowing would +increase or again for constrained + + align:start position:0% +increase or again for constrained + + + align:start position:0% +increase or again for constrained +entrepreneurs + + align:start position:0% +entrepreneurs + + + align:start position:0% +entrepreneurs +on the other hand it doesn't necessarily + + align:start position:0% +on the other hand it doesn't necessarily + + + align:start position:0% +on the other hand it doesn't necessarily +mean that with this collateral + + align:start position:0% +mean that with this collateral + + + align:start position:0% +mean that with this collateral +constraint everyone's going to be + + align:start position:0% +constraint everyone's going to be + + + align:start position:0% +constraint everyone's going to be +borrowing they may have enough wealth to + + align:start position:0% +borrowing they may have enough wealth to + + + align:start position:0% +borrowing they may have enough wealth to +entirely self-finance or they uh the + + align:start position:0% +entirely self-finance or they uh the + + + align:start position:0% +entirely self-finance or they uh the +borrowing constraint isn't binding in + + align:start position:0% +borrowing constraint isn't binding in + + + align:start position:0% +borrowing constraint isn't binding in +the sense that they don't go up to the + + align:start position:0% +the sense that they don't go up to the + + + align:start position:0% +the sense that they don't go up to the +Limit they have some wealth they borrow + + align:start position:0% +Limit they have some wealth they borrow + + + align:start position:0% +Limit they have some wealth they borrow +additional resources but they could have + + align:start position:0% +additional resources but they could have + + + align:start position:0% +additional resources but they could have +borrowed more and they don't do it on + + align:start position:0% +borrowed more and they don't do it on + + + align:start position:0% +borrowed more and they don't do it on +the other hand a different constraint is + + align:start position:0% +the other hand a different constraint is + + + align:start position:0% +the other hand a different constraint is +a moral hazard now moral hazard means + + align:start position:0% +a moral hazard now moral hazard means + + + align:start position:0% +a moral hazard now moral hazard means +that so funny terminology it's like you + + align:start position:0% +that so funny terminology it's like you + + + align:start position:0% +that so funny terminology it's like you +buy an insurance policy + + align:start position:0% +buy an insurance policy + + + align:start position:0% +buy an insurance policy +uh that's supposed to pay off if you + + align:start position:0% +uh that's supposed to pay off if you + + + align:start position:0% +uh that's supposed to pay off if you +know your house burns down but because + + align:start position:0% +know your house burns down but because + + + align:start position:0% +know your house burns down but because +you're insured and you don't pay + + align:start position:0% +you're insured and you don't pay + + + align:start position:0% +you're insured and you don't pay +attention and take the appropriate + + align:start position:0% +attention and take the appropriate + + + align:start position:0% +attention and take the appropriate +precautionary measures + + align:start position:0% +precautionary measures + + + align:start position:0% +precautionary measures +so so the house is likely to burn down + + align:start position:0% +so so the house is likely to burn down + + + align:start position:0% +so so the house is likely to burn down +for some reason in the insurance + + align:start position:0% +for some reason in the insurance + + + align:start position:0% +for some reason in the insurance +industry this is referred to as moral + + align:start position:0% +industry this is referred to as moral + + + align:start position:0% +industry this is referred to as moral +hazard as if it were quote immoral but + + align:start position:0% +hazard as if it were quote immoral but + + + align:start position:0% +hazard as if it were quote immoral but +again from our sort of business science + + align:start position:0% +again from our sort of business science + + + align:start position:0% +again from our sort of business science +economics point of review it's not + + align:start position:0% +economics point of review it's not + + + align:start position:0% +economics point of review it's not +immoral per se it's just that didn't + + align:start position:0% +immoral per se it's just that didn't + + + align:start position:0% +immoral per se it's just that didn't +have the right incentives okay and in + + align:start position:0% +have the right incentives okay and in + + + align:start position:0% +have the right incentives okay and in +this moral hazard World effort diligence + + align:start position:0% +this moral hazard World effort diligence + + + align:start position:0% +this moral hazard World effort diligence +taking care is not observed so the only + + align:start position:0% +taking care is not observed so the only + + + align:start position:0% +taking care is not observed so the only +way the land the insurance company or + + align:start position:0% +way the land the insurance company or + + + align:start position:0% +way the land the insurance company or +the lender can get the money back is + + align:start position:0% +the lender can get the money back is + + + align:start position:0% +the lender can get the money back is +when there's not an adverse event or the + + align:start position:0% +when there's not an adverse event or the + + + align:start position:0% +when there's not an adverse event or the +firm is successful in making profit now + + align:start position:0% +firm is successful in making profit now + + + align:start position:0% +firm is successful in making profit now +that means that poor borrowers who owe a + + align:start position:0% +that means that poor borrowers who owe a + + + align:start position:0% +that means that poor borrowers who owe a +lot of money are don't have an incentive + + align:start position:0% +lot of money are don't have an incentive + + + align:start position:0% +lot of money are don't have an incentive +to work very hard at being diligent + + align:start position:0% +to work very hard at being diligent + + + align:start position:0% +to work very hard at being diligent +because they're going to pay the bulk of + + align:start position:0% +because they're going to pay the bulk of + + + align:start position:0% +because they're going to pay the bulk of +their returns back if they're successful + + align:start position:0% +their returns back if they're successful + + + align:start position:0% +their returns back if they're successful +to the bank or to the insurance company + + align:start position:0% +to the bank or to the insurance company + + + align:start position:0% +to the bank or to the insurance company +so they don't take care and the + + align:start position:0% +so they don't take care and the + + + align:start position:0% +so they don't take care and the +probability of failure is high it's a + + align:start position:0% +probability of failure is high it's a + + + align:start position:0% +probability of failure is high it's a +constraint because the probability of + + align:start position:0% +constraint because the probability of + + + align:start position:0% +constraint because the probability of +failure could be high especially for low + + align:start position:0% +failure could be high especially for low + + + align:start position:0% +failure could be high especially for low +wealth agents + + align:start position:0% +wealth agents + + + align:start position:0% +wealth agents +the banks in order to break even on + + align:start position:0% +the banks in order to break even on + + + align:start position:0% +the banks in order to break even on +those loans have to charge High interest + + align:start position:0% +those loans have to charge High interest + + + align:start position:0% +those loans have to charge High interest +rates and in fact the rate could be so + + align:start position:0% +rates and in fact the rate could be so + + + align:start position:0% +rates and in fact the rate could be so +high would be high enough for the lender + + align:start position:0% +high would be high enough for the lender + + + align:start position:0% +high would be high enough for the lender +to break even but the borrower is no + + align:start position:0% +to break even but the borrower is no + + + align:start position:0% +to break even but the borrower is no +longer interested because it's just too + + align:start position:0% +longer interested because it's just too + + + align:start position:0% +longer interested because it's just too +too high of a rate + + align:start position:0% +too high of a rate + + + align:start position:0% +too high of a rate +and uh and likewise High rates they may + + align:start position:0% +and uh and likewise High rates they may + + + align:start position:0% +and uh and likewise High rates they may +not want to borrow very much even if + + align:start position:0% +not want to borrow very much even if + + + align:start position:0% +not want to borrow very much even if +they do go into business another + + align:start position:0% +they do go into business another + + + align:start position:0% +they do go into business another +difference with the collateral + + align:start position:0% +difference with the collateral + + + align:start position:0% +difference with the collateral +constraint is in the moral hazard world + + align:start position:0% +constraint is in the moral hazard world + + + align:start position:0% +constraint is in the moral hazard world +uh the incentive constraint is always + + align:start position:0% +uh the incentive constraint is always + + + align:start position:0% +uh the incentive constraint is always +binding + + align:start position:0% +binding + + + align:start position:0% +binding +that's a version of what we were just + + align:start position:0% +that's a version of what we were just + + + align:start position:0% +that's a version of what we were just +discussing full insurance is never + + align:start position:0% +discussing full insurance is never + + + align:start position:0% +discussing full insurance is never +optimal because Under full insurance you + + align:start position:0% +optimal because Under full insurance you + + + align:start position:0% +optimal because Under full insurance you +exert minimal effort so you don't offer + + align:start position:0% +exert minimal effort so you don't offer + + + align:start position:0% +exert minimal effort so you don't offer +full insurance + + align:start position:0% +full insurance + + + align:start position:0% +full insurance +but likewise then effort is lower than + + align:start position:0% +but likewise then effort is lower than + + + align:start position:0% +but likewise then effort is lower than +it would have been in a full information + + align:start position:0% +it would have been in a full information + + + align:start position:0% +it would have been in a full information +world so the incentive constraint to be + + align:start position:0% +world so the incentive constraint to be + + + align:start position:0% +world so the incentive constraint to be +diligent is always binding and the way + + align:start position:0% +diligent is always binding and the way + + + align:start position:0% +diligent is always binding and the way +out of that problem if in a + + align:start position:0% +out of that problem if in a + + + align:start position:0% +out of that problem if in a +cross-section entrepreneurs have more + + align:start position:0% +cross-section entrepreneurs have more + + + align:start position:0% +cross-section entrepreneurs have more +and more wealth comparing one to the + + align:start position:0% +and more wealth comparing one to the + + + align:start position:0% +and more wealth comparing one to the +other then they can self-finance more + + align:start position:0% +other then they can self-finance more + + + align:start position:0% +other then they can self-finance more +and the more you self-finance the less + + align:start position:0% +and the more you self-finance the less + + + align:start position:0% +and the more you self-finance the less +you have to pay back + + align:start position:0% +you have to pay back + + + align:start position:0% +you have to pay back +so in this case as wealth goes up + + align:start position:0% +so in this case as wealth goes up + + + align:start position:0% +so in this case as wealth goes up +borrowing goes down that's exactly the + + align:start position:0% +borrowing goes down that's exactly the + + + align:start position:0% +borrowing goes down that's exactly the +opposite from what we got in the limited + + align:start position:0% +opposite from what we got in the limited + + + align:start position:0% +opposite from what we got in the limited +liability case for constrained + + align:start position:0% +liability case for constrained + + + align:start position:0% +liability case for constrained +entrepreneurs when wealth went up + + align:start position:0% +entrepreneurs when wealth went up + + + align:start position:0% +entrepreneurs when wealth went up +borrowing went up so I alluded to these + + align:start position:0% +borrowing went up so I alluded to these + + + align:start position:0% +borrowing went up so I alluded to these +reduced form statistics we will see + + align:start position:0% +reduced form statistics we will see + + + align:start position:0% +reduced form statistics we will see +again at some point a summary of the + + align:start position:0% +again at some point a summary of the + + + align:start position:0% +again at some point a summary of the +data that that depending on the region + + align:start position:0% +data that that depending on the region + + + align:start position:0% +data that that depending on the region +that they're in you we will see either + + align:start position:0% +that they're in you we will see either + + + align:start position:0% +that they're in you we will see either +this one result in the cross-section or + + align:start position:0% +this one result in the cross-section or + + + align:start position:0% +this one result in the cross-section or +the other one and yeah the goal then is + + align:start position:0% +the other one and yeah the goal then is + + + align:start position:0% +the other one and yeah the goal then is +to take the full-blown model and do + + align:start position:0% +to take the full-blown model and do + + + align:start position:0% +to take the full-blown model and do +structural estimates to determine which + + align:start position:0% +structural estimates to determine which + + + align:start position:0% +structural estimates to determine which +constraint is binding it could be one it + + align:start position:0% +constraint is binding it could be one it + + + align:start position:0% +constraint is binding it could be one it +could be the other actually technically + + align:start position:0% +could be the other actually technically + + + align:start position:0% +could be the other actually technically +it could be both + + align:start position:0% +it could be both + + + align:start position:0% +it could be both +and I'm going to show you that once we + + align:start position:0% +and I'm going to show you that once we + + + align:start position:0% +and I'm going to show you that once we +review the tools we already have pending + + align:start position:0% +review the tools we already have pending + + + align:start position:0% +review the tools we already have pending +on the appropriate constraints it's + + align:start position:0% +on the appropriate constraints it's + + + align:start position:0% +on the appropriate constraints it's +actually easy to test one versus the + + align:start position:0% +actually easy to test one versus the + + + align:start position:0% +actually easy to test one versus the +other versus multiple It's relatively + + align:start position:0% +other versus multiple It's relatively + + + align:start position:0% +other versus multiple It's relatively +easy to do but we are learning some of + + align:start position:0% +easy to do but we are learning some of + + + align:start position:0% +easy to do but we are learning some of +those new tools today that's half of the + + align:start position:0% +those new tools today that's half of the + + + align:start position:0% +those new tools today that's half of the +point of the lecture so I've made + + align:start position:0% +point of the lecture so I've made + + + align:start position:0% +point of the lecture so I've made +reference to twice two differences + + align:start position:0% +reference to twice two differences + + + align:start position:0% +reference to twice two differences +across regions I think I may have shown + + align:start position:0% +across regions I think I may have shown + + + align:start position:0% +across regions I think I may have shown +you this picture before but I'm not sure + + align:start position:0% +you this picture before but I'm not sure + + + align:start position:0% +you this picture before but I'm not sure +we certainly looked at the Thai data we + + align:start position:0% +we certainly looked at the Thai data we + + + align:start position:0% +we certainly looked at the Thai data we +looked at the monthly data + + align:start position:0% +looked at the monthly data + + + align:start position:0% +looked at the monthly data +when we did risk and return in Village + + align:start position:0% +when we did risk and return in Village + + + align:start position:0% +when we did risk and return in Village +Thailand which was the second + + align:start position:0% +Thailand which was the second + + + align:start position:0% +Thailand which was the second +application of the resharing sections so + + align:start position:0% +application of the resharing sections so + + + align:start position:0% +application of the resharing sections so +anyway bangkok's over here this is + + align:start position:0% +anyway bangkok's over here this is + + + align:start position:0% +anyway bangkok's over here this is +central region these yellow provinces + + align:start position:0% +central region these yellow provinces + + + align:start position:0% +central region these yellow provinces +were ones that I had surveyed in annual + + align:start position:0% +were ones that I had surveyed in annual + + + align:start position:0% +were ones that I had surveyed in annual +data since 1997 and over here in the + + align:start position:0% +data since 1997 and over here in the + + + align:start position:0% +data since 1997 and over here in the +East but they call it the Northeast we + + align:start position:0% +East but they call it the Northeast we + + + align:start position:0% +East but they call it the Northeast we +have two other provinces that are these + + align:start position:0% +have two other provinces that are these + + + align:start position:0% +have two other provinces that are these +are predominantly rural agricultural the + + align:start position:0% +are predominantly rural agricultural the + + + align:start position:0% +are predominantly rural agricultural the +ones near Bangkok are much more + + align:start position:0% +ones near Bangkok are much more + + + align:start position:0% +ones near Bangkok are much more +industrialized + + align:start position:0% +industrialized + + + align:start position:0% +industrialized +and here's a map of sisa cat just to + + align:start position:0% +and here's a map of sisa cat just to + + + align:start position:0% +and here's a map of sisa cat just to +show you where the data are coming from + + align:start position:0% +show you where the data are coming from + + + align:start position:0% +show you where the data are coming from +we've got a lot of little Villages here + + align:start position:0% +we've got a lot of little Villages here + + + align:start position:0% +we've got a lot of little Villages here +these little dots as well as parts of + + align:start position:0% +these little dots as well as parts of + + + align:start position:0% +these little dots as well as parts of +the road Network and then the colored + + align:start position:0% +the road Network and then the colored + + + align:start position:0% +the road Network and then the colored +circles correspond to uh if they're + + align:start position:0% +circles correspond to uh if they're + + + align:start position:0% +circles correspond to uh if they're +purple you know these clusters are where + + align:start position:0% +purple you know these clusters are where + + + align:start position:0% +purple you know these clusters are where +we gather the annual data that we're + + align:start position:0% +we gather the annual data that we're + + + align:start position:0% +we gather the annual data that we're +going to be using today + + align:start position:0% +going to be using today + + + align:start position:0% +going to be using today +in the previous lectures risk and return + + align:start position:0% +in the previous lectures risk and return + + + align:start position:0% +in the previous lectures risk and return +in Village Thailand we were using the + + align:start position:0% +in Village Thailand we were using the + + + align:start position:0% +in Village Thailand we were using the +monthly data and those are stars and if + + align:start position:0% +monthly data and those are stars and if + + + align:start position:0% +monthly data and those are stars and if +you you know look really closely you'll + + align:start position:0% +you you know look really closely you'll + + + align:start position:0% +you you know look really closely you'll +eventually find a cluster uh with the + + align:start position:0% +eventually find a cluster uh with the + + + align:start position:0% +eventually find a cluster uh with the +Stars that correspond to the monthly + + align:start position:0% +Stars that correspond to the monthly + + + align:start position:0% +Stars that correspond to the monthly +data the annual data are spread out you + + align:start position:0% +data the annual data are spread out you + + + align:start position:0% +data the annual data are spread out you +know much more those stars are up here + + align:start position:0% +know much more those stars are up here + + + align:start position:0% +know much more those stars are up here +they're just not visible + + align:start position:0% +they're just not visible + + + align:start position:0% +they're just not visible +I know these provinces like the back of + + align:start position:0% +I know these provinces like the back of + + + align:start position:0% +I know these provinces like the back of +my hand because I've been there so often + + align:start position:0% +my hand because I've been there so often + + + align:start position:0% +my hand because I've been there so often +okay so again Thai data 1997 + + align:start position:0% +okay so again Thai data 1997 + + + align:start position:0% +okay so again Thai data 1997 +onwards almost 3 000 households they're + + align:start position:0% +onwards almost 3 000 households they're + + + align:start position:0% +onwards almost 3 000 households they're +running their businesses as you know + + align:start position:0% +running their businesses as you know + + + align:start position:0% +running their businesses as you know +livestock fish shrimp farm and small + + align:start position:0% +livestock fish shrimp farm and small + + + align:start position:0% +livestock fish shrimp farm and small +business like vendors and we have those + + align:start position:0% +business like vendors and we have those + + + align:start position:0% +business like vendors and we have those +two regions of the country the cool + + align:start position:0% +two regions of the country the cool + + + align:start position:0% +two regions of the country the cool +thing is that in 1997 we had the + + align:start position:0% +thing is that in 1997 we had the + + + align:start position:0% +thing is that in 1997 we had the +foresight to ask about some of the + + align:start position:0% +foresight to ask about some of the + + + align:start position:0% +foresight to ask about some of the +things that had happened in the last + + align:start position:0% +things that had happened in the last + + + align:start position:0% +things that had happened in the last +five years so we have their wealth + + align:start position:0% +five years so we have their wealth + + + align:start position:0% +five years so we have their wealth +retrospectively what it was five years + + align:start position:0% +retrospectively what it was five years + + + align:start position:0% +retrospectively what it was five years +ago before 1997 and also what kind of + + align:start position:0% +ago before 1997 and also what kind of + + + align:start position:0% +ago before 1997 and also what kind of +occupation they were engaged in five + + align:start position:0% +occupation they were engaged in five + + + align:start position:0% +occupation they were engaged in five +years before 1997. so that those are two + + align:start position:0% +years before 1997. so that those are two + + + align:start position:0% +years before 1997. so that those are two +of the key variables namely how much + + align:start position:0% +of the key variables namely how much + + + align:start position:0% +of the key variables namely how much +wealth did you have in 1992 and what + + align:start position:0% +wealth did you have in 1992 and what + + + align:start position:0% +wealth did you have in 1992 and what +business were you in in 1992 and then + + align:start position:0% +business were you in in 1992 and then + + + align:start position:0% +business were you in in 1992 and then +did you change your occupation say going + + align:start position:0% +did you change your occupation say going + + + align:start position:0% +did you change your occupation say going +from being a wage earner to going into + + align:start position:0% +from being a wage earner to going into + + + align:start position:0% +from being a wage earner to going into +business over those five-year periods + + align:start position:0% +business over those five-year periods + + + align:start position:0% +business over those five-year periods +and again we're going to find the bottom + + align:start position:0% +and again we're going to find the bottom + + + align:start position:0% +and again we're going to find the bottom +line is the data on wealth and + + align:start position:0% +line is the data on wealth and + + + align:start position:0% +line is the data on wealth and +occupation transitions as well as the + + align:start position:0% +occupation transitions as well as the + + + align:start position:0% +occupation transitions as well as the +cross-sectional data it's going to favor + + align:start position:0% +cross-sectional data it's going to favor + + + align:start position:0% +cross-sectional data it's going to favor +moral hazard as being in the constrained + + align:start position:0% +moral hazard as being in the constrained + + + align:start position:0% +moral hazard as being in the constrained +in the wealthier central region and in + + align:start position:0% +in the wealthier central region and in + + + align:start position:0% +in the wealthier central region and in +the Northeast it's going to be that + + align:start position:0% +the Northeast it's going to be that + + + align:start position:0% +the Northeast it's going to be that +limited liability although frequently + + align:start position:0% +limited liability although frequently + + + align:start position:0% +limited liability although frequently +both limited liability and moral hazard + + align:start position:0% +both limited liability and moral hazard + + + align:start position:0% +both limited liability and moral hazard +in combination + + align:start position:0% +in combination + + + align:start position:0% +in combination +so hopefully you're wondering how on + + align:start position:0% +so hopefully you're wondering how on + + + align:start position:0% +so hopefully you're wondering how on +Earth we could ever figure this all out + + align:start position:0% +Earth we could ever figure this all out + + + align:start position:0% +Earth we could ever figure this all out +here by the way is the picture of + + align:start position:0% +here by the way is the picture of + + + align:start position:0% +here by the way is the picture of +increasing wealth and increasing + + align:start position:0% +increasing wealth and increasing + + + align:start position:0% +increasing wealth and increasing +probability of making a transition into + + align:start position:0% +probability of making a transition into + + + align:start position:0% +probability of making a transition into +business so the this line here is upward + + align:start position:0% +business so the this line here is upward + + + align:start position:0% +business so the this line here is upward +sloping the higher the wealth the higher + + align:start position:0% +sloping the higher the wealth the higher + + + align:start position:0% +sloping the higher the wealth the higher +the transition but you know this could + + align:start position:0% +the transition but you know this could + + + align:start position:0% +the transition but you know this could +in theory be a very steep profile or a + + align:start position:0% +in theory be a very steep profile or a + + + align:start position:0% +in theory be a very steep profile or a +very flat one + + align:start position:0% +very flat one + + + align:start position:0% +very flat one +so part of it is estimating the profile + + align:start position:0% +so part of it is estimating the profile + + + align:start position:0% +so part of it is estimating the profile +suggested by the theory and then + + align:start position:0% +suggested by the theory and then + + + align:start position:0% +suggested by the theory and then +comparing it to the actual data here's + + align:start position:0% +comparing it to the actual data here's + + + align:start position:0% +comparing it to the actual data here's +the model so agents all these + + align:start position:0% +the model so agents all these + + + align:start position:0% +the model so agents all these +ingredients should be very familiar by + + align:start position:0% +ingredients should be very familiar by + + + align:start position:0% +ingredients should be very familiar by +now you've seen them at least twice and + + align:start position:0% +now you've seen them at least twice and + + + align:start position:0% +now you've seen them at least twice and +maybe more household that could run a + + align:start position:0% +maybe more household that could run a + + + align:start position:0% +maybe more household that could run a +firm or could just be a wage earner + + align:start position:0% +firm or could just be a wage earner + + + align:start position:0% +firm or could just be a wage earner +cares about the utility of consumption + + align:start position:0% +cares about the utility of consumption + + + align:start position:0% +cares about the utility of consumption +and effort so the consumption part is + + align:start position:0% +and effort so the consumption part is + + + align:start position:0% +and effort so the consumption part is +constant relative risk aversion + + align:start position:0% +constant relative risk aversion + + + align:start position:0% +constant relative risk aversion +and the degree of risk aversion is gamma + + align:start position:0% +and the degree of risk aversion is gamma + + + align:start position:0% +and the degree of risk aversion is gamma +when gamma is zero this thing is linear + + align:start position:0% +when gamma is zero this thing is linear + + + align:start position:0% +when gamma is zero this thing is linear +that's risk neutral so not risk-averse + + align:start position:0% +that's risk neutral so not risk-averse + + + align:start position:0% +that's risk neutral so not risk-averse +at all as gamma gets higher and higher + + align:start position:0% +at all as gamma gets higher and higher + + + align:start position:0% +at all as gamma gets higher and higher +you have more and more curvature and + + align:start position:0% +you have more and more curvature and + + + align:start position:0% +you have more and more curvature and +then entering inseparably linearly is a + + align:start position:0% +then entering inseparably linearly is a + + + align:start position:0% +then entering inseparably linearly is a +disutility of effort Z being effort + + align:start position:0% +disutility of effort Z being effort + + + align:start position:0% +disutility of effort Z being effort +taking care due diligence how hard + + align:start position:0% +taking care due diligence how hard + + + align:start position:0% +taking care due diligence how hard +you're working again raised to a power + + align:start position:0% +you're working again raised to a power + + + align:start position:0% +you're working again raised to a power +like constant relative risk aversion to + + align:start position:0% +like constant relative risk aversion to + + + align:start position:0% +like constant relative risk aversion to +a different degree gamma 2 rather than a + + align:start position:0% +a different degree gamma 2 rather than a + + + align:start position:0% +a different degree gamma 2 rather than a +gamma 1 and Kappa + + align:start position:0% +gamma 1 and Kappa + + + align:start position:0% +gamma 1 and Kappa +reflects the utility trade-off between + + align:start position:0% +reflects the utility trade-off between + + + align:start position:0% +reflects the utility trade-off between +consumption and and effort + + align:start position:0% +consumption and and effort + + + align:start position:0% +consumption and and effort +so not to say you need to memorize this + + align:start position:0% +so not to say you need to memorize this + + + align:start position:0% +so not to say you need to memorize this +but we can pay attention to the + + align:start position:0% +but we can pay attention to the + + + align:start position:0% +but we can pay attention to the +parameters we got three of them here + + align:start position:0% +parameters we got three of them here + + + align:start position:0% +parameters we got three of them here +Gamma 1 gamma 2 and Kappa so we would + + align:start position:0% +Gamma 1 gamma 2 and Kappa so we would + + + align:start position:0% +Gamma 1 gamma 2 and Kappa so we would +like to estimate those and we will start + + align:start position:0% +like to estimate those and we will start + + + align:start position:0% +like to estimate those and we will start +looking at the model when Gamma One is + + align:start position:0% +looking at the model when Gamma One is + + + align:start position:0% +looking at the model when Gamma One is +zero hence where it's neutral and then + + align:start position:0% +zero hence where it's neutral and then + + + align:start position:0% +zero hence where it's neutral and then +let them be risk-averse and estimate the + + align:start position:0% +let them be risk-averse and estimate the + + + align:start position:0% +let them be risk-averse and estimate the +model generally the estimation will use + + align:start position:0% +model generally the estimation will use + + + align:start position:0% +model generally the estimation will use +linear programming you've seen this + + align:start position:0% +linear programming you've seen this + + + align:start position:0% +linear programming you've seen this +trade-off between consumption and effort + + align:start position:0% +trade-off between consumption and effort + + + align:start position:0% +trade-off between consumption and effort +when we did the lecture on utility and + + align:start position:0% +when we did the lecture on utility and + + + align:start position:0% +when we did the lecture on utility and +preferences there was a slide at the + + align:start position:0% +preferences there was a slide at the + + + align:start position:0% +preferences there was a slide at the +very end that had the agent choosing + + align:start position:0% +very end that had the agent choosing + + + align:start position:0% +very end that had the agent choosing +between work and wheat as an output and + + align:start position:0% +between work and wheat as an output and + + + align:start position:0% +between work and wheat as an output and +we actually did that in the right hand + + align:start position:0% +we actually did that in the right hand + + + align:start position:0% +we actually did that in the right hand +side with respect to consumption and + + align:start position:0% +side with respect to consumption and + + + align:start position:0% +side with respect to consumption and +Leisure or the left hand side with + + align:start position:0% +Leisure or the left hand side with + + + align:start position:0% +Leisure or the left hand side with +respect to consumption and effort so + + align:start position:0% +respect to consumption and effort so + + + align:start position:0% +respect to consumption and effort so +that you know this is a parametric + + align:start position:0% +that you know this is a parametric + + + align:start position:0% +that you know this is a parametric +version of those same preferences okay + + align:start position:0% +version of those same preferences okay + + + align:start position:0% +version of those same preferences okay +more on the model + + align:start position:0% +more on the model + + + align:start position:0% +more on the model +households differ with respect to + + align:start position:0% +households differ with respect to + + + align:start position:0% +households differ with respect to +initial wealth as I said call that a for + + align:start position:0% +initial wealth as I said call that a for + + + align:start position:0% +initial wealth as I said call that a for +assets they differ with respect to + + align:start position:0% +assets they differ with respect to + + + align:start position:0% +assets they differ with respect to +Talent Theta some people are better at + + align:start position:0% +Talent Theta some people are better at + + + align:start position:0% +Talent Theta some people are better at +things than other people like running a + + align:start position:0% +things than other people like running a + + + align:start position:0% +things than other people like running a +business + + align:start position:0% +business + + + align:start position:0% +business +and S is the level of schooling formal + + align:start position:0% +and S is the level of schooling formal + + + align:start position:0% +and S is the level of schooling formal +education all are observed by the agents + + align:start position:0% +education all are observed by the agents + + + align:start position:0% +education all are observed by the agents +and even by the Banks that's a bit of a + + align:start position:0% +and even by the Banks that's a bit of a + + + align:start position:0% +and even by the Banks that's a bit of a +stretch + + align:start position:0% +stretch + + + align:start position:0% +stretch +but we are Imagining the bank can see + + align:start position:0% +but we are Imagining the bank can see + + + align:start position:0% +but we are Imagining the bank can see +wealth and talent and education + + align:start position:0% +wealth and talent and education + + + align:start position:0% +wealth and talent and education +we however only see what we have in the + + align:start position:0% +we however only see what we have in the + + + align:start position:0% +we however only see what we have in the +data which is wealth and schooling we do + + align:start position:0% +data which is wealth and schooling we do + + + align:start position:0% +data which is wealth and schooling we do +not see Talent as modelers but we can + + align:start position:0% +not see Talent as modelers but we can + + + align:start position:0% +not see Talent as modelers but we can +make some assumption about it namely + + align:start position:0% +make some assumption about it namely + + + align:start position:0% +make some assumption about it namely +it's log linear Talent log Theta is log + + align:start position:0% +it's log linear Talent log Theta is log + + + align:start position:0% +it's log linear Talent log Theta is log +linear in assets and schooling and we + + align:start position:0% +linear in assets and schooling and we + + + align:start position:0% +linear in assets and schooling and we +assume that error term is normally + + align:start position:0% +assume that error term is normally + + + align:start position:0% +assume that error term is normally +distributed with this mean zero and + + align:start position:0% +distributed with this mean zero and + + + align:start position:0% +distributed with this mean zero and +variance of one why are we doing this + + align:start position:0% +variance of one why are we doing this + + + align:start position:0% +variance of one why are we doing this +well we want to distinguish the + + align:start position:0% +well we want to distinguish the + + + align:start position:0% +well we want to distinguish the +constraint but the worry is that + + align:start position:0% +constraint but the worry is that + + + align:start position:0% +constraint but the worry is that +talented people in the past have been + + align:start position:0% +talented people in the past have been + + + align:start position:0% +talented people in the past have been +more successful and hence already have + + align:start position:0% +more successful and hence already have + + + align:start position:0% +more successful and hence already have +higher assets we want to be able to + + align:start position:0% +higher assets we want to be able to + + + align:start position:0% +higher assets we want to be able to +distinguish the asset part which is + + align:start position:0% +distinguish the asset part which is + + + align:start position:0% +distinguish the asset part which is +wealth which plays a role in the + + align:start position:0% +wealth which plays a role in the + + + align:start position:0% +wealth which plays a role in the +financing constraints versus Talent + + align:start position:0% +financing constraints versus Talent + + + align:start position:0% +financing constraints versus Talent +which is productivity which is entering + + align:start position:0% +which is productivity which is entering + + + align:start position:0% +which is productivity which is entering +in the production function if we didn't + + align:start position:0% +in the production function if we didn't + + + align:start position:0% +in the production function if we didn't +allow talent to depend on wealth then we + + align:start position:0% +allow talent to depend on wealth then we + + + align:start position:0% +allow talent to depend on wealth then we +could incorrectly infer that financing + + align:start position:0% +could incorrectly infer that financing + + + align:start position:0% +could incorrectly infer that financing +constraints or playing a role because + + align:start position:0% +constraints or playing a role because + + + align:start position:0% +constraints or playing a role because +higher wealth allows people to do better + + align:start position:0% +higher wealth allows people to do better + + + align:start position:0% +higher wealth allows people to do better +but actually it could be playing a role + + align:start position:0% +but actually it could be playing a role + + + align:start position:0% +but actually it could be playing a role +through this third variable namely + + align:start position:0% +through this third variable namely + + + align:start position:0% +through this third variable namely +talent that higher wealth means higher + + align:start position:0% +talent that higher wealth means higher + + + align:start position:0% +talent that higher wealth means higher +Talent reflects higher talent and it's + + align:start position:0% +Talent reflects higher talent and it's + + + align:start position:0% +Talent reflects higher talent and it's +actually higher talent that is the + + align:start position:0% +actually higher talent that is the + + + align:start position:0% +actually higher talent that is the +reason some people are in business and + + align:start position:0% +reason some people are in business and + + + align:start position:0% +reason some people are in business and +operating at a higher scale so this is + + align:start position:0% +operating at a higher scale so this is + + + align:start position:0% +operating at a higher scale so this is +kind of a shorthand way to + + align:start position:0% +kind of a shorthand way to + + + align:start position:0% +kind of a shorthand way to +allow things to be correlated and not in + + align:start position:0% +allow things to be correlated and not in + + + align:start position:0% +allow things to be correlated and not in +incorrectly infer something about + + align:start position:0% +incorrectly infer something about + + + align:start position:0% +incorrectly infer something about +causality other parts of the model + + align:start position:0% +causality other parts of the model + + + align:start position:0% +causality other parts of the model +Q is output profits it's a function of + + align:start position:0% +Q is output profits it's a function of + + + align:start position:0% +Q is output profits it's a function of +effort and capital if you refer or wage + + align:start position:0% +effort and capital if you refer or wage + + + align:start position:0% +effort and capital if you refer or wage +earners if you're not a firm + + align:start position:0% +earners if you're not a firm + + + align:start position:0% +earners if you're not a firm +this output can take on two values for + + align:start position:0% +this output can take on two values for + + + align:start position:0% +this output can take on two values for +Simplicity namely success and failure + + align:start position:0% +Simplicity namely success and failure + + + align:start position:0% +Simplicity namely success and failure +but when they're successful in the + + align:start position:0% +but when they're successful in the + + + align:start position:0% +but when they're successful in the +project the value of Q is Theta so more + + align:start position:0% +project the value of Q is Theta so more + + + align:start position:0% +project the value of Q is Theta so more +talented + + align:start position:0% +talented + + + align:start position:0% +talented +entrepreneurs have higher output + + align:start position:0% +entrepreneurs have higher output + + + align:start position:0% +entrepreneurs have higher output +conditioned on being successful and the + + align:start position:0% +conditioned on being successful and the + + + align:start position:0% +conditioned on being successful and the +other simplification is the failure + + align:start position:0% +other simplification is the failure + + + align:start position:0% +other simplification is the failure +which means they have zero output and + + align:start position:0% +which means they have zero output and + + + align:start position:0% +which means they have zero output and +you know if you have zero output then + + align:start position:0% +you know if you have zero output then + + + align:start position:0% +you know if you have zero output then +you're not going to repay a loan and + + align:start position:0% +you're not going to repay a loan and + + + align:start position:0% +you're not going to repay a loan and +there's no output with which to repay + + align:start position:0% +there's no output with which to repay + + + align:start position:0% +there's no output with which to repay +the loan so this whole branch of Q + + align:start position:0% +the loan so this whole branch of Q + + + align:start position:0% +the loan so this whole branch of Q +equals zero becomes simplistic anyway + + align:start position:0% +equals zero becomes simplistic anyway + + + align:start position:0% +equals zero becomes simplistic anyway +yeah two extremes here three really + + align:start position:0% +yeah two extremes here three really + + + align:start position:0% +yeah two extremes here three really +Talent only enters through success + + align:start position:0% +Talent only enters through success + + + align:start position:0% +Talent only enters through success +there's only two values of profitability + + align:start position:0% +there's only two values of profitability + + + align:start position:0% +there's only two values of profitability +success or failure and failure is + + align:start position:0% +success or failure and failure is + + + align:start position:0% +success or failure and failure is +corresponds with zero output so let's + + align:start position:0% +corresponds with zero output so let's + + + align:start position:0% +corresponds with zero output so let's +look then at the probability of success + + align:start position:0% +look then at the probability of success + + + align:start position:0% +look then at the probability of success +the probability of Q is equal to Theta + + align:start position:0% +the probability of Q is equal to Theta + + + align:start position:0% +the probability of Q is equal to Theta +the high one + + align:start position:0% +the high one + + + align:start position:0% +the high one +conditioned on effort and the level of + + align:start position:0% +conditioned on effort and the level of + + + align:start position:0% +conditioned on effort and the level of +capitalization of the firm and that's + + align:start position:0% +capitalization of the firm and that's + + + align:start position:0% +capitalization of the firm and that's +essentially in the numerator like a Cobb + + align:start position:0% +essentially in the numerator like a Cobb + + + align:start position:0% +essentially in the numerator like a Cobb +Douglas function you know K is capital Z + + align:start position:0% +Douglas function you know K is capital Z + + + align:start position:0% +Douglas function you know K is capital Z +is effort to the powers Alpha and one + + align:start position:0% +is effort to the powers Alpha and one + + + align:start position:0% +is effort to the powers Alpha and one +minus Alpha a function you've seen + + align:start position:0% +minus Alpha a function you've seen + + + align:start position:0% +minus Alpha a function you've seen +before now why is it being divided by + + align:start position:0% +before now why is it being divided by + + + align:start position:0% +before now why is it being divided by +something well this thing the whole + + align:start position:0% +something well this thing the whole + + + align:start position:0% +something well this thing the whole +thing is supposed to be a probability + + align:start position:0% +thing is supposed to be a probability + + + align:start position:0% +thing is supposed to be a probability +probability of success is a number + + align:start position:0% +probability of success is a number + + + align:start position:0% +probability of success is a number +between 0 and 1. okay so if K and Z were + + align:start position:0% +between 0 and 1. okay so if K and Z were + + + align:start position:0% +between 0 and 1. okay so if K and Z were +zero the numerator is zero zero divided + + align:start position:0% +zero the numerator is zero zero divided + + + align:start position:0% +zero the numerator is zero zero divided +by one is zero so that's the left + + align:start position:0% +by one is zero so that's the left + + + align:start position:0% +by one is zero so that's the left +endpoint + + align:start position:0% +endpoint + + + align:start position:0% +endpoint +and likewise if k and z are getting + + align:start position:0% +and likewise if k and z are getting + + + align:start position:0% +and likewise if k and z are getting +really really big + + align:start position:0% +really really big + + + align:start position:0% +really really big +and there's no natural bound here yet + + align:start position:0% +and there's no natural bound here yet + + + align:start position:0% +and there's no natural bound here yet +then this numerator is getting really + + align:start position:0% +then this numerator is getting really + + + align:start position:0% +then this numerator is getting really +big but so is the same term in the + + align:start position:0% +big but so is the same term in the + + + align:start position:0% +big but so is the same term in the +denominator so this whole term is going + + align:start position:0% +denominator so this whole term is going + + + align:start position:0% +denominator so this whole term is going +to one + + align:start position:0% +to one + + + align:start position:0% +to one +because the numerator and denominator + + align:start position:0% +because the numerator and denominator + + + align:start position:0% +because the numerator and denominator +are getting very very similar + + align:start position:0% +are getting very very similar + + + align:start position:0% +are getting very very similar +so this P function is a probability + + align:start position:0% +so this P function is a probability + + + align:start position:0% +so this P function is a probability +between 0 and 1 no matter what K and C + + align:start position:0% +between 0 and 1 no matter what K and C + + + align:start position:0% +between 0 and 1 no matter what K and C +are put into the to The Firm output is + + align:start position:0% +are put into the to The Firm output is + + + align:start position:0% +are put into the to The Firm output is +always going to be observed in the + + align:start position:0% +always going to be observed in the + + + align:start position:0% +always going to be observed in the +models that follow the issue is going to + + align:start position:0% +models that follow the issue is going to + + + align:start position:0% +models that follow the issue is going to +be whether this is effort Z is observed + + align:start position:0% +be whether this is effort Z is observed + + + align:start position:0% +be whether this is effort Z is observed +or not + + align:start position:0% +or not + + + align:start position:0% +or not +and whether K is restricted by the + + align:start position:0% +and whether K is restricted by the + + + align:start position:0% +and whether K is restricted by the +collateral constraint and I will show + + align:start position:0% +collateral constraint and I will show + + + align:start position:0% +collateral constraint and I will show +you that in a minute and finally the + + align:start position:0% +you that in a minute and finally the + + + align:start position:0% +you that in a minute and finally the +other Branch not to lose sight of it + + align:start position:0% +other Branch not to lose sight of it + + + align:start position:0% +other Branch not to lose sight of it +they could choose not to be a firm in + + align:start position:0% +they could choose not to be a firm in + + + align:start position:0% +they could choose not to be a firm in +which case k is equal to zero and when K + + align:start position:0% +which case k is equal to zero and when K + + + align:start position:0% +which case k is equal to zero and when K +is equal to zero the firm is NOT + + align:start position:0% +is equal to zero the firm is NOT + + + align:start position:0% +is equal to zero the firm is NOT +capitalized and effectively the + + align:start position:0% +capitalized and effectively the + + + align:start position:0% +capitalized and effectively the +household is a wage earner so earnings + + align:start position:0% +household is a wage earner so earnings + + + align:start position:0% +household is a wage earner so earnings +in the wage sector are also stochastic + + align:start position:0% +in the wage sector are also stochastic + + + align:start position:0% +in the wage sector are also stochastic +and probabilistic you can work hard to + + align:start position:0% +and probabilistic you can work hard to + + + align:start position:0% +and probabilistic you can work hard to +find a job that doesn't mean you will + + align:start position:0% +find a job that doesn't mean you will + + + align:start position:0% +find a job that doesn't mean you will +find one + + align:start position:0% +find one + + + align:start position:0% +find one +the higher effort you devote towards or + + align:start position:0% +the higher effort you devote towards or + + + align:start position:0% +the higher effort you devote towards or +finding a job the higher would be the + + align:start position:0% +finding a job the higher would be the + + + align:start position:0% +finding a job the higher would be the +probability of getting the wage + + align:start position:0% +probability of getting the wage + + + align:start position:0% +probability of getting the wage +and again this is bounded between zero + + align:start position:0% +and again this is bounded between zero + + + align:start position:0% +and again this is bounded between zero +and one now if you Refirm you may or may + + align:start position:0% +and one now if you Refirm you may or may + + + align:start position:0% +and one now if you Refirm you may or may +not borrow but if you borrow there's + + align:start position:0% +not borrow but if you borrow there's + + + align:start position:0% +not borrow but if you borrow there's +going to be an interest rate schedule + + align:start position:0% +going to be an interest rate schedule + + + align:start position:0% +going to be an interest rate schedule +that determines how much you pay back + + align:start position:0% +that determines how much you pay back + + + align:start position:0% +that determines how much you pay back +and that interest rate schedule is a + + align:start position:0% +and that interest rate schedule is a + + + align:start position:0% +and that interest rate schedule is a +function of two of the things the + + align:start position:0% +function of two of the things the + + + align:start position:0% +function of two of the things the +lending firm observes the wealth of the + + align:start position:0% +lending firm observes the wealth of the + + + align:start position:0% +lending firm observes the wealth of the +household and the household's talent and + + align:start position:0% +household and the household's talent and + + + align:start position:0% +household and the household's talent and +this schedule is going to be such that + + align:start position:0% +this schedule is going to be such that + + + align:start position:0% +this schedule is going to be such that +the banks although maximizing profits + + align:start position:0% +the banks although maximizing profits + + + align:start position:0% +the banks although maximizing profits +can at best break even and I'll show you + + align:start position:0% +can at best break even and I'll show you + + + align:start position:0% +can at best break even and I'll show you +that constraint in a minute but I + + align:start position:0% +that constraint in a minute but I + + + align:start position:0% +that constraint in a minute but I +already alluded to it in the sense of + + align:start position:0% +already alluded to it in the sense of + + + align:start position:0% +already alluded to it in the sense of +moral hazard being a problem because we + + align:start position:0% +moral hazard being a problem because we + + + align:start position:0% +moral hazard being a problem because we +came in going down and banks have a new + + align:start position:0% +came in going down and banks have a new + + + align:start position:0% +came in going down and banks have a new +raise interest rates to cover what + + align:start position:0% +raise interest rates to cover what + + + align:start position:0% +raise interest rates to cover what +otherwise would be losses to having to + + align:start position:0% +otherwise would be losses to having to + + + align:start position:0% +otherwise would be losses to having to +get enough from the successful firms to + + align:start position:0% +get enough from the successful firms to + + + align:start position:0% +get enough from the successful firms to +cover the fact that the unsuccessful + + align:start position:0% +cover the fact that the unsuccessful + + + align:start position:0% +cover the fact that the unsuccessful +ones are not paying off the loans when + + align:start position:0% +ones are not paying off the loans when + + + align:start position:0% +ones are not paying off the loans when +uh you're a worker or a firm that is not + + align:start position:0% +uh you're a worker or a firm that is not + + + align:start position:0% +uh you're a worker or a firm that is not +using all their resources to borrow you + + align:start position:0% +using all their resources to borrow you + + + align:start position:0% +using all their resources to borrow you +have some residual assets left they put + + align:start position:0% +have some residual assets left they put + + + align:start position:0% +have some residual assets left they put +it in the bank and they earn the + + align:start position:0% +it in the bank and they earn the + + + align:start position:0% +it in the bank and they earn the +riskless rate of return are so in some + + align:start position:0% +riskless rate of return are so in some + + + align:start position:0% +riskless rate of return are so in some +respects there's both borrowing and + + align:start position:0% +respects there's both borrowing and + + + align:start position:0% +respects there's both borrowing and +saving going on here depending on what + + align:start position:0% +saving going on here depending on what + + + align:start position:0% +saving going on here depending on what +occupation you choose and your + + align:start position:0% +occupation you choose and your + + + align:start position:0% +occupation you choose and your +underlying characteristics so how are we + + align:start position:0% +underlying characteristics so how are we + + + align:start position:0% +underlying characteristics so how are we +going to solve this problem we're going + + align:start position:0% +going to solve this problem we're going + + + align:start position:0% +going to solve this problem we're going +to solve for a constrained Optimum we + + align:start position:0% +to solve for a constrained Optimum we + + + align:start position:0% +to solve for a constrained Optimum we +are going to write down a quote-unquote + + align:start position:0% +are going to write down a quote-unquote + + + align:start position:0% +are going to write down a quote-unquote +planners problem which I sometimes refer + + align:start position:0% +planners problem which I sometimes refer + + + align:start position:0% +planners problem which I sometimes refer +to the math problem + + align:start position:0% +to the math problem + + + align:start position:0% +to the math problem +which is maximizing Lambda weighted sums + + align:start position:0% +which is maximizing Lambda weighted sums + + + align:start position:0% +which is maximizing Lambda weighted sums +of utilities subject to Resource + + align:start position:0% +of utilities subject to Resource + + + align:start position:0% +of utilities subject to Resource +truth-telling and liability constraints + + align:start position:0% +truth-telling and liability constraints + + + align:start position:0% +truth-telling and liability constraints +now to State restate that we're going to + + align:start position:0% +now to State restate that we're going to + + + align:start position:0% +now to State restate that we're going to +maximize the utility a weighted sum of + + align:start position:0% +maximize the utility a weighted sum of + + + align:start position:0% +maximize the utility a weighted sum of +the utility of borrowers and the utility + + align:start position:0% +the utility of borrowers and the utility + + + align:start position:0% +the utility of borrowers and the utility +of the banks the banks however could + + align:start position:0% +of the banks the banks however could + + + align:start position:0% +of the banks the banks however could +make profits so we're just + + align:start position:0% +make profits so we're just + + + align:start position:0% +make profits so we're just +distinguishing in their case profits as + + align:start position:0% +distinguishing in their case profits as + + + align:start position:0% +distinguishing in their case profits as +as a version of utility the second thing + + align:start position:0% +as a version of utility the second thing + + + align:start position:0% +as a version of utility the second thing +is and I didn't reload this picture if + + align:start position:0% +is and I didn't reload this picture if + + + align:start position:0% +is and I didn't reload this picture if +you go back to the lecture where we + + align:start position:0% +you go back to the lecture where we + + + align:start position:0% +you go back to the lecture where we +introduced the notion of Pareto + + align:start position:0% +introduced the notion of Pareto + + + align:start position:0% +introduced the notion of Pareto +optimality + + align:start position:0% +optimality + + + align:start position:0% +optimality +we had the so-called Pareto Frontier and + + align:start position:0% +we had the so-called Pareto Frontier and + + + align:start position:0% +we had the so-called Pareto Frontier and +we decided the points on the frontier + + align:start position:0% +we decided the points on the frontier + + + align:start position:0% +we decided the points on the frontier +would be Pareto optimal and you could + + align:start position:0% +would be Pareto optimal and you could + + + align:start position:0% +would be Pareto optimal and you could +achieve those points by maximizing a + + align:start position:0% +achieve those points by maximizing a + + + align:start position:0% +achieve those points by maximizing a +particular Lambda weighted sum of + + align:start position:0% +particular Lambda weighted sum of + + + align:start position:0% +particular Lambda weighted sum of +utilities or in this case a particular + + align:start position:0% +utilities or in this case a particular + + + align:start position:0% +utilities or in this case a particular +Lambda weighted sum of profits and + + align:start position:0% +Lambda weighted sum of profits and + + + align:start position:0% +Lambda weighted sum of profits and +utility of the borrower but there is + + align:start position:0% +utility of the borrower but there is + + + align:start position:0% +utility of the borrower but there is +another way to do it which is to + + align:start position:0% +another way to do it which is to + + + align:start position:0% +another way to do it which is to +maximize the utility of the borrower + + align:start position:0% +maximize the utility of the borrower + + + align:start position:0% +maximize the utility of the borrower +subject to a fixed profit level of the + + align:start position:0% +subject to a fixed profit level of the + + + align:start position:0% +subject to a fixed profit level of the +bank it's equivalent normally with these + + align:start position:0% +bank it's equivalent normally with these + + + align:start position:0% +bank it's equivalent normally with these +you know concave Frontiers then the next + + align:start position:0% +you know concave Frontiers then the next + + + align:start position:0% +you know concave Frontiers then the next +step is okay there are many many banks + + align:start position:0% +step is okay there are many many banks + + + align:start position:0% +step is okay there are many many banks +and they're competing if one + + align:start position:0% +and they're competing if one + + + align:start position:0% +and they're competing if one +representative Bank were to make a + + align:start position:0% +representative Bank were to make a + + + align:start position:0% +representative Bank were to make a +profit with respect to the borrowing + + align:start position:0% +profit with respect to the borrowing + + + align:start position:0% +profit with respect to the borrowing +customers another bank could step in and + + align:start position:0% +customers another bank could step in and + + + align:start position:0% +customers another bank could step in and +undercut the first one and do slightly + + align:start position:0% +undercut the first one and do slightly + + + align:start position:0% +undercut the first one and do slightly +better + + align:start position:0% +better + + + align:start position:0% +better +so this competitive process is going to + + align:start position:0% +so this competitive process is going to + + + align:start position:0% +so this competitive process is going to +drive the profits of the bank down to + + align:start position:0% +drive the profits of the bank down to + + + align:start position:0% +drive the profits of the bank down to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +so we're going to be looking at + + align:start position:0% +so we're going to be looking at + + + align:start position:0% +so we're going to be looking at +particular Pareto Optimum where the + + align:start position:0% +particular Pareto Optimum where the + + + align:start position:0% +particular Pareto Optimum where the +utilities of the borrowers are maximized + + align:start position:0% +utilities of the borrowers are maximized + + + align:start position:0% +utilities of the borrowers are maximized +subject to a zero profit constraint on + + align:start position:0% +subject to a zero profit constraint on + + + align:start position:0% +subject to a zero profit constraint on +the part of the lenders there are other + + align:start position:0% +the part of the lenders there are other + + + align:start position:0% +the part of the lenders there are other +Optima we're not going to look at today + + align:start position:0% +Optima we're not going to look at today + + + align:start position:0% +Optima we're not going to look at today +although it's going to be clear from the + + align:start position:0% +although it's going to be clear from the + + + align:start position:0% +although it's going to be clear from the +equations how we could have done it more + + align:start position:0% +equations how we could have done it more + + + align:start position:0% +equations how we could have done it more +generally + + align:start position:0% +generally + + + align:start position:0% +generally +okay so this is the utility of the + + align:start position:0% +okay so this is the utility of the + + + align:start position:0% +okay so this is the utility of the +borrower there are three possible + + align:start position:0% +borrower there are three possible + + + align:start position:0% +borrower there are three possible +branches + + align:start position:0% +branches + + + align:start position:0% +branches +this is again the risk neutral borrower + + align:start position:0% +this is again the risk neutral borrower + + + align:start position:0% +this is again the risk neutral borrower +to get warmed up uh if K is zero which + + align:start position:0% +to get warmed up uh if K is zero which + + + align:start position:0% +to get warmed up uh if K is zero which +is a choice + + align:start position:0% +is a choice + + + align:start position:0% +is a choice +but if the solution is k equals to zero + + align:start position:0% +but if the solution is k equals to zero + + + align:start position:0% +but if the solution is k equals to zero +then in fact the household is a wage + + align:start position:0% +then in fact the household is a wage + + + align:start position:0% +then in fact the household is a wage +earner not a firm deciding on effort + + align:start position:0% +earner not a firm deciding on effort + + + align:start position:0% +earner not a firm deciding on effort +which determines the probability of + + align:start position:0% +which determines the probability of + + + align:start position:0% +which determines the probability of +getting the wage although it comes at a + + align:start position:0% +getting the wage although it comes at a + + + align:start position:0% +getting the wage although it comes at a +disutility cost of working and they put + + align:start position:0% +disutility cost of working and they put + + + align:start position:0% +disutility cost of working and they put +all their wealth in the bank so that + + align:start position:0% +all their wealth in the bank so that + + + align:start position:0% +all their wealth in the bank so that +risk-free rate of interest times assets + + align:start position:0% +risk-free rate of interest times assets + + + align:start position:0% +risk-free rate of interest times assets +is something they get at the end of the + + align:start position:0% +is something they get at the end of the + + + align:start position:0% +is something they get at the end of the +period the savings account + + align:start position:0% +period the savings account + + + align:start position:0% +period the savings account +the second branch is they do go into + + align:start position:0% +the second branch is they do go into + + + align:start position:0% +the second branch is they do go into +business and there's capitalization is + + align:start position:0% +business and there's capitalization is + + + align:start position:0% +business and there's capitalization is +positive but it's less than their assets + + align:start position:0% +positive but it's less than their assets + + + align:start position:0% +positive but it's less than their assets +so they can basically take what's left + + align:start position:0% +so they can basically take what's left + + + align:start position:0% +so they can basically take what's left +assets minus capitalization and put it + + align:start position:0% +assets minus capitalization and put it + + + align:start position:0% +assets minus capitalization and put it +in the bank so these guys also get a + + align:start position:0% +in the bank so these guys also get a + + + align:start position:0% +in the bank so these guys also get a +return on savings but part of their + + align:start position:0% +return on savings but part of their + + + align:start position:0% +return on savings but part of their +wealth to the cape art is stuck into the + + align:start position:0% +wealth to the cape art is stuck into the + + + align:start position:0% +wealth to the cape art is stuck into the +production function so the return on + + align:start position:0% +production function so the return on + + + align:start position:0% +production function so the return on +that comes from the possibility of + + align:start position:0% +that comes from the possibility of + + + align:start position:0% +that comes from the possibility of +profits and you still have this + + align:start position:0% +profits and you still have this + + + align:start position:0% +profits and you still have this +trade-off of probability of success + + align:start position:0% +trade-off of probability of success + + + align:start position:0% +trade-off of probability of success +versus the disutility of effort and then + + align:start position:0% +versus the disutility of effort and then + + + align:start position:0% +versus the disutility of effort and then +the final Branch here is these guys have + + align:start position:0% +the final Branch here is these guys have + + + align:start position:0% +the final Branch here is these guys have +a k which is relatively large + + align:start position:0% +a k which is relatively large + + + align:start position:0% +a k which is relatively large +relative to their assets so there they + + align:start position:0% +relative to their assets so there they + + + align:start position:0% +relative to their assets so there they +got a borrow and the sign here is a bit + + align:start position:0% +got a borrow and the sign here is a bit + + + align:start position:0% +got a borrow and the sign here is a bit +confusing + + align:start position:0% +confusing + + + align:start position:0% +confusing +but if K is greater than a then a is + + align:start position:0% +but if K is greater than a then a is + + + align:start position:0% +but if K is greater than a then a is +less than K so this term is negative so + + align:start position:0% +less than K so this term is negative so + + + align:start position:0% +less than K so this term is negative so +naturally they're quote negative paying + + align:start position:0% +naturally they're quote negative paying + + + align:start position:0% +naturally they're quote negative paying +off the principal and the interest on + + align:start position:0% +off the principal and the interest on + + + align:start position:0% +off the principal and the interest on +the loan and they only pay it off if + + align:start position:0% +the loan and they only pay it off if + + + align:start position:0% +the loan and they only pay it off if +they're successful so again this + + align:start position:0% +they're successful so again this + + + align:start position:0% +they're successful so again this +modified Cobb Douglas probability + + align:start position:0% +modified Cobb Douglas probability + + + align:start position:0% +modified Cobb Douglas probability +expression is entering in there as it + + align:start position:0% +expression is entering in there as it + + + align:start position:0% +expression is entering in there as it +does for the probability of success okay + + align:start position:0% +does for the probability of success okay + + + align:start position:0% +does for the probability of success okay +so those are the three branches + + align:start position:0% +so those are the three branches + + + align:start position:0% +so those are the three branches +this is the break-even constraint of the + + align:start position:0% +this is the break-even constraint of the + + + align:start position:0% +this is the break-even constraint of the +bank which is I've said in words a + + align:start position:0% +bank which is I've said in words a + + + align:start position:0% +bank which is I've said in words a +couple of times already this is the + + align:start position:0% +couple of times already this is the + + + align:start position:0% +couple of times already this is the +risk-free rate so a bank has basically + + align:start position:0% +risk-free rate so a bank has basically + + + align:start position:0% +risk-free rate so a bank has basically +got to get funds from somewhere from + + align:start position:0% +got to get funds from somewhere from + + + align:start position:0% +got to get funds from somewhere from +depositors actually + + align:start position:0% +depositors actually + + + align:start position:0% +depositors actually +and they got to break even because of + + align:start position:0% +and they got to break even because of + + + align:start position:0% +and they got to break even because of +all that competition so they they may + + align:start position:0% +all that competition so they they may + + + align:start position:0% +all that competition so they they may +get a higher return depending on the + + align:start position:0% +get a higher return depending on the + + + align:start position:0% +get a higher return depending on the +borrower's wealth and talent but they + + align:start position:0% +borrower's wealth and talent but they + + + align:start position:0% +borrower's wealth and talent but they +only get that back when that borrower is + + align:start position:0% +only get that back when that borrower is + + + align:start position:0% +only get that back when that borrower is +successful so this is the expected + + align:start position:0% +successful so this is the expected + + + align:start position:0% +successful so this is the expected +return given the interest rate schedule + + align:start position:0% +return given the interest rate schedule + + + align:start position:0% +return given the interest rate schedule +and that is driven down to the risk-free + + align:start position:0% +and that is driven down to the risk-free + + + align:start position:0% +and that is driven down to the risk-free +rate so we have this zero profit + + align:start position:0% +rate so we have this zero profit + + + align:start position:0% +rate so we have this zero profit +constraint to impose as part of the + + align:start position:0% +constraint to impose as part of the + + + align:start position:0% +constraint to impose as part of the +solution + + align:start position:0% +solution + + + align:start position:0% +solution +so again to repeat myself instead of + + align:start position:0% +so again to repeat myself instead of + + + align:start position:0% +so again to repeat myself instead of +maximizing a Lambda weighted sum of + + align:start position:0% +maximizing a Lambda weighted sum of + + + align:start position:0% +maximizing a Lambda weighted sum of +utilities we're going to maximize the + + align:start position:0% +utilities we're going to maximize the + + + align:start position:0% +utilities we're going to maximize the +utility of the borrower subject to a + + align:start position:0% +utility of the borrower subject to a + + + align:start position:0% +utility of the borrower subject to a +particular Lambda for the bank a Lambda + + align:start position:0% +particular Lambda for the bank a Lambda + + + align:start position:0% +particular Lambda for the bank a Lambda +which is associated with making zero + + align:start position:0% +which is associated with making zero + + + align:start position:0% +which is associated with making zero +profits and we just impose a zero profit + + align:start position:0% +profits and we just impose a zero profit + + + align:start position:0% +profits and we just impose a zero profit +constraint from the get-go it's also + + align:start position:0% +constraint from the get-go it's also + + + align:start position:0% +constraint from the get-go it's also +kind of interesting in terms of where we + + align:start position:0% +kind of interesting in terms of where we + + + align:start position:0% +kind of interesting in terms of where we +are in the class because when we first + + align:start position:0% +are in the class because when we first + + + align:start position:0% +are in the class because when we first +introduced utility maximization we had + + align:start position:0% +introduced utility maximization we had + + + align:start position:0% +introduced utility maximization we had +these sort of partial equilibrium + + align:start position:0% +these sort of partial equilibrium + + + align:start position:0% +these sort of partial equilibrium +exercises in which prices and so on were + + align:start position:0% +exercises in which prices and so on were + + + align:start position:0% +exercises in which prices and so on were +taken as given although we buried them + + align:start position:0% +taken as given although we buried them + + + align:start position:0% +taken as given although we buried them +to see what the household will do + + align:start position:0% +to see what the household will do + + + align:start position:0% +to see what the household will do +likewise when we did the firm we had + + align:start position:0% +likewise when we did the firm we had + + + align:start position:0% +likewise when we did the firm we had +input prices as taken as given and we + + align:start position:0% +input prices as taken as given and we + + + align:start position:0% +input prices as taken as given and we +did some experiments and here likewise + + align:start position:0% +did some experiments and here likewise + + + align:start position:0% +did some experiments and here likewise +we're in quote unquote partial + + align:start position:0% +we're in quote unquote partial + + + align:start position:0% +we're in quote unquote partial +equilibrium in the sense that that wage + + align:start position:0% +equilibrium in the sense that that wage + + + align:start position:0% +equilibrium in the sense that that wage +and the interest rate are given to us + + align:start position:0% +and the interest rate are given to us + + + align:start position:0% +and the interest rate are given to us +we're not trying to explain them they're + + align:start position:0% +we're not trying to explain them they're + + + align:start position:0% +we're not trying to explain them they're +going to be part of the data on the + + align:start position:0% +going to be part of the data on the + + + align:start position:0% +going to be part of the data on the +other hand we're definitely doing a + + align:start position:0% +other hand we're definitely doing a + + + align:start position:0% +other hand we're definitely doing a +Contracting problem here + + align:start position:0% +Contracting problem here + + + align:start position:0% +Contracting problem here +and to do it we have to draw on those + + align:start position:0% +and to do it we have to draw on those + + + align:start position:0% +and to do it we have to draw on those +tools about Pareto optimality and so on + + align:start position:0% +tools about Pareto optimality and so on + + + align:start position:0% +tools about Pareto optimality and so on +and how to determine Pareto optimal + + align:start position:0% +and how to determine Pareto optimal + + + align:start position:0% +and how to determine Pareto optimal +outcomes via programming problems so we + + align:start position:0% +outcomes via programming problems so we + + + align:start position:0% +outcomes via programming problems so we +kind of are drawing on two different + + align:start position:0% +kind of are drawing on two different + + + align:start position:0% +kind of are drawing on two different +segments of the class that we've covered + + align:start position:0% +segments of the class that we've covered + + + align:start position:0% +segments of the class that we've covered +already in this application okay so + + align:start position:0% +already in this application okay so + + + align:start position:0% +already in this application okay so +let's talk about limited liability + + align:start position:0% +let's talk about limited liability + + + align:start position:0% +let's talk about limited liability +so limited liability let's just jump + + align:start position:0% +so limited liability let's just jump + + + align:start position:0% +so limited liability let's just jump +down here it's easier here okay that + + align:start position:0% +down here it's easier here okay that + + + align:start position:0% +down here it's easier here okay that +they can use the capitalization of the + + align:start position:0% +they can use the capitalization of the + + + align:start position:0% +they can use the capitalization of the +firm is bounded above by their assets + + align:start position:0% +firm is bounded above by their assets + + + align:start position:0% +firm is bounded above by their assets +actually it's Lambda some + + align:start position:0% +actually it's Lambda some + + + align:start position:0% +actually it's Lambda some +proportionality times asset so this is + + align:start position:0% +proportionality times asset so this is + + + align:start position:0% +proportionality times asset so this is +referred to as a borrowing constraint + + align:start position:0% +referred to as a borrowing constraint + + + align:start position:0% +referred to as a borrowing constraint +now Lambda could be greater than one + + align:start position:0% +now Lambda could be greater than one + + + align:start position:0% +now Lambda could be greater than one +they may be able to borrow more than + + align:start position:0% +they may be able to borrow more than + + + align:start position:0% +they may be able to borrow more than +their wealth but it is limited there's a + + align:start position:0% +their wealth but it is limited there's a + + + align:start position:0% +their wealth but it is limited there's a +little bit of a derivation here I was + + align:start position:0% +little bit of a derivation here I was + + + align:start position:0% +little bit of a derivation here I was +thinking about it this morning it's not + + align:start position:0% +thinking about it this morning it's not + + + align:start position:0% +thinking about it this morning it's not +really all that compelling you can + + align:start position:0% +really all that compelling you can + + + align:start position:0% +really all that compelling you can +derive this constraint by saying there's + + align:start position:0% +derive this constraint by saying there's + + + align:start position:0% +derive this constraint by saying there's +a maximum amount they can invest in The + + align:start position:0% +a maximum amount they can invest in The + + + align:start position:0% +a maximum amount they can invest in The +Firm then you write down the equation + + align:start position:0% +Firm then you write down the equation + + + align:start position:0% +Firm then you write down the equation +for borrowing which is the difference + + align:start position:0% +for borrowing which is the difference + + + align:start position:0% +for borrowing which is the difference +between capital and assets and then + + align:start position:0% +between capital and assets and then + + + align:start position:0% +between capital and assets and then +substitute in that maximum amount for + + align:start position:0% +substitute in that maximum amount for + + + align:start position:0% +substitute in that maximum amount for +Capital and derive this equation this + + align:start position:0% +Capital and derive this equation this + + + align:start position:0% +Capital and derive this equation this +now has a on both sides of the equation + + align:start position:0% +now has a on both sides of the equation + + + align:start position:0% +now has a on both sides of the equation +which you could drop and you get the + + align:start position:0% +which you could drop and you get the + + + align:start position:0% +which you could drop and you get the +equation six as a result but I'm + + align:start position:0% +equation six as a result but I'm + + + align:start position:0% +equation six as a result but I'm +perfectly happy if you want to just + + align:start position:0% +perfectly happy if you want to just + + + align:start position:0% +perfectly happy if you want to just +start with six that capital is bounded + + align:start position:0% +start with six that capital is bounded + + + align:start position:0% +start with six that capital is bounded +from above due to a collateral + + align:start position:0% +from above due to a collateral + + + align:start position:0% +from above due to a collateral +constraint related to wealth that's the + + align:start position:0% +constraint related to wealth that's the + + + align:start position:0% +constraint related to wealth that's the +limited liability version + + align:start position:0% +limited liability version + + + align:start position:0% +limited liability version +here's the moral hazard version in this + + align:start position:0% +here's the moral hazard version in this + + + align:start position:0% +here's the moral hazard version in this +case the bank does not see the + + align:start position:0% +case the bank does not see the + + + align:start position:0% +case the bank does not see the +borrower's effort so whatever the + + align:start position:0% +borrower's effort so whatever the + + + align:start position:0% +borrower's effort so whatever the +contract is in terms of that repayment + + align:start position:0% +contract is in terms of that repayment + + + align:start position:0% +contract is in terms of that repayment +schedule and whatever the level of + + align:start position:0% +schedule and whatever the level of + + + align:start position:0% +schedule and whatever the level of +capitalization that the borrower can + + align:start position:0% +capitalization that the borrower can + + + align:start position:0% +capitalization that the borrower can +manage the choice of how much to work is + + align:start position:0% +manage the choice of how much to work is + + + align:start position:0% +manage the choice of how much to work is +done by the borrower alone and cannot be + + align:start position:0% +done by the borrower alone and cannot be + + + align:start position:0% +done by the borrower alone and cannot be +dictated + + align:start position:0% +dictated + + + align:start position:0% +dictated +and it's going to be summarized by A + + align:start position:0% +and it's going to be summarized by A + + + align:start position:0% +and it's going to be summarized by A +first order condition + + align:start position:0% +first order condition + + + align:start position:0% +first order condition +which is like a solution to the sub + + align:start position:0% +which is like a solution to the sub + + + align:start position:0% +which is like a solution to the sub +problem which sub problem this sub + + align:start position:0% +problem which sub problem this sub + + + align:start position:0% +problem which sub problem this sub +problem here okay so this is the branch + + align:start position:0% +problem here okay so this is the branch + + + align:start position:0% +problem here okay so this is the branch +where the household s firm is borrowing + + align:start position:0% +where the household s firm is borrowing + + + align:start position:0% +where the household s firm is borrowing +and its payoff in curly brackets is in + + align:start position:0% +and its payoff in curly brackets is in + + + align:start position:0% +and its payoff in curly brackets is in +part a function of Z so if you + + align:start position:0% +part a function of Z so if you + + + align:start position:0% +part a function of Z so if you +differentiate this function with respect + + align:start position:0% +differentiate this function with respect + + + align:start position:0% +differentiate this function with respect +to effort you know you're going to get + + align:start position:0% +to effort you know you're going to get + + + align:start position:0% +to effort you know you're going to get +the way that the probability of success + + align:start position:0% +the way that the probability of success + + + align:start position:0% +the way that the probability of success +is increasing with effort you're going + + align:start position:0% +is increasing with effort you're going + + + align:start position:0% +is increasing with effort you're going +to get a part with a negative sign + + align:start position:0% +to get a part with a negative sign + + + align:start position:0% +to get a part with a negative sign +reflecting the disutility of effort and + + align:start position:0% +reflecting the disutility of effort and + + + align:start position:0% +reflecting the disutility of effort and +this probability of success is also + + align:start position:0% +this probability of success is also + + + align:start position:0% +this probability of success is also +entering into you know it's like the + + align:start position:0% +entering into you know it's like the + + + align:start position:0% +entering into you know it's like the +Winner's curse you win your profits are + + align:start position:0% +Winner's curse you win your profits are + + + align:start position:0% +Winner's curse you win your profits are +successful but you got to pay off the + + align:start position:0% +successful but you got to pay off the + + + align:start position:0% +successful but you got to pay off the +bank so the higher you work the more you + + align:start position:0% +bank so the higher you work the more you + + + align:start position:0% +bank so the higher you work the more you +repay so take the derivative of this and + + align:start position:0% +repay so take the derivative of this and + + + align:start position:0% +repay so take the derivative of this and +you get this first order condition over + + align:start position:0% +you get this first order condition over + + + align:start position:0% +you get this first order condition over +here + + align:start position:0% + + + + align:start position:0% + +equation seven so that's the formality + + align:start position:0% +equation seven so that's the formality + + + align:start position:0% +equation seven so that's the formality +of it that it captures the notion as + + align:start position:0% +of it that it captures the notion as + + + align:start position:0% +of it that it captures the notion as +I've said that no matter what contract + + align:start position:0% +I've said that no matter what contract + + + align:start position:0% +I've said that no matter what contract +the firm is entering into the bank + + align:start position:0% +the firm is entering into the bank + + + align:start position:0% +the firm is entering into the bank +cannot see the borrower's effort but + + align:start position:0% +cannot see the borrower's effort but + + + align:start position:0% +cannot see the borrower's effort but +knows how the borrower is determining it + + align:start position:0% +knows how the borrower is determining it + + + align:start position:0% +knows how the borrower is determining it +so so we get this equation seven is + + align:start position:0% +so so we get this equation seven is + + + align:start position:0% +so so we get this equation seven is +another constraint on the on the program + + align:start position:0% +another constraint on the on the program + + + align:start position:0% +another constraint on the on the program +if we believe moral hazard is strain so + + align:start position:0% +if we believe moral hazard is strain so + + + align:start position:0% +if we believe moral hazard is strain so +we did limited liability we did moral + + align:start position:0% +we did limited liability we did moral + + + align:start position:0% +we did limited liability we did moral +hazard we could have both and + + align:start position:0% +hazard we could have both and + + + align:start position:0% +hazard we could have both and +now I'll show you a very cool picture so + + align:start position:0% +now I'll show you a very cool picture so + + + align:start position:0% +now I'll show you a very cool picture so +it says utility of a household as a firm + + align:start position:0% +it says utility of a household as a firm + + + align:start position:0% +it says utility of a household as a firm +but on the X and Y axis are the inputs + + align:start position:0% +but on the X and Y axis are the inputs + + + align:start position:0% +but on the X and Y axis are the inputs +the capital level and the effort level + + align:start position:0% +the capital level and the effort level + + + align:start position:0% +the capital level and the effort level +if we did what we would call First best + + align:start position:0% +if we did what we would call First best + + + align:start position:0% +if we did what we would call First best +meaning that we ignore all the limited + + align:start position:0% +meaning that we ignore all the limited + + + align:start position:0% +meaning that we ignore all the limited +liability and moral hazard constraints + + align:start position:0% +liability and moral hazard constraints + + + align:start position:0% +liability and moral hazard constraints +then the borrower would maximize these + + align:start position:0% +then the borrower would maximize these + + + align:start position:0% +then the borrower would maximize these +choices of capital in effort + + align:start position:0% +choices of capital in effort + + + align:start position:0% +choices of capital in effort +choose them to have maximal utility and + + align:start position:0% +choose them to have maximal utility and + + + align:start position:0% +choose them to have maximal utility and +where is the utility maximal utility + + align:start position:0% +where is the utility maximal utility + + + align:start position:0% +where is the utility maximal utility +it's in this Bullseye over here so in + + align:start position:0% +it's in this Bullseye over here so in + + + align:start position:0% +it's in this Bullseye over here so in +other lectures we talked about Bliss + + align:start position:0% +other lectures we talked about Bliss + + + align:start position:0% +other lectures we talked about Bliss +points + + align:start position:0% +points + + + align:start position:0% +points +meaning if you're below Bliss you know + + align:start position:0% +meaning if you're below Bliss you know + + + align:start position:0% +meaning if you're below Bliss you know +utility is increasing As you move toward + + align:start position:0% +utility is increasing As you move toward + + + align:start position:0% +utility is increasing As you move toward +it or you could go above Bliss and which + + align:start position:0% +it or you could go above Bliss and which + + + align:start position:0% +it or you could go above Bliss and which +which is kind of weird in which case you + + align:start position:0% +which is kind of weird in which case you + + + align:start position:0% +which is kind of weird in which case you +want to dump stuff + + align:start position:0% +want to dump stuff + + + align:start position:0% +want to dump stuff +this is an endogenous Bliss point this + + align:start position:0% +this is an endogenous Bliss point this + + + align:start position:0% +this is an endogenous Bliss point this +this came from solving an underlying + + align:start position:0% +this came from solving an underlying + + + align:start position:0% +this came from solving an underlying +problem but we can nevertheless plot the + + align:start position:0% +problem but we can nevertheless plot the + + + align:start position:0% +problem but we can nevertheless plot the +solution this way and where do they want + + align:start position:0% +solution this way and where do they want + + + align:start position:0% +solution this way and where do they want +to be as close to the bullseye as + + align:start position:0% +to be as close to the bullseye as + + + align:start position:0% +to be as close to the bullseye as +possible but not Northeast of it + + align:start position:0% +possible but not Northeast of it + + + align:start position:0% +possible but not Northeast of it +okay so now what are the constraints on + + align:start position:0% +okay so now what are the constraints on + + + align:start position:0% +okay so now what are the constraints on +the problem + + align:start position:0% +the problem + + + align:start position:0% +the problem +there's this liability constraint which + + align:start position:0% +there's this liability constraint which + + + align:start position:0% +there's this liability constraint which +is capital times Lambda and if that's + + align:start position:0% +is capital times Lambda and if that's + + + align:start position:0% +is capital times Lambda and if that's +the constraint in the world and hence in + + align:start position:0% +the constraint in the world and hence in + + + align:start position:0% +the constraint in the world and hence in +the program it just simply says Capital + + align:start position:0% +the program it just simply says Capital + + + align:start position:0% +the program it just simply says Capital +cannot be to the right of it it can be + + align:start position:0% +cannot be to the right of it it can be + + + align:start position:0% +cannot be to the right of it it can be +to the left of it or on it so all these + + align:start position:0% +to the left of it or on it so all these + + + align:start position:0% +to the left of it or on it so all these +Solutions on the vertical line and left + + align:start position:0% +Solutions on the vertical line and left + + + align:start position:0% +Solutions on the vertical line and left +of the vertical line correspond to + + align:start position:0% +of the vertical line correspond to + + + align:start position:0% +of the vertical line correspond to +satisfying this capitalization + + align:start position:0% +satisfying this capitalization + + + align:start position:0% +satisfying this capitalization +constraint for a given value of Lambda + + align:start position:0% +constraint for a given value of Lambda + + + align:start position:0% +constraint for a given value of Lambda +which is listed down here at the bottom + + align:start position:0% +which is listed down here at the bottom + + + align:start position:0% +which is listed down here at the bottom +of the slide and where is the maximal + + align:start position:0% +of the slide and where is the maximal + + + align:start position:0% +of the slide and where is the maximal +solution at the tangency right here + + align:start position:0% +solution at the tangency right here + + + align:start position:0% +solution at the tangency right here +that's where the the slope of these + + align:start position:0% +that's where the the slope of these + + + align:start position:0% +that's where the the slope of these +concentric Rings goes vertical okay + + align:start position:0% +concentric Rings goes vertical okay + + + align:start position:0% +concentric Rings goes vertical okay +let's do the moral hazard so ignore + + align:start position:0% +let's do the moral hazard so ignore + + + align:start position:0% +let's do the moral hazard so ignore +limited liability constraint and Trace + + align:start position:0% +limited liability constraint and Trace + + + align:start position:0% +limited liability constraint and Trace +out this guy + + align:start position:0% +out this guy + + + align:start position:0% +out this guy +I did not know every priori what this + + align:start position:0% +I did not know every priori what this + + + align:start position:0% +I did not know every priori what this +constraint was going to look like + + align:start position:0% +constraint was going to look like + + + align:start position:0% +constraint was going to look like +but if you plot it in the space of K and + + align:start position:0% +but if you plot it in the space of K and + + + align:start position:0% +but if you plot it in the space of K and +and Z it looks like this it's like this + + align:start position:0% +and Z it looks like this it's like this + + + align:start position:0% +and Z it looks like this it's like this +parabola + + align:start position:0% +parabola + + + align:start position:0% +parabola +Alex was my student and ra for this + + align:start position:0% +Alex was my student and ra for this + + + align:start position:0% +Alex was my student and ra for this +project and Anna and I former student + + align:start position:0% +project and Anna and I former student + + + align:start position:0% +project and Anna and I former student +were writing this paper we shared the + + align:start position:0% +were writing this paper we shared the + + + align:start position:0% +were writing this paper we shared the +problem with Alex and Alex came up with + + align:start position:0% +problem with Alex and Alex came up with + + + align:start position:0% +problem with Alex and Alex came up with +this graph and Alex became a co-author + + align:start position:0% +this graph and Alex became a co-author + + + align:start position:0% +this graph and Alex became a co-author +of the paper and subsequent collaborator + + align:start position:0% +of the paper and subsequent collaborator + + + align:start position:0% +of the paper and subsequent collaborator +and many things anyway I love this graph + + align:start position:0% +and many things anyway I love this graph + + + align:start position:0% +and many things anyway I love this graph +so if you want to satisfy the moral + + align:start position:0% +so if you want to satisfy the moral + + + align:start position:0% +so if you want to satisfy the moral +hazard constraint you're going to be on + + align:start position:0% +hazard constraint you're going to be on + + + align:start position:0% +hazard constraint you're going to be on +the parabola and where is the maximal + + align:start position:0% +the parabola and where is the maximal + + + align:start position:0% +the parabola and where is the maximal +point it's again a tangency with a + + align:start position:0% +point it's again a tangency with a + + + align:start position:0% +point it's again a tangency with a +concentric Circle and it's right here + + align:start position:0% +concentric Circle and it's right here + + + align:start position:0% +concentric Circle and it's right here +so interestingly if you compare these + + align:start position:0% +so interestingly if you compare these + + + align:start position:0% +so interestingly if you compare these +two points the limited liability + + align:start position:0% +two points the limited liability + + + align:start position:0% +two points the limited liability +constraint solution and the moral hazard + + align:start position:0% +constraint solution and the moral hazard + + + align:start position:0% +constraint solution and the moral hazard +constraint solution limited liability + + align:start position:0% +constraint solution limited liability + + + align:start position:0% +constraint solution limited liability +involves less capital and more effort + + align:start position:0% +involves less capital and more effort + + + align:start position:0% +involves less capital and more effort +relative to the moral hazard solution + + align:start position:0% +relative to the moral hazard solution + + + align:start position:0% +relative to the moral hazard solution +which kind of makes sense because with + + align:start position:0% +which kind of makes sense because with + + + align:start position:0% +which kind of makes sense because with +moral hazard the problem is inducing + + align:start position:0% +moral hazard the problem is inducing + + + align:start position:0% +moral hazard the problem is inducing +effort not Capital with limited + + align:start position:0% +effort not Capital with limited + + + align:start position:0% +effort not Capital with limited +liability the problem is financing that + + align:start position:0% +liability the problem is financing that + + + align:start position:0% +liability the problem is financing that +level of capital and efforts fully + + align:start position:0% +level of capital and efforts fully + + + align:start position:0% +level of capital and efforts fully +observed now it turns out if you have + + align:start position:0% +observed now it turns out if you have + + + align:start position:0% +observed now it turns out if you have +both constraints in this world with risk + + align:start position:0% +both constraints in this world with risk + + + align:start position:0% +both constraints in this world with risk +neutrality there's nothing to optimize + + align:start position:0% +neutrality there's nothing to optimize + + + align:start position:0% +neutrality there's nothing to optimize +it's like two lines cross actually + + align:start position:0% +it's like two lines cross actually + + + align:start position:0% +it's like two lines cross actually +technically it's a vertical line + + align:start position:0% +technically it's a vertical line + + + align:start position:0% +technically it's a vertical line +Crossing with a parabola but it + + align:start position:0% +Crossing with a parabola but it + + + align:start position:0% +Crossing with a parabola but it +completely nails down the solution it's + + align:start position:0% +completely nails down the solution it's + + + align:start position:0% +completely nails down the solution it's +okay and z are at the crossing over here + + align:start position:0% +okay and z are at the crossing over here + + + align:start position:0% +okay and z are at the crossing over here +so what we're doing conceptually then is + + align:start position:0% +so what we're doing conceptually then is + + + align:start position:0% +so what we're doing conceptually then is +loading in these parameter values fourth + + align:start position:0% +loading in these parameter values fourth + + + align:start position:0% +loading in these parameter values fourth +in this case a particular Talent level + + align:start position:0% +in this case a particular Talent level + + + align:start position:0% +in this case a particular Talent level +particular asset level Alpha in the + + align:start position:0% +particular asset level Alpha in the + + + align:start position:0% +particular asset level Alpha in the +production function Kappa which is the + + align:start position:0% +production function Kappa which is the + + + align:start position:0% +production function Kappa which is the +disutility of effort and the powers + + align:start position:0% +disutility of effort and the powers + + + align:start position:0% +disutility of effort and the powers +Lambda Lambda 1 is 0 Etc solving the + + align:start position:0% +Lambda Lambda 1 is 0 Etc solving the + + + align:start position:0% +Lambda Lambda 1 is 0 Etc solving the +model and you know delineating what + + align:start position:0% +model and you know delineating what + + + align:start position:0% +model and you know delineating what +happens with these various constraints + + align:start position:0% +happens with these various constraints + + + align:start position:0% +happens with these various constraints +one the other or both + + align:start position:0% +one the other or both + + + align:start position:0% +one the other or both +okay so now we're going to generalize + + align:start position:0% +okay so now we're going to generalize + + + align:start position:0% +okay so now we're going to generalize +this + + align:start position:0% +this + + + align:start position:0% +this +and in particular we're going to let + + align:start position:0% +and in particular we're going to let + + + align:start position:0% +and in particular we're going to let +there be some risk well there is already + + align:start position:0% +there be some risk well there is already + + + align:start position:0% +there be some risk well there is already +risk but we're going to let the + + align:start position:0% +risk but we're going to let the + + + align:start position:0% +risk but we're going to let the +household be risk averse so their payoff + + align:start position:0% +household be risk averse so their payoff + + + align:start position:0% +household be risk averse so their payoff +can depend on Q which they now care + + align:start position:0% +can depend on Q which they now care + + + align:start position:0% +can depend on Q which they now care +about the dispersion because they're + + align:start position:0% +about the dispersion because they're + + + align:start position:0% +about the dispersion because they're +risk averse so there's a consumption + + align:start position:0% +risk averse so there's a consumption + + + align:start position:0% +risk averse so there's a consumption +this profit sharing schedule + + align:start position:0% +this profit sharing schedule + + + align:start position:0% +this profit sharing schedule +and we're going to want to solve for + + align:start position:0% +and we're going to want to solve for + + + align:start position:0% +and we're going to want to solve for +these probabilities this kind of came up + + align:start position:0% +these probabilities this kind of came up + + + align:start position:0% +these probabilities this kind of came up +in the beginning of class is pi is a + + align:start position:0% +in the beginning of class is pi is a + + + align:start position:0% +in the beginning of class is pi is a +probability number an endogenous number + + align:start position:0% +probability number an endogenous number + + + align:start position:0% +probability number an endogenous number +that reflects the solution to a + + align:start position:0% +that reflects the solution to a + + + align:start position:0% +that reflects the solution to a +programming problem so we're going to + + align:start position:0% +programming problem so we're going to + + + align:start position:0% +programming problem so we're going to +want to determine the probability of + + align:start position:0% +want to determine the probability of + + + align:start position:0% +want to determine the probability of +seeing this quadruple + + align:start position:0% +seeing this quadruple + + + align:start position:0% +seeing this quadruple +a particular value of C particular value + + align:start position:0% +a particular value of C particular value + + + align:start position:0% +a particular value of C particular value +of q a particular value of effort Z on a + + align:start position:0% +of q a particular value of effort Z on a + + + align:start position:0% +of q a particular value of effort Z on a +particular capitalization level as a + + align:start position:0% +particular capitalization level as a + + + align:start position:0% +particular capitalization level as a +function of observed and unobserved + + align:start position:0% +function of observed and unobserved + + + align:start position:0% +function of observed and unobserved +characteristics of the borrower namely + + align:start position:0% +characteristics of the borrower namely + + + align:start position:0% +characteristics of the borrower namely +Theta A and S Talon assets and schooling + + align:start position:0% +Theta A and S Talon assets and schooling + + + align:start position:0% +Theta A and S Talon assets and schooling +so again + + align:start position:0% +so again + + + align:start position:0% +so again +I don't remember what what slide it's on + + align:start position:0% +I don't remember what what slide it's on + + + align:start position:0% +I don't remember what what slide it's on +but we will determine the solution by + + align:start position:0% +but we will determine the solution by + + + align:start position:0% +but we will determine the solution by +these probabilities + + align:start position:0% +these probabilities + + + align:start position:0% +these probabilities +there are lotteries + + align:start position:0% +there are lotteries + + + align:start position:0% +there are lotteries +they will make our program and turn it + + align:start position:0% +they will make our program and turn it + + + align:start position:0% +they will make our program and turn it +into a linear program and again this is + + align:start position:0% +into a linear program and again this is + + + align:start position:0% +into a linear program and again this is +a bit of a review but now in a + + align:start position:0% +a bit of a review but now in a + + + align:start position:0% +a bit of a review but now in a +interesting applied context remember we + + align:start position:0% +interesting applied context remember we + + + align:start position:0% +interesting applied context remember we +had discrete values for consumption when + + align:start position:0% +had discrete values for consumption when + + + align:start position:0% +had discrete values for consumption when +we introduced the notion of risk and we + + align:start position:0% +we introduced the notion of risk and we + + + align:start position:0% +we introduced the notion of risk and we +talked about the probability Pi of + + align:start position:0% +talked about the probability Pi of + + + align:start position:0% +talked about the probability Pi of +choosing a certain bundle discrete + + align:start position:0% +choosing a certain bundle discrete + + + align:start position:0% +choosing a certain bundle discrete +bundle c c s or S and delineated all the + + align:start position:0% +bundle c c s or S and delineated all the + + + align:start position:0% +bundle c c s or S and delineated all the +possible discrete values of c that was + + align:start position:0% +possible discrete values of c that was + + + align:start position:0% +possible discrete values of c that was +one place that we did it and there's + + align:start position:0% +one place that we did it and there's + + + align:start position:0% +one place that we did it and there's +been others but I don't have it right + + align:start position:0% +been others but I don't have it right + + + align:start position:0% +been others but I don't have it right +off the top of my head so oh sorry in + + align:start position:0% +off the top of my head so oh sorry in + + + align:start position:0% +off the top of my head so oh sorry in +the mechanism design literature from the + + align:start position:0% +the mechanism design literature from the + + + align:start position:0% +the mechanism design literature from the +previous lecture we did it we had + + align:start position:0% +previous lecture we did it we had + + + align:start position:0% +previous lecture we did it we had +deterministic programs and programs with + + align:start position:0% +deterministic programs and programs with + + + align:start position:0% +deterministic programs and programs with +the lotteries so that's the second + + align:start position:0% +the lotteries so that's the second + + + align:start position:0% +the lotteries so that's the second +reason to have the lotteries and I made + + align:start position:0% +reason to have the lotteries and I made + + + align:start position:0% +reason to have the lotteries and I made +the point there that they were linear + + align:start position:0% +the point there that they were linear + + + align:start position:0% +the point there that they were linear +programs so this despite putting in + + align:start position:0% +programs so this despite putting in + + + align:start position:0% +programs so this despite putting in +truth-telling constraints when we have + + align:start position:0% +truth-telling constraints when we have + + + align:start position:0% +truth-telling constraints when we have +the lotteries the constraints are linear + + align:start position:0% +the lotteries the constraints are linear + + + align:start position:0% +the lotteries the constraints are linear +in the pi and so is the objective + + align:start position:0% +in the pi and so is the objective + + + align:start position:0% +in the pi and so is the objective +function so here here we're going to + + align:start position:0% +function so here here we're going to + + + align:start position:0% +function so here here we're going to +have these moral hazard constraints Etc + + align:start position:0% +have these moral hazard constraints Etc + + + align:start position:0% +have these moral hazard constraints Etc +which could turn us into a very + + align:start position:0% +which could turn us into a very + + + align:start position:0% +which could turn us into a very +non-linear problem because we have the + + align:start position:0% +non-linear problem because we have the + + + align:start position:0% +non-linear problem because we have the +original + + align:start position:0% +original + + + align:start position:0% +original +maximum the objective function subject + + align:start position:0% +maximum the objective function subject + + + align:start position:0% +maximum the objective function subject +to a derivative of part of the maximized + + align:start position:0% +to a derivative of part of the maximized + + + align:start position:0% +to a derivative of part of the maximized +function as a constraint and you know + + align:start position:0% +function as a constraint and you know + + + align:start position:0% +function as a constraint and you know +Lord knows what that looks like but we + + align:start position:0% +Lord knows what that looks like but we + + + align:start position:0% +Lord knows what that looks like but we +turn it all into a linear programming + + align:start position:0% +turn it all into a linear programming + + + align:start position:0% +turn it all into a linear programming +problem with these lotteries not only + + align:start position:0% +problem with these lotteries not only + + + align:start position:0% +problem with these lotteries not only +that we're going to imagine discrete + + align:start position:0% +that we're going to imagine discrete + + + align:start position:0% +that we're going to imagine discrete +values so it's not a semi-infinite + + align:start position:0% +values so it's not a semi-infinite + + + align:start position:0% +values so it's not a semi-infinite +program it's a finite discrete linear + + align:start position:0% +program it's a finite discrete linear + + + align:start position:0% +program it's a finite discrete linear +program and that allows capitalization + + align:start position:0% +program and that allows capitalization + + + align:start position:0% +program and that allows capitalization +to be chunky maybe you get a machine or + + align:start position:0% +to be chunky maybe you get a machine or + + + align:start position:0% +to be chunky maybe you get a machine or +you don't for example literally a + + align:start position:0% +you don't for example literally a + + + align:start position:0% +you don't for example literally a +discrete value that also causes a + + align:start position:0% +discrete value that also causes a + + + align:start position:0% +discrete value that also causes a +problem just the way chunky consumption + + align:start position:0% +problem just the way chunky consumption + + + align:start position:0% +problem just the way chunky consumption +causes a problem but never mind + + align:start position:0% +causes a problem but never mind + + + align:start position:0% +causes a problem but never mind +lotteries are the cure-all and it just + + align:start position:0% +lotteries are the cure-all and it just + + + align:start position:0% +lotteries are the cure-all and it just +always works to turn it into this + + align:start position:0% +always works to turn it into this + + + align:start position:0% +always works to turn it into this +so don't pass out each of these lines + + align:start position:0% +so don't pass out each of these lines + + + align:start position:0% +so don't pass out each of these lines +will make sense to you this is the + + align:start position:0% +will make sense to you this is the + + + align:start position:0% +will make sense to you this is the +objective function it's the utility of + + align:start position:0% +objective function it's the utility of + + + align:start position:0% +objective function it's the utility of +the household as a function of + + align:start position:0% +the household as a function of + + + align:start position:0% +the household as a function of +consumption and effort + + align:start position:0% +consumption and effort + + + align:start position:0% +consumption and effort +this is expected utility because part of + + align:start position:0% +this is expected utility because part of + + + align:start position:0% +this is expected utility because part of +the probability involves consumption and + + align:start position:0% +the probability involves consumption and + + + align:start position:0% +the probability involves consumption and +effort which may potentially be chosen + + align:start position:0% +effort which may potentially be chosen + + + align:start position:0% +effort which may potentially be chosen +at random according to Pi and then we + + align:start position:0% +at random according to Pi and then we + + + align:start position:0% +at random according to Pi and then we +sum up over all these discrete values of + + align:start position:0% +sum up over all these discrete values of + + + align:start position:0% +sum up over all these discrete values of +cqzk summing them up weighting them by + + align:start position:0% +cqzk summing them up weighting them by + + + align:start position:0% +cqzk summing them up weighting them by +pi so this whole thing is just expected + + align:start position:0% +pi so this whole thing is just expected + + + align:start position:0% +pi so this whole thing is just expected +utility in this case the borrower is + + align:start position:0% +utility in this case the borrower is + + + align:start position:0% +utility in this case the borrower is +risk-averse so we we're allowing for + + align:start position:0% +risk-averse so we we're allowing for + + + align:start position:0% +risk-averse so we we're allowing for +that now this constraint is what I call + + align:start position:0% +that now this constraint is what I call + + + align:start position:0% +that now this constraint is what I call +a mother nature constraint what Mother + + align:start position:0% +a mother nature constraint what Mother + + + align:start position:0% +a mother nature constraint what Mother +Nature is giving us is the technology + + align:start position:0% +Nature is giving us is the technology + + + align:start position:0% +Nature is giving us is the technology +that Maps C and K along with Theta into + + align:start position:0% +that Maps C and K along with Theta into + + + align:start position:0% +that Maps C and K along with Theta into +the probability of success Q + + align:start position:0% +the probability of success Q + + + align:start position:0% +the probability of success Q +so this P tilde function is given it's + + align:start position:0% +so this P tilde function is given it's + + + align:start position:0% +so this P tilde function is given it's +part of the underlying environment but + + align:start position:0% +part of the underlying environment but + + + align:start position:0% +part of the underlying environment but +you might think that in part we're + + align:start position:0% +you might think that in part we're + + + align:start position:0% +you might think that in part we're +solving for the relationship the + + align:start position:0% +solving for the relationship the + + + align:start position:0% +solving for the relationship the +probabilistic relationship between Q Z + + align:start position:0% +probabilistic relationship between Q Z + + + align:start position:0% +probabilistic relationship between Q Z +and K because everything looks + + align:start position:0% +and K because everything looks + + + align:start position:0% +and K because everything looks +endogenous up here so we need to impose + + align:start position:0% +endogenous up here so we need to impose + + + align:start position:0% +endogenous up here so we need to impose +another constraint to make sure we + + align:start position:0% +another constraint to make sure we + + + align:start position:0% +another constraint to make sure we +respect the mother nature and if you + + align:start position:0% +respect the mother nature and if you + + + align:start position:0% +respect the mother nature and if you +know little statistics this is like the + + align:start position:0% +know little statistics this is like the + + + align:start position:0% +know little statistics this is like the +probability of a conditioned on event B + + align:start position:0% +probability of a conditioned on event B + + + align:start position:0% +probability of a conditioned on event B +times the probability event B is + + align:start position:0% +times the probability event B is + + + align:start position:0% +times the probability event B is +therefore the probability of the joint + + align:start position:0% +therefore the probability of the joint + + + align:start position:0% +therefore the probability of the joint +of n a and b and on the left hand side + + align:start position:0% +of n a and b and on the left hand side + + + align:start position:0% +of n a and b and on the left hand side +it's already the join event A and B so + + align:start position:0% +it's already the join event A and B so + + + align:start position:0% +it's already the join event A and B so +this is the probability of Q conditioned + + align:start position:0% +this is the probability of Q conditioned + + + align:start position:0% +this is the probability of Q conditioned +on Z and K this is the probability of Z + + align:start position:0% +on Z and K this is the probability of Z + + + align:start position:0% +on Z and K this is the probability of Z +and K because we've integrated out the + + align:start position:0% +and K because we've integrated out the + + + align:start position:0% +and K because we've integrated out the +other objects C and Q so this is the + + align:start position:0% +other objects C and Q so this is the + + + align:start position:0% +other objects C and Q so this is the +probability of Q Z K and likewise the + + align:start position:0% +probability of Q Z K and likewise the + + + align:start position:0% +probability of Q Z K and likewise the +left hand side is the probability of Q z + + align:start position:0% +left hand side is the probability of Q z + + + align:start position:0% +left hand side is the probability of Q z +k where we've somehow integrate out the + + align:start position:0% +k where we've somehow integrate out the + + + align:start position:0% +k where we've somehow integrate out the +only other object the C so this is a + + align:start position:0% +only other object the C so this is a + + + align:start position:0% +only other object the C so this is a +mother nature constraint again it's all + + align:start position:0% +mother nature constraint again it's all + + + align:start position:0% +mother nature constraint again it's all +linear in the pies so we just code it in + + align:start position:0% +linear in the pies so we just code it in + + + align:start position:0% +linear in the pies so we just code it in +to Matlab this thing down here is to + + align:start position:0% +to Matlab this thing down here is to + + + align:start position:0% +to Matlab this thing down here is to +break even constraint for the bank and + + align:start position:0% +break even constraint for the bank and + + + align:start position:0% +break even constraint for the bank and +you can think of it as maybe the bank + + align:start position:0% +you can think of it as maybe the bank + + + align:start position:0% +you can think of it as maybe the bank +has to pay out more in consumption than + + align:start position:0% +has to pay out more in consumption than + + + align:start position:0% +has to pay out more in consumption than +output I mean this case by the way when + + align:start position:0% +output I mean this case by the way when + + + align:start position:0% +output I mean this case by the way when +the firm is not successful the output is + + align:start position:0% +the firm is not successful the output is + + + align:start position:0% +the firm is not successful the output is +zero but the borrower's risk averse and + + align:start position:0% +zero but the borrower's risk averse and + + + align:start position:0% +zero but the borrower's risk averse and +it's going to view it as a disaster to + + align:start position:0% +it's going to view it as a disaster to + + + align:start position:0% +it's going to view it as a disaster to +get zero consumption maybe even minus + + align:start position:0% +get zero consumption maybe even minus + + + align:start position:0% +get zero consumption maybe even minus +infinity utility + + align:start position:0% +infinity utility + + + align:start position:0% +infinity utility +so typically in the failure Branch + + align:start position:0% +so typically in the failure Branch + + + align:start position:0% +so typically in the failure Branch +consumption is greater than q that means + + align:start position:0% +consumption is greater than q that means + + + align:start position:0% +consumption is greater than q that means +the bank which is like taking all of the + + align:start position:0% +the bank which is like taking all of the + + + align:start position:0% +the bank which is like taking all of the +Q and giving Summit back in terms of C + + align:start position:0% +Q and giving Summit back in terms of C + + + align:start position:0% +Q and giving Summit back in terms of C +is suffering a loss on the consumption + + align:start position:0% +is suffering a loss on the consumption + + + align:start position:0% +is suffering a loss on the consumption +part on the other hand on the right hand + + align:start position:0% +part on the other hand on the right hand + + + align:start position:0% +part on the other hand on the right hand +side it's like the firm the household is + + align:start position:0% +side it's like the firm the household is + + + align:start position:0% +side it's like the firm the household is +a firm is surrendering all of its assets + + align:start position:0% +a firm is surrendering all of its assets + + + align:start position:0% +a firm is surrendering all of its assets +a to the bank to manage and only some of + + align:start position:0% +a to the bank to manage and only some of + + + align:start position:0% +a to the bank to manage and only some of +it gets used to sell to finance so the + + align:start position:0% +it gets used to sell to finance so the + + + align:start position:0% +it gets used to sell to finance so the +firms kind of make a profit on the right + + align:start position:0% +firms kind of make a profit on the right + + + align:start position:0% +firms kind of make a profit on the right +hand side times the difference the bank + + align:start position:0% +hand side times the difference the bank + + + align:start position:0% +hand side times the difference the bank +got that it didn't give back times the + + align:start position:0% +got that it didn't give back times the + + + align:start position:0% +got that it didn't give back times the +external outside interest rate so this + + align:start position:0% +external outside interest rate so this + + + align:start position:0% +external outside interest rate so this +is a zero break even constraint with the + + align:start position:0% +is a zero break even constraint with the + + + align:start position:0% +is a zero break even constraint with the +lotteries this is moral hazard it's it's + + align:start position:0% +lotteries this is moral hazard it's it's + + + align:start position:0% +lotteries this is moral hazard it's it's +akin to truth telling so what this says + + align:start position:0% +akin to truth telling so what this says + + + align:start position:0% +akin to truth telling so what this says +is the truth is that not only does the + + align:start position:0% +is the truth is that not only does the + + + align:start position:0% +is the truth is that not only does the +borrower characterize by Theta A and S + + align:start position:0% +borrower characterize by Theta A and S + + + align:start position:0% +borrower characterize by Theta A and S +the borrower contemplates doing the + + align:start position:0% +the borrower contemplates doing the + + + align:start position:0% +the borrower contemplates doing the +recommended action Z how much effort is + + align:start position:0% +recommended action Z how much effort is + + + align:start position:0% +recommended action Z how much effort is +supposed to be applied under the + + align:start position:0% +supposed to be applied under the + + + align:start position:0% +supposed to be applied under the +contract but you can't make the borrower + + align:start position:0% +contract but you can't make the borrower + + + align:start position:0% +contract but you can't make the borrower +do it the borrower has to be given + + align:start position:0% +do it the borrower has to be given + + + align:start position:0% +do it the borrower has to be given +incentive to work especially if this is + + align:start position:0% +incentive to work especially if this is + + + align:start position:0% +incentive to work especially if this is +a high level of Z but the borrower says + + align:start position:0% +a high level of Z but the borrower says + + + align:start position:0% +a high level of Z but the borrower says +Nah I might not do it so even though Z + + align:start position:0% +Nah I might not do it so even though Z + + + align:start position:0% +Nah I might not do it so even though Z +was recommended by the bank the borrower + + align:start position:0% +was recommended by the bank the borrower + + + align:start position:0% +was recommended by the bank the borrower +does something else the borrower does Z + + align:start position:0% +does something else the borrower does Z + + + align:start position:0% +does something else the borrower does Z +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +note that Z Prime is entering into the + + align:start position:0% +note that Z Prime is entering into the + + + align:start position:0% +note that Z Prime is entering into the +utility function here so he really is + + align:start position:0% +utility function here so he really is + + + align:start position:0% +utility function here so he really is +going to do that or is thinking about + + align:start position:0% +going to do that or is thinking about + + + align:start position:0% +going to do that or is thinking about +doing it and this would be the utility + + align:start position:0% +doing it and this would be the utility + + + align:start position:0% +doing it and this would be the utility +consequence this stupid thing here we + + align:start position:0% +consequence this stupid thing here we + + + align:start position:0% +consequence this stupid thing here we +have to readjust the probabilities + + align:start position:0% +have to readjust the probabilities + + + align:start position:0% +have to readjust the probabilities +because when we impose that mother + + align:start position:0% +because when we impose that mother + + + align:start position:0% +because when we impose that mother +nature constraint we embedded the + + align:start position:0% +nature constraint we embedded the + + + align:start position:0% +nature constraint we embedded the +probability of success into the + + align:start position:0% +probability of success into the + + + align:start position:0% +probability of success into the +endogenous object we would now be making + + align:start position:0% +endogenous object we would now be making + + + align:start position:0% +endogenous object we would now be making +an error if we did not adjust for the + + align:start position:0% +an error if we did not adjust for the + + + align:start position:0% +an error if we did not adjust for the +fact that the effort being taken as Z + + align:start position:0% +fact that the effort being taken as Z + + + align:start position:0% +fact that the effort being taken as Z +Prime rather than Z you know and this is + + align:start position:0% +Prime rather than Z you know and this is + + + align:start position:0% +Prime rather than Z you know and this is +derived in one of my papers hopefully + + align:start position:0% +derived in one of my papers hopefully + + + align:start position:0% +derived in one of my papers hopefully +it's somewhat intuitive that at least + + align:start position:0% +it's somewhat intuitive that at least + + + align:start position:0% +it's somewhat intuitive that at least +one needs to do an adjustment and + + align:start position:0% +one needs to do an adjustment and + + + align:start position:0% +one needs to do an adjustment and +finally this is just as the + + align:start position:0% +finally this is just as the + + + align:start position:0% +finally this is just as the +probabilities all add up to one okay so + + align:start position:0% +probabilities all add up to one okay so + + + align:start position:0% +probabilities all add up to one okay so +we're going to Max the programming + + align:start position:0% +we're going to Max the programming + + + align:start position:0% +we're going to Max the programming +problem is to maximize the expected + + align:start position:0% +problem is to maximize the expected + + + align:start position:0% +problem is to maximize the expected +utility of the borrower subject to all + + align:start position:0% +utility of the borrower subject to all + + + align:start position:0% +utility of the borrower subject to all +these constraints Mother Nature + + align:start position:0% +these constraints Mother Nature + + + align:start position:0% +these constraints Mother Nature +constraints there's a lot of them for + + align:start position:0% +constraints there's a lot of them for + + + align:start position:0% +constraints there's a lot of them for +every Q Z and K this is the break-even + + align:start position:0% +every Q Z and K this is the break-even + + + align:start position:0% +every Q Z and K this is the break-even +constraint is only one of them this is + + align:start position:0% +constraint is only one of them this is + + + align:start position:0% +constraint is only one of them this is +the moral hazard constraint to be + + align:start position:0% +the moral hazard constraint to be + + + align:start position:0% +the moral hazard constraint to be +obedient rather than Shirk and there's + + align:start position:0% +obedient rather than Shirk and there's + + + align:start position:0% +obedient rather than Shirk and there's +one of these for every K that could be + + align:start position:0% +one of these for every K that could be + + + align:start position:0% +one of these for every K that could be +assigned and for every Z and alternative + + align:start position:0% +assigned and for every Z and alternative + + + align:start position:0% +assigned and for every Z and alternative +value Z Prime and there's only one of + + align:start position:0% +value Z Prime and there's only one of + + + align:start position:0% +value Z Prime and there's only one of +these constraints 11. so I'm actually + + align:start position:0% +these constraints 11. so I'm actually + + + align:start position:0% +these constraints 11. so I'm actually +sort of enumerating the set of all + + align:start position:0% +sort of enumerating the set of all + + + align:start position:0% +sort of enumerating the set of all +constraints you can solve these things + + align:start position:0% +constraints you can solve these things + + + align:start position:0% +constraints you can solve these things +for a large number of control variables + + align:start position:0% +for a large number of control variables + + + align:start position:0% +for a large number of control variables +Pi like thousands and you can have + + align:start position:0% +Pi like thousands and you can have + + + align:start position:0% +Pi like thousands and you can have +hundreds of constraints and it's still + + align:start position:0% +hundreds of constraints and it's still + + + align:start position:0% +hundreds of constraints and it's still +solvable in things like C Plex which is + + align:start position:0% +solvable in things like C Plex which is + + + align:start position:0% +solvable in things like C Plex which is +a version of which Ruby is publicly + + align:start position:0% +a version of which Ruby is publicly + + + align:start position:0% +a version of which Ruby is publicly +available software + + align:start position:0% +available software + + + align:start position:0% +available software +so we did this for Ruby was on the + + align:start position:0% +so we did this for Ruby was on the + + + align:start position:0% +so we did this for Ruby was on the +market so we paid two thousand dollars + + align:start position:0% +market so we paid two thousand dollars + + + align:start position:0% +market so we paid two thousand dollars +to get a hold of C Plex and we saw the + + align:start position:0% +to get a hold of C Plex and we saw the + + + align:start position:0% +to get a hold of C Plex and we saw the +linear programming problem I'm going to + + align:start position:0% +linear programming problem I'm going to + + + align:start position:0% +linear programming problem I'm going to +call the solution the probability of + + align:start position:0% +call the solution the probability of + + + align:start position:0% +call the solution the probability of +being an entrepreneur it's a pretty + + align:start position:0% +being an entrepreneur it's a pretty + + + align:start position:0% +being an entrepreneur it's a pretty +Brute Force namely what is the + + align:start position:0% +Brute Force namely what is the + + + align:start position:0% +Brute Force namely what is the +probability the capital level is + + align:start position:0% +probability the capital level is + + + align:start position:0% +probability the capital level is +positive it's positive they must be + + align:start position:0% +positive it's positive they must be + + + align:start position:0% +positive it's positive they must be +affirm the way we compose the problem if + + align:start position:0% +affirm the way we compose the problem if + + + align:start position:0% +affirm the way we compose the problem if +Capital were zero they're a wage earner + + align:start position:0% +Capital were zero they're a wage earner + + + align:start position:0% +Capital were zero they're a wage earner +so ignoring everything else by summing + + align:start position:0% +so ignoring everything else by summing + + + align:start position:0% +so ignoring everything else by summing +up over everything else we only care + + align:start position:0% +up over everything else we only care + + + align:start position:0% +up over everything else we only care +about Capital being positive and we call + + align:start position:0% +about Capital being positive and we call + + + align:start position:0% +about Capital being positive and we call +that the probability of being a firm + + align:start position:0% +that the probability of being a firm + + + align:start position:0% +that the probability of being a firm +it's still condition on Talent assets + + align:start position:0% +it's still condition on Talent assets + + + align:start position:0% +it's still condition on Talent assets +and schooling so we have to solve this + + align:start position:0% +and schooling so we have to solve this + + + align:start position:0% +and schooling so we have to solve this +problem for all those stratifications in + + align:start position:0% +problem for all those stratifications in + + + align:start position:0% +problem for all those stratifications in +the data + + align:start position:0% +the data + + + align:start position:0% +the data +so let me go back again is it a moral + + align:start position:0% +so let me go back again is it a moral + + + align:start position:0% +so let me go back again is it a moral +hazard problem is it a little liability + + align:start position:0% +hazard problem is it a little liability + + + align:start position:0% +hazard problem is it a little liability +problem is it both is it neither so we + + align:start position:0% +problem is it both is it neither so we + + + align:start position:0% +problem is it both is it neither so we +have the master program here that allows + + align:start position:0% +have the master program here that allows + + + align:start position:0% +have the master program here that allows +everything all we have to do is comment + + align:start position:0% +everything all we have to do is comment + + + align:start position:0% +everything all we have to do is comment +out the relevant constraint if we want + + align:start position:0% +out the relevant constraint if we want + + + align:start position:0% +out the relevant constraint if we want +to look at the + + align:start position:0% +to look at the + + + align:start position:0% +to look at the +oh that should have been written here + + align:start position:0% +oh that should have been written here + + + align:start position:0% +oh that should have been written here +if we want to delete the moral hazard + + align:start position:0% +if we want to delete the moral hazard + + + align:start position:0% +if we want to delete the moral hazard +constraint we comment out this thing + + align:start position:0% +constraint we comment out this thing + + + align:start position:0% +constraint we comment out this thing +equation 10. and there's a limited + + align:start position:0% +equation 10. and there's a limited + + + align:start position:0% +equation 10. and there's a limited +liability constraint which somehow I'm + + align:start position:0% +liability constraint which somehow I'm + + + align:start position:0% +liability constraint which somehow I'm +not seeing in the notation but it should + + align:start position:0% +not seeing in the notation but it should + + + align:start position:0% +not seeing in the notation but it should +have been there and we can comment it + + align:start position:0% +have been there and we can comment it + + + align:start position:0% +have been there and we can comment it +out we can allow both moral hazard and + + align:start position:0% +out we can allow both moral hazard and + + + align:start position:0% +out we can allow both moral hazard and +limit liability or we could have neither + + align:start position:0% +limit liability or we could have neither + + + align:start position:0% +limit liability or we could have neither +once you go to all the trouble to code + + align:start position:0% +once you go to all the trouble to code + + + align:start position:0% +once you go to all the trouble to code +this thing up it's not hard to do all + + align:start position:0% +this thing up it's not hard to do all + + + align:start position:0% +this thing up it's not hard to do all +these different combinations and take it + + align:start position:0% +these different combinations and take it + + + align:start position:0% +these different combinations and take it +to the data so how do we go to the data + + align:start position:0% +to the data so how do we go to the data + + + align:start position:0% +to the data so how do we go to the data +we + + align:start position:0% +we + + + align:start position:0% +we +compute + + align:start position:0% +compute + + + align:start position:0% +compute +so again I'm not being shy about this + + align:start position:0% +so again I'm not being shy about this + + + align:start position:0% +so again I'm not being shy about this +because we advertise that numerical + + align:start position:0% +because we advertise that numerical + + + align:start position:0% +because we advertise that numerical +methods are important at the beginning + + align:start position:0% +methods are important at the beginning + + + align:start position:0% +methods are important at the beginning +of the class so I do one occasionally to + + align:start position:0% +of the class so I do one occasionally to + + + align:start position:0% +of the class so I do one occasionally to +show you how numerical methods can get + + align:start position:0% +show you how numerical methods can get + + + align:start position:0% +show you how numerical methods can get +used and also I know you guys are a + + align:start position:0% +used and also I know you guys are a + + + align:start position:0% +used and also I know you guys are a +great class uh so I'm not worried that + + align:start position:0% +great class uh so I'm not worried that + + + align:start position:0% +great class uh so I'm not worried that +this is necessarily too hard but it's it + + align:start position:0% +this is necessarily too hard but it's it + + + align:start position:0% +this is necessarily too hard but it's it +may be the first time that you've seen + + align:start position:0% +may be the first time that you've seen + + + align:start position:0% +may be the first time that you've seen +it which is kind of cool because you'll + + align:start position:0% +it which is kind of cool because you'll + + + align:start position:0% +it which is kind of cool because you'll +learn about maximum likelihood so what + + align:start position:0% +learn about maximum likelihood so what + + + align:start position:0% +learn about maximum likelihood so what +do we do let's fix all the parameters + + align:start position:0% +do we do let's fix all the parameters + + + align:start position:0% +do we do let's fix all the parameters +Alpha Kappa all of them a whole array of + + align:start position:0% +Alpha Kappa all of them a whole array of + + + align:start position:0% +Alpha Kappa all of them a whole array of +them I have that on the slide coming and + + align:start position:0% +them I have that on the slide coming and + + + align:start position:0% +them I have that on the slide coming and +solve that programming problem for the + + align:start position:0% +solve that programming problem for the + + + align:start position:0% +solve that programming problem for the +stratification of ability education and + + align:start position:0% +stratification of ability education and + + + align:start position:0% +stratification of ability education and +wealth and say do that for the moral + + align:start position:0% +wealth and say do that for the moral + + + align:start position:0% +wealth and say do that for the moral +hazard regime let's keep moral hazard in + + align:start position:0% +hazard regime let's keep moral hazard in + + + align:start position:0% +hazard regime let's keep moral hazard in +mind now drop limited liability now we + + align:start position:0% +mind now drop limited liability now we + + + align:start position:0% +mind now drop limited liability now we +want to construct the likelihood + + align:start position:0% +want to construct the likelihood + + + align:start position:0% +want to construct the likelihood +function which is for given parameter + + align:start position:0% +function which is for given parameter + + + align:start position:0% +function which is for given parameter +values the model predicts the + + align:start position:0% +values the model predicts the + + + align:start position:0% +values the model predicts the +probability of being a firm for + + align:start position:0% +probability of being a firm for + + + align:start position:0% +probability of being a firm for +households of this type + + align:start position:0% +households of this type + + + align:start position:0% +households of this type +the model tells us that and in the data + + align:start position:0% +the model tells us that and in the data + + + align:start position:0% +the model tells us that and in the data +we see the number + + align:start position:0% +we see the number + + + align:start position:0% +we see the number +the fraction + + align:start position:0% +the fraction + + + align:start position:0% +the fraction +of the sample that our firms in that + + align:start position:0% +of the sample that our firms in that + + + align:start position:0% +of the sample that our firms in that +wealth Talent schooling category so + + align:start position:0% +wealth Talent schooling category so + + + align:start position:0% +wealth Talent schooling category so +there may be a bit of a mismatch in the + + align:start position:0% +there may be a bit of a mismatch in the + + + align:start position:0% +there may be a bit of a mismatch in the +sense that for given parameter values + + align:start position:0% +sense that for given parameter values + + + align:start position:0% +sense that for given parameter values +the probability is low in the model and + + align:start position:0% +the probability is low in the model and + + + align:start position:0% +the probability is low in the model and +very high in the data or vice versa so + + align:start position:0% +very high in the data or vice versa so + + + align:start position:0% +very high in the data or vice versa so +then logically oh well we can play + + align:start position:0% +then logically oh well we can play + + + align:start position:0% +then logically oh well we can play +around with the parameter values we + + align:start position:0% +around with the parameter values we + + + align:start position:0% +around with the parameter values we +don't know what they are either + + align:start position:0% +don't know what they are either + + + align:start position:0% +don't know what they are either +so we bury Kappa and Alpha and all of + + align:start position:0% +so we bury Kappa and Alpha and all of + + + align:start position:0% +so we bury Kappa and Alpha and all of +those things to make the likelihood to + + align:start position:0% +those things to make the likelihood to + + + align:start position:0% +those things to make the likelihood to +maximize the probability that we would + + align:start position:0% +maximize the probability that we would + + + align:start position:0% +maximize the probability that we would +see in the data what is predicted by the + + align:start position:0% +see in the data what is predicted by the + + + align:start position:0% +see in the data what is predicted by the +model + + align:start position:0% +model + + + align:start position:0% +model +maximize the probability we would see in + + align:start position:0% +maximize the probability we would see in + + + align:start position:0% +maximize the probability we would see in +the data which is a given but it's + + align:start position:0% +the data which is a given but it's + + + align:start position:0% +the data which is a given but it's +predicted by the model and again the + + align:start position:0% +predicted by the model and again the + + + align:start position:0% +predicted by the model and again the +choices varying over all possible + + align:start position:0% +choices varying over all possible + + + align:start position:0% +choices varying over all possible +parameter values now that doesn't mean + + align:start position:0% +parameter values now that doesn't mean + + + align:start position:0% +parameter values now that doesn't mean +the likelihood will match exactly it + + align:start position:0% +the likelihood will match exactly it + + + align:start position:0% +the likelihood will match exactly it +just means the likelihood is as high as + + align:start position:0% +just means the likelihood is as high as + + + align:start position:0% +just means the likelihood is as high as +it can possibly be after searching over + + align:start position:0% +it can possibly be after searching over + + + align:start position:0% +it can possibly be after searching over +all parameter values here's a bit more + + align:start position:0% +all parameter values here's a bit more + + + align:start position:0% +all parameter values here's a bit more +of the math of it the string of + + align:start position:0% +of the math of it the string of + + + align:start position:0% +of the math of it the string of +parameter values would be risk aversion + + align:start position:0% +parameter values would be risk aversion + + + align:start position:0% +parameter values would be risk aversion +work aversion the weight on just utility + + align:start position:0% +work aversion the weight on just utility + + + align:start position:0% +work aversion the weight on just utility +in the work part Alpha in the production + + align:start position:0% +in the work part Alpha in the production + + + align:start position:0% +in the work part Alpha in the production +function Delta 0 1 2 which are the + + align:start position:0% +function Delta 0 1 2 which are the + + + align:start position:0% +function Delta 0 1 2 which are the +weights on data a Theta and S I think or + + align:start position:0% +weights on data a Theta and S I think or + + + align:start position:0% +weights on data a Theta and S I think or +the other way around Lambda being the + + align:start position:0% +the other way around Lambda being the + + + align:start position:0% +the other way around Lambda being the +limited liability constraint so we're + + align:start position:0% +limited liability constraint so we're + + + align:start position:0% +limited liability constraint so we're +going to maximize over all these + + align:start position:0% +going to maximize over all these + + + align:start position:0% +going to maximize over all these +parameters and get something like h of a + + align:start position:0% +parameters and get something like h of a + + + align:start position:0% +parameters and get something like h of a +to be the probability of being a firm + + align:start position:0% +to be the probability of being a firm + + + align:start position:0% +to be the probability of being a firm +conditioned on wealth a and it should + + align:start position:0% +conditioned on wealth a and it should + + + align:start position:0% +conditioned on wealth a and it should +have had schooling in here but not + + align:start position:0% +have had schooling in here but not + + + align:start position:0% +have had schooling in here but not +Talent we had to integrate out over 10 + + align:start position:0% +Talent we had to integrate out over 10 + + + align:start position:0% +Talent we had to integrate out over 10 +so this this object comes from the model + + align:start position:0% +so this this object comes from the model + + + align:start position:0% +so this this object comes from the model +conditioning on the stratification in + + align:start position:0% +conditioning on the stratification in + + + align:start position:0% +conditioning on the stratification in +the data and a string of parameter + + align:start position:0% +the data and a string of parameter + + + align:start position:0% +the data and a string of parameter +values so when we say maximize the + + align:start position:0% +values so when we say maximize the + + + align:start position:0% +values so when we say maximize the +likelihood L likelihood is a function of + + align:start position:0% +likelihood L likelihood is a function of + + + align:start position:0% +likelihood L likelihood is a function of +the parameter values which we will vary + + align:start position:0% +the parameter values which we will vary + + + align:start position:0% +the parameter values which we will vary +to maximize what e i is in is a + + align:start position:0% +to maximize what e i is in is a + + + align:start position:0% +to maximize what e i is in is a +statement about the data it's zero or + + align:start position:0% +statement about the data it's zero or + + + align:start position:0% +statement about the data it's zero or +one + + align:start position:0% +one + + + align:start position:0% +one +household I is either a firm or it isn't + + align:start position:0% +household I is either a firm or it isn't + + + align:start position:0% +household I is either a firm or it isn't +in the data so we count up the number + + align:start position:0% +in the data so we count up the number + + + align:start position:0% +in the data so we count up the number +every time a household is in the data as + + align:start position:0% +every time a household is in the data as + + + align:start position:0% +every time a household is in the data as +a firm we look at the associated + + align:start position:0% +a firm we look at the associated + + + align:start position:0% +a firm we look at the associated +probability of predicting that from the + + align:start position:0% +probability of predicting that from the + + + align:start position:0% +probability of predicting that from the +model this is a probability likewise + + align:start position:0% +model this is a probability likewise + + + align:start position:0% +model this is a probability likewise +logs make it the same function it's just + + align:start position:0% +logs make it the same function it's just + + + align:start position:0% +logs make it the same function it's just +a monotone function of the probability + + align:start position:0% +a monotone function of the probability + + + align:start position:0% +a monotone function of the probability +and logs are cool because they allow you + + align:start position:0% +and logs are cool because they allow you + + + align:start position:0% +and logs are cool because they allow you +to write everything is separable instead + + align:start position:0% +to write everything is separable instead + + + align:start position:0% +to write everything is separable instead +of multiplicative here's the other event + + align:start position:0% +of multiplicative here's the other event + + + align:start position:0% +of multiplicative here's the other event +a given household in the data is not a + + align:start position:0% +a given household in the data is not a + + + align:start position:0% +a given household in the data is not a +firm it's a wage earner so 1 minus zero + + align:start position:0% +firm it's a wage earner so 1 minus zero + + + align:start position:0% +firm it's a wage earner so 1 minus zero +is one so this branch is wage earner and + + align:start position:0% +is one so this branch is wage earner and + + + align:start position:0% +is one so this branch is wage earner and +what's the probability of being a wage + + align:start position:0% +what's the probability of being a wage + + + align:start position:0% +what's the probability of being a wage +earner it's one minus the probability of + + align:start position:0% +earner it's one minus the probability of + + + align:start position:0% +earner it's one minus the probability of +being a firm so this is the likelihood + + align:start position:0% +being a firm so this is the likelihood + + + align:start position:0% +being a firm so this is the likelihood +function the log likelihood function a + + align:start position:0% +function the log likelihood function a + + + align:start position:0% +function the log likelihood function a +function of the parameters and this is + + align:start position:0% +function of the parameters and this is + + + align:start position:0% +function of the parameters and this is +what where the code is maximized this is + + align:start position:0% +what where the code is maximized this is + + + align:start position:0% +what where the code is maximized this is +not linear code this is non-linear + + align:start position:0% +not linear code this is non-linear + + + align:start position:0% +not linear code this is non-linear +optimization code but there are many + + align:start position:0% +optimization code but there are many + + + align:start position:0% +optimization code but there are many +routines out there to do this and if you + + align:start position:0% +routines out there to do this and if you + + + align:start position:0% +routines out there to do this and if you +don't want to think about maximizing + + align:start position:0% +don't want to think about maximizing + + + align:start position:0% +don't want to think about maximizing +this non-linear function you can just + + align:start position:0% +this non-linear function you can just + + + align:start position:0% +this non-linear function you can just +evaluate it at you know thousands of + + align:start position:0% +evaluate it at you know thousands of + + + align:start position:0% +evaluate it at you know thousands of +these parameter configurations and pick + + align:start position:0% +these parameter configurations and pick + + + align:start position:0% +these parameter configurations and pick +the max which actually gets close to the + + align:start position:0% +the max which actually gets close to the + + + align:start position:0% +the max which actually gets close to the +to the maximum okay so too tiny to read + + align:start position:0% +to the maximum okay so too tiny to read + + + align:start position:0% +to the maximum okay so too tiny to read +but conceptually we have a moral hazard + + align:start position:0% +but conceptually we have a moral hazard + + + align:start position:0% +but conceptually we have a moral hazard +column a limited liability column and + + align:start position:0% +column a limited liability column and + + + align:start position:0% +column a limited liability column and +both constraints column and what we're + + align:start position:0% +both constraints column and what we're + + + align:start position:0% +both constraints column and what we're +doing with various specifications + + align:start position:0% +doing with various specifications + + + align:start position:0% +doing with various specifications +including this one estimating Talent is + + align:start position:0% +including this one estimating Talent is + + + align:start position:0% +including this one estimating Talent is +reporting the maximized parameter value + + align:start position:0% +reporting the maximized parameter value + + + align:start position:0% +reporting the maximized parameter value +so again that Vector string was gamma + + align:start position:0% +so again that Vector string was gamma + + + align:start position:0% +so again that Vector string was gamma +and Gamma 2 Kappa and so on and you can + + align:start position:0% +and Gamma 2 Kappa and so on and you can + + + align:start position:0% +and Gamma 2 Kappa and so on and you can +see the point estimates for risk + + align:start position:0% +see the point estimates for risk + + + align:start position:0% +see the point estimates for risk +aversion which was Gamma One we're + + align:start position:0% +aversion which was Gamma One we're + + + align:start position:0% +aversion which was Gamma One we're +getting Point estimates here of 0.06 or + + align:start position:0% +getting Point estimates here of 0.06 or + + + align:start position:0% +getting Point estimates here of 0.06 or +0.02 so almost was neutral actually but + + align:start position:0% +0.02 so almost was neutral actually but + + + align:start position:0% +0.02 so almost was neutral actually but +in parentheses is a standard error which + + align:start position:0% +in parentheses is a standard error which + + + align:start position:0% +in parentheses is a standard error which +is expressed the degree of confidence + + align:start position:0% +is expressed the degree of confidence + + + align:start position:0% +is expressed the degree of confidence +about the point estimates so those are + + align:start position:0% +about the point estimates so those are + + + align:start position:0% +about the point estimates so those are +the parameter estimates now what do we + + align:start position:0% +the parameter estimates now what do we + + + align:start position:0% +the parameter estimates now what do we +find we find at the end of the day a + + align:start position:0% +find we find at the end of the day a + + + align:start position:0% +find we find at the end of the day a +couple years of research that the + + align:start position:0% +couple years of research that the + + + align:start position:0% +couple years of research that the +central region favors moral hazard and + + align:start position:0% +central region favors moral hazard and + + + align:start position:0% +central region favors moral hazard and +likewise in the cross-section as we + + align:start position:0% +likewise in the cross-section as we + + + align:start position:0% +likewise in the cross-section as we +increased the wealth going from one + + align:start position:0% +increased the wealth going from one + + + align:start position:0% +increased the wealth going from one +household to the next an increase in + + align:start position:0% +household to the next an increase in + + + align:start position:0% +household to the next an increase in +wealth is associated with an increase in + + align:start position:0% +wealth is associated with an increase in + + + align:start position:0% +wealth is associated with an increase in +net saving which we also measured so + + align:start position:0% +net saving which we also measured so + + + align:start position:0% +net saving which we also measured so +this is consistent with moral hazard and + + align:start position:0% +this is consistent with moral hazard and + + + align:start position:0% +this is consistent with moral hazard and +the slide I showed you at the beginning + + align:start position:0% +the slide I showed you at the beginning + + + align:start position:0% +the slide I showed you at the beginning +that if it's moral hazard and you have + + align:start position:0% +that if it's moral hazard and you have + + + align:start position:0% +that if it's moral hazard and you have +higher wealth you avoid the damage + + align:start position:0% +higher wealth you avoid the damage + + + align:start position:0% +higher wealth you avoid the damage +caused by the moral hazard constraint by + + align:start position:0% +caused by the moral hazard constraint by + + + align:start position:0% +caused by the moral hazard constraint by +self-financing so you should be saving + + align:start position:0% +self-financing so you should be saving + + + align:start position:0% +self-financing so you should be saving +more as wealth goes up in the Northeast + + align:start position:0% +more as wealth goes up in the Northeast + + + align:start position:0% +more as wealth goes up in the Northeast +the story is different being constrained + + align:start position:0% +the story is different being constrained + + + align:start position:0% +the story is different being constrained +like below the constrain or at the + + align:start position:0% +like below the constrain or at the + + + align:start position:0% +like below the constrain or at the +constraint is uh not related to + + align:start position:0% +constraint is uh not related to + + + align:start position:0% +constraint is uh not related to +borrowing particularly now it is true + + align:start position:0% +borrowing particularly now it is true + + + align:start position:0% +borrowing particularly now it is true +that if you were at a constraint the + + align:start position:0% +that if you were at a constraint the + + + align:start position:0% +that if you were at a constraint the +liability constraint and wealth went up + + align:start position:0% +liability constraint and wealth went up + + + align:start position:0% +liability constraint and wealth went up +then you know they'd all be constrained + + align:start position:0% +then you know they'd all be constrained + + + align:start position:0% +then you know they'd all be constrained +by definition but there's a branch of + + align:start position:0% +by definition but there's a branch of + + + align:start position:0% +by definition but there's a branch of +entrepreneurs depending on Talent like + + align:start position:0% +entrepreneurs depending on Talent like + + + align:start position:0% +entrepreneurs depending on Talent like +if Talent was low their wealth is more + + align:start position:0% +if Talent was low their wealth is more + + + align:start position:0% +if Talent was low their wealth is more +than adequate so they may not be + + align:start position:0% +than adequate so they may not be + + + align:start position:0% +than adequate so they may not be +borrowing at all and likewise here we + + align:start position:0% +borrowing at all and likewise here we + + + align:start position:0% +borrowing at all and likewise here we +get the opposite that when wealth goes + + align:start position:0% +get the opposite that when wealth goes + + + align:start position:0% +get the opposite that when wealth goes +up for constrained entrepreneurs + + align:start position:0% +up for constrained entrepreneurs + + + align:start position:0% +up for constrained entrepreneurs +borrowing goes up but again there's this + + align:start position:0% +borrowing goes up but again there's this + + + align:start position:0% +borrowing goes up but again there's this +branch of entrepreneurs that are not + + align:start position:0% +branch of entrepreneurs that are not + + + align:start position:0% +branch of entrepreneurs that are not +necessarily borrowing so that wording on + + align:start position:0% +necessarily borrowing so that wording on + + + align:start position:0% +necessarily borrowing so that wording on +that bottom bullet point is a bit + + align:start position:0% +that bottom bullet point is a bit + + + align:start position:0% +that bottom bullet point is a bit +difficult so we have succeeded to solve + + align:start position:0% +difficult so we have succeeded to solve + + + align:start position:0% +difficult so we have succeeded to solve +the problem we've identified the + + align:start position:0% +the problem we've identified the + + + align:start position:0% +the problem we've identified the +constraints that limit small businesses + + align:start position:0% +constraints that limit small businesses + + + align:start position:0% +constraints that limit small businesses +interestingly the constraints are + + align:start position:0% +interestingly the constraints are + + + align:start position:0% +interestingly the constraints are +different in the different regions in + + align:start position:0% +different in the different regions in + + + align:start position:0% +different in the different regions in +the industrialized area near Bangkok + + align:start position:0% +the industrialized area near Bangkok + + + align:start position:0% +the industrialized area near Bangkok +which are very Urban one of these + + align:start position:0% +which are very Urban one of these + + + align:start position:0% +which are very Urban one of these +Villages is across the road from a Ford + + align:start position:0% +Villages is across the road from a Ford + + + align:start position:0% +Villages is across the road from a Ford +Motor Company Plant for example it looks + + align:start position:0% +Motor Company Plant for example it looks + + + align:start position:0% +Motor Company Plant for example it looks +like moral hazards the problem out in + + align:start position:0% +like moral hazards the problem out in + + + align:start position:0% +like moral hazards the problem out in +the Northeast the problem in which The + + align:start position:0% +the Northeast the problem in which The + + + align:start position:0% +the Northeast the problem in which The +Agrarian mostly rural the problem seems + + align:start position:0% +Agrarian mostly rural the problem seems + + + align:start position:0% +Agrarian mostly rural the problem seems +to be there's a a very limited financing + + align:start position:0% +to be there's a a very limited financing + + + align:start position:0% +to be there's a a very limited financing +constraint limited liability and they a + + align:start position:0% +constraint limited liability and they a + + + align:start position:0% +constraint limited liability and they a +lot of the households don't have a lot + + align:start position:0% +lot of the households don't have a lot + + + align:start position:0% +lot of the households don't have a lot +of wealth so they they're either + + align:start position:0% +of wealth so they they're either + + + align:start position:0% +of wealth so they they're either +constrained or don't go into business at + + align:start position:0% +constrained or don't go into business at + + + align:start position:0% +constrained or don't go into business at +all now we're not doing a policy thing + + align:start position:0% +all now we're not doing a policy thing + + + align:start position:0% +all now we're not doing a policy thing +here but it would be good for policy + + align:start position:0% +here but it would be good for policy + + + align:start position:0% +here but it would be good for policy +makers to know this because if they want + + align:start position:0% +makers to know this because if they want + + + align:start position:0% +makers to know this because if they want +to alleviate the constraints on small + + align:start position:0% +to alleviate the constraints on small + + + align:start position:0% +to alleviate the constraints on small +businesses they should direct their + + align:start position:0% +businesses they should direct their + + + align:start position:0% +businesses they should direct their +policy toward maybe in the Northeast + + align:start position:0% +policy toward maybe in the Northeast + + + align:start position:0% +policy toward maybe in the Northeast +allowing more assets to qualify as + + align:start position:0% +allowing more assets to qualify as + + + align:start position:0% +allowing more assets to qualify as +collateral not just land but you know + + align:start position:0% +collateral not just land but you know + + + align:start position:0% +collateral not just land but you know +their motorcycles which they finally did + + align:start position:0% +their motorcycles which they finally did + + + align:start position:0% +their motorcycles which they finally did +and and other things putting it in + + align:start position:0% +and and other things putting it in + + + align:start position:0% +and and other things putting it in +escrow to allow or to have the bank to + + align:start position:0% +escrow to allow or to have the bank to + + + align:start position:0% +escrow to allow or to have the bank to +have a claim on and allow to increase + + align:start position:0% +have a claim on and allow to increase + + + align:start position:0% +have a claim on and allow to increase +borrowing in the Central Area it's an + + align:start position:0% +borrowing in the Central Area it's an + + + align:start position:0% +borrowing in the Central Area it's an +information problem so there if you're + + align:start position:0% +information problem so there if you're + + + align:start position:0% +information problem so there if you're +determined to try to solve it it must be + + align:start position:0% +determined to try to solve it it must be + + + align:start position:0% +determined to try to solve it it must be +better monitoring you need better + + align:start position:0% +better monitoring you need better + + + align:start position:0% +better monitoring you need better +signals of the underlying effort by well + + align:start position:0% +signals of the underlying effort by well + + + align:start position:0% +signals of the underlying effort by well +let's try costly State verification for + + align:start position:0% +let's try costly State verification for + + + align:start position:0% +let's try costly State verification for +example which is something I talked + + align:start position:0% +example which is something I talked + + + align:start position:0% +example which is something I talked +about last time not with respect to + + align:start position:0% +about last time not with respect to + + + align:start position:0% +about last time not with respect to +verifying output but with respect to + + align:start position:0% +verifying output but with respect to + + + align:start position:0% +verifying output but with respect to +getting reliable signals of the + + align:start position:0% +getting reliable signals of the + + + align:start position:0% +getting reliable signals of the +underlying effort of the borrower okay + + align:start position:0% +underlying effort of the borrower okay + + + align:start position:0% +underlying effort of the borrower okay +so this is the economic science part of + + align:start position:0% +so this is the economic science part of + + + align:start position:0% +so this is the economic science part of +it we have models we have data we're + + align:start position:0% +it we have models we have data we're + + + align:start position:0% +it we have models we have data we're +trying to get as close to the data as + + align:start position:0% +trying to get as close to the data as + + + align:start position:0% +trying to get as close to the data as +possible we're also solving an + + align:start position:0% +possible we're also solving an + + + align:start position:0% +possible we're also solving an +interesting Finance sensing getting + + align:start position:0% +interesting Finance sensing getting + + + align:start position:0% +interesting Finance sensing getting +understanding of financing constraint + + align:start position:0% +understanding of financing constraint + + + align:start position:0% +understanding of financing constraint +and thinking about how policy would + + align:start position:0% +and thinking about how policy would + + + align:start position:0% +and thinking about how policy would +change depending on what we find out + + align:start position:0% +change depending on what we find out + + + align:start position:0% +change depending on what we find out +rather than one size fits all so that's + + align:start position:0% +rather than one size fits all so that's + + + align:start position:0% +rather than one size fits all so that's +all I have for today + + align:start position:0% +all I have for today + + + align:start position:0% +all I have for today +okay thank you very much \ No newline at end of file diff --git a/FMrYw7sgyxQ.txt b/FMrYw7sgyxQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..62628e41f332ccd9f1857e4902f42d05f1d7a6c0 --- /dev/null +++ b/FMrYw7sgyxQ.txt @@ -0,0 +1,347 @@ +align:start position:0% + +in the previous lecture we went through + + align:start position:0% +in the previous lecture we went through + + + align:start position:0% +in the previous lecture we went through +examples of inference involving some of + + align:start position:0% +examples of inference involving some of + + + align:start position:0% +examples of inference involving some of +the variations of the Bayes rule one + + align:start position:0% +the variations of the Bayes rule one + + + align:start position:0% +the variations of the Bayes rule one +case that we did not consider was the + + align:start position:0% +case that we did not consider was the + + + align:start position:0% +case that we did not consider was the +case where the unknown random variable + + align:start position:0% +case where the unknown random variable + + + align:start position:0% +case where the unknown random variable +and the observation are both continuous + + align:start position:0% +and the observation are both continuous + + + align:start position:0% +and the observation are both continuous +in this lecture we will focus + + align:start position:0% +in this lecture we will focus + + + align:start position:0% +in this lecture we will focus +exclusively on an important model of + + align:start position:0% +exclusively on an important model of + + + align:start position:0% +exclusively on an important model of +this kind and because we consider only + + align:start position:0% +this kind and because we consider only + + + align:start position:0% +this kind and because we consider only +one specific setting we will be able to + + align:start position:0% +one specific setting we will be able to + + + align:start position:0% +one specific setting we will be able to +study it in considerable detail in the + + align:start position:0% +study it in considerable detail in the + + + align:start position:0% +study it in considerable detail in the +model that we consider we start with + + align:start position:0% +model that we consider we start with + + + align:start position:0% +model that we consider we start with +some basic independent normal random + + align:start position:0% +some basic independent normal random + + + align:start position:0% +some basic independent normal random +variables some of them the theta J are + + align:start position:0% +variables some of them the theta J are + + + align:start position:0% +variables some of them the theta J are +unknown to be estimated and some of them + + align:start position:0% +unknown to be estimated and some of them + + + align:start position:0% +unknown to be estimated and some of them +the W I represent noise our observations + + align:start position:0% +the W I represent noise our observations + + + align:start position:0% +the W I represent noise our observations +X I are linear functions of these basic + + align:start position:0% +X I are linear functions of these basic + + + align:start position:0% +X I are linear functions of these basic +random variables in particular since + + align:start position:0% +random variables in particular since + + + align:start position:0% +random variables in particular since +linear functions of independent normal + + align:start position:0% +linear functions of independent normal + + + align:start position:0% +linear functions of independent normal +random variables are normal the + + align:start position:0% +random variables are normal the + + + align:start position:0% +random variables are normal the +observations are themselves normal as + + align:start position:0% +observations are themselves normal as + + + align:start position:0% +observations are themselves normal as +well this is probably the most commonly + + align:start position:0% +well this is probably the most commonly + + + align:start position:0% +well this is probably the most commonly +used type of model in all of inference + + align:start position:0% +used type of model in all of inference + + + align:start position:0% +used type of model in all of inference +and statistics this is because it is a + + align:start position:0% +and statistics this is because it is a + + + align:start position:0% +and statistics this is because it is a +reasonable approximation in many + + align:start position:0% +reasonable approximation in many + + + align:start position:0% +reasonable approximation in many +situations also it has a very clean + + align:start position:0% +situations also it has a very clean + + + align:start position:0% +situations also it has a very clean +analytical structure and a very simple + + align:start position:0% +analytical structure and a very simple + + + align:start position:0% +analytical structure and a very simple +solution for example it turns out that + + align:start position:0% +solution for example it turns out that + + + align:start position:0% +solution for example it turns out that +the posterior distribution of each theta + + align:start position:0% +the posterior distribution of each theta + + + align:start position:0% +the posterior distribution of each theta +J is itself normal and that the map and + + align:start position:0% +J is itself normal and that the map and + + + align:start position:0% +J is itself normal and that the map and +LMS estimates coincide this is because + + align:start position:0% +LMS estimates coincide this is because + + + align:start position:0% +LMS estimates coincide this is because +the peak of a normal occurs at the mean + + align:start position:0% +the peak of a normal occurs at the mean + + + align:start position:0% +the peak of a normal occurs at the mean +furthermore these estimates are given by + + align:start position:0% +furthermore these estimates are given by + + + align:start position:0% +furthermore these estimates are given by +some simple linear functions of the + + align:start position:0% +some simple linear functions of the + + + align:start position:0% +some simple linear functions of the +observations we will go over these facts + + align:start position:0% +observations we will go over these facts + + + align:start position:0% +observations we will go over these facts +by moving through a sequence of + + align:start position:0% +by moving through a sequence of + + + align:start position:0% +by moving through a sequence of +progressively more complex versions we + + align:start position:0% +progressively more complex versions we + + + align:start position:0% +progressively more complex versions we +will start with just one unknown and one + + align:start position:0% +will start with just one unknown and one + + + align:start position:0% +will start with just one unknown and one +observation and then generalize and we + + align:start position:0% +observation and then generalize and we + + + align:start position:0% +observation and then generalize and we +will illustrate the formulation and the + + align:start position:0% +will illustrate the formulation and the + + + align:start position:0% +will illustrate the formulation and the +solution through a rather realistic + + align:start position:0% +solution through a rather realistic + + + align:start position:0% +solution through a rather realistic +example where we estimate the trajectory + + align:start position:0% +example where we estimate the trajectory + + + align:start position:0% +example where we estimate the trajectory +of an object from a few noisy + + align:start position:0% +of an object from a few noisy + + + align:start position:0% +of an object from a few noisy +measurements \ No newline at end of file diff --git a/GUgIh6ff86Y.txt b/GUgIh6ff86Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..cfbde9af4a99a76554930ec91b16731e5c60bca8 --- /dev/null +++ b/GUgIh6ff86Y.txt @@ -0,0 +1,195 @@ +align:start position:0% + +people take a oh sweet class especially + + align:start position:0% +people take a oh sweet class especially + + + align:start position:0% +people take a oh sweet class especially +my version most of the students may sink + + align:start position:0% +my version most of the students may sink + + + align:start position:0% +my version most of the students may sink +uncertainty principle is actually + + align:start position:0% +uncertainty principle is actually + + + align:start position:0% +uncertainty principle is actually +related to completely related to quantum + + align:start position:0% +related to completely related to quantum + + + align:start position:0% +related to completely related to quantum +mechanics so actually it is actually + + align:start position:0% +mechanics so actually it is actually + + + align:start position:0% +mechanics so actually it is actually +another case actually uncertainty + + align:start position:0% +another case actually uncertainty + + + align:start position:0% +another case actually uncertainty +principle almost have nothing to do with + + align:start position:0% +principle almost have nothing to do with + + + align:start position:0% +principle almost have nothing to do with +quantum mechanics it has to do with just + + align:start position:0% +quantum mechanics it has to do with just + + + align:start position:0% +quantum mechanics it has to do with just +a wave description we employ when we + + align:start position:0% +a wave description we employ when we + + + align:start position:0% +a wave description we employ when we +describe the system so that's actually + + align:start position:0% +describe the system so that's actually + + + align:start position:0% +describe the system so that's actually +one of the pics in which we learn from + + align:start position:0% +one of the pics in which we learn from + + + align:start position:0% +one of the pics in which we learn from +our three the other thing which people + + align:start position:0% +our three the other thing which people + + + align:start position:0% +our three the other thing which people +will learn a lot more essentially that + + align:start position:0% +will learn a lot more essentially that + + + align:start position:0% +will learn a lot more essentially that +before they come to look us they may + + align:start position:0% +before they come to look us they may + + + align:start position:0% +before they come to look us they may +think is almost impossible to understand + + align:start position:0% +think is almost impossible to understand + + + align:start position:0% +think is almost impossible to understand +infinite number of coupled oscillators + + align:start position:0% +infinite number of coupled oscillators + + + align:start position:0% +infinite number of coupled oscillators +and it turns out that there is a very + + align:start position:0% +and it turns out that there is a very + + + align:start position:0% +and it turns out that there is a very +systematic way you can actually make use + + align:start position:0% +systematic way you can actually make use + + + align:start position:0% +systematic way you can actually make use +of simple symmetry argument and that you + + align:start position:0% +of simple symmetry argument and that you + + + align:start position:0% +of simple symmetry argument and that you +can actually create a simplified + + align:start position:0% +can actually create a simplified + + + align:start position:0% +can actually create a simplified +complicated system like infinitely long + + align:start position:0% +complicated system like infinitely long + + + align:start position:0% +complicated system like infinitely long +system so so it is actually another + + align:start position:0% +system so so it is actually another + + + align:start position:0% +system so so it is actually another +impossible task and everything can be + + align:start position:0% +impossible task and everything can be + + + align:start position:0% +impossible task and everything can be +actually understand using the concept of + + align:start position:0% +actually understand using the concept of + + + align:start position:0% +actually understand using the concept of +symmetry which we introduced in iostream \ No newline at end of file diff --git a/GUvoVvXwoOQ.txt b/GUvoVvXwoOQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..abba00413225746573c53a13bcdb1c43a20544ea --- /dev/null +++ b/GUvoVvXwoOQ.txt @@ -0,0 +1,8456 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu I let's get on with some + + align:start position:0% + + + + align:start position:0% + +Dynamics so the place + + align:start position:0% + + + + align:start position:0% + +the place I'm going to begin is just a + + align:start position:0% +the place I'm going to begin is just a + + + align:start position:0% +the place I'm going to begin is just a +comment about mechanical engineering + + align:start position:0% +comment about mechanical engineering + + + align:start position:0% +comment about mechanical engineering +courses the first and you may have heard + + align:start position:0% +courses the first and you may have heard + + + align:start position:0% +courses the first and you may have heard +this already in classes you'll be taking + + align:start position:0% +this already in classes you'll be taking + + + align:start position:0% +this already in classes you'll be taking +subjects + + align:start position:0% +subjects + + + align:start position:0% +subjects +21 if you're course two major through 29 + + align:start position:0% +21 if you're course two major through 29 + + + align:start position:0% +21 if you're course two major through 29 +and if you're 2A most of the odd ones + + align:start position:0% +and if you're 2A most of the odd ones + + + align:start position:0% +and if you're 2A most of the odd ones +but the subjects + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +through + + align:start position:0% +through + + + align:start position:0% +through +25 are really basically engineering + + align:start position:0% +25 are really basically engineering + + + align:start position:0% +25 are really basically engineering +science subject are all foundational to + + align:start position:0% +science subject are all foundational to + + + align:start position:0% +science subject are all foundational to +mechanical engineering and they all have + + align:start position:0% +mechanical engineering and they all have + + + align:start position:0% +mechanical engineering and they all have +a common sort of property to them and + + align:start position:0% +a common sort of property to them and + + + align:start position:0% +a common sort of property to them and +that is that we make observations of the + + align:start position:0% +that is that we make observations of the + + + align:start position:0% +that is that we make observations of the +world and we we ask you know we try to + + align:start position:0% +world and we we ask you know we try to + + + align:start position:0% +world and we we ask you know we try to +understand them we Poe problems you know + + align:start position:0% +understand them we Poe problems you know + + + align:start position:0% +understand them we Poe problems you know +why you know 400 years ago is the sun + + align:start position:0% +why you know 400 years ago is the sun + + + align:start position:0% +why you know 400 years ago is the sun +the center of the solar system or + + align:start position:0% +the center of the solar system or + + + align:start position:0% +the center of the solar system or +not and we try to produce + + align:start position:0% +not and we try to produce + + + align:start position:0% +not and we try to produce +models that + + align:start position:0% +models that + + + align:start position:0% +models that +explain the problem so here's the + + align:start position:0% +explain the problem so here's the + + + align:start position:0% +explain the problem so here's the +problem the question of the day we've + + align:start position:0% +problem the question of the day we've + + + align:start position:0% +problem the question of the day we've +tried to produce models to describe it + + align:start position:0% +tried to produce models to describe it + + + align:start position:0% +tried to produce models to describe it +and we make + + align:start position:0% +and we make + + + align:start position:0% +and we make +observations + + align:start position:0% + + + + align:start position:0% + +measurements to see if our models are + + align:start position:0% +measurements to see if our models are + + + align:start position:0% +measurements to see if our models are +correct and we feed that information + + align:start position:0% +correct and we feed that information + + + align:start position:0% +correct and we feed that information +back into the + + align:start position:0% +back into the + + + align:start position:0% +back into the +models we try out the models we test it + + align:start position:0% +models we try out the models we test it + + + align:start position:0% +models we try out the models we test it +against more OB observations and you go + + align:start position:0% +against more OB observations and you go + + + align:start position:0% +against more OB observations and you go +round and round and this is kind of the + + align:start position:0% +round and round and this is kind of the + + + align:start position:0% +round and round and this is kind of the +fundamental this is the way the all of + + align:start position:0% +fundamental this is the way the all of + + + align:start position:0% +fundamental this is the way the all of +these basic first five subjects use + + align:start position:0% +these basic first five subjects use + + + align:start position:0% +these basic first five subjects use +basically + + align:start position:0% +basically + + + align:start position:0% +basically +this method of + + align:start position:0% +this method of + + + align:start position:0% +this method of +inquiry so in + + align:start position:0% +inquiry so in + + + align:start position:0% +inquiry so in +two3 the way this system works my kind + + align:start position:0% +two3 the way this system works my kind + + + align:start position:0% +two3 the way this system works my kind +of + + align:start position:0% + + + + align:start position:0% + +mental conception of this modeling + + align:start position:0% +mental conception of this modeling + + + align:start position:0% +mental conception of this modeling +process is three three things and this + + align:start position:0% +process is three three things and this + + + align:start position:0% +process is three three things and this +applies to you you have a homework + + align:start position:0% +applies to you you have a homework + + + align:start position:0% +applies to you you have a homework +problem how do you attack a homework + + align:start position:0% +problem how do you attack a homework + + + align:start position:0% +problem how do you attack a homework +problem you're going to need + + align:start position:0% +problem you're going to need + + + align:start position:0% +problem you're going to need +to describe the + + align:start position:0% + + + + align:start position:0% + +motion you're going to need to choose + + align:start position:0% +motion you're going to need to choose + + + align:start position:0% +motion you're going to need to choose +the physical laws pick I'll call it + + align:start position:0% +the physical laws pick I'll call it + + + align:start position:0% +the physical laws pick I'll call it +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +short the physical + + align:start position:0% + + + + align:start position:0% + +law that you want to apply like f f + + align:start position:0% +law that you want to apply like f f + + + align:start position:0% +law that you want to apply like f f +equals ma conservation of energy + + align:start position:0% +equals ma conservation of energy + + + align:start position:0% +equals ma conservation of energy +conservation of momentum you got to know + + align:start position:0% +conservation of momentum you got to know + + + align:start position:0% +conservation of momentum you got to know +which physical laws to apply and then + + align:start position:0% +which physical laws to apply and then + + + align:start position:0% +which physical laws to apply and then +finally third you need to + + align:start position:0% + + + + align:start position:0% + +apply the correct + + align:start position:0% +apply the correct + + + align:start position:0% +apply the correct +math and that's really most most dynamic + + align:start position:0% +math and that's really most most dynamic + + + align:start position:0% +math and that's really most most dynamic +problems can be broken down this way + + align:start position:0% +problems can be broken down this way + + + align:start position:0% +problems can be broken down this way +this is the way I like to conceptually + + align:start position:0% +this is the way I like to conceptually + + + align:start position:0% +this is the way I like to conceptually +break them down you might have another + + align:start position:0% +break them down you might have another + + + align:start position:0% +break them down you might have another +model but this is the way I'm going to + + align:start position:0% +model but this is the way I'm going to + + + align:start position:0% +model but this is the way I'm going to +teach it so you need to describe the + + align:start position:0% +teach it so you need to describe the + + + align:start position:0% +teach it so you need to describe the +motion pick the correct physical laws to + + align:start position:0% +motion pick the correct physical laws to + + + align:start position:0% +motion pick the correct physical laws to +apply to the problem and apply the be + + align:start position:0% +apply to the problem and apply the be + + + align:start position:0% +apply to the problem and apply the be +able to do the correct math solving the + + align:start position:0% +able to do the correct math solving the + + + align:start position:0% +able to do the correct math solving the +equation of motion for example and this + + align:start position:0% +equation of motion for example and this + + + align:start position:0% +equation of motion for example and this +is all this is what fits in our models + + align:start position:0% +is all this is what fits in our models + + + align:start position:0% +is all this is what fits in our models +box and we test it against observations + + align:start position:0% +box and we test it against observations + + + align:start position:0% +box and we test it against observations +and measurements and improve those + + align:start position:0% +and measurements and improve those + + + align:start position:0% +and measurements and improve those +things over + + align:start position:0% +things over + + + align:start position:0% +things over +time so I'm going to give you how many + + align:start position:0% +time so I'm going to give you how many + + + align:start position:0% +time so I'm going to give you how many +of you like + + align:start position:0% +of you like + + + align:start position:0% +of you like +history I find Tech History and history + + align:start position:0% +history I find Tech History and history + + + align:start position:0% +history I find Tech History and history +of Technology kind of fun and + + align:start position:0% +of Technology kind of fun and + + + align:start position:0% +of Technology kind of fun and +interesting so I'm going to throw a + + align:start position:0% +interesting so I'm going to throw a + + + align:start position:0% +interesting so I'm going to throw a +little bit history into giving you a + + align:start position:0% +little bit history into giving you a + + + align:start position:0% +little bit history into giving you a +little quick course outline of how what + + align:start position:0% +little quick course outline of how what + + + align:start position:0% +little quick course outline of how what +we're going to do in + + align:start position:0% +we're going to do in + + + align:start position:0% +we're going to do in +this subject this + + align:start position:0% + + + + align:start position:0% + +term because the history of Dynamics and + + align:start position:0% +term because the history of Dynamics and + + + align:start position:0% +term because the history of Dynamics and +what we're going to do in the course + + align:start position:0% +what we're going to do in the course + + + align:start position:0% +what we're going to do in the course +actually F Track one another remarkably + + align:start position:0% +actually F Track one another remarkably + + + align:start position:0% +actually F Track one another remarkably +closely so if I gave you a bunch of + + align:start position:0% +closely so if I gave you a bunch of + + + align:start position:0% +closely so if I gave you a bunch of +names like Galileo Kepler decart Newton + + align:start position:0% +names like Galileo Kepler decart Newton + + + align:start position:0% +names like Galileo Kepler decart Newton +cernic Oiler lrange and + + align:start position:0% +cernic Oiler lrange and + + + align:start position:0% +cernic Oiler lrange and +Brae which one come comes + + align:start position:0% + + + + align:start position:0% + +first take a + + align:start position:0% + + + + align:start position:0% + +guess good + + align:start position:0% + + + + align:start position:0% + +cernus so cernus was polish and the + + align:start position:0% +cernus so cernus was polish and the + + + align:start position:0% +cernus so cernus was polish and the +story starts long before then but you + + align:start position:0% +story starts long before then but you + + + align:start position:0% +story starts long before then but you +know in about + + align:start position:0% +know in about + + + align:start position:0% +know in about +1500 cernus said what + + align:start position:0% + + + + align:start position:0% + +the sun's a + + align:start position:0% +the sun's a + + + align:start position:0% +the sun's a +center what is or or the Earth is the + + align:start position:0% +center what is or or the Earth is the + + + align:start position:0% +center what is or or the Earth is the +center which did he say yeah so to me + + align:start position:0% +center which did he say yeah so to me + + + align:start position:0% +center which did he say yeah so to me +you know back around 130 ad said well + + align:start position:0% +you know back around 130 ad said well + + + align:start position:0% +you know back around 130 ad said well +the sun's the Earth the center of the of + + align:start position:0% +the sun's the Earth the center of the of + + + align:start position:0% +the sun's the Earth the center of the of +the solar system Cernic's came along and + + align:start position:0% +the solar system Cernic's came along and + + + align:start position:0% +the solar system Cernic's came along and +said nope I think that in fact the sun's + + align:start position:0% +said nope I think that in fact the sun's + + + align:start position:0% +said nope I think that in fact the sun's +the center of the solar system and for + + align:start position:0% +the center of the solar system and for + + + align:start position:0% +the center of the solar system and for +the next 100 years more than a hundred + + align:start position:0% +the next 100 years more than a hundred + + + align:start position:0% +the next 100 years more than a hundred +years a couple hundred years it was a + + align:start position:0% +years a couple hundred years it was a + + + align:start position:0% +years a couple hundred years it was a +really raging controversy about that + + align:start position:0% +really raging controversy about that + + + align:start position:0% +really raging controversy about that +so + + align:start position:0% +so + + + align:start position:0% +so +cernus + + align:start position:0% +cernus + + + align:start position:0% +cernus +Brae + + align:start position:0% +Brae + + + align:start position:0% +Brae +Kepler so I'm putting him in rough + + align:start position:0% +Kepler so I'm putting him in rough + + + align:start position:0% +Kepler so I'm putting him in rough +chronological order here now I'm going + + align:start position:0% +chronological order here now I'm going + + + align:start position:0% +chronological order here now I'm going +to run out of board oh well + + align:start position:0% +to run out of board oh well + + + align:start position:0% +to run out of board oh well +um + + align:start position:0% + + + + align:start position:0% + +Galileo decart + + align:start position:0% + + + + align:start position:0% + +I'm going to + + align:start position:0% + + + + align:start position:0% + +cheat okay + + align:start position:0% +cheat okay + + + align:start position:0% +cheat okay +decart + + align:start position:0% + + + + align:start position:0% + +Newton + + align:start position:0% +Newton + + + align:start position:0% +Newton +Oiler and lrange + + align:start position:0% + + + + align:start position:0% + +so we're going to talk and say a little + + align:start position:0% +so we're going to talk and say a little + + + align:start position:0% +so we're going to talk and say a little +bit about each of them and now that I'm + + align:start position:0% +bit about each of them and now that I'm + + + align:start position:0% +bit about each of them and now that I'm +like I told you I haven't used this + + align:start position:0% +like I told you I haven't used this + + + align:start position:0% +like I told you I haven't used this +classroom before so I got to learn how + + align:start position:0% +classroom before so I got to learn how + + + align:start position:0% +classroom before so I got to learn how +to play this game I need to be able to + + align:start position:0% +to play this game I need to be able to + + + align:start position:0% +to play this game I need to be able to +reach this for a minute so Brae he was + + align:start position:0% +reach this for a minute so Brae he was + + + align:start position:0% +reach this for a minute so Brae he was +along about 1600 Brae was the + + align:start position:0% +along about 1600 Brae was the + + + align:start position:0% +along about 1600 Brae was the +mathematician the RO the Imperial + + align:start position:0% +mathematician the RO the Imperial + + + align:start position:0% +mathematician the RO the Imperial +mathematician to the emperor in Prague + + align:start position:0% +mathematician to the emperor in Prague + + + align:start position:0% +mathematician to the emperor in Prague +and he did 20 years of + + align:start position:0% +and he did 20 years of + + + align:start position:0% +and he did 20 years of +observations and he was out to prove + + align:start position:0% +observations and he was out to prove + + + align:start position:0% +observations and he was out to prove +that the Earth was the center of the + + align:start position:0% +that the Earth was the center of the + + + align:start position:0% +that the Earth was the center of the +solar system and then Kepler actually + + align:start position:0% +solar system and then Kepler actually + + + align:start position:0% +solar system and then Kepler actually +worked with him as a mathematician and + + align:start position:0% +worked with him as a mathematician and + + + align:start position:0% +worked with him as a mathematician and +then took over as the Imperial + + align:start position:0% +then took over as the Imperial + + + align:start position:0% +then took over as the Imperial +mathematician and he took bra's data 20 + + align:start position:0% +mathematician and he took bra's data 20 + + + align:start position:0% +mathematician and he took bra's data 20 +years of astronomical data without the + + align:start position:0% +years of astronomical data without the + + + align:start position:0% +years of astronomical data without the +use of a + + align:start position:0% +use of a + + + align:start position:0% +use of a +telescope and used it to come up with + + align:start position:0% +telescope and used it to come up with + + + align:start position:0% +telescope and used it to come up with +the three laws of planetary motion and + + align:start position:0% +the three laws of planetary motion and + + + align:start position:0% +the three laws of planetary motion and +so his first and second laws were put + + align:start position:0% +so his first and second laws were put + + + align:start position:0% +so his first and second laws were put +out about + + align:start position:0% + + + + align:start position:0% + +16009 and you know one of the laws is + + align:start position:0% +16009 and you know one of the laws is + + + align:start position:0% +16009 and you know one of the laws is +like equal area swept out in equal time + + align:start position:0% +like equal area swept out in equal time + + + align:start position:0% +like equal area swept out in equal time +time have you heard that one that's + + align:start position:0% +time have you heard that one that's + + + align:start position:0% +time have you heard that one that's +actually turns out to be a statement of + + align:start position:0% +actually turns out to be a statement of + + + align:start position:0% +actually turns out to be a statement of +conservation of angular momentum which + + align:start position:0% +conservation of angular momentum which + + + align:start position:0% +conservation of angular momentum which +we'll talk about quite a bit about in + + align:start position:0% +we'll talk about quite a bit about in + + + align:start position:0% +we'll talk about quite a bit about in +the course then came + + align:start position:0% +the course then came + + + align:start position:0% +the course then came +Galileo and I'm put not putting their + + align:start position:0% +Galileo and I'm put not putting their + + + align:start position:0% +Galileo and I'm put not putting their +birth and death dates here I'm kind of + + align:start position:0% +birth and death dates here I'm kind of + + + align:start position:0% +birth and death dates here I'm kind of +putting in Period of time in which kind + + align:start position:0% +putting in Period of time in which kind + + + align:start position:0% +putting in Period of time in which kind +of important things happened around him + + align:start position:0% +of important things happened around him + + + align:start position:0% +of important things happened around him +so 401 years ago a really important + + align:start position:0% +so 401 years ago a really important + + + align:start position:0% +so 401 years ago a really important +thing + + align:start position:0% +thing + + + align:start position:0% +thing +happened Galileo in 16009 turned a + + align:start position:0% +happened Galileo in 16009 turned a + + + align:start position:0% +happened Galileo in 16009 turned a +telescope on Jupiter + + align:start position:0% +telescope on Jupiter + + + align:start position:0% +telescope on Jupiter +and saw + + align:start position:0% +and saw + + + align:start position:0% +and saw +what four moons right and that then they + + align:start position:0% +what four moons right and that then they + + + align:start position:0% +what four moons right and that then they +really started having some data with + + align:start position:0% +really started having some data with + + + align:start position:0% +really started having some data with +which to really argue against the toan + + align:start position:0% +which to really argue against the toan + + + align:start position:0% +which to really argue against the toan +view of the world of the solar system + + align:start position:0% +view of the world of the solar system + + + align:start position:0% +view of the world of the solar system +the um + + align:start position:0% +the um + + + align:start position:0% +the um +deart is is an important figure to us + + align:start position:0% +deart is is an important figure to us + + + align:start position:0% +deart is is an important figure to us +and in the period of about 1630 to + + align:start position:0% +and in the period of about 1630 to + + + align:start position:0% +and in the period of about 1630 to +1644 in that period deart + + align:start position:0% +1644 in that period deart + + + align:start position:0% +1644 in that period deart +uh began what is today known as analytic + + align:start position:0% +uh began what is today known as analytic + + + align:start position:0% +uh began what is today known as analytic +geometry he was a geometer he studied + + align:start position:0% +geometry he was a geometer he studied + + + align:start position:0% +geometry he was a geometer he studied +uclid a lot but then he came up with the + + align:start position:0% +uclid a lot but then he came up with the + + + align:start position:0% +uclid a lot but then he came up with the +cartisian coordinate system XYZ and the + + align:start position:0% +cartisian coordinate system XYZ and the + + + align:start position:0% +cartisian coordinate system XYZ and the +beginnings of analytic geometry which is + + align:start position:0% +beginnings of analytic geometry which is + + + align:start position:0% +beginnings of analytic geometry which is +essentially algebra coordinates and + + align:start position:0% +essentially algebra coordinates and + + + align:start position:0% +essentially algebra coordinates and +geometry all put together and that we + + align:start position:0% +geometry all put together and that we + + + align:start position:0% +geometry all put together and that we +are going to make great use of analytic + + align:start position:0% +are going to make great use of analytic + + + align:start position:0% +are going to make great use of analytic +geometry in this course then came Newton + + align:start position:0% +geometry in this course then came Newton + + + align:start position:0% +geometry in this course then came Newton +kind of in his uh uh his actual lifespan + + align:start position:0% +kind of in his uh uh his actual lifespan + + + align:start position:0% +kind of in his uh uh his actual lifespan +16 19 43 is kind of interesting he spans + + align:start position:0% +16 19 43 is kind of interesting he spans + + + align:start position:0% +16 19 43 is kind of interesting he spans +these people and in about + + align:start position:0% + + + + align:start position:0% + +1666 is when he first the first + + align:start position:0% +1666 is when he first the first + + + align:start position:0% +1666 is when he first the first +statement of the three laws of + + align:start position:0% +statement of the three laws of + + + align:start position:0% +statement of the three laws of +motion + + align:start position:0% +motion + + + align:start position:0% +motion +okay + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +Oiler and he's + + align:start position:0% +Oiler and he's + + + align:start position:0% +Oiler and he's +1707 to 1783 that's his life span Oiler + + align:start position:0% +1707 to 1783 that's his life span Oiler + + + align:start position:0% +1707 to 1783 that's his life span Oiler +came up you know Newton never talked + + align:start position:0% +came up you know Newton never talked + + + align:start position:0% +came up you know Newton never talked +about angular momentum he mostly talked + + align:start position:0% +about angular momentum he mostly talked + + + align:start position:0% +about angular momentum he mostly talked +about particles Oiler put Newton's three + + align:start position:0% +about particles Oiler put Newton's three + + + align:start position:0% +about particles Oiler put Newton's three +laws into + + align:start position:0% +laws into + + + align:start position:0% +laws into +mathematics Oiler taught us about + + align:start position:0% +mathematics Oiler taught us about + + + align:start position:0% +mathematics Oiler taught us about +angular momentum and torque being + + align:start position:0% + + + + align:start position:0% + +dhdt in most + + align:start position:0% +dhdt in most + + + align:start position:0% +dhdt in most +cases and did he a most prolific + + align:start position:0% +cases and did he a most prolific + + + align:start position:0% +cases and did he a most prolific +mathematician of all time solve all + + align:start position:0% +mathematician of all time solve all + + + align:start position:0% +mathematician of all time solve all +sorts of important problems and then + + align:start position:0% +sorts of important problems and then + + + align:start position:0% +sorts of important problems and then +finally is lrange and lrange in about + + align:start position:0% + + + + align:start position:0% + +1788 uses an energy method energy and + + align:start position:0% +1788 uses an energy method energy and + + + align:start position:0% +1788 uses an energy method energy and +the concept of + + align:start position:0% + + + + align:start position:0% + +work to give us equations of motion so + + align:start position:0% +work to give us equations of motion so + + + align:start position:0% +work to give us equations of motion so +the + + align:start position:0% + + + + align:start position:0% + +course + + align:start position:0% +course + + + align:start position:0% +course +203 stands on the shoulders of all these + + align:start position:0% +203 stands on the shoulders of all these + + + align:start position:0% +203 stands on the shoulders of all these +people but with decart we start with + + align:start position:0% +people but with decart we start with + + + align:start position:0% +people but with decart we start with +kinematics really really this is + + align:start position:0% +kinematics really really this is + + + align:start position:0% +kinematics really really this is +analytic + + align:start position:0% +analytic + + + align:start position:0% +analytic +geometry and that's where we're going to + + align:start position:0% +geometry and that's where we're going to + + + align:start position:0% +geometry and that's where we're going to +start today is with kinematics and very + + align:start position:0% +start today is with kinematics and very + + + align:start position:0% +start today is with kinematics and very +soon therea we're going to review Newton + + align:start position:0% +soon therea we're going to review Newton + + + align:start position:0% +soon therea we're going to review Newton +the three laws and what we call the + + align:start position:0% +the three laws and what we call the + + + align:start position:0% +the three laws and what we call the +direct method for finding equations of + + align:start position:0% +direct method for finding equations of + + + align:start position:0% +direct method for finding equations of +motion conservation of momentum fact + + align:start position:0% +motion conservation of momentum fact + + + align:start position:0% +motion conservation of momentum fact +that Force sum of the forces on a object + + align:start position:0% +that Force sum of the forces on a object + + + align:start position:0% +that Force sum of the forces on a object +equals mass time acceleration or it's a + + align:start position:0% +equals mass time acceleration or it's a + + + align:start position:0% +equals mass time acceleration or it's a +Time derivative of its linear momentum + + align:start position:0% +Time derivative of its linear momentum + + + align:start position:0% +Time derivative of its linear momentum +so that's and we use that to derive + + align:start position:0% +so that's and we use that to derive + + + align:start position:0% +so that's and we use that to derive +equations of motion so we're going to go + + align:start position:0% +equations of motion so we're going to go + + + align:start position:0% +equations of motion so we're going to go +kinematics into doing the direct + + align:start position:0% +kinematics into doing the direct + + + align:start position:0% +kinematics into doing the direct +method to getting equations of + + align:start position:0% +method to getting equations of + + + align:start position:0% +method to getting equations of +motion and we go from there into angular + + align:start position:0% +motion and we go from there into angular + + + align:start position:0% +motion and we go from there into angular +momentum and what Oiler gave us the same + + align:start position:0% +momentum and what Oiler gave us the same + + + align:start position:0% +momentum and what Oiler gave us the same +thing torque we're going to do quite a + + align:start position:0% +thing torque we're going to do quite a + + + align:start position:0% +thing torque we're going to do quite a +lot with angular momentum because I know + + align:start position:0% +lot with angular momentum because I know + + + align:start position:0% +lot with angular momentum because I know +you know a lot about fals Ma and you've + + align:start position:0% +you know a lot about fals Ma and you've + + + align:start position:0% +you know a lot about fals Ma and you've +done lots of problems in 801 applying + + align:start position:0% +done lots of problems in 801 applying + + + align:start position:0% +done lots of problems in 801 applying +that done some problems use on Rigid + + align:start position:0% +that done some problems use on Rigid + + + align:start position:0% +that done some problems use on Rigid +body rotations but I think you there's a + + align:start position:0% +body rotations but I think you there's a + + + align:start position:0% +body rotations but I think you there's a +lot more you need to understand about + + align:start position:0% +lot more you need to understand about + + + align:start position:0% +lot more you need to understand about +this and we'll spend quite a bit of time + + align:start position:0% +this and we'll spend quite a bit of time + + + align:start position:0% +this and we'll spend quite a bit of time +on + + align:start position:0% +on + + + align:start position:0% +on +it and excuse me and then near the last + + align:start position:0% +it and excuse me and then near the last + + + align:start position:0% +it and excuse me and then near the last +third of the course we shift because + + align:start position:0% +third of the course we shift because + + + align:start position:0% +third of the course we shift because +lrange said that if you just write down + + align:start position:0% +lrange said that if you just write down + + + align:start position:0% +lrange said that if you just write down +expressions for + + align:start position:0% +expressions for + + + align:start position:0% +expressions for +energy kinetic and potential energy + + align:start position:0% +energy kinetic and potential energy + + + align:start position:0% +energy kinetic and potential energy +without any consideration of of Newton's + + align:start position:0% +without any consideration of of Newton's + + + align:start position:0% +without any consideration of of Newton's +laws and the direct method you can + + align:start position:0% +laws and the direct method you can + + + align:start position:0% +laws and the direct method you can +derive the equations of + + align:start position:0% +derive the equations of + + + align:start position:0% +derive the equations of +motion that's pretty remarkable so there + + align:start position:0% +motion that's pretty remarkable so there + + + align:start position:0% +motion that's pretty remarkable so there +are actually two independent roots to + + align:start position:0% +are actually two independent roots to + + + align:start position:0% +are actually two independent roots to +coming up with equations of motion and + + align:start position:0% +coming up with equations of motion and + + + align:start position:0% +coming up with equations of motion and +in this course so in about the last + + align:start position:0% +in this course so in about the last + + + align:start position:0% +in this course so in about the last +third of the course we're going to you + + align:start position:0% +third of the course we're going to you + + + align:start position:0% +third of the course we're going to you +teach you about + + align:start position:0% +teach you about + + + align:start position:0% +teach you about +lrange and all then all of these + + align:start position:0% +lrange and all then all of these + + + align:start position:0% +lrange and all then all of these +things are going to be one of the + + align:start position:0% +things are going to be one of the + + + align:start position:0% +things are going to be one of the +applications that are important to + + align:start position:0% +applications that are important to + + + align:start position:0% +applications that are important to +Engineers is a study of + + align:start position:0% + + + + align:start position:0% + +vibration so we'll be looking at + + align:start position:0% +vibration so we'll be looking at + + + align:start position:0% +vibration so we'll be looking at +vibration examples as we go through the + + align:start position:0% +vibration examples as we go through the + + + align:start position:0% +vibration examples as we go through the +course uh and applying these different + + align:start position:0% +course uh and applying these different + + + align:start position:0% +course uh and applying these different +methods + + align:start position:0% +methods + + + align:start position:0% +methods +to First modeling and then solving + + align:start position:0% +to First modeling and then solving + + + align:start position:0% +to First modeling and then solving +interesting vibration + + align:start position:0% +interesting vibration + + + align:start position:0% +interesting vibration +problems which brings ah I have a + + align:start position:0% +problems which brings ah I have a + + + align:start position:0% +problems which brings ah I have a +question for you so how many of you were + + align:start position:0% +question for you so how many of you were + + + align:start position:0% +question for you so how many of you were +in this classroom last May with + + align:start position:0% +in this classroom last May with + + + align:start position:0% +in this classroom last May with +Professor Haynes Miller and I showed up + + align:start position:0% +Professor Haynes Miller and I showed up + + + align:start position:0% +Professor Haynes Miller and I showed up +one day and we talked about + + align:start position:0% +one day and we talked about + + + align:start position:0% +one day and we talked about +vibration how many remember I told you I + + align:start position:0% +vibration how many remember I told you I + + + align:start position:0% +vibration how many remember I told you I +was going to ask this question right + + align:start position:0% +was going to ask this question right + + + align:start position:0% +was going to ask this question right +great okay it's good to see see you here + + align:start position:0% +great okay it's good to see see you here + + + align:start position:0% +great okay it's good to see see you here +again and we will talk about vibration + + align:start position:0% +again and we will talk about vibration + + + align:start position:0% +again and we will talk about vibration +in this course so there's kind of the + + align:start position:0% +in this course so there's kind of the + + + align:start position:0% +in this course so there's kind of the +subject outline built on the shoulders + + align:start position:0% +subject outline built on the shoulders + + + align:start position:0% +subject outline built on the shoulders +of these people in history that made + + align:start position:0% +of these people in history that made + + + align:start position:0% +of these people in history that made +important contributions to + + align:start position:0% + + + + align:start position:0% + +Dynamics any questions about the history + + align:start position:0% +Dynamics any questions about the history + + + align:start position:0% +Dynamics any questions about the history +if you if you want to know one of my Tas + + align:start position:0% +if you if you want to know one of my Tas + + + align:start position:0% +if you if you want to know one of my Tas +compiled a pretty neat little summary + + align:start position:0% +compiled a pretty neat little summary + + + align:start position:0% +compiled a pretty neat little summary +maybe I will see if I can go back and + + align:start position:0% +maybe I will see if I can go back and + + + align:start position:0% +maybe I will see if I can go back and +find this I just printed it out and send + + align:start position:0% +find this I just printed it out and send + + + align:start position:0% +find this I just printed it out and send +it how many of would you like to know a + + align:start position:0% +it how many of would you like to know a + + + align:start position:0% +it how many of would you like to know a +little bit more about the history these + + align:start position:0% +little bit more about the history these + + + align:start position:0% +little bit more about the history these +like like two liners on each person + + align:start position:0% +like like two liners on each person + + + align:start position:0% +like like two liners on each person +anybody want is it worth my time to send + + align:start position:0% +anybody want is it worth my time to send + + + align:start position:0% +anybody want is it worth my time to send +this out okay it's kind of + + align:start position:0% +this out okay it's kind of + + + align:start position:0% +this out okay it's kind of +fun so let's + + align:start position:0% +fun so let's + + + align:start position:0% +fun so let's +um do an + + align:start position:0% + + + + align:start position:0% + +example of this + + align:start position:0% +example of this + + + align:start position:0% +example of this +modeling describing the motion picking + + align:start position:0% +modeling describing the motion picking + + + align:start position:0% +modeling describing the motion picking +physical laws applying the + + align:start position:0% +physical laws applying the + + + align:start position:0% +physical laws applying the +math and that'll get us + + align:start position:0% +math and that'll get us + + + align:start position:0% +math and that'll get us +uh get us launched in the course and + + align:start position:0% +uh get us launched in the course and + + + align:start position:0% +uh get us launched in the course and +we'll do it using Newton and the direct + + align:start position:0% +we'll do it using Newton and the direct + + + align:start position:0% +we'll do it using Newton and the direct +method + + align:start position:0% + + + + align:start position:0% + +so last May Hayes Miller and I talked + + align:start position:0% +so last May Hayes Miller and I talked + + + align:start position:0% +so last May Hayes Miller and I talked +about + + align:start position:0% +about + + + align:start position:0% +about +vibration and so let's start I'm going + + align:start position:0% +vibration and so let's start I'm going + + + align:start position:0% +vibration and so let's start I'm going +to start with a vibration problem + + align:start position:0% + + + + align:start position:0% + +and I brought one so here's + + align:start position:0% +and I brought one so here's + + + align:start position:0% +and I brought one so here's +my couple of lead weights and a couple + + align:start position:0% +my couple of lead weights and a couple + + + align:start position:0% +my couple of lead weights and a couple +of + + align:start position:0% +of + + + align:start position:0% +of +Springs so really I just want to talk + + align:start position:0% +Springs so really I just want to talk + + + align:start position:0% +Springs so really I just want to talk +about this is the problem I want to talk + + align:start position:0% +about this is the problem I want to talk + + + align:start position:0% +about this is the problem I want to talk +about now you've done this problem + + align:start position:0% +about now you've done this problem + + + align:start position:0% +about now you've done this problem +before hannes Miller and I did it + + align:start position:0% +before hannes Miller and I did it + + + align:start position:0% +before hannes Miller and I did it +last last May and you've no doubt done + + align:start position:0% +last last May and you've no doubt done + + + align:start position:0% +last last May and you've no doubt done +it in other classes okay it's a system + + align:start position:0% +it in other classes okay it's a system + + + align:start position:0% +it in other classes okay it's a system +which has a spring a mass it exhibits + + align:start position:0% +which has a spring a mass it exhibits + + + align:start position:0% +which has a spring a mass it exhibits +something called a natural frequency but + + align:start position:0% +something called a natural frequency but + + + align:start position:0% +something called a natural frequency but +let's go let's see what it takes to just + + align:start position:0% +let's go let's see what it takes to just + + + align:start position:0% +let's go let's see what it takes to just +initially begin to follow follow this + + align:start position:0% +initially begin to follow follow this + + + align:start position:0% +initially begin to follow follow this +modeling method to arrive an equation of + + align:start position:0% +modeling method to arrive an equation of + + + align:start position:0% +modeling method to arrive an equation of +motion for this + + align:start position:0% + + + + align:start position:0% + +problem so what do I mean by when I say + + align:start position:0% +problem so what do I mean by when I say + + + align:start position:0% +problem so what do I mean by when I say +describe the motion really what that + + align:start position:0% +describe the motion really what that + + + align:start position:0% +describe the motion really what that +boils down to is you have to assign a + + align:start position:0% +boils down to is you have to assign a + + + align:start position:0% +boils down to is you have to assign a +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +system so that you can actually say + + align:start position:0% +system so that you can actually say + + + align:start position:0% +system so that you can actually say +where the object's moving and I'm going + + align:start position:0% +where the object's moving and I'm going + + + align:start position:0% +where the object's moving and I'm going +to pick one here so here's + + align:start position:0% +to pick one here so here's + + + align:start position:0% +to pick one here so here's +coordinate system can be really + + align:start position:0% +coordinate system can be really + + + align:start position:0% +coordinate system can be really +important in this + + align:start position:0% + + + + align:start position:0% + +course and + + align:start position:0% +course and + + + align:start position:0% +course and +I'll give us an + + align:start position:0% +I'll give us an + + + align:start position:0% +I'll give us an +XYZ cartisian coordinate + + align:start position:0% + + + + align:start position:0% + +system and I'm going to try to adopt the + + align:start position:0% +system and I'm going to try to adopt the + + + align:start position:0% +system and I'm going to try to adopt the +habit for the most part during the + + align:start position:0% +habit for the most part during the + + + align:start position:0% +habit for the most part during the +course that this o marks this origin but + + align:start position:0% +course that this o marks this origin but + + + align:start position:0% +course that this o marks this origin but +it also names the frame so we we have + + align:start position:0% +it also names the frame so we we have + + + align:start position:0% +it also names the frame so we we have +we're going to talk about things that + + align:start position:0% +we're going to talk about things that + + + align:start position:0% +we're going to talk about things that +are reference frames and and and most + + align:start position:0% +are reference frames and and and most + + + align:start position:0% +are reference frames and and and most +important one that we need to know about + + align:start position:0% +important one that we need to know about + + + align:start position:0% +important one that we need to know about +in the course is an inertial reference + + align:start position:0% +in the course is an inertial reference + + + align:start position:0% +in the course is an inertial reference +frame and when you can use it and when a + + align:start position:0% +frame and when you can use it and when a + + + align:start position:0% +frame and when you can use it and when a +system is inertial and is not so I'm + + align:start position:0% +system is inertial and is not so I'm + + + align:start position:0% +system is inertial and is not so I'm +going to say that this is inertial it's + + align:start position:0% +going to say that this is inertial it's + + + align:start position:0% +going to say that this is inertial it's +fixed to the Earth it's not moving and + + align:start position:0% +fixed to the Earth it's not moving and + + + align:start position:0% +fixed to the Earth it's not moving and +we're going to use this coordinate X to + + align:start position:0% +we're going to use this coordinate X to + + + align:start position:0% +we're going to use this coordinate X to +describe the motion of this mass and the + + align:start position:0% +describe the motion of this mass and the + + + align:start position:0% +describe the motion of this mass and the +motion is going to be this x is + + align:start position:0% +motion is going to be this x is + + + align:start position:0% +motion is going to be this x is +from the + + align:start position:0% +from the + + + align:start position:0% +from the +zero spring + + align:start position:0% + + + + align:start position:0% + +Force position it's actually quite + + align:start position:0% +Force position it's actually quite + + + align:start position:0% +Force position it's actually quite +important that you pick you have to say + + align:start position:0% +important that you pick you have to say + + + align:start position:0% +important that you pick you have to say +you know what's the condition in the + + align:start position:0% +you know what's the condition in the + + + align:start position:0% +you know what's the condition in the +spring of this system when you when X is + + align:start position:0% +spring of this system when you when X is + + + align:start position:0% +spring of this system when you when X is +zero so we're going to say it's when + + align:start position:0% +zero so we're going to say it's when + + + align:start position:0% +zero so we're going to say it's when +there's no force in the spring means + + align:start position:0% +there's no force in the spring means + + + align:start position:0% +there's no force in the spring means +it's not stretch that's where zero + + align:start position:0% +it's not stretch that's where zero + + + align:start position:0% +it's not stretch that's where zero +is so we've established a coordinate + + align:start position:0% + + + + align:start position:0% + +system second we need to apply physical + + align:start position:0% +system second we need to apply physical + + + align:start position:0% +system second we need to apply physical +laws + + align:start position:0% + + + + align:start position:0% + +now I'm going to do this + + align:start position:0% +now I'm going to do this + + + align:start position:0% +now I'm going to do this +problem by fals Ma Newton's Second Law + + align:start position:0% +problem by fals Ma Newton's Second Law + + + align:start position:0% +problem by fals Ma Newton's Second Law +sum the external forces is equal to math + + align:start position:0% +sum the external forces is equal to math + + + align:start position:0% +sum the external forces is equal to math +mass times the acceleration so that's + + align:start position:0% +mass times the acceleration so that's + + + align:start position:0% +mass times the acceleration so that's +the law I'm going to + + align:start position:0% +the law I'm going to + + + align:start position:0% +the law I'm going to +apply sum of the external + + align:start position:0% +apply sum of the external + + + align:start position:0% +apply sum of the external +forces it's a vector but we're just + + align:start position:0% +forces it's a vector but we're just + + + align:start position:0% +forces it's a vector but we're just +doing the X component only so we don't + + align:start position:0% +doing the X component only so we don't + + + align:start position:0% +doing the X component only so we don't +have to area along Vector notation is + + align:start position:0% +have to area along Vector notation is + + + align:start position:0% +have to area along Vector notation is +equal to this case mass time + + align:start position:0% +equal to this case mass time + + + align:start position:0% +equal to this case mass time +acceleration so that's the law we're + + align:start position:0% +acceleration so that's the law we're + + + align:start position:0% +acceleration so that's the law we're +going to apply and then finally the + + align:start position:0% +going to apply and then finally the + + + align:start position:0% +going to apply and then finally the +um the math that solve the equation of + + align:start position:0% +um the math that solve the equation of + + + align:start position:0% +um the math that solve the equation of +motion that we find that'll be the third + + align:start position:0% +motion that we find that'll be the third + + + align:start position:0% +motion that we find that'll be the third +piece but part of applying the physics + + align:start position:0% +piece but part of applying the physics + + + align:start position:0% +piece but part of applying the physics +in order to do this now we + + align:start position:0% + + + + align:start position:0% + +need what I call an + + align:start position:0% +need what I call an + + + align:start position:0% +need what I call an +fbd what do you suppose that is + + align:start position:0% +fbd what do you suppose that is + + + align:start position:0% +fbd what do you suppose that is +free body diagrams you've run you've + + align:start position:0% +free body diagrams you've run you've + + + align:start position:0% +free body diagrams you've run you've +used these many times before so we're + + align:start position:0% +used these many times before so we're + + + align:start position:0% +used these many times before so we're +going to do those + + align:start position:0% +going to do those + + + align:start position:0% +going to do those +and free body + + align:start position:0% +and free body + + + align:start position:0% +and free body +diagrams and I'm going to teach you uh + + align:start position:0% +diagrams and I'm going to teach you uh + + + align:start position:0% +diagrams and I'm going to teach you uh +at least the way I go about doing free + + align:start position:0% +at least the way I go about doing free + + + align:start position:0% +at least the way I go about doing free +body diagrams as things get more and + + align:start position:0% +body diagrams as things get more and + + + align:start position:0% +body diagrams as things get more and +more complicated you have to you're + + align:start position:0% +more complicated you have to you're + + + align:start position:0% +more complicated you have to you're +going to have to be more and more + + align:start position:0% +going to have to be more and more + + + align:start position:0% +going to have to be more and more +sophisticated in the way that you do + + align:start position:0% +sophisticated in the way that you do + + + align:start position:0% +sophisticated in the way that you do +these things so I just have some simple + + align:start position:0% +these things so I just have some simple + + + align:start position:0% +these things so I just have some simple +little rules to do free body diagrams + + align:start position:0% +little rules to do free body diagrams + + + align:start position:0% +little rules to do free body diagrams +that keep you from getting hung up up on + + align:start position:0% +that keep you from getting hung up up on + + + align:start position:0% +that keep you from getting hung up up on +sign conventions I think the thing + + align:start position:0% +sign conventions I think the thing + + + align:start position:0% +sign conventions I think the thing +people make most mistakes about is they + + align:start position:0% +people make most mistakes about is they + + + align:start position:0% +people make most mistakes about is they +get confused about signs so I'll try + + align:start position:0% +get confused about signs so I'll try + + + align:start position:0% +get confused about signs so I'll try +I'll show you how I do + + align:start position:0% +I'll show you how I do + + + align:start position:0% +I'll show you how I do +it so first you draw the you draw forces + + align:start position:0% +it so first you draw the you draw forces + + + align:start position:0% +it so first you draw the you draw forces +that you + + align:start position:0% + + + + align:start position:0% + +know basically in the direction in which + + align:start position:0% +know basically in the direction in which + + + align:start position:0% +know basically in the direction in which +they act seems obvious + + align:start position:0% +they act seems obvious + + + align:start position:0% +they act seems obvious +so when you know the + + align:start position:0% + + + + align:start position:0% + +direction so this is a really trivial + + align:start position:0% +direction so this is a really trivial + + + align:start position:0% +direction so this is a really trivial +problem but the method + + align:start position:0% + + + + align:start position:0% + +here is is very specific see in so + + align:start position:0% +here is is very specific see in so + + + align:start position:0% +here is is very specific see in so +what's an example well gravity so we'll + + align:start position:0% +what's an example well gravity so we'll + + + align:start position:0% +what's an example well gravity so we'll +start our free body + + align:start position:0% +start our free body + + + align:start position:0% +start our free body +diagram gravity acts at the center of + + align:start position:0% +diagram gravity acts at the center of + + + align:start position:0% +diagram gravity acts at the center of +mass hits downward this is what I mean + + align:start position:0% +mass hits downward this is what I mean + + + align:start position:0% +mass hits downward this is what I mean +by the direction in which it acts and it + + align:start position:0% +by the direction in which it acts and it + + + align:start position:0% +by the direction in which it acts and it +has magnitude + + align:start position:0% +has magnitude + + + align:start position:0% +has magnitude +mg okay now the other forces aren't so + + align:start position:0% +mg okay now the other forces aren't so + + + align:start position:0% +mg okay now the other forces aren't so +obvious the force that's put on by the + + align:start position:0% +obvious the force that's put on by the + + + align:start position:0% +obvious the force that's put on by the +stiffness and the damper in the spring + + align:start position:0% +stiffness and the damper in the spring + + + align:start position:0% +stiffness and the damper in the spring +which way do you draw them what's a sign + + align:start position:0% +which way do you draw them what's a sign + + + align:start position:0% +which way do you draw them what's a sign +what's the sign + + align:start position:0% +what's the sign + + + align:start position:0% +what's the sign +convention so the convention the way I + + align:start position:0% +convention so the convention the way I + + + align:start position:0% +convention so the convention the way I +go about doing these things is I + + align:start position:0% + + + + align:start position:0% + +assume positive + + align:start position:0% + + + + align:start position:0% + +positive + + align:start position:0% + + + + align:start position:0% + +values for the deflections and + + align:start position:0% +values for the deflections and + + + align:start position:0% +values for the deflections and +velocities so in this case x and x dot + + align:start position:0% +velocities so in this case x and x dot + + + align:start position:0% +velocities so in this case x and x dot +you just require that the the + + align:start position:0% +you just require that the the + + + align:start position:0% +you just require that the the +deflections that you're going to work + + align:start position:0% +deflections that you're going to work + + + align:start position:0% +deflections that you're going to work +with are positive and then from the + + align:start position:0% +with are positive and then from the + + + align:start position:0% +with are positive and then from the +positive deflection you say which way is + + align:start position:0% +positive deflection you say which way is + + + align:start position:0% +positive deflection you say which way is +the resulting Force so if the deflection + + align:start position:0% +the resulting Force so if the deflection + + + align:start position:0% +the resulting Force so if the deflection +in this is downwards which direction is + + align:start position:0% +in this is downwards which direction is + + + align:start position:0% +in this is downwards which direction is +the force that the spring applies to the + + align:start position:0% +the force that the spring applies to the + + + align:start position:0% +the force that the spring applies to the +mass up right what about if the velocity + + align:start position:0% +mass up right what about if the velocity + + + align:start position:0% +mass up right what about if the velocity +is downwards which which direction is + + align:start position:0% +is downwards which which direction is + + + align:start position:0% +is downwards which which direction is +the force that the damper puts on the + + align:start position:0% +the force that the damper puts on the + + + align:start position:0% +the force that the damper puts on the +mass also up right okay so this this + + align:start position:0% +mass also up right okay so this this + + + align:start position:0% +mass also up right okay so this this +allows this gives + + align:start position:0% +allows this gives + + + align:start position:0% +allows this gives +us so here's F spring and here's the F + + align:start position:0% +us so here's F spring and here's the F + + + align:start position:0% +us so here's F spring and here's the F +damper and are there any other forces on + + align:start position:0% +damper and are there any other forces on + + + align:start position:0% +damper and are there any other forces on +this + + align:start position:0% +this + + + align:start position:0% +this +Mass so spring Force damper force and + + align:start position:0% +Mass so spring Force damper force and + + + align:start position:0% +Mass so spring Force damper force and +the gravitational + + align:start position:0% +the gravitational + + + align:start position:0% +the gravitational +force whoops + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +third you deduce the + + align:start position:0% + + + + align:start position:0% + +signs it's basically from the direction + + align:start position:0% +signs it's basically from the direction + + + align:start position:0% +signs it's basically from the direction +of the + + align:start position:0% + + + + align:start position:0% + +arrows first we need what's called your + + align:start position:0% +arrows first we need what's called your + + + align:start position:0% +arrows first we need what's called your +constitutive relationship so so the + + align:start position:0% +constitutive relationship so so the + + + align:start position:0% +constitutive relationship so so the +spring + + align:start position:0% +spring + + + align:start position:0% +spring +Force FS well you've made X positive so + + align:start position:0% +Force FS well you've made X positive so + + + align:start position:0% +Force FS well you've made X positive so +it keeps things nice the spring + + align:start position:0% +it keeps things nice the spring + + + align:start position:0% +it keeps things nice the spring +constants a positive number so FS is k + + align:start position:0% +constants a positive number so FS is k + + + align:start position:0% +constants a positive number so FS is k +x FD is BX Dot and now we write the + + align:start position:0% +x FD is BX Dot and now we write the + + + align:start position:0% +x FD is BX Dot and now we write the +statement that the sum of the forces in + + align:start position:0% +statement that the sum of the forces in + + + align:start position:0% +statement that the sum of the forces in +the X + + align:start position:0% + + + + align:start position:0% + +direction we look at up here we say well + + align:start position:0% +direction we look at up here we say well + + + align:start position:0% +direction we look at up here we say well +that's going to + + align:start position:0% +that's going to + + + align:start position:0% +that's going to +be FS Plus FD minus + + align:start position:0% +be FS Plus FD minus + + + align:start position:0% +be FS Plus FD minus +mg so + + align:start position:0% +mg so + + + align:start position:0% +mg so +that's whoops I moved the wrong way + + align:start position:0% +that's whoops I moved the wrong way + + + align:start position:0% +that's whoops I moved the wrong way +around + + align:start position:0% +around + + + align:start position:0% +around +minus minus plus because I'm plus + + align:start position:0% +minus minus plus because I'm plus + + + align:start position:0% +minus minus plus because I'm plus +downwards right well spring minus FS is + + align:start position:0% +downwards right well spring minus FS is + + + align:start position:0% +downwards right well spring minus FS is +minus + + align:start position:0% +minus + + + align:start position:0% +minus +KX minus BX dot plus + + align:start position:0% +KX minus BX dot plus + + + align:start position:0% +KX minus BX dot plus +mg equal MX + + align:start position:0% +mg equal MX + + + align:start position:0% +mg equal MX +Dot and I rearrange this to put all the + + align:start position:0% +Dot and I rearrange this to put all the + + + align:start position:0% +Dot and I rearrange this to put all the +motion variables on one side + + align:start position:0% +motion variables on one side + + + align:start position:0% +motion variables on one side +MX dot plus BX dot plus KX + + align:start position:0% +MX dot plus BX dot plus KX + + + align:start position:0% +MX dot plus BX dot plus KX +equals + + align:start position:0% + + + + align:start position:0% + +mg so there's my equation of motion but + + align:start position:0% +mg so there's my equation of motion but + + + align:start position:0% +mg so there's my equation of motion but +with a method for doing the free body + + align:start position:0% +with a method for doing the free body + + + align:start position:0% +with a method for doing the free body +diagrams which will work with multiple + + align:start position:0% +diagrams which will work with multiple + + + align:start position:0% +diagrams which will work with multiple +bodies so you have two bodies with + + align:start position:0% +bodies so you have two bodies with + + + align:start position:0% +bodies so you have two bodies with +springs in between them this is when the + + align:start position:0% +springs in between them this is when the + + + align:start position:0% +springs in between them this is when the +confusion really comes up two bodies of + + align:start position:0% +confusion really comes up two bodies of + + + align:start position:0% +confusion really comes up two bodies of +a spring trapped between + + align:start position:0% +a spring trapped between + + + align:start position:0% +a spring trapped between +them what's the sign + + align:start position:0% +them what's the sign + + + align:start position:0% +them what's the sign +convention you do the same thing both + + align:start position:0% +convention you do the same thing both + + + align:start position:0% +convention you do the same thing both +Bodies exhibit positive motions the the + + align:start position:0% +Bodies exhibit positive motions the the + + + align:start position:0% +Bodies exhibit positive motions the the +force that results is proportional to + + align:start position:0% +force that results is proportional to + + + align:start position:0% +force that results is proportional to +the difference and you work it out and + + align:start position:0% +the difference and you work it out and + + + align:start position:0% +the difference and you work it out and +you'll get the science right okay so + + align:start position:0% +you'll get the science right okay so + + + align:start position:0% +you'll get the science right okay so +here's our equation of motion arrived at + + align:start position:0% +here's our equation of motion arrived at + + + align:start position:0% +here's our equation of motion arrived at +by doing the direct method and just + + align:start position:0% +by doing the direct method and just + + + align:start position:0% +by doing the direct method and just +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +to we could you if we went on to the + + align:start position:0% +to we could you if we went on to the + + + align:start position:0% +to we could you if we went on to the +third step which we're not going to do + + align:start position:0% +third step which we're not going to do + + + align:start position:0% +third step which we're not going to do +today and that is apply the math it + + align:start position:0% +today and that is apply the math it + + + align:start position:0% +today and that is apply the math it +might be because I want you now to + + align:start position:0% +might be because I want you now to + + + align:start position:0% +might be because I want you now to +describe the motion for me get solve for + + align:start position:0% +describe the motion for me get solve for + + + align:start position:0% +describe the motion for me get solve for +the motion means solving the + + align:start position:0% +the motion means solving the + + + align:start position:0% +the motion means solving the +differential equation and that's what we + + align:start position:0% +differential equation and that's what we + + + align:start position:0% +differential equation and that's what we +did last May in Hanes Miller's class + + align:start position:0% +did last May in Hanes Miller's class + + + align:start position:0% +did last May in Hanes Miller's class +we'll come back to this later on but for + + align:start position:0% +we'll come back to this later on but for + + + align:start position:0% +we'll come back to this later on but for +today's purposes we don't need to we + + align:start position:0% +today's purposes we don't need to we + + + align:start position:0% +today's purposes we don't need to we +don't need to go there we got something + + align:start position:0% +don't need to go there we got something + + + align:start position:0% +don't need to go there we got something +else much more important to get to about + + align:start position:0% +else much more important to get to about + + + align:start position:0% +else much more important to get to about +kinematics but I want to show you one + + align:start position:0% +kinematics but I want to show you one + + + align:start position:0% +kinematics but I want to show you one +thing and that is just just a little + + align:start position:0% +thing and that is just just a little + + + align:start position:0% +thing and that is just just a little +tiny introductory taste to this + + align:start position:0% +tiny introductory taste to this + + + align:start position:0% +tiny introductory taste to this +point so I've derived the equation of + + align:start position:0% +point so I've derived the equation of + + + align:start position:0% +point so I've derived the equation of +motion of this by saying Say by Newton's + + align:start position:0% +motion of this by saying Say by Newton's + + + align:start position:0% +motion of this by saying Say by Newton's +laws but I'm going to ignore Newton now + + align:start position:0% +laws but I'm going to ignore Newton now + + + align:start position:0% +laws but I'm going to ignore Newton now +and say I'm going to drive the equation + + align:start position:0% +and say I'm going to drive the equation + + + align:start position:0% +and say I'm going to drive the equation +of motion by another way and it's an + + align:start position:0% +of motion by another way and it's an + + + align:start position:0% +of motion by another way and it's an +energy technique and that is well let's + + align:start position:0% +energy technique and that is well let's + + + align:start position:0% +energy technique and that is well let's +talk about the total energy of this + + align:start position:0% +talk about the total energy of this + + + align:start position:0% +talk about the total energy of this +system it's going to be the sum of a + + align:start position:0% +system it's going to be the sum of a + + + align:start position:0% +system it's going to be the sum of a +kinetic energy and a potential + + align:start position:0% +kinetic energy and a potential + + + align:start position:0% +kinetic energy and a potential +energy okay and un and we'll find that + + align:start position:0% +energy okay and un and we'll find that + + + align:start position:0% +energy okay and un and we'll find that +even with lrange there's a problem with + + align:start position:0% +even with lrange there's a problem with + + + align:start position:0% +even with lrange there's a problem with +forces on systems that are what we call + + align:start position:0% +forces on systems that are what we call + + + align:start position:0% +forces on systems that are what we call +non-conservative things that either take + + align:start position:0% +non-conservative things that either take + + + align:start position:0% +non-conservative things that either take +energy out of or put it energy into the + + align:start position:0% +energy out of or put it energy into the + + + align:start position:0% +energy out of or put it energy into the +system and the dash poot does that Dash + + align:start position:0% +system and the dash poot does that Dash + + + align:start position:0% +system and the dash poot does that Dash +poot generates heat and takes energy out + + align:start position:0% +poot generates heat and takes energy out + + + align:start position:0% +poot generates heat and takes energy out +of the system so I'm going to have to + + align:start position:0% +of the system so I'm going to have to + + + align:start position:0% +of the system so I'm going to have to +ignore it for the moment so the sum of + + align:start position:0% +ignore it for the moment so the sum of + + + align:start position:0% +ignore it for the moment so the sum of +the kinetic and the potential energies + + align:start position:0% +the kinetic and the potential energies + + + align:start position:0% +the kinetic and the potential energies +in this problem is a + + align:start position:0% +in this problem is a + + + align:start position:0% +in this problem is a +half K x^2 for the potential of the + + align:start position:0% +half K x^2 for the potential of the + + + align:start position:0% +half K x^2 for the potential of the +spring plus a half m x dot squar for the + + align:start position:0% +spring plus a half m x dot squar for the + + + align:start position:0% +spring plus a half m x dot squar for the +kinetic energy of the mass and minus m g + + align:start position:0% +kinetic energy of the mass and minus m g + + + align:start position:0% +kinetic energy of the mass and minus m g +x for the potential energy that is due + + align:start position:0% +x for the potential energy that is due + + + align:start position:0% +x for the potential energy that is due +to the object moving in the + + align:start position:0% +to the object moving in the + + + align:start position:0% +to the object moving in the +gravitational field right and that's the + + align:start position:0% +gravitational field right and that's the + + + align:start position:0% +gravitational field right and that's the +total energy of the + + align:start position:0% +total energy of the + + + align:start position:0% +total energy of the +system now and I have my problem I've + + align:start position:0% +system now and I have my problem I've + + + align:start position:0% +system now and I have my problem I've +allowed no forces there's no excitation + + align:start position:0% +allowed no forces there's no excitation + + + align:start position:0% +allowed no forces there's no excitation +on here this is just free vibration only + + align:start position:0% +on here this is just free vibration only + + + align:start position:0% +on here this is just free vibration only +it's all we're talking about maybe + + align:start position:0% +it's all we're talking about maybe + + + align:start position:0% +it's all we're talking about maybe +initial displacement and it + + align:start position:0% +initial displacement and it + + + align:start position:0% +initial displacement and it +vibrates if there's no damping what can + + align:start position:0% +vibrates if there's no damping what can + + + align:start position:0% +vibrates if there's no damping what can +you say about the total energy of the + + align:start position:0% +you say about the total energy of the + + + align:start position:0% +you say about the total energy of the +system + + align:start position:0% + + + + align:start position:0% + +say it again I heard it over it's got to + + align:start position:0% +say it again I heard it over it's got to + + + align:start position:0% +say it again I heard it over it's got to +be constant right all right well so it + + align:start position:0% +be constant right all right well so it + + + align:start position:0% +be constant right all right well so it +must this must be constant therefore the + + align:start position:0% +must this must be constant therefore the + + + align:start position:0% +must this must be constant therefore the +time derivative of U my + + align:start position:0% + + + + align:start position:0% + +system it better be zero the energy is + + align:start position:0% +system it better be zero the energy is + + + align:start position:0% +system it better be zero the energy is +constant take its time deriv it's got to + + align:start position:0% +constant take its time deriv it's got to + + + align:start position:0% +constant take its time deriv it's got to +be zero + + align:start position:0% +be zero + + + align:start position:0% +be zero +apply that to the right hand side of + + align:start position:0% +apply that to the right hand side of + + + align:start position:0% +apply that to the right hand side of +this I get k x x dot plus + + align:start position:0% +this I get k x x dot plus + + + align:start position:0% +this I get k x x dot plus +m x dot X double dot minus + + align:start position:0% +m x dot X double dot minus + + + align:start position:0% +m x dot X double dot minus +mgx dot = + + align:start position:0% +mgx dot = + + + align:start position:0% +mgx dot = +Z and I now cancel out the common x dot + + align:start position:0% +Z and I now cancel out the common x dot + + + align:start position:0% +Z and I now cancel out the common x dot +terms go + + align:start position:0% +terms go + + + align:start position:0% +terms go +away and I'm left with + + align:start position:0% + + + + align:start position:0% + +and I've essentially solved for the + + align:start position:0% +and I've essentially solved for the + + + align:start position:0% +and I've essentially solved for the +equation of motion of this system + + align:start position:0% +equation of motion of this system + + + align:start position:0% +equation of motion of this system +without ever looking at conservational + + align:start position:0% +without ever looking at conservational + + + align:start position:0% +without ever looking at conservational +momentum Newton's Laws only by energy + + align:start position:0% + + + + align:start position:0% + +considerations okay so that's a very + + align:start position:0% +considerations okay so that's a very + + + align:start position:0% +considerations okay so that's a very +simple example of that you can use + + align:start position:0% +simple example of that you can use + + + align:start position:0% +simple example of that you can use +energy to derive equations of motions + + align:start position:0% +energy to derive equations of motions + + + align:start position:0% +energy to derive equations of motions +but you then have you have to go back + + align:start position:0% +but you then have you have to go back + + + align:start position:0% +but you then have you have to go back +and fix it to account for the the loss + + align:start position:0% +and fix it to account for the the loss + + + align:start position:0% +and fix it to account for the the loss +term the damping term and that you still + + align:start position:0% +term the damping term and that you still + + + align:start position:0% +term the damping term and that you still +have to consider it as a force we'll + + align:start position:0% +have to consider it as a force we'll + + + align:start position:0% +have to consider it as a force we'll +find out even with L Grange you have to + + align:start position:0% +find out even with L Grange you have to + + + align:start position:0% +find out even with L Grange you have to +go back and consider the work done by + + align:start position:0% +go back and consider the work done by + + + align:start position:0% +go back and consider the work done by +external + + align:start position:0% +external + + + align:start position:0% +external +forces + + align:start position:0% +forces + + + align:start position:0% +forces +okay so this you've just kind of seen + + align:start position:0% +okay so this you've just kind of seen + + + align:start position:0% +okay so this you've just kind of seen +the whole course we've described the + + align:start position:0% +the whole course we've described the + + + align:start position:0% +the whole course we've described the +motion we've applied Newton's Laws the + + align:start position:0% +motion we've applied Newton's Laws the + + + align:start position:0% +motion we've applied Newton's Laws the +physics to the direct method to derive + + align:start position:0% +physics to the direct method to derive + + + align:start position:0% +physics to the direct method to derive +the equations of motion we have gone to + + align:start position:0% +the equations of motion we have gone to + + + align:start position:0% +the equations of motion we have gone to +an energy method and have derive the + + align:start position:0% +an energy method and have derive the + + + align:start position:0% +an energy method and have derive the +equations of motion that way and that's + + align:start position:0% +equations of motion that way and that's + + + align:start position:0% +equations of motion that way and that's +basically what you're going to do in the + + align:start position:0% +basically what you're going to do in the + + + align:start position:0% +basically what you're going to do in the +course but now we're now you're going to + + align:start position:0% +course but now we're now you're going to + + + align:start position:0% +course but now we're now you're going to +do it with much more sophisticated + + align:start position:0% +do it with much more sophisticated + + + align:start position:0% +do it with much more sophisticated +tools you'll have multiple degree of + + align:start position:0% +tools you'll have multiple degree of + + + align:start position:0% +tools you'll have multiple degree of +Freedom systems the description + + align:start position:0% +Freedom systems the description + + + align:start position:0% +Freedom systems the description +describing the motion is maybe going to + + align:start position:0% +describing the motion is maybe going to + + + align:start position:0% +describing the motion is maybe going to +be for some of you the most challenging + + align:start position:0% +be for some of you the most challenging + + + align:start position:0% +be for some of you the most challenging +part of the course and this is a topic + + align:start position:0% +part of the course and this is a topic + + + align:start position:0% +part of the course and this is a topic +we call + + align:start position:0% + + + + align:start position:0% + +kinematics and that's what we'll turn to + + align:start position:0% + + + + align:start position:0% + +next so reference frames and vectors + + align:start position:0% +next so reference frames and vectors + + + align:start position:0% +next so reference frames and vectors +that's the topic this is now that we're + + align:start position:0% +that's the topic this is now that we're + + + align:start position:0% +that's the topic this is now that we're +talking about kinematics and this is all + + align:start position:0% +talking about kinematics and this is all + + + align:start position:0% +talking about kinematics and this is all +about describing the + + align:start position:0% +about describing the + + + align:start position:0% +about describing the +motion so + + align:start position:0% +motion so + + + align:start position:0% +motion so +decart gave us the car Ian coordinate + + align:start position:0% +decart gave us the car Ian coordinate + + + align:start position:0% +decart gave us the car Ian coordinate +system and we'll start there so + + align:start position:0% +system and we'll start there so + + + align:start position:0% +system and we'll start there so +imagine this is a fixed frame we'll talk + + align:start position:0% +imagine this is a fixed frame we'll talk + + + align:start position:0% +imagine this is a fixed frame we'll talk +about what makes an inertial frame than + + align:start position:0% +about what makes an inertial frame than + + + align:start position:0% +about what makes an inertial frame than +the next lecture but here we have an + + align:start position:0% +the next lecture but here we have an + + + align:start position:0% +the next lecture but here we have an +inertial + + align:start position:0% + + + + align:start position:0% + +frame and it's the frame we'll call O + + align:start position:0% +frame and it's the frame we'll call O + + + align:start position:0% +frame and it's the frame we'll call O +XY o XYZ or o for + + align:start position:0% +XY o XYZ or o for + + + align:start position:0% +XY o XYZ or o for +short and in this + + align:start position:0% + + + + align:start position:0% + +frame maybe this is + + align:start position:0% +frame maybe this is + + + align:start position:0% +frame maybe this is +me and up here is a + + align:start position:0% + + + + align:start position:0% + +dog and I'm going to call this point a + + align:start position:0% +dog and I'm going to call this point a + + + align:start position:0% +dog and I'm going to call this point a +and this point + + align:start position:0% + + + + align:start position:0% + +B and I'm going to describe the + + align:start position:0% +B and I'm going to describe the + + + align:start position:0% +B and I'm going to describe the +positions of + + align:start position:0% +positions of + + + align:start position:0% +positions of +these two points by vectors this one + + align:start position:0% +these two points by vectors this one + + + align:start position:0% +these two points by vectors this one +will be R and the notation that I'm + + align:start position:0% +will be R and the notation that I'm + + + align:start position:0% +will be R and the notation that I'm +going to use is the + + align:start position:0% +going to use is the + + + align:start position:0% +going to use is the +point and its measure meas with respect + + align:start position:0% +point and its measure meas with respect + + + align:start position:0% +point and its measure meas with respect +to something well it's with respect to + + align:start position:0% +to something well it's with respect to + + + align:start position:0% +to something well it's with respect to +this point O in this inertial Frame so + + align:start position:0% +this point O in this inertial Frame so + + + align:start position:0% +this point O in this inertial Frame so +this is a with respect to O is the way + + align:start position:0% +this is a with respect to O is the way + + + align:start position:0% +this is a with respect to O is the way +to read this there's another Rector here + + align:start position:0% +to read this there's another Rector here + + + align:start position:0% +to read this there's another Rector here +this is r b with respect to a and + + align:start position:0% +this is r b with respect to a and + + + align:start position:0% +this is r b with respect to a and +finally R of B with respect to O they're + + align:start position:0% +finally R of B with respect to O they're + + + align:start position:0% +finally R of B with respect to O they're +all vectors on the board I'll try to + + align:start position:0% +all vectors on the board I'll try to + + + align:start position:0% +all vectors on the board I'll try to +remember to underline them in the + + align:start position:0% +remember to underline them in the + + + align:start position:0% +remember to underline them in the +textbooks and things they're usually + + align:start position:0% +textbooks and things they're usually + + + align:start position:0% +textbooks and things they're usually +vectors are no noted as with bold + + align:start position:0% + + + + align:start position:0% + +letters and Vector allows to say the + + align:start position:0% +letters and Vector allows to say the + + + align:start position:0% +letters and Vector allows to say the +following that + + align:start position:0% + + + + align:start position:0% + +R the position of the dog and the + + align:start position:0% +R the position of the dog and the + + + align:start position:0% +R the position of the dog and the +reference with respect to O is the sum + + align:start position:0% +reference with respect to O is the sum + + + align:start position:0% +reference with respect to O is the sum +of these other two vectors R of a with + + align:start position:0% +of these other two vectors R of a with + + + align:start position:0% +of these other two vectors R of a with +respect to o plus r of B with respect to + + align:start position:0% + + + + align:start position:0% + +a and mostly to do Dynamics were really + + align:start position:0% +a and mostly to do Dynamics were really + + + align:start position:0% +a and mostly to do Dynamics were really +interested in things like velocities and + + align:start position:0% +interested in things like velocities and + + + align:start position:0% +interested in things like velocities and +accelerations so to get to velocities + + align:start position:0% +accelerations so to get to velocities + + + align:start position:0% +accelerations so to get to velocities +and accelerations we have to take a Time + + align:start position:0% +and accelerations we have to take a Time + + + align:start position:0% +and accelerations we have to take a Time +derivative of + + align:start position:0% +derivative of + + + align:start position:0% +derivative of +rbo + + align:start position:0% + + + + align:start position:0% + +DT and that's going to give us what + + align:start position:0% +DT and that's going to give us what + + + align:start position:0% +DT and that's going to give us what +we'll call the velocity I'll usually + + align:start position:0% +we'll call the velocity I'll usually + + + align:start position:0% +we'll call the velocity I'll usually +write it as V and it' be the velocity of + + align:start position:0% +write it as V and it' be the velocity of + + + align:start position:0% +write it as V and it' be the velocity of +point B with respect to + + align:start position:0% +point B with respect to + + + align:start position:0% +point B with respect to +O and no surprise it'll be the velocity + + align:start position:0% +O and no surprise it'll be the velocity + + + align:start position:0% +O and no surprise it'll be the velocity +of point + + align:start position:0% +of point + + + align:start position:0% +of point +A Plus the velocity of B with respect to + + align:start position:0% + + + + align:start position:0% + +a and finally if we take two + + align:start position:0% + + + + align:start position:0% + +derivatives dt^ + + align:start position:0% +derivatives dt^ + + + align:start position:0% +derivatives dt^ +2 we'll get the + + align:start position:0% +2 we'll get the + + + align:start position:0% +2 we'll get the +acceleration of B with respect to O and + + align:start position:0% +acceleration of B with respect to O and + + + align:start position:0% +acceleration of B with respect to O and +that'll be the sum of a the acceleration + + align:start position:0% +that'll be the sum of a the acceleration + + + align:start position:0% +that'll be the sum of a the acceleration +of a with respect to o + + align:start position:0% +of a with respect to o + + + align:start position:0% +of a with respect to o +plus the acceler eration of B with + + align:start position:0% +plus the acceler eration of B with + + + align:start position:0% +plus the acceler eration of B with +respect to a all again + + align:start position:0% + + + + align:start position:0% + +vectors now just to look ahead you know + + align:start position:0% +vectors now just to look ahead you know + + + align:start position:0% +vectors now just to look ahead you know +this seems all really triv trivial you + + align:start position:0% +this seems all really triv trivial you + + + align:start position:0% +this seems all really triv trivial you +guys are going to sleep on me + + align:start position:0% + + + + align:start position:0% + +right if these are rigid + + align:start position:0% +right if these are rigid + + + align:start position:0% +right if these are rigid +bodies this is a rigid body that is + + align:start position:0% +bodies this is a rigid body that is + + + align:start position:0% +bodies this is a rigid body that is +moving and maybe + + align:start position:0% +moving and maybe + + + align:start position:0% +moving and maybe +rotating and B is on it and a is on it + + align:start position:0% +rotating and B is on it and a is on it + + + align:start position:0% +rotating and B is on it and a is on it +and O isn't on + + align:start position:0% +and O isn't on + + + align:start position:0% +and O isn't on +it it starts getting a little + + align:start position:0% +it it starts getting a little + + + align:start position:0% +it it starts getting a little +tricky and this the + + align:start position:0% +tricky and this the + + + align:start position:0% +tricky and this the +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +of a vector that's attached to the + + align:start position:0% +of a vector that's attached to the + + + align:start position:0% +of a vector that's attached to the +body somehow has to account for the the + + align:start position:0% +body somehow has to account for the the + + + align:start position:0% +body somehow has to account for the the +fact that if + + align:start position:0% +fact that if + + + align:start position:0% +fact that if +I'm the observers on the body this other + + align:start position:0% +I'm the observers on the body this other + + + align:start position:0% +I'm the observers on the body this other +Point's on the body say it's I'm on this + + align:start position:0% +Point's on the body say it's I'm on this + + + align:start position:0% +Point's on the body say it's I'm on this +asteroid and there's and I've got a dog + + align:start position:0% +asteroid and there's and I've got a dog + + + align:start position:0% +asteroid and there's and I've got a dog +out there and the dog's running away + + align:start position:0% +out there and the dog's running away + + + align:start position:0% +out there and the dog's running away +from me the speed of the dog with + + align:start position:0% +from me the speed of the dog with + + + align:start position:0% +from me the speed of the dog with +respect to + + align:start position:0% +respect to + + + align:start position:0% +respect to +me I can measure but if I'm down here + + align:start position:0% +me I can measure but if I'm down here + + + align:start position:0% +me I can measure but if I'm down here +looking at it it'll look different + + align:start position:0% +looking at it it'll look different + + + align:start position:0% +looking at it it'll look different +because it's rotating so how do you + + align:start position:0% +because it's rotating so how do you + + + align:start position:0% +because it's rotating so how do you +account for all that so taking these + + align:start position:0% +account for all that so taking these + + + align:start position:0% +account for all that so taking these +derivatives of vectors in moving frames + + align:start position:0% +derivatives of vectors in moving frames + + + align:start position:0% +derivatives of vectors in moving frames +is where the the devil's in the details + + align:start position:0% +is where the the devil's in the details + + + align:start position:0% +is where the the devil's in the details +and that's part of what I have + + align:start position:0% +and that's part of what I have + + + align:start position:0% +and that's part of what I have +to that's part of what I'm going to be + + align:start position:0% +to that's part of what I'm going to be + + + align:start position:0% +to that's part of what I'm going to be +teaching + + align:start position:0% +teaching + + + align:start position:0% +teaching +you okay I'm still learning how to how + + align:start position:0% +you okay I'm still learning how to how + + + align:start position:0% +you okay I'm still learning how to how +to maximize you know going to optimize + + align:start position:0% +to maximize you know going to optimize + + + align:start position:0% +to maximize you know going to optimize +my board use I haven't got it perfect + + align:start position:0% +my board use I haven't got it perfect + + + align:start position:0% +my board use I haven't got it perfect +yet because I'm having to move around a + + align:start position:0% +yet because I'm having to move around a + + + align:start position:0% +yet because I'm having to move around a +lot here and improvise but we'll + + align:start position:0% +lot here and improvise but we'll + + + align:start position:0% +lot here and improvise but we'll +persevere you need to know a remember a + + align:start position:0% +persevere you need to know a remember a + + + align:start position:0% +persevere you need to know a remember a +couple things about + + align:start position:0% +couple things about + + + align:start position:0% +couple things about +vectors how to add + + align:start position:0% +vectors how to add + + + align:start position:0% +vectors how to add +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +them uh dot + + align:start position:0% +them uh dot + + + align:start position:0% +them uh dot +products if you've had forgotten these + + align:start position:0% +products if you've had forgotten these + + + align:start position:0% +products if you've had forgotten these +things you need to go back and review + + align:start position:0% +things you need to go back and review + + + align:start position:0% +things you need to go back and review +them really quickly there's usually a + + align:start position:0% +them really quickly there's usually a + + + align:start position:0% +them really quickly there's usually a +little review section in the book you + + align:start position:0% +little review section in the book you + + + align:start position:0% +little review section in the book you +need to practice that sort of + + align:start position:0% +need to practice that sort of + + + align:start position:0% +need to practice that sort of +thing couple other little facts you need + + align:start position:0% +thing couple other little facts you need + + + align:start position:0% +thing couple other little facts you need +to remember so the derivative + + align:start position:0% +to remember so the derivative + + + align:start position:0% +to remember so the derivative +of the sum of two + + align:start position:0% +of the sum of two + + + align:start position:0% +of the sum of two +vectors is just the sum of the + + align:start position:0% + + + + align:start position:0% + +derivatives + + align:start position:0% +derivatives + + + align:start position:0% +derivatives +and quite importantly we're going to + + align:start position:0% +and quite importantly we're going to + + + align:start position:0% +and quite importantly we're going to +make use of this one a lot is the + + align:start position:0% +make use of this one a lot is the + + + align:start position:0% +make use of this one a lot is the +derivative of a product of two things + + align:start position:0% +derivative of a product of two things + + + align:start position:0% +derivative of a product of two things +one of them being a vector some function + + align:start position:0% +one of them being a vector some function + + + align:start position:0% +one of them being a vector some function +maybe of time and a here + + align:start position:0% +maybe of time and a here + + + align:start position:0% +maybe of time and a here +is derivative of f with respect to T * + + align:start position:0% +is derivative of f with respect to T * + + + align:start position:0% +is derivative of f with respect to T * +a + + align:start position:0% +a + + + align:start position:0% +a +plus + + align:start position:0% +plus + + + align:start position:0% +plus +the derivative of a with respect to T + + align:start position:0% +the derivative of a with respect to T + + + align:start position:0% +the derivative of a with respect to T +time + + align:start position:0% +time + + + align:start position:0% +time +F that will make a lot of use of so just + + align:start position:0% +F that will make a lot of use of so just + + + align:start position:0% +F that will make a lot of use of so just +your basic + + align:start position:0% +your basic + + + align:start position:0% +your basic +calculus so now I want to take up let's + + align:start position:0% +calculus so now I want to take up let's + + + align:start position:0% +calculus so now I want to take up let's +talk about the simplest form of being + + align:start position:0% +talk about the simplest form of being + + + align:start position:0% +talk about the simplest form of being +able to do these derivatives and + + align:start position:0% +able to do these derivatives and + + + align:start position:0% +able to do these derivatives and +calculate these + + align:start position:0% +calculate these + + + align:start position:0% +calculate these +velocities + + align:start position:0% +velocities + + + align:start position:0% +velocities +when everything's described + + align:start position:0% +when everything's described + + + align:start position:0% +when everything's described +cribed in terms of cartisian + + align:start position:0% +cribed in terms of cartisian + + + align:start position:0% +cribed in terms of cartisian +coordinates now I'm going to give you a + + align:start position:0% +coordinates now I'm going to give you a + + + align:start position:0% +coordinates now I'm going to give you a +little look ahead because I don't I + + align:start position:0% +little look ahead because I don't I + + + align:start position:0% +little look ahead because I don't I +don't want to uh I going to try to avoid + + align:start position:0% +don't want to uh I going to try to avoid + + + align:start position:0% +don't want to uh I going to try to avoid +confusion as much as much as possible + + align:start position:0% +confusion as much as much as possible + + + align:start position:0% +confusion as much as much as possible +here the hardest problem is when you're + + align:start position:0% +here the hardest problem is when you're + + + align:start position:0% +here the hardest problem is when you're +the you have a rigid body you got the + + align:start position:0% +the you have a rigid body you got the + + + align:start position:0% +the you have a rigid body you got the +dog on it you got the Observer on it + + align:start position:0% +dog on it you got the Observer on it + + + align:start position:0% +dog on it you got the Observer on it +it's rotating and + + align:start position:0% +it's rotating and + + + align:start position:0% +it's rotating and +translating uh and to take this + + align:start position:0% +translating uh and to take this + + + align:start position:0% +translating uh and to take this +derivative you end up with a number of + + align:start position:0% +derivative you end up with a number of + + + align:start position:0% +derivative you end up with a number of +terms the simplest problem is just + + align:start position:0% +terms the simplest problem is just + + + align:start position:0% +terms the simplest problem is just +something in a fixed cartisian + + align:start position:0% +something in a fixed cartisian + + + align:start position:0% +something in a fixed cartisian +coordinate system so we're going to + + align:start position:0% +coordinate system so we're going to + + + align:start position:0% +coordinate system so we're going to +start with the simple one and build our + + align:start position:0% +start with the simple one and build our + + + align:start position:0% +start with the simple one and build our +way up to the complicated one + + align:start position:0% + + + + align:start position:0% + +okay but let's now we're going to do the + + align:start position:0% +okay but let's now we're going to do the + + + align:start position:0% +okay but let's now we're going to do the +really the the simplest one we're going + + align:start position:0% +really the the simplest one we're going + + + align:start position:0% +really the the simplest one we're going +to do velocity and + + align:start position:0% +to do velocity and + + + align:start position:0% +to do velocity and +acceleration in cartisian + + align:start position:0% + + + + align:start position:0% + +coordinates and basically I should say + + align:start position:0% +coordinates and basically I should say + + + align:start position:0% +coordinates and basically I should say +fixed + + align:start position:0% + + + + align:start position:0% + +cartisian coordinates not + + align:start position:0% + + + + align:start position:0% + +moving all right so now let's consider + + align:start position:0% +moving all right so now let's consider + + + align:start position:0% +moving all right so now let's consider +my the dog out here and his position in + + align:start position:0% +my the dog out here and his position in + + + align:start position:0% +my the dog out here and his position in +the cartisian coordinate + + align:start position:0% +the cartisian coordinate + + + align:start position:0% +the cartisian coordinate +system and I could write that and I + + align:start position:0% +system and I could write that and I + + + align:start position:0% +system and I could write that and I +you'll without any loss of generality + + align:start position:0% +you'll without any loss of generality + + + align:start position:0% +you'll without any loss of generality +here you'll know what I mean if I say + + align:start position:0% +here you'll know what I mean if I say + + + align:start position:0% +here you'll know what I mean if I say +RB X component and I'm going to stop + + align:start position:0% +RB X component and I'm going to stop + + + align:start position:0% +RB X component and I'm going to stop +writing the SL O's because this is now + + align:start position:0% +writing the SL O's because this is now + + + align:start position:0% +writing the SL O's because this is now +all in this fixed reference frame and + + align:start position:0% +all in this fixed reference frame and + + + align:start position:0% +all in this fixed reference frame and +it's in the I hat Direction and I've got + + align:start position:0% +it's in the I hat Direction and I've got + + + align:start position:0% +it's in the I hat Direction and I've got +another component + + align:start position:0% +another component + + + align:start position:0% +another component +RB + + align:start position:0% +RB + + + align:start position:0% +RB +y in the J hat and an + + align:start position:0% +y in the J hat and an + + + align:start position:0% +y in the J hat and an +RBZ in the K + + align:start position:0% +RBZ in the K + + + align:start position:0% +RBZ in the K +hat and I want to take the time + + align:start position:0% +hat and I want to take the time + + + align:start position:0% +hat and I want to take the time +derivative I'm looking for the velocity + + align:start position:0% +derivative I'm looking for the velocity + + + align:start position:0% +derivative I'm looking for the velocity +I want to calculate the + + align:start position:0% +I want to calculate the + + + align:start position:0% +I want to calculate the +velocity so the velocity here of B in + + align:start position:0% +velocity so the velocity here of B in + + + align:start position:0% +velocity so the velocity here of B in +O is d by DT of + + align:start position:0% +O is d by DT of + + + align:start position:0% +O is d by DT of +r b + + align:start position:0% +r b + + + align:start position:0% +r b +and now this is now the product of two + + align:start position:0% +and now this is now the product of two + + + align:start position:0% +and now this is now the product of two +things so I got to use that formula over + + align:start position:0% +things so I got to use that formula over + + + align:start position:0% +things so I got to use that formula over +here product one term times the other so + + align:start position:0% +here product one term times the other so + + + align:start position:0% +here product one term times the other so +forth so I I go to these and I say okay + + align:start position:0% +forth so I I go to these and I say okay + + + align:start position:0% +forth so I I go to these and I say okay +so this is r + + align:start position:0% +so this is r + + + align:start position:0% +so this is r +dot BX time + + align:start position:0% +dot BX time + + + align:start position:0% +dot BX time +I plus r dot b y * + + align:start position:0% + + + + align:start position:0% + +J plus r do bz * k + + align:start position:0% +J plus r do bz * k + + + align:start position:0% +J plus r do bz * k +and then the other the flip side of that + + align:start position:0% +and then the other the flip side of that + + + align:start position:0% +and then the other the flip side of that +is I have to take the derivatives of the + + align:start position:0% +is I have to take the derivatives of the + + + align:start position:0% +is I have to take the derivatives of the +I time RBX the derivative J and so forth + + align:start position:0% +I time RBX the derivative J and so forth + + + align:start position:0% +I time RBX the derivative J and so forth +but what's the derivative of let's say I + + align:start position:0% +but what's the derivative of let's say I + + + align:start position:0% +but what's the derivative of let's say I +I is the capital I is my unit Vector in + + align:start position:0% +I is the capital I is my unit Vector in + + + align:start position:0% +I is the capital I is my unit Vector in +the fixed reference frame my o XYZ frame + + align:start position:0% +the fixed reference frame my o XYZ frame + + + align:start position:0% +the fixed reference frame my o XYZ frame +so it's a constant it is unit length and + + align:start position:0% +so it's a constant it is unit length and + + + align:start position:0% +so it's a constant it is unit length and +it points in a direction that is fixed + + align:start position:0% +it points in a direction that is fixed + + + align:start position:0% +it points in a direction that is fixed +so what's its derivative okay it's going + + align:start position:0% +so what's its derivative okay it's going + + + align:start position:0% +so what's its derivative okay it's going +to have a zero derivative so the second + + align:start position:0% +to have a zero derivative so the second + + + align:start position:0% +to have a zero derivative so the second +part of this second bits of that is zero + + align:start position:0% +part of this second bits of that is zero + + + align:start position:0% +part of this second bits of that is zero +and that's so that's the Velocity in + + align:start position:0% +and that's so that's the Velocity in + + + align:start position:0% +and that's so that's the Velocity in +cartisian coordinates of my dog out + + align:start position:0% +cartisian coordinates of my dog out + + + align:start position:0% +cartisian coordinates of my dog out +there on running around + + align:start position:0% +there on running around + + + align:start position:0% +there on running around +okay and the acceleration in a similar + + align:start position:0% +okay and the acceleration in a similar + + + align:start position:0% +okay and the acceleration in a similar +way you get now to get the acceleration + + align:start position:0% +way you get now to get the acceleration + + + align:start position:0% +way you get now to get the acceleration +you take another derivative of this and + + align:start position:0% +you take another derivative of this and + + + align:start position:0% +you take another derivative of this and +again you'll have to take derivatives of + + align:start position:0% +again you'll have to take derivatives of + + + align:start position:0% +again you'll have to take derivatives of +i j and k and again they're going to be + + align:start position:0% +i j and k and again they're going to be + + + align:start position:0% +i j and k and again they're going to be +zero so you will find that the + + align:start position:0% +zero so you will find that the + + + align:start position:0% +zero so you will find that the +acceleration + + align:start position:0% +acceleration + + + align:start position:0% +acceleration +then is just r do X + + align:start position:0% +then is just r do X + + + align:start position:0% +then is just r do X +term in the I plus r dot by y in the J + + align:start position:0% +term in the I plus r dot by y in the J + + + align:start position:0% +term in the I plus r dot by y in the J +plus r dot bz in the K it'll be our + + align:start position:0% +plus r dot bz in the K it'll be our + + + align:start position:0% +plus r dot bz in the K it'll be our +acceleration term and it's + + align:start position:0% + + + + align:start position:0% + +easy now imagine that we were doing this + + align:start position:0% +easy now imagine that we were doing this + + + align:start position:0% +easy now imagine that we were doing this +in polar coordinates unit vectors in + + align:start position:0% +in polar coordinates unit vectors in + + + align:start position:0% +in polar coordinates unit vectors in +polar coordinates you actually let me + + align:start position:0% +polar coordinates you actually let me + + + align:start position:0% +polar coordinates you actually let me +check last year the students told me + + align:start position:0% +check last year the students told me + + + align:start position:0% +check last year the students told me +that m in your physics courses you use + + align:start position:0% +that m in your physics courses you use + + + align:start position:0% +that m in your physics courses you use +unit vectors R hat Theta hat and K is + + align:start position:0% +unit vectors R hat Theta hat and K is + + + align:start position:0% +unit vectors R hat Theta hat and K is +that right so I'll use those unit + + align:start position:0% +that right so I'll use those unit + + + align:start position:0% +that right so I'll use those unit +vectors so they look familiar because in + + align:start position:0% +vectors so they look familiar because in + + + align:start position:0% +vectors so they look familiar because in +polar coordinates people use lots of + + align:start position:0% +polar coordinates people use lots of + + + align:start position:0% +polar coordinates people use lots of +different things but think about it in + + align:start position:0% +different things but think about it in + + + align:start position:0% +different things but think about it in +polar coordinates Theta you know it's a + + align:start position:0% +polar coordinates Theta you know it's a + + + align:start position:0% +polar coordinates Theta you know it's a +fixed maybe coordinate system but now + + align:start position:0% +fixed maybe coordinate system but now + + + align:start position:0% +fixed maybe coordinate system but now +you know Theta goes like this and R + + align:start position:0% +you know Theta goes like this and R + + + align:start position:0% +you know Theta goes like this and R +moves with Theta right so the unit + + align:start position:0% +moves with Theta right so the unit + + + align:start position:0% +moves with Theta right so the unit +Vector is pointing here but over time it + + align:start position:0% +Vector is pointing here but over time it + + + align:start position:0% +Vector is pointing here but over time it +might move down to here and unit Vector + + align:start position:0% +might move down to here and unit Vector + + + align:start position:0% +might move down to here and unit Vector +has + + align:start position:0% +has + + + align:start position:0% +has +changed Direction and its derivative in + + align:start position:0% +changed Direction and its derivative in + + + align:start position:0% +changed Direction and its derivative in +time is no longer zero so it starts + + align:start position:0% +time is no longer zero so it starts + + + align:start position:0% +time is no longer zero so it starts +getting messy as soon as the unit + + align:start position:0% +getting messy as soon as the unit + + + align:start position:0% +getting messy as soon as the unit +vectors change in time and so that's one + + align:start position:0% +vectors change in time and so that's one + + + align:start position:0% +vectors change in time and so that's one +our objectives here is to get to that + + align:start position:0% +our objectives here is to get to that + + + align:start position:0% +our objectives here is to get to that +point and describe how you handle those + + align:start position:0% +point and describe how you handle those + + + align:start position:0% +point and describe how you handle those +cases + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay so quick point about + + align:start position:0% +okay so quick point about + + + align:start position:0% +okay so quick point about +velocity need to really understand what + + align:start position:0% +velocity need to really understand what + + + align:start position:0% +velocity need to really understand what +we mean by velocity so here's + + align:start position:0% +we mean by velocity so here's + + + align:start position:0% +we mean by velocity so here's +our car + + align:start position:0% +our car + + + align:start position:0% +our car +system here's this point out here + + align:start position:0% +system here's this point out here + + + align:start position:0% +system here's this point out here +B now this is the dog running around and + + align:start position:0% +B now this is the dog running around and + + + align:start position:0% +B now this is the dog running around and +the path of the dog you know might have + + align:start position:0% +the path of the dog you know might have + + + align:start position:0% +the path of the dog you know might have +been you know like this and right in + + align:start position:0% +been you know like this and right in + + + align:start position:0% +been you know like this and right in +here he's going this + + align:start position:0% +here he's going this + + + align:start position:0% +here he's going this +direction and in a little + + align:start position:0% + + + + align:start position:0% + +time in delta T + + align:start position:0% + + + + align:start position:0% + +he moves by an amount Delta + + align:start position:0% +he moves by an amount Delta + + + align:start position:0% +he moves by an amount Delta +r b with respect to + + align:start position:0% +r b with respect to + + + align:start position:0% +r b with respect to +O and that's what this + + align:start position:0% +O and that's what this + + + align:start position:0% +O and that's what this +is he's move this little bit in time + + align:start position:0% +is he's move this little bit in time + + + align:start position:0% +is he's move this little bit in time +delta T he happens to be going off in + + align:start position:0% +delta T he happens to be going off in + + + align:start position:0% +delta T he happens to be going off in +that direction so this then is our Prime + + align:start position:0% +that direction so this then is our Prime + + + align:start position:0% +that direction so this then is our Prime +I'll call it of B with respect to O and + + align:start position:0% +I'll call it of B with respect to O and + + + align:start position:0% +I'll call it of B with respect to O and +this is our original r b with respect to + + align:start position:0% +this is our original r b with respect to + + + align:start position:0% +this is our original r b with respect to +O So we can say that his new position + + align:start position:0% +O So we can say that his new position + + + align:start position:0% +O So we can say that his new position +you know + + align:start position:0% +you know + + + align:start position:0% +you know +r b with respect to O Prime is + + align:start position:0% +r b with respect to O Prime is + + + align:start position:0% +r b with respect to O Prime is +rbo plus delt + + align:start position:0% + + + + align:start position:0% + +R and these are you know all + + align:start position:0% + + + + align:start position:0% + +vectors and the + + align:start position:0% + + + + align:start position:0% + +velocity of B with respect to O is just + + align:start position:0% +velocity of B with respect to O is just + + + align:start position:0% +velocity of B with respect to O is just +equal to this limit of Delta + + align:start position:0% +equal to this limit of Delta + + + align:start position:0% +equal to this limit of Delta +rbo over delta + + align:start position:0% +rbo over delta + + + align:start position:0% +rbo over delta +T as T goes + + align:start position:0% +T as T goes + + + align:start position:0% +T as T goes +to + + align:start position:0% +to + + + align:start position:0% +to +zero so what direction is the + + align:start position:0% + + + + align:start position:0% + +velocity velocity is in the direction of + + align:start position:0% +velocity velocity is in the direction of + + + align:start position:0% +velocity velocity is in the direction of +the change not the original Vector but + + align:start position:0% +the change not the original Vector but + + + align:start position:0% +the change not the original Vector but +it's in the direction of the change and + + align:start position:0% +it's in the direction of the change and + + + align:start position:0% +it's in the direction of the change and +in fact if the path of the dog is like + + align:start position:0% +in fact if the path of the dog is like + + + align:start position:0% +in fact if the path of the dog is like +this at the point the instant you + + align:start position:0% +this at the point the instant you + + + align:start position:0% +this at the point the instant you +compute the velocity you're Computing + + align:start position:0% +compute the velocity you're Computing + + + align:start position:0% +compute the velocity you're Computing +the tangent to the path of the + + align:start position:0% +the tangent to the path of the + + + align:start position:0% +the tangent to the path of the +dog so that's what velocity is at any + + align:start position:0% +dog so that's what velocity is at any + + + align:start position:0% +dog so that's what velocity is at any +instant in time is a tangent to the path + + align:start position:0% +instant in time is a tangent to the path + + + align:start position:0% +instant in time is a tangent to the path +and that's a good concept to remember + + align:start position:0% + + + + align:start position:0% + +so we're still in this fix cartisian + + align:start position:0% +so we're still in this fix cartisian + + + align:start position:0% +so we're still in this fix cartisian +space and I have a couple of points I'll + + align:start position:0% +space and I have a couple of points I'll + + + align:start position:0% +space and I have a couple of points I'll +make it really trivial here here's B and + + align:start position:0% +make it really trivial here here's B and + + + align:start position:0% +make it really trivial here here's B and +here's a and the velocity of + + align:start position:0% +here's a and the velocity of + + + align:start position:0% +here's a and the velocity of +B where's my + + align:start position:0% + + + + align:start position:0% + +number we'll make this + + align:start position:0% +number we'll make this + + + align:start position:0% +number we'll make this +10 feet per second and + + align:start position:0% +10 feet per second and + + + align:start position:0% +10 feet per second and +it's in the J at Direction and + + align:start position:0% +it's in the J at Direction and + + + align:start position:0% +it's in the J at Direction and +a the this is the velocity of B in O the + + align:start position:0% +a the this is the velocity of B in O the + + + align:start position:0% +a the this is the velocity of B in O the +velocity of a and o + + align:start position:0% +velocity of a and o + + + align:start position:0% +velocity of a and o +we'll say is uh 4T per + + align:start position:0% + + + + align:start position:0% + +second also in the J Direction and I + + align:start position:0% +second also in the J Direction and I + + + align:start position:0% +second also in the J Direction and I +want to know what's the velocity of B + + align:start position:0% +want to know what's the velocity of B + + + align:start position:0% +want to know what's the velocity of B +with respect to a so now I'm chasing the + + align:start position:0% +with respect to a so now I'm chasing the + + + align:start position:0% +with respect to a so now I'm chasing the +dog he's running at 10 I'm running it at + + align:start position:0% +dog he's running at 10 I'm running it at + + + align:start position:0% +dog he's running at 10 I'm running it at +four and I what's my how do I perceive + + align:start position:0% +four and I what's my how do I perceive + + + align:start position:0% +four and I what's my how do I perceive +the speed of the dog well to do this in + + align:start position:0% +the speed of the dog well to do this in + + + align:start position:0% +the speed of the dog well to do this in +vectors which is the point of the + + align:start position:0% +vectors which is the point of the + + + align:start position:0% +vectors which is the point of the +exercise here is we have the uh + + align:start position:0% +exercise here is we have the uh + + + align:start position:0% +exercise here is we have the uh +Expressions we start started with over + + align:start position:0% +Expressions we start started with over + + + align:start position:0% +Expressions we start started with over +there and we're going to use these a lot + + align:start position:0% +there and we're going to use these a lot + + + align:start position:0% +there and we're going to use these a lot +in the course so the velocity of B with + + align:start position:0% +in the course so the velocity of B with + + + align:start position:0% +in the course so the velocity of B with +respect to O is the velocity of a with + + align:start position:0% +respect to O is the velocity of a with + + + align:start position:0% +respect to O is the velocity of a with +respect to o plus the velocity of B with + + align:start position:0% +respect to o plus the velocity of B with + + + align:start position:0% +respect to o plus the velocity of B with +respect to a and you can just if I want + + align:start position:0% +respect to a and you can just if I want + + + align:start position:0% +respect to a and you can just if I want +to know velocity B with respect to a I + + align:start position:0% +to know velocity B with respect to a I + + + align:start position:0% +to know velocity B with respect to a I +just solve + + align:start position:0% + + + + align:start position:0% + +this so velocity B with respect to O + + align:start position:0% +this so velocity B with respect to O + + + align:start position:0% +this so velocity B with respect to O +minus velocity of a with respect to O + + align:start position:0% +minus velocity of a with respect to O + + + align:start position:0% +minus velocity of a with respect to O +and in this case that's 10 - 4 is 6 + + align:start position:0% + + + + align:start position:0% + +in the + + align:start position:0% +in the + + + align:start position:0% +in the +J point of the exercise is to manipulate + + align:start position:0% +J point of the exercise is to manipulate + + + align:start position:0% +J point of the exercise is to manipulate +the vector expressions like this so take + + align:start position:0% +the vector expressions like this so take + + + align:start position:0% +the vector expressions like this so take +whatever known quantities you have and + + align:start position:0% +whatever known quantities you have and + + + align:start position:0% +whatever known quantities you have and +solve for the unknown one in this case I + + align:start position:0% +solve for the unknown one in this case I + + + align:start position:0% +solve for the unknown one in this case I +want to know the relative velocity + + align:start position:0% +want to know the relative velocity + + + align:start position:0% +want to know the relative velocity +between the two and it's + + align:start position:0% +between the two and it's + + + align:start position:0% +between the two and it's +this now if + + align:start position:0% +this now if + + + align:start position:0% +this now if +I that's if I'm here and I'm watching + + align:start position:0% +I that's if I'm here and I'm watching + + + align:start position:0% +I that's if I'm here and I'm watching +the dog that's how I perceive the speed + + align:start position:0% +the dog that's how I perceive the speed + + + align:start position:0% +the dog that's how I perceive the speed +of the dog relative to me right 6 feet + + align:start position:0% +of the dog relative to me right 6 feet + + + align:start position:0% +of the dog relative to me right 6 feet +per second in the J Direction what's the + + align:start position:0% +per second in the J Direction what's the + + + align:start position:0% +per second in the J Direction what's the +speed of the dog from the point of view + + align:start position:0% +speed of the dog from the point of view + + + align:start position:0% +speed of the dog from the point of view +of over here the speed of the dog + + align:start position:0% +of over here the speed of the dog + + + align:start position:0% +of over here the speed of the dog +relative + + align:start position:0% +relative + + + align:start position:0% +relative +to + + align:start position:0% + + + + align:start position:0% + +me so it's again the velocity of B with + + align:start position:0% +me so it's again the velocity of B with + + + align:start position:0% +me so it's again the velocity of B with +respect to a but from a different + + align:start position:0% +respect to a but from a different + + + align:start position:0% +respect to a but from a different +position in this fixed reference frame + + align:start position:0% + + + + align:start position:0% + +really important Point actually this is + + align:start position:0% +really important Point actually this is + + + align:start position:0% +really important Point actually this is +a really important conceptual + + align:start position:0% + + + + align:start position:0% + +Point somebody be bold what's what's the + + align:start position:0% +Point somebody be bold what's what's the + + + align:start position:0% +Point somebody be bold what's what's the +speed with respect to O the velocity of + + align:start position:0% +speed with respect to O the velocity of + + + align:start position:0% +speed with respect to O the velocity of +a b with respect to a at seen from o + + align:start position:0% +a b with respect to a at seen from o + + + align:start position:0% +a b with respect to a at seen from o +it's computed from o measured from o got + + align:start position:0% +it's computed from o measured from o got + + + align:start position:0% +it's computed from o measured from o got +radar down there and you're tracking + + align:start position:0% + + + + align:start position:0% + +them in what direction + + align:start position:0% + + + + align:start position:0% + +yeah it's a same the point is it's the + + align:start position:0% +yeah it's a same the point is it's the + + + align:start position:0% +yeah it's a same the point is it's the +same if you're in a fixed reference + + align:start position:0% +same if you're in a fixed reference + + + align:start position:0% +same if you're in a fixed reference +frame velocity of some of a a vector of + + align:start position:0% +frame velocity of some of a a vector of + + + align:start position:0% +frame velocity of some of a a vector of +velocity is the same as seen from any + + align:start position:0% +velocity is the same as seen from any + + + align:start position:0% +velocity is the same as seen from any +diff any point in the + + align:start position:0% +diff any point in the + + + align:start position:0% +diff any point in the +frame any fix point the velocity is + + align:start position:0% +frame any fix point the velocity is + + + align:start position:0% +frame any fix point the velocity is +always the same and in fact in this case + + align:start position:0% +always the same and in fact in this case + + + align:start position:0% +always the same and in fact in this case +the velocity this is IM moving point and + + align:start position:0% +the velocity this is IM moving point and + + + align:start position:0% +the velocity this is IM moving point and +the velocity of him with respect to me + + align:start position:0% +the velocity of him with respect to me + + + align:start position:0% +the velocity of him with respect to me +is is the differ 6 feet per second and I + + align:start position:0% +is is the differ 6 feet per second and I + + + align:start position:0% +is is the differ 6 feet per second and I +from here say the velocity of that guy + + align:start position:0% +from here say the velocity of that guy + + + align:start position:0% +from here say the velocity of that guy +with respect to this guy is still 6 feet + + align:start position:0% +with respect to this guy is still 6 feet + + + align:start position:0% +with respect to this guy is still 6 feet +per second any place in the in that + + align:start position:0% +per second any place in the in that + + + align:start position:0% +per second any place in the in that +frame or even any any point moving at + + align:start position:0% +frame or even any any point moving at + + + align:start position:0% +frame or even any any point moving at +constant velocity you're going to see + + align:start position:0% +constant velocity you're going to see + + + align:start position:0% +constant velocity you're going to see +the same + + align:start position:0% +the same + + + align:start position:0% +the same +answer okay so it doesn't matter where + + align:start position:0% +answer okay so it doesn't matter where + + + align:start position:0% +answer okay so it doesn't matter where +you are to compute the velocity of B + + align:start position:0% +you are to compute the velocity of B + + + align:start position:0% +you are to compute the velocity of B +with respect to a that's the that's the + + align:start position:0% +with respect to a that's the that's the + + + align:start position:0% +with respect to a that's the that's the +important point + + align:start position:0% + + + + align:start position:0% + +okay okay we got to pick up with and I + + align:start position:0% +okay okay we got to pick up with and I + + + align:start position:0% +okay okay we got to pick up with and I +may not quite finish but I am going to + + align:start position:0% +may not quite finish but I am going to + + + align:start position:0% +may not quite finish but I am going to +introduce + + align:start position:0% + + + + align:start position:0% + +the next complexity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so the what I we just what we just + + align:start position:0% +so the what I we just what we just + + + align:start position:0% +so the what I we just what we just +derived on a minute ago is that the + + align:start position:0% +derived on a minute ago is that the + + + align:start position:0% +derived on a minute ago is that the +velocity is seen from o is the same as + + align:start position:0% +velocity is seen from o is the same as + + + align:start position:0% +velocity is seen from o is the same as +the velocity is seen from a and a is me + + align:start position:0% +the velocity is seen from a and a is me + + + align:start position:0% +the velocity is seen from a and a is me +and I'm moving I'm chasing the dog so + + align:start position:0% +and I'm moving I'm chasing the dog so + + + align:start position:0% +and I'm moving I'm chasing the dog so +I'm a moving reference frame I'm what's + + align:start position:0% +I'm a moving reference frame I'm what's + + + align:start position:0% +I'm a moving reference frame I'm what's +called a translating reference frame so + + align:start position:0% +called a translating reference frame so + + + align:start position:0% +called a translating reference frame so +now we're going to step the take the + + align:start position:0% +now we're going to step the take the + + + align:start position:0% +now we're going to step the take the +next step we had a fix reference frame + + align:start position:0% +next step we had a fix reference frame + + + align:start position:0% +next step we had a fix reference frame +before purely and now I want to talk + + align:start position:0% +before purely and now I want to talk + + + align:start position:0% +before purely and now I want to talk +about having the idea concept of having + + align:start position:0% +about having the idea concept of having + + + align:start position:0% +about having the idea concept of having +a moving reference + + align:start position:0% +a moving reference + + + align:start position:0% +a moving reference +frame within a fixed one so this is a + + align:start position:0% +frame within a fixed one so this is a + + + align:start position:0% +frame within a fixed one so this is a +reference frame o capital x YZ and this + + align:start position:0% +reference frame o capital x YZ and this + + + align:start position:0% +reference frame o capital x YZ and this +little reference frame now is attached + + align:start position:0% +little reference frame now is attached + + + align:start position:0% +little reference frame now is attached +to me and it's a and I call it X Prime y + + align:start position:0% +to me and it's a and I call it X Prime y + + + align:start position:0% +to me and it's a and I call it X Prime y +Prime so just so you can it's going to + + align:start position:0% +Prime so just so you can it's going to + + + align:start position:0% +Prime so just so you can it's going to +be hard to tell my this X from this x if + + align:start position:0% +be hard to tell my this X from this x if + + + align:start position:0% +be hard to tell my this X from this x if +I don't do something like a + + align:start position:0% +I don't do something like a + + + align:start position:0% +I don't do something like a +prime so that this is the concept of a + + align:start position:0% +prime so that this is the concept of a + + + align:start position:0% +prime so that this is the concept of a +translating coordinate system attached + + align:start position:0% +translating coordinate system attached + + + align:start position:0% +translating coordinate system attached +to a body like a rigid body for example + + align:start position:0% +to a body like a rigid body for example + + + align:start position:0% +to a body like a rigid body for example +we can do of rigid body Dynamics here + + align:start position:0% +we can do of rigid body Dynamics here + + + align:start position:0% +we can do of rigid body Dynamics here +and within this coordinate system I can + + align:start position:0% +and within this coordinate system I can + + + align:start position:0% +and within this coordinate system I can +compute the velocity of B with respect + + align:start position:0% +compute the velocity of B with respect + + + align:start position:0% +compute the velocity of B with respect +to a and I'll get exactly the same + + align:start position:0% +to a and I'll get exactly the same + + + align:start position:0% +to a and I'll get exactly the same +answer I get that six feet per second in + + align:start position:0% +answer I get that six feet per second in + + + align:start position:0% +answer I get that six feet per second in +the J + + align:start position:0% +the J + + + align:start position:0% +the J +Direction so it's as if so this concept + + align:start position:0% +Direction so it's as if so this concept + + + align:start position:0% +Direction so it's as if so this concept +of being able to have a reference frame + + align:start position:0% +of being able to have a reference frame + + + align:start position:0% +of being able to have a reference frame +attached to a body and translating with + + align:start position:0% +attached to a body and translating with + + + align:start position:0% +attached to a body and translating with +it you can measure things within it get + + align:start position:0% +it you can measure things within it get + + + align:start position:0% +it you can measure things within it get +the answer and then convert that answer + + align:start position:0% +the answer and then convert that answer + + + align:start position:0% +the answer and then convert that answer +to here if you're using you know + + align:start position:0% +to here if you're using you know + + + align:start position:0% +to here if you're using you know +different coordinate you know you know + + align:start position:0% +different coordinate you know you know + + + align:start position:0% +different coordinate you know you know +one you could use polar coordinates here + + align:start position:0% +one you could use polar coordinates here + + + align:start position:0% +one you could use polar coordinates here +and rectangular here but they still can + + align:start position:0% +and rectangular here but they still can + + + align:start position:0% +and rectangular here but they still can +be related to one another we'll do + + align:start position:0% +be related to one another we'll do + + + align:start position:0% +be related to one another we'll do +problems like + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +okay so now I what I'm what I'm doing is + + align:start position:0% +okay so now I what I'm what I'm doing is + + + align:start position:0% +okay so now I what I'm what I'm doing is +I told you like in the readings the + + align:start position:0% +I told you like in the readings the + + + align:start position:0% +I told you like in the readings the +endgame is to be able to talk + + align:start position:0% +endgame is to be able to talk + + + align:start position:0% +endgame is to be able to talk +about translating rotating bodies and do + + align:start position:0% +about translating rotating bodies and do + + + align:start position:0% +about translating rotating bodies and do +Dynamics in three dimensions with + + align:start position:0% +Dynamics in three dimensions with + + + align:start position:0% +Dynamics in three dimensions with +translating and rotating objects and + + align:start position:0% +translating and rotating objects and + + + align:start position:0% +translating and rotating objects and +we're going to get there somewhat step + + align:start position:0% +we're going to get there somewhat step + + + align:start position:0% +we're going to get there somewhat step +by step but I want to show but I want + + align:start position:0% +by step but I want to show but I want + + + align:start position:0% +by step but I want to show but I want +you to understand the endgame so you + + align:start position:0% +you to understand the endgame so you + + + align:start position:0% +you to understand the endgame so you +know where we're going and you need to + + align:start position:0% +know where we're going and you need to + + + align:start position:0% +know where we're going and you need to +have a couple of Concepts in + + align:start position:0% +have a couple of Concepts in + + + align:start position:0% +have a couple of Concepts in +mind + + align:start position:0% +mind + + + align:start position:0% +mind +so so the first concept is that this is + + align:start position:0% +so so the first concept is that this is + + + align:start position:0% +so so the first concept is that this is +a rigid body + + align:start position:0% +a rigid body + + + align:start position:0% +a rigid body +now and you can describe the rigid the + + align:start position:0% +now and you can describe the rigid the + + + align:start position:0% +now and you can describe the rigid the +motion of rigid bodies by the + + align:start position:0% +motion of rigid bodies by the + + + align:start position:0% +motion of rigid bodies by the +summation the combination of a + + align:start position:0% +summation the combination of a + + + align:start position:0% +summation the combination of a +translation and a + + align:start position:0% +translation and a + + + align:start position:0% +translation and a +rotation and the rigid body if you can + + align:start position:0% +rotation and the rigid body if you can + + + align:start position:0% +rotation and the rigid body if you can +describe its translation and you can + + align:start position:0% +describe its translation and you can + + + align:start position:0% +describe its translation and you can +describe its rotation you have the + + align:start position:0% +describe its rotation you have the + + + align:start position:0% +describe its rotation you have the +complete motion so you got to understand + + align:start position:0% +complete motion so you got to understand + + + align:start position:0% +complete motion so you got to understand +what do we mean by what's it really the + + align:start position:0% +what do we mean by what's it really the + + + align:start position:0% +what do we mean by what's it really the +definition of translation so translation + + align:start position:0% +definition of translation so translation + + + align:start position:0% +definition of translation so translation +so I've got + + align:start position:0% +so I've got + + + align:start position:0% +so I've got +this call it Amer around we'll we'll use + + align:start position:0% +this call it Amer around we'll we'll use + + + align:start position:0% +this call it Amer around we'll we'll use +it we'll use using a Maro example in a + + align:start position:0% +it we'll use using a Maro example in a + + + align:start position:0% +it we'll use using a Maro example in a +minute and your observers in a fixed + + align:start position:0% +minute and your observers in a fixed + + + align:start position:0% +minute and your observers in a fixed +inertial Frame Up Above This Maro + + align:start position:0% +inertial Frame Up Above This Maro + + + align:start position:0% +inertial Frame Up Above This Maro +looking down on it okay but so you can + + align:start position:0% +looking down on it okay but so you can + + + align:start position:0% +looking down on it okay but so you can +see it I got to I got to turn it on its + + align:start position:0% +see it I got to I got to turn it on its + + + align:start position:0% +see it I got to I got to turn it on its +side so here's my marar on and if it's + + align:start position:0% +side so here's my marar on and if it's + + + align:start position:0% +side so here's my marar on and if it's +not rotating but let's say it's on a + + align:start position:0% +not rotating but let's say it's on a + + + align:start position:0% +not rotating but let's say it's on a +sitting on a + + align:start position:0% +sitting on a + + + align:start position:0% +sitting on a +train on a flat bed and moving along + + align:start position:0% +train on a flat bed and moving along + + + align:start position:0% +train on a flat bed and moving along +it's + + align:start position:0% +it's + + + align:start position:0% +it's +translating and when you say a body + + align:start position:0% +translating and when you say a body + + + align:start position:0% +translating and when you say a body +translates any two points on the body + + align:start position:0% +translates any two points on the body + + + align:start position:0% +translates any two points on the body +body move in parallel + + align:start position:0% +body move in parallel + + + align:start position:0% +body move in parallel +paths so two points my thumb and my + + align:start position:0% +paths so two points my thumb and my + + + align:start position:0% +paths so two points my thumb and my +finger if I'm just going along with this + + align:start position:0% +finger if I'm just going along with this + + + align:start position:0% +finger if I'm just going along with this +those two paths are traveling parallel + + align:start position:0% +those two paths are traveling parallel + + + align:start position:0% +those two paths are traveling parallel +to one another uh if the body does you + + align:start position:0% +to one another uh if the body does you + + + align:start position:0% +to one another uh if the body does you +know I + + align:start position:0% +know I + + + align:start position:0% +know I +got y pointing up if the body does + + align:start position:0% + + + + align:start position:0% + +this is it rotating or + + align:start position:0% +this is it rotating or + + + align:start position:0% +this is it rotating or +translating are any two points on it + + align:start position:0% +translating are any two points on it + + + align:start position:0% +translating are any two points on it +moving in parallel paths + + align:start position:0% + + + + align:start position:0% + +right okay so this called when you when + + align:start position:0% +right okay so this called when you when + + + align:start position:0% +right okay so this called when you when +it goes through curve things it's called + + align:start position:0% +it goes through curve things it's called + + + align:start position:0% +it goes through curve things it's called +curval linear translation but it's still + + align:start position:0% +curval linear translation but it's still + + + align:start position:0% +curval linear translation but it's still +just translation okay so I'll stop and + + align:start position:0% +just translation okay so I'll stop and + + + align:start position:0% +just translation okay so I'll stop and +Hold Steady the train stopped and the + + align:start position:0% +Hold Steady the train stopped and the + + + align:start position:0% +Hold Steady the train stopped and the +thing let it uh + + align:start position:0% +thing let it uh + + + align:start position:0% +thing let it uh +rotate so that's pure + + align:start position:0% +rotate so that's pure + + + align:start position:0% +rotate so that's pure +rotation and the thing to remember about + + align:start position:0% +rotation and the thing to remember about + + + align:start position:0% +rotation and the thing to remember about +pure rotation is that anywhere on the + + align:start position:0% +pure rotation is that anywhere on the + + + align:start position:0% +pure rotation is that anywhere on the +body rotates at the same rate this is + + align:start position:0% +body rotates at the same rate this is + + + align:start position:0% +body rotates at the same rate this is +going around once a second the rotation + + align:start position:0% +going around once a second the rotation + + + align:start position:0% +going around once a second the rotation +rate is one rotation per second 360 + + align:start position:0% +rate is one rotation per second 360 + + + align:start position:0% +rate is one rotation per second 360 +Degrees 2 pi radians per second is its + + align:start position:0% +Degrees 2 pi radians per second is its + + + align:start position:0% +Degrees 2 pi radians per second is its +rotation rate every point on the body + + align:start position:0% +rotation rate every point on the body + + + align:start position:0% +rotation rate every point on the body +experiences the same rotation rate + + align:start position:0% +experiences the same rotation rate + + + align:start position:0% +experiences the same rotation rate +that's a really important one to + + align:start position:0% +that's a really important one to + + + align:start position:0% +that's a really important one to +remember now this if I'm if I'm holding + + align:start position:0% +remember now this if I'm if I'm holding + + + align:start position:0% +remember now this if I'm if I'm holding +still marar round's going round and + + align:start position:0% +still marar round's going round and + + + align:start position:0% +still marar round's going round and +round it has a fixed axis of rotation + + align:start position:0% +round it has a fixed axis of rotation + + + align:start position:0% +round it has a fixed axis of rotation +right but do rotating bodies have to + + align:start position:0% +right but do rotating bodies have to + + + align:start position:0% +right but do rotating bodies have to +have fixed axes of rotation + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +if I throw that up in the + + align:start position:0% +if I throw that up in the + + + align:start position:0% +if I throw that up in the +air there's I'm not hanging on to it + + align:start position:0% +air there's I'm not hanging on to it + + + align:start position:0% +air there's I'm not hanging on to it +it's got gravity acting on it it's + + align:start position:0% +it's got gravity acting on it it's + + + align:start position:0% +it's got gravity acting on it it's +rotating what's it rotate + + align:start position:0% +rotating what's it rotate + + + align:start position:0% +rotating what's it rotate +about Center of mass okay is the center + + align:start position:0% +about Center of mass okay is the center + + + align:start position:0% +about Center of mass okay is the center +of mass + + align:start position:0% +of mass + + + align:start position:0% +of mass +moving ah so this is clearly this is an + + align:start position:0% +moving ah so this is clearly this is an + + + align:start position:0% +moving ah so this is clearly this is an +example of rotation plus + + align:start position:0% + + + + align:start position:0% + +translation it rotates about an axis but + + align:start position:0% +translation it rotates about an axis but + + + align:start position:0% +translation it rotates about an axis but +the axis can move that's another + + align:start position:0% +the axis can move that's another + + + align:start position:0% +the axis can move that's another +important concept that we we have to + + align:start position:0% +important concept that we we have to + + + align:start position:0% +important concept that we we have to +allow in order to be able to do these + + align:start position:0% +allow in order to be able to do these + + + align:start position:0% +allow in order to be able to do these +problems but this is now General motion + + align:start position:0% +problems but this is now General motion + + + align:start position:0% +problems but this is now General motion +It's a combination of translation and + + align:start position:0% +It's a combination of translation and + + + align:start position:0% +It's a combination of translation and +rotation and you we figure out each of + + align:start position:0% +rotation and you we figure out each of + + + align:start position:0% +rotation and you we figure out each of +those two pieces then we can describe + + align:start position:0% +those two pieces then we can describe + + + align:start position:0% +those two pieces then we can describe +the complete motion of the system + + align:start position:0% + + + + align:start position:0% + +okay all right the + + align:start position:0% +okay all right the + + + align:start position:0% +okay all right the +uh where we'll pick up next + + align:start position:0% +uh where we'll pick up next + + + align:start position:0% +uh where we'll pick up next +time is then doing that and and this is + + align:start position:0% +time is then doing that and and this is + + + align:start position:0% +time is then doing that and and this is +and it would help actually if you go + + align:start position:0% +and it would help actually if you go + + + align:start position:0% +and it would help actually if you go +read that reading especially up to + + align:start position:0% +read that reading especially up to + + + align:start position:0% +read that reading especially up to +chapter + + align:start position:0% +chapter + + + align:start position:0% +chapter +16 we have to get into being taking + + align:start position:0% +16 we have to get into being taking + + + align:start position:0% +16 we have to get into being taking +derivatives of vectors which are + + align:start position:0% +derivatives of vectors which are + + + align:start position:0% +derivatives of vectors which are +rotating and come up with a general + + align:start position:0% +rotating and come up with a general + + + align:start position:0% +rotating and come up with a general +formula that allows us to do velocities + + align:start position:0% +formula that allows us to do velocities + + + align:start position:0% +formula that allows us to do velocities +and accelerations under those conditions + + align:start position:0% +and accelerations under those conditions + + + align:start position:0% +and accelerations under those conditions +see you + + align:start position:0% +see you + + + align:start position:0% +see you +on Tuesday next \ No newline at end of file diff --git a/Gcb0zp82BtA.txt b/Gcb0zp82BtA.txt new file mode 100644 index 0000000000000000000000000000000000000000..4f97d6aee162f9a868281b92206f9e04053a3a1b --- /dev/null +++ b/Gcb0zp82BtA.txt @@ -0,0 +1,203 @@ +align:start position:0% + +in chapter 3 + + align:start position:0% +in chapter 3 + + + align:start position:0% +in chapter 3 +we will study epidemiological models + + align:start position:0% +we will study epidemiological models + + + align:start position:0% +we will study epidemiological models +which describe the spread of an + + align:start position:0% +which describe the spread of an + + + align:start position:0% +which describe the spread of an +infection + + align:start position:0% +infection + + + align:start position:0% +infection +and then the recovery from that + + align:start position:0% +and then the recovery from that + + + align:start position:0% +and then the recovery from that +infection + + align:start position:0% +infection + + + align:start position:0% +infection +in a population and the traditional + + align:start position:0% +in a population and the traditional + + + align:start position:0% +in a population and the traditional +epidemiological models that we will + + align:start position:0% +epidemiological models that we will + + + align:start position:0% +epidemiological models that we will +study for populations and also adapt to + + align:start position:0% +study for populations and also adapt to + + + align:start position:0% +study for populations and also adapt to +indoor spaces + + align:start position:0% +indoor spaces + + + align:start position:0% +indoor spaces +involve keeping track of compartments or + + align:start position:0% +involve keeping track of compartments or + + + align:start position:0% +involve keeping track of compartments or +subgroups of populations such as + + align:start position:0% +subgroups of populations such as + + + align:start position:0% +subgroups of populations such as +the number of susceptible people the + + align:start position:0% +the number of susceptible people the + + + align:start position:0% +the number of susceptible people the +number of infected + + align:start position:0% +number of infected + + + align:start position:0% +number of infected +exposed and recovered so for example + + align:start position:0% +exposed and recovered so for example + + + align:start position:0% +exposed and recovered so for example +an infected person can expose + + align:start position:0% +an infected person can expose + + + align:start position:0% +an infected person can expose +a susceptible and then the exposed + + align:start position:0% +a susceptible and then the exposed + + + align:start position:0% +a susceptible and then the exposed +person can themselves become infected + + align:start position:0% +person can themselves become infected + + + align:start position:0% +person can themselves become infected +or they may eventually recover and there + + align:start position:0% +or they may eventually recover and there + + + align:start position:0% +or they may eventually recover and there +are various rates for these different + + align:start position:0% +are various rates for these different + + + align:start position:0% +are various rates for these different +processes + + align:start position:0% +processes + + + align:start position:0% +processes +and this leads to a set of non-linear + + align:start position:0% +and this leads to a set of non-linear + + + align:start position:0% +and this leads to a set of non-linear +differential equations that describe the + + align:start position:0% +differential equations that describe the + + + align:start position:0% +differential equations that describe the +evolution + + align:start position:0% +evolution + + + align:start position:0% +evolution +and growth and then ultimately decay of + + align:start position:0% +and growth and then ultimately decay of + + + align:start position:0% +and growth and then ultimately decay of +an epidemic \ No newline at end of file diff --git a/H8U0a9bwxqc.txt b/H8U0a9bwxqc.txt new file mode 100644 index 0000000000000000000000000000000000000000..caa619251638e13c7530a9cce80d7f1c9af904e1 --- /dev/null +++ b/H8U0a9bwxqc.txt @@ -0,0 +1,7869 @@ +align:start position:0% + +okay why don't we get + + align:start position:0% +okay why don't we get + + + align:start position:0% +okay why don't we get +started so what I wanted to do is + + align:start position:0% +started so what I wanted to do is + + + align:start position:0% +started so what I wanted to do is +continue the discussion of inverters + + align:start position:0% +continue the discussion of inverters + + + align:start position:0% +continue the discussion of inverters +that we started last time and what I'm + + align:start position:0% +that we started last time and what I'm + + + align:start position:0% +that we started last time and what I'm +going to show you is some sort of + + align:start position:0% +going to show you is some sort of + + + align:start position:0% +going to show you is some sort of +expansions on the way you can think + + align:start position:0% +expansions on the way you can think + + + align:start position:0% +expansions on the way you can think +about uh controlling the inverters to + + align:start position:0% +about uh controlling the inverters to + + + align:start position:0% +about uh controlling the inverters to +get better performance out of the + + align:start position:0% +get better performance out of the + + + align:start position:0% +get better performance out of the +waveforms so we introduced the basic uh + + align:start position:0% +waveforms so we introduced the basic uh + + + align:start position:0% +waveforms so we introduced the basic uh +voltage source inverter structure which + + align:start position:0% +voltage source inverter structure which + + + align:start position:0% +voltage source inverter structure which +is four + + align:start position:0% +is four + + + align:start position:0% +is four +switches okay and very + + align:start position:0% +switches okay and very + + + align:start position:0% +switches okay and very +typically we'll use uh bir directional + + align:start position:0% +typically we'll use uh bir directional + + + align:start position:0% +typically we'll use uh bir directional +conducting single single directional + + align:start position:0% +conducting single single directional + + + align:start position:0% +conducting single single directional +blocking switches like + + align:start position:0% +blocking switches like + + + align:start position:0% +blocking switches like +mosfets like this for + + align:start position:0% + + + + align:start position:0% + +example and if I want to synthesize some + + align:start position:0% +example and if I want to synthesize some + + + align:start position:0% +example and if I want to synthesize some +voltage V + + align:start position:0% +voltage V + + + align:start position:0% +voltage V +X across the load if I have switches + + align:start position:0% +X across the load if I have switches + + + align:start position:0% +X across the load if I have switches +S1 S2 S3 and + + align:start position:0% +S1 S2 S3 and + + + align:start position:0% +S1 S2 S3 and +S4 right if I have + + align:start position:0% +S4 right if I have + + + align:start position:0% +S4 right if I have +um switches that are on be S1 and + + align:start position:0% +um switches that are on be S1 and + + + align:start position:0% +um switches that are on be S1 and +S2 I put positive VC across the + + align:start position:0% +S2 I put positive VC across the + + + align:start position:0% +S2 I put positive VC across the +load if I put S2 and S3 + + align:start position:0% +load if I put S2 and S3 + + + align:start position:0% +load if I put S2 and S3 +on I get zero if I have S3 + + align:start position:0% +on I get zero if I have S3 + + + align:start position:0% +on I get zero if I have S3 +S4 I get get Negative VDC across the + + align:start position:0% +S4 I get get Negative VDC across the + + + align:start position:0% +S4 I get get Negative VDC across the +load and if I have uh S4 and S1 I get + + align:start position:0% +load and if I have uh S4 and S1 I get + + + align:start position:0% +load and if I have uh S4 and S1 I get +zero again okay and we showed last + + align:start position:0% +zero again okay and we showed last + + + align:start position:0% +zero again okay and we showed last +time that we can use this to + + align:start position:0% +time that we can use this to + + + align:start position:0% +time that we can use this to +synthesize you know either plus zero or + + align:start position:0% +synthesize you know either plus zero or + + + align:start position:0% +synthesize you know either plus zero or +minus repeatedly across the load and + + align:start position:0% +minus repeatedly across the load and + + + align:start position:0% +minus repeatedly across the load and +then use that to at least very + + align:start position:0% +then use that to at least very + + + align:start position:0% +then use that to at least very +crudely approximate some kind of sine + + align:start position:0% +crudely approximate some kind of sine + + + align:start position:0% +crudely approximate some kind of sine +wave for example and why do I focus on a + + align:start position:0% +wave for example and why do I focus on a + + + align:start position:0% +wave for example and why do I focus on a +sine wave very often we want to + + align:start position:0% +sine wave very often we want to + + + align:start position:0% +sine wave very often we want to +synthesize something that if at least if + + align:start position:0% +synthesize something that if at least if + + + align:start position:0% +synthesize something that if at least if +I filter it it will look like a sine + + align:start position:0% +I filter it it will look like a sine + + + align:start position:0% +I filter it it will look like a sine +wave because for example if I'm making a + + align:start position:0% +wave because for example if I'm making a + + + align:start position:0% +wave because for example if I'm making a +UPS inverter maybe I would like to + + align:start position:0% +UPS inverter maybe I would like to + + + align:start position:0% +UPS inverter maybe I would like to +replicate what the grid does with my + + align:start position:0% +replicate what the grid does with my + + + align:start position:0% +replicate what the grid does with my +inverter okay and when I show this as a + + align:start position:0% +inverter okay and when I show this as a + + + align:start position:0% +inverter okay and when I show this as a +load you know what is + + align:start position:0% +load you know what is + + + align:start position:0% +load you know what is +this I don't know it depends on the + + align:start position:0% +this I don't know it depends on the + + + align:start position:0% +this I don't know it depends on the +application right it could be a motor + + align:start position:0% +application right it could be a motor + + + align:start position:0% +application right it could be a motor +winding it could be some low pass filter + + align:start position:0% +winding it could be some low pass filter + + + align:start position:0% +winding it could be some low pass filter +for example that's going to some load + + align:start position:0% +for example that's going to some load + + + align:start position:0% +for example that's going to some load +right so this could be + + align:start position:0% +right so this could be + + + align:start position:0% +right so this could be +VX and this could be V out across the + + align:start position:0% +VX and this could be V out across the + + + align:start position:0% +VX and this could be V out across the +load + + align:start position:0% +load + + + align:start position:0% +load +okay so we said last time that um we + + align:start position:0% +okay so we said last time that um we + + + align:start position:0% +okay so we said last time that um we +often think ese especially when we're + + align:start position:0% +often think ese especially when we're + + + align:start position:0% +often think ese especially when we're +synthesizing periodic waveforms we often + + align:start position:0% +synthesizing periodic waveforms we often + + + align:start position:0% +synthesizing periodic waveforms we often +think in terms of the 4A series then + + align:start position:0% +think in terms of the 4A series then + + + align:start position:0% +think in terms of the 4A series then +what we're doing to kind of shape the + + align:start position:0% +what we're doing to kind of shape the + + + align:start position:0% +what we're doing to kind of shape the +harmonic content of the waveforms right + + align:start position:0% +harmonic content of the waveforms right + + + align:start position:0% +harmonic content of the waveforms right +so we said okay one form of the 4A + + align:start position:0% +so we said okay one form of the 4A + + + align:start position:0% +so we said okay one form of the 4A +series for some signal F of T is simply + + align:start position:0% +series for some signal F of T is simply + + + align:start position:0% +series for some signal F of T is simply +equal um to b/ 2 plus the summation from + + align:start position:0% +equal um to b/ 2 plus the summation from + + + align:start position:0% +equal um to b/ 2 plus the summation from +1 to Infinity of a subn sin of n Omega + + align:start position:0% +1 to Infinity of a subn sin of n Omega + + + align:start position:0% +1 to Infinity of a subn sin of n Omega +t plus b subn cosine of n Omega t Okay + + align:start position:0% +t plus b subn cosine of n Omega t Okay + + + align:start position:0% +t plus b subn cosine of n Omega t Okay +where if we recall the sign terms always + + align:start position:0% +where if we recall the sign terms always + + + align:start position:0% +where if we recall the sign terms always +odd in time and the cosine terms are + + align:start position:0% +odd in time and the cosine terms are + + + align:start position:0% +odd in time and the cosine terms are +always even in time so if I happen to + + align:start position:0% +always even in time so if I happen to + + + align:start position:0% +always even in time so if I happen to +want an odd + + align:start position:0% +want an odd + + + align:start position:0% +want an odd +waveform then I should make the pattern + + align:start position:0% +waveform then I should make the pattern + + + align:start position:0% +waveform then I should make the pattern +F of + + align:start position:0% +F of + + + align:start position:0% +F of +T and that means I want the pattern of f + + align:start position:0% +T and that means I want the pattern of f + + + align:start position:0% +T and that means I want the pattern of f +of T to be odd that means um I will only + + align:start position:0% +of T to be odd that means um I will only + + + align:start position:0% +of T to be odd that means um I will only +have the as subn terms and if I want the + + align:start position:0% +have the as subn terms and if I want the + + + align:start position:0% +have the as subn terms and if I want the +pattern F of T to be even I only have + + align:start position:0% +pattern F of T to be even I only have + + + align:start position:0% +pattern F of T to be even I only have +the B subn terms okay more importantly + + align:start position:0% +the B subn terms okay more importantly + + + align:start position:0% +the B subn terms okay more importantly +we saw that + + align:start position:0% +we saw that + + + align:start position:0% +we saw that +um we can often do interesting things + + align:start position:0% +um we can often do interesting things + + + align:start position:0% +um we can often do interesting things +with halfwave + + align:start position:0% +with halfwave + + + align:start position:0% +with halfwave +symmetry okay what is halfwave Sy + + align:start position:0% +symmetry okay what is halfwave Sy + + + align:start position:0% +symmetry okay what is halfwave Sy +symmetry + + align:start position:0% +symmetry + + + align:start position:0% +symmetry +mean halfwave symmetric waveform means + + align:start position:0% +mean halfwave symmetric waveform means + + + align:start position:0% +mean halfwave symmetric waveform means +that F of + + align:start position:0% +that F of + + + align:start position:0% +that F of +T is equal to minus F of T minus t/2 + + align:start position:0% +T is equal to minus F of T minus t/2 + + + align:start position:0% +T is equal to minus F of T minus t/2 +where T is the period okay that means if + + align:start position:0% +where T is the period okay that means if + + + align:start position:0% +where T is the period okay that means if +I go back half of a cycle in the + + align:start position:0% +I go back half of a cycle in the + + + align:start position:0% +I go back half of a cycle in the +waveform the waveforms flipped so for + + align:start position:0% +waveform the waveforms flipped so for + + + align:start position:0% +waveform the waveforms flipped so for +example um + + align:start position:0% +example um + + + align:start position:0% +example um +this waveform is both odd and halfway + + align:start position:0% + + + + align:start position:0% + +symmetric why because if I go back + + align:start position:0% +symmetric why because if I go back + + + align:start position:0% +symmetric why because if I go back +that's a terrible drawing because this + + align:start position:0% +that's a terrible drawing because this + + + align:start position:0% +that's a terrible drawing because this +should go further right but if I go back + + align:start position:0% +should go further right but if I go back + + + align:start position:0% +should go further right but if I go back +at any point half a cycle I flip across + + align:start position:0% +at any point half a cycle I flip across + + + align:start position:0% +at any point half a cycle I flip across +the axis and I get to the same point on + + align:start position:0% +the axis and I get to the same point on + + + align:start position:0% +the axis and I get to the same point on +the other side okay and the reason I'm + + align:start position:0% +the other side okay and the reason I'm + + + align:start position:0% +the other side okay and the reason I'm +interested in halfway symmetry is + + align:start position:0% +interested in halfway symmetry is + + + align:start position:0% +interested in halfway symmetry is +because if it's half W of symmetry then + + align:start position:0% +because if it's half W of symmetry then + + + align:start position:0% +because if it's half W of symmetry then +the + + align:start position:0% +the + + + align:start position:0% +the +a2k and the + + align:start position:0% +a2k and the + + + align:start position:0% +a2k and the +B2K terms are + + align:start position:0% + + + + align:start position:0% + +zero right and the reason I'm interested + + align:start position:0% +zero right and the reason I'm interested + + + align:start position:0% +zero right and the reason I'm interested +in doing that is suppose I want to + + align:start position:0% +in doing that is suppose I want to + + + align:start position:0% +in doing that is suppose I want to +synthesize something that looks like a + + align:start position:0% +synthesize something that looks like a + + + align:start position:0% +synthesize something that looks like a +sine + + align:start position:0% +sine + + + align:start position:0% +sine +wave and then I want to put it through a + + align:start position:0% +wave and then I want to put it through a + + + align:start position:0% +wave and then I want to put it through a +filter it's very hard to filter out the + + align:start position:0% +filter it's very hard to filter out the + + + align:start position:0% +filter it's very hard to filter out the +second harmonic right because second + + align:start position:0% +second harmonic right because second + + + align:start position:0% +second harmonic right because second +harmonic is only a factor of two + + align:start position:0% +harmonic is only a factor of two + + + align:start position:0% +harmonic is only a factor of two +different than the fundamental in + + align:start position:0% +different than the fundamental in + + + align:start position:0% +different than the fundamental in +frequency and and you know I'm trying to + + align:start position:0% +frequency and and you know I'm trying to + + + align:start position:0% +frequency and and you know I'm trying to +use perhaps a low pass fil it just gets + + align:start position:0% +use perhaps a low pass fil it just gets + + + align:start position:0% +use perhaps a low pass fil it just gets +hard to attenuate that if I can get rid + + align:start position:0% +hard to attenuate that if I can get rid + + + align:start position:0% +hard to attenuate that if I can get rid +of the second harmonic + + align:start position:0% +of the second harmonic + + + align:start position:0% +of the second harmonic +specifically I can make my filtering + + align:start position:0% +specifically I can make my filtering + + + align:start position:0% +specifically I can make my filtering +easier and if I can get rid of the if I + + align:start position:0% +easier and if I can get rid of the if I + + + align:start position:0% +easier and if I can get rid of the if I +make it halfway symmetric I get rid of + + align:start position:0% +make it halfway symmetric I get rid of + + + align:start position:0% +make it halfway symmetric I get rid of +the second fourth six Etc and I really + + align:start position:0% +the second fourth six Etc and I really + + + align:start position:0% +the second fourth six Etc and I really +reduce the amount of stuff I have to + + align:start position:0% +reduce the amount of stuff I have to + + + align:start position:0% +reduce the amount of stuff I have to +worry about filtering so I can get much + + align:start position:0% +worry about filtering so I can get much + + + align:start position:0% +worry about filtering so I can get much +purer output waveforms by doing that + + align:start position:0% +purer output waveforms by doing that + + + align:start position:0% +purer output waveforms by doing that +okay so if we're going to synthesize + + align:start position:0% +okay so if we're going to synthesize + + + align:start position:0% +okay so if we're going to synthesize +some pattern for my inverter to + + align:start position:0% +some pattern for my inverter to + + + align:start position:0% +some pattern for my inverter to +synthesize uh con create making it + + align:start position:0% +synthesize uh con create making it + + + align:start position:0% +synthesize uh con create making it +halfway metric is significantly + + align:start position:0% +halfway metric is significantly + + + align:start position:0% +halfway metric is significantly +advantageous if I don't want any even + + align:start position:0% +advantageous if I don't want any even + + + align:start position:0% +advantageous if I don't want any even +harmonic components in my output right + + align:start position:0% +harmonic components in my output right + + + align:start position:0% +harmonic components in my output right +and + + align:start position:0% +and + + + align:start position:0% +and +um what we said was + + align:start position:0% + + + + align:start position:0% + +that you know if I come back to this + + align:start position:0% +that you know if I come back to this + + + align:start position:0% +that you know if I come back to this +kind of + + align:start position:0% + + + + align:start position:0% + +filtering right so if I think of the + + align:start position:0% +filtering right so if I think of the + + + align:start position:0% +filtering right so if I think of the +transfer function from vx to + + align:start position:0% +transfer function from vx to + + + align:start position:0% +transfer function from vx to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +V so magnitude of V over + + align:start position:0% +V so magnitude of V over + + + align:start position:0% +V so magnitude of V over +VX right ideally speaking there is going + + align:start position:0% +VX right ideally speaking there is going + + + align:start position:0% +VX right ideally speaking there is going +to be some kind of low pass filter where + + align:start position:0% +to be some kind of low pass filter where + + + align:start position:0% +to be some kind of low pass filter where +I want to put the fundamental here so + + align:start position:0% +I want to put the fundamental here so + + + align:start position:0% +I want to put the fundamental here so +it's in the pass band but 2 3 four five + + align:start position:0% +it's in the pass band but 2 3 four five + + + align:start position:0% +it's in the pass band but 2 3 four five +6 Etc you know I usually only want this + + align:start position:0% +6 Etc you know I usually only want this + + + align:start position:0% +6 Etc you know I usually only want this +component and I would like to filter + + align:start position:0% +component and I would like to filter + + + align:start position:0% +component and I would like to filter +everything + + align:start position:0% +everything + + + align:start position:0% +everything +else we can get rid of these by the + + align:start position:0% +else we can get rid of these by the + + + align:start position:0% +else we can get rid of these by the +halfwave Symmetry and then it's just the + + align:start position:0% +halfwave Symmetry and then it's just the + + + align:start position:0% +halfwave Symmetry and then it's just the +question of what about third and Fifth + + align:start position:0% +question of what about third and Fifth + + + align:start position:0% +question of what about third and Fifth +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +right what we saw last time was one more + + align:start position:0% +right what we saw last time was one more + + + align:start position:0% +right what we saw last time was one more +trick we said you know I can + + align:start position:0% +trick we said you know I can + + + align:start position:0% +trick we said you know I can +synthesize 0 plus and + + align:start position:0% +synthesize 0 plus and + + + align:start position:0% +synthesize 0 plus and +minus if I only switch once per cycle I + + align:start position:0% +minus if I only switch once per cycle I + + + align:start position:0% +minus if I only switch once per cycle I +can create a waveform that looks like + + align:start position:0% + + + + align:start position:0% + +this okay so if this is pi + + align:start position:0% +this okay so if this is pi + + + align:start position:0% +this okay so if this is pi +this is 2 pi this is some angle Omega T + + align:start position:0% +this is 2 pi this is some angle Omega T + + + align:start position:0% +this is 2 pi this is some angle Omega T +okay if I synthesize an angle I may have + + align:start position:0% +okay if I synthesize an angle I may have + + + align:start position:0% +okay if I synthesize an angle I may have +Delta Pi minus Delta pi+ Delta and 2 + + align:start position:0% +Delta Pi minus Delta pi+ Delta and 2 + + + align:start position:0% +Delta Pi minus Delta pi+ Delta and 2 +pi minus Delta right if I synthesized a + + align:start position:0% +pi minus Delta right if I synthesized a + + + align:start position:0% +pi minus Delta right if I synthesized a +waveform that looks something like this + + align:start position:0% + + + + align:start position:0% + +and so forth that is halfwave symmetric + + align:start position:0% +and so forth that is halfwave symmetric + + + align:start position:0% +and so forth that is halfwave symmetric +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +VDC this is minus + + align:start position:0% + + + + align:start position:0% + +VDC right this waveform for + + align:start position:0% + + + + align:start position:0% + +VX is halfwave + + align:start position:0% +VX is halfwave + + + align:start position:0% +VX is halfwave +symmetric and the advantage I have here + + align:start position:0% +symmetric and the advantage I have here + + + align:start position:0% +symmetric and the advantage I have here +is I can have S4 S1 + + align:start position:0% + + + + align:start position:0% + +S1 + + align:start position:0% + + + + align:start position:0% + +S2 S2 + + align:start position:0% + + + + align:start position:0% + +S3 and S3 + + align:start position:0% + + + + align:start position:0% + +S4 and then I'm back to S4 + + align:start position:0% +S4 and then I'm back to S4 + + + align:start position:0% +S4 and then I'm back to S4 +S1 I've switched each device on and off + + align:start position:0% +S1 I've switched each device on and off + + + align:start position:0% +S1 I've switched each device on and off +once per cycle and hence I've kind of + + align:start position:0% +once per cycle and hence I've kind of + + + align:start position:0% +once per cycle and hence I've kind of +got the lowest switching losses that I + + align:start position:0% +got the lowest switching losses that I + + + align:start position:0% +got the lowest switching losses that I +might get for synthesizing such a + + align:start position:0% +might get for synthesizing such a + + + align:start position:0% +might get for synthesizing such a +pattern okay so if I care a lot about + + align:start position:0% +pattern okay so if I care a lot about + + + align:start position:0% +pattern okay so if I care a lot about +the loss and switch switching which I + + align:start position:0% +the loss and switch switching which I + + + align:start position:0% +the loss and switch switching which I +might if I'm either at very high power + + align:start position:0% +might if I'm either at very high power + + + align:start position:0% +might if I'm either at very high power +where I have high voltages or very high + + align:start position:0% +where I have high voltages or very high + + + align:start position:0% +where I have high voltages or very high +frequencies this is a pretty nice + + align:start position:0% +frequencies this is a pretty nice + + + align:start position:0% +frequencies this is a pretty nice +pattern to have and we said my one + + align:start position:0% +pattern to have and we said my one + + + align:start position:0% +pattern to have and we said my one +control handle in this pattern if I use + + align:start position:0% +control handle in this pattern if I use + + + align:start position:0% +control handle in this pattern if I use +it is this angle + + align:start position:0% +it is this angle + + + align:start position:0% +it is this angle +Delta okay and by picking Delta we can + + align:start position:0% +Delta okay and by picking Delta we can + + + align:start position:0% +Delta okay and by picking Delta we can +do a few things one thing we said we + + align:start position:0% +do a few things one thing we said we + + + align:start position:0% +do a few things one thing we said we +could do is if I make Delta bigger the + + align:start position:0% +could do is if I make Delta bigger the + + + align:start position:0% +could do is if I make Delta bigger the +fundamental component gets smaller and + + align:start position:0% +fundamental component gets smaller and + + + align:start position:0% +fundamental component gets smaller and +if I make Delta smaller uh I'm sorry if + + align:start position:0% +if I make Delta smaller uh I'm sorry if + + + align:start position:0% +if I make Delta smaller uh I'm sorry if +I make Delta smaller the fun component + + align:start position:0% +I make Delta smaller the fun component + + + align:start position:0% +I make Delta smaller the fun component +gets bigger so I can control the + + align:start position:0% +gets bigger so I can control the + + + align:start position:0% +gets bigger so I can control the +fundamental of the output that way the + + align:start position:0% +fundamental of the output that way the + + + align:start position:0% +fundamental of the output that way the +other thing we said we could do is + + align:start position:0% +other thing we said we could do is + + + align:start position:0% +other thing we said we could do is +control the harmonics right because we + + align:start position:0% +control the harmonics right because we + + + align:start position:0% +control the harmonics right because we +said if I do it like this so for an odd + + align:start position:0% +said if I do it like this so for an odd + + + align:start position:0% +said if I do it like this so for an odd +waveform right and I'm only picking it + + align:start position:0% +waveform right and I'm only picking it + + + align:start position:0% +waveform right and I'm only picking it +to be odd just because it makes the 4A + + align:start position:0% +to be odd just because it makes the 4A + + + align:start position:0% +to be odd just because it makes the 4A +series description simpler right but for + + align:start position:0% +series description simpler right but for + + + align:start position:0% +series description simpler right but for +o for an odd Wade + + align:start position:0% + + + + align:start position:0% + +form right um what I get is the nth + + align:start position:0% +form right um what I get is the nth + + + align:start position:0% +form right um what I get is the nth +harmonic component is simp going to be + + align:start position:0% +harmonic component is simp going to be + + + align:start position:0% +harmonic component is simp going to be +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +uh which way did I did I do it in terms + + align:start position:0% +uh which way did I did I do it in terms + + + align:start position:0% +uh which way did I did I do it in terms +of angle or did I do it in terms of I I + + align:start position:0% +of angle or did I do it in terms of I I + + + align:start position:0% +of angle or did I do it in terms of I I +guess I did it I did it okay 2 over T + + align:start position:0% +guess I did it I did it okay 2 over T + + + align:start position:0% +guess I did it I did it okay 2 over T +integral over the period of uh VX of + + align:start position:0% +integral over the period of uh VX of + + + align:start position:0% +integral over the period of uh VX of +t s of n Omega T DT + + align:start position:0% +t s of n Omega T DT + + + align:start position:0% +t s of n Omega T DT +okay by picking Delta I can sort of + + align:start position:0% +okay by picking Delta I can sort of + + + align:start position:0% +okay by picking Delta I can sort of +choose at least one of these to mess + + align:start position:0% +choose at least one of these to mess + + + align:start position:0% +choose at least one of these to mess +with okay and so I can + + align:start position:0% +with okay and so I can + + + align:start position:0% +with okay and so I can +calculate the amplitude of the N + + align:start position:0% +calculate the amplitude of the N + + + align:start position:0% +calculate the amplitude of the N +harmonic essentially as the waveform + + align:start position:0% +harmonic essentially as the waveform + + + align:start position:0% +harmonic essentially as the waveform +times the sign of the right frequency + + align:start position:0% +times the sign of the right frequency + + + align:start position:0% +times the sign of the right frequency +integrated right and the example I + + align:start position:0% +integrated right and the example I + + + align:start position:0% +integrated right and the example I +showed you last time is if I thought + + align:start position:0% +showed you last time is if I thought + + + align:start position:0% +showed you last time is if I thought +about what say suppose I focused on the + + align:start position:0% +about what say suppose I focused on the + + + align:start position:0% +about what say suppose I focused on the +three third harmonic so n is three right + + align:start position:0% +three third harmonic so n is three right + + + align:start position:0% +three third harmonic so n is three right +the third harmonic would look like + + align:start position:0% + + + + align:start position:0% + +this or I'm sorry the the the 3 omega T + + align:start position:0% +this or I'm sorry the the the 3 omega T + + + align:start position:0% +this or I'm sorry the the the 3 omega T +would look like + + align:start position:0% + + + + align:start position:0% + +this and when I picked Delta this angle + + align:start position:0% +this and when I picked Delta this angle + + + align:start position:0% +this and when I picked Delta this angle +Delta to be exactly 30° or pi over 6 so + + align:start position:0% +Delta to be exactly 30° or pi over 6 so + + + align:start position:0% +Delta to be exactly 30° or pi over 6 so +this example is Delta equal pi over + + align:start position:0% +this example is Delta equal pi over + + + align:start position:0% +this example is Delta equal pi over + + align:start position:0% + + + align:start position:0% +okay we notice that when I look at the + + align:start position:0% +okay we notice that when I look at the + + + align:start position:0% +okay we notice that when I look at the +intersection between VX of T and I + + align:start position:0% +intersection between VX of T and I + + + align:start position:0% +intersection between VX of T and I +multiply it by the pink waveform which + + align:start position:0% +multiply it by the pink waveform which + + + align:start position:0% +multiply it by the pink waveform which +is sin 3 omega T basically I get this + + align:start position:0% +is sin 3 omega T basically I get this + + + align:start position:0% +is sin 3 omega T basically I get this +positive + + align:start position:0% + + + + align:start position:0% + +area and then I get this negative + + align:start position:0% +area and then I get this negative + + + align:start position:0% +area and then I get this negative +area multiplied by the white waveform + + align:start position:0% +area multiplied by the white waveform + + + align:start position:0% +area multiplied by the white waveform +and when I multiply them in integrate + + align:start position:0% +and when I multiply them in integrate + + + align:start position:0% +and when I multiply them in integrate +them I get + + align:start position:0% +them I get + + + align:start position:0% +them I get +zero okay so I can kind of look at this + + align:start position:0% +zero okay so I can kind of look at this + + + align:start position:0% +zero okay so I can kind of look at this +waveform and say Hey you know if I pick + + align:start position:0% +waveform and say Hey you know if I pick + + + align:start position:0% +waveform and say Hey you know if I pick +that angle just right the + + align:start position:0% +that angle just right the + + + align:start position:0% +that angle just right the +overlap with this sin 3 omega T gives me + + align:start position:0% +overlap with this sin 3 omega T gives me + + + align:start position:0% +overlap with this sin 3 omega T gives me +just such that I kill the third + + align:start position:0% +just such that I kill the third + + + align:start position:0% +just such that I kill the third +harmonic + + align:start position:0% +harmonic + + + align:start position:0% +harmonic +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and this kind of trick we're going to + + align:start position:0% +and this kind of trick we're going to + + + align:start position:0% +and this kind of trick we're going to +see we can expand in multiple ways okay + + align:start position:0% +see we can expand in multiple ways okay + + + align:start position:0% +see we can expand in multiple ways okay +to give us higher performance but before + + align:start position:0% +to give us higher performance but before + + + align:start position:0% +to give us higher performance but before +I go on is there any question about how + + align:start position:0% +I go on is there any question about how + + + align:start position:0% +I go on is there any question about how +that arises or anything up to the + + align:start position:0% +that arises or anything up to the + + + align:start position:0% +that arises or anything up to the +present Point that's sort of the quick + + align:start position:0% +present Point that's sort of the quick + + + align:start position:0% +present Point that's sort of the quick +review of last + + align:start position:0% + + + + align:start position:0% + +lecture okay so how might I go about it + + align:start position:0% +lecture okay so how might I go about it + + + align:start position:0% +lecture okay so how might I go about it +well the re the reason I did this a + + align:start position:0% +well the re the reason I did this a + + + align:start position:0% +well the re the reason I did this a +principal reason I did this was because + + align:start position:0% +principal reason I did this was because + + + align:start position:0% +principal reason I did this was because +I said okay I've gotten rid of the even + + align:start position:0% +I said okay I've gotten rid of the even + + + align:start position:0% +I said okay I've gotten rid of the even +harmonics but I've still got to worry + + align:start position:0% +harmonics but I've still got to worry + + + align:start position:0% +harmonics but I've still got to worry +about three five 7 Etc right if I picked + + align:start position:0% +about three five 7 Etc right if I picked + + + align:start position:0% +about three five 7 Etc right if I picked +my angle just this way I would pin three + + align:start position:0% +my angle just this way I would pin three + + + align:start position:0% +my angle just this way I would pin three +to zero right so that would kill the + + align:start position:0% +to zero right so that would kill the + + + align:start position:0% +to zero right so that would kill the +third + + align:start position:0% +third + + + align:start position:0% +third +harmonic okay and that means since the + + align:start position:0% +harmonic okay and that means since the + + + align:start position:0% +harmonic okay and that means since the +fourth is gone by symmetry the lowest I + + align:start position:0% +fourth is gone by symmetry the lowest I + + + align:start position:0% +fourth is gone by symmetry the lowest I +have to deal with this fifth now I'm + + align:start position:0% +have to deal with this fifth now I'm + + + align:start position:0% +have to deal with this fifth now I'm +starting to get some nice space here + + align:start position:0% +starting to get some nice space here + + + align:start position:0% +starting to get some nice space here +okay and that lets me get much more + + align:start position:0% +okay and that lets me get much more + + + align:start position:0% +okay and that lets me get much more +purer filtered waveforms at the output + + align:start position:0% +purer filtered waveforms at the output + + + align:start position:0% +purer filtered waveforms at the output +compared to this kind of pulsy shape I'm + + align:start position:0% +compared to this kind of pulsy shape I'm + + + align:start position:0% +compared to this kind of pulsy shape I'm +generating but what else could I + + align:start position:0% +generating but what else could I + + + align:start position:0% +generating but what else could I +do maybe I can play that game and get + + align:start position:0% +do maybe I can play that game and get + + + align:start position:0% +do maybe I can play that game and get +rid of more harmonics by switching + + align:start position:0% +rid of more harmonics by switching + + + align:start position:0% +rid of more harmonics by switching +more okay so I've only switched each + + align:start position:0% +more okay so I've only switched each + + + align:start position:0% +more okay so I've only switched each +device once per cycle but suppose I'm + + align:start position:0% +device once per cycle but suppose I'm + + + align:start position:0% +device once per cycle but suppose I'm +willing to give up on that and switch + + align:start position:0% +willing to give up on that and switch + + + align:start position:0% +willing to give up on that and switch +more times per cycle on and off that + + align:start position:0% +more times per cycle on and off that + + + align:start position:0% +more times per cycle on and off that +means I can sort of create more times + + align:start position:0% +means I can sort of create more times + + + align:start position:0% +means I can sort of create more times +when I have positive or zero or negative + + align:start position:0% +when I have positive or zero or negative + + + align:start position:0% +when I have positive or zero or negative +in any given time okay I would like to + + align:start position:0% +in any given time okay I would like to + + + align:start position:0% +in any given time okay I would like to +do that perhaps in a way that helps me + + align:start position:0% +do that perhaps in a way that helps me + + + align:start position:0% +do that perhaps in a way that helps me +get rid of some higher harmonics right + + align:start position:0% +get rid of some higher harmonics right + + + align:start position:0% +get rid of some higher harmonics right +so now that I've gotten rid of the third + + align:start position:0% +so now that I've gotten rid of the third + + + align:start position:0% +so now that I've gotten rid of the third +my lowest are the fifth and the seventh + + align:start position:0% +my lowest are the fifth and the seventh + + + align:start position:0% +my lowest are the fifth and the seventh +maybe I could figure out some way to get + + align:start position:0% +maybe I could figure out some way to get + + + align:start position:0% +maybe I could figure out some way to get +rid of the fifth okay well how could I + + align:start position:0% +rid of the fifth okay well how could I + + + align:start position:0% +rid of the fifth okay well how could I +do that let's think of a slightly more + + align:start position:0% +do that let's think of a slightly more + + + align:start position:0% +do that let's think of a slightly more +sophisticated pulsing waveform than the + + align:start position:0% +sophisticated pulsing waveform than the + + + align:start position:0% +sophisticated pulsing waveform than the +uh white one here's here let me do this + + align:start position:0% +uh white one here's here let me do this + + + align:start position:0% +uh white one here's here let me do this +suppose I came and I said you know what + + align:start position:0% + + + + align:start position:0% + +if I put a zero right here so let me let + + align:start position:0% +if I put a zero right here so let me let + + + align:start position:0% +if I put a zero right here so let me let +me do the same thing I + + align:start position:0% +me do the same thing I + + + align:start position:0% +me do the same thing I +will put a positive step + + align:start position:0% +will put a positive step + + + align:start position:0% +will put a positive step +here but what I'm going to do is I'm + + align:start position:0% +here but what I'm going to do is I'm + + + align:start position:0% +here but what I'm going to do is I'm +going to look at this + + align:start position:0% +going to look at this + + + align:start position:0% +going to look at this +point and if I cut out a little bit on + + align:start position:0% +point and if I cut out a little bit on + + + align:start position:0% +point and if I cut out a little bit on +each side of this I don't change the + + align:start position:0% +each side of this I don't change the + + + align:start position:0% +each side of this I don't change the +fact that the third harmonic's gone + + align:start position:0% +fact that the third harmonic's gone + + + align:start position:0% +fact that the third harmonic's gone +right because as long as I make sure the + + align:start position:0% +right because as long as I make sure the + + + align:start position:0% +right because as long as I make sure the +amount of positive in this multiple of + + align:start position:0% +amount of positive in this multiple of + + + align:start position:0% +amount of positive in this multiple of +the third harmonic balances the amount + + align:start position:0% +the third harmonic balances the amount + + + align:start position:0% +the third harmonic balances the amount +of negative area with the the third + + align:start position:0% +of negative area with the the third + + + align:start position:0% +of negative area with the the third +harmonic sine wave I will maintain zero + + align:start position:0% +harmonic sine wave I will maintain zero + + + align:start position:0% +harmonic sine wave I will maintain zero +third harmonic so maybe I could do + + align:start position:0% +third harmonic so maybe I could do + + + align:start position:0% +third harmonic so maybe I could do +something like this I will create a + + align:start position:0% +something like this I will create a + + + align:start position:0% +something like this I will create a +pulse wave form that does + + align:start position:0% + + + + align:start position:0% + +this okay and maybe I'll do that again + + align:start position:0% +this okay and maybe I'll do that again + + + align:start position:0% +this okay and maybe I'll do that again +on this + + align:start position:0% +on this + + + align:start position:0% +on this +side + + align:start position:0% +side + + + align:start position:0% +side +okay and I could and I would now want to + + align:start position:0% +okay and I could and I would now want to + + + align:start position:0% +okay and I could and I would now want to +keep my waveform halfwave symmetric so + + align:start position:0% +keep my waveform halfwave symmetric so + + + align:start position:0% +keep my waveform halfwave symmetric so +I'll do the same thing on the other side + + align:start position:0% +I'll do the same thing on the other side + + + align:start position:0% +I'll do the same thing on the other side +and do do + + align:start position:0% + + + + align:start position:0% + +this all right now if I've done this in + + align:start position:0% +this all right now if I've done this in + + + align:start position:0% +this all right now if I've done this in +a right way and I just make this + + align:start position:0% +a right way and I just make this + + + align:start position:0% +a right way and I just make this +symmetric about + + align:start position:0% +symmetric about + + + align:start position:0% +symmetric about +60° and I put in some other angle maybe + + align:start position:0% +60° and I put in some other angle maybe + + + align:start position:0% +60° and I put in some other angle maybe +I'll call that Capital + + align:start position:0% +I'll call that Capital + + + align:start position:0% +I'll call that Capital +Delta Capital + + align:start position:0% +Delta Capital + + + align:start position:0% +Delta Capital +Delta right I haven't introduced any + + align:start position:0% +Delta right I haven't introduced any + + + align:start position:0% +Delta right I haven't introduced any +third harmonic + + align:start position:0% +third harmonic + + + align:start position:0% +third harmonic +again right because the multiple of this + + align:start position:0% +again right because the multiple of this + + + align:start position:0% +again right because the multiple of this +pink colored waveform or orangey colored + + align:start position:0% +pink colored waveform or orangey colored + + + align:start position:0% +pink colored waveform or orangey colored +wave form with um this sin 3 omega T the + + align:start position:0% +wave form with um this sin 3 omega T the + + + align:start position:0% +wave form with um this sin 3 omega T the +integral of it's still going to be zero + + align:start position:0% +integral of it's still going to be zero + + + align:start position:0% +integral of it's still going to be zero +it's still orthogonal any questions + + align:start position:0% +it's still orthogonal any questions + + + align:start position:0% +it's still orthogonal any questions +about + + align:start position:0% +about + + + align:start position:0% +about +that what do I do with Delta I can pick + + align:start position:0% +that what do I do with Delta I can pick + + + align:start position:0% +that what do I do with Delta I can pick +that when I do with capital Delta + + align:start position:0% +that when I do with capital Delta + + + align:start position:0% +that when I do with capital Delta +here maybe I can pick that so the fifth + + align:start position:0% +here maybe I can pick that so the fifth + + + align:start position:0% +here maybe I can pick that so the fifth +harmonic goes + + align:start position:0% +harmonic goes + + + align:start position:0% +harmonic goes +away all right and in fact I'll show you + + align:start position:0% +away all right and in fact I'll show you + + + align:start position:0% +away all right and in fact I'll show you +the one result and this is just a kind + + align:start position:0% +the one result and this is just a kind + + + align:start position:0% +the one result and this is just a kind +of a very simple + + align:start position:0% +of a very simple + + + align:start position:0% +of a very simple +example this is what you would get + + align:start position:0% +example this is what you would get + + + align:start position:0% +example this is what you would get +and in this case I'm going to pick this + + align:start position:0% +and in this case I'm going to pick this + + + align:start position:0% +and in this case I'm going to pick this +waveform Capital Delta to be exactly + + align:start position:0% +waveform Capital Delta to be exactly + + + align:start position:0% +waveform Capital Delta to be exactly +12° okay and because my Artistry is not + + align:start position:0% +12° okay and because my Artistry is not + + + align:start position:0% +12° okay and because my Artistry is not +so good I've decided to resort to the + + align:start position:0% +so good I've decided to resort to the + + + align:start position:0% +so good I've decided to resort to the +board I mean to the + + align:start position:0% +board I mean to the + + + align:start position:0% +board I mean to the +uh to a figure from the book but this is + + align:start position:0% +uh to a figure from the book but this is + + + align:start position:0% +uh to a figure from the book but this is +the same you can see this is the third + + align:start position:0% +the same you can see this is the third + + + align:start position:0% +the same you can see this is the third +this is how I cancel third harmonic + + align:start position:0% +this is how I cancel third harmonic + + + align:start position:0% +this is how I cancel third harmonic +here's sin 5 Omega T okay and if I + + align:start position:0% +here's sin 5 Omega T okay and if I + + + align:start position:0% +here's sin 5 Omega T okay and if I +multiply this original one pulse per + + align:start position:0% +multiply this original one pulse per + + + align:start position:0% +multiply this original one pulse per +half cycle waveform by S 5 Omega T you + + align:start position:0% +half cycle waveform by S 5 Omega T you + + + align:start position:0% +half cycle waveform by S 5 Omega T you +can see that the negative area doesn't + + align:start position:0% +can see that the negative area doesn't + + + align:start position:0% +can see that the negative area doesn't +cancel the positive area and hence I + + align:start position:0% +cancel the positive area and hence I + + + align:start position:0% +cancel the positive area and hence I +have some fifth + + align:start position:0% +have some fifth + + + align:start position:0% +have some fifth +harmonic okay but if I then put in my + + align:start position:0% +harmonic okay but if I then put in my + + + align:start position:0% +harmonic okay but if I then put in my +new my nulls right here like I said + + align:start position:0% +new my nulls right here like I said + + + align:start position:0% +new my nulls right here like I said +centered about 60° it turns out if I use + + align:start position:0% +centered about 60° it turns out if I use + + + align:start position:0% +centered about 60° it turns out if I use +that Capital Delta being 12 de I can + + align:start position:0% +that Capital Delta being 12 de I can + + + align:start position:0% +that Capital Delta being 12 de I can +make the negative area exactly cancel + + align:start position:0% +make the negative area exactly cancel + + + align:start position:0% +make the negative area exactly cancel +the positive area and kill the fifth + + align:start position:0% +the positive area and kill the fifth + + + align:start position:0% +the positive area and kill the fifth +harmonic so if I use this waveform and + + align:start position:0% +harmonic so if I use this waveform and + + + align:start position:0% +harmonic so if I use this waveform and +it's again halfway symmetric has three + + align:start position:0% +it's again halfway symmetric has three + + + align:start position:0% +it's again halfway symmetric has three +pulses in each half cycle instead of one + + align:start position:0% +pulses in each half cycle instead of one + + + align:start position:0% +pulses in each half cycle instead of one +pulse in each half cycle I could not + + align:start position:0% +pulse in each half cycle I could not + + + align:start position:0% +pulse in each half cycle I could not +only keep the third harmonic killed but + + align:start position:0% +only keep the third harmonic killed but + + + align:start position:0% +only keep the third harmonic killed but +also kill off the fifth which would then + + align:start position:0% +also kill off the fifth which would then + + + align:start position:0% +also kill off the fifth which would then +leave the lowest harmonic the + + align:start position:0% +leave the lowest harmonic the + + + align:start position:0% +leave the lowest harmonic the +seventh all right + + align:start position:0% +seventh all right + + + align:start position:0% +seventh all right +um that makes it easier for this filter + + align:start position:0% +um that makes it easier for this filter + + + align:start position:0% +um that makes it easier for this filter +to kill it or equivalently for the same + + align:start position:0% +to kill it or equivalently for the same + + + align:start position:0% +to kill it or equivalently for the same +filter I get more pure sign wve at my + + align:start position:0% +filter I get more pure sign wve at my + + + align:start position:0% +filter I get more pure sign wve at my +actual output over + + align:start position:0% +actual output over + + + align:start position:0% +actual output over +here any questions about + + align:start position:0% + + + + align:start position:0% + +that this kind of trick where I'm going + + align:start position:0% +that this kind of trick where I'm going + + + align:start position:0% +that this kind of trick where I'm going +to introduce new pulses in each half + + align:start position:0% +to introduce new pulses in each half + + + align:start position:0% +to introduce new pulses in each half +cycle is called uh harmonic + + align:start position:0% + + + + align:start position:0% + +elimination and we can often view it as + + align:start position:0% +elimination and we can often view it as + + + align:start position:0% +elimination and we can often view it as +exactly through this method is how do I + + align:start position:0% +exactly through this method is how do I + + + align:start position:0% +exactly through this method is how do I +synthesize pulses that sort of satisfy + + align:start position:0% +synthesize pulses that sort of satisfy + + + align:start position:0% +synthesize pulses that sort of satisfy +this orthogonality with each + + align:start position:0% +this orthogonality with each + + + align:start position:0% +this orthogonality with each +harmonic + + align:start position:0% +harmonic + + + align:start position:0% +harmonic +okay now is this the best I could do + + align:start position:0% +okay now is this the best I could do + + + align:start position:0% +okay now is this the best I could do +well first of all if I synthesize this + + align:start position:0% +well first of all if I synthesize this + + + align:start position:0% +well first of all if I synthesize this +waveform how many times you think I + + align:start position:0% +waveform how many times you think I + + + align:start position:0% +waveform how many times you think I +switch each device per + + align:start position:0% + + + + align:start position:0% + +cycle without working it out you can + + align:start position:0% +cycle without working it out you can + + + align:start position:0% +cycle without working it out you can +essentially you know each time you get a + + align:start position:0% +essentially you know each time you get a + + + align:start position:0% +essentially you know each time you get a +pulse per half cycle you have to add on + + align:start position:0% +pulse per half cycle you have to add on + + + align:start position:0% +pulse per half cycle you have to add on +some switching transitions so you get + + align:start position:0% +some switching transitions so you get + + + align:start position:0% +some switching transitions so you get +higher switching losses right so what + + align:start position:0% +higher switching losses right so what + + + align:start position:0% +higher switching losses right so what +I'm really doing is I'm + + align:start position:0% +I'm really doing is I'm + + + align:start position:0% +I'm really doing is I'm +trading switching loss for lower + + align:start position:0% +trading switching loss for lower + + + align:start position:0% +trading switching loss for lower +filtered output + + align:start position:0% +filtered output + + + align:start position:0% +filtered output +components okay um now is this as good + + align:start position:0% +components okay um now is this as good + + + align:start position:0% +components okay um now is this as good +as I can do to get rid of the no it + + align:start position:0% +as I can do to get rid of the no it + + + align:start position:0% +as I can do to get rid of the no it +turns out that um and you can write + + align:start position:0% +turns out that um and you can write + + + align:start position:0% +turns out that um and you can write +equations and start solving them to do + + align:start position:0% +equations and start solving them to do + + + align:start position:0% +equations and start solving them to do +this and I've given in in kpvs chapter 8 + + align:start position:0% +this and I've given in in kpvs chapter 8 + + + align:start position:0% +this and I've given in in kpvs chapter 8 +there's two uh references there's a + + align:start position:0% +there's two uh references there's a + + + align:start position:0% +there's two uh references there's a +classic Patell and hoft reference that + + align:start position:0% +classic Patell and hoft reference that + + + align:start position:0% +classic Patell and hoft reference that +that introduce this general idea and + + align:start position:0% +that introduce this general idea and + + + align:start position:0% +that introduce this general idea and +then there's a more uh recent Chase and + + align:start position:0% +then there's a more uh recent Chase and + + + align:start position:0% +then there's a more uh recent Chase and +reference that really goes into detail + + align:start position:0% +reference that really goes into detail + + + align:start position:0% +reference that really goes into detail +about the the best ways to do this is + + align:start position:0% +about the the best ways to do this is + + + align:start position:0% +about the the best ways to do this is +each time you put in one pulse in a half + + align:start position:0% +each time you put in one pulse in a half + + + align:start position:0% +each time you put in one pulse in a half +cycle you can ultimately pick + + align:start position:0% +cycle you can ultimately pick + + + align:start position:0% +cycle you can ultimately pick +one harmonic to eliminate and when we + + align:start position:0% +one harmonic to eliminate and when we + + + align:start position:0% +one harmonic to eliminate and when we +talk about one harmonic we're keeping + + align:start position:0% +talk about one harmonic we're keeping + + + align:start position:0% +talk about one harmonic we're keeping +everything halfway symmetric so we care + + align:start position:0% +everything halfway symmetric so we care + + + align:start position:0% +everything halfway symmetric so we care +about one odd harmonic okay so we're + + align:start position:0% +about one odd harmonic okay so we're + + + align:start position:0% +about one odd harmonic okay so we're +assuming our evens are all gone I only + + align:start position:0% +assuming our evens are all gone I only + + + align:start position:0% +assuming our evens are all gone I only +have odds so I could actually pick this + + align:start position:0% +have odds so I could actually pick this + + + align:start position:0% +have odds so I could actually pick this +wave for and because I have two degrees + + align:start position:0% +wave for and because I have two degrees + + + align:start position:0% +wave for and because I have two degrees +of freedom uh little Delta in this + + align:start position:0% +of freedom uh little Delta in this + + + align:start position:0% +of freedom uh little Delta in this +example gamma I could kill the fifth and + + align:start position:0% +example gamma I could kill the fifth and + + + align:start position:0% +example gamma I could kill the fifth and +the second Fifth and the 7th or the + + align:start position:0% +the second Fifth and the 7th or the + + + align:start position:0% +the second Fifth and the 7th or the +third and the fifth but only have two + + align:start position:0% +third and the fifth but only have two + + + align:start position:0% +third and the fifth but only have two +pulses in a half cycle and so have fewer + + align:start position:0% +pulses in a half cycle and so have fewer + + + align:start position:0% +pulses in a half cycle and so have fewer +switching transitions than I do in this + + align:start position:0% +switching transitions than I do in this + + + align:start position:0% +switching transitions than I do in this +example waveform okay and generally the + + align:start position:0% +example waveform okay and generally the + + + align:start position:0% +example waveform okay and generally the +rule is for each pulse per half cycle I + + align:start position:0% +rule is for each pulse per half cycle I + + + align:start position:0% +rule is for each pulse per half cycle I +get to pick one odd harmonic to + + align:start position:0% +get to pick one odd harmonic to + + + align:start position:0% +get to pick one odd harmonic to +eliminate okay any questions about + + align:start position:0% +eliminate okay any questions about + + + align:start position:0% +eliminate okay any questions about +that is there like a practical limit how + + align:start position:0% +that is there like a practical limit how + + + align:start position:0% +that is there like a practical limit how +high of a + + align:start position:0% +high of a + + + align:start position:0% +high of a +harmonic yeah that is an excellent + + align:start position:0% +harmonic yeah that is an excellent + + + align:start position:0% +harmonic yeah that is an excellent +question um there is because you know if + + align:start position:0% +question um there is because you know if + + + align:start position:0% +question um there is because you know if +I want to eliminate the 97th harmonic + + align:start position:0% +I want to eliminate the 97th harmonic + + + align:start position:0% +I want to eliminate the 97th harmonic +right um what that means is I've got to + + align:start position:0% +right um what that means is I've got to + + + align:start position:0% +right um what that means is I've got to +control the timing resolution just so + + align:start position:0% +control the timing resolution just so + + + align:start position:0% +control the timing resolution just so +that I you know make that multiple with + + align:start position:0% +that I you know make that multiple with + + + align:start position:0% +that I you know make that multiple with +the 97th harmonic integrated zero right + + align:start position:0% +the 97th harmonic integrated zero right + + + align:start position:0% +the 97th harmonic integrated zero right +so the higher the number of harmonics I + + align:start position:0% +so the higher the number of harmonics I + + + align:start position:0% +so the higher the number of harmonics I +want to eliminate uh the more precise + + align:start position:0% +want to eliminate uh the more precise + + + align:start position:0% +want to eliminate uh the more precise +the timing requirements become right so + + align:start position:0% +the timing requirements become right so + + + align:start position:0% +the timing requirements become right so +you can imagine how would you do this + + align:start position:0% +you can imagine how would you do this + + + align:start position:0% +you can imagine how would you do this +you'd have a lookup table that steps + + align:start position:0% +you'd have a lookup table that steps + + + align:start position:0% +you'd have a lookup table that steps +along and it says at every time slice + + align:start position:0% +along and it says at every time slice + + + align:start position:0% +along and it says at every time slice +you know which switches should be on and + + align:start position:0% +you know which switches should be on and + + + align:start position:0% +you know which switches should be on and +and you know the the number of time + + align:start position:0% +and you know the the number of time + + + align:start position:0% +and you know the the number of time +slices I need to break it up into + + align:start position:0% +slices I need to break it up into + + + align:start position:0% +slices I need to break it up into +accurately enough to to murder those low + + align:start position:0% +accurately enough to to murder those low + + + align:start position:0% +accurately enough to to murder those low +frequency harmonics gets worse and worse + + align:start position:0% +frequency harmonics gets worse and worse + + + align:start position:0% +frequency harmonics gets worse and worse +and worse the other limit is eventually + + align:start position:0% +and worse the other limit is eventually + + + align:start position:0% +and worse the other limit is eventually +I switch so many times that it's that my + + align:start position:0% +I switch so many times that it's that my + + + align:start position:0% +I switch so many times that it's that my +switching loss goes crazy and I don't + + align:start position:0% +switching loss goes crazy and I don't + + + align:start position:0% +switching loss goes crazy and I don't +like it okay the other thing I'll point + + align:start position:0% +like it okay the other thing I'll point + + + align:start position:0% +like it okay the other thing I'll point +out is if I took this to its logical + + align:start position:0% +out is if I took this to its logical + + + align:start position:0% +out is if I took this to its logical +conclusion so suppose I came off and I + + align:start position:0% +conclusion so suppose I came off and I + + + align:start position:0% +conclusion so suppose I came off and I +said okay I want to get rid of a bunch + + align:start position:0% +said okay I want to get rid of a bunch + + + align:start position:0% +said okay I want to get rid of a bunch +of harmonics right so imagine my pulse + + align:start position:0% +of harmonics right so imagine my pulse + + + align:start position:0% +of harmonics right so imagine my pulse +waveform look like this and I'm just + + align:start position:0% +waveform look like this and I'm just + + + align:start position:0% +waveform look like this and I'm just +going to you know I'm not going to be + + align:start position:0% +going to you know I'm not going to be + + + align:start position:0% +going to you know I'm not going to be +quantitative now but maybe I would have + + align:start position:0% +quantitative now but maybe I would have + + + align:start position:0% +quantitative now but maybe I would have +something that looked like this you know + + align:start position:0% +something that looked like this you know + + + align:start position:0% +something that looked like this you know +pulse and another pulse another + + align:start position:0% +pulse and another pulse another + + + align:start position:0% +pulse and another pulse another +pulse and these are all very controlled + + align:start position:0% +pulse and these are all very controlled + + + align:start position:0% +pulse and these are all very controlled +widths right and then I do this + + align:start position:0% + + + + align:start position:0% + +right something like that right I don't + + align:start position:0% +right something like that right I don't + + + align:start position:0% +right something like that right I don't +think I have the right number of pulses + + align:start position:0% +think I have the right number of pulses + + + align:start position:0% +think I have the right number of pulses +here but you know I have something + + align:start position:0% +here but you know I have something + + + align:start position:0% +here but you know I have something +that's shaped to generate a set of + + align:start position:0% +that's shaped to generate a set of + + + align:start position:0% +that's shaped to generate a set of +pulses that make this at least it look + + align:start position:0% +pulses that make this at least it look + + + align:start position:0% +pulses that make this at least it look +frequencies when I filter it look closer + + align:start position:0% +frequencies when I filter it look closer + + + align:start position:0% +frequencies when I filter it look closer +to a sine wave okay maybe these middle + + align:start position:0% +to a sine wave okay maybe these middle + + + align:start position:0% +to a sine wave okay maybe these middle +pulses would tend to be bigger than + + align:start position:0% +pulses would tend to be bigger than + + + align:start position:0% +pulses would tend to be bigger than +these Edge pulses okay and I pick the + + align:start position:0% +these Edge pulses okay and I pick the + + + align:start position:0% +these Edge pulses okay and I pick the +pulsing times and positions exactly to + + align:start position:0% +pulsing times and positions exactly to + + + align:start position:0% +pulsing times and positions exactly to +give me this magic cancellation what I + + align:start position:0% +give me this magic cancellation what I + + + align:start position:0% +give me this magic cancellation what I +am doing if I think about this in the + + align:start position:0% +am doing if I think about this in the + + + align:start position:0% +am doing if I think about this in the +frequency domain right is you know I've + + align:start position:0% +frequency domain right is you know I've + + + align:start position:0% +frequency domain right is you know I've +got my fundamental that I + + align:start position:0% +got my fundamental that I + + + align:start position:0% +got my fundamental that I +want I've got some + + align:start position:0% +want I've got some + + + align:start position:0% +want I've got some +filter that's going to then cut off + + align:start position:0% +filter that's going to then cut off + + + align:start position:0% +filter that's going to then cut off +right and what I'm doing by Kill by + + align:start position:0% +right and what I'm doing by Kill by + + + align:start position:0% +right and what I'm doing by Kill by +doing this is I'm eliminating a bunch of + + align:start position:0% +doing this is I'm eliminating a bunch of + + + align:start position:0% +doing this is I'm eliminating a bunch of +the low order harmonics but you can see + + align:start position:0% +the low order harmonics but you can see + + + align:start position:0% +the low order harmonics but you can see +that this has a bunch of high frequency + + align:start position:0% +that this has a bunch of high frequency + + + align:start position:0% +that this has a bunch of high frequency +content right I'm switching up and down + + align:start position:0% +content right I'm switching up and down + + + align:start position:0% +content right I'm switching up and down +and up and down and up and down that + + align:start position:0% +and up and down and up and down that + + + align:start position:0% +and up and down and up and down that +sort of suggests to you there's a bunch + + align:start position:0% +sort of suggests to you there's a bunch + + + align:start position:0% +sort of suggests to you there's a bunch +of high frequency stuff there right so + + align:start position:0% +of high frequency stuff there right so + + + align:start position:0% +of high frequency stuff there right so +if I look at the original waveform VX + + align:start position:0% +if I look at the original waveform VX + + + align:start position:0% +if I look at the original waveform VX +this + + align:start position:0% +this + + + align:start position:0% +this +waveform in fact if I looked at its + + align:start position:0% +waveform in fact if I looked at its + + + align:start position:0% +waveform in fact if I looked at its +total harmonic Distortion it actually is + + align:start position:0% +total harmonic Distortion it actually is + + + align:start position:0% +total harmonic Distortion it actually is +higher what I'm doing is I'm killing off + + align:start position:0% +higher what I'm doing is I'm killing off + + + align:start position:0% +higher what I'm doing is I'm killing off +the low frequency stuff and then I'm + + align:start position:0% +the low frequency stuff and then I'm + + + align:start position:0% +the low frequency stuff and then I'm +really growing The High Frequency stuff + + align:start position:0% +really growing The High Frequency stuff + + + align:start position:0% +really growing The High Frequency stuff +right so it's not like my waveform + + align:start position:0% +right so it's not like my waveform + + + align:start position:0% +right so it's not like my waveform +actually has less harmonic content it + + align:start position:0% +actually has less harmonic content it + + + align:start position:0% +actually has less harmonic content it +actually has considerably more and + + align:start position:0% +actually has considerably more and + + + align:start position:0% +actually has considerably more and +depending upon how you choose to you + + align:start position:0% +depending upon how you choose to you + + + align:start position:0% +depending upon how you choose to you +know what angles you choose to kill off + + align:start position:0% +know what angles you choose to kill off + + + align:start position:0% +know what angles you choose to kill off +your low order harmonics you will end up + + align:start position:0% +your low order harmonics you will end up + + + align:start position:0% +your low order harmonics you will end up +with more or less stuff at high + + align:start position:0% +with more or less stuff at high + + + align:start position:0% +with more or less stuff at high +frequencies but undoubtedly you're going + + align:start position:0% +frequencies but undoubtedly you're going + + + align:start position:0% +frequencies but undoubtedly you're going +to get more highfrequency stuff because + + align:start position:0% +to get more highfrequency stuff because + + + align:start position:0% +to get more highfrequency stuff because +you've got a lot of switching going on + + align:start position:0% +you've got a lot of switching going on + + + align:start position:0% +you've got a lot of switching going on +right + + align:start position:0% +right + + + align:start position:0% +right +the thing about that is is if I think + + align:start position:0% +the thing about that is is if I think + + + align:start position:0% +the thing about that is is if I think +about a low pass filter it's easy for me + + align:start position:0% +about a low pass filter it's easy for me + + + align:start position:0% +about a low pass filter it's easy for me +to murder the high frequencies in a cut + + align:start position:0% +to murder the high frequencies in a cut + + + align:start position:0% +to murder the high frequencies in a cut +off it's hard for me to eliminate stuff + + align:start position:0% +off it's hard for me to eliminate stuff + + + align:start position:0% +off it's hard for me to eliminate stuff +that's near cut off so I'm making the + + align:start position:0% +that's near cut off so I'm making the + + + align:start position:0% +that's near cut off so I'm making the +challenge of basically pushing the + + align:start position:0% +challenge of basically pushing the + + + align:start position:0% +challenge of basically pushing the +frequency content up and kind of keeping + + align:start position:0% +frequency content up and kind of keeping + + + align:start position:0% +frequency content up and kind of keeping +the stuff that's hard to filter low okay + + align:start position:0% +the stuff that's hard to filter low okay + + + align:start position:0% +the stuff that's hard to filter low okay +so I'm not sort of getting rid of high + + align:start position:0% +so I'm not sort of getting rid of high + + + align:start position:0% +so I'm not sort of getting rid of high +frequency content I'm actually + + align:start position:0% +frequency content I'm actually + + + align:start position:0% +frequency content I'm actually +increasing it but what I am is getting + + align:start position:0% +increasing it but what I am is getting + + + align:start position:0% +increasing it but what I am is getting +rid of the stuff that's hardest to + + align:start position:0% +rid of the stuff that's hardest to + + + align:start position:0% +rid of the stuff that's hardest to +filter okay any questions about + + align:start position:0% + + + + align:start position:0% + +that okay so that's one strategy I can + + align:start position:0% +that okay so that's one strategy I can + + + align:start position:0% +that okay so that's one strategy I can +use what else could I + + align:start position:0% +use what else could I + + + align:start position:0% +use what else could I +do and actually in my original waveform + + align:start position:0% +do and actually in my original waveform + + + align:start position:0% +do and actually in my original waveform +here that we + + align:start position:0% +here that we + + + align:start position:0% +here that we +showed we saw a little bit of a hint of + + align:start position:0% +showed we saw a little bit of a hint of + + + align:start position:0% +showed we saw a little bit of a hint of +this and here's the idea um suppose I + + align:start position:0% +this and here's the idea um suppose I + + + align:start position:0% +this and here's the idea um suppose I +have some waveform uh + + align:start position:0% +have some waveform uh + + + align:start position:0% +have some waveform uh +uh X of + + align:start position:0% +uh X of + + + align:start position:0% +uh X of +T that I might Express as the summation + + align:start position:0% +T that I might Express as the summation + + + align:start position:0% +T that I might Express as the summation +of + + align:start position:0% +of + + + align:start position:0% +of +uh summation of n = 1 to infinity x + + align:start position:0% +uh summation of n = 1 to infinity x + + + align:start position:0% +uh summation of n = 1 to infinity x +subn sin of n Omega t plus 5 subn right + + align:start position:0% +subn sin of n Omega t plus 5 subn right + + + align:start position:0% +subn sin of n Omega t plus 5 subn right +it has some 4A + + align:start position:0% +it has some 4A + + + align:start position:0% +it has some 4A +series then if I had some delayed + + align:start position:0% +series then if I had some delayed + + + align:start position:0% +series then if I had some delayed +version of this waveform let me call + + align:start position:0% +version of this waveform let me call + + + align:start position:0% +version of this waveform let me call +this X of T minus + + align:start position:0% +this X of T minus + + + align:start position:0% +this X of T minus +T1 okay what would his content look like + + align:start position:0% +T1 okay what would his content look like + + + align:start position:0% +T1 okay what would his content look like +well I just go to this expression I + + align:start position:0% +well I just go to this expression I + + + align:start position:0% +well I just go to this expression I +substitute in T minus T1 right so I + + align:start position:0% +substitute in T minus T1 right so I + + + align:start position:0% +substitute in T minus T1 right so I +would get okay this is the summation of + + align:start position:0% +would get okay this is the summation of + + + align:start position:0% +would get okay this is the summation of +n = 1 to Infinity of x subn + + align:start position:0% +n = 1 to Infinity of x subn + + + align:start position:0% +n = 1 to Infinity of x subn +s of n Omega not T minus T1 so I'll say + + align:start position:0% +s of n Omega not T minus T1 so I'll say + + + align:start position:0% +s of n Omega not T minus T1 so I'll say +there's n Omega T minus n Omega T1 + 5 n + + align:start position:0% +there's n Omega T minus n Omega T1 + 5 n + + + align:start position:0% +there's n Omega T minus n Omega T1 + 5 n +right so if I + + align:start position:0% + + + + align:start position:0% + +Define some Delta 51 the phase shift at + + align:start position:0% +Define some Delta 51 the phase shift at + + + align:start position:0% +Define some Delta 51 the phase shift at +the fundamental associated with this + + align:start position:0% +the fundamental associated with this + + + align:start position:0% +the fundamental associated with this +time shift + + align:start position:0% +time shift + + + align:start position:0% +time shift +T1 okay that would simply be uh Omega + + align:start position:0% +T1 okay that would simply be uh Omega + + + align:start position:0% +T1 okay that would simply be uh Omega +T1 that is if I'm shifting by a Time T1 + + align:start position:0% +T1 that is if I'm shifting by a Time T1 + + + align:start position:0% +T1 that is if I'm shifting by a Time T1 +I'm Shifting the + + align:start position:0% +I'm Shifting the + + + align:start position:0% +I'm Shifting the +fundamental by by a + + align:start position:0% +fundamental by by a + + + align:start position:0% +fundamental by by a +phase um Omega + + align:start position:0% +phase um Omega + + + align:start position:0% +phase um Omega +T1 okay what am I Shifting the nth + + align:start position:0% +T1 okay what am I Shifting the nth + + + align:start position:0% +T1 okay what am I Shifting the nth +harmonic by this is the fundamental + + align:start position:0% + + + + align:start position:0% + +shift right the nth harmonic Delta n is + + align:start position:0% +shift right the nth harmonic Delta n is + + + align:start position:0% +shift right the nth harmonic Delta n is +equal to n + + align:start position:0% +equal to n + + + align:start position:0% +equal to n +delta1 so this is the nth + + align:start position:0% +delta1 so this is the nth + + + align:start position:0% +delta1 so this is the nth +harmonic phas + + align:start position:0% + + + + align:start position:0% + +shift okay and so you here you can see + + align:start position:0% +shift okay and so you here you can see + + + align:start position:0% +shift okay and so you here you can see +right because the nth harmonic this + + align:start position:0% +right because the nth harmonic this + + + align:start position:0% +right because the nth harmonic this +thing uh and maybe I should be careful + + align:start position:0% +thing uh and maybe I should be careful + + + align:start position:0% +thing uh and maybe I should be careful +Define delta1 is being minus Omega T1 + + align:start position:0% +Define delta1 is being minus Omega T1 + + + align:start position:0% +Define delta1 is being minus Omega T1 +and maybe this is minus n Omega delta1 + + align:start position:0% +and maybe this is minus n Omega delta1 + + + align:start position:0% +and maybe this is minus n Omega delta1 +so this is you know Delta 51 or n Delta + + align:start position:0% +so this is you know Delta 51 or n Delta + + + align:start position:0% +so this is you know Delta 51 or n Delta +51 is the amount I'm Shifting the nth + + align:start position:0% +51 is the amount I'm Shifting the nth + + + align:start position:0% +51 is the amount I'm Shifting the nth +harmonic + + align:start position:0% +harmonic + + + align:start position:0% +harmonic +okay does that make sense to + + align:start position:0% +okay does that make sense to + + + align:start position:0% +okay does that make sense to +everybody so why am I telling you this + + align:start position:0% +everybody so why am I telling you this + + + align:start position:0% +everybody so why am I telling you this +suppose I did some game like this and I + + align:start position:0% +suppose I did some game like this and I + + + align:start position:0% +suppose I did some game like this and I +would have said that this is kind of you + + align:start position:0% +would have said that this is kind of you + + + align:start position:0% +would have said that this is kind of you +know maybe not the most common way to + + align:start position:0% +know maybe not the most common way to + + + align:start position:0% +know maybe not the most common way to +play this + + align:start position:0% +play this + + + align:start position:0% +play this +game but you can actually find people + + align:start position:0% +game but you can actually find people + + + align:start position:0% +game but you can actually find people +whove built converters this way + + align:start position:0% +whove built converters this way + + + align:start position:0% +whove built converters this way +especially for high power suppose I had + + align:start position:0% +especially for high power suppose I had + + + align:start position:0% +especially for high power suppose I had +some DC input + + align:start position:0% + + + + align:start position:0% + +voltage and I will build a an + + align:start position:0% + + + + align:start position:0% + +inverter okay + + align:start position:0% +inverter okay + + + align:start position:0% +inverter okay +okay um here's a first inverter and I'll + + align:start position:0% +okay um here's a first inverter and I'll + + + align:start position:0% +okay um here's a first inverter and I'll +give him an output voltage + + align:start position:0% + + + + align:start position:0% + +vx1 okay and now let me build a second + + align:start position:0% +vx1 okay and now let me build a second + + + align:start position:0% +vx1 okay and now let me build a second +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +inverter four + + align:start position:0% + + + + align:start position:0% + +switches and I'm going to give him an + + align:start position:0% +switches and I'm going to give him an + + + align:start position:0% +switches and I'm going to give him an +output that's + + align:start position:0% +output that's + + + align:start position:0% +output that's +vx2 and what I'll do is I'll Transform a + + align:start position:0% +vx2 and what I'll do is I'll Transform a + + + align:start position:0% +vx2 and what I'll do is I'll Transform a +couple these two outputs like this + + align:start position:0% + + + + align:start position:0% + +so and let me just imagine this is a + + align:start position:0% +so and let me just imagine this is a + + + align:start position:0% +so and let me just imagine this is a +one: one + + align:start position:0% +one: one + + + align:start position:0% +one: one +Transformer okay and here's another one + + align:start position:0% +Transformer okay and here's another one + + + align:start position:0% +Transformer okay and here's another one +to1 + + align:start position:0% + + + + align:start position:0% + +Transformer okay so this is + + align:start position:0% + + + + align:start position:0% + +vx2 that's a one to one Transformer that + + align:start position:0% +vx2 that's a one to one Transformer that + + + align:start position:0% +vx2 that's a one to one Transformer that +means that this + + align:start position:0% +means that this + + + align:start position:0% +means that this +total + + align:start position:0% +total + + + align:start position:0% +total +VX is simply equal to vx1 plus VX + + align:start position:0% +VX is simply equal to vx1 plus VX + + + align:start position:0% +VX is simply equal to vx1 plus VX +X2 right so I've got a first inverter + + align:start position:0% +X2 right so I've got a first inverter + + + align:start position:0% +X2 right so I've got a first inverter +generating a first pattern and a second + + align:start position:0% +generating a first pattern and a second + + + align:start position:0% +generating a first pattern and a second +inverter generating a second pattern + + align:start position:0% +inverter generating a second pattern + + + align:start position:0% +inverter generating a second pattern +right so what is the Harmon what is the + + align:start position:0% +right so what is the Harmon what is the + + + align:start position:0% +right so what is the Harmon what is the +content if I said that you know + + align:start position:0% +content if I said that you know + + + align:start position:0% +content if I said that you know +um suppose I say + + align:start position:0% +um suppose I say + + + align:start position:0% +um suppose I say +vx1 is equal to the + + align:start position:0% +vx1 is equal to the + + + align:start position:0% +vx1 is equal to the +summation of n = 1 to Infinity let's + + align:start position:0% +summation of n = 1 to Infinity let's + + + align:start position:0% +summation of n = 1 to Infinity let's +assume I'm just doing odd waveforms of + + align:start position:0% +assume I'm just doing odd waveforms of + + + align:start position:0% +assume I'm just doing odd waveforms of +uh V subn + + align:start position:0% +uh V subn + + + align:start position:0% +uh V subn +sin uh n Omega t + 5 subn uh 5 subn + + align:start position:0% +sin uh n Omega t + 5 subn uh 5 subn + + + align:start position:0% +sin uh n Omega t + 5 subn uh 5 subn +right that means that + + align:start position:0% +right that means that + + + align:start position:0% +right that means that +vx2 if I if I shift by + + align:start position:0% + + + + align:start position:0% + +T1 right vx2 is just going to be + + align:start position:0% +T1 right vx2 is just going to be + + + align:start position:0% +T1 right vx2 is just going to be +summation of Nal 1 to Infinity of V subn + + align:start position:0% +summation of Nal 1 to Infinity of V subn + + + align:start position:0% +summation of Nal 1 to Infinity of V subn +sin n Omega t plus Del n Delta + + align:start position:0% +sin n Omega t plus Del n Delta + + + align:start position:0% +sin n Omega t plus Del n Delta +1 plus + + align:start position:0% +1 plus + + + align:start position:0% +1 plus +F where Delta 51 is just equal to Omega + + align:start position:0% +F where Delta 51 is just equal to Omega + + + align:start position:0% +F where Delta 51 is just equal to Omega +T1 + + align:start position:0% +T1 + + + align:start position:0% +T1 +okay all right so now I have these two + + align:start position:0% +okay all right so now I have these two + + + align:start position:0% +okay all right so now I have these two +waveforms and I add them right so now + + align:start position:0% +waveforms and I add them right so now + + + align:start position:0% +waveforms and I add them right so now +I'm going to get VX is simply equal + + align:start position:0% +I'm going to get VX is simply equal + + + align:start position:0% +I'm going to get VX is simply equal +to uh the + + align:start position:0% +to uh the + + + align:start position:0% +to uh the +summation of VN times s of n + + align:start position:0% +summation of VN times s of n + + + align:start position:0% +summation of VN times s of n +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +T1 I'm sorry n Omega t + 5 5 n plus sin + + align:start position:0% +T1 I'm sorry n Omega t + 5 5 n plus sin + + + align:start position:0% +T1 I'm sorry n Omega t + 5 5 n plus sin +n Omega t + f n plus Delta plus n Delta + + align:start position:0% +n Omega t + f n plus Delta plus n Delta + + + align:start position:0% +n Omega t + f n plus Delta plus n Delta +51 okay all right well what + + align:start position:0% +51 okay all right well what + + + align:start position:0% +51 okay all right well what +happens if I + + align:start position:0% +happens if I + + + align:start position:0% +happens if I +make the difference between the phase + + align:start position:0% +make the difference between the phase + + + align:start position:0% +make the difference between the phase +difference between this waveform and + + align:start position:0% +difference between this waveform and + + + align:start position:0% +difference between this waveform and +this waveform is + + align:start position:0% +this waveform is + + + align:start position:0% +this waveform is +precisely n + + align:start position:0% +precisely n + + + align:start position:0% +precisely n +delta1 right at each harmonic I've got a + + align:start position:0% +delta1 right at each harmonic I've got a + + + align:start position:0% +delta1 right at each harmonic I've got a +phase shift + + align:start position:0% +phase shift + + + align:start position:0% +phase shift +that's the nth harmonic is a phase shift + + align:start position:0% +that's the nth harmonic is a phase shift + + + align:start position:0% +that's the nth harmonic is a phase shift +that's n * Delta 51 well what happens + + align:start position:0% +that's n * Delta 51 well what happens + + + align:start position:0% +that's n * Delta 51 well what happens +when n delta1 is pi or 180 degrees + + align:start position:0% +when n delta1 is pi or 180 degrees + + + align:start position:0% +when n delta1 is pi or 180 degrees +what's going to + + align:start position:0% + + + + align:start position:0% + +happen this is going to be 180 degrees + + align:start position:0% +happen this is going to be 180 degrees + + + align:start position:0% +happen this is going to be 180 degrees +out of this + + align:start position:0% +out of this + + + align:start position:0% +out of this +and they're going to cancel all right so + + align:start position:0% +and they're going to cancel all right so + + + align:start position:0% +and they're going to cancel all right so +if I'm clever if I go build two + + align:start position:0% +if I'm clever if I go build two + + + align:start position:0% +if I'm clever if I go build two +waveforms that are shifted In + + align:start position:0% +waveforms that are shifted In + + + align:start position:0% +waveforms that are shifted In +Time by just the right IM magic amount + + align:start position:0% +Time by just the right IM magic amount + + + align:start position:0% +Time by just the right IM magic amount +such that when I add them they're 180 + + align:start position:0% +such that when I add them they're 180 + + + align:start position:0% +such that when I add them they're 180 +degrees of the harmonic that I care + + align:start position:0% +degrees of the harmonic that I care + + + align:start position:0% +degrees of the harmonic that I care +about is 180 degrees out of phase it's + + align:start position:0% +about is 180 degrees out of phase it's + + + align:start position:0% +about is 180 degrees out of phase it's +going to + + align:start position:0% +going to + + + align:start position:0% +going to +cancel okay this trick is called + + align:start position:0% +cancel okay this trick is called + + + align:start position:0% +cancel okay this trick is called +harmonic cancellation + + align:start position:0% + + + + align:start position:0% + +okay let's go see an example of + + align:start position:0% +okay let's go see an example of + + + align:start position:0% +okay let's go see an example of +this so what I've done is let's pretend + + align:start position:0% +this so what I've done is let's pretend + + + align:start position:0% +this so what I've done is let's pretend +I I've Sy synthesized those two + + align:start position:0% +I I've Sy synthesized those two + + + align:start position:0% +I I've Sy synthesized those two +waveforms okay and suppose the two + + align:start position:0% +waveforms okay and suppose the two + + + align:start position:0% +waveforms okay and suppose the two +waveforms I've synthesized for with each + + align:start position:0% +waveforms I've synthesized for with each + + + align:start position:0% +waveforms I've synthesized for with each +of those bridges each switch is + + align:start position:0% +of those bridges each switch is + + + align:start position:0% +of those bridges each switch is +switching once per cycle so it's got a + + align:start position:0% +switching once per cycle so it's got a + + + align:start position:0% +switching once per cycle so it's got a +Delta of 30 degrees and I do the first + + align:start position:0% +Delta of 30 degrees and I do the first + + + align:start position:0% +Delta of 30 degrees and I do the first +guy and then I do the second guy but I'm + + align:start position:0% +guy and then I do the second guy but I'm + + + align:start position:0% +guy and then I do the second guy but I'm +shifting him by 306 + + align:start position:0% +shifting him by 306 + + + align:start position:0% +shifting him by 306 +I'm offsetting them by + + align:start position:0% +I'm offsetting them by + + + align:start position:0% +I'm offsetting them by +36° what's 5 * + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +180 so then when I shift them then I add + + align:start position:0% +180 so then when I shift them then I add + + + align:start position:0% +180 so then when I shift them then I add +them + + align:start position:0% +them + + + align:start position:0% +them +right the bottom waveform you see the + + align:start position:0% +right the bottom waveform you see the + + + align:start position:0% +right the bottom waveform you see the +result here right in this + + align:start position:0% +result here right in this + + + align:start position:0% +result here right in this +waveform actually that kind of looks a + + align:start position:0% +waveform actually that kind of looks a + + + align:start position:0% +waveform actually that kind of looks a +lot more like a sine wave doesn't it + + align:start position:0% +lot more like a sine wave doesn't it + + + align:start position:0% +lot more like a sine wave doesn't it +right that's because I've cancelled the + + align:start position:0% +right that's because I've cancelled the + + + align:start position:0% +right that's because I've cancelled the +fifth harmonic + + align:start position:0% +fifth harmonic + + + align:start position:0% +fifth harmonic +in fact not only have I canel the fifth + + align:start position:0% +in fact not only have I canel the fifth + + + align:start position:0% +in fact not only have I canel the fifth +harmonic I've canceled the 10th although + + align:start position:0% +harmonic I've canceled the 10th although + + + align:start position:0% +harmonic I've canceled the 10th although +we didn't have 10th I've also canceled + + align:start position:0% +we didn't have 10th I've also canceled + + + align:start position:0% +we didn't have 10th I've also canceled +the 15th the 20th the 25th and + + align:start position:0% +the 15th the 20th the 25th and + + + align:start position:0% +the 15th the 20th the 25th and +everything so basically unlike harmonic + + align:start position:0% +everything so basically unlike harmonic + + + align:start position:0% +everything so basically unlike harmonic +elimination where I'm playing this game + + align:start position:0% +elimination where I'm playing this game + + + align:start position:0% +elimination where I'm playing this game +by getting something that has no low + + align:start position:0% +by getting something that has no low + + + align:start position:0% +by getting something that has no low +frequency content but has a bunch of + + align:start position:0% +frequency content but has a bunch of + + + align:start position:0% +frequency content but has a bunch of +high frequency + + align:start position:0% +high frequency + + + align:start position:0% +high frequency +stuff harmonic cancellation cancels out + + align:start position:0% +stuff harmonic cancellation cancels out + + + align:start position:0% +stuff harmonic cancellation cancels out +some waveform you care about plus + + align:start position:0% +some waveform you care about plus + + + align:start position:0% +some waveform you care about plus +multiples of that so it looks a lot more + + align:start position:0% +multiples of that so it looks a lot more + + + align:start position:0% +multiples of that so it looks a lot more +like a sine wave + + align:start position:0% +like a sine wave + + + align:start position:0% +like a sine wave +okay I've now taken each of my devices + + align:start position:0% +okay I've now taken each of my devices + + + align:start position:0% +okay I've now taken each of my devices +I've still only switched them once per + + align:start position:0% +I've still only switched them once per + + + align:start position:0% +I've still only switched them once per +cycle I've just got twice as many + + align:start position:0% +cycle I've just got twice as many + + + align:start position:0% +cycle I've just got twice as many +devices that are sort of half the size + + align:start position:0% +devices that are sort of half the size + + + align:start position:0% +devices that are sort of half the size +to process a given amount of power so + + align:start position:0% +to process a given amount of power so + + + align:start position:0% +to process a given amount of power so +I've sort of paid for this trick with a + + align:start position:0% +I've sort of paid for this trick with a + + + align:start position:0% +I've sort of paid for this trick with a +little bit of + + align:start position:0% +little bit of + + + align:start position:0% +little bit of +complexity okay but I get a waveform out + + align:start position:0% +complexity okay but I get a waveform out + + + align:start position:0% +complexity okay but I get a waveform out +that is very kind of + + align:start position:0% +that is very kind of + + + align:start position:0% +that is very kind of +um much closer to pure and much easier + + align:start position:0% +um much closer to pure and much easier + + + align:start position:0% +um much closer to pure and much easier +to filter to get what you want + + align:start position:0% +to filter to get what you want + + + align:start position:0% +to filter to get what you want +okay any questions about that as a as a + + align:start position:0% +okay any questions about that as a as a + + + align:start position:0% +okay any questions about that as a as a +trick + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +end wir that that change this worry + + align:start position:0% +end wir that that change this worry + + + align:start position:0% +end wir that that change this worry +about yeah I wouldn't worry so much + + align:start position:0% +about yeah I wouldn't worry so much + + + align:start position:0% +about yeah I wouldn't worry so much +about the the wires heating up but but + + align:start position:0% +about the the wires heating up but but + + + align:start position:0% +about the the wires heating up but but +your broader point is a good one um it's + + align:start position:0% +your broader point is a good one um it's + + + align:start position:0% +your broader point is a good one um it's +just as I'm kind of limited by timing + + align:start position:0% +just as I'm kind of limited by timing + + + align:start position:0% +just as I'm kind of limited by timing +angles with this guy how much I face + + align:start position:0% +angles with this guy how much I face + + + align:start position:0% +angles with this guy how much I face +shifted if I don't control that very + + align:start position:0% +shifted if I don't control that very + + + align:start position:0% +shifted if I don't control that very +well if there's delays between the + + align:start position:0% +well if there's delays between the + + + align:start position:0% +well if there's delays between the +circuit you know depending upon how much + + align:start position:0% +circuit you know depending upon how much + + + align:start position:0% +circuit you know depending upon how much +absolute time that is I'm limited + + align:start position:0% +absolute time that is I'm limited + + + align:start position:0% +absolute time that is I'm limited +essentially this harmonic is limited by + + align:start position:0% +essentially this harmonic is limited by + + + align:start position:0% +essentially this harmonic is limited by +how accurately I control that T1 right + + align:start position:0% +how accurately I control that T1 right + + + align:start position:0% +how accurately I control that T1 right +so I want to be very + + align:start position:0% +so I want to be very + + + align:start position:0% +so I want to be very +good about shifting this the right + + align:start position:0% +good about shifting this the right + + + align:start position:0% +good about shifting this the right +amount now I will say that + + align:start position:0% +amount now I will say that + + + align:start position:0% +amount now I will say that +um this kind of trick I do need + + align:start position:0% +um this kind of trick I do need + + + align:start position:0% +um this kind of trick I do need +some better Hardware to do it right I + + align:start position:0% +some better Hardware to do it right I + + + align:start position:0% +some better Hardware to do it right I +can't synthesize this level this level + + align:start position:0% +can't synthesize this level this level + + + align:start position:0% +can't synthesize this level this level +is sometimes called a three-level wave + + align:start position:0% +is sometimes called a three-level wave + + + align:start position:0% +is sometimes called a three-level wave +form you say well there's not three + + align:start position:0% +form you say well there's not three + + + align:start position:0% +form you say well there's not three +levels here but the way they count it is + + align:start position:0% +levels here but the way they count it is + + + align:start position:0% +levels here but the way they count it is +one half of this waveform it's you know + + align:start position:0% +one half of this waveform it's you know + + + align:start position:0% +one half of this waveform it's you know +zero plus VDC over two and plus VDC you + + align:start position:0% +zero plus VDC over two and plus VDC you + + + align:start position:0% +zero plus VDC over two and plus VDC you +know one polar side has three levels so + + align:start position:0% +know one polar side has three levels so + + + align:start position:0% +know one polar side has three levels so +they call that a three-level waveform + + align:start position:0% +they call that a three-level waveform + + + align:start position:0% +they call that a three-level waveform +with a three-level waveform I can cancel + + align:start position:0% +with a three-level waveform I can cancel + + + align:start position:0% +with a three-level waveform I can cancel +I can choose to cancel harmonic right + + align:start position:0% +I can choose to cancel harmonic right + + + align:start position:0% +I can choose to cancel harmonic right +now what we'll see later is sometimes I + + align:start position:0% +now what we'll see later is sometimes I + + + align:start position:0% +now what we'll see later is sometimes I +might choose the third sometimes I might + + align:start position:0% +might choose the third sometimes I might + + + align:start position:0% +might choose the third sometimes I might +choose the fifth it depends on what I'm + + align:start position:0% +choose the fifth it depends on what I'm + + + align:start position:0% +choose the fifth it depends on what I'm +doing and in fact even if you come back + + align:start position:0% +doing and in fact even if you come back + + + align:start position:0% +doing and in fact even if you come back +to this original waveform that I + + align:start position:0% +to this original waveform that I + + + align:start position:0% +to this original waveform that I +drew right + + align:start position:0% +drew right + + + align:start position:0% +drew right +this + + align:start position:0% +this + + + align:start position:0% +this +um this waveform the original white + + align:start position:0% +um this waveform the original white + + + align:start position:0% +um this waveform the original white +waveform that that had those 30° + + align:start position:0% +waveform that that had those 30° + + + align:start position:0% +waveform that that had those 30° +shifts um what I could really view that + + align:start position:0% +shifts um what I could really view that + + + align:start position:0% +shifts um what I could really view that +is one half of this bridge generating a + + align:start position:0% +is one half of this bridge generating a + + + align:start position:0% +is one half of this bridge generating a +square wave + + align:start position:0% +square wave + + + align:start position:0% +square wave +and the other half of the bridge + + align:start position:0% +and the other half of the bridge + + + align:start position:0% +and the other half of the bridge +generating a square wave that's 60° out + + align:start position:0% +generating a square wave that's 60° out + + + align:start position:0% +generating a square wave that's 60° out +of phase at the fundamental and send + + align:start position:0% +of phase at the fundamental and send + + + align:start position:0% +of phase at the fundamental and send +three times at three times the frequency + + align:start position:0% +three times at three times the frequency + + + align:start position:0% +three times at three times the frequency +at the third harmonic or 6th 9th 12th + + align:start position:0% +at the third harmonic or 6th 9th 12th + + + align:start position:0% +at the third harmonic or 6th 9th 12th +Etc it'll be 180 degrees out of phase so + + align:start position:0% +Etc it'll be 180 degrees out of phase so + + + align:start position:0% +Etc it'll be 180 degrees out of phase so +in fact the pulse waveform the once per + + align:start position:0% +in fact the pulse waveform the once per + + + align:start position:0% +in fact the pulse waveform the once per +one pulse per cycle waveform that I + + align:start position:0% +one pulse per cycle waveform that I + + + align:start position:0% +one pulse per cycle waveform that I +showed you you could really view it as a + + align:start position:0% +showed you you could really view it as a + + + align:start position:0% +showed you you could really view it as a +cancellation because I have two half + + align:start position:0% +cancellation because I have two half + + + align:start position:0% +cancellation because I have two half +bridges that are each generating square + + align:start position:0% +bridges that are each generating square + + + align:start position:0% +bridges that are each generating square +waves and I get a harmonic cancellation + + align:start position:0% +waves and I get a harmonic cancellation + + + align:start position:0% +waves and I get a harmonic cancellation +between those square waves killing the + + align:start position:0% +between those square waves killing the + + + align:start position:0% +between those square waves killing the +triple n + + align:start position:0% + + + + align:start position:0% + +harmonics but yes as I go up in + + align:start position:0% +harmonics but yes as I go up in + + + align:start position:0% +harmonics but yes as I go up in +frequency it becomes harder to do and I + + align:start position:0% +frequency it becomes harder to do and I + + + align:start position:0% +frequency it becomes harder to do and I +need fancier circuitry to cancel lots + + align:start position:0% +need fancier circuitry to cancel lots + + + align:start position:0% +need fancier circuitry to cancel lots +and lots of harmonics but sometimes it's + + align:start position:0% +and lots of harmonics but sometimes it's + + + align:start position:0% +and lots of harmonics but sometimes it's +worth it and people as we'll see people + + align:start position:0% +worth it and people as we'll see people + + + align:start position:0% +worth it and people as we'll see people +actually do do quite fancy circuits to + + align:start position:0% +actually do do quite fancy circuits to + + + align:start position:0% +actually do do quite fancy circuits to +help help them do + + align:start position:0% +help help them do + + + align:start position:0% +help help them do +that other + + align:start position:0% +that other + + + align:start position:0% +that other +questions in this example the harmonic + + align:start position:0% +questions in this example the harmonic + + + align:start position:0% +questions in this example the harmonic +is still canell because of the two sh + + align:start position:0% +is still canell because of the two sh + + + align:start position:0% +is still canell because of the two sh +yeah exactly that's the beautiful thing + + align:start position:0% +yeah exactly that's the beautiful thing + + + align:start position:0% +yeah exactly that's the beautiful thing +about + + align:start position:0% +about + + + align:start position:0% +about +this is once I've canceled the + + align:start position:0% +this is once I've canceled the + + + align:start position:0% +this is once I've canceled the +waveform and then I'm I take some + + align:start position:0% +waveform and then I'm I take some + + + align:start position:0% +waveform and then I'm I take some +cancellation then I add it to some other + + align:start position:0% +cancellation then I add it to some other + + + align:start position:0% +cancellation then I add it to some other +waveform I can't introduce new harmonics + + align:start position:0% +waveform I can't introduce new harmonics + + + align:start position:0% +waveform I can't introduce new harmonics +right I'm just taking some existing set + + align:start position:0% +right I'm just taking some existing set + + + align:start position:0% +right I'm just taking some existing set +of Foria coefficients the most that can + + align:start position:0% +of Foria coefficients the most that can + + + align:start position:0% +of Foria coefficients the most that can +happen is they sort of add up and stay + + align:start position:0% +happen is they sort of add up and stay + + + align:start position:0% +happen is they sort of add up and stay +constant right in other words if I take + + align:start position:0% +constant right in other words if I take + + + align:start position:0% +constant right in other words if I take +two half siiz waveforms I add the most + + align:start position:0% +two half siiz waveforms I add the most + + + align:start position:0% +two half siiz waveforms I add the most +I'm going to get is back to the original + + align:start position:0% +I'm going to get is back to the original + + + align:start position:0% +I'm going to get is back to the original +other than that I'm just going to get + + align:start position:0% +other than that I'm just going to get + + + align:start position:0% +other than that I'm just going to get +some degree of cancellation so I don't + + align:start position:0% +some degree of cancellation so I don't + + + align:start position:0% +some degree of cancellation so I don't +introduce new frequencies by doing this + + align:start position:0% +introduce new frequencies by doing this + + + align:start position:0% +introduce new frequencies by doing this +trick I just kill frequencies so yes so + + align:start position:0% +trick I just kill frequencies so yes so + + + align:start position:0% +trick I just kill frequencies so yes so +my original white waveform because it's + + align:start position:0% +my original white waveform because it's + + + align:start position:0% +my original white waveform because it's +sort of harmonic + + align:start position:0% +sort of harmonic + + + align:start position:0% +sort of harmonic +cancellation of the two half Bridges I + + align:start position:0% +cancellation of the two half Bridges I + + + align:start position:0% +cancellation of the two half Bridges I +have no triple n harmonics No 3 6 9 12 + + align:start position:0% +have no triple n harmonics No 3 6 9 12 + + + align:start position:0% +have no triple n harmonics No 3 6 9 12 +15 18 so forth right I I don't have any + + align:start position:0% +15 18 so forth right I I don't have any + + + align:start position:0% +15 18 so forth right I I don't have any +evens because of the halfway + + align:start position:0% +evens because of the halfway + + + align:start position:0% +evens because of the halfway +Symmetry and then if I do this + + align:start position:0% +Symmetry and then if I do this + + + align:start position:0% +Symmetry and then if I do this +trick I kill off all the 5n harmonics + + align:start position:0% +trick I kill off all the 5n harmonics + + + align:start position:0% +trick I kill off all the 5n harmonics +and you can keep that game up if I had a + + align:start position:0% +and you can keep that game up if I had a + + + align:start position:0% +and you can keep that game up if I had a +more complicated circuit I kill even + + align:start position:0% +more complicated circuit I kill even + + + align:start position:0% +more complicated circuit I kill even +more and the waveform just becomes you + + align:start position:0% +more and the waveform just becomes you + + + align:start position:0% +more and the waveform just becomes you +know starts to become very small Steppy + + align:start position:0% +know starts to become very small Steppy + + + align:start position:0% +know starts to become very small Steppy +close to a sine wave and you get very + + align:start position:0% +close to a sine wave and you get very + + + align:start position:0% +close to a sine wave and you get very +beautiful + + align:start position:0% + + + + align:start position:0% + +waveforms yeah does a six Dee um + + align:start position:0% +waveforms yeah does a six Dee um + + + align:start position:0% +waveforms yeah does a six Dee um +displacement matter does the wit CU it's + + align:start position:0% +displacement matter does the wit CU it's + + + align:start position:0% +displacement matter does the wit CU it's +it's a sideway but it's displaced by 6 + + align:start position:0% +it's a sideway but it's displaced by 6 + + + align:start position:0% +it's a sideway but it's displaced by 6 +so it's a way + + align:start position:0% +so it's a way + + + align:start position:0% +so it's a way +uh oh yeah okay so actually if you look + + align:start position:0% +uh oh yeah okay so actually if you look + + + align:start position:0% +uh oh yeah okay so actually if you look +in the lecture notes instead of + + align:start position:0% +in the lecture notes instead of + + + align:start position:0% +in the lecture notes instead of +displacing it by 36 Dees I displace one + + align:start position:0% +displacing it by 36 Dees I displace one + + + align:start position:0% +displacing it by 36 Dees I displace one +by + 18 and 1 by minus 18 and you get + + align:start position:0% +by + 18 and 1 by minus 18 and you get + + + align:start position:0% +by + 18 and 1 by minus 18 and you get +the same cancellation and then it stays + + align:start position:0% +the same cancellation and then it stays + + + align:start position:0% +the same cancellation and then it stays +odd yeah so you yeah I I don't have to + + align:start position:0% +odd yeah so you yeah I I don't have to + + + align:start position:0% +odd yeah so you yeah I I don't have to +have zero plus a delayed I can have + + align:start position:0% +have zero plus a delayed I can have + + + align:start position:0% +have zero plus a delayed I can have +minus half the delay and plus half the + + align:start position:0% +minus half the delay and plus half the + + + align:start position:0% +minus half the delay and plus half the +delay and it still stays stays as an odd + + align:start position:0% +delay and it still stays stays as an odd + + + align:start position:0% +delay and it still stays stays as an odd +waveform excellent question sir do you + + align:start position:0% +waveform excellent question sir do you + + + align:start position:0% +waveform excellent question sir do you +also use this trick to uh just like + + align:start position:0% +also use this trick to uh just like + + + align:start position:0% +also use this trick to uh just like +increase the AC output voltage you could + + align:start position:0% +increase the AC output voltage you could + + + align:start position:0% +increase the AC output voltage you could +yeah so so yeah what would be what would + + align:start position:0% +yeah so so yeah what would be what would + + + align:start position:0% +yeah so so yeah what would be what would +be another benefit of this um right the + + align:start position:0% +be another benefit of this um right the + + + align:start position:0% +be another benefit of this um right the +the VX has twice the amplitude of vdci + + align:start position:0% +the VX has twice the amplitude of vdci + + + align:start position:0% +the VX has twice the amplitude of vdci +could synthesize another way and that's + + align:start position:0% +could synthesize another way and that's + + + align:start position:0% +could synthesize another way and that's +just for this + + align:start position:0% +just for this + + + align:start position:0% +just for this +particular implementation which is only + + align:start position:0% +particular implementation which is only + + + align:start position:0% +particular implementation which is only +one way to do it we will see next class + + align:start position:0% +one way to do it we will see next class + + + align:start position:0% +one way to do it we will see next class +other circuits that their benefit is + + align:start position:0% +other circuits that their benefit is + + + align:start position:0% +other circuits that their benefit is +they you for a given input voltage they + + align:start position:0% +they you for a given input voltage they + + + align:start position:0% +they you for a given input voltage they +use lower voltage switches to get the + + align:start position:0% +use lower voltage switches to get the + + + align:start position:0% +use lower voltage switches to get the +same same output so there's a lot of + + align:start position:0% +same same output so there's a lot of + + + align:start position:0% +same same output so there's a lot of +ways you can you know take a advantage + + align:start position:0% +ways you can you know take a advantage + + + align:start position:0% +ways you can you know take a advantage +of the complexity you inherit the + + align:start position:0% +of the complexity you inherit the + + + align:start position:0% +of the complexity you inherit the +downside to this one is principally that + + align:start position:0% +downside to this one is principally that + + + align:start position:0% +downside to this one is principally that +I have Transformers that rated for the + + align:start position:0% +I have Transformers that rated for the + + + align:start position:0% +I have Transformers that rated for the +output that are rated for the frequency + + align:start position:0% +output that are rated for the frequency + + + align:start position:0% +output that are rated for the frequency +I'm + + align:start position:0% +I'm + + + align:start position:0% +I'm +outputting you know in some cases I + + align:start position:0% +outputting you know in some cases I + + + align:start position:0% +outputting you know in some cases I +might not like that and but there's + + align:start position:0% +might not like that and but there's + + + align:start position:0% +might not like that and but there's +other circuits that get around + + align:start position:0% +other circuits that get around + + + align:start position:0% +other circuits that get around +that let me point out that this notion + + align:start position:0% +that let me point out that this notion + + + align:start position:0% +that let me point out that this notion +this cancellation + + align:start position:0% +this cancellation + + + align:start position:0% +this cancellation +notion is a very widespread one it gets + + align:start position:0% +notion is a very widespread one it gets + + + align:start position:0% +notion is a very widespread one it gets +used in a lot of kinds of circuits let + + align:start position:0% +used in a lot of kinds of circuits let + + + align:start position:0% +used in a lot of kinds of circuits let +me show you another one that maybe + + align:start position:0% +me show you another one that maybe + + + align:start position:0% +me show you another one that maybe +um + + align:start position:0% +um + + + align:start position:0% +um +is completely different application + + align:start position:0% +is completely different application + + + align:start position:0% +is completely different application +space but + + align:start position:0% +space but + + + align:start position:0% +space but +suppose I had a um suppose I had a buck + + align:start position:0% + + + + align:start position:0% + +converter okay that looked like + + align:start position:0% +converter okay that looked like + + + align:start position:0% +converter okay that looked like +this + + align:start position:0% + + + + align:start position:0% + +okay and here's my output + + align:start position:0% +okay and here's my output + + + align:start position:0% +okay and here's my output +capacitor okay and here's my load and + + align:start position:0% +capacitor okay and here's my load and + + + align:start position:0% +capacitor okay and here's my load and +maybe output capacitor is a micro + + align:start position:0% +maybe output capacitor is a micro + + + align:start position:0% +maybe output capacitor is a micro +processor so maybe this is the 12 volts + + align:start position:0% +processor so maybe this is the 12 volts + + + align:start position:0% +processor so maybe this is the 12 volts +input and I'm delivering voltage to my + + align:start position:0% +input and I'm delivering voltage to my + + + align:start position:0% +input and I'm delivering voltage to my +microprocessor right this + + align:start position:0% +microprocessor right this + + + align:start position:0% +microprocessor right this +current here is a triangle wave right so + + align:start position:0% +current here is a triangle wave right so + + + align:start position:0% +current here is a triangle wave right so +maybe this current looks something like + + align:start position:0% +maybe this current looks something like + + + align:start position:0% +maybe this current looks something like +this it's it's uh got some DC value and + + align:start position:0% +this it's it's uh got some DC value and + + + align:start position:0% +this it's it's uh got some DC value and +it's + + align:start position:0% +it's + + + align:start position:0% +it's +got some Ripple + + align:start position:0% + + + + align:start position:0% + +okay at the switching + + align:start position:0% + + + + align:start position:0% + +frequency maybe if I came in with a + + align:start position:0% +frequency maybe if I came in with a + + + align:start position:0% +frequency maybe if I came in with a +second unit all right and I will build + + align:start position:0% +second unit all right and I will build + + + align:start position:0% +second unit all right and I will build +another parallel guy + + align:start position:0% +another parallel guy + + + align:start position:0% +another parallel guy +here and I will switch + + align:start position:0% + + + + align:start position:0% + +him with some phase shift and he'll have + + align:start position:0% +him with some phase shift and he'll have + + + align:start position:0% +him with some phase shift and he'll have +an output current and maybe I make this + + align:start position:0% +an output current and maybe I make this + + + align:start position:0% +an output current and maybe I make this +output current you know here's T + + align:start position:0% +output current you know here's T + + + align:start position:0% +output current you know here's T +over2 okay + + align:start position:0% +over2 okay + + + align:start position:0% +over2 okay +and here's got to be careful here 3T + + align:start position:0% +and here's got to be careful here 3T + + + align:start position:0% +and here's got to be careful here 3T +over2 here's 2T right maybe I will shift + + align:start position:0% +over2 here's 2T right maybe I will shift + + + align:start position:0% +over2 here's 2T right maybe I will shift +this one so that he starts half a cycle + + align:start position:0% +this one so that he starts half a cycle + + + align:start position:0% +this one so that he starts half a cycle +later like + + align:start position:0% + + + + align:start position:0% + +this okay what total current goes into + + align:start position:0% +this okay what total current goes into + + + align:start position:0% +this okay what total current goes into +the output in capacitor well it's the + + align:start position:0% +the output in capacitor well it's the + + + align:start position:0% +the output in capacitor well it's the +sum of this one and this + + align:start position:0% +sum of this one and this + + + align:start position:0% +sum of this one and this +one but if I basically make orange and + + align:start position:0% +one but if I basically make orange and + + + align:start position:0% +one but if I basically make orange and +pink + + align:start position:0% +pink + + + align:start position:0% +pink +shifted by 180 degrees of the + + align:start position:0% +shifted by 180 degrees of the + + + align:start position:0% +shifted by 180 degrees of the +fundamental that means the fundamental + + align:start position:0% +fundamental that means the fundamental + + + align:start position:0% +fundamental that means the fundamental +Ripple will + + align:start position:0% +Ripple will + + + align:start position:0% +Ripple will +cancel if there's second harmonic + + align:start position:0% +cancel if there's second harmonic + + + align:start position:0% +cancel if there's second harmonic +component in the pink + + align:start position:0% +component in the pink + + + align:start position:0% +component in the pink +waveform the second harmonic of the + + align:start position:0% +waveform the second harmonic of the + + + align:start position:0% +waveform the second harmonic of the +orange waveform will be shifted by 360 + + align:start position:0% +orange waveform will be shifted by 360 + + + align:start position:0% +orange waveform will be shifted by 360 +degrees at the second harmonic so the + + align:start position:0% +degrees at the second harmonic so the + + + align:start position:0% +degrees at the second harmonic so the +fundamentals will cancel the second + + align:start position:0% +fundamentals will cancel the second + + + align:start position:0% +fundamentals will cancel the second +harmonics will reinforce and the net + + align:start position:0% +harmonics will reinforce and the net + + + align:start position:0% +harmonics will reinforce and the net +Ripple I'm not even going to try to draw + + align:start position:0% +Ripple I'm not even going to try to draw + + + align:start position:0% +Ripple I'm not even going to try to draw +it here but it would basically be have a + + align:start position:0% +it here but it would basically be have a + + + align:start position:0% +it here but it would basically be have a +fundamental that was at twice the + + align:start position:0% +fundamental that was at twice the + + + align:start position:0% +fundamental that was at twice the +switching + + align:start position:0% +switching + + + align:start position:0% +switching +frequency right so I get something + + align:start position:0% +frequency right so I get something + + + align:start position:0% +frequency right so I get something +that's both smaller amplitude and you + + align:start position:0% +that's both smaller amplitude and you + + + align:start position:0% +that's both smaller amplitude and you +can show that the amplitude will be at + + align:start position:0% +can show that the amplitude will be at + + + align:start position:0% +can show that the amplitude will be at +most + + align:start position:0% +most + + + align:start position:0% +most +half and twice the frequency which makes + + align:start position:0% +half and twice the frequency which makes + + + align:start position:0% +half and twice the frequency which makes +it four times as easy for that capacitor + + align:start position:0% +it four times as easy for that capacitor + + + align:start position:0% +it four times as easy for that capacitor +to filter it all right so this same kind + + align:start position:0% +to filter it all right so this same kind + + + align:start position:0% +to filter it all right so this same kind +of trick of harmonic cancellation here + + align:start position:0% +of trick of harmonic cancellation here + + + align:start position:0% +of trick of harmonic cancellation here +I'm canceling the fundamentals CU what I + + align:start position:0% +I'm canceling the fundamentals CU what I + + + align:start position:0% +I'm canceling the fundamentals CU what I +would like is a DC output current this + + align:start position:0% +would like is a DC output current this + + + align:start position:0% +would like is a DC output current this +technique is called + + align:start position:0% + + + + align:start position:0% + +interleaving it's very widely used and + + align:start position:0% +interleaving it's very widely used and + + + align:start position:0% +interleaving it's very widely used and +in fact most motherboards if you look at + + align:start position:0% +in fact most motherboards if you look at + + + align:start position:0% +in fact most motherboards if you look at +them they don't have a buck converter or + + align:start position:0% +them they don't have a buck converter or + + + align:start position:0% +them they don't have a buck converter or +something driving the load they'll have + + align:start position:0% +something driving the load they'll have + + + align:start position:0% +something driving the load they'll have +a whole bunch of buck converters lined + + align:start position:0% +a whole bunch of buck converters lined + + + align:start position:0% +a whole bunch of buck converters lined +up and they phase shift them all just + + align:start position:0% +up and they phase shift them all just + + + align:start position:0% +up and they phase shift them all just +such that the first n harmonics will go + + align:start position:0% +such that the first n harmonics will go + + + align:start position:0% +such that the first n harmonics will go +away and the Ripple frequency much + + align:start position:0% +away and the Ripple frequency much + + + align:start position:0% +away and the Ripple frequency much +higher than the switching frequency of + + align:start position:0% +higher than the switching frequency of + + + align:start position:0% +higher than the switching frequency of +the individual converters that also + + align:start position:0% +the individual converters that also + + + align:start position:0% +the individual converters that also +means that you can play with response + + align:start position:0% +means that you can play with response + + + align:start position:0% +means that you can play with response +speeds of that because one will react + + align:start position:0% +speeds of that because one will react + + + align:start position:0% +speeds of that because one will react +you know sort of much quicker than if + + align:start position:0% +you know sort of much quicker than if + + + align:start position:0% +you know sort of much quicker than if +they were all in Phase if I put these + + align:start position:0% +they were all in Phase if I put these + + + align:start position:0% +they were all in Phase if I put these +two converters in Phase all I would get + + align:start position:0% +two converters in Phase all I would get + + + align:start position:0% +two converters in Phase all I would get +is twice the Ripple current at the + + align:start position:0% +is twice the Ripple current at the + + + align:start position:0% +is twice the Ripple current at the +fundamental instead I get at most half + + align:start position:0% +fundamental instead I get at most half + + + align:start position:0% +fundamental instead I get at most half +at twice the frequency right and I can + + align:start position:0% +at twice the frequency right and I can + + + align:start position:0% +at twice the frequency right and I can +play that game out to n different + + align:start position:0% +play that game out to n different + + + align:start position:0% +play that game out to n different +converters inter + + align:start position:0% + + + + align:start position:0% + +Leed so this trick of harmonic + + align:start position:0% +Leed so this trick of harmonic + + + align:start position:0% +Leed so this trick of harmonic +cancellation is really neat it's widely + + align:start position:0% +cancellation is really neat it's widely + + + align:start position:0% +cancellation is really neat it's widely +used it's used in DCd conver + + align:start position:0% +used it's used in DCd conver + + + align:start position:0% +used it's used in DCd conver +it's also used to kill off unwanted + + align:start position:0% +it's also used to kill off unwanted + + + align:start position:0% +it's also used to kill off unwanted +harmonics and inverters harmonic + + align:start position:0% +harmonics and inverters harmonic + + + align:start position:0% +harmonics and inverters harmonic +elimination is also used there's nothing + + align:start position:0% +elimination is also used there's nothing + + + align:start position:0% +elimination is also used there's nothing +that says you couldn't do the two of + + align:start position:0% +that says you couldn't do the two of + + + align:start position:0% +that says you couldn't do the two of +those together you sort of saw that + + align:start position:0% +those together you sort of saw that + + + align:start position:0% +those together you sort of saw that +right instead of using that just once + + align:start position:0% +right instead of using that just once + + + align:start position:0% +right instead of using that just once +pulse per half cycle I could use some + + align:start position:0% +pulse per half cycle I could use some + + + align:start position:0% +pulse per half cycle I could use some +pulses per half cycle to get eliminate + + align:start position:0% +pulses per half cycle to get eliminate + + + align:start position:0% +pulses per half cycle to get eliminate +some harmonics use some phase shift + + align:start position:0% +some harmonics use some phase shift + + + align:start position:0% +some harmonics use some phase shift +eliminate some more and I can intermix + + align:start position:0% +eliminate some more and I can intermix + + + align:start position:0% +eliminate some more and I can intermix +those two and they get very nicely + + align:start position:0% +those two and they get very nicely + + + align:start position:0% +those two and they get very nicely +easily filtered + + align:start position:0% +easily filtered + + + align:start position:0% +easily filtered +waveforms any questions about that + + align:start position:0% +waveforms any questions about that + + + align:start position:0% +waveforms any questions about that +okay just to demonstrate all + + align:start position:0% +okay just to demonstrate all + + + align:start position:0% +okay just to demonstrate all +this Rafa has been kind enough to set up + + align:start position:0% +this Rafa has been kind enough to set up + + + align:start position:0% +this Rafa has been kind enough to set up +a demo so I'll let her show you some + + align:start position:0% +a demo so I'll let her show you some + + + align:start position:0% +a demo so I'll let her show you some +actual experimental waveforms from an + + align:start position:0% +actual experimental waveforms from an + + + align:start position:0% +actual experimental waveforms from an +inverter that was built by a student who + + align:start position:0% +inverter that was built by a student who + + + align:start position:0% +inverter that was built by a student who +took this + + align:start position:0% +took this + + + align:start position:0% +took this +class okay so what are we looking at am + + align:start position:0% +class okay so what are we looking at am + + + align:start position:0% +class okay so what are we looking at am +I too loud sorry what are we looking at + + align:start position:0% +I too loud sorry what are we looking at + + + align:start position:0% +I too loud sorry what are we looking at +at the top + + align:start position:0% +at the top + + + align:start position:0% +at the top +is guess what what inverter is it so I + + align:start position:0% +is guess what what inverter is it so I + + + align:start position:0% +is guess what what inverter is it so I +have an inverter board that has four + + align:start position:0% +have an inverter board that has four + + + align:start position:0% +have an inverter board that has four +switches and we're probing at the output + + align:start position:0% +switches and we're probing at the output + + + align:start position:0% +switches and we're probing at the output +voltage so we had a DC input voltage of + + align:start position:0% +voltage so we had a DC input voltage of + + + align:start position:0% +voltage so we had a DC input voltage of +15 volt and then we're switching it and + + align:start position:0% +15 volt and then we're switching it and + + + align:start position:0% +15 volt and then we're switching it and +as you can see as we saw in class it + + align:start position:0% +as you can see as we saw in class it + + + align:start position:0% +as you can see as we saw in class it +uses the three levels zero positive + + align:start position:0% +uses the three levels zero positive + + + align:start position:0% +uses the three levels zero positive +negative to create something that + + align:start position:0% +negative to create something that + + + align:start position:0% +negative to create something that +somehow resembles a + + align:start position:0% +somehow resembles a + + + align:start position:0% +somehow resembles a +sinusoid and as you can see it has + + align:start position:0% +sinusoid and as you can see it has + + + align:start position:0% +sinusoid and as you can see it has +halfway symmetry so we do not have any + + align:start position:0% +halfway symmetry so we do not have any + + + align:start position:0% +halfway symmetry so we do not have any +a2k B2K or the even harmonics so we only + + align:start position:0% +a2k B2K or the even harmonics so we only + + + align:start position:0% +a2k B2K or the even harmonics so we only +have to worry about the harmonics now + + align:start position:0% +have to worry about the harmonics now + + + align:start position:0% +have to worry about the harmonics now +let's at at the bottom down here we are + + align:start position:0% +let's at at the bottom down here we are + + + align:start position:0% +let's at at the bottom down here we are +looking at the fft of the voltage Weare + + align:start position:0% +looking at the fft of the voltage Weare + + + align:start position:0% +looking at the fft of the voltage Weare +form so the voltage + + align:start position:0% +form so the voltage + + + align:start position:0% +form so the voltage +magnitudes at different + + align:start position:0% +magnitudes at different + + + align:start position:0% +magnitudes at different +harmonics now if I move my + + align:start position:0% +harmonics now if I move my + + + align:start position:0% +harmonics now if I move my +cursor at the first Spike where it + + align:start position:0% +cursor at the first Spike where it + + + align:start position:0% +cursor at the first Spike where it +happens it's really hard to see but you + + align:start position:0% +happens it's really hard to see but you + + + align:start position:0% +happens it's really hard to see but you +can see on the top right that it's + + align:start position:0% +can see on the top right that it's + + + align:start position:0% +can see on the top right that it's +happening at 600 HZ which means that's + + align:start position:0% +happening at 600 HZ which means that's + + + align:start position:0% +happening at 600 HZ which means that's +our switching frequency see and it's the + + align:start position:0% +our switching frequency see and it's the + + + align:start position:0% +our switching frequency see and it's the +fundamental and then let's see where the + + align:start position:0% +fundamental and then let's see where the + + + align:start position:0% +fundamental and then let's see where the +next Spike + + align:start position:0% + + + + align:start position:0% + +happens the second highest Spike happens + + align:start position:0% +happens the second highest Spike happens + + + align:start position:0% +happens the second highest Spike happens +at 2.9 kges which is very close to the + + align:start position:0% +at 2.9 kges which is very close to the + + + align:start position:0% +at 2.9 kges which is very close to the +fifth harmonic what does that mean that + + align:start position:0% +fifth harmonic what does that mean that + + + align:start position:0% +fifth harmonic what does that mean that +means we do not have any third harmonic + + align:start position:0% +means we do not have any third harmonic + + + align:start position:0% +means we do not have any third harmonic +so we eliminated the third harmonic from + + align:start position:0% +so we eliminated the third harmonic from + + + align:start position:0% +so we eliminated the third harmonic from +the circuit now let's do another thing + + align:start position:0% +the circuit now let's do another thing + + + align:start position:0% +the circuit now let's do another thing +it's going crazy but let's see okay now + + align:start position:0% +it's going crazy but let's see okay now + + + align:start position:0% +it's going crazy but let's see okay now +like we saw in the class if we introduce + + align:start position:0% +like we saw in the class if we introduce + + + align:start position:0% +like we saw in the class if we introduce +puls or notches on both sides of the + + align:start position:0% +puls or notches on both sides of the + + + align:start position:0% +puls or notches on both sides of the +webform it still half a symmetric so + + align:start position:0% +webform it still half a symmetric so + + + align:start position:0% +webform it still half a symmetric so +we're still doing the same thing but + + align:start position:0% +we're still doing the same thing but + + + align:start position:0% +we're still doing the same thing but +interestingly if we move to the second + + align:start position:0% +interestingly if we move to the second + + + align:start position:0% +interestingly if we move to the second +High Spike it's almost about 4.2 Kil + + align:start position:0% +High Spike it's almost about 4.2 Kil + + + align:start position:0% +High Spike it's almost about 4.2 Kil +which is the seventh harmonic so we + + align:start position:0% +which is the seventh harmonic so we + + + align:start position:0% +which is the seventh harmonic so we +erase we eliminated third and F harmonic + + align:start position:0% +erase we eliminated third and F harmonic + + + align:start position:0% +erase we eliminated third and F harmonic +now we can take this a step + + align:start position:0% +now we can take this a step + + + align:start position:0% +now we can take this a step +further let me run it and stop it + + align:start position:0% +further let me run it and stop it + + + align:start position:0% +further let me run it and stop it +okay yes so now if we move all the way + + align:start position:0% +okay yes so now if we move all the way + + + align:start position:0% +okay yes so now if we move all the way +back that will be the second Spike + + align:start position:0% +back that will be the second Spike + + + align:start position:0% +back that will be the second Spike +occurs at 5.3 khz which is like the nine + + align:start position:0% +occurs at 5.3 khz which is like the nine + + + align:start position:0% +occurs at 5.3 khz which is like the nine +therm monics so we eliminated all the + + align:start position:0% +therm monics so we eliminated all the + + + align:start position:0% +therm monics so we eliminated all the +lower third fifth seventh harmonics you + + align:start position:0% +lower third fifth seventh harmonics you + + + align:start position:0% +lower third fifth seventh harmonics you +will notice that they're getting a bit + + align:start position:0% +will notice that they're getting a bit + + + align:start position:0% +will notice that they're getting a bit +so the high higher harmonics are getting + + align:start position:0% +so the high higher harmonics are getting + + + align:start position:0% +so the high higher harmonics are getting +higher in magnitude but that's okay + + align:start position:0% +higher in magnitude but that's okay + + + align:start position:0% +higher in magnitude but that's okay +because we care about the lower + + align:start position:0% +because we care about the lower + + + align:start position:0% +because we care about the lower +harmonics more cuz um it's easier to get + + align:start position:0% +harmonics more cuz um it's easier to get + + + align:start position:0% +harmonics more cuz um it's easier to get +rid of the higher harmonics we'll need + + align:start position:0% +rid of the higher harmonics we'll need + + + align:start position:0% +rid of the higher harmonics we'll need +smaller filter components or smaller + + align:start position:0% +smaller filter components or smaller + + + align:start position:0% +smaller filter components or smaller +devices for applications that's + + align:start position:0% + + + + align:start position:0% + +all thanks so I guess what we've seen + + align:start position:0% +all thanks so I guess what we've seen + + + align:start position:0% +all thanks so I guess what we've seen +today is harmonic elimination where we + + align:start position:0% +today is harmonic elimination where we + + + align:start position:0% +today is harmonic elimination where we +introduce extra pulses carefully timed + + align:start position:0% +introduce extra pulses carefully timed + + + align:start position:0% +introduce extra pulses carefully timed +we''ve also seen harmonic cancellation + + align:start position:0% +we''ve also seen harmonic cancellation + + + align:start position:0% +we''ve also seen harmonic cancellation +where we take multiple waveforms and + + align:start position:0% +where we take multiple waveforms and + + + align:start position:0% +where we take multiple waveforms and +shift them and add them up to kind of + + align:start position:0% +shift them and add them up to kind of + + + align:start position:0% +shift them and add them up to kind of +murder the harmonics we don't like um + + align:start position:0% +murder the harmonics we don't like um + + + align:start position:0% +murder the harmonics we don't like um +those can be both used together what + + align:start position:0% +those can be both used together what + + + align:start position:0% +those can be both used together what +we'll start seeing next time is firstly + + align:start position:0% +we'll start seeing next time is firstly + + + align:start position:0% +we'll start seeing next time is firstly +well other ways we can do this kind of + + align:start position:0% +well other ways we can do this kind of + + + align:start position:0% +well other ways we can do this kind of +harmonic cancellation or harmonic + + align:start position:0% +harmonic cancellation or harmonic + + + align:start position:0% +harmonic cancellation or harmonic +elimination game more sophisticated + + align:start position:0% +elimination game more sophisticated + + + align:start position:0% +elimination game more sophisticated +circuits and after that we'll start + + align:start position:0% +circuits and after that we'll start + + + align:start position:0% +circuits and after that we'll start +talking about what happens if you know + + align:start position:0% +talking about what happens if you know + + + align:start position:0% +talking about what happens if you know +we've kind of posited this on the whole + + align:start position:0% +we've kind of posited this on the whole + + + align:start position:0% +we've kind of posited this on the whole +thing I want to make is a sine wave + + align:start position:0% +thing I want to make is a sine wave + + + align:start position:0% +thing I want to make is a sine wave +which is often true if I'm going to run + + align:start position:0% +which is often true if I'm going to run + + + align:start position:0% +which is often true if I'm going to run +a lot of what kind of Motors I want a + + align:start position:0% +a lot of what kind of Motors I want a + + + align:start position:0% +a lot of what kind of Motors I want a +sine wave if I'm trying to generate um + + align:start position:0% +sine wave if I'm trying to generate um + + + align:start position:0% +sine wave if I'm trying to generate um +you know something for the AC grid which + + align:start position:0% +you know something for the AC grid which + + + align:start position:0% +you know something for the AC grid which +is supposed to be sign soidal I want a + + align:start position:0% +is supposed to be sign soidal I want a + + + align:start position:0% +is supposed to be sign soidal I want a +sine wave but there's times we don't + + align:start position:0% +sine wave but there's times we don't + + + align:start position:0% +sine wave but there's times we don't +want to sine wave so what do we do in + + align:start position:0% +want to sine wave so what do we do in + + + align:start position:0% +want to sine wave so what do we do in +those cases and we'll we'll pick those + + align:start position:0% +those cases and we'll we'll pick those + + + align:start position:0% +those cases and we'll we'll pick those +topics up next class so have a great day \ No newline at end of file diff --git a/HxOA8HrVzPg.txt b/HxOA8HrVzPg.txt new file mode 100644 index 0000000000000000000000000000000000000000..b8c12857d6be939c7c393629cfcc1ea272446fdc --- /dev/null +++ b/HxOA8HrVzPg.txt @@ -0,0 +1,11315 @@ +align:start position:0% + +so I'm back um I guess by uh by your + + align:start position:0% +so I'm back um I guess by uh by your + + + align:start position:0% +so I'm back um I guess by uh by your +presence here you've shown that for you + + align:start position:0% +presence here you've shown that for you + + + align:start position:0% +presence here you've shown that for you +people dp1 is well under control and + + align:start position:0% +people dp1 is well under control and + + + align:start position:0% +people dp1 is well under control and +that's + + align:start position:0% +that's + + + align:start position:0% +that's +great okay so uh today's the last + + align:start position:0% +great okay so uh today's the last + + + align:start position:0% +great okay so uh today's the last +lecture on this topic on the networking + + align:start position:0% +lecture on this topic on the networking + + + align:start position:0% +lecture on this topic on the networking +uh piece of 6033 and the topic for today + + align:start position:0% +uh piece of 6033 and the topic for today + + + align:start position:0% +uh piece of 6033 and the topic for today +is something called congestion control + + align:start position:0% +is something called congestion control + + + align:start position:0% +is something called congestion control +and + + align:start position:0% +and + + + align:start position:0% +and +um what we're going to do is spend most + + align:start position:0% +um what we're going to do is spend most + + + align:start position:0% +um what we're going to do is spend most +of today talking about congestion + + align:start position:0% +of today talking about congestion + + + align:start position:0% +of today talking about congestion +control but let me um remind you of + + align:start position:0% +control but let me um remind you of + + + align:start position:0% +control but let me um remind you of +where we are in networking and so if + + align:start position:0% +where we are in networking and so if + + + align:start position:0% +where we are in networking and so if +there's one thing you take away from + + align:start position:0% +there's one thing you take away from + + + align:start position:0% +there's one thing you take away from +6033 from this networking piece you + + align:start position:0% +6033 from this networking piece you + + + align:start position:0% +6033 from this networking piece you +should remember this + + align:start position:0% +should remember this + + + align:start position:0% +should remember this +picture + + align:start position:0% +picture + + + align:start position:0% +picture +um so the way we're dealing with um + + align:start position:0% +um so the way we're dealing with um + + + align:start position:0% +um so the way we're dealing with um +networking uh and the way we always deal + + align:start position:0% +networking uh and the way we always deal + + + align:start position:0% +networking uh and the way we always deal +with networking in any complicated + + align:start position:0% +with networking in any complicated + + + align:start position:0% +with networking in any complicated +system is to layer um Network protocols + + align:start position:0% +system is to layer um Network protocols + + + align:start position:0% +system is to layer um Network protocols +and the particular layering model that + + align:start position:0% +and the particular layering model that + + + align:start position:0% +and the particular layering model that +we picked for 6033 is a subset of what + + align:start position:0% +we picked for 6033 is a subset of what + + + align:start position:0% +we picked for 6033 is a subset of what +you would see out in the real world and + + align:start position:0% +you would see out in the real world and + + + align:start position:0% +you would see out in the real world and +it's mostly accurate and the lowest + + align:start position:0% +it's mostly accurate and the lowest + + + align:start position:0% +it's mostly accurate and the lowest +layer is something called the link layer + + align:start position:0% +layer is something called the link layer + + + align:start position:0% +layer is something called the link layer +which deals with transmitting packets on + + align:start position:0% +which deals with transmitting packets on + + + align:start position:0% +which deals with transmitting packets on +a link and above that + + align:start position:0% +a link and above that + + + align:start position:0% +a link and above that +you have the network layer and the + + align:start position:0% +you have the network layer and the + + + align:start position:0% +you have the network layer and the +particular kind of network layer that + + align:start position:0% +particular kind of network layer that + + + align:start position:0% +particular kind of network layer that +we're talking about um is a very popular + + align:start position:0% +we're talking about um is a very popular + + + align:start position:0% +we're talking about um is a very popular +one which provides a kind of service + + align:start position:0% +one which provides a kind of service + + + align:start position:0% +one which provides a kind of service +called a best effort service and the + + align:start position:0% +called a best effort service and the + + + align:start position:0% +called a best effort service and the +easiest way to understand best effort + + align:start position:0% +easiest way to understand best effort + + + align:start position:0% +easiest way to understand best effort +service is it just tries to get packets + + align:start position:0% +service is it just tries to get packets + + + align:start position:0% +service is it just tries to get packets +through from one end to another but it + + align:start position:0% +through from one end to another but it + + + align:start position:0% +through from one end to another but it +doesn't get all panicked if it can't get + + align:start position:0% +doesn't get all panicked if it can't get + + + align:start position:0% +doesn't get all panicked if it can't get +package through it just lets higher + + align:start position:0% +package through it just lets higher + + + align:start position:0% +package through it just lets higher +layer um called the end to end + + align:start position:0% +layer um called the end to end + + + align:start position:0% +layer um called the end to end +layer deal with any U problems such as + + align:start position:0% +layer deal with any U problems such as + + + align:start position:0% +layer deal with any U problems such as +lost packets or missing packets + + align:start position:0% +lost packets or missing packets + + + align:start position:0% +lost packets or missing packets +corrupted packets reordered packets and + + align:start position:0% +corrupted packets reordered packets and + + + align:start position:0% +corrupted packets reordered packets and +so + + align:start position:0% +so + + + align:start position:0% +so +on and last time um when Sam um gave the + + align:start position:0% +on and last time um when Sam um gave the + + + align:start position:0% +on and last time um when Sam um gave the +lecture he talked about a few things + + align:start position:0% +lecture he talked about a few things + + + align:start position:0% +lecture he talked about a few things +that the end to end layer does and in + + align:start position:0% +that the end to end layer does and in + + + align:start position:0% +that the end to end layer does and in +particular we talked about how the end + + align:start position:0% +particular we talked about how the end + + + align:start position:0% +particular we talked about how the end +to end layer + + align:start position:0% +to end layer + + + align:start position:0% +to end layer +achieves reliability using + + align:start position:0% +achieves reliability using + + + align:start position:0% +achieves reliability using +acknowledgements so the receiver + + align:start position:0% +acknowledgements so the receiver + + + align:start position:0% +acknowledgements so the receiver +acknowledges packets that it receives + + align:start position:0% +acknowledges packets that it receives + + + align:start position:0% +acknowledges packets that it receives +from the sender and the sender uh if it + + align:start position:0% +from the sender and the sender uh if it + + + align:start position:0% +from the sender and the sender uh if it +misses an acknowledgement goes ahead and + + align:start position:0% +misses an acknowledgement goes ahead and + + + align:start position:0% +misses an acknowledgement goes ahead and +retransmits the packet and in order to + + align:start position:0% +retransmits the packet and in order to + + + align:start position:0% +retransmits the packet and in order to +do that we spend some time talking about + + align:start position:0% +do that we spend some time talking about + + + align:start position:0% +do that we spend some time talking about +timers um because you have to not try to + + align:start position:0% +timers um because you have to not try to + + + align:start position:0% +timers um because you have to not try to +retransmit immediately you have to wait + + align:start position:0% +retransmit immediately you have to wait + + + align:start position:0% +retransmit immediately you have to wait +some time until you're pretty assured + + align:start position:0% +some time until you're pretty assured + + + align:start position:0% +some time until you're pretty assured +that the packet's actually last before + + align:start position:0% +that the packet's actually last before + + + align:start position:0% +that the packet's actually last before +you go ahead and try to retransmit the + + align:start position:0% + + + + align:start position:0% + +packet the next concept at the end to + + align:start position:0% +packet the next concept at the end to + + + align:start position:0% +packet the next concept at the end to +end layer that we talked about is + + align:start position:0% +end layer that we talked about is + + + align:start position:0% +end layer that we talked about is +something called a sliding + + align:start position:0% + + + + align:start position:0% + +window where the idea was that if I send + + align:start position:0% +window where the idea was that if I send + + + align:start position:0% +window where the idea was that if I send +you a packet got an acknowledgement back + + align:start position:0% +you a packet got an acknowledgement back + + + align:start position:0% +you a packet got an acknowledgement back +and then sent you the next packet and + + align:start position:0% +and then sent you the next packet and + + + align:start position:0% +and then sent you the next packet and +did that it things are really slow uh + + align:start position:0% +did that it things are really slow uh + + + align:start position:0% +did that it things are really slow uh +and all that a sliding window is really + + align:start position:0% +and all that a sliding window is really + + + align:start position:0% +and all that a sliding window is really +is an idea that you've already seen from + + align:start position:0% +is an idea that you've already seen from + + + align:start position:0% +is an idea that you've already seen from +um an earlier chapter and probably from4 + + align:start position:0% +um an earlier chapter and probably from4 + + + align:start position:0% +um an earlier chapter and probably from4 +called pipelining which is to have + + align:start position:0% +called pipelining which is to have + + + align:start position:0% +called pipelining which is to have +multiple outstanding things um in the + + align:start position:0% +multiple outstanding things um in the + + + align:start position:0% +multiple outstanding things um in the +pipe or in the network uh at once as a + + align:start position:0% +pipe or in the network uh at once as a + + + align:start position:0% +pipe or in the network uh at once as a +way to get higher + + align:start position:0% +way to get higher + + + align:start position:0% +way to get higher +performance and the last thing that we + + align:start position:0% +performance and the last thing that we + + + align:start position:0% +performance and the last thing that we +talked about the last + + align:start position:0% +talked about the last + + + align:start position:0% +talked about the last +time was flow control and the idea here + + align:start position:0% +time was flow control and the idea here + + + align:start position:0% +time was flow control and the idea here +is to make sure that the sender doesn't + + align:start position:0% +is to make sure that the sender doesn't + + + align:start position:0% +is to make sure that the sender doesn't +send too fast because if it sent really + + align:start position:0% +send too fast because if it sent really + + + align:start position:0% +send too fast because if it sent really +fast it would swamp the receiver which + + align:start position:0% +fast it would swamp the receiver which + + + align:start position:0% +fast it would swamp the receiver which +is you know which might be slow trying + + align:start position:0% +is you know which might be slow trying + + + align:start position:0% +is you know which might be slow trying +to keep up processing um the sender + + align:start position:0% +to keep up processing um the sender + + + align:start position:0% +to keep up processing um the sender +packet so you don't want to swamp the + + align:start position:0% +packet so you don't want to swamp the + + + align:start position:0% +packet so you don't want to swamp the +receiver's buffer and we talked about + + align:start position:0% +receiver's buffer and we talked about + + + align:start position:0% +receiver's buffer and we talked about +how U with every acknowledgement the + + align:start position:0% +how U with every acknowledgement the + + + align:start position:0% +how U with every acknowledgement the +receiver can piggyback some information + + align:start position:0% +receiver can piggyback some information + + + align:start position:0% +receiver can piggyback some information +about how much space it has remaining in + + align:start position:0% +about how much space it has remaining in + + + align:start position:0% +about how much space it has remaining in +its buffer and if that clamped down to + + align:start position:0% +its buffer and if that clamped down to + + + align:start position:0% +its buffer and if that clamped down to +zero then the center would automatically + + align:start position:0% +zero then the center would automatically + + + align:start position:0% +zero then the center would automatically +slow down um sort of you would produce + + align:start position:0% +slow down um sort of you would produce + + + align:start position:0% +slow down um sort of you would produce +what's also known as back pressure back + + align:start position:0% +what's also known as back pressure back + + + align:start position:0% +what's also known as back pressure back +to the sender saying I don't have any + + align:start position:0% +to the sender saying I don't have any + + + align:start position:0% +to the sender saying I don't have any +more space slow down and the sender + + align:start position:0% +more space slow down and the sender + + + align:start position:0% +more space slow down and the sender +guarantees that it won't send more + + align:start position:0% +guarantees that it won't send more + + + align:start position:0% +guarantees that it won't send more +packets um at any given time more data + + align:start position:0% +packets um at any given time more data + + + align:start position:0% +packets um at any given time more data +at any given time than what the receiver + + align:start position:0% +at any given time than what the receiver + + + align:start position:0% +at any given time than what the receiver +says it can handle in its + + align:start position:0% +says it can handle in its + + + align:start position:0% +says it can handle in its +buffle so that was the plan and that + + align:start position:0% +buffle so that was the plan and that + + + align:start position:0% +buffle so that was the plan and that +those are the things we talked about so + + align:start position:0% +those are the things we talked about so + + + align:start position:0% +those are the things we talked about so +far for the end to end layer and what + + align:start position:0% +far for the end to end layer and what + + + align:start position:0% +far for the end to end layer and what +we're going to do today is go back to + + align:start position:0% +we're going to do today is go back to + + + align:start position:0% +we're going to do today is go back to +one of the main things about networks + + align:start position:0% +one of the main things about networks + + + align:start position:0% +one of the main things about networks +that was mentioned during the first + + align:start position:0% +that was mentioned during the first + + + align:start position:0% +that was mentioned during the first +networking lecture uh and talk about how + + align:start position:0% +networking lecture uh and talk about how + + + align:start position:0% +networking lecture uh and talk about how +we achiev that which is + + align:start position:0% + + + + align:start position:0% + +sharing ultimately it's extremely cost + + align:start position:0% +sharing ultimately it's extremely cost + + + align:start position:0% +sharing ultimately it's extremely cost +and effective extremely inefficient to + + align:start position:0% +and effective extremely inefficient to + + + align:start position:0% +and effective extremely inefficient to +build networks where every computer is + + align:start position:0% +build networks where every computer is + + + align:start position:0% +build networks where every computer is +connected to every other computer in the + + align:start position:0% +connected to every other computer in the + + + align:start position:0% +connected to every other computer in the +world by a dedicated link or a dedicated + + align:start position:0% +world by a dedicated link or a dedicated + + + align:start position:0% +world by a dedicated link or a dedicated +path of its own fundamentally networks + + align:start position:0% +path of its own fundamentally networks + + + align:start position:0% +path of its own fundamentally networks +are efficient only if they allow + + align:start position:0% +are efficient only if they allow + + + align:start position:0% +are efficient only if they allow +computers connected to each other to + + align:start position:0% +computers connected to each other to + + + align:start position:0% +computers connected to each other to +share paths underneath and the moment + + align:start position:0% +share paths underneath and the moment + + + align:start position:0% +share paths underneath and the moment +you have that um the moment you have U + + align:start position:0% +you have that um the moment you have U + + + align:start position:0% +you have that um the moment you have U +sharing of links you have to worry about + + align:start position:0% +sharing of links you have to worry about + + + align:start position:0% +sharing of links you have to worry about +um sharing the resources namely sharing + + align:start position:0% +um sharing the resources namely sharing + + + align:start position:0% +um sharing the resources namely sharing +the bandwidth of a + + align:start position:0% +the bandwidth of a + + + align:start position:0% +the bandwidth of a +link and that's what we're going to do + + align:start position:0% +link and that's what we're going to do + + + align:start position:0% +link and that's what we're going to do +today and we're going to do do this um + + align:start position:0% +today and we're going to do do this um + + + align:start position:0% +today and we're going to do do this um +basically the the goal for today is to + + align:start position:0% +basically the the goal for today is to + + + align:start position:0% +basically the the goal for today is to +talk about the problems that arise if + + align:start position:0% +talk about the problems that arise if + + + align:start position:0% +talk about the problems that arise if +you don't do sharing properly and then + + align:start position:0% +you don't do sharing properly and then + + + align:start position:0% +you don't do sharing properly and then +spend some time talking about how we + + align:start position:0% +spend some time talking about how we + + + align:start position:0% +spend some time talking about how we +solve these + + align:start position:0% + + + + align:start position:0% + +problems so imagine you have a a a + + align:start position:0% +problems so imagine you have a a a + + + align:start position:0% +problems so imagine you have a a a +network um and I'm going to start with a + + align:start position:0% +network um and I'm going to start with a + + + align:start position:0% +network um and I'm going to start with a +simple example and we're going to use + + align:start position:0% +simple example and we're going to use + + + align:start position:0% +simple example and we're going to use +that example right through because it'll + + align:start position:0% +that example right through because it'll + + + align:start position:0% +that example right through because it'll +turn out that this simple example will + + align:start position:0% +turn out that this simple example will + + + align:start position:0% +turn out that this simple example will +illustrate the essential um problem with + + align:start position:0% +illustrate the essential um problem with + + + align:start position:0% +illustrate the essential um problem with +with sharing so imagine you have a bunch + + align:start position:0% +with sharing so imagine you have a bunch + + + align:start position:0% +with sharing so imagine you have a bunch +of computers + + align:start position:0% +of computers + + + align:start position:0% +of computers +connected at one end of the network and + + align:start position:0% +connected at one end of the network and + + + align:start position:0% +connected at one end of the network and +you know at the other end you have other + + align:start position:0% +you know at the other end you have other + + + align:start position:0% +you know at the other end you have other +computers and imagine that these are + + align:start position:0% +computers and imagine that these are + + + align:start position:0% +computers and imagine that these are +senders and these are receivers and they + + align:start position:0% +senders and these are receivers and they + + + align:start position:0% +senders and these are receivers and they +share the network and you know a really + + align:start position:0% +share the network and you know a really + + + align:start position:0% +share the network and you know a really +simple form of sharing this network + + align:start position:0% +simple form of sharing this network + + + align:start position:0% +simple form of sharing this network +might be when you have all of these + + align:start position:0% +might be when you have all of these + + + align:start position:0% +might be when you have all of these +computers take their links like their + + align:start position:0% +computers take their links like their + + + align:start position:0% +computers take their links like their +ethernet connections and hook them up to + + align:start position:0% +ethernet connections and hook them up to + + + align:start position:0% +ethernet connections and hook them up to +a switch um and maybe you hook it up to + + align:start position:0% +a switch um and maybe you hook it up to + + + align:start position:0% +a switch um and maybe you hook it up to +another switch and then there's other + + align:start position:0% +another switch and then there's other + + + align:start position:0% +another switch and then there's other +pads that eventually take you to um you + + align:start position:0% +pads that eventually take you to um you + + + align:start position:0% +pads that eventually take you to um you +know the receivers that you want to talk + + align:start position:0% +know the receivers that you want to talk + + + align:start position:0% +know the receivers that you want to talk +to and imagine just for example that + + align:start position:0% +to and imagine just for example that + + + align:start position:0% +to and imagine just for example that +these are thick + + align:start position:0% +these are thick + + + align:start position:0% +these are thick +links so for example these might be 100 + + align:start position:0% +links so for example these might be 100 + + + align:start position:0% +links so for example these might be 100 +megabit per second links and then you go + + align:start position:0% +megabit per second links and then you go + + + align:start position:0% +megabit per second links and then you go +out through this you know through your + + align:start position:0% +out through this you know through your + + + align:start position:0% +out through this you know through your +Dom room and then you have something + + align:start position:0% +Dom room and then you have something + + + align:start position:0% +Dom room and then you have something +connected connecting your wherever you + + align:start position:0% +connected connecting your wherever you + + + align:start position:0% +connected connecting your wherever you +live and that might be you know um let's + + align:start position:0% +live and that might be you know um let's + + + align:start position:0% +live and that might be you know um let's +say it's a it's a megabit per second + + align:start position:0% +say it's a it's a megabit per second + + + align:start position:0% +say it's a it's a megabit per second +link so this might be one megabit per + + align:start position:0% +link so this might be one megabit per + + + align:start position:0% +link so this might be one megabit per +second and these things are 100 megabits + + align:start position:0% +second and these things are 100 megabits + + + align:start position:0% +second and these things are 100 megabits +per + + align:start position:0% + + + + align:start position:0% + +second and of course you can could have + + align:start position:0% +second and of course you can could have + + + align:start position:0% +second and of course you can could have +receivers connected with extremely fat + + align:start position:0% +receivers connected with extremely fat + + + align:start position:0% +receivers connected with extremely fat +links as well um which means that if the + + align:start position:0% +links as well um which means that if the + + + align:start position:0% +links as well um which means that if the +sender and the receiver just looked at + + align:start position:0% +sender and the receiver just looked at + + + align:start position:0% +sender and the receiver just looked at +their own access links these 100 megabit + + align:start position:0% +their own access links these 100 megabit + + + align:start position:0% +their own access links these 100 megabit +per second links and just said thought + + align:start position:0% +per second links and just said thought + + + align:start position:0% +per second links and just said thought +to themselves well I have 100 megabit + + align:start position:0% +to themselves well I have 100 megabit + + + align:start position:0% +to themselves well I have 100 megabit +per second link the sender has 100 + + align:start position:0% +per second link the sender has 100 + + + align:start position:0% +per second link the sender has 100 +megabit per second link so clearly we + + align:start position:0% +megabit per second link so clearly we + + + align:start position:0% +megabit per second link so clearly we +could exchange data at 100 megabits per + + align:start position:0% +could exchange data at 100 megabits per + + + align:start position:0% +could exchange data at 100 megabits per +second um that would be flawed because + + align:start position:0% +second um that would be flawed because + + + align:start position:0% +second um that would be flawed because +all of these things go through this + + align:start position:0% +all of these things go through this + + + align:start position:0% +all of these things go through this +relatively thin pipe of a megabit per + + align:start position:0% +relatively thin pipe of a megabit per + + + align:start position:0% +relatively thin pipe of a megabit per +second so really the goal here is to + + align:start position:0% +second so really the goal here is to + + + align:start position:0% +second so really the goal here is to +take all of these connections all of + + align:start position:0% +take all of these connections all of + + + align:start position:0% +take all of these connections all of +these end to-end transfers that might be + + align:start position:0% +these end to-end transfers that might be + + + align:start position:0% +these end to-end transfers that might be +happening at any given point in time and + + align:start position:0% +happening at any given point in time and + + + align:start position:0% +happening at any given point in time and +share every Link in the network um + + align:start position:0% +share every Link in the network um + + + align:start position:0% +share every Link in the network um +properly and I'll I'll Define what we + + align:start position:0% +properly and I'll I'll Define what we + + + align:start position:0% +properly and I'll I'll Define what we +mean by properly um as we go + + align:start position:0% +mean by properly um as we go + + + align:start position:0% +mean by properly um as we go +along so let's write some notation first + + align:start position:0% +along so let's write some notation first + + + align:start position:0% +along so let's write some notation first +because it'll help us um pose the + + align:start position:0% +because it'll help us um pose the + + + align:start position:0% +because it'll help us um pose the +problem clearly so let's say that + + align:start position:0% +problem clearly so let's say that + + + align:start position:0% +problem clearly so let's say that +there's some offered load that these + + align:start position:0% +there's some offered load that these + + + align:start position:0% +there's some offered load that these +different senders offer to the network + + align:start position:0% +different senders offer to the network + + + align:start position:0% +different senders offer to the network +so you know You' decided to download a + + align:start position:0% +so you know You' decided to download a + + + align:start position:0% +so you know You' decided to download a +bunch of files music files and web pages + + align:start position:0% +bunch of files music files and web pages + + + align:start position:0% +bunch of files music files and web pages +and each of those has you know a certain + + align:start position:0% +and each of those has you know a certain + + + align:start position:0% +and each of those has you know a certain +load that you know it's a certain size + + align:start position:0% +load that you know it's a certain size + + + align:start position:0% +load that you know it's a certain size +of a file and you can the sender can + + align:start position:0% +of a file and you can the sender can + + + align:start position:0% +of a file and you can the sender can +actually push that data through at some + + align:start position:0% +actually push that data through at some + + + align:start position:0% +actually push that data through at some +rate so that's the offered load on the + + align:start position:0% +rate so that's the offered load on the + + + align:start position:0% +rate so that's the offered load on the +network and let's assume that you have + + align:start position:0% +network and let's assume that you have + + + align:start position:0% +network and let's assume that you have +senders you know one through n here and + + align:start position:0% +senders you know one through n here and + + + align:start position:0% +senders you know one through n here and +let's say that the offered load of this + + align:start position:0% +let's say that the offered load of this + + + align:start position:0% +let's say that the offered load of this +sender is L1 this is L2 all the way + + align:start position:0% +sender is L1 this is L2 all the way + + + align:start position:0% +sender is L1 this is L2 all the way +through + + align:start position:0% +through + + + align:start position:0% +through +Ln okay so in this simple picture the + + align:start position:0% +Ln okay so in this simple picture the + + + align:start position:0% +Ln okay so in this simple picture the +total offered load um on the network + + align:start position:0% +total offered load um on the network + + + align:start position:0% +total offered load um on the network +along this path is the summation of Lis + + align:start position:0% +along this path is the summation of Lis + + + align:start position:0% +along this path is the summation of Lis +where I runs from one to n + + align:start position:0% + + + + align:start position:0% + +right and out here in the simple picture + + align:start position:0% +right and out here in the simple picture + + + align:start position:0% +right and out here in the simple picture +we have all of this offered load being + + align:start position:0% +we have all of this offered load being + + + align:start position:0% +we have all of this offered load being +going through this one common link which + + align:start position:0% +going through this one common link which + + + align:start position:0% +going through this one common link which +uh we're going to call the bottleneck + + align:start position:0% +uh we're going to call the bottleneck + + + align:start position:0% +uh we're going to call the bottleneck +link we don't actually know where it the + + align:start position:0% +link we don't actually know where it the + + + align:start position:0% +link we don't actually know where it the +centers don't know where the bottleneck + + align:start position:0% +centers don't know where the bottleneck + + + align:start position:0% +centers don't know where the bottleneck +is because it's not near them and and + + align:start position:0% +is because it's not near them and and + + + align:start position:0% +is because it's not near them and and +you know in general it's not near them + + align:start position:0% +you know in general it's not near them + + + align:start position:0% +you know in general it's not near them +it could be but in general they don't + + align:start position:0% +it could be but in general they don't + + + align:start position:0% +it could be but in general they don't +know where it is the receivers don't + + align:start position:0% +know where it is the receivers don't + + + align:start position:0% +know where it is the receivers don't +know where it is but there is some + + align:start position:0% +know where it is but there is some + + + align:start position:0% +know where it is but there is some +bottleneck link that's going to throttle + + align:start position:0% +bottleneck link that's going to throttle + + + align:start position:0% +bottleneck link that's going to throttle +the maximum rate at which you could send + + align:start position:0% +the maximum rate at which you could send + + + align:start position:0% +the maximum rate at which you could send +data and let's call that rate C + + align:start position:0% +data and let's call that rate C + + + align:start position:0% +data and let's call that rate C +so what we would like to be able to do + + align:start position:0% +so what we would like to be able to do + + + align:start position:0% +so what we would like to be able to do +is ensure at all points in time that the + + align:start position:0% +is ensure at all points in time that the + + + align:start position:0% +is ensure at all points in time that the +sum of the load that's being offered by + + align:start position:0% +sum of the load that's being offered by + + + align:start position:0% +sum of the load that's being offered by +um all senders that share any given link + + align:start position:0% +um all senders that share any given link + + + align:start position:0% +um all senders that share any given link +is less than the capacity of that link + + align:start position:0% +is less than the capacity of that link + + + align:start position:0% +is less than the capacity of that link +and so see here um in this picture this + + align:start position:0% +and so see here um in this picture this + + + align:start position:0% +and so see here um in this picture this +would be C and notice that we don't + + align:start position:0% +would be C and notice that we don't + + + align:start position:0% +would be C and notice that we don't +actually know where these things are and + + align:start position:0% +actually know where these things are and + + + align:start position:0% +actually know where these things are and +for different connections if you're + + align:start position:0% +for different connections if you're + + + align:start position:0% +for different connections if you're +surfing the web and downloading music + + align:start position:0% +surfing the web and downloading music + + + align:start position:0% +surfing the web and downloading music +and so on um the the actual bottleneck + + align:start position:0% +and so on um the the actual bottleneck + + + align:start position:0% +and so on um the the actual bottleneck +for each of those transfers might in + + align:start position:0% +for each of those transfers might in + + + align:start position:0% +for each of those transfers might in +general be + + align:start position:0% +general be + + + align:start position:0% +general be +different but the general goal for + + align:start position:0% +different but the general goal for + + + align:start position:0% +different but the general goal for +gestion control is you look at any path + + align:start position:0% +gestion control is you look at any path + + + align:start position:0% +gestion control is you look at any path +any path between a sender and receiver + + align:start position:0% +any path between a sender and receiver + + + align:start position:0% +any path between a sender and receiver +and there's some in general some + + align:start position:0% +and there's some in general some + + + align:start position:0% +and there's some in general some +bottleneck there and you have to ensure + + align:start position:0% +bottleneck there and you have to ensure + + + align:start position:0% +bottleneck there and you have to ensure +that for every bottleneck link um in + + align:start position:0% +that for every bottleneck link um in + + + align:start position:0% +that for every bottleneck link um in +fact for every link the total offered + + align:start position:0% +fact for every link the total offered + + + align:start position:0% +fact for every link the total offered +load presented to that link satisfies + + align:start position:0% +load presented to that link satisfies + + + align:start position:0% +load presented to that link satisfies +this + + align:start position:0% +this + + + align:start position:0% +this +relationship okay so that's the ultimate + + align:start position:0% +relationship okay so that's the ultimate + + + align:start position:0% +relationship okay so that's the ultimate +goal and it'll turn out we're not going + + align:start position:0% +goal and it'll turn out we're not going + + + align:start position:0% +goal and it'll turn out we're not going +to be able to perfectly solve this but + + align:start position:0% +to be able to perfectly solve this but + + + align:start position:0% +to be able to perfectly solve this but +we're going to come pretty + + align:start position:0% +we're going to come pretty + + + align:start position:0% +we're going to come pretty +close + + align:start position:0% + + + + align:start position:0% + +Okay so that's the statement of the + + align:start position:0% +Okay so that's the statement of the + + + align:start position:0% +Okay so that's the statement of the +problem + + align:start position:0% + + + + align:start position:0% + +that you want + + align:start position:0% + + + + align:start position:0% + +this this is not a trivial + + align:start position:0% +this this is not a trivial + + + align:start position:0% +this this is not a trivial +problem so one reason it's not trivial + + align:start position:0% +problem so one reason it's not trivial + + + align:start position:0% +problem so one reason it's not trivial +is something that might have been clear + + align:start position:0% +is something that might have been clear + + + align:start position:0% +is something that might have been clear +to you from the definition of the + + align:start position:0% +to you from the definition of the + + + align:start position:0% +to you from the definition of the +problem you want to assure this for all + + align:start position:0% +problem you want to assure this for all + + + align:start position:0% +problem you want to assure this for all +of the links in the network and a + + align:start position:0% +of the links in the network and a + + + align:start position:0% +of the links in the network and a +network in general might have or will + + align:start position:0% +network in general might have or will + + + align:start position:0% +network in general might have or will +have millions of links and hundreds of + + align:start position:0% +have millions of links and hundreds of + + + align:start position:0% +have millions of links and hundreds of +millions of + + align:start position:0% +millions of + + + align:start position:0% +millions of +hosts so any solution you come up with + + align:start position:0% +hosts so any solution you come up with + + + align:start position:0% +hosts so any solution you come up with +has to be scalable + + align:start position:0% + + + + align:start position:0% + +and in particular has to scale to really + + align:start position:0% +and in particular has to scale to really + + + align:start position:0% +and in particular has to scale to really +large networks um networks that um you + + align:start position:0% +large networks um networks that um you + + + align:start position:0% +large networks um networks that um you +know as big as the public internet and + + align:start position:0% +know as big as the public internet and + + + align:start position:0% +know as big as the public internet and +you know um or the public internet 10 + + align:start position:0% +you know um or the public internet 10 + + + align:start position:0% +you know um or the public internet 10 +years from now so it has to be something + + align:start position:0% +years from now so it has to be something + + + align:start position:0% +years from now so it has to be something +that scales um it has to handle large + + align:start position:0% +that scales um it has to handle large + + + align:start position:0% +that scales um it has to handle large +values so it has to handle large + + align:start position:0% + + + + align:start position:0% + +networks has to handle large values of + + align:start position:0% +networks has to handle large values of + + + align:start position:0% +networks has to handle large values of +n where you know the number of end to + + align:start position:0% +n where you know the number of end to + + + align:start position:0% +n where you know the number of end to +end connections that are transferring + + align:start position:0% +end connections that are transferring + + + align:start position:0% +end connections that are transferring +data on this network and it's an unknown + + align:start position:0% +data on this network and it's an unknown + + + align:start position:0% +data on this network and it's an unknown +value of n you don't really know what n + + align:start position:0% +value of n you don't really know what n + + + align:start position:0% +value of n you don't really know what n +is at any given point in time and it + + align:start position:0% +is at any given point in time and it + + + align:start position:0% +is at any given point in time and it +could be extremely large so you have to + + align:start position:0% +could be extremely large so you have to + + + align:start position:0% +could be extremely large so you have to +handle + + align:start position:0% +handle + + + align:start position:0% +handle +that and above all and this is actually + + align:start position:0% +that and above all and this is actually + + + align:start position:0% +that and above all and this is actually +the most important point and it's often + + align:start position:0% +the most important point and it's often + + + align:start position:0% +the most important point and it's often +missed by um you know by by a lot of + + align:start position:0% +missed by um you know by by a lot of + + + align:start position:0% +missed by um you know by by a lot of +descriptions of congestion control and + + align:start position:0% +descriptions of congestion control and + + + align:start position:0% +descriptions of congestion control and +sharing a good solution has to scale + + align:start position:0% +sharing a good solution has to scale + + + align:start position:0% +sharing a good solution has to scale +across many orders of magnitude of Link + + align:start position:0% +across many orders of magnitude of Link + + + align:start position:0% +across many orders of magnitude of Link +properties you know on the Internet or + + align:start position:0% +properties you know on the Internet or + + + align:start position:0% +properties you know on the Internet or +in any decent packet switch Network link + + align:start position:0% +in any decent packet switch Network link + + + align:start position:0% +in any decent packet switch Network link +rates vary by you know perhaps eight or + + align:start position:0% +rates vary by you know perhaps eight or + + + align:start position:0% +rates vary by you know perhaps eight or +seven or eight or nine orders of + + align:start position:0% +seven or eight or nine orders of + + + align:start position:0% +seven or eight or nine orders of +magnitude you know single Network could + + align:start position:0% +magnitude you know single Network could + + + align:start position:0% +magnitude you know single Network could +have links that send data at you know 5 + + align:start position:0% +have links that send data at you know 5 + + + align:start position:0% +have links that send data at you know 5 +or 10 kilobits per second on one extreme + + align:start position:0% +or 10 kilobits per second on one extreme + + + align:start position:0% +or 10 kilobits per second on one extreme +and 10 gbits per second or 40 gbits per + + align:start position:0% +and 10 gbits per second or 40 gbits per + + + align:start position:0% +and 10 gbits per second or 40 gbits per +second on the Other Extreme and a single + + align:start position:0% +second on the Other Extreme and a single + + + align:start position:0% +second on the Other Extreme and a single +path might actually have um might go + + align:start position:0% +path might actually have um might go + + + align:start position:0% +path might actually have um might go +through links that whose capacities vary + + align:start position:0% +through links that whose capacities vary + + + align:start position:0% +through links that whose capacities vary +by many orders of magnitude and it's + + align:start position:0% +by many orders of magnitude and it's + + + align:start position:0% +by many orders of magnitude and it's +extremely important that a solution work + + align:start position:0% +extremely important that a solution work + + + align:start position:0% +extremely important that a solution work +across this range because otherwise its + + align:start position:0% +across this range because otherwise its + + + align:start position:0% +across this range because otherwise its +generality is is not it isn't that + + align:start position:0% +generality is is not it isn't that + + + align:start position:0% +generality is is not it isn't that +General and and what you'd like is a + + align:start position:0% +General and and what you'd like is a + + + align:start position:0% +General and and what you'd like is a +very general + + align:start position:0% + + + + align:start position:0% + +solution the second reason this problem + + align:start position:0% +solution the second reason this problem + + + align:start position:0% +solution the second reason this problem +is hard is that out here we have this n + + align:start position:0% +is hard is that out here we have this n + + + align:start position:0% +is hard is that out here we have this n +but really N is a function of time you + + align:start position:0% +but really N is a function of time you + + + align:start position:0% +but really N is a function of time you +you're surfing the web you click on a + + align:start position:0% +you're surfing the web you click on a + + + align:start position:0% +you're surfing the web you click on a +link and all of a sudden 18 embedded + + align:start position:0% +link and all of a sudden 18 embedded + + + align:start position:0% +link and all of a sudden 18 embedded +objects come through in general each of + + align:start position:0% +objects come through in general each of + + + align:start position:0% +objects come through in general each of +those is a different connection um and + + align:start position:0% +those is a different connection um and + + + align:start position:0% +those is a different connection um and +then it's gone and the next time + + align:start position:0% +then it's gone and the next time + + + align:start position:0% +then it's gone and the next time +somebody else clicks on something + + align:start position:0% +somebody else clicks on something + + + align:start position:0% +somebody else clicks on something +there's a bunch more objects so n varies + + align:start position:0% +there's a bunch more objects so n varies + + + align:start position:0% +there's a bunch more objects so n varies +with time + + align:start position:0% + + + + align:start position:0% + +and as a consequence um the offered load + + align:start position:0% +and as a consequence um the offered load + + + align:start position:0% +and as a consequence um the offered load +on the system both the total offered + + align:start position:0% +on the system both the total offered + + + align:start position:0% +on the system both the total offered +load as well as the load offered by a + + align:start position:0% +load as well as the load offered by a + + + align:start position:0% +load as well as the load offered by a +single connection um uh varies with time + + align:start position:0% +single connection um uh varies with time + + + align:start position:0% +single connection um uh varies with time +so Li varies with time as + + align:start position:0% + + + + align:start position:0% + +well so it's kind of really hard to + + align:start position:0% +well so it's kind of really hard to + + + align:start position:0% +well so it's kind of really hard to +understand what the steady state + + align:start position:0% +understand what the steady state + + + align:start position:0% +understand what the steady state +behavior of a large Network like the + + align:start position:0% +behavior of a large Network like the + + + align:start position:0% +behavior of a large Network like the +internet is because there is no steady + + align:start position:0% +internet is because there is no steady + + + align:start position:0% +internet is because there is no steady +state + + align:start position:0% + + + + align:start position:0% + +Behavior and the final reason and the + + align:start position:0% +Behavior and the final reason and the + + + align:start position:0% +Behavior and the final reason and the +third reason why this problem is hard + + align:start position:0% +third reason why this problem is hard + + + align:start position:0% +third reason why this problem is hard +is the thing that we're going to come + + align:start position:0% +is the thing that we're going to come + + + align:start position:0% +is the thing that we're going to come +back to in when we talk about a solution + + align:start position:0% +back to in when we talk about a solution + + + align:start position:0% +back to in when we talk about a solution +is that if you think about this + + align:start position:0% + + + + align:start position:0% + +problem the person who can control the + + align:start position:0% +problem the person who can control the + + + align:start position:0% +problem the person who can control the +rate at which data is being sent is the + + align:start position:0% +rate at which data is being sent is the + + + align:start position:0% +rate at which data is being sent is the +sender right and maybe the receiver can + + align:start position:0% +sender right and maybe the receiver can + + + align:start position:0% +sender right and maybe the receiver can +help it control it by advertising these + + align:start position:0% +help it control it by advertising these + + + align:start position:0% +help it control it by advertising these +flow control windows so the control + + align:start position:0% +flow control windows so the control + + + align:start position:0% +flow control windows so the control +happens at these points but if you think + + align:start position:0% +happens at these points but if you think + + + align:start position:0% +happens at these points but if you think +about it the resource that's being + + align:start position:0% +about it the resource that's being + + + align:start position:0% +about it the resource that's being +shared is somewhere else it's far away + + align:start position:0% +shared is somewhere else it's far away + + + align:start position:0% +shared is somewhere else it's far away +right so there's a delay between the + + align:start position:0% +right so there's a delay between the + + + align:start position:0% +right so there's a delay between the +congestion point or the points where + + align:start position:0% +congestion point or the points where + + + align:start position:0% +congestion point or the points where +overload happens these points in the + + align:start position:0% +overload happens these points in the + + + align:start position:0% +overload happens these points in the +network and where the control can be + + align:start position:0% +network and where the control can be + + + align:start position:0% +network and where the control can be +exercised to control congestion and this + + align:start position:0% +exercised to control congestion and this + + + align:start position:0% +exercised to control congestion and this +is very different this situation is + + align:start position:0% +is very different this situation is + + + align:start position:0% +is very different this situation is +extremely different from most other + + align:start position:0% +extremely different from most other + + + align:start position:0% +extremely different from most other +resource management um schemes for other + + align:start position:0% +resource management um schemes for other + + + align:start position:0% +resource management um schemes for other +computer systems if you talk about + + align:start position:0% +computer systems if you talk about + + + align:start position:0% +computer systems if you talk about +processor Resource Management well + + align:start position:0% +processor Resource Management well + + + align:start position:0% +processor Resource Management well +there's auler that controls what runs on + + align:start position:0% +there's auler that controls what runs on + + + align:start position:0% +there's auler that controls what runs on +the processor and the processor is right + + align:start position:0% +the processor and the processor is right + + + align:start position:0% +the processor and the processor is right +there there's no long delay between the + + align:start position:0% +there there's no long delay between the + + + align:start position:0% +there there's no long delay between the +two so if the operating system decides + + align:start position:0% +two so if the operating system decides + + + align:start position:0% +two so if the operating system decides +to schedule another process well it + + align:start position:0% +to schedule another process well it + + + align:start position:0% +to schedule another process well it +doesn't take a long time before that + + align:start position:0% +doesn't take a long time before that + + + align:start position:0% +doesn't take a long time before that +happens it happens pretty quickly and + + align:start position:0% +happens it happens pretty quickly and + + + align:start position:0% +happens it happens pretty quickly and +nothing else usually happens in the + + align:start position:0% +nothing else usually happens in the + + + align:start position:0% +nothing else usually happens in the +meantime related to something else some + + align:start position:0% +meantime related to something else some + + + align:start position:0% +meantime related to something else some +other process um if you talk about dis + + align:start position:0% +other process um if you talk about dis + + + align:start position:0% +other process um if you talk about dis +scheduling well the dis scheduler is + + align:start position:0% +scheduling well the dis scheduler is + + + align:start position:0% +scheduling well the dis scheduler is +very very close to the dis it can make a + + align:start position:0% +very very close to the dis it can make a + + + align:start position:0% +very very close to the dis it can make a +decision and it exercises control + + align:start position:0% +decision and it exercises control + + + align:start position:0% +decision and it exercises control +according to whatever policy that it + + align:start position:0% +according to whatever policy that it + + + align:start position:0% +according to whatever policy that it +wants now here if the network decides + + align:start position:0% +wants now here if the network decides + + + align:start position:0% +wants now here if the network decides +it's congested and there's some plan by + + align:start position:0% +it's congested and there's some plan by + + + align:start position:0% +it's congested and there's some plan by +which the network will um want to uh + + align:start position:0% +which the network will um want to uh + + + align:start position:0% +which the network will um want to uh +react to that load um well it can't do + + align:start position:0% +react to that load um well it can't do + + + align:start position:0% +react to that load um well it can't do +very much it has to somehow arrange for + + align:start position:0% +very much it has to somehow arrange for + + + align:start position:0% +very much it has to somehow arrange for +feedback to reach the points of control + + align:start position:0% +feedback to reach the points of control + + + align:start position:0% +feedback to reach the points of control +which which are in general far away and + + align:start position:0% +which which are in general far away and + + + align:start position:0% +which which are in general far away and +are not just far away but they're I mean + + align:start position:0% +are not just far away but they're I mean + + + align:start position:0% +are not just far away but they're I mean +in terms of delay but that delay varies + + align:start position:0% +in terms of delay but that delay varies + + + align:start position:0% +in terms of delay but that delay varies +as well and that's what makes um the + + align:start position:0% +as well and that's what makes um the + + + align:start position:0% +as well and that's what makes um the +problem hard which is that the resource + + align:start position:0% +problem hard which is that the resource + + + align:start position:0% +problem hard which is that the resource +is far from the control + + align:start position:0% + + + + align:start position:0% + +point so these are the congestion points + + align:start position:0% +point so these are the congestion points + + + align:start position:0% +point so these are the congestion points +which is where the resources are and + + align:start position:0% +which is where the resources are and + + + align:start position:0% +which is where the resources are and +these are the control points which is + + align:start position:0% +these are the control points which is + + + align:start position:0% +these are the control points which is +where you can exercises and the two are + + align:start position:0% +where you can exercises and the two are + + + align:start position:0% +where you can exercises and the two are +separated + + align:start position:0% + + + + align:start position:0% + +geographically I don't think I mentioned + + align:start position:0% +geographically I don't think I mentioned + + + align:start position:0% +geographically I don't think I mentioned +this but a situation where this is what + + align:start position:0% +this but a situation where this is what + + + align:start position:0% +this but a situation where this is what +you want and any situation where Li the + + align:start position:0% +you want and any situation where Li the + + + align:start position:0% +you want and any situation where Li the +summation of Li um the offered load on a + + align:start position:0% +summation of Li um the offered load on a + + + align:start position:0% +summation of Li um the offered load on a +link is larger than the capacity that + + align:start position:0% +link is larger than the capacity that + + + align:start position:0% +link is larger than the capacity that +overload situation is some is what we're + + align:start position:0% +overload situation is some is what we're + + + align:start position:0% +overload situation is some is what we're +going to call congestion okay so anytime + + align:start position:0% +going to call congestion okay so anytime + + + align:start position:0% +going to call congestion okay so anytime +you see Li bigger than C we're going to + + align:start position:0% +you see Li bigger than C we're going to + + + align:start position:0% +you see Li bigger than C we're going to +Define that as congestion and then I'll + + align:start position:0% +Define that as congestion and then I'll + + + align:start position:0% +Define that as congestion and then I'll +make this notion a little bit more + + align:start position:0% +make this notion a little bit more + + + align:start position:0% +make this notion a little bit more +precise and you'll see why we have to + + align:start position:0% +precise and you'll see why we have to + + + align:start position:0% +precise and you'll see why we have to +make it slightly more precise but for + + align:start position:0% +make it slightly more precise but for + + + align:start position:0% +make it slightly more precise but for +now just say that if the inequality is + + align:start position:0% +now just say that if the inequality is + + + align:start position:0% +now just say that if the inequality is +swapped that means it's congest + + align:start position:0% + + + + align:start position:0% + +congested okay so that's the problem and + + align:start position:0% +congested okay so that's the problem and + + + align:start position:0% +congested okay so that's the problem and +we're we're going to want to solve the + + align:start position:0% +we're we're going to want to solve the + + + align:start position:0% +we're we're going to want to solve the +problem now every other problem that + + align:start position:0% +problem now every other problem that + + + align:start position:0% +problem now every other problem that +we've encountered in um networking so + + align:start position:0% +we've encountered in um networking so + + + align:start position:0% +we've encountered in um networking so +far we've solved by going back to that + + align:start position:0% +far we've solved by going back to that + + + align:start position:0% +far we've solved by going back to that +layered picture and saying well we need + + align:start position:0% +layered picture and saying well we need + + + align:start position:0% +layered picture and saying well we need +to deliver for example if you want to + + align:start position:0% +to deliver for example if you want to + + + align:start position:0% +to deliver for example if you want to +deliver packets across one link we say + + align:start position:0% +deliver packets across one link we say + + + align:start position:0% +deliver packets across one link we say +all right we'll take this thing as a + + align:start position:0% +all right we'll take this thing as a + + + align:start position:0% +all right we'll take this thing as a +link layer protocol we'll Define framing + + align:start position:0% +link layer protocol we'll Define framing + + + align:start position:0% +link layer protocol we'll Define framing +on top of it and Define a way by which + + align:start position:0% +on top of it and Define a way by which + + + align:start position:0% +on top of it and Define a way by which +we can um you know um do things like + + align:start position:0% +we can um you know um do things like + + + align:start position:0% +we can um you know um do things like +error correction if we need to on that + + align:start position:0% +error correction if we need to on that + + + align:start position:0% +error correction if we need to on that +link and we'll solve the problem right + + align:start position:0% +link and we'll solve the problem right + + + align:start position:0% +link and we'll solve the problem right +there then we say okay we need to + + align:start position:0% +there then we say okay we need to + + + align:start position:0% +there then we say okay we need to +connect all these computers up together + + align:start position:0% +connect all these computers up together + + + align:start position:0% +connect all these computers up together +and Route build up routing tables so we + + align:start position:0% +and Route build up routing tables so we + + + align:start position:0% +and Route build up routing tables so we +can forward data and we say okay that's + + align:start position:0% +can forward data and we say okay that's + + + align:start position:0% +can forward data and we say okay that's +the network layest problem we're going + + align:start position:0% +the network layest problem we're going + + + align:start position:0% +the network layest problem we're going +to solve the problem there then packets + + align:start position:0% +to solve the problem there then packets + + + align:start position:0% +to solve the problem there then packets +get lost well we'll deal with it at the + + align:start position:0% +get lost well we'll deal with it at the + + + align:start position:0% +get lost well we'll deal with it at the +end to endend layer and that model has + + align:start position:0% +end to endend layer and that model has + + + align:start position:0% +end to endend layer and that model has +worked out extremely well because it + + align:start position:0% +worked out extremely well because it + + + align:start position:0% +worked out extremely well because it +allows us to run arbitrary applications + + align:start position:0% +allows us to run arbitrary applications + + + align:start position:0% +allows us to run arbitrary applications +on top of this network layer without + + align:start position:0% +on top of this network layer without + + + align:start position:0% +on top of this network layer without +really having to build up forwarding + + align:start position:0% +really having to build up forwarding + + + align:start position:0% +really having to build up forwarding +tables for every application a new and + + align:start position:0% +tables for every application a new and + + + align:start position:0% +tables for every application a new and +run it on all sorts of links and you can + + align:start position:0% +run it on all sorts of links and you can + + + align:start position:0% +run it on all sorts of links and you can +have pads containing you know a variety + + align:start position:0% +have pads containing you know a variety + + + align:start position:0% +have pads containing you know a variety +of different links and everything works + + align:start position:0% +of different links and everything works + + + align:start position:0% +of different links and everything works +out like a charm but the problem with + + align:start position:0% +out like a charm but the problem with + + + align:start position:0% +out like a charm but the problem with +doing that for congestion control is + + align:start position:0% +doing that for congestion control is + + + align:start position:0% +doing that for congestion control is +that this layered picture is actually + + align:start position:0% +that this layered picture is actually + + + align:start position:0% +that this layered picture is actually +getting getting in the way of solving + + align:start position:0% +getting getting in the way of solving + + + align:start position:0% +getting getting in the way of solving +congestion control in a very clean + + align:start position:0% +congestion control in a very clean + + + align:start position:0% +congestion control in a very clean +Manner and the reason for that is that + + align:start position:0% +Manner and the reason for that is that + + + align:start position:0% +Manner and the reason for that is that +the end to endend layer runs at the end + + align:start position:0% +the end to endend layer runs at the end + + + align:start position:0% +the end to endend layer runs at the end +points and those are the points where + + align:start position:0% +points and those are the points where + + + align:start position:0% +points and those are the points where +control is exercised to control the rate + + align:start position:0% +control is exercised to control the rate + + + align:start position:0% +control is exercised to control the rate +at which traffic is being sent onto the + + align:start position:0% +at which traffic is being sent onto the + + + align:start position:0% +at which traffic is being sent onto the +network + + align:start position:0% + + + + align:start position:0% + +um but the congestion and the notice of + + align:start position:0% +um but the congestion and the notice of + + + align:start position:0% +um but the congestion and the notice of +any information about whether the + + align:start position:0% +any information about whether the + + + align:start position:0% +any information about whether the +network is overloaded is deeply buried + + align:start position:0% +network is overloaded is deeply buried + + + align:start position:0% +network is overloaded is deeply buried +inside the network at the network + + align:start position:0% +inside the network at the network + + + align:start position:0% +inside the network at the network +layer so what you need is a way by which + + align:start position:0% +layer so what you need is a way by which + + + align:start position:0% +layer so what you need is a way by which +information from the network layer about + + align:start position:0% +information from the network layer about + + + align:start position:0% +information from the network layer about +whether congestion is occurring or + + align:start position:0% +whether congestion is occurring or + + + align:start position:0% +whether congestion is occurring or +whether congestion is not occurring or + + align:start position:0% +whether congestion is not occurring or + + + align:start position:0% +whether congestion is not occurring or +whether congestion is likely to occur + + align:start position:0% +whether congestion is likely to occur + + + align:start position:0% +whether congestion is likely to occur +even though it's not yet occurred that + + align:start position:0% +even though it's not yet occurred that + + + align:start position:0% +even though it's not yet occurred that +kind of information has somehow to + + align:start position:0% +kind of information has somehow to + + + align:start position:0% +kind of information has somehow to +percolate toward the end to end layer + + align:start position:0% +percolate toward the end to end layer + + + align:start position:0% +percolate toward the end to end layer +and so far we've modularized this very + + align:start position:0% +and so far we've modularized this very + + + align:start position:0% +and so far we've modularized this very +nicely by not contr having very much + + align:start position:0% +nicely by not contr having very much + + + align:start position:0% +nicely by not contr having very much +information propagate between these + + align:start position:0% +information propagate between these + + + align:start position:0% +information propagate between these +layers but now to solve this problem of + + align:start position:0% +layers but now to solve this problem of + + + align:start position:0% +layers but now to solve this problem of +congestion precisely because of this + + align:start position:0% +congestion precisely because of this + + + align:start position:0% +congestion precisely because of this +separation between the resource and the + + align:start position:0% +separation between the resource and the + + + align:start position:0% +separation between the resource and the +control point and the fact that the + + align:start position:0% +control point and the fact that the + + + align:start position:0% +control point and the fact that the +control point is at the end to end layer + + align:start position:0% +control point is at the end to end layer + + + align:start position:0% +control point is at the end to end layer +at least in the way we're going to solve + + align:start position:0% +at least in the way we're going to solve + + + align:start position:0% +at least in the way we're going to solve +the problem and the fact that the + + align:start position:0% +the problem and the fact that the + + + align:start position:0% +the problem and the fact that the +resource is at the network layer it + + align:start position:0% +resource is at the network layer it + + + align:start position:0% +resource is at the network layer it +necessitates a cross layer solution to + + align:start position:0% +necessitates a cross layer solution to + + + align:start position:0% +necessitates a cross layer solution to +the + + align:start position:0% + + + + align:start position:0% + +problem so somehow we need information + + align:start position:0% +problem so somehow we need information + + + align:start position:0% +problem so somehow we need information +to to move uh between the two layers so + + align:start position:0% +to to move uh between the two layers so + + + align:start position:0% +to to move uh between the two layers so +here's a general + + align:start position:0% + + + + align:start position:0% + +plan so we're going to arrange for the + + align:start position:0% +plan so we're going to arrange for the + + + align:start position:0% +plan so we're going to arrange for the +end to end layer at the sender to send + + align:start position:0% +end to end layer at the sender to send + + + align:start position:0% +end to end layer at the sender to send +at a rate that you know this is going to + + align:start position:0% +at a rate that you know this is going to + + + align:start position:0% +at a rate that you know this is going to +be a rate that changes with time but + + align:start position:0% +be a rate that changes with time but + + + align:start position:0% +be a rate that changes with time but +let's say that the sender at some point + + align:start position:0% +let's say that the sender at some point + + + align:start position:0% +let's say that the sender at some point +in time sends at a rate + + align:start position:0% + + + + align:start position:0% + +RI where R is measured in bits per + + align:start position:0% +RI where R is measured in bits per + + + align:start position:0% +RI where R is measured in bits per +second and that's actually true here in + + align:start position:0% +second and that's actually true here in + + + align:start position:0% +second and that's actually true here in +in case it wasn't clear these loads are + + align:start position:0% +in case it wasn't clear these loads are + + + align:start position:0% +in case it wasn't clear these loads are +in bits per second the capacity is in + + align:start position:0% +in bits per second the capacity is in + + + align:start position:0% +in bits per second the capacity is in +bits per second as + + align:start position:0% +bits per second as + + + align:start position:0% +bits per second as +well so the plan is for the sender to + + align:start position:0% +well so the plan is for the sender to + + + align:start position:0% +well so the plan is for the sender to +send at a l rate + + align:start position:0% +send at a l rate + + + align:start position:0% +send at a l rate +RI and for the network layer for all of + + align:start position:0% +RI and for the network layer for all of + + + align:start position:0% +RI and for the network layer for all of +the switches you know inside the network + + align:start position:0% +the switches you know inside the network + + + align:start position:0% +the switches you know inside the network +to keep track in some fashion of whether + + align:start position:0% +to keep track in some fashion of whether + + + align:start position:0% +to keep track in some fashion of whether +they're being congested or not and it's + + align:start position:0% +they're being congested or not and it's + + + align:start position:0% +they're being congested or not and it's +going to be really simple after that if + + align:start position:0% +going to be really simple after that if + + + align:start position:0% +going to be really simple after that if +the senders are sending too fast or if a + + align:start position:0% +the senders are sending too fast or if a + + + align:start position:0% +the senders are sending too fast or if a +given sender is sending too fast + + align:start position:0% +given sender is sending too fast + + + align:start position:0% +given sender is sending too fast +then we're going to tell them to slow + + align:start position:0% +then we're going to tell them to slow + + + align:start position:0% +then we're going to tell them to slow +down the network lay is somehow going to + + align:start position:0% +down the network lay is somehow going to + + + align:start position:0% +down the network lay is somehow going to +tell the sender to slow + + align:start position:0% +tell the sender to slow + + + align:start position:0% +tell the sender to slow +down and likewise if they're sending too + + align:start position:0% +down and likewise if they're sending too + + + align:start position:0% +down and likewise if they're sending too +slow and we have to still we we have yet + + align:start position:0% +slow and we have to still we we have yet + + + align:start position:0% +slow and we have to still we we have yet +to figure out how you know that you're + + align:start position:0% +to figure out how you know that you're + + + align:start position:0% +to figure out how you know that you're +sending too slow and that you could send + + align:start position:0% +sending too slow and that you could send + + + align:start position:0% +sending too slow and that you could send +a little faster if you're sending too + + align:start position:0% +a little faster if you're sending too + + + align:start position:0% +a little faster if you're sending too +slow there's going to be some plan by + + align:start position:0% +slow there's going to be some plan by + + + align:start position:0% +slow there's going to be some plan by +which the sender can speed + + align:start position:0% + + + + align:start position:0% + +up and the nature of our solution is + + align:start position:0% +up and the nature of our solution is + + + align:start position:0% +up and the nature of our solution is +going to be that there is really no not + + align:start position:0% +going to be that there is really no not + + + align:start position:0% +going to be that there is really no not +going to be a steady rate at which + + align:start position:0% +going to be a steady rate at which + + + align:start position:0% +going to be a steady rate at which +senders are going to send in fact by the + + align:start position:0% +senders are going to send in fact by the + + + align:start position:0% +senders are going to send in fact by the +definition of the problem a steady rate + + align:start position:0% +definition of the problem a steady rate + + + align:start position:0% +definition of the problem a steady rate +is is is a Fool's errant because n + + align:start position:0% +is is is a Fool's errant because n + + + align:start position:0% +is is is a Fool's errant because n +varies and the load varies so that means + + align:start position:0% +varies and the load varies so that means + + + align:start position:0% +varies and the load varies so that means +the On Any Given link the traffic varies + + align:start position:0% +the On Any Given link the traffic varies + + + align:start position:0% +the On Any Given link the traffic varies +with time so you really don't want a + + align:start position:0% +with time so you really don't want a + + + align:start position:0% +with time so you really don't want a +static rate what you would like to do is + + align:start position:0% +static rate what you would like to do is + + + align:start position:0% +static rate what you would like to do is +if there's any extra capacity and a + + align:start position:0% +if there's any extra capacity and a + + + align:start position:0% +if there's any extra capacity and a +sender has load to fill that capacity + + align:start position:0% +sender has load to fill that capacity + + + align:start position:0% +sender has load to fill that capacity +you want that sender to use that + + align:start position:0% +you want that sender to use that + + + align:start position:0% +you want that sender to use that +capacity so this rate is going to adapt + + align:start position:0% +capacity so this rate is going to adapt + + + align:start position:0% +capacity so this rate is going to adapt +and change with time in response to some + + align:start position:0% +and change with time in response to some + + + align:start position:0% +and change with time in response to some +feedback that we're going to obtain + + align:start position:0% +feedback that we're going to obtain + + + align:start position:0% +feedback that we're going to obtain +based on network layer the information + + align:start position:0% +based on network layer the information + + + align:start position:0% +based on network layer the information +from essentially from the network layer + + align:start position:0% +from essentially from the network layer + + + align:start position:0% +from essentially from the network layer +about whether people are sending too + + align:start position:0% +about whether people are sending too + + + align:start position:0% +about whether people are sending too +fast or people are too slow okay and all + + align:start position:0% +fast or people are too slow okay and all + + + align:start position:0% +fast or people are too slow okay and all +congestion control schemes that people + + align:start position:0% +congestion control schemes that people + + + align:start position:0% +congestion control schemes that people +have come up with all algorithms for + + align:start position:0% +have come up with all algorithms for + + + align:start position:0% +have come up with all algorithms for +solving this problem and there have been + + align:start position:0% +solving this problem and there have been + + + align:start position:0% +solving this problem and there have been +you know dozens if not you know a few + + align:start position:0% +you know dozens if not you know a few + + + align:start position:0% +you know dozens if not you know a few +hundred of them um all of these things + + align:start position:0% +hundred of them um all of these things + + + align:start position:0% +hundred of them um all of these things +and various variants of various + + align:start position:0% +and various variants of various + + + align:start position:0% +and various variants of various +Solutions all of them are according to + + align:start position:0% +Solutions all of them are according to + + + align:start position:0% +Solutions all of them are according to +this basic plan okay the network layer + + align:start position:0% +this basic plan okay the network layer + + + align:start position:0% +this basic plan okay the network layer +gives some feedback if it's too fast + + align:start position:0% +gives some feedback if it's too fast + + + align:start position:0% +gives some feedback if it's too fast +slow down if it's too slow speed + + align:start position:0% + + + + align:start position:0% + +up the analogy is a little bit to um you + + align:start position:0% +up the analogy is a little bit to um you + + + align:start position:0% +up the analogy is a little bit to um you +know like a water pipeline Network + + align:start position:0% +know like a water pipeline Network + + + align:start position:0% +know like a water pipeline Network +imagine you have all sorts of pipes + + align:start position:0% +imagine you have all sorts of pipes + + + align:start position:0% +imagine you have all sorts of pipes +feeding water in you have this massive + + align:start position:0% +feeding water in you have this massive + + + align:start position:0% +feeding water in you have this massive +pipeline Network and what you can + + align:start position:0% +pipeline Network and what you can + + + align:start position:0% +pipeline Network and what you can +control are the valves at the end points + + align:start position:0% +control are the valves at the end points + + + align:start position:0% +control are the valves at the end points +and by controlling the valve you can + + align:start position:0% +and by controlling the valve you can + + + align:start position:0% +and by controlling the valve you can +decide whether to let water rush in or + + align:start position:0% +decide whether to let water rush in or + + + align:start position:0% +decide whether to let water rush in or +not and anytime you're getting clogged + + align:start position:0% +not and anytime you're getting clogged + + + align:start position:0% +not and anytime you're getting clogged +you have to slow down and close the + + align:start position:0% + + + + align:start position:0% + +valves so the devil's actually in the + + align:start position:0% +valves so the devil's actually in the + + + align:start position:0% +valves so the devil's actually in the +details so we're going to dive in to + + align:start position:0% +details so we're going to dive in to + + + align:start position:0% +details so we're going to dive in to +actually seeing how we're going to solve + + align:start position:0% +actually seeing how we're going to solve + + + align:start position:0% +actually seeing how we're going to solve +this problem and the first component of + + align:start position:0% +this problem and the first component of + + + align:start position:0% +this problem and the first component of +any solution to congestion control is + + align:start position:0% +any solution to congestion control is + + + align:start position:0% +any solution to congestion control is +something we've already seen + + align:start position:0% + + + + align:start position:0% + +and it's + + align:start position:0% +and it's + + + align:start position:0% +and it's +buffering any network that's that has + + align:start position:0% +buffering any network that's that has + + + align:start position:0% +buffering any network that's that has +asynchronous multiplexing um which which + + align:start position:0% +asynchronous multiplexing um which which + + + align:start position:0% +asynchronous multiplexing um which which +Sam talked about the first time any + + align:start position:0% +Sam talked about the first time any + + + align:start position:0% +Sam talked about the first time any +Network that has that has this + + align:start position:0% +Network that has that has this + + + align:start position:0% +Network that has that has this +um you know has the following effect has + + align:start position:0% +um you know has the following effect has + + + align:start position:0% +um you know has the following effect has +the following Behavior at any given + + align:start position:0% +the following Behavior at any given + + + align:start position:0% +the following Behavior at any given +point in time you might have multiple + + align:start position:0% +point in time you might have multiple + + + align:start position:0% +point in time you might have multiple +packets arriv in to a given switch and + + align:start position:0% +packets arriv in to a given switch and + + + align:start position:0% +packets arriv in to a given switch and +the switch can only send one of them out + + align:start position:0% +the switch can only send one of them out + + + align:start position:0% +the switch can only send one of them out +on an outgoing Link at any given point + + align:start position:0% +on an outgoing Link at any given point + + + align:start position:0% +on an outgoing Link at any given point +in time + + align:start position:0% +in time + + + align:start position:0% +in time +which means if you weren't careful you + + align:start position:0% +which means if you weren't careful you + + + align:start position:0% +which means if you weren't careful you +would have to drop the other packet that + + align:start position:0% +would have to drop the other packet that + + + align:start position:0% +would have to drop the other packet that +showed up and so almost everyone who + + align:start position:0% +showed up and so almost everyone who + + + align:start position:0% +showed up and so almost everyone who +builds a decent asynchronously + + align:start position:0% +builds a decent asynchronously + + + align:start position:0% +builds a decent asynchronously +multiplexed Network puts in uh some cues + + align:start position:0% +multiplexed Network puts in uh some cues + + + align:start position:0% +multiplexed Network puts in uh some cues +to buffer packets um until the link that + + align:start position:0% +to buffer packets um until the link that + + + align:start position:0% +to buffer packets um until the link that +the link is free so they can then send + + align:start position:0% +the link is free so they can then send + + + align:start position:0% +the link is free so they can then send +the packet out onto the + + align:start position:0% +the packet out onto the + + + align:start position:0% +the packet out onto the +link so the key question when it comes + + align:start position:0% +link so the key question when it comes + + + align:start position:0% +link so the key question when it comes +to buffering that you have to ask is how + + align:start position:0% +to buffering that you have to ask is how + + + align:start position:0% +to buffering that you have to ask is how +much and I don't actually mean how much + + align:start position:0% +much and I don't actually mean how much + + + align:start position:0% +much and I don't actually mean how much +in terms of how expensive it is but in + + align:start position:0% +in terms of how expensive it is but in + + + align:start position:0% +in terms of how expensive it is but in +terms of how how much should the + + align:start position:0% +terms of how how much should the + + + align:start position:0% +terms of how how much should the +buffering be I mean should you have one + + align:start position:0% +buffering be I mean should you have one + + + align:start position:0% +buffering be I mean should you have one +packet of buffering two packets four + + align:start position:0% +packet of buffering two packets four + + + align:start position:0% +packet of buffering two packets four +packets you know how big should the + + align:start position:0% +packets you know how big should the + + + align:start position:0% +packets you know how big should the +buffer + + align:start position:0% +buffer + + + align:start position:0% +buffer +be + + align:start position:0% + + + + align:start position:0% + +well so there one way to answer a + + align:start position:0% +well so there one way to answer a + + + align:start position:0% +well so there one way to answer a +question of how much first you can ask + + align:start position:0% +question of how much first you can ask + + + align:start position:0% +question of how much first you can ask +what happens if it's too little so what + + align:start position:0% +what happens if it's too little so what + + + align:start position:0% +what happens if it's too little so what +happens if the buffering is too little + + align:start position:0% +happens if the buffering is too little + + + align:start position:0% +happens if the buffering is too little +in a + + align:start position:0% + + + + align:start position:0% + +switch like you put one packet or two + + align:start position:0% +switch like you put one packet or two + + + align:start position:0% +switch like you put one packet or two +packets of buffering what + + align:start position:0% + + + + align:start position:0% + +happens I'm sorry what + + align:start position:0% + + + + align:start position:0% + +um well congestion by definition has + + align:start position:0% +um well congestion by definition has + + + align:start position:0% +um well congestion by definition has +happened when the load exceeds the + + align:start position:0% +happened when the load exceeds the + + + align:start position:0% +happened when the load exceeds the +capacity so you get congestion but + + align:start position:0% +capacity so you get congestion but + + + align:start position:0% +capacity so you get congestion but +what's the effect of that so A bunch of + + align:start position:0% +what's the effect of that so A bunch of + + + align:start position:0% +what's the effect of that so A bunch of +packets show up you got two packets of + + align:start position:0% +packets show up you got two packets of + + + align:start position:0% +packets show up you got two packets of +buffering so you lose packets this is + + align:start position:0% +buffering so you lose packets this is + + + align:start position:0% +buffering so you lose packets this is +pretty clear right good so if it's too + + align:start position:0% +pretty clear right good so if it's too + + + align:start position:0% +pretty clear right good so if it's too +little what ends up happening is that + + align:start position:0% +little what ends up happening is that + + + align:start position:0% +little what ends up happening is that +you drop + + align:start position:0% +you drop + + + align:start position:0% +you drop +packets we suggest that you can't have + + align:start position:0% +packets we suggest that you can't have + + + align:start position:0% +packets we suggest that you can't have +too little buffering okay so at the + + align:start position:0% +too little buffering okay so at the + + + align:start position:0% +too little buffering okay so at the +other end of the spectrum you could just + + align:start position:0% +other end of the spectrum you could just + + + align:start position:0% +other end of the spectrum you could just +say well I'm going to design my network + + align:start position:0% +say well I'm going to design my network + + + align:start position:0% +say well I'm going to design my network +never drops a packet memory is cheap we + + align:start position:0% +never drops a packet memory is cheap we + + + align:start position:0% +never drops a packet memory is cheap we +learned about More's law so let's just + + align:start position:0% +learned about More's law so let's just + + + align:start position:0% +learned about More's law so let's just +over-provision also called too much + + align:start position:0% +over-provision also called too much + + + align:start position:0% +over-provision also called too much +buffering okay it's not really that + + align:start position:0% +buffering okay it's not really that + + + align:start position:0% +buffering okay it's not really that +expensive so what happens if there's too + + align:start position:0% +expensive so what happens if there's too + + + align:start position:0% +expensive so what happens if there's too +much buffering + + align:start position:0% +much buffering + + + align:start position:0% +much buffering +well if you think about it the only + + align:start position:0% +well if you think about it the only + + + align:start position:0% +well if you think about it the only +thing that happens when you have too + + align:start position:0% +thing that happens when you have too + + + align:start position:0% +thing that happens when you have too +much buffering is well packets won't get + + align:start position:0% +much buffering is well packets won't get + + + align:start position:0% +much buffering is well packets won't get +lost but all you've done is traded off + + align:start position:0% +lost but all you've done is traded off + + + align:start position:0% +lost but all you've done is traded off +packet loss for packet + + align:start position:0% +packet loss for packet + + + align:start position:0% +packet loss for packet +delay you know adding more buffering + + align:start position:0% +delay you know adding more buffering + + + align:start position:0% +delay you know adding more buffering +doesn't make it your link go any + + align:start position:0% +doesn't make it your link go any + + + align:start position:0% +doesn't make it your link go any +faster they should probably learn that + + align:start position:0% +faster they should probably learn that + + + align:start position:0% +faster they should probably learn that +at Disneyland and places like that I + + align:start position:0% +at Disneyland and places like that I + + + align:start position:0% +at Disneyland and places like that I +mean these lines there are just so long + + align:start position:0% +mean these lines there are just so long + + + align:start position:0% +mean these lines there are just so long +I mean they may as well tell people to + + align:start position:0% +I mean they may as well tell people to + + + align:start position:0% +I mean they may as well tell people to +go away and come back later it's the + + align:start position:0% +go away and come back later it's the + + + align:start position:0% +go away and come back later it's the +same principle I mean just adding longer + + align:start position:0% +same principle I mean just adding longer + + + align:start position:0% +same principle I mean just adding longer +lines and longer cues doesn't mean that + + align:start position:0% +lines and longer cues doesn't mean that + + + align:start position:0% +lines and longer cues doesn't mean that +the link goes any faster so it's really + + align:start position:0% +the link goes any faster so it's really + + + align:start position:0% +the link goes any faster so it's really +problematic to add excessive buffers and + + align:start position:0% +problematic to add excessive buffers and + + + align:start position:0% +problematic to add excessive buffers and +the reason is is quite subtle the reason + + align:start position:0% +the reason is is quite subtle the reason + + + align:start position:0% +the reason is is quite subtle the reason +actually has to do with um something we + + align:start position:0% +actually has to do with um something we + + + align:start position:0% +actually has to do with um something we +talked about the last time or at least + + align:start position:0% +talked about the last time or at least + + + align:start position:0% +talked about the last time or at least +one reason a critical reason has to do + + align:start position:0% +one reason a critical reason has to do + + + align:start position:0% +one reason a critical reason has to do +with timers and retransmissions + + align:start position:0% +with timers and retransmissions + + + align:start position:0% +with timers and retransmissions +recall that all you do when you have too + + align:start position:0% +recall that all you do when you have too + + + align:start position:0% +recall that all you do when you have too +much buffering is you you eliminate + + align:start position:0% +much buffering is you you eliminate + + + align:start position:0% +much buffering is you you eliminate +packet loss or at least reduce it + + align:start position:0% +packet loss or at least reduce it + + + align:start position:0% +packet loss or at least reduce it +greatly at the expense of increasing + + align:start position:0% +greatly at the expense of increasing + + + align:start position:0% +greatly at the expense of increasing +delays but the problem with increasing + + align:start position:0% +delays but the problem with increasing + + + align:start position:0% +delays but the problem with increasing +delays is that your timers that you're + + align:start position:0% +delays is that your timers that you're + + + align:start position:0% +delays is that your timers that you're +trying to set up to figure out when to + + align:start position:0% +trying to set up to figure out when to + + + align:start position:0% +trying to set up to figure out when to +retransmit a packet you would like them + + align:start position:0% +retransmit a packet you would like them + + + align:start position:0% +retransmit a packet you would like them +to adapt to increasing delays so you + + align:start position:0% +to adapt to increasing delays so you + + + align:start position:0% +to adapt to increasing delays so you +build this exponentially weighted moving + + align:start position:0% +build this exponentially weighted moving + + + align:start position:0% +build this exponentially weighted moving +average and you pick a timeout interval + + align:start position:0% +average and you pick a timeout interval + + + align:start position:0% +average and you pick a timeout interval +that's based on it's the mean value and + + align:start position:0% +that's based on it's the mean value and + + + align:start position:0% +that's based on it's the mean value and +the standard deviation and the problem + + align:start position:0% +the standard deviation and the problem + + + align:start position:0% +the standard deviation and the problem +with too much buffering is that it makes + + align:start position:0% +with too much buffering is that it makes + + + align:start position:0% +with too much buffering is that it makes +these adaptive timers extremely hard uh + + align:start position:0% +these adaptive timers extremely hard uh + + + align:start position:0% +these adaptive timers extremely hard uh +extremely hard to implement because if + + align:start position:0% +extremely hard to implement because if + + + align:start position:0% +extremely hard to implement because if +you if because your timeout value has to + + align:start position:0% +you if because your timeout value has to + + + align:start position:0% +you if because your timeout value has to +depend on both the mean and the standard + + align:start position:0% +depend on both the mean and the standard + + + align:start position:0% +depend on both the mean and the standard +deviation and if you have too much + + align:start position:0% +deviation and if you have too much + + + align:start position:0% +deviation and if you have too much +buffering the range of roundtrip time + + align:start position:0% +buffering the range of roundtrip time + + + align:start position:0% +buffering the range of roundtrip time +values is too + + align:start position:0% +values is too + + + align:start position:0% +values is too +high and the result of that is that you + + align:start position:0% +high and the result of that is that you + + + align:start position:0% +high and the result of that is that you +end up with this potential for something + + align:start position:0% +end up with this potential for something + + + align:start position:0% +end up with this potential for something +called congestion collapse + + align:start position:0% + + + + align:start position:0% + +and let me explain this um with a + + align:start position:0% + + + + align:start position:0% + +picture so your adaptive adaptive timers + + align:start position:0% +picture so your adaptive adaptive timers + + + align:start position:0% +picture so your adaptive adaptive timers +are trying to estimate the roundt trip + + align:start position:0% +are trying to estimate the roundt trip + + + align:start position:0% +are trying to estimate the roundt trip +time and the the average roundt trip + + align:start position:0% +time and the the average roundt trip + + + align:start position:0% +time and the the average roundt trip +time and the standard deviation or the + + align:start position:0% +time and the standard deviation or the + + + align:start position:0% +time and the standard deviation or the +linear deviation of the roundt trip time + + align:start position:0% +linear deviation of the roundt trip time + + + align:start position:0% +linear deviation of the roundt trip time +um and at some point they're going to + + align:start position:0% +um and at some point they're going to + + + align:start position:0% +um and at some point they're going to +make a decision as to whether to + + align:start position:0% +make a decision as to whether to + + + align:start position:0% +make a decision as to whether to +retransmit a packet or not and they're + + align:start position:0% +retransmit a packet or not and they're + + + align:start position:0% +retransmit a packet or not and they're +going to decide to retransmit a + + align:start position:0% +going to decide to retransmit a + + + align:start position:0% +going to decide to retransmit a +packet what might + + align:start position:0% +packet what might + + + align:start position:0% +packet what might +happen and what does happen and has + + align:start position:0% +happen and what does happen and has + + + align:start position:0% +happen and what does happen and has +happened when you have too much um + + align:start position:0% +happened when you have too much um + + + align:start position:0% +happened when you have too much um +networks with too much buffering is that + + align:start position:0% +networks with too much buffering is that + + + align:start position:0% +networks with too much buffering is that +you end up with a queue that's really + + align:start position:0% +you end up with a queue that's really + + + align:start position:0% +you end up with a queue that's really +big okay and this is some link on which + + align:start position:0% +big okay and this is some link on which + + + align:start position:0% +big okay and this is some link on which +the packet's going out and you might + + align:start position:0% +the packet's going out and you might + + + align:start position:0% +the packet's going out and you might +have packet one sitting here and two + + align:start position:0% +have packet one sitting here and two + + + align:start position:0% +have packet one sitting here and two +sitting here and three and all the way + + align:start position:0% +sitting here and three and all the way + + + align:start position:0% +sitting here and three and all the way +out um there's large number of packets + + align:start position:0% +out um there's large number of packets + + + align:start position:0% +out um there's large number of packets +sitting + + align:start position:0% +sitting + + + align:start position:0% +sitting +there notice that the end to end sender + + align:start position:0% +there notice that the end to end sender + + + align:start position:0% +there notice that the end to end sender +is trying to decide whether packet one + + align:start position:0% +is trying to decide whether packet one + + + align:start position:0% +is trying to decide whether packet one +for whose acknowledgement it still + + align:start position:0% +for whose acknowledgement it still + + + align:start position:0% +for whose acknowledgement it still +hasn't heard it's trying to decide + + align:start position:0% +hasn't heard it's trying to decide + + + align:start position:0% +hasn't heard it's trying to decide +whether one is still in transit or has + + align:start position:0% +whether one is still in transit or has + + + align:start position:0% +whether one is still in transit or has +actually been dropped and it should + + align:start position:0% +actually been dropped and it should + + + align:start position:0% +actually been dropped and it should +retransmit the packet only after one has + + align:start position:0% +retransmit the packet only after one has + + + align:start position:0% +retransmit the packet only after one has +been dropped but if you have too much + + align:start position:0% +been dropped but if you have too much + + + align:start position:0% +been dropped but if you have too much +buffering the range of these values is + + align:start position:0% +buffering the range of these values is + + + align:start position:0% +buffering the range of these values is +so high that it makes these adaptive + + align:start position:0% +so high that it makes these adaptive + + + align:start position:0% +so high that it makes these adaptive +timers quite difficult to tune and the + + align:start position:0% +timers quite difficult to tune and the + + + align:start position:0% +timers quite difficult to tune and the +result often is that one is still + + align:start position:0% +result often is that one is still + + + align:start position:0% +result often is that one is still +sitting here but it had been stuck + + align:start position:0% +sitting here but it had been stuck + + + align:start position:0% +sitting here but it had been stuck +behind a large number of packets so the + + align:start position:0% +behind a large number of packets so the + + + align:start position:0% +behind a large number of packets so the +delay was extremely long and the end to + + align:start position:0% +delay was extremely long and the end to + + + align:start position:0% +delay was extremely long and the end to +end sender time out and when it times + + align:start position:0% +end sender time out and when it times + + + align:start position:0% +end sender time out and when it times +out it retransmits one into the + + align:start position:0% +out it retransmits one into the + + + align:start position:0% +out it retransmits one into the +Q and soon after that often it might + + align:start position:0% +Q and soon after that often it might + + + align:start position:0% +Q and soon after that often it might +retransmit two and retransmit three and + + align:start position:0% +retransmit two and retransmit three and + + + align:start position:0% +retransmit two and retransmit three and +retransmit four and so on and these + + align:start position:0% +retransmit four and so on and these + + + align:start position:0% +retransmit four and so on and these +packets are sort of just stuck in the + + align:start position:0% +packets are sort of just stuck in the + + + align:start position:0% +packets are sort of just stuck in the +queue they're not actually lost and if + + align:start position:0% +queue they're not actually lost and if + + + align:start position:0% +queue they're not actually lost and if +you think about what will happen then + + align:start position:0% +you think about what will happen then + + + align:start position:0% +you think about what will happen then +this link which is already a congested + + align:start position:0% +this link which is already a congested + + + align:start position:0% +this link which is already a congested +link because cues have been building up + + align:start position:0% +link because cues have been building up + + + align:start position:0% +link because cues have been building up +here long cues have been building up + + align:start position:0% +here long cues have been building up + + + align:start position:0% +here long cues have been building up +this link is now starting to do use more + + align:start position:0% +this link is now starting to do use more + + + align:start position:0% +this link is now starting to do use more +and more of its resource more and more + + align:start position:0% +and more of its resource more and more + + + align:start position:0% +and more of its resource more and more +of its capacity to send the same packet + + align:start position:0% +of its capacity to send the same packet + + + align:start position:0% +of its capacity to send the same packet +twice + + align:start position:0% +twice + + + align:start position:0% +twice +right because it sent one one out and + + align:start position:0% +right because it sent one one out and + + + align:start position:0% +right because it sent one one out and +the sender retransmitted it thinking um + + align:start position:0% +the sender retransmitted it thinking um + + + align:start position:0% +the sender retransmitted it thinking um +that it was lost when it was just stuck + + align:start position:0% +that it was lost when it was just stuck + + + align:start position:0% +that it was lost when it was just stuck +behind a long q and now one is being + + align:start position:0% +behind a long q and now one is being + + + align:start position:0% +behind a long q and now one is being +sent again and two is being sent again + + align:start position:0% +sent again and two is being sent again + + + align:start position:0% +sent again and two is being sent again +and so + + align:start position:0% +and so + + + align:start position:0% +and so +on and graphically if you look at this + + align:start position:0% +on and graphically if you look at this + + + align:start position:0% +on and graphically if you look at this +what you end up with is a picture that + + align:start position:0% +what you end up with is a picture that + + + align:start position:0% +what you end up with is a picture that +looks like the following this picture + + align:start position:0% +looks like the following this picture + + + align:start position:0% +looks like the following this picture +plots the total offer load on the x-axis + + align:start position:0% +plots the total offer load on the x-axis + + + align:start position:0% +plots the total offer load on the x-axis +and the throughput of the system on the + + align:start position:0% +and the throughput of the system on the + + + align:start position:0% +and the throughput of the system on the +Y + + align:start position:0% + + + + align:start position:0% + +AIS where the throughput is defined as + + align:start position:0% +AIS where the throughput is defined as + + + align:start position:0% +AIS where the throughput is defined as +um the number of useful bits per second + + align:start position:0% +um the number of useful bits per second + + + align:start position:0% +um the number of useful bits per second +that you get so if you send the packet + + align:start position:0% +that you get so if you send the packet + + + align:start position:0% +that you get so if you send the packet +one twice that counts not as uh you know + + align:start position:0% +one twice that counts not as uh you know + + + align:start position:0% +one twice that counts not as uh you know +only one of those packets is actually + + align:start position:0% +only one of those packets is actually + + + align:start position:0% +only one of those packets is actually +useful now initially when the offered + + align:start position:0% +useful now initially when the offered + + + align:start position:0% +useful now initially when the offered +load is low and the network is not + + align:start position:0% +load is low and the network is not + + + align:start position:0% +load is low and the network is not +congested and the offered load is less + + align:start position:0% +congested and the offered load is less + + + align:start position:0% +congested and the offered load is less +than the capacity of the link this curve + + align:start position:0% +than the capacity of the link this curve + + + align:start position:0% +than the capacity of the link this curve +is just a straight line with slope + + align:start position:0% +is just a straight line with slope + + + align:start position:0% +is just a straight line with slope +one right because everything you offer + + align:start position:0% +one right because everything you offer + + + align:start position:0% +one right because everything you offer +is below the Link's capacity and it's + + align:start position:0% +is below the Link's capacity and it's + + + align:start position:0% +is below the Link's capacity and it's +going through now at some point it hits + + align:start position:0% +going through now at some point it hits + + + align:start position:0% +going through now at some point it hits +the Link's capacity + + align:start position:0% +the Link's capacity + + + align:start position:0% +the Link's capacity +right the bottleneck links capacity and + + align:start position:0% +right the bottleneck links capacity and + + + align:start position:0% +right the bottleneck links capacity and +after that any extra offered load that + + align:start position:0% +after that any extra offered load that + + + align:start position:0% +after that any extra offered load that +you pump into the network is not going + + align:start position:0% +you pump into the network is not going + + + align:start position:0% +you pump into the network is not going +to send go out any faster the rou is + + align:start position:0% +to send go out any faster the rou is + + + align:start position:0% +to send go out any faster the rou is +still going to remain the same and it's + + align:start position:0% +still going to remain the same and it's + + + align:start position:0% +still going to remain the same and it's +just going to be flat for a + + align:start position:0% +just going to be flat for a + + + align:start position:0% +just going to be flat for a +while and the reason it's flat is that + + align:start position:0% +while and the reason it's flat is that + + + align:start position:0% +while and the reason it's flat is that +cues are building up and that's one + + align:start position:0% +cues are building up and that's one + + + align:start position:0% +cues are building up and that's one +reason that you can't send things any + + align:start position:0% +reason that you can't send things any + + + align:start position:0% +reason that you can't send things any +faster the only thing that's going on is + + align:start position:0% +faster the only thing that's going on is + + + align:start position:0% +faster the only thing that's going on is +that cues are building up so this curve + + align:start position:0% +that cues are building up so this curve + + + align:start position:0% +that cues are building up so this curve +remains flat now in a decent Network + + align:start position:0% +remains flat now in a decent Network + + + align:start position:0% +remains flat now in a decent Network +that doesn't have congestion collapse um + + align:start position:0% +that doesn't have congestion collapse um + + + align:start position:0% +that doesn't have congestion collapse um +if you don't do anything um else but + + align:start position:0% +if you don't do anything um else but + + + align:start position:0% +if you don't do anything um else but +somehow manage to keep the system + + align:start position:0% +somehow manage to keep the system + + + align:start position:0% +somehow manage to keep the system +working here this curve might remain + + align:start position:0% +working here this curve might remain + + + align:start position:0% +working here this curve might remain +flat forever no matter what the offered + + align:start position:0% +flat forever no matter what the offered + + + align:start position:0% +flat forever no matter what the offered +load you know you can pump more and more + + align:start position:0% +load you know you can pump more and more + + + align:start position:0% +load you know you can pump more and more +load at the system and the throughput + + align:start position:0% +load at the system and the throughput + + + align:start position:0% +load at the system and the throughput +remains flat at the + + align:start position:0% +remains flat at the + + + align:start position:0% +remains flat at the +capacity but the problem is that it has + + align:start position:0% +capacity but the problem is that it has + + + align:start position:0% +capacity but the problem is that it has +interactions with things that the higher + + align:start position:0% +interactions with things that the higher + + + align:start position:0% +interactions with things that the higher +layer is doing such as these + + align:start position:0% +layer is doing such as these + + + align:start position:0% +layer is doing such as these +retransmissions and timers and + + align:start position:0% +retransmissions and timers and + + + align:start position:0% +retransmissions and timers and +eventually more and more of the capacity + + align:start position:0% +eventually more and more of the capacity + + + align:start position:0% +eventually more and more of the capacity +starts being used uselessly for these + + align:start position:0% +starts being used uselessly for these + + + align:start position:0% +starts being used uselessly for these +redundant transmissions and you might + + align:start position:0% +redundant transmissions and you might + + + align:start position:0% +redundant transmissions and you might +end up in a situation where the through + + align:start position:0% +end up in a situation where the through + + + align:start position:0% +end up in a situation where the through +put Dives + + align:start position:0% +put Dives + + + align:start position:0% +put Dives +down okay and if that happens + + align:start position:0% +down okay and if that happens + + + align:start position:0% +down okay and if that happens +this situation is called congestion + + align:start position:0% + + + + align:start position:0% + +collapse there's more and more work + + align:start position:0% +collapse there's more and more work + + + align:start position:0% +collapse there's more and more work +being presented to the system and if you + + align:start position:0% +being presented to the system and if you + + + align:start position:0% +being presented to the system and if you +reach a situation where the actual + + align:start position:0% +reach a situation where the actual + + + align:start position:0% +reach a situation where the actual +amount of useful work that's being done + + align:start position:0% +amount of useful work that's being done + + + align:start position:0% +amount of useful work that's being done +starts reducing as more work gets + + align:start position:0% +starts reducing as more work gets + + + align:start position:0% +starts reducing as more work gets +presented to the system that's a + + align:start position:0% +presented to the system that's a + + + align:start position:0% +presented to the system that's a +situation of congestion + + align:start position:0% +situation of congestion + + + align:start position:0% +situation of congestion +collapse and this kind of thing shows up + + align:start position:0% +collapse and this kind of thing shows up + + + align:start position:0% +collapse and this kind of thing shows up +in many other systems for example in uh + + align:start position:0% +in many other systems for example in uh + + + align:start position:0% +in many other systems for example in uh +very fast I'm sorry in um uh things like + + align:start position:0% +very fast I'm sorry in um uh things like + + + align:start position:0% +very fast I'm sorry in um uh things like +web servers that are built out of many + + align:start position:0% +web servers that are built out of many + + + align:start position:0% +web servers that are built out of many +stages um where you have high load + + align:start position:0% +stages um where you have high load + + + align:start position:0% +stages um where you have high load +presented at the system you might see + + align:start position:0% +presented at the system you might see + + + align:start position:0% +presented at the system you might see +congestion collapse in situations where + + align:start position:0% +congestion collapse in situations where + + + align:start position:0% +congestion collapse in situations where +so let's say you get a web request and + + align:start position:0% +so let's say you get a web request and + + + align:start position:0% +so let's say you get a web request and +what you have to do is seven stages of + + align:start position:0% +what you have to do is seven stages of + + + align:start position:0% +what you have to do is seven stages of +processing on the web request but what + + align:start position:0% +processing on the web request but what + + + align:start position:0% +processing on the web request but what +you do with the processor is you take a + + align:start position:0% +you do with the processor is you take a + + + align:start position:0% +you do with the processor is you take a +request and you process it for three you + + align:start position:0% +request and you process it for three you + + + align:start position:0% +request and you process it for three you +know three of those stages and then you + + align:start position:0% +know three of those stages and then you + + + align:start position:0% +know three of those stages and then you +decide to go to the next request and + + align:start position:0% +decide to go to the next request and + + + align:start position:0% +decide to go to the next request and +process it three stages and you go to + + align:start position:0% +process it three stages and you go to + + + align:start position:0% +process it three stages and you go to +the next request and process it three + + align:start position:0% +the next request and process it three + + + align:start position:0% +the next request and process it three +stages so no request gets complete your + + align:start position:0% +stages so no request gets complete your + + + align:start position:0% +stages so no request gets complete your +CPU is 100% utilized but the throughput + + align:start position:0% +CPU is 100% utilized but the throughput + + + align:start position:0% +CPU is 100% utilized but the throughput +is essentially diving down to zero + + align:start position:0% +is essentially diving down to zero + + + align:start position:0% +is essentially diving down to zero +that's another situation where it's + + align:start position:0% +that's another situation where it's + + + align:start position:0% +that's another situation where it's +where you have congestion collapse but + + align:start position:0% +where you have congestion collapse but + + + align:start position:0% +where you have congestion collapse but +when it occurs in networks it's um it + + align:start position:0% +when it occurs in networks it's um it + + + align:start position:0% +when it occurs in networks it's um it +turns out it's more complicated to solve + + align:start position:0% +turns out it's more complicated to solve + + + align:start position:0% +turns out it's more complicated to solve +in networks because of these reasons um + + align:start position:0% +in networks because of these reasons um + + + align:start position:0% +in networks because of these reasons um +that I outlined + + align:start position:0% + + + + align:start position:0% + +before so it's has everyone seen + + align:start position:0% + + + + align:start position:0% + +this so let's go back to our problem our + + align:start position:0% +this so let's go back to our problem our + + + align:start position:0% +this so let's go back to our problem our +goal is to want we want this thing to be + + align:start position:0% +goal is to want we want this thing to be + + + align:start position:0% +goal is to want we want this thing to be +true the the aggregate offered load to + + align:start position:0% +true the the aggregate offered load to + + + align:start position:0% +true the the aggregate offered load to +be smaller than the capacity of a link + + align:start position:0% +be smaller than the capacity of a link + + + align:start position:0% +be smaller than the capacity of a link +for every Link in the + + align:start position:0% +for every Link in the + + + align:start position:0% +for every Link in the +system but it turns out that's not + + align:start position:0% +system but it turns out that's not + + + align:start position:0% +system but it turns out that's not +enough of a specification because there + + align:start position:0% +enough of a specification because there + + + align:start position:0% +enough of a specification because there +are many ways to achieve this goal for + + align:start position:0% +are many ways to achieve this goal for + + + align:start position:0% +are many ways to achieve this goal for +example a really cheesy way to achieve + + align:start position:0% +example a really cheesy way to achieve + + + align:start position:0% +example a really cheesy way to achieve +this goal is to make sure that everybody + + align:start position:0% +this goal is to make sure that everybody + + + align:start position:0% +this goal is to make sure that everybody +remains quiet nobody sends any packets + + align:start position:0% +remains quiet nobody sends any packets + + + align:start position:0% +remains quiet nobody sends any packets +you're going to get that to be true so + + align:start position:0% +you're going to get that to be true so + + + align:start position:0% +you're going to get that to be true so +we're going to actually have to define + + align:start position:0% +we're going to actually have to define + + + align:start position:0% +we're going to actually have to define +the problem a little bit more concretely + + align:start position:0% +the problem a little bit more concretely + + + align:start position:0% +the problem a little bit more concretely +let's first Define what we don't + + align:start position:0% +let's first Define what we don't + + + align:start position:0% +let's first Define what we don't +want the first thing we don't want is + + align:start position:0% +want the first thing we don't want is + + + align:start position:0% +want the first thing we don't want is +congestion + + align:start position:0% +congestion + + + align:start position:0% +congestion +collapse so any solution should have the + + align:start position:0% +collapse so any solution should have the + + + align:start position:0% +collapse so any solution should have the +property that it never gets into that + + align:start position:0% +property that it never gets into that + + + align:start position:0% +property that it never gets into that +situation and in fact good congestion + + align:start position:0% +situation and in fact good congestion + + + align:start position:0% +situation and in fact good congestion +control schemes operate at the left knee + + align:start position:0% +control schemes operate at the left knee + + + align:start position:0% +control schemes operate at the left knee +of the curve but we're not going to get + + align:start position:0% +of the curve but we're not going to get + + + align:start position:0% +of the curve but we're not going to get +too hung up on that because if we + + align:start position:0% +too hung up on that because if we + + + align:start position:0% +too hung up on that because if we +operate a little bit in the middle we're + + align:start position:0% +operate a little bit in the middle we're + + + align:start position:0% +operate a little bit in the middle we're +going to say that's fine because that'll + + align:start position:0% +going to say that's fine because that'll + + + align:start position:0% +going to say that's fine because that'll +turn out to be good enough in practice + + align:start position:0% +turn out to be good enough in practice + + + align:start position:0% +turn out to be good enough in practice +and often is just fine and the result + + align:start position:0% +and often is just fine and the result + + + align:start position:0% +and often is just fine and the result +the additional complexity that you might + + align:start position:0% +the additional complexity that you might + + + align:start position:0% +the additional complexity that you might +have to breing to bear on a solution to + + align:start position:0% +have to breing to bear on a solution to + + + align:start position:0% +have to breing to bear on a solution to +work nearer the knee might not be worth + + align:start position:0% +work nearer the knee might not be worth + + + align:start position:0% +work nearer the knee might not be worth +it okay but really we're going to worry + + align:start position:0% +it okay but really we're going to worry + + + align:start position:0% +it okay but really we're going to worry +about not getting falling off the cliff + + align:start position:0% +about not getting falling off the cliff + + + align:start position:0% +about not getting falling off the cliff +at the right Edge + + align:start position:0% +at the right Edge + + + align:start position:0% +at the right Edge +okay then having done that we're going + + align:start position:0% +okay then having done that we're going + + + align:start position:0% +okay then having done that we're going +to want reasonable + + align:start position:0% + + + + align:start position:0% + +utilization also called + + align:start position:0% +utilization also called + + + align:start position:0% +utilization also called +efficiency so what this says is if you + + align:start position:0% +efficiency so what this says is if you + + + align:start position:0% +efficiency so what this says is if you +have a network link that's often + + align:start position:0% +have a network link that's often + + + align:start position:0% +have a network link that's often +congested you want to make sure that + + align:start position:0% +congested you want to make sure that + + + align:start position:0% +congested you want to make sure that +that link isn't underutilized when there + + align:start position:0% +that link isn't underutilized when there + + + align:start position:0% +that link isn't underutilized when there +is offered load to Rong so for example + + align:start position:0% +is offered load to Rong so for example + + + align:start position:0% +is offered load to Rong so for example +you know people are presenting 100 + + align:start position:0% +you know people are presenting 100 + + + align:start position:0% +you know people are presenting 100 +kilobits per second of load and the + + align:start position:0% +kilobits per second of load and the + + + align:start position:0% +kilobits per second of load and the +network link has that capacity you don't + + align:start position:0% +network link has that capacity you don't + + + align:start position:0% +network link has that capacity you don't +want them to just be you know you want + + align:start position:0% +want them to just be you know you want + + + align:start position:0% +want them to just be you know you want +that to be used you don't want to shut + + align:start position:0% +that to be used you don't want to shut + + + align:start position:0% +that to be used you don't want to shut +them up too much so what this really + + align:start position:0% +them up too much so what this really + + + align:start position:0% +them up too much so what this really +means in practice is that um if you have + + align:start position:0% +means in practice is that um if you have + + + align:start position:0% +means in practice is that um if you have +slowed down and excess capacity has + + align:start position:0% +slowed down and excess capacity has + + + align:start position:0% +slowed down and excess capacity has +presented itself then you have to make + + align:start position:0% +presented itself then you have to make + + + align:start position:0% +presented itself then you have to make +sure that you speed up so that's that's + + align:start position:0% +sure that you speed up so that's that's + + + align:start position:0% +sure that you speed up so that's that's +what it means in + + align:start position:0% +what it means in + + + align:start position:0% +what it means in +practice and the third part of the + + align:start position:0% +practice and the third part of the + + + align:start position:0% +practice and the third part of the +solution is that is there's another + + align:start position:0% +solution is that is there's another + + + align:start position:0% +solution is that is there's another +thing we need to specify and the reason + + align:start position:0% +thing we need to specify and the reason + + + align:start position:0% +thing we need to specify and the reason +is that you can solve these two + + align:start position:0% +is that you can solve these two + + + align:start position:0% +is that you can solve these two +Problems by making sure that only one + + align:start position:0% +Problems by making sure that only one + + + align:start position:0% +Problems by making sure that only one +person transmits in the network okay if + + align:start position:0% +person transmits in the network okay if + + + align:start position:0% +person transmits in the network okay if +that person has enough offered load then + + align:start position:0% +that person has enough offered load then + + + align:start position:0% +that person has enough offered load then +you just cut everybody out altogether + + align:start position:0% +you just cut everybody out altogether + + + align:start position:0% +you just cut everybody out altogether +and essentially you know allocate that + + align:start position:0% +and essentially you know allocate that + + + align:start position:0% +and essentially you know allocate that +resource in sort of a monopolistic + + align:start position:0% +resource in sort of a monopolistic + + + align:start position:0% +resource in sort of a monopolistic +fashion to this one + + align:start position:0% +fashion to this one + + + align:start position:0% +fashion to this one +person that's not going to be very good + + align:start position:0% +person that's not going to be very good + + + align:start position:0% +person that's not going to be very good +because we would like our Network to be + + align:start position:0% +because we would like our Network to be + + + align:start position:0% +because we would like our Network to be +used by a number of people so I'm going + + align:start position:0% +used by a number of people so I'm going + + + align:start position:0% +used by a number of people so I'm going +to use um Define that as a goal of any + + align:start position:0% +to use um Define that as a goal of any + + + align:start position:0% +to use um Define that as a goal of any +good solution I'm going to call it + + align:start position:0% +good solution I'm going to call it + + + align:start position:0% +good solution I'm going to call it +Equitable allocation + + align:start position:0% + + + + align:start position:0% + +I'm not going to say fair allocation + + align:start position:0% +I'm not going to say fair allocation + + + align:start position:0% +I'm not going to say fair allocation +because Fair suggests that it's really a + + align:start position:0% +because Fair suggests that it's really a + + + align:start position:0% +because Fair suggests that it's really a +strong condition that every connection + + align:start position:0% +strong condition that every connection + + + align:start position:0% +strong condition that every connection +gets you know roughly equal throughput + + align:start position:0% +gets you know roughly equal throughput + + + align:start position:0% +gets you know roughly equal throughput +if it has that offered load we're I mean + + align:start position:0% +if it has that offered load we're I mean + + + align:start position:0% +if it has that offered load we're I mean +that turns out to be a I think in my + + align:start position:0% +that turns out to be a I think in my + + + align:start position:0% +that turns out to be a I think in my +opinion achieving perfect fairness to + + align:start position:0% +opinion achieving perfect fairness to + + + align:start position:0% +opinion achieving perfect fairness to +TCP connections is just a waste of time + + align:start position:0% +TCP connections is just a waste of time + + + align:start position:0% +TCP connections is just a waste of time +um because in reality fairness is + + align:start position:0% +um because in reality fairness is + + + align:start position:0% +um because in reality fairness is +governed by who's paying what for access + + align:start position:0% +governed by who's paying what for access + + + align:start position:0% +governed by who's paying what for access +to the network so we're not going to get + + align:start position:0% +to the network so we're not going to get + + + align:start position:0% +to the network so we're not going to get +into that in this class but we're going + + align:start position:0% +into that in this class but we're going + + + align:start position:0% +into that in this class but we're going +to want solutions that don't eliminate + + align:start position:0% +to want solutions that don't eliminate + + + align:start position:0% +to want solutions that don't eliminate +Don't Starve certain connections out and + + align:start position:0% +Don't Starve certain connections out and + + + align:start position:0% +Don't Starve certain connections out and +we'll be happy with that because that'll + + align:start position:0% +we'll be happy with that because that'll + + + align:start position:0% +we'll be happy with that because that'll +turn out to work out just fine in + + align:start position:0% + + + + align:start position:0% + +practice now to understand this problem + + align:start position:0% +practice now to understand this problem + + + align:start position:0% +practice now to understand this problem +a little bit better we're going to want + + align:start position:0% +a little bit better we're going to want + + + align:start position:0% +a little bit better we're going to want +to understand this um requirement a + + align:start position:0% +to understand this um requirement a + + + align:start position:0% +to understand this um requirement a +little bit more + + align:start position:0% +little bit more + + + align:start position:0% +little bit more +closely and the problem is that this + + align:start position:0% +closely and the problem is that this + + + align:start position:0% +closely and the problem is that this +requirement of the aggregate rate + + align:start position:0% +requirement of the aggregate rate + + + align:start position:0% +requirement of the aggregate rate +offered by the specified by the offered + + align:start position:0% +offered by the specified by the offered + + + align:start position:0% +offered by the specified by the offered +load being smaller than the link + + align:start position:0% +load being smaller than the link + + + align:start position:0% +load being smaller than the link +capacity is a condition on rates it just + + align:start position:0% +capacity is a condition on rates it just + + + align:start position:0% +capacity is a condition on rates it just +says you know the offered load is 100 + + align:start position:0% +says you know the offered load is 100 + + + align:start position:0% +says you know the offered load is 100 +kilobit per second the capacity is 150 + + align:start position:0% +kilobit per second the capacity is 150 + + + align:start position:0% +kilobit per second the capacity is 150 +kilobits per second that means it's + + align:start position:0% +kilobits per second that means it's + + + align:start position:0% +kilobits per second that means it's +fine the problem is that you have to + + align:start position:0% +fine the problem is that you have to + + + align:start position:0% +fine the problem is that you have to +really ask offered load over what time + + align:start position:0% +really ask offered load over what time + + + align:start position:0% +really ask offered load over what time +scale for example if the overall offered + + align:start position:0% +scale for example if the overall offered + + + align:start position:0% +scale for example if the overall offered +load on your on your network is um let's + + align:start position:0% +load on your on your network is um let's + + + align:start position:0% +load on your on your network is um let's +say a megabit per second and the + + align:start position:0% +say a megabit per second and the + + + align:start position:0% +say a megabit per second and the +capacity of the network is half a + + align:start position:0% +capacity of the network is half a + + + align:start position:0% +capacity of the network is half a +megabit per second and that condition + + align:start position:0% +megabit per second and that condition + + + align:start position:0% +megabit per second and that condition +lasts for a whole day okay so for a + + align:start position:0% +lasts for a whole day okay so for a + + + align:start position:0% +lasts for a whole day okay so for a +whole day you know your website got + + align:start position:0% +whole day you know your website got + + + align:start position:0% +whole day you know your website got +slash dotted take that example and you + + align:start position:0% +slash dotted take that example and you + + + align:start position:0% +slash dotted take that example and you +know you have this little wimpy Access + + align:start position:0% +know you have this little wimpy Access + + + align:start position:0% +know you have this little wimpy Access +Link through your DSL line and you know + + align:start position:0% +Link through your DSL line and you know + + + align:start position:0% +Link through your DSL line and you know +10 times that much in terms of requests + + align:start position:0% +10 times that much in terms of requests + + + align:start position:0% +10 times that much in terms of requests +are being presented to your website and + + align:start position:0% +are being presented to your website and + + + align:start position:0% +are being presented to your website and +it losts for the whole + + align:start position:0% +it losts for the whole + + + align:start position:0% +it losts for the whole +day guess what nothing we're going to + + align:start position:0% +day guess what nothing we're going to + + + align:start position:0% +day guess what nothing we're going to +talk about is really going to solve that + + align:start position:0% +talk about is really going to solve that + + + align:start position:0% +talk about is really going to solve that +problem in a way that allows every + + align:start position:0% +problem in a way that allows every + + + align:start position:0% +problem in a way that allows every +request to get through in a timely + + align:start position:0% +request to get through in a timely + + + align:start position:0% +request to get through in a timely +fashion at some point you throw up your + + align:start position:0% +fashion at some point you throw up your + + + align:start position:0% +fashion at some point you throw up your +hands and say you know what if I if I + + align:start position:0% +hands and say you know what if I if I + + + align:start position:0% +hands and say you know what if I if I +want my website to be popular I better + + align:start position:0% +want my website to be popular I better + + + align:start position:0% +want my website to be popular I better +put it on a you know me you know on a 10 + + align:start position:0% +put it on a you know me you know on a 10 + + + align:start position:0% +put it on a you know me you know on a 10 +megabit per second Network and make sure + + align:start position:0% +megabit per second Network and make sure + + + align:start position:0% +megabit per second Network and make sure +that everybody can gain access to it + + align:start position:0% +that everybody can gain access to it + + + align:start position:0% +that everybody can gain access to it +okay so you're not really going to solve + + align:start position:0% +okay so you're not really going to solve + + + align:start position:0% +okay so you're not really going to solve +the problem at that time scale on the + + align:start position:0% +the problem at that time scale on the + + + align:start position:0% +the problem at that time scale on the +other hand if you know your website + + align:start position:0% +other hand if you know your website + + + align:start position:0% +other hand if you know your website +suddenly got a little bit popular and um + + align:start position:0% +suddenly got a little bit popular and um + + + align:start position:0% +suddenly got a little bit popular and um +you know a bunch of connections came to + + align:start position:0% +you know a bunch of connections came to + + + align:start position:0% +you know a bunch of connections came to +it but it didn't last for a whole day + + align:start position:0% +it but it didn't last for a whole day + + + align:start position:0% +it but it didn't last for a whole day +but it lasted for you know a few seconds + + align:start position:0% +but it lasted for you know a few seconds + + + align:start position:0% +but it lasted for you know a few seconds +we're going to we're going to want to + + align:start position:0% +we're going to we're going to want to + + + align:start position:0% +we're going to we're going to want to +deal with that + + align:start position:0% +deal with that + + + align:start position:0% +deal with that +problem so if you think about it there + + align:start position:0% +problem so if you think about it there + + + align:start position:0% +problem so if you think about it there +are three time scales um that matter + + align:start position:0% +are three time scales um that matter + + + align:start position:0% +are three time scales um that matter +here and these time scales arise in a + + align:start position:0% +here and these time scales arise in a + + + align:start position:0% +here and these time scales arise in a +natural way because of this network + + align:start position:0% +natural way because of this network + + + align:start position:0% +natural way because of this network +where congestion happens here and then + + align:start position:0% +where congestion happens here and then + + + align:start position:0% +where congestion happens here and then +we're going to have some feedback go + + align:start position:0% +we're going to have some feedback go + + + align:start position:0% +we're going to have some feedback go +back to the cender and the cender + + align:start position:0% +back to the cender and the cender + + + align:start position:0% +back to the cender and the cender +exercises control and the only time + + align:start position:0% +exercises control and the only time + + + align:start position:0% +exercises control and the only time +scale in this whole system is the round + + align:start position:0% +scale in this whole system is the round + + + align:start position:0% +scale in this whole system is the round +trip time because that's the time scale + + align:start position:0% +trip time because that's the time scale + + + align:start position:0% +trip time because that's the time scale +the order of magnitude of the time scale + + align:start position:0% +the order of magnitude of the time scale + + + align:start position:0% +the order of magnitude of the time scale +around which any feedback is going to + + align:start position:0% +around which any feedback is going to + + + align:start position:0% +around which any feedback is going to +come to + + align:start position:0% +come to + + + align:start position:0% +come to +us so there are three time scales of + + align:start position:0% +us so there are three time scales of + + + align:start position:0% +us so there are three time scales of +Interest there's smaller than one round + + align:start position:0% +Interest there's smaller than one round + + + align:start position:0% +Interest there's smaller than one round +trip time which says this inequality is + + align:start position:0% +trip time which says this inequality is + + + align:start position:0% +trip time which says this inequality is +not satisfied for really small periods + + align:start position:0% +not satisfied for really small periods + + + align:start position:0% +not satisfied for really small periods +of time where you know there's a little + + align:start position:0% +of time where you know there's a little + + + align:start position:0% +of time where you know there's a little +spurt a burst it's also called a burst a + + align:start position:0% +spurt a burst it's also called a burst a + + + align:start position:0% +spurt a burst it's also called a burst a +burst packets show up and then they you + + align:start position:0% +burst packets show up and then they you + + + align:start position:0% +burst packets show up and then they you +know you have to handle them but then + + align:start position:0% +know you have to handle them but then + + + align:start position:0% +know you have to handle them but then +after that things get to be fine so + + align:start position:0% +after that things get to be fine so + + + align:start position:0% +after that things get to be fine so +they're smaller than one round trip time + + align:start position:0% +they're smaller than one round trip time + + + align:start position:0% +they're smaller than one round trip time +so this is summation Li is greater than + + align:start position:0% +so this is summation Li is greater than + + + align:start position:0% +so this is summation Li is greater than +C I.E the network is congested it could + + align:start position:0% +C I.E the network is congested it could + + + align:start position:0% +C I.E the network is congested it could +be congested at really short durations + + align:start position:0% +be congested at really short durations + + + align:start position:0% +be congested at really short durations +of smaller than a roundt trip time it + + align:start position:0% +of smaller than a roundt trip time it + + + align:start position:0% +of smaller than a roundt trip time it +could be between one and I'm going to + + align:start position:0% +could be between one and I'm going to + + + align:start position:0% +could be between one and I'm going to +say 100 roundt trip + + align:start position:0% + + + + align:start position:0% + +times and just for real numbers a roundt + + align:start position:0% +times and just for real numbers a roundt + + + align:start position:0% +times and just for real numbers a roundt +trip time is typically order of 100 + + align:start position:0% +trip time is typically order of 100 + + + align:start position:0% +trip time is typically order of 100 +millisecond + + align:start position:0% +millisecond + + + align:start position:0% +millisecond +so we're talking here of less than 100 + + align:start position:0% +so we're talking here of less than 100 + + + align:start position:0% +so we're talking here of less than 100 +milliseconds um up to about 10 seconds + + align:start position:0% +milliseconds um up to about 10 seconds + + + align:start position:0% +milliseconds um up to about 10 seconds +and then bigger than this number okay + + align:start position:0% +and then bigger than this number okay + + + align:start position:0% +and then bigger than this number okay +bigger than + + align:start position:0% +bigger than + + + align:start position:0% +bigger than +100 and these are all orders of + + align:start position:0% +100 and these are all orders of + + + align:start position:0% +100 and these are all orders of +magnitude I mean it could be 500 rtts + + align:start position:0% +magnitude I mean it could be 500 rtts + + + align:start position:0% +magnitude I mean it could be 500 rtts +okay those are the three time scales to + + align:start position:0% +okay those are the three time scales to + + + align:start position:0% +okay those are the three time scales to +worry + + align:start position:0% + + + + align:start position:0% + +about when congestion happens at less + + align:start position:0% +about when congestion happens at less + + + align:start position:0% +about when congestion happens at less +than one round trip time we're going to + + align:start position:0% +than one round trip time we're going to + + + align:start position:0% +than one round trip time we're going to +solve that problem using this technique + + align:start position:0% +solve that problem using this technique + + + align:start position:0% +solve that problem using this technique +we're going to solve it using buff + + align:start position:0% +we're going to solve it using buff + + + align:start position:0% +we're going to solve it using buff +offing okay and that's the plan the + + align:start position:0% +offing okay and that's the plan the + + + align:start position:0% +offing okay and that's the plan the +reason is that it's really hard to do + + align:start position:0% +reason is that it's really hard to do + + + align:start position:0% +reason is that it's really hard to do +anything else because the congestion + + align:start position:0% +anything else because the congestion + + + align:start position:0% +anything else because the congestion +lost for a certain burst and by the time + + align:start position:0% +lost for a certain burst and by the time + + + align:start position:0% +lost for a certain burst and by the time +you figure that out and tell the center + + align:start position:0% +you figure that out and tell the center + + + align:start position:0% +you figure that out and tell the center +of that the congestion has gone away + + align:start position:0% +of that the congestion has gone away + + + align:start position:0% +of that the congestion has gone away +which means telling the center that the + + align:start position:0% +which means telling the center that the + + + align:start position:0% +which means telling the center that the +congestion has gone away was sort of a + + align:start position:0% +congestion has gone away was sort of a + + + align:start position:0% +congestion has gone away was sort of a +waste because the center would have + + align:start position:0% +waste because the center would have + + + align:start position:0% +waste because the center would have +slowed down but the congestion anyway + + align:start position:0% +slowed down but the congestion anyway + + + align:start position:0% +slowed down but the congestion anyway +went away so why bother right why did + + align:start position:0% +went away so why bother right why did + + + align:start position:0% +went away so why bother right why did +you tell the center that so that's the + + align:start position:0% +you tell the center that so that's the + + + align:start position:0% +you tell the center that so that's the +kind of thing you want to solve at the + + align:start position:0% +kind of thing you want to solve at the + + + align:start position:0% +kind of thing you want to solve at the +network layer inside the switches and + + align:start position:0% +network layer inside the switches and + + + align:start position:0% +network layer inside the switches and +that's going to be done using + + align:start position:0% + + + + align:start position:0% + +buffering and that sort of suggests and + + align:start position:0% +buffering and that sort of suggests and + + + align:start position:0% +buffering and that sort of suggests and +I'm there's a bit of slight of hand here + + align:start position:0% +I'm there's a bit of slight of hand here + + + align:start position:0% +I'm there's a bit of slight of hand here +and we're not going to talk about what's + + align:start position:0% +and we're not going to talk about what's + + + align:start position:0% +and we're not going to talk about what's +uh you know why there's a slight of hand + + align:start position:0% +uh you know why there's a slight of hand + + + align:start position:0% +uh you know why there's a slight of hand +but this really suggests that if you + + align:start position:0% +but this really suggests that if you + + + align:start position:0% +but this really suggests that if you +design a network and you want to put + + align:start position:0% +design a network and you want to put + + + align:start position:0% +design a network and you want to put +buffering in the network you better not + + align:start position:0% +buffering in the network you better not + + + align:start position:0% +buffering in the network you better not +put more than about a roundt trip times + + align:start position:0% +put more than about a roundt trip times + + + align:start position:0% +put more than about a roundt trip times +worth of buffering in that switch if you + + align:start position:0% +worth of buffering in that switch if you + + + align:start position:0% +worth of buffering in that switch if you +put buffering longer than a roundt trip + + align:start position:0% +put buffering longer than a roundt trip + + + align:start position:0% +put buffering longer than a roundt trip +time you're getting in the way of things + + align:start position:0% +time you're getting in the way of things + + + align:start position:0% +time you're getting in the way of things +that the higher layers are going to be + + align:start position:0% +that the higher layers are going to be + + + align:start position:0% +that the higher layers are going to be +doing and it's going to confuse them in + + align:start position:0% +doing and it's going to confuse them in + + + align:start position:0% +doing and it's going to confuse them in +fact Sam showed this picture of like + + align:start position:0% +fact Sam showed this picture of like + + + align:start position:0% +fact Sam showed this picture of like +these roundt trip times varying a lot + + align:start position:0% +these roundt trip times varying a lot + + + align:start position:0% +these roundt trip times varying a lot +between you know yes last lecture where + + align:start position:0% +between you know yes last lecture where + + + align:start position:0% +between you know yes last lecture where +the mean was 2 and a half seconds and + + align:start position:0% +the mean was 2 and a half seconds and + + + align:start position:0% +the mean was 2 and a half seconds and +the standard deviation was one and a + + align:start position:0% +the standard deviation was one and a + + + align:start position:0% +the standard deviation was one and a +half second um that was not a madeup + + align:start position:0% +half second um that was not a madeup + + + align:start position:0% +half second um that was not a madeup +picture that was from a real wireless + + align:start position:0% +picture that was from a real wireless + + + align:start position:0% +picture that was from a real wireless +network where the designers had + + align:start position:0% +network where the designers had + + + align:start position:0% +network where the designers had +incorrectly put a huge amount of + + align:start position:0% +incorrectly put a huge amount of + + + align:start position:0% +incorrectly put a huge amount of +buffering and this is extremely common + + align:start position:0% +buffering and this is extremely common + + + align:start position:0% +buffering and this is extremely common +almost every modem that you buy um + + align:start position:0% +almost every modem that you buy um + + + align:start position:0% +almost every modem that you buy um +cellular modem or phone modem has way + + align:start position:0% +cellular modem or phone modem has way + + + align:start position:0% +cellular modem or phone modem has way +too much buffering in it and the only + + align:start position:0% +too much buffering in it and the only + + + align:start position:0% +too much buffering in it and the only +thing that happens is these cues build + + align:start position:0% +thing that happens is these cues build + + + align:start position:0% +thing that happens is these cues build +up it's just a mistake + + align:start position:0% +up it's just a mistake + + + align:start position:0% +up it's just a mistake +so less than one roundt trip time deal + + align:start position:0% +so less than one roundt trip time deal + + + align:start position:0% +so less than one roundt trip time deal +with it using + + align:start position:0% + + + + align:start position:0% + +buffering between one and 100 roundt + + align:start position:0% +buffering between one and 100 roundt + + + align:start position:0% +buffering between one and 100 roundt +trip times we're going to deal with that + + align:start position:0% +trip times we're going to deal with that + + + align:start position:0% +trip times we're going to deal with that +problem um using the techniques that + + align:start position:0% +problem um using the techniques that + + + align:start position:0% +problem um using the techniques that +we're going to talk about um today the + + align:start position:0% +we're going to talk about um today the + + + align:start position:0% +we're going to talk about um today the +next five or 10 minutes and then bigger + + align:start position:0% +next five or 10 minutes and then bigger + + + align:start position:0% +next five or 10 minutes and then bigger +than 100 round trip times or a thousand + + align:start position:0% +than 100 round trip times or a thousand + + + align:start position:0% +than 100 round trip times or a thousand +roundt trip times are things where + + align:start position:0% +roundt trip times are things where + + + align:start position:0% +roundt trip times are things where +congestion is just sort of persistent + + align:start position:0% +congestion is just sort of persistent + + + align:start position:0% +congestion is just sort of persistent +for you know many many many seconds or + + align:start position:0% +for you know many many many seconds or + + + align:start position:0% +for you know many many many seconds or +minutes or hours and there are ways of + + align:start position:0% +minutes or hours and there are ways of + + + align:start position:0% +minutes or hours and there are ways of +dealing with this problem + + align:start position:0% +dealing with this problem + + + align:start position:0% +dealing with this problem +um you know using protocols and using + + align:start position:0% +um you know using protocols and using + + + align:start position:0% +um you know using protocols and using +algorithms But ultimately you have to + + align:start position:0% +algorithms But ultimately you have to + + + align:start position:0% +algorithms But ultimately you have to +ask yourself whether you're really + + align:start position:0% +ask yourself whether you're really + + + align:start position:0% +ask yourself whether you're really +underprovision and you really ought to + + align:start position:0% +underprovision and you really ought to + + + align:start position:0% +underprovision and you really ought to +be buying or provisioning your network + + align:start position:0% +be buying or provisioning your network + + + align:start position:0% +be buying or provisioning your network +to be higher maybe put your server on a + + align:start position:0% +to be higher maybe put your server on a + + + align:start position:0% +to be higher maybe put your server on a +different network that has higher + + align:start position:0% +different network that has higher + + + align:start position:0% +different network that has higher +capacity and these are longer time scale + + align:start position:0% +capacity and these are longer time scale + + + align:start position:0% +capacity and these are longer time scale +congestion effects for which uh + + align:start position:0% +congestion effects for which uh + + + align:start position:0% +congestion effects for which uh +decisions based on um you know um + + align:start position:0% +decisions based on um you know um + + + align:start position:0% +decisions based on um you know um +provisioning have to probably come to + + align:start position:0% +provisioning have to probably come to + + + align:start position:0% +provisioning have to probably come to +play in solving um the problem + + align:start position:0% + + + + align:start position:0% + +so provisioning is certainly an + + align:start position:0% +so provisioning is certainly an + + + align:start position:0% +so provisioning is certainly an +important problem and when you have + + align:start position:0% +important problem and when you have + + + align:start position:0% +important problem and when you have +congestion lasting over really long + + align:start position:0% +congestion lasting over really long + + + align:start position:0% +congestion lasting over really long +periods of time that might be the right + + align:start position:0% +periods of time that might be the right + + + align:start position:0% +periods of time that might be the right +solution but for everything + + align:start position:0% + + + + align:start position:0% + +else there's solutions that are much + + align:start position:0% +else there's solutions that are much + + + align:start position:0% +else there's solutions that are much +easier to understand or at least as far + + align:start position:0% +easier to understand or at least as far + + + align:start position:0% +easier to understand or at least as far +as using the tools that we've built so + + align:start position:0% +as using the tools that we've built so + + + align:start position:0% +as using the tools that we've built so +far in + + align:start position:0% +far in + + + align:start position:0% +far in +6033 so the first component of the + + align:start position:0% +6033 so the first component of the + + + align:start position:0% +6033 so the first component of the +solution is some + + align:start position:0% +solution is some + + + align:start position:0% +solution is some +buffering to deal with the smaller than + + align:start position:0% +buffering to deal with the smaller than + + + align:start position:0% +buffering to deal with the smaller than +one roundt trip time + + align:start position:0% + + + + align:start position:0% + +situation and then when your buffers + + align:start position:0% +situation and then when your buffers + + + align:start position:0% +situation and then when your buffers +start getting filled up um and + + align:start position:0% +start getting filled up um and + + + align:start position:0% +start getting filled up um and +congestion is lasting for more than + + align:start position:0% +congestion is lasting for more than + + + align:start position:0% +congestion is lasting for more than +around trip time then your buffers start + + align:start position:0% +around trip time then your buffers start + + + align:start position:0% +around trip time then your buffers start +getting filled up at that point you're + + align:start position:0% +getting filled up at that point you're + + + align:start position:0% +getting filled up at that point you're +starting to see congestion that can't be + + align:start position:0% +starting to see congestion that can't be + + + align:start position:0% +starting to see congestion that can't be +hidden by pure + + align:start position:0% +hidden by pure + + + align:start position:0% +hidden by pure +buffering um and they can't be hidden + + align:start position:0% +buffering um and they can't be hidden + + + align:start position:0% +buffering um and they can't be hidden +because cues are building up and that's + + align:start position:0% +because cues are building up and that's + + + align:start position:0% +because cues are building up and that's +causing increased delay to show up at + + align:start position:0% +causing increased delay to show up at + + + align:start position:0% +causing increased delay to show up at +the center and perhaps packets may start + + align:start position:0% +the center and perhaps packets may start + + + align:start position:0% +the center and perhaps packets may start +getting dropped when the queue overflows + + align:start position:0% +getting dropped when the queue overflows + + + align:start position:0% +getting dropped when the queue overflows +and that causes is the sender to re to + + align:start position:0% +and that causes is the sender to re to + + + align:start position:0% +and that causes is the sender to re to +you know observe this congestion which + + align:start position:0% +you know observe this congestion which + + + align:start position:0% +you know observe this congestion which +means that what we want is a plan by + + align:start position:0% +means that what we want is a plan by + + + align:start position:0% +means that what we want is a plan by +which when congestion happens lasting + + align:start position:0% +which when congestion happens lasting + + + align:start position:0% +which when congestion happens lasting +over um you know half around trip time + + align:start position:0% +over um you know half around trip time + + + align:start position:0% +over um you know half around trip time +or close to around trip time we're going + + align:start position:0% +or close to around trip time we're going + + + align:start position:0% +or close to around trip time we're going +to want to provide feedback to the + + align:start position:0% +to want to provide feedback to the + + + align:start position:0% +to want to provide feedback to the +sender + + align:start position:0% +sender + + + align:start position:0% +sender +okay and then the third part of our + + align:start position:0% +okay and then the third part of our + + + align:start position:0% +okay and then the third part of our +solution is when the sender gets this + + align:start position:0% + + + + align:start position:0% + +feedback what it's going to do is + + align:start position:0% +feedback what it's going to do is + + + align:start position:0% +feedback what it's going to do is +adapt and the way it's going to adapt is + + align:start position:0% +adapt and the way it's going to adapt is + + + align:start position:0% +adapt and the way it's going to adapt is +actually easy it's going to do it by + + align:start position:0% +actually easy it's going to do it by + + + align:start position:0% +actually easy it's going to do it by +modifying the rate at which it sends + + align:start position:0% +modifying the rate at which it sends + + + align:start position:0% +modifying the rate at which it sends +packets and that's what I set up the + + align:start position:0% +packets and that's what I set up the + + + align:start position:0% +packets and that's what I set up the +center sends at rate RI um what you do + + align:start position:0% +center sends at rate RI um what you do + + + align:start position:0% +center sends at rate RI um what you do +is you change the + + align:start position:0% +is you change the + + + align:start position:0% +is you change the +rate or the speed at which the sender + + align:start position:0% +rate or the speed at which the sender + + + align:start position:0% +rate or the speed at which the sender +sends so there's two things we have to + + align:start position:0% +sends so there's two things we have to + + + align:start position:0% +sends so there's two things we have to +figure out one is how does the network + + align:start position:0% +figure out one is how does the network + + + align:start position:0% +figure out one is how does the network +give feedback and the second is what + + align:start position:0% +give feedback and the second is what + + + align:start position:0% +give feedback and the second is what +exactly is going on with changing the + + align:start position:0% +exactly is going on with changing the + + + align:start position:0% +exactly is going on with changing the +speed how does it + + align:start position:0% +speed how does it + + + align:start position:0% +speed how does it +work there are many ways to give + + align:start position:0% +work there are many ways to give + + + align:start position:0% +work there are many ways to give +feedback and the OB sort of the first + + align:start position:0% +feedback and the OB sort of the first + + + align:start position:0% +feedback and the OB sort of the first +order business things you might think + + align:start position:0% +order business things you might think + + + align:start position:0% +order business things you might think +about are well when the queue starts to + + align:start position:0% +about are well when the queue starts to + + + align:start position:0% +about are well when the queue starts to +fill up I'll send a message to the + + align:start position:0% +fill up I'll send a message to the + + + align:start position:0% +fill up I'll send a message to the +sender or I'll set a bit in the packet + + align:start position:0% +sender or I'll set a bit in the packet + + + align:start position:0% +sender or I'll set a bit in the packet +header and it'll get to the end point + + align:start position:0% +header and it'll get to the end point + + + align:start position:0% +header and it'll get to the end point +and it'll send this feedback back and + + align:start position:0% +and it'll send this feedback back and + + + align:start position:0% +and it'll send this feedback back and +all of any variant that you can think of + + align:start position:0% +all of any variant that you can think of + + + align:start position:0% +all of any variant that you can think of +in the next five or 10 minutes I can + + align:start position:0% +in the next five or 10 minutes I can + + + align:start position:0% +in the next five or 10 minutes I can +assure you has been thought of and + + align:start position:0% +assure you has been thought of and + + + align:start position:0% +assure you has been thought of and +investigated um and you might think of + + align:start position:0% +investigated um and you might think of + + + align:start position:0% +investigated um and you might think of +new ways of doing it which would be + + align:start position:0% +new ways of doing it which would be + + + align:start position:0% +new ways of doing it which would be +great I mean this is a topic of work + + align:start position:0% +great I mean this is a topic of work + + + align:start position:0% +great I mean this is a topic of work +active work people are working on this + + align:start position:0% +active work people are working on this + + + align:start position:0% +active work people are working on this +stuff still but my opinion is that the + + align:start position:0% +stuff still but my opinion is that the + + + align:start position:0% +stuff still but my opinion is that the +best way to solve this problem of + + align:start position:0% +best way to solve this problem of + + + align:start position:0% +best way to solve this problem of +feedback is the simplest possible thing + + align:start position:0% +feedback is the simplest possible thing + + + align:start position:0% +feedback is the simplest possible thing +you could think of the simplest + + align:start position:0% +you could think of the simplest + + + align:start position:0% +you could think of the simplest +technique that really works all the time + + align:start position:0% +technique that really works all the time + + + align:start position:0% +technique that really works all the time +is just drop the packet in particular if + + align:start position:0% +is just drop the packet in particular if + + + align:start position:0% +is just drop the packet in particular if +the que overflows it's going to get + + align:start position:0% +the que overflows it's going to get + + + align:start position:0% +the que overflows it's going to get +dropped anyway and that's a sign of + + align:start position:0% +dropped anyway and that's a sign of + + + align:start position:0% +dropped anyway and that's a sign of +congestion but if at any point in time + + align:start position:0% +congestion but if at any point in time + + + align:start position:0% +congestion but if at any point in time +you decide that the network is getting + + align:start position:0% +you decide that the network is getting + + + align:start position:0% +you decide that the network is getting +congested and remains so for a long + + align:start position:0% +congested and remains so for a long + + + align:start position:0% +congested and remains so for a long +enough time scale that you want the + + align:start position:0% +enough time scale that you want the + + + align:start position:0% +enough time scale that you want the +sender to react just throw the packet + + align:start position:0% +sender to react just throw the packet + + + align:start position:0% +sender to react just throw the packet +away the nice thing about throwing a + + align:start position:0% +away the nice thing about throwing a + + + align:start position:0% +away the nice thing about throwing a +packet away is that it's extremely hard + + align:start position:0% +packet away is that it's extremely hard + + + align:start position:0% +packet away is that it's extremely hard +to implement it wrong because when the + + align:start position:0% +to implement it wrong because when the + + + align:start position:0% +to implement it wrong because when the +queue overflows the packet is going to + + align:start position:0% +queue overflows the packet is going to + + + align:start position:0% +queue overflows the packet is going to +be dropped anyway so that feedback is + + align:start position:0% +be dropped anyway so that feedback is + + + align:start position:0% +be dropped anyway so that feedback is +going to be made available to the + + align:start position:0% + + + + align:start position:0% + +center so what we're going to assume for + + align:start position:0% +center so what we're going to assume for + + + align:start position:0% +center so what we're going to assume for +now is that all packet drops that happen + + align:start position:0% +now is that all packet drops that happen + + + align:start position:0% +now is that all packet drops that happen +in networks are a sign of congestion + + align:start position:0% +in networks are a sign of congestion + + + align:start position:0% +in networks are a sign of congestion +okay and when a packet gets dropped the + + align:start position:0% +okay and when a packet gets dropped the + + + align:start position:0% +okay and when a packet gets dropped the +sender gets that feedback and the reason + + align:start position:0% +sender gets that feedback and the reason + + + align:start position:0% +sender gets that feedback and the reason +it gets that feedback is remember that + + align:start position:0% +it gets that feedback is remember that + + + align:start position:0% +it gets that feedback is remember that +every packet is being acknowledged so if + + align:start position:0% +every packet is being acknowledged so if + + + align:start position:0% +every packet is being acknowledged so if +it misses an + + align:start position:0% +it misses an + + + align:start position:0% +it misses an +acknowledgement then it knows that a + + align:start position:0% +acknowledgement then it knows that a + + + align:start position:0% +acknowledgement then it knows that a +packet's been dropped and it says Ah the + + align:start position:0% +packet's been dropped and it says Ah the + + + align:start position:0% +packet's been dropped and it says Ah the +network is congested and then I'm going + + align:start position:0% +network is congested and then I'm going + + + align:start position:0% +network is congested and then I'm going +to change my speed and I'm going to + + align:start position:0% +to change my speed and I'm going to + + + align:start position:0% +to change my speed and I'm going to +change my speed by reducing the rate at + + align:start position:0% +change my speed by reducing the rate at + + + align:start position:0% +change my speed by reducing the rate at +which I'm going to send + + align:start position:0% +which I'm going to send + + + align:start position:0% +which I'm going to send +packets so now we have to ask how the + + align:start position:0% +packets so now we have to ask how the + + + align:start position:0% +packets so now we have to ask how the +sender adapts to congestion how the + + align:start position:0% +sender adapts to congestion how the + + + align:start position:0% +sender adapts to congestion how the +speed thing actually works + + align:start position:0% + + + + align:start position:0% + +out says up it's already up + + align:start position:0% + + + + align:start position:0% + +yeah it doesn't have a down + + align:start position:0% + + + + align:start position:0% + +button what's + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +Sam how many professors does it take to + + align:start position:0% + + + + align:start position:0% + +he turned the thing off he turned the + + align:start position:0% +he turned the thing off he turned the + + + align:start position:0% +he turned the thing off he turned the +light off on + + align:start position:0% + + + + align:start position:0% + +that it's not actually work can you see + + align:start position:0% + + + + align:start position:0% + +that I bet it's a race condition + + align:start position:0% +that I bet it's a race condition + + + align:start position:0% +that I bet it's a race condition +all right so can can you see that okay + + align:start position:0% +all right so can can you see that okay + + + align:start position:0% +all right so can can you see that okay +let's just move from here okay the way + + align:start position:0% +let's just move from here okay the way + + + align:start position:0% +let's just move from here okay the way +we're going to figure out the rate at + + align:start position:0% +we're going to figure out the rate at + + + align:start position:0% +we're going to figure out the rate at +which we're going to send our packets is + + align:start position:0% +which we're going to send our packets is + + + align:start position:0% +which we're going to send our packets is +to use this idea of a sliding window + + align:start position:0% +to use this idea of a sliding window + + + align:start position:0% +to use this idea of a sliding window +that we talked about the last time and + + align:start position:0% +that we talked about the last time and + + + align:start position:0% +that we talked about the last time and +since Sam did such a nice animation I'm + + align:start position:0% +since Sam did such a nice animation I'm + + + align:start position:0% +since Sam did such a nice animation I'm +going to uh just play that again just to + + align:start position:0% +going to uh just play that again just to + + + align:start position:0% +going to uh just play that again just to +refresher + + align:start position:0% +refresher + + + align:start position:0% +refresher +wonderful all + + align:start position:0% +wonderful all + + + align:start position:0% +wonderful all +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +right um and since Sam made this nice + + align:start position:0% +right um and since Sam made this nice + + + align:start position:0% +right um and since Sam made this nice +animation I'm going to play that back + + align:start position:0% +animation I'm going to play that back + + + align:start position:0% +animation I'm going to play that back +and uh I've always wanted to say played + + align:start position:0% +and uh I've always wanted to say played + + + align:start position:0% +and uh I've always wanted to say played +against + + align:start position:0% +against + + + align:start position:0% +against +Sam so uh what's going on here is that + + align:start position:0% +Sam so uh what's going on here is that + + + align:start position:0% +Sam so uh what's going on here is that +um you know whenever the send receiver + + align:start position:0% +um you know whenever the send receiver + + + align:start position:0% +um you know whenever the send receiver +receives a packet it sends an + + align:start position:0% +receives a packet it sends an + + + align:start position:0% +receives a packet it sends an +acknowledgement back and the sender's + + align:start position:0% +acknowledgement back and the sender's + + + align:start position:0% +acknowledgement back and the sender's +pipelining packets going through and + + align:start position:0% +pipelining packets going through and + + + align:start position:0% +pipelining packets going through and +whenever the sender gets an + + align:start position:0% +whenever the sender gets an + + + align:start position:0% +whenever the sender gets an +acknowledgement it sends a new packet + + align:start position:0% +acknowledgement it sends a new packet + + + align:start position:0% +acknowledgement it sends a new packet +off and that's what you see happening + + align:start position:0% +off and that's what you see happening + + + align:start position:0% +off and that's what you see happening +whenever it gets an acknowledgement a + + align:start position:0% +whenever it gets an acknowledgement a + + + align:start position:0% +whenever it gets an acknowledgement a +new packet goes out onto the other end + + align:start position:0% +new packet goes out onto the other end + + + align:start position:0% +new packet goes out onto the other end +and the window sliding by one every time + + align:start position:0% +and the window sliding by one every time + + + align:start position:0% +and the window sliding by one every time +it gets an acknowledgement so this is + + align:start position:0% +it gets an acknowledgement so this is + + + align:start position:0% +it gets an acknowledgement so this is +sort of the way in which this steady + + align:start position:0% +sort of the way in which this steady + + + align:start position:0% +sort of the way in which this steady +state thing um works out for us um in + + align:start position:0% +state thing um works out for us um in + + + align:start position:0% +state thing um works out for us um in +this + + align:start position:0% +this + + + align:start position:0% +this +network so the main point to note about + + align:start position:0% +network so the main point to note about + + + align:start position:0% +network so the main point to note about +this is that the scheme has an effect + + align:start position:0% +this is that the scheme has an effect + + + align:start position:0% +this is that the scheme has an effect +that I'll call + + align:start position:0% +that I'll call + + + align:start position:0% +that I'll call +self-pacing okay it's self-pacing + + align:start position:0% +self-pacing okay it's self-pacing + + + align:start position:0% +self-pacing okay it's self-pacing +because the sender doesn't actually have + + align:start position:0% +because the sender doesn't actually have + + + align:start position:0% +because the sender doesn't actually have +to worry very much about when it should + + align:start position:0% +to worry very much about when it should + + + align:start position:0% +to worry very much about when it should +exactly send a packet because it's being + + align:start position:0% +exactly send a packet because it's being + + + align:start position:0% +exactly send a packet because it's being +told every time an acknowledgement + + align:start position:0% +told every time an acknowledgement + + + align:start position:0% +told every time an acknowledgement +arrives it's being told that one packet + + align:start position:0% +arrives it's being told that one packet + + + align:start position:0% +arrives it's being told that one packet +the reason I got an acknowledgement is + + align:start position:0% +the reason I got an acknowledgement is + + + align:start position:0% +the reason I got an acknowledgement is +because one packet left the network + + align:start position:0% +because one packet left the network + + + align:start position:0% +because one packet left the network +which means I can send one packet into + + align:start position:0% +which means I can send one packet into + + + align:start position:0% +which means I can send one packet into +the network and as long as things + + align:start position:0% +the network and as long as things + + + align:start position:0% +the network and as long as things +weren't congested before they won't be + + align:start position:0% +weren't congested before they won't be + + + align:start position:0% +weren't congested before they won't be +congested now right because packets have + + align:start position:0% +congested now right because packets have + + + align:start position:0% +congested now right because packets have +left the pipe for every packet that + + align:start position:0% +left the pipe for every packet that + + + align:start position:0% +left the pipe for every packet that +leaves you're putting one packet in this + + align:start position:0% +leaves you're putting one packet in this + + + align:start position:0% +leaves you're putting one packet in this +is an absolutely beautiful idea um + + align:start position:0% +is an absolutely beautiful idea um + + + align:start position:0% +is an absolutely beautiful idea um +called um self-pacing and um the idea + + align:start position:0% +called um self-pacing and um the idea + + + align:start position:0% +called um self-pacing and um the idea +here is that axe essentially strobe data + + align:start position:0% +here is that axe essentially strobe data + + + align:start position:0% +here is that axe essentially strobe data +packets and like all really nice ideas + + align:start position:0% +packets and like all really nice ideas + + + align:start position:0% +packets and like all really nice ideas +it's extremely simple to to get it okay + + align:start position:0% +it's extremely simple to to get it okay + + + align:start position:0% +it's extremely simple to to get it okay +and it turns out to have lots of + + align:start position:0% +and it turns out to have lots of + + + align:start position:0% +and it turns out to have lots of +implications for why the system why the + + align:start position:0% +implications for why the system why the + + + align:start position:0% +implications for why the system why the +congestion control system is actually + + align:start position:0% +congestion control system is actually + + + align:start position:0% +congestion control system is actually +stable in reality so what this means for + + align:start position:0% +stable in reality so what this means for + + + align:start position:0% +stable in reality so what this means for +example is let's say that things are + + align:start position:0% +example is let's say that things are + + + align:start position:0% +example is let's say that things are +fine and all of a sudden a bunch of + + align:start position:0% +fine and all of a sudden a bunch of + + + align:start position:0% +fine and all of a sudden a bunch of +packets come in from somewhere else and + + align:start position:0% +packets come in from somewhere else and + + + align:start position:0% +packets come in from somewhere else and +the network starts to get congested + + align:start position:0% +the network starts to get congested + + + align:start position:0% +the network starts to get congested +what's going to happen is that cues are + + align:start position:0% +what's going to happen is that cues are + + + align:start position:0% +what's going to happen is that cues are +going to start building up but when qes + + align:start position:0% +going to start building up but when qes + + + align:start position:0% +going to start building up but when qes +start building up what happens is that + + align:start position:0% +start building up what happens is that + + + align:start position:0% +start building up what happens is that +Transmissions that are ongoing for this + + align:start position:0% +Transmissions that are ongoing for this + + + align:start position:0% +Transmissions that are ongoing for this +connection are just going to slow down a + + align:start position:0% +connection are just going to slow down a + + + align:start position:0% +connection are just going to slow down a +little bit because they're going to get + + align:start position:0% +little bit because they're going to get + + + align:start position:0% +little bit because they're going to get +you know interleaved with other packets + + align:start position:0% +you know interleaved with other packets + + + align:start position:0% +you know interleaved with other packets +in the queue which means the AXS are + + align:start position:0% +in the queue which means the AXS are + + + align:start position:0% +in the queue which means the AXS are +going to come back slower because how + + align:start position:0% +going to come back slower because how + + + align:start position:0% +going to come back slower because how +can the AXS come back any faster than + + align:start position:0% +can the AXS come back any faster than + + + align:start position:0% +can the AXS come back any faster than +the network can deliver them which means + + align:start position:0% +the network can deliver them which means + + + align:start position:0% +the network can deliver them which means +automatically the sender has a slowing + + align:start position:0% +automatically the sender has a slowing + + + align:start position:0% +automatically the sender has a slowing +down effect dealing with trans into + + align:start position:0% +down effect dealing with trans into + + + align:start position:0% +down effect dealing with trans into +congestion this is a really really nice + + align:start position:0% +congestion this is a really really nice + + + align:start position:0% +congestion this is a really really nice +behavior and um is a consequence of the + + align:start position:0% +behavior and um is a consequence of the + + + align:start position:0% +behavior and um is a consequence of the +way in which the self-pacing of um the + + align:start position:0% +way in which the self-pacing of um the + + + align:start position:0% +way in which the self-pacing of um the +way in which the sliding window thing + + align:start position:0% +way in which the sliding window thing + + + align:start position:0% +way in which the sliding window thing +here + + align:start position:0% +here + + + align:start position:0% +here +works so + + align:start position:0% + + + + align:start position:0% + +now at some point the network might + + align:start position:0% +now at some point the network might + + + align:start position:0% +now at some point the network might +become congested and a packet may get + + align:start position:0% +become congested and a packet may get + + + align:start position:0% +become congested and a packet may get +dropped so the way that manifest itself + + align:start position:0% +dropped so the way that manifest itself + + + align:start position:0% +dropped so the way that manifest itself +is when a packet gets dropped the + + align:start position:0% +is when a packet gets dropped the + + + align:start position:0% +is when a packet gets dropped the +corresponding acknowledgement doesn't + + align:start position:0% +corresponding acknowledgement doesn't + + + align:start position:0% +corresponding acknowledgement doesn't +get back to the sender and when + + align:start position:0% +get back to the sender and when + + + align:start position:0% +get back to the sender and when +knowledgement doesn't get back to the + + align:start position:0% +knowledgement doesn't get back to the + + + align:start position:0% +knowledgement doesn't get back to the +sender what the sender does is reduce + + align:start position:0% +sender what the sender does is reduce + + + align:start position:0% +sender what the sender does is reduce +its window size by + + align:start position:0% + + + + align:start position:0% + +two okay so I should mention here that + + align:start position:0% +two okay so I should mention here that + + + align:start position:0% +two okay so I should mention here that +there are really two windows going on + + align:start position:0% +there are really two windows going on + + + align:start position:0% +there are really two windows going on +one window is the window that we talked + + align:start position:0% +one window is the window that we talked + + + align:start position:0% +one window is the window that we talked +about the last time where the receiver + + align:start position:0% +about the last time where the receiver + + + align:start position:0% +about the last time where the receiver +tells the sender how much buffer space + + align:start position:0% +tells the sender how much buffer space + + + align:start position:0% +tells the sender how much buffer space +that it has and the other window is uh + + align:start position:0% +that it has and the other window is uh + + + align:start position:0% +that it has and the other window is uh +another variable that we've just + + align:start position:0% +another variable that we've just + + + align:start position:0% +another variable that we've just +introduced which is maintained by the + + align:start position:0% +introduced which is maintained by the + + + align:start position:0% +introduced which is maintained by the +sender it's also called the congestion + + align:start position:0% +sender it's also called the congestion + + + align:start position:0% +sender it's also called the congestion +window + + align:start position:0% +window + + + align:start position:0% +window +okay and this is a dynamic variable + + align:start position:0% +okay and this is a dynamic variable + + + align:start position:0% +okay and this is a dynamic variable +that's constantly changing as it gets as + + align:start position:0% +that's constantly changing as it gets as + + + align:start position:0% +that's constantly changing as it gets as +the sender gets feedback from the + + align:start position:0% +the sender gets feedback from the + + + align:start position:0% +the sender gets feedback from the +receiver and in response to a missing + + align:start position:0% +receiver and in response to a missing + + + align:start position:0% +receiver and in response to a missing +act when you determine that packet is + + align:start position:0% +act when you determine that packet is + + + align:start position:0% +act when you determine that packet is +lost you say it's congestion is going on + + align:start position:0% +lost you say it's congestion is going on + + + align:start position:0% +lost you say it's congestion is going on +and I'm going to reduce my window size + + align:start position:0% +and I'm going to reduce my window size + + + align:start position:0% +and I'm going to reduce my window size +and there are many ways to reduce it + + align:start position:0% +and there are many ways to reduce it + + + align:start position:0% +and there are many ways to reduce it +we're just going to multiplicatively + + align:start position:0% +we're just going to multiplicatively + + + align:start position:0% +we're just going to multiplicatively +decrease it and the reason for that has + + align:start position:0% +decrease it and the reason for that has + + + align:start position:0% +decrease it and the reason for that has +to do with the reason why for example on + + align:start position:0% +to do with the reason why for example on + + + align:start position:0% +to do with the reason why for example on +ethernet you found that you were doing + + align:start position:0% +ethernet you found that you were doing + + + align:start position:0% +ethernet you found that you were doing +exponential back off um you're sort of + + align:start position:0% +exponential back off um you're sort of + + + align:start position:0% +exponential back off um you're sort of +geometrically increasing the spacing + + align:start position:0% +geometrically increasing the spacing + + + align:start position:0% +geometrically increasing the spacing +with which you're sending um packets + + align:start position:0% +with which you're sending um packets + + + align:start position:0% +with which you're sending um packets +there you're doing the same kind of + + align:start position:0% +there you're doing the same kind of + + + align:start position:0% +there you're doing the same kind of +thing here reducing the rate by a factor + + align:start position:0% +thing here reducing the rate by a factor + + + align:start position:0% +thing here reducing the rate by a factor +of + + align:start position:0% +of + + + align:start position:0% +of +two so that's how you slow down at some + + align:start position:0% +two so that's how you slow down at some + + + align:start position:0% +two so that's how you slow down at some +point you might get into a situation + + align:start position:0% +point you might get into a situation + + + align:start position:0% +point you might get into a situation +where no acknowledgements come back for + + align:start position:0% +where no acknowledgements come back for + + + align:start position:0% +where no acknowledgements come back for +a while say many packets get lost right + + align:start position:0% +a while say many packets get lost right + + + align:start position:0% +a while say many packets get lost right +and that could happen all of a sudden + + align:start position:0% +and that could happen all of a sudden + + + align:start position:0% +and that could happen all of a sudden +there's a lot of congestion going on you + + align:start position:0% +there's a lot of congestion going on you + + + align:start position:0% +there's a lot of congestion going on you +get nothing back at that point you've + + align:start position:0% +get nothing back at that point you've + + + align:start position:0% +get nothing back at that point you've +lost this ability for acknowledgements + + align:start position:0% +lost this ability for acknowledgements + + + align:start position:0% +lost this ability for acknowledgements +to strobe new data packets okay so the + + align:start position:0% +to strobe new data packets okay so the + + + align:start position:0% +to strobe new data packets okay so the +AXS have acted as a clock allowing you + + align:start position:0% +AXS have acted as a clock allowing you + + + align:start position:0% +AXS have acted as a clock allowing you +to strobe packets through and You've + + align:start position:0% +to strobe packets through and You've + + + align:start position:0% +to strobe packets through and You've +Lost That + + align:start position:0% +Lost That + + + align:start position:0% +Lost That +at this point your best plan is just to + + align:start position:0% +at this point your best plan is just to + + + align:start position:0% +at this point your best plan is just to +stop and you halt for a while it's also + + align:start position:0% +stop and you halt for a while it's also + + + align:start position:0% +stop and you halt for a while it's also +called a timeout where you just be quiet + + align:start position:0% +called a timeout where you just be quiet + + + align:start position:0% +called a timeout where you just be quiet +for a while often on the order of a + + align:start position:0% +for a while often on the order of a + + + align:start position:0% +for a while often on the order of a +second or more and then you try to start + + align:start position:0% +second or more and then you try to start + + + align:start position:0% +second or more and then you try to start +over + + align:start position:0% +over + + + align:start position:0% +over +again of course now we have to figure + + align:start position:0% +again of course now we have to figure + + + align:start position:0% +again of course now we have to figure +out how you start over again and that's + + align:start position:0% +out how you start over again and that's + + + align:start position:0% +out how you start over again and that's +the same problem you have when you start + + align:start position:0% +the same problem you have when you start + + + align:start position:0% +the same problem you have when you start +a connection in the beginning when a + + align:start position:0% +a connection in the beginning when a + + + align:start position:0% +a connection in the beginning when a +connection starts up how does it know + + align:start position:0% +connection starts up how does it know + + + align:start position:0% +connection starts up how does it know +how fast to send it's the same problem + + align:start position:0% +how fast to send it's the same problem + + + align:start position:0% +how fast to send it's the same problem +as when many many packet drops happen + + align:start position:0% +as when many many packet drops happen + + + align:start position:0% +as when many many packet drops happen +and you time out and in TCP that startup + + align:start position:0% +and you time out and in TCP that startup + + + align:start position:0% +and you time out and in TCP that startup +is done using something called called a + + align:start position:0% +is done using something called called a + + + align:start position:0% +is done using something called called a +technique called slow start and I'll + + align:start position:0% +technique called slow start and I'll + + + align:start position:0% +technique called slow start and I'll +describe that algorithm it's a really + + align:start position:0% +describe that algorithm it's a really + + + align:start position:0% +describe that algorithm it's a really +elegant algorithm and it's very very + + align:start position:0% +elegant algorithm and it's very very + + + align:start position:0% +elegant algorithm and it's very very +simple um to to implement so you have a + + align:start position:0% +simple um to to implement so you have a + + + align:start position:0% +simple um to to implement so you have a +sender and receiver and the plan is + + align:start position:0% +sender and receiver and the plan is + + + align:start position:0% +sender and receiver and the plan is +initially the sender wants to initiate a + + align:start position:0% +initially the sender wants to initiate a + + + align:start position:0% +initially the sender wants to initiate a +connection to the receiver it sends a + + align:start position:0% +connection to the receiver it sends a + + + align:start position:0% +connection to the receiver it sends a +request it gets the response back with + + align:start position:0% +request it gets the response back with + + + align:start position:0% +request it gets the response back with +the flow control window which just says + + align:start position:0% +the flow control window which just says + + + align:start position:0% +the flow control window which just says +how much buffer space the receiver + + align:start position:0% +how much buffer space the receiver + + + align:start position:0% +how much buffer space the receiver +currently has okay we're not going to + + align:start position:0% +currently has okay we're not going to + + + align:start position:0% +currently has okay we're not going to +use that anymore in in this picture but + + align:start position:0% +use that anymore in in this picture but + + + align:start position:0% +use that anymore in in this picture but +it's just there saying which means the + + align:start position:0% +it's just there saying which means the + + + align:start position:0% +it's just there saying which means the +center can never send more than eight + + align:start position:0% +center can never send more than eight + + + align:start position:0% +center can never send more than eight +packets within any given round + + align:start position:0% +packets within any given round + + + align:start position:0% +packets within any given round +trip then what happens is the center + + align:start position:0% +trip then what happens is the center + + + align:start position:0% +trip then what happens is the center +sends the first segment and it gets an + + align:start position:0% +sends the first segment and it gets an + + + align:start position:0% +sends the first segment and it gets an +act so initially this congestion window + + align:start position:0% +act so initially this congestion window + + + align:start position:0% +act so initially this congestion window +value starts off at one okay you send + + align:start position:0% +value starts off at one okay you send + + + align:start position:0% +value starts off at one okay you send +one pack at one segment you get an + + align:start position:0% +one pack at one segment you get an + + + align:start position:0% +one pack at one segment you get an +acknowledgement back and now the plan is + + align:start position:0% +acknowledgement back and now the plan is + + + align:start position:0% +acknowledgement back and now the plan is +that the algorithm is as follows for + + align:start position:0% +that the algorithm is as follows for + + + align:start position:0% +that the algorithm is as follows for +every acknowledgement you get back you + + align:start position:0% +every acknowledgement you get back you + + + align:start position:0% +every acknowledgement you get back you +increase the congestion window by one + + align:start position:0% +increase the congestion window by one + + + align:start position:0% +increase the congestion window by one +okay so what this means is when you get + + align:start position:0% +okay so what this means is when you get + + + align:start position:0% +okay so what this means is when you get +this acknowledgement back you send out + + align:start position:0% +this acknowledgement back you send out + + + align:start position:0% +this acknowledgement back you send out +two + + align:start position:0% +two + + + align:start position:0% +two +packets and each of those two packets + + align:start position:0% +packets and each of those two packets + + + align:start position:0% +packets and each of those two packets +sends you back two acknowledgements + + align:start position:0% +sends you back two acknowledgements + + + align:start position:0% +sends you back two acknowledgements +now for each of those two + + align:start position:0% +now for each of those two + + + align:start position:0% +now for each of those two +acknowledgements you increase the window + + align:start position:0% +acknowledgements you increase the window + + + align:start position:0% +acknowledgements you increase the window +by one which means that after you got + + align:start position:0% +by one which means that after you got + + + align:start position:0% +by one which means that after you got +both those acknowledgements you've + + align:start position:0% +both those acknowledgements you've + + + align:start position:0% +both those acknowledgements you've +increased your window by two and + + align:start position:0% +increased your window by two and + + + align:start position:0% +increased your window by two and +previously the window was two so now you + + align:start position:0% +previously the window was two so now you + + + align:start position:0% +previously the window was two so now you +can send four packets so what happens is + + align:start position:0% +can send four packets so what happens is + + + align:start position:0% +can send four packets so what happens is +in response to the red acknowledgement + + align:start position:0% +in response to the red acknowledgement + + + align:start position:0% +in response to the red acknowledgement +you send out two packets and in response + + align:start position:0% +you send out two packets and in response + + + align:start position:0% +you send out two packets and in response +to the the light blue acknowledgement + + align:start position:0% +to the the light blue acknowledgement + + + align:start position:0% +to the the light blue acknowledgement +you send out four two more packets and + + align:start position:0% +you send out four two more packets and + + + align:start position:0% +you send out four two more packets and +now those get through to the other side + + align:start position:0% +now those get through to the other side + + + align:start position:0% +now those get through to the other side +they send back acknowledgements to you + + align:start position:0% +they send back acknowledgements to you + + + align:start position:0% +they send back acknowledgements to you +and in response to each one of those you + + align:start position:0% +and in response to each one of those you + + + align:start position:0% +and in response to each one of those you +increase the window by one so increasing + + align:start position:0% +increase the window by one so increasing + + + align:start position:0% +increase the window by one so increasing +the window by one on each + + align:start position:0% +the window by one on each + + + align:start position:0% +the window by one on each +acknowledgement means you can send two + + align:start position:0% +acknowledgement means you can send two + + + align:start position:0% +acknowledgement means you can send two +packets the reason is that one you know + + align:start position:0% +packets the reason is that one you know + + + align:start position:0% +packets the reason is that one you know +one packet went through and you got an + + align:start position:0% +one packet went through and you got an + + + align:start position:0% +one packet went through and you got an +acknowledgement so in response to that + + align:start position:0% +acknowledgement so in response to that + + + align:start position:0% +acknowledgement so in response to that +acknowledgement you could send one + + align:start position:0% +acknowledgement you could send one + + + align:start position:0% +acknowledgement you could send one +packet to fill in where what you know + + align:start position:0% +packet to fill in where what you know + + + align:start position:0% +packet to fill in where what you know +fill in that Thee the the space occupied + + align:start position:0% +fill in that Thee the the space occupied + + + align:start position:0% +fill in that Thee the the space occupied +by the packet that just got acknowledged + + align:start position:0% +by the packet that just got acknowledged + + + align:start position:0% +by the packet that just got acknowledged +in addition you increase the window by + + align:start position:0% +in addition you increase the window by + + + align:start position:0% +in addition you increase the window by +one which means you can send one more + + align:start position:0% +one which means you can send one more + + + align:start position:0% +one which means you can send one more +packet so really what's going on with + + align:start position:0% +packet so really what's going on with + + + align:start position:0% +packet so really what's going on with +this algorithm is if on each Act you + + align:start position:0% +this algorithm is if on each Act you + + + align:start position:0% +this algorithm is if on each Act you +send uh two segments which means you + + align:start position:0% +send uh two segments which means you + + + align:start position:0% +send uh two segments which means you +increase the window by one the + + align:start position:0% +increase the window by one the + + + align:start position:0% +increase the window by one the +congestion window by one really what + + align:start position:0% +congestion window by one really what + + + align:start position:0% +congestion window by one really what +happens is the rate at which this window + + align:start position:0% +happens is the rate at which this window + + + align:start position:0% +happens is the rate at which this window +op is exponential in time because in + + align:start position:0% +op is exponential in time because in + + + align:start position:0% +op is exponential in time because in +every round trip from one round trip to + + align:start position:0% +every round trip from one round trip to + + + align:start position:0% +every round trip from one round trip to +the next you're doubling the entire + + align:start position:0% +the next you're doubling the entire + + + align:start position:0% +the next you're doubling the entire +window okay so it's although it's called + + align:start position:0% +window okay so it's although it's called + + + align:start position:0% +window okay so it's although it's called +slow start it's really quite fast and + + align:start position:0% +slow start it's really quite fast and + + + align:start position:0% +slow start it's really quite fast and +it's an exponential + + align:start position:0% +it's an exponential + + + align:start position:0% +it's an exponential +increase so if you put it all together + + align:start position:0% +increase so if you put it all together + + + align:start position:0% +increase so if you put it all together +it'll turn out that the way in + + align:start position:0% +it'll turn out that the way in + + + align:start position:0% +it'll turn out that the way in +which um algorithms like TC the TCP + + align:start position:0% +which um algorithms like TC the TCP + + + align:start position:0% +which um algorithms like TC the TCP +algorithm works is it starts off at a + + align:start position:0% +algorithm works is it starts off at a + + + align:start position:0% +algorithm works is it starts off at a +value of the congestion window if this + + align:start position:0% +value of the congestion window if this + + + align:start position:0% +value of the congestion window if this +is the congestion window and this is + + align:start position:0% +is the congestion window and this is + + + align:start position:0% +is the congestion window and this is +time it starts off at some small value + + align:start position:0% +time it starts off at some small value + + + align:start position:0% +time it starts off at some small value +like one and it increases exponentially + + align:start position:0% + + + + align:start position:0% + +and then you know if you continue to + + align:start position:0% +and then you know if you continue to + + + align:start position:0% +and then you know if you continue to +increase exponentially this is the + + align:start position:0% +increase exponentially this is the + + + align:start position:0% +increase exponentially this is the +recipe for congestion it's surely going + + align:start position:0% +recipe for congestion it's surely going + + + align:start position:0% +recipe for congestion it's surely going +to overflow some buffer and slow down so + + align:start position:0% +to overflow some buffer and slow down so + + + align:start position:0% +to overflow some buffer and slow down so +what really happens in practice is after + + align:start position:0% +what really happens in practice is after + + + align:start position:0% +what really happens in practice is after +a while based on some threshold it + + align:start position:0% +a while based on some threshold it + + + align:start position:0% +a while based on some threshold it +decides that it's going you know just + + align:start position:0% +decides that it's going you know just + + + align:start position:0% +decides that it's going you know just +automatically decides it's probably not + + align:start position:0% +automatically decides it's probably not + + + align:start position:0% +automatically decides it's probably not +worth going exponentially uh fast and it + + align:start position:0% +worth going exponentially uh fast and it + + + align:start position:0% +worth going exponentially uh fast and it +turns out to go slows down to go at a + + align:start position:0% +turns out to go slows down to go at a + + + align:start position:0% +turns out to go slows down to go at a +linear increase so every roundt trip + + align:start position:0% +linear increase so every roundt trip + + + align:start position:0% +linear increase so every roundt trip +time it's increasing the window by a + + align:start position:0% +time it's increasing the window by a + + + align:start position:0% +time it's increasing the window by a +constant amount and then at some point + + align:start position:0% +constant amount and then at some point + + + align:start position:0% +constant amount and then at some point +congestion might happen and when + + align:start position:0% +congestion might happen and when + + + align:start position:0% +congestion might happen and when +congestion happens we dro the window by + + align:start position:0% +congestion happens we dro the window by + + + align:start position:0% +congestion happens we dro the window by +a factor of two so we cut down to a + + align:start position:0% +a factor of two so we cut down to a + + + align:start position:0% +a factor of two so we cut down to a +factor of two of the current window and + + align:start position:0% +factor of two of the current window and + + + align:start position:0% +factor of two of the current window and +then we continue to increase linearly + + align:start position:0% +then we continue to increase linearly + + + align:start position:0% +then we continue to increase linearly +and then we might have congestion coming + + align:start position:0% +and then we might have congestion coming + + + align:start position:0% +and then we might have congestion coming +again and this time we might have lost + + align:start position:0% +again and this time we might have lost + + + align:start position:0% +again and this time we might have lost +for instance we might have lost all of + + align:start position:0% +for instance we might have lost all of + + + align:start position:0% +for instance we might have lost all of +the acknowledgements not got any any of + + align:start position:0% +the acknowledgements not got any any of + + + align:start position:0% +the acknowledgements not got any any of +the acknowledgement losing a lot of + + align:start position:0% +the acknowledgement losing a lot of + + + align:start position:0% +the acknowledgement losing a lot of +packets which means we go down to this + + align:start position:0% +packets which means we go down to this + + + align:start position:0% +packets which means we go down to this +thing where we've lost the ACT clock so + + align:start position:0% +thing where we've lost the ACT clock so + + + align:start position:0% +thing where we've lost the ACT clock so +we have to time out and it's like a new + + align:start position:0% +we have to time out and it's like a new + + + align:start position:0% +we have to time out and it's like a new +connection so we remain silent for a + + align:start position:0% +connection so we remain silent for a + + + align:start position:0% +connection so we remain silent for a +while and this period is the timeout + + align:start position:0% +while and this period is the timeout + + + align:start position:0% +while and this period is the timeout +period That's governed by the equations + + align:start position:0% +period That's governed by the equations + + + align:start position:0% +period That's governed by the equations +that we talked about the last time based + + align:start position:0% +that we talked about the last time based + + + align:start position:0% +that we talked about the last time based +on the roundt trip time and the standard + + align:start position:0% +on the roundt trip time and the standard + + + align:start position:0% +on the roundt trip time and the standard +deviation we remain quiet for a while + + align:start position:0% +deviation we remain quiet for a while + + + align:start position:0% +deviation we remain quiet for a while +and then we start over as if it's a new + + align:start position:0% +and then we start over as if it's a new + + + align:start position:0% +and then we start over as if it's a new +connection and we increase + + align:start position:0% +connection and we increase + + + align:start position:0% +connection and we increase +exponentially and this time we don't + + align:start position:0% +exponentially and this time we don't + + + align:start position:0% +exponentially and this time we don't +exponentially increase as we did the + + align:start position:0% +exponentially increase as we did the + + + align:start position:0% +exponentially increase as we did the +very first time we actually + + align:start position:0% +very first time we actually + + + align:start position:0% +very first time we actually +exponentially increase only for a little + + align:start position:0% +exponentially increase only for a little + + + align:start position:0% +exponentially increase only for a little +bit because we knew that congestion + + align:start position:0% +bit because we knew that congestion + + + align:start position:0% +bit because we knew that congestion +happened here so we go up to some + + align:start position:0% +happened here so we go up to some + + + align:start position:0% +happened here so we go up to some +fraction of that and then increase + + align:start position:0% +fraction of that and then increase + + + align:start position:0% +fraction of that and then increase +linearly so the exact details are not + + align:start position:0% +linearly so the exact details are not + + + align:start position:0% +linearly so the exact details are not +important the thing that's important is + + align:start position:0% +important the thing that's important is + + + align:start position:0% +important the thing that's important is +just understanding that when congestion + + align:start position:0% +just understanding that when congestion + + + align:start position:0% +just understanding that when congestion +occurs you drop your window by a factor + + align:start position:0% +occurs you drop your window by a factor + + + align:start position:0% +occurs you drop your window by a factor +to some multiplicative decrease and at + + align:start position:0% +to some multiplicative decrease and at + + + align:start position:0% +to some multiplicative decrease and at +the beginning of connection you're + + align:start position:0% +the beginning of connection you're + + + align:start position:0% +the beginning of connection you're +trying to quickly figure out what the + + align:start position:0% +trying to quickly figure out what the + + + align:start position:0% +trying to quickly figure out what the +sustainable capacity is so you're going + + align:start position:0% +sustainable capacity is so you're going + + + align:start position:0% +sustainable capacity is so you're going +in this increase phase here but after a + + align:start position:0% +in this increase phase here but after a + + + align:start position:0% +in this increase phase here but after a +while you don't really want to be + + align:start position:0% +while you don't really want to be + + + align:start position:0% +while you don't really want to be +exponentially increasing all the time + + align:start position:0% +exponentially increasing all the time + + + align:start position:0% +exponentially increasing all the time +because that's almost guaranteed to + + align:start position:0% +because that's almost guaranteed to + + + align:start position:0% +because that's almost guaranteed to +overrun buffers so you want to go into a + + align:start position:0% +overrun buffers so you want to go into a + + + align:start position:0% +overrun buffers so you want to go into a +more Ginger mode and people have + + align:start position:0% +more Ginger mode and people have + + + align:start position:0% +more Ginger mode and people have +proposed congestion control schemes that + + align:start position:0% +proposed congestion control schemes that + + + align:start position:0% +proposed congestion control schemes that +do all sorts of things all sorts of + + align:start position:0% +do all sorts of things all sorts of + + + align:start position:0% +do all sorts of things all sorts of +functions but this is the thing that's + + align:start position:0% +functions but this is the thing that's + + + align:start position:0% +functions but this is the thing that's +just out there in all of the computers + + align:start position:0% +just out there in all of the computers + + + align:start position:0% +just out there in all of the computers +and it works remarkably well so there's + + align:start position:0% +and it works remarkably well so there's + + + align:start position:0% +and it works remarkably well so there's +two basic points you have to take home + + align:start position:0% +two basic points you have to take home + + + align:start position:0% +two basic points you have to take home +from here the main goal of congestion + + align:start position:0% +from here the main goal of congestion + + + align:start position:0% +from here the main goal of congestion +control is to avoid congestion collapse + + align:start position:0% +control is to avoid congestion collapse + + + align:start position:0% +control is to avoid congestion collapse +which is um the picture that's being + + align:start position:0% +which is um the picture that's being + + + align:start position:0% +which is um the picture that's being +hidden behind that which is that as + + align:start position:0% +hidden behind that which is that as + + + align:start position:0% +hidden behind that which is that as +offer load increases you don't want the + + align:start position:0% +offer load increases you don't want the + + + align:start position:0% +offer load increases you don't want the +throughput to drop like a cliff and this + + align:start position:0% +throughput to drop like a cliff and this + + + align:start position:0% +throughput to drop like a cliff and this +is a cross layer problem and the essence + + align:start position:0% +is a cross layer problem and the essence + + + align:start position:0% +is a cross layer problem and the essence +of all solutions is to use a combination + + align:start position:0% +of all solutions is to use a combination + + + align:start position:0% +of all solutions is to use a combination +of network layer feedback and end system + + align:start position:0% +of network layer feedback and end system + + + align:start position:0% +of network layer feedback and end system +control endtoend control and it works + + align:start position:0% +control endtoend control and it works + + + align:start position:0% +control endtoend control and it works +good Solutions work across eight ORD of + + align:start position:0% +good Solutions work across eight ORD of + + + align:start position:0% +good Solutions work across eight ORD of +magnitude of bandwidth and four orders + + align:start position:0% +magnitude of bandwidth and four orders + + + align:start position:0% +magnitude of bandwidth and four orders +of magnitude of delay so with that we'll + + align:start position:0% +of magnitude of delay so with that we'll + + + align:start position:0% +of magnitude of delay so with that we'll +stop dp1 is due tomorrow have a great + + align:start position:0% +stop dp1 is due tomorrow have a great + + + align:start position:0% +stop dp1 is due tomorrow have a great +spring break and see you after spring + + align:start position:0% +spring break and see you after spring + + + align:start position:0% +spring break and see you after spring +break \ No newline at end of file diff --git a/HypQZfQPtYk.txt b/HypQZfQPtYk.txt new file mode 100644 index 0000000000000000000000000000000000000000..93158baadbf6de27903bc8d9ee7929396a0dcd72 --- /dev/null +++ b/HypQZfQPtYk.txt @@ -0,0 +1,10515 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu good evening people we + + align:start position:0% +ocw.mit.edu good evening people we + + + align:start position:0% +ocw.mit.edu good evening people we +continue our discussion of neorealism by + + align:start position:0% +continue our discussion of neorealism by + + + align:start position:0% +continue our discussion of neorealism by +looking closely tonight at one classic + + align:start position:0% +looking closely tonight at one classic + + + align:start position:0% +looking closely tonight at one classic +instance of the neorealist movement Pro + + align:start position:0% +instance of the neorealist movement Pro + + + align:start position:0% +instance of the neorealist movement Pro +the single most famous film from that uh + + align:start position:0% +the single most famous film from that uh + + + align:start position:0% +the single most famous film from that uh +uh from that school bicycle thieves uh + + align:start position:0% +uh from that school bicycle thieves uh + + + align:start position:0% +uh from that school bicycle thieves uh +before we before I turn to talking a bit + + align:start position:0% +before we before I turn to talking a bit + + + align:start position:0% +before we before I turn to talking a bit +about aspects of bicycle thieves itself + + align:start position:0% +about aspects of bicycle thieves itself + + + align:start position:0% +about aspects of bicycle thieves itself +which I hope will frame your viewing in + + align:start position:0% +which I hope will frame your viewing in + + + align:start position:0% +which I hope will frame your viewing in +a way that will help you get a lot out + + align:start position:0% +a way that will help you get a lot out + + + align:start position:0% +a way that will help you get a lot out +get a lot out of the first viewing of + + align:start position:0% +get a lot out of the first viewing of + + + align:start position:0% +get a lot out of the first viewing of +the film I want to say a few words about + + align:start position:0% +the film I want to say a few words about + + + align:start position:0% +the film I want to say a few words about +Victorio Desa + + align:start position:0% + + + + align:start position:0% + +himself I mentioned this + + align:start position:0% +himself I mentioned this + + + align:start position:0% +himself I mentioned this +afternoon that the realist movement + + align:start position:0% +afternoon that the realist movement + + + align:start position:0% +afternoon that the realist movement +although it was immensely influential + + align:start position:0% +although it was immensely influential + + + align:start position:0% +although it was immensely influential +and continues to be influential in fact + + align:start position:0% +and continues to be influential in fact + + + align:start position:0% +and continues to be influential in fact +uh on on realist filmmakers and on + + align:start position:0% +uh on on realist filmmakers and on + + + align:start position:0% +uh on on realist filmmakers and on +documentarians + + align:start position:0% +documentarians + + + align:start position:0% +documentarians +um and it was especially in its in its + + align:start position:0% +um and it was especially in its in its + + + align:start position:0% +um and it was especially in its in its +earliest phases hailed uh globally as a + + align:start position:0% +earliest phases hailed uh globally as a + + + align:start position:0% +earliest phases hailed uh globally as a +very remarkable movement it incited + + align:start position:0% +very remarkable movement it incited + + + align:start position:0% +very remarkable movement it incited +criticism almost from the beginning + + align:start position:0% +criticism almost from the beginning + + + align:start position:0% +criticism almost from the beginning +inside Italy and I suggested this + + align:start position:0% +inside Italy and I suggested this + + + align:start position:0% +inside Italy and I suggested this +afternoon that some complaints against + + align:start position:0% +afternoon that some complaints against + + + align:start position:0% +afternoon that some complaints against +the movie essentially came from + + align:start position:0% +the movie essentially came from + + + align:start position:0% +the movie essentially came from +conservative forces in the society that + + align:start position:0% +conservative forces in the society that + + + align:start position:0% +conservative forces in the society that +felt that the portrait of a of Decay and + + align:start position:0% +felt that the portrait of a of Decay and + + + align:start position:0% +felt that the portrait of a of Decay and +breakdown and dislocation that was at + + align:start position:0% +breakdown and dislocation that was at + + + align:start position:0% +breakdown and dislocation that was at +the center of neorealist films after all + + align:start position:0% +the center of neorealist films after all + + + align:start position:0% +the center of neorealist films after all +they were about the Contemporary world + + align:start position:0% +they were about the Contemporary world + + + align:start position:0% +they were about the Contemporary world +and about the the the the broken + + align:start position:0% +and about the the the the broken + + + align:start position:0% +and about the the the the broken +universe that we the broken planet that + + align:start position:0% +universe that we the broken planet that + + + align:start position:0% +universe that we the broken planet that +or at least the broken Europe that we + + align:start position:0% +or at least the broken Europe that we + + + align:start position:0% +or at least the broken Europe that we +encountered after the war uh there were + + align:start position:0% +encountered after the war uh there were + + + align:start position:0% +encountered after the war uh there were +many con conservatives who F in in Italy + + align:start position:0% +many con conservatives who F in in Italy + + + align:start position:0% +many con conservatives who F in in Italy +who felt that it promulgated a bad image + + align:start position:0% +who felt that it promulgated a bad image + + + align:start position:0% +who felt that it promulgated a bad image +for the society that it made investment + + align:start position:0% +for the society that it made investment + + + align:start position:0% +for the society that it made investment +more difficult that it that it was a + + align:start position:0% +more difficult that it that it was a + + + align:start position:0% +more difficult that it that it was a +kind of Downer uh and this criticism was + + align:start position:0% +kind of Downer uh and this criticism was + + + align:start position:0% +kind of Downer uh and this criticism was +very powerful but what really undermined + + align:start position:0% +very powerful but what really undermined + + + align:start position:0% +very powerful but what really undermined +the movement in terms of getting + + align:start position:0% +the movement in terms of getting + + + align:start position:0% +the movement in terms of getting +financing why the reason that the + + align:start position:0% +financing why the reason that the + + + align:start position:0% +financing why the reason that the +movement sort of ended after about the + + align:start position:0% +movement sort of ended after about the + + + align:start position:0% +movement sort of ended after about the +time Umberto D the last of the truly + + align:start position:0% +time Umberto D the last of the truly + + + align:start position:0% +time Umberto D the last of the truly +neorealist films that Thea made was + + align:start position:0% +neorealist films that Thea made was + + + align:start position:0% +neorealist films that Thea made was +produced in + + align:start position:0% +produced in + + + align:start position:0% +produced in +1952 it's life was you know very very + + align:start position:0% +1952 it's life was you know very very + + + align:start position:0% +1952 it's life was you know very very +brief that many people would say that + + align:start position:0% +brief that many people would say that + + + align:start position:0% +brief that many people would say that +was the end of neorealism although there + + align:start position:0% +was the end of neorealism although there + + + align:start position:0% +was the end of neorealism although there +are some films that after that that have + + align:start position:0% +are some films that after that that have + + + align:start position:0% +are some films that after that that have +neorealist dimensions and elements in + + align:start position:0% +neorealist dimensions and elements in + + + align:start position:0% +neorealist dimensions and elements in +them including some by felini uh still + + align:start position:0% +them including some by felini uh still + + + align:start position:0% +them including some by felini uh still +the idea that the movement had a very + + align:start position:0% +the idea that the movement had a very + + + align:start position:0% +the idea that the movement had a very +short life despite its immense influence + + align:start position:0% +short life despite its immense influence + + + align:start position:0% +short life despite its immense influence +is is an accurate one but what I had + + align:start position:0% +is is an accurate one but what I had + + + align:start position:0% +is is an accurate one but what I had +left out this afternoon is an important + + align:start position:0% +left out this afternoon is an important + + + align:start position:0% +left out this afternoon is an important +qualification or addition which is that + + align:start position:0% +qualification or addition which is that + + + align:start position:0% +qualification or addition which is that +the films also incited criticism from + + align:start position:0% +the films also incited criticism from + + + align:start position:0% +the films also incited criticism from +the left you would think that that's + + align:start position:0% +the left you would think that that's + + + align:start position:0% +the left you would think that that's +when you see bicycle thieves you'll see + + align:start position:0% +when you see bicycle thieves you'll see + + + align:start position:0% +when you see bicycle thieves you'll see +why that might be a surprising uh fact + + align:start position:0% +why that might be a surprising uh fact + + + align:start position:0% +why that might be a surprising uh fact +because the sympathies of the film are + + align:start position:0% +because the sympathies of the film are + + + align:start position:0% +because the sympathies of the film are +so totally on the side side of the of + + align:start position:0% +so totally on the side side of the of + + + align:start position:0% +so totally on the side side of the of +the underprivileged and the underclasses + + align:start position:0% +the underprivileged and the underclasses + + + align:start position:0% +the underprivileged and the underclasses +of of the culture uh that it's it's + + align:start position:0% +of of the culture uh that it's it's + + + align:start position:0% +of of the culture uh that it's it's +difficult from our contemporary vantage + + align:start position:0% +difficult from our contemporary vantage + + + align:start position:0% +difficult from our contemporary vantage +point to see what would have offended + + align:start position:0% +point to see what would have offended + + + align:start position:0% +point to see what would have offended +leftists + + align:start position:0% +leftists + + + align:start position:0% +leftists +but there were there was a very vigorous + + align:start position:0% +but there were there was a very vigorous + + + align:start position:0% +but there were there was a very vigorous +and theoretically sophisticated + + align:start position:0% +and theoretically sophisticated + + + align:start position:0% +and theoretically sophisticated +communist movement in Italy uh uh in + + align:start position:0% +communist movement in Italy uh uh in + + + align:start position:0% +communist movement in Italy uh uh in +this period as there continues to be + + align:start position:0% +this period as there continues to be + + + align:start position:0% +this period as there continues to be +today in some degree uh and and uh many + + align:start position:0% +today in some degree uh and and uh many + + + align:start position:0% +today in some degree uh and and uh many +people on the left especially Communists + + align:start position:0% +people on the left especially Communists + + + align:start position:0% +people on the left especially Communists +but other but socialists as well + + align:start position:0% +but other but socialists as well + + + align:start position:0% +but other but socialists as well +also complained about neorealist films + + align:start position:0% +also complained about neorealist films + + + align:start position:0% +also complained about neorealist films +and in particular about the Seas films + + align:start position:0% +and in particular about the Seas films + + + align:start position:0% +and in particular about the Seas films +because they because their complaint was + + align:start position:0% +because they because their complaint was + + + align:start position:0% +because they because their complaint was +not that the difficulties of the world + + align:start position:0% +not that the difficulties of the world + + + align:start position:0% +not that the difficulties of the world +were exposed they were perfectly happy + + align:start position:0% +were exposed they were perfectly happy + + + align:start position:0% +were exposed they were perfectly happy +with that but they were angry that there + + align:start position:0% +with that but they were angry that there + + + align:start position:0% +with that but they were angry that there +wasn't a program for renovation what + + align:start position:0% +wasn't a program for renovation what + + + align:start position:0% +wasn't a program for renovation what +they were really angry about was that + + align:start position:0% +they were really angry about was that + + + align:start position:0% +they were really angry about was that +there wasn't a Marxist or a socialist + + align:start position:0% +there wasn't a Marxist or a socialist + + + align:start position:0% +there wasn't a Marxist or a socialist +program built into the films and it's I + + align:start position:0% +program built into the films and it's I + + + align:start position:0% +program built into the films and it's I +it's always struck me as a very + + align:start position:0% +it's always struck me as a very + + + align:start position:0% +it's always struck me as a very +revealing and interesting fact about the + + align:start position:0% +revealing and interesting fact about the + + + align:start position:0% +revealing and interesting fact about the +movement that it couldn't satisfy either + + align:start position:0% +movement that it couldn't satisfy either + + + align:start position:0% +movement that it couldn't satisfy either +left or right even though these films + + align:start position:0% +left or right even though these films + + + align:start position:0% +left or right even though these films +are among the most + + align:start position:0% +are among the most + + + align:start position:0% +are among the most +powerful and compassionate films about + + align:start position:0% +powerful and compassionate films about + + + align:start position:0% +powerful and compassionate films about +the lives of + + align:start position:0% +the lives of + + + align:start position:0% +the lives of +ordinary uh uh of not just ordinary + + align:start position:0% +ordinary uh uh of not just ordinary + + + align:start position:0% +ordinary uh uh of not just ordinary +people but of people without power of + + align:start position:0% +people but of people without power of + + + align:start position:0% +people but of people without power of +people without control over their lives + + align:start position:0% +people without control over their lives + + + align:start position:0% +people without control over their lives +uh that have ever been made uh so so + + align:start position:0% +uh that have ever been made uh so so + + + align:start position:0% +uh that have ever been made uh so so +it's it's it's a curious fact and it + + align:start position:0% +it's it's it's a curious fact and it + + + align:start position:0% +it's it's it's a curious fact and it +bothered Desa all his life that that uh + + align:start position:0% +bothered Desa all his life that that uh + + + align:start position:0% +bothered Desa all his life that that uh +he he seemed unable to please uh either + + align:start position:0% +he he seemed unable to please uh either + + + align:start position:0% +he he seemed unable to please uh either +side in in in that political argument + + align:start position:0% +side in in in that political argument + + + align:start position:0% +side in in in that political argument +and he and at one point in in an + + align:start position:0% +and he and at one point in in an + + + align:start position:0% +and he and at one point in in an +interview + + align:start position:0% +interview + + + align:start position:0% +interview +he said something I if I can find My + + align:start position:0% +he said something I if I can find My + + + align:start position:0% +he said something I if I can find My +Notes I'd like to quote to you he said + + align:start position:0% +Notes I'd like to quote to you he said + + + align:start position:0% +Notes I'd like to quote to you he said +in response to the to to a question that + + align:start position:0% +in response to the to to a question that + + + align:start position:0% +in response to the to to a question that +asked him why do you think the + + align:start position:0% +asked him why do you think the + + + align:start position:0% +asked him why do you think the +Socialists and the Communists were some + + align:start position:0% +Socialists and the Communists were some + + + align:start position:0% +Socialists and the Communists were some +or at least some socialists and remember + + align:start position:0% +or at least some socialists and remember + + + align:start position:0% +or at least some socialists and remember +zaatini was a socialist so he + + align:start position:0% +zaatini was a socialist so he + + + align:start position:0% +zaatini was a socialist so he +collaborated deeply with and loved uh + + align:start position:0% +collaborated deeply with and loved uh + + + align:start position:0% +collaborated deeply with and loved uh +des and collaborated with him on his + + align:start position:0% +des and collaborated with him on his + + + align:start position:0% +des and collaborated with him on his +most important film so I don't mean that + + align:start position:0% +most important film so I don't mean that + + + align:start position:0% +most important film so I don't mean that +all socialists thought ill of neorealism + + align:start position:0% +all socialists thought ill of neorealism + + + align:start position:0% +all socialists thought ill of neorealism +they did not uh but some did and and + + align:start position:0% +they did not uh but some did and and + + + align:start position:0% +they did not uh but some did and and +certainly people on the far left + + align:start position:0% +certainly people on the far left + + + align:start position:0% +certainly people on the far left +definitely did and here was the 's + + align:start position:0% +definitely did and here was the 's + + + align:start position:0% +definitely did and here was the 's +response to why he said he expressed + + align:start position:0% +response to why he said he expressed + + + align:start position:0% +response to why he said he expressed +disappointment about this but his + + align:start position:0% +disappointment about this but his + + + align:start position:0% +disappointment about this but his +response really in a way is a critique + + align:start position:0% +response really in a way is a critique + + + align:start position:0% +response really in a way is a critique +of of the programmatic demands that + + align:start position:0% +of of the programmatic demands that + + + align:start position:0% +of of the programmatic demands that +these that these people were making on + + align:start position:0% +these that these people were making on + + + align:start position:0% +these that these people were making on +his films he said my films are a + + align:start position:0% +his films he said my films are a + + + align:start position:0% +his films he said my films are a +struggle against the absence of human + + align:start position:0% +struggle against the absence of human + + + align:start position:0% +struggle against the absence of human +solidarity and you should think about + + align:start position:0% +solidarity and you should think about + + + align:start position:0% +solidarity and you should think about +this uh quotation as you're watching + + align:start position:0% +this uh quotation as you're watching + + + align:start position:0% +this uh quotation as you're watching +tonight's film because there as you'll + + align:start position:0% +tonight's film because there as you'll + + + align:start position:0% +tonight's film because there as you'll +see in the film the official + + align:start position:0% +see in the film the official + + + align:start position:0% +see in the film the official +institutions of the society seem to have + + align:start position:0% +institutions of the society seem to have + + + align:start position:0% +institutions of the society seem to have +broken down or at least to have been to + + align:start position:0% +broken down or at least to have been to + + + align:start position:0% +broken down or at least to have been to +to have become not effective they're + + align:start position:0% +to have become not effective they're + + + align:start position:0% +to have become not effective they're +they're they're they're they're U + + align:start position:0% +they're they're they're they're U + + + align:start position:0% +they're they're they're they're U +overburdened they're somewhat + + align:start position:0% +overburdened they're somewhat + + + align:start position:0% +overburdened they're somewhat +indifferent it's mostly that they're + + align:start position:0% +indifferent it's mostly that they're + + + align:start position:0% +indifferent it's mostly that they're +overburdened that the problems of the + + align:start position:0% +overburdened that the problems of the + + + align:start position:0% +overburdened that the problems of the +society are too great for the + + align:start position:0% +society are too great for the + + + align:start position:0% +society are too great for the +institutional structures that are in + + align:start position:0% +institutional structures that are in + + + align:start position:0% +institutional structures that are in +place to handle uh the problems uh but + + align:start position:0% +place to handle uh the problems uh but + + + align:start position:0% +place to handle uh the problems uh but +in any case you as you're watching the + + align:start position:0% +in any case you as you're watching the + + + align:start position:0% +in any case you as you're watching the +film uh I think you'll notice not only + + align:start position:0% +film uh I think you'll notice not only + + + align:start position:0% +film uh I think you'll notice not only +clearly this breakdown of institutions + + align:start position:0% +clearly this breakdown of institutions + + + align:start position:0% +clearly this breakdown of institutions +of very uh uh that we might expect to be + + align:start position:0% +of very uh uh that we might expect to be + + + align:start position:0% +of very uh uh that we might expect to be +helpful to REI in his quest uh but what + + align:start position:0% +helpful to REI in his quest uh but what + + + align:start position:0% +helpful to REI in his quest uh but what +we will also disc discover is that there + + align:start position:0% +we will also disc discover is that there + + + align:start position:0% +we will also disc discover is that there +are other forms of solidarity that + + align:start position:0% +are other forms of solidarity that + + + align:start position:0% +are other forms of solidarity that +emerge in the film one of them is the + + align:start position:0% +emerge in the film one of them is the + + + align:start position:0% +emerge in the film one of them is the +solidarity of husband and wife another + + align:start position:0% +solidarity of husband and wife another + + + align:start position:0% +solidarity of husband and wife another +is the solidarity very much tested in + + align:start position:0% +is the solidarity very much tested in + + + align:start position:0% +is the solidarity very much tested in +the film it's the great central theme of + + align:start position:0% +the film it's the great central theme of + + + align:start position:0% +the film it's the great central theme of +the film The solidarity of Father and + + align:start position:0% +the film The solidarity of Father and + + + align:start position:0% +the film The solidarity of Father and +Son and then there is also the + + align:start position:0% +Son and then there is also the + + + align:start position:0% +Son and then there is also the +solidarity of what we might call + + align:start position:0% +solidarity of what we might call + + + align:start position:0% +solidarity of what we might call +neighbors or neighborhoods and you'll + + align:start position:0% +neighbors or neighborhoods and you'll + + + align:start position:0% +neighbors or neighborhoods and you'll +see how that uh element Works toward the + + align:start position:0% +see how that uh element Works toward the + + + align:start position:0% +see how that uh element Works toward the +end of the film in its remarkable and + + align:start position:0% +end of the film in its remarkable and + + + align:start position:0% +end of the film in its remarkable and +surprising conclusion now here's the + + align:start position:0% +surprising conclusion now here's the + + + align:start position:0% +surprising conclusion now here's the +quotation my films are a struggle + + align:start position:0% +quotation my films are a struggle + + + align:start position:0% +quotation my films are a struggle +against the absence of human solidarity + + align:start position:0% +against the absence of human solidarity + + + align:start position:0% +against the absence of human solidarity +against the indifference of society + + align:start position:0% +against the indifference of society + + + align:start position:0% +against the indifference of society +towards suffering they are a word in + + align:start position:0% +towards suffering they are a word in + + + align:start position:0% +towards suffering they are a word in +favor of the poor and the unhappy and + + align:start position:0% +favor of the poor and the unhappy and + + + align:start position:0% +favor of the poor and the unhappy and +one reason I like the statement is it's + + align:start position:0% +one reason I like the statement is it's + + + align:start position:0% +one reason I like the statement is it's +so in a certain sense + + align:start position:0% +so in a certain sense + + + align:start position:0% +so in a certain sense +unsystematic uh it show it's they seem + + align:start position:0% +unsystematic uh it show it's they seem + + + align:start position:0% +unsystematic uh it show it's they seem +to me to be the words of an artist not a + + align:start position:0% +to me to be the words of an artist not a + + + align:start position:0% +to me to be the words of an artist not a +political pamphleteer and they partly + + align:start position:0% +political pamphleteer and they partly + + + align:start position:0% +political pamphleteer and they partly +explain the richness the reson resonance + + align:start position:0% +explain the richness the reson resonance + + + align:start position:0% +explain the richness the reson resonance +what I've been calling the multiplicity + + align:start position:0% +what I've been calling the multiplicity + + + align:start position:0% +what I've been calling the multiplicity +of bicycle + + align:start position:0% +of bicycle + + + align:start position:0% +of bicycle +thieves there's a moment in bicycle + + align:start position:0% +thieves there's a moment in bicycle + + + align:start position:0% +thieves there's a moment in bicycle +thieves + + align:start position:0% +thieves + + + align:start position:0% +thieves +uh about which Andre bazan has written + + align:start position:0% +uh about which Andre bazan has written + + + align:start position:0% +uh about which Andre bazan has written +very beautifully the same critic that + + align:start position:0% +very beautifully the same critic that + + + align:start position:0% +very beautifully the same critic that +spokes that that was a champion + + align:start position:0% +spokes that that was a champion + + + align:start position:0% +spokes that that was a champion +of French poetic realism and of Jean + + align:start position:0% +of French poetic realism and of Jean + + + align:start position:0% +of French poetic realism and of Jean +Renoir of course becomes one of the + + align:start position:0% +Renoir of course becomes one of the + + + align:start position:0% +Renoir of course becomes one of the +great champions of Italian neorealism he + + align:start position:0% +great champions of Italian neorealism he + + + align:start position:0% +great champions of Italian neorealism he +can see that that that the Italian form + + align:start position:0% +can see that that that the Italian form + + + align:start position:0% +can see that that that the Italian form +of realism is an extension and + + align:start position:0% +of realism is an extension and + + + align:start position:0% +of realism is an extension and +elaboration and in some ways a deepening + + align:start position:0% +elaboration and in some ways a deepening + + + align:start position:0% +elaboration and in some ways a deepening +of the implications of poetic realism + + align:start position:0% +of the implications of poetic realism + + + align:start position:0% +of the implications of poetic realism +and he and he he he's written + + align:start position:0% +and he and he he he's written + + + align:start position:0% +and he and he he he's written +brilliantly about the neorealist and + + align:start position:0% +brilliantly about the neorealist and + + + align:start position:0% +brilliantly about the neorealist and +especially about about the sea and + + align:start position:0% +especially about about the sea and + + + align:start position:0% +especially about about the sea and +there's one place in the film that he + + align:start position:0% +there's one place in the film that he + + + align:start position:0% +there's one place in the film that he +particularly focuses on in one of his + + align:start position:0% +particularly focuses on in one of his + + + align:start position:0% +particularly focuses on in one of his +essays uh it's a uh it's a mo I I have + + align:start position:0% +essays uh it's a uh it's a mo I I have + + + align:start position:0% +essays uh it's a uh it's a mo I I have +to give away a a small part of the plot + + align:start position:0% +to give away a a small part of the plot + + + align:start position:0% +to give away a a small part of the plot +in order to explain this but it really + + align:start position:0% +in order to explain this but it really + + + align:start position:0% +in order to explain this but it really +won't trouble you because the the plot + + align:start position:0% +won't trouble you because the the plot + + + align:start position:0% +won't trouble you because the the plot +engine gets going so early in the film + + align:start position:0% +engine gets going so early in the film + + + align:start position:0% +engine gets going so early in the film +that it's hardly a surprise in fact you + + align:start position:0% +that it's hardly a surprise in fact you + + + align:start position:0% +that it's hardly a surprise in fact you +really know what's going to happen + + align:start position:0% +really know what's going to happen + + + align:start position:0% +really know what's going to happen +almost from the opening dialogue in the + + align:start position:0% +almost from the opening dialogue in the + + + align:start position:0% +almost from the opening dialogue in the +film where people are arguing about who + + align:start position:0% +film where people are arguing about who + + + align:start position:0% +film where people are arguing about who +has bicycles and who does not + + align:start position:0% + + + + align:start position:0% + +the the the film is organized in a very + + align:start position:0% +the the the film is organized in a very + + + align:start position:0% +the the the film is organized in a very +elegant relatively simple way it covers + + align:start position:0% +elegant relatively simple way it covers + + + align:start position:0% +elegant relatively simple way it covers +essentially three days of time the first + + align:start position:0% +essentially three days of time the first + + + align:start position:0% +essentially three days of time the first +day is the day that uh in which Richi + + align:start position:0% +day is the day that uh in which Richi + + + align:start position:0% +day is the day that uh in which Richi +gets the the commission for the job uh + + align:start position:0% +gets the the commission for the job uh + + + align:start position:0% +gets the the commission for the job uh +and + + align:start position:0% +and + + + align:start position:0% +and +um then go then goes with his wife to + + align:start position:0% +um then go then goes with his wife to + + + align:start position:0% +um then go then goes with his wife to +get his bicycle out of Hawk and you'll + + align:start position:0% +get his bicycle out of Hawk and you'll + + + align:start position:0% +get his bicycle out of Hawk and you'll +see that they have to go through C + + align:start position:0% +see that they have to go through C + + + align:start position:0% +see that they have to go through C +certain kinds of tricks to find the + + align:start position:0% +certain kinds of tricks to find the + + + align:start position:0% +certain kinds of tricks to find the +money for for to to do this uh and then + + align:start position:0% +money for for to to do this uh and then + + + align:start position:0% +money for for to to do this uh and then +once he has his bicycle he goes to work + + align:start position:0% +once he has his bicycle he goes to work + + + align:start position:0% +once he has his bicycle he goes to work +uh and on his first day of work guess + + align:start position:0% +uh and on his first day of work guess + + + align:start position:0% +uh and on his first day of work guess +what + + align:start position:0% +what + + + align:start position:0% +what +happens someone guess who hasn't seen + + align:start position:0% +happens someone guess who hasn't seen + + + align:start position:0% +happens someone guess who hasn't seen +the film what do you think might get + + align:start position:0% +the film what do you think might get + + + align:start position:0% +the film what do you think might get +stolen okay right his bicycle is stolen + + align:start position:0% +stolen okay right his bicycle is stolen + + + align:start position:0% +stolen okay right his bicycle is stolen +on the first day of work okay now the + + align:start position:0% +on the first day of work okay now the + + + align:start position:0% +on the first day of work okay now the +fact is you're really not surprised when + + align:start position:0% +fact is you're really not surprised when + + + align:start position:0% +fact is you're really not surprised when +it happens because almost from that + + align:start position:0% +it happens because almost from that + + + align:start position:0% +it happens because almost from that +first scene you're aware that bicycles + + align:start position:0% +first scene you're aware that bicycles + + + align:start position:0% +first scene you're aware that bicycles +are this incredibly precious object in + + align:start position:0% +are this incredibly precious object in + + + align:start position:0% +are this incredibly precious object in +the world and yet also incredibly common + + align:start position:0% +the world and yet also incredibly common + + + align:start position:0% +the world and yet also incredibly common +and that's part of why it's such a + + align:start position:0% +and that's part of why it's such a + + + align:start position:0% +and that's part of why it's such a +resonant symbol in in the film but the + + align:start position:0% +resonant symbol in in the film but the + + + align:start position:0% +resonant symbol in in the film but the +at the center of the film the most + + align:start position:0% +at the center of the film the most + + + align:start position:0% +at the center of the film the most +fundamental and and uh uh most memorable + + align:start position:0% +fundamental and and uh uh most memorable + + + align:start position:0% +fundamental and and uh uh most memorable +parts of the film involve what I'll call + + align:start position:0% +parts of the film involve what I'll call + + + align:start position:0% +parts of the film involve what I'll call +sort of the third segment I don't know + + align:start position:0% +sort of the third segment I don't know + + + align:start position:0% +sort of the third segment I don't know +that the segments are actually equal in + + align:start position:0% +that the segments are actually equal in + + + align:start position:0% +that the segments are actually equal in +in proportion in terms of time I think + + align:start position:0% +in proportion in terms of time I think + + + align:start position:0% +in proportion in terms of time I think +the third is the longer one uh but the + + align:start position:0% +the third is the longer one uh but the + + + align:start position:0% +the third is the longer one uh but the +third sequence is the Odyssey or the + + align:start position:0% +third sequence is the Odyssey or the + + + align:start position:0% +third sequence is the Odyssey or the +quest in which Richi and his young son + + align:start position:0% +quest in which Richi and his young son + + + align:start position:0% +quest in which Richi and his young son +uh embark on in order to recover his + + align:start position:0% +uh embark on in order to recover his + + + align:start position:0% +uh embark on in order to recover his +bicycle so he spends the whole so uh I + + align:start position:0% +bicycle so he spends the whole so uh I + + + align:start position:0% +bicycle so he spends the whole so uh I +think he gets his job gets his bike + + align:start position:0% +think he gets his job gets his bike + + + align:start position:0% +think he gets his job gets his bike +starts his job on Friday has his bike + + align:start position:0% +starts his job on Friday has his bike + + + align:start position:0% +starts his job on Friday has his bike +sto on Friday uh um or maybe it's on + + align:start position:0% +sto on Friday uh um or maybe it's on + + + align:start position:0% +sto on Friday uh um or maybe it's on +Saturday in any case he he he then he + + align:start position:0% +Saturday in any case he he he then he + + + align:start position:0% +Saturday in any case he he he then he +then uh gets his bike stolen he then he + + align:start position:0% +then uh gets his bike stolen he then he + + + align:start position:0% +then uh gets his bike stolen he then he +then asks for help from various sources + + align:start position:0% +then asks for help from various sources + + + align:start position:0% +then asks for help from various sources +and the following day he spends the + + align:start position:0% +and the following day he spends the + + + align:start position:0% +and the following day he spends the +entire day walking through the city of + + align:start position:0% +entire day walking through the city of + + + align:start position:0% +entire day walking through the city of +Rome looking for the thief trying to + + align:start position:0% +Rome looking for the thief trying to + + + align:start position:0% +Rome looking for the thief trying to +find his bike he actually finds the + + align:start position:0% +find his bike he actually finds the + + + align:start position:0% +find his bike he actually finds the +thief as you'll see in the grand climax + + align:start position:0% +thief as you'll see in the grand climax + + + align:start position:0% +thief as you'll see in the grand climax +of the film although the thief turns out + + align:start position:0% +of the film although the thief turns out + + + align:start position:0% +of the film although the thief turns out +to be as as miserable and and at least + + align:start position:0% +to be as as miserable and and at least + + + align:start position:0% +to be as as miserable and and at least +as much without prospects as por + + align:start position:0% +as much without prospects as por + + + align:start position:0% +as much without prospects as por +richichi himself and something very + + align:start position:0% +richichi himself and something very + + + align:start position:0% +richichi himself and something very +interesting happens in that moment in + + align:start position:0% +interesting happens in that moment in + + + align:start position:0% +interesting happens in that moment in +the film because your sympathy shift in + + align:start position:0% +the film because your sympathy shift in + + + align:start position:0% +the film because your sympathy shift in +some way to the to the thief in in an + + align:start position:0% +some way to the to the thief in in an + + + align:start position:0% +some way to the to the thief in in an +odd way and you watch as his + + align:start position:0% +odd way and you watch as his + + + align:start position:0% +odd way and you watch as his +neighborhood gathers around the thief to + + align:start position:0% +neighborhood gathers around the thief to + + + align:start position:0% +neighborhood gathers around the thief to +protect him in certain respects so the + + align:start position:0% +protect him in certain respects so the + + + align:start position:0% +protect him in certain respects so the +so the heart of the film is this search + + align:start position:0% +so the heart of the film is this search + + + align:start position:0% +so the heart of the film is this search +that the father and the son go on + + align:start position:0% +that the father and the son go on + + + align:start position:0% +that the father and the son go on +through the third day of the of the of + + align:start position:0% +through the third day of the of the of + + + align:start position:0% +through the third day of the of the of +the plot looking looking for the bicycle + + align:start position:0% +the plot looking looking for the bicycle + + + align:start position:0% +the plot looking looking for the bicycle +and as the day wears on the father get + + align:start position:0% +and as the day wears on the father get + + + align:start position:0% +and as the day wears on the father get +the father becomes more and more nervous + + align:start position:0% +the father becomes more and more nervous + + + align:start position:0% +the father becomes more and more nervous +more and more uneasy more more and more + + align:start position:0% +more and more uneasy more more and more + + + align:start position:0% +more and more uneasy more more and more +filled with anxiety the bike seems to + + align:start position:0% +filled with anxiety the bike seems to + + + align:start position:0% +filled with anxiety the bike seems to +him the solution to all + + align:start position:0% +him the solution to all + + + align:start position:0% +him the solution to all +difficulties uh and sometimes the sun + + align:start position:0% +difficulties uh and sometimes the sun + + + align:start position:0% +difficulties uh and sometimes the sun +slows him down and there and there are + + align:start position:0% +slows him down and there and there are + + + align:start position:0% +slows him down and there and there are +scenes in which the father becomes an + + align:start position:0% +scenes in which the father becomes an + + + align:start position:0% +scenes in which the father becomes an +annoyed or angry with the son I'm + + align:start position:0% +annoyed or angry with the son I'm + + + align:start position:0% +annoyed or angry with the son I'm +getting a bit ahead of myself so I won't + + align:start position:0% +getting a bit ahead of myself so I won't + + + align:start position:0% +getting a bit ahead of myself so I won't +repeat this again but I'll come back to + + align:start position:0% +repeat this again but I'll come back to + + + align:start position:0% +repeat this again but I'll come back to +these matters the theme of Fathers and + + align:start position:0% +these matters the theme of Fathers and + + + align:start position:0% +these matters the theme of Fathers and +Sons in any case there's a moment in + + align:start position:0% +Sons in any case there's a moment in + + + align:start position:0% +Sons in any case there's a moment in +this Odyssey where the father and the + + align:start position:0% +this Odyssey where the father and the + + + align:start position:0% +this Odyssey where the father and the +son are are engaged in this search for + + align:start position:0% +son are are engaged in this search for + + + align:start position:0% +son are are engaged in this search for +the bicycle when uh it's just after I + + align:start position:0% +the bicycle when uh it's just after I + + + align:start position:0% +the bicycle when uh it's just after I +think it's exactly at a moment when + + align:start position:0% +think it's exactly at a moment when + + + align:start position:0% +think it's exactly at a moment when +there's a gigantic downpour caught in a + + align:start position:0% +there's a gigantic downpour caught in a + + + align:start position:0% +there's a gigantic downpour caught in a +terrible + + align:start position:0% +terrible + + + align:start position:0% +terrible +rainstorm I think in fact the rainstorm + + align:start position:0% +rainstorm I think in fact the rainstorm + + + align:start position:0% +rainstorm I think in fact the rainstorm +may have caused this the boy has to pee + + align:start position:0% +may have caused this the boy has to pee + + + align:start position:0% +may have caused this the boy has to pee +very badly and so he and he interrupts + + align:start position:0% +very badly and so he and he interrupts + + + align:start position:0% +very badly and so he and he interrupts +the quest to go and pee I mean he has to + + align:start position:0% +the quest to go and pee I mean he has to + + + align:start position:0% +the quest to go and pee I mean he has to +you have to go you have to go but the + + align:start position:0% +you have to go you have to go but the + + + align:start position:0% +you have to go you have to go but the +father's so upset that the boy has + + align:start position:0% +father's so upset that the boy has + + + align:start position:0% +father's so upset that the boy has +slowed him down that he slaps him and + + align:start position:0% +slowed him down that he slaps him and + + + align:start position:0% +slowed him down that he slaps him and +it's a t like you get a sense that it + + align:start position:0% +it's a t like you get a sense that it + + + align:start position:0% +it's a t like you get a sense that it +maybe the first moment that that this + + align:start position:0% +maybe the first moment that that this + + + align:start position:0% +maybe the first moment that that this +man has ever struck his + + align:start position:0% +man has ever struck his + + + align:start position:0% +man has ever struck his +son it's it's a tremendously fraught + + align:start position:0% +son it's it's a tremendously fraught + + + align:start position:0% +son it's it's a tremendously fraught +moment uh and and um this is how bazan + + align:start position:0% +moment uh and and um this is how bazan + + + align:start position:0% +moment uh and and um this is how bazan +talks about it and this is why I I I I + + align:start position:0% +talks about it and this is why I I I I + + + align:start position:0% +talks about it and this is why I I I I +mention this moment now it's an a way of + + align:start position:0% +mention this moment now it's an a way of + + + align:start position:0% +mention this moment now it's an a way of +illustrating this principle of texture + + align:start position:0% +illustrating this principle of texture + + + align:start position:0% +illustrating this principle of texture +or openness to experience that's part of + + align:start position:0% +or openness to experience that's part of + + + align:start position:0% +or openness to experience that's part of +Thea's vision of the world he is a + + align:start position:0% +Thea's vision of the world he is a + + + align:start position:0% +Thea's vision of the world he is a +socially conscious director but he's not + + align:start position:0% +socially conscious director but he's not + + + align:start position:0% +socially conscious director but he's not +a programmatic or a or a politically + + align:start position:0% +a programmatic or a or a politically + + + align:start position:0% +a programmatic or a or a politically +preachy + + align:start position:0% +preachy + + + align:start position:0% +preachy +director so bazan focuses on that moment + + align:start position:0% +director so bazan focuses on that moment + + + align:start position:0% +director so bazan focuses on that moment +I've just described to you and he says + + align:start position:0% +I've just described to you and he says + + + align:start position:0% +I've just described to you and he says +the boy needs to pee a downpour + + align:start position:0% +the boy needs to pee a downpour + + + align:start position:0% +the boy needs to pee a downpour +interrupts the chase then he says quote + + align:start position:0% +interrupts the chase then he says quote + + + align:start position:0% +interrupts the chase then he says quote +the events are not necessarily signs of + + align:start position:0% +the events are not necessarily signs of + + + align:start position:0% +the events are not necessarily signs of +something of a truth of which we are to + + align:start position:0% +something of a truth of which we are to + + + align:start position:0% +something of a truth of which we are to +be + + align:start position:0% +be + + + align:start position:0% +be +convinced they all carry their own + + align:start position:0% +convinced they all carry their own + + + align:start position:0% +convinced they all carry their own +weight the rain the need to pee the + + align:start position:0% +weight the rain the need to pee the + + + align:start position:0% +weight the rain the need to pee the +father's anger right uh they all carry + + align:start position:0% +father's anger right uh they all carry + + + align:start position:0% +father's anger right uh they all carry +their own weight their complete + + align:start position:0% +their own weight their complete + + + align:start position:0% +their own weight their complete +uniqueness they all have bazan says so + + 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be programmatic if it +if it does that and in fact the moment + + align:start position:0% +if it does that and in fact the moment + + + align:start position:0% +if it does that and in fact the moment +I'm describing is is really in some + + align:start position:0% +I'm describing is is really in some + + + align:start position:0% +I'm describing is is really in some +sense a version of what I've been + + align:start position:0% +sense a version of what I've been + + + align:start position:0% +sense a version of what I've been +calling the neorealist counterplot what + + align:start position:0% +calling the neorealist counterplot what + + + align:start position:0% +calling the neorealist counterplot what +constantly happens in good neorealist + + align:start position:0% +constantly happens in good neorealist + + + align:start position:0% +constantly happens in good neorealist +films and what what happens again and + + align:start position:0% +films and what what happens again and + + + align:start position:0% +films and what what happens again and +again in The Bicycle Thief is that the + + align:start position:0% +again in The Bicycle Thief is that the + + + align:start position:0% +again in The Bicycle Thief is that the +ongoing quest for the bicycle is + + align:start position:0% +ongoing quest for the bicycle is + + + align:start position:0% +ongoing quest for the bicycle is + or interrupted by various kinds + + align:start position:0% + or interrupted by various kinds + + + align:start position:0% + or interrupted by various kinds +of accident disturbance uh uh strange + + align:start position:0% +of accident disturbance uh uh strange + + + align:start position:0% +of accident disturbance uh uh strange +encounter so that the so that the search + + align:start position:0% +encounter so that the so that the search + + + align:start position:0% +encounter so that the so that the search +the bicycle become something much larger + + align:start position:0% +the bicycle become something much larger + + + align:start position:0% +the bicycle become something much larger +than that and every particular moment in + + align:start position:0% +than that and every particular moment in + + + align:start position:0% +than that and every particular moment in +the film has as bazan says its own + + align:start position:0% +the film has as bazan says its own + + + align:start position:0% +the film has as bazan says its own +uniqueness it's own it's you don't feel + + align:start position:0% +uniqueness it's own it's you don't feel + + + align:start position:0% +uniqueness it's own it's you don't feel +that anything is in the film to further + + align:start position:0% +that anything is in the film to further + + + align:start position:0% +that anything is in the film to further +the plot or to illuminate the character + + align:start position:0% +the plot or to illuminate the character + + + align:start position:0% +the plot or to illuminate the character +or to tell you something about what + + align:start position:0% +or to tell you something about what + + + align:start position:0% +or to tell you something about what +political attitudes you should have + + align:start position:0% +political attitudes you should have + + + align:start position:0% +political attitudes you should have +although by the time you're finished + + align:start position:0% +although by the time you're finished + + + align:start position:0% +although by the time you're finished +with the film you do have very coherent + + align:start position:0% +with the film you do have very coherent + + + align:start position:0% +with the film you do have very coherent +sense of how the society is breaking + + align:start position:0% +sense of how the society is breaking + + + align:start position:0% +sense of how the society is breaking +down of what of of how people are + + align:start position:0% +down of what of of how people are + + + align:start position:0% +down of what of of how people are +sustaining themselves of about how + + align:start position:0% +sustaining themselves of about how + + + align:start position:0% +sustaining themselves of about how +difficult life is in postwar Italy + + align:start position:0% +difficult life is in postwar Italy + + + align:start position:0% +difficult life is in postwar Italy +you're aware of all of these things + + align:start position:0% +you're aware of all of these things + + + align:start position:0% +you're aware of all of these things +uh and and and and and aware of them + + align:start position:0% +uh and and and and and aware of them + + + align:start position:0% +uh and and and and and aware of them +with a concreteness and a Clarity that + + align:start position:0% +with a concreteness and a Clarity that + + + align:start position:0% +with a concreteness and a Clarity that +you wouldn't have if you read an + + align:start position:0% +you wouldn't have if you read an + + + align:start position:0% +you wouldn't have if you read an +abstract essay you've seen them embodied + + align:start position:0% +abstract essay you've seen them embodied + + + align:start position:0% +abstract essay you've seen them embodied +in a totally believable fiction but what + + align:start position:0% +in a totally believable fiction but what + + + align:start position:0% +in a totally believable fiction but what +gives the fiction its Authority what + + align:start position:0% +gives the fiction its Authority what + + + align:start position:0% +gives the fiction its Authority what +gives it its power is precisely that you + + align:start position:0% +gives it its power is precisely that you + + + align:start position:0% +gives it its power is precisely that you +don't feel you're watching a sermon you + + align:start position:0% +don't feel you're watching a sermon you + + + align:start position:0% +don't feel you're watching a sermon you +don't feel you're watching something in + + align:start position:0% +don't feel you're watching something in + + + align:start position:0% +don't feel you're watching something in +which in in which some political + + align:start position:0% +which in in which some political + + + align:start position:0% +which in in which some political +moralist is beating you over the head + + align:start position:0% +moralist is beating you over the head + + + align:start position:0% +moralist is beating you over the head +and telling you oh you better love this + + align:start position:0% +and telling you oh you better love this + + + align:start position:0% +and telling you oh you better love this +poor guy you but and in fact as the film + + align:start position:0% +poor guy you but and in fact as the film + + + align:start position:0% +poor guy you but and in fact as the film +goes on one of the things you discover + + align:start position:0% +goes on one of the things you discover + + + align:start position:0% +goes on one of the things you discover +is that they are very they're are nasty + + align:start position:0% +is that they are very they're are nasty + + + align:start position:0% +is that they are very they're are nasty +or bad sides to poor RI we understand + + align:start position:0% +or bad sides to poor RI we understand + + + align:start position:0% +or bad sides to poor RI we understand +that he's driven by economic anxiety + + align:start position:0% +that he's driven by economic anxiety + + + align:start position:0% +that he's driven by economic anxiety +that's very deep and it partly and + + align:start position:0% +that's very deep and it partly and + + + align:start position:0% +that's very deep and it partly and +certainly mitigates his his behavior but + + align:start position:0% +certainly mitigates his his behavior but + + + align:start position:0% +certainly mitigates his his behavior but +he behaves crudely and cruy to his son + + align:start position:0% +he behaves crudely and cruy to his son + + + align:start position:0% +he behaves crudely and cruy to his son +never intending to and then of course + + align:start position:0% +never intending to and then of course + + + align:start position:0% +never intending to and then of course +there are moments when he recovers and + + align:start position:0% +there are moments when he recovers and + + + align:start position:0% +there are moments when he recovers and +tries to tries to make up with his son + + align:start position:0% +tries to tries to make up with his son + + + align:start position:0% +tries to tries to make up with his son +I'll come back to this in a moment so + + align:start position:0% +I'll come back to this in a moment so + + + align:start position:0% +I'll come back to this in a moment so +this passage from bz also calls + + align:start position:0% +this passage from bz also calls + + + align:start position:0% +this passage from bz also calls +attention then to what I think of as a + + align:start position:0% +attention then to what I think of as a + + + align:start position:0% +attention then to what I think of as a +signal feature in these films the uh and + + align:start position:0% +signal feature in these films the uh and + + + align:start position:0% +signal feature in these films the uh and +especially in The Bicycle Thief that + + align:start position:0% +especially in The Bicycle Thief that + + + align:start position:0% +especially in The Bicycle Thief that +power that that uh any moment in the + + align:start position:0% +power that that uh any moment in the + + + align:start position:0% +power that that uh any moment in the +film has to express a a kind of complete + + align:start position:0% +film has to express a a kind of complete + + + align:start position:0% +film has to express a a kind of complete +uniqueness the ambiguity that + + align:start position:0% +uniqueness the ambiguity that + + + align:start position:0% +uniqueness the ambiguity that +characterizes reality + + align:start position:0% +characterizes reality + + + align:start position:0% +characterizes reality +itself well um what I'd like to uh uh + + align:start position:0% +itself well um what I'd like to uh uh + + + align:start position:0% +itself well um what I'd like to uh uh +briefly do is give you a a partial + + align:start position:0% +briefly do is give you a a partial + + + align:start position:0% +briefly do is give you a a partial +account a a modest account of desa's own + + align:start position:0% +account a a modest account of desa's own + + + align:start position:0% +account a a modest account of desa's own +career uh and then say some things about + + align:start position:0% +career uh and then say some things about + + + align:start position:0% +career uh and then say some things about +the bicycle about bicycle + + align:start position:0% +the bicycle about bicycle + + + align:start position:0% +the bicycle about bicycle +thieves uh Desa was a stage actor uh he + + align:start position:0% +thieves uh Desa was a stage actor uh he + + + align:start position:0% +thieves uh Desa was a stage actor uh he +gave regimental performances when he + + align:start position:0% +gave regimental performances when he + + + align:start position:0% +gave regimental performances when he +served in the army in the first world + + align:start position:0% +served in the army in the first world + + + align:start position:0% +served in the army in the first world +war became a stage hand right after the + + align:start position:0% +war became a stage hand right after the + + + align:start position:0% +war became a stage hand right after the +war and an actor in + + align:start position:0% +war and an actor in + + + align:start position:0% +war and an actor in +1923 uh he joined a theater company in + + align:start position:0% +1923 uh he joined a theater company in + + + align:start position:0% +1923 uh he joined a theater company in +1925 a touring company and he became a + + align:start position:0% +1925 a touring company and he became a + + + align:start position:0% +1925 a touring company and he became a +tremendous success in a series of + + align:start position:0% +tremendous success in a series of + + + align:start position:0% +tremendous success in a series of +performances he uh in 1927 he appeared + + align:start position:0% +performances he uh in 1927 he appeared + + + align:start position:0% +performances he uh in 1927 he appeared +uh on stage in Rome in something called + + align:start position:0% +uh on stage in Rome in something called + + + align:start position:0% +uh on stage in Rome in something called +the zaboomafoo + + align:start position:0% + + + + align:start position:0% + +or at least the theater icon um he he + + align:start position:0% +or at least the theater icon um he he + + + align:start position:0% +or at least the theater icon um he he +made his first film in that same year in + + align:start position:0% +made his first film in that same year in + + + align:start position:0% +made his first film in that same year in +1922 as an actor uh and his first uh uh + + align:start position:0% +1922 as an actor uh and his first uh uh + + + align:start position:0% +1922 as an actor uh and his first uh uh +success came he he continued to act in + + align:start position:0% +success came he he continued to act in + + + align:start position:0% +success came he he continued to act in +films intermittently for the next decade + + align:start position:0% +films intermittently for the next decade + + + align:start position:0% +films intermittently for the next decade +but he didn't become a recognizably + + align:start position:0% +but he didn't become a recognizably + + + align:start position:0% +but he didn't become a recognizably +serious film actor until his first major + + align:start position:0% +serious film actor until his first major + + + align:start position:0% +serious film actor until his first major +success in + + align:start position:0% +success in + + + align:start position:0% +success in +1932 uh and then he and and then uh for + + align:start position:0% +1932 uh and then he and and then uh for + + + align:start position:0% +1932 uh and then he and and then uh for +10 years he he's a kind of matina idol + + align:start position:0% +10 years he he's a kind of matina idol + + + align:start position:0% +10 years he he's a kind of matina idol +on uh in in + + align:start position:0% +on uh in in + + + align:start position:0% +on uh in in +Italian movies he made over 40 films in + + align:start position:0% +Italian movies he made over 40 films in + + + align:start position:0% +Italian movies he made over 40 films in +the period between as an actor between + + align:start position:0% +the period between as an actor between + + + align:start position:0% +the period between as an actor between +1932 and 1942 a very handsome man as + + align:start position:0% +1932 and 1942 a very handsome man as + + + align:start position:0% +1932 and 1942 a very handsome man as +some of you may know if you've seen him + + align:start position:0% +some of you may know if you've seen him + + + align:start position:0% +some of you may know if you've seen him +uh and uh + + align:start position:0% +uh and uh + + + align:start position:0% +uh and uh +uh capable of great subtlety as an actor + + align:start position:0% +uh capable of great subtlety as an actor + + + align:start position:0% +uh capable of great subtlety as an actor +this may help to explain why he was such + + align:start position:0% +this may help to explain why he was such + + + align:start position:0% +this may help to explain why he was such +a great director of nonprofessional + + align:start position:0% +a great director of nonprofessional + + + align:start position:0% +a great director of nonprofessional +actors because he knew intuitively I + + align:start position:0% +actors because he knew intuitively I + + + align:start position:0% +actors because he knew intuitively I +think how to bring out uh a performance + + align:start position:0% +think how to bring out uh a performance + + + align:start position:0% +think how to bring out uh a performance +from a from a from someone who was not + + align:start position:0% +from a from a from someone who was not + + + align:start position:0% +from a from a from someone who was not +trained in in performing in acting he + + align:start position:0% +trained in in performing in acting he + + + align:start position:0% +trained in in performing in acting he +begins to direct in + + align:start position:0% +begins to direct in + + + align:start position:0% +begins to direct in +1940 and makes a series + + align:start position:0% +1940 and makes a series + + + align:start position:0% +1940 and makes a series +of interesting but forgettable films I + + align:start position:0% +of interesting but forgettable films I + + + align:start position:0% +of interesting but forgettable films I +suppose his first really significant + + align:start position:0% +suppose his first really significant + + + align:start position:0% +suppose his first really significant +film from one angle anyway if especially + + align:start position:0% +film from one angle anyway if especially + + + align:start position:0% +film from one angle anyway if especially +if we interested in the development of + + align:start position:0% +if we interested in the development of + + + align:start position:0% +if we interested in the development of +neorealism is a film he makes in + + align:start position:0% +neorealism is a film he makes in + + + align:start position:0% +neorealism is a film he makes in +1942 co-screenwriter + + align:start position:0% +1942 co-screenwriter + + + align:start position:0% +1942 co-screenwriter +Chesire + + align:start position:0% +Chesire + + + align:start position:0% +Chesire +zaatini entitled the children are + + align:start position:0% +zaatini entitled the children are + + + align:start position:0% +zaatini entitled the children are +watching us uh and it's it's a it's I've + + align:start position:0% +watching us uh and it's it's a it's I've + + + align:start position:0% +watching us uh and it's it's a it's I've +seen the film it's it's not a great film + + align:start position:0% +seen the film it's it's not a great film + + + align:start position:0% +seen the film it's it's not a great film +uh but it's an interesting film and + + align:start position:0% +uh but it's an interesting film and + + + align:start position:0% +uh but it's an interesting film and +there are some remarkable moments in it + + align:start position:0% +there are some remarkable moments in it + + + align:start position:0% +there are some remarkable moments in it +uh the title tells you something about + + align:start position:0% +uh the title tells you something about + + + align:start position:0% +uh the title tells you something about +the neorealist commitment to to focus on + + align:start position:0% +the neorealist commitment to to focus on + + + align:start position:0% +the neorealist commitment to to focus on +the underprivileged and the disempowered + + align:start position:0% +the underprivileged and the disempowered + + + align:start position:0% +the underprivileged and the disempowered +in society the many neorealist films + + align:start position:0% +in society the many neorealist films + + + align:start position:0% +in society the many neorealist films +Focus directly on children uh and the + + align:start position:0% +Focus directly on children uh and the + + + align:start position:0% +Focus directly on children uh and the +children are watching us as one such + + align:start position:0% +children are watching us as one such + + + align:start position:0% +children are watching us as one such +film that and it almost announces that + + align:start position:0% +film that and it almost announces that + + + align:start position:0% +film that and it almost announces that +the the idea that children are among the + + align:start position:0% +the the idea that children are among the + + + align:start position:0% +the the idea that children are among the +victims of society because they are + + align:start position:0% +victims of society because they are + + + align:start position:0% +victims of society because they are +subjected not only to all the political + + align:start position:0% +subjected not only to all the political + + + align:start position:0% +subjected not only to all the political +and social authorities of the society + + align:start position:0% +and social authorities of the society + + + align:start position:0% +and social authorities of the society +but also to the arbitrary authority of + + align:start position:0% +but also to the arbitrary authority of + + + align:start position:0% +but also to the arbitrary authority of +their own parents and their own uh and + + align:start position:0% +their own parents and their own uh and + + + align:start position:0% +their own parents and their own uh and +their own uh immediate family + + align:start position:0% +their own uh immediate family + + + align:start position:0% +their own uh immediate family +environment uh so um um so the children + + align:start position:0% +environment uh so um um so the children + + + align:start position:0% +environment uh so um um so the children +are watching us announces this uh + + align:start position:0% +are watching us announces this uh + + + align:start position:0% +are watching us announces this uh +interest in the disenfranchised and + + align:start position:0% +interest in the disenfranchised and + + + align:start position:0% +interest in the disenfranchised and +especially in children uh and it's a + + align:start position:0% +especially in children uh and it's a + + + align:start position:0% +especially in children uh and it's a +it's a film about the breakup of a + + align:start position:0% +it's a film about the breakup of a + + + align:start position:0% +it's a film about the breakup of a +middle class marriage mostly told + + align:start position:0% +middle class marriage mostly told + + + align:start position:0% +middle class marriage mostly told +Through The Eyes of the children + + align:start position:0% +Through The Eyes of the children + + + align:start position:0% +Through The Eyes of the children +so there are s certain things certain + + align:start position:0% +so there are s certain things certain + + + align:start position:0% +so there are s certain things certain +behaviors on the part of the adults are + + align:start position:0% +behaviors on the part of the adults are + + + align:start position:0% +behaviors on the part of the adults are +never fully explained because you + + align:start position:0% +never fully explained because you + + + align:start position:0% +never fully explained because you +witness and experience the film uh + + align:start position:0% +witness and experience the film uh + + + align:start position:0% +witness and experience the film uh +through the not just the eyes but + + align:start position:0% +through the not just the eyes but + + + align:start position:0% +through the not just the eyes but +through the perceptions the + + align:start position:0% +through the perceptions the + + + align:start position:0% +through the perceptions the +understanding the sensibility of + + align:start position:0% +understanding the sensibility of + + + align:start position:0% +understanding the sensibility of +children who are somewhat confused about + + align:start position:0% +children who are somewhat confused about + + + align:start position:0% +children who are somewhat confused about +what they're + + align:start position:0% +what they're + + + align:start position:0% +what they're +seeing + + align:start position:0% + + + + align:start position:0% + +um the the film that established him as + + align:start position:0% +um the the film that established him as + + + align:start position:0% +um the the film that established him as +an international figure and established + + align:start position:0% +an international figure and established + + + align:start position:0% +an international figure and established +neorealism as an international movement + + align:start position:0% +neorealism as an international movement + + + align:start position:0% +neorealism as an international movement +was one that Desa and zaatini + + align:start position:0% +was one that Desa and zaatini + + + align:start position:0% +was one that Desa and zaatini +collaborated on in + + align:start position:0% +collaborated on in + + + align:start position:0% +collaborated on in +1946 and it was entitled + + align:start position:0% +1946 and it was entitled + + + align:start position:0% +1946 and it was entitled +shuine + + align:start position:0% +shuine + + + align:start position:0% +shuine +and I sometimes have been tempted to + + align:start position:0% +and I sometimes have been tempted to + + + align:start position:0% +and I sometimes have been tempted to +show shush shine in this course even + + align:start position:0% +show shush shine in this course even + + + align:start position:0% +show shush shine in this course even +though it's a much less Perfect film + + align:start position:0% +though it's a much less Perfect film + + + align:start position:0% +though it's a much less Perfect film +than bicycle thieves because in in its + + align:start position:0% +than bicycle thieves because in in its + + + align:start position:0% +than bicycle thieves because in in its +own way it's so powerful and moving one + + align:start position:0% +own way it's so powerful and moving one + + + align:start position:0% +own way it's so powerful and moving one +of the most interesting things about uh + + align:start position:0% +of the most interesting things about uh + + + align:start position:0% +of the most interesting things about uh +neorealism uh apart from the fact that + + align:start position:0% +neorealism uh apart from the fact that + + + align:start position:0% +neorealism uh apart from the fact that +it was so short lived is how relevant + + align:start position:0% +it was so short lived is how relevant + + + align:start position:0% +it was so short lived is how relevant +the films still feel today if you watch + + align:start position:0% +the films still feel today if you watch + + + align:start position:0% +the films still feel today if you watch +shuine or another of the films that I've + + align:start position:0% +shuine or another of the films that I've + + + align:start position:0% +shuine or another of the films that I've +that I've listed here Umberto D which is + + align:start position:0% +that I've listed here Umberto D which is + + + align:start position:0% +that I've listed here Umberto D which is +about uh uh the problems of people who + + align:start position:0% +about uh uh the problems of people who + + + align:start position:0% +about uh uh the problems of people who +have gone into of old of the old it's + + align:start position:0% +have gone into of old of the old it's + + + align:start position:0% +have gone into of old of the old it's +people who are retired pensioners and + + align:start position:0% +people who are retired pensioners and + + + align:start position:0% +people who are retired pensioners and +the problems they face when there is + + align:start position:0% +the problems they face when there is + + + align:start position:0% +the problems they face when there is +horrific + + align:start position:0% +horrific + + + align:start position:0% +horrific +inflation uh Desa dedicated that film to + + align:start position:0% +inflation uh Desa dedicated that film to + + + align:start position:0% +inflation uh Desa dedicated that film to +his father and it's about an old man + + align:start position:0% +his father and it's about an old man + + + align:start position:0% +his father and it's about an old man +who's very proud he used to he dresses + + align:start position:0% +who's very proud he used to he dresses + + + align:start position:0% +who's very proud he used to he dresses +very well but he's tremendously isolated + + align:start position:0% +very well but he's tremendously isolated + + + align:start position:0% +very well but he's tremendously isolated +he's terribly poor he's almost reduced + + align:start position:0% +he's terribly poor he's almost reduced + + + align:start position:0% +he's terribly poor he's almost reduced +to begging in the course of the film and + + align:start position:0% +to begging in the course of the film and + + + align:start position:0% +to begging in the course of the film and +there's even a moment near the end of + + align:start position:0% +there's even a moment near the end of + + + align:start position:0% +there's even a moment near the end of +the film where he contemplates and then + + align:start position:0% +the film where he contemplates and then + + + align:start position:0% +the film where he contemplates and then +pulls back from + + align:start position:0% +pulls back from + + + align:start position:0% +pulls back from +suicide um uh so so but but watching + + align:start position:0% +suicide um uh so so but but watching + + + align:start position:0% +suicide um uh so so but but watching +that film today it feels much less dated + + align:start position:0% +that film today it feels much less dated + + + align:start position:0% +that film today it feels much less dated +than some films that are much later than + + align:start position:0% +than some films that are much later than + + + align:start position:0% +than some films that are much later than +that that were produced 10 15 20 25 + + align:start position:0% +that that were produced 10 15 20 25 + + + align:start position:0% +that that were produced 10 15 20 25 +years after it because the theme is so + + align:start position:0% +years after it because the theme is so + + + align:start position:0% +years after it because the theme is so +relevant I mean because we know that in + + align:start position:0% +relevant I mean because we know that in + + + align:start position:0% +relevant I mean because we know that in +society today there are so many in all + + align:start position:0% +society today there are so many in all + + + align:start position:0% +society today there are so many in all +Western societies but especially in the + + align:start position:0% +Western societies but especially in the + + + align:start position:0% +Western societies but especially in the +United States there are pensioners who + + align:start position:0% +United States there are pensioners who + + + align:start position:0% +United States there are pensioners who +can't make ends ends meet and the same + + align:start position:0% +can't make ends ends meet and the same + + + align:start position:0% +can't make ends ends meet and the same +thing is true I think in some degree of + + align:start position:0% +thing is true I think in some degree of + + + align:start position:0% +thing is true I think in some degree of +the of the of the fate of children in + + align:start position:0% +the of the of the fate of children in + + + align:start position:0% +the of the of the fate of children in +modern society so shuine although it has + + align:start position:0% +modern society so shuine although it has + + + align:start position:0% +modern society so shuine although it has +a very melodramatic and violent ending + + align:start position:0% +a very melodramatic and violent ending + + + align:start position:0% +a very melodramatic and violent ending +it's a immensely powerful film + + align:start position:0% +it's a immensely powerful film + + + align:start position:0% +it's a immensely powerful film +essentially it's a story about two boys + + align:start position:0% +essentially it's a story about two boys + + + align:start position:0% +essentially it's a story about two boys +two Roman Street urchins who are taken + + align:start position:0% +two Roman Street urchins who are taken + + + align:start position:0% +two Roman Street urchins who are taken +advantage of in some sense by by by + + align:start position:0% +advantage of in some sense by by by + + + align:start position:0% +advantage of in some sense by by by +their own relatives who are trafficking + + align:start position:0% +their own relatives who are trafficking + + + align:start position:0% +their own relatives who are trafficking +in Black Market Goods it's just the same + + align:start position:0% +in Black Market Goods it's just the same + + + align:start position:0% +in Black Market Goods it's just the same +it's said in the same moment at at the + + align:start position:0% +it's said in the same moment at at the + + + align:start position:0% +it's said in the same moment at at the +end of the war in fact the film opens + + align:start position:0% +end of the war in fact the film opens + + + align:start position:0% +end of the war in fact the film opens +with uh these these uh these + + align:start position:0% +with uh these these uh these + + + align:start position:0% +with uh these these uh these +urchins trying to make a living as + + align:start position:0% +urchins trying to make a living as + + + align:start position:0% +urchins trying to make a living as +shuine boys that's why where the title + + align:start position:0% +shuine boys that's why where the title + + + align:start position:0% +shuine boys that's why where the title +comes from uh and these shine boys are + + align:start position:0% +comes from uh and these shine boys are + + + align:start position:0% +comes from uh and these shine boys are +wandering the streets of Rome going up + + align:start position:0% +wandering the streets of Rome going up + + + align:start position:0% +wandering the streets of Rome going up +to American soldiers who are dominating + + align:start position:0% +to American soldiers who are dominating + + + align:start position:0% +to American soldiers who are dominating +the streets where it's still an occupied + + align:start position:0% +the streets where it's still an occupied + + + align:start position:0% +the streets where it's still an occupied +City uh asking soldiers if they want Sho + + align:start position:0% +City uh asking soldiers if they want Sho + + + align:start position:0% +City uh asking soldiers if they want Sho +shines um and and uh the this the + + align:start position:0% +shines um and and uh the this the + + + align:start position:0% +shines um and and uh the this the +children are unbelievable victims + + align:start position:0% +children are unbelievable victims + + + align:start position:0% +children are unbelievable victims +they're very close friends they end up + + align:start position:0% +they're very close friends they end up + + + align:start position:0% +they're very close friends they end up +buying a race race horse a broken down + + align:start position:0% +buying a race race horse a broken down + + + align:start position:0% +buying a race race horse a broken down +old racehorse that that that can't race + + align:start position:0% +old racehorse that that that can't race + + + align:start position:0% +old racehorse that that that can't race +anymore and they stable it someplace and + + align:start position:0% +anymore and they stable it someplace and + + + align:start position:0% +anymore and they stable it someplace and +it's a they're they're uh very excited + + align:start position:0% +it's a they're they're uh very excited + + + align:start position:0% +it's a they're they're uh very excited +about about their about their possession + + align:start position:0% +about about their about their possession + + + align:start position:0% +about about their about their possession +of this horse and there's some early + + align:start position:0% +of this horse and there's some early + + + align:start position:0% +of this horse and there's some early +scenes in which you see them riding on + + align:start position:0% +scenes in which you see them riding on + + + align:start position:0% +scenes in which you see them riding on +the horse with tremendous joy and so + + align:start position:0% +the horse with tremendous joy and so + + + align:start position:0% +the horse with tremendous joy and so +forth but of course this is the the dawn + + align:start position:0% +forth but of course this is the the dawn + + + align:start position:0% +forth but of course this is the the dawn +before the miserable night because what + + align:start position:0% +before the miserable night because what + + + align:start position:0% +before the miserable night because what +then happens is the kids are taken + + align:start position:0% +then happens is the kids are taken + + + align:start position:0% +then happens is the kids are taken +advantage of by one of their by by a + + align:start position:0% +advantage of by one of their by by a + + + align:start position:0% +advantage of by one of their by by a +close relative they're involved in Black + + align:start position:0% +close relative they're involved in Black + + + align:start position:0% +close relative they're involved in Black +Market activities the men the the adults + + align:start position:0% +Market activities the men the the adults + + + align:start position:0% +Market activities the men the the adults +use the children because they know that + + align:start position:0% +use the children because they know that + + + align:start position:0% +use the children because they know that +the children are less vulnerable than + + align:start position:0% +the children are less vulnerable than + + + align:start position:0% +the children are less vulnerable than +they would be if they're caught the + + align:start position:0% +they would be if they're caught the + + + align:start position:0% +they would be if they're caught the +children are caught caught they're sent + + align:start position:0% +children are caught caught they're sent + + + align:start position:0% +children are caught caught they're sent +to reform school and most of the film + + align:start position:0% +to reform school and most of the film + + + align:start position:0% +to reform school and most of the film +takes place in the reform school and you + + align:start position:0% +takes place in the reform school and you + + + align:start position:0% +takes place in the reform school and you +see these two bright-eyed beautiful + + align:start position:0% +see these two bright-eyed beautiful + + + align:start position:0% +see these two bright-eyed beautiful +young children no maybe 10 years old who + + align:start position:0% +young children no maybe 10 years old who + + + align:start position:0% +young children no maybe 10 years old who +are the fastest and closest of friends + + align:start position:0% +are the fastest and closest of friends + + + align:start position:0% +are the fastest and closest of friends +when they go into jail slowly breaking + + align:start position:0% +when they go into jail slowly breaking + + + align:start position:0% +when they go into jail slowly breaking +down you see their Humanity being beaten + + align:start position:0% +down you see their Humanity being beaten + + + align:start position:0% +down you see their Humanity being beaten +out of them by the conditions in the + + align:start position:0% +out of them by the conditions in the + + + align:start position:0% +out of them by the conditions in the +reforms in the in the in the children's + + align:start position:0% +reforms in the in the in the children's + + + align:start position:0% +reforms in the in the in the children's +prison uh it it's a it it's a terrible + + align:start position:0% +prison uh it it's a it it's a terrible + + + align:start position:0% +prison uh it it's a it it's a terrible +uh disturbing film in part because you + + align:start position:0% +uh disturbing film in part because you + + + align:start position:0% +uh disturbing film in part because you +could you can you can see that the + + align:start position:0% +could you can you can see that the + + + align:start position:0% +could you can you can see that the +people who are running the prison + + align:start position:0% +people who are running the prison + + + align:start position:0% +people who are running the prison +actually mean well they're not vicious + + align:start position:0% +actually mean well they're not vicious + + + align:start position:0% +actually mean well they're not vicious +evil people who want to harm children + + align:start position:0% +evil people who want to harm children + + + align:start position:0% +evil people who want to harm children +they just can't the the the system seems + + align:start position:0% +they just can't the the the system seems + + + align:start position:0% +they just can't the the the system seems +designed simply to cause more harm than + + align:start position:0% +designed simply to cause more harm than + + + align:start position:0% +designed simply to cause more harm than +good and to and to destroy the vitality + + align:start position:0% +good and to and to destroy the vitality + + + align:start position:0% +good and to and to destroy the vitality +and optimism in and and when I say the + + align:start position:0% +and optimism in and and when I say the + + + align:start position:0% +and optimism in and and when I say the +film ends melodramatically one one child + + align:start position:0% +film ends melodramatically one one child + + + align:start position:0% +film ends melodramatically one one child +strikes out at his Earth while best + + align:start position:0% +strikes out at his Earth while best + + + align:start position:0% +strikes out at his Earth while best +friend and knocks him down a bank and he + + align:start position:0% +friend and knocks him down a bank and he + + + align:start position:0% +friend and knocks him down a bank and he +dies so there's a in effect accidentally + + align:start position:0% +dies so there's a in effect accidentally + + + align:start position:0% +dies so there's a in effect accidentally +murders his a person who had been his + + align:start position:0% +murders his a person who had been his + + + align:start position:0% +murders his a person who had been his +dearest friend I think it's a failure in + + align:start position:0% +dearest friend I think it's a failure in + + + align:start position:0% +dearest friend I think it's a failure in +the film I think that you didn't need + + align:start position:0% +the film I think that you didn't need + + + align:start position:0% +the film I think that you didn't need +the murder for the meanings of the film + + align:start position:0% +the murder for the meanings of the film + + + align:start position:0% +the murder for the meanings of the film +to be available I think that Desa learn + + align:start position:0% +to be available I think that Desa learn + + + align:start position:0% +to be available I think that Desa learn +something from that and when you watch + + align:start position:0% +something from that and when you watch + + + align:start position:0% +something from that and when you watch +the ending of The Bicycle Thief one of + + align:start position:0% +the ending of The Bicycle Thief one of + + + align:start position:0% +the ending of The Bicycle Thief one of +the things I hope you'll ask yourself is + + align:start position:0% +the things I hope you'll ask yourself is + + + align:start position:0% +the things I hope you'll ask yourself is +why is it so apparently undramatic and + + align:start position:0% +why is it so apparently undramatic and + + + align:start position:0% +why is it so apparently undramatic and +why does that undramatic ending in the + + align:start position:0% +why does that undramatic ending in the + + + align:start position:0% +why does that undramatic ending in the +end seems so profound so moving so + + align:start position:0% +end seems so profound so moving so + + + align:start position:0% +end seems so profound so moving so +meaningful uh it's as if it's as if to + + align:start position:0% +meaningful uh it's as if it's as if to + + + align:start position:0% +meaningful uh it's as if it's as if to +seek a sort of learned his lesson as if + + align:start position:0% +seek a sort of learned his lesson as if + + + align:start position:0% +seek a sort of learned his lesson as if +he drove his point home too heavily at + + align:start position:0% +he drove his point home too heavily at + + + align:start position:0% +he drove his point home too heavily at +the end of shuine and he realized that + + align:start position:0% +the end of shuine and he realized that + + + align:start position:0% +the end of shuine and he realized that +to have a truly organic text that did + + align:start position:0% +to have a truly organic text that did + + + align:start position:0% +to have a truly organic text that did +what bazan wants text to do reflect the + + align:start position:0% +what bazan wants text to do reflect the + + + align:start position:0% +what bazan wants text to do reflect the +unique the unique ambiguity of every of + + align:start position:0% +unique the unique ambiguity of every of + + + align:start position:0% +unique the unique ambiguity of every of +every + + align:start position:0% +every + + + align:start position:0% +every +experience the ending of the bicycle of + + align:start position:0% +experience the ending of the bicycle of + + + align:start position:0% +experience the ending of the bicycle of +bicycle thieves does that much more + + align:start position:0% +bicycle thieves does that much more + + + align:start position:0% +bicycle thieves does that much more +effectively as I hope you'll watch for + + align:start position:0% +effectively as I hope you'll watch for + + + align:start position:0% +effectively as I hope you'll watch for +uh when you when you're watching the + + align:start position:0% +uh when you when you're watching the + + + align:start position:0% +uh when you when you're watching the +film so shine but shine was a made a + + align:start position:0% +film so shine but shine was a made a + + + align:start position:0% +film so shine but shine was a made a +tremendous impact and it won uh the the + + align:start position:0% +tremendous impact and it won uh the the + + + align:start position:0% +tremendous impact and it won uh the the +first of four Academy Awards that Desa + + align:start position:0% +first of four Academy Awards that Desa + + + align:start position:0% +first of four Academy Awards that Desa +won as as best director uh for this was + + align:start position:0% +won as as best director uh for this was + + + align:start position:0% +won as as best director uh for this was +for the best foreign film of the year in + + align:start position:0% +for the best foreign film of the year in + + + align:start position:0% +for the best foreign film of the year in +1946 and it put neorealism on the map um + + align:start position:0% +1946 and it put neorealism on the map um + + + align:start position:0% +1946 and it put neorealism on the map um +um and + + align:start position:0% +um and + + + align:start position:0% +um and +then two years + + align:start position:0% + + + + align:start position:0% + +later zaatini and and uh Desa followed + + align:start position:0% +later zaatini and and uh Desa followed + + + align:start position:0% +later zaatini and and uh Desa followed +with what I suppose we could call their + + align:start position:0% +with what I suppose we could call their + + + align:start position:0% +with what I suppose we could call their +Masterpiece bicycle thieves I want to + + align:start position:0% +Masterpiece bicycle thieves I want to + + + align:start position:0% +Masterpiece bicycle thieves I want to +say this is not a complet remotely + + align:start position:0% +say this is not a complet remotely + + + align:start position:0% +say this is not a complet remotely +complete list of se's films I've just + + align:start position:0% +complete list of se's films I've just + + + align:start position:0% +complete list of se's films I've just +listed some highlights here because I + + align:start position:0% +listed some highlights here because I + + + align:start position:0% +listed some highlights here because I +want to give you a sense of his work uh + + align:start position:0% +want to give you a sense of his work uh + + + align:start position:0% +want to give you a sense of his work uh +I've mentioned Umberto D already the + + align:start position:0% +I've mentioned Umberto D already the + + + align:start position:0% +I've mentioned Umberto D already the +last neorealist film according to many + + align:start position:0% +last neorealist film according to many + + + align:start position:0% +last neorealist film according to many +people uh and a very moving one about + + align:start position:0% +people uh and a very moving one about + + + align:start position:0% +people uh and a very moving one about +about an old pensioner uh the film two + + align:start position:0% +about an old pensioner uh the film two + + + align:start position:0% +about an old pensioner uh the film two +women starts Sophia Lauren one of the + + align:start position:0% +women starts Sophia Lauren one of the + + + align:start position:0% +women starts Sophia Lauren one of the +one of the great sort of uh + + align:start position:0% +one of the great sort of uh + + + align:start position:0% +one of the great sort of uh +pulchritudinous Italian movie stars of + + align:start position:0% +pulchritudinous Italian movie stars of + + + align:start position:0% +pulchritudinous Italian movie stars of +the uh 50s and 60s uh and it got a lot + + align:start position:0% +the uh 50s and 60s uh and it got a lot + + + align:start position:0% +the uh 50s and 60s uh and it got a lot +of attention and there and there were + + align:start position:0% +of attention and there and there were + + + align:start position:0% +of attention and there and there were +other interesting many other interesting + + align:start position:0% +other interesting many other interesting + + + align:start position:0% +other interesting many other interesting +films that he made but one of his great + + align:start position:0% +films that he made but one of his great + + + align:start position:0% +films that he made but one of his great +triumphs was the very last film he made + + align:start position:0% +triumphs was the very last film he made + + + align:start position:0% +triumphs was the very last film he made +and that's why I want to mention it + + align:start position:0% +and that's why I want to mention it + + + align:start position:0% +and that's why I want to mention it +zavattini returned to do an uncredited + + align:start position:0% +zavattini returned to do an uncredited + + + align:start position:0% +zavattini returned to do an uncredited +co- screenplay U uh work to do + + align:start position:0% +co- screenplay U uh work to do + + + align:start position:0% +co- screenplay U uh work to do +uncredited screenplay work on finy coni + + align:start position:0% +uncredited screenplay work on finy coni + + + align:start position:0% +uncredited screenplay work on finy coni +and you can feel Z zi's hand in many + + align:start position:0% +and you can feel Z zi's hand in many + + + align:start position:0% +and you can feel Z zi's hand in many +moments in in the film it's an + + align:start position:0% +moments in in the film it's an + + + align:start position:0% +moments in in the film it's an +adaptation of a novel and of as some of + + align:start position:0% +adaptation of a novel and of as some of + + + align:start position:0% +adaptation of a novel and of as some of +you may know it's really a holocaust U + + align:start position:0% +you may know it's really a holocaust U + + + align:start position:0% +you may know it's really a holocaust U +film it's about the buildup to the + + align:start position:0% +film it's about the buildup to the + + + align:start position:0% +film it's about the buildup to the +Holocaust and the finy coni are very + + align:start position:0% +Holocaust and the finy coni are very + + + align:start position:0% +Holocaust and the finy coni are very +wealthy Italian Jews the story is about + + align:start position:0% +wealthy Italian Jews the story is about + + + align:start position:0% +wealthy Italian Jews the story is about +a poor + + align:start position:0% +a poor + + + align:start position:0% +a poor +uh young Jewish scholar who is because + + align:start position:0% +uh young Jewish scholar who is because + + + align:start position:0% +uh young Jewish scholar who is because +of the anti-jewish laws that are + + align:start position:0% +of the anti-jewish laws that are + + + align:start position:0% +of the anti-jewish laws that are +developing in in fascist Italy is barred + + align:start position:0% +developing in in fascist Italy is barred + + + align:start position:0% +developing in in fascist Italy is barred +from using the public library and he's a + + align:start position:0% +from using the public library and he's a + + + align:start position:0% +from using the public library and he's a +very gifted young scholar he's in his + + align:start position:0% +very gifted young scholar he's in his + + + align:start position:0% +very gifted young scholar he's in his +early 20s so he gets per so he finds out + + align:start position:0% +early 20s so he gets per so he finds out + + + align:start position:0% +early 20s so he gets per so he finds out +that this very wealthy aristocratic + + align:start position:0% +that this very wealthy aristocratic + + + align:start position:0% +that this very wealthy aristocratic +family also Jewish the finy coni have a + + align:start position:0% +family also Jewish the finy coni have a + + + align:start position:0% +family also Jewish the finy coni have a +magnificent library and the finy coni + + align:start position:0% +magnificent library and the finy coni + + + align:start position:0% +magnificent library and the finy coni +opened their library to him since he's + + align:start position:0% +opened their library to him since he's + + + align:start position:0% +opened their library to him since he's +barred from going to public library and + + align:start position:0% +barred from going to public library and + + + align:start position:0% +barred from going to public library and +of course what happens is you might you + + align:start position:0% +of course what happens is you might you + + + align:start position:0% +of course what happens is you might you +might guess this too It's a Wonderful + + align:start position:0% +might guess this too It's a Wonderful + + + align:start position:0% +might guess this too It's a Wonderful +novel although the film is even more + + align:start position:0% +novel although the film is even more + + + align:start position:0% +novel although the film is even more +beautiful I think uh he falls in love + + align:start position:0% +beautiful I think uh he falls in love + + + align:start position:0% +beautiful I think uh he falls in love +with the finy coni daughter right so + + align:start position:0% +with the finy coni daughter right so + + + align:start position:0% +with the finy coni daughter right so +it's a it's a class issue you know the + + align:start position:0% +it's a it's a class issue you know the + + + align:start position:0% +it's a it's a class issue you know the +poor boy Rich Girl uh and + + align:start position:0% +poor boy Rich Girl uh and + + + align:start position:0% +poor boy Rich Girl uh and +uh the film the film so the foreground + + align:start position:0% +uh the film the film so the foreground + + + align:start position:0% +uh the film the film so the foreground +of the film is this cross-class romance + + align:start position:0% +of the film is this cross-class romance + + + align:start position:0% +of the film is this cross-class romance +but in the background of the film all + + align:start position:0% +but in the background of the film all + + + align:start position:0% +but in the background of the film all +the it's something like Cabaret but not + + align:start position:0% +the it's something like Cabaret but not + + + align:start position:0% +the it's something like Cabaret but not +as dramatic not as overt because what's + + align:start position:0% +as dramatic not as overt because what's + + + align:start position:0% +as dramatic not as overt because what's +going on in the background of the film + + align:start position:0% +going on in the background of the film + + + align:start position:0% +going on in the background of the film +is the is the growth of fascism and and + + align:start position:0% +is the is the growth of fascism and and + + + align:start position:0% +is the is the growth of fascism and and +and the the film ends with many of the + + align:start position:0% +and the the film ends with many of the + + + align:start position:0% +and the the film ends with many of the +characters we've gotten to know very + + align:start position:0% +characters we've gotten to know very + + + align:start position:0% +characters we've gotten to know very +well both young and old all of them Jews + + align:start position:0% +well both young and old all of them Jews + + + align:start position:0% +well both young and old all of them Jews +some very aristocratic and some at the + + align:start position:0% +some very aristocratic and some at the + + + align:start position:0% +some very aristocratic and some at the +bottom of the social hierarchy all being + + align:start position:0% +bottom of the social hierarchy all being + + + align:start position:0% +bottom of the social hierarchy all being +herded together being ready to be + + align:start position:0% +herded together being ready to be + + + align:start position:0% +herded together being ready to be +shipped off to the camps you don't + + align:start position:0% +shipped off to the camps you don't + + + align:start position:0% +shipped off to the camps you don't +actually go the final scenes of the film + + align:start position:0% +actually go the final scenes of the film + + + align:start position:0% +actually go the final scenes of the film +have them in the railroad station being + + align:start position:0% +have them in the railroad station being + + + align:start position:0% +have them in the railroad station being +be being prepared for their for their + + align:start position:0% +be being prepared for their for their + + + align:start position:0% +be being prepared for their for their +final Journey uh and uh the the film has + + align:start position:0% +final Journey uh and uh the the film has + + + align:start position:0% +final Journey uh and uh the the film has +a the film is also full of Comedy just + + align:start position:0% +a the film is also full of Comedy just + + + align:start position:0% +a the film is also full of Comedy just +as uh uh uh the some of the passages + + align:start position:0% +as uh uh uh the some of the passages + + + align:start position:0% +as uh uh uh the some of the passages +that I showed you in Clips this + + align:start position:0% +that I showed you in Clips this + + + align:start position:0% +that I showed you in Clips this +afternoon mix comedy with social with + + align:start position:0% +afternoon mix comedy with social with + + + align:start position:0% +afternoon mix comedy with social with +with socially serious themes this is + + align:start position:0% +with socially serious themes this is + + + align:start position:0% +with socially serious themes this is +even truer of the garden of the finsy + + align:start position:0% +even truer of the garden of the finsy + + + align:start position:0% +even truer of the garden of the finsy +cotini so one of the reasons I like the + + align:start position:0% +cotini so one of the reasons I like the + + + align:start position:0% +cotini so one of the reasons I like the +film so much is that it's a return to + + align:start position:0% +film so much is that it's a return to + + + align:start position:0% +film so much is that it's a return to +the energies and the moral passion that + + align:start position:0% +the energies and the moral passion that + + + align:start position:0% +the energies and the moral passion that +had marked desa's earlier career and I + + align:start position:0% +had marked desa's earlier career and I + + + align:start position:0% +had marked desa's earlier career and I +think that my own feeling is the finy + + align:start position:0% +think that my own feeling is the finy + + + align:start position:0% +think that my own feeling is the finy +The Garden of the finzy continuus is one + + align:start position:0% +The Garden of the finzy continuus is one + + + align:start position:0% +The Garden of the finzy continuus is one +of the great European films it's it + + align:start position:0% +of the great European films it's it + + + align:start position:0% +of the great European films it's it +certainly would be on my list of the + + align:start position:0% +certainly would be on my list of the + + + align:start position:0% +certainly would be on my list of the +best 15 or 20 uh uh European films + + align:start position:0% +best 15 or 20 uh uh European films + + + align:start position:0% +best 15 or 20 uh uh European films +of of the sound era uh and uh I I I + + align:start position:0% +of of the sound era uh and uh I I I + + + align:start position:0% +of of the sound era uh and uh I I I +think I think many of you would find it + + align:start position:0% +think I think many of you would find it + + + align:start position:0% +think I think many of you would find it +very instructive and moving but I think + + align:start position:0% +very instructive and moving but I think + + + align:start position:0% +very instructive and moving but I think +especially so after you saw some of the + + align:start position:0% +especially so after you saw some of the + + + align:start position:0% +especially so after you saw some of the +true near realist films the early + + align:start position:0% +true near realist films the early + + + align:start position:0% +true near realist films the early +neorealist films one can't really call + + align:start position:0% +neorealist films one can't really call + + + align:start position:0% +neorealist films one can't really call +The Garden of the finy coni a neorealist + + align:start position:0% +The Garden of the finy coni a neorealist + + + align:start position:0% +The Garden of the finy coni a neorealist +film although it has many elements in + + align:start position:0% +film although it has many elements in + + + align:start position:0% +film although it has many elements in +common with those earlier texts so Desa + + align:start position:0% +common with those earlier texts so Desa + + + align:start position:0% +common with those earlier texts so Desa +was a remarkable man a a significant + + align:start position:0% +was a remarkable man a a significant + + + align:start position:0% +was a remarkable man a a significant +actor a great director uh he directed + + align:start position:0% +actor a great director uh he directed + + + align:start position:0% +actor a great director uh he directed +over 25 fil he directed 25 films in his + + align:start position:0% +over 25 fil he directed 25 films in his + + + align:start position:0% +over 25 fil he directed 25 films in his +career won four Oscars for best foreign + + align:start position:0% +career won four Oscars for best foreign + + + align:start position:0% +career won four Oscars for best foreign +film he acted in more than 150 films uh + + align:start position:0% +film he acted in more than 150 films uh + + + align:start position:0% +film he acted in more than 150 films uh +mostly light uh comic social manners + + align:start position:0% +mostly light uh comic social manners + + + align:start position:0% +mostly light uh comic social manners +kind of roles but there's one exception + + align:start position:0% +kind of roles but there's one exception + + + align:start position:0% +kind of roles but there's one exception +I perhaps should mention playing in a + + align:start position:0% +I perhaps should mention playing in a + + + align:start position:0% +I perhaps should mention playing in a +film for his friend Roberto rosolini in + + align:start position:0% +film for his friend Roberto rosolini in + + + align:start position:0% +film for his friend Roberto rosolini in +1959 rosalini's greatest film a film + + align:start position:0% +1959 rosalini's greatest film a film + + + align:start position:0% +1959 rosalini's greatest film a film +called General + + align:start position:0% + + + + align:start position:0% + +Ro Desa played the lead he plays the + + align:start position:0% +Ro Desa played the lead he plays the + + + align:start position:0% +Ro Desa played the lead he plays the +general and it's it's probably his most + + align:start position:0% +general and it's it's probably his most + + + align:start position:0% +general and it's it's probably his most +memorable + + align:start position:0% +memorable + + + align:start position:0% +memorable +performance uh and it's a very very + + align:start position:0% +performance uh and it's a very very + + + align:start position:0% +performance uh and it's a very very +subtle and good film about political + + align:start position:0% +subtle and good film about political + + + align:start position:0% +subtle and good film about political +ambiguities and conflicts of loyalty + + align:start position:0% +ambiguities and conflicts of loyalty + + + align:start position:0% +ambiguities and conflicts of loyalty +it's a and human Frailty human + + align:start position:0% +it's a and human Frailty human + + + align:start position:0% +it's a and human Frailty human +inadequacy in a in in a way that's + + align:start position:0% +inadequacy in a in in a way that's + + + align:start position:0% +inadequacy in a in in a way that's +characteristic of the best neorealist + + align:start position:0% +characteristic of the best neorealist + + + align:start position:0% +characteristic of the best neorealist +work so those are all films I recommend + + align:start position:0% +work so those are all films I recommend + + + align:start position:0% +work so those are all films I recommend +and urge you to consider uh watching in + + align:start position:0% +and urge you to consider uh watching in + + + align:start position:0% +and urge you to consider uh watching in +in your in in your leisure time uh let + + align:start position:0% +in your in in your leisure time uh let + + + align:start position:0% +in your in in your leisure time uh let +me say a few words now and about about + + align:start position:0% +me say a few words now and about about + + + align:start position:0% +me say a few words now and about about +bicycle + + align:start position:0% +bicycle + + + align:start position:0% +bicycle +thieves and + + align:start position:0% +thieves and + + + align:start position:0% +thieves and +uh I've already implied or actually said + + align:start position:0% +uh I've already implied or actually said + + + align:start position:0% +uh I've already implied or actually said +a part of my what I want to say so I I I + + align:start position:0% +a part of my what I want to say so I I I + + + align:start position:0% +a part of my what I want to say so I I I +think I can be briefer than I had + + align:start position:0% +think I can be briefer than I had + + + align:start position:0% +think I can be briefer than I had +originally planned let's say let let me + + align:start position:0% +originally planned let's say let let me + + + align:start position:0% +originally planned let's say let let me +remind you again about the structure I + + align:start position:0% +remind you again about the structure I + + + align:start position:0% +remind you again about the structure I +I've mentioned to you that the structure + + align:start position:0% +I've mentioned to you that the structure + + + align:start position:0% +I've mentioned to you that the structure +of the film is elegantly simple uh that + + align:start position:0% +of the film is elegantly simple uh that + + + align:start position:0% +of the film is elegantly simple uh that +the amount of time that passes is very + + align:start position:0% +the amount of time that passes is very + + + align:start position:0% +the amount of time that passes is very +compressed uh and that's helpful because + + align:start position:0% +compressed uh and that's helpful because + + + align:start position:0% +compressed uh and that's helpful because +uh you you you you the the the time + + align:start position:0% +uh you you you you the the the time + + + align:start position:0% +uh you you you you the the the time +compression makes you aware of the + + align:start position:0% +compression makes you aware of the + + + align:start position:0% +compression makes you aware of the +urgency of the quest that the father and + + align:start position:0% +urgency of the quest that the father and + + + align:start position:0% +urgency of the quest that the father and +the son are engaged on when they Ser + + align:start position:0% +the son are engaged on when they Ser + + + align:start position:0% +the son are engaged on when they Ser +when when they're searching for the + + align:start position:0% +when when they're searching for the + + + align:start position:0% +when when they're searching for the +bicycle so one + + align:start position:0% +bicycle so one + + + align:start position:0% +bicycle so one +way uh and and as the uh uh story + + align:start position:0% +way uh and and as the uh uh story + + + align:start position:0% +way uh and and as the uh uh story +unfolds a number of things begin to + + align:start position:0% +unfolds a number of things begin to + + + align:start position:0% +unfolds a number of things begin to +happen uh the Quest for the bicycle + + align:start position:0% +happen uh the Quest for the bicycle + + + align:start position:0% +happen uh the Quest for the bicycle +becomes a kind of Odyssey in which in + + align:start position:0% +becomes a kind of Odyssey in which in + + + align:start position:0% +becomes a kind of Odyssey in which in +which several things happen one is the + + align:start position:0% +which several things happen one is the + + + align:start position:0% +which several things happen one is the +film takes you on an exploration of Rome + + align:start position:0% +film takes you on an exploration of Rome + + + align:start position:0% +film takes you on an exploration of Rome +you actually it's like one of the great + + align:start position:0% +you actually it's like one of the great + + + align:start position:0% +you actually it's like one of the great +City films it visits the city it + + align:start position:0% +City films it visits the city it + + + align:start position:0% +City films it visits the city it +explores the city you see different + + align:start position:0% +explores the city you see different + + + align:start position:0% +explores the city you see different +different it's not just that you see + + align:start position:0% +different it's not just that you see + + + align:start position:0% +different it's not just that you see +police stations and religious + + align:start position:0% +police stations and religious + + + align:start position:0% +police stations and religious +institutions and the catacombs + + align:start position:0% +institutions and the catacombs + + + align:start position:0% +institutions and the catacombs +underneath the city where the unions + + align:start position:0% +underneath the city where the unions + + + align:start position:0% +underneath the city where the unions +meet uh and where RI first goes to get + + align:start position:0% +meet uh and where RI first goes to get + + + align:start position:0% +meet uh and where RI first goes to get +help from his Union from union members + + align:start position:0% +help from his Union from union members + + + align:start position:0% +help from his Union from union members +who promise him that they'll find his + + align:start position:0% +who promise him that they'll find his + + + align:start position:0% +who promise him that they'll find his +bike very easily and they give him a + + align:start position:0% +bike very easily and they give him a + + + align:start position:0% +bike very easily and they give him a +plan and he's very excited then the next + + align:start position:0% +plan and he's very excited then the next + + + align:start position:0% +plan and he's very excited then the next +morning when they follow the + + align:start position:0% +morning when they follow the + + + align:start position:0% +morning when they follow the +instructions of the Union boss doesn't + + align:start position:0% +instructions of the Union boss doesn't + + + align:start position:0% +instructions of the Union boss doesn't +help so the unions are breaking down as + + align:start position:0% +help so the unions are breaking down as + + + align:start position:0% +help so the unions are breaking down as +well as the church as well as certain + + align:start position:0% +well as the church as well as certain + + + align:start position:0% +well as the church as well as certain +kinds of welfare organiz ganizations + + align:start position:0% +kinds of welfare organiz ganizations + + + align:start position:0% +kinds of welfare organiz ganizations +from the state and so on + + align:start position:0% +from the state and so on + + + align:start position:0% +from the state and so on +um so one thing the film becomes then is + + align:start position:0% +um so one thing the film becomes then is + + + align:start position:0% +um so one thing the film becomes then is +a kind of travel log a kind of + + align:start position:0% +a kind of travel log a kind of + + + align:start position:0% +a kind of travel log a kind of +exploration of the city the city's + + align:start position:0% +exploration of the city the city's + + + align:start position:0% +exploration of the city the city's +geography as well as the city's makeup + + align:start position:0% +geography as well as the city's makeup + + + align:start position:0% +geography as well as the city's makeup +in some way you you you you go into + + align:start position:0% +in some way you you you you go into + + + align:start position:0% +in some way you you you you go into +different neighborhoods and you hear I + + align:start position:0% +different neighborhoods and you hear I + + + align:start position:0% +different neighborhoods and you hear I +think Italians can pick up different + + align:start position:0% +think Italians can pick up different + + + align:start position:0% +think Italians can pick up different +different neighborhood speech patterns + + align:start position:0% +different neighborhood speech patterns + + + align:start position:0% +different neighborhood speech patterns +in the film at least I've been told this + + align:start position:0% +in the film at least I've been told this + + + align:start position:0% +in the film at least I've been told this +by n by native Italians uh so it's a + + align:start position:0% +by n by native Italians uh so it's a + + + align:start position:0% +by n by native Italians uh so it's a +kind of travelogue in one sense it's it + + align:start position:0% +kind of travelogue in one sense it's it + + + align:start position:0% +kind of travelogue in one sense it's it +explores this this place and part of the + + align:start position:0% +explores this this place and part of the + + + align:start position:0% +explores this this place and part of the +exploration of course part part of the + + align:start position:0% +exploration of course part part of the + + + align:start position:0% +exploration of course part part of the +exploration U um involves + + align:start position:0% + + + + align:start position:0% + +certain anary or or or or or other + + align:start position:0% +certain anary or or or or or other + + + align:start position:0% +certain anary or or or or or other +themes that are not that are that are + + align:start position:0% +themes that are not that are that are + + + align:start position:0% +themes that are not that are that are +organically linked to the to the story + + align:start position:0% +organically linked to the to the story + + + align:start position:0% +organically linked to the to the story +of looking at going through the city + + align:start position:0% +of looking at going through the city + + + align:start position:0% +of looking at going through the city +looking for the bicycle and one of these + + align:start position:0% +looking for the bicycle and one of these + + + align:start position:0% +looking for the bicycle and one of these +one of these of course is is what we + + align:start position:0% +one of these of course is is what we + + + align:start position:0% +one of these of course is is what we +might call the Social themes of the film + + align:start position:0% +might call the Social themes of the film + + + align:start position:0% +might call the Social themes of the film +because as the uh the protagonists make + + align:start position:0% +because as the uh the protagonists make + + + align:start position:0% +because as the uh the protagonists make +their way through the city searching for + + align:start position:0% +their way through the city searching for + + + align:start position:0% +their way through the city searching for +the bicycle one we what you encounter + + align:start position:0% +the bicycle one we what you encounter + + + align:start position:0% +the bicycle one we what you encounter +are little vignettes that tell you + + align:start position:0% +are little vignettes that tell you + + + align:start position:0% +are little vignettes that tell you +something about the social hierarchies + + align:start position:0% +something about the social hierarchies + + + align:start position:0% +something about the social hierarchies +of the society uh about the efficacy or + + align:start position:0% +of the society uh about the efficacy or + + + align:start position:0% +of the society uh about the efficacy or +inefficacy of its institutions right I I + + align:start position:0% +inefficacy of its institutions right I I + + + align:start position:0% +inefficacy of its institutions right I I +won't go into great detail here I want + + align:start position:0% +won't go into great detail here I want + + + align:start position:0% +won't go into great detail here I want +to I hope you'll draw your own + + align:start position:0% +to I hope you'll draw your own + + + align:start position:0% +to I hope you'll draw your own +conclusions and name some of the name + + align:start position:0% +conclusions and name some of the name + + + align:start position:0% +conclusions and name some of the name +some of the specific examples that + + align:start position:0% +some of the specific examples that + + + align:start position:0% +some of the specific examples that +reinforce this general idea but I do + + align:start position:0% +reinforce this general idea but I do + + + align:start position:0% +reinforce this general idea but I do +want to mention um at least one + + align:start position:0% +want to mention um at least one + + + align:start position:0% +want to mention um at least one +moment uh in this in in this in this + + align:start position:0% +moment uh in this in in this in this + + + align:start position:0% +moment uh in this in in this in this +Odyssey one of the most dramatic and + + align:start position:0% +Odyssey one of the most dramatic and + + + align:start position:0% +Odyssey one of the most dramatic and +and disturbingly comic moments in the + + align:start position:0% +and disturbingly comic moments in the + + + align:start position:0% +and disturbingly comic moments in the +film occurs when RI and his son actually + + align:start position:0% +film occurs when RI and his son actually + + + align:start position:0% +film occurs when RI and his son actually +think they've seen the thief they think + + align:start position:0% +think they've seen the thief they think + + + align:start position:0% +think they've seen the thief they think +they recognize him and they follow him + + align:start position:0% +they recognize him and they follow him + + + align:start position:0% +they recognize him and they follow him +and they get to a essentially a mission + + align:start position:0% +and they get to a essentially a mission + + + align:start position:0% +and they get to a essentially a mission +where uh relatively well-off uh + + align:start position:0% +where uh relatively well-off uh + + + align:start position:0% +where uh relatively well-off uh +self-satisfied Christians are serving + + align:start position:0% +self-satisfied Christians are serving + + + align:start position:0% +self-satisfied Christians are serving +meals to the Indigent and the poor right + + align:start position:0% +meals to the Indigent and the poor right + + + align:start position:0% +meals to the Indigent and the poor right +and REI gets into this institution not + + align:start position:0% +and REI gets into this institution not + + + align:start position:0% +and REI gets into this institution not +but not because he sort of wants the + + align:start position:0% +but not because he sort of wants the + + + align:start position:0% +but not because he sort of wants the +meal or because he needs the religious + + align:start position:0% +meal or because he needs the religious + + + align:start position:0% +meal or because he needs the religious +uplift but because he's chasing his + + align:start position:0% +uplift but because he's chasing his + + + align:start position:0% +uplift but because he's chasing his +Thief right and he finds once he's in + + align:start position:0% +Thief right and he finds once he's in + + + align:start position:0% +Thief right and he finds once he's in +there that he can't get out it turns out + + align:start position:0% +there that he can't get out it turns out + + + align:start position:0% +there that he can't get out it turns out +that in this institution that not only + + align:start position:0% +that in this institution that not only + + + align:start position:0% +that in this institution that not only +do they do the uh the poor have to pay + + align:start position:0% +do they do the uh the poor have to pay + + + align:start position:0% +do they do the uh the poor have to pay +for their meal by by agreeing to all + + align:start position:0% +for their meal by by agreeing to all + + + align:start position:0% +for their meal by by agreeing to all +kinds of religious behaviors prayers and + + align:start position:0% +kinds of religious behaviors prayers and + + + align:start position:0% +kinds of religious behaviors prayers and +other kinds of things but they're also + + align:start position:0% +other kinds of things but they're also + + + align:start position:0% +other kinds of things but they're also +locked into the building they're not + + align:start position:0% +locked into the building they're not + + + align:start position:0% +locked into the building they're not +allowed to eat they're not allowed to + + align:start position:0% +allowed to eat they're not allowed to + + + align:start position:0% +allowed to eat they're not allowed to +leave at least until they finish eating + + align:start position:0% +leave at least until they finish eating + + + align:start position:0% +leave at least until they finish eating +maybe they're not allowed to leave uh + + align:start position:0% +maybe they're not allowed to leave uh + + + align:start position:0% +maybe they're not allowed to leave uh +until they can be checked to make sure + + align:start position:0% +until they can be checked to make sure + + + align:start position:0% +until they can be checked to make sure +not stealing the soup bowls but in any + + align:start position:0% +not stealing the soup bowls but in any + + + align:start position:0% +not stealing the soup bowls but in any +case it's a it's it's a very interesting + + align:start position:0% +case it's a it's it's a very interesting + + + align:start position:0% +case it's a it's it's a very interesting +moment because you can see that even the + + align:start position:0% +moment because you can see that even the + + + align:start position:0% +moment because you can see that even the +people who intend to do well in the + + align:start position:0% +people who intend to do well in the + + + align:start position:0% +people who intend to do well in the +society often do more harm than good uh + + align:start position:0% +society often do more harm than good uh + + + align:start position:0% +society often do more harm than good uh +and and of course the implication is + + align:start position:0% +and and of course the implication is + + + align:start position:0% +and and of course the implication is +that the traditional religious + + align:start position:0% +that the traditional religious + + + align:start position:0% +that the traditional religious +institutions and traditional uh + + align:start position:0% +institutions and traditional uh + + + align:start position:0% +institutions and traditional uh +religious + + align:start position:0% +religious + + + align:start position:0% +religious +Arrangements uh are not sufficient to + + align:start position:0% +Arrangements uh are not sufficient to + + + align:start position:0% +Arrangements uh are not sufficient to +take care of or to or or or or + + align:start position:0% +take care of or to or or or or + + + align:start position:0% +take care of or to or or or or +adequately to respect the the + + align:start position:0% +adequately to respect the the + + + align:start position:0% +adequately to respect the the +difficulties of the poor and that's just + + align:start position:0% +difficulties of the poor and that's just + + + align:start position:0% +difficulties of the poor and that's just +one such moment I mean there there are a + + align:start position:0% +one such moment I mean there there are a + + + align:start position:0% +one such moment I mean there there are a +number there are a number of others and + + align:start position:0% +number there are a number of others and + + + align:start position:0% +number there are a number of others and +and in fact there is one other moment I + + align:start position:0% +and in fact there is one other moment I + + + align:start position:0% +and in fact there is one other moment I +should mention as a kind of + + align:start position:0% +should mention as a kind of + + + align:start position:0% +should mention as a kind of +contrast I've said that we see many + + align:start position:0% +contrast I've said that we see many + + + align:start position:0% +contrast I've said that we see many +instances in which we understand that + + align:start position:0% +instances in which we understand that + + + align:start position:0% +instances in which we understand that +the larger institutions of society like + + align:start position:0% +the larger institutions of society like + + + align:start position:0% +the larger institutions of society like +the police or the religious system uh or + + align:start position:0% +the police or the religious system uh or + + + align:start position:0% +the police or the religious system uh or +the union system are breaking down are + + align:start position:0% +the union system are breaking down are + + + align:start position:0% +the union system are breaking down are +not really helping people but I've but + + align:start position:0% +not really helping people but I've but + + + align:start position:0% +not really helping people but I've but +I've also said that there are some other + + align:start position:0% +I've also said that there are some other + + + align:start position:0% +I've also said that there are some other +sort of unofficial and + + align:start position:0% +sort of unofficial and + + + align:start position:0% +sort of unofficial and +non-institutionalized sources of + + align:start position:0% +non-institutionalized sources of + + + align:start position:0% +non-institutionalized sources of +solidarity and comfort that emerge in + + align:start position:0% +solidarity and comfort that emerge in + + + align:start position:0% +solidarity and comfort that emerge in +the course of the film and I hope you'll + + align:start position:0% +the course of the film and I hope you'll + + + align:start position:0% +the course of the film and I hope you'll +watch for them and and and and think + + align:start position:0% +watch for them and and and and think + + + align:start position:0% +watch for them and and and and think +about what they're what what their + + align:start position:0% +about what they're what what their + + + align:start position:0% +about what they're what what their +significance + + align:start position:0% + + + + align:start position:0% + +is but there's one but there but but + + align:start position:0% +is but there's one but there but but + + + align:start position:0% +is but there's one but there but but +there's one moment in which we might say + + align:start position:0% +there's one moment in which we might say + + + align:start position:0% +there's one moment in which we might say +which complicates this argument because + + align:start position:0% +which complicates this argument because + + + align:start position:0% +which complicates this argument because +we can see the social institution of the + + align:start position:0% +we can see the social institution of the + + + align:start position:0% +we can see the social institution of the +society social institutions of not + + align:start position:0% +society social institutions of not + + + align:start position:0% +society social institutions of not +actually functioning effectively but at + + align:start position:0% +actually functioning effectively but at + + + align:start position:0% +actually functioning effectively but at +least showing some compassion and it's + + align:start position:0% +least showing some compassion and it's + + + align:start position:0% +least showing some compassion and it's +an astonishingly Vivid meaningful moment + + align:start position:0% +an astonishingly Vivid meaningful moment + + + align:start position:0% +an astonishingly Vivid meaningful moment +in the film another one of these moments + + align:start position:0% +in the film another one of these moments + + + align:start position:0% +in the film another one of these moments +so full of Multiplicity that uh the + + align:start position:0% +so full of Multiplicity that uh the + + + align:start position:0% +so full of Multiplicity that uh the +meanings are are so deeply embedded in + + align:start position:0% +meanings are are so deeply embedded in + + + align:start position:0% +meanings are are so deeply embedded in +in what you dramatically see that + + align:start position:0% +in what you dramatically see that + + + align:start position:0% +in what you dramatically see that +sometimes you don't even step back to + + align:start position:0% +sometimes you don't even step back to + + + align:start position:0% +sometimes you don't even step back to +generalize on the meaning of what you've + + align:start position:0% +generalize on the meaning of what you've + + + align:start position:0% +generalize on the meaning of what you've +seen and this is a scene very early in + + align:start position:0% +seen and this is a scene very early in + + + align:start position:0% +seen and this is a scene very early in +the film where Richi actually goes to + + align:start position:0% +the film where Richi actually goes to + + + align:start position:0% +the film where Richi actually goes to +retrieve his bicycle and his wife has + + align:start position:0% +retrieve his bicycle and his wife has + + + align:start position:0% +retrieve his bicycle and his wife has +figured out a way uh basically what she + + align:start position:0% +figured out a way uh basically what she + + + align:start position:0% +figured out a way uh basically what she +figures out is we'll sell they have a + + align:start position:0% +figures out is we'll sell they have a + + + align:start position:0% +figures out is we'll sell they have a +little bit they they they sell her dowy + + align:start position:0% +little bit they they they sell her dowy + + + align:start position:0% +little bit they they they sell her dowy +she has a couple of fancy silk sheets + + align:start position:0% +she has a couple of fancy silk sheets + + + align:start position:0% +she has a couple of fancy silk sheets +and they take them to the hawk shop and + + align:start position:0% +and they take them to the hawk shop and + + + align:start position:0% +and they take them to the hawk shop and +they and they Pawn the sheets in order + + align:start position:0% +they and they Pawn the sheets in order + + + align:start position:0% +they and they Pawn the sheets in order +to get enough money to get the bicycle + + align:start position:0% +to get enough money to get the bicycle + + + align:start position:0% +to get enough money to get the bicycle +out of Hawk right means they're going to + + align:start position:0% +out of Hawk right means they're going to + + + align:start position:0% +out of Hawk right means they're going to +be sleeping on mattresses uh but so what + + align:start position:0% +be sleeping on mattresses uh but so what + + + align:start position:0% +be sleeping on mattresses uh but so what +this is more important right and so and + + align:start position:0% +this is more important right and so and + + + align:start position:0% +this is more important right and so and +you see REI and his wife go to the porn + + align:start position:0% +you see REI and his wife go to the porn + + + align:start position:0% +you see REI and his wife go to the porn +shop which is clearly it's clearly run + + align:start position:0% +shop which is clearly it's clearly run + + + align:start position:0% +shop which is clearly it's clearly run +by the state it's not like a private + + align:start position:0% +by the state it's not like a private + + + align:start position:0% +by the state it's not like a private +porn it's obviously a city institution + + align:start position:0% +porn it's obviously a city institution + + + align:start position:0% +porn it's obviously a city institution +of some kind and the and the they bring + + align:start position:0% +of some kind and the and the they bring + + + align:start position:0% +of some kind and the and the they bring +the linen up to the guy and and he he + + align:start position:0% +the linen up to the guy and and he he + + + align:start position:0% +the linen up to the guy and and he he +looks at them and he says okay I'll give + + align:start position:0% +looks at them and he says okay I'll give + + + align:start position:0% +looks at them and he says okay I'll give +you this much money and they need a + + align:start position:0% +you this much money and they need a + + + align:start position:0% +you this much money and they need a +little bit more because they need more + + align:start position:0% +little bit more because they need more + + + align:start position:0% +little bit more because they need more +to get the bike out of Po so they they + + align:start position:0% +to get the bike out of Po so they they + + + align:start position:0% +to get the bike out of Po so they they +ask him for more money and he looks at + + align:start position:0% +ask him for more money and he looks at + + + align:start position:0% +ask him for more money and he looks at +he says uh it's not really worth it okay + + align:start position:0% +he says uh it's not really worth it okay + + + align:start position:0% +he says uh it's not really worth it okay +and he gives the and it's an act of + + align:start position:0% +and he gives the and it's an act of + + + align:start position:0% +and he gives the and it's an act of +generosity on his part because he didn't + + align:start position:0% +generosity on his part because he didn't + + + align:start position:0% +generosity on his part because he didn't +have to do it he gives them just enough + + align:start position:0% +have to do it he gives them just enough + + + align:start position:0% +have to do it he gives them just enough +money for this stuff so that they can + + align:start position:0% +money for this stuff so that they can + + + align:start position:0% +money for this stuff so that they can +get his bike out of Hawk and then + + align:start position:0% +get his bike out of Hawk and then + + + align:start position:0% +get his bike out of Hawk and then +completely silent you see him pick this + + align:start position:0% +completely silent you see him pick this + + + align:start position:0% +completely silent you see him pick this +material up this this pawned bedding + + align:start position:0% +material up this this pawned bedding + + + align:start position:0% +material up this this pawned bedding +this pawned linen and he turns around I + + align:start position:0% +this pawned linen and he turns around I + + + align:start position:0% +this pawned linen and he turns around I +think he does it he may give it to + + align:start position:0% +think he does it he may give it to + + + align:start position:0% +think he does it he may give it to +another character I haven't looked at + + align:start position:0% +another character I haven't looked at + + + align:start position:0% +another character I haven't looked at +this scene in a year or two so I don't + + align:start position:0% +this scene in a year or two so I don't + + + align:start position:0% +this scene in a year or two so I don't +remember the ex but you'll recognize the + + align:start position:0% +remember the ex but you'll recognize the + + + align:start position:0% +remember the ex but you'll recognize the +scene I think it's the same man who does + + align:start position:0% +scene I think it's the same man who does + + + align:start position:0% +scene I think it's the same man who does +it or he may give it to someone else the + + align:start position:0% +it or he may give it to someone else the + + + align:start position:0% +it or he may give it to someone else the +material the the three or four sheets + + align:start position:0% +material the the three or four sheets + + + align:start position:0% +material the the three or four sheets +that are involved are taken by someone + + align:start position:0% +that are involved are taken by someone + + + align:start position:0% +that are involved are taken by someone +you walk to the back of a room and he + + align:start position:0% +you walk to the back of a room and he + + + align:start position:0% +you walk to the back of a room and he +begins to climb a ladder and as he + + align:start position:0% +begins to climb a ladder and as he + + + align:start position:0% +begins to climb a ladder and as he +climbs you realize that what he's + + align:start position:0% +climbs you realize that what he's + + + align:start position:0% +climbs you realize that what he's +climbing up is a a a he's he's climbing + + align:start position:0% +climbing up is a a a he's he's climbing + + + align:start position:0% +climbing up is a a a he's he's climbing +a ladder which + + align:start position:0% +a ladder which + + + align:start position:0% +a ladder which +is uh leaning against a series of + + align:start position:0% +is uh leaning against a series of + + + align:start position:0% +is uh leaning against a series of +shelves that seem to go on endlessly + + align:start position:0% +shelves that seem to go on endlessly + + + align:start position:0% +shelves that seem to go on endlessly +they seem to be in a in an auditorium + + align:start position:0% +they seem to be in a in an auditorium + + + align:start position:0% +they seem to be in a in an auditorium +the size of the city of Pittsburgh and + + align:start position:0% +the size of the city of Pittsburgh and + + + align:start position:0% +the size of the city of Pittsburgh and +they go up endlessly high and every + + align:start position:0% +they go up endlessly high and every + + + align:start position:0% +they go up endlessly high and every +single shelf every single inch of space + + align:start position:0% +single shelf every single inch of space + + + align:start position:0% +single shelf every single inch of space +on the Shelf is filled with bedding as + + align:start position:0% +on the Shelf is filled with bedding as + + + align:start position:0% +on the Shelf is filled with bedding as +if the entire city of Rome has pawned + + align:start position:0% +if the entire city of Rome has pawned + + + align:start position:0% +if the entire city of Rome has pawned +its bedding + + align:start position:0% +its bedding + + + align:start position:0% +its bedding +as if everybody in Rome is sleeping on + + align:start position:0% +as if everybody in Rome is sleeping on + + + align:start position:0% +as if everybody in Rome is sleeping on +mattresses now the film never makes a + + align:start position:0% +mattresses now the film never makes a + + + align:start position:0% +mattresses now the film never makes a +comment about this no one in the film + + align:start position:0% +comment about this no one in the film + + + align:start position:0% +comment about this no one in the film +says anything about it but it's an + + align:start position:0% +says anything about it but it's an + + + align:start position:0% +says anything about it but it's an +unbelievably resonant and Rich moment + + align:start position:0% +unbelievably resonant and Rich moment + + + align:start position:0% +unbelievably resonant and Rich moment +and it's and it's also it does further + + align:start position:0% +and it's and it's also it does further + + + align:start position:0% +and it's and it's also it does further +the sort of social themes of the film + + align:start position:0% +the sort of social themes of the film + + + align:start position:0% +the sort of social themes of the film +but it occurs in a moment in which you + + align:start position:0% +but it occurs in a moment in which you + + + align:start position:0% +but it occurs in a moment in which you +also see the pawn broker showing a + + align:start position:0% +also see the pawn broker showing a + + + align:start position:0% +also see the pawn broker showing a +moment of compassion and generosity and + + align:start position:0% +moment of compassion and generosity and + + + align:start position:0% +moment of compassion and generosity and +if he did not show that generosity uh + + align:start position:0% +if he did not show that generosity uh + + + align:start position:0% +if he did not show that generosity uh +they wouldn't have been able to get the + + align:start position:0% +they wouldn't have been able to get the + + + align:start position:0% +they wouldn't have been able to get the +bicycle so so it's a it's a comp at + + align:start position:0% +bicycle so so it's a it's a comp at + + + align:start position:0% +bicycle so so it's a it's a comp at +moment it does I mean if if all this + + align:start position:0% +moment it does I mean if if all this + + + align:start position:0% +moment it does I mean if if all this +linen has been pawned there's some + + align:start position:0% +linen has been pawned there's some + + + align:start position:0% +linen has been pawned there's some +question about whether or not the the + + align:start position:0% +question about whether or not the the + + + align:start position:0% +question about whether or not the the +city services are doing much good for + + align:start position:0% +city services are doing much good for + + + align:start position:0% +city services are doing much good for +anybody the the city's in obvious + + align:start position:0% +anybody the the city's in obvious + + + align:start position:0% +anybody the the city's in obvious +trouble if nobody has any bed bed linen + + align:start position:0% +trouble if nobody has any bed bed linen + + + align:start position:0% +trouble if nobody has any bed bed linen +any longer uh the implication is this is + + align:start position:0% +any longer uh the implication is this is + + + align:start position:0% +any longer uh the implication is this is +an unbelievably impoverished and and and + + align:start position:0% +an unbelievably impoverished and and and + + + align:start position:0% +an unbelievably impoverished and and and +damaged environment but it's done in + + align:start position:0% +damaged environment but it's done in + + + align:start position:0% +damaged environment but it's done in +such a quiet and there's even some it's + + align:start position:0% +such a quiet and there's even some it's + + + align:start position:0% +such a quiet and there's even some it's +done in such a quiet way there's even + + align:start position:0% +done in such a quiet way there's even + + + align:start position:0% +done in such a quiet way there's even +something almost comic about the sense + + align:start position:0% +something almost comic about the sense + + + align:start position:0% +something almost comic about the sense +you have of the Endless number of these + + align:start position:0% +you have of the Endless number of these + + + align:start position:0% +you have of the Endless number of these +things even the idea that you have to + + align:start position:0% +things even the idea that you have to + + + align:start position:0% +things even the idea that you have to +distinguish one from the other seems + + align:start position:0% +distinguish one from the other seems + + + align:start position:0% +distinguish one from the other seems +from our vantage point a bit silly even + + align:start position:0% +from our vantage point a bit silly even + + + align:start position:0% +from our vantage point a bit silly even +though each one has a ticket on it each + + align:start position:0% +though each one has a ticket on it each + + + align:start position:0% +though each one has a ticket on it each +one belongs to an individual family so + + align:start position:0% +one belongs to an individual family so + + + align:start position:0% +one belongs to an individual family so +watch for that moment it has some of + + align:start position:0% +watch for that moment it has some of + + + align:start position:0% +watch for that moment it has some of +that ambiguity that we've been that that + + align:start position:0% +that ambiguity that we've been that that + + + align:start position:0% +that ambiguity that we've been that that +bezan talks about um so the structure of + + align:start position:0% +bezan talks about um so the structure of + + + align:start position:0% +bezan talks about um so the structure of +the film is organic in the sense that + + align:start position:0% +the film is organic in the sense that + + + align:start position:0% +the film is organic in the sense that +nothing that happens in the film doesn't + + align:start position:0% +nothing that happens in the film doesn't + + + align:start position:0% +nothing that happens in the film doesn't +seem to arise naturally out of the needs + + align:start position:0% +seem to arise naturally out of the needs + + + align:start position:0% +seem to arise naturally out of the needs +of the characters we have to find our + + align:start position:0% +of the characters we have to find our + + + align:start position:0% +of the characters we have to find our +new bike we have to find our bike and in + + align:start position:0% +new bike we have to find our bike and in + + + align:start position:0% +new bike we have to find our bike and in +the course of their travels other things + + align:start position:0% +the course of their travels other things + + + align:start position:0% +the course of their travels other things +happen the boy has to pee they get + + align:start position:0% +happen the boy has to pee they get + + + align:start position:0% +happen the boy has to pee they get +hungry they have to eat or + + align:start position:0% +hungry they have to eat or + + + align:start position:0% +hungry they have to eat or +sometimes it rains they have to get out + + align:start position:0% +sometimes it rains they have to get out + + + align:start position:0% +sometimes it rains they have to get out +of the rain right and that's part that + + align:start position:0% +of the rain right and that's part that + + + align:start position:0% +of the rain right and that's part that +becomes part of the ongoing sort of + + align:start position:0% +becomes part of the ongoing sort of + + + align:start position:0% +becomes part of the ongoing sort of +organic development of the of of the + + align:start position:0% +organic development of the of of the + + + align:start position:0% +organic development of the of of the +story you never once feel I think in + + align:start position:0% +story you never once feel I think in + + + align:start position:0% +story you never once feel I think in +this film that that any event has been + + align:start position:0% +this film that that any event has been + + + align:start position:0% +this film that that any event has been +imposed from the outside every event + + align:start position:0% +imposed from the outside every event + + + align:start position:0% +imposed from the outside every event +seems to arise naturally out of the + + align:start position:0% +seems to arise naturally out of the + + + align:start position:0% +seems to arise naturally out of the +circumstances and nature of the + + align:start position:0% +circumstances and nature of the + + + align:start position:0% +circumstances and nature of the +characters and that's why I call it + + align:start position:0% +characters and that's why I call it + + + align:start position:0% +characters and that's why I call it +organic it's a deeply it's a it's a + + align:start position:0% +organic it's a deeply it's a it's a + + + align:start position:0% +organic it's a deeply it's a it's a +deeply or or organic way of thinking + + align:start position:0% +deeply or or organic way of thinking + + + align:start position:0% +deeply or or organic way of thinking +about the material but it's organic in + + align:start position:0% +about the material but it's organic in + + + align:start position:0% +about the material but it's organic in +another way too of course because it's + + align:start position:0% +another way too of course because it's + + + align:start position:0% +another way too of course because it's +deeply coherent when you finally finish + + align:start position:0% +deeply coherent when you finally finish + + + align:start position:0% +deeply coherent when you finally finish +the film and you step back you say okay + + align:start position:0% +the film and you step back you say okay + + + align:start position:0% +the film and you step back you say okay +yes the film slowed down here and yes + + align:start position:0% +yes the film slowed down here and yes + + + align:start position:0% +yes the film slowed down here and yes +the film seem to generate what thorburn + + align:start position:0% +the film seem to generate what thorburn + + + align:start position:0% +the film seem to generate what thorburn +calls a counterplot here nonetheless + + align:start position:0% +calls a counterplot here nonetheless + + + align:start position:0% +calls a counterplot here nonetheless +taken as a whole there's a profound + + align:start position:0% +taken as a whole there's a profound + + + align:start position:0% +taken as a whole there's a profound +moral and and thematic coherence in this + + align:start position:0% +moral and and thematic coherence in this + + + align:start position:0% +moral and and thematic coherence in this +organically fluid movie so the structure + + align:start position:0% +organically fluid movie so the structure + + + align:start position:0% +organically fluid movie so the structure +of the film is part of its Essence and + + align:start position:0% +of the film is part of its Essence and + + + align:start position:0% +of the film is part of its Essence and +although I haven't put this on the + + align:start position:0% +although I haven't put this on the + + + align:start position:0% +although I haven't put this on the +outline because we've talked about this + + align:start position:0% +outline because we've talked about this + + + align:start position:0% +outline because we've talked about this +so often already pay attention to the + + align:start position:0% +so often already pay attention to the + + + align:start position:0% +so often already pay attention to the +Renoir type camera Behavior I mean this + + align:start position:0% +Renoir type camera Behavior I mean this + + + align:start position:0% +Renoir type camera Behavior I mean this +the the film's visual style is like Jean + + align:start position:0% +the the film's visual style is like Jean + + + align:start position:0% +the the film's visual style is like Jean +Renoir there's a kind of there's a kind + + align:start position:0% +Renoir there's a kind of there's a kind + + + align:start position:0% +Renoir there's a kind of there's a kind +of elegant restlessness to the camera + + align:start position:0% +of elegant restlessness to the camera + + + align:start position:0% +of elegant restlessness to the camera +that's that that's that that's very much + + align:start position:0% +that's that that's that that's very much + + + align:start position:0% +that's that that's that that's very much +a part of what the film of what the film + + align:start position:0% +a part of what the film of what the film + + + align:start position:0% +a part of what the film of what the film +achieves so I in talking about the + + align:start position:0% +achieves so I in talking about the + + + align:start position:0% +achieves so I in talking about the +social themes all I meant to call your + + align:start position:0% +social themes all I meant to call your + + + align:start position:0% +social themes all I meant to call your +attention to was the extent to which in + + align:start position:0% +attention to was the extent to which in + + + align:start position:0% +attention to was the extent to which in +a variety of ways the film calls + + align:start position:0% +a variety of ways the film calls + + + align:start position:0% +a variety of ways the film calls +attention to the miserably endangered + + align:start position:0% +attention to the miserably endangered + + + align:start position:0% +attention to the miserably endangered +circumstances of ordinary people in this + + align:start position:0% +circumstances of ordinary people in this + + + align:start position:0% +circumstances of ordinary people in this +broken down War torn environment uh and + + align:start position:0% +broken down War torn environment uh and + + + align:start position:0% +broken down War torn environment uh and +it also looks to those or seems to find + + align:start position:0% +it also looks to those or seems to find + + + align:start position:0% +it also looks to those or seems to find +without even looking to those sort uh or + + align:start position:0% +without even looking to those sort uh or + + + align:start position:0% +without even looking to those sort uh or +dramatize or reveal those sources of + + align:start position:0% +dramatize or reveal those sources of + + + align:start position:0% +dramatize or reveal those sources of +support and sustenance that get us + + align:start position:0% +support and sustenance that get us + + + align:start position:0% +support and sustenance that get us +through bad times and uh as you're + + align:start position:0% +through bad times and uh as you're + + + align:start position:0% +through bad times and uh as you're +watching the ending of the film ask + + align:start position:0% +watching the ending of the film ask + + + align:start position:0% +watching the ending of the film ask +yourself what these things mean I uh + + align:start position:0% +yourself what these things mean I uh + + + align:start position:0% +yourself what these things mean I uh +what it means that the that whether I + + align:start position:0% +what it means that the that whether I + + + align:start position:0% +what it means that the that whether I +won't I won't actually tell you whether + + align:start position:0% +won't I won't actually tell you whether + + + align:start position:0% +won't I won't actually tell you whether +he recovers the bike or not let you see + + align:start position:0% +he recovers the bike or not let you see + + + align:start position:0% +he recovers the bike or not let you see +that for yourselves but ask yourself + + align:start position:0% +that for yourselves but ask yourself + + + align:start position:0% +that for yourselves but ask yourself +whether or not he recovers the bike + + align:start position:0% +whether or not he recovers the bike + + + align:start position:0% +whether or not he recovers the bike +would it have made any + + align:start position:0% +would it have made any + + + align:start position:0% +would it have made any +difference does it matter what given + + align:start position:0% +difference does it matter what given + + + align:start position:0% +difference does it matter what given +what the film is finally saying to us in + + align:start position:0% +what the film is finally saying to us in + + + align:start position:0% +what the film is finally saying to us in +those Final in those final images well + + align:start position:0% +those Final in those final images well + + + align:start position:0% +those Final in those final images well +character this is one of the great films + + align:start position:0% +character this is one of the great films + + + align:start position:0% +character this is one of the great films +about character I think and especially + + align:start position:0% +about character I think and especially + + + align:start position:0% +about character I think and especially +about about the relation between the + + align:start position:0% +about about the relation between the + + + align:start position:0% +about about the relation between the +father and the sun they're at the very + + align:start position:0% +father and the sun they're at the very + + + align:start position:0% +father and the sun they're at the very +center of the film I've already said in + + align:start position:0% +center of the film I've already said in + + + align:start position:0% +center of the film I've already said in +a way that this Odyssey that they go on + + align:start position:0% +a way that this Odyssey that they go on + + + align:start position:0% +a way that this Odyssey that they go on +is a travelogue it teaches us about the + + align:start position:0% +is a travelogue it teaches us about the + + + align:start position:0% +is a travelogue it teaches us about the +geography and social circumstances and + + align:start position:0% +geography and social circumstances and + + + align:start position:0% +geography and social circumstances and +social Arrangements uh and class system + + align:start position:0% +social Arrangements uh and class system + + + align:start position:0% +social Arrangements uh and class system +of and and institutional systems of Rome + + align:start position:0% +of and and institutional systems of Rome + + + align:start position:0% +of and and institutional systems of Rome +it does that but it also it's also an + + align:start position:0% +it does that but it also it's also an + + + align:start position:0% +it does that but it also it's also an +odyssey in which the father and the son + + align:start position:0% +odyssey in which the father and the son + + + align:start position:0% +odyssey in which the father and the son +get to know each other in the in in a + + align:start position:0% +get to know each other in the in in a + + + align:start position:0% +get to know each other in the in in a +deeper and in many ways much more + + align:start position:0% +deeper and in many ways much more + + + align:start position:0% +deeper and in many ways much more +disturbing way than has ever happened to + + align:start position:0% +disturbing way than has ever happened to + + + align:start position:0% +disturbing way than has ever happened to +them before the most poignant and + + align:start position:0% +them before the most poignant and + + + align:start position:0% +them before the most poignant and +terrible thing about this film in fact + + align:start position:0% +terrible thing about this film in fact + + + align:start position:0% +terrible thing about this film in fact +is that the Odyssey I've been describing + + align:start position:0% +is that the Odyssey I've been describing + + + align:start position:0% +is that the Odyssey I've been describing +through Rome with his son by Richi is + + align:start position:0% +through Rome with his son by Richi is + + + align:start position:0% +through Rome with his son by Richi is +also an initiation story a story about + + align:start position:0% +also an initiation story a story about + + + align:start position:0% +also an initiation story a story about +growing up but what happens to richi's + + align:start position:0% +growing up but what happens to richi's + + + align:start position:0% +growing up but what happens to richi's +son in this film doesn't happen to most + + align:start position:0% +son in this film doesn't happen to most + + + align:start position:0% +son in this film doesn't happen to most +young boys until they're much older and + + align:start position:0% +young boys until they're much older and + + + align:start position:0% +young boys until they're much older and +it happens gradually not all at once but + + align:start position:0% +it happens gradually not all at once but + + + align:start position:0% +it happens gradually not all at once but +what Richie's son discovers in the + + align:start position:0% +what Richie's son discovers in the + + + align:start position:0% +what Richie's son discovers in the +course of this day are his father's + + align:start position:0% +course of this day are his father's + + + align:start position:0% +course of this day are his father's +flaws he discovers things about his + + align:start position:0% +flaws he discovers things about his + + + align:start position:0% +flaws he discovers things about his +father that no + + align:start position:0% +father that no + + + align:start position:0% +father that no +boy really wants to know even if he's 67 + + align:start position:0% +boy really wants to know even if he's 67 + + + align:start position:0% +boy really wants to know even if he's 67 +years old like your + + align:start position:0% +years old like your + + + align:start position:0% +years old like your +professor and he discovers these things + + align:start position:0% +professor and he discovers these things + + + align:start position:0% +professor and he discovers these things +about he discovers these things about + + align:start position:0% +about he discovers these things about + + + align:start position:0% +about he discovers these things about +his father in the most stressful + + align:start position:0% +his father in the most stressful + + + align:start position:0% +his father in the most stressful +circumstance ances his father is violent + + align:start position:0% +circumstance ances his father is violent + + + align:start position:0% +circumstance ances his father is violent +toward him his father is indifferent + + align:start position:0% +toward him his father is indifferent + + + align:start position:0% +toward him his father is indifferent +toward him then there are moments when + + align:start position:0% +toward him then there are moments when + + + align:start position:0% +toward him then there are moments when +after his father feels terrible anxiety + + align:start position:0% +after his father feels terrible anxiety + + + align:start position:0% +after his father feels terrible anxiety +and grief over the way he's treated + + align:start position:0% +and grief over the way he's treated + + + align:start position:0% +and grief over the way he's treated +where his father tries to make up with + + align:start position:0% +where his father tries to make up with + + + align:start position:0% +where his father tries to make up with +him and these and you can see the boy + + align:start position:0% +him and these and you can see the boy + + + align:start position:0% +him and these and you can see the boy +not wanting to let him do it it's + + align:start position:0% +not wanting to let him do it it's + + + align:start position:0% +not wanting to let him do it it's +unbelievably rich and I don't think + + align:start position:0% +unbelievably rich and I don't think + + + align:start position:0% +unbelievably rich and I don't think +anyone who pays attention to this will + + align:start position:0% +anyone who pays attention to this will + + + align:start position:0% +anyone who pays attention to this will +fail to recognize the interactions + + align:start position:0% +fail to recognize the interactions + + + align:start position:0% +fail to recognize the interactions +between the Father and Son as + + align:start position:0% +between the Father and Son as + + + align:start position:0% +between the Father and Son as +unbelievably true marvelously accurate + + align:start position:0% +unbelievably true marvelously accurate + + + align:start position:0% +unbelievably true marvelously accurate +to the way in which loving parents and + + align:start position:0% +to the way in which loving parents and + + + align:start position:0% +to the way in which loving parents and +loving children often interact with each + + align:start position:0% +loving children often interact with each + + + align:start position:0% +loving children often interact with each +other because they have many moment + + align:start position:0% +other because they have many moment + + + align:start position:0% +other because they have many moment +where they're really not happy with each + + align:start position:0% +where they're really not happy with each + + + align:start position:0% +where they're really not happy with each +other at all what the boy discovers + + align:start position:0% +other at all what the boy discovers + + + align:start position:0% +other at all what the boy discovers +about his father are some things that no + + align:start position:0% +about his father are some things that no + + + align:start position:0% +about his father are some things that no +child ever wants to know about his + + align:start position:0% +child ever wants to know about his + + + align:start position:0% +child ever wants to know about his +father not just that he's flawed but + + align:start position:0% +father not just that he's flawed but + + + align:start position:0% +father not just that he's flawed but +that he's deeply deeply flawed that he's + + align:start position:0% +that he's deeply deeply flawed that he's + + + align:start position:0% +that he's deeply deeply flawed that he's +that that he's capable of really + + align:start position:0% +that that he's capable of really + + + align:start position:0% +that that he's capable of really +terrible Behavior Uh and the boy is and + + align:start position:0% +terrible Behavior Uh and the boy is and + + + align:start position:0% +terrible Behavior Uh and the boy is and +something then happens in this Odyssey + + align:start position:0% +something then happens in this Odyssey + + + align:start position:0% +something then happens in this Odyssey +it's one of the subtlest things about + + align:start position:0% +it's one of the subtlest things about + + + align:start position:0% +it's one of the subtlest things about +the film the Basic relations between + + align:start position:0% +the film the Basic relations between + + + align:start position:0% +the film the Basic relations between +Fathers and Sons are reversed and we + + align:start position:0% +Fathers and Sons are reversed and we + + + align:start position:0% +Fathers and Sons are reversed and we +find that the son this little child is + + align:start position:0% +find that the son this little child is + + + align:start position:0% +find that the son this little child is +twice in the film in the condition of in + + align:start position:0% +twice in the film in the condition of in + + + align:start position:0% +twice in the film in the condition of in +the position of having to rescue his + + align:start position:0% +the position of having to rescue his + + + align:start position:0% +the position of having to rescue his +father I'm I'm simplifying certain + + align:start position:0% +father I'm I'm simplifying certain + + + align:start position:0% +father I'm I'm simplifying certain +things because I don't want to give away + + align:start position:0% +things because I don't want to give away + + + align:start position:0% +things because I don't want to give away +the plot but you'll see how this works + + align:start position:0% +the plot but you'll see how this works + + + align:start position:0% +the plot but you'll see how this works +out in the film I mean there are two + + align:start position:0% +out in the film I mean there are two + + + align:start position:0% +out in the film I mean there are two +moments in the film in which richi's + + align:start position:0% +moments in the film in which richi's + + + align:start position:0% +moments in the film in which richi's +fate would be far more dire than it is + + align:start position:0% +fate would be far more dire than it is + + + align:start position:0% +fate would be far more dire than it is +because of his son's presence his son in + + align:start position:0% +because of his son's presence his son in + + + align:start position:0% +because of his son's presence his son in +a sense is his savior so that the + + align:start position:0% +a sense is his savior so that the + + + align:start position:0% +a sense is his savior so that the +fathers are supposed to protect their + + align:start position:0% +fathers are supposed to protect their + + + align:start position:0% +fathers are supposed to protect their +sons not the reverse and part of the + + align:start position:0% +sons not the reverse and part of the + + + align:start position:0% +sons not the reverse and part of the +meaning of this adventure is that Richi + + align:start position:0% +meaning of this adventure is that Richi + + + align:start position:0% +meaning of this adventure is that Richi +has been reduced to such a miserable + + align:start position:0% +has been reduced to such a miserable + + + align:start position:0% +has been reduced to such a miserable +level that he even has to rely on his + + align:start position:0% +level that he even has to rely on his + + + align:start position:0% +level that he even has to rely on his +son's help in order to get in order to + + align:start position:0% +son's help in order to get in order to + + + align:start position:0% +son's help in order to get in order to +get by this and both of them Father and + + align:start position:0% +get by this and both of them Father and + + + align:start position:0% +get by this and both of them Father and +Son experience this reversal so it's a + + align:start position:0% +Son experience this reversal so it's a + + + align:start position:0% +Son experience this reversal so it's a +it's a psychologically traumatic and + + align:start position:0% +it's a psychologically traumatic and + + + align:start position:0% +it's a psychologically traumatic and +deeply moving experience although don't + + align:start position:0% +deeply moving experience although don't + + + align:start position:0% +deeply moving experience although don't +misunderstand I'm not suggesting that + + align:start position:0% +misunderstand I'm not suggesting that + + + align:start position:0% +misunderstand I'm not suggesting that +the child doesn't come to terms with + + align:start position:0% +the child doesn't come to terms with + + + align:start position:0% +the child doesn't come to terms with +what he does come to terms with what he + + align:start position:0% +what he does come to terms with what he + + + align:start position:0% +what he does come to terms with what he +learns I think it's quite remarkable I + + align:start position:0% +learns I think it's quite remarkable I + + + align:start position:0% +learns I think it's quite remarkable I +mean I I mean I I would have had trouble + + align:start position:0% +mean I I mean I I would have had trouble + + + align:start position:0% +mean I I mean I I would have had trouble +with what that boy comes to terms with + + align:start position:0% +with what that boy comes to terms with + + + align:start position:0% +with what that boy comes to terms with +as an adult and he does it as a child + + align:start position:0% +as an adult and he does it as a child + + + align:start position:0% +as an adult and he does it as a child +but I think of course it's also + + align:start position:0% +but I think of course it's also + + + align:start position:0% +but I think of course it's also +believable as see so the so the film The + + align:start position:0% +believable as see so the so the film The + + + align:start position:0% +believable as see so the so the film The +so so the film is profound and serious + + align:start position:0% +so so the film is profound and serious + + + align:start position:0% +so so the film is profound and serious +about the social circumstances of + + align:start position:0% +about the social circumstances of + + + align:start position:0% +about the social circumstances of +postwar Italy it's profound and serious + + align:start position:0% +postwar Italy it's profound and serious + + + align:start position:0% +postwar Italy it's profound and serious +about the indifference of certain kinds + + align:start position:0% +about the indifference of certain kinds + + + align:start position:0% +about the indifference of certain kinds +of institutional arrangements to the to + + align:start position:0% +of institutional arrangements to the to + + + align:start position:0% +of institutional arrangements to the to +the real miseries of of of Human + + align:start position:0% +the real miseries of of of Human + + + align:start position:0% +the real miseries of of of Human +Experience uh and it is a powerful and + + align:start position:0% +Experience uh and it is a powerful and + + + align:start position:0% +Experience uh and it is a powerful and +deep exploration of human character and + + align:start position:0% +deep exploration of human character and + + + align:start position:0% +deep exploration of human character and +especially centrally the relation + + align:start position:0% +especially centrally the relation + + + align:start position:0% +especially centrally the relation +between Richi and his son the relation + + align:start position:0% +between Richi and his son the relation + + + align:start position:0% +between Richi and his son the relation +between fathers and Son becomes a kind + + align:start position:0% +between fathers and Son becomes a kind + + + align:start position:0% +between fathers and Son becomes a kind +of one of the great parables of of of + + align:start position:0% +of one of the great parables of of of + + + align:start position:0% +of one of the great parables of of of +the relations between adults and + + align:start position:0% +the relations between adults and + + + align:start position:0% +the relations between adults and +children between Father it's one of the + + align:start position:0% +children between Father it's one of the + + + align:start position:0% +children between Father it's one of the +great Father and Son stories of of all + + align:start position:0% +great Father and Son stories of of all + + + align:start position:0% +great Father and Son stories of of all +time let me conclude by saying a couple + + align:start position:0% +time let me conclude by saying a couple + + + align:start position:0% +time let me conclude by saying a couple +of words about the title I mean there's + + align:start position:0% +of words about the title I mean there's + + + align:start position:0% +of words about the title I mean there's +much more in the film I wish I could + + align:start position:0% +much more in the film I wish I could + + + align:start position:0% +much more in the film I wish I could +talk about but by this time in the + + align:start position:0% +talk about but by this time in the + + + align:start position:0% +talk about but by this time in the +course if you can't get this stuff + + align:start position:0% +course if you can't get this stuff + + + align:start position:0% +course if you can't get this stuff +yourself I haven't done my job I hope + + align:start position:0% +yourself I haven't done my job I hope + + + align:start position:0% +yourself I haven't done my job I hope +all of you are watching films much more + + align:start position:0% +all of you are watching films much more + + + align:start position:0% +all of you are watching films much more +attentively and carefully than you had + + align:start position:0% +attentively and carefully than you had + + + align:start position:0% +attentively and carefully than you had +before I hope that your enjoyment has + + align:start position:0% +before I hope that your enjoyment has + + + align:start position:0% +before I hope that your enjoyment has +been increased rather than decreased by + + align:start position:0% +been increased rather than decreased by + + + align:start position:0% +been increased rather than decreased by +what you've learned in this course and + + align:start position:0% +what you've learned in this course and + + + align:start position:0% +what you've learned in this course and +Let The Bicycle Thief be a test because + + align:start position:0% +Let The Bicycle Thief be a test because + + + align:start position:0% +Let The Bicycle Thief be a test because +in many ways it's not the kind of film + + align:start position:0% +in many ways it's not the kind of film + + + align:start position:0% +in many ways it's not the kind of film +most of you guys would go out to watch + + align:start position:0% +most of you guys would go out to watch + + + align:start position:0% +most of you guys would go out to watch +first of all it's only it's in black and + + align:start position:0% +first of all it's only it's in black and + + + align:start position:0% +first of all it's only it's in black and +white second it's whatever it is more + + align:start position:0% +white second it's whatever it is more + + + align:start position:0% +white second it's whatever it is more +than 50 years old but I think you'll I + + align:start position:0% +than 50 years old but I think you'll I + + + align:start position:0% +than 50 years old but I think you'll I +think you'll recognize that it that it + + align:start position:0% +think you'll recognize that it that it + + + align:start position:0% +think you'll recognize that it that it +hasn't aged that that that that that + + align:start position:0% +hasn't aged that that that that that + + + align:start position:0% +hasn't aged that that that that that +that the film is as compelling now as it + + align:start position:0% +that the film is as compelling now as it + + + align:start position:0% +that the film is as compelling now as it +was when it maybe even more compelling + + align:start position:0% +was when it maybe even more compelling + + + align:start position:0% +was when it maybe even more compelling +now than when it was made because some + + align:start position:0% +now than when it was made because some + + + align:start position:0% +now than when it was made because some +of the political turmoil has disappeared + + align:start position:0% +of the political turmoil has disappeared + + + align:start position:0% +of the political turmoil has disappeared +there's no longer there there's no + + align:start position:0% +there's no longer there there's no + + + align:start position:0% +there's no longer there there's no +longer the the taint of fascism hanging + + align:start position:0% +longer the the taint of fascism hanging + + + align:start position:0% +longer the the taint of fascism hanging +over Italian uh uh uh artistic + + align:start position:0% +over Italian uh uh uh artistic + + + align:start position:0% +over Italian uh uh uh artistic +Productions as there were at the end of + + align:start position:0% +Productions as there were at the end of + + + align:start position:0% +Productions as there were at the end of +the war there's a a historical sense of + + align:start position:0% +the war there's a a historical sense of + + + align:start position:0% +the war there's a a historical sense of +the importance of this movement so maybe + + align:start position:0% +the importance of this movement so maybe + + + align:start position:0% +the importance of this movement so maybe +we can look at these at these neorealist + + align:start position:0% +we can look at these at these neorealist + + + align:start position:0% +we can look at these at these neorealist +films with a more objective eye than + + align:start position:0% +films with a more objective eye than + + + align:start position:0% +films with a more objective eye than +than than the original audiences could + + align:start position:0% +than than the original audiences could + + + align:start position:0% +than than the original audiences could +in any case the title is an interesting + + align:start position:0% +in any case the title is an interesting + + + align:start position:0% +in any case the title is an interesting +one when it was first translated into + + align:start position:0% +one when it was first translated into + + + align:start position:0% +one when it was first translated into +English it was and in fact it's still + + align:start position:0% +English it was and in fact it's still + + + align:start position:0% +English it was and in fact it's still +widely known you might have noticed a + + align:start position:0% +widely known you might have noticed a + + + align:start position:0% +widely known you might have noticed a +few slips of the tongue on my part where + + align:start position:0% +few slips of the tongue on my part where + + + align:start position:0% +few slips of the tongue on my part where +I started to call it the B iCal thief + + align:start position:0% +I started to call it the B iCal thief + + + align:start position:0% +I started to call it the B iCal thief +and the reason is it's still often + + align:start position:0% +and the reason is it's still often + + + align:start position:0% +and the reason is it's still often +called that and when it was originally + + align:start position:0% +called that and when it was originally + + + align:start position:0% +called that and when it was originally +brought into the United States and + + align:start position:0% +brought into the United States and + + + align:start position:0% +brought into the United States and +translated both in in Great Britain and + + align:start position:0% +translated both in in Great Britain and + + + align:start position:0% +translated both in in Great Britain and +in the United States it was called The + + align:start position:0% +in the United States it was called The + + + align:start position:0% +in the United States it was called The +Bicycle Thief now the Italian is in the + + align:start position:0% +Bicycle Thief now the Italian is in the + + + align:start position:0% +Bicycle Thief now the Italian is in the +plural it's ladri + + align:start position:0% +plural it's ladri + + + align:start position:0% +plural it's ladri +DEET thieves of the bicycle would be the + + align:start position:0% +DEET thieves of the bicycle would be the + + + align:start position:0% +DEET thieves of the bicycle would be the +literal translation right uh now the + + align:start position:0% +literal translation right uh now the + + + align:start position:0% +literal translation right uh now the +question is why the plural and I think + + align:start position:0% +question is why the plural and I think + + + align:start position:0% +question is why the plural and I think +you can imagine the + + align:start position:0% +you can imagine the + + + align:start position:0% +you can imagine the +answer just from that opening sequence + + align:start position:0% +answer just from that opening sequence + + + align:start position:0% +answer just from that opening sequence +that I showed you this afternoon + + align:start position:0% +that I showed you this afternoon + + + align:start position:0% +that I showed you this afternoon +can + + align:start position:0% +can + + + align:start position:0% +can +you why why why would it be plural why + + align:start position:0% +you why why why would it be plural why + + + align:start position:0% +you why why why would it be plural why +would the title be plural one of the + + align:start position:0% +would the title be plural one of the + + + align:start position:0% +would the title be plural one of the +reasons is from the very opening + + align:start position:0% +reasons is from the very opening + + + align:start position:0% +reasons is from the very opening +sequence we see that everybody that + + align:start position:0% +sequence we see that everybody that + + + align:start position:0% +sequence we see that everybody that +first that the that the bicycle is a + + align:start position:0% +first that the that the bicycle is a + + + align:start position:0% +first that the that the bicycle is a +very ambiguous and complicated symbol in + + align:start position:0% +very ambiguous and complicated symbol in + + + align:start position:0% +very ambiguous and complicated symbol in +the film symbol is a bad word because + + align:start position:0% +the film symbol is a bad word because + + + align:start position:0% +the film symbol is a bad word because +it's such an actuality that it seems + + align:start position:0% +it's such an actuality that it seems + + + align:start position:0% +it's such an actuality that it seems +pretentious to call it a symbol you see + + align:start position:0% +pretentious to call it a symbol you see + + + align:start position:0% +pretentious to call it a symbol you see +hundreds of maybe thousands of bicycles + + align:start position:0% +hundreds of maybe thousands of bicycles + + + align:start position:0% +hundreds of maybe thousands of bicycles +in the film that's part of what makes + + align:start position:0% +in the film that's part of what makes + + + align:start position:0% +in the film that's part of what makes +richi's loss of the bicycle so poignant + + align:start position:0% +richi's loss of the bicycle so poignant + + + align:start position:0% +richi's loss of the bicycle so poignant +you have the sense as he's walking + + align:start position:0% +you have the sense as he's walking + + + align:start position:0% +you have the sense as he's walking +around the city that my God everybody + + align:start position:0% +around the city that my God everybody + + + align:start position:0% +around the city that my God everybody +has a bicycle there are 10 million + + align:start position:0% +has a bicycle there are 10 million + + + align:start position:0% +has a bicycle there are 10 million +bicycles in this city poor Richi can't + + align:start position:0% +bicycles in this city poor Richi can't + + + align:start position:0% +bicycles in this city poor Richi can't +find one can't find his it seem I mean + + align:start position:0% +find one can't find his it seem I mean + + + align:start position:0% +find one can't find his it seem I mean +there's something there's something + + align:start position:0% +there's something there's something + + + align:start position:0% +there's something there's something +horrific about the idea that an item so + + align:start position:0% +horrific about the idea that an item so + + + align:start position:0% +horrific about the idea that an item so +common could still fori be so precious + + align:start position:0% +common could still fori be so precious + + + align:start position:0% +common could still fori be so precious +as to constitute his livelihood or + + align:start position:0% +as to constitute his livelihood or + + + align:start position:0% +as to constitute his livelihood or +threat a threat against his livelihood + + align:start position:0% +threat a threat against his livelihood + + + align:start position:0% +threat a threat against his livelihood +if he can't find the bicycle and you can + + align:start position:0% +if he can't find the bicycle and you can + + + align:start position:0% +if he can't find the bicycle and you can +guess now on the basis of what I've + + align:start position:0% +guess now on the basis of what I've + + + align:start position:0% +guess now on the basis of what I've +already said one reason for why the + + align:start position:0% +already said one reason for why the + + + align:start position:0% +already said one reason for why the +title is plural why as rich is walking + + align:start position:0% +title is plural why as rich is walking + + + align:start position:0% +title is plural why as rich is walking +around looking for his bicycle walking + + align:start position:0% +around looking for his bicycle walking + + + align:start position:0% +around looking for his bicycle walking +through a City full of hundreds and + + align:start position:0% +through a City full of hundreds and + + + align:start position:0% +through a City full of hundreds and +thousands of bicycles what might he + + align:start position:0% +thousands of bicycles what might he + + + align:start position:0% +thousands of bicycles what might he +think what might you think if you needed + + align:start position:0% +think what might you think if you needed + + + align:start position:0% +think what might you think if you needed +the bicycle + + align:start position:0% +the bicycle + + + align:start position:0% +the bicycle +desperately why not pinch one right why + + align:start position:0% +desperately why not pinch one right why + + + align:start position:0% +desperately why not pinch one right why +not th so one of the reasons that the + + align:start position:0% +not th so one of the reasons that the + + + align:start position:0% +not th so one of the reasons that the +title is plural is that rich is one of + + align:start position:0% +title is plural is that rich is one of + + + align:start position:0% +title is plural is that rich is one of +the + + align:start position:0% +the + + + align:start position:0% +the +thieves right I mean I'm only suggesting + + align:start position:0% +thieves right I mean I'm only suggesting + + + align:start position:0% +thieves right I mean I'm only suggesting +that he's a thief by sort of + + align:start position:0% +that he's a thief by sort of + + + align:start position:0% +that he's a thief by sort of +psychological inclination he looks + + align:start position:0% +psychological inclination he looks + + + align:start position:0% +psychological inclination he looks +lovingly at by as you'll see the plot + + align:start position:0% +lovingly at by as you'll see the plot + + + align:start position:0% +lovingly at by as you'll see the plot +makes this even more explicit I didn't + + align:start position:0% +makes this even more explicit I didn't + + + align:start position:0% +makes this even more explicit I didn't +want I don't want to give away the plot + + align:start position:0% +want I don't want to give away the plot + + + align:start position:0% +want I don't want to give away the plot +he actually I will he actually does a + + align:start position:0% +he actually I will he actually does a + + + align:start position:0% +he actually I will he actually does a +certain sense become a thief but long + + align:start position:0% +certain sense become a thief but long + + + align:start position:0% +certain sense become a thief but long +before he becomes a literal thief and + + align:start position:0% +before he becomes a literal thief and + + + align:start position:0% +before he becomes a literal thief and +actually puts his hands on someone + + align:start position:0% +actually puts his hands on someone + + + align:start position:0% +actually puts his hands on someone +else's bicycle you you and and I even + + align:start position:0% +else's bicycle you you and and I even + + + align:start position:0% +else's bicycle you you and and I even +think that some people in the audience + + align:start position:0% +think that some people in the audience + + + align:start position:0% +think that some people in the audience +may get the idea before REI does I mean + + align:start position:0% +may get the idea before REI does I mean + + + align:start position:0% +may get the idea before REI does I mean +you're watching this guy so terrible + + align:start position:0% +you're watching this guy so terrible + + + align:start position:0% +you're watching this guy so terrible +looking for looking every place for his + + align:start position:0% +looking for looking every place for his + + + align:start position:0% +looking for looking every place for his +bicycle and he's surrounded by bicycles + + align:start position:0% +bicycle and he's surrounded by bicycles + + + align:start position:0% +bicycle and he's surrounded by bicycles +he's inundated by bicycles it's uh after + + align:start position:0% +he's inundated by bicycles it's uh after + + + align:start position:0% +he's inundated by bicycles it's uh after +he recovers the bicycle before he goes + + align:start position:0% +he recovers the bicycle before he goes + + + align:start position:0% +he recovers the bicycle before he goes +to + + align:start position:0% +to + + + align:start position:0% +to +work um his wife asks him to take him to + + align:start position:0% +work um his wife asks him to take him to + + + align:start position:0% +work um his wife asks him to take him to +a special location she wants to thank + + align:start position:0% +a special location she wants to thank + + + align:start position:0% +a special location she wants to thank +someone it turns out that that he so and + + align:start position:0% +someone it turns out that that he so and + + + align:start position:0% +someone it turns out that that he so and +they get on the bike she rides behind + + align:start position:0% +they get on the bike she rides behind + + + align:start position:0% +they get on the bike she rides behind +him and he rides over on the bike and he + + align:start position:0% +him and he rides over on the bike and he + + + align:start position:0% +him and he rides over on the bike and he +waits outside this place when his wife + + align:start position:0% +waits outside this place when his wife + + + align:start position:0% +waits outside this place when his wife +goes up his wife is taking a long time + + align:start position:0% +goes up his wife is taking a long time + + + align:start position:0% +goes up his wife is taking a long time +so he leans his bike against the wall + + align:start position:0% +so he leans his bike against the wall + + + align:start position:0% +so he leans his bike against the wall +and he starts to go up the stairs and he + + align:start position:0% +and he starts to go up the stairs and he + + + align:start position:0% +and he starts to go up the stairs and he +looks he sees that his bike is + + align:start position:0% +looks he sees that his bike is + + + align:start position:0% +looks he sees that his bike is +vulnerable so he walks down he finds a + + align:start position:0% +vulnerable so he walks down he finds a + + + align:start position:0% +vulnerable so he walks down he finds a +kid and he gives the I think he gives + + align:start position:0% +kid and he gives the I think he gives + + + align:start position:0% +kid and he gives the I think he gives +the kid a coin and tells the kid to + + align:start position:0% +the kid a coin and tells the kid to + + + align:start position:0% +the kid a coin and tells the kid to +guard the bike and then he starts + + align:start position:0% +guard the bike and then he starts + + + align:start position:0% +guard the bike and then he starts +walking up the stairs again this is very + + align:start position:0% +walking up the stairs again this is very + + + align:start position:0% +walking up the stairs again this is very +early in the film and think how clever + + align:start position:0% +early in the film and think how clever + + + align:start position:0% +early in the film and think how clever +this is and you're aware of how + + align:start position:0% +this is and you're aware of how + + + align:start position:0% +this is and you're aware of how +vulnerable the bike is from that moment + + align:start position:0% +vulnerable the bike is from that moment + + + align:start position:0% +vulnerable the bike is from that moment +long this is a day before it's stolen + + align:start position:0% +long this is a day before it's stolen + + + align:start position:0% +long this is a day before it's stolen +right and and you're you're aware of how + + align:start position:0% +right and and you're you're aware of how + + + align:start position:0% +right and and you're you're aware of how +precious it is and as he ascends the + + align:start position:0% +precious it is and as he ascends the + + + align:start position:0% +precious it is and as he ascends the +stairs you actually become afraid that + + align:start position:0% +stairs you actually become afraid that + + + align:start position:0% +stairs you actually become afraid that +his bicycle might be stolen right you be + + align:start position:0% +his bicycle might be stolen right you be + + + align:start position:0% +his bicycle might be stolen right you be +so that one of the reasons that the + + align:start position:0% +so that one of the reasons that the + + + align:start position:0% +so that one of the reasons that the +title is ambiguous is I think in the end + + align:start position:0% +title is ambiguous is I think in the end + + + align:start position:0% +title is ambiguous is I think in the end +that the title encompasses not just the + + align:start position:0% +that the title encompasses not just the + + + align:start position:0% +that the title encompasses not just the +thief who steals richi's bike and not + + align:start position:0% +thief who steals richi's bike and not + + + align:start position:0% +thief who steals richi's bike and not +just Richi himself who contemplates + + align:start position:0% +just Richi himself who contemplates + + + align:start position:0% +just Richi himself who contemplates +becoming a thief in his desperation but + + align:start position:0% +becoming a thief in his desperation but + + + align:start position:0% +becoming a thief in his desperation but +also the audience which becomes + + align:start position:0% +also the audience which becomes + + + align:start position:0% +also the audience which becomes +complicit in Rich's impulse to + + align:start position:0% +complicit in Rich's impulse to + + + align:start position:0% +complicit in Rich's impulse to +criminality + + align:start position:0% +criminality + + + align:start position:0% +criminality +because we ourselves think God steal the + + align:start position:0% +because we ourselves think God steal the + + + align:start position:0% +because we ourselves think God steal the +goddamn bike take the bike stop worrying + + align:start position:0% +goddamn bike take the bike stop worrying + + + align:start position:0% +goddamn bike take the bike stop worrying +about Get It Get Away there's a bike you + + align:start position:0% +about Get It Get Away there's a bike you + + + align:start position:0% +about Get It Get Away there's a bike you +can take and I think anyone watching the + + align:start position:0% +can take and I think anyone watching the + + + align:start position:0% +can take and I think anyone watching the +film has this feeling after a relatively + + align:start position:0% +film has this feeling after a relatively + + + align:start position:0% +film has this feeling after a relatively +short time so that we're bicycle thieves + + align:start position:0% +short time so that we're bicycle thieves + + + align:start position:0% +short time so that we're bicycle thieves +as well so part of the subtlety of the T + + align:start position:0% +as well so part of the subtlety of the T + + + align:start position:0% +as well so part of the subtlety of the T +and and you'll see as the as the film + + align:start position:0% +and and you'll see as the as the film + + + align:start position:0% +and and you'll see as the as the film +Works itself out I've already implied + + align:start position:0% +Works itself out I've already implied + + + align:start position:0% +Works itself out I've already implied +this when they finally catch up with the + + align:start position:0% +this when they finally catch up with the + + + align:start position:0% +this when they finally catch up with the +Alle with the thief the guy they think + + align:start position:0% +Alle with the thief the guy they think + + + align:start position:0% +Alle with the thief the guy they think +is the thief he turns out to be an even + + align:start position:0% +is the thief he turns out to be an even + + + align:start position:0% +is the thief he turns out to be an even +more miserable specimen than poor RI + + align:start position:0% +more miserable specimen than poor RI + + + align:start position:0% +more miserable specimen than poor RI +he's an epileptic he has he's out of + + align:start position:0% +he's an epileptic he has he's out of + + + align:start position:0% +he's an epileptic he has he's out of +work he has to be protected by his + + align:start position:0% +work he has to be protected by his + + + align:start position:0% +work he has to be protected by his +community his mother's very protective + + align:start position:0% +community his mother's very protective + + + align:start position:0% +community his mother's very protective +of him there's some modest minor + + align:start position:0% +of him there's some modest minor + + + align:start position:0% +of him there's some modest minor +possibility that he's acting that he's + + align:start position:0% +possibility that he's acting that he's + + + align:start position:0% +possibility that he's acting that he's +faking his his uh uh his his his his + + align:start position:0% +faking his his uh uh his his his his + + + align:start position:0% +faking his his uh uh his his his his +mental problems and maybe faking + + align:start position:0% +mental problems and maybe faking + + + align:start position:0% +mental problems and maybe faking +everything but I don't think so I mean + + align:start position:0% +everything but I don't think so I mean + + + align:start position:0% +everything but I don't think so I mean +and you can judge yourself whether this + + align:start position:0% +and you can judge yourself whether this + + + align:start position:0% +and you can judge yourself whether this +what is in any case the case what is any + + align:start position:0% +what is in any case the case what is any + + + align:start position:0% +what is in any case the case what is any +case surely true is that is that the + + align:start position:0% +case surely true is that is that the + + + align:start position:0% +case surely true is that is that the +neighborhood coalesces around him + + align:start position:0% +neighborhood coalesces around him + + + align:start position:0% +neighborhood coalesces around him +because Richi and his son are strangers + + align:start position:0% +because Richi and his son are strangers + + + align:start position:0% +because Richi and his son are strangers +and are attacking someone from their + + align:start position:0% +and are attacking someone from their + + + align:start position:0% +and are attacking someone from their +neighborhood right uh and and uh uh so + + align:start position:0% +neighborhood right uh and and uh uh so + + + align:start position:0% +neighborhood right uh and and uh uh so +so so when when this when this happens + + align:start position:0% +so so when when this when this happens + + + align:start position:0% +so so when when this when this happens +one of the things that you one of the + + align:start position:0% +one of the things that you one of the + + + align:start position:0% +one of the things that you one of the +things you feel is not just that uh that + + align:start position:0% +things you feel is not just that uh that + + + align:start position:0% +things you feel is not just that uh that +uh uh the thief that Richi was going + + align:start position:0% +uh uh the thief that Richi was going + + + align:start position:0% +uh uh the thief that Richi was going +going after deserves some sympathy too + + align:start position:0% +going after deserves some sympathy too + + + align:start position:0% +going after deserves some sympathy too +you begin to feel some uh U uh sense + + align:start position:0% +you begin to feel some uh U uh sense + + + align:start position:0% +you begin to feel some uh U uh sense +that his difficulties are not that you + + align:start position:0% +that his difficulties are not that you + + + align:start position:0% +that his difficulties are not that you +excuse his thievery but you understand + + align:start position:0% +excuse his thievery but you understand + + + align:start position:0% +excuse his thievery but you understand +it in a in a in a deep and generous way + + align:start position:0% +it in a in a in a deep and generous way + + + align:start position:0% +it in a in a in a deep and generous way +I think uh and that complicates your + + align:start position:0% +I think uh and that complicates your + + + align:start position:0% +I think uh and that complicates your +sense of who thieves are and what + + align:start position:0% +sense of who thieves are and what + + + align:start position:0% +sense of who thieves are and what +thieves our life and then you've come to + + align:start position:0% +thieves our life and then you've come to + + + align:start position:0% +thieves our life and then you've come to +recognize that rich is a potential thief + + align:start position:0% +recognize that rich is a potential thief + + + align:start position:0% +recognize that rich is a potential thief +and you care about Richie you see what a + + align:start position:0% +and you care about Richie you see what a + + + align:start position:0% +and you care about Richie you see what a +loving father he is what a desperate how + + align:start position:0% +loving father he is what a desperate how + + + align:start position:0% +loving father he is what a desperate how +desperate he is to take care of his + + align:start position:0% +desperate he is to take care of his + + + align:start position:0% +desperate he is to take care of his +family so you you you you sympathize + + align:start position:0% +family so you you you you sympathize + + + align:start position:0% +family so you you you you sympathize +with him and then you realize if you've + + align:start position:0% +with him and then you realize if you've + + + align:start position:0% +with him and then you realize if you've +been thinking about it that of course + + align:start position:0% +been thinking about it that of course + + + align:start position:0% +been thinking about it that of course +you've been coveting bicycles yourself + + align:start position:0% +you've been coveting bicycles yourself + + + align:start position:0% +you've been coveting bicycles yourself +as if you as so the audience and the + + align:start position:0% +as if you as so the audience and the + + + align:start position:0% +as if you as so the audience and the +real thief and reachi the wouldbe thief + + align:start position:0% +real thief and reachi the wouldbe thief + + + align:start position:0% +real thief and reachi the wouldbe thief +are all implicated together as if what + + align:start position:0% +are all implicated together as if what + + + align:start position:0% +are all implicated together as if what +he's saying is that our common humanity + + align:start position:0% +he's saying is that our common humanity + + + align:start position:0% +he's saying is that our common humanity +is what bicycle thieves suggest and + + align:start position:0% +is what bicycle thieves suggest and + + + align:start position:0% +is what bicycle thieves suggest and +that's one of the reasons that the title + + align:start position:0% +that's one of the reasons that the title + + + align:start position:0% +that's one of the reasons that the title +needs to be plural because the film is + + align:start position:0% +needs to be plural because the film is + + + align:start position:0% +needs to be plural because the film is +not about a single Bicycle Thief it's + + align:start position:0% +not about a single Bicycle Thief it's + + + align:start position:0% +not about a single Bicycle Thief it's +about The Bicycle Thief in all of + + align:start position:0% +about The Bicycle Thief in all of + + + align:start position:0% +about The Bicycle Thief in all of +us enjoy the film \ No newline at end of file diff --git a/ICBy0tTtgR4.txt b/ICBy0tTtgR4.txt new file mode 100644 index 0000000000000000000000000000000000000000..2d0bcaab3e5a2c7371ce1ab21c577bd5507e2798 --- /dev/null +++ b/ICBy0tTtgR4.txt @@ -0,0 +1,795 @@ +align:start position:0% + +the 1980s turned out to be a pivotal + + align:start position:0% +the 1980s turned out to be a pivotal + + + align:start position:0% +the 1980s turned out to be a pivotal +decade in the history of + + align:start position:0% +decade in the history of + + + align:start position:0% +decade in the history of +work so let's take a look at what + + align:start position:0% +work so let's take a look at what + + + align:start position:0% +work so let's take a look at what +happened during that decade and why we + + align:start position:0% +happened during that decade and why we + + + align:start position:0% +happened during that decade and why we +should care about these developments + + align:start position:0% +should care about these developments + + + align:start position:0% +should care about these developments +because it will affect the future of + + align:start position:0% +because it will affect the future of + + + align:start position:0% +because it will affect the future of +work going + + align:start position:0% +work going + + + align:start position:0% +work going +forward the 1970s are going to go down + + align:start position:0% +forward the 1970s are going to go down + + + align:start position:0% +forward the 1970s are going to go down +in history as a decade of status quo the + + align:start position:0% +in history as a decade of status quo the + + + align:start position:0% +in history as a decade of status quo the +pressures were building but managers and + + align:start position:0% +pressures were building but managers and + + + align:start position:0% +pressures were building but managers and +workers and unions and the government + + align:start position:0% +workers and unions and the government + + + align:start position:0% +workers and unions and the government +behaved as if the 1960s and 1950s were + + align:start position:0% +behaved as if the 1960s and 1950s were + + + align:start position:0% +behaved as if the 1960s and 1950s were +still in + + align:start position:0% +still in + + + align:start position:0% +still in +Vogue unions were declining new + + align:start position:0% +Vogue unions were declining new + + + align:start position:0% +Vogue unions were declining new +industries were coming along with new + + align:start position:0% +industries were coming along with new + + + align:start position:0% +industries were coming along with new +ways of introducing flexible job designs + + align:start position:0% +ways of introducing flexible job designs + + + align:start position:0% +ways of introducing flexible job designs +the economy was experiencing this High + + align:start position:0% +the economy was experiencing this High + + + align:start position:0% +the economy was experiencing this High +rate of inflation with no growth in + + align:start position:0% +rate of inflation with no growth in + + + align:start position:0% +rate of inflation with no growth in +wages labor law was getting outdated but + + align:start position:0% +wages labor law was getting outdated but + + + align:start position:0% +wages labor law was getting outdated but +Congress couldn't do anything about it + + align:start position:0% +Congress couldn't do anything about it + + + align:start position:0% +Congress couldn't do anything about it +so the pressures were building like this + + align:start position:0% +so the pressures were building like this + + + align:start position:0% +so the pressures were building like this +proverbial frog that was in warm water + + align:start position:0% +proverbial frog that was in warm water + + + align:start position:0% +proverbial frog that was in warm water +stayed in the water too long until it + + align:start position:0% +stayed in the water too long until it + + + align:start position:0% +stayed in the water too long until it +started to boil never jumped out because + + align:start position:0% +started to boil never jumped out because + + + align:start position:0% +started to boil never jumped out because +the challenges were only being felt + + align:start position:0% +the challenges were only being felt + + + align:start position:0% +the challenges were only being felt +incrementally until it was too + + align:start position:0% +incrementally until it was too + + + align:start position:0% +incrementally until it was too +late so what happened in the 1980s the + + align:start position:0% +late so what happened in the 1980s the + + + align:start position:0% +late so what happened in the 1980s the +president of the United States well + + align:start position:0% +president of the United States well + + + align:start position:0% +president of the United States well +Ronald Reagan got elected president a + + align:start position:0% +Ronald Reagan got elected president a + + + align:start position:0% +Ronald Reagan got elected president a +change from a Democrat to a Conservative + + align:start position:0% +change from a Democrat to a Conservative + + + align:start position:0% +change from a Democrat to a Conservative +Republican with very strong ideas about + + align:start position:0% +Republican with very strong ideas about + + + align:start position:0% +Republican with very strong ideas about +how to run the economy the second thing + + align:start position:0% +how to run the economy the second thing + + + align:start position:0% +how to run the economy the second thing +that happened is it coincided with a + + align:start position:0% +that happened is it coincided with a + + + align:start position:0% +that happened is it coincided with a +Great Recession of 1981 to + + align:start position:0% +Great Recession of 1981 to + + + align:start position:0% +Great Recession of 1981 to +1983 where the effort was to try to + + align:start position:0% +1983 where the effort was to try to + + + align:start position:0% +1983 where the effort was to try to +break the back of inflation by the + + align:start position:0% +break the back of inflation by the + + + align:start position:0% +break the back of inflation by the +Federal Reserve board the third thing + + align:start position:0% +Federal Reserve board the third thing + + + align:start position:0% +Federal Reserve board the third thing +that came along in coincidence with + + align:start position:0% +that came along in coincidence with + + + align:start position:0% +that came along in coincidence with +these pressures was the growth of + + align:start position:0% +these pressures was the growth of + + + align:start position:0% +these pressures was the growth of +Japanese and other Global competition + + align:start position:0% +Japanese and other Global competition + + + align:start position:0% +Japanese and other Global competition +now companies in Japan could build autos + + align:start position:0% +now companies in Japan could build autos + + + align:start position:0% +now companies in Japan could build autos +and other products as productively at + + align:start position:0% +and other products as productively at + + + align:start position:0% +and other products as productively at +lower cost as the United States and + + align:start position:0% +lower cost as the United States and + + + align:start position:0% +lower cost as the United States and +build them at high qualities so that + + align:start position:0% +build them at high qualities so that + + + align:start position:0% +build them at high qualities so that +they were strong competitors to this + + align:start position:0% +they were strong competitors to this + + + align:start position:0% +they were strong competitors to this +country so what did we see happen + + align:start position:0% +country so what did we see happen + + + align:start position:0% +country so what did we see happen +well somewhere in this time period that + + align:start position:0% +well somewhere in this time period that + + + align:start position:0% +well somewhere in this time period that +great social contract from the 1940s + + align:start position:0% +great social contract from the 1940s + + + align:start position:0% +great social contract from the 1940s +through the 1960s broke down this nice + + align:start position:0% +through the 1960s broke down this nice + + + align:start position:0% +through the 1960s broke down this nice +Coincidence of wages and productivity + + align:start position:0% +Coincidence of wages and productivity + + + align:start position:0% +Coincidence of wages and productivity +moving together during this time period + + align:start position:0% +moving together during this time period + + + align:start position:0% +moving together during this time period +you can see it began to fray in the 70s + + align:start position:0% +you can see it began to fray in the 70s + + + align:start position:0% +you can see it began to fray in the 70s +and then after 1980 the they depart + + align:start position:0% +and then after 1980 the they depart + + + align:start position:0% +and then after 1980 the they depart +never to return again so how did this + + align:start position:0% +never to return again so how did this + + + align:start position:0% +never to return again so how did this +happen well again it starts with Ronald + + align:start position:0% +happen well again it starts with Ronald + + + align:start position:0% +happen well again it starts with Ronald +Reagan in the August of 1981 the air + + align:start position:0% +Reagan in the August of 1981 the air + + + align:start position:0% +Reagan in the August of 1981 the air +traffic controllers went on strike + + align:start position:0% +traffic controllers went on strike + + + align:start position:0% +traffic controllers went on strike +illegally and Ronald Reagan said this is + + align:start position:0% +illegally and Ronald Reagan said this is + + + align:start position:0% +illegally and Ronald Reagan said this is +an illegal strike I'm going to take + + align:start position:0% +an illegal strike I'm going to take + + + align:start position:0% +an illegal strike I'm going to take +decisive action I'm going to fire them + + align:start position:0% +decisive action I'm going to fire them + + + align:start position:0% +decisive action I'm going to fire them +if they don't come back to work he did + + align:start position:0% +if they don't come back to work he did + + + align:start position:0% +if they don't come back to work he did +so he broke that strike and it + + align:start position:0% +so he broke that strike and it + + + align:start position:0% +so he broke that strike and it +fundamentally changed the tenor of Labor + + align:start position:0% +fundamentally changed the tenor of Labor + + + align:start position:0% +fundamentally changed the tenor of Labor +Relations companies in the private + + align:start position:0% +Relations companies in the private + + + align:start position:0% +Relations companies in the private +sector became much more aggressive + + align:start position:0% +sector became much more aggressive + + + align:start position:0% +sector became much more aggressive +building on the model of what Reagan did + + align:start position:0% +building on the model of what Reagan did + + + align:start position:0% +building on the model of what Reagan did +they demanded wage concessions to try to + + align:start position:0% +they demanded wage concessions to try to + + + align:start position:0% +they demanded wage concessions to try to +become more competitive they put in what + + align:start position:0% +become more competitive they put in what + + + align:start position:0% +become more competitive they put in what +were called two-tier contracts so new + + align:start position:0% +were called two-tier contracts so new + + + align:start position:0% +were called two-tier contracts so new +workers were starting at work at a lower + + align:start position:0% +workers were starting at work at a lower + + + align:start position:0% +workers were starting at work at a lower +wage rate than more senior workers that + + align:start position:0% +wage rate than more senior workers that + + + align:start position:0% +wage rate than more senior workers that +in fact continues today in many cases + + align:start position:0% +in fact continues today in many cases + + + align:start position:0% +in fact continues today in many cases +Auto Workers would understand this + + align:start position:0% +Auto Workers would understand this + + + align:start position:0% +Auto Workers would understand this +because new hires come in about 30% less + + align:start position:0% +because new hires come in about 30% less + + + align:start position:0% +because new hires come in about 30% less +than workers who are doing the same work + + align:start position:0% +than workers who are doing the same work + + + align:start position:0% +than workers who are doing the same work +along Ong side of them and so this + + align:start position:0% +along Ong side of them and so this + + + align:start position:0% +along Ong side of them and so this +persisted basically what happened is + + align:start position:0% +persisted basically what happened is + + + align:start position:0% +persisted basically what happened is +pattern bargaining that engine that + + align:start position:0% +pattern bargaining that engine that + + + align:start position:0% +pattern bargaining that engine that +helped to spread wage increases across + + align:start position:0% +helped to spread wage increases across + + + align:start position:0% +helped to spread wage increases across +the economy broke down the bargaining + + align:start position:0% +the economy broke down the bargaining + + + align:start position:0% +the economy broke down the bargaining +power that workers got from strikes was + + align:start position:0% +power that workers got from strikes was + + + align:start position:0% +power that workers got from strikes was +no longer there strikes became defensive + + align:start position:0% +no longer there strikes became defensive + + + align:start position:0% +no longer there strikes became defensive +weapons and companies like Greyhound bus + + align:start position:0% +weapons and companies like Greyhound bus + + + align:start position:0% +weapons and companies like Greyhound bus +lines or Eastern Airlines where strikes + + align:start position:0% +lines or Eastern Airlines where strikes + + + align:start position:0% +lines or Eastern Airlines where strikes +occurred that companies either won the + + align:start position:0% +occurred that companies either won the + + + align:start position:0% +occurred that companies either won the +strike or in Eastern's case the company + + align:start position:0% +strike or in Eastern's case the company + + + align:start position:0% +strike or in Eastern's case the company +went out of business and all the jobs + + align:start position:0% +went out of business and all the jobs + + + align:start position:0% +went out of business and all the jobs +were lost and so this has continued + + align:start position:0% +were lost and so this has continued + + + align:start position:0% +were lost and so this has continued +workers lost their source of power they + + align:start position:0% +workers lost their source of power they + + + align:start position:0% +workers lost their source of power they +don't have a new source of bargaining + + align:start position:0% +don't have a new source of bargaining + + + align:start position:0% +don't have a new source of bargaining +power in place yet and so this social + + align:start position:0% +power in place yet and so this social + + + align:start position:0% +power in place yet and so this social +contract continues to be broken the + + align:start position:0% +contract continues to be broken the + + + align:start position:0% +contract continues to be broken the +challenge that we face today the + + align:start position:0% +challenge that we face today the + + + align:start position:0% +challenge that we face today the +challenge as Next Generation workers you + + align:start position:0% +challenge as Next Generation workers you + + + align:start position:0% +challenge as Next Generation workers you +face is to figure out what is a social + + align:start position:0% +face is to figure out what is a social + + + align:start position:0% +face is to figure out what is a social +contract that might work in the modern + + align:start position:0% +contract that might work in the modern + + + align:start position:0% +contract that might work in the modern +economy for you as a modern Workforce + + align:start position:0% +economy for you as a modern Workforce + + + align:start position:0% +economy for you as a modern Workforce +and for society we have not figured that + + align:start position:0% +and for society we have not figured that + + + align:start position:0% +and for society we have not figured that +out yet that's going to be your + + align:start position:0% +out yet that's going to be your + + + align:start position:0% +out yet that's going to be your +challenge e \ No newline at end of file diff --git a/IPTyKqZpbCM.txt b/IPTyKqZpbCM.txt new file mode 100644 index 0000000000000000000000000000000000000000..3cc7f124cba416680feb609c9e197e4bf373be03 --- /dev/null +++ b/IPTyKqZpbCM.txt @@ -0,0 +1,1751 @@ +PROFESSOR: All right, let's +resume our discussion. + +And we'll finish it for sure +by the end of today. + +And as you say, you can tuck +this away for study on your + +own or for future reference or +whatever you want to do. + +So if we could assign sizes to +atoms and ions, we could do a + +lot towards predicting what sort +of structures they might + +form if we knew the +composition. + +The composition-- + +again, assuming there is only +one type of anion and one type + +of cation, the composition is +determined by the valence. + +The composition fixes the ratio +of coordination numbers. + +And the structure will have +lowest energy when we have the + +maximum number of anions around +cation and vice-versa. + +So we're in great shape. + +And this is simple, idealized, +but very powerful stuff if we + +knew the sizes that were +assumed by ions. + +And that, really, is an absurd +notion, to talk about an atom + +as though it behaved like a +sphere with finite dimensions. + +If we plotted the density of the +electrons as a function of + +distance R from an atom, it +does something like this. + +At very small distances, that +defines a shell of a rather + +small volume, so there are +not many electrons. + +Rises up to a maximum, and +then tails off gradually. + +So what is the radius? + +The maximum in the distribution +of density. + +So the notion of radius is +absolutely nonsense in terms + +of the actual distribution +of electrons on the atom. + +However, one can get from your +fraction measurements a + +determination of the +lattice constant. + +And even with routine methods, +you can get the dimension of + +the lattice to extraordinary +precision. + +The typical lattice constant +is about 10 Angstroms. + +You can get this through routine +methods to plus or + +minus 1 in the fourth +decimal point. + +So this is a precision of +1 part in 10 to the 5th. + +You can get atomic positions +when they are not fixed by + +symmetry to get a coordinate to +plus or minus 0.yyyy plus + +or minus 1 in good cases. + +So that is 1 part in +10 to the 5th. + +Missing a factor or +10 somewhere. + +This is plus or minus 1. + +That's 1 in 10 to the 4th. + +So you can get this information +very accurately. + +One thing I always like to +point out here is that a + +thermal expansion coefficient +for most inorganic materials + +is something that never gets +much lower than about 1 or 2 + +times 10 to the minus 6. + +So if you're going to push the +measurement of a lattice + +constant to the ultimate +accuracy, you'd better have a + +thermometer on the top of the +X-ray generator, or your + +measurement is meaningless. + +The thermal expansion can be +more than the uncertainty in + +your measurement. + +So you should report, for very +precise measurements, the + +temperature at which you +made your measurement. + +OK, you can get interionic +distances with very high + +precisions. + +And if you look at a series +of compounds-- + +and these are the ones that are +discussed in the notes, + +which have the rock salt +structure type. + +So here is the cation, +here is the anion. + +The anion-cation distance is +simply equal to 1/2 of A for + +the rock salt structure. + +So that's easy. + +You don't even have to know +the atomic positions. + +Just measure the lattice +constants. + +And then you would find, for +example, that R, NA plus R, CL + +is equal to 1/2 of A for NaCl. + +Very precisely know the sum. + +How do we split this up? + +Well, let's look at +another compound. + +Let's look at R, NA plus +R for bromine. + +And that would be 1/2 of the +lattice constant of NaBr. + +Hm. + +More data, but we haven't +solved anything. + +We have three radii, only +two measurements. + +And you can see, if you try to +push this further, you can + +never get enough information +to split up the interionic + +distances into sums of +individual radii in any sort + +of unique fashion. + +So you have to start +somewhere. + +And there are different sets +of ionic radii that were + +proposed early in the game. + +And they are discussed +in the notes. + +I give you an example of some +of the sums of radii for the + +oxides and sulfides +and selenides of + +the transition metals. + +You can see that as the anion +atomic number increases, the + +size of the lattice +constant goes up. + +So you could get, for example, +the difference in size between + +a sulfur and an oxygen and the +difference in radius between a + +selenium and a sulfur. + +But you could never get +the absolute values. + +There are four early +sets of radii. + +And they are tabulated for you +part way through the notes. + +And there's a cautionary +lesson here. + +One the early series +of radii-- + +see, even the old workers in +this field appreciated the + +role of ionic sizes in +determining structure. + +So they wanted to set up + +self-consistent schemes of radii. + +And the earliest one is by, +really, the founder of crystal + +chemistry, a man named +Goldschmidt. + +Linus Pauling got into the +act very early on. + +If you look at this table that +I copied from these separate + +publications, four different +people-- + +Goldschmidt, Pauling, Zacharias +and Ahrens. + +Some people left out the radii +of certain species. + +Other people left out different +radii depending on + +the compounds that +they looked at. + +If people looked at the same +ion, they very often got very, + +very different values, +depending on + +their starting point. + +Look at the size of barium, +for example. + +Zacharias said 1.29. + +Ahrens said 1.34. + +Pauling said 1.35. + +Goldschmidt said 1.43. + +Depends on the starting +point that they used + +for the initial radius. + +And once you've determined +that, + +everything falls into place. + +Another basis for determining +radii, Bragg determined a + +number of the structure of +important silicates. + +Why silicates? + +Because as you walk +along the ground, + +you're walking on silicates. + +These are part of the minerals +that form the Earth's crust, + +so there was a lot of +interest in those. + +Bragg, from his early work way +back in the late 1920s, found + +that the size and shape of the +Si04 tetrahedron forms + +tetrahedral coordination because +silicon is so small + +compared to oxygen. + +The interionic distances were +always about the same. + +The tetrahedron was +always regular. + +So what Bragg said was, a-ha, +this is a tough little nut in + +silicate structures. + +Doesn't deform. + +The size is always the same. + +It's always regular. + +The reason must be that the +oxygens are just in contact. + +So he used the dimensions of an +Si04 tetrahedron, took the + +radius of oxygen as +half the edge. + +Pauling used a different +starting point + +that has been followed. + +There's still another way +of determining radii. + +Is there any physical property +of a material which might also + +be shown to be proportional +to the size of the ion? + +And the answer to that, +which I'll pass + +over quickly, is yes. + +Quantity called the ionic +electrical polarizability, + +which is the relation between an +applied electric field and + +the dipole moment that is +induced on the atom when you + +separate the electron cloud +and the nucleus. + +And a simple model shows-- + +and this is carried +out for you-- + +that you can relate the ionic +electronic polarizability to + +the volume of the atom, and it +turns out to be beautifully + +simple, that the polarizability +is simply 4 pi + +epsilon 0 times the radius +of the ion cubed. + +So therefore, you can split up +ionic radii in proportion to + +the cube root of the +polarizability of the ions. + +Well, that trades one +problem for another. + +How do you get polarizabilities? + +It turns out that the index of +refraction of materials is + +given by the sum of the number +of each species per unit + +volume times the ionic + +polarizability of that species. + +And there is a famous +equation called the + +Lorentz-Lorenz equation. + +I can never resist calling +it not the Lorenz-Lorentz + +equation but the Lorenz-Lorentz +equation + +equation because it +sounds like you're + +saying everything twice. + +If you note that the dielectric +constant of a + +material is related to the +square of the index of + +refraction, instead of n +squared, you can replace the n + +squared by epsilon, the +dielectric constant, and then + +the equations become +known as the + +Clausius-Mossotti equations. + +And I always take that as a nice +illustration of the fact + +that a very simple change of +variables can be all it takes + +to become famous and immortal. + +[INAUDIBLE] + +what happened to Clausius +and Mossotti. + +Where do you get +polarizabilities from? + +This was looked at by +a number of people. + +One of the most complete were +three people, Tessman, Kahn, + +and Wild Bill Shockley +of transistor fame. + +So you can find these numbers, +and you can get a + +self-consistent set of radii. + +But note in the table that +I give you here that the + +individual numbers are +very different. + +And two caveats that I have to +issue is you can't mix ionic + +radii in different people's +tables because they have + +different starting assumptions +for the standard radius. + +If you do that, you're mixing +apples and oranges. + +And I wish I had a cookie for +every half-baked book on + +chemistry that said, hey, Ahrens +has got something for + +americium and Pauling doesn't. + +Let me put the value for +americium in there. + +Totally wrong that they +are established + +on different bases. + +So you can't mix apples +and oranges. + +You have to use a +self-consistent set of radii. + +The ones that were followed +until very recently are + +Pauling's radii. + +And Pauling's radii are based +on a standard radius for + +oxygen, which is 1.40 +Angstroms for + +the radius of oxygen. + +The other thing that I have to +issue as a caveat, which I + +hope you won't forget, is that +radius ratios do a pretty good + +job of predicting the expected +coordination number. + +But if you are very, very close +to a limiting critical + +radius ratio, all +bets are off. + +Because then you're really +asking the question, if I have + +this polyhedron of ions, if I +squish them a little bit so + +that I increase the coordination +number, does that + +give me a lower energy in return +for the price that I + +have to pay to deform the ions +that I'm packing together? + +And that is not possible to +answer on the basis of a rigid + +sphere model. + +So when you're very close to a +critical radius ratio, you + +really can't say for sure +whether the structure will go + +to the lower coordination +number or the higher + +coordination number. + +So you have to be +careful of that. + +Finally, people have +continued on. + +And stuck in the margin of +these older radii is a + +reference to a paper by two +people, Bob Shannon, who was a + +crystallographer at DuPont, +and Charlie Prewitt. + +I'm very proud that he became so +notable, because he was my + +office mate in graduate +school. + +So I like to promote his +radii whenever I can. + +And in Acta Crystallographica in +1969, they published a set + +of radii, which is in the nice +typeset version that's Xeroxed + +directly from their paper in +Acta Crystallographica. + +And the headings need +explanation. + +There's the ion and its valence, +then the electron + +configuration. + +And what's interesting is that +some of the transition metals, + +for example iron, can be in +a high-spin or a low-spin + +configuration depending on +whether the moments on the + +electrons are all parallel +or anti-parallel. + +High-spin and low-spin +configurations give ions with + +very, very distinct radii. + +So the second column, EC, +stands for Electron + +Configuration. + +Then comes coordination +number. + +And here is another feature +that we really should not + +overlook, that as even +rigid spheres-- + +here's an A, and here's a B-- + +acquire progressively higher +coordination numbers-- + +let's look at just coordination +number three and + +coordination number four, +because they're easy to draw. + +In addition to the attractive +force between anion and + +cation, there is also +a repulsive + +force between the anions. + +So here's the repulsive force +between this B and its + +neighboring B and this B and +its neighboring B. And the + +resultant is a force that +tends to push apart + +the A and the B ion. + +For four-coordination, remember +first of all, the Bs + +are closer, so the repulsive +force is stronger. + +But there are four +of them, as well. + +So this turns out to be a +larger repulsive force. + +So the conclusion is that the +radius of A would be expected + +to go up slightly as the +coordination number increased, + +simply because there is a +repulsive interaction between + +the coordinating Bs. + +And that will tend to push them +apart more strongly as + +the coordination goes up. + +So the third column in the +Shannon and Prewitt tables is + +coordination number. + +And if you look at several +ions, they're-- + +for example, barium has +6-coordination, + +7-coordination. + +8, 9, 10, and even 12. + +And as you go down that list +of radii, it gets larger as + +the coordination goes up. + +And it's a relatively small +effect that's on the order of + +5 or so percent. + +But still, when trying to +calculate an interionic + +distance, you should use the +radius that is appropriate for + +the coordination numbers. + +The fourth column is spin. + +And the spin stands for +high spin or low spin. + +And you will find that for the +transition metal atoms-- + +for example, CO2 plus low spin +or high spin, and note the + +rather different radii for these +two configurations of + +the electron moments. + +Yeah. + +AUDIENCE: Under coordination +number, what's the difference + +between 4SQ and just Q? + +PROFESSOR: You would guess +that the lowest energy + +configuration for +four-coordination would be + +tetrahedral, because +that keeps the + +anions most widely separated. + +There are cases where the +coordination is plainer. + +So the "SQ" stands for square, +and that's unusual. + +And you'll notice that that +appears for things like + +silver, which has a considerable +covalent + +character to it. + +For gold, 3-plus. + +That's one of the noble metals, +again, that has a + +considerable covalent +character to it. + +So you'll notice that as the +coordination number goes up, + +you get a different radius. + +Now, there are then a set of +numbers, and these are numbers + +that are based on different +starting points. + +The furthest column to the +right, quote "IR" quote, this + +is based on Pauling's +starting point. + +And Pauling's starting point, +if you go way down the list + +onto the second page, is that +for 02 minus for oxygen in + +six-coordination, the standard +radius from which everything + +else hinges is 1.40. + +The Pauling radii had been so +commonly used that Shannon and + +Prewitt decided to use 1.40, +Pauling's radii. + +So all of their numbers are +compatible with the early + +Pauling radii, except they're +based on thousands more + +crystal structure +determinations. + +There is another column, +second from the + +right, called CR. + +And that stands for +Crystal Radii. + +And there were two people that +proposed that Pauling's radii + +really didn't give a feel for +the proper sizes of the ions. + +And they went on at great +length to explain what + +"proper sizes" is. + +And the only difference for the +sizes that are based on, + +quote, "crystal radii" is that +if you go all the way down to + +oxygen, the size of the oxygen +ion in six-coordination is + +given by 1.26. + +So all of the anions in the +crystal radius column are + +smaller by 1.40 minus 1.26. + +I can do that in my head. + +That's 0.14 Angstroms. + +Run down the list. + +They're 1.4 Angstroms smaller +for the anions. + +And the cations are 0.14 +Angstroms larger. + +So there are two alternative +sets of radii, one based on + +the traditional Pauling radii, +1.40 for oxygen in + +six-coordination, and the +Fumi-Tosi radii, 1.26, which + +maybe give a better picture +of what the sphere sizes + +actually, quote, "look +like," unquote. + +But note the tendencies. + +There is a progressive +change-- + +whoever's starting point you +use, there's a progressive + +change in size with coordination +number. + +And let me give you, if I may, +at this point, give you-- + +again, a little knowledge +is a dangerous thing. + +One of the structures which I +worked on many years ago was a + +puzzle, and this was the +prototype fast ion conductor + +silver iodide. + +And nobody had been able to +determine the structure for + +several reasons. + +Nobody had ever made a single +crystal of it, and all the + +diffraction data you had +available for the structure + +were five or six intensities. + +And there were about seven +parameters necessary to fully + +describe the structure, so +you were out of luck. + +We learned how to make +single crystals. + +But before that-- + +no, he will go nameless. + +He said, OK, let's see +what's going on here. + +Oh, we'll get the radius +of silver. + +We know that in silver iodide, +the iodines are in + +body-centered cubic packing. + +And we know what the lattice +constant is, because we got + +that from powder diffraction +data. + +Huh, the silver ion is too +big to fit in either the + +tetrahedral interstitial site or +the octahedral interstitial + +site in silver iodide. + +So he said, therefore, the +structure has to distort, and + +it's really tetragonal. + +But there are going +to be domains. + +a tetragonal domain in one +orientation here, a tetragonal + +domain in another orientation +here. + +So he gets himself a random +number generator and takes + +numbers one, two, and three and +puts it on a cubic lattice + +to determine what the +distortion will be. + +Said, hey, I got a bunch of +ones here and a bunch of + +threes here. + +This crystal is built +of domains. + +And the reason the silver ions +migrate rapidly is that a + +domain can pop from one mode of +distortion to another, and + +that's essentially going to +transport the silver ion from + +one end of the domain +to another. + +This guy got two papers +out of it. + +What he had done was he looked +up the radius of silver in + +Pauling's tables. + +And he didn't realize that all +of Pauling's original radii + +were normalized to octahedral +six-hole coordination, which + +makes the radius larger. + +And that's why the silvers +didn't fit in any of the + +interstices. + +If you take the tetrahedral +radius for silver, which is + +where it actually sits in the +structure, it fits as snugly + +and nicely as you please in the +tetrahedral interstitial + +site in the body-centered +cubic arrangement. + +So this guy made an idiot of +himself because he didn't + +realize the basis on which +these tables had been + +established. + +But he's nameless, so I +can call him names. + +So anyway, again, a little +knowledge can + +be a dangerous thing. + +Moving on, in the few minutes +that we have left to devote to + +crystal chemistry. + +Pauling's radii, and even +better still now, the + +Shannon-Prewitt radii, let you +predict nearest-neighbor + +configurations-- + +coordination numbers with fair +degree of confidence. + +Pauling-- + +and this was one of the things +that he received the Nobel + +Prize for-- + +proposed a set of five rules +that are called Pauling's + +Rules for ionic structure. + +The first thing he said was +something that we've already + +stated, a coordination polyhedra +of anions is formed + +about each cation, and the +cation-anion distance is + +determined by the sum of the +radii, and the coordination + +number is determined +by radius ratio. + +So there are three principles +in here. + +The two most important ones is +that expressing faith in a set + +of radii to determine interionic +distances and the + +fact that if there are radii +that can be assigned to the + +atoms, you can predict a +coordination number. + +So that's Pauling's +first rule. + +Actually, Pauling's first +rule was first stated by + +Goldschmidt. + +But to have a complete listing +of guiding principles, he + +included that there and didn't +claim it was his own. + +But then he does something that +is rather interesting. + +This is the only one of the +rules that is quantitative. + +If you had an ionic structure, +and you could determine its + +unit cell, the structure should +be electrically neutral + +if it's composed of ions +that are charged. + +So therefore, you would not make +a structure in which all + +the cations were up in one +corner of the cell, and all + +the anions were down in the +opposite end of the cell. + +That would be something that +might be electrically neutral, + +but it would be a high-energy +configuration. + +So Pauling's second rule is a +very cute way of expressing + +the fact that a structure +should be atomistically + +electrically neutral, as well +as microscopically. + +And he did that in the +following way. + +He said, let us look at the +coordination number the + +cation, A, and look at the +coordination polyhedron. + +And let's define as the bond +strength, S, as the ratio of + +the cation charge plus Q divided +by the coordination + +number of A. + +And then he said that in a +stable structure, if we look + +at the anion, the sum of all +the bonds donated to-- + +he visualize the charge being +donated to the anion. + +The sum of all of the bonds from +the same cations or from + +different cations, if that's the +nature of the structure, + +should be equal to the +charge of the anion. + +So let me say "cation" here. + +So it's a cute way of +expressing local + +electroneutrality. + +Actually, that's been superseded +by an extension of + +this general principle. + +And I may not have time to +discuss it today, but I'll + +give you a handout next time. + +It's not in the notes, either. + +This is a relatively recent tool +that most people are not + +familiar with, so I'll return +to it briefly next time. + +The next rule says, OK, we +know how to determine the + +coordination numbers. + +To describe the structure, we +should be able to say how + +these coordination polyhedra +fit together. + +So looking at the coordination +numbers-- + +well, let me do a +three-dimensional case, + +because that's the realistic +situation. + +Let's suppose we have +coordination number eight, + +which we often do. + +And besides, that's +easy to draw. + +So he says that in a stable +structure, the coordination + +polyhedra tend to +share corners. + +And I might say also that they +tend to have the line between + +cation, anion, cation to be a +straight line, as opposed to + +sharing edges. + +So for eight-coordination, this +might be a pair of cubic + +coordination polyhedra +sharing edges. + +And especially corner sharing +is more favorable + +than sharing faces. + +It's a very specific statement +on how the coordination groups + +whose geometry is determined by +size should fit together in + +a structure. + +And it has a very +simple basis, an + +almost trivial basis. + +As the polyhedra of the given +size share corners and then + +edges and then faces, the +cations inside of these + +polyhedra are progressively +getting + +closer and closer together. + +And clearly, that increases +the repulsive energy. + +So the cations are most widely +separated if not faces, not + +edges, but corners tend +to be shared. + +Puckered a little bit. + +Maybe this is not exactly +a 180-degree bond angle. + +But corner sharing is +still favorable. + +And rule D is essentially an +appendix to that, and it says, + +and how, if the charge of the +cation is high and the + +coordination number is low, the +higher the charge of the + +cations, the stronger that +repulsive interaction. + +The smaller the coordination +number of the cation, the + +closer together they become in, +let's say, face sharing + +for tubes as opposed to face +sharing for tetrahedra. + +The lower the coordination +number, the closer together + +the cations come, regardless +of the precise shape of the + +coordination polyhedra. + +So rule D says, and how for +high charge and low + +coordination number. + +The last rule, sometimes +called the "rule of + +parsimony," the "rule of +stinginess," says that the + +number of different kinds +of atoms in a + +structure tends to be small. + +You can read in two different +interpretations of the term + +"different kinds of cations," +and both of them are right. + +You could mean different +in terms of + +different chemical species. + +In other words, if you take +a pot and dump half of the + +elements in the periodic table +into the pot, melt it up, and + +then cool it down to crystallize +the phase, you're + +not going to incorporate +all of those ions + +into one crystal structure. + +They have different sizes. + +They have different coordination +polyhedra. + +The different coordination +polyhedra + +have different sizes. + +So to try to fit all of those +things together in one + +structure is just going to +cost you a lot of energy. + +It's going to be much more +efficient to form two or more + +phases, which have much lower +energy, and then pay the price + +of an interface between them. + +So have a chemically complex +melt or solution, you're going + +to get different phases. + +You want to incorporate +everything into one structure. + +The other interpretation of +different is in terms of their + +coordination number and their +coordination polyhedra. + +If the size is such that a +particular cation wants to + +have tetrahedral coordination, +you would expect them all to + +have tetrahedral coordination +and not have a mixture of + +cubes and tetrahedra +and octahedra. + +If it works for one coordination +through the + +chemical species, it'll +work for them all. + +That rule tends to have some, +but not terribly many, + +exceptions. + +But there are cases where +you find two different + +coordination numbers. + +But very often, that's because +of a covalent character. + +So there's some discussion +and elaboration of + +each of those rules. + +I'm just about out of +time, and therefore + +out of crystal chemistry. + +Another entirely different +approach to structure is to + +say that the anions are +the big things. + +And if the energy of the +structure is lowered by taking + +ions of like charge and getting +them as close as + +possible to the larger ions, +say the anions of opposite + +charge, there is a strategy for +making the arrangement. + +And I think it's the same +strategy that I use when I'm + +packing a suitcase for a trip. + +Take the big things-- + +the books, the shoes-- + +and arrange them +in the suitcase + +as densely as possible. + +Then I take the little things-- +the toothbrush, the + +socks, and so on-- + +and I stick them into the +interstices that are left. + +And this other view of examining +structures and + +interpreting says +the same thing. + +Take the big things-- + +not the shoes but the anions-- + +and arrange them as densely +as possible. + +And this gets into +the question of + +close packing of spheres. + +Then take the little guys, the +tiny little cations, and stuff + +them into the holes that +are left in the + +close-packed arrays. + +So another way of interpreting +structures and predicting + +structures is to look at the +sort of interstices that exist + +in a close-packed array. + +Regardless of the stacking +sequence of spheres, there are + +always two kinds of interstitial +sites, one + +tetrahedral, one octahedral. + +And there are two common, but +not exclusive, types of + +packing arrangements, which +you probably know. + +There is the cubic close +packed array. + +There's a little diagram of +close-packed sheets here. + +And there are two sorts of +interstices shown in the + +figure on the first page +of the notes on packing + +considerations. + +There's one set of triangles +that points in one orientation + +that forms a hollow in which +you can drop down a second + +layer of spheres, another +triangle that is the closest + +triangle to the first +one that points in + +the opposite direction. + +Each represents a potential +location for the next + +close-packed sheet, but those +two different locations are + +too close together +to both be used. + +So you have to pick +one or another. + +And if you label those three +different locations A, B, and + +C, any arrangement of spheres +that does not place two + +letters in succession will +give you a close-packed + +arrangement with exactly +the same density. + +So ABC AC, AC, ABC, AC, AC is +a packing of close-packed + +spheres that is exactly the same +density as AB, AB, which + +is hexagonal close packed, or +ABC, ABC, ABC, which could be + +shown to be the face-centered +cubic structure. + +So that is another way of +looking at structures. + +And specifying the space +filling in simple ionic + +structures is another way of +looking at structures. + +And at that point, I'll quit. + +There are some examples of +close-packed structures and + +derivatives thereof that +form the last pictures. + +And I'm going to stop and suck +in air and mention as one last + +thought that only five +of Pauling's + +rules are stated here. + +There was a sixth Pauling's +rule, and that's + +not commonly listed. + +And I'll tell you what it is. + +The sixth rule says, massive +doses of vitamin C can cure + +the common cold. + +Actually, that was something +that Pauling pushed. + +And interestingly, about three +years before he passed away, + +Pauling came to MIT and gave +a lecture in 6120. + +And as you might expect of MIT +undergraduates, after he + +finished his lecture, there +were a few questions. + +But there were about a dozen +students who came up with + +bottles of vitamin C and +asked Pauling to + +autograph them for them. + +And he did so with good humor +and thought he had perhaps won + +a few converts in the process. + +So that's it. + +Getting silly, so it's time +for all of us to go home. \ No newline at end of file diff --git a/JWnQZrnRUGM.txt b/JWnQZrnRUGM.txt new file mode 100644 index 0000000000000000000000000000000000000000..1e0c38c3671384371ce2af58176f5f8746cd4b0f --- /dev/null +++ b/JWnQZrnRUGM.txt @@ -0,0 +1,1459 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +so in this section we talk about + + align:start position:0% +so in this section we talk about + + + align:start position:0% +so in this section we talk about +calorimetry and in contrast to + + align:start position:0% +calorimetry and in contrast to + + + align:start position:0% +calorimetry and in contrast to +the discussion of tracking detectors + + align:start position:0% +the discussion of tracking detectors + + + align:start position:0% +the discussion of tracking detectors +here + + align:start position:0% +here + + + align:start position:0% +here +what we're trying to do is measure the + + align:start position:0% +what we're trying to do is measure the + + + align:start position:0% +what we're trying to do is measure the +energy of the particles and we do this + + align:start position:0% +energy of the particles and we do this + + + align:start position:0% +energy of the particles and we do this +by basically destroying them + + align:start position:0% +by basically destroying them + + + align:start position:0% +by basically destroying them +the underlying context is rather + + align:start position:0% +the underlying context is rather + + + align:start position:0% +the underlying context is rather +straightforward we have a particle + + align:start position:0% +straightforward we have a particle + + + align:start position:0% +straightforward we have a particle +and we put a piece of material in front + + align:start position:0% +and we put a piece of material in front + + + align:start position:0% +and we put a piece of material in front +of it such that it slams into it + + align:start position:0% +of it such that it slams into it + + + align:start position:0% +of it such that it slams into it +and the energy deposited by the particle + + align:start position:0% +and the energy deposited by the particle + + + align:start position:0% +and the energy deposited by the particle +is the energy + + align:start position:0% +is the energy + + + align:start position:0% +is the energy +the measurement we try to to undertake + + align:start position:0% +the measurement we try to to undertake + + + align:start position:0% +the measurement we try to to undertake +so in nuclear and particle physics + + align:start position:0% +so in nuclear and particle physics + + + align:start position:0% +so in nuclear and particle physics +that's exactly what we refer + + align:start position:0% +that's exactly what we refer + + + align:start position:0% +that's exactly what we refer +to as calorimeters so the detection of + + align:start position:0% +to as calorimeters so the detection of + + + align:start position:0% +to as calorimeters so the detection of +particles by measuring their properties + + align:start position:0% +particles by measuring their properties + + + align:start position:0% +particles by measuring their properties +through the total absorption in the + + align:start position:0% +through the total absorption in the + + + align:start position:0% +through the total absorption in the +block of + + align:start position:0% +block of + + + align:start position:0% +block of +matter the common feature + + align:start position:0% +matter the common feature + + + align:start position:0% +matter the common feature +or the central feature is that the + + align:start position:0% +or the central feature is that the + + + align:start position:0% +or the central feature is that the +measurement is destructive + + align:start position:0% +measurement is destructive + + + align:start position:0% +measurement is destructive +so again in treating tracking detectors + + align:start position:0% +so again in treating tracking detectors + + + align:start position:0% +so again in treating tracking detectors +we try to + + align:start position:0% +we try to + + + align:start position:0% +we try to +minimally disturb the particle and then + + align:start position:0% +minimally disturb the particle and then + + + align:start position:0% +minimally disturb the particle and then +calorimeters we try to destroy them + + align:start position:0% +calorimeters we try to destroy them + + + align:start position:0% +calorimeters we try to destroy them +um the exception to this might be a muon + + align:start position:0% +um the exception to this might be a muon + + + align:start position:0% +um the exception to this might be a muon +which might at higher energies deposit + + align:start position:0% +which might at higher energies deposit + + + align:start position:0% +which might at higher energies deposit +only small fraction of its energy in a + + align:start position:0% +only small fraction of its energy in a + + + align:start position:0% +only small fraction of its energy in a +calorimeter + + align:start position:0% +calorimeter + + + align:start position:0% +calorimeter +or a neutrino which just fly through + + align:start position:0% +or a neutrino which just fly through + + + align:start position:0% +or a neutrino which just fly through +without having any interaction + + align:start position:0% +without having any interaction + + + align:start position:0% +without having any interaction +um but the the purpose is really to + + align:start position:0% +um but the the purpose is really to + + + align:start position:0% +um but the the purpose is really to +measure energies + + align:start position:0% +measure energies + + + align:start position:0% +measure energies +by destroying the particle and it's + + align:start position:0% +by destroying the particle and it's + + + align:start position:0% +by destroying the particle and it's +widely used in all kinds of areas of + + align:start position:0% +widely used in all kinds of areas of + + + align:start position:0% +widely used in all kinds of areas of +particle + + align:start position:0% +particle + + + align:start position:0% +particle +nuclear physics neutrino experiments + + align:start position:0% +nuclear physics neutrino experiments + + + align:start position:0% +nuclear physics neutrino experiments +proton decay experiments cosmic ray + + align:start position:0% +proton decay experiments cosmic ray + + + align:start position:0% +proton decay experiments cosmic ray +detectors + + align:start position:0% +detectors + + + align:start position:0% +detectors +collider experiments and so on and in + + align:start position:0% +collider experiments and so on and in + + + align:start position:0% +collider experiments and so on and in +collider experiments specifically + + align:start position:0% +collider experiments specifically + + + align:start position:0% +collider experiments specifically +the idea is to build the detector such + + align:start position:0% +the idea is to build the detector such + + + align:start position:0% +the idea is to build the detector such +that it + + align:start position:0% +that it + + + align:start position:0% +that it +completely surrounds the interaction + + align:start position:0% +completely surrounds the interaction + + + align:start position:0% +completely surrounds the interaction +region such that you don't lose + + align:start position:0% +region such that you don't lose + + + align:start position:0% +region such that you don't lose +energy from the collision um just + + align:start position:0% +energy from the collision um just + + + align:start position:0% +energy from the collision um just +passing through + + align:start position:0% +passing through + + + align:start position:0% +passing through +an un instrumented region + + align:start position:0% +an un instrumented region + + + align:start position:0% +an un instrumented region +the detection mechanism can vary quite a + + align:start position:0% +the detection mechanism can vary quite a + + + align:start position:0% +the detection mechanism can vary quite a +bit um + + align:start position:0% +bit um + + + align:start position:0% +bit um +we use scintillators a lot we use + + align:start position:0% +we use scintillators a lot we use + + + align:start position:0% +we use scintillators a lot we use +silicon in some modern detectors + + align:start position:0% +silicon in some modern detectors + + + align:start position:0% +silicon in some modern detectors +we use uh with this ionization we use to + + align:start position:0% +we use uh with this ionization we use to + + + align:start position:0% +we use uh with this ionization we use to +rank of detection + + align:start position:0% +rank of detection + + + align:start position:0% +rank of detection +we use sometimes cryogenic cryogenic + + align:start position:0% +we use sometimes cryogenic cryogenic + + + align:start position:0% +we use sometimes cryogenic cryogenic +detectors which are very sensitive to + + align:start position:0% +detectors which are very sensitive to + + + align:start position:0% +detectors which are very sensitive to +very small energy depositions and they + + align:start position:0% +very small energy depositions and they + + + align:start position:0% +very small energy depositions and they +can be quite useful + + align:start position:0% +can be quite useful + + + align:start position:0% +can be quite useful +they are used in dark matter experiments + + align:start position:0% +they are used in dark matter experiments + + + align:start position:0% +they are used in dark matter experiments +or in + + align:start position:0% +or in + + + align:start position:0% +or in +neutrinous double beta decay experiments + + align:start position:0% +neutrinous double beta decay experiments + + + align:start position:0% +neutrinous double beta decay experiments +for example + + align:start position:0% +for example + + + align:start position:0% +for example +again conceptually you can differentiate + + align:start position:0% +again conceptually you can differentiate + + + align:start position:0% +again conceptually you can differentiate +between + + align:start position:0% +between + + + align:start position:0% +between +homogeneous calorimeters and sampling + + align:start position:0% +homogeneous calorimeters and sampling + + + align:start position:0% +homogeneous calorimeters and sampling +color majors + + align:start position:0% +color majors + + + align:start position:0% +color majors +the homogeneous calorimeters um + + align:start position:0% +the homogeneous calorimeters um + + + align:start position:0% +the homogeneous calorimeters um +basically the entire absorber material + + align:start position:0% +basically the entire absorber material + + + align:start position:0% +basically the entire absorber material +is equal or is the same as the detector + + align:start position:0% +is equal or is the same as the detector + + + align:start position:0% +is equal or is the same as the detector +material + + align:start position:0% +material + + + align:start position:0% +material +so an example for this is lead glass + + align:start position:0% +so an example for this is lead glass + + + align:start position:0% +so an example for this is lead glass +which is often used + + align:start position:0% +which is often used + + + align:start position:0% +which is often used +so what you do then in the calorimeter + + align:start position:0% +so what you do then in the calorimeter + + + align:start position:0% +so what you do then in the calorimeter +is you + + align:start position:0% +is you + + + align:start position:0% +is you +induce electromagnetic and nuclear + + align:start position:0% +induce electromagnetic and nuclear + + + align:start position:0% +induce electromagnetic and nuclear +showers and then + + align:start position:0% +showers and then + + + align:start position:0% +showers and then +the energy of the incoming particle is + + align:start position:0% +the energy of the incoming particle is + + + align:start position:0% +the energy of the incoming particle is +converted into + + align:start position:0% +converted into + + + align:start position:0% +converted into +photons and then what you need is a + + align:start position:0% +photons and then what you need is a + + + align:start position:0% +photons and then what you need is a +photodetector which then measures + + align:start position:0% +photodetector which then measures + + + align:start position:0% +photodetector which then measures +the number of photons being coming out + + align:start position:0% +the number of photons being coming out + + + align:start position:0% +the number of photons being coming out +of your + + align:start position:0% +of your + + + align:start position:0% +of your +of your detector material for this to + + align:start position:0% +of your detector material for this to + + + align:start position:0% +of your detector material for this to +work + + align:start position:0% +work + + + align:start position:0% +work +the detector needs to be transparent um + + align:start position:0% +the detector needs to be transparent um + + + align:start position:0% +the detector needs to be transparent um +alternatively one can use sampling + + align:start position:0% +alternatively one can use sampling + + + align:start position:0% +alternatively one can use sampling +experiments something detectors + + align:start position:0% +experiments something detectors + + + align:start position:0% +experiments something detectors +where you have you know the the heavy + + align:start position:0% +where you have you know the the heavy + + + align:start position:0% +where you have you know the the heavy +material being used in order to induce a + + align:start position:0% +material being used in order to induce a + + + align:start position:0% +material being used in order to induce a +shower + + align:start position:0% +shower + + + align:start position:0% +shower +and then the detection material in order + + align:start position:0% +and then the detection material in order + + + align:start position:0% +and then the detection material in order +to count again the number of photons + + align:start position:0% + + + + align:start position:0% + +so homogeneous calorimeter have + + align:start position:0% +so homogeneous calorimeter have + + + align:start position:0% +so homogeneous calorimeter have +typically very good energy resolution + + align:start position:0% +typically very good energy resolution + + + align:start position:0% +typically very good energy resolution +and the reason for this is that nothing + + align:start position:0% +and the reason for this is that nothing + + + align:start position:0% +and the reason for this is that nothing +gets lost + + align:start position:0% +gets lost + + + align:start position:0% +gets lost +everything is being measured in the + + align:start position:0% +everything is being measured in the + + + align:start position:0% +everything is being measured in the +absorber which is the detector + + align:start position:0% +absorber which is the detector + + + align:start position:0% +absorber which is the detector +but that leads them to some limitations + + align:start position:0% +but that leads them to some limitations + + + align:start position:0% +but that leads them to some limitations +for example that the granularity of the + + align:start position:0% +for example that the granularity of the + + + align:start position:0% +for example that the granularity of the +detector + + align:start position:0% +detector + + + align:start position:0% +detector +is typically limited and then there's no + + align:start position:0% +is typically limited and then there's no + + + align:start position:0% +is typically limited and then there's no +longitudinal information about the + + align:start position:0% +longitudinal information about the + + + align:start position:0% +longitudinal information about the +shower development you basically have + + align:start position:0% +shower development you basically have + + + align:start position:0% +shower development you basically have +one block + + align:start position:0% +one block + + + align:start position:0% +one block +for example a lab block which is shown + + align:start position:0% +for example a lab block which is shown + + + align:start position:0% +for example a lab block which is shown +here + + align:start position:0% +here + + + align:start position:0% +here +the tungsten block which is shown here + + align:start position:0% +the tungsten block which is shown here + + + align:start position:0% +the tungsten block which is shown here +are used for the measurement + + align:start position:0% +are used for the measurement + + + align:start position:0% +are used for the measurement +right so you produce photons and so then + + align:start position:0% +right so you produce photons and so then + + + align:start position:0% +right so you produce photons and so then +the photons need to be measured + + align:start position:0% +the photons need to be measured + + + align:start position:0% +the photons need to be measured +and that that's done with photo + + align:start position:0% +and that that's done with photo + + + align:start position:0% +and that that's done with photo +detectors um here + + align:start position:0% +detectors um here + + + align:start position:0% +detectors um here +the requirements the range of + + align:start position:0% +the requirements the range of + + + align:start position:0% +the requirements the range of +requirements is quite big sometimes you + + align:start position:0% +requirements is quite big sometimes you + + + align:start position:0% +requirements is quite big sometimes you +want to be able to measure every single + + align:start position:0% +want to be able to measure every single + + + align:start position:0% +want to be able to measure every single +photon so the + + align:start position:0% +photon so the + + + align:start position:0% +photon so the +quantum efficiency needs to be quite + + align:start position:0% +quantum efficiency needs to be quite + + + align:start position:0% +quantum efficiency needs to be quite +high in others + + align:start position:0% +high in others + + + align:start position:0% +high in others +uh detectors you need to be able to put + + align:start position:0% +uh detectors you need to be able to put + + + align:start position:0% +uh detectors you need to be able to put +this detector in a radiation hard + + align:start position:0% +this detector in a radiation hard + + + align:start position:0% +this detector in a radiation hard +environment + + align:start position:0% +environment + + + align:start position:0% +environment +and so that that then changes the main + + align:start position:0% +and so that that then changes the main + + + align:start position:0% +and so that that then changes the main +types available are + + align:start position:0% +types available are + + + align:start position:0% +types available are +the old-fashioned photo multiplier tubes + + align:start position:0% +the old-fashioned photo multiplier tubes + + + align:start position:0% +the old-fashioned photo multiplier tubes +which actually become quite + + align:start position:0% +which actually become quite + + + align:start position:0% +which actually become quite +sophisticated pmts + + align:start position:0% +sophisticated pmts + + + align:start position:0% +sophisticated pmts +there's gas based photo detectors solid + + align:start position:0% +there's gas based photo detectors solid + + + align:start position:0% +there's gas based photo detectors solid +state detectors + + align:start position:0% +state detectors + + + align:start position:0% +state detectors +which are quite popular so called septum + + align:start position:0% +which are quite popular so called septum + + + align:start position:0% +which are quite popular so called septum +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +photodetectors or some hybrid modules of + + align:start position:0% +photodetectors or some hybrid modules of + + + align:start position:0% +photodetectors or some hybrid modules of +cells + + align:start position:0% +cells + + + align:start position:0% +cells +so the energy resolution in a + + align:start position:0% +so the energy resolution in a + + + align:start position:0% +so the energy resolution in a +calorimeter + + align:start position:0% +calorimeter + + + align:start position:0% +calorimeter +um depends on a number of things as i + + align:start position:0% +um depends on a number of things as i + + + align:start position:0% +um depends on a number of things as i +was saying + + align:start position:0% +was saying + + + align:start position:0% +was saying +one measures the number of particles + + align:start position:0% +one measures the number of particles + + + align:start position:0% +one measures the number of particles +being produced in a shower + + align:start position:0% +being produced in a shower + + + align:start position:0% +being produced in a shower +and so that's just a counting experiment + + align:start position:0% +and so that's just a counting experiment + + + align:start position:0% +and so that's just a counting experiment +and the uncertainty of that + + align:start position:0% +and the uncertainty of that + + + align:start position:0% +and the uncertainty of that +um scales with the square root of the + + align:start position:0% +um scales with the square root of the + + + align:start position:0% +um scales with the square root of the +number of particles produced or measured + + align:start position:0% +number of particles produced or measured + + + align:start position:0% +number of particles produced or measured +and so here we have a square root n term + + align:start position:0% +and so here we have a square root n term + + + align:start position:0% +and so here we have a square root n term +uh so the rel the relative energy + + align:start position:0% +uh so the rel the relative energy + + + align:start position:0% +uh so the rel the relative energy +measurement has an error which is + + align:start position:0% +measurement has an error which is + + + align:start position:0% +measurement has an error which is +with one over square root of the energy + + align:start position:0% +with one over square root of the energy + + + align:start position:0% +with one over square root of the energy +and then there's more contributions uh + + align:start position:0% +and then there's more contributions uh + + + align:start position:0% +and then there's more contributions uh +there's constant terms which come from + + align:start position:0% +there's constant terms which come from + + + align:start position:0% +there's constant terms which come from +in homogeneities uh those are elements + + align:start position:0% +in homogeneities uh those are elements + + + align:start position:0% +in homogeneities uh those are elements +where there's just no detector no + + align:start position:0% +where there's just no detector no + + + align:start position:0% +where there's just no detector no +equipment in in the + + align:start position:0% +equipment in in the + + + align:start position:0% +equipment in in the +direction of the of the particles those + + align:start position:0% +direction of the of the particles those + + + align:start position:0% +direction of the of the particles those +can be + + align:start position:0% +can be + + + align:start position:0% +can be +overlapped regions or regions where you + + align:start position:0% +overlapped regions or regions where you + + + align:start position:0% +overlapped regions or regions where you +have two detector modules being glued + + align:start position:0% +have two detector modules being glued + + + align:start position:0% +have two detector modules being glued +together + + align:start position:0% +together + + + align:start position:0% +together +you don't measure there and that leads + + align:start position:0% +you don't measure there and that leads + + + align:start position:0% +you don't measure there and that leads +to them in a constant term in the energy + + align:start position:0% +to them in a constant term in the energy + + + align:start position:0% +to them in a constant term in the energy +resolution and then when you translate + + align:start position:0% +resolution and then when you translate + + + align:start position:0% +resolution and then when you translate +the signal in + + align:start position:0% +the signal in + + + align:start position:0% +the signal in +the the electromagnetic signals into an + + align:start position:0% +the the electromagnetic signals into an + + + align:start position:0% +the the electromagnetic signals into an +electronic signal there can be noise in + + align:start position:0% +electronic signal there can be noise in + + + align:start position:0% +electronic signal there can be noise in +use and that noise + + align:start position:0% +use and that noise + + + align:start position:0% +use and that noise +then leads to a typical term which goes + + align:start position:0% +then leads to a typical term which goes + + + align:start position:0% +then leads to a typical term which goes +with one over the energy + + align:start position:0% +with one over the energy + + + align:start position:0% +with one over the energy +so very classical you have the three + + align:start position:0% +so very classical you have the three + + + align:start position:0% +so very classical you have the three +components to the energy + + align:start position:0% +components to the energy + + + align:start position:0% +components to the energy +three components to the energy + + align:start position:0% +three components to the energy + + + align:start position:0% +three components to the energy +resolution one is this one over the + + align:start position:0% +resolution one is this one over the + + + align:start position:0% +resolution one is this one over the +square root of the energy + + align:start position:0% +square root of the energy + + + align:start position:0% +square root of the energy +one's constant and one is depending on + + align:start position:0% +one's constant and one is depending on + + + align:start position:0% +one's constant and one is depending on +one over the energy + + align:start position:0% +one over the energy + + + align:start position:0% +one over the energy +and so when you design a detector you + + align:start position:0% +and so when you design a detector you + + + align:start position:0% +and so when you design a detector you +want to + + align:start position:0% +want to + + + align:start position:0% +want to +place it such or design it such that the + + align:start position:0% +place it such or design it such that the + + + align:start position:0% +place it such or design it such that the +most important physics you want to do + + align:start position:0% +most important physics you want to do + + + align:start position:0% +most important physics you want to do +with this detector + + align:start position:0% +with this detector + + + align:start position:0% +with this detector +is optimized towards those components + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/JaEqS1ozlHY.txt b/JaEqS1ozlHY.txt new file mode 100644 index 0000000000000000000000000000000000000000..4ff57a170eaddb191681b90e165731cee309f408 --- /dev/null +++ b/JaEqS1ozlHY.txt @@ -0,0 +1,3447 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So what +we've been trying + +to do is to develop a +description of properties + +of some system, +could be something + +like a gas, that includes +both mechanical as well + +as thermal properties. + +So the first thing +that we decided to do + +was to wait until +this system has + +properties that do not change. + +Further, with the +observation time + +that we are assigning +to this system, + +and then if it is +a gas we can say, + +OK the gas has some +pressure and volume. + +In general, we said that we +can characterize the system + +through a set of displacements +and the conjugate forces which + +are used when we describe +systems that are mechanical. + +Work on them is done. + +We can say that the work +is Jdx, for example. + +OK? + +Then we decided that this +mechanical description + +was not enough because +systems could exchange heat + +and gradually started to build +a more general prescription that + +included the exchange of heat. + +We saw that, for example, +from the zeroth law, + +we could define temperature as +a function of these quantities. + +And that we could also, from +the first law define energy. + +And in particular that +the change in energy, + +which is a function of where +you are in equilibrium. + +So once you say that you +have a system in equilibrium + +you can say what the values +of the x's and J's are. + +You know somehow what +the value of temperature + +is, what the value of energy is. + +And if you were to +make a change in energy + +by some external means +the amount of change + +would either come +from mechanical work + +that you did on the +system, or the heat + +that you supplied to the system. + +Now this expression +is the one that you + +would like to elevate somehow +and be able to compute energy + +as a function of state. + +Kind of keeping in +mind what we would + +do if there was no heat around. + +And we could do things +mechanically, then mechanically + +we could in principle build up +the energy function by changing + +displacements lightly and +calculating the amount of work + +by this formula. + +And basically we +emphasized that you + +would be able to use +a formula such as this + +if you were to make +things sufficiently slowly + +so that at each +stage in the process + +you can calculate +what Ji is, which + +means that at each +stage in the process + +you should be in some kind +of an equilibrium state. + +OK? + +If that was the case, if +you didn't have dQ then + +this would be your +energy function + +and actually once you had the +energy function you could, + +for example, calculate J +as a derivative of energy + +with respect to x. + +So then you also start +thinking about how many + +independent degrees +of freedom do I have. + +Do I really need all of the +set of x's and J's to describe + +my system in equilibrium. + +If additionally once I know the +e, I can derive all of the J's. + +So we have to also +come eventually + +to grips with how many +independent degrees of freedom + +will describe our system. + +Now the first step towards +completing this expression + +was to find what dQ is. + +So we needed another +law of thermodynamics + +beyond zeroth law and first +law that somehow related + +heat and temperature +to each other. + +As we expect that +somehow this expression + +will leave you temperature. + +And what we used was some +version of the second law. + +That was there how heat would +flow from, say, a hot air body + +to a cold air body. + +And Clausius's theorem would say +that you have only heat flowing + +in one particular direction. + +Well, we sort of +introduced the idea + +of engines, which +are machines that + +are used to do work by taking +heat from the heart air body + +to the cold air body. + +And we could define +an efficiency, + +which is work divided by heat +input, which since work is + +the difference between these +two we could write as 1 minus Qc + +over Qh. + +And then we introduced +this special class + +of engines, which were +these Carnot engines. + +And the idea of this class +was that you could run them + +forward and backward. + +They were kind of reversible. + +The were kind of a analogue +of the frictionless type + +of processes that you would use +to construct mechanical energy. + +And we found that these engines +were the most efficient. + +And so the efficiency +of these engines + +was marked only by +the two temperatures. + +So we had the functional form +potentially of efficiency + +as a function of the two +temperatures involved. + +And what we also showed +was that the efficiency + +of any random engine +was going to be + +less than the efficiency +of the Carnot engine + +that is marked by +these two temperatures. + +And by putting some +Carnot engines in series, + +we saw that the good +way to write this + +was something of this form. + +I can in principle +remove the one + +from the two sides +of this equation + +and rearrange it a +little bit into the form + +Qh over Th plus minus Qc over +Tc because of this inequality + +writing it as less +than or equal to 0. + +OK? + +What does that tell us? + +As it stands, not much. + +But then I promised you +at the end of last lecture + +then this is an example of +a much more powerful result, + +which is the Clausius Theorem. + +So let's start with writing +what that theorem is + +and how it relates to +a simple expression. + +And the theory is that +for any cyclic process + +I can, cyclic, +what does it mean? + +Is that in the set of +coordinates in principle + +that is used to +describe the system, + +I will start with the +position that is equilibrium, + +so I can put that +point in this state, + +but then I make +a transformation. + +And ultimately +return to that point. + +So the cycle is the +return to that point. + +So I carry out a set of steps. + +And I haven't indicated +the set of steps + +through a connected +continuous curve + +in this multi-dimensional +coordinate space + +because I don't want +to restrict myself + +to processes that are +even in equilibrium. + +So I may take a gas +that I have over there, + +expand it rapidly, close it +rapidly as long as I wait when + +I come back to the +same point that I + +have reached my +equilibrium again. + +I have done a cyclic process. + +Now at each stage of this +cyclic process presumably + +the system takes in a +certain amount of heat. + +So let's say that +there is a dQ that + +goes at this stage +of the process. + +So I use s to indicate, say, +stage 0, one, two, three, + +four all the way coming back. + +So this is just a +numbering process. + +The statement of +Clausius's theorem + +is that for any cyclic process +if I go out around the cycle, + +add up these elements of +heat that are delivered + +to this system and I allow +the possibility therefore + +that some of the times +these elements dQ + +will be negative just as I +did over here by writing this + +as minus Qc so +that what the dQ is + +what has gone into +whatever this black box is. + +So Qh went into this black box. + +Qc went out, which means +that minus Qc went in + +so I arranged it +in this fashion. + +You can see that +the elements of heat + +are divided by some temperature. + +I generalize that expression +over here by writing it T of S + +here. + +And the statement of +Clausius's theorem + +is that this quantity has the +same sign constraint as here + +where I told you that +dQ is heat delivered + +to system at +temperature T sub s. + +Now this particular thing +requires a certain amount + +of thinking about. + +Because I told you that your +system is not in equilibrium. + +So what is this T +sub S if you have + +a system that is +not in equilibrium? + +You can't define +its temperature. + +However, you can imagine +that whatever machine + +was delivering it had sump +particular temperature. + +And so that's the +temperature of the device + +or whatever is delivering +this heat to the system. + +And you would be +justified to say, well, + +why is that even useful? + +Because certainly if I were to +have exactly the same cycle, + +but deliver the heat elements +through a different process + +this Ts would be different. + +So this is really +also a function + +of the method through which I +want to carry out this cycle. + +So given that it doesn't sound +like a particularly useful + +theorem. + +It seems very arbitrary. + +So let's first prove it. + +The proof is simple. + +And then see whether +it's useful or not. + +Any questions at this point? + +OK. + +So how do we go proving it? + +We are going to use +these Carnot engines. + +So what I will imagine is +that I have some big vat that + +is at some, let's +say, for purposes + +of, use a high temperature, +a vat of hot water. + +And I use this +vat as the process + +that provides heat +to this entity. + +Exactly what do I mean by that? + +I will use a Carnot +engine to take heat. + +Let's call it Qh, although its +sign is not that particularly + +important. + +And convert this +into the heat element + +dQs that is delivered here. + +So since I'm using s, an +infinitesimal element here, + +let me call this dQ. + +And let's call it dQ0 +because I'm picking it + +up from the temperature of T0. + +So I have as a result +of this process + +a certain amount of work. + +All of this corresponds +to the s-th element + +through this particular cycle. + +So I divide my cycle +to lots of elements. + +Each element takes in +this amount of heat + +and I use a Carnot engine to +deliver that heat and always + +taking the Carnot engine +from the input from T0, + +but what it delivers is where +this randomness in temperature + +T of S comes about. + +Why did I use a Carnot engine? + +Because I said that +sometimes this cycle + +is going to take in heat. + +Sometimes it is going +to give out heat. + +So I want to be able to run +this both forward and backwards. + +Yes? + +AUDIENCE: Are you delivering +the work to the cycle too? + +PROFESSOR: No. + +AUDIENCE: OK. + +PROFESSOR: The work +goes whenever it goes. + +AUDIENCE: OK. + +PROFESSOR: OK? + +And indeed that's the next +step of the argument, which + +is what happened to the work? + +OK? + +So we do this. + +At the end of this story I +am back to where I started. + +AUDIENCE: Maybe I'm-- + +PROFESSOR: Yes? + +AUDIENCE: Maybe I +missed something basic, + +but I don't understand +why you can't just + +define the function dQ not of +s and ignore the Carnot engine. + +Just deliver it the key. + +What was wrong with +just the blue arrow? + +PROFESSOR: OK. + +Why can't I just take +heat from here to here? + +Because in principle +where I put it + +is at a different +temperature when I eventually + +go to equilibrium. + +And then I would run into +problems of second law, + +as to the ability +to transfer heat + +from a hotter to colder engine. + +So if you like this +intermediate stage, + +allows me ultimately two +vary this temperature Ts. + +What you say is correct as long +as the T of S is uniformly T0. + +It kind of becomes useless. + +OK? + +All right. + +So we enclose our cycle, the +Carnot engine, everything + +into a box. + +And we see what +this box is doing. + +So there is the box. + +The box takes in elements of +heat, dQ from the reservoir. + +And does elements of work, +dW at different stages. + +Now once the cycle +has been completed, + +the net result is that I have +extracted an amount of heat, + +so this is the net, +extracted heat is + +the integral over the +cycle of dQ0 of s. + +And converted it to work. + +Oh, one other step. + +Once I'm using +the Carnot engine, + +and I think I +emphasized this, there + +is a relationship between +heat and temperature. + +It is this +proportionally-- Qh is + +proportional to h for +the Carnot engine. + +Qc is proportional to Tc. + +So there is a proportionality +between the heat that I take + +and the heat that I deliver that +is related to the temperatures. + +So dQ0 is in fact T0 dQ that +goes into the engine divided + +by the temperature at which +it is delivered to the engine. + +OK? + +Now I know also +something about this + +because the second +law of thermodynamics + +says that no process is +possible whose soul result + +is the conversion +of heat to work. + +I can do the opposite. + +I can convert work +to heat, but that + +means that the integral +here has to be negative. + +OK? + +Now T0 is just a +positive constant. + +So once I divide +through by that I + +have gotten the proof of +the statement [INAUDIBLE]. + +OK? + +Questions? + +Yes? + +AUDIENCE: So how +is this is really + +going to help with the +definition of T of s + +because get theoretically +even your extraction of heat + +and your doing the work in +that black box or the opposite + +could happen +irreversibly, right? + +So you-- + +PROFESSOR: Exactly. + +AUDIENCE: --still +have a problem. + +PROFESSOR: Yeah. + +So as I have written +it here I would agree. + +It looks completely useless. + +So let's make it useful. + +How am I going to +make it useful? + +So let's start some set of +corollaries to this theorem. + +For the first thing is we +get rid of this definition + +by considering a +reversible transformation. + +OK? + +So same picture that I was +drawing before with multiple + +coordinates. + +Start some point and come back. + +But now I will draw is +solid curve in this space, + +meaning that at each +stage of the process + +I will do it sufficiently +slowly so that my system comes + +to thermal equilibrium +and I can identify it + +as a point in this +generalized phase space. + +OK? + +So now I have points in this +generalized phase space. + +To each point I can therefore +assign the equilibrium + +temperature. + +That I am at that +stage of the cycle. + +OK? + +So now I can request +my Carnot engines + +to deliver the heat at the +temperature of the system + +to be maintaining the whole +system plus the Carnot engines + +at thermal equilibrium as +I switch from one cycle + +to another cycle. + +OK? + +So now I have a +relationship that + +is pertaining to things +that are in equilibrium. + +As long as I follow the +equilibrium temperature + +of the system and do +reversible transformations + +I have the result that +dQ reversible over Ts + +is less than 0. + +But the things about-- yes? + +AUDIENCE: Could +you explain again + +why the path integral +of dQ not over s + +is smaller than [INAUDIBLE]? + +PROFESSOR: OK. + +Clausius's theorem says that +if I took heat from a vat + +and converted it to useful work +I have violated the second law. + +So the sign of the +net amount of heat + +that I extracted better +be negative, right? + +OK. + +So you are not going to +be able to have a vat + +and extract energy out of +the lake and run your engine. + +It's not allowed. + +OK? + +Now my path is reversible, which +means that I could go this way, + +or I could go the opposite way. + +And if I go the +opposite way, what + +was the definition +of reversible? + +I reverse all of a heat +exchanges inputs and outputs. + +OK? + +Which means that what I +was calling previously + +dQ becomes minus dQ. + +So the inequality holds +for both minus or plus, + +which means that as long as I +do reversible transformations + +I must have the integral +to be equal to 0. + +OK? + +Good. + +So we constructed +in a sense analog + +of doing frictionless +ways of doing work + +and increasing the +energy of the system. + +We have an idea +about reversible ways + +and their relationship +to T, well, + +one step further I need to go. + +Which is that I go +from some point A + +to some point B in +my coordinate space. + +OK? + +I can do it multiple ways. + +I can go this way +and then come back. + +Reversibly, I can go +this way and come back + +one way or the other. + +So every way I have +a number of choices. + +Essentially what it says +is that I can go from say A + +to B, dQ, reversible +over T, over some path, + +and the answer is going to +be the same for doing it + +along a different path. + +Because if I went +along this path + +I can close the reversible cycle +either by returning that way + +or by going the other way. + +So going this way +or going that way, + +the result of the integration +along reversible path + +should be the same. + +And it should be the same +also for any other path + +that I take between +these two points. + +So it kind of again reminds +us of pushing a particle + +up a hill. + +And as long as you are +doing things frictionlessly + +the amount of work that +you do in this process + +does not depend on +how you go there. + +It's just the potential +energy difference + +between the two points. + +So this entity being +independent of the path + +implies immediately +that there is + +some function like a potential +energy that only depends + +on the two end +points and this is + +how you would +decline the entropy. + +OK? + +So what we have +essentially said is + +that if I take an +infinitesimal step there's + +an infinitesimal amount of heat +that I can do reversibly, that + +is related to the change +of the state function + +through let's say dS is +dQ reversible over T. + +Or vice versa, dQ +[INAUDIBLE] TdS. + +OK? + +We've done it finally. + +We can get our +expression because we + +have now the possibility +to go from this point + +to this point reversibly using +a reversible transformation. + +And calculate the +change in energy. + +Now quite generally the change +in energy conservation lay, + +it's dW plus dQ. + +If I do this reversible +change so that each element + +I am in equilibrium. + +I know what J is. + +The dW is sum over iJidxi. + +And I have established +that as long + +as I do the reversible +transformations dQ is TdS. + +And so we have this formula. + +OK? + +So I will write that +again because really this + +is the most important +relationship + +that you need to know +from thermal dynamics. + +And we have to put all +kinds of colorful things + +around it so you remember. + +OK? + +Now in particular there is +a very common misconception + +which is that results are +relevant to transformations. + +And you derive this result for +a reversible transformation. + +So this formula is only valid +for reversible transformation. + +No. + +That's not the case. + +It is like saying, I +calculated the potential energy + +of pushing something up the hill +through a frictionless process. + +Therefore, the +potential energy is + +only relevant for +frictionless transformations. + +No. + +Potential energy exists. + +It's a function of states. + +Energy is a function of state. + +And we have been able to relate +energy as a function of state + +to all the other equilibrium +quantities that we + +have over here. + +OK? + +Any questions? + +OK. + +So now we can answer +another side question + +that I raised at +the beginning, which + +is I started with xi +and Ji, as describing + +the system in equilibrium. + +Then I gradually +added T. I added E, + +now I've added S. +How many things + +do I need to describe the +system in equilibrium? + +A lot of these are +dependent on each other. + +And in particular +saw that mechanically + +if there was the only thing +that was happening in the story, + +J's could be obtained from +the derivatives of energy + +with respect to x. + +So J's, in some sense, once +you had E were given to you. + +You didn't have to +list all of the J's. + +You just needed to add +E as a function of x's. + +But when you have thermal +transformations around, + +that's not enough. + +This equation says that if +there are n ways of doing work + +on the system, there is +one of the doing heat. + +You have n plus 1 independent +degrees of freedom.. + +So n ways of sum over i, +Ji, dxi, one way of SdT, + +you have n plus one +independent variables + +to describe your system. + +And once you realize +that you have + +a certain amount of freedom +in choosing precisely + +which n plus one +you want to select. + +So I could select all of +the x's and one temperature. + +I could select all of +the J's and one energy. + +So I have a number of choices. + +And once I have made my +choice I can rearrange things + +accordingly. + +So suppose I had chosen +the energy in xi, + +then I could write dS to +be dE over T minus sum + +over i Ji over T xi. + +So I just rearrange this +expression and solve for dS. + +So this amounts to +my having chosen + +x's and E's as independent +variables and prescribed + +through this important law s +as a function of E and x's. + +What about everything else? + +Well, everything else you +can calculate by derivatives. + +So 1 over T would be +dS by dE at constant x. + +While Ji over T would be minus +dS by dxi at constant E and xJ + +that is not equal to i. + +OK? + +Fine. + +So that's sort of +kind of extract + +the mathematical content that +we can get out of the second law + +through this Clausius's theorem. + +There is one important +corollary that + +has to do be irreversible +transformations. + +After all, in setting up +the Clausius's theorem + +I did not say anything +about the necessity + +of being in equilibrium in +order to achieve the inequality. + +Reversibility allowed me +to get it as an equality. + +So what can I do? + +I can take any +complicated space. + +I can pick a point +A and in principle, + +make an irreversible +transformation to some point B. + +And maybe in that +process I will get + +some heat inputted +through the system dQ. + +And what I would have is that +the integral going from A to B, + +dQ divided by T along the path +that I have described here + +which is irreversible. + +But I can't say anything +about it at this point. + +Clausius's theorem +has to do with cycles. + +So I can, in principle connect +back from B to A reversibly. + +So I go integral from B to +A, dQ reversible over T. + +And having completed the +cycle I know for this cycle + +that this is negative. + +If I were to take this to the +other side of the equation + +it becomes essentially the +difference of the entropies, + +or here it's also the +difference of entropies. + +But I prefer it to +be on the other side. + +And then to make +these two points very + +close to each other, +in which case, + +I can write that dQ is +less than or equal to TdS. + +This is the change in entropy +in going from A to B. OK? + +Again, there's some question +here as to what this T is. + +So let's get rid +of that uncertainty + +by looking at processes +that are adiabatic. + +So I make sure that +there is no heat + +exchange in going from A to +B. What do I conclude then? + +Is that for these processes +the change in entropy + +has to be positive. + +OK? + +Because T's are generally +positive quantities. + +OK? + +So a consequence of +Clausius's theorem + +is that entropy can only +increase in any transformation. + +Its change in entropy would +be 0 for these adiabatic + +transformations if you +have reversible processes. + +So this is actually another +one of those statements + +that you have to +think a little bit + +to see whether it +has any use or not. + +Because we all say that +entropy has to increase, + +but is that what we +have proven here? + +Not quite. + +Because what we've proven is +that if you have a system that + +is isolated, so there is +a system that is isolated + +because I want dQ to be 0. + +And I want entropy to increase. + +OK? + +So let's say we start with +some initial condition + +and we wait and go to +some final condition + +of whatever is inside the box. + +I should be able to +calculate entropy + +before and after in order to see +that this change is positive. + +OK? + +But we say entropy is +a function of state. + +And what have I done here +to change this state? + +I cannot calculate entropy +if the system is not + +in equilibrium. + +If the system is in +equilibrium it presumably + +does not change as +a function of time. + +So what is this +expression relevant to? + +The expression is +relevant to when + +you have some kind of a +constraint that you remove. + +So imagine that +let's say there is + +a gas in this room and some +kind of piston that is initially + +clamped to some position. + +Then I can calculate +the entropy of what's + +on the left side, what's +on the right hand side, + +and that would be +my initial entropy. + +I remove the clamp. + +I remove the constraint so +this can slide back and forth. + +And eventually it comes +to another position. + +So then I can again +calculate the final entropy + +from the sum of what's +on the left side + +and what's on the +right hand side. + +And I can see that +entropy is increased. + +So basically this +statement really + +is useful when there is +some internal constraint + +that you can remove. + +And as you remove the +internal constraint, + +the entropy increases. + +So I guess that image +that we all have + +is that if I give you two +pictures of a room, one + +with books nicely arranged +on a shelf and one + +with books randomly +distributed you + +would have no problem +to time order them. + +And actually presumably +there was some constraint + +from the shelf that +was removed and then + +these things fell down. + +So that's the kind +of process for which + +this statement of the +second law is appropriate. + +Any questions? + +OK. + +So that statement is something +about approach to equilibrium. + +But as I said that there was +some initial configuration + +with some constraint and +as a function of removing + +that constraint +the system would go + +from one sort of equilibrium, +constrained equilibrium + +to an unconstrained equilibrium +and this increase of entropy + +tells us in which +direction it would go. + +You can time order +the various processes. + +Now sometimes this adiabatic +way of doing things + +is not the best way. + +And so depending on what it +is that you are looking at, + +rather than looking +at entropy you + +will be looking at +different functions. + +And so the next step is to +construct different types + +of functions that are +useful for telling us + +something about equilibrium. + +Now I'll start doing that by +some function with which you + +are very familiar. + +And has practically +nothing to do + +with entropy and temperature. + +So we are going to look +at mechanical equilibrium. + +OK. + +And so the kind of +prototype of this, + +since we've been thinking in +terms of springs or wires, + +is let's imagine that +I have a wire that + +has some natural lent. + +And it is sitting there +happily in equilibrium. + +And then I attach, let's +say a mast to it and because + +of that I'm pulling +it with a force + +that I will indicate by J. + +So J, if you are +in gravity, would + +be mass of this times J. OK? + +Now if you were doing +things in vacuum, + +what would happen +to your x, which + +is the distortion +that you would have + +from the equilibrium +as a function of time? + +What would happen is +presumably the thing + +would start to oscillate and you +would get something like this. + +But certainly not +equilibrium, but in real world + +there is always friction +that is operating. + +And so if there is +a lot of friction + +what is going to +happen is that your x + +will come to some final value. + +So again, this is a constraint, +which I allowed this to move. + +And because of that +constraint I went + +from the initial equilibrium +that corresponded to x + +equals to 0 to some +final equilibrium. + +And you say, well, if +I want to calculate + +that final equilibrium, +what I need + +to do is to remove all +of the kinetic energy + +so that the thing +does not move anymore, + +which means that I have to +minimize the potential energy. + +I'll give it the +symbol H for reasons + +to become apparent shortly. + +And that is the +sum of the energy + +that I have in the spring. + +Let's imagine that it +is a hook end spring. + +We would have a formula such as +this, plus the potential energy + +that I have in my +mass, which is related + +to how far I go up and down. + +And say an appropriate +description is minus Jx. + +OK? + +So this is the net potential +energy of the spring plus + +whatever is supplying +the mass that + +is applying in the +external force. + +And so in this case, what +you have is that minimizing + +H with respect to +the constraint x + +will give you that the x +equilibrium is J over K. OK? + +So basically it comes +down to J over K. + +And that the value of this +function, potential energy + +function in equilibrium +substituting this over here + +is minus J squared over K. 2K. + +OK? + +So in many processes that +involve thermodynamics + +we are going to do +essentially the same thing. + +And we are going to call this +net potential central energy, + +in fact, an enthalpy. + +OK? + +And the generalized version +of what I wrote down for you + +is the following, in the +process that I described + +which was related to +the increase in entropy + +we were dealing with a +system that was isolated. + +dQ was 0 and there was no work +because the coordinates were + +not changing. dW was 0. + +Whereas here, I am +looking at a process + +where there is a +certain amount of work + +because this external +J that I am putting + +is doing work on the spring. + +It is adding energy +to the spring. + +And the thing is that +because of the friction + +it doesn't continue +to oscillate. + +So some of the energy that I +would have put in the system, + +if I really were using the +formula Jidxi is lost somehow. + +We can see those +oscillations have gone away. + +Now I'm always doing this +process at constant J. Right? + +So if I prescribe for you some +path of x as a function of T, + +Jdx is the same thing as d of +Jx because J does not change. + +x changes. + +OK? + +I'm going to also +imagine processes + +where mechanical equilibrium, +but with no heat so that dQ + +is 0. + +If I were to add +these two together, + +then I will get an +inequality involving + +dE, which is less than or equal +to d of Jixi, which I can write + +as the change in e minus +Jixi has to be negative. + +So appropriate to +processes, which + +are conducted so that +there is mechanical work + +at constant force, +is this function + +that is usually +called H for enthalpy. + +And what we find is that the +dH is going to be negative. + +And again, if you +think about it this + +is precisely this +enthalpy is none other + +than the potential +energy that is + +in the mechanical +degrees of freedom. + +And there's always +loss in the universe. + +And so the direction naturally +is for this potential energy + +to decrease. + +One thing to note +is that dH is dE. + +Thinking of it not now as a +process going on at constant J, + +but as a change in +a function of state + +because we said that +once I prescribe where + +I am in the coordinate +space I know what, say e is. + +I know what J is. + +I can certainly construct a +function, which is e minus Jx. + +It's another function of state. + +And I can ask what happens +if I make a change from one + +point in space to another point. + +Along the path that potentially +allows variations in J dE + +I know, is Jidxi. + +And then, actually I'm +using summation conversion. + +So let's remove that, +plus TdS and here + +it becomes minus +Jidxi minus xidJi. + +Jidxi is cancelled. + +And we that if I construct +the function H as e minus Jx, + +the natural variations +of it are TdS, just + +like dE but rather than +Jdx I have minus xdJ. + +OK? + +So H is naturally expressed as +a function of variables that are + +s and the Ji's. + +And remember that we said we +are doing things at constant J. + +So it's nice that +it happens that way. + +And in particular if I +do partial derivatives + +I find that my xi is minus +dH by dJi at constant s. + +So that in the same +way before I said + +that if you have the energy +function dE by dx will give J, + +if you have the H functions, +dH by dJ would give you x. + +Let's check. + +Here we had an H function. + +If I do a dH by dJ with a +minus sign, what do I get? + +I will get J over K. What +was my equilibrium x? + +It was J over K. OK? + +Now both of these functions +that we have encountered so far + +were expressing +the system energy + +or enthalpy have as +their argument entropy. + +Now if I give you a box you will +have a hard time potentially + +figuring out what entropy +is, but varying temperature + +is something that +we do all the time. + +So it would be great if we +could start expressing things + +not in terms of entropy, +in terms of anything else. + +Well, what's the natural +thing if not entropy? + +Here we went from x to +the conjugate variable + +J. I can make a transformation +that goes from s + +to the conjugate variable, +which is temperature. + +And that would be +relevant, therefore, + +when I'm thinking about +isothermal processes. + +And so what I'm going to do is +to reverse the role of the two + +elements of energy +that I had previously + +for mechanical processes. + +So what we had there +was that dQ was 0, + +but I want dQ to be non-0. + +What we had there was +that dW was non-0. + +So let's figure out +processes where dW is 0, + +but dQ, the same way that +previously we were doing dW + +at constant J, let's do dQ +not equals to 0 at constant T. + +And constant T is where the +isothermal expression comes + +into play. + +OK? + +So if dW is 0, I have a natural +inequality that involves dQ. + +I just erased it, I think. + +Yeah. + +It's not here. + +dQ is less than or equal to TdS. + +And if T is a constant +throughout the process, + +I can write this as d of TS. + +Add these two together +to get that dE less than + +or equal to d of TS, or +taking it to the other side, + +I can define a function which +is the Helmholtz free energy. + +F, which is E minus TS. + +And what we have is that +the natural direction + +of flow for free +energy when we remove + +some kind of a constraint +at constant temperature + +is that we will tend to +minimize the free energy. + +And then again doing +the manipulation of dF + +is dE minus d of TS in general +will have minus TdS minus SdT. + +The TdS part of the E will +vanish and what I will have + +is Jidxi minus SdT. + +So now we can see that +finally for the free energy, + +the Helmholtz free energy, +and natural variable + +rather than being entropy +is the temperature and all + +set of displacements. + +And then if you ask, well, +what happened to the entropy? + +You say, well, I can get +the entropy as minus dF + +by dT at constant x. + +If I take this +picture of the gas + +that I had put at the beginning, +which was just erased, + +picture of a piston +that can slide. + +And I think of that +as a box that I + +bring into this room, well, +then if you'll quickly + +adjust to the +temperature of the room, + +as well as the +pressure of the room. + +So this is going to be a +general transformation in which + +both heat and the +work are exchanged. + +If is at external temperature +and pressure that is fixed. + +So it's a transformation that +is isothermal and constant J. + +In pressure you would +call it [INAUDIBLE]. + +OK? + +And then quite +generally you would + +say extending what +we had before, + +in this case dQ is, again, less +than TdS because of Clausius. + +dW is less than Jdx +because you always + +lose something to friction. + +You always lose +something to friction. + +You add the two things +together, and you + +get that dE is less than or +equal to TdS, plus Jidxi. + +For the transformations +that we are considering + +that are at constant +t and J I can + +take these expressions to +mean the same thing as d + +of ts plus Jixi, which +means that more generally, + +I can define a function which +is the Gibbs free energy, G, + +which is the energy minus ts. + +This part is the Helmholtz +free energy, minus Jixi. + +And that if I regard this as +a function of state, which + +certainly will be minimized +under conditions of constant J + +and T for some constraint +that is removed. + +Quite generally as +a state function + +depending on all +of these variables, + +it's variations +would be able to be + +expressed as minus +SdT minus Jidxi. + +ie, our G is naturally a +function of temperature + +and the set of displacements. + +OK. + +I don't think music was +appropriate at this point. + +I would have put it +earlier, but such is life. + +OK. + +Now there is something +that I kind of + +did not pay sufficient-- yes? + +AUDIENCE: Sorry. + +Didn't you get it backwards +between the J's and the x's? + +PROFESSOR: I did. + +I did. + +I wrote it wrong here. + +So maybe that's what +the music was for. + +OK. + +Is it fine? + +Anything else? + +OK. + +The thing that I wasn't +sufficiently careful with + +was the list of things that +goes into mechanical work. + +And one additional care +that what needs to have, + +which is that suppose +I were to tell you, + +let's say, the pressure +and temperature as my two + +variables, and I guess this +is what I would have here + +if I go and look at +pressure as my force. + +Then have I told you +everything that I + +need to know about the system? + +So I have a box, let's +say, in this room + +that is at the +pressure of this room + +and at the temperature +of this room. + +Have I completely +specified the box? + +What have I left? + +AUDIENCE: The size. [INAUDIBLE]. + +PROFESSOR: How big is it, yes. + +So what I have left, +previously maybe I had volume, + +but I sort of +discarded the volume + +in terms of the pressure. + +So what I'd really need is to +have the number of particles. + +I have to specify something. + +Maybe the mass, +something that has + +still is going to +distinguish these boxes + +in terms of their size. + +Now it is most useful +to think in terms + +of the number of particles. + +So I give you a box and I +can say that within this box + +I have so many molecules +of oxygen and nitrogen, + +or whatever is the composition, +but then we sort of start + +to get into the realm of +chemistry and the fact + +that the different chemical +components can start + +to react with each +other, maybe even + +if you have a box +that is one component, + +some of the molecules are going +to get absorbed on the surface. + +So precisely what the +number is is potentially + +something that is a variable. + +And in order to specify +exactly what the energy + +content of a system +is you have to specify + +how many particles +and the energy + +carried by those particles. + +So the list of things +that appears here, + +especially when you think in +terms of chemical systems, + +has an additional +element that is typically + +called chemical work. + +And so let's separate mechanical +work from the chemical work. + +So mechanical work +was sum over iJidxi + +where these were +real displacements + +and we can actually +write an expression that + +is very similar here where +the displacements are + +the number of particles +of different species, + +allowing potentially there +going to other species + +through chemical reactions +provided we multiply these + +by some appropriate +chemical potential. + +So these mu's are a +chemical potential. + +So for the reason +that I stated before + +that if I were to +just-- this ambiguity + +that I had about +the size of the box + +tells me that I should +have at least one thing + +left in my system +describing the variables + +that is proportional to +the size of the system. + +So typically what you +do when you construct + +a Gibbs free energy is that you +subtract the mechanical work, + +but you don't subtract +the chemical work. + +So the ends will +remain and can tell you + +how big your system is. + +OK? + +Now there is a conjugate way I +can certainly do the other way. + +So here I constructed something +in which mechanical work was + +removed, but chemical +work remained. + +I could do it the +other way around. + +I can define a function +that is obtained + +by subtracting from the +energy the chemical work, + +but leaving the mechanical +component aside. + +So this function dG, OK, I +should go one step before. + +So once we separate out +the contributions of Jidxi + +into mechanical and +chemical components, + +I would write dE as TdS +plus sum over iJidxi, + +plus sum over alpha +mu alpha dN alpha. + +OK? + +I just explicitly separating +out those two sources of work. + +Now when I constructed G, +which subtracts from e, the mu, + +but not the J, what happens? + +I will get a minus TdS. + +This will remain unchanged. + +This will get transformed +to N alpha, d mu alpha. + +Just hold on a second. + +So this entity that is called +the grand potential actually + +completes the list of +these functions of state + +that I wanted to +tell you is naturally + +a function of T, the +chemical potentials + +as well as the displacement. + +For example, if it's a +gas the displacements + +will include the +volume which tell you + +how much material you have. + +Yes? + +AUDIENCE: In that +case, do you need + +to subtract an additional +TS from E and [INAUDIBLE]? + +PROFESSOR: Very good. + +These are all examples +of the energies + +so that you define them as +a function of temperature + +rather than entropy. + +The only things +that really remain, + +the one function +that you sort of keep + +as a function of entropy +is energy itself. + +Enthalpy, too. + +Yes, it has its uses. + +Yes? + +AUDIENCE: So I have many +questions about [INAUDIBLE]. + +PROFESSOR: OK. + +AUDIENCE: [INAUDIBLE]. + +Right now I wanted to ask you +say that so a particle is added + +to the system, a +particle of some species. + +And this is going to change +the energy of the system. + +So my question is while this +particle can bring energy + +in several ways, +like kinetic energy, + +or maybe it's this chemical +bound that's been broken-- + +PROFESSOR: Yes. + +AUDIENCE: between +energy from there. + +PROFESSOR: Absolutely. + +AUDIENCE: Or also +it's rest energy + +from special [INAUDIBLE]. + +PROFESSOR: Yes. + +AUDIENCE: So which +ones are we counting? + +Which ones are we not counting? + +PROFESSOR: OK. + +So what you see is that when +we do all of these calculations + +we definitely need +to include when + +we are talking about a gas, +the kinetic energy component. + +The change in the covalent +bond energy definitely + +has to be there if I +take an oxygen molecule + +and separate it to +two oxygen atoms. + +There is that change +in the energy that + +has to be included +corresponding kinetic energies. + +Typically the rest +mass is not included. + +And so if I were to include that +it will be a shift of chemical + +potential by an amount +that is mc squared. + +Why do people not bother? + +Because typically what we +will be trying to look at + +is the change when +something happens. + +And you have to bring +those particles presumably + +from somewhere. + +So as long as you bring in +particles from somewhere then + +there's the difference +between the rest mass + +that you had outside +and rest mass + +that you have here, that's 0. + +It's really all of +the other things that + +contribute to useful quantities +that you would be involved + +with like temperature, pressure. + +The rest mass is irrelevant. + +Now I can't rule out +that you will come up it + +some process that is going on +in [INAUDIBLE] for whatever + +where the rest mass is an +important contribution. + +So it may, to some extent, +depend on the circumstance + +that you are looking at. + +But if you are asking +truly what should I + +include in the +chemical potential, + +it will include the rest mass. + +AUDIENCE: So for example in-- +I don't know, in cosmology + +they often talk of +the chemical potential + +of the different species, +like elementary particles + +in the cosmos. + +PROFESSOR: Right. + +AUDIENCE: They say that the +chemical potential of photons + +is 0. + +PROFESSOR: Yes. + +AUDIENCE: So here they have +fixed some kind convention? + +PROFESSOR: No. + +You see there is a +difference between photons + +and other particles such as +electrons or whatever, which + +is that you have value in +number or some other number + +conservation that is applicable. + +So any process that +you have will not + +change the number +of [INAUDIBLE]. + +Whereas there are processes in +which there is something that + +is heated and will give +you whatever number of + +photons that you wish. + +So there is a distinction +between things + +that are conserved and things +that are not conserved. + +So We will get to +that maybe later on as + +to why it is appropriate to +set chemical potential to 0 + +for non-conserved things. + +OK? + +Yeah, but it's +certainly something + +that we have immediately a +feel for what the pressure is + +for what the +temperature is, so we + +have our senses seem +to sort of tell you + +the reality of +temperature and pressure, + +but maybe not so much +the chemical potential. + +So I tried to see whether we +have a sense that actually + +is sensitive to +chemical potential + +and we do to some extent. + +As you drink +something and you say + +it's too salty, or +whatever, so somehow you + +are measuring the chemical +potential of sort. + +So if you like that, that would +be your sensual equivalent + +of chemical potential. + +OK? + +Yes? + +AUDIENCE: Is there +a potential where + +you have both chemical +and mechanical work? + +[INAUDIBLE] + +PROFESSOR: OK. + +So that will run +into the problem + +of if I do that, +then my parameter is + +going to be T, J, and mu. + +And then I can ask you, +how much do I have? + +Because all of these +quantities are intensive. + +Right? + +So it could be a box this +is one cubic centimeters + +or miles long. + +So I am not allowed to do that. + +And there is a mathematical +reason for that + +that I was going +to come to shortly. + +Other questions? + +OK. + +So We are going to +take an interlude. + +Actually, the last question +is quite relevant to what + +we are going to do next, +which is that we have + +these functions defined, +many coordinates, + +and one of the things that +thermodynamics allows you to do + +is to relate measurements +of one set of quantities, + +another set of quantities. + +And it does so +through developing + +mathematical +relationships that you + +can have between these +different functions of state. + +So the next segment has to +do with mathematical results, + +which I will subdivide into +two sets of statements. + +One set of statement +follow from the discussion + +that we have had so far, which +has to do with extensivity. + +What do I mean? + +Let's take a look at our most +fundamental expression, which + +is dE is TdS plus +sum over iJdxi, + +plus sum over alpha +mu alpha dN alpha. + +Now you recognize that certainly +as the amount of material + +gets increased, the number +of particles increases. + +The typical sizes and +displacements get bigger. + +The energy content gets bigger. + +The entropy content is +related to the heat content + +and so that gets bigger. + +So these differential forms +that I have on this expression, + +they're all proportional +to the size of the system. + +What does that mean? + +It means that e, the +way that I have it + +here has as its natural +variables S, x, N. + +And extensivity means that if I +were to make my system twice as + +large, so that all +of these quantities + +would get multiplied +by a factor of two, + +the energy content would get +multiplied by a factor of two. + +OK? + +Now it is important to state +that this is not a requirement. + +OK? + +This is a statement +about most things + +that we encounter around +us, but once you go, + +let's say, to the cosmos, +and you have a star, + +the gravitational +energy of the star + +is not proportional +to its volume. + +It goes the size to +some fractional power. + +So that is an example of a +system because of the way + +gravity works as a +long range force, that + +is not extensive system. + +Typically this +would work as long + +as you have interactions +among your elements + +that are sufficiently +short-ranged + +so that you don't +get non-extensivity. + +If that's the case then +I can take a derivative + +of this expression with respect +to lambda, evaluated at lambda + +equals 2, 1. + +If I take a derivative +with respect to lambda + +here I will have dE by +dS, times S. I mean, + +the argument here +is lambda S. I am + +taking a derivative with +respect to the first argument. + +So I bring out a factor of +S. dE by dS at constant x + +and N. And then the next +term is xi dE with respect + +to all the different +xi's at constant S and N. + +Next one is going to be +N alpha, dE by dN alpha + +at constant x and S. And +there's only one lambda + +on this side, which is +going to give me E of Sx. + +OK? + +Now if I look at my +initial expression + +I can immediately see that +dE by dS at constant x + +and N is none other +than T. So this + +is the same thing as T. +dE by dxi at constant s + +and n is none other than Ji. + +dE by dN alpha at constant x and +Js is none other than mu alpha. + +So once I set the argument to be +1, so that all of these things + +are evaluated at +lambda equals to 1, + +I have the result that e is +equal to TS plus Jixi, plus mu + +alpha N alpha. + +So in some sense all I did was +I took the more fundamental + +expression and removed +all of the d's. + +So some places, this is called +the fundamental relation, + +but I don't like that because it +is only valued for systems that + +are extensive, whereas +the initial formula + +is valued irrespective of that. + +OK? + +Now once I have +this what I can do + +is I can think of +this as a relationship + +among different +functions of state. + +Take a derivative and +write it as dE is d of TS. + +D of TS is TdS plus SdT, plus +d of Jixi, which gives me + +Jidxi plus xidJi, +plus d of mu alpha. + +And alpha will give +me mu alpha dn alpha, + +plus N alpha d mu alpha. + +OK? + +This is just a rewriting +of this expression + +in differential form. + +But I know that dE is the +same thing as TdS plus Jdx + +plus mu n alpha. + +So immediately what it tells me +is that the intensive variables + +T, J, and mu our constrained +to satisfy this relation, which + +is called a +Gibbs-Duhem relation. + +OK? + +So this is, if you like, +the mathematical reason + +for my answer before. + +That I cannot choose this set of +variables to describe my system + +because this set of variables +are not independent. + +If I vary two of them the +variation of the other one + +is fixed. + +And I said I need N plus 1 +independent degrees of freedom. + +If I choose all of +the intensive ones + +I'm really using one additional +relationship that relates them, + +makes them dependent. + +And of course this +also goes to the fact + +that I won't know what the size +of the system is, both of them + +reflections of extensivity. + +Just as an example, let's see. + +Chemical potential +along isotherm. + +So for a gas, what would I have? + +I would write SdT minus Vdp. + +That is my contribution from +the work here remembering + +that hydrostatic work +at the wrong side. + +And then I have N +d mu equals to 0. + +I said how do these +vary along an isotherm? + +Isotherm means that I have +to set dT equals to 0. + +If I'm along an isotherm +then I have that d mu + +is rearranging +things a little bit. + +Mu over NdP. + +So this is the formula +that I will have to use. + +Now let's specialize to +the case of an ideal gas. + +So I'm going to use +here an ideal gas. + +For the case of the ideal +gas we had the relationship + +that PV was NKT. + +So v over n is the same +thing as kT over p. + +Remember that we are +dealing with an isotherm, + +so T is constant. + +dp over pi can +integrate, and therefore + +conclude that mu at a +constant along an isotherm, + +as a function of the other two +intensive variables T and P, + +is some reference that comes +from a constant of integration. + +And then I have KT, +integral of dP over P + +is log of P divided by sum. + +Actually, I already +put the constant. + +OK? + +Very briefly to be +expanded upon next lecture, + +the other set of +mathematical relations + +go under the name of +Maxwell relations. + +And they follow from the +following observation. + +If I have a function of +more than one variable, + +let's say, f of x and y, two +variables, then the natural way + +to write this +consistent with what + +we had before is that df is df +by dx partial at constant ydx, + +plus dfy, the y +at constant x dy. + +But one thing that +we know from calculus + +is that these are +first derivatives, + +and there are a bunch +of second derivatives. + +In particular, the second +derivative d2 f, dx, dy + +is independent of the order +of taking the derivatives. + +Which means that if I take +a derivative of this object + +with respect to y, I +will get the same thing + +if I were to take a derivative +of the second object + +with respect to x. + +So in particular if I go back +to my fundamental equation, + +dE, let's forget about +the chemical potential + +because time is running +short, Jidxi plus TdS. + +I identify T and Ji as +the first derivatives. + +That is, Ji is the +first derivative of e + +with respect to xi +at constant S. T + +is the first derivative +of E, with respect + +to S at constant x. + +Then if I were to take a second +derivative to construct d2E + +with respect to x and T, and +S, I could do it two ways. + +I already have a derivative with +respect to x that gave me Ji, + +so I take another +derivative of J + +with respect to S, +now at constant x. + +Or I can take a +derivative here, which + +is dT by dxi at constant +S. And depending + +on which one of the many +functions of state that we + +introduced, E, F, G, +H, you can certainly + +make corresponding second +derivative inequalities. + +And the key to sort of +understanding all of them + +is this equality of +second derivatives. + +So what I will start +next time around + +is to just give you a set +of things on the left hand + +side, the analog of this. + +So for example, I could +choose dS by dxi at constant T + +and show that just by +looking at the form of this + +how we will be able to construct +what this thing is related + +through a Maxwell construction. + +OK? + +Thank you. \ No newline at end of file diff --git a/JyYoXu0cJwA.txt b/JyYoXu0cJwA.txt new file mode 100644 index 0000000000000000000000000000000000000000..dda890760fd409d6e152def0f89646a310c8e09f --- /dev/null +++ b/JyYoXu0cJwA.txt @@ -0,0 +1,611 @@ +align:start position:0% + +so now that we understand at a high + + align:start position:0% +so now that we understand at a high + + + align:start position:0% +so now that we understand at a high +level what Market segmentation is the + + align:start position:0% +level what Market segmentation is the + + + align:start position:0% +level what Market segmentation is the +question now is how do you do Market + + align:start position:0% +question now is how do you do Market + + + align:start position:0% +question now is how do you do Market +segmentation and this is actually quite + + align:start position:0% +segmentation and this is actually quite + + + align:start position:0% +segmentation and this is actually quite +a fun process if you do it correctly um + + align:start position:0% +a fun process if you do it correctly um + + + align:start position:0% +a fun process if you do it correctly um +if you already have a technology and + + align:start position:0% +if you already have a technology and + + + align:start position:0% +if you already have a technology and +people are buying it and experiencing it + + align:start position:0% +people are buying it and experiencing it + + + align:start position:0% +people are buying it and experiencing it +you can actually just go to them and say + + align:start position:0% +you can actually just go to them and say + + + align:start position:0% +you can actually just go to them and say +what are you using it for and that will + + align:start position:0% +what are you using it for and that will + + + align:start position:0% +what are you using it for and that will +start to give you input um if you have + + align:start position:0% +start to give you input um if you have + + + align:start position:0% +start to give you input um if you have +an idea it's not as easy to do that but + + align:start position:0% +an idea it's not as easy to do that but + + + align:start position:0% +an idea it's not as easy to do that but +really what we're going to do here is + + align:start position:0% +really what we're going to do here is + + + align:start position:0% +really what we're going to do here is +we're not going to be limited just by + + align:start position:0% +we're not going to be limited just by + + + align:start position:0% +we're not going to be limited just by +what's already being done we're going to + + align:start position:0% +what's already being done we're going to + + + align:start position:0% +what's already being done we're going to +get the team together and we're going to + + align:start position:0% +get the team together and we're going to + + + align:start position:0% +get the team together and we're going to +think out of the box what are all the + + align:start position:0% +think out of the box what are all the + + + align:start position:0% +think out of the box what are all the +different potential things and no idea + + align:start position:0% +different potential things and no idea + + + align:start position:0% +different potential things and no idea +is too crazy brainstorming is a very + + align:start position:0% +is too crazy brainstorming is a very + + + align:start position:0% +is too crazy brainstorming is a very +good thing um the crazier idea the + + align:start position:0% +good thing um the crazier idea the + + + align:start position:0% +good thing um the crazier idea the +better because it opens the aperture and + + align:start position:0% +better because it opens the aperture and + + + align:start position:0% +better because it opens the aperture and +so then you're going to systematically + + align:start position:0% +so then you're going to systematically + + + align:start position:0% +so then you're going to systematically +make a list or lay out all the different + + align:start position:0% +make a list or lay out all the different + + + align:start position:0% +make a list or lay out all the different +opportunities that you could that you + + align:start position:0% +opportunities that you could that you + + + align:start position:0% +opportunities that you could that you +you can think of and it's interesting + + align:start position:0% +you can think of and it's interesting + + + align:start position:0% +you can think of and it's interesting +because in my company some of the first + + align:start position:0% +because in my company some of the first + + + align:start position:0% +because in my company some of the first +ones that we thought thought we're so + + align:start position:0% +ones that we thought thought we're so + + + align:start position:0% +ones that we thought thought we're so +obvious we're going to do this ends up + + align:start position:0% +obvious we're going to do this ends up + + + align:start position:0% +obvious we're going to do this ends up +being ones that we didn't do it was some + + align:start position:0% +being ones that we didn't do it was some + + + align:start position:0% +being ones that we didn't do it was some +other idea that came up in brainstorming + + align:start position:0% +other idea that came up in brainstorming + + + align:start position:0% +other idea that came up in brainstorming +but once we lay out what the different + + align:start position:0% +but once we lay out what the different + + + align:start position:0% +but once we lay out what the different +opportunities are now that was just + + align:start position:0% +opportunities are now that was just + + + align:start position:0% +opportunities are now that was just +brainstorming in a room they might not + + align:start position:0% +brainstorming in a room they might not + + + align:start position:0% +brainstorming in a room they might not +be good ideas we have to go out and the + + align:start position:0% +be good ideas we have to go out and the + + + align:start position:0% +be good ideas we have to go out and the +answer relies in doing primary customer + + align:start position:0% +answer relies in doing primary customer + + + align:start position:0% +answer relies in doing primary customer +research so we're going to go out and + + align:start position:0% +research so we're going to go out and + + + align:start position:0% +research so we're going to go out and +talk to real customers to find out what + + align:start position:0% +talk to real customers to find out what + + + align:start position:0% +talk to real customers to find out what +their problems are what they think of + + align:start position:0% +their problems are what they think of + + + align:start position:0% +their problems are what they think of +this idea it's not we have to understand + + align:start position:0% +this idea it's not we have to understand + + + align:start position:0% +this idea it's not we have to understand +their needs as well because they they're + + align:start position:0% +their needs as well because they they're + + + align:start position:0% +their needs as well because they they're +not going to be able to design the + + align:start position:0% +not going to be able to design the + + + align:start position:0% +not going to be able to design the +product for us so doing primary + + align:start position:0% +product for us so doing primary + + + align:start position:0% +product for us so doing primary +observational market research is + + align:start position:0% +observational market research is + + + align:start position:0% +observational market research is +fundamental my thesis at MIT was on this + + align:start position:0% +fundamental my thesis at MIT was on this + + + align:start position:0% +fundamental my thesis at MIT was on this +and what I saw was that you know you + + align:start position:0% +and what I saw was that you know you + + + align:start position:0% +and what I saw was that you know you +have to have a good process but it's not + + align:start position:0% +have to have a good process but it's not + + + align:start position:0% +have to have a good process but it's not +just the process that matters it's + + align:start position:0% +just the process that matters it's + + + align:start position:0% +just the process that matters it's +actually walking in the customer shoes + + align:start position:0% +actually walking in the customer shoes + + + align:start position:0% +actually walking in the customer shoes +and using good inquiry techniques not + + align:start position:0% +and using good inquiry techniques not + + + align:start position:0% +and using good inquiry techniques not +advocating for your product but + + align:start position:0% +advocating for your product but + + + align:start position:0% +advocating for your product but +understanding what they're about you + + align:start position:0% +understanding what they're about you + + + align:start position:0% +understanding what they're about you +need to walk in the customer shoes you + + align:start position:0% +need to walk in the customer shoes you + + + align:start position:0% +need to walk in the customer shoes you +need to understand them rationally of + + align:start position:0% +need to understand them rationally of + + + align:start position:0% +need to understand them rationally of +course emotionally and also socially + + align:start position:0% +course emotionally and also socially + + + align:start position:0% +course emotionally and also socially +what drives them what do you know what + + align:start position:0% +what drives them what do you know what + + + align:start position:0% +what drives them what do you know what +do they kind of fear most in the world + + align:start position:0% +do they kind of fear most in the world + + + align:start position:0% +do they kind of fear most in the world +but now we're going to understand their + + align:start position:0% +but now we're going to understand their + + + align:start position:0% +but now we're going to understand their +job as well by watching them and this is + + align:start position:0% +job as well by watching them and this is + + + align:start position:0% +job as well by watching them and this is +what we call primary customer research + + align:start position:0% +what we call primary customer research + + + align:start position:0% +what we call primary customer research +um then we're going to narrow down the + + align:start position:0% +um then we're going to narrow down the + + + align:start position:0% +um then we're going to narrow down the +you know these markets so we might have + + align:start position:0% +you know these markets so we might have + + + align:start position:0% +you know these markets so we might have +20 and we're going to do a first pass on + + align:start position:0% +20 and we're going to do a first pass on + + + align:start position:0% +20 and we're going to do a first pass on +market research and then we're going to + + align:start position:0% +market research and then we're going to + + + align:start position:0% +market research and then we're going to +say all right we can't do 20 we can only + + align:start position:0% +say all right we can't do 20 we can only + + + align:start position:0% +say all right we can't do 20 we can only +do six to eight of them and then once we + + align:start position:0% +do six to eight of them and then once we + + + align:start position:0% +do six to eight of them and then once we +do that we've narrow the field and then + + align:start position:0% +do that we've narrow the field and then + + + align:start position:0% +do that we've narrow the field and then +we do another push of market research + + align:start position:0% +we do another push of market research + + + align:start position:0% +we do another push of market research +primary market research to do this do + + align:start position:0% +primary market research to do this do + + + align:start position:0% +primary market research to do this do +not trust you know what you just see on + + align:start position:0% +not trust you know what you just see on + + + align:start position:0% +not trust you know what you just see on +the internet do not trust you know a + + align:start position:0% +the internet do not trust you know a + + + align:start position:0% +the internet do not trust you know a +report from a group as reputable as + + align:start position:0% +report from a group as reputable as + + + align:start position:0% +report from a group as reputable as +Gardner might be go out and see for + + align:start position:0% +Gardner might be go out and see for + + + align:start position:0% +Gardner might be go out and see for +yourself because the answer lies with + + align:start position:0% +yourself because the answer lies with + + + align:start position:0% +yourself because the answer lies with +the customer you have to do this + + align:start position:0% +the customer you have to do this + + + align:start position:0% +the customer you have to do this +yourself don't download your eyes and + + align:start position:0% +yourself don't download your eyes and + + + align:start position:0% +yourself don't download your eyes and +ears this primary market research is one + + align:start position:0% +ears this primary market research is one + + + align:start position:0% +ears this primary market research is one +of the most fundamental important things + + align:start position:0% +of the most fundamental important things + + + align:start position:0% +of the most fundamental important things +that you're going to do \ No newline at end of file diff --git a/K-iHODiS0-8.txt b/K-iHODiS0-8.txt new file mode 100644 index 0000000000000000000000000000000000000000..f0c4c9106e000d555b03f9ac9796a4c86b8e88af --- /dev/null +++ b/K-iHODiS0-8.txt @@ -0,0 +1,3470 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu + +PROFESSOR: OK, we have +a busy day today, + +so let's get started. + +Want to go through Chernoff +bounds and the Wald identity, + +which are closely related, as +you'll see, and that involves + +coming back to the TG1Q a little +bit and making use of + +what we did for that. + +It also means coming +back to hypothesis + +testing and using that. + +Would probably have been better +to start out with + +Wald's identity and the Chernoff +bound and then do the + +applications when it was at +the natural time for them. + +But anyway, this is the way it +is this time, and next time + +we'll probably do +it differently. + +Suppose you have a random +variable z. + +It has a moment generating +function. + +Remember, not all random +variables have moment + +generating functions. + +It's a pretty strong +restriction. + +You need a variance. + +You need moments +of all orders. + +You need all sorts of things, +s but we'll assume it exists + +in some region between +r and r plus. + +There's always a question, +with moment generating + +functions, if they exist up +to some maximum value of r + +because some of them exist at +that value of r and then + +disappear immediately after +that, and others just sort of + +peter away as r approaches +r plus from below. + +I think in the homework this +week, you have an example of + +both of those. + +I mean, it's a very +simple issue. + +If you have an exponential +distribution, then as r + +approaches, the rate of that +exponential distribution, + +obviously, the moment generating +function blows up + +because you're taking e to the +minus lambda x, and you're + +multiplying it by a the r x. + +And when r is equal to lambda, +bingo, you're integrating 1 + +over an infinite range, so +you've got infinity. + +If you multiply that exponential +by something which + +makes the integral finite when +you set r equal to lambda, + +then of course, you have +something which + +is finite at r star. + +That is a big pain +in the neck. + +It's usually not important. + +The notes deal with it very +carefully, so we're not going + +to deal with it here. + +We will just assume here that +we're talking about r less + +than r plus and not worry about +that special case, which + +usually is not all +that important. + +But sometimes you have +to worry about it. + +OK, the Chernoff bound says +that the probability that + +random variable is greater than +or equal to alpha is less + +than or equal to the moment +generating function evaluated + +at some arbitrary value r times +e to the minus r alpha. + +And if you put it in terms of +the semi invariant moment + +generating function, the log +of the moment generating + +function, then the bound +is e to the gamma z of + +r minus alpha r. + +When you see something like +that, you ought to look at it + +and say, gee, that looks funny +because here, we're taking an + +arbitrary random variable and +saying the tails of it have to + +go down exponentially. + +That's exactly what this says. + +It says that a z takes +on very large values. + +This is a fixed quantity here +for a given value of r, and + +it's going down as e to the +minus r times alpha. + +As you make alpha larger and +larger, this goes down faster + +and faster. + +So what's going on? + +How do you take an arbitrary +random variable and say the + +tails of it is exponentially +decreasing? + +That's why you have to insist +that the moment generating + +function exists because when the +moment generating function + +exists for some r, it means +that the tail of that + +distribution is, in fact, going +down at least that fast, + +so you get something +that exists. + +So the question is what's the +best bound of this sort of + +when you optimize o for r? + +Then the next thing we did is +we said that z is a sum of + +IID, then the semi invariant +moment generating function for + +that sum is equal to n times +the semi invariant moment + +generating function for the +underlying random variable x. + +S of n is n of these IID +random variable. + +So one thing you see +immediately, and ought to be + +second nature to you now, is +that if a random variable has + +a moment generating function +over some range, the sum of a + +bunch of those IID random +variables also has a moment + +generating function over +that same range. + +You can just count on that +because the semi invariant + +moment generating function +is just n times this b. + +OK, so then what we've said is +the probability that sn is + +greater than or equal to na, +where na is playing the role + +of alpha and sn is playing the +role of z, is just a minimum + +over r of e to the n times gamma +x of r minus ra, and the + +n is multiplying the ra +as well as the n. + +OK, this is exponential +n for a fixed a. + +In other words, what you do in +this minimization, if you + +don't worry about the special +cases or anything, how do you + +minimize something? + +Well, obviously, you want to +minimize the exponent here, so + +you take the derivative of this +gamma prime of r has to + +be equal to a. + +Then n can be whatever it wants +to be when you find that + +optimum r, which is where gamma +prime of r equals a, + +then this goes down +exponentially with a. + +Now, however, we're interested +in something else. + +We're interested in threshold +crossings. + +We're not interested in picking +a particular value of + +a and asking, as n gets very, +very big, what's the + +probability that the sum of +random variable is greater + +than or equal to n times a. + +That is exponential in n, but +what we're interested in is + +the probability that s of n is +greater than or equal to just + +some constant alpha, and what +we're doing, now, is instead + +of varying n and varying +this with n also, + +we're holding the stick. + +So we're asking as n gets very, +very large, but you hold + +this alpha fixed, what happens +on this bound over here? + +Well, when you minimize this, +taking the same simple-minded + +view, now the n is not +multiplied by the ra. + +It's just multiplied +by the gamma x. + +You get n times gamma prime of +r is equal to alpha s where + +the minimum is so that it says +gamma prime of r is optimized + +when you pick gamma prime of r +equal to alpha over and n. + +This quantity is minimized when +you pick gamma prime of r + +equal to alpha over n. + +So if you look at this bound as +n changes, what's happening + +is, as n changes, r is changing +also, so this is a + +harder thing to deal with +for variable n. + +But graphically, it's quite +easy to deal with. + +I'm not sure you all got the +graphical argument last time + +when we went through it, so I +want to go through it again. + +Let's look at this exponent r +minus n over alpha times gamma + +of r, and see what +it looks like. + +We'll take r, pick +any old r, there. + +What we want to do is show that +this, if you take a slope + +of alpha over n, and take an +arbitrary r, come down to + +gamma of x of r, draw a line +in this slope, and look at + +where it hits the horizontal +axis here, that point is r + +plus the length of +this line here. + +The length of this line here +is gamma of r, that's a + +negative value, times 1 over +that slope of this line. + +And 1 over the slope of this +line is n over alpha, so when + +I pick a particular value of r, +the value of the experiment + +I have is this value here. + +How do I optimize this over r? + +How do I get the largest +exponent here? + +Well, I think of varying r, as +I vary r from 0, and each + +time, I take this straight +line here. + +And I start here, draw a +straight line over there, + +start here, draw a straight +line over, start at this + +tangent here, draw a +straight line over. + +And what happens when I come +to larger values of r? + +Just because gamma of s of r is +convex, what happens is I + +start taking these slope lines, +slope alpha over n, and + +they intercept the horizontal +axis at a smaller value. + +So this is optimized over r +at the value of r0, which + +satisfies alpha over n equals +gamma prime of r0. + +That's the same answer we got +before when we just used + +elementary calculus. + +Here, we're using a more +sophisticated argument, which + +you learned about probably +in 10th grade. + +I would argue that you learned +mostly really sophisticated + +things when you're in high +school, and then when you get + +to study engineering in college, +somehow you always + +study these mundane things. + +But anyway, aside from +that, why is this + +geometric argument better? + +Well, when you look at these +special cases of what happens + +when gamma of r comes around +like this, and then suddenly + +it stops in midair and just +doesn't exist anymore? + +So it comes around here, it's +still convex, but then + +suddenly it goes off +to infinity. + +How do you do that optimization +then? + +Well, the graphical argument +makes it clear how you do it, + +and makes it perfectly rigorous +how to do it, whereas + +if you're doing it by calculus, +you've got a really + +think it through, and it +becomes fairly tricky. + +OK, so anyway, now, the next +question we want to ask-- + +I mean, at this point, we've +seen how to minimize this + +quantity over r, so we know what +this exponent is for a + +particular value of n. + +Now, what happens +when we vary n? + +As you vary n, the thing that +happens is we have this + +tangent line here, a +slope alpha over n. + +When you start making n larger, +alpha over n becomes + +smaller, so the slope +becomes smaller. + +And as n approaches infinity, +you wind up going way, + +way the heck out. + +As n gets smaller, you +come in again. + +You keep coming in until you +get to this point here. + +And what happens then? + +We're talking about +a line of-- + +maybe I ought to draw +it on the board. + +It would be clearer, I think. + +As n gets smaller, you +get a point which is + +tangent here, this here. + +When you're here, the tangent +gets right here, so we've + +moved all the way into this +quantity we call r star, which + +is the root of the equation +gamma of r equals 0. + +Gamma of r equals 0 typically +has two roots, one + +here, and one at 0. + +It always has a root at 0 +because moment generating + +function evaluated is 0 is +always 1, so the log of + +it is always 0. + +There should be another root +because this is convex, unless + +it drops off suddenly, and even +if it drops off suddenly, + +you can visualize it +as a straight line + +going off to infinity. + +So when you get down to this +point, what happens? + +Well, we just keep +moving along. + +So as n increases, we start +out very large. + +We come in. + +We hit this point, and then +we start coming out again. + +I mean, if you think about it, +that makes perfect sense + +because what we're doing here is +we're imagining experiment + +where this random variable has +a negative expected value. + +That's what's indicated by +this quantity there. + +We're asking what's the +probability that the sum of a + +large number of IID random +variables with a negative + +expected value ever rises above +some positive threshold? + +Well, the law of large numbers +says it's not going to do that + +when n is very, very large, +and this says that, too. + +It says the probability of +it for n very large is + +extraordinarily small. + +It's e to the minus 10 times +an exponent, which is very, + +very large. + +So as n gets very small, it's +not going to happen either + +because it doesn't have time +to get to the threshold. + +So there's some intermediate +value at which it's most + +likely to cross the threshold, +if you're going to cross the + +threshold, and that intermediate +value is just + +that value at which gamma of +r star is equal to zero. + +So the probability this union +of terms, namely the + +probability you ever cross +alpha, is going to be, in some + +sense, approximately a to the +minus alpha r star because + +that's where the dominant +term is. + +The dominant term is where +alpha over n is + +equal to gamma prime. + +Blah, blah, blah, blah, blah, +where'd I put that? + +r star satisfies gamma +of r star equals 0. + +When you look at the line of +slope, gamma prime of r plus + +of r star, that's where you get +this critical value of n + +where it's most likely the +cross the threshold. + +OK, I put that somewhere. + +I thought it was on this slide, +but it's the n, the + +critical n, let's call it n +crit, is equal to gamma prime. + +Is at right? + +Alpha over m is the +gamma prime. + +Alpha over n, 1 over n crit. + +n crit, this says, is alpha over +gamma prime of r star. + +OK, so that sort of nails down +everything you want to know + +about the Chernoff bound accept +for the fact that it is + +exponentially tight. + +The text proves that. + +I'm not going to go +through that here. + +Exponentially tight means, if +you take an exponent which is + +just a little bit larger than +the one you found here, and + +look what happens as alpha +gets very, very + +large, then you lose. + +OK, let's go on, and at this +point, we're ready to talk + +about Wald's identity. + +And we'll prove Wald's identity +at the end of the + +lecture today. + +Turns out there's a very, +very simple proof of it. + +There's hardly anything to it, +but it seems more important to + +use it in several ways first so +that you get a sense that + +it, in fact, is sort +of important. + +OK, so we want to think about +a random walk, s sub n and + +greater than or equal to n, so +it's a sequence of sums of + +random variable, s sub +n is equal to x1 + +plus up to x sub n. + +The x's are all IID. + +This is the thing we've been +talking about all term. + +We have a bunch of IID +random variables. + +We look at the partial +sums of them. + +We're interested in what happens +to that sequence of + +partial sums. + +The question we're asking here +is does that sequence of + +partial sums ever cross +a positive threshold? + +And now we're asking does +it ever cross a positive + +threshold, or does it cross a +negative threshold, and which + +does it cross first? + +So the probability that it +crosses this threshold is the + +probability that it +goes up, first. + +The probability that it crosses +this threshold is the + +probability that it +goes down, first. + +Now, what Wald's identity says +is the following thing. + +We're going to assume that +x is not identically 0. + +If x is identically +0, then it's never + +going to go any place. + +We're going to assume that it +has a semi invariant moment + +generating function in some +region, r minus to r plus. + +That's the same as assuming +that it has a generating + +function in that region, so it +exists from some value less + +than zero to some value +greater than zero. + +And we picked two thresholds, +one of them positive, one of + +them negative, and we let j be +the smallest value of n. j is + +a random variable, now, because +we've start to run + +this random walk. + +We run it until it crosses one +of these thresholds, and if it + +crosses the positive threshold, +j is the time at + +which it crosses the +positive threshold. + +If it crosses the negative +threshold, j is the time that + +it crosses the negative +threshold. + +We're only looking at the first + +threshold that it crosses. + +Now, notice that j is +a stopping trial. + +In other words, what that means +is you can determine + +whether you've crossed a +threshold at time n solely in + +terms of s1 up to s sub n. + +If you see all these sums, then +you know that you haven't + +crossed a threshold +up until time n. + +You know you have crossed +it at time n. + +Doesn't make any difference +what happens at times + +greater than n. + +OK, so it's a stopping trial +in the same sense as the + +stopping trials we talked +about before. + +You get the sense that Wald's +identity, which we're talking + +about here, is sort of like +Wald's equality, which we + +talked about before. + +Both of them have to do with +these stopping trials. + +Both of them have everything +to do with stopping trials. + +Wald was a famous statistician, +not all that + +much before your era. + +He didn't die too long ago. + +I forget when, but he was one +of the good statisticians. + +See, he was a statistician who +recognized that you wanted to + +look at lots of different +models to understand the + +problem, rather than a +statistician who only wanted + +to take data and think that he +wasn't assuming anything. + +So Wald was a good guy. + +And what his identity says is, +and the trouble with his + +identity, is you look at +it, and you blink. + +The expected value of +e to the r s sub j. + +s sub j is the value of the +random walk at the time when + +you cross a threshold minus +the time at which you've + +crossed a threshold +times gamma of r. + +So when you take the expected +value of e to the this, you're + +averaging over j over the time +that you crossed the + +threshold, and also at the value +at which you crossed the + +threshold, so you're averaging +over both of these things. + +And Wald says this expectation +not is less than or equal to + +1, but it's exactly 1, and it's +exactly 1 for every r + +between r minus and r plus. + +So it's a very surprising +result. + +Yes? + +AUDIENCE: Can you +please explain + +why j cannot be defective? + +I don't really see it. + +PROFESSOR: Oh, it's because +we were looking at two + +thresholds. + +If we only had one threshold, +then it could be defective. + +Since we're looking at two +thresholds, you keep adding + +random variables in, and the +sum starts to have a larger + +and larger variance. + +Now, even with a large variance, +you're not sure that + +you crossed a threshold, +but you see why you + +must cross a threshold. + +Yes? + +AUDIENCE: If the MGF is defined +at r minus, r plus, + +then is that also [INAUDIBLE] +quality? + +PROFESSOR: Yes. + +Oh, if it's defined at r plus. + +I don't know. + +I don't remember, and I would +have to think about it hard. + +Funny things happen right at the +ends of where these moment + +generating functions are +defined, and you'll see why + +when we prove it. + +I can give you a clue as to how +we're going to prove it. + +What we're going to do is, for +this random variable x, we're + +going to define another random +variable which has the same + +distribution as x except +it's tilted. + +For large values of x, you +multiply it by e to the rx. + +For small values of +x, you multiply it + +by e to the rx also. + +But if r is positive, that +means the positive values + +could shifted up, and the small +values get shifted down. + +So you're taking some of the +density that looks like this, + +and when you shift it to this +tilted value, you're shifting + +the whole thing upward. + +When r is negative, +you're shifting + +the whole thing downward. + +Now, what this says is that +tilted random variable, when + +it crosses the threshold, the +time of crossing the threshold + +is still a random variable. + +You will see that this simply +says that the expected value + +of that tilted random variable +is equal to-- + +it says that tilted random +variable is, in fact, the + +random variable. + +It's not defective. + +And it's the same argument as +before, that has a finite + +variance, and therefore, since +it has a finite variance, it + +keeps expanding. + +It will cross one of the +thresholds eventually. + +OK, so the other thing you can +do here is to say, suppose + +instead of crossing a threshold, +you just fix this + +stopping rule to say we'll +stop at time 100. + +If you stop at time 100, then +what this says is expected + +value of e to the r100 minus +100 times gamma of + +r is equal to 1. + +But that's obvious because the +expected value of e to the r + +is j is, in fact-- + +it's j times the expected value +of rx, so then you're + +subtracting off j times +the log of the + +expected value of rx. + +So it's a trivial identity +if x is fixed. + +OK, so Wald's identity +says this. + +Let's see what it means in terms +of crossing a threshold. + +We'll assume both thresholds +are there. + +Incidentally, Wald's identity +is valid in a much broader + +range of circumstances than +just where you have two + +thresholds, and you're looking +at a threshold crossing. + +It's just that's a particularly +valuable form of + +the Wald identity. + +So that's the only thing +we're going to use. + +But now, if we assume further +that this random variable x + +has a negative expectation, +when x has a negative + +expectation, gamma of r +starts off going down. + +Usually, it comes +back up again. + +We're going to assume that this +quantity r star here, + +where it crosses 0 again, we're +going to assume there is + +some value of r, for which +gamma of r star equals 0. + +Mainly, we're going to assume +this typical case in which it + +comes back up and crosses +the 0 point. + +And in that case, what it says +is the probability that sj is + +greater than or equal to alpha +is just less than or equal to + +e to the minus r star +times alpha. + +Very, very simple bound +at this point. + +You look at this, and you sort +of see why we're looking, now, + +not at r in general, +but just r star. + +At r star, gamma of r +star is equal to 0. + +So this term goes away, so we're +only talking about the + +expected value of e to the r +sj, e to the r star sj is + +equal to 1. + +So let's see what happens. + +We know that e to the r star sj +is greater than or equal to + +0 for all values of sj because +e to the anything real is + +going to be positive. + +OK, since e to the r star sj is +greater than or equal to 0, + +what we can do is break this +expected value here, this term + +is 0, now, remember, break +it into two terms. + +Break it into the term where s +sub j is bigger than alpha, + +and break it into the +term where s sub j + +is less than beta. + +So I'm just going to ignore the +case where it's less than + +or equal to beta. + +I'm going to take this +expected value. + +I'm going to write it as the +probability that s sub j is + +greater than or equal to alpha +times e times the expected + +value of either the r star s +sub j given s sub j greater + +than or equal to alpha. + +There should be another term +in here to make this equal, + +and that's the probability that +s sub j is less than or + +equal to beta times e to the r +star s sub j, given that s sub + +j is less than or +equal to beta. + +We're going to ignore that, and +that's why we get the less + +than or equal to 1 here. + +Now, you can lower bound +e to the r star + +sj under this condition. + +What's a lower bound to s sub +j given that s sub j is + +greater than or equal +to alpha? + +Alpha. + +OK, we're looking at all cases +where s sub j is greater than + +or equal to alpha, and we're +going to stop this experiment + +at the point where it +first exceeds alpha. + +So we're going to lower bound +the point where it first + +exceeds alpha by alpha itself, +so this quantity is lower + +bounded, again, by taking the +probability that s sub j + +greater than or equal to alpha +times e to the r star alpha, + +and that whole thing is less +than or equal to 1. + +That says the probability that +sj is greater than or equal to + +alpha is less than or equal to +e to the minus r star alpha, + +which is what this inequality +says here. + +OK, so this is not +rocket science. + +This is a fairly simple result +if you believe in Wald's + +identity, which we'll +prove later. + +OK, so it's valid +for all choices + +of this lower threshold. + +And remember, this probability +here, it doesn't look like + +it's a function of both alpha +and beta, but it is because + +you're asking what's the +probability that you cross the + +threshold alpha before you +cross the threshold beta. + +And if you make beta very, very +large, it makes it more + +likely that you're going +to cross the threshold. + +If you make beta very close to +0, then you're probably going + +to cross beta first, so this +inequality here, this quantity + +here, depends on beta also. + +But we know that this inequality +is valid no matter + +what beta is, so we can let beta +approach minus infinity, + +and we can still have +this inequality. + +There's a little bit tricky +math involved in that. + +There's an exercise in the text +which goes through that + +slightly tricky math, but what +you find is that this bound is + +valid with only one threshold, +as well as with two + +thresholds. + +But this proof here that we've +given depends on a lower + +threshold, which is somewhere. + +We don't care where. + +Valid for all choices of +beta, so it's valid + +without a lower threshold. + +The probability that the union +overall n of sn less than or + +equal to alpha. + +In other words, the probability +that we ever + +crossed a threshold alpha-- + +AUDIENCE: It's not true equal. + +PROFESSOR: What? + +AUDIENCE: It's supposed to +be sn larger [INAUDIBLE] + +as the last time? + +PROFESSOR: It's less than or +equal to e to the minus r star + +alpha, which is-- + +AUDIENCE: Oh, sn? + +sn? + +PROFESSOR: n. + +AUDIENCE: You just [INAUDIBLE] + +[? the quantity? ?] + +PROFESSOR: Oh, it's a union +overall n greater than or + +equal to 1. + +OK, in other words, this +quantity we're dealing with + +here is the probability +that sn--- + +oh, I see what you're saying. + +This quantity here +should be greater + +than or equal to alpha. + +You're right. + +Sorry about that. + +I think it's right +most places. + +Yes, it's right. + +We have it right here. + +The probability of this union +is really the same as the + +probability that the value of +it, after it crosses the + +threshold, is greater than +or equal to alpha. + +OK, now, we saw before that the +probability that s sub n + +is greater than or +equal to alpha. + +Excuse me, that's the same. + +When you're writing things in +LaTeX, the symbol for less + +than or equal to is so similar +to that for greater than or + +equal to that's hard to +keep them straight. + +That quantity there is a greater +than or equal to sign, + +if you're going from right to +left instead of right to left. + +So all we're doing here is +simply using this, well, + +greater than or equal to. + +OK, the corollary makes a +stronger and cleaner statement + +that the probability that you +ever cross alpha is less than + +or equal to-- + +my heavens, my evil twin got +a hold of these slides. + +And let me rewrite that one. + +The probability that the union +overall n of the event s sub n + +greater than or equal to alpha +is less than or equal to e to + +the minus r star alpha. + +OK, so we've seen from the +Chernoff bound that for every + +n this bound has satisfied, this +says that it's not only + +satisfied for each n, but it +says it's satisfied overall n + +collectively. + +Otherwise, if we were using the +Chernoff bound, what would + +we have to do to get a handle +on this quantity? + +We'd have to use the union +bound, and then when we use + +the union bound, we can show +that for every n, the + +probability that sn is greater +than or equal to alpha is less + +than or equal to +this quantity. + +But then we'd have to add all +those terms, and we would have + +to somehow diddle around with +them to show that there are + +only a few of them which are +close to this value, and all + +the rest are negligible. + +And the number that are close to +that value is only growing + +with n and goes through +a lot of headache. + +Here, we don't have to do this +anymore because the Wald + +identity has saved is from +all that difficulty. + +OK, we talked about +the G/G/1 queue. + +We're going to apply this +corollary to the G/G/1 queue + +to the queueing time, namely to +the time w sub i that the + +i's arrival spends in +the queue before + +starting to be served. + +You remember, when we looked at +that, we found that if we + +define u sub i to be equal to +the ith interarrival time + +minus the i minus first service +time, those are + +independent of each other, +so this is the + +difference between those. + +So ui is the difference between +the i's arrival time + +and the previous service time. + +What we showed was that this +sequence, u sub i, the + +sequence of the sums of u sub +i as a modification of a + +random walk. + +In other words, the sums of +the u sub i behave exactly + +like a random walk does, but +every time it gets down to 0, + +if it crosses 0, it +resets to 0 again. + +So it keeps bouncing up again. + +If you look in the text, what +it shows is that if you look + +at this sequence of u sub i's, +and you look at the sum of + +them, and you look at them +backward, if you look at the + +sum of u sub i plus u sub i +minus 1 plus u sub i minus 2, + +and so forth, when you look at +the sum that way, it actually + +becomes a random walk. + +Therefore, we can apply this +bound to the random walk, and + +what we find is that the +probability that the waiting + +time of n queue, of the nth +customer, is probability that + +it's greater than or equal to +an arbitrary number alpha is + +less than or equal to the +probability that w sub + +infinity is greater than or +equal to alpha, and it's less + +than e to the minus +r star alpha. + +So again, all you have to do is +you have this inner arrival + +time x, you have this service +time y, you take the + +difference of the two, that's a +random variable, you find a + +moment generating function of +that random variable, you find + +the point of r star at which +that moment generating + +function equals 1, and then +the bound says that the + +probability that the queueing +time that you're going to be + +dealing with is less than +or equal to this + +quantity alpha here. + +Yes? + +AUDIENCE: What do you work with +when you have the gamma + +function go like this, and thus +have infinity, and you + +cross it there. + +[INAUDIBLE] points that +we're looking for? + +PROFESSOR: For that, you +have to read the text. + +I mean, effectively, you can +think of it just as if gamma + +of r is a convex function +like anything else. + +It just has a discontinuity in +it, and bingo, it shoots off + +to infinity. + +So when you take these slope +arguments, what happens is + +that for all slopes beyond that +point, they just seesaw + +around at one point. + +But the same bound holds. + +OK, so that's the +Kingman bound. + +Then we talked about +large deviations + +for hypothesis test. + +Well, actually we just talked +about hypothesis test, but not + +large deviation for them. + +Let's review where +we were on that. + +Let's let the vector y be an n +tuple of IID random variables, + +y1 up to y sub n. + +They're IID conditional +on hypothesis 0. + +They're also IID conditional on +hypothesis 1, so the game + +is nature chooses either +hypothesis 0 or hypothesis 1. + +You take n samples of some IID +random variable, and those n + +samples are IID conditional on +either nature choosing 0 or + +nature choosing 1. + +At the end of choosing those n +samples, you're supposed to + +guess whether h0 is the right +hypothesis or 1 is a right + +hypothesis. + +Invest in Apple stock 10 years +ago, and one hypothesis is + +it's going to go broke. + +The other hypothesis is it's +going to invent marvelous + +things, and your stock will +go up by a factor of 50. + +You take some samples, you make +your decision on that. + +Fortunately, with that, you can +make a separate decision + +each year, but that's the +kind of thing that + +we're talking about. + +We're just restricting it to +this case where you have n + +sample values that you're taking +one after the other, + +and they're all IID when the +particular value of the + +hypothesis that happens +to be there. + +OK, so we said there +is something called + +a likelihood ratio. + +The likelihood ratio for a +particular sequence y is + +lambda of y is equal to the +density of y given h1 divided + +by the density of y given h0. + +Why is it h1 on the top +and h0 on the bottom? + +Purely convention, +nothing else. + +The only thing that +distinguishes hypothesis 1 + +from hypothesis 0 is you choose +one and call it 1, and + +you choose the other +and call it 0. + +Doesn't make any difference +how you do it. + +So after we make that choice, +the likelihood + +ratio is that ratio. + +Now, the reason for using semi +invariant moment generating + +functions is that this +density here is + +a product of densities. + +This density is a product of +densities, and therefore when + +you take the log of this ratio +of products, you get the sum + +from i equals 1 to n of this log +likelihood ratio for just + +a single experiment. + +It's a single experiment that +you're taking based on the + +fact that all n experiments +are based on the same + +hypothesis, either h0 or h1. + +So the game that you're playing, +and please remember + +what the game is if you forget +everything else about this + +game, is the hypothesis gets +chosen, and at the same time, + +you take n sample values. + +All n sample values correspond +to the same value of the + +hypothesis. + +OK, so when you do that, we're +going to call z sub i, this + +logarithm here, this log +likelihood ratio. + +And then we showed last time +that a threshold test is-- + +well, we define the threshold +test as comparing the sum with + +the logarithm of a threshold. + +And the threshold is equal to +p0 over p sub 1, if in fact + +you're doing a maximum a +posteriori probability test, + +and p0 and p1 are the +probabilities of hypothesis. + +Remember how we did that. + +It was a very simple thing. + +You just write out what the +probability is of hypothesis 0 + +and a sequence of +n values of y. + +You write out what the +probability is of hypotheses 1 + +and that same sequence of values +with the appropriate + +probability on that sequence for +h equals 1 and h equals 0. + +And what you get out of that +is that the threshold test + +sums up all the z sub i's, +compares it with the + +threshold, and makes a choice, +and that is the map choice. + +OK, so conditional on h0, you're +going to make an error + +if the sum of the z sub i's +is greater than the + +logarithm of eta. + +And conditional on h1, you're +going to make an error if the + +sum is less than or +equal to log eta. + +I denote these as the random +variable z sub i 0 to make + +sure that you recognize that +this random variable here is + +conditional on h0 in this case, +and it's conditional on + +h1 in the opposite case. + +OK, so the exponential bound +for z sub i sub 0-- + +OK, so what we're doing now is +we're saying, OK, suppose that + +0 is the actual value +of this hypothesis. + +0 is the value of +the hypothesis. + +The experimenter doesn't +know this. + +What the experimenter does is +does what the experimenter has + +been told to do, namely the +experimenter take these n + +values, y1 up to y sub n, finds +the likelihood ratio, + +compares that likelihood ratio +with the threshold, and if the + +threshold is larger than the +threshold, it decides 1. + +If it's smaller than the +threshold, that decides + +opposite thing. + +It decides 1 if it's above +the threshold, 0 if + +it's below the threshold. + +Well, first thing we want to do, +then, is to find the log + +likelihood ratio under the +assumption that 0 is the + +correct hypothesis, and +something very remarkable + +happens here. + +Gamma sub 0 of r is now the +logarithm because it's a semi + +invariant moment generating +function of the expected value + +of this quantity of e to +the r times z sub i. + +When we take the expected value, +we integrate over f of + +y given h0 times e to the r +times log of f of y given h1 + +over f of y given h0. + +You look at this, and +what do you get? + +This quantity here is e +to the r times log of + +f of y given h1. + +That whole quantity in there +is just f of y given + +h1 to the rth power. + +So what we have is, in this +quantity here, is f of y given + +h0 to the minus r power. + +So this term combined with +this term gives us f of 1 + +minus r of y given h0, and this +quantity here is f to the + +r of y given h1 dy. + +So the semi invariant moment +generating function is this + +quantity here. + +At r equals 1, this is just f +of y given h1, so the log of + +it is equal to 0. + +So what we're saying is that, +for any old detection problem + +in the world, so long as this +moment generating function + +exists, what happens is it +starts at 0, it comes down, + +comes back up again, and +r star is equal to 1. + +That's what we've just shown. + +When r is equal to 1, this whole +thing is equal to 1, so + +the log of 1 is equal to 0. + +For every one of these problems, +you know where this + +intercept is, you know where +this intercept is, one is at + +0, one is at 1. + +What we're going to do now is +try to find out what the + +probability of error is given +that h is 0, h equals 0, is + +the correct hypothesis. + +So we're assuming that the +probabilities are actually f + +of y given h0. + +We calculate this quantity that +looks like this, and we + +ask what is the probability +that this sum of random + +variables exceeds the threshold, +exceeds the + +threshold eta. + +So the thing that we do is we +draw a line, a slope, natural + +log of eta divided by eta. + +We draw that slope along here, +and we find that the + +probability of error is upper +bounded by gamma 0 of this + +quantity, defined by the slope, +minus r0 times log of + +eta divided by eta. + +That's all there is to it. + +Any questions about that? + +Seem obvious? + +Seem strange? + +OK, so the probability of r +conditional on h equals 0 is e + +to the n times gamma 0 of +r0 minus r0, natural + +log of eta over eta. + +And ql of eta is the probability +of error given + +that h is equal to l. + +OK, we can do the same thing +for hypothesis 1. + +We're asking what's the +probability of error given + +that h equals 1 is the correct +hypothesis, and given that we + +choose a threshold, say +we know the a priori + +probabilities, so we choose +a threshold that way. + +OK, we go through the same +argument, z1 of s is the + +natural log of f of y given F1 +times e to the s, we're using + +s in place of r here, times +the natural log of f of y + +given h1 over f of y given h0. + +And this quantity, now, f of y +given h1, the f of y given h1 + +is upstairs, so we have f of +1 plus s of y given h1. + +This quantity is down here, +so we have f of minus + +s of y given h0. + +And we notice that when s is +equal to minus 1, this is + +again equal to 0, and we notice +also, if you compare + +this, gamma 1 of s is equal +to gamma 0 of r minus 1. + +These two functions are the +same, just shifts it by one. + +OK, so this one of the very +strange things about + +hypothesis testing, namely you +are calculating these expected + +values, but you're calculating +the expected value of a + +likelihood ratio. + +And the likelihood ratio +involves the probabilities of + +the hypotheses also, so when you +calculate that ratio, what + +you get this is funny quantity +here, which is related to what + +you get when you calculate +the semi invariant moment + +generating function given +the other hypothesis. + +So that now, what we wind up +with is a gamma 1 of the eta, + +is e to the n times +gamma 0 of r0. + +I'm using the fact that gamma 1 +of s is equal to gamma 0 of + +r minus 1, s is just r shifted +over by 1, so I can do the + +same optimization for each. + +So what I wind up with is +the probability of error + +conditional on hypothesis 0, +is this quantity down here. + +That's this one, and the +probability of error + +conditional on the other +hypothesis, the exponent is + +equal to this quantity here. + +OK, so what that says is that +as you shift the threshold-- + +in other words, suppose instead +of using a map test, + +you say, well, I want the +probability of error to be + +small when hypothesis +0 correct. + +I want it to be small when +hypothesis 1 is correct. + +I have a trade off between +those two. + +How do I choose my threshold in +order to get the smallest + +value overall? + +So you say, well, +you're stuck. + +You have one exponent +under hypothesis 0. + +You have another exponent +under hypothesis 1. + +You have this curve here. + +You can take whatever value you +want over here, and that + +sticks you with a value here. + +You can rock things around this +inverted seesaw, and you + +can make one probability of +error bigger by making the + +other one smaller, or you make +the other one bigger by making + +the other one smaller. + +Namely, what you're doing is +changing the threshold, and as + +you change the threshold, as +you make the threshold + +positive, what you're doing is +making it harder to accept h1, + +h equals 1, and easier +to accept h equals 0. + +When you move the threshold the +other way, you're making + +it easier the other way. + +This, in fact, gives you the +choice between the two. + +You decide you're going +to take n tests. + +You can make both of these +smaller by making n bigger. + +But there's a trade off between +the two, and the trade + +off is given by this tangent +line to this curve here. + +And you're always stuck with +r star equals 1 and + +all of these problems. + +So the only question is what +does this curve look like? + +Notice that the expected value +of the likelihood ratio given + +h equals 0 is negative. + +The expected value given h +equals 1 is positive, and + +that's just because of the form +of the likelihood ratio. + +OK, so this actually shows +these two exponents. + +These are the exponents for +the two kinds of errors. + +You can view this as a large +deviation form of the Neyman + +Pearson test. + +In the Neyman Pearson test, +you're doing things in a very + +detailed way, and you're +taking a choice between + +choosing different thresholds +to make the probability of + +error of one type bigger or less +than the other one, just + +the other way. + +Here, we're looking at the large +deviation form of it + +that becomes an upper bound +rather than an exact + +calculation, but it tells you +much, much more because for + +most of these threshold tests, +you're going to do enough + +experiments that your +probability of error is going + +to be very small. + +So the only question is where +do you really want the error + +probability to be small? + +You can make it very small one +way by shifting the curve this + +way, and make it very small the +other way by shifting the + +curve the other way. + +And you take your choice +of which you want. + +OK, the a priori probabilities +are usually not the essential + +characteristic when you're +dealing with this large + +deviation kind of result +because, when you take a large + +number of tests, this threshold, +log eta over eta + +over n, when n becomes very +large, when you have a large + +number of experiments, +log eta over n + +becomes relatively small. + +So that's not the thing you're +usually concerned with. + +What you're concerned with is +whether one test, the patient + +dies, and the other tests costs +a lot of money; or one + +test, the nuclear plant blows +up, and the other test, you + +waste a lot of money, +which you wouldn't + +have had to pay otherwise. + +OK, now, here's the important +part of all of this. + +So far, it looked like there +wasn't any way to get out of + +this trade off between choosing +a threshold to make + +the error probability small one +way, or making the error + +probability small +the other way. + +And you think, well, +yes, there is a way + +to get around it. + +What I should do is what I do +in real life, namely if I'm + +trying to decide about +something, what I'm normally + +going to do, I don't like to +waste my time deciding about + +it, so as soon as the decision +becomes relatively + +straightforward, I +make up my mind. + +If the decision is not +straightforward, if I don't + +have enough evidence, I keep +doing more tests, so + +sequential tests are an obvious +thing to try to do if + +you can do it. + +What we have here, what we've +shown, is we have two coupled + +random walks. + +Given hypothesis h equals 0, we +have one random walk, and + +that random walk is typically +going to go down. + +Given h equals 1, we have +another random walk. + +That random walk is typically +going to go up. + +And one is going to go down, one +is going to go up, because + +we've defined the random +variable involved is a log of + +f of y given h1 divided by f +of y given h0, which is why + +the 1 walk goes up, and +the 0 walk goes down. + +Now, the thing we're going to +do is do a sequential test. + +We're going to keep +doing experiments + +until we cross a threshold. + +We're going to decide what +threshold is going to give us + +a small enough probability of +error under each condition, + +and then we choose +that threshold. + +And we continue to test +until we get there. + +So we want to find out whether +we've gained anything by that, + +how much we've gained +if we gain something + +by it, and so forth. + +OK, when you use two thresholds, +alpha's going to + +be bigger than 0. + +Beta's going to be +less than 0. + +The expected value of z given +h0 is less than 0, but the + +value of z given h1 +is greater than 0. + +That's why the walks are +coupled, so we can handle each + +of them separately until we can +get the answers for one + +from the answers +for the other. + +Crossing alpha is a rare event +for the random walk with h0 + +because a random walk +with h0, you're + +going to go down typically. + +You hardly ever go up. + +Yes? + +AUDIENCE: Can you please +explain again sign of + +expectations? + +PROFESSOR: The sign of +the expectations? + +Yes, z is the log, so that when +we actually have h equals + +1, the expected value of this +is going to be lined up with + +this term on top. + +We have f of y. + +When we have h equals 0, +this lined up with + +the term on the bottom. + +I mean, actually, you have to +go through and actually show + +that the integral of f of y +given h1 of this quantity is + +greater than 0, and the other +one is less than 0. + +We don't really have to do that +because, if we calculate + +this moment generating +function, we can + +pick it off of there. + +When we look at this moment +generating function, that + +slope there is the expected +value of z conditional on h + +equals 0, and because of the +shifting property, this slope + +here is the expected value of +z given h equals 1, just + +because the 1 curve is shifted +from the other by one unit. + +It's really because +of that ratio. + +If you defined it the other +way, you just changed the + +sign, so nothing important +would happen. + +OK, so r start equals 1 for +the h0 walk, so the + +probability of error, given h0, +is less than or equal to e + +to the minus alpha. + +Well, that's a nice simple +result, isn't it? + +In fact, that's really +beautifully. + +You just calculate this moment +generating function, you find + +the root of it, and +you're done. + +You have a nice bound, and in +fact, it's an exponentially + +tight bound. + +And on the other hand, when you +deal with the probability + +of error given h1 by symmetry, +it's less than or equal to e + +to the beta. + +Beta is a negative number, +remember, so this is + +exponentially going +down as you choose + +beta, smaller and smaller. + +So the thing that we're getting +is we can make each of + +these error probabilities as +small as we want, this one, by + +making alpha big. + +We can make this one as +small as we want by + +making beta big negative. + +There must be a cost to this. + +OK, but what's the cost? + +What happens when you +make alpha big? + +When hypothesis 1 is the correct +hypothesis, what + +normally happens is that this +random walk is going to go up + +roughly at a slope of the +expected value of z + +given h equals 0. + +So when you make alpha very, +very large, you're forced to + +make a very large number of +tests when h is equal to 1. + +When you make beta very, very +large, you're forced to take a + +large number of tests when +h is equal to 0. + +So the trade off here is +a little bit funny. + +You make your error probability +for h equals 0 + +very, very small by costing more +money when hypotheses 1 + +is the correct hypothesis +because you don't make a + +decision until you've +really climb way up + +on this random walk. + +And that means it takes a long +time when you have h equals 1. + +Since when h is equal to 1, the +probability of crossing + +this lower threshold is it is +almost negligible, this + +expected time that it takes +is really just a + +function of h equals 1. + +I'm going to show that +in the next slide. + +When you increase alpha, it +lowers the probability of + +error given h equals 0. + +Excuse me, I should have h +equals 0 instead of h sub 0. + +Exponentially, it increases the +expected number of steps + +until you make a decision +given h1. + +Expected value of j given h1 is +effectively equal to alpha + +divided by expected value +of z given h1. + +Why is that? + +That's essentially +Wald's equality. + +Not Wald's identity, but Wald's +equality because-- + +Yes, it says from Wald's +equality, since alpha is + +essentially equal to the +expected value of s of j given + +h equals 1, the number of +testing you have to take when + +h is equal to 1, when alpha +is very, very large, is + +effectively the amount of time +that it takes you to get up to + +the point alpha. + +That expected amount of time is +typically pretty close to + +the mean value. + +So alpha there is close to the +expected value of s of j given + +h equals 1. + +So Wald's equality, given h +equals 1, says the expected + +value of j given h1 is equal +to the expected value of sj + +given h equals 1, that's alpha, +divided by the expected + +value of z given h1, +which is just the + +underlying likelihood ratio. + +So to get this result, we just +substitute alpha for the + +expected value. + +And then the probability of +error, given h equals 0, if we + +write it this way, we see +the cost immediately. + +That's the expected value +of j given h equal to 1. + +In other words, the expected +number of tests given h equals + +1 times the expected value of +the log likelihood ratio given + +h equals 1. + +When you decrease beta, that +lowers the probability of + +error given h1 exponentially, +but it increases the number of + +tests when h0 is the +correct hypothesis. + +So in that case, you get the +probability of error given h + +equals 1 is effectively equal to +the expected value e to the + +expected value of j +equals j equals 0. + +This is just the number of tests +you have to do when h is + +equal to 0. + +This is the expected value of +the log likelihood ratio when + +h is equal to 0. + +This is very approximate, but +this is how you would actually + +choose how big you make alpha, +how big do you make beta if + +you want to do a test between +these two hypotheses. + +Now, this shows what you're +gaining by the sequential test + +over what you're gaining by +the non-sequential test. + +You don't have this in your +notes, so you might just jot + +it down quickly. + +The expected value of z, +conditional on h equals 0, is + +this slope here, the slope of +the moment generating function + +is z equals 0. + +That's the slope of the +underlying random variable. + +Since this point is r equal to +1, this point down here is the + +expected value of z +given h equals 0. + +That's the exponents that you +get when h equals 0 is, in + +fact, the correct exponent. + +When given the probability of +error given that h is equal to + +0, namely the probability that +you choose hypothesis 1. + +Same way over here. + +This slope here is the expected +value of the log + +likelihood ratio given +h equals 1. + +This hits down here at minus +expected value of z + +given h equals 1. + +So you have this exponent going +one way, you have this + +exponent going the other way +when the thing multiplying the + +exponent is not an absolute +value but is, in fact, the + +number of tests you have to +do than the other test. + +Now, if we do the fix test, +what we're fixed with is a + +test where you take a line +tangent to this curve, which + +goes from here across +here to there. + +We can see-saw it around. + +When we see-saw it all the way +in the limit, we can get this + +result here. + +But we get this result here at +the cost of an error, which is + +almost one in the other +case, so that's + +not a very good deal. + +This says that sequential +testing, well, it shows you + +how much you gain by doing +a sequential test. + +I mean, it might not be +intuitively obvious why this + +is happening. + +I mean, really the reason it's +happening is that the times + +when you want to make the test +very long are those times when + +if h is equal to 0, you +normally go down. + +The next most normal thing is +you wobble around without + +doing anything for a long time, +in which case you want + +to keep doing additional tests +until finally it falls down, + +or finally it goes up. + +But by taking additional +tests, you make it very + +unlikely that you're ever going +to cross that threshold. + +So that's the thing +you're gaining. + +You are gaining the fact that +the error is small in those + +situations where the sum of +these random variables stays + +close to 0 for a long time, and +then you don't make errors + +in those cases. + +We now have just a little +bit of time to + +prove Wald's identity. + +I don't want to have a lot of +time to prove it because + +proofs of theorems are things +you really have to look at + +yourselves. + +This one, you almost don't +have to look at it. + +This one is almost obvious as +soon as you understand what a + +tilted probability is. + +So let's suppose that x sub n is +a sequence of IID discrete + +random variables. + +It has a moment generating +function for some given r. + +We're going to assume that these +random variables are + +discrete now to make this +argument simple. + +If they're not discrete, this +whole argument has to be + +replaced with all sorts +of [INAUDIBLE] + +integrals and all +of that stuff. + +It's exactly the same idea, +but it just is messy + +mathematically. + +So what we're going to do is +we're going to define a tilted + +random variable. + +A tilted random variable is a +random variable in a different + +probability space. + +OK, we start out with this +probability space that we're + +interested in, and then we say, +OK, suppose that we, just + +to satisfy our imaginations, we +suppose the probabilities + +are different. + +We assume that the probabilities +for a given r is + +the probability that the random +variable X is equal to + +little x, namely this quantity +here, is equal to the original + +probability that X is +equal to little x. + +All the sample values are +the same, it's just the + +probability's changed, times e +to the rx minus gamma of r. + +So we're taking these +probabilities when X is large. + +We're magnifying them +when x is small. + +We're knocking them down. + +What's the purpose of this? + +It's just a normalization +factor. + +e to the minus gamma of r is 1 +over the moment generating + +function of r, so you take +p of x, e to the rx, + +divide it by g of r. + +So this is a probability mass +function, as well as this. + +This is the correct probability +mass function for + +the model you're looking at. + +This is an imaginary one, but +you can always imagine. + +You can say let's suppose that +we had this model instead of + +the other model. + +All the sample values are the +same, but the probabilities + +are different. + +So we want to see what we can +find out from these different + +probabilities in this different +probability model. + +If you sum over x here, +this sum is equal to + +1, as we just said. + +So we'll view q sub xr of x as +the probability mass function + +on x in a new probability +space. + +We can use all the laws of +probability in this new space, + +and that's exactly what +we're going to do. + +And we're going to say things +about the new space, but then + +we can always come back to the +old space from this formula + +here because whatever we find +out in the new space will work + +in the old space. + +One thing we'd like to do is +to be able to find the + +expected value of the random +variable x in this new + +probability space, so this isn't +the expected value in + +the old space. + +It's a probability +in the new space. + +It's the sum over x of x +times q sub xr of x. + +That's what the expected +value is. + +X is the same in both spaces. + +That's just the probabilities +that have changed. + +These are p of x times z to the +rx minus gamma of r, so + +when you sum this, what you get +is 1 over g of xr, which + +is that term, times the +derivative of p sub x + +of x, e to the rx. + +When you take this derivative, +then you get an x in front, + +which is that x there. + +So you get g prime of xr +over gx of r, which is + +gamma prime of r. + +OK, so in terms of that graph +we've drawn, when you take + +these tilted probabilities, you +move that slope, that r + +equals 0, and now you're looking +at a slope at whatever + +r you're looking at. + +And that gives you the +expected value there. + +OK, if you have a joint tilted +probability mass function-- + +and don't think it gets +any more complicated. + +It doesn't. + +I mean, you've already gone +through the major complication + +of this argument. + +The joint tilted PMF is the +probability of x1 to xn is the + +old probability of x1 to xn +times all of these tilted + +factors here. + +If you let a of sn be the set +of n tuples which have the + +same sum, then all these terms +become r times s sub n. + +So what you get is that for each +xn for which the sum is + +sn, this tilted probability +becomes the old probability + +times e to the r sn minus n +gamma of r, which says that + +when we look at the tilted +probability of the sum, namely + +we said that when we tilt these +probabilities, we can do + +everything in a new space that +we could do in the old space. + +We can do everything that +probability theory allows us + +to do, so we can look at the +probability of s sub n in the + +new space also. + +The probability of sn in the +old space, namely we're + +summing this quantity, overall +xn in a of sn, so we sum up + +all of those as the probability +sub s sub n at sn + +times this quantity, +which is fixed. + +So this is the key to a lot +of large deviation theory. + +Any time you're dealing with a +difficult problem, and you + +want to see what's happening +way, way away from the mean, + +you want to see what these +sums look like for these + +exceptional cases, what we do +is we look at a new model + +where we tilt the probability so +that the region of concern + +becomes the main region +for that tilted model. + +So for r equals 0, we're +tilting the probability + +towards large values, and you +can use the law of large + +numbers, essential limit +theorem, whatever you want to, + +in that new space, then. + +Now, we can prove +Wald's equality. + +What Wald's identity is is the +statement that when you tilt + +these probabilities, a stopping +rule in this tilted + +world is still the stopping +time is still a random + +variable, namely you still +stop with probability 1. + +Somebody questioned whether you +stop with probability 1 in + +the old world. + +Like I said, you do because +you have this positive + +variance, and the thing with two +thresholds keeps growing + +and growing. + +Here, you have the same thing. + +I mean, the mean doesn't make +any difference at all. + +I mean, you're looking at trying +to exceed one of two + +different thresholds, and +eventually, you exceed one of + +them no matter where +you set r. + +So what this is saying is the +probability that j is equal to + +n in this tilted space is equal +to the probability that + +j is equal to n in the old +space times z to the r sn + +minus gamma of r. + +So this quantity is equal to the +expected value of e to the + +r sn minus gamma of r. + +Given j equals n times the +probability that j is equal to + +n, you sum this over n +and, bingo, you're + +back at the Wald identity. + +So that's all the Wald identity +is, is just a + +statement that when you tilt a +probability, and you have a + +stopping rule on the original +probabilities, you then have a + +stopping rule on the +new probabilities. + +And Wald's identity says-- + +well, Wald's identity holds +whenever that tilted stopping + +rule is a random variable. + +OK, that's it for today. + +We will do martingales +on Wednesday. \ No newline at end of file diff --git a/Kw-FtXrG3WA.txt b/Kw-FtXrG3WA.txt new file mode 100644 index 0000000000000000000000000000000000000000..8252cdcb490a850ed68f8054bca4691e852ead15 --- /dev/null +++ b/Kw-FtXrG3WA.txt @@ -0,0 +1,731 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a creative commons license + + align:start position:0% +a creative commons license + + + align:start position:0% +a creative commons license +your support will help mit + + align:start position:0% +your support will help mit + + + align:start position:0% +your support will help mit +opencourseware continue to offer high + + align:start position:0% +opencourseware continue to offer high + + + align:start position:0% +opencourseware continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of mit courses + + align:start position:0% +materials from hundreds of mit courses + + + align:start position:0% +materials from hundreds of mit courses +visit mit open courseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +this is the course about paradox + + align:start position:0% +this is the course about paradox + + + align:start position:0% +this is the course about paradox +the idea is to start with a number of + + align:start position:0% +the idea is to start with a number of + + + align:start position:0% +the idea is to start with a number of +philosophical problems that seem + + align:start position:0% +philosophical problems that seem + + + align:start position:0% +philosophical problems that seem +intractable at first + + align:start position:0% +intractable at first + + + align:start position:0% +intractable at first +and see what can be done with them when + + align:start position:0% +and see what can be done with them when + + + align:start position:0% +and see what can be done with them when +we think rigorously about them and when + + align:start position:0% +we think rigorously about them and when + + + align:start position:0% +we think rigorously about them and when +we bring + + align:start position:0% +we bring + + + align:start position:0% +we bring +all the powerful tools that logicians + + align:start position:0% +all the powerful tools that logicians + + + align:start position:0% +all the powerful tools that logicians +have developed + + align:start position:0% +have developed + + + align:start position:0% +have developed +into the picture + + align:start position:0% +into the picture + + + align:start position:0% +into the picture +one example of a paradox is infinity + + align:start position:0% +one example of a paradox is infinity + + + align:start position:0% +one example of a paradox is infinity +so + + align:start position:0% + + + + align:start position:0% + +people tended to be + + align:start position:0% +people tended to be + + + align:start position:0% +people tended to be +perplexed by infinity because of + + align:start position:0% +perplexed by infinity because of + + + align:start position:0% +perplexed by infinity because of +problems like the following + + align:start position:0% +problems like the following + + + align:start position:0% +problems like the following +so take on the one hand + + align:start position:0% +so take on the one hand + + + align:start position:0% +so take on the one hand +the prime numbers and on the other hand + + align:start position:0% +the prime numbers and on the other hand + + + align:start position:0% +the prime numbers and on the other hand +the natural numbers 0 1 2 3 etc + + align:start position:0% +the natural numbers 0 1 2 3 etc + + + align:start position:0% +the natural numbers 0 1 2 3 etc +there's a sense in which there are more + + align:start position:0% +there's a sense in which there are more + + + align:start position:0% +there's a sense in which there are more +natural numbers and prime numbers + + align:start position:0% +natural numbers and prime numbers + + + align:start position:0% +natural numbers and prime numbers +because + + align:start position:0% +because + + + align:start position:0% +because +all of the prime numbers are natural + + align:start position:0% +all of the prime numbers are natural + + + align:start position:0% +all of the prime numbers are natural +numbers and then there's more + + align:start position:0% +numbers and then there's more + + + align:start position:0% +numbers and then there's more +but on the other hand + + align:start position:0% +but on the other hand + + + align:start position:0% +but on the other hand +you can pair up + + align:start position:0% +you can pair up + + + align:start position:0% +you can pair up +the natural numbers and the prime + + align:start position:0% +the natural numbers and the prime + + + align:start position:0% +the natural numbers and the prime +numbers you just assign + + align:start position:0% +numbers you just assign + + + align:start position:0% +numbers you just assign +zero to the first prime number + + align:start position:0% +zero to the first prime number + + + align:start position:0% +zero to the first prime number +and one to the second prime number + + align:start position:0% +and one to the second prime number + + + align:start position:0% +and one to the second prime number +and two to the third + + align:start position:0% +and two to the third + + + align:start position:0% +and two to the third +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +so there's this other sense in which + + align:start position:0% +so there's this other sense in which + + + align:start position:0% +so there's this other sense in which +they're just as many prime numbers as + + align:start position:0% +they're just as many prime numbers as + + + align:start position:0% +they're just as many prime numbers as +natural numbers + + align:start position:0% +natural numbers + + + align:start position:0% +natural numbers +and people tended to think that because + + align:start position:0% +and people tended to think that because + + + align:start position:0% +and people tended to think that because +of this where infinity began + + align:start position:0% +of this where infinity began + + + align:start position:0% +of this where infinity began +as a sensible argument ended + + align:start position:0% +as a sensible argument ended + + + align:start position:0% +as a sensible argument ended +so one one of the things we try to do in + + align:start position:0% +so one one of the things we try to do in + + + align:start position:0% +so one one of the things we try to do in +the course is tame the infinite + + align:start position:0% +the course is tame the infinite + + + align:start position:0% +the course is tame the infinite +i divide the class in sessions of two + + align:start position:0% +i divide the class in sessions of two + + + align:start position:0% +i divide the class in sessions of two +kinds so each week there's two sessions + + align:start position:0% +kinds so each week there's two sessions + + + align:start position:0% +kinds so each week there's two sessions +and i see the first session as an + + align:start position:0% +and i see the first session as an + + + align:start position:0% +and i see the first session as an +inspirational one so the idea is to + + align:start position:0% +inspirational one so the idea is to + + + align:start position:0% +inspirational one so the idea is to +brainstorm to put ideas on the table and + + align:start position:0% +brainstorm to put ideas on the table and + + + align:start position:0% +brainstorm to put ideas on the table and +get people to participate and see what + + align:start position:0% +get people to participate and see what + + + align:start position:0% +get people to participate and see what +people think + + align:start position:0% +people think + + + align:start position:0% +people think +and + + align:start position:0% +and + + + align:start position:0% +and +the second session of the week is an + + align:start position:0% +the second session of the week is an + + + align:start position:0% +the second session of the week is an +effort to bring things together so + + align:start position:0% +effort to bring things together so + + + align:start position:0% +effort to bring things together so +people will have to have completed a + + align:start position:0% +people will have to have completed a + + + align:start position:0% +people will have to have completed a +problem set by then + + align:start position:0% +problem set by then + + + align:start position:0% +problem set by then +and what we do is try and get down to + + align:start position:0% +and what we do is try and get down to + + + align:start position:0% +and what we do is try and get down to +details and see what we can make of the + + align:start position:0% +details and see what we can make of the + + + align:start position:0% +details and see what we can make of the +progress we made in the first session + + align:start position:0% +progress we made in the first session + + + align:start position:0% +progress we made in the first session +so one way in which i teach the course + + align:start position:0% +so one way in which i teach the course + + + align:start position:0% +so one way in which i teach the course +differently is that participation is key + + align:start position:0% +differently is that participation is key + + + align:start position:0% +differently is that participation is key +so i don't plan my lectures very + + align:start position:0% +so i don't plan my lectures very + + + align:start position:0% +so i don't plan my lectures very +precisely in advance what i do is think + + align:start position:0% +precisely in advance what i do is think + + + align:start position:0% +precisely in advance what i do is think +of a number of interrelated topics that + + align:start position:0% +of a number of interrelated topics that + + + align:start position:0% +of a number of interrelated topics that +we might talk about and then just see + + align:start position:0% +we might talk about and then just see + + + align:start position:0% +we might talk about and then just see +what the students want students are + + align:start position:0% +what the students want students are + + + align:start position:0% +what the students want students are +interested in one thing that's where i + + align:start position:0% +interested in one thing that's where i + + + align:start position:0% +interested in one thing that's where i +go + + align:start position:0% +go + + + align:start position:0% +go +if someone was thinking about taking + + align:start position:0% +if someone was thinking about taking + + + align:start position:0% +if someone was thinking about taking +this course independently + + align:start position:0% +this course independently + + + align:start position:0% +this course independently +one thing i would recommend + + align:start position:0% +one thing i would recommend + + + align:start position:0% +one thing i would recommend +is that they use the various puzzles the + + align:start position:0% +is that they use the various puzzles the + + + align:start position:0% +is that they use the various puzzles the +syllabus focuses on + + align:start position:0% +syllabus focuses on + + + align:start position:0% +syllabus focuses on +as + + align:start position:0% +as + + + align:start position:0% +as +doors + + align:start position:0% +doors + + + align:start position:0% +doors +into larger subfields of philosophy + + align:start position:0% +into larger subfields of philosophy + + + align:start position:0% +into larger subfields of philosophy +so that for example + + align:start position:0% +so that for example + + + align:start position:0% +so that for example +when + + align:start position:0% +when + + + align:start position:0% +when +they + + align:start position:0% +they + + + align:start position:0% +they +think about infinity that they then go + + align:start position:0% +think about infinity that they then go + + + align:start position:0% +think about infinity that they then go +on + + align:start position:0% +on + + + align:start position:0% +on +to find a textbook about the infinite + + align:start position:0% +to find a textbook about the infinite + + + align:start position:0% +to find a textbook about the infinite +and learn more about that + + align:start position:0% +and learn more about that + + + align:start position:0% +and learn more about that +or that when we consider paradoxes to do + + align:start position:0% +or that when we consider paradoxes to do + + + align:start position:0% +or that when we consider paradoxes to do +with truth + + align:start position:0% +with truth + + + align:start position:0% +with truth +that they then + + align:start position:0% +that they then + + + align:start position:0% +that they then +go and find + + align:start position:0% +go and find + + + align:start position:0% +go and find +a text on the philosophy of language and + + align:start position:0% +a text on the philosophy of language and + + + align:start position:0% +a text on the philosophy of language and +think more about that \ No newline at end of file diff --git a/L7ywsci9ujo.txt b/L7ywsci9ujo.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e3d520c854463f132fee4907c87db82a4556bb6 --- /dev/null +++ b/L7ywsci9ujo.txt @@ -0,0 +1,4220 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT +courses, visit MIT + +OpenCourseWare at ocw.mit.edu, + +ERIK DEMAINE: Today we continue +our theme of dynamic graphs. + +This is the second +of three lectures. + +And this will be the main +lecture about upper bounds + +for general graphs. + +Last class was about +link cut trees. + +And we saw, essentially, +how to solve + +a problem called dynamic +connectivity, which + +is where you can +insert into lead edges + +and you want to know +what's connected to what. + +For trees, we solved it. + +We're going to solve it again +for trees in an easier way. + +Because we need a slightly +simpler data structure + +we can augment in different +ways, called Euler-tour trees. + +And then we'll solve +trees, yet again, + +in a setting where you +can only delete edges. + +Then we can get from log +n time to constant time. + +So we'll still talk about +trees for quite awhile. + +But then we'll finally +get to general graphs. + +And we'll do a log squared n +solution for general graphs. + +So just another log +factor more, you + +can generalize from trees +to undirected graphs. + +And then I'll give you a +flavor of what's out there. + +Dynamic graphs is a big world. + +It has lots of results. + +And I'll give you some idea +of what other problems have + +been studied in dynamic graphs, +both undirected and directed. + +Though for directed graphs, +things get pretty slow. + +Yeah, next class will be +about lower bounds, which + +will prove that this log +stuff is actually necessary, + +in case you were wondering. + +Because a lot of +the time, we've been + +able to get better +than log in this class. + +And dynamic graphs, you can't. + +They're log lower bounds. + +So let's start out with a +definition of the problem. + +We'll be focusing, today, mostly +on this dynamic connectivity + +problem. + +Maintain an undirected +graph subject to [INAUDIBLE] + +insertion and deletion. + +And you can also insert and +delete degree-0 vertices. + +But we're not really going +to worry about vertices. + +It's easy to add vertices +that have no edges to them. + +Also easy to delete them. + +It'll be more about adding +and removing edges incident + +to those vertices. + +And then the query connectivity +query is given two vertices. + +Is there a v to w path? + +So this is asking are +two vertices, v and w, + +in the same connected component? + +That's a strong query. + +In some sense, a weaker query +is just to know globally, + +is the graph connected? + +That's another interpretation +of dynamic connectivity. + +It turns out, both +of these problems + +are interesting and useful +for solving problems. + +But they also turn out to +be, more or less, equivalent. + +All the upper bounds +we know for one + +apply to the other +and vice versa. + +So it doesn't seem to make much +difference which kind of query + +you want. + +So might as well take both. + +We'll focus on the v, w query. + +OK. + +So that's the +problem, in general. + +And I want to introduce +some terminology, + +like when we had partially +and full persistence, + +there's also a partial +and full dynamicness. + +A fully dynamic +data structure is + +one where you can do inserts +and deletes of edges. + +And a partially +dynamic data structure + +is one where you can +do inserts or deletes. + +So you can only do +inserts, or you can only + +do deletes throughout the +lifetime of the data structure. + +And these have specific names. + +Because usually you use +different data structures + +for just insertions +or just deletions. + +Just insertions is +called incremental. + +And just deletions is +called decremental. + +The idea of +incremental algorithms + +is definitely not a new one. + +But in dynamic graphs, +it always makes sense. + +So in general, a +dynamic graph problem + +is defined usually by insertion +and deletion of edges, + +and either fully dynamic +or partially dynamic. + +And then the query +is what can vary. + +We're going to focus on +connectivity queries. + +But you could do others. + +So this explains, for +decremental, we're + +going to solve trees +in constant time. + +For fully dynamic, we're +going to solve general graphs + +in log squared n time. + +I guess these three are sort +of the meat of the lecture. + +But before I go +into that, I want + +to tell you where this dynamic +connectivity results fit + +into the literature in general +on dynamic connectivity. + +This is part of our survey, but +just on dynamic connectivity. + +Well, for trees, this +is the best we know. + +This is the best, +possible really. + +You can do log n in general, +and then decremental. + +You can do constant. + +We actually already know how to +do trees with lint cut trees. + +It's not totally obvious, +but you can use links + +to simulate edge insertions. + +And you can use cuts to +simulate edge deletions. + +It's not totally obvious +because the link operation + +requires that one +of the vertices + +is the root of its tree. + +So that's not so trivial. + +But we'll see an easy way to +do that in Euler-tour trees + +later on. + +So this we kind of +already know how to do. + +But we're going to see +another simpler way. + +The constant time +amortized decremental + +we're going to do today. + +So we're also going +to do this today. + +Incremental, I don't think it's +known, how to do constant time. + +But I'll tell you +another result. + +You can get almost +constant time. + +Another special type of +graph you could consider + +is a plane graph. + +This is a graph with +planar embedding. + +So as you're inserting edges +or adding vertices and whatnot, + +you say which face they live in. + +And so you have a +fixed planar embedding. + +It's being constructed +as you go along. + +These are easy to maintain. + +You can get order log n. + +I guess, in some sense, +that generalizes trees. + +Because they also have pretty +obvious planar embedding. + +So that's something +you can do, in log n. + +But the big question +is, for general graphs, + +can you do log n per operation? + +That's an open problem, probably +the central open problem + +in dynamic connectivity. + +But we're not so +far away from that. + +As I said, you can +get log squared. + +Let me say what the +log squared result is. + +It's a little bit better +than just log squared. + +You get log squared +update, but query + +is actually sub logarithmic. + +You got a log n over +log log n query. + +And another result is +you can do a little bit + +better than log squared. + +You can do log times +log log n cube update. + +So roughly log n update, but +there's some poly log log term. + +And query slows +down very slightly. + +It becomes log n +over a log log log n. + +Well, it'll sort of makes +sense why in a moment. + +So the lowest update time known +is this one, log times log + +log cubed. + +Big open question is whether +you can get log for update, + +and any kind of +reasonable query time. + +But ideally, log for both. + +So that's for a fully dynamic. + +If I don't say any +otherwise, fully dynamic + +is always the default. +Result, that's + +the case you usually care about. + +Cool. + +But if you want +to do incremental, + +you can achieve an alpha bound. + +Because incremental dynamic +connectivity is really + +the union find problem. + +Union find, you have a +bunch of sets of elements. + +You can take two of them +and union them together. + +Once they're unioned, they +can never be split apart. + +And find is tell +me what set I'm in. + +So if I do find +on two vertices, I + +can find which connected +components there + +and check whether +they're the same. + +That will give me +connectivity query. + +Insertion corresponds to +merging two connected components + +unless they were +already together. + +And it's known you can get +an alpha amortized bound. + +And that's optimal +for that problem. + +So I guess that's +actually a theta. + +So that's sort of +well-known stuff. + +It's a complicated analysis, +but already been done. + +So in particular, that's, +I believe, the best way + +we know how to solve incremental +connectivity in trees. + +Though I'm curious whether you +can do constant incremental. + +Decremental, there's +essentially a log n solution. + +Not quite, but for dense graphs, +there's a log n solution. + +So I'm stating, instead +of a bound per operation, + +this is a total bound. + +Let's say you start +with an m-edge graph + +and you delete all the edges. + +Then you pay log +n for each edge. + +But you also have to pay +this n poly log n cost. + +So if m is a bit bigger +than n, then this dominates. + +And so it's log n per operation. + +But if you have a +sparse graph, it's + +still poly log per operation. + +So decremental, we can kind +of get log for general graphs. + +Another goal you might +have is what if I wanted + +to get worse-case bounds? + +Everything I've said +so far is amortized. + +If you want to get worse +case, not much is known. + +Big open question is, can I +get a poly log updating query. + +So it was actually a pretty big +breakthrough to get poly log + +whatsoever. + +This first result +is from 2001 or so, + +after people have worked on +dynamic graphs for probably + +a decade. + +So it took quite a while to +find this any kind of poly log. + +That still hasn't +been made worse case. + +So the best results +are state of the art + +at the time, before +the poly log came out, + +which is square root of +n update, constant query. + +There's one other result +for worse case, which + +is if you want to do an +incremental solution, + +so you're just inserting edges. + +Then there's a bound. + +It's actually a whole trade off +between updates and queries. + +If you have updates +to take order x time, + +then you get queries that +take log n over log x time. + +So log base x of n. + +And that's optimal. + +These are theta. + +There's matching lower bounds. + +So this is again, +really union find. + +And so union find has +been well studied, + +even in the worse-case setting. + +Can't do as well as +alpha, basically. + +OK. + +And then finally, I want +to talk about lower bounds. + +So there are two +complementary results. + +But maybe first I'll +summarize by saying you need + +omega log n update or query. + +One of them has to +be at least log n + +to do dynamic connectivity. + +As you see, queries +can be sublogarithmic. + +We don't know how to make +updates sublogarithmic + +and get any +reasonable query time. + +But one of them has +to be at least log. + +And here's the specific +theorems that imply that. + +That's actually similar to this +result, but not quite the same. + +Because there's a log +on the left-hand side. + +And these results hold +for amortized solutions. + +Whoops. + +Key word's missing here. + +This is an update bound. + +And this is a query bound. + +So these are basically +symmetric results. + +Says if you have super +logarithmic update, + +so you have some x bigger +than 1 times log n update, + +then you get log n +over log x query. + +That's a lower bound. + +If you have a super +logarithmic query, + +so let's say it's x +times larger than log n, + +then you need at least a log +n over log x update time. + +So this result is +the one of relevance. + +Because we don't know any +sublogarithmic updates. + +But we do know +sublogarithmic queries. + +So this is the +regime that we have, + +essentially, matching +upper bounds. + +Let me show you. + +This result, this +result, and this result, + +even, are, in some sense, +tight against this trade-off, + +this update query trade-off. + +So this update is +log n times log n. + +So x is log n. + +And over here we get +log n over log log n. + +So that's tight against that. + +Here, also, we have here +x is log log n cubed. + +So you take a log of log log n +cubed, you get log log log n. + +So that's why there's a +log log log n down here. + +That's the best +you could hope for, + +given that update time, +that's the best query + +time you can get. + +Same over here. + +Given an update time of root +n, well, of course, the best + +you can hope for +is constant query. + +But indeed, it works out. + +As you're taking log n +divided it by 1/2 log n, + +you get constant. + +So these results, they +may sound suboptimal. + +But a certain sense, +they're optimal. + +Of course, these are just single +points on the trade-off curve. + +We still really care +about the situation of-- + +where's the open +problem here-- log n + +update and query, that +would still be ideal. + +But these are not as bad +as they look, is the point. + +Of course, it'd be better +if this wasn't a 3, + +it was only a 1. + +But they're still, +in a certain sense, + +tight against this, the +query bound that you get. + +Another open problem +here is whether this, + +the reverse situation, +is ever relevant. + +Can you have a +sublogarithmic update time + +and get any poly log query time? + +So this is another open problem. + +Little o of log n query. + +Sorry, little o of log n update, +and let's say poly log query. + +The lower bound kind of predicts +that something like this + +ought to exist. + +But it may be it's +just impossible. + +And there's a different lower +bound that makes it impossible. + +Some theta I wanted to add here. + +OK. + +Another fun thing +about this lower bound, + +is that it holds even if +your graphs are paths. + +So in particular, that tells us +that this dynamic tree result + +that we covered last +class, say, you need log n. + +If you're going to do +both operations and log n, + +that's optimal. + +Even if your trees +are paths, which + +is like the really easy case. + +And we're going to prove +this theorem next class. + +So if you want, that'll +be our last class, + +our last lower bound. + +That's next time. + +Tune in next time. + +But today we're going to +focus on upper bounds, namely + +these two and this one. + +So let's do them. + +The first one is +Euler-tour trees, + +which is another way +to do the log n bound. + +It's something we need. + +We'll need it for doing +the log squared solution, + +for a reason we'll +see in a moment. + +So Euler-tour tress go back +to 1995, Henzinger and King. + +They're simpler dynamic +trees, simpler than link cut, + +even though they're newer. + +And the key difference +compared to link cut trees + +is that they let you +do stuff with subtrees + +of the tree instead +of paths of the tree. + +Link cut trees are great. + +We could compute +the min or the max + +or the sum of a bunch +of weights on any path + +that we cared about. + +But for various reasons, we +want to do the same thing + +on subtrees. + +And this turns out to be easier. + +So what do we do with +Euler-tour trees? + +We take an Euler-tour. + +Remember Euler-tour from-- I +can never remember-- lecture 15. + +[LAUGHS] + +I don't quite remember +what that lecture was. + +When did we do Euler-tours? + +Well, doesn't matter. + +You remember the idea +of an Euler-tour. + +It was just walk around the +tree, do a depth for search, + +and keep track of every +time you visit a node. + +So you visit some +nodes multiple times. + +In general, the +degree of the node + +is the number of +times you visit it. + +Every edge gets +visited exactly twice. + +So it's the linear +number of visits total. + +I just want to take that +linear order of visits, + +pull it out straight, store +that in a balanced binary search + +tree. + +That's Euler-tour trees. + +They're very simple. + +Store the node visits +by the Euler-tour, + +and a balanced +binary search tree. + +What's the order? + +We're storing them +in order by the order + +that the Euler-tour +visits, the visits. + +So this will be the left-most, +the min in the tree. + +This will be the +next and then next. + +So if you do an in-order +traversal of the tree, + +you should get the +visits in this order. + +This is, of course, a way to +balance a tree, in some sense. + +I drew a balanced +tree as the thing + +we're trying to represent. + +But again, it could be a +totally unbalanced thing. + +But when you do an Euler-tour, +you get order n visits. + +And you throw them into +a balanced binary search + +tree, it's balanced, of course. + +It's a bit of a weird thing, +because you're not really + +preserving the structure +in an obvious way. + +But there's one +more thing we store, + +which will let us do, +essentially, whatever we want. + +Each node stores two +pointers into this structure + +to the first and last visit. + +So like this node has a +pointer to its first visit + +and its last visit +along this structure. + +It doesn't keep track +of any middle visits. + +Because there could +be a lot of those. + +And we just want to have a +constant number of pointers. + +This is going to be a pointer +machine data structure + +just like link cut trees. + +Let's see. + +How do we solve our operations, +inserting and deleting + +of edges and connectivity? + +Actually, I'll start +with just phrasing it + +like link cut trees. + +We can do most of the +link cut tree operations. + +Remember, there was a +find root, link and cut + +were our main operations. + +Than there was aggregation. + +But that will have to change. + +But if we want to do find root-- + +so we're given one of these +balanced binary search trees. + +In it is the node v. +Well, actually, it's + +a little weirder here. + +But we have some +node v in our tree. + +And really, we have +our pointers into this. + +This is a balanced +binary search tree here. + +We have pointers to the +first and last visit in here. + +I don't care. + +Just take any visit, +anything in here, + +just say the first visit of +v. Then walk up the tree. + +Then walk down the +tree on the left spine. + +That is the min. + +And that's going to be the +first visit of the root node. + +And so this has a pointer, +in turn, to the root node. + +Boom, you found the +root of your tree. + +Again, we're maintaining +forest of trees. + +And so we just need to +find which tree v is in, + +walk up, walk down, +that's order log + +n, because this +thing is balanced, + +and we found the root. + +So that's easy. + +Turns out, the other +operations are not too easy + +if you can split and +concatenate your tree. + +So let's start with cut. + +We need a bigger diagram. + +So here's v. Here's the +parent of v. I'll call it w. + +Here's the edge. + +And our goal, and +the cut operation + +is to delete that edge, separate +this tree from that tree. + +So what I need to do is +isolate this subtree of v. + +But conveniently, if you +think of the Euler-tour, + +the Euler-tour, it +does some stuff here. + +Eventually it follows this edge. + +Visits v for the +first time here. + +Then it visits all +the stuff down here. + +Then it visits v +for the last time. + +Then it follows this edge +and then does other stuff. + +So the v subtree is a contiguous +interval of the Euler-tour. + +So we just cut it +open, cut it apart. + +So we split the BST at +the first and last visits + +to v, which is +exactly what we know. + +We have a pointer from v to +its first and last visits + +in the Euler-tour. + +So split the tree there. + +Split the tree there. + +You know split in a +binary search tree. + +You're given a particular +key value, let's say, x. + +And you split into +everything less than x, + +and everything great than +or equal to x, or something + +like that. + +That's a split operation. + +It can be done in +log n time, and pick + +your favorite balanced +binary search tree. + +Red-black trees, AVL +trees, they can all + +do this and maintain +balance in these two things. + +Even though they might +be very different sizes, + +they'll both be log height +relative to their own size. + +This is obviously +not quite enough. + +Because what we've +done is basically + +cut here and cut here. + +Now we have three trees. + +We have the one we want +for v, v is subtree. + +That will correspond +to the Euler-tour + +of exactly that thing. + +So this is the represented +tree I'm talking about. + +And this is the balanced +binary search tree. + +But the rest of the +tree is in two parts. + +There's the part +to the left of v, + +before we visited v, the +part after we visited + +v. Those we just have +to stick back together, + +so we concatenate them. + +Yeah. + +So I'll call them the before-v +tree and the after-v tree. + +There is actually a tiny +thing that has to happen here, + +which I just remembered. + +Which is we need, somewhere, +to delete one occurrence of w, + +of the parent of v. + +Because it used to be we +visit w, then we visit v, + +blah, blah, blah. + +Then we visit w again. + +If we cut out this +part, we're going + +to have two visits +to w in a row. + +We really just want one visit. + +So this is a minor thing, but +we need to do a delete in there. + +So each of these is log n time. + +So the overall time is log n. + +Easy. + +This is a cut-and-paste kind +of argument, all pretty cheap. + +OK, now let's do link. + +Concatenate is the reverse +of split, by the way. + +You have two trees. + +All the things in +the left are smaller + +than all things in the right. + +You just want to +join them together + +like a very restrictive +kind of merge. + +So join, recall, is you have a +node v. And you want to make it + +a new child of w. + +w might have other children. + +It lives in some bigger tree. + +We want to add v +as a child of w. + +So we're assuming here +v is a root, for now. + +So what do we do? + +Sort of the same thing. + +We sort of know we want to +put v in here somewhere. + +It actually doesn't really +matter where we put it. + +We're not keeping track of +the order of nodes in here. + +So I'm going to simplify +my life and say, + +let's put v at the end. + +I want to make v the last +child of w, like this. + +So we can find the last +child, in some sense. + +After we visit the last +child, we come back + +and do the last visit to w. + +So I'm going to look +at the last visit of w, + +cut the tree open there, +and stick this part in. + +Cut the Euler-tour +in half there. + +So split. + +w is tree at w's last visit. + +Right? + +And then we do +omega concatenate. + +We're going to +concatenate, basically, + +before w's last visit. + +We're going to concatenate +a single occurrence of w. + +Because there's a new +occurrence of w now. + +We do it before and after v. + +So we add another w. + +Then we add v's +Euler-tour, v's BST, + +and then we do after +whatever used to be there + +after w's last visit. + +Let's say, after and +including that w visit. + +So just the symmetric +of this, here + +we had to delete +one occurrence of w. + +Here we have to add one back in. + +But you just cut, paste +in the thing you need, + +and rejoin everything. + +So again, very easy. + +It's a constant number +of log n time operations, + +if you can do split and +concatenate in log n time. + +So you see this, it's like wow, +why do we spend so much time + +with link cut trees? + +This is really easy. + +But they have their +different applications. + +If you want to compute +aggregates on paths + +you need to use link cut tress. + +It's the best we know. + +This structure will not +do aggregates on paths. + +But it will do +aggregates on subtrees. + +Because subtrees are +represented by these intervals + +in the Euler-tour tree. + +So if you have a weight +on all the nodes in here, + +say, you can easily +find this interval + +and do a range query there. + +So you take the min +of all those things. + +If you have subtree +mins, you can + +take the min of log n +things and in log n time, + +compute the min in an +interval, or min over + +a subtree rooted at a node, +or max or sum, or whatever. + +So here you can do subtree +aggregation in log n time. + +And we're going to need that +for the log squared solution. + +One other thing I +wanted to maybe mention, + +here we did join. + +And join assumed that v +was the root of its tree. + +What if v is not +the root of its tree + +and we still want +to insert an edge? + +Because insert, when +we're maintaining + +an undirected graph, +there is no rootedness. + +That rootedness is just a tool. + +You could say at the first +step here, just root the tree + +somewhere so that we can +have a well-defined beginning + +and end to the Euler-tour. + +Of course, Euler-tour in +it's the most natural form, + +is actually a cycle. + +And it would only +have one visit here. + +So you can think of it that way. + +I'd still like to have the +two visits conceptually, + +because that makes even the +subtree rooted at the root + +an interval between the +beginning and the end. + +But the nice thing +of the cycle view + +is if I wanted to +change who the root is, + +say I want this node to +be the root, that's just + +a cyclic shift of everything. + +It just means I want to start +the cycle here and end it here. + +So I'd basically duplicate this +copy of the vertex, singlify + +this one. + +There's only one copy. + +That's the constant number +of inserts and deletes. + +And now rotate. + +[LAUGHS] + +What does it rotate mean? + +Well, before it was +a sequential order, + +starting here, ending here. + +Now, I want it to be a +sequential order, say, + +starting here, continuing this +way, and then ending back here. + +So if you look at what +that requires, maybe + +use another color, +I want this part. + +That's an interval of the old +tree, of the old sequence. + +And then I want this part. + +So there's two pieces +of the old tree. + +And I just want to +change their order. + +It's a cyclic shift. + +Cyclic shift is just a cut and +then a rejoin the other way. + +So I can reroute a tree +in log n time as well. + +So this is why, in this world, +join is equivalent to insert. + +If I want to do +a general insert, + +first I reroute v's tree. + +I do a cyclic shift with +one split one concatenate, + +like this. + +And I get v to be the root. + +Then I can do the join. + +So again, constant number +of splits and concatenates. + +So it's another operation +we can do, in log in. + +Everything here is log n. + +Cool. + +Any questions about +Euler-tour trees. + +That's all I'll say about them. + +We will next move +on to next result. + +AUDIENCE: Can link cut +trees also do a reroute? + +ERIK DEMAINE: Can link cut +tress also do a reroute? + +I haven't thought about that. + +I would guess so. + +[LAUGHS] + +But it's going to require +some more thought. + +So let's see, link cut tree, +we can do a little aside here. + +Link cut tree, we +do an axis on v. + +So now we get that v is +up here, right at the root + +of the tree of oxx trees. + +Now we've got other trees of +[INAUDIBLE] trees hanging off + +here. + +But in particular, this +thing represents a path. + +It represents the +route to v path. + +It actually has no right child. + +So it's a little bit +emptier, like that. + +So now we want to flip things +around and say v is the root. + +We basically want +to reverse the order + +of all the nodes in this tree. + +So reversing the order of +nodes in a binary search tree, + +you can't regularly do. + +But if you augment your +data structure to say, + +I could basically mark +these nodes as all inverted, + +treat left as right +and right as left. + +It's basically the +dyslexic approach. + +You have a bit +saying from here down + +to here, mark +everything as dyslexic. + +And so you invert +left and right. + +So I think, with this +appropriate augmentation, + +you can reroute the +tree in log n time. + +But of course, there's +some details to check. + +It might even be that's in the +original link cut tree paper. + +But I don't remember offhand. + +So I'm pretty sure it +works, and therefore, + +gives you dynamic connectivity. + +But if it doesn't, +Euler-tour trees do it too. + +So we're covered either way. + +So that's Euler-tour trees. + +Next on our list is decremental +connectivity in trees. + +So we're going to solve +a weaker problem, which + +is just deletions only instead +of inserts and deletes. + +We're going to solve it faster. + +Constant time per operation. + +This is just a +fun little result. + +It's fun because it uses +some techniques we know. + +So bound is constant amortized, +assuming all edges get deleted. + +We need to assume +this, essentially, + +because we're amortizing +against the future. + +So we need to get all +the way to the end. + +Overall, over n operations it's +going to take order n time. + +This is, again, a +series of refinements, + +or a bunch of pieces of +the solution that get + +combined together, not +a sequential algorithm. + +So the first observation is, of +course, we can do order log n. + +We know, now, maybe +two ways to do it. + +But you can use Euler-tour trees +and only do cuts, life is easy. + +Link cut trees, you +could also just do cuts. + +You don't even need rerouting. + +Rerouting was only for joins. + +So that may seem obvious. + +But how do we reduce +the log n to a constant? + +In general, in this class? + +AUDIENCE: Make up tables. + +ERIK DEMAINE: Indirection, +and maybe look up tables. + +Yep. + +How do we do +indirection in a tree? + +AUDIENCE: Leaf pruning? + +ERIK DEMAINE: Leaf +pruning, leaf trimming, + +whatever you want to call it. + +Should call it the Edward +Scissorhands approach, + +or something. + +So leaf trimming, +what I want to do + +is cut below +maximally deep nodes + +that are [INAUDIBLE] log n. + +Say with greater than +log n descendants. + +So we have our top tree. + +And then hanging +off some nodes here, + +we're going to have +some bottom trees. + +These each have, at +most, log n nodes. + +These have bigger than +log n nodes below them. + +So we can charge every +leaf in the structure + +to the log n nodes below it. + +And so up here we have at most, +sorry, n over log n leaves. + +Not nodes. + +Nodes could still be linear +if the graph is a path. + +But at most, n +over log n leaves. + +So we have, at most, n over +log n branching nodes up here. + +So what we need is a +structure for dealing + +with long paths in +the top, a structure + +for dealing with log n +size things down here, + +and a structure for +combining the paths together. + +And that's the easy part. + +If we treat each long +path as a single edge, + +basically, we look at +the compressed top tree, + +in the sense of +compressed tries. + +But it's now a tree +instead of a try. + +I guess it's a try. + +Whatever + +We look at the +compressed tree up here. + +That will have +size, n over log n. + +And then we can afford +to use structure one. + +Why? + +Because in some +sense, there only + +be n over log n +operations performed. + +So it's not a space issue +there we're trying to save. + +It's a time issue. + +So a little different +from the past. + +There are only n +over log n times + +that you can destroy +a path up here. + +Because there's only +n over log n paths. + +Each time you destroy a path, +I do an operation up here, + +I pay log n. + +But if the total number of +operations n over log n, + +total cost is linear. + +So constant amortized +against the future. + +So I'm going to use structure +one on the compressed top tree. + +And what remains is what +I do in the bottom trees? + +What I do on the paths? + +And then how do I combine +all those results together? + +Let's first talk about how +to combine the results. + +There are a couple +of different cases. + +It So we're doing +a query on v, w, + +and we want to do +connectivity query. + +So it could be that v and w +are in the same bottom tree. + +In that case, we just need to +do a query within a bottom tree. + +So as long as we can solve +the bottom tree case quickly, + +we're happy. + +Constant time, I guess. + +That will turn out +to be pretty easy. + +That's the easy case. + +Otherwise they could be +in different bottom trees. + +So it could be v's down here and +w's in some other bottom tree. + +So then we have three +queries we need to do. + +One is like this. + +We need to test the single +edge, but that's trivial. + +And then we need to +do a query in the top. + +Can you get from here to here? + +Now, these nodes are +a little bit special, + +because they are leaves. + +They will be at +the ends of paths. + +So this is really just a query +we can do using structure one. + +Because we take either an +entire path or no path at all. + +So we can look at +the compressed tree + +and that's enough, +because the leaves + +exist on the compressed tree. + +That's not always the case. + +A different situation is this. + +We might have, for example, +v up here, w up here, + +and v and w are not down here. + +So these are irrelevant. + +We just want to know, in the +top tree, can I get from v to w? + +Now, this is a +little more awkward + +because v is going +to live on some path. + +w is going to live on some path. + +But it might be in +the middle of a path. + +And so there's now three +queries we need to do. + +One is can I get to +the top of my path? + +And then can I get from +one path to the other? + +So these are +branching nodes here. + +And can I get from +this branching node + +to that branching node? + +It might not always be going up. + +Sometimes you have to go down. + +But point is, a constant number +of queries to path structures, + +to compressed structures. + +This is, again, +the one structure. + +And a constant number of +calls to a bottom structure + +will suffice to +answer the query. + +There's a few more cases +that I haven't drawn. + +If you could be half of +this and half of this. + +But it can all be +done, as long as we + +can solve bottom and paths. + +So let's solve paths +first, I think. + +Oh no, bottom trees, fine. + +So part 3 of the solution +is solve a bottom tree. + +Here we can do it in +constant worse case. + +So this is essentially +the lookup table thing, + +although it's a pretty +simple lookup table. + +What we do, bottom tree +has only log n nodes. + +So we can represent 1 bit +per node in a single word. + +And what we'll do, store +bit vector of which + +edges have been deleted. + +In what order? + +I don't really care. + +Just pick some fixed order +on the edges down here, + +and store the bits +in that order. + +And say every edge +knows its sequence. + +So you could do a depth first +search at the beginning, + +to label the edges in +some canonical order. + +And then every edge knows +what its bit position + +is in the vector. + +So when I go to +delete an edge, I just + +set that one bit +using an or operation. + +Cool. + +So I can delete edges. + +I can actually even insert edges +down here that used to exist. + +I could undelete an edge. + +But that only works in +the bottom structure. + +So not generally useful. + +OK, so it's clear how to do +an update, how to do a delete. + +I just mark a bit. + +How do I do a query? + +I want to know, given two +nodes, v and w, one of them + +could be the root of the tree. + +I want to know can +I get from v to w? + +Or there's only a single +path that might exist. + +So it's a matter of has any edge +along this path been deleted? + +So a general way to +write that is I have w. + +I look at v's path to the root. + +I look at w's path to the root. + +At some point, +we've reach the LCA. + +What I want to know is, have +any of these edges been deleted? + +If yes, I can't get there. + +If none of them have been +deleted, I can get there. + +It's an if and only if. + +I don't care about these +edges up here above the LCA. + +Because I only need to go +to the LCA and back down. + +So what do I do? + +Each vertex stores a bit +vector of its ancestors, + +of the ancestor edges. + +Well, ancestor edges +is kind of weird. + +It stores a bit vector +representing its path + +to the root. + +That's this red stuff. + +I want to know, +for vertex v, what + +are the edges along the path to +the root of this bottom tree? + +Just preprocessed. + +You can build this thing as +you do the depth first search + +and store it. + +Again, it's one word per vertex. + +So I can fit it +with constant space. + +It's constant space overhead. + +And now, if I have +two vertices, I + +take the XOR of those two paths. + +That will give me this part. + +And then I use that as a mask +into the bit vector, say, + +are any of these 1? + +How do I do that? + +I just mask. + +And if the result is the 0 word, +then I know none of them are 1. + +Otherwise, I know some edge +was deleted and I'm screwed. + +So I take XOR of v's +path and w's path. + +And then I mask this thing, +which stores which edges + +were deleted. + +And then I check whether +that word equals 0. + +If it equals 0, yes, +I can get there. + +If it doesn't equal +0, I can't get there + +because some edge was deleted. + +So very easy, because we can +fit log n bits in a word. + +OK, that's the bottom +tree structure. + +Next we need a path structure. + +Here we can use due constant +amortized with a similar trick. + +So here's our path. + +We're going to use, +essentially, indirection again. + +Again, we know how to +solve this in log n. + +When we have a sequential thing, +our usual way of indirection + +is to split into chunks. + +Each chunk here, I need +to be about log n in size. + +So I'll just make it +exactly log n in size. + +So there's n over log n chunks. + +So if I store a +summary vector, we + +can think of these +as being 0, 1, 0, 1, + +whatever, where the 1's mean +this edge has been deleted. + +0 means it hasn't been deleted. + +All right, let me write n over +log n chunks, each log n edges. + +And I'm going to store +each chunk as a bit vector. + +Bit vector has log n bits. + +w's at least log n. + +So I can do the same sort +of things I could do before. + +If I delete an edge, I just set +a 1 bit in the chunk vector. + +Now, that's good +for local queries. + +If I want to do a +long-distance query, + +I need to basically summarize, +are any of these edges deleted? + +If so, I'll put a 1 up here. + +Any of these edges deleted? + +If not, put a 0. + +And now, I want to +structure over-- this, + +you might call the summary +vector, like in [INAUDIBLE].. + +Done that before with +indirection as well. + +Now, this summary vector +has size n over log n. + +So I can afford to use our log +n solution that we started with. + +So use 1 on summary +vector of chunks. + +Because again, the first time +I set one of the bits in here, + +I have to do an update up here. + +But only then. + +Once it's been done once, I +don't have to update again. + +So there will only be +n over log n updates. + +So I can afford +log n per update. + +It'll still be linear time +total, constant per operation + +amortized. + +So this is my solution. + +If I have a query, let's say +I want to know between here + +and here, I first check, can +I get to the right endpoint + +locally? + +Which is a query +within the chunk. + +Which is again, I just +mask out these bits. + +I say and now do I +have the 0 vector? + +In which case, nothing I +care about has been deleted + +and I can get there? + +Or if I don't have the 0 +vector, I can't get there. + +I want to know, can I get +to the left from here? + +Again it's a mask and +a check against 0. + +And then I want to +know, can I go over + +this interval of chunks? + +And that, I can use +the summary vector for. + +And again, that is a +mask of a subinterval, + +and then checking +whether it has 0. + +So I take the and of these +three results, and I'm done. + +That gives me a +query over a path. + +So it's kind of fun. + +We use two levels +of indirection. + +One to reduce the +number of leaves. + +And then these were +sort of trivial. + +And then within the structure, +we could only afford things + +on the non-branching +part, so we had + +to deal with paths separately. + +And there we use another +level of indirection. + +But in the end, we get +rid of all of our logs. + +And it's constant amortized +for deletions in a tree. + +Questions about that? + +That was our second +result. We have one more. + +Last result we're +going to talk about + +is log squared n +update, log over log log + +query, for general graphs. + +Finally, we graduate from +trees to general graphs. + +This is a result by Holm, +de Lichtenberg, and Thorup, + +2001 is the journal version. + +So we want to solve +dynamic connectivity. + +We want to understand, +in general, + +when two vertices are in +the same connected component + +or not. + +That sounds tricky. + +We're going to do that +in a pretty simple way + +at a high level. + +High level is, we want to +store a spanning forest. + +You know what a +spanning tree is. + +Spanning forest, well, your +graph might be disconnected. + +That's the whole point +of the data structure. + +If it's not disconnected, +you answer yes all the time. + +When it's disconnected +you say, OK, I'll + +have a spanning tree for +this connected component, + +spanning tree for every +connected component. + +Together we call that +a spanning forest. + +That's the maximal connectivity +you can get, but represented + +as a tree. + +Now, we have a great +way to represent + +trees, Euler-tour trees. + +And if you somehow connected +together two components, + +that is an insertion of an edge +in an Euler-tour structure. + +Great. + +So we can maintain all +these connected components + +and merge them if we +have to, using an insert + +in Euler-tour structure. + +And to do a connectivity query-- + +I don't think I mentioned this-- +you do find root on v and w, + +see whether they're +the same root. + +Because root is a canonical name +for the connected component. + +You can solve connectivity using +find root in constant time. + +Well, constant extra time, +log for the find root. + +OK, so everything looks great. + +I can connectivity. + +I can do insertion. + +What about deletion? + +If I delete an edge that is +not in my spanning forest, + +I'm happy. + +I have exactly the same +connectivity as before, + +as proved by the +spanning forest. + +The trouble is when I +delete an edge that's + +in the spanning forest. + +Then it's like, uh, maybe. + +So here's spanning +tree, whatever. + +And now let's say I +delete this edge here. + +Then there's a +couple possibilities. + +It was a graph, it's not a tree. + +So there could be +some other edge + +that connects those two trees. + +Then I have to find it. + +Oh, I'm going to find it. + +That's going to be annoying. + +Or it could be +there's no such edge. + +Then I'm fine. + +Then it's just a cut. + +But distinguishing +those two cases + +is going to be our challenge. + +And that's where we're going +to lose another log factor, + +but only another log factor. + +To only lose another log +factor, what we're going to do + +is not just store +one spanning forest. + +We will store the +spanning forest, + +but then we're going to +hierarchically decompose it + +and say, well, yeah, +there's this big tree. + +But some of the edges I'm going +to put in the next level down. + +Some I won't. + +So some subset of this forest +will be at the next level down. + +And there's going +to be log n levels. + +That's where we +lose our log factor. + +And the weird thing is, +there's no real reason + +to put things down, except we'll +use it as a charging scheme. + +We'll prove that an edge can +only go down log n levels. + +And then it has to get deleted +before it becomes relevant + +again. + +So it will let us charge +only log n times per edge. + +OK, that's about as +good as I can give you + +a high-level overview. + +Now we have to see the details. + +It's kind of amazing that +this works, but it does. + +So we're going to talk +about the level of an edge. + +This is not a +definition, per se. + +But it's a change in +quantity over time. + +As you do edge +deletions, some edges + +are going to decrease in level. + +They all start at log n. + +Log n is going to +be the top level. + +That's the whole +spanning forest. + +They will only decrease, +so it's monotone. + +And they can never get below 0. + +So we start at log n. + +They could go down. + +And the lowest value is 0. + +Now, Gi is my graph. + +And G is going to be the +subgraph of lower-level edges. + +It's going to say, level +less than or equal to i. + +So in particular, G log +n is the whole graph. + +So we always include +lower-level edges. + +So level 0 is going to +appear in all the Gi's. + +But if we look at G 0, +it's only level 0 edges. + +G1 is level 0 and 1. + +And so this is sort of a +hierarchical decomposition + +of the graph. + +We have fewer edges +at the bottom levels. + +And there's going to +be two key invariants + +we have over these structures. + +In variant one it's is going +to be every connected component + +of Gi is small. + +It's going to be size, +at most, 2 to the i. + +This is really +what's going to let + +us charge against something. + +Whenever you go down +a level, the max size + +of a connected component +goes down by a factor of 2. + +So at level 0, all +components have size 1. + +There are no edges at level 0. + +So I kind of lied. + +I guess the lowest level is 1. + +At level 1, you can +have two vertices. + +So there can be +isolated edges in Gi. + +But that's it. + +You can't have a path of length +2 in G1, and so on up the tree. + +At G log n, you can +have the whole graph. + +Whole thing could be connected. + +But this will let us +charge to something + +as we go down in the tree. + +As we go down in +levels, I should say. + +So next thing we need is a +spanning forest for each Gi. + +Fi is going to be +spanning forest of Gi. + +So it's going to maintain the +connected components of Gi. + +And we're going to store that +using an Euler-tour tree. + +There's this issue +of pluralization. + +I'll say trees. + +Because Fi is disconnected. + +Each connected +component you use, + +you store using an +Euler-tour tree. + +Together, it's an Euler-tour +forest, I suppose. + +So that way we can do a query. + +And so given two +nodes, we can know + +whether they're in the same +connected component in Fi, + +just by saying whether they +live under the same root. + +Well, in particular, +that means that f + +log n, which is a +spanning forest of G log + +n, which is everything, that +will let me solve queries. + +This is the desired +spanning forest + +that will let me ask +connectivity queries. + +So all this +infrastructure is in order + +to support deletes efficiently. + +But queries are easy. + +We just look at the top forest. + +That's the one we want. + +OK, now second +invariant, this is + +where things get interesting. + +Variant 2. + +The forests have to nest. + +So F log n, of course, +has the most edges. + +F0 is going to have +the fewest edges. + +But I want them to be contained +in this nested structure. + +All this is saying is +that there's really only + +one spanning forest, F log n. + +Fi is just F log n, but +restricted to the edges of Gi. + +So really we're trying +to represent this forest. + +But then, as we look +at lower levels, + +we just forget about +the higher-level edges. + +Restrict to the lower edges of +level less than or equal to i, + +that's our smaller force. + +This is, in some sense, the +hierarchical decomposition + +of the forest. + +Because there's really +only one forest. + +That would make our +lives way easier. + +Fun fact, is that that +forest, then, is actually not + +just any spanning forest. + +It's a minimum spanning +forest, with respect to level. + +You've probably heard of +minimum spanning tree. + +Minimum spanning forest +is just the analog + +for disconnected graphs. + +So we're defining the weight +of an edge to be it's level. + +And so F log n can't just +be any spanning forest. + +It has to prefer +lower-level edges. + +Otherwise, this nesting +structure won't be true. + +Now, that doesn't uniquely +define the forest or anything. + +Because maybe all +the levels are log n. + +And then every spanning forest +is a minimum spanning forest. + +But it's a constraint +on spanning forest. + +Cool Let's go over here. + +Let me quickly say how to do an +insert and how to do a query. + +These are really easy. + +Delete is really +where the action is, + +but just to make sure +we're on the same page, + +and to introduce a +little bit of notation, + +and say a little bit +about what we do. + +We are going to store +incidence lists, which + +is for every vertex, we +have a list of the incident + +edges in a linked list. + +So in constant time, we +can add our edge to v + +and w's incidence lists. + +That's not maintaining any +order or anything special. + +Then we also set the level +of the edge to the log n. + +That's what I said, every +edge starts at level log n. + +And then there's one +more thing, which + +is if v and w are +disconnected, and F log n, + +we can tell that because we +can do a connectivity query + +on F log n. + +We have that as an +Euler-tour tree. + +So we can see whether v and w +are in different components. + +If they are, we +have to merge them. + +So we merge them. + +We This is what you +call an edge insertion. + +So this is an Euler-tour +tree insertion, + +that we know how to do in log n. + +We reroute and we do a join. + +So that's cheap. + +And that's it. + +So insertion is easy to do +in log n time, actually. + +Its deletion that's +going to be painful. + +Actually, we're going to +charge through the inserts. + +So it'll be end up being +log squared amortized. + +But worst case, it's log n. + +Great. + +I want to say a little +bit about connectivity. + +Now we know how to solve +connectivity already. + +We do find root on v +and w and in log n time, + +we determine whether they're +in the same component. + +But I actually claimed-- +it's maybe erased by now. + +Yeah. + +But I claim not to log n query. + +I claimed a log +over log log query. + +Turns out, that's +really easy to do. + +You just change the top +level minimum spanning forest + +slightly. + +So I want to make F log +n equal to a B-tree. + +Or actually, it's +a bunch of B-trees, + +one per connected component, +of branching factor log n. + +I guess it's a B-tree, so +I have to have some slop. + +Theta log n, let's say. + +Usually we said with +Euler-tour trees, + +it was a balanced +binary search tree. + +I'm going to make this +particular forest use a log n + +way, B-tree. + +This is going to +slow down updates. + +But it actually +speeds up queries. + +So to do a find root is +now a little bit easier. + +Find root should just +be log base log n of n, + +which is log n over log log n. + +Because find root, you just +need to go to your parent, + +to your parent, to your parent. + +Go to the top. + +And then you have to go +to the leftmost place. + +But it's easy, in a +B-tree, to always go + +to the leftmost place. + +If I had to do a +search within the node, + +that would be annoying. + +But going to the +leftmost, that's easy. + +So I only pay log over +log log for query, + +so I got my desired query time. + +And I claim the +update is kind of OK. + +Because it's slowed down, but +we're already going to pay + +log square eventually. + +And here we were doing log. + +So we don't need +to be that fast. + +Update is now going to be-- + +let's see-- the +height of the tree + +times the branching factor. + +If we touch nodes in +a root-to-leaf path, + +there's log over +log log of them. + +For each one, we have to +rewrite the whole node. + +So we pay log. + +But this is less +than log squared. + +So this won't end up hurting us. + +Because we only do this +at the top forest level. + +We don't do it at +all the levels. + +If we did it at +all the levels, we + +would lose another log factor, +log over log log factor. + +But here, we do this +once at the top, + +pay log squared over log log. + +Then we have to update log n +other levels, each paying log. + +So we're already paying log +squared for the lower level. + +So if we increase the top +level a bit, not a big deal. + +So that's how you improve +connectivity queries slightly. + +And now, finally, +we get to deletes. + +This is the moment +you've been waiting for. + +How do we do a delete +in this structure? + +What are all these +levels good for? + +So we're deleting an edge e. + +Its endpoints are v and w. + +First thing we do is remove +e from the incidence list. + +If every edge stores +a pointer to where + +it lives in the +incidence list, you + +can do that deletion +in constant time. + +Great. + +So as I said, if e is +not in this forest-- + +what if it's in a +lower level of forest? + +Oh, I see, right. + +I forgot. + +In variant two, variant two +says the forests are nested. + +So if it's in any forest, it's +going to be in the last one. + +So if it's not in +the last one, that + +means it's not in +any of the forests. + +That means we're done. + +We do nothing. + +That's the easy case. + +We didn't destroy +any connectivity, + +because the forests represent +maximal connectivity. + +They're spanning. + +But if it's in the forest, +then something changed. + +Then we need to determine, +like in this picture, + +is there a replacement edge? + +Or is there no replacement edge? + +In which case, when there's +no replacement edge, + +we basically don't do anything. + +We have to do a bunch of +deletes in the forests. + +But yeah, is that what +I want to say next? + +Yes, we always do that. + +We're going to delete e. + +We have to delete e. + +So we're going to recursively +delete it from f sub e dot + +level up to F log n. e +dot level is the earliest + +forest it appears in. + +And we have to delete +it from all those. + +Each of those is an Euler-tour +tree deletion, or cut. + +And so each of them pays log +n total cost log squared n. + +So this is where the log +squared's coming from. + +That's great. + +Now we've successfully +deleted the edge. + +But now we need to know, +is there a replacement? + +And at what level is +there a replacement? + +Now, we know by invariant +2, that there could be + +no replacement of lower level. + +The point is, this is a +minimum spanning tree. + +So e was the lowest +level edge that + +could connect the two sides, +these two connected components + +of the forest. + +So if there's any replacements +at e's level or higher, + +there might not be a +replacement at e dot level. + +But there might be a +replacement at a higher level. + +We want to find the smallest +level for which there + +is a replacement. + +That will preserve +invariant 2, that we + +have a minimum spanning forest. + +So that's what we're going +to do, loop over the levels + +to try to find a +replacement edge. + +So we're going to start +at e dot level, loop + +potentially up to log +n, call it a level i. + +Then I want to identify, +at level i, the two + +sides of the edge. + +Let Tv and Tw be the trees +of Fi, containing v and w, + +respectively. + +We just deleted the edge +connecting those two sides. + +So we know that they're in two +different trees, Tv and Tw. + +And one of them is +smaller than the other. + +I'd like to relabel v and +w so that the size of Tv + +is less than or equal +to the size of Tw, size, + +in terms of number of vertices +from there in the tree. + +So swapped v and w if necessary. + +Here's the fun thing. + +If we apply invariant +1, then we learn + +these sizes are not so big. + +Claim, at most, 2 to the i. + +As you realize it's +almost 2 to the i, + +you have to imagine the moment +before this deletion happened, + +before we deleted the edge. + +Because at that point, Tv and +Tw were actually one tree. + +They were connected by edge e. + +We've just deleted them. + +But the moment before we +deleted them, invariant 1 held. + +And so that was a +connected component. + +It should have size, +at most, 2 to the i. + +Now, we split it. + +But that's all we've done. + +So the sum of those sizes +has to be at most 2 to the i. + +Because that used to be +a connected component. + +Cool + +So that means that size of Tv +is 1/2 that, at most 2 to i + +minus 1. + +Because Tv is less +than or equal to Tw. + +So it's, at most, +1/2 of the total. + +So Tv is even smaller. + +In particular, what +that tells us-- + +now we have Tv and Tw as +kind of separate components + +temporarily-- + +we don't really know that +they're separate at level i. + +But we know at level i +minus 1 they are separate. + +At level i minus 1, there +is no replacement edge, + +by the minimum spanning +forest property. + +So what we could +do, at this point, + +is take Tv, take all of +the edges internal to Tv, + +and push them down +to level i minus 1. + +We could afford that. + +What do I mean by we +could afford that? + +We wouldn't destroy invariant 1. + +Because we're taking +2 to the i minus 1 + +vertices, pushing +all those edges down. + +We don't have to +push all of them. + +We could push some +subset of the edges down. + +Whatever connectivity +component we make at that level + +will be of size at +most 2 to d, i minus 1, + +and so invariant 1 +will be preserved. + +So great. + +We can afford in +this certain sense of + +"afford," to push all of Tv's +edges to level i minus 1. + +Great + +We don't actually +need to do this. + +But what we're going to do +is use it to pay for stuff. + +We have this scary +goal, which is + +we want to find is there +a replacement edge? + +I don't know a good way to +find a replacement edge, + +except to do, basically, +a depth first search + +and look at all the edges. + +That's going to +take a lot of time. + +But the good news +is, if we search + +from Tv, every edge +that's useless, + +we can just decrease its level. + +And whenever we decrease +the level of an edge, + +we basically get a +free coin to continue. + +So you get a free +life every time you + +push an edge down by one level. + +Because overall, +number of pushes + +can be number +insertions times log n. + +Because every edge can only +be pushed long n times. + +So whenever we push down an +edge, we get a free bonus life, + +so we can keep doing our search. + +So here's how the search works. + +I'm going to say, for each-- + +this is a little bit +tricky to implement. + +I'm going to first tell +you what we want to do + +and why that's OK. + +And then we'll see +how we actually do it. + +So I want to search +from every vertex in Fv. + +I want to look at all the +outgoing edges from there + +of level i. + +Never mind how to +find those edges. + +Just pretend you could find +it in constant time per edge. + +It's going to be +log n time per edge. + +But that's OK. + +It's two cases. + +Either y is in Tw. + +Otherwise, y is +going to be in Tv. + +Because we have Tv here. + +We have Tw. + +We just deleted this edge, e. + +Sadly, we want to find +a replacement edge. + +So if we look at all the edges +coming out of a vertex in Tv, + +this is, I guess, x. + +It could be it's an edge +that stays within Tv. + +Or could be it's an +edge that goes to Tw. + +There are no other options, +because of our invariants. + +If it's in Tv, oh, +that's kind of annoying. + +Doesn't help us. + +But then we can just set +the level of that edge, + +e-prime, to be i minus 1. + +Because we can afford +to push all of these + +edges down by one level. + +So that pays for this +round of the loop. + +What about the other case? + +The other cases +is the good case. + +That means we've found a +replacement edge for e. + +If we have an edge +from Tv to Tw. + +And at level i, we did +these levels in order. + +Did I say that? + +Yeah, we're doing +levels in order. + +So if we can find this is the +lowest level replacement edge, + +so we do it. + +We insert that edge into +Fi using an Euler-tour tree + +insertion. + +And then we're done. + +So we stop the algorithm. + +The moment we find a +desired edge we're happy. + +Now, maybe there +are lots of edges. + +So we've got to stop when +we find the first one. + +Then we've restored our minimum +spanning forest property. + +We have maximal connectivity, +all these great things. + +As long as we +don't find an edge, + +we can push things down a +level and pay for this round. + +So it's constant time or log +n time to do the last step. + +But all the other steps are paid +for by the decrease in level. + +So the claim is overall, +we pay log squared n. + +Because we had to do log +squared n for these deletions. + +Plus log n times the +number of level decreases. + +That's for this step. + +I claim that each round +of this loop cost log n. + +So that's why we've +get log n times + +number of level decreases. + +But number of level +decreases is, at most, + +number of edge +insertions times log n. + +Because each edge can +only decrease in level + +log n times, by +definition of levels. + +And so we can charge to +the insert operations + +at a factor of log n. + +So there's two log n's here. + +So inserts now cost log +squared amortized as well. + +To deletes costs log +squared amortized. + +And we get log squared overall. + +One last issue though, which +is how do we do this step? + +Actually, there's another +step that's not so trivial, + +this one. + +We need to know the size +of Tv and the size of Tw. + +Well, that's easy. + +I just store subtree +sizes at every node. + +So then I look at +the root of the BST, + +and it tells me how +big that tree is. + +And so I can see which is +bigger and switch accordingly. + +But that's trivial. + +This one requires a +different augmentation + +for Euler-tour trees. + +And again, in both +of these situations, + +we're using the fact that we +can augment on subtrees, not + +on paths. + +That's why we need Euler-tour +trees, not link cut trees. + +So what we store in F-- + +why did I write Fv? + +I mean Tv here. + +So in Fi-- this is for each i, +but at the forest at level i-- + +what I'm going to store is at +every node in the Euler-tour + +tree, I want to know in the +subtree rooted in that node-- + +so here's Euler-tour tree. + +Here's a node, v. +This is a tree in Fi. + +I want to know, in +this subtree, in here, + +is there any node that has a +level i edge incident to it? + +So I want to know, are +there any level i edges? + +If there aren't any +level i edges, then + +for the purposes +of this search, I + +should just skip that subtree. + +It's as if the +subtree was erased. + +So I have some tree. + +It has height log n overall. + +I erase some of the +subtrees according + +to this bit, which is an +easy thing to keep track of. + +It's an augmentation, +constant factor overhead. + +Then I basically want to +do an in-order traversal + +of this tree, but +skipping the stuff below. + +So I mean, one way to think of +it is you just repeatedly call + +successor, like successor +in a binary search tree. + +But whenever I see that there's +no level edges below me, + +I just skip. + +So in log n time you can +basically find the next place + +where there's an outgoing edge. + +I guess also, the +incidence lists + +have to be stored +separately for each level. + +So you can say, what are +your outgoing level i + +edges from a vertex? + +This lets you find +the vertex quickly, + +but then you have to +find the edges quickly. + +So the instance lists are not +just stored as one single link + +lists, one link list per level. + +But that's easy to do. + +So then from this, vertex we +can find all the outgoing level + +i edges. + +And we can do this +4 loop efficiently. + +And whenever it's +low, we get to charge. + +In the remaining +negative two minutes, + +let me tell you briefly +about other problems that + +have been solved. + +So this finishes log squared +n fully dynamic connectivity. + +I wasn't planning to spend +much time on this anyway. + +There are notes. + +If you're interested in +the specific problems, + +I'll just tell you +what the problems are. + +Generalization of connectivity +is k connectivity. + +I don't just want to know, is +there one path from v to w? + +I want to know are there k +disjoint paths from v to w? + +So they could be edge-disjoint +or vertex-disjoint paths, + +might be your goal. + +In that case, poly +log solutions are + +known for 2 connectivity +edge or vertex. + +This is the result, actually, +I used in my very first graph + +algorithms papers, where I first +learned about dynamic graphs. + +In log to the fourth n time, +you can maintain 2 edge + +connectivity. + +It's open for k equals +3, even, whether you + +can achieve that bound. + +So kind of lame. + +Another problem is +minimum spanning forest. + +So you don't just want to +maintain some spanning forest. + +Maybe you actually have +weights on the edges + +and you want the +minimum spanning for us. + +That it turns out, you can +solve with a couple extra log + +factors. + +So in log to the fourth +n time, with an extra log + +squared factor, you can +reduce to the problem + +of dynamic connectivity. + +And so log to the +forth overall, you + +can maintain minimum +spanning forest. + +Another problem is +planarity testing. + +You want to insert or delete +edges and, at all points, + +know whether your +graph is planar. + +And that, there's no great +results known for that. + +It's like n to the 2/3. + +Directed graphs, +things get really hard. + +There are two problems +I've surveyed here. + +There's probably more. + +But the most +fundamental questions + +are the analog of +connectivity is + +what I call dynamic +transitive closure, which + +means given two vertices, +v and w, I want to know, + +is there a directed path from +v to w instead of undirected? + +At the moment, a +bunch of results + +match a trade-off curve +which should be update times + +query is roughly m times n, a +number of edges times number + +of vertices. + +This is big. + +But there are a bunch of results +that achieve this trade-off. + +I don't think I'm +matching lower bound. + +But it's also open, whether +this entire trade-off + +curve could be achieved. + +There's various points on +the curve where you pay + +square root of n for an update. + +Then you pay like, +m times square root + +of n for the query or vice +versa, stuff like that. + +And then a harder +version of this + +is you have weights +on the edges. + +And now the query is +not just find a path, + +find the shortest path. + +This is what I call dynamic +all pairs shortest paths. + +This is even harder. + +There are some results where you +can do like, roughly, n squared + +time updates constant query. + +So it's maybe similar +type of trade-off curves, + +not really known. + +When all the weights +of the edges are 1, + +you just want to find the +shortest path in terms + +of the number of edges, you can +do not really that much better. + +Still, this is the product. + +But at least more of the +trade curve has been solved. + +So that's a quick overview of +dynamic graphs, more generally. + +Dynamic graphs come up all +over the place, obviously. + +You have network where the +links are changing, or Facebook, + +you want to maintain +connections but people friend + +and de-friend all the time. + +So you want to maintain whatever +structure you care about. + +Anyway, that's dynamic +graphs upper bounds. + +Next class will be +lower bounds, the log n. \ No newline at end of file diff --git a/LaTbPEKrE-8.txt b/LaTbPEKrE-8.txt new file mode 100644 index 0000000000000000000000000000000000000000..7f5dc205c39369e4973664f0cafdf5881a01f9da --- /dev/null +++ b/LaTbPEKrE-8.txt @@ -0,0 +1,1347 @@ +align:start position:0% + +welcome back to a20 special relativity + + align:start position:0% +welcome back to a20 special relativity + + + align:start position:0% +welcome back to a20 special relativity +in this section and also the next one we + + align:start position:0% +in this section and also the next one we + + + align:start position:0% +in this section and also the next one we +talk about electromagnetism + + align:start position:0% +talk about electromagnetism + + + align:start position:0% +talk about electromagnetism +electromagnetism is not part of the core + + align:start position:0% +electromagnetism is not part of the core + + + align:start position:0% +electromagnetism is not part of the core +of a20 we are not requiring + + align:start position:0% +of a20 we are not requiring + + + align:start position:0% +of a20 we are not requiring +electromagnetism and electromagnetism as + + align:start position:0% +electromagnetism and electromagnetism as + + + align:start position:0% +electromagnetism and electromagnetism as +part of the prerequisite i will not test + + align:start position:0% +part of the prerequisite i will not test + + + align:start position:0% +part of the prerequisite i will not test +or include electromagnetism in the final + + align:start position:0% +or include electromagnetism in the final + + + align:start position:0% +or include electromagnetism in the final +but nevertheless it's interesting to + + align:start position:0% +but nevertheless it's interesting to + + + align:start position:0% +but nevertheless it's interesting to +discuss electromagnetic effects in the + + align:start position:0% +discuss electromagnetic effects in the + + + align:start position:0% +discuss electromagnetic effects in the +context of special relativity as there + + align:start position:0% +context of special relativity as there + + + align:start position:0% +context of special relativity as there +led to the development of special + + align:start position:0% +led to the development of special + + + align:start position:0% +led to the development of special +activity in the first + + align:start position:0% +activity in the first + + + align:start position:0% +activity in the first +after all the paper which describes + + align:start position:0% +after all the paper which describes + + + align:start position:0% +after all the paper which describes +special the theory of special relativity + + align:start position:0% +special the theory of special relativity + + + align:start position:0% +special the theory of special relativity +is about + + align:start position:0% +is about + + + align:start position:0% +is about +the electrodynamics of moving bodies and + + align:start position:0% +the electrodynamics of moving bodies and + + + align:start position:0% +the electrodynamics of moving bodies and +so let's have a look at the + + align:start position:0% +so let's have a look at the + + + align:start position:0% +so let's have a look at the +electrodynamics of moving body + + align:start position:0% +electrodynamics of moving body + + + align:start position:0% +electrodynamics of moving body +and so here we have a source + + align:start position:0% +and so here we have a source + + + align:start position:0% +and so here we have a source +a charge which is moving with a velocity + + align:start position:0% +a charge which is moving with a velocity + + + align:start position:0% +a charge which is moving with a velocity +v + + align:start position:0% +v + + + align:start position:0% +v +and moving charges or currents create + + align:start position:0% +and moving charges or currents create + + + align:start position:0% +and moving charges or currents create +magnetic fields you can use your right + + align:start position:0% +magnetic fields you can use your right + + + align:start position:0% +magnetic fields you can use your right +hand and see + + align:start position:0% +hand and see + + + align:start position:0% +hand and see +particles are moving in this direction + + align:start position:0% +particles are moving in this direction + + + align:start position:0% +particles are moving in this direction +here the electric field lines are + + align:start position:0% +here the electric field lines are + + + align:start position:0% +here the electric field lines are +curling around + + align:start position:0% +curling around + + + align:start position:0% +curling around +good so now i have a second charge a + + align:start position:0% +good so now i have a second charge a + + + align:start position:0% +good so now i have a second charge a +test charge which is moving with the + + align:start position:0% +test charge which is moving with the + + + align:start position:0% +test charge which is moving with the +velocity u + + align:start position:0% +velocity u + + + align:start position:0% +velocity u +that test charge will experience a + + align:start position:0% +that test charge will experience a + + + align:start position:0% +that test charge will experience a +magnetic force the force is equal to the + + align:start position:0% +magnetic force the force is equal to the + + + align:start position:0% +magnetic force the force is equal to the +test charge itself q t + + align:start position:0% +test charge itself q t + + + align:start position:0% +test charge itself q t +times u cross b the velocity across the + + align:start position:0% +times u cross b the velocity across the + + + align:start position:0% +times u cross b the velocity across the +magnetic field + + align:start position:0% +magnetic field + + + align:start position:0% +magnetic field +all right so there is clearly a magnetic + + align:start position:0% +all right so there is clearly a magnetic + + + align:start position:0% +all right so there is clearly a magnetic +force acting on this charge + + align:start position:0% +force acting on this charge + + + align:start position:0% +force acting on this charge +in this reference however if i now move + + align:start position:0% +in this reference however if i now move + + + align:start position:0% +in this reference however if i now move +into a reference frame where the source + + align:start position:0% +into a reference frame where the source + + + align:start position:0% +into a reference frame where the source +charge is stationary + + align:start position:0% +charge is stationary + + + align:start position:0% +charge is stationary +a stationary charge is not creating a + + align:start position:0% +a stationary charge is not creating a + + + align:start position:0% +a stationary charge is not creating a +magnetic field so the magnetic field is + + align:start position:0% +magnetic field so the magnetic field is + + + align:start position:0% +magnetic field so the magnetic field is +zero hence the magnetic force on the + + align:start position:0% +zero hence the magnetic force on the + + + align:start position:0% +zero hence the magnetic force on the +test charge is here i can alternatively + + align:start position:0% +test charge is here i can alternatively + + + align:start position:0% +test charge is here i can alternatively +look at the reference frame in which the + + align:start position:0% +look at the reference frame in which the + + + align:start position:0% +look at the reference frame in which the +test charge is stationary and so also + + align:start position:0% +test charge is stationary and so also + + + align:start position:0% +test charge is stationary and so also +here because u is equal to zero the + + align:start position:0% +here because u is equal to zero the + + + align:start position:0% +here because u is equal to zero the +magnetic force is here + + align:start position:0% +magnetic force is here + + + align:start position:0% +magnetic force is here +so clearly we do have to treat magnetic + + align:start position:0% +so clearly we do have to treat magnetic + + + align:start position:0% +so clearly we do have to treat magnetic +and electric fields + + align:start position:0% +and electric fields + + + align:start position:0% +and electric fields +instead of a consistent matter as we + + align:start position:0% +instead of a consistent matter as we + + + align:start position:0% +instead of a consistent matter as we +treat time and space and energy momentum + + align:start position:0% +treat time and space and energy momentum + + + align:start position:0% +treat time and space and energy momentum +in a consistent manner so we need a + + align:start position:0% +in a consistent manner so we need a + + + align:start position:0% +in a consistent manner so we need a +concept of electromagnetic fields and + + align:start position:0% +concept of electromagnetic fields and + + + align:start position:0% +concept of electromagnetic fields and +previously in this class we look at + + align:start position:0% +previously in this class we look at + + + align:start position:0% +previously in this class we look at +electromagnetic fields light on before + + align:start position:0% +electromagnetic fields light on before + + + align:start position:0% +electromagnetic fields light on before +the difference here is and that's + + align:start position:0% +the difference here is and that's + + + align:start position:0% +the difference here is and that's +context of the next section is that we + + align:start position:0% +context of the next section is that we + + + align:start position:0% +context of the next section is that we +want to understand how we create those + + align:start position:0% +want to understand how we create those + + + align:start position:0% +want to understand how we create those +fields how we can create electric and + + align:start position:0% +fields how we can create electric and + + + align:start position:0% +fields how we can create electric and +magnetic fields and how this all works + + align:start position:0% +magnetic fields and how this all works + + + align:start position:0% +magnetic fields and how this all works +together + + align:start position:0% +together + + + align:start position:0% +together +at the first activity i want you can to + + align:start position:0% +at the first activity i want you can to + + + align:start position:0% +at the first activity i want you can to +consider the cube of length l + + align:start position:0% +consider the cube of length l + + + align:start position:0% +consider the cube of length l +with n electrons if n charges inside and + + align:start position:0% +with n electrons if n charges inside and + + + align:start position:0% +with n electrons if n charges inside and +everything is at rest + + align:start position:0% +everything is at rest + + + align:start position:0% +everything is at rest +and what i want you to figure out is + + align:start position:0% +and what i want you to figure out is + + + align:start position:0% +and what i want you to figure out is +what is the charge and current density + + align:start position:0% +what is the charge and current density + + + align:start position:0% +what is the charge and current density +wrote not and j naught + + align:start position:0% +wrote not and j naught + + + align:start position:0% +wrote not and j naught +of this cube + + align:start position:0% +of this cube + + + align:start position:0% +of this cube +and the second step as you can imagine + + align:start position:0% +and the second step as you can imagine + + + align:start position:0% +and the second step as you can imagine +i ask you to consider the very same + + align:start position:0% +i ask you to consider the very same + + + align:start position:0% +i ask you to consider the very same +thing from a moving reference frame as + + align:start position:0% +thing from a moving reference frame as + + + align:start position:0% +thing from a moving reference frame as +prime with some velocity u which is the + + align:start position:0% +prime with some velocity u which is the + + + align:start position:0% +prime with some velocity u which is the +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +um + + align:start position:0% +um + + + align:start position:0% +um +of s prime with respect to s + + align:start position:0% +of s prime with respect to s + + + align:start position:0% +of s prime with respect to s +what is the charge in the current + + align:start position:0% +what is the charge in the current + + + align:start position:0% +what is the charge in the current +density now in this new reference frame + + align:start position:0% +density now in this new reference frame + + + align:start position:0% +density now in this new reference frame +okay i'd like you to figure this out + + align:start position:0% +okay i'd like you to figure this out + + + align:start position:0% +okay i'd like you to figure this out +okay so now we look at this + + align:start position:0% +okay so now we look at this + + + align:start position:0% +okay so now we look at this +cube + + align:start position:0% +cube + + + align:start position:0% +cube +and the total number of charges is n the + + align:start position:0% +and the total number of charges is n the + + + align:start position:0% +and the total number of charges is n the +length or the volume is l naught cube + + align:start position:0% +length or the volume is l naught cube + + + align:start position:0% +length or the volume is l naught cube +and so the density is n divided by l + + align:start position:0% +and so the density is n divided by l + + + align:start position:0% +and so the density is n divided by l +naught q the current is zero nothing is + + align:start position:0% +naught q the current is zero nothing is + + + align:start position:0% +naught q the current is zero nothing is +moving there's no moving charges current + + align:start position:0% +moving there's no moving charges current + + + align:start position:0% +moving there's no moving charges current +is zero + + align:start position:0% +is zero + + + align:start position:0% +is zero +all right this was rather + + align:start position:0% +all right this was rather + + + align:start position:0% +all right this was rather +straightforward but now in our moving + + align:start position:0% +straightforward but now in our moving + + + align:start position:0% +straightforward but now in our moving +reference frame the situation changes + + align:start position:0% +reference frame the situation changes + + + align:start position:0% +reference frame the situation changes +here + + align:start position:0% +here + + + align:start position:0% +here +one of the direction the direction in + + align:start position:0% +one of the direction the direction in + + + align:start position:0% +one of the direction the direction in +which we are moving is lawrence + + align:start position:0% +which we are moving is lawrence + + + align:start position:0% +which we are moving is lawrence +contracted so we have lx equal to lx + + align:start position:0% +contracted so we have lx equal to lx + + + align:start position:0% +contracted so we have lx equal to lx +naught or l naught + + align:start position:0% +naught or l naught + + + align:start position:0% +naught or l naught +times + + align:start position:0% +times + + + align:start position:0% +times +divided by gamma or times square root 1 + + align:start position:0% +divided by gamma or times square root 1 + + + align:start position:0% +divided by gamma or times square root 1 +minus u square over c squared the volume + + align:start position:0% +minus u square over c squared the volume + + + align:start position:0% +minus u square over c squared the volume +then + + align:start position:0% +then + + + align:start position:0% +then +of the same cube in the + + align:start position:0% +of the same cube in the + + + align:start position:0% +of the same cube in the +s prime reference frame is in a cube + + align:start position:0% +s prime reference frame is in a cube + + + align:start position:0% +s prime reference frame is in a cube +divided by gamma + + align:start position:0% +divided by gamma + + + align:start position:0% +divided by gamma +the number of electrons however is + + align:start position:0% +the number of electrons however is + + + align:start position:0% +the number of electrons however is +unchanged so the charge density + + align:start position:0% +unchanged so the charge density + + + align:start position:0% +unchanged so the charge density +is the previous charged entity divided + + align:start position:0% +is the previous charged entity divided + + + align:start position:0% +is the previous charged entity divided +by the volume and if you + + align:start position:0% +by the volume and if you + + + align:start position:0% +by the volume and if you +if you compare + + align:start position:0% +if you compare + + + align:start position:0% +if you compare +sorry the charge divided by the new + + align:start position:0% +sorry the charge divided by the new + + + align:start position:0% +sorry the charge divided by the new +volume which is + + align:start position:0% +volume which is + + + align:start position:0% +volume which is +the um + + align:start position:0% +the um + + + align:start position:0% +the um +density times gamma + + align:start position:0% +density times gamma + + + align:start position:0% +density times gamma +for the new charge density + + align:start position:0% +for the new charge density + + + align:start position:0% +for the new charge density +we simply have to multiply the mutual + + align:start position:0% +we simply have to multiply the mutual + + + align:start position:0% +we simply have to multiply the mutual +the current density + + align:start position:0% +the current density + + + align:start position:0% +the current density +for the + + align:start position:0% +for the + + + align:start position:0% +for the +current density we have to multiply the + + align:start position:0% +current density we have to multiply the + + + align:start position:0% +current density we have to multiply the +charge then t times the velocity and + + align:start position:0% +charge then t times the velocity and + + + align:start position:0% +charge then t times the velocity and +again we find + + align:start position:0% +again we find + + + align:start position:0% +again we find +rho naught times u + + align:start position:0% +rho naught times u + + + align:start position:0% +rho naught times u +times gamma + + align:start position:0% +times gamma + + + align:start position:0% +times gamma +okay good so if you look at those + + align:start position:0% +okay good so if you look at those + + + align:start position:0% +okay good so if you look at those +relations they look very much like the + + align:start position:0% +relations they look very much like the + + + align:start position:0% +relations they look very much like the +relay relations between the current and + + align:start position:0% +relay relations between the current and + + + align:start position:0% +relay relations between the current and +the density charge density they look + + align:start position:0% +the density charge density they look + + + align:start position:0% +the density charge density they look +very much like the relations we had + + align:start position:0% +very much like the relations we had + + + align:start position:0% +very much like the relations we had +between momentum and energy and time and + + align:start position:0% +between momentum and energy and time and + + + align:start position:0% +between momentum and energy and time and +space and lauren's transformation look + + align:start position:0% +space and lauren's transformation look + + + align:start position:0% +space and lauren's transformation look +very similar so we can + + align:start position:0% +very similar so we can + + + align:start position:0% +very similar so we can +motivate it by this + + align:start position:0% +motivate it by this + + + align:start position:0% +motivate it by this +uh write a four vector which is the + + align:start position:0% +uh write a four vector which is the + + + align:start position:0% +uh write a four vector which is the +first component theta c times the + + align:start position:0% +first component theta c times the + + + align:start position:0% +first component theta c times the +density + + align:start position:0% +density + + + align:start position:0% +density +and that's the first second and third + + align:start position:0% +and that's the first second and third + + + align:start position:0% +and that's the first second and third +component + + align:start position:0% +component + + + align:start position:0% +component +the + + align:start position:0% +the + + + align:start position:0% +the +current + + align:start position:0% +current + + + align:start position:0% +current +and you find that the invariant here is + + align:start position:0% +and you find that the invariant here is + + + align:start position:0% +and you find that the invariant here is +very similar to time in space energy and + + align:start position:0% +very similar to time in space energy and + + + align:start position:0% +very similar to time in space energy and +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +given as the density + + align:start position:0% +given as the density + + + align:start position:0% +given as the density +where the charges are at rest + + align:start position:0% +where the charges are at rest + + + align:start position:0% +where the charges are at rest +and that's in the invariance and you can + + align:start position:0% +and that's in the invariance and you can + + + align:start position:0% +and that's in the invariance and you can +calculate this for multiplying + + align:start position:0% +calculate this for multiplying + + + align:start position:0% +calculate this for multiplying +the four + + align:start position:0% +the four + + + align:start position:0% +the four +often squaring the volume + + align:start position:0% +often squaring the volume + + + align:start position:0% +often squaring the volume +okay so concept questions + + align:start position:0% +okay so concept questions + + + align:start position:0% +okay so concept questions +is the electric charge conserved on the + + align:start position:0% +is the electric charge conserved on the + + + align:start position:0% +is the electric charge conserved on the +lawrence transformation + + align:start position:0% +lawrence transformation + + + align:start position:0% +lawrence transformation +but did we actually change the charge so + + align:start position:0% +but did we actually change the charge so + + + align:start position:0% +but did we actually change the charge so +we have the charge density here and the + + align:start position:0% +we have the charge density here and the + + + align:start position:0% +we have the charge density here and the +current here but did we actually change + + align:start position:0% +current here but did we actually change + + + align:start position:0% +current here but did we actually change +the charge on the lawn transformation + + align:start position:0% +the charge on the lawn transformation + + + align:start position:0% +the charge on the lawn transformation +the answer is no we did not change them + + align:start position:0% +the answer is no we did not change them + + + align:start position:0% +the answer is no we did not change them +so + + align:start position:0% +so + + + align:start position:0% +so +the charge is conserved or the charge is + + align:start position:0% +the charge is conserved or the charge is + + + align:start position:0% +the charge is conserved or the charge is +invariant on the launch transformation + + align:start position:0% +invariant on the launch transformation + + + align:start position:0% +invariant on the launch transformation +is the electric current conserved on the + + align:start position:0% +is the electric current conserved on the + + + align:start position:0% +is the electric current conserved on the +lower dimension + + align:start position:0% +lower dimension + + + align:start position:0% +lower dimension +or invariant on the lens transformation + + align:start position:0% +or invariant on the lens transformation + + + align:start position:0% +or invariant on the lens transformation +it should rather use invariant + + align:start position:0% +it should rather use invariant + + + align:start position:0% +it should rather use invariant +and the answer is no it's not so we have + + align:start position:0% +and the answer is no it's not so we have + + + align:start position:0% +and the answer is no it's not so we have +seen from the very first example that we + + align:start position:0% +seen from the very first example that we + + + align:start position:0% +seen from the very first example that we +start with the current zero and then in + + align:start position:0% +start with the current zero and then in + + + align:start position:0% +start with the current zero and then in +the s prime frame the current is of a + + align:start position:0% +the s prime frame the current is of a + + + align:start position:0% +the s prime frame the current is of a +certain value so certainly the current + + align:start position:0% +certain value so certainly the current + + + align:start position:0% +certain value so certainly the current +as seen from two different observers + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/MOcWRURkmS0.txt b/MOcWRURkmS0.txt new file mode 100644 index 0000000000000000000000000000000000000000..014486570c8b77b931b68d7b7ae89e142b539657 --- /dev/null +++ b/MOcWRURkmS0.txt @@ -0,0 +1,11181 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu anyway + + align:start position:0% +ocw.mit.edu anyway + + + align:start position:0% +ocw.mit.edu anyway +we I'd + + align:start position:0% +we I'd + + + align:start position:0% +we I'd +better abbreviate all the stuff that I + + align:start position:0% +better abbreviate all the stuff that I + + + align:start position:0% +better abbreviate all the stuff that I +want to cover today the next three + + align:start position:0% +want to cover today the next three + + + align:start position:0% +want to cover today the next three +classes are going to + + align:start position:0% +classes are going to + + + align:start position:0% +classes are going to +cover cases of very PR + + align:start position:0% +cover cases of very PR + + + align:start position:0% +cover cases of very PR +just + + align:start position:0% + + + + align:start position:0% + +very uh complex but very direct + + align:start position:0% +very uh complex but very direct + + + align:start position:0% +very uh complex but very direct +relationships between social and spatial + + align:start position:0% +relationships between social and spatial + + + align:start position:0% +relationships between social and spatial +structure + + align:start position:0% + + + + align:start position:0% + +there is a a + + align:start position:0% +there is a a + + + align:start position:0% +there is a a +literature largely from the left side of + + align:start position:0% +literature largely from the left side of + + + align:start position:0% +literature largely from the left side of +the + + align:start position:0% +the + + + align:start position:0% +the +market uh on these issues + + align:start position:0% +market uh on these issues + + + align:start position:0% +market uh on these issues +I don't have time to go through much of + + align:start position:0% +I don't have time to go through much of + + + align:start position:0% +I don't have time to go through much of +this + + align:start position:0% +this + + + align:start position:0% +this +here + + align:start position:0% +here + + + align:start position:0% +here +um you should read the required reading + + align:start position:0% +um you should read the required reading + + + align:start position:0% +um you should read the required reading +for this class Kevin Lynch's piece + + align:start position:0% +for this class Kevin Lynch's piece + + + align:start position:0% +for this class Kevin Lynch's piece +chapter on social and spatial structure + + align:start position:0% +chapter on social and spatial structure + + + align:start position:0% +chapter on social and spatial structure +relation + + align:start position:0% +relation + + + align:start position:0% +relation +ships + + align:start position:0% +ships + + + align:start position:0% +ships +um on + + align:start position:0% +um on + + + align:start position:0% +um on +the on the left I + + align:start position:0% + + + + align:start position:0% + +would assume + + align:start position:0% + + + + align:start position:0% + +the AR the arguments that space is an + + align:start position:0% +the AR the arguments that space is an + + + align:start position:0% +the AR the arguments that space is an +active agent that + + align:start position:0% +active agent that + + + align:start position:0% +active agent that +it's involves + + align:start position:0% +it's involves + + + align:start position:0% +it's involves +conflict that it's + + align:start position:0% +conflict that it's + + + align:start position:0% +conflict that it's +political and this is an argument that + + align:start position:0% +political and this is an argument that + + + align:start position:0% +political and this is an argument that +is + + align:start position:0% +is + + + align:start position:0% +is +articulated very well by AR Le in the + + align:start position:0% +articulated very well by AR Le in the + + + align:start position:0% +articulated very well by AR Le in the +translation of his writing into + + align:start position:0% +translation of his writing into + + + align:start position:0% +translation of his writing into +English David Harvey's first book social + + align:start position:0% +English David Harvey's first book social + + + align:start position:0% +English David Harvey's first book social +justice in the city augus that under + + align:start position:0% + + + + align:start position:0% + +capitalism investment will never stream + + align:start position:0% +capitalism investment will never stream + + + align:start position:0% +capitalism investment will never stream +towards the poorest sections of the + + align:start position:0% +towards the poorest sections of the + + + align:start position:0% +towards the poorest sections of the +society because capitalism has so many + + align:start position:0% +society because capitalism has so many + + + align:start position:0% +society because capitalism has so many +circuits of + + align:start position:0% +circuits of + + + align:start position:0% +circuits of +investment to an object of capitalist + + align:start position:0% +investment to an object of capitalist + + + align:start position:0% +investment to an object of capitalist +investment is always maximizing + + align:start position:0% +investment is always maximizing + + + align:start position:0% +investment is always maximizing +profit there + + align:start position:0% +profit there + + + align:start position:0% +profit there +are less attractive writings by Manuel + + align:start position:0% +are less attractive writings by Manuel + + + align:start position:0% +are less attractive writings by Manuel +castels in his + + align:start position:0% + + + + align:start position:0% + +pre Berkeley + + align:start position:0% +pre Berkeley + + + align:start position:0% +pre Berkeley +stage the book the urban + + align:start position:0% +stage the book the urban + + + align:start position:0% +stage the book the urban +question uh and so on and so + + align:start position:0% +question uh and so on and so + + + align:start position:0% +question uh and so on and so +on uh there's David Gordon's writing + + align:start position:0% +on uh there's David Gordon's writing + + + align:start position:0% +on uh there's David Gordon's writing +about + + align:start position:0% +about + + + align:start position:0% +about +um the origins of American + + align:start position:0% +um the origins of American + + + align:start position:0% +um the origins of American +Suburbia as being the result of Labor + + align:start position:0% +Suburbia as being the result of Labor + + + align:start position:0% +Suburbia as being the result of Labor +friction in the central business area + + align:start position:0% +friction in the central business area + + + align:start position:0% +friction in the central business area +and the bosses wanting to move as far + + align:start position:0% +and the bosses wanting to move as far + + + align:start position:0% +and the bosses wanting to move as far +away from the workers as possible and + + align:start position:0% +away from the workers as possible and + + + align:start position:0% +away from the workers as possible and +there many histories of this kind + + align:start position:0% +there many histories of this kind + + + align:start position:0% +there many histories of this kind +there's castel's piece the wild city + + align:start position:0% +there's castel's piece the wild city + + + align:start position:0% +there's castel's piece the wild city +which argues that + + align:start position:0% +which argues that + + + align:start position:0% +which argues that +suburbian is a form of advanced + + align:start position:0% +suburbian is a form of advanced + + + align:start position:0% +suburbian is a form of advanced +capitalist investment in which + + align:start position:0% + + + + align:start position:0% + +you have to create markets + + align:start position:0% +you have to create markets + + + align:start position:0% +you have to create markets +for prolific domestic goods and suburbia + + align:start position:0% +for prolific domestic goods and suburbia + + + align:start position:0% +for prolific domestic goods and suburbia +is an attractive Avenue for this kind of + + align:start position:0% +is an attractive Avenue for this kind of + + + align:start position:0% +is an attractive Avenue for this kind of +Market he writing is called the wild + + align:start position:0% +Market he writing is called the wild + + + align:start position:0% +Market he writing is called the wild +City claims the American city is wild in + + align:start position:0% +City claims the American city is wild in + + + align:start position:0% +City claims the American city is wild in +the sense that it uh oys the uh + + align:start position:0% +the sense that it uh oys the uh + + + align:start position:0% +the sense that it uh oys the uh +consequences of Market action in a very + + align:start position:0% +consequences of Market action in a very + + + align:start position:0% +consequences of Market action in a very +obvious kind of + + align:start position:0% +obvious kind of + + + align:start position:0% +obvious kind of +way uh it's not uh hidden or + + align:start position:0% +way uh it's not uh hidden or + + + align:start position:0% +way uh it's not uh hidden or +transformed um there's an enormous + + align:start position:0% +transformed um there's an enormous + + + align:start position:0% +transformed um there's an enormous +amount of writing there's less writing + + align:start position:0% +amount of writing there's less writing + + + align:start position:0% +amount of writing there's less writing +and from this from the center and the + + align:start position:0% +and from this from the center and the + + + align:start position:0% +and from this from the center and the +right um in Sunday's New York Times + + align:start position:0% +right um in Sunday's New York Times + + + align:start position:0% +right um in Sunday's New York Times +there's a piece called Suburban D this + + align:start position:0% +there's a piece called Suburban D this + + + align:start position:0% +there's a piece called Suburban D this +equilibrium I don't know if anybody + + align:start position:0% +equilibrium I don't know if anybody + + + align:start position:0% +equilibrium I don't know if anybody +looks at these things + + align:start position:0% + + + + align:start position:0% + +it simply says that suburbs are + + align:start position:0% + + + + align:start position:0% + +unequal something that one would presume + + align:start position:0% +unequal something that one would presume + + + align:start position:0% +unequal something that one would presume +to + + align:start position:0% +to + + + align:start position:0% +to +know and the reason suburbs are unequal + + align:start position:0% +know and the reason suburbs are unequal + + + align:start position:0% +know and the reason suburbs are unequal +or given and they haven't changed and + + align:start position:0% +or given and they haven't changed and + + + align:start position:0% +or given and they haven't changed and +not much has changed she cites examples + + align:start position:0% +not much has changed she cites examples + + + align:start position:0% +not much has changed she cites examples +of suburbs close together in Los Angeles + + align:start position:0% +of suburbs close together in Los Angeles + + + align:start position:0% +of suburbs close together in Los Angeles +where in one their house C for 68 + + align:start position:0% +where in one their house C for 68 + + + align:start position:0% +where in one their house C for 68 +million dollars and there's a few miles + + align:start position:0% +million dollars and there's a few miles + + + align:start position:0% +million dollars and there's a few miles +away there's a suburb of Mexican amican + + align:start position:0% +away there's a suburb of Mexican amican + + + align:start position:0% +away there's a suburb of Mexican amican +workers who can barely for to buy their + + align:start position:0% +workers who can barely for to buy their + + + align:start position:0% +workers who can barely for to buy their +house + + align:start position:0% +house + + + align:start position:0% +house +um in + + align:start position:0% +um in + + + align:start position:0% +um in +teaching this material I found over the + + align:start position:0% +teaching this material I found over the + + + align:start position:0% +teaching this material I found over the +years + + align:start position:0% +years + + + align:start position:0% +years +that + + align:start position:0% +that + + + align:start position:0% +that +um the material is + + align:start position:0% +um the material is + + + align:start position:0% +um the material is +very much Str to + + align:start position:0% +very much Str to + + + align:start position:0% +very much Str to +large ideas about economic science and + + align:start position:0% +large ideas about economic science and + + + align:start position:0% +large ideas about economic science and +social policy uh there's very little + + align:start position:0% +social policy uh there's very little + + + align:start position:0% +social policy uh there's very little +discussion of the meaning of place um + + align:start position:0% +discussion of the meaning of place um + + + align:start position:0% +discussion of the meaning of place um +Donald Appleyard has written about that + + align:start position:0% +Donald Appleyard has written about that + + + align:start position:0% +Donald Appleyard has written about that +and so some of + + align:start position:0% +and so some of + + + align:start position:0% +and so some of +others uh what place means what space + + align:start position:0% +others uh what place means what space + + + align:start position:0% +others uh what place means what space +means to people and and so on so I've + + align:start position:0% +means to people and and so on so I've + + + align:start position:0% +means to people and and so on so I've +decided to follow a different rout in + + align:start position:0% +decided to follow a different rout in + + + align:start position:0% +decided to follow a different rout in +dealing with this um I've + + align:start position:0% +dealing with this um I've + + + align:start position:0% +dealing with this um I've +established uh a notion called + + align:start position:0% +established uh a notion called + + + align:start position:0% +established uh a notion called +bipolarity + + align:start position:0% +bipolarity + + + align:start position:0% +bipolarity +um + + align:start position:0% +um + + + align:start position:0% +um +and chosen cases + + align:start position:0% +and chosen cases + + + align:start position:0% +and chosen cases +where the conflict + + align:start position:0% +where the conflict + + + align:start position:0% +where the conflict +between various groups in the city is + + align:start position:0% +between various groups in the city is + + + align:start position:0% +between various groups in the city is +very + + align:start position:0% + + + + align:start position:0% + +explicit and + + align:start position:0% +explicit and + + + align:start position:0% +explicit and +uh under different + + align:start position:0% +uh under different + + + align:start position:0% +uh under different +conditions so we will examine + + align:start position:0% +conditions so we will examine + + + align:start position:0% +conditions so we will examine +Jan + + align:start position:0% +Jan + + + align:start position:0% +Jan +isburg from its origins in + + align:start position:0% +isburg from its origins in + + + align:start position:0% +isburg from its origins in +1876 I think to + + align:start position:0% +1876 I think to + + + align:start position:0% +1876 I think to +today following a path of explicit + + align:start position:0% +today following a path of explicit + + + align:start position:0% +today following a path of explicit +racial policy so the + + align:start position:0% +racial policy so the + + + align:start position:0% +racial policy so the +Africa + + align:start position:0% +Africa + + + align:start position:0% +Africa +invented or formalized racial policy to + + align:start position:0% +invented or formalized racial policy to + + + align:start position:0% +invented or formalized racial policy to +an extent that no other country in no + + align:start position:0% +an extent that no other country in no + + + align:start position:0% +an extent that no other country in no +other state in the world ever has so we + + align:start position:0% +other state in the world ever has so we + + + align:start position:0% +other state in the world ever has so we +should look at Johannesburg what the + + align:start position:0% +should look at Johannesburg what the + + + align:start position:0% +should look at Johannesburg what the +space of Johannesburg looks like as a + + align:start position:0% +space of Johannesburg looks like as a + + + align:start position:0% +space of Johannesburg looks like as a +result of the enforcement of absolute + + align:start position:0% +result of the enforcement of absolute + + + align:start position:0% +result of the enforcement of absolute +inequities between white and + + align:start position:0% +inequities between white and + + + align:start position:0% +inequities between white and +black we should look at the colonial + + align:start position:0% +black we should look at the colonial + + + align:start position:0% +black we should look at the colonial +City and we look at Delhi and New Delhi + + align:start position:0% +City and we look at Delhi and New Delhi + + + align:start position:0% +City and we look at Delhi and New Delhi +we look at the border between Mexico and + + align:start position:0% +we look at the border between Mexico and + + + align:start position:0% +we look at the border between Mexico and +the United + + align:start position:0% +the United + + + align:start position:0% +the United +States and + + align:start position:0% +States and + + + align:start position:0% +States and +uh look at + + align:start position:0% +uh look at + + + align:start position:0% +uh look at +the polarity between between country and + + align:start position:0% +the polarity between between country and + + + align:start position:0% +the polarity between between country and +city in the development of + + align:start position:0% +city in the development of + + + align:start position:0% +city in the development of +Havana um to today's + + align:start position:0% +Havana um to today's + + + align:start position:0% +Havana um to today's +class is really dealing with a mother of + + align:start position:0% +class is really dealing with a mother of + + + align:start position:0% +class is really dealing with a mother of +all social complexities and that's + + align:start position:0% +all social complexities and that's + + + align:start position:0% +all social complexities and that's +Jerusalem I want to do a case study on + + align:start position:0% +Jerusalem I want to do a case study on + + + align:start position:0% +Jerusalem I want to do a case study on +Jerusalem and + + align:start position:0% +Jerusalem and + + + align:start position:0% +Jerusalem and +just for those of you haven't read the + + align:start position:0% +just for those of you haven't read the + + + align:start position:0% +just for those of you haven't read the +required reading for + + align:start position:0% +required reading for + + + align:start position:0% +required reading for +today which is a long piece which I + + align:start position:0% +today which is a long piece which I + + + align:start position:0% +today which is a long piece which I +wrote after months of work + + align:start position:0% +wrote after months of work + + + align:start position:0% +wrote after months of work +and I'm so sad that you haven't read it + + align:start position:0% +and I'm so sad that you haven't read it + + + align:start position:0% +and I'm so sad that you haven't read it +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um I'll go through these very let me + + align:start position:0% +um I'll go through these very let me + + + align:start position:0% +um I'll go through these very let me +just explain what I've handed out to you + + align:start position:0% +just explain what I've handed out to you + + + align:start position:0% +just explain what I've handed out to you +after this the map of the history of + + align:start position:0% +after this the map of the history of + + + align:start position:0% +after this the map of the history of +Jerusalem simplified history on the next + + align:start position:0% +Jerusalem simplified history on the next + + + align:start position:0% +Jerusalem simplified history on the next +page is a + + align:start position:0% +page is a + + + align:start position:0% +page is a +drawing it's a drawing on a napkin by + + align:start position:0% +drawing it's a drawing on a napkin by + + + align:start position:0% +drawing it's a drawing on a napkin by +the head of the + + align:start position:0% +the head of the + + + align:start position:0% +the head of the +of of the planning section of mopic the + + align:start position:0% +of of the planning section of mopic the + + + align:start position:0% +of of the planning section of mopic the +Palestinian organization after the Oslo + + align:start position:0% +Palestinian organization after the Oslo + + + align:start position:0% +Palestinian organization after the Oslo +cords which I worked with for a while uh + + align:start position:0% +cords which I worked with for a while uh + + + align:start position:0% +cords which I worked with for a while uh +this was his depiction of the future of + + align:start position:0% +this was his depiction of the future of + + + align:start position:0% +this was his depiction of the future of +Jerusalem as one metropolitan area with + + align:start position:0% +Jerusalem as one metropolitan area with + + + align:start position:0% +Jerusalem as one metropolitan area with +two with the Jewish sector on the west + + align:start position:0% +two with the Jewish sector on the west + + + align:start position:0% +two with the Jewish sector on the west +and the Palestinian sect on the right + + align:start position:0% +and the Palestinian sect on the right + + + align:start position:0% +and the Palestinian sect on the right +and the historic Center in the middle + + align:start position:0% +and the historic Center in the middle + + + align:start position:0% +and the historic Center in the middle +below that is data which is + + align:start position:0% +below that is data which is + + + align:start position:0% +below that is data which is +obvious + + align:start position:0% + + + + align:start position:0% + +um uh pointing out the stupidity + + align:start position:0% +um uh pointing out the stupidity + + + align:start position:0% +um uh pointing out the stupidity +of some of the writing on this issue so + + align:start position:0% +of some of the writing on this issue so + + + align:start position:0% +of some of the writing on this issue so +what I'm going to do + + align:start position:0% +what I'm going to do + + + align:start position:0% +what I'm going to do +is try to take you through a history + + align:start position:0% +is try to take you through a history + + + align:start position:0% +is try to take you through a history +of which starts off as a history of for + + align:start position:0% +of which starts off as a history of for + + + align:start position:0% +of which starts off as a history of for +a long time a history of religious + + align:start position:0% + + + + align:start position:0% + +consequence and transforms much later + + align:start position:0% +consequence and transforms much later + + + align:start position:0% +consequence and transforms much later +and in recent time certainly in this + + align:start position:0% +and in recent time certainly in this + + + align:start position:0% +and in recent time certainly in this +Century into a + + align:start position:0% +Century into a + + + align:start position:0% +Century into a +geopolitical + + align:start position:0% +geopolitical + + + align:start position:0% +geopolitical +conflict and we end up with this status + + align:start position:0% + + + + align:start position:0% + +quo + + align:start position:0% +quo + + + align:start position:0% +quo +um let's follow + + align:start position:0% +um let's follow + + + align:start position:0% +um let's follow +this map very briefly + + align:start position:0% + + + + align:start position:0% + +the origins of Jerusalem are again + + align:start position:0% +the origins of Jerusalem are again + + + align:start position:0% +the origins of Jerusalem are again +political + + align:start position:0% +political + + + align:start position:0% +political +for Palestinians it talks about the + + align:start position:0% +for Palestinians it talks about the + + + align:start position:0% +for Palestinians it talks about the +jebusites and the + + align:start position:0% +jebusites and the + + + align:start position:0% +jebusites and the +Canaanites and the + + align:start position:0% +Canaanites and the + + + align:start position:0% +Canaanites and the +origins of the city prior to + + align:start position:0% +origins of the city prior to + + + align:start position:0% +origins of the city prior to +1,000 + + align:start position:0% +1,000 + + + align:start position:0% +1,000 +BC which is at the date + + align:start position:0% +BC which is at the date + + + align:start position:0% +BC which is at the date +that the dividian city the city of + + align:start position:0% +that the dividian city the city of + + + align:start position:0% +that the dividian city the city of +David argues as its + + align:start position:0% + + + + align:start position:0% + +beginning David captures Jerusalem + + align:start position:0% +beginning David captures Jerusalem + + + align:start position:0% +beginning David captures Jerusalem +according to this this is an Israeli + + align:start position:0% +according to this this is an Israeli + + + align:start position:0% +according to this this is an Israeli +map uh according to + + align:start position:0% +map uh according to + + + align:start position:0% +map uh according to +the to Israeli + + align:start position:0% +the to Israeli + + + align:start position:0% +the to Israeli +history David bought the threshing + + align:start position:0% +history David bought the threshing + + + align:start position:0% +history David bought the threshing +fields on the Temple Mount from the + + align:start position:0% +fields on the Temple Mount from the + + + align:start position:0% +fields on the Temple Mount from the +jebus sdes for 15 shekels the equivalent + + align:start position:0% +jebus sdes for 15 shekels the equivalent + + + align:start position:0% +jebus sdes for 15 shekels the equivalent +amount of money + + align:start position:0% +amount of money + + + align:start position:0% +amount of money +and in order to unify the spread + + align:start position:0% +and in order to unify the spread + + + align:start position:0% +and in order to unify the spread +out Jewish + + align:start position:0% +out Jewish + + + align:start position:0% +out Jewish +tribes he built the first he uh he + + align:start position:0% +tribes he built the first he uh he + + + align:start position:0% +tribes he built the first he uh he +was a lover and a poet and uh General + + align:start position:0% +was a lover and a poet and uh General + + + align:start position:0% +was a lover and a poet and uh General +and according to strict Hebrew law was + + align:start position:0% +and according to strict Hebrew law was + + + align:start position:0% +and according to strict Hebrew law was +not able to build a temple so his son + + align:start position:0% +not able to build a temple so his son + + + align:start position:0% +not able to build a temple so his son +Solomon was the author of the first + + align:start position:0% +Solomon was the author of the first + + + align:start position:0% +Solomon was the author of the first +temple I'll show you a drawing of by kiz + + align:start position:0% +temple I'll show you a drawing of by kiz + + + align:start position:0% +temple I'll show you a drawing of by kiz +of the + + align:start position:0% +of the + + + align:start position:0% +of the +tribal + + align:start position:0% +tribal + + + align:start position:0% +tribal +environment + + align:start position:0% +environment + + + align:start position:0% +environment +which the Jews and most people + + align:start position:0% +which the Jews and most people + + + align:start position:0% +which the Jews and most people +established at that time and the drawing + + align:start position:0% +established at that time and the drawing + + + align:start position:0% +established at that time and the drawing +shows the temple as the + + align:start position:0% +shows the temple as the + + + align:start position:0% +shows the temple as the +first physical + + align:start position:0% +first physical + + + align:start position:0% +first physical +presence in a + + align:start position:0% + + + + align:start position:0% + +city seeing that the religion City for a + + align:start position:0% +city seeing that the religion City for a + + + align:start position:0% +city seeing that the religion City for a +long time just depended on a religious + + align:start position:0% +long time just depended on a religious + + + align:start position:0% +long time just depended on a religious +infrastructure it's clear that the first + + align:start position:0% + + + + align:start position:0% + +temple this + + align:start position:0% +temple this + + + align:start position:0% +temple this +Temple exists for about 500 + + align:start position:0% +Temple exists for about 500 + + + align:start position:0% +Temple exists for about 500 +years uh during which time + + align:start position:0% +years uh during which time + + + align:start position:0% +years uh during which time +it the Middle East + + align:start position:0% +it the Middle East + + + align:start position:0% +it the Middle East +undergoes sieges and invasions the most + + align:start position:0% +undergoes sieges and invasions the most + + + align:start position:0% +undergoes sieges and invasions the most +significant invasion is by Nezar in six + + align:start position:0% +significant invasion is by Nezar in six + + + align:start position:0% +significant invasion is by Nezar in six +in the 6th Century this has enormous + + align:start position:0% +in the 6th Century this has enormous + + + align:start position:0% +in the 6th Century this has enormous +consequences + + align:start position:0% +consequences + + + align:start position:0% +consequences +historically and I tend to exaggerate + + align:start position:0% +historically and I tend to exaggerate + + + align:start position:0% +historically and I tend to exaggerate +some of + + align:start position:0% +some of + + + align:start position:0% +some of +them + + align:start position:0% +them + + + align:start position:0% +them +Nebuchadnezzar came from the world's + + align:start position:0% +Nebuchadnezzar came from the world's + + + align:start position:0% +Nebuchadnezzar came from the world's +greatest City at the time + + align:start position:0% +greatest City at the time + + + align:start position:0% +greatest City at the time +Babylon the most advanced city of + + align:start position:0% +Babylon the most advanced city of + + + align:start position:0% +Babylon the most advanced city of +all instead of killing the Jews he took + + align:start position:0% +all instead of killing the Jews he took + + + align:start position:0% +all instead of killing the Jews he took +a back with him as + + align:start position:0% +a back with him as + + + align:start position:0% +a back with him as +prisoners and allowed the Jews to + + align:start position:0% +prisoners and allowed the Jews to + + + align:start position:0% +prisoners and allowed the Jews to +establish themselves in Babylon in a + + align:start position:0% +establish themselves in Babylon in a + + + align:start position:0% +establish themselves in Babylon in a +relatively free manner why he did that + + align:start position:0% +relatively free manner why he did that + + + align:start position:0% +relatively free manner why he did that +which was very contrary + + align:start position:0% +which was very contrary + + + align:start position:0% +which was very contrary +to social inter + + align:start position:0% +to social inter + + + align:start position:0% +to social inter +International Behavior at the time I + + align:start position:0% +International Behavior at the time I + + + align:start position:0% +International Behavior at the time I +don't know what happened was so + + align:start position:0% +don't know what happened was so + + + align:start position:0% +don't know what happened was so +significant for the + + align:start position:0% +significant for the + + + align:start position:0% +significant for the +Jews not having a temple not having + + align:start position:0% +Jews not having a temple not having + + + align:start position:0% +Jews not having a temple not having +priests you must understand the + + align:start position:0% +priests you must understand the + + + align:start position:0% +priests you must understand the +organization of the social structure + + align:start position:0% +organization of the social structure + + + align:start position:0% +organization of the social structure +around the temple the temple was run by + + align:start position:0% +around the temple the temple was run by + + + align:start position:0% +around the temple the temple was run by +priests there were there was no + + align:start position:0% +priests there were there was no + + + align:start position:0% +priests there were there was no +democracy in + + align:start position:0% +democracy in + + + align:start position:0% +democracy in +religion + + align:start position:0% +religion + + + align:start position:0% +religion +you took what the priests gave you and + + align:start position:0% +you took what the priests gave you and + + + align:start position:0% +you took what the priests gave you and +the priests + + align:start position:0% +the priests + + + align:start position:0% +the priests +were were monitors of the holy of the + + align:start position:0% +were were monitors of the holy of the + + + align:start position:0% +were were monitors of the holy of the +holies if you look at the plans pated + + align:start position:0% +holies if you look at the plans pated + + + align:start position:0% +holies if you look at the plans pated +for the first temple you will see that + + align:start position:0% +for the first temple you will see that + + + align:start position:0% +for the first temple you will see that +structure + + align:start position:0% +structure + + + align:start position:0% +structure +um the Jews didn't have + + align:start position:0% +um the Jews didn't have + + + align:start position:0% +um the Jews didn't have +temples they either had to give up their + + align:start position:0% +temples they either had to give up their + + + align:start position:0% +temples they either had to give up their +religion or + + align:start position:0% +religion or + + + align:start position:0% +religion or +convert to some other Pagan religion + + align:start position:0% +convert to some other Pagan religion + + + align:start position:0% +convert to some other Pagan religion +having been the first Mono Mono + + align:start position:0% +having been the first Mono Mono + + + align:start position:0% +having been the first Mono Mono +Mono + + align:start position:0% +Mono + + + align:start position:0% +Mono +Mono + + align:start position:0% +Mono + + + align:start position:0% +Mono +ethicists of + + align:start position:0% +ethicists of + + + align:start position:0% +ethicists of +all having monotheism was founded in + + align:start position:0% +all having monotheism was founded in + + + align:start position:0% +all having monotheism was founded in +Jerusalem nobody quite knows how but the + + align:start position:0% +Jerusalem nobody quite knows how but the + + + align:start position:0% +Jerusalem nobody quite knows how but the +idea that many gods were dysfunctional + + align:start position:0% +idea that many gods were dysfunctional + + + align:start position:0% +idea that many gods were dysfunctional +and that a single God an invisible + + align:start position:0% +and that a single God an invisible + + + align:start position:0% +and that a single God an invisible +single God was the proper course for + + align:start position:0% +single God was the proper course for + + + align:start position:0% +single God was the proper course for +religious + + align:start position:0% +religious + + + align:start position:0% +religious +Faith so the Jews prayed in houses and + + align:start position:0% +Faith so the Jews prayed in houses and + + + align:start position:0% +Faith so the Jews prayed in houses and +in schools wherever they + + align:start position:0% +in schools wherever they + + + align:start position:0% +in schools wherever they +could this type substitution was an + + align:start position:0% +could this type substitution was an + + + align:start position:0% +could this type substitution was an +extraordinary idea + + align:start position:0% +extraordinary idea + + + align:start position:0% +extraordinary idea +the in the history of the + + align:start position:0% +the in the history of the + + + align:start position:0% +the in the history of the +church I found a reference to saying + + align:start position:0% +church I found a reference to saying + + + align:start position:0% +church I found a reference to saying +that this was the beginning of the idea + + 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align:start position:0% +in fact the conflict towards the end of + + + align:start position:0% +in fact the conflict towards the end of +the Jewish reign in Jerusalem at the + + align:start position:0% +the Jewish reign in Jerusalem at the + + + align:start position:0% +the Jewish reign in Jerusalem at the +time of Jesus it was very much a + + align:start position:0% +time of Jesus it was very much a + + + align:start position:0% +time of Jesus it was very much a +conflict between the priests of the + + align:start position:0% +conflict between the priests of the + + + align:start position:0% +conflict between the priests of the +second + + align:start position:0% +second + + + align:start position:0% +second +temple and the Pharisees who are + + align:start position:0% +temple and the Pharisees who are + + + align:start position:0% +temple and the Pharisees who are +advocating a beginning to Advocate a + + align:start position:0% +advocating a beginning to Advocate a + + + align:start position:0% +advocating a beginning to Advocate a +democratic religion in the form of the + + align:start position:0% +democratic religion in the form of the + + + align:start position:0% +democratic religion in the form of the +synagogue so the synagogue emerges in + + align:start position:0% +synagogue so the synagogue emerges in + + + align:start position:0% +synagogue so the synagogue emerges in +primitive form in the Exile of a Jewish + + align:start position:0% +primitive form in the Exile of a Jewish + + + align:start position:0% +primitive form in the Exile of a Jewish +group + + align:start position:0% +group + + + align:start position:0% +group +from the + + align:start position:0% +from the + + + align:start position:0% +from the +temple there + + align:start position:0% +temple there + + + align:start position:0% +temple there +it there's a second phenomenon which + + align:start position:0% +it there's a second phenomenon which + + + align:start position:0% +it there's a second phenomenon which +occurs during this period in the + + align:start position:0% +occurs during this period in the + + + align:start position:0% +occurs during this period in the +judeo-christian Bible there are seven + + align:start position:0% +judeo-christian Bible there are seven + + + align:start position:0% +judeo-christian Bible there are seven +chapters devoted to Ezekiel who was + + align:start position:0% +chapters devoted to Ezekiel who was + + + align:start position:0% +chapters devoted to Ezekiel who was +Ezekiel what role did he play in + + align:start position:0% +Ezekiel what role did he play in + + + align:start position:0% +Ezekiel what role did he play in +the you should know these things you are + + align:start position:0% +the you should know these things you are + + + align:start position:0% +the you should know these things you are +Christians or or Muslims or or other any + + align:start position:0% +Christians or or Muslims or or other any + + + align:start position:0% +Christians or or Muslims or or other any +other form of religion you know nothing + + align:start position:0% +other form of religion you know nothing + + + align:start position:0% +other form of religion you know nothing +about your own + + align:start position:0% +about your own + + + align:start position:0% +about your own +religion maybe all + + align:start position:0% + + + + align:start position:0% + +pagans which would be refreshing I + + align:start position:0% +pagans which would be refreshing I + + + align:start position:0% +pagans which would be refreshing I +suppose he was + + align:start position:0% +suppose he was + + + align:start position:0% +suppose he was +Captain + + align:start position:0% +Captain + + + align:start position:0% +Captain +well + + align:start position:0% +well + + + align:start position:0% +well +Ezekiel had a dream he was a prophet he + + align:start position:0% +Ezekiel had a dream he was a prophet he + + + align:start position:0% +Ezekiel had a dream he was a prophet he +had a dream that God and he encountered + + align:start position:0% +had a dream that God and he encountered + + + align:start position:0% +had a dream that God and he encountered +each other and he had instructions to de + + align:start position:0% +each other and he had instructions to de + + + align:start position:0% +each other and he had instructions to de +de to devise a new Temple there are six + + align:start position:0% +de to devise a new Temple there are six + + + align:start position:0% +de to devise a new Temple there are six +chapters in your Bible on + + align:start position:0% +chapters in your Bible on + + + align:start position:0% +chapters in your Bible on +ezekiel's dimensions for this for this + + align:start position:0% +ezekiel's dimensions for this for this + + + align:start position:0% +ezekiel's dimensions for this for this +new Temple imagine dreaming of a temple + + align:start position:0% +new Temple imagine dreaming of a temple + + + align:start position:0% +new Temple imagine dreaming of a temple +when you in Exile and designing it in + + align:start position:0% +when you in Exile and designing it in + + + align:start position:0% +when you in Exile and designing it in +your mind as a + + align:start position:0% +your mind as a + + + align:start position:0% +your mind as a +text anyway strange things + + align:start position:0% +text anyway strange things + + + align:start position:0% +text anyway strange things +happen ezekiel's Temple as I'll show you + + align:start position:0% +happen ezekiel's Temple as I'll show you + + + align:start position:0% +happen ezekiel's Temple as I'll show you +in the slides has been re redrawn and + + align:start position:0% +in the slides has been re redrawn and + + + align:start position:0% +in the slides has been re redrawn and +reimagined from these Dimensions over + + align:start position:0% +reimagined from these Dimensions over + + + align:start position:0% +reimagined from these Dimensions over +time the Jews return and the third + + align:start position:0% +time the Jews return and the third + + + align:start position:0% +time the Jews return and the third +significance of the stay in + + align:start position:0% +significance of the stay in + + + align:start position:0% +significance of the stay in +Babylon the Jewish + + align:start position:0% +Babylon the Jewish + + + align:start position:0% +Babylon the Jewish +talmood the book of laws + + align:start position:0% +talmood the book of laws + + + align:start position:0% +talmood the book of laws +has two versions the Palestinian version + + align:start position:0% +has two versions the Palestinian version + + + align:start position:0% +has two versions the Palestinian version +at least the Jerusalem version and the + + align:start position:0% +at least the Jerusalem version and the + + + align:start position:0% +at least the Jerusalem version and the +Babylonian version the Babylonian + + align:start position:0% +Babylonian version the Babylonian + + + align:start position:0% +Babylonian version the Babylonian +version is considered to be the + + align:start position:0% +version is considered to be the + + + align:start position:0% +version is considered to be the +preferred + + align:start position:0% +preferred + + + align:start position:0% +preferred +version so the Jews in Exile established + + align:start position:0% +version so the Jews in Exile established + + + align:start position:0% +version so the Jews in Exile established +a culture which they brought back to + + align:start position:0% +a culture which they brought back to + + + align:start position:0% +a culture which they brought back to +Jerusalem having been freed and Israel + + align:start position:0% +Jerusalem having been freed and Israel + + + align:start position:0% +Jerusalem having been freed and Israel +read the Bible to the people for the + + align:start position:0% +read the Bible to the people for the + + + align:start position:0% +read the Bible to the people for the +first time and they according to the + + align:start position:0% +first time and they according to the + + + align:start position:0% +first time and they according to the +text they wept + + align:start position:0% + + + + align:start position:0% + +the beginning of the idea that religion + + align:start position:0% +the beginning of the idea that religion + + + align:start position:0% +the beginning of the idea that religion +is a democratic + + align:start position:0% +is a democratic + + + align:start position:0% +is a democratic +phenomenon is my explanation for the + + align:start position:0% +phenomenon is my explanation for the + + + align:start position:0% +phenomenon is my explanation for the +problem of + + align:start position:0% +problem of + + + align:start position:0% +problem of +Jesus I have a rather excentric version + + align:start position:0% +Jesus I have a rather excentric version + + + align:start position:0% +Jesus I have a rather excentric version +of the + + align:start position:0% +of the + + + align:start position:0% +of the +story what happens we we jump a th we + + align:start position:0% +story what happens we we jump a th we + + + align:start position:0% +story what happens we we jump a th we +jump 500 years and Herod builds rebuilds + + align:start position:0% +jump 500 years and Herod builds rebuilds + + + align:start position:0% +jump 500 years and Herod builds rebuilds +the temple he build an enormous Temple + + align:start position:0% +the temple he build an enormous Temple + + + align:start position:0% +the temple he build an enormous Temple +bigger than + + align:start position:0% + + + + align:start position:0% + +before the priests are again now in + + align:start position:0% + + + + align:start position:0% + +control they control + + align:start position:0% +control they control + + + align:start position:0% +control they control +Power they control the artifacts of + + align:start position:0% +Power they control the artifacts of + + + align:start position:0% +Power they control the artifacts of +religion they control property they + + align:start position:0% +religion they control property they + + + align:start position:0% +religion they control property they +control everything in the + + align:start position:0% + + + + align:start position:0% + +city Along Comes a Jew + + align:start position:0% +city Along Comes a Jew + + + align:start position:0% +city Along Comes a Jew +a radical Jew has another ver vision of + + align:start position:0% +a radical Jew has another ver vision of + + + align:start position:0% +a radical Jew has another ver vision of +the + + align:start position:0% + + + + align:start position:0% + +world Jesus doesn't threaten the Romans + + align:start position:0% +world Jesus doesn't threaten the Romans + + + align:start position:0% +world Jesus doesn't threaten the Romans +very + + align:start position:0% +very + + + align:start position:0% +very +much the Romans are used to dealing with + + align:start position:0% +much the Romans are used to dealing with + + + align:start position:0% +much the Romans are used to dealing with +all over the Empire with infidels they + + align:start position:0% +all over the Empire with infidels they + + + align:start position:0% +all over the Empire with infidels they +just block them up or cut their heads + + align:start position:0% +just block them up or cut their heads + + + align:start position:0% +just block them up or cut their heads +off very explicit + + align:start position:0% +off very explicit + + + align:start position:0% +off very explicit +rules others they in a rather difficult + + align:start position:0% +rules others they in a rather difficult + + + align:start position:0% +rules others they in a rather difficult +situation + + align:start position:0% +situation + + + align:start position:0% +situation +the + + align:start position:0% +the + + + align:start position:0% +the +priests are more threatened by Jesus + + align:start position:0% +priests are more threatened by Jesus + + + align:start position:0% +priests are more threatened by Jesus +than are the + + align:start position:0% +than are the + + + align:start position:0% +than are the +Romans the priests therefore + + align:start position:0% +Romans the priests therefore + + + align:start position:0% +Romans the priests therefore +connive with the Romans to execute + + align:start position:0% +connive with the Romans to execute + + + align:start position:0% +connive with the Romans to execute +Jesus the notion of execution of your + + align:start position:0% +Jesus the notion of execution of your + + + align:start position:0% +Jesus the notion of execution of your +son occurs in the geic Christian Bible + + align:start position:0% +son occurs in the geic Christian Bible + + + align:start position:0% +son occurs in the geic Christian Bible +beforeand although it wasn't legal the + + align:start position:0% +beforeand although it wasn't legal the + + + align:start position:0% +beforeand although it wasn't legal the +IDE aidea of passing your son on as a + + align:start position:0% + + + + align:start position:0% + +gift the use of + + align:start position:0% +gift the use of + + + align:start position:0% +gift the use of +blood 22,000 oxen were killed in the + + align:start position:0% +blood 22,000 oxen were killed in the + + + align:start position:0% +blood 22,000 oxen were killed in the +dedication of the Temple of + + align:start position:0% +dedication of the Temple of + + + align:start position:0% +dedication of the Temple of +Solomon the whole idea of giving + + align:start position:0% +Solomon the whole idea of giving + + + align:start position:0% +Solomon the whole idea of giving +something to God as a gift if you were + + align:start position:0% +something to God as a gift if you were + + + align:start position:0% +something to God as a gift if you were +poor you brought a a + + align:start position:0% +poor you brought a a + + + align:start position:0% +poor you brought a a +chicken to the temple to the priests if + + align:start position:0% +chicken to the temple to the priests if + + + align:start position:0% +chicken to the temple to the priests if +if you were wealthy you brought a cow an + + align:start position:0% +if you were wealthy you brought a cow an + + + align:start position:0% +if you were wealthy you brought a cow an +ox if you were very wealthy go Lord le + + align:start position:0% +ox if you were very wealthy go Lord le + + + align:start position:0% +ox if you were very wealthy go Lord le +as you donated your son the story of + + align:start position:0% +as you donated your son the story of + + + align:start position:0% +as you donated your son the story of +Abraham and Isaac is that same version + + align:start position:0% +Abraham and Isaac is that same version + + + align:start position:0% +Abraham and Isaac is that same version +of the of that + + align:start position:0% +of the of that + + + align:start position:0% +of the of that +giftgiving the Supreme gift is the gift + + align:start position:0% +giftgiving the Supreme gift is the gift + + + align:start position:0% +giftgiving the Supreme gift is the gift +of your son and the Jesus story is the + + align:start position:0% +of your son and the Jesus story is the + + + align:start position:0% +of your son and the Jesus story is the +Su is archetypally the story of God + + align:start position:0% +Su is archetypally the story of God + + + align:start position:0% +Su is archetypally the story of God +donating his + + align:start position:0% +donating his + + + align:start position:0% +donating his +son again + + align:start position:0% + + + + align:start position:0% + +for the Improvement of the + + align:start position:0% +for the Improvement of the + + + align:start position:0% +for the Improvement of the +world the Christianity is based on many + + align:start position:0% +world the Christianity is based on many + + + align:start position:0% +world the Christianity is based on many +mythical + + align:start position:0% +mythical + + + align:start position:0% +mythical +stories which emanate from the history + + align:start position:0% +stories which emanate from the history + + + align:start position:0% +stories which emanate from the history +of Jerusalem and he's the second + + align:start position:0% +of Jerusalem and he's the second + + + align:start position:0% +of Jerusalem and he's the second +monotheistic religion to emerge out of + + align:start position:0% +monotheistic religion to emerge out of + + + align:start position:0% +monotheistic religion to emerge out of +the + + align:start position:0% + + + + align:start position:0% + +city Muhammad is is born in 570 + + align:start position:0% +city Muhammad is is born in 570 + + + align:start position:0% +city Muhammad is is born in 570 +BC fights his battles in Mecca and + + align:start position:0% +BC fights his battles in Mecca and + + + align:start position:0% +BC fights his battles in Mecca and +Medina spreads the idea of Islam as a + + align:start position:0% +Medina spreads the idea of Islam as a + + + align:start position:0% +Medina spreads the idea of Islam as a +the third great monistic + + align:start position:0% +the third great monistic + + + align:start position:0% +the third great monistic +religion through the Arabian + + align:start position:0% +religion through the Arabian + + + align:start position:0% +religion through the Arabian +Peninsula and soon + + align:start position:0% +Peninsula and soon + + + align:start position:0% +Peninsula and soon +afterwards Jerusalem is invaded by the + + align:start position:0% +afterwards Jerusalem is invaded by the + + + align:start position:0% +afterwards Jerusalem is invaded by the +first Arab + + align:start position:0% + + + + align:start position:0% + +group significant the + + align:start position:0% +group significant the + + + align:start position:0% +group significant the +Christians had chosen a site for their + + align:start position:0% +Christians had chosen a site for their + + + align:start position:0% +Christians had chosen a site for their +great + + align:start position:0% +great + + + align:start position:0% +great +church constantin's mother Helena from + + align:start position:0% +church constantin's mother Helena from + + + align:start position:0% +church constantin's mother Helena from +Istanbul or + + align:start position:0% +Istanbul or + + + align:start position:0% +Istanbul or +Constantinople drifted down to Jerusalem + + align:start position:0% +Constantinople drifted down to Jerusalem + + + align:start position:0% +Constantinople drifted down to Jerusalem +and is supposed to have selected the + + align:start position:0% +and is supposed to have selected the + + + align:start position:0% +and is supposed to have selected the +site where Jesus was + + align:start position:0% +site where Jesus was + + + align:start position:0% +site where Jesus was +killed on the basis of that information + + align:start position:0% +killed on the basis of that information + + + align:start position:0% +killed on the basis of that information +the Church of the Holy sepula was built + + align:start position:0% +the Church of the Holy sepula was built + + + align:start position:0% +the Church of the Holy sepula was built +and is still in existence today having + + align:start position:0% +and is still in existence today having + + + align:start position:0% +and is still in existence today having +been destroyed seven times and + + align:start position:0% + + + + align:start position:0% + +rebuilt the Arabs arrive in Jerusalem + + align:start position:0% +rebuilt the Arabs arrive in Jerusalem + + + align:start position:0% +rebuilt the Arabs arrive in Jerusalem +they're the + + align:start position:0% + + + + align:start position:0% + +newcomers they they ask the Christian + + align:start position:0% +newcomers they they ask the Christian + + + align:start position:0% +newcomers they they ask the Christian +Bishop uh about sites for their own + + align:start position:0% + + + + align:start position:0% + +mosque the Temple Mount which had been + + align:start position:0% +mosque the Temple Mount which had been + + + align:start position:0% +mosque the Temple Mount which had been +the site of the Jewish temp Temple had + + align:start position:0% +the site of the Jewish temp Temple had + + + align:start position:0% +the site of the Jewish temp Temple had +been raised by the Romans and there was + + align:start position:0% +been raised by the Romans and there was + + + align:start position:0% +been raised by the Romans and there was +nothing left for 500 years the Temple + + align:start position:0% +nothing left for 500 years the Temple + + + align:start position:0% +nothing left for 500 years the Temple +Mount was a rubbish dump of old parts of + + align:start position:0% +Mount was a rubbish dump of old parts of + + + align:start position:0% +Mount was a rubbish dump of old parts of +buildings and so on the Christians + + align:start position:0% +buildings and so on the Christians + + + align:start position:0% +buildings and so on the Christians +wanted nothing to do with it in fact the + + align:start position:0% +wanted nothing to do with it in fact the + + + align:start position:0% +wanted nothing to do with it in fact the +Church of the Holy sepa which is you was + + align:start position:0% +Church of the Holy sepa which is you was + + + align:start position:0% +Church of the Holy sepa which is you was +usually under the Roman city entered + + align:start position:0% +usually under the Roman city entered + + + align:start position:0% +usually under the Roman city entered +from the C on the west at least on the + + align:start position:0% +from the C on the west at least on the + + + align:start position:0% +from the C on the west at least on the +East was closed and you now enter the + + align:start position:0% +East was closed and you now enter the + + + align:start position:0% +East was closed and you now enter the +Church of the Holy Seer only from the + + align:start position:0% +Church of the Holy Seer only from the + + + align:start position:0% +Church of the Holy Seer only from the +south on the East now there's the best + + align:start position:0% +south on the East now there's the best + + + align:start position:0% +south on the East now there's the best +candy store in Jerusalem on the + + align:start position:0% +candy store in Jerusalem on the + + + align:start position:0% +candy store in Jerusalem on the +cardo + + align:start position:0% +cardo + + + align:start position:0% +cardo +um so the + + align:start position:0% +um so the + + + align:start position:0% +um so the 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+penetrators thought that the that the + + + align:start position:0% +penetrators thought that the that the +mythological origins of the use of the + + align:start position:0% +mythological origins of the use of the + + + align:start position:0% +mythological origins of the use of the +Temple Mount was sufficient for them to + + align:start position:0% +Temple Mount was sufficient for them to + + + align:start position:0% +Temple Mount was sufficient for them to +follow the Jewish tradition of the + + align:start position:0% +follow the Jewish tradition of the + + + align:start position:0% +follow the Jewish tradition of the +destroyed + + align:start position:0% +destroyed + + + align:start position:0% +destroyed +Temple so they rebuild the Temple + + align:start position:0% +Temple so they rebuild the Temple + + + align:start position:0% +Temple so they rebuild the Temple +Mountain about + + align:start position:0% +Mountain about + + + align:start position:0% +Mountain about +100 years + + align:start position:0% +100 years + + + align:start position:0% +100 years +after uh M Muhammad's + + align:start position:0% +after uh M Muhammad's + + + align:start position:0% +after uh M Muhammad's +birth and build the two buildings which + + align:start position:0% +birth and build the two buildings which + + + align:start position:0% +birth and build the two buildings which +are still there today the Dome of the + + align:start position:0% +are still there today the Dome of the + + + align:start position:0% +are still there today the Dome of the +Rock and the alaka + + align:start position:0% + + + + align:start position:0% + +mosque in my writing I go through + + align:start position:0% +mosque in my writing I go through + + + align:start position:0% +mosque in my writing I go through +detailed history of the idea of + + align:start position:0% +detailed history of the idea of + + + align:start position:0% +detailed history of the idea of +resilience how under in these + + align:start position:0% +resilience how under in these + + + align:start position:0% +resilience how under in these +occupations each religion plays around + + align:start position:0% +occupations each religion plays around + + + align:start position:0% +occupations each religion plays around +with the idea of permanence + + align:start position:0% + + + + align:start position:0% + +the Christians in the in the Holy + + align:start position:0% +the Christians in the in the Holy + + + align:start position:0% +the Christians in the in the Holy +sepa never + + align:start position:0% +sepa never + + + align:start position:0% +sepa never +really agree on the fundamentals of the + + align:start position:0% +really agree on the fundamentals of the + + + align:start position:0% +really agree on the fundamentals of the +Christian faith May whilst they may + + align:start position:0% +Christian faith May whilst they may + + + align:start position:0% +Christian faith May whilst they may +agree on the fundamentals they don't + + align:start position:0% +agree on the fundamentals they don't + + + align:start position:0% +agree on the fundamentals they don't +agree on its + + align:start position:0% +agree on its + + + align:start position:0% +agree on its +application so 70% of the Holy SE is + + align:start position:0% +application so 70% of the Holy SE is + + + align:start position:0% +application so 70% of the Holy SE is +still under Greek + + align:start position:0% +still under Greek + + + align:start position:0% +still under Greek +Christian the poor + + align:start position:0% +Christian the poor + + + align:start position:0% +Christian the poor +African Ethiopian Christians live on the + + align:start position:0% +African Ethiopian Christians live on the + + + align:start position:0% +African Ethiopian Christians live on the +roof and are not only allowed to enter + + align:start position:0% +roof and are not only allowed to enter + + + align:start position:0% +roof and are not only allowed to enter +the major Tabernacle by a small + + align:start position:0% +the major Tabernacle by a small + + + align:start position:0% +the major Tabernacle by a small +staircase um as one of the writers + + align:start position:0% +staircase um as one of the writers + + + align:start position:0% +staircase um as one of the writers +right + + align:start position:0% +right + + + align:start position:0% +right +uh they are all divided by + + align:start position:0% +uh they are all divided by + + + align:start position:0% +uh they are all divided by +faith or something of this kind so you + + align:start position:0% +faith or something of this kind so you + + + align:start position:0% +faith or something of this kind so you +have the notion of + + align:start position:0% +have the notion of + + + align:start position:0% +have the notion of +a of of of of of the three major + + align:start position:0% +a of of of of of the three major + + + align:start position:0% +a of of of of of the three major +religions having in the case of the + + align:start position:0% +religions having in the case of the + + + align:start position:0% +religions having in the case of the +Christians an artifact which + + align:start position:0% +Christians an artifact which + + + align:start position:0% +Christians an artifact which +is houses divided aspects of the + + align:start position:0% +is houses divided aspects of the + + + align:start position:0% +is houses divided aspects of the +religion they are fires they are people + + align:start position:0% +religion they are fires they are people + + + align:start position:0% +religion they are fires they are people +killed they are all kinds of dis + + align:start position:0% +killed they are all kinds of dis + + + align:start position:0% +killed they are all kinds of dis +disjunctions between these groups but + + align:start position:0% +disjunctions between these groups but + + + align:start position:0% +disjunctions between these groups but +Christianity + + align:start position:0% +Christianity + + + align:start position:0% +Christianity +survives on the Islamic front you have + + align:start position:0% +survives on the Islamic front you have + + + align:start position:0% +survives on the Islamic front you have +the + + align:start position:0% +the + + + align:start position:0% +the +church the Dome of The Rock and the AL + + align:start position:0% +church the Dome of The Rock and the AL + + + align:start position:0% +church the Dome of The Rock and the AL +MOS which survived to this day + + align:start position:0% +MOS which survived to this day + + + align:start position:0% +MOS which survived to this day +unblemished in 1099 the Crusaders under + + align:start position:0% +unblemished in 1099 the Crusaders under + + + align:start position:0% +unblemished in 1099 the Crusaders under +the pressure from the popes of Europe + + align:start position:0% +the pressure from the popes of Europe + + + align:start position:0% +the pressure from the popes of Europe +attempt to re restore + + align:start position:0% +attempt to re restore + + + align:start position:0% +attempt to re restore +Christianity um instead of disant they + + align:start position:0% +Christianity um instead of disant they + + + align:start position:0% +Christianity um instead of disant they +are absolutely ruthless to the degree + + align:start position:0% +are absolutely ruthless to the degree + + + align:start position:0% +are absolutely ruthless to the degree +that they kill everybody in their sight + + align:start position:0% +that they kill everybody in their sight + + + align:start position:0% +that they kill everybody in their sight +they kill Muslims and Jews + + align:start position:0% +they kill Muslims and Jews + + + align:start position:0% +they kill Muslims and Jews +and in the blood of their boots they + + align:start position:0% +and in the blood of their boots they + + + align:start position:0% +and in the blood of their boots they +walk to the holy sepil and + + align:start position:0% +walk to the holy sepil and + + + align:start position:0% +walk to the holy sepil and +pray there's always this kind of + + align:start position:0% +pray there's always this kind of + + + align:start position:0% +pray there's always this kind of +biblical in in interest interesting + + align:start position:0% +biblical in in interest interesting + + + align:start position:0% +biblical in in interest interesting +biblical thing which I focus on also + + align:start position:0% +biblical thing which I focus on also + + + align:start position:0% +biblical thing which I focus on also +that the interpretation of God is always + + align:start position:0% +that the interpretation of God is always + + + align:start position:0% +that the interpretation of God is always +ambiguous God is + + align:start position:0% +ambiguous God is + + + align:start position:0% +ambiguous God is +always punishing people for doing the + + align:start position:0% +always punishing people for doing the + + + align:start position:0% +always punishing people for doing the +wrong things but he's also forgiving if + + align:start position:0% +wrong things but he's also forgiving if + + + align:start position:0% +wrong things but he's also forgiving if +you come to terms with him + + align:start position:0% +you come to terms with him + + + align:start position:0% +you come to terms with him +or + + align:start position:0% +or + + + align:start position:0% +or +her depending on what you + + align:start position:0% +her depending on what you + + + align:start position:0% +her depending on what you +believe so the Crusaders behave in this + + align:start position:0% +believe so the Crusaders behave in this + + + align:start position:0% +believe so the Crusaders behave in this +apparently bifocal way they destroy + + align:start position:0% +apparently bifocal way they destroy + + + align:start position:0% +apparently bifocal way they destroy +everybody whom they see in their sight + + align:start position:0% +everybody whom they see in their sight + + + align:start position:0% +everybody whom they see in their sight +violently and at the same time they they + + align:start position:0% +violently and at the same time they they + + + align:start position:0% +violently and at the same time they they +go and sing hymns in their + + align:start position:0% +go and sing hymns in their + + + align:start position:0% +go and sing hymns in their +church now there may be parallels in + + align:start position:0% +church now there may be parallels in + + + align:start position:0% +church now there may be parallels in +contemporary violence as well I don't + + align:start position:0% +contemporary violence as well I don't + + + align:start position:0% +contemporary violence as well I don't +know if it's a Bor in Instinct in + + align:start position:0% +know if it's a Bor in Instinct in + + + align:start position:0% +know if it's a Bor in Instinct in +humankind that you modify your behavior + + align:start position:0% +humankind that you modify your behavior + + + align:start position:0% +humankind that you modify your behavior +in two distinct ways according to your + + align:start position:0% +in two distinct ways according to your + + + align:start position:0% +in two distinct ways according to your +belief + + align:start position:0% +belief + + + align:start position:0% +belief +system the Jews have lost two temples + + align:start position:0% +system the Jews have lost two temples + + + align:start position:0% +system the Jews have lost two temples +they're now in + + align:start position:0% +they're now in + + + align:start position:0% +they're now in +Exile they take with them books that's + + align:start position:0% +Exile they take with them books that's + + + align:start position:0% +Exile they take with them books that's +the only property they + + align:start position:0% +the only property they + + + align:start position:0% +the only property they +have there's writers + + align:start position:0% +have there's writers + + + align:start position:0% +have there's writers +here shall + + align:start position:0% +here shall + + + align:start position:0% +here shall +the + + align:start position:0% +the + + + align:start position:0% +the +American Jewish theolog liberal + + align:start position:0% +American Jewish theolog liberal + + + align:start position:0% +American Jewish theolog liberal +theological Rabbi Mitchell schwarer did + + align:start position:0% +theological Rabbi Mitchell schwarer did + + + align:start position:0% +theological Rabbi Mitchell schwarer did +his PhD at MIT write about the idea of + + align:start position:0% +his PhD at MIT write about the idea of + + + align:start position:0% +his PhD at MIT write about the idea of +the Jewish + + align:start position:0% +the Jewish + + + align:start position:0% +the Jewish +book as the significant property of + + align:start position:0% +book as the significant property of + + + align:start position:0% +book as the significant property of +memory they argue that in fact the uh I + + align:start position:0% +memory they argue that in fact the uh I + + + align:start position:0% +memory they argue that in fact the uh I +think aelu talks about the Jewish + + align:start position:0% +think aelu talks about the Jewish + + + align:start position:0% +think aelu talks about the Jewish +religion as being a religion of the + + align:start position:0% +religion as being a religion of the + + + align:start position:0% +religion as being a religion of the +architecture of + + align:start position:0% +architecture of + + + align:start position:0% +architecture of +time if you look at the layout of a text + + align:start position:0% +time if you look at the layout of a text + + + align:start position:0% +time if you look at the layout of a text +in the mishna you'll see a body of + + align:start position:0% +in the mishna you'll see a body of + + + align:start position:0% +in the mishna you'll see a body of +writing and on the sides + + align:start position:0% +writing and on the sides + + + align:start position:0% +writing and on the sides +of talmudic interpretations by rabbis + + align:start position:0% +of talmudic interpretations by rabbis + + + align:start position:0% +of talmudic interpretations by rabbis +over time so that the truth is never + + align:start position:0% +over time so that the truth is never + + + align:start position:0% +over time so that the truth is never +absolute in this one sense that it's + + align:start position:0% +absolute in this one sense that it's + + + align:start position:0% +absolute in this one sense that it's +always open to to + + align:start position:0% +always open to to + + + align:start position:0% +always open to to +discussion it's also that the Jews took + + align:start position:0% +discussion it's also that the Jews took + + + align:start position:0% +discussion it's also that the Jews took +upon themselves and Freud himself who at + + align:start position:0% +upon themselves and Freud himself who at + + + align:start position:0% +upon themselves and Freud himself who at +one time decided thought about going to + + align:start position:0% +one time decided thought about going to + + + align:start position:0% +one time decided thought about going to +live in + + align:start position:0% +live in + + + align:start position:0% +live in +Jerusalem + + align:start position:0% +Jerusalem + + + align:start position:0% +Jerusalem +um says that the + + align:start position:0% +um says that the + + + align:start position:0% +um says that the +Jews preoccupied themselves with + + align:start position:0% +Jews preoccupied themselves with + + + align:start position:0% +Jews preoccupied themselves with +avoiding pictorial imagery you cannot + + align:start position:0% +avoiding pictorial imagery you cannot + + + align:start position:0% +avoiding pictorial imagery you cannot +decorate to + + align:start position:0% +decorate to + + + align:start position:0% +decorate to +synagogue the text has to be absolutely + + align:start position:0% +synagogue the text has to be absolutely + + + align:start position:0% +synagogue the text has to be absolutely +pure + + align:start position:0% +pure + + + align:start position:0% +pure +Jews didn't become Architects they were + + align:start position:0% +Jews didn't become Architects they were + + + align:start position:0% +Jews didn't become Architects they were +never in a power position in exile for + + align:start position:0% +never in a power position in exile for + + + align:start position:0% +never in a power position in exile for +thousands of years well thousands of + + align:start position:0% +thousands of years well thousands of + + + align:start position:0% +thousands of years well thousands of +years Peter Eisen Eisenman is frankia + + align:start position:0% +years Peter Eisen Eisenman is frankia + + + align:start position:0% +years Peter Eisen Eisenman is frankia +Jewish and I suppose that we made up for + + align:start position:0% +Jewish and I suppose that we made up for + + + align:start position:0% +Jewish and I suppose that we made up for +all of that last + + align:start position:0% +all of that last + + + align:start position:0% +all of that last +time + + align:start position:0% +time + + + align:start position:0% +time +uh + + align:start position:0% +uh + + + align:start position:0% +uh +but the Jewish presence after 70 AD was + + align:start position:0% +but the Jewish presence after 70 AD was + + + align:start position:0% +but the Jewish presence after 70 AD was +in Exile + + align:start position:0% +in Exile + + + align:start position:0% +in Exile +until the slow Return of the Jews in the + + align:start position:0% +until the slow Return of the Jews in the + + + align:start position:0% +until the slow Return of the Jews in the +otoman period which lasted from about + + align:start position:0% +otoman period which lasted from about + + + align:start position:0% +otoman period which lasted from about +1500 to + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +um I hope you've following all of these + + align:start position:0% +um I hope you've following all of these + + + align:start position:0% +um I hope you've following all of these +detailed stories + + align:start position:0% +detailed stories + + + align:start position:0% +detailed stories +but in a sense it's only by looking at + + align:start position:0% +but in a sense it's only by looking at + + + align:start position:0% +but in a sense it's only by looking at +the detailed sides of these stories that + + align:start position:0% +the detailed sides of these stories that + + + align:start position:0% +the detailed sides of these stories that +you really get a good idea of the + + align:start position:0% +you really get a good idea of the + + + align:start position:0% +you really get a good idea of the +complex of the situation to say Arab I + + align:start position:0% +complex of the situation to say Arab I + + + align:start position:0% +complex of the situation to say Arab I +mean of the 3,000 years of the history + + align:start position:0% +mean of the 3,000 years of the history + + + align:start position:0% +mean of the 3,000 years of the history +of jerusalm 1200 years have been under + + align:start position:0% +of jerusalm 1200 years have been under + + + align:start position:0% +of jerusalm 1200 years have been under +the Israelites or the Jews and 1200 + + align:start position:0% +the Israelites or the Jews and 1200 + + + align:start position:0% +the Israelites or the Jews and 1200 +years under the Arabs or + + align:start position:0% + + + + align:start position:0% + +Islam whatever that means the rest is + + align:start position:0% +Islam whatever that means the rest is + + + align:start position:0% +Islam whatever that means the rest is +divided amongst the Christians and the + + align:start position:0% +divided amongst the Christians and the + + + align:start position:0% +divided amongst the Christians and the +Romans Jerusalem was in the first place + + align:start position:0% +Romans Jerusalem was in the first place + + + align:start position:0% +Romans Jerusalem was in the first place +not a particularly important city + + align:start position:0% + + + + align:start position:0% + +it was too + + align:start position:0% +it was too + + + align:start position:0% +it was too +steep it was the + + align:start position:0% +steep it was the + + + align:start position:0% +steep it was the +main circulation path was to the e to + + align:start position:0% +main circulation path was to the e to + + + align:start position:0% +main circulation path was to the e to +the West along the + + align:start position:0% +the West along the + + + align:start position:0% +the West along the +Mediterranean Jerusalem was the was the + + align:start position:0% +Mediterranean Jerusalem was the was the + + + align:start position:0% +Mediterranean Jerusalem was the was the +last connector + + align:start position:0% +last connector + + + align:start position:0% +last connector +between the coastal plane and the + + align:start position:0% +between the coastal plane and the + + + align:start position:0% +between the coastal plane and the +endless desert which stretched all the + + align:start position:0% +endless desert which stretched all the + + + align:start position:0% +endless desert which stretched all the +way to + + align:start position:0% + + + + align:start position:0% + +India the Dead Sea close to Jerusalem + + align:start position:0% +India the Dead Sea close to Jerusalem + + + align:start position:0% +India the Dead Sea close to Jerusalem +was the lowest point on + + align:start position:0% +was the lowest point on + + + align:start position:0% +was the lowest point on +Earth so there was I'll show you a slide + + align:start position:0% +Earth so there was I'll show you a slide + + + align:start position:0% +Earth so there was I'll show you a slide +indicating this division of geographical + + align:start position:0% +indicating this division of geographical + + + align:start position:0% +indicating this division of geographical +division on which Jerusalem + + align:start position:0% +division on which Jerusalem + + + align:start position:0% +division on which Jerusalem +sits Alexander the Great visited + + align:start position:0% +sits Alexander the Great visited + + + align:start position:0% +sits Alexander the Great visited +Jerusalem this was an + + align:start position:0% +Jerusalem this was an + + + align:start position:0% +Jerusalem this was an +enormous victory for the Jews many Jews + + align:start position:0% +enormous victory for the Jews many Jews + + + align:start position:0% +enormous victory for the Jews many Jews +including my son are named + + align:start position:0% +including my son are named + + + align:start position:0% +including my son are named +Alexander because of that tradition + + align:start position:0% +Alexander because of that tradition + + + align:start position:0% +Alexander because of that tradition +his first name is + + align:start position:0% +his first name is + + + align:start position:0% +his first name is +Peter but his second name is Alexander I + + align:start position:0% +Peter but his second name is Alexander I + + + align:start position:0% +Peter but his second name is Alexander I +named him + + align:start position:0% +named him + + + align:start position:0% +named him +after + + align:start position:0% +after + + + align:start position:0% +after +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Russian Russian Giants rather than + + align:start position:0% +Russian Russian Giants rather than + + + align:start position:0% +Russian Russian Giants rather than +Jewish + + align:start position:0% + + + + align:start position:0% + +hero + + align:start position:0% + + + + align:start position:0% + +so Zionism as a + + align:start position:0% +so Zionism as a + + + align:start position:0% +so Zionism as a +phenomenon + + align:start position:0% +phenomenon + + + align:start position:0% +phenomenon +occurs in + + align:start position:0% +occurs in + + + align:start position:0% +occurs in +Europe as this cont consequence of the + + align:start position:0% +Europe as this cont consequence of the + + + align:start position:0% +Europe as this cont consequence of the +marginalization of Jews in Central + + align:start position:0% +marginalization of Jews in Central + + + align:start position:0% +marginalization of Jews in Central +Europe and all the way to England and + + align:start position:0% +Europe and all the way to England and + + + align:start position:0% +Europe and all the way to England and +France the disposition of Jewish land + + align:start position:0% +France the disposition of Jewish land + + + align:start position:0% +France the disposition of Jewish land +the Jews under under one of the early I + + align:start position:0% +the Jews under under one of the early I + + + align:start position:0% +the Jews under under one of the early I +think 12th century English kings had to + + align:start position:0% +think 12th century English kings had to + + + align:start position:0% +think 12th century English kings had to +wear labels marking them as + + align:start position:0% +wear labels marking them as + + + align:start position:0% +wear labels marking them as +Jews uh the pgms of Eastern Europe I + + align:start position:0% +Jews uh the pgms of Eastern Europe I + + + align:start position:0% +Jews uh the pgms of Eastern Europe I +mean it's a long history which precedes + + align:start position:0% +mean it's a long history which precedes + + + align:start position:0% +mean it's a long history which precedes +the so the + + align:start position:0% +the so the + + + align:start position:0% +the so the +Holocaust uh and Jewish reaction to P + + align:start position:0% +Holocaust uh and Jewish reaction to P + + + align:start position:0% +Holocaust uh and Jewish reaction to P +persecution and + + align:start position:0% +persecution and + + + align:start position:0% +persecution and +Punishment took the form of a Biblical + + align:start position:0% +Punishment took the form of a Biblical + + + align:start position:0% +Punishment took the form of a Biblical +notion of next year in + + align:start position:0% +notion of next year in + + + align:start position:0% +notion of next year in +Jerusalem in the Jewish Passover service + + align:start position:0% +Jerusalem in the Jewish Passover service + + + align:start position:0% +Jerusalem in the Jewish Passover service +there's this phrase next year in + + align:start position:0% +there's this phrase next year in + + + align:start position:0% +there's this phrase next year in +Jerusalem the Jewish Passover unlike the + + align:start position:0% +Jerusalem the Jewish Passover unlike the + + + align:start position:0% +Jerusalem the Jewish Passover unlike the +Christian Easter is not dedicated very + + align:start position:0% +Christian Easter is not dedicated very + + + align:start position:0% +Christian Easter is not dedicated very +much to + + align:start position:0% +much to + + + align:start position:0% +much to +religious idea + + align:start position:0% +religious idea + + + align:start position:0% +religious idea +but related to The Escape Under Moses + + align:start position:0% +but related to The Escape Under Moses + + + align:start position:0% +but related to The Escape Under Moses +from + + align:start position:0% +from + + + align:start position:0% +from +Egypt and God parting the Red Sea to + + align:start position:0% +Egypt and God parting the Red Sea to + + + align:start position:0% +Egypt and God parting the Red Sea to +allow the Jews to + + align:start position:0% +allow the Jews to + + + align:start position:0% +allow the Jews to +escape how true that story is whether + + align:start position:0% +escape how true that story is whether + + + align:start position:0% +escape how true that story is whether +Freud claims that Moses was in fact a + + align:start position:0% +Freud claims that Moses was in fact a + + + align:start position:0% +Freud claims that Moses was in fact a +Egyptian uh who had learned + + align:start position:0% +Egyptian uh who had learned + + + align:start position:0% +Egyptian uh who had learned +about anyway I'm there too many + + align:start position:0% +about anyway I'm there too many + + + align:start position:0% +about anyway I'm there too many +stories when you get all of these people + + align:start position:0% +stories when you get all of these people + + + align:start position:0% +stories when you get all of these people +having been involved in this dialogue on + + align:start position:0% +having been involved in this dialogue on + + + align:start position:0% +having been involved in this dialogue on +this + + align:start position:0% +this + + + align:start position:0% +this +multilog you have many + + align:start position:0% +multilog you have many + + + align:start position:0% +multilog you have many +stories the Ottoman Empire chooses to + + align:start position:0% +stories the Ottoman Empire chooses to + + + align:start position:0% +stories the Ottoman Empire chooses to +take the wrong side in the 1418 War and + + align:start position:0% +take the wrong side in the 1418 War and + + + align:start position:0% +take the wrong side in the 1418 War and +the British take over + + align:start position:0% +the British take over + + + align:start position:0% +the British take over +Jerusalem they maintained Jerusalem as a + + align:start position:0% +Jerusalem they maintained Jerusalem as a + + + align:start position:0% +Jerusalem they maintained Jerusalem as a +mandate until + + align:start position:0% +mandate until + + + align:start position:0% +mandate until +1948 when the is + + align:start position:0% +1948 when the is + + + align:start position:0% +1948 when the is +the war of + + align:start position:0% +the war of + + + align:start position:0% +the war of +independence and the Jewish state of + + align:start position:0% +independence and the Jewish state of + + + align:start position:0% +independence and the Jewish state of +Israel is founded 70 years ago + + align:start position:0% + + + + align:start position:0% + +now East Jerusalem is is belongs to + + align:start position:0% +now East Jerusalem is is belongs to + + + align:start position:0% +now East Jerusalem is is belongs to +Jordan West Jerusalem + + align:start position:0% +Jordan West Jerusalem + + + align:start position:0% +Jordan West Jerusalem +to Israel + + align:start position:0% +to Israel + + + align:start position:0% +to Israel +1967 Another War this time the Jews + + align:start position:0% + + + + align:start position:0% + +Jews expelled Jordan from East + + align:start position:0% +Jews expelled Jordan from East + + + align:start position:0% +Jews expelled Jordan from East +Jerusalem and in fact Annex the West + + align:start position:0% +Jerusalem and in fact Annex the West + + + align:start position:0% +Jerusalem and in fact Annex the West +Bank to United + + align:start position:0% + + + + align:start position:0% + +Israel the United Nations + + align:start position:0% +Israel the United Nations + + + align:start position:0% +Israel the United Nations +proposes that Jerusalem be a + + align:start position:0% +proposes that Jerusalem be a + + + align:start position:0% +proposes that Jerusalem be a +international + + align:start position:0% +international + + + align:start position:0% +international +City they actually have a diagram of the + + align:start position:0% +City they actually have a diagram of the + + + align:start position:0% +City they actually have a diagram of the +form of Jerusalem as an international + + align:start position:0% +form of Jerusalem as an international + + + align:start position:0% +form of Jerusalem as an international +City neither side did neither Arab nor + + align:start position:0% +City neither side did neither Arab nor + + + align:start position:0% +City neither side did neither Arab nor +Jewish + + align:start position:0% +Jewish + + + align:start position:0% +Jewish +politics accept that as a + + align:start position:0% +politics accept that as a + + + align:start position:0% +politics accept that as a +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +um the Jews start after the Oslo + + align:start position:0% +um the Jews start after the Oslo + + + align:start position:0% +um the Jews start after the Oslo +Accords which presumably sets out that + + align:start position:0% +Accords which presumably sets out that + + + align:start position:0% +Accords which presumably sets out that +there will be a independent Palestinian + + align:start position:0% +there will be a independent Palestinian + + + align:start position:0% +there will be a independent Palestinian +State and uh talks about the 67 boundary + + align:start position:0% +State and uh talks about the 67 boundary + + + align:start position:0% +State and uh talks about the 67 boundary +lines and zones for the future + + align:start position:0% +lines and zones for the future + + + align:start position:0% +lines and zones for the future +States um + + align:start position:0% + + + + align:start position:0% + +Israel politics combination of religious + + align:start position:0% +Israel politics combination of religious + + + align:start position:0% +Israel politics combination of religious +pressure + + align:start position:0% +pressure + + + align:start position:0% +pressure +and uh all kinds of other + + align:start position:0% +and uh all kinds of other + + + align:start position:0% +and uh all kinds of other +internal + + align:start position:0% +internal + + + align:start position:0% +internal +Israeli social + + align:start position:0% +Israeli social + + + align:start position:0% +Israeli social +issues promote a expansion program which + + align:start position:0% +issues promote a expansion program which + + + align:start position:0% +issues promote a expansion program which +now has reached + + align:start position:0% +now has reached + + + align:start position:0% +now has reached +300,000 settlers living on land + + align:start position:0% +300,000 settlers living on land + + + align:start position:0% +300,000 settlers living on land +which is east of the + + align:start position:0% +which is east of the + + + align:start position:0% +which is east of the +partition line set by the Oslo + + align:start position:0% + + + + align:start position:0% + +Accords many American + + align:start position:0% +Accords many American + + + align:start position:0% +Accords many American +presidents since Harry Truman I think + + align:start position:0% +presidents since Harry Truman I think + + + align:start position:0% +presidents since Harry Truman I think +have objected to Israeli settlement + + align:start position:0% +have objected to Israeli settlement + + + align:start position:0% +have objected to Israeli settlement +expansion with no results + + align:start position:0% +expansion with no results + + + align:start position:0% +expansion with no results +whatsoever uh the status quo at the end + + align:start position:0% +whatsoever uh the status quo at the end + + + align:start position:0% +whatsoever uh the status quo at the end +of all of my long story of 3,000 years + + align:start position:0% +of all of my long story of 3,000 years + + + align:start position:0% +of all of my long story of 3,000 years +is + + align:start position:0% +is + + + align:start position:0% +is +a situation in which + + align:start position:0% +a situation in which + + + align:start position:0% +a situation in which +Jerusalem is claimed by Israel to be the + + align:start position:0% +Jerusalem is claimed by Israel to be the + + + align:start position:0% +Jerusalem is claimed by Israel to be the +unique capital of Israel although as you + + align:start position:0% +unique capital of Israel although as you + + + align:start position:0% +unique capital of Israel although as you +will read in my letter many of the + + align:start position:0% +will read in my letter many of the + + + align:start position:0% +will read in my letter many of the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +Israeli presidents have looked for + + align:start position:0% +Israeli presidents have looked for + + + align:start position:0% +Israeli presidents have looked for +alternative sites to Israel to + + align:start position:0% +alternative sites to Israel to + + + align:start position:0% +alternative sites to Israel to +Jerusalem uh at least for the capital of + + align:start position:0% +Jerusalem uh at least for the capital of + + + align:start position:0% +Jerusalem uh at least for the capital of +Israel including boran's choice of KOB + + align:start position:0% +Israel including boran's choice of KOB + + + align:start position:0% +Israel including boran's choice of KOB +in the + + align:start position:0% +in the + + + align:start position:0% +in the +netive + + align:start position:0% + + + + align:start position:0% + +uh the present the + + align:start position:0% +uh the present the + + + align:start position:0% +uh the present the +Palestinian + + align:start position:0% +Palestinian + + + align:start position:0% +Palestinian +position is a slightly more complex + + align:start position:0% +position is a slightly more complex + + + align:start position:0% +position is a slightly more complex +position but they would like to share + + align:start position:0% +position but they would like to share + + + align:start position:0% +position but they would like to share +Palestine + + align:start position:0% +Palestine + + + align:start position:0% +Palestine +Jerusalem as the capital of their state + + align:start position:0% +Jerusalem as the capital of their state + + + align:start position:0% +Jerusalem as the capital of their state +as + + align:start position:0% +as + + + align:start position:0% +as +well so you have a ocean which I don't + + align:start position:0% +well so you have a ocean which I don't + + + align:start position:0% +well so you have a ocean which I don't +think exists anywhere else in the world + + align:start position:0% +think exists anywhere else in the world + + + align:start position:0% +think exists anywhere else in the world +where one city is the capital of two + + align:start position:0% +where one city is the capital of two + + + align:start position:0% +where one city is the capital of two +countries you get St Louis Missouri and + + align:start position:0% +countries you get St Louis Missouri and + + + align:start position:0% +countries you get St Louis Missouri and +St Louis Kansas City you + + align:start position:0% +St Louis Kansas City you + + + align:start position:0% +St Louis Kansas City you +have + + align:start position:0% +have + + + align:start position:0% +have +divisions in other parts of the world + + align:start position:0% +divisions in other parts of the world + + + align:start position:0% +divisions in other parts of the world +but you have no claim for a city as + + align:start position:0% +but you have no claim for a city as + + + align:start position:0% +but you have no claim for a city as +being the capital of two + + align:start position:0% +being the capital of two + + + align:start position:0% +being the capital of two +states in fact the notion of two states + + align:start position:0% +states in fact the notion of two states + + + align:start position:0% +states in fact the notion of two states +is now + + align:start position:0% +is now + + + align:start position:0% +is now +under + + align:start position:0% +under + + + align:start position:0% +under +discussion there's a new relatively new + + align:start position:0% +discussion there's a new relatively new + + + align:start position:0% +discussion there's a new relatively new +movement which argues for the existence + + align:start position:0% +movement which argues for the existence + + + align:start position:0% +movement which argues for the existence +of a single + + align:start position:0% +of a single + + + align:start position:0% +of a single +state which would alleviate the problem + + align:start position:0% +state which would alleviate the problem + + + align:start position:0% +state which would alleviate the problem +of the settlements but deny Zionist + + align:start position:0% +of the settlements but deny Zionist + + + align:start position:0% +of the settlements but deny Zionist +Ambitions because + + align:start position:0% + + + + align:start position:0% + +demographically the Jewish position is + + align:start position:0% +demographically the Jewish position is + + + align:start position:0% +demographically the Jewish position is +more vulnerable + + align:start position:0% +more vulnerable + + + align:start position:0% +more vulnerable +demographically um this two-state + + align:start position:0% +demographically um this two-state + + + align:start position:0% +demographically um this two-state +solution which the United States and + + align:start position:0% +solution which the United States and + + + align:start position:0% +solution which the United States and +most + + align:start position:0% +most + + + align:start position:0% +most +liberal uh politician + + align:start position:0% +liberal uh politician + + + align:start position:0% +liberal uh politician +uh support is for there to be an + + align:start position:0% +uh support is for there to be an + + + align:start position:0% +uh support is for there to be an +independent Palestinian + + align:start position:0% +independent Palestinian + + + align:start position:0% +independent Palestinian +State uh the Palestinians wish to go + + align:start position:0% +State uh the Palestinians wish to go + + + align:start position:0% +State uh the Palestinians wish to go +back to the 1967 boundary uh there'll + + align:start position:0% +back to the 1967 boundary uh there'll + + + align:start position:0% +back to the 1967 boundary uh there'll +have to be some compromise God leers how + + align:start position:0% +have to be some compromise God leers how + + + align:start position:0% +have to be some compromise God leers how +that compromise is going to be worked + + align:start position:0% +that compromise is going to be worked + + + align:start position:0% +that compromise is going to be worked +out uh between the size of the + + align:start position:0% +out uh between the size of the + + + align:start position:0% +out uh between the size of the +settlement population and the + + align:start position:0% +settlement population and the + + + align:start position:0% +settlement population and the +emaciated + + align:start position:0% +emaciated + + + align:start position:0% +emaciated +fragmented you can see in the last map + + align:start position:0% +fragmented you can see in the last map + + + align:start position:0% +fragmented you can see in the last map +in your hand out just in the case of the + + align:start position:0% +in your hand out just in the case of the + + + align:start position:0% +in your hand out just in the case of the +periphery of + + align:start position:0% +periphery of + + + align:start position:0% +periphery of +Jerusalem how much this land has + + align:start position:0% +Jerusalem how much this land has + + + align:start position:0% +Jerusalem how much this land has +[Music] + + align:start position:0% + + + + align:start position:0% + +become paralized in and fragmented + + align:start position:0% +become paralized in and fragmented + + + align:start position:0% +become paralized in and fragmented +rather than + + align:start position:0% + + + + align:start position:0% + +unified my son's book + + align:start position:0% + + + + align:start position:0% + +which tackles this Pro problem much more + + align:start position:0% +which tackles this Pro problem much more + + + align:start position:0% +which tackles this Pro problem much more +eloquently than than I + + align:start position:0% +eloquently than than I + + + align:start position:0% +eloquently than than I +can argues that for a Palestinian state + + align:start position:0% +can argues that for a Palestinian state + + + align:start position:0% +can argues that for a Palestinian state +which is liberal and + + align:start position:0% +which is liberal and + + + align:start position:0% +which is liberal and +not imposing military law onto its the + + align:start position:0% +not imposing military law onto its the + + + align:start position:0% +not imposing military law onto its the +Palestinians in the West Bank and so on + + align:start position:0% +Palestinians in the West Bank and so on + + + align:start position:0% +Palestinians in the West Bank and so on +and so on he's probably the most + + align:start position:0% +and so on he's probably the most + + + align:start position:0% +and so on he's probably the most +coherent liberal position on the subject + + align:start position:0% +coherent liberal position on the subject + + + align:start position:0% +coherent liberal position on the subject +of at the moment the future of Jerusalem + + align:start position:0% +of at the moment the future of Jerusalem + + + align:start position:0% +of at the moment the future of Jerusalem +May well be never + + align:start position:0% + + + + align:start position:0% + +resolved it may be the result of too + + align:start position:0% +resolved it may be the result of too + + + align:start position:0% +resolved it may be the result of too +much history and too much + + align:start position:0% +much history and too much + + + align:start position:0% +much history and too much +mythology mythology becomes + + align:start position:0% +mythology mythology becomes + + + align:start position:0% +mythology mythology becomes +history at a certain point let me give + + align:start position:0% +history at a certain point let me give + + + align:start position:0% +history at a certain point let me give +you an + + align:start position:0% +you an + + + align:start position:0% +you an +example + + align:start position:0% +example + + + align:start position:0% +example +Christians at Easter today celebrate the + + align:start position:0% +Christians at Easter today celebrate the + + + align:start position:0% +Christians at Easter today celebrate the +way of the cross they carry the cross + + align:start position:0% +way of the cross they carry the cross + + + align:start position:0% +way of the cross they carry the cross +symbolically from the pretorium where + + align:start position:0% +symbolically from the pretorium where + + + align:start position:0% +symbolically from the pretorium where +Jesus was housed to where he was a + + align:start position:0% + + + + align:start position:0% + +crucified the sight of crucifixion is + + align:start position:0% +crucified the sight of crucifixion is + + + align:start position:0% +crucified the sight of crucifixion is +not absolutely clear but most people now + + align:start position:0% +not absolutely clear but most people now + + + align:start position:0% +not absolutely clear but most people now +assume it to be somewhere around where + + align:start position:0% +assume it to be somewhere around where + + + align:start position:0% +assume it to be somewhere around where +the holy sepula + + align:start position:0% +the holy sepula + + + align:start position:0% +the holy sepula +is one of the Stations of the + + align:start position:0% +is one of the Stations of the + + + align:start position:0% +is one of the Stations of the +Cross station number + + align:start position:0% +Cross station number + + + align:start position:0% +Cross station number +I don't know what number seven I'm not + + align:start position:0% +I don't know what number seven I'm not + + + align:start position:0% +I don't know what number seven I'm not +sure exactly it's called the eomo + + align:start position:0% +sure exactly it's called the eomo + + + align:start position:0% +sure exactly it's called the eomo +station that's where the + + align:start position:0% + + + + align:start position:0% + +Roman legion + + align:start position:0% +Roman legion + + + align:start position:0% +Roman legion +Commander pointed down to to Jesus and + + align:start position:0% +Commander pointed down to to Jesus and + + + align:start position:0% +Commander pointed down to to Jesus and +said eom look at that man look at this + + align:start position:0% +said eom look at that man look at this + + + align:start position:0% +said eom look at that man look at this +man in a derisive manner carrying the + + align:start position:0% +man in a derisive manner carrying the + + + align:start position:0% +man in a derisive manner carrying the +cross in fact history proves there to be + + align:start position:0% +cross in fact history proves there to be + + + align:start position:0% +cross in fact history proves there to be +absolutely nonsense but complete myth + + align:start position:0% +absolutely nonsense but complete myth + + + align:start position:0% +absolutely nonsense but complete myth +archaeologists say that the + + align:start position:0% +archaeologists say that the + + + align:start position:0% +archaeologists say that the +eomo arch was only Built long after + + align:start position:0% +eomo arch was only Built long after + + + align:start position:0% +eomo arch was only Built long after +after Jesus's death and didn't exist at + + align:start position:0% +after Jesus's death and didn't exist at + + + align:start position:0% +after Jesus's death and didn't exist at +the time of + + align:start position:0% +the time of + + + align:start position:0% +the time of +Jesus + + align:start position:0% +Jesus + + + align:start position:0% +Jesus +so the + + align:start position:0% +so the + + + align:start position:0% +so the +other conf conflations of the of + + align:start position:0% +other conf conflations of the of + + + align:start position:0% +other conf conflations of the of +reality the + + align:start position:0% +reality the + + + align:start position:0% +reality the +Jews on near the The Citadel of + + align:start position:0% +Jews on near the The Citadel of + + + align:start position:0% +Jews on near the The Citadel of +David have the sight of David's + + align:start position:0% +David have the sight of David's + + + align:start position:0% +David have the sight of David's +tomb above which Christians claim the + + align:start position:0% +tomb above which Christians claim the + + + align:start position:0% +tomb above which Christians claim the +Last Supper of Jesus with + + align:start position:0% +Last Supper of Jesus with + + + align:start position:0% +Last Supper of Jesus with +his followers took + + align:start position:0% +his followers took + + + align:start position:0% +his followers took +place it is now the site of the dorm + + align:start position:0% +place it is now the site of the dorm + + + align:start position:0% +place it is now the site of the dorm +Miss AB + + align:start position:0% +Miss AB + + + align:start position:0% +Miss AB +Abbey which is where Mary was supposedly + + align:start position:0% +Abbey which is where Mary was supposedly + + + align:start position:0% +Abbey which is where Mary was supposedly +died dor Mary dor being the Italian word + + align:start position:0% +died dor Mary dor being the Italian word + + + align:start position:0% +died dor Mary dor being the Italian word +to sleep dor Mission Abbey so you have a + + align:start position:0% +to sleep dor Mission Abbey so you have a + + + align:start position:0% +to sleep dor Mission Abbey so you have a +vertical as the history of the city is + + align:start position:0% +vertical as the history of the city is + + + align:start position:0% +vertical as the history of the city is +grown and layered upon each other + + align:start position:0% +grown and layered upon each other + + + align:start position:0% +grown and layered upon each other +physically you have Jewish David at the + + align:start position:0% +physically you have Jewish David at the + + + align:start position:0% +physically you have Jewish David at the +bottom Jesus next on top and the Ottoman + + align:start position:0% +bottom Jesus next on top and the Ottoman + + + align:start position:0% +bottom Jesus next on top and the Ottoman +Empire and Mary's memory on the + + align:start position:0% +Empire and Mary's memory on the + + + align:start position:0% +Empire and Mary's memory on the +top what do you do about a place like + + align:start position:0% +top what do you do about a place like + + + align:start position:0% +top what do you do about a place like +this you Foster ize it in my letter in + + align:start position:0% +this you Foster ize it in my letter in + + + align:start position:0% +this you Foster ize it in my letter in +the new Republic I say that it's not + + align:start position:0% +the new Republic I say that it's not + + + align:start position:0% +the new Republic I say that it's not +only a religious City it's a everyday + + align:start position:0% +only a religious City it's a everyday + + + align:start position:0% +only a religious City it's a everyday +City in which people go to school people + + align:start position:0% +City in which people go to school people + + + align:start position:0% +City in which people go to school people +have transportation problems the Jews + + align:start position:0% +have transportation problems the Jews + + + align:start position:0% +have transportation problems the Jews +have just built a light rail + + align:start position:0% +have just built a light rail + + + align:start position:0% +have just built a light rail +system + + align:start position:0% + + + + align:start position:0% + +um it's a political City it never was + + align:start position:0% +um it's a political City it never was + + + align:start position:0% +um it's a political City it never was +the capital of any of + + align:start position:0% +the capital of any of + + + align:start position:0% +the capital of any of +the countries Arab countries that + + align:start position:0% +the countries Arab countries that + + + align:start position:0% +the countries Arab countries that +conquered + + align:start position:0% +conquered + + + align:start position:0% +conquered +Jerusalem I'll show you a slide + + align:start position:0% +Jerusalem I'll show you a slide + + + align:start position:0% +Jerusalem I'll show you a slide +of Jerusalem only being the capital of + + align:start position:0% +of Jerusalem only being the capital of + + + align:start position:0% +of Jerusalem only being the capital of +the Crusader Empire and the Jewish + + align:start position:0% +the Crusader Empire and the Jewish + + + align:start position:0% +the Crusader Empire and the Jewish +Empire what justification that makes for + + align:start position:0% +Empire what justification that makes for + + + align:start position:0% +Empire what justification that makes for +arguing that Jerusalem should be the + + align:start position:0% +arguing that Jerusalem should be the + + + align:start position:0% +arguing that Jerusalem should be the +unique capital of Israel is for you to + + align:start position:0% +unique capital of Israel is for you to + + + align:start position:0% +unique capital of Israel is for you to +decide + + align:start position:0% + + + + align:start position:0% + +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +most I mean I can give you many detailed + + align:start position:0% +most I mean I can give you many detailed + + + align:start position:0% +most I mean I can give you many detailed +stories and versions of the any of these + + align:start position:0% +stories and versions of the any of these + + + align:start position:0% +stories and versions of the any of these +events um for + + align:start position:0% + + + + align:start position:0% + +instance + + align:start position:0% +instance + + + align:start position:0% +instance +in in a religious environment of this + + align:start position:0% +in in a religious environment of this + + + align:start position:0% +in in a religious environment of this +kind it's amazing how + + align:start position:0% +kind it's amazing how + + + align:start position:0% +kind it's amazing how +frequently people build on the SES of + + align:start position:0% +frequently people build on the SES of + + + align:start position:0% +frequently people build on the SES of +other of previous religious institution + + align:start position:0% +other of previous religious institution + + + align:start position:0% +other of previous religious institution +the Church of the hly sepa + + align:start position:0% +the Church of the hly sepa + + + align:start position:0% +the Church of the hly sepa +is built on the site of the Roman Temple + + align:start position:0% +is built on the site of the Roman Temple + + + align:start position:0% +is built on the site of the Roman Temple +of + + align:start position:0% +of + + + align:start position:0% +of +Aphrodite when the Crusaders capture + + align:start position:0% +Aphrodite when the Crusaders capture + + + align:start position:0% +Aphrodite when the Crusaders capture +Jerusalem in + + align:start position:0% +Jerusalem in + + + align:start position:0% +Jerusalem in +1099 they go they March to the to the + + align:start position:0% +1099 they go they March to the to the + + + align:start position:0% +1099 they go they March to the to the +Dome of the Rock and theak of mque and + + align:start position:0% +Dome of the Rock and theak of mque and + + + align:start position:0% +Dome of the Rock and theak of mque and +instead of putting them down they put a + + align:start position:0% +instead of putting them down they put a + + + align:start position:0% +instead of putting them down they put a +Christian flag on top of the Dome of the + + align:start position:0% +Christian flag on top of the Dome of the + + + align:start position:0% +Christian flag on top of the Dome of the +Rock and called a temple + + align:start position:0% +Rock and called a temple + + + align:start position:0% +Rock and called a temple +Dominus and Theos becomes Temple + + align:start position:0% +Dominus and Theos becomes Temple + + + align:start position:0% +Dominus and Theos becomes Temple +solonus the sasque was as its + + align:start position:0% +solonus the sasque was as its + + + align:start position:0% +solonus the sasque was as its +foundations in Solomon's Temple + + align:start position:0% +foundations in Solomon's Temple + + + align:start position:0% +foundations in Solomon's Temple +Stables it is + + align:start position:0% +Stables it is + + + align:start position:0% +Stables it is +constantly its roof is constantly its + + align:start position:0% +constantly its roof is constantly its + + + align:start position:0% +constantly its roof is constantly its +lead roof is constantly having to be + + align:start position:0% +lead roof is constantly having to be + + + align:start position:0% +lead roof is constantly having to be +repaired because its foundations are St + + align:start position:0% +repaired because its foundations are St + + + align:start position:0% +repaired because its foundations are St +unstable this is the city which is + + align:start position:0% +unstable this is the city which is + + + align:start position:0% +unstable this is the city which is +built I write in the last part of my + + align:start position:0% +built I write in the last part of my + + + align:start position:0% +built I write in the last part of my +writing on Lou Khan's KVA + + align:start position:0% +writing on Lou Khan's KVA + + + align:start position:0% +writing on Lou Khan's KVA +synagogue but if you haven't read it I'm + + align:start position:0% +synagogue but if you haven't read it I'm + + + align:start position:0% +synagogue but if you haven't read it I'm +not I'm going to tell you the story of + + align:start position:0% +not I'm going to tell you the story of + + + align:start position:0% +not I'm going to tell you the story of +lon's interpretation of how you building + + align:start position:0% +lon's interpretation of how you building + + + align:start position:0% +lon's interpretation of how you building +Jerusalem his his theory of + + align:start position:0% + + + + align:start position:0% + +ruins so today + + align:start position:0% +ruins so today + + + align:start position:0% +ruins so today +the Islam has three two permanent + + align:start position:0% +the Islam has three two permanent + + + align:start position:0% +the Islam has three two permanent +monuments where his people can + + align:start position:0% +monuments where his people can + + + align:start position:0% +monuments where his people can +pray the Jews don't have any they pray + + align:start position:0% +pray the Jews don't have any they pray + + + align:start position:0% +pray the Jews don't have any they pray +in the open + + align:start position:0% +in the open + + + align:start position:0% +in the open +air the holiest presence is in the + + align:start position:0% +air the holiest presence is in the + + + align:start position:0% +air the holiest presence is in the +western War which is erodian + + align:start position:0% +western War which is erodian + + + align:start position:0% +western War which is erodian +in in in in in in + + align:start position:0% +in in in in in in + + + align:start position:0% +in in in in in in +ancestry and the Christians still have + + align:start position:0% +ancestry and the Christians still have + + + align:start position:0% +ancestry and the Christians still have +the desiccated + + align:start position:0% +the desiccated + + + align:start position:0% +the desiccated +holy place of the + + align:start position:0% +holy place of the + + + align:start position:0% +holy place of the +Seiler Christ's passion the location of + + align:start position:0% +Seiler Christ's passion the location of + + + align:start position:0% +Seiler Christ's passion the location of +Christ's + + align:start position:0% +Christ's + + + align:start position:0% +Christ's +passion + + align:start position:0% + + + + align:start position:0% + +and such is this such as an abbreviated + + align:start position:0% +and such is this such as an abbreviated + + + align:start position:0% +and such is this such as an abbreviated +story in Jerusalem now what do you + + align:start position:0% + + + + align:start position:0% + +do I've worked for the Palestinian side + + align:start position:0% +do I've worked for the Palestinian side + + + align:start position:0% +do I've worked for the Palestinian side +I've worked not for the Israeli + + align:start position:0% +I've worked not for the Israeli + + + align:start position:0% +I've worked not for the Israeli +government but for the mayor of + + align:start position:0% +government but for the mayor of + + + align:start position:0% +government but for the mayor of +Jerusalem over time so my investment in + + align:start position:0% +Jerusalem over time so my investment in + + + align:start position:0% +Jerusalem over time so my investment in +the city + + align:start position:0% +the city + + + align:start position:0% +the city +is more than just knowing its history + + align:start position:0% +is more than just knowing its history + + + align:start position:0% +is more than just knowing its history +which I only know partially history of + + align:start position:0% +which I only know partially history of + + + align:start position:0% +which I only know partially history of +religion is so + + align:start position:0% +religion is so + + + align:start position:0% +religion is so +extensive that to understand it all I + + align:start position:0% +extensive that to understand it all I + + + align:start position:0% +extensive that to understand it all I +don't think even understand who Gabriel + + align:start position:0% +don't think even understand who Gabriel + + + align:start position:0% +don't think even understand who Gabriel +was he figures in some story + + align:start position:0% +was he figures in some story + + + align:start position:0% +was he figures in some story +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +uh I + + align:start position:0% + + + + align:start position:0% + +mean the books about the Last Supper + + align:start position:0% +mean the books about the Last Supper + + + align:start position:0% +mean the books about the Last Supper +which talk about the tradition of eating + + align:start position:0% +which talk about the tradition of eating + + + align:start position:0% +which talk about the tradition of eating +together and what that means the books + + align:start position:0% +together and what that means the books + + + align:start position:0% +together and what that means the books +about the killing of your first + + align:start position:0% + + + + align:start position:0% + +son remember one of the plagues that + + align:start position:0% +son remember one of the plagues that + + + align:start position:0% +son remember one of the plagues that +uh the Egyptians or God cast on the + + align:start position:0% +uh the Egyptians or God cast on the + + + align:start position:0% +uh the Egyptians or God cast on the +Egyptians for the persecution of the + + align:start position:0% +Egyptians for the persecution of the + + + align:start position:0% +Egyptians for the persecution of the +Jews was the killing of the first son + + align:start position:0% +Jews was the killing of the first son + + + align:start position:0% +Jews was the killing of the first son +that's why the Baby Moses was hidden in + + align:start position:0% +that's why the Baby Moses was hidden in + + + align:start position:0% +that's why the Baby Moses was hidden in +the + + align:start position:0% + + + + align:start position:0% + +reads we can go on and on and on and on + + align:start position:0% +reads we can go on and on and on and on + + + align:start position:0% +reads we can go on and on and on and on +and on religion is a business which + + align:start position:0% +and on religion is a business which + + + align:start position:0% +and on religion is a business which +produces lots of myths and realities and + + align:start position:0% +produces lots of myths and realities and + + + align:start position:0% +produces lots of myths and realities and +interpretations to keep itself + + align:start position:0% +interpretations to keep itself + + + align:start position:0% +interpretations to keep itself +going + + align:start position:0% +going + + + align:start position:0% +going +uh + + align:start position:0% + + + + align:start position:0% + +okay we should look at some of these + + align:start position:0% +okay we should look at some of these + + + align:start position:0% +okay we should look at some of these +pictures so you get a better idea of + + align:start position:0% +pictures so you get a better idea of + + + align:start position:0% +pictures so you get a better idea of +what this place looks + + align:start position:0% + + + + align:start position:0% + +like the options are simple + + align:start position:0% + + + + align:start position:0% + +this is the present Israeli option for + + align:start position:0% +this is the present Israeli option for + + + align:start position:0% +this is the present Israeli option for +Jerusalem if this is Palestine and this + + align:start position:0% +Jerusalem if this is Palestine and this + + + align:start position:0% +Jerusalem if this is Palestine and this +is Israel Jerusalem has a secure border + + align:start position:0% +is Israel Jerusalem has a secure border + + + align:start position:0% +is Israel Jerusalem has a secure border +on its West on its East + + align:start position:0% +on its West on its East + + + align:start position:0% +on its West on its East +side this is a + + align:start position:0% +side this is a + + + align:start position:0% +side this is a +metropolitan city as indicated the + + align:start position:0% +metropolitan city as indicated the + + + align:start position:0% +metropolitan city as indicated the +drawing of the Palestinian planner with + + align:start position:0% +drawing of the Palestinian planner with + + + align:start position:0% +drawing of the Palestinian planner with +the + + align:start position:0% +the + + + align:start position:0% +the +central the problem of what happens on a + + align:start position:0% +central the problem of what happens on a + + + align:start position:0% +central the problem of what happens on a +boundary between two countries in terms + + align:start position:0% +boundary between two countries in terms + + + align:start position:0% +boundary between two countries in terms +of security and Customs isn't answered + + align:start position:0% +of security and Customs isn't answered + + + align:start position:0% +of security and Customs isn't answered +by + + align:start position:0% +by + + + align:start position:0% +by +one you have to dispense with it you can + + align:start position:0% +one you have to dispense with it you can + + + align:start position:0% +one you have to dispense with it you can +only dispense with that if you if you + + align:start position:0% +only dispense with that if you if you + + + align:start position:0% +only dispense with that if you if you +have secure + + align:start position:0% + + + + align:start position:0% + +relationships the European Union is + + align:start position:0% +relationships the European Union is + + + align:start position:0% +relationships the European Union is +dispensed with + + align:start position:0% +dispensed with + + + align:start position:0% +dispensed with +passport by virtue of an assumption that + + align:start position:0% +passport by virtue of an assumption that + + + align:start position:0% +passport by virtue of an assumption that +there's no + + align:start position:0% + + + + align:start position:0% + +reason to + + align:start position:0% +reason to + + + align:start position:0% +reason to +maintain fortified borders any + + align:start position:0% +maintain fortified borders any + + + align:start position:0% +maintain fortified borders any +longer between France and Belgium for + + align:start position:0% +longer between France and Belgium for + + + align:start position:0% +longer between France and Belgium for +instance but can you conceive of this + + align:start position:0% +instance but can you conceive of this + + + align:start position:0% +instance but can you conceive of this +being a solution in relation to pretty + + align:start position:0% +being a solution in relation to pretty + + + align:start position:0% +being a solution in relation to pretty +two pretty hostile + + align:start position:0% +two pretty hostile + + + align:start position:0% +two pretty hostile +entities how you going to deal with + + align:start position:0% +entities how you going to deal with + + + align:start position:0% +entities how you going to deal with +security in a unified + + align:start position:0% + + + + align:start position:0% + +City small details of + + align:start position:0% + + + + align:start position:0% + +the the Historic Site + + align:start position:0% + + + + align:start position:0% + +has ifan if + + align:start position:0% +has ifan if + + + align:start position:0% +has ifan if +anaki wishes + + align:start position:0% +anaki wishes + + + align:start position:0% +anaki wishes +to visit the Dome of the + + align:start position:0% +to visit the Dome of the + + + align:start position:0% +to visit the Dome of the +Rock he or she has to + + align:start position:0% +Rock he or she has to + + + align:start position:0% +Rock he or she has to +penetrate some kind of + + align:start position:0% + + + + align:start position:0% + +line or presumably there's no line which + + align:start position:0% +line or presumably there's no line which + + + align:start position:0% +line or presumably there's no line which +is has to be penetrated at + + align:start position:0% +is has to be penetrated at + + + align:start position:0% +is has to be penetrated at +all this + + align:start position:0% +all this + + + align:start position:0% +all this +is a position where + + align:start position:0% +is a position where + + + align:start position:0% +is a position where +Palestine in circles Jerusalem in the in + + align:start position:0% +Palestine in circles Jerusalem in the in + + + align:start position:0% +Palestine in circles Jerusalem in the in +the counter point to this proposal are + + align:start position:0% +the counter point to this proposal are + + + align:start position:0% +the counter point to this proposal are +there any other + + align:start position:0% + + + + align:start position:0% + +possibili what do you think at the back + + align:start position:0% + + + + align:start position:0% + +there possibility H + + align:start position:0% +there possibility H + + + align:start position:0% +there possibility H +possibility for the the future of + + align:start position:0% +possibility for the the future of + + + align:start position:0% +possibility for the the future of +Jerusalem given either one or given one + + align:start position:0% +Jerusalem given either one or given one + + + align:start position:0% +Jerusalem given either one or given one +one state solution there's no problem + + align:start position:0% +one state solution there's no problem + + + align:start position:0% +one state solution there's no problem +it's the capital of a single state but + + align:start position:0% +it's the capital of a single state but + + + align:start position:0% +it's the capital of a single state but +if it's + + align:start position:0% +if it's + + + align:start position:0% +if it's +the another solution is a version of + + align:start position:0% +the another solution is a version of + + + align:start position:0% +the another solution is a version of +number + + align:start position:0% + + + + align:start position:0% + +one that + + align:start position:0% +one that + + + align:start position:0% +one that +rala the United States and the European + + align:start position:0% +rala the United States and the European + + + align:start position:0% +rala the United States and the European +Union give a billion dollars to the + + align:start position:0% +Union give a billion dollars to the + + + align:start position:0% +Union give a billion dollars to the +Palestinians to build a new capital + + align:start position:0% +Palestinians to build a new capital + + + align:start position:0% +Palestinians to build a new capital +it's a question of where other people + + align:start position:0% +it's a question of where other people + + + align:start position:0% +it's a question of where other people +want them to put the + + align:start position:0% +want them to put the + + + align:start position:0% +want them to put the +capital they want the + + align:start position:0% +capital they want the + + + align:start position:0% +capital they want the +capital Place put it for Israel the + + align:start position:0% +capital Place put it for Israel the + + + align:start position:0% +capital Place put it for Israel the +same there's two sides of + + align:start position:0% +same there's two sides of + + + align:start position:0% +same there's two sides of +Jerusalem I understand a place to divide + + align:start position:0% +Jerusalem I understand a place to divide + + + align:start position:0% +Jerusalem I understand a place to divide +it or is it divide without there being a + + align:start position:0% +it or is it divide without there being a + + + align:start position:0% +it or is it divide without there being a +political division there's a there's a + + align:start position:0% +political division there's a there's a + + + align:start position:0% +political division there's a there's a +community that's + + align:start position:0% +community that's + + + align:start position:0% +community that's +divided problem + + align:start position:0% +divided problem + + + align:start position:0% +divided problem +issue of security and to whether + + align:start position:0% +issue of security and to whether + + + align:start position:0% +issue of security and to whether +everybody from whe the Palestinians can + + align:start position:0% +everybody from whe the Palestinians can + + + align:start position:0% +everybody from whe the Palestinians can +control who comes right up to the edge + + align:start position:0% +control who comes right up to the edge + + + align:start position:0% +control who comes right up to the edge +of the Israeli side or the Jewish side + + align:start position:0% +of the Israeli side or the Jewish side + + + align:start position:0% +of the Israeli side or the Jewish side +that's the problem I + + align:start position:0% +that's the problem I + + + align:start position:0% +that's the problem I +understand what we what I'm concluding + + align:start position:0% +understand what we what I'm concluding + + + align:start position:0% +understand what we what I'm concluding +is that there is no + + align:start position:0% +is that there is no + + + align:start position:0% +is that there is no +solution and that that this will just + + align:start position:0% +solution and that that this will just + + + align:start position:0% +solution and that that this will just +perpetuate itself in history causing + + align:start position:0% +perpetuate itself in history causing + + + align:start position:0% +perpetuate itself in history causing +Bloodshed as + + align:start position:0% +Bloodshed as + + + align:start position:0% +Bloodshed as +blood was + + align:start position:0% +blood was + + + align:start position:0% +blood was +accompanied accompanies the history of + + align:start position:0% +accompanied accompanies the history of + + + align:start position:0% +accompanied accompanies the history of +Jerusalem for two 3,000 years that it'll + + align:start position:0% +Jerusalem for two 3,000 years that it'll + + + align:start position:0% +Jerusalem for two 3,000 years that it'll +just continue to + + align:start position:0% +just continue to + + + align:start position:0% +just continue to +be it is too intoxicated a sight by the + + align:start position:0% +be it is too intoxicated a sight by the + + + align:start position:0% +be it is too intoxicated a sight by the +virtue of the three major religions in + + align:start position:0% +virtue of the three major religions in + + + align:start position:0% +virtue of the three major religions in +the + + align:start position:0% +the + + + align:start position:0% +the +world forgive me if I leave the others + + align:start position:0% + + + + align:start position:0% + +out that the in to use Al the Ros this + + align:start position:0% +out that the in to use Al the Ros this + + + align:start position:0% +out that the in to use Al the Ros this +term the locus is such that it is + + align:start position:0% + + + + align:start position:0% + +irresolvable it's a bleak future for + + align:start position:0% +irresolvable it's a bleak future for + + + align:start position:0% +irresolvable it's a bleak future for +both Palestine and + + align:start position:0% + + + + align:start position:0% + +Israel maybe there's a solution which + + align:start position:0% +Israel maybe there's a solution which + + + align:start position:0% +Israel maybe there's a solution which +doesn't include Jerusalem this is the + + align:start position:0% +doesn't include Jerusalem this is the + + + align:start position:0% +doesn't include Jerusalem this is the +one which I'm indicating + + align:start position:0% +one which I'm indicating + + + align:start position:0% +one which I'm indicating +here which East Jerusalem is a suburb of + + align:start position:0% +here which East Jerusalem is a suburb of + + + align:start position:0% +here which East Jerusalem is a suburb of +another + + align:start position:0% +another + + + align:start position:0% +another +state of a city in another state + + align:start position:0% +state of a city in another state + + + align:start position:0% +state of a city in another state +but that's a + + align:start position:0% +but that's a + + + align:start position:0% +but that's a +farfetched + + align:start position:0% +farfetched + + + align:start position:0% +farfetched +resolution there's the West versus the + + align:start position:0% +resolution there's the West versus the + + + align:start position:0% +resolution there's the West versus the +East the countries of Palestine versus + + align:start position:0% +East the countries of Palestine versus + + + align:start position:0% +East the countries of Palestine versus +Israel the race Arab versus Hebrew + + align:start position:0% +Israel the race Arab versus Hebrew + + + align:start position:0% +Israel the race Arab versus Hebrew +language Hebrew versus Arabic religion + + align:start position:0% +language Hebrew versus Arabic religion + + + align:start position:0% +language Hebrew versus Arabic religion +Islam and Christianity + + align:start position:0% +Islam and Christianity + + + align:start position:0% +Islam and Christianity +versus + + align:start position:0% +versus + + + align:start position:0% +versus +Judaism Israel's relationship with the + + align:start position:0% +Judaism Israel's relationship with the + + + align:start position:0% +Judaism Israel's relationship with the +West there Palestinians association with + + align:start position:0% +West there Palestinians association with + + + align:start position:0% +West there Palestinians association with +the Middle East and the Arab + + align:start position:0% +the Middle East and the Arab + + + align:start position:0% +the Middle East and the Arab +world Israel's preoccupation with + + align:start position:0% +world Israel's preoccupation with + + + align:start position:0% +world Israel's preoccupation with +Western industrial + + align:start position:0% +Western industrial + + + align:start position:0% +Western industrial +growth palestine's developing economy in + + align:start position:0% +growth palestine's developing economy in + + + align:start position:0% +growth palestine's developing economy in +agriculture and in + + align:start position:0% +agriculture and in + + + align:start position:0% +agriculture and in +technical + + align:start position:0% +technical + + + align:start position:0% +technical +industry the Jewish background of the + + align:start position:0% +industry the Jewish background of the + + + align:start position:0% +industry the Jewish background of the +Holocaust and the Arab treatment of Jews + + align:start position:0% +Holocaust and the Arab treatment of Jews + + + align:start position:0% +Holocaust and the Arab treatment of Jews +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in uh in Arab countries + + align:start position:0% +in uh in Arab countries + + + align:start position:0% +in uh in Arab countries +palestine's Heritage of + + align:start position:0% +palestine's Heritage of + + + align:start position:0% +palestine's Heritage of +colonialism + + align:start position:0% + + + + align:start position:0% + +exploitation and so on and so on and so + + align:start position:0% +exploitation and so on and so on and so + + + align:start position:0% +exploitation and so on and so on and so +on and so on they just travel the world + + align:start position:0% +on and so on they just travel the world + + + align:start position:0% +on and so on they just travel the world +of + + align:start position:0% +of + + + align:start position:0% +of +imagery it's + + align:start position:0% + + + + align:start position:0% + +cheaper Jerusalem like 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align:start position:0% +1213 all of these schools and Community + + + align:start position:0% +1213 all of these schools and Community +places as a result of the islamization + + align:start position:0% +places as a result of the islamization + + + align:start position:0% +places as a result of the islamization +of the + + align:start position:0% +of the + + + align:start position:0% +of the +space + + align:start position:0% +space + + + align:start position:0% +space +1917 Jerusalem prior at the time of the + + align:start position:0% +1917 Jerusalem prior at the time of the + + + align:start position:0% +1917 Jerusalem prior at the time of the +British Invasion next + + align:start position:0% + + + + align:start position:0% + +I mentioned the example of the duplicate + + align:start position:0% +I mentioned the example of the duplicate + + + align:start position:0% +I mentioned the example of the duplicate +the M the layering + + align:start position:0% +the M the layering + + + align:start position:0% +the M the layering +of the the David's tomb the dorm Mission + + align:start position:0% +of the the David's tomb the dorm Mission + + + align:start position:0% +of the the David's tomb the dorm Mission +Abbey in the house of Kus one of + + align:start position:0% +Abbey in the house of Kus one of + + + align:start position:0% +Abbey in the house of Kus one of +the agents in the death of + + align:start position:0% +the agents in the death of + + + align:start position:0% +the agents in the death of +Jesus but the Last Supper takes place + + align:start position:0% +Jesus but the Last Supper takes place + + + align:start position:0% +Jesus but the Last Supper takes place +there as well here is the dorm missan + + align:start position:0% +there as well here is the dorm missan + + + align:start position:0% +there as well here is the dorm missan +Abbey which has these three layers of + + align:start position:0% +Abbey which has these three layers of + + + align:start position:0% +Abbey which has these three layers of +the vertical space belonging to + + align:start position:0% +the vertical space belonging to + + + align:start position:0% +the vertical space belonging to +different religions + + align:start position:0% + + + + align:start position:0% + +next the final subdivision of the holy + + align:start position:0% +next the final subdivision of the holy + + + align:start position:0% +next the final subdivision of the holy +city into four + + align:start position:0% +city into four + + + align:start position:0% +city into four +sectors the Dome of the Rock and Thea + + align:start position:0% +sectors the Dome of the Rock and Thea + + + align:start position:0% +sectors the Dome of the Rock and Thea +mque penetrating into the Jewish protor + + align:start position:0% +mque penetrating into the Jewish protor + + + align:start position:0% +mque penetrating into the Jewish protor +with a d gate as its gate the Golden + + align:start position:0% +with a d gate as its gate the Golden + + + align:start position:0% +with a d gate as its gate the Golden +Gate which is not open any + + align:start position:0% +Gate which is not open any + + + align:start position:0% +Gate which is not open any +longer to the Islamic section which has + + align:start position:0% +longer to the Islamic section which has + + + align:start position:0% +longer to the Islamic section which has +the the Damascus gate on the North as + + align:start position:0% +the the Damascus gate on the North as + + + align:start position:0% +the the Damascus gate on the North as +its + + align:start position:0% +its + + + align:start position:0% +its +major uh entrance the Church of the Holy + + align:start position:0% +major uh entrance the Church of the Holy + + + align:start position:0% +major uh entrance the Church of the Holy +sepa and the Christian sector and the + + align:start position:0% +sepa and the Christian sector and the + + + align:start position:0% +sepa and the Christian sector and the +arm median + + align:start position:0% +arm median + + + align:start position:0% +arm median +sector the Jaffer gate leads to is the + + align:start position:0% +sector the Jaffer gate leads to is the + + + align:start position:0% +sector the Jaffer gate leads to is the +prim if you extend these lines the + + align:start position:0% +prim if you extend these lines the + + + align:start position:0% +prim if you extend these lines the +Jaffer gate extends to + + align:start position:0% +Jaffer gate extends to + + + align:start position:0% +Jaffer gate extends to +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +Mediterranean the dung gate extends down + + align:start position:0% +Mediterranean the dung gate extends down + + + align:start position:0% +Mediterranean the dung gate extends down +to Egypt Damascus gate extends upwards + + align:start position:0% +to Egypt Damascus gate extends upwards + + + align:start position:0% +to Egypt Damascus gate extends upwards +to Syria and this closed Golden + + align:start position:0% +to Syria and this closed Golden + + + align:start position:0% +to Syria and this closed Golden +Gate potentially + + align:start position:0% +Gate potentially + + + align:start position:0% +Gate potentially +extends eastwards to + + align:start position:0% +extends eastwards to + + + align:start position:0% +extends eastwards to +Iraq + + align:start position:0% + + + + align:start position:0% + +next the Contemporary City on the left + + align:start position:0% +next the Contemporary City on the left + + + align:start position:0% +next the Contemporary City on the left +the coexistence of uh tall skyscrapers + + align:start position:0% +the coexistence of uh tall skyscrapers + + + align:start position:0% +the coexistence of uh tall skyscrapers +on the West in the je + + align:start position:0% + + + + align:start position:0% + +City + + align:start position:0% + + + + align:start position:0% + +next the British occupation the mlan + + align:start position:0% +next the British occupation the mlan + + + align:start position:0% +next the British occupation the mlan +plan it's not very + + align:start position:0% +plan it's not very + + + align:start position:0% +plan it's not very +clear but + + align:start position:0% +clear but + + + align:start position:0% +clear but +it's an attempt to recognize the western + + align:start position:0% +it's an attempt to recognize the western + + + align:start position:0% +it's an attempt to recognize the western +part the Jewish part and and developing + + align:start position:0% +part the Jewish part and and developing + + + align:start position:0% +part the Jewish part and and developing +it according to a Garden City + + align:start position:0% +it according to a Garden City + + + align:start position:0% +it according to a Garden City +model the Arab side is left + + align:start position:0% +model the Arab side is left + + + align:start position:0% +model the Arab side is left +gray reasons I don't understand + + align:start position:0% +gray reasons I don't understand + + + align:start position:0% +gray reasons I don't understand +restricted building and open + + align:start position:0% +restricted building and open + + + align:start position:0% +restricted building and open +space extraordinary + + align:start position:0% + + + + align:start position:0% + +plan and the United + + align:start position:0% +plan and the United + + + align:start position:0% +plan and the United +Nations plan which encloses a larger + + align:start position:0% +Nations plan which encloses a larger + + + align:start position:0% +Nations plan which encloses a larger +area than the municipality it encloses + + align:start position:0% +area than the municipality it encloses + + + align:start position:0% +area than the municipality it encloses +bethle + + align:start position:0% + + + + align:start position:0% + +uh on the East including hadasa Hospital + + align:start position:0% +uh on the East including hadasa Hospital + + + align:start position:0% +uh on the East including hadasa Hospital +Hebrew University on the + + align:start position:0% +Hebrew University on the + + + align:start position:0% +Hebrew University on the +North + + align:start position:0% +North + + + align:start position:0% +North +East um rejected by both + + align:start position:0% + + + + align:start position:0% + +sides + + align:start position:0% + + + + align:start position:0% + +next judism rul is from 587 that's + + align:start position:0% +next judism rul is from 587 that's + + + align:start position:0% +next judism rul is from 587 that's +Nebuchadnezzar in Babylon to + + align:start position:0% +Nebuchadnezzar in Babylon to + + + align:start position:0% +Nebuchadnezzar in Babylon to + + align:start position:0% + + + align:start position:0% +ad showing that + + align:start position:0% +ad showing that + + + align:start position:0% +ad showing that +Jerusalem had consequence at a + + align:start position:0% +Jerusalem had consequence at a + + + align:start position:0% +Jerusalem had consequence at a +distance the + + align:start position:0% +distance the + + + align:start position:0% +distance the +19 the + + align:start position:0% +19 the + + + align:start position:0% +19 the +19667 dividing of the city in east and + + align:start position:0% +19667 dividing of the city in east and + + + align:start position:0% +19667 dividing of the city in east and +west with a boundary between the two + + align:start position:0% +west with a boundary between the two + + + align:start position:0% +west with a boundary between the two +next the boundary taken over in the map + + align:start position:0% + + + + align:start position:0% + +showing map by + + align:start position:0% +showing map by + + + align:start position:0% +showing map by +protagonists of + + align:start position:0% +protagonists of + + + align:start position:0% +protagonists of +the Arab caes arguing that the Jews have + + align:start position:0% +the Arab caes arguing that the Jews have + + + align:start position:0% +the Arab caes arguing that the Jews have +always try to locate + + align:start position:0% +always try to locate + + + align:start position:0% +always try to locate +settlements in an pattern which causes + + align:start position:0% +settlements in an pattern which causes + + + align:start position:0% +settlements in an pattern which causes +the city not to be + + align:start position:0% +the city not to be + + + align:start position:0% +the city not to be +unified next + + align:start position:0% + + + + align:start position:0% + +dyon's one of dyon's great buildings + + align:start position:0% +dyon's one of dyon's great buildings + + + align:start position:0% +dyon's one of dyon's great buildings +which you never built and these very + + align:start position:0% + + + + align:start position:0% + +interesting you interpretation of the + + align:start position:0% +interesting you interpretation of the + + + align:start position:0% +interesting you interpretation of the +use of ruins in a city + + align:start position:0% +use of ruins in a city + + + align:start position:0% +use of ruins in a city +of could you just turn on those lights + + align:start position:0% +of could you just turn on those lights + + + align:start position:0% +of could you just turn on those lights +please + + align:start position:0% + + + + align:start position:0% + +when you have the intersection of + + align:start position:0% + + + + align:start position:0% + +religion + + align:start position:0% +religion + + + align:start position:0% +religion +politics geography and + + align:start position:0% +politics geography and + + + align:start position:0% +politics geography and +history you cannot do + + align:start position:0% + + + + align:start position:0% + +anything he's + + align:start position:0% +anything he's + + + align:start position:0% +anything he's +Frozen I don't know if a situation which + + align:start position:0% +Frozen I don't know if a situation which + + + align:start position:0% +Frozen I don't know if a situation which +has managed to overcome maybe Belgium + + align:start position:0% + + + + align:start position:0% + +I suppose + + align:start position:0% + + + + align:start position:0% + +the in Europe at least the elimination + + align:start position:0% +the in Europe at least the elimination + + + align:start position:0% +the in Europe at least the elimination +of obstacles towards the creation of a + + align:start position:0% +of obstacles towards the creation of a + + + align:start position:0% +of obstacles towards the creation of a +plane of General + + align:start position:0% +plane of General + + + align:start position:0% +plane of General +Acceptance in the European Union is + + align:start position:0% +Acceptance in the European Union is + + + align:start position:0% +Acceptance in the European Union is +perhaps the most modern example of the + + align:start position:0% +perhaps the most modern example of the + + + align:start position:0% +perhaps the most modern example of the +breaking down of + + align:start position:0% +breaking down of + + + align:start position:0% +breaking down of +barriers the barriers are still + + align:start position:0% +barriers the barriers are still + + + align:start position:0% +barriers the barriers are still +between alers + + align:start position:0% +between alers + + + align:start position:0% +between alers +and + + align:start position:0% +and + + + align:start position:0% +and +Paris it's between the interland of + + align:start position:0% +Paris it's between the interland of + + + align:start position:0% +Paris it's between the interland of +countries turkey and the European Union + + align:start position:0% +countries turkey and the European Union + + + align:start position:0% +countries turkey and the European Union +sending migrant labor back and + + align:start position:0% +sending migrant labor back and + + + align:start position:0% +sending migrant labor back and +forth but this is + + align:start position:0% +forth but this is + + + align:start position:0% +forth but this is +a phenomenon + + align:start position:0% +a phenomenon + + + align:start position:0% +a phenomenon +which is not easily apply to + + align:start position:0% +which is not easily apply to + + + align:start position:0% +which is not easily apply to +Jerusalem in the case of Johannesburg + + align:start position:0% +Jerusalem in the case of Johannesburg + + + align:start position:0% +Jerusalem in the case of Johannesburg +you'll see that absence of religion it + + align:start position:0% +you'll see that absence of religion it + + + align:start position:0% +you'll see that absence of religion it +is purely a question of + + align:start position:0% +is purely a question of + + + align:start position:0% +is purely a question of +race once you eliminate religion and you + + align:start position:0% +race once you eliminate religion and you + + + align:start position:0% +race once you eliminate religion and you +only deal with race you find it easier + + align:start position:0% +only deal with race you find it easier + + + align:start position:0% +only deal with race you find it easier +to resolve even although South Africa + + align:start position:0% +to resolve even although South Africa + + + align:start position:0% +to resolve even although South Africa +struggled to the to the into the post + + align:start position:0% +struggled to the to the into the post + + + align:start position:0% +struggled to the to the into the post +aparte + + align:start position:0% +aparte + + + align:start position:0% +aparte +democracy took enormous resources and + + align:start position:0% +democracy took enormous resources and + + + align:start position:0% +democracy took enormous resources and +time and bloodshed + + align:start position:0% +time and bloodshed + + + align:start position:0% +time and bloodshed +and jandsburg is not artifact of + + align:start position:0% + + + + align:start position:0% + +race and so on so we look at these + + align:start position:0% +race and so on so we look at these + + + align:start position:0% +race and so on so we look at these +others in a slightly different light + + align:start position:0% +others in a slightly different light + + + align:start position:0% +others in a slightly different light +than Jerusalem but Jerusalem is the + + align:start position:0% +than Jerusalem but Jerusalem is the + + + align:start position:0% +than Jerusalem but Jerusalem is the +great metaphysical city of the world + + align:start position:0% +great metaphysical city of the world + + + align:start position:0% +great metaphysical city of the world +it's the most important metaphysical + + align:start position:0% + + + + align:start position:0% + +presence what that means meaning + + align:start position:0% +presence what that means meaning + + + align:start position:0% +presence what that means meaning +wise it's difficult to + + align:start position:0% +wise it's difficult to + + + align:start position:0% +wise it's difficult to +say there are Parts where you trade and + + align:start position:0% +say there are Parts where you trade and + + + align:start position:0% +say there are Parts where you trade and +walk softly and slowly because you have + + align:start position:0% +walk softly and slowly because you have + + + align:start position:0% +walk softly and slowly because you have +a history of associations with that + + align:start position:0% +a history of associations with that + + + align:start position:0% +a history of associations with that +particular + + align:start position:0% +particular + + + align:start position:0% +particular +place and these associations are kept + + align:start position:0% +place and these associations are kept + + + align:start position:0% +place and these associations are kept +very + + align:start position:0% + + + + align:start position:0% + +Vivid they've + + align:start position:0% +Vivid they've + + + align:start position:0% +Vivid they've +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +been Palestinian riots around around the + + align:start position:0% +been Palestinian riots around around the + + + align:start position:0% +been Palestinian riots around around the +archaeology + + align:start position:0% +archaeology + + + align:start position:0% +archaeology +of certain regions in the olden + + align:start position:0% +of certain regions in the olden + + + align:start position:0% +of certain regions in the olden +city + + align:start position:0% +city + + + align:start position:0% +city +um somebody one day will try to excavate + + align:start position:0% +um somebody one day will try to excavate + + + align:start position:0% +um somebody one day will try to excavate +under the hly mount to see if the H of + + align:start position:0% +under the hly mount to see if the H of + + + align:start position:0% +under the hly mount to see if the H of +hodies is still + + align:start position:0% +hodies is still + + + align:start position:0% +hodies is still +there Steven + + align:start position:0% +there Steven + + + align:start position:0% +there Steven +Spielberg's probably likely to to do the + + align:start position:0% +Spielberg's probably likely to to do the + + + align:start position:0% +Spielberg's probably likely to to do the +movie although he's done a movie + + align:start position:0% +movie although he's done a movie + + + align:start position:0% +movie although he's done a movie +which is + + align:start position:0% +which is + + + align:start position:0% +which is +similar anyway any thoughts about all of + + align:start position:0% + + + + align:start position:0% + +this complexity is a easy + + align:start position:0% + + + + align:start position:0% + +evasion you know wherever I go around + + align:start position:0% +evasion you know wherever I go around + + + align:start position:0% +evasion you know wherever I go around +the world hearing people talk about + + align:start position:0% +the world hearing people talk about + + + align:start position:0% +the world hearing people talk about +cities the modern interpretation is + + align:start position:0% +cities the modern interpretation is + + + align:start position:0% +cities the modern interpretation is +they're too complex to have theories + + align:start position:0% +they're too complex to have theories + + + align:start position:0% +they're too complex to have theories +about + + align:start position:0% +about + + + align:start position:0% +about +them and the no city is more complex + + align:start position:0% +them and the no city is more complex + + + align:start position:0% +them and the no city is more complex +than + + align:start position:0% +than + + + align:start position:0% +than +Jerusalem no no city has been the site + + align:start position:0% +Jerusalem no no city has been the site + + + align:start position:0% +Jerusalem no no city has been the site +of three major + + align:start position:0% +of three major + + + align:start position:0% +of three major +religions no city has been the site + + align:start position:0% +religions no city has been the site + + + align:start position:0% +religions no city has been the site +of 3,000 years + + align:start position:0% +of 3,000 years + + + align:start position:0% +of 3,000 years +of invasion and succession resilience + + align:start position:0% + + + + align:start position:0% + +and the building up of history and + + align:start position:0% + + + + align:start position:0% + +myths you should go and visit it + + align:start position:0% +myths you should go and visit it + + + align:start position:0% +myths you should go and visit it +that's all I can recommend see if you + + align:start position:0% +that's all I can recommend see if you + + + align:start position:0% +that's all I can recommend see if you +can make any sense of + + align:start position:0% +can make any sense of + + + align:start position:0% +can make any sense of +it you've lived in Jerusalem haven't + + align:start position:0% +it you've lived in Jerusalem haven't + + + align:start position:0% +it you've lived in Jerusalem haven't +you you + + align:start position:0% + + + + align:start position:0% + +never + + align:start position:0% +never + + + align:start position:0% +never +yeah + + align:start position:0% + + + + align:start position:0% + +yeah the the first immigrant zionists + + align:start position:0% +yeah the the first immigrant zionists + + + align:start position:0% +yeah the the first immigrant zionists +saw Jerusalem as an + + align:start position:0% +saw Jerusalem as an + + + align:start position:0% +saw Jerusalem as an +oldfashioned historic ly bound City + + align:start position:0% +oldfashioned historic ly bound City + + + align:start position:0% +oldfashioned historic ly bound City +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and + + align:start position:0% +and + + + align:start position:0% +and +leaders chose to make t Aviv the capital + + align:start position:0% +leaders chose to make t Aviv the capital + + + align:start position:0% +leaders chose to make t Aviv the capital +or highi the capital facing the + + align:start position:0% +or highi the capital facing the + + + align:start position:0% +or highi the capital facing the +Mediterranean or in the case of binur + + align:start position:0% +Mediterranean or in the case of binur + + + align:start position:0% +Mediterranean or in the case of binur +and the city the the new city of + + align:start position:0% +and the city the the new city of + + + align:start position:0% +and the city the the new city of +k + + align:start position:0% +k + + + align:start position:0% +k +um vitman + + align:start position:0% +um vitman + + + align:start position:0% +um vitman +found Jerusalem to be ar and and + + align:start position:0% +found Jerusalem to be ar and and + + + align:start position:0% +found Jerusalem to be ar and and +medieval and the new Jewish sinus Spirit + + align:start position:0% +medieval and the new Jewish sinus Spirit + + + align:start position:0% +medieval and the new Jewish sinus Spirit +was in favor of novelty and social + + align:start position:0% +was in favor of novelty and social + + + align:start position:0% +was in favor of novelty and social +equity + + align:start position:0% + + + + align:start position:0% + +and some of the things which it hasn't + + align:start position:0% +and some of the things which it hasn't + + + align:start position:0% +and some of the things which it hasn't +been able to per to + + align:start position:0% +been able to per to + + + align:start position:0% +been able to per to +perpetuate okay we'll do Johannesburg on + + align:start position:0% +perpetuate okay we'll do Johannesburg on + + + align:start position:0% +perpetuate okay we'll do Johannesburg on +Thursday and see if there's any + + align:start position:0% +Thursday and see if there's any + + + align:start position:0% +Thursday and see if there's any +comparison \ No newline at end of file diff --git a/N46RKNbKf2s.txt b/N46RKNbKf2s.txt new file mode 100644 index 0000000000000000000000000000000000000000..e8df148d3e940dd3b443a54b2724861294dc0283 --- /dev/null +++ b/N46RKNbKf2s.txt @@ -0,0 +1,1699 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu kul's Force law can be the + + align:start position:0% +ocw.mit.edu kul's Force law can be the + + + align:start position:0% +ocw.mit.edu kul's Force law can be the +basis for estimating the net charge on + + align:start position:0% +basis for estimating the net charge on + + + align:start position:0% +basis for estimating the net charge on +an + + align:start position:0% +an + + + align:start position:0% +an +object conservation of charge and + + align:start position:0% +object conservation of charge and + + + align:start position:0% +object conservation of charge and +gauss's law are also the basis for the + + align:start position:0% +gauss's law are also the basis for the + + + align:start position:0% +gauss's law are also the basis for the +measurement of + + align:start position:0% + + + + align:start position:0% + +charge kul's Force law states that a + + align:start position:0% +charge kul's Force law states that a + + + align:start position:0% +charge kul's Force law states that a +particle or object carrying a net charge + + align:start position:0% +particle or object carrying a net charge + + + align:start position:0% +particle or object carrying a net charge +Q2 in an electric field due to a second + + align:start position:0% +Q2 in an electric field due to a second + + + align:start position:0% +Q2 in an electric field due to a second +charge + + align:start position:0% +charge + + + align:start position:0% +charge +q1 experiences a + + align:start position:0% +q1 experiences a + + + align:start position:0% +q1 experiences a +force proportional to the product of the + + align:start position:0% +force proportional to the product of the + + + align:start position:0% +force proportional to the product of the +charges and inversely proportional to + + align:start position:0% +charges and inversely proportional to + + + align:start position:0% +charges and inversely proportional to +the square of the distance R + + align:start position:0% +the square of the distance R + + + align:start position:0% +the square of the distance R +between charges of the same polarity + + align:start position:0% + + + + align:start position:0% + +repel in this demonstration the + + align:start position:0% +repel in this demonstration the + + + align:start position:0% +repel in this demonstration the +particles are air filled + + align:start position:0% +particles are air filled + + + align:start position:0% +particles are air filled +balloons of the variety used at + + align:start position:0% + + + + align:start position:0% + +parties they can be charged by rubbing + + align:start position:0% +parties they can be charged by rubbing + + + align:start position:0% +parties they can be charged by rubbing +them with a dry cloth + + align:start position:0% + + + + align:start position:0% + +they repel each other because they've + + align:start position:0% +they repel each other because they've + + + align:start position:0% +they repel each other because they've +been charged to the same + + align:start position:0% + + + + align:start position:0% + +polarity let's use measure measurements + + align:start position:0% +polarity let's use measure measurements + + + align:start position:0% +polarity let's use measure measurements +of the separation distance and the + + align:start position:0% +of the separation distance and the + + + align:start position:0% +of the separation distance and the +weight of the balloon to approximate the + + align:start position:0% +weight of the balloon to approximate the + + + align:start position:0% +weight of the balloon to approximate the +charge that's been left on one of the + + align:start position:0% + + + + align:start position:0% + +balloons the threads that have been used + + align:start position:0% +balloons the threads that have been used + + + align:start position:0% +balloons the threads that have been used +to suspend them are tied at a common + + align:start position:0% + + + + align:start position:0% + +point we can measure the vertical + + align:start position:0% +point we can measure the vertical + + + align:start position:0% +point we can measure the vertical +distance L between the height of the + + align:start position:0% +distance L between the height of the + + + align:start position:0% +distance L between the height of the +balloons and the point where the threads + + align:start position:0% +balloons and the point where the threads + + + align:start position:0% +balloons and the point where the threads +are tied + + align:start position:0% +are tied + + + align:start position:0% +are tied +we can also measure the distance R + + align:start position:0% +we can also measure the distance R + + + align:start position:0% +we can also measure the distance R +between the + + align:start position:0% +between the + + + align:start position:0% +between the +balloons the balloons are not all that + + align:start position:0% +balloons the balloons are not all that + + + align:start position:0% +balloons the balloons are not all that +small compared to these distances + + align:start position:0% +small compared to these distances + + + align:start position:0% +small compared to these distances +however for the purpose of estimating + + align:start position:0% +however for the purpose of estimating + + + align:start position:0% +however for the purpose of estimating +the charge we'll represent them as point + + align:start position:0% +the charge we'll represent them as point + + + align:start position:0% +the charge we'll represent them as point +charges and point + + align:start position:0% + + + + align:start position:0% + +masses there are three forces acting on + + align:start position:0% +masses there are three forces acting on + + + align:start position:0% +masses there are three forces acting on +the right balloon the downward vertical + + align:start position:0% +the right balloon the downward vertical + + + align:start position:0% +the right balloon the downward vertical +force of + + align:start position:0% +force of + + + align:start position:0% +force of +gravity the balloon mass times the + + align:start position:0% +gravity the balloon mass times the + + + align:start position:0% +gravity the balloon mass times the +acceleration of gravity + + align:start position:0% +acceleration of gravity + + + align:start position:0% +acceleration of gravity +G the horizont izontal Kum force of + + align:start position:0% +G the horizont izontal Kum force of + + + align:start position:0% +G the horizont izontal Kum force of +repulsion and the tension supplied by + + align:start position:0% +repulsion and the tension supplied by + + + align:start position:0% +repulsion and the tension supplied by +the + + align:start position:0% + + + + align:start position:0% + +thread to have the tension of the thread + + align:start position:0% +thread to have the tension of the thread + + + align:start position:0% +thread to have the tension of the thread +balance the gravitational and electric + + align:start position:0% +balance the gravitational and electric + + + align:start position:0% +balance the gravitational and electric +forces the ratio of the kulum force to + + align:start position:0% +forces the ratio of the kulum force to + + + align:start position:0% +forces the ratio of the kulum force to +the gravitational force must be equal to + + align:start position:0% +the gravitational force must be equal to + + + align:start position:0% +the gravitational force must be equal to +the ratio of half the distance between + + align:start position:0% +the ratio of half the distance between + + + align:start position:0% +the ratio of half the distance between +the balloons + + align:start position:0% +the balloons + + + align:start position:0% +the balloons +r/2 to the vertical distance from from + + align:start position:0% +r/2 to the vertical distance from from + + + align:start position:0% +r/2 to the vertical distance from from +the balloon to where the thread is + + align:start position:0% + + + + align:start position:0% + +tied if we assume that the balloons are + + align:start position:0% +tied if we assume that the balloons are + + + align:start position:0% +tied if we assume that the balloons are +equally charged we can express the kulum + + align:start position:0% +equally charged we can express the kulum + + + align:start position:0% +equally charged we can express the kulum +force in terms of the spacing between + + align:start position:0% +force in terms of the spacing between + + + align:start position:0% +force in terms of the spacing between +balloons R and the desired charge + + align:start position:0% + + + + align:start position:0% + +Q this expression can be solved for Q as + + align:start position:0% +Q this expression can be solved for Q as + + + align:start position:0% +Q this expression can be solved for Q as +a function of the quantities that we can + + align:start position:0% + + + + align:start position:0% + +measure having measured the balloon mass + + align:start position:0% +measure having measured the balloon mass + + + align:start position:0% +measure having measured the balloon mass +m + + align:start position:0% +m + + + align:start position:0% +m +the spacing R and the height L we can + + align:start position:0% +the spacing R and the height L we can + + + align:start position:0% +the spacing R and the height L we can +deduce + + align:start position:0% +deduce + + + align:start position:0% +deduce +Q first we weigh a typical + + align:start position:0% + + + + align:start position:0% + +balloon the mass m of this balloon is 73 + + align:start position:0% +balloon the mass m of this balloon is 73 + + + align:start position:0% +balloon the mass m of this balloon is 73 +G in MKS units + + align:start position:0% + + + + align:start position:0% + +the gravitational acceleration is 9.8 + + align:start position:0% +the gravitational acceleration is 9.8 + + + align:start position:0% +the gravitational acceleration is 9.8 +m/s + + align:start position:0% + + + + align:start position:0% + +squared the spacing between balloon + + align:start position:0% +squared the spacing between balloon + + + align:start position:0% +squared the spacing between balloon +centers is about 50 cm it's not possible + + align:start position:0% +centers is about 50 cm it's not possible + + + align:start position:0% +centers is about 50 cm it's not possible +to put the meter stick close to the + + align:start position:0% +to put the meter stick close to the + + + align:start position:0% +to put the meter stick close to the +balloons without they're being attracted + + align:start position:0% +balloons without they're being attracted + + + align:start position:0% +balloons without they're being attracted +to Professor Zan his body's a good + + align:start position:0% +to Professor Zan his body's a good + + + align:start position:0% +to Professor Zan his body's a good +conductor the charges on the balloons + + align:start position:0% +conductor the charges on the balloons + + + align:start position:0% +conductor the charges on the balloons +induce image charge es of opposite + + align:start position:0% +induce image charge es of opposite + + + align:start position:0% +induce image charge es of opposite +polarity on conducting surfaces to which + + align:start position:0% +polarity on conducting surfaces to which + + + align:start position:0% +polarity on conducting surfaces to which +they're + + align:start position:0% + + + + align:start position:0% + +attracted the height L is roughly 1 + + align:start position:0% +attracted the height L is roughly 1 + + + align:start position:0% +attracted the height L is roughly 1 +meter + + align:start position:0% + + + + align:start position:0% + +finally the permitivity of free space is + + align:start position:0% +finally the permitivity of free space is + + + align:start position:0% +finally the permitivity of free space is +8.85 * + + align:start position:0% +8.85 * + + + align:start position:0% +8.85 * +10-2 farads per + + align:start position:0% + + + + align:start position:0% + +meter evaluation gives a charge + + align:start position:0% + + + + align:start position:0% + +Q of about + + align:start position:0% +Q of about + + + align:start position:0% +Q of about +220 nanocs + + align:start position:0% + + + + align:start position:0% + +conservation of charge and gauss's law + + align:start position:0% +conservation of charge and gauss's law + + + align:start position:0% +conservation of charge and gauss's law +can also be used to deduce the charge on + + align:start position:0% +can also be used to deduce the charge on + + + align:start position:0% +can also be used to deduce the charge on +the + + align:start position:0% +the + + + align:start position:0% +the +balloons this will be done by putting + + align:start position:0% +balloons this will be done by putting + + + align:start position:0% +balloons this will be done by putting +the balloon inside a conducting + + align:start position:0% +the balloon inside a conducting + + + align:start position:0% +the balloon inside a conducting +enclosure and measuring the charge + + align:start position:0% +enclosure and measuring the charge + + + align:start position:0% +enclosure and measuring the charge +induced on the + + align:start position:0% + + + + align:start position:0% + +enclosure note that this induced charge + + align:start position:0% +enclosure note that this induced charge + + + align:start position:0% +enclosure note that this induced charge +is opposite in sign to that of the + + align:start position:0% +is opposite in sign to that of the + + + align:start position:0% +is opposite in sign to that of the +balloon + + align:start position:0% + + + + align:start position:0% + +this image charge is just that + + align:start position:0% +this image charge is just that + + + align:start position:0% +this image charge is just that +responsible for attracting the balloons + + align:start position:0% +responsible for attracting the balloons + + + align:start position:0% +responsible for attracting the balloons +to any essentially grounded conductor in + + align:start position:0% +to any essentially grounded conductor in + + + align:start position:0% +to any essentially grounded conductor in +its + + align:start position:0% + + + + align:start position:0% + +vicinity by making this metal enclosure + + align:start position:0% +vicinity by making this metal enclosure + + + align:start position:0% +vicinity by making this metal enclosure +which is called a faraday cage enclose + + align:start position:0% +which is called a faraday cage enclose + + + align:start position:0% +which is called a faraday cage enclose +the charge we make all of the field + + align:start position:0% +the charge we make all of the field + + + align:start position:0% +the charge we make all of the field +lines from the balloon charge terminate + + align:start position:0% +lines from the balloon charge terminate + + + align:start position:0% +lines from the balloon charge terminate +on the surrounding walls + + align:start position:0% +on the surrounding walls + + + align:start position:0% +on the surrounding walls +the Faraday cage is insulated from a + + align:start position:0% +the Faraday cage is insulated from a + + + align:start position:0% +the Faraday cage is insulated from a +surrounding grounded + + align:start position:0% + + + + align:start position:0% + +shield and itself connected to ground + + align:start position:0% +shield and itself connected to ground + + + align:start position:0% +shield and itself connected to ground +through the low impedance of an + + align:start position:0% + + + + align:start position:0% + +integrator The Shield is necessary to + + align:start position:0% +integrator The Shield is necessary to + + + align:start position:0% +integrator The Shield is necessary to +prevent field lines from outside charges + + align:start position:0% +prevent field lines from outside charges + + + align:start position:0% +prevent field lines from outside charges +terminating on the cage such as from + + align:start position:0% +terminating on the cage such as from + + + align:start position:0% +terminating on the cage such as from +Professor Zan's having walked on the + + align:start position:0% + + + + align:start position:0% + +carpet because the enclosure is itself + + align:start position:0% +carpet because the enclosure is itself + + + align:start position:0% +carpet because the enclosure is itself +essentially grounded there is little + + align:start position:0% +essentially grounded there is little + + + align:start position:0% +essentially grounded there is little +electric field between it and and its + + align:start position:0% + + + + align:start position:0% + +Shield the integral form of charge + + align:start position:0% +Shield the integral form of charge + + + align:start position:0% +Shield the integral form of charge +conservation shows how the charge + + align:start position:0% +conservation shows how the charge + + + align:start position:0% +conservation shows how the charge +induced on the Faraday cage is related + + align:start position:0% +induced on the Faraday cage is related + + + align:start position:0% +induced on the Faraday cage is related +to the current I to the + + align:start position:0% +to the current I to the + + + align:start position:0% +to the current I to the +integrator the surface + + align:start position:0% +integrator the surface + + + align:start position:0% +integrator the surface +s encloses the + + align:start position:0% +s encloses the + + + align:start position:0% +s encloses the +cage + + align:start position:0% +cage + + + align:start position:0% +cage +completely and cuts Through the + + align:start position:0% + + + + align:start position:0% + +Wire the only contribution to the + + align:start position:0% +Wire the only contribution to the + + + align:start position:0% +Wire the only contribution to the +integral of the current + + align:start position:0% +integral of the current + + + align:start position:0% +integral of the current +density is where the wire passes through + + align:start position:0% +density is where the wire passes through + + + align:start position:0% +density is where the wire passes through +the + + align:start position:0% +the + + + align:start position:0% +the +surface and is the current + + align:start position:0% + + + + align:start position:0% + +I because the charge on the outside of + + align:start position:0% +I because the charge on the outside of + + + align:start position:0% +I because the charge on the outside of +the Faraday cage is + + align:start position:0% +the Faraday cage is + + + align:start position:0% +the Faraday cage is +zero the net charge in the volume v + + align:start position:0% +zero the net charge in the volume v + + + align:start position:0% +zero the net charge in the volume v +enclosed by this surface is the negative + + align:start position:0% +enclosed by this surface is the negative + + + align:start position:0% +enclosed by this surface is the negative +of that brought Inside the Cage as the + + align:start position:0% +of that brought Inside the Cage as the + + + align:start position:0% +of that brought Inside the Cage as the +balloon is + + align:start position:0% + + + + align:start position:0% + +introduced thus the the current Through + + align:start position:0% +introduced thus the the current Through + + + align:start position:0% +introduced thus the the current Through +the Wire is the time rate of change of + + align:start position:0% +the Wire is the time rate of change of + + + align:start position:0% +the Wire is the time rate of change of +the charge introduced into the enclosure + + align:start position:0% +the charge introduced into the enclosure + + + align:start position:0% +the charge introduced into the enclosure +with the + + align:start position:0% +with the + + + align:start position:0% +with the +balloon if the balloon is finally + + align:start position:0% +balloon if the balloon is finally + + + align:start position:0% +balloon if the balloon is finally +completely enclosed by the cage then the + + align:start position:0% +completely enclosed by the cage then the + + + align:start position:0% +completely enclosed by the cage then the +final value of this charge is just that + + align:start position:0% +final value of this charge is just that + + + align:start position:0% +final value of this charge is just that +on the + + align:start position:0% +on the + + + align:start position:0% +on the +balloon this is true even if the balloon + + align:start position:0% +balloon this is true even if the balloon + + + align:start position:0% +balloon this is true even if the balloon +makes no electrical contact with the + + align:start position:0% +makes no electrical contact with the + + + align:start position:0% +makes no electrical contact with the +Faraday + + align:start position:0% +Faraday + + + align:start position:0% +Faraday +cage the integrator is made from an + + align:start position:0% +cage the integrator is made from an + + + align:start position:0% +cage the integrator is made from an +operational + + align:start position:0% +operational + + + align:start position:0% +operational +amplifier and the integrated signal + + align:start position:0% +amplifier and the integrated signal + + + align:start position:0% +amplifier and the integrated signal +could be displayed on an oscilloscope + + align:start position:0% + + + + align:start position:0% + +instead we'll use an integrating + + align:start position:0% +instead we'll use an integrating + + + align:start position:0% +instead we'll use an integrating +electrometer in kulum measurement + + align:start position:0% +electrometer in kulum measurement + + + align:start position:0% +electrometer in kulum measurement +mode it's designed to display the charge + + align:start position:0% +mode it's designed to display the charge + + + align:start position:0% +mode it's designed to display the charge +that would account for the integral of + + align:start position:0% +that would account for the integral of + + + align:start position:0% +that would account for the integral of +the current into its + + align:start position:0% + + + + align:start position:0% + +input the shapes of the Faraday cage and + + align:start position:0% +input the shapes of the Faraday cage and + + + align:start position:0% +input the shapes of the Faraday cage and +grounded Shield do not matter in our + + align:start position:0% +grounded Shield do not matter in our + + + align:start position:0% +grounded Shield do not matter in our +experiment the Faraday cage is a waste + + align:start position:0% +experiment the Faraday cage is a waste + + + align:start position:0% +experiment the Faraday cage is a waste +paper basket sized rectangular aluminum + + align:start position:0% +paper basket sized rectangular aluminum + + + align:start position:0% +paper basket sized rectangular aluminum +box + + align:start position:0% +box + + + align:start position:0% +box +and the surrounding Shield is a metal + + align:start position:0% + + + + align:start position:0% + +screen by now one of our balloons is + + align:start position:0% +screen by now one of our balloons is + + + align:start position:0% +screen by now one of our balloons is +broken but with new balloons and A + + align:start position:0% +broken but with new balloons and A + + + align:start position:0% +broken but with new balloons and A +Renewed charge the spacing looks to be + + align:start position:0% +Renewed charge the spacing looks to be + + + align:start position:0% +Renewed charge the spacing looks to be +about what we had + + align:start position:0% +about what we had + + + align:start position:0% +about what we had +before here's what happens when we + + align:start position:0% +before here's what happens when we + + + align:start position:0% +before here's what happens when we +insert the balloon in the Faraday + + align:start position:0% + + + + align:start position:0% + +cage watch the meter too + + align:start position:0% + + + + align:start position:0% + +our charge conservation statement can be + + align:start position:0% +our charge conservation statement can be + + + align:start position:0% +our charge conservation statement can be +used to see that it makes no difference + + align:start position:0% +used to see that it makes no difference + + + align:start position:0% +used to see that it makes no difference +to the measurement whether the balloon + + align:start position:0% +to the measurement whether the balloon + + + align:start position:0% +to the measurement whether the balloon +makes physical and electrical contact + + align:start position:0% +makes physical and electrical contact + + + align:start position:0% +makes physical and electrical contact +with the inner + + align:start position:0% +with the inner + + + align:start position:0% +with the inner +box from the dial settings on the top + + align:start position:0% +box from the dial settings on the top + + + align:start position:0% +box from the dial settings on the top +scale a full scale deflection is a + + align:start position:0% +scale a full scale deflection is a + + + align:start position:0% +scale a full scale deflection is a +charge of minus 1,000 + + align:start position:0% +charge of minus 1,000 + + + align:start position:0% +charge of minus 1,000 +nanocs the measured charge is 220 or + + align:start position:0% +nanocs the measured charge is 220 or + + + align:start position:0% +nanocs the measured charge is 220 or +30 nanocs + + align:start position:0% + + + + align:start position:0% + +let's see what we get for the other + + align:start position:0% + + + + align:start position:0% + +balloon the reading is about the same + + align:start position:0% +balloon the reading is about the same + + + align:start position:0% +balloon the reading is about the same +about 220 + + align:start position:0% + + + + align:start position:0% + +nanocom remember from our Force + + align:start position:0% +nanocom remember from our Force + + + align:start position:0% +nanocom remember from our Force +experiment we estimated 220 + + align:start position:0% +experiment we estimated 220 + + + align:start position:0% +experiment we estimated 220 +nanocs of course given the informality + + align:start position:0% +nanocs of course given the informality + + + align:start position:0% +nanocs of course given the informality +of our experiments this agreement is + + align:start position:0% +of our experiments this agreement is + + + align:start position:0% +of our experiments this agreement is +somewhat + + align:start position:0% + + + + align:start position:0% + +Fortes both the electromechanical and + + align:start position:0% +Fortes both the electromechanical and + + + align:start position:0% +Fortes both the electromechanical and +Faraday cage measurements that we have + + align:start position:0% +Faraday cage measurements that we have + + + align:start position:0% +Faraday cage measurements that we have +Illustrated can be made very + + align:start position:0% +Illustrated can be made very + + + align:start position:0% +Illustrated can be made very +precise here we've Illustrated how kul's + + align:start position:0% +precise here we've Illustrated how kul's + + + align:start position:0% +precise here we've Illustrated how kul's +Force law the law of charge conservation + + align:start position:0% +Force law the law of charge conservation + + + align:start position:0% +Force law the law of charge conservation +and gauss's law can also be used to make + + align:start position:0% +and gauss's law can also be used to make + + + align:start position:0% +and gauss's law can also be used to make +rough estimates + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +when the balloon is removed the meter + + align:start position:0% +when the balloon is removed the meter + + + align:start position:0% +when the balloon is removed the meter +reading almost goes back to + + align:start position:0% + + + + align:start position:0% + +zero apparently the charge is + + align:start position:0% +zero apparently the charge is + + + align:start position:0% +zero apparently the charge is +essentially removed with the balloon + + align:start position:0% + + + + align:start position:0% + +balloon what happens to the charge on + + align:start position:0% +balloon what happens to the charge on + + + align:start position:0% +balloon what happens to the charge on +the balloon if it's broken while in the + + align:start position:0% +the balloon if it's broken while in the + + + align:start position:0% +the balloon if it's broken while in the +Faraday cage and then + + align:start position:0% + + + + align:start position:0% + +removed we've used Scotch tape to hold + + align:start position:0% +removed we've used Scotch tape to hold + + + align:start position:0% +removed we've used Scotch tape to hold +the balloon together + + align:start position:0% + + + + align:start position:0% + +Professor Zan feels that most of the + + align:start position:0% +Professor Zan feels that most of the + + + align:start position:0% +Professor Zan feels that most of the +balloon was removed the charge was not \ No newline at end of file diff --git a/NwPOhzDPHKc.txt b/NwPOhzDPHKc.txt new file mode 100644 index 0000000000000000000000000000000000000000..f52fb5635cafd1bb3df6863a4a0e92112bff983f --- /dev/null +++ b/NwPOhzDPHKc.txt @@ -0,0 +1,1539 @@ +align:start position:0% + +the next thing I want to save her and + + align:start position:0% +the next thing I want to save her and + + + align:start position:0% +the next thing I want to save her and +talk to or for a few minutes is about + + align:start position:0% +talk to or for a few minutes is about + + + align:start position:0% +talk to or for a few minutes is about +the node theorem theorem and it's + + align:start position:0% +the node theorem theorem and it's + + + align:start position:0% +the node theorem theorem and it's +something we've seen before we've heard + + align:start position:0% +something we've seen before we've heard + + + align:start position:0% +something we've seen before we've heard +if you have a one-dimensional potential + + align:start position:0% +if you have a one-dimensional potential + + + align:start position:0% +if you have a one-dimensional potential +you have bound States the ground state + + align:start position:0% +you have bound States the ground state + + + align:start position:0% +you have bound States the ground state +has no nodes the first excited state has + + align:start position:0% +has no nodes the first excited state has + + + align:start position:0% +has no nodes the first excited state has +one node second two three four all I + + align:start position:0% +one node second two three four all I + + + align:start position:0% +one node second two three four all I +want to do is give you a little + + align:start position:0% +want to do is give you a little + + + align:start position:0% +want to do is give you a little +intuition as to why this happens so this + + align:start position:0% +intuition as to why this happens so this + + + align:start position:0% +intuition as to why this happens so this +will be an argument that is not + + align:start position:0% +will be an argument that is not + + + align:start position:0% +will be an argument that is not +mathematically very rigorous but it's + + align:start position:0% +mathematically very rigorous but it's + + + align:start position:0% +mathematically very rigorous but it's +fairly intuitive and it captures the + + align:start position:0% +fairly intuitive and it captures the + + + align:start position:0% +fairly intuitive and it captures the +physics of the problem so it begins by + + align:start position:0% +physics of the problem so it begins by + + + align:start position:0% +physics of the problem so it begins by +making two observations so in the node + + align:start position:0% +making two observations so in the node + + + align:start position:0% +making two observations so in the node +theorem is they if you have psy 1 psy - + + align:start position:0% +theorem is they if you have psy 1 psy - + + + align:start position:0% +theorem is they if you have psy 1 psy - +psy 3 all energy energy eigenstates of a + + align:start position:0% +psy 3 all energy energy eigenstates of a + + + align:start position:0% +psy 3 all energy energy eigenstates of a +one dimensional potential bound States + + align:start position:0% +one dimensional potential bound States + + + align:start position:0% +one dimensional potential bound States +bound state with energy e1 less than V 2 + + align:start position:0% +bound state with energy e1 less than V 2 + + + align:start position:0% +bound state with energy e1 less than V 2 +less than e 3 in for sy n has n minus 1 + + align:start position:0% +less than e 3 in for sy n has n minus 1 + + + align:start position:0% +less than e 3 in for sy n has n minus 1 +nodes those are points where the wave + + align:start position:0% +nodes those are points where the wave + + + align:start position:0% +nodes those are points where the wave +function vanishes inside the range of X + + align:start position:0% +function vanishes inside the range of X + + + align:start position:0% +function vanishes inside the range of X +so for the square well you've proven + + align:start position:0% +so for the square well you've proven + + + align:start position:0% +so for the square well you've proven +this by calculating all the energy + + align:start position:0% +this by calculating all the energy + + + align:start position:0% +this by calculating all the energy +eigenstates the first state is the + + align:start position:0% +eigenstates the first state is the + + + align:start position:0% +eigenstates the first state is the +ground state has no note + + align:start position:0% +ground state has no note + + + align:start position:0% +ground state has no note +the next state is the first excited + + align:start position:0% +the next state is the first excited + + + align:start position:0% +the next state is the first excited +state has one note and you can write all + + align:start position:0% +state has one note and you can write all + + + align:start position:0% +state has one note and you can write all +of them and we saw that each one has one + + align:start position:0% +of them and we saw that each one has one + + + align:start position:0% +of them and we saw that each one has one +more node than the next now I want to + + align:start position:0% +more node than the next now I want to + + + align:start position:0% +more node than the next now I want to +argue that in an arbitrary potential + + align:start position:0% +argue that in an arbitrary potential + + + align:start position:0% +argue that in an arbitrary potential +that has bound States this is also true + + align:start position:0% +that has bound States this is also true + + + align:start position:0% +that has bound States this is also true +so why would that be true for an + + align:start position:0% +so why would that be true for an + + + align:start position:0% +so why would that be true for an +arbitrary potential the argument we're + + align:start position:0% +arbitrary potential the argument we're + + + align:start position:0% +arbitrary potential the argument we're +gonna make is based on continuity + + align:start position:0% +gonna make is based on continuity + + + align:start position:0% +gonna make is based on continuity +suppose you have a potential like this V + + align:start position:0% +suppose you have a potential like this V + + + align:start position:0% +suppose you have a potential like this V +of X and I want to argue that this + + align:start position:0% +of X and I want to argue that this + + + align:start position:0% +of X and I want to argue that this +potential will have bound States and + + align:start position:0% +potential will have bound States and + + + align:start position:0% +potential will have bound States and +will have no node 1 node 2 node 3 nodes + + align:start position:0% +will have no node 1 node 2 node 3 nodes + + + align:start position:0% +will have no node 1 node 2 node 3 nodes +how how could I argue that well I would + + align:start position:0% +how how could I argue that well I would + + + align:start position:0% +how how could I argue that well I would +do the following here is the argument + + align:start position:0% +do the following here is the argument + + + align:start position:0% +do the following here is the argument +identify the minimum here call this x + + align:start position:0% +identify the minimum here call this x + + + align:start position:0% +identify the minimum here call this x +equals 0 oh I want to say one more thing + + align:start position:0% +equals 0 oh I want to say one more thing + + + align:start position:0% +equals 0 oh I want to say one more thing +remind you for another fact that I'm + + align:start position:0% +remind you for another fact that I'm + + + align:start position:0% +remind you for another fact that I'm +going to use so this is the first thing + + align:start position:0% +going to use so this is the first thing + + + align:start position:0% +going to use so this is the first thing +that the square well realizes this + + align:start position:0% +that the square well realizes this + + + align:start position:0% +that the square well realizes this +theorem and the second is that sigh at X + + align:start position:0% +theorem and the second is that sigh at X + + + align:start position:0% +theorem and the second is that sigh at X +naught being equal to psi Prime at X + + align:start position:0% +naught being equal to psi Prime at X + + + align:start position:0% +naught being equal to psi Prime at X +naught being equal to 0 is not possible + + align:start position:0% +naught being equal to 0 is not possible + + + align:start position:0% +naught being equal to 0 is not possible +the wave function and it's derivative + + align:start position:0% +the wave function and it's derivative + + + align:start position:0% +the wave function and it's derivative +cannot vanish at the same point please + + align:start position:0% +cannot vanish at the same point please + + + align:start position:0% +cannot vanish at the same point please +see the notes about this there's an + + align:start position:0% +see the notes about this there's an + + + align:start position:0% +see the notes about this there's an +explanation in last lectures notes it is + + align:start position:0% +explanation in last lectures notes it is + + + align:start position:0% +explanation in last lectures notes it is +the fact that for a second order + + align:start position:0% +the fact that for a second order + + + align:start position:0% +the fact that for a second order +differential equation + + align:start position:0% +differential equation + + + align:start position:0% +differential equation +sigh I'm side Prime tell you how to + + align:start position:0% +sigh I'm side Prime tell you how to + + + align:start position:0% +sigh I'm side Prime tell you how to +start the solution and if both times I + + align:start position:0% +start the solution and if both times I + + + align:start position:0% +start the solution and if both times I +primary equal to 0 the general solution + + align:start position:0% +primary equal to 0 the general solution + + + align:start position:0% +primary equal to 0 the general solution +of the differential equation is always 0 + + align:start position:0% +of the differential equation is always 0 + + + align:start position:0% +of the differential equation is always 0 +everywhere so this kind of thing doesn't + + align:start position:0% +everywhere so this kind of thing doesn't + + + align:start position:0% +everywhere so this kind of thing doesn't +happen to a wave function the point + + align:start position:0% +happen to a wave function the point + + + align:start position:0% +happen to a wave function the point +where it's zero on the derivative is 0 + + align:start position:0% +where it's zero on the derivative is 0 + + + align:start position:0% +where it's zero on the derivative is 0 +that never happens this happens zero + + align:start position:0% +that never happens this happens zero + + + align:start position:0% +that never happens this happens zero +wave function but a derivative but this + + align:start position:0% +wave function but a derivative but this + + + align:start position:0% +wave function but a derivative but this +no never happens so those two facts and + + align:start position:0% +no never happens so those two facts and + + + align:start position:0% +no never happens so those two facts and +now let's do the following let's invent + + align:start position:0% +now let's do the following let's invent + + + align:start position:0% +now let's do the following let's invent +a new potential not this potential but + + align:start position:0% +a new potential not this potential but + + + align:start position:0% +a new potential not this potential but +the new one that I'll mark the point - a + + align:start position:0% +the new one that I'll mark the point - a + + + align:start position:0% +the new one that I'll mark the point - a +here and the point a here and invent a + + align:start position:0% +here and the point a here and invent a + + + align:start position:0% +here and the point a here and invent a +new potential that is infinite here + + align:start position:0% +new potential that is infinite here + + + align:start position:0% +new potential that is infinite here +infinite there and has this part or or + + align:start position:0% +infinite there and has this part or or + + + align:start position:0% +infinite there and has this part or or +right there so this will be called the + + align:start position:0% +right there so this will be called the + + + align:start position:0% +right there so this will be called the +screened potential screened potential V + + align:start position:0% +screened potential screened potential V + + + align:start position:0% +screened potential screened potential V +a of X in which V a of X is equal to V + + align:start position:0% +a of X in which V a of X is equal to V + + + align:start position:0% +a of X in which V a of X is equal to V +of X for X less than a and it's infinity + + align:start position:0% +of X for X less than a and it's infinity + + + align:start position:0% +of X for X less than a and it's infinity +for X greater than a so that's a + + align:start position:0% +for X greater than a so that's a + + + align:start position:0% +for X greater than a so that's a +potential in which you sort of turn your + + align:start position:0% +potential in which you sort of turn your + + + align:start position:0% +potential in which you sort of turn your +potential into an infinite square well + + align:start position:0% +potential into an infinite square well + + + align:start position:0% +potential into an infinite square well +whose bottom follows the potential is + + align:start position:0% +whose bottom follows the potential is + + + align:start position:0% +whose bottom follows the potential is +not flat and now we intuitively argue + + align:start position:0% +not flat and now we intuitively argue + + + align:start position:0% +not flat and now we intuitively argue +that as I take a to infinity the bound + + align:start position:0% +that as I take a to infinity the bound + + + align:start position:0% +that as I take a to infinity the bound +states of the screen potentials become + + align:start position:0% +states of the screen potentials become + + + align:start position:0% +states of the screen potentials become +the bound states of your original + + align:start position:0% +the bound states of your original + + + align:start position:0% +the bound states of your original +potential because when the screen is + + align:start position:0% +potential because when the screen is + + + align:start position:0% +potential because when the screen is +very very very far away up to infinity + + align:start position:0% +very very very far away up to infinity + + + align:start position:0% +very very very far away up to infinity +you got all your potential and by the + + align:start position:0% +you got all your potential and by the + + + align:start position:0% +you got all your potential and by the +time you have bounced taser decaying so + + align:start position:0% +time you have bounced taser decaying so + + + align:start position:0% +time you have bounced taser decaying so +the screen is not gonna do much at + + align:start position:0% +the screen is not gonna do much at + + + align:start position:0% +the screen is not gonna do much at +infinity and anyway you can move it even + + align:start position:0% +infinity and anyway you can move it even + + + align:start position:0% +infinity and anyway you can move it even +further away if you move it one + + align:start position:0% +further away if you move it one + + + align:start position:0% +further away if you move it one +light-year away or two light-years away + + align:start position:0% +light-year away or two light-years away + + + align:start position:0% +light-year away or two light-years away +should matter so the idea is that the + + align:start position:0% +should matter so the idea is that the + + + align:start position:0% +should matter so the idea is that the +bound States bound States of V a of X as + + align:start position:0% +bound States bound States of V a of X as + + + align:start position:0% +bound States bound States of V a of X as +a goes to infinity + + align:start position:0% +a goes to infinity + + + align:start position:0% +a goes to infinity +are the bound States + + align:start position:0% + + + + align:start position:0% + +of VFX and moreover as you slowly and + + align:start position:0% +of VFX and moreover as you slowly and + + + align:start position:0% +of VFX and moreover as you slowly and +increase the width of the screen the + + align:start position:0% +increase the width of the screen the + + + align:start position:0% +increase the width of the screen the +both states evolve but they evolve + + align:start position:0% +both states evolve but they evolve + + + align:start position:0% +both states evolve but they evolve +continuously at no point a bound state + + align:start position:0% +continuously at no point a bound state + + + align:start position:0% +continuously at no point a bound state +sort of blows up and reappears or does + + align:start position:0% +sort of blows up and reappears or does + + + align:start position:0% +sort of blows up and reappears or does +something like that + + align:start position:0% +something like that + + + align:start position:0% +something like that +it just goes continuously these are + + align:start position:0% +it just goes continuously these are + + + align:start position:0% +it just goes continuously these are +physically reasonable but a + + align:start position:0% +physically reasonable but a + + + align:start position:0% +physically reasonable but a +mathematician would demand better + + align:start position:0% +mathematician would demand better + + + align:start position:0% +mathematician would demand better +explanation but that's okay we will + + align:start position:0% +explanation but that's okay we will + + + align:start position:0% +explanation but that's okay we will +stick to this so let's continue there so + + align:start position:0% +stick to this so let's continue there so + + + align:start position:0% +stick to this so let's continue there so +here is the idea simply stated if a is + + align:start position:0% +here is the idea simply stated if a is + + + align:start position:0% +here is the idea simply stated if a is +going to 0 if the length of the screen + + align:start position:0% +going to 0 if the length of the screen + + + align:start position:0% +going to 0 if the length of the screen +is vary the width of the screen is + + align:start position:0% +is vary the width of the screen is + + + align:start position:0% +is vary the width of the screen is +extremely narrow you're sitting at the + + align:start position:0% +extremely narrow you're sitting at the + + + align:start position:0% +extremely narrow you're sitting at the +bottom of the potential at x equals 0 + + align:start position:0% +bottom of the potential at x equals 0 + + + align:start position:0% +bottom of the potential at x equals 0 +and the screen potential is basically a + + align:start position:0% +and the screen potential is basically a + + + align:start position:0% +and the screen potential is basically a +very very narrow thing and here there's + + align:start position:0% +very very narrow thing and here there's + + + align:start position:0% +very very narrow thing and here there's +the bottom of the potential and for + + align:start position:0% +the bottom of the potential and for + + + align:start position:0% +the bottom of the potential and for +sufficiently small a since you pick the + + align:start position:0% +sufficiently small a since you pick the + + + align:start position:0% +sufficiently small a since you pick the +bottom of the potential there it's + + align:start position:0% +bottom of the potential there it's + + + align:start position:0% +bottom of the potential there it's +basically flat and then I can use the + + align:start position:0% +basically flat and then I can use the + + + align:start position:0% +basically flat and then I can use the +state of the infinite square well + + align:start position:0% +state of the infinite square well + + + align:start position:0% +state of the infinite square well +potential as a goes to 0 yes you have a + + align:start position:0% +potential as a goes to 0 yes you have a + + + align:start position:0% +potential as a goes to 0 yes you have a +ground state with no note a first + + align:start position:0% +ground state with no note a first + + + align:start position:0% +ground state with no note a first +excited state with one note and all the + + align:start position:0% +excited state with one note and all the + + + align:start position:0% +excited state with one note and all the +states have the right number of notes + + align:start position:0% +states have the right number of notes + + + align:start position:0% +states have the right number of notes +because they are the states of the + + align:start position:0% +because they are the states of the + + + align:start position:0% +because they are the states of the +infinite square well however narrow it + + align:start position:0% +infinite square well however narrow it + + + align:start position:0% +infinite square well however narrow it +is so the only thing we have to now show + + align:start position:0% +is so the only thing we have to now show + + + align:start position:0% +is so the only thing we have to now show +is that if you have a wave function say + + align:start position:0% +is that if you have a wave function say + + + align:start position:0% +is that if you have a wave function say +let's begin with one with no notes as + + align:start position:0% +let's begin with one with no notes as + + + align:start position:0% +let's begin with one with no notes as +you increase the width of the screen you + + align:start position:0% +you increase the width of the screen you + + + align:start position:0% +you increase the width of the screen you +cannot get + + align:start position:0% +cannot get + + + align:start position:0% +cannot get +more nodes it's impossible to change the + + align:start position:0% +more nodes it's impossible to change the + + + align:start position:0% +more nodes it's impossible to change the +number of nodes continuously so here it + + align:start position:0% +number of nodes continuously so here it + + + align:start position:0% +number of nodes continuously so here it +is I'm gonna do a little diagram so for + + align:start position:0% +is I'm gonna do a little diagram so for + + + align:start position:0% +is I'm gonna do a little diagram so for +example let's assume the screen is this + + align:start position:0% +example let's assume the screen is this + + + align:start position:0% +example let's assume the screen is this +big at this moment that you have some + + align:start position:0% +big at this moment that you have some + + + align:start position:0% +big at this moment that you have some +ground state like this you've been + + align:start position:0% +ground state like this you've been + + + align:start position:0% +ground state like this you've been +growing this and then as the screen + + align:start position:0% +growing this and then as the screen + + + align:start position:0% +growing this and then as the screen +grows bigger you somehow have maybe a + + align:start position:0% +grows bigger you somehow have maybe a + + + align:start position:0% +grows bigger you somehow have maybe a +node could this have happened + + align:start position:0% +node could this have happened + + + align:start position:0% +node could this have happened +as you increase this screen you get a + + align:start position:0% +as you increase this screen you get a + + + align:start position:0% +as you increase this screen you get a +node now I made it on this point which + + align:start position:0% +node now I made it on this point which + + + align:start position:0% +node now I made it on this point which +is not I didn't intend to do that so let + + align:start position:0% +is not I didn't intend to do that so let + + + align:start position:0% +is not I didn't intend to do that so let +me borrow do it again you know somewhere + + align:start position:0% +me borrow do it again you know somewhere + + + align:start position:0% +me borrow do it again you know somewhere +do you get a node well here was the + + align:start position:0% +do you get a node well here was the + + + align:start position:0% +do you get a node well here was the +original screen and here the derivative + + align:start position:0% +original screen and here the derivative + + + align:start position:0% +original screen and here the derivative +Tsai prime is negative sy prime is + + align:start position:0% +Tsai prime is negative sy prime is + + + align:start position:0% +Tsai prime is negative sy prime is +negative on the other hand side prime + + align:start position:0% +negative on the other hand side prime + + + align:start position:0% +negative on the other hand side prime +here is already positive + + align:start position:0% +here is already positive + + + align:start position:0% +here is already positive +so as you rule the screen this sort of + + align:start position:0% +so as you rule the screen this sort of + + + align:start position:0% +so as you rule the screen this sort of +sy prime that was here must have turned + + align:start position:0% +sy prime that was here must have turned + + + align:start position:0% +sy prime that was here must have turned +from passi from negative to positive the + + align:start position:0% +from passi from negative to positive the + + + align:start position:0% +from passi from negative to positive the +way it looks here but for that there + + align:start position:0% +way it looks here but for that there + + + align:start position:0% +way it looks here but for that there +must have been a point somewhere here + + align:start position:0% +must have been a point somewhere here + + + align:start position:0% +must have been a point somewhere here +when it was horizontal if it's + + align:start position:0% +when it was horizontal if it's + + + align:start position:0% +when it was horizontal if it's +continuous and therefore there must have + + align:start position:0% +continuous and therefore there must have + + + align:start position:0% +continuous and therefore there must have +been some point at which sy and sy prime + + align:start position:0% +been some point at which sy and sy prime + + + align:start position:0% +been some point at which sy and sy prime +were both 0 at at the end by X equal a + + align:start position:0% +were both 0 at at the end by X equal a + + + align:start position:0% +were both 0 at at the end by X equal a +whatever the value of a was because sy + + align:start position:0% +whatever the value of a was because sy + + + align:start position:0% +whatever the value of a was because sy +prime here is positive and he + + align:start position:0% +prime here is positive and he + + + align:start position:0% +prime here is positive and he +is negative so at some point it was zero + + align:start position:0% +is negative so at some point it was zero + + + align:start position:0% +is negative so at some point it was zero +but since it's at the point where you + + align:start position:0% +but since it's at the point where you + + + align:start position:0% +but since it's at the point where you +have the infinite square well prize also + + align:start position:0% +have the infinite square well prize also + + + align:start position:0% +have the infinite square well prize also +zero and you would have both science try + + align:start position:0% +zero and you would have both science try + + + align:start position:0% +zero and you would have both science try +prime equals zero which is impossible so + + align:start position:0% +prime equals zero which is impossible so + + + align:start position:0% +prime equals zero which is impossible so +basically you can't quite flip this and + + align:start position:0% +basically you can't quite flip this and + + + align:start position:0% +basically you can't quite flip this and +producer note because you would have to + + align:start position:0% +producer note because you would have to + + + align:start position:0% +producer note because you would have to +flip here and you can't do it you could + + align:start position:0% +flip here and you can't do it you could + + + align:start position:0% +flip here and you can't do it you could +you know one could try to make a very + + align:start position:0% +you know one could try to make a very + + + align:start position:0% +you know one could try to make a very +precise rigorous argument but if you + + align:start position:0% +precise rigorous argument but if you + + + align:start position:0% +precise rigorous argument but if you +have another possibility you might think + + align:start position:0% +have another possibility you might think + + + align:start position:0% +have another possibility you might think +well you have this wave function maybe + + align:start position:0% +well you have this wave function maybe + + + align:start position:0% +well you have this wave function maybe +and then suddenly it starts doing this + + align:start position:0% +and then suddenly it starts doing this + + + align:start position:0% +and then suddenly it starts doing this +and at some stage it's going to try to + + align:start position:0% +and at some stage it's going to try to + + + align:start position:0% +and at some stage it's going to try to +do this but before it does that at some + + align:start position:0% +do this but before it does that at some + + + align:start position:0% +do this but before it does that at some +point will have to be just like this and + + align:start position:0% +point will have to be just like this and + + + align:start position:0% +point will have to be just like this and +cross but at this point science i prime + + align:start position:0% +cross but at this point science i prime + + + align:start position:0% +cross but at this point science i prime +would be zero so you can intuitively + + align:start position:0% +would be zero so you can intuitively + + + align:start position:0% +would be zero so you can intuitively +convince yourself that this thing + + align:start position:0% +convince yourself that this thing + + + align:start position:0% +convince yourself that this thing +doesn't allow you to produce a node so + + align:start position:0% +doesn't allow you to produce a node so + + + align:start position:0% +doesn't allow you to produce a node so +if you start with whatever wavefunction + + align:start position:0% +if you start with whatever wavefunction + + + align:start position:0% +if you start with whatever wavefunction +that has no note as we increase the + + align:start position:0% +that has no note as we increase the + + + align:start position:0% +that has no note as we increase the +screen you just can't produce a node so + + align:start position:0% +screen you just can't produce a node so + + + align:start position:0% +screen you just can't produce a node so +the ground state of the whole bit + + align:start position:0% +the ground state of the whole bit + + + align:start position:0% +the ground state of the whole bit +potential will have no nodes and if you + + align:start position:0% +potential will have no nodes and if you + + + align:start position:0% +potential will have no nodes and if you +start with the first excited state that + + align:start position:0% +start with the first excited state that + + + align:start position:0% +start with the first excited state that +has one node as you increase the screen + + align:start position:0% +has one node as you increase the screen + + + align:start position:0% +has one node as you increase the screen +you still keep one node so the next + + align:start position:0% +you still keep one node so the next + + + align:start position:0% +you still keep one node so the next +state of the full potential have one + + align:start position:0% +state of the full potential have one + + + align:start position:0% +state of the full potential have one +node as well and that way you argue that + + align:start position:0% +node as well and that way you argue that + + + align:start position:0% +node as well and that way you argue that +all your bound states of the complete + + align:start position:0% +all your bound states of the complete + + + align:start position:0% +all your bound states of the complete +potential will just have the right + + align:start position:0% +potential will just have the right + + + align:start position:0% +potential will just have the right +number of nodes which is 0 1 2 3 4 and + + align:start position:0% +number of nodes which is 0 1 2 3 4 and + + + align:start position:0% +number of nodes which is 0 1 2 3 4 and +it all came essentially from the + + align:start position:0% +it all came essentially from the + + + align:start position:0% +it all came essentially from the +infinite square well and continuity \ No newline at end of file diff --git a/OGtElTMJidE.txt b/OGtElTMJidE.txt new file mode 100644 index 0000000000000000000000000000000000000000..e2275cb650271ec8c8d905727d2ec04b70621c50 --- /dev/null +++ b/OGtElTMJidE.txt @@ -0,0 +1,7235 @@ +align:start position:0% + +so I'll try it again at the end of this + + align:start position:0% +so I'll try it again at the end of this + + + align:start position:0% +so I'll try it again at the end of this +lecture and show you that stuff + + align:start position:0% +lecture and show you that stuff + + + align:start position:0% +lecture and show you that stuff +hopefully uh next time okay so for + + align:start position:0% +hopefully uh next time okay so for + + + align:start position:0% +hopefully uh next time okay so for +today uh we're going to start with + + align:start position:0% +today uh we're going to start with + + + align:start position:0% +today uh we're going to start with +nonlinear analysis okay uh before we do + + align:start position:0% +nonlinear analysis okay uh before we do + + + align:start position:0% +nonlinear analysis okay uh before we do +that I wanted to uh do a little bit of + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +review so um I wanted give you the uh + + align:start position:0% +review so um I wanted give you the uh + + + align:start position:0% +review so um I wanted give you the uh +the past 3 weeks in perspective and show + + align:start position:0% +the past 3 weeks in perspective and show + + + align:start position:0% +the past 3 weeks in perspective and show +you how all of these things fit into the + + align:start position:0% +you how all of these things fit into the + + + align:start position:0% +you how all of these things fit into the +grand scheme of things so um we began + + align:start position:0% + + + + align:start position:0% + +by building the great little playground + + align:start position:0% +by building the great little playground + + + align:start position:0% +by building the great little playground +and within that playground we said + + align:start position:0% +and within that playground we said + + + align:start position:0% +and within that playground we said +that by enforcing upon ourselves the + + align:start position:0% +that by enforcing upon ourselves the + + + align:start position:0% +that by enforcing upon ourselves the +lump matter discipline we created the + + align:start position:0% +lump matter discipline we created the + + + align:start position:0% +lump matter discipline we created the +lump circuit + + align:start position:0% +lump circuit + + + align:start position:0% +lump circuit +abstraction So within that Playfield we + + align:start position:0% +abstraction So within that Playfield we + + + align:start position:0% +abstraction So within that Playfield we +assume that we had DQ by DT and D5 by DT + + align:start position:0% +assume that we had DQ by DT and D5 by DT + + + align:start position:0% +assume that we had DQ by DT and D5 by DT +to be zero and so that gave us the lump + + align:start position:0% +to be zero and so that gave us the lump + + + align:start position:0% +to be zero and so that gave us the lump +circuit abstraction and within the lump + + align:start position:0% +circuit abstraction and within the lump + + + align:start position:0% +circuit abstraction and within the lump +circuit abstraction within this + + align:start position:0% +circuit abstraction within this + + + align:start position:0% +circuit abstraction within this +playground we looked at several methods + + align:start position:0% +playground we looked at several methods + + + align:start position:0% +playground we looked at several methods +of analyzing circuits uh + + align:start position:0% +of analyzing circuits uh + + + align:start position:0% +of analyzing circuits uh +including the kvl KCl + + align:start position:0% +including the kvl KCl + + + align:start position:0% +including the kvl KCl +method we also + + align:start position:0% + + + + align:start position:0% + +learned the method involving composing + + align:start position:0% +learned the method involving composing + + + align:start position:0% +learned the method involving composing +uh resistors the voltage dividers and so + + align:start position:0% +uh resistors the voltage dividers and so + + + align:start position:0% +uh resistors the voltage dividers and so +on and solving circuits intuitively and + + align:start position:0% +on and solving circuits intuitively and + + + align:start position:0% +on and solving circuits intuitively and +we + + align:start position:0% +we + + + align:start position:0% +we +also looked at the node method which is + + align:start position:0% +also looked at the node method which is + + + align:start position:0% +also looked at the node method which is +kind of the Workhorse of the circuits + + align:start position:0% +kind of the Workhorse of the circuits + + + align:start position:0% +kind of the Workhorse of the circuits +industry so when in doubt apply the node + + align:start position:0% +industry so when in doubt apply the node + + + align:start position:0% +industry so when in doubt apply the node +method and it will get you uh where you + + align:start position:0% +method and it will get you uh where you + + + align:start position:0% +method and it will get you uh where you +want to go now we also said that that + + align:start position:0% +want to go now we also said that that + + + align:start position:0% +want to go now we also said that that +this was good here's our playground we + + align:start position:0% +this was good here's our playground we + + + align:start position:0% +this was good here's our playground we +said hey if we focus on those circuits + + align:start position:0% +said hey if we focus on those circuits + + + align:start position:0% +said hey if we focus on those circuits +that are linear + + align:start position:0% + + + + align:start position:0% + +we come to the left part of our + + align:start position:0% +we come to the left part of our + + + align:start position:0% +we come to the left part of our +playground okay and we said that for + + align:start position:0% +playground okay and we said that for + + + align:start position:0% +playground okay and we said that for +linear circuits in this part of the + + align:start position:0% +linear circuits in this part of the + + + align:start position:0% +linear circuits in this part of the +playground we can further use a couple + + align:start position:0% +playground we can further use a couple + + + align:start position:0% +playground we can further use a couple +of techniques a few + + align:start position:0% +of techniques a few + + + align:start position:0% +of techniques a few +techniques + + align:start position:0% + + + + align:start position:0% + +superposition + + align:start position:0% +superposition + + + align:start position:0% +superposition +T Norton and so on so these techniques + + align:start position:0% +T Norton and so on so these techniques + + + align:start position:0% +T Norton and so on so these techniques +allow you to very quickly analyze + + align:start position:0% +allow you to very quickly analyze + + + align:start position:0% +allow you to very quickly analyze +complicated circuits especially when + + align:start position:0% +complicated circuits especially when + + + align:start position:0% +complicated circuits especially when +you're looking to find a single current + + align:start position:0% +you're looking to find a single current + + + align:start position:0% +you're looking to find a single current +or voltage or some parameter of Interest + + align:start position:0% + + + + align:start position:0% + +whenever you see if you see a circuit + + align:start position:0% +whenever you see if you see a circuit + + + align:start position:0% +whenever you see if you see a circuit +containing multiple voltage sources or + + align:start position:0% +containing multiple voltage sources or + + + align:start position:0% +containing multiple voltage sources or +two or more voltage sources the current + + align:start position:0% +two or more voltage sources the current + + + align:start position:0% +two or more voltage sources the current +sources as a first step think + + align:start position:0% +sources as a first step think + + + align:start position:0% +sources as a first step think +superposition okay and uh so in these + + align:start position:0% +superposition okay and uh so in these + + + align:start position:0% +superposition okay and uh so in these +are very powerful techniques that let + + align:start position:0% +are very powerful techniques that let + + + align:start position:0% +are very powerful techniques that let +you analyze very complicated circuits + + align:start position:0% +you analyze very complicated circuits + + + align:start position:0% +you analyze very complicated circuits +very + + align:start position:0% +very + + + align:start position:0% +very +effectively so after we did this we said + + align:start position:0% +effectively so after we did this we said + + + align:start position:0% +effectively so after we did this we said +uh oh um let me draw another playground + + align:start position:0% +uh oh um let me draw another playground + + + align:start position:0% +uh oh um let me draw another playground +here uh this is the + + align:start position:0% + + + + align:start position:0% + +another piece of our playground and if + + align:start position:0% +another piece of our playground and if + + + align:start position:0% +another piece of our playground and if +this is linear circuits then this half + + align:start position:0% +this is linear circuits then this half + + + align:start position:0% +this is linear circuits then this half +of the playground is nonlinear circuits + + align:start position:0% +of the playground is nonlinear circuits + + + align:start position:0% +of the playground is nonlinear circuits +and we said that if you further Focus if + + align:start position:0% +and we said that if you further Focus if + + + align:start position:0% +and we said that if you further Focus if +you further focus on discretized + + align:start position:0% + + + + align:start position:0% + +values if you discretized values and + + align:start position:0% +values if you discretized values and + + + align:start position:0% +values if you discretized values and +focused only on circuits that dealt with + + align:start position:0% +focused only on circuits that dealt with + + + align:start position:0% +focused only on circuits that dealt with +binary signals highs and lows then we + + align:start position:0% +binary signals highs and lows then we + + + align:start position:0% +binary signals highs and lows then we +came into this small regime of the + + align:start position:0% +came into this small regime of the + + + align:start position:0% +came into this small regime of the +playground and notice that digital + + align:start position:0% +playground and notice that digital + + + align:start position:0% +playground and notice that digital +circuits are by the very nature + + align:start position:0% +circuits are by the very nature + + + align:start position:0% +circuits are by the very nature +nonlinear okay remember uh remember the + + align:start position:0% + + + + align:start position:0% + +circuit a b uh this was one of our nor + + align:start position:0% +circuit a b uh this was one of our nor + + + align:start position:0% +circuit a b uh this was one of our nor +gate circuits and uh if you look at a + + align:start position:0% +gate circuits and uh if you look at a + + + align:start position:0% +gate circuits and uh if you look at a +transfer functions that is if I plot + + align:start position:0% +transfer functions that is if I plot + + + align:start position:0% +transfer functions that is if I plot +let's say for + + align:start position:0% +let's say for + + + align:start position:0% +let's say for +example for some combination of + + align:start position:0% +example for some combination of + + + align:start position:0% +example for some combination of +uh input input values let's say I plot V + + align:start position:0% +uh input input values let's say I plot V + + + align:start position:0% +uh input input values let's say I plot V +inverse V out uh let's say for example I + + align:start position:0% +inverse V out uh let's say for example I + + + align:start position:0% +inverse V out uh let's say for example I +turn this guy off by setting B to zero + + align:start position:0% +turn this guy off by setting B to zero + + + align:start position:0% +turn this guy off by setting B to zero +and then I simply apply a low to high + + align:start position:0% +and then I simply apply a low to high + + + align:start position:0% +and then I simply apply a low to high +transition at uh VN then what I would + + align:start position:0% +transition at uh VN then what I would + + + align:start position:0% +transition at uh VN then what I would +see at the output is a transfer function + + align:start position:0% +see at the output is a transfer function + + + align:start position:0% +see at the output is a transfer function +of the following sort where as V changes + + align:start position:0% +of the following sort where as V changes + + + align:start position:0% +of the following sort where as V changes +the output switches at some point and + + align:start position:0% +the output switches at some point and + + + align:start position:0% +the output switches at some point and +then stays at a low value Okay so when V + + align:start position:0% +then stays at a low value Okay so when V + + + align:start position:0% +then stays at a low value Okay so when V +in is low V out is high and VN is high V + + align:start position:0% +in is low V out is high and VN is high V + + + align:start position:0% +in is low V out is high and VN is high V +out is uh low so that's kind of the V + + align:start position:0% +out is uh low so that's kind of the V + + + align:start position:0% +out is uh low so that's kind of the V +out versus VN when B is set at zero so + + align:start position:0% +out versus VN when B is set at zero so + + + align:start position:0% +out versus VN when B is set at zero so +notice that this is a + + align:start position:0% +notice that this is a + + + align:start position:0% +notice that this is a +nonlinear curve okay this is not a + + align:start position:0% +nonlinear curve okay this is not a + + + align:start position:0% +nonlinear curve okay this is not a +straight line uh it's a nonlinear curve + + align:start position:0% +straight line uh it's a nonlinear curve + + + align:start position:0% +straight line uh it's a nonlinear curve +and so therefore in the digital domain + + align:start position:0% +and so therefore in the digital domain + + + align:start position:0% +and so therefore in the digital domain +we see functions highly nonlinear + + align:start position:0% +we see functions highly nonlinear + + + align:start position:0% +we see functions highly nonlinear +functions that look like this and so + + align:start position:0% +functions that look like this and so + + + align:start position:0% +functions that look like this and so +on however however take a look at this + + align:start position:0% +on however however take a look at this + + + align:start position:0% +on however however take a look at this +circuit suppose + + align:start position:0% +circuit suppose + + + align:start position:0% +circuit suppose +I focus on the circuit for a given set + + align:start position:0% +I focus on the circuit for a given set + + + align:start position:0% +I focus on the circuit for a given set +of switch + + align:start position:0% +of switch + + + align:start position:0% +of switch +settings okay so let's say for example I + + align:start position:0% +settings okay so let's say for example I + + + align:start position:0% +settings okay so let's say for example I +focus on the circuit When A and B are + + align:start position:0% +focus on the circuit When A and B are + + + align:start position:0% +focus on the circuit When A and B are +both + + align:start position:0% +both + + + align:start position:0% +both +ones for a given set of switch settings + + align:start position:0% +ones for a given set of switch settings + + + align:start position:0% +ones for a given set of switch settings +notice that I'm going to be either in + + align:start position:0% +notice that I'm going to be either in + + + align:start position:0% +notice that I'm going to be either in +this region or in this region notice + + align:start position:0% +this region or in this region notice + + + align:start position:0% +this region or in this region notice +that uh this region is a straight + + align:start position:0% +that uh this region is a straight + + + align:start position:0% +that uh this region is a straight +line okay so if I focus on let's say + + align:start position:0% +line okay so if I focus on let's say + + + align:start position:0% +line okay so if I focus on let's say +both A and B are ones + + align:start position:0% + + + + align:start position:0% + +then I get something like + + align:start position:0% + + + + align:start position:0% + +this okay and in this situation for a + + align:start position:0% +this okay and in this situation for a + + + align:start position:0% +this okay and in this situation for a +given set of switch settings notice that + + align:start position:0% +given set of switch settings notice that + + + align:start position:0% +given set of switch settings notice that +my digital circuit now can be analyzed + + align:start position:0% +my digital circuit now can be analyzed + + + align:start position:0% +my digital circuit now can be analyzed +using linear techniques so + + align:start position:0% + + + + align:start position:0% + +therefore my digital gets moved into the + + align:start position:0% +therefore my digital gets moved into the + + + align:start position:0% +therefore my digital gets moved into the +linear domain for a given set of switch + + align:start position:0% +linear domain for a given set of switch + + + align:start position:0% +linear domain for a given set of switch +settings + + align:start position:0% + + + + align:start position:0% + +okay so if I fix my switch settings and + + align:start position:0% +okay so if I fix my switch settings and + + + align:start position:0% +okay so if I fix my switch settings and +look at the circuit then each circuit + + align:start position:0% +look at the circuit then each circuit + + + align:start position:0% +look at the circuit then each circuit +for a given set of switch settings is + + align:start position:0% +for a given set of switch settings is + + + align:start position:0% +for a given set of switch settings is +comprised of voltage sources and some + + align:start position:0% +comprised of voltage sources and some + + + align:start position:0% +comprised of voltage sources and some +resistors and it's a linear circuit so + + align:start position:0% +resistors and it's a linear circuit so + + + align:start position:0% +resistors and it's a linear circuit so +again I can go back and apply all my + + align:start position:0% +again I can go back and apply all my + + + align:start position:0% +again I can go back and apply all my +linear technique to techniques to + + align:start position:0% +linear technique to techniques to + + + align:start position:0% +linear technique to techniques to +virtually all the digital circuits that + + align:start position:0% +virtually all the digital circuits that + + + align:start position:0% +virtually all the digital circuits that +you will be dealing with in + + align:start position:0% +you will be dealing with in + + + align:start position:0% +you will be dealing with in +62 okay again remember if I fix my + + align:start position:0% +62 okay again remember if I fix my + + + align:start position:0% +62 okay again remember if I fix my +switch settings if I fix the inputs + + align:start position:0% +switch settings if I fix the inputs + + + align:start position:0% +switch settings if I fix the inputs +then the output can be determined using + + align:start position:0% +then the output can be determined using + + + align:start position:0% +then the output can be determined using +linear techniques because the the + + align:start position:0% +linear techniques because the the + + + align:start position:0% +linear techniques because the the +digital circuits we're showing you in 62 + + align:start position:0% +digital circuits we're showing you in 62 + + + align:start position:0% +digital circuits we're showing you in 62 +uh simply comprise linear elements like + + align:start position:0% +uh simply comprise linear elements like + + + align:start position:0% +uh simply comprise linear elements like +voltage sources and resistors and so on + + align:start position:0% +voltage sources and resistors and so on + + + align:start position:0% +voltage sources and resistors and so on +you'll see some more later but you can + + align:start position:0% +you'll see some more later but you can + + + align:start position:0% +you'll see some more later but you can +apply your linear techniques and analyze + + align:start position:0% +apply your linear techniques and analyze + + + align:start position:0% +apply your linear techniques and analyze +them so uh the cool thing here is that + + align:start position:0% +them so uh the cool thing here is that + + + align:start position:0% +them so uh the cool thing here is that +with just two weeks of stuff that you've + + align:start position:0% +with just two weeks of stuff that you've + + + align:start position:0% +with just two weeks of stuff that you've +learned in 62 you are well on your way + + align:start position:0% +learned in 62 you are well on your way + + + align:start position:0% +learned in 62 you are well on your way +to being able to analyze certain classes + + align:start position:0% +to being able to analyze certain classes + + + align:start position:0% +to being able to analyze certain classes +of digital circuits for a given set of + + align:start position:0% +of digital circuits for a given set of + + + align:start position:0% +of digital circuits for a given set of +switch settings and many many many + + align:start position:0% +switch settings and many many many + + + align:start position:0% +switch settings and many many many +linear circuits + + align:start position:0% + + + + align:start position:0% + +okay what we'll do + + align:start position:0% +okay what we'll do + + + align:start position:0% +okay what we'll do +today is focus + + align:start position:0% +today is focus + + + align:start position:0% +today is focus +on nonlinear + + align:start position:0% +on nonlinear + + + align:start position:0% +on nonlinear +circuits okay so we look at this + + align:start position:0% + + + + align:start position:0% + +space notice again that up to now we + + align:start position:0% +space notice again that up to now we + + + align:start position:0% +space notice again that up to now we +dealt with these three methods which + + align:start position:0% +dealt with these three methods which + + + align:start position:0% +dealt with these three methods which +apply to all circuits within this + + align:start position:0% +apply to all circuits within this + + + align:start position:0% +apply to all circuits within this +playground the lump circuit playground + + align:start position:0% +playground the lump circuit playground + + + align:start position:0% +playground the lump circuit playground +and the subset of that is the linear + + align:start position:0% +and the subset of that is the linear + + + align:start position:0% +and the subset of that is the linear +domain we can analyze many we can + + align:start position:0% +domain we can analyze many we can + + + align:start position:0% +domain we can analyze many we can +analyze linear circuits in this way and + + align:start position:0% +analyze linear circuits in this way and + + + align:start position:0% +analyze linear circuits in this way and +digital circuits for a given set of + + align:start position:0% +digital circuits for a given set of + + + align:start position:0% +digital circuits for a given set of +switch settings also fall within this + + align:start position:0% +switch settings also fall within this + + + align:start position:0% +switch settings also fall within this +category so notice that uh you can go + + align:start position:0% +category so notice that uh you can go + + + align:start position:0% +category so notice that uh you can go +ahead and analyze the digital circuits + + align:start position:0% +ahead and analyze the digital circuits + + + align:start position:0% +ahead and analyze the digital circuits +using superposition or you know other U + + align:start position:0% +using superposition or you know other U + + + align:start position:0% +using superposition or you know other U +other techniques like that so the next + + align:start position:0% +other techniques like that so the next + + + align:start position:0% +other techniques like that so the next +big step for us is to begin our analysis + + align:start position:0% +big step for us is to begin our analysis + + + align:start position:0% +big step for us is to begin our analysis +of nonlinear circuits today + + align:start position:0% + + + + align:start position:0% + +the important thing to remember is that + + align:start position:0% +the important thing to remember is that + + + align:start position:0% +the important thing to remember is that +nonlinear circuits are also within this + + align:start position:0% +nonlinear circuits are also within this + + + align:start position:0% +nonlinear circuits are also within this +big playground in which we have assumed + + align:start position:0% +big playground in which we have assumed + + + align:start position:0% +big playground in which we have assumed +the uh in which we are going under the + + align:start position:0% +the uh in which we are going under the + + + align:start position:0% +the uh in which we are going under the +lump matter discipline okay so nonlinear + + align:start position:0% +lump matter discipline okay so nonlinear + + + align:start position:0% +lump matter discipline okay so nonlinear +circuits are also lump circuits and + + align:start position:0% +circuits are also lump circuits and + + + align:start position:0% +circuits are also lump circuits and +therefore because we are in that + + align:start position:0% +therefore because we are in that + + + align:start position:0% +therefore because we are in that +playground we can use any one of our + + align:start position:0% +playground we can use any one of our + + + align:start position:0% +playground we can use any one of our +techniques kvl KCl or the node method to + + align:start position:0% +techniques kvl KCl or the node method to + + + align:start position:0% +techniques kvl KCl or the node method to +analyze a nonlinear circuits so if you + + align:start position:0% +analyze a nonlinear circuits so if you + + + align:start position:0% +analyze a nonlinear circuits so if you +see a nonlinear circuit don't get + + align:start position:0% +see a nonlinear circuit don't get + + + align:start position:0% +see a nonlinear circuit don't get +daunted say just remember you know this + + align:start position:0% +daunted say just remember you know this + + + align:start position:0% +daunted say just remember you know this +is meant to be simple stuff so let's let + + align:start position:0% +is meant to be simple stuff so let's let + + + align:start position:0% +is meant to be simple stuff so let's let +me simply write down the node equation + + align:start position:0% +me simply write down the node equation + + + align:start position:0% +me simply write down the node equation +and analyze it okay there's nothing + + align:start position:0% +and analyze it okay there's nothing + + + align:start position:0% +and analyze it okay there's nothing +there's really nothing new in today's + + align:start position:0% +there's really nothing new in today's + + + align:start position:0% +there's really nothing new in today's +lecture I'm just going to show you a + + align:start position:0% +lecture I'm just going to show you a + + + align:start position:0% +lecture I'm just going to show you a +nonlinear circuit and analyzing using + + align:start position:0% +nonlinear circuit and analyzing using + + + align:start position:0% +nonlinear circuit and analyzing using +techniques that uh you already + + align:start position:0% +techniques that uh you already + + + align:start position:0% +techniques that uh you already +know so + + align:start position:0% + + + + align:start position:0% + +today uh nonlinear + + align:start position:0% +today uh nonlinear + + + align:start position:0% +today uh nonlinear +circuits and we look at several methods + + align:start position:0% +circuits and we look at several methods + + + align:start position:0% +circuits and we look at several methods +of analyzing nonlinear circuits we look + + align:start position:0% +of analyzing nonlinear circuits we look + + + align:start position:0% +of analyzing nonlinear circuits we look +at + + align:start position:0% + + + + align:start position:0% + +the analytic + + align:start position:0% +the analytic + + + align:start position:0% +the analytic +method we look at a graphical + + align:start position:0% + + + + align:start position:0% + +method you will look at a piece-wise + + align:start position:0% +method you will look at a piece-wise + + + align:start position:0% +method you will look at a piece-wise +linear method in the uh in the + + align:start position:0% + + + + align:start position:0% + +book I won't be covering this in lecture + + align:start position:0% +book I won't be covering this in lecture + + + align:start position:0% +book I won't be covering this in lecture +you can read the section 4.4 for the + + align:start position:0% +you can read the section 4.4 for the + + + align:start position:0% +you can read the section 4.4 for the +piecewise linear method uh in this + + align:start position:0% +piecewise linear method uh in this + + + align:start position:0% +piecewise linear method uh in this +method uh you take uh you take your + + align:start position:0% +method uh you take uh you take your + + + align:start position:0% +method uh you take uh you take your +curves and you approximate them with a + + align:start position:0% +curves and you approximate them with a + + + align:start position:0% +curves and you approximate them with a +bunch of straight line segments um you + + align:start position:0% +bunch of straight line segments um you + + + align:start position:0% +bunch of straight line segments um you +know kind of uh like uh the v outv in + + align:start position:0% +know kind of uh like uh the v outv in + + + align:start position:0% +know kind of uh like uh the v outv in +curve I've shown you there and analyze + + align:start position:0% +curve I've shown you there and analyze + + + align:start position:0% +curve I've shown you there and analyze +the circuit using linear techniques + + align:start position:0% +the circuit using linear techniques + + + align:start position:0% +the circuit using linear techniques +within any given straight line segment + + align:start position:0% +within any given straight line segment + + + align:start position:0% +within any given straight line segment +okay um we'll also do incremental + + align:start position:0% + + + + align:start position:0% + +analysis this is also called small + + align:start position:0% +analysis this is also called small + + + align:start position:0% +analysis this is also called small +signal + + align:start position:0% + + + + align:start position:0% + +analysis okay so we'll cover these two + + align:start position:0% +analysis okay so we'll cover these two + + + align:start position:0% +analysis okay so we'll cover these two +today I will in introduce this one today + + align:start position:0% +today I will in introduce this one today + + + align:start position:0% +today I will in introduce this one today +and wrap that up uh on during the next + + align:start position:0% + + + + align:start position:0% + +lecture okay so let's uh let's start + + align:start position:0% +lecture okay so let's uh let's start + + + align:start position:0% +lecture okay so let's uh let's start +with a simple example + + align:start position:0% + + + + align:start position:0% + +okay so I have some voltage uh V it's + + align:start position:0% +okay so I have some voltage uh V it's + + + align:start position:0% +okay so I have some voltage uh V it's +some voltage source + + align:start position:0% +some voltage source + + + align:start position:0% +some voltage source +V and I have some resistor R and I have + + align:start position:0% +V and I have some resistor R and I have + + + align:start position:0% +V and I have some resistor R and I have +a fictitious device here that I that I + + align:start position:0% +a fictitious device here that I that I + + + align:start position:0% +a fictitious device here that I that I +labeled the okay let's call this + + align:start position:0% +labeled the okay let's call this + + + align:start position:0% +labeled the okay let's call this +fictitious device the Expo + + align:start position:0% + + + + align:start position:0% + +DB okay perfectly chosen a funky name + + align:start position:0% +DB okay perfectly chosen a funky name + + + align:start position:0% +DB okay perfectly chosen a funky name +because this is a fictitious device okay + + align:start position:0% +because this is a fictitious device okay + + + align:start position:0% +because this is a fictitious device okay +let's call it the export dweb and uh let + + align:start position:0% +let's call it the export dweb and uh let + + + align:start position:0% +let's call it the export dweb and uh let +me write down the associated variables + + align:start position:0% +me write down the associated variables + + + align:start position:0% +me write down the associated variables +for this device as + + align:start position:0% +for this device as + + + align:start position:0% +for this device as +follows ID is the current flowing uh + + align:start position:0% +follows ID is the current flowing uh + + + align:start position:0% +follows ID is the current flowing uh +into this terminal and VD is the voltage + + align:start position:0% +into this terminal and VD is the voltage + + + align:start position:0% +into this terminal and VD is the voltage +across uh this device so this is a + + align:start position:0% +across uh this device so this is a + + + align:start position:0% +across uh this device so this is a +nonlinear device and uh + + align:start position:0% + + + + align:start position:0% + +and uh this device is characterized by + + align:start position:0% +and uh this device is characterized by + + + align:start position:0% +and uh this device is characterized by +the following + + align:start position:0% +the following + + + align:start position:0% +the following +equation much like resistors were + + align:start position:0% +equation much like resistors were + + + align:start position:0% +equation much like resistors were +characterized by a IV relation V is + + align:start position:0% +characterized by a IV relation V is + + + align:start position:0% +characterized by a IV relation V is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +iir or I is equal to uh V / by R uh this + + align:start position:0% +iir or I is equal to uh V / by R uh this + + + align:start position:0% +iir or I is equal to uh V / by R uh this +device is also characterized by the + + align:start position:0% +device is also characterized by the + + + align:start position:0% +device is also characterized by the +following element relationship it's a e + + align:start position:0% +following element relationship it's a e + + + align:start position:0% +following element relationship it's a e +ra to + + align:start position:0% + + + + align:start position:0% + +B okay so there the exponentiation here + + align:start position:0% +B okay so there the exponentiation here + + + align:start position:0% +B okay so there the exponentiation here +and again remember this a fictitious + + align:start position:0% +and again remember this a fictitious + + + align:start position:0% +and again remember this a fictitious +device and I'll show you some funky + + align:start position:0% +device and I'll show you some funky + + + align:start position:0% +device and I'll show you some funky +things that it does in a second so um + + align:start position:0% +things that it does in a second so um + + + align:start position:0% +things that it does in a second so um +it's a very simple relation the + + align:start position:0% +it's a very simple relation the + + + align:start position:0% +it's a very simple relation the +exponential relation where the current + + align:start position:0% +exponential relation where the current + + + align:start position:0% +exponential relation where the current +relates to the uh exponentiated value of + + align:start position:0% +relates to the uh exponentiated value of + + + align:start position:0% +relates to the uh exponentiated value of +the voltage VD across the uh element so + + align:start position:0% +the voltage VD across the uh element so + + + align:start position:0% +the voltage VD across the uh element so +I can + + align:start position:0% + + + + align:start position:0% + +plot ID versus ID versus VD for this uh + + align:start position:0% +plot ID versus ID versus VD for this uh + + + align:start position:0% +plot ID versus ID versus VD for this uh +element as follows uh notice that uh + + align:start position:0% +element as follows uh notice that uh + + + align:start position:0% +element as follows uh notice that uh +when VD is zero ID is + + align:start position:0% +when VD is zero ID is + + + align:start position:0% +when VD is zero ID is +a so I have a here and it looks like + + align:start position:0% +a so I have a here and it looks like + + + align:start position:0% +a so I have a here and it looks like +looks like + + align:start position:0% +looks like + + + align:start position:0% +looks like +this okay it's a funny device a + + align:start position:0% +this okay it's a funny device a + + + align:start position:0% +this okay it's a funny device a +fictitious device so when VD is zero um + + align:start position:0% +fictitious device so when VD is zero um + + + align:start position:0% +fictitious device so when VD is zero um +I have some current flowing through the + + align:start position:0% +I have some current flowing through the + + + align:start position:0% +I have some current flowing through the +device and as VD increases I get an + + align:start position:0% +device and as VD increases I get an + + + align:start position:0% +device and as VD increases I get an +exponential increase in the current + + align:start position:0% +exponential increase in the current + + + align:start position:0% +exponential increase in the current +through that uh + + align:start position:0% +through that uh + + + align:start position:0% +through that uh +device um this device is funny in the + + align:start position:0% +device um this device is funny in the + + + align:start position:0% +device um this device is funny in the +sense that it is not a passive device in + + align:start position:0% +sense that it is not a passive device in + + + align:start position:0% +sense that it is not a passive device in +that notice that when VD and ID are + + align:start position:0% +that notice that when VD and ID are + + + align:start position:0% +that notice that when VD and ID are +positive the product is positive which + + align:start position:0% +positive the product is positive which + + + align:start position:0% +positive the product is positive which +is fine which says that uh it is + + align:start position:0% +is fine which says that uh it is + + + align:start position:0% +is fine which says that uh it is +consuming power on the other hand on the + + align:start position:0% +consuming power on the other hand on the + + + align:start position:0% +consuming power on the other hand on the +left hand side notice that the vi + + align:start position:0% +left hand side notice that the vi + + + align:start position:0% +left hand side notice that the vi +relation is negative which means that + + align:start position:0% +relation is negative which means that + + + align:start position:0% +relation is negative which means that +when I put a negative voltage on it it + + align:start position:0% +when I put a negative voltage on it it + + + align:start position:0% +when I put a negative voltage on it it +can still sustain a positive current + + align:start position:0% +can still sustain a positive current + + + align:start position:0% +can still sustain a positive current +this must imply that the device is + + align:start position:0% +this must imply that the device is + + + align:start position:0% +this must imply that the device is +producing power okay but for the purpose + + align:start position:0% +producing power okay but for the purpose + + + align:start position:0% +producing power okay but for the purpose +of a nonlinear analysis uh we we don't + + align:start position:0% +of a nonlinear analysis uh we we don't + + + align:start position:0% +of a nonlinear analysis uh we we don't +have to worry about that let's just do + + align:start position:0% +have to worry about that let's just do + + + align:start position:0% +have to worry about that let's just do +it uh mathematically and find out what + + align:start position:0% +it uh mathematically and find out what + + + align:start position:0% +it uh mathematically and find out what +it looks + + align:start position:0% +it looks + + + align:start position:0% +it looks +like so uh back to this again a voltage + + align:start position:0% +like so uh back to this again a voltage + + + align:start position:0% +like so uh back to this again a voltage +source resistor and my export dwee + + align:start position:0% +source resistor and my export dwee + + + align:start position:0% +source resistor and my export dwee +connected in that manner now again + + align:start position:0% +connected in that manner now again + + + align:start position:0% +connected in that manner now again +reflect on this pattern a voltage source + + align:start position:0% +reflect on this pattern a voltage source + + + align:start position:0% +reflect on this pattern a voltage source +or a current Source uh uh a resistor and + + align:start position:0% +or a current Source uh uh a resistor and + + + align:start position:0% +or a current Source uh uh a resistor and +some device this is a very standard + + align:start position:0% +some device this is a very standard + + + align:start position:0% +some device this is a very standard +pattern you will see again and again and + + align:start position:0% +pattern you will see again and again and + + + align:start position:0% +pattern you will see again and again and +again in particular if you look at this + + align:start position:0% +again in particular if you look at this + + + align:start position:0% +again in particular if you look at this +device the nonlinear device here and + + align:start position:0% +device the nonlinear device here and + + + align:start position:0% +device the nonlinear device here and +facing the nonlinear device is a voltage + + align:start position:0% +facing the nonlinear device is a voltage + + + align:start position:0% +facing the nonlinear device is a voltage +source in series with a resistor now the + + align:start position:0% +source in series with a resistor now the + + + align:start position:0% +source in series with a resistor now the +reason I said that this is an incredibly + + align:start position:0% +reason I said that this is an incredibly + + + align:start position:0% +reason I said that this is an incredibly +important + + align:start position:0% +important + + + align:start position:0% +important +parent is the + + align:start position:0% +parent is the + + + align:start position:0% +parent is the +following notice that + + align:start position:0% + + + + align:start position:0% + +suppose notice that if on the left hand + + align:start position:0% +suppose notice that if on the left hand + + + align:start position:0% +suppose notice that if on the left hand +side I had any linear circuit okay and I + + align:start position:0% +side I had any linear circuit okay and I + + + align:start position:0% +side I had any linear circuit okay and I +had a single nonlinear element in that + + align:start position:0% +had a single nonlinear element in that + + + align:start position:0% +had a single nonlinear element in that +circuit notice that by a tent reduction + + align:start position:0% +circuit notice that by a tent reduction + + + align:start position:0% +circuit notice that by a tent reduction +that you've learned you can take this + + align:start position:0% +that you've learned you can take this + + + align:start position:0% +that you've learned you can take this +entire mess + + align:start position:0% +entire mess + + + align:start position:0% +entire mess +if all you care about is the behavior of + + align:start position:0% +if all you care about is the behavior of + + + align:start position:0% +if all you care about is the behavior of +the nonlinear device for the purpose of + + align:start position:0% +the nonlinear device for the purpose of + + + align:start position:0% +the nonlinear device for the purpose of +analyzing this nonlinear device you can + + align:start position:0% +analyzing this nonlinear device you can + + + align:start position:0% +analyzing this nonlinear device you can +take this entire linear circuit okay no + + align:start position:0% +take this entire linear circuit okay no + + + align:start position:0% +take this entire linear circuit okay no +matter how complicated it is you know + + align:start position:0% +matter how complicated it is you know + + + align:start position:0% +matter how complicated it is you know +voltage sources current sources + + align:start position:0% +voltage sources current sources + + + align:start position:0% +voltage sources current sources +resistors and a bunch of other funky + + align:start position:0% +resistors and a bunch of other funky + + + align:start position:0% +resistors and a bunch of other funky +stuff you can boil all of that down to a + + align:start position:0% +stuff you can boil all of that down to a + + + align:start position:0% +stuff you can boil all of that down to a +t equivalent a voltage and a resistor in + + align:start position:0% +t equivalent a voltage and a resistor in + + + align:start position:0% +t equivalent a voltage and a resistor in +series okay so so so we can trick you + + align:start position:0% +series okay so so so we can trick you + + + align:start position:0% +series okay so so so we can trick you +okay we can give you a complicated + + align:start position:0% +okay we can give you a complicated + + + align:start position:0% +okay we can give you a complicated +circuit and say aha tell me what the + + align:start position:0% +circuit and say aha tell me what the + + + align:start position:0% +circuit and say aha tell me what the +current is through this device if I + + align:start position:0% +current is through this device if I + + + align:start position:0% +current is through this device if I +apply you know some voltage three volts + + align:start position:0% +apply you know some voltage three volts + + + align:start position:0% +apply you know some voltage three volts +there what you can do is you can say aha + + align:start position:0% +there what you can do is you can say aha + + + align:start position:0% +there what you can do is you can say aha +I don't care about what happens here so + + align:start position:0% +I don't care about what happens here so + + + align:start position:0% +I don't care about what happens here so +I'm just going to replace the whole + + align:start position:0% +I'm just going to replace the whole + + + align:start position:0% +I'm just going to replace the whole +thing with the tein equivalent okay and + + align:start position:0% +thing with the tein equivalent okay and + + + align:start position:0% +thing with the tein equivalent okay and +you've done a homework now and you can + + align:start position:0% +you've done a homework now and you can + + + align:start position:0% +you've done a homework now and you can +calculate thin equivalent for circuits + + align:start position:0% +calculate thin equivalent for circuits + + + align:start position:0% +calculate thin equivalent for circuits +and simply replace this and then go + + align:start position:0% +and simply replace this and then go + + + align:start position:0% +and simply replace this and then go +ahead and solve the circuit again + + align:start position:0% +ahead and solve the circuit again + + + align:start position:0% +ahead and solve the circuit again +remember uh we are Engineers okay we are + + align:start position:0% +remember uh we are Engineers okay we are + + + align:start position:0% +remember uh we are Engineers okay we are +we are looking for answers we are + + align:start position:0% +we are looking for answers we are + + + align:start position:0% +we are looking for answers we are +looking to build interesting systems + + align:start position:0% +looking to build interesting systems + + + align:start position:0% +looking to build interesting systems +okay and in general we like to take the + + align:start position:0% +okay and in general we like to take the + + + align:start position:0% +okay and in general we like to take the +simplest path possible to the solution + + align:start position:0% +simplest path possible to the solution + + + align:start position:0% +simplest path possible to the solution +okay so simplify your lives and create a + + align:start position:0% +okay so simplify your lives and create a + + + align:start position:0% +okay so simplify your lives and create a +simple ton coupled to a nonlinear device + + align:start position:0% +simple ton coupled to a nonlinear device + + + align:start position:0% +simple ton coupled to a nonlinear device +and then you will be uh you will be + + align:start position:0% +and then you will be uh you will be + + + align:start position:0% +and then you will be uh you will be +rolling so when we talk about a variety + + align:start position:0% +rolling so when we talk about a variety + + + align:start position:0% +rolling so when we talk about a variety +of other circuits okay nonlinear + + align:start position:0% +of other circuits okay nonlinear + + + align:start position:0% +of other circuits okay nonlinear +circuits time varing circuits and so on + + align:start position:0% +circuits time varing circuits and so on + + + align:start position:0% +circuits time varing circuits and so on +in the rest of this course we will look + + align:start position:0% +in the rest of this course we will look + + + align:start position:0% +in the rest of this course we will look +at this pattern again and again and + + align:start position:0% +at this pattern again and again and + + + align:start position:0% +at this pattern again and again and +again and again to be blue in the + + align:start position:0% +again and again to be blue in the + + + align:start position:0% +again and again to be blue in the +face and just remember the reason we + + align:start position:0% +face and just remember the reason we + + + align:start position:0% +face and just remember the reason we +keep looking at this pattern is that + + align:start position:0% +keep looking at this pattern is that + + + align:start position:0% +keep looking at this pattern is that +whenever you have + + align:start position:0% + + + + align:start position:0% + +some big linear Mass okay connected + + align:start position:0% + + + + align:start position:0% + +to some interesting + + align:start position:0% +to some interesting + + + align:start position:0% +to some interesting +device okay what you can do is if all + + align:start position:0% +device okay what you can do is if all + + + align:start position:0% +device okay what you can do is if all +you care about is analyzing the behavior + + align:start position:0% +you care about is analyzing the behavior + + + align:start position:0% +you care about is analyzing the behavior +of that device you can take this linear + + align:start position:0% +of that device you can take this linear + + + align:start position:0% +of that device you can take this linear +mass and simply figure + + align:start position:0% +mass and simply figure + + + align:start position:0% +mass and simply figure +out the T + + align:start position:0% +out the T + + + align:start position:0% +out the T +equivalent or the N equivalent if you + + align:start position:0% +equivalent or the N equivalent if you + + + align:start position:0% +equivalent or the N equivalent if you +like and replace this whole thing with + + align:start position:0% +like and replace this whole thing with + + + align:start position:0% +like and replace this whole thing with +its equivalent and then go ahead and + + align:start position:0% +its equivalent and then go ahead and + + + align:start position:0% +its equivalent and then go ahead and +analyze it okay so boil boil a + + align:start position:0% +analyze it okay so boil boil a + + + align:start position:0% +analyze it okay so boil boil a +arbitrarily complicated circuit down to + + align:start position:0% +arbitrarily complicated circuit down to + + + align:start position:0% +arbitrarily complicated circuit down to +a very simple pattern of the + + align:start position:0% +a very simple pattern of the + + + align:start position:0% +a very simple pattern of the +sort okay what this means is because of + + align:start position:0% +sort okay what this means is because of + + + align:start position:0% +sort okay what this means is because of +this brilliant tant + + align:start position:0% +this brilliant tant + + + align:start position:0% +this brilliant tant +simplification going forward through the + + align:start position:0% +simplification going forward through the + + + align:start position:0% +simplification going forward through the +rest of this course we mostly deal with + + align:start position:0% +rest of this course we mostly deal with + + + align:start position:0% +rest of this course we mostly deal with +very simple circuits like this voltage + + align:start position:0% +very simple circuits like this voltage + + + align:start position:0% +very simple circuits like this voltage +source resistor and the device that's + + align:start position:0% +source resistor and the device that's + + + align:start position:0% +source resistor and the device that's +it very very very very rarely will you + + align:start position:0% +it very very very very rarely will you + + + align:start position:0% +it very very very very rarely will you +see multiple sources uh you know and + + align:start position:0% +see multiple sources uh you know and + + + align:start position:0% +see multiple sources uh you know and +lots of resistors in a circuit usually + + align:start position:0% +lots of resistors in a circuit usually + + + align:start position:0% +lots of resistors in a circuit usually +going to be simple stuff and and + + align:start position:0% +going to be simple stuff and and + + + align:start position:0% +going to be simple stuff and and +remember how we got here okay by making + + align:start position:0% +remember how we got here okay by making + + + align:start position:0% +remember how we got here okay by making +a tant simplification of a linear Mass + + align:start position:0% +a tant simplification of a linear Mass + + + align:start position:0% +a tant simplification of a linear Mass +all + + align:start position:0% +all + + + align:start position:0% +all +right so U so if in homeworks or quizzes + + align:start position:0% +right so U so if in homeworks or quizzes + + + align:start position:0% +right so U so if in homeworks or quizzes +or in real life if you find that or in + + align:start position:0% +or in real life if you find that or in + + + align:start position:0% +or in real life if you find that or in +many examples of real life if you find + + align:start position:0% +many examples of real life if you find + + + align:start position:0% +many examples of real life if you find +that you have to deal with a lot of + + align:start position:0% +that you have to deal with a lot of + + + align:start position:0% +that you have to deal with a lot of +grunge and a lot of mess uh step back + + align:start position:0% +grunge and a lot of mess uh step back + + + align:start position:0% +grunge and a lot of mess uh step back +and think a little bit okay try to use + + align:start position:0% +and think a little bit okay try to use + + + align:start position:0% +and think a little bit okay try to use +intuition and see if you can simplify + + align:start position:0% +intuition and see if you can simplify + + + align:start position:0% +intuition and see if you can simplify +things using some clever trick or uh uh + + align:start position:0% +things using some clever trick or uh uh + + + align:start position:0% +things using some clever trick or uh uh +method + + align:start position:0% + + + + align:start position:0% + +okay method one of analysis so let's go + + align:start position:0% +okay method one of analysis so let's go + + + align:start position:0% +okay method one of analysis so let's go +ahead and analyze this uh pattern here + + align:start position:0% +ahead and analyze this uh pattern here + + + align:start position:0% +ahead and analyze this uh pattern here +this template circuit if you will a + + align:start position:0% +this template circuit if you will a + + + align:start position:0% +this template circuit if you will a +voltage source resistor and a nonlinear + + align:start position:0% +voltage source resistor and a nonlinear + + + align:start position:0% +voltage source resistor and a nonlinear +device so + + align:start position:0% +device so + + + align:start position:0% +device so +uh this is the uh analytical + + align:start position:0% + + + + align:start position:0% + +method and uh remember the node the node + + align:start position:0% +method and uh remember the node the node + + + align:start position:0% +method and uh remember the node the node +equation the node method applies so let + + align:start position:0% +equation the node method applies so let + + + align:start position:0% +equation the node method applies so let +me go ahead and apply the uh node method + + align:start position:0% +me go ahead and apply the uh node method + + + align:start position:0% +me go ahead and apply the uh node method +so to apply the node method what do I do + + align:start position:0% +so to apply the node method what do I do + + + align:start position:0% +so to apply the node method what do I do +I first have to select a ground node + + align:start position:0% +I first have to select a ground node + + + align:start position:0% +I first have to select a ground node +okay let me select this as my ground + + align:start position:0% +okay let me select this as my ground + + + align:start position:0% +okay let me select this as my ground +node let me label all the nodes with + + align:start position:0% +node let me label all the nodes with + + + align:start position:0% +node let me label all the nodes with +their voltages so this node has voltage + + align:start position:0% +their voltages so this node has voltage + + + align:start position:0% +their voltages so this node has voltage +V and this node has uh a label V capital + + align:start position:0% +V and this node has uh a label V capital + + + align:start position:0% +V and this node has uh a label V capital +D okay so let me go ahead and analyze + + align:start position:0% +D okay so let me go ahead and analyze + + + align:start position:0% +D okay so let me go ahead and analyze +this using the node method so node + + align:start position:0% +this using the node method so node + + + align:start position:0% +this using the node method so node +method says for each of the nodes in the + + align:start position:0% +method says for each of the nodes in the + + + align:start position:0% +method says for each of the nodes in the +circuit whose voltage is not known go + + align:start position:0% +circuit whose voltage is not known go + + + align:start position:0% +circuit whose voltage is not known go +ahead and write down + + align:start position:0% +ahead and write down + + + align:start position:0% +ahead and write down +KCl implicitly applying the element + + align:start position:0% +KCl implicitly applying the element + + + align:start position:0% +KCl implicitly applying the element +relationships to replace the current + + align:start position:0% +relationships to replace the current + + + align:start position:0% +relationships to replace the current +values with the voltage values okay so + + align:start position:0% +values with the voltage values okay so + + + align:start position:0% +values with the voltage values okay so +let's start with the the current going + + align:start position:0% +let's start with the the current going + + + align:start position:0% +let's start with the the current going +in that direction current going uh from + + align:start position:0% +in that direction current going uh from + + + align:start position:0% +in that direction current going uh from +the VD node through resistor R looks as + + align:start position:0% +the VD node through resistor R looks as + + + align:start position:0% +the VD node through resistor R looks as +follows is VD minus V divided by R + + align:start position:0% +follows is VD minus V divided by R + + + align:start position:0% +follows is VD minus V divided by R +that's the current going data wayase and + + align:start position:0% +that's the current going data wayase and + + + align:start position:0% +that's the current going data wayase and +the current going down is + + align:start position:0% +the current going down is + + + align:start position:0% +the current going down is +ID okay in general when I apply the node + + align:start position:0% +ID okay in general when I apply the node + + + align:start position:0% +ID okay in general when I apply the node +method I don't write ID here but I go + + align:start position:0% +method I don't write ID here but I go + + + align:start position:0% +method I don't write ID here but I go +ahead and write + + align:start position:0% +ahead and write + + + align:start position:0% +ahead and write +the element relation a is the BVD here + + align:start position:0% +the element relation a is the BVD here + + + align:start position:0% +the element relation a is the BVD here +okay I have an then I get an equation in + + align:start position:0% +okay I have an then I get an equation in + + + align:start position:0% +okay I have an then I get an equation in +VD and I just solve for it solve for the + + align:start position:0% +VD and I just solve for it solve for the + + + align:start position:0% +VD and I just solve for it solve for the +node voltage however um just to make a + + align:start position:0% +node voltage however um just to make a + + + align:start position:0% +node voltage however um just to make a +couple of extra points later let me go + + align:start position:0% +couple of extra points later let me go + + + align:start position:0% +couple of extra points later let me go +ahead and do that in two steps uh write + + align:start position:0% +ahead and do that in two steps uh write + + + align:start position:0% +ahead and do that in two steps uh write +down uh this and then go ahead and write + + align:start position:0% +down uh this and then go ahead and write + + + align:start position:0% +down uh this and then go ahead and write +down ID separately as a e to the b v + + align:start position:0% + + + + align:start position:0% + +d again remember uh don't get confused + + align:start position:0% +d again remember uh don't get confused + + + align:start position:0% +d again remember uh don't get confused +here in the node method I don't write + + align:start position:0% +here in the node method I don't write + + + align:start position:0% +here in the node method I don't write +down a second step I directly write down + + align:start position:0% +down a second step I directly write down + + + align:start position:0% +down a second step I directly write down +a e to the BVD in place of ID I get one + + align:start position:0% +a e to the BVD in place of ID I get one + + + align:start position:0% +a e to the BVD in place of ID I get one +equation in VD I go solve it um just for + + align:start position:0% +equation in VD I go solve it um just for + + + align:start position:0% +equation in VD I go solve it um just for +fun today I'm writing taking two steps + + align:start position:0% +fun today I'm writing taking two steps + + + align:start position:0% +fun today I'm writing taking two steps +here writing ID here and explicitly + + align:start position:0% +here writing ID here and explicitly + + + align:start position:0% +here writing ID here and explicitly +putting down ID as a e to the BBD okay + + align:start position:0% +putting down ID as a e to the BBD okay + + + align:start position:0% +putting down ID as a e to the BBD okay +now that's it Ian this is all there is + + align:start position:0% +now that's it Ian this is all there is + + + align:start position:0% +now that's it Ian this is all there is +to it okay you guys can now go ahead and + + align:start position:0% +to it okay you guys can now go ahead and + + + align:start position:0% +to it okay you guys can now go ahead and +analyze nonlinear circuits okay you get + + align:start position:0% +analyze nonlinear circuits okay you get + + + align:start position:0% +analyze nonlinear circuits okay you get +a bunch of equations a bunch of unknowns + + align:start position:0% +a bunch of equations a bunch of unknowns + + + align:start position:0% +a bunch of equations a bunch of unknowns +you know go solve + + align:start position:0% +you know go solve + + + align:start position:0% +you know go solve +I have two equations here VD and ID are + + align:start position:0% +I have two equations here VD and ID are + + + align:start position:0% +I have two equations here VD and ID are +my unknowns and I can just go ahead and + + align:start position:0% +my unknowns and I can just go ahead and + + + align:start position:0% +my unknowns and I can just go ahead and +uh solve for + + align:start position:0% +uh solve for + + + align:start position:0% +uh solve for +them now in + + align:start position:0% +them now in + + + align:start position:0% +them now in +general with nonlinear circuits often + + align:start position:0% +general with nonlinear circuits often + + + align:start position:0% +general with nonlinear circuits often +times it's hard to get a close form + + align:start position:0% +times it's hard to get a close form + + + align:start position:0% +times it's hard to get a close form +solution okay so uh you may have to use + + align:start position:0% +solution okay so uh you may have to use + + + align:start position:0% +solution okay so uh you may have to use +a bunch of methods you can try a close + + align:start position:0% +a bunch of methods you can try a close + + + align:start position:0% +a bunch of methods you can try a close +form solution or you can try numerical + + align:start position:0% +form solution or you can try numerical + + + align:start position:0% +form solution or you can try numerical +Solutions okay or you can do trial and + + align:start position:0% +Solutions okay or you can do trial and + + + align:start position:0% +Solutions okay or you can do trial and +error okay in this case I'll just go + + align:start position:0% +error okay in this case I'll just go + + + align:start position:0% +error okay in this case I'll just go +ahead and tell you suppose I choose V is + + align:start position:0% +ahead and tell you suppose I choose V is + + + align:start position:0% +ahead and tell you suppose I choose V is +uh uh one volt + + align:start position:0% +uh uh one volt + + + align:start position:0% +uh uh one volt +R is 1 + + align:start position:0% +R is 1 + + + align:start position:0% +R is 1 +ohm and B is uh + + align:start position:0% +ohm and B is uh + + + align:start position:0% +ohm and B is uh +one uh 1 over volt and a is + + align:start position:0% +one uh 1 over volt and a is + + + align:start position:0% +one uh 1 over volt and a is +1/4 amps for those values um + + align:start position:0% +1/4 amps for those values um + + + align:start position:0% +1/4 amps for those values um +approximately VD is roughly .5 volts and + + align:start position:0% +approximately VD is roughly .5 volts and + + + align:start position:0% +approximately VD is roughly .5 volts and +ID is + + align:start position:0% +ID is + + + align:start position:0% +ID is +roughly .4 volts okay you can do this + + align:start position:0% +roughly .4 volts okay you can do this + + + align:start position:0% +roughly .4 volts okay you can do this +you know using trial and error or other + + align:start position:0% +you know using trial and error or other + + + align:start position:0% +you know using trial and error or other +other methods um in 62 we don't dwell on + + align:start position:0% +other methods um in 62 we don't dwell on + + + align:start position:0% +other methods um in 62 we don't dwell on +having uh working too hard to solve + + align:start position:0% +having uh working too hard to solve + + + align:start position:0% +having uh working too hard to solve +equations of this sort if you cannot + + align:start position:0% +equations of this sort if you cannot + + + align:start position:0% +equations of this sort if you cannot +substitute this in here and solve it + + align:start position:0% +substitute this in here and solve it + + + align:start position:0% +substitute this in here and solve it +directly uh we don't ask you to go and + + align:start position:0% +directly uh we don't ask you to go and + + + align:start position:0% +directly uh we don't ask you to go and +learn numerical method techniques and so + + align:start position:0% +learn numerical method techniques and so + + + align:start position:0% +learn numerical method techniques and so +on to solve it but just remember that uh + + align:start position:0% +on to solve it but just remember that uh + + + align:start position:0% +on to solve it but just remember that uh +you can use trial and error or you know + + align:start position:0% +you can use trial and error or you know + + + align:start position:0% +you can use trial and error or you know +you can use back substitution and other + + align:start position:0% +you can use back substitution and other + + + align:start position:0% +you can use back substitution and other +techniques that you'll learn in future + + align:start position:0% +techniques that you'll learn in future + + + align:start position:0% +techniques that you'll learn in future +uh numerical methods classes uh and + + align:start position:0% +uh numerical methods classes uh and + + + align:start position:0% +uh numerical methods classes uh and +apply them here but suffice it to say + + align:start position:0% +apply them here but suffice it to say + + + align:start position:0% +apply them here but suffice it to say +that you know for here well we can stick + + align:start position:0% +that you know for here well we can stick + + + align:start position:0% +that you know for here well we can stick +with trial and error if you like and uh + + align:start position:0% +with trial and error if you like and uh + + + align:start position:0% +with trial and error if you like and uh +for these values VD and ID are 0.5 and + + align:start position:0% +for these values VD and ID are 0.5 and + + + align:start position:0% +for these values VD and ID are 0.5 and +uh approximately point4 you're done it's + + align:start position:0% +uh approximately point4 you're done it's + + + align:start position:0% +uh approximately point4 you're done it's +it's really that simple + + align:start position:0% +it's really that simple + + + align:start position:0% +it's really that simple +yes oh I'm sorry I'm sorry good + + align:start position:0% + + + + align:start position:0% + +catch I know at least one person ain't + + align:start position:0% +catch I know at least one person ain't + + + align:start position:0% +catch I know at least one person ain't +sleeping here okay good so + + align:start position:0% + + + + align:start position:0% + +um so so as I said there's not a whole + + align:start position:0% +um so so as I said there's not a whole + + + align:start position:0% +um so so as I said there's not a whole +lot to it you know whether it's a non + + align:start position:0% +lot to it you know whether it's a non + + + align:start position:0% +lot to it you know whether it's a non +linear circuit or a linear circuit and + + align:start position:0% +linear circuit or a linear circuit and + + + align:start position:0% +linear circuit or a linear circuit and +as long as I am inside this playground + + align:start position:0% +as long as I am inside this playground + + + align:start position:0% +as long as I am inside this playground +here where the lump circuit abstraction + + align:start position:0% +here where the lump circuit abstraction + + + align:start position:0% +here where the lump circuit abstraction +holds um I can apply my node equations + + align:start position:0% +holds um I can apply my node equations + + + align:start position:0% +holds um I can apply my node equations +and then go ahead and solve + + align:start position:0% + + + + align:start position:0% + +it let me show you a few more methods U + + align:start position:0% +it let me show you a few more methods U + + + align:start position:0% +it let me show you a few more methods U +so so we can uh articulate your repto of + + align:start position:0% +so so we can uh articulate your repto of + + + align:start position:0% +so so we can uh articulate your repto of +tools for non linger circuits and uh + + align:start position:0% + + + + align:start position:0% + +I'd like to show you a graphical + + align:start position:0% +I'd like to show you a graphical + + + align:start position:0% +I'd like to show you a graphical +technique um I personally rarely use a + + align:start position:0% +technique um I personally rarely use a + + + align:start position:0% +technique um I personally rarely use a +graphical technique to solve + + align:start position:0% +graphical technique to solve + + + align:start position:0% +graphical technique to solve +circuits okay then uh you know why why + + align:start position:0% +circuits okay then uh you know why why + + + align:start position:0% +circuits okay then uh you know why why +am I sharing this with you it turns out + + align:start position:0% +am I sharing this with you it turns out + + + align:start position:0% +am I sharing this with you it turns out +that uh often times by looking at things + + align:start position:0% +that uh often times by looking at things + + + align:start position:0% +that uh often times by looking at things +graphically you you you can get some + + align:start position:0% +graphically you you you can get some + + + align:start position:0% +graphically you you you can get some +better insights into circuit Behavior + + align:start position:0% +better insights into circuit Behavior + + + align:start position:0% +better insights into circuit Behavior +okay uh you can also show cool demos + + align:start position:0% +okay uh you can also show cool demos + + + align:start position:0% +okay uh you can also show cool demos +when you show graphs of circuit you know + + align:start position:0% +when you show graphs of circuit you know + + + align:start position:0% +when you show graphs of circuit you know +graphs of responses kind of playing with + + align:start position:0% +graphs of responses kind of playing with + + + align:start position:0% +graphs of responses kind of playing with +each other and so on so uh so this is + + align:start position:0% +each other and so on so uh so this is + + + align:start position:0% +each other and so on so uh so this is +fun for doing you know getting intuition + + align:start position:0% +fun for doing you know getting intuition + + + align:start position:0% +fun for doing you know getting intuition +and things like that so graphically all + + align:start position:0% +and things like that so graphically all + + + align:start position:0% +and things like that so graphically all +I'm really going to do is solve those + + align:start position:0% +I'm really going to do is solve those + + + align:start position:0% +I'm really going to do is solve those +two equations graphically um so I'm + + align:start position:0% +two equations graphically um so I'm + + + align:start position:0% +two equations graphically um so I'm +going to + + align:start position:0% +going to + + + align:start position:0% +going to +plot uh equation one uh let me rewrite + + align:start position:0% +plot uh equation one uh let me rewrite + + + align:start position:0% +plot uh equation one uh let me rewrite +equation one as follows + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +ID + + align:start position:0% + + + + align:start position:0% + +is I'm just rewriting equation one uh um + + align:start position:0% +is I'm just rewriting equation one uh um + + + align:start position:0% +is I'm just rewriting equation one uh um +as follows v v by R minus VD by IDE by r + + align:start position:0% +as follows v v by R minus VD by IDE by r + + + align:start position:0% +as follows v v by R minus VD by IDE by r +and + + align:start position:0% +and + + + align:start position:0% +and +u uh + + align:start position:0% +u uh + + + align:start position:0% +u uh +oops okay and I can also draw the second + + align:start position:0% + + + + align:start position:0% + +guy okay I can do this uh uh do this as + + align:start position:0% +guy okay I can do this uh uh do this as + + + align:start position:0% +guy okay I can do this uh uh do this as +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +well I can do it + + align:start position:0% + + + + align:start position:0% + +id id versus uh VD + + align:start position:0% +id id versus uh VD + + + align:start position:0% +id id versus uh VD +plot and in this particular situation + + align:start position:0% +plot and in this particular situation + + + align:start position:0% +plot and in this particular situation +you've seen this + + align:start position:0% + + + + align:start position:0% + +already okay that's my uh ID versus VD + + align:start position:0% +already okay that's my uh ID versus VD + + + align:start position:0% +already okay that's my uh ID versus VD +curve right there and I can do the same + + align:start position:0% +curve right there and I can do the same + + + align:start position:0% +curve right there and I can do the same +for this one here uh let me find uh so + + align:start position:0% +for this one here uh let me find uh so + + + align:start position:0% +for this one here uh let me find uh so +this this equation establishes uh the + + align:start position:0% +this this equation establishes uh the + + + align:start position:0% +this this equation establishes uh the +following straight line relationship uh + + align:start position:0% +following straight line relationship uh + + + align:start position:0% +following straight line relationship uh +it says that uh when VD is zero + + align:start position:0% +it says that uh when VD is zero + + + align:start position:0% +it says that uh when VD is zero +when VD is zero ID is V / R + + align:start position:0% +when VD is zero ID is V / R + + + align:start position:0% +when VD is zero ID is V / R +so that's here and similarly when ID is + + align:start position:0% +so that's here and similarly when ID is + + + align:start position:0% +so that's here and similarly when ID is +zero then VD is equal to V so I get + + align:start position:0% +zero then VD is equal to V so I get + + + align:start position:0% +zero then VD is equal to V so I get +something + + align:start position:0% +something + + + align:start position:0% +something +here okay so that's my straight line + + align:start position:0% +here okay so that's my straight line + + + align:start position:0% +here okay so that's my straight line +relationship uh corresponding to this + + align:start position:0% +relationship uh corresponding to this + + + align:start position:0% +relationship uh corresponding to this +equation here so what I can do is I can + + align:start position:0% +equation here so what I can do is I can + + + align:start position:0% +equation here so what I can do is I can +simply solve these by superimposing the + + align:start position:0% +simply solve these by superimposing the + + + align:start position:0% +simply solve these by superimposing the +two curves on the same VD ID uh template + + align:start position:0% +two curves on the same VD ID uh template + + + align:start position:0% +two curves on the same VD ID uh template +here and finding the intersection of the + + align:start position:0% +here and finding the intersection of the + + + align:start position:0% +here and finding the intersection of the +curves so I can take this + + align:start position:0% +curves so I can take this + + + align:start position:0% +curves so I can take this +curve corresponding to two and I can + + align:start position:0% +curve corresponding to two and I can + + + align:start position:0% +curve corresponding to two and I can +take this + + align:start position:0% +take this + + + align:start position:0% +take this +curve corresponding to one and this is + + align:start position:0% +curve corresponding to one and this is + + + align:start position:0% +curve corresponding to one and this is +uh V / R and this is V zero and I can + + align:start position:0% +uh V / R and this is V zero and I can + + + align:start position:0% +uh V / R and this is V zero and I can +find the intersection + + align:start position:0% + + + + align:start position:0% + +Point uh this curve + + align:start position:0% +Point uh this curve + + + align:start position:0% +Point uh this curve +here for reasons that will be obvious uh + + align:start position:0% +here for reasons that will be obvious uh + + + align:start position:0% +here for reasons that will be obvious uh +about three weeks from now is called uh + + align:start position:0% +about three weeks from now is called uh + + + align:start position:0% +about three weeks from now is called uh +the load line okay it's called the load + + align:start position:0% +the load line okay it's called the load + + + align:start position:0% +the load line okay it's called the load +line uh you'll understand uh why that is + + align:start position:0% +line uh you'll understand uh why that is + + + align:start position:0% +line uh you'll understand uh why that is +so uh in a later in a later + + align:start position:0% +so uh in a later in a later + + + align:start position:0% +so uh in a later in a later +lecture okay so uh so you um I've given + + align:start position:0% +lecture okay so uh so you um I've given + + + align:start position:0% +lecture okay so uh so you um I've given +you a template on page six to uh boil + + align:start position:0% +you a template on page six to uh boil + + + align:start position:0% +you a template on page six to uh boil +these two down onto one uh one equation + + align:start position:0% +these two down onto one uh one equation + + + align:start position:0% +these two down onto one uh one equation +so there again you know you can + + align:start position:0% +so there again you know you can + + + align:start position:0% +so there again you know you can +substitute the values for uh V is one + + align:start position:0% +substitute the values for uh V is one + + + align:start position:0% +substitute the values for uh V is one +volt and R is one and so on and so forth + + align:start position:0% +volt and R is one and so on and so forth + + + align:start position:0% +volt and R is one and so on and so forth +and get the same kind of uh result as + + align:start position:0% +and get the same kind of uh result as + + + align:start position:0% +and get the same kind of uh result as +you did uh + + align:start position:0% + + + + align:start position:0% + +previously so there's really nothing new + + align:start position:0% +previously so there's really nothing new + + + align:start position:0% +previously so there's really nothing new +here all I've done in the second method + + align:start position:0% +here all I've done in the second method + + + align:start position:0% +here all I've done in the second method +is combined the two equations + + align:start position:0% +is combined the two equations + + + align:start position:0% +is combined the two equations +graphically and found the solution by + + align:start position:0% +graphically and found the solution by + + + align:start position:0% +graphically and found the solution by +looking at where the two curves + + align:start position:0% + + + + align:start position:0% + +intersect okay + + align:start position:0% + + + + align:start position:0% + +um the start of the lecture I also told + + align:start position:0% +um the start of the lecture I also told + + + align:start position:0% +um the start of the lecture I also told +you that that uh uh you may want to go + + align:start position:0% +you that that uh uh you may want to go + + + align:start position:0% +you that that uh uh you may want to go +and check out the peie + + align:start position:0% +and check out the peie + + + align:start position:0% +and check out the peie +wise linear + + align:start position:0% + + + + align:start position:0% + +technique in section 4.4 of the uh + + align:start position:0% +technique in section 4.4 of the uh + + + align:start position:0% +technique in section 4.4 of the uh +course + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +notes all right + + align:start position:0% + + + + align:start position:0% + +so for + + align:start position:0% +so for + + + align:start position:0% +so for +today let me do a third method called + + align:start position:0% +today let me do a third method called + + + align:start position:0% +today let me do a third method called +incremental + + align:start position:0% + + + + align:start position:0% + +analysis okay this technique is also + + align:start position:0% +analysis okay this technique is also + + + align:start position:0% +analysis okay this technique is also +called uh the small signal + + align:start position:0% + + + + align:start position:0% + +method + + align:start position:0% +method + + + align:start position:0% +method +okay so + + align:start position:0% + + + + align:start position:0% + +um I'm going to show you uh before I go + + align:start position:0% +um I'm going to show you uh before I go + + + align:start position:0% +um I'm going to show you uh before I go +into the method uh in today's lecture + + align:start position:0% +into the method uh in today's lecture + + + align:start position:0% +into the method uh in today's lecture +what I'll do is I'll give you a + + align:start position:0% +what I'll do is I'll give you a + + + align:start position:0% +what I'll do is I'll give you a +motivating example okay for why we need + + align:start position:0% +motivating example okay for why we need + + + align:start position:0% +motivating example okay for why we need +the small signal approach get a m + + align:start position:0% +the small signal approach get a m + + + align:start position:0% +the small signal approach get a m +motivating example and show you a little + + align:start position:0% +motivating example and show you a little + + + align:start position:0% +motivating example and show you a little +demo okay and then I will close with uh + + align:start position:0% +demo okay and then I will close with uh + + + align:start position:0% +demo okay and then I will close with uh +showing you a problem with applying a + + align:start position:0% +showing you a problem with applying a + + + align:start position:0% +showing you a problem with applying a +standard approach and I'll ask you to + + align:start position:0% +standard approach and I'll ask you to + + + align:start position:0% +standard approach and I'll ask you to +see if you can figure out a way to + + align:start position:0% +see if you can figure out a way to + + + align:start position:0% +see if you can figure out a way to +handle it uh you know in time for next + + align:start position:0% +handle it uh you know in time for next + + + align:start position:0% +handle it uh you know in time for next +lecture okay so let me let me give you + + align:start position:0% +lecture okay so let me let me give you + + + align:start position:0% +lecture okay so let me let me give you +the motivation + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +here so here's what I want to + + align:start position:0% +here so here's what I want to + + + align:start position:0% +here so here's what I want to +do so many of youve have seen a uh one + + align:start position:0% +do so many of youve have seen a uh one + + + align:start position:0% +do so many of youve have seen a uh one +of those uh electric eye garage door + + align:start position:0% +of those uh electric eye garage door + + + align:start position:0% +of those uh electric eye garage door +openers right so you have a uh uh a + + align:start position:0% +openers right so you have a uh uh a + + + align:start position:0% +openers right so you have a uh uh a +receiver at one end and you have uh some + + align:start position:0% +receiver at one end and you have uh some + + + align:start position:0% +receiver at one end and you have uh some +kind of a light beam at the other and + + align:start position:0% +kind of a light beam at the other and + + + align:start position:0% +kind of a light beam at the other and +when you uh when you walk through it's + + align:start position:0% +when you uh when you walk through it's + + + align:start position:0% +when you uh when you walk through it's +stops or rather it cuts the circuit and + + align:start position:0% +stops or rather it cuts the circuit and + + + align:start position:0% +stops or rather it cuts the circuit and +stops the door from closing and when you + + align:start position:0% +stops the door from closing and when you + + + align:start position:0% +stops the door from closing and when you +uh you know when no one's going through + + align:start position:0% +uh you know when no one's going through + + + align:start position:0% +uh you know when no one's going through +it maintains a uh connection and lets + + align:start position:0% +it maintains a uh connection and lets + + + align:start position:0% +it maintains a uh connection and lets +the door close so uh what we did is we + + align:start position:0% +the door close so uh what we did is we + + + align:start position:0% +the door close so uh what we did is we +went to the we went to Home Depot or one + + align:start position:0% +went to the we went to Home Depot or one + + + align:start position:0% +went to the we went to Home Depot or one +of the stores and bought a very standard + + align:start position:0% +of the stores and bought a very standard + + + align:start position:0% +of the stores and bought a very standard +uh uh device that uh essentially has uh + + align:start position:0% +uh uh device that uh essentially has uh + + + align:start position:0% +uh uh device that uh essentially has uh +produces some response when light + + align:start position:0% +produces some response when light + + + align:start position:0% +produces some response when light +impinges on it and my goal will be to + + align:start position:0% +impinges on it and my goal will be to + + + align:start position:0% +impinges on it and my goal will be to +see if I can send music over a uh you + + align:start position:0% +see if I can send music over a uh you + + + align:start position:0% +see if I can send music over a uh you +know over a light beam uh using a simple + + align:start position:0% +know over a light beam uh using a simple + + + align:start position:0% +know over a light beam uh using a simple +garage door opener uh device okay so + + align:start position:0% +garage door opener uh device okay so + + + align:start position:0% +garage door opener uh device okay so +here's here's the little circuit that + + align:start position:0% +here's here's the little circuit that + + + align:start position:0% +here's here's the little circuit that +I'll do so we actually went and built + + align:start position:0% +I'll do so we actually went and built + + + align:start position:0% +I'll do so we actually went and built +this I'll also show you a demo + + align:start position:0% +this I'll also show you a demo + + + align:start position:0% +this I'll also show you a demo +um + + align:start position:0% + + + + align:start position:0% + +so so here's my time varing voltage VT + + align:start position:0% +so so here's my time varing voltage VT + + + align:start position:0% +so so here's my time varing voltage VT +uh VI and uh this is some music some + + align:start position:0% +uh VI and uh this is some music some + + + align:start position:0% +uh VI and uh this is some music some +music music signal + + align:start position:0% + + + + align:start position:0% + +get some music signal and uh I'm going + + align:start position:0% +get some music signal and uh I'm going + + + align:start position:0% +get some music signal and uh I'm going +to connect this to my + + align:start position:0% +to connect this to my + + + align:start position:0% +to connect this to my +uh to this + + align:start position:0% +uh to this + + + align:start position:0% +uh to this +device okay which is uh which is a + + align:start position:0% +device okay which is uh which is a + + + align:start position:0% +device okay which is uh which is a +device found in garage door + + align:start position:0% +device found in garage door + + + align:start position:0% +device found in garage door +openers I'm going to call it a uh LED uh + + align:start position:0% +openers I'm going to call it a uh LED uh + + + align:start position:0% +openers I'm going to call it a uh LED uh +if you like you can view it as a this is + + align:start position:0% +if you like you can view it as a this is + + + align:start position:0% +if you like you can view it as a this is +very similar to our export dweb uh this + + align:start position:0% +very similar to our export dweb uh this + + + align:start position:0% +very similar to our export dweb uh this +is called a light emitting export dwee + + align:start position:0% +is called a light emitting export dwee + + + align:start position:0% +is called a light emitting export dwee +okay that's why it's LED so uh so what + + align:start position:0% +okay that's why it's LED so uh so what + + + align:start position:0% +okay that's why it's LED so uh so what +the light emitting export dwe does is um + + align:start position:0% +the light emitting export dwe does is um + + + align:start position:0% +the light emitting export dwe does is um +as I apply this voltage across + + align:start position:0% + + + + align:start position:0% + +it that same voltage appears across the + + align:start position:0% +it that same voltage appears across the + + + align:start position:0% +it that same voltage appears across the +uh uh light emitting export D and uh + + align:start position:0% +uh uh light emitting export D and uh + + + align:start position:0% +uh uh light emitting export D and uh +there's some current that flows through + + align:start position:0% +there's some current that flows through + + + align:start position:0% +there's some current that flows through +the device okay and for for our analysis + + align:start position:0% +the device okay and for for our analysis + + + align:start position:0% +the device okay and for for our analysis +we will assume that this device is + + align:start position:0% +we will assume that this device is + + + align:start position:0% +we will assume that this device is +virtually has an identical IV + + align:start position:0% +virtually has an identical IV + + + align:start position:0% +virtually has an identical IV +characteristic to the uh export wee just + + align:start position:0% +characteristic to the uh export wee just + + + align:start position:0% +characteristic to the uh export wee just +that it image light okay so when I pass + + align:start position:0% +that it image light okay so when I pass + + + align:start position:0% +that it image light okay so when I pass +a current through it it IM light okay + + align:start position:0% +a current through it it IM light okay + + + align:start position:0% +a current through it it IM light okay +and the light intensity is proportional + + align:start position:0% +and the light intensity is proportional + + + align:start position:0% +and the light intensity is proportional +to the current that flows through okay + + align:start position:0% +to the current that flows through okay + + + align:start position:0% +to the current that flows through okay +so it emits light and light intensity LD + + align:start position:0% +so it emits light and light intensity LD + + + align:start position:0% +so it emits light and light intensity LD +is proportional to + + align:start position:0% + + + + align:start position:0% + +ID okay so here's my little light + + align:start position:0% +ID okay so here's my little light + + + align:start position:0% +ID okay so here's my little light +emiting device which when current flows + + align:start position:0% +emiting device which when current flows + + + align:start position:0% +emiting device which when current flows +through it it produces light whose + + align:start position:0% +through it it produces light whose + + + align:start position:0% +through it it produces light whose +intensity is proportional to the current + + align:start position:0% +intensity is proportional to the current + + + align:start position:0% +intensity is proportional to the current +and what I'll do is I'll stick in theer + + align:start position:0% + + + + align:start position:0% + +here okay think of it as a uh uh photo + + align:start position:0% +here okay think of it as a uh uh photo + + + align:start position:0% +here okay think of it as a uh uh photo +resistor or you know some other uh + + align:start position:0% +resistor or you know some other uh + + + align:start position:0% +resistor or you know some other uh +device + + align:start position:0% +device + + + align:start position:0% +device +where I'm going to connect that in a + + align:start position:0% + + + + align:start position:0% + +circuit not going to spend too much time + + align:start position:0% +circuit not going to spend too much time + + + align:start position:0% +circuit not going to spend too much time +on this side I'm going to focus on the + + align:start position:0% +on this side I'm going to focus on the + + + align:start position:0% +on this side I'm going to focus on the +left hand side here and let's say I have + + align:start position:0% +left hand side here and let's say I have + + + align:start position:0% +left hand side here and let's say I have +some kind of + + align:start position:0% +some kind of + + + align:start position:0% +some kind of +amplifier and speakers and so on and so + + align:start position:0% +amplifier and speakers and so on and so + + + align:start position:0% +amplifier and speakers and so on and so +forth suffice it to say that + + align:start position:0% +forth suffice it to say that + + + align:start position:0% +forth suffice it to say that +when the when the light falls on this + + align:start position:0% +when the when the light falls on this + + + align:start position:0% +when the when the light falls on this +device PR uh that + + align:start position:0% +device PR uh that + + + align:start position:0% +device PR uh that +IR that uh goes through here is + + align:start position:0% +IR that uh goes through here is + + + align:start position:0% +IR that uh goes through here is +proportional to the received light + + align:start position:0% +proportional to the received light + + + align:start position:0% +proportional to the received light +intensity okay so um if the current is + + align:start position:0% +intensity okay so um if the current is + + + align:start position:0% +intensity okay so um if the current is +proportional to the received light + + align:start position:0% +proportional to the received light + + + align:start position:0% +proportional to the received light +intensity then I amplify that signal in + + align:start position:0% +intensity then I amplify that signal in + + + align:start position:0% +intensity then I amplify that signal in +my amplifier and I get the music playing + + align:start position:0% +my amplifier and I get the music playing + + + align:start position:0% +my amplifier and I get the music playing +out here okay and uh notice that uh the + + align:start position:0% +out here okay and uh notice that uh the + + + align:start position:0% +out here okay and uh notice that uh the +following chain of dependences apply + + align:start position:0% +following chain of dependences apply + + + align:start position:0% +following chain of dependences apply +so I have an input music signal + + align:start position:0% + + + + align:start position:0% + +VI that gets converted to some uh ID + + align:start position:0% +VI that gets converted to some uh ID + + + align:start position:0% +VI that gets converted to some uh ID +these are all time varing signals okay + + align:start position:0% +these are all time varing signals okay + + + align:start position:0% +these are all time varing signals okay +so VI is a Time varing signal so is ID + + align:start position:0% +so VI is a Time varing signal so is ID + + + align:start position:0% +so VI is a Time varing signal so is ID +and + + align:start position:0% +and + + + align:start position:0% +and +uh ID gets converted to + + align:start position:0% +uh ID gets converted to + + + align:start position:0% +uh ID gets converted to +light of some intensity + + align:start position:0% + + + + align:start position:0% + +LD okay this in + + align:start position:0% +LD okay this in + + + align:start position:0% +LD okay this in +turn uh gets attenuated somewhat and is + + align:start position:0% +turn uh gets attenuated somewhat and is + + + align:start position:0% +turn uh gets attenuated somewhat and is +received at the uh photo + + align:start position:0% +received at the uh photo + + + align:start position:0% +received at the uh photo +resistor and uh I get some intensity LR + + align:start position:0% +resistor and uh I get some intensity LR + + + align:start position:0% +resistor and uh I get some intensity LR +impinging on that uh that device there + + align:start position:0% +impinging on that uh that device there + + + align:start position:0% +impinging on that uh that device there +and that in turn produces a current ir + + align:start position:0% +and that in turn produces a current ir + + + align:start position:0% +and that in turn produces a current ir +and an + + align:start position:0% + + + + align:start position:0% + +IR is Amplified and goes through a + + align:start position:0% +IR is Amplified and goes through a + + + align:start position:0% +IR is Amplified and goes through a +speaker and so on and produce the sound + + align:start position:0% +speaker and so on and produce the sound + + + align:start position:0% +speaker and so on and produce the sound +so notice that using this chain I've + + align:start position:0% +so notice that using this chain I've + + + align:start position:0% +so notice that using this chain I've +taken a music signal here and I'm + + align:start position:0% +taken a music signal here and I'm + + + align:start position:0% +taken a music signal here and I'm +playing it here okay and just just + + align:start position:0% +playing it here okay and just just + + + align:start position:0% +playing it here okay and just just +imagine that this is your garage door + + align:start position:0% +imagine that this is your garage door + + + align:start position:0% +imagine that this is your garage door +opener uh device here where + + align:start position:0% +opener uh device here where + + + align:start position:0% +opener uh device here where +the light being emitted is being + + align:start position:0% +the light being emitted is being + + + align:start position:0% +the light being emitted is being +articulated by the voltage signal VI and + + align:start position:0% +articulated by the voltage signal VI and + + + align:start position:0% +articulated by the voltage signal VI and +received here and so notice that if I + + align:start position:0% +received here and so notice that if I + + + align:start position:0% +received here and so notice that if I +cut this if I if I I stick something in + + align:start position:0% +cut this if I if I I stick something in + + + align:start position:0% +cut this if I if I I stick something in +here I block it then I get no response + + align:start position:0% +here I block it then I get no response + + + align:start position:0% +here I block it then I get no response +here but if I take my hand away then I + + align:start position:0% +here but if I take my hand away then I + + + align:start position:0% +here but if I take my hand away then I +do get uh some response so this is fine + + align:start position:0% +do get uh some response so this is fine + + + align:start position:0% +do get uh some response so this is fine +okay so this should + + align:start position:0% +okay so this should + + + align:start position:0% +okay so this should +work you can try this at home if you + + align:start position:0% +work you can try this at home if you + + + align:start position:0% +work you can try this at home if you +like you know but if you have a garage + + align:start position:0% +like you know but if you have a garage + + + align:start position:0% +like you know but if you have a garage +door opener just you know stick a little + + align:start position:0% +door opener just you know stick a little + + + align:start position:0% +door opener just you know stick a little +circuit like this and it should simply + + align:start position:0% +circuit like this and it should simply + + + align:start position:0% +circuit like this and it should simply +work we have a problem though + + align:start position:0% +work we have a problem though + + + align:start position:0% +work we have a problem though +the problem + + align:start position:0% +the problem + + + align:start position:0% +the problem +is that as I said I'm using the export + + align:start position:0% +is that as I said I'm using the export + + + align:start position:0% +is that as I said I'm using the export +DB here the light emitting Expo dwe and + + align:start position:0% +DB here the light emitting Expo dwe and + + + align:start position:0% +DB here the light emitting Expo dwe and +its characteristics are as + + align:start position:0% +its characteristics are as + + + align:start position:0% +its characteristics are as +follows okay ID is exponentially related + + align:start position:0% +follows okay ID is exponentially related + + + align:start position:0% +follows okay ID is exponentially related +to the voltage + + align:start position:0% +to the voltage + + + align:start position:0% +to the voltage +VD okay so this is + + align:start position:0% + + + + align:start position:0% + +nonlinear and that a real + + align:start position:0% +nonlinear and that a real + + + align:start position:0% +nonlinear and that a real +problem okay because this is nonlinear I + + align:start position:0% +problem okay because this is nonlinear I + + + align:start position:0% +problem okay because this is nonlinear I +am going to get a uh distorted + + align:start position:0% +am going to get a uh distorted + + + align:start position:0% +am going to get a uh distorted +output let me show you a little uh + + align:start position:0% +output let me show you a little uh + + + align:start position:0% +output let me show you a little uh +waveform a little graph to show you how + + align:start position:0% +waveform a little graph to show you how + + + align:start position:0% +waveform a little graph to show you how +the Distortion happens and then show you + + align:start position:0% +the Distortion happens and then show you + + + align:start position:0% +the Distortion happens and then show you +a little demo + + align:start position:0% +a little demo + + + align:start position:0% +a little demo +uh showing you the + + align:start position:0% +uh showing you the + + + align:start position:0% +uh showing you the +Distortion so uh let me graphically show + + align:start position:0% +Distortion so uh let me graphically show + + + align:start position:0% +Distortion so uh let me graphically show +you the kind of distortion that's + + align:start position:0% +you the kind of distortion that's + + + align:start position:0% +you the kind of distortion that's +happening here and I'll do it by drawing + + align:start position:0% +happening here and I'll do it by drawing + + + align:start position:0% +happening here and I'll do it by drawing +the following uh + + align:start position:0% + + + + align:start position:0% + +graph okay so this is the VD ID curve + + align:start position:0% +graph okay so this is the VD ID curve + + + align:start position:0% +graph okay so this is the VD ID curve +for our device okay and what I'm going + + align:start position:0% +for our device okay and what I'm going + + + align:start position:0% +for our device okay and what I'm going +tol for you is if I have a Time varing + + align:start position:0% +tol for you is if I have a Time varing + + + align:start position:0% +tol for you is if I have a Time varing +VD voltage I just want to see what the + + align:start position:0% +VD voltage I just want to see what the + + + align:start position:0% +VD voltage I just want to see what the +time varing ID current looks like and a + + align:start position:0% +time varing ID current looks like and a + + + align:start position:0% +time varing ID current looks like and a +trick to plot that is to take your input + + align:start position:0% + + + + align:start position:0% + +voltage like so and uh you know let's + + align:start position:0% +voltage like so and uh you know let's + + + align:start position:0% +voltage like so and uh you know let's +say apply a + + align:start position:0% + + + + align:start position:0% + +sinusoid so I'm just taking a uh a Time + + align:start position:0% +sinusoid so I'm just taking a uh a Time + + + align:start position:0% +sinusoid so I'm just taking a uh a Time +wearing sin voltage and plotting it + + align:start position:0% +wearing sin voltage and plotting it + + + align:start position:0% +wearing sin voltage and plotting it +rotating the plot 90° like so so I can + + align:start position:0% +rotating the plot 90° like so so I can + + + align:start position:0% +rotating the plot 90° like so so I can +see where these points correspond to on + + align:start position:0% +see where these points correspond to on + + + align:start position:0% +see where these points correspond to on +that curve okay so what this says is + + align:start position:0% +that curve okay so what this says is + + + align:start position:0% +that curve okay so what this says is +that at some point here for example + + align:start position:0% +that at some point here for example + + + align:start position:0% +that at some point here for example +where uh Vi at this point in time when + + align:start position:0% +where uh Vi at this point in time when + + + align:start position:0% +where uh Vi at this point in time when +VI is here notice VI and VD are the same + + align:start position:0% +VI is here notice VI and VD are the same + + + align:start position:0% +VI is here notice VI and VD are the same +thing okay because VI is applied across + + align:start position:0% +thing okay because VI is applied across + + + align:start position:0% +thing okay because VI is applied across +VD okay VI directly applies across the + + align:start position:0% +VD okay VI directly applies across the + + + align:start position:0% +VD okay VI directly applies across the +uh device and so VI equals VD at all + + align:start position:0% +uh device and so VI equals VD at all + + + align:start position:0% +uh device and so VI equals VD at all +time so uh so this this voltage here + + align:start position:0% +time so uh so this this voltage here + + + align:start position:0% +time so uh so this this voltage here +corresponds to uh this voltage which + + align:start position:0% +corresponds to uh this voltage which + + + align:start position:0% +corresponds to uh this voltage which +corresponds to this current and then I + + align:start position:0% +corresponds to this current and then I + + + align:start position:0% +corresponds to this current and then I +can find out what the current is for + + align:start position:0% +can find out what the current is for + + + align:start position:0% +can find out what the current is for +that uh that voltage using the same + + align:start position:0% +that uh that voltage using the same + + + align:start position:0% +that uh that voltage using the same +artifice that me I can plot uh the + + align:start position:0% +artifice that me I can plot uh the + + + align:start position:0% +artifice that me I can plot uh the +output current ID like so + + align:start position:0% +output current ID like so + + + align:start position:0% +output current ID like so +um so for this value I get uh some + + align:start position:0% +um so for this value I get uh some + + + align:start position:0% +um so for this value I get uh some +current + + align:start position:0% +current + + + align:start position:0% +current +here and uh so that at time t0 I start + + align:start position:0% +here and uh so that at time t0 I start + + + align:start position:0% +here and uh so that at time t0 I start +here and notice that as + + align:start position:0% +here and notice that as + + + align:start position:0% +here and notice that as +this signal moves up here I can find out + + align:start position:0% +this signal moves up here I can find out + + + align:start position:0% +this signal moves up here I can find out +the corresponding values of ID by + + align:start position:0% +the corresponding values of ID by + + + align:start position:0% +the corresponding values of ID by +looking at where a straight line from me + + align:start position:0% +looking at where a straight line from me + + + align:start position:0% +looking at where a straight line from me +intersects here and plotting the values + + align:start position:0% +intersects here and plotting the values + + + align:start position:0% +intersects here and plotting the values +here I had a nice little graphical + + align:start position:0% +here I had a nice little graphical + + + align:start position:0% +here I had a nice little graphical +animation to show you this uh hopefully + + align:start position:0% +animation to show you this uh hopefully + + + align:start position:0% +animation to show you this uh hopefully +the laptop will tomorrow and uh we can + + align:start position:0% +the laptop will tomorrow and uh we can + + + align:start position:0% +the laptop will tomorrow and uh we can +check that I'm I'm doing nothing new + + align:start position:0% +check that I'm I'm doing nothing new + + + align:start position:0% +check that I'm I'm doing nothing new +here just showing you a a trick to be + + align:start position:0% +here just showing you a a trick to be + + + align:start position:0% +here just showing you a a trick to be +able to plot VI versus V out + + align:start position:0% +able to plot VI versus V out + + + align:start position:0% +able to plot VI versus V out +relationships Bas of VI versus other + + align:start position:0% +relationships Bas of VI versus other + + + align:start position:0% +relationships Bas of VI versus other +relationships based on uh some kind of a + + align:start position:0% +relationships based on uh some kind of a + + + align:start position:0% +relationships based on uh some kind of a +transfer function so uh what you end up + + align:start position:0% +transfer function so uh what you end up + + + align:start position:0% +transfer function so uh what you end up +getting is something that looks like + + align:start position:0% + + + + align:start position:0% + +this why is that notice + + align:start position:0% +this why is that notice + + + align:start position:0% +this why is that notice +that + + align:start position:0% +that + + + align:start position:0% +that +uh this curve here corresponds to the + + align:start position:0% +uh this curve here corresponds to the + + + align:start position:0% +uh this curve here corresponds to the +signal as this signal moves from to here + + align:start position:0% +signal as this signal moves from to here + + + align:start position:0% +signal as this signal moves from to here +this point moves from here to here and + + align:start position:0% +this point moves from here to here and + + + align:start position:0% +this point moves from here to here and +that corresponds to uh this + + align:start position:0% +that corresponds to uh this + + + align:start position:0% +that corresponds to uh this +ID when this moves from here to here + + align:start position:0% +ID when this moves from here to here + + + align:start position:0% +ID when this moves from here to here +that corresponds to uh a point moving + + align:start position:0% +that corresponds to uh a point moving + + + align:start position:0% +that corresponds to uh a point moving +from this part of the curve to here and + + align:start position:0% +from this part of the curve to here and + + + align:start position:0% +from this part of the curve to here and +that looks like so and then for the + + align:start position:0% +that looks like so and then for the + + + align:start position:0% +that looks like so and then for the +whole negative incursion notice that the + + align:start position:0% +whole negative incursion notice that the + + + align:start position:0% +whole negative incursion notice that the +whole negative incursion uh moves + + align:start position:0% +whole negative incursion uh moves + + + align:start position:0% +whole negative incursion uh moves +here okay so for that entire negative + + align:start position:0% +here okay so for that entire negative + + + align:start position:0% +here okay so for that entire negative +incursion I get an output that looks + + align:start position:0% +incursion I get an output that looks + + + align:start position:0% +incursion I get an output that looks +like this notice that this this device + + align:start position:0% +like this notice that this this device + + + align:start position:0% +like this notice that this this device +has completely cut off and hammered um + + align:start position:0% +has completely cut off and hammered um + + + align:start position:0% +has completely cut off and hammered um +negative going signals okay what it's + + align:start position:0% +negative going signals okay what it's + + + align:start position:0% +negative going signals okay what it's +done is that rather than giving me a + + align:start position:0% +done is that rather than giving me a + + + align:start position:0% +done is that rather than giving me a +nice little negative uh Spike um + + align:start position:0% +nice little negative uh Spike um + + + align:start position:0% +nice little negative uh Spike um +incursion here or Excursion here what + + align:start position:0% +incursion here or Excursion here what + + + align:start position:0% +incursion here or Excursion here what +this is doing is that it's taking this + + align:start position:0% +this is doing is that it's taking this + + + align:start position:0% +this is doing is that it's taking this +excursion and simply slamming it down to + + align:start position:0% +excursion and simply slamming it down to + + + align:start position:0% +excursion and simply slamming it down to +uh this value here okay and then again + + align:start position:0% +uh this value here okay and then again + + + align:start position:0% +uh this value here okay and then again +when I go back up I get this peak here + + align:start position:0% +when I go back up I get this peak here + + + align:start position:0% +when I go back up I get this peak here +so notice that what was a nice little + + align:start position:0% +so notice that what was a nice little + + + align:start position:0% +so notice that what was a nice little +sinusoid out there gets uh hammered and + + align:start position:0% +sinusoid out there gets uh hammered and + + + align:start position:0% +sinusoid out there gets uh hammered and +squished into this funny curve here okay + + align:start position:0% +squished into this funny curve here okay + + + align:start position:0% +squished into this funny curve here okay +what this device is doing is for + + align:start position:0% +what this device is doing is for + + + align:start position:0% +what this device is doing is for +positive values it tends to produce + + align:start position:0% +positive values it tends to produce + + + align:start position:0% +positive values it tends to produce +exponentially greater current so I get + + align:start position:0% +exponentially greater current so I get + + + align:start position:0% +exponentially greater current so I get +you know boom high-rising Peaks + + align:start position:0% +you know boom high-rising Peaks + + + align:start position:0% +you know boom high-rising Peaks +corresponding to these two and for + + align:start position:0% +corresponding to these two and for + + + align:start position:0% +corresponding to these two and for +negative going currents negative going + + align:start position:0% +negative going currents negative going + + + align:start position:0% +negative going currents negative going +voltages it simply compresses them to a + + align:start position:0% +voltages it simply compresses them to a + + + align:start position:0% +voltages it simply compresses them to a +low positive value here and that's what + + align:start position:0% +low positive value here and that's what + + + align:start position:0% +low positive value here and that's what +I see here corresponding to negative + + align:start position:0% +I see here corresponding to negative + + + align:start position:0% +I see here corresponding to negative +excursions so notice so what this will + + align:start position:0% +excursions so notice so what this will + + + align:start position:0% +excursions so notice so what this will +do is if I if I view sound if I input + + align:start position:0% +do is if I if I view sound if I input + + + align:start position:0% +do is if I if I view sound if I input +sound here when sound has negative going + + align:start position:0% +sound here when sound has negative going + + + align:start position:0% +sound here when sound has negative going +excursions it will simply scrunch them + + align:start position:0% +excursions it will simply scrunch them + + + align:start position:0% +excursions it will simply scrunch them +okay and but more or less let the + + align:start position:0% +okay and but more or less let the + + + align:start position:0% +okay and but more or less let the +positive things through and uh that is + + align:start position:0% +positive things through and uh that is + + + align:start position:0% +positive things through and uh that is +going to give rise to a bunch of + + align:start position:0% +going to give rise to a bunch of + + + align:start position:0% +going to give rise to a bunch of +distortion in my in my signal so I'd + + align:start position:0% +distortion in my in my signal so I'd + + + align:start position:0% +distortion in my in my signal so I'd +like to show you a little demo um + + align:start position:0% +like to show you a little demo um + + + align:start position:0% +like to show you a little demo um +actually we've gone ahead and built a + + align:start position:0% +actually we've gone ahead and built a + + + align:start position:0% +actually we've gone ahead and built a +little device like + + align:start position:0% +little device like + + + align:start position:0% +little device like +this okay we have an honest to goodness + + align:start position:0% +this okay we have an honest to goodness + + + align:start position:0% +this okay we have an honest to goodness +little device you know costing you know + + align:start position:0% +little device you know costing you know + + + align:start position:0% +little device you know costing you know +I don't know 50 cents or a buck or + + align:start position:0% +I don't know 50 cents or a buck or + + + align:start position:0% +I don't know 50 cents or a buck or +something um which is a little voltage + + align:start position:0% +something um which is a little voltage + + + align:start position:0% +something um which is a little voltage +uh uh it's a uh it's a device that emits + + align:start position:0% +uh uh it's a uh it's a device that emits + + + align:start position:0% +uh uh it's a uh it's a device that emits +light proportional to the current + + align:start position:0% +light proportional to the current + + + align:start position:0% +light proportional to the current +flowing through it I have a receiver and + + align:start position:0% +flowing through it I have a receiver and + + + align:start position:0% +flowing through it I have a receiver and +uh I'm going to play some music and you + + align:start position:0% +uh I'm going to play some music and you + + + align:start position:0% +uh I'm going to play some music and you +will listen to uh the output here okay + + align:start position:0% +will listen to uh the output here okay + + + align:start position:0% +will listen to uh the output here okay +and uh hopefully you should see a bunch + + align:start position:0% +and uh hopefully you should see a bunch + + + align:start position:0% +and uh hopefully you should see a bunch +of distortion because of that uh that + + align:start position:0% +of distortion because of that uh that + + + align:start position:0% +of distortion because of that uh that +effect that I showed + + align:start position:0% + + + + align:start position:0% + +you okay and uh what I'll do is uh um + + align:start position:0% +you okay and uh what I'll do is uh um + + + align:start position:0% +you okay and uh what I'll do is uh um +before we do that uh you'll see two + + align:start position:0% +before we do that uh you'll see two + + + align:start position:0% +before we do that uh you'll see two +curves up there the yellow I believe is + + align:start position:0% +curves up there the yellow I believe is + + + align:start position:0% +curves up there the yellow I believe is +the vi is the input and the green I + + align:start position:0% +the vi is the input and the green I + + + align:start position:0% +the vi is the input and the green I +believe is a signal proportional to uh + + align:start position:0% +believe is a signal proportional to uh + + + align:start position:0% +believe is a signal proportional to uh +other way oh I see so green is the input + + align:start position:0% +other way oh I see so green is the input + + + align:start position:0% +other way oh I see so green is the input +so green the lower one is the input and + + align:start position:0% +so green the lower one is the input and + + + align:start position:0% +so green the lower one is the input and +the upper one is the distorted output + + align:start position:0% +the upper one is the distorted output + + + align:start position:0% +the upper one is the distorted output +okay so we're going to play some sound + + align:start position:0% +okay so we're going to play some sound + + + align:start position:0% +okay so we're going to play some sound +through it and uh music through it and + + align:start position:0% +through it and uh music through it and + + + align:start position:0% +through it and uh music through it and +uh you can + + align:start position:0% +uh you can + + + align:start position:0% +uh you can +listen through a little CD player + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +volume turn on some more so uh so so a + + align:start position:0% +volume turn on some more so uh so so a + + + align:start position:0% +volume turn on some more so uh so so a +couple things the good news the the good + + align:start position:0% +couple things the good news the the good + + + align:start position:0% +couple things the good news the the good +news is that it + + align:start position:0% +news is that it + + + align:start position:0% +news is that it +works + + align:start position:0% +works + + + align:start position:0% +works +okay however I doubt that uh you know uh + + align:start position:0% +okay however I doubt that uh you know uh + + + align:start position:0% +okay however I doubt that uh you know uh +that music artist will come to my studio + + align:start position:0% +that music artist will come to my studio + + + align:start position:0% +that music artist will come to my studio +to uh to record if this is the quality + + align:start position:0% +to uh to record if this is the quality + + + align:start position:0% +to uh to record if this is the quality +of what I produce so do notice that uh + + align:start position:0% +of what I produce so do notice that uh + + + align:start position:0% +of what I produce so do notice that uh +there are hardly any negative going + + align:start position:0% +there are hardly any negative going + + + align:start position:0% +there are hardly any negative going +excursions in that curve up there right + + align:start position:0% +excursions in that curve up there right + + + align:start position:0% +excursions in that curve up there right +all the negative negative ones have been + + align:start position:0% +all the negative negative ones have been + + + align:start position:0% +all the negative negative ones have been +like you know scrunched up down into a + + align:start position:0% +like you know scrunched up down into a + + + align:start position:0% +like you know scrunched up down into a +flat line there and that's the reason I + + align:start position:0% +flat line there and that's the reason I + + + align:start position:0% +flat line there and that's the reason I +get this Distortion and just to prove to + + align:start position:0% +get this Distortion and just to prove to + + + align:start position:0% +get this Distortion and just to prove to +you that I am indeed using a garage door + + align:start position:0% +you that I am indeed using a garage door + + + align:start position:0% +you that I am indeed using a garage door +open or device and you know not faking + + align:start position:0% +open or device and you know not faking + + + align:start position:0% +open or device and you know not faking +it here here um I'm going to just you + + align:start position:0% +it here here um I'm going to just you + + + align:start position:0% +it here here um I'm going to just you +know shut the music shut the uh signal + + align:start position:0% +know shut the music shut the uh signal + + + align:start position:0% +know shut the music shut the uh signal +off by stopping the light you know using + + align:start position:0% +off by stopping the light you know using + + + align:start position:0% +off by stopping the light you know using +a piece of paper + + align:start position:0% +a piece of paper + + + align:start position:0% +a piece of paper +here so notice that uh this device here + + align:start position:0% +here so notice that uh this device here + + + align:start position:0% +here so notice that uh this device here +uh is a little device that uh has a + + align:start position:0% +uh is a little device that uh has a + + + align:start position:0% +uh is a little device that uh has a +light beam going through the center and + + align:start position:0% +light beam going through the center and + + + align:start position:0% +light beam going through the center and +I'm going to take this piece of paper + + align:start position:0% +I'm going to take this piece of paper + + + align:start position:0% +I'm going to take this piece of paper +and uh turn it up + + align:start position:0% +and uh turn it up + + + align:start position:0% +and uh turn it up +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so what should happen is so let's have + + align:start position:0% +so what should happen is so let's have + + + align:start position:0% +so what should happen is so let's have +some fun with this so if I were to put + + align:start position:0% +some fun with this so if I were to put + + + align:start position:0% +some fun with this so if I were to put +this piece of paper halfway down I + + align:start position:0% +this piece of paper halfway down I + + + align:start position:0% +this piece of paper halfway down I +should get half the intensity right so + + align:start position:0% +should get half the intensity right so + + + align:start position:0% +should get half the intensity right so +my sound should you know diminish in + + align:start position:0% +my sound should you know diminish in + + + align:start position:0% +my sound should you know diminish in +volume a little bit let's maybe that'll + + align:start position:0% +volume a little bit let's maybe that'll + + + align:start position:0% +volume a little bit let's maybe that'll +work let's let's see if it work nothing + + align:start position:0% +work let's let's see if it work nothing + + + align:start position:0% +work let's let's see if it work nothing +to a double it's just + + align:start position:0% +to a double it's just + + + align:start position:0% +to a double it's just +fun + + align:start position:0% +fun + + + align:start position:0% +fun +louder can make it loud my louder + + align:start position:0% +louder can make it loud my louder + + + align:start position:0% +louder can make it loud my louder +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +do much coffee hand shaking so + + align:start position:0% +do much coffee hand shaking so + + + align:start position:0% +do much coffee hand shaking so +uh so I guess you did see uh the the + + align:start position:0% +uh so I guess you did see uh the the + + + align:start position:0% +uh so I guess you did see uh the the +lowering of volume right + + align:start position:0% + + + + align:start position:0% + +okay okay so uh no just way too much + + align:start position:0% +okay okay so uh no just way too much + + + align:start position:0% +okay okay so uh no just way too much +coffee and so my hand was sh shaking too + + align:start position:0% +coffee and so my hand was sh shaking too + + + align:start position:0% +coffee and so my hand was sh shaking too +fast so uh okay imposing its own sign + + align:start position:0% +fast so uh okay imposing its own sign + + + align:start position:0% +fast so uh okay imposing its own sign +wave on top of the uh signal okay so um + + align:start position:0% +wave on top of the uh signal okay so um + + + align:start position:0% +wave on top of the uh signal okay so um +what did I show you I this was uh this + + align:start position:0% +what did I show you I this was uh this + + + align:start position:0% +what did I show you I this was uh this +was garbage right we had U we had a nice + + align:start position:0% +was garbage right we had U we had a nice + + + align:start position:0% +was garbage right we had U we had a nice +little uh signal input and the output + + align:start position:0% +little uh signal input and the output + + + align:start position:0% +little uh signal input and the output +was completely distorted because I was + + align:start position:0% +was completely distorted because I was + + + align:start position:0% +was completely distorted because I was +playing sound over this and uh this is + + align:start position:0% +playing sound over this and uh this is + + + align:start position:0% +playing sound over this and uh this is +what happened + + align:start position:0% +what happened + + + align:start position:0% +what happened +switch to page nine now this is what I + + align:start position:0% +switch to page nine now this is what I + + + align:start position:0% +switch to page nine now this is what I +would have liked to have + + align:start position:0% + + + + align:start position:0% + +happened so on page nine what I would + + align:start position:0% +happened so on page nine what I would + + + align:start position:0% +happened so on page nine what I would +have liked to see happen is + + align:start position:0% + + + + align:start position:0% + +this suppose I had a light emitting + + align:start position:0% +this suppose I had a light emitting + + + align:start position:0% +this suppose I had a light emitting +device that looked + + align:start position:0% +device that looked + + + align:start position:0% +device that looked +linear okay straight + + align:start position:0% +linear okay straight + + + align:start position:0% +linear okay straight +line okay where the current was linearly + + align:start position:0% +line okay where the current was linearly + + + align:start position:0% +line okay where the current was linearly +related to VD then what I would see is + + align:start position:0% +related to VD then what I would see is + + + align:start position:0% +related to VD then what I would see is +if I had aoid here then I would + + align:start position:0% +if I had aoid here then I would + + + align:start position:0% +if I had aoid here then I would +get a signus soid + + align:start position:0% +get a signus soid + + + align:start position:0% +get a signus soid +here no Distortion there right + + align:start position:0% +here no Distortion there right + + + align:start position:0% +here no Distortion there right +but if only things were you know like I + + align:start position:0% +but if only things were you know like I + + + align:start position:0% +but if only things were you know like I +wanted them if I had a linear device but + + align:start position:0% +wanted them if I had a linear device but + + + align:start position:0% +wanted them if I had a linear device but +I don't have a linear device I have a I + + align:start position:0% +I don't have a linear device I have a I + + + align:start position:0% +I don't have a linear device I have a I +have an export D now now you know why I + + align:start position:0% +have an export D now now you know why I + + + align:start position:0% +have an export D now now you know why I +call it a d it's not you know I'd like a + + align:start position:0% +call it a d it's not you know I'd like a + + + align:start position:0% +call it a d it's not you know I'd like a +linear device and it's exponential but + + align:start position:0% +linear device and it's exponential but + + + align:start position:0% +linear device and it's exponential but +this is what I'd like + + align:start position:0% + + + + align:start position:0% + +and if I had this I won't show it to you + + align:start position:0% +and if I had this I won't show it to you + + + align:start position:0% +and if I had this I won't show it to you +today if I had this uh my music would go + + align:start position:0% +today if I had this uh my music would go + + + align:start position:0% +today if I had this uh my music would go +through without any Distortion and uh + + align:start position:0% +through without any Distortion and uh + + + align:start position:0% +through without any Distortion and uh +you know I wouldn't have to run cables + + align:start position:0% +you know I wouldn't have to run cables + + + align:start position:0% +you know I wouldn't have to run cables +through my uh attic I could just use my + + align:start position:0% +through my uh attic I could just use my + + + align:start position:0% +through my uh attic I could just use my +garage door open or to play signals from + + align:start position:0% +garage door open or to play signals from + + + align:start position:0% +garage door open or to play signals from +my bedroom in our living room and so on + + align:start position:0% +my bedroom in our living room and so on + + + align:start position:0% +my bedroom in our living room and so on +right so uh so key thing here is how do + + align:start position:0% +right so uh so key thing here is how do + + + align:start position:0% +right so uh so key thing here is how do +I get this okay and uh what I'd like you + + align:start position:0% +I get this okay and uh what I'd like you + + + align:start position:0% +I get this okay and uh what I'd like you +to do is uh think about it yourselves + + align:start position:0% +to do is uh think about it yourselves + + + align:start position:0% +to do is uh think about it yourselves +what I'm given is something like this + + align:start position:0% +what I'm given is something like this + + + align:start position:0% +what I'm given is something like this +think about yourself you know what would + + align:start position:0% +think about yourself you know what would + + + align:start position:0% +think about yourself you know what would +you do um see if you can come come to me + + align:start position:0% +you do um see if you can come come to me + + + align:start position:0% +you do um see if you can come come to me +before lecture tomorrow on Thursday and + + align:start position:0% +before lecture tomorrow on Thursday and + + + align:start position:0% +before lecture tomorrow on Thursday and +tell me the answer okay \ No newline at end of file diff --git a/OKAsxiE8ziY.txt b/OKAsxiE8ziY.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b1e851d40b6ff1d8789cdd0c9b89ee5e4a23013 --- /dev/null +++ b/OKAsxiE8ziY.txt @@ -0,0 +1,1907 @@ +align:start position:0% + +because like a lot of the in some sense + + align:start position:0% +because like a lot of the in some sense + + + align:start position:0% +because like a lot of the in some sense +like the emerence of cre happened in the + + align:start position:0% +like the emerence of cre happened in the + + + align:start position:0% +like the emerence of cre happened in the +last 200 300 I don't know how like 300 + + align:start position:0% +last 200 300 I don't know how like 300 + + + align:start position:0% +last 200 300 I don't know how like 300 +years like four 4 yeah not 17th century + + align:start position:0% +years like four 4 yeah not 17th century + + + align:start position:0% +years like four 4 yeah not 17th century +roughly in Haiti is there any other + + align:start position:0% +roughly in Haiti is there any other + + + align:start position:0% +roughly in Haiti is there any other +language that are not Crees that like we + + align:start position:0% +language that are not Crees that like we + + + align:start position:0% +language that are not Crees that like we +know developed in this + + align:start position:0% +know developed in this + + + align:start position:0% +know developed in this +like in the last 400 years like well if + + align:start position:0% +like in the last 400 years like well if + + + align:start position:0% +like in the last 400 years like well if +what I'm saying is is right then then + + align:start position:0% +what I'm saying is is right then then + + + align:start position:0% +what I'm saying is is right then then +yeah so so then well English itself + + align:start position:0% +yeah so so then well English itself + + + align:start position:0% +yeah so so then well English itself +Modern English has developed not that + + align:start position:0% +Modern English has developed not that + + + align:start position:0% +Modern English has developed not that +long ago right because Middle English + + align:start position:0% +long ago right because Middle English + + + align:start position:0% +long ago right because Middle English +was up to 14 15 16th Century Modern + + align:start position:0% +was up to 14 15 16th Century Modern + + + align:start position:0% +was up to 14 15 16th Century Modern +English that developing in the 16th + + align:start position:0% +English that developing in the 16th + + + align:start position:0% +English that developing in the 16th +century 17th century English the way we + + align:start position:0% +century 17th century English the way we + + + align:start position:0% +century 17th century English the way we +know it so that that that variety of + + align:start position:0% +know it so that that that variety of + + + align:start position:0% +know it so that that that variety of +English is relatively much younger than + + align:start position:0% +English is relatively much younger than + + + align:start position:0% +English is relatively much younger than +than what Cher spoke right so so so + + align:start position:0% +than what Cher spoke right so so so + + + align:start position:0% +than what Cher spoke right so so so +right there is a notion of uh the fact + + align:start position:0% +right there is a notion of uh the fact + + + align:start position:0% +right there is a notion of uh the fact +that we we call English + + align:start position:0% +that we we call English + + + align:start position:0% +that we we call English +English can be an illusion because + + align:start position:0% +English can be an illusion because + + + align:start position:0% +English can be an illusion because +there's been many englishes throughout + + align:start position:0% +there's been many englishes throughout + + + align:start position:0% +there's been many englishes throughout +throughout the centuries if we focus on + + align:start position:0% +throughout the centuries if we focus on + + + align:start position:0% +throughout the centuries if we focus on +English as a broader umbrella then of + + align:start position:0% +English as a broader umbrella then of + + + align:start position:0% +English as a broader umbrella then of +course it's old but if we focus on + + align:start position:0% +course it's old but if we focus on + + + align:start position:0% +course it's old but if we focus on +English as we speak it now it's + + align:start position:0% +English as we speak it now it's + + + align:start position:0% +English as we speak it now it's +relatively recent so even that might not + + align:start position:0% +relatively recent so even that might not + + + align:start position:0% +relatively recent so even that might not +make the the right cut between say and + + align:start position:0% +make the the right cut between say and + + + align:start position:0% +make the the right cut between say and +actually sign languages did you mention + + align:start position:0% +actually sign languages did you mention + + + align:start position:0% +actually sign languages did you mention +sign languages yes yeah + + align:start position:0% +sign languages yes yeah + + + align:start position:0% +sign languages yes yeah +yeah in some sense like maybe like maybe + + align:start position:0% +yeah in some sense like maybe like maybe + + + align:start position:0% +yeah in some sense like maybe like maybe +like part of the bias like could be + + align:start position:0% +like part of the bias like could be + + + align:start position:0% +like part of the bias like could be +like like uh even the first in like the + + align:start position:0% +like like uh even the first in like the + + + align:start position:0% +like like uh even the first in like the +first hatian like I don't know like I + + align:start position:0% +first hatian like I don't know like I + + + align:start position:0% +first hatian like I don't know like I +mean at some point like we we we saying + + align:start position:0% +mean at some point like we we we saying + + + align:start position:0% +mean at some point like we we we saying +that hian c is a separate language from + + align:start position:0% +that hian c is a separate language from + + + align:start position:0% +that hian c is a separate language from +French so like at some point like there + + align:start position:0% +French so like at some point like there + + + align:start position:0% +French so like at some point like there +was a there was a break yeah yeah like + + align:start position:0% +was a there was a break yeah yeah like + + + align:start position:0% +was a there was a break yeah yeah like +the the first instance that we consider + + align:start position:0% +the the first instance that we consider + + + align:start position:0% +the the first instance that we consider +this like a different language like + + align:start position:0% +this like a different language like + + + align:start position:0% +this like a different language like +happened veryy recently that's right + + align:start position:0% +happened veryy recently that's right + + + align:start position:0% +happened veryy recently that's right +that's right yeah so like I was + + align:start position:0% +that's right yeah so like I was + + + align:start position:0% +that's right yeah so like I was +wondering if like U Can I to give more + + align:start position:0% +wondering if like U Can I to give more + + + align:start position:0% +wondering if like U Can I to give more +evidence that this bias could be racial + + align:start position:0% +evidence that this bias could be racial + + + align:start position:0% +evidence that this bias could be racial +um is there any other language that like + + align:start position:0% +um is there any other language that like + + + align:start position:0% +um is there any other language that like +we know has merged fairly recently and + + align:start position:0% +we know has merged fairly recently and + + + align:start position:0% +we know has merged fairly recently and +like see how they treat that differently + + align:start position:0% +like see how they treat that differently + + + align:start position:0% +like see how they treat that differently +compared to K well Spanglish you + + align:start position:0% +compared to K well Spanglish you + + + align:start position:0% +compared to K well Spanglish you +mentioned Spanglish right one could say + + align:start position:0% +mentioned Spanglish right one could say + + + align:start position:0% +mentioned Spanglish right one could say +that Spanglish might be even younger + + align:start position:0% +that Spanglish might be even younger + + + align:start position:0% +that Spanglish might be even younger +right a lot it's + + align:start position:0% +right a lot it's + + + align:start position:0% +right a lot it's +not maybe 30 40 yeah but it's + + align:start position:0% +not maybe 30 40 yeah but it's + + + align:start position:0% +not maybe 30 40 yeah but it's +it's but the thing is it's not + + align:start position:0% +it's but the thing is it's not + + + align:start position:0% +it's but the thing is it's not +considered a language well actually it + + align:start position:0% +considered a language well actually it + + + align:start position:0% +considered a language well actually it +it's changing I I heard recently that um + + align:start position:0% +it's changing I I heard recently that um + + + align:start position:0% +it's changing I I heard recently that um +at some University on the west coast in + + align:start position:0% +at some University on the west coast in + + + align:start position:0% +at some University on the west coast in +fact I was told that by uh Fran parasa + + align:start position:0% +fact I was told that by uh Fran parasa + + + align:start position:0% +fact I was told that by uh Fran parasa +she she told she told us I me and N + + align:start position:0% +she she told she told us I me and N + + + align:start position:0% +she she told she told us I me and N +chumsky had an interview with with n and + + align:start position:0% +chumsky had an interview with with n and + + + align:start position:0% +chumsky had an interview with with n and +she gave us the news that is at + + align:start position:0% +she gave us the news that is at + + + align:start position:0% +she gave us the news that is at +University we going to start teaching + + align:start position:0% +University we going to start teaching + + + align:start position:0% +University we going to start teaching +Spanglish as a language do you know + + align:start position:0% +Spanglish as a language do you know + + + align:start position:0% +Spanglish as a language do you know +which one you know I have to listen to + + align:start position:0% +which one you know I have to listen to + + + align:start position:0% +which one you know I have to listen to +the interview again she did tell us but + + align:start position:0% +the interview again she did tell us but + + + align:start position:0% +the interview again she did tell us but +I don't remember which one but it's it's + + align:start position:0% +I don't remember which one but it's it's + + + align:start position:0% +I don't remember which one but it's it's +it's the first it's the first in the + + align:start position:0% +it's the first it's the first in the + + + align:start position:0% +it's the first it's the first in the +history of Spanglish you know final + + align:start position:0% +history of Spanglish you know final + + + align:start position:0% +history of Spanglish you know final +there one University that's that's + + align:start position:0% +there one University that's that's + + + align:start position:0% +there one University that's that's +agreed to teach Spanglish as a language + + align:start position:0% +agreed to teach Spanglish as a language + + + align:start position:0% +agreed to teach Spanglish as a language +you know and and I think that's it's not + + align:start position:0% +you know and and I think that's it's not + + + align:start position:0% +you know and and I think that's it's not +that's remarkable right yeah awesome but + + align:start position:0% +that's remarkable right yeah awesome but + + + align:start position:0% +that's remarkable right yeah awesome but +it's not what um is talking about just + + align:start position:0% +it's not what um is talking about just + + + align:start position:0% +it's not what um is talking about just +because English and Spanish were + + align:start position:0% +because English and Spanish were + + + align:start position:0% +because English and Spanish were +somewhat prestigious languages in and of + + align:start position:0% +somewhat prestigious languages in and of + + + align:start position:0% +somewhat prestigious languages in and of +themselves and like the whole point of + + align:start position:0% +themselves and like the whole point of + + + align:start position:0% +themselves and like the whole point of +CR is that it's like not prestigious + + align:start position:0% +CR is that it's like not prestigious + + + align:start position:0% +CR is that it's like not prestigious +plus prestigious yeah not like so I have + + align:start position:0% +plus prestigious yeah not like so I have + + + align:start position:0% +plus prestigious yeah not like so I have +to think cuz like I at the same time I + + align:start position:0% +to think cuz like I at the same time I + + + align:start position:0% +to think cuz like I at the same time I +know like I don't want to I have to like + + align:start position:0% +know like I don't want to I have to like + + + align:start position:0% +know like I don't want to I have to like +like cuz like I know there's a lot of + + align:start position:0% +like cuz like I know there's a lot of + + + align:start position:0% +like cuz like I know there's a lot of +people in hes who like them themselves + + align:start position:0% +people in hes who like them themselves + + + align:start position:0% +people in hes who like them themselves +don't think language yeah so like maybe + + align:start position:0% +don't think language yeah so like maybe + + + align:start position:0% +don't think language yeah so like maybe +I'm like being like Oh Spanish is not + + align:start position:0% +I'm like being like Oh Spanish is not + + + align:start position:0% +I'm like being like Oh Spanish is not +langage like I don't want + + align:start position:0% +langage like I don't want + + + align:start position:0% +langage like I don't want +to but in some s like it is like the + + align:start position:0% +to but in some s like it is like the + + + align:start position:0% +to but in some s like it is like the +like it's like when people speak like + + align:start position:0% +like it's like when people speak like + + + align:start position:0% +like it's like when people speak like +it's because it's you know two languages + + align:start position:0% +it's because it's you know two languages + + + align:start position:0% +it's because it's you know two languages +and you're just like you like purposely + + align:start position:0% +and you're just like you like purposely + + + align:start position:0% +and you're just like you like purposely +mix them because like it's convenient + + align:start position:0% +mix them because like it's convenient + + + align:start position:0% +mix them because like it's convenient +but like I feel like nobody would say + + align:start position:0% +but like I feel like nobody would say + + + align:start position:0% +but like I feel like nobody would say +that that is a like you know but + + align:start position:0% +that that is a like you know but + + + align:start position:0% +that that is a like you know but +actually language that emerg like that + + align:start position:0% +actually language that emerg like that + + + align:start position:0% +actually language that emerg like that +so in in Canada there is a language + + align:start position:0% +so in in Canada there is a language + + + align:start position:0% +so in in Canada there is a language +called mief mief is + + align:start position:0% +called mief mief is + + + align:start position:0% +called mief mief is +also uh a mix of of French and some + + align:start position:0% +also uh a mix of of French and some + + + align:start position:0% +also uh a mix of of French and some +agunan language there's one in in the in + + align:start position:0% +agunan language there's one in in the in + + + align:start position:0% +agunan language there's one in in the in +the Indies called media langa in fact + + align:start position:0% +the Indies called media langa in fact + + + align:start position:0% +the Indies called media langa in fact +even the name tells you that it's a it's + + align:start position:0% +even the name tells you that it's a it's + + + align:start position:0% +even the name tells you that it's a it's +a mix of the same sort right you know + + align:start position:0% +a mix of the same sort right you know + + + align:start position:0% +a mix of the same sort right you know +it's called media langua what's media + + align:start position:0% +it's called media langua what's media + + + align:start position:0% +it's called media langua what's media +langua it's a mix between Spanish and + + align:start position:0% +langua it's a mix between Spanish and + + + align:start position:0% +langua it's a mix between Spanish and +ketua you see so so and and and media + + align:start position:0% +ketua you see so so and and and media + + + align:start position:0% +ketua you see so so and and and media +langua is now it's the language of the + + align:start position:0% +langua is now it's the language of the + + + align:start position:0% +langua is now it's the language of the +community + + align:start position:0% +community + + + align:start position:0% +community +you know and actually that case is very + + align:start position:0% +you know and actually that case is very + + + align:start position:0% +you know and actually that case is very +interesting actually because medua was + + align:start position:0% +interesting actually because medua was + + + align:start position:0% +interesting actually because medua was +created really Midway because you had + + align:start position:0% +created really Midway because you had + + + align:start position:0% +created really Midway because you had +the in the valley you had the rich + + align:start position:0% +the in the valley you had the rich + + + align:start position:0% +the in the valley you had the rich +colonizers the Spanish people and in the + + align:start position:0% +colonizers the Spanish people and in the + + + align:start position:0% +colonizers the Spanish people and in the +in the top of the mountains you had the + + align:start position:0% +in the top of the mountains you had the + + + align:start position:0% +in the top of the mountains you had the +Keta speakers and then in between you + + align:start position:0% +Keta speakers and then in between you + + + align:start position:0% +Keta speakers and then in between you +had these people were in terms of the + + align:start position:0% +had these people were in terms of the + + + align:start position:0% +had these people were in terms of the +social class in the in the as a mid in + + align:start position:0% +social class in the in the as a mid in + + + align:start position:0% +social class in the in the as a mid in +the midpoint between the rich Spaniards + + align:start position:0% +the midpoint between the rich Spaniards + + + align:start position:0% +the midpoint between the rich Spaniards +and the oppressed ketua speakers and and + + align:start position:0% +and the oppressed ketua speakers and and + + + align:start position:0% +and the oppressed ketua speakers and and +they bless you and they Dev media langua + + align:start position:0% +they bless you and they Dev media langua + + + align:start position:0% +they bless you and they Dev media langua +as a as a way to show that they were + + align:start position:0% +as a as a way to show that they were + + + align:start position:0% +as a as a way to show that they were +different that they were not exactly + + align:start position:0% +different that they were not exactly + + + align:start position:0% +different that they were not exactly +like the Keta speakers but they were not + + align:start position:0% +like the Keta speakers but they were not + + + align:start position:0% +like the Keta speakers but they were not +at this at the level yet of the Spanish + + align:start position:0% +at this at the level yet of the Spanish + + + align:start position:0% +at this at the level yet of the Spanish +speakers and they use that mixing of of + + align:start position:0% +speakers and they use that mixing of of + + + align:start position:0% +speakers and they use that mixing of of +so at first one could imagine that at + + align:start position:0% +so at first one could imagine that at + + + align:start position:0% +so at first one could imagine that at +first you know people would say well + + align:start position:0% +first you know people would say well + + + align:start position:0% +first you know people would say well +it's on the language right it's just + + align:start position:0% +it's on the language right it's just + + + align:start position:0% +it's on the language right it's just +that this random mix of kitua words and + + align:start position:0% +that this random mix of kitua words and + + + align:start position:0% +that this random mix of kitua words and +and Spanish words but now media langua + + align:start position:0% +and Spanish words but now media langua + + + align:start position:0% +and Spanish words but now media langua +is a language spoken by a community of + + align:start position:0% +is a language spoken by a community of + + + align:start position:0% +is a language spoken by a community of +of people who at first were bilingual + + align:start position:0% +of people who at first were bilingual + + + align:start position:0% +of people who at first were bilingual +but now they're the main language is + + align:start position:0% +but now they're the main language is + + + align:start position:0% +but now they're the main language is +ketua is is medua it's like with with + + align:start position:0% +ketua is is medua it's like with with + + + align:start position:0% +ketua is is medua it's like with with +like when you combine English and such + + align:start position:0% +like when you combine English and such + + + align:start position:0% +like when you combine English and such +like that's how it feel like it doesn't + + align:start position:0% +like that's how it feel like it doesn't + + + align:start position:0% +like that's how it feel like it doesn't +feel like like it exactly feels like + + align:start position:0% +feel like like it exactly feels like + + + align:start position:0% +feel like like it exactly feels like +you're like sometimes i' say like uh + + align:start position:0% +you're like sometimes i' say like uh + + + align:start position:0% +you're like sometimes i' say like uh +like I like I really only combine + + align:start position:0% +like I like I really only combine + + + align:start position:0% +like I like I really only combine +English and Spanish when I know the + + align:start position:0% +English and Spanish when I know the + + + align:start position:0% +English and Spanish when I know the +other person like feels most comfortable + + align:start position:0% +other person like feels most comfortable + + + align:start position:0% +other person like feels most comfortable +speaking that like uh it's like it just + + align:start position:0% +speaking that like uh it's like it just + + + align:start position:0% +speaking that like uh it's like it just +like so so I think you so say you'll be + + align:start position:0% +like so so I think you so say you'll be + + + align:start position:0% +like so so I think you so say you'll be +interested to read about the history of + + align:start position:0% +interested to read about the history of + + + align:start position:0% +interested to read about the history of +mea because I think what you're + + align:start position:0% +mea because I think what you're + + + align:start position:0% +mea because I think what you're +describing in terms of that feeling that + + align:start position:0% +describing in terms of that feeling that + + + align:start position:0% +describing in terms of that feeling that +you know both and that you're speaking + + align:start position:0% +you know both and that you're speaking + + + align:start position:0% +you know both and that you're speaking +to someone who can understand both + + align:start position:0% +to someone who can understand both + + + align:start position:0% +to someone who can understand both +that's what it's been described by + + align:start position:0% +that's what it's been described by + + + align:start position:0% +that's what it's been described by +people who've looked at so so so the key + + align:start position:0% +people who've looked at so so so the key + + + align:start position:0% +people who've looked at so so so the key +language here that you should look at + + align:start position:0% +language here that you should look at + + + align:start position:0% +language here that you should look at +his name is um his name is p uh let me + + align:start position:0% +his name is um his name is p uh let me + + + align:start position:0% +his name is um his name is p uh let me +Peter + + align:start position:0% + + + + align:start position:0% + +Morin okay so so look up Peter moin yeah + + align:start position:0% +Morin okay so so look up Peter moin yeah + + + align:start position:0% +Morin okay so so look up Peter moin yeah +okay so it was some beautiful work + + align:start position:0% +okay so it was some beautiful work + + + align:start position:0% +okay so it was some beautiful work +describing uh the origins the structures + + align:start position:0% +describing uh the origins the structures + + + align:start position:0% +describing uh the origins the structures +of media langua and then and then you + + align:start position:0% +of media langua and then and then you + + + align:start position:0% +of media langua and then and then you +have to do as you read that ask yourself + + align:start position:0% +have to do as you read that ask yourself + + + align:start position:0% +have to do as you read that ask yourself +about is he describing what I feel now + + align:start position:0% +about is he describing what I feel now + + + align:start position:0% +about is he describing what I feel now +when I speak Spanglish I don't know what + + align:start position:0% +when I speak Spanglish I don't know what + + + align:start position:0% +when I speak Spanglish I don't know what +the the answer is but that's what brings + + align:start position:0% +the the answer is but that's what brings + + + align:start position:0% +the the answer is but that's what brings +comes to my mind as you describe + + align:start position:0% +comes to my mind as you describe + + + align:start position:0% +comes to my mind as you describe +Spanglish I think of media langua like + + align:start position:0% +Spanglish I think of media langua like + + + align:start position:0% +Spanglish I think of media langua like +it like it like for example like most + + align:start position:0% +it like it like for example like most + + + align:start position:0% +it like it like for example like most +Mexicans like don't identify too much + + align:start position:0% +Mexicans like don't identify too much + + + align:start position:0% +Mexicans like don't identify too much +with like the use of Spanish Spanglish + + align:start position:0% +with like the use of Spanish Spanglish + + + align:start position:0% +with like the use of Spanish Spanglish +like it's more like well that's exactly + + align:start position:0% +like it's more like well that's exactly + + + align:start position:0% +like it's more like well that's exactly +that's exactly the way this was created + + align:start position:0% +that's exactly the way this was created + + + align:start position:0% +that's exactly the way this was created +because Meda the speakers wanted to + + align:start position:0% +because Meda the speakers wanted to + + + align:start position:0% +because Meda the speakers wanted to +create a new identity for them talking + + align:start position:0% +create a new identity for them talking + + + align:start position:0% +create a new identity for them talking +about identity see that they didn't only + + align:start position:0% +about identity see that they didn't only + + + align:start position:0% +about identity see that they didn't only +see themselves as if they were purely + + align:start position:0% +see themselves as if they were purely + + + align:start position:0% +see themselves as if they were purely +ketua speakers nor were they Europeans + + align:start position:0% +ketua speakers nor were they Europeans + + + align:start position:0% +ketua speakers nor were they Europeans +so they wanted to create this middle + + align:start position:0% +so they wanted to create this middle + + + align:start position:0% +so they wanted to create this middle +this compromise between the two + + align:start position:0% +this compromise between the two + + + align:start position:0% +this compromise between the two +identities and they use that mix of of + + align:start position:0% +identities and they use that mix of of + + + align:start position:0% +identities and they use that mix of of +ketua and and Spanish to to create a new + + align:start position:0% +ketua and and Spanish to to create a new + + + align:start position:0% +ketua and and Spanish to to create a new +Badge of identity so so I now I don't + + align:start position:0% +Badge of identity so so I now I don't + + + align:start position:0% +Badge of identity so so I now I don't +know whether that is the same thing for + + align:start position:0% +know whether that is the same thing for + + + align:start position:0% +know whether that is the same thing for +Spanglish but but from what you describe + + align:start position:0% +Spanglish but but from what you describe + + + align:start position:0% +Spanglish but but from what you describe +it sounds interestingly reminiscent to + + align:start position:0% +it sounds interestingly reminiscent to + + + align:start position:0% +it sounds interestingly reminiscent to +that story you may have just touched on + + align:start position:0% +that story you may have just touched on + + + align:start position:0% +that story you may have just touched on +it U but I was going to ask if he's if + + align:start position:0% +it U but I was going to ask if he's if + + + align:start position:0% +it U but I was going to ask if he's if +uh he's talking about how Spanish + + align:start position:0% +uh he's talking about how Spanish + + + align:start position:0% +uh he's talking about how Spanish +speakers and English speakers + + align:start position:0% +speakers and English speakers + + + align:start position:0% +speakers and English speakers +don't Mexican don't identify with + + align:start position:0% +don't Mexican don't identify with + + + align:start position:0% +don't Mexican don't identify with +Spanglish and and they don't speak it + + align:start position:0% +Spanglish and and they don't speak it + + + align:start position:0% +Spanglish and and they don't speak it +but is that is that how these speakers + + align:start position:0% +but is that is that how these speakers + + + align:start position:0% +but is that is that how these speakers +of French in alanin yeah me Chief is + + align:start position:0% +of French in alanin yeah me Chief is + + + align:start position:0% +of French in alanin yeah me Chief is +that how they felt in development of + + align:start position:0% +that how they felt in development of + + + align:start position:0% +that how they felt in development of +that language well I think so so so + + align:start position:0% +that language well I think so so so + + + align:start position:0% +that language well I think so so so +right so there yeah so so so in the + + align:start position:0% +right so there yeah so so so in the + + + align:start position:0% +right so there yeah so so so in the +history waying own right right so in get + + align:start position:0% +history waying own right right so in get + + + align:start position:0% +history waying own right right so in get +cut so I think the history of Mischief + + align:start position:0% +cut so I think the history of Mischief + + + align:start position:0% +cut so I think the history of Mischief +has another twist which is that there + + align:start position:0% +has another twist which is that there + + + align:start position:0% +has another twist which is that there +was a gender issue I think there were an + + align:start position:0% +was a gender issue I think there were an + + + align:start position:0% +was a gender issue I think there were an +issue of um there were aonan women um + + align:start position:0% +issue of um there were aonan women um + + + align:start position:0% +issue of um there were aonan women um +meeting with uh French French speakers + + align:start position:0% +meeting with uh French French speakers + + + align:start position:0% +meeting with uh French French speakers +so so there is another aspect that's + + align:start position:0% +so so there is another aspect that's + + + align:start position:0% +so so there is another aspect that's +that's not part of neither Spanglish nor + + align:start position:0% +that's not part of neither Spanglish nor + + + align:start position:0% +that's not part of neither Spanglish nor +nor media langua which is the gender the + + align:start position:0% +nor media langua which is the gender the + + + align:start position:0% +nor media langua which is the gender the +gender part of it having to do with um + + align:start position:0% +gender part of it having to do with um + + + align:start position:0% +gender part of it having to do with um +know who spoke Alon and who spoke French + + align:start position:0% +know who spoke Alon and who spoke French + + + align:start position:0% +know who spoke Alon and who spoke French +and and it was mostly women who spoke + + align:start position:0% +and and it was mostly women who spoke + + + align:start position:0% +and and it was mostly women who spoke +Alon + + align:start position:0% +Alon + + + align:start position:0% +Alon +and okay okay go ahead + + align:start position:0% +and okay okay go ahead + + + align:start position:0% +and okay okay go ahead +this I feel like there are certain + + align:start position:0% +this I feel like there are certain + + + align:start position:0% +this I feel like there are certain +dialects of Spanish that in some ways + + align:start position:0% +dialects of Spanish that in some ways + + + align:start position:0% +dialects of Spanish that in some ways +use Spanglish like legitimately like + + align:start position:0% +use Spanglish like legitimately like + + + align:start position:0% +use Spanglish like legitimately like +maybe that's how it be like that which + + align:start position:0% +maybe that's how it be like that which + + + align:start position:0% +maybe that's how it be like that which +is like not how you actually say to like + + align:start position:0% +is like not how you actually say to like + + + align:start position:0% +is like not how you actually say to like +park a car but like that's that would be + + align:start position:0% +park a car but like that's that would be + + + align:start position:0% +park a car but like that's that would be +like considered Spanglish wouldn't it + + align:start position:0% +like considered Spanglish wouldn't it + + + align:start position:0% +like considered Spanglish wouldn't it +like it's + + align:start position:0% +like it's + + + align:start position:0% +like it's +combination I don't know if it's like + + align:start position:0% +combination I don't know if it's like + + + align:start position:0% +combination I don't know if it's like +for example I'm from like the Border + + align:start position:0% +for example I'm from like the Border + + + align:start position:0% +for example I'm from like the Border +like in like we definitely use like like + + align:start position:0% +like in like we definitely use like like + + + align:start position:0% +like in like we definitely use like like +I'm from I'm from SE like exactly the + + align:start position:0% +I'm from I'm from SE like exactly the + + + align:start position:0% +I'm from I'm from SE like exactly the +and like we definitely use a lot of + + align:start position:0% +and like we definitely use a lot of + + + align:start position:0% +and like we definitely use a lot of +words that like have English origin like + + align:start position:0% +words that like have English origin like + + + align:start position:0% +words that like have English origin like +par like yeah like there like tra we use + + align:start position:0% +par like yeah like there like tra we use + + + align:start position:0% +par like yeah like there like tra we use +tra instead OFA H tra I didn't know that + + align:start position:0% +tra instead OFA H tra I didn't know that + + + align:start position:0% +tra instead OFA H tra I didn't know that +was like the origin until like I was + + align:start position:0% +was like the origin until like I was + + + align:start position:0% +was like the origin until like I was +like 17 18 for me so you using tra + + align:start position:0% +like 17 18 for me so you using tra + + + align:start position:0% +like 17 18 for me so you using tra +without knowing that it was yeah yeah + + align:start position:0% +without knowing that it was yeah yeah + + + align:start position:0% +without knowing that it was yeah yeah +and like because it doesn't feel like an + + align:start position:0% +and like because it doesn't feel like an + + + align:start position:0% +and like because it doesn't feel like an +English you just tra yeah you're like + + align:start position:0% +English you just tra yeah you're like + + + align:start position:0% +English you just tra yeah you're like +okay of course that's like a Spanish + + align:start position:0% +okay of course that's like a Spanish + + + align:start position:0% +okay of course that's like a Spanish +word um it doesn't feel like it it just + + align:start position:0% +word um it doesn't feel like it it just + + + align:start position:0% +word um it doesn't feel like it it just +feels like you're borrowing words or + + align:start position:0% +feels like you're borrowing words or + + + align:start position:0% +feels like you're borrowing words or +like they're like more than like + + align:start position:0% +like they're like more than like + + + align:start position:0% +like they're like more than like +something independent you like sometimes + + align:start position:0% +something independent you like sometimes + + + align:start position:0% +something independent you like sometimes +I like I know like like I only really + + align:start position:0% +I like I know like like I only really + + + align:start position:0% +I like I know like like I only really +like combine English and Spanish when + + align:start position:0% +like combine English and Spanish when + + + align:start position:0% +like combine English and Spanish when +I'm speaking with somebody who like the + + align:start position:0% +I'm speaking with somebody who like the + + + align:start position:0% +I'm speaking with somebody who like the +Baseline is English but like I kind of + + align:start position:0% +Baseline is English but like I kind of + + + align:start position:0% +Baseline is English but like I kind of +have to alate but right I don't know it + + align:start position:0% +have to alate but right I don't know it + + + align:start position:0% +have to alate but right I don't know it +doesn't like I don't know okay so that + + align:start position:0% +doesn't like I don't know okay so that + + + align:start position:0% +doesn't like I don't know okay so that +could be an interesting research project + + align:start position:0% +could be an interesting research project + + + align:start position:0% +could be an interesting research project +because in this case you would be your + + align:start position:0% +because in this case you would be your + + + align:start position:0% +because in this case you would be your +own subject right so I think that's + + align:start position:0% +own subject right so I think that's + + + align:start position:0% +own subject right so I think that's +that's a fascinating question that you + + align:start position:0% +that's a fascinating question that you + + + align:start position:0% +that's a fascinating question that you +could ask \ No newline at end of file diff --git a/OWAEr2egtsI.txt b/OWAEr2egtsI.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ef09270a53a5adfbc8a2a0096f274fed786a26c --- /dev/null +++ b/OWAEr2egtsI.txt @@ -0,0 +1,1459 @@ +align:start position:0% + +let's take a brief look at how to think + + align:start position:0% +let's take a brief look at how to think + + + align:start position:0% +let's take a brief look at how to think +about submitting your photographs as + + align:start position:0% +about submitting your photographs as + + + align:start position:0% +about submitting your photographs as +potential cover art in their + + align:start position:0% +potential cover art in their + + + align:start position:0% +potential cover art in their +presentations the first thing that's + + align:start position:0% +presentations the first thing that's + + + align:start position:0% +presentations the first thing that's +essential is for you to study the + + align:start position:0% +essential is for you to study the + + + align:start position:0% +essential is for you to study the +journal layout to which you are + + align:start position:0% +journal layout to which you are + + + align:start position:0% +journal layout to which you are +submitting your image how they might be + + align:start position:0% +submitting your image how they might be + + + align:start position:0% +submitting your image how they might be +placed in the particular cover format + + align:start position:0% +placed in the particular cover format + + + align:start position:0% +placed in the particular cover format +most covers these days are full bleeds + + align:start position:0% +most covers these days are full bleeds + + + align:start position:0% +most covers these days are full bleeds +that is the image takes up the whole + + align:start position:0% +that is the image takes up the whole + + + align:start position:0% +that is the image takes up the whole +cover and is therefore vertical some of + + align:start position:0% +cover and is therefore vertical some of + + + align:start position:0% +cover and is therefore vertical some of +them still have let's say rectangle + + align:start position:0% +them still have let's say rectangle + + + align:start position:0% +them still have let's say rectangle +places within the larger vertical format + + align:start position:0% +places within the larger vertical format + + + align:start position:0% +places within the larger vertical format +but most of them are bleeds at this + + align:start position:0% +but most of them are bleeds at this + + + align:start position:0% +but most of them are bleeds at this +point so you have to think about that + + align:start position:0% +point so you have to think about that + + + align:start position:0% +point so you have to think about that +when you do submit an idea for a cover + + align:start position:0% +when you do submit an idea for a cover + + + align:start position:0% +when you do submit an idea for a cover +think about where the journals logo is + + align:start position:0% +think about where the journals logo is + + + align:start position:0% +think about where the journals logo is +placed where additional text might be + + align:start position:0% +placed where additional text might be + + + align:start position:0% +placed where additional text might be +dropped you have to take all these + + align:start position:0% +dropped you have to take all these + + + align:start position:0% +dropped you have to take all these +things into consideration to help the + + align:start position:0% +things into consideration to help the + + + align:start position:0% +things into consideration to help the +art director decide whether or not the + + align:start position:0% +art director decide whether or not the + + + align:start position:0% +art director decide whether or not the +image is good enough for a cover but I + + align:start position:0% +image is good enough for a cover but I + + + align:start position:0% +image is good enough for a cover but I +do suggest not submitting a cover idea + + align:start position:0% +do suggest not submitting a cover idea + + + align:start position:0% +do suggest not submitting a cover idea +with the journal logo just let the folks + + align:start position:0% +with the journal logo just let the folks + + + align:start position:0% +with the journal logo just let the folks +at the journal use their imaginations + + align:start position:0% +at the journal use their imaginations + + + align:start position:0% +at the journal use their imaginations +let's start with something I did fairly + + align:start position:0% +let's start with something I did fairly + + + align:start position:0% +let's start with something I did fairly +recently here I was given a number of + + align:start position:0% +recently here I was given a number of + + + align:start position:0% +recently here I was given a number of +samples of material they're all + + align:start position:0% +samples of material they're all + + + align:start position:0% +samples of material they're all +fabricated pieces that respond + + align:start position:0% +fabricated pieces that respond + + + align:start position:0% +fabricated pieces that respond +differently to pressure trying to think + + align:start position:0% +differently to pressure trying to think + + + align:start position:0% +differently to pressure trying to think +of how in the world i was going to come + + align:start position:0% +of how in the world i was going to come + + + align:start position:0% +of how in the world i was going to come +up with an interesting cover design so i + + align:start position:0% +up with an interesting cover design so i + + + align:start position:0% +up with an interesting cover design so i +decided to play around with the shapes + + align:start position:0% +decided to play around with the shapes + + + align:start position:0% +decided to play around with the shapes +here i'm using my flatbed scanner and + + align:start position:0% +here i'm using my flatbed scanner and + + + align:start position:0% +here i'm using my flatbed scanner and +i'm adding a few pieces here and there + + align:start position:0% +i'm adding a few pieces here and there + + + align:start position:0% +i'm adding a few pieces here and there +and finally wound up with this + + align:start position:0% +and finally wound up with this + + + align:start position:0% +and finally wound up with this +composition which i thought had the + + align:start position:0% +composition which i thought had the + + + align:start position:0% +composition which i thought had the +potential of being considered for this + + align:start position:0% +potential of being considered for this + + + align:start position:0% +potential of being considered for this +particular journal cover and I did + + align:start position:0% +particular journal cover and I did + + + align:start position:0% +particular journal cover and I did +digitally add a gradient to the + + align:start position:0% +digitally add a gradient to the + + + align:start position:0% +digitally add a gradient to the +background as you can see in the end yes + + align:start position:0% +background as you can see in the end yes + + + align:start position:0% +background as you can see in the end yes +it did make a cover which is always nice + + align:start position:0% +it did make a cover which is always nice + + + align:start position:0% +it did make a cover which is always nice +but do keep in mind it's not just the + + align:start position:0% +but do keep in mind it's not just the + + + align:start position:0% +but do keep in mind it's not just the +image that will get you on the cover + + align:start position:0% +image that will get you on the cover + + + align:start position:0% +image that will get you on the cover +it's the science in the article that + + align:start position:0% +it's the science in the article that + + + align:start position:0% +it's the science in the article that +informs the journal selection maybe some + + align:start position:0% +informs the journal selection maybe some + + + align:start position:0% +informs the journal selection maybe some +other things as well which none of us + + align:start position:0% +other things as well which none of us + + + align:start position:0% +other things as well which none of us +are privy to so it's not just the + + align:start position:0% +are privy to so it's not just the + + + align:start position:0% +are privy to so it's not just the +aesthetics mostly about the importance + + align:start position:0% +aesthetics mostly about the importance + + + align:start position:0% +aesthetics mostly about the importance +of the research which should be the case + + align:start position:0% +of the research which should be the case + + + align:start position:0% +of the research which should be the case +here's another example which you've seen + + align:start position:0% +here's another example which you've seen + + + align:start position:0% +here's another example which you've seen +before showing the flexible circuitry + + align:start position:0% +before showing the flexible circuitry + + + align:start position:0% +before showing the flexible circuitry +imprinted on transparent material and + + align:start position:0% +imprinted on transparent material and + + + align:start position:0% +imprinted on transparent material and +again we were delighted to get the cover + + align:start position:0% +again we were delighted to get the cover + + + align:start position:0% +again we were delighted to get the cover +of the journal probably because of the + + align:start position:0% +of the journal probably because of the + + + align:start position:0% +of the journal probably because of the +importance of the science and by the way + + align:start position:0% +importance of the science and by the way + + + align:start position:0% +importance of the science and by the way +that journal now has another format + + align:start position:0% +that journal now has another format + + + align:start position:0% +that journal now has another format +where the cover art takes a completely + + align:start position:0% +where the cover art takes a completely + + + align:start position:0% +where the cover art takes a completely +different shape than what you're seeing + + align:start position:0% +different shape than what you're seeing + + + align:start position:0% +different shape than what you're seeing +here so again it's very important to + + align:start position:0% +here so again it's very important to + + + align:start position:0% +here so again it's very important to +match your images format with the + + align:start position:0% +match your images format with the + + + align:start position:0% +match your images format with the +journals format for this image another + + align:start position:0% +journals format for this image another + + + align:start position:0% +journals format for this image another +one that you've seen before it still is + + align:start position:0% +one that you've seen before it still is + + + align:start position:0% +one that you've seen before it still is +one of my favorites after all these + + align:start position:0% +one of my favorites after all these + + + align:start position:0% +one of my favorites after all these +years bit unusual because I don't + + align:start position:0% +years bit unusual because I don't + + + align:start position:0% +years bit unusual because I don't +usually like old stuff but they used it + + align:start position:0% +usually like old stuff but they used it + + + align:start position:0% +usually like old stuff but they used it +for the cover of a textbook in chemistry + + align:start position:0% +for the cover of a textbook in chemistry + + + align:start position:0% +for the cover of a textbook in chemistry +after all this is very very much about + + align:start position:0% +after all this is very very much about + + + align:start position:0% +after all this is very very much about +chemistry and notice how they crop the + + align:start position:0% +chemistry and notice how they crop the + + + align:start position:0% +chemistry and notice how they crop the +image to fit the format and of course I + + align:start position:0% +image to fit the format and of course I + + + align:start position:0% +image to fit the format and of course I +gave the publisher permission to do that + + align:start position:0% +gave the publisher permission to do that + + + align:start position:0% +gave the publisher permission to do that +and here this image was made by the + + align:start position:0% +and here this image was made by the + + + align:start position:0% +and here this image was made by the +researchers hundreds of miles from my + + align:start position:0% +researchers hundreds of miles from my + + + align:start position:0% +researchers hundreds of miles from my +studio but we communicated closely + + align:start position:0% +studio but we communicated closely + + + align:start position:0% +studio but we communicated closely +through email with my making suggestions + + align:start position:0% +through email with my making suggestions + + + align:start position:0% +through email with my making suggestions +on how to photograph and light the word + + align:start position:0% +on how to photograph and light the word + + + align:start position:0% +on how to photograph and light the word +in this next image the researchers + + align:start position:0% +in this next image the researchers + + + align:start position:0% +in this next image the researchers +shined a laser on to the container with + + align:start position:0% +shined a laser on to the container with + + + align:start position:0% +shined a laser on to the container with +no additional room light and we see new + + align:start position:0% +no additional room light and we see new + + + align:start position:0% +no additional room light and we see new +material showing up we couldn't see it + + align:start position:0% +material showing up we couldn't see it + + + align:start position:0% +material showing up we couldn't see it +before because those balls have the same + + align:start position:0% +before because those balls have the same + + + align:start position:0% +before because those balls have the same +index of refraction as the solution in + + align:start position:0% +index of refraction as the solution in + + + align:start position:0% +index of refraction as the solution in +which they were floating that's the + + align:start position:0% +which they were floating that's the + + + align:start position:0% +which they were floating that's the +point of this research the researchers + + align:start position:0% +point of this research the researchers + + + align:start position:0% +point of this research the researchers +wanted to show this image with a hand in + + align:start position:0% +wanted to show this image with a hand in + + + align:start position:0% +wanted to show this image with a hand in +place suggesting that the laser is + + align:start position:0% +place suggesting that the laser is + + + align:start position:0% +place suggesting that the laser is +turned off ready to be turned on and i + + align:start position:0% +turned off ready to be turned on and i + + + align:start position:0% +turned off ready to be turned on and i +said no please no hands I believe that + + align:start position:0% +said no please no hands I believe that + + + align:start position:0% +said no please no hands I believe that +hands generally distract and detract + + align:start position:0% +hands generally distract and detract + + + align:start position:0% +hands generally distract and detract +from the rest of the image it's just + + align:start position:0% +from the rest of the image it's just + + + align:start position:0% +from the rest of the image it's just +another distraction please don't use + + align:start position:0% +another distraction please don't use + + + align:start position:0% +another distraction please don't use +hands so I suggested starting with a + + align:start position:0% +hands so I suggested starting with a + + + align:start position:0% +hands so I suggested starting with a +container under a lamp as before and + + align:start position:0% +container under a lamp as before and + + + align:start position:0% +container under a lamp as before and +then take another picture with just the + + align:start position:0% +then take another picture with just the + + + align:start position:0% +then take another picture with just the +laser shining through the lower part of + + align:start position:0% +laser shining through the lower part of + + + align:start position:0% +laser shining through the lower part of +the image to see the hidden material so + + align:start position:0% +the image to see the hidden material so + + + align:start position:0% +the image to see the hidden material so +this is the first image and this is the + + align:start position:0% +this is the first image and this is the + + + align:start position:0% +this is the first image and this is the +second image I selected the + + align:start position:0% +second image I selected the + + + align:start position:0% +second image I selected the +or part of the second image copied it + + align:start position:0% +or part of the second image copied it + + + align:start position:0% +or part of the second image copied it +and pasted it on to the first image so + + align:start position:0% +and pasted it on to the first image so + + + align:start position:0% +and pasted it on to the first image so +that we have a sort of photo + + align:start position:0% +that we have a sort of photo + + + align:start position:0% +that we have a sort of photo +illustration which you're going to see + + align:start position:0% +illustration which you're going to see + + + align:start position:0% +illustration which you're going to see +more of next week in that we will show + + align:start position:0% +more of next week in that we will show + + + align:start position:0% +more of next week in that we will show +what it is without the laser and what it + + align:start position:0% +what it is without the laser and what it + + + align:start position:0% +what it is without the laser and what it +is with the lasers side by side + + align:start position:0% +is with the lasers side by side + + + align:start position:0% +is with the lasers side by side +comparing the two with the information + + align:start position:0% +comparing the two with the information + + + align:start position:0% +comparing the two with the information +in the caption the idea was to make the + + align:start position:0% +in the caption the idea was to make the + + + align:start position:0% +in the caption the idea was to make the +cover and we did which was nice I think + + align:start position:0% +cover and we did which was nice I think + + + align:start position:0% +cover and we did which was nice I think +it worked well you know some images look + + align:start position:0% +it worked well you know some images look + + + align:start position:0% +it worked well you know some images look +even better when they are made into + + align:start position:0% +even better when they are made into + + + align:start position:0% +even better when they are made into +covers with the addition of text they + + align:start position:0% +covers with the addition of text they + + + align:start position:0% +covers with the addition of text they +might not be spectacular on their own + + align:start position:0% +might not be spectacular on their own + + + align:start position:0% +might not be spectacular on their own +but often in my opinion are enhanced + + align:start position:0% +but often in my opinion are enhanced + + + align:start position:0% +but often in my opinion are enhanced +with well-placed text as what happens + + align:start position:0% +with well-placed text as what happens + + + align:start position:0% +with well-placed text as what happens +here this is not a very exciting image + + align:start position:0% +here this is not a very exciting image + + + align:start position:0% +here this is not a very exciting image +that I made it's a detail of equipment + + align:start position:0% +that I made it's a detail of equipment + + + align:start position:0% +that I made it's a detail of equipment +that's used in this particular lab I was + + align:start position:0% +that's used in this particular lab I was + + + align:start position:0% +that's used in this particular lab I was +delighted that they liked the abstract + + align:start position:0% +delighted that they liked the abstract + + + align:start position:0% +delighted that they liked the abstract +quality of the image and used it well in + + align:start position:0% +quality of the image and used it well in + + + align:start position:0% +quality of the image and used it well in +fact with good placement of text in this + + align:start position:0% +fact with good placement of text in this + + + align:start position:0% +fact with good placement of text in this +image I was working on some print + + align:start position:0% +image I was working on some print + + + align:start position:0% +image I was working on some print +material for what was then called the + + align:start position:0% +material for what was then called the + + + align:start position:0% +material for what was then called the +DuPont MIT Alliance which funded + + align:start position:0% +DuPont MIT Alliance which funded + + + align:start position:0% +DuPont MIT Alliance which funded +research about bio inspired material I + + align:start position:0% +research about bio inspired material I + + + align:start position:0% +research about bio inspired material I +made a picture of a sea urchin which is + + align:start position:0% +made a picture of a sea urchin which is + + + align:start position:0% +made a picture of a sea urchin which is +a fascinating story in itself I made it + + align:start position:0% +a fascinating story in itself I made it + + + align:start position:0% +a fascinating story in itself I made it +straight on I also tried it with the + + align:start position:0% +straight on I also tried it with the + + + align:start position:0% +straight on I also tried it with the +flatbed scanner in the end the very + + align:start position:0% +flatbed scanner in the end the very + + + align:start position:0% +flatbed scanner in the end the very +talented graphic designer he created a + + align:start position:0% +talented graphic designer he created a + + + align:start position:0% +talented graphic designer he created a +pretty stunning brochure place the + + align:start position:0% +pretty stunning brochure place the + + + align:start position:0% +pretty stunning brochure place the +scanner image on the cover and it worked + + align:start position:0% +scanner image on the cover and it worked + + + align:start position:0% +scanner image on the cover and it worked +well in terms of the whole design of the + + align:start position:0% +well in terms of the whole design of the + + + align:start position:0% +well in terms of the whole design of the +brochure and in this image which was + + align:start position:0% +brochure and in this image which was + + + align:start position:0% +brochure and in this image which was +also part of the same project a + + align:start position:0% +also part of the same project a + + + align:start position:0% +also part of the same project a +bioreactor where liver cells grow in + + align:start position:0% +bioreactor where liver cells grow in + + + align:start position:0% +bioreactor where liver cells grow in +three-dimensional space I did like the + + align:start position:0% +three-dimensional space I did like the + + + align:start position:0% +three-dimensional space I did like the +picture as I made it but once again the + + align:start position:0% +picture as I made it but once again the + + + align:start position:0% +picture as I made it but once again the +graphic designer took it to another + + align:start position:0% +graphic designer took it to another + + + align:start position:0% +graphic designer took it to another +level using the image as is and also + + align:start position:0% +level using the image as is and also + + + align:start position:0% +level using the image as is and also +associating it on the page with a + + align:start position:0% +associating it on the page with a + + + align:start position:0% +associating it on the page with a +drawing of the same reactor a very + + align:start position:0% +drawing of the same reactor a very + + + align:start position:0% +drawing of the same reactor a very +interesting way of reinforcing the + + align:start position:0% +interesting way of reinforcing the + + + align:start position:0% +interesting way of reinforcing the +structure for our book no small matter I + + align:start position:0% +structure for our book no small matter I + + + align:start position:0% +structure for our book no small matter I +made a photograph of beer the idea was + + align:start position:0% +made a photograph of beer the idea was + + + align:start position:0% +made a photograph of beer the idea was +to kill + + align:start position:0% +to kill + + + align:start position:0% +to kill +sitter the molecular or nanostructure of + + align:start position:0% +sitter the molecular or nanostructure of + + + align:start position:0% +sitter the molecular or nanostructure of +bubbles now notice that I include the + + align:start position:0% +bubbles now notice that I include the + + + align:start position:0% +bubbles now notice that I include the +wall of the rectangular container in + + align:start position:0% +wall of the rectangular container in + + + align:start position:0% +wall of the rectangular container in +image on the right the final cover + + align:start position:0% +image on the right the final cover + + + align:start position:0% +image on the right the final cover +wrapped the image around the full book + + align:start position:0% +wrapped the image around the full book + + + align:start position:0% +wrapped the image around the full book +and use the container area as the front + + align:start position:0% +and use the container area as the front + + + align:start position:0% +and use the container area as the front +book flap which i think is kind of cool + + align:start position:0% +book flap which i think is kind of cool + + + align:start position:0% +book flap which i think is kind of cool +here's an image you've seen before and + + align:start position:0% +here's an image you've seen before and + + + align:start position:0% +here's an image you've seen before and +here it's used in the title page of the + + align:start position:0% +here it's used in the title page of the + + + align:start position:0% +here it's used in the title page of the +Chinese version of our book no small + + align:start position:0% +Chinese version of our book no small + + + align:start position:0% +Chinese version of our book no small +matter and here's the american title + + align:start position:0% +matter and here's the american title + + + align:start position:0% +matter and here's the american title +page again just showing you how + + align:start position:0% +page again just showing you how + + + align:start position:0% +page again just showing you how +photographs can be used with text once + + align:start position:0% +photographs can be used with text once + + + align:start position:0% +photographs can be used with text once +again dropping text I think can make an + + align:start position:0% +again dropping text I think can make an + + + align:start position:0% +again dropping text I think can make an +okay image which this is of bubbles into + + align:start position:0% +okay image which this is of bubbles into + + + align:start position:0% +okay image which this is of bubbles into +a more interesting cover the left side + + align:start position:0% +a more interesting cover the left side + + + align:start position:0% +a more interesting cover the left side +is the back cover of this booklet I + + align:start position:0% +is the back cover of this booklet I + + + align:start position:0% +is the back cover of this booklet I +think that worked pretty well and this + + align:start position:0% +think that worked pretty well and this + + + align:start position:0% +think that worked pretty well and this +photograph is a straight highly + + align:start position:0% +photograph is a straight highly + + + align:start position:0% +photograph is a straight highly +documentary image showing the presence + + align:start position:0% +documentary image showing the presence + + + align:start position:0% +documentary image showing the presence +of material in an assay and I simply use + + align:start position:0% +of material in an assay and I simply use + + + align:start position:0% +of material in an assay and I simply use +the image in a more expanded idea for a + + align:start position:0% +the image in a more expanded idea for a + + + align:start position:0% +the image in a more expanded idea for a +cover illustratively giving more + + align:start position:0% +cover illustratively giving more + + + align:start position:0% +cover illustratively giving more +information about the material I don't + + align:start position:0% +information about the material I don't + + + align:start position:0% +information about the material I don't +use illustrator very often but in this + + align:start position:0% +use illustrator very often but in this + + + align:start position:0% +use illustrator very often but in this +case it seemed to work and finally here + + align:start position:0% +case it seemed to work and finally here + + + align:start position:0% +case it seemed to work and finally here +is another image you've seen before used + + align:start position:0% +is another image you've seen before used + + + align:start position:0% +is another image you've seen before used +both as a cover and back cover for an + + align:start position:0% +both as a cover and back cover for an + + + align:start position:0% +both as a cover and back cover for an +MIT publication I was quite pleased that + + align:start position:0% +MIT publication I was quite pleased that + + + align:start position:0% +MIT publication I was quite pleased that +the image i made fifteen years ago still + + align:start position:0% +the image i made fifteen years ago still + + + align:start position:0% +the image i made fifteen years ago still +had a life frankly because of the + + align:start position:0% +had a life frankly because of the + + + align:start position:0% +had a life frankly because of the +importance of nanocrystal or quantum + + align:start position:0% +importance of nanocrystal or quantum + + + align:start position:0% +importance of nanocrystal or quantum +dots science yeah the picture was good + + align:start position:0% +dots science yeah the picture was good + + + align:start position:0% +dots science yeah the picture was good +but the science is even better if you + + align:start position:0% +but the science is even better if you + + + align:start position:0% +but the science is even better if you +are lucky to work with researchers whose + + align:start position:0% +are lucky to work with researchers whose + + + align:start position:0% +are lucky to work with researchers whose +work is timeless then your photographs + + align:start position:0% +work is timeless then your photographs + + + align:start position:0% +work is timeless then your photographs +might become timeless as well if you are + + align:start position:0% +might become timeless as well if you are + + + align:start position:0% +might become timeless as well if you are +lucky \ No newline at end of file diff --git a/O_M8asN10oQ.txt b/O_M8asN10oQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..9e77f5b7fb958873be739c408afa0b171697ae35 --- /dev/null +++ b/O_M8asN10oQ.txt @@ -0,0 +1,1291 @@ +align:start position:0% + +we now would like to consider the motion + + align:start position:0% +we now would like to consider the motion + + + align:start position:0% +we now would like to consider the motion +of a rigid body that's undergoing + + align:start position:0% +of a rigid body that's undergoing + + + align:start position:0% +of a rigid body that's undergoing +angular acceleration about some axis so + + align:start position:0% +angular acceleration about some axis so + + + align:start position:0% +angular acceleration about some axis so +let's consider for Simplicity a + + align:start position:0% +let's consider for Simplicity a + + + align:start position:0% +let's consider for Simplicity a +dis and we have an axis that's passing + + align:start position:0% +dis and we have an axis that's passing + + + align:start position:0% +dis and we have an axis that's passing +through some point s here it's the + + align:start position:0% +through some point s here it's the + + + align:start position:0% +through some point s here it's the +center but that's not + + align:start position:0% +center but that's not + + + align:start position:0% +center but that's not +crucial + + align:start position:0% +crucial + + + align:start position:0% +crucial +and we want to consider the fact that + + align:start position:0% +and we want to consider the fact that + + + align:start position:0% +and we want to consider the fact that +this object we call this our z-axis K + + align:start position:0% +this object we call this our z-axis K + + + align:start position:0% +this object we call this our z-axis K +hat unit Vector in that direction so + + align:start position:0% +hat unit Vector in that direction so + + + align:start position:0% +hat unit Vector in that direction so +it's pointing up and this object is + + align:start position:0% +it's pointing up and this object is + + + align:start position:0% +it's pointing up and this object is +undergoing an angular acceleration where + + align:start position:0% +undergoing an angular acceleration where + + + align:start position:0% +undergoing an angular acceleration where +Alpha Z is the Z component of the + + align:start position:0% +Alpha Z is the Z component of the + + + align:start position:0% +Alpha Z is the Z component of the +angular + + align:start position:0% +angular + + + align:start position:0% +angular +acceleration now what we'd like to + + align:start position:0% +acceleration now what we'd like to + + + align:start position:0% +acceleration now what we'd like to +consider is the torque on this object so + + align:start position:0% +consider is the torque on this object so + + + align:start position:0% +consider is the torque on this object so +the way we'll do it is we'll divide the + + align:start position:0% +the way we'll do it is we'll divide the + + + align:start position:0% +the way we'll do it is we'll divide the +object into a bunch of pieces and let's + + align:start position:0% +object into a bunch of pieces and let's + + + align:start position:0% +object into a bunch of pieces and let's +identify a piece here as Delta + + align:start position:0% +identify a piece here as Delta + + + align:start position:0% +identify a piece here as Delta +MJ that's that piece and this piece is + + align:start position:0% +MJ that's that piece and this piece is + + + align:start position:0% +MJ that's that piece and this piece is +has some force acting on it + + align:start position:0% +has some force acting on it + + + align:start position:0% +has some force acting on it +now this force can be a vector but the + + align:start position:0% +now this force can be a vector but the + + + align:start position:0% +now this force can be a vector but the +important thing to realize is that this + + align:start position:0% +important thing to realize is that this + + + align:start position:0% +important thing to realize is that this +force is only the external Force because + + align:start position:0% +force is only the external Force because + + + align:start position:0% +force is only the external Force because +we've already going to make the + + align:start position:0% +we've already going to make the + + + align:start position:0% +we've already going to make the +assumption that all internal torqus + + align:start position:0% +assumption that all internal torqus + + + align:start position:0% +assumption that all internal torqus +cancel in pairs and we'll show that in a + + align:start position:0% +cancel in pairs and we'll show that in a + + + align:start position:0% +cancel in pairs and we'll show that in a +video a little bit later so we're only + + align:start position:0% +video a little bit later so we're only + + + align:start position:0% +video a little bit later so we're only +considering the external forces that are + + align:start position:0% +considering the external forces that are + + + align:start position:0% +considering the external forces that are +acting on this element and recall that + + align:start position:0% +acting on this element and recall that + + + align:start position:0% +acting on this element and recall that +we have the vector RS to J is the vector + + align:start position:0% +we have the vector RS to J is the vector + + + align:start position:0% +we have the vector RS to J is the vector +from point s to where this Mass element + + align:start position:0% +from point s to where this Mass element + + + align:start position:0% +from point s to where this Mass element +is and now what we'd like to do is + + align:start position:0% +is and now what we'd like to do is + + + align:start position:0% +is and now what we'd like to do is +calculate the torque in general torque + + align:start position:0% +calculate the torque in general torque + + + align:start position:0% +calculate the torque in general torque +is given by the expression we'll sum + + align:start position:0% +is given by the expression we'll sum + + + align:start position:0% +is given by the expression we'll sum +over all the elements J goes from 1 to + + align:start position:0% +over all the elements J goes from 1 to + + + align:start position:0% +over all the elements J goes from 1 to +n and it's the vect cross product of our + + align:start position:0% +n and it's the vect cross product of our + + + align:start position:0% +n and it's the vect cross product of our +SJ cross FJ + + align:start position:0% +SJ cross FJ + + + align:start position:0% +SJ cross FJ +external now what we're trying our goal + + align:start position:0% +external now what we're trying our goal + + + align:start position:0% +external now what we're trying our goal +here is only to calculate the Z + + align:start position:0% +here is only to calculate the Z + + + align:start position:0% +here is only to calculate the Z +component of the torque so we can + + align:start position:0% +component of the torque so we can + + + align:start position:0% +component of the torque so we can +simplify our understanding a little bit + + align:start position:0% +simplify our understanding a little bit + + + align:start position:0% +simplify our understanding a little bit +by writing out this Vector F + + align:start position:0% +by writing out this Vector F + + + align:start position:0% +by writing out this Vector F +external J as a component in the plane + + align:start position:0% +external J as a component in the plane + + + align:start position:0% +external J as a component in the plane +and in order to describe that we'll + + align:start position:0% +and in order to describe that we'll + + + align:start position:0% +and in order to describe that we'll +choose some unit + + align:start position:0% +choose some unit + + + align:start position:0% +choose some unit +vectors R + + align:start position:0% +vectors R + + + align:start position:0% +vectors R +hat Theta hat going into the plane we + + align:start position:0% +hat Theta hat going into the plane we + + + align:start position:0% +hat Theta hat going into the plane we +make another picture in a moment so our + + align:start position:0% +make another picture in a moment so our + + + align:start position:0% +make another picture in a moment so our +Vector can have a r + + align:start position:0% +Vector can have a r + + + align:start position:0% +Vector can have a r +component and I'll keep the external in + + align:start position:0% +component and I'll keep the external in + + + align:start position:0% +component and I'll keep the external in +there it can have a Theta hack component + + align:start position:0% +there it can have a Theta hack component + + + align:start position:0% +there it can have a Theta hack component +and it can also have a z + + align:start position:0% +and it can also have a z + + + align:start position:0% +and it can also have a z +component but + + align:start position:0% +component but + + + align:start position:0% +component but +recall that a cross product is always + + align:start position:0% +recall that a cross product is always + + + align:start position:0% +recall that a cross product is always +perpendicular to either the elements so + + align:start position:0% +perpendicular to either the elements so + + + align:start position:0% +perpendicular to either the elements so +when I cross r with anything in the K + + align:start position:0% +when I cross r with anything in the K + + + align:start position:0% +when I cross r with anything in the K +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +then that component will give a + + align:start position:0% +then that component will give a + + + align:start position:0% +then that component will give a +component that's not in the Z Direction + + align:start position:0% +component that's not in the Z Direction + + + align:start position:0% +component that's not in the Z Direction +and so I can ignore that so my first + + align:start position:0% +and so I can ignore that so my first + + + align:start position:0% +and so I can ignore that so my first +simp simplification is to say that the Z + + align:start position:0% +simp simplification is to say that the Z + + + align:start position:0% +simp simplification is to say that the Z +component will only come from the cross + + align:start position:0% +component will only come from the cross + + + align:start position:0% +component will only come from the cross +product of R SJ with these two pieces so + + align:start position:0% +product of R SJ with these two pieces so + + + align:start position:0% +product of R SJ with these two pieces so +that's cross + + align:start position:0% +that's cross + + + align:start position:0% +that's cross +FJR R hat plus FJ Theta Theta + + align:start position:0% +FJR R hat plus FJ Theta Theta + + + align:start position:0% +FJR R hat plus FJ Theta Theta +head now again we can make another + + align:start position:0% +head now again we can make another + + + align:start position:0% +head now again we can make another +simplification and perhaps here it's + + align:start position:0% +simplification and perhaps here it's + + + align:start position:0% +simplification and perhaps here it's +helpful to have another overhead + + align:start position:0% +helpful to have another overhead + + + align:start position:0% +helpful to have another overhead +view and here's our Mass + + align:start position:0% +view and here's our Mass + + + align:start position:0% +view and here's our Mass +element Delta + + align:start position:0% +element Delta + + + align:start position:0% +element Delta +MJ that's our Vector from s from the + + align:start position:0% +MJ that's our Vector from s from the + + + align:start position:0% +MJ that's our Vector from s from the +center to Delta MJ we have unit vectors + + align:start position:0% +center to Delta MJ we have unit vectors + + + align:start position:0% +center to Delta MJ we have unit vectors +R hat and Theta hat and so we see that + + align:start position:0% +R hat and Theta hat and so we see that + + + align:start position:0% +R hat and Theta hat and so we see that +this Vector are + + align:start position:0% +this Vector are + + + align:start position:0% +this Vector are +RS J has some length in the r hat + + align:start position:0% +RS J has some length in the r hat + + + align:start position:0% +RS J has some length in the r hat +Direction now so we're not we're picking + + align:start position:0% +Direction now so we're not we're picking + + + align:start position:0% +Direction now so we're not we're picking +S as the origin of our coordinate system + + align:start position:0% +S as the origin of our coordinate system + + + align:start position:0% +S as the origin of our coordinate system +Um this can generalize so we don't worry + + align:start position:0% +Um this can generalize so we don't worry + + + align:start position:0% +Um this can generalize so we don't worry +about if the object is not + + align:start position:0% +about if the object is not + + + align:start position:0% +about if the object is not +symmetric so when you take the cross + + align:start position:0% +symmetric so when you take the cross + + + align:start position:0% +symmetric so when you take the cross +product of R hat versus R hat that also + + align:start position:0% +product of R hat versus R hat that also + + + align:start position:0% +product of R hat versus R hat that also +is zero and so we see our simplification + + align:start position:0% +is zero and so we see our simplification + + + align:start position:0% +is zero and so we see our simplification +is quite nice that the Z component of + + align:start position:0% +is quite nice that the Z component of + + + align:start position:0% +is quite nice that the Z component of +the torque is only arising from the sum + + align:start position:0% +the torque is only arising from the sum + + + align:start position:0% +the torque is only arising from the sum +of J goes from 1 to n of R SJ well we've + + align:start position:0% +of J goes from 1 to n of R SJ well we've + + + align:start position:0% +of J goes from 1 to n of R SJ well we've +already we'll write this all as vectors + + align:start position:0% +already we'll write this all as vectors + + + align:start position:0% +already we'll write this all as vectors +R Hat Cross f j Theta Theta + + align:start position:0% +R Hat Cross f j Theta Theta + + + align:start position:0% +R Hat Cross f j Theta Theta +hat now again um even if our external + + align:start position:0% +hat now again um even if our external + + + align:start position:0% +hat now again um even if our external +Force by the way we're dropping external + + align:start position:0% +Force by the way we're dropping external + + + align:start position:0% +Force by the way we're dropping external +we could always say external but I think + + align:start position:0% +we could always say external but I think + + + align:start position:0% +we could always say external but I think +for Simplicity we'll now drop the + + align:start position:0% +for Simplicity we'll now drop the + + + align:start position:0% +for Simplicity we'll now drop the +external um and what we're considering + + align:start position:0% +external um and what we're considering + + + align:start position:0% +external um and what we're considering +is just the component of the force we + + align:start position:0% +is just the component of the force we + + + align:start position:0% +is just the component of the force we +can write that f j this is a little + + align:start position:0% +can write that f j this is a little + + + align:start position:0% +can write that f j this is a little +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +Theta just the Theta hat component of + + align:start position:0% +Theta just the Theta hat component of + + + align:start position:0% +Theta just the Theta hat component of +that + + align:start position:0% +that + + + align:start position:0% +that +Force this is the only piece of the + + align:start position:0% +Force this is the only piece of the + + + align:start position:0% +Force this is the only piece of the +force that matters in contributing to + + align:start position:0% +force that matters in contributing to + + + align:start position:0% +force that matters in contributing to +the Z component of the torque + + align:start position:0% +the Z component of the torque + + + align:start position:0% +the Z component of the torque +and this cross product is very direct + + align:start position:0% +and this cross product is very direct + + + align:start position:0% +and this cross product is very direct +because we've chosen a right-handed + + align:start position:0% +because we've chosen a right-handed + + + align:start position:0% +because we've chosen a right-handed +system where R Hat Cross Theta hat is K + + align:start position:0% + + + + align:start position:0% + +hat so we see that this + + align:start position:0% +hat so we see that this + + + align:start position:0% +hat so we see that this +becomes J = 1 to n of R SJ FJ Theta in + + align:start position:0% +becomes J = 1 to n of R SJ FJ Theta in + + + align:start position:0% +becomes J = 1 to n of R SJ FJ Theta in +the K hat + + align:start position:0% +the K hat + + + align:start position:0% +the K hat +Direction now that's just the + + align:start position:0% +Direction now that's just the + + + align:start position:0% +Direction now that's just the +calculation of the torque but as always + + align:start position:0% +calculation of the torque but as always + + + align:start position:0% +calculation of the torque but as always +always it's crucial to understand where + + align:start position:0% +always it's crucial to understand where + + + align:start position:0% +always it's crucial to understand where +Newton's Second Law appears in these + + align:start position:0% +Newton's Second Law appears in these + + + align:start position:0% +Newton's Second Law appears in these +calculations and Newton's second law for + + align:start position:0% +calculations and Newton's second law for + + + align:start position:0% +calculations and Newton's second law for +this Mass element Delta MJ so the second + + align:start position:0% +this Mass element Delta MJ so the second + + + align:start position:0% +this Mass element Delta MJ so the second +law is telling us that the tangential + + align:start position:0% +law is telling us that the tangential + + + align:start position:0% +law is telling us that the tangential +force is proportional to the mass + + align:start position:0% +force is proportional to the mass + + + align:start position:0% +force is proportional to the mass +element times the tangential + + align:start position:0% +element times the tangential + + + align:start position:0% +element times the tangential +acceleration of that mass element now + + align:start position:0% +acceleration of that mass element now + + + align:start position:0% +acceleration of that mass element now +for this type of rotation about the + + align:start position:0% +for this type of rotation about the + + + align:start position:0% +for this type of rotation about the +z-axis + + align:start position:0% +z-axis + + + align:start position:0% +z-axis +so when we're rotating about that z-axis + + align:start position:0% +so when we're rotating about that z-axis + + + align:start position:0% +so when we're rotating about that z-axis +we know that + + align:start position:0% +we know that + + + align:start position:0% +we know that +a j Theta so the acceleration of this + + align:start position:0% +a j Theta so the acceleration of this + + + align:start position:0% +a j Theta so the acceleration of this +tangential element is just proportional + + align:start position:0% +tangential element is just proportional + + + align:start position:0% +tangential element is just proportional +to r + + align:start position:0% +to r + + + align:start position:0% +to r +j the distance from well we've called + + align:start position:0% +j the distance from well we've called + + + align:start position:0% +j the distance from well we've called +that R SJ so how far away from the + + align:start position:0% +that R SJ so how far away from the + + + align:start position:0% +that R SJ so how far away from the +center and here's the key thing it's + + align:start position:0% +center and here's the key thing it's + + + align:start position:0% +center and here's the key thing it's +also proportional to the Z component of + + align:start position:0% +also proportional to the Z component of + + + align:start position:0% +also proportional to the Z component of +the angular acceleration and every Mass + + align:start position:0% +the angular acceleration and every Mass + + + align:start position:0% +the angular acceleration and every Mass +element in the body has the same Alpha Z + + align:start position:0% +element in the body has the same Alpha Z + + + align:start position:0% +element in the body has the same Alpha Z +and so our sum for the torque can now be + + align:start position:0% +and so our sum for the torque can now be + + + align:start position:0% +and so our sum for the torque can now be +written in the following way the Z + + align:start position:0% +written in the following way the Z + + + align:start position:0% +written in the following way the Z +component of the torque now I'm going to + + align:start position:0% +component of the torque now I'm going to + + + align:start position:0% +component of the torque now I'm going to +do something here which is I'll write J + + align:start position:0% +do something here which is I'll write J + + + align:start position:0% +do something here which is I'll write J += 1 to n a parentheses Mark I have one + + align:start position:0% += 1 to n a parentheses Mark I have one + + + align:start position:0% += 1 to n a parentheses Mark I have one +of the rsjs I have another rsj a Delta + + align:start position:0% +of the rsjs I have another rsj a Delta + + + align:start position:0% +of the rsjs I have another rsj a Delta +MJ so I have Delta MJ rsj squ + + align:start position:0% +MJ so I have Delta MJ rsj squ + + + align:start position:0% +MJ so I have Delta MJ rsj squ +but every single component has the same + + align:start position:0% +but every single component has the same + + + align:start position:0% +but every single component has the same +Alpha Z and we're in the K hat + + align:start position:0% +Alpha Z and we're in the K hat + + + align:start position:0% +Alpha Z and we're in the K hat +Direction now because we have a + + align:start position:0% +Direction now because we have a + + + align:start position:0% +Direction now because we have a +continuous body we have to again + + align:start position:0% +continuous body we have to again + + + align:start position:0% +continuous body we have to again +consider a limit so let's call the limit + + align:start position:0% +consider a limit so let's call the limit + + + align:start position:0% +consider a limit so let's call the limit +as Delta MJ goes to zero of this sum + + align:start position:0% +as Delta MJ goes to zero of this sum + + + align:start position:0% +as Delta MJ goes to zero of this sum +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +MJ R SJ SAR well that's an + + align:start position:0% +MJ R SJ SAR well that's an + + + align:start position:0% +MJ R SJ SAR well that's an +integral over the body of DM RS s and we + + align:start position:0% +integral over the body of DM RS s and we + + + align:start position:0% +integral over the body of DM RS s and we +identified that before as the moment of + + align:start position:0% +identified that before as the moment of + + + align:start position:0% +identified that before as the moment of +inertia about the + + align:start position:0% +inertia about the + + + align:start position:0% +inertia about the +z-axis so the quaning parentheses is + + align:start position:0% +z-axis so the quaning parentheses is + + + align:start position:0% +z-axis so the quaning parentheses is +just a measure of the mass distribution + + align:start position:0% +just a measure of the mass distribution + + + align:start position:0% +just a measure of the mass distribution +about the axis you see the r s the Delta + + align:start position:0% +about the axis you see the r s the Delta + + + align:start position:0% +about the axis you see the r s the Delta +MJ and so in conclusion we have that the + + align:start position:0% +MJ and so in conclusion we have that the + + + align:start position:0% +MJ and so in conclusion we have that the +Z component of the torque is equal to is + + align:start position:0% +Z component of the torque is equal to is + + + align:start position:0% +Z component of the torque is equal to is +Alpha ZK hat which is now a vector + + align:start position:0% +Alpha ZK hat which is now a vector + + + align:start position:0% +Alpha ZK hat which is now a vector +because that's the vector Alpha and this + + align:start position:0% +because that's the vector Alpha and this + + + align:start position:0% +because that's the vector Alpha and this +is our crucial result for a body that's + + align:start position:0% +is our crucial result for a body that's + + + align:start position:0% +is our crucial result for a body that's +rotating about the + + align:start position:0% +rotating about the + + + align:start position:0% +rotating about the +z-axis this result can generalize to not + + align:start position:0% +z-axis this result can generalize to not + + + align:start position:0% +z-axis this result can generalize to not +just a dis but any body that's and + + align:start position:0% +just a dis but any body that's and + + + align:start position:0% +just a dis but any body that's and +looking at the Z + + align:start position:0% +looking at the Z + + + align:start position:0% +looking at the Z +component for this fixed axis rotation \ No newline at end of file diff --git a/P_av1O1HTk8.txt b/P_av1O1HTk8.txt new file mode 100644 index 0000000000000000000000000000000000000000..127a21bc134981cb685bb3ae68141603b5f62cfc --- /dev/null +++ b/P_av1O1HTk8.txt @@ -0,0 +1,6475 @@ +align:start position:0% + +I'm trying to remember exactly well I + + align:start position:0% +I'm trying to remember exactly well I + + + align:start position:0% +I'm trying to remember exactly well I +remember there was for + + align:start position:0% +remember there was for + + + align:start position:0% +remember there was for +instance the uh I don't want to do that + + align:start position:0% +instance the uh I don't want to do that + + + align:start position:0% +instance the uh I don't want to do that +but I did um there was less of an + + align:start position:0% +but I did um there was less of an + + + align:start position:0% +but I did um there was less of an +entrance in here uh of course this was + + align:start position:0% +entrance in here uh of course this was + + + align:start position:0% +entrance in here uh of course this was +here and this is been gotten much more + + align:start position:0% +here and this is been gotten much more + + + align:start position:0% +here and this is been gotten much more +articulate than what it was which I need + + align:start position:0% +articulate than what it was which I need + + + align:start position:0% +articulate than what it was which I need +to know about but this was coming up and + + align:start position:0% +to know about but this was coming up and + + + align:start position:0% +to know about but this was coming up and +went down and then we suggested that it + + align:start position:0% +went down and then we suggested that it + + + align:start position:0% +went down and then we suggested that it +didn't happens of the ordinary coming + + align:start position:0% +didn't happens of the ordinary coming + + + align:start position:0% +didn't happens of the ordinary coming +over that was one thing and we suggested + + align:start position:0% +over that was one thing and we suggested + + + align:start position:0% +over that was one thing and we suggested +that the back court the corner Court + + align:start position:0% +that the back court the corner Court + + + align:start position:0% +that the back court the corner Court +which still is not got a little larger + + align:start position:0% +which still is not got a little larger + + + align:start position:0% +which still is not got a little larger +yeah it's it's more open it's just yeah + + align:start position:0% +yeah it's it's more open it's just yeah + + + align:start position:0% +yeah it's it's more open it's just yeah +okay I'll okay um so right to make this + + align:start position:0% +okay I'll okay um so right to make this + + + align:start position:0% +okay I'll okay um so right to make this +entrance bigger and you know as matching + + align:start position:0% +entrance bigger and you know as matching + + + align:start position:0% +entrance bigger and you know as matching +FL coming out of here I just moved the + + align:start position:0% +FL coming out of here I just moved the + + + align:start position:0% +FL coming out of here I just moved the +main volume of this back I think I just + + align:start position:0% +main volume of this back I think I just + + + align:start position:0% +main volume of this back I think I just +made it shorter it was pretty long + + align:start position:0% +made it shorter it was pretty long + + + align:start position:0% +made it shorter it was pretty long +before so + + align:start position:0% +before so + + + align:start position:0% +before so +um and then this volume sort of goes + + align:start position:0% +um and then this volume sort of goes + + + align:start position:0% +um and then this volume sort of goes +from here to there and ends there and + + align:start position:0% +from here to there and ends there and + + + align:start position:0% +from here to there and ends there and +then that volume starts so this is sort + + align:start position:0% +then that volume starts so this is sort + + + align:start position:0% +then that volume starts so this is sort +of the + + align:start position:0% +of the + + + align:start position:0% +of the +artists um rooms and + + align:start position:0% +artists um rooms and + + + align:start position:0% +artists um rooms and +centers and + + align:start position:0% +centers and + + + align:start position:0% +centers and +um this one is basically one floor this + + align:start position:0% +um this one is basically one floor this + + + align:start position:0% +um this one is basically one floor this +one will'll be three floors and so the + + align:start position:0% +one will'll be three floors and so the + + + align:start position:0% +one will'll be three floors and so the +bottom floor for both of them it's going + + align:start position:0% +bottom floor for both of them it's going + + + align:start position:0% +bottom floor for both of them it's going +to be like the bigger rooms like a big + + align:start position:0% +to be like the bigger rooms like a big + + + align:start position:0% +to be like the bigger rooms like a big +wood shop or metal shop or something + + align:start position:0% +wood shop or metal shop or something + + + align:start position:0% +wood shop or metal shop or something +that'll be more directly connected to in + + align:start position:0% +that'll be more directly connected to in + + + align:start position:0% +that'll be more directly connected to in +here and then as you go up you get more + + align:start position:0% +here and then as you go up you get more + + + align:start position:0% +here and then as you go up you get more +smaller spaces more individual work and + + align:start position:0% +smaller spaces more individual work and + + + align:start position:0% +smaller spaces more individual work and +then as far as sort of this axis goes I + + align:start position:0% +then as far as sort of this axis goes I + + + align:start position:0% +then as far as sort of this axis goes I +let the full yeah um I tried to figure + + align:start position:0% +let the full yeah um I tried to figure + + + align:start position:0% +let the full yeah um I tried to figure +out the stairs they're still kind of + + align:start position:0% +out the stairs they're still kind of + + + align:start position:0% +out the stairs they're still kind of +iffy but um I thought well I thought it + + align:start position:0% +iffy but um I thought well I thought it + + + align:start position:0% +iffy but um I thought well I thought it +would be interesting this piece first of + + align:start position:0% +would be interesting this piece first of + + + align:start position:0% +would be interesting this piece first of +all is it's actually a step lower than + + align:start position:0% +all is it's actually a step lower than + + + align:start position:0% +all is it's actually a step lower than +the first step but it's on the sidewalk + + align:start position:0% +the first step but it's on the sidewalk + + + align:start position:0% +the first step but it's on the sidewalk +and so instead of um concrete you'll + + align:start position:0% +and so instead of um concrete you'll + + + align:start position:0% +and so instead of um concrete you'll +start walking on the stone over here um + + align:start position:0% +start walking on the stone over here um + + + align:start position:0% +start walking on the stone over here um +I'm imagining this to be Stone and so + + align:start position:0% +I'm imagining this to be Stone and so + + + align:start position:0% +I'm imagining this to be Stone and so +you'll kind of be walking on it without + + align:start position:0% +you'll kind of be walking on it without + + + align:start position:0% +you'll kind of be walking on it without +even realizing it and then you'll be + + align:start position:0% +even realizing it and then you'll be + + + align:start position:0% +even realizing it and then you'll be +brought into it and I was Imaging little + + align:start position:0% +brought into it and I was Imaging little + + + align:start position:0% +brought into it and I was Imaging little +platforms maybe little pools of water so + + align:start position:0% +platforms maybe little pools of water so + + + align:start position:0% +platforms maybe little pools of water so +people are sitting around here and it's + + align:start position:0% +people are sitting around here and it's + + + align:start position:0% +people are sitting around here and it's +kind of a a nice meeting place and then + + align:start position:0% +kind of a a nice meeting place and then + + + align:start position:0% +kind of a a nice meeting place and then +it leads you up to this plane this floor + + align:start position:0% +it leads you up to this plane this floor + + + align:start position:0% +it leads you up to this plane this floor +which starts becoming in ior around here + + align:start position:0% +which starts becoming in ior around here + + + align:start position:0% +which starts becoming in ior around here +wherever the roof kind of lands and it's + + align:start position:0% +wherever the roof kind of lands and it's + + + align:start position:0% +wherever the roof kind of lands and it's +sort of the tourist + + align:start position:0% +sort of the tourist + + + align:start position:0% +sort of the tourist +information um area and underneath here + + align:start position:0% +information um area and underneath here + + + align:start position:0% +information um area and underneath here +I was thinking this should be some sort + + align:start position:0% +I was thinking this should be some sort + + + align:start position:0% +I was thinking this should be some sort +of supply store place because obviously + + align:start position:0% +of supply store place because obviously + + + align:start position:0% +of supply store place because obviously +they're going to need lots of supplies + + align:start position:0% +they're going to need lots of supplies + + + align:start position:0% +they're going to need lots of supplies +so I got that be a good place for that + + align:start position:0% +so I got that be a good place for that + + + align:start position:0% +so I got that be a good place for that +to go um and then from here they can + + align:start position:0% +to go um and then from here they can + + + align:start position:0% +to go um and then from here they can +come up to this this is a roof deck this + + align:start position:0% +come up to this this is a roof deck this + + + align:start position:0% +come up to this this is a roof deck this +actually is just holding it up somehow + + align:start position:0% +actually is just holding it up somehow + + + align:start position:0% +actually is just holding it up somehow +this will be hel you go under mhm yeah + + align:start position:0% +this will be hel you go under mhm yeah + + + align:start position:0% +this will be hel you go under mhm yeah +so you can walk all the way AC across + + align:start position:0% +so you can walk all the way AC across + + + align:start position:0% +so you can walk all the way AC across +here and there'll be food up here and + + align:start position:0% +here and there'll be food up here and + + + align:start position:0% +here and there'll be food up here and +everything and then you can I'm thinking + + align:start position:0% +everything and then you can I'm thinking + + + align:start position:0% +everything and then you can I'm thinking +of maybe a little Bridge or something to + + align:start position:0% +of maybe a little Bridge or something to + + + align:start position:0% +of maybe a little Bridge or something to +get into here and this I was thinking + + align:start position:0% +get into here and this I was thinking + + + align:start position:0% +get into here and this I was thinking +would be um some sort of a theater like + + align:start position:0% +would be um some sort of a theater like + + + align:start position:0% +would be um some sort of a theater like +a movie theater or this BL yeah it's + + align:start position:0% +a movie theater or this BL yeah it's + + + align:start position:0% +a movie theater or this BL yeah it's +actually pretty tall so I think youd + + align:start position:0% +actually pretty tall so I think youd + + + align:start position:0% +actually pretty tall so I think youd +have room for like a bigger theater and + + align:start position:0% +have room for like a bigger theater and + + + align:start position:0% +have room for like a bigger theater and +like a small lecture hall or something + + align:start position:0% +like a small lecture hall or something + + + align:start position:0% +like a small lecture hall or something +so you could show an Italian classic or + + align:start position:0% +so you could show an Italian classic or + + + align:start position:0% +so you could show an Italian classic or +something I don't know um and then as + + align:start position:0% +something I don't know um and then as + + + align:start position:0% +something I don't know um and then as +far as this plane you can uh get on to + + align:start position:0% +far as this plane you can uh get on to + + + align:start position:0% +far as this plane you can uh get on to +it from in here so I'm not quite sure if + + align:start position:0% +it from in here so I'm not quite sure if + + + align:start position:0% +it from in here so I'm not quite sure if +these two will be connected so you can + + align:start position:0% +these two will be connected so you can + + + align:start position:0% +these two will be connected so you can +go from here to here you'll definitely + + align:start position:0% +go from here to here you'll definitely + + + align:start position:0% +go from here to here you'll definitely +be a to come out on both of those and + + align:start position:0% +be a to come out on both of those and + + + align:start position:0% +be a to come out on both of those and +then the way let's put this back so + + align:start position:0% +then the way let's put this back so + + + align:start position:0% +then the way let's put this back so +because I + + align:start position:0% +because I + + + align:start position:0% +because I +can yep go on and then um the way these + + align:start position:0% +can yep go on and then um the way these + + + align:start position:0% +can yep go on and then um the way these +spaces here work this one is kind of + + align:start position:0% +spaces here work this one is kind of + + + align:start position:0% +spaces here work this one is kind of +nice you can enter it right from the + + align:start position:0% +nice you can enter it right from the + + + align:start position:0% +nice you can enter it right from the +street in here and there'll probably be + + align:start position:0% +street in here and there'll probably be + + + align:start position:0% +street in here and there'll probably be +an entrance to the movie theater back + + align:start position:0% +an entrance to the movie theater back + + + align:start position:0% +an entrance to the movie theater back +here so you can watch the movie come out + + align:start position:0% +here so you can watch the movie come out + + + align:start position:0% +here so you can watch the movie come out +here rest um whatever I do with the + + align:start position:0% +here rest um whatever I do with the + + + align:start position:0% +here rest um whatever I do with the +water is sort of happen again + + align:start position:0% +water is sort of happen again + + + align:start position:0% +water is sort of happen again +here um and then this space it's + + align:start position:0% +here um and then this space it's + + + align:start position:0% +here um and then this space it's +actually pretty open it's it's all this + + align:start position:0% +actually pretty open it's it's all this + + + align:start position:0% +actually pretty open it's it's all this +is just I this building and here so it's + + align:start position:0% +is just I this building and here so it's + + + align:start position:0% +is just I this building and here so it's +all that I just gave it a little bit of + + align:start position:0% +all that I just gave it a little bit of + + + align:start position:0% +all that I just gave it a little bit of +a loop so it's more of a you know the + + align:start position:0% +a loop so it's more of a you know the + + + align:start position:0% +a loop so it's more of a you know the +personal space for the artists which is + + align:start position:0% +personal space for the artists which is + + + align:start position:0% +personal space for the artists which is +then very much connected to here but you + + align:start position:0% +then very much connected to here but you + + + align:start position:0% +then very much connected to here but you +know this will sort of be at the + + align:start position:0% +know this will sort of be at the + + + align:start position:0% +know this will sort of be at the +evening um and'll be full of people + + align:start position:0% +evening um and'll be full of people + + + align:start position:0% +evening um and'll be full of people +coming to the movie coming to eat up + + align:start position:0% +coming to the movie coming to eat up + + + align:start position:0% +coming to the movie coming to eat up +here and and then you can go back there + + align:start position:0% +here and and then you can go back there + + + align:start position:0% +here and and then you can go back there +and it'll be more + + align:start position:0% +and it'll be more + + + align:start position:0% +and it'll be more +quiet and as far as the roof is going + + align:start position:0% +quiet and as far as the roof is going + + + align:start position:0% +quiet and as far as the roof is going +I'm sort of + + align:start position:0% +I'm sort of + + + align:start position:0% +I'm sort of +imagining you kind of see it but just a + + align:start position:0% +imagining you kind of see it but just a + + + align:start position:0% +imagining you kind of see it but just a +a bunch of planes kind of connecting or + + align:start position:0% +a bunch of planes kind of connecting or + + + align:start position:0% +a bunch of planes kind of connecting or +intersecting put pieces on + + align:start position:0% +intersecting put pieces on + + + align:start position:0% +intersecting put pieces on +here see better you have this one plane + + align:start position:0% +here see better you have this one plane + + + align:start position:0% +here see better you have this one plane +here and another one they s of build + + align:start position:0% +here and another one they s of build + + + align:start position:0% +here and another one they s of build +down I didn't want anything curved or + + align:start position:0% +down I didn't want anything curved or + + + align:start position:0% +down I didn't want anything curved or +anything so I'm trying to keep planes + + align:start position:0% +anything so I'm trying to keep planes + + + align:start position:0% +anything so I'm trying to keep planes +and keep varying the + + align:start position:0% +and keep varying the + + + align:start position:0% +and keep varying the +levels um obviously it's not very + + align:start position:0% +levels um obviously it's not very + + + align:start position:0% +levels um obviously it's not very +defined yet and then I can understand + + align:start position:0% +defined yet and then I can understand + + + align:start position:0% +defined yet and then I can understand +right and so then the columns will help + + align:start position:0% +right and so then the columns will help + + + align:start position:0% +right and so then the columns will help +sort of Define the interior spaces + + align:start position:0% +sort of Define the interior spaces + + + align:start position:0% +sort of Define the interior spaces +better couple questions do I come across + + align:start position:0% +better couple questions do I come across + + + align:start position:0% +better couple questions do I come across +the street here and down um no I hadn't + + align:start position:0% +the street here and down um no I hadn't + + + align:start position:0% +the street here and down um no I hadn't +it doesn't completely reach across the + + align:start position:0% +it doesn't completely reach across the + + + align:start position:0% +it doesn't completely reach across the +street so I + + align:start position:0% +street so I + + + align:start position:0% +street so I +didn't but it's a platform that comes + + align:start position:0% +didn't but it's a platform that comes + + + align:start position:0% +didn't but it's a platform that comes +out it's a platform yeah you can come + + align:start position:0% +out it's a platform yeah you can come + + + align:start position:0% +out it's a platform yeah you can come +out right and of course I can go under + + align:start position:0% +out right and of course I can go under + + + align:start position:0% +out right and of course I can go under +it right right but I want to review a + + align:start position:0% +it right right but I want to review a + + + align:start position:0% +it right right but I want to review a +little + + align:start position:0% +little + + + align:start position:0% +little +bit part of this project is building + + align:start position:0% +bit part of this project is building + + + align:start position:0% +bit part of this project is building +nature in the city right how are you + + align:start position:0% +nature in the city right how are you + + + align:start position:0% +nature in the city right how are you +doing + + align:start position:0% +doing + + + align:start position:0% +doing +that yeah um so I feel that the sort of + + align:start position:0% +that yeah um so I feel that the sort of + + + align:start position:0% +that yeah um so I feel that the sort of +the outdoor areas + + align:start position:0% +the outdoor areas + + + align:start position:0% +the outdoor areas +of this this this this will all have + + align:start position:0% +of this this this this will all have + + + align:start position:0% +of this this this this will all have +elements of well this is all Stone first + + align:start position:0% +elements of well this is all Stone first + + + align:start position:0% +elements of well this is all Stone first +of all so that's of the ground element + + align:start position:0% +of all so that's of the ground element + + + align:start position:0% +of all so that's of the ground element +and then I want to incorporate some sort + + align:start position:0% +and then I want to incorporate some sort + + + align:start position:0% +and then I want to incorporate some sort +of pools of + + align:start position:0% +of pools of + + + align:start position:0% +of pools of +water things like that into here that I + + align:start position:0% +water things like that into here that I + + + align:start position:0% +water things like that into here that I +haven't figured out very much and then + + align:start position:0% +haven't figured out very much and then + + + align:start position:0% +haven't figured out very much and then +also this structure I'm kind of thinking + + align:start position:0% +also this structure I'm kind of thinking + + + align:start position:0% +also this structure I'm kind of thinking +it should be wood + + align:start position:0% +it should be wood + + + align:start position:0% +it should be wood +because you know not only is it more + + align:start position:0% +because you know not only is it more + + + align:start position:0% +because you know not only is it more +sort of organic but the floats that are + + align:start position:0% +sort of organic but the floats that are + + + align:start position:0% +sort of organic but the floats that are +being built they probably out of wood so + + align:start position:0% +being built they probably out of wood so + + + align:start position:0% +being built they probably out of wood so +kind of relate a little bit so I think + + align:start position:0% +kind of relate a little bit so I think + + + align:start position:0% +kind of relate a little bit so I think +through the materials and kind of the + + align:start position:0% +through the materials and kind of the + + + align:start position:0% +through the materials and kind of the +colors that I'm going to try to use you + + align:start position:0% +colors that I'm going to try to use you + + + align:start position:0% +colors that I'm going to try to use you +know stone wood water so it won't be you + + align:start position:0% +know stone wood water so it won't be you + + + align:start position:0% +know stone wood water so it won't be you +know big masses of trees and stuff but + + align:start position:0% +know big masses of trees and stuff but + + + align:start position:0% +know big masses of trees and stuff but +it'll be more just Su + + align:start position:0% +it'll be more just Su + + + align:start position:0% +it'll be more just Su +materials all + + align:start position:0% +materials all + + + align:start position:0% +materials all +right uh again um I think everybody is + + align:start position:0% +right uh again um I think everybody is + + + align:start position:0% +right uh again um I think everybody is +settling into General organization which + + align:start position:0% +settling into General organization which + + + align:start position:0% +settling into General organization which +is good and particularly the change of + + align:start position:0% +is good and particularly the change of + + + align:start position:0% +is good and particularly the change of +this and also the use of this which is + + align:start position:0% +this and also the use of this which is + + + align:start position:0% +this and also the use of this which is +kind of a perfect use in a way related + + align:start position:0% +kind of a perfect use in a way related + + + align:start position:0% +kind of a perfect use in a way related +to this of the AUD of the theater + + align:start position:0% +to this of the AUD of the theater + + + align:start position:0% +to this of the AUD of the theater +because then + + align:start position:0% +because then + + + align:start position:0% +because then +in terms of the elevation I can do + + align:start position:0% +in terms of the elevation I can do + + + align:start position:0% +in terms of the elevation I can do +something related to that so the + + align:start position:0% +something related to that so the + + + align:start position:0% +something related to that so the +ordinary is moving into this extremely + + align:start position:0% +ordinary is moving into this extremely + + + align:start position:0% +ordinary is moving into this extremely +extraordinary thing that you + + align:start position:0% +extraordinary thing that you + + + align:start position:0% +extraordinary thing that you +have uh three issues at least the first + + align:start position:0% +have uh three issues at least the first + + + align:start position:0% +have uh three issues at least the first +is that you gave a big clue when you + + align:start position:0% +is that you gave a big clue when you + + + align:start position:0% +is that you gave a big clue when you +said you're going to make this in the + + align:start position:0% +said you're going to make this in the + + + align:start position:0% +said you're going to make this in the +street a different + + align:start position:0% +street a different + + + align:start position:0% +street a different +behaving what I think should happen uh + + align:start position:0% +behaving what I think should happen uh + + + align:start position:0% +behaving what I think should happen uh +picking up on what you just + + align:start position:0% +picking up on what you just + + + align:start position:0% +picking up on what you just +said is that what I call the building of + + align:start position:0% +said is that what I call the building of + + + align:start position:0% +said is that what I call the building of +the Mind meaning that the building + + align:start position:0% +the Mind meaning that the building + + + align:start position:0% +the Mind meaning that the building +starts long before I get there mhm that + + align:start position:0% +starts long before I get there mhm that + + + align:start position:0% +starts long before I get there mhm that +this triangular condition might actually + + align:start position:0% +this triangular condition might actually + + + align:start position:0% +this triangular condition might actually +stretch down the street even farther + + align:start position:0% +stretch down the street even farther + + + align:start position:0% +stretch down the street even farther +than what you + + align:start position:0% +than what you + + + align:start position:0% +than what you +have and be exactly as I can't do it + + align:start position:0% +have and be exactly as I can't do it + + + align:start position:0% +have and be exactly as I can't do it +with this but be exactly what you + + align:start position:0% +with this but be exactly what you + + + align:start position:0% +with this but be exactly what you +saidh uh but down in here I start to + + align:start position:0% +saidh uh but down in here I start to + + + align:start position:0% +saidh uh but down in here I start to +realize that I'm in a territory which is + + align:start position:0% +realize that I'm in a territory which is + + + align:start position:0% +realize that I'm in a territory which is +part of this building and is not part of + + align:start position:0% +part of this building and is not part of + + + align:start position:0% +part of this building and is not part of +something else but just a slight change + + align:start position:0% +something else but just a slight change + + + align:start position:0% +something else but just a slight change +that perhaps that starts to Elevate just + + align:start position:0% +that perhaps that starts to Elevate just + + + align:start position:0% +that perhaps that starts to Elevate just +slightly uhu so I'm starting to move up + + align:start position:0% +slightly uhu so I'm starting to move up + + + align:start position:0% +slightly uhu so I'm starting to move up +so when I get to here I'm almost as I + + align:start position:0% +so when I get to here I'm almost as I + + + align:start position:0% +so when I get to here I'm almost as I +have it here at the same level where + + align:start position:0% +have it here at the same level where + + + align:start position:0% +have it here at the same level where +there's going to be a wall here + + align:start position:0% +there's going to be a wall here + + + align:start position:0% +there's going to be a wall here +obviously right um the reason I say that + + align:start position:0% +obviously right um the reason I say that + + + align:start position:0% +obviously right um the reason I say that +is that and the reason I asked you the + + align:start position:0% +is that and the reason I asked you the + + + align:start position:0% +is that and the reason I asked you the +question about nature is that there + + align:start position:0% +question about nature is that there + + + align:start position:0% +question about nature is that there +could be the beginning of some kind of + + align:start position:0% +could be the beginning of some kind of + + + align:start position:0% +could be the beginning of some kind of +continuous natural experience which + + align:start position:0% +continuous natural experience which + + + align:start position:0% +continuous natural experience which +could be trees or water for instance + + align:start position:0% +could be trees or water for instance + + + align:start position:0% +could be trees or water for instance +water could be moving down through this + + align:start position:0% +water could be moving down through this + + + align:start position:0% +water could be moving down through this +along the way and maybe there's a pool I + + align:start position:0% +along the way and maybe there's a pool I + + + align:start position:0% +along the way and maybe there's a pool I +know we're in the street but still it + + align:start position:0% +know we're in the street but still it + + + align:start position:0% +know we're in the street but still it +could be uh the Street's over here so + + align:start position:0% +could be uh the Street's over here so + + + align:start position:0% +could be uh the Street's over here so +there might be enough room to do it so + + align:start position:0% +there might be enough room to do it so + + + align:start position:0% +there might be enough room to do it so +that the water is the thing that ties it + + align:start position:0% +that the water is the thing that ties it + + + align:start position:0% +that the water is the thing that ties it +together in this case and the trees are + + align:start position:0% +together in this case and the trees are + + + align:start position:0% +together in this case and the trees are +the thing that ties it together so I'm + + align:start position:0% +the thing that ties it together so I'm + + + align:start position:0% +the thing that ties it together so I'm +moving up right now the pro the places + + align:start position:0% +moving up right now the pro the places + + + align:start position:0% +moving up right now the pro the places +that I have problems with that if that's + + align:start position:0% +that I have problems with that if that's + + + align:start position:0% +that I have problems with that if that's +the the case and I think that's what + + align:start position:0% +the the case and I think that's what + + + align:start position:0% +the the case and I think that's what +you're trying to do and that's what you + + align:start position:0% +you're trying to do and that's what you + + + align:start position:0% +you're trying to do and that's what you +sort of told me is that it seems very + + align:start position:0% +sort of told me is that it seems very + + + align:start position:0% +sort of told me is that it seems very +very gentle and uh just the right + + align:start position:0% +very gentle and uh just the right + + + align:start position:0% +very gentle and uh just the right +change of elevation in here and maybe + + align:start position:0% +change of elevation in here and maybe + + + align:start position:0% +change of elevation in here and maybe +over here but here it's very abrupt yeah + + align:start position:0% +over here but here it's very abrupt yeah + + + align:start position:0% +over here but here it's very abrupt yeah +and there may be a way that you can make + + align:start position:0% +and there may be a way that you can make + + + align:start position:0% +and there may be a way that you can make +that transition from this vertical + + align:start position:0% +that transition from this vertical + + + align:start position:0% +that transition from this vertical +horizontal to this one in a vertical + + align:start position:0% +horizontal to this one in a vertical + + + align:start position:0% +horizontal to this one in a vertical +way not like this of course but a little + + align:start position:0% +way not like this of course but a little + + + align:start position:0% +way not like this of course but a little +less abrupt so that I can move up more + + align:start position:0% +less abrupt so that I can move up more + + + align:start position:0% +less abrupt so that I can move up more +slowly if that's the case then + + align:start position:0% +slowly if that's the case then + + + align:start position:0% +slowly if that's the case then +conceptually what you've always talked + + align:start position:0% +conceptually what you've always talked + + + align:start position:0% +conceptually what you've always talked +about is relating to the street this way + + align:start position:0% +about is relating to the street this way + + + align:start position:0% +about is relating to the street this way +and relating it this way then there's a + + align:start position:0% +and relating it this way then there's a + + + align:start position:0% +and relating it this way then there's a +crossing of the two and just as you've + + align:start position:0% +crossing of the two and just as you've + + + align:start position:0% +crossing of the two and just as you've +shown on your model one's gray and one's + + align:start position:0% +shown on your model one's gray and one's + + + align:start position:0% +shown on your model one's gray and one's +copper um we would recognize it as that + + align:start position:0% +copper um we would recognize it as that + + + align:start position:0% +copper um we would recognize it as that +Crossing whereas that's why I ask you + + align:start position:0% +Crossing whereas that's why I ask you + + + align:start position:0% +Crossing whereas that's why I ask you +this one might be a cross overpass with + + align:start position:0% +this one might be a cross overpass with + + + align:start position:0% +this one might be a cross overpass with +a spiral stair or a stair that I can get + + align:start position:0% +a spiral stair or a stair that I can get + + + align:start position:0% +a spiral stair or a stair that I can get +over and up through um and it's + + align:start position:0% +over and up through um and it's + + + align:start position:0% +over and up through um and it's +different than than this one but the two + + align:start position:0% +different than than this one but the two + + + align:start position:0% +different than than this one but the two +are going Crossing each one one is + + align:start position:0% +are going Crossing each one one is + + + align:start position:0% +are going Crossing each one one is +natural one is more urban that's the + + align:start position:0% +natural one is more urban that's the + + + align:start position:0% +natural one is more urban that's the +first + + align:start position:0% +first + + + align:start position:0% +first +the second thing is that you solved a + + align:start position:0% +the second thing is that you solved a + + + align:start position:0% +the second thing is that you solved a +problem I think from last time in terms + + align:start position:0% +problem I think from last time in terms + + + align:start position:0% +problem I think from last time in terms +of the entrance and in the process + + align:start position:0% +of the entrance and in the process + + + align:start position:0% +of the entrance and in the process +created a problem and and I'll explain + + align:start position:0% +created a problem and and I'll explain + + + align:start position:0% +created a problem and and I'll explain +why you've got a very nice entrance in + + align:start position:0% +why you've got a very nice entrance in + + + align:start position:0% +why you've got a very nice entrance in +the sense of space huh a big can't + + align:start position:0% +the sense of space huh a big can't + + + align:start position:0% +the sense of space huh a big can't +believe well you do but assuming that + + align:start position:0% +believe well you do but assuming that + + + align:start position:0% +believe well you do but assuming that +you can deal with that no I'm more + + align:start position:0% +you can deal with that no I'm more + + + align:start position:0% +you can deal with that no I'm more +concerned about it being very + + align:start position:0% +concerned about it being very + + + align:start position:0% +concerned about it being very +dark yeah um right okay let me talk + + align:start position:0% +dark yeah um right okay let me talk + + + align:start position:0% +dark yeah um right okay let me talk +these I was actually imagining + + align:start position:0% +these I was actually imagining + + + align:start position:0% +these I was actually imagining +translucent material so that you can see + + align:start position:0% +translucent material so that you can see + + + align:start position:0% +translucent material so that you can see +people working M Etc um which would also + + align:start position:0% +people working M Etc um which would also + + + align:start position:0% +people working M Etc um which would also +help with the light so they wouldn't be + + align:start position:0% +help with the light so they wouldn't be + + + align:start position:0% +help with the light so they wouldn't be +these dark M + + align:start position:0% +these dark M + + + align:start position:0% +these dark M +cardboard um but down that's only on the + + align:start position:0% +cardboard um but down that's only on the + + + align:start position:0% +cardboard um but down that's only on the +lower level though no sort of the whole + + align:start position:0% +lower level though no sort of the whole + + + align:start position:0% +lower level though no sort of the whole +volume almost I mean I'm just picturing + + align:start position:0% +volume almost I mean I'm just picturing + + + align:start position:0% +volume almost I mean I'm just picturing +this translucent completely um like + + align:start position:0% +this translucent completely um like + + + align:start position:0% +this translucent completely um like +these volumes and + + align:start position:0% +these volumes and + + + align:start position:0% +these volumes and +then so I don't know if that well it + + align:start position:0% +then so I don't know if that well it + + + align:start position:0% +then so I don't know if that well it +does but what I'm trying to get is some + + align:start position:0% +does but what I'm trying to get is some + + + align:start position:0% +does but what I'm trying to get is some +light down into this + + align:start position:0% +light down into this + + + align:start position:0% +light down into this +somehow + + align:start position:0% +somehow + + + align:start position:0% +somehow +where um this may become slightly + + align:start position:0% +where um this may become slightly + + + align:start position:0% +where um this may become slightly +smaller here so that there's a vertical + + align:start position:0% +smaller here so that there's a vertical + + + align:start position:0% +smaller here so that there's a vertical +shaft of light that's anchoring the + + align:start position:0% +shaft of light that's anchoring the + + + align:start position:0% +shaft of light that's anchoring the +space at the place where you need it the + + align:start position:0% +space at the place where you need it the + + + align:start position:0% +space at the place where you need it the +most which is the corner right so that + + align:start position:0% +most which is the corner right so that + + + align:start position:0% +most which is the corner right so that +when I'm here like a moth towards a + + align:start position:0% +when I'm here like a moth towards a + + + align:start position:0% +when I'm here like a moth towards a +light bulb I'm drawn towards the light + + align:start position:0% +light bulb I'm drawn towards the light + + + align:start position:0% +light bulb I'm drawn towards the light +to there and then once I'm there I'm + + align:start position:0% +to there and then once I'm there I'm + + + align:start position:0% +to there and then once I'm there I'm +drawn into there right I guess I was + + align:start position:0% +drawn into there right I guess I was + + + align:start position:0% +drawn into there right I guess I was +going directly like I was just piing + + align:start position:0% +going directly like I was just piing + + + align:start position:0% +going directly like I was just piing +yeah well which is good and and that's + + align:start position:0% +yeah well which is good and and that's + + + align:start position:0% +yeah well which is good and and that's +another that's a secondary um part of it + + align:start position:0% +another that's a secondary um part of it + + + align:start position:0% +another that's a secondary um part of it +but I'm talking about just I'm not so + + align:start position:0% +but I'm talking about just I'm not so + + + align:start position:0% +but I'm talking about just I'm not so +sure um in spite of everything you said + + align:start position:0% +sure um in spite of everything you said + + + align:start position:0% +sure um in spite of everything you said +but I'm still a little concerned that + + align:start position:0% +but I'm still a little concerned that + + + align:start position:0% +but I'm still a little concerned that +this space is preg good size without + + align:start position:0% +this space is preg good size without + + + align:start position:0% +this space is preg good size without +light coming from above right right so + + align:start position:0% +light coming from above right right so + + + align:start position:0% +light coming from above right right so +that's but I don't think that's a major + + align:start position:0% +that's but I don't think that's a major + + + align:start position:0% +that's but I don't think that's a major +um change I think that's a slight change + + align:start position:0% +um change I think that's a slight change + + + align:start position:0% +um change I think that's a slight change +in the organization and I think it's in + + align:start position:0% +in the organization and I think it's in + + + align:start position:0% +in the organization and I think it's in +that point yeah I mean there's I guess + + align:start position:0% +that point yeah I mean there's I guess + + + align:start position:0% +that point yeah I mean there's I guess +there's space between this plane and + + align:start position:0% +there's space between this plane and + + + align:start position:0% +there's space between this plane and +that building yeah you could do that too + + align:start position:0% +that building yeah you could do that too + + + align:start position:0% +that building yeah you could do that too +yeah and and even better because then + + align:start position:0% +yeah and and even better because then + + + align:start position:0% +yeah and and even better because then +the light would come down and wash that + + align:start position:0% +the light would come down and wash that + + + align:start position:0% +the light would come down and wash that +wall right so you get light down into + + align:start position:0% +wall right so you get light down into + + + align:start position:0% +wall right so you get light down into +the space and it's washing the wall at + + align:start position:0% +the space and it's washing the wall at + + + align:start position:0% +the space and it's washing the wall at +the same time which is would be would be + + align:start position:0% +the same time which is would be would be + + + align:start position:0% +the same time which is would be would be +the best because when I'm out here then + + align:start position:0% +the best because when I'm out here then + + + align:start position:0% +the best because when I'm out here then +I see that daylight hitting the side of + + align:start position:0% +I see that daylight hitting the side of + + + align:start position:0% +I see that daylight hitting the side of +the wall coming down okay now the biggie + + align:start position:0% +the wall coming down okay now the biggie + + + align:start position:0% +the wall coming down okay now the biggie +ready + + align:start position:0% +ready + + + align:start position:0% +ready +yeah the way you explained this and the + + align:start position:0% +yeah the way you explained this and the + + + align:start position:0% +yeah the way you explained this and the +way these guys are sitting here and I + + align:start position:0% +way these guys are sitting here and I + + + align:start position:0% +way these guys are sitting here and I +know they're just taped up and all that + + align:start position:0% +know they're just taped up and all that + + + align:start position:0% +know they're just taped up and all that +M which are quite uh + + align:start position:0% +M which are quite uh + + + align:start position:0% +M which are quite uh +beautiful but the immediate reaction + + align:start position:0% +beautiful but the immediate reaction + + + align:start position:0% +beautiful but the immediate reaction +that I have to it which I want you just + + align:start position:0% +that I have to it which I want you just + + + align:start position:0% +that I have to it which I want you just +consider mhm there is a configuration + + align:start position:0% +consider mhm there is a configuration + + + align:start position:0% +consider mhm there is a configuration +underneath this of geometric forms which + + align:start position:0% +underneath this of geometric forms which + + + align:start position:0% +underneath this of geometric forms which +producing the spaces all things we + + align:start position:0% +producing the spaces all things we + + + align:start position:0% +producing the spaces all things we +talked + + align:start position:0% +talked + + + align:start position:0% +talked +about in reality what you've done is you + + align:start position:0% +about in reality what you've done is you + + + align:start position:0% +about in reality what you've done is you +put like leaves on top of this to cover + + align:start position:0% +put like leaves on top of this to cover + + + align:start position:0% +put like leaves on top of this to cover +it and you talked about I probably can't + + align:start position:0% +it and you talked about I probably can't + + + align:start position:0% +it and you talked about I probably can't +do it different Heights of these + + align:start position:0% +do it different Heights of these + + + align:start position:0% +do it different Heights of these +yeah okay but unfortunately there's it's + + align:start position:0% +yeah okay but unfortunately there's it's + + + align:start position:0% +yeah okay but unfortunately there's it's +a bit like a crossword puzzle here this + + align:start position:0% +a bit like a crossword puzzle here this + + + align:start position:0% +a bit like a crossword puzzle here this +one should go under that one probably in + + align:start position:0% +one should go under that one probably in + + + align:start position:0% +one should go under that one probably in +order to make it work can I do that no I + + align:start position:0% +order to make it work can I do that no I + + + align:start position:0% +order to make it work can I do that no I +can no I + + align:start position:0% +can no I + + + align:start position:0% +can no I +can't I'm going to can I take this off + + align:start position:0% + + + + align:start position:0% + +okay so these are like petals mhm + + align:start position:0% +okay so these are like petals mhm + + + align:start position:0% +okay so these are like petals mhm +if this and you want to cover these GL + + align:start position:0% +if this and you want to cover these GL + + + align:start position:0% +if this and you want to cover these GL +and glass and but they're different + + align:start position:0% +and glass and but they're different + + + align:start position:0% +and glass and but they're different +levels just for the moment imagine + + align:start position:0% +levels just for the moment imagine + + + align:start position:0% +levels just for the moment imagine +there's no columns uhhuh instead there's + + align:start position:0% +there's no columns uhhuh instead there's + + + align:start position:0% +there's no columns uhhuh instead there's +tension uhhuh going up onto the + + align:start position:0% + + + + align:start position:0% + +wall so this part of the building which + + align:start position:0% +wall so this part of the building which + + + align:start position:0% +wall so this part of the building which +is what I would call Sky form is in fact + + align:start position:0% +is what I would call Sky form is in fact + + + align:start position:0% +is what I would call Sky form is in fact +separated to a certain extent from this + + align:start position:0% +separated to a certain extent from this + + + align:start position:0% +separated to a certain extent from this +mhm and it's acting like like a tent + + align:start position:0% +mhm and it's acting like like a tent + + + align:start position:0% +mhm and it's acting like like a tent +like + + align:start position:0% +like + + + align:start position:0% +like +covering therefore no columns going down + + align:start position:0% +covering therefore no columns going down + + + align:start position:0% +covering therefore no columns going down +and therefore where this is meeting the + + align:start position:0% +and therefore where this is meeting the + + + align:start position:0% +and therefore where this is meeting the +ever is a glass petition obviously but + + align:start position:0% +ever is a glass petition obviously but + + + align:start position:0% +ever is a glass petition obviously but +it's free to + + align:start position:0% +it's free to + + + align:start position:0% +it's free to +meet so well underneath this is a space + + align:start position:0% +meet so well underneath this is a space + + + align:start position:0% +meet so well underneath this is a space +obviously so the line of + + align:start position:0% +obviously so the line of + + + align:start position:0% +obviously so the line of +the of the wall might say coming up + + align:start position:0% +the of the wall might say coming up + + + align:start position:0% +the of the wall might say coming up +against this form underneath hit here + + align:start position:0% +against this form underneath hit here + + + align:start position:0% +against this form underneath hit here +then it might Zig back back and hit this + + align:start position:0% +then it might Zig back back and hit this + + + align:start position:0% +then it might Zig back back and hit this +one and Zig back and hit that one Zig + + align:start position:0% +one and Zig back and hit that one Zig + + + align:start position:0% +one and Zig back and hit that one Zig +back and hit this one right okay yeah so + + align:start position:0% +back and hit this one right okay yeah so + + + align:start position:0% +back and hit this one right okay yeah so +the walls which are glass I think I I + + align:start position:0% +the walls which are glass I think I I + + + align:start position:0% +the walls which are glass I think I I +would assume you you + + align:start position:0% +would assume you you + + + align:start position:0% +would assume you you +met are transparent + + align:start position:0% +met are transparent + + + align:start position:0% +met are transparent +yeah and it's being held up with cables + + align:start position:0% +yeah and it's being held up with cables + + + align:start position:0% +yeah and it's being held up with cables +which it can be + + align:start position:0% +which it can be + + + align:start position:0% +which it can be +done and at night this is like a little + + align:start position:0% +done and at night this is like a little + + + align:start position:0% +done and at night this is like a little +and this might be uh copper roofs I + + align:start position:0% +and this might be uh copper roofs I + + + align:start position:0% +and this might be uh copper roofs I +don't know what it is it's light metal + + align:start position:0% +don't know what it is it's light metal + + + align:start position:0% +don't know what it is it's light metal +maybe or glass uh or maybe it doesn't + + align:start position:0% +maybe or glass uh or maybe it doesn't + + + align:start position:0% +maybe or glass uh or maybe it doesn't +have to be glass maybe it's just the + + align:start position:0% +have to be glass maybe it's just the + + + align:start position:0% +have to be glass maybe it's just the +light coming through it is at night I + + align:start position:0% +light coming through it is at night I + + + align:start position:0% +light coming through it is at night I +see this glow underneath of + + align:start position:0% +see this glow underneath of + + + align:start position:0% +see this glow underneath of +these uh forums coming off this this + + align:start position:0% +these uh forums coming off this this + + + align:start position:0% +these uh forums coming off this this +building and therefore I don't have a + + align:start position:0% +building and therefore I don't have a + + + align:start position:0% +building and therefore I don't have a +force of columns coming down F I was + + align:start position:0% +force of columns coming down F I was + + + align:start position:0% +force of columns coming down F I was +kind of worried about well the point is + + align:start position:0% +kind of worried about well the point is + + + align:start position:0% +kind of worried about well the point is +is that you see there's + + align:start position:0% +is that you see there's + + + align:start position:0% +is that you see there's +two I think there are two structures + + align:start position:0% +two I think there are two structures + + + align:start position:0% +two I think there are two structures +here I think there's + + align:start position:0% +here I think there's + + + align:start position:0% +here I think there's +this and then there's this M and so by + + align:start position:0% +this and then there's this M and so by + + + align:start position:0% +this and then there's this M and so by +not having + + align:start position:0% +not having + + + align:start position:0% +not having +columns I don't have to try to get those + + align:start position:0% +columns I don't have to try to get those + + + align:start position:0% +columns I don't have to try to get those +columns down through that right and I + + align:start position:0% +columns down through that right and I + + + align:start position:0% +columns down through that right and I +know that David can help you on this but + + align:start position:0% +know that David can help you on this but + + + align:start position:0% +know that David can help you on this but +I know that we can do that + + align:start position:0% +I know that we can do that + + + align:start position:0% +I know that we can do that +architecturally we can hang these + + align:start position:0% +architecturally we can hang these + + + align:start position:0% +architecturally we can hang these +guys and and by the way it might look + + align:start position:0% +guys and and by the way it might look + + + align:start position:0% +guys and and by the way it might look +very + + align:start position:0% +very + + + align:start position:0% +very +beautiful um if I saw a bunch of cables + + align:start position:0% +beautiful um if I saw a bunch of cables + + + align:start position:0% +beautiful um if I saw a bunch of cables +coming + + align:start position:0% + + + + align:start position:0% + +across yeah with the roofs on top uhhuh + + align:start position:0% +across yeah with the roofs on top uhhuh + + + align:start position:0% +across yeah with the roofs on top uhhuh +H now does that uh yeah I like that does + + align:start position:0% +H now does that uh yeah I like that does + + + align:start position:0% +H now does that uh yeah I like that does +that uh cuz I you know imagine just like + + align:start position:0% +that uh cuz I you know imagine just like + + + align:start position:0% +that uh cuz I you know imagine just like +sort of floating yeah well I think + + align:start position:0% +sort of floating yeah well I think + + + align:start position:0% +sort of floating yeah well I think +that's what you imagine them as floating + + align:start position:0% +that's what you imagine them as floating + + + align:start position:0% +that's what you imagine them as floating +but if they got columns on them they're + + align:start position:0% +but if they got columns on them they're + + + align:start position:0% +but if they got columns on them they're +not exactly floating it's a it's it's + + align:start position:0% +not exactly floating it's a it's it's + + + align:start position:0% +not exactly floating it's a it's it's +still okay but it's not quite the + + align:start position:0% +still okay but it's not quite the + + + align:start position:0% +still okay but it's not quite the +same okay so think about that one before + + align:start position:0% +same okay so think about that one before + + + align:start position:0% +same okay so think about that one before +you do it but it it might uh it might + + align:start position:0% +you do it but it it might uh it might + + + align:start position:0% +you do it but it it might uh it might +make your idea even stronger yeah I like + + align:start position:0% +make your idea even stronger yeah I like + + + align:start position:0% +make your idea even stronger yeah I like +it um um we got a Troublesome spot here + + align:start position:0% +it um um we got a Troublesome spot here + + + align:start position:0% +it um um we got a Troublesome spot here +that I think you can Sol yeah I think + + align:start position:0% +that I think you can Sol yeah I think + + + align:start position:0% +that I think you can Sol yeah I think +opening of that right there might have + + align:start position:0% +opening of that right there might have + + + align:start position:0% +opening of that right there might have +and by the way I that's up there then I + + align:start position:0% +and by the way I that's up there then I + + + align:start position:0% +and by the way I that's up there then I +have more to I can play more with them + + align:start position:0% +have more to I can play more with them + + + align:start position:0% +have more to I can play more with them +uh I think the land form needs to be + + align:start position:0% +uh I think the land form needs to be + + + align:start position:0% +uh I think the land form needs to be +more articulate uhhm ter get yeah + + align:start position:0% +more articulate uhhm ter get yeah + + + align:start position:0% +more articulate uhhm ter get yeah +getting up through and the copper uh L + + align:start position:0% +getting up through and the copper uh L + + + align:start position:0% +getting up through and the copper uh L +copper passageway for instance this + + align:start position:0% +copper passageway for instance this + + + align:start position:0% +copper passageway for instance this +might come down it might be narrower and + + align:start position:0% +might come down it might be narrower and + + + align:start position:0% +might come down it might be narrower and +narrower and then it comes down to the + + align:start position:0% +narrower and then it comes down to the + + + align:start position:0% +narrower and then it comes down to the +other side of the street which should be + + align:start position:0% +other side of the street which should be + + + align:start position:0% +other side of the street which should be +about + + align:start position:0% +about + + + align:start position:0% +about +there okay and you're uh and you and by + + align:start position:0% +there okay and you're uh and you and by + + + align:start position:0% +there okay and you're uh and you and by +the way there's a + + align:start position:0% +the way there's a + + + align:start position:0% +the way there's a +wall I'm saying somewhere in here you + + align:start position:0% +wall I'm saying somewhere in here you + + + align:start position:0% +wall I'm saying somewhere in here you +start up but there's also a wall in + + align:start position:0% + + + + align:start position:0% + +here but it may not be as high as that + + align:start position:0% +here but it may not be as high as that + + + align:start position:0% +here but it may not be as high as that +of + + align:start position:0% +of + + + align:start position:0% +of +course so what it is is is that I'm + + align:start position:0% +course so what it is is is that I'm + + + align:start position:0% +course so what it is is is that I'm +moving down the street and I'm slowly + + align:start position:0% +moving down the street and I'm slowly + + + align:start position:0% +moving down the street and I'm slowly +making a transition from the street into + + align:start position:0% +making a transition from the street into + + + align:start position:0% +making a transition from the street into +this world of yours and I may not even + + align:start position:0% +this world of yours and I may not even + + + align:start position:0% +this world of yours and I may not even +know I do it + + align:start position:0% +know I do it + + + align:start position:0% +know I do it +yeah I wanted them to be like oh wait I + + align:start position:0% +yeah I wanted them to be like oh wait I + + + align:start position:0% +yeah I wanted them to be like oh wait I +didn't want to be on the right but then + + align:start position:0% +didn't want to be on the right but then + + + align:start position:0% +didn't want to be on the right but then +all of a sudden I find this incredible + + align:start position:0% +all of a sudden I find this incredible + + + align:start position:0% +all of a sudden I find this incredible +thing they're working in they building + + align:start position:0% +thing they're working in they building + + + align:start position:0% +thing they're working in they building +this unbelievable float that I can + + align:start position:0% +this unbelievable float that I can + + + align:start position:0% +this unbelievable float that I can +see so what you need to do now is to + + align:start position:0% +see so what you need to do now is to + + + align:start position:0% +see so what you need to do now is to +beyond what I just said is also start to + + align:start position:0% +beyond what I just said is also start to + + + align:start position:0% +beyond what I just said is also start to +make some articulation of what the + + align:start position:0% +make some articulation of what the + + + align:start position:0% +make some articulation of what the +materials are or at least not materials + + align:start position:0% +materials are or at least not materials + + + align:start position:0% +materials are or at least not materials +at this stage but at least opaque + + align:start position:0% +at this stage but at least opaque + + + align:start position:0% +at this stage but at least opaque +transparent translucent yeah not this by + + align:start position:0% +transparent translucent yeah not this by + + + align:start position:0% +transparent translucent yeah not this by +the way this is open is it not yeah yeah + + align:start position:0% +the way this is open is it not yeah yeah + + + align:start position:0% +the way this is open is it not yeah yeah +yeah which I think it it should be yeah + + align:start position:0% +yeah which I think it it should be yeah + + + align:start position:0% +yeah which I think it it should be yeah +it's outdoor it's not heated right + + align:start position:0% +it's outdoor it's not heated right + + + align:start position:0% +it's outdoor it's not heated right +exactly I think it's uh I think it's + + align:start position:0% +exactly I think it's uh I think it's + + + align:start position:0% +exactly I think it's uh I think it's +neat and I think it's interesting + + align:start position:0% +neat and I think it's interesting + + + align:start position:0% +neat and I think it's interesting +because it has a relationship to your + + align:start position:0% +because it has a relationship to your + + + align:start position:0% +because it has a relationship to your +previous projects and uh uh in + + align:start position:0% +previous projects and uh uh in + + + align:start position:0% +previous projects and uh uh in +a in a strange way it's the billboard on + + align:start position:0% +a in a strange way it's the billboard on + + + align:start position:0% +a in a strange way it's the billboard on +its side it's the it's the Sals floating + + align:start position:0% +its side it's the it's the Sals floating + + + align:start position:0% +its side it's the it's the Sals floating +and it's kind of like it's a summary of + + align:start position:0% +and it's kind of like it's a summary of + + + align:start position:0% +and it's kind of like it's a summary of +book project that you're + + align:start position:0% +book project that you're + + + align:start position:0% +book project that you're +done okay so go to it + + align:start position:0% + + + + align:start position:0% + +I guess I started um from the plan and + + align:start position:0% +I guess I started um from the plan and + + + align:start position:0% +I guess I started um from the plan and +tried to do like use the + + align:start position:0% +tried to do like use the + + + align:start position:0% +tried to do like use the +existing lines to create the the shapes + + align:start position:0% +existing lines to create the the shapes + + + align:start position:0% +existing lines to create the the shapes +for the planes and my different floors + + align:start position:0% +for the planes and my different floors + + + align:start position:0% +for the planes and my different floors +and so a lot of them came out of being a + + align:start position:0% +and so a lot of them came out of being a + + + align:start position:0% +and so a lot of them came out of being a +perpendicular from the building or + + align:start position:0% +perpendicular from the building or + + + align:start position:0% +perpendicular from the building or +parallel to or perpendicular parallel to + + align:start position:0% +parallel to or perpendicular parallel to + + + align:start position:0% +parallel to or perpendicular parallel to +the street and and then from there I + + align:start position:0% +the street and and then from there I + + + align:start position:0% +the street and and then from there I +just like kind of cut them and and um + + align:start position:0% +just like kind of cut them and and um + + + align:start position:0% +just like kind of cut them and and um +kept trying to figure out what shapes + + align:start position:0% +kept trying to figure out what shapes + + + align:start position:0% +kept trying to figure out what shapes +would work with the program and + + align:start position:0% +would work with the program and + + + align:start position:0% +would work with the program and +circulation and compositionally I guess + + align:start position:0% +circulation and compositionally I guess + + + align:start position:0% +circulation and compositionally I guess +and this is like him up with so + + align:start position:0% +and this is like him up with so + + + align:start position:0% +and this is like him up with so +um is kind of imagining like the you + + align:start position:0% +um is kind of imagining like the you + + + align:start position:0% +um is kind of imagining like the you +know the bottom floor to be where like + + align:start position:0% +know the bottom floor to be where like + + + align:start position:0% +know the bottom floor to be where like +the restaurant is and there's like that + + align:start position:0% +the restaurant is and there's like that + + + align:start position:0% +the restaurant is and there's like that +there's access from the + + align:start position:0% +there's access from the + + + align:start position:0% +there's access from the +back also so you can go directly from + + align:start position:0% +back also so you can go directly from + + + align:start position:0% +back also so you can go directly from +the bottom and also it's you know the + + align:start position:0% +the bottom and also it's you know the + + + align:start position:0% +the bottom and also it's you know the +ambiguous is it the skate park or is it + + align:start position:0% +ambiguous is it the skate park or is it + + + align:start position:0% +ambiguous is it the skate park or is it +for function of the building and + + align:start position:0% +for function of the building and + + + align:start position:0% +for function of the building and +um and then it's kind of hard to see + + align:start position:0% +um and then it's kind of hard to see + + + align:start position:0% +um and then it's kind of hard to see +with it like this but no but I can see + + align:start position:0% +with it like this but no but I can see + + + align:start position:0% +with it like this but no but I can see +it don't take it apart but so transition + + align:start position:0% +it don't take it apart but so transition + + + align:start position:0% +it don't take it apart but so transition +space still also from the two spaces and + + align:start position:0% +space still also from the two spaces and + + + align:start position:0% +space still also from the two spaces and +then I focused on having I figured a lot + + align:start position:0% +then I focused on having I figured a lot + + + align:start position:0% +then I focused on having I figured a lot +of people would spend a lot of time like + + align:start position:0% +of people would spend a lot of time like + + + align:start position:0% +of people would spend a lot of time like +I wanted to integrate the skating aspect + + align:start position:0% +I wanted to integrate the skating aspect + + + align:start position:0% +I wanted to integrate the skating aspect +and the rock climbing aspect more + + align:start position:0% +and the rock climbing aspect more + + + align:start position:0% +and the rock climbing aspect more +because cuz the way I had it before is + + align:start position:0% +because cuz the way I had it before is + + + align:start position:0% +because cuz the way I had it before is +kind of just like skating on or below + + align:start position:0% +kind of just like skating on or below + + + align:start position:0% +kind of just like skating on or below +the grade and then the building was rock + + align:start position:0% +the grade and then the building was rock + + + align:start position:0% +the grade and then the building was rock +climbing so I wanted to bring in more of + + align:start position:0% +climbing so I wanted to bring in more of + + + align:start position:0% +climbing so I wanted to bring in more of +the um skating into it so I had a + + align:start position:0% +the um skating into it so I had a + + + align:start position:0% +the um skating into it so I had a +halfpipe in there which I figured a lot + + align:start position:0% +halfpipe in there which I figured a lot + + + align:start position:0% +halfpipe in there which I figured a lot +of people spend a lot of time in um it's + + align:start position:0% +of people spend a lot of time in um it's + + + align:start position:0% +of people spend a lot of time in um it's +more stationary of a skating area since + + align:start position:0% +more stationary of a skating area since + + + align:start position:0% +more stationary of a skating area since +you're staying within it and then the + + align:start position:0% +you're staying within it and then the + + + align:start position:0% +you're staying within it and then the +part where you come up + + align:start position:0% +part where you come up + + + align:start position:0% +part where you come up +is kind of has a relationship to this + + align:start position:0% +is kind of has a relationship to this + + + align:start position:0% +is kind of has a relationship to this +part down here where the largest + + align:start position:0% +part down here where the largest + + + align:start position:0% +part down here where the largest +Climbing Center about walls where people + + align:start position:0% +Climbing Center about walls where people + + + align:start position:0% +Climbing Center about walls where people +would be standing here to blay the + + align:start position:0% +would be standing here to blay the + + + align:start position:0% +would be standing here to blay the +people climbing so you have like the + + align:start position:0% +people climbing so you have like the + + + align:start position:0% +people climbing so you have like the +rock climbers and skaters being able to + + align:start position:0% +rock climbers and skaters being able to + + + align:start position:0% +rock climbers and skaters being able to +see more of what's going on between the + + align:start position:0% +see more of what's going on between the + + + align:start position:0% +see more of what's going on between the +two activities um and then I also had + + align:start position:0% +two activities um and then I also had + + + align:start position:0% +two activities um and then I also had +mentioned in the um pinup for the + + align:start position:0% +mentioned in the um pinup for the + + + align:start position:0% +mentioned in the um pinup for the +posters that I had wanted an area where + + align:start position:0% +posters that I had wanted an area where + + + align:start position:0% +posters that I had wanted an area where +people could learn how to rock + + align:start position:0% +people could learn how to rock + + + align:start position:0% +people could learn how to rock +climb I so I see like this Center being + + align:start position:0% +climb I so I see like this Center being + + + align:start position:0% +climb I so I see like this Center being +like + + align:start position:0% +like + + + align:start position:0% +like +so the wall extends all the way through + + align:start position:0% +so the wall extends all the way through + + + align:start position:0% +so the wall extends all the way through +but it'll be a smaller wall for lessons + + align:start position:0% +but it'll be a smaller wall for lessons + + + align:start position:0% +but it'll be a smaller wall for lessons +and stuff that you could also see the + + align:start position:0% +and stuff that you could also see the + + + align:start position:0% +and stuff that you could also see the +main wall so I guess everything kind of + + align:start position:0% +main wall so I guess everything kind of + + + align:start position:0% +main wall so I guess everything kind of +ended up being like focused around being + + align:start position:0% +ended up being like focused around being + + + align:start position:0% +ended up being like focused around being +able to always have a view of these two + + align:start position:0% +able to always have a view of these two + + + align:start position:0% +able to always have a view of these two +activities but being as open to the + + align:start position:0% +activities but being as open to the + + + align:start position:0% +activities but being as open to the +outside as as possible also and I + + align:start position:0% +outside as as possible also and I + + + align:start position:0% +outside as as possible also and I +haven't done the um I'm working on + + align:start position:0% +haven't done the um I'm working on + + + align:start position:0% +haven't done the um I'm working on +seeing what full walls I want and so I + + align:start position:0% +seeing what full walls I want and so I + + + align:start position:0% +seeing what full walls I want and so I +started doing like the railing so I + + align:start position:0% +started doing like the railing so I + + + align:start position:0% +started doing like the railing so I +could put in the main wall to start to + + align:start position:0% +could put in the main wall to start to + + + align:start position:0% +could put in the main wall to start to +take have the outer structure take for + + align:start position:0% +take have the outer structure take for + + + align:start position:0% +take have the outer structure take for +like right now I see it as being cuz I + + align:start position:0% +like right now I see it as being cuz I + + + align:start position:0% +like right now I see it as being cuz I +purposely I wanted to have a lot of + + align:start position:0% +purposely I wanted to have a lot of + + + align:start position:0% +purposely I wanted to have a lot of +faces to it kind of like um how I talk + + align:start position:0% +faces to it kind of like um how I talk + + + align:start position:0% +faces to it kind of like um how I talk +about in my presentation um is + + align:start position:0% +about in my presentation um is + + + align:start position:0% +about in my presentation um is +having the the skate area suggest the + + align:start position:0% +having the the skate area suggest the + + + align:start position:0% +having the the skate area suggest the +the pools and the water and fluidity and + + align:start position:0% +the pools and the water and fluidity and + + + align:start position:0% +the pools and the water and fluidity and +then the building more of like a a MK so + + align:start position:0% +then the building more of like a a MK so + + + align:start position:0% +then the building more of like a a MK so +kind of like how the rock how rocks are + + align:start position:0% +kind of like how the rock how rocks are + + + align:start position:0% +kind of like how the rock how rocks are +I want it to have like a lot of faces um + + align:start position:0% +I want it to have like a lot of faces um + + + align:start position:0% +I want it to have like a lot of faces um +each face like having different material + + align:start position:0% +each face like having different material + + + align:start position:0% +each face like having different material +maybe according to what I see need um + + align:start position:0% +maybe according to what I see need um + + + align:start position:0% +maybe according to what I see need um +and so I think like these different + + align:start position:0% +and so I think like these different + + + align:start position:0% +and so I think like these different +edges will provide that and have some + + align:start position:0% +edges will provide that and have some + + + align:start position:0% +edges will provide that and have some +like coming in and out mhm I'm just not + + align:start position:0% +like coming in and out mhm I'm just not + + + align:start position:0% +like coming in and out mhm I'm just not +sure how + + align:start position:0% +sure how + + + align:start position:0% +sure how +exactly I'm going to do it like if I'm + + align:start position:0% +exactly I'm going to do it like if I'm + + + align:start position:0% +exactly I'm going to do it like if I'm +going to have this be inside to outside + + align:start position:0% +going to have this be inside to outside + + + align:start position:0% +going to have this be inside to outside +structure or had it like have inside or + + align:start position:0% +structure or had it like have inside or + + + align:start position:0% +structure or had it like have inside or +like I did have these kind + + align:start position:0% +like I did have these kind + + + align:start position:0% +like I did have these kind +of on here um as like the different + + align:start position:0% +of on here um as like the different + + + align:start position:0% +of on here um as like the different +areas that I might have like have this + + align:start position:0% +areas that I might have like have this + + + align:start position:0% +areas that I might have like have this +be one IND section and then like this + + align:start position:0% +be one IND section and then like this + + + align:start position:0% +be one IND section and then like this +another and then this another so they'd + + align:start position:0% +another and then this another so they'd + + + align:start position:0% +another and then this another so they'd +be at different levels but I haven't + + align:start position:0% +be at different levels but I haven't + + + align:start position:0% +be at different levels but I haven't +quite figured that out yet I'm not sure + + align:start position:0% +quite figured that out yet I'm not sure + + + align:start position:0% +quite figured that out yet I'm not sure +about like if I want to have and then + + align:start position:0% +about like if I want to have and then + + + align:start position:0% +about like if I want to have and then +like I wanted to be in as much light as + + align:start position:0% +like I wanted to be in as much light as + + + align:start position:0% +like I wanted to be in as much light as +possible of course so those are all the + + align:start position:0% +possible of course so those are all the + + + align:start position:0% +possible of course so those are all the +different factors I'm trying to consider + + align:start position:0% +different factors I'm trying to consider + + + align:start position:0% +different factors I'm trying to consider +when I do the walls and move I guess and + + align:start position:0% +when I do the walls and move I guess and + + + align:start position:0% +when I do the walls and move I guess and +this is outside and of course this one + + align:start position:0% +this is outside and of course this one + + + align:start position:0% +this is outside and of course this one +is outside but most + + align:start position:0% +is outside but most + + + align:start position:0% +is outside but most +likely is this this is outside too most + + align:start position:0% +likely is this this is outside too most + + + align:start position:0% +likely is this this is outside too most +likely or not most likely inside right + + align:start position:0% +likely or not most likely inside right + + + align:start position:0% +likely or not most likely inside right +now so I'm inside and then I go outside + + align:start position:0% +now so I'm inside and then I go outside + + + align:start position:0% +now so I'm inside and then I go outside +here something yeah there' be a door + + align:start position:0% +here something yeah there' be a door + + + align:start position:0% +here something yeah there' be a door +right here mhm + + align:start position:0% +right here mhm + + + align:start position:0% +right here mhm +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +okay and then inside I think I see it + + align:start position:0% +okay and then inside I think I see it + + + align:start position:0% +okay and then inside I think I see it +but there's a set of steps that kind of + + align:start position:0% +but there's a set of steps that kind of + + + align:start position:0% +but there's a set of steps that kind of +take me from here to here and then from + + align:start position:0% +take me from here to here and then from + + + align:start position:0% +take me from here to here and then from +there to there yeah basically there's + + align:start position:0% +there to there yeah basically there's + + + align:start position:0% +there to there yeah basically there's +only really three levels in it there's + + align:start position:0% +only really three levels in it there's + + + align:start position:0% +only really three levels in it there's +one below it but there's three levels M + + align:start position:0% +one below it but there's three levels M + + + align:start position:0% +one below it but there's three levels M +getting up through where do + + align:start position:0% +getting up through where do + + + align:start position:0% +getting up through where do +I I don't know this building I have + + align:start position:0% +I I don't know this building I have + + + align:start position:0% +I I don't know this building I have +never been here before how do I know + + align:start position:0% +never been here before how do I know + + + align:start position:0% +never been here before how do I know +where to come in uh well I was going to + + align:start position:0% +where to come in uh well I was going to + + + align:start position:0% +where to come in uh well I was going to +have um this area be solid like how that + + align:start position:0% +have um this area be solid like how that + + + align:start position:0% +have um this area be solid like how that +one is or less transparent um so you can + + align:start position:0% +one is or less transparent um so you can + + + align:start position:0% +one is or less transparent um so you can +clim on it yeah and then this would be + + align:start position:0% +clim on it yeah and then this would be + + + align:start position:0% +clim on it yeah and then this would be +very um and I like had it tilted slanted + + align:start position:0% +very um and I like had it tilted slanted + + + align:start position:0% +very um and I like had it tilted slanted +this way so when cuz most of the traffic + + align:start position:0% +this way so when cuz most of the traffic + + + align:start position:0% +this way so when cuz most of the traffic +is coming this way so you will be able + + align:start position:0% +is coming this way so you will be able + + + align:start position:0% +is coming this way so you will be able +to see like steps and to clear like + + align:start position:0% +to see like steps and to clear like + + + align:start position:0% +to see like steps and to clear like +maybe automatic doors and then I was + + align:start position:0% +maybe automatic doors and then I was + + + align:start position:0% +maybe automatic doors and then I was +hoping that this would catch people's + + align:start position:0% +hoping that this would catch people's + + + align:start position:0% +hoping that this would catch people's +attention being able to see this inside + + align:start position:0% +attention being able to see this inside + + + align:start position:0% +attention being able to see this inside +the building and wanting to go look at + + align:start position:0% +the building and wanting to go look at + + + align:start position:0% +the building and wanting to go look at +it and then um like the pattern on the + + align:start position:0% +it and then um like the pattern on the + + + align:start position:0% +it and then um like the pattern on the +floor following it out over here and I + + align:start position:0% +floor following it out over here and I + + + align:start position:0% +floor following it out over here and I +can saw kind of like a reception place + + align:start position:0% +can saw kind of like a reception place + + + align:start position:0% +can saw kind of like a reception place +here and then the food place so from + + align:start position:0% +here and then the food place so from + + + align:start position:0% +here and then the food place so from +that angle I kind of see like that um + + align:start position:0% +that angle I kind of see like that um + + + align:start position:0% +that angle I kind of see like that um +and hopefully like from any of the + + align:start position:0% +and hopefully like from any of the + + + align:start position:0% +and hopefully like from any of the +angles you see the St + + align:start position:0% + + + + align:start position:0% + +mov okay I got it first of all it's a + + align:start position:0% +mov okay I got it first of all it's a + + + align:start position:0% +mov okay I got it first of all it's a +it's a great jump from a + + align:start position:0% +it's a great jump from a + + + align:start position:0% +it's a great jump from a +Tuesday and uh making it + + align:start position:0% +Tuesday and uh making it + + + align:start position:0% +Tuesday and uh making it +smaller by that factor but bigger than + + align:start position:0% +smaller by that factor but bigger than + + + align:start position:0% +smaller by that factor but bigger than +this one mhm is just to me about the + + align:start position:0% +this one mhm is just to me about the + + + align:start position:0% +this one mhm is just to me about the +right size for the right side the other + + align:start position:0% +right size for the right side the other + + + align:start position:0% +right size for the right side the other +thing that you had but we didn't see it + + align:start position:0% +thing that you had but we didn't see it + + + align:start position:0% +thing that you had but we didn't see it +entirely which I think is really + + align:start position:0% +entirely which I think is really + + + align:start position:0% +entirely which I think is really +powerful here is this bridge or this + + align:start position:0% +powerful here is this bridge or this + + + align:start position:0% +powerful here is this bridge or this +Lookout acting as kind of a continuity + + align:start position:0% +Lookout acting as kind of a continuity + + + align:start position:0% +Lookout acting as kind of a continuity +around the building MH and even to the + + align:start position:0% +around the building MH and even to the + + + align:start position:0% +around the building MH and even to the +point where if we could see another one + + align:start position:0% +point where if we could see another one + + + align:start position:0% +point where if we could see another one +of these someplace over here if that + + align:start position:0% +of these someplace over here if that + + + align:start position:0% +of these someplace over here if that +were + + align:start position:0% +were + + + align:start position:0% +were +possible um so that these being outside + + align:start position:0% +possible um so that these being outside + + + align:start position:0% +possible um so that these being outside +I go into the building I come out and I + + align:start position:0% +I go into the building I come out and I + + + align:start position:0% +I go into the building I come out and I +see different views this one was the + + align:start position:0% +see different views this one was the + + + align:start position:0% +see different views this one was the +viewing platform from way back but maybe + + align:start position:0% +viewing platform from way back but maybe + + + align:start position:0% +viewing platform from way back but maybe +there's one another one over there or + + align:start position:0% +there's one another one over there or + + + align:start position:0% +there's one another one over there or +maybe there's one from even from the + + align:start position:0% +maybe there's one from even from the + + + align:start position:0% +maybe there's one from even from the +second floor but that's all um to me + + align:start position:0% +second floor but that's all um to me + + + align:start position:0% +second floor but that's all um to me +that's very strong this + + align:start position:0% +that's very strong this + + + align:start position:0% +that's very strong this +part the other part that's strong is the + + align:start position:0% +part the other part that's strong is the + + + align:start position:0% +part the other part that's strong is the +uh the landscape that's being created + + align:start position:0% +uh the landscape that's being created + + + align:start position:0% +uh the landscape that's being created +because of this which is beautiful + + align:start position:0% +because of this which is beautiful + + + align:start position:0% +because of this which is beautiful +underneath this this is + + align:start position:0% +underneath this this is + + + align:start position:0% +underneath this this is +terrific uh and here and and the copper + + align:start position:0% +terrific uh and here and and the copper + + + align:start position:0% +terrific uh and here and and the copper +Tu I think is great because you'd be + + align:start position:0% +Tu I think is great because you'd be + + + align:start position:0% +Tu I think is great because you'd be +standing here and you would know what + + align:start position:0% +standing here and you would know what + + + align:start position:0% +standing here and you would know what +would be coming in or out you somebody + + align:start position:0% +would be coming in or out you somebody + + + align:start position:0% +would be coming in or out you somebody +be coming through you hear the noise + + align:start position:0% +be coming through you hear the noise + + + align:start position:0% +be coming through you hear the noise +you'd hear the noise and then wow it + + align:start position:0% +you'd hear the noise and then wow it + + + align:start position:0% +you'd hear the noise and then wow it +come through which would be I think very + + align:start position:0% +come through which would be I think very + + + align:start position:0% +come through which would be I think very +powerful um so it seems to me that the + + align:start position:0% +powerful um so it seems to me that the + + + align:start position:0% +powerful um so it seems to me that the +the landscape issue of this and the + + align:start position:0% +the landscape issue of this and the + + + align:start position:0% +the landscape issue of this and the +building are integrated very well and by + + align:start position:0% +building are integrated very well and by + + + align:start position:0% +building are integrated very well and by +the way much better than it was the + + align:start position:0% +the way much better than it was the + + + align:start position:0% +the way much better than it was the +other day when you were talking with + + align:start position:0% +other day when you were talking with + + + align:start position:0% +other day when you were talking with +curves it's the + + align:start position:0% +curves it's the + + + align:start position:0% +curves it's the +wrong wrong way to go I think couple + + align:start position:0% +wrong wrong way to go I think couple + + + align:start position:0% +wrong wrong way to go I think couple +things that I see that just bring to you + + align:start position:0% +things that I see that just bring to you + + + align:start position:0% +things that I see that just bring to you +attention + + align:start position:0% +attention + + + align:start position:0% +attention +MH I am still somewhat bothered by the + + align:start position:0% +MH I am still somewhat bothered by the + + + align:start position:0% +MH I am still somewhat bothered by the +notion that the little kids are over + + align:start position:0% +notion that the little kids are over + + + align:start position:0% +notion that the little kids are over +here hanging out at the very edge of the + + align:start position:0% +here hanging out at the very edge of the + + + align:start position:0% +here hanging out at the very edge of the +site so to speak MH and the big kids + + align:start position:0% +site so to speak MH and the big kids + + + align:start position:0% +site so to speak MH and the big kids +stop I assume and go around here and + + align:start position:0% +stop I assume and go around here and + + + align:start position:0% +stop I assume and go around here and +come + + align:start position:0% +come + + + align:start position:0% +come +back well it's kind of um seeing this as + + align:start position:0% +back well it's kind of um seeing this as + + + align:start position:0% +back well it's kind of um seeing this as +a transition space between two different + + align:start position:0% +a transition space between two different + + + align:start position:0% +a transition space between two different +kinds of skating like the pool skating + + align:start position:0% +kinds of skating like the pool skating + + + align:start position:0% +kinds of skating like the pool skating +and then more like the street trick you + + align:start position:0% +and then more like the street trick you + + + align:start position:0% +and then more like the street trick you +do like Street tricks skating like it'll + + align:start position:0% +do like Street tricks skating like it'll + + + align:start position:0% +do like Street tricks skating like it'll +be more like rails and steps that kind + + align:start position:0% +be more like rails and steps that kind + + + align:start position:0% +be more like rails and steps that kind +of like slower speed okay so not + + align:start position:0% +of like slower speed okay so not + + + align:start position:0% +of like slower speed okay so not +necessarily little kids as opposed to + + align:start position:0% +necessarily little kids as opposed to + + + align:start position:0% +necessarily little kids as opposed to +big kids yeah like little kids just so + + align:start position:0% +big kids yeah like little kids just so + + + align:start position:0% +big kids yeah like little kids just so +in the sense that like this is all very + + align:start position:0% +in the sense that like this is all very + + + align:start position:0% +in the sense that like this is all very +high speed and a little more dangerous I + + align:start position:0% +high speed and a little more dangerous I + + + align:start position:0% +high speed and a little more dangerous I +guess but this is it still has like the + + align:start position:0% +guess but this is it still has like the + + + align:start position:0% +guess but this is it still has like the +slopes they can work on but like the big + + align:start position:0% +slopes they can work on but like the big + + + align:start position:0% +slopes they can work on but like the big +kids would go here to work on Street + + align:start position:0% +kids would go here to work on Street + + + align:start position:0% +kids would go here to work on Street +skating anyway um it's just not as high + + align:start position:0% +skating anyway um it's just not as high + + + align:start position:0% +skating anyway um it's just not as high +speed as this area well fine another way + + align:start position:0% +speed as this area well fine another way + + + align:start position:0% +speed as this area well fine another way +of doing it however would have been not + + align:start position:0% +of doing it however would have been not + + + align:start position:0% +of doing it however would have been not +to do here but to do that someplace else + + align:start position:0% +to do here but to do that someplace else + + + align:start position:0% +to do here but to do that someplace else +like back there or even + + align:start position:0% +like back there or even + + + align:start position:0% +like back there or even +inside and let this thing become much + + align:start position:0% +inside and let this thing become much + + + align:start position:0% +inside and let this thing become much +more of a counterbalance to the other + + align:start position:0% +more of a counterbalance to the other + + + align:start position:0% +more of a counterbalance to the other +side so that I would come out of this + + align:start position:0% +side so that I would come out of this + + + align:start position:0% +side so that I would come out of this +tube around and then I would assume back + + align:start position:0% +tube around and then I would assume back + + + align:start position:0% +tube around and then I would assume back +into the building and around so if + + align:start position:0% +into the building and around so if + + + align:start position:0% +into the building and around so if +that's what you if that's a possibility + + align:start position:0% +that's what you if that's a possibility + + + align:start position:0% +that's what you if that's a possibility +that it's more of a continuous surface + + align:start position:0% +that it's more of a continuous surface + + + align:start position:0% +that it's more of a continuous surface +if I if I got it right is it right that + + align:start position:0% +if I if I got it right is it right that + + + align:start position:0% +if I if I got it right is it right that +I could in theory go from here through + + align:start position:0% +I could in theory go from here through + + + align:start position:0% +I could in theory go from here through +the building and come out yeah so the + + align:start position:0% +the building and come out yeah so the + + + align:start position:0% +the building and come out yeah so the +notion of almost this figure eight kind + + align:start position:0% +notion of almost this figure eight kind + + + align:start position:0% +notion of almost this figure eight kind +of notion coming through the + + align:start position:0% +of notion coming through the + + + align:start position:0% +of notion coming through the +building + + align:start position:0% +building + + + align:start position:0% +building +um might be another way of doing it + + align:start position:0% +um might be another way of doing it + + + align:start position:0% +um might be another way of doing it +which means that this is not + + align:start position:0% +which means that this is not + + + align:start position:0% +which means that this is not +here a comment or two that I think is + + align:start position:0% +here a comment or two that I think is + + + align:start position:0% +here a comment or two that I think is +not good these guys look like leftover + + align:start position:0% +not good these guys look like leftover + + + align:start position:0% +not good these guys look like leftover +places the seats and this wall not + + align:start position:0% +places the seats and this wall not + + + align:start position:0% +places the seats and this wall not +nearly as integrated into the landscape + + align:start position:0% +nearly as integrated into the landscape + + + align:start position:0% +nearly as integrated into the landscape +say is what you're doing in here or even + + align:start position:0% +say is what you're doing in here or even + + + align:start position:0% +say is what you're doing in here or even +there which is very powerful okay the + + align:start position:0% +there which is very powerful okay the + + + align:start position:0% +there which is very powerful okay the +mountain or the climbing wall there this + + align:start position:0% +mountain or the climbing wall there this + + + align:start position:0% +mountain or the climbing wall there this +one + + align:start position:0% +one + + + align:start position:0% +one +is very strong U it could be + + align:start position:0% +is very strong U it could be + + + align:start position:0% +is very strong U it could be +higher it seems to me I'm going to have + + align:start position:0% +higher it seems to me I'm going to have + + + align:start position:0% +higher it seems to me I'm going to have +a what happened to I used to have a + + align:start position:0% +a what happened to I used to have a + + + align:start position:0% +a what happened to I used to have a +screen oh that's right there's a screen + + align:start position:0% +screen oh that's right there's a screen + + + align:start position:0% +screen oh that's right there's a screen +up there okay terrific okay so then + + align:start position:0% +up there okay terrific okay so then + + + align:start position:0% +up there okay terrific okay so then +maybe if there's a screen there we don't + + align:start position:0% +maybe if there's a screen there we don't + + + align:start position:0% +maybe if there's a screen there we don't +we don't have it higher but it I was + + align:start position:0% +we don't have it higher but it I was + + + align:start position:0% +we don't have it higher but it I was +going to suggest it could be narrower + + align:start position:0% +going to suggest it could be narrower + + + align:start position:0% +going to suggest it could be narrower +and a little higher and still do that + + align:start position:0% +and a little higher and still do that + + + align:start position:0% +and a little higher and still do that +because it's taking up quite a bit of + + align:start position:0% +because it's taking up quite a bit of + + + align:start position:0% +because it's taking up quite a bit of +the land + + align:start position:0% +the land + + + align:start position:0% +the land +here um + + align:start position:0% +here um + + + align:start position:0% +here um +narrower this way yeah narrower that way + + align:start position:0% +narrower this way yeah narrower that way + + + align:start position:0% +narrower this way yeah narrower that way +vertically um I don't know how you + + align:start position:0% +vertically um I don't know how you + + + align:start position:0% +vertically um I don't know how you +justify my concern yet oh I do know how + + align:start position:0% +justify my concern yet oh I do know how + + + align:start position:0% +justify my concern yet oh I do know how +you do it of wanting to make the + + align:start position:0% +you do it of wanting to make the + + + align:start position:0% +you do it of wanting to make the +connection between the ordinary and the + + align:start position:0% +connection between the ordinary and the + + + align:start position:0% +connection between the ordinary and the +extraordinary this face is not + + align:start position:0% +extraordinary this face is not + + + align:start position:0% +extraordinary this face is not +necessarily + + align:start position:0% +necessarily + + + align:start position:0% +necessarily +climbing it's this face so therefore + + align:start position:0% +climbing it's this face so therefore + + + align:start position:0% +climbing it's this face so therefore +this could be some kind of yeah that a + + align:start position:0% +this could be some kind of yeah that a + + + align:start position:0% +this could be some kind of yeah that a +wall that's coming in from the ordinary + + align:start position:0% +wall that's coming in from the ordinary + + + align:start position:0% +wall that's coming in from the ordinary +of this + + align:start position:0% +of this + + + align:start position:0% +of this +and then wow all of a sudden in fact + + align:start position:0% +and then wow all of a sudden in fact + + + align:start position:0% +and then wow all of a sudden in fact +yeah I turned the corner in fact this + + align:start position:0% +yeah I turned the corner in fact this + + + align:start position:0% +yeah I turned the corner in fact this +could go even a little bit farther + + align:start position:0% +could go even a little bit farther + + + align:start position:0% +could go even a little bit farther +MH making this world just a little bit + + align:start position:0% +MH making this world just a little bit + + + align:start position:0% +MH making this world just a little bit +more hidden than what you got and there + + align:start position:0% +more hidden than what you got and there + + + align:start position:0% +more hidden than what you got and there +because I don't use that + + align:start position:0% +because I don't use that + + + align:start position:0% +because I don't use that +face now that's one thing the second + + align:start position:0% +face now that's one thing the second + + + align:start position:0% +face now that's one thing the second +thing is that this is a if I'm not + + align:start position:0% +thing is that this is a if I'm not + + + align:start position:0% +thing is that this is a if I'm not +mistaken is an inside climbing + + align:start position:0% +mistaken is an inside climbing + + + align:start position:0% +mistaken is an inside climbing +wall it all of a sudden now looks very + + align:start position:0% +wall it all of a sudden now looks very + + + align:start position:0% +wall it all of a sudden now looks very +token and very small in relationship to + + align:start position:0% +token and very small in relationship to + + + align:start position:0% +token and very small in relationship to +the space it seems it seems like it + + align:start position:0% +the space it seems it seems like it + + + align:start position:0% +the space it seems it seems like it +could have been much larger or even be + + align:start position:0% +could have been much larger or even be + + + align:start position:0% +could have been much larger or even be +more commanding in size for the space + + align:start position:0% +more commanding in size for the space + + + align:start position:0% +more commanding in size for the space +that you have inside MH assuming that it + + align:start position:0% +that you have inside MH assuming that it + + + align:start position:0% +that you have inside MH assuming that it +works for the + + align:start position:0% +works for the + + + align:start position:0% +works for the +climbers so it could become much more of + + align:start position:0% +climbers so it could become much more of + + + align:start position:0% +climbers so it could become much more of +an architectural issue as this one is by + + align:start position:0% +an architectural issue as this one is by + + + align:start position:0% +an architectural issue as this one is by +the way + + align:start position:0% +the way + + + align:start position:0% +the way +outside uh this got done first I think + + align:start position:0% +outside uh this got done first I think + + + align:start position:0% +outside uh this got done first I think +or maybe not but it feels like it didn't + + align:start position:0% +or maybe not but it feels like it didn't + + + align:start position:0% +or maybe not but it feels like it didn't +get done in relationship to the + + align:start position:0% +get done in relationship to the + + + align:start position:0% +get done in relationship to the +magnitude of that space it actually got + + align:start position:0% +magnitude of that space it actually got + + + align:start position:0% +magnitude of that space it actually got +done this but it was + + align:start position:0% + + + + align:start position:0% + +because well I figured like I had this + + align:start position:0% +because well I figured like I had this + + + align:start position:0% +because well I figured like I had this +all worked out and then the height of + + align:start position:0% +all worked out and then the height of + + + align:start position:0% +all worked out and then the height of +this I figured would I knew the + + align:start position:0% +this I figured would I knew the + + + align:start position:0% +this I figured would I knew the +approximate height I want it to be but + + align:start position:0% +approximate height I want it to be but + + + align:start position:0% +approximate height I want it to be but +then knowing the height that I wanted + + align:start position:0% +then knowing the height that I wanted + + + align:start position:0% +then knowing the height that I wanted +this room to be I just made + + align:start position:0% +this room to be I just made + + + align:start position:0% +this room to be I just made +I well based on what I'm seeing here and + + align:start position:0% +I well based on what I'm seeing here and + + + align:start position:0% +I well based on what I'm seeing here and +back here to me I think the building + + align:start position:0% +back here to me I think the building + + + align:start position:0% +back here to me I think the building +could be up in here somewhere okay + + align:start position:0% +could be up in here somewhere okay + + + align:start position:0% +could be up in here somewhere okay +therefore that could be higher and + + align:start position:0% +therefore that could be higher and + + + align:start position:0% +therefore that could be higher and +therefore it could be much more of of a + + align:start position:0% +therefore it could be much more of of a + + + align:start position:0% +therefore it could be much more of of a +physic + + align:start position:0% +physic + + + align:start position:0% +physic +feature of the + + align:start position:0% +feature of the + + + align:start position:0% +feature of the +building now I want to congratulate you + + align:start position:0% +building now I want to congratulate you + + + align:start position:0% +building now I want to congratulate you +on something which I think is just + + align:start position:0% +on something which I think is just + + + align:start position:0% +on something which I think is just +incredible you have chosen a rectangular + + align:start position:0% +incredible you have chosen a rectangular + + + align:start position:0% +incredible you have chosen a rectangular +base system MH which I think is just is + + align:start position:0% +base system MH which I think is just is + + + align:start position:0% +base system MH which I think is just is +is just beautiful because it's playing + + align:start position:0% +is just beautiful because it's playing + + + align:start position:0% +is just beautiful because it's playing +against the angularity of the + + align:start position:0% +against the angularity of the + + + align:start position:0% +against the angularity of the +other and you do not have to which is + + align:start position:0% +other and you do not have to which is + + + align:start position:0% +other and you do not have to which is +what you're starting to struggle with + + align:start position:0% +what you're starting to struggle with + + + align:start position:0% +what you're starting to struggle with +think about enclosure related to this + + align:start position:0% +think about enclosure related to this + + + align:start position:0% +think about enclosure related to this +they can be enclosure walls m can be + + align:start position:0% +they can be enclosure walls m can be + + + align:start position:0% +they can be enclosure walls m can be +separate MH from the structure so and + + align:start position:0% +separate MH from the structure so and + + + align:start position:0% +separate MH from the structure so and +these guys just as we've done here can + + align:start position:0% +these guys just as we've done here can + + + align:start position:0% +these guys just as we've done here can +be poking through at different way at + + align:start position:0% +be poking through at different way at + + + align:start position:0% +be poking through at different way at +different places so you've got an + + align:start position:0% +different places so you've got an + + + align:start position:0% +different places so you've got an +ordering device here several ordering + + align:start position:0% +ordering device here several ordering + + + align:start position:0% +ordering device here several ordering +devices one off this which is + + align:start position:0% +devices one off this which is + + + align:start position:0% +devices one off this which is +fractional U uh another one is is + + align:start position:0% +fractional U uh another one is is + + + align:start position:0% +fractional U uh another one is is +angular related to another set of angles + + align:start position:0% +angular related to another set of angles + + + align:start position:0% +angular related to another set of angles +this one which is + + align:start position:0% +this one which is + + + align:start position:0% +this one which is +rectangular uh and they're starting to + + align:start position:0% +rectangular uh and they're starting to + + + align:start position:0% +rectangular uh and they're starting to +work with each and then of course this + + align:start position:0% +work with each and then of course this + + + align:start position:0% +work with each and then of course this +one down here which is is just another + + align:start position:0% +one down here which is is just another + + + align:start position:0% +one down here which is is just another +world they're starting work with each + + align:start position:0% +world they're starting work with each + + + align:start position:0% +world they're starting work with each +other and I think that's brilliant I + + align:start position:0% +other and I think that's brilliant I + + + align:start position:0% +other and I think that's brilliant I +think now you having done that you are + + align:start position:0% +think now you having done that you are + + + align:start position:0% +think now you having done that you are +now + + align:start position:0% +now + + + align:start position:0% +now +free to play + + align:start position:0% +free to play + + + align:start position:0% +free to play +if if I could say so with how the the + + align:start position:0% +if if I could say so with how the the + + + align:start position:0% +if if I could say so with how the the +facades of this is going to be mhm but + + align:start position:0% +facades of this is going to be mhm but + + + align:start position:0% +facades of this is going to be mhm but +never think that you have to connect two + + align:start position:0% +never think that you have to connect two + + + align:start position:0% +never think that you have to connect two +columns they can be all curtain walls + + align:start position:0% +columns they can be all curtain walls + + + align:start position:0% +columns they can be all curtain walls +basically and by doing so you have to + + align:start position:0% +basically and by doing so you have to + + + align:start position:0% +basically and by doing so you have to +get back to you will get back to some of + + align:start position:0% +get back to you will get back to some of + + + align:start position:0% +get back to you will get back to some of +the original Notions that you have and + + align:start position:0% +the original Notions that you have and + + + align:start position:0% +the original Notions that you have and +by the way back to your old + + align:start position:0% +by the way back to your old + + + align:start position:0% +by the way back to your old +projects + + align:start position:0% +projects + + + align:start position:0% +projects +um I think it's very good I think it's + + align:start position:0% +um I think it's very good I think it's + + + align:start position:0% +um I think it's very good I think it's +very powerful now the question is what + + align:start position:0% +very powerful now the question is what + + + align:start position:0% +very powerful now the question is what +is the material of these + + align:start position:0% +is the material of these + + + align:start position:0% +is the material of these +roofs I'm not sure I was thinking + + align:start position:0% +roofs I'm not sure I was thinking + + + align:start position:0% +roofs I'm not sure I was thinking +because I do want it to be to let as + + align:start position:0% +because I do want it to be to let as + + + align:start position:0% +because I do want it to be to let as +much light as possible a nature + + align:start position:0% +much light as possible a nature + + + align:start position:0% +much light as possible a nature +your of some kind of reflective like + + align:start position:0% +your of some kind of reflective like + + + align:start position:0% +your of some kind of reflective like +metal with transparent materials um I + + align:start position:0% +metal with transparent materials um I + + + align:start position:0% +metal with transparent materials um I +was thinking like if I were going to + + align:start position:0% +was thinking like if I were going to + + + align:start position:0% +was thinking like if I were going to +have different layers like if I had the + + align:start position:0% +have different layers like if I had the + + + align:start position:0% +have different layers like if I had the +back one lower than this top one then + + align:start position:0% +back one lower than this top one then + + + align:start position:0% +back one lower than this top one then +you know maybe this would be solid but + + align:start position:0% +you know maybe this would be solid but + + + align:start position:0% +you know maybe this would be solid but +then a face of this would be clear to + + align:start position:0% +then a face of this would be clear to + + + align:start position:0% +then a face of this would be clear to +let the light in that kind of thing or + + align:start position:0% +let the light in that kind of thing or + + + align:start position:0% +let the light in that kind of thing or +there could be a metal + + align:start position:0% +there could be a metal + + + align:start position:0% +there could be a metal +frame almost like a honeycomb frame that + + align:start position:0% +frame almost like a honeycomb frame that + + + align:start position:0% +frame almost like a honeycomb frame that +reflects light and then has translucent + + align:start position:0% +reflects light and then has translucent + + + align:start position:0% +reflects light and then has translucent +material over it and and it's like a + + align:start position:0% +material over it and and it's like a + + + align:start position:0% +material over it and and it's like a +sandwich almost so that these are um + + align:start position:0% +sandwich almost so that these are um + + + align:start position:0% +sandwich almost so that these are um +here they're very + + align:start position:0% +here they're very + + + align:start position:0% +here they're very +thin the roofs MH they could have more + + align:start position:0% +thin the roofs MH they could have more + + + align:start position:0% +thin the roofs MH they could have more +Dimension to them without being solid + + align:start position:0% +Dimension to them without being solid + + + align:start position:0% +Dimension to them without being solid +looking + + align:start position:0% +looking + + + align:start position:0% +looking +MH hanging over this MH and light coming + + align:start position:0% +MH hanging over this MH and light coming + + + align:start position:0% +MH hanging over this MH and light coming +through them so they could have a + + align:start position:0% +through them so they could have a + + + align:start position:0% +through them so they could have a +dimension like that as an + + align:start position:0% +dimension like that as an + + + align:start position:0% +dimension like that as an +example which might be a nice complement + + align:start position:0% +example which might be a nice complement + + + align:start position:0% +example which might be a nice complement +to what's going on in the ground + + align:start position:0% +to what's going on in the ground + + + align:start position:0% +to what's going on in the ground +yeah and then of course they're held up + + align:start position:0% +yeah and then of course they're held up + + + align:start position:0% +yeah and then of course they're held up +by The Columns so the columns by the way + + align:start position:0% +by The Columns so the columns by the way + + + align:start position:0% +by The Columns so the columns by the way +the columns are about the right size mhm + + align:start position:0% +the columns are about the right size mhm + + + align:start position:0% +the columns are about the right size mhm +uh so the columns are then connecting to + + align:start position:0% +uh so the columns are then connecting to + + + align:start position:0% +uh so the columns are then connecting to +this in some way on the grid of the of + + align:start position:0% +this in some way on the grid of the of + + + align:start position:0% +this in some way on the grid of the of +the framework of the of the roof which + + align:start position:0% +the framework of the of the roof which + + + align:start position:0% +the framework of the of the roof which +is metal + + align:start position:0% +is metal + + + align:start position:0% +is metal +okay uh you're on your way so good yeah + + align:start position:0% +okay uh you're on your way so good yeah + + + align:start position:0% +okay uh you're on your way so good yeah +any suggestions as to like how the + + align:start position:0% +any suggestions as to like how the + + + align:start position:0% +any suggestions as to like how the +overall form of the outside should be + + align:start position:0% +overall form of the outside should be + + + align:start position:0% +overall form of the outside should be +like having like I think I do want to + + align:start position:0% +like having like I think I do want to + + + align:start position:0% +like having like I think I do want to +make this like higher here um so maybe + + align:start position:0% +make this like higher here um so maybe + + + align:start position:0% +make this like higher here um so maybe +this like air be higher and this lower + + align:start position:0% +this like air be higher and this lower + + + align:start position:0% +this like air be higher and this lower +so you can have like get in the high + + align:start position:0% +so you can have like get in the high + + + align:start position:0% +so you can have like get in the high +place but then like yes I do I would be + + align:start position:0% +place but then like yes I do I would be + + + align:start position:0% +place but then like yes I do I would be +careful that it does not become + + align:start position:0% +careful that it does not become + + + align:start position:0% +careful that it does not become +so literal in the sense that it's one + + align:start position:0% +so literal in the sense that it's one + + + align:start position:0% +so literal in the sense that it's one +two three as I go down in fact I could + + align:start position:0% +two three as I go down in fact I could + + + align:start position:0% +two three as I go down in fact I could +imagine that maybe this one is higher + + align:start position:0% +imagine that maybe this one is higher + + + align:start position:0% +imagine that maybe this one is higher +even though it's over this is over the + + align:start position:0% +even though it's over this is over the + + + align:start position:0% +even though it's over this is over the +highest space m so that and then it goes + + align:start position:0% +highest space m so that and then it goes + + + align:start position:0% +highest space m so that and then it goes +down yeah otherwise this you may end up + + align:start position:0% +down yeah otherwise this you may end up + + + align:start position:0% +down yeah otherwise this you may end up +with something that is too Central with + + align:start position:0% +with something that is too Central with + + + align:start position:0% +with something that is too Central with +things radiating around it and I don't + + align:start position:0% +things radiating around it and I don't + + + align:start position:0% +things radiating around it and I don't +think that's the intention of what you + + align:start position:0% +think that's the intention of what you + + + align:start position:0% +think that's the intention of what you +want to do I think you have something in + + align:start position:0% +want to do I think you have something in + + + align:start position:0% +want to do I think you have something in +mind that's a little bit more Freer than + + align:start position:0% +mind that's a little bit more Freer than + + + align:start position:0% +mind that's a little bit more Freer than +that do you think it'd be a pro if this + + align:start position:0% +that do you think it'd be a pro if this + + + align:start position:0% +that do you think it'd be a pro if this +area was higher there'd be a problem + + align:start position:0% +area was higher there'd be a problem + + + align:start position:0% +area was higher there'd be a problem +with getting light in this no because in + + align:start position:0% +with getting light in this no because in + + + align:start position:0% +with getting light in this no because in +fact I was thinking if it was higher + + align:start position:0% +fact I was thinking if it was higher + + + align:start position:0% +fact I was thinking if it was higher +light could come through that and down + + align:start position:0% +light could come through that and down + + + align:start position:0% +light could come through that and down +into yeah okay so uh I don't think it + + align:start position:0% +into yeah okay so uh I don't think it + + + align:start position:0% +into yeah okay so uh I don't think it +would be wrong I mean I guess this one + + align:start position:0% +would be wrong I mean I guess this one + + + align:start position:0% +would be wrong I mean I guess this one +was supposed to be here I don't know + + align:start position:0% +was supposed to be here I don't know + + + align:start position:0% +was supposed to be here I don't know +what you're + + align:start position:0% +what you're + + + align:start position:0% +what you're +but it could be like + + align:start position:0% +but it could be like + + + align:start position:0% +but it could be like +that um how many of them I don't know is + + align:start position:0% +that um how many of them I don't know is + + + align:start position:0% +that um how many of them I don't know is +there three four five that's up to you + + align:start position:0% +there three four five that's up to you + + + align:start position:0% +there three four five that's up to you +but this is the fun part you get to play + + align:start position:0% +but this is the fun part you get to play + + + align:start position:0% +but this is the fun part you get to play +oh this is the part that you get to play + + align:start position:0% +oh this is the part that you get to play + + + align:start position:0% +oh this is the part that you get to play +with uh how these forms are at + + align:start position:0% + + + + align:start position:0% + +top the thing that again that's + + align:start position:0% +top the thing that again that's + + + align:start position:0% +top the thing that again that's +interesting is that structurally and + + align:start position:0% +interesting is that structurally and + + + align:start position:0% +interesting is that structurally and +architecturally there's an ordering + + align:start position:0% +architecturally there's an ordering + + + align:start position:0% +architecturally there's an ordering +framework that's holding all this + + align:start position:0% +framework that's holding all this + + + align:start position:0% +framework that's holding all this +together with these guys + + align:start position:0% +together with these guys + + + align:start position:0% +together with these guys +as opposed + + align:start position:0% +as opposed + + + align:start position:0% +as opposed +to um which you could have done which I + + align:start position:0% +to um which you could have done which I + + + align:start position:0% +to um which you could have done which I +think would have been a mistake is that + + align:start position:0% +think would have been a mistake is that + + + align:start position:0% +think would have been a mistake is that +the columns would have tried to follow + + align:start position:0% +the columns would have tried to follow + + + align:start position:0% +the columns would have tried to follow +the forms of the that's a disaster or + + align:start position:0% +the forms of the that's a disaster or + + + align:start position:0% +the forms of the that's a disaster or +could be you you would uh never get that + + align:start position:0% +could be you you would uh never get that + + + align:start position:0% +could be you you would uh never get that +one right \ No newline at end of file diff --git a/PfxuFD4ML9s.txt b/PfxuFD4ML9s.txt new file mode 100644 index 0000000000000000000000000000000000000000..364ae86a9f870b49b42dcc8a4c468fcfb399efdd --- /dev/null +++ b/PfxuFD4ML9s.txt @@ -0,0 +1,1611 @@ +align:start position:0% + +since the Industrial Revolution began + + align:start position:0% +since the Industrial Revolution began + + + align:start position:0% +since the Industrial Revolution began +250 years ago people have been burning + + align:start position:0% +250 years ago people have been burning + + + align:start position:0% +250 years ago people have been burning +fossil fuels like coal and oil to + + align:start position:0% +fossil fuels like coal and oil to + + + align:start position:0% +fossil fuels like coal and oil to +generate + + align:start position:0% +generate + + + align:start position:0% +generate +electricity hi I'm Professor nor AA s + + align:start position:0% +electricity hi I'm Professor nor AA s + + + align:start position:0% +electricity hi I'm Professor nor AA s +Amin professor of chemical engineering + + align:start position:0% +Amin professor of chemical engineering + + + align:start position:0% +Amin professor of chemical engineering +and a visiting fellow with the MIT UTM + + align:start position:0% +and a visiting fellow with the MIT UTM + + + align:start position:0% +and a visiting fellow with the MIT UTM +sustainable cities program my research + + align:start position:0% +sustainable cities program my research + + + align:start position:0% +sustainable cities program my research +is focused on renewable energy and today + + align:start position:0% +is focused on renewable energy and today + + + align:start position:0% +is focused on renewable energy and today +I am going to talk about climate change + + align:start position:0% +I am going to talk about climate change + + + align:start position:0% +I am going to talk about climate change +and renewable energy the primary product + + align:start position:0% +and renewable energy the primary product + + + align:start position:0% +and renewable energy the primary product +of burning of fossil fuels is carbon + + align:start position:0% +of burning of fossil fuels is carbon + + + align:start position:0% +of burning of fossil fuels is carbon +dioxide for centuries the amount of + + align:start position:0% +dioxide for centuries the amount of + + + align:start position:0% +dioxide for centuries the amount of +carbon dioxide emissions in the + + align:start position:0% +carbon dioxide emissions in the + + + align:start position:0% +carbon dioxide emissions in the +atmosphere was 300 parts per million but + + align:start position:0% +atmosphere was 300 parts per million but + + + align:start position:0% +atmosphere was 300 parts per million but +carbon dioxide levels have increased + + align:start position:0% +carbon dioxide levels have increased + + + align:start position:0% +carbon dioxide levels have increased +dramatically and reached an + + align:start position:0% +dramatically and reached an + + + align:start position:0% +dramatically and reached an +unprecedented value of about 400 parts + + align:start position:0% +unprecedented value of about 400 parts + + + align:start position:0% +unprecedented value of about 400 parts +per million high levels of carbon + + align:start position:0% +per million high levels of carbon + + + align:start position:0% +per million high levels of carbon +dioxide emissions are linked to climate + + align:start position:0% +dioxide emissions are linked to climate + + + align:start position:0% +dioxide emissions are linked to climate +change which has led to increasing + + align:start position:0% +change which has led to increasing + + + align:start position:0% +change which has led to increasing +temperatures melting glaciers rising sea + + align:start position:0% +temperatures melting glaciers rising sea + + + align:start position:0% +temperatures melting glaciers rising sea +level changing rain and snow patterns + + align:start position:0% +level changing rain and snow patterns + + + align:start position:0% +level changing rain and snow patterns +and also drought flood and Other Extreme + + align:start position:0% +and also drought flood and Other Extreme + + + align:start position:0% +and also drought flood and Other Extreme +events climate change is an important + + align:start position:0% +events climate change is an important + + + align:start position:0% +events climate change is an important +issue and reducing carbon emission is a + + align:start position:0% +issue and reducing carbon emission is a + + + align:start position:0% +issue and reducing carbon emission is a +challenge in December 2015 world leaders + + align:start position:0% +challenge in December 2015 world leaders + + + align:start position:0% +challenge in December 2015 world leaders +convened in Paris to discuss the + + align:start position:0% +convened in Paris to discuss the + + + align:start position:0% +convened in Paris to discuss the +reduction of carbon emissions and and + + align:start position:0% +reduction of carbon emissions and and + + + align:start position:0% +reduction of carbon emissions and and +climate change impacts at a United + + align:start position:0% +climate change impacts at a United + + + align:start position:0% +climate change impacts at a United +Nations Global Climate + + align:start position:0% + + + + align:start position:0% + +conference there is no doubt that the + + align:start position:0% +conference there is no doubt that the + + + align:start position:0% +conference there is no doubt that the +global climate change agreement we seek + + align:start position:0% +global climate change agreement we seek + + + align:start position:0% +global climate change agreement we seek +must be part of what Paris has become + + align:start position:0% +must be part of what Paris has become + + + align:start position:0% +must be part of what Paris has become +even Hollywood is taking a public stand + + align:start position:0% +even Hollywood is taking a public stand + + + align:start position:0% +even Hollywood is taking a public stand +on this issue and the Oscar goes to + + align:start position:0% +on this issue and the Oscar goes to + + + align:start position:0% +on this issue and the Oscar goes to +Leonardo + + align:start position:0% + + + + align:start position:0% + +DiCaprio climate change is real it is + + align:start position:0% +DiCaprio climate change is real it is + + + align:start position:0% +DiCaprio climate change is real it is +happening right now it is the most + + align:start position:0% +happening right now it is the most + + + align:start position:0% +happening right now it is the most +urgent threat facing our entire + + align:start position:0% +urgent threat facing our entire + + + align:start position:0% +urgent threat facing our entire +species one of the ways to address + + align:start position:0% +species one of the ways to address + + + align:start position:0% +species one of the ways to address +climate change is to replace fossil + + align:start position:0% +climate change is to replace fossil + + + align:start position:0% +climate change is to replace fossil +fuels with renewable energy for + + align:start position:0% +fuels with renewable energy for + + + align:start position:0% +fuels with renewable energy for +electricity production carbon emissions + + align:start position:0% +electricity production carbon emissions + + + align:start position:0% +electricity production carbon emissions +from renewable energy power plants are + + align:start position:0% +from renewable energy power plants are + + + align:start position:0% +from renewable energy power plants are +much lower compared to those that run + + align:start position:0% +much lower compared to those that run + + + align:start position:0% +much lower compared to those that run +with fossil fuels according to the + + align:start position:0% +with fossil fuels according to the + + + align:start position:0% +with fossil fuels according to the +Energy Information + + align:start position:0% +Energy Information + + + align:start position:0% +Energy Information +Administration although there are plenty + + align:start position:0% +Administration although there are plenty + + + align:start position:0% +Administration although there are plenty +of renewable resources available on + + align:start position:0% +of renewable resources available on + + + align:start position:0% +of renewable resources available on +Earth only 10% of the world's energy + + align:start position:0% +Earth only 10% of the world's energy + + + align:start position:0% +Earth only 10% of the world's energy +output is from renewable sources types + + align:start position:0% +output is from renewable sources types + + + align:start position:0% +output is from renewable sources types +of renewable energy include solar + + align:start position:0% +of renewable energy include solar + + + align:start position:0% +of renewable energy include solar +geothermal wind and + + align:start position:0% +geothermal wind and + + + align:start position:0% +geothermal wind and +biomass there are many lessons that can + + align:start position:0% +biomass there are many lessons that can + + + align:start position:0% +biomass there are many lessons that can +be learned from Malaysia's success with + + align:start position:0% +be learned from Malaysia's success with + + + align:start position:0% +be learned from Malaysia's success with +using renewable energy given Malaysia's + + align:start position:0% +using renewable energy given Malaysia's + + + align:start position:0% +using renewable energy given Malaysia's +tropical biod diversity conversion of + + align:start position:0% +tropical biod diversity conversion of + + + align:start position:0% +tropical biod diversity conversion of +biomass to energy is a promising + + align:start position:0% +biomass to energy is a promising + + + align:start position:0% +biomass to energy is a promising +approach to establishing sustainable + + align:start position:0% +approach to establishing sustainable + + + align:start position:0% +approach to establishing sustainable +energy production Malaysia would also be + + align:start position:0% +energy production Malaysia would also be + + + align:start position:0% +energy production Malaysia would also be +an excellent example where there is + + align:start position:0% +an excellent example where there is + + + align:start position:0% +an excellent example where there is +plenty of agricultural waste and it + + align:start position:0% +plenty of agricultural waste and it + + + align:start position:0% +plenty of agricultural waste and it +could be a wonderful idea to try to use + + align:start position:0% +could be a wonderful idea to try to use + + + align:start position:0% +could be a wonderful idea to try to use +that waste um in uh a way which brings a + + align:start position:0% +that waste um in uh a way which brings a + + + align:start position:0% +that waste um in uh a way which brings a +little bit of value to community to the + + align:start position:0% +little bit of value to community to the + + + align:start position:0% +little bit of value to community to the +country but at the same time can help us + + align:start position:0% +country but at the same time can help us + + + align:start position:0% +country but at the same time can help us +to reduce carbon dioxide emissions + + align:start position:0% +to reduce carbon dioxide emissions + + + align:start position:0% +to reduce carbon dioxide emissions +situated in joho the most southern state + + align:start position:0% +situated in joho the most southern state + + + align:start position:0% +situated in joho the most southern state +in Peninsula Malaysia isanda Malaysia is + + align:start position:0% +in Peninsula Malaysia isanda Malaysia is + + + align:start position:0% +in Peninsula Malaysia isanda Malaysia is +a new development region that Advocates + + align:start position:0% +a new development region that Advocates + + + align:start position:0% +a new development region that Advocates +low carbon emission most of its carbon + + align:start position:0% +low carbon emission most of its carbon + + + align:start position:0% +low carbon emission most of its carbon +dioxide emission are from the + + align:start position:0% +dioxide emission are from the + + + align:start position:0% +dioxide emission are from the +electricity and heating sector as + + align:start position:0% +electricity and heating sector as + + + align:start position:0% +electricity and heating sector as +documented in the low carbon plan + + align:start position:0% +documented in the low carbon plan + + + align:start position:0% +documented in the low carbon plan +iscandar Malaysia is projected to be a + + align:start position:0% +iscandar Malaysia is projected to be a + + + align:start position:0% +iscandar Malaysia is projected to be a +sustainable City by 2025 with only 18.9 + + align:start position:0% +sustainable City by 2025 with only 18.9 + + + align:start position:0% +sustainable City by 2025 with only 18.9 +million tons of carbon dioxide emissions + + align:start position:0% +million tons of carbon dioxide emissions + + + align:start position:0% +million tons of carbon dioxide emissions +a 40% reduction from 2005 level how can + + align:start position:0% +a 40% reduction from 2005 level how can + + + align:start position:0% +a 40% reduction from 2005 level how can +iscandal Malaysia achieve this target + + align:start position:0% +iscandal Malaysia achieve this target + + + align:start position:0% +iscandal Malaysia achieve this target +one of the methods is to utilize waste + + align:start position:0% +one of the methods is to utilize waste + + + align:start position:0% +one of the methods is to utilize waste +from the oil pump industry to generate + + align:start position:0% +from the oil pump industry to generate + + + align:start position:0% +from the oil pump industry to generate +heat and electricity iscandar Malaysia + + align:start position:0% +heat and electricity iscandar Malaysia + + + align:start position:0% +heat and electricity iscandar Malaysia +is easily accessible to large areas of + + align:start position:0% +is easily accessible to large areas of + + + align:start position:0% +is easily accessible to large areas of +oil pump Plantation the oil pump + + align:start position:0% +oil pump Plantation the oil pump + + + align:start position:0% +oil pump Plantation the oil pump +industry produces waste such as empty + + align:start position:0% +industry produces waste such as empty + + + align:start position:0% +industry produces waste such as empty +fruit bunch and palm oil mil affluent + + align:start position:0% +fruit bunch and palm oil mil affluent + + + align:start position:0% +fruit bunch and palm oil mil affluent +empty fruit bunch is the residue + + align:start position:0% +empty fruit bunch is the residue + + + align:start position:0% +empty fruit bunch is the residue +produced when palm fruit is taken from a + + align:start position:0% +produced when palm fruit is taken from a + + + align:start position:0% +produced when palm fruit is taken from a +fresh fruit bunch in the initial process + + align:start position:0% +fresh fruit bunch in the initial process + + + align:start position:0% +fresh fruit bunch in the initial process +of palm oil production palm oil mil + + align:start position:0% +of palm oil production palm oil mil + + + align:start position:0% +of palm oil production palm oil mil +affluent is the voluminous liquid waste + + align:start position:0% +affluent is the voluminous liquid waste + + + align:start position:0% +affluent is the voluminous liquid waste +that comes from the sterilization and + + align:start position:0% +that comes from the sterilization and + + + align:start position:0% +that comes from the sterilization and +clarification processes in Milling oil + + align:start position:0% +clarification processes in Milling oil + + + align:start position:0% +clarification processes in Milling oil +palm by utilizing waste carbon dioxide + + align:start position:0% +palm by utilizing waste carbon dioxide + + + align:start position:0% +palm by utilizing waste carbon dioxide +emissions can be significantly reduced + + align:start position:0% +emissions can be significantly reduced + + + align:start position:0% +emissions can be significantly reduced +and make the air in the region cleaner + + align:start position:0% +and make the air in the region cleaner + + + align:start position:0% +and make the air in the region cleaner +and healthier one way to measure carbon + + align:start position:0% +and healthier one way to measure carbon + + + align:start position:0% +and healthier one way to measure carbon +dioxide emissions is to use an + + align:start position:0% +dioxide emissions is to use an + + + align:start position:0% +dioxide emissions is to use an +integrated model that takes into account + + align:start position:0% +integrated model that takes into account + + + align:start position:0% +integrated model that takes into account +direct and indirect carbon dioxide + + align:start position:0% +direct and indirect carbon dioxide + + + align:start position:0% +direct and indirect carbon dioxide +emissions the concept of the model is to + + align:start position:0% +emissions the concept of the model is to + + + align:start position:0% +emissions the concept of the model is to +provide a systematic and comprehensive + + align:start position:0% +provide a systematic and comprehensive + + + align:start position:0% +provide a systematic and comprehensive +carbon accounting to evaluate carbon + + align:start position:0% +carbon accounting to evaluate carbon + + + align:start position:0% +carbon accounting to evaluate carbon +performance as well as to determine the + + align:start position:0% +performance as well as to determine the + + + align:start position:0% +performance as well as to determine the +potential carbon emission reduction in + + align:start position:0% +potential carbon emission reduction in + + + align:start position:0% +potential carbon emission reduction in +the + + align:start position:0% +the + + + align:start position:0% +the +process the model calculates carbon + + align:start position:0% +process the model calculates carbon + + + align:start position:0% +process the model calculates carbon +dioxide emissions from three biomass + + align:start position:0% +dioxide emissions from three biomass + + + align:start position:0% +dioxide emissions from three biomass +power plants the bio EXL plant kolim + + align:start position:0% +power plants the bio EXL plant kolim + + + align:start position:0% +power plants the bio EXL plant kolim +Group Plant and ronza biog gas plant + + align:start position:0% +Group Plant and ronza biog gas plant + + + align:start position:0% +Group Plant and ronza biog gas plant +initially Caron accounting centers for + + align:start position:0% +initially Caron accounting centers for + + + align:start position:0% +initially Caron accounting centers for +each process is divided into smaller + + align:start position:0% +each process is divided into smaller + + + align:start position:0% +each process is divided into smaller +units next the total monthly carbon + + align:start position:0% +units next the total monthly carbon + + + align:start position:0% +units next the total monthly carbon +emission equivalent is determined + + align:start position:0% +emission equivalent is determined + + + align:start position:0% +emission equivalent is determined +followed by calculation of the carbon + + align:start position:0% +followed by calculation of the carbon + + + align:start position:0% +followed by calculation of the carbon +dioxide emissions and carbon emission + + align:start position:0% +dioxide emissions and carbon emission + + + align:start position:0% +dioxide emissions and carbon emission +index across the carbon performance + + align:start position:0% +index across the carbon performance + + + align:start position:0% +index across the carbon performance +indicators strategies for reduction of + + align:start position:0% +indicators strategies for reduction of + + + align:start position:0% +indicators strategies for reduction of +carbon emissions are then implemented + + align:start position:0% +carbon emissions are then implemented + + + align:start position:0% +carbon emissions are then implemented +the five main emission contributors are + + align:start position:0% +the five main emission contributors are + + + align:start position:0% +the five main emission contributors are +identified as carbon performance + + align:start position:0% +identified as carbon performance + + + align:start position:0% +identified as carbon performance +indicators these are fuel water and + + align:start position:0% +indicators these are fuel water and + + + align:start position:0% +indicators these are fuel water and +electricity consumption and also waste + + align:start position:0% +electricity consumption and also waste + + + align:start position:0% +electricity consumption and also waste +water and solid waste generation empty + + align:start position:0% +water and solid waste generation empty + + + align:start position:0% +water and solid waste generation empty +fruit banch is fed into bio EXL plant to + + align:start position:0% +fruit banch is fed into bio EXL plant to + + + align:start position:0% +fruit banch is fed into bio EXL plant to +generate Steam and + + align:start position:0% +generate Steam and + + + align:start position:0% +generate Steam and +electricity empty fruit bunch is + + align:start position:0% +electricity empty fruit bunch is + + + align:start position:0% +electricity empty fruit bunch is +shredded and then formed as solid + + align:start position:0% +shredded and then formed as solid + + + align:start position:0% +shredded and then formed as solid +pallets the pellets are used as fuels + + align:start position:0% +pallets the pellets are used as fuels + + + align:start position:0% +pallets the pellets are used as fuels +for the boilers to produce steam the + + align:start position:0% +for the boilers to produce steam the + + + align:start position:0% +for the boilers to produce steam the +steam turbine then generates + + align:start position:0% +steam turbine then generates + + + align:start position:0% +steam turbine then generates +electricity meanwhile Kim andron utilize + + align:start position:0% +electricity meanwhile Kim andron utilize + + + align:start position:0% +electricity meanwhile Kim andron utilize +palm oil mill affluent the affluent is + + align:start position:0% +palm oil mill affluent the affluent is + + + align:start position:0% +palm oil mill affluent the affluent is +retained in an anerobic digestor to + + align:start position:0% +retained in an anerobic digestor to + + + align:start position:0% +retained in an anerobic digestor to +produce bio gas the gas runs the turbine + + align:start position:0% +produce bio gas the gas runs the turbine + + + align:start position:0% +produce bio gas the gas runs the turbine +to generate electricity the total + + align:start position:0% +to generate electricity the total + + + align:start position:0% +to generate electricity the total +monthly carbon dioxide emissions before + + align:start position:0% +monthly carbon dioxide emissions before + + + align:start position:0% +monthly carbon dioxide emissions before +and after the implementation of the + + align:start position:0% +and after the implementation of the + + + align:start position:0% +and after the implementation of the +reduction strategies are exhibited in + + align:start position:0% +reduction strategies are exhibited in + + + align:start position:0% +reduction strategies are exhibited in +figure one showing a 27% emissions + + align:start position:0% +figure one showing a 27% emissions + + + align:start position:0% +figure one showing a 27% emissions +reduction at bio Exel 15% at kulim and + + align:start position:0% +reduction at bio Exel 15% at kulim and + + + align:start position:0% +reduction at bio Exel 15% at kulim and +41% at ronza + + align:start position:0% +41% at ronza + + + align:start position:0% +41% at ronza +figure two compress the carbon emission + + align:start position:0% +figure two compress the carbon emission + + + align:start position:0% +figure two compress the carbon emission +index after implementing the reduction + + align:start position:0% +index after implementing the reduction + + + align:start position:0% +index after implementing the reduction +strategies in general all performance + + align:start position:0% +strategies in general all performance + + + align:start position:0% +strategies in general all performance +indicators show reduced emissions after + + align:start position:0% +indicators show reduced emissions after + + + align:start position:0% +indicators show reduced emissions after +Innovative strategies are implemented in + + align:start position:0% +Innovative strategies are implemented in + + + align:start position:0% +Innovative strategies are implemented in +BIO Exel the carbon emission index for + + align:start position:0% +BIO Exel the carbon emission index for + + + align:start position:0% +BIO Exel the carbon emission index for +fuel and water consumption decreased + + align:start position:0% +fuel and water consumption decreased + + + align:start position:0% +fuel and water consumption decreased +significantly after solid empty fruit + + align:start position:0% +significantly after solid empty fruit + + + align:start position:0% +significantly after solid empty fruit +punches replace the shredded ones in + + align:start position:0% +punches replace the shredded ones in + + + align:start position:0% +punches replace the shredded ones in +addition a reduction of solid waste + + align:start position:0% +addition a reduction of solid waste + + + align:start position:0% +addition a reduction of solid waste +generation in ronza biogas gas was also + + align:start position:0% +generation in ronza biogas gas was also + + + align:start position:0% +generation in ronza biogas gas was also +registered after water from the affluent + + align:start position:0% +registered after water from the affluent + + + align:start position:0% +registered after water from the affluent +is recycled carbon dioxide emissions can + + align:start position:0% +is recycled carbon dioxide emissions can + + + align:start position:0% +is recycled carbon dioxide emissions can +be easily predicted using the income + + align:start position:0% +be easily predicted using the income + + + align:start position:0% +be easily predicted using the income +model a power plant that utilizes + + align:start position:0% +model a power plant that utilizes + + + align:start position:0% +model a power plant that utilizes +biomass contributes less to climate + + align:start position:0% +biomass contributes less to climate + + + align:start position:0% +biomass contributes less to climate +change since the carbon dioxide released + + align:start position:0% +change since the carbon dioxide released + + + align:start position:0% +change since the carbon dioxide released +is absorbed by trees through + + align:start position:0% +is absorbed by trees through + + + align:start position:0% +is absorbed by trees through +photosynthesis the process is cyclical + + align:start position:0% +photosynthesis the process is cyclical + + + align:start position:0% +photosynthesis the process is cyclical +the industry could play a big role in + + align:start position:0% +the industry could play a big role in + + + align:start position:0% +the industry could play a big role in +reducing carbon dioxide emissions by + + align:start position:0% +reducing carbon dioxide emissions by + + + align:start position:0% +reducing carbon dioxide emissions by +switching to renewable energy for + + align:start position:0% +switching to renewable energy for + + + align:start position:0% +switching to renewable energy for +generating electricity + + align:start position:0% + + + + align:start position:0% + +the key prayers the key prayers for CO2 + + align:start position:0% +the key prayers the key prayers for CO2 + + + align:start position:0% +the key prayers the key prayers for CO2 +reduction has to be also from the + + align:start position:0% +reduction has to be also from the + + + align:start position:0% +reduction has to be also from the +private sector globally electricity + + align:start position:0% +private sector globally electricity + + + align:start position:0% +private sector globally electricity +generation from Renewables and + + align:start position:0% +generation from Renewables and + + + align:start position:0% +generation from Renewables and +particularly from biomass is increasing + + align:start position:0% +particularly from biomass is increasing + + + align:start position:0% +particularly from biomass is increasing +biomass Supply such as palm oil mil + + align:start position:0% +biomass Supply such as palm oil mil + + + align:start position:0% +biomass Supply such as palm oil mil +affluence is steady due to the number of + + align:start position:0% +affluence is steady due to the number of + + + align:start position:0% +affluence is steady due to the number of +oil pum Mills in the region as stated by + + align:start position:0% +oil pum Mills in the region as stated by + + + align:start position:0% +oil pum Mills in the region as stated by +Dr AA AIS of G run Kai company I would + + align:start position:0% +Dr AA AIS of G run Kai company I would + + + align:start position:0% +Dr AA AIS of G run Kai company I would +say is very very reliable very + + align:start position:0% +say is very very reliable very + + + align:start position:0% +say is very very reliable very +significantly reliable because based on + + align:start position:0% +significantly reliable because based on + + + align:start position:0% +significantly reliable because based on +the number of uh palm oil Mills in the + + align:start position:0% +the number of uh palm oil Mills in the + + + align:start position:0% +the number of uh palm oil Mills in the +country as of + + align:start position:0% +country as of + + + align:start position:0% +country as of +2014 they are at least 480 meals in the + + align:start position:0% +2014 they are at least 480 meals in the + + + align:start position:0% +2014 they are at least 480 meals in the +country including uh in Peninsula Mania + + align:start position:0% +country including uh in Peninsula Mania + + + align:start position:0% +country including uh in Peninsula Mania +as well as Sabah and Shak East Malaysia + + align:start position:0% +as well as Sabah and Shak East Malaysia + + + align:start position:0% +as well as Sabah and Shak East Malaysia +so from from this huge number of oil + + align:start position:0% +so from from this huge number of oil + + + align:start position:0% +so from from this huge number of oil +Mills they are + + align:start position:0% +Mills they are + + + align:start position:0% +Mills they are +off is it's just a matter of how we + + align:start position:0% +off is it's just a matter of how we + + + align:start position:0% +off is it's just a matter of how we +going to maximize this because so to me + + align:start position:0% +going to maximize this because so to me + + + align:start position:0% +going to maximize this because so to me +it's not being maximized in terms of uh + + align:start position:0% +it's not being maximized in terms of uh + + + align:start position:0% +it's not being maximized in terms of uh +effort to reducing the uh carbon + + align:start position:0% +effort to reducing the uh carbon + + + align:start position:0% +effort to reducing the uh carbon +emission in the country the significant + + align:start position:0% +emission in the country the significant + + + align:start position:0% +emission in the country the significant +decline in capital cost for electrical + + align:start position:0% +decline in capital cost for electrical + + + align:start position:0% +decline in capital cost for electrical +generation suggest that investment in + + align:start position:0% +generation suggest that investment in + + + align:start position:0% +generation suggest that investment in +renewable energy is economically viable + + align:start position:0% +renewable energy is economically viable + + + align:start position:0% +renewable energy is economically viable +the utilization of renewable energy + + align:start position:0% +the utilization of renewable energy + + + align:start position:0% +the utilization of renewable energy +waste for repowering power plants could + + align:start position:0% +waste for repowering power plants could + + + align:start position:0% +waste for repowering power plants could +help realize iscandar Malaysia's low + + align:start position:0% +help realize iscandar Malaysia's low + + + align:start position:0% +help realize iscandar Malaysia's low +carbon goals since biomass emits less + + align:start position:0% +carbon goals since biomass emits less + + + align:start position:0% +carbon goals since biomass emits less +carbon dioxide compared to fossil fuel + + align:start position:0% +carbon dioxide compared to fossil fuel + + + align:start position:0% +carbon dioxide compared to fossil fuel +the move to clean energy could reduce + + align:start position:0% +the move to clean energy could reduce + + + align:start position:0% +the move to clean energy could reduce +the magnitude of climate change risk + + align:start position:0% +the magnitude of climate change risk + + + align:start position:0% +the magnitude of climate change risk +renewable energy is the way forward to a + + align:start position:0% +renewable energy is the way forward to a + + + align:start position:0% +renewable energy is the way forward to a +wonderful more sustainable world + + align:start position:0% +wonderful more sustainable world + + + align:start position:0% +wonderful more sustainable world +[Music] \ No newline at end of file diff --git a/PvNHQCOR7V0.txt b/PvNHQCOR7V0.txt new file mode 100644 index 0000000000000000000000000000000000000000..3072ccab9e9782e258c62ee8abc4e32a2161a41f --- /dev/null +++ b/PvNHQCOR7V0.txt @@ -0,0 +1,7403 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay if some of you don't + + align:start position:0% +ocw.mit.edu okay if some of you don't + + + align:start position:0% +ocw.mit.edu okay if some of you don't +have your quizzes yet the graded quizzes + + align:start position:0% +have your quizzes yet the graded quizzes + + + align:start position:0% +have your quizzes yet the graded quizzes +um + + align:start position:0% +um + + + align:start position:0% +um +Michael and Hannah have them with them + + align:start position:0% +Michael and Hannah have them with them + + + align:start position:0% +Michael and Hannah have them with them +so make sure you pick them up before you + + align:start position:0% + + + + align:start position:0% + +leave okay now we've been going + + align:start position:0% +leave okay now we've been going + + + align:start position:0% +leave okay now we've been going +over reading from the conre Lawrence + + align:start position:0% +over reading from the conre Lawrence + + + align:start position:0% +over reading from the conre Lawrence +book that I posted + + align:start position:0% +book that I posted + + + align:start position:0% +book that I posted +online I am going to give you a quiz on + + align:start position:0% +online I am going to give you a quiz on + + + align:start position:0% +online I am going to give you a quiz on +Wednesday + + align:start position:0% +Wednesday + + + align:start position:0% +Wednesday +uh covering that + + align:start position:0% + + + + align:start position:0% + +material very sparsely of course with + + align:start position:0% +material very sparsely of course with + + + align:start position:0% +material very sparsely of course with +only a few + + align:start position:0% + + + + align:start position:0% + +questions if you've read it and listened + + align:start position:0% +questions if you've read it and listened + + + align:start position:0% +questions if you've read it and listened +to the classes it should not be a + + align:start position:0% +to the classes it should not be a + + + align:start position:0% +to the classes it should not be a +difficult + + align:start position:0% + + + + align:start position:0% + +quiz and there will also be a homework + + align:start position:0% +quiz and there will also be a homework + + + align:start position:0% +quiz and there will also be a homework +due early next week okay + + align:start position:0% +due early next week okay + + + align:start position:0% +due early next week okay +I'll try to get that posted by Wednesday + + align:start position:0% +I'll try to get that posted by Wednesday + + + align:start position:0% +I'll try to get that posted by Wednesday +as + + align:start position:0% + + + + align:start position:0% + +well so you'll have plenty of time to + + align:start position:0% +well so you'll have plenty of time to + + + align:start position:0% +well so you'll have plenty of time to +work on the + + align:start position:0% +work on the + + + align:start position:0% +work on the +homework okay now this + + align:start position:0% + + + + align:start position:0% + +uh this was the initial slide for the + + align:start position:0% +uh this was the initial slide for the + + + align:start position:0% +uh this was the initial slide for the +last class and we we talked about the + + align:start position:0% +last class and we we talked about the + + + align:start position:0% +last class and we we talked about the +models we talked about hierarchies and + + align:start position:0% +models we talked about hierarchies and + + + align:start position:0% +models we talked about hierarchies and +chains of + + align:start position:0% +chains of + + + align:start position:0% +chains of +behavior and we started with this + + align:start position:0% +behavior and we started with this + + + align:start position:0% +behavior and we started with this +topic talking + + align:start position:0% +topic talking + + + align:start position:0% +topic talking +about spatial + + align:start position:0% +about spatial + + + align:start position:0% +about spatial +orientation by means of reflexes and + + align:start position:0% +orientation by means of reflexes and + + + align:start position:0% +orientation by means of reflexes and +what they call taxis which are automatic + + align:start position:0% +what they call taxis which are automatic + + + align:start position:0% +what they call taxis which are automatic +orientation during + + align:start position:0% + + + + align:start position:0% + +Locomotion we've not talked about the + + align:start position:0% +Locomotion we've not talked about the + + + align:start position:0% +Locomotion we've not talked about the +role of cognitive behavior the internal + + align:start position:0% +role of cognitive behavior the internal + + + align:start position:0% +role of cognitive behavior the internal +model but we will do that + + align:start position:0% +model but we will do that + + + align:start position:0% +model but we will do that +today + + align:start position:0% +today + + + align:start position:0% +today +and then finally we'll talk + + align:start position:0% +and then finally we'll talk + + + align:start position:0% +and then finally we'll talk +about the way organisms handle + + align:start position:0% +about the way organisms handle + + + align:start position:0% +about the way organisms handle +multiple simultaneous + + align:start position:0% + + + + align:start position:0% + +motivations so this was the + + align:start position:0% +motivations so this was the + + + align:start position:0% +motivations so this was the +last thing we talked + + align:start position:0% +last thing we talked + + + align:start position:0% +last thing we talked +about a goldfish seems to pretty + + align:start position:0% +about a goldfish seems to pretty + + + align:start position:0% +about a goldfish seems to pretty +intelligently solve this problem he's + + align:start position:0% +intelligently solve this problem he's + + + align:start position:0% +intelligently solve this problem he's +he's on one side of a barrier food is on + + align:start position:0% +he's on one side of a barrier food is on + + + align:start position:0% +he's on one side of a barrier food is on +the other he can see the + + align:start position:0% +the other he can see the + + + align:start position:0% +the other he can see the +food so he moves towards it but but he + + align:start position:0% +food so he moves towards it but but he + + + align:start position:0% +food so he moves towards it but but he +runs into the + + align:start position:0% +runs into the + + + align:start position:0% +runs into the +barrier but he has an automatic response + + align:start position:0% +barrier but he has an automatic response + + + align:start position:0% +barrier but he has an automatic response +to the + + align:start position:0% +to the + + + align:start position:0% +to the +barrier it's a response called negative + + align:start position:0% +barrier it's a response called negative + + + align:start position:0% +barrier it's a response called negative +thigmotaxis it's it's a kind of reflex + + align:start position:0% +thigmotaxis it's it's a kind of reflex + + + align:start position:0% +thigmotaxis it's it's a kind of reflex +involving + + align:start position:0% +involving + + + align:start position:0% +involving +Locomotion in which he moves away in + + align:start position:0% +Locomotion in which he moves away in + + + align:start position:0% +Locomotion in which he moves away in +change + + align:start position:0% +change + + + align:start position:0% +change +directions uh so he ends up you know + + align:start position:0% +directions uh so he ends up you know + + + align:start position:0% +directions uh so he ends up you know +moving along the + + align:start position:0% +moving along the + + + align:start position:0% +moving along the +barrier until he clears + + align:start position:0% +barrier until he clears + + + align:start position:0% +barrier until he clears +it so he appears to know what to do but + + align:start position:0% +it so he appears to know what to do but + + + align:start position:0% +it so he appears to know what to do but +in fact he's just using these simple + + align:start position:0% +in fact he's just using these simple + + + align:start position:0% +in fact he's just using these simple +automatic responses now I asked at the + + align:start position:0% +automatic responses now I asked at the + + + align:start position:0% +automatic responses now I asked at the +end here why does a dog often fail in + + align:start position:0% +end here why does a dog often fail in + + + align:start position:0% +end here why does a dog often fail in +such a + + align:start position:0% + + + + align:start position:0% + +situation what does the dog do here the + + align:start position:0% +situation what does the dog do here the + + + align:start position:0% +situation what does the dog do here the +dog's here + + align:start position:0% +dog's here + + + align:start position:0% +dog's here +now what does the dog do trying to get + + align:start position:0% +now what does the dog do trying to get + + + align:start position:0% +now what does the dog do trying to get +to that food and there's he's it's on + + align:start position:0% +to that food and there's he's it's on + + + align:start position:0% +to that food and there's he's it's on +the other side of a + + align:start position:0% +the other side of a + + + align:start position:0% +the other side of a +fence let's say an inexperienced + + align:start position:0% +fence let's say an inexperienced + + + align:start position:0% +fence let's say an inexperienced +dog because I'll admit an experienced + + align:start position:0% +dog because I'll admit an experienced + + + align:start position:0% +dog because I'll admit an experienced +dog can learn methods of + + align:start position:0% + + + + align:start position:0% + +Sol he can go around the end but an + + align:start position:0% +Sol he can go around the end but an + + + align:start position:0% +Sol he can go around the end but an +inexperienced dog will not do + + align:start position:0% +inexperienced dog will not do + + + align:start position:0% +inexperienced dog will not do +that at least not for quite a while long + + align:start position:0% +that at least not for quite a while long + + + align:start position:0% +that at least not for quite a while long +he will persist trying to get through + + align:start position:0% +he will persist trying to get through + + + align:start position:0% +he will persist trying to get through +that fence + + align:start position:0% + + + + align:start position:0% + +long after the Goldfish has already + + align:start position:0% +long after the Goldfish has already + + + align:start position:0% +long after the Goldfish has already +solved a similar problem so what does he + + align:start position:0% +solved a similar problem so what does he + + + align:start position:0% +solved a similar problem so what does he +do what has the dog + + align:start position:0% +do what has the dog + + + align:start position:0% +do what has the dog +inherited that he can + + align:start position:0% +inherited that he can + + + align:start position:0% +inherited that he can +use to solve the + + align:start position:0% + + + + align:start position:0% + +problem without thinking about it + + align:start position:0% +problem without thinking about it + + + align:start position:0% +problem without thinking about it +without learning anything what does he + + align:start position:0% +without learning anything what does he + + + align:start position:0% +without learning anything what does he +do + + align:start position:0% +do + + + align:start position:0% +do +automatically come on you have dogs some + + align:start position:0% +automatically come on you have dogs some + + + align:start position:0% +automatically come on you have dogs some +of + + align:start position:0% +of + + + align:start position:0% +of +you + + align:start position:0% + + + + align:start position:0% + +sorry yeah he he he either jumps to jump + + align:start position:0% +sorry yeah he he he either jumps to jump + + + align:start position:0% +sorry yeah he he he either jumps to jump +over the fence or go under it frequently + + align:start position:0% +over the fence or go under it frequently + + + align:start position:0% +over the fence or go under it frequently +under it they they try to dig under the + + align:start position:0% +under it they they try to dig under the + + + align:start position:0% +under it they they try to dig under the +fence and anybody that's kept dogs in a + + align:start position:0% +fence and anybody that's kept dogs in a + + + align:start position:0% +fence and anybody that's kept dogs in a +fence backyard knows this problem they + + align:start position:0% +fence backyard knows this problem they + + + align:start position:0% +fence backyard knows this problem they +they they do get out sometimes and they + + align:start position:0% +they they do get out sometimes and they + + + align:start position:0% +they they do get out sometimes and they +frequently try to dig under the Thum if + + align:start position:0% +frequently try to dig under the Thum if + + + align:start position:0% +frequently try to dig under the Thum if +there + + align:start position:0% +there + + + align:start position:0% +there +something that attracts them usually + + align:start position:0% +something that attracts them usually + + + align:start position:0% +something that attracts them usually +it's not food because they're well fed + + align:start position:0% +it's not food because they're well fed + + + align:start position:0% +it's not food because they're well fed +if they're pets but uh for a male it's + + align:start position:0% +if they're pets but uh for a male it's + + + align:start position:0% +if they're pets but uh for a male it's +usually female dog and I've had male + + align:start position:0% +usually female dog and I've had male + + + align:start position:0% +usually female dog and I've had male +dogs that either dig under fences or + + align:start position:0% +dogs that either dig under fences or + + + align:start position:0% +dogs that either dig under fences or +leap over + + align:start position:0% +leap over + + + align:start position:0% +leap over +them females are a little + + align:start position:0% +them females are a little + + + align:start position:0% +them females are a little +easier so anyway + + align:start position:0% + + + + align:start position:0% + +uh I thought I had + + align:start position:0% +uh I thought I had + + + align:start position:0% +uh I thought I had +described but anyway what is if the dog + + align:start position:0% +described but anyway what is if the dog + + + align:start position:0% +described but anyway what is if the dog +does the dog ever solve the problem an + + align:start position:0% +does the dog ever solve the problem an + + + align:start position:0% +does the dog ever solve the problem an +inexperienced dog well he keeps cying + + align:start position:0% +inexperienced dog well he keeps cying + + + align:start position:0% +inexperienced dog well he keeps cying +and + + align:start position:0% +and + + + align:start position:0% +and +eventually he's exhausted and he gives + + align:start position:0% +eventually he's exhausted and he gives + + + align:start position:0% +eventually he's exhausted and he gives +up and he starts wandering + + align:start position:0% +up and he starts wandering + + + align:start position:0% +up and he starts wandering +around and in his wandering he does find + + align:start position:0% +around and in his wandering he does find + + + align:start position:0% +around and in his wandering he does find +the end of the + + align:start position:0% +the end of the + + + align:start position:0% +the end of the +fence and then he will probably see that + + align:start position:0% +fence and then he will probably see that + + + align:start position:0% +fence and then he will probably see that +the food is still there and he will get + + align:start position:0% +the food is still there and he will get + + + align:start position:0% +the food is still there and he will get +to it it doesn't take more than once or + + align:start position:0% +to it it doesn't take more than once or + + + align:start position:0% +to it it doesn't take more than once or +twice going through that when the dog + + align:start position:0% +twice going through that when the dog + + + align:start position:0% +twice going through that when the dog +will learn it's kind of trial and error + + align:start position:0% +will learn it's kind of trial and error + + + align:start position:0% +will learn it's kind of trial and error +learning you could say + + align:start position:0% +learning you could say + + + align:start position:0% +learning you could say +but he doesn't solve it when he's in a + + align:start position:0% +but he doesn't solve it when he's in a + + + align:start position:0% +but he doesn't solve it when he's in a +really highly motivated State because + + align:start position:0% +really highly motivated State because + + + align:start position:0% +really highly motivated State because +then he's dominated by these instinctive + + align:start position:0% +then he's dominated by these instinctive + + + align:start position:0% +then he's dominated by these instinctive +behaviors you know think of the way dogs + + align:start position:0% +behaviors you know think of the way dogs + + + align:start position:0% +behaviors you know think of the way dogs +evolve initially as + + align:start position:0% +evolve initially as + + + align:start position:0% +evolve initially as +wol and they normally aren't confronted + + align:start position:0% +wol and they normally aren't confronted + + + align:start position:0% +wol and they normally aren't confronted +with things like + + align:start position:0% +with things like + + + align:start position:0% +with things like +fences the barriers they're faced with + + align:start position:0% +fences the barriers they're faced with + + + align:start position:0% +fences the barriers they're faced with +they uh + + align:start position:0% +they uh + + + align:start position:0% +they uh +streams + + align:start position:0% +streams + + + align:start position:0% +streams +streams Lakes uh Ravines mountains I + + align:start position:0% +streams Lakes uh Ravines mountains I + + + align:start position:0% +streams Lakes uh Ravines mountains I +mean they're certainly adapted to + + align:start position:0% +mean they're certainly adapted to + + + align:start position:0% +mean they're certainly adapted to +dealing with those things but not things + + align:start position:0% +dealing with those things but not things + + + align:start position:0% +dealing with those things but not things +like + + align:start position:0% +like + + + align:start position:0% +like +fences okay but yet they're also very + + align:start position:0% +fences okay but yet they're also very + + + align:start position:0% +fences okay but yet they're also very +intelligent is the fish then as + + align:start position:0% +intelligent is the fish then as + + + align:start position:0% +intelligent is the fish then as +intelligent as it more intelligent than + + align:start position:0% +intelligent as it more intelligent than + + + align:start position:0% +intelligent as it more intelligent than +the dog because it can solve those + + align:start position:0% +the dog because it can solve those + + + align:start position:0% +the dog because it can solve those +problems remember we talked about the + + align:start position:0% +problems remember we talked about the + + + align:start position:0% +problems remember we talked about the +intelligence of + + align:start position:0% +intelligence of + + + align:start position:0% +intelligence of +instinct what seems like intelligent + + align:start position:0% +instinct what seems like intelligent + + + align:start position:0% +instinct what seems like intelligent +Behavior and we think of intelligence as + + align:start position:0% +Behavior and we think of intelligence as + + + align:start position:0% +Behavior and we think of intelligence as +involving + + align:start position:0% +involving + + + align:start position:0% +involving +cognition may not involve cognition at + + align:start position:0% +cognition may not involve cognition at + + + align:start position:0% +cognition may not involve cognition at +all it's + + align:start position:0% +all it's + + + align:start position:0% +all it's +simply instinctive Behavior that's + + align:start position:0% +simply instinctive Behavior that's + + + align:start position:0% +simply instinctive Behavior that's +highly adapted to the + + align:start position:0% + + + + align:start position:0% + +situation so let's talk now + + align:start position:0% +situation so let's talk now + + + align:start position:0% +situation so let's talk now +about cognitive behavior how do human + + align:start position:0% +about cognitive behavior how do human + + + align:start position:0% +about cognitive behavior how do human +languages give Clues to the nature of + + align:start position:0% +languages give Clues to the nature of + + + align:start position:0% +languages give Clues to the nature of +what we call Insight + + align:start position:0% +what we call Insight + + + align:start position:0% +what we call Insight +we've got to think about what Insight + + align:start position:0% + + + + align:start position:0% + +is and this is what Lawrence says about + + align:start position:0% +is and this is what Lawrence says about + + + align:start position:0% +is and this is what Lawrence says about +it he quotes + + align:start position:0% +it he quotes + + + align:start position:0% +it he quotes +uh uh foric who wrote in 1950 that our + + align:start position:0% +uh uh foric who wrote in 1950 that our + + + align:start position:0% +uh uh foric who wrote in 1950 that our +language translates everything that + + align:start position:0% +language translates everything that + + + align:start position:0% +language translates everything that +cannot be visualized into spatial + + align:start position:0% +cannot be visualized into spatial + + + align:start position:0% +cannot be visualized into spatial +Concepts it's not just done by by one + + align:start position:0% +Concepts it's not just done by by one + + + align:start position:0% +Concepts it's not just done by by one +language but by all + + align:start position:0% + + + + align:start position:0% + +languages concepts for space and time + + align:start position:0% +languages concepts for space and time + + + align:start position:0% +languages concepts for space and time +use the same spatial + + align:start position:0% +use the same spatial + + + align:start position:0% +use the same spatial +terms for orientation all orientation is + + align:start position:0% +terms for orientation all orientation is + + + align:start position:0% +terms for orientation all orientation is +always concerned with both space and + + align:start position:0% +always concerned with both space and + + + align:start position:0% +always concerned with both space and +time of course we move through + + align:start position:0% +time of course we move through + + + align:start position:0% +time of course we move through +multiple spaces both physical spaces and + + align:start position:0% +multiple spaces both physical spaces and + + + align:start position:0% +multiple spaces both physical spaces and +conceptual + + align:start position:0% + + + + align:start position:0% + +spaces these are represented in a + + align:start position:0% +spaces these are represented in a + + + align:start position:0% +spaces these are represented in a +memory as our concept both conceptual + + align:start position:0% +memory as our concept both conceptual + + + align:start position:0% +memory as our concept both conceptual +and physical spaces or memory for + + align:start position:0% +and physical spaces or memory for + + + align:start position:0% +and physical spaces or memory for +them because we think in conceptual + + align:start position:0% +them because we think in conceptual + + + align:start position:0% +them because we think in conceptual +spaces in + + align:start position:0% +spaces in + + + align:start position:0% +spaces in +fact the part of the brain involved in + + align:start position:0% +fact the part of the brain involved in + + + align:start position:0% +fact the part of the brain involved in +what we call cognitive + + align:start position:0% +what we call cognitive + + + align:start position:0% +what we call cognitive +Maps we believe is involved and there's + + align:start position:0% +Maps we believe is involved and there's + + + align:start position:0% +Maps we believe is involved and there's +plenty of evidence now from Imaging + + align:start position:0% +plenty of evidence now from Imaging + + + align:start position:0% +plenty of evidence now from Imaging +studies is involved in both kinds of + + align:start position:0% + + + + align:start position:0% + +navigation when we solve + + align:start position:0% +navigation when we solve + + + align:start position:0% +navigation when we solve +problems or when we think about going + + align:start position:0% +problems or when we think about going + + + align:start position:0% +problems or when we think about going +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +physically it involves Association cour + + align:start position:0% +physically it involves Association cour + + + align:start position:0% +physically it involves Association cour +and hample form in the temple + + align:start position:0% + + + + align:start position:0% + +lobe so let's talk about this term in + + align:start position:0% +lobe so let's talk about this term in + + + align:start position:0% +lobe so let's talk about this term in +Insight + + align:start position:0% + + + + align:start position:0% + +now if you search search under Google + + align:start position:0% +now if you search search under Google + + + align:start position:0% +now if you search search under Google +you can find how they deal with inside + + align:start position:0% +you can find how they deal with inside + + + align:start position:0% +you can find how they deal with inside +in animals I did searches on inside in + + align:start position:0% +in animals I did searches on inside in + + + align:start position:0% +in animals I did searches on inside in +Apes uh on examples of both Tim and + + align:start position:0% +Apes uh on examples of both Tim and + + + align:start position:0% +Apes uh on examples of both Tim and +gorilla + + align:start position:0% +gorilla + + + align:start position:0% +gorilla +problem solving some of them are well + + align:start position:0% +problem solving some of them are well + + + align:start position:0% +problem solving some of them are well +known and I read some of these studies + + align:start position:0% +known and I read some of these studies + + + align:start position:0% +known and I read some of these studies +as a graduate + + align:start position:0% + + + + align:start position:0% + +student + + align:start position:0% +student + + + align:start position:0% +student +um it's very interesting because they + + align:start position:0% +um it's very interesting because they + + + align:start position:0% +um it's very interesting because they +give evidence that even in in these Apes + + align:start position:0% +give evidence that even in in these Apes + + + align:start position:0% +give evidence that even in in these Apes +just like in humans it's evidence that + + align:start position:0% +just like in humans it's evidence that + + + align:start position:0% +just like in humans it's evidence that +they + + align:start position:0% + + + + align:start position:0% + +uh form plans within some kind of an + + align:start position:0% +uh form plans within some kind of an + + + align:start position:0% +uh form plans within some kind of an +internal model of the world and they can + + align:start position:0% +internal model of the world and they can + + + align:start position:0% +internal model of the world and they can +end anticipate events and they can + + align:start position:0% +end anticipate events and they can + + + align:start position:0% +end anticipate events and they can +consider alternatives and act on + + align:start position:0% +consider alternatives and act on + + + align:start position:0% +consider alternatives and act on +them + + align:start position:0% +them + + + align:start position:0% +them +uh I think these websites that I'm + + align:start position:0% +uh I think these websites that I'm + + + align:start position:0% +uh I think these websites that I'm +giving here still work these are the + + align:start position:0% +giving here still work these are the + + + align:start position:0% +giving here still work these are the +some pictures that I + + align:start position:0% +some pictures that I + + + align:start position:0% +some pictures that I +found uh this is + + align:start position:0% +found uh this is + + + align:start position:0% +found uh this is +from this kind of work that this isn't + + align:start position:0% +from this kind of work that this isn't + + + align:start position:0% +from this kind of work that this isn't +from his studies but uh the work was + + align:start position:0% +from his studies but uh the work was + + + align:start position:0% +from his studies but uh the work was +initiated by wul gon Couer in World War + + align:start position:0% +initiated by wul gon Couer in World War + + + align:start position:0% +initiated by wul gon Couer in World War +I + + align:start position:0% +I + + + align:start position:0% +I +and it was carried further by Paul + + align:start position:0% +and it was carried further by Paul + + + align:start position:0% +and it was carried further by Paul +killer Peter Killer's father uh and + + align:start position:0% +killer Peter Killer's father uh and + + + align:start position:0% +killer Peter Killer's father uh and +later by his wife Claire + + align:start position:0% +later by his wife Claire + + + align:start position:0% +later by his wife Claire +killer and + + align:start position:0% + + + + align:start position:0% + +uh but this was the nature of the work + + align:start position:0% +uh but this was the nature of the work + + + align:start position:0% +uh but this was the nature of the work +you see chimpanzees here um here's a + + align:start position:0% +you see chimpanzees here um here's a + + + align:start position:0% +you see chimpanzees here um here's a +chimp that's using a stick + + align:start position:0% +chimp that's using a stick + + + align:start position:0% +chimp that's using a stick +to he's learning there that he can poke + + align:start position:0% +to he's learning there that he can poke + + + align:start position:0% +to he's learning there that he can poke +that stick under the fence and get at + + align:start position:0% +that stick under the fence and get at + + + align:start position:0% +that stick under the fence and get at +things the more famous problem was the + + align:start position:0% +things the more famous problem was the + + + align:start position:0% +things the more famous problem was the +hanging a banana this was done first + + align:start position:0% +hanging a banana this was done first + + + align:start position:0% +hanging a banana this was done first +with gorillas and here you see chimp + + align:start position:0% +with gorillas and here you see chimp + + + align:start position:0% +with gorillas and here you see chimp +solving a similar problem there are + + align:start position:0% +solving a similar problem there are + + + align:start position:0% +solving a similar problem there are +bananas hanging up + + align:start position:0% +bananas hanging up + + + align:start position:0% +bananas hanging up +high and uh what is the chimp doing + + align:start position:0% +high and uh what is the chimp doing + + + align:start position:0% +high and uh what is the chimp doing +there he's piling up boxes which were + + align:start position:0% +there he's piling up boxes which were + + + align:start position:0% +there he's piling up boxes which were +present in the pen but they weren't + + align:start position:0% +present in the pen but they weren't + + + align:start position:0% +present in the pen but they weren't +piled up they were scattered + + align:start position:0% +piled up they were scattered + + + align:start position:0% +piled up they were scattered +about and the the chimp eventually will + + align:start position:0% +about and the the chimp eventually will + + + align:start position:0% +about and the the chimp eventually will +pile the boxes up so he can do what you + + align:start position:0% +pile the boxes up so he can do what you + + + align:start position:0% +pile the boxes up so he can do what you +see the chimp doing here and climb up on + + align:start position:0% +see the chimp doing here and climb up on + + + align:start position:0% +see the chimp doing here and climb up on +the + + align:start position:0% +the + + + align:start position:0% +the +boxes it looks like these are about to + + align:start position:0% +boxes it looks like these are about to + + + align:start position:0% +boxes it looks like these are about to +fall over but he's reaching the + + align:start position:0% +fall over but he's reaching the + + + align:start position:0% +fall over but he's reaching the +bananas there you see it happening to + + align:start position:0% +bananas there you see it happening to + + + align:start position:0% +bananas there you see it happening to +her another one is involved + + align:start position:0% +her another one is involved + + + align:start position:0% +her another one is involved +also and Claire Schiller wrote an + + align:start position:0% +also and Claire Schiller wrote an + + + align:start position:0% +also and Claire Schiller wrote an +interesting analysis of this Behavior + + align:start position:0% +interesting analysis of this Behavior + + + align:start position:0% +interesting analysis of this Behavior +because it had been interpreted as sort + + align:start position:0% +because it had been interpreted as sort + + + align:start position:0% +because it had been interpreted as sort +of a denovo problem solving like they + + align:start position:0% +of a denovo problem solving like they + + + align:start position:0% +of a denovo problem solving like they +figured it out + + align:start position:0% +figured it out + + + align:start position:0% +figured it out +they looked at the boxes they looked at + + align:start position:0% +they looked at the boxes they looked at + + + align:start position:0% +they looked at the boxes they looked at +the bananas they couldn't reach the + + align:start position:0% +the bananas they couldn't reach the + + + align:start position:0% +the bananas they couldn't reach the +bananas and they figured out in their + + align:start position:0% +bananas and they figured out in their + + + align:start position:0% +bananas and they figured out in their +minds that they could climb on boxes and + + align:start position:0% +minds that they could climb on boxes and + + + align:start position:0% +minds that they could climb on boxes and +get to it but she + + align:start position:0% +get to it but she + + + align:start position:0% +get to it but she +asked does that mean they were there's + + align:start position:0% +asked does that mean they were there's + + + align:start position:0% +asked does that mean they were there's +no instinctive Behavior involved at + + align:start position:0% +no instinctive Behavior involved at + + + align:start position:0% +no instinctive Behavior involved at +all he said she didn't think it meant + + align:start position:0% +all he said she didn't think it meant + + + align:start position:0% +all he said she didn't think it meant +that at all because simps and gorillas + + align:start position:0% +that at all because simps and gorillas + + + align:start position:0% +that at all because simps and gorillas +both make + + align:start position:0% +both make + + + align:start position:0% +both make +nests twice a day at least least to + + align:start position:0% +nests twice a day at least least to + + + align:start position:0% +nests twice a day at least least to +sleep they take naps in the middle of + + align:start position:0% +sleep they take naps in the middle of + + + align:start position:0% +sleep they take naps in the middle of +the day they sleep at night and every + + align:start position:0% +the day they sleep at night and every + + + align:start position:0% +the day they sleep at night and every +night they make a nest in a different + + align:start position:0% +night they make a nest in a different + + + align:start position:0% +night they make a nest in a different +place uh they do the same thing for + + align:start position:0% +place uh they do the same thing for + + + align:start position:0% +place uh they do the same thing for +their naps they construct these things + + align:start position:0% +their naps they construct these things + + + align:start position:0% +their naps they construct these things +and they're they pile leaves + + align:start position:0% +and they're they pile leaves + + + align:start position:0% +and they're they pile leaves +branches uh up and making the + + align:start position:0% +branches uh up and making the + + + align:start position:0% +branches uh up and making the +nest so + + align:start position:0% +nest so + + + align:start position:0% +nest so +they have that in their instinctive + + align:start position:0% +they have that in their instinctive + + + align:start position:0% +they have that in their instinctive +Behavior it's not that far from that to + + align:start position:0% +Behavior it's not that far from that to + + + align:start position:0% +Behavior it's not that far from that to +pile anything especially wooden boxes + + align:start position:0% +pile anything especially wooden boxes + + + align:start position:0% +pile anything especially wooden boxes +and + + align:start position:0% + + + + align:start position:0% + +uh what the connection had when they + + align:start position:0% +uh what the connection had when they + + + align:start position:0% +uh what the connection had when they +piled + + align:start position:0% +piled + + + align:start position:0% +piled +them and they often don't they seem to + + align:start position:0% +them and they often don't they seem to + + + align:start position:0% +them and they often don't they seem to +be acting rather randomly they almost + + align:start position:0% +be acting rather randomly they almost + + + align:start position:0% +be acting rather randomly they almost +seem to be forgetting about the bananas + + align:start position:0% +seem to be forgetting about the bananas + + + align:start position:0% +seem to be forgetting about the bananas +when they first play around with the + + align:start position:0% +when they first play around with the + + + align:start position:0% +when they first play around with the +boxes but they figure out pretty quickly + + align:start position:0% +boxes but they figure out pretty quickly + + + align:start position:0% +boxes but they figure out pretty quickly +they make the connection that they can + + align:start position:0% +they make the connection that they can + + + align:start position:0% +they make the connection that they can +get up a lot + + align:start position:0% +get up a lot + + + align:start position:0% +get up a lot +higher so it's definitely a kind of + + align:start position:0% +higher so it's definitely a kind of + + + align:start position:0% +higher so it's definitely a kind of +insight they do figure out they make + + align:start position:0% +insight they do figure out they make + + + align:start position:0% +insight they do figure out they make +that connection they can get higher by + + align:start position:0% +that connection they can get higher by + + + align:start position:0% +that connection they can get higher by +piling the boxes and they can you then + + align:start position:0% +piling the boxes and they can you then + + + align:start position:0% +piling the boxes and they can you then +they figure out they this it is a way to + + align:start position:0% +they figure out they this it is a way to + + + align:start position:0% +they figure out they this it is a way to +get at those + + align:start position:0% + + + + align:start position:0% + +bananas so when Lawrence talks about + + align:start position:0% +bananas so when Lawrence talks about + + + align:start position:0% +bananas so when Lawrence talks about +what he calls higher animals he + + align:start position:0% +what he calls higher animals he + + + align:start position:0% +what he calls higher animals he +said he has the hypotheses that there's + + align:start position:0% +said he has the hypotheses that there's + + + align:start position:0% +said he has the hypotheses that there's +a higher control center in higher + + align:start position:0% +a higher control center in higher + + + align:start position:0% +a higher control center in higher +animals he says superimposed on all + + align:start position:0% +animals he says superimposed on all + + + align:start position:0% +animals he says superimposed on all +these orienting + + align:start position:0% +these orienting + + + align:start position:0% +these orienting +mechanisms and of course the mechanisms + + align:start position:0% +mechanisms and of course the mechanisms + + + align:start position:0% +mechanisms and of course the mechanisms +for instinctive + + align:start position:0% + + + + align:start position:0% + +behavior and also remembers changes in + + align:start position:0% +behavior and also remembers changes in + + + align:start position:0% +behavior and also remembers changes in +the environment and is able to judge the + + align:start position:0% +the environment and is able to judge the + + + align:start position:0% +the environment and is able to judge the +priority of incoming Insight + + align:start position:0% +priority of incoming Insight + + + align:start position:0% +priority of incoming Insight +information well that's pretty General + + align:start position:0% +information well that's pretty General + + + align:start position:0% +information well that's pretty General +and difficult to get a grip on how do + + align:start position:0% +and difficult to get a grip on how do + + + align:start position:0% +and difficult to get a grip on how do +you define a + + align:start position:0% +you define a + + + align:start position:0% +you define a +higher versus a lower animal + + align:start position:0% +higher versus a lower animal + + + align:start position:0% +higher versus a lower animal +can you think of any way to do + + align:start position:0% + + + + align:start position:0% + +that it's not an easy + + align:start position:0% +that it's not an easy + + + align:start position:0% +that it's not an easy +issue we already saw how a goldfish if + + align:start position:0% +issue we already saw how a goldfish if + + + align:start position:0% +issue we already saw how a goldfish if +you just use a single problem like that + + align:start position:0% +you just use a single problem like that + + + align:start position:0% +you just use a single problem like that +you could say a goldfish is a higher + + align:start position:0% +you could say a goldfish is a higher + + + align:start position:0% +you could say a goldfish is a higher +animal than a dog but most of us would + + align:start position:0% +animal than a dog but most of us would + + + align:start position:0% +animal than a dog but most of us would +realize that that's not very + + align:start position:0% +realize that that's not very + + + align:start position:0% +realize that that's not very +likely think of the brain for + + align:start position:0% +likely think of the brain for + + + align:start position:0% +likely think of the brain for +example the dog has a extremely large + + align:start position:0% +example the dog has a extremely large + + + align:start position:0% +example the dog has a extremely large +end brain in compared to the + + align:start position:0% + + + + align:start position:0% + +Goldfish the lower parts of the brain + + align:start position:0% +Goldfish the lower parts of the brain + + + align:start position:0% +Goldfish the lower parts of the brain +the the midbrain and midbrain is + + align:start position:0% +the the midbrain and midbrain is + + + align:start position:0% +the the midbrain and midbrain is +relatively larger in the Goldfish and + + align:start position:0% +relatively larger in the Goldfish and + + + align:start position:0% +relatively larger in the Goldfish and +the hindbrain is pretty similar all the + + align:start position:0% +the hindbrain is pretty similar all the + + + align:start position:0% +the hindbrain is pretty similar all the +same basic + + align:start position:0% +same basic + + + align:start position:0% +same basic +structures all the way from really + + align:start position:0% +structures all the way from really + + + align:start position:0% +structures all the way from really +across the + + align:start position:0% + + + + align:start position:0% + +vertebrates but the end brains are very + + align:start position:0% +vertebrates but the end brains are very + + + align:start position:0% +vertebrates but the end brains are very +different we know higher can't mean + + align:start position:0% +different we know higher can't mean + + + align:start position:0% +different we know higher can't mean +better better adapted because all + + align:start position:0% +better better adapted because all + + + align:start position:0% +better better adapted because all +existing species are highly adapted to + + align:start position:0% +existing species are highly adapted to + + + align:start position:0% +existing species are highly adapted to +their particular environmental + + align:start position:0% +their particular environmental + + + align:start position:0% +their particular environmental +need you could Define it in terms of + + align:start position:0% +need you could Define it in terms of + + + align:start position:0% +need you could Define it in terms of +ability to + + align:start position:0% +ability to + + + align:start position:0% +ability to +anticipate and these anticipation + + align:start position:0% +anticipate and these anticipation + + + align:start position:0% +anticipate and these anticipation +abilities we've talked about a little + + align:start position:0% +abilities we've talked about a little + + + align:start position:0% +abilities we've talked about a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +before uh we talked mentioned that here + + align:start position:0% +before uh we talked mentioned that here + + + align:start position:0% +before uh we talked mentioned that here +talking about the + + align:start position:0% +talking about the + + + align:start position:0% +talking about the +Apes and when we deal with anticipation + + align:start position:0% +Apes and when we deal with anticipation + + + align:start position:0% +Apes and when we deal with anticipation +ability to anticipate tanks in the + + align:start position:0% +ability to anticipate tanks in the + + + align:start position:0% +ability to anticipate tanks in the +future we know the parts of the brain + + align:start position:0% +future we know the parts of the brain + + + align:start position:0% +future we know the parts of the brain +association areas of the neocortex that + + align:start position:0% +association areas of the neocortex that + + + align:start position:0% +association areas of the neocortex that +are primarily involved and especially + + align:start position:0% +are primarily involved and especially + + + align:start position:0% +are primarily involved and especially +prefrontal areas because they're + + align:start position:0% +prefrontal areas because they're + + + align:start position:0% +prefrontal areas because they're +involved in planning + + align:start position:0% +involved in planning + + + align:start position:0% +involved in planning +movement movement the animal will make + + align:start position:0% +movement movement the animal will make + + + align:start position:0% +movement movement the animal will make +in the + + align:start position:0% +in the + + + align:start position:0% +in the +future so we can ask now a neurological + + align:start position:0% +future so we can ask now a neurological + + + align:start position:0% +future so we can ask now a neurological +question well what animal has the + + align:start position:0% +question well what animal has the + + + align:start position:0% +question well what animal has the +relatively largest prefrontal + + align:start position:0% +relatively largest prefrontal + + + align:start position:0% +relatively largest prefrontal +cortex and up until recently if IID + + align:start position:0% +cortex and up until recently if IID + + + align:start position:0% +cortex and up until recently if IID +given this question in this class I + + align:start position:0% +given this question in this class I + + + align:start position:0% +given this question in this class I +immediately would have said well it + + align:start position:0% +immediately would have said well it + + + align:start position:0% +immediately would have said well it +appears that humans have the largest + + align:start position:0% +appears that humans have the largest + + + align:start position:0% +appears that humans have the largest +relatively largest preal + + align:start position:0% + + + + align:start position:0% + +cortex but look + + align:start position:0% +cortex but look + + + align:start position:0% +cortex but look +here I've drawn the prefrontal cortex + + align:start position:0% +here I've drawn the prefrontal cortex + + + align:start position:0% +here I've drawn the prefrontal cortex +I've taken this from the literature A + + align:start position:0% +I've taken this from the literature A + + + align:start position:0% +I've taken this from the literature A +study of a monot an egg laying + + align:start position:0% +study of a monot an egg laying + + + align:start position:0% +study of a monot an egg laying +animal very primitive in evolution this + + align:start position:0% +animal very primitive in evolution this + + + align:start position:0% +animal very primitive in evolution this +is the + + align:start position:0% +is the + + + align:start position:0% +is the +Akida and I've + + align:start position:0% +Akida and I've + + + align:start position:0% +Akida and I've +colored the prefrontal areas in + + align:start position:0% + + + + align:start position:0% + +pink these are motor + + align:start position:0% +pink these are motor + + + align:start position:0% +pink these are motor +areas this is a seata sensory area + + align:start position:0% +areas this is a seata sensory area + + + align:start position:0% +areas this is a seata sensory area +visual area and auditory + + align:start position:0% + + + + align:start position:0% + +area so you get an idea there of the + + align:start position:0% +area so you get an idea there of the + + + align:start position:0% +area so you get an idea there of the +relative size of the prefrontal cortex + + align:start position:0% +relative size of the prefrontal cortex + + + align:start position:0% +relative size of the prefrontal cortex +now look at human look at the side view + + align:start position:0% +now look at human look at the side view + + + align:start position:0% +now look at human look at the side view +here prefrontal cortex here is in this + + align:start position:0% +here prefrontal cortex here is in this + + + align:start position:0% +here prefrontal cortex here is in this +model + + align:start position:0% +model + + + align:start position:0% +model +pink there's centry motor premotor + + align:start position:0% +pink there's centry motor premotor + + + align:start position:0% +pink there's centry motor premotor +there's the prefrontal cortex and now + + align:start position:0% +there's the prefrontal cortex and now + + + align:start position:0% +there's the prefrontal cortex and now +the posterior Association cortex is very + + align:start position:0% +the posterior Association cortex is very + + + align:start position:0% +the posterior Association cortex is very +large so if you took all the association + + align:start position:0% +large so if you took all the association + + + align:start position:0% +large so if you took all the association +cortex okay maybe human is even larger + + align:start position:0% +cortex okay maybe human is even larger + + + align:start position:0% +cortex okay maybe human is even larger +than a kidney but if you just took the + + align:start position:0% +than a kidney but if you just took the + + + align:start position:0% +than a kidney but if you just took the +prefrontal + + align:start position:0% +prefrontal + + + align:start position:0% +prefrontal +areas the kidney beats us + + align:start position:0% +areas the kidney beats us + + + align:start position:0% +areas the kidney beats us +all what does that + + align:start position:0% + + + + align:start position:0% + +mean well I wish I could answer + + align:start position:0% +mean well I wish I could answer + + + align:start position:0% +mean well I wish I could answer +there's almost no behavioral study of + + align:start position:0% +there's almost no behavioral study of + + + align:start position:0% +there's almost no behavioral study of +the + + align:start position:0% +the + + + align:start position:0% +the +Akida and yet they're present in some of + + align:start position:0% +Akida and yet they're present in some of + + + align:start position:0% +Akida and yet they're present in some of +our + + align:start position:0% +our + + + align:start position:0% +our +zoos it's only fairly recently but you + + align:start position:0% +zoos it's only fairly recently but you + + + align:start position:0% +zoos it's only fairly recently but you +know + + align:start position:0% +know + + + align:start position:0% +know +and that depends on how old you are to + + align:start position:0% +and that depends on how old you are to + + + align:start position:0% +and that depends on how old you are to +you it it would be a long time ago when + + align:start position:0% +you it it would be a long time ago when + + + align:start position:0% +you it it would be a long time ago when +they first discovered this these facts + + align:start position:0% +they first discovered this these facts + + + align:start position:0% +they first discovered this these facts +about the prefrontal cortex and the + + align:start position:0% +about the prefrontal cortex and the + + + align:start position:0% +about the prefrontal cortex and the +corresponding nucleus and Thalamus this + + align:start position:0% +corresponding nucleus and Thalamus this + + + align:start position:0% +corresponding nucleus and Thalamus this +MD area that projects to the prefontal + + align:start position:0% +MD area that projects to the prefontal + + + align:start position:0% +MD area that projects to the prefontal +cortex that's also hued in the + + align:start position:0% +cortex that's also hued in the + + + align:start position:0% +cortex that's also hued in the +aido okay so the fact + + align:start position:0% +aido okay so the fact + + + align:start position:0% +aido okay so the fact +is + + align:start position:0% + + + + align:start position:0% + +uh with that neurological substrate the + + align:start position:0% +uh with that neurological substrate the + + + align:start position:0% +uh with that neurological substrate the +animal must have evolved that for some + + align:start position:0% +animal must have evolved that for some + + + align:start position:0% +animal must have evolved that for some +reason what do humans use all this + + align:start position:0% +reason what do humans use all this + + + align:start position:0% +reason what do humans use all this +prefrontal cortex 4 we know it's for + + align:start position:0% +prefrontal cortex 4 we know it's for + + + align:start position:0% +prefrontal cortex 4 we know it's for +planning for + + align:start position:0% +planning for + + + align:start position:0% +planning for +future uh anticipation of events as is + + align:start position:0% +future uh anticipation of events as is + + + align:start position:0% +future uh anticipation of events as is +posterior cortex but it's the frontal + + align:start position:0% +posterior cortex but it's the frontal + + + align:start position:0% +posterior cortex but it's the frontal +where we plan our + + align:start position:0% + + + + align:start position:0% + +actions okay but there's one other thing + + align:start position:0% +actions okay but there's one other thing + + + align:start position:0% +actions okay but there's one other thing +we use that for and that is the language + + align:start position:0% +we use that for and that is the language + + + align:start position:0% +we use that for and that is the language +system it + + align:start position:0% +system it + + + align:start position:0% +system it +involves this region of the frontal lobe + + align:start position:0% +involves this region of the frontal lobe + + + align:start position:0% +involves this region of the frontal lobe +in this region of the posterior + + align:start position:0% +in this region of the posterior + + + align:start position:0% +in this region of the posterior +Association + + align:start position:0% +Association + + + align:start position:0% +Association +cortex basically auditory association + + align:start position:0% +cortex basically auditory association + + + align:start position:0% +cortex basically auditory association +areas but also Visual and SM sensory are + + align:start position:0% +areas but also Visual and SM sensory are + + + align:start position:0% +areas but also Visual and SM sensory are +part of it in other words multi + + align:start position:0% +part of it in other words multi + + + align:start position:0% +part of it in other words multi +multimodal association areas and + + align:start position:0% +multimodal association areas and + + + align:start position:0% +multimodal association areas and +auditory association areas that are + + align:start position:0% +auditory association areas that are + + + align:start position:0% +auditory association areas that are +highly + + align:start position:0% + + + + align:start position:0% + +connected with that paral + + align:start position:0% +connected with that paral + + + align:start position:0% +connected with that paral +lobe nothing like that in the Akida that + + align:start position:0% +lobe nothing like that in the Akida that + + + align:start position:0% +lobe nothing like that in the Akida that +we know + + align:start position:0% +we know + + + align:start position:0% +we know +of so humans with the language system it + + align:start position:0% +of so humans with the language system it + + + align:start position:0% +of so humans with the language system it +seems to be sort of super imposed on and + + align:start position:0% +seems to be sort of super imposed on and + + + align:start position:0% +seems to be sort of super imposed on and +highly + + align:start position:0% +highly + + + align:start position:0% +highly +connected with the other brain + + align:start position:0% +connected with the other brain + + + align:start position:0% +connected with the other brain +systems and we know that it enables + + align:start position:0% +systems and we know that it enables + + + align:start position:0% +systems and we know that it enables +social + + align:start position:0% +social + + + align:start position:0% +social +communication so in a + + align:start position:0% +communication so in a + + + align:start position:0% +communication so in a +sense even the way it's connected it is + + align:start position:0% +sense even the way it's connected it is + + + align:start position:0% +sense even the way it's connected it is +sort of a higher + + align:start position:0% +sort of a higher + + + align:start position:0% +sort of a higher +system so is that a way to define higher + + align:start position:0% +system so is that a way to define higher + + + align:start position:0% +system so is that a way to define higher +and lower animals well maybe it's a + + align:start position:0% +and lower animals well maybe it's a + + + align:start position:0% +and lower animals well maybe it's a +possibility I'm just pointing out how + + align:start position:0% +possibility I'm just pointing out how + + + align:start position:0% +possibility I'm just pointing out how +difficult this issue is but at least + + align:start position:0% +difficult this issue is but at least + + + align:start position:0% +difficult this issue is but at least +because I'm a neuron anatomist as well + + align:start position:0% +because I'm a neuron anatomist as well + + + align:start position:0% +because I'm a neuron anatomist as well +as an animal behavior + + align:start position:0% +as an animal behavior + + + align:start position:0% +as an animal behavior +I sort of can't help but use the anatomy + + align:start position:0% +I sort of can't help but use the anatomy + + + align:start position:0% +I sort of can't help but use the anatomy +to uh make a stab at it but I really + + align:start position:0% +to uh make a stab at it but I really + + + align:start position:0% +to uh make a stab at it but I really +would like to see I would like to do it + + align:start position:0% +would like to see I would like to do it + + + align:start position:0% +would like to see I would like to do it +myself if I had any kidas around here to + + align:start position:0% +myself if I had any kidas around here to + + + align:start position:0% +myself if I had any kidas around here to +study here's what I would + + align:start position:0% +study here's what I would + + + align:start position:0% +study here's what I would +guess it can't be that it's a very + + align:start position:0% +guess it can't be that it's a very + + + align:start position:0% +guess it can't be that it's a very +social animal we know frontal lob and + + align:start position:0% +social animal we know frontal lob and + + + align:start position:0% +social animal we know frontal lob and +it's been proposed front L became so big + + align:start position:0% +it's been proposed front L became so big + + + align:start position:0% +it's been proposed front L became so big +in humans because of social life and + + align:start position:0% +in humans because of social life and + + + align:start position:0% +in humans because of social life and +that characterizes our higher + + align:start position:0% +that characterizes our higher + + + align:start position:0% +that characterizes our higher +cognition well is the Aida there very + + align:start position:0% +cognition well is the Aida there very + + + align:start position:0% +cognition well is the Aida there very +social animal no mostly a solitary + + align:start position:0% +social animal no mostly a solitary + + + align:start position:0% +social animal no mostly a solitary +animal of course all all these animals + + align:start position:0% +animal of course all all these animals + + + align:start position:0% +animal of course all all these animals +even the solitary ones have to mate to + + align:start position:0% +even the solitary ones have to mate to + + + align:start position:0% +even the solitary ones have to mate to +reproduce and so yes they they have that + + align:start position:0% +reproduce and so yes they they have that + + + align:start position:0% +reproduce and so yes they they have that +but they don't have the complex social + + align:start position:0% +but they don't have the complex social + + + align:start position:0% +but they don't have the complex social +life of humans in fact of primes and of + + align:start position:0% +life of humans in fact of primes and of + + + align:start position:0% +life of humans in fact of primes and of +most + + align:start position:0% + + + + align:start position:0% + +Prat what does he eat + + align:start position:0% +Prat what does he eat + + + align:start position:0% +Prat what does he eat +he's an ante eater this is the spiny the + + align:start position:0% +he's an ante eater this is the spiny the + + + align:start position:0% +he's an ante eater this is the spiny the +Australian spiny ante + + align:start position:0% +Australian spiny ante + + + align:start position:0% +Australian spiny ante +eater what's so difficult about hunting + + align:start position:0% +eater what's so difficult about hunting + + + align:start position:0% +eater what's so difficult about hunting +ants one is they're very small they move + + align:start position:0% +ants one is they're very small they move + + + align:start position:0% +ants one is they're very small they move +very fast and when you get them they + + align:start position:0% +very fast and when you get them they + + + align:start position:0% +very fast and when you get them they +don't stay around very long my guess is + + align:start position:0% +don't stay around very long my guess is + + + align:start position:0% +don't stay around very long my guess is +he can very rapidly not only see many + + align:start position:0% +he can very rapidly not only see many + + + align:start position:0% +he can very rapidly not only see many +many ants he can remember where they + + align:start position:0% +many ants he can remember where they + + + align:start position:0% +many ants he can remember where they +are that takes our pre fontal cortex + + align:start position:0% +are that takes our pre fontal cortex + + + align:start position:0% +are that takes our pre fontal cortex +that we call it working + + align:start position:0% +that we call it working + + + align:start position:0% +that we call it working +memory and he can guide multiple actions + + align:start position:0% +memory and he can guide multiple actions + + + align:start position:0% +memory and he can guide multiple actions +very very quickly and get as many ants + + align:start position:0% +very very quickly and get as many ants + + + align:start position:0% +very very quickly and get as many ants +as possible it seems awfully simplistic + + align:start position:0% +as possible it seems awfully simplistic + + + align:start position:0% +as possible it seems awfully simplistic +could that result in this enormous + + align:start position:0% +could that result in this enormous + + + align:start position:0% +could that result in this enormous +Evolution I don't know but that's one of + + align:start position:0% +Evolution I don't know but that's one of + + + align:start position:0% +Evolution I don't know but that's one of +the things I would go after that would + + align:start position:0% +the things I would go after that would + + + align:start position:0% +the things I would go after that would +that would be one thing I would like to + + align:start position:0% +that would be one thing I would like to + + + align:start position:0% +that would be one thing I would like to +test I would like to observe their + + align:start position:0% +test I would like to observe their + + + align:start position:0% +test I would like to observe their +feeding Behavior exactly how they do + + align:start position:0% +feeding Behavior exactly how they do + + + align:start position:0% +feeding Behavior exactly how they do +it compare other animals other anteaters + + align:start position:0% +it compare other animals other anteaters + + + align:start position:0% +it compare other animals other anteaters +to see if they're as good as in a kidna + + align:start position:0% +to see if they're as good as in a kidna + + + align:start position:0% +to see if they're as good as in a kidna +and what kind of PR pral cakes they have + + align:start position:0% + + + + align:start position:0% + +okay let's deal with multiple + + align:start position:0% +okay let's deal with multiple + + + align:start position:0% +okay let's deal with multiple +simultaneous motivational + + align:start position:0% + + + + align:start position:0% + +States and talk + + align:start position:0% +States and talk + + + align:start position:0% +States and talk +about how they resolve the conflict if + + align:start position:0% +about how they resolve the conflict if + + + align:start position:0% +about how they resolve the conflict if +they do at + + align:start position:0% + + + + align:start position:0% + +all and I think I've already pointed out + + align:start position:0% +all and I think I've already pointed out + + + align:start position:0% +all and I think I've already pointed out +that we don't always resolve our + + align:start position:0% +that we don't always resolve our + + + align:start position:0% +that we don't always resolve our +conflicts uh but there are we talked + + align:start position:0% +conflicts uh but there are we talked + + + align:start position:0% +conflicts uh but there are we talked +when we remember the model of tinbergen + + align:start position:0% +when we remember the model of tinbergen + + + align:start position:0% +when we remember the model of tinbergen +where he shows the hierarchy of + + align:start position:0% +where he shows the hierarchy of + + + align:start position:0% +where he shows the hierarchy of +instinctive behavior and he shows at the + + align:start position:0% +instinctive behavior and he shows at the + + + align:start position:0% +instinctive behavior and he shows at the +lower levels where you have multiple + + align:start position:0% +lower levels where you have multiple + + + align:start position:0% +lower levels where you have multiple +different actions at approximately the + + align:start position:0% +different actions at approximately the + + + align:start position:0% +different actions at approximately the +same level of a hierarchy of instinctive + + align:start position:0% +same level of a hierarchy of instinctive + + + align:start position:0% +same level of a hierarchy of instinctive +Behavior he shows these interconnections + + align:start position:0% +Behavior he shows these interconnections + + + align:start position:0% +Behavior he shows these interconnections +among them largely inhibitory + + align:start position:0% +among them largely inhibitory + + + align:start position:0% +among them largely inhibitory +connections so that only one of them + + align:start position:0% +connections so that only one of them + + + align:start position:0% +connections so that only one of them +becomes dominant in any one + + align:start position:0% +becomes dominant in any one + + + align:start position:0% +becomes dominant in any one +time so the way you see that what + + align:start position:0% +time so the way you see that what + + + align:start position:0% +time so the way you see that what +happens in Behavior if you deal with two + + align:start position:0% +happens in Behavior if you deal with two + + + align:start position:0% +happens in Behavior if you deal with two +very highly aroused States you can get + + align:start position:0% +very highly aroused States you can get + + + align:start position:0% +very highly aroused States you can get +different ways to solve it you might + + align:start position:0% +different ways to solve it you might + + + align:start position:0% +different ways to solve it you might +just just superimpose + + align:start position:0% +just just superimpose + + + align:start position:0% +just just superimpose +them we'll show examples of + + align:start position:0% +them we'll show examples of + + + align:start position:0% +them we'll show examples of +that what happens if the the a + + align:start position:0% +that what happens if the the a + + + align:start position:0% +that what happens if the the a +motivation to + + align:start position:0% +motivation to + + + align:start position:0% +motivation to +approach let's say it's a dog and he's + + align:start position:0% +approach let's say it's a dog and he's + + + align:start position:0% +approach let's say it's a dog and he's +highly motivated to + + align:start position:0% +highly motivated to + + + align:start position:0% +highly motivated to +attack but he's also afraid so he's also + + align:start position:0% +attack but he's also afraid so he's also + + + align:start position:0% +attack but he's also afraid so he's also +highly motivated to run + + align:start position:0% +highly motivated to run + + + align:start position:0% +highly motivated to run +away what does he do often you get a + + align:start position:0% +away what does he do often you get a + + + align:start position:0% +away what does he do often you get a +superimposition of the motor patterns + + align:start position:0% +superimposition of the motor patterns + + + align:start position:0% +superimposition of the motor patterns +the fixed motor patterns of those two + + align:start position:0% +the fixed motor patterns of those two + + + align:start position:0% +the fixed motor patterns of those two +fixed action patterns you can also get + + align:start position:0% +fixed action patterns you can also get + + + align:start position:0% +fixed action patterns you can also get +Mutual + + align:start position:0% +Mutual + + + align:start position:0% +Mutual +inhibition which can lead to either one + + align:start position:0% +inhibition which can lead to either one + + + align:start position:0% +inhibition which can lead to either one +dominating or you can get two states + + align:start position:0% +dominating or you can get two states + + + align:start position:0% +dominating or you can get two states +alternating so you can get + + align:start position:0% +alternating so you can get + + + align:start position:0% +alternating so you can get +oscillations and then interestingly you + + align:start position:0% +oscillations and then interestingly you + + + align:start position:0% +oscillations and then interestingly you +can also + + align:start position:0% +can also + + + align:start position:0% +can also +get displacement activity a third + + align:start position:0% +get displacement activity a third + + + align:start position:0% +get displacement activity a third +behavior that seems to have nothing to + + align:start position:0% +behavior that seems to have nothing to + + + align:start position:0% +behavior that seems to have nothing to +do with the motivational States under + + align:start position:0% +do with the motivational States under + + + align:start position:0% +do with the motivational States under +lying this suddenly a third Behavior + + align:start position:0% +lying this suddenly a third Behavior + + + align:start position:0% +lying this suddenly a third Behavior +will emerge and the animal shows display + + align:start position:0% +will emerge and the animal shows display + + + align:start position:0% +will emerge and the animal shows display +placement let's talk about each of + + align:start position:0% + + + + align:start position:0% + +these if you talk + + align:start position:0% +these if you talk + + + align:start position:0% +these if you talk +about approach and avoidance behavior in + + align:start position:0% +about approach and avoidance behavior in + + + align:start position:0% +about approach and avoidance behavior in +geese or in fish it's very interesting I + + align:start position:0% +geese or in fish it's very interesting I + + + align:start position:0% +geese or in fish it's very interesting I +think fish are about the most + + align:start position:0% +think fish are about the most + + + align:start position:0% +think fish are about the most +interesting if you take a little sickid + + align:start position:0% +interesting if you take a little sickid + + + align:start position:0% +interesting if you take a little sickid +fish these beautiful tropical + + align:start position:0% +fish these beautiful tropical + + + align:start position:0% +fish these beautiful tropical +fish uh and get an animal that's trying + + align:start position:0% +fish uh and get an animal that's trying + + + align:start position:0% +fish uh and get an animal that's trying +to approach food but + + align:start position:0% +to approach food but + + + align:start position:0% +to approach food but +also he's afraid because uh there's + + align:start position:0% +also he's afraid because uh there's + + + align:start position:0% +also he's afraid because uh there's +something novel there that makes him + + align:start position:0% +something novel there that makes him + + + align:start position:0% +something novel there that makes him +avoid it what does the fish + + align:start position:0% +avoid it what does the fish + + + align:start position:0% +avoid it what does the fish +do you can literally see a fish where + + align:start position:0% +do you can literally see a fish where + + + align:start position:0% +do you can literally see a fish where +the front end of the fish represented by + + align:start position:0% +the front end of the fish represented by + + + align:start position:0% +the front end of the fish represented by +his pectoral fins is moving back and his + + align:start position:0% +his pectoral fins is moving back and his + + + align:start position:0% +his pectoral fins is moving back and his +tail is swimming + + align:start position:0% +tail is swimming + + + align:start position:0% +tail is swimming +forward so you see the simultaneous + + align:start position:0% +forward so you see the simultaneous + + + align:start position:0% +forward so you see the simultaneous +appearance of elements of both fixed AC + + align:start position:0% +appearance of elements of both fixed AC + + + align:start position:0% +appearance of elements of both fixed AC +both fixed motor patterns under lying + + align:start position:0% +both fixed motor patterns under lying + + + align:start position:0% +both fixed motor patterns under lying +these two different motivational + + align:start position:0% +these two different motivational + + + align:start position:0% +these two different motivational +States in + + align:start position:0% +States in + + + align:start position:0% +States in +geese and you see this a lot when you're + + align:start position:0% +geese and you see this a lot when you're + + + align:start position:0% +geese and you see this a lot when you're +trying to feed geese and you're novel to + + align:start position:0% +trying to feed geese and you're novel to + + + align:start position:0% +trying to feed geese and you're novel to +them they want the food but they're + + align:start position:0% +them they want the food but they're + + + align:start position:0% +them they want the food but they're +afraid of you because you're novel you + + align:start position:0% +afraid of you because you're novel you + + + align:start position:0% +afraid of you because you're novel you +might be a danger to them + + align:start position:0% +might be a danger to them + + + align:start position:0% +might be a danger to them +uh they you can actually see + + align:start position:0% +uh they you can actually see + + + align:start position:0% +uh they you can actually see +oscillations of their + + align:start position:0% + + + + align:start position:0% + +neck like both actions are being + + align:start position:0% +neck like both actions are being + + + align:start position:0% +neck like both actions are being +simultaneously triggered so you get this + + align:start position:0% +simultaneously triggered so you get this + + + align:start position:0% +simultaneously triggered so you get this +weird oscillation in the + + align:start position:0% +weird oscillation in the + + + align:start position:0% +weird oscillation in the +fish you get a lot of trembling of the + + align:start position:0% +fish you get a lot of trembling of the + + + align:start position:0% +fish you get a lot of trembling of the +neck is described by + + align:start position:0% + + + + align:start position:0% + +Lawrence I think that's not always clear + + align:start position:0% +Lawrence I think that's not always clear + + + align:start position:0% +Lawrence I think that's not always clear +when it's happening what it is but that + + align:start position:0% +when it's happening what it is but that + + + align:start position:0% +when it's happening what it is but that +appears to be how it originated the fish + + align:start position:0% +appears to be how it originated the fish + + + align:start position:0% +appears to be how it originated the fish +it's clear because you get both actions + + align:start position:0% +it's clear because you get both actions + + + align:start position:0% +it's clear because you get both actions +very clearly in different parts of the + + align:start position:0% +very clearly in different parts of the + + + align:start position:0% +very clearly in different parts of the +fit the part that's closer tries to run + + align:start position:0% +fit the part that's closer tries to run + + + align:start position:0% +fit the part that's closer tries to run +away the part that's farther please it + + align:start position:0% +away the part that's farther please it + + + align:start position:0% +away the part that's farther please it +tries to go + + align:start position:0% + + + + align:start position:0% + +forward here's + + align:start position:0% + + + + align:start position:0% + +uh superimpositions in the dog where + + align:start position:0% +uh superimpositions in the dog where + + + align:start position:0% +uh superimpositions in the dog where +Lawrence has + + align:start position:0% +Lawrence has + + + align:start position:0% +Lawrence has +described his hypothesis of how gestures + + align:start position:0% +described his hypothesis of how gestures + + + align:start position:0% +described his hypothesis of how gestures +of threat Behavior must have evolved in + + align:start position:0% +of threat Behavior must have evolved in + + + align:start position:0% +of threat Behavior must have evolved in +dogs and this is his very nice + + align:start position:0% +dogs and this is his very nice + + + align:start position:0% +dogs and this is his very nice +illustration of it he's + + align:start position:0% +illustration of it he's + + + align:start position:0% +illustration of it he's +arranged uh showed the different + + align:start position:0% +arranged uh showed the different + + + align:start position:0% +arranged uh showed the different +expressions of a dog and silhouette + + align:start position:0% +expressions of a dog and silhouette + + + align:start position:0% +expressions of a dog and silhouette +Expressions representing increasing + + align:start position:0% +Expressions representing increasing + + + align:start position:0% +Expressions representing increasing +motivation to flee so here's a dog + + align:start position:0% +motivation to flee so here's a dog + + + align:start position:0% +motivation to flee so here's a dog +that's purely + + align:start position:0% +that's purely + + + align:start position:0% +that's purely +afraid ears flattened back mouth fairly + + align:start position:0% +afraid ears flattened back mouth fairly + + + align:start position:0% +afraid ears flattened back mouth fairly +straight + + align:start position:0% +straight + + + align:start position:0% +straight +eyes not + + align:start position:0% + + + + align:start position:0% + +wide if you're very familiar with dogs + + align:start position:0% +wide if you're very familiar with dogs + + + align:start position:0% +wide if you're very familiar with dogs +you look at that you say that dog's + + align:start position:0% +you look at that you say that dog's + + + align:start position:0% +you look at that you say that dog's +afraid of something here's the normal + + align:start position:0% +afraid of something here's the normal + + + align:start position:0% +afraid of something here's the normal +Cal + + align:start position:0% +Cal + + + align:start position:0% +Cal +dog here's + + align:start position:0% +dog here's + + + align:start position:0% +dog here's +increasing motivation to flee here's + + align:start position:0% +increasing motivation to flee here's + + + align:start position:0% +increasing motivation to flee here's +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +aggression so here's the dog that's + + align:start position:0% +aggression so here's the dog that's + + + align:start position:0% +aggression so here's the dog that's +doesn't have any tendency to flee you + + align:start position:0% +doesn't have any tendency to flee you + + + align:start position:0% +doesn't have any tendency to flee you +see his ears come + + align:start position:0% +see his ears come + + + align:start position:0% +see his ears come +forward his lips curl he shows his teeth + + align:start position:0% +forward his lips curl he shows his teeth + + + align:start position:0% +forward his lips curl he shows his teeth +and he + + align:start position:0% +and he + + + align:start position:0% +and he +growls that's the + + align:start position:0% +growls that's the + + + align:start position:0% +growls that's the +dog that you don't want to get any + + align:start position:0% +dog that you don't want to get any + + + align:start position:0% +dog that you don't want to get any +closer + + align:start position:0% +closer + + + align:start position:0% +closer +to okay he's a dog about to + + align:start position:0% +to okay he's a dog about to + + + align:start position:0% +to okay he's a dog about to +attack but now with increasing + + align:start position:0% +attack but now with increasing + + + align:start position:0% +attack but now with increasing +motivation to flee at the same + + align:start position:0% +motivation to flee at the same + + + align:start position:0% +motivation to flee at the same +time he shows a dog here that + + align:start position:0% +time he shows a dog here that + + + align:start position:0% +time he shows a dog here that +shows maximal aggression and maximal + + align:start position:0% +shows maximal aggression and maximal + + + align:start position:0% +shows maximal aggression and maximal +motivation to flee you just + + align:start position:0% +motivation to flee you just + + + align:start position:0% +motivation to flee you just +superimpose the two types of + + align:start position:0% +superimpose the two types of + + + align:start position:0% +superimpose the two types of +actions you get almost flat in the ears + + align:start position:0% +actions you get almost flat in the ears + + + align:start position:0% +actions you get almost flat in the ears +but not completely they're still turned + + align:start position:0% +but not completely they're still turned + + + align:start position:0% +but not completely they're still turned +up at the ends as they are here and a + + align:start position:0% +up at the ends as they are here and a + + + align:start position:0% +up at the ends as they are here and a +very aggressive dog he still is showing + + align:start position:0% +very aggressive dog he still is showing + + + align:start position:0% +very aggressive dog he still is showing +teeth but notice nothing like this + + align:start position:0% +teeth but notice nothing like this + + + align:start position:0% +teeth but notice nothing like this +animal where he just widened his mouth + + align:start position:0% +animal where he just widened his mouth + + + align:start position:0% +animal where he just widened his mouth +so you can see all his his his big teeth + + align:start position:0% +so you can see all his his his big teeth + + + align:start position:0% +so you can see all his his his big teeth +here you don't see them all in fact his + + align:start position:0% +here you don't see them all in fact his + + + align:start position:0% +here you don't see them all in fact his +lips are curled back more like this + + align:start position:0% +lips are curled back more like this + + + align:start position:0% +lips are curled back more like this +animal and so forth and he doesn't sound + + align:start position:0% +animal and so forth and he doesn't sound + + + align:start position:0% +animal and so forth and he doesn't sound +quite the same either and this is a + + align:start position:0% +quite the same either and this is a + + + align:start position:0% +quite the same either and this is a +threatening dog when you see dogs + + align:start position:0% +threatening dog when you see dogs + + + align:start position:0% +threatening dog when you see dogs +fighting you will see them threatening + + align:start position:0% +fighting you will see them threatening + + + align:start position:0% +fighting you will see them threatening +each other with this kind of expression + + align:start position:0% +each other with this kind of expression + + + align:start position:0% +each other with this kind of expression +you see this superimposition of the two + + align:start position:0% + + + + align:start position:0% + +motivations I say here that Mutual + + align:start position:0% +motivations I say here that Mutual + + + align:start position:0% +motivations I say here that Mutual +inhibition usually occurs when between + + align:start position:0% +inhibition usually occurs when between + + + align:start position:0% +inhibition usually occurs when between +action patterns at the same level of or + + align:start position:0% +action patterns at the same level of or + + + align:start position:0% +action patterns at the same level of or +of organization and Lawrence discusses + + align:start position:0% +of organization and Lawrence discusses + + + align:start position:0% +of organization and Lawrence discusses +this I give you the page there but so + + align:start position:0% +this I give you the page there but so + + + align:start position:0% +this I give you the page there but so +that only one can be expressed at anyone + + align:start position:0% +that only one can be expressed at anyone + + + align:start position:0% +that only one can be expressed at anyone +one time but there is one action pattern + + align:start position:0% +one time but there is one action pattern + + + align:start position:0% +one time but there is one action pattern +that's almost always given absolute + + align:start position:0% +that's almost always given absolute + + + align:start position:0% +that's almost always given absolute +priority what do you what do you think + + align:start position:0% +priority what do you what do you think + + + align:start position:0% +priority what do you what do you think +that + + align:start position:0% +that + + + align:start position:0% +that +is what's the action pattern you're most + + align:start position:0% +is what's the action pattern you're most + + + align:start position:0% +is what's the action pattern you're most +likely and what an an not just you but + + align:start position:0% +likely and what an an not just you but + + + align:start position:0% +likely and what an an not just you but +any animal they give priority + + align:start position:0% + + + + align:start position:0% + +to it's not + + align:start position:0% + + + + align:start position:0% + +sex life + + align:start position:0% +sex life + + + align:start position:0% +sex life +preserving you're attach by a predator + + align:start position:0% +preserving you're attach by a predator + + + align:start position:0% +preserving you're attach by a predator +who can kill + + align:start position:0% +who can kill + + + align:start position:0% +who can kill +you you lose your other motivations and + + align:start position:0% +you you lose your other motivations and + + + align:start position:0% +you you lose your other motivations and +the motivation to Clee the Predator to + + align:start position:0% +the motivation to Clee the Predator to + + + align:start position:0% +the motivation to Clee the Predator to +escape from the Predator will be + + align:start position:0% +escape from the Predator will be + + + align:start position:0% +escape from the Predator will be +absolutely dominant and this is true in + + align:start position:0% +absolutely dominant and this is true in + + + align:start position:0% +absolutely dominant and this is true in +almost every + + align:start position:0% +almost every + + + align:start position:0% +almost every +animal if the animal has absolutely + + align:start position:0% +animal if the animal has absolutely + + + align:start position:0% +animal if the animal has absolutely +no + + align:start position:0% +no + + + align:start position:0% +no +Predators which is very + + align:start position:0% +Predators which is very + + + align:start position:0% +Predators which is very +unusual you can imagine an animal that + + align:start position:0% +unusual you can imagine an animal that + + + align:start position:0% +unusual you can imagine an animal that +might + + align:start position:0% +might + + + align:start position:0% +might +not you might not see this tendency to + + align:start position:0% + + + + align:start position:0% + +plea maybe Tyrannosaurus Rex was like + + align:start position:0% +plea maybe Tyrannosaurus Rex was like + + + align:start position:0% +plea maybe Tyrannosaurus Rex was like +that but they're they're pretty unusual + + align:start position:0% +that but they're they're pretty unusual + + + align:start position:0% +that but they're they're pretty unusual +when you see + + align:start position:0% + + + + align:start position:0% + +that but Mutual inhibition can also + + align:start position:0% +that but Mutual inhibition can also + + + align:start position:0% +that but Mutual inhibition can also +cause oscillation as I mentioned before + + align:start position:0% +cause oscillation as I mentioned before + + + align:start position:0% +cause oscillation as I mentioned before +two two fixed action patterns can + + align:start position:0% +two two fixed action patterns can + + + align:start position:0% +two two fixed action patterns can +oscillate and this + + align:start position:0% + + + + align:start position:0% + +oscillation can become rich visualized + + align:start position:0% +oscillation can become rich visualized + + + align:start position:0% +oscillation can become rich visualized +in evolution they can become social + + align:start position:0% +in evolution they can become social + + + align:start position:0% +in evolution they can become social +signals so these are examples here's + + align:start position:0% +signals so these are examples here's + + + align:start position:0% +signals so these are examples here's +a here's a + + align:start position:0% +a here's a + + + align:start position:0% +a here's a +female pygm or dwarf + + align:start position:0% +female pygm or dwarf + + + align:start position:0% +female pygm or dwarf +cichlid beautiful little + + align:start position:0% +cichlid beautiful little + + + align:start position:0% +cichlid beautiful little +fish uh it's got a prepared Nest site + + align:start position:0% +fish uh it's got a prepared Nest site + + + align:start position:0% +fish uh it's got a prepared Nest site +and it's attracting a male but how does + + align:start position:0% +and it's attracting a male but how does + + + align:start position:0% +and it's attracting a male but how does +it do that it attacks the male and then + + align:start position:0% +it do that it attacks the male and then + + + align:start position:0% +it do that it attacks the male and then +immediately + + align:start position:0% +immediately + + + align:start position:0% +immediately +reverses and tries to guide it to the + + align:start position:0% +reverses and tries to guide it to the + + + align:start position:0% +reverses and tries to guide it to the +nest he gets his attention by attacking + + align:start position:0% +nest he gets his attention by attacking + + + align:start position:0% +nest he gets his attention by attacking +him and it's very similar in the male + + align:start position:0% +him and it's very similar in the male + + + align:start position:0% +him and it's very similar in the male +stickleback fish we talked about that + + align:start position:0% +stickleback fish we talked about that + + + align:start position:0% +stickleback fish we talked about that +the male stickleback fish builds the + + align:start position:0% +the male stickleback fish builds the + + + align:start position:0% +the male stickleback fish builds the +nest then he swims out uses a female + + align:start position:0% +nest then he swims out uses a female + + + align:start position:0% +nest then he swims out uses a female +that looks the most gravid the most + + align:start position:0% +that looks the most gravid the most + + + align:start position:0% +that looks the most gravid the most +ready to lay eggs because of her swollen + + align:start position:0% +ready to lay eggs because of her swollen + + + align:start position:0% +ready to lay eggs because of her swollen +belly uh + + align:start position:0% +belly uh + + + align:start position:0% +belly uh +he'll pick the one and they've tested + + align:start position:0% +he'll pick the one and they've tested + + + align:start position:0% +he'll pick the one and they've tested +remember with the dummy stimuli that he + + align:start position:0% +remember with the dummy stimuli that he + + + align:start position:0% +remember with the dummy stimuli that he +will tend to chose the one with the most + + align:start position:0% +will tend to chose the one with the most + + + align:start position:0% +will tend to chose the one with the most +eggs uh and he starts an attack but then + + align:start position:0% +eggs uh and he starts an attack but then + + + align:start position:0% +eggs uh and he starts an attack but then +immediately changes his whole movement + + align:start position:0% +immediately changes his whole movement + + + align:start position:0% +immediately changes his whole movement +it's become more ritualized in + + align:start position:0% +it's become more ritualized in + + + align:start position:0% +it's become more ritualized in +the in the male stickle back than in + + align:start position:0% +the in the male stickle back than in + + + align:start position:0% +the in the male stickle back than in +these + + align:start position:0% +these + + + align:start position:0% +these +cichlids because he has a very + + align:start position:0% +cichlids because he has a very + + + align:start position:0% +cichlids because he has a very +characteristic dance he uses we call it + + align:start position:0% +characteristic dance he uses we call it + + + align:start position:0% +characteristic dance he uses we call it +a dance it's a + + align:start position:0% +a dance it's a + + + align:start position:0% +a dance it's a +ritual kind of swimming the zigzag + + align:start position:0% +ritual kind of swimming the zigzag + + + align:start position:0% +ritual kind of swimming the zigzag +dance that the female has evolved the + + align:start position:0% +dance that the female has evolved the + + + align:start position:0% +dance that the female has evolved the +specific response to a following + + align:start position:0% +specific response to a following + + + align:start position:0% +specific response to a following +response if she's the one he attacked + + align:start position:0% +response if she's the one he attacked + + + align:start position:0% +response if she's the one he attacked +she's the one will pay the most + + align:start position:0% +she's the one will pay the most + + + align:start position:0% +she's the one will pay the most +attention and often will follow him to + + align:start position:0% +attention and often will follow him to + + + align:start position:0% +attention and often will follow him to +the + + align:start position:0% +the + + + align:start position:0% +the +nest um he leads her right into the nest + + align:start position:0% +nest um he leads her right into the nest + + + align:start position:0% +nest um he leads her right into the nest +she swims through the nest and deposits + + align:start position:0% +she swims through the nest and deposits + + + align:start position:0% +she swims through the nest and deposits +her + + align:start position:0% +her + + + align:start position:0% +her +eggs + + align:start position:0% +eggs + + + align:start position:0% +eggs +uh which elicits + + align:start position:0% +uh which elicits + + + align:start position:0% +uh which elicits +his following through the nest and he + + align:start position:0% +his following through the nest and he + + + align:start position:0% +his following through the nest and he +inseminates the fertilizes the + + align:start position:0% + + + + align:start position:0% + +eggs + + align:start position:0% +eggs + + + align:start position:0% +eggs +so this this + + align:start position:0% +so this this + + + align:start position:0% +so this this +ritualization is common in evolution + + align:start position:0% +ritualization is common in evolution + + + align:start position:0% +ritualization is common in evolution +where you get you can trace the origins + + align:start position:0% +where you get you can trace the origins + + + align:start position:0% +where you get you can trace the origins +by looking at closely related species + + align:start position:0% +by looking at closely related species + + + align:start position:0% +by looking at closely related species +because in some + + align:start position:0% +because in some + + + align:start position:0% +because in some +some species you will find the ritual to + + align:start position:0% +some species you will find the ritual to + + + align:start position:0% +some species you will find the ritual to +be a little different or less less + + align:start position:0% +be a little different or less less + + + align:start position:0% +be a little different or less less +ritualized perhaps just like in the + + align:start position:0% +ritualized perhaps just like in the + + + align:start position:0% +ritualized perhaps just like in the +cichlids here you don't find as much + + align:start position:0% +cichlids here you don't find as much + + + align:start position:0% +cichlids here you don't find as much +ritualization uh as you find in the + + align:start position:0% +ritualization uh as you find in the + + + align:start position:0% +ritualization uh as you find in the +stickle bags where the females have + + align:start position:0% +stickle bags where the females have + + + align:start position:0% +stickle bags where the females have +evolved a very specific response to that + + align:start position:0% +evolved a very specific response to that + + + align:start position:0% +evolved a very specific response to that +male uh movement and the movement itself + + align:start position:0% +male uh movement and the movement itself + + + align:start position:0% +male uh movement and the movement itself +is a little different from normal + + align:start position:0% +is a little different from normal + + + align:start position:0% +is a little different from normal +swimming Behavior + + align:start position:0% + + + + align:start position:0% + +okay talk about displacement activity + + align:start position:0% +okay talk about displacement activity + + + align:start position:0% +okay talk about displacement activity +but what are two situations where + + align:start position:0% +but what are two situations where + + + align:start position:0% +but what are two situations where +displacement activity occurs there's a + + align:start position:0% +displacement activity occurs there's a + + + align:start position:0% +displacement activity occurs there's a +diagram of the causes of that that I I + + align:start position:0% +diagram of the causes of that that I I + + + align:start position:0% +diagram of the causes of that that I I +didn't try to reproduce here because it + + align:start position:0% +didn't try to reproduce here because it + + + align:start position:0% +didn't try to reproduce here because it +just doesn't go far enough in explaining + + align:start position:0% +just doesn't go far enough in explaining + + + align:start position:0% +just doesn't go far enough in explaining +it and the reason it doesn't is + + align:start position:0% +it and the reason it doesn't is + + + align:start position:0% +it and the reason it doesn't is +displacement activities + + align:start position:0% +displacement activities + + + align:start position:0% +displacement activities +are in some species it's always the same + + align:start position:0% +are in some species it's always the same + + + align:start position:0% +are in some species it's always the same +thing whereas the theory that you see + + align:start position:0% +thing whereas the theory that you see + + + align:start position:0% +thing whereas the theory that you see +outlined there by + + align:start position:0% +outlined there by + + + align:start position:0% +outlined there by +some um computational + + align:start position:0% +some um computational + + + align:start position:0% +some um computational +ethologist um really doesn't predict the + + align:start position:0% +ethologist um really doesn't predict the + + + align:start position:0% +ethologist um really doesn't predict the +species typical nature of some + + align:start position:0% +species typical nature of some + + + align:start position:0% +species typical nature of some +displacement activities but when do they + + align:start position:0% +displacement activities but when do they + + + align:start position:0% +displacement activities but when do they +occur two simultaneous + + align:start position:0% +occur two simultaneous + + + align:start position:0% +occur two simultaneous +motivations we mentioned this + + align:start position:0% +motivations we mentioned this + + + align:start position:0% +motivations we mentioned this +before you want to stay and hear what + + align:start position:0% +before you want to stay and hear what + + + align:start position:0% +before you want to stay and hear what +I'm going to say at the very end but you + + align:start position:0% +I'm going to say at the very end but you + + + align:start position:0% +I'm going to say at the very end but you +also want to leave so what do you do you + + align:start position:0% +also want to leave so what do you do you + + + align:start position:0% +also want to leave so what do you do you +do a third thing you know you know you + + align:start position:0% +do a third thing you know you know you + + + align:start position:0% +do a third thing you know you know you +engage in other activities you might + + align:start position:0% +engage in other activities you might + + + align:start position:0% +engage in other activities you might +increase the chewing of your + + align:start position:0% +increase the chewing of your + + + align:start position:0% +increase the chewing of your +pencil you might scratch your + + align:start position:0% +pencil you might scratch your + + + align:start position:0% +pencil you might scratch your +head I'm impatient I want to finish this + + align:start position:0% +head I'm impatient I want to finish this + + + align:start position:0% +head I'm impatient I want to finish this +lecture and leave I might Pace a little + + align:start position:0% +lecture and leave I might Pace a little + + + align:start position:0% +lecture and leave I might Pace a little +more I might scratch my head a little + + align:start position:0% +more I might scratch my head a little + + + align:start position:0% +more I might scratch my head a little +more these are all displacement + + align:start position:0% +more these are all displacement + + + align:start position:0% +more these are all displacement +activities so when you have two + + align:start position:0% +activities so when you have two + + + align:start position:0% +activities so when you have two +simultaneous + + align:start position:0% +simultaneous + + + align:start position:0% +simultaneous +motivations you often engage you you're + + align:start position:0% +motivations you often engage you you're + + + align:start position:0% +motivations you often engage you you're +likelihood that you'll engage in a third + + align:start position:0% +likelihood that you'll engage in a third + + + align:start position:0% +likelihood that you'll engage in a third +thing are increase and the thing we + + align:start position:0% +thing are increase and the thing we + + + align:start position:0% +thing are increase and the thing we +talked about before is when just one + + align:start position:0% +talked about before is when just one + + + align:start position:0% +talked about before is when just one +motivation is very high okay but then + + align:start position:0% +motivation is very high okay but then + + + align:start position:0% +motivation is very high okay but then +something blocks the + + align:start position:0% +something blocks the + + + align:start position:0% +something blocks the +stimulus that blocks the key stimuli + + align:start position:0% +stimulus that blocks the key stimuli + + + align:start position:0% +stimulus that blocks the key stimuli +that elicit the fix motor pattern but + + align:start position:0% +that elicit the fix motor pattern but + + + align:start position:0% +that elicit the fix motor pattern but +then like the the bear he's angry but + + align:start position:0% +then like the the bear he's angry but + + + align:start position:0% +then like the the bear he's angry but +there's nothing to vent his anger at so + + align:start position:0% +there's nothing to vent his anger at so + + + align:start position:0% +there's nothing to vent his anger at so +he vents it at anything + + align:start position:0% +he vents it at anything + + + align:start position:0% +he vents it at anything +near a man who's extremely angry at his + + align:start position:0% +near a man who's extremely angry at his + + + align:start position:0% +near a man who's extremely angry at his +boss but he's also + + align:start position:0% +boss but he's also + + + align:start position:0% +boss but he's also +afraid or his boss isn't right there or + + align:start position:0% +afraid or his boss isn't right there or + + + align:start position:0% +afraid or his boss isn't right there or +he becomes angry when he gets a letter + + align:start position:0% +he becomes angry when he gets a letter + + + align:start position:0% +he becomes angry when he gets a letter +from his boss he gets very angry but the + + align:start position:0% +from his boss he gets very angry but the + + + align:start position:0% +from his boss he gets very angry but the +boss isn't there he can't take out his + + align:start position:0% +boss isn't there he can't take out his + + + align:start position:0% +boss isn't there he can't take out his +anger + + align:start position:0% +anger + + + align:start position:0% +anger +directly he's likely to yell at his wife + + align:start position:0% +directly he's likely to yell at his wife + + + align:start position:0% +directly he's likely to yell at his wife +he's likely to hit something and so on + + align:start position:0% +he's likely to hit something and so on + + + align:start position:0% +he's likely to hit something and so on +and so forth some people get so engaged + + align:start position:0% +and so forth some people get so engaged + + + align:start position:0% +and so forth some people get so engaged +in sports that they they have a they + + align:start position:0% +in sports that they they have a they + + + align:start position:0% +in sports that they they have a they +have a rubber baseball bat just to hit + + align:start position:0% +have a rubber baseball bat just to hit + + + align:start position:0% +have a rubber baseball bat just to hit +the TV with they don't want to ruin + + align:start position:0% +the TV with they don't want to ruin + + + align:start position:0% +the TV with they don't want to ruin +their TV so that's they actually sell + + align:start position:0% + + + + align:start position:0% + +those do any of you have + + align:start position:0% + + + + align:start position:0% + +that but even if you + + align:start position:0% +that but even if you + + + align:start position:0% +that but even if you +don't that + + align:start position:0% +don't that + + + align:start position:0% +don't that +directly so that kind of displacement + + align:start position:0% +directly so that kind of displacement + + + align:start position:0% +directly so that kind of displacement +activity you're likely to do + + align:start position:0% + + + + align:start position:0% + +something express some kind of action + + align:start position:0% +something express some kind of action + + + align:start position:0% +something express some kind of action +because of the motivation + + align:start position:0% + + + + align:start position:0% + +after discharge displacements are what + + align:start position:0% +after discharge displacements are what + + + align:start position:0% +after discharge displacements are what +they're called if the it's a single + + align:start position:0% +they're called if the it's a single + + + align:start position:0% +they're called if the it's a single +motivation that's highly aroused but + + align:start position:0% +motivation that's highly aroused but + + + align:start position:0% +motivation that's highly aroused but +then no specific stimuli to elicit the + + align:start position:0% +then no specific stimuli to elicit the + + + align:start position:0% +then no specific stimuli to elicit the +normal motor + + align:start position:0% +normal motor + + + align:start position:0% +normal motor +pattern so uh other actions + + align:start position:0% + + + + align:start position:0% + +occur displacement activity was + + align:start position:0% +occur displacement activity was + + + align:start position:0% +occur displacement activity was +originally given this long German name + + align:start position:0% +originally given this long German name + + + align:start position:0% +originally given this long German name +Uber Springs but they + + align:start position:0% + + + + align:start position:0% + +the the springing over + + align:start position:0% +the the springing over + + + align:start position:0% +the the springing over +activity uh sparking over activity in + + align:start position:0% +activity uh sparking over activity in + + + align:start position:0% +activity uh sparking over activity in +German it was studied a lot by tinbergen + + align:start position:0% +German it was studied a lot by tinbergen + + + align:start position:0% +German it was studied a lot by tinbergen +as well as by + + align:start position:0% + + + + align:start position:0% + +Lawrence and these are the two + + align:start position:0% +Lawrence and these are the two + + + align:start position:0% +Lawrence and these are the two +situations that I was talking about + + align:start position:0% +situations that I was talking about + + + align:start position:0% +situations that I was talking about +let's give examples of the species + + align:start position:0% +let's give examples of the species + + + align:start position:0% +let's give examples of the species +typical nature of displacement + + align:start position:0% +typical nature of displacement + + + align:start position:0% +typical nature of displacement +activities + + align:start position:0% +activities + + + align:start position:0% +activities +first of all here's the ganders of three + + align:start position:0% +first of all here's the ganders of three + + + align:start position:0% +first of all here's the ganders of three +different types of geese that are in + + align:start position:0% +different types of geese that are in + + + align:start position:0% +different types of geese that are in +conflict between escape and defense of + + align:start position:0% +conflict between escape and defense of + + + align:start position:0% +conflict between escape and defense of +their nest a very common conflict that a + + align:start position:0% +their nest a very common conflict that a + + + align:start position:0% +their nest a very common conflict that a +female goose is faced with with a gry + + align:start position:0% +female goose is faced with with a gry + + + align:start position:0% +female goose is faced with with a gry +leg Goose she engages in in Wing + + align:start position:0% +leg Goose she engages in in Wing + + + align:start position:0% +leg Goose she engages in in Wing +shaking very vigorous Wing shaking the + + align:start position:0% +shaking very vigorous Wing shaking the + + + align:start position:0% +shaking very vigorous Wing shaking the +pink foot + + align:start position:0% +pink foot + + + align:start position:0% +pink foot +goose uh she engages in pining movements + + align:start position:0% +goose uh she engages in pining movements + + + align:start position:0% +goose uh she engages in pining movements +movements that are have evolved for + + align:start position:0% +movements that are have evolved for + + + align:start position:0% +movements that are have evolved for +Distributing oil from glands under her + + align:start position:0% +Distributing oil from glands under her + + + align:start position:0% +Distributing oil from glands under her +Wing cover feathers and distributing the + + align:start position:0% +Wing cover feathers and distributing the + + + align:start position:0% +Wing cover feathers and distributing the +oil on the flank + + align:start position:0% +oil on the flank + + + align:start position:0% +oil on the flank +feathers the greater snow goose engages + + align:start position:0% +feathers the greater snow goose engages + + + align:start position:0% +feathers the greater snow goose engages +in bathing movements and she'll do this + + align:start position:0% +in bathing movements and she'll do this + + + align:start position:0% +in bathing movements and she'll do this +right on dry ground even though there's + + align:start position:0% +right on dry ground even though there's + + + align:start position:0% +right on dry ground even though there's +no water to bathe no water to bathe with + + align:start position:0% +no water to bathe no water to bathe with + + + align:start position:0% +no water to bathe no water to bathe with +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +displacement bathing + + align:start position:0% + + + + align:start position:0% + +here's one that many of you have seen + + align:start position:0% +here's one that many of you have seen + + + align:start position:0% +here's one that many of you have seen +hamsters in + + align:start position:0% +hamsters in + + + align:start position:0% +hamsters in +conflict between especially if you're + + align:start position:0% +conflict between especially if you're + + + align:start position:0% +conflict between especially if you're +novel let's say you you're approaching + + align:start position:0% +novel let's say you you're approaching + + + align:start position:0% +novel let's say you you're approaching +hamsters are not always very + + align:start position:0% +hamsters are not always very + + + align:start position:0% +hamsters are not always very +Cain yes they're pets but unless they're + + align:start position:0% +Cain yes they're pets but unless they're + + + align:start position:0% +Cain yes they're pets but unless they're +very familiar with you you know you will + + align:start position:0% +very familiar with you you know you will + + + align:start position:0% +very familiar with you you know you will +see this kind of thing you try to give + + align:start position:0% +see this kind of thing you try to give + + + align:start position:0% +see this kind of thing you try to give +them a seed we know it's their favorite + + align:start position:0% +them a seed we know it's their favorite + + + align:start position:0% +them a seed we know it's their favorite +food so they're very attracted to + + align:start position:0% +food so they're very attracted to + + + align:start position:0% +food so they're very attracted to +sunflower seeds but you smell a little + + align:start position:0% +sunflower seeds but you smell a little + + + align:start position:0% +sunflower seeds but you smell a little +different they're a little cautious so + + align:start position:0% +different they're a little cautious so + + + align:start position:0% +different they're a little cautious so +they're in + + align:start position:0% +they're in + + + align:start position:0% +they're in +Conflict they approach they avoid what + + align:start position:0% +Conflict they approach they avoid what + + + align:start position:0% +Conflict they approach they avoid what +do they + + align:start position:0% +do they + + + align:start position:0% +do they +do almost always they will start + + align:start position:0% +do almost always they will start + + + align:start position:0% +do almost always they will start +grooming they'll throw displacement + + align:start position:0% +grooming they'll throw displacement + + + align:start position:0% +grooming they'll throw displacement +grooming and you if you keep hamers you + + align:start position:0% +grooming and you if you keep hamers you + + + align:start position:0% +grooming and you if you keep hamers you +can you learn to discriminate between + + align:start position:0% +can you learn to discriminate between + + + align:start position:0% +can you learn to discriminate between +real grooming and displacement grooming + + align:start position:0% +real grooming and displacement grooming + + + align:start position:0% +real grooming and displacement grooming +it's not always + + align:start position:0% +it's not always + + + align:start position:0% +it's not always +easy especially once the displacement + + align:start position:0% +easy especially once the displacement + + + align:start position:0% +easy especially once the displacement +groom groming starts he goes on for a + + align:start position:0% +groom groming starts he goes on for a + + + align:start position:0% +groom groming starts he goes on for a +long time but in some cases because they + + align:start position:0% +long time but in some cases because they + + + align:start position:0% +long time but in some cases because they +The Grooming itself seems to calm them + + align:start position:0% +The Grooming itself seems to calm them + + + align:start position:0% +The Grooming itself seems to calm them +down but when they start their + + align:start position:0% +down but when they start their + + + align:start position:0% +down but when they start their +displacement grooming it's so vigorous + + align:start position:0% +displacement grooming it's so vigorous + + + align:start position:0% +displacement grooming it's so vigorous +it's more + + align:start position:0% +it's more + + + align:start position:0% +it's more +vigorous uh more animated than real + + align:start position:0% +vigorous uh more animated than real + + + align:start position:0% +vigorous uh more animated than real +grooming and not not + + align:start position:0% +grooming and not not + + + align:start position:0% +grooming and not not +always they don't always go through all + + align:start position:0% +always they don't always go through all + + + align:start position:0% +always they don't always go through all +the Motions of real + + align:start position:0% +the Motions of real + + + align:start position:0% +the Motions of real +grooming + + align:start position:0% +grooming + + + align:start position:0% +grooming +okay this the ones with the larger + + align:start position:0% +okay this the ones with the larger + + + align:start position:0% +okay this the ones with the larger +movements in it becomes very + + align:start position:0% +movements in it becomes very + + + align:start position:0% +movements in it becomes very +obvious so similarly you can have + + align:start position:0% +obvious so similarly you can have + + + align:start position:0% +obvious so similarly you can have +displacement Wing shaking and normal + + align:start position:0% +displacement Wing shaking and normal + + + align:start position:0% +displacement Wing shaking and normal +Wing + + align:start position:0% + + + + align:start position:0% + +shaking normal oil distribution + + align:start position:0% +shaking normal oil distribution + + + align:start position:0% +shaking normal oil distribution +displacement oil distribution and so + + align:start position:0% + + + + align:start position:0% + +forth so think of the various examples + + align:start position:0% +forth so think of the various examples + + + align:start position:0% +forth so think of the various examples +of the human displacement + + align:start position:0% +of the human displacement + + + align:start position:0% +of the human displacement +activities I've just listed some of them + + align:start position:0% +activities I've just listed some of them + + + align:start position:0% +activities I've just listed some of them +here facing the floor we mentioned head + + align:start position:0% +here facing the floor we mentioned head + + + align:start position:0% +here facing the floor we mentioned head +scratching biting a + + align:start position:0% +scratching biting a + + + align:start position:0% +scratching biting a +pencil I didn't mention the oscillations + + align:start position:0% +pencil I didn't mention the oscillations + + + align:start position:0% +pencil I didn't mention the oscillations +of a + + align:start position:0% + + + + align:start position:0% + +foot just saw the guy over + + align:start position:0% +foot just saw the guy over + + + align:start position:0% +foot just saw the guy over +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +uh nail + + align:start position:0% +uh nail + + + align:start position:0% +uh nail +biting nail biting often originates as + + align:start position:0% +biting nail biting often originates as + + + align:start position:0% +biting nail biting often originates as +displacement and of course they can + + align:start position:0% +displacement and of course they can + + + align:start position:0% +displacement and of course they can +become + + align:start position:0% +become + + + align:start position:0% +become +habits but they're displ placement + + align:start position:0% +habits but they're displ placement + + + align:start position:0% +habits but they're displ placement +activity habits so just like these birds + + align:start position:0% +activity habits so just like these birds + + + align:start position:0% +activity habits so just like these birds +always they show a certain thing well + + align:start position:0% +always they show a certain thing well + + + align:start position:0% +always they show a certain thing well +people can develop habits of showing + + align:start position:0% +people can develop habits of showing + + + align:start position:0% +people can develop habits of showing +certain displacement + + align:start position:0% + + + + align:start position:0% + +activities so why might displacement + + align:start position:0% +activities so why might displacement + + + align:start position:0% +activities so why might displacement +activities then sometimes become + + align:start position:0% +activities then sometimes become + + + align:start position:0% +activities then sometimes become +ritualized and actually undergo changes + + align:start position:0% +ritualized and actually undergo changes + + + align:start position:0% +ritualized and actually undergo changes +in evolution from the original fixed + + align:start position:0% +in evolution from the original fixed + + + align:start position:0% +in evolution from the original fixed +action patterns that they + + align:start position:0% +action patterns that they + + + align:start position:0% +action patterns that they +represent can you think of a + + align:start position:0% +represent can you think of a + + + align:start position:0% +represent can you think of a +reason + + align:start position:0% + + + + align:start position:0% + +because it leads to the next topic next + + align:start position:0% +because it leads to the next topic next + + + align:start position:0% +because it leads to the next topic next +major topic we want to talk + + align:start position:0% +major topic we want to talk + + + align:start position:0% +major topic we want to talk +about the changes occur because they + + align:start position:0% +about the changes occur because they + + + align:start position:0% +about the changes occur because they +conserve the Socialist + + align:start position:0% + + + + align:start position:0% + +signs it results in benefit Mutual + + align:start position:0% +signs it results in benefit Mutual + + + align:start position:0% +signs it results in benefit Mutual +benefit because it can promote the + + align:start position:0% +benefit because it can promote the + + + align:start position:0% +benefit because it can promote the +survival of the of an animal if he can + + align:start position:0% +survival of the of an animal if he can + + + align:start position:0% +survival of the of an animal if he can +detect the displacement activities in + + align:start position:0% +detect the displacement activities in + + + align:start position:0% +detect the displacement activities in +another animal and realize that the + + align:start position:0% +another animal and realize that the + + + align:start position:0% +another animal and realize that the +animals in some kind of + + align:start position:0% +animals in some kind of + + + align:start position:0% +animals in some kind of +conflict so he then becomes more + + align:start position:0% +conflict so he then becomes more + + + align:start position:0% +conflict so he then becomes more +cautious even if he doesn't notice + + align:start position:0% +cautious even if he doesn't notice + + + align:start position:0% +cautious even if he doesn't notice +what's causing all that in the first + + align:start position:0% +what's causing all that in the first + + + align:start position:0% +what's causing all that in the first +animal it serves as a social + + align:start position:0% +animal it serves as a social + + + align:start position:0% +animal it serves as a social +signal and when we so we'll talk about + + align:start position:0% +signal and when we so we'll talk about + + + align:start position:0% +signal and when we so we'll talk about +communication and when we talk about + + align:start position:0% +communication and when we talk about + + + align:start position:0% +communication and when we talk about +mating behavior we'll talk about + + align:start position:0% +mating behavior we'll talk about + + + align:start position:0% +mating behavior we'll talk about +courtship and many courtship rituals + + align:start position:0% +courtship and many courtship rituals + + + align:start position:0% +courtship and many courtship rituals +That You observe in animals originated + + align:start position:0% +That You observe in animals originated + + + align:start position:0% +That You observe in animals originated +as you know either displacement + + align:start position:0% +as you know either displacement + + + align:start position:0% +as you know either displacement +activities or as + + align:start position:0% +activities or as + + + align:start position:0% +activities or as +as + + align:start position:0% +as + + + align:start position:0% +as +conflict resolution s too simultaneous + + align:start position:0% +conflict resolution s too simultaneous + + + align:start position:0% +conflict resolution s too simultaneous +of uh aroused fix action pattern that + + align:start position:0% +of uh aroused fix action pattern that + + + align:start position:0% +of uh aroused fix action pattern that +then and then you'll see the two fix + + align:start position:0% +then and then you'll see the two fix + + + align:start position:0% +then and then you'll see the two fix +action patterns oscillating in the + + align:start position:0% +action patterns oscillating in the + + + align:start position:0% +action patterns oscillating in the +courtship ritual because courtship does + + align:start position:0% +courtship ritual because courtship does + + + align:start position:0% +courtship ritual because courtship does +involve both approach and avoidance and + + align:start position:0% +involve both approach and avoidance and + + + align:start position:0% +involve both approach and avoidance and +often the ritual you see that in the + + align:start position:0% +often the ritual you see that in the + + + align:start position:0% +often the ritual you see that in the +ritual and we see that we'll talk about + + align:start position:0% +ritual and we see that we'll talk about + + + align:start position:0% +ritual and we see that we'll talk about +we'll bring that up again when we uh + + align:start position:0% +we'll bring that up again when we uh + + + align:start position:0% +we'll bring that up again when we uh +when we talk about the uh + + align:start position:0% +when we talk about the uh + + + align:start position:0% +when we talk about the uh +courtship + + align:start position:0% +courtship + + + align:start position:0% +courtship +Behavior okay about the a little more + + align:start position:0% +Behavior okay about the a little more + + + align:start position:0% +Behavior okay about the a little more +about the + + align:start position:0% + + + + align:start position:0% + +quiz I know there's quite a bit of + + align:start position:0% +quiz I know there's quite a bit of + + + align:start position:0% +quiz I know there's quite a bit of +reading in lawence + + align:start position:0% +reading in lawence + + + align:start position:0% +reading in lawence +uh but emphasize Concepts I've talked + + align:start position:0% +uh but emphasize Concepts I've talked + + + align:start position:0% +uh but emphasize Concepts I've talked +about at least mentioned in the + + align:start position:0% +about at least mentioned in the + + + align:start position:0% +about at least mentioned in the +class + + align:start position:0% +class + + + align:start position:0% +class +uh one of the clues I can give you is I + + align:start position:0% +uh one of the clues I can give you is I + + + align:start position:0% +uh one of the clues I can give you is I +think I want to ask you some something + + align:start position:0% +think I want to ask you some something + + + align:start position:0% +think I want to ask you some something +about those models at least know what + + align:start position:0% +about those models at least know what + + + align:start position:0% +about those models at least know what +what the major differences are between + + align:start position:0% +what the major differences are between + + + align:start position:0% +what the major differences are between +the tinbergen models and the Lawrence + + align:start position:0% +the tinbergen models and the Lawrence + + + align:start position:0% +the tinbergen models and the Lawrence +model I want to ask you about the + + align:start position:0% +model I want to ask you about the + + + align:start position:0% +model I want to ask you about the +computational models that been done we + + align:start position:0% +computational models that been done we + + + align:start position:0% +computational models that been done we +only talked in class about the Timber + + align:start position:0% +only talked in class about the Timber + + + align:start position:0% +only talked in class about the Timber +and Lawrence models but I also said they + + align:start position:0% +and Lawrence models but I also said they + + + align:start position:0% +and Lawrence models but I also said they +each have + + align:start position:0% +each have + + + align:start position:0% +each have +advantages uh so you should know you + + align:start position:0% +advantages uh so you should know you + + + align:start position:0% +advantages uh so you should know you +know what is the value of learning about + + align:start position:0% + + + + align:start position:0% + +both okay + + align:start position:0% +both okay + + + align:start position:0% +both okay +and uh if you focus on the study + + align:start position:0% +and uh if you focus on the study + + + align:start position:0% +and uh if you focus on the study +questions in the list of questions I've + + align:start position:0% +questions in the list of questions I've + + + align:start position:0% +questions in the list of questions I've +given you most of them we've brought up + + align:start position:0% +given you most of them we've brought up + + + align:start position:0% +given you most of them we've brought up +in class um I think you'll be pretty + + align:start position:0% +in class um I think you'll be pretty + + + align:start position:0% +in class um I think you'll be pretty +well + + align:start position:0% +well + + + align:start position:0% +well +prepared and I'm not finished with the + + align:start position:0% +prepared and I'm not finished with the + + + align:start position:0% +prepared and I'm not finished with the +homework yet because I want to add a + + align:start position:0% +homework yet because I want to add a + + + align:start position:0% +homework yet because I want to add a +couple of questions on the things we'll + + align:start position:0% +couple of questions on the things we'll + + + align:start position:0% +couple of questions on the things we'll +be covering the rest of this + + align:start position:0% +be covering the rest of this + + + align:start position:0% +be covering the rest of this +week all + + align:start position:0% + + + + align:start position:0% + +right that's it for today \ No newline at end of file diff --git a/Q3v_2znHCvg.txt b/Q3v_2znHCvg.txt new file mode 100644 index 0000000000000000000000000000000000000000..04d9aeb0caf32a07a858f06fb928b075016042a7 --- /dev/null +++ b/Q3v_2znHCvg.txt @@ -0,0 +1,363 @@ +align:start position:0% + +let's consider a two-dimensional motion + + align:start position:0% +let's consider a two-dimensional motion + + + align:start position:0% +let's consider a two-dimensional motion +suppose we have something like a + + align:start position:0% +suppose we have something like a + + + align:start position:0% +suppose we have something like a +projectile motion and we have an object + + align:start position:0% +projectile motion and we have an object + + + align:start position:0% +projectile motion and we have an object +moving let's now describe how we can + + align:start position:0% +moving let's now describe how we can + + + align:start position:0% +moving let's now describe how we can +just describe this motion with vectors + + align:start position:0% +just describe this motion with vectors + + + align:start position:0% +just describe this motion with vectors +so the first thing we always want to do + + align:start position:0% +so the first thing we always want to do + + + align:start position:0% +so the first thing we always want to do +and let's remind ourselves of the steps + + align:start position:0% +and let's remind ourselves of the steps + + + align:start position:0% +and let's remind ourselves of the steps +is we want to choose a coordinate system + + align:start position:0% +is we want to choose a coordinate system + + + align:start position:0% +is we want to choose a coordinate system +now what is a coordinate system consists + + align:start position:0% +now what is a coordinate system consists + + + align:start position:0% +now what is a coordinate system consists +of it consists of An Origin it consists + + align:start position:0% +of it consists of An Origin it consists + + + align:start position:0% +of it consists of An Origin it consists +of two axes in this case we'll identify + + align:start position:0% +of two axes in this case we'll identify + + + align:start position:0% +of two axes in this case we'll identify +these the positive direction for each + + align:start position:0% +these the positive direction for each + + + align:start position:0% +these the positive direction for each +axis is plus X and plus Y and at every + + align:start position:0% +axis is plus X and plus Y and at every + + + align:start position:0% +axis is plus X and plus Y and at every +single point in space so if we had any + + align:start position:0% +single point in space so if we had any + + + align:start position:0% +single point in space so if we had any +arbitrary Point P here P let's call this + + align:start position:0% +arbitrary Point P here P let's call this + + + align:start position:0% +arbitrary Point P here P let's call this +P1 we have a choice of unit vectors i1 + + align:start position:0% +P1 we have a choice of unit vectors i1 + + + align:start position:0% +P1 we have a choice of unit vectors i1 +and J hat one now what makes cartisian + + align:start position:0% +and J hat one now what makes cartisian + + + align:start position:0% +and J hat one now what makes cartisian +coordinates unique is that no matter + + align:start position:0% +coordinates unique is that no matter + + + align:start position:0% +coordinates unique is that no matter +what point we're at the unit vectors are + + align:start position:0% +what point we're at the unit vectors are + + + align:start position:0% +what point we're at the unit vectors are +all the same so we could erase all these + + align:start position:0% +all the same so we could erase all these + + + align:start position:0% +all the same so we could erase all these +indices for that particular point and + + align:start position:0% +indices for that particular point and + + + align:start position:0% +indices for that particular point and +just have an abstract set of unit + + align:start position:0% +just have an abstract set of unit + + + align:start position:0% +just have an abstract set of unit +vectors IAD and J hat now normally what + + align:start position:0% +vectors IAD and J hat now normally what + + + align:start position:0% +vectors IAD and J hat now normally what +we'll do is we'll just put those off to + + align:start position:0% +we'll do is we'll just put those off to + + + align:start position:0% +we'll do is we'll just put those off to +the + + align:start position:0% +the + + + align:start position:0% +the +side so in our cartisian + + align:start position:0% +side so in our cartisian + + + align:start position:0% +side so in our cartisian +coordinates we now want to define the + + align:start position:0% +coordinates we now want to define the + + + align:start position:0% +coordinates we now want to define the +position vector and the position Vector + + align:start position:0% +position vector and the position Vector + + + align:start position:0% +position vector and the position Vector +is a vector from the origin to where the + + align:start position:0% +is a vector from the origin to where the + + + align:start position:0% +is a vector from the origin to where the +object is so we'll write that position + + align:start position:0% +object is so we'll write that position + + + align:start position:0% +object is so we'll write that position +Vector we'll denote it by R of T because + + align:start position:0% +Vector we'll denote it by R of T because + + + align:start position:0% +Vector we'll denote it by R of T because +as this object moves along its + + align:start position:0% +as this object moves along its + + + align:start position:0% +as this object moves along its +trajectory that position Vector is + + align:start position:0% +trajectory that position Vector is + + + align:start position:0% +trajectory that position Vector is +changing and we'll write down R of T in + + align:start position:0% +changing and we'll write down R of T in + + + align:start position:0% +changing and we'll write down R of T in +terms of two coordinate functions X of + + align:start position:0% +terms of two coordinate functions X of + + + align:start position:0% +terms of two coordinate functions X of +T and Y of T and so our Vector position + + align:start position:0% +T and Y of T and so our Vector position + + + align:start position:0% +T and Y of T and so our Vector position +Vector of the object R of T is equal to + + align:start position:0% +Vector of the object R of T is equal to + + + align:start position:0% +Vector of the object R of T is equal to +X of T IAT plus y of T J hat and one of + + align:start position:0% +X of T IAT plus y of T J hat and one of + + + align:start position:0% +X of T IAT plus y of T J hat and one of +our main goals is to figure out what + + align:start position:0% +our main goals is to figure out what + + + align:start position:0% +our main goals is to figure out what +these position functions are for the + + align:start position:0% +these position functions are for the + + + align:start position:0% +these position functions are for the +motion of + + align:start position:0% +motion of + + + align:start position:0% +motion of +objects so this is we describe an object + + align:start position:0% +objects so this is we describe an object + + + align:start position:0% +objects so this is we describe an object +in a cartisian coordinate system + + align:start position:0% +in a cartisian coordinate system + + + align:start position:0% +in a cartisian coordinate system +undergoing two-dimensional motion what + + align:start position:0% +undergoing two-dimensional motion what + + + align:start position:0% +undergoing two-dimensional motion what +we want to analyze next is what is the + + align:start position:0% +we want to analyze next is what is the + + + align:start position:0% +we want to analyze next is what is the +velocity of that object \ No newline at end of file diff --git a/QGOLnKZTFEQ.txt b/QGOLnKZTFEQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1fe5d590a626d8ee026646dc5b34276b46dbb71 --- /dev/null +++ b/QGOLnKZTFEQ.txt @@ -0,0 +1,15155 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu my name is Dr heish Fraser + + align:start position:0% +ocw.mit.edu my name is Dr heish Fraser + + + align:start position:0% +ocw.mit.edu my name is Dr heish Fraser +and as said I'm the director of + + align:start position:0% +and as said I'm the director of + + + align:start position:0% +and as said I'm the director of +informatics and medicine atart and + + align:start position:0% +informatics and medicine atart and + + + align:start position:0% +informatics and medicine atart and +health and I'm also assistant professor + + align:start position:0% +health and I'm also assistant professor + + + align:start position:0% +health and I'm also assistant professor +at H medical school and the Britain + + align:start position:0% +at H medical school and the Britain + + + align:start position:0% +at H medical school and the Britain +women's hospital so um I'm actually been + + align:start position:0% +women's hospital so um I'm actually been + + + align:start position:0% +women's hospital so um I'm actually been +interest this area for about a decade or + + align:start position:0% +interest this area for about a decade or + + + align:start position:0% +interest this area for about a decade or +so um surprisingly I think when we + + align:start position:0% +so um surprisingly I think when we + + + align:start position:0% +so um surprisingly I think when we +started people thought we were a little + + align:start position:0% +started people thought we were a little + + + align:start position:0% +started people thought we were a little +bit crazy um I think even Joy thought I + + align:start position:0% +bit crazy um I think even Joy thought I + + + align:start position:0% +bit crazy um I think even Joy thought I +was little bit crazy and + + align:start position:0% + + + + align:start position:0% + +so well for some reason the rest of the + + align:start position:0% +so well for some reason the rest of the + + + align:start position:0% +so well for some reason the rest of the +world seems to be believing that there's + + align:start position:0% +world seems to be believing that there's + + + align:start position:0% +world seems to be believing that there's +something interesting going on with + + align:start position:0% +something interesting going on with + + + align:start position:0% +something interesting going on with +information technology in development + + align:start position:0% +information technology in development + + + align:start position:0% +information technology in development +and one of the pieces of that is the use + + align:start position:0% +and one of the pieces of that is the use + + + align:start position:0% +and one of the pieces of that is the use +of Information Systems to support + + align:start position:0% +of Information Systems to support + + + align:start position:0% +of Information Systems to support +expansion of healthare in very + + align:start position:0% +expansion of healthare in very + + + align:start position:0% +expansion of healthare in very +resourceful environments in developing + + align:start position:0% +resourceful environments in developing + + + align:start position:0% +resourceful environments in developing +countries so um today what we wanted to + + align:start position:0% +countries so um today what we wanted to + + + align:start position:0% +countries so um today what we wanted to +start with is really a background about + + align:start position:0% +start with is really a background about + + + align:start position:0% +start with is really a background about +the challenges of Healthcare in + + align:start position:0% +the challenges of Healthcare in + + + align:start position:0% +the challenges of Healthcare in +developing countries and we're extremely + + align:start position:0% +developing countries and we're extremely + + + align:start position:0% +developing countries and we're extremely +fortunate that Joy M who's a colleague + + align:start position:0% +fortunate that Joy M who's a colleague + + + align:start position:0% +fortunate that Joy M who's a colleague +of mine and a friend um who's also uh + + align:start position:0% +of mine and a friend um who's also uh + + + align:start position:0% +of mine and a friend um who's also uh +the medical director of Partners and + + align:start position:0% +the medical director of Partners and + + + align:start position:0% +the medical director of Partners and +health has agreed to talk today about + + align:start position:0% +health has agreed to talk today about + + + align:start position:0% +health has agreed to talk today about +her experiences and about the challenges + + align:start position:0% +her experiences and about the challenges + + + align:start position:0% +her experiences and about the challenges +that partners and health and our + + align:start position:0% +that partners and health and our + + + align:start position:0% +that partners and health and our +colleagues own world faced so joer is an + + align:start position:0% +colleagues own world faced so joer is an + + + align:start position:0% +colleagues own world faced so joer is an +associate professor at the BR W hospital + + align:start position:0% +associate professor at the BR W hospital + + + align:start position:0% +associate professor at the BR W hospital +and Harvard medical school and she's + + align:start position:0% +and Harvard medical school and she's + + + align:start position:0% +and Harvard medical school and she's +also been working with Parton health for + + align:start position:0% +also been working with Parton health for + + + align:start position:0% +also been working with Parton health for +actually over a decade now isn't it just + + align:start position:0% +actually over a decade now isn't it just + + + align:start position:0% +actually over a decade now isn't it just +over yeah and I'll just tell you a + + align:start position:0% +over yeah and I'll just tell you a + + + align:start position:0% +over yeah and I'll just tell you a +little bit about Partners in Health + + align:start position:0% +little bit about Partners in Health + + + align:start position:0% +little bit about Partners in Health +itself if you're not familiar with the + + align:start position:0% +itself if you're not familiar with the + + + align:start position:0% +itself if you're not familiar with the +organization so it was founded in 1987 + + align:start position:0% +organization so it was founded in 1987 + + + align:start position:0% +organization so it was founded in 1987 +by Paul Farmer Jim Kim and ailia d and + + align:start position:0% +by Paul Farmer Jim Kim and ailia d and + + + align:start position:0% +by Paul Farmer Jim Kim and ailia d and +really it focuses on providing healthare + + align:start position:0% +really it focuses on providing healthare + + + align:start position:0% +really it focuses on providing healthare +to the poorest and most vulnerable + + align:start position:0% +to the poorest and most vulnerable + + + align:start position:0% +to the poorest and most vulnerable +people in the developing world and Par + + align:start position:0% +people in the developing world and Par + + + align:start position:0% +people in the developing world and Par +and health uh started working in in the + + align:start position:0% +and health uh started working in in the + + + align:start position:0% +and health uh started working in in the +central Plateau area of hati and of + + align:start position:0% +central Plateau area of hati and of + + + align:start position:0% +central Plateau area of hati and of +course it's still very much one of the + + align:start position:0% +course it's still very much one of the + + + align:start position:0% +course it's still very much one of the +focus areas of ours particularly of the + + align:start position:0% +focus areas of ours particularly of the + + + align:start position:0% +focus areas of ours particularly of the +last year with the the earthquake and + + align:start position:0% +last year with the the earthquake and + + + align:start position:0% +last year with the the earthquake and +the color outbreak there um we focus + + align:start position:0% +the color outbreak there um we focus + + + align:start position:0% +the color outbreak there um we focus +very much on U the roots of disease as + + align:start position:0% +very much on U the roots of disease as + + + align:start position:0% +very much on U the roots of disease as +well as the treatment of disease so we + + align:start position:0% +well as the treatment of disease so we + + + align:start position:0% +well as the treatment of disease so we +focus on social justice on providing um + + align:start position:0% +focus on social justice on providing um + + + align:start position:0% +focus on social justice on providing um +better housing access to clean water and + + align:start position:0% +better housing access to clean water and + + + align:start position:0% +better housing access to clean water and +food and we also look at the interaction + + align:start position:0% +food and we also look at the interaction + + + align:start position:0% +food and we also look at the interaction +between Elite um institutions like MIT + + align:start position:0% +between Elite um institutions like MIT + + + align:start position:0% +between Elite um institutions like MIT +and Harvard and the the kind of + + align:start position:0% +and Harvard and the the kind of + + + align:start position:0% +and Harvard and the the kind of +technology and medical education that + + align:start position:0% +technology and medical education that + + + align:start position:0% +technology and medical education that +these organizations can provide and the + + align:start position:0% +these organizations can provide and the + + + align:start position:0% +these organizations can provide and the +challenges and the lived experience of + + align:start position:0% +challenges and the lived experience of + + + align:start position:0% +challenges and the lived experience of +people in very poor countries um on a + + align:start position:0% +people in very poor countries um on a + + + align:start position:0% +people in very poor countries um on a +day-to-day basis and we're particularly + + align:start position:0% +day-to-day basis and we're particularly + + + align:start position:0% +day-to-day basis and we're particularly +interested in this interaction between + + align:start position:0% +interested in this interaction between + + + align:start position:0% +interested in this interaction between +how we can actually learn different ways + + align:start position:0% +how we can actually learn different ways + + + align:start position:0% +how we can actually learn different ways +of providing Healthcare rather than + + align:start position:0% +of providing Healthcare rather than + + + align:start position:0% +of providing Healthcare rather than +scaling down what we have in the US or + + align:start position:0% +scaling down what we have in the US or + + + align:start position:0% +scaling down what we have in the US or +in other developed countries but + + align:start position:0% +in other developed countries but + + + align:start position:0% +in other developed countries but +actually thinking about what are the + + align:start position:0% +actually thinking about what are the + + + align:start position:0% +actually thinking about what are the +experience what are the real needs in + + align:start position:0% +experience what are the real needs in + + + align:start position:0% +experience what are the real needs in +those communities and also what are the + + align:start position:0% +those communities and also what are the + + + align:start position:0% +those communities and also what are the +strengths of those commun communities + + align:start position:0% +strengths of those commun communities + + + align:start position:0% +strengths of those commun communities +and uh Joy has also been working this + + align:start position:0% +and uh Joy has also been working this + + + align:start position:0% +and uh Joy has also been working this +area um particularly medical education + + align:start position:0% +area um particularly medical education + + + align:start position:0% +area um particularly medical education +and is um in addition to her work as a + + align:start position:0% +and is um in addition to her work as a + + + align:start position:0% +and is um in addition to her work as a +medical director is the head of the + + align:start position:0% +medical director is the head of the + + + align:start position:0% +medical director is the head of the +Institute of Health and Social Justice + + align:start position:0% +Institute of Health and Social Justice + + + align:start position:0% +Institute of Health and Social Justice +at Pi uh she's published or Au more than + + align:start position:0% +at Pi uh she's published or Au more than + + + align:start position:0% +at Pi uh she's published or Au more than +50 Journal articles peerreview Journal + + align:start position:0% +50 Journal articles peerreview Journal + + + align:start position:0% +50 Journal articles peerreview Journal +articles and I think really it's a great + + align:start position:0% +articles and I think really it's a great + + + align:start position:0% +articles and I think really it's a great +choice for this class particularly + + align:start position:0% +choice for this class particularly + + + align:start position:0% +choice for this class particularly +because she's not tied particularly to + + align:start position:0% +because she's not tied particularly to + + + align:start position:0% +because she's not tied particularly to +technology um Joya really focuses on a + + align:start position:0% +technology um Joya really focuses on a + + + align:start position:0% +technology um Joya really focuses on a +whole range of different areas um she's + + align:start position:0% +whole range of different areas um she's + + + align:start position:0% +whole range of different areas um she's +B certified in Pediatrics internal + + align:start position:0% +B certified in Pediatrics internal + + + align:start position:0% +B certified in Pediatrics internal +medicine and infectious diseases and + + align:start position:0% +medicine and infectious diseases and + + + align:start position:0% +medicine and infectious diseases and +also has an um mph so uh what we want to + + align:start position:0% +also has an um mph so uh what we want to + + + align:start position:0% +also has an um mph so uh what we want to +do here is not to focus this course on + + align:start position:0% +do here is not to focus this course on + + + align:start position:0% +do here is not to focus this course on +the technology but to focus it on the + + align:start position:0% +the technology but to focus it on the + + + align:start position:0% +the technology but to focus it on the +problem and the real needs that people + + align:start position:0% +problem and the real needs that people + + + align:start position:0% +problem and the real needs that people +have and then to to look at how we can + + align:start position:0% +have and then to to look at how we can + + + align:start position:0% +have and then to to look at how we can +actually find creative ways of solving + + align:start position:0% +actually find creative ways of solving + + + align:start position:0% +actually find creative ways of solving +those and one little secret about Jo + + align:start position:0% +those and one little secret about Jo + + + align:start position:0% +those and one little secret about Jo +which not many people know is that one + + align:start position:0% +which not many people know is that one + + + align:start position:0% +which not many people know is that one +she was in fact doing um medical + + align:start position:0% +she was in fact doing um medical + + + align:start position:0% +she was in fact doing um medical +engineering and I believe a little + + align:start position:0% +engineering and I believe a little + + + align:start position:0% +engineering and I believe a little +software M at some startup company so + + align:start position:0% +software M at some startup company so + + + align:start position:0% +software M at some startup company so +you know just have a little + + align:start position:0% +you know just have a little + + + align:start position:0% +you know just have a little +understanding about the kind of geeky + + align:start position:0% +understanding about the kind of geeky + + + align:start position:0% +understanding about the kind of geeky +stuff that we'll be focusing on here Z + + align:start position:0% +stuff that we'll be focusing on here Z + + + align:start position:0% +stuff that we'll be focusing on here Z +thank you so much for + + align:start position:0% +thank you so much for + + + align:start position:0% +thank you so much for +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +coming well I'm myself as a recipient of + + align:start position:0% +coming well I'm myself as a recipient of + + + align:start position:0% +coming well I'm myself as a recipient of +some very high technology just this week + + align:start position:0% +some very high technology just this week + + + align:start position:0% +some very high technology just this week +I had a um electrical ablation of my + + align:start position:0% +I had a um electrical ablation of my + + + align:start position:0% +I had a um electrical ablation of my +part of my conducting system in my heart + + align:start position:0% +part of my conducting system in my heart + + + align:start position:0% +part of my conducting system in my heart +so if I seem a little short of breath + + align:start position:0% +so if I seem a little short of breath + + + align:start position:0% +so if I seem a little short of breath +I'm just still the men um so really one + + align:start position:0% +I'm just still the men um so really one + + + align:start position:0% +I'm just still the men um so really one +of the most high-tech outpatient + + align:start position:0% +of the most high-tech outpatient + + + align:start position:0% +of the most high-tech outpatient +procedures you can have I was out of the + + align:start position:0% +procedures you can have I was out of the + + + align:start position:0% +procedures you can have I was out of the +hospital the same day after fascina so + + align:start position:0% +hospital the same day after fascina so + + + align:start position:0% +hospital the same day after fascina so +actually um what I what I thought I + + align:start position:0% +actually um what I what I thought I + + + align:start position:0% +actually um what I what I thought I +would talk about just to give a sense of + + align:start position:0% +would talk about just to give a sense of + + + align:start position:0% +would talk about just to give a sense of +you know heish asked me to talk about + + align:start position:0% +you know heish asked me to talk about + + + align:start position:0% +you know heish asked me to talk about +our work but what I wanted to do is + + align:start position:0% +our work but what I wanted to do is + + + align:start position:0% +our work but what I wanted to do is +focus on not only the work of delivering + + align:start position:0% +focus on not only the work of delivering + + + align:start position:0% +focus on not only the work of delivering +health care but how we use the interface + + align:start position:0% +health care but how we use the interface + + + align:start position:0% +health care but how we use the interface +of Academia to sort of promote our work + + align:start position:0% +of Academia to sort of promote our work + + + align:start position:0% +of Academia to sort of promote our work +and even promote social change um + + align:start position:0% +and even promote social change um + + + align:start position:0% +and even promote social change um +because for us it's not yeah yeah sure + + align:start position:0% +because for us it's not yeah yeah sure + + + align:start position:0% +because for us it's not yeah yeah sure +for for us it's definitely not only + + align:start position:0% +for for us it's definitely not only + + + align:start position:0% +for for us it's definitely not only +about um don't really have a good place + + align:start position:0% +about um don't really have a good place + + + align:start position:0% +about um don't really have a good place +oh for us it's not it's not only about + + align:start position:0% +oh for us it's not it's not only about + + + align:start position:0% +oh for us it's not it's not only about +sort of providing Health Care to the + + align:start position:0% +sort of providing Health Care to the + + + align:start position:0% +sort of providing Health Care to the +people in front of us but really + + align:start position:0% +people in front of us but really + + + align:start position:0% +people in front of us but really +changing how how health care as a basic + + align:start position:0% +changing how how health care as a basic + + + align:start position:0% +changing how how health care as a basic +right is perceived um I think some of + + align:start position:0% +right is perceived um I think some of + + + align:start position:0% +right is perceived um I think some of +you know that the standard of care + + align:start position:0% +you know that the standard of care + + + align:start position:0% +you know that the standard of care +resource poor settings is to do very + + align:start position:0% +resource poor settings is to do very + + + align:start position:0% +resource poor settings is to do very +little the standard of care in resource + + align:start position:0% +little the standard of care in resource + + + align:start position:0% +little the standard of care in resource +poor settings focuses on prevention um + + align:start position:0% +poor settings focuses on prevention um + + + align:start position:0% +poor settings focuses on prevention um +not generally treatment and is limited + + align:start position:0% +not generally treatment and is limited + + + align:start position:0% +not generally treatment and is limited +Often by the GDP of the country and as a + + align:start position:0% +Often by the GDP of the country and as a + + + align:start position:0% +Often by the GDP of the country and as a +result the life expectancy in some of + + align:start position:0% +result the life expectancy in some of + + + align:start position:0% +result the life expectancy in some of +the world's Forest countries is under 40 + + align:start position:0% +the world's Forest countries is under 40 + + + align:start position:0% +the world's Forest countries is under 40 +and and sort of our philosophy is that's + + align:start position:0% +and and sort of our philosophy is that's + + + align:start position:0% +and and sort of our philosophy is that's +just not appropriate that we have you + + align:start position:0% +just not appropriate that we have you + + + align:start position:0% +just not appropriate that we have you +know the idea of appropriate technology + + align:start position:0% +know the idea of appropriate technology + + + align:start position:0% +know the idea of appropriate technology +as heish said being a dumbed Down + + align:start position:0% +as heish said being a dumbed Down + + + align:start position:0% +as heish said being a dumbed Down +version is not working to improve life + + align:start position:0% +version is not working to improve life + + + align:start position:0% +version is not working to improve life +expectancy for the poorest people in the + + align:start position:0% +expectancy for the poorest people in the + + + align:start position:0% +expectancy for the poorest people in the +world so what we have sort of the + + align:start position:0% +world so what we have sort of the + + + align:start position:0% +world so what we have sort of the +inverse way of looking at it by saying + + align:start position:0% +inverse way of looking at it by saying + + + align:start position:0% +inverse way of looking at it by saying +what are the + + align:start position:0% +what are the + + + align:start position:0% +what are the +needs how do we address them doing the + + align:start position:0% +needs how do we address them doing the + + + align:start position:0% +needs how do we address them doing the +scholarship needed around addressing + + align:start position:0% +scholarship needed around addressing + + + align:start position:0% +scholarship needed around addressing +those needs and then really trying to + + align:start position:0% +those needs and then really trying to + + + align:start position:0% +those needs and then really trying to +push the envelope for money for + + align:start position:0% +push the envelope for money for + + + align:start position:0% +push the envelope for money for +resources and for change because you + + align:start position:0% +resources and for change because you + + + align:start position:0% +resources and for change because you +know for for Partners in Health we we + + align:start position:0% +know for for Partners in Health we we + + + align:start position:0% +know for for Partners in Health we we +really look at um the medical context as + + align:start position:0% +really look at um the medical context as + + + align:start position:0% +really look at um the medical context as +as sort of a thermometer for social + + align:start position:0% +as sort of a thermometer for social + + + align:start position:0% +as sort of a thermometer for social +inequality and so rather than just try + + align:start position:0% +inequality and so rather than just try + + + align:start position:0% +inequality and so rather than just try +to you know bring the fever down we want + + align:start position:0% +to you know bring the fever down we want + + + align:start position:0% +to you know bring the fever down we want +to deal with the root cause which all + + align:start position:0% +to deal with the root cause which all + + + align:start position:0% +to deal with the root cause which all +often is a social context so I'm going + + align:start position:0% +often is a social context so I'm going + + + align:start position:0% +often is a social context so I'm going +to talk a little bit about sort of how + + align:start position:0% +to talk a little bit about sort of how + + + align:start position:0% +to talk a little bit about sort of how +we built up over time different chains + + align:start position:0% +we built up over time different chains + + + align:start position:0% +we built up over time different chains +of evidence scholarly evidence um that + + align:start position:0% +of evidence scholarly evidence um that + + + align:start position:0% +of evidence scholarly evidence um that +is a fairly novel um type of scholarship + + align:start position:0% +is a fairly novel um type of scholarship + + + align:start position:0% +is a fairly novel um type of scholarship +I mean I would say even 10 or so years + + align:start position:0% +I mean I would say even 10 or so years + + + align:start position:0% +I mean I would say even 10 or so years +ago when heish and I started a Partners + + align:start position:0% +ago when heish and I started a Partners + + + align:start position:0% +ago when heish and I started a Partners +in Health um the kind of work we do was + + align:start position:0% +in Health um the kind of work we do was + + + align:start position:0% +in Health um the kind of work we do was +not really considered scholarly research + + align:start position:0% +not really considered scholarly research + + + align:start position:0% +not really considered scholarly research +but more and more people are realizing + + align:start position:0% +but more and more people are realizing + + + align:start position:0% +but more and more people are realizing +that in the implementation and in the + + align:start position:0% +that in the implementation and in the + + + align:start position:0% +that in the implementation and in the +application and in the description of + + align:start position:0% +application and in the description of + + + align:start position:0% +application and in the description of +the work we do there's there's value in + + align:start position:0% +the work we do there's there's value in + + + align:start position:0% +the work we do there's there's value in +terms of teaching and learning so that's + + align:start position:0% +terms of teaching and learning so that's + + + align:start position:0% +terms of teaching and learning so that's +what I'm going to talk about um this is + + align:start position:0% +what I'm going to talk about um this is + + + align:start position:0% +what I'm going to talk about um this is +one of my favorite slides does everyone + + align:start position:0% +one of my favorite slides does everyone + + + align:start position:0% +one of my favorite slides does everyone +know what this + + align:start position:0% + + + + align:start position:0% + +is oh come + + align:start position:0% +is oh come + + + align:start position:0% +is oh come +on what does it look like what if it + + align:start position:0% +on what does it look like what if it + + + align:start position:0% +on what does it look like what if it +look like you're going to have to talk + + align:start position:0% +look like you're going to have to talk + + + align:start position:0% +look like you're going to have to talk +to me because I don't believe in around + + align:start position:0% +to me because I don't believe in around + + + align:start position:0% +to me because I don't believe in around +the world it's night time around the + + align:start position:0% +the world it's night time around the + + + align:start position:0% +the world it's night time around the +world and and it's interesting right so + + align:start position:0% +world and and it's interesting right so + + + align:start position:0% +world and and it's interesting right so +what does it show you it's not possible + + align:start position:0% +what does it show you it's not possible + + + align:start position:0% +what does it show you it's not possible +yeah it kind of does show you it's not + + align:start position:0% +yeah it kind of does show you it's not + + + align:start position:0% +yeah it kind of does show you it's not +who said that not possible Right it kind + + align:start position:0% +who said that not possible Right it kind + + + align:start position:0% +who said that not possible Right it kind +of says well you know here in the + + align:start position:0% +of says well you know here in the + + + align:start position:0% +of says well you know here in the +Northeast we have electricity and we can + + align:start position:0% +Northeast we have electricity and we can + + + align:start position:0% +Northeast we have electricity and we can +do a lot of stuff so so this is a sort + + align:start position:0% +do a lot of stuff so so this is a sort + + + align:start position:0% +do a lot of stuff so so this is a sort +of map to me of of low + + align:start position:0% +of map to me of of low + + + align:start position:0% +of map to me of of low +expectations right now interestingly + + align:start position:0% +expectations right now interestingly + + + align:start position:0% +expectations right now interestingly +keep this in your head okay here's + + align:start position:0% +keep this in your head okay here's + + + align:start position:0% +keep this in your head okay here's +another + + align:start position:0% + + + + align:start position:0% + +map isn't that interestingly the inverse + + align:start position:0% +map isn't that interestingly the inverse + + + align:start position:0% +map isn't that interestingly the inverse +of the electric electricity grid so do + + align:start position:0% +of the electric electricity grid so do + + + align:start position:0% +of the electric electricity grid so do +you think that there's more + + align:start position:0% +you think that there's more + + + align:start position:0% +you think that there's more +AIDS in Dark Places because people don't + + align:start position:0% +AIDS in Dark Places because people don't + + + align:start position:0% +AIDS in Dark Places because people don't +have + + align:start position:0% +have + + + align:start position:0% +have +electricity maybe they just have more + + align:start position:0% +electricity maybe they just have more + + + align:start position:0% +electricity maybe they just have more +sex in the dark I don't know we could + + align:start position:0% +sex in the dark I don't know we could + + + align:start position:0% +sex in the dark I don't know we could +test that + + align:start position:0% +test that + + + align:start position:0% +test that +hypothesis so what do you think this is + + align:start position:0% +hypothesis so what do you think this is + + + align:start position:0% +hypothesis so what do you think this is +about I mean this is this is kind of to + + align:start position:0% +about I mean this is this is kind of to + + + align:start position:0% +about I mean this is this is kind of to +me I love this I me I love these kind of + + align:start position:0% +me I love this I me I love these kind of + + + align:start position:0% +me I love this I me I love these kind of +things superimposed I like to do it + + align:start position:0% +things superimposed I like to do it + + + align:start position:0% +things superimposed I like to do it +together you know but haven't done that + + align:start position:0% +together you know but haven't done that + + + align:start position:0% +together you know but haven't done that +yet what do you think that's + + align:start position:0% + + + + align:start position:0% + +about yeah it's about uh level income + + align:start position:0% +about yeah it's about uh level income + + + align:start position:0% +about yeah it's about uh level income +poverty uh lack of Education yeah so so + + align:start position:0% +poverty uh lack of Education yeah so so + + + align:start position:0% +poverty uh lack of Education yeah so so +for for in the beginning of the AIDS + + align:start position:0% +for for in the beginning of the AIDS + + + align:start position:0% +for for in the beginning of the AIDS +epidemic that there was this focus on + + align:start position:0% +epidemic that there was this focus on + + + align:start position:0% +epidemic that there was this focus on +prevention + + align:start position:0% +prevention + + + align:start position:0% +prevention +right and I and so we're saying well + + align:start position:0% +right and I and so we're saying well + + + align:start position:0% +right and I and so we're saying well +what about just bring electricity no I'm + + align:start position:0% +what about just bring electricity no I'm + + + align:start position:0% +what about just bring electricity no I'm +just kidding but so whoops sorry I went + + align:start position:0% +just kidding but so whoops sorry I went + + + align:start position:0% +just kidding but so whoops sorry I went +all the way to the end you just see all + + align:start position:0% +all the way to the end you just see all + + + align:start position:0% +all the way to the end you just see all +the how did that happen so much for my + + align:start position:0% +the how did that happen so much for my + + + align:start position:0% +the how did that happen so much for my +geeky + + align:start position:0% +geeky + + + align:start position:0% +geeky +side um so you know I mean come on look + + align:start position:0% +side um so you know I mean come on look + + + align:start position:0% +side um so you know I mean come on look +at that you could say well just bring + + align:start position:0% +at that you could say well just bring + + + align:start position:0% +at that you could say well just bring +electricity would fix it would that fix + + align:start position:0% +electricity would fix it would that fix + + + align:start position:0% +electricity would fix it would that fix +it would that fix the E ID + + align:start position:0% +it would that fix the E ID + + + align:start position:0% +it would that fix the E ID +number no how did these places get + + align:start position:0% +number no how did these places get + + + align:start position:0% +number no how did these places get +electricity + + align:start position:0% + + + + align:start position:0% + +so that's what we're going to talk about + + align:start position:0% +so that's what we're going to talk about + + + align:start position:0% +so that's what we're going to talk about +so of of course I don't think + + align:start position:0% +so of of course I don't think + + + align:start position:0% +so of of course I don't think +electricity would fix the ID but I do + + align:start position:0% +electricity would fix the ID but I do + + + align:start position:0% +electricity would fix the ID but I do +think that decreasing extreme poverty + + align:start position:0% +think that decreasing extreme poverty + + + align:start position:0% +think that decreasing extreme poverty +would minimize people's risk of epidemic + + align:start position:0% +would minimize people's risk of epidemic + + + align:start position:0% +would minimize people's risk of epidemic +diseases like Aid and TB and malaria + + align:start position:0% +diseases like Aid and TB and malaria + + + align:start position:0% +diseases like Aid and TB and malaria +right because we know that a lot of the + + align:start position:0% +right because we know that a lot of the + + + align:start position:0% +right because we know that a lot of the +risks are embedded in the social context + + align:start position:0% +risks are embedded in the social context + + + align:start position:0% +risks are embedded in the social context +and in fact most of what I teach is + + align:start position:0% +and in fact most of what I teach is + + + align:start position:0% +and in fact most of what I teach is +social medicine which is really looking + + align:start position:0% +social medicine which is really looking + + + align:start position:0% +social medicine which is really looking +at the social context of disease and so + + align:start position:0% +at the social context of disease and so + + + align:start position:0% +at the social context of disease and so +I always think this is a very + + align:start position:0% +I always think this is a very + + + align:start position:0% +I always think this is a very +interesting way to start the discussion + + align:start position:0% +interesting way to start the discussion + + + align:start position:0% +interesting way to start the discussion +to say what is it about the electrical + + align:start position:0% +to say what is it about the electrical + + + align:start position:0% +to say what is it about the electrical +Grid or the lack thereof that really + + align:start position:0% +Grid or the lack thereof that really + + + align:start position:0% +Grid or the lack thereof that really +predisposes people so this is kind of a + + align:start position:0% +predisposes people so this is kind of a + + + align:start position:0% +predisposes people so this is kind of a +timeline of the work of Partners in + + align:start position:0% +timeline of the work of Partners in + + + align:start position:0% +timeline of the work of Partners in +Health and in the early years we were + + align:start position:0% +Health and in the early years we were + + + align:start position:0% +Health and in the early years we were +just focused on delivering Primary + + align:start position:0% +just focused on delivering Primary + + + align:start position:0% +just focused on delivering Primary +Health Care to a population in rural + + align:start position:0% +Health Care to a population in rural + + + align:start position:0% +Health Care to a population in rural +Haiti in fact a displaced population a + + align:start position:0% +Haiti in fact a displaced population a + + + align:start position:0% +Haiti in fact a displaced population a +bunch of people who were displaced by a + + align:start position:0% +bunch of people who were displaced by a + + + align:start position:0% +bunch of people who were displaced by a +hydroelectric Dam kind of ran up this + + align:start position:0% +hydroelectric Dam kind of ran up this + + + align:start position:0% +hydroelectric Dam kind of ran up this +Rocky Hill couldn't Farm couldn't do + + align:start position:0% +Rocky Hill couldn't Farm couldn't do + + + align:start position:0% +Rocky Hill couldn't Farm couldn't do +anything and they were sick and they + + align:start position:0% +anything and they were sick and they + + + align:start position:0% +anything and they were sick and they +were dying now the first thing we always + + align:start position:0% +were dying now the first thing we always + + + align:start position:0% +were dying now the first thing we always +do in a community is sit with the + + align:start position:0% +do in a community is sit with the + + + align:start position:0% +do in a community is sit with the +community and say so what do you + + align:start position:0% +community and say so what do you + + + align:start position:0% +community and say so what do you +need and so in this community when we + + align:start position:0% +need and so in this community when we + + + align:start position:0% +need and so in this community when we +ask so what do you need what do you + + align:start position:0% +ask so what do you need what do you + + + align:start position:0% +ask so what do you need what do you +think they said what do you think they + + align:start position:0% + + + + align:start position:0% + +said Mercedes Benz no what food water + + align:start position:0% +said Mercedes Benz no what food water + + + align:start position:0% +said Mercedes Benz no what food water +Food Water Shelter shelter + + align:start position:0% + + + + align:start position:0% + +two more things probably three schools + + align:start position:0% + + + + align:start position:0% + +schools + + align:start position:0% + + + + align:start position:0% + +healthare jobs okay so these six + + align:start position:0% +healthare jobs okay so these six + + + align:start position:0% +healthare jobs okay so these six +things um are those do I don't know how + + align:start position:0% +things um are those do I don't know how + + + align:start position:0% +things um are those do I don't know how +much you know about the public health + + align:start position:0% +much you know about the public health + + + align:start position:0% +much you know about the public health +Paradigm but how much of that is in like + + align:start position:0% +Paradigm but how much of that is in like + + + align:start position:0% +Paradigm but how much of that is in like +the public health paradigm + + align:start position:0% + + + + align:start position:0% + +almost none right maybe + + align:start position:0% +almost none right maybe + + + align:start position:0% +almost none right maybe +water water and + + align:start position:0% +water water and + + + align:start position:0% +water water and +sanitation so you could do A needs + + align:start position:0% +sanitation so you could do A needs + + + align:start position:0% +sanitation so you could do A needs +assessment which is often done in + + align:start position:0% +assessment which is often done in + + + align:start position:0% +assessment which is often done in +research per settings and you could say + + align:start position:0% +research per settings and you could say + + + align:start position:0% +research per settings and you could say +well these are the things people need + + align:start position:0% +well these are the things people need + + + align:start position:0% +well these are the things people need +they need schools they need health care + + align:start position:0% +they need schools they need health care + + + align:start position:0% +they need schools they need health care +they need jobs they need appropriate + + align:start position:0% +they need jobs they need appropriate + + + align:start position:0% +they need jobs they need appropriate +shelter sanitation + + align:start position:0% +shelter sanitation + + + align:start position:0% +shelter sanitation +um and so what what might you do well we + + align:start position:0% +um and so what what might you do well we + + + align:start position:0% +um and so what what might you do well we +decided at Partners in Health to build a + + align:start position:0% +decided at Partners in Health to build a + + + align:start position:0% +decided at Partners in Health to build a +clinic and a school and to employ local + + align:start position:0% +clinic and a school and to employ local + + + align:start position:0% +clinic and a school and to employ local +people and and a + + align:start position:0% +people and and a + + + align:start position:0% +people and and a +was and to employ local people um to be + + align:start position:0% +was and to employ local people um to be + + + align:start position:0% +was and to employ local people um to be +engaged in the work of providing health + + align:start position:0% +engaged in the work of providing health + + + align:start position:0% +engaged in the work of providing health +care and the school and the water system + + align:start position:0% +care and the school and the water system + + + align:start position:0% +care and the school and the water system +so does that sound kind of logical + + align:start position:0% + + + + align:start position:0% + +or I think in the context of developed + + align:start position:0% +or I think in the context of developed + + + align:start position:0% +or I think in the context of developed +country you have to + + align:start position:0% +country you have to + + + align:start position:0% +country you have to +approach you cannot like in in + + align:start position:0% +approach you cannot like in in + + + align:start position:0% +approach you cannot like in in +Haiti uh medicine is like vertical and + + align:start position:0% +Haiti uh medicine is like vertical and + + + align:start position:0% +Haiti uh medicine is like vertical and +you have to in the context of + + align:start position:0% +you have to in the context of + + + align:start position:0% +you have to in the context of +development you have to see Health + + align:start position:0% +development you have to see Health + + + align:start position:0% +development you have to see Health +development you have to see care with + + align:start position:0% +development you have to see care with + + + align:start position:0% +development you have to see care with +development + + align:start position:0% +development + + + align:start position:0% +development +yeah so so we one of the ways we address + + align:start position:0% +yeah so so we one of the ways we address + + + align:start position:0% +yeah so so we one of the ways we address +that is to say that education is + + align:start position:0% +that is to say that education is + + + align:start position:0% +that is to say that education is +critical development and jobs are + + align:start position:0% +critical development and jobs are + + + align:start position:0% +critical development and jobs are +critical development and we can employ + + align:start position:0% +critical development and we can employ + + + align:start position:0% +critical development and we can employ +local people to do that so I think + + align:start position:0% +local people to do that so I think + + + align:start position:0% +local people to do that so I think +you're right what what else do you think + + align:start position:0% +you're right what what else do you think + + + align:start position:0% +you're right what what else do you think +I mean is this sort of um let's say + + align:start position:0% +I mean is this sort of um let's say + + + align:start position:0% +I mean is this sort of um let's say +you're UNICEF or the wh and you go into + + align:start position:0% +you're UNICEF or the wh and you go into + + + align:start position:0% +you're UNICEF or the wh and you go into +a community and do A needs assessment + + align:start position:0% +a community and do A needs assessment + + + align:start position:0% +a community and do A needs assessment +what might you plan what are sort of + + align:start position:0% +what might you plan what are sort of + + + align:start position:0% +what might you plan what are sort of +typical Public Health kind of programs + + align:start position:0% +typical Public Health kind of programs + + + align:start position:0% +typical Public Health kind of programs +to address the needs + + align:start position:0% + + + + align:start position:0% + +assessment I think you want to know of + + align:start position:0% +assessment I think you want to know of + + + align:start position:0% +assessment I think you want to know of +what they have on the ground they have + + align:start position:0% +what they have on the ground they have + + + align:start position:0% +what they have on the ground they have +on the ground systems not necessarily do + + align:start position:0% +on the ground systems not necessarily do + + + align:start position:0% +on the ground systems not necessarily do +the new ones and if um they have + + align:start position:0% +the new ones and if um they have + + + align:start position:0% +the new ones and if um they have +dysfunctional educational system you + + align:start position:0% +dysfunctional educational system you + + + align:start position:0% +dysfunctional educational system you +could go around walk around the factors + + align:start position:0% +could go around walk around the factors + + + align:start position:0% +could go around walk around the factors +that make basic it dysfunctional and try + + align:start position:0% +that make basic it dysfunctional and try + + + align:start position:0% +that make basic it dysfunctional and try +to um provide provide some form of + + align:start position:0% +to um provide provide some form of + + + align:start position:0% +to um provide provide some form of +support systems for this yeah I mean I + + align:start position:0% +support systems for this yeah I mean I + + + align:start position:0% +support systems for this yeah I mean I +think that's a terrific approach I I + + align:start position:0% +think that's a terrific approach I I + + + align:start position:0% +think that's a terrific approach I I +think that's a terrific approach I think + + align:start position:0% +think that's a terrific approach I think + + + align:start position:0% +think that's a terrific approach I think +we have to be intellectually honest when + + align:start position:0% +we have to be intellectually honest when + + + align:start position:0% +we have to be intellectually honest when +we do this kind of needs assessment to + + align:start position:0% +we do this kind of needs assessment to + + + align:start position:0% +we do this kind of needs assessment to +actually say what is the real need + + align:start position:0% +actually say what is the real need + + + align:start position:0% +actually say what is the real need +unfortunately unfortunately that has not + + align:start position:0% +unfortunately unfortunately that has not + + + align:start position:0% +unfortunately unfortunately that has not +been the health related view of A needs + + align:start position:0% +been the health related view of A needs + + + align:start position:0% +been the health related view of A needs +assessment or development so where are + + align:start position:0% +assessment or development so where are + + + align:start position:0% +assessment or development so where are +you from Nigeria okay I thought you + + align:start position:0% +you from Nigeria okay I thought you + + + align:start position:0% +you from Nigeria okay I thought you +might be not perfect I'm so glad you're + + align:start position:0% +might be not perfect I'm so glad you're + + + align:start position:0% +might be not perfect I'm so glad you're +from Nigeria what happened when uh the + + align:start position:0% +from Nigeria what happened when uh the + + + align:start position:0% +from Nigeria what happened when uh the +The Who and UNICEF tried to do the polio + + align:start position:0% +The Who and UNICEF tried to do the polio + + + align:start position:0% +The Who and UNICEF tried to do the polio +eradication in Nigeria Nigeria oh they + + align:start position:0% +eradication in Nigeria Nigeria oh they + + + align:start position:0% +eradication in Nigeria Nigeria oh they +had um this they had it was + + align:start position:0% +had um this they had it was + + + align:start position:0% +had um this they had it was +Su it planned out to be a political um + + align:start position:0% +Su it planned out to be a political um + + + align:start position:0% +Su it planned out to be a political um +um political um war between between the + + align:start position:0% +um political um war between between the + + + align:start position:0% +um political um war between between the +the government officials and the donors + + align:start position:0% +the government officials and the donors + + + align:start position:0% +the government officials and the donors +from wh and the UN at the end of the day + + align:start position:0% +from wh and the UN at the end of the day + + + align:start position:0% +from wh and the UN at the end of the day +it became kind of vertical program and + + align:start position:0% +it became kind of vertical program and + + + align:start position:0% +it became kind of vertical program and +some some people argue that it worked + + align:start position:0% +some some people argue that it worked + + + align:start position:0% +some some people argue that it worked +and and and they were the the figur + + align:start position:0% +and and and they were the the figur + + + align:start position:0% +and and and they were the the figur +worked but but back home um you could + + align:start position:0% +worked but but back home um you could + + + align:start position:0% +worked but but back home um you could +feel that um that that that that bad + + align:start position:0% +feel that um that that that that bad + + + align:start position:0% +feel that um that that that that bad +blood between the government officials + + align:start position:0% +blood between the government officials + + + align:start position:0% +blood between the government officials +and the people from W that there was no + + align:start position:0% +and the people from W that there was no + + + align:start position:0% +and the people from W that there was no +really so much of communication does + + align:start position:0% +really so much of communication does + + + align:start position:0% +really so much of communication does +everyone know this story no it's a great + + align:start position:0% +everyone know this story no it's a great + + + align:start position:0% +everyone know this story no it's a great +story so UNICEF wh comes into Nigeria + + align:start position:0% +story so UNICEF wh comes into Nigeria + + + align:start position:0% +story so UNICEF wh comes into Nigeria +and they say Nigeria is probably the + + align:start position:0% +and they say Nigeria is probably the + + + align:start position:0% +and they say Nigeria is probably the +main country in Africa that still has + + align:start position:0% +main country in Africa that still has + + + align:start position:0% +main country in Africa that still has +real polio real endemic polio and so we + + align:start position:0% +real polio real endemic polio and so we + + + align:start position:0% +real polio real endemic polio and so we +really want to focus polar eradication + + align:start position:0% +really want to focus polar eradication + + + align:start position:0% +really want to focus polar eradication +in Nigeria okay because that's how we're + + align:start position:0% +in Nigeria okay because that's how we're + + + align:start position:0% +in Nigeria okay because that's how we're +going to eradicate Global eradication + + align:start position:0% +going to eradicate Global eradication + + + align:start position:0% +going to eradicate Global eradication +polar seems like a good idea right so + + align:start position:0% +polar seems like a good idea right so + + + align:start position:0% +polar seems like a good idea right so +they brought big trucks with people with + + align:start position:0% +they brought big trucks with people with + + + align:start position:0% +they brought big trucks with people with +the cold chain with Etc and did you know + + align:start position:0% +the cold chain with Etc and did you know + + + align:start position:0% +the cold chain with Etc and did you know +wanted to do these Mass polio + + align:start position:0% +wanted to do these Mass polio + + + align:start position:0% +wanted to do these Mass polio +vaccinations and in some places in the + + align:start position:0% +vaccinations and in some places in the + + + align:start position:0% +vaccinations and in some places in the +poorest places in Northern Nigeria the + + align:start position:0% +poorest places in Northern Nigeria the + + + align:start position:0% +poorest places in Northern Nigeria the +communities + + align:start position:0% +communities + + + align:start position:0% +communities +refused they + + align:start position:0% +refused they + + + align:start position:0% +refused they +refused you looking puzzled right but + + align:start position:0% +refused you looking puzzled right but + + + align:start position:0% +refused you looking puzzled right but +why did they refuse because we're + + align:start position:0% +why did they refuse because we're + + + align:start position:0% +why did they refuse because we're +hearing there was a lot of bad blood + + align:start position:0% +hearing there was a lot of bad blood + + + align:start position:0% +hearing there was a lot of bad blood +maybe it worked maybe it was worked so + + align:start position:0% +maybe it worked maybe it was worked so + + + align:start position:0% +maybe it worked maybe it was worked so +I'll tell tell what the paper said the + + align:start position:0% +I'll tell tell what the paper said the + + + align:start position:0% +I'll tell tell what the paper said the +initial report so you're giving a better + + align:start position:0% +initial report so you're giving a better + + + align:start position:0% +initial report so you're giving a better +Nuance thing the initial report said the + + align:start position:0% +Nuance thing the initial report said the + + + align:start position:0% +Nuance thing the initial report said the +Muslim clerics don't believe in + + align:start position:0% +Muslim clerics don't believe in + + + align:start position:0% +Muslim clerics don't believe in +vaccination it's a health belief problem + + align:start position:0% +vaccination it's a health belief problem + + + align:start position:0% +vaccination it's a health belief problem +but what you're saying is different it + + align:start position:0% +but what you're saying is different it + + + align:start position:0% +but what you're saying is different it +wasn't a health belief problem what was + + align:start position:0% +wasn't a health belief problem what was + + + align:start position:0% +wasn't a health belief problem what was +it lack of health + + align:start position:0% +it lack of health + + + align:start position:0% +it lack of health +promotion it was this whole idea of a + + align:start position:0% +promotion it was this whole idea of a + + + align:start position:0% +promotion it was this whole idea of a +vertical program these people our + + align:start position:0% +vertical program these people our + + + align:start position:0% +vertical program these people our +community leaders they're sitting in a + + align:start position:0% +community leaders they're sitting in a + + + align:start position:0% +community leaders they're sitting in a +poor community that has you know open + + align:start position:0% +poor community that has you know open + + + align:start position:0% +poor community that has you know open +sewage + + align:start position:0% +sewage + + + align:start position:0% +sewage +right they have no quality of water they + + align:start position:0% +right they have no quality of water they + + + align:start position:0% +right they have no quality of water they +have absolutely no healthare and some + + align:start position:0% +have absolutely no healthare and some + + + align:start position:0% +have absolutely no healthare and some +foreigners come in and want to give + + align:start position:0% +foreigners come in and want to give + + + align:start position:0% +foreigners come in and want to give +polio not really the highest thing on + + align:start position:0% +polio not really the highest thing on + + + align:start position:0% +polio not really the highest thing on +their + + align:start position:0% +their + + + align:start position:0% +their +agenda right so this idea of sort of + + align:start position:0% +agenda right so this idea of sort of + + + align:start position:0% +agenda right so this idea of sort of +really discussing with the community the + + align:start position:0% +really discussing with the community the + + + align:start position:0% +really discussing with the community the +needs and trying to address the needs + + align:start position:0% +needs and trying to address the needs + + + align:start position:0% +needs and trying to address the needs +had that been done I believe it would + + align:start position:0% +had that been done I believe it would + + + align:start position:0% +had that been done I believe it would +have been much different I mean you tell + + align:start position:0% +have been much different I mean you tell + + + align:start position:0% +have been much different I mean you tell +me you're Nigerian but that there wasn't + + align:start position:0% +me you're Nigerian but that there wasn't + + + align:start position:0% +me you're Nigerian but that there wasn't +a discussion with the community is this + + align:start position:0% +a discussion with the community is this + + + align:start position:0% +a discussion with the community is this +a priority how do we embed this in + + align:start position:0% +a priority how do we embed this in + + + align:start position:0% +a priority how do we embed this in +something that really works + + align:start position:0% +something that really works + + + align:start position:0% +something that really works +right I mean do you think that that was + + align:start position:0% +right I mean do you think that that was + + + align:start position:0% +right I mean do you think that that was +yes at the time they had they just felt + + align:start position:0% +yes at the time they had they just felt + + + align:start position:0% +yes at the time they had they just felt +that it was a place where you just come + + align:start position:0% +that it was a place where you just come + + + align:start position:0% +that it was a place where you just come +D vacines um not taken into + + align:start position:0% +D vacines um not taken into + + + align:start position:0% +D vacines um not taken into +consideration people the stakeholders on + + align:start position:0% +consideration people the stakeholders on + + + align:start position:0% +consideration people the stakeholders on +ground so what happened was that over + + align:start position:0% +ground so what happened was that over + + + align:start position:0% +ground so what happened was that over +time they were rumors of the vaccine + + align:start position:0% +time they were rumors of the vaccine + + + align:start position:0% +time they were rumors of the vaccine +causing other comorbidities and the + + align:start position:0% +causing other comorbidities and the + + + align:start position:0% +causing other comorbidities and the +vaccines um causing things like + + align:start position:0% +vaccines um causing things like + + + align:start position:0% +vaccines um causing things like +infertility yeah when you get older and + + align:start position:0% +infertility yeah when you get older and + + + align:start position:0% +infertility yeah when you get older and +and basically I I I knew that that was + + align:start position:0% +and basically I I I knew that that was + + + align:start position:0% +and basically I I I knew that that was +just propaganda from the people that + + align:start position:0% +just propaganda from the people that + + + align:start position:0% +just propaganda from the people that +really who were mad about it yes they + + align:start position:0% +really who were mad about it yes they + + + align:start position:0% +really who were mad about it yes they +were really mad about it so they had to + + align:start position:0% +were really mad about it so they had to + + + align:start position:0% +were really mad about it so they had to +come out every story they could come up + + align:start position:0% +come out every story they could come up + + + align:start position:0% +come out every story they could come up +so generally they didn't want to know + + align:start position:0% +so generally they didn't want to know + + + align:start position:0% +so generally they didn't want to know +what the people there and it ended up go + + align:start position:0% +what the people there and it ended up go + + + align:start position:0% +what the people there and it ended up go +ahead yeah do you like small vacination + + align:start position:0% +ahead yeah do you like small vacination + + + align:start position:0% +ahead yeah do you like small vacination +is having similar failures I do is that + + align:start position:0% +is having similar failures I do is that + + + align:start position:0% +is having similar failures I do is that +controversial tell me what you think + + align:start position:0% +controversial tell me what you think + + + align:start position:0% +controversial tell me what you think +yeah I think they critical part in the + + align:start position:0% +yeah I think they critical part in the + + + align:start position:0% +yeah I think they critical part in the +small PX history where they turn out + + align:start position:0% +small PX history where they turn out + + + align:start position:0% +small PX history where they turn out +from uh institutional activities to + + align:start position:0% +from uh institutional activities to + + + align:start position:0% +from uh institutional activities to +community outreach when go and find like + + align:start position:0% +community outreach when go and find like + + + align:start position:0% +community outreach when go and find like +do active um screening with Community + + align:start position:0% +do active um screening with Community + + + align:start position:0% +do active um screening with Community +workers this was the the U-turn that + + align:start position:0% +workers this was the the U-turn that + + + align:start position:0% +workers this was the the U-turn that +make the small pox of success right and + + align:start position:0% +make the small pox of success right and + + + align:start position:0% +make the small pox of success right and +it's cool that we don't have small pox I + + align:start position:0% +it's cool that we don't have small pox I + + + align:start position:0% +it's cool that we don't have small pox I +mean I'm an infectious disease doctor + + align:start position:0% +mean I'm an infectious disease doctor + + + align:start position:0% +mean I'm an infectious disease doctor +once in a blue moon someone will throw a + + align:start position:0% +once in a blue moon someone will throw a + + + align:start position:0% +once in a blue moon someone will throw a +picture of a small pox case up there to + + align:start position:0% +picture of a small pox case up there to + + + align:start position:0% +picture of a small pox case up there to +throw off somebody you know it doesn't + + align:start position:0% +throw off somebody you know it doesn't + + + align:start position:0% +throw off somebody you know it doesn't +exist it's awesome but what was + + align:start position:0% +exist it's awesome but what was + + + align:start position:0% +exist it's awesome but what was +built with the eradication of small pox + + align:start position:0% +built with the eradication of small pox + + + align:start position:0% +built with the eradication of small pox +almost + + align:start position:0% +almost + + + align:start position:0% +almost +nothing and so I don't think the + + align:start position:0% +nothing and so I don't think the + + + align:start position:0% +nothing and so I don't think the +eradication of small pox was a failure + + align:start position:0% +eradication of small pox was a failure + + + align:start position:0% +eradication of small pox was a failure +it was a success in eradicating of + + align:start position:0% +it was a success in eradicating of + + + align:start position:0% +it was a success in eradicating of +disease but the same children who would + + align:start position:0% +disease but the same children who would + + + align:start position:0% +disease but the same children who would +have died of small pox die of measles + + align:start position:0% +have died of small pox die of measles + + + align:start position:0% +have died of small pox die of measles +today and die of malnutrition so I think + + align:start position:0% +today and die of malnutrition so I think + + + align:start position:0% +today and die of malnutrition so I think +what part of what I think your course + + align:start position:0% +what part of what I think your course + + + align:start position:0% +what part of what I think your course +organizers wants you to come away with + + align:start position:0% +organizers wants you to come away with + + + align:start position:0% +organizers wants you to come away with +is we would like to capture + + align:start position:0% +is we would like to capture + + + align:start position:0% +is we would like to capture +complexity we we would like not to dumb + + align:start position:0% +complexity we we would like not to dumb + + + align:start position:0% +complexity we we would like not to dumb +down the delivery of Health Care and + + align:start position:0% +down the delivery of Health Care and + + + align:start position:0% +down the delivery of Health Care and +addressing the social context of Health + + align:start position:0% +addressing the social context of Health + + + align:start position:0% +addressing the social context of Health +Care to poor people so so try to raise + + align:start position:0% +Care to poor people so so try to raise + + + align:start position:0% +Care to poor people so so try to raise +your sights I mean you're lucky because + + align:start position:0% +your sights I mean you're lucky because + + + align:start position:0% +your sights I mean you're lucky because +a lot of you are not necessarily + + align:start position:0% +a lot of you are not necessarily + + + align:start position:0% +a lot of you are not necessarily +inculcated in the public health + + align:start position:0% +inculcated in the public health + + + align:start position:0% +inculcated in the public health +prevention only method some of you may + + align:start position:0% +prevention only method some of you may + + + align:start position:0% +prevention only method some of you may +be and it's going to be a little jarring + + align:start position:0% +be and it's going to be a little jarring + + + align:start position:0% +be and it's going to be a little jarring +right because we're talking about + + align:start position:0% +right because we're talking about + + + align:start position:0% +right because we're talking about +investing money we're talking about you + + align:start position:0% +investing money we're talking about you + + + align:start position:0% +investing money we're talking about you +know bringing resources and Technology + + align:start position:0% +know bringing resources and Technology + + + align:start position:0% +know bringing resources and Technology +to communities that really were sort of + + align:start position:0% +to communities that really were sort of + + + align:start position:0% +to communities that really were sort of +have just GI dumped a vaccine right and + + align:start position:0% +have just GI dumped a vaccine right and + + + align:start position:0% +have just GI dumped a vaccine right and +vaccination is good I myself have given + + align:start position:0% +vaccination is good I myself have given + + + align:start position:0% +vaccination is good I myself have given +thousands of polio vaccines in my life + + align:start position:0% +thousands of polio vaccines in my life + + + align:start position:0% +thousands of polio vaccines in my life +love it love it but not in the absence + + align:start position:0% +love it love it but not in the absence + + + align:start position:0% +love it love it but not in the absence +of treating HIV tuberculosis uh making + + align:start position:0% +of treating HIV tuberculosis uh making + + + align:start position:0% +of treating HIV tuberculosis uh making +sure women don't die in childbirth um + + align:start position:0% +sure women don't die in childbirth um + + + align:start position:0% +sure women don't die in childbirth um +finding a child who needs to be treated + + align:start position:0% +finding a child who needs to be treated + + + align:start position:0% +finding a child who needs to be treated +for malnutrition so I'm going to kind of + + align:start position:0% +for malnutrition so I'm going to kind of + + + align:start position:0% +for malnutrition so I'm going to kind of +talk about taking each of those steps + + align:start position:0% +talk about taking each of those steps + + + align:start position:0% +talk about taking each of those steps +through a process of delivery and then + + align:start position:0% +through a process of delivery and then + + + align:start position:0% +through a process of delivery and then +scholar ship and then sort of trying to + + align:start position:0% +scholar ship and then sort of trying to + + + align:start position:0% +scholar ship and then sort of trying to +change the Paradigm so when about the + + align:start position:0% +change the Paradigm so when about the + + + align:start position:0% +change the Paradigm so when about the +time haish and I started a Partners in + + align:start position:0% +time haish and I started a Partners in + + + align:start position:0% +time haish and I started a Partners in +Health we were asked by a very small + + align:start position:0% +Health we were asked by a very small + + + align:start position:0% +Health we were asked by a very small +poor community in the slums of Peru to + + align:start position:0% +poor community in the slums of Peru to + + + align:start position:0% +poor community in the slums of Peru to +do the same kind of work that we did in + + align:start position:0% +do the same kind of work that we did in + + + align:start position:0% +do the same kind of work that we did in +Haiti which was to sit with the + + align:start position:0% +Haiti which was to sit with the + + + align:start position:0% +Haiti which was to sit with the +community and sort of say what is it you + + align:start position:0% +community and sort of say what is it you + + + align:start position:0% +community and sort of say what is it you +need and plan a community based like you + + align:start position:0% +need and plan a community based like you + + + align:start position:0% +need and plan a community based like you +said sort of the strength of the + + align:start position:0% +said sort of the strength of the + + + align:start position:0% +said sort of the strength of the +community we certainly believe has been + + align:start position:0% +community we certainly believe has been + + + align:start position:0% +community we certainly believe has been +a positive aspect of things like small + + align:start position:0% +a positive aspect of things like small + + + align:start position:0% +a positive aspect of things like small +talks eradication and say What are the + + align:start position:0% +talks eradication and say What are the + + + align:start position:0% +talks eradication and say What are the +key problems in this community well lo + + align:start position:0% +key problems in this community well lo + + + align:start position:0% +key problems in this community well lo +and behold what what became a real shock + + align:start position:0% +and behold what what became a real shock + + + align:start position:0% +and behold what what became a real shock +to us was one of the biggest problems + + align:start position:0% +to us was one of the biggest problems + + + align:start position:0% +to us was one of the biggest problems +faced by this very poor uh Community was + + align:start position:0% +faced by this very poor uh Community was + + + align:start position:0% +faced by this very poor uh Community was +tuberculosis and that struck us as very + + align:start position:0% +tuberculosis and that struck us as very + + + align:start position:0% +tuberculosis and that struck us as very +strange because at the time the program + + align:start position:0% +strange because at the time the program + + + align:start position:0% +strange because at the time the program +tuberculosis program in Peru was raided + + align:start position:0% +tuberculosis program in Peru was raided + + + align:start position:0% +tuberculosis program in Peru was raided +by The Who the best in the world okay + + align:start position:0% +by The Who the best in the world okay + + + align:start position:0% +by The Who the best in the world okay +the best in the world so we had all + + align:start position:0% +the best in the world so we had all + + + align:start position:0% +the best in the world so we had all +these community members that themselves + + align:start position:0% +these community members that themselves + + + align:start position:0% +these community members that themselves +were dying of + + align:start position:0% +were dying of + + + align:start position:0% +were dying of +tuberculosis while on + + align:start position:0% +tuberculosis while on + + + align:start position:0% +tuberculosis while on +treatment + + align:start position:0% +treatment + + + align:start position:0% +treatment +so what was going on I mean you can read + + align:start position:0% +so what was going on I mean you can read + + + align:start position:0% +so what was going on I mean you can read +the slide so what do you think was going + + align:start position:0% +the slide so what do you think was going + + + align:start position:0% +the slide so what do you think was going +on these people are dying of + + align:start position:0% +on these people are dying of + + + align:start position:0% +on these people are dying of +tuberculosis while on treatment this + + align:start position:0% +tuberculosis while on treatment this + + + align:start position:0% +tuberculosis while on treatment this +yeah they had resistance so we said to + + align:start position:0% +yeah they had resistance so we said to + + + align:start position:0% +yeah they had resistance so we said to +the government we think these people + + align:start position:0% +the government we think these people + + + align:start position:0% +the government we think these people +have resistant + + align:start position:0% +have resistant + + + align:start position:0% +have resistant +tuberculosis we said that to the wh I + + align:start position:0% +tuberculosis we said that to the wh I + + + align:start position:0% +tuberculosis we said that to the wh I +mean at the time Partners in Health was + + align:start position:0% +mean at the time Partners in Health was + + + align:start position:0% +mean at the time Partners in Health was +Tiny I was the first physan Partners in + + align:start position:0% +Tiny I was the first physan Partners in + + + align:start position:0% +Tiny I was the first physan Partners in +Health ever h + + align:start position:0% +Health ever h + + + align:start position:0% +Health ever h +like you know 99 it was Paul Farmer was + + align:start position:0% +like you know 99 it was Paul Farmer was + + + align:start position:0% +like you know 99 it was Paul Farmer was +already a pool Professor Jim Kim was + + align:start position:0% +already a pool Professor Jim Kim was + + + align:start position:0% +already a pool Professor Jim Kim was +still Moonlighting at to bring him to + + align:start position:0% +still Moonlighting at to bring him to + + + align:start position:0% +still Moonlighting at to bring him to +pay a salary and I was like fulltime so + + align:start position:0% +pay a salary and I was like fulltime so + + + align:start position:0% +pay a salary and I was like fulltime so +we had like this tiny staff right 75 you + + align:start position:0% +we had like this tiny staff right 75 you + + + align:start position:0% +we had like this tiny staff right 75 you +know community health workers in Peru + + align:start position:0% +know community health workers in Peru + + + align:start position:0% +know community health workers in Peru +about 200 in Haiti and a tiny little + + align:start position:0% +about 200 in Haiti and a tiny little + + + align:start position:0% +about 200 in Haiti and a tiny little +clinic and we said the who these people + + align:start position:0% +clinic and we said the who these people + + + align:start position:0% +clinic and we said the who these people +have drug resistance and what do you + + align:start position:0% +have drug resistance and what do you + + + align:start position:0% +have drug resistance and what do you +think their response + + align:start position:0% +think their response + + + align:start position:0% +think their response +was you're shaking your head no they + + align:start position:0% +was you're shaking your head no they + + + align:start position:0% +was you're shaking your head no they +don't first of all no they don't so we + + align:start position:0% +don't first of all no they don't so we + + + align:start position:0% +don't first of all no they don't so we +actually had to bring this them back to + + align:start position:0% +actually had to bring this them back to + + + align:start position:0% +actually had to bring this them back to +the United States which by the way is + + align:start position:0% +the United States which by the way is + + + align:start position:0% +the United States which by the way is +against the law um without a permit and + + align:start position:0% +against the law um without a permit and + + + align:start position:0% +against the law um without a permit and +bring it to the Massachusetts state + + align:start position:0% +bring it to the Massachusetts state + + + align:start position:0% +bring it to the Massachusetts state +laboratory again trying to leverage + + align:start position:0% +laboratory again trying to leverage + + + align:start position:0% +laboratory again trying to leverage +technology because even in PR they we + + align:start position:0% +technology because even in PR they we + + + align:start position:0% +technology because even in PR they we +don't have the technology to do TB + + align:start position:0% +don't have the technology to do TB + + + align:start position:0% +don't have the technology to do TB +Culture by the way TB culture was + + align:start position:0% +Culture by the way TB culture was + + + align:start position:0% +Culture by the way TB culture was +invented in + + align:start position:0% + + + + align:start position:0% + +1888 you know how much it costs to do a + + align:start position:0% +1888 you know how much it costs to do a + + + align:start position:0% +1888 you know how much it costs to do a +TB culture a dollar so why couldn't you + + align:start position:0% +TB culture a dollar so why couldn't you + + + align:start position:0% +TB culture a dollar so why couldn't you +guys do huh why couldn't you guys do it + + align:start position:0% +guys do huh why couldn't you guys do it + + + align:start position:0% +guys do huh why couldn't you guys do it +there they didn't have they they said + + align:start position:0% +there they didn't have they they said + + + align:start position:0% +there they didn't have they they said +they didn't have the facilities to do + + align:start position:0% +they didn't have the facilities to do + + + align:start position:0% +they didn't have the facilities to do +it because nobody had ever put money + + align:start position:0% +it because nobody had ever put money + + + align:start position:0% +it because nobody had ever put money +into that real the health sector it + + align:start position:0% +into that real the health sector it + + + align:start position:0% +into that real the health sector it +wasn't considered the sustainable route + + align:start position:0% +wasn't considered the sustainable route + + + align:start position:0% +wasn't considered the sustainable route +for a country like Peru to have a real + + align:start position:0% +for a country like Peru to have a real + + + align:start position:0% +for a country like Peru to have a real +TB lab even though to Peru at the + + align:start position:0% +TB lab even though to Peru at the + + + align:start position:0% +TB lab even though to Peru at the +time with only 5% of the population of + + align:start position:0% +time with only 5% of the population of + + + align:start position:0% +time with only 5% of the population of +South America had 25% of the TV + + align:start position:0% +South America had 25% of the TV + + + align:start position:0% +South America had 25% of the TV +cases so highest one of the highest + + align:start position:0% +cases so highest one of the highest + + + align:start position:0% +cases so highest one of the highest +burden countries in the world per capita + + align:start position:0% +burden countries in the world per capita + + + align:start position:0% +burden countries in the world per capita +with tuberculosis no functioning TB lab + + align:start position:0% +with tuberculosis no functioning TB lab + + + align:start position:0% +with tuberculosis no functioning TB lab +because it's too expensive too Hightech + + align:start position:0% +because it's too expensive too Hightech + + + align:start position:0% +because it's too expensive too Hightech +too demanding of human resource so we + + align:start position:0% +too demanding of human resource so we + + + align:start position:0% +too demanding of human resource so we +brought it back to Mass state lab did + + align:start position:0% +brought it back to Mass state lab did + + + align:start position:0% +brought it back to Mass state lab did +the thing thought oh my God these people + + align:start position:0% +the thing thought oh my God these people + + + align:start position:0% +the thing thought oh my God these people +have highly resistant TB so we started + + align:start position:0% +have highly resistant TB so we started + + + align:start position:0% +have highly resistant TB so we started +to show this data to the government of + + align:start position:0% +to show this data to the government of + + + align:start position:0% +to show this data to the government of +brew and to The Who and saying we we + + align:start position:0% +brew and to The Who and saying we we + + + align:start position:0% +brew and to The Who and saying we we +could treat this I mean in the United + + align:start position:0% +could treat this I mean in the United + + + align:start position:0% +could treat this I mean in the United +States we had a little outbreak TV a + + align:start position:0% +States we had a little outbreak TV a + + + align:start position:0% +States we had a little outbreak TV a +little outbreak of drug resistant TB in + + align:start position:0% +little outbreak of drug resistant TB in + + + align:start position:0% +little outbreak of drug resistant TB in +the '90s and you know it's a treatable + + align:start position:0% +the '90s and you know it's a treatable + + + align:start position:0% +the '90s and you know it's a treatable +disease it's not that you have + + align:start position:0% +disease it's not that you have + + + align:start position:0% +disease it's not that you have +died and we were roundly + + align:start position:0% +died and we were roundly + + + align:start position:0% +died and we were roundly +criticized and in fact it changed + + align:start position:0% +criticized and in fact it changed + + + align:start position:0% +criticized and in fact it changed +Partners in Health a lot because it + + align:start position:0% +Partners in Health a lot because it + + + align:start position:0% +Partners in Health a lot because it +vaulted us from this kind of tiny + + align:start position:0% +vaulted us from this kind of tiny + + + align:start position:0% +vaulted us from this kind of tiny +Community Based solidarity based group + + align:start position:0% +Community Based solidarity based group + + + align:start position:0% +Community Based solidarity based group +to sort of being involved in these huge + + align:start position:0% +to sort of being involved in these huge + + + align:start position:0% +to sort of being involved in these huge +political policy debates around who + + align:start position:0% +political policy debates around who + + + align:start position:0% +political policy debates around who +should get treatment of + + align:start position:0% +should get treatment of + + + align:start position:0% +should get treatment of +what okay so why do you think people + + align:start position:0% +what okay so why do you think people + + + align:start position:0% +what okay so why do you think people +didn't want to treat tuberculosis drug + + align:start position:0% +didn't want to treat tuberculosis drug + + + align:start position:0% +didn't want to treat tuberculosis drug +resistant tuberculosis we treated these + + align:start position:0% +resistant tuberculosis we treated these + + + align:start position:0% +resistant tuberculosis we treated these +patients + + align:start position:0% +patients + + + align:start position:0% +patients +um and so you know what what now crew + + align:start position:0% +um and so you know what what now crew + + + align:start position:0% +um and so you know what what now crew +kept saying but we have the best TV + + align:start position:0% +kept saying but we have the best TV + + + align:start position:0% +kept saying but we have the best TV +program in the world we have the best TV + + align:start position:0% +program in the world we have the best TV + + + align:start position:0% +program in the world we have the best TV +control program in the world so why are + + align:start position:0% +control program in the world so why are + + + align:start position:0% +control program in the world so why are +those people getting drug res in + + align:start position:0% + + + + align:start position:0% + +TV why do you think you would if you're + + align:start position:0% +TV why do you think you would if you're + + + align:start position:0% +TV why do you think you would if you're +a public health official what might you + + align:start position:0% +a public health official what might you + + + align:start position:0% +a public health official what might you +say no I have a degree in public health + + align:start position:0% +say no I have a degree in public health + + + align:start position:0% +say no I have a degree in public health +so I'm allowed to slam Public Health + + align:start position:0% +so I'm allowed to slam Public Health + + + align:start position:0% +so I'm allowed to slam Public Health +which I often do + + align:start position:0% + + + + align:start position:0% + +compliance this is the best excuse how + + align:start position:0% +compliance this is the best excuse how + + + align:start position:0% +compliance this is the best excuse how +many doctors are in the room this is the + + align:start position:0% +many doctors are in the room this is the + + + align:start position:0% +many doctors are in the room this is the +best thing to do if you know if a do if + + align:start position:0% +best thing to do if you know if a do if + + + align:start position:0% +best thing to do if you know if a do if +a patient doesn't do well you say it's + + align:start position:0% +a patient doesn't do well you say it's + + + align:start position:0% +a patient doesn't do well you say it's +their fault right that's how you wash + + align:start position:0% +their fault right that's how you wash + + + align:start position:0% +their fault right that's how you wash +your hands of the responsibility for a + + align:start position:0% +your hands of the responsibility for a + + + align:start position:0% +your hands of the responsibility for a +bad outcome right so they said these are + + align:start position:0% +bad outcome right so they said these are + + + align:start position:0% +bad outcome right so they said these are +stupid poor people and they're not + + align:start position:0% +stupid poor people and they're not + + + align:start position:0% +stupid poor people and they're not +taking their medicines and that's why + + align:start position:0% +taking their medicines and that's why + + + align:start position:0% +taking their medicines and that's why +they have nttb so we don't care about + + align:start position:0% +they have nttb so we don't care about + + + align:start position:0% +they have nttb so we don't care about +them now first of all it's a cont it it + + align:start position:0% +them now first of all it's a cont it it + + + align:start position:0% +them now first of all it's a cont it it +it's it doesn't make sense because here + + align:start position:0% +it's it doesn't make sense because here + + + align:start position:0% +it's it doesn't make sense because here +Peru is saying they have the best TV + + align:start position:0% +Peru is saying they have the best TV + + + align:start position:0% +Peru is saying they have the best TV +program in the world and they're saying + + align:start position:0% +program in the world and they're saying + + + align:start position:0% +program in the world and they're saying +these people are taking their medicines + + align:start position:0% +these people are taking their medicines + + + align:start position:0% +these people are taking their medicines +the reason Peru had the best TV uh + + align:start position:0% +the reason Peru had the best TV uh + + + align:start position:0% +the reason Peru had the best TV uh +program in the world is everyone took + + align:start position:0% +program in the world is everyone took + + + align:start position:0% +program in the world is everyone took +their medes they would go find you they + + align:start position:0% +their medes they would go find you they + + + align:start position:0% +their medes they would go find you they +would hunt you down so we had the + + align:start position:0% +would hunt you down so we had the + + + align:start position:0% +would hunt you down so we had the +records that all of these people were in + + align:start position:0% +records that all of these people were in + + + align:start position:0% +records that all of these people were in +fact taking their medicines + + align:start position:0% +fact taking their medicines + + + align:start position:0% +fact taking their medicines +religiously religiously under penalty of + + align:start position:0% +religiously religiously under penalty of + + + align:start position:0% +religiously religiously under penalty of +imprisonment right so we knew they were + + align:start position:0% +imprisonment right so we knew they were + + + align:start position:0% +imprisonment right so we knew they were +taking their medicine so then why so + + align:start position:0% +taking their medicine so then why so + + + align:start position:0% +taking their medicine so then why so +then why did they have MTV + + align:start position:0% + + + + align:start position:0% + +yeah see there in lies the rubel it + + align:start position:0% +yeah see there in lies the rubel it + + + align:start position:0% +yeah see there in lies the rubel it +turned out a couple huh of the drugs + + align:start position:0% +turned out a couple huh of the drugs + + + align:start position:0% +turned out a couple huh of the drugs +quality of the drugs is certainly a + + align:start position:0% +quality of the drugs is certainly a + + + align:start position:0% +quality of the drugs is certainly a +factor in a lot of places it probably + + align:start position:0% +factor in a lot of places it probably + + + align:start position:0% +factor in a lot of places it probably +wasn't in Peru as much um so that could + + align:start position:0% +wasn't in Peru as much um so that could + + + align:start position:0% +wasn't in Peru as much um so that could +be yeah you don't have the good quality + + align:start position:0% +be yeah you don't have the good quality + + + align:start position:0% +be yeah you don't have the good quality +drugs I think + + align:start position:0% +drugs I think + + + align:start position:0% +drugs I think +um really correlation between + + align:start position:0% +um really correlation between + + + align:start position:0% +um really correlation between +nutritional yeah like so this is the + + align:start position:0% +nutritional yeah like so this is the + + + align:start position:0% +nutritional yeah like so this is the +quote unquote house that these patients + + align:start position:0% +quote unquote house that these patients + + + align:start position:0% +quote unquote house that these patients +were living in often 10 to a one room + + align:start position:0% +were living in often 10 to a one room + + + align:start position:0% +were living in often 10 to a one room +house they're poor they have bad + + align:start position:0% +house they're poor they have bad + + + align:start position:0% +house they're poor they have bad +nutrition they they um have no real + + align:start position:0% +nutrition they they um have no real + + + align:start position:0% +nutrition they they um have no real +ventilation to speak of I mean I don't + + align:start position:0% +ventilation to speak of I mean I don't + + + align:start position:0% +ventilation to speak of I mean I don't +know if you I don't know this doesn't + + align:start position:0% +know if you I don't know this doesn't + + + align:start position:0% +know if you I don't know this doesn't +even but this is this what the slums of + + align:start position:0% +even but this is this what the slums of + + + align:start position:0% +even but this is this what the slums of +L look like um and so let's say one + + align:start position:0% +L look like um and so let's say one + + + align:start position:0% +L look like um and so let's say one +person didn't take their medicines in + + align:start position:0% +person didn't take their medicines in + + + align:start position:0% +person didn't take their medicines in +this + + align:start position:0% +this + + + align:start position:0% +this +house and they were spreading resistant + + align:start position:0% +house and they were spreading resistant + + + align:start position:0% +house and they were spreading resistant +tuberculosis T now + + align:start position:0% +tuberculosis T now + + + align:start position:0% +tuberculosis T now +so then we so we we we said look they + + align:start position:0% +so then we so we we we said look they + + + align:start position:0% +so then we so we we we said look they +all have drug resistant TB and here's + + align:start position:0% +all have drug resistant TB and here's + + + align:start position:0% +all have drug resistant TB and here's +their treatment card and these people + + align:start position:0% +their treatment card and these people + + + align:start position:0% +their treatment card and these people +all took their their TB and still people + + align:start position:0% +all took their their TB and still people + + + align:start position:0% +all took their their TB and still people +didn't believe it they didn't want to + + align:start position:0% +didn't believe it they didn't want to + + + align:start position:0% +didn't believe it they didn't want to +believe it because it made the situation + + align:start position:0% +believe it because it made the situation + + + align:start position:0% +believe it because it made the situation +more complex so we actually had to do um + + align:start position:0% +more complex so we actually had to do um + + + align:start position:0% +more complex so we actually had to do um +rflp restriction fragment uh length + + align:start position:0% +rflp restriction fragment uh length + + + align:start position:0% +rflp restriction fragment uh length +polymorphisms which was a genetic test + + align:start position:0% +polymorphisms which was a genetic test + + + align:start position:0% +polymorphisms which was a genetic test +of the strain to show who had the same + + align:start position:0% +of the strain to show who had the same + + + align:start position:0% +of the strain to show who had the same +strain in the family because people were + + align:start position:0% +strain in the family because people were + + + align:start position:0% +strain in the family because people were +saying well you know drug resistant TB + + align:start position:0% +saying well you know drug resistant TB + + + align:start position:0% +saying well you know drug resistant TB +is not um it's not + + align:start position:0% +is not um it's not + + + align:start position:0% +is not um it's not +transmissible you know it's like so we + + align:start position:0% +transmissible you know it's like so we + + + align:start position:0% +transmissible you know it's like so we +had to yeah I know it's stupid h i I + + align:start position:0% +had to yeah I know it's stupid h i I + + + align:start position:0% +had to yeah I know it's stupid h i I +used to just lose it I can't go to TV uh + + align:start position:0% +used to just lose it I can't go to TV uh + + + align:start position:0% +used to just lose it I can't go to TV uh +meetings anymore because I get so angry + + align:start position:0% +meetings anymore because I get so angry + + + align:start position:0% +meetings anymore because I get so angry +at the TV still like I I hate them um so + + align:start position:0% +at the TV still like I I hate them um so + + + align:start position:0% +at the TV still like I I hate them um so +they said well it's not transmissible um + + align:start position:0% +they said well it's not transmissible um + + + align:start position:0% +they said well it's not transmissible um +so there's some weird technicality that + + align:start position:0% +so there's some weird technicality that + + + align:start position:0% +so there's some weird technicality that +you know occasionally the kind of + + align:start position:0% +you know occasionally the kind of + + + align:start position:0% +you know occasionally the kind of +resistance that develops in a TB strain + + align:start position:0% +resistance that develops in a TB strain + + + align:start position:0% +resistance that develops in a TB strain +makes it less fit but that's not even + + align:start position:0% +makes it less fit but that's not even + + + align:start position:0% +makes it less fit but that's not even +the norm it's just like one small type + + align:start position:0% +the norm it's just like one small type + + + align:start position:0% +the norm it's just like one small type +of mutation I mean these people had + + align:start position:0% +of mutation I mean these people had + + + align:start position:0% +of mutation I mean these people had +seven drug resistant five 10 drug + + align:start position:0% +seven drug resistant five 10 drug + + + align:start position:0% +seven drug resistant five 10 drug +resistant you know drug to which there + + align:start position:0% +resistant you know drug to which there + + + align:start position:0% +resistant you know drug to which there +Str resist so the primary here are all + + align:start position:0% +Str resist so the primary here are all + + + align:start position:0% +Str resist so the primary here are all +the people who had the same restriction + + align:start position:0% +the people who had the same restriction + + + align:start position:0% +the people who had the same restriction +length uh fragment length polymorphism + + align:start position:0% +length uh fragment length polymorphism + + + align:start position:0% +length uh fragment length polymorphism +or + + align:start position:0% +or + + + align:start position:0% +or +FP um so probably this person these two + + align:start position:0% +FP um so probably this person these two + + + align:start position:0% +FP um so probably this person these two +people in 9091 maybe had developed + + align:start position:0% +people in 9091 maybe had developed + + + align:start position:0% +people in 9091 maybe had developed +resistant uh TB from not taking their + + align:start position:0% +resistant uh TB from not taking their + + + align:start position:0% +resistant uh TB from not taking their +meds or whatever the actually good best + + align:start position:0% +meds or whatever the actually good best + + + align:start position:0% +meds or whatever the actually good best +TB program in the world started in 1990 + + align:start position:0% +TB program in the world started in 1990 + + + align:start position:0% +TB program in the world started in 1990 +so it may have been people were infected + + align:start position:0% +so it may have been people were infected + + + align:start position:0% +so it may have been people were infected +before got poor quality drugs or didn't + + align:start position:0% +before got poor quality drugs or didn't + + + align:start position:0% +before got poor quality drugs or didn't +have the adequate treatment but then + + align:start position:0% +have the adequate treatment but then + + + align:start position:0% +have the adequate treatment but then +everyone else in the family had that + + align:start position:0% +everyone else in the family had that + + + align:start position:0% +everyone else in the family had that +same strength so if we had not had + + align:start position:0% +same strength so if we had not had + + + align:start position:0% +same strength so if we had not had +access to kind of that technology no one + + align:start position:0% +access to kind of that technology no one + + + align:start position:0% +access to kind of that technology no one +would have believed this you know and so + + align:start position:0% +would have believed this you know and so + + + align:start position:0% +would have believed this you know and so +for us we felt like it's it's good it's + + align:start position:0% +for us we felt like it's it's good it's + + + align:start position:0% +for us we felt like it's it's good it's +like a good samaritan thing to do to + + align:start position:0% +like a good samaritan thing to do to + + + align:start position:0% +like a good samaritan thing to do to +treat these people but we also had to do + + align:start position:0% +treat these people but we also had to do + + + align:start position:0% +treat these people but we also had to do +the scholarship to show that in Peru in + + align:start position:0% +the scholarship to show that in Peru in + + + align:start position:0% +the scholarship to show that in Peru in +a place where people we knew that their + + align:start position:0% +a place where people we knew that their + + + align:start position:0% +a place where people we knew that their +compliance was excellent if they were + + align:start position:0% +compliance was excellent if they were + + + align:start position:0% +compliance was excellent if they were +failing therapy which the average length + + align:start position:0% +failing therapy which the average length + + + align:start position:0% +failing therapy which the average length +of time that our original 75 patients + + align:start position:0% +of time that our original 75 patients + + + align:start position:0% +of time that our original 75 patients +had been treated for tuberculosis was 14 + + align:start position:0% +had been treated for tuberculosis was 14 + + + align:start position:0% +had been treated for tuberculosis was 14 +months okay we had some people had been + + align:start position:0% +months okay we had some people had been + + + align:start position:0% +months okay we had some people had been +treat on treatment for TB for 5 years + + align:start position:0% +treat on treatment for TB for 5 years + + + align:start position:0% +treat on treatment for TB for 5 years +ineffective treatment making them more + + align:start position:0% +ineffective treatment making them more + + + align:start position:0% +ineffective treatment making them more +and more resistant each time so so we + + align:start position:0% +and more resistant each time so so we + + + align:start position:0% +and more resistant each time so so we +showed that in a place where you know + + align:start position:0% +showed that in a place where you know + + + align:start position:0% +showed that in a place where you know +the TV program works you know people are + + align:start position:0% +the TV program works you know people are + + + align:start position:0% +the TV program works you know people are +getting their medicines if they are + + align:start position:0% +getting their medicines if they are + + + align:start position:0% +getting their medicines if they are +failing at month three they probably + + align:start position:0% +failing at month three they probably + + + align:start position:0% +failing at month three they probably +have drug resistant TB and you need to + + align:start position:0% +have drug resistant TB and you need to + + + align:start position:0% +have drug resistant TB and you need to +do + + align:start position:0% +do + + + align:start position:0% +do +something so this was a way we really + + align:start position:0% +something so this was a way we really + + + align:start position:0% +something so this was a way we really +pushed the envelope to say it's not okay + + align:start position:0% +pushed the envelope to say it's not okay + + + align:start position:0% +pushed the envelope to say it's not okay +just to kind of pick the cheapest + + align:start position:0% +just to kind of pick the cheapest + + + align:start position:0% +just to kind of pick the cheapest +intervention and apply that so when we + + align:start position:0% +intervention and apply that so when we + + + align:start position:0% +intervention and apply that so when we +first started treating this disease the + + align:start position:0% +first started treating this disease the + + + align:start position:0% +first started treating this disease the +treatment cost was + + align:start position:0% +treatment cost was + + + align:start position:0% +treatment cost was +$30,000 per patient for a + + align:start position:0% +$30,000 per patient for a + + + align:start position:0% +$30,000 per patient for a +cure so what are you going to say about + + align:start position:0% + + + + align:start position:0% + +that money yeah where' you get the money + + align:start position:0% +that money yeah where' you get the money + + + align:start position:0% +that money yeah where' you get the money +like how you so we just said look we can + + align:start position:0% +like how you so we just said look we can + + + align:start position:0% +like how you so we just said look we can +find the money and we had an amazing + + align:start position:0% +find the money and we had an amazing + + + align:start position:0% +find the money and we had an amazing +benefactor who really cared about poor + + align:start position:0% +benefactor who really cared about poor + + + align:start position:0% +benefactor who really cared about poor +people and he said yeah okay I'll pay + + align:start position:0% +people and he said yeah okay I'll pay + + + align:start position:0% +people and he said yeah okay I'll pay +for it but but more importantly we use + + align:start position:0% +for it but but more importantly we use + + + align:start position:0% +for it but but more importantly we use +this + + align:start position:0% +this + + + align:start position:0% +this +research and other pieces of data + + align:start position:0% +research and other pieces of data + + + align:start position:0% +research and other pieces of data +showing that it was curable showing that + + align:start position:0% +showing that it was curable showing that + + + align:start position:0% +showing that it was curable showing that +there was a global pandemic going on at + + align:start position:0% +there was a global pandemic going on at + + + align:start position:0% +there was a global pandemic going on at +the time um I mean this is a little kid + + align:start position:0% +the time um I mean this is a little kid + + + align:start position:0% +the time um I mean this is a little kid +this a little kid for Dr this classic po + + align:start position:0% +this a little kid for Dr this classic po + + + align:start position:0% +this a little kid for Dr this classic po +dis use on an MRI and this is a little + + align:start position:0% +dis use on an MRI and this is a little + + + align:start position:0% +dis use on an MRI and this is a little +kid after treatment and and we actually + + align:start position:0% +kid after treatment and and we actually + + + align:start position:0% +kid after treatment and and we actually +did another study just showing that the + + align:start position:0% +did another study just showing that the + + + align:start position:0% +did another study just showing that the +in the first 16 kids that we treated + + align:start position:0% +in the first 16 kids that we treated + + + align:start position:0% +in the first 16 kids that we treated +they all had been on treatment for a + + align:start position:0% +they all had been on treatment for a + + + align:start position:0% +they all had been on treatment for a +really long time because there was no + + align:start position:0% +really long time because there was no + + + align:start position:0% +really long time because there was no +way to move them to drug resistant TB + + align:start position:0% +way to move them to drug resistant TB + + + align:start position:0% +way to move them to drug resistant TB +treatment so you know this kid was + + align:start position:0% +treatment so you know this kid was + + + align:start position:0% +treatment so you know this kid was +paralyzed now he's fine he's probably 14 + + align:start position:0% +paralyzed now he's fine he's probably 14 + + + align:start position:0% +paralyzed now he's fine he's probably 14 +or 15 now I haven't seen him in years um + + align:start position:0% +or 15 now I haven't seen him in years um + + + align:start position:0% +or 15 now I haven't seen him in years um +so we but but what we did is sort of + + align:start position:0% +so we but but what we did is sort of + + + align:start position:0% +so we but but what we did is sort of +make sorry make a documentation around + + align:start position:0% +make sorry make a documentation around + + + align:start position:0% +make sorry make a documentation around +the world of the prevalence of drug + + align:start position:0% +the world of the prevalence of drug + + + align:start position:0% +the world of the prevalence of drug +resistance to say this is a real Public + + align:start position:0% +resistance to say this is a real Public + + + align:start position:0% +resistance to say this is a real Public +Health threet it it is possible so we + + align:start position:0% +Health threet it it is possible so we + + + align:start position:0% +Health threet it it is possible so we +first show the overall burden of disease + + align:start position:0% +first show the overall burden of disease + + + align:start position:0% +first show the overall burden of disease +then we show it's feasable then we try + + align:start position:0% +then we show it's feasable then we try + + + align:start position:0% +then we show it's feasable then we try +to develop protocols and all of these + + align:start position:0% +to develop protocols and all of these + + + align:start position:0% +to develop protocols and all of these +things again you need that sort of + + align:start position:0% +things again you need that sort of + + + align:start position:0% +things again you need that sort of +feedback loop some is the electronic dat + + align:start position:0% +feedback loop some is the electronic dat + + + align:start position:0% +feedback loop some is the electronic dat +some is the laboratory technology some + + align:start position:0% +some is the laboratory technology some + + + align:start position:0% +some is the laboratory technology some +is ETC um and then what was interesting + + align:start position:0% +is ETC um and then what was interesting + + + align:start position:0% +is ETC um and then what was interesting +is once we showed the need the prices of + + align:start position:0% +is once we showed the need the prices of + + + align:start position:0% +is once we showed the need the prices of +the drugs + + align:start position:0% +the drugs + + + align:start position:0% +the drugs +dropped you know why why would the + + align:start position:0% +dropped you know why why would the + + + align:start position:0% +dropped you know why why would the +prices of the drugs dropped drop after + + align:start position:0% +prices of the drugs dropped drop after + + + align:start position:0% +prices of the drugs dropped drop after +we show the need we actually one of the + + align:start position:0% +we show the need we actually one of the + + + align:start position:0% +we show the need we actually one of the +ways we did it we did this overall um um + + align:start position:0% +ways we did it we did this overall um um + + + align:start position:0% +ways we did it we did this overall um um +review of how much MDR there was in the + + align:start position:0% +review of how much MDR there was in the + + + align:start position:0% +review of how much MDR there was in the +world we showed it was everywhere and + + align:start position:0% +world we showed it was everywhere and + + + align:start position:0% +world we showed it was everywhere and +then we fought to get the second line + + align:start position:0% +then we fought to get the second line + + + align:start position:0% +then we fought to get the second line +drugs on on the essential med list of + + align:start position:0% +drugs on on the essential med list of + + + align:start position:0% +drugs on on the essential med list of +the wh what is that a drug resistant TV + + align:start position:0% +the wh what is that a drug resistant TV + + + align:start position:0% +the wh what is that a drug resistant TV +sorry multi- drug resistant TV + + align:start position:0% + + + + align:start position:0% + +yeah I was going to say the + + align:start position:0% +yeah I was going to say the + + + align:start position:0% +yeah I was going to say the +manufacturers of drugs know that they + + align:start position:0% +manufacturers of drugs know that they + + + align:start position:0% +manufacturers of drugs know that they +can sell a lot more now because it's + + align:start position:0% +can sell a lot more now because it's + + + align:start position:0% +can sell a lot more now because it's +going to be encouraged at low prices + + align:start position:0% +going to be encouraged at low prices + + + align:start position:0% +going to be encouraged at low prices +that's right so Li Tak is going to be a + + align:start position:0% +that's right so Li Tak is going to be a + + + align:start position:0% +that's right so Li Tak is going to be a +lot higher so in other words part of + + align:start position:0% +lot higher so in other words part of + + + align:start position:0% +lot higher so in other words part of +this advocacy was pushing the price down + + align:start position:0% +this advocacy was pushing the price down + + + align:start position:0% +this advocacy was pushing the price down +and now you can cure somebody with a + + align:start position:0% +and now you can cure somebody with a + + + align:start position:0% +and now you can cure somebody with a +drug resistant TB for about $1,700 the + + align:start position:0% +drug resistant TB for about $1,700 the + + + align:start position:0% +drug resistant TB for about $1,700 the +price is still quite High probably too + + align:start position:0% +price is still quite High probably too + + + align:start position:0% +price is still quite High probably too +high given the burden of disease around + + align:start position:0% +high given the burden of disease around + + + align:start position:0% +high given the burden of disease around +the world we think there are somewhere + + align:start position:0% +the world we think there are somewhere + + + align:start position:0% +the world we think there are somewhere +in the neighborhood of a half a million + + align:start position:0% +in the neighborhood of a half a million + + + align:start position:0% +in the neighborhood of a half a million +cases that need to be treated but uh you + + align:start position:0% +cases that need to be treated but uh you + + + align:start position:0% +cases that need to be treated but uh you +know certainly more than a tenfold drop + + align:start position:0% +know certainly more than a tenfold drop + + + align:start position:0% +know certainly more than a tenfold drop +in a span of just a couple of years by + + align:start position:0% +in a span of just a couple of years by + + + align:start position:0% +in a span of just a couple of years by +showing the need and the economies of + + align:start position:0% +showing the need and the economies of + + + align:start position:0% +showing the need and the economies of +scale and what's interesting with drug + + align:start position:0% +scale and what's interesting with drug + + + align:start position:0% +scale and what's interesting with drug +resistant TV is none of the drugs are + + align:start position:0% +resistant TV is none of the drugs are + + + align:start position:0% +resistant TV is none of the drugs are +even on + + align:start position:0% +even on + + + align:start position:0% +even on +patents right so it wasn't even a patent + + align:start position:0% +patents right so it wasn't even a patent + + + align:start position:0% +patents right so it wasn't even a patent +issue it was just a supply and demand + + align:start position:0% +issue it was just a supply and demand + + + align:start position:0% +issue it was just a supply and demand +issue we showed the demand was there and + + align:start position:0% +issue we showed the demand was there and + + + align:start position:0% +issue we showed the demand was there and +then of course this was tied with + + align:start position:0% +then of course this was tied with + + + align:start position:0% +then of course this was tied with +advocacy for more money for epidemic + + align:start position:0% +advocacy for more money for epidemic + + + align:start position:0% +advocacy for more money for epidemic +diseases and the global fund to fight + + align:start position:0% +diseases and the global fund to fight + + + align:start position:0% +diseases and the global fund to fight +AIDS TB and malaria provides the + + align:start position:0% +AIDS TB and malaria provides the + + + align:start position:0% +AIDS TB and malaria provides the +majority of money to countries to treat + + align:start position:0% +majority of money to countries to treat + + + align:start position:0% +majority of money to countries to treat +Pro resistant TV today so again just + + align:start position:0% +Pro resistant TV today so again just + + + align:start position:0% +Pro resistant TV today so again just +sort of talking about so you know we + + align:start position:0% +sort of talking about so you know we + + + align:start position:0% +sort of talking about so you know we +have this kind of crazy idea that wow we + + align:start position:0% +have this kind of crazy idea that wow we + + + align:start position:0% +have this kind of crazy idea that wow we +we won this fight we were this tiny + + align:start position:0% +we won this fight we were this tiny + + + align:start position:0% +we won this fight we were this tiny +little like Don keot size organization + + align:start position:0% +little like Don keot size organization + + + align:start position:0% +little like Don keot size organization +taking on the wh and we won actually we + + align:start position:0% +taking on the wh and we won actually we + + + align:start position:0% +taking on the wh and we won actually we +won saying this treatment should be + + align:start position:0% +won saying this treatment should be + + + align:start position:0% +won saying this treatment should be +available to people in resource for + + align:start position:0% +available to people in resource for + + + align:start position:0% +available to people in resource for +settings now I don't think it was that + + align:start position:0% +settings now I don't think it was that + + + align:start position:0% +settings now I don't think it was that +big of a success because in fact this is + + align:start position:0% +big of a success because in fact this is + + + align:start position:0% +big of a success because in fact this is +a more complicated disease to treat than + + align:start position:0% +a more complicated disease to treat than + + + align:start position:0% +a more complicated disease to treat than +HIV to be frank and the drugs still + + align:start position:0% +HIV to be frank and the drugs still + + + align:start position:0% +HIV to be frank and the drugs still +haven't come down enough in price and + + align:start position:0% +haven't come down enough in price and + + + align:start position:0% +haven't come down enough in price and +the accessibility of this treatment is + + align:start position:0% +the accessibility of this treatment is + + + align:start position:0% +the accessibility of this treatment is +not what I would like it to be relevant + + align:start position:0% +not what I would like it to be relevant + + + align:start position:0% +not what I would like it to be relevant +but it gave us sort of this sense that + + align:start position:0% +but it gave us sort of this sense that + + + align:start position:0% +but it gave us sort of this sense that +maybe these questions are solvable if we + + align:start position:0% +maybe these questions are solvable if we + + + align:start position:0% +maybe these questions are solvable if we +do show the burden of disease show the + + align:start position:0% +do show the burden of disease show the + + + align:start position:0% +do show the burden of disease show the +feasibility of this develop Pro calls + + align:start position:0% +feasibility of this develop Pro calls + + + align:start position:0% +feasibility of this develop Pro calls +for it to be sort of scaled up and then + + align:start position:0% +for it to be sort of scaled up and then + + + align:start position:0% +for it to be sort of scaled up and then +document that and and that advocacy can + + align:start position:0% +document that and and that advocacy can + + + align:start position:0% +document that and and that advocacy can +be connected with that kind of chain of + + align:start position:0% +be connected with that kind of chain of + + + align:start position:0% +be connected with that kind of chain of +scholarship and so for me what I'm + + align:start position:0% +scholarship and so for me what I'm + + + align:start position:0% +scholarship and so for me what I'm +talking about now a lot is a new kind of + + align:start position:0% +talking about now a lot is a new kind of + + + align:start position:0% +talking about now a lot is a new kind of +translational research because we think + + align:start position:0% +translational research because we think + + + align:start position:0% +translational research because we think +of translational research as bench to + + align:start position:0% +of translational research as bench to + + + align:start position:0% +of translational research as bench to +bedside or sometimes like bedside to + + align:start position:0% +bedside or sometimes like bedside to + + + align:start position:0% +bedside or sometimes like bedside to +adaptation in the US but nobody really + + align:start position:0% +adaptation in the US but nobody really + + + align:start position:0% +adaptation in the US but nobody really +thinks of translational research is + + align:start position:0% +thinks of translational research is + + + align:start position:0% +thinks of translational research is +something that we know works but we have + + align:start position:0% +something that we know works but we have + + + align:start position:0% +something that we know works but we have +to get it to the majority of the world + + align:start position:0% +to get it to the majority of the world + + + align:start position:0% +to get it to the majority of the world +and and there is a needed scholarship + + align:start position:0% +and and there is a needed scholarship + + + align:start position:0% +and and there is a needed scholarship +and understanding of how you develop + + align:start position:0% +and understanding of how you develop + + + align:start position:0% +and understanding of how you develop +systems to do this so about the same + + align:start position:0% +systems to do this so about the same + + + align:start position:0% +systems to do this so about the same +time about 98 a similar thing happened + + align:start position:0% +time about 98 a similar thing happened + + + align:start position:0% +time about 98 a similar thing happened +in Haiti which is a lot of our own + + align:start position:0% +in Haiti which is a lot of our own + + + align:start position:0% +in Haiti which is a lot of our own +healthcare workers and people who lived + + align:start position:0% +healthcare workers and people who lived + + + align:start position:0% +healthcare workers and people who lived +in this little community of + + align:start position:0% +in this little community of + + + align:start position:0% +in this little community of +college and actually was an MIT + + align:start position:0% +college and actually was an MIT + + + align:start position:0% +college and actually was an MIT +underground I think or Harvard + + align:start position:0% +underground I think or Harvard + + + align:start position:0% +underground I think or Harvard +underground sanj sonj the MIT an MIT + + align:start position:0% +underground sanj sonj the MIT an MIT + + + align:start position:0% +underground sanj sonj the MIT an MIT +undergrad great guy who's an AIDS doctor + + align:start position:0% +undergrad great guy who's an AIDS doctor + + + align:start position:0% +undergrad great guy who's an AIDS doctor +now um sanj Basu who said you know I'm + + align:start position:0% +now um sanj Basu who said you know I'm + + + align:start position:0% +now um sanj Basu who said you know I'm +going to try to get some drugs for you + + align:start position:0% +going to try to get some drugs for you + + + align:start position:0% +going to try to get some drugs for you +we we thought we have to treat these + + align:start position:0% +we we thought we have to treat these + + + align:start position:0% +we we thought we have to treat these +people these are our people these are + + align:start position:0% +people these are our people these are + + + align:start position:0% +people these are our people these are +our health workers these are our friends + + align:start position:0% +our health workers these are our friends + + + align:start position:0% +our health workers these are our friends +so we started treating them with highly + + align:start position:0% +so we started treating them with highly + + + align:start position:0% +so we started treating them with highly +active anti-retro therapy which by the + + align:start position:0% +active anti-retro therapy which by the + + + align:start position:0% +active anti-retro therapy which by the +way was one of the most miraculous + + align:start position:0% +way was one of the most miraculous + + + align:start position:0% +way was one of the most miraculous +things in medicine in in the 20th + + align:start position:0% +things in medicine in in the 20th + + + align:start position:0% +things in medicine in in the 20th +century um so for people like me who + + align:start position:0% +century um so for people like me who + + + align:start position:0% +century um so for people like me who +started medical school in the in the + + align:start position:0% +started medical school in the in the + + + align:start position:0% +started medical school in the in the +peak of the AIDS epidemic and then + + align:start position:0% +peak of the AIDS epidemic and then + + + align:start position:0% +peak of the AIDS epidemic and then +suddenly in '95 we stop seeing people + + align:start position:0% +suddenly in '95 we stop seeing people + + + align:start position:0% +suddenly in '95 we stop seeing people +die you know suddenly in '95 you're + + align:start position:0% +die you know suddenly in '95 you're + + + align:start position:0% +die you know suddenly in '95 you're +invited to people's weddings and + + align:start position:0% +invited to people's weddings and + + + align:start position:0% +invited to people's weddings and +graduations instead of funerals totally + + align:start position:0% +graduations instead of funerals totally + + + align:start position:0% +graduations instead of funerals totally +change everything now I myself had + + align:start position:0% +change everything now I myself had + + + align:start position:0% +change everything now I myself had +worked in + + align:start position:0% +worked in + + + align:start position:0% +worked in +Africa before coming to Pi and I was in + + align:start position:0% +Africa before coming to Pi and I was in + + + align:start position:0% +Africa before coming to Pi and I was in +Uganda in + + align:start position:0% +Uganda in + + + align:start position:0% +Uganda in +9495 which was really Uganda was the + + align:start position:0% +9495 which was really Uganda was the + + + align:start position:0% +9495 which was really Uganda was the +epicenter of the epidemic and 9495 there + + align:start position:0% +epicenter of the epidemic and 9495 there + + + align:start position:0% +epicenter of the epidemic and 9495 there +was no treatment in the US or anywhere + + align:start position:0% +was no treatment in the US or anywhere + + + align:start position:0% +was no treatment in the US or anywhere +else in the world so the best you could + + align:start position:0% +else in the world so the best you could + + + align:start position:0% +else in the world so the best you could +do anywhere was prevention + + align:start position:0% +do anywhere was prevention + + + align:start position:0% +do anywhere was prevention +so about the the same time you know + + align:start position:0% +so about the the same time you know + + + align:start position:0% +so about the the same time you know +everybody's focused on prevention you're + + align:start position:0% +everybody's focused on prevention you're + + + align:start position:0% +everybody's focused on prevention you're +looking at that map of the global AIDS + + align:start position:0% +looking at that map of the global AIDS + + + align:start position:0% +looking at that map of the global AIDS +epidemic and they're saying we've got to + + align:start position:0% +epidemic and they're saying we've got to + + + align:start position:0% +epidemic and they're saying we've got to +do prevention prevention + + align:start position:0% +do prevention prevention + + + align:start position:0% +do prevention prevention +prevention and there was this little + + align:start position:0% +prevention and there was this little + + + align:start position:0% +prevention and there was this little +window that + + align:start position:0% +window that + + + align:start position:0% +window that +occurred um where we started to see + + align:start position:0% +occurred um where we started to see + + + align:start position:0% +occurred um where we started to see +these success of treatment so this um + + align:start position:0% +these success of treatment so this um + + + align:start position:0% +these success of treatment so this um +there are two people who've taught me + + align:start position:0% +there are two people who've taught me + + + align:start position:0% +there are two people who've taught me +more about HIV than than anyone El + + align:start position:0% +more about HIV than than anyone El + + + align:start position:0% +more about HIV than than anyone El +because I spent a lot of my life doing + + align:start position:0% +because I spent a lot of my life doing + + + align:start position:0% +because I spent a lot of my life doing +prevention I spent two years working in + + align:start position:0% +prevention I spent two years working in + + + align:start position:0% +prevention I spent two years working in +mural Uganda doing prevention um I did + + align:start position:0% +mural Uganda doing prevention um I did + + + align:start position:0% +mural Uganda doing prevention um I did +tons of HIV prevention I mean I used to + + align:start position:0% +tons of HIV prevention I mean I used to + + + align:start position:0% +tons of HIV prevention I mean I used to +I'm from an Indian family so you know + + align:start position:0% +I'm from an Indian family so you know + + + align:start position:0% +I'm from an Indian family so you know +just talking about sex is sort of not + + align:start position:0% +just talking about sex is sort of not + + + align:start position:0% +just talking about sex is sort of not +even really permitted and then I would + + align:start position:0% +even really permitted and then I would + + + align:start position:0% +even really permitted and then I would +send my dad pictures like with a box of + + align:start position:0% +send my dad pictures like with a box of + + + align:start position:0% +send my dad pictures like with a box of +6,000 condoms mared usaid say having a + + align:start position:0% +6,000 condoms mared usaid say having a + + + align:start position:0% +6,000 condoms mared usaid say having a +great time now um but there were two + + align:start position:0% +great time now um but there were two + + + align:start position:0% +great time now um but there were two +people this little + + align:start position:0% +people this little + + + align:start position:0% +people this little +girl who's + + align:start position:0% +girl who's + + + align:start position:0% +girl who's +nine who's the head of a + + align:start position:0% +nine who's the head of a + + + align:start position:0% +nine who's the head of a +family these are her siblings who she is + + align:start position:0% +family these are her siblings who she is + + + align:start position:0% +family these are her siblings who she is +raising a + + align:start position:0% +raising a + + + align:start position:0% +raising a +loone okay this was a not uncommon + + align:start position:0% +loone okay this was a not uncommon + + + align:start position:0% +loone okay this was a not uncommon +scenario in subsaharan Africa + + align:start position:0% +scenario in subsaharan Africa + + + align:start position:0% +scenario in subsaharan Africa +particularly at the height of + + align:start position:0% +particularly at the height of + + + align:start position:0% +particularly at the height of +AES child headed + + align:start position:0% +AES child headed + + + align:start position:0% +AES child headed +household nine-year-old girl okay and + + align:start position:0% +household nine-year-old girl okay and + + + align:start position:0% +household nine-year-old girl okay and +this + + align:start position:0% +this + + + align:start position:0% +this +guy you know who this guy is the guy who + + align:start position:0% +guy you know who this guy is the guy who + + + align:start position:0% +guy you know who this guy is the guy who +snorted his father's ashes right so why + + align:start position:0% +snorted his father's ashes right so why + + + align:start position:0% +snorted his father's ashes right so why +Keith Richards you know he's rolling + + align:start position:0% +Keith Richards you know he's rolling + + + align:start position:0% +Keith Richards you know he's rolling +stone just wrote a really kind of crazy + + align:start position:0% +stone just wrote a really kind of crazy + + + align:start position:0% +stone just wrote a really kind of crazy +book that like has supported all my + + align:start position:0% +book that like has supported all my + + + align:start position:0% +book that like has supported all my +hypothesis of talking about him all + + align:start position:0% +hypothesis of talking about him all + + + align:start position:0% +hypothesis of talking about him all +these years + + align:start position:0% +these years + + + align:start position:0% +these years +so does Keith Richards have + + align:start position:0% +so does Keith Richards have + + + align:start position:0% +so does Keith Richards have +HIV no no he doesn't so here's the + + align:start position:0% +HIV no no he doesn't so here's the + + + align:start position:0% +HIV no no he doesn't so here's the +contrast AG totally promiscuous drug + + align:start position:0% +contrast AG totally promiscuous drug + + + align:start position:0% +contrast AG totally promiscuous drug +addicted wacko rock and roll + + align:start position:0% +addicted wacko rock and roll + + + align:start position:0% +addicted wacko rock and roll +star + + align:start position:0% +star + + + align:start position:0% +star +versus girl under 15 who's an orphan in + + align:start position:0% +versus girl under 15 who's an orphan in + + + align:start position:0% +versus girl under 15 who's an orphan in +the head of the household who + + align:start position:0% +the head of the household who + + + align:start position:0% +the head of the household who +statistically had more risk of having + + align:start position:0% +statistically had more risk of having + + + align:start position:0% +statistically had more risk of having +HIV that little + + align:start position:0% +HIV that little + + + align:start position:0% +HIV that little +girl that little girl so while + + align:start position:0% +girl that little girl so while + + + align:start position:0% +girl that little girl so while +everyone's telling us you've got to do + + align:start position:0% +everyone's telling us you've got to do + + + align:start position:0% +everyone's telling us you've got to do +prevention and prevention we're like + + align:start position:0% +prevention and prevention we're like + + + align:start position:0% +prevention and prevention we're like +this is not about + + align:start position:0% +this is not about + + + align:start position:0% +this is not about +Behavior like why is this little girl at + + align:start position:0% +Behavior like why is this little girl at + + + align:start position:0% +Behavior like why is this little girl at +risk for + + align:start position:0% +risk for + + + align:start position:0% +risk for +HIV cuz she's having so much + + align:start position:0% + + + + align:start position:0% + +fun just whing around I mean why why is + + align:start position:0% +fun just whing around I mean why why is + + + align:start position:0% +fun just whing around I mean why why is +that little girl she's more vulnerable + + align:start position:0% +that little girl she's more vulnerable + + + align:start position:0% +that little girl she's more vulnerable +what what makes her vulnerable + + align:start position:0% +what what makes her vulnerable + + + align:start position:0% +what what makes her vulnerable +vulnerable to what vulner + + align:start position:0% +vulnerable to what vulner + + + align:start position:0% +vulnerable to what vulner +to social context in settings probably + + align:start position:0% +to social context in settings probably + + + align:start position:0% +to social context in settings probably +the it's an embedment of several uh + + align:start position:0% +the it's an embedment of several uh + + + align:start position:0% +the it's an embedment of several uh +social issues for developing countries + + align:start position:0% +social issues for developing countries + + + align:start position:0% +social issues for developing countries +like gender issues + + align:start position:0% +like gender issues + + + align:start position:0% +like gender issues +like like uh and you guys yeah exactly + + align:start position:0% +like like uh and you guys yeah exactly + + + align:start position:0% +like like uh and you guys yeah exactly +and you guys are lucky cuz in this + + align:start position:0% +and you guys are lucky cuz in this + + + align:start position:0% +and you guys are lucky cuz in this +little class here it's a pretty diverse + + align:start position:0% +little class here it's a pretty diverse + + + align:start position:0% +little class here it's a pretty diverse +group but I used to talk about this 10 + + align:start position:0% +group but I used to talk about this 10 + + + align:start position:0% +group but I used to talk about this 10 +years ago and I tell you the Harvard + + align:start position:0% +years ago and I tell you the Harvard + + + align:start position:0% +years ago and I tell you the Harvard +students you know the medical students + + align:start position:0% +students you know the medical students + + + align:start position:0% +students you know the medical students +they did not get it at all they really + + align:start position:0% +they did not get it at all they really + + + align:start position:0% +they did not get it at all they really +didn't get it I think the ethos about + + align:start position:0% +didn't get it I think the ethos about + + + align:start position:0% +didn't get it I think the ethos about +this has really changed in 10 years um + + align:start position:0% +this has really changed in 10 years um + + + align:start position:0% +this has really changed in 10 years um +but it is in fact the social Factor so + + align:start position:0% +but it is in fact the social Factor so + + + align:start position:0% +but it is in fact the social Factor so +not to say that prevention doesn't work + + align:start position:0% +not to say that prevention doesn't work + + + align:start position:0% +not to say that prevention doesn't work +but what we documented using work from + + align:start position:0% +but what we documented using work from + + + align:start position:0% +but what we documented using work from +Haiti using work from other places was + + align:start position:0% +Haiti using work from other places was + + + align:start position:0% +Haiti using work from other places was +that prevention is absolutely + + align:start position:0% +that prevention is absolutely + + + align:start position:0% +that prevention is absolutely +insufficient for dealing with this + + align:start position:0% +insufficient for dealing with this + + + align:start position:0% +insufficient for dealing with this +epidemic because the only prevention we + + align:start position:0% +epidemic because the only prevention we + + + align:start position:0% +epidemic because the only prevention we +talk about is individual Behavior change + + align:start position:0% +talk about is individual Behavior change + + + align:start position:0% +talk about is individual Behavior change +and if you are a 9-year-old head of a + + align:start position:0% +and if you are a 9-year-old head of a + + + align:start position:0% +and if you are a 9-year-old head of a +household your individual behavior is + + align:start position:0% +household your individual behavior is + + + align:start position:0% +household your individual behavior is +not what's putting you at risk it's the + + align:start position:0% +not what's putting you at risk it's the + + + align:start position:0% +not what's putting you at risk it's the +risk of predators it's the fact that you + + align:start position:0% +risk of predators it's the fact that you + + + align:start position:0% +risk of predators it's the fact that you +have no money to support your little + + align:start position:0% +have no money to support your little + + + align:start position:0% +have no money to support your little +siblings it's the fact that maybe you + + align:start position:0% +siblings it's the fact that maybe you + + + align:start position:0% +siblings it's the fact that maybe you +know one of the things I learned in + + align:start position:0% +know one of the things I learned in + + + align:start position:0% +know one of the things I learned in +Uganda I don't think I have this picture + + align:start position:0% +Uganda I don't think I have this picture + + + align:start position:0% +Uganda I don't think I have this picture +but one of my favorite um sort of my my + + align:start position:0% +but one of my favorite um sort of my my + + + align:start position:0% +but one of my favorite um sort of my my +biggest lesson in my life was working + + align:start position:0% +biggest lesson in my life was working + + + align:start position:0% +biggest lesson in my life was working +with these kids 11 to 14 years + + align:start position:0% +with these kids 11 to 14 years + + + align:start position:0% +with these kids 11 to 14 years +old and we taught them about how AIDS + + align:start position:0% +old and we taught them about how AIDS + + + align:start position:0% +old and we taught them about how AIDS +was prevented how it was transmitted how + + align:start position:0% +was prevented how it was transmitted how + + + align:start position:0% +was prevented how it was transmitted how +they could protect themselves Etc and + + align:start position:0% +they could protect themselves Etc and + + + align:start position:0% +they could protect themselves Etc and +when we got to asking them okay what are + + align:start position:0% +when we got to asking them okay what are + + + align:start position:0% +when we got to asking them okay what are +your risk factors and this was like an + + align:start position:0% +your risk factors and this was like an + + + align:start position:0% +your risk factors and this was like an +intensive educational course for peer + + align:start position:0% +intensive educational course for peer + + + align:start position:0% +intensive educational course for peer +Educators it was two weeks they'd all be + + align:start position:0% +Educators it was two weeks they'd all be + + + align:start position:0% +Educators it was two weeks they'd all be +together with their teachers and + + align:start position:0% +together with their teachers and + + + align:start position:0% +together with their teachers and +everything we'd ask them what's your + + align:start position:0% +everything we'd ask them what's your + + + align:start position:0% +everything we'd ask them what's your +main risk factor and these kids said + + align:start position:0% +main risk factor and these kids said + + + align:start position:0% +main risk factor and these kids said +poverty and for me I could have said oh + + align:start position:0% +poverty and for me I could have said oh + + + align:start position:0% +poverty and for me I could have said oh +they're ignorant they don't get what I + + align:start position:0% +they're ignorant they don't get what I + + + align:start position:0% +they're ignorant they don't get what I +just was trying to teach them but + + align:start position:0% +just was trying to teach them but + + + align:start position:0% +just was trying to teach them but +instead I said oh they're teaching me + + align:start position:0% +instead I said oh they're teaching me + + + align:start position:0% +instead I said oh they're teaching me +something and particularly for girls + + align:start position:0% +something and particularly for girls + + + align:start position:0% +something and particularly for girls +what they said is look I'm I know I'm an + + align:start position:0% +what they said is look I'm I know I'm an + + + align:start position:0% +what they said is look I'm I know I'm an +orphan + + align:start position:0% +orphan + + + align:start position:0% +orphan +already and if I don't ever learn to + + align:start position:0% +already and if I don't ever learn to + + + align:start position:0% +already and if I don't ever learn to +read and write I will definitely get + + align:start position:0% +read and write I will definitely get + + + align:start position:0% +read and write I will definitely get +AIDS I mean in the community I lived in + + align:start position:0% +AIDS I mean in the community I lived in + + + align:start position:0% +AIDS I mean in the community I lived in +35% of people were HIV + + align:start position:0% +35% of people were HIV + + + align:start position:0% +35% of people were HIV +infected okay so most of these kids new + + align:start position:0% +infected okay so most of these kids new + + + align:start position:0% +infected okay so most of these kids new +people had lost People sisters brothers + + align:start position:0% +people had lost People sisters brothers + + + align:start position:0% +people had lost People sisters brothers +Aunts Uncles parents so they knew that + + align:start position:0% +Aunts Uncles parents so they knew that + + + align:start position:0% +Aunts Uncles parents so they knew that +if if they as an orphan didn't know how + + align:start position:0% +if if they as an orphan didn't know how + + + align:start position:0% +if if they as an orphan didn't know how +to read and write what is the future for + + align:start position:0% +to read and write what is the future for + + + align:start position:0% +to read and write what is the future for +them to be a servant to be a domestic + + align:start position:0% +them to be a servant to be a domestic + + + align:start position:0% +them to be a servant to be a domestic +servant in which case they have + + align:start position:0% +servant in which case they have + + + align:start position:0% +servant in which case they have +absolutely no Neal right they'll be + + align:start position:0% +absolutely no Neal right they'll be + + + align:start position:0% +absolutely no Neal right they'll be +raped they'll be abused they'll be + + align:start position:0% +raped they'll be abused they'll be + + + align:start position:0% +raped they'll be abused they'll be +violated but if there's some nice man in + + align:start position:0% +violated but if there's some nice man in + + + align:start position:0% +violated but if there's some nice man in +the community who will pay for them to + + align:start position:0% +the community who will pay for them to + + + align:start position:0% +the community who will pay for them to +go to school and maybe they'll learn to + + align:start position:0% +go to school and maybe they'll learn to + + + align:start position:0% +go to school and maybe they'll learn to +read and write maybe they can make + + align:start position:0% +read and write maybe they can make + + + align:start position:0% +read and write maybe they can make +something of themselves and if that man + + align:start position:0% +something of themselves and if that man + + + align:start position:0% +something of themselves and if that man +wants to have sexual + + align:start position:0% +wants to have sexual + + + align:start position:0% +wants to have sexual +relationship it's not a bad choice right + + align:start position:0% +relationship it's not a bad choice right + + + align:start position:0% +relationship it's not a bad choice right +I mean it's not a choice you'd want + + align:start position:0% +I mean it's not a choice you'd want + + + align:start position:0% +I mean it's not a choice you'd want +anyone to have to make but in comparison + + align:start position:0% +anyone to have to make but in comparison + + + align:start position:0% +anyone to have to make but in comparison +these girls were actually choosing + + align:start position:0% +these girls were actually choosing + + + align:start position:0% +these girls were actually choosing +probably a safer option but it's sick + + align:start position:0% +probably a safer option but it's sick + + + align:start position:0% +probably a safer option but it's sick +it's sick it's sick because school isn't + + align:start position:0% +it's sick it's sick because school isn't + + + align:start position:0% +it's sick it's sick because school isn't +free because all of these things we + + align:start position:0% +free because all of these things we + + + align:start position:0% +free because all of these things we +talked about at the beginning what we + + align:start position:0% +talked about at the beginning what we + + + align:start position:0% +talked about at the beginning what we +need to do is change the social context + + align:start position:0% +need to do is change the social context + + + align:start position:0% +need to do is change the social context +you know that school becomes a basic + + align:start position:0% +you know that school becomes a basic + + + align:start position:0% +you know that school becomes a basic +right that you know because school fees + + align:start position:0% +right that you know because school fees + + + align:start position:0% +right that you know because school fees +have been a huge issue for young girls + + align:start position:0% +have been a huge issue for young girls + + + align:start position:0% +have been a huge issue for young girls +and boys particularly girls in in poor + + align:start position:0% +and boys particularly girls in in poor + + + align:start position:0% +and boys particularly girls in in poor +countries that put them at risk for HIV + + align:start position:0% +countries that put them at risk for HIV + + + align:start position:0% +countries that put them at risk for HIV +and so they're trying to better + + align:start position:0% +and so they're trying to better + + + align:start position:0% +and so they're trying to better +themselves you know what I mean so you + + align:start position:0% +themselves you know what I mean so you + + + align:start position:0% +themselves you know what I mean so you +know we we wrote a paper and it got + + align:start position:0% +know we we wrote a paper and it got + + + align:start position:0% +know we we wrote a paper and it got +published in the British medical journal + + align:start position:0% +published in the British medical journal + + + align:start position:0% +published in the British medical journal +saying you know prevention isn't + + align:start position:0% +saying you know prevention isn't + + + align:start position:0% +saying you know prevention isn't +sufficient now look at when we wrote + + align:start position:0% +sufficient now look at when we wrote + + + align:start position:0% +sufficient now look at when we wrote +this in 2003 in 2003 there was still + + align:start position:0% +this in 2003 in 2003 there was still + + + align:start position:0% +this in 2003 in 2003 there was still +almost no movement just starting to + + align:start position:0% +almost no movement just starting to + + + align:start position:0% +almost no movement just starting to +provide treatment for + + align:start position:0% +provide treatment for + + + align:start position:0% +provide treatment for +HIV remember I said the treatment came + + align:start position:0% +HIV remember I said the treatment came + + + align:start position:0% +HIV remember I said the treatment came +about in + + align:start position:0% +about in + + + align:start position:0% +about in +95 so you have eight years of + + align:start position:0% +95 so you have eight years of + + + align:start position:0% +95 so you have eight years of +essentially 3 to six million people + + align:start position:0% +essentially 3 to six million people + + + align:start position:0% +essentially 3 to six million people +dying per year of a treatable disease + + align:start position:0% +dying per year of a treatable disease + + + align:start position:0% +dying per year of a treatable disease +you know so we we published that we we + + align:start position:0% +you know so we we published that we we + + + align:start position:0% +you know so we we published that we we +published something that was + + align:start position:0% +published something that was + + + align:start position:0% +published something that was +oxymoronically called the Harvard + + align:start position:0% +oxymoronically called the Harvard + + + align:start position:0% +oxymoronically called the Harvard +consensus statement because you can't + + align:start position:0% +consensus statement because you can't + + + align:start position:0% +consensus statement because you can't +have a consensus at Harvard it's + + align:start position:0% +have a consensus at Harvard it's + + + align:start position:0% +have a consensus at Harvard it's +actually illegal um and we did that for + + align:start position:0% +actually illegal um and we did that for + + + align:start position:0% +actually illegal um and we did that for +one reason only to show this + + align:start position:0% +one reason only to show this + + + align:start position:0% +one reason only to show this +graph which was showing that little red + + align:start position:0% +graph which was showing that little red + + + align:start position:0% +graph which was showing that little red +line was the massive which seemed to us + + align:start position:0% +line was the massive which seemed to us + + + align:start position:0% +line was the massive which seemed to us +massive change in death + + align:start position:0% +massive change in death + + + align:start position:0% +massive change in death +rate but when you put it on the scale of + + align:start position:0% +rate but when you put it on the scale of + + + align:start position:0% +rate but when you put it on the scale of +what was happening for the untreated + + align:start position:0% +what was happening for the untreated + + + align:start position:0% +what was happening for the untreated +epidemic in sub Subs Africa it just like + + align:start position:0% +epidemic in sub Subs Africa it just like + + + align:start position:0% +epidemic in sub Subs Africa it just like +vanishes in significance + + align:start position:0% +vanishes in significance + + + align:start position:0% +vanishes in significance +so we really said look we as Harvard + + align:start position:0% +so we really said look we as Harvard + + + align:start position:0% +so we really said look we as Harvard +faculty members would like to see + + align:start position:0% +faculty members would like to see + + + align:start position:0% +faculty members would like to see +treatment become part of the + + align:start position:0% +treatment become part of the + + + align:start position:0% +treatment become part of the +debate and we published it in a stupid + + align:start position:0% +debate and we published it in a stupid + + + align:start position:0% +debate and we published it in a stupid +Journal that nobody reads called topics + + align:start position:0% +Journal that nobody reads called topics + + + align:start position:0% +Journal that nobody reads called topics +in HIV medicine and it went viral before + + align:start position:0% +in HIV medicine and it went viral before + + + align:start position:0% +in HIV medicine and it went viral before +things could even go viral and went + + align:start position:0% +things could even go viral and went + + + align:start position:0% +things could even go viral and went +viral who made it viral who do you think + + align:start position:0% +viral who made it viral who do you think + + + align:start position:0% +viral who made it viral who do you think +made it + + align:start position:0% +made it + + + align:start position:0% +made it +viral was before YouTube believe it or + + align:start position:0% +viral was before YouTube believe it or + + + align:start position:0% +viral was before YouTube believe it or +not it wasn't academics I'll give you a + + align:start position:0% +not it wasn't academics I'll give you a + + + align:start position:0% +not it wasn't academics I'll give you a +hint huh patience patience activism and + + align:start position:0% +hint huh patience patience activism and + + + align:start position:0% +hint huh patience patience activism and +and to me this is what has really made a + + align:start position:0% +and to me this is what has really made a + + + align:start position:0% +and to me this is what has really made a +big difference between HIV and other + + align:start position:0% +big difference between HIV and other + + + align:start position:0% +big difference between HIV and other +problems we face and I I would like us + + align:start position:0% +problems we face and I I would like us + + + align:start position:0% +problems we face and I I would like us +all to learn how as as scholars in this + + align:start position:0% +all to learn how as as scholars in this + + + align:start position:0% +all to learn how as as scholars in this +work we can we can harness that activism + + align:start position:0% +work we can we can harness that activism + + + align:start position:0% +work we can we can harness that activism +um toward other things because it was + + align:start position:0% +um toward other things because it was + + + align:start position:0% +um toward other things because it was +the patients people living with AIDS who + + align:start position:0% +the patients people living with AIDS who + + + align:start position:0% +the patients people living with AIDS who +were activists in the US in Europe and + + align:start position:0% +were activists in the US in Europe and + + + align:start position:0% +were activists in the US in Europe and +in the south in Uganda in South Africa + + align:start position:0% +in the south in Uganda in South Africa + + + align:start position:0% +in the south in Uganda in South Africa +and Zambia who really forced this stuff + + align:start position:0% +and Zambia who really forced this stuff + + + align:start position:0% +and Zambia who really forced this stuff +down the throats of the politicians and + + align:start position:0% +down the throats of the politicians and + + + align:start position:0% +down the throats of the politicians and +policy + + align:start position:0% +policy + + + align:start position:0% +policy +makers um so who is your audience you + + align:start position:0% +makers um so who is your audience you + + + align:start position:0% +makers um so who is your audience you +know so you know we're dealing with + + align:start position:0% +know so you know we're dealing with + + + align:start position:0% +know so you know we're dealing with +these things like it's too hard I mean + + align:start position:0% +these things like it's too hard I mean + + + align:start position:0% +these things like it's too hard I mean +the head of + + align:start position:0% +the head of + + + align:start position:0% +the head of +usid who you guys live in Boston so + + align:start position:0% +usid who you guys live in Boston so + + + align:start position:0% +usid who you guys live in Boston so +you'll know is the same man that brought + + align:start position:0% +you'll know is the same man that brought + + + align:start position:0% +you'll know is the same man that brought +us the big + + align:start position:0% +us the big + + + align:start position:0% +us the big +dig you're a little too young okay um + + align:start position:0% +dig you're a little too young okay um + + + align:start position:0% +dig you're a little too young okay um +Andrew naio said this many PE this is + + align:start position:0% +Andrew naio said this many PE this is + + + align:start position:0% +Andrew naio said this many PE this is +why we can't do AIDS treatment many + + align:start position:0% +why we can't do AIDS treatment many + + + align:start position:0% +why we can't do AIDS treatment many +people in Africa there are some Africans + + align:start position:0% +people in Africa there are some Africans + + + align:start position:0% +people in Africa there are some Africans +here right have never seen a clock or a + + align:start position:0% +here right have never seen a clock or a + + + align:start position:0% +here right have never seen a clock or a +watch in their entire lives and if you + + align:start position:0% +watch in their entire lives and if you + + + align:start position:0% +watch in their entire lives and if you +say 1:00 in the afternoon they don't + + align:start position:0% +say 1:00 in the afternoon they don't + + + align:start position:0% +say 1:00 in the afternoon they don't +know what you're talking + + align:start position:0% +know what you're talking + + + align:start position:0% +know what you're talking +about 2000 in the New York + + align:start position:0% +about 2000 in the New York + + + align:start position:0% +about 2000 in the New York +Times 200000 the year + + align:start position:0% +Times 200000 the year + + + align:start position:0% +Times 200000 the year +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +2000 what is this it's a + + align:start position:0% + + + + align:start position:0% + +lot you think about this is the man who + + align:start position:0% +lot you think about this is the man who + + + align:start position:0% +lot you think about this is the man who +holds the keys to all us + + align:start position:0% +holds the keys to all us + + + align:start position:0% +holds the keys to all us +assistants right crazy so what do you do + + align:start position:0% +assistants right crazy so what do you do + + + align:start position:0% +assistants right crazy so what do you do +to combat that I mean you could protest + + align:start position:0% +to combat that I mean you could protest + + + align:start position:0% +to combat that I mean you could protest +and that certainly happened but the + + align:start position:0% +and that certainly happened but the + + + align:start position:0% +and that certainly happened but the +other thing you could do if you're a + + align:start position:0% +other thing you could do if you're a + + + align:start position:0% +other thing you could do if you're a +geek you know is you can start writing + + align:start position:0% +geek you know is you can start writing + + + align:start position:0% +geek you know is you can start writing +articles and papers and so we wrote our + + align:start position:0% +articles and papers and so we wrote our + + + align:start position:0% +articles and papers and so we wrote our +first scholarly article about HIV + + align:start position:0% +first scholarly article about HIV + + + align:start position:0% +first scholarly article about HIV +treatment in rural Haiti with just 60 + + align:start position:0% +treatment in rural Haiti with just 60 + + + align:start position:0% +treatment in rural Haiti with just 60 +patients and we said we had no Labs we + + align:start position:0% +patients and we said we had no Labs we + + + align:start position:0% +patients and we said we had no Labs we +had no v no cob nothing and we said you + + align:start position:0% +had no v no cob nothing and we said you + + + align:start position:0% +had no v no cob nothing and we said you +know but the patients didn't die and + + align:start position:0% +know but the patients didn't die and + + + align:start position:0% +know but the patients didn't die and +they went back to their + + align:start position:0% +they went back to their + + + align:start position:0% +they went back to their +families um and you know I was kind of + + align:start position:0% +families um and you know I was kind of + + + align:start position:0% +families um and you know I was kind of +excited this was like the first paper I + + align:start position:0% +excited this was like the first paper I + + + align:start position:0% +excited this was like the first paper I +ever wrote and you know this was the + + align:start position:0% +ever wrote and you know this was the + + + align:start position:0% +ever wrote and you know this was the +most universally hated paper although + + align:start position:0% +most universally hated paper although + + + align:start position:0% +most universally hated paper although +it's by the way of the things I've + + align:start position:0% +it's by the way of the things I've + + + align:start position:0% +it's by the way of the things I've +written is the by far the most cited but + + align:start position:0% +written is the by far the most cited but + + + align:start position:0% +written is the by far the most cited but +Public Health people medical people said + + align:start position:0% +Public Health people medical people said + + + align:start position:0% +Public Health people medical people said +this is ridiculous in fact they invited + + align:start position:0% +this is ridiculous in fact they invited + + + align:start position:0% +this is ridiculous in fact they invited +us to write a second article for the wh + + align:start position:0% +us to write a second article for the wh + + + align:start position:0% +us to write a second article for the wh +bulletin is uh they have a feature + + align:start position:0% +bulletin is uh they have a feature + + + align:start position:0% +bulletin is uh they have a feature +called the round table which is like um + + align:start position:0% +called the round table which is like um + + + align:start position:0% +called the round table which is like um +morbidity mortality around so you write + + align:start position:0% +morbidity mortality around so you write + + + align:start position:0% +morbidity mortality around so you write +this thing people just make fun of you + + align:start position:0% +this thing people just make fun of you + + + align:start position:0% +this thing people just make fun of you +so we're like okay we can do that um and + + align:start position:0% +so we're like okay we can do that um and + + + align:start position:0% +so we're like okay we can do that um and +they Mak in making fun of us they said + + align:start position:0% +they Mak in making fun of us they said + + + align:start position:0% +they Mak in making fun of us they said +this is silly this is gold plated this + + align:start position:0% +this is silly this is gold plated this + + + align:start position:0% +this is silly this is gold plated this +is why what was the deal by the way + + align:start position:0% +is why what was the deal by the way + + + align:start position:0% +is why what was the deal by the way +activists were jumping up and down + + align:start position:0% +activists were jumping up and down + + + align:start position:0% +activists were jumping up and down +yeah maybe they want to believe it this + + align:start position:0% +yeah maybe they want to believe it this + + + align:start position:0% +yeah maybe they want to believe it this +is + + align:start position:0% +is + + + align:start position:0% +is +actually happening why wouldn't they + + align:start position:0% +actually happening why wouldn't they + + + align:start position:0% +actually happening why wouldn't they +want I mean you know it's like kind of + + align:start position:0% +want I mean you know it's like kind of + + + align:start position:0% +want I mean you know it's like kind of +like the see no evil like you're right + + align:start position:0% +like the see no evil like you're right + + + align:start position:0% +like the see no evil like you're right +it make it more complex it makes it it's + + align:start position:0% +it make it more complex it makes it it's + + + align:start position:0% +it make it more complex it makes it it's +like mdtv there can't must be the + + align:start position:0% +like mdtv there can't must be the + + + align:start position:0% +like mdtv there can't must be the +patient B at least mdtv someone could be + + align:start position:0% +patient B at least mdtv someone could be + + + align:start position:0% +patient B at least mdtv someone could be +blamed but for this you know so how + + align:start position:0% +blamed but for this you know so how + + + align:start position:0% +blamed but for this you know so how +could they don't believe it what what's + + align:start position:0% +could they don't believe it what what's + + + align:start position:0% +could they don't believe it what what's +the critique you get in medicine or in + + align:start position:0% +the critique you get in medicine or in + + + align:start position:0% +the critique you get in medicine or in +science if people don't believe + + align:start position:0% +science if people don't believe + + + align:start position:0% +science if people don't believe +it not a good study not controlled not + + align:start position:0% +it not a good study not controlled not + + + align:start position:0% +it not a good study not controlled not +randomized you need more data right so + + align:start position:0% +randomized you need more data right so + + + align:start position:0% +randomized you need more data right so +that was all that was there what else + + align:start position:0% +that was all that was there what else + + + align:start position:0% +that was all that was there what else +why + + align:start position:0% + + + + align:start position:0% + +else like you said just 60 you too small + + align:start position:0% +else like you said just 60 you too small + + + align:start position:0% +else like you said just 60 you too small +all you know and by the way at this time + + align:start position:0% +all you know and by the way at this time + + + align:start position:0% +all you know and by the way at this time +in + + align:start position:0% +in + + + align:start position:0% +in +2001 paper after paper after paper you + + align:start position:0% +2001 paper after paper after paper you + + + align:start position:0% +2001 paper after paper after paper you +can look hundreds of papers were being + + align:start position:0% +can look hundreds of papers were being + + + align:start position:0% +can look hundreds of papers were being +published every year about the natural + + align:start position:0% +published every year about the natural + + + align:start position:0% +published every year about the natural +history of untreated HIV infection in + + align:start position:0% +history of untreated HIV infection in + + + align:start position:0% +history of untreated HIV infection in +Africa oh in Nigeria people die of AIDS + + align:start position:0% +Africa oh in Nigeria people die of AIDS + + + align:start position:0% +Africa oh in Nigeria people die of AIDS +too oh in South Africa people die of a + + align:start position:0% +too oh in South Africa people die of a + + + align:start position:0% +too oh in South Africa people die of a +too oh and Zia look at this people die I + + align:start position:0% +too oh and Zia look at this people die I + + + align:start position:0% +too oh and Zia look at this people die I +mean this and nobody's bad than I + + align:start position:0% +mean this and nobody's bad than I + + + align:start position:0% +mean this and nobody's bad than I +right and we publish this and we're kind + + align:start position:0% +right and we publish this and we're kind + + + align:start position:0% +right and we publish this and we're kind +of totally beaten up by what else so + + align:start position:0% +of totally beaten up by what else so + + + align:start position:0% +of totally beaten up by what else so +it's like too small non + + align:start position:0% + + + + align:start position:0% + +scientific it wasn't even publish in + + align:start position:0% +scientific it wasn't even publish in + + + align:start position:0% +scientific it wasn't even publish in +like a research thing it's publish in + + align:start position:0% +like a research thing it's publish in + + + align:start position:0% +like a research thing it's publish in +Viewpoint this is our Viewpoint in the + + align:start position:0% + + + + align:start position:0% + +L what so why else were people so + + align:start position:0% +L what so why else were people so + + + align:start position:0% +L what so why else were people so +critical yeah if that was scalable not + + align:start position:0% +critical yeah if that was scalable not + + + align:start position:0% +critical yeah if that was scalable not +scalable not sustainable you're doing + + align:start position:0% +scalable not sustainable you're doing + + + align:start position:0% +scalable not sustainable you're doing +something so + + align:start position:0% +something so + + + align:start position:0% +something so +so what do you say to that is that + + align:start position:0% +so what do you say to that is that + + + align:start position:0% +so what do you say to that is that +legitimate you can say it's legitimate I + + align:start position:0% +legitimate you can say it's legitimate I + + + align:start position:0% +legitimate you can say it's legitimate I +mean my politics are obvious and my + + align:start position:0% +mean my politics are obvious and my + + + align:start position:0% +mean my politics are obvious and my +son's name is Chas so you know anything + + align:start position:0% +son's name is Chas so you know anything + + + align:start position:0% +son's name is Chas so you know anything +you say is going to be slightly to the + + align:start position:0% +you say is going to be slightly to the + + + align:start position:0% +you say is going to be slightly to the +right of of me so don't worry and I'm + + align:start position:0% +right of of me so don't worry and I'm + + + align:start position:0% +right of of me so don't worry and I'm +not critical of that so so what do you + + align:start position:0% +not critical of that so so what do you + + + align:start position:0% +not critical of that so so what do you +say about that is it scalable is it + + align:start position:0% + + + + align:start position:0% + +sustainable what is what does + + align:start position:0% +sustainable what is what does + + + align:start position:0% +sustainable what is what does +sustainable mean in this context you + + align:start position:0% +sustainable mean in this context you + + + align:start position:0% +sustainable mean in this context you +guys have heard this + + align:start position:0% + + + + align:start position:0% + +yeah well you know it's funny that's + + align:start position:0% +yeah well you know it's funny that's + + + align:start position:0% +yeah well you know it's funny that's +what it should mean mean that's what I + + align:start position:0% +what it should mean mean that's what I + + + align:start position:0% +what it should mean mean that's what I +would like it to mean but really in a + + align:start position:0% +would like it to mean but really in a + + + align:start position:0% +would like it to mean but really in a +public health context to dat what + + align:start position:0% +public health context to dat what + + + align:start position:0% +public health context to dat what +sustainable means is that a country can + + align:start position:0% +sustainable means is that a country can + + + align:start position:0% +sustainable means is that a country can +sustain it on their own + + align:start position:0% +sustain it on their own + + + align:start position:0% +sustain it on their own +resources so what is what is the health + + align:start position:0% +resources so what is what is the health + + + align:start position:0% +resources so what is what is the health +budget of most heavily indebted very + + align:start position:0% +budget of most heavily indebted very + + + align:start position:0% +budget of most heavily indebted very +poor countries per anim per capital you + + align:start position:0% +poor countries per anim per capital you + + + align:start position:0% +poor countries per anim per capital you +know five + + align:start position:0% +know five + + + align:start position:0% +know five +bucks okay $5 per person per year so how + + align:start position:0% +bucks okay $5 per person per year so how + + + align:start position:0% +bucks okay $5 per person per year so how +much do even TB treatment cost you have + + align:start position:0% +much do even TB treatment cost you have + + + align:start position:0% +much do even TB treatment cost you have +an idea good to know these things 12 + + align:start position:0% +an idea good to know these things 12 + + + align:start position:0% +an idea good to know these things 12 +bucks infant vaccination anybody + + align:start position:0% +bucks infant vaccination anybody + + + align:start position:0% +bucks infant vaccination anybody +$240 so you know you quickly run out of + + align:start position:0% +$240 so you know you quickly run out of + + + align:start position:0% +$240 so you know you quickly run out of +that Health budget so anything else will + + align:start position:0% +that Health budget so anything else will + + + align:start position:0% +that Health budget so anything else will +break the + + align:start position:0% +break the + + + align:start position:0% +break the +budget and in some countries like Haiti + + align:start position:0% +budget and in some countries like Haiti + + + align:start position:0% +budget and in some countries like Haiti +the annual Health budget was + + align:start position:0% +the annual Health budget was + + + align:start position:0% +the annual Health budget was +$1.75 per person per year so the + + align:start position:0% +$1.75 per person per year so the + + + align:start position:0% +$1.75 per person per year so the +government couldn't even sustain infant + + align:start position:0% +government couldn't even sustain infant + + + align:start position:0% +government couldn't even sustain infant +vaccination because the government buys + + align:start position:0% +vaccination because the government buys + + + align:start position:0% +vaccination because the government buys +the vaccination for $2.40 the whole + + align:start position:0% +the vaccination for $2.40 the whole + + + align:start position:0% +the vaccination for $2.40 the whole +package from + + align:start position:0% +package from + + + align:start position:0% +package from +UNICEF um but they couldn't do it so + + align:start position:0% +UNICEF um but they couldn't do it so + + + align:start position:0% +UNICEF um but they couldn't do it so +even the very most basic so we have + + align:start position:0% +even the very most basic so we have + + + align:start position:0% +even the very most basic so we have +constrained poor countries to that as + + align:start position:0% +constrained poor countries to that as + + + align:start position:0% +constrained poor countries to that as +the optimization function right this is + + align:start position:0% +the optimization function right this is + + + align:start position:0% +the optimization function right this is +your health spending everything that + + align:start position:0% +your health spending everything that + + + align:start position:0% +your health spending everything that +sustainable you do within your rubric of + + align:start position:0% +sustainable you do within your rubric of + + + align:start position:0% +sustainable you do within your rubric of +what you have the life expectancy in + + align:start position:0% +what you have the life expectancy in + + + align:start position:0% +what you have the life expectancy in +these countries is + + align:start position:0% +these countries is + + + align:start position:0% +these countries is +39 right and now you have AIDS and you + + align:start position:0% +39 right and now you have AIDS and you + + + align:start position:0% +39 right and now you have AIDS and you +you have tuberculosis and you have all + + align:start position:0% +you have tuberculosis and you have all + + + align:start position:0% +you have tuberculosis and you have all +these things and many of them are + + align:start position:0% +these things and many of them are + + + align:start position:0% +these things and many of them are +treatable but somehow we've got to + + align:start position:0% +treatable but somehow we've got to + + + align:start position:0% +treatable but somehow we've got to +change the optimization function you + + align:start position:0% +change the optimization function you + + + align:start position:0% +change the optimization function you +know when I was in high school + + align:start position:0% +know when I was in high school + + + align:start position:0% +know when I was in high school +physics this my geeky reference that + + align:start position:0% +physics this my geeky reference that + + + align:start position:0% +physics this my geeky reference that +what I learned is the only state of the + + align:start position:0% +what I learned is the only state of the + + + align:start position:0% +what I learned is the only state of the +universe that's + + align:start position:0% +universe that's + + + align:start position:0% +universe that's +sustainable without inputting energy is + + align:start position:0% +sustainable without inputting energy is + + + align:start position:0% +sustainable without inputting energy is +what high school physics anyone + + align:start position:0% +what high school physics anyone + + + align:start position:0% +what high school physics anyone +entropy chaos that's what we've got + + align:start position:0% +entropy chaos that's what we've got + + + align:start position:0% +entropy chaos that's what we've got +we've got + + align:start position:0% +we've got + + + align:start position:0% +we've got +chaos and and you have to input energy + + align:start position:0% +chaos and and you have to input energy + + + align:start position:0% +chaos and and you have to input energy +which is human resources which is + + align:start position:0% +which is human resources which is + + + align:start position:0% +which is human resources which is +capital if if you want to change the + + align:start position:0% +capital if if you want to change the + + + align:start position:0% +capital if if you want to change the +chaotic nature of healthcare for the + + align:start position:0% +chaotic nature of healthcare for the + + + align:start position:0% +chaotic nature of healthcare for the +poor you're going to have to input + + align:start position:0% +poor you're going to have to input + + + align:start position:0% +poor you're going to have to input +energy technology you know medicines + + align:start position:0% +energy technology you know medicines + + + align:start position:0% +energy technology you know medicines +Commodities uh + + align:start position:0% +Commodities uh + + + align:start position:0% +Commodities uh +electricity right back to the + + align:start position:0% +electricity right back to the + + + align:start position:0% +electricity right back to the +electricity SL so we um this was totally + + align:start position:0% +electricity SL so we um this was totally + + + align:start position:0% +electricity SL so we um this was totally +about the sustainability argument so + + align:start position:0% +about the sustainability argument so + + + align:start position:0% +about the sustainability argument so +while people didn't quote unquote + + align:start position:0% +while people didn't quote unquote + + + align:start position:0% +while people didn't quote unquote +believe it of course they believed it + + align:start position:0% +believe it of course they believed it + + + align:start position:0% +believe it of course they believed it +they believe of course they knew if you + + align:start position:0% +they believe of course they knew if you + + + align:start position:0% +they believe of course they knew if you +treat a Haitian with HIV they will do + + align:start position:0% +treat a Haitian with HIV they will do + + + align:start position:0% +treat a Haitian with HIV they will do +just as well as an American in fact + + align:start position:0% +just as well as an American in fact + + + align:start position:0% +just as well as an American in fact +better because they they only have one + + align:start position:0% +better because they they only have one + + + align:start position:0% +better because they they only have one +shot and they're really really + + align:start position:0% +shot and they're really really + + + align:start position:0% +shot and they're really really +compliant you know Americans 50% of + + align:start position:0% +compliant you know Americans 50% of + + + align:start position:0% +compliant you know Americans 50% of +Americans after one year of therapy are + + align:start position:0% +Americans after one year of therapy are + + + align:start position:0% +Americans after one year of therapy are +already resistant to their drugs because + + align:start position:0% +already resistant to their drugs because + + + align:start position:0% +already resistant to their drugs because +they don't take them that has not been + + align:start position:0% +they don't take them that has not been + + + align:start position:0% +they don't take them that has not been +the case in the developing + + align:start position:0% +the case in the developing + + + align:start position:0% +the case in the developing +world and and just to go back to our + + align:start position:0% +world and and just to go back to our + + + align:start position:0% +world and and just to go back to our +sanj bosu so sanj was like scr Grand + + align:start position:0% +sanj bosu so sanj was like scr Grand + + + align:start position:0% +sanj bosu so sanj was like scr Grand +because at this time the treatment was + + align:start position:0% +because at this time the treatment was + + + align:start position:0% +because at this time the treatment was +$10,000 per patient per + + align:start position:0% + + + + align:start position:0% + +year so sanj's running around Cambridge + + align:start position:0% +year so sanj's running around Cambridge + + + align:start position:0% +year so sanj's running around Cambridge +collecting unexpired anti rets and + + align:start position:0% +collecting unexpired anti rets and + + + align:start position:0% +collecting unexpired anti rets and +giving them to us to treat + + align:start position:0% +giving them to us to treat + + + align:start position:0% +giving them to us to treat +patients and you know where sanji's name + + align:start position:0% +patients and you know where sanji's name + + + align:start position:0% +patients and you know where sanji's name +comes up about six months into this the + + align:start position:0% +comes up about six months into this the + + + align:start position:0% +comes up about six months into this the +Wall Street + + align:start position:0% +Wall Street + + + align:start position:0% +Wall Street +Journal this is an MIT undergrad a + + align:start position:0% +Journal this is an MIT undergrad a + + + align:start position:0% +Journal this is an MIT undergrad a +little dude named sanj bosu is in the + + align:start position:0% +little dude named sanj bosu is in the + + + align:start position:0% +little dude named sanj bosu is in the +front page above the fold in the Wall + + align:start position:0% +front page above the fold in the Wall + + + align:start position:0% +front page above the fold in the Wall +Street Journal for + + align:start position:0% + + + + align:start position:0% + +what it was a positive + + align:start position:0% + + + + align:start position:0% + +article violating International property + + align:start position:0% +article violating International property + + + align:start position:0% +article violating International property +intellectual property laws and by the + + align:start position:0% +intellectual property laws and by the + + + align:start position:0% +intellectual property laws and by the +way Haiti had no Pats Hai has no Pats no + + align:start position:0% +way Haiti had no Pats Hai has no Pats no + + + align:start position:0% +way Haiti had no Pats Hai has no Pats no +Pat on + + align:start position:0% +Pat on + + + align:start position:0% +Pat on +ha so why do you why would the Wall + + align:start position:0% +ha so why do you why would the Wall + + + align:start position:0% +ha so why do you why would the Wall +Street this is 60 patients this is a kid + + align:start position:0% +Street this is 60 patients this is a kid + + + align:start position:0% +Street this is 60 patients this is a kid +in Cambridge running around getting + + align:start position:0% +in Cambridge running around getting + + + align:start position:0% +in Cambridge running around getting +unexpired TR why would the Wall Street + + align:start position:0% +unexpired TR why would the Wall Street + + + align:start position:0% +unexpired TR why would the Wall Street +Journal put an article about him above + + align:start position:0% +Journal put an article about him above + + + align:start position:0% +Journal put an article about him above +the fold I'm all into the above and + + align:start position:0% +the fold I'm all into the above and + + + align:start position:0% +the fold I'm all into the above and +below the fold which was kind of dated + + align:start position:0% +below the fold which was kind of dated + + + align:start position:0% +below the fold which was kind of dated +right cuz we don't have the fold anymore + + align:start position:0% +right cuz we don't have the fold anymore + + + align:start position:0% +right cuz we don't have the fold anymore +I got my + + align:start position:0% +I got my + + + align:start position:0% +I got my +iPad + + align:start position:0% +iPad + + + align:start position:0% +iPad +um I I but I I like that so what what + + align:start position:0% +um I I but I I like that so what what + + + align:start position:0% +um I I but I I like that so what what +what do you think the Wall Street + + align:start position:0% +what do you think the Wall Street + + + align:start position:0% +what do you think the Wall Street +Journal was thinking are they paying + + align:start position:0% +Journal was thinking are they paying + + + align:start position:0% +Journal was thinking are they paying +attention to this I mean why why would + + align:start position:0% +attention to this I mean why why would + + + align:start position:0% +attention to this I mean why why would +the Wall Street Journal is you know + + align:start position:0% +the Wall Street Journal is you know + + + align:start position:0% +the Wall Street Journal is you know +pretty respectable if you like that sort + + align:start position:0% +pretty respectable if you like that sort + + + align:start position:0% +pretty respectable if you like that sort +of + + align:start position:0% +of + + + align:start position:0% +of +thing what do you think they were + + align:start position:0% +thing what do you think they were + + + align:start position:0% +thing what do you think they were +thinking why pick on + + align:start position:0% +thinking why pick on + + + align:start position:0% +thinking why pick on +Sanji they like to write about the + + align:start position:0% +Sanji they like to write about the + + + align:start position:0% +Sanji they like to write about the +profits of drug companies right so sanj + + align:start position:0% +profits of drug companies right so sanj + + + align:start position:0% +profits of drug companies right so sanj +was undercutting them right so little + + align:start position:0% +was undercutting them right so little + + + align:start position:0% +was undercutting them right so little +but they saw it they're smart people + + align:start position:0% +but they saw it they're smart people + + + align:start position:0% +but they saw it they're smart people +these these these capitalists are very + + align:start position:0% +these these these capitalists are very + + + align:start position:0% +these these these capitalists are very +smart I know that they're tricky and + + align:start position:0% +smart I know that they're tricky and + + + align:start position:0% +smart I know that they're tricky and +they're smart and they see that this is + + align:start position:0% +they're smart and they see that this is + + + align:start position:0% +they're smart and they see that this is +a terrible + + align:start position:0% +a terrible + + + align:start position:0% +a terrible +example this is a terrible + + align:start position:0% +example this is a terrible + + + align:start position:0% +example this is a terrible +example you know and so it just tells + + align:start position:0% +example you know and so it just tells + + + align:start position:0% +example you know and so it just tells +you how entrenched these systems are + + align:start position:0% +you how entrenched these systems are + + + align:start position:0% +you how entrenched these systems are +that you need this really you to attack + + align:start position:0% +that you need this really you to attack + + + align:start position:0% +that you need this really you to attack +them you really need to have a complex + + align:start position:0% +them you really need to have a complex + + + align:start position:0% +them you really need to have a complex +system of attacks um so when we you know + + align:start position:0% +system of attacks um so when we you know + + + align:start position:0% +system of attacks um so when we you know +other things we dealt with people said + + align:start position:0% +other things we dealt with people said + + + align:start position:0% +other things we dealt with people said +oh my gosh you know like the patients + + align:start position:0% +oh my gosh you know like the patients + + + align:start position:0% +oh my gosh you know like the patients +won't be able to take their meds they + + align:start position:0% +won't be able to take their meds they + + + align:start position:0% +won't be able to take their meds they +have no watches they have no you know we + + align:start position:0% +have no watches they have no you know we + + + align:start position:0% +have no watches they have no you know we +had one picture with all our patients + + align:start position:0% +had one picture with all our patients + + + align:start position:0% +had one picture with all our patients +with watches + + align:start position:0% +with watches + + + align:start position:0% +with watches +on but we also had community health + + align:start position:0% +on but we also had community health + + + align:start position:0% +on but we also had community health +workers back to your concept with small + + align:start position:0% +workers back to your concept with small + + + align:start position:0% +workers back to your concept with small +pots because one of the positive things + + align:start position:0% +pots because one of the positive things + + + align:start position:0% +pots because one of the positive things +we all learned in public health is by + + align:start position:0% +we all learned in public health is by + + + align:start position:0% +we all learned in public health is by +harnessing the enthusiasm of community + + align:start position:0% +harnessing the enthusiasm of community + + + align:start position:0% +harnessing the enthusiasm of community +you could really get out to the most + + align:start position:0% +you could really get out to the most + + + align:start position:0% +you could really get out to the most +difficult to read patients but we also + + align:start position:0% +difficult to read patients but we also + + + align:start position:0% +difficult to read patients but we also +paid Community Health which was highly + + align:start position:0% +paid Community Health which was highly + + + align:start position:0% +paid Community Health which was highly +controversial and remains so to this day + + align:start position:0% +controversial and remains so to this day + + + align:start position:0% +controversial and remains so to this day +because the idea is people should + + align:start position:0% +because the idea is people should + + + align:start position:0% +because the idea is people should +volunteer to do that what do you think + + align:start position:0% +volunteer to do that what do you think + + + align:start position:0% +volunteer to do that what do you think +about + + align:start position:0% +about + + + align:start position:0% +about +that + + align:start position:0% +that + + + align:start position:0% +that +just you were talking about Community + + align:start position:0% +just you were talking about Community + + + align:start position:0% +just you were talking about Community +workers and you know a lot of for + + align:start position:0% +workers and you know a lot of for + + + align:start position:0% +workers and you know a lot of for +example in Haiti the the the the + + align:start position:0% +example in Haiti the the the the + + + align:start position:0% +example in Haiti the the the the +strategy of community outreach is not + + align:start position:0% +strategy of community outreach is not + + + align:start position:0% +strategy of community outreach is not +even includ in the National Health yeah + + align:start position:0% +even includ in the National Health yeah + + + align:start position:0% +even includ in the National Health yeah +what's up with that and it has been we + + align:start position:0% +what's up with that and it has been we + + + align:start position:0% +what's up with that and it has been we +had a lot of results because I'm from ha + + align:start position:0% +had a lot of results because I'm from ha + + + align:start position:0% +had a lot of results because I'm from ha +we had a lot of results Partners in + + align:start position:0% +we had a lot of results Partners in + + + align:start position:0% +we had a lot of results Partners in +Health and a lot + + align:start position:0% +Health and a lot + + + align:start position:0% +Health and a lot +of so it's all so why do you think that + + align:start position:0% +of so it's all so why do you think that + + + align:start position:0% +of so it's all so why do you think that +why why do you think that I think still + + align:start position:0% +why why do you think that I think still + + + align:start position:0% +why why do you think that I think still +uh they see Public Health as + + align:start position:0% +uh they see Public Health as + + + align:start position:0% +uh they see Public Health as +institutions and not + + align:start position:0% +institutions and not + + + align:start position:0% +institutions and not +really uh public Heth has to be also a + + align:start position:0% +really uh public Heth has to be also a + + + align:start position:0% +really uh public Heth has to be also a +lake for the community and the health + + align:start position:0% +lake for the community and the health + + + align:start position:0% +lake for the community and the health +insti and they're begging they're + + align:start position:0% +insti and they're begging they're + + + align:start position:0% +insti and they're begging they're +begging us for it now I'll tell you Dr + + align:start position:0% +begging us for it now I'll tell you Dr + + + align:start position:0% +begging us for it now I'll tell you Dr +lson the the minister of health is + + align:start position:0% +lson the the minister of health is + + + align:start position:0% +lson the the minister of health is +saying Help Us figure out how to do this + + align:start position:0% +saying Help Us figure out how to do this + + + align:start position:0% +saying Help Us figure out how to do this +on the national level we have to because + + align:start position:0% +on the national level we have to because + + + align:start position:0% +on the national level we have to because +it has to be legitimate yeah what about + + align:start position:0% +it has to be legitimate yeah what about + + + align:start position:0% +it has to be legitimate yeah what about +pay what about compensation of these + + align:start position:0% +pay what about compensation of these + + + align:start position:0% +pay what about compensation of these +community health + + align:start position:0% +community health + + + align:start position:0% +community health +workers because that's the standard + + align:start position:0% +workers because that's the standard + + + align:start position:0% +workers because that's the standard +public health approach is volunteers so + + align:start position:0% +public health approach is volunteers so + + + align:start position:0% +public health approach is volunteers so +much time does it take well for our guys + + align:start position:0% +much time does it take well for our guys + + + align:start position:0% +much time does it take well for our guys +it's a full-time job I mean you know + + align:start position:0% +it's a full-time job I mean you know + + + align:start position:0% +it's a full-time job I mean you know +there Haiti is a very rural Haiti is + + align:start position:0% +there Haiti is a very rural Haiti is + + + align:start position:0% +there Haiti is a very rural Haiti is +extremely um sparsely populated un like + + align:start position:0% +extremely um sparsely populated un like + + + align:start position:0% +extremely um sparsely populated un like +Randa and so you really are hiking for 6 + + align:start position:0% +Randa and so you really are hiking for 6 + + + align:start position:0% +Randa and so you really are hiking for 6 +seven hours day you have to think about + + align:start position:0% +seven hours day you have to think about + + + align:start position:0% +seven hours day you have to think about +sustainability recruit retention these + + align:start position:0% +sustainability recruit retention these + + + align:start position:0% +sustainability recruit retention these +health workers paying them goes Long Way + + align:start position:0% +health workers paying them goes Long Way + + + align:start position:0% +health workers paying them goes Long Way +doing right so we definitely there's + + align:start position:0% +doing right so we definitely there's + + + align:start position:0% +doing right so we definitely there's +plenty of data that shows the attrition + + align:start position:0% +plenty of data that shows the attrition + + + align:start position:0% +plenty of data that shows the attrition +rate for volunteer Health work is + + align:start position:0% +rate for volunteer Health work is + + + align:start position:0% +rate for volunteer Health work is +profound very quick yeah there's a + + align:start position:0% +profound very quick yeah there's a + + + align:start position:0% +profound very quick yeah there's a +status associated with proving healthare + + align:start position:0% +status associated with proving healthare + + + align:start position:0% +status associated with proving healthare +and there's strong + + align:start position:0% +and there's strong + + + align:start position:0% +and there's strong +histor what is train can be + + align:start position:0% +histor what is train can be + + + align:start position:0% +histor what is train can be +trision time you start talking about t + + align:start position:0% +trision time you start talking about t + + + align:start position:0% +trision time you start talking about t +shifting from an expert to the community + + align:start position:0% +shifting from an expert to the community + + + align:start position:0% +shifting from an expert to the community +yeah you run into un established yeah so + + align:start position:0% +yeah you run into un established yeah so + + + align:start position:0% +yeah you run into un established yeah so +there is definitely this sort of + + align:start position:0% +there is definitely this sort of + + + align:start position:0% +there is definitely this sort of +protection of trade um you know nurses + + align:start position:0% +protection of trade um you know nurses + + + align:start position:0% +protection of trade um you know nurses +are worried if community health workers + + align:start position:0% +are worried if community health workers + + + align:start position:0% +are worried if community health workers +give Depo fora don't they'll be out of + + align:start position:0% +give Depo fora don't they'll be out of + + + align:start position:0% +give Depo fora don't they'll be out of +the job that kind of thing so we've got + + align:start position:0% +the job that kind of thing so we've got + + + align:start position:0% +the job that kind of thing so we've got +the attrition thing so we really felt + + align:start position:0% +the attrition thing so we really felt + + + align:start position:0% +the attrition thing so we really felt +like paying people it's a full-time job + + align:start position:0% +like paying people it's a full-time job + + + align:start position:0% +like paying people it's a full-time job +in Haiti not true in all of our sites in + + align:start position:0% +in Haiti not true in all of our sites in + + + align:start position:0% +in Haiti not true in all of our sites in +Haiti and LU definitely hold in MA + + align:start position:0% +Haiti and LU definitely hold in MA + + + align:start position:0% +Haiti and LU definitely hold in MA +definitely job other + + align:start position:0% +definitely job other + + + align:start position:0% +definitely job other +thoughts I mean I think one of the the + + align:start position:0% +thoughts I mean I think one of the the + + + align:start position:0% +thoughts I mean I think one of the the +pieces of what you said also is by + + align:start position:0% +pieces of what you said also is by + + + align:start position:0% +pieces of what you said also is by +providing work as a health worker in the + + align:start position:0% +providing work as a health worker in the + + + align:start position:0% +providing work as a health worker in the +community you can Elevate the person's + + align:start position:0% +community you can Elevate the person's + + + align:start position:0% +community you can Elevate the person's +status too so the large majority of our + + align:start position:0% +status too so the large majority of our + + + align:start position:0% +status too so the large majority of our +community health workers in in most + + align:start position:0% +community health workers in in most + + + align:start position:0% +community health workers in in most +countries particularly in southern + + align:start position:0% +countries particularly in southern + + + align:start position:0% +countries particularly in southern +Africa in lutu in in um in Mala are + + align:start position:0% +Africa in lutu in in um in Mala are + + + align:start position:0% +Africa in lutu in in um in Mala are +women so in terms of attacking gender + + align:start position:0% +women so in terms of attacking gender + + + align:start position:0% +women so in terms of attacking gender +disparity and providing jobs for women + + align:start position:0% +disparity and providing jobs for women + + + align:start position:0% +disparity and providing jobs for women +like it's part of our social strategy + + align:start position:0% +like it's part of our social strategy + + + align:start position:0% +like it's part of our social strategy +actually to have you know and and we we + + align:start position:0% +actually to have you know and and we we + + + align:start position:0% +actually to have you know and and we we +have a very high preference for people + + align:start position:0% +have a very high preference for people + + + align:start position:0% +have a very high preference for people +who are living themselves with HIV um so + + align:start position:0% +who are living themselves with HIV um so + + + align:start position:0% +who are living themselves with HIV um so +you know trying to do a progressively + + align:start position:0% +you know trying to do a progressively + + + align:start position:0% +you know trying to do a progressively +structured Recruitment and Retention for + + align:start position:0% +structured Recruitment and Retention for + + + align:start position:0% +structured Recruitment and Retention for +the most vulnerable um is also job + + align:start position:0% +the most vulnerable um is also job + + + align:start position:0% +the most vulnerable um is also job +creation strategy and today like we have + + align:start position:0% +creation strategy and today like we have + + + align:start position:0% +creation strategy and today like we have +5,500 patients working for zombie Los + + align:start position:0% +5,500 patients working for zombie Los + + + align:start position:0% +5,500 patients working for zombie Los +Sante and more than 3,000 of them are + + align:start position:0% +Sante and more than 3,000 of them are + + + align:start position:0% +Sante and more than 3,000 of them are +community health workers so these people + + align:start position:0% +community health workers so these people + + + align:start position:0% +community health workers so these people +are that's the only job they've ever had + + align:start position:0% +are that's the only job they've ever had + + + align:start position:0% +are that's the only job they've ever had +often in the formal economy um you know + + align:start position:0% +often in the formal economy um you know + + + align:start position:0% +often in the formal economy um you know +the main critique of it is too expensive + + align:start position:0% +the main critique of it is too expensive + + + align:start position:0% +the main critique of it is too expensive +not sustainable that's the main critique + + align:start position:0% +not sustainable that's the main critique + + + align:start position:0% +not sustainable that's the main critique +that governments with a health care + + align:start position:0% +that governments with a health care + + + align:start position:0% +that governments with a health care +budget of $1.75 per person per anom they + + align:start position:0% +budget of $1.75 per person per anom they + + + align:start position:0% +budget of $1.75 per person per anom they +can't afford that for us you know HIV + + align:start position:0% +can't afford that for us you know HIV + + + align:start position:0% +can't afford that for us you know HIV +has given us a window to say well you + + align:start position:0% +has given us a window to say well you + + + align:start position:0% +has given us a window to say well you +know we're doing all this you know the + + align:start position:0% +know we're doing all this you know the + + + align:start position:0% +know we're doing all this you know the +healthcare doesn't add that much to this + + align:start position:0% +healthcare doesn't add that much to this + + + align:start position:0% +healthcare doesn't add that much to this +but we'll talk a little about so we you + + align:start position:0% +but we'll talk a little about so we you + + + align:start position:0% +but we'll talk a little about so we you +know we've written about the healthcare + + align:start position:0% +know we've written about the healthcare + + + align:start position:0% +know we've written about the healthcare +workers again to say not only you know + + align:start position:0% +workers again to say not only you know + + + align:start position:0% +workers again to say not only you know +is the payment worth it and in this + + align:start position:0% +is the payment worth it and in this + + + align:start position:0% +is the payment worth it and in this +article we put some charts of if you + + align:start position:0% +article we put some charts of if you + + + align:start position:0% +article we put some charts of if you +save for every year you save a patient + + align:start position:0% +save for every year you save a patient + + + align:start position:0% +save for every year you save a patient +from going to Second Line drugs which + + align:start position:0% +from going to Second Line drugs which + + + align:start position:0% +from going to Second Line drugs which +are tfold more expensive because today + + align:start position:0% +are tfold more expensive because today + + + align:start position:0% +are tfold more expensive because today +the price of First Line anti- retral + + align:start position:0% +the price of First Line anti- retral + + + align:start position:0% +the price of First Line anti- retral +drugs is less than $90 per person per + + align:start position:0% +drugs is less than $90 per person per + + + align:start position:0% +drugs is less than $90 per person per +year and it was 10,000 in the son Basu + + align:start position:0% +year and it was 10,000 in the son Basu + + + align:start position:0% +year and it was 10,000 in the son Basu +era right so yes so 10,000 to 90 right + + align:start position:0% +era right so yes so 10,000 to 90 right + + + align:start position:0% +era right so yes so 10,000 to 90 right +to see that drop of a 100 fold more than + + align:start position:0% +to see that drop of a 100 fold more than + + + align:start position:0% +to see that drop of a 100 fold more than +100 fold price in your lifetime makes + + align:start position:0% +100 fold price in your lifetime makes + + + align:start position:0% +100 fold price in your lifetime makes +you feel like you can do it anything + + align:start position:0% +you feel like you can do it anything + + + align:start position:0% +you feel like you can do it anything +makes you + + align:start position:0% +makes you + + + align:start position:0% +makes you +very optimistic I would say cocky might + + align:start position:0% +very optimistic I would say cocky might + + + align:start position:0% +very optimistic I would say cocky might +be another uh descriptor of burgers + + align:start position:0% +be another uh descriptor of burgers + + + align:start position:0% +be another uh descriptor of burgers +andoun sometimes but um so you know we + + align:start position:0% +andoun sometimes but um so you know we + + + align:start position:0% +andoun sometimes but um so you know we +we wrote this to say it's feasible again + + align:start position:0% +we wrote this to say it's feasible again + + + align:start position:0% +we wrote this to say it's feasible again +it's feasible this is how we do it this + + align:start position:0% +it's feasible this is how we do it this + + + align:start position:0% +it's feasible this is how we do it this +is the benefits we think it makes this + + align:start position:0% +is the benefits we think it makes this + + + align:start position:0% +is the benefits we think it makes this +is how you can end up saving the + + align:start position:0% +is how you can end up saving the + + + align:start position:0% +is how you can end up saving the +government of Haiti money because + + align:start position:0% +government of Haiti money because + + + align:start position:0% +government of Haiti money because +they've already committed to now + + align:start position:0% +they've already committed to now + + + align:start position:0% +they've already committed to now +treating HIV see as we were able to push + + align:start position:0% +treating HIV see as we were able to push + + + align:start position:0% +treating HIV see as we were able to push +the envelope on HIV even more than + + align:start position:0% +the envelope on HIV even more than + + + align:start position:0% +the envelope on HIV even more than +tuberculosis the government had plans to + + align:start position:0% +tuberculosis the government had plans to + + + align:start position:0% +tuberculosis the government had plans to +treat everyone and treat everyone for + + align:start position:0% +treat everyone and treat everyone for + + + align:start position:0% +treat everyone and treat everyone for +free and in places like Nigeria in + + align:start position:0% +free and in places like Nigeria in + + + align:start position:0% +free and in places like Nigeria in +places like mosan Beque in places like + + align:start position:0% +places like mosan Beque in places like + + + align:start position:0% +places like mosan Beque in places like +Malawi you can get HIV medicines for + + align:start position:0% +Malawi you can get HIV medicines for + + + align:start position:0% +Malawi you can get HIV medicines for +free + + align:start position:0% +free + + + align:start position:0% +free +anywhere crazy like think about that I + + align:start position:0% +anywhere crazy like think about that I + + + align:start position:0% +anywhere crazy like think about that I +mean that is just a massive sea change + + align:start position:0% +mean that is just a massive sea change + + + align:start position:0% +mean that is just a massive sea change +um and we also documented this what this + + align:start position:0% +um and we also documented this what this + + + align:start position:0% +um and we also documented this what this +massive price drop did for our ability + + align:start position:0% +massive price drop did for our ability + + + align:start position:0% +massive price drop did for our ability +to provide universal access so this is + + align:start position:0% +to provide universal access so this is + + + align:start position:0% +to provide universal access so this is +you know the + + align:start position:0% +you know the + + + align:start position:0% +you know the +$10,000 and in a span of less than4 + + align:start position:0% +$10,000 and in a span of less than4 + + + align:start position:0% +$10,000 and in a span of less than4 +years we were at $150 per capita and all + + align:start position:0% +years we were at $150 per capita and all + + + align:start position:0% +years we were at $150 per capita and all +of that was advocacy was getting the + + align:start position:0% +of that was advocacy was getting the + + + align:start position:0% +of that was advocacy was getting the +drugs on the who essential drug list it + + align:start position:0% +drugs on the who essential drug list it + + + align:start position:0% +drugs on the who essential drug list it +was AIDS activists you know shutting + + align:start position:0% +was AIDS activists you know shutting + + + align:start position:0% +was AIDS activists you know shutting +down conferences in South Africa you + + align:start position:0% +down conferences in South Africa you + + + align:start position:0% +down conferences in South Africa you +know falling around Al Gore and chucking + + align:start position:0% +know falling around Al Gore and chucking + + + align:start position:0% +know falling around Al Gore and chucking +blood on him and I mean you know this I + + align:start position:0% +blood on him and I mean you know this I + + + align:start position:0% +blood on him and I mean you know this I +love these guys you know and they have + + align:start position:0% +love these guys you know and they have + + + align:start position:0% +love these guys you know and they have +the Good Sense often to not be the front + + align:start position:0% +the Good Sense often to not be the front + + + align:start position:0% +the Good Sense often to not be the front +man you know they'll put me up well you + + align:start position:0% +man you know they'll put me up well you + + + align:start position:0% +man you know they'll put me up well you +she cleans up good let's put her there + + align:start position:0% +she cleans up good let's put her there + + + align:start position:0% +she cleans up good let's put her there +and then they're back and you know + + align:start position:0% +and then they're back and you know + + + align:start position:0% +and then they're back and you know +throwing blood and stuff I never had to + + align:start position:0% +throwing blood and stuff I never had to + + + align:start position:0% +throwing blood and stuff I never had to +throw + + align:start position:0% +throw + + + align:start position:0% +throw +it's kind of disappointingly I would say + + align:start position:0% +it's kind of disappointingly I would say + + + align:start position:0% +it's kind of disappointingly I would say +um you know so we also published this + + align:start position:0% +um you know so we also published this + + + align:start position:0% +um you know so we also published this +showing that if you have large scale + + align:start position:0% +showing that if you have large scale + + + align:start position:0% +showing that if you have large scale +procurement if you demonstrate demand if + + align:start position:0% +procurement if you demonstrate demand if + + + align:start position:0% +procurement if you demonstrate demand if +you go with this sort of rights based + + align:start position:0% +you go with this sort of rights based + + + align:start position:0% +you go with this sort of rights based +argument you will see a price drop this + + align:start position:0% +argument you will see a price drop this + + + align:start position:0% +argument you will see a price drop this +is what happened in TB and this is what + + align:start position:0% +is what happened in TB and this is what + + + align:start position:0% +is what happened in TB and this is what +happened in HIV and we're hoping it will + + align:start position:0% +happened in HIV and we're hoping it will + + + align:start position:0% +happened in HIV and we're hoping it will +happen other places and then the other + + align:start position:0% +happen other places and then the other + + + align:start position:0% +happen other places and then the other +argument we said because as this started + + align:start position:0% +argument we said because as this started + + + align:start position:0% +argument we said because as this started +rolling out we're back in the same + + align:start position:0% +rolling out we're back in the same + + + align:start position:0% +rolling out we're back in the same +rubric reverence saying well governments + + align:start position:0% +rubric reverence saying well governments + + + align:start position:0% +rubric reverence saying well governments +can't afford it to you have to put some + + align:start position:0% +can't afford it to you have to put some + + + align:start position:0% +can't afford it to you have to put some +cost recovery you have to get people to + + align:start position:0% +cost recovery you have to get people to + + + align:start position:0% +cost recovery you have to get people to +pay something otherwise they won't + + align:start position:0% +pay something otherwise they won't + + + align:start position:0% +pay something otherwise they won't +appreciate it and what we saw everywhere + + align:start position:0% +appreciate it and what we saw everywhere + + + align:start position:0% +appreciate it and what we saw everywhere +is anywhere that people had to pay they + + align:start position:0% +is anywhere that people had to pay they + + + align:start position:0% +is anywhere that people had to pay they +didn't stay on the drugs they had to pay + + align:start position:0% +didn't stay on the drugs they had to pay + + + align:start position:0% +didn't stay on the drugs they had to pay +for tests if they had to pay for + + align:start position:0% +for tests if they had to pay for + + + align:start position:0% +for tests if they had to pay for +transport thing so that the whole idea + + align:start position:0% +transport thing so that the whole idea + + + align:start position:0% +transport thing so that the whole idea +we said know let's right now we are + + align:start position:0% +we said know let's right now we are + + + align:start position:0% +we said know let's right now we are +rationing care worldwide by ability to + + align:start position:0% +rationing care worldwide by ability to + + + align:start position:0% +rationing care worldwide by ability to +pay how do you make the delivery of HIV + + align:start position:0% +pay how do you make the delivery of HIV + + + align:start position:0% +pay how do you make the delivery of HIV +Services a right and we showed that you + + align:start position:0% +Services a right and we showed that you + + + align:start position:0% +Services a right and we showed that you +do that through the public sector so + + align:start position:0% +do that through the public sector so + + + align:start position:0% +do that through the public sector so +even though Partners in Health started + + align:start position:0% +even though Partners in Health started + + + align:start position:0% +even though Partners in Health started +with you know this private beautiful + + align:start position:0% +with you know this private beautiful + + + align:start position:0% +with you know this private beautiful +private clinic in the middle of nowhere + + align:start position:0% +private clinic in the middle of nowhere + + + align:start position:0% +private clinic in the middle of nowhere +we now facilitate have revitalized + + align:start position:0% +we now facilitate have revitalized + + + align:start position:0% +we now facilitate have revitalized +operate 60 public facilities around the + + align:start position:0% +operate 60 public facilities around the + + + align:start position:0% +operate 60 public facilities around the +world with governments because we said + + align:start position:0% +world with governments because we said + + + align:start position:0% +world with governments because we said +the right to healthcare demands on the + + align:start position:0% +the right to healthcare demands on the + + + align:start position:0% +the right to healthcare demands on the +government being able to deliver and + + align:start position:0% +government being able to deliver and + + + align:start position:0% +government being able to deliver and +we're going to help to capacitate the + + align:start position:0% +we're going to help to capacitate the + + + align:start position:0% +we're going to help to capacitate the +government our view is a rights based + + align:start position:0% +government our view is a rights based + + + align:start position:0% +government our view is a rights based +approach takes two pieces one is the + + align:start position:0% +approach takes two pieces one is the + + + align:start position:0% +approach takes two pieces one is the +engage of the community and that's kind + + align:start position:0% +engage of the community and that's kind + + + align:start position:0% +engage of the community and that's kind +of bread and butter human rights work + + align:start position:0% +of bread and butter human rights work + + + align:start position:0% +of bread and butter human rights work +everyone believes that that's really + + align:start position:0% +everyone believes that that's really + + + align:start position:0% +everyone believes that that's really +good that's what's going on in Egypt now + + align:start position:0% +good that's what's going on in Egypt now + + + align:start position:0% +good that's what's going on in Egypt now +we're happy to see it but the other one + + align:start position:0% +we're happy to see it but the other one + + + align:start position:0% +we're happy to see it but the other one +is you have to enable the government to + + align:start position:0% +is you have to enable the government to + + + align:start position:0% +is you have to enable the government to +deliver on rights because if the + + align:start position:0% +deliver on rights because if the + + + align:start position:0% +deliver on rights because if the +government can't deliver People Can + + align:start position:0% +government can't deliver People Can + + + align:start position:0% +government can't deliver People Can +chout chant and Shout up and down till + + align:start position:0% +chout chant and Shout up and down till + + + align:start position:0% +chout chant and Shout up and down till +they're blew in the face nothing's going + + align:start position:0% +they're blew in the face nothing's going + + + align:start position:0% +they're blew in the face nothing's going +to happen so we made the concrete + + align:start position:0% +to happen so we made the concrete + + + align:start position:0% +to happen so we made the concrete +decision when AIDS money started coming + + align:start position:0% +decision when AIDS money started coming + + + align:start position:0% +decision when AIDS money started coming +and even before that in Peru with TB + + align:start position:0% +and even before that in Peru with TB + + + align:start position:0% +and even before that in Peru with TB +that the real effect of our program was + + align:start position:0% +that the real effect of our program was + + + align:start position:0% +that the real effect of our program was +not as an NGO + + align:start position:0% +not as an NGO + + + align:start position:0% +not as an NGO +it was as a a lever to Encon that into a + + align:start position:0% +it was as a a lever to Encon that into a + + + align:start position:0% +it was as a a lever to Encon that into a +government program so in Peru for + + align:start position:0% +government program so in Peru for + + + align:start position:0% +government program so in Peru for +example we started out showing + + align:start position:0% +example we started out showing + + + align:start position:0% +example we started out showing +feasibility with 75 patients like in + + align:start position:0% +feasibility with 75 patients like in + + + align:start position:0% +feasibility with 75 patients like in +Haiti we showed feasibility with 60 + + align:start position:0% +Haiti we showed feasibility with 60 + + + align:start position:0% +Haiti we showed feasibility with 60 +patients but today in Pro more than + + align:start position:0% +patients but today in Pro more than + + + align:start position:0% +patients but today in Pro more than +10,000 people have been treated for drug + + align:start position:0% +10,000 people have been treated for drug + + + align:start position:0% +10,000 people have been treated for drug +ex list and TV all on the government's + + align:start position:0% +ex list and TV all on the government's + + + align:start position:0% +ex list and TV all on the government's +program so we worked with the government + + align:start position:0% +program so we worked with the government + + + align:start position:0% +program so we worked with the government +to train them and to work on it and + + align:start position:0% +to train them and to work on it and + + + align:start position:0% +to train them and to work on it and +protocols Etc and that's how we develop + + align:start position:0% +protocols Etc and that's how we develop + + + align:start position:0% +protocols Etc and that's how we develop +scale but that scale depends on + + align:start position:0% +scale but that scale depends on + + + align:start position:0% +scale but that scale depends on +governments being able to get more money + + align:start position:0% +governments being able to get more money + + + align:start position:0% +governments being able to get more money +into health and that's usually the + + align:start position:0% +into health and that's usually the + + + align:start position:0% +into health and that's usually the +international financial institutions + + align:start position:0% +international financial institutions + + + align:start position:0% +international financial institutions +like the World Bank the IMF the US + + align:start position:0% +like the World Bank the IMF the US + + + align:start position:0% +like the World Bank the IMF the US +government Etc so you know fighting all + + align:start position:0% +government Etc so you know fighting all + + + align:start position:0% +government Etc so you know fighting all +these fights simultaneous is very + + align:start position:0% +these fights simultaneous is very + + + align:start position:0% +these fights simultaneous is very +complex but what we showed is let's take + + align:start position:0% +complex but what we showed is let's take + + + align:start position:0% +complex but what we showed is let's take +this HIV money and instead of developing + + align:start position:0% +this HIV money and instead of developing + + + align:start position:0% +this HIV money and instead of developing +the vertical programs like the polio + + align:start position:0% +the vertical programs like the polio + + + align:start position:0% +the vertical programs like the polio +thing we're going to say you know you + + align:start position:0% +thing we're going to say you know you + + + align:start position:0% +thing we're going to say you know you +can't find HIV unless you have a + + align:start position:0% +can't find HIV unless you have a + + + align:start position:0% +can't find HIV unless you have a +functioning Clinic you can't treat HIV + + align:start position:0% +functioning Clinic you can't treat HIV + + + align:start position:0% +functioning Clinic you can't treat HIV +unless you have a functioning Clinic a + + align:start position:0% +unless you have a functioning Clinic a + + + align:start position:0% +unless you have a functioning Clinic a +lot of the clinics that we worked in I + + align:start position:0% +lot of the clinics that we worked in I + + + align:start position:0% +lot of the clinics that we worked in I +remember our visit in 2003 to buan CR I + + align:start position:0% +remember our visit in 2003 to buan CR I + + + align:start position:0% +remember our visit in 2003 to buan CR I +mean two room clinic closed most of the + + align:start position:0% +mean two room clinic closed most of the + + + align:start position:0% +mean two room clinic closed most of the +time the doctor that worked for us was + + align:start position:0% +time the doctor that worked for us was + + + align:start position:0% +time the doctor that worked for us was +selling radios in the market because he + + align:start position:0% +selling radios in the market because he + + + align:start position:0% +selling radios in the market because he +hadn't been paid for nine months right + + align:start position:0% +hadn't been paid for nine months right + + + align:start position:0% +hadn't been paid for nine months right +and then everyone well no one else F + + align:start position:0% +and then everyone well no one else F + + + align:start position:0% +and then everyone well no one else F +faith in the public sector who would + + align:start position:0% +faith in the public sector who would + + + align:start position:0% +faith in the public sector who would +have faith in that it's that it's that + + align:start position:0% +have faith in that it's that it's that + + + align:start position:0% +have faith in that it's that it's that +you know the the you know the world + + align:start position:0% +you know the the you know the world + + + align:start position:0% +you know the the you know the world +doesn't have faith in the ability of you + + align:start position:0% +doesn't have faith in the ability of you + + + align:start position:0% +doesn't have faith in the ability of you +know the delivery of healthcare as a + + align:start position:0% +know the delivery of healthcare as a + + + align:start position:0% +know the delivery of healthcare as a +basic right so we said we're going to + + align:start position:0% +basic right so we said we're going to + + + align:start position:0% +basic right so we said we're going to +use HIV money to make this Clinic work + + align:start position:0% +use HIV money to make this Clinic work + + + align:start position:0% +use HIV money to make this Clinic work +and then by the way we'll provide HIV + + align:start position:0% +and then by the way we'll provide HIV + + + align:start position:0% +and then by the way we'll provide HIV +testing and treatment but but that in + + align:start position:0% +testing and treatment but but that in + + + align:start position:0% +testing and treatment but but that in +fact it's the strengthening of the + + align:start position:0% +fact it's the strengthening of the + + + align:start position:0% +fact it's the strengthening of the +health system that's key to providing + + align:start position:0% +health system that's key to providing + + + align:start position:0% +health system that's key to providing +real scale up for HIV and and we we we + + align:start position:0% +real scale up for HIV and and we we we + + + align:start position:0% +real scale up for HIV and and we we we +showed that you know you integrate HIV + + align:start position:0% +showed that you know you integrate HIV + + + align:start position:0% +showed that you know you integrate HIV +in Primary + + align:start position:0% +in Primary + + + align:start position:0% +in Primary +Care through provider initiate testing + + align:start position:0% +Care through provider initiate testing + + + align:start position:0% +Care through provider initiate testing +you integrate HIV through tuberculosis + + align:start position:0% +you integrate HIV through tuberculosis + + + align:start position:0% +you integrate HIV through tuberculosis +you integrate HIV in women's health and + + align:start position:0% +you integrate HIV in women's health and + + + align:start position:0% +you integrate HIV in women's health and +uh sexually transmitted disease and + + align:start position:0% +uh sexually transmitted disease and + + + align:start position:0% +uh sexually transmitted disease and +child health and that sort of gives you + + align:start position:0% +child health and that sort of gives you + + + align:start position:0% +child health and that sort of gives you +the whole gamut and so we Justified huge + + align:start position:0% +the whole gamut and so we Justified huge + + + align:start position:0% +the whole gamut and so we Justified huge +Investments of global fund money and + + align:start position:0% +Investments of global fund money and + + + align:start position:0% +Investments of global fund money and +even pep far money which was trickier + + align:start position:0% +even pep far money which was trickier + + + align:start position:0% +even pep far money which was trickier +into Health System strengthening to meet + + align:start position:0% +into Health System strengthening to meet + + + align:start position:0% +into Health System strengthening to meet +our HIV targets and um what we saw was + + align:start position:0% +our HIV targets and um what we saw was + + + align:start position:0% +our HIV targets and um what we saw was +really remarkable this was the clinic I + + align:start position:0% +really remarkable this was the clinic I + + + align:start position:0% +really remarkable this was the clinic I +was talking about heish and I visiting + + align:start position:0% +was talking about heish and I visiting + + + align:start position:0% +was talking about heish and I visiting +in 2003 and and this is what the clinic + + align:start position:0% +in 2003 and and this is what the clinic + + + align:start position:0% +in 2003 and and this is what the clinic +looked like right and this is three + + align:start position:0% +looked like right and this is three + + + align:start position:0% +looked like right and this is three +months later and now you know I didn't + + align:start position:0% +months later and now you know I didn't + + + align:start position:0% +months later and now you know I didn't +randomize for the rainbow colored onx so + + align:start position:0% +randomize for the rainbow colored onx so + + + align:start position:0% +randomize for the rainbow colored onx so +maybe it's just that but that we have a + + align:start position:0% +maybe it's just that but that we have a + + + align:start position:0% +maybe it's just that but that we have a +confounder you know is Rainbow you know + + align:start position:0% +confounder you know is Rainbow you know + + + align:start position:0% +confounder you know is Rainbow you know +Nations like + + align:start position:0% +Nations like + + + align:start position:0% +Nations like +rainbows I don't know but but we did + + align:start position:0% +rainbows I don't know but but we did + + + align:start position:0% +rainbows I don't know but but we did +four things with HIV money in this + + align:start position:0% +four things with HIV money in this + + + align:start position:0% +four things with HIV money in this +public facility four things one we put + + align:start position:0% +public facility four things one we put + + + align:start position:0% +public facility four things one we put +in a package of essential drugs not only + + align:start position:0% +in a package of essential drugs not only + + + align:start position:0% +in a package of essential drugs not only +HIV drugs so penicillin you know + + align:start position:0% +HIV drugs so penicillin you know + + + align:start position:0% +HIV drugs so penicillin you know +paracetamol anti- Waring medicines and + + align:start position:0% +paracetamol anti- Waring medicines and + + + align:start position:0% +paracetamol anti- Waring medicines and +in fact that investment was quite pretty + + align:start position:0% +in fact that investment was quite pretty + + + align:start position:0% +in fact that investment was quite pretty +cheap the second thing we did was get + + align:start position:0% +cheap the second thing we did was get + + + align:start position:0% +cheap the second thing we did was get +rid of work consolidate the user fees + + align:start position:0% +rid of work consolidate the user fees + + + align:start position:0% +rid of work consolidate the user fees +because any fee for service for + + align:start position:0% +because any fee for service for + + + align:start position:0% +because any fee for service for +utilization is a barrier to poor people + + align:start position:0% +utilization is a barrier to poor people + + + align:start position:0% +utilization is a barrier to poor people +and that's been documented all over the + + align:start position:0% +and that's been documented all over the + + + align:start position:0% +and that's been documented all over the +world okay and I say Consolidated + + align:start position:0% +world okay and I say Consolidated + + + align:start position:0% +world okay and I say Consolidated +because often when you're working in a + + align:start position:0% +because often when you're working in a + + + align:start position:0% +because often when you're working in a +public Clinic you can't get rid of the + + align:start position:0% +public Clinic you can't get rid of the + + + align:start position:0% +public Clinic you can't get rid of the +fees because the government has made a + + align:start position:0% +fees because the government has made a + + + align:start position:0% +fees because the government has made a +deal with the World Bank that they have + + align:start position:0% +deal with the World Bank that they have + + + align:start position:0% +deal with the World Bank that they have +to have cost recovery as part of their + + align:start position:0% +to have cost recovery as part of their + + + align:start position:0% +to have cost recovery as part of their +health strategy so what we try to do is + + align:start position:0% +health strategy so what we try to do is + + + align:start position:0% +health strategy so what we try to do is +I I'd love to get rid of them in Malawi + + align:start position:0% +I I'd love to get rid of them in Malawi + + + align:start position:0% +I I'd love to get rid of them in Malawi +they have no user fees the only country + + align:start position:0% +they have no user fees the only country + + + align:start position:0% +they have no user fees the only country +we work in with no user fees um but in + + align:start position:0% +we work in with no user fees um but in + + + align:start position:0% +we work in with no user fees um but in +every other country we try to sort of + + align:start position:0% +every other country we try to sort of + + + align:start position:0% +every other country we try to sort of +help the clinics have large exemptions + + align:start position:0% +help the clinics have large exemptions + + + align:start position:0% +help the clinics have large exemptions +so you know HIV patients TB patients + + align:start position:0% +so you know HIV patients TB patients + + + align:start position:0% +so you know HIV patients TB patients +kids under five pregnant women anyone + + align:start position:0% +kids under five pregnant women anyone + + + align:start position:0% +kids under five pregnant women anyone +with one teeth you know people with + + align:start position:0% +with one teeth you know people with + + + align:start position:0% +with one teeth you know people with +maybe fungal nail infections I mean we + + align:start position:0% +maybe fungal nail infections I mean we + + + align:start position:0% +maybe fungal nail infections I mean we +try to exempt about everybody because + + align:start position:0% +try to exempt about everybody because + + + align:start position:0% +try to exempt about everybody because +what these user fees bring in is so + + align:start position:0% +what these user fees bring in is so + + + align:start position:0% +what these user fees bring in is so +little it doesn't even matter it's an + + align:start position:0% +little it doesn't even matter it's an + + + align:start position:0% +little it doesn't even matter it's an +ideology it's not really a A system that + + align:start position:0% +ideology it's not really a A system that + + + align:start position:0% +ideology it's not really a A system that +works anyway so we so so consolidating + + align:start position:0% +works anyway so we so so consolidating + + + align:start position:0% +works anyway so we so so consolidating +user fees essential drugs paying the + + align:start position:0% +user fees essential drugs paying the + + + align:start position:0% +user fees essential drugs paying the +staff to do their + + align:start position:0% +staff to do their + + + align:start position:0% +staff to do their +work helping the government to pay this + + align:start position:0% +work helping the government to pay this + + + align:start position:0% +work helping the government to pay this +STA and then the fourth thing is the + + align:start position:0% +STA and then the fourth thing is the + + + align:start position:0% +STA and then the fourth thing is the +community health and within doing + + align:start position:0% +community health and within doing + + + align:start position:0% +community health and within doing +nothing physically to the clinic now + + align:start position:0% +nothing physically to the clinic now + + + align:start position:0% +nothing physically to the clinic now +this is now a beautiful Hospital book + + align:start position:0% +this is now a beautiful Hospital book + + + align:start position:0% +this is now a beautiful Hospital book +actually but but with doing nothing to + + align:start position:0% +actually but but with doing nothing to + + + align:start position:0% +actually but but with doing nothing to +the infrastructure just providing + + align:start position:0% +the infrastructure just providing + + + align:start position:0% +the infrastructure just providing +Services drove up utilization and then + + align:start position:0% +Services drove up utilization and then + + + align:start position:0% +Services drove up utilization and then +we could do thousands of HIV tests and + + align:start position:0% +we could do thousands of HIV tests and + + + align:start position:0% +we could do thousands of HIV tests and +get people in treatment and so here's my + + align:start position:0% +get people in treatment and so here's my + + + align:start position:0% +get people in treatment and so here's my +gratuitous picture of + + align:start position:0% +gratuitous picture of + + + align:start position:0% +gratuitous picture of +Alor on you're supposed to laugh don't + + align:start position:0% +Alor on you're supposed to laugh don't + + + align:start position:0% +Alor on you're supposed to laugh don't +you think I mean isn't it good you got + + align:start position:0% +you think I mean isn't it good you got + + + align:start position:0% +you think I mean isn't it good you got +Keith Richards you got Al Gore um did he + + align:start position:0% +Keith Richards you got Al Gore um did he + + + align:start position:0% +Keith Richards you got Al Gore um did he +invent the internet I mean you guys + + align:start position:0% +invent the internet I mean you guys + + + align:start position:0% +invent the internet I mean you guys +should know you're in MIT what do you + + align:start position:0% +should know you're in MIT what do you + + + align:start position:0% +should know you're in MIT what do you +think he did he invent the internet no + + align:start position:0% +think he did he invent the internet no + + + align:start position:0% +think he did he invent the internet no +okay so so you know how do we use + + align:start position:0% +okay so so you know how do we use + + + align:start position:0% +okay so so you know how do we use +technology to sort of you know harness + + align:start position:0% +technology to sort of you know harness + + + align:start position:0% +technology to sort of you know harness +technology to help us with this system + + align:start position:0% +technology to help us with this system + + + align:start position:0% +technology to help us with this system +and we made a very strong early + + align:start position:0% +and we made a very strong early + + + align:start position:0% +and we made a very strong early +commitment that heish was you know + + align:start position:0% +commitment that heish was you know + + + align:start position:0% +commitment that heish was you know +really the lead on to say you cannot + + align:start position:0% +really the lead on to say you cannot + + + align:start position:0% +really the lead on to say you cannot +deliver care of this complexity without + + align:start position:0% +deliver care of this complexity without + + + align:start position:0% +deliver care of this complexity without +an electron electronic medical reference + + align:start position:0% +an electron electronic medical reference + + + align:start position:0% +an electron electronic medical reference +system and heish talked to me until I + + align:start position:0% +system and heish talked to me until I + + + align:start position:0% +system and heish talked to me until I +was blew in the face about open mrss and + + align:start position:0% +was blew in the face about open mrss and + + + align:start position:0% +was blew in the face about open mrss and +I have to tell you I didn't get it until + + align:start position:0% +I have to tell you I didn't get it until + + + align:start position:0% +I have to tell you I didn't get it until +maybe three years ago I was like w + + align:start position:0% +maybe three years ago I was like w + + + align:start position:0% +maybe three years ago I was like w +that's brilliant you know but um but we + + align:start position:0% +that's brilliant you know but um but we + + + align:start position:0% +that's brilliant you know but um but we +did it um for HIV for TB we're doing it + + align:start position:0% +did it um for HIV for TB we're doing it + + + align:start position:0% +did it um for HIV for TB we're doing it +more and more for other things why well + + align:start position:0% +more and more for other things why well + + + align:start position:0% +more and more for other things why well +one is public health had never taken on + + align:start position:0% +one is public health had never taken on + + + align:start position:0% +one is public health had never taken on +chronic diseases and once you take on a + + align:start position:0% +chronic diseases and once you take on a + + + align:start position:0% +chronic diseases and once you take on a +chronic disease you need a longitudinal + + align:start position:0% +chronic disease you need a longitudinal + + + align:start position:0% +chronic disease you need a longitudinal +record and anyone who's ever been in a + + align:start position:0% +record and anyone who's ever been in a + + + align:start position:0% +record and anyone who's ever been in a +clinic in a poor country knows there + + align:start position:0% +clinic in a poor country knows there + + + align:start position:0% +clinic in a poor country knows there +ain't no record keeping right I mean + + align:start position:0% +ain't no record keeping right I mean + + + align:start position:0% +ain't no record keeping right I mean +there's files like this and some poor + + align:start position:0% +there's files like this and some poor + + + align:start position:0% +there's files like this and some poor +person who's pay like a dollar a day + + align:start position:0% +person who's pay like a dollar a day + + + align:start position:0% +person who's pay like a dollar a day +who's going down and can't even read + + align:start position:0% +who's going down and can't even read + + + align:start position:0% +who's going down and can't even read +it's like a nightmare right everybody's + + align:start position:0% +it's like a nightmare right everybody's + + + align:start position:0% +it's like a nightmare right everybody's +got six is this + + align:start position:0% +got six is this + + + align:start position:0% +got six is this +true okay so so you know we said this + + align:start position:0% +true okay so so you know we said this + + + align:start position:0% +true okay so so you know we said this +has to be incon in that and we're + + align:start position:0% +has to be incon in that and we're + + + align:start position:0% +has to be incon in that and we're +fighting for not only the the electronic + + align:start position:0% +fighting for not only the the electronic + + + align:start position:0% +fighting for not only the the electronic +medical system but the whole technology + + align:start position:0% +medical system but the whole technology + + + align:start position:0% +medical system but the whole technology +framework to put that in which is + + align:start position:0% +framework to put that in which is + + + align:start position:0% +framework to put that in which is +satellite internet what is you think + + align:start position:0% +satellite internet what is you think + + + align:start position:0% +satellite internet what is you think +satellite internet does for a + + align:start position:0% +satellite internet does for a + + + align:start position:0% +satellite internet does for a +clinic take out the record + + align:start position:0% + + + + align:start position:0% + +system decision support so definitely + + align:start position:0% +system decision support so definitely + + + align:start position:0% +system decision support so definitely +you can you can help you can do tele + + align:start position:0% +you can you can help you can do tele + + + align:start position:0% +you can you can help you can do tele +medicine you can do decision support I + + align:start position:0% +medicine you can do decision support I + + + align:start position:0% +medicine you can do decision support I +get even today even though you know no + + align:start position:0% +get even today even though you know no + + + align:start position:0% +get even today even though you know no +one really needs me anymore I still get + + align:start position:0% +one really needs me anymore I still get + + + align:start position:0% +one really needs me anymore I still get +you what do you think about this patient + + align:start position:0% +you what do you think about this patient + + + align:start position:0% +you what do you think about this patient +kind of thing you know casual or formal + + align:start position:0% +kind of thing you know casual or formal + + + align:start position:0% +kind of thing you know casual or formal +decision support what + + align:start position:0% + + + + align:start position:0% + +else what do you use the internet what + + align:start position:0% +else what do you use the internet what + + + align:start position:0% +else what do you use the internet what +so the + + align:start position:0% +so the + + + align:start position:0% +so the +employees practice absolutely so up + + align:start position:0% +employees practice absolutely so up + + + align:start position:0% +employees practice absolutely so up +toate looking at Medline searching + + align:start position:0% +toate looking at Medline searching + + + align:start position:0% +toate looking at Medline searching +articles you know our physicians and + + align:start position:0% +articles you know our physicians and + + + align:start position:0% +articles you know our physicians and +nurses want to be good you know they + + align:start position:0% +nurses want to be good you know they + + + align:start position:0% +nurses want to be good you know they +want to participate in the global debate + + align:start position:0% +want to participate in the global debate + + + align:start position:0% +want to participate in the global debate +about HIV or TB or malaria so so that + + align:start position:0% +about HIV or TB or malaria so so that + + + align:start position:0% +about HIV or TB or malaria so so that +you know can can make them not feel so + + align:start position:0% +you know can can make them not feel so + + + align:start position:0% +you know can can make them not feel so +isolated in every country in the world + + align:start position:0% +isolated in every country in the world + + + align:start position:0% +isolated in every country in the world +doctors and nurses do not want to work + + align:start position:0% +doctors and nurses do not want to work + + + align:start position:0% +doctors and nurses do not want to work +in the middle of nowhere and that's one + + align:start position:0% +in the middle of nowhere and that's one + + + align:start position:0% +in the middle of nowhere and that's one +of the reasons why else what else would + + align:start position:0% +of the reasons why else what else would + + + align:start position:0% +of the reasons why else what else would +it be helpful for it yeah so AR of the + + align:start position:0% +it be helpful for it yeah so AR of the + + + align:start position:0% +it be helpful for it yeah so AR of the +EMR yeah so you know having the history + + align:start position:0% +EMR yeah so you know having the history + + + align:start position:0% +EMR yeah so you know having the history +of what we've done um very + + align:start position:0% +of what we've done um very + + + align:start position:0% +of what we've done um very +important tracking the patients yeah and + + align:start position:0% +important tracking the patients yeah and + + + align:start position:0% +important tracking the patients yeah and +really yeah go ahead new yes quality of + + align:start position:0% +really yeah go ahead new yes quality of + + + align:start position:0% +really yeah go ahead new yes quality of +life for the + + align:start position:0% +life for the + + + align:start position:0% +life for the +staff like doesn't the internet kind of + + align:start position:0% +staff like doesn't the internet kind of + + + align:start position:0% +staff like doesn't the internet kind of +help your quality of life I mean the + + align:start position:0% +help your quality of life I mean the + + + align:start position:0% +help your quality of life I mean the +fact is these are people in the middle + + align:start position:0% +fact is these are people in the middle + + + align:start position:0% +fact is these are people in the middle +of nowhere now you know we have some + + align:start position:0% +of nowhere now you know we have some + + + align:start position:0% +of nowhere now you know we have some +problems occasionally with downloading a + + align:start position:0% +problems occasionally with downloading a + + + align:start position:0% +problems occasionally with downloading a +porn but okay all right as long as I do + + align:start position:0% +porn but okay all right as long as I do + + + align:start position:0% +porn but okay all right as long as I do +it + + align:start position:0% +it + + + align:start position:0% +it +safely um but no seriously for people to + + align:start position:0% +safely um but no seriously for people to + + + align:start position:0% +safely um but no seriously for people to +keep in touch with their families by + + align:start position:0% +keep in touch with their families by + + + align:start position:0% +keep in touch with their families by +Skype for people to have friends on + + align:start position:0% +Skype for people to have friends on + + + align:start position:0% +Skype for people to have friends on +Facebook in other countries this is also + + align:start position:0% +Facebook in other countries this is also + + + align:start position:0% +Facebook in other countries this is also +a really important way to make people's + + align:start position:0% +a really important way to make people's + + + align:start position:0% +a really important way to make people's +quality of life in a poor isolated reg + + align:start position:0% +quality of life in a poor isolated reg + + + align:start position:0% +quality of life in a poor isolated reg +reasonable and we think that's also a + + align:start position:0% +reasonable and we think that's also a + + + align:start position:0% +reasonable and we think that's also a +valid thing and then the last thing that + + align:start position:0% +valid thing and then the last thing that + + + align:start position:0% +valid thing and then the last thing that +was quite a surprise to us was how much + + align:start position:0% +was quite a surprise to us was how much + + + align:start position:0% +was quite a surprise to us was how much +it helped um maternal mortality + + align:start position:0% +it helped um maternal mortality + + + align:start position:0% +it helped um maternal mortality +issues when we first put up our first + + align:start position:0% +issues when we first put up our first + + + align:start position:0% +issues when we first put up our first +list serve the aliance that's gone down + + align:start position:0% +list serve the aliance that's gone down + + + align:start position:0% +list serve the aliance that's gone down +several times because of strangeness the + + align:start position:0% +several times because of strangeness the + + + align:start position:0% +several times because of strangeness the +number one call for help was a + + align:start position:0% +number one call for help was a + + + align:start position:0% +number one call for help was a +obstructed labor Hemorrhage right we + + align:start position:0% +obstructed labor Hemorrhage right we + + + align:start position:0% +obstructed labor Hemorrhage right we +don't have cerian section every site but + + align:start position:0% +don't have cerian section every site but + + + align:start position:0% +don't have cerian section every site but +we have some places you can do cerian + + align:start position:0% +we have some places you can do cerian + + + align:start position:0% +we have some places you can do cerian +section and we could get rapidly deploy + + align:start position:0% +section and we could get rapidly deploy + + + align:start position:0% +section and we could get rapidly deploy +ambulances and get women to hospitals so + + align:start position:0% +ambulances and get women to hospitals so + + + align:start position:0% +ambulances and get women to hospitals so +the the emergency you know you think + + align:start position:0% +the the emergency you know you think + + + align:start position:0% +the the emergency you know you think +about we call 911 we take it for granted + + align:start position:0% +about we call 911 we take it for granted + + + align:start position:0% +about we call 911 we take it for granted +but there is no emergency in Medical + + align:start position:0% +but there is no emergency in Medical + + + align:start position:0% +but there is no emergency in Medical +Response and that was very much + + align:start position:0% +Response and that was very much + + + align:start position:0% +Response and that was very much +facilitating it's critical as you're + + align:start position:0% +facilitating it's critical as you're + + + align:start position:0% +facilitating it's critical as you're +developing these new health centers to + + align:start position:0% +developing these new health centers to + + + align:start position:0% +developing these new health centers to +be able to prevent death right because + + align:start position:0% +be able to prevent death right because + + + align:start position:0% +be able to prevent death right because +you want people to have faith in what + + align:start position:0% +you want people to have faith in what + + + align:start position:0% +you want people to have faith in what +you're doing and you see these kids that + + align:start position:0% +you're doing and you see these kids that + + + align:start position:0% +you're doing and you see these kids that +need blood transfusions because they + + align:start position:0% +need blood transfusions because they + + + align:start position:0% +need blood transfusions because they +have malaria you see you know women who + + align:start position:0% +have malaria you see you know women who + + + align:start position:0% +have malaria you see you know women who +are dying Etc so you know for us this + + align:start position:0% +are dying Etc so you know for us this + + + align:start position:0% +are dying Etc so you know for us this +was something about medical records but + + align:start position:0% +was something about medical records but + + + align:start position:0% +was something about medical records but +it was also something about quality of + + align:start position:0% +it was also something about quality of + + + align:start position:0% +it was also something about quality of +life it was something about developing A + + align:start position:0% +life it was something about developing A + + + align:start position:0% +life it was something about developing A +system that could provide emergency care + + align:start position:0% +system that could provide emergency care + + + align:start position:0% +system that could provide emergency care +um so I'm actually just going to talk uh + + align:start position:0% +um so I'm actually just going to talk uh + + + align:start position:0% +um so I'm actually just going to talk uh +for the last 5 minutes about so what is + + align:start position:0% +for the last 5 minutes about so what is + + + align:start position:0% +for the last 5 minutes about so what is +our plan for scale well you know in 2005 + + align:start position:0% +our plan for scale well you know in 2005 + + + align:start position:0% +our plan for scale well you know in 2005 +because of the work in Haiti we were + + align:start position:0% +because of the work in Haiti we were + + + align:start position:0% +because of the work in Haiti we were +invited by the government of Rwanda to + + align:start position:0% +invited by the government of Rwanda to + + + align:start position:0% +invited by the government of Rwanda to +help them develop a rural Health Plan + + align:start position:0% +help them develop a rural Health Plan + + + align:start position:0% +help them develop a rural Health Plan +not around HIV although HIV was part of + + align:start position:0% +not around HIV although HIV was part of + + + align:start position:0% +not around HIV although HIV was part of +it but really how do you harness the + + align:start position:0% +it but really how do you harness the + + + align:start position:0% +it but really how do you harness the +community and the public sector and and + + align:start position:0% +community and the public sector and and + + + align:start position:0% +community and the public sector and and +what the government really liked is they + + align:start position:0% +what the government really liked is they + + + align:start position:0% +what the government really liked is they +said oh this is an NGO that's not + + align:start position:0% +said oh this is an NGO that's not + + + align:start position:0% +said oh this is an NGO that's not +setting up a separate system they're + + align:start position:0% +setting up a separate system they're + + + align:start position:0% +setting up a separate system they're +actually helping us to do what we're + + align:start position:0% +actually helping us to do what we're + + + align:start position:0% +actually helping us to do what we're +supposed to be doing like what what our + + align:start position:0% +supposed to be doing like what what our + + + align:start position:0% +supposed to be doing like what what our +constitutional mandate is and so we went + + align:start position:0% +constitutional mandate is and so we went + + + align:start position:0% +constitutional mandate is and so we went +through the same model meet with the + + align:start position:0% +through the same model meet with the + + + align:start position:0% +through the same model meet with the +community see what it is the community + + align:start position:0% +community see what it is the community + + + align:start position:0% +community see what it is the community +needs and needs were often really pretty + + align:start position:0% +needs and needs were often really pretty + + + align:start position:0% +needs and needs were often really pretty +similar but still the exercise is very + + align:start position:0% +similar but still the exercise is very + + + align:start position:0% +similar but still the exercise is very +important um in fact the guy standing up + + align:start position:0% +important um in fact the guy standing up + + + align:start position:0% +important um in fact the guy standing up +in the gray shirt is is our head of hibb + + align:start position:0% +in the gray shirt is is our head of hibb + + + align:start position:0% +in the gray shirt is is our head of hibb +for our work in Haiti and he was one of + + align:start position:0% +for our work in Haiti and he was one of + + + align:start position:0% +for our work in Haiti and he was one of +our chief is continues to be one of our + + align:start position:0% +our chief is continues to be one of our + + + align:start position:0% +our chief is continues to be one of our +chief consultants in Moana so a lot of + + align:start position:0% +chief consultants in Moana so a lot of + + + align:start position:0% +chief consultants in Moana so a lot of +our patient staff who had developed this + + align:start position:0% +our patient staff who had developed this + + + align:start position:0% +our patient staff who had developed this +expertise really have helped a lot in + + align:start position:0% +expertise really have helped a lot in + + + align:start position:0% +expertise really have helped a lot in +Rwanda and other places revitalizing the + + align:start position:0% +Rwanda and other places revitalizing the + + + align:start position:0% +Rwanda and other places revitalizing the +hospital saying you know this system is + + align:start position:0% +hospital saying you know this system is + + + align:start position:0% +hospital saying you know this system is +broken like you can't attract people to + + align:start position:0% +broken like you can't attract people to + + + align:start position:0% +broken like you can't attract people to +care if it's not dignified um working + + align:start position:0% +care if it's not dignified um working + + + align:start position:0% +care if it's not dignified um working +with the public sector and then sort of + + align:start position:0% +with the public sector and then sort of + + + align:start position:0% +with the public sector and then sort of +how you engage community health workers + + align:start position:0% +how you engage community health workers + + + align:start position:0% +how you engage community health workers +and um I'm not going to talk about all + + align:start position:0% +and um I'm not going to talk about all + + + align:start position:0% +and um I'm not going to talk about all +this stuff but I just want to uh say + + align:start position:0% +this stuff but I just want to uh say + + + align:start position:0% +this stuff but I just want to uh say +something about child malnutrition + + align:start position:0% +something about child malnutrition + + + align:start position:0% +something about child malnutrition +before I start is at Heart of + + align:start position:0% +before I start is at Heart of + + + align:start position:0% +before I start is at Heart of +pediatrician so you know I think for + + align:start position:0% +pediatrician so you know I think for + + + align:start position:0% +pediatrician so you know I think for +each of these stages you know we we've + + align:start position:0% +each of these stages you know we we've + + + align:start position:0% +each of these stages you know we we've +sort of seen a problem that is + + align:start position:0% +sort of seen a problem that is + + + align:start position:0% +sort of seen a problem that is +insolvable given the resources that are + + align:start position:0% +insolvable given the resources that are + + + align:start position:0% +insolvable given the resources that are +available we've tried to document how + + align:start position:0% +available we've tried to document how + + + align:start position:0% +available we've tried to document how +you could deliver those resources and + + align:start position:0% +you could deliver those resources and + + + align:start position:0% +you could deliver those resources and +how much it would cost and then have a + + align:start position:0% +how much it would cost and then have a + + + align:start position:0% +how much it would cost and then have a +strategy to mobilize these resources so + + align:start position:0% +strategy to mobilize these resources so + + + align:start position:0% +strategy to mobilize these resources so +one of the things we're very involved in + + align:start position:0% +one of the things we're very involved in + + + align:start position:0% +one of the things we're very involved in +now is child + + align:start position:0% +now is child + + + align:start position:0% +now is child +malnutrition and you know + + align:start position:0% +malnutrition and you know + + + align:start position:0% +malnutrition and you know +24,000 kids die every day + + align:start position:0% +24,000 kids die every day + + + align:start position:0% +24,000 kids die every day +of malnutrition related preventable + + align:start position:0% +of malnutrition related preventable + + + align:start position:0% +of malnutrition related preventable +diseases so 60% of them are related to + + align:start position:0% +diseases so 60% of them are related to + + + align:start position:0% +diseases so 60% of them are related to +malnutrition what do they die they die + + align:start position:0% +malnutrition what do they die they die + + + align:start position:0% +malnutrition what do they die they die +of diarrhea they die of colds + + align:start position:0% +of diarrhea they die of colds + + + align:start position:0% +of diarrhea they die of colds +respiratory infections they die of + + align:start position:0% +respiratory infections they die of + + + align:start position:0% +respiratory infections they die of +malaria all these things are one + + align:start position:0% +malaria all these things are one + + + align:start position:0% +malaria all these things are one +preventable and two would not kill them + + align:start position:0% +preventable and two would not kill them + + + align:start position:0% +preventable and two would not kill them +if they were well-nourished + + align:start position:0% +if they were well-nourished + + + align:start position:0% +if they were well-nourished +but the what do you know what the public + + align:start position:0% +but the what do you know what the public + + + align:start position:0% +but the what do you know what the public +health strategy is for kids for to deal + + align:start position:0% +health strategy is for kids for to deal + + + align:start position:0% +health strategy is for kids for to deal +with kids who have + + align:start position:0% +with kids who have + + + align:start position:0% +with kids who have +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +malnutrition something I mean is a sort + + align:start position:0% +malnutrition something I mean is a sort + + + align:start position:0% +malnutrition something I mean is a sort +of standard Public Health strategy for + + align:start position:0% +of standard Public Health strategy for + + + align:start position:0% +of standard Public Health strategy for +kids under five is something called GOI + + align:start position:0% +kids under five is something called GOI + + + align:start position:0% +kids under five is something called GOI +growth monitoring oral rehydration if + + align:start position:0% +growth monitoring oral rehydration if + + + align:start position:0% +growth monitoring oral rehydration if +they have diarrhea um uh promotion of + + align:start position:0% +they have diarrhea um uh promotion of + + + align:start position:0% +they have diarrhea um uh promotion of +exclusive breastfeeding until age six + + align:start position:0% +exclusive breastfeeding until age six + + + align:start position:0% +exclusive breastfeeding until age six +months until two years of life um and + + align:start position:0% +months until two years of life um and + + + align:start position:0% +months until two years of life um and +immunization and that's the + + align:start position:0% +immunization and that's the + + + align:start position:0% +immunization and that's the +package but here's the problem when + + align:start position:0% +package but here's the problem when + + + align:start position:0% +package but here's the problem when +you're doing growth monitoring so this + + align:start position:0% +you're doing growth monitoring so this + + + align:start position:0% +you're doing growth monitoring so this +is like a standard uh growth chart + + align:start position:0% +is like a standard uh growth chart + + + align:start position:0% +is like a standard uh growth chart +standard everybody's seen this shim + + align:start position:0% +standard everybody's seen this shim + + + align:start position:0% +standard everybody's seen this shim +lante but it's in it's in whatever + + align:start position:0% +lante but it's in it's in whatever + + + align:start position:0% +lante but it's in it's in whatever +language your Ruba it's it's in every + + align:start position:0% +language your Ruba it's it's in every + + + align:start position:0% +language your Ruba it's it's in every +language youu hand me out like candy + + align:start position:0% +language youu hand me out like candy + + + align:start position:0% +language youu hand me out like candy +this is the intervention right so you + + align:start position:0% +this is the intervention right so you + + + align:start position:0% +this is the intervention right so you +weigh a kid in that little gaffing hook + + align:start position:0% +weigh a kid in that little gaffing hook + + + align:start position:0% +weigh a kid in that little gaffing hook +right you put him in that little blue + + align:start position:0% +right you put him in that little blue + + + align:start position:0% +right you put him in that little blue +thing and they kind and then you put him + + align:start position:0% +thing and they kind and then you put him + + + align:start position:0% +thing and they kind and then you put him +on the chart now by the way this yellow + + align:start position:0% +on the chart now by the way this yellow + + + align:start position:0% +on the chart now by the way this yellow +goes to zero like I think that's not + + align:start position:0% +goes to zero like I think that's not + + + align:start position:0% +goes to zero like I think that's not +compatible with light last I + + align:start position:0% +compatible with light last I + + + align:start position:0% +compatible with light last I +checked + + align:start position:0% +checked + + + align:start position:0% +checked +but you put them on this chart if + + align:start position:0% +but you put them on this chart if + + + align:start position:0% +but you put them on this chart if +they're in the red they're okay + + align:start position:0% +they're in the red they're okay + + + align:start position:0% +they're in the red they're okay +if they're in the orange they're um low + + align:start position:0% +if they're in the orange they're um low + + + align:start position:0% +if they're in the orange they're um low +weight for age and you have to do + + align:start position:0% +weight for age and you have to do + + + align:start position:0% +weight for age and you have to do +something and if they're yellow they're + + align:start position:0% +something and if they're yellow they're + + + align:start position:0% +something and if they're yellow they're +severely low weight R so what do you do + + align:start position:0% +severely low weight R so what do you do + + + align:start position:0% +severely low weight R so what do you do +when you find out the kid is in the + + align:start position:0% +when you find out the kid is in the + + + align:start position:0% +when you find out the kid is in the +orange or the yellow what do you think + + align:start position:0% +orange or the yellow what do you think + + + align:start position:0% +orange or the yellow what do you think +you do growth monitoring or + + align:start position:0% +you do growth monitoring or + + + align:start position:0% +you do growth monitoring or +overhydration blast feeding + + align:start position:0% +overhydration blast feeding + + + align:start position:0% +overhydration blast feeding +immunization so you've monitored their + + align:start position:0% +immunization so you've monitored their + + + align:start position:0% +immunization so you've monitored their +growth check so what what will you do + + align:start position:0% +growth check so what what will you do + + + align:start position:0% +growth check so what what will you do +when you find out that they're in the + + align:start position:0% +when you find out that they're in the + + + align:start position:0% +when you find out that they're in the +orange or yellow we should do or what do + + align:start position:0% +orange or yellow we should do or what do + + + align:start position:0% +orange or yellow we should do or what do +you yeah what do they traditionally what + + align:start position:0% +you yeah what do they traditionally what + + + align:start position:0% +you yeah what do they traditionally what +do we + + align:start position:0% +do we + + + align:start position:0% +do we +do no it's not feed them this is the + + align:start position:0% +do no it's not feed them this is the + + + align:start position:0% +do no it's not feed them this is the +crazy thing did just keep the records + + align:start position:0% +crazy thing did just keep the records + + + align:start position:0% +crazy thing did just keep the records +keep the records which as we know are + + align:start position:0% +keep the records which as we know are + + + align:start position:0% +keep the records which as we know are +sitting over here going piling up and + + align:start position:0% +sitting over here going piling up and + + + align:start position:0% +sitting over here going piling up and +what else what else might you + + align:start position:0% +what else what else might you + + + align:start position:0% +what else what else might you +do + + align:start position:0% +do + + + align:start position:0% +do +ladies any Mothers besides me + + align:start position:0% + + + + align:start position:0% + +Ellen you might tell to breastfeed the + + align:start position:0% +Ellen you might tell to breastfeed the + + + align:start position:0% +Ellen you might tell to breastfeed the +breastfeed more that you might do that + + align:start position:0% +breastfeed more that you might do that + + + align:start position:0% +breastfeed more that you might do that +CU that's in your goby framework + + align:start position:0% +CU that's in your goby framework + + + align:start position:0% +CU that's in your goby framework +breastfeeding by the way is not so easy + + align:start position:0% +breastfeeding by the way is not so easy + + + align:start position:0% +breastfeeding by the way is not so easy +I would just like to point that out + + align:start position:0% +I would just like to point that out + + + align:start position:0% +I would just like to point that out +especially if you're dehydrated which + + align:start position:0% +especially if you're dehydrated which + + + align:start position:0% +especially if you're dehydrated which +most women are in for countries they + + align:start position:0% +most women are in for countries they + + + align:start position:0% +most women are in for countries they +don't make L the + + align:start position:0% +don't make L the + + + align:start position:0% +don't make L the +mother educate the mother so you go with + + align:start position:0% +mother educate the mother so you go with + + + align:start position:0% +mother educate the mother so you go with +this chart this is real this really what + + align:start position:0% +this chart this is real this really what + + + align:start position:0% +this chart this is real this really what +you do come on you guys have done this + + align:start position:0% +you do come on you guys have done this + + + align:start position:0% +you do come on you guys have done this +right it's a chart it has four food + + align:start position:0% +right it's a chart it has four food + + + align:start position:0% +right it's a chart it has four food +groups on it so you have an orange or + + align:start position:0% +groups on it so you have an orange or + + + align:start position:0% +groups on it so you have an orange or +yellow baby and you go okay here's your + + align:start position:0% +yellow baby and you go okay here's your + + + align:start position:0% +yellow baby and you go okay here's your +chart this is green vegetables these are + + align:start position:0% +chart this is green vegetables these are + + + align:start position:0% +chart this is green vegetables these are +good this chicken leg or egg that's + + align:start position:0% +good this chicken leg or egg that's + + + align:start position:0% +good this chicken leg or egg that's +protein very important your kid is not + + align:start position:0% +protein very important your kid is not + + + align:start position:0% +protein very important your kid is not +getting enough of that this grain right + + align:start position:0% +getting enough of that this grain right + + + align:start position:0% +getting enough of that this grain right +this is fat Dairy okay Mom can you do + + align:start position:0% +this is fat Dairy okay Mom can you do + + + align:start position:0% +this is fat Dairy okay Mom can you do +that cuz your kid is + + align:start position:0% +that cuz your kid is + + + align:start position:0% +that cuz your kid is +really do you see that chart is that + + align:start position:0% +really do you see that chart is that + + + align:start position:0% +really do you see that chart is that +helping + + align:start position:0% +helping + + + align:start position:0% +helping +you why + + align:start position:0% + + + + align:start position:0% + +not you don't have access to those foods + + align:start position:0% +not you don't have access to those foods + + + align:start position:0% +not you don't have access to those foods +like mothers know that the kids need to + + align:start position:0% +like mothers know that the kids need to + + + align:start position:0% +like mothers know that the kids need to +eat I mean I have a skinny kid he's not + + align:start position:0% +eat I mean I have a skinny kid he's not + + + align:start position:0% +eat I mean I have a skinny kid he's not +so skinny anymore I mean there is + + align:start position:0% +so skinny anymore I mean there is + + + align:start position:0% +so skinny anymore I mean there is +nothing that makes you feel worse as a + + align:start position:0% +nothing that makes you feel worse as a + + + align:start position:0% +nothing that makes you feel worse as a +mother than having a skinny kid and the + + align:start position:0% +mother than having a skinny kid and the + + + align:start position:0% +mother than having a skinny kid and the +poorer you are the more true that is + + align:start position:0% +poorer you are the more true that is + + + align:start position:0% +poorer you are the more true that is +right because your whole like success as + + align:start position:0% +right because your whole like success as + + + align:start position:0% +right because your whole like success as +a mother is about feeding your kid like + + align:start position:0% +a mother is about feeding your kid like + + + align:start position:0% +a mother is about feeding your kid like +they don't care about anything else you + + align:start position:0% +they don't care about anything else you + + + align:start position:0% +they don't care about anything else you +got to feed them so the idea that that + + align:start position:0% +got to feed them so the idea that that + + + align:start position:0% +got to feed them so the idea that that +is the strategy well we said so two + + align:start position:0% +is the strategy well we said so two + + + align:start position:0% +is the strategy well we said so two +problems with that one is you just don't + + align:start position:0% +problems with that one is you just don't + + + align:start position:0% +problems with that one is you just don't +have access here's the other secret + + align:start position:0% +have access here's the other secret + + + align:start position:0% +have access here's the other secret +problem and this is where we need your + + align:start position:0% +problem and this is where we need your + + + align:start position:0% +problem and this is where we need your +help so I was doing this chart one + + align:start position:0% +help so I was doing this chart one + + + align:start position:0% +help so I was doing this chart one +day and I said to one of my Haitian + + align:start position:0% +day and I said to one of my Haitian + + + align:start position:0% +day and I said to one of my Haitian +colleagues he's a big tall guy a + + align:start position:0% +colleagues he's a big tall guy a + + + align:start position:0% +colleagues he's a big tall guy a +pediatrician I said this kid is so tiny + + align:start position:0% +pediatrician I said this kid is so tiny + + + align:start position:0% +pediatrician I said this kid is so tiny +he says no he's in the red I said that's + + align:start position:0% +he says no he's in the red I said that's + + + align:start position:0% +he says no he's in the red I said that's +weird and for the first time ever I + + align:start position:0% +weird and for the first time ever I + + + align:start position:0% +weird and for the first time ever I +opened my herit Lane handbook which is + + align:start position:0% +opened my herit Lane handbook which is + + + align:start position:0% +opened my herit Lane handbook which is +an American Pediatric handbook and I put + + align:start position:0% +an American Pediatric handbook and I put + + + align:start position:0% +an American Pediatric handbook and I put +the kid on the growth chart and he was + + align:start position:0% +the kid on the growth chart and he was + + + align:start position:0% +the kid on the growth chart and he was +in the less than 5% and so I superimpose + + align:start position:0% + + + + align:start position:0% + +these why all these kids are + + align:start position:0% +these why all these kids are + + + align:start position:0% +these why all these kids are +dying if any kid in the US is below the + + align:start position:0% +dying if any kid in the US is below the + + + align:start position:0% +dying if any kid in the US is below the +perc they get admitted to the + + align:start position:0% +perc they get admitted to the + + + align:start position:0% +perc they get admitted to the +hospital they would get admitted under + + align:start position:0% +hospital they would get admitted under + + + align:start position:0% +hospital they would get admitted under +Child Protection to the + + align:start position:0% +Child Protection to the + + + align:start position:0% +Child Protection to the +hospital okay this is the majority of + + align:start position:0% +hospital okay this is the majority of + + + align:start position:0% +hospital okay this is the majority of +children so one of the things we're + + align:start position:0% +children so one of the things we're + + + align:start position:0% +children so one of the things we're +really fighting for is trying to + + align:start position:0% +really fighting for is trying to + + + align:start position:0% +really fighting for is trying to +document that this is just not + + align:start position:0% +document that this is just not + + + align:start position:0% +document that this is just not +compatible with + + align:start position:0% +compatible with + + + align:start position:0% +compatible with +survival you know this is resulting in + + align:start position:0% +survival you know this is resulting in + + + align:start position:0% +survival you know this is resulting in +stunting and cognitive delay and death + + align:start position:0% +stunting and cognitive delay and death + + + align:start position:0% +stunting and cognitive delay and death +and um you know the world doesn't want + + align:start position:0% +and um you know the world doesn't want + + + align:start position:0% +and um you know the world doesn't want +to hear this this is kind of going back + + align:start position:0% +to hear this this is kind of going back + + + align:start position:0% +to hear this this is kind of going back +to that we're not going to see this + + align:start position:0% +to that we're not going to see this + + + align:start position:0% +to that we're not going to see this +we're not going to hear it because what + + align:start position:0% +we're not going to hear it because what + + + align:start position:0% +we're not going to hear it because what +it says is places like Haiti 80% of the + + align:start position:0% +it says is places like Haiti 80% of the + + + align:start position:0% +it says is places like Haiti 80% of the +kids are + + align:start position:0% +kids are + + + align:start position:0% +kids are +stunted you know and this tall + + align:start position:0% +stunted you know and this tall + + + align:start position:0% +stunted you know and this tall +pediatrician said well you know Haitians + + align:start position:0% +pediatrician said well you know Haitians + + + align:start position:0% +pediatrician said well you know Haitians +are smaller I said + + align:start position:0% +are smaller I said + + + align:start position:0% +are smaller I said +no he said well not my kind of Haitian + + align:start position:0% +no he said well not my kind of Haitian + + + align:start position:0% +no he said well not my kind of Haitian +not middle class as right so you know + + align:start position:0% +not middle class as right so you know + + + align:start position:0% +not middle class as right so you know +I'll stop there but saying you know we + + align:start position:0% +I'll stop there but saying you know we + + + align:start position:0% +I'll stop there but saying you know we +have you know and so so one of the + + align:start position:0% +have you know and so so one of the + + + align:start position:0% +have you know and so so one of the +things we've done with this is really + + align:start position:0% +things we've done with this is really + + + align:start position:0% +things we've done with this is really +move toward actual feeding with ready to + + align:start position:0% +move toward actual feeding with ready to + + + align:start position:0% +move toward actual feeding with ready to +use therapeutic food which is + + align:start position:0% +use therapeutic food which is + + + align:start position:0% +use therapeutic food which is +nutritionally fortified peanut butter + + align:start position:0% +nutritionally fortified peanut butter + + + align:start position:0% +nutritionally fortified peanut butter +that we can make locally that we can + + align:start position:0% +that we can make locally that we can + + + align:start position:0% +that we can make locally that we can +Source locally that we can pay local + + align:start position:0% +Source locally that we can pay local + + + align:start position:0% +Source locally that we can pay local +farmers to produce and make you we're + + align:start position:0% +farmers to produce and make you we're + + + align:start position:0% +farmers to produce and make you we're +going even put a a big Factory for it + + align:start position:0% +going even put a a big Factory for it + + + align:start position:0% +going even put a a big Factory for it +and you know treat malnutrition as a + + align:start position:0% +and you know treat malnutrition as a + + + align:start position:0% +and you know treat malnutrition as a +disease put that ready cheese + + align:start position:0% +disease put that ready cheese + + + align:start position:0% +disease put that ready cheese +therapeutic food on an essential drug + + align:start position:0% +therapeutic food on an essential drug + + + align:start position:0% +therapeutic food on an essential drug +list because those kids under five if + + align:start position:0% +list because those kids under five if + + + align:start position:0% +list because those kids under five if +you don't if you don't get them up to + + align:start position:0% +you don't if you don't get them up to + + + align:start position:0% +you don't if you don't get them up to +their right height and weight by the + + align:start position:0% +their right height and weight by the + + + align:start position:0% +their right height and weight by the +time they're two you have lost a big + + align:start position:0% +time they're two you have lost a big + + + align:start position:0% +time they're two you have lost a big +chunk of their potential thank you very + + align:start position:0% +chunk of their potential thank you very + + + align:start position:0% +chunk of their potential thank you very +much Jo I always enjoy this meeting and + + align:start position:0% +much Jo I always enjoy this meeting and + + + align:start position:0% +much Jo I always enjoy this meeting and +uh one of the the key things here was to + + align:start position:0% +uh one of the the key things here was to + + + align:start position:0% +uh one of the the key things here was to +to really get you thinking and also in + + align:start position:0% +to really get you thinking and also in + + + align:start position:0% +to really get you thinking and also in +you know this is a class where we really + + align:start position:0% +you know this is a class where we really + + + align:start position:0% +you know this is a class where we really +want people to think about problems out + + align:start position:0% +want people to think about problems out + + + align:start position:0% +want people to think about problems out +box and to really to to question the way + + align:start position:0% +box and to really to to question the way + + + align:start position:0% +box and to really to to question the way +that Health Care is been provided + + align:start position:0% +that Health Care is been provided + + + align:start position:0% +that Health Care is been provided +question the the structures we have at + + align:start position:0% +question the the structures we have at + + + align:start position:0% +question the the structures we have at +the moment and how can we use new + + align:start position:0% +the moment and how can we use new + + + align:start position:0% +the moment and how can we use new +approaches new technology to address + + align:start position:0% +approaches new technology to address + + + align:start position:0% +approaches new technology to address +those and I think you know there are + + align:start position:0% +those and I think you know there are + + + align:start position:0% +those and I think you know there are +many things that Jo actually has BC out + + align:start position:0% +many things that Jo actually has BC out + + + align:start position:0% +many things that Jo actually has BC out +here which we'll talk about more but one + + align:start position:0% +here which we'll talk about more but one + + + align:start position:0% +here which we'll talk about more but one +I one just sort of caught me was this + + align:start position:0% +I one just sort of caught me was this + + + align:start position:0% +I one just sort of caught me was this +question about the U use of satellite + + align:start position:0% +question about the U use of satellite + + + align:start position:0% +question about the U use of satellite +internet we went into places like bukon + + align:start position:0% +internet we went into places like bukon + + + align:start position:0% +internet we went into places like bukon +car and K and all the other sites in the + + align:start position:0% +car and K and all the other sites in the + + + align:start position:0% +car and K and all the other sites in the +central Plateau region of Haiti in the + + align:start position:0% +central Plateau region of Haiti in the + + + align:start position:0% +central Plateau region of Haiti in the +early part of the last decade these were + + align:start position:0% +early part of the last decade these were + + + align:start position:0% +early part of the last decade these were +places that had absolutely no + + align:start position:0% +places that had absolutely no + + + align:start position:0% +places that had absolutely no +communication no cell no cell phones no + + align:start position:0% +communication no cell no cell phones no + + + align:start position:0% +communication no cell no cell phones no +land lines you might get radio from the + + align:start position:0% +land lines you might get radio from the + + + align:start position:0% +land lines you might get radio from the +capital and that was basically it and so + + align:start position:0% +capital and that was basically it and so + + + align:start position:0% +capital and that was basically it and so +the question about what what changed in + + align:start position:0% +the question about what what changed in + + + align:start position:0% +the question about what what changed in +the way you can provide care and the way + + align:start position:0% +the way you can provide care and the way + + + align:start position:0% +the way you can provide care and the way +an Healthcare organization is working + + align:start position:0% +an Healthcare organization is working + + + align:start position:0% +an Healthcare organization is working +with the ability to actually communicate + + align:start position:0% +with the ability to actually communicate + + + align:start position:0% +with the ability to actually communicate +is absolutely critical and it's only now + + align:start position:0% +is absolutely critical and it's only now + + + align:start position:0% +is absolutely critical and it's only now +that cell phone systems have starting to + + align:start position:0% +that cell phone systems have starting to + + + align:start position:0% +that cell phone systems have starting to +really Rampage across the developing + + align:start position:0% +really Rampage across the developing + + + align:start position:0% +really Rampage across the developing +World in really amazing ways that people + + align:start position:0% +World in really amazing ways that people + + + align:start position:0% +World in really amazing ways that people +are starting to question what is that + + align:start position:0% +are starting to question what is that + + + align:start position:0% +are starting to question what is that +doing to change the nature of what we + + align:start position:0% +doing to change the nature of what we + + + align:start position:0% +doing to change the nature of what we +can do and how we think about Healthcare + + align:start position:0% +can do and how we think about Healthcare + + + align:start position:0% +can do and how we think about Healthcare +and how we run organizations and what we + + align:start position:0% +and how we run organizations and what we + + + align:start position:0% +and how we run organizations and what we +can do with drugs Supply and what we can + + align:start position:0% +can do with drugs Supply and what we can + + + align:start position:0% +can do with drugs Supply and what we can +do to get critical information to the + + align:start position:0% +do to get critical information to the + + + align:start position:0% +do to get critical information to the +places it needs so that patients don't + + align:start position:0% +places it needs so that patients don't + + + align:start position:0% +places it needs so that patients don't +fall through the gaps particularly for + + align:start position:0% +fall through the gaps particularly for + + + align:start position:0% +fall through the gaps particularly for +example pregnant women who may need + + align:start position:0% +example pregnant women who may need + + + align:start position:0% +example pregnant women who may need +cesarian section or instructed labor so + + align:start position:0% +cesarian section or instructed labor so + + + align:start position:0% +cesarian section or instructed labor so +these are the kind of questions that we + + align:start position:0% +these are the kind of questions that we + + + align:start position:0% +these are the kind of questions that we +want you to think about and to sort of + + align:start position:0% +want you to think about and to sort of + + + align:start position:0% +want you to think about and to sort of +really go just consider how differently + + align:start position:0% +really go just consider how differently + + + align:start position:0% +really go just consider how differently +we could provide care and also what + + align:start position:0% +we could provide care and also what + + + align:start position:0% +we could provide care and also what +other Technologies might be available to + + align:start position:0% +other Technologies might be available to + + + align:start position:0% +other Technologies might be available to +help with that process \ No newline at end of file diff --git a/QPV-DmpGXeQ.txt b/QPV-DmpGXeQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..1cff623aada227182fd85080eabd2dedbe88b82d --- /dev/null +++ b/QPV-DmpGXeQ.txt @@ -0,0 +1,627 @@ +align:start position:0% + +I'd now like to talk about the velocity + + align:start position:0% +I'd now like to talk about the velocity + + + align:start position:0% +I'd now like to talk about the velocity +of the center of mass for a system of + + align:start position:0% +of the center of mass for a system of + + + align:start position:0% +of the center of mass for a system of +particles so let's take a system which + + align:start position:0% +particles so let's take a system which + + + align:start position:0% +particles so let's take a system which +I'll just Outline by this and in that + + align:start position:0% +I'll just Outline by this and in that + + + align:start position:0% +I'll just Outline by this and in that +system we have a bunch of particles + + align:start position:0% +system we have a bunch of particles + + + align:start position:0% +system we have a bunch of particles +particle one particle two let refer to + + align:start position:0% +particle one particle two let refer to + + + align:start position:0% +particle one particle two let refer to +this as the J particle and some point x + + align:start position:0% +this as the J particle and some point x + + + align:start position:0% +this as the J particle and some point x +cm and if I want to talk about the + + align:start position:0% +cm and if I want to talk about the + + + align:start position:0% +cm and if I want to talk about the +position of the center of mass I can + + align:start position:0% +position of the center of mass I can + + + align:start position:0% +position of the center of mass I can +choose a point s and if I want to Define + + align:start position:0% +choose a point s and if I want to Define + + + align:start position:0% +choose a point s and if I want to Define +that Vector RCM then what I have to do + + align:start position:0% +that Vector RCM then what I have to do + + + align:start position:0% +that Vector RCM then what I have to do +is draw a vector to each object R SJ and + + align:start position:0% +is draw a vector to each object R SJ and + + + align:start position:0% +is draw a vector to each object R SJ and +we saw that this velocity the position + + align:start position:0% +we saw that this velocity the position + + + align:start position:0% +we saw that this velocity the position +of the center of mass with respect to + + align:start position:0% +of the center of mass with respect to + + + align:start position:0% +of the center of mass with respect to +this origin s is the sum MJ R + + align:start position:0% +this origin s is the sum MJ R + + + align:start position:0% +this origin s is the sum MJ R +SJ and that's divided by the total mass + + align:start position:0% +SJ and that's divided by the total mass + + + align:start position:0% +SJ and that's divided by the total mass +n + + align:start position:0% +n + + + align:start position:0% +n +total and J goes from 1 to n where n is + + align:start position:0% +total and J goes from 1 to n where n is + + + align:start position:0% +total and J goes from 1 to n where n is +the number of particles in the + + align:start position:0% +the number of particles in the + + + align:start position:0% +the number of particles in the +system now if I want to find the + + align:start position:0% +system now if I want to find the + + + align:start position:0% +system now if I want to find the +velocity of the center of mass then I + + align:start position:0% +velocity of the center of mass then I + + + align:start position:0% +velocity of the center of mass then I +can just differentiate this um and I'm + + align:start position:0% +can just differentiate this um and I'm + + + align:start position:0% +can just differentiate this um and I'm +dropping the point s for the moment but + + align:start position:0% +dropping the point s for the moment but + + + align:start position:0% +dropping the point s for the moment but +let's just + + align:start position:0% +let's just + + + align:start position:0% +let's just +differentiate 1 to n you'll see Y and + + align:start position:0% +differentiate 1 to n you'll see Y and + + + align:start position:0% +differentiate 1 to n you'll see Y and +when I differentiate the position Vector + + align:start position:0% +when I differentiate the position Vector + + + align:start position:0% +when I differentiate the position Vector +of the object that's the velocity of the + + align:start position:0% +of the object that's the velocity of the + + + align:start position:0% +of the object that's the velocity of the +object divided by J goes from 1 to n the + + align:start position:0% +object divided by J goes from 1 to n the + + + align:start position:0% +object divided by J goes from 1 to n the +total mass now why did I drop the + + align:start position:0% +total mass now why did I drop the + + + align:start position:0% +total mass now why did I drop the +position because if you have any two + + align:start position:0% +position because if you have any two + + + align:start position:0% +position because if you have any two +fixed points so if I chose another fixed + + align:start position:0% +fixed points so if I chose another fixed + + + align:start position:0% +fixed points so if I chose another fixed +Point say over here um + + align:start position:0% +Point say over here um + + + align:start position:0% +Point say over here um +P then this + + align:start position:0% +P then this + + + align:start position:0% +P then this +distance R we'll call a vector from s to + + align:start position:0% +distance R we'll call a vector from s to + + + align:start position:0% +distance R we'll call a vector from s to +P RSP this is a + + align:start position:0% +P RSP this is a + + + align:start position:0% +P RSP this is a +constant and if I draw the position + + align:start position:0% +constant and if I draw the position + + + align:start position:0% +constant and if I draw the position +Vector with to P now the point here is + + align:start position:0% +Vector with to P now the point here is + + + align:start position:0% +Vector with to P now the point here is +that this is + + align:start position:0% +that this is + + + align:start position:0% +that this is +constant distance because this is a + + align:start position:0% +constant distance because this is a + + + align:start position:0% +constant distance because this is a +fixed these are fixed + + align:start position:0% +fixed these are fixed + + + align:start position:0% +fixed these are fixed +points then if you were to draw your + + align:start position:0% +points then if you were to draw your + + + align:start position:0% +points then if you were to draw your +vector triangle which is the position of + + align:start position:0% +vector triangle which is the position of + + + align:start position:0% +vector triangle which is the position of +the object with respect to S that's this + + align:start position:0% +the object with respect to S that's this + + + align:start position:0% +the object with respect to S that's this +Vector is equal to that fixed position + + align:start position:0% +Vector is equal to that fixed position + + + align:start position:0% +Vector is equal to that fixed position +Vector from s to P plus the vector from + + align:start position:0% +Vector from s to P plus the vector from + + + align:start position:0% +Vector from s to P plus the vector from +P to J and I differentiate this + + align:start position:0% +P to J and I differentiate this + + + align:start position:0% +P to J and I differentiate this +DRS J + + align:start position:0% +DRS J + + + align:start position:0% +DRS J +DT well + + align:start position:0% +DT well + + + align:start position:0% +DT well +this derivative of a constant + + align:start position:0% +this derivative of a constant + + + align:start position:0% +this derivative of a constant +Vector this is + + align:start position:0% +Vector this is + + + align:start position:0% +Vector this is +zero plus + + align:start position:0% +zero plus + + + align:start position:0% +zero plus +DRP J DT and so we see that the velocity + + align:start position:0% +DRP J DT and so we see that the velocity + + + align:start position:0% +DRP J DT and so we see that the velocity +J is + + align:start position:0% + + + + align:start position:0% + +independent of the + + align:start position:0% + + + + align:start position:0% + +choice of Point + + align:start position:0% +choice of Point + + + align:start position:0% +choice of Point +s you choose any other fixed point and + + align:start position:0% +s you choose any other fixed point and + + + align:start position:0% +s you choose any other fixed point and +you get that these velocities D + + align:start position:0% +you get that these velocities D + + + align:start position:0% +you get that these velocities D +rsj DT equals Dr r p j DT for + + align:start position:0% +rsj DT equals Dr r p j DT for + + + align:start position:0% +rsj DT equals Dr r p j DT for +all fixed + + align:start position:0% +all fixed + + + align:start position:0% +all fixed +points p and that's why in this + + align:start position:0% +points p and that's why in this + + + align:start position:0% +points p and that's why in this +expression when we differentiate the + + align:start position:0% +expression when we differentiate the + + + align:start position:0% +expression when we differentiate the +velocity even though we had an index s + + align:start position:0% +velocity even though we had an index s + + + align:start position:0% +velocity even though we had an index s +we dropped that and so our conclusion is + + align:start position:0% +we dropped that and so our conclusion is + + + align:start position:0% +we dropped that and so our conclusion is +that we can treat that we have the + + align:start position:0% +that we can treat that we have the + + + align:start position:0% +that we can treat that we have the +velocity of the center of mass of this + + align:start position:0% +velocity of the center of mass of this + + + align:start position:0% +velocity of the center of mass of this +system is equal to the sum + + align:start position:0% +system is equal to the sum + + + align:start position:0% +system is equal to the sum +MJ BJ J goes from 1 to n divid by the + + align:start position:0% +MJ BJ J goes from 1 to n divid by the + + + align:start position:0% +MJ BJ J goes from 1 to n divid by the +total + + align:start position:0% +total + + + align:start position:0% +total +mass now what's interesting here is why + + align:start position:0% +mass now what's interesting here is why + + + align:start position:0% +mass now what's interesting here is why +is this an important quantity let's just + + align:start position:0% +is this an important quantity let's just + + + align:start position:0% +is this an important quantity let's just +add that if we want to talk about the + + align:start position:0% +add that if we want to talk about the + + + align:start position:0% +add that if we want to talk about the +acceleration of the center of mass I do + + align:start position:0% +acceleration of the center of mass I do + + + align:start position:0% +acceleration of the center of mass I do +exactly the same type of calculation I + + align:start position:0% +exactly the same type of calculation I + + + align:start position:0% +exactly the same type of calculation I +just differentiate and I get the mass of + + align:start position:0% +just differentiate and I get the mass of + + + align:start position:0% +just differentiate and I get the mass of +the jth particle times the acceleration + + align:start position:0% +the jth particle times the acceleration + + + align:start position:0% +the jth particle times the acceleration +of the jth particle divid by the total + + align:start position:0% + + + + align:start position:0% + +mass and our next step is to understand + + align:start position:0% +mass and our next step is to understand + + + align:start position:0% +mass and our next step is to understand +why this is an important quantity for a + + align:start position:0% +why this is an important quantity for a + + + align:start position:0% +why this is an important quantity for a +system of particles \ No newline at end of file diff --git a/QTJuzevTGkQ.txt b/QTJuzevTGkQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..1cdd63c7311f41fbad723a600de66b5d0e6d9775 --- /dev/null +++ b/QTJuzevTGkQ.txt @@ -0,0 +1,659 @@ +align:start position:0% + +have you ever wondered how all the + + align:start position:0% +have you ever wondered how all the + + + align:start position:0% +have you ever wondered how all the +chemical elements are made then join me + + align:start position:0% +chemical elements are made then join me + + + align:start position:0% +chemical elements are made then join me +as we are lifting all the status secrets + + align:start position:0% +as we are lifting all the status secrets + + + align:start position:0% +as we are lifting all the status secrets +to understand the cosmic origin of the + + align:start position:0% +to understand the cosmic origin of the + + + align:start position:0% +to understand the cosmic origin of the +chemical elements we want to talk about + + align:start position:0% +chemical elements we want to talk about + + + align:start position:0% +chemical elements we want to talk about +the cosmic origin of the chemical + + align:start position:0% +the cosmic origin of the chemical + + + align:start position:0% +the cosmic origin of the chemical +elements today + + align:start position:0% +elements today + + + align:start position:0% +elements today +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in order to understand where the + + align:start position:0% +in order to understand where the + + + align:start position:0% +in order to understand where the +elements come from we need to consider + + align:start position:0% +elements come from we need to consider + + + align:start position:0% +elements come from we need to consider +two different components one is nuclear + + align:start position:0% +two different components one is nuclear + + + align:start position:0% +two different components one is nuclear +physics and one is astrophysics and + + align:start position:0% +physics and one is astrophysics and + + + align:start position:0% +physics and one is astrophysics and +they're nicely combined when we want to + + align:start position:0% +they're nicely combined when we want to + + + align:start position:0% +they're nicely combined when we want to +understand where the chemical elements + + align:start position:0% +understand where the chemical elements + + + align:start position:0% +understand where the chemical elements +come from and so let's look at that in + + align:start position:0% +come from and so let's look at that in + + + align:start position:0% +come from and so let's look at that in +more detail we have nuclear physics part + + align:start position:0% + + + + align:start position:0% + +and we have astrophysics + + align:start position:0% + + + + align:start position:0% + +and on the nuclear physics side we have + + align:start position:0% +and on the nuclear physics side we have + + + align:start position:0% +and on the nuclear physics side we have +two things that we want to consider or + + align:start position:0% +two things that we want to consider or + + + align:start position:0% +two things that we want to consider or +learn about namely how the light + + align:start position:0% +learn about namely how the light + + + align:start position:0% +learn about namely how the light +elements are formed light elements up to + + align:start position:0% +elements are formed light elements up to + + + align:start position:0% +elements are formed light elements up to +iron and they are formed in in fusion + + align:start position:0% +iron and they are formed in in fusion + + + align:start position:0% +iron and they are formed in in fusion +processes in stars + + align:start position:0% + + + + align:start position:0% + +and so this is one and then we have also + + align:start position:0% +and so this is one and then we have also + + + align:start position:0% +and so this is one and then we have also +lots and lots of elements in the + + align:start position:0% +lots and lots of elements in the + + + align:start position:0% +lots and lots of elements in the +periodic table that are heavier than + + align:start position:0% +periodic table that are heavier than + + + align:start position:0% +periodic table that are heavier than +iron so how are they heavy elements + + align:start position:0% +iron so how are they heavy elements + + + align:start position:0% +iron so how are they heavy elements +formed and so they are made in what's + + align:start position:0% +formed and so they are made in what's + + + align:start position:0% +formed and so they are made in what's +called a neutron capture process and + + align:start position:0% +called a neutron capture process and + + + align:start position:0% +called a neutron capture process and +that's a really neat way of making big + + align:start position:0% +that's a really neat way of making big + + + align:start position:0% +that's a really neat way of making big +heavy nuclei and so these two parts here + + align:start position:0% +heavy nuclei and so these two parts here + + + align:start position:0% +heavy nuclei and so these two parts here +together really explain how most of the + + align:start position:0% +together really explain how most of the + + + align:start position:0% +together really explain how most of the +elements in the periodic table I mean + + align:start position:0% +elements in the periodic table I mean + + + align:start position:0% +elements in the periodic table I mean +there are few extra processes that we + + align:start position:0% +there are few extra processes that we + + + align:start position:0% +there are few extra processes that we +will not consider that this gets us up + + align:start position:0% +will not consider that this gets us up + + + align:start position:0% +will not consider that this gets us up +almost there then we have the + + align:start position:0% +almost there then we have the + + + align:start position:0% +almost there then we have the +astrophysics because this is this is + + align:start position:0% +astrophysics because this is this is + + + align:start position:0% +astrophysics because this is this is +basically a lot of theory and we need to + + align:start position:0% +basically a lot of theory and we need to + + + align:start position:0% +basically a lot of theory and we need to +put this to the test and one test that + + align:start position:0% +put this to the test and one test that + + + align:start position:0% +put this to the test and one test that +the universe offers us is investigating + + align:start position:0% +the universe offers us is investigating + + + align:start position:0% +the universe offers us is investigating +chemical evolution + + align:start position:0% + + + + align:start position:0% + +Emme call evolution is the successive + + align:start position:0% +Emme call evolution is the successive + + + align:start position:0% +Emme call evolution is the successive +build-up of heavy elements in the + + align:start position:0% +build-up of heavy elements in the + + + align:start position:0% +build-up of heavy elements in the +universe with time with cosmic time over + + align:start position:0% +universe with time with cosmic time over + + + align:start position:0% +universe with time with cosmic time over +the last 13.8 billion years and we can + + align:start position:0% +the last 13.8 billion years and we can + + + align:start position:0% +the last 13.8 billion years and we can +observe stars at different times and + + align:start position:0% +observe stars at different times and + + + align:start position:0% +observe stars at different times and +thus trace the signatures of these + + align:start position:0% +thus trace the signatures of these + + + align:start position:0% +thus trace the signatures of these +nuclear seconds process is here and + + align:start position:0% +nuclear seconds process is here and + + + align:start position:0% +nuclear seconds process is here and +reconstruct how the nuclear physics + + align:start position:0% +reconstruct how the nuclear physics + + + align:start position:0% +reconstruct how the nuclear physics +operated that works particularly well at + + align:start position:0% +operated that works particularly well at + + + align:start position:0% +operated that works particularly well at +at early times when the universe was a + + align:start position:0% +at early times when the universe was a + + + align:start position:0% +at early times when the universe was a +much less messy place and it's now and + + align:start position:0% +much less messy place and it's now and + + + align:start position:0% +much less messy place and it's now and +so the second portion here is going to + + align:start position:0% +so the second portion here is going to + + + align:start position:0% +so the second portion here is going to +be the oldest stars because they are the + + align:start position:0% +be the oldest stars because they are the + + + align:start position:0% +be the oldest stars because they are the +tool for us to really figure out how the + + align:start position:0% +tool for us to really figure out how the + + + align:start position:0% +tool for us to really figure out how the +elements were made first in the universe + + align:start position:0% +elements were made first in the universe + + + align:start position:0% +elements were made first in the universe +that allows us we can obtain clean + + align:start position:0% +that allows us we can obtain clean + + + align:start position:0% +that allows us we can obtain clean +signatures of these processes there and + + align:start position:0% +signatures of these processes there and + + + align:start position:0% +signatures of these processes there and +that's a very exciting and timely Avenue + + align:start position:0% +that's a very exciting and timely Avenue + + + align:start position:0% +that's a very exciting and timely Avenue +fast stony and together with the older + + align:start position:0% +fast stony and together with the older + + + align:start position:0% +fast stony and together with the older +stars comes the concept of stellar + + align:start position:0% +stars comes the concept of stellar + + + align:start position:0% +stars comes the concept of stellar +archaeology and that sort of encompass + + align:start position:0% +archaeology and that sort of encompass + + + align:start position:0% +archaeology and that sort of encompass +us how we use stars that still available + + align:start position:0% +us how we use stars that still available + + + align:start position:0% +us how we use stars that still available +in shining today to study the early + + align:start position:0% +in shining today to study the early + + + align:start position:0% +in shining today to study the early +universe when everything got started and + + align:start position:0% +universe when everything got started and + + + align:start position:0% +universe when everything got started and +and in order to study chemical evolution + + align:start position:0% +and in order to study chemical evolution + + + align:start position:0% +and in order to study chemical evolution +with all stars we actually need to use a + + align:start position:0% +with all stars we actually need to use a + + + align:start position:0% +with all stars we actually need to use a +scientific method called spectroscopy so + + align:start position:0% +scientific method called spectroscopy so + + + align:start position:0% +scientific method called spectroscopy so +we're also going to look at spectroscopy + + align:start position:0% +we're also going to look at spectroscopy + + + align:start position:0% +we're also going to look at spectroscopy +and how how that works + + align:start position:0% +and how how that works + + + align:start position:0% +and how how that works +observing all the little stellar little + + align:start position:0% +observing all the little stellar little + + + align:start position:0% +observing all the little stellar little +rainbows and because we do that with big + + align:start position:0% +rainbows and because we do that with big + + + align:start position:0% +rainbows and because we do that with big +telescopes we're also going to look at + + align:start position:0% +telescopes we're also going to look at + + + align:start position:0% +telescopes we're also going to look at +what it's like to use the telescopes and + + align:start position:0% +what it's like to use the telescopes and + + + align:start position:0% +what it's like to use the telescopes and +observing because all of this work is + + align:start position:0% +observing because all of this work is + + + align:start position:0% +observing because all of this work is +based on astronomical observations with + + align:start position:0% +based on astronomical observations with + + + align:start position:0% +based on astronomical observations with +the largest telescopes in mostly in + + align:start position:0% +the largest telescopes in mostly in + + + align:start position:0% +the largest telescopes in mostly in +Chile and I will explain all these + + align:start position:0% +Chile and I will explain all these + + + align:start position:0% +Chile and I will explain all these +different parts one by one and then in + + align:start position:0% +different parts one by one and then in + + + align:start position:0% +different parts one by one and then in +the end we're going to put it all + + align:start position:0% +the end we're going to put it all + + + align:start position:0% +the end we're going to put it all +together to understand the origin of the + + align:start position:0% +together to understand the origin of the + + + align:start position:0% +together to understand the origin of the +elements + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/QTb6YsxMbBY.txt b/QTb6YsxMbBY.txt new file mode 100644 index 0000000000000000000000000000000000000000..21f5fbb69bec81ca91646a006de78f081b0a8437 --- /dev/null +++ b/QTb6YsxMbBY.txt @@ -0,0 +1,2189 @@ +ERIC LANDER: Good morning. + +Good morning. + +So we've been talking about +recombinant DNA. + +And really what it does +to our picture here-- + +function, gene, protein-- + +is for the first time take +something that's a theoretical + +relationship and make +it operational. + +Being able to go from a function +like the ability to + +make your own arginine, to a +specific gene, to a specific + +protein, and to be able +to connect those up. + +In principle, by the time we're +done with recombinant + +DNA, one should be able to go +from any vertex of that + +triangle to any other vertex +of that triangle. + +Given a function, +find the genes. + +Given a gene, find +the proteins. + +Given a protein, +find the genes. + +Given a protein, find +the function. + +That's really the goal of +recombinant DNA is to be able + +to start at any vertex +and reach any other + +vertex of that triangle. + +We're not there yet. + +But we will be in the next +couple of days, to the point + +where we can move freely about +this whole picture. + +So we've talked about +DNA sequencing. + +And I want to pick up a little +bit with DNA sequencing. + +And I'll probably end with DNA +sequencing again, as I tell + +you where things stand today. + +How did we use DNA sequencing? + +Well, we found us a clone. + +Maybe our clone was a clone that +conferred the ability to + +grow without arginine. + +That was cloning by +complementation. + +Maybe it was a clone that +encoded beta globin. + +There we found an antibody that +recognized beta globin. + +We made a cDNA library with +an appropriate promoter. + +And we asked E. coli to produce +those human proteins + +from those cDNAs. + +And then we use our antibody +to recognize which clone. + +One way or the other, we found +ourselves a clone. + +The clone had this vector. + +It had this insert. + +The insert is now of +interest to us. + +We wish to sequence it. + +And we talked before about +taking that piece of DNA and + +subjecting it to sequencing. + +We started with a primer. + +From that primer, we extended. + +And we hit a point, let's say, +opposite an A or maybe + +opposite the next A or opposite +the A after that or + +opposite the A after that. + +And we had this clever trick, +for which Fred Sanger actually + +won a Nobel Prize, of using +a defective version of the + +nucleotide T that would +stop at that point. + +But remember, we didn't use only +defective T. We used a + +mixture of good T and defective +T. Let's say + +defective T was 1% of the whole +mixture, whenever we + +encountered a defective T and +put it in, the chain would + +stop because it couldn't +be extended. + +Whenever we put in a good +T, it would keep going. + +And so since we're making-- + +Of course, we have millions and +millions of copies of our + +template sitting there +in the test tube. + +We're always working-- when I +talk about "a" molecule, and I + +draw a picture of a molecule, +we should always know that + +there's millions of copies +of those things. + +Some of them are +stopping here. + +Some of them are going +here, et cetera, + +et cetera, et cetera. + +And we end up with a +large collection. + +And if we separate it on a gel, +we can detect the lengths + +of those fragments. + +If we attach a fluorescent dye, +then those fragments are + +fluorescently labeled. + +We could all run them +in the same lane + +with different colors. + +And we could put our little +fluorescence detector and see + +what goes by. + +And the traces you would get, +the actual pictures that + +emerge from this, look +something like this. + +And you'd see colored traces +like that emerging from that + +electrophoretic detector. + +And you could read off the +sequence by the colors-- + +really very gorgeous, very +simple, beautiful technology, + +all this taking place in a +little capillary tube. + +You remember how we made +a defective T, right? + +How did we make a defective T? + +Sorry? + +STUDENT: Dideoxy. + +ERIC LANDER: To dideoxy. + +Because remember, we need +that 3-prime hydroxyl in + +order to extend it. + +No 3-prime hydroxyl, +no extension. + +So if you make that deoxy +at the 3-prime + +position, you can extend. + +And since it was originally +2-prime deoxy, it's now + +2-prime, 3-prime dideoxy. + +That's all it takes +in order to block + +the extension reaction. + +And they sell the stuff, +and you can use it. + +All right. + +I had another question +for you guys. + +Where did the primer +come from? + +Sorry? + +Sorry? + +STUDENT: We put it in. + +ERIC LANDER: We put it in. + +How did we know what +to put in? + +STUDENT: [INAUDIBLE] catalog. + +ERIC LANDER: Well, the catalog's +very smart, but it + +doesn't tell us what we need. + +How do we know what +sequence it is? + +Actually, it turns out that so +many different sequences might + +be needed for different purposes +in molecular biology + +that they don't stock them all +in the catalog because you + +might order any sequence. + +So it really turns out that if +you want to order a specific + +20-letter sequence, you go on +the web, type it in, and then + +the machine will make it for +you, and you get it the next + +day, it turns out. + +But they don't actually put it +in the catalog because it + +would be too big an inventory. + +Although ones that people use +a lot they keep in the + +catalog, otherwise they just +make it on the spot for you. + +But how do we know +what sequence + +we're supposed to use? + +Here's my clone, let's say +arginine, the ARG1 gene. + +How did I know what sequence +to start with? + +You let me get away with just +put a primer there. + +And what does it match? + +Yeah? + +STUDENT: Could you use the +EcoR1 [INAUDIBLE]? + +ERIC LANDER: I did use EcoR1. + +STUDENT: [INAUDIBLE] + +ERIC LANDER: EcoR1 site +here, GAATTC-- + +GAATTC-- + +I'm going to cut in this site. + +I'm sorry, I'm going +to cut in this site + +like that, let's say. + +Yeah, like that. + +And this fragment here-- + +sorry, like that-- + +the fragment here that I'm going +to start sequencing from + +it starts with a G, right? + +Because it's opposite that C. + +So because I cut with EcoR1, I'm +pretty sure it starts with + +a G. It's not a very big +primer to use, though. + +I could start with a C, but I +don't think that's going to + +have enough binding +energy to do it. + +STUDENT: Doesn't a bacteria +already replicate that DNA? + +ERIC LANDER: It replicates +that DNA just fine. + +STUDENT: So there's already +a primer in there. + +Why do you [INAUDIBLE]? + +ERIC LANDER: Well, +because I've now + +purified out my insert. + +And I'm going to subject +it to sequencing. + +And I need to start +with a primer. + +I've got that fragment. + +I need to know how that +fragment starts. + +And I don't know how that +fragment starts. + +STUDENT: Is there a place you +could cut in a little bit + +after that? + +ERIC LANDER: Oh! + +What if I was really smart and +put in a different restriction + +site back here? + +And I use that restriction +enzyme, and I cut there? + +Then what would you be +able to tell me? + +Well, then the fragment +would start with a + +known vector sequence. + +Bingo. + +That'll work. + +Good. + +Good engineering. + +Since I don't know what the +sequence is of the thing I'm + +reading, I'd better back up a +little bit and use a known + +sequence from the vector. + +And then I keep going. + +This is all just to give +you a sense of all the + +tricks you can do. + +So now it's easy. + +Now, in fact if that's the +vector I use a lot, all the + +time, then bingo! + +I can go to the catalog +because they + +will stock that one. + +And I'll use it. + +And I can use my green primer +there to get going. + +All right. + +Now here's the problem. + +As I start sequencing, coming +down this capillary tube are + +fragments of different +lengths. + +The speed of migration depends +on the logarithm of the length + +of the fragment. + +Big fragments goes slower. + +It's inversely proportional +to the log of the + +length of the fragment. + +So big fragments go slower. + +And as they get bigger and +bigger and bigger, they go + +slower and slower and slower. + +But the difference between log +of 1,000 and log of 1,001 is + +pretty small. + +And then log of 1,001 and +1,002, very small. + +Actually, those peaks over there +start bunching up, and I + +can't tell them apart. + +So I can actually only go with +this electrophoretic process + +maybe 1,000 letters before the +peaks get too bunched up + +because the different speeds are +not so different anymore. + +So I can only read 1,000 +bases, let's say. + +In practice, we would tend to +read 700, 800 bases because it + +started getting scruffy. + +But let's make it round, and +we'll say 1,000 bases. + +Now, suppose this fragment that +I got that's the ARG1 + +gene is 3,000 bases. + +Well, we've got our clever trick +that you've introduced + +here of cutting back over here +at some previous site, using + +our primer here and reading. + +But it kind of dies at +about 1,000 bases. + +I can't read any further. + +What do I do? + +STUDENT: [INAUDIBLE] + +ERIC LANDER: What if there's +not a perfect + +restriction site there? + +But you're on the right track. + +Keep going. + +Once I've sequenced the first +1,000 bases, what do I know? + +The sequence of the +first 1,000 bases. + +What primer could I use then? + +STUDENT: [INAUDIBLE]. + +ERIC LANDER: I can just make +a new primer based on those + +bases, right? + +So I don't even need my +restriction site anymore. + +You've got it exactly right. + +I use my knowledge. + +And then I could use +a new primer, and I + +could go more bases. + +Then I could use a new primer +and go more bases. + +Then a new primer, and +go more bases. + +And I can do what's +called "primer + +walking" along the clone. + +Will that work? + +You bet. + +That works just fine. + +It's also very slow. + +Because I had to get my first +bases, analyze them, order a + +new primer, and the next day +set up my next reaction. + +Take a couple days, get +my next reaction. + +Take a couple days, +next reaction. + +Imagine sequencing the human +genome like this. + +This could take a long time +if I do it in serial. + +So what else could I do? + +This works, by the way. + +This totally works. + +It's a good procedure, and it's + +used for certain purposes. + +But what else could I do? + +Here's the cool thing. + +We've got biology. + +But you guys, being MIT +students, you've also got + +computer science and other +tricks available. + +Here's a cool trick. + +I have my clone, 3,000 bases. + +I like my clone. + +I'm going to take my clone, my +fragment, of 3,000 bases, and + +maybe instead of sequencing it, +I'm going to shred it up + +into a lot of smaller pieces. + +Suppose I shred this up +into fragments of, + +say, size 800 bases. + +This was 3,000 bases. + +Now let me shred it up. + +I'll just take 800 +as a number. + +Now remember, I had a lot of +copies of this clone, right? + +So I'm going to get shreds like +this and shreds like that + +and a shred like that. + +It's not just one copy. + +I've got a lot of copies of +this piece of DNA there. + +I'm going to shred it up. + +And there are ways to shred it +up by forcing it through a + +needle or treating it meanly, +or things like that. + +I'm going to get lots +of little fragments. + +And what I could do is I could +clone all of those little + +subfragments. + +I take my big fragment, and what +I'm going to do is I'm + +going to make a new library +of subfragments. + +Got it? + +Now I have a whole lot of +subfragments, each taken from + +my 3,000 bases. + +And they're all kind +of smallish. + +What could I do to all of those +little subfragments? + +They're all living +in a vector. + +Each is in its own vector. + +I've spread them out. + +I've made a library. + +They're each in their +own bacteria. + +They're each in a vector. + +That vector has a known +sequence at its + +end, the green primer. + +Couldn't I just sequence a lot +of different random subclones + +and paste them together? + +See, that's where it pays to +have computer science as well. + +Because what I could do is +by subcloning these into + +individual little +random pieces-- + +I have no idea how they've +been broken up. + +I don't care-- + +I just take the total DNA, shred +it up into pieces, sub + +clone it into a vector. + +And now because it's in the +vector, I could read this one + +and that one and this one +and that one and this + +one and that one. + +Do I actually know which +ones I'm reading? + +No. + +It's totally random. + +I take my 3,000 bases, shred +it up into lots of smaller + +pieces, and I just read +a lot of them. + +When I get a whole lot of +these pieces, maybe 800 + +letters each, what do I do? + +I write me a piece of code +that looks for overlaps + +between them and start +pasting it together. + +And that's called assembly. + +You assemble the sequence out +of its little pieces. + +And so you can assemble +things. + +And this gets referred to +as shotgun sequencing. + +That's what it's really called, +because it's like you + +shoot it out of the end of +the shotgun or something. + +It's broken up into +a lot of pieces. + +It's just a shotgun, random +approach where I take + +individual random clones, +and I assemble them. + +Any questions about that? + +It's really a way to do it. + +And the big difference there is +you can do it in parallel. + +Rather than doing it one step +at a time, which sounds so + +logical but takes +so much time-- + +easier. + +Just shred it up, read lots of +them all the same afternoon, + +and then assemble them +by computer. + +So that's nice. + +So I do that. + +I get my clone. + +I'm going to now do my computer +assembly of it. + +And I'm going to get +my 3,000 bases. + +How do I analyze my clone, +my clone sequence? + +Now I have 3,000 letters +in order, nicely done. + +What do I do with it? + +That clone, let's say, is able +to confer the ability to grow + +without arginine. + +It encodes some enzyme that +lets you make arginine. + +I've got 3,000 letters. + +How do I tell what it's doing? + +What do I look for? + +Yep? + +STUDENT: Compare it with +something that doesn't have + +[INAUDIBLE]? + +ERIC LANDER: Well, so tell +me what I'm looking for? + +I'm looking for a gene? + +STUDENT: Yes, [INAUDIBLE]. + +ERIC LANDER: Yeah. + +So what about that gene? + +What's distinctive +about genes? + +How do I recognize a gene? + +It's tricky. + +STUDENT: The sequence? + +ERIC LANDER: How can I just + +recognize it from the sequence? + +Can I tell that something +is a gene? + +STUDENT: Start codon. + +ERIC LANDER: I could look +for a start codon, ATG. + +Do you think that'll happen +just by chance, though? + +There'll be a lot ATGs running +around, because you've got two + +strands, three reading frames. + +It'll happen pretty often. + +But that's a start. + +What happens after +the start codon. + +STUDENT: There's a stop codon. + +ERIC LANDER: There's a stop +codon, at some point. + +And what's in between +the start codon + +and the stop codon? + +STUDENT: [INAUDIBLE]. + +ERIC LANDER: Well, +no stop codons. + +A gene should look like ATG +and a whole lot of codons + +without any stops in the +reading frame, until + +you get to a stop. + +That's called an open reading +frame, a long stretch without + +stop codons. + +So I could look for an +open reading frame. + +So by an open reading frame, +I mean a long stretch that + +starts with an ATG and +then goes on and on + +and on and on with-- + +How frequent are stops? + +There are three stops +out of 64. + +One codon in 20 is a +stop, on average. + +So if I go 20 codons, I might +see a stop, on average. + +But suppose I run for 100 +codons, and there's no stop--- + +without a stop codon. + +That's pretty impressive, isn't +it, if I can read 100 + +codons in a row, and +I never see a stop, + +that's pretty unusual. + +So I say, that's an open +reading frame. + +That's one way to recognize +the gene in there. + +The problem is introns. + +What happens if there's +an intron? + +Yikes. + +Then it'll be spliced there. + +That'll be spliced out, but I +won't initially know that, + +reading the sequence. + +And there could be stop codons +in the intron because it's not + +part of the final message. + +So I'm in trouble. + +So happily, in yeast, which has +very small introns, not + +very many introns, I can +actually almost get away by + +looking for open +reading frames. + +In human DNA, this +is kind of lousy. + +Well, it's really problematic +because + +there'll be too many introns. + +There, other tricks +that get used-- + +I could make cDNA and compare +it to cDNAs, which have + +already spliced everything out, +and look for the open + +reading frame. + +Other tricks that get used-- + +I can compare it to the +database of everything + +everybody has ever sequenced +before and start looking for + +similarities. + +And today there are +massive databases. + +So many years ago, a +postdoctoral fellow in my lab + +cloned a gene related +to a human disease. + +And she didn't know +what the gene did. + +And she found it. + +And it had exons, but +she didn't know + +where they were yet. + +But she just took the whole +sequence and said, this + +sequence here, is it similar to +anything that's ever been + +seen before? + +This was a gene that was in +people who had a really severe + +form of dwarfism with twisted +bones and things, called + +diastrophic dysplasia. + +And she put it against the +computer database. + +And the computer came back and +said, the sequence you just + +gave me has a whole lot of +patches that looks just like + +sulfate transporters +in a fungus. + +She instantly knew what +her gene did. + +Because it turns out that bones +have a lot of sulfated + +proteoglycans, et cetera, et +cetera, whatever those are. + +And she instantly knew, because +my sequence was + +similar to something-- it's a +human sequence similar to + +something in a fungus that does +sulfate transport, I've + +probably got a sulfate +transporter. + +That's probably the basis +of my disease. + +She took her cells from her +patients, added sulfate, found + +that the cells couldn't take +up sulfate very well, and + +bingo-- had found the cause +of her disease. + +One of the most powerful +ways-- + +it's sort of Google, +of course, right?-- + +it's Google before Google. + +You take your sequence and you +Google it against all other + +sequences and see +what it's like. + +And by googling all of life's +sequences against each other, + +if somebody else has already +solved your problem for you, + +you can find out about +your problem. + +And it's just this wonderful +network effect that is so + +characteristic of information +technologies. + +So anyway, you can do that +by searching databases. + +And we will not, +in this class. + +So you can write code for +looking for open reading + +frames, you can search databases +for similarities + +across organisms or +within organisms, + +or things like that. + +We won't here, but there are at +MIT some great courses on + +computational biology that, +for example, you can write + +algorithms for detecting +these sorts of things. + +It's an interesting question. + +How do you write an algorithm +for comparing two strings + +which might have insertions and +deletions and changes and + +things like that? + +There's a whole rich field of +computational mathematics + +associated with genome +comparisons. + +All right. + +So we've got it. + +Bingo! + +Now, here's our next problem. + +Our next problem, we +cloned the gene for + +beta globin from you. + +You were kind enough. + +You signed an informed consent +allowing us to take some DNA, + +prepare a library. + +We made our antibody, +we found your beta + +globin gene, et cetera. + +Now we're going to conduct a +study of beta globin in a + +larger population. + +Maybe we're going to ask +multiple people in the class, + +would they be willing to sign +an informed consent to have + +their beta globin +gene sequenced? + +It's an interesting gene. + +There are variants in it that +confer risk of sickle cell. + +There are variants in it that +confer risks of other things. + +There are fascinating things +about that gene. + +Maybe we'd like to see +the beta globin + +sequence of many people. + +How do we get the beta globin +sequence of a second person? + +Well, how'd we get the +beta globin sequence + +from the first person? + +Took DNA, cut it up, cloned it +in our vector, spread it out + +on the plate, washed +over the antibody-- + +actually, we took cDNA-- + +washed it over, et cetera, +et cetera, et cetera. + +It's a lot of work. + +If we wanted to do 100 people +in this class, do we have to + +get DNA from each of you, +prepare a library, maybe a + +cDNA library even, and do the +same exact process to discover + +your beta globe gene? + +Or is there any way where after +we've done your beta + +globin gene, we could now do +everybody's beta globin gene a + +lot easier? + +STUDENT: [INAUDIBLE] + +ERIC LANDER: Actually, I +do know the sequence. + +That's the thing that's +different is having found it + +once, I know the +whole sequence. + +The question is, can I use the +sequence to save me the + +trouble of making an entire +library of everything? + +How can I use the knowledge I've +just gained to make it so + +much easier? + +Well, the answer occurred to +a chemist working at Cetus + +corporation in the mid 1980s. + +He was driving along, and he was +thinking about this very + +problem and thinking about +sequencing and how they do it. + +And he had the following +thought. + +His following thought was, +suppose we've got the whole + +human genome. + +There's a whole human genome. + +And I'm just going to melt it +for you, for a second, into + +two strands. + +And suppose we've already +discovered + +the beta globin gene. + +The beta globin gene is right +over here, it turns out. + +That's beta globin. + +Well, we know this +whole sequence. + +This is total DNA. + +I haven't done anything +right now. + +This is the whole human +genome that runs + +over 3 billion bases. + +But it's the whole genome. + +I know the sequence, right? + +I could make a primer to that +part of the sequence. + +And suppose I just make a primer +to that part of the + +sequence, throw it into your +total DNA, and I add + +polymerase and nucleotides. + +Maybe it'll start copying. + +At some point, it'll fall off. + +But notice, I've made an extra +copy of beta globin-- + +of course, mixed into the whole, +total human genome. + +But there's a little bit +extra beta globin now. + +Suppose I also made a +primer over here. + +I'd get that. + +I'd now have two double strands +of beta globin, + +whereas before, I +only had one. + +Let's call this step 1. + +What do you think step 1 +should be followed by? + +STUDENT: Step 2. + +ERIC LANDER: Step 2. + +Very good. + +Excellent. + +You guys have learned +induction. + +So let me melt the DNA and +now throw back my primer. + +Actually, if you'll allow me, +I'm going to make the two + +primers different colors. + +Let's make that one +a different color. + +There we go. + +So now what will happen is +this primer goes here. + +This green primer goes here. + +This guy sits down here. + +And this guy goes like that. + +Well, that didn't come +out very good. + +I'll just draw it a little +more clearly here. + +What happens is this guy will +start copying this way. + +This guy starts copying +this way. + +This guy starts copying +this way. + +This guy starts copying +this way. + +Now, after step 2, how +many copies of + +beta globin do I have? + +Four copies. + +What's the next step? + +STUDENT: Step 3. + +ERIC LANDER: Step 3. + +Very good. + +No putting anything +over on you. + +And after we melt the DNA and +we add back the primers, how + +many copies of beta globin +will we now have? + +STUDENT: Eight. + +ERIC LANDER: Eight, because +it's doubling every time. + +Step 4? + +Step 10? + +2 the 10th. + +2 to the 10th, because +we're doubling. + +2 to the 10th. + +Step 20? + +2 to the 20th, which +is about a million. + +Step 30? + +2 to the 30th is about +a billion. + +Oh. + +After 30 steps, I have 2 to +the 30th copies, which is + +about a billion copies. + +And at that point, the majority +of the DNA in my tube + +is beta globin. + +The rest of the human genome +is still there, but beta + +globin started out being one + +one-hundred-millionth of the genome. + +And I've just amplified +it a billionfold. + +So it's now 90% of what's +in the tube. + +Pretty cool. + +This is like a chain reaction. + +You do it once, you do +it again, you do it + +again, you do it again. + +You just throw in polymerase, +and you run a chain reaction. + +This therefore is called the +polymerase chain reaction, or + +as it is universally +known, PCR. + +That's PCR. + +That's the polymerase +chain reaction. + +Kary Mullis, who invented this +thing, won a Nobel Prize in + +chemistry for it. + +Because notice what +he's just done. + +He's cloned your beta globin +gene without cloning. + +It's cloning without cloning. + +I didn't need any vectors, I +didn't need any bacteria, I + +didn't need no nothing. + +All I needed was the sequence +that I got once by cloning, + +and then I'm off to the races. + +I throw in two primers-- + +choop-choop-choop-choop-choop-- + +bingo! + +Where do my primers come from? + +They're not in the catalogs. + +We don't keep all +that inventory. + +You just type them in, and they +come to you the next day + +by an automatic synthesis +machine. + +So anyplace in the human genome +or the yeast genome or + +any other thing that you want +to PCR, just give me the two + +primers and piece it out. + +How do we do this? + +There are a couple of the +details that I have to worry + +about here. + +Cooking details here +for the recipe. + +What I have to do is I have to +take my test tube, and I have + +to heat it up so high that the +double helix melts and comes + +apart, so that the primers +can get in there. + +So I have to heat +to 97 degrees. + +Then it comes apart. + +I cool it down, I add +my polymerase. + +I cool it, I add polymerase +and nucleotides. + +And then it does +its extension. + +Then I heat it up to 97. + +Now the problem is when I heat +it up to 97, you know what + +happens to my polymerase? + +STUDENT: Denatured. + +ERIC LANDER: It gets denatured, + +and it doesn't come. + +It's ruined. + +So what I have to do is I have +to pop open my two-- + +Sorry, you had a question? + +STUDENT: [INAUDIBLE] + +ERIC LANDER: Why do +I heat it up? + +There are ways you might +be able to avoid it. + +But the traditional technique +is you heat it up. + +But you're right, there might +be other solution. + +But now I'm going heat it up. + +And my polymerase +gets denatured. + +So I have to pop open the test +tube, throw in some more + +polymerase, let it do its work, +heat it up again, pop + +open the test tube, put some +more polymerase in. + +And it gets really boring. + +Every one of these 30 steps, +I have to keep adding + +polymerase. + +So the engineers in you will +say, why don't we just design + +a polymerase that doesn't +denature at 97 degrees? + +So we should go to an expert +and say, please make us a + +polymerase that doesn't denature +at 97 degrees, even + +that doesn't mind +being boiled. + +So what expert do we go to? + +STUDENT: Bacteria. + +ERIC LANDER: Bacteria. + +What bacteria do you think has +a DNA polymerase that doesn't + +mind being boiled? + +STUDENT: [INAUDIBLE]. + +ERIC LANDER: Bacteria +that live in, say, + +geysers, hot springs. + +So you go to a hot spring. + +You go to geyser, you go to +Yosemite, and you fish out + +some water, and you see what's +growing there, and you find + +the bacteria growing +there that has the + +name Thermus aquaticus. + +And you purify DNA from +Thermus aquaticus. + +Thermus aquaticus just goes by +name TAQ, T-A-Q. You purify + +TAQ polymerase. + +And now, no problem. + +You just use TAQ polymerase, +throw it in your test tube. + +And you go heat, cool, heat, +cool, heat,cool, heat, cool, + +heat, cool, and you're +all done. + +You just put it on a little +heating block. + +And the heating block +automatically goes hot, cold, + +hot, cold, hot, cold, +hot, cold. + +And that's called the +thermocycler. + +The thermocycler does it. + +And of course, nowadays, +do you have to yourself + +personally go to the hot spring +and risk your life + +fishing out the bacteria? + +No. + +Because it's in--? + +STUDENT: The catalog. + +ERIC LANDER: The catalog. + +Exactly. + +Very good. + +TAQ polymerase is +in the catalog. + +All right. + +I'll tell you a story. + +The statute of limitations has +already expired, so it's OK. + +TAQ polymerase used to +be very expensive. + +So we needed a lot +of it in our lab. + +And we couldn't afford +all of it. + +So what we did was we just +looked up the sequence of the + +TAQ polymerase in Thermus +aquaticus, got primers, used + +PCR to get the gene for TAQ +polymerase, and then expressed + +it to make a lot of +TAQ polymerase. + +So it's kind of cool. + +Anyway, that was about +15 years ago. + +We produced in a few days what +was then worth about $4 + +million worth of +TAQ polymerase. + +[LAUGHTER] + +That was why we went to the +trouble of doing it. + +We didn't end up getting in +any real trouble about it. + +OK. + +So now, why is this +stuff cool? + +This stuff is cool because +you're able to amplify tiny + +amounts of DNA. + +So if I want to purify any human +gene now, and I know its + +sequence initially, +PCR it out. + +No problem. + +Suppose a patient presents with +a bacterial infection. + +And you're a physician. + +And you suspect that there might +be a specific bacterial + +infection or maybe a specific +viral infection. + +So applications of PCR. + +Application of PCR? + +Well, resequencing a +known gene, yes. + +Resequencing beta globin. + +But infectious disease. + +I have a patient. + +I think there might be a +bacteria, there might be a + +virus in the blood. + +What do I do? + +Make primers, do PCR. + +I have a detection technique. + +I can detect the presence +of a viral infection + +or a bacterial infection. + +For example, HIV testing +can be done by PCR. + +Because it doesn't take +very much there in + +order to detect it. + +Water contamination. + +You can test for bugs that +shouldn't be in the water, by + +PCR because you don't +need much. + +How little do you need? + +Suppose I take a tube of DNA, +and I start diluting it and + +diluting it and diluting it. + +How far down do you think I can +go and still PCR back up, + +say, beta globin? + +Suppose I dilute it so that +there's only like 1,000 copies + +of beta globin left, +on average. + +Can I still PCR it? + +100 copies? + +10 copies? + +Suppose I dilute it so on +average there's only one copy + +of the beta globin +molecule there. + +Can I PCR it? + +How can I prove that? + +An easy way to prove that-- + +I could do it statistically by +just diluting it so that on + +average there's only +one beta globin. + +But how can I get one +copy of beta globin + +packaged up very nicely? + +STUDENT: Order it. + +ERIC LANDER: Sorry? + +STUDENT: Order it. + +ERIC LANDER: No. + +Can't order that. + +Where do you know that there's +just exactly one copy of the + +beta globin gene? + +One human sperm. + +Suppose with a micromanipulator, +I purify a + +single human sperm, one sperm. + +It's haploid. + +It's got exactly one +beta globin. + +Throw it in a test tube, crack +it open, do PCR, it works. + +That's how I demonstrate that +a single copy is enough. + +I can make that work. + +Pretty impressive. + +Not only that, that +I can do it from a + +single copy in a sperm. + +If someone is doing in +vitro fertilization-- + +remember, in vitro fertilization +won the Nobel + +Prize this semester-- + +in vitro. + +Suppose a couple has a 1 in 4 +chance of having a baby with + +some terrible lethal disorder. + +The couple might use in vitro +fertilization to make multiple + +independent embryos. + +The doctor, then, is deciding +which embryo should we implant + +back in mom? + +Well, how could they tell at +this eight-cell stage which + +embryo carries the +genetic disease? + +Suppose this genetic disease +they already knew the + +molecular mutation causing it. + +Pull off a cell. + +Pull off one cell, pull off one +cell, pull off one cell. + +This is at the eight-cell +stage, let's say. + +If I pull off one of those cells +at the eight-cell stage, + +does that mean the baby doesn't +have an ear or an arm + +or something? + +No, it doesn't. + +Because at that stage, none +of the cells have + +taken up any identity. + +It regulates. + +There's no problem. + +It turns out you can pull off an +individual cell, and it has + +no impact on the embryo. + +And I do PCR. + +And I can figure out that that +one carries the severe genetic + +disease that's going +to cause the baby + +to die at five months. + +And the couple says, we're not +going to implant that one. + +We'll implant the other ones. + +That's called preimplantation +diagnostics. + +Or suppose somebody's being +treated for cancer. + +And the cancer cells that had +previously been there are no + +longer detectable. + +The drug therapy has apparently +killed this blood + +cancer that somebody has. + +Maybe they have a cancer +of the blood. + +Now what I'm going to do is +monitor that patient every + +several months by getting a +blood sample and seeing if the + +distinct mutations that +were present in + +the cancer were there. + +And I can begin to see if that's +coming back, if those + +cells are now recurring. + +It's an incredibly sensitive +technique. + +And then of course, where does +this stuff get used that you + +guys all surely we know about? + +Forensics. + +CSI and all that +kind of stuff. + +If I lick an envelope-- + +I used to say, licking a stamp, +but stamps just peel + +off these days. + +But people still do lick +an envelope sometimes. + +If you lick an envelope, more +than enough DNA comes off when + +you lick the envelope that you +can use PCR to determine who + +do the licking. + +ERIC LANDER: You can. + +It works. + +All right. + +So that's PCR. \ No newline at end of file diff --git a/QcRteDU9Eco.txt b/QcRteDU9Eco.txt new file mode 100644 index 0000000000000000000000000000000000000000..69364435d03adc5fd0661821cffab7c8e417892d --- /dev/null +++ b/QcRteDU9Eco.txt @@ -0,0 +1,5410 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK today, teaching +with blackboards and slides. + +And also several questions +from the last time. + +And, related to that, a handout, +which I've put + +online, which is on how +to make a lesson plan. + +So I'll do all that through +the questions. + +So now just a quick bit about +lesson planning, because a + +couple of you pointed out that +you'd have liked to know more + +about lesson planning. + +And reminded me that when I +taught the chemistry TA + +workshops, I actually gave +everyone a handout on how to + +plan a lesson. + +So I've put that handout online, +and I'll just show you + +what it looks like here. + +So this is basically the sheet I +use for planning any kind of + +lecture recitation. + +At the top, you need some kind +of course, and date. + +And then the objective. + +So that's quite important. + +You'll see the exact sheet. + +And there's a PDF file, you +can just use it yourself. + +There's a course objective for +that particular session. + +And that relates to your overall +goals for the course. + +So, for example, in this +problem, my objective might be + +something like, to show +that easy cases-- + +in fact, this was +my objective-- + +I wanted to show that +easy cases-- + +extreme cases-- are useful not +just for checking formulas, + +but also for generating +formulas. + +OK, so I write that +on the top. + +So I remind myself, +why am I here? + +What am I doing? + +Then there's a three-column +table. + +Basically you just plan +items in your lecture. + +The first column is minutes-- + +how long you expect each +thing to take. + +And then the middle column, most +of the space is, what's + +your goal in this local +part of the lecture? + +And what are you going +to do for that? + +So here's my overall +objective. + +And my local goal may be, +just this example-- + +getting that one third. + +And then here in the third +column is props. + +So there's actually +a piece here, too. + +So props are anything that +I need to bring. + +So I just stick that +in the margin. + +OK, bring the cones, +or the pyramids, + +whatever they may be. + +And so then, when you're filling +this piece in, about + +what to bring, you just scan +down this last column, and + +just write everything here. + +OK, cones. + +Homework three, solution set +two-- whatever it may be. + +So now, at a glance, before you +go to your session, you + +review these two things. + +Make sure you have everything, +your know why you're here. + +But then here, you're going +to follow your script. + +Which is a loose script. + +It's not exactly a word-for-word +script. + +It's, maybe, a few equations. + +Suppose there's a question. + +What is this constant? + +OK, so that's my overall, +what I'm going to do + +for, say, ten minutes. + +And then I break it into +sub-questions. + +OK. + +What is H and B? + +How many pyramids do I need? + +What's my goal shape? + +So these are questions +that I ask students. + +And for each one, I write +down the minutes. + +Maybe in parentheses, put +the total up here. + +So now, when I've done my two +or three pages-- and by the + +way I find, just at the level of +detail I use, if I ever go + +beyond three pages, I never +get to that material. + +So it's just sort of for a +security blanket by the time + +I'm beyond three pages. + +It depends how detailed you +write these things, but I've + +generally found that's +where I am. + +And then, you estimate +the time. + +And what you'll find is, the +first time you do stuff, + +you'll massively underestimate +the time. + +You'll be off by a +factor of two. + +So, in other words, if you think +it takes five minutes, + +it'll really take ten minutes. + +And that's true even after you +take account of this rule. + +Sort of. + +OK, so then you put down all +your minutes on this page, and + +the next page. + +You add them up, and you make +sure that you're not over 50, + +or whatever the amount is. + +And then what you'll find is +what you thought was 50 really + +is going to take you 130. + +So the next time, when you +evaluate minutes, you'll have + +a better idea. + +And you'll find yourself +actually tuning your time + +sense pretty well. + +So now I've got my time sense +that I don't really need to + +put the minutes down, because +I can just do it + +by number of pages. + +Three pages, too much. + +And so you'll find your own +writing level, and detail + +level, how many pages to use. + +Now the other point is, where do +these questions come from? + +OK, well this is a way you can +turn any regular lecture into + +an interactive one. + +So suppose you have a +long derivation that + +you're going to do. + +Or, for example, suppose the +first way I planned this, was + +I wanted to show people that +this was 1/3 over here, this + +is three here. + +And the way I was going to do +it, was I was going to draw + +six pyramids, show them in a +cube, and show that 6V, and do + +all this showing. + +Well, first draft, write it all +out like that, with times + +and everything, without +questions. + +Then, any time you come to +something interesting-- + +so here. + +So before you have [? tel. ?] + +So now you look at your sheet, +and you say, hmm, where did + +something interesting happen? + +Hopefully, there is at +least one point. + +Because if there isn't, maybe +you shouldn't be giving the + +lecture at all. + +So now, let's just say, by +construction, you found some + +interesting things. + +OK, so that's interesting. + +Oh, it's interesting that +it makes a cube-- + +it's not obvious. + +So just think, where does +something require thought, and + +that you're short-circuiting +the thought by telling. + +So then, what I do is I have a +green pen, and I turn it into + +a question. + +So I'll circle it in green, and +write, "ask" next to it. + +OK, or you can just rewrite +your sheet. + +Telling something, then asking, +and then continuing. + +OK so that's how you can turn +any regular lecture into an + +interactive one. + +And that's your sheet that +you walk into class with. + +And what you'll find, is that +the first time you do it that + +way, there will be a bunch more +spots you realize were + +actually subtle. + +Because, for example, at the end +of class session, when you + +collect your feedback sheets, +people will have questions + +about different parts. + +You'll realize, oh, there was +actually something interesting + +that happened that wasn't +obvious in one of these + +telling points. + +And you'll be able to turn that +into a question, as well. + +The master sheet with all that +formatted for you is online, + +on the course website. + +And you're welcome to use that +in your own teaching, and + +distribute it to everyone you +know Any questions about that? + +Yes. + +AUDIENCE: When you run over +time, then you have to shift + +some of the things to +the next lecture. + +So how do you do that? + +PROFESSOR: What happens when +you run over time. + +The first time you teach the +course, you basically find out + +there's just twice as much +material in the course as + +there should be. + +And you'll always be running +over time if you try to cover + +every single thing. + +So, the first time you +run out of time-- + +there's two approaches to it. + +One is just to slow the entire +pace down, and cover half of + +the amount of material. + +So that's quite a reasonable +approach. + +The other is to sort of keep +rhythm, but not cover every + +single thing. + +So my piano teacher, a while +ago, she said, when you're + +sight-reading new piano music, +the most important thing is, + +keep rhythm. + +So don't just stop, and then +think for like ten seconds + +about one measure, and +then continue in + +this herk and jerk. + +Just keep playing at speed, but +skip some of the notes, + +and do whatever you have +to do to keep rhythm. + +So you can try that +approach too. + +And then, what you do is you +say, OK look I'm not going to + +cover every single +thing in lecture. + +A lot of stuff is in the book. + +And that's good to do anyway. + +So a mix of the two approaches +is one way to deal with + +running over time. + +AUDIENCE: [INAUDIBLE] + +So each lecture you have +some objective. + +And then, if you run over +time, then in the first + +lecture, you only finish +half of it. + +And then, the second one seems +to start from the middle of + +[INAUDIBLE]. + +PROFESSOR: Right. + +OK. + +So that's one reason +it's worth writing + +the objective first. + +Because then you know what +the main goal is. + +So one way to do it, +which I do like, is + +to make sure that-- + +right away-- the objective +is reached. + +So you do it as sort +of a layer cake. + +So the first example-- + +maybe the first two examples-- + +just from those, if everybody +just doesn't do anything else + +but the first two examples, +which you expect will only + +take 15 minutes-- + +but it takes 40 minutes, +it's okay. + +Because the first two examples +reach your objective. + +Now they don't reach the +objective 100%, but they give + +you 80% of the objective. + +So you want to plan your lecture +structure like a layer + +cake, or like JPEG. + +People know how JPEG +compression works? + +So JPEG, the way you do it, is +the low-frequency, quote, + +"most important" terms, +come first. + +And then the higher-frequency, +say, less important terms, + +come later. + +So sometimes you see things +rendered in your browser + +step-by-step, and they just +sort of take focus. + +And it gets better and better as +you wait longer and longer. + +So you want to plan your +lecture a bit that way. + +So that it's robust +to time shortage. + +So that if, for example, there's +a fire alarm halfway + +through your lecture, still +the main point got across. + +Now it didn't get across in +all the detail, and the + +beautiful glory of that you +wanted, but the main point + +still got across. + +So then, if you run out +of time, it's OK. + +You say, look, there's two more +examples of this which we + +didn't do, but they further +illustrate the main point. + +See the notes. + +And then you can keep +to your plan. + +Assuming that your plan +is a reasonable one. + +If your plan is that, I'm going +to do f equals ma today, + +and I'm going to do rigid body +rotation tomorrow, that's + +probably not a reasonable +plan. + +And the fact that you ran out of +time on day one is probably + +a good sign that you should +actually spend a little more + +time on f equals ma. + +Does that answer +your question? + +Other questions? + +Yes. + +AUDIENCE: I have a question +about [INAUDIBLE]? + +A lot of people have told me +over the years that it's good + +to write really big. + +And I know you're constrained by +that the people have to be + +able to see. + +But, given that you're writing +large enough for them to see, + +what's the advantage of writing +any bigger than that? + +As opposed to having +the [INAUDIBLE]? + +PROFESSOR: OK, so that's +a good question. + +Actually, why don't +we save that. + +We'll talk about that today. + +So the question was, how +big should you write? + +Just enough so people +can see, or bigger? + +So that you can keep the +full story there. + +OK, so, any other questions +on the lecture planning? + +And blackboard, and slides, +we'll come to + +starting right now. + +Teaching with slides +and blackboards. + +What are the advantages, and +disadvantages of each. + +I'll tell you my bottom line, +which is that my zero-th order + +term, so this is +my objective-- + +if the lecture ends after the +next two minutes, at least + +you'll have the zero-th +order term. + +The zero-th order term is +that, if you can't help + +yourself, use slides, but +otherwise, use blackboard. + +For 90% of things, blackboard +is much better for teaching + +than slides. + +There are some cases where +slides are useful, and you can + +make an argument for it. + +There's some cases where maybe +the slide is as good as a + +blackboard, few cases where it's +better than a blackboard. + +But the default is, blackboards + +are better than slides. + +Now let me show you an example +of why that's true. + +Suppose you're teaching the-- + +an example I've done with you +before, slightly, is the + +Navier-Stokes equation. + +Let me write it down, +to start with. + +Actually, I'll put it on +a separate blackboard. + +So there's our topic. + +So we always know what our +topic is, because it's up + +there, and it's just going +to live there for a bit. + +And in fact, in some +classrooms-- + +you can't do it so easily +here, but my favorite + +classroom is 4-265 because it +has pretty much this much + +blackboards in the front, and it +has blackboards all around + +the side, and on the back. + +So I don't use the back ones so +much, but the side ones are + +really, really useful. + +Because you can, for example, +put the topic, like I've done + +here, on the side blackboard, +and just let it stay there the + +entire time. + +You can put an outline +of the lecture. + +OK, so let's say we +have a lecture on + +Navier-Stokes equation. + +We want to look at them, +try to understand them. + +So here are the equation. + +Well "are," "is," the plural +is a bit ambiguous. + +This is actually three +equations, one because it's a + +vector, vector, vector. + +Already there, you see something +that's harder to do + +with slides. + +You'd have to work harder +to do that in slides. + +You can just go back, and +annotate as you go. + +And here, you can see the entire +topic while you're + +looking at this. + +So, for example, the student has +now got overwhelmed by all + +the little symbols here-- + +the del squared, the partial +derivative, the v dot grad-- + +that part always scared me when +I was a physics student. + +I knew what del dot v is, +but what's v dot del? + +So you get scared by all that. + +And then people forget, +they panic. + +Because their short-term term +memory got filled with every + +single, little, chunk here. + +Their chunks are, remember, +very small. + +And they forgot, what +are they doing? + +Navier-Stokes equation +fluid mechanics. + +OK. + +And now, you can even improve +that first blackboard by + +talking about, what does +this apply to? + +Drag, turbulence, river +flow, airplanes. + +So here, you can have a + +reminder of why it's important. + +So now that just stays up +there the whole time. + +And people can re-center +themselves every time they get + +confused of what they're +doing, just by that. + +And then, you can continue. + +You can say, OK, let me +try to explain the + +meaning of these terms. + +So let's do the terms +one at a time. + +What's this? + +So this term here is Dvdt. + +We've seen things like that-- +that's sort of like an + +acceleration. + +You can annotate the equation +right there. + +That's also hard to +do on a slide. + +I mean, you can do it, you can +work at it, but it's very + +natural on a chalkboard. + +Now, there's some things that +are common to chalkboards and + +slides, which is the +use of color. + +So now this, unfortunately, +is blue, which is + +not the ideal color. + +Unfortunately, I +don't have my-- + +orange is generally better, +but anyway I have blue. + +Can you see the blue? + +So marginally? + +Maybe this orange, even though +it's not as big, will be + +better than the blue. + +OK, well this shows you an +example of color, and the + +importance of choosing +the right color. + +There used to be a green +one here, but + +they're isn't green anymore. + +Blue is not ideal, I +won't use the blue. + +Let's try this. + +Is that better? + +OK. + +So let me use this orange one, +and I'll try to write large, + +even though it's not as bold. + +OK, so the use of color. + +That's important in both +slides and blackboard. + +What's the use of color here? + +Is it just because it's nice +to have a pretty picture? + +No. + +The reason for using the color +is that you get layering. + +So again, remember the +students' dilemma. + +Pretty much all students' +dilemma come from the + +following problem, which +is that their + +chunk size is one symbol. + +You've been teaching the +Navier-Stokes equation for 20 + +years, your chunk size is +the entire equation. + +Right? + +So that's one chunk to you, +you just write it + +down, like I just did. + +But for the student, every +single, little + +thing is one symbol. + +So now, if you then write all +of this stuff in the same + +color, as your rest of your +equation, it just + +becomes more stuff. + +They don't know how to +separate it into + +two different objects. + +But, if you write your labels in +a different color, it pops + +out in a different layer. + +They know that lives in a +different space, so you're + +already helping them chunk. + +So what is this? + +This is also a change in v. +So it's sort of like an + +acceleration. + +Well, it's part of the +acceleration, actually. + +So this is another +acceleration. + +It's a change in v, but it's a +change in v because you've + +moved to a new place. + +So this is a change in v +because you waited-- + +you move to a new time. + +This is a change in v because a +little piece of fluid moved + +to new place, where the fluid +velocity is different. + +So these two things together +are two different + +contributions to the change in +v. So we'll actually call this + +whole thing D of vdt, which is +actually its actual name. + +So this is an acceleration. + +These are the two pieces of it-- +this is the acceleration. + +What's on the other side? + +Well, this guy, pressure-- + +p is pressure-- + +grading of pressure. + +So that's the differences +in pressure. + +So that's going to do some kind +of thing, like a force. + +And row is density. + +So you're taking a force-- + +I'll put it in quotes, because +it's not quite a force, it's + +sort of force per area. + +But now you divide by density, +and you get f over m. + +So f over m. + +So we have, here this guy-- + +acceleration is equal +to f over m. + +Do you recognize that +equation before? + +Yes, Newton's Second Law. + +So this whole thing, so far +here, is just this is a + +equals f over m. + +So this is the pressure forces, +and this must be the-- + +and this is the viscous forces +divided by the mass. + +So these are the two +contributors to the forces-- + +pressure forces, viscous +forces-- + +and those produce the +acceleration. + +So the Navier-Stokes equation +comes out just as Newton's + +Second Law all over again. + +So now, this kind of drawing +is quite difficult + +to do in the slide. + +Yes. + +AUDIENCE: So I actually +would argue with you. + +You could prepare a set of +slides with annotations, and + +then you could do everything. + +You could put all the +information [INAUDIBLE] in a + +slide, or in multiple slides. + +[INAUDIBLE] animation. + +PROFESSOR: Yeah. + +So you could put them on +multiple slides, and then flip + +to it, one by one That's true. + +So you can do it, which is +why I said you can do + +it, but it's hard. + +Because it is a bit of a pain, +and you can do it. + +OK but then the problem is, you +want to now leave that on. + +So now you want to have not only +this, but you also want + +to have this, and leave it on +for the entire lecture. + +Because this is the meaning +of the terms. + +And now you're going to leave it +there, and talk about each + +term, one by one. + +Yes + +AUDIENCE: But you could also +give them a handout, with all + +the slides there, so +they would have + +everything in front of them. + +And if they ever want to go +back, they can look back on + +the previous slide. + +[INAUDIBLE] but I think so far +this is not a strong argument + +against the slides. + +Maybe the question's about +interactivity. + +If somebody asks you +a question, what + +about the third term? + +If you don't have a slide +for that, then-- + +PROFESSOR: Right. + +And this is the point +I'm coming to. + +So there's that. + +And I agree with you, you can +do this with slides, you can + +give people a handout. + +Though the problem with +the handout-- + +suppose you put all of this on +the handout for them, so that + +now, when you erase this screen, +and that screen, you + +go to another thing they +still have something to + +refer back to you. + +The problem is that you want +it all in one visual field. + +And you don't have that when +it's on a handout. + +So you have a problem +of split attention. + +So now the student's attention +is switching between the + +screen, and the handout-- + +screen and handout. + +And when they look at the +screen, they're trying to + +remember what they're +confused about. + +And now they look +at the handout. + +This is the analogy. + +When I was in Prague, I would +look at a street sign, and I + +would read the word, and look +at all the letters. + +[INAUDIBLE] + +or something like that. + +And I would look away. + +Two seconds later, I could not +remember more than one letter + +that I saw on the +street sign-- + +on the street name. + +The reason is, because each of +the letters was random to me. + +So, yes, someone who's Czech, +just says, oh yeah, that's + +Main Street, of course. + +No big deal. + +What's there to remember? + +It's Main Street, it's +in the Main Square. + +Whereas me, as the foreigner, +has no clue. + +And it's all new data to me. + +So it's the same way +for the students. + +This is all new to them. + +So when they're looking +at something else, + +you're talking about-- + +you're going to discuss, +what's the + +dimensions of this term? + +They look at this thing, and now +you have a big analysis of + +the dimensions of this, you +want to check that all the + +dimensions are right, and your +goal is eventually to work out + +the dimensions of this-- + +viscosity, let's say. + +They might be frightened +of the partial. + +So they look at this, and they +say, oh, yeah, where does the + +Dvdt come from? + +And then they look back at their +handout, and they've + +already forgotten pretty +much what this was. + +Because they are +the foreigner. + +They are the tourist +in this land. + +AUDIENCE: Yes. + +I was just going say that +I would have said + +something very similar. + +The annotation part of it is to +[INAUDIBLE] slides at all, + +because if I was making slides +for this lecture, I would've + +done exactly what you did. + +But it would all be nicely +spaced, and there would be no + +handwriting issues. + +So if anything, slides would +be better for that. + +But I think that the argument +for slides is [INAUDIBLE] + +having them linger on, +but also pacing. + +Like, the fact that it doesn't +flip up so quickly, because + +the [INAUDIBLE] that I've taken +where they use slides + +and use [INAUDIBLE], it goes by +so quickly that you have no + +chance to internalize. + +The fact that you have to write +it out by hand forces + +you to slow down, in a +way that is really + +helpful for the listener. + +And so that's something that's +really important [INAUDIBLE] + +difference. + +PROFESSOR: Right. + +And that's a fundamentally +important point about pacing. + +And this partly addresses +your question about how + +big should you write. + +So one of the reasons for +writing big, is that you're + +writing slower. + +And writing slower, generally +forces your pace to match the + +pace that is absorbable +by the students. + +So I'll come back to that point +in just one second. + +So let me just finish the point +about the visual field. + +The good thing about the +blackboard is, you could call + +it cognitive offloading. + +In one glance, everything +that the students + +need, can be there. + +So they don't really have +to remember much. + +And the short-term memory +isn't overfull. + +They're registers. + +They're a low-register +machine. + +Or rather, they have the same +number of registers as us, but + +they don't store as much + +information in their registers. + +So their registers don't get +overfull, because everything's + +right there. + +Whereas there is a much bigger +danger of register overfilling + +with slides. + +Then, as you point out, +there's the issue of + +interactivity. + +So this is partly a performance +question. + +Slides, not only are they +much more pre-prepared-- + +I mean, you can prepare your +blackboards, as well, but you + +actually do have to re-perform +it each time. + +Whereas a slide, as you say, you +just click to Return, or + +Next, and there you are, +at the next slide. + +So there's much less +performance in it. + +And it seems much more +pre-scripted. + +Now, what does that signal +to the students? + +The pre-scripting. + +It says to the students, look, +this is all one, tight thing. + +It's sort of like a play on +a stage, that you're only + +supposed to applaud at +particular times. + +A modern-day play. + +Back in Elizabethan times, in +Shakespeare's time, people + +cheered, and screamed, and +cat-called, and it was a much + +more lively thing +on the stage. + +But now, everyone sits really +quiet, God help you if you + +cough, you try to wait, and you +think about your coughing, + +and then you don't think about +the play, and you try to + +prevent your coughing. + +So all that transfers a bit. + +That same mentality comes when +you're using slides. + +People think, oh my God, this is +a pre-scripted thing-- how + +dare I intervene, and +break into that. + +So if your goal is to encourage +students to + +question, it's harder to +do that with slides. + +You still can do it. + +You can, for example, put +questions on the slides-- and + +you definitely should do that +you're going to use slides-- + +but the random, spontaneous +character of your session-- + +the good side of that, +is going to be + +minimized by the slides. + +So this one was just to continue +saying, OK, now we're + +going to leave these two on, +and we're going to do the + +dimensions of each term. + +I have one, two, three, +four, let's say-- + +four terms I want +to talk about. + +I'll do the dimensions of +two terms on this board, + +dimensions of two terms on that +board, now I'll have all + +the dimensions there. + +And now I can start, for +example, doing dimensional + +analysis on this side +of the room. + +And we'll eventually get to the +Reynolds number, which is + +vr over nu. + +Once we know this guy's +dimensions. + +And v, we know his dimensions, +r the size of + +your sphere or something. + +So this is dimensionless. + +Now you've got the Reynolds +number, you've also got, say, + +drag coefficient, which is +f over 1/2 [INAUDIBLE] + +v squared times some area. + +So this is also dimensionless. + +So now, you have two +dimensionless things. + +And then finally, +the finale is-- + +So now, let's say by the end of +the lecture, you get to the + +point where you've plotted +the drag coefficient, a + +dimensionless thing, versus +the Reynolds number, on a + +log-log scale. + +And then you can talk about +this, you can go back and you + +say, OK, well what is this? + +This is really interesting. + +It looks like it was constant. + +And then what happened? + +Well, you can go back +and talk about that. + +And as you talk about it, the +entire graph is visible to + +everyone, as well as the source +of all the pieces of + +the graph, which is all the-- + +why is everything +dimensionless? + +Well, you have it on +these two boards. + +And what are the terms +that you used? + +Well, those are all on there. + +So all of that is visible +in one glance. + +So that's an example of +something that is hard to do + +in the slides. + +Now, it's not easy to +get it right on + +the blackboard, either. + +You do have to plan. + +You have to plan by saying, +what am I going + +to put on each board? + +And how am I going to structure +the boards? + +But you can do that on your +lesson plan, for example, on + +the back of the lesson plan. + +Say, OK, how many boards +do I have? + +And what am I going to use? + +And then, if you want to take +advantage of the fact that + +everything is visible all the +time, you generally don't want + +to use the up-and-down +nature of the board. + +You just want to use two boards +on each of the regions. + +If you push this up, and start +writing on this guy, you're + +now OK, still. + +But then, when you push this +up, and you write on here, + +you've covered this guy up. + +And yes, you've lost some +of that advantage. + +Again, you can plan it out, +and do a trade off. + +But that is harder to +do with slides. + +Now, your question about how big +you should write so that + +everyone can see, versus telling +the whole story. + +I think it is important to try +to tell the whole story. + +It doesn't have to be the entire +lecture sits on the set + +of blackboards, but a coherent +chunk of the lecture should + +sit on the blackboards. + +You have two things +you could control. + +One you can control is the +writing size, and the other is + +what you write down. + +So this is a similarity +between slides and + +blackboards, which is +you don't want to + +write everything down. + +Because if you write everything +down, then you say, + +well for example, did +I write every single + +thing I said here? + +No, because I want the main +ideas to come across. + +Every little detail that I say, +that should be either in + +the notes, or in some book. + +But the main point should be on +the blackboard at a level + +of detail that people +can absorb. + +It's the same thing +with slides. + +You don't want to put everything +on the slides. + +So, you can still write big, +if you just cut down + +how much you write. + +And generally, that is more +suited to what students need. + +Because, again, they are living +in the dirt of what is + +this, and what is this. + +And you want to try to +bring them up higher. + +So you don't want to spend a +whole bunch of time on all + +these little guys. + +You want to try to bring them +up higher, and put some + +high-level chunks onto the +little bits that they have. + +So use a big chalk, write, +large, just don't write + +everything. + +And try to fit a coherent +piece onto all the + +blackboards. + +It doesn't have to be +a whole lecture. + +Although Feynman, at +Caltech, when he + +gave the Feynman Lectures-- + +well, what later became the +Feynman Lectures-- he did + +actually plan it so that he +would start at one corner, and + +he would end all the way here. + +And I find that's too hard to +do if you're also going to + +make the lecture at +all interactive. + +For example, if you're going to +have questions where you're + +going to have the students give +answers, and you're going + +to write down the answers. + +Well, you're not necessarily +going to keep all the answers + +for the rest of the class. + +So the goal of corner-to-corner, +I think, is + +a bit too strict. + +But the general idea is sound. + +Any questions about that before +we take a break, and + +then go onto slides, +and slide design? + +Yes. + +AUDIENCE: I just wanted to +comment that also, a lot of + +students, if there are slides, +and they're available online, + +they will just print them out, +and not come to lectures. + +PROFESSOR: That's true. + +A lot of students will just +print the lecture slides, and + +then just think they can thumb +through them, and understand + +the lecture. + +So that's partly-- + +you could call it the +optimism of youth. + +That they don't realize how +much they're actually not + +seeing, because they didn't +actually come. + +They think if they just follow +each slide, they've understood + +everything. + +But there's no way to put +everything in a slide. + +If you packed a slide with +everything you said that was + +worth remembering, or that was +actually part of the structure + +of the argument, then it +would become not a + +slide, but a book chapter. + +And so, yeah. + +I think there is a reasonable +argument that if there's a + +book chapter-- + +maybe they don't want to come to +lecture if all you're doing + +is reading the book chapter. + +But slide, and lecture, +are so different. + +It's sort of like, if you just +take a few photographs of the + +blackboard, could you +replace the lecture? + +No, but you're right, students +do think that. + +So actually I don't like giving +them handouts of the + +slides, if I do happen +to use slides. + +Because it's really not a +substitute for a lecture. + +It's an aid to the lecture, just +like the blackboard is an + +aide to the lecture. + +But what's important about the +lecture is, what are you + +having them do in the lecture? + +And that's the reason they +should come into lecture. + +Because in lecture, they're +actually struggling with some + +stuff, and you've structured +it so that they + +struggle, and learn. + +And somehow you have +to convince them + +that that's the value. + +And it's hard, because +of what you say. + +Other comments or questions? + +One second, in the back. + +AUDIENCE: [INAUDIBLE] + +But at the same time, I've +probably taken at least half a + +dozen classes where every single +word that the lecturer + +spoke, was present +on the slide. + +And then it felt kind of +worthless going, because you + +show up, you pick up the slide +handouts, and you can read the + +slides during the lecture. + +You pay no attention to the +lecture, because he's not + +saying anything that +isn't there. + +PROFESSOR: Right. + +So that's sort of the worst +of both worlds. + +So now, what they've done, is +they've taken the constraints + +of the slide format-- + +because there's only so many +words you can put on the + +slide, and make it even +at all readable-- + +and often they don't make it +readable, and I'll show you an + +example when we come back. + +And so then they've torqued the +lecture to be basically + +reading out the slide. + +So now they messed up the +lecture, and the slide still + +isn't really a good +substitute. + +It's a huge problem. + +I think the answer to that, is +that if you're going to use + +slides, they're really an aide, +but the students really + +need to learn how to read +a book, or your notes. + +Or something that's actually +a coherent + +presentation of the material. + +Yes. + +AUDIENCE: So when you write +something on the board to + +respond to a comment, and it +[INAUDIBLE] some of your space + +that you could otherwise use to +plan for the usual stuff. + +So when do you erase +that comment? + +PROFESSOR: That's +a good question. + +So how temporary should +stuff be? + +One way to do it is to think +about the number of minutes + +each thing deserves. + +So that-- + +I like things like that to be +on the board the whole time, + +if possible. + +And now it may be that, halfway +through, I might + +reclaim that board if I +don't have a choice. + +But I'd like that to be there +for a while, at least, because + +that's really the main reason +we're doing all this stuff. + +And what are we doing. + +So ideally, I'd put that on the +side blackboard, and just + +leave it there forever. + +Something like this, I would +like it to stay there the + +whole time, so we remember. + +So this, I would +mark as, "don't + +erase," if at all possible. + +So when I'm writing stuff +down, I would know, how + +perishable is the material? + +That's the word I'm +looking for. + +So suppose I ask people +a question, + +like the wood blocks. + +OK, what's the frequency +going to be? + +And we get a bunch of reasons. + +I think the reasons are +quite perishable. + +After we write them down, and +we talk about them, and then + +we reconcile everything, I'm +perfectly happy to erase all + +the reasons, and just +have the reconciled + +picture on the board. + +But while I'm reconciling, +I want them all visible. + +So then, what I would do, is I +would try to have all those + +reasons go, say, here. + +I might cover that +up temporarily. + +What I would do, is I would +write the reasons here, and + +then do the reconciliation +here. + +And then-- + +so let's call this +Reconciliation-- + +so this is actually the picture +that I would use for + +the wood blocks, +which is this. + +And I would draw a bunch of +arrows, and stuff, dot, dot, + +dots, and spring [? bogs ?] + +OK. + +And now, I need to reclaim this +board with perishable + +material on it. + +So now I reclaim the board. + +So this had reasons before. + +Lots of reasons. + +OK, and then, reclaim this. + +And I still have that +reconciliation up there, and I + +have this board back. + +AUDIENCE: So you think it is +a good idea to separate the + +perishable things on one board, +and then the more + +permanent things on +the other board? + +PROFESSOR: Yes. + +I think it is a good idea. + +That's a good point. + +I hadn't thought of it that way, +but that is a good idea. + +Because that way you can reclaim +the entire board back, + +and then replace it with +more permanent things. + +Or, if something perishable +is going to go back + +on it, put it here. + +And then, when it's done, to +erase it, until a permanent + +thing goes on there. + +And then you move onto +the next board. + +So it does require some +board planning. + +But what you find, basically, +is the first time you teach + +the course, you wish you'd +planned it more + +in the first lecture. + +But then you start to be more +automatic about it. + +Yes. + +AUDIENCE: I have a comment +on the performance + +aspect of the board. + +So when you were writing these +equations, and then as you + +went back in the vector symbols, +and also when you're + +circling things, because if +you're doing it right, the + +students are engaged. + +Their focus is [INAUDIBLE] +chalk. + +PROFESSOR: That's +a good point. + +AUDIENCE: It's as much of an +interactive activity as they + +can with you writing +on the board. + +Whereas with a slide, certainly +[INAUDIBLE] a + +physical pointer, you might +circle something, but then + +there's nothing there. + +A laser pointer's even worse, +because you're not actually + +touching anything. + +Even if you have an animation +drawing, you're still + +separate from it. + +So I think that's a big +advantage of the board. + +If their attention is at your +chalk tip, then that's some + +degree of engagement +with that action. + +PROFESSOR: Yeah that's +a really good point. + +So the point is that when I'm, +for example, circling this, it + +directs people's attention, and +then there's a permanent + +trace left. + +So you can, kind of, +do it on a slide. + +If you knew you were going to do +that ahead of time, you can + +make an animation that +goes, circle. + +So you can do that, +but it's hard. + +So one of the cures for that is +this tablet, a kind of PC. + +So you can actually write +on the tablet as you go. + +AUDIENCE: Yeah. + +But even so, the thing is that +you're still over there + +[INAUDIBLE]. + +PROFESSOR: I know. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I think +that's true. + +That, actually, we are +together, doing + +this, on the object. + +AUDIENCE: Yeah that's exactly +what I was not saying very + +well earlier, was you can do all +this, what you're saying, + +on a slide, just as well. + +When I do [INAUDIBLE] +presentations, I do actually + +animate the circle. + +I find that that's the +most intuitive way + +for me to do something. + +But it's not the same as +actually drawing it yourself. + +It's not the same level +of activity. + +And obviously you kind of have +to use slides for [INAUDIBLE], + +but in a classroom you +don't have to. + +PROFESSOR: Right. + +OK, so that's what we'll talk +about when we come back-- the + +difference being technical +presentation, and teaching. + +And then we'll actually look at +an example of slides, and + +we'll critique them, and I'll +show you how to redraw them. + +OK so break for 10 minutes. + +We'll start at 10:18 sharp, +by that clock. + +So you can set your clocks +accordingly. + +And I will erase all this, and +put up a slide that we're + +going to critique. + +And then we'll talk +about technical + +presentations versus teaching. + +Because there's a lot of +misconceptions that come from + +technical presentations. + +And therefore, people +think we should + +use slides for teaching. + +OK, so see in 10 minutes, or +if people have questions + +during the break. + +OK, so our next task is to +figure out, if you are going + +to use slides, what +should you do. + +And related to that point is, +when are slides appropriate. + +People have the idea the slides +are always appropriate + +for teaching, because they +see them used all + +the time for seminars. + +So if you go, and give a talk +at a conference, you go to a + +conference, most-- + +almost all the talks-- + +or at the department seminars, +basically people now come with + +some form of slides. + +When I was an undergraduate, it +was sort of transitional-- + +people came with overhead +projector foils. + +And it was sort of shifting, +from seminars used to be + +blackboard seminars, and then +they shifted to overhead + +projectors, at least +in physics. + +And now it's pretty much slides +all the way through. + +But there's a fundamental +difference between seminar + +presentation, and teaching. + +And seminar presentation-- + +basically you're talking +to people + +who are sort of experts. + +They may not be experts in that +particular area you've + +understood. + +Probably not, otherwise they +would have invited one of them + +to talk, instead of you. + +So now, you're the expert +locally, on that local area. + +But in the broader area, you're +talking to basically + +people who are already +interested in, and are + +professionals in the field. + +And maybe some apprentices in +the field, who are going to + +soon be professionals, like +graduate students. + +So your goal is not to slowly, +necessarily, uncover one or + +two ideas, especially if it's +a 10-minute conference + +presentation. + +Your goal is something like, +here are the core, main + +ideas-- one or two points-- and +here's something to show + +you that really interesting +stuff is going on. + +And you should pay more +attention to me is part of the + +goal of the seminar. + +Now that's very different +in teaching. + +In teaching, your goal really is +to kindle some new thoughts + +in the student. + +And who are very different +from a seminar audience. + +They are not professionals. + +Maybe they would like to +eventually be, but part of + +your job is to kindle that +interest so they would like to + +become professionals. + +So you have a very, very +different audience, and + +generally much different +time constraint. + +In a seminar, maybe it's 10 +minutes, maybe 15 minutes. + +Rarely, once you start getting +well known, maybe you get + +invited to give a 50-minute +seminar. + +But, teaching, you generally +will have 50 minutes. + +So your time is different, your +audience is different. + +So just because slides are used +so much for seminars, + +does not mean they should be +used so much for teaching. + +You should really use them when +you don't really have a + +choice, and when it seems like +it's the optimal thing to do. + +So for example, art +history class. + +Now, an art history class, it +would be fantastic to go to + +Sienna, and look at all the +tapestries, and take the whole + +class with you. + +Now that's just too expensive. + +So, instead, you show slides. + +That's exactly why they're +called slides-- they + +originally were 35 millimeter +slides. + +35 millimeter? + +Yeah, 35 millimeter slides. + +So for something like that, +yes, slides are ideal. + +And drawing the tapestries of +Sienna on the blackboard is + +not even close to showing +the actual pictures. + +So, in that case, 100% +go with slides. + +Other cases generally go towards +blackboards, but there + +are cases where, for example, +there are no blackboards in + +the room, and you have +to teach with slides. + +There's no whiteboard, either. + +Whiteboards are not as good as +blackboards, but they're a + +reasonable substitute. + +But there's neither, and +it's just slides. + +Or, yes-- + +AUDIENCE: Why aren't whiteboards +as good as + +blackboards? + +PROFESSOR: I find the markers +always dry out, whereas chalk + +always works. + +So blackboard markers never +quite work as well. + +And the other problem, just +me personally, is that I'm + +sensitive to the chemicals +in them. + +So I eventually just get +a bit dizzy using them. + +So I don't like him +for that reason. + +And there's quite +a few people. + +I'm sort of the canary, so I'm +more sensitive, maybe, than + +many people, because I have +lots of allergies. + +But I think lots of people are +bit sensitive to them. + +But, generally, I find +the markers just + +don't work as well. + +And, also, there's very rare +room has lots of whiteboards. + +Whereas many, many, classrooms +have this many blackboards. + +When they replace them with +whiteboards, usually it'll be + +one whiteboard. + +So then you're back to many of +the disadvantages of slides, + +which is that you can't get +a big field of view. + +But now let's say you are +going to use slides. + +How do we make good slides? + +Well, one way to figure out what +constitutes good slides, + +is to look at what constitutes +bad slides. + +So this, here, is +a horrid slide. + +So what we're going to do is, +I'm going to show you how to + +re-write the slide. + +But first, let's figure out what +are some of the problems + +with this slide. + +So, take a couple minutes +with your neighbors. + +You can all see the slide. + +What are the things that just +don't work about it? + +And there's many. + +It's a very competitive field. + +And I'll write some stuff +down on here. + +By the way, one thing is +that the JIT, that I + +just actually shortened. + +It actually was, "Just +in Time Learning". + +I've just shortened it to +improve the typesetting, + +assuming that the audience +knows what it means. + +So the original slide didn't +have that problem. + +So I see you found +lots of trouble. + +Give me one thing +that's wrong. + +Adrian. + +AUDIENCE: There's no message. + +PROFESSOR: What do you +mean by message? + +AUDIENCE: What is the person +trying to tell you here. + +You have to infer what the +person is trying to tell you + +by analysing it yourself. + +PROFESSOR: OK, no message. + +So, the reader, the viewer, +the student-- + +this was actually used in a +class, never mind where, but + +it's not here. + +Yeah, what is the teacher +trying to communicate? + +So Jean-Luc Doumont, if you +saw him during IAP-- + +he has a great way of talking +about what's a message, versus + +what's information. + +So the message-- + +so information, that's +what that slide has. + +It has lots of information. + +That's the "what." Message +is the "so what." + +His native language +is not English. + +I wish I could come up +with things like + +that in other languages. + +I think it's fantastic, because +there's lots of + +"what." Well, 12% said Just +in Time Learning-- + +JIT Learning-- was a bad idea. + +But your question is, so what? + +And there's no answer +to that question. + +So there's no message. + +Yes. + +AUDIENCE: So a counterpoint +to that would be, this is + +documentation, this +isn't propaganda. + +Right? + +You don't want to say, this is +what you should all think + +about this data, instead of, +look at the data yourself, and + +make your own conclusion. + +Presenting the data in an +accessible manner is a + +different issue. + +But I don't know if I agree +with this, "so what" idea. + +PROFESSOR: And some of that is +that, yeah, definitely in a + +seminar, you lean much more +towards the "so what." And you + +would put in the "so what," +really first. + +And in teaching, maybe you start +with the "what," and + +then you lead to the "so what." +So, for example, the + +wood blocks. + +Here's the "what--" what do you +think is going to happen? + +And I haven't said, +"so what," really. + +And then we talk about a whole +bunch of ways of analyzing it, + +and then we finally lead +up to the "so what.". + +But at some point, you +do want a "so what." + +So, yeah, without seeing the +entire lecture, it's hard to + +know if they ever gave a "so +what." But I can tell you that + +the succeeding slides just +went on to other topics. + +So it wasn't that they +were using that + +to develop the point-- + +what do you think about Just +in Time Learning, or how + +should we analyze Just +in Time Learning. + +They just moved on. + +Yes. + +AUDIENCE: Going back to your art +history example as a good + +use of slides, that doesn't have +anything in it that gives + +you "so what." It gives the +presentation of information, + +and then the discussion of +it is what gives that. + +So I don't necessarily think +there's something inherently + +wrong with giving information +on a slide, and having not + +answered the discussion +in the slide. + +PROFESSOR: It's not inherently +wrong, and + +that's a good point. + +So the art history one, +it's sort of a + +different use of the slide. + +So there, it's really like +you're bringing in a prop. + +So the cones, these pyramids +themselves, didn't have a "so + +what." They only got a "so +what" as we used them. + +So it's the same way with +the art history slide. + +It would get its "so what" in +how you discussed the slide. + +But here, the slide +is really the + +alternative to the lecture-- + +to the blackboard. + +If you've gone to slide talks, +or slide teaching, which + +aren't art history. + +I think art history is really +a separate example. + +It's, I'm telling you stuff, +I'm telling you stuff, I'm + +just telling you in a way +that you don't really + +know what I'm telling. + +Like, I may be telling it to +you verbally, but the slide + +doesn't match what +I'm telling you. + +Sorry, you're next. + +Go ahead first. + +AUDIENCE: You may have already +said this, but is this slide + +supposed to be for the students, +or is this for a + +faculty meeting? + +PROFESSOR: No, this was +for a course about-- + +what was the course about? + +It was a computer science +course somewhere. + +Maybe it was a discussion +of a-- + +no, it was a computer science +course, or a teaching course. + +I forget exactly what course +it was, but it was from a + +particular course. + +So it's a slide used +in teaching. + +Yes. + +AUDIENCE: That partially +answers what I + +was going to say. + +This material doesn't belong in +the lecture in any course, + +unless it's a course +on teaching. + +The surveys are filled out, so +they benefitted the lecturer + +so that they know what +to do when planning + +and running the course. + +The students don't need to know +what the results are. + +PROFESSOR: I think it wasn't for +the course itself, it was + +for the students in a teaching +course, is what I + +think it was for. + +And either way, whether it's +for a seminar, or for a + +teaching course, it has the +same problem, which is you + +don't even know what +to think about it. + +You just have a lot of data. + +And there's no integration. + +OK, so that's the no message-- + +the "what," versus "so what." + +What else is wrong? + +Yeah, Wendy? + +AUDIENCE: The data is just +terribly organized. + +[INAUDIBLE] + +One thing is that there's +bullets under bullets. + +By the time I get to +[INAUDIBLE], I'd rather skip, + +I've forgotten [INAUDIBLE], I +don't remember what we were + +talking about. + +PROFESSOR: Right, so the +organization is ghastly. + +AUDIENCE: And another good +comment, which is that the + +numbers of the percentages are +not organized in any way. + +They're not going from +highest to lowest, + +or lowest to highest. + +So you've seen, maybe 52, you're +like, I assume this is + +going in descending +order, and then + +things get flipped around. + +PROFESSOR: Right. + +So the percentages are +kind of random. + +It's sort of like the "what." To +organize it towards the "so + +what," you would put +some theme in it. + +But there isn't any, or +none that's obvious. + +And the typesetting, yes, is +related to the organization. + +The typesetting is a bit off. + +Yeah. + +AUDIENCE: So related to that, +[INAUDIBLE] the numbers and + +the questions are given +completely equal footing, + +because the numbers are +organized, [INAUDIBLE]. + +And so the numbers just follow +better to worse. + +I'm sorry, the answers to the +questions are organized from + +better to worse. + +[INAUDIBLE] + +PROFESSOR: OK, so then +it comes out. + +OK. + +AUDIENCE: And then it comes +out, but that's not + +[INAUDIBLE]. + +PROFESSOR: So the Likert +scale isn't obvious. + +The Likert scale is the +better-to-worse scale of how + +much you agree with +this statement. + +Right. + +So you're saying, also, the +answers have equal prominence + +to the questions. + +AUDIENCE: Equal prominence +to the percentages. + +You have no clue what's +organizing the information. + +PROFESSOR: Right OK. + +So the emphasis is random. + +Yes. + +AUDIENCE: So [INAUDIBLE] + +so she suggested [INAUDIBLE] + +or [INAUDIBLE]. + +PROFESSOR: OK, so +it's not visual. + +A pie chart, or a histogram, +or something would help you + +see much more. + +So that's one of our principles, +right, that your + +perceptual system is so much +smarter than your symbolic + +processing system. + +So you're actually slowing +everyone down, and making them + +much dumber, by forcing them +to try to extract-- + +basically build a mental +picture which you + +could build for them. + +Yes. + +AUDIENCE: I'd say there's +too much. + +PROFESSOR: Too much. + +So what do you think +is too much? + +AUDIENCE: All at once, you're +getting lots of text, and it's + +all these different things. + +Too much [? given ?]. + +PROFESSOR: Yeah, it's +too many chunks. + +It just overloads you. + +You don't relate it to +the lack of messages. + +If there are messages +in there, there + +are too many messages. + +You don't know what's important, +and what to pay + +attention to. + +Other problems? + +Yes. + +AUDIENCE: Format switches +midstream. + +PROFESSOR: Where? + +AUDIENCE: At the bottom, +the last question. + +PROFESSOR: Oh yeah. + +You're right. + +OK So the format. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Right. + +It's sort of related +to too much. + +Right, I tried to put too much +on my slide, and I really + +tried, really hard. + +So the format changes at the +end, right, so they could fit + +everything onto one slide. + +Yes. + +AUDIENCE: Extraneous use of +bullets, colons, [INAUDIBLE]. + +Not helping. + +PROFESSOR: So a random use +of colons and bullets. + +And it's not clear how +those actually help. + +Other problems. + +Yeah. + +AUDIENCE: Is that all bold? + +PROFESSOR: Yeah. + +I think it is all bold. + +So everything's equally +emphasized. + +So all bold. + +So again, it's presenting all +the information, right? + +It's just you don't know what's +important-- what's the + +"so what." Yep. + +AUDIENCE: The numbers are very +far away from the text, so by + +the time you get over there, +you don't know. + +PROFESSOR: Right, it's sort of +like a table of contents. + +And that's OK, for a +table of contents. + +It's not ideal, but there are +ways of doing table of + +contents that don't +have that problem. + +For a table of contents +it's OK. + +You don't need to sort of +get the entire table + +at a glance, right? + +You just want to know where +chapter five begins, and you + +just scan across, and +you go there. + +Whereas here, you can't +match the things. + +You want to try to match it all +together, and you can't, + +because the numbers are so +far away from the text. + +AUDIENCE: I don't know +what PI means. + +PROFESSOR: Sorry, that +was my fault, too. + +I just tried to shift it. + +Peer instruction. + +Yeah, you're right, so there's +a lot of use of acronyms. + +Yeah, so the JIT, and the PI +were my contributions to it. + +So maybe I made it a +little bit worse. + +Yeah. + +AUDIENCE: So how would you do +this on the blackboard, + +instead, if you had a chance? + +PROFESSOR: So this one, +actually, if I were going to + +present this, I would either +draw the thing I'm about to + +show you, or I would +use a slide for it. + +Either way. + +AUDIENCE: A slide with what? + +PROFESSOR: I'll show you what +the redrawn slide is. + +OK, so now let's redraw +the slide. + +So I think the slide +that I redrew-- + +I'll show it to you-- + +basically answers most +of these objections, + +though maybe not all. + +I think most of them. + +So what I'm going to show you +is what Michael Alley calls + +the Assertion-Evidence +design for slides. + +So Michael Alley, I'll +write his name down. + +So Michael Alley, and his book +is called The Craft of + +Scientific Presentation, +I think. + +And this is to get around +many of these problems. + +So the idea is, first of all, +so related to what Jean-luc + +says, talking about messages +versus information, each slide + +should have one message-- + +one assertion. + +So that's the assertion +part of the slide. + +And the body of the slide +is the evidence. + +And it should ideally be visual +evidence, because of + +all the reasons we talked about +for visual evidence. + +So here is an example of that. + +There. + +Is this the entire slide? + +No. + +This is just one, basically, +third of it. + +But you can redraw the rest of +the slide, with two more + +slides, this way. + +So this is one slide, +with one message-- + +most students like in-class +concept tests. + +If that's the point you're +trying to make. + +The problem is, it's +hard to redraw + +slides with no messages. + +Because you don't actually know +what the message was, so + +you have to sort of infer it. + +But hopefully the author could +actually infer it, and redraw + +it themself. + +So here you have to +play author, and + +I guessed the message-- + +most students like in-class +concept tests. + +The presentation is here, +with a pie chart. + +And you notice all of the tags, +the "I like them", the + +"please skip them," "I dislike +them." They're all right next + +to their percentages. + +And then, what's +color used for? + +There, color is used to +emphasize the like. + +So the green, and the light +green, are both + +categories of like. + +As asserted by the author. + +I mean, you could say, well, no +"enjoy and learn from them" + +is the only category that +matters, "like" isn't strong + +enough, or really you shouldn't +lump them together. + +You can have those debates. + +But what the author-- + +the teacher-- is trying +to say, is that most + +students like them. + +And you can see it just at a +glance, because most of the + +pie chart is colored in. + +So this solves most +of the problems. + +First of all, you don't have the +ghastly typesetting that + +you have here. + +The typesetting here is just +horrendous, this is sort of + +typical PowerPoint +typesetting. + +The alignment is nonexistent. + +There's random alignment +lines everywhere. + +If you look, for example, at +the way top, the yellow bar + +doesn't align with +anything else. + +The left edge of +it just doesn't + +align with the bullets. + +The open bullets are +just random. + +It's just a big mess, +as you pointed out. + +So here, just get +rid of all that. + +And you can do this +with any program. + +You can make your figure +however you want. + +You can put one assertion +at the top. + +So now assertion, another +synonym for that is "sentence + +headlines." So you want +your title of your + +slide to be a sentence. + +If you're not writing a +sentence, you're probably + +writing a topic. + +You're just mentioning +something-- you're giving them + +"what." To give "so what," you +really need a sentence. + +So fit a sentence of one or +two lines there, and then, + +give visual evidence. + +Yes. + +AUDIENCE: To sort of play +devil's advocate, I mean, I + +agree [INAUDIBLE], but the +advantage of having all the + +information on one slide is +you can see the different + +things, and see the different +conclusions. + +PROFESSOR: If you could +actually see them. + +The problem is, you can't +actually see all the + +conclusions. + +I agree it's nice to see all +the conclusions at once. + +So to do that, what I would +do is, I would make-- + +I think there are really +three messages here-- + +one for each of the questions. + +So I made a slide for the first +one, which is about the + +concept test. + +You'd make another slide for +the Just in Time learning, + +another one for, do lectures +cover too much material. + +So now you have three. + +And now, basically you want an +overall message of, overall + +these instructional changes +were well liked. + +Then you could have one summary +slide, which just + +lists those three points. + +And with maybe three small pie +charts, to remind people of + +each pie chart, to fit +it all together. + +But to try to pull it out of +that, the people won't + +actually get the +three messages. + +So you have to guide +them towards it. + +Hopefully you can use this for +your seminars as well, not + +just for your teaching. + +This works for teaching, +as well seminars. + +Now, how would you actually put +this into practice, in a + +teaching example? + +So that's what comes up next. + +I'll show you a mathematical +example, which you could do on + +the blackboard, or I sort of +optimized it so you could do + +it on slides too. + +And we can see how that goes. + +OK, so here is just the +comparison, side by side, of + +the two slides. + +Just at a glance. + +I don't actually mean for people +to be able to read the + +words, just to see that one has +enough information that + +you can get a point, but doesn't +overload you, and the + +other is just a rat's nest. + +OK, so then the mathematical +example-- + +actually, a statistical +mechanics example as well-- + +is the log of n factorial. + +So we're going to approximate +the log of n + +factorial using pictures. + +Now why n factorial? + +Well, what is n factorial? + +5 factorial is 5 times 4 times +3 times 2 times 1. + +Why do we care about it? + +It's the most important function +in statistical + +mechanics when you're +counting objects. + +And it shows up in probability +theory all the time. + +And statistical mechanics +has a lot of + +particles, so the n is big. + +So we'd like to approximate +how big n factorial is, + +because it's so big we +take the logarithm. + +OK, let's see if we can +approximate the logarithm + +using pictures. + +So log of n factorial is the +area of those rectangles. + +You can see rectangle for log +2, log 3, log 4, log 5, + +log 6, and log 7. + +And log of n factorial is just +the sum of all of those. + +Say, 3 factorial is 3 times 2 +times 1, so log of 3 factorial + +is log of 3, plus log +of 2, plus log of 1. + +Log of 1 is 0, so all you +have left is those + +rectangles to add up. + +OK, so now let's add them +up, approximately. + +So the area under the curve is +your first approximation. + +So the curve is just log k. + +So let's see what that is. + +Well, OK, that's just the +integral of log k from 1 to n, + +from the lower limit +to the upper limit. + +So that we can just do +symbolically, you get n log n + +minus n plus 1. + +OK, now the error. + +Where does the error +come from? + +Well, it comes from +the protrusions + +beyond the log n curve. + +So there you have +the protrusions. + +so we'd like to add up all +those protrusions. + +Well, how are we going +to do that? + +Each piece is almost +a triangle. + +So let's just straighten out +each little piece of log k + +curve, and make triangles. + +And now, it turns out they're +much easier to add up if you + +double them, and make every +triangle into a rectangle. + +OK, so now I'm going to stop +here, and see if you can + +figure out how to add up +all of those pieces. + +What's the sum of all of +those shaded regions? + +Take a minute and check +with your neighbor. + +OK, when you see it, +raise your hand. + +Find someone around who sees +it, if you haven't seen it, + +and check with them. + +Because it is fun to see. + +I don't want to spoil +it unnecessarily. + +Here's a little hint. + +So what you do, is you hold your +hand at the right page, + +and you whack all of the +rectangles, and they slide + +across, and go psssssh, and +stack, and form the last one. + +So that means the sum of all the +corrections, times 2, is + +the last rectangle. + +So log 7, or log n, is twice +your error, roughly. + +So now you just combine the +integral, which is the piece + +under the curve, with the +approximated protrusion, and + +you get that for log +of n factorial. + +So let's see. + +So that is actually very close +to Stirling's formula. + +Let's see how close it is. + +Well where's the error? + +Well, the error comes from when +we straightened out the + +pieces of the log k curve, and +made triangles instead of the + +funny-shaped region. + +So the error is those shaded +guys, which is not very big. + +And most of the error happens +low down, so if you just + +corrected for that, pretty much +it would all go So here + +is the total error. + +Here's an example. + +The picture method, so we get 7 +factorial, gives you 8.594. + +The exact answer for the logs +of 7 factorial, 8.525. + +So it's an error only 0.07. + +So all of this just +adds up to 0.07. + +Which ends up being a 7% error +in seven factorial. + +So the moral of the story is +that pictures can help you + +approximate log of n factorial, +and here is your + +approximation. + +So one of the most important +functions + +in statistical mechanics. + +95% with pictures, and +one tiny integral. + +OK, now. + +That's an example or something +you could do if you wanted to + +teach it using slides. + +You could easily do that on the +blackboard, and normally I + +teach it on the blackboard. + +But I made this as an exercise +for myself to say, OK, well + +suppose I have to teach it with +slides, what would I do? + +And you notice here. + +So when I first drafted it, +this slide was missing. + +And I went from here +to there directly. + +And then I thought, +oh, actually-- + +so this is about the +interactivity question-- + +oh, actually I'm depriving +people of a chance to think + +about something, +and realize it. + +On the board, it's really +easy to pause. + +You just put the picture +up, and you wait. + +And you say, OK, what +do you think? + +And then you start +drawing stuff. + +So I thought, OK, well you can +actually simulate that on + +slides, too. + +So I put the intervening slide +in there, so that people had a + +chance to stop here, and think +about the result before we + +continued on to the solution, +where it adds + +up to the last guy. + +So that's an example of +basically somewhat interactive + +slide teaching of a +mathematical idea. + +Yes. + +AUDIENCE: So why didn't you +animate a slide [INAUDIBLE] + +with boxes to take advantage? + +PROFESSOR: That's +a good question. + +Why didn't I? + +Actually, because, A, I +didn't think of it, + +but it's a good idea. + +I should have probably +done it. + +The problem is that I'm showing +it as a PDF file, + +rather than through +any program. + +So PDF animations-- + +I don't know if PDF has +animations in it. + +It probably doesn't. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes, that's true, +it's sort of against the + +purpose of PDF, which +is a stable format. + +Yes. + +AUDIENCE: I actually thought +this entire presentation was + +really clear, and would be just +as good as if you did it + +on a blackboard. + +Because it was interactive, +slow, had pacing, the suspense + +of having us ask +the questions. + +So I think one of the major +reasons why I would be opposed + +[? to teaching ?] in this way, +is just because it takes you + +more time to create the slide. + +From my own experience, it +takes a long time to make + +really good slides, just +fiddling around with + +[INAUDIBLE]. + +So I think if you could spend +all the energy we're spending + +on slides instead +on [INAUDIBLE]-- + +PROFESSOR: That's +a good point. + +AUDIENCE: --or whatever, +I think that might be + +[INAUDIBLE]. + +PROFESSOR: I think that is +a really good point. + +And I hadn't thought of it until +you mentioned it, but + +you're right. + +It took me a long time to +make the slides right. + +To do slides well, you have to +really think about the visual + +presentation, make everything +visual, you're + +making a lot of diagrams. + +There's all kinds of +little tweaks. + +Like, I made sure that all the +diagrams are exactly the same + +size, so that when you flip from +slide to slide, you don't + +get a shift. + +So all those things, you don't +have to worry about on the + +chalkboard. + +And yes, I would advise people, +just as you do, to + +spend that time thinking about +your teaching, and where + +you're going to put the +interactivity in. + +And do it on the blackboard. + +So this is something where, +with a lot of effort, the + +slide reaches to the level +of the blackboard. + +But with colored chalk, and +lots of blackboard, the + +blackboard is just as +good, and quicker. + +And the blackboard has the +advantage that this could be + +two blackboards in your class. + +Say it's a class about visual +representations, and you have + +two blackboards for +this thing. + +The middle two blackboards for +yet another example, the end + +two blackboards for yet +another example. + +And you have all of +them at once. + +Yes. + +AUDIENCE: Last time I taught a +class where I used all slides, + +and when I put the amount of +time that, things like you put + +into this, to make them all so +they perfectly line up, and + +the animations were really +helpful and everything, just + +creating the slides probably +took half the overall time + +that I put into the class. + +But I think the one advantage +was I was able to use + +printouts of those handouts +as class notes. + +Which I handed out +after the class. + +They didn't have them +during class. + +So that's the only advantage, is +you can reuse all of these + +[INAUDIBLE]. + +PROFESSOR: And that's +exactly true. + +So all these nice figures, we +did it for this class, and for + +a seminar on making slides. + +And then I used them verbatim +in my Street-Fighting + +Mathematics textbook. + +So basically, to make good +slides requires making + +something pretty much +publication quality. + +And then, you do have something +publication quality, + +but maybe the first time you +teach it, that's not where you + +want to be spending your time. + +There was one other point that +was raised in an email + +beforehand, which is, in +Jean-luc's paper, he mentioned + +that he uses less popular +alternatives to the Microsoft + +software for making slides. + +So, yeah, I highly do not +recommend using Microsoft + +software, because it's +not free software. + +And it's, I think, unethical +to use non-free software. + +Free software meaning freely +licensed, so you change the + +source code, view the source +code, make your own versions, + +do whatever you want. + +And it's none of that. + +Second, it's all proprietary +formats. + +So you're encouraging +other people to + +use proprietary formats. + +No one has fully debugged, and +decoded, all the formats that + +Microsoft uses. + +So you should use open +formats at least. + +Now, you could use Open Office, +but the problem is + +Open Office, the whole model of +the way it does slides is + +kind of yuck, because it's +just copied from + +the Microsoft way. + +So actually I prefer-- + +maybe it's because of my +computer science math + +background-- + +what I prefer is to program +all the slides. + +So let's see. + +[? Log.tech. ?] + +Where are the-- yeah. + +OK. + +So I actually write in +[? Tech, ?] or version of + +[? Tech. ?] + +And here is your title +of the slide. + +And I can change the +formatting later. + +AUDIENCE: Maybe that's what +took you so long. + +PROFESSOR: Maybe. + +Maybe. + +But the thing is, +you can't make + +publication-quality stuff otherwise. + +So if you're going to actually +do a good slide, basically you + +want to do that. + +Otherwise, I don't think +people should bother. + +And mathematical typesetting is +just ghastly unless you use + +[? Tech ?]. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Oh. + +And I don't think you can +make it look as nice. + +And I'm speaking here about Open +Office, and it's probably + +a clone of rubbish +that it replaces. + +The mathematical typesetting +is just not as good. + +And so for technical +presentations, + +it's just not as good. + +So now, making the figures, I +have the same philosophy. + +So the figures I actually +program as well. + +Where is that fig [INAUDIBLE]. + +So here are the figures. + +So this is a function that +draws logarithm graphs. + +And then I tell it which parts +of the graph to put in. + +So that's how I do the-- + +you draw all the lines, you +drew all the pieces. + +And then here I call it with +different arguments, and I get + +different figures. + +So I'll put all the source code +up for you guys, so you + +can see an alternative +way of doing it. + +And some links, so you +can try it yourself. + +And some templates. + +But it's not for everyone. + +Though it is a public format. + +It produces PDF, which +is a public format. + +So I actually highly recommend +it for those who have at all + +some programming affinity. + +AUDIENCE: [INAUDIBLE] programs +that ends up as PDF format. + +PROFESSOR: That has +the advantage of + +PDF, which is good. + +So I do recommend presenting +things as PDF because you can + +view it on anything. + +It's just, you have the problem +of, do you have good + +mathematical typesetting. + +And that's hard to find, +except [? in Tech, ?] + +basically. + +That's the only thing +that does it right. + +OK, so if you could just +take one minute, + +fill out the sheets. + +I'll answer the questions +next time. + +I'll have office +hours as usual. + +We'll meet outside that door. + +And then we'll go to the cafe +area, and have a chat at the + +tables, as long as people +have questions. + +OK, so, the moral the story is +use the blackboard if you can. + +Use the big visual field. + +But if you're going to use +slides, Assertion-Evidence. + +Sentence headline. + +Visual evidence. + +One message per slide. + +Answers from lecture +nine, to questions + +generated in lecture eight. + +Audio quality for this video +is poor due to technical + +difficulties. + +PROFESSOR: [INAUDIBLE] + +is I'd like to go through the +questions from before. + +There's one question from the +time before, which is, could I + +get the reference for the works +that said, there's a + +difference between telling +people that they have + +intrinsic abilities-- saying, +oh, you did that because you + +are really smart, versus, oh you +did that because you tried + +really hard. + +And how those two ways of +talking to people-- and + +children especially-- + +produced different interests, +and confidence + +in trying new problems. + +I mentioned that that work was +done a lot by a Professor at + +Stanford, in the Psychology +Department. + +Could I get a reference +for it? + +The next update of the website +will have the reference, with + +the reference is Carol Dweck, +D-W-E-C-K. And she's written a + +ton of books, and papers. + +But the one that [INAUDIBLE] +popular, [INAUDIBLE] + +is called Mindset. + +Which is a really, really +fascinating read. + +So that will be on +the website. + +OK. + +First question was, you +mentioned many times, problems + +that are PDF-- pass, D, or F, +where P is made a decent + +effort, D is made an indecent +effort, and F is + +didn't make an effort. + +That's great, but then how do +you balance that with the fact + +that exams become high-stakes, +hit-or-miss performances that + +completely determine grades. + +I don't use the exams +that way. + +I give exams, they're balanced +with the problem sets. + +The problem sets are PDF, and if +you do P on all the problem + +sets, that contributes a large +part of your grade, towards + +getting an A. So there's no +necessity to make the exams + +all or nothing. + +Problem sets still account +for quite a bit. + +[INAUDIBLE] + +It's just you're not forcing the +students to get every last + +T, and dot every last I, which +often means going through + +[INAUDIBLE] to try +to do all that. + +Instead, you're saying, look, +I want you to try to learn + +something big, important. + +If you take responsibility, +then, you get a reward for + +that, by saying, OK, that'll +help your grade, too. + +About slide talks. + +Were there any questions about +slides talks versus teaching, + +versus blackboards. + +So one of the papers says that +the best usage of slides is as + +a completed form that's +understandable without the + +talk that comes with it. + +Is that for a research talk? + +Yes, for a research seminar, +that's what you want. + +You want two channels. + +You want the auditory channel, +and the slide channel, or the + +visual channel-- + +whatever's on the blackboard, +however you do it. + +You want them to stand +independently. + +So if people are deaf, and they +just see the slides, they + +get something out of the talk. + +And if they're blind, and they +just hear your speech, they + +get something out of the talk. + +That's, I would say, less +true for teaching. + +The slides tend not to be so, +message, message, message. + +You may develop a point, build +up a bit of suspense, and then + +give a final message. + +So there's more interaction that +happens from the lecture, + +generally, when you're +teaching, than + +in a research seminar. + +So those are somewhat +different. + +But generally, you do want +your slides, or your + +blackboard work, to somehow +stand independently. + +Although I've just violated that +principle right there. + +This is meaningless unless +you've heard what I said. + +But as I said, it's not +an absolute rule. + +It's just that there's +tendencies that are different + +between [INAUDIBLE] talks, +and teaching. + +What do you do if you're +assigned to a classroom with a + +bad blackboard situation. + +In other words, not like this. + +This is fantastic. + +It would be even more ideal if +there was a slide [INAUDIBLE]. + +But what do you do if you go +to a classroom with, for + +example, just one whiteboard, +or just one or two + +blackboards? + +Then you have to work harder. + +Then you have to plan even more +carefully, how are you + +going to use the blackboard. + +And be more telegraphic. + +Put coarser details +on the boards, not + +every single detail. + +Use the notes more. + +So you optimize the constraints +that you have. + +Should you only use the front +half of the room. + +Suppose you're in a room which +has blackboards all around. + +Should you only use the front +half of the room? + +Yeah, I generally try to use +only the front half of the + +room, because people can look at +that, and glance out of the + +side of their eye at the side, +and then, the front as well. + +The back forces people to turn +around, so they're much less + +likely to use it. + +So it's sort of like putting +something on the ceiling. + +[INAUDIBLE] never see it. + +So generally, yeah, I use the +front of the room, and + +[INAUDIBLE] the side. + +Should all slides have a "so +what" element, or is that only + +for research talks? + +Definitely for a research talk, +all the slides should + +have a "so what," so people +know what the point is. + +And ideally, for teaching, +you should have two. + +Now, last time, I didn't mention +one of the fundamental + +benefits of putting +a "so what," an + +assertion, in every slide. + +So that was the idea. + +So the slide title is +the "so what.". + +And then here is the evidence, +maybe a picture, or a graph. + +Some kind of, ideally +visual, evidence. + +So what's the advantage +of doing that? + +It's not just for +the audience-- + +it's for you, as well. + +What you do, after you make your +series of slides, with + +your sentences, your "so what." +You extract just the + +sentences, which is easy to do +if you're using a program + +[? like Tech. ?] + +You just [INAUDIBLE], +just the titles. + +However you do it. + +You make a list of sentences. + +And then you see whether +the sentences flow. + +With a sentence, you can tell, +very well, because whether + +your presentation, your +teaching, your seminar is well + +organized, if it herks and +jerks, if sentence one and + +sentence two seem to have +nothing to do with each other, + +there's no transition between +them, well, maybe you need a + +sentence one and a half, a slide +that goes in between. + +Or maybe sentence two belongs +down here, next to something + +that relates better. + +So you can see not just at the +level of the individual + +slides, but at the level of +the entire presentation, + +whether there's a thread +that goes through. + +And if you remember, one of +the principles of good + +teaching is having +a good story. + +So this helps you make +a good story. + +When you're teaching a class +that has expectations for + +teaching lots of material, how +do you reconcile your desire + +to teach the important things +really well, and keep a + +reasonable pace? + +Some things aren't really +reconcilable. + +Classes that, for example, say, +OK, we're going to go + +through the 1,600-page textbook, +there's really not + +much you can do to help that. + +And students are just hosed. + +But try to avoid that, +mitigate it. + +Sometimes it seems like, just +out of habit, everyone does + +that 1,600-page textbook. + +But you could find out, what are +the actual requirements? + +What do people need +for [INAUDIBLE]? + +If may be a lot less. + +It may be that a bunch of stuff +was just put in there + +historically, and could +be taken out. + +So you might have some freedom +to reduce that. + +The other thing is you put more +stuff in the notes, and + +you give the higher-level +ideas in the lecture. + +Can I put my slides on +the course web page? + +Yes, I'll do that, with the +reference, on the next update. + +What about having slides that +scroll rather than flip? + +This was a suggestion to avoid +the problem I mentioned of + +signal overload, where you fill +up the short-term memory + +with a slide, and then +you've forgotten + +what's on the old slide. + +And so, [INAUDIBLE] + +too small to remember +the whole slide. + +So what about having slides that +scroll, instead of flip. + +And this may be a critique +of the PDF format, which + +organizes things +in [? pages. ?] + +I think it's actually not a +critique of the PDF format, + +it's just a critique +of the PDF viewers. + +So if you have a PDF viewer that +can scroll, which many + +can, you could actually +use that. + +The problem is that screens +are not big enough. + +That's really the fundamental +issue. + +So if this slide is taking up +the entire screen space, when + +you scroll it, stuff goes off +these screens, and gets + +replaced by new stuff. + +So that problem is really +hard to work around. + +What you really need is multiple +screens, and multiple + +projectors. + +Many questions asked, what do +you do if you're in a room + +with a bad blackboard situation, +where you just have + +one or two blackboards. + +Well, almost every room has a +bad slide situation, because + +you only have one +slide projector. + +So you only use a small +part of the room. + +So that's the really fundamental +problem. + +And if you could get around +that, it wouldn't really + +matter so much whether the +slides scrolled or flipped. + +You'd put one over there, +one over there, + +maybe one over there. + +Of course now [INAUDIBLE]. + +My guess is that the t prepare +is probably proportional to n + +cubed, or something like that. + +Depending on the number of +slide projectors you + +have to deal with. + +Because you have to do all the +coupling of [INAUDIBLE] n + +squared [INAUDIBLE]. + +You'd have to do all the +coupling between all the + +slides, and it will probably +take you twelve hours for + +every lecture that you +give, of one hour. + +Which is kind of [INAUDIBLE]. + +Do I think the video camera for +OCW impacts the style of + +my lectures, blackboards, +pacing, et cetera? + +If anything, it probably +improves it. + +Because I'm a little more +conscious that I write + +clearly, and maybe it improves +my dress code a bit, because I + +make sure to wear a tie. + +But other than that, it doesn't +really affect, too + +much, what I do. + +And I usually forget that +it's even there. + +It's much easier to write +equations [? in Tech, ?] and + +then copy and paste them into a +presentation, than doing the + +entire presentation +[? in Tech. ?] + +Actually, I disagree. + +This is a case of start-up +costs, versus running costs. + +So there's many examples +of that, here at issue. + +It's actually a general +principle worth knowing, + +because you can analyze +lots of stuff. + +Another example of this +principle is, suppose you see + +a book that you really like, +that's available in print, + +from publisher n, and there's +also a PDF file online. + +Well, you could just print it +out and replace your printer. + +Or, you could buy the thing +from the publisher. + +Now, unless the publisher's a +total thief -- unfortunately, + +many of them are, but many +of them aren't-- + +it's usually much better to +buy it at the bookstore, + +because it's much cheaper, than +to print it on your laser + +printer, get all the paper +trimmed to the right size, and + +have it all bound. + +So the running cost for you to +do one book-- you have no + +start-up cost, you just do it. + +There's no fixed amount you +have to pay, no matter how + +many books you do. + +But there's a running cost, +and your running cost is + +pretty high. + +Whereas the publisher, they +have a big start-up cost. + +What they do, is they make all +these plates, they take them + +to a PDF file, [INAUDIBLE], +they make all these metal + +plates, and they ink +the metal plates, + +stamp it onto the paper. + +So they do all that. + +That's a big start-up cost. + +But their running cost +is much lower. + +They're much more efficient +printing, per book. + +But it requires all that +start-up cost. + +So there's a contrast between +book publishers and you. + +So it's the same thing, +actually, with doing + +[? Tech, ?] + +versus doing, say, regular +word processing. + +With [? Tech, ?] there's +a lot of start-up cost. + +No doubt about that. + +It's not what most people +are used to, you end up + +programming your documents. + +And so, if you're only making +one document, if you only + +write one letter in your life, +no question it's faster to + +write the letter. + +Your have lower running costs. + +You don't have to worry about +the start-up costs if you + +write it using a word +processing program-- + +Open Office, for example. + +You just type, and you make it +look like you want, and just + +spit it out. + +But, if you have to write 50 +letters that all have a + +roughly similar format, +it's much + +better to get the template. + +You pay the start-up cost once, +learn [? Tech, ?] learn + +some kind of program template. + +And then, you just enter the +blanks into the template. + +The text, dear who, the +address, and all that. + +[INAUDIBLE] + +formatting, that's all +dealt with once. + +So you pay start-up costs, +in return for + +lower running costs. + +And that's basically true +of lectures, too. + +Once you have all your templates +ready, it's much + +faster to do everything +[? in Tech, ?] or in some kind + +of programming, text-processing +system, rather + +than in a word processor. + +The problem is that, because +of the start-up costs, + +[INAUDIBLE] + +lecture the day before, +or two days before. + +Because of the start-up costs, +you always say, well, I could + +learn [? Tech, ?], and do this +properly, and it would save me + +a lot of time later, but I don't +have the time right now. + +And then you end up paying the +higher running cost to do it + +some other way. + +But each time, before each +lecture, it happens again, + +over and over and over again And +you would have been better + +off [INAUDIBLE] actually paying +the start-up cost. + +So, to that end, I will put my +templates up, so other people + +can use them. + +So you don't have to pay so much +start-up cost, and you + +can just take them, and use them +for your own [INAUDIBLE]. + +So I think that was the main +questions for this time. + +Any questions that have been +created since then? \ No newline at end of file diff --git a/Qo2B2y6cLf4.txt b/Qo2B2y6cLf4.txt new file mode 100644 index 0000000000000000000000000000000000000000..5fec0480ef8f4d32517c8b408b957e9673fe4a94 --- /dev/null +++ b/Qo2B2y6cLf4.txt @@ -0,0 +1,17043 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free to make a donation or to view + + align:start position:0% +for free to make a donation or to view + + + align:start position:0% +for free to make a donation or to view +additional materials from hundreds of + + align:start position:0% +additional materials from hundreds of + + + align:start position:0% +additional materials from hundreds of +MIT courses visit MIT opencourseware at + + align:start position:0% +MIT courses visit MIT opencourseware at + + + align:start position:0% +MIT courses visit MIT opencourseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so today we really kind of talked more + + align:start position:0% +so today we really kind of talked more + + + align:start position:0% +so today we really kind of talked more +about the system the kind of third + + align:start position:0% +about the system the kind of third + + + align:start position:0% +about the system the kind of third +direct innovation factor and then about + + align:start position:0% +direct innovation factor and then about + + + align:start position:0% +direct innovation factor and then about +these indirect factors that are + + align:start position:0% +these indirect factors that are + + + align:start position:0% +these indirect factors that are +important than significant but not as + + align:start position:0% +important than significant but not as + + + align:start position:0% +important than significant but not as +powerful I'd argue as the direct factors + + align:start position:0% +powerful I'd argue as the direct factors + + + align:start position:0% +powerful I'd argue as the direct factors +so but first and let me just you know + + align:start position:0% +so but first and let me just you know + + + align:start position:0% +so but first and let me just you know +recap last week just really in a few + + align:start position:0% +recap last week just really in a few + + + align:start position:0% +recap last week just really in a few +seconds and then give us a glimpse of + + align:start position:0% +seconds and then give us a glimpse of + + + align:start position:0% +seconds and then give us a glimpse of +what we're getting into so last week + + align:start position:0% + + + + align:start position:0% + +Robert Solow the great growth economist + + align:start position:0% +Robert Solow the great growth economist + + + align:start position:0% +Robert Solow the great growth economist +developed really created growth + + align:start position:0% +developed really created growth + + + align:start position:0% +developed really created growth +economics + + align:start position:0% + + + + align:start position:0% + +developed the theory that the + + align:start position:0% +developed the theory that the + + + align:start position:0% +developed the theory that the +dominant causative factor in economic + + align:start position:0% +dominant causative factor in economic + + + align:start position:0% +dominant causative factor in economic +growth was quote technological and + + align:start position:0% +growth was quote technological and + + + align:start position:0% +growth was quote technological and +related innovation phrased it you'll + + align:start position:0% +related innovation phrased it you'll + + + align:start position:0% +related innovation phrased it you'll +hear all the time here and we followed + + align:start position:0% +hear all the time here and we followed + + + align:start position:0% +hear all the time here and we followed +up that discussion with talk about Paul + + align:start position:0% +up that discussion with talk about Paul + + + align:start position:0% +up that discussion with talk about Paul +Romer and his work on human capital + + align:start position:0% +Romer and his work on human capital + + + align:start position:0% +Romer and his work on human capital +engaged in research as a kind of second + + align:start position:0% +engaged in research as a kind of second + + + align:start position:0% +engaged in research as a kind of second +key direct innovation factor that's the + + align:start position:0% +key direct innovation factor that's the + + + align:start position:0% +key direct innovation factor that's the +talent base that has to be behind the + + align:start position:0% +talent base that has to be behind the + + + align:start position:0% +talent base that has to be behind the +R&D system we read Dale Jorgenson who + + align:start position:0% +R&D system we read Dale Jorgenson who + + + align:start position:0% +R&D system we read Dale Jorgenson who +told us that yes in fact this innovation + + align:start position:0% +told us that yes in fact this innovation + + + align:start position:0% +told us that yes in fact this innovation +based economic growth model is in fact + + align:start position:0% +based economic growth model is in fact + + + align:start position:0% +based economic growth model is in fact +correct that's what happened in the I T + + align:start position:0% +correct that's what happened in the I T + + + align:start position:0% +correct that's what happened in the I T +wave and he showed us in effect you know + + align:start position:0% +wave and he showed us in effect you know + + + align:start position:0% +wave and he showed us in effect you know +how that occurred + + align:start position:0% +how that occurred + + + align:start position:0% +how that occurred +the model was + + align:start position:0% +the model was + + + align:start position:0% +the model was +you do an invention or a core group of + + align:start position:0% +you do an invention or a core group of + + + align:start position:0% +you do an invention or a core group of +inventions they begin to scale up + + align:start position:0% +inventions they begin to scale up + + + align:start position:0% +inventions they begin to scale up +applications pile on them they enter + + align:start position:0% +applications pile on them they enter + + + align:start position:0% +applications pile on them they enter +into the economy and really begin to + + align:start position:0% +into the economy and really begin to + + + align:start position:0% +into the economy and really begin to +scale up in the economy and eventually + + align:start position:0% +scale up in the economy and eventually + + + align:start position:0% +scale up in the economy and eventually +over time become a true innovation wave + + align:start position:0% +over time become a true innovation wave + + + align:start position:0% +over time become a true innovation wave +and we'll talk more today as you know + + align:start position:0% +and we'll talk more today as you know + + + align:start position:0% +and we'll talk more today as you know +about innovation wave theory we also + + align:start position:0% +about innovation wave theory we also + + + align:start position:0% +about innovation wave theory we also +read a piece by some Merrill Lynch + + align:start position:0% +read a piece by some Merrill Lynch + + + align:start position:0% +read a piece by some Merrill Lynch +analysts and the + + align:start position:0% +analysts and the + + + align:start position:0% +analysts and the +fundamental point in that piece was that + + align:start position:0% +fundamental point in that piece was that + + + align:start position:0% +fundamental point in that piece was that +industry is very interested in + + align:start position:0% +industry is very interested in + + + align:start position:0% +industry is very interested in +innovation but they're only prepared to + + align:start position:0% +innovation but they're only prepared to + + + align:start position:0% +innovation but they're only prepared to +fund the very short late stage of it + + align:start position:0% +fund the very short late stage of it + + + align:start position:0% +fund the very short late stage of it +so somehow even though + + align:start position:0% +so somehow even though + + + align:start position:0% +so somehow even though +the evolutions innovation is a very + + align:start position:0% +the evolutions innovation is a very + + + align:start position:0% +the evolutions innovation is a very +long-term process + + align:start position:0% +long-term process + + + align:start position:0% +long-term process +the financial sector is only going to + + align:start position:0% +the financial sector is only going to + + + align:start position:0% +the financial sector is only going to +dive in as close as they can to + + align:start position:0% +dive in as close as they can to + + + align:start position:0% +dive in as close as they can to +certainty in other words at a very late + + align:start position:0% +certainty in other words at a very late + + + align:start position:0% +certainty in other words at a very late +stage so those were kind of our four + + align:start position:0% +stage so those were kind of our four + + + align:start position:0% +stage so those were kind of our four +core readings and + + align:start position:0% +core readings and + + + align:start position:0% +core readings and +one other idea and then Merrill Lynch + + align:start position:0% +one other idea and then Merrill Lynch + + + align:start position:0% +one other idea and then Merrill Lynch +piece was this notion that + + align:start position:0% +piece was this notion that + + + align:start position:0% +piece was this notion that +innovation needs to move through a + + align:start position:0% +innovation needs to move through a + + + align:start position:0% +innovation needs to move through a +series of stages to kind of get there + + align:start position:0% +series of stages to kind of get there + + + align:start position:0% +series of stages to kind of get there +there needs to be an early vision + + align:start position:0% +there needs to be an early vision + + + align:start position:0% +there needs to be an early vision +kind of a visionary he will set out what + + align:start position:0% +kind of a visionary he will set out what + + + align:start position:0% +kind of a visionary he will set out what +could happen and then enabling + + align:start position:0% +could happen and then enabling + + + align:start position:0% +could happen and then enabling +technologies evolve that become enablers + + align:start position:0% +technologies evolve that become enablers + + + align:start position:0% +technologies evolve that become enablers +technical enablers for the evolution to + + align:start position:0% +technical enablers for the evolution to + + + align:start position:0% +technical enablers for the evolution to +to an innovation wave and then there's + + align:start position:0% +to an innovation wave and then there's + + + align:start position:0% +to an innovation wave and then there's +got to be substantial talent on task in + + align:start position:0% +got to be substantial talent on task in + + + align:start position:0% +got to be substantial talent on task in +other words people have got to be + + align:start position:0% +other words people have got to be + + + align:start position:0% +other words people have got to be +researches they've got to be work honest + + align:start position:0% +researches they've got to be work honest + + + align:start position:0% +researches they've got to be work honest +in significant depth in order for this + + align:start position:0% +in significant depth in order for this + + + align:start position:0% +in significant depth in order for this +thing to evolve so it's going to take a + + align:start position:0% +thing to evolve so it's going to take a + + + align:start position:0% +thing to evolve so it's going to take a +community scale kind of effort so + + align:start position:0% +community scale kind of effort so + + + align:start position:0% +community scale kind of effort so +the first class left us with two direct + + align:start position:0% +the first class left us with two direct + + + align:start position:0% +the first class left us with two direct +or explicit innovation factors and we + + align:start position:0% +or explicit innovation factors and we + + + align:start position:0% +or explicit innovation factors and we +could you know + + align:start position:0% +could you know + + + align:start position:0% +could you know +oversimplify them and put them in + + align:start position:0% +oversimplify them and put them in + + + align:start position:0% +oversimplify them and put them in +shorthand but we could say you've got to + + align:start position:0% +shorthand but we could say you've got to + + + align:start position:0% +shorthand but we could say you've got to +do R&D and you've got to have a talent + + align:start position:0% +do R&D and you've got to have a talent + + + align:start position:0% +do R&D and you've got to have a talent +based staffing that R&D system and + + align:start position:0% +based staffing that R&D system and + + + align:start position:0% +based staffing that R&D system and +we worked on a definition of innovation + + align:start position:0% +we worked on a definition of innovation + + + align:start position:0% +we worked on a definition of innovation +as a system for introducing technical + + align:start position:0% +as a system for introducing technical + + + align:start position:0% +as a system for introducing technical +advance and we talked briefly about + + align:start position:0% +advance and we talked briefly about + + + align:start position:0% +advance and we talked briefly about +innovation waves + + align:start position:0% +innovation waves + + + align:start position:0% +innovation waves +which will spend more time on today so + + align:start position:0% +which will spend more time on today so + + + align:start position:0% +which will spend more time on today so +that's a quick recap of last week's + + align:start position:0% +that's a quick recap of last week's + + + align:start position:0% +that's a quick recap of last week's +discussion and + + align:start position:0% +discussion and + + + align:start position:0% +discussion and +Chris you and I can follow up so you + + align:start position:0% +Chris you and I can follow up so you + + + align:start position:0% +Chris you and I can follow up so you +catch up on some of this some of the + + align:start position:0% +catch up on some of this some of the + + + align:start position:0% +catch up on some of this some of the +issues that came up there and I've + + align:start position:0% +issues that came up there and I've + + + align:start position:0% +issues that came up there and I've +posted the slides to the stellar site + + align:start position:0% +posted the slides to the stellar site + + + align:start position:0% +posted the slides to the stellar site +which will help as well but I'd be happy + + align:start position:0% +which will help as well but I'd be happy + + + align:start position:0% +which will help as well but I'd be happy +to talk to you further about it + + align:start position:0% + + + + align:start position:0% + +so let me just do a quick snapshot to + + align:start position:0% +so let me just do a quick snapshot to + + + align:start position:0% +so let me just do a quick snapshot to +open up today's discussion so that's + + align:start position:0% +open up today's discussion so that's + + + align:start position:0% +open up today's discussion so that's +Thomas Edison + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% + + + + align:start position:0% + +his idea Factory + + align:start position:0% +his idea Factory + + + align:start position:0% +his idea Factory +so and that's the group right that does + + align:start position:0% +so and that's the group right that does + + + align:start position:0% +so and that's the group right that does +the lightbulb + + align:start position:0% +the lightbulb + + + align:start position:0% +the lightbulb +right it's the light bulb and + + align:start position:0% +right it's the light bulb and + + + align:start position:0% +right it's the light bulb and +you know you can see the idea Factory + + align:start position:0% +you know you can see the idea Factory + + + align:start position:0% +you know you can see the idea Factory +this building in that scheme at the top + + align:start position:0% +this building in that scheme at the top + + + align:start position:0% +this building in that scheme at the top +moneda see the farmhouse back behind + + align:start position:0% +moneda see the farmhouse back behind + + + align:start position:0% +moneda see the farmhouse back behind +which is where Edison lived with his + + align:start position:0% +which is where Edison lived with his + + + align:start position:0% +which is where Edison lived with his +wife except that he never spent any time + + align:start position:0% +wife except that he never spent any time + + + align:start position:0% +wife except that he never spent any time +there he was on the idea factory pretty + + align:start position:0% +there he was on the idea factory pretty + + + align:start position:0% +there he was on the idea factory pretty +much 24/7 I just wanted to give you a + + align:start position:0% +much 24/7 I just wanted to give you a + + + align:start position:0% +much 24/7 I just wanted to give you a +feel for what innovation is like when it + + align:start position:0% +feel for what innovation is like when it + + + align:start position:0% +feel for what innovation is like when it +starts to take off and this is a good + + align:start position:0% +starts to take off and this is a good + + + align:start position:0% +starts to take off and this is a good +you know Edison is a classic example so + + align:start position:0% +you know Edison is a classic example so + + + align:start position:0% +you know Edison is a classic example so +he + + align:start position:0% +he + + + align:start position:0% +he +very limited education + + align:start position:0% +very limited education + + + align:start position:0% +very limited education +he was homeschooled by his mother he's + + align:start position:0% +he was homeschooled by his mother he's + + + align:start position:0% +he was homeschooled by his mother he's +probably pretty dyslexic right we don't + + align:start position:0% +probably pretty dyslexic right we don't + + + align:start position:0% +probably pretty dyslexic right we don't +quite know that but it's probably the + + align:start position:0% +quite know that but it's probably the + + + align:start position:0% +quite know that but it's probably the +case as a kid he understands that you + + align:start position:0% +case as a kid he understands that you + + + align:start position:0% +case as a kid he understands that you +know early evolution of the Telegraph + + align:start position:0% +know early evolution of the Telegraph + + + align:start position:0% +know early evolution of the Telegraph +and he develops kind of a newspaper + + align:start position:0% +and he develops kind of a newspaper + + + align:start position:0% +and he develops kind of a newspaper +sales scheme during the civil war + + align:start position:0% +sales scheme during the civil war + + + align:start position:0% +sales scheme during the civil war +where he gets the newspapers ahead of + + align:start position:0% +where he gets the newspapers ahead of + + + align:start position:0% +where he gets the newspapers ahead of +time in Cleveland gets them out to the + + align:start position:0% +time in Cleveland gets them out to the + + + align:start position:0% +time in Cleveland gets them out to the +trains coming into Cleveland and then + + align:start position:0% +trains coming into Cleveland and then + + + align:start position:0% +trains coming into Cleveland and then +sells them on the trains and he's keys + + align:start position:0% +sells them on the trains and he's keys + + + align:start position:0% +sells them on the trains and he's keys +kind of kept in other words he kind of + + align:start position:0% +kind of kept in other words he kind of + + + align:start position:0% +kind of kept in other words he kind of +beats the news cycle and then unloads + + align:start position:0% +beats the news cycle and then unloads + + + align:start position:0% +beats the news cycle and then unloads +newspapers on these early commuting + + align:start position:0% +newspapers on these early commuting + + + align:start position:0% +newspapers on these early commuting +efforts as people are coming into the + + align:start position:0% +efforts as people are coming into the + + + align:start position:0% +efforts as people are coming into the +city + + align:start position:0% +city + + + align:start position:0% +city +he gets his big break by scooping up the + + align:start position:0% +he gets his big break by scooping up the + + + align:start position:0% +he gets his big break by scooping up the +child of a telegraph operator so trains + + align:start position:0% +child of a telegraph operator so trains + + + align:start position:0% +child of a telegraph operator so trains +had to operate by telegraph systems they + + align:start position:0% +had to operate by telegraph systems they + + + align:start position:0% +had to operate by telegraph systems they +were a crucial technology to enable + + align:start position:0% +were a crucial technology to enable + + + align:start position:0% +were a crucial technology to enable +trains to work and + + align:start position:0% + + + + align:start position:0% + +the telegraph operator for a train + + align:start position:0% +the telegraph operator for a train + + + align:start position:0% +the telegraph operator for a train +system is very important but also + + align:start position:0% +system is very important but also + + + align:start position:0% +system is very important but also +obviously serves a larger community + + align:start position:0% +obviously serves a larger community + + + align:start position:0% +obviously serves a larger community +communications purpose so this the kid + + align:start position:0% +communications purpose so this the kid + + + align:start position:0% +communications purpose so this the kid +of the telegraph operator is down on the + + align:start position:0% +of the telegraph operator is down on the + + + align:start position:0% +of the telegraph operator is down on the +tracks train is coming down the tracks + + align:start position:0% +tracks train is coming down the tracks + + + align:start position:0% +tracks train is coming down the tracks +Edison as a boy sees what's happening + + align:start position:0% +Edison as a boy sees what's happening + + + align:start position:0% +Edison as a boy sees what's happening +rushes scoops the child up barely + + align:start position:0% +rushes scoops the child up barely + + + align:start position:0% +rushes scoops the child up barely +escapes the Train needless to say the + + align:start position:0% +escapes the Train needless to say the + + + align:start position:0% +escapes the Train needless to say the +telegraph operator is appreciative so he + + align:start position:0% +telegraph operator is appreciative so he + + + align:start position:0% +telegraph operator is appreciative so he +trains Edison in Morse code and how + + align:start position:0% +trains Edison in Morse code and how + + + align:start position:0% +trains Edison in Morse code and how +telegraph operations work so he becomes + + align:start position:0% +telegraph operations work so he becomes + + + align:start position:0% +telegraph operations work so he becomes +an expert on telegraph which is + + align:start position:0% +an expert on telegraph which is + + + align:start position:0% +an expert on telegraph which is +obviously early electrical technology + + align:start position:0% +obviously early electrical technology + + + align:start position:0% +obviously early electrical technology +and + + align:start position:0% +and + + + align:start position:0% +and +he becomes a master at it and then he + + align:start position:0% +he becomes a master at it and then he + + + align:start position:0% +he becomes a master at it and then he +becomes very interested in technology + + align:start position:0% +becomes very interested in technology + + + align:start position:0% +becomes very interested in technology +itself so over time he goes to New York + + align:start position:0% +itself so over time he goes to New York + + + align:start position:0% +itself so over time he goes to New York +he develops what becomes in if an early + + align:start position:0% +he develops what becomes in if an early + + + align:start position:0% +he develops what becomes in if an early +stock ticker which can what we would + + align:start position:0% +stock ticker which can what we would + + + align:start position:0% +stock ticker which can what we would +call multiplex in other which you could + + align:start position:0% +call multiplex in other which you could + + + align:start position:0% +call multiplex in other which you could +receive multiple + + align:start position:0% +receive multiple + + + align:start position:0% +receive multiple +telegraphing signals and communications + + align:start position:0% +telegraphing signals and communications + + + align:start position:0% +telegraphing signals and communications +over the same line right which obviously + + align:start position:0% +over the same line right which obviously + + + align:start position:0% +over the same line right which obviously +was a key enabler for keeping track of + + align:start position:0% +was a key enabler for keeping track of + + + align:start position:0% +was a key enabler for keeping track of +stocks so he becomes very close to the + + align:start position:0% +stocks so he becomes very close to the + + + align:start position:0% +stocks so he becomes very close to the +science of Wall Street including JP + + align:start position:0% +science of Wall Street including JP + + + align:start position:0% +science of Wall Street including JP +Morgan he gets to know them all because + + align:start position:0% +Morgan he gets to know them all because + + + align:start position:0% +Morgan he gets to know them all because +he's like their enabler and then he sees + + align:start position:0% +he's like their enabler and then he sees + + + align:start position:0% +he's like their enabler and then he sees +this thing in Ansonia Connecticut + + align:start position:0% +this thing in Ansonia Connecticut + + + align:start position:0% +this thing in Ansonia Connecticut +it's not it's a much bigger version of + + align:start position:0% +it's not it's a much bigger version of + + + align:start position:0% +it's not it's a much bigger version of +this but there's this kind of gimmick + + align:start position:0% +this but there's this kind of gimmick + + + align:start position:0% +this but there's this kind of gimmick +this nine foot tall + + align:start position:0% +this nine foot tall + + + align:start position:0% +this nine foot tall +you know poles with the spark because + + align:start position:0% +you know poles with the spark because + + + align:start position:0% +you know poles with the spark because +they're you know positive and negative + + align:start position:0% +they're you know positive and negative + + + align:start position:0% +they're you know positive and negative +and a spark travels across looks really + + align:start position:0% +and a spark travels across looks really + + + align:start position:0% +and a spark travels across looks really +cool right people are wandering around + + align:start position:0% +cool right people are wandering around + + + align:start position:0% +cool right people are wandering around +they don't know what to do with it but + + align:start position:0% +they don't know what to do with it but + + + align:start position:0% +they don't know what to do with it but +they're awestruck by this kind of + + align:start position:0% +they're awestruck by this kind of + + + align:start position:0% +they're awestruck by this kind of +electric lighting this electric movement + + align:start position:0% +electric lighting this electric movement + + + align:start position:0% +electric lighting this electric movement +of lightning going across the two poles + + align:start position:0% +of lightning going across the two poles + + + align:start position:0% +of lightning going across the two poles +Edison has the idea Oh light right so he + + align:start position:0% +Edison has the idea Oh light right so he + + + align:start position:0% +Edison has the idea Oh light right so he +takes that he makes his money on Wall + + align:start position:0% +takes that he makes his money on Wall + + + align:start position:0% +takes that he makes his money on Wall +Street he takes all his money out he + + align:start position:0% +Street he takes all his money out he + + + align:start position:0% +Street he takes all his money out he +goes off into a farm in Menlo Park New + + align:start position:0% +goes off into a farm in Menlo Park New + + + align:start position:0% +goes off into a farm in Menlo Park New +Jersey out in his rural area + + align:start position:0% +Jersey out in his rural area + + + align:start position:0% +Jersey out in his rural area +he hires this team which consists of an + + align:start position:0% +he hires this team which consists of an + + + align:start position:0% +he hires this team which consists of an +interesting mix of artisans like there's + + align:start position:0% +interesting mix of artisans like there's + + + align:start position:0% +interesting mix of artisans like there's +an incredibly important glass blower + + align:start position:0% +an incredibly important glass blower + + + align:start position:0% +an incredibly important glass blower +here and Harold you know it which + + align:start position:0% +here and Harold you know it which + + + align:start position:0% +here and Harold you know it which +Harold's back to the MIT glass lab which + + align:start position:0% +Harold's back to the MIT glass lab which + + + align:start position:0% +Harold's back to the MIT glass lab which +I always buy stuff from and + + align:start position:0% +I always buy stuff from and + + + align:start position:0% +I always buy stuff from and +there's also scientists and engineers in + + align:start position:0% +there's also scientists and engineers in + + + align:start position:0% +there's also scientists and engineers in +here but a lot of people are just know + + align:start position:0% +here but a lot of people are just know + + + align:start position:0% +here but a lot of people are just know +how to do things who were very good at + + align:start position:0% +how to do things who were very good at + + + align:start position:0% +how to do things who were very good at +sort of mechanical tinkering and it's + + align:start position:0% +sort of mechanical tinkering and it's + + + align:start position:0% +sort of mechanical tinkering and it's +it's an interesting team and he has to + + align:start position:0% +it's an interesting team and he has to + + + align:start position:0% +it's an interesting team and he has to +take this idea of this weird art that he + + align:start position:0% +take this idea of this weird art that he + + + align:start position:0% +take this idea of this weird art that he +saw his 9 foot tall couple pulls this on + + align:start position:0% +saw his 9 foot tall couple pulls this on + + + align:start position:0% +saw his 9 foot tall couple pulls this on +and and Sony and Connecticut and turn it + + align:start position:0% +and and Sony and Connecticut and turn it + + + align:start position:0% +and and Sony and Connecticut and turn it +into a light bulb it's not an easy job + + align:start position:0% +into a light bulb it's not an easy job + + + align:start position:0% +into a light bulb it's not an easy job +and + + align:start position:0% + + + + align:start position:0% + +it's very intense there's only a certain + + align:start position:0% +it's very intense there's only a certain + + + align:start position:0% +it's very intense there's only a certain +amount of money the money's gonna run + + align:start position:0% +amount of money the money's gonna run + + + align:start position:0% +amount of money the money's gonna run +out he's got to get this thing done + + align:start position:0% +out he's got to get this thing done + + + align:start position:0% +out he's got to get this thing done +before he runs out of cash and + + align:start position:0% +before he runs out of cash and + + + align:start position:0% +before he runs out of cash and +they work literally you know all the + + align:start position:0% +they work literally you know all the + + + align:start position:0% +they work literally you know all the +time they're always on it but they're + + align:start position:0% +time they're always on it but they're + + + align:start position:0% +time they're always on it but they're +having the time of their lives right + + align:start position:0% +having the time of their lives right + + + align:start position:0% +having the time of their lives right +so there's a wood stove in here over and + + align:start position:0% +so there's a wood stove in here over and + + + align:start position:0% +so there's a wood stove in here over and +I'm not sure can't maybe it's in another + + align:start position:0% +I'm not sure can't maybe it's in another + + + align:start position:0% +I'm not sure can't maybe it's in another +corner but around midnight they all + + align:start position:0% +corner but around midnight they all + + + align:start position:0% +corner but around midnight they all +gather around the wood stove and their + + align:start position:0% +gather around the wood stove and their + + + align:start position:0% +gather around the wood stove and their +rap music has not been invented yet so + + align:start position:0% +rap music has not been invented yet so + + + align:start position:0% +rap music has not been invented yet so +they do doggerel verses which they throw + + align:start position:0% +they do doggerel verses which they throw + + + align:start position:0% +they do doggerel verses which they throw +at one another you know insulting and + + align:start position:0% +at one another you know insulting and + + + align:start position:0% +at one another you know insulting and +funny and this incredible dog world + + align:start position:0% +funny and this incredible dog world + + + align:start position:0% +funny and this incredible dog world +verse back and forth going on and they + + align:start position:0% +verse back and forth going on and they + + + align:start position:0% +verse back and forth going on and they +all have big you know like cherry pies + + align:start position:0% +all have big you know like cherry pies + + + align:start position:0% +all have big you know like cherry pies +and apple pies at midnight and gather + + align:start position:0% +and apple pies at midnight and gather + + + align:start position:0% +and apple pies at midnight and gather +around the wood stove + + align:start position:0% +around the wood stove + + + align:start position:0% +around the wood stove +it's a very intense effort and + + align:start position:0% +it's a very intense effort and + + + align:start position:0% +it's a very intense effort and +actually Edison is away for so long from + + align:start position:0% +actually Edison is away for so long from + + + align:start position:0% +actually Edison is away for so long from +the farmhouse just further back on the + + align:start position:0% +the farmhouse just further back on the + + + align:start position:0% +the farmhouse just further back on the +property that at one point when he comes + + align:start position:0% +property that at one point when he comes + + + align:start position:0% +property that at one point when he comes +in at like two o'clock in the morning + + align:start position:0% +in at like two o'clock in the morning + + + align:start position:0% +in at like two o'clock in the morning +his wife pulls a revolver on him think + + align:start position:0% +his wife pulls a revolver on him think + + + align:start position:0% +his wife pulls a revolver on him think +he's an intruder because she's seen him + + align:start position:0% +he's an intruder because she's seen him + + + align:start position:0% +he's an intruder because she's seen him +so rarely right fortunately she doesn't + + align:start position:0% +so rarely right fortunately she doesn't + + + align:start position:0% +so rarely right fortunately she doesn't +shoot but you know they're they are + + align:start position:0% +shoot but you know they're they are + + + align:start position:0% +shoot but you know they're they are +gathered on the idea Factory and you + + align:start position:0% +gathered on the idea Factory and you + + + align:start position:0% +gathered on the idea Factory and you +know eventually they come up with the + + align:start position:0% +know eventually they come up with the + + + align:start position:0% +know eventually they come up with the +core concepts being the vacuum tube + + align:start position:0% +core concepts being the vacuum tube + + + align:start position:0% +core concepts being the vacuum tube +obviously is core here and the right + + align:start position:0% +obviously is core here and the right + + + align:start position:0% +obviously is core here and the right +filament is court here they come up with + + align:start position:0% +filament is court here they come up with + + + align:start position:0% +filament is court here they come up with +a working model and electric light + + align:start position:0% +a working model and electric light + + + align:start position:0% +a working model and electric light +there's only one problem there's no + + align:start position:0% +there's only one problem there's no + + + align:start position:0% +there's only one problem there's no +electrical system right there's no like + + align:start position:0% +electrical system right there's no like + + + align:start position:0% +electrical system right there's no like +right so they've got a wonderful + + align:start position:0% +right so they've got a wonderful + + + align:start position:0% +right so they've got a wonderful +application for a non existent system so + + align:start position:0% +application for a non existent system so + + + align:start position:0% +application for a non existent system so +the real innovation here is not simply + + align:start position:0% +the real innovation here is not simply + + + align:start position:0% +the real innovation here is not simply +the + + align:start position:0% +the + + + align:start position:0% +the +invention it's creating the whole system + + align:start position:0% +invention it's creating the whole system + + + align:start position:0% +invention it's creating the whole system +so they have to envision they have to + + align:start position:0% +so they have to envision they have to + + + align:start position:0% +so they have to envision they have to +think of what an electric utility might + + align:start position:0% +think of what an electric utility might + + + align:start position:0% +think of what an electric utility might +be right they envision the utility right + + align:start position:0% +be right they envision the utility right + + + align:start position:0% +be right they envision the utility right +they envision what a generator would be + + align:start position:0% +they envision what a generator would be + + + align:start position:0% +they envision what a generator would be +they have to think through all this + + align:start position:0% +they have to think through all this + + + align:start position:0% +they have to think through all this +early safety requirements so it's an + + align:start position:0% +early safety requirements so it's an + + + align:start position:0% +early safety requirements so it's an +incredibly big thing that they're + + align:start position:0% +incredibly big thing that they're + + + align:start position:0% +incredibly big thing that they're +launching they're launching the + + align:start position:0% +launching they're launching the + + + align:start position:0% +launching they're launching the +electrical system not simply the light + + align:start position:0% +electrical system not simply the light + + + align:start position:0% +electrical system not simply the light +bulb but the light bulbs the enabler + + align:start position:0% +bulb but the light bulbs the enabler + + + align:start position:0% +bulb but the light bulbs the enabler +that's going to enable them to sell the + + align:start position:0% +that's going to enable them to sell the + + + align:start position:0% +that's going to enable them to sell the +system eventually they do a big + + align:start position:0% +system eventually they do a big + + + align:start position:0% +system eventually they do a big +demonstration on a couple of city blocks + + align:start position:0% +demonstration on a couple of city blocks + + + align:start position:0% +demonstration on a couple of city blocks +in New York everybody loves it you know + + align:start position:0% +in New York everybody loves it you know + + + align:start position:0% +in New York everybody loves it you know +gas lighting is not what you call + + align:start position:0% +gas lighting is not what you call + + + align:start position:0% +gas lighting is not what you call +optimal since you have a good chance of + + align:start position:0% +optimal since you have a good chance of + + + align:start position:0% +optimal since you have a good chance of +blowing yourself up and + + align:start position:0% +blowing yourself up and + + + align:start position:0% +blowing yourself up and +you know the nation eventually switches + + align:start position:0% +you know the nation eventually switches + + + align:start position:0% +you know the nation eventually switches +over but I just wanted you to see what + + align:start position:0% +over but I just wanted you to see what + + + align:start position:0% +over but I just wanted you to see what +that innovation moment looks like right + + align:start position:0% +that innovation moment looks like right + + + align:start position:0% +that innovation moment looks like right +and we'll talk about great group theory + + align:start position:0% +and we'll talk about great group theory + + + align:start position:0% +and we'll talk about great group theory +and this is certainly a great group + + align:start position:0% +and this is certainly a great group + + + align:start position:0% +and this is certainly a great group +but that's that's the moment we're after + + align:start position:0% +but that's that's the moment we're after + + + align:start position:0% +but that's that's the moment we're after +in this class that's the moment we want + + align:start position:0% +in this class that's the moment we want + + + align:start position:0% +in this class that's the moment we want +to stand we want to understand how that + + align:start position:0% +to stand we want to understand how that + + + align:start position:0% +to stand we want to understand how that +innovation emerges from the group but + + align:start position:0% +innovation emerges from the group but + + + align:start position:0% +innovation emerges from the group but +importantly how it scales right what + + align:start position:0% +importantly how it scales right what + + + align:start position:0% +importantly how it scales right what +happens to it so that's kind of a little + + align:start position:0% +happens to it so that's kind of a little + + + align:start position:0% +happens to it so that's kind of a little +that's story time for today's class and + + align:start position:0% +that's story time for today's class and + + + align:start position:0% +that's story time for today's class and +they'll do serious work I want to get + + align:start position:0% +they'll do serious work I want to get + + + align:start position:0% +they'll do serious work I want to get +some other basic ideas down so we talked + + align:start position:0% +some other basic ideas down so we talked + + + align:start position:0% +some other basic ideas down so we talked +us about some basic concepts last time I + + align:start position:0% +us about some basic concepts last time I + + + align:start position:0% +us about some basic concepts last time I +want to put a few more on the table + + align:start position:0% + + + + align:start position:0% + +steps in the technology development + + align:start position:0% +steps in the technology development + + + align:start position:0% +steps in the technology development +process + + align:start position:0% +process + + + align:start position:0% +process +so we talked a little bit last week + + align:start position:0% +so we talked a little bit last week + + + align:start position:0% +so we talked a little bit last week +about + + align:start position:0% +about + + + align:start position:0% +about +three of those steps + + align:start position:0% +three of those steps + + + align:start position:0% +three of those steps +but let me put them in into a larger + + align:start position:0% +but let me put them in into a larger + + + align:start position:0% +but let me put them in into a larger +context so typically you're gonna have + + align:start position:0% +context so typically you're gonna have + + + align:start position:0% +context so typically you're gonna have +to go through a series of + + align:start position:0% +to go through a series of + + + align:start position:0% +to go through a series of +steps here to actually get to really + + align:start position:0% +steps here to actually get to really + + + align:start position:0% +steps here to actually get to really +scaling a technology up we talked last + + align:start position:0% +scaling a technology up we talked last + + + align:start position:0% +scaling a technology up we talked last +week about having a vision + + align:start position:0% +week about having a vision + + + align:start position:0% +week about having a vision +we talked last week about the supporting + + align:start position:0% +we talked last week about the supporting + + + align:start position:0% +we talked last week about the supporting +enabling technologies + + align:start position:0% +enabling technologies + + + align:start position:0% +enabling technologies +then you're gonna do your particular + + align:start position:0% +then you're gonna do your particular + + + align:start position:0% +then you're gonna do your particular +invention idea you're going to need to + + align:start position:0% +invention idea you're going to need to + + + align:start position:0% +invention idea you're going to need to +do some research to perfect it you're + + align:start position:0% +do some research to perfect it you're + + + align:start position:0% +do some research to perfect it you're +gonna need to develop a prototype of it + + align:start position:0% +gonna need to develop a prototype of it + + + align:start position:0% +gonna need to develop a prototype of it +then you're going to need to go through + + align:start position:0% +then you're going to need to go through + + + align:start position:0% +then you're going to need to go through +engineering development + + align:start position:0% +engineering development + + + align:start position:0% +engineering development +then you can start to think about + + align:start position:0% +then you can start to think about + + + align:start position:0% +then you can start to think about +production and manufacturing that + + align:start position:0% +production and manufacturing that + + + align:start position:0% +production and manufacturing that +prototype and then eventually scaling up + + align:start position:0% +prototype and then eventually scaling up + + + align:start position:0% +prototype and then eventually scaling up +to commercial production you've got to + + align:start position:0% +to commercial production you've got to + + + align:start position:0% +to commercial production you've got to +have a supporting infrastructure system + + align:start position:0% +have a supporting infrastructure system + + + align:start position:0% +have a supporting infrastructure system +right and there may be additional + + align:start position:0% +right and there may be additional + + + align:start position:0% +right and there may be additional +applications that you can use and pile + + align:start position:0% +applications that you can use and pile + + + align:start position:0% +applications that you can use and pile +on here and then you got to go through a + + align:start position:0% +on here and then you got to go through a + + + align:start position:0% +on here and then you got to go through a +series of generations of the product + + align:start position:0% +series of generations of the product + + + align:start position:0% +series of generations of the product +right so that's a lot of stuff to get + + align:start position:0% +right so that's a lot of stuff to get + + + align:start position:0% +right so that's a lot of stuff to get +through + + align:start position:0% +through + + + align:start position:0% +through +so the u.s. typically + + align:start position:0% +so the u.s. typically + + + align:start position:0% +so the u.s. typically +thinks about innovation as is like in + + align:start position:0% +thinks about innovation as is like in + + + align:start position:0% +thinks about innovation as is like in +the vision idea research realm right but + + align:start position:0% +the vision idea research realm right but + + + align:start position:0% +the vision idea research realm right but +it's a much more complex process that + + align:start position:0% +it's a much more complex process that + + + align:start position:0% +it's a much more complex process that +has to be mastered to actually get from + + align:start position:0% +has to be mastered to actually get from + + + align:start position:0% +has to be mastered to actually get from +the discovery to the innovation + + align:start position:0% +the discovery to the innovation + + + align:start position:0% +the discovery to the innovation +so there's models for technology change + + align:start position:0% +so there's models for technology change + + + align:start position:0% +so there's models for technology change +and we'll talk more about those in a + + align:start position:0% +and we'll talk more about those in a + + + align:start position:0% +and we'll talk more about those in a +later class but just a couple of core + + align:start position:0% +later class but just a couple of core + + + align:start position:0% +later class but just a couple of core +ideas to put on the table right now + + align:start position:0% +ideas to put on the table right now + + + align:start position:0% +ideas to put on the table right now +technology push + + align:start position:0% +technology push + + + align:start position:0% +technology push +okay so we talked a bit about the + + align:start position:0% +okay so we talked a bit about the + + + align:start position:0% +okay so we talked a bit about the +innovation pipeline last week + + align:start position:0% +innovation pipeline last week + + + align:start position:0% +innovation pipeline last week +technology pushes typically where you + + align:start position:0% +technology pushes typically where you + + + align:start position:0% +technology pushes typically where you +support research something emerges and + + align:start position:0% +support research something emerges and + + + align:start position:0% +support research something emerges and +that research in effect and then enters + + align:start position:0% +that research in effect and then enters + + + align:start position:0% +that research in effect and then enters +into widespread use you know typically + + align:start position:0% +into widespread use you know typically + + + align:start position:0% +into widespread use you know typically +our commercializable product right so in + + align:start position:0% +our commercializable product right so in + + + align:start position:0% +our commercializable product right so in +effect you're your nurturing and + + align:start position:0% +effect you're your nurturing and + + + align:start position:0% +effect you're your nurturing and +developing and technology and you're + + align:start position:0% +developing and technology and you're + + + align:start position:0% +developing and technology and you're +pushing it towards the economy + + align:start position:0% +pushing it towards the economy + + + align:start position:0% +pushing it towards the economy +technology pull are sometimes called + + align:start position:0% +technology pull are sometimes called + + + align:start position:0% +technology pull are sometimes called +demand pull as a different model so in + + align:start position:0% +demand pull as a different model so in + + + align:start position:0% +demand pull as a different model so in +this case the market will create an + + align:start position:0% +this case the market will create an + + + align:start position:0% +this case the market will create an +opportunity the market may create a + + align:start position:0% +opportunity the market may create a + + + align:start position:0% +opportunity the market may create a +niche right or someone may spot the + + align:start position:0% +niche right or someone may spot the + + + align:start position:0% +niche right or someone may spot the +opportunity or the niche and in effect + + align:start position:0% +opportunity or the niche and in effect + + + align:start position:0% +opportunity or the niche and in effect +the market is going to pull that + + align:start position:0% +the market is going to pull that + + + align:start position:0% +the market is going to pull that +technology out it's going to be in a way + + align:start position:0% +technology out it's going to be in a way + + + align:start position:0% +technology out it's going to be in a way +the enabler for that technology to + + align:start position:0% +the enabler for that technology to + + + align:start position:0% +the enabler for that technology to +evolve right so these are two very + + align:start position:0% +evolve right so these are two very + + + align:start position:0% +evolve right so these are two very +different processes and we'll talk more + + align:start position:0% +different processes and we'll talk more + + + align:start position:0% +different processes and we'll talk more +about who does which incurs incremental + + align:start position:0% +about who does which incurs incremental + + + align:start position:0% +about who does which incurs incremental +innovation and there's radical + + align:start position:0% +innovation and there's radical + + + align:start position:0% +innovation and there's radical +innovation so incremental innovation + + align:start position:0% +innovation so incremental innovation + + + align:start position:0% +innovation so incremental innovation +as the definition here it improves + + align:start position:0% +as the definition here it improves + + + align:start position:0% +as the definition here it improves +function aesthetics performance + + align:start position:0% +function aesthetics performance + + + align:start position:0% +function aesthetics performance +efficiency manufacturability and so + + align:start position:0% +efficiency manufacturability and so + + + align:start position:0% +efficiency manufacturability and so +forth right in other words modest + + align:start position:0% +forth right in other words modest + + + align:start position:0% +forth right in other words modest +incremental steps right it's very + + align:start position:0% +incremental steps right it's very + + + align:start position:0% +incremental steps right it's very +important + + align:start position:0% +important + + + align:start position:0% +important +we all kind of love radical innovation + + align:start position:0% +we all kind of love radical innovation + + + align:start position:0% +we all kind of love radical innovation +right and there's actually good evidence + + align:start position:0% +right and there's actually good evidence + + + align:start position:0% +right and there's actually good evidence +that radical innovation will lead you a + + align:start position:0% +that radical innovation will lead you a + + + align:start position:0% +that radical innovation will lead you a +really lead to a really disproportionate + + align:start position:0% +really lead to a really disproportionate + + + align:start position:0% +really lead to a really disproportionate +profit impact in other words if you can + + align:start position:0% +profit impact in other words if you can + + + align:start position:0% +profit impact in other words if you can +launch a radical innovation the gains + + align:start position:0% +launch a radical innovation the gains + + + align:start position:0% +launch a radical innovation the gains +can really be big right and that will + + align:start position:0% +can really be big right and that will + + + align:start position:0% +can really be big right and that will +become an important idea when we talk + + align:start position:0% +become an important idea when we talk + + + align:start position:0% +become an important idea when we talk +about venture capital later in the class + + align:start position:0% + + + + align:start position:0% + +now you're calling on me to really look + + align:start position:0% +now you're calling on me to really look + + + align:start position:0% +now you're calling on me to really look +closely I don't know how many years this + + align:start position:0% +closely I don't know how many years this + + + align:start position:0% +closely I don't know how many years this +is a 97 study out of the Harvard + + align:start position:0% +is a 97 study out of the Harvard + + + align:start position:0% +is a 97 study out of the Harvard +Business School and I just don't + + align:start position:0% +Business School and I just don't + + + align:start position:0% +Business School and I just don't +remember + + align:start position:0% +remember + + + align:start position:0% +remember +Martyna how many years this covers but + + align:start position:0% +Martyna how many years this covers but + + + align:start position:0% +Martyna how many years this covers but +I'll be happy to look that up for you + + align:start position:0% +I'll be happy to look that up for you + + + align:start position:0% +I'll be happy to look that up for you +because I don't see it on here but it's + + align:start position:0% +because I don't see it on here but it's + + + align:start position:0% +because I don't see it on here but it's +got to be you know it's got to be at + + align:start position:0% +got to be you know it's got to be at + + + align:start position:0% +got to be you know it's got to be at +least a 10 year look I think to be + + align:start position:0% +least a 10 year look I think to be + + + align:start position:0% +least a 10 year look I think to be +meaningful + + align:start position:0% +meaningful + + + align:start position:0% +meaningful +so I don't want you to get the idea + + align:start position:0% +so I don't want you to get the idea + + + align:start position:0% +so I don't want you to get the idea +though that one is better than the other + + align:start position:0% +though that one is better than the other + + + align:start position:0% +though that one is better than the other +than or radical or better than one + + align:start position:0% +than or radical or better than one + + + align:start position:0% +than or radical or better than one +another right just think + + align:start position:0% +another right just think + + + align:start position:0% +another right just think +the Wright brothers aircraft would be + + align:start position:0% +the Wright brothers aircraft would be + + + align:start position:0% +the Wright brothers aircraft would be +good a good example of a radical + + align:start position:0% +good a good example of a radical + + + align:start position:0% +good a good example of a radical +innovation right but you and I would not + + align:start position:0% +innovation right but you and I would not + + + align:start position:0% +innovation right but you and I would not +want to take the Wright brothers + + align:start position:0% +want to take the Wright brothers + + + align:start position:0% +want to take the Wright brothers +aircraft across the Atlantic Ocean we + + align:start position:0% +aircraft across the Atlantic Ocean we + + + align:start position:0% +aircraft across the Atlantic Ocean we +would rather do the 787 right so + + align:start position:0% +would rather do the 787 right so + + + align:start position:0% +would rather do the 787 right so +incremental can be extremely important + + align:start position:0% +incremental can be extremely important + + + align:start position:0% +incremental can be extremely important +historically industry does the + + align:start position:0% +historically industry does the + + + align:start position:0% +historically industry does the +incremental right that's more of a + + align:start position:0% +incremental right that's more of a + + + align:start position:0% +incremental right that's more of a +technology demand kind of model a + + align:start position:0% +technology demand kind of model a + + + align:start position:0% +technology demand kind of model a +technology pull kind of model as opposed + + align:start position:0% +technology pull kind of model as opposed + + + align:start position:0% +technology pull kind of model as opposed +to the + + align:start position:0% +to the + + + align:start position:0% +to the +radical which tends to be more out of a + + align:start position:0% +radical which tends to be more out of a + + + align:start position:0% +radical which tends to be more out of a +technology push research base and + + align:start position:0% +technology push research base and + + + align:start position:0% +technology push research base and +we'll talk more about those things as + + align:start position:0% +we'll talk more about those things as + + + align:start position:0% +we'll talk more about those things as +time goes by but I wanted to get those + + align:start position:0% +time goes by but I wanted to get those + + + align:start position:0% +time goes by but I wanted to get those +out on the table + + align:start position:0% +out on the table + + + align:start position:0% +out on the table +so although radical may be more + + align:start position:0% +so although radical may be more + + + align:start position:0% +so although radical may be more +profitable incremental is easier and + + align:start position:0% +profitable incremental is easier and + + + align:start position:0% +profitable incremental is easier and +obviously there's much more incremental + + align:start position:0% +obviously there's much more incremental + + + align:start position:0% +obviously there's much more incremental +advance max + + align:start position:0% + + + + align:start position:0% + +right because in our system as we talked + + align:start position:0% +right because in our system as we talked + + + align:start position:0% +right because in our system as we talked +a bit about last week + + align:start position:0% +a bit about last week + + + align:start position:0% +a bit about last week +research is predominantly funded by + + align:start position:0% +research is predominantly funded by + + + align:start position:0% +research is predominantly funded by +government and and the and the actors + + align:start position:0% +government and and the and the actors + + + align:start position:0% +government and and the and the actors +are universities and + + align:start position:0% +are universities and + + + align:start position:0% +are universities and +development is predominantly funded by + + align:start position:0% +development is predominantly funded by + + + align:start position:0% +development is predominantly funded by +industry right which tends to be more + + align:start position:0% +industry right which tends to be more + + + align:start position:0% +industry right which tends to be more +incremental advanced + + align:start position:0% + + + + align:start position:0% + +and there's something also that you just + + align:start position:0% +and there's something also that you just + + + align:start position:0% +and there's something also that you just +kind of need to keep in the back of your + + align:start position:0% +kind of need to keep in the back of your + + + align:start position:0% +kind of need to keep in the back of your +minds which is product cycle theory + + align:start position:0% +minds which is product cycle theory + + + align:start position:0% +minds which is product cycle theory +that products go through cycles go + + align:start position:0% +that products go through cycles go + + + align:start position:0% +that products go through cycles go +through evolutionary stages so a firm + + align:start position:0% +through evolutionary stages so a firm + + + align:start position:0% +through evolutionary stages so a firm +develops defines a product it develops a + + align:start position:0% +develops defines a product it develops a + + + align:start position:0% +develops defines a product it develops a +market for it then it standardizes the + + align:start position:0% +market for it then it standardizes the + + + align:start position:0% +market for it then it standardizes the +product and then typically over time one + + align:start position:0% +product and then typically over time one + + + align:start position:0% +product and then typically over time one +design will tend to dominate right and + + align:start position:0% +design will tend to dominate right and + + + align:start position:0% +design will tend to dominate right and +then the number of competing companies + + align:start position:0% +then the number of competing companies + + + align:start position:0% +then the number of competing companies +with varying designs will tend to shrink + + align:start position:0% +with varying designs will tend to shrink + + + align:start position:0% +with varying designs will tend to shrink +so and over time the product will + + align:start position:0% +so and over time the product will + + + align:start position:0% +so and over time the product will +sometimes become a true commodity + + align:start position:0% +sometimes become a true commodity + + + align:start position:0% +sometimes become a true commodity +product right high-volume the price goes + + align:start position:0% +product right high-volume the price goes + + + align:start position:0% +product right high-volume the price goes +significantly down and the profit margin + + align:start position:0% +significantly down and the profit margin + + + align:start position:0% +significantly down and the profit margin +is much lower + + align:start position:0% +is much lower + + + align:start position:0% +is much lower +so the uniqueness of the product kind of + + align:start position:0% +so the uniqueness of the product kind of + + + align:start position:0% +so the uniqueness of the product kind of +ebbs + + align:start position:0% +ebbs + + + align:start position:0% +ebbs +at that stage in the u.s. system often + + align:start position:0% +at that stage in the u.s. system often + + + align:start position:0% +at that stage in the u.s. system often +the production often goes offshore right + + align:start position:0% +the production often goes offshore right + + + align:start position:0% +the production often goes offshore right +that's the moment where it occurs where + + align:start position:0% +that's the moment where it occurs where + + + align:start position:0% +that's the moment where it occurs where +the commodity production begins + + align:start position:0% +the commodity production begins + + + align:start position:0% +the commodity production begins +barriers to entry increase at this point + + align:start position:0% +barriers to entry increase at this point + + + align:start position:0% +barriers to entry increase at this point +because only a modest number of firms on + + align:start position:0% +because only a modest number of firms on + + + align:start position:0% +because only a modest number of firms on +a standardized product tend to dominate + + align:start position:0% +a standardized product tend to dominate + + + align:start position:0% +a standardized product tend to dominate +and the surviving firms have to have the + + align:start position:0% +and the surviving firms have to have the + + + align:start position:0% +and the surviving firms have to have the +capacity to keep advancing their + + align:start position:0% +capacity to keep advancing their + + + align:start position:0% +capacity to keep advancing their +technology keep making incremental + + align:start position:0% +technology keep making incremental + + + align:start position:0% +technology keep making incremental +advances they've got to be able to + + align:start position:0% +advances they've got to be able to + + + align:start position:0% +advances they've got to be able to +master large-scale production they've + + align:start position:0% +master large-scale production they've + + + align:start position:0% +master large-scale production they've +got to have strong distribution and + + align:start position:0% +got to have strong distribution and + + + align:start position:0% +got to have strong distribution and +marketing arms and they've got to have + + align:start position:0% +marketing arms and they've got to have + + + align:start position:0% +marketing arms and they've got to have +the management talent to kind of work + + align:start position:0% +the management talent to kind of work + + + align:start position:0% +the management talent to kind of work +across all those pieces + + align:start position:0% + + + + align:start position:0% + +yeah I mean think about things you see + + align:start position:0% +yeah I mean think about things you see + + + align:start position:0% +yeah I mean think about things you see +all the time right like search engines + + align:start position:0% +all the time right like search engines + + + align:start position:0% +all the time right like search engines +how was it that Google really came to + + align:start position:0% +how was it that Google really came to + + + align:start position:0% +how was it that Google really came to +dominate the search engine business or + + align:start position:0% +dominate the search engine business or + + + align:start position:0% +dominate the search engine business or +think about operating systems how was it + + align:start position:0% +think about operating systems how was it + + + align:start position:0% +think about operating systems how was it +that Microsoft really came to dominate + + align:start position:0% +that Microsoft really came to dominate + + + align:start position:0% +that Microsoft really came to dominate +the operating system world + + align:start position:0% +the operating system world + + + align:start position:0% +the operating system world +so that just you know consumers tend to + + align:start position:0% +so that just you know consumers tend to + + + align:start position:0% +so that just you know consumers tend to +lock in to the dominant product you know + + align:start position:0% +lock in to the dominant product you know + + + align:start position:0% +lock in to the dominant product you know +how was it that Apple came to dominate + + align:start position:0% +how was it that Apple came to dominate + + + align:start position:0% +how was it that Apple came to dominate +iPhones although that's you know + + align:start position:0% +iPhones although that's you know + + + align:start position:0% +iPhones although that's you know +obviously up for grabs every few years + + align:start position:0% +obviously up for grabs every few years + + + align:start position:0% +obviously up for grabs every few years +it's not to say there can't be entry of + + align:start position:0% +it's not to say there can't be entry of + + + align:start position:0% +it's not to say there can't be entry of +others into these fields but the berries + + align:start position:0% +others into these fields but the berries + + + align:start position:0% +others into these fields but the berries +at barriers to entry tend to get higher + + align:start position:0% +at barriers to entry tend to get higher + + + align:start position:0% +at barriers to entry tend to get higher +because how many firms can really master + + align:start position:0% +because how many firms can really master + + + align:start position:0% +because how many firms can really master +all these skill sets right that's that's + + align:start position:0% +all these skill sets right that's that's + + + align:start position:0% +all these skill sets right that's that's +pretty sophisticated + + align:start position:0% +pretty sophisticated + + + align:start position:0% +pretty sophisticated +does that help yeah + + align:start position:0% + + + + align:start position:0% + +yeah it's + + align:start position:0% +yeah it's + + + align:start position:0% +yeah it's +so you really have to systemize the + + align:start position:0% +so you really have to systemize the + + + align:start position:0% +so you really have to systemize the +opéra systematize the operation to be + + align:start position:0% +opéra systematize the operation to be + + + align:start position:0% +opéra systematize the operation to be +able to continue to make strong gains + + align:start position:0% +able to continue to make strong gains + + + align:start position:0% +able to continue to make strong gains +out of that + + align:start position:0% +out of that + + + align:start position:0% +out of that +out of that more commodity product line + + align:start position:0% +out of that more commodity product line + + + align:start position:0% +out of that more commodity product line +and then typically you've got to keep + + align:start position:0% +and then typically you've got to keep + + + align:start position:0% +and then typically you've got to keep +driving the cost down as well + + align:start position:0% +driving the cost down as well + + + align:start position:0% +driving the cost down as well +now this is this is not eternally true + + align:start position:0% +now this is this is not eternally true + + + align:start position:0% +now this is this is not eternally true +and you began to poke at some of the + + align:start position:0% +and you began to poke at some of the + + + align:start position:0% +and you began to poke at some of the +problems in this model right you can + + align:start position:0% +problems in this model right you can + + + align:start position:0% +problems in this model right you can +think about ways of disrupting this + + align:start position:0% +think about ways of disrupting this + + + align:start position:0% +think about ways of disrupting this +pattern right + + align:start position:0% +pattern right + + + align:start position:0% +pattern right +for example some companies are learning + + align:start position:0% +for example some companies are learning + + + align:start position:0% +for example some companies are learning +how to do + + align:start position:0% +how to do + + + align:start position:0% +how to do +continuing radical innovations right + + align:start position:0% +continuing radical innovations right + + + align:start position:0% +continuing radical innovations right +that was frankly Apple is a good example + + align:start position:0% +that was frankly Apple is a good example + + + align:start position:0% +that was frankly Apple is a good example +of that that was Apple's magic right you + + align:start position:0% +of that that was Apple's magic right you + + + align:start position:0% +of that that was Apple's magic right you +know it does the Mac and then it does + + align:start position:0% +know it does the Mac and then it does + + + align:start position:0% +know it does the Mac and then it does +the iPod and then it does the iPhone and + + align:start position:0% +the iPod and then it does the iPhone and + + + align:start position:0% +the iPod and then it does the iPhone and +so forth right in other words it's able + + align:start position:0% +so forth right in other words it's able + + + align:start position:0% +so forth right in other words it's able +to continue to do pretty radical + + align:start position:0% +to continue to do pretty radical + + + align:start position:0% +to continue to do pretty radical +innovations on a continuing basis + + align:start position:0% +innovations on a continuing basis + + + align:start position:0% +innovations on a continuing basis +what enables a company to keep that + + align:start position:0% +what enables a company to keep that + + + align:start position:0% +what enables a company to keep that +ability to to keep innovating right + + align:start position:0% +ability to to keep innovating right + + + align:start position:0% +ability to to keep innovating right +because it's not + + align:start position:0% +because it's not + + + align:start position:0% +because it's not +there are only a handful of companies in + + align:start position:0% +there are only a handful of companies in + + + align:start position:0% +there are only a handful of companies in +the world that are over a hundred years + + align:start position:0% +the world that are over a hundred years + + + align:start position:0% +the world that are over a hundred years +old + + align:start position:0% +old + + + align:start position:0% +old +they burn themselves out + + align:start position:0% + + + + align:start position:0% + +globalization obviously Spurs + + align:start position:0% +globalization obviously Spurs + + + align:start position:0% +globalization obviously Spurs +competitiveness and it spurs entry right + + align:start position:0% +competitiveness and it spurs entry right + + + align:start position:0% +competitiveness and it spurs entry right +and increase competition it speeds the + + align:start position:0% +and increase competition it speeds the + + + align:start position:0% +and increase competition it speeds the +product cycle so it can be disruptive + + align:start position:0% +product cycle so it can be disruptive + + + align:start position:0% +product cycle so it can be disruptive +this of this traditional product cycle + + align:start position:0% +this of this traditional product cycle + + + align:start position:0% +this of this traditional product cycle +there may be and we'll talk about it + + align:start position:0% +there may be and we'll talk about it + + + align:start position:0% +there may be and we'll talk about it +more in our next class but a kind of + + align:start position:0% +more in our next class but a kind of + + + align:start position:0% +more in our next class but a kind of +rebirth of manufacturing process + + align:start position:0% +rebirth of manufacturing process + + + align:start position:0% +rebirth of manufacturing process +improvements that could disrupt this + + align:start position:0% +improvements that could disrupt this + + + align:start position:0% +improvements that could disrupt this +cycle and change it and there's now a + + align:start position:0% +cycle and change it and there's now a + + + align:start position:0% +cycle and change it and there's now a +very interesting + + align:start position:0% +very interesting + + + align:start position:0% +very interesting +service sector that's not hard product + + align:start position:0% +service sector that's not hard product + + + align:start position:0% +service sector that's not hard product +based that's emerging and the + + align:start position:0% +based that's emerging and the + + + align:start position:0% +based that's emerging and the +possibility of tying + + align:start position:0% +possibility of tying + + + align:start position:0% +possibility of tying +services to hardware so you know an + + align:start position:0% +services to hardware so you know an + + + align:start position:0% +services to hardware so you know an +Apple iPhone is a classic example of a + + align:start position:0% +Apple iPhone is a classic example of a + + + align:start position:0% +Apple iPhone is a classic example of a +hard technology that is also a service + + align:start position:0% +hard technology that is also a service + + + align:start position:0% +hard technology that is also a service +delivery model right so we're getting + + align:start position:0% +delivery model right so we're getting + + + align:start position:0% +delivery model right so we're getting +these combinations and interesting new + + align:start position:0% +these combinations and interesting new + + + align:start position:0% +these combinations and interesting new +ways that will change this product cycle + + align:start position:0% +ways that will change this product cycle + + + align:start position:0% +ways that will change this product cycle +as well so it's not a tunnel but I want + + align:start position:0% +as well so it's not a tunnel but I want + + + align:start position:0% +as well so it's not a tunnel but I want +you to get an idea product cycle theory + + align:start position:0% +you to get an idea product cycle theory + + + align:start position:0% +you to get an idea product cycle theory +and then our final idea before we dig in + + align:start position:0% +and then our final idea before we dig in + + + align:start position:0% +and then our final idea before we dig in +on the readings + + align:start position:0% +on the readings + + + align:start position:0% +on the readings +dynamic versus static competitive + + align:start position:0% +dynamic versus static competitive + + + align:start position:0% +dynamic versus static competitive +advantage so David Ricardo great + + align:start position:0% +advantage so David Ricardo great + + + align:start position:0% +advantage so David Ricardo great +economist of the 19th century + + align:start position:0% +economist of the 19th century + + + align:start position:0% +economist of the 19th century +develops essentially a theory of + + align:start position:0% +develops essentially a theory of + + + align:start position:0% +develops essentially a theory of +static comparative advantage that + + align:start position:0% +static comparative advantage that + + + align:start position:0% +static comparative advantage that +advantage would be intrinsic to a + + align:start position:0% +advantage would be intrinsic to a + + + align:start position:0% +advantage would be intrinsic to a +country typically based on natural + + align:start position:0% +country typically based on natural + + + align:start position:0% +country typically based on natural +resources and his famous economic + + align:start position:0% +resources and his famous economic + + + align:start position:0% +resources and his famous economic +example was you know and we we talked + + align:start position:0% +example was you know and we we talked + + + align:start position:0% +example was you know and we we talked +about it + + align:start position:0% +about it + + + align:start position:0% +about it +a little bit last week but you know + + align:start position:0% +a little bit last week but you know + + + align:start position:0% +a little bit last week but you know +England has a lot of rain has a lot of + + align:start position:0% +England has a lot of rain has a lot of + + + align:start position:0% +England has a lot of rain has a lot of +grass it can have sheep it can do wool + + align:start position:0% +grass it can have sheep it can do wool + + + align:start position:0% +grass it can have sheep it can do wool +very well right and Portugal doesn't + + align:start position:0% +very well right and Portugal doesn't + + + align:start position:0% +very well right and Portugal doesn't +have that much rain doesn't have that + + align:start position:0% +have that much rain doesn't have that + + + align:start position:0% +have that much rain doesn't have that +much grass + + align:start position:0% +much grass + + + align:start position:0% +much grass +but it's great for growing grapes so + + align:start position:0% +but it's great for growing grapes so + + + align:start position:0% +but it's great for growing grapes so +it's gonna do wine England adieu we'll + + align:start position:0% +it's gonna do wine England adieu we'll + + + align:start position:0% +it's gonna do wine England adieu we'll +we'll each has a natural comparative + + align:start position:0% +we'll each has a natural comparative + + + align:start position:0% +we'll each has a natural comparative +advantage based on a resource advantage + + align:start position:0% +advantage based on a resource advantage + + + align:start position:0% +advantage based on a resource advantage +and it benefits both to trade right + + align:start position:0% +and it benefits both to trade right + + + align:start position:0% +and it benefits both to trade right +Portugal expands its market from wine by + + align:start position:0% +Portugal expands its market from wine by + + + align:start position:0% +Portugal expands its market from wine by +growing outside its own borders England + + align:start position:0% +growing outside its own borders England + + + align:start position:0% +growing outside its own borders England +expands its market for wool by growing + + align:start position:0% +expands its market for wool by growing + + + align:start position:0% +expands its market for wool by growing +out its borders there's a benefit to + + align:start position:0% +out its borders there's a benefit to + + + align:start position:0% +out its borders there's a benefit to +each so that's the kind of 19th century + + align:start position:0% +each so that's the kind of 19th century + + + align:start position:0% +each so that's the kind of 19th century +concept that's the heart of free trade + + align:start position:0% +concept that's the heart of free trade + + + align:start position:0% +concept that's the heart of free trade +theory ok that's a static static + + align:start position:0% +theory ok that's a static static + + + align:start position:0% +theory ok that's a static static +comparative advantage starting around + + align:start position:0% +comparative advantage starting around + + + align:start position:0% +comparative advantage starting around +the middle of the 20th century something + + align:start position:0% +the middle of the 20th century something + + + align:start position:0% +the middle of the 20th century something +very different began to evolve a dynamic + + align:start position:0% +very different began to evolve a dynamic + + + align:start position:0% +very different began to evolve a dynamic +comparative advantage and + + align:start position:0% +comparative advantage and + + + align:start position:0% +comparative advantage and +this is based on growth theory in other + + align:start position:0% +this is based on growth theory in other + + + align:start position:0% +this is based on growth theory in other +words if you can be innovative and you + + align:start position:0% +words if you can be innovative and you + + + align:start position:0% +words if you can be innovative and you +can lead innovation waves you can + + align:start position:0% +can lead innovation waves you can + + + align:start position:0% +can lead innovation waves you can +capture a lot of the early gains of that + + align:start position:0% +capture a lot of the early gains of that + + + align:start position:0% +capture a lot of the early gains of that +innovation wave its solo innovation + + align:start position:0% +innovation wave its solo innovation + + + align:start position:0% +innovation wave its solo innovation +based growth theory so that is a dynamic + + align:start position:0% +based growth theory so that is a dynamic + + + align:start position:0% +based growth theory so that is a dynamic +advantage created by and we're still we + + align:start position:0% +advantage created by and we're still we + + + align:start position:0% +advantage created by and we're still we +have to understand the menu but + + align:start position:0% +have to understand the menu but + + + align:start position:0% +have to understand the menu but +investments in R&D in education and + + align:start position:0% +investments in R&D in education and + + + align:start position:0% +investments in R&D in education and +efficient governance those could all be + + align:start position:0% +efficient governance those could all be + + + align:start position:0% +efficient governance those could all be +inputs and we'll talk more about the + + align:start position:0% +inputs and we'll talk more about the + + + align:start position:0% +inputs and we'll talk more about the +system later today into a dynamic + + align:start position:0% +system later today into a dynamic + + + align:start position:0% +system later today into a dynamic +comparative advantage now a dynamic + + align:start position:0% +comparative advantage now a dynamic + + + align:start position:0% +comparative advantage now a dynamic +comparative advantage is not eternal + + align:start position:0% +comparative advantage is not eternal + + + align:start position:0% +comparative advantage is not eternal +right it may get lost and we're gonna + + align:start position:0% +right it may get lost and we're gonna + + + align:start position:0% +right it may get lost and we're gonna +talk about some work by Paul Samuelson + + align:start position:0% +talk about some work by Paul Samuelson + + + align:start position:0% +talk about some work by Paul Samuelson +who lays a lot of that thinking out and + + align:start position:0% +who lays a lot of that thinking out and + + + align:start position:0% +who lays a lot of that thinking out and +I'm famous 2004 article in one of the + + align:start position:0% +I'm famous 2004 article in one of the + + + align:start position:0% +I'm famous 2004 article in one of the +next couple of classes so + + align:start position:0% +next couple of classes so + + + align:start position:0% +next couple of classes so +the u.s. created in many ways the + + align:start position:0% +the u.s. created in many ways the + + + align:start position:0% +the u.s. created in many ways the +biggest innovating economy in the world + + align:start position:0% +biggest innovating economy in the world + + + align:start position:0% +biggest innovating economy in the world +coming out of that war to period + + align:start position:0% +coming out of that war to period + + + align:start position:0% +coming out of that war to period +so it built built a competitive + + align:start position:0% +so it built built a competitive + + + align:start position:0% +so it built built a competitive +advantage + + align:start position:0% +advantage + + + align:start position:0% +advantage +based on innovation + + align:start position:0% +based on innovation + + + align:start position:0% +based on innovation +right which was you know had been + + align:start position:0% +right which was you know had been + + + align:start position:0% +right which was you know had been +evolving in Europe and countries like + + align:start position:0% +evolving in Europe and countries like + + + align:start position:0% +evolving in Europe and countries like +Britain and Germany had been doing some + + align:start position:0% +Britain and Germany had been doing some + + + align:start position:0% +Britain and Germany had been doing some +things similar and you know starting in + + align:start position:0% +things similar and you know starting in + + + align:start position:0% +things similar and you know starting in +the second half of the nineteenth + + align:start position:0% +the second half of the nineteenth + + + align:start position:0% +the second half of the nineteenth +century but the u.s. really scaled that + + align:start position:0% +century but the u.s. really scaled that + + + align:start position:0% +century but the u.s. really scaled that +model up and really built a very strong + + align:start position:0% +model up and really built a very strong + + + align:start position:0% +model up and really built a very strong +early stage innovation system it became + + align:start position:0% +early stage innovation system it became + + + align:start position:0% +early stage innovation system it became +the richest nation on earth right that + + align:start position:0% +the richest nation on earth right that + + + align:start position:0% +the richest nation on earth right that +was its model that was its comparative + + align:start position:0% +was its model that was its comparative + + + align:start position:0% +was its model that was its comparative +advantage now the problem with a + + align:start position:0% +advantage now the problem with a + + + align:start position:0% +advantage now the problem with a +comparative advantage + + align:start position:0% +comparative advantage + + + align:start position:0% +comparative advantage +based on innovation is that others can + + align:start position:0% +based on innovation is that others can + + + align:start position:0% +based on innovation is that others can +figure out how to innovate right its + + align:start position:0% +figure out how to innovate right its + + + align:start position:0% +figure out how to innovate right its +England is always gonna have rain and + + align:start position:0% +England is always gonna have rain and + + + align:start position:0% +England is always gonna have rain and +sheep and wool and Portugal is always + + align:start position:0% +sheep and wool and Portugal is always + + + align:start position:0% +sheep and wool and Portugal is always +gonna have Sun and grapes and wine + + align:start position:0% +gonna have Sun and grapes and wine + + + align:start position:0% +gonna have Sun and grapes and wine +those are inherent static comparative + + align:start position:0% +those are inherent static comparative + + + align:start position:0% +those are inherent static comparative +advantages they are not going to change + + align:start position:0% +advantages they are not going to change + + + align:start position:0% +advantages they are not going to change +an innovation advantage can change right + + align:start position:0% +an innovation advantage can change right + + + align:start position:0% +an innovation advantage can change right +so the US had an incredible mass + + align:start position:0% +so the US had an incredible mass + + + align:start position:0% +so the US had an incredible mass +production system coming out at the end + + align:start position:0% +production system coming out at the end + + + align:start position:0% +production system coming out at the end +of World War two Japan figures out a + + align:start position:0% +of World War two Japan figures out a + + + align:start position:0% +of World War two Japan figures out a +bigger better innovation model based on + + align:start position:0% +bigger better innovation model based on + + + align:start position:0% +bigger better innovation model based on +quality production and takes + + align:start position:0% +quality production and takes + + + align:start position:0% +quality production and takes +consumer electronics and large parts of + + align:start position:0% +consumer electronics and large parts of + + + align:start position:0% +consumer electronics and large parts of +the auto sector right so that's how a + + align:start position:0% +the auto sector right so that's how a + + + align:start position:0% +the auto sector right so that's how a +comparative innovation advantage can + + align:start position:0% +comparative innovation advantage can + + + align:start position:0% +comparative innovation advantage can +erode + + align:start position:0% +erode + + + align:start position:0% +erode +so it's powerful you can get very rich + + align:start position:0% +so it's powerful you can get very rich + + + align:start position:0% +so it's powerful you can get very rich +as a nation and as a society but it's + + align:start position:0% +as a nation and as a society but it's + + + align:start position:0% +as a nation and as a society but it's +also up for grabs + + align:start position:0% +also up for grabs + + + align:start position:0% +also up for grabs +all right anything so far + + align:start position:0% +all right anything so far + + + align:start position:0% +all right anything so far +on this any questions so far + + align:start position:0% +on this any questions so far + + + align:start position:0% +on this any questions so far +all right and these slides will be + + align:start position:0% +all right and these slides will be + + + align:start position:0% +all right and these slides will be +parked on the stellar site and + + align:start position:0% +parked on the stellar site and + + + align:start position:0% +parked on the stellar site and +accessible to use these underlying + + align:start position:0% +accessible to use these underlying + + + align:start position:0% +accessible to use these underlying +foundational ideas will be around feet + + align:start position:0% +foundational ideas will be around feet + + + align:start position:0% +foundational ideas will be around feet +at glance at so today we move to our + + align:start position:0% +at glance at so today we move to our + + + align:start position:0% +at glance at so today we move to our +discussion leader system and so here's + + align:start position:0% +discussion leader system and so here's + + + align:start position:0% +discussion leader system and so here's +how it's gonna work I'm gonna talk for + + align:start position:0% +how it's gonna work I'm gonna talk for + + + align:start position:0% +how it's gonna work I'm gonna talk for +10 minutes or so 12 minutes something + + align:start position:0% +10 minutes or so 12 minutes something + + + align:start position:0% +10 minutes or so 12 minutes something +like that about the readings and then + + align:start position:0% +like that about the readings and then + + + align:start position:0% +like that about the readings and then +each of our able discussion leaders + + align:start position:0% +each of our able discussion leaders + + + align:start position:0% +each of our able discussion leaders +is going to you know gonna in turn take + + align:start position:0% +is going to you know gonna in turn take + + + align:start position:0% +is going to you know gonna in turn take +that reading so Beth has got Nelson and + + align:start position:0% +that reading so Beth has got Nelson and + + + align:start position:0% +that reading so Beth has got Nelson and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +did you have Atkinson Beth somehow got + + align:start position:0% +did you have Atkinson Beth somehow got + + + align:start position:0% +did you have Atkinson Beth somehow got +the really too hard readings on an a she + + align:start position:0% +the really too hard readings on an a she + + + align:start position:0% +the really too hard readings on an a she +lost in the jump ball but Lily well that + + align:start position:0% +lost in the jump ball but Lily well that + + + align:start position:0% +lost in the jump ball but Lily well that +will take the next couple of readings + + align:start position:0% +will take the next couple of readings + + + align:start position:0% +will take the next couple of readings +and then Martine willful up with + + align:start position:0% +and then Martine willful up with + + + align:start position:0% +and then Martine willful up with +actually the really fun stuff as we get + + align:start position:0% +actually the really fun stuff as we get + + + align:start position:0% +actually the really fun stuff as we get +towards the end of the class we'll have + + align:start position:0% +towards the end of the class we'll have + + + align:start position:0% +towards the end of the class we'll have +to make sure we find full time for it + + align:start position:0% +to make sure we find full time for it + + + align:start position:0% +to make sure we find full time for it +but let me start with Nelson and he's + + align:start position:0% +but let me start with Nelson and he's + + + align:start position:0% +but let me start with Nelson and he's +that he's our third great growth + + align:start position:0% +that he's our third great growth + + + align:start position:0% +that he's our third great growth +economist a Columbia professor of + + align:start position:0% +economist a Columbia professor of + + + align:start position:0% +economist a Columbia professor of +economics and he writes in 1993 this + + align:start position:0% +economics and he writes in 1993 this + + + align:start position:0% +economics and he writes in 1993 this +really interesting + + align:start position:0% +really interesting + + + align:start position:0% +really interesting +book about national innovation systems a + + align:start position:0% +book about national innovation systems a + + + align:start position:0% +book about national innovation systems a +comparative analysis and + + align:start position:0% + + + + align:start position:0% + +he essentially puts out another a third + + align:start position:0% +he essentially puts out another a third + + + align:start position:0% +he essentially puts out another a third +innovation factus we've got solos and + + align:start position:0% +innovation factus we've got solos and + + + align:start position:0% +innovation factus we've got solos and +robbers and Nelson really adds a third + + align:start position:0% +robbers and Nelson really adds a third + + + align:start position:0% +robbers and Nelson really adds a third +he develops this term national + + align:start position:0% +he develops this term national + + + align:start position:0% +he develops this term national +innovation system he's not the first one + + align:start position:0% +innovation system he's not the first one + + + align:start position:0% +innovation system he's not the first one +to use it an economist named chris + + align:start position:0% +to use it an economist named chris + + + align:start position:0% +to use it an economist named chris +freeman at the University of Sussex in + + align:start position:0% +freeman at the University of Sussex in + + + align:start position:0% +freeman at the University of Sussex in +Britain actually is probably the first + + align:start position:0% +Britain actually is probably the first + + + align:start position:0% +Britain actually is probably the first +to use that term in looking at the + + align:start position:0% +to use that term in looking at the + + + align:start position:0% +to use that term in looking at the +Japanese economy + + align:start position:0% +Japanese economy + + + align:start position:0% +Japanese economy +but he really in this book really kind + + align:start position:0% +but he really in this book really kind + + + align:start position:0% +but he really in this book really kind +of spells that out + + align:start position:0% +of spells that out + + + align:start position:0% +of spells that out +so he talks about how the technological + + align:start position:0% +so he talks about how the technological + + + align:start position:0% +so he talks about how the technological +capabilities of a nation's firms and + + align:start position:0% +capabilities of a nation's firms and + + + align:start position:0% +capabilities of a nation's firms and +other innovation actors are a key source + + align:start position:0% +other innovation actors are a key source + + + align:start position:0% +other innovation actors are a key source +of the nation's competitive Palace + + align:start position:0% +of the nation's competitive Palace + + + align:start position:0% +of the nation's competitive Palace +does the term national innovation system + + align:start position:0% +does the term national innovation system + + + align:start position:0% +does the term national innovation system +still makes sense in what is a much more + + align:start position:0% +still makes sense in what is a much more + + + align:start position:0% +still makes sense in what is a much more +globalized world + + align:start position:0% +globalized world + + + align:start position:0% +globalized world +right this is after all being written + + align:start position:0% +right this is after all being written + + + align:start position:0% +right this is after all being written +back in 1993 a lot has changed there's a + + align:start position:0% +back in 1993 a lot has changed there's a + + + align:start position:0% +back in 1993 a lot has changed there's a +much more integrated globalized world is + + align:start position:0% +much more integrated globalized world is + + + align:start position:0% +much more integrated globalized world is +it still a term that you can look at + + align:start position:0% +it still a term that you can look at + + + align:start position:0% +it still a term that you can look at +if Nelson was sitting here I think he + + align:start position:0% +if Nelson was sitting here I think he + + + align:start position:0% +if Nelson was sitting here I think he +would argue yes he would say that + + align:start position:0% + + + + align:start position:0% + +enough of the factors that go into an + + align:start position:0% +enough of the factors that go into an + + + align:start position:0% +enough of the factors that go into an +innovation system are still tied to + + align:start position:0% +innovation system are still tied to + + + align:start position:0% +innovation system are still tied to +national investments + + align:start position:0% +national investments + + + align:start position:0% +national investments +that you can still do a national + + align:start position:0% +that you can still do a national + + + align:start position:0% +that you can still do a national +analysis but it's harder right and we'll + + align:start position:0% +analysis but it's harder right and we'll + + + align:start position:0% +analysis but it's harder right and we'll +talk about what some of those national + + align:start position:0% +talk about what some of those national + + + align:start position:0% +talk about what some of those national +factors are in a bit and Nelson here + + align:start position:0% +factors are in a bit and Nelson here + + + align:start position:0% +factors are in a bit and Nelson here +uses the same broad definition of + + align:start position:0% +uses the same broad definition of + + + align:start position:0% +uses the same broad definition of +innovation that we've been using so far + + align:start position:0% +innovation that we've been using so far + + + align:start position:0% +innovation that we've been using so far +in our first two classes and he refers + + align:start position:0% +in our first two classes and he refers + + + align:start position:0% +in our first two classes and he refers +to it as the process by which firms + + align:start position:0% +to it as the process by which firms + + + align:start position:0% +to it as the process by which firms +master and get into practice product + + align:start position:0% +master and get into practice product + + + align:start position:0% +master and get into practice product +designs and new manufacturing processes + + align:start position:0% +designs and new manufacturing processes + + + align:start position:0% +designs and new manufacturing processes +so it's not the invention it's something + + align:start position:0% +so it's not the invention it's something + + + align:start position:0% +so it's not the invention it's something +much larger + + align:start position:0% +much larger + + + align:start position:0% +much larger +so let's do some background some of his + + align:start position:0% +so let's do some background some of his + + + align:start position:0% +so let's do some background some of his +background points + + align:start position:0% +background points + + + align:start position:0% +background points +he argues that + + align:start position:0% +he argues that + + + align:start position:0% +he argues that +capitalism is + + align:start position:0% +capitalism is + + + align:start position:0% +capitalism is +destructive and disruptive that's a term + + align:start position:0% +destructive and disruptive that's a term + + + align:start position:0% +destructive and disruptive that's a term +from a great economist named Jean Pater + + align:start position:0% +from a great economist named Jean Pater + + + align:start position:0% +from a great economist named Jean Pater +destructive capitalism occurs via + + align:start position:0% +destructive capitalism occurs via + + + align:start position:0% +destructive capitalism occurs via +innovation it's not necessarily the + + align:start position:0% +innovation it's not necessarily the + + + align:start position:0% +innovation it's not necessarily the +first innovator that gets all of the + + align:start position:0% +first innovator that gets all of the + + + align:start position:0% +first innovator that gets all of the +rewards or even most of the rewards + + align:start position:0% +rewards or even most of the rewards + + + align:start position:0% +rewards or even most of the rewards +sometimes the second follow-on innovator + + align:start position:0% +sometimes the second follow-on innovator + + + align:start position:0% +sometimes the second follow-on innovator +captures a lot of the rewards because + + align:start position:0% +captures a lot of the rewards because + + + align:start position:0% +captures a lot of the rewards because +they pick up from what the first + + align:start position:0% +they pick up from what the first + + + align:start position:0% +they pick up from what the first +innovators mistakes were and improve + + align:start position:0% +innovators mistakes were and improve + + + align:start position:0% +innovators mistakes were and improve +them but a nation's concern therefore + + align:start position:0% +them but a nation's concern therefore + + + align:start position:0% +them but a nation's concern therefore +shouldn't be necessarily with sponsoring + + align:start position:0% +shouldn't be necessarily with sponsoring + + + align:start position:0% +shouldn't be necessarily with sponsoring +the first innovator it's got to have a + + align:start position:0% +the first innovator it's got to have a + + + align:start position:0% +the first innovator it's got to have a +broader concern about innovative + + align:start position:0% +broader concern about innovative + + + align:start position:0% +broader concern about innovative +capability so again if the dominant + + align:start position:0% +capability so again if the dominant + + + align:start position:0% +capability so again if the dominant +causative factor of economic growth is + + align:start position:0% +causative factor of economic growth is + + + align:start position:0% +causative factor of economic growth is +technological and related innovation as + + align:start position:0% +technological and related innovation as + + + align:start position:0% +technological and related innovation as +Sola taught all of us + + align:start position:0% +Sola taught all of us + + + align:start position:0% +Sola taught all of us +Nelson goes on to start to think about + + align:start position:0% +Nelson goes on to start to think about + + + align:start position:0% +Nelson goes on to start to think about +what do you do to make sure you're + + align:start position:0% +what do you do to make sure you're + + + align:start position:0% +what do you do to make sure you're +getting a lot of that okay and + + align:start position:0% +getting a lot of that okay and + + + align:start position:0% +getting a lot of that okay and +his point is that you need a system to + + align:start position:0% +his point is that you need a system to + + + align:start position:0% +his point is that you need a system to +be able to do that a + + align:start position:0% +be able to do that a + + + align:start position:0% +be able to do that a +system of actors + + align:start position:0% +system of actors + + + align:start position:0% +system of actors +that can be connected and influence and + + align:start position:0% +that can be connected and influence and + + + align:start position:0% +that can be connected and influence and +affect and drive your innovative + + align:start position:0% +affect and drive your innovative + + + align:start position:0% +affect and drive your innovative +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +so who are these institutional actors + + align:start position:0% +so who are these institutional actors + + + align:start position:0% +so who are these institutional actors +universities firms government agencies + + align:start position:0% +universities firms government agencies + + + align:start position:0% +universities firms government agencies +and the policies around them right and + + align:start position:0% +and the policies around them right and + + + align:start position:0% +and the policies around them right and +he argues that yes there can be a common + + align:start position:0% +he argues that yes there can be a common + + + align:start position:0% +he argues that yes there can be a common +analytical frame framework across + + align:start position:0% +analytical frame framework across + + + align:start position:0% +analytical frame framework across +nations by looking at these actors so + + align:start position:0% +nations by looking at these actors so + + + align:start position:0% +nations by looking at these actors so +this is a really important idea that's + + align:start position:0% +this is a really important idea that's + + + align:start position:0% +this is a really important idea that's +you know at the heart of today's class + + align:start position:0% +you know at the heart of today's class + + + align:start position:0% +you know at the heart of today's class +here it is + + align:start position:0% +here it is + + + align:start position:0% +here it is +innovation is a system and you can look + + align:start position:0% +innovation is a system and you can look + + + align:start position:0% +innovation is a system and you can look +at the strength of that system based on + + align:start position:0% +at the strength of that system based on + + + align:start position:0% +at the strength of that system based on +the strength and connectedness of the + + align:start position:0% +the strength and connectedness of the + + + align:start position:0% +the strength and connectedness of the +actors in that system + + align:start position:0% +actors in that system + + + align:start position:0% +actors in that system +so you can now go to any nation region + + align:start position:0% +so you can now go to any nation region + + + align:start position:0% +so you can now go to any nation region +area and you can start doing an analysis + + align:start position:0% +area and you can start doing an analysis + + + align:start position:0% +area and you can start doing an analysis +of just how strong that innovation + + align:start position:0% +of just how strong that innovation + + + align:start position:0% +of just how strong that innovation +system is by looking at the strength of + + align:start position:0% +system is by looking at the strength of + + + align:start position:0% +system is by looking at the strength of +the actors + + align:start position:0% +the actors + + + align:start position:0% +the actors +things like the firms government + + align:start position:0% +things like the firms government + + + align:start position:0% +things like the firms government +agencies universities related policies + + align:start position:0% +agencies universities related policies + + + align:start position:0% +agencies universities related policies +you can do an assessment on innovation + + align:start position:0% +you can do an assessment on innovation + + + align:start position:0% +you can do an assessment on innovation +strengths right so this is a key tool + + align:start position:0% +strengths right so this is a key tool + + + align:start position:0% +strengths right so this is a key tool +and a lot of your a lot of the paper in + + align:start position:0% +and a lot of your a lot of the paper in + + + align:start position:0% +and a lot of your a lot of the paper in +this class is gonna be built around this + + align:start position:0% +this class is gonna be built around this + + + align:start position:0% +this class is gonna be built around this +Nelson system idea + + align:start position:0% +Nelson system idea + + + align:start position:0% +Nelson system idea +he goes off and makes some interesting + + align:start position:0% +he goes off and makes some interesting + + + align:start position:0% +he goes off and makes some interesting +points about the relationship between + + align:start position:0% +points about the relationship between + + + align:start position:0% +points about the relationship between +science and technology which is also + + align:start position:0% +science and technology which is also + + + align:start position:0% +science and technology which is also +really a point about the relationship + + align:start position:0% +really a point about the relationship + + + align:start position:0% +really a point about the relationship +between basic research and applied + + align:start position:0% +between basic research and applied + + + align:start position:0% +between basic research and applied +research and development and between + + align:start position:0% +research and development and between + + + align:start position:0% +research and development and between +university research government-sponsored + + align:start position:0% +university research government-sponsored + + + align:start position:0% +university research government-sponsored +research and firms and his point is that + + align:start position:0% +research and firms and his point is that + + + align:start position:0% +research and firms and his point is that +new science can give rise to new + + align:start position:0% +new science can give rise to new + + + align:start position:0% +new science can give rise to new +technology and vice versa + + align:start position:0% + + + + align:start position:0% + +so he cites an example of science + + align:start position:0% +so he cites an example of science + + + align:start position:0% +so he cites an example of science +leading + + align:start position:0% +leading + + + align:start position:0% +leading +to a technology as electricity and he + + align:start position:0% +to a technology as electricity and he + + + align:start position:0% +to a technology as electricity and he +cites Faraday and so forth he cites + + align:start position:0% +cites Faraday and so forth he cites + + + align:start position:0% +cites Faraday and so forth he cites +chemistry as science as a follower right + + align:start position:0% +chemistry as science as a follower right + + + align:start position:0% +chemistry as science as a follower right +that you know it really came out of a + + align:start position:0% +that you know it really came out of a + + + align:start position:0% +that you know it really came out of a +whole series of pretty practical + + align:start position:0% +whole series of pretty practical + + + align:start position:0% +whole series of pretty practical +professions some other examples you know + + align:start position:0% +professions some other examples you know + + + align:start position:0% +professions some other examples you know +Gibbs creates the whole science of + + align:start position:0% +Gibbs creates the whole science of + + + align:start position:0% +Gibbs creates the whole science of +thermodynamics + + align:start position:0% +thermodynamics + + + align:start position:0% +thermodynamics +because he's analyzing steam engines + + align:start position:0% +because he's analyzing steam engines + + + align:start position:0% +because he's analyzing steam engines +right that's where he develops his + + align:start position:0% +right that's where he develops his + + + align:start position:0% +right that's where he develops his +thesis + + align:start position:0% +thesis + + + align:start position:0% +thesis +Edison is the other way around Edison is + + align:start position:0% +Edison is the other way around Edison is + + + align:start position:0% +Edison is the other way around Edison is +trying to do a very practical electrical + + align:start position:0% +trying to do a very practical electrical + + + align:start position:0% +trying to do a very practical electrical +technology light bulb but he stumbles + + align:start position:0% +technology light bulb but he stumbles + + + align:start position:0% +technology light bulb but he stumbles +into science something called the Edison + + align:start position:0% +into science something called the Edison + + + align:start position:0% +into science something called the Edison +effect which actually is kind of an + + align:start position:0% +effect which actually is kind of an + + + align:start position:0% +effect which actually is kind of an +early way of looking at electron theory + + align:start position:0% +early way of looking at electron theory + + + align:start position:0% +early way of looking at electron theory +as part of that but this development of + + align:start position:0% +as part of that but this development of + + + align:start position:0% +as part of that but this development of +electricity yields all kinds of + + align:start position:0% +electricity yields all kinds of + + + align:start position:0% +electricity yields all kinds of +follow-on scientific advances aircraft + + align:start position:0% +follow-on scientific advances aircraft + + + align:start position:0% +follow-on scientific advances aircraft +technology starts with the Wright + + align:start position:0% +technology starts with the Wright + + + align:start position:0% +technology starts with the Wright +brothers who are these are mechanics + + align:start position:0% +brothers who are these are mechanics + + + align:start position:0% +brothers who are these are mechanics +these are tinkerers but then leads to + + align:start position:0% +these are tinkerers but then leads to + + + align:start position:0% +these are tinkerers but then leads to +very deep + + align:start position:0% +very deep + + + align:start position:0% +very deep +aerospace engineering the transistor is + + align:start position:0% +aerospace engineering the transistor is + + + align:start position:0% +aerospace engineering the transistor is +an attempt to solve a practical problem + + align:start position:0% +an attempt to solve a practical problem + + + align:start position:0% +an attempt to solve a practical problem +you know high speed switching + + align:start position:0% +you know high speed switching + + + align:start position:0% +you know high speed switching +and yet that leads directly to solid + + align:start position:0% +and yet that leads directly to solid + + + align:start position:0% +and yet that leads directly to solid +state physics a whole whole new field in + + align:start position:0% +state physics a whole whole new field in + + + align:start position:0% +state physics a whole whole new field in +physics + + align:start position:0% +physics + + + align:start position:0% +physics +computing yields computing science so + + align:start position:0% +computing yields computing science so + + + align:start position:0% +computing yields computing science so +it's a two-way street here science can + + align:start position:0% +it's a two-way street here science can + + + align:start position:0% +it's a two-way street here science can +yield technology but technology can also + + align:start position:0% +yield technology but technology can also + + + align:start position:0% +yield technology but technology can also +yield science so you've got to have that + + align:start position:0% +yield science so you've got to have that + + + align:start position:0% +yield science so you've got to have that +two-way street operating right which + + align:start position:0% +two-way street operating right which + + + align:start position:0% +two-way street operating right which +means that you've got to have some + + align:start position:0% +means that you've got to have some + + + align:start position:0% +means that you've got to have some +connection between the force and your + + align:start position:0% +connection between the force and your + + + align:start position:0% +connection between the force and your +society that are more focused on + + align:start position:0% +society that are more focused on + + + align:start position:0% +society that are more focused on +technology which is typically firms and + + align:start position:0% +technology which is typically firms and + + + align:start position:0% +technology which is typically firms and +the research side and vice-versa + + align:start position:0% + + + + align:start position:0% + +the limits of science + + align:start position:0% + + + + align:start position:0% + +again innovation is not simply the + + align:start position:0% +again innovation is not simply the + + + align:start position:0% +again innovation is not simply the +invention it's bigger and it includes + + align:start position:0% +invention it's bigger and it includes + + + align:start position:0% +invention it's bigger and it includes +design so you engineers in the room will + + align:start position:0% +design so you engineers in the room will + + + align:start position:0% +design so you engineers in the room will +know what we're talking about here but + + align:start position:0% +know what we're talking about here but + + + align:start position:0% +know what we're talking about here but +that really means choosing the right + + align:start position:0% +that really means choosing the right + + + align:start position:0% +that really means choosing the right +quote mix of performance characteristics + + align:start position:0% +quote mix of performance characteristics + + + align:start position:0% +quote mix of performance characteristics +for example in designing a modern + + align:start position:0% +for example in designing a modern + + + align:start position:0% +for example in designing a modern +aircraft wing + + align:start position:0% +aircraft wing + + + align:start position:0% +aircraft wing +it's not enough to get the discovery + + align:start position:0% +it's not enough to get the discovery + + + align:start position:0% +it's not enough to get the discovery +right you've got to get the design right + + align:start position:0% +right you've got to get the design right + + + align:start position:0% +right you've got to get the design right +- in other words you need to select the + + align:start position:0% +- in other words you need to select the + + + align:start position:0% +- in other words you need to select the +right mix of performance characteristics + + align:start position:0% + + + + align:start position:0% + +who are these innovation actors + + align:start position:0% +who are these innovation actors + + + align:start position:0% +who are these innovation actors +first and foremost and + + align:start position:0% +first and foremost and + + + align:start position:0% +first and foremost and +this was written in 1993 is the industry + + align:start position:0% +this was written in 1993 is the industry + + + align:start position:0% +this was written in 1993 is the industry +lab so in 1993 something like bell labs + + align:start position:0% +lab so in 1993 something like bell labs + + + align:start position:0% +lab so in 1993 something like bell labs +are the great GE labs or the great IBM + + align:start position:0% +are the great GE labs or the great IBM + + + align:start position:0% +are the great GE labs or the great IBM +labs + + align:start position:0% +labs + + + align:start position:0% +labs +these dominated in many ways the + + align:start position:0% +these dominated in many ways the + + + align:start position:0% +these dominated in many ways the +industrial innovation + + align:start position:0% +industrial innovation + + + align:start position:0% +industrial innovation +landscape they are by and large gone + + align:start position:0% +landscape they are by and large gone + + + align:start position:0% +landscape they are by and large gone +that is dramatically changed since 1993 + + align:start position:0% +that is dramatically changed since 1993 + + + align:start position:0% +that is dramatically changed since 1993 +no it's not that large firms don't do + + align:start position:0% +no it's not that large firms don't do + + + align:start position:0% +no it's not that large firms don't do +or Indy they do a lot of it and that + + align:start position:0% +or Indy they do a lot of it and that + + + align:start position:0% +or Indy they do a lot of it and that +number is growing but it's increasingly + + align:start position:0% +number is growing but it's increasingly + + + align:start position:0% +number is growing but it's increasingly +D and les are + + align:start position:0% + + + + align:start position:0% + +also there's a reminder here that + + align:start position:0% +also there's a reminder here that + + + align:start position:0% +also there's a reminder here that +R&D is only part of a larger innovation + + align:start position:0% +R&D is only part of a larger innovation + + + align:start position:0% +R&D is only part of a larger innovation +picture so things like management and + + align:start position:0% +picture so things like management and + + + align:start position:0% +picture so things like management and +management organization organization of + + align:start position:0% +management organization organization of + + + align:start position:0% +management organization organization of +R&D can have major roles here - so actor + + align:start position:0% +R&D can have major roles here - so actor + + + align:start position:0% +R&D can have major roles here - so actor +number one is industry and at the time + + align:start position:0% +number one is industry and at the time + + + align:start position:0% +number one is industry and at the time +he writes its industry labs now that's a + + align:start position:0% +he writes its industry labs now that's a + + + align:start position:0% +he writes its industry labs now that's a +much more dispersed model now because + + align:start position:0% +much more dispersed model now because + + + align:start position:0% +much more dispersed model now because +industries have largely abandoned their + + align:start position:0% +industries have largely abandoned their + + + align:start position:0% +industries have largely abandoned their +old labs to use do a lot of more + + align:start position:0% +old labs to use do a lot of more + + + align:start position:0% +old labs to use do a lot of more +fundamental work to really development + + align:start position:0% +fundamental work to really development + + + align:start position:0% +fundamental work to really development +processes and rounding up innovators and + + align:start position:0% +processes and rounding up innovators and + + + align:start position:0% +processes and rounding up innovators and +in some cases acquiring them like in the + + align:start position:0% +in some cases acquiring them like in the + + + align:start position:0% +in some cases acquiring them like in the +biotech sector + + align:start position:0% +biotech sector + + + align:start position:0% +biotech sector +but industry is still a central player + + align:start position:0% +but industry is still a central player + + + align:start position:0% +but industry is still a central player +obviously there were also university + + align:start position:0% +obviously there were also university + + + align:start position:0% +obviously there were also university +laboratories you all are familiar with + + align:start position:0% +laboratories you all are familiar with + + + align:start position:0% +laboratories you all are familiar with +those the government laboratories like + + align:start position:0% +those the government laboratories like + + + align:start position:0% +those the government laboratories like +the great labs for the Department of + + align:start position:0% +the great labs for the Department of + + + align:start position:0% +the great labs for the Department of +Energy of the Department of Defense + + align:start position:0% +Energy of the Department of Defense + + + align:start position:0% +Energy of the Department of Defense +then there's a whole public sector + + align:start position:0% +then there's a whole public sector + + + align:start position:0% +then there's a whole public sector +support system that's an actor here as + + align:start position:0% +support system that's an actor here as + + + align:start position:0% +support system that's an actor here as +well + + align:start position:0% +well + + + align:start position:0% +well +for R&D and + + align:start position:0% +for R&D and + + + align:start position:0% +for R&D and +there's an element historically that has + + align:start position:0% +there's an element historically that has + + + align:start position:0% +there's an element historically that has +supported industry R&D particularly + + align:start position:0% +supported industry R&D particularly + + + align:start position:0% +supported industry R&D particularly +through the Defense Department + + align:start position:0% +through the Defense Department + + + align:start position:0% +through the Defense Department +so + + align:start position:0% +so + + + align:start position:0% +so +that's one way to look at this is the + + align:start position:0% +that's one way to look at this is the + + + align:start position:0% +that's one way to look at this is the +actors the actors will be different in + + align:start position:0% +actors the actors will be different in + + + align:start position:0% +actors the actors will be different in +different industrial sectors they're + + align:start position:0% +different industrial sectors they're + + + align:start position:0% +different industrial sectors they're +going to look different and there'll be + + align:start position:0% +going to look different and there'll be + + + align:start position:0% +going to look different and there'll be +a different mix and they're going to be + + align:start position:0% +a different mix and they're going to be + + + align:start position:0% +a different mix and they're going to be +organized differently in different + + align:start position:0% +organized differently in different + + + align:start position:0% +organized differently in different +industrial sectors so + + align:start position:0% +industrial sectors so + + + align:start position:0% +industrial sectors so +you know steel is really different than + + align:start position:0% +you know steel is really different than + + + align:start position:0% +you know steel is really different than +aviation right these are differently + + align:start position:0% +aviation right these are differently + + + align:start position:0% +aviation right these are differently +organized things but you can see you can + + align:start position:0% +organized things but you can see you can + + + align:start position:0% +organized things but you can see you can +nonetheless look at the innovation + + align:start position:0% +nonetheless look at the innovation + + + align:start position:0% +nonetheless look at the innovation +actors in the system and look at their + + align:start position:0% +actors in the system and look at their + + + align:start position:0% +actors in the system and look at their +strengths and weaknesses + + align:start position:0% +strengths and weaknesses + + + align:start position:0% +strengths and weaknesses +complex technologies require supply + + align:start position:0% +complex technologies require supply + + + align:start position:0% +complex technologies require supply +chains and therefore customers and users + + align:start position:0% +chains and therefore customers and users + + + align:start position:0% +chains and therefore customers and users +play a role in the innovation system + + align:start position:0% +play a role in the innovation system + + + align:start position:0% +play a role in the innovation system +because there's a whole feedback system + + align:start position:0% +because there's a whole feedback system + + + align:start position:0% +because there's a whole feedback system +that comes in right + + align:start position:0% +that comes in right + + + align:start position:0% +that comes in right +so the customers play a role for complex + + align:start position:0% +so the customers play a role for complex + + + align:start position:0% +so the customers play a role for complex +technologies particularly so it's not + + align:start position:0% +technologies particularly so it's not + + + align:start position:0% +technologies particularly so it's not +only the actors have gone through so far + + align:start position:0% +only the actors have gone through so far + + + align:start position:0% +only the actors have gone through so far +customers can be brought in and users + + align:start position:0% +customers can be brought in and users + + + align:start position:0% +customers can be brought in and users +can be brought in so you've got much + + align:start position:0% +can be brought in so you've got much + + + align:start position:0% +can be brought in so you've got much +closer to an idea of an innovation + + align:start position:0% +closer to an idea of an innovation + + + align:start position:0% +closer to an idea of an innovation +network here and we'll talk in a bit + + align:start position:0% +network here and we'll talk in a bit + + + align:start position:0% +network here and we'll talk in a bit +about Rycroft encash to kind of spell + + align:start position:0% +about Rycroft encash to kind of spell + + + align:start position:0% +about Rycroft encash to kind of spell +that out so he does a comparison he + + align:start position:0% +that out so he does a comparison he + + + align:start position:0% +that out so he does a comparison he +compares the u.s. innovation system in + + align:start position:0% +compares the u.s. innovation system in + + + align:start position:0% +compares the u.s. innovation system in +the 1945 to 1975 timeframe compares that + + align:start position:0% +the 1945 to 1975 timeframe compares that + + + align:start position:0% +the 1945 to 1975 timeframe compares that +to the Japanese innovation system in the + + align:start position:0% +to the Japanese innovation system in the + + + align:start position:0% +to the Japanese innovation system in the +70s and 80s + + align:start position:0% +70s and 80s + + + align:start position:0% +70s and 80s +so very different innovation systems + + align:start position:0% + + + + align:start position:0% + +hence helped driving the theory of + + align:start position:0% +hence helped driving the theory of + + + align:start position:0% +hence helped driving the theory of +national innovation system so in that + + align:start position:0% +national innovation system so in that + + + align:start position:0% +national innovation system so in that +time period the US firms tended to be + + align:start position:0% +time period the US firms tended to be + + + align:start position:0% +time period the US firms tended to be +larger in scale they served a continent + + align:start position:0% +larger in scale they served a continent + + + align:start position:0% +larger in scale they served a continent +sized market the firm's spent more in + + align:start position:0% +sized market the firm's spent more in + + + align:start position:0% +sized market the firm's spent more in +the US on R&D the government spends a + + align:start position:0% +the US on R&D the government spends a + + + align:start position:0% +the US on R&D the government spends a +lot more on Rd at the time particularly + + align:start position:0% +lot more on Rd at the time particularly + + + align:start position:0% +lot more on Rd at the time particularly +because the defense mission u.s. + + align:start position:0% +because the defense mission u.s. + + + align:start position:0% +because the defense mission u.s. +university research was stronger as a + + align:start position:0% +university research was stronger as a + + + align:start position:0% +university research was stronger as a +result of some post-war decision-making + + align:start position:0% +result of some post-war decision-making + + + align:start position:0% +result of some post-war decision-making +that the u.s. made and most US goods + + align:start position:0% +that the u.s. made and most US goods + + + align:start position:0% +that the u.s. made and most US goods +were sold into US markets so that's some + + align:start position:0% +were sold into US markets so that's some + + + align:start position:0% +were sold into US markets so that's some +framing ideas around the u.s. model + + align:start position:0% +framing ideas around the u.s. model + + + align:start position:0% +framing ideas around the u.s. model +Japan is really different Japan is very + + align:start position:0% +Japan is really different Japan is very + + + align:start position:0% +Japan is really different Japan is very +resource poor so it has to have strong + + align:start position:0% +resource poor so it has to have strong + + + align:start position:0% +resource poor so it has to have strong +exports to be able to get the resources + + align:start position:0% +exports to be able to get the resources + + + align:start position:0% +exports to be able to get the resources +so it's got to be an export-led economy + + align:start position:0% +so it's got to be an export-led economy + + + align:start position:0% +so it's got to be an export-led economy +whereas the US can organize essentially + + align:start position:0% +whereas the US can organize essentially + + + align:start position:0% +whereas the US can organize essentially +on national consumer markets Japan has + + align:start position:0% +on national consumer markets Japan has + + + align:start position:0% +on national consumer markets Japan has +got expand globally + + align:start position:0% +got expand globally + + + align:start position:0% +got expand globally +R&D in Japan in this time period and + + align:start position:0% +R&D in Japan in this time period and + + + align:start position:0% +R&D in Japan in this time period and +still pretty much to this day is more + + align:start position:0% +still pretty much to this day is more + + + align:start position:0% +still pretty much to this day is more +tied to industry then it's the case with + + align:start position:0% +tied to industry then it's the case with + + + align:start position:0% +tied to industry then it's the case with +us there's less fundamental research + + align:start position:0% +us there's less fundamental research + + + align:start position:0% +us there's less fundamental research +there's much more applied and + + align:start position:0% +there's much more applied and + + + align:start position:0% +there's much more applied and +development support from government and + + align:start position:0% +development support from government and + + + align:start position:0% +development support from government and +there are from government very explicit + + align:start position:0% +there are from government very explicit + + + align:start position:0% +there are from government very explicit +technology development politic policies + + align:start position:0% +technology development politic policies + + + align:start position:0% +technology development politic policies +at this time + + align:start position:0% +at this time + + + align:start position:0% +at this time +so that's just a way of looking at two + + align:start position:0% +so that's just a way of looking at two + + + align:start position:0% +so that's just a way of looking at two +different countries and beginning to + + align:start position:0% +different countries and beginning to + + + align:start position:0% +different countries and beginning to +think about their different innovation + + align:start position:0% +think about their different innovation + + + align:start position:0% +think about their different innovation +systems and some of the underlying + + align:start position:0% +systems and some of the underlying + + + align:start position:0% +systems and some of the underlying +factors that will drive them he argues + + align:start position:0% +factors that will drive them he argues + + + align:start position:0% +factors that will drive them he argues +that there are several basic categories + + align:start position:0% +that there are several basic categories + + + align:start position:0% +that there are several basic categories +of countries large high-income small + + align:start position:0% +of countries large high-income small + + + align:start position:0% +of countries large high-income small +high income and then lower-income + + align:start position:0% +high income and then lower-income + + + align:start position:0% +high income and then lower-income +countries + + align:start position:0% +countries + + + align:start position:0% +countries +countries without resources have to have + + align:start position:0% +countries without resources have to have + + + align:start position:0% +countries without resources have to have +an export orientation and he cites + + align:start position:0% +an export orientation and he cites + + + align:start position:0% +an export orientation and he cites +Germany Japan Korea + + align:start position:0% +Germany Japan Korea + + + align:start position:0% +Germany Japan Korea +the US and to some extent the UK and + + align:start position:0% +the US and to some extent the UK and + + + align:start position:0% +the US and to some extent the UK and +France have a national security + + align:start position:0% +France have a national security + + + align:start position:0% +France have a national security +orientation for their innovation systems + + align:start position:0% +orientation for their innovation systems + + + align:start position:0% +orientation for their innovation systems +we justify a lot of R&D investment for + + align:start position:0% +we justify a lot of R&D investment for + + + align:start position:0% +we justify a lot of R&D investment for +national security reasons in the u.s. + + align:start position:0% +national security reasons in the u.s. + + + align:start position:0% +national security reasons in the u.s. +other countries don't do that + + align:start position:0% +other countries don't do that + + + align:start position:0% +other countries don't do that +there's differences in the governmental + + align:start position:0% +there's differences in the governmental + + + align:start position:0% +there's differences in the governmental +role the US government tends to be a lot + + align:start position:0% +role the US government tends to be a lot + + + align:start position:0% +role the US government tends to be a lot +less interventionist + + align:start position:0% +less interventionist + + + align:start position:0% +less interventionist +in the innovation system in the economy + + align:start position:0% +in the innovation system in the economy + + + align:start position:0% +in the innovation system in the economy +in general then for example Japan was in + + align:start position:0% +in general then for example Japan was in + + + align:start position:0% +in general then for example Japan was in +this time period so their country + + align:start position:0% +this time period so their country + + + align:start position:0% +this time period so their country +differences what's innovations success + + align:start position:0% +differences what's innovations success + + + align:start position:0% +differences what's innovations success +strong firms in Nelson mine is the + + align:start position:0% +strong firms in Nelson mine is the + + + align:start position:0% +strong firms in Nelson mine is the +critical factor they have got to do all + + align:start position:0% +critical factor they have got to do all + + + align:start position:0% +critical factor they have got to do all +the translation moving from discovery to + + align:start position:0% +the translation moving from discovery to + + + align:start position:0% +the translation moving from discovery to +fit a whole raft of + + align:start position:0% +fit a whole raft of + + + align:start position:0% +fit a whole raft of +tasks that they've got to perform in + + align:start position:0% +tasks that they've got to perform in + + + align:start position:0% +tasks that they've got to perform in +this translation task so without strong + + align:start position:0% +this translation task so without strong + + + align:start position:0% +this translation task so without strong +firms you got a serious problem in your + + align:start position:0% +firms you got a serious problem in your + + + align:start position:0% +firms you got a serious problem in your +innovation assistant but there are other + + align:start position:0% +innovation assistant but there are other + + + align:start position:0% +innovation assistant but there are other +factors education and training + + align:start position:0% +factors education and training + + + align:start position:0% +factors education and training +trade policy fiscal policy public + + align:start position:0% +trade policy fiscal policy public + + + align:start position:0% +trade policy fiscal policy public +support of university research these are + + align:start position:0% +support of university research these are + + + align:start position:0% +support of university research these are +all elements again in the system but he + + align:start position:0% +all elements again in the system but he + + + align:start position:0% +all elements again in the system but he +places the firm you know kind of front + + align:start position:0% +places the firm you know kind of front + + + align:start position:0% +places the firm you know kind of front +and center and given what firms look + + align:start position:0% +and center and given what firms look + + + align:start position:0% +and center and given what firms look +like in 1993 you can kind of see why + + align:start position:0% +like in 1993 you can kind of see why + + + align:start position:0% +like in 1993 you can kind of see why +it's a more complicated complex story + + align:start position:0% +it's a more complicated complex story + + + align:start position:0% +it's a more complicated complex story +now + + align:start position:0% + + + + align:start position:0% + +how about an explicit governmental role + + align:start position:0% +how about an explicit governmental role + + + align:start position:0% +how about an explicit governmental role +in innovation + + align:start position:0% +in innovation + + + align:start position:0% +in innovation +right how direct should that + + align:start position:0% +right how direct should that + + + align:start position:0% +right how direct should that +governmental role be so he's fine with + + align:start position:0% +governmental role be so he's fine with + + + align:start position:0% +governmental role be so he's fine with +the earlier stages he notes that there's + + align:start position:0% +the earlier stages he notes that there's + + + align:start position:0% +the earlier stages he notes that there's +a whole ongoing debate about how far + + align:start position:0% +a whole ongoing debate about how far + + + align:start position:0% +a whole ongoing debate about how far +down the innovation pipeline the + + align:start position:0% +down the innovation pipeline the + + + align:start position:0% +down the innovation pipeline the +government should intervene that's been + + align:start position:0% +government should intervene that's been + + + align:start position:0% +government should intervene that's been +a long-standing u.s. debate and we'll + + align:start position:0% +a long-standing u.s. debate and we'll + + + align:start position:0% +a long-standing u.s. debate and we'll +get more into that as the class goes on + + align:start position:0% +get more into that as the class goes on + + + align:start position:0% +get more into that as the class goes on +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +that's our Nelson story and Beth why + + align:start position:0% +that's our Nelson story and Beth why + + + align:start position:0% +that's our Nelson story and Beth why +don't I turn it over to you to raise + + align:start position:0% +don't I turn it over to you to raise + + + align:start position:0% +don't I turn it over to you to raise +some ideas about Nelson that you saw and + + align:start position:0% +some ideas about Nelson that you saw and + + + align:start position:0% +some ideas about Nelson that you saw and +to lead us and some Q&A + + align:start position:0% + + + + align:start position:0% + +second main topic area that came up a + + align:start position:0% +second main topic area that came up a + + + align:start position:0% +second main topic area that came up a +lot was just what are the best policies + + align:start position:0% +lot was just what are the best policies + + + align:start position:0% +lot was just what are the best policies +for innovation now given that this paper + + align:start position:0% +for innovation now given that this paper + + + align:start position:0% +for innovation now given that this paper +is a little bit older as the world has + + align:start position:0% +is a little bit older as the world has + + + align:start position:0% +is a little bit older as the world has +changed what do we see is the best ways + + align:start position:0% +changed what do we see is the best ways + + + align:start position:0% +changed what do we see is the best ways +to move forward + + align:start position:0% +to move forward + + + align:start position:0% +to move forward +third theme that came up was technology + + align:start position:0% +third theme that came up was technology + + + align:start position:0% +third theme that came up was technology +spillover and how that can be used as an + + align:start position:0% +spillover and how that can be used as an + + + align:start position:0% +spillover and how that can be used as an +advantage and last was balancing these + + align:start position:0% +advantage and last was balancing these + + + align:start position:0% +advantage and last was balancing these +national interests first the + + align:start position:0% +national interests first the + + + align:start position:0% +national interests first the +international relationships that have + + align:start position:0% +international relationships that have + + + align:start position:0% +international relationships that have +emerged in firms and so just a few + + align:start position:0% +emerged in firms and so just a few + + + align:start position:0% +emerged in firms and so just a few +summary points before we go into those + + align:start position:0% +summary points before we go into those + + + align:start position:0% +summary points before we go into those +kind of I'll read through some of the + + align:start position:0% +kind of I'll read through some of the + + + align:start position:0% +kind of I'll read through some of the +questions that I thought were especially + + align:start position:0% +questions that I thought were especially + + + align:start position:0% +questions that I thought were especially +enlightening + + align:start position:0% +enlightening + + + align:start position:0% +enlightening +just the basis of using national + + align:start position:0% +just the basis of using national + + + align:start position:0% +just the basis of using national +innovation systems + + align:start position:0% +innovation systems + + + align:start position:0% +innovation systems +from Nelson's point of view is that + + align:start position:0% +from Nelson's point of view is that + + + align:start position:0% +from Nelson's point of view is that +countries have some similarities but + + align:start position:0% +countries have some similarities but + + + align:start position:0% +countries have some similarities but +because of their differences in history + + align:start position:0% +because of their differences in history + + + align:start position:0% +because of their differences in history +culture their infrastructure laws + + align:start position:0% +culture their infrastructure laws + + + align:start position:0% +culture their infrastructure laws +financial institutions policies and + + align:start position:0% +financial institutions policies and + + + align:start position:0% +financial institutions policies and +investing we see that there are inherent + + align:start position:0% +investing we see that there are inherent + + + align:start position:0% +investing we see that there are inherent +differences to innovation systems in + + align:start position:0% +differences to innovation systems in + + + align:start position:0% +differences to innovation systems in +different countries and that for these + + align:start position:0% +different countries and that for these + + + align:start position:0% +different countries and that for these +countries to be successful it's not just + + align:start position:0% +countries to be successful it's not just + + + align:start position:0% +countries to be successful it's not just +enough to have manufacturing it's not + + align:start position:0% +enough to have manufacturing it's not + + + align:start position:0% +enough to have manufacturing it's not +that's not a substitute for a + + align:start position:0% +that's not a substitute for a + + + align:start position:0% +that's not a substitute for a +technological innovation so you need + + align:start position:0% +technological innovation so you need + + + align:start position:0% +technological innovation so you need +these strong firms that are constantly + + align:start position:0% +these strong firms that are constantly + + + align:start position:0% +these strong firms that are constantly +innovating + + align:start position:0% +innovating + + + align:start position:0% +innovating +and so he comes the conclusion that + + align:start position:0% +and so he comes the conclusion that + + + align:start position:0% +and so he comes the conclusion that +national innovation systems while they + + align:start position:0% +national innovation systems while they + + + align:start position:0% +national innovation systems while they +may seem a somewhat contradictory term + + align:start position:0% +may seem a somewhat contradictory term + + + align:start position:0% +may seem a somewhat contradictory term +considering policies are different for + + align:start position:0% +considering policies are different for + + + align:start position:0% +considering policies are different for +different industries within a nation are + + align:start position:0% +different industries within a nation are + + + align:start position:0% +different industries within a nation are +still useful for comparing how nations + + align:start position:0% +still useful for comparing how nations + + + align:start position:0% +still useful for comparing how nations +foster innovation and so first I just + + align:start position:0% +foster innovation and so first I just + + + align:start position:0% +foster innovation and so first I just +think it'd be interesting to hear what + + align:start position:0% +think it'd be interesting to hear what + + + align:start position:0% +think it'd be interesting to hear what +people see as the appropriate way to + + align:start position:0% +people see as the appropriate way to + + + align:start position:0% +people see as the appropriate way to +treat innovation systems is it at this + + align:start position:0% +treat innovation systems is it at this + + + align:start position:0% +treat innovation systems is it at this +national level is it at an industry + + align:start position:0% +national level is it at an industry + + + align:start position:0% +national level is it at an industry +level should it just be international + + align:start position:0% +level should it just be international + + + align:start position:0% +level should it just be international +interactions with each other so I'd like + + align:start position:0% +interactions with each other so I'd like + + + align:start position:0% +interactions with each other so I'd like +to open it up to some that + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +think + + align:start position:0% + + + + align:start position:0% + +it sort of depends on the industry + + align:start position:0% + + + + align:start position:0% + +takes place on that national level or + + align:start position:0% +takes place on that national level or + + + align:start position:0% +takes place on that national level or +firmly certain things like airspace + + align:start position:0% +firmly certain things like airspace + + + align:start position:0% +firmly certain things like airspace +we're often working fine so and things + + align:start position:0% +we're often working fine so and things + + + align:start position:0% +we're often working fine so and things +were very + + align:start position:0% +were very + + + align:start position:0% +were very +isolated to the nation in question but + + align:start position:0% +isolated to the nation in question but + + + align:start position:0% +isolated to the nation in question but +other like biotech picks up could be + + align:start position:0% +other like biotech picks up could be + + + align:start position:0% +other like biotech picks up could be +more + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +think it depends on what I'm doing + + align:start position:0% +think it depends on what I'm doing + + + align:start position:0% +think it depends on what I'm doing +you're analyzing because a lot of the + + align:start position:0% +you're analyzing because a lot of the + + + align:start position:0% +you're analyzing because a lot of the +things about past economic trends and + + align:start position:0% +things about past economic trends and + + + align:start position:0% +things about past economic trends and +some ways + + align:start position:0% + + + + align:start position:0% + +reading stated a lot of more global + + align:start position:0% +reading stated a lot of more global + + + align:start position:0% +reading stated a lot of more global +connection be possible the idea of a + + align:start position:0% +connection be possible the idea of a + + + align:start position:0% +connection be possible the idea of a +national level + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% + + + + align:start position:0% + +wait + + align:start position:0% + + + + align:start position:0% + +alright so you think it might be more + + align:start position:0% +alright so you think it might be more + + + align:start position:0% +alright so you think it might be more +rather than trying to make a + + align:start position:0% +rather than trying to make a + + + align:start position:0% +rather than trying to make a +generalization for how innovation has + + align:start position:0% +generalization for how innovation has + + + align:start position:0% +generalization for how innovation has +always happened it's kind of depending + + align:start position:0% +always happened it's kind of depending + + + align:start position:0% +always happened it's kind of depending +on what kind of innovation we're seeing + + align:start position:0% +on what kind of innovation we're seeing + + + align:start position:0% +on what kind of innovation we're seeing +that might be how we want to describe + + align:start position:0% +that might be how we want to describe + + + align:start position:0% +that might be how we want to describe +the innovation systems going forward + + align:start position:0% +the innovation systems going forward + + + align:start position:0% +the innovation systems going forward +and then thinking about policies for + + align:start position:0% +and then thinking about policies for + + + align:start position:0% +and then thinking about policies for +innovation one interesting question that + + align:start position:0% +innovation one interesting question that + + + align:start position:0% +innovation one interesting question that +came up was how does national technology + + align:start position:0% +came up was how does national technology + + + align:start position:0% +came up was how does national technology +policy shape the focus of research being + + align:start position:0% +policy shape the focus of research being + + + align:start position:0% +policy shape the focus of research being +conducted and company pursuits and then + + align:start position:0% +conducted and company pursuits and then + + + align:start position:0% +conducted and company pursuits and then +going off that how should national + + align:start position:0% +going off that how should national + + + align:start position:0% +going off that how should national +technology policy is shaped the focus of + + align:start position:0% +technology policy is shaped the focus of + + + align:start position:0% +technology policy is shaped the focus of +research + + align:start position:0% +research + + + align:start position:0% +research +so that kind of comes into that to be of + + align:start position:0% +so that kind of comes into that to be of + + + align:start position:0% +so that kind of comes into that to be of +how far in the pipeline should the + + align:start position:0% +how far in the pipeline should the + + + align:start position:0% +how far in the pipeline should the +government be intervening or should it + + align:start position:0% +government be intervening or should it + + + align:start position:0% +government be intervening or should it +be kind of a societal call for action + + align:start position:0% +be kind of a societal call for action + + + align:start position:0% +be kind of a societal call for action +where should this come up + + align:start position:0% + + + + align:start position:0% + +in general the history of innovation + + align:start position:0% +in general the history of innovation + + + align:start position:0% +in general the history of innovation +like early on usually it's not an expert + + align:start position:0% +like early on usually it's not an expert + + + align:start position:0% +like early on usually it's not an expert +anything that does it like + + align:start position:0% +anything that does it like + + + align:start position:0% +anything that does it like +the Wright brothers weren't really + + align:start position:0% +the Wright brothers weren't really + + + align:start position:0% +the Wright brothers weren't really +experts in flight and the reason that + + align:start position:0% +experts in flight and the reason that + + + align:start position:0% +experts in flight and the reason that +because they weren't experts to where it + + align:start position:0% +because they weren't experts to where it + + + align:start position:0% +because they weren't experts to where it +was able to figure out different way of + + align:start position:0% +was able to figure out different way of + + + align:start position:0% +was able to figure out different way of +doing it so probably like the right area + + align:start position:0% +doing it so probably like the right area + + + align:start position:0% +doing it so probably like the right area +for governments after like an initial + + align:start position:0% +for governments after like an initial + + + align:start position:0% +for governments after like an initial +innovation it's been figured out when + + align:start position:0% +innovation it's been figured out when + + + align:start position:0% +innovation it's been figured out when +I'm kind of know there's something there + + align:start position:0% +I'm kind of know there's something there + + + align:start position:0% +I'm kind of know there's something there +and now you can start pulling in + + align:start position:0% +and now you can start pulling in + + + align:start position:0% +and now you can start pulling in +resources but innovation and you know it + + align:start position:0% +resources but innovation and you know it + + + align:start position:0% +resources but innovation and you know it +could be like making a sculpture or give + + align:start position:0% +could be like making a sculpture or give + + + align:start position:0% +could be like making a sculpture or give +you that you need to make a house so + + align:start position:0% +you that you need to make a house so + + + align:start position:0% +you that you need to make a house so +like when it's time to kind of make a + + align:start position:0% +like when it's time to kind of make a + + + align:start position:0% +like when it's time to kind of make a +house we need a lot of hammers like I + + align:start position:0% +house we need a lot of hammers like I + + + align:start position:0% +house we need a lot of hammers like I +think that's a good time for government + + align:start position:0% +think that's a good time for government + + + align:start position:0% +think that's a good time for government +policy thus for mine it's like chiseling + + align:start position:0% +policy thus for mine it's like chiseling + + + align:start position:0% +policy thus for mine it's like chiseling +that's better select individuals or + + align:start position:0% +that's better select individuals or + + + align:start position:0% +that's better select individuals or +firms back to the idea of industry being + + align:start position:0% +firms back to the idea of industry being + + + align:start position:0% +firms back to the idea of industry being +in sin to us through government funds in + + align:start position:0% +in sin to us through government funds in + + + align:start position:0% +in sin to us through government funds in +general industry will do their own + + align:start position:0% +general industry will do their own + + + align:start position:0% +general industry will do their own +research and they have enough monopolies + + align:start position:0% +research and they have enough monopolies + + + align:start position:0% +research and they have enough monopolies +I guess if what used to happen which was + + align:start position:0% +I guess if what used to happen which was + + + align:start position:0% +I guess if what used to happen which was +I forget what company Apple took graphic + + align:start position:0% +I forget what company Apple took graphic + + + align:start position:0% +I forget what company Apple took graphic +user interface from but that was all hmm + + align:start position:0% +user interface from but that was all hmm + + + align:start position:0% +user interface from but that was all hmm +yeah Xerox parlors but they're famous + + align:start position:0% +yeah Xerox parlors but they're famous + + + align:start position:0% +yeah Xerox parlors but they're famous +for having a lot of innovations that + + align:start position:0% +for having a lot of innovations that + + + align:start position:0% +for having a lot of innovations that +they can never take to the product stage + + align:start position:0% +they can never take to the product stage + + + align:start position:0% +they can never take to the product stage +which is back to the point that you made + + align:start position:0% +which is back to the point that you made + + + align:start position:0% +which is back to the point that you made +on being able to take an innovation and + + align:start position:0% +on being able to take an innovation and + + + align:start position:0% +on being able to take an innovation and +they also make it a product and put in + + align:start position:0% +they also make it a product and put in + + + align:start position:0% +they also make it a product and put in +some kind of industrial cycle but + + align:start position:0% +some kind of industrial cycle but + + + align:start position:0% +some kind of industrial cycle but +government grants like SBIR grants are + + align:start position:0% +government grants like SBIR grants are + + + align:start position:0% +government grants like SBIR grants are +pretty good too for in it lefur creating + + align:start position:0% +pretty good too for in it lefur creating + + + align:start position:0% +pretty good too for in it lefur creating +that kind of Industry innovation I guess + + align:start position:0% +that kind of Industry innovation I guess + + + align:start position:0% +that kind of Industry innovation I guess +I'm much better with better incentives + + align:start position:0% + + + + align:start position:0% + +so martini it's a make a series of + + align:start position:0% +so martini it's a make a series of + + + align:start position:0% +so martini it's a make a series of +interesting points that let me go back + + align:start position:0% +interesting points that let me go back + + + align:start position:0% +interesting points that let me go back +to the first one which I made and he + + align:start position:0% +to the first one which I made and he + + + align:start position:0% +to the first one which I made and he +made this interesting distinction + + align:start position:0% +made this interesting distinction + + + align:start position:0% +made this interesting distinction +between the sculpture in the building + + align:start position:0% +between the sculpture in the building + + + align:start position:0% +between the sculpture in the building +and I think historically in the US the + + align:start position:0% +and I think historically in the US the + + + align:start position:0% +and I think historically in the US the +attitude is even though logic would say + + align:start position:0% +attitude is even though logic would say + + + align:start position:0% +attitude is even though logic would say +let's think about the building that + + align:start position:0% +let's think about the building that + + + align:start position:0% +let's think about the building that +might be the moment for government + + align:start position:0% +might be the moment for government + + + align:start position:0% +might be the moment for government +support historically + + align:start position:0% +support historically + + + align:start position:0% +support historically +the government support has been at the + + align:start position:0% +the government support has been at the + + + align:start position:0% +the government support has been at the +earlier stage at that sculpture moments + + align:start position:0% +earlier stage at that sculpture moments + + + align:start position:0% +earlier stage at that sculpture moments +before it turns into a building and + + align:start position:0% +before it turns into a building and + + + align:start position:0% +before it turns into a building and +that's pretty deep in our system so it's + + align:start position:0% +that's pretty deep in our system so it's + + + align:start position:0% +that's pretty deep in our system so it's +historically been okay for government to + + align:start position:0% +historically been okay for government to + + + align:start position:0% +historically been okay for government to +support basic research but when it gets + + align:start position:0% +support basic research but when it gets + + + align:start position:0% +support basic research but when it gets +within range of commercialization that + + align:start position:0% +within range of commercialization that + + + align:start position:0% +within range of commercialization that +would be a governmental interference in + + align:start position:0% +would be a governmental interference in + + + align:start position:0% +would be a governmental interference in +the marketplace so + + align:start position:0% +the marketplace so + + + align:start position:0% +the marketplace so +most countries don't do that but that + + align:start position:0% +most countries don't do that but that + + + align:start position:0% +most countries don't do that but that +historically has been a limit on the way + + align:start position:0% +historically has been a limit on the way + + + align:start position:0% +historically has been a limit on the way +in which we think about this stuff so + + align:start position:0% +in which we think about this stuff so + + + align:start position:0% +in which we think about this stuff so +when + + align:start position:0% +when + + + align:start position:0% +when +Nelson talks about whether there should + + align:start position:0% +Nelson talks about whether there should + + + align:start position:0% +Nelson talks about whether there should +be an explicit role for government in + + align:start position:0% +be an explicit role for government in + + + align:start position:0% +be an explicit role for government in +what he calls high-tech innovation on + + align:start position:0% +what he calls high-tech innovation on + + + align:start position:0% +what he calls high-tech innovation on +there was later stage work that + + align:start position:0% +there was later stage work that + + + align:start position:0% +there was later stage work that +controversial topic going to take on and + + align:start position:0% +controversial topic going to take on and + + + align:start position:0% +controversial topic going to take on and +when we talk about Charles Schulz later + + align:start position:0% +when we talk about Charles Schulz later + + + align:start position:0% +when we talk about Charles Schulz later +you know we'll see kind of the + + align:start position:0% +you know we'll see kind of the + + + align:start position:0% +you know we'll see kind of the +dimensions of this this big come further + + align:start position:0% +dimensions of this this big come further + + + align:start position:0% +dimensions of this this big come further +but what do you think is that what I'm + + align:start position:0% +but what do you think is that what I'm + + + align:start position:0% +but what do you think is that what I'm +curious is so there's two kinds of I + + align:start position:0% +curious is so there's two kinds of I + + + align:start position:0% +curious is so there's two kinds of I +guess that kind of sculpture innovation + + align:start position:0% +guess that kind of sculpture innovation + + + align:start position:0% +guess that kind of sculpture innovation +well the only one I can think of that + + align:start position:0% +well the only one I can think of that + + + align:start position:0% +well the only one I can think of that +was successful with government + + align:start position:0% +was successful with government + + + align:start position:0% +was successful with government +intervention was kind of like when + + align:start position:0% +intervention was kind of like when + + + align:start position:0% +intervention was kind of like when +they're making the atomic bomb is that + + align:start position:0% +they're making the atomic bomb is that + + + align:start position:0% +they're making the atomic bomb is that +was very much that we need a technology + + align:start position:0% +was very much that we need a technology + + + align:start position:0% +was very much that we need a technology +push but in other cases it's rigid for + + align:start position:0% +push but in other cases it's rigid for + + + align:start position:0% +push but in other cases it's rigid for +the Wright brothers I forget what the + + align:start position:0% +the Wright brothers I forget what the + + + align:start position:0% +the Wright brothers I forget what the +name of the person that the government + + align:start position:0% +name of the person that the government + + + align:start position:0% +name of the person that the government +was funding he was like the expert in + + align:start position:0% +was funding he was like the expert in + + + align:start position:0% +was funding he was like the expert in +aerodynamics at the time but because he + + align:start position:0% +aerodynamics at the time but because he + + + align:start position:0% +aerodynamics at the time but because he +put his equations didn't work out he + + align:start position:0% +put his equations didn't work out he + + + align:start position:0% +put his equations didn't work out he +couldn't he didn't do it + + align:start position:0% +couldn't he didn't do it + + + align:start position:0% +couldn't he didn't do it +all those aircraft landed in the + + align:start position:0% +all those aircraft landed in the + + + align:start position:0% +all those aircraft landed in the +Anacostia River yeah well but well the + + align:start position:0% +Anacostia River yeah well but well the + + + align:start position:0% +Anacostia River yeah well but well the +way I think about it they say an expert + + align:start position:0% +way I think about it they say an expert + + + align:start position:0% +way I think about it they say an expert +is an expert in a field that's already + + align:start position:0% +is an expert in a field that's already + + + align:start position:0% +is an expert in a field that's already +been created and a lot of time this + + align:start position:0% +been created and a lot of time this + + + align:start position:0% +been created and a lot of time this +innovator is not gonna look like an + + align:start position:0% +innovator is not gonna look like an + + + align:start position:0% +innovator is not gonna look like an +expert at all because the field has not + + align:start position:0% +expert at all because the field has not + + + align:start position:0% +expert at all because the field has not +been made like Edison you wouldn't you + + align:start position:0% +been made like Edison you wouldn't you + + + align:start position:0% +been made like Edison you wouldn't you +really wouldn't say he was like a genius + + align:start position:0% +really wouldn't say he was like a genius + + + align:start position:0% +really wouldn't say he was like a genius +in any field but he did figure out + + align:start position:0% +in any field but he did figure out + + + align:start position:0% +in any field but he did figure out +something and then he took it as far as + + align:start position:0% +something and then he took it as far as + + + align:start position:0% +something and then he took it as far as +you could go but and another distinction + + align:start position:0% +you could go but and another distinction + + + align:start position:0% +you could go but and another distinction +tubes that there's gonna be who that are + + align:start position:0% +tubes that there's gonna be who that are + + + align:start position:0% +tubes that there's gonna be who that are +gonna team up with them example with + + align:start position:0% +gonna team up with them example with + + + align:start position:0% +gonna team up with them example with +Edison is that gee II had a lot of + + align:start position:0% +Edison is that gee II had a lot of + + + align:start position:0% +Edison is that gee II had a lot of +issues with their transmission lines and + + align:start position:0% +issues with their transmission lines and + + + align:start position:0% +issues with their transmission lines and +it wasn't until they got this one + + align:start position:0% +it wasn't until they got this one + + + align:start position:0% +it wasn't until they got this one +I realize first name but it's lasting + + align:start position:0% +I realize first name but it's lasting + + + align:start position:0% +I realize first name but it's lasting +this Steinman's he's like it's very + + align:start position:0% +this Steinman's he's like it's very + + + align:start position:0% +this Steinman's he's like it's very +hunchback he's famous for like never + + align:start position:0% +hunchback he's famous for like never + + + align:start position:0% +hunchback he's famous for like never +being in pictures because it was just + + align:start position:0% +being in pictures because it was just + + + align:start position:0% +being in pictures because it was just +very much bad to make short but he came + + align:start position:0% +very much bad to make short but he came + + + align:start position:0% +very much bad to make short but he came +up with these equations and he figured + + align:start position:0% +up with these equations and he figured + + + align:start position:0% +up with these equations and he figured +out all the he saw up all the main + + align:start position:0% +out all the he saw up all the main + + + align:start position:0% +out all the he saw up all the main +problems with the technology + + align:start position:0% +problems with the technology + + + align:start position:0% +problems with the technology +so I definitely think there's probably + + align:start position:0% +so I definitely think there's probably + + + align:start position:0% +so I definitely think there's probably +more study I guess on that and like when + + align:start position:0% +more study I guess on that and like when + + + align:start position:0% +more study I guess on that and like when +was it over most successful than what + + align:start position:0% +was it over most successful than what + + + align:start position:0% +was it over most successful than what +their investments I know if they do that + + align:start position:0% +their investments I know if they do that + + + align:start position:0% +their investments I know if they do that +I don't really know how that works with + + align:start position:0% +I don't really know how that works with + + + align:start position:0% +I don't really know how that works with +innovation + + align:start position:0% +innovation + + + align:start position:0% +innovation +but in general be story you'll be an + + align:start position:0% +but in general be story you'll be an + + + align:start position:0% +but in general be story you'll be an +expert okay well in general VCS will + + align:start position:0% +expert okay well in general VCS will + + + align:start position:0% +expert okay well in general VCS will +look at their investments and then + + align:start position:0% +look at their investments and then + + + align:start position:0% +look at their investments and then +figure out why they won with their + + align:start position:0% +figure out why they won with their + + + align:start position:0% +figure out why they won with their +investment so that might be a good way + + align:start position:0% +investment so that might be a good way + + + align:start position:0% +investment so that might be a good way +of looking into it like in the history + + align:start position:0% +of looking into it like in the history + + + align:start position:0% +of looking into it like in the history +of the US when do we make investments + + align:start position:0% +of the US when do we make investments + + + align:start position:0% +of the US when do we make investments +and how do they pay off and also like + + align:start position:0% +and how do they pay off and also like + + + align:start position:0% +and how do they pay off and also like +what do we measure the success because + + align:start position:0% +what do we measure the success because + + + align:start position:0% +what do we measure the success because +it probably won't be economic returns + + align:start position:0% +it probably won't be economic returns + + + align:start position:0% +it probably won't be economic returns +because the nature of the problem but if + + align:start position:0% +because the nature of the problem but if + + + align:start position:0% +because the nature of the problem but if +you look at in terms of what development + + align:start position:0% +you look at in terms of what development + + + align:start position:0% +you look at in terms of what development +there's gonna be a lot of hidden + + align:start position:0% +there's gonna be a lot of hidden + + + align:start position:0% +there's gonna be a lot of hidden +variables that we don't account for I + + align:start position:0% +variables that we don't account for I + + + align:start position:0% +variables that we don't account for I +wouldn't shoot me to account for when we + + align:start position:0% +wouldn't shoot me to account for when we + + + align:start position:0% +wouldn't shoot me to account for when we +measure that success + + align:start position:0% +measure that success + + + align:start position:0% +measure that success +yeah I think once you hit on something + + align:start position:0% +yeah I think once you hit on something + + + align:start position:0% +yeah I think once you hit on something +which is like how does it go + + align:start position:0% + + + + align:start position:0% + +the only example on my app is SpaceX + + align:start position:0% +the only example on my app is SpaceX + + + align:start position:0% +the only example on my app is SpaceX +because they get a lot of support + + align:start position:0% +because they get a lot of support + + + align:start position:0% +because they get a lot of support +because that's just the way big + + align:start position:0% +because that's just the way big + + + align:start position:0% +because that's just the way big +transitions sort of out of the space + + align:start position:0% +transitions sort of out of the space + + + align:start position:0% +transitions sort of out of the space +race we have like a lot of + + align:start position:0% +race we have like a lot of + + + align:start position:0% +race we have like a lot of +infrastructure at NASA we like no longer + + align:start position:0% +infrastructure at NASA we like no longer + + + align:start position:0% +infrastructure at NASA we like no longer +wants to focus specifically sort of on + + align:start position:0% +wants to focus specifically sort of on + + + align:start position:0% +wants to focus specifically sort of on +space exploration in a way that might be + + align:start position:0% +space exploration in a way that might be + + + align:start position:0% +space exploration in a way that might be +sort of private commercially available + + align:start position:0% +sort of private commercially available + + + align:start position:0% +sort of private commercially available +but you have this sort of Technology + + align:start position:0% +but you have this sort of Technology + + + align:start position:0% +but you have this sort of Technology +spillover and all these resources exist + + align:start position:0% +spillover and all these resources exist + + + align:start position:0% +spillover and all these resources exist +in massive a long paths everywhere that + + align:start position:0% +in massive a long paths everywhere that + + + align:start position:0% +in massive a long paths everywhere that +they can't really you know take + + align:start position:0% +they can't really you know take + + + align:start position:0% +they can't really you know take +advantage of cuz it's not what they're + + align:start position:0% +advantage of cuz it's not what they're + + + align:start position:0% +advantage of cuz it's not what they're +but you have this infrastructure + + align:start position:0% +but you have this infrastructure + + + align:start position:0% +but you have this infrastructure +leftover I started sort of leasing it + + align:start position:0% +leftover I started sort of leasing it + + + align:start position:0% +leftover I started sort of leasing it +out to companies like SpaceX just sort + + align:start position:0% +out to companies like SpaceX just sort + + + align:start position:0% +out to companies like SpaceX just sort +of you launch demonstrations and things + + align:start position:0% +of you launch demonstrations and things + + + align:start position:0% +of you launch demonstrations and things +like that and so I think but that only + + align:start position:0% +like that and so I think but that only + + + align:start position:0% +like that and so I think but that only +comes I don't know exactly how that came + + align:start position:0% +comes I don't know exactly how that came + + + align:start position:0% +comes I don't know exactly how that came +about but I think you might be able to + + align:start position:0% +about but I think you might be able to + + + align:start position:0% +about but I think you might be able to +facilitate those roles where the + + align:start position:0% +facilitate those roles where the + + + align:start position:0% +facilitate those roles where the +government sort of has resources built + + align:start position:0% +government sort of has resources built + + + align:start position:0% +government sort of has resources built +up from sort of things previously and + + align:start position:0% +up from sort of things previously and + + + align:start position:0% +up from sort of things previously and +the industry met moving in a different + + align:start position:0% +the industry met moving in a different + + + align:start position:0% +the industry met moving in a different +direction and it might see more + + align:start position:0% +direction and it might see more + + + align:start position:0% +direction and it might see more +advantageous ways to kind of pass off + + align:start position:0% +advantageous ways to kind of pass off + + + align:start position:0% +advantageous ways to kind of pass off +use facilities and things like that sort + + align:start position:0% +use facilities and things like that sort + + + align:start position:0% +use facilities and things like that sort +of we have you know these launch pads + + align:start position:0% +of we have you know these launch pads + + + align:start position:0% +of we have you know these launch pads +that NASA was trying to get away from + + align:start position:0% +that NASA was trying to get away from + + + align:start position:0% +that NASA was trying to get away from +legacy of National Labs now which are + + align:start position:0% +legacy of National Labs now which are + + + align:start position:0% +legacy of National Labs now which are +traditionally more basic research but + + align:start position:0% +traditionally more basic research but + + + align:start position:0% +traditionally more basic research but +could be used to sort of bring in + + align:start position:0% +could be used to sort of bring in + + + align:start position:0% +could be used to sort of bring in +companies as sort of testing grounds for + + align:start position:0% +companies as sort of testing grounds for + + + align:start position:0% +companies as sort of testing grounds for +a lot of + + align:start position:0% + + + + align:start position:0% + +more useful anyone biotech using + + align:start position:0% +more useful anyone biotech using + + + align:start position:0% +more useful anyone biotech using +supercomputers that are children but + + align:start position:0% +supercomputers that are children but + + + align:start position:0% +supercomputers that are children but +it's important to kind of identify that + + align:start position:0% +it's important to kind of identify that + + + align:start position:0% +it's important to kind of identify that +point which technologies might be a + + align:start position:0% +point which technologies might be a + + + align:start position:0% +point which technologies might be a +little bit more receptive to sort of + + align:start position:0% +little bit more receptive to sort of + + + align:start position:0% +little bit more receptive to sort of +that breaks me out and I think it comes + + align:start position:0% +that breaks me out and I think it comes + + + align:start position:0% +that breaks me out and I think it comes +from maybe with a little readings where + + align:start position:0% +from maybe with a little readings where + + + align:start position:0% +from maybe with a little readings where +it's like you have to identify + + align:start position:0% +it's like you have to identify + + + align:start position:0% +it's like you have to identify +who's in the market and what are their + + align:start position:0% +who's in the market and what are their + + + align:start position:0% +who's in the market and what are their +sort of needs and that conversation + + align:start position:0% +sort of needs and that conversation + + + align:start position:0% +sort of needs and that conversation +doesn't really happen because they're + + align:start position:0% +doesn't really happen because they're + + + align:start position:0% +doesn't really happen because they're +medicine to sort of choose winners but I + + align:start position:0% +medicine to sort of choose winners but I + + + align:start position:0% +medicine to sort of choose winners but I +think at some point it's going to be + + align:start position:0% +think at some point it's going to be + + + align:start position:0% +think at some point it's going to be +necessary to kind of consult the + + align:start position:0% +necessary to kind of consult the + + + align:start position:0% +necessary to kind of consult the +necessary or consult like I'm going to + + align:start position:0% +necessary or consult like I'm going to + + + align:start position:0% +necessary or consult like I'm going to +use the word experts here you know you + + align:start position:0% +use the word experts here you know you + + + align:start position:0% +use the word experts here you know you +don't really know who they're bizarre + + align:start position:0% +don't really know who they're bizarre + + + align:start position:0% +don't really know who they're bizarre +and so you kind of bring the Wright + + align:start position:0% +and so you kind of bring the Wright + + + align:start position:0% +and so you kind of bring the Wright +brothers and they make you know I jump + + align:start position:0% +brothers and they make you know I jump + + + align:start position:0% +brothers and they make you know I jump +relieved but I think like it could have + + align:start position:0% +relieved but I think like it could have + + + align:start position:0% +relieved but I think like it could have +been facilitated if they had brought + + align:start position:0% +been facilitated if they had brought + + + align:start position:0% +been facilitated if they had brought +this guy in and found they found that + + align:start position:0% +this guy in and found they found that + + + align:start position:0% +this guy in and found they found that +maybe like all of this experiment + + align:start position:0% +maybe like all of this experiment + + + align:start position:0% +maybe like all of this experiment +passionately out across the river so by + + align:start position:0% +passionately out across the river so by + + + align:start position:0% +passionately out across the river so by +the government of initially okay these + + align:start position:0% +the government of initially okay these + + + align:start position:0% +the government of initially okay these +expression we need + + align:start position:0% +expression we need + + + align:start position:0% +expression we need +and so I think it's this + + align:start position:0% +and so I think it's this + + + align:start position:0% +and so I think it's this +the emphasis has to be on sort of these + + align:start position:0% +the emphasis has to be on sort of these + + + align:start position:0% +the emphasis has to be on sort of these +public-private partnerships facilitation + + align:start position:0% +public-private partnerships facilitation + + + align:start position:0% +public-private partnerships facilitation +owes a little bit maybe a little bit + + align:start position:0% +owes a little bit maybe a little bit + + + align:start position:0% +owes a little bit maybe a little bit +earlier and bringing inside of these + + align:start position:0% +earlier and bringing inside of these + + + align:start position:0% +earlier and bringing inside of these +ministry experts who are shifting gears + + align:start position:0% +ministry experts who are shifting gears + + + align:start position:0% +ministry experts who are shifting gears +to new directions to figure out what is + + align:start position:0% +to new directions to figure out what is + + + align:start position:0% +to new directions to figure out what is +the best role because it's been a very + + align:start position:0% +the best role because it's been a very + + + align:start position:0% +the best role because it's been a very +sector by sector because obviously + + align:start position:0% +sector by sector because obviously + + + align:start position:0% +sector by sector because obviously +maybe the Wright brothers much good if + + align:start position:0% +maybe the Wright brothers much good if + + + align:start position:0% +maybe the Wright brothers much good if +they had access + + align:start position:0% +they had access + + + align:start position:0% +they had access +but might be + + align:start position:0% + + + + align:start position:0% + +waiting zones are like large areas of + + align:start position:0% +waiting zones are like large areas of + + + align:start position:0% +waiting zones are like large areas of +space + + align:start position:0% + + + + align:start position:0% + +but kind of going back to your point in + + align:start position:0% +but kind of going back to your point in + + + align:start position:0% +but kind of going back to your point in +playing devil's advocate there + + align:start position:0% +playing devil's advocate there + + + align:start position:0% +playing devil's advocate there +if we're not funding the sculptors + + align:start position:0% +if we're not funding the sculptors + + + align:start position:0% +if we're not funding the sculptors +originally do we have concerns that + + align:start position:0% +originally do we have concerns that + + + align:start position:0% +originally do we have concerns that +there won't be enough that are taking + + align:start position:0% +there won't be enough that are taking + + + align:start position:0% +there won't be enough that are taking +the risk on their own to make the first + + align:start position:0% +the risk on their own to make the first + + + align:start position:0% +the risk on their own to make the first +steps before commercialization like do + + align:start position:0% +steps before commercialization like do + + + align:start position:0% +steps before commercialization like do +we need to consider that balance a + + align:start position:0% +we need to consider that balance a + + + align:start position:0% +we need to consider that balance a +little bit I think that's an interesting + + align:start position:0% +little bit I think that's an interesting + + + align:start position:0% +little bit I think that's an interesting +question in terms of if the Wright + + align:start position:0% +question in terms of if the Wright + + + align:start position:0% +question in terms of if the Wright +brothers were alive today will really be + + align:start position:0% +brothers were alive today will really be + + + align:start position:0% +brothers were alive today will really be +able to get any kind of government + + align:start position:0% +able to get any kind of government + + + align:start position:0% +able to get any kind of government +support right and then that and then you + + align:start position:0% +support right and then that and then you + + + align:start position:0% +support right and then that and then you +can think about like well what kind of + + align:start position:0% +can think about like well what kind of + + + align:start position:0% +can think about like well what kind of +support or how should the government be + + align:start position:0% +support or how should the government be + + + align:start position:0% +support or how should the government be +structured to support that kind of + + align:start position:0% +structured to support that kind of + + + align:start position:0% +structured to support that kind of +interior + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so I'm gonna ask everybody to identify + + align:start position:0% +so I'm gonna ask everybody to identify + + + align:start position:0% +so I'm gonna ask everybody to identify +themselves because well myself + + align:start position:0% +themselves because well myself + + + align:start position:0% +themselves because well myself +to just throw out your first name before + + align:start position:0% +to just throw out your first name before + + + align:start position:0% +to just throw out your first name before +you start so we all get + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +optimizing resources when it's not + + align:start position:0% +optimizing resources when it's not + + + align:start position:0% +optimizing resources when it's not +really nervous to use them all the time + + align:start position:0% +really nervous to use them all the time + + + align:start position:0% +really nervous to use them all the time +but these announced + + align:start position:0% +but these announced + + + align:start position:0% +but these announced +but I think they do still sort of choose + + align:start position:0% +but I think they do still sort of choose + + + align:start position:0% +but I think they do still sort of choose +winners and in + + align:start position:0% +winners and in + + + align:start position:0% +winners and in +Wright brothers in the world it's like + + align:start position:0% +Wright brothers in the world it's like + + + align:start position:0% +Wright brothers in the world it's like +there's a lot of + + align:start position:0% +there's a lot of + + + align:start position:0% +there's a lot of +put out like a big for you know maybe a + + align:start position:0% +put out like a big for you know maybe a + + + align:start position:0% +put out like a big for you know maybe a +certain spacecraft bus or something and + + align:start position:0% +certain spacecraft bus or something and + + + align:start position:0% +certain spacecraft bus or something and +maybe Lockheed and + + align:start position:0% +maybe Lockheed and + + + align:start position:0% +maybe Lockheed and +like a bunch of different companies + + align:start position:0% +like a bunch of different companies + + + align:start position:0% +like a bunch of different companies +could submit proposals for how they + + align:start position:0% +could submit proposals for how they + + + align:start position:0% +could submit proposals for how they +might fulfill those design requirements + + align:start position:0% +might fulfill those design requirements + + + align:start position:0% +might fulfill those design requirements +cheapest and like the most + + align:start position:0% +cheapest and like the most + + + align:start position:0% +cheapest and like the most +technologically successful so every bit + + align:start position:0% +technologically successful so every bit + + + align:start position:0% +technologically successful so every bit +I might not be choosing winners but is + + align:start position:0% +I might not be choosing winners but is + + + align:start position:0% +I might not be choosing winners but is +sort of one way that the government can + + align:start position:0% +sort of one way that the government can + + + align:start position:0% +sort of one way that the government can +support + + align:start position:0% +support + + + align:start position:0% +support +innovation I + + align:start position:0% + + + + align:start position:0% + +think Chris I think where government has + + align:start position:0% +think Chris I think where government has + + + align:start position:0% +think Chris I think where government has +a really important role is probably + + align:start position:0% +a really important role is probably + + + align:start position:0% +a really important role is probably +galvanizing support and especially like + + align:start position:0% +galvanizing support and especially like + + + align:start position:0% +galvanizing support and especially like +initial funding for potentially riskier + + align:start position:0% +initial funding for potentially riskier + + + align:start position:0% +initial funding for potentially riskier +kind of ventures at earlier stages for + + align:start position:0% +kind of ventures at earlier stages for + + + align:start position:0% +kind of ventures at earlier stages for +example I know in like biotech + + align:start position:0% +example I know in like biotech + + + align:start position:0% +example I know in like biotech +for example cystic fibrosis that was a + + align:start position:0% +for example cystic fibrosis that was a + + + align:start position:0% +for example cystic fibrosis that was a +huge push by the government in some + + align:start position:0% +huge push by the government in some + + + align:start position:0% +huge push by the government in some +pretty national groups to get research + + align:start position:0% +pretty national groups to get research + + + align:start position:0% +pretty national groups to get research +on the ground and really focus and it + + align:start position:0% +on the ground and really focus and it + + + align:start position:0% +on the ground and really focus and it +took like ten or twelve years one + + align:start position:0% +took like ten or twelve years one + + + align:start position:0% +took like ten or twelve years one +hundreds of millions of dollars but they + + align:start position:0% +hundreds of millions of dollars but they + + + align:start position:0% +hundreds of millions of dollars but they +finally came up with a drug Hawaii Co + + align:start position:0% +finally came up with a drug Hawaii Co + + + align:start position:0% +finally came up with a drug Hawaii Co +which is produced iceberg tech so like + + align:start position:0% +which is produced iceberg tech so like + + + align:start position:0% +which is produced iceberg tech so like +that kind of initiative I think is + + align:start position:0% +that kind of initiative I think is + + + align:start position:0% +that kind of initiative I think is +really useful and like national policy + + align:start position:0% +really useful and like national policy + + + align:start position:0% +really useful and like national policy +is like for example I know like cancer + + align:start position:0% +is like for example I know like cancer + + + align:start position:0% +is like for example I know like cancer +moon shoot or something like that that + + align:start position:0% +moon shoot or something like that that + + + align:start position:0% +moon shoot or something like that that +said look at presidents and like places + + align:start position:0% +said look at presidents and like places + + + align:start position:0% +said look at presidents and like places +importance on like development of these + + align:start position:0% +importance on like development of these + + + align:start position:0% +importance on like development of these +kind of drugs and kind of creates some + + align:start position:0% +kind of drugs and kind of creates some + + + align:start position:0% +kind of drugs and kind of creates some +sort of importance and path for them to + + align:start position:0% +sort of importance and path for them to + + + align:start position:0% +sort of importance and path for them to +incentivize development throughout oh no + + align:start position:0% +incentivize development throughout oh no + + + align:start position:0% +incentivize development throughout oh no +like + + align:start position:0% +like + + + align:start position:0% +like +expedited patent approval and kind of + + align:start position:0% +expedited patent approval and kind of + + + align:start position:0% +expedited patent approval and kind of +maybe tax breaks or support for the R&D + + align:start position:0% +maybe tax breaks or support for the R&D + + + align:start position:0% +maybe tax breaks or support for the R&D +process I think those can really help + + align:start position:0% +process I think those can really help + + + align:start position:0% +process I think those can really help +guide technology development as well as + + align:start position:0% +guide technology development as well as + + + align:start position:0% +guide technology development as well as +you know innovation especially as firms + + align:start position:0% +you know innovation especially as firms + + + align:start position:0% +you know innovation especially as firms +are looking to you know what to do next + + align:start position:0% +are looking to you know what to do next + + + align:start position:0% +are looking to you know what to do next +but to kind of put their money + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +interesting + + align:start position:0% + + + + align:start position:0% + +because I think cooperation and + + align:start position:0% +because I think cooperation and + + + align:start position:0% +because I think cooperation and +inclusion from the design research + + align:start position:0% +inclusion from the design research + + + align:start position:0% +inclusion from the design research +standpoint and incredibly important in + + align:start position:0% +standpoint and incredibly important in + + + align:start position:0% +standpoint and incredibly important in +identifying the competitive and dynamic + + align:start position:0% +identifying the competitive and dynamic + + + align:start position:0% +identifying the competitive and dynamic +and static advantages and I see this + + align:start position:0% +and static advantages and I see this + + + align:start position:0% +and static advantages and I see this +particularly being an issue in + + align:start position:0% +particularly being an issue in + + + align:start position:0% +particularly being an issue in +manufacturing with robotics right the + + align:start position:0% +manufacturing with robotics right the + + + align:start position:0% +manufacturing with robotics right the +United States is not invested as much + + align:start position:0% +United States is not invested as much + + + align:start position:0% +United States is not invested as much +number of audience in the search + + align:start position:0% +number of audience in the search + + + align:start position:0% +number of audience in the search +leader in the nights you know that and + + align:start position:0% +leader in the nights you know that and + + + align:start position:0% +leader in the nights you know that and +it's really fascinating to think about + + align:start position:0% +it's really fascinating to think about + + + align:start position:0% +it's really fascinating to think about +the ways in which the United States is + + align:start position:0% +the ways in which the United States is + + + align:start position:0% +the ways in which the United States is +not really cooperating with the United + + align:start position:0% +not really cooperating with the United + + + align:start position:0% +not really cooperating with the United +States + + align:start position:0% +States + + + align:start position:0% +States +to sort of dominate international + + align:start position:0% +to sort of dominate international + + + align:start position:0% +to sort of dominate international +markets as well as domestic markets + + align:start position:0% +markets as well as domestic markets + + + align:start position:0% +markets as well as domestic markets +right so that corporation is really + + align:start position:0% +right so that corporation is really + + + align:start position:0% +right so that corporation is really +important and it's not really something + + align:start position:0% +important and it's not really something + + + align:start position:0% +important and it's not really something +that I solo Romer and Elsa + + align:start position:0% + + + + align:start position:0% + +so great discussion so far you're really + + align:start position:0% +so great discussion so far you're really + + + align:start position:0% +so great discussion so far you're really +driving and I think to get at best + + align:start position:0% +driving and I think to get at best + + + align:start position:0% +driving and I think to get at best +underlying point + + align:start position:0% +underlying point + + + align:start position:0% +underlying point +which is you know what is the + + align:start position:0% +which is you know what is the + + + align:start position:0% +which is you know what is the +governmental role going to be in this + + align:start position:0% +governmental role going to be in this + + + align:start position:0% +governmental role going to be in this +mix where do you draw the lines how far + + align:start position:0% +mix where do you draw the lines how far + + + align:start position:0% +mix where do you draw the lines how far +should extend down the innovation + + align:start position:0% +should extend down the innovation + + + align:start position:0% +should extend down the innovation +pipeline what are the different + + align:start position:0% +pipeline what are the different + + + align:start position:0% +pipeline what are the different +controversies so you all have laid out I + + align:start position:0% +controversies so you all have laid out I + + + align:start position:0% +controversies so you all have laid out I +think really nicely all set of + + align:start position:0% +think really nicely all set of + + + align:start position:0% +think really nicely all set of +examples about how we start that debate + + align:start position:0% +examples about how we start that debate + + + align:start position:0% +examples about how we start that debate +but that'll be a central kind of issue + + align:start position:0% +but that'll be a central kind of issue + + + align:start position:0% +but that'll be a central kind of issue +and the class as we go along so Beth do + + align:start position:0% +and the class as we go along so Beth do + + + align:start position:0% +and the class as we go along so Beth do +you want to give us a couple some + + align:start position:0% +you want to give us a couple some + + + align:start position:0% +you want to give us a couple some +closing thoughts here + + align:start position:0% + + + + align:start position:0% + +so I guess we have been viewing this in + + align:start position:0% +so I guess we have been viewing this in + + + align:start position:0% +so I guess we have been viewing this in +a very much like us context and that's + + align:start position:0% +a very much like us context and that's + + + align:start position:0% +a very much like us context and that's +obviously what we're most familiar with + + align:start position:0% +obviously what we're most familiar with + + + align:start position:0% +obviously what we're most familiar with +but it is very important to think about + + align:start position:0% +but it is very important to think about + + + align:start position:0% +but it is very important to think about +like what actions other countries are + + align:start position:0% +like what actions other countries are + + + align:start position:0% +like what actions other countries are +taking compared to what we're doing and + + align:start position:0% +taking compared to what we're doing and + + + align:start position:0% +taking compared to what we're doing and +how we could learn from them and best + + align:start position:0% +how we could learn from them and best + + + align:start position:0% +how we could learn from them and best +compete with them + + align:start position:0% +compete with them + + + align:start position:0% +compete with them +if the American system tends to lean a + + align:start position:0% +if the American system tends to lean a + + + align:start position:0% +if the American system tends to lean a +little bit more towards the kind of + + align:start position:0% +little bit more towards the kind of + + + align:start position:0% +little bit more towards the kind of +capitalist free-market once these + + align:start position:0% +capitalist free-market once these + + + align:start position:0% +capitalist free-market once these +companies emerge it is seen as kind of + + align:start position:0% +companies emerge it is seen as kind of + + + align:start position:0% +companies emerge it is seen as kind of +unfair to support certain industries and + + align:start position:0% +unfair to support certain industries and + + + align:start position:0% +unfair to support certain industries and +certain companies well in other + + align:start position:0% +certain companies well in other + + + align:start position:0% +certain companies well in other +countries that's more acceptable and it + + align:start position:0% +countries that's more acceptable and it + + + align:start position:0% +countries that's more acceptable and it +is worthwhile to think about is that + + align:start position:0% +is worthwhile to think about is that + + + align:start position:0% +is worthwhile to think about is that +something that we would want to move + + align:start position:0% +something that we would want to move + + + align:start position:0% +something that we would want to move +towards or is it better to kind of let + + align:start position:0% +towards or is it better to kind of let + + + align:start position:0% +towards or is it better to kind of let +these firms fight it out on their own + + align:start position:0% +these firms fight it out on their own + + + align:start position:0% +these firms fight it out on their own +and + + align:start position:0% +and + + + align:start position:0% +and +as far as the relationship between + + align:start position:0% +as far as the relationship between + + + align:start position:0% +as far as the relationship between +national interests and international + + align:start position:0% +national interests and international + + + align:start position:0% +national interests and international +partnerships kind of one like closing + + align:start position:0% +partnerships kind of one like closing + + + align:start position:0% +partnerships kind of one like closing +question to consider is how much the + + align:start position:0% +question to consider is how much the + + + align:start position:0% +question to consider is how much the +government's be intervening and + + align:start position:0% +government's be intervening and + + + align:start position:0% +government's be intervening and +protecting their companies versus + + align:start position:0% +protecting their companies versus + + + align:start position:0% +protecting their companies versus +if that limits them from being able to + + align:start position:0% +if that limits them from being able to + + + align:start position:0% +if that limits them from being able to +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +function on the international market + + align:start position:0% +function on the international market + + + align:start position:0% +function on the international market +such as like terrorists and other things + + align:start position:0% +such as like terrorists and other things + + + align:start position:0% +such as like terrorists and other things +that are protecting industries that's + + align:start position:0% +that are protecting industries that's + + + align:start position:0% +that are protecting industries that's +something that governments should be + + align:start position:0% +something that governments should be + + + align:start position:0% +something that governments should be +able to do that fair if other countries + + align:start position:0% +able to do that fair if other countries + + + align:start position:0% +able to do that fair if other countries +don't have those policies in place and + + align:start position:0% +don't have those policies in place and + + + align:start position:0% +don't have those policies in place and +are we limiting which technologies are + + align:start position:0% +are we limiting which technologies are + + + align:start position:0% +are we limiting which technologies are +successful on the market by protecting + + align:start position:0% +successful on the market by protecting + + + align:start position:0% +successful on the market by protecting +ones that might not be as productive + + align:start position:0% +ones that might not be as productive + + + align:start position:0% +ones that might not be as productive +great great closing thoughts + + align:start position:0% + + + + align:start position:0% + +the discussion leader system is working + + align:start position:0% +the discussion leader system is working + + + align:start position:0% +the discussion leader system is working +thank you for getting us off to a good + + align:start position:0% +thank you for getting us off to a good + + + align:start position:0% +thank you for getting us off to a good +start + + align:start position:0% +start + + + align:start position:0% +start +let me do some just some quick summaries + + align:start position:0% +let me do some just some quick summaries + + + align:start position:0% +let me do some just some quick summaries +and then lead into an the Atkins and + + align:start position:0% +and then lead into an the Atkins and + + + align:start position:0% +and then lead into an the Atkins and +material and death will come back to you + + align:start position:0% +material and death will come back to you + + + align:start position:0% +material and death will come back to you +in a minute + + align:start position:0% +in a minute + + + align:start position:0% +in a minute +so in last week's class we talked about + + align:start position:0% +so in last week's class we talked about + + + align:start position:0% +so in last week's class we talked about +these direct innovation factors in other + + align:start position:0% +these direct innovation factors in other + + + align:start position:0% +these direct innovation factors in other +words these these factors that you + + align:start position:0% +words these these factors that you + + + align:start position:0% +words these these factors that you +really can't do without if you want to + + align:start position:0% +really can't do without if you want to + + + align:start position:0% +really can't do without if you want to +have a strong innovation system and the + + align:start position:0% +have a strong innovation system and the + + + align:start position:0% +have a strong innovation system and the +purpose that would be to drive economic + + align:start position:0% +purpose that would be to drive economic + + + align:start position:0% +purpose that would be to drive economic +growth to grow economic well-being in + + align:start position:0% +growth to grow economic well-being in + + + align:start position:0% +growth to grow economic well-being in +your society in your economy so + + align:start position:0% +your society in your economy so + + + align:start position:0% +your society in your economy so +government plays a role in some of these + + align:start position:0% +government plays a role in some of these + + + align:start position:0% +government plays a role in some of these +direct factors it supports + + align:start position:0% +direct factors it supports + + + align:start position:0% +direct factors it supports +almost all of university R&D it supports + + align:start position:0% +almost all of university R&D it supports + + + align:start position:0% +almost all of university R&D it supports +governmental laboratories it provides + + align:start position:0% +governmental laboratories it provides + + + align:start position:0% +governmental laboratories it provides +lots of support for the education system + + align:start position:0% +lots of support for the education system + + + align:start position:0% +lots of support for the education system +and then it provides + + align:start position:0% +and then it provides + + + align:start position:0% +and then it provides +support for + + align:start position:0% +support for + + + align:start position:0% +support for +industry R&D in some areas particularly + + align:start position:0% +industry R&D in some areas particularly + + + align:start position:0% +industry R&D in some areas particularly +defense at some extent in agriculture so + + align:start position:0% +defense at some extent in agriculture so + + + align:start position:0% +defense at some extent in agriculture so +those are kind of those are if + + align:start position:0% +those are kind of those are if + + + align:start position:0% +those are kind of those are if +the solo + + align:start position:0% +the solo + + + align:start position:0% +the solo +factor of + + align:start position:0% +factor of + + + align:start position:0% +factor of +doing R&D is a core factor then you can + + align:start position:0% +doing R&D is a core factor then you can + + + align:start position:0% +doing R&D is a core factor then you can +see the governmental role here but + + align:start position:0% +see the governmental role here but + + + align:start position:0% +see the governmental role here but +there's also a private sector an + + align:start position:0% +there's also a private sector an + + + align:start position:0% +there's also a private sector an +industry role on that + + align:start position:0% +industry role on that + + + align:start position:0% +industry role on that +initial factor of course there's + + align:start position:0% +initial factor of course there's + + + align:start position:0% +initial factor of course there's +industry Rd which as we discussed is + + align:start position:0% +industry Rd which as we discussed is + + + align:start position:0% +industry Rd which as we discussed is +predominantly D + + align:start position:0% +predominantly D + + + align:start position:0% +predominantly D +but that's what takes you through the + + align:start position:0% +but that's what takes you through the + + + align:start position:0% +but that's what takes you through the +prototyping and engineering and + + align:start position:0% +prototyping and engineering and + + + align:start position:0% +prototyping and engineering and +production stages and then industry + + align:start position:0% +production stages and then industry + + + align:start position:0% +production stages and then industry +provides the dominant role in training + + align:start position:0% + + + + align:start position:0% + +okay so those are + + align:start position:0% +okay so those are + + + align:start position:0% +okay so those are +direct solo Roemer factors then + + align:start position:0% +direct solo Roemer factors then + + + align:start position:0% +direct solo Roemer factors then +that are tied to industry and tied to + + align:start position:0% +that are tied to industry and tied to + + + align:start position:0% +that are tied to industry and tied to +the private sector but then there is a + + align:start position:0% +the private sector but then there is a + + + align:start position:0% +the private sector but then there is a +raft + + align:start position:0% +raft + + + align:start position:0% +raft +of + + align:start position:0% +of + + + align:start position:0% +of +indirect or we could call them implicit + + align:start position:0% +indirect or we could call them implicit + + + align:start position:0% +indirect or we could call them implicit +innovation factors + + align:start position:0% +innovation factors + + + align:start position:0% +innovation factors +so if Nelson is right that there's an + + align:start position:0% +so if Nelson is right that there's an + + + align:start position:0% +so if Nelson is right that there's an +innovation ecosystem then there's a lot + + align:start position:0% +innovation ecosystem then there's a lot + + + align:start position:0% +innovation ecosystem then there's a lot +of pieces in that complex system and + + align:start position:0% +of pieces in that complex system and + + + align:start position:0% +of pieces in that complex system and +government is supplying some of those + + align:start position:0% +government is supplying some of those + + + align:start position:0% +government is supplying some of those +pieces that have a role in the + + align:start position:0% +pieces that have a role in the + + + align:start position:0% +pieces that have a role in the +innovation process but are not as direct + + align:start position:0% +innovation process but are not as direct + + + align:start position:0% +innovation process but are not as direct +as the first thing we talked about + + align:start position:0% +as the first thing we talked about + + + align:start position:0% +as the first thing we talked about +so government is providing + + align:start position:0% +so government is providing + + + align:start position:0% +so government is providing +fiscal tax monetary policy is providing + + align:start position:0% +fiscal tax monetary policy is providing + + + align:start position:0% +fiscal tax monetary policy is providing +trade policy technology standards + + align:start position:0% +trade policy technology standards + + + align:start position:0% +trade policy technology standards +technology transfer policies it's + + align:start position:0% +technology transfer policies it's + + + align:start position:0% +technology transfer policies it's +providing government procurement which + + align:start position:0% +providing government procurement which + + + align:start position:0% +providing government procurement which +buys a lot of technology particularly in + + align:start position:0% +buys a lot of technology particularly in + + + align:start position:0% +buys a lot of technology particularly in +defense it sets up the intellectual + + align:start position:0% +defense it sets up the intellectual + + + align:start position:0% +defense it sets up the intellectual +property system the whole legal + + align:start position:0% +property system the whole legal + + + align:start position:0% +property system the whole legal +contracting liability system + + align:start position:0% +contracting liability system + + + align:start position:0% +contracting liability system +the regulatory system in many many areas + + align:start position:0% +the regulatory system in many many areas + + + align:start position:0% +the regulatory system in many many areas +accounting standards export controls + + align:start position:0% +accounting standards export controls + + + align:start position:0% +accounting standards export controls +these all will have an effect on the + + align:start position:0% +these all will have an effect on the + + + align:start position:0% +these all will have an effect on the +innovation system and your ability to + + align:start position:0% +innovation system and your ability to + + + align:start position:0% +innovation system and your ability to +innovate + + align:start position:0% + + + + align:start position:0% + +but then there are these indirect + + align:start position:0% +but then there are these indirect + + + align:start position:0% +but then there are these indirect +factors that are is less critical than + + align:start position:0% +factors that are is less critical than + + + align:start position:0% +factors that are is less critical than +the two we've talked about but + + align:start position:0% +the two we've talked about but + + + align:start position:0% +the two we've talked about but +nonetheless part of that system right so + + align:start position:0% +nonetheless part of that system right so + + + align:start position:0% +nonetheless part of that system right so +the private sector sets some really + + align:start position:0% +the private sector sets some really + + + align:start position:0% +the private sector sets some really +important ones that includes investment + + align:start position:0% +important ones that includes investment + + + align:start position:0% +important ones that includes investment +capital which can be angel or venture or + + align:start position:0% +capital which can be angel or venture or + + + align:start position:0% +capital which can be angel or venture or +IPO or equity or lending markets is a + + align:start position:0% +IPO or equity or lending markets is a + + + align:start position:0% +IPO or equity or lending markets is a +private sector function obviously + + align:start position:0% +private sector function obviously + + + align:start position:0% +private sector function obviously +management and management organization + + align:start position:0% +management and management organization + + + align:start position:0% +management and management organization +is really a private sector function in + + align:start position:0% +is really a private sector function in + + + align:start position:0% +is really a private sector function in +our system the whole reward system the + + align:start position:0% +our system the whole reward system the + + + align:start position:0% +our system the whole reward system the +compensation system for talent is + + align:start position:0% +compensation system for talent is + + + align:start position:0% +compensation system for talent is +largely a private sector set so the + + align:start position:0% +largely a private sector set so the + + + align:start position:0% +largely a private sector set so the +private sector plays a huge role too and + + align:start position:0% +private sector plays a huge role too and + + + align:start position:0% +private sector plays a huge role too and +this complex ecosystem mix so the + + align:start position:0% +this complex ecosystem mix so the + + + align:start position:0% +this complex ecosystem mix so the +picture I want you to have is of a + + align:start position:0% +picture I want you to have is of a + + + align:start position:0% +picture I want you to have is of a +complex innovation + + align:start position:0% +complex innovation + + + align:start position:0% +complex innovation +system there's direct factors and now + + align:start position:0% +system there's direct factors and now + + + align:start position:0% +system there's direct factors and now +we've talked about if we include Nelson + + align:start position:0% +we've talked about if we include Nelson + + + align:start position:0% +we've talked about if we include Nelson +we've talked about three + + align:start position:0% +we've talked about three + + + align:start position:0% +we've talked about three +but there's a whole mix of other stuff + + align:start position:0% +but there's a whole mix of other stuff + + + align:start position:0% +but there's a whole mix of other stuff +there and you want to get as many of + + align:start position:0% +there and you want to get as many of + + + align:start position:0% +there and you want to get as many of +those right in your innovation system as + + align:start position:0% +those right in your innovation system as + + + align:start position:0% +those right in your innovation system as +you can to have a strong functioning + + align:start position:0% +you can to have a strong functioning + + + align:start position:0% +you can to have a strong functioning +innovation system so it's not only the + + align:start position:0% +innovation system so it's not only the + + + align:start position:0% +innovation system so it's not only the +actors right you've also got it to take + + align:start position:0% +actors right you've also got it to take + + + align:start position:0% +actors right you've also got it to take +into account this larger system as well + + align:start position:0% +into account this larger system as well + + + align:start position:0% +into account this larger system as well +and + + align:start position:0% +and + + + align:start position:0% +and +you know we'll get in in a few minutes + + align:start position:0% +you know we'll get in in a few minutes + + + align:start position:0% +you know we'll get in in a few minutes +into some of the indirect factors and + + align:start position:0% +into some of the indirect factors and + + + align:start position:0% +into some of the indirect factors and +how to look at those but first we're + + align:start position:0% +how to look at those but first we're + + + align:start position:0% +how to look at those but first we're +gonna do innovation wave theory that's + + align:start position:0% +gonna do innovation wave theory that's + + + align:start position:0% +gonna do innovation wave theory that's +Rob Atkinson who's head of iti F a think + + align:start position:0% +Rob Atkinson who's head of iti F a think + + + align:start position:0% +Rob Atkinson who's head of iti F a think +tank in Washington + + align:start position:0% +tank in Washington + + + align:start position:0% +tank in Washington +we talked about and I drew a scribble + + align:start position:0% +we talked about and I drew a scribble + + + align:start position:0% +we talked about and I drew a scribble +last week on the blackboard but this is + + align:start position:0% +last week on the blackboard but this is + + + align:start position:0% +last week on the blackboard but this is +a better rendition of it we talked you + + align:start position:0% +a better rendition of it we talked you + + + align:start position:0% +a better rendition of it we talked you +know what is an innovation wave look + + align:start position:0% +know what is an innovation wave look + + + align:start position:0% +know what is an innovation wave look +like and just to recap from our + + align:start position:0% +like and just to recap from our + + + align:start position:0% +like and just to recap from our +discussion last week + + align:start position:0% +discussion last week + + + align:start position:0% +discussion last week +there's a long build-up and that can be + + align:start position:0% +there's a long build-up and that can be + + + align:start position:0% +there's a long build-up and that can be +15-20 years it can be longer right and + + align:start position:0% +15-20 years it can be longer right and + + + align:start position:0% +15-20 years it can be longer right and +then at some point it hits a moment work + + align:start position:0% +then at some point it hits a moment work + + + align:start position:0% +then at some point it hits a moment work +and start to scale up pretty quickly and + + align:start position:0% +and start to scale up pretty quickly and + + + align:start position:0% +and start to scale up pretty quickly and +spread into the society and economy so + + align:start position:0% +spread into the society and economy so + + + align:start position:0% +spread into the society and economy so +there is a fast growth period here maybe + + align:start position:0% +there is a fast growth period here maybe + + + align:start position:0% +there is a fast growth period here maybe +that's a decade all right + + align:start position:0% +that's a decade all right + + + align:start position:0% +that's a decade all right +then there's a period of more stay but + + align:start position:0% +then there's a period of more stay but + + + align:start position:0% +then there's a period of more stay but +there's always a bubble and then there's + + align:start position:0% +there's always a bubble and then there's + + + align:start position:0% +there's always a bubble and then there's +a period of more stable growth + + align:start position:0% +a period of more stable growth + + + align:start position:0% +a period of more stable growth +eventually and maybe that's 20 years + + align:start position:0% +eventually and maybe that's 20 years + + + align:start position:0% +eventually and maybe that's 20 years +maybe that's more then eventually you + + align:start position:0% +maybe that's more then eventually you + + + align:start position:0% +maybe that's more then eventually you +reached kind of technological maturity + + align:start position:0% +reached kind of technological maturity + + + align:start position:0% +reached kind of technological maturity +right so the IT wave the one you all are + + align:start position:0% +right so the IT wave the one you all are + + + align:start position:0% +right so the IT wave the one you all are +most familiar with that's still ongoing + + align:start position:0% +most familiar with that's still ongoing + + + align:start position:0% +most familiar with that's still ongoing +long build-up when do we start it from + + align:start position:0% +long build-up when do we start it from + + + align:start position:0% +long build-up when do we start it from +you know do we start from Babbage do we + + align:start position:0% +you know do we start from Babbage do we + + + align:start position:0% +you know do we start from Babbage do we +started from veneer bush's differential + + align:start position:0% +started from veneer bush's differential + + + align:start position:0% +started from veneer bush's differential +analyzer in the 1930s till we started + + align:start position:0% +analyzer in the 1930s till we started + + + align:start position:0% +analyzer in the 1930s till we started +from ENIAC right 1946 the first + + align:start position:0% +from ENIAC right 1946 the first + + + align:start position:0% +from ENIAC right 1946 the first +functioning mainframe computer you know + + align:start position:0% +functioning mainframe computer you know + + + align:start position:0% +functioning mainframe computer you know +we can started at various points but you + + align:start position:0% +we can started at various points but you + + + align:start position:0% +we can started at various points but you +get a sense for how long that buildup is + + align:start position:0% +get a sense for how long that buildup is + + + align:start position:0% +get a sense for how long that buildup is +and then finally we hit the 1990s and + + align:start position:0% +and then finally we hit the 1990s and + + + align:start position:0% +and then finally we hit the 1990s and +that incredible decade of growth in the + + align:start position:0% +that incredible decade of growth in the + + + align:start position:0% +that incredible decade of growth in the +1990s very rapid scale-up + + align:start position:0% + + + + align:start position:0% + +right it depends on when you date it + + align:start position:0% +right it depends on when you date it + + + align:start position:0% +right it depends on when you date it +from you know because everybody stands + + align:start position:0% +from you know because everybody stands + + + align:start position:0% +from you know because everybody stands +on everybody else's shoulders in the + + align:start position:0% +on everybody else's shoulders in the + + + align:start position:0% +on everybody else's shoulders in the +innovation process maybe we ought to + + align:start position:0% +innovation process maybe we ought to + + + align:start position:0% +innovation process maybe we ought to +dated Newtonian physics right + + align:start position:0% +dated Newtonian physics right + + + align:start position:0% +dated Newtonian physics right +I you know I think ENIAC is a pretty + + align:start position:0% +I you know I think ENIAC is a pretty + + + align:start position:0% +I you know I think ENIAC is a pretty +reasonable start date but there's a long + + align:start position:0% +reasonable start date but there's a long + + + align:start position:0% +reasonable start date but there's a long +time between 1946 and 1990 right very + + align:start position:0% +time between 1946 and 1990 right very + + + align:start position:0% +time between 1946 and 1990 right very +long period of time so it's a longer + + align:start position:0% +long period of time so it's a longer + + + align:start position:0% +long period of time so it's a longer +period frankly than this in many many + + align:start position:0% +period frankly than this in many many + + + align:start position:0% +period frankly than this in many many +cases + + align:start position:0% +cases + + + align:start position:0% +cases +but then after the bubble and that in + + align:start position:0% +but then after the bubble and that in + + + align:start position:0% +but then after the bubble and that in +the IT world that's the dot-com bust of + + align:start position:0% +the IT world that's the dot-com bust of + + + align:start position:0% +the IT world that's the dot-com bust of +2001 right then all kinds of comms fail + + align:start position:0% +2001 right then all kinds of comms fail + + + align:start position:0% +2001 right then all kinds of comms fail +and then the surviving firms are + + align:start position:0% +and then the surviving firms are + + + align:start position:0% +and then the surviving firms are +stronger and they go on a period of + + align:start position:0% +stronger and they go on a period of + + + align:start position:0% +stronger and they go on a period of +stable continued growth I would argue + + align:start position:0% +stable continued growth I would argue + + + align:start position:0% +stable continued growth I would argue +that that's what we're on now in the IT + + align:start position:0% +that that's what we're on now in the IT + + + align:start position:0% +that that's what we're on now in the IT +innovation wave you know eventually + + align:start position:0% +innovation wave you know eventually + + + align:start position:0% +innovation wave you know eventually +we'll reach technology maturity the IT + + align:start position:0% +we'll reach technology maturity the IT + + + align:start position:0% +we'll reach technology maturity the IT +wave is complicated because + + align:start position:0% +wave is complicated because + + + align:start position:0% +wave is complicated because +information is a core organizing + + align:start position:0% +information is a core organizing + + + align:start position:0% +information is a core organizing +principle of the universe I you know + + align:start position:0% +principle of the universe I you know + + + align:start position:0% +principle of the universe I you know +it's like mass and energy right it's one + + align:start position:0% +it's like mass and energy right it's one + + + align:start position:0% +it's like mass and energy right it's one +of those big things and if you're tying + + align:start position:0% +of those big things and if you're tying + + + align:start position:0% +of those big things and if you're tying +your innovation wave to something as + + align:start position:0% +your innovation wave to something as + + + align:start position:0% +your innovation wave to something as +fundamental and powerful as that maybe + + align:start position:0% +fundamental and powerful as that maybe + + + align:start position:0% +fundamental and powerful as that maybe +it's more enduring and we haven't begun + + align:start position:0% +it's more enduring and we haven't begun + + + align:start position:0% +it's more enduring and we haven't begun +to touch artificial intelligence yet so + + align:start position:0% +to touch artificial intelligence yet so + + + align:start position:0% +to touch artificial intelligence yet so +maybe we'll get a lot longer run Mac's + + align:start position:0% +maybe we'll get a lot longer run Mac's + + + align:start position:0% +maybe we'll get a lot longer run Mac's +in our stable growth period right I mean + + align:start position:0% +in our stable growth period right I mean + + + align:start position:0% +in our stable growth period right I mean +we have a lot more to go but think about + + align:start position:0% +we have a lot more to go but think about + + + align:start position:0% +we have a lot more to go but think about +railroads you can think about somewhere + + align:start position:0% +railroads you can think about somewhere + + + align:start position:0% +railroads you can think about somewhere +in the in the first half of the 20th + + align:start position:0% +in the in the first half of the 20th + + + align:start position:0% +in the in the first half of the 20th +century we reached a fair amount of + + align:start position:0% +century we reached a fair amount of + + + align:start position:0% +century we reached a fair amount of +technological maturity to pick with the + + align:start position:0% +technological maturity to pick with the + + + align:start position:0% +technological maturity to pick with the +advent of the diesel electric engine + + align:start position:0% +advent of the diesel electric engine + + + align:start position:0% +advent of the diesel electric engine +so their incremental advances in + + align:start position:0% +so their incremental advances in + + + align:start position:0% +so their incremental advances in +railroads but the but the real + + align:start position:0% +railroads but the but the real + + + align:start position:0% +railroads but the but the real +challenging period is probably over for + + align:start position:0% +challenging period is probably over for + + + align:start position:0% +challenging period is probably over for +the time being + + align:start position:0% +the time being + + + align:start position:0% +the time being +death we're looking at the stable growth + + align:start position:0% +death we're looking at the stable growth + + + align:start position:0% +death we're looking at the stable growth +here + + align:start position:0% + + + + align:start position:0% + +an example + + align:start position:0% + + + + align:start position:0% + +of upward trend where we expect to see + + align:start position:0% +of upward trend where we expect to see + + + align:start position:0% +of upward trend where we expect to see +some ups and downs from other causes or + + align:start position:0% +some ups and downs from other causes or + + + align:start position:0% +some ups and downs from other causes or +how have you capture those effects + + align:start position:0% +how have you capture those effects + + + align:start position:0% +how have you capture those effects +yeah I mean there's we could call them + + align:start position:0% +yeah I mean there's we could call them + + + align:start position:0% +yeah I mean there's we could call them +Black Swan elements that pop up + + align:start position:0% +Black Swan elements that pop up + + + align:start position:0% +Black Swan elements that pop up +periodically that disrupt everything + + align:start position:0% +periodically that disrupt everything + + + align:start position:0% +periodically that disrupt everything +like crazy + + align:start position:0% +like crazy + + + align:start position:0% +like crazy +you could I'd argue that you could + + align:start position:0% +you could I'd argue that you could + + + align:start position:0% +you could I'd argue that you could +actually treat the + + align:start position:0% + + + + align:start position:0% + +growth and financial services as an + + align:start position:0% +growth and financial services as an + + + align:start position:0% +growth and financial services as an +innovation way that there were a whole + + align:start position:0% +innovation way that there were a whole + + + align:start position:0% +innovation way that there were a whole +series of technological areas of advance + + align:start position:0% +series of technological areas of advance + + + align:start position:0% +series of technological areas of advance +right in areas like mathematics and in + + align:start position:0% +right in areas like mathematics and in + + + align:start position:0% +right in areas like mathematics and in +particular but IT revolution accompanies + + align:start position:0% +particular but IT revolution accompanies + + + align:start position:0% +particular but IT revolution accompanies +that you could actually have the + + align:start position:0% +that you could actually have the + + + align:start position:0% +that you could actually have the +technology foundation and the processes + + align:start position:0% +technology foundation and the processes + + + align:start position:0% +technology foundation and the processes +to really create global financial + + align:start position:0% +to really create global financial + + + align:start position:0% +to really create global financial +services system + + align:start position:0% +services system + + + align:start position:0% +services system +and you plot that growth and sure enough + + align:start position:0% +and you plot that growth and sure enough + + + align:start position:0% +and you plot that growth and sure enough +they have a bubble the problem with the + + align:start position:0% +they have a bubble the problem with the + + + align:start position:0% +they have a bubble the problem with the +bubble and the financial services bust + + align:start position:0% +bubble and the financial services bust + + + align:start position:0% +bubble and the financial services bust +is that it just doesn't bring down a + + align:start position:0% +is that it just doesn't bring down a + + + align:start position:0% +is that it just doesn't bring down a +bunch of dot-coms you know it brings + + align:start position:0% +bunch of dot-coms you know it brings + + + align:start position:0% +bunch of dot-coms you know it brings +down the entire economy so be careful + + align:start position:0% +down the entire economy so be careful + + + align:start position:0% +down the entire economy so be careful +about innovation waves in the financial + + align:start position:0% +about innovation waves in the financial + + + align:start position:0% +about innovation waves in the financial +services sector be very careful because + + align:start position:0% +services sector be very careful because + + + align:start position:0% +services sector be very careful because +it messes everything up but I think you + + align:start position:0% +it messes everything up but I think you + + + align:start position:0% +it messes everything up but I think you +can actually I think that one actually + + align:start position:0% +can actually I think that one actually + + + align:start position:0% +can actually I think that one actually +works is a way biotech for sure works as + + align:start position:0% +works is a way biotech for sure works as + + + align:start position:0% +works is a way biotech for sure works as +a wave suddenly as big as IT but + + align:start position:0% +a wave suddenly as big as IT but + + + align:start position:0% +a wave suddenly as big as IT but +nonetheless is significant Matt + + align:start position:0% + + + + align:start position:0% + +very good point right they modulate + + align:start position:0% +very good point right they modulate + + + align:start position:0% +very good point right they modulate +through the process right + + align:start position:0% +through the process right + + + align:start position:0% +through the process right +Atkinson argues that in US history there + + align:start position:0% +Atkinson argues that in US history there + + + align:start position:0% +Atkinson argues that in US history there +are essentially four phases for long + + align:start position:0% +are essentially four phases for long + + + align:start position:0% +are essentially four phases for long +waves + + align:start position:0% +waves + + + align:start position:0% +waves +in the US economy so he argues that and + + align:start position:0% +in the US economy so he argues that and + + + align:start position:0% +in the US economy so he argues that and +different people can look at this + + align:start position:0% +different people can look at this + + + align:start position:0% +different people can look at this +differently and look there's big ways in + + align:start position:0% +differently and look there's big ways in + + + align:start position:0% +differently and look there's big ways in +the small ways and there's wavelets with + + align:start position:0% +the small ways and there's wavelets with + + + align:start position:0% +the small ways and there's wavelets with +in a way right so it's not absolutely + + align:start position:0% +in a way right so it's not absolutely + + + align:start position:0% +in a way right so it's not absolutely +straightforward but he argues that in + + align:start position:0% +straightforward but he argues that in + + + align:start position:0% +straightforward but he argues that in +the 1840s the development of small local + + align:start position:0% +the 1840s the development of small local + + + align:start position:0% +the 1840s the development of small local +manufacturing industries in New England + + align:start position:0% +manufacturing industries in New England + + + align:start position:0% +manufacturing industries in New England +around textiles and early machines + + align:start position:0% +around textiles and early machines + + + align:start position:0% +around textiles and early machines +that's one wave by the 1880s and 90's + + align:start position:0% +that's one wave by the 1880s and 90's + + + align:start position:0% +that's one wave by the 1880s and 90's +that's regional factory based systems + + align:start position:0% +that's regional factory based systems + + + align:start position:0% +that's regional factory based systems +and you know what those 19th century's + + align:start position:0% +and you know what those 19th century's + + + align:start position:0% +and you know what those 19th century's +cities look like think about Pittsburgh + + align:start position:0% +cities look like think about Pittsburgh + + + align:start position:0% +cities look like think about Pittsburgh +by the 1940s were moving towards + + align:start position:0% +by the 1940s were moving towards + + + align:start position:0% +by the 1940s were moving towards +corporate mass production in areas like + + align:start position:0% +corporate mass production in areas like + + + align:start position:0% +corporate mass production in areas like +automobiles and aircraft then in the + + align:start position:0% +automobiles and aircraft then in the + + + align:start position:0% +automobiles and aircraft then in the +1990s he argues the new economy which is + + align:start position:0% +1990s he argues the new economy which is + + + align:start position:0% +1990s he argues the new economy which is +an IT based + + align:start position:0% +an IT based + + + align:start position:0% +an IT based +innovation wave + + align:start position:0% +innovation wave + + + align:start position:0% +innovation wave +emerges that's global that's + + align:start position:0% +emerges that's global that's + + + align:start position:0% +emerges that's global that's +entrepreneurial + + align:start position:0% +entrepreneurial + + + align:start position:0% +entrepreneurial +that's knowledge-based but that's his + + align:start position:0% +that's knowledge-based but that's his + + + align:start position:0% +that's knowledge-based but that's his +way of + + align:start position:0% +way of + + + align:start position:0% +way of +looking at innovation waves in the US + + align:start position:0% +looking at innovation waves in the US + + + align:start position:0% +looking at innovation waves in the US +economy + + align:start position:0% + + + + align:start position:0% + +you know we're familiar with the 1990s + + align:start position:0% +you know we're familiar with the 1990s + + + align:start position:0% +you know we're familiar with the 1990s +we just discussed that one so I won't + + align:start position:0% +we just discussed that one so I won't + + + align:start position:0% +we just discussed that one so I won't +dwell on in here the political system + + align:start position:0% +dwell on in here the political system + + + align:start position:0% +dwell on in here the political system +typically is slow to react to these + + align:start position:0% +typically is slow to react to these + + + align:start position:0% +typically is slow to react to these +innovation ways it does not see them + + align:start position:0% +innovation ways it does not see them + + + align:start position:0% +innovation ways it does not see them +john maynard keynes the great economist + + align:start position:0% +john maynard keynes the great economist + + + align:start position:0% +john maynard keynes the great economist +who created you know Keynesian theory + + align:start position:0% +who created you know Keynesian theory + + + align:start position:0% +who created you know Keynesian theory +once said practical men who believe + + align:start position:0% +once said practical men who believe + + + align:start position:0% +once said practical men who believe +themselves to be quite exempt from any + + align:start position:0% +themselves to be quite exempt from any + + + align:start position:0% +themselves to be quite exempt from any +intellectual influences are usually + + align:start position:0% +intellectual influences are usually + + + align:start position:0% +intellectual influences are usually +slaves of some defunct economist right + + align:start position:0% +slaves of some defunct economist right + + + align:start position:0% +slaves of some defunct economist right +in other words they're operating off old + + align:start position:0% +in other words they're operating off old + + + align:start position:0% +in other words they're operating off old +economics and tend to perpetrate them + + align:start position:0% +economics and tend to perpetrate them + + + align:start position:0% +economics and tend to perpetrate them +atkinson argues that the american old + + align:start position:0% +atkinson argues that the american old + + + align:start position:0% +atkinson argues that the american old +left was focused essentially on a mass + + align:start position:0% +left was focused essentially on a mass + + + align:start position:0% +left was focused essentially on a mass +production economy which had been + + align:start position:0% +production economy which had been + + + align:start position:0% +production economy which had been +eclipsed t' by the time the IT wave + + align:start position:0% +eclipsed t' by the time the IT wave + + + align:start position:0% +eclipsed t' by the time the IT wave +emerges the conservative political + + align:start position:0% +emerges the conservative political + + + align:start position:0% +emerges the conservative political +elements the republican party at this + + align:start position:0% +elements the republican party at this + + + align:start position:0% +elements the republican party at this +time the time and he's writing in was + + align:start position:0% +time the time and he's writing in was + + + align:start position:0% +time the time and he's writing in was +very supply-side classical economics + + align:start position:0% +very supply-side classical economics + + + align:start position:0% +very supply-side classical economics +based they were worried about capital + + align:start position:0% +based they were worried about capital + + + align:start position:0% +based they were worried about capital +supply and they were worried + + align:start position:0% +supply and they were worried + + + align:start position:0% +supply and they were worried +particularly about marginal tax rates + + align:start position:0% +particularly about marginal tax rates + + + align:start position:0% +particularly about marginal tax rates +affecting that capital supply so that + + align:start position:0% +affecting that capital supply so that + + + align:start position:0% +affecting that capital supply so that +wasn't organized to run an innovation + + align:start position:0% +wasn't organized to run an innovation + + + align:start position:0% +wasn't organized to run an innovation +wave that was organized around old + + align:start position:0% +wave that was organized around old + + + align:start position:0% +wave that was organized around old +classical economics right so in a way + + align:start position:0% +classical economics right so in a way + + + align:start position:0% +classical economics right so in a way +both parties got organized around the + + align:start position:0% +both parties got organized around the + + + align:start position:0% +both parties got organized around the +two fundamental bases in classical + + align:start position:0% +two fundamental bases in classical + + + align:start position:0% +two fundamental bases in classical +economic theory the democratic party + + align:start position:0% +economic theory the democratic party + + + align:start position:0% +economic theory the democratic party +around a broad definition of labor + + align:start position:0% +around a broad definition of labor + + + align:start position:0% +around a broad definition of labor +supply that includes education and + + align:start position:0% +supply that includes education and + + + align:start position:0% +supply that includes education and +health and things like that in the + + align:start position:0% +health and things like that in the + + + align:start position:0% +health and things like that in the +republican party around a theory of + + align:start position:0% +republican party around a theory of + + + align:start position:0% +republican party around a theory of +capital supply which was translated in + + align:start position:0% +capital supply which was translated in + + + align:start position:0% +capital supply which was translated in +tax policy it's largely where those + + align:start position:0% +tax policy it's largely where those + + + align:start position:0% +tax policy it's largely where those +parties are today they missed + + align:start position:0% +parties are today they missed + + + align:start position:0% +parties are today they missed +innovation base growth theory i + + align:start position:0% + + + + align:start position:0% + +say that the parties had locked into + + align:start position:0% +say that the parties had locked into + + + align:start position:0% +say that the parties had locked into +this by you know pretty early on in the + + align:start position:0% +this by you know pretty early on in the + + + align:start position:0% +this by you know pretty early on in the +20th century by the time of Franklin + + align:start position:0% +20th century by the time of Franklin + + + align:start position:0% +20th century by the time of Franklin +Roosevelt it's when the Democratic Party + + align:start position:0% +Roosevelt it's when the Democratic Party + + + align:start position:0% +Roosevelt it's when the Democratic Party +locks in to look there's nothing wrong + + align:start position:0% +locks in to look there's nothing wrong + + + align:start position:0% +locks in to look there's nothing wrong +with capital and it's nothing wrong with + + align:start position:0% +with capital and it's nothing wrong with + + + align:start position:0% +with capital and it's nothing wrong with +labor supply right there are important + + align:start position:0% +labor supply right there are important + + + align:start position:0% +labor supply right there are important +elements and they need to be considered + + align:start position:0% +elements and they need to be considered + + + align:start position:0% +elements and they need to be considered +in their contributors we just know + + align:start position:0% +in their contributors we just know + + + align:start position:0% +in their contributors we just know +however that innovation based growth is + + align:start position:0% +however that innovation based growth is + + + align:start position:0% +however that innovation based growth is +the larger factor in growth right and + + align:start position:0% +the larger factor in growth right and + + + align:start position:0% +the larger factor in growth right and +the political parties haven't gotten + + align:start position:0% +the political parties haven't gotten + + + align:start position:0% +the political parties haven't gotten +there yet all right it's a real + + align:start position:0% +there yet all right it's a real + + + align:start position:0% +there yet all right it's a real +structural problem in the US system + + align:start position:0% +structural problem in the US system + + + align:start position:0% +structural problem in the US system +neither then embrace growth economics + + align:start position:0% +neither then embrace growth economics + + + align:start position:0% +neither then embrace growth economics +and spurring innovation + + align:start position:0% + + + + align:start position:0% + +and that leads us to some interesting + + align:start position:0% +and that leads us to some interesting + + + align:start position:0% +and that leads us to some interesting +ideas of a social organization right so + + align:start position:0% +ideas of a social organization right so + + + align:start position:0% +ideas of a social organization right so +technology and technological + + align:start position:0% +technology and technological + + + align:start position:0% +technology and technological +organization is going to drive social + + align:start position:0% +organization is going to drive social + + + align:start position:0% +organization is going to drive social +and economic structures + + align:start position:0% +and economic structures + + + align:start position:0% +and economic structures +so it's a really important point that he + + align:start position:0% +so it's a really important point that he + + + align:start position:0% +so it's a really important point that he +raises here and it's I think one of the + + align:start position:0% +raises here and it's I think one of the + + + align:start position:0% +raises here and it's I think one of the +reasons why the subject of this class is + + align:start position:0% +reasons why the subject of this class is + + + align:start position:0% +reasons why the subject of this class is +actually really important it's bigger + + align:start position:0% +actually really important it's bigger + + + align:start position:0% +actually really important it's bigger +than standing up cool technologies it's + + align:start position:0% +than standing up cool technologies it's + + + align:start position:0% +than standing up cool technologies it's +a lot bigger than that because this + + align:start position:0% +a lot bigger than that because this + + + align:start position:0% +a lot bigger than that because this +class is not only about + + align:start position:0% +class is not only about + + + align:start position:0% +class is not only about +technology development it is about the + + align:start position:0% +technology development it is about the + + + align:start position:0% +technology development it is about the +way society organizes itself around + + align:start position:0% +way society organizes itself around + + + align:start position:0% +way society organizes itself around +those technologies + + align:start position:0% +those technologies + + + align:start position:0% +those technologies +so Hegel right + + align:start position:0% +so Hegel right + + + align:start position:0% +so Hegel right +great German philosopher Western society + + align:start position:0% +great German philosopher Western society + + + align:start position:0% +great German philosopher Western society +is driven by the competition of ideas + + align:start position:0% +is driven by the competition of ideas + + + align:start position:0% +is driven by the competition of ideas +thesis antithesis you all know the story + + align:start position:0% +thesis antithesis you all know the story + + + align:start position:0% +thesis antithesis you all know the story +Marx introduces a very different concept + + align:start position:0% +Marx introduces a very different concept + + + align:start position:0% +Marx introduces a very different concept +into that + + align:start position:0% +into that + + + align:start position:0% +into that +conversation he argues that in acquiring + + align:start position:0% +conversation he argues that in acquiring + + + align:start position:0% +conversation he argues that in acquiring +new productive forces people change + + align:start position:0% +new productive forces people change + + + align:start position:0% +new productive forces people change +their mode of production and in changing + + align:start position:0% +their mode of production and in changing + + + align:start position:0% +their mode of production and in changing +their mode of production they change + + align:start position:0% +their mode of production they change + + + align:start position:0% +their mode of production they change +their way of living and they change + + align:start position:0% +their way of living and they change + + + align:start position:0% +their way of living and they change +their social relations okay so that's + + align:start position:0% +their social relations okay so that's + + + align:start position:0% +their social relations okay so that's +fundamental Marx philosophical + + align:start position:0% +fundamental Marx philosophical + + + align:start position:0% +fundamental Marx philosophical +perspective that is called determinism + + align:start position:0% +perspective that is called determinism + + + align:start position:0% +perspective that is called determinism +in philosophy in other words the + + align:start position:0% +in philosophy in other words the + + + align:start position:0% +in philosophy in other words the +technological order of your society will + + align:start position:0% +technological order of your society will + + + align:start position:0% +technological order of your society will +be determinative of the kind of society + + align:start position:0% +be determinative of the kind of society + + + align:start position:0% +be determinative of the kind of society +you have right and that's how Marxism of + + align:start position:0% +you have right and that's how Marxism of + + + align:start position:0% +you have right and that's how Marxism of +all that's the fundamental philosophical + + align:start position:0% +all that's the fundamental philosophical + + + align:start position:0% +all that's the fundamental philosophical +underpinning and he is seeing the + + align:start position:0% +underpinning and he is seeing the + + + align:start position:0% +underpinning and he is seeing the +Industrial Revolution drive systemic + + align:start position:0% +Industrial Revolution drive systemic + + + align:start position:0% +Industrial Revolution drive systemic +change in society in that in the late + + align:start position:0% +change in society in that in the late + + + align:start position:0% +change in society in that in the late +18th through the 19th century that's + + align:start position:0% +18th through the 19th century that's + + + align:start position:0% +18th through the 19th century that's +what he's seeing right he's seeing this + + align:start position:0% +what he's seeing right he's seeing this + + + align:start position:0% +what he's seeing right he's seeing this +incredible class order evolve to match + + align:start position:0% +incredible class order evolve to match + + + align:start position:0% +incredible class order evolve to match +the very hierarchical structure than + + align:start position:0% +the very hierarchical structure than + + + align:start position:0% +the very hierarchical structure than +industrial organization driven by the + + align:start position:0% +industrial organization driven by the + + + align:start position:0% +industrial organization driven by the +Industrial Revolution requires at that + + align:start position:0% +Industrial Revolution requires at that + + + align:start position:0% +Industrial Revolution requires at that +time Stephanie oh you had a question + + align:start position:0% + + + + align:start position:0% + +I'll get it + + align:start position:0% + + + + align:start position:0% + +sort of + + align:start position:0% + + + + align:start position:0% + +retreats technology technology works + + align:start position:0% +retreats technology technology works + + + align:start position:0% +retreats technology technology works +perpetuate capitalism I think there's + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so I thought + + align:start position:0% +so I thought + + + align:start position:0% +so I thought +at this point I + + align:start position:0% +at this point I + + + align:start position:0% +at this point I +gave you an opening + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% +you + + + align:start position:0% +you +know that is really a big question I + + align:start position:0% +know that is really a big question I + + + align:start position:0% +know that is really a big question I +guess I I guess I opened myself up to + + align:start position:0% +guess I I guess I opened myself up to + + + align:start position:0% +guess I I guess I opened myself up to +that by bringing determinism in using + + align:start position:0% +that by bringing determinism in using + + + align:start position:0% +that by bringing determinism in using +the excuse that Atkinson raised the + + align:start position:0% +the excuse that Atkinson raised the + + + align:start position:0% +the excuse that Atkinson raised the +subject + + align:start position:0% +subject + + + align:start position:0% +subject +look that's not a quite that's not a + + align:start position:0% +look that's not a quite that's not a + + + align:start position:0% +look that's not a quite that's not a +dialogue that the US has had for some + + align:start position:0% +dialogue that the US has had for some + + + align:start position:0% +dialogue that the US has had for some +decades right we thought the Cold War is + + align:start position:0% +decades right we thought the Cold War is + + + align:start position:0% +decades right we thought the Cold War is +over so and we thought capitalism won + + align:start position:0% +over so and we thought capitalism won + + + align:start position:0% +over so and we thought capitalism won +it's only in fairly recent years that + + align:start position:0% +it's only in fairly recent years that + + + align:start position:0% +it's only in fairly recent years that +we're actually starting to think hmm + + align:start position:0% +we're actually starting to think hmm + + + align:start position:0% +we're actually starting to think hmm +maybe there's some more elements here + + align:start position:0% +maybe there's some more elements here + + + align:start position:0% +maybe there's some more elements here +that we need to consider + + align:start position:0% +that we need to consider + + + align:start position:0% +that we need to consider +look I think that's an open question + + align:start position:0% +look I think that's an open question + + + align:start position:0% +look I think that's an open question +obviously this class is about innovation + + align:start position:0% +obviously this class is about innovation + + + align:start position:0% +obviously this class is about innovation +and it's with about innovation in a + + align:start position:0% +and it's with about innovation in a + + + align:start position:0% +and it's with about innovation in a +largely capitalistic systems right which + + align:start position:0% +largely capitalistic systems right which + + + align:start position:0% +largely capitalistic systems right which +obviously is the direction of the world + + align:start position:0% +obviously is the direction of the world + + + align:start position:0% +obviously is the direction of the world +economies have gone in + + align:start position:0% +economies have gone in + + + align:start position:0% +economies have gone in +worldwide so I think that's the reality + + align:start position:0% +worldwide so I think that's the reality + + + align:start position:0% +worldwide so I think that's the reality +that's the reality we have + + align:start position:0% +that's the reality we have + + + align:start position:0% +that's the reality we have +you know my personal view is that that's + + align:start position:0% +you know my personal view is that that's + + + align:start position:0% +you know my personal view is that that's +essentially a positive + + align:start position:0% +essentially a positive + + + align:start position:0% +essentially a positive +but you know there are different views + + align:start position:0% +but you know there are different views + + + align:start position:0% +but you know there are different views +here and we have to keep in mind how + + align:start position:0% +here and we have to keep in mind how + + + align:start position:0% +here and we have to keep in mind how +powerful the technologies that are + + align:start position:0% +powerful the technologies that are + + + align:start position:0% +powerful the technologies that are +coming out of these innovation systems + + align:start position:0% +coming out of these innovation systems + + + align:start position:0% +coming out of these innovation systems +can be for how we relate to one another + + align:start position:0% +can be for how we relate to one another + + + align:start position:0% +can be for how we relate to one another +as people right how we organize our + + align:start position:0% +as people right how we organize our + + + align:start position:0% +as people right how we organize our +social lives + + align:start position:0% + + + + align:start position:0% + +so the prevailing technology system + + align:start position:0% +so the prevailing technology system + + + align:start position:0% +so the prevailing technology system +really sets parameters on the + + align:start position:0% +really sets parameters on the + + + align:start position:0% +really sets parameters on the +fundamentals of social organization + + align:start position:0% +fundamentals of social organization + + + align:start position:0% +fundamentals of social organization +few other thoughts along those lines + + align:start position:0% +few other thoughts along those lines + + + align:start position:0% +few other thoughts along those lines +Condrey F who developed the fundamentals + + align:start position:0% +Condrey F who developed the fundamentals + + + align:start position:0% +Condrey F who developed the fundamentals +of wave theory back at the beginning of + + align:start position:0% +of wave theory back at the beginning of + + + align:start position:0% +of wave theory back at the beginning of +the 20th century + + align:start position:0% + + + + align:start position:0% + +you know he viewed depression as a + + align:start position:0% +you know he viewed depression as a + + + align:start position:0% +you know he viewed depression as a +trough + + align:start position:0% +trough + + + align:start position:0% +trough +in a + + align:start position:0% +in a + + + align:start position:0% +in a +50 year wave cycle right classical + + align:start position:0% +50 year wave cycle right classical + + + align:start position:0% +50 year wave cycle right classical +economists view depression was that you + + align:start position:0% +economists view depression was that you + + + align:start position:0% +economists view depression was that you +know they were waiting for wages and + + align:start position:0% +know they were waiting for wages and + + + align:start position:0% +know they were waiting for wages and +prices to fall far enough to enable a + + align:start position:0% +prices to fall far enough to enable a + + + align:start position:0% +prices to fall far enough to enable a +rebound right eventually everything is + + align:start position:0% +rebound right eventually everything is + + + align:start position:0% +rebound right eventually everything is +cheap enough somebody will buy it right + + align:start position:0% +cheap enough somebody will buy it right + + + align:start position:0% +cheap enough somebody will buy it right +Keynes took on that attitude right this + + align:start position:0% +Keynes took on that attitude right this + + + align:start position:0% +Keynes took on that attitude right this +is this is the point back to what you + + align:start position:0% +is this is the point back to what you + + + align:start position:0% +is this is the point back to what you +raised mad about it how does that + + align:start position:0% +raised mad about it how does that + + + align:start position:0% +raised mad about it how does that +comment economic cycle theory interact + + align:start position:0% +comment economic cycle theory interact + + + align:start position:0% +comment economic cycle theory interact +with innovation wave theory so we're + + align:start position:0% +with innovation wave theory so we're + + + align:start position:0% +with innovation wave theory so we're +right exactly at that point that you + + align:start position:0% +right exactly at that point that you + + + align:start position:0% +right exactly at that point that you +raised so Keynes agreed but you know in + + align:start position:0% +raised so Keynes agreed but you know in + + + align:start position:0% +raised so Keynes agreed but you know in +the end he argued better intervene + + align:start position:0% +the end he argued better intervene + + + align:start position:0% +the end he argued better intervene +because in a longer range were all dead + + align:start position:0% +because in a longer range were all dead + + + align:start position:0% +because in a longer range were all dead +right so don't wait that long better get + + align:start position:0% +right so don't wait that long better get + + + align:start position:0% +right so don't wait that long better get +on with it + + align:start position:0% +on with it + + + align:start position:0% +on with it +Sean payer definitely saw who's that the + + align:start position:0% +Sean payer definitely saw who's that the + + + align:start position:0% +Sean payer definitely saw who's that the +advocate and economics of disruptive + + align:start position:0% +advocate and economics of disruptive + + + align:start position:0% +advocate and economics of disruptive +capitalism destructive capitalism he saw + + align:start position:0% +capitalism destructive capitalism he saw + + + align:start position:0% +capitalism destructive capitalism he saw +country have long waves theory but he + + align:start position:0% +country have long waves theory but he + + + align:start position:0% +country have long waves theory but he +saw them as driven by innovation not + + align:start position:0% +saw them as driven by innovation not + + + align:start position:0% +saw them as driven by innovation not +just in technology but in the + + align:start position:0% +just in technology but in the + + + align:start position:0% +just in technology but in the +accompanying aspects of production and + + align:start position:0% +accompanying aspects of production and + + + align:start position:0% +accompanying aspects of production and +distribution so it's not only the + + align:start position:0% +distribution so it's not only the + + + align:start position:0% +distribution so it's not only the +technology but it's the production and + + align:start position:0% +technology but it's the production and + + + align:start position:0% +technology but it's the production and +distribution system too that he would + + align:start position:0% +distribution system too that he would + + + align:start position:0% +distribution system too that he would +add to that mix so destructive + + align:start position:0% +add to that mix so destructive + + + align:start position:0% +add to that mix so destructive +capitalism in the end is based on + + align:start position:0% +capitalism in the end is based on + + + align:start position:0% +capitalism in the end is based on +radical innovation right as opposed to + + align:start position:0% +radical innovation right as opposed to + + + align:start position:0% +radical innovation right as opposed to +incremental innovation which means that + + align:start position:0% +incremental innovation which means that + + + align:start position:0% +incremental innovation which means that +if you really want disruptive capitalism + + align:start position:0% +if you really want disruptive capitalism + + + align:start position:0% +if you really want disruptive capitalism +and the potential gains of innovation + + align:start position:0% +and the potential gains of innovation + + + align:start position:0% +and the potential gains of innovation +that can derive from it you've got to + + align:start position:0% +that can derive from it you've got to + + + align:start position:0% +that can derive from it you've got to +think hard about radical innovation not + + align:start position:0% +think hard about radical innovation not + + + align:start position:0% +think hard about radical innovation not +just incremental advance + + align:start position:0% +just incremental advance + + + align:start position:0% +just incremental advance +right so that in our system that means + + align:start position:0% +right so that in our system that means + + + align:start position:0% +right so that in our system that means +in turn you got to think about that + + align:start position:0% +in turn you got to think about that + + + align:start position:0% +in turn you got to think about that +early stage R&D to because that's the + + align:start position:0% +early stage R&D to because that's the + + + align:start position:0% +early stage R&D to because that's the +real contributor to radical advance as + + align:start position:0% +real contributor to radical advance as + + + align:start position:0% +real contributor to radical advance as +opposed to industry's development which + + align:start position:0% +opposed to industry's development which + + + align:start position:0% +opposed to industry's development which +is largely incremental with me + + align:start position:0% + + + + align:start position:0% + +so Atkinson argues that technology is + + align:start position:0% +so Atkinson argues that technology is + + + align:start position:0% +so Atkinson argues that technology is +the skeleton on which an economy is + + align:start position:0% +the skeleton on which an economy is + + + align:start position:0% +the skeleton on which an economy is +formed and every 1/2 seconds centuries + + align:start position:0% +formed and every 1/2 seconds centuries + + + align:start position:0% +formed and every 1/2 seconds centuries +so the skeleton changes right as these + + align:start position:0% +so the skeleton changes right as these + + + align:start position:0% +so the skeleton changes right as these +waves come about + + align:start position:0% +waves come about + + + align:start position:0% +waves come about +the changes are not steady they can be + + align:start position:0% +the changes are not steady they can be + + + align:start position:0% +the changes are not steady they can be +very clustered right this is not a + + align:start position:0% +very clustered right this is not a + + + align:start position:0% +very clustered right this is not a +smooth wave there should have been lots + + align:start position:0% +smooth wave there should have been lots + + + align:start position:0% +smooth wave there should have been lots +of erratic lines and the wave theory + + align:start position:0% +of erratic lines and the wave theory + + + align:start position:0% +of erratic lines and the wave theory +diagram I showed you + + align:start position:0% + + + + align:start position:0% + +now Carlota Perez is a great growth + + align:start position:0% +now Carlota Perez is a great growth + + + align:start position:0% +now Carlota Perez is a great growth +economist who taught at the University + + align:start position:0% +economist who taught at the University + + + align:start position:0% +economist who taught at the University +of Sussex and worked with Chris Freeman + + align:start position:0% +of Sussex and worked with Chris Freeman + + + align:start position:0% +of Sussex and worked with Chris Freeman +there and + + align:start position:0% + + + + align:start position:0% + +she argues that it's not just the + + align:start position:0% +she argues that it's not just the + + + align:start position:0% +she argues that it's not just the +economy changes but the politics social + + align:start position:0% +economy changes but the politics social + + + align:start position:0% +economy changes but the politics social +relations and how and where we live the + + align:start position:0% +relations and how and where we live the + + + align:start position:0% +relations and how and where we live the +changes and it's also how we organize + + align:start position:0% +changes and it's also how we organize + + + align:start position:0% +changes and it's also how we organize +our education system and how our culture + + align:start position:0% +our education system and how our culture + + + align:start position:0% +our education system and how our culture +in turn which is driven by some of these + + align:start position:0% +in turn which is driven by some of these + + + align:start position:0% +in turn which is driven by some of these +factors shapes our belief so quote the + + align:start position:0% +factors shapes our belief so quote the + + + align:start position:0% +factors shapes our belief so quote the +logic of the techno economic paradigm + + align:start position:0% +logic of the techno economic paradigm + + + align:start position:0% +logic of the techno economic paradigm +reaches well beyond the economic sphere + + align:start position:0% +reaches well beyond the economic sphere + + + align:start position:0% +reaches well beyond the economic sphere +to become a general and shared + + align:start position:0% +to become a general and shared + + + align:start position:0% +to become a general and shared +organization common sense of the period + + align:start position:0% +organization common sense of the period + + + align:start position:0% +organization common sense of the period +so here's an idea here right a techno + + align:start position:0% +so here's an idea here right a techno + + + align:start position:0% +so here's an idea here right a techno +economic paradigm a + + align:start position:0% + + + + align:start position:0% + +paradigm that includes technology but + + align:start position:0% +paradigm that includes technology but + + + align:start position:0% +paradigm that includes technology but +therefore reaches deep into economics so + + align:start position:0% +therefore reaches deep into economics so + + + align:start position:0% +therefore reaches deep into economics so +there's a paradigm my driving paradigm + + align:start position:0% +there's a paradigm my driving paradigm + + + align:start position:0% +there's a paradigm my driving paradigm +in the society that connects these two + + align:start position:0% +in the society that connects these two + + + align:start position:0% +in the society that connects these two +I'll argue later in class that the + + align:start position:0% +I'll argue later in class that the + + + align:start position:0% +I'll argue later in class that the +paradigm is even bigger than this + + align:start position:0% +paradigm is even bigger than this + + + align:start position:0% +paradigm is even bigger than this +and that becomes in a way the order of + + align:start position:0% +and that becomes in a way the order of + + + align:start position:0% +and that becomes in a way the order of +things so I + + align:start position:0% +things so I + + + align:start position:0% +things so I +think we'll kind of we'll wrap it up + + align:start position:0% +think we'll kind of we'll wrap it up + + + align:start position:0% +think we'll kind of we'll wrap it up +here in terms of talking about Atkinson + + align:start position:0% +here in terms of talking about Atkinson + + + align:start position:0% +here in terms of talking about Atkinson +because + + align:start position:0% +because + + + align:start position:0% +because +we need to move on but Beth you've got + + align:start position:0% +we need to move on but Beth you've got + + + align:start position:0% +we need to move on but Beth you've got +Atkinson as well right and I think + + align:start position:0% +Atkinson as well right and I think + + + align:start position:0% +Atkinson as well right and I think +actually if you speak into the mic in + + align:start position:0% +actually if you speak into the mic in + + + align:start position:0% +actually if you speak into the mic in +the center and I'll move + + align:start position:0% +the center and I'll move + + + align:start position:0% +the center and I'll move +this laptop slightly so you've got a + + align:start position:0% +this laptop slightly so you've got a + + + align:start position:0% +this laptop slightly so you've got a +direct line there okay + + align:start position:0% + + + + align:start position:0% + +thanks + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +about countries + + align:start position:0% + + + + align:start position:0% + +are there actually + + align:start position:0% +are there actually + + + align:start position:0% +are there actually +minimize these troughs + + align:start position:0% + + + + align:start position:0% + +and then a lot of just about what what + + align:start position:0% +and then a lot of just about what what + + + align:start position:0% +and then a lot of just about what what +is technology's effect on society and + + align:start position:0% +is technology's effect on society and + + + align:start position:0% +is technology's effect on society and +what should be should the government be + + align:start position:0% +what should be should the government be + + + align:start position:0% +what should be should the government be +doing things to + + align:start position:0% +doing things to + + + align:start position:0% +doing things to +counteract technology's effect on + + align:start position:0% +counteract technology's effect on + + + align:start position:0% +counteract technology's effect on +society or + + align:start position:0% +society or + + + align:start position:0% +society or +it's a good thing that we're seeing + + align:start position:0% +it's a good thing that we're seeing + + + align:start position:0% +it's a good thing that we're seeing +these effects + + align:start position:0% +these effects + + + align:start position:0% +these effects +there's just a few points before we go + + align:start position:0% +there's just a few points before we go + + + align:start position:0% +there's just a few points before we go +into that + + align:start position:0% + + + + align:start position:0% + +so a concern rights with the new economy + + align:start position:0% + + + + align:start position:0% + +I think that's something that we've been + + align:start position:0% +I think that's something that we've been + + + align:start position:0% +I think that's something that we've been +kind of bored with some assumption when + + align:start position:0% +kind of bored with some assumption when + + + align:start position:0% +kind of bored with some assumption when +we discuss this + + align:start position:0% + + + + align:start position:0% + +so the concept that this new economy + + align:start position:0% +so the concept that this new economy + + + align:start position:0% +so the concept that this new economy +forms new businesses labor organizations + + align:start position:0% +forms new businesses labor organizations + + + align:start position:0% +forms new businesses labor organizations +educational systems + + align:start position:0% +educational systems + + + align:start position:0% +educational systems +cultural beliefs I think is especially + + align:start position:0% +cultural beliefs I think is especially + + + align:start position:0% +cultural beliefs I think is especially +relevant today is there's not going to + + align:start position:0% +relevant today is there's not going to + + + align:start position:0% +relevant today is there's not going to +be a lot of interesting political things + + align:start position:0% +be a lot of interesting political things + + + align:start position:0% +be a lot of interesting political things +arise and + + align:start position:0% +arise and + + + align:start position:0% +arise and +it says like with every disruption + + align:start position:0% +it says like with every disruption + + + align:start position:0% +it says like with every disruption +entrenched interests will push back and + + align:start position:0% +entrenched interests will push back and + + + align:start position:0% +entrenched interests will push back and +may resist change and so + + align:start position:0% + + + + align:start position:0% + +I want to say Beth I really like that + + align:start position:0% +I want to say Beth I really like that + + + align:start position:0% +I want to say Beth I really like that +right your last point here in other + + align:start position:0% +right your last point here in other + + + align:start position:0% +right your last point here in other +words we are seeing very significant + + align:start position:0% +words we are seeing very significant + + + align:start position:0% +words we are seeing very significant +social disruption today and we may be + + align:start position:0% +social disruption today and we may be + + + align:start position:0% +social disruption today and we may be +able to connect it back to the IT + + align:start position:0% +able to connect it back to the IT + + + align:start position:0% +able to connect it back to the IT +innovation wave which frankly the upper + + align:start position:0% +innovation wave which frankly the upper + + + align:start position:0% +innovation wave which frankly the upper +middle class has written to unparalleled + + align:start position:0% +middle class has written to unparalleled + + + align:start position:0% +middle class has written to unparalleled +success but left a lot of people behind + + align:start position:0% +success but left a lot of people behind + + + align:start position:0% +success but left a lot of people behind +maybe right is that what you're driving + + align:start position:0% +maybe right is that what you're driving + + + align:start position:0% +maybe right is that what you're driving +at + + align:start position:0% +at + + + align:start position:0% +at +right + + align:start position:0% + + + + align:start position:0% + +the national scale + + align:start position:0% + + + + align:start position:0% + +so should the government have + + align:start position:0% +so should the government have + + + align:start position:0% +so should the government have +responsibility for correcting this + + align:start position:0% +responsibility for correcting this + + + align:start position:0% +responsibility for correcting this +inequity should it just be focusing on + + align:start position:0% +inequity should it just be focusing on + + + align:start position:0% +inequity should it just be focusing on +total efficiency for the nation as a + + align:start position:0% +total efficiency for the nation as a + + + align:start position:0% +total efficiency for the nation as a +whole and how can it balance the idea + + align:start position:0% +whole and how can it balance the idea + + + align:start position:0% +whole and how can it balance the idea +that in some parts of the country may be + + align:start position:0% +that in some parts of the country may be + + + align:start position:0% +that in some parts of the country may be +worse off waters are better off so it's + + align:start position:0% +worse off waters are better off so it's + + + align:start position:0% +worse off waters are better off so it's +very broad and open so + + align:start position:0% +very broad and open so + + + align:start position:0% +very broad and open so +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so the paper claims that these long ways + + align:start position:0% +so the paper claims that these long ways + + + align:start position:0% +so the paper claims that these long ways +have increase the general quality of + + align:start position:0% +have increase the general quality of + + + align:start position:0% +have increase the general quality of +life maybe at like the national scale + + align:start position:0% +life maybe at like the national scale + + + align:start position:0% +life maybe at like the national scale +but the benefits are likely to be not + + align:start position:0% +but the benefits are likely to be not + + + align:start position:0% +but the benefits are likely to be not +even based on + + align:start position:0% +even based on + + + align:start position:0% +even based on +maybe who's most prepared to take on + + align:start position:0% +maybe who's most prepared to take on + + + align:start position:0% +maybe who's most prepared to take on +technological changes so should the + + align:start position:0% +technological changes so should the + + + align:start position:0% +technological changes so should the +government have a responsibility to + + align:start position:0% +government have a responsibility to + + + align:start position:0% +government have a responsibility to +increase the equity should they be more + + align:start position:0% +increase the equity should they be more + + + align:start position:0% +increase the equity should they be more +focused on this total efficiency how do + + align:start position:0% +focused on this total efficiency how do + + + align:start position:0% +focused on this total efficiency how do +we handle this the societal changes that + + align:start position:0% +we handle this the societal changes that + + + align:start position:0% +we handle this the societal changes that +arise from it I think there is some talk + + align:start position:0% +arise from it I think there is some talk + + + align:start position:0% +arise from it I think there is some talk +that that's kind of that wave of + + align:start position:0% +that that's kind of that wave of + + + align:start position:0% +that that's kind of that wave of +populism has been very evident in recent + + align:start position:0% +populism has been very evident in recent + + + align:start position:0% +populism has been very evident in recent +elections so that's something that the + + align:start position:0% +elections so that's something that the + + + align:start position:0% +elections so that's something that the +government should be interviewing + + align:start position:0% +government should be interviewing + + + align:start position:0% +government should be interviewing +whether should it be up to the three + + align:start position:0% +whether should it be up to the three + + + align:start position:0% +whether should it be up to the three +markets + + align:start position:0% + + + + align:start position:0% + +is just that which always be nervous + + align:start position:0% +is just that which always be nervous + + + align:start position:0% +is just that which always be nervous +because we don't get the next wave + + align:start position:0% + + + + align:start position:0% + +in the future is like the there's + + align:start position:0% +in the future is like the there's + + + align:start position:0% +in the future is like the there's +certain asteroid belts that we're + + align:start position:0% +certain asteroid belts that we're + + + align:start position:0% +certain asteroid belts that we're +playing + + align:start position:0% +playing + + + align:start position:0% +playing +millions of dollars so if we happen to + + align:start position:0% +millions of dollars so if we happen to + + + align:start position:0% +millions of dollars so if we happen to +say oh you know what we're just gonna + + align:start position:0% +say oh you know what we're just gonna + + + align:start position:0% +say oh you know what we're just gonna +not really focus on having rapid + + align:start position:0% +not really focus on having rapid + + + align:start position:0% +not really focus on having rapid +innovation in Japan or China says no + + align:start position:0% +innovation in Japan or China says no + + + align:start position:0% +innovation in Japan or China says no +actually they're not really focusing on + + align:start position:0% +actually they're not really focusing on + + + align:start position:0% +actually they're not really focusing on +this at all like let's just go up let's + + align:start position:0% +this at all like let's just go up let's + + + align:start position:0% +this at all like let's just go up let's +go let's do a Manhattan Project for + + align:start position:0% +go let's do a Manhattan Project for + + + align:start position:0% +go let's do a Manhattan Project for +going into space and being able to find + + align:start position:0% +going into space and being able to find + + + align:start position:0% +going into space and being able to find +and they can go in and they can get + + align:start position:0% +and they can go in and they can get + + + align:start position:0% +and they can go in and they can get +billion dollars into their economy the + + align:start position:0% +billion dollars into their economy the + + + align:start position:0% +billion dollars into their economy the +key is pretty good + + align:start position:0% +key is pretty good + + + align:start position:0% +key is pretty good +other implications are saving some + + align:start position:0% +other implications are saving some + + + align:start position:0% +other implications are saving some +people who + + align:start position:0% + + + + align:start position:0% + +we're never + + align:start position:0% + + + + align:start position:0% + +we could say yeah we're number one but + + align:start position:0% +we could say yeah we're number one but + + + align:start position:0% +we could say yeah we're number one but +also say we really need to think + + align:start position:0% +also say we really need to think + + + align:start position:0% +also say we really need to think +about how our structure because the + + align:start position:0% +about how our structure because the + + + align:start position:0% +about how our structure because the +future is + + align:start position:0% +future is + + + align:start position:0% +future is +full-time + + align:start position:0% +full-time + + + align:start position:0% +full-time +pretty much indicating this change + + align:start position:0% +pretty much indicating this change + + + align:start position:0% +pretty much indicating this change +so we probably won't be where we're at + + align:start position:0% +so we probably won't be where we're at + + + align:start position:0% +so we probably won't be where we're at +probably thinking we don't want to go + + align:start position:0% +probably thinking we don't want to go + + + align:start position:0% +probably thinking we don't want to go +down but that that's really up to the US + + align:start position:0% +down but that that's really up to the US + + + align:start position:0% +down but that that's really up to the US +and I + + align:start position:0% + + + + align:start position:0% + +think I might + + align:start position:0% + + + + align:start position:0% + +be talking a lot about + + align:start position:0% +be talking a lot about + + + align:start position:0% +be talking a lot about +certainly capitalist innovation and how + + align:start position:0% +certainly capitalist innovation and how + + + align:start position:0% +certainly capitalist innovation and how +that might see things might be a little + + align:start position:0% +that might see things might be a little + + + align:start position:0% +that might see things might be a little +different structured o my capital side + + align:start position:0% +different structured o my capital side + + + align:start position:0% +different structured o my capital side +we might just tell look at the effect of + + align:start position:0% +we might just tell look at the effect of + + + align:start position:0% +we might just tell look at the effect of +a survey like I think there's an + + align:start position:0% +a survey like I think there's an + + + align:start position:0% +a survey like I think there's an +important piece here where we see a lot + + align:start position:0% +important piece here where we see a lot + + + align:start position:0% +important piece here where we see a lot +of growth in the upper middle class to + + align:start position:0% +of growth in the upper middle class to + + + align:start position:0% +of growth in the upper middle class to +be prepared to handle + + align:start position:0% +be prepared to handle + + + align:start position:0% +be prepared to handle +a lot of the sort of more human aspects + + align:start position:0% +a lot of the sort of more human aspects + + + align:start position:0% +a lot of the sort of more human aspects +where we're going that you see these + + align:start position:0% +where we're going that you see these + + + align:start position:0% +where we're going that you see these +sort of this transition transition as we + + align:start position:0% +sort of this transition transition as we + + + align:start position:0% +sort of this transition transition as we +look forward into certain management + + align:start position:0% +look forward into certain management + + + align:start position:0% +look forward into certain management +styles and kind of structuring things + + align:start position:0% +styles and kind of structuring things + + + align:start position:0% +styles and kind of structuring things +which is a little bit more high-level + + align:start position:0% +which is a little bit more high-level + + + align:start position:0% +which is a little bit more high-level +which + + align:start position:0% +which + + + align:start position:0% +which +which I think if we were looking to + + align:start position:0% +which I think if we were looking to + + + align:start position:0% +which I think if we were looking to +serve as a corrective measure + + align:start position:0% + + + + align:start position:0% + +there is this sort of public need for + + align:start position:0% +there is this sort of public need for + + + align:start position:0% +there is this sort of public need for +the smoothing and transition sort of + + align:start position:0% +the smoothing and transition sort of + + + align:start position:0% +the smoothing and transition sort of +like you see the eyes for those that are + + align:start position:0% +like you see the eyes for those that are + + + align:start position:0% +like you see the eyes for those that are +I don't see the aggressive + + align:start position:0% +I don't see the aggressive + + + align:start position:0% +I don't see the aggressive +sort of Passover or made obsolete + + align:start position:0% +sort of Passover or made obsolete + + + align:start position:0% +sort of Passover or made obsolete +structurally I + + align:start position:0% +structurally I + + + align:start position:0% +structurally I +think there's a greater need for + + align:start position:0% +think there's a greater need for + + + align:start position:0% +think there's a greater need for +kind of renewed investment + + align:start position:0% + + + + align:start position:0% + +kind of a lot of folks + + align:start position:0% +kind of a lot of folks + + + align:start position:0% +kind of a lot of folks +sort of public education or + + align:start position:0% +sort of public education or + + + align:start position:0% +sort of public education or +educational or secondary education at + + align:start position:0% +educational or secondary education at + + + align:start position:0% +educational or secondary education at +postgraduate increased sort of on that + + align:start position:0% + + + + align:start position:0% + +right away into + + align:start position:0% +right away into + + + align:start position:0% +right away into +but + + align:start position:0% + + + + align:start position:0% + +so there's like less room for error you + + align:start position:0% +so there's like less room for error you + + + align:start position:0% +so there's like less room for error you +can't prove + + align:start position:0% + + + + align:start position:0% + +what is a general running summary I + + align:start position:0% +what is a general running summary I + + + align:start position:0% +what is a general running summary I +think you get a lot of these interesting + + align:start position:0% +think you get a lot of these interesting + + + align:start position:0% +think you get a lot of these interesting +they're quickly + + align:start position:0% +they're quickly + + + align:start position:0% +they're quickly +the highest you get higher a lot faster + + align:start position:0% + + + + align:start position:0% + +probably smoothing + + align:start position:0% +probably smoothing + + + align:start position:0% +probably smoothing +or insurance + + align:start position:0% + + + + align:start position:0% + +so rushy that's really interesting and + + align:start position:0% +so rushy that's really interesting and + + + align:start position:0% +so rushy that's really interesting and +you're driving us to a perspective here + + align:start position:0% +you're driving us to a perspective here + + + align:start position:0% +you're driving us to a perspective here +that innovation waves maybe away at + + align:start position:0% +that innovation waves maybe away at + + + align:start position:0% +that innovation waves maybe away at +least in the shorter term for the rich + + align:start position:0% +least in the shorter term for the rich + + + align:start position:0% +least in the shorter term for the rich +to get richer and to create a larger + + align:start position:0% +to get richer and to create a larger + + + align:start position:0% +to get richer and to create a larger +underclass right if we look at the + + align:start position:0% +underclass right if we look at the + + + align:start position:0% +underclass right if we look at the +Industrial Revolution you know the work + + align:start position:0% +Industrial Revolution you know the work + + + align:start position:0% +Industrial Revolution you know the work +out period of doing the adjustments for + + align:start position:0% +out period of doing the adjustments for + + + align:start position:0% +out period of doing the adjustments for +the workforce I mean that's a hundred + + align:start position:0% +the workforce I mean that's a hundred + + + align:start position:0% +the workforce I mean that's a hundred +year long project all right + + align:start position:0% +year long project all right + + + align:start position:0% +year long project all right +you know I think the recent election + + align:start position:0% +you know I think the recent election + + + align:start position:0% +you know I think the recent election +results may tell us that we don't have + + align:start position:0% +results may tell us that we don't have + + + align:start position:0% +results may tell us that we don't have +the kind of play time to play with as we + + align:start position:0% +the kind of play time to play with as we + + + align:start position:0% +the kind of play time to play with as we +work out the latest innovation waves now + + align:start position:0% +work out the latest innovation waves now + + + align:start position:0% +work out the latest innovation waves now +is an alternative to bring on another + + align:start position:0% +is an alternative to bring on another + + + align:start position:0% +is an alternative to bring on another +wave + + align:start position:0% +wave + + + align:start position:0% +wave +right and then maybe all waves are not + + align:start position:0% +right and then maybe all waves are not + + + align:start position:0% +right and then maybe all waves are not +the same in terms of their class and + + align:start position:0% +the same in terms of their class and + + + align:start position:0% +the same in terms of their class and +structural effects and deterministic + + align:start position:0% +structural effects and deterministic + + + align:start position:0% +structural effects and deterministic +effects right so if Martha's innovation + + align:start position:0% +effects right so if Martha's innovation + + + align:start position:0% +effects right so if Martha's innovation +wave around new energy technology that + + align:start position:0% +wave around new energy technology that + + + align:start position:0% +wave around new energy technology that +she spends her life on comes about that + + align:start position:0% +she spends her life on comes about that + + + align:start position:0% +she spends her life on comes about that +may be a big net generator of employment + + align:start position:0% +may be a big net generator of employment + + + align:start position:0% +may be a big net generator of employment +overall right as opposed to an IT + + align:start position:0% +overall right as opposed to an IT + + + align:start position:0% +overall right as opposed to an IT +software way which appears to be less so + + align:start position:0% +software way which appears to be less so + + + align:start position:0% +software way which appears to be less so +so different waves may have different + + align:start position:0% +so different waves may have different + + + align:start position:0% +so different waves may have different +kind of underlying structural features + + align:start position:0% +kind of underlying structural features + + + align:start position:0% +kind of underlying structural features +for the for the society + + align:start position:0% + + + + align:start position:0% + +unless we get on it + + align:start position:0% +unless we get on it + + + align:start position:0% +unless we get on it +Martha you better hurry up that's all I + + align:start position:0% +Martha you better hurry up that's all I + + + align:start position:0% +Martha you better hurry up that's all I +can say + + align:start position:0% +can say + + + align:start position:0% +can say +what do you say this + + align:start position:0% + + + + align:start position:0% + +colder + + align:start position:0% + + + + align:start position:0% + +well lilium habit you know I worked in + + align:start position:0% +well lilium habit you know I worked in + + + align:start position:0% +well lilium habit you know I worked in +the Senate for 15 years I wasn't able to + + align:start position:0% +the Senate for 15 years I wasn't able to + + + align:start position:0% +the Senate for 15 years I wasn't able to +persuade them you know I was able to + + align:start position:0% +persuade them you know I was able to + + + align:start position:0% +persuade them you know I was able to +bring it about + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +no make a comment Alberto + + align:start position:0% + + + + align:start position:0% + +you know the big old beast of the + + align:start position:0% +you know the big old beast of the + + + align:start position:0% +you know the big old beast of the +military-industrial complex which like + + align:start position:0% +military-industrial complex which like + + + align:start position:0% +military-industrial complex which like +from my understanding drives not on + + align:start position:0% +from my understanding drives not on + + + align:start position:0% +from my understanding drives not on +radical innovation they really love the + + align:start position:0% +radical innovation they really love the + + + align:start position:0% +radical innovation they really love the +incremental thing because it can suck + + align:start position:0% +incremental thing because it can suck + + + align:start position:0% +incremental thing because it can suck +out as much money as they can from the + + align:start position:0% +out as much money as they can from the + + + align:start position:0% +out as much money as they can from the +government and if they can just stay + + align:start position:0% +government and if they can just stay + + + align:start position:0% +government and if they can just stay +like that if they can convince all the + + align:start position:0% +like that if they can convince all the + + + align:start position:0% +like that if they can convince all the +politicians to give them onion + + align:start position:0% + + + + align:start position:0% + +this doesn't work best for them but to + + align:start position:0% +this doesn't work best for them but to + + + align:start position:0% +this doesn't work best for them but to +go back to an IRA she said so Alberto + + align:start position:0% +go back to an IRA she said so Alberto + + + align:start position:0% +go back to an IRA she said so Alberto +I'd contest with you because I think + + align:start position:0% +I'd contest with you because I think + + + align:start position:0% +I'd contest with you because I think +it's fair to say that the military is + + align:start position:0% +it's fair to say that the military is + + + align:start position:0% +it's fair to say that the military is +brought on actually most of the big + + align:start position:0% +brought on actually most of the big + + + align:start position:0% +brought on actually most of the big +radical innovation ways + + align:start position:0% +radical innovation ways + + + align:start position:0% +radical innovation ways +the second half of the 19th so well + + align:start position:0% +the second half of the 19th so well + + + align:start position:0% +the second half of the 19th so well +radar turned out to be consumer + + align:start position:0% +radar turned out to be consumer + + + align:start position:0% +radar turned out to be consumer +electronics right and so what's come out + + align:start position:0% +electronics right and so what's come out + + + align:start position:0% +electronics right and so what's come out +of f-35 I don't know yeah what's coming + + align:start position:0% +of f-35 I don't know yeah what's coming + + + align:start position:0% +of f-35 I don't know yeah what's coming +I don't know what + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +maybe I'm wrong no but it's a very good + + align:start position:0% +maybe I'm wrong no but it's a very good + + + align:start position:0% +maybe I'm wrong no but it's a very good +point and I think the answer is that + + align:start position:0% +point and I think the answer is that + + + align:start position:0% +point and I think the answer is that +there's different forces in the military + + align:start position:0% +there's different forces in the military + + + align:start position:0% +there's different forces in the military +there is there's huge conservative + + align:start position:0% +there is there's huge conservative + + + align:start position:0% +there is there's huge conservative +forces that want to perpetuate their + + align:start position:0% +forces that want to perpetuate their + + + align:start position:0% +forces that want to perpetuate their +existing operating systems right and + + align:start position:0% +existing operating systems right and + + + align:start position:0% +existing operating systems right and +it's actually hard to do disruptive + + align:start position:0% +it's actually hard to do disruptive + + + align:start position:0% +it's actually hard to do disruptive +innovation in the military because it + + align:start position:0% +innovation in the military because it + + + align:start position:0% +innovation in the military because it +really is a legacy sector so I think + + align:start position:0% +really is a legacy sector so I think + + + align:start position:0% +really is a legacy sector so I think +this play out between how you bring + + align:start position:0% +this play out between how you bring + + + align:start position:0% +this play out between how you bring +innovation into a legacy sector which + + align:start position:0% +innovation into a legacy sector which + + + align:start position:0% +innovation into a legacy sector which +the military is actually solved a few + + align:start position:0% +the military is actually solved a few + + + align:start position:0% +the military is actually solved a few +times right is kind of an interesting + + align:start position:0% +times right is kind of an interesting + + + align:start position:0% +times right is kind of an interesting +you know idea and we'll keep playing + + align:start position:0% +you know idea and we'll keep playing + + + align:start position:0% +you know idea and we'll keep playing +with this idea as we go on so yes the + + align:start position:0% +with this idea as we go on so yes the + + + align:start position:0% +with this idea as we go on so yes the +military has been able to launch + + align:start position:0% +military has been able to launch + + + align:start position:0% +military has been able to launch +disruptive innovation but overall it's a + + align:start position:0% +disruptive innovation but overall it's a + + + align:start position:0% +disruptive innovation but overall it's a +legatus legacy sector and a lot of it is + + align:start position:0% +legatus legacy sector and a lot of it is + + + align:start position:0% +legatus legacy sector and a lot of it is +resistant innovation just as you suggest + + align:start position:0% +resistant innovation just as you suggest + + + align:start position:0% +resistant innovation just as you suggest +so it's a very interesting balance well + + align:start position:0% +so it's a very interesting balance well + + + align:start position:0% +so it's a very interesting balance well +I wanted to go back to the sheets of my + + align:start position:0% +I wanted to go back to the sheets of my + + + align:start position:0% +I wanted to go back to the sheets of my +education that innovation waves don't + + align:start position:0% +education that innovation waves don't + + + align:start position:0% +education that innovation waves don't +have to like cause of destruction over + + align:start position:0% +have to like cause of destruction over + + + align:start position:0% +have to like cause of destruction over +like classes of people as long as + + align:start position:0% +like classes of people as long as + + + align:start position:0% +like classes of people as long as +people are educated with the new skills + + align:start position:0% +people are educated with the new skills + + + align:start position:0% +people are educated with the new skills +are associated like you brought the + + align:start position:0% +are associated like you brought the + + + align:start position:0% +are associated like you brought the +story up about like + + align:start position:0% +story up about like + + + align:start position:0% +story up about like +someone teaching someone else in Morse + + align:start position:0% +someone teaching someone else in Morse + + + align:start position:0% +someone teaching someone else in Morse +code and like how people would not be + + align:start position:0% +code and like how people would not be + + + align:start position:0% +code and like how people would not be +left behind by railroads maybe even + + align:start position:0% +left behind by railroads maybe even + + + align:start position:0% +left behind by railroads maybe even +learn to the Morse code operators + + align:start position:0% +learn to the Morse code operators + + + align:start position:0% +learn to the Morse code operators +and then in the future I've just read a + + align:start position:0% +and then in the future I've just read a + + + align:start position:0% +and then in the future I've just read a +lot of things about what if + + align:start position:0% +lot of things about what if + + + align:start position:0% +lot of things about what if +coding and + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +about connecting the legacy sector + + align:start position:0% +about connecting the legacy sector + + + align:start position:0% +about connecting the legacy sector +recommendation + + align:start position:0% +recommendation + + + align:start position:0% +recommendation +to pre-trip even particularly when you + + align:start position:0% +to pre-trip even particularly when you + + + align:start position:0% +to pre-trip even particularly when you +see modern company that regulation + + align:start position:0% +see modern company that regulation + + + align:start position:0% +see modern company that regulation +squandering fluid like to + + align:start position:0% +squandering fluid like to + + + align:start position:0% +squandering fluid like to +write human sponsoring + + align:start position:0% + + + + align:start position:0% + +so I think it would be really curious to + + align:start position:0% +so I think it would be really curious to + + + align:start position:0% +so I think it would be really curious to +see the ways in which commercial through + + align:start position:0% +see the ways in which commercial through + + + align:start position:0% +see the ways in which commercial through +this election is how encouraging + + align:start position:0% + + + + align:start position:0% + +and also the nation + + align:start position:0% + + + + align:start position:0% + +which precisely legacy sector innovation + + align:start position:0% +which precisely legacy sector innovation + + + align:start position:0% +which precisely legacy sector innovation +is + + align:start position:0% + + + + align:start position:0% + +pushing almost preventing I + + align:start position:0% + + + + align:start position:0% + +actually wanted to mention winder point + + align:start position:0% +actually wanted to mention winder point + + + align:start position:0% +actually wanted to mention winder point +said that it would be difficult to have + + align:start position:0% +said that it would be difficult to have + + + align:start position:0% +said that it would be difficult to have +people decide okay I want to save your + + align:start position:0% +people decide okay I want to save your + + + align:start position:0% +people decide okay I want to save your +job today versus like future well maybe + + align:start position:0% +job today versus like future well maybe + + + align:start position:0% +job today versus like future well maybe +that's is that the purpose of government + + align:start position:0% +that's is that the purpose of government + + + align:start position:0% +that's is that the purpose of government +in the first place is sometimes + + align:start position:0% + + + + align:start position:0% + +actually + + align:start position:0% + + + + align:start position:0% + +it's not answer but I + + align:start position:0% +it's not answer but I + + + align:start position:0% +it's not answer but I +at least think that + + align:start position:0% +at least think that + + + align:start position:0% +at least think that +that's why we're not that's why we're + + align:start position:0% +that's why we're not that's why we're + + + align:start position:0% +that's why we're not that's why we're +more representative democracy rather + + align:start position:0% +more representative democracy rather + + + align:start position:0% +more representative democracy rather +than just straight-up demise because + + align:start position:0% +than just straight-up demise because + + + align:start position:0% +than just straight-up demise because +then we want these we want these people + + align:start position:0% +then we want these we want these people + + + align:start position:0% +then we want these we want these people +to actually represent us in action or + + align:start position:0% + + + + align:start position:0% + +ideally we would say that okay we + + align:start position:0% +ideally we would say that okay we + + + align:start position:0% +ideally we would say that okay we +actually trust these people to + + align:start position:0% +actually trust these people to + + + align:start position:0% +actually trust these people to +see it what our messenger saw + + align:start position:0% + + + + align:start position:0% + +so I'm gonna curtail this conversation + + align:start position:0% +so I'm gonna curtail this conversation + + + align:start position:0% +so I'm gonna curtail this conversation +because we have five readings to go and + + align:start position:0% +because we have five readings to go and + + + align:start position:0% +because we have five readings to go and +we're more than halfway through the + + align:start position:0% +we're more than halfway through the + + + align:start position:0% +we're more than halfway through the +class + + align:start position:0% +class + + + align:start position:0% +class +so this is gonna be a standard problem + + align:start position:0% +so this is gonna be a standard problem + + + align:start position:0% +so this is gonna be a standard problem +we're gonna have all year so what we can + + align:start position:0% +we're gonna have all year so what we can + + + align:start position:0% +we're gonna have all year so what we can +get used to it but why don't we take a + + align:start position:0% +get used to it but why don't we take a + + + align:start position:0% +get used to it but why don't we take a +quick you know like five minute break + + align:start position:0% +quick you know like five minute break + + + align:start position:0% +quick you know like five minute break +now and come back and then and then + + align:start position:0% +now and come back and then and then + + + align:start position:0% +now and come back and then and then +we'll well tackle the next round \ No newline at end of file diff --git a/Qw4SkvZ03cc.txt b/Qw4SkvZ03cc.txt new file mode 100644 index 0000000000000000000000000000000000000000..d6936a36ee2816553593eae717d2b31477ace8ba --- /dev/null +++ b/Qw4SkvZ03cc.txt @@ -0,0 +1,4760 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +mitopencourseware at + +ocw.mit.edu. + +PROFESSOR: In some ways, I won't +be able to compete with + +live demonstrations of children +from last week. + +But I will try to talk about +adult development. + +And we will really sweep through +your minds and brains + +from when you were not yet born +until you're going to be + +in your '90s. + +So here's your life from the +beginning to the end viewed in + +different ways. + +And we'll touch on a number +of different topics. + +So you know this question about +people have talked for a + +long time about the development +that one goes + +throughout one's life. + +What walks on four legs in the +morning, two legs in the + +afternoon, three legs +in the evening? + +You know the answer +to this, right? + +People. + +They're crawling, they're +standing up, and then + +you get to my age. + +And we need an extra little +prop to move around + +successfully. + +So sort of thinking about this, +that different things + +matter to people at different +ages, that there's different + +priorities, different +ways of thought. + +Erik Erickson is often given +credit for trying to + +articulate that. + +And we'll just walk through +it for a moment. + +Where he said at different +ages, at infancy, early + +childhood, through school, +adolescence, young adulthood, + +people are dealing with +different kinds of issues and + +different developmental tasks +in front of them. + +Your life is a constant +development. + +Not maybe as dramatic as infancy +where we saw last time + +that children really see +the world differently. + +But there's different +challenges in front + +of you at all ages. + +At infancy, you're deciding +who can you + +trust, who can you love. + +Is it a good world? + +And then the drama of potty +training, independence. + +How much are you becoming a +free agent in the world? + +Early school, where you start +to interact with other + +children, and play, and make +friendships, and think about + +social groups. + +Later in schools, you're +becoming more advanced in + +terms of what you're learning in +school and more complex in + +terms of the social networks +that you're developing. + +We'll come back to this at the +end, a period of high anxiety + +and drama of adolescents. + +Then there's something about +young adulthood. + +You may have heard recently +people are speculating that + +what used to be the beginning of +young adulthood culturally, + +at least in the US, and maybe +Europe, and industrialized + +parts of the world, that whereas +the '20s used to be + +considered a decade of +adulthood, there are now + +theories floating around or +impressions floating around + +that '20s are the +new adolescence. + +What are you guys think? + +Everybody says, oh my '20s, I'm +going to discover this and + +discover that. + +But when I get to 30, that's +when we're playing for keeps. + +Is it? + +Well, and part of it's because +you live longer, on average. + +Or you count on living longer. + +And you do, on average, +live longer. + +For a person who's counting on +living to 90, which many of + +you are sort of, another decade +of finding your way, + +your 20s, seems reasonable. + +In a world where people didn't +live nearly as long, didn't + +have as many options, by the +time you finished college-- + +or many people didn't go to +college-- it's roll up your + +sleeves and get to adulthood. + +So there's all these sort of +magazine discussions, are the + +20s the new teens in terms of +whether people feel they have + +responsibilities they have to +execute as a young adult. + +And this a little bit timed +also, a little bit + +anachronistic, then +having a family. + +Although, I think we're much +more thinking about that's not + +necessarily the root for +everybody at all. + +And then old age where +you give other + +people lots of advice. + +So we're going to talk about +brain development from infancy + +to young adulthood, cognitive +stability + +and decline in adulthood. + +We've talked a little +bit about that. + +We'll talk a bit more. + +Alterations in hemispheric +specializations + +that come with aging. + +A bunch of remarkable results +about exercise in the brain. + +All of us want as we get older, +or just even when + +you're younger maybe, just +a pill you pop and + +you're ready to go. + +That would be the best. + +It turns out there's remarkable +evidence about what + +physical exercise does +for the brain. + +I'll share that with you-- +especially in regards to + +aging, but at all ages-- + +ideas about how as you get +older, your social and + +emotional goals will tend to +change, a little bit about + +rewards, and a little bit about +back to adolescence and + +some thoughts about what's going +on in the adolescent + +mind and brain. + +So we know if there's one thing +about the brain that's + +stunning, and challenging to +grasp, and empowers us to be + +humans, it's this complexity. + +There's a huge number of +neurons, fantastic number of + +connections among the neurons. + +So there's just a phenomenal +complexity that all starts + +with a single cell. + +And how does the brain +become this + +dramatically complex organ? + +And how does it organize in the +right way to let you be an + +effective learner, an effective +partner in your + +family, and so on? + +So we start with the idea of +neurogenesis, a magical word, + +the neurons being born. + +And they have to make this +crawl, there's a huge path the + +size of a neuron from the +ventricular surface, the + +ventricle, the fluid-filled +space, to get to the place + +you're going to be +in the brain. + +It's a huge adventure +per neuron. + +Cells dividing there, the +earliest neurons are existing + +by the second embryonic week. + +So that's when you began +to produce your + +neurons in your brain. + +By the seventh embryonic week-- +so you're just two + +months of pregnancy-- + +you're producing an estimated +500,000 neurons a minute. + +We said the neuron is kind of +like a moderate computer. + +Except unlike iPhones, it can't +keep track of where + +you're going all the time. + +We said it's a moderate +computer. + +So 500,000 of those every +minute, I mean, staggering. + +That it all works out +is staggering. + +By the 18th week, you've mostly +made all the neurons + +you're ever going to make for +the rest of your life except + +in two brain regions. + +And there's been a big debate +in the last decade about + +another brain region. + +I'll share those with you. + +But people have been taught for +many, many, many years in + +medical school, and college, and +graduate school, that all + +the neurons you get are +by the 18th week. + +So hang on to them +through healthy + +living and wise behavior. + +Because you have what +you have, right? + +So don't lose them. + +But we'll talk about that +you lose the vast + +majority of them anyway. + +I still recommend +healthy living. + +Because you know, perhaps from +other courses, that the brain + +does this wild thing. + +It excessively overproduces, by +massive scales, the number + +of neurons and the connections +among the neurons. + +And then through use, it gets +rid of neurons and gets rid of + +connections among neurons. + +It's exactly the opposite way +if you build a building. + +If you build a building, +what do you do? + +You construct every bit of it +you need, and you're done. + +Well you don't do is say, I +need a two-story building. + +So I'm going to do a 40-story +building or a 90-story + +building and then knock +off the stories + +as they're not needed. + +You say, well, that's wild. + +Why would I do that? + +But the brain brilliantly makes +many more neurons and + +many more connections on epic +scales and then only uses the + +ones that seem to be +useful for the + +functions of the brain. + +And so for that reason, the +density of the neurons in the + +brain is much higher in a +two-year-old than in you, + +where it was much higher when +you were two than it is now. + +So in a two-year-old, they +have 55% more gray matter + +density in the frontal +lobe than an adult. + +Even at age five, even +at age seven, + +they're 10% percent more. + +From a peak of around before +birth, you're constantly + +shedding neurons and their +connections and keeping the + +ones that seem to be +effective somehow. + +Now, for many years people said, +is there neurogenesis in + +the adult brain? + +Is everything you get before +you're born and + +that's pretty much it? + +And there's many reasons to +be interested in that. + +One is just how does +the brain work? + +How do people work? + +The second is for diseases +like Alzheimer's disease, + +Parkinson's disease, +and other diseases. + +We would love to replace neurons +that have died to help + +people do better. + +So can the brain make new +neurons before birth? + +There's compelling evidence in +animals, and some indirect + +evidence in people too, that +neurogenesis does continue + +into adulthood in the olfactory +bulb and in this + +particular part-- and I'll come +back to this-- in the + +hippocampus, a small part of +the hippocampus called the + +dentate gyrus. + +Everybody's in pretty much +agreement on this for the + +moment, which is kind +of interesting. + +Why those two areas amongst all +the areas in the brain? + +What makes them different that +they can produce neurons all + +throughout your life? + +And then about a decade ago, +Elizabeth Gould at Princeton + +said, oh, when I do the right +kind of experiment, I see new + +neurons in the prefrontal cortex +of monkeys, and for + +human primates. + +That was a giant revolution. + +Because they said, +wait a minute. + +Maybe if monkeys are doing it, +people might be doing it, + +making neurons throughout +their life. + +We just did know that. + +It's not so easy to measure. + +If you think about it, the kind +of experiment to know for + +certain if a human is making a +new neuron is not so easy. + +Because brain imaging +is very far from the + +single neuron level. + +And even if we saw a neuron, +how could we tell it's new? + +And then Pasko Rakic, a big +developmental researcher at + +Yale said, that what she +really saw was glia. + +The glia are the other cells in +the brain, not the neurons. + +They support the neurons. + +Everybody agrees that you make +glia all through your life. + +There's no debate about that. + +But glia are not the stuff +of thoughts and feelings. + +Neurons are. + +So what do we understand +about that whole story? + +Here is an unbelievable +experiment, I think. + +It's really not an experiment. + +But it's a measurement. + +Published in 2006, it's one +approach to asking, do adults + +make new neurons? + +So the nuclear bomb tests that +occur during the Cold War sent + +a carbon-14 into the atmosphere +from 1955 to 1963 + +until there was an international +test ban treaty. + +And then these decreased +and stopped. + +But there was a lot of nuclear +bomb testing in the + +late '50s and '60s. + +That released carbon-14 +into the atmosphere. + +And that integrates with DNA and +forms a date mark for the + +cell of a birth. + +So this is not an experiment +we would want to do again, + +atmospheric nuclear testing, +and having nuclear stuff + +floating around in +the atmosphere. + +I'll tell you the bottom line, +and I'll show you how they + +figured this out. + +What they figured out is looking +at people who died a + +few years ago, that + +nonneuronal cells are generated. + +That was found before glial +cells are made throughout your + +lifetime is the inference +from the finding. + +But neurons are not generated +in adult neocortex. + +The commentary in this article +said, no new neurons for you. + +OK, that's not quite true. + +We know these two little areas +in the brain do it but not in + +most of the brain. + +And they also looked at +something called BrdU, + +B-R-D-U, which is another +way to take a + +brain if you have it. + +It marks newly synthesized +DNA. + +So if you have the brain +directly to measure it, you + +have a couple of measures of +newly synthesized DNA, which + +would be the marker +of new neurons. + +So here's a fantastically +interesting thing. + +They took people who were born +in different times, took + +postmortem samples, and measured +carbon-14 relative to + +what was expected-- + +there's a line here-- it was +relative to what was expected + +by the amount of carbon +in the atmosphere. + +And here's what they found. + +If they look for somebody born +after 1963, they have, in + +their neurons, exactly the +amount that you would expect + +if they made all their neurons +around here and the decrease + +here didn't affect the +neurons at all. + +The glia are here, which is kind +of an average of here and + +the rest of life. + +So if you measure the average +age of the glia, it was about + +the average age of the life of +the person the carbon was + +being picked up in the DNA, +because it's being made. + +It's being kept, +and being made. + +But the neurons all looked like +one value, the value that + +has to do with when +you're born. + +So it's not changing the number +of neurons that are + +showing the carbon-14. + +As if whatever you've got +at birth, that's it. + +On the other hand, here is +somebody born before 1963, + +having essentially zero carbon +that's being showing up in + +their neuronal DNA, and having +again the expected average + +glial DNA as if glia +kept going. + +So this is fantastic. + +It's looking at the carbon-14 +in the DNA of neurons and + +glial of people who +have passed away. + +And saying the carbon-14 dating +looks like neurons. + +You get them all before +you're born. + +That's it. + +Glia, you keep making. + +And they can look at it more +directly by looking at this + +thing that shows you recent +DNA, again, showing you + +impressively that glia keep +making new glia with new DNA + +but not new neurons. + +So the current conclusion in the +field, as far as anybody + +can tell, is no new neurons for +you except in your dentate + +gyrus and olfactory bulb. + +Now here's something +fantastic though. + +It appears that exercise-- + +I'll just show you one example +in animals and humans-- + +there's evidence that exercise +will pump up the number of new + +neurons you make in the +dentate gyrus of the + +hippocampus. + +And we know that the +hippocampus is + +important for memory. + +So that's not a bad place +to make new neurons. + +So you know that going to +exercise will strengthen you + +in various ways. + +But you never realized, unless +you follow this line of work, + +that when you exercise, you're +enhancing the number of new + +neurons that you're producing +in your dentate gyrus. + +So here's a couple ways people +have approached this. + +So one way is to measure +cerebral blood volume, how + +much blood is in the dentate. + +And I'm going to show you +evidence that mice that are + +allowed to exercise push +up the blood volume. + +And that seems to go with +direct evidence of + +neurogenesis. + +Because you can do that +in the animals. + +You can look up sacrificed +animals. + +And then in humans, some +indirect evidence that + +exercise is, again, pushing +up the blood volume in the + +dentate and pushing up a little +bit of memory abilities + +that go with the part +of the brain. + +We can't go in and measure +neurons in the humans. + +So here are mice who exercise +or didn't exercise. + +They measured the +blood volume. + +Here in red is the dentate +part of the hippocampus. + +You can see it's the hottest +spot for blood volume. + +And it's the only part that +responds to exercise. + +So they had some mice +not get to exercise, + +some mice get to exercise. + +The blood volume increases +within the hippocampus + +selectively in a small component +of the hippocampus, + +the dentate gyrus. + +Exercise is pushing up +the blood volume. + +Now that's not direct evidence +about what's happening at the + +cellular level. + +But they can sacrifice these +animals and show you that if + +you look at this binding that +goes with new neurons, with + +new DNA, that's pushed up +the exercise animals. + +Here's the statistics. + +Here's the picture. + +So in the animals, they can +correlate directly. + +More blood volume and more new +neurons going with more + +physical exercise. + +In humans, they can measure +the blood volume. + +And so they had some people do +more exercise, some people + +less exercise. + +Again, it was a dentate +gyrus selectively. + +It showed an increase in +blood volume in humans. + +And now they give them +a memory test. + +And it's not overwhelming. + +But at least in some cases, the +people who did exercising, + +who pushed up their blood +volume, also pushed up a + +little bit their memory +performance. + +So in humans it has to be more +indirect, but all the data + +aligned with the idea that +exercise is pushing up your + +own neuronal genesis, the +creation of new neurons in one + +of the two regions everybody +agrees we make new neurons, + +the dentate gyrus and +the hippocampus. + +But cells have to go incredible +distances at the + +cellular size. + +Neurons have to travel to +the intended location. + +Migration occurs over many +months including eight months + +postnatally. + +Here's this neuron following +it's little path to where it's + +going to go. + +There's glial tracks following +molecular cues as to their + +ultimate target location +to get organized. + +Its initial destination and +function are predetermined at + +the start of the migration. + +People can measure things in +these that tell you where this + +is going to end up. + +It's programed in these cells. + +Unless there's something that +blocks them, they know where + +they're going to go and +make up different + +parts of the brain. + +And then they form synapses, the +part where information is + +sent from one neuron +to another. + +It occurs throughout the brain, +but at different rates + +and different areas. + +So very early, you see +it in spinal cord. + +Very late, you see it in higher +cortical areas like + +prefrontal cortex. + +At the peak growth, there's an +estimate-- these are all gross + +estimates-- + +that you may be forming 1.8 +million synapses per second. + +It's stunning, 1.8 million +synapses per second. + +And do you know how many +molecules are in an average + +synapse by current +estimations? + +1,000. + +There's 1,000 different +molecules in a synapse for it + +to do it has to do. + +Multiply that times 1.8 +million per second. + +It's spectacular biology. + +And then they keep getting more +and more until two years. + +And then you start +just losing them. + +By age 16, you'll have +lost a lot of them. + +And so the people have this +idea we mentioned before, + +pruning and selection. + +That we overgrow the number +of neurons, the number of + +connections. + +What stays is activity +dependence, or this use it or + +lose it neural Darwinism. + +Here's something amazing. + +There's an estimate that we lose +20 billion synapses per + +day through adolescence. + +And that's not a bad thing. + +That's not the worst behaving +adolescents doing the worst + +things they can do. + +That's the brain getting rid of + +connections that aren't useful. + +It's an incredibly interesting +way to + +construct a powerful brain. + +It's to get everybody +to way overbuild. + +And then eliminate the ones that +aren't powerfully useful. + +And another marker of +development is myelination. + +That's the growth of the fatty +sheath that surrounds the + +neurons that are extending +distances. + +It insulates them and +accelerates their signal. + +It looks like white matter +in the postmortem brain. + +What happens through +adolescence-- + +here's age four to 22-- + +is that white matter goes up, +and gray matter goes down. + +So quite interesting, the total +brain size from about + +age six to about 20-- young +adulthood, most of you-- + +stays about the same, the +total brain size. + +What you're doing is you're +getting rid of gray matter. + +And you're enhancing +white matter. + +You're getting rid of the +neurons that are nonproductive + +and the synapses that +are nonproductive. + +And you're increasing the +strength with which different + +parts of the brain can +communicate with one another + +through the white matter. + +And so here's the kinds of +pictures of this growth. + +And some of the parts of the +brain that mature latest by + +these kinds of measures of +getting rid of the overgrowth, + +are in prefrontal cortex. + +And we've talked about +that before. + +So many people are interested +always in thinking about + +developmental issues and +the biology of them. + +And here's a kind of +a stunning finding. + +And we don't know exactly how +it would relate to humans. + +But I thought it would be +interesting to share with you + +and think about this +just a little bit. + +So the title of the paper in +science was "Good Memories of + +Bad Events in Infancy." So we +know from before, and just + +common sense, that fear is +important for the survival. + +So we start at the amygdala, +which seems essential for + +learning what's to be feared. + +Because what's to be feared is +what injures you, or worst + +case, could kill you. + +So the amygdala is essential +for learned fear. + +And we know that one example, a +fear condition that depends + +on the amygdala, would +be a neutral + +stimulus like an odor-- + +odor that's not particularly +good or bad, just an odor-- + +and then a shock that makes +an aversive stimulus. + +So you pair them through +conditioning, odor, shock, + +odor, shock. + +So the odor predicts +the shock. + +Now, they looked at young rats +and looked at attachments. + +And here's what they find +kind of remarkably. + +Up to postnatal day nine for +these rats, if they were + +exposed to the odors and the +shocks, here's what they do. + +They know through pairings +odor, shock, odor, shock, + +odor, shock, here +comes the odor. + +Here comes the shock. + +They still approach the odors. + +That's what's in this graph. + +Up to nine days, the +rats, the mice-- + +sorry-- + +are still approaching this odor +even though it will lead + +to a shock. + +But on the 10th day, +just one day later, + +it completely reverses. + +And they avoid the odors +that predict the + +shock, a complete reversal. + +So they keep going to the +odors with the shock. + +And on the 10th today, the +pups stop going there. + +And what they also +find is this. + +If they look at metabolic +activity in the amygdala, for + +the nine-day olds, it's the +same for the odor and the + +shock, where a neutral order. + +It's not selective to +what's to be feared. + +And the 10-day old, here's a big +response in the amygdala + +for the odor that predicts the +shock, for the fearful + +learning, to know what's +scary, and + +injurious and dangerous. + +So how do people think +about this? + +Well, this is an animal +experiment up to nine days. + +We can't really know how +it relates to people. + +But the speculation was this. + +And maybe there's something +to it on a + +different scale on people. + +Why would an animal approach +something injurious, up to the + +amygdala seems to get more +mature, and then + +avoid what's injurious. + +Why would that happen in such +a predictable evolutionary + +determined way? + +And the hypothesis is this. + +That if you're a very helpless +newborn, you have to go to + +things no matter what. + +Because you're so dependent +on things in your + +environment to survive. + +But at some moment you mature +enough that you + +say no thank you. + +If it's going to be shocking +and painful, I'm + +going to avoid it. + +You become kind of independent +in that sense, in + +the concrete sense. + +And so the author said, well, +could it be helpful for + +newborns to know, no matter +what, approach a caregiver, + +not respond to things that are +negative, because you need the + +care, because you're +so dependent. + +And now this is super +speculatively. + +A thing that's been noted is +that even in families where + +there's unfortunate tremendous +abuse for a young child, the + +abuse victims so commonly +remain powerful + +loyal to their parents. + +Is this kind of a mechanism that +mixes up attachment and + +fear especially when you're +young and can't separate them + +out so well? + +So it's a huge leap from +the mice to the people. + +But it's a mechanism that we +can understand might be + +involved in how attachment +and fear can have unusual + +relationships with +one another. + +All right. + +You can't avoid reading in the +newspapers, or seeing on your + +computer screen, discussions +about the deficit and older + +people like me demanding a lot +of medical care that's paid + +for by the wages you're going +to get in a couple years. + +I mean that's how +I look at it. + +So you are entering a world, +we're all entering a world, + +where the changing ages +demography of our society is + +spectacular. + +Japan is ahead of us in +this a little bit. + +The rest of the world +is following. + +And China is going to +be unbelievable when + +it happens on scale. + +But the United States right +now, right now. + +And here's why. + +For most of human history, the +average life expectancy was up + +to 20 years old. + +That's why you had +to be an adult. + +Because at 20, who knows +how much time I have. + +I better do my adult things. + +Some people lived +for a long time. + +This is really interesting. + +It wasn't that everybody +perished by 30. + +Some people lived to +60, 70, 80, 90. + +But many people fell ill to +many diseases that are now + +readily cured. + +So the average age was 20. + +In the 1800s, it became the +'30s, just a couple hundred + +years ago in all of +human history. + +By 2000, the average person +in the US lived until 77. + +By 2010, 78. + +So we're having a spectacular +growth in the proportion of + +humans in our society who are +living a long, long time, + +which is a wonderful thing. + +But it's radically changing the +world we live in and the + +world for those people who +are older as well. + +So, for example, 100-year-old +people, there's 50,000 of them + +in the US, which is triple what +there was a time ago. + +And it's expected to be a +million people in the US who + +are 100 years and older by +2050, which is in your + +lifetime, a million people +in the US alone + +will be 100 or older. + +And maybe 50% of girls born in +2000 will live for a century. + +Spectacular changes are +occurring right this moment. + +The baby boom generation, huge +numbers of us are approaching + +retirement and the kind of +medical support that gets + +heavier when you get older on +average, huge numbers of us. + +How's it changing? + +One way it's changing is that +families often have-- and you + +might hear this-- an issue of +families feeling that they're + +a sandwich generation. + +They're taking care of their +children and the elderly. + +And you can bet if you have +parents who are living to 120, + +you're doing that. + +Giant effects on education, +pension, work, financial + +markets, I mean these are +epic societal effects. + +So you're hearing the discussion +now about how the + +US is going to deal with this. + +So there used to be kind +of an old model. + +And even this is not that old. + +This is from the mid-1950s. + +Your job was to go to college, +have a career, have a mate, + +take care of a kid, retire +at 65, and put your + +feet up on the desk. + +But all of a sudden, if +everybody's living-- + +not everybody, but huge numbers +of people are living-- + +until 70, 80, 90, 100, many in +pretty good health-- not + +everybody we wish for-- but many +in pretty good health, + +that's a fantastically +different thing. + +65 is no longer the retirement +moment, and you're + +glad you made it. + +65 is something like the +halfway point of your + +potential work life. + +20 to 60, 60 to 100, something +like this. + +It's an unbelievable change. + +You cannot overestimate how it's +changing the world around + +you, and how it will affect the +economics and the politics + +of the world that the rest of us +will be in for many years. + +There's about 10% of the +population over 65 now. + +In 20 years, one out of every +four people will be over 65 by + +current estimates. + +So we're going to elect whatever +president we want. + +And older people go vote a lot +more than younger people. + +You can change that. + +But that's how it is. + +So let's talk about +adult development. + +I can tell you that if you +compare adult development, + +very little is understood +from 20 to 80. + +Almost all the research is +taking something like college + +students, and something +like 80-year-olds, + +and comparing them. + +So pretty much minimal +information is available about + +everything between 20 and 80. + +But we'll look at what we can. + +And one of the things we'll talk +about for a moment is the + +two kinds of studies we could +look at for development. + +This could be about infants. + +But we're going to talk +about adults. + +Cross-sectional versus +longitudinal, so + +cross-sectional is I look +at you as 20-year-olds. + +I look at some 80-year-olds in +the Boston community and + +compare them. + +That's very different than +looking at you at 20 and + +seeing you at 80. + +Because that's much +more controlled. + +That's you with everything +that's special and particular + +about you at 20 and 80. + +When you go get people who are +20-year-olds from one place + +and 80-year-olds from another, +a cross-sectional , study, + +that's going to have all +the differences that + +go with those cohorts. + +So what do we see in these +kinds of things? + +So here's some measures. + +You've seen this kind +of stuff before. + +For things like working memory, +speed of processing, + +and long-term memory. + +Here's people in their '20s, +people in their '80s, a ski + +scope of decline. + +Here's things like knowledge +of vocabulary. + +And that stays more steady, +so the crystallized fluid + +distinction you've already +heard about before. + +So what are the strengths and +limitations of cross-sectional + +versus longitudinal studies. + +So for cross-sectional studies, +they're fast. + +If you're a scientist like a +graduate student who has to do + +a Ph.D. thesis in a mere six or +seven years, you can go to + +experiment with 20-year-olds +and 80-year-olds and have a + +conclusion. + +If you're a graduate student +who would have to test this + +class of 20 and come back to you +in 60 years from now and + +see how you're doing, that's +going to be slow progress. + +So that's why an overwhelming +amount of evidence is + +cross-sectional. + +The problem with it +is cohort effects. + +We discussed, for example, that +IQ scores go up year by + +year throughout the world. + +So you're not really comparing +equal things in terms of + +educational opportunities, +nutrition, exposure to + +information on the internet. + +A 20-year-old and an 80-year-old +have lived through + +different worlds. + +So it's all mixed up in +the measurements. + +Not just age, it's different +worlds that + +people have lived in. + +Longitudinal studies +are painfully slow. + +They're more accurate, because +you're looking at change + +within a person. + +You're holding all the world +things constant. + +You have one other weird +thing, which is you get + +practice effects. + +If you test somebody in the same +test, if you're 60 years + +apart, you don't get much. + +But if it's maybe three or four +years apart, you take a + +test twice, you get +better at it. + +So that's a problem with +longitudinal affects when you + +retest somebody. + +So there's been a few studies +that have looked at relatively + +short-term longitudinal and +cross-sectional data. + +And here's a ski slope on +the values of fluid + +intelligence things. + +And it's just made a bit milder +by a longitudinal + +design, but not dramatically +different. + +So it's not the case of +longitudinal studies. + +People used to think oh, these +longitudinal studies are + +overestimating that. + +Especially if you're older, +you like that thought. + +It's a messed up +study approach. + +But unfortunately, +cross-sectional ones just + +diminish the difference +a little bit. + +So people have said, +though, there's + +an interesting trade-off. + +What's the trade-off, then-- + +I'll ask you for a moment-- + +between most of you +are like 18 to 22. + +I'll bracket it 17 to 25. + +Is that fair? + +What advantage do you have +versus somebody in their + +mid-'50s like me? + +And what disadvantage do you +have in some global sense? + +Oh. + +That was painful. + +The answer was you guys +are physically able. + +All right. + +That would be true. + +There's not many Olympian +sprinters who + +are in their mid-'50s. + +How about in terms of +cognitive things? + +So we just said, for speed +of mental processing, + +it's good to be 20. + +And then 30-year-olds +are a little slower. + +40-year-olds, a little slower. + +50, 60, 70, every decade a +little bit slower for speed of + +mental processing. + +But there's one thing +that's an advantage + +with time for cognition. + +What's the advantage? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Sorry? + +AUDIENCE: Experience. + +PROFESSOR: Experience. + +Thank you. + +Oh yes. + +Yes. + +Over time, you learn stuff, +especially stuff that you're + +exposed to a lot. + +So time is a trade-off +within adulthood. + +You lose some speeded +capacities. + +You gain some specific knowledge +or experience. + +So they looked at studies +like these, air traffic + +controllers in Canada. + +And this is very relevant. + +Especially now, air traffic +controllers are in the news + +more than they want to be. + +You've seen them? + +Unfortunately, they're +napping. + +They're playing movies, +some of them. + +I'm sure it's a tiny minority. + +But it's worrisome if you're a +member of the flying public. + +So here's another question. + +At what age should you tell +somebody, well, I think we + +don't need you to be an air +controller anymore, because + +you're not with it enough +for us to feel safe. + +So people are probing +this all the time. + +The average retirement age in +the US is 55, in Canada, 65. + +Is one more correct +than the other? + +And so here's what they found +when they looked at air + +traffic controllers. + +Age influences processing +speed but not task + +performance. + +So what we're thinking is older +people aren't better. + +But they're not worse. + +Maybe there's a trade-off +between speed and experience. + +And it kind of evens out until +some age where it will no + +longer even out. + +118 pilots, 40 to 69, they +took place in flight + +simulators and tested three +times across three years. + +It's a longitudinal design +and a flight simulator. + +The older pilots were worse the +first time they did it. + +Now some time is passing. + +But then they outperformed +the younger pilots in + +years two and three. + +That is, once they had some +experience with the new + +situation, they could apply, +presumably, their prior + +experience. + +But the very first time they did +it when they have to use + +their fluid intelligence to +figure out what's going on, + +they were worse. + +So you can see some trade-offs +between raw processing, speed, + +and flexibility that goes with +the young adulthood and some + +degree of knowledge +and expertise + +that's gained over time. + +There's trade-offs +on these things. + +How about in memory, declarative +memory that we + +talked about, every +day memory. + +I'll show you in a moment. + +There's mild, steady decline +in healthy aging severe in + +Alzheimer's. + +Implicit memory, we +talked about that. + +It can be more steady +across ages. + +But let me focus on explicit +memory, declarative memory. + +We're going to figure out why +the projector is washing these + +things out so much. + +But here's a slide that +you don't have to see + +very much to know. + +Long-term memory performance +is going down quite sharply + +year by year as you get older. + +But here's something that was +a huge surprise from brain + +imaging, a huge surprise. + +And the thing that if you didn't +have brain imaging, you + +wouldn't even conceive that +it could have existed. + +So many studies have done +brain imaging as people + +perform various kinds of tasks, +memory tasks in this + +case, with young adults +and older adults. + +And + +what they found, unexpectedly, +was this. + +Young adults would typically +activate one side of the + +prefrontal cortex typically in +regards to whether it was + +verbal or spatial. + +So here's young adults mostly +on one side, mostly on one + +side, mostly on one side, +mostly on one side. + +Healthy older adults in good +health characteristically + +turned on both sides of the +brain as they were performing + +these memory tasks. + +So you wouldn't have known +that if you didn't have + +imaging, because who could +have thought about that? + +So then there was a little bit +of a debate in the field with + +the fact that adults were +turning on both sides of their + +hemispheres whereas adults +were just picking one + +or just using one. + +Was that a good thing +or a bad thing? + +So people said, well, +it's a bad thing. + +Because maybe as you get +older, you lose your + +specializations, and you're +using the wrong stuff. + +It's as if I need +my physics book. + +And I'm going to grab +my chemistry book. + +Well, just grab your +physics book. + +Just grab the right thing. + +Why are you getting other stuff +that's not relevant that + +could mess you up and +slow you down? + +So some people said, you're +sort of losing the + +specializations of peak +young adulthood. + +You're leaking brain activity +in the wrong places. + +It's yet another sad sign +of getting older. + +Here's an alternative one. + +Well, you get older. + +But maybe you get some +compensatory mechanisms. + +You realize at some level in +your brain that you can't do + +what you could when +you were 20. + +And you make up for that by +somehow using two sides of + +your brain instead of one. + +So that would be a good thing. + +So how would you decide that? + +How would you decide whether +using the two sides of your + +brain when you're an older adult +is a helpful thing, part + +of the solution to keeping your +cognition going, or is it + +part of the problem of losing +long-term memory abilities as + +you get older while +they're declining. + +How would you decide that? + +There's kind of an +easy answer. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Sorry. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: You what? + +AUDIENCE: Like, split +their brains. + +PROFESSOR: Yes. + +It's a suggestion we should take +older people, split their + +brains, and see how +they're doing. + +Well, older people, +their long-term + +memory is not that bad. + +So here was the approach. + +It seems reasonable. + +They say amongst older people, +some people do better and + +worse in terms of the memory. + +Does better memory go with using +two sides or one side? + +And what was found, and +here's one example. + +Here's young people using one +side of their frontal cortex + +as they perform a memory task. + +Here's older people whose +memory was not so good. + +Here's older people whose +memory was good. + +And here's a similar finding. + +So the suggestion was that older +people who used both + +frontal cortices were actually +doing better. + +They were having less of an +effective age on cognition. + +So the answer seems to be, +it's a good thing. + +And if you're older, you somehow +compensate for some of + +the decrease in long-term +ability by applying more + +neural systems to support +your performance. + +Older adults are really +interested in this. + +You are not. + +In about 30 years, +you might be. + +But older adults are really +interested in what can I do to + +keep myself going? + +Because I'm going to live to be +80, 90, or 100 with just a + +little bit of luck. + +How can I keep my quality +of life high in terms of + +cognition and mental +abilities? + +So one thing that people have +found is that, on average, + +higher education is correlated +with-- and there's many + +interpretations of this-- + +better cognitive abilities and +less likelihood of getting + +Alzheimer's, or getting +Alzheimer's, if you're going + +to get it, at an older age. + +So that's kind of interesting. + +It's good to go to college. + +It's good to keep being educated +in some sense. + +It doesn't have to be formal. + +But formal education correlates +with that. + +Now here was a surprise. + +And now you tell +me what it is. + +So how would that work? + +How would sitting there and +listening to me really + +carefully right now give you an +extra decade of cognitive + +ability when you're 80? + +All right, now I've got +your attention. + +How would that work +biologically? + +Is education kind of going in +your brain and saying, we're + +knocking all these things in. + +And we're keeping them here. + +And we're not going to let +you have any injury when + +you're 40 or 50. + +How does that work? + +So I'm going to tell you one +more piece of information, + +which is this. + +And you tell me what +you think. + +So the other thing that we know +is there's evidence that + +once you get the diagnosis of +Alzheimer's disease, then the + +more educated you are, the +faster you decline. + +And I don't think the story +is all done yet. + +Because people are +complicated. + +But this is the current +evidence. + +So how do you interpret that? + +So here's the interpretation. + +The interpretation is more +education gives you more + +mental tools, what people will +call cognitive reserve. + +You have more things going for +you like maybe the ability to + +use two hemispheres. + +That will protect you as +something like some brain + +injury happens over time, like +an Alzheimer's disease, or + +other causes of slowed +or diminished + +cognition in old age. + +That will help you. + +You have more tools with +which to keep operating + +successfully. + +But once Alzheimer's disease +become severe enough in the + +brain that those tools are no +longer available to you, then + +the more educated you are, +the more you plummet. + +Because everything's done. + +So we now know something-- +and I'll just say + +a word about this-- + +Alzheimer's disease-- and +this is compelling + +evidence for this-- + +starts in your brain +about 15 years + +before you get the diagnosis. + +And it could be more +than that. + +That's how far we can track +it back by brain imaging. + +So if an adult is diagnosed +with Alzheimer's at 70, + +somewhere around 55, something +has started that will + +ultimately be injury enough +to lead to dementia and + +Alzheimer's disease. + +And that's why there's such +a big emphasis on early + +identification. + +Because it's very hard to +treat a brain that's + +had a lot of injury. + +You want to catch the +people at 55 or 60. + +So we also know that lifelong +cognitively is good. + +Conscientious, we talked +about that. + +And here, again, +comes exercise. + +So they took a study. + +This is now a random assignment +study, finally a + +full on experiment, where they +took sedentary people, people + +who were not exercising over 60, +and assigned them to two + +groups, an aerobic training +group who did walking and + +swimming, so some really +exercise, and non-aerobic + +group who did toning +and stretching. + +So they thought they +were special. + +They were active. + +But they weren't doing +the aerobic exercise. + +And they didn't do it a +phenomenal amount of time, an + +hour a day, a few times +a week for months. + +It's not a brutal exercise +schedule. + +What happens? + +It's kind of amazing +what happened. + +These are healthy people +but not very active. + +What's shown here in the red +bars are the cognitive + +performances after the +exercise of the + +healthy older people. + +And blue bars are the people +who did the stretching and + +toning, not the aerobic +exercise. + +So very substantial gains in +cognitive abilities from a few + +months of moderate exercise. + +And in the brain, both by +functional MRI and by + +structural MRI, in gray matter, +and white matter, + +physically measurable changes +in the brain for the group + +that did the aerobic exercise +a couple times a week for a + +few months compared to +the group that did + +the less active exercises. + +That's amazing. + +The brain changes. + +Cognition changes. + +Again, no pill you can pop. + +And you're making new neurons in +your dentate gyrus to boot. + +So all of us want +the easy out. + +But exercise is the most +compelling story for keeping + +your brain optimized +that we know. + +Now here's a remarkable thing. + +Exercise, we kind of get. + +Actually, if you think about +it, we don't know the + +mechanism at all. + +I mean, you're running +around like this. + +Now how is that pushing up your +neurons in your brain? + +But here's something +very psychological + +that's kind of stunning. + +And at first, I almost didn't +believe it when I read it. + +But there's been a few +other studies that + +have supported this. + +We often think, well, exercise +is something real. + +Attitudes, even in a psychology +course, attitudes, + +they're just attitudes. + +So look at this. + +And then you can think +about this. + +So they looked in a longitudinal +study of over 400 + +in the Baltimore Longitudinal +Study of Aging. + +They started under 50. + +But they kept going with them. + +They gave them a questionnaire +on attitudes about aging. + +So they said, are older people, +for example, more + +absent-minded or less +intelligent? + +And some people say, +oh my gosh. + +Older people are very +absent-minded. + +They're very less intelligent. + +Other people think it's +just a milder think. + +People vary in their estimates +of how severe these changes + +are in old age. + +Then they measured something +very concrete and real, the + +number of cardiovascular events, +like stroke or heart + +attack, over the +next 38 years. + +So this is a real physical +measurement. + +This isn't an attitude. + +How powerful is an attitude? + +Well, it's kind of stunning, +unbelievably + +powerful in some ways. + +We don't know if it's the +attitude or something + +correlated. + +But here's the percent with +strokes or heart attacks. + +Here's the people who had +negative age stereotypes. + +And here's the people who had +positive age stereotypes. + +So one always has to be +worried about the + +chicken and egg issue. + +Maybe if you had a lot of +strokes and heart attacks, + +you're not so optimistic +about your old age. + +But they were measuring these +things at the beginning, they + +were very similar. + +So they weren't starting +out with + +different health problems. + +So something about attitudes +seems to chip in to the most + +core aspects of physical +health. + +But none of us understand +the mechanism. + +Yes? + +AUDIENCE: Wouldn't family +history have a + +lot to do with that? + +PROFESSOR: So the question is +how about family history? + +It could be mixed into that. + +AUDIENCE: [INTERPOSING VOICES]. + +PROFESSOR: Yeah. + +That's a very good. + +Then it's not just +attitudes, right? + +Or it could be not +attitudes it all. + +And here's the concept. + +That regardless of your age-- +but age is one of the most + +powerful pieces of the story-- + +when your time is limited, +people focus on social goals + +related to emotional meaning and +emotional satisfaction and + +less related to knowledge +acquisition. + +That depending on the moment of +your life on average, when + +you're in adolescence, and +you're in college and graduate + +school, and you're beginning +your residency, or becoming a + +junior partner at a law firm, +you're at an age of huge + +information acquisition. + +What you want to know is what +do I need to know to do + +something important, +significant, + +valuable in my life? + +You're sitting here acquiring +knowledge. + +College is four years of +acquiring knowledge in terms + +of classrooms and majors. + +You guys do other things too. + +But the number one mission is +acquire that knowledge. + +Now when you get older, you +don't really want so much + +information anymore. + +And maybe what you're much more +interested in is how you + +regulate your feelings, how +positive can you make your + +life, not by being adventurous, +taking risks, and + +all this kind of stuff, +but by finding + +a way towards happiness. + +And I'm going to show you +a bunch of research that + +suggests that young adulthood +is full about acquisition of + +information through adventure. + +And old age, on average you're +focused to regulate your + +emotions in positive ways. + +And so sometimes people +will call that wisdom. + +Although, you could just say +it's different things for + +different ages are desirable. + +And part of the support came +from the following result, + +which has been found many, +many, many times. + +But it was kind of stunning when +it was first reported. + +So this is where people were +asked, how happy are you? + +Are you satisfied +with your life? + +So here's a younger adults, +18 to 50 basically. + +About half of them said they're +very satisfied. + +But it zooms up if +you're older. + +How many people are satisfied +with their standard of living? + +40 if you're younger. + +60 if you're older. + +Frequency of depression, +for example, never. + +Let's pick often. + +It's higher for younger +people. + +They have more frequent thoughts +about suicide. + +By every measure you can make, +if we give you a questionnaire + +like this, on average, for +20-year-olds or 30-year-olds, + +you would report more +unhappiness than older people, + +on average. + +Of course, it varies. + +But that's kind of a surprise +maybe or not. + +And everybody has found that. + +No, not a surprise? + +AUDIENCE: I mean, just because +they report something, doesn't + +mean that's the way it is. + +PROFESSOR: Ah well we'll come +back to this again. + +Yes. + +Just because you say +you're happier + +doesn't mean you're happier. + +We don't have a better +way than that though. + +We can't say, oh, you +think you're happy. + +But you'd be so happy if +you were at Caltech. + +You'd be just so happy. + +I'm a brain measurer. + +So I like objective measures. + +I think if a person tells +you they're happy, + +they probably are. + +There are certain moments, +I know, when + +people tell you that. + +Well, we'll see. + +Who knows? + +I agree with you. + +It's a concern. + +So here's the thought, that +motivation and goals are set + +by temporal context. + +At times, they're perceived +as limited. + +And all this will come that the +older you get, the more + +you focus on the positive +things in the world. + +And what makes you happy is to +focus on positive things and + +ignore the negative. + +So how true might this +be experimentally? + +So they had students-- ah, this +is really washed out-- + +capture these special moments, +this same ad. + +And this one says, "Capture the +special moments." And this + +one says, "Capture the +unexplored world." + +So if you're an information +seeker, which is better? the + +unexplored world or the special + +moments, which is better? + +The unexplored world, right? + +You're a 20-year-old. + +Unexplored Is awesome. + +Young people prefer this ad. + +Older people prefer the +special moments. + +And by special moments, we mean +emotionally satisfying. + +Right? + +OK. + +Here's another one. + +They show you up pictures of +a positive and negative + +expression. + +It flashes away. + +And there's a dot left. + +If the dot appears on the +right, you push your + +right-hand button. + +If the dot appears on +the left, you push + +the left-hand button. + +It's simply pushing to a dot. + +But if the dot is in the place +where you just saw, either a + +negative or a neutral face. + +And what they find is for +younger people, they're about + +as fast whether the dot appears +where the neutral or + +negative face was. + +They don't really care. + +For the older people, they're +much faster if the dot appears + +where the positive face +had just been. + +As if their attention was locked +to the positive face. + +Oh, the dot appears there. + +I'm ready to go. + +Locked on the positive face +if the dot appears here. + +You go, whoa, whoa, whoa. + +You shift your attention. + +And that takes extra time. + +So you're locked to the positive +when you see a + +positive and a negative face. + +Here's another one where you're +doing positive and + +negative car options, +things that are good + +or bad about a car. + +This line goes up. + +This line goes down. + +Younger people focus more on the +negative options relative + +to older people who focus more +on the positive options. + +Here's another one. + +You show pictures of happy +scenes, or neutral scenes, are + +negative scenes. + +This is a graveyard. + +Young people's memory for +positive, negative, and + +neutral things, they remember +emotional things better. + +Let's go to the older people. + +Look at this line way up here. + +That's memory for the +positive scenes. + +And here's the negative +scenes. + +Do you see the focus on the +positivity and the sort of + +lack of interest in the +negative stuff? + +For young people, equally +interesting if it's positive + +or negative. + +For older people, much more +interesting, and sticking in + +your memory if it's positive. + +And not sticking in your memory +if it's negative. + +So one of the big questions +is, is this simply about + +getting older? + +And I'm going to ask you to +think back, if I can, to your + +last days in high school, your +last days in high school. + +For those last days-- + +and I'm sure it will vary +depending on your experience + +in different ways-- + +were you primarily interested +in getting that last little + +bit of information about +US history or calculus? + +I mean, you might have been. + +That could have been the +critical bit of information + +that will make college +work out. + +Or did you have a sudden-- + +and it's kind of embarrassing +when you're 16, 17, 18-- + +enhanced sense of nostalgia? + +Oh, this is the last time the +three of us, or the six of us, + +or the eight of us, or the two +of us will be together. + +Then we're spreading across +the world to go + +to different colleges. + +Nobody had that feeling? + +OK. + +It's kind of embarrassing +when you're 18. + +Because you're not supposed +to say that kind of stuff. + +And it will happen to you at the +end the college for most + +of you most of the time. + +I remember senior year, it crept +up on us in college. + +And we started college. + +Oh my gosh. + +This is the last year +we're together. + +And it seemed very emotionally +important. + +So age or time. + +So is it simply age? + +Or is it time? + +So they did experiments where +they asked people, are you + +focusing on adventure +and content? + +Or are you focusing on emotion +and satisfaction? + +When you're about to move from +one city to another, people + +waned to spend time +with people they + +really cared about. + +And they were not interested +in getting new information. + +Two more tragic studies, if +people are near death, and + +they're asked this question, +of course time with people, + +not acquiring information. + +But here's another one, +inner-city gangs study in Los + +Angeles, inner-city gangs +involved in violence are much + +more interested in time with +people than in information. + +And partly that goes with what +is viewed from the outside. + +Sometimes this kind of insane +loyalty that inner-city gang + +members have for one another is +because they're so focused + +given their situation on this +relations with the other + +people in their group compared +to everything that's rational + +about a safe growing up. + +And, tragically, you know if you +ask a member of inner-city + +gangs how long they think +they'll live, they often tell + +you not very long. + +I'm counting on not +living very long. + +So it's not whether you're +20, or 60, or 80. + +It's how long you sense +time is in front of + +you, a temporal horizon. + +Here's one study that +I had a hand in. + +We took older and younger people +and put them inside an + +MRI and show them positive, +neutral, + +and negative pictures. + +Here's a couple different +points. + +When they said, how intense +is this picture? + +Look at younger people. + +The positive, neutral, and the +negative are really intense. + +This goes down. + +So the older people, as they see +the pictures, experienced + +by their own report, the +negative pictures as being + +less intense. + +They're sort of downplaying +the negative. + +And if we asked their memory, +here's younger people. + +Positive, and negative things, +neutral things, same for + +positive and negative. + +Look at older people, much +more focused in memory, + +retaining in memory +the positive and + +not so much the negative. + +And if we look at their +amygdala, which we know is a + +structure that's essential for +how emotion modulates the + +formation of memory, here's +young people. + +Here's a positive picture. + +Here's a negative picture. + +Here's a neutral picture. + +So emotion counts. + +Positive and negative count +about the same. + +Look at older people. + +Here's positive, and +here's negative. + +So this partly addresses the +question for some people. + +Are older people pretending +they're positive? + +Well, it doesn't +look like that. + +This is their amygdala as +they're looking at it. + +I don't know if their +amygdala can pretend + +to look at the positive. + +So here's the good +news for you. + +What will happen as you get +older, on average, is that for + +whatever reason it happens-- and +we don't really know why-- + +you will focus more and +more on the positive + +things in your life. + +And you'll feel better +for that, on average. + +So that's the kind of +quiet satisfaction. + +Now I'm focusing on +the positive. + +That's the zen satisfaction. + +Let's talk about fantastic +satisfaction, reward system. + +When you really want to do +something, because it's going + +to feel so wonderful, +the reward system. + +So let me tell you a little bit +about what we understand + +about that. + +It involves dopamine as the +critical neurotransmitter. + +It starts in the ventral +tegmental + +area of your brainstem. + +And that projects to something +called the nucleus accumbens, + +an inferior portion of +the basal ganglia. + +And this is reward central. + +If you love something from +opera, to chocolate, to video + +games, this turns on. + +Every experiment that people +have ever done shows in humans + +if something really turns +you on, this area + +really gets turned on. + +What's more powerful for us +than what we find deeply + +emotionally rewarding? + +This is that rewards system. + +And the dopamine runs +from there. + +And look at how cells respond. + +I'm going to show you an example +from monkeys where we + +can look at single cells. + +And then brain imaging, +back to people. + +So here's the experiment +with monkeys. + +And there's a message in this +that's both biologically true + +and compelling about +human life. + +So what's biologically true in +science what's compelling + +about life is a story. + +So here's the experiment. + +The monkey sits there and gets +various cues, different visual + +things that tell them +what's coming up. + +Let's pretend this is a cue +that's something wonderful is + +coming up, highly +desired food. + +So they're recording +electrically why + +the animal sees this. + +There's waiting for what we call +the anticipation period. + +And now here comes the reward. + +And here's something sort of +deep, I think, about reward, + +and learning, and people, +and things like this. + +So here's the neurons firing. + +This is the sum of the neurons +firing in the ventral + +tegmental area. + +So right now they're +just sitting there. + +Oops, here comes the reward. + +And boom, dopamine +is released. + +The dopaminergic cells are +firing like crazy. + +They're getting food +they really want. + +We're thrilled. + +We're hungry, and we're getting +something delicious. + +Not much more rewarding +can happen when + +you're really hungry. + +Now they predict the arrival +with the cue that you saw, a + +meaningless stimulus. + +And look what happens. + +When do these neurons fire? + +Not for the food arriving, but +for the visual signal that + +predicts the food will come. + +What's delicious for the brain +is the anticipation of + +something that's rewarding. + +And this morning when I was +thinking about this lecture, I + +was thinking. + +You might say this. + +Think about experiences +you've had that you've + +looked forward to. + +And almost the most delicious +part, you might say, is the + +anticipation of something +delightful. + +Often the event itself is more +mixed and anticlimactic than + +you would've thought. + +Is that fair? + +I think there's nothing better +like I'm anticipating + +something wonderful. + +And the event can +be wonderful. + +But often it's a little +more complicated. + +That anticipation is like +pure joy, because you're + +dopaminergic system is +firing freely away. + +And it protests also. + +So you get the visual +signal that, oh, the + +reward's coming up. + +Here it is. + +Here comes the food. + +The food doesn't come. + +Look at the silence. + +These cells are protesting +because they didn't get what + +they expected to get. + +So it's very compelling that the +reward in you occurs not + +even so much for the reward +itself, but the anticipation + +of the reward is where it's +biologically occurring when + +you can anticipate and count +on it correctly. + +So, in humans, it's harder to +deliver-- not impossible-- + +food in a scanner. + +So a very simple thing is done +for a reward, which is + +offering people money. + +So in a given trial on a +scanner, you might see a + +meaningless cue like this. + +But you learn that this box +predicts that at the end of + +this trial-- + +you do many trials-- + +you're going to get $1.00. + +Another one might be $0.10. + +Another one they might +take away $1.00. + +So this is like a +good one to get. + +I'm going to get $1 +just sitting here. + +I'm going to get $1. + +It's not huge. + +It's not the biggest reward +in the world. + +But it's something for +just laying in the + +scanner doing nothing. + +And here's what happens. + +Your nucleus accumbens gets +activated, where dopamine + +flows from the ventral tegmental +area when you + +anticipate a reward. + +This is not when the +reward comes. + +This is when you're anticipating +the reward. + +Here's another picture. + +It's most powerful +for when people + +anticipate a gain, a reward. + +And it's less responsive when +people anticipate a loss. + +So it's about gains. + +Then the same system projects to +the inferior parts of your + +frontal lobe. + +So now we're moving into +the neocortex. + +And that part of the brain +seems to respond most + +powerfully if you +get the reward. + +So this is really interesting, +a part of your brain that + +responds to the anticipation, +the + +dopaminergic reward system. + +And then another part of their +brain that responds not + +whether you anticipate it. + +But sometimes they trick you. + +They say we're going +to give you $1. + +And then they go, oops. + +We're not giving it to you. + +This part of the brain seems to +register the receipt of the + +reward or not. + +So there's a separation of the +brain between the anticipation + +of the reward and the response +to whether you get + +the reward or not. + +Older people, when they look +at these kinds of similar + +reward paradigms, they're less +responsive to potential loss + +but equally responsive +to potential + +gain as young adults. + +So that's exactly responding to +positive things and showing + +less of a response to potential +negative things. + +So let's switch to +adolescents. + +We're going to focus on +adolescents now mostly for the + +next 10 minutes. + +You just got through that. + +So let's reflect back for the +last couple of years. + +And they make the experiments +because they want to put + +children into a little +bit more of a vivid. + +Here's pirates. + +Here's not much reward. + +Here's some reward. + +Here's a lot of reward +in the scanner. + +And your children are +adolescents or young adults. + +And they look in the +nucleus accumbens. + +This is that reward region. + +And look who's firing +like crazy? + +Adolescents, teenagers. + +But they're not firing like +crazy in the frontal cortex. + +So this is very speculative. + +These are partly just +wide stories. + +But one hypothesis is this. + +And we're going to say in a +minute more about this. + +Adolescence is a really +interesting period. + +Because it's not only when +you're deciding who you are in + +the world in many ways +independently. + +It's also, worrisomely for +parents, grandparents, + +cousins, siblings, the period +in life when people are most + +likely to put themselves +at great risk. + +And one version of that is that +the subcortical reward + +areas are developing way faster +than the cortical areas + +that control and regulate +your behavior. + +This goes with the stereotype +which is probably as unfair as + +any other stereotype of the +out of control teenager. + +But imagine if it were true +that your reward system is + +very turned up. + +And your cortical control system +were not yet caught up + +to the adult level. + +Well, that would make you a +little bit more likely to do + +adventuresome things. + +Because the reward +is powerful. + +And the control of your thoughts +about how to approach + +or reject that reward +are less powerful. + +So here's some things +to think about. + +And people worry about +for adolescents. + +40% of adult alcoholics report +having initial alcoholism + +between 15 and 19. + +Between 16 and 20, both sexes +are twice as likely to be in + +accidents than drivers between +20 and 50, twice the + +accidental rate. + +Adolescents are more likely to +engage in impulsive sexual + +behavior and multiple +partners. + +Annually, three million +adolescents contract a sexual + +transmitted disease. + +So lots of things that are risky +behaviors occur with + +high frequency in a demonstrable +way, on average, + +among adolescents. + +Young kids don't drive yet. + +20-year-olds are a bit more +mature in their driving. + +So part of this is, again, +attitudinal. + +Here's a question that people +were asked about future + +perspectives. + +They were asked, I would rather +save my money for a + +rainy day than spend it on +something fun right now. + +In your 20s, a little bit. + +That's growing. + +You'll keep the dollar. + +But the younger you are in your +teenage years, the more + +like who wants to wait. + +Let's do it now. + +So moving from something fun +to something experimental, + +let's put together a +couple last things. + +So here's a thing we did before +several times in this + +class, creating false +memories. + +And you remember the way they +create false memories in the + +laboratory is they pick a word +they don't present to you, + +like sweet. + +Then they ask many students to +say what words go with that + +word, like sour, or +candy, or sugar? + +They present you this list. + +And then they test +you for this word + +that was not presented. + +And people often imagine +incorrectly that they heard or + +saw this word. + +We've done that a +couple of times. + +It's a way to show +illusory memory. + +And the way we understand +it is basically this. + +Your memory, your mind, mostly +thinks about the essence of + +things, not the details +of things. + +The essence of things was +everything is sweet. + +The details were the specific +words in the list. + +So let's look at older adults +versus younger adults, + +80-year-olds versus 20-year-olds +and exactly this + +experiment. + +Older adults have many +more false memories. + +And they perform less well. + +So to a scary extend, the +healthy 70-year-olds, here's + +their real memories. + +Here's their false memories. + +It's dead even. + +Here's young people having lots +of false memories, but + +not as many as older +people, and having + +more correct memories. + +So older adults have more +false memories, because + +they're encoding the +gist a lot, but + +they're losing the specifics. + +Does that make sense? + +And you're really vulnerable +to false memories. + +Children, you might think, +well children, + +what do they know? + +Children have less false +memories than you do. + +You would have less false +memories at age five than you + +would right now, which +is kind of amazing. + +If you didn't do the experiment, +you'd imagine + +children would be totally +confused. + +They'd get a big +list of words. + +Was sweet on the list? + +I don't know. + +Yeah, sure. + +A five-year-old does better than +a seven, does better than + +an 11-year-old, does better +than a 20-year-old. + +Why? + +Why does a five-year-old have +less false memories under the + +circumstances? + +Well, we understand that to be +the price of having a mind + +that understands +a lot of gist. + +As you become older, you +understand what's important, + +what counts. + +It's not the little details. + +It's the big concepts. + +So here's an example of, for +example, how well people can + +relate words across sentences. + +And that grows from +six to nine. + +And that's what we want. + +You don't want to read +word, word, word. + +You want to say, what's the +point of the sentence? + +That process of saying, I don't +care about the detail. + +I care about the concept, the +gist of the concept, it's like + +the chess players. + +You shed the specific +details to gain the + +overall knowledge advantage. + +But the five-year-old is not +making the big picture. + +They're just getting +the little details. + +So they're less prone to +the illusory memories. + +We can't see that. + +But this is just showing that +when it comes to organizing + +memories, you see that develop +across a childhood. + +Last couple of things. + +Because when I heard this a few +years ago at a conference, + +I was so surprised by +these findings. + +And I've been around long enough +that i don't get as + +surprised as often +as I used to. + +But it's kind of really +interesting. + +It's a total twist. + +And you can make a judgment +call about how + +to interpret it. + +But here's the experiments +and the data. + +So, again, we have this picture +that everybody likes + +because it fits with the +stereotype, which is the + +teenager out of control. + +Their dopamine is going up. + +And they're saying, let's do a +lot of inappropriate things. + +Because it will be rewarding. + +I know everybody's against it. + +So that's the stereotype. + +And probably there's something +true about that. + +Literally, in the brain +imaging, it + +looks somewhat true. + +But let's think about +this for a moment. + +You're going to be +good at this. + +If line a-- + +these are lines-- is longer than +b, and line b is longer + +than line c, is a +longer than c? + +Yes. + +All right. + +This is MIT. + +Now answer this question +truly. + +Think about it for a moment. + +Person a is a friend +or person b. + +So let's pretend you're person +b and your friend was a. + +You're also a friend with c. + +Are a and c likely +to be friends? + +Let's think about this. + +Is it mathematically transitive +like this one? + +No. + +Let's think about +it for a moment. + +In your experience through life, +on average, are your + +friends mostly kind of going +to like each other? + +Kind of, not all the +time, but kind of? + +Yeah, probably. + +Because if one person likes you, +and another person likes + +you, you share interests. + +You share background to a +certain extent, in a loose + +statistical way. + +It's not definitive like this. + +So let's take a look at what +happens when you ask you two + +questions to grades +one through four. + +OK, these kids are just +making mistakes. + +And they're getting smarter. + +But look at this one go +up just like that. + +So we can say this is a growth +in logical ability. + +This is a growth in your +everyday sense that I hang out + +with a certain kind of person. + +Maybe they like football. + +Maybe they like skating. + +Maybe they like psychology. + +but that's the group I tend +to hang out with. + +And, on average, if I have a +friend, it's because we share + +some interests, or +style of being. + +And if I have another friend, +we probably share that too. + +So more than chance, they +might like each other. + +So this is this idea that you +can separate out what you + +might call purely logical +analysis of things versus a + +growth of social experience, +basically. + +So the last three +slides or so. + +You remember this from a bit +back, from a prior example. + +We said there's a framing +heuristic. + +People are risk averse +for gains. + +But they're risk-taking +for losses. + +If we said here's a program. + +We did this before. + +If Program A is adopted, +200 people are saved. + +Or here's 400 people will +die out of 600. + +That's the same statement. + +But because this is stated +as a gain, people + +usually like this. + +Because this is stated +as a loss, people + +usually don't like this. + +Adults are risk averse for +gains, and they're risk-taking + +for losses. + +If something looks like +a loss, roll the dice. + +If something looks like it's +going to work out, go with it, + +even though numerically, +these are identical. + +You can't see this. + +I can tell you. + +It's not present in + +preschoolers or second graders. + +Preschoolers or second graders, +when you give them + +these kinds of problems, they +don't show the asymmetry for + +losses and gains. + +That's something that +happens over time. + +And it's not a logical one. + +Logically, it should be that. + +So in that weird sense, the +preschooler is more logical + +than you and I, more logical +than you and I. Because + +there's no reason to be +statistically different for + +losses and gains. + +That's purely an attitudinal +emotional perspective. + +First of all, you can hear +the information-seeking. + +Let's check it out. + +That's kind of interesting, +swimming with sharks. + +I can assure you 70-year-olds +are not going to go, hey, that + +can be kind of interesting. + +They're going, no! + +Terrible idea! + +Don't do it! + +Yeah? + +AUDIENCE: Were they asked +in a group collectively? + +PROFESSOR: Yeah. + +You see some peer influence. + +Yeah. + +And that doesn't happen with +adolescents, right? + +They do this. + +They go, oh my gosh. + +These are these teenagers who +are going to go do all these + +things, and get horrible sexual +diseases, and drive + +while they are impaired. + +And that's just the beginning +of their weekend. + +Because they're not going to +follow all the advice that we + +gave them for years, and years, +and years, and years, + +at home and in school. + +So here's the flip on this. + +And just think about +it for a moment. + +It's complicated. + +Swimming with sharks, the adults +say, you don't have to + +tell me any more. + +It's a bad idea. + +The gist is sharks, bad. + +I don't even need to hear +the rest of the story. + +Adolescents start to +weigh the factors. + +We'd be safer in a group. + +Is it dark or night outside? + +How shallow is the water? + +And you can say, well, it's +kind of ridiculous. + +But it's not totally +ridiculous. + +Because when we talk about +danger, those are some of the + +things you might start +to think about. + +So by this analysis, having +unprotected sex. + +Adults, bad, bad, bad. + +OK? + +I mean really bad. + +Adolescents, well, let's +think about this. + +What's the gain? + +Well, we hear that sex is +highly pleasurable. + +What's the loss? + +All these things everybody's +telling us. + +What's the odds, purely +statistically, that for a + +single, sexual experience, you +will have the pleasure of sex, + +but you will end up with +a terrible disease? + +What's the odds for +one outing? + +What do you think? + +Here's the complexity. + +Some people argue that +adolescents are actually more + +accurate in their assessment +of risk, not + +wise in their choice. + +Do you understand the point? + +They're actually doing the +calculations, whereas adults + +just go, sharks bad. + +Sexually transmitted +diseases, avoid. + +You're not parsing through the +exact odds and circumstances, + +the trade-offs between +exploration and pleasure and + +responsibility and safety. + +You just have the gist, +the line, that's it. + +That's my wisdom that +I've gotten. + +Sharks, bad. + +Sexually transmitted +disease, bad. + +That's it. + +And these teenagers are kind +of curiously thinking about + +what are the factors. + +And you could say, it's +not the best analysis. + +But you could say it's +almost more rational. + +Just like the older adults will +make more gist errors in + +memory, they will be more +emotional in their + +avoidance of risk. + +So it's very complicated. + +It's not just dopamine +flushing. + +It's also in the brain. + +It's also something about how +risk is perceived at different + +ages and what information +is available to you. + +All right. + +Thanks very much. \ No newline at end of file diff --git a/RAyFaeJCYWA.txt b/RAyFaeJCYWA.txt new file mode 100644 index 0000000000000000000000000000000000000000..db4e9c913bab5871b86e764bbad2b730923faa11 --- /dev/null +++ b/RAyFaeJCYWA.txt @@ -0,0 +1,12723 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +break + + align:start position:0% + + + + align:start position:0% + +um so before the break we talked about + + align:start position:0% +um so before the break we talked about + + + align:start position:0% +um so before the break we talked about +The Rock equation so we introduced the + + align:start position:0% +The Rock equation so we introduced the + + + align:start position:0% +The Rock equation so we introduced the +equation + + align:start position:0% +equation + + + align:start position:0% +equation +we we showed that it is + + align:start position:0% +we we showed that it is + + + align:start position:0% +we we showed that it is +no rents covarent + + align:start position:0% +no rents covarent + + + align:start position:0% +no rents covarent +and then we started talking about the + + align:start position:0% +and then we started talking about the + + + align:start position:0% +and then we started talking about the +classical Solutions of the rock equation + + align:start position:0% +classical Solutions of the rock equation + + + align:start position:0% +classical Solutions of the rock equation +uh because the + + align:start position:0% +uh because the + + + align:start position:0% +uh because the +um + + align:start position:0% +um + + + align:start position:0% +um +finding the the complete set of + + align:start position:0% +finding the the complete set of + + + align:start position:0% +finding the the complete set of +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +for the rock equation is the necessary + + align:start position:0% +for the rock equation is the necessary + + + align:start position:0% +for the rock equation is the necessary +step for quantizing it okay so uh so let + + align:start position:0% +step for quantizing it okay so uh so let + + + align:start position:0% +step for quantizing it okay so uh so let +us continue + + align:start position:0% +us continue + + + align:start position:0% +us continue +consider the + + align:start position:0% +consider the + + + align:start position:0% +consider the +classical Solutions + + align:start position:0% + + + + align:start position:0% + +of the rock equations + + align:start position:0% + + + + align:start position:0% + +and we call the direct equation is given + + align:start position:0% +and we call the direct equation is given + + + align:start position:0% +and we call the direct equation is given +by the following + + align:start position:0% + + + + align:start position:0% + +okay so this gamma Matrix is so this + + align:start position:0% +okay so this gamma Matrix is so this + + + align:start position:0% +okay so this gamma Matrix is so this +gamma matrices are four by four matrices + + align:start position:0% +gamma matrices are four by four matrices + + + align:start position:0% +gamma matrices are four by four matrices +and PSI is a four complex vector + + align:start position:0% +and PSI is a four complex vector + + + align:start position:0% +and PSI is a four complex vector +and we already know just from setting up + + align:start position:0% +and we already know just from setting up + + + align:start position:0% +and we already know just from setting up +the Iraq equation and the properties of + + align:start position:0% +the Iraq equation and the properties of + + + align:start position:0% +the Iraq equation and the properties of +the gamma matrices + + align:start position:0% +the gamma matrices + + + align:start position:0% +the gamma matrices +that this should have Solutions + + align:start position:0% +that this should have Solutions + + + align:start position:0% +that this should have Solutions +proportional to say plane wave + + align:start position:0% +proportional to say plane wave + + + align:start position:0% +proportional to say plane wave +with K Square + + align:start position:0% +with K Square + + + align:start position:0% +with K Square +so equal to minus M squared okay + + align:start position:0% +so equal to minus M squared okay + + + align:start position:0% +so equal to minus M squared okay +so our goal + + align:start position:0% +so our goal + + + align:start position:0% +so our goal +is to find the + + align:start position:0% +is to find the + + + align:start position:0% +is to find the +yeah the pre-factors okay + + align:start position:0% +yeah the pre-factors okay + + + align:start position:0% +yeah the pre-factors okay +so so here we separating the two kinds + + align:start position:0% +so so here we separating the two kinds + + + align:start position:0% +so so here we separating the two kinds +of solutions + + align:start position:0% +of solutions + + + align:start position:0% +of solutions +so this just reminds you + + align:start position:0% +so this just reminds you + + + align:start position:0% +so this just reminds you +we discussed at the end of last lecture + + align:start position:0% +we discussed at the end of last lecture + + + align:start position:0% +we discussed at the end of last lecture +we call UK + + align:start position:0% +we call UK + + + align:start position:0% +we call UK +corresponding to the positive so we + + align:start position:0% +corresponding to the positive so we + + + align:start position:0% +corresponding to the positive so we +always take + + align:start position:0% +always take + + + align:start position:0% +always take +k to have positive + + align:start position:0% + + + + align:start position:0% + +time component okay + + align:start position:0% +time component okay + + + align:start position:0% +time component okay +and so so this is the positive energy + + align:start position:0% +and so so this is the positive energy + + + align:start position:0% +and so so this is the positive energy +solution + + align:start position:0% +solution + + + align:start position:0% +solution +then we have also so-called selective + + align:start position:0% +then we have also so-called selective + + + align:start position:0% +then we have also so-called selective +Energy Solution so these are just Flames + + align:start position:0% +Energy Solution so these are just Flames + + + align:start position:0% +Energy Solution so these are just Flames +okay it does not + + align:start position:0% +okay it does not + + + align:start position:0% +okay it does not +really means that they have positive + + align:start position:0% +really means that they have positive + + + align:start position:0% +really means that they have positive +energy or Active Energy okay just means + + align:start position:0% +energy or Active Energy okay just means + + + align:start position:0% +energy or Active Energy okay just means +the sign here + + align:start position:0% +the sign here + + + align:start position:0% +the sign here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so now if you plug this + + align:start position:0% +so so now if you plug this + + + align:start position:0% +so so now if you plug this +into the direct equation + + align:start position:0% +into the direct equation + + + align:start position:0% +into the direct equation +and then you get the algebraic equation + + align:start position:0% +and then you get the algebraic equation + + + align:start position:0% +and then you get the algebraic equation +for Q + + align:start position:0% +for Q + + + align:start position:0% +for Q +you get the algebraic equation for U and + + align:start position:0% +you get the algebraic equation for U and + + + align:start position:0% +you get the algebraic equation for U and +then you find + + align:start position:0% +then you find + + + align:start position:0% +then you find +A Clash + + align:start position:0% +A Clash + + + align:start position:0% +A Clash +I slide ik slash m u equal to zero + + align:start position:0% +I slide ik slash m u equal to zero + + + align:start position:0% +I slide ik slash m u equal to zero +and the ik Slash + + align:start position:0% +and the ik Slash + + + align:start position:0% +and the ik Slash +plus m b equal to zero okay so u and v + + align:start position:0% +plus m b equal to zero okay so u and v + + + align:start position:0% +plus m b equal to zero okay so u and v +satisfy those equations okay + + align:start position:0% +satisfy those equations okay + + + align:start position:0% +satisfy those equations okay +and so so I + + align:start position:0% +and so so I + + + align:start position:0% +and so so I +I suppose you already familiar with the + + align:start position:0% +I suppose you already familiar with the + + + align:start position:0% +I suppose you already familiar with the +uh with the rotation say this case slash + + align:start position:0% +uh with the rotation say this case slash + + + align:start position:0% +uh with the rotation say this case slash +okay + + align:start position:0% + + + + align:start position:0% + +so those equations in principle you can + + align:start position:0% +so those equations in principle you can + + + align:start position:0% +so those equations in principle you can +just solve them okay so so these are + + align:start position:0% +just solve them okay so so these are + + + align:start position:0% +just solve them okay so so these are +just linear equations + + align:start position:0% +just linear equations + + + align:start position:0% +just linear equations +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +yeah uh in principle you can just solve + + align:start position:0% +yeah uh in principle you can just solve + + + align:start position:0% +yeah uh in principle you can just solve +them but but still there's uh there are + + align:start position:0% +them but but still there's uh there are + + + align:start position:0% +them but but still there's uh there are +tricks how we solve them say so that + + align:start position:0% +tricks how we solve them say so that + + + align:start position:0% +tricks how we solve them say so that +it's mostly uh transparent so there are + + align:start position:0% +it's mostly uh transparent so there are + + + align:start position:0% +it's mostly uh transparent so there are +two methods of finding the U and K + + align:start position:0% + + + + align:start position:0% + +so the one method is we first go to the + + align:start position:0% +so the one method is we first go to the + + + align:start position:0% +so the one method is we first go to the +rest frame + + align:start position:0% + + + + align:start position:0% + +say we take K mu + + align:start position:0% + + + + align:start position:0% + +say to uh to have zero spatial momentum + + align:start position:0% +say to uh to have zero spatial momentum + + + align:start position:0% +say to uh to have zero spatial momentum +and then the K mu will be just equal to + + align:start position:0% +and then the K mu will be just equal to + + + align:start position:0% +and then the K mu will be just equal to +m + + align:start position:0% +m + + + align:start position:0% +m +zero okay + + align:start position:0% +zero okay + + + align:start position:0% +zero okay +so in this case those equations become + + align:start position:0% +so in this case those equations become + + + align:start position:0% +so in this case those equations become +particularly simple + + align:start position:0% +particularly simple + + + align:start position:0% +particularly simple +and also before we uh solve them + + align:start position:0% +and also before we uh solve them + + + align:start position:0% +and also before we uh solve them +actually we should also specify the + + align:start position:0% +actually we should also specify the + + + align:start position:0% +actually we should also specify the +gamma matrices we need to use so so the + + align:start position:0% +gamma matrices we need to use so so the + + + align:start position:0% +gamma matrices we need to use so so the +government matches ability to + + align:start position:0% +government matches ability to + + + align:start position:0% +government matches ability to +we will use is given by the following + + align:start position:0% + + + + align:start position:0% + +again each are the two by two block + + align:start position:0% +again each are the two by two block + + + align:start position:0% +again each are the two by two block +okay + + align:start position:0% + + + + align:start position:0% + +okay so so this is the gamma matrices + + align:start position:0% +okay so so this is the gamma matrices + + + align:start position:0% +okay so so this is the gamma matrices +we're going to use + + align:start position:0% +we're going to use + + + align:start position:0% +we're going to use +and yeah as we discussed before there + + align:start position:0% +and yeah as we discussed before there + + + align:start position:0% +and yeah as we discussed before there +are many many different choices of java + + align:start position:0% +are many many different choices of java + + + align:start position:0% +are many many different choices of java +matrices + + align:start position:0% +matrices + + + align:start position:0% +matrices +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +some of them are convenient for a + + align:start position:0% +some of them are convenient for a + + + align:start position:0% +some of them are convenient for a +certain purpose and as we will see this + + align:start position:0% +certain purpose and as we will see this + + + align:start position:0% +certain purpose and as we will see this +one actually makes the non-rativistic + + align:start position:0% +one actually makes the non-rativistic + + + align:start position:0% +one actually makes the non-rativistic +limit more manifest okay so it's a + + align:start position:0% +limit more manifest okay so it's a + + + align:start position:0% +limit more manifest okay so it's a +conveniently reduced to + + align:start position:0% +conveniently reduced to + + + align:start position:0% +conveniently reduced to +non-reactivistic limit + + align:start position:0% +non-reactivistic limit + + + align:start position:0% +non-reactivistic limit +and so so in the rest frame those + + align:start position:0% +and so so in the rest frame those + + + align:start position:0% +and so so in the rest frame those +equations simplify + + align:start position:0% +equations simplify + + + align:start position:0% +equations simplify +essentially you just becomes the + + align:start position:0% +essentially you just becomes the + + + align:start position:0% +essentially you just becomes the +eigenvalue equations for gamma zero okay + + align:start position:0% +eigenvalue equations for gamma zero okay + + + align:start position:0% +eigenvalue equations for gamma zero okay +so you find + + align:start position:0% + + + + align:start position:0% + +say say this equation for U + + align:start position:0% + + + + align:start position:0% + +so let's load the rest frame by by zero + + align:start position:0% +so let's load the rest frame by by zero + + + align:start position:0% +so let's load the rest frame by by zero +and then + + align:start position:0% +and then + + + align:start position:0% +and then +so the equation for for you just become + + align:start position:0% +so the equation for for you just become + + + align:start position:0% +so the equation for for you just become +this in the rest frame + + align:start position:0% +this in the rest frame + + + align:start position:0% +this in the rest frame +and the V + + align:start position:0% + + + + align:start position:0% + +given by this okay so essentially + + align:start position:0% +given by this okay so essentially + + + align:start position:0% +given by this okay so essentially +so essentially uh this is just + + align:start position:0% +so essentially uh this is just + + + align:start position:0% +so essentially uh this is just +corresponding essentially see that u and + + align:start position:0% +corresponding essentially see that u and + + + align:start position:0% +corresponding essentially see that u and +v u zero and V 0 just corresponding to + + align:start position:0% +v u zero and V 0 just corresponding to + + + align:start position:0% +v u zero and V 0 just corresponding to +eigenvalues of gamma zero + + align:start position:0% +eigenvalues of gamma zero + + + align:start position:0% +eigenvalues of gamma zero +okay because this is comma zero times U + + align:start position:0% +okay because this is comma zero times U + + + align:start position:0% +okay because this is comma zero times U +give you a constant okay I can be moved + + align:start position:0% +give you a constant okay I can be moved + + + align:start position:0% +give you a constant okay I can be moved +that constant to the right hand side it + + align:start position:0% +that constant to the right hand side it + + + align:start position:0% +that constant to the right hand side it +just looks like an eigenvalue equation + + align:start position:0% +just looks like an eigenvalue equation + + + align:start position:0% +just looks like an eigenvalue equation +okay + + align:start position:0% + + + + align:start position:0% + +and uh so so you can just easily you can + + align:start position:0% +and uh so so you can just easily you can + + + align:start position:0% +and uh so so you can just easily you can +plug this in and easily solve them which + + align:start position:0% +plug this in and easily solve them which + + + align:start position:0% +plug this in and easily solve them which +we already discussed + + align:start position:0% +we already discussed + + + align:start position:0% +we already discussed +last time + + align:start position:0% +last time + + + align:start position:0% +last time +say for example you find that there are + + align:start position:0% +say for example you find that there are + + + align:start position:0% +say for example you find that there are +two independent equations so so this is + + align:start position:0% +two independent equations so so this is + + + align:start position:0% +two independent equations so so this is +the four by four Matrix + + align:start position:0% +the four by four Matrix + + + align:start position:0% +the four by four Matrix +so gamma zero is a four by four Matrix + + align:start position:0% +so gamma zero is a four by four Matrix + + + align:start position:0% +so gamma zero is a four by four Matrix +and uh and actually have two uh + + align:start position:0% +and uh and actually have two uh + + + align:start position:0% +and uh and actually have two uh +eigenvalues say uh so so each u and v + + align:start position:0% +eigenvalues say uh so so each u and v + + + align:start position:0% +eigenvalues say uh so so each u and v +have two say independent + + align:start position:0% +have two say independent + + + align:start position:0% +have two say independent +Solutions okay so um so you find that + + align:start position:0% +Solutions okay so um so you find that + + + align:start position:0% +Solutions okay so um so you find that +the + + align:start position:0% +the + + + align:start position:0% +the +say for example + + align:start position:0% +say for example + + + align:start position:0% +say for example +one solution + + align:start position:0% +one solution + + + align:start position:0% +one solution +it's just given by one zero zero zero + + align:start position:0% +it's just given by one zero zero zero + + + align:start position:0% +it's just given by one zero zero zero +Q2 + + align:start position:0% + + + + align:start position:0% + +so this one we all just discussed at the + + align:start position:0% +so this one we all just discussed at the + + + align:start position:0% +so this one we all just discussed at the +end of last lecture here I'm just + + align:start position:0% +end of last lecture here I'm just + + + align:start position:0% +end of last lecture here I'm just +trying to remind you + + align:start position:0% + + + + align:start position:0% + +okay so in this rest frame the solutions + + align:start position:0% +okay so in this rest frame the solutions + + + align:start position:0% +okay so in this rest frame the solutions +are particularly simple + + align:start position:0% +are particularly simple + + + align:start position:0% +are particularly simple +and so essentially you have two + + align:start position:0% +and so essentially you have two + + + align:start position:0% +and so essentially you have two +independent Solutions and then you take + + align:start position:0% +independent Solutions and then you take + + + align:start position:0% +independent Solutions and then you take +and take actually arbitrary and linear + + align:start position:0% +and take actually arbitrary and linear + + + align:start position:0% +and take actually arbitrary and linear +superposition of them because we are + + align:start position:0% +superposition of them because we are + + + align:start position:0% +superposition of them because we are +solving linear equations but similarly + + align:start position:0% +solving linear equations but similarly + + + align:start position:0% +solving linear equations but similarly +for V and you can take the arbitrary + + align:start position:0% +for V and you can take the arbitrary + + + align:start position:0% +for V and you can take the arbitrary +linear superpositions of this and then + + align:start position:0% +linear superpositions of this and then + + + align:start position:0% +linear superpositions of this and then +and then you will solved there okay + + align:start position:0% + + + + align:start position:0% + +and then for the um + + align:start position:0% + + + + align:start position:0% + +for General UK and V K you can just + + align:start position:0% +for General UK and V K you can just + + + align:start position:0% +for General UK and V K you can just +perform an orange transformation + + align:start position:0% +perform an orange transformation + + + align:start position:0% +perform an orange transformation +so you can perform lowering + + align:start position:0% +so you can perform lowering + + + align:start position:0% +so you can perform lowering +transformation say the UK + + align:start position:0% + + + + align:start position:0% + +is obtained by + + align:start position:0% +is obtained by + + + align:start position:0% +is obtained by +say s Lambda + + align:start position:0% +say s Lambda + + + align:start position:0% +say s Lambda +uk0 u0 + + align:start position:0% +uk0 u0 + + + align:start position:0% +uk0 u0 +okay and and the BK + + align:start position:0% +okay and and the BK + + + align:start position:0% +okay and and the BK +is given by S Lambda + + align:start position:0% +is given by S Lambda + + + align:start position:0% +is given by S Lambda +b0 + + align:start position:0% +b0 + + + align:start position:0% +b0 +okay so so the Lambda is to remember our + + align:start position:0% +okay so so the Lambda is to remember our + + + align:start position:0% +okay so so the Lambda is to remember our +rotation s Lambda is low range + + align:start position:0% +rotation s Lambda is low range + + + align:start position:0% +rotation s Lambda is low range +transformation on The Spinners + + align:start position:0% +transformation on The Spinners + + + align:start position:0% +transformation on The Spinners +okay it's a low range transmission on + + align:start position:0% +okay it's a low range transmission on + + + align:start position:0% +okay it's a low range transmission on +the spindles and the Lambda is just + + align:start position:0% +the spindles and the Lambda is just + + + align:start position:0% +the spindles and the Lambda is just +determined by the Lowrance + + align:start position:0% +determined by the Lowrance + + + align:start position:0% +determined by the Lowrance +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +to take + + align:start position:0% + + + + align:start position:0% + +this k0 + + align:start position:0% +this k0 + + + align:start position:0% +this k0 +to K okay so so for arbitrary + + align:start position:0% +to K okay so so for arbitrary + + + align:start position:0% +to K okay so so for arbitrary +so we take this zero + + align:start position:0% +so we take this zero + + + align:start position:0% +so we take this zero +so you make the lower range + + align:start position:0% +so you make the lower range + + + align:start position:0% +so you make the lower range +transformation to K and then and then + + align:start position:0% +transformation to K and then and then + + + align:start position:0% +transformation to K and then and then +and then the corresponding UK then then + + align:start position:0% +and then the corresponding UK then then + + + align:start position:0% +and then the corresponding UK then then +it's getting by that okay + + align:start position:0% + + + + align:start position:0% + +but in practice + + align:start position:0% +but in practice + + + align:start position:0% +but in practice +if I give your arbitrary say yeah okay + + align:start position:0% +if I give your arbitrary say yeah okay + + + align:start position:0% +if I give your arbitrary say yeah okay +keep the arbitrary k + + align:start position:0% +keep the arbitrary k + + + align:start position:0% +keep the arbitrary k +and you first work out the Lambda then + + align:start position:0% +and you first work out the Lambda then + + + align:start position:0% +and you first work out the Lambda then +you then you have to work out this s + + align:start position:0% +you then you have to work out this s + + + align:start position:0% +you then you have to work out this s +Lambda so working s m the uh is possible + + align:start position:0% +Lambda so working s m the uh is possible + + + align:start position:0% +Lambda so working s m the uh is possible +but again take some effort okay but but + + align:start position:0% +but again take some effort okay but but + + + align:start position:0% +but again take some effort okay but but +there's still a lot of shortcuts we can + + align:start position:0% +there's still a lot of shortcuts we can + + + align:start position:0% +there's still a lot of shortcuts we can +actually Define the solution so this is + + align:start position:0% +actually Define the solution so this is + + + align:start position:0% +actually Define the solution so this is +one way to do it and this alternative + + align:start position:0% +one way to do it and this alternative + + + align:start position:0% +one way to do it and this alternative +way + + align:start position:0% + + + + align:start position:0% + +so before I talk about this alternative + + align:start position:0% +so before I talk about this alternative + + + align:start position:0% +so before I talk about this alternative +I do have any questions so so this is + + align:start position:0% +I do have any questions so so this is + + + align:start position:0% +I do have any questions so so this is +more or less where we stopped so at the + + align:start position:0% +more or less where we stopped so at the + + + align:start position:0% +more or less where we stopped so at the +end of the before the break + + align:start position:0% +end of the before the break + + + align:start position:0% +end of the before the break +um + + align:start position:0% + + + + align:start position:0% + +any questions + + align:start position:0% + + + + align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +so + + align:start position:0% +so + + + align:start position:0% +so +so alternative will be we can actually + + align:start position:0% +so alternative will be we can actually + + + align:start position:0% +so alternative will be we can actually +find the simpler way + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so this simpler way is by + + align:start position:0% +so this simpler way is by + + + align:start position:0% +so this simpler way is by +by observing + + align:start position:0% +by observing + + + align:start position:0% +by observing +an identity okay + + align:start position:0% + + + + align:start position:0% + +you say if you look at the K slash + + align:start position:0% +you say if you look at the K slash + + + align:start position:0% +you say if you look at the K slash +Square + + align:start position:0% +Square + + + align:start position:0% +Square +so you have done something similar in + + align:start position:0% +so you have done something similar in + + + align:start position:0% +so you have done something similar in +your preset + + align:start position:0% +your preset + + + align:start position:0% +your preset +okay if you look at the case last Square + + align:start position:0% +okay if you look at the case last Square + + + align:start position:0% +okay if you look at the case last Square +so this quantity by definition is K mu + + align:start position:0% +so this quantity by definition is K mu + + + align:start position:0% +so this quantity by definition is K mu +gamma mu + + align:start position:0% +gamma mu + + + align:start position:0% +gamma mu +okay new gamma Lu + + align:start position:0% +okay new gamma Lu + + + align:start position:0% +okay new gamma Lu +okay and then you use the properties of + + align:start position:0% +okay and then you use the properties of + + + align:start position:0% +okay and then you use the properties of +gamma mu and the gamma Nu okay and then + + align:start position:0% +gamma mu and the gamma Nu okay and then + + + align:start position:0% +gamma mu and the gamma Nu okay and then +you + + align:start position:0% +you + + + align:start position:0% +you +can easily convince yourself this is + + align:start position:0% +can easily convince yourself this is + + + align:start position:0% +can easily convince yourself this is +just giving you the K Square + + align:start position:0% +just giving you the K Square + + + align:start position:0% +just giving you the K Square +okay this just gives you the K square + + align:start position:0% +okay this just gives you the K square + + + align:start position:0% +okay this just gives you the K square +and then + + align:start position:0% +and then + + + align:start position:0% +and then +because we are looking + + align:start position:0% +because we are looking + + + align:start position:0% +because we are looking +at the unshare solution so this is just + + align:start position:0% +at the unshare solution so this is just + + + align:start position:0% +at the unshare solution so this is just +equal to minus M squared okay + + align:start position:0% + + + + align:start position:0% + +then this means + + align:start position:0% + + + + align:start position:0% + +then this means + + align:start position:0% +then this means + + + align:start position:0% +then this means +that if I have i k slash plus m + + align:start position:0% + + + + align:start position:0% + +so which so appearing in the equation + + align:start position:0% +so which so appearing in the equation + + + align:start position:0% +so which so appearing in the equation +for u and v are a k slash plasma or + + align:start position:0% +for u and v are a k slash plasma or + + + align:start position:0% +for u and v are a k slash plasma or +minus m + + align:start position:0% +minus m + + + align:start position:0% +minus m +and then then if I multiply by a k slash + + align:start position:0% +and then then if I multiply by a k slash + + + align:start position:0% +and then then if I multiply by a k slash +minus m + + align:start position:0% +minus m + + + align:start position:0% +minus m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then essentially I have + + align:start position:0% +and then essentially I have + + + align:start position:0% +and then essentially I have +minus case slash Square minus M Square + + align:start position:0% +minus case slash Square minus M Square + + + align:start position:0% +minus case slash Square minus M Square +okay and this is actually equal to zero + + align:start position:0% +okay and this is actually equal to zero + + + align:start position:0% +okay and this is actually equal to zero +because of this equation + + align:start position:0% +because of this equation + + + align:start position:0% +because of this equation +okay + + align:start position:0% + + + + align:start position:0% + +so so now we can immediately observe + + align:start position:0% +so so now we can immediately observe + + + align:start position:0% +so so now we can immediately observe +okay so now we can immediately observe + + align:start position:0% + + + + align:start position:0% + +if I take a solution + + align:start position:0% + + + + align:start position:0% + +if I just uh to solve that equation + + align:start position:0% + + + + align:start position:0% + +we can just write U + + align:start position:0% + + + + align:start position:0% + +as say some normalization constant n + + align:start position:0% +as say some normalization constant n + + + align:start position:0% +as say some normalization constant n +would be normalization constant + + align:start position:0% +would be normalization constant + + + align:start position:0% +would be normalization constant +and ik slash plus m + + align:start position:0% + + + + align:start position:0% + +okay and then the acting on some + + align:start position:0% +okay and then the acting on some + + + align:start position:0% +okay and then the acting on some +arbitrary + + align:start position:0% +arbitrary + + + align:start position:0% +arbitrary +say you tilde okay some arbitrary + + align:start position:0% +say you tilde okay some arbitrary + + + align:start position:0% +say you tilde okay some arbitrary +spinder and then this equation that + + align:start position:0% +spinder and then this equation that + + + align:start position:0% +spinder and then this equation that +equation automatically satisfied + + align:start position:0% +equation automatically satisfied + + + align:start position:0% +equation automatically satisfied +okay automatically satisfied and + + align:start position:0% +okay automatically satisfied and + + + align:start position:0% +okay automatically satisfied and +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +V + + align:start position:0% +V + + + align:start position:0% +V +if I take some normalization constant + + align:start position:0% +if I take some normalization constant + + + align:start position:0% +if I take some normalization constant +and then take a minus i k slash plus m + + align:start position:0% +and then take a minus i k slash plus m + + + align:start position:0% +and then take a minus i k slash plus m +say some V tilde + + align:start position:0% +say some V tilde + + + align:start position:0% +say some V tilde +okay so that equates you again automatic + + align:start position:0% +okay so that equates you again automatic + + + align:start position:0% +okay so that equates you again automatic +the V equation of the Matrix result is + + align:start position:0% +the V equation of the Matrix result is + + + align:start position:0% +the V equation of the Matrix result is +five okay because of this identity + + align:start position:0% +five okay because of this identity + + + align:start position:0% +five okay because of this identity +and now we know that there's only two + + align:start position:0% +and now we know that there's only two + + + align:start position:0% +and now we know that there's only two +independent equations two independent + + align:start position:0% +independent equations two independent + + + align:start position:0% +independent equations two independent +solutions for both u and v okay + + align:start position:0% +solutions for both u and v okay + + + align:start position:0% +solutions for both u and v okay +and uh of both u and v + + align:start position:0% +and uh of both u and v + + + align:start position:0% +and uh of both u and v +so so so we can choose a basis for you + + align:start position:0% +so so so we can choose a basis for you + + + align:start position:0% +so so so we can choose a basis for you +and just by taking this to be + + align:start position:0% +and just by taking this to be + + + align:start position:0% +and just by taking this to be +say U S zero + + align:start position:0% + + + + align:start position:0% + +so so and then this would be a basis + + align:start position:0% +so so and then this would be a basis + + + align:start position:0% +so so and then this would be a basis +a complete the basis of solutions okay + + align:start position:0% +a complete the basis of solutions okay + + + align:start position:0% +a complete the basis of solutions okay +so s will go one to two Okay so because + + align:start position:0% +so s will go one to two Okay so because + + + align:start position:0% +so s will go one to two Okay so because +we have and for each of them we have two + + align:start position:0% +we have and for each of them we have two + + + align:start position:0% +we have and for each of them we have two +independent Solutions + + align:start position:0% + + + + align:start position:0% + +okay and uh so the reason we can choose + + align:start position:0% +okay and uh so the reason we can choose + + + align:start position:0% +okay and uh so the reason we can choose +us here you can also check that when you + + align:start position:0% +us here you can also check that when you + + + align:start position:0% +us here you can also check that when you +take the M uh when you take the 2B uh uh + + align:start position:0% +take the M uh when you take the 2B uh uh + + + align:start position:0% +take the M uh when you take the 2B uh uh +yeah yeah so so so so so when you take K + + align:start position:0% +yeah yeah so so so so so when you take K + + + align:start position:0% +yeah yeah so so so so so when you take K +to be k0 so you can easily check + + align:start position:0% +to be k0 so you can easily check + + + align:start position:0% +to be k0 so you can easily check +yourself that this equate uh this + + align:start position:0% +yourself that this equate uh this + + + align:start position:0% +yourself that this equate uh this +essentially just reduced to a a US zero + + align:start position:0% +essentially just reduced to a a US zero + + + align:start position:0% +essentially just reduced to a a US zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah this is consistent yeah I just say + + align:start position:0% +yeah this is consistent yeah I just say + + + align:start position:0% +yeah this is consistent yeah I just say +when you uh take that you just reduce to + + align:start position:0% +when you uh take that you just reduce to + + + align:start position:0% +when you uh take that you just reduce to +these spaces okay + + align:start position:0% + + + + align:start position:0% + +so n is the normalization constant + + align:start position:0% + + + + align:start position:0% + +and so us + + align:start position:0% +and so us + + + align:start position:0% +and so us +BS + + align:start position:0% +BS + + + align:start position:0% +BS +then provide a basis + + align:start position:0% +then provide a basis + + + align:start position:0% +then provide a basis +then this is a basis of solutions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and we can be sure these are the + + align:start position:0% +and we can be sure these are the + + + align:start position:0% +and we can be sure these are the +complete bases because the because + + align:start position:0% +complete bases because the because + + + align:start position:0% +complete bases because the because +that's the only yeah essentially or we + + align:start position:0% +that's the only yeah essentially or we + + + align:start position:0% +that's the only yeah essentially or we +already know the solution like okay at + + align:start position:0% +already know the solution like okay at + + + align:start position:0% +already know the solution like okay at +the rest frame and and we just have the + + align:start position:0% +the rest frame and and we just have the + + + align:start position:0% +the rest frame and and we just have the +right number of the uh the independent + + align:start position:0% +right number of the uh the independent + + + align:start position:0% +right number of the uh the independent +Solutions yes + + align:start position:0% + + + + align:start position:0% + +oh yeah yeah yeah here we don't know + + align:start position:0% +oh yeah yeah yeah here we don't know + + + align:start position:0% +oh yeah yeah yeah here we don't know +but you can guess why it should be the + + align:start position:0% +but you can guess why it should be the + + + align:start position:0% +but you can guess why it should be the +same it's just essentially uh + + align:start position:0% +same it's just essentially uh + + + align:start position:0% +same it's just essentially uh +so this you yeah because the equation + + align:start position:0% +so this you yeah because the equation + + + align:start position:0% +so this you yeah because the equation +looks pretty symmetric and the + + align:start position:0% +looks pretty symmetric and the + + + align:start position:0% +looks pretty symmetric and the +normalization constant don't depend on + + align:start position:0% +normalization constant don't depend on + + + align:start position:0% +normalization constant don't depend on +the sign of M essentially yeah + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah in principle uh I should + + align:start position:0% +yeah yeah yeah in principle uh I should + + + align:start position:0% +yeah yeah yeah in principle uh I should +write N1 and Q yeah just + + align:start position:0% +write N1 and Q yeah just + + + align:start position:0% +write N1 and Q yeah just +um but in the end they are the same + + align:start position:0% +um but in the end they are the same + + + align:start position:0% +um but in the end they are the same +good any + + align:start position:0% +good any + + + align:start position:0% +good any +other questions + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +so you can also + + align:start position:0% +so you can also + + + align:start position:0% +so you can also +yeah if you take the conjugate then you + + align:start position:0% +yeah if you take the conjugate then you + + + align:start position:0% +yeah if you take the conjugate then you +can get the uh the what's the U dagger + + align:start position:0% +can get the uh the what's the U dagger + + + align:start position:0% +can get the uh the what's the U dagger +or the U Bar or V dagger V bar okay + + align:start position:0% +or the U Bar or V dagger V bar okay + + + align:start position:0% +or the U Bar or V dagger V bar okay +so for example you just take the + + align:start position:0% +so for example you just take the + + + align:start position:0% +so for example you just take the +conjugate then you find the U.S bar + + align:start position:0% +conjugate then you find the U.S bar + + + align:start position:0% +conjugate then you find the U.S bar +so I hope you still remember the + + align:start position:0% +so I hope you still remember the + + + align:start position:0% +so I hope you still remember the +notation the US bar which is a U.S + + align:start position:0% +notation the US bar which is a U.S + + + align:start position:0% +notation the US bar which is a U.S +stagger times gamma zero in the US bar + + align:start position:0% +stagger times gamma zero in the US bar + + + align:start position:0% +stagger times gamma zero in the US bar +okay so this is for the conjugate + + align:start position:0% +okay so this is for the conjugate + + + align:start position:0% +okay so this is for the conjugate +solution will be a and the same n we can + + align:start position:0% +solution will be a and the same n we can + + + align:start position:0% +solution will be a and the same n we can +take n to be real say u s + + align:start position:0% +take n to be real say u s + + + align:start position:0% +take n to be real say u s +bar 0. it's an ik slash + + align:start position:0% +bar 0. it's an ik slash + + + align:start position:0% +bar 0. it's an ik slash +plus m okay so you just use the + + align:start position:0% +plus m okay so you just use the + + + align:start position:0% +plus m okay so you just use the +properties of the + + align:start position:0% + + + + align:start position:0% + +okay so you can also find this + + align:start position:0% + + + + align:start position:0% + +so now you can easily check yourself + + align:start position:0% +so now you can easily check yourself + + + align:start position:0% +so now you can easily check yourself +okay using again using this equation + + align:start position:0% + + + + align:start position:0% + +you can check that the U Bar and the V + + align:start position:0% +you can check that the U Bar and the V + + + align:start position:0% +you can check that the U Bar and the V +bar are actually U and the v orthogonal + + align:start position:0% +bar are actually U and the v orthogonal + + + align:start position:0% +bar are actually U and the v orthogonal +in the following sense and u r bar v s + + align:start position:0% +in the following sense and u r bar v s + + + align:start position:0% +in the following sense and u r bar v s +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +V bar r u s is equal to zero for + + align:start position:0% +V bar r u s is equal to zero for + + + align:start position:0% +V bar r u s is equal to zero for +arbitrary r r s equal to one and two + + align:start position:0% +arbitrary r r s equal to one and two + + + align:start position:0% +arbitrary r r s equal to one and two +okay so so U and the V orthogonal uh + + align:start position:0% +okay so so U and the V orthogonal uh + + + align:start position:0% +okay so so U and the V orthogonal uh +um + + align:start position:0% + + + + align:start position:0% + +and we can also + + align:start position:0% +and we can also + + + align:start position:0% +and we can also +and then + + align:start position:0% +and then + + + align:start position:0% +and then +we need to fix the normalization of u + + align:start position:0% +we need to fix the normalization of u + + + align:start position:0% +we need to fix the normalization of u +and v okay so it's convenient to fix the + + align:start position:0% +and v okay so it's convenient to fix the + + + align:start position:0% +and v okay so it's convenient to fix the +normalization as follows + + align:start position:0% +normalization as follows + + + align:start position:0% +normalization as follows +so we will use the following convention + + align:start position:0% +so we will use the following convention + + + align:start position:0% +so we will use the following convention +say U S Bar + + align:start position:0% +say U S Bar + + + align:start position:0% +say U S Bar +k + + align:start position:0% +k + + + align:start position:0% +k +say you are + + align:start position:0% +say you are + + + align:start position:0% +say you are +okay U Bar and u s k + + align:start position:0% +okay U Bar and u s k + + + align:start position:0% +okay U Bar and u s k +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +iqm + + align:start position:0% +iqm + + + align:start position:0% +iqm +Delta r s okay + + align:start position:0% +Delta r s okay + + + align:start position:0% +Delta r s okay +and similarly + + align:start position:0% +and similarly + + + align:start position:0% +and similarly +VR bar okay + + align:start position:0% +VR bar okay + + + align:start position:0% +VR bar okay +and the v s okay + + align:start position:0% + + + + align:start position:0% + +minus I + + align:start position:0% + + + + align:start position:0% + +q n + + align:start position:0% + + + + align:start position:0% + +okay so so this 2m just for for + + align:start position:0% +okay so so this 2m just for for + + + align:start position:0% +okay so so this 2m just for for +convenience okay + + align:start position:0% +convenience okay + + + align:start position:0% +convenience okay +so it just convention for convenience + + align:start position:0% +so it just convention for convenience + + + align:start position:0% +so it just convention for convenience +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so so so you can check yourself that + + align:start position:0% +so so so you can check yourself that + + + align:start position:0% +so so so you can check yourself that +actually uh um + + align:start position:0% +actually uh um + + + align:start position:0% +actually uh um +yeah uh uh uh so so different you + + align:start position:0% +yeah uh uh uh so so different you + + + align:start position:0% +yeah uh uh uh so so different you +different value of R and S they're also + + align:start position:0% +different value of R and S they're also + + + align:start position:0% +different value of R and S they're also +going to each other you can already see + + align:start position:0% +going to each other you can already see + + + align:start position:0% +going to each other you can already see +already in the in the rest frame okay + + align:start position:0% +already in the in the rest frame okay + + + align:start position:0% +already in the in the rest frame okay +you can just easily check using those + + align:start position:0% +you can just easily check using those + + + align:start position:0% +you can just easily check using those +extractions but you can also check again + + align:start position:0% +extractions but you can also check again + + + align:start position:0% +extractions but you can also check again +using this identity that the different + + align:start position:0% +using this identity that the different + + + align:start position:0% +using this identity that the different +value of R and S they're talking to each + + align:start position:0% +value of R and S they're talking to each + + + align:start position:0% +value of R and S they're talking to each +other and when they are the same and + + align:start position:0% +other and when they are the same and + + + align:start position:0% +other and when they are the same and +then we normalize the constant to be 2m + + align:start position:0% +then we normalize the constant to be 2m + + + align:start position:0% +then we normalize the constant to be 2m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +and from here you deduce + + align:start position:0% +and from here you deduce + + + align:start position:0% +and from here you deduce +and n + + align:start position:0% +and n + + + align:start position:0% +and n +is equal to 1 over + + align:start position:0% +is equal to 1 over + + + align:start position:0% +is equal to 1 over +square root e plus m + + align:start position:0% +square root e plus m + + + align:start position:0% +square root e plus m +so from now on I will also use the this + + align:start position:0% +so from now on I will also use the this + + + align:start position:0% +so from now on I will also use the this +notation for e + + align:start position:0% +notation for e + + + align:start position:0% +notation for e +so the E the energy + + align:start position:0% +so the E the energy + + + align:start position:0% +so the E the energy +this is Omega k + + align:start position:0% +this is Omega k + + + align:start position:0% +this is Omega k +okay so so now I will also use this + + align:start position:0% +okay so so now I will also use this + + + align:start position:0% +okay so so now I will also use this +notation okay + + align:start position:0% + + + + align:start position:0% + +good so this gives you a complete + + align:start position:0% +good so this gives you a complete + + + align:start position:0% +good so this gives you a complete +basis of solutions to the direct + + align:start position:0% +basis of solutions to the direct + + + align:start position:0% +basis of solutions to the direct +equations okay + + align:start position:0% +equations okay + + + align:start position:0% +equations okay +so so now let me just write them down to + + align:start position:0% +so so now let me just write them down to + + + align:start position:0% +so so now let me just write them down to +give you a little bit + + align:start position:0% +give you a little bit + + + align:start position:0% +give you a little bit +uh intuition about the explicit + + align:start position:0% +uh intuition about the explicit + + + align:start position:0% +uh intuition about the explicit +expression so so with those gamma + + align:start position:0% +expression so so with those gamma + + + align:start position:0% +expression so so with those gamma +matrices + + align:start position:0% +matrices + + + align:start position:0% +matrices +we can just plug in here + + align:start position:0% +we can just plug in here + + + align:start position:0% +we can just plug in here +okay and we know what's us 0 v s 0 we + + align:start position:0% +okay and we know what's us 0 v s 0 we + + + align:start position:0% +okay and we know what's us 0 v s 0 we +low n so so in principle log you can + + align:start position:0% +low n so so in principle log you can + + + align:start position:0% +low n so so in principle log you can +write them down explicitly so you find + + align:start position:0% +write them down explicitly so you find + + + align:start position:0% +write them down explicitly so you find +that in that basis + + align:start position:0% +that in that basis + + + align:start position:0% +that in that basis +then the usk is given by the following + + align:start position:0% + + + + align:start position:0% + +given by the square root + + align:start position:0% + + + + align:start position:0% + +e plus m + + align:start position:0% +e plus m + + + align:start position:0% +e plus m +PSI s + + align:start position:0% +PSI s + + + align:start position:0% +PSI s +and the sigma + + align:start position:0% +and the sigma + + + align:start position:0% +and the sigma +dot k + + align:start position:0% +dot k + + + align:start position:0% +dot k +divided by square root + + align:start position:0% +divided by square root + + + align:start position:0% +divided by square root +e plus m + + align:start position:0% + + + + align:start position:0% + +x i s + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and uh and the vs + + align:start position:0% + + + + align:start position:0% + +K is given by + + align:start position:0% + + + + align:start position:0% + +Sigma + + align:start position:0% +Sigma + + + align:start position:0% +Sigma +dot k + + align:start position:0% +dot k + + + align:start position:0% +dot k +divided by square root e plus m + + align:start position:0% +divided by square root e plus m + + + align:start position:0% +divided by square root e plus m +also cosine is + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +U plus m + + align:start position:0% +U plus m + + + align:start position:0% +U plus m +side s okay + + align:start position:0% +side s okay + + + align:start position:0% +side s okay +and x i s is a two + + align:start position:0% +and x i s is a two + + + align:start position:0% +and x i s is a two +so so s from 1 to 2 + + align:start position:0% +so so s from 1 to 2 + + + align:start position:0% +so so s from 1 to 2 +and x i one it's so s are two components + + align:start position:0% +and x i one it's so s are two components + + + align:start position:0% +and x i one it's so s are two components +vectors Y is given by one zero + + align:start position:0% +vectors Y is given by one zero + + + align:start position:0% +vectors Y is given by one zero +and the other + + align:start position:0% +and the other + + + align:start position:0% +and the other +is given by zero one okay + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +so that you get + + align:start position:0% +so that you get + + + align:start position:0% +so that you get +so so you can see + + align:start position:0% +so so you can see + + + align:start position:0% +so so you can see +in the rest frame + + align:start position:0% +in the rest frame + + + align:start position:0% +in the rest frame +k equal to zero essentially for you you + + align:start position:0% +k equal to zero essentially for you you + + + align:start position:0% +k equal to zero essentially for you you +just left with the upper half + + align:start position:0% +just left with the upper half + + + align:start position:0% +just left with the upper half +because this is zero and then and then + + align:start position:0% +because this is zero and then and then + + + align:start position:0% +because this is zero and then and then +we have with the one zero and the zero + + align:start position:0% +we have with the one zero and the zero + + + align:start position:0% +we have with the one zero and the zero +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +and then when k equal to zero and for V + + align:start position:0% +and then when k equal to zero and for V + + + align:start position:0% +and then when k equal to zero and for V +just left with the lower half and again + + align:start position:0% +just left with the lower half and again + + + align:start position:0% +just left with the lower half and again +we have the one zero and the zero one + + align:start position:0% +we have the one zero and the zero one + + + align:start position:0% +we have the one zero and the zero one +okay so this is consistent with the rest + + align:start position:0% +okay so this is consistent with the rest + + + align:start position:0% +okay so this is consistent with the rest +frame without or obtained earlier + + align:start position:0% +frame without or obtained earlier + + + align:start position:0% +frame without or obtained earlier +good any questions on this yes + + align:start position:0% +good any questions on this yes + + + align:start position:0% +good any questions on this yes +or Sigma just the sigma Matrix + + align:start position:0% +or Sigma just the sigma Matrix + + + align:start position:0% +or Sigma just the sigma Matrix +so this Sigma just pounding matrices + + align:start position:0% +so this Sigma just pounding matrices + + + align:start position:0% +so this Sigma just pounding matrices +Sigma 1 Sigma 2 Sigma 3 only matrices + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +good okay + + align:start position:0% +good okay + + + align:start position:0% +good okay +so so let me just mention a few make a + + align:start position:0% +so so let me just mention a few make a + + + align:start position:0% +so so let me just mention a few make a +few remarks on the solutions + + align:start position:0% +few remarks on the solutions + + + align:start position:0% +few remarks on the solutions +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +to + + align:start position:0% +to + + + align:start position:0% +to +to + + align:start position:0% +to + + + align:start position:0% +to +um + + align:start position:0% +um + + + align:start position:0% +um +yeah to be familiar with the properties + + align:start position:0% +yeah to be familiar with the properties + + + align:start position:0% +yeah to be familiar with the properties +of the solutions uh actually will be + + align:start position:0% +of the solutions uh actually will be + + + align:start position:0% +of the solutions uh actually will be +very useful when later you do farm and + + align:start position:0% +very useful when later you do farm and + + + align:start position:0% +very useful when later you do farm and +diagram calculations + + align:start position:0% +diagram calculations + + + align:start position:0% +diagram calculations +because the different uh when you + + align:start position:0% +because the different uh when you + + + align:start position:0% +because the different uh when you +involve say electron fermions and now + + align:start position:0% +involve say electron fermions and now + + + align:start position:0% +involve say electron fermions and now +it's no longer plane wave okay so so + + align:start position:0% +it's no longer plane wave okay so so + + + align:start position:0% +it's no longer plane wave okay so so +this u and v will enter your family + + align:start position:0% +this u and v will enter your family + + + align:start position:0% +this u and v will enter your family +diagram calculations and if you are + + align:start position:0% +diagram calculations and if you are + + + align:start position:0% +diagram calculations and if you are +familiar with their properties and will + + align:start position:0% +familiar with their properties and will + + + align:start position:0% +familiar with their properties and will +help you to uh do such calculations Okay + + align:start position:0% +help you to uh do such calculations Okay + + + align:start position:0% +help you to uh do such calculations Okay +so + + align:start position:0% +so + + + align:start position:0% +so +so let me just first mention some + + align:start position:0% +so let me just first mention some + + + align:start position:0% +so let me just first mention some +properties + + align:start position:0% + + + + align:start position:0% + +some remarks + + align:start position:0% +some remarks + + + align:start position:0% +some remarks +so first is that if we consider the long + + align:start position:0% +so first is that if we consider the long + + + align:start position:0% +so first is that if we consider the long +activistic limits + + align:start position:0% + + + + align:start position:0% + +okay the long right basic limits so + + align:start position:0% +okay the long right basic limits so + + + align:start position:0% +okay the long right basic limits so +that's corresponding to you take + + align:start position:0% +that's corresponding to you take + + + align:start position:0% +that's corresponding to you take +the magnitude of K divided by m goes to + + align:start position:0% +the magnitude of K divided by m goes to + + + align:start position:0% +the magnitude of K divided by m goes to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and then in this limit e would be + + align:start position:0% +and then in this limit e would be + + + align:start position:0% +and then in this limit e would be +approximately equal to m + + align:start position:0% +approximately equal to m + + + align:start position:0% +approximately equal to m +okay oops oximeter equal to m + + align:start position:0% +okay oops oximeter equal to m + + + align:start position:0% +okay oops oximeter equal to m +and then you find the leading order when + + align:start position:0% +and then you find the leading order when + + + align:start position:0% +and then you find the leading order when +you expand + + align:start position:0% +you expand + + + align:start position:0% +you expand +say in in yeah so you can expand this in + + align:start position:0% +say in in yeah so you can expand this in + + + align:start position:0% +say in in yeah so you can expand this in +1 over m + + align:start position:0% +1 over m + + + align:start position:0% +1 over m +so so so so sorry the leading order + + align:start position:0% + + + + align:start position:0% + +you find + + align:start position:0% +you find + + + align:start position:0% +you find +that the usk so you can just easily do + + align:start position:0% +that the usk so you can just easily do + + + align:start position:0% +that the usk so you can just easily do +this too okay and uh yeah so so this + + align:start position:0% +this too okay and uh yeah so so this + + + align:start position:0% +this too okay and uh yeah so so this +term certainly you can just ignore + + align:start position:0% +term certainly you can just ignore + + + align:start position:0% +term certainly you can just ignore +because e so this is M and so this is K + + align:start position:0% +because e so this is M and so this is K + + + align:start position:0% +because e so this is M and so this is K +divided by square root n so this is + + align:start position:0% +divided by square root n so this is + + + align:start position:0% +divided by square root n so this is +higher order than this one and here is + + align:start position:0% +higher order than this one and here is + + + align:start position:0% +higher order than this one and here is +the square root m + + align:start position:0% +the square root m + + + align:start position:0% +the square root m +so so to reading order you have square + + align:start position:0% +so so to reading order you have square + + + align:start position:0% +so so to reading order you have square +root 2m + + align:start position:0% +root 2m + + + align:start position:0% +root 2m +PSI s is zero + + align:start position:0% +PSI s is zero + + + align:start position:0% +PSI s is zero +okay similarly vsk + + align:start position:0% + + + + align:start position:0% + +equal to square root 2 m eating order + + align:start position:0% +equal to square root 2 m eating order + + + align:start position:0% +equal to square root 2 m eating order +0 psi s + + align:start position:0% +0 psi s + + + align:start position:0% +0 psi s +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so essentially what you see + + align:start position:0% +so essentially what you see + + + align:start position:0% +so essentially what you see +in the um + + align:start position:0% +in the um + + + align:start position:0% +in the um +in the in the longer activistic limit + + align:start position:0% +in the in the longer activistic limit + + + align:start position:0% +in the in the longer activistic limit +for example if we look at this positive + + align:start position:0% +for example if we look at this positive + + + align:start position:0% +for example if we look at this positive +energy solutions + + align:start position:0% +energy solutions + + + align:start position:0% +energy solutions +so this just reduced to arbitrary + + align:start position:0% + + + + align:start position:0% + +so u s k + + align:start position:0% +so u s k + + + align:start position:0% +so u s k +you yeah now you can do linear + + align:start position:0% +you yeah now you can do linear + + + align:start position:0% +you yeah now you can do linear +superposition just UK just reduce to + + align:start position:0% +superposition just UK just reduce to + + + align:start position:0% +superposition just UK just reduce to +arbitrary + + align:start position:0% + + + + align:start position:0% + +two component + + align:start position:0% + + + + align:start position:0% + +complex vector + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah so so you just so this is just some + + align:start position:0% +yeah so so you just so this is just some + + + align:start position:0% +yeah so so you just so this is just some +constant and as a basis you just have + + align:start position:0% +constant and as a basis you just have + + + align:start position:0% +constant and as a basis you just have +these basis and then you can just now do + + align:start position:0% +these basis and then you can just now do + + + align:start position:0% +these basis and then you can just now do +arbitrary com yeah just become the + + align:start position:0% +arbitrary com yeah just become the + + + align:start position:0% +arbitrary com yeah just become the +arbitrary complex Vector so D so this + + align:start position:0% +arbitrary complex Vector so D so this + + + align:start position:0% +arbitrary complex Vector so D so this +should remind you how we describe a spin + + align:start position:0% +should remind you how we describe a spin + + + align:start position:0% +should remind you how we describe a spin +half particle + + align:start position:0% +half particle + + + align:start position:0% +half particle +in our activistic limit okay in another + + align:start position:0% +in our activistic limit okay in another + + + align:start position:0% +in our activistic limit okay in another +basic limit + + align:start position:0% +basic limit + + + align:start position:0% +basic limit +the way we describe the uh a spin half + + align:start position:0% +the way we describe the uh a spin half + + + align:start position:0% +the way we describe the uh a spin half +particle and it's precisely a a two + + align:start position:0% +particle and it's precisely a a two + + + align:start position:0% +particle and it's precisely a a two +component a vector okay so so this is + + align:start position:0% +component a vector okay so so this is + + + align:start position:0% +component a vector okay so so this is +exactly + + align:start position:0% + + + + align:start position:0% + +as the description + + align:start position:0% + + + + align:start position:0% + +of a spin half + + align:start position:0% + + + + align:start position:0% + +particle + + align:start position:0% + + + + align:start position:0% + +yeah the wave function + + align:start position:0% +yeah the wave function + + + align:start position:0% +yeah the wave function +yeah here you should understand as the + + align:start position:0% +yeah here you should understand as the + + + align:start position:0% +yeah here you should understand as the +wave function description + + align:start position:0% +wave function description + + + align:start position:0% +wave function description +of the spin half particle okay in + + align:start position:0% +of the spin half particle okay in + + + align:start position:0% +of the spin half particle okay in +non-relativistic quantum mechanics + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so I will not go through here but + + align:start position:0% +and so I will not go through here but + + + align:start position:0% +and so I will not go through here but +you can show + + align:start position:0% +you can show + + + align:start position:0% +you can show +you can show in the language limits + + align:start position:0% +you can show in the language limits + + + align:start position:0% +you can show in the language limits +this solution actually decoupled + + align:start position:0% +this solution actually decoupled + + + align:start position:0% +this solution actually decoupled +okay in the end when you solve the + + align:start position:0% +okay in the end when you solve the + + + align:start position:0% +okay in the end when you solve the +equation only one half of the equation + + align:start position:0% +equation only one half of the equation + + + align:start position:0% +equation only one half of the equation +above half of the solution remain and + + align:start position:0% +above half of the solution remain and + + + align:start position:0% +above half of the solution remain and +actually this is no longer yeah + + align:start position:0% +actually this is no longer yeah + + + align:start position:0% +actually this is no longer yeah +I just get the positive energy solution + + align:start position:0% +I just get the positive energy solution + + + align:start position:0% +I just get the positive energy solution +so uh so in that image you you + + align:start position:0% +so uh so in that image you you + + + align:start position:0% +so uh so in that image you you +essentially only reduce to two + + align:start position:0% +essentially only reduce to two + + + align:start position:0% +essentially only reduce to two +components okay + + align:start position:0% + + + + align:start position:0% + +so this is the first remark so this is + + align:start position:0% +so this is the first remark so this is + + + align:start position:0% +so this is the first remark so this is +the first indication + + align:start position:0% +the first indication + + + align:start position:0% +the first indication +we see that this should likely describe + + align:start position:0% +we see that this should likely describe + + + align:start position:0% +we see that this should likely describe +a spring half particle okay uh the rock + + align:start position:0% +a spring half particle okay uh the rock + + + align:start position:0% +a spring half particle okay uh the rock +theory uh uh likely describes uh a spin + + align:start position:0% +theory uh uh likely describes uh a spin + + + align:start position:0% +theory uh uh likely describes uh a spin +half particle + + align:start position:0% + + + + align:start position:0% + +so the second limit we can consider + + align:start position:0% + + + + align:start position:0% + +is considered the the actual + + align:start position:0% +is considered the the actual + + + align:start position:0% +is considered the the actual +relativistic limit + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is an image which e is much + + align:start position:0% +so this is an image which e is much + + + align:start position:0% +so this is an image which e is much +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +energy is much greater than m okay and E + + align:start position:0% +energy is much greater than m okay and E + + + align:start position:0% +energy is much greater than m okay and E +and then will be approximate + + align:start position:0% +and then will be approximate + + + align:start position:0% +and then will be approximate +say to K to the magnitude of K + + align:start position:0% +say to K to the magnitude of K + + + align:start position:0% +say to K to the magnitude of K +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now let's also Define the direction + + align:start position:0% +and now let's also Define the direction + + + align:start position:0% +and now let's also Define the direction +of K by just k + + align:start position:0% + + + + align:start position:0% + +very by its magnitude okay + + align:start position:0% +very by its magnitude okay + + + align:start position:0% +very by its magnitude okay +so we also introduced the K hat + + align:start position:0% +so we also introduced the K hat + + + align:start position:0% +so we also introduced the K hat +is the unit Vector along the direction + + align:start position:0% +is the unit Vector along the direction + + + align:start position:0% +is the unit Vector along the direction +of the K so in this case you can do a a + + align:start position:0% +of the K so in this case you can do a a + + + align:start position:0% +of the K so in this case you can do a a +small M expansion + + align:start position:0% +small M expansion + + + align:start position:0% +small M expansion +okay just do a small em expression these + + align:start position:0% +okay just do a small em expression these + + + align:start position:0% +okay just do a small em expression these +two expressions for v u and v + + align:start position:0% +two expressions for v u and v + + + align:start position:0% +two expressions for v u and v +and then you then you find your leading + + align:start position:0% +and then you then you find your leading + + + align:start position:0% +and then you then you find your leading +order + + align:start position:0% + + + + align:start position:0% + +usk given by + + align:start position:0% +usk given by + + + align:start position:0% +usk given by +square root e + + align:start position:0% +square root e + + + align:start position:0% +square root e +okay and then you have PSI s + + align:start position:0% +okay and then you have PSI s + + + align:start position:0% +okay and then you have PSI s +and then you have Sigma + + align:start position:0% +and then you have Sigma + + + align:start position:0% +and then you have Sigma +k + + align:start position:0% +k + + + align:start position:0% +k +hat + + align:start position:0% +hat + + + align:start position:0% +hat +PSI s + + align:start position:0% +PSI s + + + align:start position:0% +PSI s +okay this is for the US + + align:start position:0% +okay this is for the US + + + align:start position:0% +okay this is for the US +and for the vs you find + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's the so you find that solution + + align:start position:0% +so that's the so you find that solution + + + align:start position:0% +so that's the so you find that solution +simplify + + align:start position:0% +simplify + + + align:start position:0% +simplify +and so that's the result you get okay + + align:start position:0% + + + + align:start position:0% + +so so it's not manifest + + align:start position:0% +so so it's not manifest + + + align:start position:0% +so so it's not manifest +from this expression + + align:start position:0% +from this expression + + + align:start position:0% +from this expression +but actually there's something very + + align:start position:0% +but actually there's something very + + + align:start position:0% +but actually there's something very +special + + align:start position:0% +special + + + align:start position:0% +special +in this question in this simplified + + align:start position:0% +in this question in this simplified + + + align:start position:0% +in this question in this simplified +expression in algebraith basic limit + + align:start position:0% +expression in algebraith basic limit + + + align:start position:0% +expression in algebraith basic limit +so if you look at + + align:start position:0% + + + + align:start position:0% + +so the expression for u and v + + align:start position:0% +so the expression for u and v + + + align:start position:0% +so the expression for u and v +these are linearly independent + + align:start position:0% +these are linearly independent + + + align:start position:0% +these are linearly independent +in the sense that no matter how you do + + align:start position:0% +in the sense that no matter how you do + + + align:start position:0% +in the sense that no matter how you do +linear superposition of U you will not + + align:start position:0% +linear superposition of U you will not + + + align:start position:0% +linear superposition of U you will not +be able to get V okay and also how you + + align:start position:0% +be able to get V okay and also how you + + + align:start position:0% +be able to get V okay and also how you +do a linear solution of V you won't get + + align:start position:0% +do a linear solution of V you won't get + + + align:start position:0% +do a linear solution of V you won't get +U okay + + align:start position:0% +U okay + + + align:start position:0% +U okay +but in this limit even though it's not + + align:start position:0% +but in this limit even though it's not + + + align:start position:0% +but in this limit even though it's not +clear uh not manifest in this form but + + align:start position:0% +clear uh not manifest in this form but + + + align:start position:0% +clear uh not manifest in this form but +in fact this dual linearly related to + + align:start position:0% +in fact this dual linearly related to + + + align:start position:0% +in fact this dual linearly related to +each other + + align:start position:0% +each other + + + align:start position:0% +each other +so so this can be seen as follows + + align:start position:0% +so so this can be seen as follows + + + align:start position:0% +so so this can be seen as follows +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so if you + + align:start position:0% + + + + align:start position:0% + +so if you uh use the identity + + align:start position:0% +so if you uh use the identity + + + align:start position:0% +so if you uh use the identity +that's Sigma + + align:start position:0% + + + + align:start position:0% + +dot dot k + + align:start position:0% +dot dot k + + + align:start position:0% +dot dot k +Square + + align:start position:0% +Square + + + align:start position:0% +Square +okay so this is the analog of this + + align:start position:0% +okay so this is the analog of this + + + align:start position:0% +okay so this is the analog of this +equation + + align:start position:0% + + + + align:start position:0% + +for the sigma matrices okay for the + + align:start position:0% +for the sigma matrices okay for the + + + align:start position:0% +for the sigma matrices okay for the +party matrices + + align:start position:0% +party matrices + + + align:start position:0% +party matrices +and this you can easily again using the + + align:start position:0% +and this you can easily again using the + + + align:start position:0% +and this you can easily again using the +property of poly matrices you can + + align:start position:0% +property of poly matrices you can + + + align:start position:0% +property of poly matrices you can +convince yourself that this is just + + align:start position:0% +convince yourself that this is just + + + align:start position:0% +convince yourself that this is just +giving you K hat squared + + align:start position:0% +giving you K hat squared + + + align:start position:0% +giving you K hat squared +okay give you K hat squared + + align:start position:0% +okay give you K hat squared + + + align:start position:0% +okay give you K hat squared +and this is actually if you go this is a + + align:start position:0% +and this is actually if you go this is a + + + align:start position:0% +and this is actually if you go this is a +unit Vector this is just one + + align:start position:0% +unit Vector this is just one + + + align:start position:0% +unit Vector this is just one +okay so now if you use this property + + align:start position:0% +okay so now if you use this property + + + align:start position:0% +okay so now if you use this property +this is equal to 1 + + align:start position:0% +this is equal to 1 + + + align:start position:0% +this is equal to 1 +and then we find + + align:start position:0% +and then we find + + + align:start position:0% +and then we find +and then that + + align:start position:0% + + + + align:start position:0% + +ETA s equal to + + align:start position:0% +ETA s equal to + + + align:start position:0% +ETA s equal to +Sigma k + + align:start position:0% +Sigma k + + + align:start position:0% +Sigma k +Sigma dot k hat PSI s + + align:start position:0% + + + + align:start position:0% + +and then you find the vsk + + align:start position:0% +and then you find the vsk + + + align:start position:0% +and then you find the vsk +can be written it in the exactly form as + + align:start position:0% +can be written it in the exactly form as + + + align:start position:0% +can be written it in the exactly form as +u s k just replace e to S by uh by + + align:start position:0% +u s k just replace e to S by uh by + + + align:start position:0% +u s k just replace e to S by uh by +cosine s by ETA s and then you can have + + align:start position:0% +cosine s by ETA s and then you can have + + + align:start position:0% +cosine s by ETA s and then you can have +it + + align:start position:0% +it + + + align:start position:0% +it +in the following form + + align:start position:0% +in the following form + + + align:start position:0% +in the following form +square root e + + align:start position:0% + + + + align:start position:0% + +ETA s + + align:start position:0% +ETA s + + + align:start position:0% +ETA s +igma + + align:start position:0% +igma + + + align:start position:0% +igma +dot k + + align:start position:0% +dot k + + + align:start position:0% +dot k +is s + + align:start position:0% +is s + + + align:start position:0% +is s +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this is obviously this is equivalent to + + align:start position:0% +this is obviously this is equivalent to + + + align:start position:0% +this is obviously this is equivalent to +that once you plug in the E to S equal + + align:start position:0% +that once you plug in the E to S equal + + + align:start position:0% +that once you plug in the E to S equal +to Sigma k sorry because this just give + + align:start position:0% +to Sigma k sorry because this just give + + + align:start position:0% +to Sigma k sorry because this just give +you that and when you plug into here you + + align:start position:0% +you that and when you plug into here you + + + align:start position:0% +you that and when you plug into here you +get the sigma K square and the grid 1 + + align:start position:0% +get the sigma K square and the grid 1 + + + align:start position:0% +get the sigma K square and the grid 1 +and again you reduce to that okay + + align:start position:0% +and again you reduce to that okay + + + align:start position:0% +and again you reduce to that okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but now these have exactly the same form + + align:start position:0% + + + + align:start position:0% + +as this one + + align:start position:0% + + + + align:start position:0% + +except now ETA s + + align:start position:0% +except now ETA s + + + align:start position:0% +except now ETA s +is a linear so position of the PSI s + + align:start position:0% +is a linear so position of the PSI s + + + align:start position:0% +is a linear so position of the PSI s +then that means that the vs is a linear + + align:start position:0% +then that means that the vs is a linear + + + align:start position:0% +then that means that the vs is a linear +superposition of the U.S + + align:start position:0% +superposition of the U.S + + + align:start position:0% +superposition of the U.S +okay so this means that the vs is a + + align:start position:0% +okay so this means that the vs is a + + + align:start position:0% +okay so this means that the vs is a +linear solution of vs + + align:start position:0% +linear solution of vs + + + align:start position:0% +linear solution of vs +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so vs now is + + align:start position:0% + + + + align:start position:0% + +superposition + + align:start position:0% + + + + align:start position:0% + +obvious of us + + align:start position:0% +obvious of us + + + align:start position:0% +obvious of us +so they are no longer independent okay + + align:start position:0% +so they are no longer independent okay + + + align:start position:0% +so they are no longer independent okay +so so they are not + + align:start position:0% + + + + align:start position:0% + +linear independent + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so actually + + align:start position:0% + + + + align:start position:0% + +if you remember one of the Basin we have + + align:start position:0% +if you remember one of the Basin we have + + + align:start position:0% +if you remember one of the Basin we have +discussed before this may not appear + + align:start position:0% +discussed before this may not appear + + + align:start position:0% +discussed before this may not appear +surprise to you + + align:start position:0% +surprise to you + + + align:start position:0% +surprise to you +because previously we already discussed + + align:start position:0% +because previously we already discussed + + + align:start position:0% +because previously we already discussed +when we derived with the diracy equation + + align:start position:0% +when we derived with the diracy equation + + + align:start position:0% +when we derived with the diracy equation +so direct equation + + align:start position:0% +so direct equation + + + align:start position:0% +so direct equation +in order to satisfy all the properties + + align:start position:0% +in order to satisfy all the properties + + + align:start position:0% +in order to satisfy all the properties +for long zero m + + align:start position:0% +for long zero m + + + align:start position:0% +for long zero m +we did a four + + align:start position:0% +we did a four + + + align:start position:0% +we did a four +dimensional matrices okay so that means + + align:start position:0% +dimensional matrices okay so that means + + + align:start position:0% +dimensional matrices okay so that means +PSI is a four vector + + align:start position:0% +PSI is a four vector + + + align:start position:0% +PSI is a four vector +but we also mentioned that if you + + align:start position:0% +but we also mentioned that if you + + + align:start position:0% +but we also mentioned that if you +in the message case said m equal to zero + + align:start position:0% +in the message case said m equal to zero + + + align:start position:0% +in the message case said m equal to zero +in the message case actually you can use + + align:start position:0% +in the message case actually you can use + + + align:start position:0% +in the message case actually you can use +two components just use gamma matrices + + align:start position:0% +two components just use gamma matrices + + + align:start position:0% +two components just use gamma matrices +so that means that if you solve a mass + + align:start position:0% +so that means that if you solve a mass + + + align:start position:0% +so that means that if you solve a mass +list Rock equation you only need you + + align:start position:0% +list Rock equation you only need you + + + align:start position:0% +list Rock equation you only need you +only have two independent Solutions + + align:start position:0% +only have two independent Solutions + + + align:start position:0% +only have two independent Solutions +and this actually basically limit is + + align:start position:0% +and this actually basically limit is + + + align:start position:0% +and this actually basically limit is +precisely like the Master's limit + + align:start position:0% +precisely like the Master's limit + + + align:start position:0% +precisely like the Master's limit +because the mass the energy is much + + align:start position:0% +because the mass the energy is much + + + align:start position:0% +because the mass the energy is much +greater than the mass and then you can + + align:start position:0% +greater than the mass and then you can + + + align:start position:0% +greater than the mass and then you can +neglect the effect of mass + + align:start position:0% +neglect the effect of mass + + + align:start position:0% +neglect the effect of mass +okay so so this is consistent + + align:start position:0% + + + + align:start position:0% + +means that the massive Rock equation + + align:start position:0% + + + + align:start position:0% + +with that the only + + align:start position:0% +with that the only + + + align:start position:0% +with that the only +requests + + align:start position:0% + + + + align:start position:0% + +two components + + align:start position:0% +two components + + + align:start position:0% +two components +okay rather than four components okay + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah then you have to be a little + + align:start position:0% +yeah yeah then you have to be a little + + + align:start position:0% +yeah yeah then you have to be a little +bit careful yeah yeah + + align:start position:0% + + + + align:start position:0% + +so that's a very good question so so you + + align:start position:0% +so that's a very good question so so you + + + align:start position:0% +so that's a very good question so so you +have to be careful a little bit and when + + align:start position:0% +have to be careful a little bit and when + + + align:start position:0% +have to be careful a little bit and when +you take the limit in uh in deriving + + align:start position:0% +you take the limit in uh in deriving + + + align:start position:0% +you take the limit in uh in deriving +that relation yeah + + align:start position:0% +that relation yeah + + + align:start position:0% +that relation yeah +yeah yeah just you have to be a little + + align:start position:0% +yeah yeah just you have to be a little + + + align:start position:0% +yeah yeah just you have to be a little +more careful uh in understanding yeah I + + align:start position:0% +more careful uh in understanding yeah I + + + align:start position:0% +more careful uh in understanding yeah I +forgot the exact uh what exactly + + align:start position:0% +forgot the exact uh what exactly + + + align:start position:0% +forgot the exact uh what exactly +happened to that equation but I remember + + align:start position:0% +happened to that equation but I remember + + + align:start position:0% +happened to that equation but I remember +this uncertainties yeah you have to be + + align:start position:0% +this uncertainties yeah you have to be + + + align:start position:0% +this uncertainties yeah you have to be +yep + + align:start position:0% + + + + align:start position:0% + +good other questions + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +okay so also there are some other useful + + align:start position:0% +okay so also there are some other useful + + + align:start position:0% +okay so also there are some other useful +relations + + align:start position:0% +relations + + + align:start position:0% +relations +which will be useful later + + align:start position:0% +which will be useful later + + + align:start position:0% +which will be useful later +so so one of them + + align:start position:0% +so so one of them + + + align:start position:0% +so so one of them +so so let me also list some useful + + align:start position:0% +so so let me also list some useful + + + align:start position:0% +so so let me also list some useful +relations + + align:start position:0% + + + + align:start position:0% + +so so why you said if you look at you + + align:start position:0% +so so why you said if you look at you + + + align:start position:0% +so so why you said if you look at you +are dagger + + align:start position:0% +are dagger + + + align:start position:0% +are dagger +and U.S + + align:start position:0% +and U.S + + + align:start position:0% +and U.S +so this is K + + align:start position:0% +so this is K + + + align:start position:0% +so this is K +u s k + + align:start position:0% +u s k + + + align:start position:0% +u s k +okay again this is orthogonal + + align:start position:0% +okay again this is orthogonal + + + align:start position:0% +okay again this is orthogonal +between r and s + + align:start position:0% +between r and s + + + align:start position:0% +between r and s +and then it's given by 2E dot RS + + align:start position:0% +and then it's given by 2E dot RS + + + align:start position:0% +and then it's given by 2E dot RS +okay so here a spa so the difference + + align:start position:0% +okay so here a spa so the difference + + + align:start position:0% +okay so here a spa so the difference +here is bar + + align:start position:0% +here is bar + + + align:start position:0% +here is bar +and so so when you have a bar you have + + align:start position:0% +and so so when you have a bar you have + + + align:start position:0% +and so so when you have a bar you have +additional gamma zero + + align:start position:0% +additional gamma zero + + + align:start position:0% +additional gamma zero +okay and then and then here is 2m then + + align:start position:0% +okay and then and then here is 2m then + + + align:start position:0% +okay and then and then here is 2m then +here become QE and here you have + + align:start position:0% +here become QE and here you have + + + align:start position:0% +here become QE and here you have +additional I because you have a gamma + + align:start position:0% +additional I because you have a gamma + + + align:start position:0% +additional I because you have a gamma +zero + + align:start position:0% +zero + + + align:start position:0% +zero +because comma zero remember comma zero + + align:start position:0% +because comma zero remember comma zero + + + align:start position:0% +because comma zero remember comma zero +squared to minus one so so gamma Zero + + align:start position:0% +squared to minus one so so gamma Zero + + + align:start position:0% +squared to minus one so so gamma Zero +have actually eigenvalue to be pure + + align:start position:0% +have actually eigenvalue to be pure + + + align:start position:0% +have actually eigenvalue to be pure +imaginary so so that's why there's a + + align:start position:0% +imaginary so so that's why there's a + + + align:start position:0% +imaginary so so that's why there's a +difference in y here okay + + align:start position:0% +difference in y here okay + + + align:start position:0% +difference in y here okay +and similarly + + align:start position:0% +and similarly + + + align:start position:0% +and similarly +the VR + + align:start position:0% +the VR + + + align:start position:0% +the VR +dagger k + + align:start position:0% +dagger k + + + align:start position:0% +dagger k +and vsk + + align:start position:0% +and vsk + + + align:start position:0% +and vsk +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +2E + + align:start position:0% +2E + + + align:start position:0% +2E +dot is okay + + align:start position:0% + + + + align:start position:0% + +so so those expressions + + align:start position:0% +so so those expressions + + + align:start position:0% +so so those expressions +to um + + align:start position:0% + + + + align:start position:0% + +yeah will be very useful later + + align:start position:0% + + + + align:start position:0% + +when you actually + + align:start position:0% +when you actually + + + align:start position:0% +when you actually +do two calculations + + align:start position:0% + + + + align:start position:0% + +all right right yeah yeah I forgot to + + align:start position:0% +all right right yeah yeah I forgot to + + + align:start position:0% +all right right yeah yeah I forgot to +mention yeah the reason is that the the + + align:start position:0% +mention yeah the reason is that the the + + + align:start position:0% +mention yeah the reason is that the the +reason that the limit is start home into + + align:start position:0% +reason that the limit is start home into + + + align:start position:0% +reason that the limit is start home into +that is because the I remember the + + align:start position:0% +that is because the I remember the + + + align:start position:0% +that is because the I remember the +normalization we do here is m + + align:start position:0% +normalization we do here is m + + + align:start position:0% +normalization we do here is m +so and so you have to change your + + align:start position:0% +so and so you have to change your + + + align:start position:0% +so and so you have to change your +normalization when you go to the + + align:start position:0% +normalization when you go to the + + + align:start position:0% +normalization when you go to the +Masterpiece case yeah so yeah so this + + align:start position:0% +Masterpiece case yeah so yeah so this + + + align:start position:0% +Masterpiece case yeah so yeah so this +worries since you have to be careful + + align:start position:0% +worries since you have to be careful + + + align:start position:0% +worries since you have to be careful +okay + + align:start position:0% +okay + + + align:start position:0% +okay +very since you have to be careful + + align:start position:0% +very since you have to be careful + + + align:start position:0% +very since you have to be careful +so so you have that + + align:start position:0% +so so you have that + + + align:start position:0% +so so you have that +and then you also have the relation + + align:start position:0% + + + + align:start position:0% + +that the you are dagger + + align:start position:0% +that the you are dagger + + + align:start position:0% +that the you are dagger +k + + align:start position:0% +k + + + align:start position:0% +k +so so because the everything is on here + + align:start position:0% +so so because the everything is on here + + + align:start position:0% +so so because the everything is on here +so in principle I can only I only need + + align:start position:0% +so in principle I can only I only need + + + align:start position:0% +so in principle I can only I only need +to specify the spatial momentum okay so + + align:start position:0% +to specify the spatial momentum okay so + + + align:start position:0% +to specify the spatial momentum okay so +it's of convenience let me just specify + + align:start position:0% +it's of convenience let me just specify + + + align:start position:0% +it's of convenience let me just specify +the spatial momentum + + align:start position:0% +the spatial momentum + + + align:start position:0% +the spatial momentum +and which is easier in notation + + align:start position:0% +and which is easier in notation + + + align:start position:0% +and which is easier in notation +so so now + + align:start position:0% + + + + align:start position:0% + +it turns out u r and v s it's a nice + + align:start position:0% +it turns out u r and v s it's a nice + + + align:start position:0% +it turns out u r and v s it's a nice +dagger when you have bar the the + + align:start position:0% +dagger when you have bar the the + + + align:start position:0% +dagger when you have bar the the +orthoglo we have the expression there + + align:start position:0% +orthoglo we have the expression there + + + align:start position:0% +orthoglo we have the expression there +but then you have dagger it it turns out + + align:start position:0% +but then you have dagger it it turns out + + + align:start position:0% +but then you have dagger it it turns out +it's also going to minus k + + align:start position:0% +it's also going to minus k + + + align:start position:0% +it's also going to minus k +okay you have to reverse your spatial + + align:start position:0% +okay you have to reverse your spatial + + + align:start position:0% +okay you have to reverse your spatial +momentum okay and this is equal to + + align:start position:0% +momentum okay and this is equal to + + + align:start position:0% +momentum okay and this is equal to +VR + + align:start position:0% +VR + + + align:start position:0% +VR +k + + align:start position:0% + + + + align:start position:0% + +and the U.S + + align:start position:0% +and the U.S + + + align:start position:0% +and the U.S +minus K so this is equal to zero + + align:start position:0% +minus K so this is equal to zero + + + align:start position:0% +minus K so this is equal to zero +but this is actually not equal to zero + + align:start position:0% +but this is actually not equal to zero + + + align:start position:0% +but this is actually not equal to zero +okay + + align:start position:0% + + + + align:start position:0% + +you are dagger okay + + align:start position:0% +you are dagger okay + + + align:start position:0% +you are dagger okay +us + + align:start position:0% +us + + + align:start position:0% +us +vs + + align:start position:0% +vs + + + align:start position:0% +vs +k + + align:start position:0% +k + + + align:start position:0% +k +it's actually not the Future Okay so so + + align:start position:0% +it's actually not the Future Okay so so + + + align:start position:0% +it's actually not the Future Okay so so +they're not also okay only the bar + + align:start position:0% +they're not also okay only the bar + + + align:start position:0% +they're not also okay only the bar +relation is also low and then and then + + align:start position:0% +relation is also low and then and then + + + align:start position:0% +relation is also low and then and then +this inflation is so good okay + + align:start position:0% + + + + align:start position:0% + +and and similarly with the conjugate of + + align:start position:0% +and and similarly with the conjugate of + + + align:start position:0% +and and similarly with the conjugate of +this okay + + align:start position:0% +this okay + + + align:start position:0% +this okay +so so those relations you can just check + + align:start position:0% +so so those relations you can just check + + + align:start position:0% +so so those relations you can just check +them + + align:start position:0% +them + + + align:start position:0% +them +using explicit reform of those + + align:start position:0% +using explicit reform of those + + + align:start position:0% +using explicit reform of those +expression okay and we have this + + align:start position:0% +expression okay and we have this + + + align:start position:0% +expression okay and we have this +question here you can just check that + + align:start position:0% +question here you can just check that + + + align:start position:0% +question here you can just check that +the expression is true okay and so we + + align:start position:0% +the expression is true okay and so we + + + align:start position:0% +the expression is true okay and so we +are not going to uh that + + align:start position:0% +are not going to uh that + + + align:start position:0% +are not going to uh that +but actually more remarkably + + align:start position:0% +but actually more remarkably + + + align:start position:0% +but actually more remarkably +expressions so when we derive this + + align:start position:0% +expressions so when we derive this + + + align:start position:0% +expressions so when we derive this +expression + + align:start position:0% +expression + + + align:start position:0% +expression +we actually use the expressive form of + + align:start position:0% +we actually use the expressive form of + + + align:start position:0% +we actually use the expressive form of +the gamma matrices okay it depends on + + align:start position:0% +the gamma matrices okay it depends on + + + align:start position:0% +the gamma matrices okay it depends on +the expression for uh so those + + align:start position:0% +the expression for uh so those + + + align:start position:0% +the expression for uh so those +expressions depend on expressive form of + + align:start position:0% +expressions depend on expressive form of + + + align:start position:0% +expressions depend on expressive form of +this comma matrices so if you have a + + align:start position:0% +this comma matrices so if you have a + + + align:start position:0% +this comma matrices so if you have a +different set of government matrices + + align:start position:0% +different set of government matrices + + + align:start position:0% +different set of government matrices +then you get different forms okay + + align:start position:0% +then you get different forms okay + + + align:start position:0% +then you get different forms okay +but but of course physically they're all + + align:start position:0% +but but of course physically they're all + + + align:start position:0% +but but of course physically they're all +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +very tenderize a lot of relations + + align:start position:0% + + + + align:start position:0% + +okay so those regulations actually are + + align:start position:0% +okay so those regulations actually are + + + align:start position:0% +okay so those regulations actually are +independent of choice of gamma matrices + + align:start position:0% +independent of choice of gamma matrices + + + align:start position:0% +independent of choice of gamma matrices +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so so so let me just + + align:start position:0% +so so so let me just + + + align:start position:0% +so so so let me just +enable them by + + align:start position:0% +enable them by + + + align:start position:0% +enable them by +let me call it star + + align:start position:0% +let me call it star + + + align:start position:0% +let me call it star +and here by star star + + align:start position:0% + + + + align:start position:0% + +so star and star + + align:start position:0% + + + + align:start position:0% + +s are actually independent + + align:start position:0% + + + + align:start position:0% + +of choice + + align:start position:0% + + + + align:start position:0% + +of reputations + + align:start position:0% +of reputations + + + align:start position:0% +of reputations +of gamma matrices okay + + align:start position:0% + + + + align:start position:0% + +so so they actually are Universal for + + align:start position:0% +so so they actually are Universal for + + + align:start position:0% +so so they actually are Universal for +any choice of government matrices so + + align:start position:0% +any choice of government matrices so + + + align:start position:0% +any choice of government matrices so +this is very useful okay because because + + align:start position:0% +this is very useful okay because because + + + align:start position:0% +this is very useful okay because because +when you do calculations then you don't + + align:start position:0% +when you do calculations then you don't + + + align:start position:0% +when you do calculations then you don't +have to worry uh uh of each choice of uh + + align:start position:0% +have to worry uh uh of each choice of uh + + + align:start position:0% +have to worry uh uh of each choice of uh +gamma matrices you make and those + + align:start position:0% +gamma matrices you make and those + + + align:start position:0% +gamma matrices you make and those +expressions are + + align:start position:0% +expressions are + + + align:start position:0% +expressions are +at you + + align:start position:0% + + + + align:start position:0% + +so so you can actually + + align:start position:0% +so so you can actually + + + align:start position:0% +so so you can actually +so you can actually derive + + align:start position:0% + + + + align:start position:0% + +those expressions + + align:start position:0% +those expressions + + + align:start position:0% +those expressions +okay without using gamma matrices just + + align:start position:0% +okay without using gamma matrices just + + + align:start position:0% +okay without using gamma matrices just +abstract 3 you only using the properties + + align:start position:0% +abstract 3 you only using the properties + + + align:start position:0% +abstract 3 you only using the properties +of the + + align:start position:0% +of the + + + align:start position:0% +of the +the rocky equation itself and the + + align:start position:0% +the rocky equation itself and the + + + align:start position:0% +the rocky equation itself and the +general properties of gamma matrices + + align:start position:0% +general properties of gamma matrices + + + align:start position:0% +general properties of gamma matrices +without using explicit representations + + align:start position:0% +without using explicit representations + + + align:start position:0% +without using explicit representations +okay uh um yes + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +no no that also does not depend on + + align:start position:0% +no no that also does not depend on + + + align:start position:0% +no no that also does not depend on +repetition yeah yeah that also does not + + align:start position:0% +repetition yeah yeah that also does not + + + align:start position:0% +repetition yeah yeah that also does not +yeah all this normalization does not + + align:start position:0% +yeah all this normalization does not + + + align:start position:0% +yeah all this normalization does not +depend on the reputation + + align:start position:0% +depend on the reputation + + + align:start position:0% +depend on the reputation +but but this expression somehow is + + align:start position:0% +but but this expression somehow is + + + align:start position:0% +but but this expression somehow is +yeah that's just our definition we just + + align:start position:0% +yeah that's just our definition we just + + + align:start position:0% +yeah that's just our definition we just +Define them this way + + align:start position:0% +Define them this way + + + align:start position:0% +Define them this way +we Define them this way so this just + + align:start position:0% +we Define them this way so this just + + + align:start position:0% +we Define them this way so this just +follows from uh from those General + + align:start position:0% +follows from uh from those General + + + align:start position:0% +follows from uh from those General +expressions from just from this equation + + align:start position:0% +expressions from just from this equation + + + align:start position:0% +expressions from just from this equation +but but this equation is not obvious + + align:start position:0% +but but this equation is not obvious + + + align:start position:0% +but but this equation is not obvious +because wizard gamma zero then it's a + + align:start position:0% +because wizard gamma zero then it's a + + + align:start position:0% +because wizard gamma zero then it's a +less directory related to the to the + + align:start position:0% +less directory related to the to the + + + align:start position:0% +less directory related to the to the +wrong equation itself and by Tanda the + + align:start position:0% +wrong equation itself and by Tanda the + + + align:start position:0% +wrong equation itself and by Tanda the +uh this expression also independent of + + align:start position:0% +uh this expression also independent of + + + align:start position:0% +uh this expression also independent of +the choice of car matrices + + align:start position:0% + + + + align:start position:0% + +any other questions + + align:start position:0% + + + + align:start position:0% + +okay I can give you a derivation + + align:start position:0% +okay I can give you a derivation + + + align:start position:0% +okay I can give you a derivation +of this uh without using gamma matrices + + align:start position:0% +of this uh without using gamma matrices + + + align:start position:0% +of this uh without using gamma matrices +and yeah but that takes a few minutes I + + align:start position:0% +and yeah but that takes a few minutes I + + + align:start position:0% +and yeah but that takes a few minutes I +I will skip that you can read it in + + align:start position:0% +I will skip that you can read it in + + + align:start position:0% +I will skip that you can read it in +passing so passing has a derivation + + align:start position:0% +passing so passing has a derivation + + + align:start position:0% +passing so passing has a derivation +of this + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +so so but but you should remember this + + align:start position:0% +so so but but you should remember this + + + align:start position:0% +so so but but you should remember this +yourself okay just remember it + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +so the fourth remark + + align:start position:0% +so the fourth remark + + + align:start position:0% +so the fourth remark +you said often we actually need to use + + align:start position:0% +you said often we actually need to use + + + align:start position:0% +you said often we actually need to use +the projection + + align:start position:0% +the projection + + + align:start position:0% +the projection +so you can also construct projections + + align:start position:0% +so you can also construct projections + + + align:start position:0% +so you can also construct projections +projectors + + align:start position:0% +projectors + + + align:start position:0% +projectors +to + + align:start position:0% +to + + + align:start position:0% +to +the positive + + align:start position:0% +the positive + + + align:start position:0% +the positive +and elective + + align:start position:0% + + + + align:start position:0% + +solution space okay + + align:start position:0% + + + + align:start position:0% + +species + + align:start position:0% +species + + + align:start position:0% +species +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so consider so the projector + + align:start position:0% + + + + align:start position:0% + +to the space + + align:start position:0% + + + + align:start position:0% + +spanned by us + + align:start position:0% + + + + align:start position:0% + +can be defined as the followers so let + + align:start position:0% +can be defined as the followers so let + + + align:start position:0% +can be defined as the followers so let +me call it plot P plus + + align:start position:0% +me call it plot P plus + + + align:start position:0% +me call it plot P plus +so so this just from + + align:start position:0% +so so this just from + + + align:start position:0% +so so this just from +QAM so that's come from the luminization + + align:start position:0% +QAM so that's come from the luminization + + + align:start position:0% +QAM so that's come from the luminization +then just sum s + + align:start position:0% +then just sum s + + + align:start position:0% +then just sum s +equal to one and two + + align:start position:0% +equal to one and two + + + align:start position:0% +equal to one and two +usk + + align:start position:0% + + + + align:start position:0% + +and the US bar k + + align:start position:0% +and the US bar k + + + align:start position:0% +and the US bar k +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so you can easily check yourself okay + + align:start position:0% +so so you can easily check yourself okay + + + align:start position:0% +so so you can easily check yourself okay +because the orthogonal relations + + align:start position:0% +because the orthogonal relations + + + align:start position:0% +because the orthogonal relations +because u and v are orthogonal when you + + align:start position:0% +because u and v are orthogonal when you + + + align:start position:0% +because u and v are orthogonal when you +act this on the uh on the general + + align:start position:0% +act this on the uh on the general + + + align:start position:0% +act this on the uh on the general +solution we have just project into + + align:start position:0% +solution we have just project into + + + align:start position:0% +solution we have just project into +Solutions proportional and only involve + + align:start position:0% +Solutions proportional and only involve + + + align:start position:0% +Solutions proportional and only involve +linear superpositions of U okay + + align:start position:0% + + + + align:start position:0% + +so so now you can check + + align:start position:0% +so so now you can check + + + align:start position:0% +so so now you can check +you can check yourself explicitly + + align:start position:0% + + + + align:start position:0% + +with this + + align:start position:0% +with this + + + align:start position:0% +with this +so just use the worries use property of + + align:start position:0% +so just use the worries use property of + + + align:start position:0% +so just use the worries use property of +this view you can check yourself + + align:start position:0% +this view you can check yourself + + + align:start position:0% +this view you can check yourself +explicitly video where I will not do + + align:start position:0% +explicitly video where I will not do + + + align:start position:0% +explicitly video where I will not do +there and you um + + align:start position:0% +there and you um + + + align:start position:0% +there and you um +you can check that this is indeed the + + align:start position:0% +you can check that this is indeed the + + + align:start position:0% +you can check that this is indeed the +projector okay if you look at P Square + + align:start position:0% +projector okay if you look at P Square + + + align:start position:0% +projector okay if you look at P Square +it gives back to itself + + align:start position:0% + + + + align:start position:0% + +and with a little bit more effort + + align:start position:0% +and with a little bit more effort + + + align:start position:0% +and with a little bit more effort +you can further show + + align:start position:0% + + + + align:start position:0% + +that the P plus can be written in the + + align:start position:0% +that the P plus can be written in the + + + align:start position:0% +that the P plus can be written in the +following form + + align:start position:0% +following form + + + align:start position:0% +following form +AK slash plus m + + align:start position:0% +AK slash plus m + + + align:start position:0% +AK slash plus m +divided by 2m + + align:start position:0% +divided by 2m + + + align:start position:0% +divided by 2m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this requires a little bit more + + align:start position:0% +so so this requires a little bit more + + + align:start position:0% +so so this requires a little bit more +efforts that we leave as exercise for + + align:start position:0% +efforts that we leave as exercise for + + + align:start position:0% +efforts that we leave as exercise for +yourself okay + + align:start position:0% + + + + align:start position:0% + +or you can + + align:start position:0% +or you can + + + align:start position:0% +or you can +look at it from the from the books okay + + align:start position:0% +look at it from the from the books okay + + + align:start position:0% +look at it from the from the books okay +yeah + + align:start position:0% + + + + align:start position:0% + +and similarly you can Define the + + align:start position:0% +and similarly you can Define the + + + align:start position:0% +and similarly you can Define the +projector + + align:start position:0% +projector + + + align:start position:0% +projector +to the to the space of V + + align:start position:0% +to the to the space of V + + + align:start position:0% +to the to the space of V +so the P minus + + align:start position:0% +so the P minus + + + align:start position:0% +so the P minus +you can also Define p minus to be + + align:start position:0% +you can also Define p minus to be + + + align:start position:0% +you can also Define p minus to be +minus 2 High m + + align:start position:0% +minus 2 High m + + + align:start position:0% +minus 2 High m +because of the minus sign here + + align:start position:0% +because of the minus sign here + + + align:start position:0% +because of the minus sign here +so one over minus two I am + + align:start position:0% +so one over minus two I am + + + align:start position:0% +so one over minus two I am +sum s + + align:start position:0% +sum s + + + align:start position:0% +sum s +v s k + + align:start position:0% +v s k + + + align:start position:0% +v s k +we as far k + + align:start position:0% +we as far k + + + align:start position:0% +we as far k +and you can show that this is also have + + align:start position:0% +and you can show that this is also have + + + align:start position:0% +and you can show that this is also have +a + + align:start position:0% +a + + + align:start position:0% +a +can be written as something like this + + align:start position:0% +can be written as something like this + + + align:start position:0% +can be written as something like this +minus ik slash + + align:start position:0% +minus ik slash + + + align:start position:0% +minus ik slash +plus m divided by 2m + + align:start position:0% +plus m divided by 2m + + + align:start position:0% +plus m divided by 2m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so again this I will leave as + + align:start position:0% +so so again this I will leave as + + + align:start position:0% +so so again this I will leave as +exercise to yourself + + align:start position:0% +exercise to yourself + + + align:start position:0% +exercise to yourself +so this is a projector to the to the + + align:start position:0% +so this is a projector to the to the + + + align:start position:0% +so this is a projector to the to the +space of V's + + align:start position:0% +space of V's + + + align:start position:0% +space of V's +and then + + align:start position:0% + + + + align:start position:0% + +from these two expression + + align:start position:0% +from these two expression + + + align:start position:0% +from these two expression +p plus P minus you easily see + + align:start position:0% +p plus P minus you easily see + + + align:start position:0% +p plus P minus you easily see +p plus plus three minus equal to one + + align:start position:0% + + + + align:start position:0% + +and use the Expression I just erased + + align:start position:0% +and use the Expression I just erased + + + align:start position:0% +and use the Expression I just erased +so from the taking the product and the P + + align:start position:0% +so from the taking the product and the P + + + align:start position:0% +so from the taking the product and the P +plus P minus + + align:start position:0% +plus P minus + + + align:start position:0% +plus P minus +is equal to P minus P plus equal to zero + + align:start position:0% +is equal to P minus P plus equal to zero + + + align:start position:0% +is equal to P minus P plus equal to zero +okay so in this they are just projectors + + align:start position:0% +okay so in this they are just projectors + + + align:start position:0% +okay so in this they are just projectors +orthogonal projectors into different + + align:start position:0% +orthogonal projectors into different + + + align:start position:0% +orthogonal projectors into different +space + + align:start position:0% + + + + align:start position:0% + +okay so this concludes our discussion + + align:start position:0% +okay so this concludes our discussion + + + align:start position:0% +okay so this concludes our discussion +of the classical Solutions of the rock + + align:start position:0% +of the classical Solutions of the rock + + + align:start position:0% +of the classical Solutions of the rock +equations and their properties so do you + + align:start position:0% +equations and their properties so do you + + + align:start position:0% +equations and their properties so do you +have other questions + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah that you need to quantize the + + align:start position:0% +yeah yeah that you need to quantize the + + + align:start position:0% +yeah yeah that you need to quantize the +theory first right but we haven't + + align:start position:0% +theory first right but we haven't + + + align:start position:0% +theory first right but we haven't +context this here + + align:start position:0% +context this here + + + align:start position:0% +context this here +yeah so yeah that would be our next step + + align:start position:0% +yeah so yeah that would be our next step + + + align:start position:0% +yeah so yeah that would be our next step +so so once we have find the full set of + + align:start position:0% +so so once we have find the full set of + + + align:start position:0% +so so once we have find the full set of +classical Solutions and now we can + + align:start position:0% +classical Solutions and now we can + + + align:start position:0% +classical Solutions and now we can +quantize it and once quantize it then we + + align:start position:0% +quantize it and once quantize it then we + + + align:start position:0% +quantize it and once quantize it then we +can actually really uh find this angle + + align:start position:0% +can actually really uh find this angle + + + align:start position:0% +can actually really uh find this angle +moment + + align:start position:0% + + + + align:start position:0% + +other questions and indeed actually I + + align:start position:0% +other questions and indeed actually I + + + align:start position:0% +other questions and indeed actually I +think that would be a one of your preset + + align:start position:0% +think that would be a one of your preset + + + align:start position:0% +think that would be a one of your preset +problem + + align:start position:0% +problem + + + align:start position:0% +problem +yeah to to show yourself that this is + + align:start position:0% +yeah to to show yourself that this is + + + align:start position:0% +yeah to to show yourself that this is +screen half + + align:start position:0% + + + + align:start position:0% + +yeah but uh yeah other questions + + align:start position:0% + + + + align:start position:0% + +okay good + + align:start position:0% + + + + align:start position:0% + +good so so now we conclude the + + align:start position:0% +good so so now we conclude the + + + align:start position:0% +good so so now we conclude the +discussion now we can quantize the + + align:start position:0% +discussion now we can quantize the + + + align:start position:0% +discussion now we can quantize the +theory + + align:start position:0% + + + + align:start position:0% + +now we can go to the quantity Quantum + + align:start position:0% +now we can go to the quantity Quantum + + + align:start position:0% +now we can go to the quantity Quantum +system + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so the uh remember the action + + align:start position:0% +so so the uh remember the action + + + align:start position:0% +so so the uh remember the action +for the Iraq + + align:start position:0% +for the Iraq + + + align:start position:0% +for the Iraq +is d4ox + + align:start position:0% + + + + align:start position:0% + +PSI bar + + align:start position:0% +PSI bar + + + align:start position:0% +PSI bar +gamma mu partial mu + + align:start position:0% +gamma mu partial mu + + + align:start position:0% +gamma mu partial mu +PSI partial mu minus m + + align:start position:0% +PSI partial mu minus m + + + align:start position:0% +PSI partial mu minus m +side okay so this is the this is the + + align:start position:0% +side okay so this is the this is the + + + align:start position:0% +side okay so this is the this is the +action which give us the the rank + + align:start position:0% +action which give us the the rank + + + align:start position:0% +action which give us the the rank +equation + + align:start position:0% +equation + + + align:start position:0% +equation +so + + align:start position:0% +so + + + align:start position:0% +so +so in order to contact it the first + + align:start position:0% +so in order to contact it the first + + + align:start position:0% +so in order to contact it the first +remember our procedure to quantize a + + align:start position:0% +remember our procedure to quantize a + + + align:start position:0% +remember our procedure to quantize a +theory + + align:start position:0% +theory + + + align:start position:0% +theory +so we we need to First find the + + align:start position:0% +so we we need to First find the + + + align:start position:0% +so we we need to First find the +canonical momentum + + align:start position:0% +canonical momentum + + + align:start position:0% +canonical momentum +and we also need to impose the canonical + + align:start position:0% +and we also need to impose the canonical + + + align:start position:0% +and we also need to impose the canonical +commutation relation + + align:start position:0% +commutation relation + + + align:start position:0% +commutation relation +and then we then expand your operators + + align:start position:0% +and then we then expand your operators + + + align:start position:0% +and then we then expand your operators +in terms of complete sets of classical + + align:start position:0% +in terms of complete sets of classical + + + align:start position:0% +in terms of complete sets of classical +Solutions and then that's corresponding + + align:start position:0% +Solutions and then that's corresponding + + + align:start position:0% +Solutions and then that's corresponding +to the solutions to the operating + + align:start position:0% +to the solutions to the operating + + + align:start position:0% +to the solutions to the operating +equations okay so so let's try to find + + align:start position:0% +equations okay so so let's try to find + + + align:start position:0% +equations okay so so let's try to find +out what's the canonical momentum of PSI + + align:start position:0% + + + + align:start position:0% + +so so as in the complex scalar case we + + align:start position:0% +so so as in the complex scalar case we + + + align:start position:0% +so so as in the complex scalar case we +can treat the PSI and percent dagger as + + align:start position:0% +can treat the PSI and percent dagger as + + + align:start position:0% +can treat the PSI and percent dagger as +independent variables okay because of + + align:start position:0% +independent variables okay because of + + + align:start position:0% +independent variables okay because of +the um yeah so so then the canonical + + align:start position:0% +the um yeah so so then the canonical + + + align:start position:0% +the um yeah so so then the canonical +momentum for PSI + + align:start position:0% +momentum for PSI + + + align:start position:0% +momentum for PSI +if you look at this expression + + align:start position:0% +if you look at this expression + + + align:start position:0% +if you look at this expression +so so you look at the partial zero on + + align:start position:0% +so so you look at the partial zero on + + + align:start position:0% +so so you look at the partial zero on +PSI then you find yeah so so the + + align:start position:0% +PSI then you find yeah so so the + + + align:start position:0% +PSI then you find yeah so so the +lagrangian density + + align:start position:0% +lagrangian density + + + align:start position:0% +lagrangian density +if you look at that if I write a bit + + align:start position:0% +if you look at that if I write a bit + + + align:start position:0% +if you look at that if I write a bit +of the form + + align:start position:0% +of the form + + + align:start position:0% +of the form +it's a dagger + + align:start position:0% +it's a dagger + + + align:start position:0% +it's a dagger +so this diagram comma zero + + align:start position:0% +so this diagram comma zero + + + align:start position:0% +so this diagram comma zero +and then comma zero side zero + + align:start position:0% + + + + align:start position:0% + +PSI then plus the rest of the terms okay + + align:start position:0% +PSI then plus the rest of the terms okay + + + align:start position:0% +PSI then plus the rest of the terms okay +so so in order to find the canonical + + align:start position:0% +so so in order to find the canonical + + + align:start position:0% +so so in order to find the canonical +momentum we are only interested in the + + align:start position:0% +momentum we are only interested in the + + + align:start position:0% +momentum we are only interested in the +part of the + + align:start position:0% +part of the + + + align:start position:0% +part of the +uh the logonian density which are + + align:start position:0% +uh the logonian density which are + + + align:start position:0% +uh the logonian density which are +related to the derivative of PSI well at + + align:start position:0% +related to the derivative of PSI well at + + + align:start position:0% +related to the derivative of PSI well at +the time derivative okay and so that's + + align:start position:0% +the time derivative okay and so that's + + + align:start position:0% +the time derivative okay and so that's +the only term involving time derivative + + align:start position:0% +the only term involving time derivative + + + align:start position:0% +the only term involving time derivative +of either side of PSI bar or opposite + + align:start position:0% +of either side of PSI bar or opposite + + + align:start position:0% +of either side of PSI bar or opposite +diagram okay + + align:start position:0% +diagram okay + + + align:start position:0% +diagram okay +so so this + + align:start position:0% +so so this + + + align:start position:0% +so so this +comma 0 square equal to minus one so + + align:start position:0% +comma 0 square equal to minus one so + + + align:start position:0% +comma 0 square equal to minus one so +this is just I side dagger partial zero + + align:start position:0% +this is just I side dagger partial zero + + + align:start position:0% +this is just I side dagger partial zero +PSI + + align:start position:0% +PSI + + + align:start position:0% +PSI +so now we can + + align:start position:0% +so now we can + + + align:start position:0% +so now we can +immediately find out + + align:start position:0% +immediately find out + + + align:start position:0% +immediately find out +that the conjugate momentum + + align:start position:0% +that the conjugate momentum + + + align:start position:0% +that the conjugate momentum +for PSI + + align:start position:0% +for PSI + + + align:start position:0% +for PSI +is given by Ipsy dagger + + align:start position:0% +is given by Ipsy dagger + + + align:start position:0% +is given by Ipsy dagger +because you take a derivative on PSI + + align:start position:0% +because you take a derivative on PSI + + + align:start position:0% +because you take a derivative on PSI +zero uh partial zero percent just get a + + align:start position:0% +zero uh partial zero percent just get a + + + align:start position:0% +zero uh partial zero percent just get a +percent angle but the conjugate momentum + + align:start position:0% +percent angle but the conjugate momentum + + + align:start position:0% +percent angle but the conjugate momentum +stagger + + align:start position:0% + + + + align:start position:0% + +is actually equal to what + + align:start position:0% + + + + align:start position:0% + +so so what is this + + align:start position:0% + + + + align:start position:0% + +this is equal to zero because there's no + + align:start position:0% +this is equal to zero because there's no + + + align:start position:0% +this is equal to zero because there's no +time derivative on on side diagram + + align:start position:0% +time derivative on on side diagram + + + align:start position:0% +time derivative on on side diagram +so so this tells you + + align:start position:0% +so so this tells you + + + align:start position:0% +so so this tells you +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this so fact that this + + align:start position:0% +so so this so fact that this + + + align:start position:0% +so so this so fact that this +you could do zero + + align:start position:0% +you could do zero + + + align:start position:0% +you could do zero +because you + + align:start position:0% +because you + + + align:start position:0% +because you +actually the direct system okay the + + align:start position:0% +actually the direct system okay the + + + align:start position:0% +actually the direct system okay the +action uh this direct system is actually + + align:start position:0% +action uh this direct system is actually + + + align:start position:0% +action uh this direct system is actually +a constraint system + + align:start position:0% + + + + align:start position:0% + +so this is considered to be a constraint + + align:start position:0% +so this is considered to be a constraint + + + align:start position:0% +so this is considered to be a constraint +okay because you can no longer normally + + align:start position:0% +okay because you can no longer normally + + + align:start position:0% +okay because you can no longer normally +so remember + + align:start position:0% +so remember + + + align:start position:0% +so remember +when you are when we uh say from the + + align:start position:0% +when you are when we uh say from the + + + align:start position:0% +when you are when we uh say from the +lagrangian + + align:start position:0% +lagrangian + + + align:start position:0% +lagrangian +you find the canonical momentum + + align:start position:0% +you find the canonical momentum + + + align:start position:0% +you find the canonical momentum +and then you you invert the canonical + + align:start position:0% +and then you you invert the canonical + + + align:start position:0% +and then you you invert the canonical +momentum to find the hamiltonian okay + + align:start position:0% +momentum to find the hamiltonian okay + + + align:start position:0% +momentum to find the hamiltonian okay +but but when you have this equal to zero + + align:start position:0% +but but when you have this equal to zero + + + align:start position:0% +but but when you have this equal to zero +you cannot invert it okay you cannot + + align:start position:0% +you cannot invert it okay you cannot + + + align:start position:0% +you cannot invert it okay you cannot +express your say PSI or PSI Diagon in + + align:start position:0% +express your say PSI or PSI Diagon in + + + align:start position:0% +express your say PSI or PSI Diagon in +terms of pipes that diagram okay and so + + align:start position:0% +terms of pipes that diagram okay and so + + + align:start position:0% +terms of pipes that diagram okay and so +so this is a constraint + + align:start position:0% +so this is a constraint + + + align:start position:0% +so this is a constraint +so that means we actually have a + + align:start position:0% +so that means we actually have a + + + align:start position:0% +so that means we actually have a +constraint system okay + + align:start position:0% +constraint system okay + + + align:start position:0% +constraint system okay +means you have a constraint system + + align:start position:0% +means you have a constraint system + + + align:start position:0% +means you have a constraint system +and frankly constrained systems + + align:start position:0% +and frankly constrained systems + + + align:start position:0% +and frankly constrained systems +are very annoying + + align:start position:0% +are very annoying + + + align:start position:0% +are very annoying +okay very annoying and uh but but so uh + + align:start position:0% +okay very annoying and uh but but so uh + + + align:start position:0% +okay very annoying and uh but but so uh +have involved a lot of + + align:start position:0% +have involved a lot of + + + align:start position:0% +have involved a lot of +involve a lot of formalism in order to + + align:start position:0% +involve a lot of formalism in order to + + + align:start position:0% +involve a lot of formalism in order to +say treat the constraint system to + + align:start position:0% +say treat the constraint system to + + + align:start position:0% +say treat the constraint system to +contact them Etc + + align:start position:0% +contact them Etc + + + align:start position:0% +contact them Etc +okay but fortunately in this case this + + align:start position:0% +okay but fortunately in this case this + + + align:start position:0% +okay but fortunately in this case this +is actually a simple trick to go to go + + align:start position:0% +is actually a simple trick to go to go + + + align:start position:0% +is actually a simple trick to go to go +around it okay and so now now I will not + + align:start position:0% +around it okay and so now now I will not + + + align:start position:0% +around it okay and so now now I will not +use + + align:start position:0% +use + + + align:start position:0% +use +this full-fledged constrained + + align:start position:0% +this full-fledged constrained + + + align:start position:0% +this full-fledged constrained +quantization to do the job I will just + + align:start position:0% +quantization to do the job I will just + + + align:start position:0% +quantization to do the job I will just +use a simple trick which will reach the + + align:start position:0% +use a simple trick which will reach the + + + align:start position:0% +use a simple trick which will reach the +same answer yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah so there's ambiguity so so + + align:start position:0% +yeah yeah so there's ambiguity so so + + + align:start position:0% +yeah yeah so there's ambiguity so so +that's part of the reflection that this + + align:start position:0% +that's part of the reflection that this + + + align:start position:0% +that's part of the reflection that this +is a constraint system yeah + + align:start position:0% +is a constraint system yeah + + + align:start position:0% +is a constraint system yeah +so this is actually typical + + align:start position:0% +so this is actually typical + + + align:start position:0% +so this is actually typical +to have this kind of constraints + + align:start position:0% +to have this kind of constraints + + + align:start position:0% +to have this kind of constraints +is typical whenever you have a first + + align:start position:0% +is typical whenever you have a first + + + align:start position:0% +is typical whenever you have a first +order system so here it's different from + + align:start position:0% +order system so here it's different from + + + align:start position:0% +order system so here it's different from +the client golden action is because here + + align:start position:0% +the client golden action is because here + + + align:start position:0% +the client golden action is because here +only only involved in the first + + align:start position:0% +only only involved in the first + + + align:start position:0% +only only involved in the first +derivative okay a one derivative rather + + align:start position:0% +derivative okay a one derivative rather + + + align:start position:0% +derivative okay a one derivative rather +than two derivatives + + align:start position:0% +than two derivatives + + + align:start position:0% +than two derivatives +and so this is not our standard system + + align:start position:0% +and so this is not our standard system + + + align:start position:0% +and so this is not our standard system +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so the way + + align:start position:0% +so so the way + + + align:start position:0% +so so the way +to go around this is the following + + align:start position:0% + + + + align:start position:0% + +okay the way to go around is the volume + + align:start position:0% +okay the way to go around is the volume + + + align:start position:0% +okay the way to go around is the volume +is now + + align:start position:0% +is now + + + align:start position:0% +is now +so this equation if we look at this + + align:start position:0% +so this equation if we look at this + + + align:start position:0% +so this equation if we look at this +equation + + align:start position:0% + + + + align:start position:0% + +so this equation tells you that the + + align:start position:0% +so this equation tells you that the + + + align:start position:0% +so this equation tells you that the +canonical momentum conjugate to psi + + align:start position:0% +canonical momentum conjugate to psi + + + align:start position:0% +canonical momentum conjugate to psi +is actually dagger + + align:start position:0% +is actually dagger + + + align:start position:0% +is actually dagger +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so also here is a little bit uh funny + + align:start position:0% +so also here is a little bit uh funny + + + align:start position:0% +so also here is a little bit uh funny +because you remember in the in the + + align:start position:0% +because you remember in the in the + + + align:start position:0% +because you remember in the in the +standard the story The canonical + + align:start position:0% +standard the story The canonical + + + align:start position:0% +standard the story The canonical +momentum is related to the time + + align:start position:0% +momentum is related to the time + + + align:start position:0% +momentum is related to the time +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +okay and here there's no time derivative + + align:start position:0% +okay and here there's no time derivative + + + align:start position:0% +okay and here there's no time derivative +here just side diagram itself okay and + + align:start position:0% +here just side diagram itself okay and + + + align:start position:0% +here just side diagram itself okay and +this is another uh indication that this + + align:start position:0% +this is another uh indication that this + + + align:start position:0% +this is another uh indication that this +is a constraint uh rather than uh um + + align:start position:0% +is a constraint uh rather than uh um + + + align:start position:0% +is a constraint uh rather than uh um +yeah so so anyway + + align:start position:0% +yeah so so anyway + + + align:start position:0% +yeah so so anyway +so here tells you that the percent + + align:start position:0% +so here tells you that the percent + + + align:start position:0% +so here tells you that the percent +dagger + + align:start position:0% +dagger + + + align:start position:0% +dagger +is in fact the canonical momentum to psi + + align:start position:0% +is in fact the canonical momentum to psi + + + align:start position:0% +is in fact the canonical momentum to psi +and now we can just + + align:start position:0% +and now we can just + + + align:start position:0% +and now we can just +now in this equation we can just try to + + align:start position:0% +now in this equation we can just try to + + + align:start position:0% +now in this equation we can just try to +interpret the side diagram as the + + align:start position:0% +interpret the side diagram as the + + + align:start position:0% +interpret the side diagram as the +momentum rather than as a configuration + + align:start position:0% +momentum rather than as a configuration + + + align:start position:0% +momentum rather than as a configuration +variable okay so now let's rewrite the + + align:start position:0% +variable okay so now let's rewrite the + + + align:start position:0% +variable okay so now let's rewrite the +uh lagrangian so the lagrangian has + + align:start position:0% +uh lagrangian so the lagrangian has + + + align:start position:0% +uh lagrangian so the lagrangian has +foreign form + + align:start position:0% +foreign form + + + align:start position:0% +foreign form +minus I PSI bar + + align:start position:0% +minus I PSI bar + + + align:start position:0% +minus I PSI bar +gamma mu partial mu + + align:start position:0% +gamma mu partial mu + + + align:start position:0% +gamma mu partial mu +minus M PSI okay so this is the + + align:start position:0% +minus M PSI okay so this is the + + + align:start position:0% +minus M PSI okay so this is the +laguanian density + + align:start position:0% +laguanian density + + + align:start position:0% +laguanian density +so I will rewrite it as a following + + align:start position:0% +so I will rewrite it as a following + + + align:start position:0% +so I will rewrite it as a following +so let's first separate the time + + align:start position:0% +so let's first separate the time + + + align:start position:0% +so let's first separate the time +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +so this is a dagger so so just this term + + align:start position:0% +so this is a dagger so so just this term + + + align:start position:0% +so this is a dagger so so just this term +you move in the time derivative + + align:start position:0% +you move in the time derivative + + + align:start position:0% +you move in the time derivative +and then the rest I have PSI bar + + align:start position:0% +and then the rest I have PSI bar + + + align:start position:0% +and then the rest I have PSI bar +comma I partial I minus M side but here + + align:start position:0% +comma I partial I minus M side but here + + + align:start position:0% +comma I partial I minus M side but here +the the no longer involved in the the + + align:start position:0% +the the no longer involved in the the + + + align:start position:0% +the the no longer involved in the the +time derivative + + align:start position:0% +time derivative + + + align:start position:0% +time derivative +and now we just interpret this + + align:start position:0% +and now we just interpret this + + + align:start position:0% +and now we just interpret this +as the canonical random for PSI + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then this is just some something + + align:start position:0% +and then this is just some something + + + align:start position:0% +and then this is just some something +involving spatial duty of PSI + + align:start position:0% +involving spatial duty of PSI + + + align:start position:0% +involving spatial duty of PSI +and I just interpret this as a + + align:start position:0% +and I just interpret this as a + + + align:start position:0% +and I just interpret this as a +hamiltonian flip side + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so so so this expression just involves + + align:start position:0% +so so so this expression just involves + + + align:start position:0% +so so so this expression just involves +inside diagram and the PSI it moving + + align:start position:0% +inside diagram and the PSI it moving + + + align:start position:0% +inside diagram and the PSI it moving +some spatial derivative so so this is + + align:start position:0% +some spatial derivative so so this is + + + align:start position:0% +some spatial derivative so so this is +essentially just some some functions of + + align:start position:0% +essentially just some some functions of + + + align:start position:0% +essentially just some some functions of +PSI a pipe side and the PSI and maybe + + align:start position:0% +PSI a pipe side and the PSI and maybe + + + align:start position:0% +PSI a pipe side and the PSI and maybe +with some spatial derivatives okay so + + align:start position:0% +with some spatial derivatives okay so + + + align:start position:0% +with some spatial derivatives okay so +now you see that this is not grounding + + align:start position:0% +now you see that this is not grounding + + + align:start position:0% +now you see that this is not grounding +density + + align:start position:0% +density + + + align:start position:0% +density +actually + + align:start position:0% +actually + + + align:start position:0% +actually +if I interpret the diagram as the + + align:start position:0% +if I interpret the diagram as the + + + align:start position:0% +if I interpret the diagram as the +canonic momentum then has the form of + + align:start position:0% +canonic momentum then has the form of + + + align:start position:0% +canonic momentum then has the form of +this canonical transformation to go from + + align:start position:0% +this canonical transformation to go from + + + align:start position:0% +this canonical transformation to go from +the lagonian density to hamiltonian and + + align:start position:0% +the lagonian density to hamiltonian and + + + align:start position:0% +the lagonian density to hamiltonian and +then I can just interpret this as a + + align:start position:0% +then I can just interpret this as a + + + align:start position:0% +then I can just interpret this as a +hamiltonian + + align:start position:0% +hamiltonian + + + align:start position:0% +hamiltonian +okay I can just interpret this as a + + align:start position:0% +okay I can just interpret this as a + + + align:start position:0% +okay I can just interpret this as a +hamiltonian + + align:start position:0% +hamiltonian + + + align:start position:0% +hamiltonian +okay so so now I can just interpret this + + align:start position:0% +okay so so now I can just interpret this + + + align:start position:0% +okay so so now I can just interpret this +as my hometownin + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +we just treat + + align:start position:0% + + + + align:start position:0% + +so now + + align:start position:0% + + + + align:start position:0% + +we just um + + align:start position:0% +we just um + + + align:start position:0% +we just um +so this is + + align:start position:0% + + + + align:start position:0% + +so PSI diagram of PSI and now this is a + + align:start position:0% +so PSI diagram of PSI and now this is a + + + align:start position:0% +so PSI diagram of PSI and now this is a +full face space + + align:start position:0% +full face space + + + align:start position:0% +full face space +okay so this is the momentum and this is + + align:start position:0% +okay so this is the momentum and this is + + + align:start position:0% +okay so this is the momentum and this is +the coordinate so this is the full space + + align:start position:0% +the coordinate so this is the full space + + + align:start position:0% +the coordinate so this is the full space +okay rather than previously uh uh uh we + + align:start position:0% +okay rather than previously uh uh uh we + + + align:start position:0% +okay rather than previously uh uh uh we +would interpret them as a configuration + + align:start position:0% +would interpret them as a configuration + + + align:start position:0% +would interpret them as a configuration +space okay + + align:start position:0% +space okay + + + align:start position:0% +space okay +manipulate them as configuration space + + align:start position:0% +manipulate them as configuration space + + + align:start position:0% +manipulate them as configuration space +and then and then the hamiltonian + + align:start position:0% + + + + align:start position:0% + +just equal to + + align:start position:0% +just equal to + + + align:start position:0% +just equal to +I + + align:start position:0% +I + + + align:start position:0% +I +PSI bar + + align:start position:0% +PSI bar + + + align:start position:0% +PSI bar +gamma I partial I minus M side okay + + align:start position:0% + + + + align:start position:0% + +so this is the Hamilton intensity + + align:start position:0% + + + + align:start position:0% + +okay so so so we now then have now this + + align:start position:0% +okay so so so we now then have now this + + + align:start position:0% +okay so so so we now then have now this +just go back to the standard formulation + + align:start position:0% +just go back to the standard formulation + + + align:start position:0% +just go back to the standard formulation +okay + + align:start position:0% + + + + align:start position:0% + +any questions on this + + align:start position:0% +any questions on this + + + align:start position:0% +any questions on this +yes + + align:start position:0% + + + + align:start position:0% + +momentum + + align:start position:0% + + + + align:start position:0% + +yeah it's no longer two different fields + + align:start position:0% +yeah it's no longer two different fields + + + align:start position:0% +yeah it's no longer two different fields +for example if you have two different + + align:start position:0% +for example if you have two different + + + align:start position:0% +for example if you have two different +fields then PSI and side they should + + align:start position:0% +fields then PSI and side they should + + + align:start position:0% +fields then PSI and side they should +commute + + align:start position:0% +commute + + + align:start position:0% +commute +but now since they become canonic + + align:start position:0% +but now since they become canonic + + + align:start position:0% +but now since they become canonic +momentum they no longer compute yeah + + align:start position:0% +momentum they no longer compute yeah + + + align:start position:0% +momentum they no longer compute yeah +yeah yes + + align:start position:0% + + + + align:start position:0% + +right hand side of the like our earlier + + align:start position:0% +right hand side of the like our earlier + + + align:start position:0% +right hand side of the like our earlier +version of the drag equation the one + + align:start position:0% +version of the drag equation the one + + + align:start position:0% +version of the drag equation the one +where you like + + align:start position:0% + + + + align:start position:0% + +the one with the alpha and beta like the + + align:start position:0% +the one with the alpha and beta like the + + + align:start position:0% +the one with the alpha and beta like the +other direction we wrote that earlier + + align:start position:0% +other direction we wrote that earlier + + + align:start position:0% +other direction we wrote that earlier +yeah okay yeah yeah that's right yeah + + align:start position:0% +yeah okay yeah yeah that's right yeah + + + align:start position:0% +yeah okay yeah yeah that's right yeah +yeah yeah it's very yeah he's saying + + align:start position:0% +yeah yeah it's very yeah he's saying + + + align:start position:0% +yeah yeah it's very yeah he's saying +here you just left Hamilton yeah that's + + align:start position:0% +here you just left Hamilton yeah that's + + + align:start position:0% +here you just left Hamilton yeah that's +right yeah yeah yes + + align:start position:0% + + + + align:start position:0% + +yeah so when you + + align:start position:0% + + + + align:start position:0% + +golden equation uh in the in the scalar + + align:start position:0% +golden equation uh in the in the scalar + + + align:start position:0% +golden equation uh in the in the scalar +Theory when you quantize you always have + + align:start position:0% +Theory when you quantize you always have + + + align:start position:0% +Theory when you quantize you always have +to treat time differently and then then + + align:start position:0% +to treat time differently and then then + + + align:start position:0% +to treat time differently and then then +the uh then the lorenzymmetry is come + + align:start position:0% +the uh then the lorenzymmetry is come + + + align:start position:0% +the uh then the lorenzymmetry is come +out uh uh uh in the property of the + + align:start position:0% +out uh uh uh in the property of the + + + align:start position:0% +out uh uh uh in the property of the +states right + + align:start position:0% +states right + + + align:start position:0% +states right +yeah but you always uh when you quantize + + align:start position:0% +yeah but you always uh when you quantize + + + align:start position:0% +yeah but you always uh when you quantize +you always have to treat time separately + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah exactly + + align:start position:0% + + + + align:start position:0% + +yeah yeah it's a it's a + + align:start position:0% +yeah yeah it's a it's a + + + align:start position:0% +yeah yeah it's a it's a +yeah it's a + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yeah yeah this just uh yeah so that's + + align:start position:0% +yeah yeah this just uh yeah so that's + + + align:start position:0% +yeah yeah this just uh yeah so that's +why we call this a constraint system but + + align:start position:0% +why we call this a constraint system but + + + align:start position:0% +why we call this a constraint system but +now I'm just giving you a shortcut so + + align:start position:0% +now I'm just giving you a shortcut so + + + align:start position:0% +now I'm just giving you a shortcut so +that we have to don't have to go through + + align:start position:0% +that we have to don't have to go through + + + align:start position:0% +that we have to don't have to go through +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +yeah the the conjugate the intricacy of + + align:start position:0% +yeah the the conjugate the intricacy of + + + align:start position:0% +yeah the the conjugate the intricacy of +a constrained condensation + + align:start position:0% + + + + align:start position:0% + +okay so now the canonical quantization + + align:start position:0% +okay so now the canonical quantization + + + align:start position:0% +okay so now the canonical quantization +become easy so now this is my momentum + + align:start position:0% +become easy so now this is my momentum + + + align:start position:0% +become easy so now this is my momentum +so now we just have + + align:start position:0% +so now we just have + + + align:start position:0% +so now we just have +the canonical quantitation + + align:start position:0% + + + + align:start position:0% + +I think today we may have unfortunate + + align:start position:0% +I think today we may have unfortunate + + + align:start position:0% +I think today we may have unfortunate +timing + + align:start position:0% +timing + + + align:start position:0% +timing +so so now become PSI it is coordinate + + align:start position:0% + + + + align:start position:0% + +and now we have PSI dagger we have pi + + align:start position:0% +and now we have PSI dagger we have pi + + + align:start position:0% +and now we have PSI dagger we have pi +PSI which is the momentum + + align:start position:0% +PSI which is the momentum + + + align:start position:0% +PSI which is the momentum +so this definition by definition should + + align:start position:0% +so this definition by definition should + + + align:start position:0% +so this definition by definition should +give you + + align:start position:0% +give you + + + align:start position:0% +give you +say + + align:start position:0% +say + + + align:start position:0% +say +the data function + + align:start position:0% +the data function + + + align:start position:0% +the data function +so equal time correlation function so + + align:start position:0% +so equal time correlation function so + + + align:start position:0% +so equal time correlation function so +here we should + + align:start position:0% +here we should + + + align:start position:0% +here we should +because remember this is the four Vector + + align:start position:0% +because remember this is the four Vector + + + align:start position:0% +because remember this is the four Vector +so this has also have four components so + + align:start position:0% +so this has also have four components so + + + align:start position:0% +so this has also have four components so +let me just uh uh now suppress this + + align:start position:0% +let me just uh uh now suppress this + + + align:start position:0% +let me just uh uh now suppress this +subscript side because there's only one + + align:start position:0% +subscript side because there's only one + + + align:start position:0% +subscript side because there's only one +variable here now okay so so so so here + + align:start position:0% +variable here now okay so so so so here + + + align:start position:0% +variable here now okay so so so so here +there's also coefficient so this is also + + align:start position:0% +there's also coefficient so this is also + + + align:start position:0% +there's also coefficient so this is also +four Vector beta and then here should be + + align:start position:0% +four Vector beta and then here should be + + + align:start position:0% +four Vector beta and then here should be +Delta alphabet okay so Alpha Beta our + + align:start position:0% +Delta alphabet okay so Alpha Beta our + + + align:start position:0% +Delta alphabet okay so Alpha Beta our +spinner indices + + align:start position:0% + + + + align:start position:0% + +indices + + align:start position:0% + + + + align:start position:0% + +so if you impose and this is equivalent + + align:start position:0% + + + + align:start position:0% + +just to psi Alpha + + align:start position:0% +just to psi Alpha + + + align:start position:0% +just to psi Alpha +TX + + align:start position:0% +TX + + + align:start position:0% +TX +dagger beta + + align:start position:0% +dagger beta + + + align:start position:0% +dagger beta +TX Prime + + align:start position:0% +TX Prime + + + align:start position:0% +TX Prime +equal to + + align:start position:0% + + + + align:start position:0% + +I Delta Alpha Beta + + align:start position:0% + + + + align:start position:0% + +x minus Prime okay + + align:start position:0% + + + + align:start position:0% + +and so we can now expand PSI X + + align:start position:0% + + + + align:start position:0% + +in terms of complete set of solutions + + align:start position:0% +in terms of complete set of solutions + + + align:start position:0% +in terms of complete set of solutions +so this is the first step + + align:start position:0% +so this is the first step + + + align:start position:0% +so this is the first step +of the quantization + + align:start position:0% +of the quantization + + + align:start position:0% +of the quantization +so first is this is the commutation + + align:start position:0% +so first is this is the commutation + + + align:start position:0% +so first is this is the commutation +relation + + align:start position:0% +relation + + + align:start position:0% +relation +so the Second Step remember we can + + align:start position:0% +so the Second Step remember we can + + + align:start position:0% +so the Second Step remember we can +expand the PSI in terms of complete the + + align:start position:0% +expand the PSI in terms of complete the + + + align:start position:0% +expand the PSI in terms of complete the +basis of classical Solutions + + align:start position:0% +basis of classical Solutions + + + align:start position:0% +basis of classical Solutions +so we say X + + align:start position:0% +so we say X + + + align:start position:0% +so we say X +just equal to + + align:start position:0% +just equal to + + + align:start position:0% +just equal to +again we integrate over all spatial + + align:start position:0% +again we integrate over all spatial + + + align:start position:0% +again we integrate over all spatial +momentum + + align:start position:0% + + + + align:start position:0% + +again we use this factor for convenience + + align:start position:0% +again we use this factor for convenience + + + align:start position:0% +again we use this factor for convenience +as in the scalar case + + align:start position:0% +as in the scalar case + + + align:start position:0% +as in the scalar case +and now we just lead to some of all + + align:start position:0% +and now we just lead to some of all + + + align:start position:0% +and now we just lead to some of all +possible solutions + + align:start position:0% +possible solutions + + + align:start position:0% +possible solutions +so so here we have a sum over s + + align:start position:0% + + + + align:start position:0% + +equal to 1 and Q + + align:start position:0% +equal to 1 and Q + + + align:start position:0% +equal to 1 and Q +okay so we have + + align:start position:0% +okay so we have + + + align:start position:0% +okay so we have +then we have a k + + align:start position:0% +then we have a k + + + align:start position:0% +then we have a k +s + + align:start position:0% +s + + + align:start position:0% +s +u u s + + align:start position:0% +u u s + + + align:start position:0% +u u s +ikx + + align:start position:0% +ikx + + + align:start position:0% +ikx +and then Plus + + align:start position:0% +and then Plus + + + align:start position:0% +and then Plus +b k + + align:start position:0% + + + + align:start position:0% + +should be here sorry b k + + align:start position:0% +should be here sorry b k + + + align:start position:0% +should be here sorry b k +s + + align:start position:0% +s + + + align:start position:0% +s +and V + + align:start position:0% +and V + + + align:start position:0% +and V +s + + align:start position:0% +s + + + align:start position:0% +s +expenditure minus i k x + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so these are the uh Complete because the + + align:start position:0% +so these are the uh Complete because the + + + align:start position:0% +so these are the uh Complete because the +company set up solution that u and v + + align:start position:0% +company set up solution that u and v + + + align:start position:0% +company set up solution that u and v +and then we call the coefficient of A + + align:start position:0% +and then we call the coefficient of A + + + align:start position:0% +and then we call the coefficient of A +and B so let me call it B dagger as we + + align:start position:0% +and B so let me call it B dagger as we + + + align:start position:0% +and B so let me call it B dagger as we +did for the complex scalar case before + + align:start position:0% +did for the complex scalar case before + + + align:start position:0% +did for the complex scalar case before +okay so so be so the coefficient we call + + align:start position:0% +okay so so be so the coefficient we call + + + align:start position:0% +okay so so be so the coefficient we call +them A and B actually it doesn't matter + + align:start position:0% +them A and B actually it doesn't matter + + + align:start position:0% +them A and B actually it doesn't matter +we call it B actually let me just call + + align:start position:0% +we call it B actually let me just call + + + align:start position:0% +we call it B actually let me just call +it B okay yeah so you can just uh you + + align:start position:0% +it B okay yeah so you can just uh you + + + align:start position:0% +it B okay yeah so you can just uh you +have u and v and then the caution will + + align:start position:0% +have u and v and then the caution will + + + align:start position:0% +have u and v and then the caution will +be a and b okay + + align:start position:0% + + + + align:start position:0% + +and uh and so um + + align:start position:0% + + + + align:start position:0% + +so now + + align:start position:0% +so now + + + align:start position:0% +so now +you can just plug this + + align:start position:0% + + + + align:start position:0% + +so if this equation is one + + align:start position:0% +so if this equation is one + + + align:start position:0% +so if this equation is one +and this equation is 2 + + align:start position:0% +and this equation is 2 + + + align:start position:0% +and this equation is 2 +and you take the complex conjugate side + + align:start position:0% +and you take the complex conjugate side + + + align:start position:0% +and you take the complex conjugate side +diagram you can plug in here to find + + align:start position:0% +diagram you can plug in here to find + + + align:start position:0% +diagram you can plug in here to find +what's the commutation relation between + + align:start position:0% +what's the commutation relation between + + + align:start position:0% +what's the commutation relation between +a and b + + align:start position:0% +a and b + + + align:start position:0% +a and b +okay + + align:start position:0% + + + + align:start position:0% + +so you find + + align:start position:0% + + + + align:start position:0% + +so uh you find that the um + + align:start position:0% +so uh you find that the um + + + align:start position:0% +so uh you find that the um +uh yeah so Planck + + align:start position:0% + + + + align:start position:0% + +2 into 1 + + align:start position:0% + + + + align:start position:0% + +so you find the computation relation + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +s + + align:start position:0% + + + + align:start position:0% + +and K Prime + + align:start position:0% +and K Prime + + + align:start position:0% +and K Prime +p + + align:start position:0% +p + + + align:start position:0% +p +then equal to + + align:start position:0% +then equal to + + + align:start position:0% +then equal to +V K + + align:start position:0% +V K + + + align:start position:0% +V K +as + + align:start position:0% +as + + + align:start position:0% +as +and the b k Prime + + align:start position:0% +and the b k Prime + + + align:start position:0% +and the b k Prime +t + + align:start position:0% +t + + + align:start position:0% +t +then equal to 2 pi + + align:start position:0% +then equal to 2 pi + + + align:start position:0% +then equal to 2 pi +cubed + + align:start position:0% +cubed + + + align:start position:0% +cubed +dot St + + align:start position:0% +dot St + + + align:start position:0% +dot St +Delta 3 + + align:start position:0% +Delta 3 + + + align:start position:0% +Delta 3 +K minus K Prime + + align:start position:0% +K minus K Prime + + + align:start position:0% +K minus K Prime +okay + + align:start position:0% + + + + align:start position:0% + +so now + + align:start position:0% + + + + align:start position:0% + +and you can also Define the vacuum + + align:start position:0% + + + + align:start position:0% + +you can also Define the vacuum + + align:start position:0% + + + + align:start position:0% + +so and yeah and all other commutators + + align:start position:0% +so and yeah and all other commutators + + + align:start position:0% +so and yeah and all other commutators +are zero okay + + align:start position:0% +are zero okay + + + align:start position:0% +are zero okay +with all others zero + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +and you can also Define the vacuum + + align:start position:0% + + + + align:start position:0% + +as we did for the scalar case + + align:start position:0% +as we did for the scalar case + + + align:start position:0% +as we did for the scalar case +to be elevated + + align:start position:0% +to be elevated + + + align:start position:0% +to be elevated +by AK + + align:start position:0% + + + + align:start position:0% + +and b k + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now you can in principle build the + + align:start position:0% +and now you can in principle build the + + + align:start position:0% +and now you can in principle build the +Ohio space okay + + align:start position:0% +Ohio space okay + + + align:start position:0% +Ohio space okay +yes + + align:start position:0% + + + + align:start position:0% + +momentum is I side + + align:start position:0% +momentum is I side + + + align:start position:0% +momentum is I side +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +oh right right sorry so there's no yeah + + align:start position:0% +oh right right sorry so there's no yeah + + + align:start position:0% +oh right right sorry so there's no yeah +yeah thank you there's no I here yeah + + align:start position:0% +yeah thank you there's no I here yeah + + + align:start position:0% +yeah thank you there's no I here yeah +because the momentum is upside diagram + + align:start position:0% +because the momentum is upside diagram + + + align:start position:0% +because the momentum is upside diagram +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah there's no I anymore just + + align:start position:0% +yeah there's no I anymore just + + + align:start position:0% +yeah there's no I anymore just +just the dirt off a bit + + align:start position:0% +just the dirt off a bit + + + align:start position:0% +just the dirt off a bit +okay so oh look + + align:start position:0% +okay so oh look + + + align:start position:0% +okay so oh look +pretty straightforward + + align:start position:0% +pretty straightforward + + + align:start position:0% +pretty straightforward +okay but you actually have + + align:start position:0% +okay but you actually have + + + align:start position:0% +okay but you actually have +problems + + align:start position:0% +problems + + + align:start position:0% +problems +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you actually have problems + + align:start position:0% +you actually have problems + + + align:start position:0% +you actually have problems +so the first problem some of you may be + + align:start position:0% +so the first problem some of you may be + + + align:start position:0% +so the first problem some of you may be +already asked him + + align:start position:0% + + + + align:start position:0% + +in your head + + align:start position:0% + + + + align:start position:0% + +he said are we supposed to describe spin + + align:start position:0% +he said are we supposed to describe spin + + + align:start position:0% +he said are we supposed to describe spin +one half particles + + align:start position:0% +one half particles + + + align:start position:0% +one half particles +but if we are supposed to describe + + align:start position:0% +but if we are supposed to describe + + + align:start position:0% +but if we are supposed to describe +swimming one half particles + + align:start position:0% +swimming one half particles + + + align:start position:0% +swimming one half particles +then why do we find the bosons okay so + + align:start position:0% +then why do we find the bosons okay so + + + align:start position:0% +then why do we find the bosons okay so +these are commutation relations for + + align:start position:0% +these are commutation relations for + + + align:start position:0% +these are commutation relations for +bosons + + align:start position:0% +bosons + + + align:start position:0% +bosons +okay because they commute okay so so + + align:start position:0% +okay because they commute okay so so + + + align:start position:0% +okay because they commute okay so so +different okay they + + align:start position:0% +different okay they + + + align:start position:0% +different okay they +sorry I think + + align:start position:0% +sorry I think + + + align:start position:0% +sorry I think +I'm missing dagger sorry + + align:start position:0% + + + + align:start position:0% + +so different AK + + align:start position:0% +so different AK + + + align:start position:0% +so different AK +they commute with each other + + align:start position:0% +they commute with each other + + + align:start position:0% +they commute with each other +as we discussed in the scalar case when + + align:start position:0% +as we discussed in the scalar case when + + + align:start position:0% +as we discussed in the scalar case when +the a mu or a or commute with each other + + align:start position:0% +the a mu or a or commute with each other + + + align:start position:0% +the a mu or a or commute with each other +uh this is this is boson means the + + align:start position:0% +uh this is this is boson means the + + + align:start position:0% +uh this is this is boson means the +particle you created you can exchange + + align:start position:0% +particle you created you can exchange + + + align:start position:0% +particle you created you can exchange +them + + align:start position:0% +them + + + align:start position:0% +them +and they don't uh uh uh yeah you can + + align:start position:0% +and they don't uh uh uh yeah you can + + + align:start position:0% +and they don't uh uh uh yeah you can +arbitrarily exchange them okay it's + + align:start position:0% +arbitrarily exchange them okay it's + + + align:start position:0% +arbitrarily exchange them okay it's +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +but fermions they're supposed to be + + align:start position:0% +but fermions they're supposed to be + + + align:start position:0% +but fermions they're supposed to be +party principle okay + + align:start position:0% +party principle okay + + + align:start position:0% +party principle okay +so so so so you're supposed to get the + + align:start position:0% +so so so so you're supposed to get the + + + align:start position:0% +so so so so you're supposed to get the +minus sign when you exchange them + + align:start position:0% +minus sign when you exchange them + + + align:start position:0% +minus sign when you exchange them +so this cannot this doesn't look to be + + align:start position:0% +so this cannot this doesn't look to be + + + align:start position:0% +so this cannot this doesn't look to be +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +so this is the first + + align:start position:0% +so this is the first + + + align:start position:0% +so this is the first +thing simply we will find in both zones + + align:start position:0% +thing simply we will find in both zones + + + align:start position:0% +thing simply we will find in both zones +okay rather than fermions + + align:start position:0% + + + + align:start position:0% + +and the second is that now if you find + + align:start position:0% +and the second is that now if you find + + + align:start position:0% +and the second is that now if you find +the hamiltonian + + align:start position:0% + + + + align:start position:0% + +so now if you try to find the + + align:start position:0% +so now if you try to find the + + + align:start position:0% +so now if you try to find the +hamiltonian + + align:start position:0% + + + + align:start position:0% + +so H is just a + + align:start position:0% +so H is just a + + + align:start position:0% +so H is just a +integration of the uh this hamiltonian + + align:start position:0% +integration of the uh this hamiltonian + + + align:start position:0% +integration of the uh this hamiltonian +density + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +and you can just plug it in okay plug + + align:start position:0% +and you can just plug it in okay plug + + + align:start position:0% +and you can just plug it in okay plug +that expression for hamiltonian density + + align:start position:0% +that expression for hamiltonian density + + + align:start position:0% +that expression for hamiltonian density +in + + align:start position:0% +in + + + align:start position:0% +in +where is my hamiltonian density yeah + + align:start position:0% +where is my hamiltonian density yeah + + + align:start position:0% +where is my hamiltonian density yeah +yeah plug that in + + align:start position:0% +yeah plug that in + + + align:start position:0% +yeah plug that in +okay + + align:start position:0% + + + + align:start position:0% + +and then you will find the uh + + align:start position:0% +and then you will find the uh + + + align:start position:0% +and then you will find the uh +um + + align:start position:0% +um + + + align:start position:0% +um +yeah so so you find just this just given + + align:start position:0% +yeah so so you find just this just given + + + align:start position:0% +yeah so so you find just this just given +by + + align:start position:0% +by + + + align:start position:0% +by +i d 3x + + align:start position:0% + + + + align:start position:0% + +minus M PSI okay + + align:start position:0% + + + + align:start position:0% + +so so now if you plug them in okay you + + align:start position:0% +so so now if you plug them in okay you + + + align:start position:0% +so so now if you plug them in okay you +just plug them in plug this mode + + align:start position:0% +just plug them in plug this mode + + + align:start position:0% +just plug them in plug this mode +expansion in + + align:start position:0% +expansion in + + + align:start position:0% +expansion in +and then you find actually + + align:start position:0% + + + + align:start position:0% + +okay then you find the following + + align:start position:0% +okay then you find the following + + + align:start position:0% +okay then you find the following +expression + + align:start position:0% + + + + align:start position:0% + +Omega k + + align:start position:0% +Omega k + + + align:start position:0% +Omega k +and you sum over s + + align:start position:0% +and you sum over s + + + align:start position:0% +and you sum over s +from 1 to 2 + + align:start position:0% +from 1 to 2 + + + align:start position:0% +from 1 to 2 +and then you find it's given by + + align:start position:0% +and then you find it's given by + + + align:start position:0% +and then you find it's given by +a k + + align:start position:0% +a k + + + align:start position:0% +a k +s + + align:start position:0% + + + + align:start position:0% + +dagger AK + + align:start position:0% + + + + align:start position:0% + +s + + align:start position:0% +s + + + align:start position:0% +s +okay + + align:start position:0% +okay + + + align:start position:0% +okay +minus + + align:start position:0% +minus + + + align:start position:0% +minus +b k + + align:start position:0% +b k + + + align:start position:0% +b k +s dagger + + align:start position:0% +s dagger + + + align:start position:0% +s dagger +PK + + align:start position:0% + + + + align:start position:0% + +s + + align:start position:0% +s + + + align:start position:0% +s +okay and then up to some infinite + + align:start position:0% +okay and then up to some infinite + + + align:start position:0% +okay and then up to some infinite +constants + + align:start position:0% + + + + align:start position:0% + +so now you see something problematic + + align:start position:0% +so now you see something problematic + + + align:start position:0% +so now you see something problematic +here + + align:start position:0% + + + + align:start position:0% + +so what's problematic you see + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah energy is not positive definite + + align:start position:0% +yeah energy is not positive definite + + + align:start position:0% +yeah energy is not positive definite +because of this minus sign + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because this minus sign + + align:start position:0% +because this minus sign + + + align:start position:0% +because this minus sign +so so this minus sign + + align:start position:0% +so so this minus sign + + + align:start position:0% +so so this minus sign +tells you that if you excite a lot of + + align:start position:0% +tells you that if you excite a lot of + + + align:start position:0% +tells you that if you excite a lot of +these B particles + + align:start position:0% + + + + align:start position:0% + +you can make the energy selective as you + + align:start position:0% +you can make the energy selective as you + + + align:start position:0% +you can make the energy selective as you +want + + align:start position:0% +want + + + align:start position:0% +want +and in the series don't make sense okay + + align:start position:0% +and in the series don't make sense okay + + + align:start position:0% +and in the series don't make sense okay +and then this is a series with energy + + align:start position:0% +and then this is a series with energy + + + align:start position:0% +and then this is a series with energy +unbounded from Below + + align:start position:0% +unbounded from Below + + + align:start position:0% +unbounded from Below +okay it's a theory with energy + + align:start position:0% +okay it's a theory with energy + + + align:start position:0% +okay it's a theory with energy +unbounded from below so that means + + align:start position:0% +unbounded from below so that means + + + align:start position:0% +unbounded from below so that means +this vacuum is unstable + + align:start position:0% + + + + align:start position:0% + +okay so I've been on sleep + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so uh uh so so there must be something + + align:start position:0% +so uh uh so so there must be something + + + align:start position:0% +so uh uh so so there must be something +wrong with this procedure okay something + + align:start position:0% +wrong with this procedure okay something + + + align:start position:0% +wrong with this procedure okay something +wrong with this procedure + + align:start position:0% +wrong with this procedure + + + align:start position:0% +wrong with this procedure +so so it turns out that there's a very + + align:start position:0% +so so it turns out that there's a very + + + align:start position:0% +so so it turns out that there's a very +quick fix to this problem + + align:start position:0% +quick fix to this problem + + + align:start position:0% +quick fix to this problem +and and this quick fix was uh invented + + align:start position:0% +and and this quick fix was uh invented + + + align:start position:0% +and and this quick fix was uh invented +by + + align:start position:0% +by + + + align:start position:0% +by +by Jordan + + align:start position:0% +by Jordan + + + align:start position:0% +by Jordan +so so he recognized + + align:start position:0% +so so he recognized + + + align:start position:0% +so so he recognized +that if you don't do the standard + + align:start position:0% +that if you don't do the standard + + + align:start position:0% +that if you don't do the standard +commutation relation + + align:start position:0% +commutation relation + + + align:start position:0% +commutation relation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +if you do instead of commutator + + align:start position:0% +if you do instead of commutator + + + align:start position:0% +if you do instead of commutator +here you change it to anti-commutator + + align:start position:0% + + + + align:start position:0% + +okay remember this bracket uh this curly + + align:start position:0% +okay remember this bracket uh this curly + + + align:start position:0% +okay remember this bracket uh this curly +Brack means anti-communator + + align:start position:0% +Brack means anti-communator + + + align:start position:0% +Brack means anti-communator +and that means that here you change it + + align:start position:0% +and that means that here you change it + + + align:start position:0% +and that means that here you change it +to anti-commutator + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then still with the same scene + + align:start position:0% + + + + align:start position:0% + +0 is the same scene + + align:start position:0% + + + + align:start position:0% + +and now + + align:start position:0% +and now + + + align:start position:0% +and now +this becomes anti-commutator + + align:start position:0% + + + + align:start position:0% + +okay so let me see + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +I just want to make sure I get the + + align:start position:0% + + + + align:start position:0% + +yeah we change the anagram is also from + + align:start position:0% +yeah we change the anagram is also from + + + align:start position:0% +yeah we change the anagram is also from +the commission you change this to dagger + + align:start position:0% +the commission you change this to dagger + + + align:start position:0% +the commission you change this to dagger +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now you change this to diagram as we did + + align:start position:0% +now you change this to diagram as we did + + + align:start position:0% +now you change this to diagram as we did +for the complex case and then and then + + align:start position:0% +for the complex case and then and then + + + align:start position:0% +for the complex case and then and then +you just get this and now if you do that + + align:start position:0% +you just get this and now if you do that + + + align:start position:0% +you just get this and now if you do that +and then this becomes plus sign + + align:start position:0% + + + + align:start position:0% + +and that's this become plus sign + + align:start position:0% +and that's this become plus sign + + + align:start position:0% +and that's this become plus sign +and now not only this become plus sign + + align:start position:0% +and now not only this become plus sign + + + align:start position:0% +and now not only this become plus sign +and also all different AK + + align:start position:0% +and also all different AK + + + align:start position:0% +and also all different AK +for different s + + align:start position:0% + + + + align:start position:0% + +and T + + align:start position:0% +and T + + + align:start position:0% +and T +the anti-commute with each other + + align:start position:0% + + + + align:start position:0% + +the anti-commute each other + + align:start position:0% +the anti-commute each other + + + align:start position:0% +the anti-commute each other +so anti-commute each other + + align:start position:0% +so anti-commute each other + + + align:start position:0% +so anti-commute each other +means that if you create a particle for + + align:start position:0% +means that if you create a particle for + + + align:start position:0% +means that if you create a particle for +example AK dagger + + align:start position:0% +example AK dagger + + + align:start position:0% +example AK dagger +and UK the other a particle AK Prime + + align:start position:0% +and UK the other a particle AK Prime + + + align:start position:0% +and UK the other a particle AK Prime +dagger on zero + + align:start position:0% +dagger on zero + + + align:start position:0% +dagger on zero +and now these two anti-commute + + align:start position:0% +and now these two anti-commute + + + align:start position:0% +and now these two anti-commute +means when you exchange order you get + + align:start position:0% +means when you exchange order you get + + + align:start position:0% +means when you exchange order you get +the minus sign + + align:start position:0% +the minus sign + + + align:start position:0% +the minus sign +that precisely give you the the minus + + align:start position:0% +that precisely give you the the minus + + + align:start position:0% +that precisely give you the the minus +sign in the body principle okay in the + + align:start position:0% +sign in the body principle okay in the + + + align:start position:0% +sign in the body principle okay in the +in the in the uh + + align:start position:0% +in the in the uh + + + align:start position:0% +in the in the uh +in the statistic for fermions + + align:start position:0% +in the statistic for fermions + + + align:start position:0% +in the statistic for fermions +and so so changing this uh scene to the + + align:start position:0% +and so so changing this uh scene to the + + + align:start position:0% +and so so changing this uh scene to the +to the anti-commutator + + align:start position:0% +to the anti-commutator + + + align:start position:0% +to the anti-commutator +and so so solves all your problems and + + align:start position:0% +and so so solves all your problems and + + + align:start position:0% +and so so solves all your problems and +your energy now expanded from Below + + align:start position:0% +your energy now expanded from Below + + + align:start position:0% +your energy now expanded from Below +and then you actually now actually + + align:start position:0% +and then you actually now actually + + + align:start position:0% +and then you actually now actually +describe some particles which obey the + + align:start position:0% +describe some particles which obey the + + + align:start position:0% +describe some particles which obey the +uh the body principle + + align:start position:0% +uh the body principle + + + align:start position:0% +uh the body principle +okay which obey is the poly principle + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so yeah + + align:start position:0% +so yeah + + + align:start position:0% +so yeah +um + + align:start position:0% +um + + + align:start position:0% +um +I think + + align:start position:0% +I think + + + align:start position:0% +I think +we still have + + align:start position:0% +we still have + + + align:start position:0% +we still have +one minute left but we but it's a good + + align:start position:0% +one minute left but we but it's a good + + + align:start position:0% +one minute left but we but it's a good +time to stop because otherwise other + + align:start position:0% +time to stop because otherwise other + + + align:start position:0% +time to stop because otherwise other +scenes will take more time so let me + + align:start position:0% +scenes will take more time so let me + + + align:start position:0% +scenes will take more time so let me +just make a couple remark + + align:start position:0% +just make a couple remark + + + align:start position:0% +just make a couple remark +why the commutator why here you need to + + align:start position:0% +why the commutator why here you need to + + + align:start position:0% +why the commutator why here you need to +do something uh unconventional + + align:start position:0% + + + + align:start position:0% + +okay why you have to do something + + align:start position:0% +okay why you have to do something + + + align:start position:0% +okay why you have to do something +unconventional + + align:start position:0% + + + + align:start position:0% + +so so if you look at this hamiltonian + + align:start position:0% +so so if you look at this hamiltonian + + + align:start position:0% +so so if you look at this hamiltonian +density + + align:start position:0% + + + + align:start position:0% + +so if you look at this hamiltonian + + align:start position:0% +so if you look at this hamiltonian + + + align:start position:0% +so if you look at this hamiltonian +density + + align:start position:0% +density + + + align:start position:0% +density +so even with us doing this calculation + + align:start position:0% + + + + align:start position:0% + +okay even without doing this calculation + + align:start position:0% +okay even without doing this calculation + + + align:start position:0% +okay even without doing this calculation +you can + + align:start position:0% +you can + + + align:start position:0% +you can +already conclude from here that this age + + align:start position:0% +already conclude from here that this age + + + align:start position:0% +already conclude from here that this age +cannot be bonded From Below okay for the + + align:start position:0% +cannot be bonded From Below okay for the + + + align:start position:0% +cannot be bonded From Below okay for the +following reason + + align:start position:0% +following reason + + + align:start position:0% +following reason +for the following reason + + align:start position:0% +for the following reason + + + align:start position:0% +for the following reason +so from the diracy equation + + align:start position:0% +so from the diracy equation + + + align:start position:0% +so from the diracy equation +yeah let me just Erase here + + align:start position:0% + + + + align:start position:0% + +so from the direct equation + + align:start position:0% +so from the direct equation + + + align:start position:0% +so from the direct equation +you have gamma mu partial mu minus m + + align:start position:0% +you have gamma mu partial mu minus m + + + align:start position:0% +you have gamma mu partial mu minus m +PSI equal to zero + + align:start position:0% +PSI equal to zero + + + align:start position:0% +PSI equal to zero +so that means that the gamma I partial I + + align:start position:0% +so that means that the gamma I partial I + + + align:start position:0% +so that means that the gamma I partial I +minus m + + align:start position:0% +minus m + + + align:start position:0% +minus m +PSI is equal to minus gamma zero partial + + align:start position:0% +PSI is equal to minus gamma zero partial + + + align:start position:0% +PSI is equal to minus gamma zero partial +zero of PSI + + align:start position:0% +zero of PSI + + + align:start position:0% +zero of PSI +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now if you plug this + + align:start position:0% +so now if you plug this + + + align:start position:0% +so now if you plug this +equation into here + + align:start position:0% + + + + align:start position:0% + +into here + + align:start position:0% +into here + + + align:start position:0% +into here +and then what you get + + align:start position:0% +and then what you get + + + align:start position:0% +and then what you get +if you find that H is equal to + + align:start position:0% + + + + align:start position:0% + +i d 3x + + align:start position:0% +i d 3x + + + align:start position:0% +i d 3x +PSI dagger partial zero percent + + align:start position:0% + + + + align:start position:0% + +okay so so because the uh the the PSI + + align:start position:0% +okay so so because the uh the the PSI + + + align:start position:0% +okay so so because the uh the the PSI +now this becomes operate equation then + + align:start position:0% +now this becomes operate equation then + + + align:start position:0% +now this becomes operate equation then +satisfy this equation and now I find H + + align:start position:0% +satisfy this equation and now I find H + + + align:start position:0% +satisfy this equation and now I find H +become this form + + align:start position:0% +become this form + + + align:start position:0% +become this form +and which is side diagram times the time + + align:start position:0% +and which is side diagram times the time + + + align:start position:0% +and which is side diagram times the time +derivative of PSI + + align:start position:0% +derivative of PSI + + + align:start position:0% +derivative of PSI +and times you upside remember PSI + + align:start position:0% +and times you upside remember PSI + + + align:start position:0% +and times you upside remember PSI +expanded both in terms of the positive + + align:start position:0% +expanded both in terms of the positive + + + align:start position:0% +expanded both in terms of the positive +energy solutions + + align:start position:0% +energy solutions + + + align:start position:0% +energy solutions +and the Active Energy Solutions + + align:start position:0% +and the Active Energy Solutions + + + align:start position:0% +and the Active Energy Solutions +so depends on which Omega you have you + + align:start position:0% +so depends on which Omega you have you + + + align:start position:0% +so depends on which Omega you have you +can have either positive Omega or + + align:start position:0% +can have either positive Omega or + + + align:start position:0% +can have either positive Omega or +laxative Omega okay because this is the + + align:start position:0% +laxative Omega okay because this is the + + + align:start position:0% +laxative Omega okay because this is the +first derivative a first time Duty + + align:start position:0% +first derivative a first time Duty + + + align:start position:0% +first derivative a first time Duty +percent and so and so this cannot be a + + align:start position:0% +percent and so and so this cannot be a + + + align:start position:0% +percent and so and so this cannot be a +positive definite okay so this quantity + + align:start position:0% +positive definite okay so this quantity + + + align:start position:0% +positive definite okay so this quantity +cannot be positive definite anyway so uh + + align:start position:0% +cannot be positive definite anyway so uh + + + align:start position:0% +cannot be positive definite anyway so uh +uh um so so so you have to do something + + align:start position:0% +uh um so so so you have to do something + + + align:start position:0% +uh um so so so you have to do something +more radical okay if these are + + align:start position:0% +more radical okay if these are + + + align:start position:0% +more radical okay if these are +conventional functions + + align:start position:0% +conventional functions + + + align:start position:0% +conventional functions +and then and then this won't be positive + + align:start position:0% +and then and then this won't be positive + + + align:start position:0% +and then and then this won't be positive +definite + + align:start position:0% +definite + + + align:start position:0% +definite +but now what we did is that we make this + + align:start position:0% +but now what we did is that we make this + + + align:start position:0% +but now what we did is that we make this +into functions with anti-compute + + align:start position:0% +into functions with anti-compute + + + align:start position:0% +into functions with anti-compute +when the Envy commute turns out it needs + + align:start position:0% +when the Envy commute turns out it needs + + + align:start position:0% +when the Envy commute turns out it needs +to be a positive definite quantity + + align:start position:0% +to be a positive definite quantity + + + align:start position:0% +to be a positive definite quantity +okay as an ordinary function this cannot + + align:start position:0% +okay as an ordinary function this cannot + + + align:start position:0% +okay as an ordinary function this cannot +be positive template but if the + + align:start position:0% +be positive template but if the + + + align:start position:0% +be positive template but if the +anti-commute doesn't become a positive + + align:start position:0% +anti-commute doesn't become a positive + + + align:start position:0% +anti-commute doesn't become a positive +definite okay so let's stop here \ No newline at end of file diff --git a/T6EpmS2sWcM.txt b/T6EpmS2sWcM.txt new file mode 100644 index 0000000000000000000000000000000000000000..aca56c9de0a4f861aa734af96f4e364aa697b4ce --- /dev/null +++ b/T6EpmS2sWcM.txt @@ -0,0 +1,15035 @@ +align:start position:0% + +go ahead and get started we want to + + align:start position:0% +go ahead and get started we want to + + + align:start position:0% +go ahead and get started we want to +start with looking at the schedule get + + align:start position:0% +start with looking at the schedule get + + + align:start position:0% +start with looking at the schedule get +ourselves reoriented + + align:start position:0% +ourselves reoriented + + + align:start position:0% +ourselves reoriented +um this is uh November + + align:start position:0% +um this is uh November + + + align:start position:0% +um this is uh November +16th and uh we have our final lecture + + align:start position:0% +16th and uh we have our final lecture + + + align:start position:0% +16th and uh we have our final lecture +today on chapter nine chapter nine has + + align:start position:0% +today on chapter nine chapter nine has + + + align:start position:0% +today on chapter nine chapter nine has +three lectures we'll talk about modeling + + align:start position:0% +three lectures we'll talk about modeling + + + align:start position:0% +three lectures we'll talk about modeling +uh the Topography of uh + + align:start position:0% +uh the Topography of uh + + + align:start position:0% +uh the Topography of uh +deposition and you're working on + + align:start position:0% +deposition and you're working on + + + align:start position:0% +deposition and you're working on +hopefully everybody's working on + + align:start position:0% +hopefully everybody's working on + + + align:start position:0% +hopefully everybody's working on +homework number + + align:start position:0% +homework number + + + align:start position:0% +homework number +five uh that homework du uh next lecture + + align:start position:0% +five uh that homework du uh next lecture + + + align:start position:0% +five uh that homework du uh next lecture +on the 18th and uh anybody have any + + align:start position:0% +on the 18th and uh anybody have any + + + align:start position:0% +on the 18th and uh anybody have any +questions on the homework or if you do + + align:start position:0% +questions on the homework or if you do + + + align:start position:0% +questions on the homework or if you do +make sure you see me after class or send + + align:start position:0% +make sure you see me after class or send + + + align:start position:0% +make sure you see me after class or send +me an + + align:start position:0% +me an + + + align:start position:0% +me an +email um in addition to the homework uh + + align:start position:0% +email um in addition to the homework uh + + + align:start position:0% +email um in addition to the homework uh +everyone has now except one person on on + + align:start position:0% +everyone has now except one person on on + + + align:start position:0% +everyone has now except one person on on +the clipboard has a topic and I had my + + align:start position:0% +the clipboard has a topic and I had my + + + align:start position:0% +the clipboard has a topic and I had my +assistant um type it up I'll put it on + + align:start position:0% +assistant um type it up I'll put it on + + + align:start position:0% +assistant um type it up I'll put it on +the web everybody signed up for a FAL + + align:start position:0% +the web everybody signed up for a FAL + + + align:start position:0% +the web everybody signed up for a FAL +report topic and uh you can verify that + + align:start position:0% +report topic and uh you can verify that + + + align:start position:0% +report topic and uh you can verify that +she got it right uh and then uh if + + align:start position:0% +she got it right uh and then uh if + + + align:start position:0% +she got it right uh and then uh if +you're doing an oral + + align:start position:0% +you're doing an oral + + + align:start position:0% +you're doing an oral +presentation uh I'll start this week + + align:start position:0% +presentation uh I'll start this week + + + align:start position:0% +presentation uh I'll start this week +I'll start making up a schedule so you + + align:start position:0% +I'll start making up a schedule so you + + + align:start position:0% +I'll start making up a schedule so you +know which day you're you're going to + + align:start position:0% +know which day you're you're going to + + + align:start position:0% +know which day you're you're going to +speak um + + align:start position:0% +speak um + + + align:start position:0% +speak um +okay so hopefully uh everybody recovered + + align:start position:0% +okay so hopefully uh everybody recovered + + + align:start position:0% +okay so hopefully uh everybody recovered +from the snowstorm we had over the + + align:start position:0% +from the snowstorm we had over the + + + align:start position:0% +from the snowstorm we had over the +weekend and uh we'll go ahead and start + + align:start position:0% +weekend and uh we'll go ahead and start + + + align:start position:0% +weekend and uh we'll go ahead and start +this lecture uh with handout number + + align:start position:0% +this lecture uh with handout number + + + align:start position:0% +this lecture uh with handout number +32 as I mentioned this is the final uh + + align:start position:0% +32 as I mentioned this is the final uh + + + align:start position:0% +32 as I mentioned this is the final uh +lecture on chapter nine so far we've uh + + align:start position:0% +lecture on chapter nine so far we've uh + + + align:start position:0% +lecture on chapter nine so far we've uh +in in the way of by way of thin film + + align:start position:0% +in in the way of by way of thin film + + + align:start position:0% +in in the way of by way of thin film +deposition epit we talked uh at least a + + align:start position:0% +deposition epit we talked uh at least a + + + align:start position:0% +deposition epit we talked uh at least a +little bit about silicon epitaxial + + align:start position:0% +little bit about silicon epitaxial + + + align:start position:0% +little bit about silicon epitaxial +growth we discussed the uh low pressure + + align:start position:0% +growth we discussed the uh low pressure + + + align:start position:0% +growth we discussed the uh low pressure +chemical vapor deposition of three the + + align:start position:0% +chemical vapor deposition of three the + + + align:start position:0% +chemical vapor deposition of three the +three most important films in front end + + align:start position:0% +three most important films in front end + + + align:start position:0% +three most important films in front end +processing that's polysilicon oxide you + + align:start position:0% +processing that's polysilicon oxide you + + + align:start position:0% +processing that's polysilicon oxide you +know low temperature oxide and silicon + + align:start position:0% +know low temperature oxide and silicon + + + align:start position:0% +know low temperature oxide and silicon +nitride and we introduced uh some PV PVD + + align:start position:0% +nitride and we introduced uh some PV PVD + + + align:start position:0% +nitride and we introduced uh some PV PVD +techniques such as sputtering we talked + + align:start position:0% +techniques such as sputtering we talked + + + align:start position:0% +techniques such as sputtering we talked +about systems for dcn RF sputtering uh + + align:start position:0% +about systems for dcn RF sputtering uh + + + align:start position:0% +about systems for dcn RF sputtering uh +which is the most commonly used PVD + + align:start position:0% +which is the most commonly used PVD + + + align:start position:0% +which is the most commonly used PVD +technique in in modern Fabs um the nice + + align:start position:0% +technique in in modern Fabs um the nice + + + align:start position:0% +technique in in modern Fabs um the nice +thing about it is it can be adjusted to + + align:start position:0% +thing about it is it can be adjusted to + + + align:start position:0% +thing about it is it can be adjusted to +give reasonably good step coverage this + + align:start position:0% +give reasonably good step coverage this + + + align:start position:0% +give reasonably good step coverage this +is in contrast to evaporation thermal + + align:start position:0% +is in contrast to evaporation thermal + + + align:start position:0% +is in contrast to evaporation thermal +evaporation is typically not used in in + + align:start position:0% +evaporation is typically not used in in + + + align:start position:0% +evaporation is typically not used in in +seamoss + + align:start position:0% +seamoss + + + align:start position:0% +seamoss +processing today what I want to talk + + align:start position:0% +processing today what I want to talk + + + align:start position:0% +processing today what I want to talk +about though is is uh modeling of these + + align:start position:0% +about though is is uh modeling of these + + + align:start position:0% +about though is is uh modeling of these +processes and you'll see how these + + align:start position:0% +processes and you'll see how these + + + align:start position:0% +processes and you'll see how these +models are a little bit different + + align:start position:0% +models are a little bit different + + + align:start position:0% +models are a little bit different +they're much more quasi empirical than + + align:start position:0% +they're much more quasi empirical than + + + align:start position:0% +they're much more quasi empirical than +the models we had for iron + + align:start position:0% +the models we had for iron + + + align:start position:0% +the models we had for iron +implantation uh but there are methods to + + align:start position:0% +implantation uh but there are methods to + + + align:start position:0% +implantation uh but there are methods to +do modeling of these processes and we'll + + align:start position:0% +do modeling of these processes and we'll + + + align:start position:0% +do modeling of these processes and we'll +give a couple of specific uh + + align:start position:0% +give a couple of specific uh + + + align:start position:0% +give a couple of specific uh +examples okay let's go on to uh to uh + + align:start position:0% +examples okay let's go on to uh to uh + + + align:start position:0% +examples okay let's go on to uh to uh +slide number two uh within the last 10 + + align:start position:0% +slide number two uh within the last 10 + + + align:start position:0% +slide number two uh within the last 10 +to 15 years ago or so there have been a + + align:start position:0% +to 15 years ago or so there have been a + + + align:start position:0% +to 15 years ago or so there have been a +a number of simulation tools have been + + align:start position:0% +a number of simulation tools have been + + + align:start position:0% +a number of simulation tools have been +developed for topography simulation now + + align:start position:0% +developed for topography simulation now + + + align:start position:0% +developed for topography simulation now +I want to make clear topography + + align:start position:0% +I want to make clear topography + + + align:start position:0% +I want to make clear topography +simulation is not what Supreme 4 does + + align:start position:0% +simulation is not what Supreme 4 does + + + align:start position:0% +simulation is not what Supreme 4 does +you you've all been using Supreme 4 uh + + align:start position:0% +you you've all been using Supreme 4 uh + + + align:start position:0% +you you've all been using Supreme 4 uh +to model ion implantation oxidation + + align:start position:0% +to model ion implantation oxidation + + + align:start position:0% +to model ion implantation oxidation +diffusion a lot of the frontend + + align:start position:0% +diffusion a lot of the frontend + + + align:start position:0% +diffusion a lot of the frontend +processing Supreme for doesn't have any + + align:start position:0% +processing Supreme for doesn't have any + + + align:start position:0% +processing Supreme for doesn't have any +topography simulation of of any sort if + + align:start position:0% +topography simulation of of any sort if + + + align:start position:0% +topography simulation of of any sort if +you tell it to make an etch it assumes + + align:start position:0% +you tell it to make an etch it assumes + + + align:start position:0% +you tell it to make an etch it assumes +it's etched at a certain angle you tell + + align:start position:0% +it's etched at a certain angle you tell + + + align:start position:0% +it's etched at a certain angle you tell +at the angle it doesn't make any effort + + align:start position:0% +at the angle it doesn't make any effort + + + align:start position:0% +at the angle it doesn't make any effort +to calculate those angles or if you tell + + align:start position:0% +to calculate those angles or if you tell + + + align:start position:0% +to calculate those angles or if you tell +it that something is deposited um it + + align:start position:0% +it that something is deposited um it + + + align:start position:0% +it that something is deposited um it +assumes conformal deposition unless you + + align:start position:0% +assumes conformal deposition unless you + + + align:start position:0% +assumes conformal deposition unless you +say otherwise so it's not a simulator + + align:start position:0% +say otherwise so it's not a simulator + + + align:start position:0% +say otherwise so it's not a simulator +for topography um there are other + + align:start position:0% +for topography um there are other + + + align:start position:0% +for topography um there are other +simulators and one of the ones that um + + align:start position:0% +simulators and one of the ones that um + + + align:start position:0% +simulators and one of the ones that um +also came out of Stanford is called + + align:start position:0% +also came out of Stanford is called + + + align:start position:0% +also came out of Stanford is called +speedy and there are some examples in + + align:start position:0% +speedy and there are some examples in + + + align:start position:0% +speedy and there are some examples in +this lecture from the Speedy simulator + + align:start position:0% +this lecture from the Speedy simulator + + + align:start position:0% +this lecture from the Speedy simulator +and from your in your + + align:start position:0% +and from your in your + + + align:start position:0% +and from your in your +textbook okay so what is it that we need + + align:start position:0% +textbook okay so what is it that we need + + + align:start position:0% +textbook okay so what is it that we need +to f about if we want to do topography + + align:start position:0% +to f about if we want to do topography + + + align:start position:0% +to f about if we want to do topography +simulation let's say we are trying to + + align:start position:0% +simulation let's say we are trying to + + + align:start position:0% +simulation let's say we are trying to +model the Topography of deposition of + + align:start position:0% +model the Topography of deposition of + + + align:start position:0% +model the Topography of deposition of +some film this particular uh example on + + align:start position:0% +some film this particular uh example on + + + align:start position:0% +some film this particular uh example on +slide two is shown assuming we're doing + + align:start position:0% +slide two is shown assuming we're doing + + + align:start position:0% +slide two is shown assuming we're doing +a deposition of aluminum say in a + + align:start position:0% +a deposition of aluminum say in a + + + align:start position:0% +a deposition of aluminum say in a +sputtering chamber um and this is the + + align:start position:0% +sputtering chamber um and this is the + + + align:start position:0% +sputtering chamber um and this is the +surface this this is the surface where + + align:start position:0% +surface this this is the surface where + + + align:start position:0% +surface this this is the surface where +um that we're depositing the aluminum + + align:start position:0% +um that we're depositing the aluminum + + + align:start position:0% +um that we're depositing the aluminum +for instance uh onto that surface has + + align:start position:0% +for instance uh onto that surface has + + + align:start position:0% +for instance uh onto that surface has +some starting uh initial uh + + align:start position:0% +some starting uh initial uh + + + align:start position:0% +some starting uh initial uh +topography well uh this is sort of a + + align:start position:0% +topography well uh this is sort of a + + + align:start position:0% +topography well uh this is sort of a +generalized picture of what's involved + + align:start position:0% +generalized picture of what's involved + + + align:start position:0% +generalized picture of what's involved +in the deposition and you'll see that + + align:start position:0% +in the deposition and you'll see that + + + align:start position:0% +in the deposition and you'll see that +modeling topography ends up being a lot + + align:start position:0% +modeling topography ends up being a lot + + + align:start position:0% +modeling topography ends up being a lot +of bookkeeping of the different fluxes + + align:start position:0% +of bookkeeping of the different fluxes + + + align:start position:0% +of bookkeeping of the different fluxes +involved uh in general we are not going + + align:start position:0% +involved uh in general we are not going + + + align:start position:0% +involved uh in general we are not going +to consider gas phase boundary layer in + + align:start position:0% +to consider gas phase boundary layer in + + + align:start position:0% +to consider gas phase boundary layer in +in this in these simple models so this + + align:start position:0% +in this in these simple models so this + + + align:start position:0% +in this in these simple models so this +picture will not be AC accurate for for + + align:start position:0% +picture will not be AC accurate for for + + + align:start position:0% +picture will not be AC accurate for for +example atmospheric pressure CBD where + + align:start position:0% +example atmospheric pressure CBD where + + + align:start position:0% +example atmospheric pressure CBD where +the fusion through a boundary layer is + + align:start position:0% +the fusion through a boundary layer is + + + align:start position:0% +the fusion through a boundary layer is +very important we're not taking into + + align:start position:0% +very important we're not taking into + + + align:start position:0% +very important we're not taking into +account um uh but it will be reasonably + + align:start position:0% +account um uh but it will be reasonably + + + align:start position:0% +account um uh but it will be reasonably +useful for modeling low pressure CBD uh + + align:start position:0% +useful for modeling low pressure CBD uh + + + align:start position:0% +useful for modeling low pressure CBD uh +or for modeling sputtering which also + + align:start position:0% +or for modeling sputtering which also + + + align:start position:0% +or for modeling sputtering which also +takes place at reasonably low pressures + + align:start position:0% +takes place at reasonably low pressures + + + align:start position:0% +takes place at reasonably low pressures +so these are the the fluxes involved for + + align:start position:0% +so these are the the fluxes involved for + + + align:start position:0% +so these are the the fluxes involved for +example if we're depositing aluminum on + + align:start position:0% +example if we're depositing aluminum on + + + align:start position:0% +example if we're depositing aluminum on +this surface we have a direct flux uh to + + align:start position:0% +this surface we have a direct flux uh to + + + align:start position:0% +this surface we have a direct flux uh to +the surface of neutral alumin aluminum + + align:start position:0% +the surface of neutral alumin aluminum + + + align:start position:0% +the surface of neutral alumin aluminum +atoms we also have a direct flux of ions + + align:start position:0% +atoms we also have a direct flux of ions + + + align:start position:0% +atoms we also have a direct flux of ions +that we need to keep track of uh + + align:start position:0% +that we need to keep track of uh + + + align:start position:0% +that we need to keep track of uh +aluminum can come down and it can + + align:start position:0% +aluminum can come down and it can + + + align:start position:0% +aluminum can come down and it can +actually we can have any desorbed it can + + align:start position:0% +actually we can have any desorbed it can + + + align:start position:0% +actually we can have any desorbed it can +desorb aluminum that has already been + + align:start position:0% +desorb aluminum that has already been + + + align:start position:0% +desorb aluminum that has already been +deposited at a point and then we have a + + align:start position:0% +deposited at a point and then we have a + + + align:start position:0% +deposited at a point and then we have a +desorbed or emitted flux that can be + + align:start position:0% +desorbed or emitted flux that can be + + + align:start position:0% +desorbed or emitted flux that can be +redeposited Elsewhere on the surface so + + align:start position:0% +redeposited Elsewhere on the surface so + + + align:start position:0% +redeposited Elsewhere on the surface so +that's a flux we need to take account of + + align:start position:0% +that's a flux we need to take account of + + + align:start position:0% +that's a flux we need to take account of +uh argon ions because again this is in + + align:start position:0% +uh argon ions because again this is in + + + align:start position:0% +uh argon ions because again this is in +the sputtering system argon is not only + + align:start position:0% +the sputtering system argon is not only + + + align:start position:0% +the sputtering system argon is not only +supposed to be directed towards the + + align:start position:0% +supposed to be directed towards the + + + align:start position:0% +supposed to be directed towards the +target not towards the wafer but it's + + align:start position:0% +target not towards the wafer but it's + + + align:start position:0% +target not towards the wafer but it's +possible that it would be directed + + align:start position:0% +possible that it would be directed + + + align:start position:0% +possible that it would be directed +towards the wafer argon ions some of + + align:start position:0% +towards the wafer argon ions some of + + + align:start position:0% +towards the wafer argon ions some of +them and that they would sputter off + + align:start position:0% +them and that they would sputter off + + + align:start position:0% +them and that they would sputter off +aluminum that had already been deposited + + align:start position:0% +aluminum that had already been deposited + + + align:start position:0% +aluminum that had already been deposited +and then that can redeposit elsewhere + + align:start position:0% +and then that can redeposit elsewhere + + + align:start position:0% +and then that can redeposit elsewhere +and there's a surface diffusion flux + + align:start position:0% +and there's a surface diffusion flux + + + align:start position:0% +and there's a surface diffusion flux +aluminum can diffuse along the surface + + align:start position:0% +aluminum can diffuse along the surface + + + align:start position:0% +aluminum can diffuse along the surface +uh at a certain distance and then then + + align:start position:0% +uh at a certain distance and then then + + + align:start position:0% +uh at a certain distance and then then +deposit at a different point um so these + + align:start position:0% +deposit at a different point um so these + + + align:start position:0% +deposit at a different point um so these +we end up just taking doing a lot of + + align:start position:0% +we end up just taking doing a lot of + + + align:start position:0% +we end up just taking doing a lot of +Bookkeeping on all the different fluxes + + align:start position:0% +Bookkeeping on all the different fluxes + + + align:start position:0% +Bookkeeping on all the different fluxes +and uh it'd be good if you think about + + align:start position:0% +and uh it'd be good if you think about + + + align:start position:0% +and uh it'd be good if you think about +this picture because we're going to use + + align:start position:0% +this picture because we're going to use + + + align:start position:0% +this picture because we're going to use +the exact same picture when we talk + + align:start position:0% +the exact same picture when we talk + + + align:start position:0% +the exact same picture when we talk +about etching when you think about it in + + align:start position:0% +about etching when you think about it in + + + align:start position:0% +about etching when you think about it in +this uh terminology etching is sort of + + align:start position:0% +this uh terminology etching is sort of + + + align:start position:0% +this uh terminology etching is sort of +just the opposite instead of depositing + + align:start position:0% +just the opposite instead of depositing + + + align:start position:0% +just the opposite instead of depositing +we're talking about REM uh fluxes coming + + align:start position:0% +we're talking about REM uh fluxes coming + + + align:start position:0% +we're talking about REM uh fluxes coming +down reacting and removing films uh but + + align:start position:0% +down reacting and removing films uh but + + + align:start position:0% +down reacting and removing films uh but +it's not that much difference it's sort + + align:start position:0% +it's not that much difference it's sort + + + align:start position:0% +it's not that much difference it's sort +of mathematically the inverse of + + align:start position:0% +of mathematically the inverse of + + + align:start position:0% +of mathematically the inverse of +deposition so in order to simulate that + + align:start position:0% +deposition so in order to simulate that + + + align:start position:0% +deposition so in order to simulate that +process that I just showed + + align:start position:0% +process that I just showed + + + align:start position:0% +process that I just showed +uh on slide three here we need to + + align:start position:0% +uh on slide three here we need to + + + align:start position:0% +uh on slide three here we need to +simulate uh we need some kind of + + align:start position:0% +simulate uh we need some kind of + + + align:start position:0% +simulate uh we need some kind of +mathematical description of all of these + + align:start position:0% +mathematical description of all of these + + + align:start position:0% +mathematical description of all of these +fluxes and then we need to add them and + + align:start position:0% +fluxes and then we need to add them and + + + align:start position:0% +fluxes and then we need to add them and +uh add them all up and see what we get + + align:start position:0% +uh add them all up and see what we get + + + align:start position:0% +uh add them all up and see what we get +at any given + + align:start position:0% +at any given + + + align:start position:0% +at any given +point so what we write is this equation + + align:start position:0% +point so what we write is this equation + + + align:start position:0% +point so what we write is this equation +shown at the top of of slide three that + + align:start position:0% +shown at the top of of slide three that + + + align:start position:0% +shown at the top of of slide three that +that we say the net flux at any point I + + align:start position:0% +that we say the net flux at any point I + + + align:start position:0% +that we say the net flux at any point I +so point I point I is just if I go back + + align:start position:0% +so point I point I is just if I go back + + + align:start position:0% +so point I point I is just if I go back +one point I is just at some point on the + + align:start position:0% +one point I is just at some point on the + + + align:start position:0% +one point I is just at some point on the +surface that's it could be at this point + + align:start position:0% +surface that's it could be at this point + + + align:start position:0% +surface that's it could be at this point +right here could be at that point right + + align:start position:0% +right here could be at that point right + + + align:start position:0% +right here could be at that point right +there it's just said at some point on + + align:start position:0% +there it's just said at some point on + + + align:start position:0% +there it's just said at some point on +the surface + + align:start position:0% +the surface + + + align:start position:0% +the surface +the net flux is well it's the flux + + align:start position:0% +the net flux is well it's the flux + + + align:start position:0% +the net flux is well it's the flux +deposited at that point minus everything + + align:start position:0% +deposited at that point minus everything + + + align:start position:0% +deposited at that point minus everything +that was emitted right and that gives + + align:start position:0% +that was emitted right and that gives + + + align:start position:0% +that was emitted right and that gives +you the total atoms per square + + align:start position:0% +you the total atoms per square + + + align:start position:0% +you the total atoms per square +centimeter per unit time so this is the + + align:start position:0% +centimeter per unit time so this is the + + + align:start position:0% +centimeter per unit time so this is the +you add up the direct Flux Of neutrals + + align:start position:0% +you add up the direct Flux Of neutrals + + + align:start position:0% +you add up the direct Flux Of neutrals +the direct flux of ions any flux that's + + align:start position:0% +the direct flux of ions any flux that's + + + align:start position:0% +the direct flux of ions any flux that's +redeposited that's coming off uh from + + align:start position:0% +redeposited that's coming off uh from + + + align:start position:0% +redeposited that's coming off uh from +another area uh any flux that's due to + + align:start position:0% +another area uh any flux that's due to + + + align:start position:0% +another area uh any flux that's due to +surface diffusion all those are positive + + align:start position:0% +surface diffusion all those are positive + + + align:start position:0% +surface diffusion all those are positive +terms you subtract off any flux that's + + align:start position:0% +terms you subtract off any flux that's + + + align:start position:0% +terms you subtract off any flux that's +emitted from that point uh any flux that + + align:start position:0% +emitted from that point uh any flux that + + + align:start position:0% +emitted from that point uh any flux that +diffuses out or that's sputter from that + + align:start position:0% +diffuses out or that's sputter from that + + + align:start position:0% +diffuses out or that's sputter from that +point by virtue of uh argon ions coming + + align:start position:0% +point by virtue of uh argon ions coming + + + align:start position:0% +point by virtue of uh argon ions coming +down or something so you can see this is + + align:start position:0% +down or something so you can see this is + + + align:start position:0% +down or something so you can see this is +going to amount to basically a lot of + + align:start position:0% +going to amount to basically a lot of + + + align:start position:0% +going to amount to basically a lot of +bookkeeping and this is something that + + align:start position:0% +bookkeeping and this is something that + + + align:start position:0% +bookkeeping and this is something that +computers are very good at doing and you + + align:start position:0% +computers are very good at doing and you + + + align:start position:0% +computers are very good at doing and you +can and you can model those fluxes + + align:start position:0% +can and you can model those fluxes + + + align:start position:0% +can and you can model those fluxes +across the + + align:start position:0% +across the + + + align:start position:0% +across the +surface so um usually what we need to do + + align:start position:0% +surface so um usually what we need to do + + + align:start position:0% +surface so um usually what we need to do +for a specific system let's say you're + + align:start position:0% +for a specific system let's say you're + + + align:start position:0% +for a specific system let's say you're +doing lpcvd or something uh we have to + + align:start position:0% +doing lpcvd or something uh we have to + + + align:start position:0% +doing lpcvd or something uh we have to +figure out which one of these fluxes is + + align:start position:0% +figure out which one of these fluxes is + + + align:start position:0% +figure out which one of these fluxes is +important and ignore all the others so + + align:start position:0% +important and ignore all the others so + + + align:start position:0% +important and ignore all the others so +we don't so we can simplify the models + + align:start position:0% +we don't so we can simplify the models + + + align:start position:0% +we don't so we can simplify the models +to a certain extent uh um and this + + align:start position:0% +to a certain extent uh um and this + + + align:start position:0% +to a certain extent uh um and this +picture gives you a rough idea of of how + + align:start position:0% +picture gives you a rough idea of of how + + + align:start position:0% +picture gives you a rough idea of of how +we do the + + align:start position:0% +we do the + + + align:start position:0% +we do the +modeling um what we have what we + + align:start position:0% +modeling um what we have what we + + + align:start position:0% +modeling um what we have what we +consider is uh we draw this dash line + + align:start position:0% +consider is uh we draw this dash line + + + align:start position:0% +consider is uh we draw this dash line +here right above the surface of the + + align:start position:0% +here right above the surface of the + + + align:start position:0% +here right above the surface of the +wafer and um so it's a plane just above + + align:start position:0% +wafer and um so it's a plane just above + + + align:start position:0% +wafer and um so it's a plane just above +the surface and we first thing we need + + align:start position:0% +the surface and we first thing we need + + + align:start position:0% +the surface and we first thing we need +to look at is what's the arrival angle + + align:start position:0% +to look at is what's the arrival angle + + + align:start position:0% +to look at is what's the arrival angle +distribution of atoms and ions that are + + align:start position:0% +distribution of atoms and ions that are + + + align:start position:0% +distribution of atoms and ions that are +coming down in that plane and then later + + align:start position:0% +coming down in that plane and then later + + + align:start position:0% +coming down in that plane and then later +on the next step will take into account + + align:start position:0% +on the next step will take into account + + + align:start position:0% +on the next step will take into account +topography so first you do it assuming + + align:start position:0% +topography so first you do it assuming + + + align:start position:0% +topography so first you do it assuming +you have a plane just above the + + align:start position:0% +you have a plane just above the + + + align:start position:0% +you have a plane just above the +surface um and now what we need to take + + align:start position:0% +surface um and now what we need to take + + + align:start position:0% +surface um and now what we need to take +into account are these direct Flux Of + + align:start position:0% +into account are these direct Flux Of + + + align:start position:0% +into account are these direct Flux Of +neutrals and the direct flux of ions + + align:start position:0% +neutrals and the direct flux of ions + + + align:start position:0% +neutrals and the direct flux of ions +these we generally model uh with some + + align:start position:0% +these we generally model uh with some + + + align:start position:0% +these we generally model uh with some +kind of arrival angle distribution just + + align:start position:0% +kind of arrival angle distribution just + + + align:start position:0% +kind of arrival angle distribution just +above the wafer uh and I've noted here + + align:start position:0% +above the wafer uh and I've noted here + + + align:start position:0% +above the wafer uh and I've noted here +what it says it doesn't model the + + align:start position:0% +what it says it doesn't model the + + + align:start position:0% +what it says it doesn't model the +equipment what that means is um you have + + align:start position:0% +equipment what that means is um you have + + + align:start position:0% +equipment what that means is um you have +to put in the arrival angle distribution + + align:start position:0% +to put in the arrival angle distribution + + + align:start position:0% +to put in the arrival angle distribution +you can't save the simulator oh yes I + + align:start position:0% +you can't save the simulator oh yes I + + + align:start position:0% +you can't save the simulator oh yes I +have an applyed material sputtering tool + + align:start position:0% +have an applyed material sputtering tool + + + align:start position:0% +have an applyed material sputtering tool +in the Endura and now tell me what it's + + align:start position:0% +in the Endura and now tell me what it's + + + align:start position:0% +in the Endura and now tell me what it's +going to look like it it doesn't have + + align:start position:0% +going to look like it it doesn't have + + + align:start position:0% +going to look like it it doesn't have +that level of knowledge of the + + align:start position:0% +that level of knowledge of the + + + align:start position:0% +that level of knowledge of the +individual tools what you do is you put + + align:start position:0% +individual tools what you do is you put + + + align:start position:0% +individual tools what you do is you put +in flux the direct flux as a function of + + align:start position:0% +in flux the direct flux as a function of + + + align:start position:0% +in flux the direct flux as a function of +the angle Theta and that's measured with + + align:start position:0% +the angle Theta and that's measured with + + + align:start position:0% +the angle Theta and that's measured with +respect to the normal and you give it + + align:start position:0% +respect to the normal and you give it + + + align:start position:0% +respect to the normal and you give it +usually um it's some normal flux times a + + align:start position:0% +usually um it's some normal flux times a + + + align:start position:0% +usually um it's some normal flux times a +cosine Theta to the end power uh so + + align:start position:0% +cosine Theta to the end power uh so + + + align:start position:0% +cosine Theta to the end power uh so +that's that's a variable that you need + + align:start position:0% +that's that's a variable that you need + + + align:start position:0% +that's that's a variable that you need +to put into the uh into the simulator uh + + align:start position:0% +to put into the uh into the simulator uh + + + align:start position:0% +to put into the uh into the simulator uh +but there are some guidelines on on for + + align:start position:0% +but there are some guidelines on on for + + + align:start position:0% +but there are some guidelines on on for +different systems different types of + + align:start position:0% +different systems different types of + + + align:start position:0% +different systems different types of +systems what kind of uh arrival angle + + align:start position:0% +systems what kind of uh arrival angle + + + align:start position:0% +systems what kind of uh arrival angle +distribution for neutrals and ions you + + align:start position:0% +distribution for neutrals and ions you + + + align:start position:0% +distribution for neutrals and ions you +might use + + align:start position:0% + + + + align:start position:0% + +so let's look at a couple different + + align:start position:0% +so let's look at a couple different + + + align:start position:0% +so let's look at a couple different +types of of uh flux uh distributions the + + align:start position:0% +types of of uh flux uh distributions the + + + align:start position:0% +types of of uh flux uh distributions the +first one here shown on slide number + + align:start position:0% +first one here shown on slide number + + + align:start position:0% +first one here shown on slide number +four is what we call isotropic flux + + align:start position:0% +four is what we call isotropic flux + + + align:start position:0% +four is what we call isotropic flux +arrival as the name suggests the flux is + + align:start position:0% +arrival as the name suggests the flux is + + + align:start position:0% +arrival as the name suggests the flux is +um is essentially uh + + align:start position:0% +um is essentially uh + + + align:start position:0% +um is essentially uh +isotropic uh and this we use and n + + align:start position:0% +isotropic uh and this we use and n + + + align:start position:0% +isotropic uh and this we use and n +equals 1 in the formula of cosine Theta + + align:start position:0% +equals 1 in the formula of cosine Theta + + + align:start position:0% +equals 1 in the formula of cosine Theta +the N uh so what we get is that the + + align:start position:0% +the N uh so what we get is that the + + + align:start position:0% +the N uh so what we get is that the +direct flux f as a function of angle + + align:start position:0% +direct flux f as a function of angle + + + align:start position:0% +direct flux f as a function of angle +Theta so Theta is measured with respect + + align:start position:0% +Theta so Theta is measured with respect + + + align:start position:0% +Theta so Theta is measured with respect +to the normal is whatever the flux is in + + align:start position:0% +to the normal is whatever the flux is in + + + align:start position:0% +to the normal is whatever the flux is in +the normal Direction F0 so it's this + + align:start position:0% +the normal Direction F0 so it's this + + + align:start position:0% +the normal Direction F0 so it's this +flux number here times cosine uh Theta + + align:start position:0% +flux number here times cosine uh Theta + + + align:start position:0% +flux number here times cosine uh Theta +to the end so what's happening is I'm + + align:start position:0% +to the end so what's happening is I'm + + + align:start position:0% +to the end so what's happening is I'm +moving from normal I have a certain flux + + align:start position:0% +moving from normal I have a certain flux + + + align:start position:0% +moving from normal I have a certain flux +in and as I go this direction as I + + align:start position:0% +in and as I go this direction as I + + + align:start position:0% +in and as I go this direction as I +coming in at shallower Shang shallower + + align:start position:0% +coming in at shallower Shang shallower + + + align:start position:0% +coming in at shallower Shang shallower +angles um the the flux uh goes down + + align:start position:0% +angles um the the flux uh goes down + + + align:start position:0% +angles um the the flux uh goes down +according to this cosine Theta yeah and + + align:start position:0% +according to this cosine Theta yeah and + + + align:start position:0% +according to this cosine Theta yeah and +this little derivation that I've shown + + align:start position:0% +this little derivation that I've shown + + + align:start position:0% +this little derivation that I've shown +mathematically on the second half of + + align:start position:0% +mathematically on the second half of + + + align:start position:0% +mathematically on the second half of +slide four kind of explains where that + + align:start position:0% +slide four kind of explains where that + + + align:start position:0% +slide four kind of explains where that +comes from uh what we're interested in + + align:start position:0% +comes from uh what we're interested in + + + align:start position:0% +comes from uh what we're interested in +when we're looking at deposition we're + + align:start position:0% +when we're looking at deposition we're + + + align:start position:0% +when we're looking at deposition we're +interested in uh the normal component of + + align:start position:0% +interested in uh the normal component of + + + align:start position:0% +interested in uh the normal component of +the + + align:start position:0% +the + + + align:start position:0% +the +flux okay so let's say this is my wafer + + align:start position:0% +flux okay so let's say this is my wafer + + + align:start position:0% +flux okay so let's say this is my wafer +down here this solid line here + + align:start position:0% +down here this solid line here + + + align:start position:0% +down here this solid line here +represents the wafer um or the surface + + align:start position:0% +represents the wafer um or the surface + + + align:start position:0% +represents the wafer um or the surface +uh that I'm depositing on and if we look + + align:start position:0% +uh that I'm depositing on and if we look + + + align:start position:0% +uh that I'm depositing on and if we look +at this little red region that + + align:start position:0% +at this little red region that + + + align:start position:0% +at this little red region that +represents a certain normal flux coming + + align:start position:0% +represents a certain normal flux coming + + + align:start position:0% +represents a certain normal flux coming +and that would be my f super zero uh and + + align:start position:0% +and that would be my f super zero uh and + + + align:start position:0% +and that would be my f super zero uh and +this I'm I'm drawing this for the N + + align:start position:0% +this I'm I'm drawing this for the N + + + align:start position:0% +this I'm I'm drawing this for the N +equals 1 case so have a certain flux + + align:start position:0% +equals 1 case so have a certain flux + + + align:start position:0% +equals 1 case so have a certain flux +coming in uh Norm in normal now at some + + align:start position:0% +coming in uh Norm in normal now at some + + + align:start position:0% +coming in uh Norm in normal now at some +other angle Theta I have that same flux + + align:start position:0% +other angle Theta I have that same flux + + + align:start position:0% +other angle Theta I have that same flux +you notice I drew those same number of + + align:start position:0% +you notice I drew those same number of + + + align:start position:0% +you notice I drew those same number of +arrows so it's at the coming in this + + align:start position:0% +arrows so it's at the coming in this + + + align:start position:0% +arrows so it's at the coming in this +direction normal to this plane here + + align:start position:0% +direction normal to this plane here + + + align:start position:0% +direction normal to this plane here +normal to this plane I have the same + + align:start position:0% +normal to this plane I have the same + + + align:start position:0% +normal to this plane I have the same +number of atoms per square centimeter uh + + align:start position:0% +number of atoms per square centimeter uh + + + align:start position:0% +number of atoms per square centimeter uh +per unit time but I need to project that + + align:start position:0% +per unit time but I need to project that + + + align:start position:0% +per unit time but I need to project that +now uh onto this surface so when I + + align:start position:0% +now uh onto this surface so when I + + + align:start position:0% +now uh onto this surface so when I +project this uh this distance here uh of + + align:start position:0% +project this uh this distance here uh of + + + align:start position:0% +project this uh this distance here uh of +length L onto the surface I have this + + align:start position:0% +length L onto the surface I have this + + + align:start position:0% +length L onto the surface I have this +sort of distance this it spread out over + + align:start position:0% +sort of distance this it spread out over + + + align:start position:0% +sort of distance this it spread out over +a lateral Dimension + + align:start position:0% +a lateral Dimension + + + align:start position:0% +a lateral Dimension +H uh now we have right triangles here + + align:start position:0% +H uh now we have right triangles here + + + align:start position:0% +H uh now we have right triangles here +with angle Theta here and and uh Theta + + align:start position:0% +with angle Theta here and and uh Theta + + + align:start position:0% +with angle Theta here and and uh Theta +here and you can write it's very simply + + align:start position:0% +here and you can write it's very simply + + + align:start position:0% +here and you can write it's very simply +that the coine of the angle Theta it's + + align:start position:0% +that the coine of the angle Theta it's + + + align:start position:0% +that the coine of the angle Theta it's +just this uh distance L divided by the + + align:start position:0% +just this uh distance L divided by the + + + align:start position:0% +just this uh distance L divided by the +distance H where H represents how far + + align:start position:0% +distance H where H represents how far + + + align:start position:0% +distance H where H represents how far +that unit flux is spread uh across the + + align:start position:0% +that unit flux is spread uh across the + + + align:start position:0% +that unit flux is spread uh across the +wafer um okay so now it's just + + align:start position:0% +wafer um okay so now it's just + + + align:start position:0% +wafer um okay so now it's just +bookkeeping if I want to know what what + + align:start position:0% +bookkeeping if I want to know what what + + + align:start position:0% +bookkeeping if I want to know what what +is the flux here um in this region it's + + align:start position:0% +is the flux here um in this region it's + + + align:start position:0% +is the flux here um in this region it's +just the number per unit area per unit + + align:start position:0% +just the number per unit area per unit + + + align:start position:0% +just the number per unit area per unit +time it's going to be proportional to + + align:start position:0% +time it's going to be proportional to + + + align:start position:0% +time it's going to be proportional to +the + + align:start position:0% +the + + + align:start position:0% +the +number uh per unit time divided by H + + align:start position:0% +number uh per unit time divided by H + + + align:start position:0% +number uh per unit time divided by H +right because it's spread out over the + + align:start position:0% +right because it's spread out over the + + + align:start position:0% +right because it's spread out over the +distance H but you can substitute in for + + align:start position:0% +distance H but you can substitute in for + + + align:start position:0% +distance H but you can substitute in for +H H is cosine Theta over + + align:start position:0% +H H is cosine Theta over + + + align:start position:0% +H H is cosine Theta over +L uh or L over cosine Theta right so you + + align:start position:0% +L uh or L over cosine Theta right so you + + + align:start position:0% +L uh or L over cosine Theta right so you +can you can substitute that in so you + + align:start position:0% +can you can substitute that in so you + + + align:start position:0% +can you can substitute that in so you +get the fact that this for for isotropic + + align:start position:0% +get the fact that this for for isotropic + + + align:start position:0% +get the fact that this for for isotropic +so assuming you have just as much + + align:start position:0% +so assuming you have just as much + + + align:start position:0% +so assuming you have just as much +intensity in this red bar as I had uh in + + align:start position:0% +intensity in this red bar as I had uh in + + + align:start position:0% +intensity in this red bar as I had uh in +this um in this direction Theta in the + + align:start position:0% +this um in this direction Theta in the + + + align:start position:0% +this um in this direction Theta in the +black bar assuming that then I get this + + align:start position:0% +black bar assuming that then I get this + + + align:start position:0% +black bar assuming that then I get this +simple formula which shows that the flux + + align:start position:0% +simple formula which shows that the flux + + + align:start position:0% +simple formula which shows that the flux +as a function of theta is just the + + align:start position:0% +as a function of theta is just the + + + align:start position:0% +as a function of theta is just the +normal flux times the cosine Theta um + + align:start position:0% +normal flux times the cosine Theta um + + + align:start position:0% +normal flux times the cosine Theta um +now if for some that's assuming that the + + align:start position:0% +now if for some that's assuming that the + + + align:start position:0% +now if for some that's assuming that the +source is isotropic like this if for + + align:start position:0% +source is isotropic like this if for + + + align:start position:0% +source is isotropic like this if for +some reason your Source varies and you + + align:start position:0% +some reason your Source varies and you + + + align:start position:0% +some reason your Source varies and you +have much greater intensity over here + + align:start position:0% +have much greater intensity over here + + + align:start position:0% +have much greater intensity over here +and over here or whatever this cosine + + align:start position:0% +and over here or whatever this cosine + + + align:start position:0% +and over here or whatever this cosine +Theta term will be modified but again + + align:start position:0% +Theta term will be modified but again + + + align:start position:0% +Theta term will be modified but again +this is assuming um uh + + align:start position:0% +this is assuming um uh + + + align:start position:0% +this is assuming um uh +isotropic an isotropic source and the + + align:start position:0% +isotropic an isotropic source and the + + + align:start position:0% +isotropic an isotropic source and the +cosine Theta just comes from a geometry + + align:start position:0% +cosine Theta just comes from a geometry + + + align:start position:0% +cosine Theta just comes from a geometry +a + + align:start position:0% +a + + + align:start position:0% +a +factor okay you can sit down and stare + + align:start position:0% +factor okay you can sit down and stare + + + align:start position:0% +factor okay you can sit down and stare +at that for a little while hopefully + + align:start position:0% +at that for a little while hopefully + + + align:start position:0% +at that for a little while hopefully +it'll it'll make sense to + + align:start position:0% +it'll it'll make sense to + + + align:start position:0% +it'll it'll make sense to +you let go to slide five um so th in + + align:start position:0% +you let go to slide five um so th in + + + align:start position:0% +you let go to slide five um so th in +contrast to that on the left side I + + align:start position:0% +contrast to that on the left side I + + + align:start position:0% +contrast to that on the left side I +showed what I just derived which is the + + align:start position:0% +showed what I just derived which is the + + + align:start position:0% +showed what I just derived which is the +isotropic flux arrival Distribution on + + align:start position:0% +isotropic flux arrival Distribution on + + + align:start position:0% +isotropic flux arrival Distribution on +the right side uh for some systems you + + align:start position:0% +the right side uh for some systems you + + + align:start position:0% +the right side uh for some systems you +may have very anisotropic flux most of + + align:start position:0% +may have very anisotropic flux most of + + + align:start position:0% +may have very anisotropic flux most of +the atoms or ions coming down may be + + align:start position:0% +the atoms or ions coming down may be + + + align:start position:0% +the atoms or ions coming down may be +directed mostly normal to the surface + + align:start position:0% +directed mostly normal to the surface + + + align:start position:0% +directed mostly normal to the surface +there may be very few coming out at + + align:start position:0% +there may be very few coming out at + + + align:start position:0% +there may be very few coming out at +shallow angles depending on the the the + + align:start position:0% +shallow angles depending on the the the + + + align:start position:0% +shallow angles depending on the the the +particular machine that you're using so + + align:start position:0% +particular machine that you're using so + + + align:start position:0% +particular machine that you're using so +here we we in the cosine Theta the N we + + align:start position:0% +here we we in the cosine Theta the N we + + + align:start position:0% +here we we in the cosine Theta the N we +make n greater than one and you can see + + align:start position:0% +make n greater than one and you can see + + + align:start position:0% +make n greater than one and you can see +just based on the way these arrows are + + align:start position:0% +just based on the way these arrows are + + + align:start position:0% +just based on the way these arrows are +distributed most of them are coming in + + align:start position:0% +distributed most of them are coming in + + + align:start position:0% +distributed most of them are coming in +normal the flux coming in at Angles + + align:start position:0% +normal the flux coming in at Angles + + + align:start position:0% +normal the flux coming in at Angles +higher angles Theta is is much smaller + + align:start position:0% +higher angles Theta is is much smaller + + + align:start position:0% +higher angles Theta is is much smaller +you can see that from the length of the + + align:start position:0% +you can see that from the length of the + + + align:start position:0% +you can see that from the length of the +arrow so the length of these arrows here + + align:start position:0% +arrow so the length of these arrows here + + + align:start position:0% +arrow so the length of these arrows here +is supposed to represent uh the the flux + + align:start position:0% +is supposed to represent uh the the flux + + + align:start position:0% +is supposed to represent uh the the flux +at any given + + align:start position:0% +at any given + + + align:start position:0% +at any given +angle so generally we have this arrival + + align:start position:0% +angle so generally we have this arrival + + + align:start position:0% +angle so generally we have this arrival +angle distribution at a plane just above + + align:start position:0% +angle distribution at a plane just above + + + align:start position:0% +angle distribution at a plane just above +the wafer it has some Co cosine Theta + + align:start position:0% +the wafer it has some Co cosine Theta + + + align:start position:0% +the wafer it has some Co cosine Theta +the N uh type of dependence and again + + align:start position:0% +the N uh type of dependence and again + + + align:start position:0% +the N uh type of dependence and again +it's the normal component normal to the + + align:start position:0% +it's the normal component normal to the + + + align:start position:0% +it's the normal component normal to the +surface uh that strikes the surface that + + align:start position:0% +surface uh that strikes the surface that + + + align:start position:0% +surface uh that strikes the surface that +determines the deposition + + align:start position:0% + + + + align:start position:0% + +rate so let's take a look at at at + + align:start position:0% +rate so let's take a look at at at + + + align:start position:0% +rate so let's take a look at at at +examples of distribution of flux uh + + align:start position:0% +examples of distribution of flux uh + + + align:start position:0% +examples of distribution of flux uh +arrival uh distribution functions here's + + align:start position:0% +arrival uh distribution functions here's + + + align:start position:0% +arrival uh distribution functions here's +that formula I just uh mentioned and um + + align:start position:0% +that formula I just uh mentioned and um + + + align:start position:0% +that formula I just uh mentioned and um +for some for example if you have a high + + align:start position:0% +for some for example if you have a high + + + align:start position:0% +for some for example if you have a high +pressure system reasonably high pressure + + align:start position:0% +pressure system reasonably high pressure + + + align:start position:0% +pressure system reasonably high pressure +you're going to have a lot of gas phase + + align:start position:0% +you're going to have a lot of gas phase + + + align:start position:0% +you're going to have a lot of gas phase +collisions uh which means you have a + + align:start position:0% +collisions uh which means you have a + + + align:start position:0% +collisions uh which means you have a +short mean-free path and you're going to + + align:start position:0% +short mean-free path and you're going to + + + align:start position:0% +short mean-free path and you're going to +get tend to get isotropic arrival + + align:start position:0% +get tend to get isotropic arrival + + + align:start position:0% +get tend to get isotropic arrival +because those atoms are all bouncing + + align:start position:0% +because those atoms are all bouncing + + + align:start position:0% +because those atoms are all bouncing +around and regardless of where they're + + align:start position:0% +around and regardless of where they're + + + align:start position:0% +around and regardless of where they're +coming from it's just sort of the flux + + align:start position:0% +coming from it's just sort of the flux + + + align:start position:0% +coming from it's just sort of the flux +is equally distributed uh for all angles + + align:start position:0% +is equally distributed uh for all angles + + + align:start position:0% +is equally distributed uh for all angles +if you're in a very low pressure system + + align:start position:0% +if you're in a very low pressure system + + + align:start position:0% +if you're in a very low pressure system +where you have a very um uh fewer gas + + align:start position:0% +where you have a very um uh fewer gas + + + align:start position:0% +where you have a very um uh fewer gas +phase collisions a long mean-free path + + align:start position:0% +phase collisions a long mean-free path + + + align:start position:0% +phase collisions a long mean-free path +and it's going to be closer to one + + align:start position:0% +and it's going to be closer to one + + + align:start position:0% +and it's going to be closer to one +you're going to get more like line of + + align:start position:0% +you're going to get more like line of + + + align:start position:0% +you're going to get more like line of +sight from The Source whatever that + + align:start position:0% +sight from The Source whatever that + + + align:start position:0% +sight from The Source whatever that +happen whatever that Source happens to + + align:start position:0% +happen whatever that Source happens to + + + align:start position:0% +happen whatever that Source happens to +it could be a point source it could be a + + align:start position:0% +it could be a point source it could be a + + + align:start position:0% +it could be a point source it could be a +plane if it's sputtering but you're + + align:start position:0% +plane if it's sputtering but you're + + + align:start position:0% +plane if it's sputtering but you're +going to have n greater than + + align:start position:0% +going to have n greater than + + + align:start position:0% +going to have n greater than +one that that's all assuming neutrals if + + align:start position:0% +one that that's all assuming neutrals if + + + align:start position:0% +one that that's all assuming neutrals if +you have ionic species and the wafer is + + align:start position:0% +you have ionic species and the wafer is + + + align:start position:0% +you have ionic species and the wafer is +biased imagine the wafer has some bias + + align:start position:0% +biased imagine the wafer has some bias + + + align:start position:0% +biased imagine the wafer has some bias +and you have an ion the ion can be + + align:start position:0% +and you have an ion the ion can be + + + align:start position:0% +and you have an ion the ion can be +attracted to it by the electric field + + align:start position:0% +attracted to it by the electric field + + + align:start position:0% +attracted to it by the electric field +okay that's set up in that case for + + align:start position:0% +okay that's set up in that case for + + + align:start position:0% +okay that's set up in that case for +ioniz species it tends to be very + + align:start position:0% +ioniz species it tends to be very + + + align:start position:0% +ioniz species it tends to be very +anisotropic because again there's a + + align:start position:0% +anisotropic because again there's a + + + align:start position:0% +anisotropic because again there's a +there's a a force driving it towards the + + align:start position:0% +there's a a force driving it towards the + + + align:start position:0% +there's a a force driving it towards the +wafer so it doesn't tend to to uh to + + align:start position:0% +wafer so it doesn't tend to to uh to + + + align:start position:0% +wafer so it doesn't tend to to uh to +bounce around the species tend to go + + align:start position:0% +bounce around the species tend to go + + + align:start position:0% +bounce around the species tend to go +right to the wafer so these are just + + align:start position:0% +right to the wafer so these are just + + + align:start position:0% +right to the wafer so these are just +some examples um of flux distribution so + + align:start position:0% +some examples um of flux distribution so + + + align:start position:0% +some examples um of flux distribution so +you can see what it what it looks like + + align:start position:0% +you can see what it what it looks like + + + align:start position:0% +you can see what it what it looks like +for different values of + + align:start position:0% +for different values of + + + align:start position:0% +for different values of +n so this is the relative flux so it's + + align:start position:0% +n so this is the relative flux so it's + + + align:start position:0% +n so this is the relative flux so it's +the flux at any given uh angle uh Theta + + align:start position:0% +the flux at any given uh angle uh Theta + + + align:start position:0% +the flux at any given uh angle uh Theta +uh divided by the normal flux divided by + + align:start position:0% +uh divided by the normal flux divided by + + + align:start position:0% +uh divided by the normal flux divided by +F0 and this is what it looks like so it + + align:start position:0% +F0 and this is what it looks like so it + + + align:start position:0% +F0 and this is what it looks like so it +starts here at at theta equals z so + + align:start position:0% +starts here at at theta equals z so + + + align:start position:0% +starts here at at theta equals z so +that's normal uh is one and you can see + + align:start position:0% +that's normal uh is one and you can see + + + align:start position:0% +that's normal uh is one and you can see +for n equals 1 it drops down and the + + align:start position:0% +for n equals 1 it drops down and the + + + align:start position:0% +for n equals 1 it drops down and the +flux finally goes to zero at 90° you're + + align:start position:0% +flux finally goes to zero at 90° you're + + + align:start position:0% +flux finally goes to zero at 90° you're +just skimming along the surface + + align:start position:0% +just skimming along the surface + + + align:start position:0% +just skimming along the surface +obviously then normal component is + + align:start position:0% +obviously then normal component is + + + align:start position:0% +obviously then normal component is +zero n equal + + align:start position:0% +zero n equal + + + align:start position:0% +zero n equal +3 uh which is slight anisotropy looks + + align:start position:0% +3 uh which is slight anisotropy looks + + + align:start position:0% +3 uh which is slight anisotropy looks +something like this it's start the flux + + align:start position:0% +something like this it's start the flux + + + align:start position:0% +something like this it's start the flux +really dies down dramatically after 60 + + align:start position:0% +really dies down dramatically after 60 + + + align:start position:0% +really dies down dramatically after 60 +degrees that equals 15 uh which could be + + align:start position:0% +degrees that equals 15 uh which could be + + + align:start position:0% +degrees that equals 15 uh which could be +appropriate for some ionized um + + align:start position:0% +appropriate for some ionized um + + + align:start position:0% +appropriate for some ionized um +deposition systems you can see really + + align:start position:0% +deposition systems you can see really + + + align:start position:0% +deposition systems you can see really +the flux Goes To Zero by the time you + + align:start position:0% +the flux Goes To Zero by the time you + + + align:start position:0% +the flux Goes To Zero by the time you +get to about 30 degrees so it's very uh + + align:start position:0% +get to about 30 degrees so it's very uh + + + align:start position:0% +get to about 30 degrees so it's very uh +anisotropic uh arrival at that plane and + + align:start position:0% +anisotropic uh arrival at that plane and + + + align:start position:0% +anisotropic uh arrival at that plane and +again these in in most models these are + + align:start position:0% +again these in in most models these are + + + align:start position:0% +again these in in most models these are +these are uh inputs that uh parameters + + align:start position:0% +these are uh inputs that uh parameters + + + align:start position:0% +these are uh inputs that uh parameters +that you can + + align:start position:0% + + + + align:start position:0% + +vary okay so that gives us an idea of + + align:start position:0% +vary okay so that gives us an idea of + + + align:start position:0% +vary okay so that gives us an idea of +the direct fluxes and their angular + + align:start position:0% +the direct fluxes and their angular + + + align:start position:0% +the direct fluxes and their angular +dependence the next thing we have to do + + align:start position:0% +dependence the next thing we have to do + + + align:start position:0% +dependence the next thing we have to do +is to take into account uh the surface + + align:start position:0% +is to take into account uh the surface + + + align:start position:0% +is to take into account uh the surface +to topography and uh just to give you an + + align:start position:0% +to topography and uh just to give you an + + + align:start position:0% +to topography and uh just to give you an +example of that I'm showing here imagine + + align:start position:0% +example of that I'm showing here imagine + + + align:start position:0% +example of that I'm showing here imagine +your surface is not flat but that you + + align:start position:0% +your surface is not flat but that you + + + align:start position:0% +your surface is not flat but that you +have a wafer and you are sputtering + + align:start position:0% +have a wafer and you are sputtering + + + align:start position:0% +have a wafer and you are sputtering +aluminum into it and you have a via or + + align:start position:0% +aluminum into it and you have a via or + + + align:start position:0% +aluminum into it and you have a via or +you have um a hole contact hole so it's + + align:start position:0% +you have um a hole contact hole so it's + + + align:start position:0% +you have um a hole contact hole so it's +like this and then you have this hole + + align:start position:0% +like this and then you have this hole + + + align:start position:0% +like this and then you have this hole +right here well if you have imagine each + + align:start position:0% +right here well if you have imagine each + + + align:start position:0% +right here well if you have imagine each +one of these um little uh regions + + align:start position:0% +one of these um little uh regions + + + align:start position:0% +one of these um little uh regions +corresponds to an emitter uh with a + + align:start position:0% +corresponds to an emitter uh with a + + + align:start position:0% +corresponds to an emitter uh with a +certain flux depending uh any point ey + + align:start position:0% +certain flux depending uh any point ey + + + align:start position:0% +certain flux depending uh any point ey +on this on this vertical surface is + + align:start position:0% +on this on this vertical surface is + + + align:start position:0% +on this on this vertical surface is +going to have a certain viewing angle uh + + align:start position:0% +going to have a certain viewing angle uh + + + align:start position:0% +going to have a certain viewing angle uh +and if you're beyond that viewing angle + + align:start position:0% +and if you're beyond that viewing angle + + + align:start position:0% +and if you're beyond that viewing angle +you're going to be shadowed so this is a + + align:start position:0% +you're going to be shadowed so this is a + + + align:start position:0% +you're going to be shadowed so this is a +shadowing effect uh on the sidewall of + + align:start position:0% +shadowing effect uh on the sidewall of + + + align:start position:0% +shadowing effect uh on the sidewall of +the trench it's not not that uncommon + + align:start position:0% +the trench it's not not that uncommon + + + align:start position:0% +the trench it's not not that uncommon +depending on the depth and the aspect + + align:start position:0% +depending on the depth and the aspect + + + align:start position:0% +depending on the depth and the aspect +ratio of the + + align:start position:0% +ratio of the + + + align:start position:0% +ratio of the +trench um so we have to take into + + align:start position:0% +trench um so we have to take into + + + align:start position:0% +trench um so we have to take into +account the orientation of the surface + + align:start position:0% +account the orientation of the surface + + + align:start position:0% +account the orientation of the surface +what its angle is uh this viewing angle + + align:start position:0% +what its angle is uh this viewing angle + + + align:start position:0% +what its angle is uh this viewing angle +uh and and shadowing and um typically in + + align:start position:0% +uh and and shadowing and um typically in + + + align:start position:0% +uh and and shadowing and um typically in +the near uh near wafer surface region we + + align:start position:0% +the near uh near wafer surface region we + + + align:start position:0% +the near uh near wafer surface region we +will neglect the gas phase collisions on + + align:start position:0% +will neglect the gas phase collisions on + + + align:start position:0% +will neglect the gas phase collisions on +that so if if you uh if you will you can + + align:start position:0% +that so if if you uh if you will you can + + + align:start position:0% +that so if if you uh if you will you can +think of this imagine my reference plane + + align:start position:0% +think of this imagine my reference plane + + + align:start position:0% +think of this imagine my reference plane +remember that reference plane is sort of + + align:start position:0% +remember that reference plane is sort of + + + align:start position:0% +remember that reference plane is sort of +a plane uh just above the wafer + + align:start position:0% +a plane uh just above the wafer + + + align:start position:0% +a plane uh just above the wafer +surface um and each small area on this + + align:start position:0% +surface um and each small area on this + + + align:start position:0% +surface um and each small area on this +reference plane uh can be treated as an + + align:start position:0% +reference plane uh can be treated as an + + + align:start position:0% +reference plane uh can be treated as an +emission source so if you have emission + + align:start position:0% +emission source so if you have emission + + + align:start position:0% +emission source so if you have emission +coming down you have all these little + + align:start position:0% +coming down you have all these little + + + align:start position:0% +coming down you have all these little +emission + + align:start position:0% +emission + + + align:start position:0% +emission +sources um and the each source is + + align:start position:0% +sources um and the each source is + + + align:start position:0% +sources um and the each source is +emitting to the topography below it and + + align:start position:0% +emitting to the topography below it and + + + align:start position:0% +emitting to the topography below it and +then the total direct Point uh flux at + + align:start position:0% +then the total direct Point uh flux at + + + align:start position:0% +then the total direct Point uh flux at +any point I uh can be calculated by just + + align:start position:0% +any point I uh can be calculated by just + + + align:start position:0% +any point I uh can be calculated by just +adding up the flux from each one of + + align:start position:0% +adding up the flux from each one of + + + align:start position:0% +adding up the flux from each one of +these little miniature uh emission + + align:start position:0% +these little miniature uh emission + + + align:start position:0% +these little miniature uh emission +sources which each one of which has a + + align:start position:0% +sources which each one of which has a + + + align:start position:0% +sources which each one of which has a +certain angular distribution depending + + align:start position:0% +certain angular distribution depending + + + align:start position:0% +certain angular distribution depending +on the type of system that you're um + + align:start position:0% +on the type of system that you're um + + + align:start position:0% +on the type of system that you're um +that you're + + align:start position:0% +that you're + + + align:start position:0% +that you're +modeling so you can now begin to see how + + align:start position:0% +modeling so you can now begin to see how + + + align:start position:0% +modeling so you can now begin to see how +in a computer model you can build + + align:start position:0% +in a computer model you can build + + + align:start position:0% +in a computer model you can build +equations and you can and you can build + + align:start position:0% +equations and you can and you can build + + + align:start position:0% +equations and you can and you can build +uh structures that would be able to + + align:start position:0% +uh structures that would be able to + + + align:start position:0% +uh structures that would be able to +model this type of + + align:start position:0% +model this type of + + + align:start position:0% +model this type of +deposition let's go on to slide eight + + align:start position:0% +deposition let's go on to slide eight + + + align:start position:0% +deposition let's go on to slide eight +and I wanted to give you a practical + + align:start position:0% +and I wanted to give you a practical + + + align:start position:0% +and I wanted to give you a practical +example we're talking about all these + + align:start position:0% +example we're talking about all these + + + align:start position:0% +example we're talking about all these +mathematical things but um a practical + + align:start position:0% +mathematical things but um a practical + + + align:start position:0% +mathematical things but um a practical +example which should will be somewhat + + align:start position:0% +example which should will be somewhat + + + align:start position:0% +example which should will be somewhat +intuitive uh here on slide eight is the + + align:start position:0% +intuitive uh here on slide eight is the + + + align:start position:0% +intuitive uh here on slide eight is the +impact of having a finite Target size uh + + align:start position:0% +impact of having a finite Target size uh + + + align:start position:0% +impact of having a finite Target size uh +compared to the wafer on if you're doing + + align:start position:0% +compared to the wafer on if you're doing + + + align:start position:0% +compared to the wafer on if you're doing +sputter deposition on asymmetry across a + + align:start position:0% +sputter deposition on asymmetry across a + + + align:start position:0% +sputter deposition on asymmetry across a +wafer so if you look at this + + align:start position:0% +wafer so if you look at this + + + align:start position:0% +wafer so if you look at this +illustration imagine I have a Target uh + + align:start position:0% +illustration imagine I have a Target uh + + + align:start position:0% +illustration imagine I have a Target uh +that I'm doing sputtering and this could + + align:start position:0% +that I'm doing sputtering and this could + + + align:start position:0% +that I'm doing sputtering and this could +be aluminum and it's up here it has this + + align:start position:0% +be aluminum and it's up here it has this + + + align:start position:0% +be aluminum and it's up here it has this +Dimension uh it's relatively small + + align:start position:0% +Dimension uh it's relatively small + + + align:start position:0% +Dimension uh it's relatively small +compared to say I'm doing a six or8 inch + + align:start position:0% +compared to say I'm doing a six or8 inch + + + align:start position:0% +compared to say I'm doing a six or8 inch +wafer um so what's going to happen and + + align:start position:0% +wafer um so what's going to happen and + + + align:start position:0% +wafer um so what's going to happen and +you have the wafer sitting there and + + align:start position:0% +you have the wafer sitting there and + + + align:start position:0% +you have the wafer sitting there and +you're sputtering into a trench on the + + align:start position:0% +you're sputtering into a trench on the + + + align:start position:0% +you're sputtering into a trench on the +left side of the wafer and you have a + + align:start position:0% +left side of the wafer and you have a + + + align:start position:0% +left side of the wafer and you have a +diey over here on the right side of the + + align:start position:0% +diey over here on the right side of the + + + align:start position:0% +diey over here on the right side of the +wafer and let's say for now you're not + + align:start position:0% +wafer and let's say for now you're not + + + align:start position:0% +wafer and let's say for now you're not +rotating the Wafers or anything so you + + align:start position:0% +rotating the Wafers or anything so you + + + align:start position:0% +rotating the Wafers or anything so you +can imagine what's going to happen here + + align:start position:0% +can imagine what's going to happen here + + + align:start position:0% +can imagine what's going to happen here +on the this trench this uh White region + + align:start position:0% +on the this trench this uh White region + + + align:start position:0% +on the this trench this uh White region +indicates the region that you've + + align:start position:0% +indicates the region that you've + + + align:start position:0% +indicates the region that you've +sputtered the material you've sputtered + + align:start position:0% +sputtered the material you've sputtered + + + align:start position:0% +sputtered the material you've sputtered +you get an asymmetry on the sidewall + + align:start position:0% +you get an asymmetry on the sidewall + + + align:start position:0% +you get an asymmetry on the sidewall +because you've got here at this point in + + align:start position:0% +because you've got here at this point in + + + align:start position:0% +because you've got here at this point in +the wafer you have more flux coming from + + align:start position:0% +the wafer you have more flux coming from + + + align:start position:0% +the wafer you have more flux coming from +from this direction and so you're going + + align:start position:0% +from this direction and so you're going + + + align:start position:0% +from this direction and so you're going +to get uh because of shadowing you're + + align:start position:0% +to get uh because of shadowing you're + + + align:start position:0% +to get uh because of shadowing you're +going to not get much deposition on this + + align:start position:0% +going to not get much deposition on this + + + align:start position:0% +going to not get much deposition on this +wall they'll get more on this wall on + + align:start position:0% +wall they'll get more on this wall on + + + align:start position:0% +wall they'll get more on this wall on +the right side of the wafer we have just + + align:start position:0% +the right side of the wafer we have just + + + align:start position:0% +the right side of the wafer we have just +the opposite type of + + align:start position:0% +the opposite type of + + + align:start position:0% +the opposite type of +shadowing so you will tend to get + + align:start position:0% +shadowing so you will tend to get + + + align:start position:0% +shadowing so you will tend to get +asymmetric deposition uh on the left + + align:start position:0% +asymmetric deposition uh on the left + + + align:start position:0% +asymmetric deposition uh on the left +side of the wafer as opposed to the + + align:start position:0% +side of the wafer as opposed to the + + + align:start position:0% +side of the wafer as opposed to the +right side of the wafer with this + + align:start position:0% +right side of the wafer with this + + + align:start position:0% +right side of the wafer with this +particular geometry so what do people do + + align:start position:0% +particular geometry so what do people do + + + align:start position:0% +particular geometry so what do people do +in a real system because we obviously + + align:start position:0% +in a real system because we obviously + + + align:start position:0% +in a real system because we obviously +this is not desirable we want to have it + + align:start position:0% +this is not desirable we want to have it + + + align:start position:0% +this is not desirable we want to have it +this each side of the wafer should look + + align:start position:0% +this each side of the wafer should look + + + align:start position:0% +this each side of the wafer should look +the same well you can widen the target + + align:start position:0% +the same well you can widen the target + + + align:start position:0% +the same well you can widen the target +size so I can take this Target and make + + align:start position:0% +size so I can take this Target and make + + + align:start position:0% +size so I can take this Target and make +it much bigger make it larger than the + + align:start position:0% +it much bigger make it larger than the + + + align:start position:0% +it much bigger make it larger than the +wafer or you can take the same size + + align:start position:0% +wafer or you can take the same size + + + align:start position:0% +wafer or you can take the same size +Target and move it further from the + + align:start position:0% +Target and move it further from the + + + align:start position:0% +Target and move it further from the +wafer um so so in either case you're + + align:start position:0% +wafer um so so in either case you're + + + align:start position:0% +wafer um so so in either case you're +going to get an arrival angle + + align:start position:0% +going to get an arrival angle + + + align:start position:0% +going to get an arrival angle +distribution that is more symmetric + + align:start position:0% +distribution that is more symmetric + + + align:start position:0% +distribution that is more symmetric +across the + + align:start position:0% +across the + + + align:start position:0% +across the +wafer uh another thing people sometimes + + align:start position:0% +wafer uh another thing people sometimes + + + align:start position:0% +wafer uh another thing people sometimes +do is to rotate the Wafers so you can + + align:start position:0% +do is to rotate the Wafers so you can + + + align:start position:0% +do is to rotate the Wafers so you can +put the W Wafers on a PL and that + + align:start position:0% +put the W Wafers on a PL and that + + + align:start position:0% +put the W Wafers on a PL and that +rotates with respect to the source which + + align:start position:0% +rotates with respect to the source which + + + align:start position:0% +rotates with respect to the source which +is essentially similar to widening you + + align:start position:0% +is essentially similar to widening you + + + align:start position:0% +is essentially similar to widening you +know increasing the effective size of + + align:start position:0% +know increasing the effective size of + + + align:start position:0% +know increasing the effective size of +your target this is why sputtering + + align:start position:0% +your target this is why sputtering + + + align:start position:0% +your target this is why sputtering +systems are very large because they tend + + align:start position:0% +systems are very large because they tend + + + align:start position:0% +systems are very large because they tend +to have huge targets imagine today + + align:start position:0% +to have huge targets imagine today + + + align:start position:0% +to have huge targets imagine today +people are processing 6inch Wafers up 6 + + align:start position:0% +people are processing 6inch Wafers up 6 + + + align:start position:0% +people are processing 6inch Wafers up 6 +in here at Mt we're processing 6 in 12in + + align:start position:0% +in here at Mt we're processing 6 in 12in + + + align:start position:0% +in here at Mt we're processing 6 in 12in +wafers in Industry that Target has to be + + align:start position:0% +wafers in Industry that Target has to be + + + align:start position:0% +wafers in Industry that Target has to be +huge uh basically and then you would be + + align:start position:0% +huge uh basically and then you would be + + + align:start position:0% +huge uh basically and then you would be +rotating the Wafers and so this is why + + align:start position:0% +rotating the Wafers and so this is why + + + align:start position:0% +rotating the Wafers and so this is why +the equipment in the Fabs is getting + + align:start position:0% +the equipment in the Fabs is getting + + + align:start position:0% +the equipment in the Fabs is getting +larger and larger you're fundamentally + + align:start position:0% +larger and larger you're fundamentally + + + align:start position:0% +larger and larger you're fundamentally +limited by some of these uh processes to + + align:start position:0% +limited by some of these uh processes to + + + align:start position:0% +limited by some of these uh processes to +obtain + + align:start position:0% +obtain + + + align:start position:0% +obtain +uniformity and on slide nine in fact + + align:start position:0% +uniformity and on slide nine in fact + + + align:start position:0% +uniformity and on slide nine in fact +there's just an example of how we would + + align:start position:0% +there's just an example of how we would + + + align:start position:0% +there's just an example of how we would +how we would ameliorate this a symmetry + + align:start position:0% +how we would ameliorate this a symmetry + + + align:start position:0% +how we would ameliorate this a symmetry +from the left and the right side of the + + align:start position:0% +from the left and the right side of the + + + align:start position:0% +from the left and the right side of the +wafer here's an example where the + + align:start position:0% +wafer here's an example where the + + + align:start position:0% +wafer here's an example where the +target's been made as large as the wafer + + align:start position:0% +target's been made as large as the wafer + + + align:start position:0% +target's been made as large as the wafer +in fact most targets today are much + + align:start position:0% +in fact most targets today are much + + + align:start position:0% +in fact most targets today are much +bigger than the size of the wafer and + + align:start position:0% +bigger than the size of the wafer and + + + align:start position:0% +bigger than the size of the wafer and +this is also why they cost a lot of + + align:start position:0% +this is also why they cost a lot of + + + align:start position:0% +this is also why they cost a lot of +money if you have a target of platinum + + align:start position:0% +money if you have a target of platinum + + + align:start position:0% +money if you have a target of platinum +if you're sputtering Platinum it has to + + align:start position:0% +if you're sputtering Platinum it has to + + + align:start position:0% +if you're sputtering Platinum it has to +be 2 feet by 10 in or something like + + align:start position:0% +be 2 feet by 10 in or something like + + + align:start position:0% +be 2 feet by 10 in or something like +that that's a lot of platinum that's a + + align:start position:0% +that that's a lot of platinum that's a + + + align:start position:0% +that that's a lot of platinum that's a +very large sheet of platinum so it costs + + align:start position:0% +very large sheet of platinum so it costs + + + align:start position:0% +very large sheet of platinum so it costs +quite a bit of money or if you want + + align:start position:0% +quite a bit of money or if you want + + + align:start position:0% +quite a bit of money or if you want +instead of making a Target so big you + + align:start position:0% +instead of making a Target so big you + + + align:start position:0% +instead of making a Target so big you +can move it further away and you'll get + + align:start position:0% +can move it further away and you'll get + + + align:start position:0% +can move it further away and you'll get +a little better symmetry between the + + align:start position:0% +a little better symmetry between the + + + align:start position:0% +a little better symmetry between the +left and the right side of the wafer but + + align:start position:0% +left and the right side of the wafer but + + + align:start position:0% +left and the right side of the wafer but +that makes the tool the machine really + + align:start position:0% +that makes the tool the machine really + + + align:start position:0% +that makes the tool the machine really +big you know and you can only have so + + align:start position:0% +big you know and you can only have so + + + align:start position:0% +big you know and you can only have so +much size and your in your clean room so + + align:start position:0% +much size and your in your clean room so + + + align:start position:0% +much size and your in your clean room so +it's they kind of trade-offs here so in + + align:start position:0% +it's they kind of trade-offs here so in + + + align:start position:0% +it's they kind of trade-offs here so in +practice people use larger targets at + + align:start position:0% +practice people use larger targets at + + + align:start position:0% +practice people use larger targets at +some reasonable distance and and scale + + align:start position:0% +some reasonable distance and and scale + + + align:start position:0% +some reasonable distance and and scale +the tool size and and rotate the Wafers + + align:start position:0% +the tool size and and rotate the Wafers + + + align:start position:0% +the tool size and and rotate the Wafers +to + + align:start position:0% +to + + + align:start position:0% +to +help so there's a practical example okay + + align:start position:0% +help so there's a practical example okay + + + align:start position:0% +help so there's a practical example okay +so um we talked about how to calculate + + align:start position:0% +so um we talked about how to calculate + + + align:start position:0% +so um we talked about how to calculate +the direct flux basically you're just + + align:start position:0% +the direct flux basically you're just + + + align:start position:0% +the direct flux basically you're just +taking it's it's like a geometry problem + + align:start position:0% +taking it's it's like a geometry problem + + + align:start position:0% +taking it's it's like a geometry problem +essentially and you have to have a + + align:start position:0% +essentially and you have to have a + + + align:start position:0% +essentially and you have to have a +cosine Theta to the end dependence how + + align:start position:0% +cosine Theta to the end dependence how + + + align:start position:0% +cosine Theta to the end dependence how +about the indirect flux first of all on + + align:start position:0% +about the indirect flux first of all on + + + align:start position:0% +about the indirect flux first of all on +slide 10 what do I mean by indirect well + + align:start position:0% +slide 10 what do I mean by indirect well + + + align:start position:0% +slide 10 what do I mean by indirect well +I mean all those processes that occur on + + align:start position:0% +I mean all those processes that occur on + + + align:start position:0% +I mean all those processes that occur on +the surface or near the surface of the + + align:start position:0% +the surface or near the surface of the + + + align:start position:0% +the surface or near the surface of the +wafer during the deposition so these + + align:start position:0% +wafer during the deposition so these + + + align:start position:0% +wafer during the deposition so these +indirect fluxes include surface + + align:start position:0% +indirect fluxes include surface + + + align:start position:0% +indirect fluxes include surface +diffusion so I could have an aluminum + + align:start position:0% +diffusion so I could have an aluminum + + + align:start position:0% +diffusion so I could have an aluminum +atom that's that ended up that started + + align:start position:0% +atom that's that ended up that started + + + align:start position:0% +atom that's that ended up that started +here but it can diffuse along the + + align:start position:0% +here but it can diffuse along the + + + align:start position:0% +here but it can diffuse along the +surface and end up somewhere else so + + align:start position:0% +surface and end up somewhere else so + + + align:start position:0% +surface and end up somewhere else so +that represents a flux to that point um + + align:start position:0% +that represents a flux to that point um + + + align:start position:0% +that represents a flux to that point um +emission + + align:start position:0% +emission + + + align:start position:0% +emission +species come down but they don't always + + align:start position:0% +species come down but they don't always + + + align:start position:0% +species come down but they don't always +stick they don't always um stick where + + align:start position:0% +stick they don't always um stick where + + + align:start position:0% +stick they don't always um stick where +they land they might actually go there + + align:start position:0% +they land they might actually go there + + + align:start position:0% +they land they might actually go there +and then be reemitted so that's an + + align:start position:0% +and then be reemitted so that's an + + + align:start position:0% +and then be reemitted so that's an +indirect flux called reemission uh + + align:start position:0% +indirect flux called reemission uh + + + align:start position:0% +indirect flux called reemission uh +sputtering incoming atoms can knock off + + align:start position:0% +sputtering incoming atoms can knock off + + + align:start position:0% +sputtering incoming atoms can knock off +uh you could have a film of aluminum + + align:start position:0% +uh you could have a film of aluminum + + + align:start position:0% +uh you could have a film of aluminum +already on the wafer but incoming atoms + + align:start position:0% +already on the wafer but incoming atoms + + + align:start position:0% +already on the wafer but incoming atoms +could knock them off and uh redeposition + + align:start position:0% +could knock them off and uh redeposition + + + align:start position:0% +could knock them off and uh redeposition +sputtered atoms can be redeposited + + align:start position:0% +sputtered atoms can be redeposited + + + align:start position:0% +sputtered atoms can be redeposited +Elsewhere for here here's an example + + align:start position:0% +Elsewhere for here here's an example + + + align:start position:0% +Elsewhere for here here's an example +aluminum comes down it hits an aluminum + + align:start position:0% +aluminum comes down it hits an aluminum + + + align:start position:0% +aluminum comes down it hits an aluminum +atom that was already deposited on the + + align:start position:0% +atom that was already deposited on the + + + align:start position:0% +atom that was already deposited on the +surface it's then + + align:start position:0% +surface it's then + + + align:start position:0% +surface it's then +um uh desorbed or emitted and + + align:start position:0% +um uh desorbed or emitted and + + + align:start position:0% +um uh desorbed or emitted and +redeposited down here so there's a + + align:start position:0% +redeposited down here so there's a + + + align:start position:0% +redeposited down here so there's a +number of processes we call these + + align:start position:0% +number of processes we call these + + + align:start position:0% +number of processes we call these +indirect because they're not directly + + align:start position:0% +indirect because they're not directly + + + align:start position:0% +indirect because they're not directly +coming from the source they're coming + + align:start position:0% +coming from the source they're coming + + + align:start position:0% +coming from the source they're coming +from other regions on the surface but + + align:start position:0% +from other regions on the surface but + + + align:start position:0% +from other regions on the surface but +they need to be taken into account in + + align:start position:0% +they need to be taken into account in + + + align:start position:0% +they need to be taken into account in +the + + align:start position:0% +the + + + align:start position:0% +the +topography so let's go through each one + + align:start position:0% +topography so let's go through each one + + + align:start position:0% +topography so let's go through each one +of these surface processes the diffusion + + align:start position:0% +of these surface processes the diffusion + + + align:start position:0% +of these surface processes the diffusion +uh and the redeposition and things and + + align:start position:0% +uh and the redeposition and things and + + + align:start position:0% +uh and the redeposition and things and +talk about how we might model them um if + + align:start position:0% +talk about how we might model them um if + + + align:start position:0% +talk about how we might model them um if +we go on to slide 11 um surface + + align:start position:0% +we go on to slide 11 um surface + + + align:start position:0% +we go on to slide 11 um surface +diffusion well surface diffusion and I + + align:start position:0% +diffusion well surface diffusion and I + + + align:start position:0% +diffusion well surface diffusion and I +I'll refer to your text I'm not going to + + align:start position:0% +I'll refer to your text I'm not going to + + + align:start position:0% +I'll refer to your text I'm not going to +derive this equation but it turns out + + align:start position:0% +derive this equation but it turns out + + + align:start position:0% +derive this equation but it turns out +diffusion along the surface is different + + align:start position:0% +diffusion along the surface is different + + + align:start position:0% +diffusion along the surface is different +from diffusion the bulk we spent a lot + + align:start position:0% +from diffusion the bulk we spent a lot + + + align:start position:0% +from diffusion the bulk we spent a lot +of time talking about diffusion in the + + align:start position:0% +of time talking about diffusion in the + + + align:start position:0% +of time talking about diffusion in the +bulk of of single Crystal silicon um + + align:start position:0% +bulk of of single Crystal silicon um + + + align:start position:0% +bulk of of single Crystal silicon um +surface diffusion has different slightly + + align:start position:0% +surface diffusion has different slightly + + + align:start position:0% +surface diffusion has different slightly +different driving forces um not always + + align:start position:0% +different driving forces um not always + + + align:start position:0% +different driving forces um not always +just driven by a gradient but it can + + align:start position:0% +just driven by a gradient but it can + + + align:start position:0% +just driven by a gradient but it can +actually be driven by the shape of the + + align:start position:0% +actually be driven by the shape of the + + + align:start position:0% +actually be driven by the shape of the +of the surface it can actually be the + + align:start position:0% +of the surface it can actually be the + + + align:start position:0% +of the surface it can actually be the +fusion could be driven by the local + + align:start position:0% +fusion could be driven by the local + + + align:start position:0% +fusion could be driven by the local +curvature of the surface uh if you're + + align:start position:0% +curvature of the surface uh if you're + + + align:start position:0% +curvature of the surface uh if you're +depositing a film in order to minimize + + align:start position:0% +depositing a film in order to minimize + + + align:start position:0% +depositing a film in order to minimize +surface free + + align:start position:0% +surface free + + + align:start position:0% +surface free +energy so we have a different type of + + align:start position:0% +energy so we have a different type of + + + align:start position:0% +energy so we have a different type of +equation from what you're used to seeing + + align:start position:0% +equation from what you're used to seeing + + + align:start position:0% +equation from what you're used to seeing +perhaps for diffusion um we we see that + + align:start position:0% +perhaps for diffusion um we we see that + + + align:start position:0% +perhaps for diffusion um we we see that +the there if there's a flux into a point + + align:start position:0% +the there if there's a flux into a point + + + align:start position:0% +the there if there's a flux into a point +on the surface minus the flux diffusion + + align:start position:0% +on the surface minus the flux diffusion + + + align:start position:0% +on the surface minus the flux diffusion +flux out so that's the net diffusion + + align:start position:0% +flux out so that's the net diffusion + + + align:start position:0% +flux out so that's the net diffusion +flux to a point um it actually depends + + align:start position:0% +flux to a point um it actually depends + + + align:start position:0% +flux to a point um it actually depends +on a Surface diffusion coefficient D + + align:start position:0% +on a Surface diffusion coefficient D + + + align:start position:0% +on a Surface diffusion coefficient D +Subs uh diffusivity uh but it also it + + align:start position:0% +Subs uh diffusivity uh but it also it + + + align:start position:0% +Subs uh diffusivity uh but it also it +depends on this curvature this + + align:start position:0% +depends on this curvature this + + + align:start position:0% +depends on this curvature this +derivative uh which has to do with the + + align:start position:0% +derivative uh which has to do with the + + + align:start position:0% +derivative uh which has to do with the +curvature of the surface and and what I + + align:start position:0% +curvature of the surface and and what I + + + align:start position:0% +curvature of the surface and and what I +would do I don't want to go through + + align:start position:0% +would do I don't want to go through + + + align:start position:0% +would do I don't want to go through +through it detail in class but uh if you + + align:start position:0% +through it detail in class but uh if you + + + align:start position:0% +through it detail in class but uh if you +look at equation 1137 and um and the + + align:start position:0% +look at equation 1137 and um and the + + + align:start position:0% +look at equation 1137 and um and the +associated text in in chapter 11 they + + align:start position:0% +associated text in in chapter 11 they + + + align:start position:0% +associated text in in chapter 11 they +they talk a little bit more about + + align:start position:0% +they talk a little bit more about + + + align:start position:0% +they talk a little bit more about +surface diffusion and where this + + align:start position:0% +surface diffusion and where this + + + align:start position:0% +surface diffusion and where this +equation comes + + align:start position:0% +equation comes + + + align:start position:0% +equation comes +from uh but the the main point is + + align:start position:0% +from uh but the the main point is + + + align:start position:0% +from uh but the the main point is +because it increases with curvature + + align:start position:0% +because it increases with curvature + + + align:start position:0% +because it increases with curvature +during deposition uh filling in of + + align:start position:0% +during deposition uh filling in of + + + align:start position:0% +during deposition uh filling in of +Corners may be enhanced and and you can + + align:start position:0% +Corners may be enhanced and and you can + + + align:start position:0% +Corners may be enhanced and and you can +sometimes get more uh smoother uh more + + align:start position:0% +sometimes get more uh smoother uh more + + + align:start position:0% +sometimes get more uh smoother uh more +conformal deposition of course you have + + align:start position:0% +conformal deposition of course you have + + + align:start position:0% +conformal deposition of course you have +to be at a high enough temperature that + + align:start position:0% +to be at a high enough temperature that + + + align:start position:0% +to be at a high enough temperature that +these species can diffuse and depending + + align:start position:0% +these species can diffuse and depending + + + align:start position:0% +these species can diffuse and depending +on the material and the temperature it + + align:start position:0% +on the material and the temperature it + + + align:start position:0% +on the material and the temperature it +may not it may not be diffusing you may + + align:start position:0% +may not it may not be diffusing you may + + + align:start position:0% +may not it may not be diffusing you may +have to raise the targ the uh the wafer + + align:start position:0% +have to raise the targ the uh the wafer + + + align:start position:0% +have to raise the targ the uh the wafer +temperature slightly if you want to get + + align:start position:0% +temperature slightly if you want to get + + + align:start position:0% +temperature slightly if you want to get +U more surface diffusion so you can + + align:start position:0% +U more surface diffusion so you can + + + align:start position:0% +U more surface diffusion so you can +think of it this way if I raise the + + align:start position:0% +think of it this way if I raise the + + + align:start position:0% +think of it this way if I raise the +temperature of the wafer I can smooth + + align:start position:0% +temperature of the wafer I can smooth + + + align:start position:0% +temperature of the wafer I can smooth +out and get a little more conformal + + align:start position:0% +out and get a little more conformal + + + align:start position:0% +out and get a little more conformal +deposition by virtue of surface + + align:start position:0% +deposition by virtue of surface + + + align:start position:0% +deposition by virtue of surface +diffusion + + align:start position:0% +diffusion + + + align:start position:0% +diffusion +processes so that's something that can + + align:start position:0% +processes so that's something that can + + + align:start position:0% +processes so that's something that can +be modeled in uh topography + + align:start position:0% + + + + align:start position:0% + +simulators uh page 12 a little bit + + align:start position:0% +simulators uh page 12 a little bit + + + align:start position:0% +simulators uh page 12 a little bit +simpler this is this is is a very this + + align:start position:0% +simpler this is this is is a very this + + + align:start position:0% +simpler this is this is is a very this +is very much a bookkeeping thing uh + + align:start position:0% +is very much a bookkeeping thing uh + + + align:start position:0% +is very much a bookkeeping thing uh +there's surf something called surface + + align:start position:0% +there's surf something called surface + + + align:start position:0% +there's surf something called surface +sticking and and + + align:start position:0% +sticking and and + + + align:start position:0% +sticking and and +emission uh and a sticking coefficient + + align:start position:0% +emission uh and a sticking coefficient + + + align:start position:0% +emission uh and a sticking coefficient +um so there's this flux at any given + + align:start position:0% +um so there's this flux at any given + + + align:start position:0% +um so there's this flux at any given +point I that's emitted that arises + + align:start position:0% +point I that's emitted that arises + + + align:start position:0% +point I that's emitted that arises +because not all molecules stick when + + align:start position:0% +because not all molecules stick when + + + align:start position:0% +because not all molecules stick when +they arrive at the surface and so in + + align:start position:0% +they arrive at the surface and so in + + + align:start position:0% +they arrive at the surface and so in +fact we write the emitted flux from any + + align:start position:0% +fact we write the emitted flux from any + + + align:start position:0% +fact we write the emitted flux from any +point as being equal to 1 minus s + + align:start position:0% +point as being equal to 1 minus s + + + align:start position:0% +point as being equal to 1 minus s +subc uh so the fraction emitted is 1 + + align:start position:0% +subc uh so the fraction emitted is 1 + + + align:start position:0% +subc uh so the fraction emitted is 1 +minus s subc where s subc is cul + + align:start position:0% +minus s subc where s subc is cul + + + align:start position:0% +minus s subc where s subc is cul +coefficient times the flux going + + align:start position:0% +coefficient times the flux going + + + align:start position:0% +coefficient times the flux going +in so what is sfc well it's a very + + align:start position:0% +in so what is sfc well it's a very + + + align:start position:0% +in so what is sfc well it's a very +simple thing it's a fraction that stick + + align:start position:0% +simple thing it's a fraction that stick + + + align:start position:0% +simple thing it's a fraction that stick +basically so uh sticking coefficient + + align:start position:0% +basically so uh sticking coefficient + + + align:start position:0% +basically so uh sticking coefficient +here sfc is it's the flux that react and + + align:start position:0% +here sfc is it's the flux that react and + + + align:start position:0% +here sfc is it's the flux that react and +stay put divided by the total incident + + align:start position:0% +stay put divided by the total incident + + + align:start position:0% +stay put divided by the total incident +flux um so to give yourself an idea um + + align:start position:0% +flux um so to give yourself an idea um + + + align:start position:0% +flux um so to give yourself an idea um +if you have uh a high s subc so s subc + + align:start position:0% +if you have uh a high s subc so s subc + + + align:start position:0% +if you have uh a high s subc so s subc +is a number between 0 and one really + + align:start position:0% +is a number between 0 and one really + + + align:start position:0% +is a number between 0 and one really +because it's a fraction if you have a + + align:start position:0% +because it's a fraction if you have a + + + align:start position:0% +because it's a fraction if you have a +high sfc like sfc equals 1 basically you + + align:start position:0% +high sfc like sfc equals 1 basically you + + + align:start position:0% +high sfc like sfc equals 1 basically you +have line of site deposition everything + + align:start position:0% +have line of site deposition everything + + + align:start position:0% +have line of site deposition everything +that comes down just stops and sticks on + + align:start position:0% +that comes down just stops and sticks on + + + align:start position:0% +that comes down just stops and sticks on +the surface if you have a type of + + align:start position:0% +the surface if you have a type of + + + align:start position:0% +the surface if you have a type of +deposition with a low sticking + + align:start position:0% +deposition with a low sticking + + + align:start position:0% +deposition with a low sticking +coefficient what happens is atoms come + + align:start position:0% +coefficient what happens is atoms come + + + align:start position:0% +coefficient what happens is atoms come +down they they may touch the surface but + + align:start position:0% +down they they may touch the surface but + + + align:start position:0% +down they they may touch the surface but +they don't stick they don't react + + align:start position:0% +they don't stick they don't react + + + align:start position:0% +they don't stick they don't react +they're kind of inert in which case + + align:start position:0% +they're kind of inert in which case + + + align:start position:0% +they're kind of inert in which case +they'll be reemitted they touch + + align:start position:0% +they'll be reemitted they touch + + + align:start position:0% +they'll be reemitted they touch +somewhere else and then they they they + + align:start position:0% +somewhere else and then they they they + + + align:start position:0% +somewhere else and then they they they +don't react and then finally they might + + align:start position:0% +don't react and then finally they might + + + align:start position:0% +don't react and then finally they might +be emitted and stuck at this point so + + align:start position:0% +be emitted and stuck at this point so + + + align:start position:0% +be emitted and stuck at this point so +when you have a low sticking coefficient + + align:start position:0% +when you have a low sticking coefficient + + + align:start position:0% +when you have a low sticking coefficient +much much less than one and sticking + + align:start position:0% +much much less than one and sticking + + + align:start position:0% +much much less than one and sticking +coefficients can be you know 01 it means + + align:start position:0% +coefficients can be you know 01 it means + + + align:start position:0% +coefficients can be you know 01 it means +the things bounc around a lot uh before + + align:start position:0% +the things bounc around a lot uh before + + + align:start position:0% +the things bounc around a lot uh before +they actually stick on the surface uh so + + align:start position:0% +they actually stick on the surface uh so + + + align:start position:0% +they actually stick on the surface uh so +you're going to have um more conformal + + align:start position:0% +you're going to have um more conformal + + + align:start position:0% +you're going to have um more conformal +type deposition so this depends a lot on + + align:start position:0% +type deposition so this depends a lot on + + + align:start position:0% +type deposition so this depends a lot on +the deposition system on the temperature + + align:start position:0% +the deposition system on the temperature + + + align:start position:0% +the deposition system on the temperature +on the chemistry again we don't model + + align:start position:0% +on the chemistry again we don't model + + + align:start position:0% +on the chemistry again we don't model +all that we don't say oh I'm putting a + + align:start position:0% +all that we don't say oh I'm putting a + + + align:start position:0% +all that we don't say oh I'm putting a +wafer into an lpcvd system the sticking + + align:start position:0% +wafer into an lpcvd system the sticking + + + align:start position:0% +wafer into an lpcvd system the sticking +coefficient must be 0.1 or 0.1 um we + + align:start position:0% +coefficient must be 0.1 or 0.1 um we + + + align:start position:0% +coefficient must be 0.1 or 0.1 um we +don't know that for any given tool you + + align:start position:0% +don't know that for any given tool you + + + align:start position:0% +don't know that for any given tool you +can put it in as a variable in the model + + align:start position:0% +can put it in as a variable in the model + + + align:start position:0% +can put it in as a variable in the model +and then you can compare that to what + + align:start position:0% +and then you can compare that to what + + + align:start position:0% +and then you can compare that to what +you get you can compare the modeled + + align:start position:0% +you get you can compare the modeled + + + align:start position:0% +you get you can compare the modeled +deposition to the profile of what you + + align:start position:0% +deposition to the profile of what you + + + align:start position:0% +deposition to the profile of what you +get and then you get get an idea of what + + align:start position:0% +get and then you get get an idea of what + + + align:start position:0% +get and then you get get an idea of what +your sticking coefficient is it's not + + align:start position:0% +your sticking coefficient is it's not + + + align:start position:0% +your sticking coefficient is it's not +it's not a number you can calculate from + + align:start position:0% +it's not a number you can calculate from + + + align:start position:0% +it's not a number you can calculate from +a first principal uh point of view but + + align:start position:0% +a first principal uh point of view but + + + align:start position:0% +a first principal uh point of view but +people have uh have derived sticking + + align:start position:0% +people have uh have derived sticking + + + align:start position:0% +people have uh have derived sticking +coefficients for various types of + + align:start position:0% + + + + align:start position:0% + +deposition okay so uh slide 13 so this + + align:start position:0% +deposition okay so uh slide 13 so this + + + align:start position:0% +deposition okay so uh slide 13 so this +is the formula we said the the the flux + + align:start position:0% +is the formula we said the the the flux + + + align:start position:0% +is the formula we said the the the flux +emitted is just one minus the sticking + + align:start position:0% +emitted is just one minus the sticking + + + align:start position:0% +emitted is just one minus the sticking +coefficient uh it's those that don't + + align:start position:0% +coefficient uh it's those that don't + + + align:start position:0% +coefficient uh it's those that don't +stick times the flux incident at the + + align:start position:0% +stick times the flux incident at the + + + align:start position:0% +stick times the flux incident at the +point we make some assumptions generally + + align:start position:0% +point we make some assumptions generally + + + align:start position:0% +point we make some assumptions generally +we assume that ions stick so if we have + + align:start position:0% +we assume that ions stick so if we have + + + align:start position:0% +we assume that ions stick so if we have +an ion coming down we assume sticking + + align:start position:0% +an ion coming down we assume sticking + + + align:start position:0% +an ion coming down we assume sticking +coefficient is one why is that ions tend + + align:start position:0% +coefficient is one why is that ions tend + + + align:start position:0% +coefficient is one why is that ions tend +to be very reactive um and they also + + align:start position:0% +to be very reactive um and they also + + + align:start position:0% +to be very reactive um and they also +often come down with a certain amount of + + align:start position:0% +often come down with a certain amount of + + + align:start position:0% +often come down with a certain amount of +energy so we we usually say that they + + align:start position:0% +energy so we we usually say that they + + + align:start position:0% +energy so we we usually say that they +have the sticking coefficient one + + align:start position:0% +have the sticking coefficient one + + + align:start position:0% +have the sticking coefficient one +neutrals can have any any number one or + + align:start position:0% +neutrals can have any any number one or + + + align:start position:0% +neutrals can have any any number one or +less um and they're often assumed to be + + align:start position:0% +less um and they're often assumed to be + + + align:start position:0% +less um and they're often assumed to be +emitted uh with some kind of a cosine + + align:start position:0% +emitted uh with some kind of a cosine + + + align:start position:0% +emitted uh with some kind of a cosine +Theta angle distribution so that is they + + align:start position:0% +Theta angle distribution so that is they + + + align:start position:0% +Theta angle distribution so that is they +may have no memory of their arrival + + align:start position:0% +may have no memory of their arrival + + + align:start position:0% +may have no memory of their arrival +angle so don't think of this for example + + align:start position:0% +angle so don't think of this for example + + + align:start position:0% +angle so don't think of this for example +in here don't think of this as a little + + align:start position:0% +in here don't think of this as a little + + + align:start position:0% +in here don't think of this as a little +trough uh like like a pool uh that way + + align:start position:0% +trough uh like like a pool uh that way + + + align:start position:0% +trough uh like like a pool uh that way +you've taken all the water out and you + + align:start position:0% +you've taken all the water out and you + + + align:start position:0% +you've taken all the water out and you +have a pingpong ball and it's bouncing + + align:start position:0% +have a pingpong ball and it's bouncing + + + align:start position:0% +have a pingpong ball and it's bouncing +around with sort of bilard ball kind of + + align:start position:0% +around with sort of bilard ball kind of + + + align:start position:0% +around with sort of bilard ball kind of +collisions it's not supposed to be + + align:start position:0% +collisions it's not supposed to be + + + align:start position:0% +collisions it's not supposed to be +thought like that this atom is supposed + + align:start position:0% +thought like that this atom is supposed + + + align:start position:0% +thought like that this atom is supposed +to come down and then uh atoms are + + align:start position:0% +to come down and then uh atoms are + + + align:start position:0% +to come down and then uh atoms are +coming down continuously say at this + + align:start position:0% +coming down continuously say at this + + + align:start position:0% +coming down continuously say at this +point and then it's re-emitting at some + + align:start position:0% +point and then it's re-emitting at some + + + align:start position:0% +point and then it's re-emitting at some +with some angular distribution but it's + + align:start position:0% +with some angular distribution but it's + + + align:start position:0% +with some angular distribution but it's +not necessarily a billiard ball kind of + + align:start position:0% +not necessarily a billiard ball kind of + + + align:start position:0% +not necessarily a billiard ball kind of +collision type of thing happening + + align:start position:0% +collision type of thing happening + + + align:start position:0% +collision type of thing happening +um so you need to put in a reemission + + align:start position:0% +um so you need to put in a reemission + + + align:start position:0% +um so you need to put in a reemission +flux distribution + + align:start position:0% + + + + align:start position:0% + +so this uh at any point I we get a flux + + align:start position:0% +so this uh at any point I we get a flux + + + align:start position:0% +so this uh at any point I we get a flux +of redeposited material uh because the + + align:start position:0% +of redeposited material uh because the + + + align:start position:0% +of redeposited material uh because the +admitted flux can land somewhere else uh + + align:start position:0% +admitted flux can land somewhere else uh + + + align:start position:0% +admitted flux can land somewhere else uh +on the surface so uh we have this sort + + align:start position:0% +on the surface so uh we have this sort + + + align:start position:0% +on the surface so uh we have this sort +of again this end up being bookkeeping + + align:start position:0% +of again this end up being bookkeeping + + + align:start position:0% +of again this end up being bookkeeping +we have this something we express as F + + align:start position:0% +we have this something we express as F + + + align:start position:0% +we have this something we express as F +super i k um redep redeposited and what + + align:start position:0% +super i k um redep redeposited and what + + + align:start position:0% +super i k um redep redeposited and what +this is is um you take the flux the + + align:start position:0% +this is is um you take the flux the + + + align:start position:0% +this is is um you take the flux the +direct flux F sub K that's coming into a + + align:start position:0% +direct flux F sub K that's coming into a + + + align:start position:0% +direct flux F sub K that's coming into a +Point K on the surface let's say it's + + align:start position:0% +Point K on the surface let's say it's + + + align:start position:0% +Point K on the surface let's say it's +right here and we're looking at um then + + align:start position:0% +right here and we're looking at um then + + + align:start position:0% +right here and we're looking at um then +point I the um it's desorbed from point + + align:start position:0% +point I the um it's desorbed from point + + + align:start position:0% +point I the um it's desorbed from point +K and it's Depo redeposited at point I + + align:start position:0% +K and it's Depo redeposited at point I + + + align:start position:0% +K and it's Depo redeposited at point I +so this redeposited flux depends on some + + align:start position:0% +so this redeposited flux depends on some + + + align:start position:0% +so this redeposited flux depends on some +geometry Factor g i k so it has to do + + align:start position:0% +geometry Factor g i k so it has to do + + + align:start position:0% +geometry Factor g i k so it has to do +with the geometry between point I and + + align:start position:0% +with the geometry between point I and + + + align:start position:0% +with the geometry between point I and +point K times F subk that's emitted so + + align:start position:0% +point K times F subk that's emitted so + + + align:start position:0% +point K times F subk that's emitted so +times this this um emitted flux from + + align:start position:0% +times this this um emitted flux from + + + align:start position:0% +times this this um emitted flux from +this point + + align:start position:0% +this point + + + align:start position:0% +this point +K well the emitted flux from point K + + align:start position:0% +K well the emitted flux from point K + + + align:start position:0% +K well the emitted flux from point K +just depends on the incoming flux to + + align:start position:0% +just depends on the incoming flux to + + + align:start position:0% +just depends on the incoming flux to +point K times the one minus the sticking + + align:start position:0% +point K times the one minus the sticking + + + align:start position:0% +point K times the one minus the sticking +coefficient so the nice thing is here I + + align:start position:0% +coefficient so the nice thing is here I + + + align:start position:0% +coefficient so the nice thing is here I +can I can uh for point I I can take any + + align:start position:0% +can I can uh for point I I can take any + + + align:start position:0% +can I can uh for point I I can take any +point K and figure out if I know the + + align:start position:0% +point K and figure out if I know the + + + align:start position:0% +point K and figure out if I know the +geometry factor between the two um how + + align:start position:0% +geometry factor between the two um how + + + align:start position:0% +geometry factor between the two um how +much uh is redeposited at this is + + align:start position:0% +much uh is redeposited at this is + + + align:start position:0% +much uh is redeposited at this is +deposited at this point I resulting from + + align:start position:0% +deposited at this point I resulting from + + + align:start position:0% +deposited at this point I resulting from +uh having come from being emitted from + + align:start position:0% +uh having come from being emitted from + + + align:start position:0% +uh having come from being emitted from +point + + align:start position:0% +point + + + align:start position:0% +point +K and then what you do is you you take + + align:start position:0% +K and then what you do is you you take + + + align:start position:0% +K and then what you do is you you take +all of these at this point I you take + + align:start position:0% +all of these at this point I you take + + + align:start position:0% +all of these at this point I you take +redeposited fluxes from all points of + + align:start position:0% +redeposited fluxes from all points of + + + align:start position:0% +redeposited fluxes from all points of +the surface so the all points of a + + align:start position:0% +the surface so the all points of a + + + align:start position:0% +the surface so the all points of a +surface could be redepositing at this + + align:start position:0% +surface could be redepositing at this + + + align:start position:0% +surface could be redepositing at this +point so you sum up for all I and K uh + + align:start position:0% +point so you sum up for all I and K uh + + + align:start position:0% +point so you sum up for all I and K uh +and uh and you figure out what's deposit + + align:start position:0% +and uh and you figure out what's deposit + + + align:start position:0% +and uh and you figure out what's deposit +so g i k then accounts for the geometry + + align:start position:0% +so g i k then accounts for the geometry + + + align:start position:0% +so g i k then accounts for the geometry +between any point I and K because + + align:start position:0% +between any point I and K because + + + align:start position:0% +between any point I and K because +obviously if you're over here let's say + + align:start position:0% +obviously if you're over here let's say + + + align:start position:0% +obviously if you're over here let's say +I'm over here my point K we're up at + + align:start position:0% +I'm over here my point K we're up at + + + align:start position:0% +I'm over here my point K we're up at +this surface and it's re-emitting well + + align:start position:0% +this surface and it's re-emitting well + + + align:start position:0% +this surface and it's re-emitting well +chances of it coming back down over to + + align:start position:0% +chances of it coming back down over to + + + align:start position:0% +chances of it coming back down over to +this point are are dramatically lower + + align:start position:0% +this point are are dramatically lower + + + align:start position:0% +this point are are dramatically lower +than if it's re-emitting from the walls + + align:start position:0% +than if it's re-emitting from the walls + + + align:start position:0% +than if it's re-emitting from the walls +just just by based on + + align:start position:0% +just just by based on + + + align:start position:0% +just just by based on +Geometry + + align:start position:0% + + + + align:start position:0% + +okay so let's look at take a look at + + align:start position:0% +okay so let's look at take a look at + + + align:start position:0% +okay so let's look at take a look at +some examples on slide 14 um so and and + + align:start position:0% +some examples on slide 14 um so and and + + + align:start position:0% +some examples on slide 14 um so and and +hopefully this will become intuitive but + + align:start position:0% +hopefully this will become intuitive but + + + align:start position:0% +hopefully this will become intuitive but +if you have a low sticking coefficient s + + align:start position:0% +if you have a low sticking coefficient s + + + align:start position:0% +if you have a low sticking coefficient s +subc much less than one you can end up + + align:start position:0% +subc much less than one you can end up + + + align:start position:0% +subc much less than one you can end up +with more conformal deposition or + + align:start position:0% +with more conformal deposition or + + + align:start position:0% +with more conformal deposition or +conformal coverage of the step because + + align:start position:0% +conformal coverage of the step because + + + align:start position:0% +conformal coverage of the step because +of the redeposition + + align:start position:0% +of the redeposition + + + align:start position:0% +of the redeposition +process um redeposition and this low + + align:start position:0% +process um redeposition and this low + + + align:start position:0% +process um redeposition and this low +sticking coefficient is usually more + + align:start position:0% +sticking coefficient is usually more + + + align:start position:0% +sticking coefficient is usually more +important than surface diffusion because + + align:start position:0% +important than surface diffusion because + + + align:start position:0% +important than surface diffusion because +most of the time in these processes uh + + align:start position:0% +most of the time in these processes uh + + + align:start position:0% +most of the time in these processes uh +the wafer temperature is low enough that + + align:start position:0% +the wafer temperature is low enough that + + + align:start position:0% +the wafer temperature is low enough that +the surface diffusion is not all that + + align:start position:0% +the surface diffusion is not all that + + + align:start position:0% +the surface diffusion is not all that +high especially if you're doing pbd um + + align:start position:0% +high especially if you're doing pbd um + + + align:start position:0% +high especially if you're doing pbd um +but let's let's just take a look here at + + align:start position:0% +but let's let's just take a look here at + + + align:start position:0% +but let's let's just take a look here at +um the case uh a where I have a high + + align:start position:0% +um the case uh a where I have a high + + + align:start position:0% +um the case uh a where I have a high +sticking coefficient so a sticking + + align:start position:0% +sticking coefficient so a sticking + + + align:start position:0% +sticking coefficient so a sticking +coefficient is one everything comes down + + align:start position:0% +coefficient is one everything comes down + + + align:start position:0% +coefficient is one everything comes down +and sticks so what do I get based if I'm + + align:start position:0% +and sticks so what do I get based if I'm + + + align:start position:0% +and sticks so what do I get based if I'm +if I'm depositing in this trench well I + + align:start position:0% +if I'm depositing in this trench well I + + + align:start position:0% +if I'm depositing in this trench well I +get very non-conformable deposition I + + align:start position:0% +get very non-conformable deposition I + + + align:start position:0% +get very non-conformable deposition I +get a film deposited at the bottom of + + align:start position:0% +get a film deposited at the bottom of + + + align:start position:0% +get a film deposited at the bottom of +the trench uh there' probably be a film + + align:start position:0% +the trench uh there' probably be a film + + + align:start position:0% +the trench uh there' probably be a film +up here too it should have been shown + + align:start position:0% +up here too it should have been shown + + + align:start position:0% +up here too it should have been shown +but we're only looking at what's + + align:start position:0% +but we're only looking at what's + + + align:start position:0% +but we're only looking at what's +happening in the trench um but nothing + + align:start position:0% +happening in the trench um but nothing + + + align:start position:0% +happening in the trench um but nothing +on the + + align:start position:0% +on the + + + align:start position:0% +on the +sidewalls why because I really don't + + align:start position:0% +sidewalls why because I really don't + + + align:start position:0% +sidewalls why because I really don't +have any opportunity uh for uh for + + align:start position:0% +have any opportunity uh for uh for + + + align:start position:0% +have any opportunity uh for uh for +redeposition um whereas I can have that + + align:start position:0% +redeposition um whereas I can have that + + + align:start position:0% +redeposition um whereas I can have that +same angular arrival distribution so + + align:start position:0% +same angular arrival distribution so + + + align:start position:0% +same angular arrival distribution so +with the exact same angular arrival + + align:start position:0% +with the exact same angular arrival + + + align:start position:0% +with the exact same angular arrival +distribution if I have a low sticking + + align:start position:0% +distribution if I have a low sticking + + + align:start position:0% +distribution if I have a low sticking +coefficient things can move around a lot + + align:start position:0% +coefficient things can move around a lot + + + align:start position:0% +coefficient things can move around a lot +and and hit the sidewalls and then you + + align:start position:0% +and and hit the sidewalls and then you + + + align:start position:0% +and and hit the sidewalls and then you +can end up with more conformal uh + + align:start position:0% +can end up with more conformal uh + + + align:start position:0% +can end up with more conformal uh +deposition and again you would use this + + align:start position:0% +deposition and again you would use this + + + align:start position:0% +deposition and again you would use this +type of equation in the computer uh to + + align:start position:0% +type of equation in the computer uh to + + + align:start position:0% +type of equation in the computer uh to +be able to model that you just vary the + + align:start position:0% +be able to model that you just vary the + + + align:start position:0% +be able to model that you just vary the +sticking coefficient and you need to + + align:start position:0% +sticking coefficient and you need to + + + align:start position:0% +sticking coefficient and you need to +calculate the geometry Factor as part of + + align:start position:0% +calculate the geometry Factor as part of + + + align:start position:0% +calculate the geometry Factor as part of +that so low sticking coefficient is good + + align:start position:0% +that so low sticking coefficient is good + + + align:start position:0% +that so low sticking coefficient is good +if you want to coat a trench now that + + align:start position:0% +if you want to coat a trench now that + + + align:start position:0% +if you want to coat a trench now that +may not be what you want you may want to + + align:start position:0% +may not be what you want you may want to + + + align:start position:0% +may not be what you want you may want to +just deposit at the bottom but again it + + align:start position:0% +just deposit at the bottom but again it + + + align:start position:0% +just deposit at the bottom but again it +depends on the process that you're uh + + align:start position:0% +depends on the process that you're uh + + + align:start position:0% +depends on the process that you're uh +you're trying to + + align:start position:0% +you're trying to + + + align:start position:0% +you're trying to +do okay so that has to do with sticking + + align:start position:0% +do okay so that has to do with sticking + + + align:start position:0% +do okay so that has to do with sticking +coefficient that's an important Concept + + align:start position:0% +coefficient that's an important Concept + + + align:start position:0% +coefficient that's an important Concept +in in basic surface physics um and we + + align:start position:0% +in in basic surface physics um and we + + + align:start position:0% +in in basic surface physics um and we +talked about surface diffusion the third + + align:start position:0% +talked about surface diffusion the third + + + align:start position:0% +talked about surface diffusion the third +concept is is + + align:start position:0% +concept is is + + + align:start position:0% +concept is is +sputtering what happens on the surface + + align:start position:0% +sputtering what happens on the surface + + + align:start position:0% +sputtering what happens on the surface +and that we talk about here on slide 15 + + align:start position:0% +and that we talk about here on slide 15 + + + align:start position:0% +and that we talk about here on slide 15 +um uh this there's a sputtered flux at + + align:start position:0% +um uh this there's a sputtered flux at + + + align:start position:0% +um uh this there's a sputtered flux at +any point I is caused by energetic + + align:start position:0% +any point I is caused by energetic + + + align:start position:0% +any point I is caused by energetic +usually in incoming ions why do we care + + align:start position:0% +usually in incoming ions why do we care + + + align:start position:0% +usually in incoming ions why do we care +about ions well Mo the neutrals usually + + align:start position:0% +about ions well Mo the neutrals usually + + + align:start position:0% +about ions well Mo the neutrals usually +come down with low enough energy they do + + align:start position:0% +come down with low enough energy they do + + + align:start position:0% +come down with low enough energy they do +a little bit of sputtering but not much + + align:start position:0% +a little bit of sputtering but not much + + + align:start position:0% +a little bit of sputtering but not much +but an incoming ion can come in and it + + align:start position:0% +but an incoming ion can come in and it + + + align:start position:0% +but an incoming ion can come in and it +might have a couple hundred electron + + align:start position:0% +might have a couple hundred electron + + + align:start position:0% +might have a couple hundred electron +volts of energy with it with enough + + align:start position:0% +volts of energy with it with enough + + + align:start position:0% +volts of energy with it with enough +energy it can then hit something at the + + align:start position:0% +energy it can then hit something at the + + + align:start position:0% +energy it can then hit something at the +surface and cause it to be uh sputtered + + align:start position:0% +surface and cause it to be uh sputtered + + + align:start position:0% +surface and cause it to be uh sputtered +or or emitted so what we typically say + + align:start position:0% +or or emitted so what we typically say + + + align:start position:0% +or or emitted so what we typically say +as any point eye the sputtered flux + + align:start position:0% +as any point eye the sputtered flux + + + align:start position:0% +as any point eye the sputtered flux +depends on the sputtering yield why uh Y + + align:start position:0% +depends on the sputtering yield why uh Y + + + align:start position:0% +depends on the sputtering yield why uh Y +is just the number sputter divided by + + align:start position:0% +is just the number sputter divided by + + + align:start position:0% +is just the number sputter divided by +the number incident so uh and this tells + + align:start position:0% +the number incident so uh and this tells + + + align:start position:0% +the number incident so uh and this tells +you this plot tells you how the + + align:start position:0% +you this plot tells you how the + + + align:start position:0% +you this plot tells you how the +sputtering yield barriers with angle + + align:start position:0% +sputtering yield barriers with angle + + + align:start position:0% +sputtering yield barriers with angle +depends on y times the um Flux Of + + align:start position:0% +depends on y times the um Flux Of + + + align:start position:0% +depends on y times the um Flux Of +incident argon ions um uh flux of argon + + align:start position:0% +incident argon ions um uh flux of argon + + + align:start position:0% +incident argon ions um uh flux of argon +and the flux of uh direct uh direct flux + + align:start position:0% +and the flux of uh direct uh direct flux + + + align:start position:0% +and the flux of uh direct uh direct flux +of ions so the total ionic flux is what + + align:start position:0% +of ions so the total ionic flux is what + + + align:start position:0% +of ions so the total ionic flux is what +we add + + align:start position:0% +we add + + + align:start position:0% +we add +up so uh you might be curious to say all + + align:start position:0% +up so uh you might be curious to say all + + + align:start position:0% +up so uh you might be curious to say all +right well how does the sputtering yield + + align:start position:0% +right well how does the sputtering yield + + + align:start position:0% +right well how does the sputtering yield +depend on the angle because that's going + + align:start position:0% +depend on the angle because that's going + + + align:start position:0% +depend on the angle because that's going +to tell you um if you have a trench with + + align:start position:0% +to tell you um if you have a trench with + + + align:start position:0% +to tell you um if you have a trench with +a certain angle and the atoms are coming + + align:start position:0% +a certain angle and the atoms are coming + + + align:start position:0% +a certain angle and the atoms are coming +in the ions are coming in how is this + + align:start position:0% +in the ions are coming in how is this + + + align:start position:0% +in the ions are coming in how is this +sping yield going to vary well this is a + + align:start position:0% +sping yield going to vary well this is a + + + align:start position:0% +sping yield going to vary well this is a +plot a typical plot of yield uh versus + + align:start position:0% +plot a typical plot of yield uh versus + + + align:start position:0% +plot a typical plot of yield uh versus +angle so again a yield of one means it's + + align:start position:0% +angle so again a yield of one means it's + + + align:start position:0% +angle so again a yield of one means it's +one to one uh what for every one that's + + align:start position:0% +one to one uh what for every one that's + + + align:start position:0% +one to one uh what for every one that's +incident on that point one comes + + align:start position:0% +incident on that point one comes + + + align:start position:0% +incident on that point one comes +off uh and you can see and this is all + + align:start position:0% +off uh and you can see and this is all + + + align:start position:0% +off uh and you can see and this is all +measured with respect to the surface + + align:start position:0% +measured with respect to the surface + + + align:start position:0% +measured with respect to the surface +normal so theta equals zero means normal + + align:start position:0% +normal so theta equals zero means normal + + + align:start position:0% +normal so theta equals zero means normal +normal sputtering so it's coming + + align:start position:0% +normal sputtering so it's coming + + + align:start position:0% +normal sputtering so it's coming +straight + + align:start position:0% +straight + + + align:start position:0% +straight +down um so at theta equals z for this + + align:start position:0% +down um so at theta equals z for this + + + align:start position:0% +down um so at theta equals z for this +particular example the spattering yield + + align:start position:0% +particular example the spattering yield + + + align:start position:0% +particular example the spattering yield +is one and look what happens as you + + align:start position:0% +is one and look what happens as you + + + align:start position:0% +is one and look what happens as you +increase Theta so you're coming in a + + align:start position:0% +increase Theta so you're coming in a + + + align:start position:0% +increase Theta so you're coming in a +little more grazing I'm increasing Theta + + align:start position:0% +little more grazing I'm increasing Theta + + + align:start position:0% +little more grazing I'm increasing Theta +it Peaks somewhere here around 50 or 60 + + align:start position:0% +it Peaks somewhere here around 50 or 60 + + + align:start position:0% +it Peaks somewhere here around 50 or 60 +65 degrees gets up to about two two and + + align:start position:0% +65 degrees gets up to about two two and + + + align:start position:0% +65 degrees gets up to about two two and +a half and then uh eventually at your + + align:start position:0% +a half and then uh eventually at your + + + align:start position:0% +a half and then uh eventually at your +very glancing incidence there's really + + align:start position:0% +very glancing incidence there's really + + + align:start position:0% +very glancing incidence there's really +no sputtering at all it really drops + + align:start position:0% +no sputtering at all it really drops + + + align:start position:0% +no sputtering at all it really drops +dramatically so this angular sensitive + + align:start position:0% +dramatically so this angular sensitive + + + align:start position:0% +dramatically so this angular sensitive +and uh you can use this to achieve more + + align:start position:0% +and uh you can use this to achieve more + + + align:start position:0% +and uh you can use this to achieve more +planer surfaces during a deposition in + + align:start position:0% +planer surfaces during a deposition in + + + align:start position:0% +planer surfaces during a deposition in +fact we'll show some examples where we + + align:start position:0% +fact we'll show some examples where we + + + align:start position:0% +fact we'll show some examples where we +use ionized uh species during deposition + + align:start position:0% +use ionized uh species during deposition + + + align:start position:0% +use ionized uh species during deposition +to to give you a little uh better + + align:start position:0% +to to give you a little uh better + + + align:start position:0% +to to give you a little uh better +planarity but but so this angular + + align:start position:0% +planarity but but so this angular + + + align:start position:0% +planarity but but so this angular +dependence is something we want to keep + + align:start position:0% +dependence is something we want to keep + + + align:start position:0% +dependence is something we want to keep +in + + align:start position:0% + + + + align:start position:0% + +mind okay and now on slide 16 so what + + align:start position:0% +mind okay and now on slide 16 so what + + + align:start position:0% +mind okay and now on slide 16 so what +happens so let's say you do sputter that + + align:start position:0% +happens so let's say you do sputter that + + + align:start position:0% +happens so let's say you do sputter that +off then you have redeposition of the + + align:start position:0% +off then you have redeposition of the + + + align:start position:0% +off then you have redeposition of the +sputtered molecules how do you model + + align:start position:0% +sputtered molecules how do you model + + + align:start position:0% +sputtered molecules how do you model +that you the exact same way you model + + align:start position:0% +that you the exact same way you model + + + align:start position:0% +that you the exact same way you model +reemission when you were just coming off + + align:start position:0% +reemission when you were just coming off + + + align:start position:0% +reemission when you were just coming off +due to low sticking coefficient uh you + + align:start position:0% +due to low sticking coefficient uh you + + + align:start position:0% +due to low sticking coefficient uh you +just say the redeposit flux between I at + + align:start position:0% +just say the redeposit flux between I at + + + align:start position:0% +just say the redeposit flux between I at +point I due to whatever is buttering off + + align:start position:0% +point I due to whatever is buttering off + + + align:start position:0% +point I due to whatever is buttering off +from point K is just a geometry Factor G + + align:start position:0% +from point K is just a geometry Factor G + + + align:start position:0% +from point K is just a geometry Factor G +K which you which end up summing over + + align:start position:0% +K which you which end up summing over + + + align:start position:0% +K which you which end up summing over +the Surface Times the uh sputter flux + + align:start position:0% +the Surface Times the uh sputter flux + + + align:start position:0% +the Surface Times the uh sputter flux +from point K and that sputter flux from + + align:start position:0% +from point K and that sputter flux from + + + align:start position:0% +from point K and that sputter flux from +point point K depends on the flux + + align:start position:0% +point point K depends on the flux + + + align:start position:0% +point point K depends on the flux +incident of ions times the sputtering + + align:start position:0% +incident of ions times the sputtering + + + align:start position:0% +incident of ions times the sputtering +yield y to see how the sputtering yield + + align:start position:0% +yield y to see how the sputtering yield + + + align:start position:0% +yield y to see how the sputtering yield +comes into + + align:start position:0% +comes into + + + align:start position:0% +comes into +it and finally if you want to substitute + + align:start position:0% +it and finally if you want to substitute + + + align:start position:0% +it and finally if you want to substitute +in uh the sticking coefficients what you + + align:start position:0% +in uh the sticking coefficients what you + + + align:start position:0% +in uh the sticking coefficients what you +say is the redeposited at point I um + + align:start position:0% +say is the redeposited at point I um + + + align:start position:0% +say is the redeposited at point I um +depends on the emitted from K which + + align:start position:0% +depends on the emitted from K which + + + align:start position:0% +depends on the emitted from K which +depends on um one minus the sticking + + align:start position:0% +depends on um one minus the sticking + + + align:start position:0% +depends on um one minus the sticking +coefficient so we have this + + align:start position:0% +coefficient so we have this + + + align:start position:0% +coefficient so we have this +redeposited uh due to emission is very + + align:start position:0% +redeposited uh due to emission is very + + + align:start position:0% +redeposited uh due to emission is very +very similar to the redeposited uh due + + align:start position:0% +very similar to the redeposited uh due + + + align:start position:0% +very similar to the redeposited uh due +to the + + align:start position:0% +to the + + + align:start position:0% +to the +sputtering um and there's a a final term + + align:start position:0% +sputtering um and there's a a final term + + + align:start position:0% +sputtering um and there's a a final term +in a lot of these and this is the + + align:start position:0% +in a lot of these and this is the + + + align:start position:0% +in a lot of these and this is the +biggest fudge factor I would say in the + + align:start position:0% +biggest fudge factor I would say in the + + + align:start position:0% +biggest fudge factor I would say in the +whole model which is that ions coming + + align:start position:0% +whole model which is that ions coming + + + align:start position:0% +whole model which is that ions coming +down on the surface can sometimes + + align:start position:0% +down on the surface can sometimes + + + align:start position:0% +down on the surface can sometimes +enhance the deposition rate in a way + + align:start position:0% +enhance the deposition rate in a way + + + align:start position:0% +enhance the deposition rate in a way +that's uh not completely obvious the + + align:start position:0% +that's uh not completely obvious the + + + align:start position:0% +that's uh not completely obvious the +ions may come down they must they may + + align:start position:0% +ions may come down they must they may + + + align:start position:0% +ions may come down they must they may +supply enough energy to drive a chemical + + align:start position:0% +supply enough energy to drive a chemical + + + align:start position:0% +supply enough energy to drive a chemical +reaction that might take place at the + + align:start position:0% +reaction that might take place at the + + + align:start position:0% +reaction that might take place at the +surface so we have um a deposition flux + + align:start position:0% +surface so we have um a deposition flux + + + align:start position:0% +surface so we have um a deposition flux +so we can have a deposition rate that is + + align:start position:0% +so we can have a deposition rate that is + + + align:start position:0% +so we can have a deposition rate that is +called ion enhanced or ion + + align:start position:0% +called ion enhanced or ion + + + align:start position:0% +called ion enhanced or ion +induced um uh chemical reaction so it's + + align:start position:0% +induced um uh chemical reaction so it's + + + align:start position:0% +induced um uh chemical reaction so it's +kind of a fudge Factor we have this an + + align:start position:0% +kind of a fudge Factor we have this an + + + align:start position:0% +kind of a fudge Factor we have this an +additional flux and a term with a K subi + + align:start position:0% +additional flux and a term with a K subi + + + align:start position:0% +additional flux and a term with a K subi +where K subi is a fitting parameter + + align:start position:0% +where K subi is a fitting parameter + + + align:start position:0% +where K subi is a fitting parameter +times the flux of ions coming at any + + align:start position:0% +times the flux of ions coming at any + + + align:start position:0% +times the flux of ions coming at any +given point + + align:start position:0% +given point + + + align:start position:0% +given point +so you can have this extra ion induced + + align:start position:0% +so you can have this extra ion induced + + + align:start position:0% +so you can have this extra ion induced +uh deposition rate obviously that's only + + align:start position:0% +uh deposition rate obviously that's only + + + align:start position:0% +uh deposition rate obviously that's only +important in systems with ionized uh + + align:start position:0% +important in systems with ionized uh + + + align:start position:0% +important in systems with ionized uh +ionized type of + + align:start position:0% +ionized type of + + + align:start position:0% +ionized type of +deposition okay so those are all the + + align:start position:0% +deposition okay so those are all the + + + align:start position:0% +deposition okay so those are all the +different processes at the surface and + + align:start position:0% +different processes at the surface and + + + align:start position:0% +different processes at the surface and +the direct flux and now I wanted to give + + align:start position:0% +the direct flux and now I wanted to give + + + align:start position:0% +the direct flux and now I wanted to give +starting on slide 17 I want to give a + + align:start position:0% +starting on slide 17 I want to give a + + + align:start position:0% +starting on slide 17 I want to give a +couple of examples because it seems like + + align:start position:0% +couple of examples because it seems like + + + align:start position:0% +couple of examples because it seems like +there's a lot of different equations but + + align:start position:0% +there's a lot of different equations but + + + align:start position:0% +there's a lot of different equations but +it turns out a lot of them simplify for + + align:start position:0% +it turns out a lot of them simplify for + + + align:start position:0% +it turns out a lot of them simplify for +most + + align:start position:0% +most + + + align:start position:0% +most +systems so let's do an example of low + + align:start position:0% +systems so let's do an example of low + + + align:start position:0% +systems so let's do an example of low +pressure CBD remember LP CBD is probably + + align:start position:0% +pressure CBD remember LP CBD is probably + + + align:start position:0% +pressure CBD remember LP CBD is probably +the most most common process um uh + + align:start position:0% +the most most common process um uh + + + align:start position:0% +the most most common process um uh +deposition process in a Fab typically + + align:start position:0% +deposition process in a Fab typically + + + align:start position:0% +deposition process in a Fab typically +takes place in a furnace that's pumped + + align:start position:0% +takes place in a furnace that's pumped + + + align:start position:0% +takes place in a furnace that's pumped +down to low pressure say 10 to 100 + + align:start position:0% +down to low pressure say 10 to 100 + + + align:start position:0% +down to low pressure say 10 to 100 +millor the Wafers are usually stacked in + + align:start position:0% +millor the Wafers are usually stacked in + + + align:start position:0% +millor the Wafers are usually stacked in +a batch uh people do 25 50 Wafers at a + + align:start position:0% +a batch uh people do 25 50 Wafers at a + + + align:start position:0% +a batch uh people do 25 50 Wafers at a +time it's in a resistively heated + + align:start position:0% +time it's in a resistively heated + + + align:start position:0% +time it's in a resistively heated +furnace um there are no ions this is not + + align:start position:0% +furnace um there are no ions this is not + + + align:start position:0% +furnace um there are no ions this is not +a plasma system so we can get rid of all + + align:start position:0% +a plasma system so we can get rid of all + + + align:start position:0% +a plasma system so we can get rid of all +ionized processes so we can ignore + + align:start position:0% +ionized processes so we can ignore + + + align:start position:0% +ionized processes so we can ignore +sputtering because again we're going to + + align:start position:0% +sputtering because again we're going to + + + align:start position:0% +sputtering because again we're going to +say that only in the presence of ions do + + align:start position:0% +say that only in the presence of ions do + + + align:start position:0% +say that only in the presence of ions do +you have enough energy to sputter + + align:start position:0% +you have enough energy to sputter + + + align:start position:0% +you have enough energy to sputter +something off so we get rid of the + + align:start position:0% +something off so we get rid of the + + + align:start position:0% +something off so we get rid of the +sputtering uh usually long range surface + + align:start position:0% +sputtering uh usually long range surface + + + align:start position:0% +sputtering uh usually long range surface +diffusion is not that important so we + + align:start position:0% +diffusion is not that important so we + + + align:start position:0% +diffusion is not that important so we +can also ignore the surface diffusion so + + align:start position:0% +can also ignore the surface diffusion so + + + align:start position:0% +can also ignore the surface diffusion so +if in my bookkeeping I have all these + + align:start position:0% +if in my bookkeeping I have all these + + + align:start position:0% +if in my bookkeeping I have all these +different fluxes most of them are all + + align:start position:0% +different fluxes most of them are all + + + align:start position:0% +different fluxes most of them are all +not present there's only two that + + align:start position:0% +not present there's only two that + + + align:start position:0% +not present there's only two that +dominate at any point uh it's the + + align:start position:0% +dominate at any point uh it's the + + + align:start position:0% +dominate at any point uh it's the +emitted flux yes because we have a + + align:start position:0% +emitted flux yes because we have a + + + align:start position:0% +emitted flux yes because we have a +finite sticking coefficient and the + + align:start position:0% +finite sticking coefficient and the + + + align:start position:0% +finite sticking coefficient and the +redeposited flux yes we need to take + + align:start position:0% +redeposited flux yes we need to take + + + align:start position:0% +redeposited flux yes we need to take +that into account uh and the neutral + + align:start position:0% +that into account uh and the neutral + + + align:start position:0% +that into account uh and the neutral +direct flux so really in this example + + align:start position:0% +direct flux so really in this example + + + align:start position:0% +direct flux so really in this example +I'm really only going to have three + + align:start position:0% +I'm really only going to have three + + + align:start position:0% +I'm really only going to have three +fluxes I need to worry about all the + + align:start position:0% +fluxes I need to worry about all the + + + align:start position:0% +fluxes I need to worry about all the +rest of these um we don't have to we + + align:start position:0% +rest of these um we don't have to we + + + align:start position:0% +rest of these um we don't have to we +don't have to take into account in the + + align:start position:0% +don't have to take into account in the + + + align:start position:0% +don't have to take into account in the +simulation so then we can write down + + align:start position:0% +simulation so then we can write down + + + align:start position:0% +simulation so then we can write down +those fluxes pretty simply and and the + + align:start position:0% +those fluxes pretty simply and and the + + + align:start position:0% +those fluxes pretty simply and and the +net flux here on on slide 18 so at any + + align:start position:0% +net flux here on on slide 18 so at any + + + align:start position:0% +net flux here on on slide 18 so at any +point I on the surface F super I the net + + align:start position:0% +point I on the surface F super I the net + + + align:start position:0% +point I on the surface F super I the net +flux is again the flux coming in minus + + align:start position:0% +flux is again the flux coming in minus + + + align:start position:0% +flux is again the flux coming in minus +the flux going out so it's the Flux Of + + align:start position:0% +the flux going out so it's the Flux Of + + + align:start position:0% +the flux going out so it's the Flux Of +directs neutral species the redepositing + + align:start position:0% +directs neutral species the redepositing + + + align:start position:0% +directs neutral species the redepositing +flux that come from other areas of the + + align:start position:0% +flux that come from other areas of the + + + align:start position:0% +flux that come from other areas of the +surface minus the flux that goes out + + align:start position:0% +surface minus the flux that goes out + + + align:start position:0% +surface minus the flux that goes out +well this those that don't stick that's + + align:start position:0% +well this those that don't stick that's + + + align:start position:0% +well this those that don't stick that's +one minus the sticking coefficient times + + align:start position:0% +one minus the sticking coefficient times + + + align:start position:0% +one minus the sticking coefficient times +um the direct Flux Of neutrals and the + + align:start position:0% +um the direct Flux Of neutrals and the + + + align:start position:0% +um the direct Flux Of neutrals and the +and the redeposited uh direct flux okay + + align:start position:0% +and the redeposited uh direct flux okay + + + align:start position:0% +and the redeposited uh direct flux okay +so these are the ones that that that + + align:start position:0% +so these are the ones that that that + + + align:start position:0% +so these are the ones that that that +come in and these are the ones that go + + align:start position:0% +come in and these are the ones that go + + + align:start position:0% +come in and these are the ones that go +out that's and there's a negative sign + + align:start position:0% +out that's and there's a negative sign + + + align:start position:0% +out that's and there's a negative sign +in between the two so you can rearrange + + align:start position:0% +in between the two so you can rearrange + + + align:start position:0% +in between the two so you can rearrange +this a little bit and you can write it + + align:start position:0% +this a little bit and you can write it + + + align:start position:0% +this a little bit and you can write it +then as shown here the net flux at any + + align:start position:0% +then as shown here the net flux at any + + + align:start position:0% +then as shown here the net flux at any +point I is the sticking coefficient s + + align:start position:0% +point I is the sticking coefficient s + + + align:start position:0% +point I is the sticking coefficient s +subc times the uh direct flux at that + + align:start position:0% +subc times the uh direct flux at that + + + align:start position:0% +subc times the uh direct flux at that +point of neutral R plus um a term that + + align:start position:0% +point of neutral R plus um a term that + + + align:start position:0% +point of neutral R plus um a term that +relates a geometric term is g i k * 1us + + align:start position:0% +relates a geometric term is g i k * 1us + + + align:start position:0% +relates a geometric term is g i k * 1us +S Sub C that's those that don't stick + + align:start position:0% +S Sub C that's those that don't stick + + + align:start position:0% +S Sub C that's those that don't stick +times the flux into that into the uh + + align:start position:0% +times the flux into that into the uh + + + align:start position:0% +times the flux into that into the uh +some other point on the surface + + align:start position:0% +some other point on the surface + + + align:start position:0% +some other point on the surface +K and then we just need to sum this up + + align:start position:0% +K and then we just need to sum this up + + + align:start position:0% +K and then we just need to sum this up +all over uh Over All Points K on the + + align:start position:0% +all over uh Over All Points K on the + + + align:start position:0% +all over uh Over All Points K on the +surface now what you can do to simplify + + align:start position:0% +surface now what you can do to simplify + + + align:start position:0% +surface now what you can do to simplify +this a little bit you can Define uh F + + align:start position:0% +this a little bit you can Define uh F + + + align:start position:0% +this a little bit you can Define uh F +subd to be the deposition flux at each + + align:start position:0% +subd to be the deposition flux at each + + + align:start position:0% +subd to be the deposition flux at each +point uh to be equal to the direct Flux + + align:start position:0% +point uh to be equal to the direct Flux + + + align:start position:0% +point uh to be equal to the direct Flux +Of neutrals uh plus the um the + + align:start position:0% +Of neutrals uh plus the um the + + + align:start position:0% +Of neutrals uh plus the um the +redeposited flux if you want to do that + + align:start position:0% +redeposited flux if you want to do that + + + align:start position:0% +redeposited flux if you want to do that +and then you can write the deposition + + align:start position:0% +and then you can write the deposition + + + align:start position:0% +and then you can write the deposition +rate more simply as uh the sticking + + align:start position:0% +rate more simply as uh the sticking + + + align:start position:0% +rate more simply as uh the sticking +coefficient uh so this is the depth rate + + align:start position:0% +coefficient uh so this is the depth rate + + + align:start position:0% +coefficient uh so this is the depth rate +then the sticking coefficient times the + + align:start position:0% +then the sticking coefficient times the + + + align:start position:0% +then the sticking coefficient times the +flux uh at any given point I divided by + + align:start position:0% +flux uh at any given point I divided by + + + align:start position:0% +flux uh at any given point I divided by +n so we can then calculate the + + align:start position:0% +n so we can then calculate the + + + align:start position:0% +n so we can then calculate the +deposition rate at any point I on the + + align:start position:0% +deposition rate at any point I on the + + + align:start position:0% +deposition rate at any point I on the +surface and we use a cosine Theta to the + + align:start position:0% +surface and we use a cosine Theta to the + + + align:start position:0% +surface and we use a cosine Theta to the +end distribution for the incoming + + align:start position:0% +end distribution for the incoming + + + align:start position:0% +end distribution for the incoming +molecules so it's a relatively simple + + align:start position:0% +molecules so it's a relatively simple + + + align:start position:0% +molecules so it's a relatively simple +uh formula can be used for + + align:start position:0% + + + + align:start position:0% + +lpcb and in fact on slide 19 I just + + align:start position:0% +lpcb and in fact on slide 19 I just + + + align:start position:0% +lpcb and in fact on slide 19 I just +wanted to go through an example this I + + align:start position:0% +wanted to go through an example this I + + + align:start position:0% +wanted to go through an example this I +took directly from your + + align:start position:0% +took directly from your + + + align:start position:0% +took directly from your +text um what we're asked to do is + + align:start position:0% +text um what we're asked to do is + + + align:start position:0% +text um what we're asked to do is +calculate the depth rate uh using this + + align:start position:0% +calculate the depth rate uh using this + + + align:start position:0% +calculate the depth rate uh using this +lpcvd expression that we just derived + + align:start position:0% +lpcvd expression that we just derived + + + align:start position:0% +lpcvd expression that we just derived +sticking coefficient times a flux + + align:start position:0% +sticking coefficient times a flux + + + align:start position:0% +sticking coefficient times a flux +divided by density for silicon dioxide + + align:start position:0% +divided by density for silicon dioxide + + + align:start position:0% +divided by density for silicon dioxide +so this is low temperature oxide and we + + align:start position:0% +so this is low temperature oxide and we + + + align:start position:0% +so this is low temperature oxide and we +have a flat circus so this is nice + + align:start position:0% +have a flat circus so this is nice + + + align:start position:0% +have a flat circus so this is nice +there's there's no topography um we are + + align:start position:0% +there's there's no topography um we are + + + align:start position:0% +there's there's no topography um we are +to that the sticking coefficient + + align:start position:0% +to that the sticking coefficient + + + align:start position:0% +to that the sticking coefficient +is.3 um um and that the maximum + + align:start position:0% +is.3 um um and that the maximum + + + align:start position:0% +is.3 um um and that the maximum +unobstructed flux that's the maximum + + align:start position:0% +unobstructed flux that's the maximum + + + align:start position:0% +unobstructed flux that's the maximum +flux is coming straight down is equal to + + align:start position:0% +flux is coming straight down is equal to + + + align:start position:0% +flux is coming straight down is equal to +3 * 10 15th molecules per square + + align:start position:0% +3 * 10 15th molecules per square + + + align:start position:0% +3 * 10 15th molecules per square +centimet per second so that's that's a + + align:start position:0% +centimet per second so that's that's a + + + align:start position:0% +centimet per second so that's that's a +molecular flux and we're given the + + align:start position:0% +molecular flux and we're given the + + + align:start position:0% +molecular flux and we're given the +density of the film that's deposited uh + + align:start position:0% +density of the film that's deposited uh + + + align:start position:0% +density of the film that's deposited uh +2.27 gam per cubic + + align:start position:0% +2.27 gam per cubic + + + align:start position:0% +2.27 gam per cubic +cmet so this is a relatively simple + + align:start position:0% +cmet so this is a relatively simple + + + align:start position:0% +cmet so this is a relatively simple +calculation um we want to get the + + align:start position:0% +calculation um we want to get the + + + align:start position:0% +calculation um we want to get the +deposition rate on a flat surface + + align:start position:0% +deposition rate on a flat surface + + + align:start position:0% +deposition rate on a flat surface +therefore there is no shadowing effect + + align:start position:0% +therefore there is no shadowing effect + + + align:start position:0% +therefore there is no shadowing effect +there's no redeposited flux because + + align:start position:0% +there's no redeposited flux because + + + align:start position:0% +there's no redeposited flux because +we're not we're not coming off of a side + + align:start position:0% +we're not we're not coming off of a side + + + align:start position:0% +we're not we're not coming off of a side +wall of a trench and each surface + + align:start position:0% +wall of a trench and each surface + + + align:start position:0% +wall of a trench and each surface +position is in a horizontal orientation + + align:start position:0% +position is in a horizontal orientation + + + align:start position:0% +position is in a horizontal orientation +so we're only concerned about the direct + + align:start position:0% +so we're only concerned about the direct + + + align:start position:0% +so we're only concerned about the direct +flux um so F subd the deposited uh flux + + align:start position:0% +flux um so F subd the deposited uh flux + + + align:start position:0% +flux um so F subd the deposited uh flux +is just equal everywhere to the maximum + + align:start position:0% +is just equal everywhere to the maximum + + + align:start position:0% +is just equal everywhere to the maximum +value which is this 3 * 10 15th + + align:start position:0% +value which is this 3 * 10 15th + + + align:start position:0% +value which is this 3 * 10 15th +molecules per square centimeter per + + align:start position:0% +molecules per square centimeter per + + + align:start position:0% +molecules per square centimeter per +second um and you can look up equation + + align:start position:0% +second um and you can look up equation + + + align:start position:0% +second um and you can look up equation +9.53 in fact that's exactly what I just + + align:start position:0% +9.53 in fact that's exactly what I just + + + align:start position:0% +9.53 in fact that's exactly what I just +uh was showing down here for the depth + + align:start position:0% +uh was showing down here for the depth + + + align:start position:0% +uh was showing down here for the depth +rate U so we have that equation the rate + + align:start position:0% +rate U so we have that equation the rate + + + align:start position:0% +rate U so we have that equation the rate +is just the sticking coefficient times + + align:start position:0% +is just the sticking coefficient times + + + align:start position:0% +is just the sticking coefficient times +the flux divided by n we need to do um a + + align:start position:0% +the flux divided by n we need to do um a + + + align:start position:0% +the flux divided by n we need to do um a +little bit bit of conversion here uh to + + align:start position:0% +little bit bit of conversion here uh to + + + align:start position:0% +little bit bit of conversion here uh to +get ourselves from grams per cubic + + align:start position:0% +get ourselves from grams per cubic + + + align:start position:0% +get ourselves from grams per cubic +centimeter into molecule and the way we + + align:start position:0% +centimeter into molecule and the way we + + + align:start position:0% +centimeter into molecule and the way we +do that is we take the density of S2 + + align:start position:0% +do that is we take the density of S2 + + + align:start position:0% +do that is we take the density of S2 +being 2.27 G per cubic cm we multiply + + align:start position:0% +being 2.27 G per cubic cm we multiply + + + align:start position:0% +being 2.27 G per cubic cm we multiply +that by alad's number number uh divided + + align:start position:0% +that by alad's number number uh divided + + + align:start position:0% +that by alad's number number uh divided +by the number of GRS per mole of + + align:start position:0% +by the number of GRS per mole of + + + align:start position:0% +by the number of GRS per mole of +si2 um so we need to do a little + + align:start position:0% +si2 um so we need to do a little + + + align:start position:0% +si2 um so we need to do a little +conversion to convert this density of + + align:start position:0% +conversion to convert this density of + + + align:start position:0% +conversion to convert this density of +grams per cubic centimeter into a number + + align:start position:0% +grams per cubic centimeter into a number + + + align:start position:0% +grams per cubic centimeter into a number +of molecules per cubic centimeter for SI + + align:start position:0% +of molecules per cubic centimeter for SI + + + align:start position:0% +of molecules per cubic centimeter for SI +of 2 so you get 2 * 10 22 molecules um + + align:start position:0% +of 2 so you get 2 * 10 22 molecules um + + + align:start position:0% +of 2 so you get 2 * 10 22 molecules um +of + + align:start position:0% +of + + + align:start position:0% +of +sio2 those units per cubic + + align:start position:0% +sio2 those units per cubic + + + align:start position:0% +sio2 those units per cubic +centimeter and then you just use the + + align:start position:0% +centimeter and then you just use the + + + align:start position:0% +centimeter and then you just use the +simple formula the rate is just sticking + + align:start position:0% +simple formula the rate is just sticking + + + align:start position:0% +simple formula the rate is just sticking +coefficient times the flux the maximum + + align:start position:0% +coefficient times the flux the maximum + + + align:start position:0% +coefficient times the flux the maximum +flux Over N you plug in the numbers you + + align:start position:0% +flux Over N you plug in the numbers you + + + align:start position:0% +flux Over N you plug in the numbers you +were given and you get about something + + align:start position:0% +were given and you get about something + + + align:start position:0% +were given and you get about something +like + + align:start position:0% +like + + + align:start position:0% +like +.23 microns uh 023 microns per minute um + + align:start position:0% +.23 microns uh 023 microns per minute um + + + align:start position:0% +.23 microns uh 023 microns per minute um +but now if you had a deposition on a + + align:start position:0% +but now if you had a deposition on a + + + align:start position:0% +but now if you had a deposition on a +non-f flat surface if you had a trench + + align:start position:0% +non-f flat surface if you had a trench + + + align:start position:0% +non-f flat surface if you had a trench +or something like that on the side wall + + align:start position:0% +or something like that on the side wall + + + align:start position:0% +or something like that on the side wall +for example the local depth rate would + + align:start position:0% +for example the local depth rate would + + + align:start position:0% +for example the local depth rate would +be less so this gives you a maximum a + + align:start position:0% +be less so this gives you a maximum a + + + align:start position:0% +be less so this gives you a maximum a +rough idea of a + + align:start position:0% +rough idea of a + + + align:start position:0% +rough idea of a +maximum um so it just gives you uh we'll + + align:start position:0% +maximum um so it just gives you uh we'll + + + align:start position:0% +maximum um so it just gives you uh we'll +we'll talk later about Speedy + + align:start position:0% +we'll talk later about Speedy + + + align:start position:0% +we'll talk later about Speedy +simulations more complex topographies + + align:start position:0% +simulations more complex topographies + + + align:start position:0% +simulations more complex topographies +but it gives you a rough idea of how you + + align:start position:0% +but it gives you a rough idea of how you + + + align:start position:0% +but it gives you a rough idea of how you +can uh model this simple type of process + + align:start position:0% + + + + align:start position:0% + +okay um let's go on to slide 20 and we + + align:start position:0% +okay um let's go on to slide 20 and we + + + align:start position:0% +okay um let's go on to slide 20 and we +we'll give us some more examples now + + align:start position:0% +we'll give us some more examples now + + + align:start position:0% +we'll give us some more examples now +we're going to do PVD um so we'd already + + align:start position:0% +we're going to do PVD um so we'd already + + + align:start position:0% +we're going to do PVD um so we'd already +talked about physical vapor deposition + + align:start position:0% +talked about physical vapor deposition + + + align:start position:0% +talked about physical vapor deposition +systems we said there could be DC or RF + + align:start position:0% +systems we said there could be DC or RF + + + align:start position:0% +systems we said there could be DC or RF +sputtering or + + align:start position:0% +sputtering or + + + align:start position:0% +sputtering or +evaporation uh typically um ions do not + + align:start position:0% +evaporation uh typically um ions do not + + + align:start position:0% +evaporation uh typically um ions do not +play a significant role in these kind of + + align:start position:0% +play a significant role in these kind of + + + align:start position:0% +play a significant role in these kind of +PVD systems most of the time so the + + align:start position:0% +PVD systems most of the time so the + + + align:start position:0% +PVD systems most of the time so the +modeling of simple PVD is very much + + align:start position:0% +modeling of simple PVD is very much + + + align:start position:0% +modeling of simple PVD is very much +analogous to lpcvd the parameters of + + align:start position:0% +analogous to lpcvd the parameters of + + + align:start position:0% +analogous to lpcvd the parameters of +different + + align:start position:0% +different + + + align:start position:0% +different +though um so here's an example of a + + align:start position:0% +though um so here's an example of a + + + align:start position:0% +though um so here's an example of a +simple um DC uh um sputtering system + + align:start position:0% +simple um DC uh um sputtering system + + + align:start position:0% +simple um DC uh um sputtering system +which we talked about a couple of + + align:start position:0% +which we talked about a couple of + + + align:start position:0% +which we talked about a couple of +lectures ago and these are the processes + + align:start position:0% +lectures ago and these are the processes + + + align:start position:0% +lectures ago and these are the processes +uh that go on so just like lpcvd we can + + align:start position:0% +uh that go on so just like lpcvd we can + + + align:start position:0% +uh that go on so just like lpcvd we can +say a rate any point on the surface is a + + align:start position:0% +say a rate any point on the surface is a + + + align:start position:0% +say a rate any point on the surface is a +sticking coefficient times the flux uh + + align:start position:0% +sticking coefficient times the flux uh + + + align:start position:0% +sticking coefficient times the flux uh +the total deposi of flux divided by the + + align:start position:0% +the total deposi of flux divided by the + + + align:start position:0% +the total deposi of flux divided by the +density however the the key difference + + align:start position:0% +density however the the key difference + + + align:start position:0% +density however the the key difference +is the sticking coefficient sfc and the + + align:start position:0% +is the sticking coefficient sfc and the + + + align:start position:0% +is the sticking coefficient sfc and the +arrival angle distribution cosine Theta + + align:start position:0% +arrival angle distribution cosine Theta + + + align:start position:0% +arrival angle distribution cosine Theta +the N will be very different between + + align:start position:0% +the N will be very different between + + + align:start position:0% +the N will be very different between +lpcvd and P PVD systems and that's where + + align:start position:0% +lpcvd and P PVD systems and that's where + + + align:start position:0% +lpcvd and P PVD systems and that's where +the real differences um tend to come + + align:start position:0% + + + + align:start position:0% + +about um there is one other type of + + align:start position:0% +about um there is one other type of + + + align:start position:0% +about um there is one other type of +system for PVD though where you do have + + align:start position:0% +system for PVD though where you do have + + + align:start position:0% +system for PVD though where you do have +to pay attention to a little more + + align:start position:0% +to pay attention to a little more + + + align:start position:0% +to pay attention to a little more +complex processes then you would an + + align:start position:0% +complex processes then you would an + + + align:start position:0% +complex processes then you would an +lpcvd and that's shown on slide 21 when + + align:start position:0% +lpcvd and that's shown on slide 21 when + + + align:start position:0% +lpcvd and that's shown on slide 21 when +you have ionized pbd we did talk about + + align:start position:0% +you have ionized pbd we did talk about + + + align:start position:0% +you have ionized pbd we did talk about +the case uh where we um yeah systems + + align:start position:0% +the case uh where we um yeah systems + + + align:start position:0% +the case uh where we um yeah systems +that are more + + align:start position:0% +that are more + + + align:start position:0% +that are more +complex uh this because ions and + + align:start position:0% +complex uh this because ions and + + + align:start position:0% +complex uh this because ions and +neutrals both play a role here's an + + align:start position:0% +neutrals both play a role here's an + + + align:start position:0% +neutrals both play a role here's an +example of an ionized PVD system so you + + align:start position:0% +example of an ionized PVD system so you + + + align:start position:0% +example of an ionized PVD system so you +have sputtering uh of aluminum coming + + align:start position:0% +have sputtering uh of aluminum coming + + + align:start position:0% +have sputtering uh of aluminum coming +off this target but then you have an + + align:start position:0% +off this target but then you have an + + + align:start position:0% +off this target but then you have an +additional in addition to that um you + + align:start position:0% +additional in addition to that um you + + + align:start position:0% +additional in addition to that um you +have uh a coil that goes around that + + align:start position:0% +have uh a coil that goes around that + + + align:start position:0% +have uh a coil that goes around that +ionizes the aluminum as it comes off now + + align:start position:0% +ionizes the aluminum as it comes off now + + + align:start position:0% +ionizes the aluminum as it comes off now +you have aluminum ions that are being a + + align:start position:0% +you have aluminum ions that are being a + + + align:start position:0% +you have aluminum ions that are being a +large density of aluminum ions that are + + align:start position:0% +large density of aluminum ions that are + + + align:start position:0% +large density of aluminum ions that are +being created and then these can be + + align:start position:0% +being created and then these can be + + + align:start position:0% +being created and then these can be +accelerated towards the + + align:start position:0% +accelerated towards the + + + align:start position:0% +accelerated towards the +substrate so um this is not that + + align:start position:0% +substrate so um this is not that + + + align:start position:0% +substrate so um this is not that +uncommon for metal deposition so you you + + align:start position:0% +uncommon for metal deposition so you you + + + align:start position:0% +uncommon for metal deposition so you you +have aluminum or maybe titanium ions + + align:start position:0% +have aluminum or maybe titanium ions + + + align:start position:0% +have aluminum or maybe titanium ions +will be present therefore when you have + + align:start position:0% +will be present therefore when you have + + + align:start position:0% +will be present therefore when you have +ions you do have to take into account + + align:start position:0% +ions you do have to take into account + + + align:start position:0% +ions you do have to take into account +sputtering and other processes that will + + align:start position:0% +sputtering and other processes that will + + + align:start position:0% +sputtering and other processes that will +not be present uh in lpcvd or the + + align:start position:0% +not be present uh in lpcvd or the + + + align:start position:0% +not be present uh in lpcvd or the +simpler P PVD systems so ionized PVD + + align:start position:0% +simpler P PVD systems so ionized PVD + + + align:start position:0% +simpler P PVD systems so ionized PVD +inductively coupled ionized PVD is a + + align:start position:0% +inductively coupled ionized PVD is a + + + align:start position:0% +inductively coupled ionized PVD is a +little bit more complicated uh to model + + align:start position:0% +little bit more complicated uh to model + + + align:start position:0% +little bit more complicated uh to model +just more bookkeeping in the + + align:start position:0% + + + + align:start position:0% + +equations here's an example in fact on + + align:start position:0% +equations here's an example in fact on + + + align:start position:0% +equations here's an example in fact on +slide 22 if we do ionize pbd of all the + + align:start position:0% +slide 22 if we do ionize pbd of all the + + + align:start position:0% +slide 22 if we do ionize pbd of all the +different fluxes that really do need to + + align:start position:0% +different fluxes that really do need to + + + align:start position:0% +different fluxes that really do need to +be taken into account and you see we + + align:start position:0% +be taken into account and you see we + + + align:start position:0% +be taken into account and you see we +have yes on all of them the direct + + align:start position:0% +have yes on all of them the direct + + + align:start position:0% +have yes on all of them the direct +neutrals the direct ions the emitted the + + align:start position:0% +neutrals the direct ions the emitted the + + + align:start position:0% +neutrals the direct ions the emitted the +only one we don't we're not taking into + + align:start position:0% +only one we don't we're not taking into + + + align:start position:0% +only one we don't we're not taking into +account in this case because we're + + align:start position:0% +account in this case because we're + + + align:start position:0% +account in this case because we're +assuming the wafer is low enough + + align:start position:0% +assuming the wafer is low enough + + + align:start position:0% +assuming the wafer is low enough +temperature that we can ignore surface + + align:start position:0% +temperature that we can ignore surface + + + align:start position:0% +temperature that we can ignore surface +diffusion uh but all these fluxes um + + align:start position:0% +diffusion uh but all these fluxes um + + + align:start position:0% +diffusion uh but all these fluxes um +would need to be taken into account and + + align:start position:0% +would need to be taken into account and + + + align:start position:0% +would need to be taken into account and +if you do that um shown here on slide 22 + + align:start position:0% +if you do that um shown here on slide 22 + + + align:start position:0% +if you do that um shown here on slide 22 +this is the example of the possible + + align:start position:0% +this is the example of the possible + + + align:start position:0% +this is the example of the possible +terms that could be included in your + + align:start position:0% +terms that could be included in your + + + align:start position:0% +terms that could be included in your +model your computer model so you would + + align:start position:0% +model your computer model so you would + + + align:start position:0% +model your computer model so you would +say that the rate at any point I depends + + align:start position:0% +say that the rate at any point I depends + + + align:start position:0% +say that the rate at any point I depends +on the sticking coefficient times the + + align:start position:0% +on the sticking coefficient times the + + + align:start position:0% +on the sticking coefficient times the +the the direct maximum deposited uh flux + + align:start position:0% +the the direct maximum deposited uh flux + + + align:start position:0% +the the direct maximum deposited uh flux +where FD includes the direct and the + + align:start position:0% +where FD includes the direct and the + + + align:start position:0% +where FD includes the direct and the +redeposited neutral + + align:start position:0% +redeposited neutral + + + align:start position:0% +redeposited neutral +fluxes plus F + + align:start position:0% +fluxes plus F + + + align:start position:0% +fluxes plus F +subi uh includes the direct redeposit + + align:start position:0% +subi uh includes the direct redeposit + + + align:start position:0% +subi uh includes the direct redeposit +and ion induced flux so there's the F + + align:start position:0% +and ion induced flux so there's the F + + + align:start position:0% +and ion induced flux so there's the F +subi and again F subi doesn't have a + + align:start position:0% +subi and again F subi doesn't have a + + + align:start position:0% +subi and again F subi doesn't have a +sticking coefficient Associated we say + + align:start position:0% +sticking coefficient Associated we say + + + align:start position:0% +sticking coefficient Associated we say +for ions we include all of them we say + + align:start position:0% +for ions we include all of them we say + + + align:start position:0% +for ions we include all of them we say +they just come down and + + align:start position:0% +they just come down and + + + align:start position:0% +they just come down and +stick um and then you have a minus those + + align:start position:0% +stick um and then you have a minus those + + + align:start position:0% +stick um and then you have a minus those +that are sputtered off you have a + + align:start position:0% +that are sputtered off you have a + + + align:start position:0% +that are sputtered off you have a +sputtered + + align:start position:0% +sputtered + + + align:start position:0% +sputtered +term um plus a redeposited term so this + + align:start position:0% +term um plus a redeposited term so this + + + align:start position:0% +term um plus a redeposited term so this +FD models the redeposition due to + + align:start position:0% +FD models the redeposition due to + + + align:start position:0% +FD models the redeposition due to +sputtering so you have extra terms here + + align:start position:0% +sputtering so you have extra terms here + + + align:start position:0% +sputtering so you have extra terms here +uh divided by the density end so you + + align:start position:0% +uh divided by the density end so you + + + align:start position:0% +uh divided by the density end so you +have a positive term and a negative + + align:start position:0% +have a positive term and a negative + + + align:start position:0% +have a positive term and a negative +terms some of which uh depending on the + + align:start position:0% +terms some of which uh depending on the + + + align:start position:0% +terms some of which uh depending on the +point I and the surface uh and the + + align:start position:0% +point I and the surface uh and the + + + align:start position:0% +point I and the surface uh and the +angles involved um May cancel each other + + align:start position:0% + + + + align:start position:0% + +out okay so those are some + + align:start position:0% +out okay so those are some + + + align:start position:0% +out okay so those are some +basic bookkeeping models let's I want to + + align:start position:0% +basic bookkeeping models let's I want to + + + align:start position:0% +basic bookkeeping models let's I want to +actually do some examples of the values + + align:start position:0% +actually do some examples of the values + + + align:start position:0% +actually do some examples of the values +of these parameters um that are useful + + align:start position:0% +of these parameters um that are useful + + + align:start position:0% +of these parameters um that are useful +for specific systems and so far we've + + align:start position:0% +for specific systems and so far we've + + + align:start position:0% +for specific systems and so far we've +talked about two parameters that that + + align:start position:0% +talked about two parameters that that + + + align:start position:0% +talked about two parameters that that +are most important the um n value which + + align:start position:0% +are most important the um n value which + + + align:start position:0% +are most important the um n value which +is the expon exponent in the cosine uh + + align:start position:0% +is the expon exponent in the cosine uh + + + align:start position:0% +is the expon exponent in the cosine uh +Theta to the N arrival angle + + align:start position:0% +Theta to the N arrival angle + + + align:start position:0% +Theta to the N arrival angle +distribution and the sticking + + align:start position:0% +distribution and the sticking + + + align:start position:0% +distribution and the sticking +coefficient s subc uh those are the two + + align:start position:0% +coefficient s subc uh those are the two + + + align:start position:0% +coefficient s subc uh those are the two +kind of most critical in in modeling + + align:start position:0% +kind of most critical in in modeling + + + align:start position:0% +kind of most critical in in modeling +simple systems so uh and there are a + + align:start position:0% +simple systems so uh and there are a + + + align:start position:0% +simple systems so uh and there are a +couple different model systems shown + + align:start position:0% +couple different model systems shown + + + align:start position:0% +couple different model systems shown +here on the top we're talking about + + align:start position:0% +here on the top we're talking about + + + align:start position:0% +here on the top we're talking about +sputter deposition either standard or + + align:start position:0% +sputter deposition either standard or + + + align:start position:0% +sputter deposition either standard or +ionized uh and evaporation so these are + + align:start position:0% +ionized uh and evaporation so these are + + + align:start position:0% +ionized uh and evaporation so these are +PVD systems in the bottom we have the um + + align:start position:0% +PVD systems in the bottom we have the um + + + align:start position:0% +PVD systems in the bottom we have the um +cvd uh systems so let's look at PVD Well + + align:start position:0% +cvd uh systems so let's look at PVD Well + + + align:start position:0% +cvd uh systems so let's look at PVD Well +Physical vapor deposition it tends to + + align:start position:0% +Physical vapor deposition it tends to + + + align:start position:0% +Physical vapor deposition it tends to +have much more vertical arrival angle + + align:start position:0% +have much more vertical arrival angle + + + align:start position:0% +have much more vertical arrival angle +distribution so the end value is Big + + align:start position:0% +distribution so the end value is Big + + + align:start position:0% +distribution so the end value is Big +right almost everything in PVD is coming + + align:start position:0% +right almost everything in PVD is coming + + + align:start position:0% +right almost everything in PVD is coming +straight down um certainly in + + align:start position:0% +straight down um certainly in + + + align:start position:0% +straight down um certainly in +evaporation you have very low pressure + + align:start position:0% +evaporation you have very low pressure + + + align:start position:0% +evaporation you have very low pressure +so you have line of sight even in + + align:start position:0% +so you have line of sight even in + + + align:start position:0% +so you have line of sight even in +sputtering we tend to have closer uh + + align:start position:0% +sputtering we tend to have closer uh + + + align:start position:0% +sputtering we tend to have closer uh +very uh anisotropic so for sputter + + align:start position:0% +very uh anisotropic so for sputter + + + align:start position:0% +very uh anisotropic so for sputter +deposition um depending you know you + + align:start position:0% +deposition um depending you know you + + + align:start position:0% +deposition um depending you know you +could have n equals up to five maybe uh + + align:start position:0% +could have n equals up to five maybe uh + + + align:start position:0% +could have n equals up to five maybe uh +if you're ionized you can get up into + + align:start position:0% +if you're ionized you can get up into + + + align:start position:0% +if you're ionized you can get up into +the uh the range of 50 or + + align:start position:0% +the uh the range of 50 or + + + align:start position:0% +the uh the range of 50 or +so so n is but in any case n is usually + + align:start position:0% +so so n is but in any case n is usually + + + align:start position:0% +so so n is but in any case n is usually +greater than one for pbd um um in in + + align:start position:0% +greater than one for pbd um um in in + + + align:start position:0% +greater than one for pbd um um in in +contrast CBD systems tend to have pretty + + align:start position:0% +contrast CBD systems tend to have pretty + + + align:start position:0% +contrast CBD systems tend to have pretty +much isotopic arrival angle um PVD again + + align:start position:0% +much isotopic arrival angle um PVD again + + + align:start position:0% +much isotopic arrival angle um PVD again +takes place your sputtering uh in a 10 + + align:start position:0% +takes place your sputtering uh in a 10 + + + align:start position:0% +takes place your sputtering uh in a 10 +Theus 5 tour or something or or 1 time + + align:start position:0% +Theus 5 tour or something or or 1 time + + + align:start position:0% +Theus 5 tour or something or or 1 time +10 minus 3 tour something like that um + + align:start position:0% +10 minus 3 tour something like that um + + + align:start position:0% +10 minus 3 tour something like that um +cvd uh usually much higher hundreds of + + align:start position:0% +cvd uh usually much higher hundreds of + + + align:start position:0% +cvd uh usually much higher hundreds of +millor uh 0.1 tour or something like + + align:start position:0% +millor uh 0.1 tour or something like + + + align:start position:0% +millor uh 0.1 tour or something like +that so you usually have higher pressure + + align:start position:0% +that so you usually have higher pressure + + + align:start position:0% +that so you usually have higher pressure +uh you have a lot of gas-based + + align:start position:0% +uh you have a lot of gas-based + + + align:start position:0% +uh you have a lot of gas-based +collisions that randomize things and + + align:start position:0% +collisions that randomize things and + + + align:start position:0% +collisions that randomize things and +mostly neutrals you don't usually in CV + + align:start position:0% +mostly neutrals you don't usually in CV + + + align:start position:0% +mostly neutrals you don't usually in CV +don't have many ions so n is usually one + + align:start position:0% +don't have many ions so n is usually one + + + align:start position:0% +don't have many ions so n is usually one +in CBD so the cosine Theta the N is is + + align:start position:0% +in CBD so the cosine Theta the N is is + + + align:start position:0% +in CBD so the cosine Theta the N is is +usually fairly + + align:start position:0% +usually fairly + + + align:start position:0% +usually fairly +isotropic uh what about PB pbd well the + + align:start position:0% +isotropic uh what about PB pbd well the + + + align:start position:0% +isotropic uh what about PB pbd well the +sticking coefficient in PVD tends to be + + align:start position:0% +sticking coefficient in PVD tends to be + + + align:start position:0% +sticking coefficient in PVD tends to be +close to one there really isn't much + + align:start position:0% +close to one there really isn't much + + + align:start position:0% +close to one there really isn't much +surface chemistry involved the aluminum + + align:start position:0% +surface chemistry involved the aluminum + + + align:start position:0% +surface chemistry involved the aluminum +or whatever it is that's being + + align:start position:0% +or whatever it is that's being + + + align:start position:0% +or whatever it is that's being +evaporated or sputtered usually comes + + align:start position:0% +evaporated or sputtered usually comes + + + align:start position:0% +evaporated or sputtered usually comes +down and pretty close to Sticks um there + + align:start position:0% +down and pretty close to Sticks um there + + + align:start position:0% +down and pretty close to Sticks um there +is a whole lot there can be but uh most + + align:start position:0% +is a whole lot there can be but uh most + + + align:start position:0% +is a whole lot there can be but uh most +of the time the atoms arrive and stick + + align:start position:0% +of the time the atoms arrive and stick + + + align:start position:0% +of the time the atoms arrive and stick +very very different though in the case + + align:start position:0% +very very different though in the case + + + align:start position:0% +very very different though in the case +of lpcvd look at lpcvd the sticking + + align:start position:0% +of lpcvd look at lpcvd the sticking + + + align:start position:0% +of lpcvd look at lpcvd the sticking +coefficients depending on what you're uh + + align:start position:0% +coefficients depending on what you're uh + + + align:start position:0% +coefficients depending on what you're uh +chemistry using if you're using a + + align:start position:0% +chemistry using if you're using a + + + align:start position:0% +chemistry using if you're using a +silicon source of silene you might have + + align:start position:0% +silicon source of silene you might have + + + align:start position:0% +silicon source of silene you might have +a sticking coefficient of 0.5 or 03 for + + align:start position:0% +a sticking coefficient of 0.5 or 03 for + + + align:start position:0% +a sticking coefficient of 0.5 or 03 for +teos we mentioned there's other ways of + + align:start position:0% +teos we mentioned there's other ways of + + + align:start position:0% +teos we mentioned there's other ways of +doing low temperature oxide not just + + align:start position:0% +doing low temperature oxide not just + + + align:start position:0% +doing low temperature oxide not just +with um Sil but uh this other um silicon + + align:start position:0% +with um Sil but uh this other um silicon + + + align:start position:0% +with um Sil but uh this other um silicon +sources um sticking coefficient is is + + align:start position:0% +sources um sticking coefficient is is + + + align:start position:0% +sources um sticking coefficient is is +can be much lower + + align:start position:0% +can be much lower + + + align:start position:0% +can be much lower +uh lpcvd tungsten or polysilicon you + + align:start position:0% +uh lpcvd tungsten or polysilicon you + + + align:start position:0% +uh lpcvd tungsten or polysilicon you +have much lower um sticking coefficients + + align:start position:0% +have much lower um sticking coefficients + + + align:start position:0% +have much lower um sticking coefficients +so very different from + + align:start position:0% +so very different from + + + align:start position:0% +so very different from +PVD that same chart is reproduced here + + align:start position:0% +PVD that same chart is reproduced here + + + align:start position:0% +PVD that same chart is reproduced here +again on slide 23 it's exact same chart + + align:start position:0% +again on slide 23 it's exact same chart + + + align:start position:0% +again on slide 23 it's exact same chart +I just wanted to reproduce it and talk a + + align:start position:0% +I just wanted to reproduce it and talk a + + + align:start position:0% +I just wanted to reproduce it and talk a +little bit more about the CBD saying + + align:start position:0% +little bit more about the CBD saying + + + align:start position:0% +little bit more about the CBD saying +that because they have surface chemistry + + align:start position:0% +that because they have surface chemistry + + + align:start position:0% +that because they have surface chemistry +um sticking coefficient much much less + + align:start position:0% +um sticking coefficient much much less + + + align:start position:0% +um sticking coefficient much much less +than one um and things often evaporate + + align:start position:0% +than one um and things often evaporate + + + align:start position:0% +than one um and things often evaporate +uh before they react what does this mean + + align:start position:0% +uh before they react what does this mean + + + align:start position:0% +uh before they react what does this mean +well just by looking at these numbers + + align:start position:0% +well just by looking at these numbers + + + align:start position:0% +well just by looking at these numbers +you know that CBD systems with their + + align:start position:0% +you know that CBD systems with their + + + align:start position:0% +you know that CBD systems with their +small sticking coefficients are going to + + align:start position:0% +small sticking coefficients are going to + + + align:start position:0% +small sticking coefficients are going to +tend to have more formal deposition if + + align:start position:0% +tend to have more formal deposition if + + + align:start position:0% +tend to have more formal deposition if +you want to cover a step and you want to + + align:start position:0% +you want to cover a step and you want to + + + align:start position:0% +you want to cover a step and you want to +cover it very conformally what does that + + align:start position:0% +cover it very conformally what does that + + + align:start position:0% +cover it very conformally what does that +mean that means the thickness along the + + align:start position:0% +mean that means the thickness along the + + + align:start position:0% +mean that means the thickness along the +flat part of the wafer is exactly equal + + align:start position:0% +flat part of the wafer is exactly equal + + + align:start position:0% +flat part of the wafer is exactly equal +to the thickness of the film along the + + align:start position:0% +to the thickness of the film along the + + + align:start position:0% +to the thickness of the film along the +uh the trench wall is exactly equal on + + align:start position:0% +uh the trench wall is exactly equal on + + + align:start position:0% +uh the trench wall is exactly equal on +the bottom it's just completely + + align:start position:0% +the bottom it's just completely + + + align:start position:0% +the bottom it's just completely +conformal in that case you probably want + + align:start position:0% +conformal in that case you probably want + + + align:start position:0% +conformal in that case you probably want +to use cvd now that may not be what you + + align:start position:0% +to use cvd now that may not be what you + + + align:start position:0% +to use cvd now that may not be what you +want but this is what we mean by + + align:start position:0% +want but this is what we mean by + + + align:start position:0% +want but this is what we mean by +conformal deposition that equal + + align:start position:0% +conformal deposition that equal + + + align:start position:0% +conformal deposition that equal +thickness and cvd tends to give you um + + align:start position:0% +thickness and cvd tends to give you um + + + align:start position:0% +thickness and cvd tends to give you um +more con + + align:start position:0% +more con + + + align:start position:0% +more con +conformality just because of this um + + align:start position:0% +conformality just because of this um + + + align:start position:0% +conformality just because of this um +sticking coefficient + + align:start position:0% +sticking coefficient + + + align:start position:0% +sticking coefficient +argument okay now I want to show some + + align:start position:0% +argument okay now I want to show some + + + align:start position:0% +argument okay now I want to show some +actual examples of simulations to + + align:start position:0% +actual examples of simulations to + + + align:start position:0% +actual examples of simulations to +convince you of of some of these things + + align:start position:0% +convince you of of some of these things + + + align:start position:0% +convince you of of some of these things +that we've been talking about and we're + + align:start position:0% +that we've been talking about and we're + + + align:start position:0% +that we've been talking about and we're +going to vary the parameters in and s + + align:start position:0% +going to vary the parameters in and s + + + align:start position:0% +going to vary the parameters in and s +subc in the model uh so on on slide 25 + + align:start position:0% +subc in the model uh so on on slide 25 + + + align:start position:0% +subc in the model uh so on on slide 25 +these are topography simulations that + + align:start position:0% +these are topography simulations that + + + align:start position:0% +these are topography simulations that +are uh taken from the simulator that I + + align:start position:0% +are uh taken from the simulator that I + + + align:start position:0% +are uh taken from the simulator that I +mentioned called speedy again that's a + + align:start position:0% +mentioned called speedy again that's a + + + align:start position:0% +mentioned called speedy again that's a +topography simulator you cannot simulate + + align:start position:0% +topography simulator you cannot simulate + + + align:start position:0% +topography simulator you cannot simulate +this type of topography uh in sueme 4 + + align:start position:0% +this type of topography uh in sueme 4 + + + align:start position:0% +this type of topography uh in sueme 4 +Supreme 4 doesn't doesn't do topography + + align:start position:0% +Supreme 4 doesn't doesn't do topography + + + align:start position:0% +Supreme 4 doesn't doesn't do topography +um so this is an example of you're doing + + align:start position:0% +um so this is an example of you're doing + + + align:start position:0% +um so this is an example of you're doing +a deposition uh using lpcvd of si2 and + + align:start position:0% +a deposition uh using lpcvd of si2 and + + + align:start position:0% +a deposition uh using lpcvd of si2 and +you originally have a trench that you + + align:start position:0% +you originally have a trench that you + + + align:start position:0% +you originally have a trench that you +have etched that looks like this and + + align:start position:0% +have etched that looks like this and + + + align:start position:0% +have etched that looks like this and +each contour line it's a little bit hard + + align:start position:0% +each contour line it's a little bit hard + + + align:start position:0% +each contour line it's a little bit hard +to see uh but each contour line + + align:start position:0% +to see uh but each contour line + + + align:start position:0% +to see uh but each contour line +represents the deposited topography uh + + align:start position:0% +represents the deposited topography uh + + + align:start position:0% +represents the deposited topography uh +at different time intervals so this + + align:start position:0% +at different time intervals so this + + + align:start position:0% +at different time intervals so this +might be after you know each one might + + align:start position:0% +might be after you know each one might + + + align:start position:0% +might be after you know each one might +be after a one minute interval so you + + align:start position:0% +be after a one minute interval so you + + + align:start position:0% +be after a one minute interval so you +get an idea of how the topography + + align:start position:0% +get an idea of how the topography + + + align:start position:0% +get an idea of how the topography +develops over time + + align:start position:0% +develops over time + + + align:start position:0% +develops over time +um in this particular example we did a + + align:start position:0% +um in this particular example we did a + + + align:start position:0% +um in this particular example we did a +speedy simulation with a sticking + + align:start position:0% +speedy simulation with a sticking + + + align:start position:0% +speedy simulation with a sticking +coefficient of one um actually the + + align:start position:0% +coefficient of one um actually the + + + align:start position:0% +coefficient of one um actually the +sticking Co efficient of one is probably + + align:start position:0% +sticking Co efficient of one is probably + + + align:start position:0% +sticking Co efficient of one is probably +more typical of PVD so this really + + align:start position:0% +more typical of PVD so this really + + + align:start position:0% +more typical of PVD so this really +should be PVD uh in your mind um and all + + align:start position:0% +should be PVD uh in your mind um and all + + + align:start position:0% +should be PVD uh in your mind um and all +we did mathematically is vary the + + align:start position:0% +we did mathematically is vary the + + + align:start position:0% +we did mathematically is vary the +arrival angle distribution uh the N + + align:start position:0% +arrival angle distribution uh the N + + + align:start position:0% +arrival angle distribution uh the N +value so this is for n equals 1 that's + + align:start position:0% +value so this is for n equals 1 that's + + + align:start position:0% +value so this is for n equals 1 that's +isotropic here's for n equals 3 somewhat + + align:start position:0% +isotropic here's for n equals 3 somewhat + + + align:start position:0% +isotropic here's for n equals 3 somewhat +an isotropic N equals + + align:start position:0% +an isotropic N equals + + + align:start position:0% +an isotropic N equals +10 um so let's look at this even for + + align:start position:0% +10 um so let's look at this even for + + + align:start position:0% +10 um so let's look at this even for +isot Tropic arrival distribution because + + align:start position:0% +isot Tropic arrival distribution because + + + align:start position:0% +isot Tropic arrival distribution because +of shadowing effects and things uh + + align:start position:0% +of shadowing effects and things uh + + + align:start position:0% +of shadowing effects and things uh +conformal coverage is not achieved with + + align:start position:0% +conformal coverage is not achieved with + + + align:start position:0% +conformal coverage is not achieved with +the sticking coefficient once that is + + align:start position:0% +the sticking coefficient once that is + + + align:start position:0% +the sticking coefficient once that is +what do I mean by conformal coverage is + + align:start position:0% +what do I mean by conformal coverage is + + + align:start position:0% +what do I mean by conformal coverage is +not achieved well the thickness of the + + align:start position:0% +not achieved well the thickness of the + + + align:start position:0% +not achieved well the thickness of the +film here at the surface on the flat + + align:start position:0% +film here at the surface on the flat + + + align:start position:0% +film here at the surface on the flat +portions is not equal to the thickness + + align:start position:0% +portions is not equal to the thickness + + + align:start position:0% +portions is not equal to the thickness +um uh along the uh the sidewall the + + align:start position:0% +um uh along the uh the sidewall the + + + align:start position:0% +um uh along the uh the sidewall the +sidewall is thinner not even for n + + align:start position:0% +sidewall is thinner not even for n + + + align:start position:0% +sidewall is thinner not even for n +equals + + align:start position:0% +equals + + + align:start position:0% +equals +1 um and so for this what this implies + + align:start position:0% +1 um and so for this what this implies + + + align:start position:0% +1 um and so for this what this implies +that if you have a sticking Co efficient + + align:start position:0% +that if you have a sticking Co efficient + + + align:start position:0% +that if you have a sticking Co efficient +s subc uh equal to one uh the geometry + + align:start position:0% +s subc uh equal to one uh the geometry + + + align:start position:0% +s subc uh equal to one uh the geometry +and line of sight issues are still going + + align:start position:0% +and line of sight issues are still going + + + align:start position:0% +and line of sight issues are still going +to be very are going to be very + + align:start position:0% +to be very are going to be very + + + align:start position:0% +to be very are going to be very +important so for example for PVD you + + align:start position:0% +important so for example for PVD you + + + align:start position:0% +important so for example for PVD you +really need to take into account the + + align:start position:0% +really need to take into account the + + + align:start position:0% +really need to take into account the +geometry of what you're depositing into + + align:start position:0% +geometry of what you're depositing into + + + align:start position:0% +geometry of what you're depositing into +um look at this one for n equals 10 you + + align:start position:0% +um look at this one for n equals 10 you + + + align:start position:0% +um look at this one for n equals 10 you +almost get no deposition on the sidewall + + align:start position:0% +almost get no deposition on the sidewall + + + align:start position:0% +almost get no deposition on the sidewall +you get quite a bit on the bottom and + + align:start position:0% +you get quite a bit on the bottom and + + + align:start position:0% +you get quite a bit on the bottom and +notice this is for an aspect ratio + + align:start position:0% +notice this is for an aspect ratio + + + align:start position:0% +notice this is for an aspect ratio +that's pretty pretty gentle I mean + + align:start position:0% +that's pretty pretty gentle I mean + + + align:start position:0% +that's pretty pretty gentle I mean +pretty not that sophisticated this + + align:start position:0% +pretty not that sophisticated this + + + align:start position:0% +pretty not that sophisticated this +aspect ratio of3 what does that mean + + align:start position:0% +aspect ratio of3 what does that mean + + + align:start position:0% +aspect ratio of3 what does that mean +that means the the trend inch is three + + align:start position:0% +that means the the trend inch is three + + + align:start position:0% +that means the the trend inch is three +times wider than it is tall so it's only + + align:start position:0% +times wider than it is tall so it's only + + + align:start position:0% +times wider than it is tall so it's only +one micron tall but it's three microns + + align:start position:0% +one micron tall but it's three microns + + + align:start position:0% +one micron tall but it's three microns +wide and you're already seeing these + + align:start position:0% +wide and you're already seeing these + + + align:start position:0% +wide and you're already seeing these +sort of these non-c conformality types + + align:start position:0% +sort of these non-c conformality types + + + align:start position:0% +sort of these non-c conformality types +of of of issues so this is what you'd + + align:start position:0% +of of of issues so this is what you'd + + + align:start position:0% +of of of issues so this is what you'd +expect from pbd with these + + align:start position:0% +expect from pbd with these + + + align:start position:0% +expect from pbd with these +parameters just to remind you on page 26 + + align:start position:0% +parameters just to remind you on page 26 + + + align:start position:0% +parameters just to remind you on page 26 +what we're talking about the N equals 1 + + align:start position:0% +what we're talking about the N equals 1 + + + align:start position:0% +what we're talking about the N equals 1 +the flux as a function of angle looks + + align:start position:0% +the flux as a function of angle looks + + + align:start position:0% +the flux as a function of angle looks +like this n equals 3 looks something it + + align:start position:0% +like this n equals 3 looks something it + + + align:start position:0% +like this n equals 3 looks something it +it cuts out after about 60° and the Nal + + align:start position:0% +it cuts out after about 60° and the Nal + + + align:start position:0% +it cuts out after about 60° and the Nal +15 cuts out after about 30° so this is + + align:start position:0% +15 cuts out after about 30° so this is + + + align:start position:0% +15 cuts out after about 30° so this is +close to N equal 15 so when I was + + align:start position:0% +close to N equal 15 so when I was + + + align:start position:0% +close to N equal 15 so when I was +getting more than about 30° so from a + + align:start position:0% +getting more than about 30° so from a + + + align:start position:0% +getting more than about 30° so from a +normal you can imagine going onto this + + align:start position:0% +normal you can imagine going onto this + + + align:start position:0% +normal you can imagine going onto this +surface there is not a whole lot of flux + + align:start position:0% +surface there is not a whole lot of flux + + + align:start position:0% +surface there is not a whole lot of flux +um and and that's the problem that's why + + align:start position:0% +um and and that's the problem that's why + + + align:start position:0% +um and and that's the problem that's why +we're getting such low um um uh with + + align:start position:0% +we're getting such low um um uh with + + + align:start position:0% +we're getting such low um um uh with +with a sticking coefficient of one uh + + align:start position:0% +with a sticking coefficient of one uh + + + align:start position:0% +with a sticking coefficient of one uh +you're getting such low deposition along + + align:start position:0% +you're getting such low deposition along + + + align:start position:0% +you're getting such low deposition along +those vertical + + align:start position:0% + + + + align:start position:0% + +walls let's let's um let's uh make it a + + align:start position:0% +walls let's let's um let's uh make it a + + + align:start position:0% +walls let's let's um let's uh make it a +little more difficult even uh let's take + + align:start position:0% +little more difficult even uh let's take + + + align:start position:0% +little more difficult even uh let's take +an aspect ratio we're going to take + + align:start position:0% +an aspect ratio we're going to take + + + align:start position:0% +an aspect ratio we're going to take +those same parameters so the same + + align:start position:0% +those same parameters so the same + + + align:start position:0% +those same parameters so the same +parameters that we just uh just saw + + align:start position:0% +parameters that we just uh just saw + + + align:start position:0% +parameters that we just uh just saw +sticking coefficient equals one here on + + align:start position:0% +sticking coefficient equals one here on + + + align:start position:0% +sticking coefficient equals one here on +slide + + align:start position:0% +slide + + + align:start position:0% +slide +27 um but now I've increased the aspect + + align:start position:0% +27 um but now I've increased the aspect + + + align:start position:0% +27 um but now I've increased the aspect +ratio from3 up to 1.3 or 1.25 so now the + + align:start position:0% +ratio from3 up to 1.3 or 1.25 so now the + + + align:start position:0% +ratio from3 up to 1.3 or 1.25 so now the +trench uh is 1.25 times tall compared to + + align:start position:0% +trench uh is 1.25 times tall compared to + + + align:start position:0% +trench uh is 1.25 times tall compared to +what it is wide so it's much taller than + + align:start position:0% +what it is wide so it's much taller than + + + align:start position:0% +what it is wide so it's much taller than +it is wide just the opposite of what I + + align:start position:0% +it is wide just the opposite of what I + + + align:start position:0% +it is wide just the opposite of what I +had + + align:start position:0% + + + + align:start position:0% + +before um now what you do once what you + + align:start position:0% +before um now what you do once what you + + + align:start position:0% +before um now what you do once what you +you see again is less deposition on the + + align:start position:0% +you see again is less deposition on the + + + align:start position:0% +you see again is less deposition on the +sidewalks here this is um uh a here on + + align:start position:0% +sidewalks here this is um uh a here on + + + align:start position:0% +sidewalks here this is um uh a here on +the left is for isotropic arrival n + + align:start position:0% +the left is for isotropic arrival n + + + align:start position:0% +the left is for isotropic arrival n +equals 1 and B is for anisotropic n + + align:start position:0% +equals 1 and B is for anisotropic n + + + align:start position:0% +equals 1 and B is for anisotropic n +equals 10 so let's look at the N equals + + align:start position:0% +equals 10 so let's look at the N equals + + + align:start position:0% +equals 10 so let's look at the N equals +1 well what's happening you see um for + + align:start position:0% +1 well what's happening you see um for + + + align:start position:0% +1 well what's happening you see um for +isotropic arrival angle you're not + + align:start position:0% +isotropic arrival angle you're not + + + align:start position:0% +isotropic arrival angle you're not +getting much material down at the bottom + + align:start position:0% +getting much material down at the bottom + + + align:start position:0% +getting much material down at the bottom +of that narrow trench um because again + + align:start position:0% +of that narrow trench um because again + + + align:start position:0% +of that narrow trench um because again +it's it's reasonably isotropic arrival + + align:start position:0% +it's it's reasonably isotropic arrival + + + align:start position:0% +it's it's reasonably isotropic arrival +you're getting material coming deposited + + align:start position:0% +you're getting material coming deposited + + + align:start position:0% +you're getting material coming deposited +along here and you're sort of developing + + align:start position:0% +along here and you're sort of developing + + + align:start position:0% +along here and you're sort of developing +these lobes up at the top uh which if + + align:start position:0% +these lobes up at the top uh which if + + + align:start position:0% +these lobes up at the top uh which if +you had a narrow enough trench you can + + align:start position:0% +you had a narrow enough trench you can + + + align:start position:0% +you had a narrow enough trench you can +imagine these might cut off and you end + + align:start position:0% +imagine these might cut off and you end + + + align:start position:0% +imagine these might cut off and you end +up with a big void um if you're more an + + align:start position:0% +up with a big void um if you're more an + + + align:start position:0% +up with a big void um if you're more an +isotropic you're coming down straight so + + align:start position:0% +isotropic you're coming down straight so + + + align:start position:0% +isotropic you're coming down straight so +you do get quite a bit at the bottom of + + align:start position:0% +you do get quite a bit at the bottom of + + + align:start position:0% +you do get quite a bit at the bottom of +the trench you get quite a bit on the + + align:start position:0% +the trench you get quite a bit on the + + + align:start position:0% +the trench you get quite a bit on the +flats but you get nothing on the very + + align:start position:0% +flats but you get nothing on the very + + + align:start position:0% +flats but you get nothing on the very +little on the + + align:start position:0% +little on the + + + align:start position:0% +little on the +sidewalls so as you go to narrow and + + align:start position:0% +sidewalls so as you go to narrow and + + + align:start position:0% +sidewalls so as you go to narrow and +narrow trenches you can imagine you + + align:start position:0% +narrow trenches you can imagine you + + + align:start position:0% +narrow trenches you can imagine you +might end up not being able to fill them + + align:start position:0% +might end up not being able to fill them + + + align:start position:0% +might end up not being able to fill them +at all you might end up with voiding if + + align:start position:0% +at all you might end up with voiding if + + + align:start position:0% +at all you might end up with voiding if +you have a sticking coefficient of one + + align:start position:0% +you have a sticking coefficient of one + + + align:start position:0% +you have a sticking coefficient of one +is what really what this boils down to + + align:start position:0% +is what really what this boils down to + + + align:start position:0% +is what really what this boils down to +for high aspect ratio trenches + + align:start position:0% +for high aspect ratio trenches + + + align:start position:0% +for high aspect ratio trenches +so if you if you want to avoid that + + align:start position:0% +so if you if you want to avoid that + + + align:start position:0% +so if you if you want to avoid that +let's say you really want to the the + + align:start position:0% +let's say you really want to the the + + + align:start position:0% +let's say you really want to the the +purpose of your deposition is to fill + + align:start position:0% +purpose of your deposition is to fill + + + align:start position:0% +purpose of your deposition is to fill +this trench you haven't done a very good + + align:start position:0% +this trench you haven't done a very good + + + align:start position:0% +this trench you haven't done a very good +job in this case and you're not going to + + align:start position:0% +job in this case and you're not going to + + + align:start position:0% +job in this case and you're not going to +do a good job in this case at all you're + + align:start position:0% +do a good job in this case at all you're + + + align:start position:0% +do a good job in this case at all you're +going to pinch it off what do we need to + + align:start position:0% +going to pinch it off what do we need to + + + align:start position:0% +going to pinch it off what do we need to +do well we need to lower the sticking + + align:start position:0% +do well we need to lower the sticking + + + align:start position:0% +do well we need to lower the sticking +coefficient we need to have not such a + + align:start position:0% +coefficient we need to have not such a + + + align:start position:0% +coefficient we need to have not such a +line of sight distribution we need to + + align:start position:0% +line of sight distribution we need to + + + align:start position:0% +line of sight distribution we need to +for atams to come down come in here and + + align:start position:0% +for atams to come down come in here and + + + align:start position:0% +for atams to come down come in here and +not stick and move around so they can + + align:start position:0% +not stick and move around so they can + + + align:start position:0% +not stick and move around so they can +eventually cover these + + align:start position:0% +eventually cover these + + + align:start position:0% +eventually cover these +sidewalls and that's exactly what is + + align:start position:0% +sidewalls and that's exactly what is + + + align:start position:0% +sidewalls and that's exactly what is +shown um on slide uh 28 in the Speedy + + align:start position:0% +shown um on slide uh 28 in the Speedy + + + align:start position:0% +shown um on slide uh 28 in the Speedy +simulations here's an example of um now + + align:start position:0% +simulations here's an example of um now + + + align:start position:0% +simulations here's an example of um now +I've got that same trench that same high + + align:start position:0% +I've got that same trench that same high + + + align:start position:0% +I've got that same trench that same high +aspect ratio 1.25 but on the left here a + + align:start position:0% +aspect ratio 1.25 but on the left here a + + + align:start position:0% +aspect ratio 1.25 but on the left here a +I have a sticking coefficient of 0.1 so + + align:start position:0% +I have a sticking coefficient of 0.1 so + + + align:start position:0% +I have a sticking coefficient of 0.1 so +only one in 10 atoms sticks the other + + align:start position:0% +only one in 10 atoms sticks the other + + + align:start position:0% +only one in 10 atoms sticks the other +nine when they hit a point they go + + align:start position:0% +nine when they hit a point they go + + + align:start position:0% +nine when they hit a point they go +somewhere else and they continue to + + align:start position:0% +somewhere else and they continue to + + + align:start position:0% +somewhere else and they continue to +bounce around until they finally stick + + align:start position:0% +bounce around until they finally stick + + + align:start position:0% +bounce around until they finally stick +here's one and a 100 + + align:start position:0% +here's one and a 100 + + + align:start position:0% +here's one and a 100 +sticking um so again this is with n + + align:start position:0% +sticking um so again this is with n + + + align:start position:0% +sticking um so again this is with n +equals 1 so it's isotropic arrival but + + align:start position:0% +equals 1 so it's isotropic arrival but + + + align:start position:0% +equals 1 so it's isotropic arrival but +with different values of the sticking + + align:start position:0% +with different values of the sticking + + + align:start position:0% +with different values of the sticking +coefficient so sticking coefficient is + + align:start position:0% +coefficient so sticking coefficient is + + + align:start position:0% +coefficient so sticking coefficient is +the knob you want to turn when you want + + align:start position:0% +the knob you want to turn when you want + + + align:start position:0% +the knob you want to turn when you want +if you want to fill a trench um changing + + align:start position:0% +if you want to fill a trench um changing + + + align:start position:0% +if you want to fill a trench um changing +the N value helped but not not a whole + + align:start position:0% +the N value helped but not not a whole + + + align:start position:0% +the N value helped but not not a whole +lot it was really the very lowering the + + align:start position:0% +lot it was really the very lowering the + + + align:start position:0% +lot it was really the very lowering the +sticking coefficient uh you get much + + align:start position:0% +sticking coefficient uh you get much + + + align:start position:0% +sticking coefficient uh you get much +more conformal coverage so you get on a + + align:start position:0% +more conformal coverage so you get on a + + + align:start position:0% +more conformal coverage so you get on a +side wall just about what you had um uh + + align:start position:0% +side wall just about what you had um uh + + + align:start position:0% +side wall just about what you had um uh +so this is typical on a uh this this + + align:start position:0% +so this is typical on a uh this this + + + align:start position:0% +so this is typical on a uh this this +this sort of view of things the + + align:start position:0% +this sort of view of things the + + + align:start position:0% +this sort of view of things the +parameter values n equals 1 and sticking + + align:start position:0% +parameter values n equals 1 and sticking + + + align:start position:0% +parameter values n equals 1 and sticking +coefficient of 0.1 is very typical of uh + + align:start position:0% +coefficient of 0.1 is very typical of uh + + + align:start position:0% +coefficient of 0.1 is very typical of uh +lto so low temperature oxid or CBD sao2 + + align:start position:0% +lto so low temperature oxid or CBD sao2 + + + align:start position:0% +lto so low temperature oxid or CBD sao2 +B with a sticking coefficient of one in + + align:start position:0% +B with a sticking coefficient of one in + + + align:start position:0% +B with a sticking coefficient of one in +100 is more typical of tungsten + + align:start position:0% +100 is more typical of tungsten + + + align:start position:0% +100 is more typical of tungsten +CBD so when we need to reduce sticking + + align:start position:0% +CBD so when we need to reduce sticking + + + align:start position:0% +CBD so when we need to reduce sticking +coefficient if you need uh more + + align:start position:0% +coefficient if you need uh more + + + align:start position:0% +coefficient if you need uh more +conformal + + align:start position:0% + + + + align:start position:0% + +deposition how about the side wall angle + + align:start position:0% +deposition how about the side wall angle + + + align:start position:0% +deposition how about the side wall angle +so even if if I even uh go back here I + + align:start position:0% +so even if if I even uh go back here I + + + align:start position:0% +so even if if I even uh go back here I +look at this um I didn't do a perfect + + align:start position:0% +look at this um I didn't do a perfect + + + align:start position:0% +look at this um I didn't do a perfect +job in this case of filling this trench + + align:start position:0% +job in this case of filling this trench + + + align:start position:0% +job in this case of filling this trench +you look like it's going to pinch off in + + align:start position:0% +you look like it's going to pinch off in + + + align:start position:0% +you look like it's going to pinch off in +form of void before I get the whole + + align:start position:0% +form of void before I get the whole + + + align:start position:0% +form of void before I get the whole +thing filled even here it doesn't look + + align:start position:0% +thing filled even here it doesn't look + + + align:start position:0% +thing filled even here it doesn't look +all necessarily that perfect so what can + + align:start position:0% +all necessarily that perfect so what can + + + align:start position:0% +all necessarily that perfect so what can +we do you only have so much latitude + + align:start position:0% +we do you only have so much latitude + + + align:start position:0% +we do you only have so much latitude +your sticking coefficient you can change + + align:start position:0% +your sticking coefficient you can change + + + align:start position:0% +your sticking coefficient you can change +the pressure and do things in your + + align:start position:0% +the pressure and do things in your + + + align:start position:0% +the pressure and do things in your +reactor but you only have so much + + align:start position:0% +reactor but you only have so much + + + align:start position:0% +reactor but you only have so much +latitude well what you do is you change + + align:start position:0% +latitude well what you do is you change + + + align:start position:0% +latitude well what you do is you change +the topography that you're starting with + + align:start position:0% +the topography that you're starting with + + + align:start position:0% +the topography that you're starting with +so uh these examples are results of + + align:start position:0% +so uh these examples are results of + + + align:start position:0% +so uh these examples are results of +Speedy simulations where you're doing uh + + align:start position:0% +Speedy simulations where you're doing uh + + + align:start position:0% +Speedy simulations where you're doing uh +lpcvd into a trench and we've changed + + align:start position:0% +lpcvd into a trench and we've changed + + + align:start position:0% +lpcvd into a trench and we've changed +the sidewall angle here the trench has + + align:start position:0% +the sidewall angle here the trench has + + + align:start position:0% +the sidewall angle here the trench has +has a 90° angle so the side walls go + + align:start position:0% +has a 90° angle so the side walls go + + + align:start position:0% +has a 90° angle so the side walls go +straight down here it's opened up + + align:start position:0% +straight down here it's opened up + + + align:start position:0% +straight down here it's opened up +slightly by 5° so this is an 85° angle + + align:start position:0% +slightly by 5° so this is an 85° angle + + + align:start position:0% +slightly by 5° so this is an 85° angle +and here you open up a little bit more + + align:start position:0% +and here you open up a little bit more + + + align:start position:0% +and here you open up a little bit more +80° angle um this has a sticking + + align:start position:0% +80° angle um this has a sticking + + + align:start position:0% +80° angle um this has a sticking +coefficient of 02 and an N of one so + + align:start position:0% +coefficient of 02 and an N of one so + + + align:start position:0% +coefficient of 02 and an N of one so +this is very typical of low temperature + + align:start position:0% +this is very typical of low temperature + + + align:start position:0% +this is very typical of low temperature +oxide deposition uh for example into a + + align:start position:0% +oxide deposition uh for example into a + + + align:start position:0% +oxide deposition uh for example into a +trench um so if you decrease the angle + + align:start position:0% +trench um so if you decrease the angle + + + align:start position:0% +trench um so if you decrease the angle +um from 90 to 80 degre you greatly + + align:start position:0% +um from 90 to 80 degre you greatly + + + align:start position:0% +um from 90 to 80 degre you greatly +improve the filling see at 90 degrees + + align:start position:0% +improve the filling see at 90 degrees + + + align:start position:0% +improve the filling see at 90 degrees +you're going to pinch off and you're + + align:start position:0% +you're going to pinch off and you're + + + align:start position:0% +you're going to pinch off and you're +going to get a void at 80 degrees you're + + align:start position:0% +going to get a void at 80 degrees you're + + + align:start position:0% +going to get a void at 80 degrees you're +not going to so it's very common in + + align:start position:0% +not going to so it's very common in + + + align:start position:0% +not going to so it's very common in +etching when you go to etch to try to + + align:start position:0% +etching when you go to etch to try to + + + align:start position:0% +etching when you go to etch to try to +etch a contact hole in a via you never + + align:start position:0% +etch a contact hole in a via you never + + + align:start position:0% +etch a contact hole in a via you never +want to etch it straight down you always + + align:start position:0% +want to etch it straight down you always + + + align:start position:0% +want to etch it straight down you always +want to have a slight angle say make it + + align:start position:0% +want to have a slight angle say make it + + + align:start position:0% +want to have a slight angle say make it +make it uh 80 degrees uh to slope this + + align:start position:0% +make it uh 80 degrees uh to slope this + + + align:start position:0% +make it uh 80 degrees uh to slope this +so that you can get much better um uh + + align:start position:0% +so that you can get much better um uh + + + align:start position:0% +so that you can get much better um uh +filling of the hole or if you're trying + + align:start position:0% +filling of the hole or if you're trying + + + align:start position:0% +filling of the hole or if you're trying +to make um you want uh metal lines to go + + align:start position:0% +to make um you want uh metal lines to go + + + align:start position:0% +to make um you want uh metal lines to go +over a step on your wafer um you never + + align:start position:0% +over a step on your wafer um you never + + + align:start position:0% +over a step on your wafer um you never +want to make the step look like this you + + align:start position:0% +want to make the step look like this you + + + align:start position:0% +want to make the step look like this you +usually want to have it more sloped so + + align:start position:0% +usually want to have it more sloped so + + + align:start position:0% +usually want to have it more sloped so +you somehow you know slope the step when + + align:start position:0% +you somehow you know slope the step when + + + align:start position:0% +you somehow you know slope the step when +you etch it or you put in sidewall + + align:start position:0% +you etch it or you put in sidewall + + + align:start position:0% +you etch it or you put in sidewall +spacers or do something so the general + + align:start position:0% +spacers or do something so the general + + + align:start position:0% +spacers or do something so the general +idea if you want good step coverage + + align:start position:0% +idea if you want good step coverage + + + align:start position:0% +idea if you want good step coverage +don't make such abrupt + + align:start position:0% +don't make such abrupt + + + align:start position:0% +don't make such abrupt +steps um if you're doing vs you can you + + align:start position:0% +steps um if you're doing vs you can you + + + align:start position:0% +steps um if you're doing vs you can you +can just uh decrease your angle from 90 + + align:start position:0% +can just uh decrease your angle from 90 + + + align:start position:0% +can just uh decrease your angle from 90 +to to 80 and you get much better um + + align:start position:0% +to to 80 and you get much better um + + + align:start position:0% +to to 80 and you get much better um +filling of the + + align:start position:0% + + + + align:start position:0% + +trench okay how about um there is there + + align:start position:0% +trench okay how about um there is there + + + align:start position:0% +trench okay how about um there is there +are a little bit more complicated cases + + align:start position:0% +are a little bit more complicated cases + + + align:start position:0% +are a little bit more complicated cases +I've just shown very simple cases uh PVD + + align:start position:0% +I've just shown very simple cases uh PVD + + + align:start position:0% +I've just shown very simple cases uh PVD +without ions or lpcvd without ions how + + align:start position:0% +without ions or lpcvd without ions how + + + align:start position:0% +without ions or lpcvd without ions how +about the case where you do have an ion + + align:start position:0% +about the case where you do have an ion + + + align:start position:0% +about the case where you do have an ion +flux and there is there are a couple of + + align:start position:0% +flux and there is there are a couple of + + + align:start position:0% +flux and there is there are a couple of +cases like that there's what's called + + align:start position:0% +cases like that there's what's called + + + align:start position:0% +cases like that there's what's called +hdp high density plasma CBD this has a + + align:start position:0% +hdp high density plasma CBD this has a + + + align:start position:0% +hdp high density plasma CBD this has a +very high ion flux um could be three or + + align:start position:0% +very high ion flux um could be three or + + + align:start position:0% +very high ion flux um could be three or +four orders of magnitude higher than + + align:start position:0% +four orders of magnitude higher than + + + align:start position:0% +four orders of magnitude higher than +what you have in ordinary um uh ordinary + + align:start position:0% +what you have in ordinary um uh ordinary + + + align:start position:0% +what you have in ordinary um uh ordinary +um CBD so what what what how does this + + align:start position:0% +um CBD so what what what how does this + + + align:start position:0% +um CBD so what what what how does this +work well I think we mentioned this at + + align:start position:0% +work well I think we mentioned this at + + + align:start position:0% +work well I think we mentioned this at +one point uh this particular one has a + + align:start position:0% +one point uh this particular one has a + + + align:start position:0% +one point uh this particular one has a +microwave W Source um what we have is we + + align:start position:0% +microwave W Source um what we have is we + + + align:start position:0% +microwave W Source um what we have is we +have a plasma up here um and there's a + + align:start position:0% +have a plasma up here um and there's a + + + align:start position:0% +have a plasma up here um and there's a +microwave Supply that's creating those + + align:start position:0% +microwave Supply that's creating those + + + align:start position:0% +microwave Supply that's creating those +ions uh but then we all it's created + + align:start position:0% +ions uh but then we all it's created + + + align:start position:0% +ions uh but then we all it's created +remotely so this ionized plasma has a + + align:start position:0% +remotely so this ionized plasma has a + + + align:start position:0% +remotely so this ionized plasma has a +very high density but it's created + + align:start position:0% +very high density but it's created + + + align:start position:0% +very high density but it's created +remotely not directly over the wafer and + + align:start position:0% +remotely not directly over the wafer and + + + align:start position:0% +remotely not directly over the wafer and +then you have an RF bias and you extract + + align:start position:0% +then you have an RF bias and you extract + + + align:start position:0% +then you have an RF bias and you extract +those ions towards the wafer so the nice + + align:start position:0% +those ions towards the wafer so the nice + + + align:start position:0% +those ions towards the wafer so the nice +thing about this is that you can get a + + align:start position:0% +thing about this is that you can get a + + + align:start position:0% +thing about this is that you can get a +very high density without having huge + + align:start position:0% +very high density without having huge + + + align:start position:0% +very high density without having huge +energies huge voltages to extract them + + align:start position:0% +energies huge voltages to extract them + + + align:start position:0% +energies huge voltages to extract them +to the + + align:start position:0% +to the + + + align:start position:0% +to the +wafer um so you don't get so much damage + + align:start position:0% +wafer um so you don't get so much damage + + + align:start position:0% +wafer um so you don't get so much damage +uh so and this high density um high + + align:start position:0% +uh so and this high density um high + + + align:start position:0% +uh so and this high density um high +density U plasma can give you a very + + align:start position:0% +density U plasma can give you a very + + + align:start position:0% +density U plasma can give you a very +high cvd depth rate uh even down to room + + align:start position:0% +high cvd depth rate uh even down to room + + + align:start position:0% +high cvd depth rate uh even down to room +temperature um with relatively low + + align:start position:0% +temperature um with relatively low + + + align:start position:0% +temperature um with relatively low +pressures so the key is you have a + + align:start position:0% +pressures so the key is you have a + + + align:start position:0% +pressures so the key is you have a +separate RF bias applied to the + + align:start position:0% +separate RF bias applied to the + + + align:start position:0% +separate RF bias applied to the +substrate um that controls the angular + + align:start position:0% +substrate um that controls the angular + + + align:start position:0% +substrate um that controls the angular +dependence of what comes down and of ion + + align:start position:0% +dependence of what comes down and of ion + + + align:start position:0% +dependence of what comes down and of ion +sputtering during deposition so we have + + align:start position:0% +sputtering during deposition so we have + + + align:start position:0% +sputtering during deposition so we have +a direct ion flux coming down like this + + align:start position:0% +a direct ion flux coming down like this + + + align:start position:0% +a direct ion flux coming down like this +on the surface and we have ions that + + align:start position:0% +on the surface and we have ions that + + + align:start position:0% +on the surface and we have ions that +come down and sputter off and now here's + + align:start position:0% +come down and sputter off and now here's + + + align:start position:0% +come down and sputter off and now here's +where our reutter flux becomes important + + align:start position:0% +where our reutter flux becomes important + + + align:start position:0% +where our reutter flux becomes important +from these highdensity plasma systems + + align:start position:0% +from these highdensity plasma systems + + + align:start position:0% +from these highdensity plasma systems +and the thing that we need to realize is + + align:start position:0% +and the thing that we need to realize is + + + align:start position:0% +and the thing that we need to realize is +because of the angular dependence of + + align:start position:0% +because of the angular dependence of + + + align:start position:0% +because of the angular dependence of +sputtering sputtering occurs + + align:start position:0% +sputtering sputtering occurs + + + align:start position:0% +sputtering sputtering occurs +preferentially on a slope surface rather + + align:start position:0% +preferentially on a slope surface rather + + + align:start position:0% +preferentially on a slope surface rather +than a surface that's either vertical or + + align:start position:0% +than a surface that's either vertical or + + + align:start position:0% +than a surface that's either vertical or +horizontal uh because remember that + + align:start position:0% +horizontal uh because remember that + + + align:start position:0% +horizontal uh because remember that +sputter uh sputtering rate sort of + + align:start position:0% +sputter uh sputtering rate sort of + + + align:start position:0% +sputter uh sputtering rate sort of +peaked at around 60° so if you have a + + align:start position:0% +peaked at around 60° so if you have a + + + align:start position:0% +peaked at around 60° so if you have a +slope surface you get preferential + + align:start position:0% +slope surface you get preferential + + + align:start position:0% +slope surface you get preferential +sputtering so you can actually use these + + align:start position:0% +sputtering so you can actually use these + + + align:start position:0% +sputtering so you can actually use these +highdensity plasma systems to do + + align:start position:0% +highdensity plasma systems to do + + + align:start position:0% +highdensity plasma systems to do +planarization now all along I've been + + align:start position:0% +planarization now all along I've been + + + align:start position:0% +planarization now all along I've been +talking about conformal deposition you + + align:start position:0% +talking about conformal deposition you + + + align:start position:0% +talking about conformal deposition you +may not want to get conformal deposition + + align:start position:0% +may not want to get conformal deposition + + + align:start position:0% +may not want to get conformal deposition +you may want planarized so what do I + + align:start position:0% +you may want planarized so what do I + + + align:start position:0% +you may want planarized so what do I +mean by planarized deposition well if + + align:start position:0% +mean by planarized deposition well if + + + align:start position:0% +mean by planarized deposition well if +you start out let's say your surface + + align:start position:0% +you start out let's say your surface + + + align:start position:0% +you start out let's say your surface +topography looks like + + align:start position:0% +topography looks like + + + align:start position:0% +topography looks like +this you have a metal line or something + + align:start position:0% +this you have a metal line or something + + + align:start position:0% +this you have a metal line or something +and you want to cover it with oxide but + + align:start position:0% +and you want to cover it with oxide but + + + align:start position:0% +and you want to cover it with oxide but +you want it to be planer when you're + + align:start position:0% +you want it to be planer when you're + + + align:start position:0% +you want it to be planer when you're +done you like the surface to look like + + align:start position:0% +done you like the surface to look like + + + align:start position:0% +done you like the surface to look like +that after deposition completely flat + + align:start position:0% +that after deposition completely flat + + + align:start position:0% +that after deposition completely flat +that's not that's just the opposite of + + align:start position:0% +that's not that's just the opposite of + + + align:start position:0% +that's not that's just the opposite of +conformal if it were conformal right it + + align:start position:0% +conformal if it were conformal right it + + + align:start position:0% +conformal if it were conformal right it +would have looked like this it would + + align:start position:0% +would have looked like this it would + + + align:start position:0% +would have looked like this it would +have it would reproduce that big hump + + align:start position:0% +have it would reproduce that big hump + + + align:start position:0% +have it would reproduce that big hump +but if you're trying to do planarization + + align:start position:0% +but if you're trying to do planarization + + + align:start position:0% +but if you're trying to do planarization +during deposition without using CMP + + align:start position:0% +during deposition without using CMP + + + align:start position:0% +during deposition without using CMP +you'd love a process that would deposit + + align:start position:0% +you'd love a process that would deposit + + + align:start position:0% +you'd love a process that would deposit +like this how well how can you do that + + align:start position:0% +like this how well how can you do that + + + align:start position:0% +like this how well how can you do that +well there are some process processes + + align:start position:0% +well there are some process processes + + + align:start position:0% +well there are some process processes +that are self- planarizing during + + align:start position:0% +that are self- planarizing during + + + align:start position:0% +that are self- planarizing during +deposition and here's an here's an + + align:start position:0% +deposition and here's an here's an + + + align:start position:0% +deposition and here's an here's an +example of such a process you need these + + align:start position:0% +example of such a process you need these + + + align:start position:0% +example of such a process you need these +ionized techniques which in addition to + + align:start position:0% +ionized techniques which in addition to + + + align:start position:0% +ionized techniques which in addition to +depositing are doing sputtering uh + + align:start position:0% +depositing are doing sputtering uh + + + align:start position:0% +depositing are doing sputtering uh +preferentially so here's an example uh + + align:start position:0% +preferentially so here's an example uh + + + align:start position:0% +preferentially so here's an example uh +on slide 31 of two Speedy simulations on + + align:start position:0% +on slide 31 of two Speedy simulations on + + + align:start position:0% +on slide 31 of two Speedy simulations on +my left I have low pressure CBD regular + + align:start position:0% +my left I have low pressure CBD regular + + + align:start position:0% +my left I have low pressure CBD regular +low pressure CBD so I have a line like + + align:start position:0% +low pressure CBD so I have a line like + + + align:start position:0% +low pressure CBD so I have a line like +this and I'm trying to cover it with + + align:start position:0% +this and I'm trying to cover it with + + + align:start position:0% +this and I'm trying to cover it with +oxide and you see you started out with a + + align:start position:0% +oxide and you see you started out with a + + + align:start position:0% +oxide and you see you started out with a +bump and you end up with a bump there is + + align:start position:0% +bump and you end up with a bump there is + + + align:start position:0% +bump and you end up with a bump there is +no planarization it's perfectly + + align:start position:0% +no planarization it's perfectly + + + align:start position:0% +no planarization it's perfectly +conformant in B we we've simulated this + + align:start position:0% +conformant in B we we've simulated this + + + align:start position:0% +conformant in B we we've simulated this +highdensity plasma CBD deposition um and + + align:start position:0% +highdensity plasma CBD deposition um and + + + align:start position:0% +highdensity plasma CBD deposition um and +it has a directed ion flux and the key + + align:start position:0% +it has a directed ion flux and the key + + + align:start position:0% +it has a directed ion flux and the key +is it has this angle dependent + + align:start position:0% +is it has this angle dependent + + + align:start position:0% +is it has this angle dependent +sputtering um which and you end up with + + align:start position:0% +sputtering um which and you end up with + + + align:start position:0% +sputtering um which and you end up with +a little bump but much more planarize + + align:start position:0% +a little bump but much more planarize + + + align:start position:0% +a little bump but much more planarize +topography after deposition so if you + + align:start position:0% +topography after deposition so if you + + + align:start position:0% +topography after deposition so if you +had to do CMP to planarize on this one + + align:start position:0% +had to do CMP to planarize on this one + + + align:start position:0% +had to do CMP to planarize on this one +you'd have to CMP quite a bit on this + + align:start position:0% +you'd have to CMP quite a bit on this + + + align:start position:0% +you'd have to CMP quite a bit on this +one you'd probably have to CMP only a + + align:start position:0% +one you'd probably have to CMP only a + + + align:start position:0% +one you'd probably have to CMP only a +little bit uh just a small amount and + + align:start position:0% +little bit uh just a small amount and + + + align:start position:0% +little bit uh just a small amount and +that's very desirable because CMP is a + + align:start position:0% +that's very desirable because CMP is a + + + align:start position:0% +that's very desirable because CMP is a +tricky process introduces non-uniformity + + align:start position:0% +tricky process introduces non-uniformity + + + align:start position:0% +tricky process introduces non-uniformity +and it's fairly expensive so if you can + + align:start position:0% +and it's fairly expensive so if you can + + + align:start position:0% +and it's fairly expensive so if you can +do self- planarizing deposition with + + align:start position:0% +do self- planarizing deposition with + + + align:start position:0% +do self- planarizing deposition with +these fancy ionized deposition systems + + align:start position:0% +these fancy ionized deposition systems + + + align:start position:0% +these fancy ionized deposition systems +um you're much better + + align:start position:0% +um you're much better + + + align:start position:0% +um you're much better +off and I'll actually show some some + + align:start position:0% +off and I'll actually show some some + + + align:start position:0% +off and I'll actually show some some +real examples of that so besides um + + align:start position:0% +real examples of that so besides um + + + align:start position:0% +real examples of that so besides um +depositing overall line you can also use + + align:start position:0% +depositing overall line you can also use + + + align:start position:0% +depositing overall line you can also use +this highdensity plasma CBD is very good + + align:start position:0% +this highdensity plasma CBD is very good + + + align:start position:0% +this highdensity plasma CBD is very good +at filling Open Spaces uh and reducing + + align:start position:0% +at filling Open Spaces uh and reducing + + + align:start position:0% +at filling Open Spaces uh and reducing +void + + align:start position:0% +void + + + align:start position:0% +void +formation so here's an example here + + align:start position:0% +formation so here's an example here + + + align:start position:0% +formation so here's an example here +again a speedy simulation on the left I + + align:start position:0% +again a speedy simulation on the left I + + + align:start position:0% +again a speedy simulation on the left I +had a trench with a relatively High + + align:start position:0% +had a trench with a relatively High + + + align:start position:0% +had a trench with a relatively High +aspect ratio this was that + + align:start position:0% +aspect ratio this was that + + + align:start position:0% +aspect ratio this was that +1.25 aspect ratio um by lpcvd you see it + + align:start position:0% +1.25 aspect ratio um by lpcvd you see it + + + align:start position:0% +1.25 aspect ratio um by lpcvd you see it +pinches off and you end up up with a + + align:start position:0% +pinches off and you end up up with a + + + align:start position:0% +pinches off and you end up up with a +void um and in order to do this we we um + + align:start position:0% +void um and in order to do this we we um + + + align:start position:0% +void um and in order to do this we we um +use a sticking coefficient of 02 in in + + align:start position:0% +use a sticking coefficient of 02 in in + + + align:start position:0% +use a sticking coefficient of 02 in in +isotropic arrival angle on the one on + + align:start position:0% +isotropic arrival angle on the one on + + + align:start position:0% +isotropic arrival angle on the one on +the left on the right I'm sorry is high + + align:start position:0% +the left on the right I'm sorry is high + + + align:start position:0% +the left on the right I'm sorry is high +density plasma deposition in the trench + + align:start position:0% +density plasma deposition in the trench + + + align:start position:0% +density plasma deposition in the trench +and you look and we have you get much + + align:start position:0% +and you look and we have you get much + + + align:start position:0% +and you look and we have you get much +better um filling you don't see the + + align:start position:0% +better um filling you don't see the + + + align:start position:0% +better um filling you don't see the +void uh well why does it do this well + + align:start position:0% +void uh well why does it do this well + + + align:start position:0% +void uh well why does it do this well +highdensity plasma gives you better + + align:start position:0% +highdensity plasma gives you better + + + align:start position:0% +highdensity plasma gives you better +filling because you combine this highly + + align:start position:0% +filling because you combine this highly + + + align:start position:0% +filling because you combine this highly +directed ion flux so a lot of the ions + + align:start position:0% +directed ion flux so a lot of the ions + + + align:start position:0% +directed ion flux so a lot of the ions +are coming straight down that helps they + + align:start position:0% +are coming straight down that helps they + + + align:start position:0% +are coming straight down that helps they +get into the trench so they're towards + + align:start position:0% +get into the trench so they're towards + + + align:start position:0% +get into the trench so they're towards +the surface with this angle dependent + + align:start position:0% +the surface with this angle dependent + + + align:start position:0% +the surface with this angle dependent +sputtering so the angular dependent + + align:start position:0% +sputtering so the angular dependent + + + align:start position:0% +sputtering so the angular dependent +sputtering tends to etch off any of + + align:start position:0% +sputtering tends to etch off any of + + + align:start position:0% +sputtering tends to etch off any of +these overhangs as they form they get + + align:start position:0% +these overhangs as they form they get + + + align:start position:0% +these overhangs as they form they get +etched off by the sputtering + + align:start position:0% +etched off by the sputtering + + + align:start position:0% +etched off by the sputtering +preferentially so overhangs that develop + + align:start position:0% +preferentially so overhangs that develop + + + align:start position:0% +preferentially so overhangs that develop +get sputtered away and you end up being + + align:start position:0% +get sputtered away and you end up being + + + align:start position:0% +get sputtered away and you end up being +able to fill the trench pretty well + + align:start position:0% +able to fill the trench pretty well + + + align:start position:0% +able to fill the trench pretty well +without + + align:start position:0% +without + + + align:start position:0% +without +aoid often you do not want voids in the + + align:start position:0% +aoid often you do not want voids in the + + + align:start position:0% +aoid often you do not want voids in the +film you don't want air spaces in your + + align:start position:0% +film you don't want air spaces in your + + + align:start position:0% +film you don't want air spaces in your +chips so this is a way to do it is that + + align:start position:0% +chips so this is a way to do it is that + + + align:start position:0% +chips so this is a way to do it is that +high density + + align:start position:0% + + + + align:start position:0% + +plasma here's an example on slide 33 + + align:start position:0% +plasma here's an example on slide 33 + + + align:start position:0% +plasma here's an example on slide 33 +this just to show you that instead of + + align:start position:0% +this just to show you that instead of + + + align:start position:0% +this just to show you that instead of +just showing Speedy simulations actual + + align:start position:0% +just showing Speedy simulations actual + + + align:start position:0% +just showing Speedy simulations actual +data um these are uh scanning electron + + align:start position:0% +data um these are uh scanning electron + + + align:start position:0% +data um these are uh scanning electron +micrograph images of hdp oxide + + align:start position:0% +micrograph images of hdp oxide + + + align:start position:0% +micrograph images of hdp oxide +deposition and on the left uh this was a + + align:start position:0% +deposition and on the left uh this was a + + + align:start position:0% +deposition and on the left uh this was a +metal line you can see and I was try + + align:start position:0% +metal line you can see and I was try + + + align:start position:0% +metal line you can see and I was try +we're trying to deposit oxide over that + + align:start position:0% +we're trying to deposit oxide over that + + + align:start position:0% +we're trying to deposit oxide over that +and again if it had been conformal you'd + + align:start position:0% +and again if it had been conformal you'd + + + align:start position:0% +and again if it had been conformal you'd +have a big hump in your oxide but with + + align:start position:0% +have a big hump in your oxide but with + + + align:start position:0% +have a big hump in your oxide but with +high density plasma CBD which is not + + align:start position:0% +high density plasma CBD which is not + + + align:start position:0% +high density plasma CBD which is not +conformal uh you end up with pretty + + align:start position:0% +conformal uh you end up with pretty + + + align:start position:0% +conformal uh you end up with pretty +plainer oxide you still have a little + + align:start position:0% +plainer oxide you still have a little + + + align:start position:0% +plainer oxide you still have a little +bit of a bump there a very small little + + align:start position:0% +bit of a bump there a very small little + + + align:start position:0% +bit of a bump there a very small little +bump that you uh would have to um + + align:start position:0% +bump that you uh would have to um + + + align:start position:0% +bump that you uh would have to um +planarize away but the amount of CNP + + align:start position:0% +planarize away but the amount of CNP + + + align:start position:0% +planarize away but the amount of CNP +you'd have to do on that would be very + + align:start position:0% +you'd have to do on that would be very + + + align:start position:0% +you'd have to do on that would be very +minimal um and again so that's the case + + align:start position:0% +minimal um and again so that's the case + + + align:start position:0% +minimal um and again so that's the case +of depositing overall line if you're + + align:start position:0% +of depositing overall line if you're + + + align:start position:0% +of depositing overall line if you're +depositing oxide in a trench so here's + + align:start position:0% +depositing oxide in a trench so here's + + + align:start position:0% +depositing oxide in a trench so here's +an example of kind of a trench you have + + align:start position:0% +an example of kind of a trench you have + + + align:start position:0% +an example of kind of a trench you have +two metal lines one on the right one on + + align:start position:0% +two metal lines one on the right one on + + + align:start position:0% +two metal lines one on the right one on +the left they're separated by half + + align:start position:0% +the left they're separated by half + + + align:start position:0% +the left they're separated by half +Micron or so you want to completely fill + + align:start position:0% +Micron or so you want to completely fill + + + align:start position:0% +Micron or so you want to completely fill +this without voids you can see you've + + align:start position:0% +this without voids you can see you've + + + align:start position:0% +this without voids you can see you've +gotten excellent filling um uh you did + + align:start position:0% +gotten excellent filling um uh you did + + + align:start position:0% +gotten excellent filling um uh you did +get some of these strange you know + + align:start position:0% +get some of these strange you know + + + align:start position:0% +get some of these strange you know +topographies because of these these ion + + align:start position:0% +topographies because of these these ion + + + align:start position:0% +topographies because of these these ion +uh the ion effects but that would have + + align:start position:0% +uh the ion effects but that would have + + + align:start position:0% +uh the ion effects but that would have +to be cmpd off but the key is you were + + align:start position:0% +to be cmpd off but the key is you were + + + align:start position:0% +to be cmpd off but the key is you were +able to fill a very small space um + + align:start position:0% +able to fill a very small space um + + + align:start position:0% +able to fill a very small space um +without without inducing the voids that + + align:start position:0% +without without inducing the voids that + + + align:start position:0% +without without inducing the voids that +would be a problem if you're trying to + + align:start position:0% +would be a problem if you're trying to + + + align:start position:0% +would be a problem if you're trying to +use say an lpcvd + + align:start position:0% +use say an lpcvd + + + align:start position:0% +use say an lpcvd +system so you can imagine looking at + + align:start position:0% +system so you can imagine looking at + + + align:start position:0% +system so you can imagine looking at +these topographies simulating and then + + align:start position:0% +these topographies simulating and then + + + align:start position:0% +these topographies simulating and then +going back in + + align:start position:0% +going back in + + + align:start position:0% +going back in +Speedy uh and varying your models to try + + align:start position:0% +Speedy uh and varying your models to try + + + align:start position:0% +Speedy uh and varying your models to try +to get something that looks like what + + align:start position:0% +to get something that looks like what + + + align:start position:0% +to get something that looks like what +you actually U what you actually got um + + align:start position:0% +you actually U what you actually got um + + + align:start position:0% +you actually U what you actually got um +from semm and that's what exactly what + + align:start position:0% +from semm and that's what exactly what + + + align:start position:0% +from semm and that's what exactly what +people do in topography simulation again + + align:start position:0% +people do in topography simulation again + + + align:start position:0% +people do in topography simulation again +it's not first principles you vary all + + align:start position:0% +it's not first principles you vary all + + + align:start position:0% +it's not first principles you vary all +these different uh parameters the + + align:start position:0% +these different uh parameters the + + + align:start position:0% +these different uh parameters the +sputtering yield is a function of angle + + align:start position:0% +sputtering yield is a function of angle + + + align:start position:0% +sputtering yield is a function of angle +the N value which is the cosine Theta + + align:start position:0% +the N value which is the cosine Theta + + + align:start position:0% +the N value which is the cosine Theta +the N distribution the sticking + + align:start position:0% +the N distribution the sticking + + + align:start position:0% +the N distribution the sticking +coefficient you vary all those until you + + align:start position:0% +coefficient you vary all those until you + + + align:start position:0% +coefficient you vary all those until you +get something in your simulation that + + align:start position:0% +get something in your simulation that + + + align:start position:0% +get something in your simulation that +looks somewhat close to what you + + align:start position:0% +looks somewhat close to what you + + + align:start position:0% +looks somewhat close to what you +actually uh + + align:start position:0% + + + + align:start position:0% + +deposited slide 34 shows um the case we + + align:start position:0% +deposited slide 34 shows um the case we + + + align:start position:0% +deposited slide 34 shows um the case we +haven't had much chance to talk about it + + align:start position:0% +haven't had much chance to talk about it + + + align:start position:0% +haven't had much chance to talk about it +but this whole idea of surface diffusion + + align:start position:0% +but this whole idea of surface diffusion + + + align:start position:0% +but this whole idea of surface diffusion +um + + align:start position:0% +um + + + align:start position:0% +um +and this becomes important only when + + align:start position:0% +and this becomes important only when + + + align:start position:0% +and this becomes important only when +you're usually doing a high temperature + + align:start position:0% +you're usually doing a high temperature + + + align:start position:0% +you're usually doing a high temperature +uh PVD say for aluminum that's a + + align:start position:0% +uh PVD say for aluminum that's a + + + align:start position:0% +uh PVD say for aluminum that's a +practical example that people sometimes + + align:start position:0% +practical example that people sometimes + + + align:start position:0% +practical example that people sometimes +do um again all these issues tend to + + align:start position:0% +do um again all these issues tend to + + + align:start position:0% +do um again all these issues tend to +arise when you're we try we have high + + align:start position:0% +arise when you're we try we have high + + + align:start position:0% +arise when you're we try we have high +aspect ratios on the wafer so you have a + + align:start position:0% +aspect ratios on the wafer so you have a + + + align:start position:0% +aspect ratios on the wafer so you have a +very high aspect ratio trench uh like + + align:start position:0% +very high aspect ratio trench uh like + + + align:start position:0% +very high aspect ratio trench uh like +this uh and you're trying to uh fill + + align:start position:0% +this uh and you're trying to uh fill + + + align:start position:0% +this uh and you're trying to uh fill +that with + + align:start position:0% +that with + + + align:start position:0% +that with +aluminum uh and so um on a on the left + + align:start position:0% +aluminum uh and so um on a on the left + + + align:start position:0% +aluminum uh and so um on a on the left +is High aspect ratio trench using PVD so + + align:start position:0% +is High aspect ratio trench using PVD so + + + align:start position:0% +is High aspect ratio trench using PVD so +we have a sticking coefficient of one uh + + align:start position:0% +we have a sticking coefficient of one uh + + + align:start position:0% +we have a sticking coefficient of one uh +n equals 4 um so this could be a + + align:start position:0% +n equals 4 um so this could be a + + + align:start position:0% +n equals 4 um so this could be a +sputtered situation and you have very + + align:start position:0% +sputtered situation and you have very + + + align:start position:0% +sputtered situation and you have very +poor filling in fact uh you don't have + + align:start position:0% +poor filling in fact uh you don't have + + + align:start position:0% +poor filling in fact uh you don't have +much at all aluminum on the sidewalls if + + align:start position:0% +much at all aluminum on the sidewalls if + + + align:start position:0% +much at all aluminum on the sidewalls if +uh you weren't able to fill the trench + + align:start position:0% +uh you weren't able to fill the trench + + + align:start position:0% +uh you weren't able to fill the trench +well at all um in + + align:start position:0% +well at all um in + + + align:start position:0% +well at all um in +b um this is again uh now this we have + + align:start position:0% +b um this is again uh now this we have + + + align:start position:0% +b um this is again uh now this we have +high temperature PVD where we've raised + + align:start position:0% +high temperature PVD where we've raised + + + align:start position:0% +high temperature PVD where we've raised +the surface of the wafer up to about + + align:start position:0% +the surface of the wafer up to about + + + align:start position:0% +the surface of the wafer up to about +400° uh much better uh filling not + + align:start position:0% +400° uh much better uh filling not + + + align:start position:0% +400° uh much better uh filling not +completely but but much better and + + align:start position:0% +completely but but much better and + + + align:start position:0% +completely but but much better and +finally if you do to a deposition + + align:start position:0% +finally if you do to a deposition + + + align:start position:0% +finally if you do to a deposition +temperature of 550 and you can't go too + + align:start position:0% +temperature of 550 and you can't go too + + + align:start position:0% +temperature of 550 and you can't go too +hot aluminum melts at six something uh + + align:start position:0% +hot aluminum melts at six something uh + + + align:start position:0% +hot aluminum melts at six something uh +you'd be in trouble but at 550 you get a + + align:start position:0% +you'd be in trouble but at 550 you get a + + + align:start position:0% +you'd be in trouble but at 550 you get a +lot of surface diffusion and you get a + + align:start position:0% +lot of surface diffusion and you get a + + + align:start position:0% +lot of surface diffusion and you get a +lot of Reflow of the aluminum + + align:start position:0% +lot of Reflow of the aluminum + + + align:start position:0% +lot of Reflow of the aluminum +essentially and you completely filled uh + + align:start position:0% +essentially and you completely filled uh + + + align:start position:0% +essentially and you completely filled uh +the trench so much better much smoother + + align:start position:0% +the trench so much better much smoother + + + align:start position:0% +the trench so much better much smoother +topography so that's an example when you + + align:start position:0% +topography so that's an example when you + + + align:start position:0% +topography so that's an example when you +get to very high aspect ratios you + + align:start position:0% +get to very high aspect ratios you + + + align:start position:0% +get to very high aspect ratios you +cannot rely just simply on + + align:start position:0% +cannot rely just simply on + + + align:start position:0% +cannot rely just simply on +sputtering um and so you need to do add + + align:start position:0% +sputtering um and so you need to do add + + + align:start position:0% +sputtering um and so you need to do add +something to the system you add the + + align:start position:0% +something to the system you add the + + + align:start position:0% +something to the system you add the +surface diffusion uh component uh by + + align:start position:0% +surface diffusion uh component uh by + + + align:start position:0% +surface diffusion uh component uh by +raising the wafer temperature so then + + align:start position:0% +raising the wafer temperature so then + + + align:start position:0% +raising the wafer temperature so then +then you need a special system where the + + align:start position:0% +then you need a special system where the + + + align:start position:0% +then you need a special system where the +sputtering system is designed so it can + + align:start position:0% +sputtering system is designed so it can + + + align:start position:0% +sputtering system is designed so it can +can heat the wafer up to reasonably um + + align:start position:0% +can heat the wafer up to reasonably um + + + align:start position:0% +can heat the wafer up to reasonably um +high temperatures at which the the + + align:start position:0% +high temperatures at which the the + + + align:start position:0% +high temperatures at which the the +species will surface + + align:start position:0% + + + + align:start position:0% + +diffuse okay so on slide um 35 I just + + align:start position:0% +diffuse okay so on slide um 35 I just + + + align:start position:0% +diffuse okay so on slide um 35 I just +want to summarize this is as I mentioned + + align:start position:0% +want to summarize this is as I mentioned + + + align:start position:0% +want to summarize this is as I mentioned +this is the last uh lecture on chapter + + align:start position:0% +this is the last uh lecture on chapter + + + align:start position:0% +this is the last uh lecture on chapter +nine um we talked about important issues + + align:start position:0% +nine um we talked about important issues + + + align:start position:0% +nine um we talked about important issues +for thin film deposition we said there + + align:start position:0% +for thin film deposition we said there + + + align:start position:0% +for thin film deposition we said there +are two different uh properties the + + align:start position:0% +are two different uh properties the + + + align:start position:0% +are two different uh properties the +physical properties and theem chemical + + align:start position:0% +physical properties and theem chemical + + + align:start position:0% +physical properties and theem chemical +properties of the film um the coverage + + align:start position:0% +properties of the film um the coverage + + + align:start position:0% +properties of the film um the coverage +um of topography for example this + + align:start position:0% +um of topography for example this + + + align:start position:0% +um of topography for example this +conformal deposition and step coverage + + align:start position:0% +conformal deposition and step coverage + + + align:start position:0% +conformal deposition and step coverage +we said were very important uh there are + + align:start position:0% +we said were very important uh there are + + + align:start position:0% +we said were very important uh there are +two main techniques you need to keep in + + align:start position:0% +two main techniques you need to keep in + + + align:start position:0% +two main techniques you need to keep in +mind chemical vapor and physical vapor + + align:start position:0% +mind chemical vapor and physical vapor + + + align:start position:0% +mind chemical vapor and physical vapor +deposition uh if you have simple CBD + + align:start position:0% +deposition uh if you have simple CBD + + + align:start position:0% +deposition uh if you have simple CBD +models the depth rate is limited by + + align:start position:0% +models the depth rate is limited by + + + align:start position:0% +models the depth rate is limited by +either the surface reaction rate that's + + align:start position:0% +either the surface reaction rate that's + + + align:start position:0% +either the surface reaction rate that's +usually at low temperatures or the mass + + align:start position:0% +usually at low temperatures or the mass + + + align:start position:0% +usually at low temperatures or the mass +transer through the uh gas phase + + align:start position:0% +transer through the uh gas phase + + + align:start position:0% +transer through the uh gas phase +boundary layer that's usually at high + + align:start position:0% +boundary layer that's usually at high + + + align:start position:0% +boundary layer that's usually at high +temperatures um uh uh and uh but you do + + align:start position:0% +temperatures um uh uh and uh but you do + + + align:start position:0% +temperatures um uh uh and uh but you do +have to take into account shadowing and + + align:start position:0% +have to take into account shadowing and + + + align:start position:0% +have to take into account shadowing and +service features um to model the actual + + align:start position:0% +service features um to model the actual + + + align:start position:0% +service features um to model the actual +coverage uh for PVD these processes + + align:start position:0% +coverage uh for PVD these processes + + + align:start position:0% +coverage uh for PVD these processes +again their names is very physical + + align:start position:0% +again their names is very physical + + + align:start position:0% +again their names is very physical +rather than chemical the arrival angle + + align:start position:0% +rather than chemical the arrival angle + + + align:start position:0% +rather than chemical the arrival angle +distribution in the way uh at the wa for + + align:start position:0% +distribution in the way uh at the wa for + + + align:start position:0% +distribution in the way uh at the wa for +surface is important that cosine Theta + + align:start position:0% +surface is important that cosine Theta + + + align:start position:0% +surface is important that cosine Theta +to the end term um in a lot of these + + align:start position:0% +to the end term um in a lot of these + + + align:start position:0% +to the end term um in a lot of these +techniques the species arrive more + + align:start position:0% +techniques the species arrive more + + + align:start position:0% +techniques the species arrive more +vertical uh to the way for surface and + + align:start position:0% +vertical uh to the way for surface and + + + align:start position:0% +vertical uh to the way for surface and +the the sticking coefficient tends to be + + align:start position:0% +the the sticking coefficient tends to be + + + align:start position:0% +the the sticking coefficient tends to be +one for pbd so PVD has a lot lot of + + align:start position:0% +one for pbd so PVD has a lot lot of + + + align:start position:0% +one for pbd so PVD has a lot lot of +shadowing uh issues that you need to + + align:start position:0% +shadowing uh issues that you need to + + + align:start position:0% +shadowing uh issues that you need to +keep into uh keep in + + align:start position:0% +keep into uh keep in + + + align:start position:0% +keep into uh keep in +mind uh we model these uh by having a + + align:start position:0% +mind uh we model these uh by having a + + + align:start position:0% +mind uh we model these uh by having a +sticking coefficient s subc uh and um uh + + align:start position:0% +sticking coefficient s subc uh and um uh + + + align:start position:0% +sticking coefficient s subc uh and um uh +if you have a low sticking coefficient + + align:start position:0% +if you have a low sticking coefficient + + + align:start position:0% +if you have a low sticking coefficient +say much less than 1.01 or something + + align:start position:0% +say much less than 1.01 or something + + + align:start position:0% +say much less than 1.01 or something +like that or 0.1 and you have an + + align:start position:0% +like that or 0.1 and you have an + + + align:start position:0% +like that or 0.1 and you have an +isotropic arrival distribution you'll + + align:start position:0% +isotropic arrival distribution you'll + + + align:start position:0% +isotropic arrival distribution you'll +get much better filling of + + align:start position:0% +get much better filling of + + + align:start position:0% +get much better filling of +holes uh but there are new techniques + + align:start position:0% +holes uh but there are new techniques + + + align:start position:0% +holes uh but there are new techniques +but but this only works to a certain + + align:start position:0% +but but this only works to a certain + + + align:start position:0% +but but this only works to a certain +extent this filling so the latest + + align:start position:0% +extent this filling so the latest + + + align:start position:0% +extent this filling so the latest +techniques use these high density + + align:start position:0% +techniques use these high density + + + align:start position:0% +techniques use these high density +plasma um and these ionized sputtering + + align:start position:0% +plasma um and these ionized sputtering + + + align:start position:0% +plasma um and these ionized sputtering +techniques which have simultaneously + + align:start position:0% +techniques which have simultaneously + + + align:start position:0% +techniques which have simultaneously +sputtering going on uh at the same time + + align:start position:0% +sputtering going on uh at the same time + + + align:start position:0% +sputtering going on uh at the same time +as deposition and this can can be used + + align:start position:0% +as deposition and this can can be used + + + align:start position:0% +as deposition and this can can be used +to get good Gap filling and + + align:start position:0% +to get good Gap filling and + + + align:start position:0% +to get good Gap filling and +planarization so these are the most + + align:start position:0% +planarization so these are the most + + + align:start position:0% +planarization so these are the most +modern techniques people use + + align:start position:0% +modern techniques people use + + + align:start position:0% +modern techniques people use +today um there's a lot of things I we + + align:start position:0% +today um there's a lot of things I we + + + align:start position:0% +today um there's a lot of things I we +didn't get to talk about in in chapter + + align:start position:0% +didn't get to talk about in in chapter + + + align:start position:0% +didn't get to talk about in in chapter +nine in this course 6774 is about + + align:start position:0% +nine in this course 6774 is about + + + align:start position:0% +nine in this course 6774 is about +front-end processing uh but we give the + + align:start position:0% +front-end processing uh but we give the + + + align:start position:0% +front-end processing uh but we give the +Lion Share of the time to oxidation + + align:start position:0% +Lion Share of the time to oxidation + + + align:start position:0% +Lion Share of the time to oxidation +diffusion and I implantation and most of + + align:start position:0% +diffusion and I implantation and most of + + + align:start position:0% +diffusion and I implantation and most of +the lectures are on that um if you + + align:start position:0% +the lectures are on that um if you + + + align:start position:0% +the lectures are on that um if you +really want to know a lot more if if + + align:start position:0% +really want to know a lot more if if + + + align:start position:0% +really want to know a lot more if if +you're a thesis research is going to be + + align:start position:0% +you're a thesis research is going to be + + + align:start position:0% +you're a thesis research is going to be +on thin films for example um we didn't + + align:start position:0% +on thin films for example um we didn't + + + align:start position:0% +on thin films for example um we didn't +cover a lot of things we didn't talk at + + align:start position:0% +cover a lot of things we didn't talk at + + + align:start position:0% +cover a lot of things we didn't talk at +all about the grain structure the + + align:start position:0% +all about the grain structure the + + + align:start position:0% +all about the grain structure the +density the the stress in the film none + + align:start position:0% +density the the stress in the film none + + + align:start position:0% +density the the stress in the film none +of these things did we have time to + + align:start position:0% +of these things did we have time to + + + align:start position:0% +of these things did we have time to +cover and how to model these properties + + align:start position:0% +cover and how to model these properties + + + align:start position:0% +cover and how to model these properties +um there are courses that are more thin + + align:start position:0% +um there are courses that are more thin + + + align:start position:0% +um there are courses that are more thin +film oriented courses like in the + + align:start position:0% +film oriented courses like in the + + + align:start position:0% +film oriented courses like in the +material science department and if you + + align:start position:0% +material science department and if you + + + align:start position:0% +material science department and if you +really want to know about thin films uh + + align:start position:0% +really want to know about thin films uh + + + align:start position:0% +really want to know about thin films uh +Beyond what's in chapter 9 um I would I + + align:start position:0% +Beyond what's in chapter 9 um I would I + + + align:start position:0% +Beyond what's in chapter 9 um I would I +would recommend uh you look towards some + + align:start position:0% +would recommend uh you look towards some + + + align:start position:0% +would recommend uh you look towards some +of those classes but I just wanted to + + align:start position:0% +of those classes but I just wanted to + + + align:start position:0% +of those classes but I just wanted to +make it clear that this is the sort of + + align:start position:0% +make it clear that this is the sort of + + + align:start position:0% +make it clear that this is the sort of +the minimum amount of information you + + align:start position:0% +the minimum amount of information you + + + align:start position:0% +the minimum amount of information you +need to know for front-end processing as + + align:start position:0% +need to know for front-end processing as + + + align:start position:0% +need to know for front-end processing as +far as thin film Depp and epig + + align:start position:0% +far as thin film Depp and epig + + + align:start position:0% +far as thin film Depp and epig +goes okay I think that's about all I + + align:start position:0% +goes okay I think that's about all I + + + align:start position:0% +goes okay I think that's about all I +have um in this for today's lecture um + + align:start position:0% +have um in this for today's lecture um + + + align:start position:0% +have um in this for today's lecture um +as I mentioned at the beginning if you + + align:start position:0% +as I mentioned at the beginning if you + + + align:start position:0% +as I mentioned at the beginning if you +came in late uh hopefully you're working + + align:start position:0% +came in late uh hopefully you're working + + + align:start position:0% +came in late uh hopefully you're working +on hand on uh on um homework number five + + align:start position:0% +on hand on uh on um homework number five + + + align:start position:0% +on hand on uh on um homework number five +is due Thursday and uh I did bring the + + align:start position:0% +is due Thursday and uh I did bring the + + + align:start position:0% +is due Thursday and uh I did bring the +clip forward my assistant has typed up + + align:start position:0% +clip forward my assistant has typed up + + + align:start position:0% +clip forward my assistant has typed up +um her version of what she thinks you're + + align:start position:0% +um her version of what she thinks you're + + + align:start position:0% +um her version of what she thinks you're +going to be uh either talking about or + + align:start position:0% +going to be uh either talking about or + + + align:start position:0% +going to be uh either talking about or +writing up you can check that I've + + align:start position:0% +writing up you can check that I've + + + align:start position:0% +writing up you can check that I've +approved all of them there's only one + + align:start position:0% +approved all of them there's only one + + + align:start position:0% +approved all of them there's only one +person doesn't have anything listed + + align:start position:0% +person doesn't have anything listed + + + align:start position:0% +person doesn't have anything listed +there uh and if you're giving an o + + align:start position:0% +there uh and if you're giving an o + + + align:start position:0% +there uh and if you're giving an o +report what I'm going to do this week is + + align:start position:0% +report what I'm going to do this week is + + + align:start position:0% +report what I'm going to do this week is +start scheduling the uh for the last + + align:start position:0% +start scheduling the uh for the last + + + align:start position:0% +start scheduling the uh for the last +week of classes so you know which day + + align:start position:0% +week of classes so you know which day + + + align:start position:0% +week of classes so you know which day +you have to give your oral + + align:start position:0% +you have to give your oral + + + align:start position:0% +you have to give your oral +report okay good well I'll look forward + + align:start position:0% +report okay good well I'll look forward + + + align:start position:0% +report okay good well I'll look forward +to seeing you on Thursday + + align:start position:0% +to seeing you on Thursday + + + align:start position:0% +to seeing you on Thursday +then \ No newline at end of file diff --git a/TIWE0DaOlzU.txt b/TIWE0DaOlzU.txt new file mode 100644 index 0000000000000000000000000000000000000000..a6f4ceaaa9efb10428875fe7454841f368d61d63 --- /dev/null +++ b/TIWE0DaOlzU.txt @@ -0,0 +1,2616 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: All right, so today +we're going to continue our + +discussion of consumer choice. + +If you remember the set-up +from last time, the main + +motivation is you're trying to +understand what underlies + +demand curves, how consumers +ultimately decide to trade off + +price and quantity of goods. + +We said that ultimately that +came from the principle of + +utility maximization, and that +utility is maximized when + +individuals maximize the utility +function, which is + +this mathematical representation +of preferences. + +And last time we talked about +how if individuals were + +unconstrained how they choose +what they want, they would + +just like more of everything, +and their ranking across + +different bundles would +depend on that + +underlying utility function. + +Now, of course, what's stopping +individuals from + +consuming everything they want +is their budget constraints. + +And so today we're going to turn +to the second part of the + +problem, which is talking about +budget constraints. + +Now, we're going to make a very +simplifying assumption + +here for most of the semester, +which is we are going to + +assume that your income +equals your budget. + +That is, you spend your +entire income. + +That is, we're going to ignore +the possibility of savings + +until about the third lecture +from the end. + +Now, this turns out not to be a +terrible assumption for the + +typical American. + +The typical American doesn't +save. So actually, it's not a + +terrible assumption for us to +work with if we think about + +typical consumers. + +In practice, savings is going +to turn out to be a very + +critical part of what we're +going to do to think about + +economics, so we'll +come back to that. + +But we're going to ignore +savings for now and assume + +that your budget equals +your income. + +So let's say that your parents, +probably a good model + +is you guys, you guys probably +aren't in saving mode. + +You've got some budget saved +from your parents. + +Let's call it y. + +And let's say that your parents +give you some budget + +at the start of the semester, +y, and they say this is your + +money you have to spend, +say each month or + +for the whole semester. + +And let's imagine that you have +to allocate that budget + +only across two goods, +pizza and movies. + +So once again, unrealistic, +but this is the kind of + +simplifying assumption that lets +us understand how people + +make decisions. + +So that gives you your +budget constraint. + +You've got some income y that +your parents have given you, + +and you can allocate that +across pizza and movies. + +So how do you allocate that? + +Well, you can buy movies, the +number of movies you can get, + +plus the number of pizzas. + +Well, how many of each +you can get, that + +depends on their price. + +In particular, budget constraint +is the number of + +movies times the price +per movie plus the + +number of pizzas -- + +plus the number of pizzas times +the price for pizza. + +That's your budget constraint. + +It's the number of movies times +the price per movie or + +the number of pizzas times +the price for pizza. + +And this is easiest to +see graphically. + +If you go to figure 5-1, this is +a graphical illustration of + +a budget constraint. + +Now, let's just carefully talk +through this for a moment. + +You're going to be really good +at dealing with budget + +constraints. + +You're going to have to +be this semester. + +So let's carefully talk about +where this comes from. + +OK, the x-axis is going to be +how many movies you could have + +if all you did with your income +was consume movies. + +Well, if all you did with your +income was consume movies, you + +could have y over +p sub m movies. + +If you decided to devote your +income solely to movies, then + +you could have y times y +over p sub m movies. + +If instead you decided to devote +all your income to + +pizza, then you could have +y over p sub p pizza. + +So the y-axis is going to be +the point where you consume + +zero movies and all pizza. + +It's going to be where +you devote your + +entire budget to pizzas. + +And then there'll be some +combination in between, which + +is our budget line. + +Which is the combinations of +pizzas and movies you can + +consume given your +total income y. + +And the slope of that line is +going to be the price ratio. + +Or the negative of +the price ratio. + +The slope of that line is going +to be minus pp over pm. + +The slope of that line is going +to be the change in the + +ratio of the price of pizza +to the price of movies. + +OK, what am I doing +wrong here? + +Negative of the price ratio. + +Have I got this right? + +Rise over run. + +Yeah. + +Have I got this right? + +Yeah. + +AUDIENCE: I think that the pp +and the pm's are in the + +denominators, because it's y +over pp [INAUDIBLE PHRASE]. + +PROFESSOR: Right. + +It's the denominators, that's +what I did wrong. + +Right, so it is pm over pp. + +Sorry, my bad. + +OK, right. + +Because they're the +denominators. + +Because it's the rise over run +in terms of the quantity. + +So that's what I did wrong. + +OK, so basically it's the +negative of the price ratio, + +minus the price of movies over +the price of pizzas because + +they're in the denominators as +you said, because as the price + +goes up, the quantity +goes down. + +So the negative of the price +ratio of the price of movies + +to the price of pizzas +is the slope. + +So let's just do a +simple example. + +Imagine that income +equals $96. + +Imagine your parents +give you $96, say + +a month or a semester. + +Imagine that the price of movies +is $8 and imagine the + +price of a pizza is $16. + +It's a good pizza. + +So what this means is that with +your income of $96, you + +could either get eight +pizzas or 12 movies. + +So that means that the price +ratio of the slope of your + +budget constraint +is minus 1/2. + +The price ratio is minus 1/2. + +So the slope of that budget +constraint is minus 1/2. + +Now, we have a name +for this slope. + +We're going to call this +the marginal rate of + +transformation. + +The marginal rate of +transformation is our label + +for this slope. + +Now, why do we use that name? + +Well, it means that's the +marginal rate at which you can + +transform pizzas into movies. + +The rate at which you can +turn pizzas into movies. + +Now, once again, like I talked +about last time, you're not an + +alchemist. You're not actually +turning pizzas into movies. + +But the market essentially is +giving you a rate at which you + +can do that given a budget, +given that you have a certain + +amount of money. + +Given that you have a certain +amount of money, $96, and + +given the prices that you face +in the market, you could + +transform pizzas into movies +by trading one + +pizza for 1/2 a movie. + +Now, once again, you're not +actually doing the physical + +transformation, but that's the +trade-off that you face when + +you're trying to transform +one to the other. + +So effectively, it's the same as +if you're trading them for + +each other. + +As I talked about last time. + +it's essentially the same as +you're trading, and that's + +because of the key economic +concept we'll come back to + +over and over again +in this course-- + +the concept of opportunity +cost. + +The opportunity cost is the +value of the forgone + +alternative. + +The value of the forgone +alternative is the opportunity + +cost. So basically what that +means is if you decide to + +forgo a pizza, that's the same +as forgoing two movies. + +Likewise, if you decide to forgo +a movie, it's the same + +as forgoing half a pizza. + +So the opportunity cost of a +movie, what essentially the + +movie is costing you, +is 1/2 a pizza. + +Now, really it's costing you $8 +and a pizza costs you $16. + +But when we think about +trading off goods, the + +opportunity cost of that movie +is that you've forgone the + +ability to eat half a pizza. + +That's the opportunity cost +of the situation. + +So that's basically +how we're going to + +think about this trade-off. + +We're going to think about +trading off goods as the + +opportunity cost of consuming +one good instead of another. + +The opportunity cost of that +movie is that you haven't + +gotten to eat 1/2 a pizza. + +The opportunity cost of the +pizza is that you've forgone + +seeing two movies. + +And the reason is because +you have a fixed budget. + +If you had an infinite budget, +there'd be no opportunity + +cost. But because you have a +fixed budget and you have to + +allocate that budget, there's +an opportunity cost. If you + +choose not to decide, you've +still made a choice. + +I don't know whether that +quote's due to Shakespeare or + +Rush, I'm not sure. + +I have to look that up. + +But basically, if you choose +to have one thing, then by + +definition you're forgoing +another. + +Now, to understand the budget +constraint, let's talk about + +what happens when we shock +the budget constraint. + +Let's imagine the price of +pizzas rose from $16 to $24. + +Pizzas got really expensive. + +We decided we only want gourmet +pizzas or something. + +The price of pizzas went +from $16 to $24. + +What does this do? + +Well, let's look +at figure 5-2. + +It'll show what that does. + +What that does is it says our +new budget constraint, instead + +of being 16p plus 8m equals 96, +which is what the budget + +constraint was in our example, +it's now 24p + +plus 8m equals 96. + +That's the new equation for +the budget constraint. + +Or, more relevantly, the slope +of the budget constraint has + +flattened from minus +1/2 to minus 1/3. + +The slope has fallen from +minus 1/2 to minus 1/3. + +The price ratio has been reduced +from 1/2 to 1/3. + +Now, forget utility +for a second. + +Forget the fact that we +thought about utility. + +Just looking at this, can you +tell whether you are better or + +worse off from this +price change? + +You shook your head +no, why not? + +AUDIENCE: Because you don't know +if you like pizzas enough + +to get any. + +PROFESSOR: OK, well +in particular, + +you can almost tell. + +Who's the only person +who doesn't care + +about this price change? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: No, no no. + +Think about consumers, people +with different preferences for + +pizzas and movies. + +What would your preference for +pizzas and movies have to be + +for you not to care about +this price change? + +All movies. + +So long as you care about +pizza at all, + +you're worse off. + +So in fact, the answer is your +opportunity set has been + +restricted. + +So we can think about +the opportunity set. + +Your opportunity set is the set +of choices you can make + +given your budget. + +Before, you could make choices +all the way up + +to the upper line. + +Now your set of choices +that are + +available have just fallen. + +Now, you're no poorer-- it's +not like your parents + +have cut you off. + +They still give you the $96. + +But you're effectively poorer. + +You're effectively worse +off, and why is that? + +Because the set of things you +could afford with that $96 has + +just been restricted. + +And unless you truly have no +value on pizza, unless all you + +care about's the movie-- + +you're gluten and cheese +allergic or something, you + +have no value on pizza-- + +then you're worse off. + +Your opportunity set's +restricted. + +And that's the key insight here, +is that you are worse + +off because the price +has increased. + +A price increase makes +you worse off. + +It restricts your opportunity +set, because with the same + +amount of income, you can +now afford fewer goods. + +Your opportunity set has +been restricted. + +Likewise, now let's talk +about what happens + +when your income falls. + +That's the next figure. + +Now, let's suppose your parents +are pissed at you and + +they cut you down to $80. + +Because you didn't +do something. + +You don't write enough or +call enough, so they + +cut you down to $80. + +Well, here the slope +of the budget + +constraint has not changed. + +Because what determines the +slope of the budget + +constraint? + +It's prices, and no prices +have changed. + +The slope of the budget +constraint is unchanged + +because prices haven't changed, +but your opportunity + +set is once again restricted +because you + +now have lower income. + +So you can now afford fewer +pizzas and movies. + +So now, instead of being able to +afford up to six pizzas and + +up to 12 movies, you can now +only afford up to five pizzas + +and up to 10 movies because +your income has fallen. + +So once again, you're +unambiguously worse off. + +Your opportunity set +has contracted. + +So your opportunity set will +contract whenever income falls + +or whenever price increases. + +And how it affects the graph +will depend on whether it + +affects prices, which affects +the slope, or just income, + +which affects the intercepts. + +Now, questions about the +budget constraints and + +opportunity sets? + +Armed with that-- + +Yeah, I'm sorry, go ahead. + +AUDIENCE: Is the area under +the curve at all + +indicative of utility? + +PROFESSOR:No, it's not, because +that's going to be + +determined by your +preferences. + +It's indicative of, if you +will, potential utility, + +because that's your +opportunity set. + +But as the example here points +out, if you don't like pizzas + +at all, you'll feel very +differently than if you like + +pizzas a lot. + +So it's indicative of sort of +your potential utility, but + +not your actual well-being. + +But now that's a great segue +to the next step. + +Let's put that together and talk +about constrained choice. + +Which is now, let's +put together-- + +we know what your preferences +are, we've mathematically + +represented those by +utility function. + +We know what your budget set +is, we've mathematically + +represented that based on +your income and prices. + +Now let's put them together +and talk about + +how you make choices. + +And the basic question you want +to ask is, what's the + +highest utility you can achieve +given the constraints + +your budget constraints +put on you? + +Or, graphically-- + +so let's say you wanted to +understand this intuitively, + +graphically, and +mathematically. + +Intuitively the idea is quite +simple, I think, which is + +just, what's the most you can +have given the constraints + +that are placed on you? + +Graphically, we represent that +as asking, what is the + +furthest out indifference +curve you can achieve? + +Because remember, +more is better. + +Indifference curves that are +further out make you happier. + +So what's the furthest out +indifference curve that you + +can achieve given your +budget constraint? + +So to do that, let's actually +do an example. + +Let's imagine, as last time, +your utility is the square + +root of pizza times movies. + +Once again, this has no +fundamental meaning, it's just + +a mathematical representation +of your preferences. + +So your preferences are +mathematically represented by + +utility equals square root +of pizza times movies. + +And let's have the same +budget constraint + +that we have up here. + +Income is $96, price of movies +is $8, price of pizza is $16. + +Now let's go to the +next graph. + +Figure 5-4. + +What this does is put together +our indifference curve + +analysis with our budget +constraint analysis. + +It's a little complicated. + +The budget constraint line is +the vertical line running from + +a y-intercept of six to +an x-intercept of 12. + +The-- not the vertical line, the +straight line running from + +a y-intercept of six to +an x-intercept of 12. + +That's your budget constraint. + +We saw that before. + +Then we have here a series +of indifference curves. + +These curves are drawn-- these +are a mathematical + +representative of this +utility function. + +These are points among which +you're indifferent if you have + +that utility function. + +And what we see is that the best +you can do is to choose + +point D. Point D, with six +movies and three pizzas-- + +OK, that should be p on the +y-axis, not C. It should be + +movies on the x-axis and +pizzas on the y-axis. + +That should be p +on the y-axis. + +The best you can do is +to choose a point D. + +Now, to see that. + +And that gives utility. + +What's the value of your +utility at point D? + +We understand value's +meaningless, but just so we + +can compare, what's the value +of your utility at point D? + +The square root of 18. + +The value of utility is the +square root of 6 times 3, + +which is the square +root of 18. + +Which is going to be square root +of two, or three times + +square root of two, but we'll +just call it square root of 18 + +for comparison. + +Now, let's talk about why that's +the best point for you. + +Let's think about some +alternative points. + +For instance, why is that +better than point E? + +Somebody raise their hand and +tell me, why is point D better + +than point E? + +Yeah? + +AUDIENCE: E is unattainable +with your budget. + +PROFESSOR: E would be better, +that'd be great. + +We'd love eight movies +and four pizzas, but + +we can't reach it. + +So E's unattainable. + +Why is it better than point A? + +Point A you can afford. + +So why's point E better +than point A? + +You could afford point +A just like you can + +afford point D. Yeah? + +AUDIENCE: Because the utility's +only root 10. + +PROFESSOR: Because what? + +AUDIENCE: It's only root 10. + +PROFESSOR: Yes, exactly, because +the utilitity's only + +the square root of 10. + +You're on a lower indifference +curve at point A. So it's true + +you could afford point A, +but you're on a lower + +indifference curve. + +Your utility's a lower value, +it's only square root of 10. + +So point A is dominated by point +D. What about point C? + +Well, point C you +have the same-- + +point C is just an inward shift +from point D, but here + +that's a dominated choice. + +Once again your utility's +lower. + +It's the square root +of 4.5 times 2.2. + +And basically that's dominated +because you could afford more. + +So basically, the point is that +the point which will make + +you happiest is the point at +which your indifference curve + +is tangent to the budget +constraint. + +Because that is the point of the +farthest out indifference + +curve that you can reach given +your budget constraint. + +The tangency of the indifference +curve and the + +budget constraint is the point +which makes you best off given + +your available budget and +the available prices. + +And that's the point where the +slope of the indifference + +curve equals the slope of +the budget constraint. + +The tangency is the point +where the slope of the + +indifference curve equals +the slope of the budget + +constraint. + +Or, more relevantly-- + +OK, let me stop there. + +That's the graphic intuition. + +With a sloping indifference +curve because the slope of the + +budget constraint is the +optimum, because by + +definition, that is the point +of the furthest out + +indifference curve you can +reach given your budget. + +The point of tangency is the +point of equal slopes. + +Are there questions about the +graphical analysis here? + +This is very, very +important, so. + +Yeah? + +AUDIENCE: This is sort of about +the graphical analysis, + +but if it only matters in terms +of the ordinal values of + +the utility function and p and M +are always positive, does it + +matter if you got rid +of the square root? + +Would anything change if +it was u equals pm? + +Because the the marginal +rate of substitution, + +transformation, all that would +still be the same, right? + +PROFESSOR: In this particular +example, it would not. + +So actually, you're asking +a great question. + +Because it's ordinal, you can +typically do transformations + +for the ranking of bundles. + +You will always get the same +ranking with a monotone + +transformation of the +utility function. + +That's exactly right. + +Later in the course, we'll show +different ways why the + +functional form matters, and +I'll show you why I did square + +root, because it's going +to turn out that + +that's going to matter. + +But for other things-- +but for the ranking + +bundles, you're right. + +The ranking of bundles is +consistent with the + +transformation. + +So that's the graphical. + +Now let's come to +the mathematical + +derivation of this. + +So let's talk about the +mathematics of utility + +maximization. + +Now what I'm going to do here +is, I'm going to do this sort + +of casually, as is my wont. + +Friday in section, you're +going to work on the + +underlying calculus that lies +behind the mathematics that + +I'm going to present here. + +Now, let's talk about +what it means that + +these slopes are equal. + +Well, remember, what is-- does +anyone remember what the slope + +of the indifference curve is? + +What do we call the slope of +the indifference curve? + +Yeah? + +AUDIENCE: The MRS. + +PROFESSOR: The MRS. The slope +of the indifference curve is + +the marginal rate +of substitution. + +Which is defined as what? + +What is the marginal rate +of substitution? + +The ratio of what? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: No, the marginal +rate of substitution. + +This is just about +preferences. + +What's the marginal rate of +substitution defined as? + +It's the ratio of +what to what? + +Yeah? + +AUDIENCE: The amount of one good +you have to get to give + +up a unit of the other good. + +PROFESSOR: I'm sorry? + +AUDIENCE: The amount of one good +you have to get to give + +up a unit of the other good. + +PROFESSOR: So graphically +that's what + +it's defined as, exactly. + +It's the slope of the +indifference curve. + +Mathematically, what was it? + +What was it in terms +of utility? + +Does anyone remember? + +Yeah. + +AUDIENCE: The ratio +of the partials. + +PROFESSOR: Ratio of the +marginal utilities. + +In particular, it's the negative +of the marginal + +utility of movies over the +marginal utility of pizza. + +Remember, it's the negative of +the marginal utility of the + +x-axis over the marginal +utility of the y-axis. + +So marginal rate of substitution +is the rate at + +which you're willing to +substitute between movies and + +pizza, which is a function of +your marginal utilities. + +If your marginal utility for +movies is very high, then you + +need a lot of pizzas. + +Then you wouldn't trade a movie +unless you get a lot of + +pizza for it. + +If your marginal utility of +movies is very low, you'd be + +happy to give up a movie +even for a small + +fraction of a pizza. + +So that's the marginal +rate of substitution. + +That's about preferences only. + +At the same time, we're saying +that that marginal rate of + +substitution is equal to-- + +this slope is equal to the +slope of the budget + +constraint. + +Well, the slope of the budget +constraint we call the + +marginal rate of transformation, +which is the + +price ratio. + +The slope of the budget +constraint is the negative of + +the price ratio. + +That's where you were sort of +one step ahead of us here. + +So preferences give us this, +the marginal rate of + +substitution. + +The mechanics of the market give +us the marginal rate of + +transformation. + +And utility maximization gives +us that those are equal, + +because they're equal +at that tangency. + +At that tangency is where you +get to the highest possible + +indifference curve. + +So at the optimum, you get that +the ratio of marginal + +utility equals the +ratio of prices. + +Now, I want to try to see you +understand this a bit more + +intuitively, given +this mathematics. + +The way I like to think about +this is, think about the ratio + +of the marginal utilities +as the marginal benefit. + +So it's the benefit of another +movie in terms of pizza. + +The marginal rate of +substitution is the benefit of + +another movie in +terms of pizza. + +It's how much you like that +next movie relative to how + +much you like that next pizza. + +The marginal rate of +transformation, the cost, is + +the price of that next movie +relative to the price of that + +next pizza. + +So what we're saying here is +we're setting benefits equal + +to the costs. + +In particular, we're setting +marginal benefits equal to + +marginal cost. + +The marginal benefit, the +benefit to that next movie in + +terms of pizza, has got to be +equal to the marginal cost, + +the cost to you in terms +of that next + +movie in terms of pizza. + +And this notion that the optimum +will be where marginal + +benefit equals marginal +cost will pervade + +through the whole course. + +When we do firm maximization, +it'll be the same thing. + +Any maximization we'll do in +this course, any optimization, + +will be about equating +these margins. + +Setting the marginal benefits +equal to marginal costs. + +Now, this is different than +benefits equals cost, because + +it's about the next unit. + +It's saying, how do we feel +about that next movie compared + +to the price of that +next movie. + +Now, prices here we have +being constant. + +You could imagine prices of +movies changing as you see + +more, but that gets +complicated. + +We'll worry about that later. + +For now, the price +is constant. + +But the marginal utilities +are not constant. + +Marginal utilities are obviously +changing the more + +moves you see. + +Once again, with intuition, +you have to + +develop your own intuition. + +The way that I like to think +about this intuitively is to + +actually rewrite this a little +bit, and rewrite it as saying + +that the marginal utility of +movies over the price of + +movies equals the marginal +utility of pizza over the + +price of pizza. + +At the optimum, this'll +be true. + +I like this because to me this +term sort of says, look, the + +bang for the buck has to be +the same across all goods. + +For each dollar of movie +expenditure, what's it buying? + +What's that next dollar of movie +expenditure buying you? + +This is saying, what's that +next dollar of pizza + +expenditure buying you? + +And they've got to be equal. + +If the next dollar of movie +expenditure buys you a lot + +more happiness than the next +dollar of pizza expenditure, + +then you're not at +the right place. + +You should shift your money and +spend more on movies and + +less on pizza. + +If the next dollar of pizza +expenditure buys you a lot + +more happiness than the next +dollar of movie expenditure, + +then you're not in the +right place either. + +You should see fewer movies +and buy more pizza. + +So basically, it's where the +marginal benefit to you-- + +the bang for the buck of that +next movie is the same as the + +bang for the buck of +that next pizza. + +So to see this, let's go back +to figure 5-4 and let's + +actually think through the +mathematics of a couple of + +these points. + +Let's take point A. At point +A, you have two pizzas and + +five movies. + +So pizza equals two, movies +equals five at point A. So + +utility is equal to square +root of 10 at point A. + +Now, in particular, your +marginal utility for pizzas at + +that point-- + +what's the marginal utility +for pizzas? + +Well, we can differentiate. + +That's the derivative of the +utility function with respect + +to prices, du/dp. + +Which is going to be 0.5 times +movies over the square root of + +p times m, which at these values +is going to be one over + +the square root of 10. + +That's your marginal +utility of pizzas. + +Your marginal utility of movies +is going to be du/dm, + +which is going to be 0.5 times +p over square root of p times + +m, which is going to be 2.5 +over square root of 10. + +So the marginal rate of +substitution between + +these two is 2.5. + +The marginal rate of +substitution, 2.5. + +What does that mean +intuitively? + +Can someone tell me what that +means intuitively, the + +marginal rate of substitution +is 2.5? + +What does that mean? + +Someone explain that like you'd +explain it to someone + +who's speaking English. + +What does it mean that +the marginal rate of + +substitution is 2.5? + +Yeah? + +AUDIENCE: You'd give up one +pizza for 2.5 movies. + +Yes. + +No, actually, the opposite. + +You'd give up two +and 1/2 pizzas-- + +the marginal rate of +substitution is 2.5-- + +no, that's right. + +You would give up 2.5-- + +one second, let's make sure +I have this right. + +Right, so you would give up one +pizza to see 2 and 1/2-- + +no, it's the other way around. + +You're getting a lot of pizza +and not enough movies. + +So you would give up two +and 1/2 pizzas to + +get one more movie. + +This is confusing, OK? + +You'd give up two and 1/2 pizzas +to get one more movie. + +That's what it means. + +You would give up two and 1/2 +pizzas to see one more movie, + +and why is that? + +Why at a point like A would you +give up two and 1/2 pizzas + +to see one more movie? + +Yeah? + +AUDIENCE: Well, if you just look +at the line tangent to + +the indifference curve +at A, it's really + +not a downward slope. + +PROFESSOR: It's really steep, +which means what? + +AUDIENCE: Which means you get +a lot more benefit--like you + +don't care if you +give up a lot of + +pizzas to see more movies. + +PROFESSOR: Exactly. + +Actually, that's a great way to +bring the graphics and the + +intuition together. + +Here's thinking of +it intuitively. + +I'm getting a lot of pizza +at point A. I'm not + +getting a lot of movies. + +So I would happily give +up a lot of pizza + +to get my next movie. + +What you pointed out is the +tie to the graphics here. + +The indifference curve is very +steep at that point through A. + +A steep indifference curve in +that way means I don't really + +care a whole lot at this point +about how many pizzas I get, + +but I care a lot about +getting more movies. + +So at a point like A where +it's very steep, you are + +willing to give up two and 1/2 +pizzas to see a movie. + +But what do you have +to give up? + +What's the market telling +you you have to + +give up to see a movie? + +How much pizza do you actually +have to give up to see a movie + +in practice? + +You're willing to give up two +and 1/2 pizzas to see a movie, + +but how many pizzas do you +actually have to give up? + +AUDIENCE: 1/2. + +PROFESSOR: 1/2 a pizza +to see a movie. + +So that can't be the optimum. + +You're willing to give up two +and 1/2 pizzas to see a movie, + +but you only have to give up +1/2 a pizza to see a movie. + +So you can't be at +the right place. + +You should be changing your +consumption bundle. + +You should be changing your +consumption bundle, because + +the market is only asking for +1/2 a pizza to see a movie, + +but you're willing to +give up two and 1/2 + +pizzas to see a movie. + +So at a point like A, you're +clearly not at the optimum. + +Because you are willing +to make a trade. + +Remember, we talked about-- we +can go all the way back to the + +first lecture. + +The key point was-- the first +or second lecture-- + +inefficiency happens +when trades aren't + +made that people value. + +Here's a trade that you value. + +You're willing to give up two +and 1/2 pizzas to see a movie. + +The market only wants 1/2 +a pizza to see a movie. + +You're not making a trade you +value, so that's not the + +efficient outcome. + +Likewise, let's do the same +mathematics at point B. Well, + +at point B, if you do the math +and work it out, you see that + +the marginal utility of +pizza is five over + +square root of ten. + +The marginal utility of +movies is 0.5 over the + +square root of 10. + +So the MRS is 0.1. + +At this point, you'd only be +willing to give up 0.1 pizzas + +to see a movie. + +At a point like B, +the indifference + +curve is very flat. + +You're only willing to give up +0.1 pizzas to see a movie. + +But remember, the market is +willing to say, look-- + +you can flip it around, the +market's willing to say, look, + +you can get a movie. + +You're only willing to give up +0.1 pizzas to see a movie. + +Well, that means clearly that +you have too many movies and + +not enough pizza. + +You're clearly at that point +happy to say, wow, you mean + +that I can gain a whole pizza by +just giving up two movies? + +Heck, I'd be willing to give up +10 movies to get a pizza. + +At the point I'm at right there, +I'd be willing to give + +up 10 movies to get a pizza. + +You're telling me we only +have to give up two + +movies to get a pizza? + +Great. + +I'm going to do that trade. + +I'm going to move back towards +point D. So that's why this + +idea of what you're willing to +do, which is the MRS, and what + +the market's making you do, you +want to equilibrate those + +to decide how much you +want to consume. + +Now, obviously a point like-- + +let's talk about point C. +Point C is interesting, + +because at point +C, what's true? + +The marginal rate of +substitution is equal to the + +marginal rate of transformation +at point C. The + +slope of the indifference +curve and the budget + +constraint are equal. + +That's why you have to check +two conditions for + +optimization. + +First of all, those slopes +have to be equal. + +Second of all, you've got +to spend all your money. + +So it's true there's a whole +host of points-- in fact, + +there's a vector running through +CDE, all which are + +points where the margin rate +of substitution equals the + +margin rate of transformation. + +But only D is optimal, because +you also have to + +remember more is better. + +You never want to leave +money on the table. + +So the two conditions you have +to meet is that you're at the + +point where your desired +trade-off between pizzas and + +movies is the same as the +market's, and where you're + +spending all your budget. + +And that's the optimum. + +OK, questions about that? + +So that's basically how we +think about optimization. + +That's how we think about +consumers making their + +decisions deciding between +consuming pizzas and movies. + +Now, let's come back-- however, +this is a particular + +case we've looked at. + +This is a case in particular +where we've imposed that + +there's an interior solution. + +In fact, in practice you could +end up in these kinds of + +choices with corner solutions. + +So let's take a look at the +last figure, figure 5-5. + +We've chosen a case where your +optimal bundle includes both + +pizza and movies. + +But you could imagine +a situation where + +your optimal bundle-- + +and once again, that should be +a p, not a c in figure 5-5, + +that should be p +on the y-axis-- + +where your optimal +bundle includes + +only one or the other. + +So this is a particular case-- +we have the same budget line + +as before, which is you're +trading off pizza and movies. + +You have an income of 96, the +price of pizzas is 16, the + +price of movies is 8. + +So same budget line as before. + +But now your indifference curves +look very different. + +Now your preferences are such +that you've got these linear + +difference curves of the +form I1, I2, I3. + +You've got these linear +indifference curves. + +What that means is +you've got-- + +these indifference curves mean +that you have a constant rate + +at which you're willing to trade +off pizza for movies. + +If we go back to figure 5.4, +the rate at which you're + +willing to trade off pizza +for movies changes. + +Your preferences +are such that-- + +because the square root function +as pointed out-- + +your preferences are such that +you are willing to make + +different rates of trade +at different amounts. + +In figure 5-5, your preferences +are constant, no + +matter how many movies or pizzas +you have. You're always + +willing to make that trade-off +at the same rate. + +Well, in that case you can end +up with a corner solution, + +where in fact, you're going +to consume only six + +pizzas and no movies. + +And why is that? + +That's because this is a +person who loves pizza + +relative to movies. + +It's a very flat indifference +curve. + +They love pizza relative +to movies. + +And they love pizza so much +relative to movies that given + +the prices they face, they'll +just go ahead and choose six + +pizzas and no movies. + +So that's a corner solution. + +So mathematically, as you'll +go through a section on + +Friday, you're going to have to +check for corner solutions. + +You may solve these problems +and end up with negative + +quantities and be befuddled +about what happens. + +Well, if an answer looks +wrong, it is wrong. + +If you solve problems with +negative quantities, that's + +probably because there's a +corner solution to the + +problem, and actually the +optimal quantity is to have + +zero of one thing and spend +your entire budget on + +something else. + +Questions about that? + +So now let's think about +applying this to the kinds of + +decisions that you +all have to make. + +So I talked about this +particular example of pizza + +and movies. + +And in fact, you might say, +well, that's sort of + +unrealistic. + +Gee, I spend my budget +on lots of things, + +and how do I do this? + +Well, in practice, what you'd +have to do is you'd have to + +draw a multi-dimensional +graph and solve a + +multi-dimensional problem. + +And that's a bear. + +But in practice, in fact, we can +often think about breaking + +down the choices we make +into pairs of choices. + +In practice, you could think +about saying, look-- + +many people do what a lot of +psychologists call mental + +accounting, where basically they +say, look, yes, I have a + +whole budget and lots +of things I can buy. + +But in fact, I like to think +of my budget in sort of + +subcategories. + +I think of a certain amount +I'm willing to spend on + +entertainment and a +certain amount I'm + +willing to spend on food. + +And I take my budget and +I mentally put it + +in different buckets. + +And within each of those +buckets, you can then do the + +same kind of optimization +problem that we've done here. + +So even though in reality we +choose across a whole host of + +goods, in practice what you're +going to see is that people + +will do this kind of mental +accounting, where they sort of + +divide their goods into +different buckets and optimize + +within each of those buckets. + +What this means in practice is +that in fact, if we now stop + +for a second and think about +the government, and how it + +affects our consumption +decisions, what this means is + +that in practice, +the government-- + +so, one way we typically of +the government affecting + +consumption decisions is through +the power of taxation. + +So let's say for example, +the government decided + +that pizzas were bad. + +They caused obesity. + +That there's too much obesity +because people are eating too + +much pizza, and we need to +deal with that through a + +government policy that +involves taxation. + +Somebody talk me through the +analysis of how we'd think + +about analyzing a tax on pizza +given these diagrams. + +Let's go to figure 5-4. + +And imagine I said that +we're going to place + +a 50% tax on pizza. + +So we're going to say that every +dollar you pay on pizza, + +you're going to have to pay +$0.50 to the government. + +Because we're really +worried people are + +eating too much pizza. + +What would that do the +budget constraint? + +Yeah. + +AUDIENCE: Well, effectively +you're increasing + +the price of pizza. + +PROFESSOR: Effectively you're +increasing the price of pizza + +to the consumer. + +AUDIENCE: The budget +constraint would + +shift down like this. + +PROFESSOR: It's actually going +to have the same effect as we + +saw in figure 5-2. + +In fact, I've just replicated +figure 5-2. + +Because in figure 5-2, the price +of pizza went up by 50%, + +from $16 to $24. + +That's the same thing that the +government's just done. + +It's raised the price of pizza +effectively from $16 a pizza + +to $24 because instead of paying +your $16, you're also + +going to pay $8 to the +government in tax. + +So what's that going to do? + +That is going to, in general, +lower consumption of pizza. + +So that kind of price increase +is going to, in general, lower + +the consumption of pizza. + +So the government has tried +to accomplish its goal by + +shifting people away from pizza +towards movies, away + +from pizza toward +other things. + +Yeah? + +AUDIENCE: Would it be meaningful +to say that it also + +affects the utility curves? + +PROFESSOR: It would not be +meaningful, actually-- + +it will affect your +optimal choice. + +In general, you will choose +a different amount + +of pizza and movies. + +We'll talk about +that next time. + +But it's very important, it +would not be right to say it + +affects utility. + +Utility is like what you're +born with, it's an innate + +concept about your underlying +preferences. + +However, you're actually getting +to my point, which is + +in fact, the way economists +typically think about this is + +the government can't affect +your preferences. + +But in fact, if people do +mental accounting, the + +government maybe can affect +your preferences. + +So let's say that basically the +way I think about it is, + +let's say I think I have a +budget for food and I have a + +budget for entertainment. + +And let's say I think my budget +for entertainment's + +pretty small because +I'm low income. + +I've gotta have a +budget for food. + +And so let's say I put pizza +in my budget for food, so I + +allocate some of my budget +for food to pizza. + +And the government can then +cause me to eat less + +pizza by taxing it. + +But what if somehow the +government could get me to + +think of pizza differently? + +What if somehow the government +could get me to think of pizza + +as entertainment? + +And suddenly I put it in that +bucket, where I'm trading it + +off not against other food, but +against the fact that I + +want to see a movie and I +want to download stuff + +from iTunes, et cetera. + +Maybe then I'd buy less pizza at +the same price because I'm + +putting it in the bucket where +I have less money. + +So in other words, +we've imagined a + +world with two goods. + +And the only way you can affect +the choice across those + +two goods is to lower your +income or your price. + +But in fact, if people have lots +of different bundles of + +goods, somehow I could shift you +mentally from considering + +pizza in a bucket where you have +a lot of money to putting + +pizza in a bucket where you +don't have as much money. + +I can lower your consumption +of pizza without affecting + +prices, without an obtrusive +government tax policy. + +This is the kind of thing +that we call in + +economic policy a nudge. + +And there's a new book called +Nudge by Richard Thaler, who's + +a famous behavioral economist, +basically bringing psychology + +into economics. + +There's this very important +field now in economics called + +behavioral economics, which is +all about, how can we bring + +the lessons of psychology +into economics? + +We don't do that in 14.01. + +14.01's all about, we assume +everybody's these perfectly + +rational people who would never +really be fooled into + +thinking about pizza differently +just because of + +what the government told them. + +But in fact, in reality people +think about things differently + +based on the kinds of +information they have. And + +given that tax policies can feel +very intrusive-- imagine + +some of you are like, wow, +they're raising my pizza to + +$24, that seems very +intrusive. + +If the government could somehow +through nudging you to + +think about pizza differently +change your pizza consumption, + +that might be a much more +acceptable and palatable + +policy to many people. + +And that's the kind of role the +government can play, or + +policy-makers can play, is not +just by changing your prices + +or income, but by actually +changing how you categorize + +things mentally, they can change +the choices you make. \ No newline at end of file diff --git a/TuXFwKrWQg8.txt b/TuXFwKrWQg8.txt new file mode 100644 index 0000000000000000000000000000000000000000..225b2226a88d8bb568e713684ded2341cb3c10fb --- /dev/null +++ b/TuXFwKrWQg8.txt @@ -0,0 +1,13459 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + 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align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so today the the general + + align:start position:0% +ocw.mit.edu so today the the general + + + align:start position:0% +ocw.mit.edu so today the the general +theme is going to be to try to + + align:start position:0% +theme is going to be to try to + + + align:start position:0% +theme is going to be to try to +understand uh how how bacteria uh find + + align:start position:0% +understand uh how how bacteria uh find + + + align:start position:0% +understand uh how how bacteria uh find +food and uh in particular how do they uh + + align:start position:0% +food and uh in particular how do they uh + + + align:start position:0% +food and uh in particular how do they uh +how do they know which direction to swim + + align:start position:0% +how do they know which direction to swim + + + align:start position:0% +how do they know which direction to swim +how do they swim given that they're + + align:start position:0% +how do they swim given that they're + + + align:start position:0% +how do they swim given that they're +operating this low Reynolds number + + align:start position:0% +operating this low Reynolds number + + + align:start position:0% +operating this low Reynolds number +regime that uh that you read about uh + + align:start position:0% +regime that uh that you read about uh + + + align:start position:0% +regime that uh that you read about uh +maybe last night uh what what did you + + align:start position:0% +maybe last night uh what what did you + + + align:start position:0% +maybe last night uh what what did you +guys think of the life at L Reynolds + + align:start position:0% +guys think of the life at L Reynolds + + + align:start position:0% +guys think of the life at L Reynolds +number uh yeah it's kind of fun right + + align:start position:0% +number uh yeah it's kind of fun right + + + align:start position:0% +number uh yeah it's kind of fun right +you know it's it's you very much get the + + align:start position:0% +you know it's it's you very much get the + + + align:start position:0% +you know it's it's you very much get the +impression that you are kind of there in + + align:start position:0% +impression that you are kind of there in + + + align:start position:0% +impression that you are kind of there in +that lecture hall with him you know you + + align:start position:0% +that lecture hall with him you know you + + + align:start position:0% +that lecture hall with him you know you +know they do say that you know some + + align:start position:0% +know they do say that you know some + + + align:start position:0% +know they do say that you know some +essential arm waving was not reproduced + + align:start position:0% +essential arm waving was not reproduced + + + align:start position:0% +essential arm waving was not reproduced +or so right but but you kind of Imagine + + align:start position:0% +or so right but but you kind of Imagine + + + align:start position:0% +or so right but but you kind of Imagine +his arms waving as as he does as he as + + align:start position:0% +his arms waving as as he does as he as + + + align:start position:0% +his arms waving as as he does as he as +he talks even though you don't get to + + align:start position:0% +he talks even though you don't get to + + + align:start position:0% +he talks even though you don't get to +hear him talk + + align:start position:0% +hear him talk + + + align:start position:0% +hear him talk +um right so I think yeah so that that's + + align:start position:0% +um right so I think yeah so that that's + + + align:start position:0% +um right so I think yeah so that that's +uh that's fun and you it's a surprising + + align:start position:0% +uh that's fun and you it's a surprising + + + align:start position:0% +uh that's fun and you it's a surprising +number of typos you know given that + + align:start position:0% +number of typos you know given that + + + align:start position:0% +number of typos you know given that +right every time I read that I'm um + + align:start position:0% +right every time I read that I'm um + + + align:start position:0% +right every time I read that I'm um +somehow this is still the best version + + align:start position:0% +somehow this is still the best version + + + align:start position:0% +somehow this is still the best version +that I've been able to find of of that + + align:start position:0% +that I've been able to find of of that + + + align:start position:0% +that I've been able to find of of that +uh of that talk but I think that it's + + align:start position:0% +uh of that talk but I think that it's + + + align:start position:0% +uh of that talk but I think that it's +just a neat example of how uh well + + align:start position:0% +just a neat example of how uh well + + + align:start position:0% +just a neat example of how uh well +clearly a talented physicist can kind of + + align:start position:0% +clearly a talented physicist can kind of + + + align:start position:0% +clearly a talented physicist can kind of +from a naive perspective say interesting + + align:start position:0% +from a naive perspective say interesting + + + align:start position:0% +from a naive perspective say interesting +things about the way that life has to + + align:start position:0% +things about the way that life has to + + + align:start position:0% +things about the way that life has to +work right now um + + align:start position:0% +work right now um + + + align:start position:0% +work right now um +today so we we will be talking indeed + + align:start position:0% +today so we we will be talking indeed + + + align:start position:0% +today so we we will be talking indeed +about how bacteria are swimm but we we + + align:start position:0% +about how bacteria are swimm but we we + + + align:start position:0% +about how bacteria are swimm but we we +we want to start by just making sure we + + align:start position:0% +we want to start by just making sure we + + + align:start position:0% +we want to start by just making sure we +understand something about uh how + + align:start position:0% +understand something about uh how + + + align:start position:0% +understand something about uh how +diffusion Works uh what life is like in + + align:start position:0% +diffusion Works uh what life is like in + + + align:start position:0% +diffusion Works uh what life is like in +this low reyolds number regime and for + + align:start position:0% +this low reyolds number regime and for + + + align:start position:0% +this low reyolds number regime and for +these sorts of problems it's really very + + align:start position:0% +these sorts of problems it's really very + + + align:start position:0% +these sorts of problems it's really very +very valuable if you can just apply some + + align:start position:0% +very valuable if you can just apply some + + + align:start position:0% +very valuable if you can just apply some +simple dimensional analysis ideas and so + + align:start position:0% +simple dimensional analysis ideas and so + + + align:start position:0% +simple dimensional analysis ideas and so +we're going to uh we're going to + + align:start position:0% +we're going to uh we're going to + + + align:start position:0% +we're going to uh we're going to +practice that in a few different cases + + align:start position:0% +practice that in a few different cases + + + align:start position:0% +practice that in a few different cases +right that dimensional analysis can + + align:start position:0% +right that dimensional analysis can + + + align:start position:0% +right that dimensional analysis can +often tell you a great deal right in + + align:start position:0% +often tell you a great deal right in + + + align:start position:0% +often tell you a great deal right in +many cases you can discover new + + align:start position:0% +many cases you can discover new + + + align:start position:0% +many cases you can discover new +physical laws you can figure out how + + align:start position:0% +physical laws you can figure out how + + + align:start position:0% +physical laws you can figure out how +things have to scale and in some cases + + align:start position:0% +things have to scale and in some cases + + + align:start position:0% +things have to scale and in some cases +the scalings are rather surprising + + align:start position:0% +the scalings are rather surprising + + + align:start position:0% +the scalings are rather surprising +okay um and uh given given some of the + + align:start position:0% +okay um and uh given given some of the + + + align:start position:0% +okay um and uh given given some of the +constraints that uh that microscopic + + align:start position:0% +constraints that uh that microscopic + + + align:start position:0% +constraints that uh that microscopic +life is facing right in this low reyolds + + align:start position:0% +life is facing right in this low reyolds + + + align:start position:0% +life is facing right in this low reyolds +number regime where defusion is very + + align:start position:0% +number regime where defusion is very + + + align:start position:0% +number regime where defusion is very +important viscous forces are dominating + + align:start position:0% +important viscous forces are dominating + + + align:start position:0% +important viscous forces are dominating +over these inertial forces right it + + align:start position:0% +over these inertial forces right it + + + align:start position:0% +over these inertial forces right it +really constrains uh what bacteria for + + align:start position:0% +really constrains uh what bacteria for + + + align:start position:0% +really constrains uh what bacteria for +example are able to do and it really + + align:start position:0% +example are able to do and it really + + + align:start position:0% +example are able to do and it really +constraints how they uh how they have to + + align:start position:0% +constraints how they uh how they have to + + + align:start position:0% +constraints how they uh how they have to +go about solving uh the challenges of + + align:start position:0% +go about solving uh the challenges of + + + align:start position:0% +go about solving uh the challenges of +life + + align:start position:0% +life + + + align:start position:0% +life +okay so what I want to do is is start by + + align:start position:0% +okay so what I want to do is is start by + + + align:start position:0% +okay so what I want to do is is start by +uh by ask uh thinking about just a very + + align:start position:0% +uh by ask uh thinking about just a very + + + align:start position:0% +uh by ask uh thinking about just a very +kind of simple situation which is if we + + align:start position:0% +kind of simple situation which is if we + + + align:start position:0% +kind of simple situation which is if we +have um in we'll say water there's we + + align:start position:0% +have um in we'll say water there's we + + + align:start position:0% +have um in we'll say water there's we +have a a non-permeable membrane that is + + align:start position:0% +have a a non-permeable membrane that is + + + align:start position:0% +have a a non-permeable membrane that is +separating two + + align:start position:0% +separating two + + + align:start position:0% +separating two +compartments okay whereas over here we + + align:start position:0% +compartments okay whereas over here we + + + align:start position:0% +compartments okay whereas over here we +have maybe salt or something uh on the + + align:start position:0% +have maybe salt or something uh on the + + + align:start position:0% +have maybe salt or something uh on the +right you know okay so this is say salty + + align:start position:0% +right you know okay so this is say salty + + + align:start position:0% +right you know okay so this is say salty +solution + + align:start position:0% + + + + align:start position:0% + +all right and this is pure + + align:start position:0% + + + + align:start position:0% + +water now uh this is a a non-permeable + + align:start position:0% +water now uh this is a a non-permeable + + + align:start position:0% +water now uh this is a a non-permeable +uh non-permeable membrane so it doesn't + + align:start position:0% +uh non-permeable membrane so it doesn't + + + align:start position:0% +uh non-permeable membrane so it doesn't +allow the salt to cross okay but the + + align:start position:0% +allow the salt to cross okay but the + + + align:start position:0% +allow the salt to cross okay but the +question is well what happens if I + + align:start position:0% +question is well what happens if I + + + align:start position:0% +question is well what happens if I +puncture and I put a little hole in the + + align:start position:0% +puncture and I put a little hole in the + + + align:start position:0% +puncture and I put a little hole in the +membrane of uh some radius a say uh now + + align:start position:0% +membrane of uh some radius a say uh now + + + align:start position:0% +membrane of uh some radius a say uh now +the question is uh what will be the uh + + align:start position:0% +the question is uh what will be the uh + + + align:start position:0% +the question is uh what will be the uh +flow rate the net uh net flow of uh of + + align:start position:0% +flow rate the net uh net flow of uh of + + + align:start position:0% +flow rate the net uh net flow of uh of +salt in this case uh from the right to + + align:start position:0% +salt in this case uh from the right to + + + align:start position:0% +salt in this case uh from the right to +the + + align:start position:0% + + + + align:start position:0% + +left right so first of all can + + align:start position:0% +left right so first of all can + + + align:start position:0% +left right so first of all can +somebody uh kind of answer you know at + + align:start position:0% +somebody uh kind of answer you know at + + + align:start position:0% +somebody uh kind of answer you know at +least for a couple you know what are + + align:start position:0% +least for a couple you know what are + + + align:start position:0% +least for a couple you know what are +possible things that might be relevant + + align:start position:0% +possible things that might be relevant + + + align:start position:0% +possible things that might be relevant +if we're going to if we're going to try + + align:start position:0% +if we're going to if we're going to try + + + align:start position:0% +if we're going to if we're going to try +to figure this out what quantities will + + align:start position:0% +to figure this out what quantities will + + + align:start position:0% +to figure this out what quantities will +we need to know or measure Concentra + + align:start position:0% +we need to know or measure Concentra + + + align:start position:0% +we need to know or measure Concentra +concentration seems like relevant + + align:start position:0% + + + + align:start position:0% + +yeah right and in this case there's only + + align:start position:0% +yeah right and in this case there's only + + + align:start position:0% +yeah right and in this case there's only +one concentration because well I mean + + align:start position:0% +one concentration because well I mean + + + align:start position:0% +one concentration because well I mean +this concentration is zero here and some + + align:start position:0% +this concentration is zero here and some + + + align:start position:0% +this concentration is zero here and some +concentration C over here okay what what + + align:start position:0% +concentration C over here okay what what + + + align:start position:0% +concentration C over here okay what what +else might we need to + + align:start position:0% +else might we need to + + + align:start position:0% +else might we need to +know the poe size Perfect all right + + align:start position:0% +know the poe size Perfect all right + + + align:start position:0% +know the poe size Perfect all right +we'll say uh we'll use a as the radius + + align:start position:0% +we'll say uh we'll use a as the radius + + + align:start position:0% +we'll say uh we'll use a as the radius +of the pore + + align:start position:0% + + + + align:start position:0% + +uh and is that going to is that going to + + align:start position:0% +uh and is that going to is that going to + + + align:start position:0% +uh and is that going to is that going to +do + + align:start position:0% + + + + align:start position:0% + +it we need a time right because we want + + align:start position:0% +it we need a time right because we want + + + align:start position:0% +it we need a time right because we want +what we want is something you know some + + align:start position:0% +what we want is something you know some + + + align:start position:0% +what we want is something you know some +number of molecules per unit time that + + align:start position:0% +number of molecules per unit time that + + + align:start position:0% +number of molecules per unit time that +is going to be Crossing from the right + + align:start position:0% +is going to be Crossing from the right + + + align:start position:0% +is going to be Crossing from the right +to the left so we need something that + + align:start position:0% +to the left so we need something that + + + align:start position:0% +to the left so we need something that +has a + + align:start position:0% +has a + + + align:start position:0% +has a +time + + align:start position:0% +time + + + align:start position:0% +time +yes all right the diffusivity right so + + align:start position:0% +yes all right the diffusivity right so + + + align:start position:0% +yes all right the diffusivity right so +you so D so we'll say d which is uh the + + align:start position:0% +you so D so we'll say d which is uh the + + + align:start position:0% +you so D so we'll say d which is uh the +diffusion coefficient okay + + align:start position:0% + + + + align:start position:0% + +how many s's + + align:start position:0% +how many s's + + + align:start position:0% +how many s's +diffusion all + + align:start position:0% + + + + align:start position:0% + +right all right now other things that + + align:start position:0% +right all right now other things that + + + align:start position:0% +right all right now other things that +might be + + align:start position:0% + + + + align:start position:0% + +relevant temperature temperature okay I + + align:start position:0% +relevant temperature temperature okay I + + + align:start position:0% +relevant temperature temperature okay I +guess it's + + align:start position:0% +guess it's + + + align:start position:0% +guess it's +probably exactly right so indeed the + + align:start position:0% +probably exactly right so indeed the + + + align:start position:0% +probably exactly right so indeed the +flow rate will be dependent upon the uh + + align:start position:0% +flow rate will be dependent upon the uh + + + align:start position:0% +flow rate will be dependent upon the uh +on the temperature but the way that that + + align:start position:0% +on the temperature but the way that that + + + align:start position:0% +on the temperature but the way that that +manifests is by uh doing what to + + align:start position:0% + + + + align:start position:0% + +D in general if we go up to higher + + align:start position:0% +D in general if we go up to higher + + + align:start position:0% +D in general if we go up to higher +temperature how will D + + align:start position:0% +temperature how will D + + + align:start position:0% +temperature how will D +change should bigger should get bigger + + align:start position:0% +change should bigger should get bigger + + + align:start position:0% +change should bigger should get bigger +in yeah so indeed D will um be typically + + align:start position:0% +in yeah so indeed D will um be typically + + + align:start position:0% +in yeah so indeed D will um be typically +given by this einin of relation of KT + + align:start position:0% +given by this einin of relation of KT + + + align:start position:0% +given by this einin of relation of KT +over gamma we'll talk more about this uh + + align:start position:0% +over gamma we'll talk more about this uh + + + align:start position:0% +over gamma we'll talk more about this uh +in a little bit right but for now let's + + align:start position:0% +in a little bit right but for now let's + + + align:start position:0% +in a little bit right but for now let's +just say the D is something that we've + + align:start position:0% +just say the D is something that we've + + + align:start position:0% +just say the D is something that we've +measured + + align:start position:0% +measured + + + align:start position:0% +measured +right right now uh other things that may + + align:start position:0% +right right now uh other things that may + + + align:start position:0% +right right now uh other things that may +that may enter into the + + align:start position:0% + + + + align:start position:0% + +expression all right so this is uh this + + align:start position:0% +expression all right so this is uh this + + + align:start position:0% +expression all right so this is uh this +is pretty simple right we have three + + align:start position:0% +is pretty simple right we have three + + + align:start position:0% +is pretty simple right we have three +things now uh the question is uh if we + + align:start position:0% +things now uh the question is uh if we + + + align:start position:0% +things now uh the question is uh if we +uh if we double the size of the poe I if + + align:start position:0% +uh if we double the size of the poe I if + + + align:start position:0% +uh if we double the size of the poe I if +we double if we double A how does the + + align:start position:0% +we double if we double A how does the + + + align:start position:0% +we double if we double A how does the +flow rate change okay so we'll go ahead + + align:start position:0% +flow rate change okay so we'll go ahead + + + align:start position:0% +flow rate change okay so we'll go ahead +and do a vote since we like to do + + align:start position:0% +and do a vote since we like to do + + + align:start position:0% +and do a vote since we like to do +this right + + align:start position:0% + + + + align:start position:0% + +right all right so we double a the flow + + align:start position:0% +right all right so we double a the flow + + + align:start position:0% +right all right so we double a the flow +goes uh up by what + + align:start position:0% + + + + align:start position:0% + +factor right maybe not at + + align:start position:0% + + + + align:start position:0% + +all all right and if you think it's + + align:start position:0% +all all right and if you think it's + + + align:start position:0% +all all right and if you think it's +uh something else you can + + align:start position:0% +uh something else you can + + + align:start position:0% +uh something else you can +uh you know SP your cards out right now + + align:start position:0% +uh you know SP your cards out right now + + + align:start position:0% +uh you know SP your cards out right now +now the idea here is that uh using + + align:start position:0% +now the idea here is that uh using + + + align:start position:0% +now the idea here is that uh using +dimensional analysis we should be able + + align:start position:0% +dimensional analysis we should be able + + + align:start position:0% +dimensional analysis we should be able +to figure this out okay now I'll give + + align:start position:0% +to figure this out okay now I'll give + + + align:start position:0% +to figure this out okay now I'll give +you just uh a minute to try to think + + align:start position:0% +you just uh a minute to try to think + + + align:start position:0% +you just uh a minute to try to think +think through this + + align:start position:0% + + + + align:start position:0% + +all right so I'm yeah so you don't even + + align:start position:0% +all right so I'm yeah so you don't even + + + align:start position:0% +all right so I'm yeah so you don't even +need to know this in principle I'm going + + align:start position:0% +need to know this in principle I'm going + + + align:start position:0% +need to know this in principle I'm going +to give you something else that may + + align:start position:0% + + + + align:start position:0% + +help uh + + align:start position:0% +help uh + + + align:start position:0% +help uh +yeah so this is the mean uh the mean + + align:start position:0% +yeah so this is the mean uh the mean + + + align:start position:0% +yeah so this is the mean uh the mean +squared uh distance that something will + + align:start position:0% +squared uh distance that something will + + + align:start position:0% +squared uh distance that something will +diffuse yeah + + align:start position:0% +diffuse yeah + + + align:start position:0% +diffuse yeah +uh yeah so I I I I wasn't explaining + + align:start position:0% +uh yeah so I I I I wasn't explaining + + + align:start position:0% +uh yeah so I I I I wasn't explaining +because that was sort of a hint in the + + align:start position:0% +because that was sort of a hint in the + + + align:start position:0% +because that was sort of a hint in the +sense that I was just you know in case + + align:start position:0% +sense that I was just you know in case + + + align:start position:0% +sense that I was just you know in case +you might remember something like an + + align:start position:0% +you might remember something like an + + + align:start position:0% +you might remember something like an +equation yeah but + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +yes uh right okay so the yeah so there's + + align:start position:0% +yes uh right okay so the yeah so there's + + + align:start position:0% +yes uh right okay so the yeah so there's +going to be some question of time scales + + align:start position:0% +going to be some question of time scales + + + align:start position:0% +going to be some question of time scales +here okay so I it's it's really that + + align:start position:0% +here okay so I it's it's really that + + + align:start position:0% +here okay so I it's it's really that +after you puncture the hole you know + + align:start position:0% +after you puncture the hole you know + + + align:start position:0% +after you puncture the hole you know +very rapidly it's G to it's going to + + align:start position:0% +very rapidly it's G to it's going to + + + align:start position:0% +very rapidly it's G to it's going to +assume some kind of steady state right + + align:start position:0% +assume some kind of steady state right + + + align:start position:0% +assume some kind of steady state right +and then uh then the flow rate will be + + align:start position:0% +and then uh then the flow rate will be + + + align:start position:0% +and then uh then the flow rate will be +constant for some rather long time but + + align:start position:0% +constant for some rather long time but + + + align:start position:0% +constant for some rather long time but +then eventually the concentration will + + align:start position:0% +then eventually the concentration will + + + align:start position:0% +then eventually the concentration will +on this half will will decrease right so + + align:start position:0% +on this half will will decrease right so + + + align:start position:0% +on this half will will decrease right so +we're we're thinking about the flow rate + + align:start position:0% +we're we're thinking about the flow rate + + + align:start position:0% +we're we're thinking about the flow rate +after you've reached that steady state + + align:start position:0% +after you've reached that steady state + + + align:start position:0% +after you've reached that steady state +but before you know you've equilibrated + + align:start position:0% +but before you know you've equilibrated + + + align:start position:0% +but before you know you've equilibrated +across across the two uh the two sides + + align:start position:0% +across across the two uh the two sides + + + align:start position:0% +across across the two uh the two sides +of the um of the + + align:start position:0% +of the um of the + + + align:start position:0% +of the um of the +tube okay + + align:start position:0% + + + + align:start position:0% + +all right do you need more time all + + align:start position:0% +all right do you need more time all + + + align:start position:0% +all right do you need more time all +right let's go ahead and see where we + + align:start position:0% +right let's go ahead and see where we + + + align:start position:0% +right let's go ahead and see where we +are uh + + align:start position:0% +are uh + + + align:start position:0% +are uh +ready three two + + align:start position:0% + + + + align:start position:0% + +one all right so we have um + + align:start position:0% +one all right so we have um + + + align:start position:0% +one all right so we have um +pretty good agreement it seems that it's + + align:start position:0% +pretty good agreement it seems that it's + + + align:start position:0% +pretty good agreement it seems that it's +D right um + + align:start position:0% + + + + align:start position:0% + +but didn't I tell you how to do the + + align:start position:0% +but didn't I tell you how to do the + + + align:start position:0% +but didn't I tell you how to do the +problem already and + + align:start position:0% +problem already and + + + align:start position:0% +problem already and +no all right + + align:start position:0% + + + + align:start position:0% + +uh okay so uh it's it's uh it's not uh + + align:start position:0% +uh okay so uh it's it's uh it's not uh + + + align:start position:0% +uh okay so uh it's it's uh it's not uh +so the naive thing I guess + + align:start position:0% +so the naive thing I guess + + + align:start position:0% +so the naive thing I guess +DC oh + + align:start position:0% + + + + align:start position:0% + +sorry well + + align:start position:0% + + + + align:start position:0% + +I all right so I'm I'm going to give you + + align:start position:0% +I all right so I'm I'm going to give you + + + align:start position:0% +I all right so I'm I'm going to give you +another um uh collaborate with a + + align:start position:0% +another um uh collaborate with a + + + align:start position:0% +another um uh collaborate with a +neighbor and I'll tell you that it's not + + align:start position:0% +neighbor and I'll tell you that it's not + + + align:start position:0% +neighbor and I'll tell you that it's not +D to uh to nudge you in in the right + + align:start position:0% +D to uh to nudge you in in the right + + + align:start position:0% +D to uh to nudge you in in the right +direction okay so spend a minute + + align:start position:0% + + + + align:start position:0% + +and oh number br + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +all right let's go ahead and and uh and + + align:start position:0% +all right let's go ahead and and uh and + + + align:start position:0% +all right let's go ahead and and uh and +reconvene okay + + align:start position:0% +reconvene okay + + + align:start position:0% +reconvene okay +all all right I just want to see where + + align:start position:0% +all all right I just want to see where + + + align:start position:0% +all all right I just want to see where +we are now all right so given that you + + align:start position:0% +we are now all right so given that you + + + align:start position:0% +we are now all right so given that you +know you if if you still believe it's D + + align:start position:0% +know you if if you still believe it's D + + + align:start position:0% +know you if if you still believe it's D +despite my telling you that I don't + + align:start position:0% +despite my telling you that I don't + + + align:start position:0% +despite my telling you that I don't +think it's D you can still vote D and + + align:start position:0% +think it's D you can still vote D and + + + align:start position:0% +think it's D you can still vote D and +then we can argue about it and that's + + align:start position:0% +then we can argue about it and that's + + + align:start position:0% +then we can argue about it and that's +fine too all right ready 3 2 + + align:start position:0% + + + + align:start position:0% + +1 okay so now okay so there there's + + align:start position:0% +1 okay so now okay so there there's + + + align:start position:0% +1 okay so now okay so there there's +maybe a disagree between a and C now uh + + align:start position:0% +maybe a disagree between a and C now uh + + + align:start position:0% +maybe a disagree between a and C now uh +all right well nobody liked my route + + align:start position:0% +all right well nobody liked my route + + + align:start position:0% +all right well nobody liked my route +two all right maybe you saw me hesitate + + align:start position:0% +two all right maybe you saw me hesitate + + + align:start position:0% +two all right maybe you saw me hesitate +a little bit before I wrote it you was + + align:start position:0% +a little bit before I wrote it you was + + + align:start position:0% +a little bit before I wrote it you was +like oh let me throw in a root okay um + + align:start position:0% +like oh let me throw in a root okay um + + + align:start position:0% +like oh let me throw in a root okay um +right okay so indeed + + align:start position:0% + + + + align:start position:0% + +this uh the flow rate does not scale as + + align:start position:0% +this uh the flow rate does not scale as + + + align:start position:0% +this uh the flow rate does not scale as +the area it only scales with a linear + + align:start position:0% +the area it only scales with a linear + + + align:start position:0% +the area it only scales with a linear +dimension of this hole okay this is + + align:start position:0% +dimension of this hole okay this is + + + align:start position:0% +dimension of this hole okay this is +weird right which is why everybody says + + align:start position:0% +weird right which is why everybody says + + + align:start position:0% +weird right which is why everybody says +D and even after you've done this + + align:start position:0% +D and even after you've done this + + + align:start position:0% +D and even after you've done this +problem you still think it's D in your + + align:start position:0% +problem you still think it's D in your + + + align:start position:0% +problem you still think it's D in your +intuition you know but you have to like + + align:start position:0% +intuition you know but you have to like + + + align:start position:0% +intuition you know but you have to like +pound that intuition away from you we + + align:start position:0% +pound that intuition away from you we + + + align:start position:0% +pound that intuition away from you we +we'll try to understand in multiple + + align:start position:0% +we'll try to understand in multiple + + + align:start position:0% +we'll try to understand in multiple +different ways why this might be okay + + align:start position:0% +different ways why this might be okay + + + align:start position:0% +different ways why this might be okay +what I want to do first is just make + + align:start position:0% +what I want to do first is just make + + + align:start position:0% +what I want to do first is just make +sure that we understand from dimensional + + align:start position:0% +sure that we understand from dimensional + + + align:start position:0% +sure that we understand from dimensional +analysis why this has to be the case + + align:start position:0% +analysis why this has to be the case + + + align:start position:0% +analysis why this has to be the case +okay now the first thing you need to + + align:start position:0% +okay now the first thing you need to + + + align:start position:0% +okay now the first thing you need to +know for dimensional analysis is the + + align:start position:0% +know for dimensional analysis is the + + + align:start position:0% +know for dimensional analysis is the +units of your answer right we're looking + + align:start position:0% +units of your answer right we're looking + + + align:start position:0% +units of your answer right we're looking +for something that is going to be units + + align:start position:0% +for something that is going to be units + + + align:start position:0% +for something that is going to be units +of you know some number of molecules + + align:start position:0% +of you know some number of molecules + + + align:start position:0% +of you know some number of molecules +over time but you know number there's no + + align:start position:0% +over time but you know number there's no + + + align:start position:0% +over time but you know number there's no +units attach that so the answer is + + align:start position:0% +units attach that so the answer is + + + align:start position:0% +units attach that so the answer is +supposed to be just a one over time and + + align:start position:0% +supposed to be just a one over time and + + + align:start position:0% +supposed to be just a one over time and +this is why we needed something that had + + align:start position:0% +this is why we needed something that had + + + align:start position:0% +this is why we needed something that had +some unit of time somewhere in order to + + align:start position:0% +some unit of time somewhere in order to + + + align:start position:0% +some unit of time somewhere in order to +get an answer that could possibly do + + align:start position:0% +get an answer that could possibly do + + + align:start position:0% +get an answer that could possibly do +this right and indeed we know that the + + align:start position:0% +this right and indeed we know that the + + + align:start position:0% +this right and indeed we know that the +diffusion coefficient has units of for + + align:start position:0% +diffusion coefficient has units of for + + + align:start position:0% +diffusion coefficient has units of for +example Micron squar per second right so + + align:start position:0% +example Micron squar per second right so + + + align:start position:0% +example Micron squar per second right so +it's a length squared over a time okay + + align:start position:0% +it's a length squared over a time okay + + + align:start position:0% +it's a length squared over a time okay +now I think one barrier that people have + + align:start position:0% +now I think one barrier that people have + + + align:start position:0% +now I think one barrier that people have +to use dimensional analysis is because + + align:start position:0% +to use dimensional analysis is because + + + align:start position:0% +to use dimensional analysis is because +we have trouble remembering what the + + align:start position:0% +we have trouble remembering what the + + + align:start position:0% +we have trouble remembering what the +units of things are right so if you + + align:start position:0% +units of things are right so if you + + + align:start position:0% +units of things are right so if you +don't remember something like the units + + align:start position:0% +don't remember something like the units + + + align:start position:0% +don't remember something like the units +of a diffusion coefficient then what you + + align:start position:0% +of a diffusion coefficient then what you + + + align:start position:0% +of a diffusion coefficient then what you +have to do is you have to REM try to + + align:start position:0% +have to do is you have to REM try to + + + align:start position:0% +have to do is you have to REM try to +find some equation in your brain where + + align:start position:0% +find some equation in your brain where + + + align:start position:0% +find some equation in your brain where +that you know that that symbol is used + + align:start position:0% +that you know that that symbol is used + + + align:start position:0% +that you know that that symbol is used +right and it of course it should be the + + align:start position:0% +right and it of course it should be the + + + align:start position:0% +right and it of course it should be the +the correct use of the symbol right but + + align:start position:0% +the correct use of the symbol right but + + + align:start position:0% +the correct use of the symbol right but +um right okay so so here this is why + + align:start position:0% +um right okay so so here this is why + + + align:start position:0% +um right okay so so here this is why +this is why I'm saying right you know + + align:start position:0% +this is why I'm saying right you know + + + align:start position:0% +this is why I'm saying right you know +this is like essentially the definition + + align:start position:0% +this is like essentially the definition + + + align:start position:0% +this is like essentially the definition +of this kind of linear diffusion + + align:start position:0% +of this kind of linear diffusion + + + align:start position:0% +of this kind of linear diffusion +coefficient right and from that you get + + align:start position:0% +coefficient right and from that you get + + + align:start position:0% +coefficient right and from that you get +you get the units okay and this is just + + align:start position:0% +you get the units okay and this is just + + + align:start position:0% +you get the units okay and this is just +very very common that you know something + + align:start position:0% +very very common that you know something + + + align:start position:0% +very very common that you know something +like + + align:start position:0% +like + + + align:start position:0% +like +viscosity impossible to remember what + + align:start position:0% +viscosity impossible to remember what + + + align:start position:0% +viscosity impossible to remember what +the units of that thing are right but + + align:start position:0% +the units of that thing are right but + + + align:start position:0% +the units of that thing are right but +then you just you know you have + + align:start position:0% +then you just you know you have + + + align:start position:0% +then you just you know you have +equations in your in your brain where + + align:start position:0% +equations in your in your brain where + + + align:start position:0% +equations in your in your brain where +you know the viscosity enters and then + + align:start position:0% +you know the viscosity enters and then + + + align:start position:0% +you know the viscosity enters and then +you can figure it out + + align:start position:0% + + + + align:start position:0% + +okay all right so then if you want to + + align:start position:0% +okay all right so then if you want to + + + align:start position:0% +okay all right so then if you want to +use this dimensional analysis idea you + + align:start position:0% +use this dimensional analysis idea you + + + align:start position:0% +use this dimensional analysis idea you +you you just be very clear you know + + align:start position:0% +you you just be very clear you know + + + align:start position:0% +you you just be very clear you know +write down what all the dimensions are + + align:start position:0% +write down what all the dimensions are + + + align:start position:0% +write down what all the dimensions are +and then the answer just comes screaming + + align:start position:0% +and then the answer just comes screaming + + + align:start position:0% +and then the answer just comes screaming +out at you in general all right now we + + align:start position:0% +out at you in general all right now we + + + align:start position:0% +out at you in general all right now we +see that we want something one over time + + align:start position:0% +see that we want something one over time + + + align:start position:0% +see that we want something one over time +there's only one of these symbols that + + align:start position:0% +there's only one of these symbols that + + + align:start position:0% +there's only one of these symbols that +has a time in there right so we know + + align:start position:0% +has a time in there right so we know + + + align:start position:0% +has a time in there right so we know +exactly how the diffusion coefficient + + align:start position:0% +exactly how the diffusion coefficient + + + align:start position:0% +exactly how the diffusion coefficient +has to enter right we know that the flow + + align:start position:0% +has to enter right we know that the flow + + + align:start position:0% +has to enter right we know that the flow +is going to have to be something where + + align:start position:0% +is going to have to be something where + + + align:start position:0% +is going to have to be something where +we know that D has to enter in there + + align:start position:0% +we know that D has to enter in there + + + align:start position:0% +we know that D has to enter in there +line linearly because if it was any + + align:start position:0% +line linearly because if it was any + + + align:start position:0% +line linearly because if it was any +other way then the time would have some + + align:start position:0% +other way then the time would have some + + + align:start position:0% +other way then the time would have some +weird units or you know it' be time + + align:start position:0% +weird units or you know it' be time + + + align:start position:0% +weird units or you know it' be time +squared or square root of time or + + align:start position:0% +squared or square root of time or + + + align:start position:0% +squared or square root of time or +something right + + align:start position:0% +something right + + + align:start position:0% +something right +now okay it's true that we can do we + + align:start position:0% +now okay it's true that we can do we + + + align:start position:0% +now okay it's true that we can do we +could in principle dream up something uh + + align:start position:0% +could in principle dream up something uh + + + align:start position:0% +could in principle dream up something uh +crazy between concentration and um and + + align:start position:0% +crazy between concentration and um and + + + align:start position:0% +crazy between concentration and um and +the poe size okay in the sense that if + + align:start position:0% +the poe size okay in the sense that if + + + align:start position:0% +the poe size okay in the sense that if +we wanted to we + + align:start position:0% +we wanted to we + + + align:start position:0% +we wanted to we +could put it well we + + align:start position:0% +could put it well we + + + align:start position:0% +could put it well we +could do + + align:start position:0% +could do + + + align:start position:0% +could do +c times we can always add a c * a cubed + + align:start position:0% +c times we can always add a c * a cubed + + + align:start position:0% +c times we can always add a c * a cubed +or something like that right but of + + align:start position:0% +or something like that right but of + + + align:start position:0% +or something like that right but of +course this is diffusion where what that + + align:start position:0% +course this is diffusion where what that + + + align:start position:0% +course this is diffusion where what that +means is that if these are + + align:start position:0% +means is that if these are + + + align:start position:0% +means is that if these are +non-interacting diffusing molecules + + align:start position:0% +non-interacting diffusing molecules + + + align:start position:0% +non-interacting diffusing molecules +right that means that if we double the + + align:start position:0% +right that means that if we double the + + + align:start position:0% +right that means that if we double the +number of the molecules over on the + + align:start position:0% +number of the molecules over on the + + + align:start position:0% +number of the molecules over on the +right hand side we have to double the + + align:start position:0% +right hand side we have to double the + + + align:start position:0% +right hand side we have to double the +flow rate right because in in this + + align:start position:0% +flow rate right because in in this + + + align:start position:0% +flow rate right because in in this +diffusion equation and for diffusion + + align:start position:0% +diffusion equation and for diffusion + + + align:start position:0% +diffusion equation and for diffusion +these molecules are not not interacting + + align:start position:0% +these molecules are not not interacting + + + align:start position:0% +these molecules are not not interacting +at all they don't see each other and + + align:start position:0% +at all they don't see each other and + + + align:start position:0% +at all they don't see each other and +that means if you if you just double the + + align:start position:0% +that means if you if you just double the + + + align:start position:0% +that means if you if you just double the +concentration on the right you have to + + align:start position:0% +concentration on the right you have to + + + align:start position:0% +concentration on the right you have to +double the flow rate okay right so that + + align:start position:0% +double the flow rate okay right so that + + + align:start position:0% +double the flow rate okay right so that +means we know that it has to show up as + + align:start position:0% +means we know that it has to show up as + + + align:start position:0% +means we know that it has to show up as +a single C + + align:start position:0% +a single C + + + align:start position:0% +a single C +okay and all we're left with is going to + + align:start position:0% +okay and all we're left with is going to + + + align:start position:0% +okay and all we're left with is going to +be one unit of length that we have to + + align:start position:0% +be one unit of length that we have to + + + align:start position:0% +be one unit of length that we have to +have to get rid of okay right now this + + align:start position:0% +have to get rid of okay right now this + + + align:start position:0% +have to get rid of okay right now this +is not of course a rigorous definition + + align:start position:0% +is not of course a rigorous definition + + + align:start position:0% +is not of course a rigorous definition +this and and and does this have to be + + align:start position:0% +this and and and does this have to be + + + align:start position:0% +this and and and does this have to be +actually an equal + + align:start position:0% +actually an equal + + + align:start position:0% +actually an equal +sign no so what we can actually say is + + align:start position:0% +sign no so what we can actually say is + + + align:start position:0% +sign no so what we can actually say is +that it has to be proportional to this + + align:start position:0% +that it has to be proportional to this + + + align:start position:0% +that it has to be proportional to this +so + + align:start position:0% +so + + + align:start position:0% +so +I'll + + align:start position:0% +I'll + + + align:start position:0% +I'll +um + + align:start position:0% +um + + + align:start position:0% +um +okay but actually just from dimensional + + align:start position:0% +okay but actually just from dimensional + + + align:start position:0% +okay but actually just from dimensional +analysis and this idea of say + + align:start position:0% +analysis and this idea of say + + + align:start position:0% +analysis and this idea of say +superposition of of the concentrations + + align:start position:0% +superposition of of the concentrations + + + align:start position:0% +superposition of of the concentrations +you can get something that's really kind + + align:start position:0% +you can get something that's really kind + + + align:start position:0% +you can get something that's really kind +of a deep statement about how diffusion + + align:start position:0% +of a deep statement about how diffusion + + + align:start position:0% +of a deep statement about how diffusion +is going to + + align:start position:0% +is going to + + + align:start position:0% +is going to +operate + + align:start position:0% +operate + + + align:start position:0% +operate +yes it seems to me that we can break + + align:start position:0% +yes it seems to me that we can break + + + align:start position:0% +yes it seems to me that we can break +that there's like this degeneracy like + + align:start position:0% +that there's like this degeneracy like + + + align:start position:0% +that there's like this degeneracy like +we can't quite sort out the powers of + + align:start position:0% +we can't quite sort out the powers of + + + align:start position:0% +we can't quite sort out the powers of +CNA well right so that's what I was + + align:start position:0% +CNA well right so that's what I was + + + align:start position:0% +CNA well right so that's what I was +that's what I was saying that in just + + align:start position:0% +that's what I was saying that in just + + + align:start position:0% +that's what I was saying that in just +from the units alone we could always add + + align:start position:0% +from the units alone we could always add + + + align:start position:0% +from the units alone we could always add +a c * a cubed or or to some power right + + align:start position:0% +a c * a cubed or or to some power right + + + align:start position:0% +a c * a cubed or or to some power right +no but that and that's why I'm saying + + align:start position:0% +no but that and that's why I'm saying + + + align:start position:0% +no but that and that's why I'm saying +that you you have to be able to invoke + + align:start position:0% +that you you have to be able to invoke + + + align:start position:0% +that you you have to be able to invoke +this idea that that if you double the + + align:start position:0% +this idea that that if you double the + + + align:start position:0% +this idea that that if you double the +concentration of this salt on the right + + align:start position:0% +concentration of this salt on the right + + + align:start position:0% +concentration of this salt on the right +you'll double the flow rate because + + align:start position:0% +you'll double the flow rate because + + + align:start position:0% +you'll double the flow rate because +these These are non-interacting + + align:start position:0% +these These are non-interacting + + + align:start position:0% +these These are non-interacting +molecules because they're just diffusing + + align:start position:0% +molecules because they're just diffusing + + + align:start position:0% +molecules because they're just diffusing +around in + + align:start position:0% +around in + + + align:start position:0% +around in +solution I was going to say that we + + align:start position:0% +solution I was going to say that we + + + align:start position:0% +solution I was going to say that we +could if we simply chose to measure flow + + align:start position:0% +could if we simply chose to measure flow + + + align:start position:0% +could if we simply chose to measure flow +in not in units of number of atoms but + + align:start position:0% +in not in units of number of atoms but + + + align:start position:0% +in not in units of number of atoms but +in units of mass per unit time and + + align:start position:0% +in units of mass per unit time and + + + align:start position:0% +in units of mass per unit time and +concentration unit of mass then we could + + align:start position:0% +concentration unit of mass then we could + + + align:start position:0% +concentration unit of mass then we could +then we clearly see + + align:start position:0% + + + + align:start position:0% + +what right it's an interesting I I think + + align:start position:0% +what right it's an interesting I I think + + + align:start position:0% +what right it's an interesting I I think +I'm going to disagree with you but I I'm + + align:start position:0% +I'm going to disagree with you but I I'm + + + align:start position:0% +I'm going to disagree with you but I I'm +but I want to make sure that I + + align:start position:0% +but I want to make sure that I + + + align:start position:0% +but I want to make sure that I +um all right so you want to say okay + + align:start position:0% +um all right so you want to say okay + + + align:start position:0% +um all right so you want to say okay +you're entering yeah but if if the + + align:start position:0% +you're entering yeah but if if the + + + align:start position:0% +you're entering yeah but if if the +diffusion coefficient is is about what + + align:start position:0% +diffusion coefficient is is about what + + + align:start position:0% +diffusion coefficient is is about what +the molecule is doing so I'm just I'm + + align:start position:0% +the molecule is doing so I'm just I'm + + + align:start position:0% +the molecule is doing so I'm just I'm +you know I'm not sure how we're going to + + align:start position:0% +you know I'm not sure how we're going to + + + align:start position:0% +you know I'm not sure how we're going to +do if we measure concentration and units + + align:start position:0% +do if we measure concentration and units + + + align:start position:0% +do if we measure concentration and units +of you're saying all right migs per Mill + + align:start position:0% +of you're saying all right migs per Mill + + + align:start position:0% +of you're saying all right migs per Mill +of some protein or so right then you + + align:start position:0% +of some protein or so right then you + + + align:start position:0% +of some protein or so right then you +know then it's you're really saying that + + align:start position:0% +know then it's you're really saying that + + + align:start position:0% +know then it's you're really saying that +there's some mass density + + align:start position:0% +there's some mass density + + + align:start position:0% +there's some mass density +um and I guess you can always Define + + align:start position:0% +um and I guess you can always Define + + + align:start position:0% +um and I guess you can always Define +diffusion coefficient as uh because I + + align:start position:0% +diffusion coefficient as uh because I + + + align:start position:0% +diffusion coefficient as uh because I +guess you know even in even even from + + align:start position:0% +guess you know even in even even from + + + align:start position:0% +guess you know even in even even from +the standpoint of a uh because we don't + + align:start position:0% +the standpoint of a uh because we don't + + + align:start position:0% +the standpoint of a uh because we don't +even need numbers in order to we could + + align:start position:0% +even need numbers in order to we could + + + align:start position:0% +even need numbers in order to we could +measure do you know some you know + + align:start position:0% +measure do you know some you know + + + align:start position:0% +measure do you know some you know +fluoresence or something and how it + + align:start position:0% +fluoresence or something and how it + + + align:start position:0% +fluoresence or something and how it +diffuses across right so that doesn't + + align:start position:0% +diffuses across right so that doesn't + + + align:start position:0% +diffuses across right so that doesn't +even require numbers uh you know I'm + + align:start position:0% +even require numbers uh you know I'm + + + align:start position:0% +even require numbers uh you know I'm +trying to think if this is going to end + + align:start position:0% +trying to think if this is going to end + + + align:start position:0% +trying to think if this is going to end +up being different from the argument + + align:start position:0% + + + + align:start position:0% + +of I'd have to yeah if we if we put in + + align:start position:0% +of I'd have to yeah if we if we put in + + + align:start position:0% +of I'd have to yeah if we if we put in +the number of molecules then it's going + + align:start position:0% +the number of molecules then it's going + + + align:start position:0% +the number of molecules then it's going +to have to be number of molecules per + + align:start position:0% +to have to be number of molecules per + + + align:start position:0% +to have to be number of molecules per +time and then C has to be linear because + + align:start position:0% +time and then C has to be linear because + + + align:start position:0% +time and then C has to be linear because +C is number of molecules per something + + align:start position:0% +C is number of molecules per something + + + align:start position:0% +C is number of molecules per something +right okay yeah yeah right so if if you + + align:start position:0% +right okay yeah yeah right so if if you + + + align:start position:0% +right okay yeah yeah right so if if you +could you could you know say you know + + align:start position:0% +could you could you know say you know + + + align:start position:0% +could you could you know say you know +you could say treat molecules as a as a + + align:start position:0% +you could say treat molecules as a as a + + + align:start position:0% +you could say treat molecules as a as a +unit and then it all then that also ends + + align:start position:0% +unit and then it all then that also ends + + + align:start position:0% +unit and then it all then that also ends +up having to requiring that it's um yeah + + align:start position:0% +up having to requiring that it's um yeah + + + align:start position:0% +up having to requiring that it's um yeah +no I think that that's fair + + align:start position:0% +no I think that that's fair + + + align:start position:0% +no I think that that's fair +uh know but I I'd have to think about + + align:start position:0% +uh know but I I'd have to think about + + + align:start position:0% +uh know but I I'd have to think about +this Ma you know how how how it play out + + align:start position:0% +this Ma you know how how how it play out + + + align:start position:0% +this Ma you know how how how it play out +if you try to measure things in terms of + + align:start position:0% +if you try to measure things in terms of + + + align:start position:0% +if you try to measure things in terms of +you know Mass PR + + align:start position:0% + + + + align:start position:0% + +volume all right of course you should be + + align:start position:0% +volume all right of course you should be + + + align:start position:0% +volume all right of course you should be +able to calculate this explicitly and + + align:start position:0% +able to calculate this explicitly and + + + align:start position:0% +able to calculate this explicitly and +then also to figure out what the + + align:start position:0% +then also to figure out what the + + + align:start position:0% +then also to figure out what the +proportionality constant is and but + + align:start position:0% +proportionality constant is and but + + + align:start position:0% +proportionality constant is and but +indeed what you find is that is that it + + align:start position:0% +indeed what you find is that is that it + + + align:start position:0% +indeed what you find is that is that it +it it scales linearly with the radius + + align:start position:0% +it it scales linearly with the radius + + + align:start position:0% +it it scales linearly with the radius +instead of as the area right so which is + + align:start position:0% +instead of as the area right so which is + + + align:start position:0% +instead of as the area right so which is +I think very surprising yes uh we can + + align:start position:0% +I think very surprising yes uh we can + + + align:start position:0% +I think very surprising yes uh we can +also say d scal with a s + + align:start position:0% + + + + align:start position:0% + +um oh you're saying that maybe we don't + + align:start position:0% +um oh you're saying that maybe we don't + + + align:start position:0% +um oh you're saying that maybe we don't +need the con the conentration is not + + align:start position:0% +need the con the conentration is not + + + align:start position:0% +need the con the conentration is not +relevant is is that uh if we look at + + align:start position:0% +relevant is is that uh if we look at + + + align:start position:0% +relevant is is that uh if we look at +that way then + + align:start position:0% +that way then + + + align:start position:0% +that way then +answer okay um all + + align:start position:0% +answer okay um all + + + align:start position:0% +answer okay um all +right right what you what you're saying + + align:start position:0% +right right what you what you're saying + + + align:start position:0% +right right what you what you're saying +is that maybe somehow the flow is just + + align:start position:0% +is that maybe somehow the flow is just + + + align:start position:0% +is that maybe somehow the flow is just +equal to or proportional goes as D * a + + align:start position:0% +equal to or proportional goes as D * a + + + align:start position:0% +equal to or proportional goes as D * a +2qu in the sense that you would say that + + align:start position:0% +2qu in the sense that you would say that + + + align:start position:0% +2qu in the sense that you would say that +or + + align:start position:0% +or + + + align:start position:0% +or +okay + + align:start position:0% + + + + align:start position:0% + +um right I I I think that it re I think + + align:start position:0% +um right I I I think that it re I think + + + align:start position:0% +um right I I I think that it re I think +that it really has to you know this + + align:start position:0% +that it really has to you know this + + + align:start position:0% +that it really has to you know this +non-interacting particle business I + + align:start position:0% +non-interacting particle business I + + + align:start position:0% +non-interacting particle business I +think it really does tell you that the + + align:start position:0% +think it really does tell you that the + + + align:start position:0% +think it really does tell you that the +flow has to be proportional to the + + align:start position:0% +flow has to be proportional to the + + + align:start position:0% +flow has to be proportional to the +concentration uh + + align:start position:0% +concentration uh + + + align:start position:0% +concentration uh +and you so so I think the yeah I think + + align:start position:0% +and you so so I think the yeah I think + + + align:start position:0% +and you so so I think the yeah I think +that is sufficient already I agree that + + align:start position:0% +that is sufficient already I agree that + + + align:start position:0% +that is sufficient already I agree that +just from units you could do this + + align:start position:0% +just from units you could do this + + + align:start position:0% +just from units you could do this +but I think well it's not true and it's + + align:start position:0% +but I think well it's not true and it's + + + align:start position:0% +but I think well it's not true and it's +nonsensical and it's not proportional to + + align:start position:0% +nonsensical and it's not proportional to + + + align:start position:0% +nonsensical and it's not proportional to +C all right okay + + align:start position:0% +C all right okay + + + align:start position:0% +C all right okay +um all right I I let's move on um okay + + align:start position:0% +um all right I I let's move on um okay + + + align:start position:0% +um all right I I let's move on um okay +no but okay but I think that this is but + + align:start position:0% +no but okay but I think that this is but + + + align:start position:0% +no but okay but I think that this is but +I think it's it's important that to be + + align:start position:0% +I think it's it's important that to be + + + align:start position:0% +I think it's it's important that to be +that it's possible to say something + + align:start position:0% +that it's possible to say something + + + align:start position:0% +that it's possible to say something +that's a deep kind of physical principle + + align:start position:0% +that's a deep kind of physical principle + + + align:start position:0% +that's a deep kind of physical principle +just based on analysis of of units right + + align:start position:0% +just based on analysis of of units right + + + align:start position:0% +just based on analysis of of units right +and and then of course can somebody + + align:start position:0% +and and then of course can somebody + + + align:start position:0% +and and then of course can somebody +offer the intuitive explanation for why + + align:start position:0% +offer the intuitive explanation for why + + + align:start position:0% +offer the intuitive explanation for why +this might be I mean why is it that it + + align:start position:0% +this might be I mean why is it that it + + + align:start position:0% +this might be I mean why is it that it +goes as uh a instead of a + + align:start position:0% + + + + align:start position:0% + +squ you know I know and this is a little + + align:start position:0% +squ you know I know and this is a little + + + align:start position:0% +squ you know I know and this is a little +bit weird given the fact that we all say + + align:start position:0% +bit weird given the fact that we all say + + + align:start position:0% +bit weird given the fact that we all say +you know we all check our intuition we + + align:start position:0% +you know we all check our intuition we + + + align:start position:0% +you know we all check our intuition we +all say d right but you know but you + + align:start position:0% +all say d right but you know but you + + + align:start position:0% +all say d right but you know but you +know but the thing is once you know an + + align:start position:0% +know but the thing is once you know an + + + align:start position:0% +know but the thing is once you know an +answer you should still try to figure + + align:start position:0% +answer you should still try to figure + + + align:start position:0% +answer you should still try to figure +out what the intuition might have been + + align:start position:0% +out what the intuition might have been + + + align:start position:0% +out what the intuition might have been +right that you missed when you + + align:start position:0% +right that you missed when you + + + align:start position:0% +right that you missed when you +originally said d + + align:start position:0% + + + + align:start position:0% + +yes okay this might not make so say um + + align:start position:0% +yes okay this might not make so say um + + + align:start position:0% +yes okay this might not make so say um +you would first think it goes like a s + + align:start position:0% +you would first think it goes like a s + + + align:start position:0% +you would first think it goes like a s +because the area like a s that's right + + align:start position:0% +because the area like a s that's right + + + align:start position:0% +because the area like a s that's right +but then maybe the fact that the + + align:start position:0% +but then maybe the fact that the + + + align:start position:0% +but then maybe the fact that the +perimeter grows like a and the perimeter + + align:start position:0% +perimeter grows like a and the perimeter + + + align:start position:0% +perimeter grows like a and the perimeter +add drag maybe that would subtract like + + align:start position:0% +add drag maybe that would subtract like + + + align:start position:0% +add drag maybe that would subtract like +cancel + + align:start position:0% + + + + align:start position:0% + +sense + + align:start position:0% +sense + + + align:start position:0% +sense +yeah well + + align:start position:0% +yeah well + + + align:start position:0% +yeah well +okay yeah okay so I I don't think that's + + align:start position:0% +okay yeah okay so I I don't think that's + + + align:start position:0% +okay yeah okay so I I don't think that's +the intuition that I would use um but + + align:start position:0% +the intuition that I would use um but + + + align:start position:0% +the intuition that I would use um but +but okay but then we have to figure out + + align:start position:0% +but okay but then we have to figure out + + + align:start position:0% +but okay but then we have to figure out +okay well what what might be wrong okay + + align:start position:0% +okay well what what might be wrong okay + + + align:start position:0% +okay well what what might be wrong okay +well first I don't think you can + + align:start position:0% +well first I don't think you can + + + align:start position:0% +well first I don't think you can +subtract an A but but also we haven't + + align:start position:0% +subtract an A but but also we haven't + + + align:start position:0% +subtract an A but but also we haven't +invoked anything any actual drag quite + + align:start position:0% +invoked anything any actual drag quite + + + align:start position:0% +invoked anything any actual drag quite +in the sense that there's no sense that + + align:start position:0% +in the sense that there's no sense that + + + align:start position:0% +in the sense that there's no sense that +the perimeter should be right + + align:start position:0% + + + + align:start position:0% + +um all right so this is so mysterious + + align:start position:0% +um all right so this is so mysterious + + + align:start position:0% +um all right so this is so mysterious +that we're uh okay it's fine all right + + align:start position:0% +that we're uh okay it's fine all right + + + align:start position:0% +that we're uh okay it's fine all right +so I I think that the the way that I + + align:start position:0% +so I I think that the the way that I + + + align:start position:0% +so I I think that the the way that I +that I like to think about this is that + + align:start position:0% +that I like to think about this is that + + + align:start position:0% +that I like to think about this is that +uh there's because of you know we're not + + align:start position:0% +uh there's because of you know we're not + + + align:start position:0% +uh there's because of you know we're not +it's not that we're shooting like + + align:start position:0% +it's not that we're shooting like + + + align:start position:0% +it's not that we're shooting like +bullets at this memory right if we were + + align:start position:0% +bullets at this memory right if we were + + + align:start position:0% +bullets at this memory right if we were +shooting bullets or you know these were + + align:start position:0% +shooting bullets or you know these were + + + align:start position:0% +shooting bullets or you know these were +this were raindrops coming then indeed + + align:start position:0% +this were raindrops coming then indeed + + + align:start position:0% +this were raindrops coming then indeed +it would scale as as the area right but + + align:start position:0% +it would scale as as the area right but + + + align:start position:0% +it would scale as as the area right but +because it's diffusion right diffusion + + align:start position:0% +because it's diffusion right diffusion + + + align:start position:0% +because it's diffusion right diffusion +operates on uh on gradients of + + align:start position:0% +operates on uh on gradients of + + + align:start position:0% +operates on uh on gradients of +concentration okay and what's happen + + align:start position:0% +concentration okay and what's happen + + + align:start position:0% +concentration okay and what's happen +Happening Here is that you get a local + + align:start position:0% +Happening Here is that you get a local + + + align:start position:0% +Happening Here is that you get a local +depletion of the concentration at the at + + align:start position:0% +depletion of the concentration at the at + + + align:start position:0% +depletion of the concentration at the at +the pore okay so it's not the case that + + align:start position:0% +the pore okay so it's not the case that + + + align:start position:0% +the pore okay so it's not the case that +you have concentration C all the way + + align:start position:0% +you have concentration C all the way + + + align:start position:0% +you have concentration C all the way +until you get to the pore and then all + + align:start position:0% +until you get to the pore and then all + + + align:start position:0% +until you get to the pore and then all +of a sudden you have a linear gradient + + align:start position:0% +of a sudden you have a linear gradient + + + align:start position:0% +of a sudden you have a linear gradient +of C across that little pore but rather + + align:start position:0% +of C across that little pore but rather + + + align:start position:0% +of C across that little pore but rather +that you have a depletion of the + + align:start position:0% +that you have a depletion of the + + + align:start position:0% +that you have a depletion of the +concentration as you approach as you + + align:start position:0% +concentration as you approach as you + + + align:start position:0% +concentration as you approach as you +approach the poe right and so there as + + align:start position:0% +approach the poe right and so there as + + + align:start position:0% +approach the poe right and so there as +you as you grow the pore you're somehow + + align:start position:0% +you as you grow the pore you're somehow + + + align:start position:0% +you as you grow the pore you're somehow +competing with + + align:start position:0% + + + + align:start position:0% + +yourself think another way to think + + align:start position:0% +yourself think another way to think + + + align:start position:0% +yourself think another way to think +about this is + + align:start position:0% +about this is + + + align:start position:0% +about this is +if we to think about what happens if we + + align:start position:0% +if we to think about what happens if we + + + align:start position:0% +if we to think about what happens if we +have two pores + + align:start position:0% + + + + align:start position:0% + +okay so for example let's imagine that + + align:start position:0% +okay so for example let's imagine that + + + align:start position:0% +okay so for example let's imagine that +we have this pore here of size a but now + + align:start position:0% +we have this pore here of size a but now + + + align:start position:0% +we have this pore here of size a but now +I'm going to add a second pore over here + + align:start position:0% +I'm going to add a second pore over here + + + align:start position:0% +I'm going to add a second pore over here +far away same + + align:start position:0% +far away same + + + align:start position:0% +far away same +size so what should this do to the total + + align:start position:0% +size so what should this do to the total + + + align:start position:0% +size so what should this do to the total +flow rate right A B CDE + + align:start position:0% +flow rate right A B CDE + + + align:start position:0% +flow rate right A B CDE +e give you 10 seconds to come up with an + + align:start position:0% +e give you 10 seconds to come up with an + + + align:start position:0% +e give you 10 seconds to come up with an +opinion right so I'm adding a second Poe + + align:start position:0% +opinion right so I'm adding a second Poe + + + align:start position:0% +opinion right so I'm adding a second Poe +far + + align:start position:0% + + + + align:start position:0% + +away all right + + align:start position:0% +away all right + + + align:start position:0% +away all right +ready three two + + align:start position:0% +ready three two + + + align:start position:0% +ready three two +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one all right so we're all agreeing that + + align:start position:0% +one all right so we're all agreeing that + + + align:start position:0% +one all right so we're all agreeing that +this this should be 2x right again all + + align:start position:0% +this this should be 2x right again all + + + align:start position:0% +this this should be 2x right again all +right so this is the this is for two + + align:start position:0% +right so this is the this is for two + + + align:start position:0% +right so this is the this is for two +pores now right we also we get twox and + + align:start position:0% +pores now right we also we get twox and + + + align:start position:0% +pores now right we also we get twox and +this is because if the two two pores are + + align:start position:0% +this is because if the two two pores are + + + align:start position:0% +this is because if the two two pores are +far away from each other you know as + + align:start position:0% +far away from each other you know as + + + align:start position:0% +far away from each other you know as +relative to that the size of the pores + + align:start position:0% +relative to that the size of the pores + + + align:start position:0% +relative to that the size of the pores +then these are really non- + + align:start position:0% +then these are really non- + + + align:start position:0% +then these are really non- +interacting right in the sense that this + + align:start position:0% +interacting right in the sense that this + + + align:start position:0% +interacting right in the sense that this +is there's no there's none of this + + align:start position:0% +is there's no there's none of this + + + align:start position:0% +is there's no there's none of this +depletion effect that I was telling you + + align:start position:0% +depletion effect that I was telling you + + + align:start position:0% +depletion effect that I was telling you +about whereas as we bring these pores + + align:start position:0% +about whereas as we bring these pores + + + align:start position:0% +about whereas as we bring these pores +together right then they they start they + + align:start position:0% +together right then they they start they + + + align:start position:0% +together right then they they start they +start kind of interfering with each + + align:start position:0% +start kind of interfering with each + + + align:start position:0% +start kind of interfering with each +other because they they each involve + + align:start position:0% +other because they they each involve + + + align:start position:0% +other because they they each involve +some local depletion of the + + align:start position:0% +some local depletion of the + + + align:start position:0% +some local depletion of the +concentration and once that that kind of + + align:start position:0% +concentration and once that that kind of + + + align:start position:0% +concentration and once that that kind of +depletion area starts to overlap then + + align:start position:0% +depletion area starts to overlap then + + + align:start position:0% +depletion area starts to overlap then +the point is that there was some + + align:start position:0% +the point is that there was some + + + align:start position:0% +the point is that there was some +molecule that was diffusing and if you + + align:start position:0% +molecule that was diffusing and if you + + + align:start position:0% +molecule that was diffusing and if you +have the pores right next to each other + + align:start position:0% +have the pores right next to each other + + + align:start position:0% +have the pores right next to each other +you know that you're not going to get + + align:start position:0% +you know that you're not going to get + + + align:start position:0% +you know that you're not going to get +twice the twice the net flow because + + align:start position:0% +twice the twice the net flow because + + + align:start position:0% +twice the twice the net flow because +that molecule it might have diffused + + align:start position:0% +that molecule it might have diffused + + + align:start position:0% +that molecule it might have diffused +through the other the other pore even if + + align:start position:0% +through the other the other pore even if + + + align:start position:0% +through the other the other pore even if +it uh right if you were if if if one + + align:start position:0% +it uh right if you were if if if one + + + align:start position:0% +it uh right if you were if if if one +pore were not there then it might have + + align:start position:0% +pore were not there then it might have + + + align:start position:0% +pore were not there then it might have +diffused through the other + + align:start position:0% + + + + align:start position:0% + +Poe okay can think of it as the fact + + align:start position:0% +Poe okay can think of it as the fact + + + align:start position:0% +Poe okay can think of it as the fact +that that under a random walk the dis + + align:start position:0% +that that under a random walk the dis + + + align:start position:0% +that that under a random walk the dis +goes time so if you double the number if + + align:start position:0% +goes time so if you double the number if + + + align:start position:0% +goes time so if you double the number if +you + + align:start position:0% +you + + + align:start position:0% +you +um yeah increase the number of molecules + + align:start position:0% +um yeah increase the number of molecules + + + align:start position:0% +um yeah increase the number of molecules +going through by the square of + + align:start position:0% +going through by the square of + + + align:start position:0% +going through by the square of +parameter then actually the like total + + align:start position:0% +parameter then actually the like total + + + align:start position:0% +parameter then actually the like total +molecule displacement through I + + align:start position:0% +molecule displacement through I + + + align:start position:0% +molecule displacement through I +think actually only go larly in that + + align:start position:0% +think actually only go larly in that + + + align:start position:0% +think actually only go larly in that +because whichs the fact mole coming + + align:start position:0% +because whichs the fact mole coming + + + align:start position:0% +because whichs the fact mole coming +back right so it's true that the + + align:start position:0% +back right so it's true that the + + + align:start position:0% +back right so it's true that the +molecules coming back across you always + + align:start position:0% +molecules coming back across you always + + + align:start position:0% +molecules coming back across you always +have to worry about but I don't well I + + align:start position:0% +have to worry about but I don't well I + + + align:start position:0% +have to worry about but I don't well I +don't I don't see this argument actually + + align:start position:0% +don't I don't see this argument actually + + + align:start position:0% +don't I don't see this argument actually +necessarily + + align:start position:0% +necessarily + + + align:start position:0% +necessarily +I okay yeah it might it might it might + + align:start position:0% +I okay yeah it might it might it might + + + align:start position:0% +I okay yeah it might it might it might +work but it's a one like one double oh I + + align:start position:0% +work but it's a one like one double oh I + + + align:start position:0% +work but it's a one like one double oh I +see yeah yeah yeah I think that it it's + + align:start position:0% +see yeah yeah yeah I think that it it's + + + align:start position:0% +see yeah yeah yeah I think that it it's +it may be connected although I'm not + + align:start position:0% +it may be connected although I'm not + + + align:start position:0% +it may be connected although I'm not +sure if I'm if I'm sold on the argument + + align:start position:0% +sure if I'm if I'm sold on the argument + + + align:start position:0% +sure if I'm if I'm sold on the argument +you + + align:start position:0% + + + + align:start position:0% + +and yeah I think it's a little bit it's + + align:start position:0% +and yeah I think it's a little bit it's + + + align:start position:0% +and yeah I think it's a little bit it's +a little bit dangerous um + + align:start position:0% + + + + align:start position:0% + +mention okay right and this is why uh + + align:start position:0% +mention okay right and this is why uh + + + align:start position:0% +mention okay right and this is why uh +there was this question of time scales + + align:start position:0% +there was this question of time scales + + + align:start position:0% +there was this question of time scales +that immediately after you puncture the + + align:start position:0% +that immediately after you puncture the + + + align:start position:0% +that immediately after you puncture the +hole then uh then the flow rate will + + align:start position:0% +hole then uh then the flow rate will + + + align:start position:0% +hole then uh then the flow rate will +actually be higher than it'll be at that + + align:start position:0% +actually be higher than it'll be at that + + + align:start position:0% +actually be higher than it'll be at that +steady state so + + align:start position:0% +steady state so + + + align:start position:0% +steady state so +it's a s yeah I think right um right I + + align:start position:0% +it's a s yeah I think right um right I + + + align:start position:0% +it's a s yeah I think right um right I +think that the the flow right after you + + align:start position:0% +think that the the flow right after you + + + align:start position:0% +think that the the flow right after you +puncture indeed will will will scale as + + align:start position:0% +puncture indeed will will will scale as + + + align:start position:0% +puncture indeed will will will scale as +a squ because then because what you're + + align:start position:0% +a squ because then because what you're + + + align:start position:0% +a squ because then because what you're +doing is you're like taking there really + + align:start position:0% +doing is you're like taking there really + + + align:start position:0% +doing is you're like taking there really +is you're taking the number of molecules + + align:start position:0% +is you're taking the number of molecules + + + align:start position:0% +is you're taking the number of molecules +across this area and you're half of them + + align:start position:0% +across this area and you're half of them + + + align:start position:0% +across this area and you're half of them +are going to come through right you know + + align:start position:0% +are going to come through right you know + + + align:start position:0% +are going to come through right you know +so there and there's just more molecules + + align:start position:0% +so there and there's just more molecules + + + align:start position:0% +so there and there's just more molecules +in that area when you first puncture + + align:start position:0% +in that area when you first puncture + + + align:start position:0% +in that area when you first puncture +right but that's that's going to + + align:start position:0% +right but that's that's going to + + + align:start position:0% +right but that's that's going to +equilibrate in you know whatever micr + + align:start position:0% +equilibrate in you know whatever micr + + + align:start position:0% +equilibrate in you know whatever micr +you know it's really that'll be really + + align:start position:0% +you know it's really that'll be really + + + align:start position:0% +you know it's really that'll be really +fast whereas the this this the steady + + align:start position:0% +fast whereas the this this the steady + + + align:start position:0% +fast whereas the this this the steady +state flow rate that's that's that will + + align:start position:0% +state flow rate that's that's that will + + + align:start position:0% +state flow rate that's that's that will +that could go for you know in principle + + align:start position:0% +that could go for you know in principle + + + align:start position:0% +that could go for you know in principle +forever if you know a large + + align:start position:0% +forever if you know a large + + + align:start position:0% +forever if you know a large +Reservoir + + align:start position:0% +Reservoir + + + align:start position:0% +Reservoir +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +right so I want to I want to move on but + + align:start position:0% +right so I want to I want to move on but + + + align:start position:0% +right so I want to I want to move on but +I I I want to make sure that uh we we + + align:start position:0% +I I I want to make sure that uh we we + + + align:start position:0% +I I I want to make sure that uh we we +understand how this basic principle + + align:start position:0% +understand how this basic principle + + + align:start position:0% +understand how this basic principle +allows us to to say some interesting + + align:start position:0% +allows us to to say some interesting + + + align:start position:0% +allows us to to say some interesting +things right for example there's a + + align:start position:0% +things right for example there's a + + + align:start position:0% +things right for example there's a +related problem which is uh how much + + align:start position:0% +related problem which is uh how much + + + align:start position:0% +related problem which is uh how much +food could a could a cell possibly + + align:start position:0% + + + + align:start position:0% + +eat right and can can somebody say why + + align:start position:0% +eat right and can can somebody say why + + + align:start position:0% +eat right and can can somebody say why +there might be a a an upper upper bound + + align:start position:0% +there might be a a an upper upper bound + + + align:start position:0% +there might be a a an upper upper bound +on this + + align:start position:0% + + + + align:start position:0% + +I'm + + align:start position:0% +I'm + + + align:start position:0% +I'm +Sorry's get many the cell and oh no this + + align:start position:0% +Sorry's get many the cell and oh no this + + + align:start position:0% +Sorry's get many the cell and oh no this +is a super hungry cell it no I mean it + + align:start position:0% +is a super hungry cell it no I mean it + + + align:start position:0% +is a super hungry cell it no I mean it +can uh you know it can in principle it + + align:start position:0% +can uh you know it can in principle it + + + align:start position:0% +can uh you know it can in principle it +would be able to use every glucose + + align:start position:0% +would be able to use every glucose + + + align:start position:0% +would be able to use every glucose +molecule that came in no but I'm saying + + align:start position:0% +molecule that came in no but I'm saying + + + align:start position:0% +molecule that came in no but I'm saying +the diffus the osmosis water + + align:start position:0% + + + + align:start position:0% + +oh oh okay we're talking about osmotic + + align:start position:0% +oh oh okay we're talking about osmotic + + + align:start position:0% +oh oh okay we're talking about osmotic +effects okay yeah um all right but we + + align:start position:0% +effects okay yeah um all right but we + + + align:start position:0% +effects okay yeah um all right but we +can just say that it's going to um you + + align:start position:0% +can just say that it's going to um you + + + align:start position:0% +can just say that it's going to um you +know it's a super it's got a super tough + + align:start position:0% +know it's a super it's got a super tough + + + align:start position:0% +know it's a super it's got a super tough +cell wall so it can take well we'll say + + align:start position:0% +cell wall so it can take well we'll say + + + align:start position:0% +cell wall so it can take well we'll say +infinite you know but even you know no I + + align:start position:0% +infinite you know but even you know no I + + + align:start position:0% +infinite you know but even you know no I +I guess what I'm saying is there's + + align:start position:0% +I guess what I'm saying is there's + + + align:start position:0% +I guess what I'm saying is there's +something you know even if I invoke such + + align:start position:0% +something you know even if I invoke such + + + align:start position:0% +something you know even if I invoke such +a thing that there still is a limit I + + align:start position:0% +a thing that there still is a limit I + + + align:start position:0% +a thing that there still is a limit I +guess that's really what I'm trying to + + align:start position:0% + + + + align:start position:0% + +sayc well the the glucose is going to + + align:start position:0% +sayc well the the glucose is going to + + + align:start position:0% +sayc well the the glucose is going to +get imported and then it's going to be + + align:start position:0% +get imported and then it's going to be + + + align:start position:0% +get imported and then it's going to be +immediately converted into useful + + align:start position:0% +immediately converted into useful + + + align:start position:0% +immediately converted into useful +things all right so but then still + + align:start position:0% +things all right so but then still + + + align:start position:0% +things all right so but then still +there's a limit what is + + align:start position:0% + + + + align:start position:0% + +maximum right so this is the maximum + + align:start position:0% +maximum right so this is the maximum + + + align:start position:0% +maximum right so this is the maximum +kind of Poss nutrient + + align:start position:0% + + + + align:start position:0% + +uptake + + align:start position:0% + + + + align:start position:0% + +yes okay right right so okay so so maybe + + align:start position:0% +yes okay right right so okay so so maybe + + + align:start position:0% +yes okay right right so okay so so maybe +it could be somehow diffusion limited + + align:start position:0% +it could be somehow diffusion limited + + + align:start position:0% +it could be somehow diffusion limited +right and what's the best that a cell + + align:start position:0% +right and what's the best that a cell + + + align:start position:0% +right and what's the best that a cell +could possibly do in this regard all + + align:start position:0% +could possibly do in this regard all + + + align:start position:0% +could possibly do in this regard all +right so here's a + + align:start position:0% +right so here's a + + + align:start position:0% +right so here's a +cell right and now um maybe we will + + align:start position:0% +cell right and now um maybe we will + + + align:start position:0% +cell right and now um maybe we will +again have it be radius a so now is the + + align:start position:0% +again have it be radius a so now is the + + + align:start position:0% +again have it be radius a so now is the +cell of radius a okay now what what you + + align:start position:0% +cell of radius a okay now what what you + + + align:start position:0% +cell of radius a okay now what what you +know what if it if it were the just the + + align:start position:0% +know what if it if it were the just the + + + align:start position:0% +know what if it if it were the just the +best the best of it can be what how + + align:start position:0% +best the best of it can be what how + + + align:start position:0% +best the best of it can be what how +would you describe that relative to + + align:start position:0% +would you describe that relative to + + + align:start position:0% +would you describe that relative to +diffusion + + align:start position:0% + + + + align:start position:0% + +well I mean everything like all could be + + align:start position:0% +well I mean everything like all could be + + + align:start position:0% +well I mean everything like all could be +absorbing that's right yeah so that's + + align:start position:0% +absorbing that's right yeah so that's + + + align:start position:0% +absorbing that's right yeah so that's +what I yeah so the best they could + + align:start position:0% +what I yeah so the best they could + + + align:start position:0% +what I yeah so the best they could +possibly be is a perfect absorber okay + + align:start position:0% +possibly be is a perfect absorber okay + + + align:start position:0% +possibly be is a perfect absorber okay +what we mean by that is something where + + align:start position:0% +what we mean by that is something where + + + align:start position:0% +what we mean by that is something where +the moment that a molecule touches it it + + align:start position:0% +the moment that a molecule touches it it + + + align:start position:0% +the moment that a molecule touches it it +gets imported + + align:start position:0% + + + + align:start position:0% + +okay now of course a cell is not a + + align:start position:0% +okay now of course a cell is not a + + + align:start position:0% +okay now of course a cell is not a +perfect absorber but what's fascinating + + align:start position:0% +perfect absorber but what's fascinating + + + align:start position:0% +perfect absorber but what's fascinating +is that even if it were even if it were + + align:start position:0% +is that even if it were even if it were + + + align:start position:0% +is that even if it were even if it were +then it does not mean that it's going to + + align:start position:0% +then it does not mean that it's going to + + + align:start position:0% +then it does not mean that it's going to +be consuming say glucose at an infinite + + align:start position:0% +be consuming say glucose at an infinite + + + align:start position:0% +be consuming say glucose at an infinite +rate + + align:start position:0% +rate + + + align:start position:0% +rate +okay in particular we can ask well if we + + align:start position:0% +okay in particular we can ask well if we + + + align:start position:0% +okay in particular we can ask well if we +have a situation like this where we have + + align:start position:0% +have a situation like this where we have + + + align:start position:0% +have a situation like this where we have +a cell a sphere of size a it's a perfect + + align:start position:0% +a cell a sphere of size a it's a perfect + + + align:start position:0% +a cell a sphere of size a it's a perfect +absorber how will its uptake + + align:start position:0% +absorber how will its uptake + + + align:start position:0% +absorber how will its uptake +rate uh scale with its + + align:start position:0% + + + + align:start position:0% + +size all right in particular if we + + align:start position:0% +size all right in particular if we + + + align:start position:0% +size all right in particular if we +double A what is it going to do for the + + align:start position:0% +double A what is it going to do for the + + + align:start position:0% +double A what is it going to do for the +flow all right we're going to have 10 + + align:start position:0% +flow all right we're going to have 10 + + + align:start position:0% +flow all right we're going to have 10 +seconds to think about + + align:start position:0% + + + + align:start position:0% + +this right if we we're imagining a cell + + align:start position:0% +this right if we we're imagining a cell + + + align:start position:0% +this right if we we're imagining a cell +is a perfect absorber the moment that + + align:start position:0% +is a perfect absorber the moment that + + + align:start position:0% +is a perfect absorber the moment that +this nutrient touches it gets imported + + align:start position:0% +this nutrient touches it gets imported + + + align:start position:0% +this nutrient touches it gets imported +and chewed up and the question is how + + align:start position:0% +and chewed up and the question is how + + + align:start position:0% +and chewed up and the question is how +does that maximum uptake rate change if + + align:start position:0% +does that maximum uptake rate change if + + + align:start position:0% +does that maximum uptake rate change if +I double the U the size of the cell + + align:start position:0% +I double the U the size of the cell + + + align:start position:0% +I double the U the size of the cell +double double the radius are we + + align:start position:0% + + + + align:start position:0% + +ready okay let's see where we are ready + + align:start position:0% +ready okay let's see where we are ready + + + align:start position:0% +ready okay let's see where we are ready +three two + + align:start position:0% +three two + + + align:start position:0% +three two +one okay all right so now it is a bit + + align:start position:0% +one okay all right so now it is a bit + + + align:start position:0% +one okay all right so now it is a bit +more of a mixture of A's C's D's + + align:start position:0% +more of a mixture of A's C's D's + + + align:start position:0% +more of a mixture of A's C's D's +although it is a majority we're getting + + align:start position:0% +although it is a majority we're getting + + + align:start position:0% +although it is a majority we're getting +a majority C uh and + + align:start position:0% +a majority C uh and + + + align:start position:0% +a majority C uh and +again okay + + align:start position:0% +again okay + + + align:start position:0% +again okay +uh this is cell double cell doubles size + + align:start position:0% +uh this is cell double cell doubles size + + + align:start position:0% +uh this is cell double cell doubles size +okay and indeed this is just from the + + align:start position:0% +okay and indeed this is just from the + + + align:start position:0% +okay and indeed this is just from the +standpoint of dimensional analysis this + + align:start position:0% +standpoint of dimensional analysis this + + + align:start position:0% +standpoint of dimensional analysis this +is the same problem as that pore that we + + align:start position:0% +is the same problem as that pore that we + + + align:start position:0% +is the same problem as that pore that we +just did right because again it's + + align:start position:0% +just did right because again it's + + + align:start position:0% +just did right because again it's +diffusion right we're interested in + + align:start position:0% +diffusion right we're interested in + + + align:start position:0% +diffusion right we're interested in +uptake now it's not a flow across a + + align:start position:0% +uptake now it's not a flow across a + + + align:start position:0% +uptake now it's not a flow across a +membrane but this is uptake rate by the + + align:start position:0% +membrane but this is uptake rate by the + + + align:start position:0% +membrane but this is uptake rate by the +cell it's going to be numbers of + + align:start position:0% +cell it's going to be numbers of + + + align:start position:0% +cell it's going to be numbers of +molecules per unit time again there's + + align:start position:0% +molecules per unit time again there's + + + align:start position:0% +molecules per unit time again there's +diffusion the concentration is still + + align:start position:0% +diffusion the concentration is still + + + align:start position:0% +diffusion the concentration is still +relevant you know and and so the all the + + align:start position:0% +relevant you know and and so the all the + + + align:start position:0% +relevant you know and and so the all the +same arguments apply right and indeed + + align:start position:0% +same arguments apply right and indeed + + + align:start position:0% +same arguments apply right and indeed +this um this is again proportional to + + align:start position:0% +this um this is again proportional to + + + align:start position:0% +this um this is again proportional to +the area or + + align:start position:0% +the area or + + + align:start position:0% +the area or +sorry proportional to the radius + + align:start position:0% +sorry proportional to the radius + + + align:start position:0% +sorry proportional to the radius +a and + + align:start position:0% +a and + + + align:start position:0% +a and +remember and we're you know we're + + align:start position:0% +remember and we're you know we're + + + align:start position:0% +remember and we're you know we're +following the uh Convention of purcel + + align:start position:0% +following the uh Convention of purcel + + + align:start position:0% +following the uh Convention of purcel +and calling this a because Reynold's + + align:start position:0% +and calling this a because Reynold's + + + align:start position:0% +and calling this a because Reynold's +number is an r and then problems arise + + align:start position:0% +number is an r and then problems arise + + + align:start position:0% +number is an r and then problems arise +okay okay are there any questions about + + align:start position:0% +okay okay are there any questions about + + + align:start position:0% +okay okay are there any questions about +why why this argument why the argument + + align:start position:0% +why why this argument why the argument + + + align:start position:0% +why why this argument why the argument +is the same + + align:start position:0% +is the same + + + align:start position:0% +is the same +here as it was + + align:start position:0% + + + + align:start position:0% + +there okay now there's something + + align:start position:0% +there okay now there's something + + + align:start position:0% +there okay now there's something +interesting about this though which is + + align:start position:0% +interesting about this though which is + + + align:start position:0% +interesting about this though which is +that you can + + align:start position:0% + + + + align:start position:0% + +imagine the fact that this only scale + + align:start position:0% +imagine the fact that this only scale + + + align:start position:0% +imagine the fact that this only scale +scales as as the radius of the cell + + align:start position:0% +scales as as the radius of the cell + + + align:start position:0% +scales as as the radius of the cell +tells you that there there's some sense + + align:start position:0% +tells you that there there's some sense + + + align:start position:0% +tells you that there there's some sense +in which we're wasting an awful lot of + + align:start position:0% +in which we're wasting an awful lot of + + + align:start position:0% +in which we're wasting an awful lot of +that uh of that surface area right + + align:start position:0% +that uh of that surface area right + + + align:start position:0% +that uh of that surface area right +because we have a bit you know know this + + align:start position:0% +because we have a bit you know know this + + + align:start position:0% +because we have a bit you know know this +large surface area but we're you know + + align:start position:0% +large surface area but we're you know + + + align:start position:0% +large surface area but we're you know +we're just kind of it's not as good as + + align:start position:0% +we're just kind of it's not as good as + + + align:start position:0% +we're just kind of it's not as good as +you would have thought it would have + + align:start position:0% +you would have thought it would have + + + align:start position:0% +you would have thought it would have +been and what that means is in + + align:start position:0% +been and what that means is in + + + align:start position:0% +been and what that means is in +principle you could have a smaller + + align:start position:0% +principle you could have a smaller + + + align:start position:0% +principle you could have a smaller +fraction of the + + align:start position:0% +fraction of the + + + align:start position:0% +fraction of the +area covered by a bunch of + + align:start position:0% +area covered by a bunch of + + + align:start position:0% +area covered by a bunch of +little think pores or Transporters that + + align:start position:0% +little think pores or Transporters that + + + align:start position:0% +little think pores or Transporters that +kind of analogous to this situation that + + align:start position:0% +kind of analogous to this situation that + + + align:start position:0% +kind of analogous to this situation that +we had before with the salt crossing the + + align:start position:0% +we had before with the salt crossing the + + + align:start position:0% +we had before with the salt crossing the +membrane okay and indeed if you if you + + align:start position:0% +membrane okay and indeed if you if you + + + align:start position:0% +membrane okay and indeed if you if you +just imagine that these are each little + + align:start position:0% +just imagine that these are each little + + + align:start position:0% +just imagine that these are each little +absor + + align:start position:0% +absor + + + align:start position:0% +absor +patches that are perhaps 1 nmet in size + + align:start position:0% +patches that are perhaps 1 nmet in size + + + align:start position:0% +patches that are perhaps 1 nmet in size +you know + + align:start position:0% +you know + + + align:start position:0% +you know +small okay there's a an amusing + + align:start position:0% +small okay there's a an amusing + + + align:start position:0% +small okay there's a an amusing +calculation you can do which is you can + + align:start position:0% +calculation you can do which is you can + + + align:start position:0% +calculation you can do which is you can +ask well how is it that + + align:start position:0% + + + + align:start position:0% + +the this is now uptake + + align:start position:0% + + + + align:start position:0% + +rate now we want to know how is it that + + align:start position:0% +rate now we want to know how is it that + + + align:start position:0% +rate now we want to know how is it that +that uh is going to change as a function + + align:start position:0% +that uh is going to change as a function + + + align:start position:0% +that uh is going to change as a function +of the fraction of the surface area that + + align:start position:0% +of the fraction of the surface area that + + + align:start position:0% +of the fraction of the surface area that +we have covered with these um with these + + align:start position:0% +we have covered with these um with these + + + align:start position:0% +we have covered with these um with these +Transporters right with these little + + align:start position:0% +Transporters right with these little + + + align:start position:0% +Transporters right with these little +perfectly absorbing + + align:start position:0% +perfectly absorbing + + + align:start position:0% +perfectly absorbing +patches so we can imagine the cell is + + align:start position:0% +patches so we can imagine the cell is + + + align:start position:0% +patches so we can imagine the cell is +one to 10 uh microns kind of in size + + align:start position:0% +one to 10 uh microns kind of in size + + + align:start position:0% +one to 10 uh microns kind of in size +then now we have a bunch of these little + + align:start position:0% +then now we have a bunch of these little + + + align:start position:0% +then now we have a bunch of these little +uh little pores that we're going to go + + align:start position:0% +uh little pores that we're going to go + + + align:start position:0% +uh little pores that we're going to go +on and you know and of course this is + + align:start position:0% +on and you know and of course this is + + + align:start position:0% +on and you know and of course this is +going + + align:start position:0% +going + + + align:start position:0% +going +to this is going to saturate + + align:start position:0% +to this is going to saturate + + + align:start position:0% +to this is going to saturate +somewhere right and it's going to + + align:start position:0% +somewhere right and it's going to + + + align:start position:0% +somewhere right and it's going to +saturate as it turns out this goes as 4 + + align:start position:0% +saturate as it turns out this goes as 4 + + + align:start position:0% +saturate as it turns out this goes as 4 +Pi D I think yeah right so the uptake + + align:start position:0% +Pi D I think yeah right so the uptake + + + align:start position:0% +Pi D I think yeah right so the uptake +rate is it's actually equal to 4 Pi C + + align:start position:0% +rate is it's actually equal to 4 Pi C + + + align:start position:0% +rate is it's actually equal to 4 Pi C +D for a sphere okay right so this is + + align:start position:0% +D for a sphere okay right so this is + + + align:start position:0% +D for a sphere okay right so this is +this is the part that we could not have + + align:start position:0% +this is the part that we could not have + + + align:start position:0% +this is the part that we could not have +figured out from uh from dimensional + + align:start position:0% +figured out from uh from dimensional + + + align:start position:0% +figured out from uh from dimensional +analysis right so indeed the uptake rate + + align:start position:0% +analysis right so indeed the uptake rate + + + align:start position:0% +analysis right so indeed the uptake rate +once we get up to this is a fraction + + align:start position:0% +once we get up to this is a fraction + + + align:start position:0% +once we get up to this is a fraction +that's covered once that's one + + align:start position:0% +that's covered once that's one + + + align:start position:0% +that's covered once that's one +indeed it's going to be 4 Pi + + align:start position:0% + + + + align:start position:0% + +CDA okay now the question is how does it + + align:start position:0% +CDA okay now the question is how does it + + + align:start position:0% +CDA okay now the question is how does it +behave over + + align:start position:0% +behave over + + + align:start position:0% +behave over +here now you might have thought that + + align:start position:0% +here now you might have thought that + + + align:start position:0% +here now you might have thought that +would just + + align:start position:0% +would just + + + align:start position:0% +would just +be some line like that right you know + + align:start position:0% +be some line like that right you know + + + align:start position:0% +be some line like that right you know +it's just oh the more of + + align:start position:0% +it's just oh the more of + + + align:start position:0% +it's just oh the more of +these + + align:start position:0% +these + + + align:start position:0% +these +Transporters that you have maybe you + + align:start position:0% +Transporters that you have maybe you + + + align:start position:0% +Transporters that you have maybe you +know you just get a linear increase in + + align:start position:0% +know you just get a linear increase in + + + align:start position:0% +know you just get a linear increase in +your your total uptake + + align:start position:0% +your your total uptake + + + align:start position:0% +your your total uptake +rate but it turns out that that's not + + align:start position:0% +rate but it turns out that that's not + + + align:start position:0% +rate but it turns out that that's not +true because even at just having say 1% + + align:start position:0% + + + + align:start position:0% + +roughly of uh of the surface covered by + + align:start position:0% +roughly of uh of the surface covered by + + + align:start position:0% +roughly of uh of the surface covered by +this transporter you can get something + + align:start position:0% +this transporter you can get something + + + align:start position:0% +this transporter you can get something +like 50% + + align:start position:0% + + + + align:start position:0% + +of the total maximal uptake rate and + + align:start position:0% +of the total maximal uptake rate and + + + align:start position:0% +of the total maximal uptake rate and +that's because these guys are not + + align:start position:0% +that's because these guys are not + + + align:start position:0% +that's because these guys are not +competing with each other so much + + align:start position:0% +competing with each other so much + + + align:start position:0% +competing with each other so much +because they're far away right so this + + align:start position:0% +because they're far away right so this + + + align:start position:0% +because they're far away right so this +curve really looks something + + align:start position:0% + + + + align:start position:0% + +like + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% + + + + align:start position:0% + +okay okay now this is I think especially + + align:start position:0% +okay okay now this is I think especially + + + align:start position:0% +okay okay now this is I think especially +interesting because a cell is not trying + + align:start position:0% +interesting because a cell is not trying + + + align:start position:0% +interesting because a cell is not trying +to import just one thing in principle + + align:start position:0% +to import just one thing in principle + + + align:start position:0% +to import just one thing in principle +it's trying to import many different + + align:start position:0% +it's trying to import many different + + + align:start position:0% +it's trying to import many different +things right so you need you need carbon + + align:start position:0% +things right so you need you need carbon + + + align:start position:0% +things right so you need you need carbon +sources you need uh you need all sorts + + align:start position:0% +sources you need uh you need all sorts + + + align:start position:0% +sources you need uh you need all sorts +of Trace Metals you need nitrogen right + + align:start position:0% +of Trace Metals you need nitrogen right + + + align:start position:0% +of Trace Metals you need nitrogen right +so in principle there are many many many + + align:start position:0% +so in principle there are many many many + + + align:start position:0% +so in principle there are many many many +things that a cell is trying to get from + + align:start position:0% +things that a cell is trying to get from + + + align:start position:0% +things that a cell is trying to get from +the environment and by Simply Having + + align:start position:0% +the environment and by Simply Having + + + align:start position:0% +the environment and by Simply Having +different Transporters specific to + + align:start position:0% +different Transporters specific to + + + align:start position:0% +different Transporters specific to +different things all right so here are + + align:start position:0% +different things all right so here are + + + align:start position:0% +different things all right so here are +some squares that uptake something else + + align:start position:0% +some squares that uptake something else + + + align:start position:0% +some squares that uptake something else +and + + align:start position:0% +and + + + align:start position:0% +and +little I don't know have some triangles + + align:start position:0% +little I don't know have some triangles + + + align:start position:0% +little I don't know have some triangles +all right whatever right so you can have + + align:start position:0% +all right whatever right so you can have + + + align:start position:0% +all right whatever right so you can have +many many many of these different + + align:start position:0% +many many many of these different + + + align:start position:0% +many many many of these different +transform ERS on the cell surface and + + align:start position:0% +transform ERS on the cell surface and + + + align:start position:0% +transform ERS on the cell surface and +they're each uptaking their own thing + + align:start position:0% +they're each uptaking their own thing + + + align:start position:0% +they're each uptaking their own thing +and kind of surprisingly you can get + + align:start position:0% +and kind of surprisingly you can get + + + align:start position:0% +and kind of surprisingly you can get +near optimal uptake rates of many many + + align:start position:0% +near optimal uptake rates of many many + + + align:start position:0% +near optimal uptake rates of many many +different + + align:start position:0% +different + + + align:start position:0% +different +things + + align:start position:0% +things + + + align:start position:0% +things +okay I'm I I feel that I've + + align:start position:0% +okay I'm I I feel that I've + + + align:start position:0% +okay I'm I I feel that I've +lost can some somebody ask a question of + + align:start position:0% +lost can some somebody ask a question of + + + align:start position:0% +lost can some somebody ask a question of +yes + + align:start position:0% + + + + align:start position:0% + +thisf right so this right so this this + + align:start position:0% +thisf right so this right so this this + + + align:start position:0% +thisf right so this right so this this +initial thing this increases linearly + + align:start position:0% +initial thing this increases linearly + + + align:start position:0% +initial thing this increases linearly +for for small areas because just like + + align:start position:0% +for for small areas because just like + + + align:start position:0% +for for small areas because just like +what we said before is that if you had + + align:start position:0% +what we said before is that if you had + + + align:start position:0% +what we said before is that if you had +these two little holes in the membrane + + align:start position:0% +these two little holes in the membrane + + + align:start position:0% +these two little holes in the membrane +that are far away from each other then + + align:start position:0% +that are far away from each other then + + + align:start position:0% +that are far away from each other then +uh then they don't compete what that + + align:start position:0% +uh then they don't compete what that + + + align:start position:0% +uh then they don't compete what that +means is that you get you do get an + + align:start position:0% +means is that you get you do get an + + + align:start position:0% +means is that you get you do get an +initial linear increase here guess + + align:start position:0% +initial linear increase here guess + + + align:start position:0% +initial linear increase here guess +question how get + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +um oh no we can do we can do it uh yeah + + align:start position:0% +um oh no we can do we can do it uh yeah + + + align:start position:0% +um oh no we can do we can do it uh yeah +um yeah because + + align:start position:0% +um yeah because + + + align:start position:0% +um yeah because +actually uh I I think + + align:start position:0% +actually uh I I think + + + align:start position:0% +actually uh I I think +that the most straightforward way to do + + align:start position:0% +that the most straightforward way to do + + + align:start position:0% +that the most straightforward way to do +this is to ask what is the uh kind of + + align:start position:0% +this is to ask what is the uh kind of + + + align:start position:0% +this is to ask what is the uh kind of +absorbing rate of a + + align:start position:0% +absorbing rate of a + + + align:start position:0% +absorbing rate of a +um you know of a little patch let's say + + align:start position:0% +um you know of a little patch let's say + + + align:start position:0% +um you know of a little patch let's say +a circular patch right and we already + + align:start position:0% +a circular patch right and we already + + + align:start position:0% +a circular patch right and we already +figured out that when as uh as well okay + + align:start position:0% +figured out that when as uh as well okay + + + align:start position:0% +figured out that when as uh as well okay +so these are very related problems as + + align:start position:0% +so these are very related problems as + + + align:start position:0% +so these are very related problems as +you can kind of see from the you know I + + align:start position:0% +you can kind of see from the you know I + + + align:start position:0% +you can kind of see from the you know I +I just don't remember whether it's 2 pi + + align:start position:0% +I just don't remember whether it's 2 pi + + + align:start position:0% +I just don't remember whether it's 2 pi +or if it's 4 Pi for that particular + + align:start position:0% +or if it's 4 Pi for that particular + + + align:start position:0% +or if it's 4 Pi for that particular +problem + + align:start position:0% + + + + align:start position:0% + +um yeah but uh right because this this + + align:start position:0% +um yeah but uh right because this this + + + align:start position:0% +um yeah but uh right because this this +is some this is some uh this is an let's + + align:start position:0% +is some this is some uh this is an let's + + + align:start position:0% +is some this is some uh this is an let's +say this is uptake of a um of a patch + + align:start position:0% +say this is uptake of a um of a patch + + + align:start position:0% +say this is uptake of a um of a patch +we'll say you know and this is it's + + align:start position:0% +we'll say you know and this is it's + + + align:start position:0% +we'll say you know and this is it's +going to + + align:start position:0% +going to + + + align:start position:0% +going to +be either one two or four Pi DCA right + + align:start position:0% +be either one two or four Pi DCA right + + + align:start position:0% +be either one two or four Pi DCA right +but uh you so there there's some uptake + + align:start position:0% +but uh you so there there's some uptake + + + align:start position:0% +but uh you so there there's some uptake +rate from each patch right and the then + + align:start position:0% +rate from each patch right and the then + + + align:start position:0% +rate from each patch right and the then +but then that means just the the uptake + + align:start position:0% +but then that means just the the uptake + + + align:start position:0% +but then that means just the the uptake +total for small numbers is indeed just + + align:start position:0% +total for small numbers is indeed just + + + align:start position:0% +total for small numbers is indeed just +going to be equal to the number of + + align:start position:0% +going to be equal to the number of + + + align:start position:0% +going to be equal to the number of +patches or Transporters times the optic + + align:start position:0% +patches or Transporters times the optic + + + align:start position:0% +patches or Transporters times the optic +rate of each one right because they're + + align:start position:0% +rate of each one right because they're + + + align:start position:0% +rate of each one right because they're +they're just not not competing against + + align:start position:0% +they're just not not competing against + + + align:start position:0% +they're just not not competing against +each other and the Striking thing is + + align:start position:0% +each other and the Striking thing is + + + align:start position:0% +each other and the Striking thing is +that because of this difference in + + align:start position:0% +that because of this difference in + + + align:start position:0% +that because of this difference in +scaling between uh the radius and the + + align:start position:0% +scaling between uh the radius and the + + + align:start position:0% +scaling between uh the radius and the +area this can be a this can give you a + + align:start position:0% +area this can be a this can give you a + + + align:start position:0% +area this can be a this can give you a +lot of uptake rate while only occupying + + align:start position:0% +lot of uptake rate while only occupying + + + align:start position:0% +lot of uptake rate while only occupying +a small fraction of the + + align:start position:0% +a small fraction of the + + + align:start position:0% +a small fraction of the +area okay this is + + align:start position:0% +area okay this is + + + align:start position:0% +area okay this is +a fraction of + + align:start position:0% + + + + align:start position:0% + +area covered + + align:start position:0% + + + + align:start position:0% + +okay do you see why that ends up being + + align:start position:0% +okay do you see why that ends up being + + + align:start position:0% +okay do you see why that ends up being +the case yes + + align:start position:0% + + + + align:start position:0% + +that's well you know it depends on what + + align:start position:0% +that's well you know it depends on what + + + align:start position:0% +that's well you know it depends on what +you mean by soon I mean it's soon on the + + align:start position:0% +you mean by soon I mean it's soon on the + + + align:start position:0% +you mean by soon I mean it's soon on the +scale of the amount of area but it could + + align:start position:0% +scale of the amount of area but it could + + + align:start position:0% +scale of the amount of area but it could +be that you can have you know a thousand + + align:start position:0% +be that you can have you know a thousand + + + align:start position:0% +be that you can have you know a thousand +of them or so right you know so um you + + align:start position:0% +of them or so right you know so um you + + + align:start position:0% +of them or so right you know so um you +know I guess what I what I the way I + + align:start position:0% +know I guess what I what I the way I + + + align:start position:0% +know I guess what I what I the way I +would think about it is that uh you + + align:start position:0% +would think about it is that uh you + + + align:start position:0% +would think about it is that uh you +don't have to cover up very much of the + + align:start position:0% +don't have to cover up very much of the + + + align:start position:0% +don't have to cover up very much of the +cell surface in order to get really good + + align:start position:0% +cell surface in order to get really good + + + align:start position:0% +cell surface in order to get really good +upate + + align:start position:0% + + + + align:start position:0% + +connects all + + align:start position:0% + + + + align:start position:0% + +right now all right so the these are + + align:start position:0% +right now all right so the these are + + + align:start position:0% +right now all right so the these are +some some say fundamental limits to the + + align:start position:0% +some some say fundamental limits to the + + + align:start position:0% +some some say fundamental limits to the +way that bacteria for example and other + + align:start position:0% +way that bacteria for example and other + + + align:start position:0% +way that bacteria for example and other +cells can uh can uptake food and other + + align:start position:0% +cells can uh can uptake food and other + + + align:start position:0% +cells can uh can uptake food and other +other nutrients + + align:start position:0% +other nutrients + + + align:start position:0% +other nutrients +but from the standpoint of trying to + + align:start position:0% +but from the standpoint of trying to + + + align:start position:0% +but from the standpoint of trying to +find where the nutrients are better what + + align:start position:0% +find where the nutrients are better what + + + align:start position:0% +find where the nutrients are better what +you need to be able to do is uh you need + + align:start position:0% +you need to be able to do is uh you need + + + align:start position:0% +you need to be able to do is uh you need +to be able to measure the + + align:start position:0% + + + + align:start position:0% + +concentration now the basic way that you + + align:start position:0% +concentration now the basic way that you + + + align:start position:0% +concentration now the basic way that you +could for example measure a + + align:start position:0% +could for example measure a + + + align:start position:0% +could for example measure a +concentration of something is if you + + align:start position:0% +concentration of something is if you + + + align:start position:0% +concentration of something is if you +were the best that you could do is if + + align:start position:0% +were the best that you could do is if + + + align:start position:0% +were the best that you could do is if +you're a perfect + + align:start position:0% +you're a perfect + + + align:start position:0% +you're a perfect +absorber you uptake molecules at this + + align:start position:0% +absorber you uptake molecules at this + + + align:start position:0% +absorber you uptake molecules at this +rate okay and then you uh count the + + align:start position:0% +rate okay and then you uh count the + + + align:start position:0% +rate okay and then you uh count the +number of molecules that that you uptake + + align:start position:0% +number of molecules that that you uptake + + + align:start position:0% +number of molecules that that you uptake +over some time + + align:start position:0% +over some time + + + align:start position:0% +over some time +T right indeed the number that you + + align:start position:0% +T right indeed the number that you + + + align:start position:0% +T right indeed the number that you +uptake over sometime + + align:start position:0% +uptake over sometime + + + align:start position:0% +uptake over sometime +T will uh just be given by + + align:start position:0% + + + + align:start position:0% + +this what will be the distribution of + + align:start position:0% +this what will be the distribution of + + + align:start position:0% +this what will be the distribution of +these + + align:start position:0% + + + + align:start position:0% + +numbers all right I should just have + + align:start position:0% +numbers all right I should just have + + + align:start position:0% +numbers all right I should just have +somewhere up on the always a bunch of + + align:start position:0% +somewhere up on the always a bunch of + + + align:start position:0% +somewhere up on the always a bunch of +probability distributions that we can uh + + align:start position:0% +probability distributions that we can uh + + + align:start position:0% +probability distributions that we can uh +we can + + align:start position:0% +we can + + + align:start position:0% +we can +vote but think about it for a moment and + + align:start position:0% +vote but think about it for a moment and + + + align:start position:0% +vote but think about it for a moment and +then we'll + + align:start position:0% + + + + align:start position:0% + +vote all right ready + + align:start position:0% +vote all right ready + + + align:start position:0% +vote all right ready +three two one what is going to be the + + align:start position:0% +three two one what is going to be the + + + align:start position:0% +three two one what is going to be the +probability distribution of the number + + align:start position:0% +probability distribution of the number + + + align:start position:0% +probability distribution of the number +of these things + + align:start position:0% +of these things + + + align:start position:0% +of these things +absorbed over some time right it's going + + align:start position:0% +absorbed over some time right it's going + + + align:start position:0% +absorbed over some time right it's going +to be distributed + + align:start position:0% + + + + align:start position:0% + +Pon right what is going to be + + align:start position:0% +Pon right what is going to be + + + align:start position:0% +Pon right what is going to be +the distribution of times between + + align:start position:0% +the distribution of times between + + + align:start position:0% +the distribution of times between +successive absorption + + align:start position:0% +successive absorption + + + align:start position:0% +successive absorption +events ready three two + + align:start position:0% + + + + align:start position:0% + +one all right yeah this one that that is + + align:start position:0% +one all right yeah this one that that is + + + align:start position:0% +one all right yeah this one that that is +going to end up being exponential right + + align:start position:0% +going to end up being exponential right + + + align:start position:0% +going to end up being exponential right +and this is all confusing so this is a + + align:start position:0% +and this is all confusing so this is a + + + align:start position:0% +and this is all confusing so this is a +pant process these things are occurring + + align:start position:0% +pant process these things are occurring + + + align:start position:0% +pant process these things are occurring +at random times you know at some rate + + align:start position:0% +at random times you know at some rate + + + align:start position:0% +at random times you know at some rate +and if you have such such a process + + align:start position:0% +and if you have such such a process + + + align:start position:0% +and if you have such such a process +that's random and you ask how many + + align:start position:0% +that's random and you ask how many + + + align:start position:0% +that's random and you ask how many +events or sometime T that is the + + align:start position:0% +events or sometime T that is the + + + align:start position:0% +events or sometime T that is the +definition of a + + align:start position:0% +definition of a + + + align:start position:0% +definition of a +Pon okay if this is a large + + align:start position:0% +Pon okay if this is a large + + + align:start position:0% +Pon okay if this is a large +number then the probability distribution + + align:start position:0% +number then the probability distribution + + + align:start position:0% +number then the probability distribution +is going to look like something else + + align:start position:0% +is going to look like something else + + + align:start position:0% +is going to look like something else +what is it going to look like ready + + align:start position:0% +what is it going to look like ready + + + align:start position:0% +what is it going to look like ready +three two + + align:start position:0% + + + + align:start position:0% + +one all right most people are trying to + + align:start position:0% +one all right most people are trying to + + + align:start position:0% +one all right most people are trying to +find the D okay it's the Cent limit + + align:start position:0% +find the D okay it's the Cent limit + + + align:start position:0% +find the D okay it's the Cent limit +theorem there all + + align:start position:0% +theorem there all + + + align:start position:0% +theorem there all +right what is going to be uh what's + + align:start position:0% +right what is going to be uh what's + + + align:start position:0% +right what is going to be uh what's +going to be what's going to determine + + align:start position:0% +going to be what's going to determine + + + align:start position:0% +going to be what's going to determine +the resolution of that measurement that + + align:start position:0% +the resolution of that measurement that + + + align:start position:0% +the resolution of that measurement that +we that we + + align:start position:0% + + + + align:start position:0% + +make right so in some ways what what you + + align:start position:0% +make right so in some ways what what you + + + align:start position:0% +make right so in some ways what what you +would like to know is well what's the + + align:start position:0% +would like to know is well what's the + + + align:start position:0% +would like to know is well what's the +standard deviation in your measurement + + align:start position:0% +standard deviation in your measurement + + + align:start position:0% +standard deviation in your measurement +of the + + align:start position:0% +of the + + + align:start position:0% +of the +concentration okay divided by the + + align:start position:0% +concentration okay divided by the + + + align:start position:0% +concentration okay divided by the +concentration right so this is maybe a a + + align:start position:0% +concentration right so this is maybe a a + + + align:start position:0% +concentration right so this is maybe a a +fractional error in your measurement of + + align:start position:0% +fractional error in your measurement of + + + align:start position:0% +fractional error in your measurement of +the + + align:start position:0% + + + + align:start position:0% + +concentration does it do you guys + + align:start position:0% +concentration does it do you guys + + + align:start position:0% +concentration does it do you guys +understand why this is the + + align:start position:0% + + + + align:start position:0% + +error in in the + + align:start position:0% + + + + align:start position:0% + +measurement + + align:start position:0% +measurement + + + align:start position:0% +measurement +right well this actually will go as the + + align:start position:0% +right well this actually will go as the + + + align:start position:0% +right well this actually will go as the +standard deviation in our measurement of + + align:start position:0% +standard deviation in our measurement of + + + align:start position:0% +standard deviation in our measurement of +the number divided by kind of the number + + align:start position:0% +the number divided by kind of the number + + + align:start position:0% +the number divided by kind of the number +that we + + align:start position:0% + + + + align:start position:0% + +measure okay what's going to be the + + align:start position:0% +measure okay what's going to be the + + + align:start position:0% +measure okay what's going to be the +standard deviation of this + + align:start position:0% + + + + align:start position:0% + +number what's + + align:start position:0% +number what's + + + align:start position:0% +number what's +that the mean yes it's close to yeah + + align:start position:0% +that the mean yes it's close to yeah + + + align:start position:0% +that the mean yes it's close to yeah +yeah it's the square root of of the the + + align:start position:0% +yeah it's the square root of of the the + + + align:start position:0% +yeah it's the square root of of the the +mean number right what that means is + + align:start position:0% +mean number right what that means is + + + align:start position:0% +mean number right what that means is +that this thing is going to be the + + align:start position:0% +that this thing is going to be the + + + align:start position:0% +that this thing is going to be the +square root of a 4 Pi c d a t and this + + align:start position:0% +square root of a 4 Pi c d a t and this + + + align:start position:0% +square root of a 4 Pi c d a t and this +is which is 4 Pi + + align:start position:0% +is which is 4 Pi + + + align:start position:0% +is which is 4 Pi +CD + + align:start position:0% +CD + + + align:start position:0% +CD +T right + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay this is this the number that you + + align:start position:0% +okay this is this the number that you + + + align:start position:0% +okay this is this the number that you +measure here when the number that you + + align:start position:0% +measure here when the number that you + + + align:start position:0% +measure here when the number that you +uptake over some time period T that's + + align:start position:0% +uptake over some time period T that's + + + align:start position:0% +uptake over some time period T that's +going to be distributed as a Plus on and + + align:start position:0% +going to be distributed as a Plus on and + + + align:start position:0% +going to be distributed as a Plus on and +plus on the variance is equal to the + + align:start position:0% +plus on the variance is equal to the + + + align:start position:0% +plus on the variance is equal to the +mean + + align:start position:0% +mean + + + align:start position:0% +mean +which means the standard deviation which + + align:start position:0% +which means the standard deviation which + + + align:start position:0% +which means the standard deviation which +is the square root of the + + align:start position:0% +is the square root of the + + + align:start position:0% +is the square root of the +variance is going to be this okay + + align:start position:0% +variance is going to be this okay + + + align:start position:0% +variance is going to be this okay +yesing the first step where you change + + align:start position:0% +yesing the first step where you change + + + align:start position:0% +yesing the first step where you change +the C for right uh okay so the + + align:start position:0% +the C for right uh okay so the + + + align:start position:0% +the C for right uh okay so the +uh right okay so from the standpoint of + + align:start position:0% +uh right okay so from the standpoint of + + + align:start position:0% +uh right okay so from the standpoint of +the cell what the cell is doing is it's + + align:start position:0% +the cell what the cell is doing is it's + + + align:start position:0% +the cell what the cell is doing is it's +counting you know the number of these + + align:start position:0% +counting you know the number of these + + + align:start position:0% +counting you know the number of these +things that have have come right and + + align:start position:0% +things that have have come right and + + + align:start position:0% +things that have have come right and +it's true that that from that number to + + align:start position:0% +it's true that that from that number to + + + align:start position:0% +it's true that that from that number to +get an absolute from the number of of + + align:start position:0% +get an absolute from the number of of + + + align:start position:0% +get an absolute from the number of of +say molecules that are absorbed absorbed + + align:start position:0% +say molecules that are absorbed absorbed + + + align:start position:0% +say molecules that are absorbed absorbed +uh to to get a concentration units of + + align:start position:0% +uh to to get a concentration units of + + + align:start position:0% +uh to to get a concentration units of +you know of of number per cubic Micron + + align:start position:0% +you know of of number per cubic Micron + + + align:start position:0% +you know of of number per cubic Micron +or whatnot you need to you would need + + align:start position:0% +or whatnot you need to you would need + + + align:start position:0% +or whatnot you need to you would need +the cell would need to know kind of how + + align:start position:0% +the cell would need to know kind of how + + + align:start position:0% +the cell would need to know kind of how +big it is what the diffusion coefficient + + align:start position:0% +big it is what the diffusion coefficient + + + align:start position:0% +big it is what the diffusion coefficient +is and so forth but in terms of the + + align:start position:0% +is and so forth but in terms of the + + + align:start position:0% +is and so forth but in terms of the +fractional error those all end up + + align:start position:0% +fractional error those all end up + + + align:start position:0% +fractional error those all end up +disappearing okay because the fractional + + align:start position:0% +disappearing okay because the fractional + + + align:start position:0% +disappearing okay because the fractional +error is telling us well if if this time + + align:start position:0% +error is telling us well if if this time + + + align:start position:0% +error is telling us well if if this time +I measure it and I get 10 and next time + + align:start position:0% +I measure it and I get 10 and next time + + + align:start position:0% +I measure it and I get 10 and next time +I measure it I get 20 then this is this + + align:start position:0% +I measure it I get 20 then this is this + + + align:start position:0% +I measure it I get 20 then this is this +is telling us about how much error this + + align:start position:0% +is telling us about how much error this + + + align:start position:0% +is telling us about how much error this +is indeed just fractional error in in + + align:start position:0% +is indeed just fractional error in in + + + align:start position:0% +is indeed just fractional error in in +our measurement of the concentration and + + align:start position:0% +our measurement of the concentration and + + + align:start position:0% +our measurement of the concentration and +irrespective of what the uh whether the + + align:start position:0% +irrespective of what the uh whether the + + + align:start position:0% +irrespective of what the uh whether the +cell is able able to estimate the re you + + align:start position:0% +cell is able able to estimate the re you + + + align:start position:0% +cell is able able to estimate the re you +know the the concentration units of of a + + align:start position:0% +know the the concentration units of of a + + + align:start position:0% +know the the concentration units of of a +physical quantity right because these + + align:start position:0% +physical quantity right because these + + + align:start position:0% +physical quantity right because these +things uh yeah because they that that + + align:start position:0% +things uh yeah because they that that + + + align:start position:0% +things uh yeah because they that that +sort of error would scale together I'm + + align:start position:0% +sort of error would scale together I'm + + + align:start position:0% +sort of error would scale together I'm +worried that I'm not helping you though + + align:start position:0% +worried that I'm not helping you though + + + align:start position:0% +worried that I'm not helping you though +um so you're kind of saying because CNN + + align:start position:0% +um so you're kind of saying because CNN + + + align:start position:0% +um so you're kind of saying because CNN +are larly related um any proportionality + + align:start position:0% +are larly related um any proportionality + + + align:start position:0% +are larly related um any proportionality +factors would cancel out yeah yep + + align:start position:0% + + + + align:start position:0% + +would I be right to think that is dist + + align:start position:0% +would I be right to think that is dist + + + align:start position:0% +would I be right to think that is dist +as + + align:start position:0% +as + + + align:start position:0% +as +c yeah our our our estimate of C would + + align:start position:0% +c yeah our our our estimate of C would + + + align:start position:0% +c yeah our our our estimate of C would +be because because ultimately what what + + align:start position:0% +be because because ultimately what what + + + align:start position:0% +be because because ultimately what what +the cell would do is it would measure + + align:start position:0% +the cell would do is it would measure + + + align:start position:0% +the cell would do is it would measure +some number and then it would say all + + align:start position:0% +some number and then it would say all + + + align:start position:0% +some number and then it would say all +right well I multiply by all these + + align:start position:0% +right well I multiply by all these + + + align:start position:0% +right well I multiply by all these +things and then that that results in an + + align:start position:0% +things and then that that results in an + + + align:start position:0% +things and then that that results in an +error in C that is distributed the same + + align:start position:0% +error in C that is distributed the same + + + align:start position:0% +error in C that is distributed the same +way as the error in N but it's it's you + + align:start position:0% +way as the error in N but it's it's you + + + align:start position:0% +way as the error in N but it's it's you +know they're kind of proportional to + + align:start position:0% +know they're kind of proportional to + + + align:start position:0% +know they're kind of proportional to +each other + + align:start position:0% +each other + + + align:start position:0% +each other +yeah confus + + align:start position:0% +yeah confus + + + align:start position:0% +yeah confus +C is plus distributed and then our + + align:start position:0% +C is plus distributed and then our + + + align:start position:0% +C is plus distributed and then our +original ratio that we want Sig c c + + align:start position:0% +original ratio that we want Sig c c + + + align:start position:0% +original ratio that we want Sig c c +should go like one + + align:start position:0% + + + + align:start position:0% + +should yeah I mean I that's got sure + + align:start position:0% +should yeah I mean I that's got sure + + + align:start position:0% +should yeah I mean I that's got sure +okay so um and okay I think we have to + + align:start position:0% +okay so um and okay I think we have to + + + align:start position:0% +okay so um and okay I think we have to +be careful so it's not that the C is + + align:start position:0% +be careful so it's not that the C is + + + align:start position:0% +be careful so it's not that the C is +actually Plus on distributed because you + + align:start position:0% +actually Plus on distributed because you + + + align:start position:0% +actually Plus on distributed because you +can't it it's um it's really that you + + align:start position:0% +can't it it's um it's really that you + + + align:start position:0% +can't it it's um it's really that you +take a Pon distribution and multiply by + + align:start position:0% +take a Pon distribution and multiply by + + + align:start position:0% +take a Pon distribution and multiply by +something to get an estimate of C right + + align:start position:0% +something to get an estimate of C right + + + align:start position:0% +something to get an estimate of C right +but if you take an if you take a + + align:start position:0% +but if you take an if you take a + + + align:start position:0% +but if you take an if you take a +distribution and you multiply it by + + align:start position:0% +distribution and you multiply it by + + + align:start position:0% +distribution and you multiply it by +multiply the numbers by 10 then it's no + + align:start position:0% +multiply the numbers by 10 then it's no + + + align:start position:0% +multiply the numbers by 10 then it's no +longer Pon distribution because because + + align:start position:0% +longer Pon distribution because because + + + align:start position:0% +longer Pon distribution because because +the mean goes up by 10 but the variance + + align:start position:0% +the mean goes up by 10 but the variance + + + align:start position:0% +the mean goes up by 10 but the variance +goes up by 100 right so then then the + + align:start position:0% +goes up by 100 right so then then the + + + align:start position:0% +goes up by 100 right so then then the +variance is no longer equal to the mean + + align:start position:0% +variance is no longer equal to the mean + + + align:start position:0% +variance is no longer equal to the mean +so it's not a Pon anymore right so you + + align:start position:0% +so it's not a Pon anymore right so you + + + align:start position:0% +so it's not a Pon anymore right so you +can't just multiply number times a Pon + + align:start position:0% +can't just multiply number times a Pon + + + align:start position:0% +can't just multiply number times a Pon +to get you know + + align:start position:0% + + + + align:start position:0% + +thanks and this expression kind of makes + + align:start position:0% +thanks and this expression kind of makes + + + align:start position:0% +thanks and this expression kind of makes +sense and that you know the longer that + + align:start position:0% +sense and that you know the longer that + + + align:start position:0% +sense and that you know the longer that +the cell measures the you know the less + + align:start position:0% +the cell measures the you know the less + + + align:start position:0% +the cell measures the you know the less +error there is you know if there's more + + align:start position:0% +error there is you know if there's more + + + align:start position:0% +error there is you know if there's more +diffusion or higher concent ation less + + align:start position:0% +diffusion or higher concent ation less + + + align:start position:0% +diffusion or higher concent ation less +error right and this is really in some + + align:start position:0% +error right and this is really in some + + + align:start position:0% +error right and this is really in some +ways uh some some estimate of the best + + align:start position:0% +ways uh some some estimate of the best + + + align:start position:0% +ways uh some some estimate of the best +the cell could do and surprisingly cells + + align:start position:0% +the cell could do and surprisingly cells + + + align:start position:0% +the cell could do and surprisingly cells +can get close to this okay now you might + + align:start position:0% +can get close to this okay now you might + + + align:start position:0% +can get close to this okay now you might +also ask okay this this is this is a + + align:start position:0% +also ask okay this this is this is a + + + align:start position:0% +also ask okay this this is this is a +measurement of concentration for a + + align:start position:0% +measurement of concentration for a + + + align:start position:0% +measurement of concentration for a +perfectly absorbing sphere is a cell now + + align:start position:0% +perfectly absorbing sphere is a cell now + + + align:start position:0% +perfectly absorbing sphere is a cell now +you might ask well how would our error + + align:start position:0% +you might ask well how would our error + + + align:start position:0% +you might ask well how would our error +change if instead of absorbing the + + align:start position:0% +change if instead of absorbing the + + + align:start position:0% +change if instead of absorbing the +molecules we simply had um a detector + + align:start position:0% +molecules we simply had um a detector + + + align:start position:0% +molecules we simply had um a detector +right we had something so that just + + align:start position:0% +right we had something so that just + + + align:start position:0% +right we had something so that just +asked okay each time that the molecule + + align:start position:0% +asked okay each time that the molecule + + + align:start position:0% +asked okay each time that the molecule +bounces against my cell I count + + align:start position:0% +bounces against my cell I count + + + align:start position:0% +bounces against my cell I count +one do you understand the difference + + align:start position:0% +one do you understand the difference + + + align:start position:0% +one do you understand the difference +right so this is for a perfect + + align:start position:0% + + + + align:start position:0% + +absorber so what about a perfect I think + + align:start position:0% +absorber so what about a perfect I think + + + align:start position:0% +absorber so what about a perfect I think +you might call it a perfect + + align:start position:0% + + + + align:start position:0% + +monitor right does the question there is + + align:start position:0% +monitor right does the question there is + + + align:start position:0% +monitor right does the question there is +does a perfect monitor do better or + + align:start position:0% +does a perfect monitor do better or + + + align:start position:0% +does a perfect monitor do better or +worse than a perfect + + align:start position:0% +worse than a perfect + + + align:start position:0% +worse than a perfect +detector + + align:start position:0% +detector + + + align:start position:0% +detector +okay so we'll say + + align:start position:0% +okay so we'll say + + + align:start position:0% +okay so we'll say +better + + align:start position:0% +better + + + align:start position:0% +better +worse or no + + align:start position:0% +worse or no + + + align:start position:0% +worse or no +change and it's of course not possible + + align:start position:0% +change and it's of course not possible + + + align:start position:0% +change and it's of course not possible +for you to actually do this calculation + + align:start position:0% +for you to actually do this calculation + + + align:start position:0% +for you to actually do this calculation +but it's useful to imagine the situation + + align:start position:0% +but it's useful to imagine the situation + + + align:start position:0% +but it's useful to imagine the situation +and and uh make your best + + align:start position:0% +and and uh make your best + + + align:start position:0% +and and uh make your best +guess better worse and + + align:start position:0% +guess better worse and + + + align:start position:0% +guess better worse and +same I'll give you I'll give you five 10 + + align:start position:0% +same I'll give you I'll give you five 10 + + + align:start position:0% +same I'll give you I'll give you five 10 +seconds to think about it because it's + + align:start position:0% +seconds to think about it because it's + + + align:start position:0% +seconds to think about it because it's +it's interesting to imagine the + + align:start position:0% + + + + align:start position:0% + +situation all right let's see where we + + align:start position:0% +situation all right let's see where we + + + align:start position:0% +situation all right let's see where we +are ready three two + + align:start position:0% + + + + align:start position:0% + +one oh it's a we have a fair a fair + + align:start position:0% +one oh it's a we have a fair a fair + + + align:start position:0% +one oh it's a we have a fair a fair +range of answers all right I think every + + align:start position:0% +range of answers all right I think every + + + align:start position:0% +range of answers all right I think every +everybody agrees it's going to do + + align:start position:0% +everybody agrees it's going to do + + + align:start position:0% +everybody agrees it's going to do +something because it would be kind of a + + align:start position:0% +something because it would be kind of a + + + align:start position:0% +something because it would be kind of a +coincidence if it didn't if it didn't + + align:start position:0% +coincidence if it didn't if it didn't + + + align:start position:0% +coincidence if it didn't if it didn't +change things all right can uh can I get + + align:start position:0% +change things all right can uh can I get + + + align:start position:0% +change things all right can uh can I get +uh somebody to volunteer of what their + + align:start position:0% +uh somebody to volunteer of what their + + + align:start position:0% +uh somebody to volunteer of what their +neighbor is thinking I know you didn't + + align:start position:0% +neighbor is thinking I know you didn't + + + align:start position:0% +neighbor is thinking I know you didn't +actually talk to your neighbor yet but + + align:start position:0% +actually talk to your neighbor yet but + + + align:start position:0% +actually talk to your neighbor yet but +you can you can still invoke + + align:start position:0% + + + + align:start position:0% + +that yes well so I don't know about this + + align:start position:0% +that yes well so I don't know about this + + + align:start position:0% +that yes well so I don't know about this +so much but I was the first thing I was + + align:start position:0% +so much but I was the first thing I was + + + align:start position:0% +so much but I was the first thing I was +thinking is that maybe this monitor + + align:start position:0% +thinking is that maybe this monitor + + + align:start position:0% +thinking is that maybe this monitor +might um at a different rate like + + align:start position:0% +might um at a different rate like + + + align:start position:0% +might um at a different rate like +proportional to its area than + + align:start position:0% +proportional to its area than + + + align:start position:0% +proportional to its area than +the just I don't know it seemed like it + + align:start position:0% +the just I don't know it seemed like it + + + align:start position:0% +the just I don't know it seemed like it +wouldn't change a concent the + + align:start position:0% +wouldn't change a concent the + + + align:start position:0% +wouldn't change a concent the +concentration gradient because it + + align:start position:0% +concentration gradient because it + + + align:start position:0% +concentration gradient because it +wouldn't be subtracting any and so then + + align:start position:0% +wouldn't be subtracting any and so then + + + align:start position:0% +wouldn't be subtracting any and so then +just things would bounce off it and that + + align:start position:0% +just things would bounce off it and that + + + align:start position:0% +just things would bounce off it and that +would be proportional to area okay + + align:start position:0% +would be proportional to area okay + + + align:start position:0% +would be proportional to area okay +that's interesting so so you're you're + + align:start position:0% +that's interesting so so you're you're + + + align:start position:0% +that's interesting so so you're you're +um you're arguing for a different + + align:start position:0% +um you're arguing for a different + + + align:start position:0% +um you're arguing for a different +scaling and then and then then it would + + align:start position:0% +scaling and then and then then it would + + + align:start position:0% +scaling and then and then then it would +actually be either it could you know + + align:start position:0% +actually be either it could you know + + + align:start position:0% +actually be either it could you know +depending on the area then it would be + + align:start position:0% +depending on the area then it would be + + + align:start position:0% +depending on the area then it would be +different because yeah so that seemed + + align:start position:0% +different because yeah so that seemed + + + align:start position:0% +different because yeah so that seemed +weird to me which is why I wanted to + + align:start position:0% +weird to me which is why I wanted to + + + align:start position:0% +weird to me which is why I wanted to +just check where + + align:start position:0% +just check where + + + align:start position:0% +just check where +people yeah no no that's fair that's + + align:start position:0% +people yeah no no that's fair that's + + + align:start position:0% +people yeah no no that's fair that's +right yeah no in the end the scaling is + + align:start position:0% +right yeah no in the end the scaling is + + + align:start position:0% +right yeah no in the end the scaling is +the same although this is very + + align:start position:0% +the same although this is very + + + align:start position:0% +the same although this is very +complicated confusing something can can + + align:start position:0% +complicated confusing something can can + + + align:start position:0% +complicated confusing something can can +I hear uh somebody else argue for one or + + align:start position:0% +I hear uh somebody else argue for one or + + + align:start position:0% +I hear uh somebody else argue for one or +the other he actually argued for both + + align:start position:0% +the other he actually argued for both + + + align:start position:0% +the other he actually argued for both +right so that's you + + align:start position:0% +right so that's you + + + align:start position:0% +right so that's you +know um I just thought like + + align:start position:0% +know um I just thought like + + + align:start position:0% +know um I just thought like +if if it's not taking up the molecules + + align:start position:0% +if if it's not taking up the molecules + + + align:start position:0% +if if it's not taking up the molecules +then it could bounce against the same + + align:start position:0% +then it could bounce against the same + + + align:start position:0% +then it could bounce against the same +molecule yeah right and yeah and and + + align:start position:0% +molecule yeah right and yeah and and + + + align:start position:0% +molecule yeah right and yeah and and +therefore so which one are you arguing + + align:start position:0% +therefore so which one are you arguing + + + align:start position:0% +therefore so which one are you arguing +for for work yeah for Worse okay yeah + + align:start position:0% +for for work yeah for Worse okay yeah + + + align:start position:0% +for for work yeah for Worse okay yeah +indeed it it does end up being worse and + + align:start position:0% +indeed it it does end up being worse and + + + align:start position:0% +indeed it it does end up being worse and +it's actually significantly worse it's + + align:start position:0% +it's actually significantly worse it's + + + align:start position:0% +it's actually significantly worse it's +uh it's something like 10 times worse + + align:start position:0% +uh it's something like 10 times worse + + + align:start position:0% +uh it's something like 10 times worse +yeah so U and and and and I think the + + align:start position:0% +yeah so U and and and and I think the + + + align:start position:0% +yeah so U and and and and I think the +intuitive explanation is indeed what you + + align:start position:0% +intuitive explanation is indeed what you + + + align:start position:0% +intuitive explanation is indeed what you +just said that a perfect monitor you + + align:start position:0% +just said that a perfect monitor you + + + align:start position:0% +just said that a perfect monitor you +know that's great except for the fact + + align:start position:0% +know that's great except for the fact + + + align:start position:0% +know that's great except for the fact +that you know it's it's it's counting + + align:start position:0% +that you know it's it's it's counting + + + align:start position:0% +that you know it's it's it's counting +every time something hits but then it + + align:start position:0% +every time something hits but then it + + + align:start position:0% +every time something hits but then it +doesn't know if it already you know + + align:start position:0% +doesn't know if it already you know + + + align:start position:0% +doesn't know if it already you know +counted that molecule or not right so + + align:start position:0% +counted that molecule or not right so + + + align:start position:0% +counted that molecule or not right so +then there's some there's extra + + align:start position:0% +then there's some there's extra + + + align:start position:0% +then there's some there's extra +uncertainty that results from + + align:start position:0% +uncertainty that results from + + + align:start position:0% +uncertainty that results from +that okay of course ultimately you have + + align:start position:0% +that okay of course ultimately you have + + + align:start position:0% +that okay of course ultimately you have +to go and do the calculation if you want + + align:start position:0% +to go and do the calculation if you want + + + align:start position:0% +to go and do the calculation if you want +to be convinced do something like this + + align:start position:0% +to be convinced do something like this + + + align:start position:0% +to be convinced do something like this +but uh but indeed the perfect absorber + + align:start position:0% +but uh but indeed the perfect absorber + + + align:start position:0% +but uh but indeed the perfect absorber +is the best that you can possibly + + align:start position:0% +is the best that you can possibly + + + align:start position:0% +is the best that you can possibly +do + + align:start position:0% + + + + align:start position:0% + +okay unless + + align:start position:0% + + + + align:start position:0% + +itag that's right but that that's right + + align:start position:0% +itag that's right but that that's right + + + align:start position:0% +itag that's right but that that's right +so that's equivalent to being a perfect + + align:start position:0% +so that's equivalent to being a perfect + + + align:start position:0% +so that's equivalent to being a perfect +absorber right oh okay yeah well no + + align:start position:0% +absorber right oh okay yeah well no + + + align:start position:0% +absorber right oh okay yeah well no +because then yeah because these are non- + + align:start position:0% +because then yeah because these are non- + + + align:start position:0% +because then yeah because these are non- +interacting molecule so if you tag it + + align:start position:0% +interacting molecule so if you tag it + + + align:start position:0% +interacting molecule so if you tag it +green then all that you do is when the + + align:start position:0% +green then all that you do is when the + + + align:start position:0% +green then all that you do is when the +green molecule comes back you say I'm + + align:start position:0% +green molecule comes back you say I'm + + + align:start position:0% +green molecule comes back you say I'm +going to ignore that and that but then + + align:start position:0% +going to ignore that and that but then + + + align:start position:0% +going to ignore that and that but then +that's equivalent to if you if you just + + align:start position:0% +that's equivalent to if you if you just + + + align:start position:0% +that's equivalent to if you if you just +absorbed it yeah but there's no local + + align:start position:0% +absorbed it yeah but there's no local + + + align:start position:0% +absorbed it yeah but there's no local +dep yeah so there's no local there's no + + align:start position:0% +dep yeah so there's no local there's no + + + align:start position:0% +dep yeah so there's no local there's no +local depletion but because the diffus + + align:start position:0% +local depletion but because the diffus + + + align:start position:0% +local depletion but because the diffus +these are all non-interacting particles + + align:start position:0% +these are all non-interacting particles + + + align:start position:0% +these are all non-interacting particles +then it can't make a difference and I + + align:start position:0% +then it can't make a difference and I + + + align:start position:0% +then it can't make a difference and I +agree that this is + + align:start position:0% +agree that this is + + + align:start position:0% +agree that this is +confusing but I'm pretty confident what + + align:start position:0% +confusing but I'm pretty confident what + + + align:start position:0% +confusing but I'm pretty confident what +I said is true yeah because I you know + + align:start position:0% +I said is true yeah because I you know + + + align:start position:0% +I said is true yeah because I you know +since they're all non- interacted + + align:start position:0% +since they're all non- interacted + + + align:start position:0% +since they're all non- interacted +there's just no no no more information + + align:start position:0% + + + + align:start position:0% + +yeah right so okay yeah so this is + + align:start position:0% +yeah right so okay yeah so this is + + + align:start position:0% +yeah right so okay yeah so this is +asking uh all right so over some period + + align:start position:0% +asking uh all right so over some period + + + align:start position:0% +asking uh all right so over some period +of time I count the number of molecules + + align:start position:0% +of time I count the number of molecules + + + align:start position:0% +of time I count the number of molecules +that say I that hit me or that I absorb + + align:start position:0% +that say I that hit me or that I absorb + + + align:start position:0% +that say I that hit me or that I absorb +right and then I I say okay well I think + + align:start position:0% +right and then I I say okay well I think + + + align:start position:0% +right and then I I say okay well I think +that there are you know I counted 20 and + + align:start position:0% +that there are you know I counted 20 and + + + align:start position:0% +that there are you know I counted 20 and +the and the question is really well if I + + align:start position:0% +the and the question is really well if I + + + align:start position:0% +the and the question is really well if I +did this again how close to 20 would I + + align:start position:0% +did this again how close to 20 would I + + + align:start position:0% +did this again how close to 20 would I +would I + + align:start position:0% +would I + + + align:start position:0% +would I +get right would I get again you know 20 + + align:start position:0% +get right would I get again you know 20 + + + align:start position:0% +get right would I get again you know 20 +or 21 or would I next time get would I + + align:start position:0% +or 21 or would I next time get would I + + + align:start position:0% +or 21 or would I next time get would I +get 10 or 50 you know right so and that + + align:start position:0% +get 10 or 50 you know right so and that + + + align:start position:0% +get 10 or 50 you know right so and that +that's that's the real question how how + + align:start position:0% +that's that's the real question how how + + + align:start position:0% +that's that's the real question how how +repeatable are my + + align:start position:0% +repeatable are my + + + align:start position:0% +repeatable are my +measurements right so if I plot a + + align:start position:0% +measurements right so if I plot a + + + align:start position:0% +measurements right so if I plot a +histogram of a bunch of + + align:start position:0% +histogram of a bunch of + + + align:start position:0% +histogram of a bunch of +numbers that I get over this + + align:start position:0% +numbers that I get over this + + + align:start position:0% +numbers that I get over this +time right this is this is the number or + + align:start position:0% +time right this is this is the number or + + + align:start position:0% +time right this is this is the number or +the frequency that I observe a + + align:start position:0% +the frequency that I observe a + + + align:start position:0% +the frequency that I observe a +particular number of molecules over some + + align:start position:0% +particular number of molecules over some + + + align:start position:0% +particular number of molecules over some +period of time T you know I get some + + align:start position:0% +period of time T you know I get some + + + align:start position:0% +period of time T you know I get some +histogram and this is telling us about + + align:start position:0% +histogram and this is telling us about + + + align:start position:0% +histogram and this is telling us about +the width of that histogram relative to + + align:start position:0% +the width of that histogram relative to + + + align:start position:0% +the width of that histogram relative to +the + + align:start position:0% + + + + align:start position:0% + +mean all right now let's imagine that + + align:start position:0% +mean all right now let's imagine that + + + align:start position:0% +mean all right now let's imagine that +you're the cell and you calculated the + + align:start position:0% +you're the cell and you calculated the + + + align:start position:0% +you're the cell and you calculated the +concentration in a really wonderful way + + align:start position:0% +concentration in a really wonderful way + + + align:start position:0% +concentration in a really wonderful way +right now uh the question is do you know + + align:start position:0% +right now uh the question is do you know + + + align:start position:0% +right now uh the question is do you know +where you should go to get more + + align:start position:0% +where you should go to get more + + + align:start position:0% +where you should go to get more +food no right so you know the + + align:start position:0% +food no right so you know the + + + align:start position:0% +food no right so you know the +concentration at your location that + + align:start position:0% +concentration at your location that + + + align:start position:0% +concentration at your location that +doesn't tell you what you need to know + + align:start position:0% +doesn't tell you what you need to know + + + align:start position:0% +doesn't tell you what you need to know +uh for that purpose is a gradient okay + + align:start position:0% +uh for that purpose is a gradient okay + + + align:start position:0% +uh for that purpose is a gradient okay +and I'm trying to remember if in this + + align:start position:0% +and I'm trying to remember if in this + + + align:start position:0% +and I'm trying to remember if in this +paper they maybe are not very explicit + + align:start position:0% +paper they maybe are not very explicit + + + align:start position:0% +paper they maybe are not very explicit +uh why is it that a bacteria a bacterial + + align:start position:0% +uh why is it that a bacteria a bacterial + + + align:start position:0% +uh why is it that a bacteria a bacterial +cell might do this biased random walk + + align:start position:0% +cell might do this biased random walk + + + align:start position:0% +cell might do this biased random walk +that's described in the paper instead of + + align:start position:0% +that's described in the paper instead of + + + align:start position:0% +that's described in the paper instead of +just you know measure the gradient right + + align:start position:0% +just you know measure the gradient right + + + align:start position:0% +just you know measure the gradient right +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +cell yeah right so bacteria just small I + + align:start position:0% +cell yeah right so bacteria just small I + + + align:start position:0% +cell yeah right so bacteria just small I +think is is is the argument that we + + align:start position:0% +think is is is the argument that we + + + align:start position:0% +think is is is the argument that we +often give and that's just saying that + + align:start position:0% +often give and that's just saying that + + + align:start position:0% +often give and that's just saying that +uh if you want to measure a gradient + + align:start position:0% +uh if you want to measure a gradient + + + align:start position:0% +uh if you want to measure a gradient +then what you would do is if you're a + + align:start position:0% +then what you would do is if you're a + + + align:start position:0% +then what you would do is if you're a +sphere like this you might say okay I'm + + align:start position:0% +sphere like this you might say okay I'm + + + align:start position:0% +sphere like this you might say okay I'm +going to measure I'm going to count the + + align:start position:0% +going to measure I'm going to count the + + + align:start position:0% +going to measure I'm going to count the +number of the molecules that hit me over + + align:start position:0% +number of the molecules that hit me over + + + align:start position:0% +number of the molecules that hit me over +here and I'm going to compare that to + + align:start position:0% +here and I'm going to compare that to + + + align:start position:0% +here and I'm going to compare that to +the number of molecules hit me over + + align:start position:0% +the number of molecules hit me over + + + align:start position:0% +the number of molecules hit me over +there right and all right so you get two + + align:start position:0% +there right and all right so you get two + + + align:start position:0% +there right and all right so you get two +measurements of concentration okay but + + align:start position:0% +measurements of concentration okay but + + + align:start position:0% +measurements of concentration okay but +then in order to get a gradient what's + + align:start position:0% +then in order to get a gradient what's + + + align:start position:0% +then in order to get a gradient what's +is uh you have to look at look at this + + align:start position:0% +is uh you have to look at look at this + + + align:start position:0% +is uh you have to look at look at this +distance and of course uh if you have a + + align:start position:0% +distance and of course uh if you have a + + + align:start position:0% +distance and of course uh if you have a +long a bigger cell than a given gradient + + align:start position:0% +long a bigger cell than a given gradient + + + align:start position:0% +long a bigger cell than a given gradient +shows up is a larger difference in + + align:start position:0% +shows up is a larger difference in + + + align:start position:0% +shows up is a larger difference in +concentration or lar larger difference + + align:start position:0% +concentration or lar larger difference + + + align:start position:0% +concentration or lar larger difference +in the number of molecules that are + + align:start position:0% +in the number of molecules that are + + + align:start position:0% +in the number of molecules that are +going to hit the cell right and that in + + align:start position:0% +going to hit the cell right and that in + + + align:start position:0% +going to hit the cell right and that in +does that + + align:start position:0% +does that + + + align:start position:0% +does that +scale linearly or quadratically with + + align:start position:0% + + + + align:start position:0% + +a linearly right difference in + + align:start position:0% +a linearly right difference in + + + align:start position:0% +a linearly right difference in +concentration is going to be equal to + + align:start position:0% +concentration is going to be equal to + + + align:start position:0% +concentration is going to be equal to +kind of the size of the cell maybe 2 A + + align:start position:0% +kind of the size of the cell maybe 2 A + + + align:start position:0% +kind of the size of the cell maybe 2 A +Time D oops DC DX sorry so there's some + + align:start position:0% +Time D oops DC DX sorry so there's some + + + align:start position:0% +Time D oops DC DX sorry so there's some +gradient that's out there right and then + + align:start position:0% +gradient that's out there right and then + + + align:start position:0% +gradient that's out there right and then +we you know so we get a linear kind of + + align:start position:0% +we you know so we get a linear kind of + + + align:start position:0% +we you know so we get a linear kind of +amplification of our signal based on the + + align:start position:0% +amplification of our signal based on the + + + align:start position:0% +amplification of our signal based on the +size of the cell okay so if you look at + + align:start position:0% +size of the cell okay so if you look at + + + align:start position:0% +size of the cell okay so if you look at +many eukariotic cells for example dict + + align:start position:0% +many eukariotic cells for example dict + + + align:start position:0% +many eukariotic cells for example dict +and other others they indeed often do + + align:start position:0% +and other others they indeed often do + + + align:start position:0% +and other others they indeed often do +this direct gradient measurement and + + align:start position:0% +this direct gradient measurement and + + + align:start position:0% +this direct gradient measurement and +then from that they decide where to + + align:start position:0% +then from that they decide where to + + + align:start position:0% +then from that they decide where to +go okay uh bacteria on the other hand + + align:start position:0% +go okay uh bacteria on the other hand + + + align:start position:0% +go okay uh bacteria on the other hand +they do this this other thing that is + + align:start position:0% +they do this this other thing that is + + + align:start position:0% +they do this this other thing that is +described in uh in the paper where where + + align:start position:0% +described in uh in the paper where where + + + align:start position:0% +described in uh in the paper where where +they have a biased random Walk we're + + align:start position:0% +they have a biased random Walk we're + + + align:start position:0% +they have a biased random Walk we're +going to be talking much more about this + + align:start position:0% +going to be talking much more about this + + + align:start position:0% +going to be talking much more about this +and the G network that allows Sals to do + + align:start position:0% +and the G network that allows Sals to do + + + align:start position:0% +and the G network that allows Sals to do +it on on Tuesday but the basic idea is + + align:start position:0% +it on on Tuesday but the basic idea is + + + align:start position:0% +it on on Tuesday but the basic idea is +that the bacteria they're swimming in + + align:start position:0% +that the bacteria they're swimming in + + + align:start position:0% +that the bacteria they're swimming in +some random Direction okay and then they + + align:start position:0% +some random Direction okay and then they + + + align:start position:0% +some random Direction okay and then they +ask instead of whether directly + + align:start position:0% +ask instead of whether directly + + + align:start position:0% +ask instead of whether directly +measuring the concentration as a + + align:start position:0% +measuring the concentration as a + + + align:start position:0% +measuring the concentration as a +dcx which which you might do as a UK + + align:start position:0% +dcx which which you might do as a UK + + + align:start position:0% +dcx which which you might do as a UK +carotic cell instead where they they + + align:start position:0% +carotic cell instead where they they + + + align:start position:0% +carotic cell instead where they they +measure as a change in concentration + + align:start position:0% +measure as a change in concentration + + + align:start position:0% +measure as a change in concentration +with respect to time right because they + + align:start position:0% +with respect to time right because they + + + align:start position:0% +with respect to time right because they +are moving so they ask are things + + align:start position:0% +are moving so they ask are things + + + align:start position:0% +are moving so they ask are things +getting better they getting worse + + align:start position:0% +getting better they getting worse + + + align:start position:0% +getting better they getting worse +right if things are getting better you + + align:start position:0% +right if things are getting better you + + + align:start position:0% +right if things are getting better you +keep on going if things are getting + + align:start position:0% +keep on going if things are getting + + + align:start position:0% +keep on going if things are getting +worse then you randomize your direction + + align:start position:0% +worse then you randomize your direction + + + align:start position:0% +worse then you randomize your direction +and you try again okay and this + + align:start position:0% +and you try again okay and this + + + align:start position:0% +and you try again okay and this +implements a biased random walk okay + + align:start position:0% +implements a biased random walk okay + + + align:start position:0% +implements a biased random walk okay +we'll talk about the the kind of + + align:start position:0% +we'll talk about the the kind of + + + align:start position:0% +we'll talk about the the kind of +decision-making circuit in the cell that + + align:start position:0% +decision-making circuit in the cell that + + + align:start position:0% +decision-making circuit in the cell that +allows it to do that uh on Tuesday but + + align:start position:0% +allows it to do that uh on Tuesday but + + + align:start position:0% +allows it to do that uh on Tuesday but +um but that's uh that's the basic the + + align:start position:0% +um but that's uh that's the basic the + + + align:start position:0% +um but that's uh that's the basic the +basic notion there okay and uh can + + align:start position:0% +basic notion there okay and uh can + + + align:start position:0% +basic notion there okay and uh can +someone remind us how long is a typical + + align:start position:0% +someone remind us how long is a typical + + + align:start position:0% +someone remind us how long is a typical +run for E + + align:start position:0% + + + + align:start position:0% + +coli yeah it's yeah maybe 30 microns + + align:start position:0% +coli yeah it's yeah maybe 30 microns + + + align:start position:0% +coli yeah it's yeah maybe 30 microns +right so there's this idea + + align:start position:0% +right so there's this idea + + + align:start position:0% +right so there's this idea +that + + align:start position:0% + + + + align:start position:0% + +um okay all right so a cell might go + + align:start position:0% +um okay all right so a cell might go + + + align:start position:0% +um okay all right so a cell might go +like this for 30 microns and it takes + + align:start position:0% +like this for 30 microns and it takes + + + align:start position:0% +like this for 30 microns and it takes +about a second for it to do that but + + align:start position:0% +about a second for it to do that but + + + align:start position:0% +about a second for it to do that but +then it it that's a + + align:start position:0% +then it it that's a + + + align:start position:0% +then it it that's a +run but then it'll engage in some random + + align:start position:0% +run but then it'll engage in some random + + + align:start position:0% +run but then it'll engage in some random +tumble that leads it to go some other + + align:start position:0% +tumble that leads it to go some other + + + align:start position:0% +tumble that leads it to go some other +direction uh and then another tumble and + + align:start position:0% +direction uh and then another tumble and + + + align:start position:0% +direction uh and then another tumble and +then it kind of goes different direction + + align:start position:0% +then it kind of goes different direction + + + align:start position:0% +then it kind of goes different direction +and so + + align:start position:0% +and so + + + align:start position:0% +and so +forth okay so these are runs and + + align:start position:0% + + + + align:start position:0% + +tumbles now the nice thing here is that + + align:start position:0% +tumbles now the nice thing here is that + + + align:start position:0% +tumbles now the nice thing here is that +you can see that to measure this + + align:start position:0% +you can see that to measure this + + + align:start position:0% +you can see that to measure this +concentration over here the this the + + align:start position:0% +concentration over here the this the + + + align:start position:0% +concentration over here the this the +change of concentration across the cell + + align:start position:0% +change of concentration across the cell + + + align:start position:0% +change of concentration across the cell +when is a which might only be one or two + + align:start position:0% +when is a which might only be one or two + + + align:start position:0% +when is a which might only be one or two +microns whereas here now the eoli can + + align:start position:0% +microns whereas here now the eoli can + + + align:start position:0% +microns whereas here now the eoli can +measure a change in a concentration over + + align:start position:0% +measure a change in a concentration over + + + align:start position:0% +measure a change in a concentration over +tens of microns right so it's in some + + align:start position:0% +tens of microns right so it's in some + + + align:start position:0% +tens of microns right so it's in some +ways like a longer antenna right that + + align:start position:0% +ways like a longer antenna right that + + + align:start position:0% +ways like a longer antenna right that +allows it to pick up the signal better + + align:start position:0% + + + + align:start position:0% + +okay there's a comment about what um + + align:start position:0% +okay there's a comment about what um + + + align:start position:0% +okay there's a comment about what um +what happens here in the sense that if + + align:start position:0% +what happens here in the sense that if + + + align:start position:0% +what happens here in the sense that if +you imagine you have a + + align:start position:0% +you imagine you have a + + + align:start position:0% +you imagine you have a +cell right it's a few microns in + + align:start position:0% +cell right it's a few microns in + + + align:start position:0% +cell right it's a few microns in +size fella is pushing it right it's + + align:start position:0% +size fella is pushing it right it's + + + align:start position:0% +size fella is pushing it right it's +going at 30 microns per + + align:start position:0% +going at 30 microns per + + + align:start position:0% +going at 30 microns per +second and the question is um if at some + + align:start position:0% +second and the question is um if at some + + + align:start position:0% +second and the question is um if at some +time it stops + + align:start position:0% +time it stops + + + align:start position:0% +time it stops +spinning the uh its + + align:start position:0% +spinning the uh its + + + align:start position:0% +spinning the uh its +flagellum how far will it + + align:start position:0% +flagellum how far will it + + + align:start position:0% +flagellum how far will it +Coast + + align:start position:0% + + + + align:start position:0% + +okay all right we'll sell coast and this + + align:start position:0% +okay all right we'll sell coast and this + + + align:start position:0% +okay all right we'll sell coast and this +is after stopping swimming + + align:start position:0% + + + + align:start position:0% + +right um all right + + align:start position:0% + + + + align:start position:0% + +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +is so I know and we'll do approximate so + + align:start position:0% +is so I know and we'll do approximate so + + + align:start position:0% +is so I know and we'll do approximate so +10 Micron + + align:start position:0% + + + + align:start position:0% + +maybe all + + align:start position:0% + + + + align:start position:0% + +right all right how yeah how many + + align:start position:0% +right all right how yeah how many + + + align:start position:0% +right all right how yeah how many +microns does a cell Coast after it stops + + align:start position:0% +microns does a cell Coast after it stops + + + align:start position:0% +microns does a cell Coast after it stops +swimming + + align:start position:0% +swimming + + + align:start position:0% +swimming +cell this is a bacterial cell yeah this + + align:start position:0% +cell this is a bacterial cell yeah this + + + align:start position:0% +cell this is a bacterial cell yeah this +is eoli and you know this is you we'll + + align:start position:0% +is eoli and you know this is you we'll + + + align:start position:0% +is eoli and you know this is you we'll +say three microns in + + align:start position:0% + + + + align:start position:0% + +size okay ready three two + + align:start position:0% +size okay ready three two + + + align:start position:0% +size okay ready three two +one all right okay so everybody says + + align:start position:0% +one all right okay so everybody says + + + align:start position:0% +one all right okay so everybody says +short and is this the is this actually + + align:start position:0% +short and is this the is this actually + + + align:start position:0% +short and is this the is this actually +the right answer no it's not okay okay + + align:start position:0% +the right answer no it's not okay okay + + + align:start position:0% +the right answer no it's not okay okay +so this is the closest it's true but + + align:start position:0% +so this is the closest it's true but + + + align:start position:0% +so this is the closest it's true but +it's like this you know none of these + + align:start position:0% +it's like this you know none of these + + + align:start position:0% +it's like this you know none of these +are true so how how far does it + + align:start position:0% + + + + align:start position:0% + +Coast right yeah so yeah I mean it's + + align:start position:0% +Coast right yeah so yeah I mean it's + + + align:start position:0% +Coast right yeah so yeah I mean it's +something ridiculous I mean you know + + align:start position:0% +something ridiculous I mean you know + + + align:start position:0% +something ridiculous I mean you know +it's um you know and this is really + + align:start position:0% +it's um you know and this is really + + + align:start position:0% +it's um you know and this is really +really weird right that the this guy you + + align:start position:0% +really weird right that the this guy you + + + align:start position:0% +really weird right that the this guy you +know it's 30 microns a second so this is + + align:start position:0% +know it's 30 microns a second so this is + + + align:start position:0% +know it's 30 microns a second so this is +M you know 10 times its body length + + align:start position:0% +M you know 10 times its body length + + + align:start position:0% +M you know 10 times its body length +every second it's really shooting along + + align:start position:0% +every second it's really shooting along + + + align:start position:0% +every second it's really shooting along +right but the moment that it stops + + align:start position:0% +right but the moment that it stops + + + align:start position:0% +right but the moment that it stops +swimming it stops moving okay so it's + + align:start position:0% +swimming it stops moving okay so it's + + + align:start position:0% +swimming it stops moving okay so it's +none of these things it was was it one + + align:start position:0% +none of these things it was was it one + + + align:start position:0% +none of these things it was was it one +or less than an angstrom I + + align:start position:0% +or less than an angstrom I + + + align:start position:0% +or less than an angstrom I +was yeah okay 0.1 + + align:start position:0% +was yeah okay 0.1 + + + align:start position:0% +was yeah okay 0.1 +angstroms which Micron this is 10us 5 + + align:start position:0% +angstroms which Micron this is 10us 5 + + + align:start position:0% +angstroms which Micron this is 10us 5 +microns is + + align:start position:0% + + + + align:start position:0% + +that okay right so it's orders of + + align:start position:0% +that okay right so it's orders of + + + align:start position:0% +that okay right so it's orders of +magnitude smaller than you would ever + + align:start position:0% +magnitude smaller than you would ever + + + align:start position:0% +magnitude smaller than you would ever +imagine right and that's because our + + align:start position:0% +imagine right and that's because our + + + align:start position:0% +imagine right and that's because our +intuition comes from um you know kind of + + align:start position:0% +intuition comes from um you know kind of + + + align:start position:0% +intuition comes from um you know kind of +our length scales where you know if if I + + align:start position:0% +our length scales where you know if if I + + + align:start position:0% +our length scales where you know if if I +were swimming this fast you know I would + + align:start position:0% +were swimming this fast you know I would + + + align:start position:0% +were swimming this fast you know I would +keep on drifting right if I you know + + align:start position:0% +keep on drifting right if I you know + + + align:start position:0% +keep on drifting right if I you know +after I stop swimming but um that's not + + align:start position:0% +after I stop swimming but um that's not + + + align:start position:0% +after I stop swimming but um that's not +the world that bacteria live in okay and + + align:start position:0% +the world that bacteria live in okay and + + + align:start position:0% +the world that bacteria live in okay and +that's because of the small the low + + align:start position:0% +that's because of the small the low + + + align:start position:0% +that's because of the small the low +Reynolds number + + align:start position:0% + + + + align:start position:0% + +okay all right the reyolds number is + + align:start position:0% +okay all right the reyolds number is + + + align:start position:0% +okay all right the reyolds number is +much much less than one right so this + + align:start position:0% +much much less than one right so this + + + align:start position:0% +much much less than one right so this +thing is the dimensionless number that + + align:start position:0% +thing is the dimensionless number that + + + align:start position:0% +thing is the dimensionless number that +quantifies the relative importance of + + align:start position:0% +quantifies the relative importance of + + + align:start position:0% +quantifies the relative importance of +inertial forces to viscous + + align:start position:0% +inertial forces to viscous + + + align:start position:0% +inertial forces to viscous +forces okay now there there was some + + align:start position:0% +forces okay now there there was some + + + align:start position:0% +forces okay now there there was some +discussion of the Reynolds number in uh + + align:start position:0% +discussion of the Reynolds number in uh + + + align:start position:0% +discussion of the Reynolds number in uh +in your reading + + align:start position:0% +in your reading + + + align:start position:0% +in your reading +I maybe won't get into too much detail + + align:start position:0% +I maybe won't get into too much detail + + + align:start position:0% +I maybe won't get into too much detail +about it but what I what I'll say is + + align:start position:0% +about it but what I what I'll say is + + + align:start position:0% +about it but what I what I'll say is +that you know if anybody wants to talk + + align:start position:0% +that you know if anybody wants to talk + + + align:start position:0% +that you know if anybody wants to talk +about a way of thinking about the + + align:start position:0% +about a way of thinking about the + + + align:start position:0% +about a way of thinking about the +rynolds number maybe you can ask me + + align:start position:0% +rynolds number maybe you can ask me + + + align:start position:0% +rynolds number maybe you can ask me +after class and I can explain to you why + + align:start position:0% +after class and I can explain to you why + + + align:start position:0% +after class and I can explain to you why +this weird uh why this weird expression + + align:start position:0% +this weird uh why this weird expression + + + align:start position:0% +this weird uh why this weird expression +can be thought of as the ratio of the uh + + align:start position:0% +can be thought of as the ratio of the uh + + + align:start position:0% +can be thought of as the ratio of the uh +of the inertial liscus forces um but I I + + align:start position:0% +of the inertial liscus forces um but I I + + + align:start position:0% +of the inertial liscus forces um but I I +want to + + align:start position:0% + + + + align:start position:0% + +um I I want to think a little bit more + + align:start position:0% +um I I want to think a little bit more + + + align:start position:0% +um I I want to think a little bit more +about the strategy that these uh these + + align:start position:0% +about the strategy that these uh these + + + align:start position:0% +about the strategy that these uh these +cells are following which + + align:start position:0% +cells are following which + + + align:start position:0% +cells are following which +um is you know why is it that a run is + + align:start position:0% +um is you know why is it that a run is + + + align:start position:0% +um is you know why is it that a run is +of the length scale that it is in + + align:start position:0% +of the length scale that it is in + + + align:start position:0% +of the length scale that it is in +particular why not um why not go further + + align:start position:0% +particular why not um why not go further + + + align:start position:0% +particular why not um why not go further +right we already said that the its + + align:start position:0% +right we already said that the its + + + align:start position:0% +right we already said that the its +ability to measure a + + align:start position:0% +ability to measure a + + + align:start position:0% +ability to measure a +concentration is somehow it's going to + + align:start position:0% +concentration is somehow it's going to + + + align:start position:0% +concentration is somehow it's going to +if you did a direct measurement it would + + align:start position:0% +if you did a direct measurement it would + + + align:start position:0% +if you did a direct measurement it would +scale with the size of the cell in this + + align:start position:0% +scale with the size of the cell in this + + + align:start position:0% +scale with the size of the cell in this +case it sort of scales like the length + + align:start position:0% +case it sort of scales like the length + + + align:start position:0% +case it sort of scales like the length +of the run right so why not run for 10 + + align:start position:0% +of the run right so why not run for 10 + + + align:start position:0% +of the run right so why not run for 10 +times longer 100 times longer you know + + align:start position:0% +times longer 100 times longer you know + + + align:start position:0% +times longer 100 times longer you know +so you can get a really good measurement + + align:start position:0% +so you can get a really good measurement + + + align:start position:0% +so you can get a really good measurement +of a + + align:start position:0% +of a + + + align:start position:0% +of a +gradient if you're going you go times + + align:start position:0% +gradient if you're going you go times + + + align:start position:0% +gradient if you're going you go times +right okay so it could be yeah it's just + + align:start position:0% +right okay so it could be yeah it's just + + + align:start position:0% +right okay so it could be yeah it's just +if you're going the wrong way although + + align:start position:0% +if you're going the wrong way although + + + align:start position:0% +if you're going the wrong way although +then we could maybe even be just more + + align:start position:0% +then we could maybe even be just more + + + align:start position:0% +then we could maybe even be just more +sensitive in that in that we could say + + align:start position:0% +sensitive in that in that we could say + + + align:start position:0% +sensitive in that in that we could say +because what's striking is that even + + align:start position:0% +because what's striking is that even + + + align:start position:0% +because what's striking is that even +when it's going in the right direction + + align:start position:0% +when it's going in the right direction + + + align:start position:0% +when it's going in the right direction +it still tumbles of you know the the + + align:start position:0% +it still tumbles of you know the the + + + align:start position:0% +it still tumbles of you know the the +difference between the Run lengths in + + align:start position:0% +difference between the Run lengths in + + + align:start position:0% +difference between the Run lengths in +the correct and incorrect direction are + + align:start position:0% +the correct and incorrect direction are + + + align:start position:0% +the correct and incorrect direction are +are kind of modest I guess right so + + align:start position:0% +are kind of modest I guess right so + + + align:start position:0% +are kind of modest I guess right so +maybe we we could come up with a + + align:start position:0% +maybe we we could come up with a + + + align:start position:0% +maybe we we could come up with a +different strategy where we say all + + align:start position:0% +different strategy where we say all + + + align:start position:0% +different strategy where we say all +right well if I feel like things are + + align:start position:0% +right well if I feel like things are + + + align:start position:0% +right well if I feel like things are +getting worse I'll I'll tumble quickly + + align:start position:0% +getting worse I'll I'll tumble quickly + + + align:start position:0% +getting worse I'll I'll tumble quickly +right but if I feel like things are + + align:start position:0% +right but if I feel like things are + + + align:start position:0% +right but if I feel like things are +going great maybe then I'll just then + + align:start position:0% +going great maybe then I'll just then + + + align:start position:0% +going great maybe then I'll just then +I'll I'll I'll I'll go in the same + + align:start position:0% +I'll I'll I'll I'll go in the same + + + align:start position:0% +I'll I'll I'll I'll go in the same +direction and I'll measure that gradient + + align:start position:0% +direction and I'll measure that gradient + + + align:start position:0% +direction and I'll measure that gradient +really finely so I can get precisely the + + align:start position:0% +really finely so I can get precisely the + + + align:start position:0% +really finely so I can get precisely the +right direction so I guess the question + + align:start position:0% +right direction so I guess the question + + + align:start position:0% +right direction so I guess the question +is is there any is there anything that's + + align:start position:0% +is is there any is there anything that's + + + align:start position:0% +is is there any is there anything that's +going to limit how useful it is to go uh + + align:start position:0% +going to limit how useful it is to go uh + + + align:start position:0% +going to limit how useful it is to go uh +swimming even in uh even in a good + + align:start position:0% +swimming even in uh even in a good + + + align:start position:0% +swimming even in uh even in a good +direction in + + align:start position:0% +direction in + + + align:start position:0% +direction in +principle yeah it's so small + + align:start position:0% + + + + align:start position:0% + +yeah and this is a weird thing right + + align:start position:0% +yeah and this is a weird thing right + + + align:start position:0% +yeah and this is a weird thing right +that um not only does diffusion act uh + + align:start position:0% +that um not only does diffusion act uh + + + align:start position:0% +that um not only does diffusion act uh +kind of uh in say linear Sense on the + + align:start position:0% +kind of uh in say linear Sense on the + + + align:start position:0% +kind of uh in say linear Sense on the +center of mass position of an object but + + align:start position:0% +center of mass position of an object but + + + align:start position:0% +center of mass position of an object but +it also acts + + align:start position:0% +it also acts + + + align:start position:0% +it also acts +rotationally which means that the cell + + align:start position:0% +rotationally which means that the cell + + + align:start position:0% +rotationally which means that the cell +and other objects in liquid uh lose uh + + align:start position:0% +and other objects in liquid uh lose uh + + + align:start position:0% +and other objects in liquid uh lose uh +their orientational um order and what + + align:start position:0% +their orientational um order and what + + + align:start position:0% +their orientational um order and what +that means is that if this cell starts + + align:start position:0% +that means is that if this cell starts + + + align:start position:0% +that means is that if this cell starts +swimming in One Direction it's actually + + align:start position:0% +swimming in One Direction it's actually + + + align:start position:0% +swimming in One Direction it's actually +the case that after a few seconds it + + align:start position:0% +the case that after a few seconds it + + + align:start position:0% +the case that after a few seconds it +forgets where it was going right so it + + align:start position:0% +forgets where it was going right so it + + + align:start position:0% +forgets where it was going right so it +actually does you can't actually collect + + align:start position:0% +actually does you can't actually collect + + + align:start position:0% +actually does you can't actually collect +information about uh the gradient in + + align:start position:0% +information about uh the gradient in + + + align:start position:0% +information about uh the gradient in +that direction because you're actually + + align:start position:0% +that direction because you're actually + + + align:start position:0% +that direction because you're actually +going in a different direction from what + + align:start position:0% +going in a different direction from what + + + align:start position:0% +going in a different direction from what +you were a few seconds ago right this is + + align:start position:0% +you were a few seconds ago right this is + + + align:start position:0% +you were a few seconds ago right this is +actually a pretty fine and this is + + align:start position:0% +actually a pretty fine and this is + + + align:start position:0% +actually a pretty fine and this is +actually a pretty tough limitation that + + align:start position:0% +actually a pretty tough limitation that + + + align:start position:0% +actually a pretty tough limitation that +that these cells are facing right on the + + align:start position:0% +that these cells are facing right on the + + + align:start position:0% +that these cells are facing right on the +one hand they're small so it's really + + align:start position:0% +one hand they're small so it's really + + + align:start position:0% +one hand they're small so it's really +hard to measure gradients on the other + + align:start position:0% +hard to measure gradients on the other + + + align:start position:0% +hard to measure gradients on the other +hand every few seconds they get turned + + align:start position:0% +hand every few seconds they get turned + + + align:start position:0% +hand every few seconds they get turned +around right and if you imagine trying + + align:start position:0% +around right and if you imagine trying + + + align:start position:0% +around right and if you imagine trying +to navigate in that kind of situation be + + align:start position:0% +to navigate in that kind of situation be + + + align:start position:0% +to navigate in that kind of situation be +pretty hard all right now I want to um + + align:start position:0% +pretty hard all right now I want to um + + + align:start position:0% +pretty hard all right now I want to um +make sure that we understand how to how + + align:start position:0% +make sure that we understand how to how + + + align:start position:0% +make sure that we understand how to how +to figure out what that um the the time + + align:start position:0% +to figure out what that um the the time + + + align:start position:0% +to figure out what that um the the time +scale is that that uh this orientational + + align:start position:0% +scale is that that uh this orientational + + + align:start position:0% +scale is that that uh this orientational +order is lost and um and again we're + + align:start position:0% +order is lost and um and again we're + + + align:start position:0% +order is lost and um and again we're +going to use dimensional analysis + + align:start position:0% +going to use dimensional analysis + + + align:start position:0% +going to use dimensional analysis +because I love it and um and I can tell + + align:start position:0% +because I love it and um and I can tell + + + align:start position:0% +because I love it and um and I can tell +that you guys are big fans as well all + + align:start position:0% +that you guys are big fans as well all + + + align:start position:0% +that you guys are big fans as well all +right + + align:start position:0% +right + + + align:start position:0% +right +um okay so the I'll I will tell you + + align:start position:0% +um okay so the I'll I will tell you + + + align:start position:0% +um okay so the I'll I will tell you +something that + + align:start position:0% + + + + align:start position:0% + +hopefully how much do I want to tell you + + align:start position:0% +hopefully how much do I want to tell you + + + align:start position:0% +hopefully how much do I want to tell you +all right um + + align:start position:0% + + + + align:start position:0% + +all right what I'll tell you is this + + align:start position:0% +all right what I'll tell you is this + + + align:start position:0% +all right what I'll tell you is this +that uh the the diffusion coefficient + + align:start position:0% +that uh the the diffusion coefficient + + + align:start position:0% +that uh the the diffusion coefficient +for + + align:start position:0% +for + + + align:start position:0% +for +angular uh fluctuations okay um is + + align:start position:0% +angular uh fluctuations okay um is + + + align:start position:0% +angular uh fluctuations okay um is +defined just the way it is for uh for + + align:start position:0% +defined just the way it is for uh for + + + align:start position:0% +defined just the way it is for uh for +diffusion coefficient for the say the + + align:start position:0% +diffusion coefficient for the say the + + + align:start position:0% +diffusion coefficient for the say the +center of + + align:start position:0% +center of + + + align:start position:0% +center of +mass okay all right given that the + + align:start position:0% +mass okay all right given that the + + + align:start position:0% +mass okay all right given that the +question is if I have a sphere again + + align:start position:0% +question is if I have a sphere again + + + align:start position:0% +question is if I have a sphere again +size + + align:start position:0% +size + + + align:start position:0% +size +a now I want to know + + align:start position:0% +a now I want to know + + + align:start position:0% +a now I want to know +um you know how how does uh the typical + + align:start position:0% +um you know how how does uh the typical + + + align:start position:0% +um you know how how does uh the typical +the this correlation time how does this + + align:start position:0% +the this correlation time how does this + + + align:start position:0% +the this correlation time how does this +the time to + + align:start position:0% + + + + align:start position:0% + +randomize randomize + + align:start position:0% +randomize randomize + + + align:start position:0% +randomize randomize +orientation how does it + + align:start position:0% +orientation how does it + + + align:start position:0% +orientation how does it +scale with the radius + + align:start position:0% + + + + align:start position:0% + +okay all right so it could be that this + + align:start position:0% +okay all right so it could be that this + + + align:start position:0% +okay all right so it could be that this +time scale tow could goes a to + + align:start position:0% + + + + align:start position:0% + +zero all right and you should be + + align:start position:0% +zero all right and you should be + + + align:start position:0% +zero all right and you should be +starting to think + + align:start position:0% + + + + align:start position:0% + +SC + + align:start position:0% + + + + align:start position:0% + +all right do you need more time + + align:start position:0% + + + + align:start position:0% + +I why don't we go and see where uh see + + align:start position:0% +I why don't we go and see where uh see + + + align:start position:0% +I why don't we go and see where uh see +where the group + + align:start position:0% +where the group + + + align:start position:0% +where the group +is all right if you're um and it's okay + + align:start position:0% +is all right if you're um and it's okay + + + align:start position:0% +is all right if you're um and it's okay +if you if you've not figured it out make + + align:start position:0% +if you if you've not figured it out make + + + align:start position:0% +if you if you've not figured it out make +your best guess you know ready three two + + align:start position:0% +your best guess you know ready three two + + + align:start position:0% +your best guess you know ready three two +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one okay we + + align:start position:0% +one okay we + + + align:start position:0% +one okay we +got + + align:start position:0% +got + + + align:start position:0% +got +yeah um okay so I'd say it might be a + + align:start position:0% +yeah um okay so I'd say it might be a + + + align:start position:0% +yeah um okay so I'd say it might be a +slight majority B but then it's actually + + align:start position:0% +slight majority B but then it's actually + + + align:start position:0% +slight majority B but then it's actually +there are fair numbers spread around + + align:start position:0% +there are fair numbers spread around + + + align:start position:0% +there are fair numbers spread around +okay um yeah no there's there's a + + align:start position:0% +okay um yeah no there's there's a + + + align:start position:0% +okay um yeah no there's there's a +there's a b c's D's and e um + + align:start position:0% + + + + align:start position:0% + +all right maybe I I I'll let you I'll + + align:start position:0% +all right maybe I I I'll let you I'll + + + align:start position:0% +all right maybe I I I'll let you I'll +give you a minute to talk to your + + align:start position:0% +give you a minute to talk to your + + + align:start position:0% +give you a minute to talk to your +neighbor and I'm just going to um give + + align:start position:0% +neighbor and I'm just going to um give + + + align:start position:0% +neighbor and I'm just going to um give +you an extra hint which is uh you know + + align:start position:0% +you an extra hint which is uh you know + + + align:start position:0% +you an extra hint which is uh you know +it's good to look at the units of the + + align:start position:0% +it's good to look at the units of the + + + align:start position:0% +it's good to look at the units of the +diffusion + + align:start position:0% +diffusion + + + align:start position:0% +diffusion +coefficient which is why I wrote this + + align:start position:0% +coefficient which is why I wrote this + + + align:start position:0% +coefficient which is why I wrote this +[Music] + + align:start position:0% + + + + align:start position:0% + +equation no yes + + align:start position:0% +equation no yes + + + align:start position:0% +equation no yes +no you did that that's what we did okay + + align:start position:0% +no you did that that's what we did okay + + + align:start position:0% +no you did that that's what we did okay +um okay well I'll give you another + + align:start position:0% +um okay well I'll give you another + + + align:start position:0% +um okay well I'll give you another +minute CU I think that it's it's it's + + align:start position:0% +minute CU I think that it's it's it's + + + align:start position:0% +minute CU I think that it's it's it's +important to to like worked through this + + align:start position:0% +important to to like worked through this + + + align:start position:0% +important to to like worked through this +at least you know some way mentally + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Def + + align:start position:0% + + + + align:start position:0% + +okay all right why don't why don't we go + + align:start position:0% +okay all right why don't why don't we go + + + align:start position:0% +okay all right why don't why don't we go +ahead and reconvene even I know that you + + align:start position:0% +ahead and reconvene even I know that you + + + align:start position:0% +ahead and reconvene even I know that you +may not have had time to fully uh fully + + align:start position:0% +may not have had time to fully uh fully + + + align:start position:0% +may not have had time to fully uh fully +Converge on this um right but it turns + + align:start position:0% +Converge on this um right but it turns + + + align:start position:0% +Converge on this um right but it turns +out that this actually goes as a + + align:start position:0% +out that this actually goes as a + + + align:start position:0% +out that this actually goes as a +cubed no one would have guessed + + align:start position:0% +cubed no one would have guessed + + + align:start position:0% +cubed no one would have guessed +that so + + align:start position:0% +that so + + + align:start position:0% +that so +upset sphere it's for sphere yeah yeah + + align:start position:0% +upset sphere it's for sphere yeah yeah + + + align:start position:0% +upset sphere it's for sphere yeah yeah +it's a sphere so it's not a + + align:start position:0% + + + + align:start position:0% + +b um I I don't I don't know what to say + + align:start position:0% +b um I I don't I don't know what to say + + + align:start position:0% +b um I I don't I don't know what to say +where's the mass where's the mass the + + align:start position:0% +where's the mass where's the mass the + + + align:start position:0% +where's the mass where's the mass the +mass on the surface or is the mass in + + align:start position:0% +mass on the surface or is the mass in + + + align:start position:0% +mass on the surface or is the mass in +the + + align:start position:0% +the + + + align:start position:0% +the +middle um no no no um no no right so + + align:start position:0% +middle um no no no um no no right so + + + align:start position:0% +middle um no no no um no no right so +because we're we're in the we're right + + align:start position:0% +because we're we're in the we're right + + + align:start position:0% +because we're we're in the we're right +we're right we're in the low Reynolds + + align:start position:0% +we're right we're in the low Reynolds + + + align:start position:0% +we're right we're in the low Reynolds +number regime right so that what that + + align:start position:0% +number regime right so that what that + + + align:start position:0% +number regime right so that what that +means is that um is that you know this + + align:start position:0% +means is that um is that you know this + + + align:start position:0% +means is that um is that you know this +this is all dominated by the + + align:start position:0% +this is all dominated by the + + + align:start position:0% +this is all dominated by the +interactions between the object and the + + align:start position:0% +interactions between the object and the + + + align:start position:0% +interactions between the object and the +fluid okay so it actually doesn't Mass + + align:start position:0% +fluid okay so it actually doesn't Mass + + + align:start position:0% +fluid okay so it actually doesn't Mass +it doesn't enter into yeah mass is + + align:start position:0% +it doesn't enter into yeah mass is + + + align:start position:0% +it doesn't enter into yeah mass is +irrelevant okay right so oh that's yeah + + align:start position:0% +irrelevant okay right so oh that's yeah + + + align:start position:0% +irrelevant okay right so oh that's yeah +so it doesn't scale with that would have + + align:start position:0% +so it doesn't scale with that would have + + + align:start position:0% +so it doesn't scale with that would have +been a fine question as well but okay + + align:start position:0% +been a fine question as well but okay + + + align:start position:0% +been a fine question as well but okay +right so a cubed all right so this is + + align:start position:0% +right so a cubed all right so this is + + + align:start position:0% +right so a cubed all right so this is +this is weird all right um now I okay + + align:start position:0% +this is weird all right um now I okay + + + align:start position:0% +this is weird all right um now I okay +you know of course you can think about + + align:start position:0% +you know of course you can think about + + + align:start position:0% +you know of course you can think about +things in many different ways but the + + align:start position:0% +things in many different ways but the + + + align:start position:0% +things in many different ways but the +the key thing that you can see maybe is + + align:start position:0% +the key thing that you can see maybe is + + + align:start position:0% +the key thing that you can see maybe is +that um before for the sort of linear + + align:start position:0% +that um before for the sort of linear + + + align:start position:0% +that um before for the sort of linear +diffusion so d d linear respect of time + + align:start position:0% +diffusion so d d linear respect of time + + + align:start position:0% +diffusion so d d linear respect of time +you can see that the difference in units + + align:start position:0% +you can see that the difference in units + + + align:start position:0% +you can see that the difference in units +between these two diffusion + + align:start position:0% +between these two diffusion + + + align:start position:0% +between these two diffusion +coefficients uh is a factor of there + + align:start position:0% +coefficients uh is a factor of there + + + align:start position:0% +coefficients uh is a factor of there +there's a length squared difference + + align:start position:0% +there's a length squared difference + + + align:start position:0% +there's a length squared difference +between those two okay and it's that + + align:start position:0% +between those two okay and it's that + + + align:start position:0% +between those two okay and it's that +length squared that that turns the just + + align:start position:0% +length squared that that turns the just + + + align:start position:0% +length squared that that turns the just +linear dependence of a for uh for normal + + align:start position:0% +linear dependence of a for uh for normal + + + align:start position:0% +linear dependence of a for uh for normal +linear uh diffusion up to to an a cubed + + align:start position:0% +linear uh diffusion up to to an a cubed + + + align:start position:0% +linear uh diffusion up to to an a cubed +okay now you there you know of course + + align:start position:0% +okay now you there you know of course + + + align:start position:0% +okay now you there you know of course +there are other things we can write down + + align:start position:0% +there are other things we can write down + + + align:start position:0% +there are other things we can write down +that may be useful right so remember so + + align:start position:0% +that may be useful right so remember so + + + align:start position:0% +that may be useful right so remember so +this D linear Einstein told us this is + + align:start position:0% +this D linear Einstein told us this is + + + align:start position:0% +this D linear Einstein told us this is +KT over gamma + + align:start position:0% +KT over gamma + + + align:start position:0% +KT over gamma +linear right so this is if we try to + + align:start position:0% +linear right so this is if we try to + + + align:start position:0% +linear right so this is if we try to +move it this this tells us how hard do + + align:start position:0% +move it this this tells us how hard do + + + align:start position:0% +move it this this tells us how hard do +we have to move some how hard do we have + + align:start position:0% +we have to move some how hard do we have + + + align:start position:0% +we have to move some how hard do we have +to push to get something to move right + + align:start position:0% +to push to get something to move right + + + align:start position:0% +to push to get something to move right +so this is if you apply Force + + align:start position:0% +so this is if you apply Force + + + align:start position:0% +so this is if you apply Force +then gamma linear tells you how fast it + + align:start position:0% +then gamma linear tells you how fast it + + + align:start position:0% +then gamma linear tells you how fast it +will move in this uh uh in this low Ral + + align:start position:0% +will move in this uh uh in this low Ral + + + align:start position:0% +will move in this uh uh in this low Ral +number + + align:start position:0% +number + + + align:start position:0% +number +regime and now uh there's a similar set + + align:start position:0% +regime and now uh there's a similar set + + + align:start position:0% +regime and now uh there's a similar set +of things that we can say here I'm going + + align:start position:0% +of things that we can say here I'm going + + + align:start position:0% +of things that we can say here I'm going +to erase this just because um right so + + align:start position:0% +to erase this just because um right so + + + align:start position:0% +to erase this just because um right so +we can still say it's actually Einstein + + align:start position:0% +we can still say it's actually Einstein + + + align:start position:0% +we can still say it's actually Einstein +is just always right so the D rotational + + align:start position:0% +is just always right so the D rotational + + + align:start position:0% +is just always right so the D rotational +again is going to be KT but now this is + + align:start position:0% +again is going to be KT but now this is + + + align:start position:0% +again is going to be KT but now this is +a gamma + + align:start position:0% +a gamma + + + align:start position:0% +a gamma +rotational okay but instead of thinking + + align:start position:0% +rotational okay but instead of thinking + + + align:start position:0% +rotational okay but instead of thinking +about forces now this is torqus right so + + align:start position:0% +about forces now this is torqus right so + + + align:start position:0% +about forces now this is torqus right so +what's what's relevant is that if you + + align:start position:0% +what's what's relevant is that if you + + + align:start position:0% +what's what's relevant is that if you +apply oh I already used a + + align:start position:0% +apply oh I already used a + + + align:start position:0% +apply oh I already used a +towel oh okay I'll just say + + align:start position:0% +towel oh okay I'll just say + + + align:start position:0% +towel oh okay I'll just say +torque all right so if you apply torque + + align:start position:0% +torque all right so if you apply torque + + + align:start position:0% +torque all right so if you apply torque +on say a sphere or this object then this + + align:start position:0% +on say a sphere or this object then this + + + align:start position:0% +on say a sphere or this object then this +will cause uh an angular velocity so + + align:start position:0% +will cause uh an angular velocity so + + + align:start position:0% +will cause uh an angular velocity so +gamma rotational times some omega around + + align:start position:0% +gamma rotational times some omega around + + + align:start position:0% +gamma rotational times some omega around +okay + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +now okay for uh for concreteness I I + + align:start position:0% +now okay for uh for concreteness I I + + + align:start position:0% +now okay for uh for concreteness I I +will say if you have a sphere + + align:start position:0% +will say if you have a sphere + + + align:start position:0% +will say if you have a sphere +Stokes drag tells us this is this is 6 + + align:start position:0% +Stokes drag tells us this is this is 6 + + + align:start position:0% +Stokes drag tells us this is this is 6 +Pi Ada a * V right so this thing is how + + align:start position:0% +Pi Ada a * V right so this thing is how + + + align:start position:0% +Pi Ada a * V right so this thing is how +tells us how hard we have to push an + + align:start position:0% +tells us how hard we have to push an + + + align:start position:0% +tells us how hard we have to push an +object in order to make it move some + + align:start position:0% +object in order to make it move some + + + align:start position:0% +object in order to make it move some +velocity if it's a if it's a + + align:start position:0% +velocity if it's a if it's a + + + align:start position:0% +velocity if it's a if it's a +sphere okay + + align:start position:0% + + + + align:start position:0% + +uh whereas the gamma rotational here + + align:start position:0% +uh whereas the gamma rotational here + + + align:start position:0% +uh whereas the gamma rotational here +this thing is ends up being 8 Pi Ada a + + align:start position:0% +this thing is ends up being 8 Pi Ada a + + + align:start position:0% +this thing is ends up being 8 Pi Ada a +cubed Omega right so the gamma + + align:start position:0% +cubed Omega right so the gamma + + + align:start position:0% +cubed Omega right so the gamma +rotational ends up being that + + align:start position:0% + + + + align:start position:0% + +okay right so you can you can see that + + align:start position:0% +okay right so you can you can see that + + + align:start position:0% +okay right so you can you can see that +uh in terms of uh in terms of the + + align:start position:0% +uh in terms of uh in terms of the + + + align:start position:0% +uh in terms of uh in terms of the +rotational diffusion or rotational order + + align:start position:0% +rotational diffusion or rotational order + + + align:start position:0% +rotational diffusion or rotational order +uh objects uh scale the what do I to say + + align:start position:0% +uh objects uh scale the what do I to say + + + align:start position:0% +uh objects uh scale the what do I to say +that the the scaling is even is slower + + align:start position:0% +that the the scaling is even is slower + + + align:start position:0% +that the the scaling is even is slower +than you would expect somehow or no + + align:start position:0% +than you would expect somehow or no + + + align:start position:0% +than you would expect somehow or no +sorry the SC well the scaling here is + + align:start position:0% +sorry the SC well the scaling here is + + + align:start position:0% +sorry the SC well the scaling here is +larger than you would expect whereas the + + align:start position:0% +larger than you would expect whereas the + + + align:start position:0% +larger than you would expect whereas the +scaling here is smaller than you would + + align:start position:0% +scaling here is smaller than you would + + + align:start position:0% +scaling here is smaller than you would +expect right + + align:start position:0% + + + + align:start position:0% + +U + + align:start position:0% +U + + + align:start position:0% +U +yes + + align:start position:0% +yes + + + align:start position:0% +yes +sh um yes it's always different but not + + align:start position:0% +sh um yes it's always different but not + + + align:start position:0% +sh um yes it's always different but not +by very much okay all right so for + + align:start position:0% +by very much okay all right so for + + + align:start position:0% +by very much okay all right so for +example um I me so this thing the stok + + align:start position:0% +example um I me so this thing the stok + + + align:start position:0% +example um I me so this thing the stok +drug is only true for a sphere okay but + + align:start position:0% +drug is only true for a sphere okay but + + + align:start position:0% +drug is only true for a sphere okay but +uh but this linear on a is true for you + + align:start position:0% +uh but this linear on a is true for you + + + align:start position:0% +uh but this linear on a is true for you +know any of these objects so it's really + + align:start position:0% +know any of these objects so it's really + + + align:start position:0% +know any of these objects so it's really +that it's a is some typical length scale + + align:start position:0% +that it's a is some typical length scale + + + align:start position:0% +that it's a is some typical length scale +and in particular it's actually the + + align:start position:0% +and in particular it's actually the + + + align:start position:0% +and in particular it's actually the +larger of the two length + + align:start position:0% +larger of the two length + + + align:start position:0% +larger of the two length +scales so for example if you take a long + + align:start position:0% +scales so for example if you take a long + + + align:start position:0% +scales so for example if you take a long +kind of like cylinder + + align:start position:0% + + + + align:start position:0% + +pipe + + align:start position:0% +pipe + + + align:start position:0% +pipe +okay right now you can ask well now you + + align:start position:0% +okay right now you can ask well now you + + + align:start position:0% +okay right now you can ask well now you +know it's not isotropic anymore so + + align:start position:0% +know it's not isotropic anymore so + + + align:start position:0% +know it's not isotropic anymore so +there's going to actually be two + + align:start position:0% +there's going to actually be two + + + align:start position:0% +there's going to actually be two +different gamas there's going to be a + + align:start position:0% +different gamas there's going to be a + + + align:start position:0% +different gamas there's going to be a +gamma that we might call parallel + + align:start position:0% +gamma that we might call parallel + + + align:start position:0% +gamma that we might call parallel +if you want to push it in this direction + + align:start position:0% +if you want to push it in this direction + + + align:start position:0% +if you want to push it in this direction +and a gamma perpendicular if you want to + + align:start position:0% +and a gamma perpendicular if you want to + + + align:start position:0% +and a gamma perpendicular if you want to +push it in this direction + + align:start position:0% +push it in this direction + + + align:start position:0% +push it in this direction +right what's what's fascinating is that + + align:start position:0% +right what's what's fascinating is that + + + align:start position:0% +right what's what's fascinating is that +you know if this is something that say a + + align:start position:0% +you know if this is something that say a + + + align:start position:0% +you know if this is something that say a +nanometer in size here but a micron here + + align:start position:0% +nanometer in size here but a micron here + + + align:start position:0% +nanometer in size here but a micron here +so aspect ratio thousand to one okay + + align:start position:0% +so aspect ratio thousand to one okay + + + align:start position:0% +so aspect ratio thousand to one okay +still the difference between gamma + + align:start position:0% +still the difference between gamma + + + align:start position:0% +still the difference between gamma +parallel and Gamma perpendicular is + + align:start position:0% +parallel and Gamma perpendicular is + + + align:start position:0% +parallel and Gamma perpendicular is +still just a factor of two or so right + + align:start position:0% +still just a factor of two or so right + + + align:start position:0% +still just a factor of two or so right +because in both cases it's dominated by + + align:start position:0% +because in both cases it's dominated by + + + align:start position:0% +because in both cases it's dominated by +the longest linear Dimension okay so + + align:start position:0% +the longest linear Dimension okay so + + + align:start position:0% +the longest linear Dimension okay so +what's relevant + + align:start position:0% +what's relevant + + + align:start position:0% +what's relevant +is um is this is this big thing the + + align:start position:0% +is um is this is this big thing the + + + align:start position:0% +is um is this is this big thing the +length Okay so this is again an aspect + + align:start position:0% +length Okay so this is again an aspect + + + align:start position:0% +length Okay so this is again an aspect +of uh the surprising nature of the low + + align:start position:0% +of uh the surprising nature of the low + + + align:start position:0% +of uh the surprising nature of the low +Reynolds number regime right this is not + + align:start position:0% +Reynolds number regime right this is not + + + align:start position:0% +Reynolds number regime right this is not +true if you were you know a sky diver or + + align:start position:0% +true if you were you know a sky diver or + + + align:start position:0% +true if you were you know a sky diver or +something right but uh the reason is + + align:start position:0% +something right but uh the reason is + + + align:start position:0% +something right but uh the reason is +that this longest Dimension kind of + + align:start position:0% +that this longest Dimension kind of + + + align:start position:0% +that this longest Dimension kind of +tells you how much water you're going to + + align:start position:0% +tells you how much water you're going to + + + align:start position:0% +tells you how much water you're going to +be pulling with you right what's + + align:start position:0% +be pulling with you right what's + + + align:start position:0% +be pulling with you right what's +relevant is not the cross-sectional area + + align:start position:0% +relevant is not the cross-sectional area + + + align:start position:0% +relevant is not the cross-sectional area +that you're kind of you're pushing but + + align:start position:0% +that you're kind of you're pushing but + + + align:start position:0% +that you're kind of you're pushing but +rather uh it's kind of telling you kind + + align:start position:0% +rather uh it's kind of telling you kind + + + align:start position:0% +rather uh it's kind of telling you kind +of how much fluid are you kind of + + align:start position:0% +of how much fluid are you kind of + + + align:start position:0% +of how much fluid are you kind of +disturbing along the whole the whole + + align:start position:0% +disturbing along the whole the whole + + + align:start position:0% +disturbing along the whole the whole +length + + align:start position:0% +length + + + align:start position:0% +length +Okay + + align:start position:0% +Okay + + + align:start position:0% +Okay +okay there any questions about what I + + align:start position:0% +okay there any questions about what I + + + align:start position:0% +okay there any questions about what I +mean by + + align:start position:0% + + + + align:start position:0% + +this okay oh yeah yeah all right so + + align:start position:0% +this okay oh yeah yeah all right so + + + align:start position:0% +this okay oh yeah yeah all right so +you're wondering how I actually get get + + align:start position:0% +you're wondering how I actually get get + + + align:start position:0% +you're wondering how I actually get get +to a time from this yeah okay sorry I + + align:start position:0% +to a time from this yeah okay sorry I + + + align:start position:0% +to a time from this yeah okay sorry I +should have um yeah finished this okay + + align:start position:0% +should have um yeah finished this okay + + + align:start position:0% +should have um yeah finished this okay +so let let me just show you what I meant + + align:start position:0% +so let let me just show you what I meant + + + align:start position:0% +so let let me just show you what I meant +um right so one way to think about this + + align:start position:0% +um right so one way to think about this + + + align:start position:0% +um right so one way to think about this +is okay so we we we know that U this + + align:start position:0% +is okay so we we we know that U this + + + align:start position:0% +is okay so we we we know that U this +this is that this is where we start and + + align:start position:0% +this is that this is where we start and + + + align:start position:0% +this is that this is where we start and +what you could say is well the typical + + align:start position:0% +what you could say is well the typical + + + align:start position:0% +what you could say is well the typical +time to randomize that's that's when + + align:start position:0% +time to randomize that's that's when + + + align:start position:0% +time to randomize that's that's when +we've gone to enough time so that change + + align:start position:0% +we've gone to enough time so that change + + + align:start position:0% +we've gone to enough time so that change +in Theta squared is say of order you + + align:start position:0% +in Theta squared is say of order you + + + align:start position:0% +in Theta squared is say of order you +know a radian squared right so it's it's + + align:start position:0% +know a radian squared right so it's it's + + + align:start position:0% +know a radian squared right so it's it's +enough that you know that's sort of a + + align:start position:0% +enough that you know that's sort of a + + + align:start position:0% +enough that you know that's sort of a +characteristic reorientation right so + + align:start position:0% +characteristic reorientation right so + + + align:start position:0% +characteristic reorientation right so +you just say okay well we're going to + + align:start position:0% +you just say okay well we're going to + + + align:start position:0% +you just say okay well we're going to +set this equal to around one so 2dr + + align:start position:0% +set this equal to around one so 2dr + + + align:start position:0% +set this equal to around one so 2dr +times this reorientation time to will be + + align:start position:0% +times this reorientation time to will be + + + align:start position:0% +times this reorientation time to will be +of around + + align:start position:0% +of around + + + align:start position:0% +of around +one okay so that gives us that the + + align:start position:0% +one okay so that gives us that the + + + align:start position:0% +one okay so that gives us that the +reorientation time you know it's going + + align:start position:0% +reorientation time you know it's going + + + align:start position:0% +reorientation time you know it's going +to be + + align:start position:0% +to be + + + align:start position:0% +to be +around so we have a half and then D + + align:start position:0% +around so we have a half and then D + + + align:start position:0% +around so we have a half and then D +rotation now we have 8 Pi Ada a + + align:start position:0% +rotation now we have 8 Pi Ada a + + + align:start position:0% +rotation now we have 8 Pi Ada a +cubed over + + align:start position:0% +cubed over + + + align:start position:0% +cubed over +KT is that KT + + align:start position:0% +KT is that KT + + + align:start position:0% +KT is that KT +get yeah + + align:start position:0% +get yeah + + + align:start position:0% +get yeah +all right um and and actually in units I + + align:start position:0% +all right um and and actually in units I + + + align:start position:0% +all right um and and actually in units I +mean so I I grew up in the single + + align:start position:0% +mean so I I grew up in the single + + + align:start position:0% +mean so I I grew up in the single +molecule world where everything was in + + align:start position:0% +molecule world where everything was in + + + align:start position:0% +molecule world where everything was in +units of pons nanometers + + align:start position:0% +units of pons nanometers + + + align:start position:0% +units of pons nanometers +seconds and in those units we could + + align:start position:0% +seconds and in those units we could + + + align:start position:0% +seconds and in those units we could +actually write okay this is a you know + + align:start position:0% +actually write okay this is a you know + + + align:start position:0% +actually write okay this is a you know +we have a 4 Pi KT is actually 4.1 Pon + + align:start position:0% +we have a 4 Pi KT is actually 4.1 Pon + + + align:start position:0% +we have a 4 Pi KT is actually 4.1 Pon +nanometers so it's around four in these + + align:start position:0% +nanometers so it's around four in these + + + align:start position:0% +nanometers so it's around four in these +units and then Ada is actually 10us 9 in + + align:start position:0% +units and then Ada is actually 10us 9 in + + + align:start position:0% +units and then Ada is actually 10us 9 in +those units a for a for a bacteria you + + align:start position:0% +those units a for a for a bacteria you + + + align:start position:0% +those units a for a for a bacteria you +know it's around a micron right so it's + + align:start position:0% +know it's around a micron right so it's + + + align:start position:0% +know it's around a micron right so it's +a thous in but this is in P nanometer + + align:start position:0% +a thous in but this is in P nanometer + + + align:start position:0% +a thous in but this is in P nanometer +second units so this is we have to do 10 + + align:start position:0% +second units so this is we have to do 10 + + + align:start position:0% +second units so this is we have to do 10 +3 cubed because you know we a micron is + + align:start position:0% +3 cubed because you know we a micron is + + + align:start position:0% +3 cubed because you know we a micron is +10 3 nanometers right conveniently 10 3 + + align:start position:0% +10 3 nanometers right conveniently 10 3 + + + align:start position:0% +10 3 nanometers right conveniently 10 3 +the 3 10us 9 we can just cross these out + + align:start position:0% +the 3 10us 9 we can just cross these out + + + align:start position:0% +the 3 10us 9 we can just cross these out +we can cross the fours out all right so + + align:start position:0% +we can cross the fours out all right so + + + align:start position:0% +we can cross the fours out all right so +we get Pi + + align:start position:0% + + + + align:start position:0% + +seconds all right should we take the pi + + align:start position:0% +seconds all right should we take the pi + + + align:start position:0% +seconds all right should we take the pi +seriously no okay yeah so you know but + + align:start position:0% +seriously no okay yeah so you know but + + + align:start position:0% +seriously no okay yeah so you know but +the point is that it's it's of order + + align:start position:0% +the point is that it's it's of order + + + align:start position:0% +the point is that it's it's of order +you know 1 to 10 seconds right this is + + align:start position:0% +you know 1 to 10 seconds right this is + + + align:start position:0% +you know 1 to 10 seconds right this is +and you get from such a back envelope + + align:start position:0% +and you get from such a back envelope + + + align:start position:0% +and you get from such a back envelope +calculation right but this is saying + + align:start position:0% +calculation right but this is saying + + + align:start position:0% +calculation right but this is saying +that from the standpoint of the + + align:start position:0% +that from the standpoint of the + + + align:start position:0% +that from the standpoint of the +bacterial cell it starts going and it + + align:start position:0% +bacterial cell it starts going and it + + + align:start position:0% +bacterial cell it starts going and it +forgets which direction it started going + + align:start position:0% +forgets which direction it started going + + + align:start position:0% +forgets which direction it started going +over the time scale of a few + + align:start position:0% +over the time scale of a few + + + align:start position:0% +over the time scale of a few +seconds right so it doesn't it does it's + + align:start position:0% +seconds right so it doesn't it does it's + + + align:start position:0% +seconds right so it doesn't it does it's +not worth it for the cell to actually + + align:start position:0% +not worth it for the cell to actually + + + align:start position:0% +not worth it for the cell to actually +have a run that's longer than that + + align:start position:0% +have a run that's longer than that + + + align:start position:0% +have a run that's longer than that +because it will have lost its way + + align:start position:0% +because it will have lost its way + + + align:start position:0% +because it will have lost its way +anyways + + align:start position:0% + + + + align:start position:0% + +okay all right um all right so uh what + + align:start position:0% +okay all right um all right so uh what + + + align:start position:0% +okay all right um all right so uh what +we're going to do on Tuesday is we're + + align:start position:0% +we're going to do on Tuesday is we're + + + align:start position:0% +we're going to do on Tuesday is we're +going to try to understand something + + align:start position:0% +going to try to understand something + + + align:start position:0% +going to try to understand something +about how how bacteria use this + + align:start position:0% +about how how bacteria use this + + + align:start position:0% +about how how bacteria use this +combination of runs and tumbles in order + + align:start position:0% +combination of runs and tumbles in order + + + align:start position:0% +combination of runs and tumbles in order +to uh kind of perform these exquisitly + + align:start position:0% +to uh kind of perform these exquisitly + + + align:start position:0% +to uh kind of perform these exquisitly +sensitive uh uh kind of travels to find + + align:start position:0% +sensitive uh uh kind of travels to find + + + align:start position:0% +sensitive uh uh kind of travels to find +uh to find food sources if you have any + + align:start position:0% +uh to find food sources if you have any + + + align:start position:0% +uh to find food sources if you have any +questions about anything that we talked + + align:start position:0% +questions about anything that we talked + + + align:start position:0% +questions about anything that we talked +about please come on up \ No newline at end of file diff --git a/VHVsCE9XmQk.txt b/VHVsCE9XmQk.txt new file mode 100644 index 0000000000000000000000000000000000000000..1871b16acc2574478ddfe92a15b533c474b2f6ae --- /dev/null +++ b/VHVsCE9XmQk.txt @@ -0,0 +1,98 @@ +Given the CMOS circuit with pull-down shown +here, we can generate the corresponding function + +that this CMOS circuit represents which is +NOT(F) = (A+B)C + D. + +So F = ((A+B)C + D) the whole thing negated. +This function can be expressed as a truth + +table which describes the output that the +function produces for any set of inputs. + +All of the possible input combinations are +enumerated, and then the value of F is specified + +for each of those combinations. +For this function, F, for example, if A=0 + +B=0 C=0 and D=0, then (A+B)C = 0 that ORed +with D = 0, and finally the entire thing is + +negated, so F = 1. +For A=0 B=0 C=0 and D=1, (A+B)C = 0 + D=1 + +gives us 1 and the whole thing negated is +F=0. + +In the same way, we can complete the rest +of the truth table, and we get. + +1 0 1 0 0 0 1 0 0 0 1 0 0 0 +Given a truth table, one can be asked if the + +function F that this truth table defines, +can be implemented using a single CMOS gate. + +To figure that out, we first convert the truth +table to a logical equation for F. + +Given this truth table, the function F can +be expressed as a sum of products by listing + +all terms that make F=1 and ORing them together. +For this truth table F = NOT(A) NOT(B) NOT(C) + ++ NOT(A) B NOT(C) + A NOT(B) NOT(C). +In order to determine if this function can + +be implemented as a single CMOS circuit, the +function F needs to be manipulated through + +logic simplifications in order to see if NOT(F) +can be written as a function of just the inputs + +A, B, and C (without any negations of those +inputs) together with ANDs and ORs. + +We start with our function for F. +Factoring out NOT(C), that equals NOT(C) (NOT(A) + +NOT(B) + NOT(A) B + A NOT(B)). +Rearranging the terms and repeating the first + +one continues to produce the same function. +So F = NOT(C) (NOT(A) NOT(B) + A NOT(B) + + +NOT(A) B + NOT(A) NOT(B)). +Noting that A X + NOT(A) X = X, this reduces + +to: F = NOT(C) (NOT(B) + NOT(A)). +We are almost there, we now want to convert + +F to NOT(F) by negating the entire thing, +so NOT(F) = NOT (NOT(C) (NOT(B) + NOT(A)). + +To simplify this we make use of De Morgan's +Law which states that NOT(AB) = NOT(A) + NOT(B). + +And that NOT(A+B) = NOT(A) AND NOT(B). +So NOT(F) = C + NOT(NOT(B) + NOT(A)), and + +finally NOT(F) = C + (B A). +Now that we have found that NOT(F) = C + BA, + +we know that F can be implemented as a single +CMOS gate because we were able to express + +NOT(F) as a function that consists purely +of our non-negated inputs, A, B, and C, together + +with ANDs and ORs. +The pull-down for this circuit would basically + +implement NOT(F) so it would be series(A,B) +in parallel with C. + +The pull-up would be the inverse of that which +is parallel(A,B) in series with C. \ No newline at end of file diff --git a/W1lxlbJ0BZU.txt b/W1lxlbJ0BZU.txt new file mode 100644 index 0000000000000000000000000000000000000000..1564181cbd5412b3ce6467fe68929d1d0a8b3a73 --- /dev/null +++ b/W1lxlbJ0BZU.txt @@ -0,0 +1,483 @@ +align:start position:0% + +now that we've described the position + + align:start position:0% +now that we've described the position + + + align:start position:0% +now that we've described the position +Vector of the runner let's try to + + align:start position:0% +Vector of the runner let's try to + + + align:start position:0% +Vector of the runner let's try to +describe what happens in time as the + + align:start position:0% +describe what happens in time as the + + + align:start position:0% +describe what happens in time as the +runner moves along our road suppose at a + + align:start position:0% +runner moves along our road suppose at a + + + align:start position:0% +runner moves along our road suppose at a +later time our runner has gone down the + + align:start position:0% +later time our runner has gone down the + + + align:start position:0% +later time our runner has gone down the +road just a little bit and + + align:start position:0% +road just a little bit and + + + align:start position:0% +road just a little bit and +so Runner has moved a little bit + + align:start position:0% +so Runner has moved a little bit + + + align:start position:0% +so Runner has moved a little bit +remember at time T we described the + + align:start position:0% +remember at time T we described the + + + align:start position:0% +remember at time T we described the +position Vector R of T was equal to the + + align:start position:0% +position Vector R of T was equal to the + + + align:start position:0% +position Vector R of T was equal to the +coordinate function X is a function of + + align:start position:0% +coordinate function X is a function of + + + align:start position:0% +coordinate function X is a function of +time I hat and this distance here was + + align:start position:0% +time I hat and this distance here was + + + align:start position:0% +time I hat and this distance here was +our X of T now our position Vector a + + align:start position:0% +our X of T now our position Vector a + + + align:start position:0% +our X of T now our position Vector a +little bit later so here we're at time t + + align:start position:0% +little bit later so here we're at time t + + + align:start position:0% +little bit later so here we're at time t ++ delta T the runner has moved a little + + align:start position:0% ++ delta T the runner has moved a little + + + align:start position:0% ++ delta T the runner has moved a little +bit and we'll now describe the position + + align:start position:0% +bit and we'll now describe the position + + + align:start position:0% +bit and we'll now describe the position +Vector because I don't want to overlap + + align:start position:0% +Vector because I don't want to overlap + + + align:start position:0% +Vector because I don't want to overlap +it that Center Point is up here it's + + align:start position:0% +it that Center Point is up here it's + + + align:start position:0% +it that Center Point is up here it's +going to point in this direction and + + align:start position:0% +going to point in this direction and + + + align:start position:0% +going to point in this direction and +this is what we call R of t plus delta T + + align:start position:0% +this is what we call R of t plus delta T + + + align:start position:0% +this is what we call R of t plus delta T +and that Vector R of t plus delta T the + + align:start position:0% +and that Vector R of t plus delta T the + + + align:start position:0% +and that Vector R of t plus delta T the +coordinate function is no longer at time + + align:start position:0% +coordinate function is no longer at time + + + align:start position:0% +coordinate function is no longer at time +T but t plus delta T I had and we would + + align:start position:0% +T but t plus delta T I had and we would + + + align:start position:0% +T but t plus delta T I had and we would +now like to describe the displacement + + align:start position:0% +now like to describe the displacement + + + align:start position:0% +now like to describe the displacement +Vector so our next step is to describe + + align:start position:0% +Vector so our next step is to describe + + + align:start position:0% +Vector so our next step is to describe +displacement + + align:start position:0% +displacement + + + align:start position:0% +displacement +Vector for the interval T to t + delta T + + align:start position:0% +Vector for the interval T to t + delta T + + + align:start position:0% +Vector for the interval T to t + delta T +and that displacement Vector is Define + + align:start position:0% +and that displacement Vector is Define + + + align:start position:0% +and that displacement Vector is Define +we use the symbol delt R and what we + + align:start position:0% +we use the symbol delt R and what we + + + align:start position:0% +we use the symbol delt R and what we +mean is the vector R of t plus delta T + + align:start position:0% +mean is the vector R of t plus delta T + + + align:start position:0% +mean is the vector R of t plus delta T +minus the vector R of T now what that + + align:start position:0% +minus the vector R of T now what that + + + align:start position:0% +minus the vector R of T now what that +Vector corresponds to is the vector + + align:start position:0% +Vector corresponds to is the vector + + + align:start position:0% +Vector corresponds to is the vector +right here this is our Delta + + align:start position:0% +right here this is our Delta + + + align:start position:0% +right here this is our Delta +R and if we now use our two definitions + + align:start position:0% +R and if we now use our two definitions + + + align:start position:0% +R and if we now use our two definitions +here then this becomes X of t plus delta + + align:start position:0% +here then this becomes X of t plus delta + + + align:start position:0% +here then this becomes X of t plus delta +T minus + + align:start position:0% +T minus + + + align:start position:0% +T minus +X of + + align:start position:0% +X of + + + align:start position:0% +X of +t i and this quantity here we refer to + + align:start position:0% +t i and this quantity here we refer to + + + align:start position:0% +t i and this quantity here we refer to +as the component of the displacement + + align:start position:0% +as the component of the displacement + + + align:start position:0% +as the component of the displacement +Vector so Delta X is the + + align:start position:0% + + + + align:start position:0% + +component of the displacement + + align:start position:0% + + + + align:start position:0% + +vector and as before the component can + + align:start position:0% +vector and as before the component can + + + align:start position:0% +vector and as before the component can +be positive which would correspond to + + align:start position:0% +be positive which would correspond to + + + align:start position:0% +be positive which would correspond to +the person moving a positive component + + align:start position:0% +the person moving a positive component + + + align:start position:0% +the person moving a positive component +positive IAT Direction in the positive X + + align:start position:0% +positive IAT Direction in the positive X + + + align:start position:0% +positive IAT Direction in the positive X +direction as shown in this figure if the + + align:start position:0% +direction as shown in this figure if the + + + align:start position:0% +direction as shown in this figure if the +displacement Vector is zero the person + + align:start position:0% +displacement Vector is zero the person + + + align:start position:0% +displacement Vector is zero the person +could have run forward and come back and + + align:start position:0% +could have run forward and come back and + + + align:start position:0% +could have run forward and come back and +at time t plus delta T be in exactly the + + align:start position:0% +at time t plus delta T be in exactly the + + + align:start position:0% +at time t plus delta T be in exactly the +same spot as time T the displacement + + align:start position:0% +same spot as time T the displacement + + + align:start position:0% +same spot as time T the displacement +Vector is + + align:start position:0% +Vector is + + + align:start position:0% +Vector is +zero in that case the displacement + + align:start position:0% +zero in that case the displacement + + + align:start position:0% +zero in that case the displacement +Vector could have a component that's + + align:start position:0% +Vector could have a component that's + + + align:start position:0% +Vector could have a component that's +negative and would negative means is at + + align:start position:0% +negative and would negative means is at + + + align:start position:0% +negative and would negative means is at +the end of this interval t plus delta T + + align:start position:0% +the end of this interval t plus delta T + + + align:start position:0% +the end of this interval t plus delta T +that the person is on to the left of the + + align:start position:0% +that the person is on to the left of the + + + align:start position:0% +that the person is on to the left of the +runner and so this quantity would be + + align:start position:0% +runner and so this quantity would be + + + align:start position:0% +runner and so this quantity would be +negative and so this is our crucial + + align:start position:0% +negative and so this is our crucial + + + align:start position:0% +negative and so this is our crucial +displacement Vector that describes only + + align:start position:0% +displacement Vector that describes only + + + align:start position:0% +displacement Vector that describes only +the difference in positions between the + + align:start position:0% +the difference in positions between the + + + align:start position:0% +the difference in positions between the +person between time t plus delta T and + + align:start position:0% +person between time t plus delta T and + + + align:start position:0% +person between time t plus delta T and +time t \ No newline at end of file diff --git a/Wlfd5wjFyYw.txt b/Wlfd5wjFyYw.txt new file mode 100644 index 0000000000000000000000000000000000000000..740856613deb140dd84d375b21b44d953fbb4578 --- /dev/null +++ b/Wlfd5wjFyYw.txt @@ -0,0 +1,971 @@ +align:start position:0% + +the study state magnetic levitation of + + align:start position:0% +the study state magnetic levitation of + + + align:start position:0% +the study state magnetic levitation of +current carrying conductor zovirax + + align:start position:0% +current carrying conductor zovirax + + + align:start position:0% +current carrying conductor zovirax +magnetic forces due to conduction + + align:start position:0% +magnetic forces due to conduction + + + align:start position:0% +magnetic forces due to conduction +currents here is the actual experiment + + align:start position:0% +currents here is the actual experiment + + + align:start position:0% +currents here is the actual experiment +with the pancake coil excited by 60 + + align:start position:0% +with the pancake coil excited by 60 + + + align:start position:0% +with the pancake coil excited by 60 +Hertz current from this very act the + + align:start position:0% +Hertz current from this very act the + + + align:start position:0% +Hertz current from this very act the +current is measured with this clip on a + + align:start position:0% +current is measured with this clip on a + + + align:start position:0% +current is measured with this clip on a +meter and indicated on the oscilloscope + + align:start position:0% + + + + align:start position:0% + +the ground plane is this aluminum sheet + + align:start position:0% +the ground plane is this aluminum sheet + + + align:start position:0% +the ground plane is this aluminum sheet +its thickness is 1.2 seven centimeters + + align:start position:0% +its thickness is 1.2 seven centimeters + + + align:start position:0% +its thickness is 1.2 seven centimeters +the coil has a thickness of about one + + align:start position:0% +the coil has a thickness of about one + + + align:start position:0% +the coil has a thickness of about one +and a half centimeters + + align:start position:0% + + + + align:start position:0% + +a typical current in the coil is 20 to + + align:start position:0% +a typical current in the coil is 20 to + + + align:start position:0% +a typical current in the coil is 20 to +30 amperes so it's made of large + + align:start position:0% +30 amperes so it's made of large + + + align:start position:0% +30 amperes so it's made of large +diameter wire to reduce its resistance + + align:start position:0% +diameter wire to reduce its resistance + + + align:start position:0% +diameter wire to reduce its resistance +the 250 turns are of number 10 aluminum + + align:start position:0% +the 250 turns are of number 10 aluminum + + + align:start position:0% +the 250 turns are of number 10 aluminum +wire aluminum is chosen for its light + + align:start position:0% +wire aluminum is chosen for its light + + + align:start position:0% +wire aluminum is chosen for its light +weight its density is 2.7 grams per + + align:start position:0% +weight its density is 2.7 grams per + + + align:start position:0% +weight its density is 2.7 grams per +cubic centimeter so that for a given + + align:start position:0% +cubic centimeter so that for a given + + + align:start position:0% +cubic centimeter so that for a given +current and thus magnetic force the coil + + align:start position:0% +current and thus magnetic force the coil + + + align:start position:0% +current and thus magnetic force the coil +will rise higher than if made of copper + + align:start position:0% +will rise higher than if made of copper + + + align:start position:0% +will rise higher than if made of copper +although copper is a better conductor by + + align:start position:0% +although copper is a better conductor by + + + align:start position:0% +although copper is a better conductor by +a factor of about 1.6 its density is + + align:start position:0% +a factor of about 1.6 its density is + + + align:start position:0% +a factor of about 1.6 its density is +about 3.3 times greater than aluminum + + align:start position:0% +about 3.3 times greater than aluminum + + + align:start position:0% +about 3.3 times greater than aluminum +the scope trace indicates the coil + + align:start position:0% +the scope trace indicates the coil + + + align:start position:0% +the scope trace indicates the coil +current here again is what happens as + + align:start position:0% +current here again is what happens as + + + align:start position:0% +current here again is what happens as +the current is raised + + align:start position:0% + + + + align:start position:0% + +the force on the conductor results in + + align:start position:0% +the force on the conductor results in + + + align:start position:0% +the force on the conductor results in +vibrations which we hear is telltale + + align:start position:0% +vibrations which we hear is telltale + + + align:start position:0% +vibrations which we hear is telltale +evidence that the current is being + + align:start position:0% +evidence that the current is being + + + align:start position:0% +evidence that the current is being +increased the force is proportional to + + align:start position:0% +increased the force is proportional to + + + align:start position:0% +increased the force is proportional to +the square of the 60 Hertz current these + + align:start position:0% +the square of the 60 Hertz current these + + + align:start position:0% +the square of the 60 Hertz current these +vibrations result from the 120 Hertz + + align:start position:0% +vibrations result from the 120 Hertz + + + align:start position:0% +vibrations result from the 120 Hertz +second harmonic component of the force + + align:start position:0% +second harmonic component of the force + + + align:start position:0% +second harmonic component of the force +when the RMS current is large enough + + align:start position:0% +when the RMS current is large enough + + + align:start position:0% +when the RMS current is large enough +that the Lorentz force can overcome the + + align:start position:0% +that the Lorentz force can overcome the + + + align:start position:0% +that the Lorentz force can overcome the +coil weight the coil lifts off the + + align:start position:0% +coil weight the coil lifts off the + + + align:start position:0% +coil weight the coil lifts off the +ground plane increasing the current + + align:start position:0% +ground plane increasing the current + + + align:start position:0% +ground plane increasing the current +further results in an increase in the + + align:start position:0% +further results in an increase in the + + + align:start position:0% +further results in an increase in the +levitation force at a given altitude so + + align:start position:0% +levitation force at a given altitude so + + + align:start position:0% +levitation force at a given altitude so +the coil rises to make the upwards + + align:start position:0% +the coil rises to make the upwards + + + align:start position:0% +the coil rises to make the upwards +magnetic force equal to that of the coil + + align:start position:0% +magnetic force equal to that of the coil + + + align:start position:0% +magnetic force equal to that of the coil +weight let's see if we can estimate how + + align:start position:0% +weight let's see if we can estimate how + + + align:start position:0% +weight let's see if we can estimate how +high the pancake coil will rise for a + + align:start position:0% +high the pancake coil will rise for a + + + align:start position:0% +high the pancake coil will rise for a +given coil current we are limited in + + align:start position:0% +given coil current we are limited in + + + align:start position:0% +given coil current we are limited in +height by the maximum current before we + + align:start position:0% +height by the maximum current before we + + + align:start position:0% +height by the maximum current before we +blow a fuse + + align:start position:0% + + + + align:start position:0% + +focusing attention on a single turn of + + align:start position:0% +focusing attention on a single turn of + + + align:start position:0% +focusing attention on a single turn of +the circular coil with radius a with a + + align:start position:0% +the circular coil with radius a with a + + + align:start position:0% +the circular coil with radius a with a +much larger than the wire diameter we + + align:start position:0% +much larger than the wire diameter we + + + align:start position:0% +much larger than the wire diameter we +can approximately use our inductance + + align:start position:0% +can approximately use our inductance + + + align:start position:0% +can approximately use our inductance +formula for a straight wire of length L + + align:start position:0% +formula for a straight wire of length L + + + align:start position:0% +formula for a straight wire of length L +if we take L to just be the coil + + align:start position:0% +if we take L to just be the coil + + + align:start position:0% +if we take L to just be the coil +circumference to PI a we reconnect the + + align:start position:0% +circumference to PI a we reconnect the + + + align:start position:0% +circumference to PI a we reconnect the +pancake coil to the variac the clip on + + align:start position:0% +pancake coil to the variac the clip on + + + align:start position:0% +pancake coil to the variac the clip on +ammeter measures the current which is + + align:start position:0% +ammeter measures the current which is + + + align:start position:0% +ammeter measures the current which is +displayed on the oscilloscope we raise + + align:start position:0% +displayed on the oscilloscope we raise + + + align:start position:0% +displayed on the oscilloscope we raise +the current slowly and find the coil + + align:start position:0% +the current slowly and find the coil + + + align:start position:0% +the current slowly and find the coil +lifts off at about fifteen point five + + align:start position:0% +lifts off at about fifteen point five + + + align:start position:0% +lifts off at about fifteen point five +amperes RMS what we predicted was + + align:start position:0% +amperes RMS what we predicted was + + + align:start position:0% +amperes RMS what we predicted was +fourteen point three amperes rms as we + + align:start position:0% +fourteen point three amperes rms as we + + + align:start position:0% +fourteen point three amperes rms as we +raise the current further the coil + + align:start position:0% +raise the current further the coil + + + align:start position:0% +raise the current further the coil +height above the ground plane increases + + align:start position:0% + + + + align:start position:0% + +here the coil sent arises by two point + + align:start position:0% +here the coil sent arises by two point + + + align:start position:0% +here the coil sent arises by two point +two five centimeters at twenty amperes + + align:start position:0% +two five centimeters at twenty amperes + + + align:start position:0% +two five centimeters at twenty amperes +RMS we take other data points by + + align:start position:0% +RMS we take other data points by + + + align:start position:0% +RMS we take other data points by +increasing the current further + + align:start position:0% + + + + align:start position:0% + +the skin depth in aluminum at 60 Hertz + + align:start position:0% +the skin depth in aluminum at 60 Hertz + + + align:start position:0% +the skin depth in aluminum at 60 Hertz +is 1.1 centimeters at first one may + + align:start position:0% +is 1.1 centimeters at first one may + + + align:start position:0% +is 1.1 centimeters at first one may +think that for the assumption of a + + align:start position:0% +think that for the assumption of a + + + align:start position:0% +think that for the assumption of a +perfectly conducting ground plane to be + + align:start position:0% +perfectly conducting ground plane to be + + + align:start position:0% +perfectly conducting ground plane to be +accurate the frequency must be high + + align:start position:0% +accurate the frequency must be high + + + align:start position:0% +accurate the frequency must be high +enough that the ground plane thickness + + align:start position:0% +enough that the ground plane thickness + + + align:start position:0% +enough that the ground plane thickness +is greater than the skin depth for our + + align:start position:0% +is greater than the skin depth for our + + + align:start position:0% +is greater than the skin depth for our +experiments thus far the aluminum ground + + align:start position:0% +experiments thus far the aluminum ground + + + align:start position:0% +experiments thus far the aluminum ground +plane thickness has been one point 27 + + align:start position:0% +plane thickness has been one point 27 + + + align:start position:0% +plane thickness has been one point 27 +centimeters this thickness is about a + + align:start position:0% +centimeters this thickness is about a + + + align:start position:0% +centimeters this thickness is about a +skin depth to demonstrate the dependence + + align:start position:0% +skin depth to demonstrate the dependence + + + align:start position:0% +skin depth to demonstrate the dependence +and ground plane thickness we can try a + + align:start position:0% +and ground plane thickness we can try a + + + align:start position:0% +and ground plane thickness we can try a +ground plane with half the thickness + + align:start position:0% +ground plane with half the thickness + + + align:start position:0% +ground plane with half the thickness +this plate has a thickness of six point + + align:start position:0% +this plate has a thickness of six point + + + align:start position:0% +this plate has a thickness of six point +three five millimeters this is about + + align:start position:0% +three five millimeters this is about + + + align:start position:0% +three five millimeters this is about +half the skin depth remember that with + + align:start position:0% +half the skin depth remember that with + + + align:start position:0% +half the skin depth remember that with +1.2 7 centimeter thickness liftoff + + align:start position:0% +1.2 7 centimeter thickness liftoff + + + align:start position:0% +1.2 7 centimeter thickness liftoff +occurred at fifteen point five amperes + + align:start position:0% +occurred at fifteen point five amperes + + + align:start position:0% +occurred at fifteen point five amperes +with this half skin depth thick ground + + align:start position:0% +with this half skin depth thick ground + + + align:start position:0% +with this half skin depth thick ground +plane lifts off occurs at 16.3 rather + + align:start position:0% +plane lifts off occurs at 16.3 rather + + + align:start position:0% +plane lifts off occurs at 16.3 rather +than fifteen point five amperes RMS this + + align:start position:0% +than fifteen point five amperes RMS this + + + align:start position:0% +than fifteen point five amperes RMS this +current is only slightly higher than + + align:start position:0% +current is only slightly higher than + + + align:start position:0% +current is only slightly higher than +with the 1.2 7 centimeter thick round + + align:start position:0% +with the 1.2 7 centimeter thick round + + + align:start position:0% +with the 1.2 7 centimeter thick round +plane even though the ground plane + + align:start position:0% +plane even though the ground plane + + + align:start position:0% +plane even though the ground plane +thickness is now about half the skin + + align:start position:0% +thickness is now about half the skin + + + align:start position:0% +thickness is now about half the skin +death it still lacks essentially as a + + align:start position:0% +death it still lacks essentially as a + + + align:start position:0% +death it still lacks essentially as a +perfect conductor + + align:start position:0% + + + + align:start position:0% + +with a one millimeter thick plane the + + align:start position:0% +with a one millimeter thick plane the + + + align:start position:0% +with a one millimeter thick plane the +coil does not lift up even at 30 amperes + + align:start position:0% +coil does not lift up even at 30 amperes + + + align:start position:0% +coil does not lift up even at 30 amperes +RMS the ground blind is now so thin that + + align:start position:0% +RMS the ground blind is now so thin that + + + align:start position:0% +RMS the ground blind is now so thin that +most of the magnetic field penetrates + + align:start position:0% +most of the magnetic field penetrates + + + align:start position:0% +most of the magnetic field penetrates +through the ground plane we just blew a + + align:start position:0% +through the ground plane we just blew a + + + align:start position:0% +through the ground plane we just blew a +fuse again but this time because of an + + align:start position:0% +fuse again but this time because of an + + + align:start position:0% +fuse again but this time because of an +arc the enamel insulation on the wires + + align:start position:0% +arc the enamel insulation on the wires + + + align:start position:0% +arc the enamel insulation on the wires +may not be enough to prevent arcing to + + align:start position:0% +may not be enough to prevent arcing to + + + align:start position:0% +may not be enough to prevent arcing to +the sheet we have just seen an example + + align:start position:0% +the sheet we have just seen an example + + + align:start position:0% +the sheet we have just seen an example +of this let's try it again now with some + + align:start position:0% +of this let's try it again now with some + + + align:start position:0% +of this let's try it again now with some +gaffers tape for better insulation on + + align:start position:0% +gaffers tape for better insulation on + + + align:start position:0% +gaffers tape for better insulation on +the bottom + + align:start position:0% + + + + align:start position:0% + +here it is again with a current of 30 to + + align:start position:0% +here it is again with a current of 30 to + + + align:start position:0% +here it is again with a current of 30 to +40 amperes + + align:start position:0% + + + + align:start position:0% + +the coil doesn't lift off but the + + align:start position:0% +the coil doesn't lift off but the + + + align:start position:0% +the coil doesn't lift off but the +induced current does make the ground + + align:start position:0% +induced current does make the ground + + + align:start position:0% +induced current does make the ground +plane very hot our coil has the making + + align:start position:0% +plane very hot our coil has the making + + + align:start position:0% +plane very hot our coil has the making +of a burner first stove our thin sheet + + align:start position:0% +of a burner first stove our thin sheet + + + align:start position:0% +of a burner first stove our thin sheet +could be the bottom of a pan our + + align:start position:0% +could be the bottom of a pan our + + + align:start position:0% +could be the bottom of a pan our +experiment has been turned upside down + + align:start position:0% +experiment has been turned upside down + + + align:start position:0% +experiment has been turned upside down +the protective border prevent spillage + + align:start position:0% +the protective border prevent spillage + + + align:start position:0% +the protective border prevent spillage +let's turn the current up and let it + + align:start position:0% +let's turn the current up and let it + + + align:start position:0% +let's turn the current up and let it +heat for a while + + align:start position:0% + + + + align:start position:0% + +it takes a while but it does cook + + align:start position:0% + + + + align:start position:0% + +the experiment demonstrates the magnetic + + align:start position:0% +the experiment demonstrates the magnetic + + + align:start position:0% +the experiment demonstrates the magnetic +induction of current in conductors and + + align:start position:0% +induction of current in conductors and + + + align:start position:0% +induction of current in conductors and +both the resulting Lorenz magnetic force + + align:start position:0% +both the resulting Lorenz magnetic force + + + align:start position:0% +both the resulting Lorenz magnetic force +of repulsion and the heating \ No newline at end of file diff --git a/Y8zx1tWEbeI.txt b/Y8zx1tWEbeI.txt new file mode 100644 index 0000000000000000000000000000000000000000..5cfe574c0bd5e8d3e67a3cf990f99ac21836231b --- /dev/null +++ b/Y8zx1tWEbeI.txt @@ -0,0 +1,547 @@ +Hi. + +In this problem, we'll get +more practice using + +conditioning to help +us calculate + +expectations of variances. + +We'll see that in this problem, +which deals with + +widgets and crates, it's +actually similar in flavor to + +an earlier problem that we +did, involving breaking a + +stick twice. + +And you'll see that in this +problem, we'll again use the + +law of iterated expectations and +the law of total variance + +to help us calculate +expectations of variances. + +And again, we'll be taking the +approach of attacking the + +problem by splitting into the +stages and building up from + +the bottom up. + +So in this problem, what we +have is a crate, which + +contains some number of boxes. + +And we don't know how +many boxes are. + +It's random. + +And it's given by some discrete +random variable, n. + +And in each box, there are +some number of widgets. + +And again, this is +also random. + +And in each box, say for Box +I, there are xi number of + +widgets in each one. + +What we're really interested +in in this problem is, how + +many widgets are there +total in this crate? + +So in the crate, there are +boxes, and in the boxes, there + +are widgets. + +How many widgets are there +total within the crate? + +And we'll call that a +random variable, t. + +And the problem gives +us some information. + +It tells us that the expectation +of the number of + +widgets in each box for all +the boxes is the same. + +It's 10. + +And also, the expectation +of the number of + +boxes is also 10. + +And furthermore, the variance of +x of the number of widgets + +and the number of +boxes is all 16. + +And lastly, an important fact +is that all the xi's, so all + +the widgets for each box, and +the total number of boxes, + +these random variables +are all independent. + +So to calculate t, t is just +a sum of x1 through xn. + +So x1 is the number of widgets +in Box 1, z2 is the number of + +widgets in Box 2, and all +the way through Box n. + +So what makes this difficult +is that the + +n is actually random. + +We don't actually know how +many boxes there are. + +So we don't even know how many +terms there are in the sum. + +Well, let's take a slightly +simpler problem. + +Let's pretend that we +actually know there + +are exactly 12 boxes. + +And in that case, the only thing +that's random now is how + +many widgets there +are in each box. + +And so let's call [? sum ?] a +new random variable, s, the + +sum of x1 through x12. + +So this would tell us, +this is the number of + +widgets in 12 boxes. + +All right. + +And because each of these xi's +are independent, and they have + +the same expectation, just by +linearity of expectations, we + +know that the expectation of s +is just 12 copies of the same + +expectation of xi. + +And similarly, because we also +assume that all the xi's are + +independent, the variance of +s, we can just add the + +variances of each +of these terms. + +So again, there are 12 copies +of the variance of xi. + +So we've done a simpler version +of this problem, where + +we've assumed we know what +n is, that n is 12. + +And we've seen that in this +simpler case, it's pretty + +simple to calculate what the +expectation of the sum is. + +So let's try to use that +knowledge to help us calculate + +the actual problem, where +n is actually random. + + + +So what we'll do is use the law +of iterated expectations. + +And so this is written in terms +of x and y, but we can + +very easily just substitute in +for the random variables that + +we care about. + +Where in this case, what we see +is that in order to build + +things up, it would be helpful +if we condition on something + +that is useful. + +And in this case, it's fairly +clear that it would be helpful + +if we condition on n, +the number of boxes. + +So if we knew how many boxes +there were, then we can drop + +down to the level of widgets +within each box. + +And then once we have that, we +can build up and average over + +the total number of boxes. + +So what we should do +is condition on n, + +the number of boxes. + +So what have we discovered +through this + +simpler exercise earlier? + +Well, we've discovered that if +we knew the number of boxes, + +then the expectation of the +total number of widgets is + +just the number of boxes times +the number of widgets in each + +one, or the expectation of the +number of widgets in each one. + +So we can use that information +to help us here. + +Because now, this is basically +the same scenario, except that + +the number of boxes +is now random. + +Instead of being 12, it +could be anything. + +But if we just condition on +the number of boxes being + +equal to n, then we know +that there are + +exactly n copies of this. + +But notice that n here +is still random. + +And so what we get is that the +expectation is n times the + +expectation of the number of +widgets in each box, which we + +know is 10. + +So it's expectation of 10 +times n or 10 times the + +expectation of n, which +gives us 100. + +Because there are, on +expectation, 10 boxes. + +So this, again, makes +intuitive sense. + +Because we know that on average, +there are 10 boxes. + +And on average, each box +has 10 widgets inside. + +And so on average, +we expect that + +there will be 100 widgets. + +And the key thing here is that +we actually relied on this + +independence. + +So if the number of widgets in +each box vary depending on-- + +or if the distribution of the +number of widgets in each box + +vary depending on how many +boxes there were, then we + +wouldn't be able to +do it this simply. + + + +OK, so that gives us the answer +to the first part, the + +expectation of the total +number of widgets. + +Now let's do the second part, +which is the variance. + +The variance, we'll again use +this idea of conditioning and + +splitting things up, and use +the law of total variance. + +So the variance of t is going to +be equal to the expectation + +of the conditional variance +plus the variance of the + +conditional expectation. + + + +So what we have to do now is +just to calculate what all of + +these pieces are. + +So let's start with +this thing here, + +the conditional variance. + +So what is the conditional +variance? + + + +Well, again, let's go back +to our simpler case. + +We know that if we knew what n +is, then the variance would + +just be n times the variance +of each xi. + +So what does that tell us? + +That tells us that, well, if +we knew what n was, so + +condition on n, the variance +would just be n times the + +variance of each xi. + +So we've just taken this analogy +and generalized it to + +the case where we don't actually +know what n is. + +We just condition on n, and we +still have a random variable. + + + +So then from that, we know that +the expectation now, to + +get this first term, take +the expectation of this + +conditional variance, it's just +the expectation of n and + +the variance of xi, +we're given that. + +That's equal to 16. + +So it's n times 16, which we +know is 160, because the + +expectation of n, we +also know, is 10. + +All right, let's do this +second term now. + +We need the variance +of the conditional + +expectation of t given n. + +Well, what is the conditional +expectation of t given n? + +We've already kind of +used that here. + +And again, it's using the fact +that if we knew what n was, + +the expectation would just be n +times the expectation of the + +number of widgets in each box. + +So it would be n times the +expectation of each xi. + + + +Now, to get the second +term, we just take + +the variance of this. + +So the variance is the variance +of n times the + +expectation of each xi. + +And the expectation +of each xi is 10. + +So it's n times 10. + +And now remember, when you +calculate variances, + +[? if you ?] have a constant +term inside, when you pull it + +out, you have to square it. + +So you get 100 times +the variance of n. + +And we know that the variance +of n is also 16. + +So this gives us 1600. + +All right. + +So now we've calculated +both terms here. + +The first term is +equal to 160. + +The second term is +equal to 1600. + +So to get the final answer, +all we have to + +do is add this up. + +So we get that the final answer +is equal to 1760. + +And this is not as obvious as +the expectation, where you + +could have just kind +of guessed that it + +was equal to 100. + +So again, this was just another +example of using + +conditioning and the laws of +total variance and iterated + +expectations in order to help +you solve a problem. + +And in this case, you could kind +of see that there is a + +hierarchy, where you +start with widgets. + +Widgets are contained in boxes, +and then crates contain + +some number of boxes. + +And so it's easy to +just condition and + +do it level by level. + +So you condition on the +number of boxes. + +If you know what the number of +boxes are, then you can easily + +calculate how many widgets +there are, on average. + +And then you average over the +number of boxes to get the + +final answer. + +So I hope that was helpful. + +And we'll see you next time. \ No newline at end of file diff --git a/YenDB3yOfDc.txt b/YenDB3yOfDc.txt new file mode 100644 index 0000000000000000000000000000000000000000..d67c34d5956f87442ee8baa8f9e020950e822dec --- /dev/null +++ b/YenDB3yOfDc.txt @@ -0,0 +1,779 @@ +align:start position:0% + +this is a simple example where we want + + align:start position:0% +this is a simple example where we want + + + align:start position:0% +this is a simple example where we want +to just apply the formula for + + align:start position:0% +to just apply the formula for + + + align:start position:0% +to just apply the formula for +conditional probabilities and see what + + align:start position:0% +conditional probabilities and see what + + + align:start position:0% +conditional probabilities and see what +we get + + align:start position:0% +we get + + + align:start position:0% +we get +the example involves a four-sided die if + + align:start position:0% +the example involves a four-sided die if + + + align:start position:0% +the example involves a four-sided die if +you can imagine such an object which we + + align:start position:0% +you can imagine such an object which we + + + align:start position:0% +you can imagine such an object which we +roll twice and we record the first roll + + align:start position:0% +roll twice and we record the first roll + + + align:start position:0% +roll twice and we record the first roll +and the second roll so there are 16 + + align:start position:0% +and the second roll so there are 16 + + + align:start position:0% +and the second roll so there are 16 +possible outcomes we assume to keep + + align:start position:0% +possible outcomes we assume to keep + + + align:start position:0% +possible outcomes we assume to keep +things simple that each one of those 16 + + align:start position:0% +things simple that each one of those 16 + + + align:start position:0% +things simple that each one of those 16 +possible outcomes each one of them has + + align:start position:0% +possible outcomes each one of them has + + + align:start position:0% +possible outcomes each one of them has +the same probability so each outcome has + + align:start position:0% +the same probability so each outcome has + + + align:start position:0% +the same probability so each outcome has +probability 1 over 16 let us consider + + align:start position:0% +probability 1 over 16 let us consider + + + align:start position:0% +probability 1 over 16 let us consider +now a particular event B on which we're + + align:start position:0% +now a particular event B on which we're + + + align:start position:0% +now a particular event B on which we're +going to condition this is the event + + align:start position:0% +going to condition this is the event + + + align:start position:0% +going to condition this is the event +under which the smaller of the two die + + align:start position:0% +under which the smaller of the two die + + + align:start position:0% +under which the smaller of the two die +rolls is equal to 2 which means that one + + align:start position:0% +rolls is equal to 2 which means that one + + + align:start position:0% +rolls is equal to 2 which means that one +of the dice must have resulted in 2 and + + align:start position:0% +of the dice must have resulted in 2 and + + + align:start position:0% +of the dice must have resulted in 2 and +the other die has resulted in something + + align:start position:0% +the other die has resulted in something + + + align:start position:0% +the other die has resulted in something +which is 2 or larger so this can happen + + align:start position:0% +which is 2 or larger so this can happen + + + align:start position:0% +which is 2 or larger so this can happen +in multiple ways and here are the + + align:start position:0% +in multiple ways and here are the + + + align:start position:0% +in multiple ways and here are the +different ways that it can happen so a 2 + + align:start position:0% +different ways that it can happen so a 2 + + + align:start position:0% +different ways that it can happen so a 2 +2 or 2 3 a 2 4 then a 3 2 and the 4 2 + + align:start position:0% +2 or 2 3 a 2 4 then a 3 2 and the 4 2 + + + align:start position:0% +2 or 2 3 a 2 4 then a 3 2 and the 4 2 +all these are outcomes in which one of + + align:start position:0% +all these are outcomes in which one of + + + align:start position:0% +all these are outcomes in which one of +the dice has a value equal to 2 and the + + align:start position:0% +the dice has a value equal to 2 and the + + + align:start position:0% +the dice has a value equal to 2 and the +other die is at least as large so we + + align:start position:0% +other die is at least as large so we + + + align:start position:0% +other die is at least as large so we +condition on this event these results in + + align:start position:0% +condition on this event these results in + + + align:start position:0% +condition on this event these results in +a conditional model where each one of + + align:start position:0% +a conditional model where each one of + + + align:start position:0% +a conditional model where each one of +those five outcomes are equally likely + + align:start position:0% +those five outcomes are equally likely + + + align:start position:0% +those five outcomes are equally likely +Cindy since they used to be equally + + align:start position:0% +Cindy since they used to be equally + + + align:start position:0% +Cindy since they used to be equally +likely in the original model now let us + + align:start position:0% +likely in the original model now let us + + + align:start position:0% +likely in the original model now let us +look at this quantity the maximum of the + + align:start position:0% +look at this quantity the maximum of the + + + align:start position:0% +look at this quantity the maximum of the +two die rolls that is the largest of the + + align:start position:0% +two die rolls that is the largest of the + + + align:start position:0% +two die rolls that is the largest of the +results and let us try to calculate the + + align:start position:0% +results and let us try to calculate the + + + align:start position:0% +results and let us try to calculate the +following quantity the conditional + + align:start position:0% +following quantity the conditional + + + align:start position:0% +following quantity the conditional +probability that the maximum is equal to + + align:start position:0% +probability that the maximum is equal to + + + align:start position:0% +probability that the maximum is equal to +1 given that the minimum is equal to 2 + + align:start position:0% +1 given that the minimum is equal to 2 + + + align:start position:0% +1 given that the minimum is equal to 2 +so this is the conditional probability + + align:start position:0% +so this is the conditional probability + + + align:start position:0% +so this is the conditional probability +of this particular outcome well this + + align:start position:0% +of this particular outcome well this + + + align:start position:0% +of this particular outcome well this +particular outcome cannot happen if I + + align:start position:0% +particular outcome cannot happen if I + + + align:start position:0% +particular outcome cannot happen if I +tell you that the smaller number is 2 + + align:start position:0% +tell you that the smaller number is 2 + + + align:start position:0% +tell you that the smaller number is 2 +then the larger number cannot be equal + + align:start position:0% +then the larger number cannot be equal + + + align:start position:0% +then the larger number cannot be equal +to 1 so this outcome is impossible and + + align:start position:0% +to 1 so this outcome is impossible and + + + align:start position:0% +to 1 so this outcome is impossible and +therefore this conditional probability + + align:start position:0% +therefore this conditional probability + + + align:start position:0% +therefore this conditional probability +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +zero let's do something a little more + + align:start position:0% +zero let's do something a little more + + + align:start position:0% +zero let's do something a little more +interesting let us now look at the + + align:start position:0% +interesting let us now look at the + + + align:start position:0% +interesting let us now look at the +conditional probability that the maximum + + align:start position:0% +conditional probability that the maximum + + + align:start position:0% +conditional probability that the maximum +is equal to three given the information + + align:start position:0% +is equal to three given the information + + + align:start position:0% +is equal to three given the information +that event B has occurred it's best to + + align:start position:0% +that event B has occurred it's best to + + + align:start position:0% +that event B has occurred it's best to +draw a picture and see what that event + + align:start position:0% +draw a picture and see what that event + + + align:start position:0% +draw a picture and see what that event +corresponds to M is equal to three the + + align:start position:0% +corresponds to M is equal to three the + + + align:start position:0% +corresponds to M is equal to three the +maximum is equal to three if one of the + + align:start position:0% +maximum is equal to three if one of the + + + align:start position:0% +maximum is equal to three if one of the +dies resulted in a three and the other + + align:start position:0% +dies resulted in a three and the other + + + align:start position:0% +dies resulted in a three and the other +died resulting in something that's three + + align:start position:0% +died resulting in something that's three + + + align:start position:0% +died resulting in something that's three +or less so this event here corresponds + + align:start position:0% +or less so this event here corresponds + + + align:start position:0% +or less so this event here corresponds +to the blue region in this diagram now + + align:start position:0% +to the blue region in this diagram now + + + align:start position:0% +to the blue region in this diagram now +let us try to calculate the conditional + + align:start position:0% +let us try to calculate the conditional + + + align:start position:0% +let us try to calculate the conditional +probability by just following the + + align:start position:0% +probability by just following the + + + align:start position:0% +probability by just following the +definition the conditional probability + + align:start position:0% +definition the conditional probability + + + align:start position:0% +definition the conditional probability +of one event given another is the + + align:start position:0% +of one event given another is the + + + align:start position:0% +of one event given another is the +probability that both of them both of + + align:start position:0% +probability that both of them both of + + + align:start position:0% +probability that both of them both of +the two events occur divided by the + + align:start position:0% +the two events occur divided by the + + + align:start position:0% +the two events occur divided by the +probability of the conditioning event + + align:start position:0% +probability of the conditioning event + + + align:start position:0% +probability of the conditioning event +that is out of the probable total + + align:start position:0% +that is out of the probable total + + + align:start position:0% +that is out of the probable total +probability in the conditioning event we + + align:start position:0% +probability in the conditioning event we + + + align:start position:0% +probability in the conditioning event we +ask what fraction of that probability is + + align:start position:0% +ask what fraction of that probability is + + + align:start position:0% +ask what fraction of that probability is +assigned to outcomes in which the event + + align:start position:0% +assigned to outcomes in which the event + + + align:start position:0% +assigned to outcomes in which the event +of interest is also happening so what is + + align:start position:0% +of interest is also happening so what is + + + align:start position:0% +of interest is also happening so what is +this event the maximum is equal to 3 + + align:start position:0% +this event the maximum is equal to 3 + + + align:start position:0% +this event the maximum is equal to 3 +which is the blue event and + + align:start position:0% +which is the blue event and + + + align:start position:0% +which is the blue event and +simultaneously the red event is + + align:start position:0% +simultaneously the red event is + + + align:start position:0% +simultaneously the red event is +happening these two events intersect + + align:start position:0% +happening these two events intersect + + + align:start position:0% +happening these two events intersect +only in two places this is the + + align:start position:0% +only in two places this is the + + + align:start position:0% +only in two places this is the +intersection of the two events and the + + align:start position:0% +intersection of the two events and the + + + align:start position:0% +intersection of the two events and the +probability of that intersection is two + + align:start position:0% +probability of that intersection is two + + + align:start position:0% +probability of that intersection is two +out of 16 since there's 16 outcomes and + + align:start position:0% +out of 16 since there's 16 outcomes and + + + align:start position:0% +out of 16 since there's 16 outcomes and +that event happens only with two + + align:start position:0% +that event happens only with two + + + align:start position:0% +that event happens only with two +particular outcomes so this gives us 2 + + align:start position:0% +particular outcomes so this gives us 2 + + + align:start position:0% +particular outcomes so this gives us 2 +over 16 in the numerator how about the + + align:start position:0% +over 16 in the numerator how about the + + + align:start position:0% +over 16 in the numerator how about the +denominator event B consists of a total + + align:start position:0% +denominator event B consists of a total + + + align:start position:0% +denominator event B consists of a total +of 5 possible outcomes each one has + + align:start position:0% +of 5 possible outcomes each one has + + + align:start position:0% +of 5 possible outcomes each one has +probability 1/16 so this is 5 over 16 so + + align:start position:0% +probability 1/16 so this is 5 over 16 so + + + align:start position:0% +probability 1/16 so this is 5 over 16 so +the final answer is 2 over 5 we could + + align:start position:0% +the final answer is 2 over 5 we could + + + align:start position:0% +the final answer is 2 over 5 we could +have gotten that same answer in a simple + + align:start position:0% +have gotten that same answer in a simple + + + align:start position:0% +have gotten that same answer in a simple +and more perhaps more intuitive way in + + align:start position:0% +and more perhaps more intuitive way in + + + align:start position:0% +and more perhaps more intuitive way in +the original model all outcomes were + + align:start position:0% +the original model all outcomes were + + + align:start position:0% +the original model all outcomes were +equally likely therefore in the + + align:start position:0% +equally likely therefore in the + + + align:start position:0% +equally likely therefore in the +conditional model the five outcomes that + + align:start position:0% +conditional model the five outcomes that + + + align:start position:0% +conditional model the five outcomes that +belong to B should also be equally + + align:start position:0% +belong to B should also be equally + + + align:start position:0% +belong to B should also be equally +likely + + align:start position:0% +likely + + + align:start position:0% +likely +out of those five there's two of them + + align:start position:0% +out of those five there's two of them + + + align:start position:0% +out of those five there's two of them +that make the event of interest to occur + + align:start position:0% +that make the event of interest to occur + + + align:start position:0% +that make the event of interest to occur +so given that we live in B there's two + + align:start position:0% +so given that we live in B there's two + + + align:start position:0% +so given that we live in B there's two +ways out of five that the event of + + align:start position:0% +ways out of five that the event of + + + align:start position:0% +ways out of five that the event of +interest will materialize so the event + + align:start position:0% +interest will materialize so the event + + + align:start position:0% +interest will materialize so the event +of interest has conditional probability + + align:start position:0% +of interest has conditional probability + + + align:start position:0% +of interest has conditional probability +equals to 2/5 \ No newline at end of file diff --git a/YfmVSPS7EFI.txt b/YfmVSPS7EFI.txt new file mode 100644 index 0000000000000000000000000000000000000000..55eb788921ba186302567fdec284c8ef8fc6f3dd --- /dev/null +++ b/YfmVSPS7EFI.txt @@ -0,0 +1,7601 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Welcome to +STS.050, History of MIT. + +I'm Professor Mindell. + +This is Professor Smith. + +And before we introduce +ourselves or say anything + +about the class, I just +want to do a little exercise + +about what do you know +about the history of MIT, + +either big picture stuff +or even random facts. + +Yep. + +AUDIENCE: Used to be in Boston. + +PROFESSOR: Sorry. + +Used to be in Boston. + +OK. + +That is correct. + +PROFESSOR: Used to be +called [INAUDIBLE] Boston. + +As sort of a nickname. + +AUDIENCE: Don't remember. + +AUDIENCE: Boston Tech. + +PROFESSOR: Boston Tech. + +Yep. + +AUDIENCE: I think it +was founded in 1861. + +PROFESSOR: That's correct. + +PROFESSOR: Jeez. + +You don't need this class. + +PROFESSOR: Yep. + +AUDIENCE: I think +because of the Civil War, + +it had to wait to open. + +PROFESSOR: OK. + +That's correct, too. + +The American Civil War started +right after the founding. + +And there weren't any classes +taught for about four years. + +AUDIENCE: It was founded +by William Barton Rogers. + +PROFESSOR: OK. + +That's also good. + +PROFESSOR: What +was his nickname? + +AUDIENCE: Barty? + +[LAUGHTER] + +AUDIENCE: William Rogers. + +PROFESSOR: I don't +think he had a nickname. + +AUDIENCE: William Bart Rogers. + +PROFESSOR: Cool. + +Bart. + +PROFESSOR: What was it? + +Do you know? + +PROFESSOR: No. + +PROFESSOR: Billy? + +PROFESSOR: We had a house +master over at Burton Conner. + +We had a reunion the +other day, and they + +had a big picture +William Barton Rogers. + +And one of the students +came up and put a ID clip on + +and it said Billy. + +So maybe it's Billy. + +PROFESSOR: Somebody +sent me-- there + +is one sentence in all +of his papers and letters + +and records which shows +any amount of cheerfulness + +or playfulness, +which is, I think + +it was after his brother +died, he wrote to someone + +about six months later +said, I'm finally + +starting to feel brisk again. + +He was a serious guy. + +What else do we know about MIT? + +AUDIENCE: They got one of +the federal land grants. + +PROFESSOR: OK. + +Good. + +We'll certainly talk +about what that means. + +Yep. + +AUDIENCE: Me? + +PROFESSOR: Yep. + +AUDIENCE: I think at +least when it started out, + +there weren't any +female students. + +PROFESSOR: OK. + +That's true. + +No women at first, but later on. + +We'll also talk +a lot about that. + +Yep. + +AUDIENCE: At some point +there was discussion + +about wanting to +merge with Harvard. + +PROFESSOR: Oh, OK. + +Many points as it turns out. + +PROFESSOR: Yeah. + +Five or six. + +We don't have to just +talk about the founding + +in the early years. + +There's a lot of +time in between. + +So. + +Yep. + +AUDIENCE: It got a lot +of money from Polaroid + +to build a new campus. + +PROFESSOR: OK. + +MERRITT ROE SMITH: Polaroid? + +PROFESSOR: Polaroid? + +AUDIENCE: It was one of +the guys who started Kodak. + +PROFESSOR: Eastman Kodak. + +PROFESSOR: Kodak. + +Eastman Kodak. + +See, I knew he was gonna +jump on you because he's + +from Rochester, New York, +home of Eastman Kodak. + +PROFESSOR: That's right. + +Yeah. + +Polaroid is a Boston +company with ties to MIT, + +although not specifically +an MIT spin-off, + +starting in the +1930s, really getting + +going in the '50s and '60s. + +Whereas Eastman Kodak +started around the turn + +of the 20th century. + +Anybody know the +year that MIT moved + +across the river from +Boston to Cambridge? + +AUDIENCE: 1916. + +PROFESSOR: 1916. + +Right. + +So that's also a +pretty important date. + +Nobody's mentioned anything +that was invented here. + +Maybe nothing was. + +AUDIENCE: Radar. + +PROFESSOR: Sorry. + +AUDIENCE: There was a lot of +development for the radar-- + +PROFESSOR: OK. + +Radar, certainly. + +Anybody know where +the radar development + +took place physically? + +AUDIENCE: W 20. + +Or not W 20, Building 20. + +PROFESSOR: Yeah. + +PROFESSOR: Anybody +know where that was? + +AUDIENCE: Where +Stata is right now. + +PROFESSOR: Yeah. + +Right there. + +PROFESSOR: To give you an +idea how long I've been here, + +my first office +was in Building 20. + +And, the offices +in that building, + +it was like a WWII barracks. + +It was all made of +wood, basically. + +It's a wonder it +didn't burn down, + +all this stuff that +went on in there. + +But my office was huge. + +But the problem was +that by the time + +I got there, it was +pretty well run down. + +And there was a hole in +the wall and squirrels used + +to run around inside +and then dash out. + +Our colleague, Leo Marks, +you'll hear about today, + +had an even bigger-- +his office was + +like a one bedroom +apartment over there. + +It's really cool. + +A lot of stuff went on there. + +AUDIENCE: Which building +is better, 20 or Stata? + +PROFESSOR: I haven't had +enough experience in Stata + +to tell you. + +Stata visually, of course, +is far more interesting, + +but I hear it leaks. + +Building 20 didn't leak. + +AUDIENCE: Except +for the squirrels. + +PROFESSOR: Pardon? + +AUDIENCE: Except +for the squirrels. + +PROFESSOR: I still didn't hear. + +AUDIENCE: Except +for the squirrels. + +PROFESSOR: Except +for the squirrels. + +Yes. + +PROFESSOR: Building 20 was built +in, I think, under six months + +in 1940, 1941. + +PROFESSOR: Yeah. + +PROFESSOR: And it +lasted for 50 years. + +PROFESSOR: Well, it +was torn down what? + +10 years ago, maybe? + +PROFESSOR: Yeah, +not that long ago. + +PROFESSOR: Not so long ago. + +Long ago in your lifetimes. + +But in mine, a mere drop. + +PROFESSOR: Anything else? + +AUDIENCE: The +departments here have + +gone through a lot of changes. + +PROFESSOR: OK. + +The departments certainly have. + +Although a lot of them +are also quite similar. + +Yep. + +AUDIENCE: During the 1960s, +the basement of Building 10 + +was excavated for +a super laser that + +was designed to +bounce off a orbiting + +satellite out to +the Soviet Union. + +That was one of our +weapons in the Cold War + +that no one ever knew of. + +PROFESSOR: Oh. + +That's news to me. + +I didn't know about that. + +Ah. + +AUDIENCE: That's awesome. + +PROFESSOR: Is it still there? + +AUDIENCE: Yeah. + +It's a secret sub-basement. + +[LAUGHTER] + +PROFESSOR: You got +to take us on a tour. + +Does anybody know how much +secret research goes on + +on this campus? + +Military secret research? + +AUDIENCE: None anymore? + +PROFESSOR: That's right, none. + +Does MIT do any secret research? + +PROFESSOR: Yeah. + +AUDIENCE: Not that we know of. + +PROFESSOR: Well. + +[LAUGHTER] + +PROFESSOR: No? + +PROFESSOR: No? + +PROFESSOR: Actually, MIT does +a lot of secret research. + +It's just not-- + +PROFESSOR: Here. + +PROFESSOR: Here. + +Where is it? + +AUDIENCE: Lincoln Labs. + +PROFESSOR: Lincoln Labs +out in the suburbs. + +Yeah. + +So that's certainly a +thing we'll come across, + +too, is Cold War and +generally the relationships + +with the military. + +Anybody know what MIT's +budget is roughly? + +$100 billion? + +$100 million? + +AUDIENCE: Endowment's +like $8 billion. + +PROFESSOR: Yeah. + +Endowment's between $8 +billion and $10 billion, + +depending on how you count. + +What do we spend every year? + +About $1 billion. + +PROFESSOR: Really? + +My god. + +I didn't know it was that much. + +PROFESSOR: A big part of that +is actually at Lincoln Labs. + +I forget exactly. + +10% or 20%. + +AUDIENCE: I wonder +how many people-- + +PROFESSOR: Work. + +Including students? + +How many students are +there, first of all? + +Anybody know how +many undergrads? + +AUDIENCE: 4,000? + +PROFESSOR: What is it? + +It's like 4,100 today or-- + +PROFESSOR: Is it? + +Really. + +PROFESSOR: Around. + +It's about to grow a +little bit to about 4,500. + +How many grad students? + +AUDIENCE: 6,000. + +PROFESSOR: About the +same, 5,000 to 6,000. + +Then another 5,000 or so +faculty and staff people + +and other kinds of researchers. + +Anybody know how many +faculty there are? + +Roughly about 1,000. + +About 960 maybe. + +PROFESSOR: Does that +include adjuncts? + +PROFESSOR: No. + +AUDIENCE: Just straight +regular faculty. + +PROFESSOR: There aren't very +many adjunct faculty, actually. + +So, about 1,000 faculty. + +Interestingly, that number +has not grown more than 10% + +in the last 20 years. + +Whereas the budget and +the general size of MIT + +has about tripled +in that time frame. + +So, if you ever wonder why +the professor seem overworked, + +that's why. + +Anything else about +the history of MIT? + +Big accomplishments. + +AUDIENCE: Nobel Prize winners. + +PROFESSOR: Lots of Nobel +Prize winners for sure. + +AUDIENCE: Instrumentations +Lab during the Apollo program. + +And apparently like a +third of NASA's astronauts + +have been MIT educated +at some point. + +PROFESSOR: OK. + +Big connection to NASA. + +MIT built the computers +that landed on the Moon. + +I think about a third of the +people who walked on the Moon + +were MIT graduates. + +And about a third of the +total American astronauts + +had been MIT graduates, +which I think + +is more than anywhere else. + +And I think that also I +read a statistic where-- + +AUDIENCE: Other than +military academies. + +PROFESSOR: Sorry. + +AUDIENCE: Other than military-- + +PROFESSOR: Other than +the military academy. + +A third of all US +human space flights + +have had MIT graduates on them. + +We're gonna have a big astronaut +reunion this spring, actually, + +which you'll all be invited +to as part of the class. + +Not all of them but quite a good +number of them are coming back. + +So a lot of connections +to the space program. + +What else? + +PROFESSOR: Do you know who's +chairing the 150th anniversary? + +[LAUGHTER] + +PROFESSOR: So we'll talk +a little bit about that. + +Other facts about MIT? + +AUDIENCE: Was +high-speed photography + +developed by an MIT Professor? + +PROFESSOR: Not +exactly high-speed + +photography, but close. + +Anybody know what the actual +technical part of that is? + +AUDIENCE: He did the strobes. + +PROFESSOR: Electronic strobes. + +So up until not that long +ago, certainly in my lifetime, + +if you bought a camera, +it came with flashbulbs + +which were like +in a little cube. + +Anybody ever seen a flash cube? + +And they go pshh. + +And that was it. + +One picture and then +they'd turn around. + +And you'd get four per cube. + +And Edgerton invented what is +now on not only on your cameras + +but maybe even on your phones, +the actual electronic strobe. + +Which means that you could +fire it with a battery + +and it was basically usable +hundreds of thousands of times, + +which had made possible +high-speed photography. + +We'll talk about +that a little bit. + +Other interesting +facts about MIT? + +Anybody name a company that +was started by MIT graduates? + +AUDIENCE: Analog Devices. + +PROFESSOR: Analog +Devices is one. + +Sorry. + +AUDIENCE: Bose. + +PROFESSOR: Bose is one. + +AUDIENCE: iRobot? + +PROFESSOR: Sorry. + +AUDIENCE: iRobot. + +PROFESSOR: IRobot. + +AUDIENCE: A123 Systems. + +PROFESSOR: A123. + +AUDIENCE: Harmonics. + +PROFESSOR: Harmonics. + +AUDIENCE: TerraFusion. + +PROFESSOR: Sorry. + +AUDIENCE: TerraFusion. + +PROFESSOR: TerraFusion. + +AUDIENCE: Dropbox. + +PROFESSOR: Dropbox. + +That's right. + +I use Dropbox all the time. + +Not actually Polaroid. + +Raytheon was started +partly by MIT folks. + +MERRITT ROE SMITH: Miter. + +PROFESSOR: The +Miter Corporation. + +I'm just trying to think +a little bit further back + +into time. + +Anybody ever hear of the +Digital Equipment Corporation? + +That's kind of before this +generation a little bit. + +So obviously, nobody +said anything too much + +about computers. + +Lot of the work in +computing was done here, + +software, artificial +intelligence, robotics. + +Human Genome Project. + +Anybody ever hear of that? + +Significant fraction +of that was here. + +We'll come across 1,000 +things that you didn't even + +think of were here. + +OK. + +PROFESSOR: I think one +of the great inventors + +is still living here-- I mean +of the fairly distant past-- + +and that's Jay Forrester. + +Have you ever heard of him? + +What do you recollect, Eric? + +Pardon. + +AUDIENCE: The +Whirlwind computer. + +PROFESSOR: Whirlwind, yes. + +And why was that a +significant development? + +Do you remember? + +Well, you got the +Whirlwind all right. + +It's the first core memory. + +One of the first random-access +core memories, as I recollect. + +So it had great +significance to the building + +of the type of computers +that you're using + +and the desktops +and all of that. + +It was very, very basic. + +It's said that IBM +really made its money + +off the use of that development. + +And I was in conversations +many years ago + +in which President +Wiesner expressed + +some discontent about the fact +that IBM had not ponied up + +enough support money for +MIT because it had gotten so + +much from MIT in terms +of it's technical. + +I don't know how true that is. + +But Jerry Wiesner sure +was not happy about + +that, I know that much. + +PROFESSOR: Also, Whirlwind was +sort of the first real-time + +interactive-- + +PROFESSOR: Yeah. + +PROFESSOR: --computer, +which was-- + +PROFESSOR: Where did +the money come from it? + +Who supported that? + +AUDIENCE: Navy? + +PROFESSOR: Pardon. + +AUDIENCE: The navy? + +PROFESSOR: Well, partly +navy, partly air force. + +Yeah. + +A lot of military contracting +down here after World War II. + +We'll see that. + +I mean that's a big +part of the system. + +PROFESSOR: Anybody know where +the Whirlwind computer was back + +in the days when computers had +entire buildings themselves? + +It was on Mass Ave. in +the Barta Building, which + +is now where IS&T is. + +Anybody know where that is? + +PROFESSOR: Some people are +shaking their heads almost + +in disgust. + +[LAUGHTER] + +PROFESSOR: OK. + +So I just want to start with a +little brainstorming about some + +of the things that +are gonna come up + +over the course of the term. + +Maybe we'll introduce +ourselves first. + +I'll ask Professor Smith +to introduce himself, + +say a little bit about +his research and stuff. + +PROFESSOR: OK. + +Hi. + +My name full name is +Merritt Roe Smith, + +but I go by my middle name, Roe. + +And I'm a member +of two faculties + +here, the STS faculty that David +chairs and also the history + +faculty. + +And I've been here since 1979. + +So I've been here quite a while. + +And my research +interests are primarily + +in 19th century industrial +history and technology. + +And as I've said +to many friends, + +my expertise falls off +rapidly after World War I. + +But the good news is +that his picks up rapidly + +in that period. + +And so David is the +expert on the modern era + +of MIT's history. + +So we make a fairly good team. + +I will give the earlier +lectures on William Barton + +Rogers and things like that. + +I guess my main my +main research has + +been about machine tools +and the development + +of interchangeable +parts manufacturing. + +And I'm particularly +interested in that subject + +because that, too, was a +military-sponsored technology + +that had a tremendous +spin-off effect + +that once these new techniques +were developed for making guns, + +the machine tools and gauging +methods and things like that, + +were disseminated into all +sorts of manufacturing, + +one of the first +being sewing machines. + +So it was primarily +a technology used + +by women in which this gun +making technology found + +it's earliest applications. + +And then you can see it +spreading further out + +until you see the earliest +automobiles in the United + +States being made with very +similar methods that come right + +out of this old +gun-making industry. + +So those are the sorts +of things that I'm + +interested in basically is +how new technologies develop + +and how they get disseminated. + +PROFESSOR: So I'm David Mindell. + +As Roe mentioned, I'm in the +program in Science, Technology, + +and Society as an +historian of technology, + +which I'm the +director of, and also + +in aeronautics and astronautics. + +I'm actually an +electrical engineer + +interested in electronics +and control systems. + +But these days a lot +of my work in that area + +happens in the aerospace world +so I'm dual in AeroAstro. + +Most of my research is +focused, as Roe mentioned, + +on 20th century, some of +it military technology, + +particularly control +systems and feedback control + +and digital computers. + +And I wrote a book +about the Apollo program + +and the computers +that we mentioned + +before that were used +to land on the moon. + +And I'm generally interested +in human machine interaction + +and the ways the evolving +technology changes + +the rules of the users +and of the people who + +are operating systems. + +And that's still something +that I study today. + +Done a lot of work +in the undersea world + +doing exploration of the +deep ocean with robots. + +Anybody here ever participate +in the JASON project? + +In junior high? + +No. + +Did a lot of work with deep-sea +robots exploring shipwrecks + +around the world. + +And that still interests me. + +And now I work a +lot on space flight + +in aviation, too, and +what roles people have + +in technological systems +and how those roles change + +as technologies evolve +and how the engineers who + +build those technologies +think about people. + +There's really sort +of two or three things + +that led us to begin +teaching this class. + +This is the second +time we've taught it. + +We taught it last +spring as well. + +And one of them +is obvious, which + +is that, as you +probably all know, + +this semester is MIT's 150th +anniversary celebrations. + +And I've been chairing +the planning committee + +for those celebrations +for the last few years. + +And when I started doing that, I +didn't know anything about MIT. + +And in grand tradition, +when you don't know anything + +about a subject, you get a bunch +of students in a room and start + +teaching about it and you +all sort of learn together. + +And so that was part of +the idea for the class. + +And then another part of +the idea for the class + +was there's actually been only +in the last few years enough + +really professionally +written history about MIT. + +So that we won't spend +the whole term talking + +about just the +fraternities and sororities + +and the great inventions +and the sort of great man + +history of MIT. + +We'll do some of that. + +But there's also been +enough professional history + +where you can really +talk about what + +is the history of +science and technology? + +How does it evolve? + +How do technologies +and knowledge + +evolve-- which is really +what both Roe and I study + +in our different contexts-- +and use MIT as a lens + +through which to look at that +issue over the last 150 years. + +So we will be looking at some +of those larger questions. + +What counts as knowledge? + +How do engineers work? + +How do scientists work? + +How do they interact with +the larger society, both + +the politics and the culture +and the social questions? + +And how do they actually carry +on their work day to day? + +And what does it mean to invent +something or create a new idea? + +And fortunately, there's enough +material out there on MIT + +that we can examine +those questions + +through the history of MIT. + +And then it happened +that because Roe + +is a 19th-century expert and I +work more on the 20th century, + +we kind of got together and +roughly split the material. + +We'll go back and +forth quite a bit + +as well, especially this term. + +This term is a +little bit special, + +more than a little bit. + +It's a lot special and +a little bit different + +from last term in that the +actual 150th celebrations are + +going on as we're taking the +class and teaching the class. + +And so you'll see a +little bit about that + +as we pass out the syllabus. + +So that's just sort of a rough +introduction to the class. + +I also wanted to ask Michaela +Thompson to introduce herself + +as our teaching assistant. + +MICHAELA THOMPSON: Hi. + +I'm Michaela Thompson. + +I'm a third-year PhD +student in the HASS program. + +And I study, +basically, the history + +of biology and +environmental history. + +PROFESSOR: And among many +other cool facts about Michaela + +is that if you go to +the Boston Aquarium + +and see the penguins +swimming around-- + +MICHAELA THOMPSON: I'm +down in there with them. + +PROFESSOR: She's the lady in +the wetsuit feeding the penguins + +and swimming around with them. + +Maybe we'll take a field +trip and come see her + +when she's working one day. + +MICHAELA THOMPSON: +I will be there + +and I will wave at all of you. + +PROFESSOR: So maybe we +should pass out the syllabus + +and we can sort of walk through. + +Any questions on what +we've talked about so far? + +MICHAELA THOMPSON: Is +anybody missing a syllabus? + +PROFESSOR: Oh, we +already passed out. + +OK, good. + +I don't have one yet. + +So just to go through +the top, we really + +talked about this description. + +Again, there are +a number of themes + +that are in this sort +of first paragraph + +that will keep coming +up again and again. + +The relationship of MIT +to the surrounding city + +and the region and the country. + +Stories about MIT +students and professors. + +The student body and +who is an MIT student + +and how does that +person-- there is + +no typical profile, +or really at any time, + +but the student body +changes quite a bit + +over the course of +these 150 years. + +That's something +we'll be looking at. + +The physical development +of the campus. + +We talked about the move a +little bit across the river. + +MIT's relationship +with industry. + +That's a big one, which +is kind of a pendulum that + +swings every 10 years or so. + +Too much industrial involvement, +not enough relevance + +to industry, too much +industrial involvement, + +not enough-- practically +see-- maybe somebody + +can calculate the period +of that pendulum for us. + +It's pretty +predictable, actually. + +And then, also, +MIT's relationship + +to the government, +which you might guess + +moves almost exactly the same +as the relationship to industry + +but in the opposite direction. + +Where are we now in that swing? + +Does anybody want to +have a guess on that? + +I would say that we're probably +at the point of just beginning + +the swing beginning away from +government back toward industry + +for a while. + +Because the stimulus package +that Obama passed in 2008 + +was very, very +supportive of MIT. + +And that's about to run out. + +And generally the government +is about to run out + +of money altogether. + +And that's gonna be a big issue +for MIT in the coming five + +years or so. + +And naturally that swings +back toward industry. + +A little bit about requirements. + +We do want you to come +to class every week. + +We do want you to participate +in the discussions. + +We will ask for you to close +your laptops when we're + +having a class discussion, +which is generally + +gonna be the second +half of the class. + +You can use them for +the notes and things + +in the first half of the class. + +And then there's a series +of reflection papers, which + +is a significant amount of the +work over the course the term. + +We want you to submit +them online to the TA. + +And, let's see what's +the actual number. + +There are 11 class sessions +where there is actually + +reading that's assigned. + +And so we're gonna ask you to +submit eight reflection papers. + +So you can opt out +of any three weeks + +over the course of the term. + +And when you do +submit the papers, + +we would like them to have them +the night before by 5 o'clock. + +And there's a reason +for that, which is then + +we'll compile all the questions +and the thoughts the people + +have from those +reflection papers + +and use them as the starting +point for the discussion + +the following day. + +So we need to have those then. + +We're not gonna grade +them A, B, C, or D, + +but we do want to +see people thinking + +through what's on +the reflections. + +One to two pages is +all that is required. + +Then of those eight +reflection papers-- + +you'll notice when we +come to the syllabus + +that a number of the days +that we meet in class + +are concurrent with +the MIT 150th Symposia. + +And so if you like, you +can write reflection paper + +on the symposia instead of on +the readings for that week, + +with basically the +same requirements. + +And then they're going to be two +writing assignments, basically + +two papers, which we'll +send out the assignments + +for as the time goes closer. + +And one of the really nice +things about teaching it + +this term, even as +opposed to a year ago, + +is-- I'll show you +in a few minutes. + +There's a vast amount of +material, just raw material, + +on the web that's been made +available from which we can use + +as research materials +for these papers. + +So there's the breakdown of +the grading, 20% on the papers, + +big band on the +writing assignment, + +and then class participation. + +Although, somehow that +doesn't add up to 100. + +We must have missed a +line from last year. + +[LAUGHTER] + +PROFESSOR: We'll get +back to you on that one. + +Somehow we must have +edited something. + +Oh no, sorry, there's two +writing assignments, 70 + +and then 30. + +There's the absence policy. + +There's really only +one required book. + +I see one person's picked +it up already, which + +is the book that David +Kaiser-- our colleague-- edited + +called Moments of +Decision, which they had + +no intention of this when +they put this book together. + +But it really comes +out almost perfectly + +as a textbook for the course. + +Do you want to say anything +more about the book, Roe? + +PROFESSOR: Well, the +essays in it are not long. + +I'll tell you that. + +Each essay's around 15 printed +pages, 17, somewhere in there. + +So they're easily read. + +I've read the entire +book twice now. + +And I contributed +an essay to it. + +But quite apart from +my essay, I actually + +think these essays +are pretty damn good. + +And it's the sort of book that +you can use in this class. + +And then you could +turn around and give it + +to your parents or somebody +like that because it + +does a good encapsulated +history of MIT at certain-- + +it's not a complete +history of MIT. + +But it looks at the +critical moments. + +And I think it's a +good little book. + +I'll say that much. + +PROFESSOR: Good, I agree. + +I should say also next Tuesday, +February 15, from 4:00 to 6:00 + +we're having an event as +part of the 150th that + +is more or less the authors from +these books getting together + +to talk about the +history of MIT. + +And so you'd be welcome +to join us for that. + +And then there are going to be +additional readings, a fairly + +significant amount of them, +available on the MIT site. + +I'm sure you've all taken +humanities classes at MIT + +before. + +There's a lot of reading +in the humanities. + +That's sort of the equivalent +of the problem sets + +is reading through a fairly +large amount of material + +and absorbing it +and then fitting it + +into the rest of the material. + +So that's a very important +part of the class. + +And we do expect you to +spend sort of the equivalent + +amount of time that you +would spend on a problem set + +in a science class +on the reading. + +So just to go +through a little bit + +week by week, what +we'll do today, + +when we're done going +through the syllabus, + +I want to show you a little +video about the founding of MIT + +and then a little bit +about web resources. + +And then we'll take a +break, which we'll always + +do about halfway through +the three hour period + +because it is a +long time period. + +And during the break, +we'll give you extra time + +to read an article +that we'll pass out + +which is about the birth and +the idea of technology, which + +turns out is not a very old +idea and is almost exactly + +the same age as MIT. + +The t in MIT was one of the +very significant first uses + +of the word technology. + +And then we'll come back +for a little discussion + +of the ideas in that article. + +And then toward the +end of the class, + +Karen Arenson will come in. + +And she actually +is past president + +of the MIT Alumni +Association and Brass + +member of the Corporation. + +But also is a +journalist who conducted + +100 or so oral history +interviews with people + +about the last 40 years of MIT. + +And she'll talk a little +bit about that process. + +Then next week, we go way +back before even the founding. + +Do you want to say anything +about that week, Roe? + +PROFESSOR: Well +yeah, the second week + +is basically trying to put +MIT in a larger context. + +So I'm going to give a lecture +about the United States + +circa 1850, 1860, the years +that William Barton Rogers was + +beginning to formulate +this plan for what + +he called a +"polytechnic institute." + +And so the readings here, +there are two readings. + +One of them is from +a textbook that I + +was one of the co-authors of. + +It's the one that's listed +under Pauline Maier's name. + +Actually, the pages +you'll be reading + +there are pages +that I've written + +in the text on the +1850's basically. + +So you'll get my take on that +period from the textbook, + +basically. + +And then the other +reading is, I would say, + +a broader cultural, political +look at the United States + +between 1820 and 1860 that +looks very broadly at society. + +So that's even a bigger +picture of the United States + +during this period. + +And the idea here is +just to kind of immerse + +you in that period +to get you thinking + +about why was a +technical institute + +necessary at this point in time? + +Why 1861 and not 1900 +or sometime like that? + +It turns out that +MIT's founding, + +it occurs at a very +important moment in history. + +And one of the things I want +to talk about in my lecture + +is why 1861 basically. + +Why is this the +right moment to found + +an institute of technology? + +There's none other like +it prior to the Civil War. + +There were other engineering +schools, but not like MIT. + +MIT was different. + +And I'll say one thing +too about this place. + +The more I learn about MIT, +the more I'm amazed by it. + +It's really an +interesting place. + +And I didn't know much +about MIT's history + +until about two years +ago when I started + +preparing for this essay +on William Barton Rogers. + +But the more I learn about +it, the more captivated + +I've become by the history of +this place and all the things + +that it's done. + +I don't think there's another +educational institution, + +or surely a higher +educational institution, + +in the United +States that has had + +a more interesting history +than this place has. + +We're sure to get arguments +from people up the street. + +But that's just my own +personal perspective. + +It's quite a +remarkable institution. + +And it takes root in the +middle of the American Civil + +War of all times, one of +the worst possible moments + +to try to found a college. + +How did that happen? + +So that's what that second +week is basically about + +is how did this +place get started? + +And why? + +PROFESSOR: Because we'll +come across this then, too. + +The actual date of the +signing of the charter for MIT + +is April 10, 1861. + +April 12, 1861 is the +firing on Fort Sumter, which + +is the first combat +of the Civil War. + +So you'll see this next week. + +Poor William Barton Rogers +spends 30 years pursuing + +his dream and +finally achieves it. + +And then the whole country +blows up in his face basically. + +PROFESSOR: Not a good time. + +PROFESSOR: So the next +week too then we also + +focus on the founding +and the early years. + +You want to just walk through +this part of the syllabus? + +PROFESSOR: Yeah, the +third week will be mainly + +about William Barton Rogers and +his vision for the institute + +and how this place gets started. + +And in the essay you'll read +in this little book here, + +you'll see that I have some +things to say about the role + +the government played in +giving MIT the wherewithal + +to get started. + +The state of Massachusetts +grants it land over in Boston. + +And then it subvents it to the +tune of-- I don't know how many + +current dollars. + +But I think it's +around $300,000, + +a lot of money in those days. + +But without that money, +initial seed money + +basically, MIT would have had +an almost impossible time. + +Because once the +government of Massachusetts + +signed on to this place and +said, we'll give you a charter. + +We'll give you some land. + +And we'll give you some money. + +That gave a signal +to private donors + +that this place had a future. + +And that it was +worth investing in. + +And then, of course, there +were private donations + +that were very important too. + +But it's that sort of +story I want to talk about + +is how did Rogers get +the place started? + +And then who were the early +faculty that he recruited? + +Because it takes off in an +extremely interesting way + +and in a way that +really comports + +nicely with what MIT +is all about today. + +The original ideals of MIT +in 1865 and those today + +are not that different +in my opinion. + +There are differences. + +But the Mens et Manus +theme in the seal + +is a very interesting +and revealing way + +to think about this place. + +It hasn't changed. + +Well, it's changed, but-- +so that's the third week. + +And then the fourth week +is basically-- well, + +it's about two things. + +One of you mentioned +earlier about Harvard + +trying to take over MIT. + +And that's a fascinating story. + +Harvard makes that attempt +at least five times, + +if not six, starting in +1872 and continuing up + +until World War +I or thereabouts. + +And each time-- well, it comes +very close once in the early + +1900's. + +There was actually +a time when you + +could get a joint degree +from Harvard and MIT. + +And it was looking +very much like the two + +places might merge. + +But it never happened. + +But that's an interesting +story that all MIT alums like + +to talk about and +students I suppose. + +And then the other +part of it is how + +this new campus, the so-called +campus, that we're on today, + +how did that come about? + +And of course, it +wouldn't have happened + +without George +Eastman first of all. + +George Eastman put up an +amazing number of dollars + +to build the main part +of the campus here. + +The big dome +buildings and all that + +were all built +with Eastman money. + +And it's an interesting story +because I forget exactly how + +much he granted MIT initially. + +But President Maclaurin, +who was the president of MIT + +at that time, kept +going back to him. + +George, could you put a +little more on the till here? + +And each time he'd write a +check, very, very generous. + +And he wasn't a MIT graduate. + +I don't think he had +any MIT affiliation. + +But he employed +some MIT graduates. + +And I think that was +what-- he thought, + +they produce a good +product down there. + +I'm going to +support that school. + +And so that's basically +why he put up so much money + +to build a campus. + +But we'll have Mark +Jarzombek come in. + +He's written a book about the +physical facility or the campus + +itself, the building +of the campus. + +And he'll be the guest +speaker that day. + +And he has really +interesting things to say. + +He's written a book +about that topic. + +But they'll be some +good visuals that you'll + +be able to see in this too. + +PROFESSOR: And +that's really kind + +of the end of the +beginning for MIT. + +PROFESSOR: Yep. + +PROFESSOR: In that. + +And people at the +time, you'll see + +them say, up until that point +there was always money trouble. + +We never knew if we were going +to be around in five years. + +But once they move over +to this side of the campus + +and they build the +buildings, which + +puts them in a bit +of a hole for a while + +financially, but really is +the time that MIT arrived. + +And they feel like +that it's really + +become something that's +going to be lasting, + +only 50 years +after the founding. + +Then the next week we move +into what people sometimes + +call the progressive era, +the age of big business also. + +And actually our guest +speaker is Ross Bassett, + +who was a colleague of +ours, not from here. + +He's written a very interesting +piece, which we'll read, + +about students from India +coming to MIT in the 1930's. + +And there were only +about 20 or 30 students + +from India coming to MIT during +that whole 10 year period. + +But they were all from the 20 +or 30 most prominent families + +in India and went back +and did amazing things + +in their own countries as well. + +And that's the +sort of jumping off + +point for our conversation +about MIT's relationships + +with the rest of the world +and the positioning of MIT + +as a global university, which +is obviously a very big thing + +today. + +And again, there's +a lot of issues + +there during that +period about industry + +and the appropriate +role of industry. + +And people are +feeling at the time + +that MIT has gotten much +too close to industry. + +And professors are behaving +more like consultants + +than they are like scientists. + +And that all sort of +turns around in 1930. + +We'll talk about +that in week six, + +both the relationships with +the military during World War I + +and the hiring of +Karl Compton in 1930, + +who was the first +scientist-- I think + +he's the first scientist or the +first physical scientist who + +leads MIT and really +brings the institute back + +toward a basic science +foundation, which is still + +something that you'll see +in your own educations, + +and sets it up for the +second World War in a way. + +So that's the middle of March. + +Then in week seven there's one +of the symposia for the 150th. + +There are six symposia +over the course + +of the semester about +the 150th anniversary. + +And two or three +of them are meeting + +on a time that happens +to be a Monday. + +And I have to be +there all day anyway + +because I'm introducing it +and sort of put it together. + +And what we'll do is +we'll have class time just + +be attend the symposium. + +Now, you don't have to +actually attend the three hours + +1:00 to 4:00. + +We happen to know that's +free in your schedule. + +So that's a good time to go. + +But any three hours over +the course of those two days + +will be fine. + +And that one is about women +in science and engineering + +at MIT, which is a +pretty major part + +of the history in +the last 10 years + +here starting just about +10 years ago with a very + +famous report that came +out, which was, in a sense, + +nothing short of revolutionary. + +And actually, Lotte Bailyn, +who wrote the article + +in this book-- the Kaiser +book-- about that moment + +also was one of the key authors +of that women in science report + +and is one of the organizers +of that symposium. + +PROFESSOR: One other point +is to note now week six, + +we're dealing with +the '20s and '30s. + +And now in week +seven, we're kind + +of jumping chronological +a little bit + +to more current events. + +We have to do that +because the symposia is + +scheduled at this time. + +So there's going to be +some jumping around here + +that we can't avoid. + +But the themes are +sufficiently important that we + +think that going +to that symposia + +would be extremely +interesting and educational. + +PROFESSOR: Yeah, +on the one hand, + +we're roughly moving +chronologically + +over the course of the term. + +But inevitably, even as we've +been doing already today, + +we're going to jump around +throughout the 150 year history + +because things will come +up that are relevant today + +or things that were past. + +So the class is not organized +around the idea of suspense + +where wait and see what +happens in the 1980s + +that you'll only learn +in the last week. + +You're going to incorporate that +over the course of the term. + +Then on week eight, we're +going to actually meet + +at the MIT Museum +where they have + +a special exhibition about MIT. + +Has anybody been to +the exhibition so far? + +So they put that together +for the 150th anniversary. + +It almost reads like a syllabus +for the class in some ways + +and also does a really good +job of tying these larger + +themes together about +different kinds of innovation + +and education and how those +two things tie together. + +And Debbie Douglas, who was the +curator who put that together, + +will give us our personal +tour through that exhibit. + +It's not actually +part of class time. + +But then I just put on +the syllabus April 10 + +is the convocation, which +is the ceremonial center + +of the 150th anniversary. + +It's open to all faculty, +staff, and students and alums + +and happens down at the +Boston convention center. + +So I certainly +encourage you all to go. + +The governor of +Massachusetts will be there. + +Quite a number of other high +profile speakers will be there. + +And I'll show you +a little bit later + +about the mid-century +convocation, which + +happened in 1949, which +it's roughly modeled on. + +Then that very week, +actually it's the day after, + +is a symposium on computation +and the transformation + +of practically everything. + +Again, that one happens +to meet on a Monday. + +So class will just be attending +the symposium that day. + +Excuse me. + +Then we kind of pick up +our historical thread + +again with World War +II, also really quite + +a critical turning +point for the institute. + +One that I've done a +lot of work on that + +really begins to see +where we are today. + +Then we'll go into the Cold War. + +Again, one could teach an entire +class on MIT in the Cold War + +as one of our +colleagues, David Kaiser, + +actually teaches a class on +science and the Cold War. + +And then week 12, +we sort of bring it + +up to the last 40 years or so. + +And in a way, that's been +the hardest part of the class + +to teach because it's +not yet history as much + +as the rest of it is. + +And yet, it's still +in the making. + +And actually, the final +writing assignment really + +is partly to ask +you guys to help + +make that history of +the last 40 years or so. + +Because there's a +lot of things that + +haven't been written +about that we don't really + +know that some research +into the archives + +will really help us with. + +Although this year, we +have the oral histories + +that we didn't have last year. + +And I'll show you +those in a moment. + +So it's actually going to +be a pretty packed semester. + +There's a lot going on. + +It's a big history. + +There's a lot that happened. + +But we'll hope you'll get +some sense both for where + +the place that you're +going to school at + +came from, why you are expected +to take the classes that you're + +expected to take-- the +GIRs in particular-- what + +is the philosophy +behind the education + +that you're getting, no +matter what major you're in. + +How many people are +undergrads here by the way? + +Any grad students? + +Couple of grad students. + +And those are two +things-- we'll talk + +about how those two +things, the undergrad + +and the grad experience, +relate to each other. + +And hopefully at +the end of the term + +it will all make perfect +sense to all of you. + +Any questions about the +syllabus or assignments or any + +of those things? + +One of the really interesting +things about the 150th + +and about teaching the +class and writing this book + +and a lot of the other +things we're doing + +is that there isn't really +a fixed history of MIT. + +And as any historian +will tell you, + +what constitutes the history +of any subject changes + +in each generation and in a +sense is constantly rewritten. + +We like to think we don't +write too much of it + +according to today's +values and points of view. + +And at the same +time, we always know + +that we see things +from our point of view. + +And so you look back. + +And you see things that are +important in one generation + +that were less important in +another generation and vice + +versa. + +And what's been +really interesting + +about the last couple years +and the next few months + +is that we are again +rewriting the history of MIT. + +This book is one +attempt to do that. + +And one of the things +that came out of that + +was this little +video that I want + +to show you which, in a +way, really will anticipate + +a lot of the themes for +the reading for next week. + +It really gets us started on +how we think about these things. + +And over the course +of the 150 you'll + +see we put together about +five or six 12 minute videos + +on different aspects +of the institute. + +Some of them are +more historical. + +Some of them are +more current day. + +One of them focuses on +students and student life. + +One of them focuses +on entrepreneurship. + +And this one focuses +on the founding of MIT. + +And you'll see, maybe, a +familiar name or face in there. + +[VIDEO PLAYBACK] + +-Today's Massachusetts +Institute of Technology + +is a world class center +for teaching and research. + +Faculty, students, +and researchers + +are united in their +goal to advance + +the frontiers of knowledge and +solve contemporary real world + +problems, following the vision +laid out for MIT 150 years ago. + +But the place +itself has certainly + +evolved and flourished +since those early days. + +It's hard to imagine how much +the scientific landscape has + +changed from when founder +William Barton Rogers first + +started thinking about a new +kind of polytechnic institute. + +-William Barton Rogers +was born at the beginning + +of the 19th century. + +And that marks the beginning +of an extraordinary time + +in US history. + +It's really the +transition that we're + +going to witness over a century +from an agrarian, rural country + +into an urban and +industrial country. + +-We're beginning to see the +emergence of large cities, + +factories, railroads, canals, +all the early instruments + +of big time industry +in the United States. + +-There's surveying involved. + +There's mechanical engineering. + +There's geology. + +There's all kinds of +civil engineering. + +-The sense of possibility of +what this new technology would + +mean for the country was +very much on Rogers' mind. + +-William Barton Rogers had a +lifelong interest in education. + +And by 1835, he's a professor +at the University of Virginia. + +He soon signs on to +lead a geological survey + +for the state. + +Though he loves the project, +he has a big problem + +finding qualified workers. + +-Rogers' inability to hire +workers for his survey, + +that combined scientific +knowledge and the ability + +to use technical apparatus, +was a great problem + +to his way of thinking. + +He wasn't the only person +that needed an individual + +with that skill. + +The world was filled +with new industries. + +And they all needed people +that combined smarts and skill. + +-Eventually, Rogers +decides to leave behind + +the frustrations and +political turmoil + +he's encountered in +Virginia's slave society + +and moved north to the +vibrant city of Boston. + +-Boston was one of the +leading commercial centers + +of the country. + +And the area surrounding +Boston was without question + +the most developed industrially +of any state in the union. + +-There probably was +not an American city + +that had more of a need +for engineers than Boston. + +The city itself was +being transformed + +by one of the +greatest engineering + +projects of the 19th century, +the filling in of the back bay. + +-And then you had +these reform movements, + +temperance movements, +pacifist movements, + +and of course the famous +anti-slavery abolitionist + +movement. + +This was the place. + +Boston was so radical +in its reform spirit. + +-The wealth generated +by all of this industry + +Bostonians put into various +philanthropic enterprises, + +endowing schools, hospitals, +libraries, museums, + +various institutions which +benefit the broader community. + +-Rogers writes in +his memoirs how much + +he likes the so-called +enterprising spirit + +and even uses the word knowledge +seeking spirit of this area. + +-For decades, Rogers had been +talking with his brother Henry + +about a new kind of +polytechnic institution. + +-At the time, the +ideals of science + +really focused on fundamental +principles somewhat + +disconnected from the +real problems of industry + +and the people who +worked in industry. + +-They began thinking about +how to incorporate science + +into what they referred +to as the useful arts. + +Today we would call +that technology. + +-It's a revolutionary +idea that someone + +will go to school +to get training + +to become an architect, +an engineer, a scientist. + +These are typically +occupations that people + +would learn by doing. + +-This was experimental +from the get go. + +Even the word technology +was new at that time. + +-He wanted students who had +a grasp of human nature, + +of basic sciences, +of mathematics far + +beyond the requirements for +making this or that machine + +work. + +He wanted to train students who +would be able to kind of guide + +the nation through +industrialization, + +not just build the widgets. + +-Different players +are coming together, + +trying to bring a bunch of +different scientific and + +practical institutions together. + +And Rogers proves very skilled +at taking that set of people + +and orienting their ideas +toward his proposal. + +-They knew it was +going to be in Boston, + +and the land in Back Bay +was the place to put it. + +So they were going to have +to convince the Massachusetts + +state legislature +that not only was + +the school worth establishing, +but that it was worth + +designating a piece of land for. + +-The proposal was brought to +the state of Massachusetts. + +And the first step is to +essentially incorporate it + +as a state corporation. + +And that's what we celebrate on +the founding day of April 10, + +1861, when the governor +finally signs the MIT charter. + +-Just two days after MIT's +founding on April 10 in 1861, + +the first shots are fired on +Fort Sumter in South Carolina. + +And with the start +of the Civil War, + +it meant that classes at MIT +could not start right away. + +This proved fortuitous +for MIT, because it + +allowed them the opportunity +to raise additional funds-- + +to acquire the land, to start +construction, to hire faculty. + +-One can imagine that when +Rogers tried to raise money-- + +it's wartime, and energies are +being devoted to other things. + +Yet on the other +hand, if we have + +optimism about the +outcome of the war, + +we can see the necessity +for young men and women + +to become engineers +and scientists, + +to be able to solve +these other problems. + +-When the Morrill Act is +passed in Washington in 1862, + +it grants every state +some land that then they + +can either use or sell to found +an agricultural or mechanical + +institution. + +-Rogers and his +colleagues won support + +from the state +legislature that a portion + +of the funds from +the Land Grant Act + +would be dedicated +to this new school, + +assuming that they could raise +the other funds successfully. + +And then they had to go +out, house by house, factory + +to factory, and convince +people one at a time + +to donate funds to +support this enterprise. + +-As the war is ending in 1865, +the Massachusetts Institute + +of Technology holds +its first classes + +in rented space in downtown +Boston's Mercantile Building + +while constructing its own +buildings near Copley Square. + +Rogers' vision for a +new kind of education, + +with its emphasis on +hands on learning, + +made it crucial to establish +cutting edge laboratories. + +-Rogers had a very +strong reaction + +against what he +considered rote learning. + +And so from the beginning, +MIT was a great innovator + +in getting laboratory +work right down + +to the earliest levels +of the curriculum. + +Entry undergraduate +students would + +be entitled to do a lot of +work in the laboratories + +with their own hands, not +just seeing someone else + +demonstrate some effect. + +-Rogers needed +faculty who were going + +to be willing to invent +a new kind of curriculum. + +That they were going to +have to cobble together + +for the first time ever +laboratory exercises. + +-He allowed his professors to +basically experiment with it, + +tinker with it, adjust +it, and build the program. + +I think of Pickering in +physics, for example. + +Professor Storer, who was one +of the early chemists at MIT. + +And both of them +become very famous. + +And they're producing +textbooks to accompany + +the lab oriented +educational process. + +-You look at the +curriculum offered + +in that very first set of +classes at MIT in 1865-- + +it looks a lot like what we +call the GIRs today, the General + +Institute Requirements, that +still every freshman has + +to take. + +Mathematics, +chemistry, physics-- + +those are all required +at MIT from day one. + +-There was an emphasis on +combining basic science + +with applied things +in the field. + +Students took field trips to +all kinds of working places, + +where the technological +world was being built. + +And Barton Rogers +wanted all that right + +in the curriculum for +his undergraduates, + +right from the start. + +-As a young startup, +MIT had its share + +of hurdles-- ongoing money +troubles, takeover attempts + +by neighboring Harvard. + +But with every passing year, +with every successful student + +who went on to make his +or her mark in the world, + +MIT's reputation grew, +and the school's standing + +became more and more secure. + +By 1894, President +Francis Amasa Walker + +was able to declare +in his annual report + +that the battle of +the new education + +is won, proclaiming that +the influence of MIT + +and its innovative ways are +now recognized far and wide. + +-In the early years, the +MIT way of doing business, + +with a great deal of emphasis +on hands on and doing things + +in reality, contrasted +very substantially + +with the more classically +oriented education. + +But today, even for +those institutions + +which are more classically +oriented liberal arts, + +they have moved, +actually, towards MIT. + +-By the time operations +moved across the Charles + +to the brand new +Cambridge campus in 1916, + +MIT's ongoing future +seemed assured. + +Over the decades, the roadmap +Rogers laid out for his school + +has proved flexible +enough to stay + +true to his founding +ideals while incorporating + +new fields as they emerge. + +-There have been a +lot of continuities + +in the history of +MIT, especially + +around the type of +curriculum that students + +are required to follow. + +There's surely a greater +range choice today, + +but the emphasis on combining +science with practice + +is still an important +dimension of what + +is happening around +the Institute today. + +-That idea of mind and +hands-- mens et manus-- + +that goes right back to +the beginnings of MIT. + +And it's coincident +with the idea + +that learning takes place by +doing, as well just by seeing. + +-MIT today shows +remarkable commitment + +to the original vision +articulated by William Barton + +Rogers of a place that solves +great problems, that educates + +students who have +the capacity to be + +independent in their thinking. + +Those commitments are timeless, +and stretch across 150 years. + +[MUSIC PLAYING] + +[END VIDEO PLAYBACK] + +AUDIENCE: Is this part +of a bigger series, + +or is this just one? + +PROFESSOR: So as I +mentioned, there's + +five or six of these coming out. + +But it's not like the class. + +They're not going +chronologically. + +One is on entrepreneurship. + +One is on the student body. + +They'll each have a +little history in them, + +but it's not a +consecutive series. + +When they first +wanted to do this, + +they said, well, we'll +do one from 1861 to 1916. + +And we really pushed +them to go back + +into that earlier period, and +the background of the founding, + +and spend more time on that. + +Because the context, which +we'll read about next week, + +is so interesting and important. + +AUDIENCE: I feel like there were +three people who kept talking, + +and two of them were you two. + +Who was the third one? + +PROFESSOR: The third one-- the +woman was Debbie Douglas, who + +is the curator at +the museum, who + +we'll meet when +we go over there. + +And we'll also read a chapter +of hers, I think, in the book. + +AUDIENCE: How recently +did this come out? + +PROFESSOR: Two months ago. + +It was just released. + +It was released on +the day that 150th + +opened, which was January 7. + +So it's brand new, basically. + +Yeah, Michelle? + +AUDIENCE: Who produced it? + +PROFESSOR: Who produced it? + +Larry Gallagher, who +heads AV, produced it. + +And then it was directed +by a woman named-- + +PROFESSOR: Maggie Villiger. + +PROFESSOR: Maggie Villiger. + +Actually, one of the interesting +things that we're doing + +is for each of five +of these videos, + +they're directed by +a different person. + +So it's not going to be a +consistent style across them. + +They're all going to have a +slightly different style, which + +should make it kind +of interesting. + +AUDIENCE: At the beginning, +I saw a lot of pictures + +with women in, for +instance, classrooms. + +Is that-- + +PROFESSOR: Good question. + +That's a good question. + +MIT actually admitted women as +special students quite early. + +Ellen Swallow Richards, who +was the first actual graduate, + +also graduated quite early. + +I think 1878 was the +year she graduated. + +PROFESSOR: Somewhere +around there. + +Somewhere in there. + +PROFESSOR: My alma +mater, which is + +Yale-- they started +admitting students in 1969. + +But MIT was way +ahead of that curve. + +Now, actually, it's +a good question + +to ask Karen about when she +comes here in a little while. + +Because she was a student here +in the early '70s, I think. + +And it was very different +from what it is today. + +It's not like there were-- +and I think even-- I got here + +in 1991, and I believe at +the undergraduate level, + +it was still only +about 30% women. + +And now it's more like +50% or 55% women, I think. + +So it's come up a lot +even in that period. + +So there have always +been women here, + +but the proportions +that you know of today + +are fairly recent. + +But again, if you look at +the Ivy League schools, + +they were in the +Stone Age compared + +to MIT with how they +handled and treated women. + +AUDIENCE: So you +guys in that video + +are saying that MIT sort of +grew out of and contributed + +to the Boston area at +the beginning, mostly. + +When did it sort of hit +international and national + +prominence and become like a +huge international technology + +institution? + +PROFESSOR: That's a really +good question, actually, + +and one of the +things we'll look at + +again and again all semester. + +I think as the +video talks about, + +New England was really +attractive to William Barton + +Rogers. + +There's every reason that +we could be celebrating + +the Virginia Institute of +Technology's 150th anniversary, + +but we're not. + +He felt Virginia was +not the place for this. + +That New England, +for reasons that Roe + +will talk about next week, +was much more suited to it. + +I would guess that already +by the late 19th century, + +a lot of the MIT graduates +are going out west, and doing + +the surveys and engineering +on the railroads + +and dams and water supplies. + +Fremont, one of the great +surveyor engineers of the west, + +was an MIT graduate. + +He was maybe even a faculty +member here, wasn't he? + +PROFESSOR: John Fremont? + +PROFESSOR: John Fremont. + +PROFESSOR: No, I don't think so. + +But I'm trying to remember who-- +there is someone in that guise, + +but it's not Fremont. + +I think, with reference +to your question + +about when does MIT +start to achieve + +an international reputation, +probably the real reputation + +comes during and +after World War II. + +I mean, that's +when MIT is really + +recognized as being a big +time place internationally. + +There were surely +hints of recognition + +in the late 19th +century, the 1890s. + +When Francis Amasa Walker, after +whom the Walker building is + +named, makes his +annual report-- I + +think it's in 1894 or +thereabouts-- in which he says + +the battle of the +new education is won, + +clearly he was making +a reference to the fact + +that MIT was being recognized +not only by American higher + +educational institutions, +but by that time, + +there were foreign +students beginning to come. + +It's very small +numbers, but still. + +So it's increasing, +but it really + +doesn't hit the big +center spot until-- I + +was going to say centerfold. + +That's not quite the right word. + +[LAUGHTER] + +PROFESSOR: But +until, I would say, + +World War II, +after World War II. + +So much was happening here, +and it really became famous. + +PROFESSOR: If you look in the +sciences, well into the 1930s, + +if you're a bright +young physicist, + +you're basically sent to +Germany to get your PhD. + +And that changes, +obviously, during the course + +of the second World +War, not least + +because the Germans kicked out +a lot of the good physicists + +and they all came here. + +And also in 1940, when Vannevar +Bush goes to Washington-- + +we'll talk about +this-- and really + +founds the whole wartime +research establishment, which + +includes the Manhattan Project, +includes the radiation lab, + +includes the whole modern way +that the federal government + +supports research, that's +when you see MIT people really + +literally at the right +hand of the president. + +I don't know that there +would be any senior MIT + +person in a national political +role before about then. + +We'll see over the course of the +term, but I don't think of one. + +Whereas after that, the first +presidential science adviser + +ever appointed is James +Killian, president of MIT. + +The second one, +under John F Kennedy, + +is Jerry Wiesner, who later +becomes president of MIT. + +On and on and on. + +And for the period +of the '50s and '60s, + +the place really acquires +that national-- but also + +during the '50s, MIT faculty, +much like they're doing today, + +are off abroad founding +engineering schools + +in the MIT model +all over the world. + +I once went to a conference +where I was seated at dinner-- + +it was an oil +industry conference-- + +the guy I was next to was +the associate oil minister + +for Iran, which is not the sort +of person that Americans meet + +very often at conferences, +because there aren't too many + +conferences where-- + +PROFESSOR: --you +have the Iranians. + +PROFESSOR: And I was +sort of like, gee, + +what is this going +to conversation. + +And he said, oh, MIT. + +My technical institute +in Tehran that I went to + +was founded by MIT +faculty on the MIT model. + +He had an enormous +respect for what + +MIT represented in that country. + +And that's true in a lot of +places in the Middle East, + +a lot of so-called developing +nations during that period. + +The Indian Institutes +of Technology-- + +it's not a coincidence, +IIT is what they're called. + +There are many of them. + +And so that's one of the ways. + +And it's of course +happening today in Singapore + +and other places in +Asia, particularly, + +that new institutes +are being founded + +with MIT's influence there. + +AUDIENCE: So did we do Caltech? + +PROFESSOR: Well, +Caltech-- anybody + +know what it was called +before it was the California + +Institute of +Technology, which has + +some resonance to the +name of this institution? + +It was called Throop College. + +And in the '20s or +in the '30s-- I'm + +forgetting exactly when-- +they changed the name to it + +California Institute +of Technology. + +For many years, just the +word "tech" meant MIT. + +And then gradually, all +these other institutes + +formed, where they became +Georgia Tech or Caltech + +or other places like that. + +And then the word, the +"tech" term, became generic. + +Most of you probably +don't refer to this place + +as "Tech," do you? + +When you're home +on break, you say, + +I've got to go back +to Tech for this. + +But for many years, that's +what people referred to it. + +Or they referred to +it as "Technology" + +in the 19th century. + +So yes, Caltech and +Stanford, very much so. + +The father of Silicon +Valley was a guy + +named Frederick Terman, who got +his PhD here in Vannevar Bush's + +lab in the late '20s and early +'30s, and then moved out west. + +And Stanford, again, +had been founded-- + +he didn't found +Stanford-- but he really + +built up the model +of a university + +as the center of a kind +of industrial region, + +with Hewlett and +Packard and many + +of those other +early entrepreneurs. + +And so there's a lot of that +kind of influence there. + +You'll see this a lot in the +reading in the next couple + +weeks-- useful arts. + +That's a phrase that +Leo talked about that + +comes up all the time. + +It's in the MIT +charter, I believe. + +And a useful way to think of +that is not art as in fine art, + +like you'd go to the Museum +of Fine Arts to see today, + +but art as in +artisanal, artisans-- + +you know, a brick layer, +a tile layer, a carpenter. + +Those were sort of more +what people referred + +to when they used the term +the "useful arts" then. + +The steam engine and the +locomotive is a machine. + +But a locomotive is +only a very small part + +of what it takes +to make a railroad. + +There's all this +civil engineering + +that goes involved in +laying the tracks, and maybe + +some surveying, and thinking +about it as a system. + +And then railroads +and telegraphs + +came up really +very much together. + +All the early telegraphs went +along the railroad routes + +in this country. + +And so you almost can't even +think about the railroad + +without thinking +about a telegraph. + +There was even a +book out recently + +called The Victorian Internet, +a kind of early information + +network that ran around. + +There's a famous +book by a guy named + +Alfred Chandler at +Harvard Business School. + +He talks about-- modern +management arose as actually + +between the Worcester +to Albany railroad. + +It was one of the first +long railroads in the world, + +in Western Massachusetts +and New York state. + +When that railroad was built, +it was longer than 60 miles. + +And they started running +into each other, the trains. + +And he said when you started +building railroads that + +were bigger than 60 miles, +all of a sudden-- hi, Karen. + +This is our speaker +for our next hour. + +But we're talking a little bit +about the idea of technology. + +When the railroad became +longer than 60 miles, + +it needed a whole +new organization just + +to coordinate who was +on the tracks when + +and keep the trains from +running into each other. + +And that's exactly the +same kind of period + +about which Leo Marx +is talking about, + +where suddenly you have +these people called managers. + +There's nobody in the +world called a "manager" + +before about 1840. + +And even then, they +rise only gradually + +over the course of +the 19th century. + +You have these people +called "managers." + +You have this +whole organization. + +Yes, you have machines. + +But a machine is not a +great way to describe it. + +And sure enough, right +about then, if you look, + +you have this word-- +it's not actually + +coined in 1829 by Jacob +Bigelow, but it is sort of + +brought into a modern usage-- +this word "technology." + +And Leo really writes +about why was it + +at this point in history you +needed a new word for this, + +and what did this new +word come to stand for. + +And even after 1829, the +word wasn't used very much + +until the T in MIT. + +It was really one of the first +significant uses of the word. + +And even then, you wouldn't +see people using the word + +technology like +they use it today + +until after World +War II, really. + +So you'd see a student +today in a lab might say, + +I made a new technology +for handling micropayments + +on the internet, or +something like that. + +You'd never see that in 1940. + +They would say, I +built an apparatus. + +They used that +phrase a lot, even + +though they were working at MIT. + +Technology is an abstraction. + +[INAUDIBLE] sort of [INAUDIBLE] +these different things. + +And then when people +start using it as a noun + +that actually has active agency +in the world, what is that? + +It's a very strange way to talk. + +And we won't talk about +it this way in the class. + +Technology doesn't force +people to do things. + +People build technologies. + +People like you +build technologies. + +People do things with machines. + +People are influenced by +certain kinds of forces. + +But technology itself is +this sort of invisible thing + +that exists out +there, that doesn't + +think, it doesn't have a mind, +it doesn't have an address, + +doesn't pay taxes. + +It doesn't order anybody around. + +Now, interestingly, +in his conception + +when he wrote this +paper, he had this idea + +that technology conjures up an +idea of white men in lab coats + +sort of sitting at lab benches. + +More and more, personal +technologies-- PCs + +and cellphones and things-- +if you look in the technology + +section of either the +bookstore or the newspaper, + +they don't even talk about +airplanes and railroads + +and ships and submarines. + +They talk about basically +personal information technology + +almost exclusively. + +So that word has come. + +And if you talk about +the tech sector, + +they almost always +mean the companies + +in Silicon Valley +and a few companies + +around here who do +this kind of stuff. + +I once had an experience-- +it was about 10 years ago + +already-- where Microsoft +gave a whole bunch of money + +to MIT-- I think +they still do it, + +it was what became what +is now called iCampus-- + +to do research projects in +technology and education. + +And the guy from +Microsoft came and said, + +OK, we'll give +$25 million to MIT + +for experiments in +technology in education, + +technology in education, +technology in education-- + +he kept repeating that phrase. + +I said, oh, that's interesting. + +And I raised my hand and I said, +what do you mean by technology? + +Do you mean like helicopters +and submarines and ships? + +And the guy said, oh, no, +no, I should clarify that. + +What we mean is +personal computers + +running Microsoft software. + +Oh, OK. + +As long as we're +clear on what we + +mean by technology in education. + +That's helpful. + +That was sort of +an extreme case, + +but you see that around a lot. + +But even then, it's +still worth-- I + +happen to be reading +a book by my colleague + +Sherry Turkle, which +you may have seen. + +It's been in the news a lot. + +She was on Stephen +Colbert a couple weeks ago + +talking about cellphone +use, and particularly + +teenagers and technology. + +It says, "Why do we expect +more from technology + +and less from each other?" + +She's a close colleague of mine +and of Leo Marx's, but she's + +constantly using the word +technology makes us do this, + +technology makes us do +that, when actually, + +it's how we relate +to our machines + +in a slightly different way. + +So we sort of start out +the class with this piece. + +And if you haven't finished it, +please do read the rest of it + +between now and +next week, to give + +a little bit of +historical perspective + +on what is the thing. + +We're at this Institute +of Technology-- + +what do we really mean by that? + +And the word can become so big +that it can kind of encompass + +anything and everything. + +You can ask the +same, by the way, + +about the word engineering. + +How many people are +here engineering + +majors of one kind or another? + +So almost everybody. + +Science majors? + +Any? + +One, two? + +And actually, the +profession of engineering + +has almost the exact same kind +of chronology as both the word + +technology and the +history of MIT. + +Does anybody know what +the first engineering + +school in the United States was? + +AUDIENCE: West Point. + +PROFESSOR: Yeah, West Point. + +1804. + +It was not MIT. + +Second one was Rensselaer +Polytechnic, RPI. + +And MIT was pretty much the +third one, but almost 50 years + +later-- almost 60 years +later from West Point. + +So engineering as +we know it today + +has its origins in what today +we call civil engineering, + +but actually was really +called military engineering. + +And all engineering +was basically-- + +up until the beginning +of the 19th century, + +all engineering was +civil engineering, + +which meant roads, +bridges, fortifications, + +a little bit of artillery work. + +And it's only in the course +of the mid 19th century + +that you get-- in fact, the +profession, the discipline + +of mechanical engineering, is a +post Civil War thing, organized + +around steam engines +and steam engineering. + +In fact, the MIT department +of mechanical engineering, + +as like many other departments +of mechanical engineering, + +is formed by Navy +steam engineers + +who come out of +the Civil War Navy. + +Electrical engineering +is even later. + +And all the other +kinds of engineering + +are even later after that. + +So you're all familiar with +the course number story at MIT, + +right? + +That the course +numbers are basically + +the chronology on +which they were added. + +So course one is what? + +AUDIENCE: Civil. + +PROFESSOR: Civil. + +The environmental +is added later. + +Actually pretty +recently, I think + +within the last 10 or 15 years. + +Course two, Mechanical +Engineering, comes next. + +Course three, Material +Science, anybody + +know when the phrase +"material science" comes from? + +That's a 1960s, +'70s, '80s phrase. + +What was it before that? + +AUDIENCE: Didn't it +used to be mining? + +PROFESSOR: Mining +and Metallurgy. + +So that's a much +more traditional way + +of thinking about that kind +of engineering, very, very + +old way of kind of engineering, +straight of alchemy, really. + +What's four? + +AUDIENCE: Architecture. + +PROFESSOR: Architecture, +also very early. + +Five is Chemistry, +also very early. + +Electrical Engineering, getting +to be a little bit later. + +That's an effect of the 1880s. + +And then, on up from there. + +AUDIENCE: Did course six used +to be something different? + +PROFESSOR: I think +course six was always + +Electrical Engineering. + +I'm not exactly sure when the +department itself was founded. + +It was probably around +the turn of the century. + +But certainly, mechanical +engineering is much older. + +And mechanical engineering +exists more or less prior + +to the science that supports it. + +In fact, most of the fundamental +science in thermodynamics + +is done because of problems +raised by steam engines. + +So it's not like the physicists +worked out the thermo + +and then they built +the steam engines. + +It's exactly the +other way around. + +Engineers built steam engines. + +And then, that raised +problems of thermo + +that people needed to solve. + +Whereas, electrical +engineering is much more-- + +you almost can't have +it without the physics. + +And it's much more +intimately tied with science, + +from its very foundings. + +So it's quite, in a way, +a much more different kind + +of engineering. + +Then you have AeroAstro as +Course 16, much later on. + +AUDIENCE: How can +Electrical Engineering + +come before Biology? + +PROFESSOR: Sorry? + +AUDIENCE: Or Physics? + +AUDIENCE: Yeah, why would +Electrical Engineering + +come before Biology? + +PROFESSOR: That's +a good question. + +And I think, A, +there were things + +that were taught at MIT +that weren't necessarily + +departments, so +various things at work. + +And we'll see, as we look +in the next few weeks, + +the early MIT is +a teaching school. + +It doesn't really become +a research institution + +until rather later, +in a fundamental way. + +And so biology was +the sort of thing-- + +and we'll see this-- that +they did at Harvard because it + +had very little practical +application, compared + +to other things. + +And Louis Agassiz, who was +the great Harvard biologist, + +got into a very public a war +with Charles Elliott, who + +was the president of MIT, +over the issue of evolution. + +And Physics-- you would think-- +would be an earlier department. + +And I'm not exactly +sure why that one + +was founded a little bit later. + +That's a good question. + +Yeah. + +AUDIENCE: What about those +that do not have numbers? + +PROFESSOR: Those are +mostly added later. + +Like my course, STS, +comes from the '70s. + +And I think also, in +general, you probably + +can find that +around the 15s, 16s, + +the numbering system +starts to break down. + +And it doesn't follow as +much of a rational pattern. + +Like, Course 21 is Humanities. + +Humanities have been around +for a long time at MIT. + +But they weren't incorporated +into a particular course, + +until after World War II. + +And again, then, some +of the earlier ones, + +like Mining and +Metallurgy, is transformed + +into Material Science and stuff. + +So past the first +15 or so, I think + +the chronology is a +little more complicated. + +AUDIENCE: Isn't course +nine fairly new, + +Brain and Cognitive Science? + +PROFESSOR: It is, but it +was Psychology before. + +So psychology has a +kind of older pedigree. + +And then, there were other +courses that were cancelled, + +like Applied Biology, famously +so, not that long ago. + +Another interesting way +to look at the history. + +So now, I would +like to introduce + +my friend and colleague, +Karen Arenson. + +And maybe, as I do, I'll call +up the page of the oral history. + +So people get a sense for what +the actual accomplishment looks + +like. + +And as I did mention +before, Karen + +is a former member of the +MIT Corporation, an alum, + +from I'm not quite +sure which year. + +KAREN ARENSON: '70. + +PROFESSOR: '70. + +So she has a lot of interesting +perspective on women at MIT, + +which we talked about +a little bit before, + +as well as a former +higher education + +journalist for The +New York Times. + +So she's seen what MIT looks +like in the context of a larger + +picture, as well as a member +the Council of the Arts, + +here at MIT. + +And in all of those +sort of capacities, + +we did this oral +history project. + +And she conducted not +all but a large fraction + +of these oral histories. + +So she's, at the +moment, probably + +heard more about the last +40 years of MIT's history + +than almost anybody +and maybe will + +incorporate all those things +in what she has to say. + +But while she's +starting to talk, + +let me call up the +oral history page + +because it's worth +having a look. + +And it's this +incredibly rich thing. + +KAREN ARENSON: Have any of +you looked at the oral history + +thing? + +I've just begun to. + +Hi, I was in your seat, not +in this room, many years ago. + +And when I was walking here +and passed near 26-100, + +I thought, 801, 802. + +They existed back +when I was a student. + +I've been asked to talk +today a little about who I am + +and where I came from, a little +about the Oral History Project, + +specifically, and then a little +about what I learned from it. + +And that's been the +challenging part. + +I fell in love with MIT when I +first visited it as an admitted + +freshman, back in +1966 and discovered + +that other people +talked my language. + +They thought quantitatively +and analytically. + +And they liked to +solve problems. + +And I think that's +still true today. + +And although many of +them were brilliant, + +they also turned out to be +nice people and friendly + +and unpretentious-- +I think a distinction + +from another place in +Cambridge-- and helpful. + +And I've never fallen out +of love with the Institute. + +And the Oral History +Project gave me + +a chance to explore areas +that I was familiar with, + +like economics and the +Alumni Association, + +and also areas that I knew +nothing about, like STS, which + +didn't exist when I was +here; Biotechnology, which + +didn't exist anywhere; +Engineering Systems. + +I applied to MIT +because I liked math. + +And I wanted to focus +on social problems. + +I didn't come here thinking +I would major in math. + +I thought Economics. + +And this place had the best +Economics Department then. + +It still does. + +And I majored in Economics +and in student government + +and in the newspaper. + +And lived at The +Tech an awful lot. + +I was one of 50 women +in a class to 900. + +They had built McCormick +Hall a few years before. + +And all of a sudden, the +numbers shot up to 50 + +per class, that had been +less than 20 before that. + +And by the time I graduated, +after all the Vietnam turmoil + +and society turning +inside out, they + +decided to make the +other dorms co-ed. + +And all of a sudden, there +was more room for women. + +The number of women shot +up, gradually, into the 30%. + +You're about mid +40s now, in terms + +of undergraduate population. + +I went from the +Economics Department + +here to the Public +Policy School at Harvard + +and did a master's degree. + +And the one thing I +learned was that I + +didn't want to +sit behind a desk, + +and maybe I should +be a journalist. + +I had lived at The +Tech all those years + +and at my student newspaper +in the high school. + +And it took me about +a year to land a job. + +But I landed it +at Business Week. + +I was lucky. + +I spent five years +there and then moved + +to The New York Times. + +Business journalism was +becoming more important. + +I love numbers. + +And it was a wonderful +career for me. + +Along the way, I remained +involved with MIT + +because I like the people. + +And as Professor +Mindell said, I served + +on the corporation and +the executive committee + +and discovered that +businessmen, who made up + +most of the corporation, +are actually + +pretty interesting people. + +And they had other lives. + +And they weren't the kind of bad +people we thought in the 1960s, + +when all business was bad. + +And nobody wanted to +go to business school. + +Because of my involvement with +MIT, The Times, at some point, + +they asked me to start writing +about higher education. + +That was an interesting topic. + +The only trouble was I had +to cut my ties with MIT. + +Because it would +have been perceived + +as a conflict of +interest or might + +have been a conflict +of interest. + +And so I had a period of about +13 years, when I pulled back. + +And I took a buy-out +from The Times in 2008 + +and began to reengage. + +And one day, I got a phone +call from out of the blue, + +from a guy named Paul Gray. + +Maybe some of you +have encountered him, + +a former president of MIT. + +And he asked if I would +conduct some interviews + +for this project they +had, oral history. + +And I didn't know +what oral history was. + +But it sounded interesting. + +And I'm not good at saying "no." + +And I said, sure. + +I hung up. + +And I started googling. + +And I discovered that +Columbia University + +was the center of oral history. + +They had this big +archive of world figures. + +A history professor +in the 1940s had + +started to do this thing +that hadn't existed before. + +So I visited Colombia +and talked with them + +and discovered that +what we were doing + +wasn't really oral +history, which + +tends to be much +more open ended. + +These things go one +for 40, 50, 100 hours. + +It's sort of sit back +and dump everything, + +in a very relaxed fashion. + +The MIT ones were +about two hours each, + +tied to the sesquicentennial. + +There had been a +planning committee that + +started about five +years ago, to say, + +150th anniversary is coming up. + +What should we do? + +And one of the things +they came up with + +was to gather some +interviews with people + +who had been important in the +development of the Institute, + +over the last 50 years. + +And they put together a +list of about 75 people + +and had hired a guy named +John Hockenberry, who + +has been on ABC, I think, +and National Public Radio. + +But he was a visiting +professor in the Media Lab. + +And he was the main person who +was going to do the interviews. + +They had a couple of +other people helping him. + +And at some point, +he got a new program. + +And he said, so +long, can't do both. + +And that's when I +got the phone call. + +So I came in part way through. + +He had already done a handful +of interviews, probably six + +or eight or 10, including +the former presidents who + +were still living. + +They had laid out a sort +of rough template of seven + +broad topic areas. + +They wanted to make +sure we asked people + +where they were born +and how they grew up; + +how they got to MIT, whether it +was as a student or a faculty + +member; whatever their +impressions of MIT; + +their role in the world of +MIT; how it had changed; + +and how it had +affected their lives. + +So if you sign on +to these things. + +And there are, I +think, about 102. + +I did 40 of them, over about +2 and 1/2 years, including + +your professor and +your other professor. + +He isn't here today. + +PROFESSOR: He had +to run out for-- + +KAREN ARENSON: OK. + +Anyway, I did both of them. + +Unfortunately, my +thesis adviser, + +Bob Solow, one of the +Nobel Prize winners, + +subsequently had +already been done. + +Samuelson had been done. + +I did Jim Poterba, +Lester Thurow. + +It was a sort of hit or miss. + +It depended on their +scheduling and mine. + +So I got to do some people I +knew and got thrown into some. + +I said, I don't know +anything about that. + +So I learned. + +And that actually +was the fun of it. + +As a journalist, I was very +used to interviewing people. + +I've been doing it +professionally for 35 years. + +But it was very different. + +I never had to do it +in front of a camera. + +And these interviews +were videotaped. + +I never had to worry about +a beginning, a middle, + +and an end. + +I could sort of start +somewhere and sort of go + +and come back to +it, say thank you. + +And if I forgot +something, I call up again + +or email and say, +oops, what about this. + +These were two-hour +sound bytes that + +were pretty much as +they were recorded. + +They weren't edited. + +Except for maybe, they took +out some "ums" and "you knows." + +But other than that, they're +pretty much as recorded. + +I was pretty compulsive +about preparing for them. + +I tried to learn +as much as possible + +about the people I was +going to interview. + +And I usually drew up about +12 to 14 pages of questions. + +Because I didn't want to +get to an hour and a half + +and have half an hour to fill +and think, oh, my goodness. + +What am I going to ask? + +It's not that I've ever had a +problem thinking of questions. + +But when you're on camera, +you can't just sort of + +sit there and think, hm. + +What do I do next? + +Some of the interviewees +answered questions + +at length, two, three, +five paragraphs. + +Sometimes, people answered +in two or three words. + +And the trouble +was I didn't know + +which it was going to be +because I didn't know them. + +When I prepared to +interview Noam Chomsky, + +the famous linguist and the +highly-visible political + +activist, there +was more material + +than you could +absorb in a lifetime. + +He'd written so many books. + +There were several +biographies about him, + +including his life at MIT +and what he thought about it. + +I think he's the most +interviewed man on earth, + +literally. + +I mean, there are days +when he'll schedule three + +or four interviews, five, +six, seven days a week. + +If you google Noam +Chomsky, there's + +a whole website where lots +of them are available. + +So if you're into that, +he's a fascinating man. + +But there was a lot more +than I could digest. + +I dipped into some of it. + +I ordered some of his books. + +I had some of them on my shelf. + +I read about him. + +But there was no way I was +going to understand it all. + +And then, at the other +end of the spectrum, + +there were people where you +could find almost nothing, + +like your provost Rafael Reif. + +I had a short biographical +sketch of him. + +I had a news release, +announcing that he + +was going to be provost. + +And then, there was this blank. + +Where did he come from? + +What did he do? + +It turned out, he was a +pretty interesting fellow, + +whose parents had +fled Nazi Europe + +and moved around Latin America. + +He grew up in Venezuela. + +He was a chess expert, +all this stuff. + +But you couldn't +find it anywhere. + +So I began to learn +about it by calling + +some of the people he worked +with, and little by little. + +I could've gone +into the interviews + +without knowing all this +and just sort of said, so + +tell me where you were +born and where you grew up + +and what you liked +to do as a kid. + +And did you tinker? + +But I liked to know +as much as I could. + +Because maybe he +wouldn't think something + +was interesting or +important that I would. + +And if I knew about it, I +could say, but what about this. + +So I did as much learning as +possible before each interview. + +And then, the two +biggest challenges + +were to figure out +what was important + +and how to pace the interview. + +There were all these topics +I was supposed to cover. + +And you didn't know +if they were going + +to talk fast or talk slowly. + +At the end of 40 interviews, +I still couldn't tell you how. + +I used to sit there very tense. + +The first hour +was OK because you + +figured whatever we covered. + +But then, it began to +be, do I have enough. + +Are we going to +have way too much? + +And how do I get everything in? + +So that's the process. + +What did I learn? + +I didn't have any +of these interviews + +to look at until +January 7, when they all + +went up on the website. + +And then, I said, I have to +do this panel on February 15. + +And it would be +really helpful if I + +could look at the interviews +and have the transcripts. + +Because the videos are +interesting, but it's hard. + +It's slow. + +They take two hours. + +If you read them, it's faster. + +And if you go to the +little unlock feature, + +it turns out you can +disengage from the voice. + +And you can even turn it off, +by just lowering your voice. + +It's a little hard to read down. + +I called the people who +are running them and said, + +can people download the +voice and listen on an iPod, + +while they're on treadmill? + +And they said, +hm, good idea, no. + +This is MIT. + +So anyway, I've begun +to go through them. + +They all meld together, +in a funny way. + +They were all my favorite +because pretty much all of them + +were fascinating +in different ways. + +So lessons I learned, +and I'm going + +to tell you some stories +and maybe too many. + +Probably the most +important lesson + +was that MIT is +indeed filled with + +amazing, brilliant, +creative people. + +For me, it was a dream +to be able to talk + +with so many of them. + +But it's actually +important because MIT + +is a special and +important institution. + +Because somehow, it manages +to attract them and hold them. + +It includes the students. + +Faculty say over and over +again that they stay here + +because they get +students like you, + +who are just really bright and +really interested and really + +driven. + +But the staff, the +alumni, the trustees. + +And when you begin to +put people like this + +in some kind of environment, +innovation happens. + +And that's what +MIT is known for. + +And it's not a coincidence. + +And you need an +environment where + +they can mix with +each other and create. + +And many of the interviewees +talk about that, + +during their two hours. + +One example is Bob Langer, +the chemical engineer + +and biotechnologist. + +When they called me and said, +he's this biotechnologist. + +I said, ew. + +I don't know anything +about that subject. + +But I fell in love with him. + +He's just amazing. + +He has more than 750 patents. + +He runs the biggest lab at MIT. + +And he's one of the guys who +said that what holds him here-- + +and I'm sure he's had offers +from anywhere and everywhere. + +He said, "It's the best place. + +It has exceptional students, +exceptional colleagues. + +I feel I can have the +greatest impact because + +of all those people." + +Or Donald Sadoway, I +don't know if any of you + +took his 3.091, which satisfies +the chemistry requirement. + +He talked about arriving here +as a post-doc from Toronto. + +He said, "I remember +when I first arrived. + +And I walked up the stairs, +the steps from that crosswalk + +at 77, and looked up at those +pillars and thought, well, + +you've really done it. + +This is high stakes, no more +big fish in a small pond." + +He'd been up in Toronto. + +"This is the real deal." + +So here's this big +guy and telling + +us what went through his mind. + +"And the early days +were very heady. + +I mean to be surrounded +with super bright people. + +I was postdocing with Julian. + +And the kinds of +people would come + +to visit him was just +a different world + +from the University of Toronto." + +So it's not only the people who +are here, but the people who + +came to see them, who +added to that whole, what + +makes MIT special. + +There were other common themes. + +Many of the people +at MIT started + +from really modest backgrounds. + +Many of them were +immigrants or children + +of immigrants, Joel Moses, the +former provost, Rafael Reif, + +the current provost, Claude +Canizares, the vice president + +for research and +associate provost. + +Many of them pointed +to serendipity, + +in the shaping of their +lives and their careers. + +That's a wonderful word, one +that the sociologist, Merton, + +who's the father of the Merton +here, did a whole book about. + +I think he called +it Serendipity. + +It would be easy to think that +all these brilliant people knew + +what they wanted to do +from the age of three + +and that they followed a +smooth, predictable path. + +When you're trying to figure +out should I do this or that, + +you think everyone +else knows what + +they're doing except for me. + +It ain't so. + +If you watch these videos, +over and over again, + +people talk about well, +I was going along. + +And then this happened. + +And suddenly, I was going along. + +And this happened. + +It really is striking. + +Most of them said +they had no grand plan + +and that luck +played a large role. + +One example was Bob +Horvitz, the MIT professor + +who won a Nobel Prize for +his research on worms. + +He was actually one of my +news editors at The Tech. + +He was two years ahead of me. + +He double majored in +Math and Economics. + +And he was ready to graduate +after three years anyway. + +But he got elected president +of the student government. + +So he stayed for another year. + +So he had to fill out a +fourth year of classes. + +He didn't know what to take. + +And one of his +fraternity brothers + +said, why don't you try a +biology class, course seven. + +So he took a bio course. + +And he fell in love with it. + +And six weeks into +the term, he thought, + +this is what I want to do, +not math, not economics. + +I want to do biology. + +But he was kind of embarrassed. + +Here he was a senior. + +And he was taking +his first class. + +And he wanted to +go to grad school. + +So we went up to his professor. + +And he was sort of apologetic. + +And he said, I want to go to +grad school, but you know. + +And the professor, whose +name was Cy Leventhal, + +told him not to worry. + +He had been a physics major. + +And he had gone to +graduate school in physics + +and gotten his PhD in Physics. + +And here he was +teaching biology at MIT. + +He said, so you're +starting early. + +So it really isn't +too late to figure out + +what you like to do and try +things and keep exploring. + +Woodie Flowers, the mechanical +engineering professor + +who started the big contest, +where you get a bag of stuff. + +And you have to build a +gadget that does something. + +And then, they have a +big contest at the end. + +And the different +little robotic machines + +compete with each other. + +That was Woodie Flowers. + +He didn't even plan +to go to college. + +I think he grew up in Alabama +or Arkansas, in a poor family. + +His family couldn't afford it. + +But his senior year in high +school, one of his teachers + +noticed that his arm +wasn't set right. + +He had broken it when he fell +out of a tree in second grade. + +And it had never +been fixed properly. + +And some teacher took +an interested in him + +and got it set right, I guess. + +They had to re-break +it or something. + +I don't know. + +But then, the orthopedic surgeon +looked at the elbow and said, + +you really need some rehab. + +You can't just walk out of here. + +And he wrote some kind +of letter to the state. + +And the state gave +Woodie Flowers + +what he called a rehabilitation +scholarship to college. + +And so we went to college. + +And at the end of college, +he was doing well. + +And his professor +said, you really + +ought to think +about grad school. + +And you really ought +to think about MIT. + +I mean, this isn't all Woodie +doing lots of homework. + +It's some chance +meeting with people + +who took an interest in him. + +Now undoubtedly, he worked hard. + +He was smart. + +He was creative. + +And so I don't think it's +a coincidence that people + +were taking an interest in him. + +But it wasn't his +planning out his life. + +Rafael Reif, the provost +I was telling you about, + +had several other older +brothers and one of them + +had come to study in the states. + +This is way before the internet. + +How do you learn about +colleges in the states? + +You go to the American embassy. + +They have a bunch +of college catalogs. + +And the one thing +he knew was that he + +didn't think he wanted +to experience winter. + +Venezuela's not a +place of winters. + +So he looked at California +schools, ended up at Stanford, + +didn't know a lot of English +when he came, translated hard + +for lots of hours the first +two semesters, did pretty well. + +And he was going to go home +to Venezuela to be a teacher. + +Only, he had a +brother at MIT and he + +thought he'd come visit +him before he went back + +to Venezuela. + +And one of his former +colleagues said, + +I thought you were going home? + +And he said, yeah, but +I'm going to go visit MIT. + +And the guy said, there's +a spot open there. + +So he said, well, +maybe I'll look at it. + +Of course, he got the +offer, told his wife, + +I think we're +going to stay here. + +Somebody told him you +put on lots of layers + +and you deal with +winter, so he's + +dealt with winter ever since. + +But again, sort of a chance +meeting with a former colleague + +who said, I know about a spot. + +But for that, he'd probably +be back in Venezuela teaching. + +He summed it up +by saying, "I had + +to change all the plans +at the last minute. + +It was just one of those +accidents of history + +that helped me a great deal." + +But you get this over and +over again in these videos. + +And it's really +kind of stunning. + +Other lessons from +the interviews-- + +I learned a lot +about MIT's history. + +You know, I'd heard of +William Barton Rogers, + +but it wasn't until I +started reading the Decisions + +book, which is +really a good read, + +and talked to Professor Smith, +for example, that I understood + +a lot more about MIT's +early years, the emphasis + +that William Barton Rogers put +on real scientific research, + +the people he drew +to support him, + +the efforts to merge Harvard +and MIT, several times. + +Luckily, it didn't happen. + +There was an interesting +chapter on MIT's Center + +for International Studies, +which had links to the CIA + +for a while. + +The CIA essentially +got it off the ground. + +By the end of World +War II, MIT was + +used to collaborating +with the government. + +It had provided lots of +help on things like radar. + +And so, when the +CIA asked for help + +in learning more about +communications and propaganda-- + +because it was +the Cold War, late + +'40s-- MIT said, sure, +why worry about it? + +So two of the interviews +are with people + +who were involved with the +center-- Donald Blackmer + +and Jean Shkolnikov. + +And they talk about the +center, and the protests + +against the center. + +There was a bombing in +the Herman building, + +and the eventual +break with the CIA. + +And they talk about +the development + +of political science at MIT. + +You were talking about how +different courses evolve, + +so course 14, 15, and 17 all +used to be glommed together-- + +economics, political +science, and management. + +At some point they were +separated, economics + +and management, first, +political science later. + +Probably would make a +good project for somebody + +to explore the different +courses and how they came along. + +Another historical chapter that +some interviewees talked about + +was the huge disruption +during Vietnam. + +The anti-war protests +that tore the campus apart + +in the late 1960s. + +So Noam Chomsky talked about +it from the perspective + +of an activist professor. + +Larry Bacow and I, I +got interviewed too, + +talked about it +from the perspective + +of the students who were there. + +Howard Johnson talks +about that period + +from the perspective +of a president. + +And then there was a guy +named Bill Pounds, who + +was dean of the Sloan +School at that point, who + +had followed Howard Johnson +as Dean of Sloan, who suddenly + +found himself appointed +by the president + +to head a committee to study the +role of MIT's two defense labs. + +He said that Howard +Johnson went out of his way + +to ensure that the membership +of this committee, which + +was sort of meant to placate +everybody as much as to figure + +out what to do, that the +president had gone out + +of his way to make sure +there were radicals + +and conservatives, that the +whole spectrum was represented. + +He said it was kind of +like a Noah's Ark, two + +by two, a radical, a +conservative, a radical, + +a conservative. + +And Bill stood up during +a raucous faculty meeting + +and announced that +the committee would + +start meeting the +following day-- a Saturday. + +I think he'd been given +two or three days notice. + +And this wasn't an area +he knew anything about. + +They would meet every +day from 9:00 to 5:00 + +until they reached a conclusion. + +He said that one +step that cleared + +the way for the +commission to even begin + +to talk to each other was +to give them as much time + +as they needed at the front +end, just to go around the room + +and let everybody talk about +their views on war and peace, + +universities and truth, +and all the other kinds + +of profundities, as he put it. + +And then they got down to +work, because they'd all + +sort of cleared their throats. + +He said it took about a +week or a week and a half. + +He also made observation about +being made dean of the Sloan + +School just a few years +after he'd arrived at MIT. + +And he said he hadn't +really understood the place. + +We all look up to deans as these +are all-knowing creatures who + +have put in lots of +time and get promoted. + +He said, here he was +dean, and he didn't really + +have much of a clue. + +And he said he thought +that becoming dean, quote, + +"might pull back +the curtain on MIT." + +Instead, he said, he +discovered that quote, + +"there was neither a curtain +nor anyone behind it." + +Kind of like the Wizard of Oz. + +He was an interesting +guy because he also + +headed the Rockefeller +Brothers office for a decade + +but was attached enough to MIT +so he commuted between Boston + +and New York the whole time, +running the Rockefeller's + +business and still +remaining here. + +Anyway, he's very articulate. + +It's another fun one to look +at, even if you've never + +heard of him before today. + +Another theme that +came up repeatedly + +was MIT's unusual +openness and flexibility. + +It seemed to be better +than many universities + +at accepting people whose work +didn't fit into neat boxes. + +And it was better +than most universities + +and allowing people to +cut across boundaries. + +I think when you're here, +you take it for granted + +that it doesn't matter +what school you're in. + +On other campuses, +it matters a lot + +you never see the other people. + +Again and again, +these were cited + +as really important +factors in allowing people + +to do innovative work. + +And I'm sure MIT isn't +perfect on this score, + +but it does appear to +really be different + +from other institutions. + +Chomsky, for example, +recalled his early efforts + +to have his ground breaking +work in linguistics published, + +only to be told that +there was no such field. + +I mean, he was the father +of modern linguistics. + +But MIT provided a +home from for him. + +His first teaching job was to +help graduate students cram + +for the language exams they +had to pass to get their PhDs. + +I don't know if PhDs +are still required + +to pass one or two languages, +but they were back in the '50s. + +He said, "in your +early 20s, you're + +thinking about +what you are doing. + +You don't really care +what the world thinks." + +Gradually, of course, his work +drew attention and respect + +and got published. + +Bob Langer, the biotech guy +I was talking to you about, + +had a similar story. + +He was a doctoral student +here in chemical engineering. + +And most of his classmates +went from chemical engineering + +to the petroleum industry. + +This is what you did. + +So he flew to Louisiana +to interview with Exxon. + +And the executives +there explained + +that if they could increase the +yield of some petrochemicals + +by one one hundredth +of a percent, + +they would make +billions of dollars. + +On his flight home he +was thinking of that. + +And he realized he had no +interest in doing any of that. + +But what would he do? + +Well, he kind of +wanted to change + +the shape of chemical +engineering and chemistry. + +So he started applying +for jobs to look + +like they would do that. + +But they didn't want him. + +Exxon would have +taken him, but-- so he + +kept looking and looking, +and eventually someone + +suggested that he go talk +to this cancer researcher + +at Harvard named Judah Folkman. + +Hiring a chemical +engineer in a cancer lab + +doesn't sound like +an obvious thing + +to do, especially back +when he was coming out. + +But Folkman was a +risk taker, and Langer + +made a stunning breakthrough +in finding a new approach + +to controlled drug delivery. + +That was his post-doc. + +He came back to MIT. + +He got hired, but his +path was still bumpy. + +He actually didn't get hired +into chemical engineering. + +They didn't think he was doing +chemical engineering type + +work, like petrochemicals. + +He went into this applied +biology, course 20 at the time. + +And they didn't love him either. + +But somehow he kept on. + +He said, "the path I wanted +to follow didn't exist," + +but he was hired. + +And there was +enough room for him + +to run and to start +publishing and earn tenure. + +And today he's one of the most +venerated figures in the field. + +You are another example +of crossing boundaries. + +I mean, I don't know if he's +told you about his background. + +He studied literature. + +He double majored in literature +and electrical engineering + +at Yale. + +That's a pretty unusual +set of double majors. + +And even after he +got here, he's been + +a bridge between the humanities +department and the engineering + +school. + +I think he's the only professor +with full appointments + +in both schools. + +So you'll have to get him +to talk during the semester + +about being this kind of bridge. + +But during the +interview, you said + +STS is not a discipline +for people trying + +to escape science +and engineering. + +It's really about +pulling them together. + +People talked about +their backgrounds. + +Lots of them were tinkerers. + +There are lots of good +stories about that. + +A lot of them did ham radio. + +Even the women who came-- as +a young girl, Brit d'Arbeloff, + +who holds a master's degree in +mechanical engineering from MIT + +and is a life member +of the MIT Corporation, + +her late husband was chairman +of MIT's Corporation, + +founded a big company +called Teradyne. + +But when she was a +little girl, her father + +was an engineer at this +appliance company in Chicago. + +And he brought home the +machines that he invented, + +things like the mix master. + +He worked on the hair +dryer and the toaster. + +So she used to play with them. + +She got out to Stanford. + +She said I was looking to get as +far from my parents as I could. + +And the engineering +professors there said, + +you don't want to +major in engineering. + +They didn't want a girl. + +But one of my favorite +tales that she + +told, she had to take welding, +and foundry, and machine shop-- + +only girls at Stanford had +to wear dresses and skirts. + +There was a dress code. + +So she knew she didn't want +to do welding in a skirt. + +So she used to put on her +jeans, and roll them up, and put + +a trenchcoat over them, +so nobody could see, + +even if it was 90 degrees +out, and go to class. + +They didn't give +her trouble there. + +Of course, she graduated +number one in her class. + +PROFESSOR: I walked by the +glass lab on Saturday afternoon + +and she was in there. + +KAREN ARENSON: She was there. + +She's now chair of the +Arts Council at MIT. + +Let me get one or two +others and then-- there + +were some incredible personal +stories in these interviews. + +And I think the one that +move me the most was + +Wesley Harris, who's a +professor of Aero and Astro. + +He's now associate provost +for faculty equity, + +as in diversity. + +He's the descendant of +slaves in the South. + +He grew up in segregated +Richmond, Virginia in the '50s. + +He was a good student. + +And in the '50s, the +University of Virginia + +simply didn't take blacks. + +They said go to one of the +historically black colleges. + +One exception was +engineering because there + +was no separate but equal. + +So his physics +teacher in high school + +said, you've got to go to +UVA and study engineering + +because they've got to +see that blacks can excel. + +So even though he wanted to +study physics, he went to UVA + +and studied engineering +to make the point. + +Some of this +professors, I don't know + +if they were the +ones he had teaching, + +but some of the professors there +threw cigarette butts at him. + +They spit on him. + +I mean, just an incredible tale. + +But he had mentors. + +And they helped him get through. + +They pushed him on to Princeton. + +He had an offer to come to +MIT, but his good old physics + +teacher from high school said, +you've got to go back to UVA + +and make a point that you can +be a professor and do it well. + +So here he was, sort +of, pushing his life + +in directions he probably +didn't really want to take + +and suffering because-- +to make a point. + +It's a kind of +civil rights battle. + +And he talks about this +during the interview. + +It made me go back +and look-- there's + +a big told by a guy named +Clarence Williams who + +did a lot of interviews +with blacks at MIT. + +I'd never read them before +I started reading them. + +It's amazing. + +Anyway, actually, the chairman +of the board, John Reed, + +who I also interviewed, +who was also + +the former chairman of +Citicorp, is an interesting set + +of personal tales. + +His parents were +American but his father + +was in the meat business. + +They lived in Latin America +most of his childhood. + +He grew up in Brazil +and Argentina. + +His father had gone to MIT. + +But to ease the transition +back to the states, + +he enrolled in +MIT's 3-2 program, + +started at a small liberal arts +college and then came here. + +And he describes his years +at MIT as being invisible. + +He said I would go to classes +and go back to my apartment. + +This is the guy who later became +head of Citicorp, head of MIT. + +He loved physical +chemistry but was + +too awed by the formidable +professor to even talk to him. + +He worked at Goodyear Tire for +a year on the assembly line. + +He had a rubber +workers union card. + +Amazing stories. + +When he was in the army, +he did something wrong + +and was assigned to clean +garbage pails for three days. + +He said, I assure you +that no one has ever + +washed them as well as I did. + +I was always enthusiastic +about whatever I was doing. + +It's a great skill. + +So these tales are buried +through these interviews. + +Anyway, I'd better wind down. + +There are more than +200 hours of video. + +They're fascinating +in different ways. + +They humanize this place in a +way it doesn't do for itself. + +I don't think there are +any plans to do a book + +or to keep going. + +I think it would be a shame to +stop the chronicling process. + +But I know that we'll be doing +some of your own probing, + +maybe the oral histories +will help a little. + +I just came from a meeting of +the council of the arts, which + +is having its 40th +anniversary next year. + +I'm doing a one line +commercial, if I may. + +Part of that, we were +thinking about doing + +a history of the council +and the arts at MIT. + +There are lots of documents +there are living people. + +As you all go about +figuring out what you're + +going to delve into for your +projects later, if any of you + +like the arts, this +would be a fun topic. + +And we'd love to +have one or more + +of you do a history of +the council for the arts. + +And we'd feature it next year. + +I don't know if there's any +time left for questions, + +but if there are. + +PROFESSOR: I want to take +a little time for questions + +but I also want to play this +little farm video they made. + +KAREN ARENSON: Oh, +that's a wonderful-- + +PROFESSOR: I'll show you, +you can look yourself + +at the interface +because you can actually + +search through-- you can do text +searches of all the interviews + +altogether. + +And you can search on a +particular keyword or topic. + +And then it'll also take +you right to that point + +in the video, of any video. + +And the video guys just +searched on the word farm. + +And from that little search, +they made this a little video. + +KAREN ARENSON: The first +guy is Bill Pounds, + +who I was telling you about, +the former dean of the Sloan + +school and Rockefeller. + +They don't identify him. + +[VIDEO PLAYBACK] + +-I grew up in Pennsylvania. + +And I have the distinction of +having been born on a farm. + +-I grew up on a farm. + +-So I was born on a +farm, if you will. + +-I grew up in Montana. + +I'm a cowboy at heart. + +-Father was a farmer. + +-We were in Sunbury, PA, +which is a rural community, + +farming community. + +-When my parents were +about 20 years old, + +they decided to +live a simpler life. + +And they basically moved +to rural West Virginia + +as a way of going +back to the land. + +-I rode and trained +horses as a child. + +-Well, I was brought up in +farm country of Pennsylvania. + +And I had my share of work +picking tomatoes and doing + +farm work. + +-So I grew up in +the bush, very much. + +I come from a fifth +generation Australian family + +and always very +much in the bush. + +-Between the time +I was 17 months old + +and five or six years +old, I spent on a farm. + +-So we went to Idaho when +I was nine years old. + +And we settled in a +little farming village. + +-We lived on a mini farm. + +-Well, I was born +on a cattle ranch, + +spent my youth on +a cattle ranch. + +-I think it had an +influence in the sense + +that farmers are entrepreneurs. + +And they are their own boss. + +And so I think that's sort +of settled into my psyche. + +-Hard work. + +You learn how to +focus on a farm. + +-People in the cities +romanticize the bush + +in the same way that Americans +romanticize the west. + +It's not to be +romanticized, actually, + +it's a pretty tough +and rough place. + +-It is kind of +strange for someone + +to grow up in a house with +not a lot of technology + +to become a faculty +member at MIT. + +But I became an +engineer, in part, + +because I was good at math, +and I liked problem solving. + +But I think the childhood +has influenced me + +in terms of how I +bias technologies. + +That is, I give +value to technologies + +that are maybe simpler or local. + +And I think that does come out +of my research and my work. + +[END VIDEO PLAYBACK] + +KAREN ARENSON: So, if you +go on the MIT 150 website, + +there's something called +Infinite History, which + +has the 100 oral histories. + +There's a separate +little category + +called Multimedia, which is +where this is tucked away, + +way at the bottom of +the right hand column. + +It's a bunch of videos that +include some oral history + +snippets, which this +was, and other stuff. + +PROFESSOR: If we have +the right interface, + +and I talked to the company to +do that, I would love to have, + +if you wanted, +for an assignment, + +to make little videos +like that snipping + +from these oral histories. + +But at the moment, we don't +quite have the interface to it. + +KAREN ARENSON: That +would be fabulous. + +PROFESSOR: But let's have +a few minutes for questions + +before we're all +done or comments. + +KAREN ARENSON: Three hours. + +Yeah. + +AUDIENCE: You said you +did 40 of the interviews, + +and there are 100 or so. + +KAREN ARENSON: I did 40. + +AUDIENCE: So who +did the other 60? + +KAREN ARENSON: There were +actually four other people, + +a graduate of MIT, he had been +an undergraduate in engineering + +and STS, did the +first dozen or so + +as a kind of feasibility study. + +And then John +Hockenberry, the NPR guy, + +got pulled in to do the project. + +And he probably did 8 or 10 +before he went out the door. + +He came back and +did one or two more. + +They had hired a local +journalist, Toby Smith, + +and she did, I think, +40, 45 of them. + +And them one of the guys in +the video lab, Larry Gallagher, + +did a handful. + +And the styles are different. + +Nobody was looking at them. + +My lead-ins are way too slow. + +I never saw one of them before. + +I kept thinking, these are +going into the archive. + +I need an intro to say, why +are we talking to this person. + +So I have pretty +substantial intros, + +and I talk way too slowly. + +But I had no idea until January +7, which is a real shame. + +I'd love to rerecord them. + +But Hockenberry's are more +like radio interviews. + +Toby pretty much starts +with where were you born? + +How did you grow up? + +So anyway, there are +several different styles-- + +probably good. + +Any other? + +AUDIENCE: You said you did +economics when you were here? + +So for people like +yourself, probably + +the majority of graduates, +who do something completely + +different than what +they studied, like, + +is there sort of a general +thing that you still + +retain from your +undergraduate education? + +I mean, obviously, +you don't really + +use economics day-to-day. + +What are the basic +things that people + +who go on to do different +things keep from MIT? + +KAREN ARENSON: You +mean just in general? + +AUDIENCE: Yeah, was it +a complete wast of time? + +KAREN ARENSON: Lots of people +go into law, medicine, business, + +a few people go into +journalism, not very many. + +I did economics and finance +journalism for 35 years + +before I did higher ed, so I was +using my economics background. + +I actually went back +to school and took + +finance, and accounting, +and financial institutions + +because I realized there +was a certain amount I just + +didn't know. + +But I did use my +economics background. + +And as a journalist, +a lot of journalists + +come from being English majors. + +Some of them are +journalism majors. + +There aren't very +many economics majors, + +but I was very analytical. + +So they all learned +how to write. + +I learned how to +look at numbers, + +and we sort of came +together in the middle. + +I had to learn how +to write on the job. + +Some of them learned +to use numbers. + +Some of them never did. + +When I was editing, I can +remember the first couple weeks + +I ran the Sunday business +section for the New York Times. + +And I got a big story in, and +one of the editors under me + +had worked it. + +And it came to me. + +And the story wasn't bad. + +And at the last minute, +the graphic arrived. + +And the story said this, and +the graphic looked like this. + +And I said, they don't agree. + +I killed it at that point. + +People, a lot of +journalists, at least back + +when I was starting +just were number-phobic. + +But I like to look at +stories as puzzles. + +In other words, how +did this happen? + +How did the pieces +come together? + +Kind of like an MIT +education trains + +you to look at the world. + +And that's how I looked +at it, even higher ed. + +So it was fun. + +PROFESSOR: Let's leave +it at that for today. + +Please join me in +thanking Karen. + +KAREN ARENSON: Good luck. + +[APPLAUSE] + +KAREN ARENSON: Thank you. \ No newline at end of file diff --git a/ZUU57Q3CFOU.txt b/ZUU57Q3CFOU.txt new file mode 100644 index 0000000000000000000000000000000000000000..0cd42b862b2d28d3c7d288cf25acf54d9c80f4fd --- /dev/null +++ b/ZUU57Q3CFOU.txt @@ -0,0 +1,6339 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +well ok so first important things about + + align:start position:0% +well ok so first important things about + + + align:start position:0% +well ok so first important things about +the course plans for the course and then + + align:start position:0% +the course plans for the course and then + + + align:start position:0% +the course plans for the course and then +I'm today I'm going to move to the new + + align:start position:0% +I'm today I'm going to move to the new + + + align:start position:0% +I'm today I'm going to move to the new +next section of the notes section 2 or + + align:start position:0% +next section of the notes section 2 or + + + align:start position:0% +next section of the notes section 2 or +part 2 I should say and actually I'll + + align:start position:0% +part 2 I should say and actually I'll + + + align:start position:0% +part 2 I should say and actually I'll +skip for the moment section 2 1 and go + + align:start position:0% +skip for the moment section 2 1 and go + + + align:start position:0% +skip for the moment section 2 1 and go +to section 2 2 and all the SEC's all of + + align:start position:0% +to section 2 2 and all the SEC's all of + + + align:start position:0% +to section 2 2 and all the SEC's all of +chapter 2 will come to you probably + + align:start position:0% +chapter 2 will come to you probably + + + align:start position:0% +chapter 2 will come to you probably +today or latest tomorrow so that's where + + align:start position:0% +today or latest tomorrow so that's where + + + align:start position:0% +today or latest tomorrow so that's where +we're going next we're following the + + align:start position:0% +we're going next we're following the + + + align:start position:0% +we're going next we're following the +notes pretty carefully except I'm going + + align:start position:0% +notes pretty carefully except I'm going + + + align:start position:0% +notes pretty carefully except I'm going +to skip the section on tensors until I + + align:start position:0% +to skip the section on tensors until I + + + align:start position:0% +to skip the section on tensors until I +learn more + + align:start position:0% +learn more + + + align:start position:0% +learn more +basically yeah yeah I could say a little + + align:start position:0% +basically yeah yeah I could say a little + + + align:start position:0% +basically yeah yeah I could say a little +about tensors but this flows this flows + + align:start position:0% +about tensors but this flows this flows + + + align:start position:0% +about tensors but this flows this flows +naturally using the SVD so it's just + + align:start position:0% +naturally using the SVD so it's just + + + align:start position:0% +naturally using the SVD so it's just +terribly important problem least squares + + align:start position:0% +terribly important problem least squares + + + align:start position:0% +terribly important problem least squares +and of course I know that you've seen + + align:start position:0% +and of course I know that you've seen + + + align:start position:0% +and of course I know that you've seen +one or two ways to do least squares and + + align:start position:0% +one or two ways to do least squares and + + + align:start position:0% +one or two ways to do least squares and +it's really the whole subject comes + + align:start position:0% +it's really the whole subject comes + + + align:start position:0% +it's really the whole subject comes +together here I want to say something + + align:start position:0% +together here I want to say something + + + align:start position:0% +together here I want to say something +before I send out a plan for looking + + align:start position:0% +before I send out a plan for looking + + + align:start position:0% +before I send out a plan for looking +ahead for the course as a whole so + + align:start position:0% +ahead for the course as a whole so + + + align:start position:0% +ahead for the course as a whole so +there's no final exam and I don't really + + align:start position:0% +there's no final exam and I don't really + + + align:start position:0% +there's no final exam and I don't really +see how to examine you how to give tests + + align:start position:0% +see how to examine you how to give tests + + + align:start position:0% +see how to examine you how to give tests +I could of course create our tests use + + align:start position:0% +I could of course create our tests use + + + align:start position:0% +I could of course create our tests use +it on about the linear algebra part but + + align:start position:0% +it on about the linear algebra part but + + + align:start position:0% +it on about the linear algebra part but +I don't think it's it's not sort of the + + align:start position:0% +I don't think it's it's not sort of the + + + align:start position:0% +I don't think it's it's not sort of the +style of this course to + + align:start position:0% +style of this course to + + + align:start position:0% +style of this course to +to expect you quickly to create a proof + + align:start position:0% +to expect you quickly to create a proof + + + align:start position:0% +to expect you quickly to create a proof +or something in in our class but I think + + align:start position:0% +or something in in our class but I think + + + align:start position:0% +or something in in our class but I think +so I think and especially looking at + + align:start position:0% +so I think and especially looking at + + + align:start position:0% +so I think and especially looking at +what we're headed for and moving quite + + align:start position:0% +what we're headed for and moving quite + + + align:start position:0% +what we're headed for and moving quite +steadily in that direction is all these + + align:start position:0% +steadily in that direction is all these + + + align:start position:0% +steadily in that direction is all these +all the problems that these this linear + + align:start position:0% +all the problems that these this linear + + + align:start position:0% +all the problems that these this linear +algebra is is aimed at right up to an + + align:start position:0% +algebra is is aimed at right up to an + + + align:start position:0% +algebra is is aimed at right up to an +including conjugate gradient descent and + + align:start position:0% +including conjugate gradient descent and + + + align:start position:0% +including conjugate gradient descent and +and deep learning the the big the + + align:start position:0% +and deep learning the the big the + + + align:start position:0% +and deep learning the the big the +overwhelmingly important and lively + + align:start position:0% +overwhelmingly important and lively + + + align:start position:0% +overwhelmingly important and lively +active research area that's I couldn't + + align:start position:0% +active research area that's I couldn't + + + align:start position:0% +active research area that's I couldn't +do better than to get keep the course + + align:start position:0% +do better than to get keep the course + + + align:start position:0% +do better than to get keep the course +going in that direction so I think what + + align:start position:0% +going in that direction so I think what + + + align:start position:0% +going in that direction so I think what +I would ask you to do is late late and + + align:start position:0% +I would ask you to do is late late and + + + align:start position:0% +I would ask you to do is late late and +sort of april/may the regular homeworks + + align:start position:0% +sort of april/may the regular homeworks + + + align:start position:0% +sort of april/may the regular homeworks +I'll discontinue at a certain point and + + align:start position:0% +I'll discontinue at a certain point and + + + align:start position:0% +I'll discontinue at a certain point and +then instead I'll be asking and + + align:start position:0% +then instead I'll be asking and + + + align:start position:0% +then instead I'll be asking and +encouraging a project I don't know if + + align:start position:0% +encouraging a project I don't know if + + + align:start position:0% +encouraging a project I don't know if +that's the right word to be using in + + align:start position:0% +that's the right word to be using in + + + align:start position:0% +that's the right word to be using in +which you use what we've done for and + + align:start position:0% +which you use what we've done for and + + + align:start position:0% +which you use what we've done for and +I'll send out a message on stellar + + align:start position:0% +I'll send out a message on stellar + + + align:start position:0% +I'll send out a message on stellar +listing like five or six areas and only + + align:start position:0% +listing like five or six areas and only + + + align:start position:0% +listing like five or six areas and only +I mean one of them is the machine + + align:start position:0% +I mean one of them is the machine + + + align:start position:0% +I mean one of them is the machine +learning deep learning part but they're + + align:start position:0% +learning deep learning part but they're + + + align:start position:0% +learning deep learning part but they're +all the other parts that that that + + align:start position:0% +all the other parts that that that + + + align:start position:0% +all the other parts that that that +things we've learned to are learning how + + align:start position:0% +things we've learned to are learning how + + + align:start position:0% +things we've learned to are learning how +to do how to find sparse solutions for + + align:start position:0% +to do how to find sparse solutions for + + + align:start position:0% +to do how to find sparse solutions for +example or or something about the + + align:start position:0% +example or or something about the + + + align:start position:0% +example or or something about the +pseudo-inverse all kinds of things so + + align:start position:0% +pseudo-inverse all kinds of things so + + + align:start position:0% +pseudo-inverse all kinds of things so +that's my goal is to would give you + + align:start position:0% +that's my goal is to would give you + + + align:start position:0% +that's my goal is to would give you +something to do which uses the material + + align:start position:0% +something to do which uses the material + + + align:start position:0% +something to do which uses the material +you've learned and look I I'm not + + align:start position:0% +you've learned and look I I'm not + + + align:start position:0% +you've learned and look I I'm not +expecting a thesis but it's a it's a + + align:start position:0% +expecting a thesis but it's a it's a + + + align:start position:0% +expecting a thesis but it's a it's a +good chance so it will be more than just + + align:start position:0% +good chance so it will be more than just + + + align:start position:0% +good chance so it will be more than just +like drag in some code for deep learning + + align:start position:0% +like drag in some code for deep learning + + + align:start position:0% +like drag in some code for deep learning +and and some data matrix and do it + + align:start position:0% +and and some data matrix and do it + + + align:start position:0% +and and some data matrix and do it +but we'll chalk amaura that's a time + + align:start position:0% +but we'll chalk amaura that's a time + + + align:start position:0% +but we'll chalk amaura that's a time +comes + + align:start position:0% +comes + + + align:start position:0% +comes +so like I just thought I'd say before + + align:start position:0% +so like I just thought I'd say before + + + align:start position:0% +so like I just thought I'd say before +sending out the announcement I would say + + align:start position:0% +sending out the announcement I would say + + + align:start position:0% +sending out the announcement I would say +it's coming about what as a as a larger + + align:start position:0% +it's coming about what as a as a larger + + + align:start position:0% +it's coming about what as a as a larger +scale than single one week homeworks + + align:start position:0% +scale than single one week homeworks + + + align:start position:0% +scale than single one week homeworks +would be here before and he saw it's + + align:start position:0% +would be here before and he saw it's + + + align:start position:0% +would be here before and he saw it's +about that I haven't given it I haven't + + align:start position:0% +about that I haven't given it I haven't + + + align:start position:0% +about that I haven't given it I haven't +given you details so let me do that with + + align:start position:0% +given you details so let me do that with + + + align:start position:0% +given you details so let me do that with +a message and then ask again but I'm + + align:start position:0% +a message and then ask again but I'm + + + align:start position:0% +a message and then ask again but I'm +open to I hope you've understood I think + + align:start position:0% +open to I hope you've understood I think + + + align:start position:0% +open to I hope you've understood I think +you have that that if you make + + align:start position:0% +you have that that if you make + + + align:start position:0% +you have that that if you make +suggestions either directly to my email + + align:start position:0% +suggestions either directly to my email + + + align:start position:0% +suggestions either directly to my email +or on Piazza or whatever they get paid + + align:start position:0% +or on Piazza or whatever they get paid + + + align:start position:0% +or on Piazza or whatever they get paid +attention to okay Michelle you just go + + align:start position:0% +attention to okay Michelle you just go + + + align:start position:0% +attention to okay Michelle you just go +forward with least squares so what's the + + align:start position:0% +forward with least squares so what's the + + + align:start position:0% +forward with least squares so what's the +least squares problem and what are these + + align:start position:0% +least squares problem and what are these + + + align:start position:0% +least squares problem and what are these +four ways each each bringing so let me + + align:start position:0% +four ways each each bringing so let me + + + align:start position:0% +four ways each each bringing so let me +speak about the pseudo-inverse first + + align:start position:0% +speak about the pseudo-inverse first + + + align:start position:0% +speak about the pseudo-inverse first +okay the pseudo inverse of a matrix + + align:start position:0% +okay the pseudo inverse of a matrix + + + align:start position:0% +okay the pseudo inverse of a matrix +alright good so we have a matrix a M by + + align:start position:0% +alright good so we have a matrix a M by + + + align:start position:0% +alright good so we have a matrix a M by +N and the pseudo-inverse I'm going to + + align:start position:0% +N and the pseudo-inverse I'm going to + + + align:start position:0% +N and the pseudo-inverse I'm going to +call a plus and it naturally it's gonna + + align:start position:0% +call a plus and it naturally it's gonna + + + align:start position:0% +call a plus and it naturally it's gonna +be n by M I'm going to multiply those + + align:start position:0% +be n by M I'm going to multiply those + + + align:start position:0% +be n by M I'm going to multiply those +together and I'm gonna get as near to + + align:start position:0% +together and I'm gonna get as near to + + + align:start position:0% +together and I'm gonna get as near to +the identity as I can that's the idea of + + align:start position:0% +the identity as I can that's the idea of + + + align:start position:0% +the identity as I can that's the idea of +course of the pseudo-inverse the word + + align:start position:0% +course of the pseudo-inverse the word + + + align:start position:0% +course of the pseudo-inverse the word +pseudo is in there so so no one's + + align:start position:0% +pseudo is in there so so no one's + + + align:start position:0% +pseudo is in there so so no one's +deceived it's not an actual inverse oh + + align:start position:0% +deceived it's not an actual inverse oh + + + align:start position:0% +deceived it's not an actual inverse oh +if the matrix is square and has an + + align:start position:0% +if the matrix is square and has an + + + align:start position:0% +if the matrix is square and has an +inverse of course then if if a inverse + + align:start position:0% +inverse of course then if if a inverse + + + align:start position:0% +inverse of course then if if a inverse +exists which which requires a everybody + + align:start position:0% +exists which which requires a everybody + + + align:start position:0% +exists which which requires a everybody +remembers it requires the matrix to be + + align:start position:0% +remembers it requires the matrix to be + + + align:start position:0% +remembers it requires the matrix to be +square because I mean inverse on both + + align:start position:0% +square because I mean inverse on both + + + align:start position:0% +square because I mean inverse on both +sides and and it requires rank in full + + align:start position:0% +sides and and it requires rank in full + + + align:start position:0% +sides and and it requires rank in full +rank then the inverse will exist you can + + align:start position:0% +rank then the inverse will exist you can + + + align:start position:0% +rank then the inverse will exist you can +check it MATLAB would check it by + + align:start position:0% +check it MATLAB would check it by + + + align:start position:0% +check it MATLAB would check it by +computing the pivots in elimination + + align:start position:0% +computing the pivots in elimination + + + align:start position:0% +computing the pivots in elimination +finding and pivots so if a inverse + + align:start position:0% +finding and pivots so if a inverse + + + align:start position:0% +finding and pivots so if a inverse +exists which means a and a times a + + align:start position:0% +exists which means a and a times a + + + align:start position:0% +exists which means a and a times a +inverse and a inverse times a both give + + align:start position:0% +inverse and a inverse times a both give + + + align:start position:0% +inverse and a inverse times a both give +I then a plus is a inverse of course the + + align:start position:0% +I then a plus is a inverse of course the + + + align:start position:0% +I then a plus is a inverse of course the +pseudo inverse is the inverse when there + + align:start position:0% +pseudo inverse is the inverse when there + + + align:start position:0% +pseudo inverse is the inverse when there +is one but I'm thinking about cases + + align:start position:0% +is one but I'm thinking about cases + + + align:start position:0% +is one but I'm thinking about cases +where either the matrix is rectangular + + align:start position:0% +where either the matrix is rectangular + + + align:start position:0% +where either the matrix is rectangular +or or it has zero eigenvalues it it's it + + align:start position:0% +or or it has zero eigenvalues it it's it + + + align:start position:0% +or or it has zero eigenvalues it it's it +could be square but has a null space + + align:start position:0% +could be square but has a null space + + + align:start position:0% +could be square but has a null space +other than just the zero vector in other + + align:start position:0% +other than just the zero vector in other + + + align:start position:0% +other than just the zero vector in other +words the columns are dependent what can + + align:start position:0% +words the columns are dependent what can + + + align:start position:0% +words the columns are dependent what can +we do then about inverting it we can't + + align:start position:0% +we do then about inverting it we can't + + + align:start position:0% +we do then about inverting it we can't +literally invert it if if a has a null + + align:start position:0% +literally invert it if if a has a null + + + align:start position:0% +literally invert it if if a has a null +space then when I multiply by a vector X + + align:start position:0% +space then when I multiply by a vector X + + + align:start position:0% +space then when I multiply by a vector X +in that null space ax will be zero and + + align:start position:0% +in that null space ax will be zero and + + + align:start position:0% +in that null space ax will be zero and +when I multiply by a inverse still zero + + align:start position:0% +when I multiply by a inverse still zero + + + align:start position:0% +when I multiply by a inverse still zero +that can't change the zero so if there + + align:start position:0% +that can't change the zero so if there + + + align:start position:0% +that can't change the zero so if there +is an X in the null space then this + + align:start position:0% +is an X in the null space then this + + + align:start position:0% +is an X in the null space then this +can't happen but so we just do the best + + align:start position:0% +can't happen but so we just do the best + + + align:start position:0% +can't happen but so we just do the best +we can and that's what the pseudo + + align:start position:0% +we can and that's what the pseudo + + + align:start position:0% +we can and that's what the pseudo +inverse is and so let me draw a picture + + align:start position:0% +inverse is and so let me draw a picture + + + align:start position:0% +inverse is and so let me draw a picture +of the the picture you know of the row + + align:start position:0% +of the the picture you know of the row + + + align:start position:0% +of the the picture you know of the row +space and the null space okay and it's + + align:start position:0% +space and the null space okay and it's + + + align:start position:0% +space and the null space okay and it's +there you see there is a null space and + + align:start position:0% +there you see there is a null space and + + + align:start position:0% +there you see there is a null space and +over here I have the column space and + + align:start position:0% +over here I have the column space and + + + align:start position:0% +over here I have the column space and +the null space of a transpose okay so + + align:start position:0% +the null space of a transpose okay so + + + align:start position:0% +the null space of a transpose okay so +this is the row space of course that's a + + align:start position:0% +this is the row space of course that's a + + + align:start position:0% +this is the row space of course that's a +column space of a and of a transpose and + + align:start position:0% +column space of a and of a transpose and + + + align:start position:0% +column space of a and of a transpose and +there's the column space of a okay so + + align:start position:0% +there's the column space of a okay so + + + align:start position:0% +there's the column space of a okay so +which part of that picture is invertible + + align:start position:0% +which part of that picture is invertible + + + align:start position:0% +which part of that picture is invertible +and which part of the picture is + + align:start position:0% +and which part of the picture is + + + align:start position:0% +and which part of the picture is +hopeless the top part is invertible this + + align:start position:0% +hopeless the top part is invertible this + + + align:start position:0% +hopeless the top part is invertible this +is the are sort of our dimensional row + + align:start position:0% +is the are sort of our dimensional row + + + align:start position:0% +is the are sort of our dimensional row +space our dimensional column space a + + align:start position:0% +space our dimensional column space a + + + align:start position:0% +space our dimensional column space a +takes a vector in here zaps it into + + align:start position:0% +takes a vector in here zaps it into + + + align:start position:0% +takes a vector in here zaps it into +every oh you always end up in the column + + align:start position:0% +every oh you always end up in the column + + + align:start position:0% +every oh you always end up in the column +space here here here I take a vector in + + align:start position:0% +space here here here I take a vector in + + + align:start position:0% +space here here here I take a vector in +the + + align:start position:0% +the + + + align:start position:0% +the +row space say X and it gets mapped to ax + + align:start position:0% +row space say X and it gets mapped to ax + + + align:start position:0% +row space say X and it gets mapped to ax +and between those two spaces a is + + align:start position:0% +and between those two spaces a is + + + align:start position:0% +and between those two spaces a is +entirely invertible you know you you get + + align:start position:0% +entirely invertible you know you you get + + + align:start position:0% +entirely invertible you know you you get +separate vectors here go to separate + + align:start position:0% +separate vectors here go to separate + + + align:start position:0% +separate vectors here go to separate +vectors in the column space and the + + align:start position:0% +vectors in the column space and the + + + align:start position:0% +vectors in the column space and the +inverse just brings it back so we know + + align:start position:0% +inverse just brings it back so we know + + + align:start position:0% +inverse just brings it back so we know +what the pseudo-inverse should do + + align:start position:0% +what the pseudo-inverse should do + + + align:start position:0% +what the pseudo-inverse should do +it'll take a we'll take go that way and + + align:start position:0% +it'll take a we'll take go that way and + + + align:start position:0% +it'll take a we'll take go that way and +a plus the pseudo-inverse will be just + + align:start position:0% +a plus the pseudo-inverse will be just + + + align:start position:0% +a plus the pseudo-inverse will be just +it will give us on the top half of the + + align:start position:0% +it will give us on the top half of the + + + align:start position:0% +it will give us on the top half of the +picture it'll give us a plus we'll take + + align:start position:0% +picture it'll give us a plus we'll take + + + align:start position:0% +picture it'll give us a plus we'll take +ax back to x4 in the in the top half now + + align:start position:0% +ax back to x4 in the in the top half now + + + align:start position:0% +ax back to x4 in the in the top half now +what about here that's where we have + + align:start position:0% +what about here that's where we have + + + align:start position:0% +what about here that's where we have +trouble we don't have that's what spoils + + align:start position:0% +trouble we don't have that's what spoils + + + align:start position:0% +trouble we don't have that's what spoils +our inverse if there's a null space + + align:start position:0% +our inverse if there's a null space + + + align:start position:0% +our inverse if there's a null space +vector then it goes where when you + + align:start position:0% +vector then it goes where when you + + + align:start position:0% +vector then it goes where when you +multiply by a this guy in the null space + + align:start position:0% +multiply by a this guy in the null space + + + align:start position:0% +multiply by a this guy in the null space +goes to zero usually along a straighter + + align:start position:0% +goes to zero usually along a straighter + + + align:start position:0% +goes to zero usually along a straighter +line than I've drawn but go there gets + + align:start position:0% +line than I've drawn but go there gets + + + align:start position:0% +line than I've drawn but go there gets +to zero so you you can't raise it from + + align:start position:0% +to zero so you you can't raise it from + + + align:start position:0% +to zero so you you can't raise it from +the dead so to speak you can't recover + + align:start position:0% +the dead so to speak you can't recover + + + align:start position:0% +the dead so to speak you can't recover +it one of you there's no way inverse so + + align:start position:0% +it one of you there's no way inverse so + + + align:start position:0% +it one of you there's no way inverse so +we have to think what shall a inverse do + + align:start position:0% +we have to think what shall a inverse do + + + align:start position:0% +we have to think what shall a inverse do +to this space here where nobody's + + align:start position:0% +to this space here where nobody's + + + align:start position:0% +to this space here where nobody's +hitting it so it's this was this would + + align:start position:0% +hitting it so it's this was this would + + + align:start position:0% +hitting it so it's this was this would +be the null space of a transpose because + + align:start position:0% +be the null space of a transpose because + + + align:start position:0% +be the null space of a transpose because +8/8 sorry yeah what should the + + align:start position:0% +8/8 sorry yeah what should the + + + align:start position:0% +8/8 sorry yeah what should the +pseudo-inverse do I said what should the + + align:start position:0% +pseudo-inverse do I said what should the + + + align:start position:0% +pseudo-inverse do I said what should the +inverse do the inverse is helpless but + + align:start position:0% +inverse do the inverse is helpless but + + + align:start position:0% +inverse do the inverse is helpless but +we have to to define a plus I've said + + align:start position:0% +we have to to define a plus I've said + + + align:start position:0% +we have to to define a plus I've said +what it should do on that guy on the + + align:start position:0% +what it should do on that guy on the + + + align:start position:0% +what it should do on that guy on the +column space it should take everything + + align:start position:0% +column space it should take everything + + + align:start position:0% +column space it should take everything +in the column space back where it came + + align:start position:0% +in the column space back where it came + + + align:start position:0% +in the column space back where it came +from but what should it do on this + + align:start position:0% +from but what should it do on this + + + align:start position:0% +from but what should it do on this +orthogonal space where yeah just tell me + + align:start position:0% +orthogonal space where yeah just tell me + + + align:start position:0% +orthogonal space where yeah just tell me +what what what do you think if I have + + align:start position:0% +what what what do you think if I have + + + align:start position:0% +what what what do you think if I have +some vector here that's it's called that + + align:start position:0% +some vector here that's it's called that + + + align:start position:0% +some vector here that's it's called that +V R plus one that would + + align:start position:0% +V R plus one that would + + + align:start position:0% +V R plus one that would +be like so here here I have a basis of a + + align:start position:0% +be like so here here I have a basis of a + + + align:start position:0% +be like so here here I have a basis of a +nice a nice basis for the column space + + align:start position:0% +nice a nice basis for the column space + + + align:start position:0% +nice a nice basis for the column space +this V's I would use V's for the for the + + align:start position:0% +this V's I would use V's for the for the + + + align:start position:0% +this V's I would use V's for the for the +ones that come up in the SVD they're + + align:start position:0% +ones that come up in the SVD they're + + + align:start position:0% +ones that come up in the SVD they're +orthogonal and they come from orthogonal + + align:start position:0% +orthogonal and they come from orthogonal + + + align:start position:0% +orthogonal and they come from orthogonal +use so that top half is great what shall + + align:start position:0% +use so that top half is great what shall + + + align:start position:0% +use so that top half is great what shall +I do with this stuff I'm gonna send that + + align:start position:0% +I do with this stuff I'm gonna send that + + + align:start position:0% +I do with this stuff I'm gonna send that +back by a plus and where am I going what + + align:start position:0% +back by a plus and where am I going what + + + align:start position:0% +back by a plus and where am I going what +am I gonna do with it send it to know + + align:start position:0% +am I gonna do with it send it to know + + + align:start position:0% +am I gonna do with it send it to know +where else could it go zero is the right + + align:start position:0% +where else could it go zero is the right + + + align:start position:0% +where else could it go zero is the right +answer all this stuff goes back to zero + + align:start position:0% +answer all this stuff goes back to zero + + + align:start position:0% +answer all this stuff goes back to zero +I'm looking for a linear Mayton linear + + align:start position:0% +I'm looking for a linear Mayton linear + + + align:start position:0% +I'm looking for a linear Mayton linear +operator a matrix and I have to think of + + align:start position:0% +operator a matrix and I have to think of + + + align:start position:0% +operator a matrix and I have to think of +once I've decided what to do with all + + align:start position:0% +once I've decided what to do with all + + + align:start position:0% +once I've decided what to do with all +those and what to do with all these then + + align:start position:0% +those and what to do with all these then + + + align:start position:0% +those and what to do with all these then +I know what to do with any combination + + align:start position:0% +I know what to do with any combination + + + align:start position:0% +I know what to do with any combination +so I've got it I've got it so so the + + align:start position:0% +so I've got it I've got it so so the + + + align:start position:0% +so I've got it I've got it so so the +idea will be this is true for X in the + + align:start position:0% +idea will be this is true for X in the + + + align:start position:0% +idea will be this is true for X in the +row space for X in the row space if X is + + align:start position:0% +row space for X in the row space if X is + + + align:start position:0% +row space for X in the row space if X is +in the row space ax is in the column + + align:start position:0% +in the row space ax is in the column + + + align:start position:0% +in the row space ax is in the column +space and a inverse just brings it back + + align:start position:0% +space and a inverse just brings it back + + + align:start position:0% +space and a inverse just brings it back +as it should and and in a in the case of + + align:start position:0% +as it should and and in a in the case of + + + align:start position:0% +as it should and and in a in the case of +an invertible matrix a what happens to + + align:start position:0% +an invertible matrix a what happens to + + + align:start position:0% +an invertible matrix a what happens to +my picture what does this picture + + align:start position:0% +my picture what does this picture + + + align:start position:0% +my picture what does this picture +looking like if a is actually a six by + + align:start position:0% +looking like if a is actually a six by + + + align:start position:0% +looking like if a is actually a six by +six invertible matrix in that case + + align:start position:0% +six invertible matrix in that case + + + align:start position:0% +six invertible matrix in that case +what's what's in my picture and what is + + align:start position:0% +what's what's in my picture and what is + + + align:start position:0% +what's what's in my picture and what is +not in my picture all this null space + + align:start position:0% +not in my picture all this null space + + + align:start position:0% +not in my picture all this null space +stuff isn't there a null space is just + + align:start position:0% +stuff isn't there a null space is just + + + align:start position:0% +stuff isn't there a null space is just +the zero vector but all that I don't + + align:start position:0% +the zero vector but all that I don't + + + align:start position:0% +the zero vector but all that I don't +have to worry about but in general I do + + align:start position:0% +have to worry about but in general I do + + + align:start position:0% +have to worry about but in general I do +have to say so that the point is that a + + align:start position:0% +have to say so that the point is that a + + + align:start position:0% +have to say so that the point is that a +plus on the what what am i calling this + + align:start position:0% +plus on the what what am i calling this + + + align:start position:0% +plus on the what what am i calling this +ooh it's a null space of a transpose or + + align:start position:0% +ooh it's a null space of a transpose or + + + align:start position:0% +ooh it's a null space of a transpose or +or whatever on on V R plus 1 to the N + + align:start position:0% +or whatever on on V R plus 1 to the N + + + align:start position:0% +or whatever on on V R plus 1 to the N +those those though + + align:start position:0% +those those though + + + align:start position:0% +those those though +those all those vectors the the guys + + align:start position:0% +those all those vectors the the guys + + + align:start position:0% +those all those vectors the the guys +that are not in the orthogonal to the + + align:start position:0% +that are not in the orthogonal to the + + + align:start position:0% +that are not in the orthogonal to the +column space then your your we have to + + align:start position:0% +column space then your your we have to + + + align:start position:0% +column space then your your we have to +say what does a plus do to them and the + + align:start position:0% +say what does a plus do to them and the + + + align:start position:0% +say what does a plus do to them and the +answer is it takes them all to zero so + + align:start position:0% +answer is it takes them all to zero so + + + align:start position:0% +answer is it takes them all to zero so +there's a picture using the what I call + + align:start position:0% +there's a picture using the what I call + + + align:start position:0% +there's a picture using the what I call +the big picture of linear algebra the + + align:start position:0% +the big picture of linear algebra the + + + align:start position:0% +the big picture of linear algebra the +four spaces you see what a plus should + + align:start position:0% +four spaces you see what a plus should + + + align:start position:0% +four spaces you see what a plus should +do now I need a little formula for it + + align:start position:0% +do now I need a little formula for it + + + align:start position:0% +do now I need a little formula for it +I've got a I've got the plan for what it + + align:start position:0% +I've got a I've got the plan for what it + + + align:start position:0% +I've got a I've got the plan for what it +should be and it's they're sort of a + + align:start position:0% +should be and it's they're sort of a + + + align:start position:0% +should be and it's they're sort of a +natural thing so A plus a is you could + + align:start position:0% +natural thing so A plus a is you could + + + align:start position:0% +natural thing so A plus a is you could +say up it's a projection matrix it's not + + align:start position:0% +say up it's a projection matrix it's not + + + align:start position:0% +say up it's a projection matrix it's not +the identity matrix because because if X + + align:start position:0% +the identity matrix because because if X + + + align:start position:0% +the identity matrix because because if X +is in the null space a plus ay ay ay + + align:start position:0% +is in the null space a plus ay ay ay + + + align:start position:0% +is in the null space a plus ay ay ay +plus a will take it to zero but so so + + align:start position:0% +plus a will take it to zero but so so + + + align:start position:0% +plus a will take it to zero but so so +it's a project a plus a is the identity + + align:start position:0% +it's a project a plus a is the identity + + + align:start position:0% +it's a project a plus a is the identity +on the top half and zero on the bottom + + align:start position:0% +on the top half and zero on the bottom + + + align:start position:0% +on the top half and zero on the bottom +half that's that's really what the + + align:start position:0% +half that's that's really what the + + + align:start position:0% +half that's that's really what the +matrix is and now I want a simple + + align:start position:0% +matrix is and now I want a simple + + + align:start position:0% +matrix is and now I want a simple +formula for it and I guess my message + + align:start position:0% +formula for it and I guess my message + + + align:start position:0% +formula for it and I guess my message +here is that if we're looking for a nice + + align:start position:0% +here is that if we're looking for a nice + + + align:start position:0% +here is that if we're looking for a nice +expression start with the SVD because + + align:start position:0% +expression start with the SVD because + + + align:start position:0% +expression start with the SVD because +the SVD works for any matrix and it + + align:start position:0% +the SVD works for any matrix and it + + + align:start position:0% +the SVD works for any matrix and it +writes it as an orthogonal matrix times + + align:start position:0% +writes it as an orthogonal matrix times + + + align:start position:0% +writes it as an orthogonal matrix times +the diagonal matrix times an orthogonal + + align:start position:0% +the diagonal matrix times an orthogonal + + + align:start position:0% +the diagonal matrix times an orthogonal +matrix and now I want to invert it well + + align:start position:0% +matrix and now I want to invert it well + + + align:start position:0% +matrix and now I want to invert it well +suppose a had an inverse what would that + + align:start position:0% +suppose a had an inverse what would that + + + align:start position:0% +suppose a had an inverse what would that +be if this is F invertible what would be + + align:start position:0% +be if this is F invertible what would be + + + align:start position:0% +be if this is F invertible what would be +the SVD of a inverse what would be the + + align:start position:0% +the SVD of a inverse what would be the + + + align:start position:0% +the SVD of a inverse what would be the +singular value decomposition if if this + + align:start position:0% +singular value decomposition if if this + + + align:start position:0% +singular value decomposition if if this +is good so when is this going to be good + + align:start position:0% +is good so when is this going to be good + + + align:start position:0% +is good so when is this going to be good +that what would that make what would I + + align:start position:0% +that what would that make what would I + + + align:start position:0% +that what would that make what would I +have to know about that matrix Sigma + + align:start position:0% +have to know about that matrix Sigma + + + align:start position:0% +have to know about that matrix Sigma +that diagonal matrix in the middle if + + align:start position:0% +that diagonal matrix in the middle if + + + align:start position:0% +that diagonal matrix in the middle if +this is truly an invertible matrix well + + align:start position:0% +this is truly an invertible matrix well + + + align:start position:0% +this is truly an invertible matrix well +know what's its name those are not + + align:start position:0% +know what's its name those are not + + + align:start position:0% +know what's its name those are not +eigenvalues well there I can values of + + align:start position:0% +eigenvalues well there I can values of + + + align:start position:0% +eigenvalues well there I can values of +a transpose a but their singular value + + align:start position:0% +a transpose a but their singular value + + + align:start position:0% +a transpose a but their singular value +singular violets fine so that's the + + align:start position:0% +singular violets fine so that's the + + + align:start position:0% +singular violets fine so that's the +singular value matrix and what would be + + align:start position:0% +singular value matrix and what would be + + + align:start position:0% +singular value matrix and what would be +the situation if if a had an inverse + + align:start position:0% +the situation if if a had an inverse + + + align:start position:0% +the situation if if a had an inverse +there would be no zeros all their + + align:start position:0% +there would be no zeros all their + + + align:start position:0% +there would be no zeros all their +singular values would be sitting there + + align:start position:0% +singular values would be sitting there + + + align:start position:0% +singular values would be sitting there +Sigma 1 2 Sigma N what would be the + + align:start position:0% +Sigma 1 2 Sigma N what would be the + + + align:start position:0% +Sigma 1 2 Sigma N what would be the +shape of this Sigma matrix if if if I + + align:start position:0% +shape of this Sigma matrix if if if I + + + align:start position:0% +shape of this Sigma matrix if if if I +have an inverse then I've it's got to be + + align:start position:0% +have an inverse then I've it's got to be + + + align:start position:0% +have an inverse then I've it's got to be +square and by N so what's the shape of + + align:start position:0% +square and by N so what's the shape of + + + align:start position:0% +square and by N so what's the shape of +the Sigma guy also square and by n so so + + align:start position:0% +the Sigma guy also square and by n so so + + + align:start position:0% +the Sigma guy also square and by n so so +the invertible case would be and I'm + + align:start position:0% +the invertible case would be and I'm + + + align:start position:0% +the invertible case would be and I'm +gonna erase this in a minute the + + align:start position:0% +gonna erase this in a minute the + + + align:start position:0% +gonna erase this in a minute the +invertible case would be when Sigma is + + align:start position:0% +invertible case would be when Sigma is + + + align:start position:0% +invertible case would be when Sigma is +just that that would be the invertible + + align:start position:0% +just that that would be the invertible + + + align:start position:0% +just that that would be the invertible +case so let's see can you finish this + + align:start position:0% +case so let's see can you finish this + + + align:start position:0% +case so let's see can you finish this +formula what would be the SVD of a + + align:start position:0% +formula what would be the SVD of a + + + align:start position:0% +formula what would be the SVD of a +inverse so I've given the SVD of a I'm + + align:start position:0% +inverse so I've given the SVD of a I'm + + + align:start position:0% +inverse so I've given the SVD of a I'm +given the U and this Sigma is cool and + + align:start position:0% +given the U and this Sigma is cool and + + + align:start position:0% +given the U and this Sigma is cool and +the V transpose what's the inverse of + + align:start position:0% +the V transpose what's the inverse of + + + align:start position:0% +the V transpose what's the inverse of +that + + align:start position:0% +that + + + align:start position:0% +that +well yeah I'm just really asking you + + align:start position:0% +well yeah I'm just really asking you + + + align:start position:0% +well yeah I'm just really asking you +what's the inverse of that product of + + align:start position:0% +what's the inverse of that product of + + + align:start position:0% +what's the inverse of that product of +three matrices what comes first here V + + align:start position:0% +three matrices what comes first here V + + + align:start position:0% +three matrices what comes first here V +the inverse of V transpose is V that's + + align:start position:0% +the inverse of V transpose is V that's + + + align:start position:0% +the inverse of V transpose is V that's +because V is a orthogonal matrix the + + align:start position:0% +because V is a orthogonal matrix the + + + align:start position:0% +because V is a orthogonal matrix the +inverse of Sigma I just 1 over it is + + align:start position:0% +inverse of Sigma I just 1 over it is + + + align:start position:0% +inverse of Sigma I just 1 over it is +just the Sigma inverse it's obvious what + + align:start position:0% +just the Sigma inverse it's obvious what + + + align:start position:0% +just the Sigma inverse it's obvious what +that means and the inverse of U would go + + align:start position:0% +that means and the inverse of U would go + + + align:start position:0% +that means and the inverse of U would go +here and that is U transpose great ok so + + align:start position:0% +here and that is U transpose great ok so + + + align:start position:0% +here and that is U transpose great ok so +this is f invertible if invertible we + + align:start position:0% +this is f invertible if invertible we + + + align:start position:0% +this is f invertible if invertible we +know what the SVD of a inverse is it + + align:start position:0% +know what the SVD of a inverse is it + + + align:start position:0% +know what the SVD of a inverse is it +just takes the V's back to the eu's + + align:start position:0% +just takes the V's back to the eu's + + + align:start position:0% +just takes the V's back to the eu's +takes it or they use back to the V's + + align:start position:0% +takes it or they use back to the V's + + + align:start position:0% +takes it or they use back to the V's +whichever ok ok now we've got to do it + + align:start position:0% +whichever ok ok now we've got to do it + + + align:start position:0% +whichever ok ok now we've got to do it +if we're going to allow if we're gonna + + align:start position:0% +if we're going to allow if we're gonna + + + align:start position:0% +if we're going to allow if we're gonna +get beyond this limit the situation + + align:start position:0% +get beyond this limit the situation + + + align:start position:0% +get beyond this limit the situation +allow the matrix Sigma to be rectangular + + align:start position:0% +allow the matrix Sigma to be rectangular + + + align:start position:0% +allow the matrix Sigma to be rectangular +then let me just show you how the idea + + align:start position:0% +then let me just show you how the idea + + + align:start position:0% +then let me just show you how the idea +here + + align:start position:0% +here + + + align:start position:0% +here +so so now I'm gonna say now Sigma in + + align:start position:0% +so so now I'm gonna say now Sigma in + + + align:start position:0% +so so now I'm gonna say now Sigma in +general its rectangular it's got our non + + align:start position:0% +general its rectangular it's got our non + + + align:start position:0% +general its rectangular it's got our non +zeros on the diagonal but then it quits + + align:start position:0% +zeros on the diagonal but then it quits + + + align:start position:0% +zeros on the diagonal but then it quits +so it's it's got a bunch of zeros that + + align:start position:0% +so it's it's got a bunch of zeros that + + + align:start position:0% +so it's it's got a bunch of zeros that +to make it not invertible but let's do + + align:start position:0% +to make it not invertible but let's do + + + align:start position:0% +to make it not invertible but let's do +our best and pseudo-inverse okay so now + + align:start position:0% +our best and pseudo-inverse okay so now + + + align:start position:0% +our best and pseudo-inverse okay so now +I'll help me get started on a formula + + align:start position:0% +I'll help me get started on a formula + + + align:start position:0% +I'll help me get started on a formula +for using I want to write this a plus + + align:start position:0% +for using I want to write this a plus + + + align:start position:0% +for using I want to write this a plus +which are described up there in terms of + + align:start position:0% +which are described up there in terms of + + + align:start position:0% +which are described up there in terms of +the subspaces now I'm going to describe + + align:start position:0% +the subspaces now I'm going to describe + + + align:start position:0% +the subspaces now I'm going to describe +a plus in terms of you Sigma and V the + + align:start position:0% +a plus in terms of you Sigma and V the + + + align:start position:0% +a plus in terms of you Sigma and V the +in the SVD guys okay so what what shall + + align:start position:0% +in the SVD guys okay so what what shall + + + align:start position:0% +in the SVD guys okay so what what shall +I start with here well let me give a + + align:start position:0% +I start with here well let me give a + + + align:start position:0% +I start with here well let me give a +hint I'll just that was a great start my + + align:start position:0% +hint I'll just that was a great start my + + + align:start position:0% +hint I'll just that was a great start my +V is still an orthogonal matrix V + + align:start position:0% +V is still an orthogonal matrix V + + + align:start position:0% +V is still an orthogonal matrix V +transpose is still an orthogonal matrix + + align:start position:0% +transpose is still an orthogonal matrix + + + align:start position:0% +transpose is still an orthogonal matrix +I'll invert it at the end + + align:start position:0% +I'll invert it at the end + + + align:start position:0% +I'll invert it at the end +the U was no problem all the problems + + align:start position:0% +the U was no problem all the problems + + + align:start position:0% +the U was no problem all the problems +are in Sigma and Sigma remember Sigma so + + align:start position:0% +are in Sigma and Sigma remember Sigma so + + + align:start position:0% +are in Sigma and Sigma remember Sigma so +it's it's rectangular maybe I'll make it + + align:start position:0% +it's it's rectangular maybe I'll make it + + + align:start position:0% +it's it's rectangular maybe I'll make it +like wide for to wide and maybe I'll + + align:start position:0% +like wide for to wide and maybe I'll + + + align:start position:0% +like wide for to wide and maybe I'll +only give it to non zeros and then all + + align:start position:0% +only give it to non zeros and then all + + + align:start position:0% +only give it to non zeros and then all +the rest so the rank of my matrix a is 2 + + align:start position:0% +the rest so the rank of my matrix a is 2 + + + align:start position:0% +the rest so the rank of my matrix a is 2 +but the m and n are bigger than 2 it's + + align:start position:0% +but the m and n are bigger than 2 it's + + + align:start position:0% +but the m and n are bigger than 2 it's +it's just got two independent columns + + align:start position:0% +it's just got two independent columns + + + align:start position:0% +it's just got two independent columns +and then then it's just sort of totally + + align:start position:0% +and then then it's just sort of totally + + + align:start position:0% +and then then it's just sort of totally +singular okay so my question is what am + + align:start position:0% +singular okay so my question is what am + + + align:start position:0% +singular okay so my question is what am +I going to put there and I've described + + align:start position:0% +I going to put there and I've described + + + align:start position:0% +I going to put there and I've described +it one way but now I'm gonna describe it + + align:start position:0% +it one way but now I'm gonna describe it + + + align:start position:0% +it one way but now I'm gonna describe it +another way well let me just say what I + + align:start position:0% +another way well let me just say what I + + + align:start position:0% +another way well let me just say what I +what I'll put there is the pseudo + + align:start position:0% +what I'll put there is the pseudo + + + align:start position:0% +what I'll put there is the pseudo +inverse of Sigma I can't put Sigma + + align:start position:0% +inverse of Sigma I can't put Sigma + + + align:start position:0% +inverse of Sigma I can't put Sigma +inverse you using that symbol because it + + align:start position:0% +inverse you using that symbol because it + + + align:start position:0% +inverse you using that symbol because it +there is no such thing with this I can't + + align:start position:0% +there is no such thing with this I can't + + + align:start position:0% +there is no such thing with this I can't +invert it so that's the best I can do so + + align:start position:0% +invert it so that's the best I can do so + + + align:start position:0% +invert it so that's the best I can do so +I'm almost done but to finish I have to + + align:start position:0% +I'm almost done but to finish I have to + + + align:start position:0% +I'm almost done but to finish I have to +tell you what does that + + align:start position:0% +tell you what does that + + + align:start position:0% +tell you what does that +what what is this thing so Sigma plus + + align:start position:0% +what what is this thing so Sigma plus + + + align:start position:0% +what what is this thing so Sigma plus +I'm now going to tell you Sigma plus and + + align:start position:0% +I'm now going to tell you Sigma plus and + + + align:start position:0% +I'm now going to tell you Sigma plus and +then that's what should sit there in the + + align:start position:0% +then that's what should sit there in the + + + align:start position:0% +then that's what should sit there in the +middle so if Sigma is this diagonal + + align:start position:0% +middle so if Sigma is this diagonal + + + align:start position:0% +middle so if Sigma is this diagonal +matrix which quits after two Sigma's + + align:start position:0% +matrix which quits after two Sigma's + + + align:start position:0% +matrix which quits after two Sigma's +what should Sigma plus be well first of + + align:start position:0% +what should Sigma plus be well first of + + + align:start position:0% +what should Sigma plus be well first of +all it should be rectangular the other + + align:start position:0% +all it should be rectangular the other + + + align:start position:0% +all it should be rectangular the other +way if this was M by n column and + + align:start position:0% +way if this was M by n column and + + + align:start position:0% +way if this was M by n column and +columns and M rows now I want to have n + + align:start position:0% +columns and M rows now I want to have n + + + align:start position:0% +columns and M rows now I want to have n +rows and M columns and yeah here's the + + align:start position:0% +rows and M columns and yeah here's the + + + align:start position:0% +rows and M columns and yeah here's the +question what's the best inverse you + + align:start position:0% +question what's the best inverse you + + + align:start position:0% +question what's the best inverse you +could come up with for that Sigma I mean + + align:start position:0% +could come up with for that Sigma I mean + + + align:start position:0% +could come up with for that Sigma I mean +if somebody independent of 1806 five if + + align:start position:0% +if somebody independent of 1806 five if + + + align:start position:0% +if somebody independent of 1806 five if +somebody asks you do your best to invert + + align:start position:0% +somebody asks you do your best to invert + + + align:start position:0% +somebody asks you do your best to invert +that matrix I think we'd all agree it is + + align:start position:0% +that matrix I think we'd all agree it is + + + align:start position:0% +that matrix I think we'd all agree it is +yeah one over the Sigma one would come + + align:start position:0% +yeah one over the Sigma one would come + + + align:start position:0% +yeah one over the Sigma one would come +there and one over Sigma two then non + + align:start position:0% +there and one over Sigma two then non + + + align:start position:0% +there and one over Sigma two then non +zeros and then zeros I think you just + + align:start position:0% +zeros and then zeros I think you just + + + align:start position:0% +zeros and then zeros I think you just +the way up there we didn't we didn't + + align:start position:0% +the way up there we didn't we didn't + + + align:start position:0% +the way up there we didn't we didn't +know what to do + + align:start position:0% +know what to do + + + align:start position:0% +know what to do +when there was nothing good to do zero + + align:start position:0% +when there was nothing good to do zero + + + align:start position:0% +when there was nothing good to do zero +was there was the right answer so so + + align:start position:0% +was there was the right answer so so + + + align:start position:0% +was there was the right answer so so +this is all zeroes of course it's + + align:start position:0% +this is all zeroes of course it's + + + align:start position:0% +this is all zeroes of course it's +rectangular the other way but do you see + + align:start position:0% +rectangular the other way but do you see + + + align:start position:0% +rectangular the other way but do you see +that if I multiply Sigma plus times + + align:start position:0% +that if I multiply Sigma plus times + + + align:start position:0% +that if I multiply Sigma plus times +Sigma if I multiply the pseudo inverse + + align:start position:0% +Sigma if I multiply the pseudo inverse + + + align:start position:0% +Sigma if I multiply the pseudo inverse +times the matrix what do I get if I + + align:start position:0% +times the matrix what do I get if I + + + align:start position:0% +times the matrix what do I get if I +multiply that by that what does that + + align:start position:0% +multiply that by that what does that + + + align:start position:0% +multiply that by that what does that +multiplication produce can you describe + + align:start position:0% +multiplication produce can you describe + + + align:start position:0% +multiplication produce can you describe +the well or I can when you tell me what + + align:start position:0% +the well or I can when you tell me what + + + align:start position:0% +the well or I can when you tell me what +it looks like I'll write it down so what + + align:start position:0% +it looks like I'll write it down so what + + + align:start position:0% +it looks like I'll write it down so what +is Sigma plus time Sigma if Sigma is a + + align:start position:0% +is Sigma plus time Sigma if Sigma is a + + + align:start position:0% +is Sigma plus time Sigma if Sigma is a +diagonal Sigma plus is a diagonal and + + align:start position:0% +diagonal Sigma plus is a diagonal and + + + align:start position:0% +diagonal Sigma plus is a diagonal and +they both quit after two guys what do I + + align:start position:0% +they both quit after two guys what do I + + + align:start position:0% +they both quit after two guys what do I +have one because Sigma 1 times 1 over + + align:start position:0% +have one because Sigma 1 times 1 over + + + align:start position:0% +have one because Sigma 1 times 1 over +Sigma 1 is a 1 and the other next guy is + + align:start position:0% +Sigma 1 is a 1 and the other next guy is + + + align:start position:0% +Sigma 1 is a 1 and the other next guy is +a 1 and the rest are all 0 that's right + + align:start position:0% +a 1 and the rest are all 0 that's right + + + align:start position:0% +a 1 and the rest are all 0 that's right +it's the best I could do the rank was + + align:start position:0% +it's the best I could do the rank was + + + align:start position:0% +it's the best I could do the rank was +only two so I couldn't get anywhere so + + align:start position:0% +only two so I couldn't get anywhere so + + + align:start position:0% +only two so I couldn't get anywhere so +that tells you what Sigma plus is okay + + align:start position:0% +that tells you what Sigma plus is okay + + + align:start position:0% +that tells you what Sigma plus is okay +so I described the pseudo-inverse then + + align:start position:0% +so I described the pseudo-inverse then + + + align:start position:0% +so I described the pseudo-inverse then +with a picture of spaces and then with a + + align:start position:0% +with a picture of spaces and then with a + + + align:start position:0% +with a picture of spaces and then with a +formula of matrices and now I want to + + align:start position:0% +formula of matrices and now I want to + + + align:start position:0% +formula of matrices and now I want to +use it in least squares so now I'm going + + align:start position:0% +use it in least squares so now I'm going + + + align:start position:0% +use it in least squares so now I'm going +to say what is the least squares problem + + align:start position:0% +to say what is the least squares problem + + + align:start position:0% +to say what is the least squares problem +and the first way to solve it will be to + + align:start position:0% +and the first way to solve it will be to + + + align:start position:0% +and the first way to solve it will be to +let do to involve a plus will give the + + align:start position:0% +let do to involve a plus will give the + + + align:start position:0% +let do to involve a plus will give the +solution okay so what is the what is the + + align:start position:0% +solution okay so what is the what is the + + + align:start position:0% +solution okay so what is the what is the +least squares problem let me put it here + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay the least squares problem is simply + + align:start position:0% +okay the least squares problem is simply + + + align:start position:0% +okay the least squares problem is simply +you have an equation ax equal B but a is + + align:start position:0% +you have an equation ax equal B but a is + + + align:start position:0% +you have an equation ax equal B but a is +not invertible so you can't solve it of + + align:start position:0% +not invertible so you can't solve it of + + + align:start position:0% +not invertible so you can't solve it of +course for which yeah you could find you + + align:start position:0% +course for which yeah you could find you + + + align:start position:0% +course for which yeah you could find you +could solve it for certain B's if B is + + align:start position:0% +could solve it for certain B's if B is + + + align:start position:0% +could solve it for certain B's if B is +in the column space of a then just by + + align:start position:0% +in the column space of a then just by + + + align:start position:0% +in the column space of a then just by +the meaning of column space this has a + + align:start position:0% +the meaning of column space this has a + + + align:start position:0% +the meaning of column space this has a +solution the vectors in the column space + + align:start position:0% +solution the vectors in the column space + + + align:start position:0% +solution the vectors in the column space +are the guys that you can get but the + + align:start position:0% +are the guys that you can get but the + + + align:start position:0% +are the guys that you can get but the +vectors in the orthogonal space you + + align:start position:0% +vectors in the orthogonal space you + + + align:start position:0% +vectors in the orthogonal space you +cannot get all the rest of the vectors + + align:start position:0% +cannot get all the rest of the vectors + + + align:start position:0% +cannot get all the rest of the vectors +you cannot get so suppose this is like + + align:start position:0% +you cannot get so suppose this is like + + + align:start position:0% +you cannot get so suppose this is like +so but always a is M by n rank R and + + align:start position:0% +so but always a is M by n rank R and + + + align:start position:0% +so but always a is M by n rank R and +that that then we get a inverse when M + + align:start position:0% +that that then we get a inverse when M + + + align:start position:0% +that that then we get a inverse when M +equals N equals R that's the invertible + + align:start position:0% +equals N equals R that's the invertible + + + align:start position:0% +equals N equals R that's the invertible +case ok what do we do with a system of + + align:start position:0% +case ok what do we do with a system of + + + align:start position:0% +case ok what do we do with a system of +equations when we can't solve it that's + + align:start position:0% +equations when we can't solve it that's + + + align:start position:0% +equations when we can't solve it that's +this is probably the main application in + + align:start position:0% +this is probably the main application in + + + align:start position:0% +this is probably the main application in +1806 so you've seen this problem before + + align:start position:0% +1806 so you've seen this problem before + + + align:start position:0% +1806 so you've seen this problem before +what do we do if ax equal B has no + + align:start position:0% +what do we do if ax equal B has no + + + align:start position:0% +what do we do if ax equal B has no +solution + + align:start position:0% +solution + + + align:start position:0% +solution +so typically B would be a vector of + + align:start position:0% +so typically B would be a vector of + + + align:start position:0% +so typically B would be a vector of +measurements like we're tracking a + + align:start position:0% +measurements like we're tracking a + + + align:start position:0% +measurements like we're tracking a +satellite and we get some measurements + + align:start position:0% +satellite and we get some measurements + + + align:start position:0% +satellite and we get some measurements +but and often we get too many + + align:start position:0% +but and often we get too many + + + align:start position:0% +but and often we get too many +measurements and of course there's a + + align:start position:0% +measurements and of course there's a + + + align:start position:0% +measurements and of course there's a +little noise in them and a little noise + + align:start position:0% +little noise in them and a little noise + + + align:start position:0% +little noise in them and a little noise +means that we can't solve the equations + + align:start position:0% +means that we can't solve the equations + + + align:start position:0% +means that we can't solve the equations +that maybe we're the case everybody + + align:start position:0% +that maybe we're the case everybody + + + align:start position:0% +that maybe we're the case everybody +knows is where a where this this + + align:start position:0% +knows is where a where this this + + + align:start position:0% +knows is where a where this this +equation is like expressing a straight + + align:start position:0% +equation is like expressing a straight + + + align:start position:0% +equation is like expressing a straight +line going through the data point so the + + align:start position:0% +line going through the data point so the + + + align:start position:0% +line going through the data point so the +the famous example of these squares is + + align:start position:0% +the famous example of these squares is + + + align:start position:0% +the famous example of these squares is +fit a straight line a straight line to + + align:start position:0% +fit a straight line a straight line to + + + align:start position:0% +fit a straight line a straight line to +the B's 2 B 1 B 2 we've got em + + align:start position:0% +the B's 2 B 1 B 2 we've got em + + + align:start position:0% +the B's 2 B 1 B 2 we've got em +measurements we've got em measurements + + align:start position:0% +measurements we've got em measurements + + + align:start position:0% +measurements we've got em measurements +the physics or the mechanics of the + + align:start position:0% +the physics or the mechanics of the + + + align:start position:0% +the physics or the mechanics of the +problem is pretty well linear but of + + align:start position:0% +problem is pretty well linear but of + + + align:start position:0% +problem is pretty well linear but of +course there's noise and the straight + + align:start position:0% +course there's noise and the straight + + + align:start position:0% +course there's noise and the straight +line only has two degrees of freedom + + align:start position:0% +line only has two degrees of freedom + + + align:start position:0% +line only has two degrees of freedom +however so we're going to have only two + + align:start position:0% +however so we're going to have only two + + + align:start position:0% +however so we're going to have only two +columns in our matrix a will be only two + + align:start position:0% +columns in our matrix a will be only two + + + align:start position:0% +columns in our matrix a will be only two +columns with many rows highly + + align:start position:0% +columns with many rows highly + + + align:start position:0% +columns with many rows highly +rectangular so fit a straight line let + + align:start position:0% +rectangular so fit a straight line let + + + align:start position:0% +rectangular so fit a straight line let +me call that line CX Plus D say this is + + align:start position:0% +me call that line CX Plus D say this is + + + align:start position:0% +me call that line CX Plus D say this is +the X direction this is the the bees + + align:start position:0% +the X direction this is the the bees + + + align:start position:0% +the X direction this is the the bees +direction and we've got a whole bunch of + + align:start position:0% +direction and we've got a whole bunch of + + + align:start position:0% +direction and we've got a whole bunch of +data points and they're not on a line or + + align:start position:0% +data points and they're not on a line or + + + align:start position:0% +data points and they're not on a line or +they are in a line what how would I how + + align:start position:0% +they are in a line what how would I how + + + align:start position:0% +they are in a line what how would I how +what suppose those did lie on the line + + align:start position:0% +what suppose those did lie on the line + + + align:start position:0% +what suppose those did lie on the line +what would that tell me about ax equal B + + align:start position:0% +what would that tell me about ax equal B + + + align:start position:0% +what would that tell me about ax equal B +I haven't said everything I need to but + + align:start position:0% +I haven't said everything I need to but + + + align:start position:0% +I haven't said everything I need to but +maybe the insight is what I'm after here + + align:start position:0% +maybe the insight is what I'm after here + + + align:start position:0% +maybe the insight is what I'm after here +if I if my points are right on a line so + + align:start position:0% +if I if my points are right on a line so + + + align:start position:0% +if I if my points are right on a line so +there is a straight line through them + + align:start position:0% +there is a straight line through them + + + align:start position:0% +there is a straight line through them +the unknowns here is so low B so ax the + + align:start position:0% +the unknowns here is so low B so ax the + + + align:start position:0% +the unknowns here is so low B so ax the +unknowns here are + + align:start position:0% +unknowns here are + + + align:start position:0% +unknowns here are +C&D and the right hand side is all my + + align:start position:0% +C&D and the right hand side is all my + + + align:start position:0% +C&D and the right hand side is all my +measurements okay suppose without my + + align:start position:0% +measurements okay suppose without my + + + align:start position:0% +measurements okay suppose without my +drawing a picture + + align:start position:0% +drawing a picture + + + align:start position:0% +drawing a picture +suppose the these points are on the line + + align:start position:0% +suppose the these points are on the line + + + align:start position:0% +suppose the these points are on the line +here here's the different X's the + + align:start position:0% +here here's the different X's the + + + align:start position:0% +here here's the different X's the +measurement x here's the different + + align:start position:0% +measurement x here's the different + + + align:start position:0% +measurement x here's the different +measurements but if they're on a line + + align:start position:0% +measurements but if they're on a line + + + align:start position:0% +measurements but if they're on a line +what does that tell me about my linear + + align:start position:0% +what does that tell me about my linear + + + align:start position:0% +what does that tell me about my linear +system ax equal B it has a solution + + align:start position:0% +system ax equal B it has a solution + + + align:start position:0% +system ax equal B it has a solution +being on a line means everything's + + align:start position:0% +being on a line means everything's + + + align:start position:0% +being on a line means everything's +perfect there is a solution but will + + align:start position:0% +perfect there is a solution but will + + + align:start position:0% +perfect there is a solution but will +there usually be a solution certainly + + align:start position:0% +there usually be a solution certainly + + + align:start position:0% +there usually be a solution certainly +not if I have only two parameters two + + align:start position:0% +not if I have only two parameters two + + + align:start position:0% +not if I have only two parameters two +unknowns two columns here the rank is + + align:start position:0% +unknowns two columns here the rank is + + + align:start position:0% +unknowns two columns here the rank is +going to be two and here I'm trying to + + align:start position:0% +going to be two and here I'm trying to + + + align:start position:0% +going to be two and here I'm trying to +hit any noisy set of measurements so of + + align:start position:0% +hit any noisy set of measurements so of + + + align:start position:0% +hit any noisy set of measurements so of +course in general the picture will look + + align:start position:0% +course in general the picture will look + + + align:start position:0% +course in general the picture will look +like that and I'm gonna look for the + + align:start position:0% +like that and I'm gonna look for the + + + align:start position:0% +like that and I'm gonna look for the +best C and D so I'll call it C X C CX + + align:start position:0% +best C and D so I'll call it C X C CX + + + align:start position:0% +best C and D so I'll call it C X C CX +Plus D yeah right sorry that's that's my + + align:start position:0% +Plus D yeah right sorry that's that's my + + + align:start position:0% +Plus D yeah right sorry that's that's my +line so those are my equation so oh + + align:start position:0% +line so those are my equation so oh + + + align:start position:0% +line so those are my equation so oh +sorry I often write it C plus D X do you + + align:start position:0% +sorry I often write it C plus D X do you + + + align:start position:0% +sorry I often write it C plus D X do you +mind if I put the constant term first in + + align:start position:0% +mind if I put the constant term first in + + + align:start position:0% +mind if I put the constant term first in +the in the highly difficult equation + + align:start position:0% +the in the highly difficult equation + + + align:start position:0% +the in the highly difficult equation +here for a straight line so let me tell + + align:start position:0% +here for a straight line so let me tell + + + align:start position:0% +here for a straight line so let me tell +you what I'm so these are the the points + + align:start position:0% +you what I'm so these are the the points + + + align:start position:0% +you what I'm so these are the the points +where you have a measurement X 1 X 2 up + + align:start position:0% +where you have a measurement X 1 X 2 up + + + align:start position:0% +where you have a measurement X 1 X 2 up +to X M and these are the actual + + align:start position:0% +to X M and these are the actual + + + align:start position:0% +to X M and these are the actual +measurements B 1 up to BM let's say and + + align:start position:0% +measurements B 1 up to BM let's say and + + + align:start position:0% +measurements B 1 up to BM let's say and +then my equations are yeah + + align:start position:0% +then my equations are yeah + + + align:start position:0% +then my equations are yeah +I'm just want to set up your matrix here + + align:start position:0% +I'm just want to set up your matrix here + + + align:start position:0% +I'm just want to set up your matrix here +I just want to set up the matrix so I + + align:start position:0% +I just want to set up the matrix so I + + + align:start position:0% +I just want to set up the matrix so I +want C to get multiplied by ones every + + align:start position:0% +want C to get multiplied by ones every + + + align:start position:0% +want C to get multiplied by ones every +time and I want deed + + align:start position:0% +time and I want deed + + + align:start position:0% +time and I want deed +get multiplied by these X's X 1 X 2 X 3 + + align:start position:0% +get multiplied by these X's X 1 X 2 X 3 + + + align:start position:0% +get multiplied by these X's X 1 X 2 X 3 +X M the measurement places and there was + + align:start position:0% +X M the measurement places and there was + + + align:start position:0% +X M the measurement places and there was +a measurements anyway and the part my + + align:start position:0% +a measurements anyway and the part my + + + align:start position:0% +a measurements anyway and the part my +problem is this has no solution and so + + align:start position:0% +problem is this has no solution and so + + + align:start position:0% +problem is this has no solution and so +so what do I do when there's no solution + + align:start position:0% +so what do I do when there's no solution + + + align:start position:0% +so what do I do when there's no solution +well well I'll do what gauss did he was + + align:start position:0% +well well I'll do what gauss did he was + + + align:start position:0% +well well I'll do what gauss did he was +a good mathematician so i'll follow his + + align:start position:0% +a good mathematician so i'll follow his + + + align:start position:0% +a good mathematician so i'll follow his +advice and I won't do it all semester as + + align:start position:0% +advice and I won't do it all semester as + + + align:start position:0% +advice and I won't do it all semester as +you know + + align:start position:0% +you know + + + align:start position:0% +you know +so but Gauss's advice was minimize I'll + + align:start position:0% +so but Gauss's advice was minimize I'll + + + align:start position:0% +so but Gauss's advice was minimize I'll +blame it on the Gauss the distance + + align:start position:0% +blame it on the Gauss the distance + + + align:start position:0% +blame it on the Gauss the distance +between a x + B squared the l2 norm + + align:start position:0% +between a x + B squared the l2 norm + + + align:start position:0% +between a x + B squared the l2 norm +squared which was which is just a X + + align:start position:0% +squared which was which is just a X + + + align:start position:0% +squared which was which is just a X +minus B transpose ax minus B it's a + + align:start position:0% +minus B transpose ax minus B it's a + + + align:start position:0% +minus B transpose ax minus B it's a +quadratic and minimizing it gives me a + + align:start position:0% +quadratic and minimizing it gives me a + + + align:start position:0% +quadratic and minimizing it gives me a +system of linear equations so in the end + + align:start position:0% +system of linear equations so in the end + + + align:start position:0% +system of linear equations so in the end +they will have a solution so that's the + + align:start position:0% +they will have a solution so that's the + + + align:start position:0% +they will have a solution so that's the +whole point of these squares we have an + + align:start position:0% +whole point of these squares we have an + + + align:start position:0% +whole point of these squares we have an +unsolvable problem not no solution we + + align:start position:0% +unsolvable problem not no solution we + + + align:start position:0% +unsolvable problem not no solution we +follow a Gauss's advice to get the best + + align:start position:0% +follow a Gauss's advice to get the best + + + align:start position:0% +follow a Gauss's advice to get the best +we can and that does produce an answer + + align:start position:0% +we can and that does produce an answer + + + align:start position:0% +we can and that does produce an answer +so this is this is if I multiply this as + + align:start position:0% +so this is this is if I multiply this as + + + align:start position:0% +so this is this is if I multiply this as +out as X transpose a transpose ax that + + align:start position:0% +out as X transpose a transpose ax that + + + align:start position:0% +out as X transpose a transpose ax that +comes from the square term and then I + + align:start position:0% +comes from the square term and then I + + + align:start position:0% +comes from the square term and then I +have probably these actually will + + align:start position:0% + + + + align:start position:0% + +probably I'll get two of those and then + + align:start position:0% +probably I'll get two of those and then + + + align:start position:0% +probably I'll get two of those and then +a constant term that has derivative 0 so + + align:start position:0% +a constant term that has derivative 0 so + + + align:start position:0% +a constant term that has derivative 0 so +it doesn't enter so this is what I'm + + align:start position:0% +it doesn't enter so this is what I'm + + + align:start position:0% +it doesn't enter so this is what I'm +minimizing this is the loss function and + + align:start position:0% +minimizing this is the loss function and + + + align:start position:0% +minimizing this is the loss function and +it leads to let's just jump to the so + + align:start position:0% +it leads to let's just jump to the so + + + align:start position:0% +it leads to let's just jump to the so +the to the key here what equation do I + + align:start position:0% +the to the key here what equation do I + + + align:start position:0% +the to the key here what equation do I +get when I + + align:start position:0% +get when I + + + align:start position:0% +get when I +for what equation is solved by the best + + align:start position:0% +for what equation is solved by the best + + + align:start position:0% +for what equation is solved by the best +X the best X the best act solves the + + align:start position:0% +X the best X the best act solves the + + + align:start position:0% +X the best X the best act solves the +famous so this is regression and + + align:start position:0% +famous so this is regression and + + + align:start position:0% +famous so this is regression and +statistics linear regression + + align:start position:0% + + + + align:start position:0% + +one of the main computations and + + align:start position:0% +one of the main computations and + + + align:start position:0% +one of the main computations and +statistics not of course just for + + align:start position:0% +statistics not of course just for + + + align:start position:0% +statistics not of course just for +straight line fits but for any system ax + + align:start position:0% +straight line fits but for any system ax + + + align:start position:0% +straight line fits but for any system ax +equal B that will lead to this minimum + + align:start position:0% +equal B that will lead to this minimum + + + align:start position:0% +equal B that will lead to this minimum +will lead to a system of equations that + + align:start position:0% +will lead to a system of equations that + + + align:start position:0% +will lead to a system of equations that +I'm going to put a box around because + + align:start position:0% +I'm going to put a box around because + + + align:start position:0% +I'm going to put a box around because +it's so fundamental and are you willing + + align:start position:0% +it's so fundamental and are you willing + + + align:start position:0% +it's so fundamental and are you willing +to tell me what that equation is yes + + align:start position:0% +to tell me what that equation is yes + + + align:start position:0% +to tell me what that equation is yes +thanks a transpose a it's gonna come + + align:start position:0% +thanks a transpose a it's gonna come + + + align:start position:0% +thanks a transpose a it's gonna come +from there you see it times the best x + + align:start position:0% +from there you see it times the best x + + + align:start position:0% +from there you see it times the best x +equals a transpose B that gives the + + align:start position:0% +equals a transpose B that gives the + + + align:start position:0% +equals a transpose B that gives the +minimum + + align:start position:0% +minimum + + + align:start position:0% +minimum +let me forego checking that you you see + + align:start position:0% +let me forego checking that you you see + + + align:start position:0% +let me forego checking that you you see +that the quadratic term has the matrix + + align:start position:0% +that the quadratic term has the matrix + + + align:start position:0% +that the quadratic term has the matrix +in it so it's derivative is may be may + + align:start position:0% +in it so it's derivative is may be may + + + align:start position:0% +in it so it's derivative is may be may +be the derivative of this is to a + + align:start position:0% +be the derivative of this is to a + + + align:start position:0% +be the derivative of this is to a +transpose ax and then the two cancels + + align:start position:0% +transpose ax and then the two cancels + + + align:start position:0% +transpose ax and then the two cancels +that two and this could also be written + + align:start position:0% +that two and this could also be written + + + align:start position:0% +that two and this could also be written +as X transpose a transpose B so it's X + + align:start position:0% +as X transpose a transpose B so it's X + + + align:start position:0% +as X transpose a transpose B so it's X +transpose against a transpose B that's + + align:start position:0% +transpose against a transpose B that's + + + align:start position:0% +transpose against a transpose B that's +linear so when I take the derivative + + align:start position:0% +linear so when I take the derivative + + + align:start position:0% +linear so when I take the derivative +it's that country that's pretty fast + + align:start position:0% +it's that country that's pretty fast + + + align:start position:0% +it's that country that's pretty fast +1806 would patiently derive that but + + align:start position:0% +1806 would patiently derive that but + + + align:start position:0% +1806 would patiently derive that but +here I let me give you the picture that + + align:start position:0% +here I let me give you the picture that + + + align:start position:0% +here I let me give you the picture that +goes with it the geometry so we have we + + align:start position:0% +goes with it the geometry so we have we + + + align:start position:0% +goes with it the geometry so we have we +have the problem no solution we have + + align:start position:0% +have the problem no solution we have + + + align:start position:0% +have the problem no solution we have +Gauss's + + align:start position:0% +Gauss's + + + align:start position:0% +Gauss's +best answer minimize the to norm of the + + align:start position:0% +best answer minimize the to norm of the + + + align:start position:0% +best answer minimize the to norm of the +error we have the conclusion the matrix + + align:start position:0% +error we have the conclusion the matrix + + + align:start position:0% +error we have the conclusion the matrix +that we get in and now I want to draw a + + align:start position:0% +that we get in and now I want to draw a + + + align:start position:0% +that we get in and now I want to draw a +picture that goes with it okay so here + + align:start position:0% +picture that goes with it okay so here + + + align:start position:0% +picture that goes with it okay so here +is a picture I want to I want to have + + align:start position:0% +is a picture I want to I want to have + + + align:start position:0% +is a picture I want to I want to have +column space of a there in that picture + + align:start position:0% +column space of a there in that picture + + + align:start position:0% +column space of a there in that picture +of course the zero vectors in the column + + align:start position:0% +of course the zero vectors in the column + + + align:start position:0% +of course the zero vectors in the column +space of a so this is this is all + + align:start position:0% +space of a so this is this is all + + + align:start position:0% +space of a so this is this is all +possible vectors ax right + + align:start position:0% +possible vectors ax right + + + align:start position:0% +possible vectors ax right +you're never forgetting that the column + + align:start position:0% +you're never forgetting that the column + + + align:start position:0% +you're never forgetting that the column +space is all the a X's now I've got to + + align:start position:0% +space is all the a X's now I've got to + + + align:start position:0% +space is all the a X's now I've got to +put B in the picture so where does this + + align:start position:0% +put B in the picture so where does this + + + align:start position:0% +put B in the picture so where does this +vector B so I'm trying to solve ax equal + + align:start position:0% +vector B so I'm trying to solve ax equal + + + align:start position:0% +vector B so I'm trying to solve ax equal +B but failing so what if I draw B in + + align:start position:0% +B but failing so what if I draw B in + + + align:start position:0% +B but failing so what if I draw B in +this picture how do I draw B where do I + + align:start position:0% +this picture how do I draw B where do I + + + align:start position:0% +this picture how do I draw B where do I +put it + + align:start position:0% +put it + + + align:start position:0% +put it +shall I put it in the column space no + + align:start position:0% +shall I put it in the column space no + + + align:start position:0% +shall I put it in the column space no +the whole point is it's not in the + + align:start position:0% +the whole point is it's not in the + + + align:start position:0% +the whole point is it's not in the +column space it's not an ax it's out + + align:start position:0% +column space it's not an ax it's out + + + align:start position:0% +column space it's not an ax it's out +there somewhere B okay and then what's + + align:start position:0% +there somewhere B okay and then what's + + + align:start position:0% +there somewhere B okay and then what's +the geometry that goes with these + + align:start position:0% +the geometry that goes with these + + + align:start position:0% +the geometry that goes with these +squares and the normal equations and + + align:start position:0% +squares and the normal equations and + + + align:start position:0% +squares and the normal equations and +Gauss's suggestion to minimize the error + + align:start position:0% +Gauss's suggestion to minimize the error + + + align:start position:0% +Gauss's suggestion to minimize the error +what will where will ax be the best ax + + align:start position:0% +what will where will ax be the best ax + + + align:start position:0% +what will where will ax be the best ax +that I can do + + align:start position:0% +that I can do + + + align:start position:0% +that I can do +where will so so so Gauss is what Gauss + + align:start position:0% +where will so so so Gauss is what Gauss + + + align:start position:0% +where will so so so Gauss is what Gauss +has produced is a an a the other he + + align:start position:0% +has produced is a an a the other he + + + align:start position:0% +has produced is a an a the other he +can't find an X he'll do his best he can + + align:start position:0% +can't find an X he'll do his best he can + + + align:start position:0% +can't find an X he'll do his best he can +and we're calling that guy X hat and + + align:start position:0% +and we're calling that guy X hat and + + + align:start position:0% +and we're calling that guy X hat and +this is the algebra to find X hat and + + align:start position:0% +this is the algebra to find X hat and + + + align:start position:0% +this is the algebra to find X hat and +now where's the picture here where is + + align:start position:0% +now where's the picture here where is + + + align:start position:0% +now where's the picture here where is +this vector ax hat which is the best ik + + align:start position:0% +this vector ax hat which is the best ik + + + align:start position:0% +this vector ax hat which is the best ik +ax we can get so it has to be + + align:start position:0% +ax we can get so it has to be + + + align:start position:0% +ax we can get so it has to be +in the column space because it's a times + + align:start position:0% +in the column space because it's a times + + + align:start position:0% +in the column space because it's a times +something and where is it in the column + + align:start position:0% +something and where is it in the column + + + align:start position:0% +something and where is it in the column +space + + align:start position:0% +space + + + align:start position:0% +space +it's the projection that's a x half and + + align:start position:0% +it's the projection that's a x half and + + + align:start position:0% +it's the projection that's a x half and +here's the error which you couldn't do + + align:start position:0% +here's the error which you couldn't do + + + align:start position:0% +here's the error which you couldn't do +anything about B minus a X F yeah so + + align:start position:0% +anything about B minus a X F yeah so + + + align:start position:0% +anything about B minus a X F yeah so +it's the projection right so that all + + align:start position:0% +it's the projection right so that all + + + align:start position:0% +it's the projection right so that all +this is justifying the so we're we're in + + align:start position:0% +this is justifying the so we're we're in + + + align:start position:0% +this is justifying the so we're we're in +the second approach to these squares + + align:start position:0% +the second approach to these squares + + + align:start position:0% +the second approach to these squares +solves the normal equations solve the + + align:start position:0% +solves the normal equations solve the + + + align:start position:0% +solves the normal equations solve the +normal equations yeah that would be the + + align:start position:0% +normal equations yeah that would be the + + + align:start position:0% +normal equations yeah that would be the +second approach to least squares and + + align:start position:0% + + + + align:start position:0% + +most examples if they're not very big or + + align:start position:0% +most examples if they're not very big or + + + align:start position:0% +most examples if they're not very big or +very difficult you just creates a matrix + + align:start position:0% +very difficult you just creates a matrix + + + align:start position:0% +very difficult you just creates a matrix +a transpose a and you call MATLAB and + + align:start position:0% +a transpose a and you call MATLAB and + + + align:start position:0% +a transpose a and you call MATLAB and +solve that linear system you create the + + align:start position:0% +solve that linear system you create the + + + align:start position:0% +solve that linear system you create the +matrix you create the right hand side + + align:start position:0% +matrix you create the right hand side + + + align:start position:0% +matrix you create the right hand side +and you solve it so that's the ordinary + + align:start position:0% +and you solve it so that's the ordinary + + + align:start position:0% +and you solve it so that's the ordinary +run-of-the-mill + + align:start position:0% +run-of-the-mill + + + align:start position:0% +run-of-the-mill +these squares problems just do it so + + align:start position:0% +these squares problems just do it so + + + align:start position:0% +these squares problems just do it so +that's method 2 just do it + + align:start position:0% + + + + align:start position:0% + +what's method 3 for the same we're + + align:start position:0% +what's method 3 for the same we're + + + align:start position:0% +what's method 3 for the same we're +talking about the same problem here but + + align:start position:0% +talking about the same problem here but + + + align:start position:0% +talking about the same problem here but +now I'm thinking it may be a little more + + align:start position:0% +now I'm thinking it may be a little more + + + align:start position:0% +now I'm thinking it may be a little more +difficult this matrix a transpose a + + align:start position:0% +difficult this matrix a transpose a + + + align:start position:0% +difficult this matrix a transpose a +might be nearly singular Gauss is + + align:start position:0% +might be nearly singular Gauss is + + + align:start position:0% +might be nearly singular Gauss is +assuming that yeah yeah when did this + + align:start position:0% +assuming that yeah yeah when did this + + + align:start position:0% +assuming that yeah yeah when did this +work when did this work and it will + + align:start position:0% +work when did this work and it will + + + align:start position:0% +work when did this work and it will +continue to work in the next three this + + align:start position:0% +continue to work in the next three this + + + align:start position:0% +continue to work in the next three this +works this is good if assuming a has + + align:start position:0% +works this is good if assuming a has + + + align:start position:0% +works this is good if assuming a has +independent columns + + align:start position:0% + + + + align:start position:0% + +ya better just make clear I'm claiming + + align:start position:0% +ya better just make clear I'm claiming + + + align:start position:0% +ya better just make clear I'm claiming +that when a hasn't so what's the what's + + align:start position:0% +that when a hasn't so what's the what's + + + align:start position:0% +that when a hasn't so what's the what's +the reasoning if a has independent + + align:start position:0% +the reasoning if a has independent + + + align:start position:0% +the reasoning if a has independent +columns but maybe not enough columns + + align:start position:0% +columns but maybe not enough columns + + + align:start position:0% +columns but maybe not enough columns +like here it's only got two columns + + align:start position:0% +like here it's only got two columns + + + align:start position:0% +like here it's only got two columns +that's obviously not going to be able to + + align:start position:0% +that's obviously not going to be able to + + + align:start position:0% +that's obviously not going to be able to +match any right hand side but it's got + + align:start position:0% +match any right hand side but it's got + + + align:start position:0% +match any right hand side but it's got +independent columns when a has + + align:start position:0% +independent columns when a has + + + align:start position:0% +independent columns when a has +independent columns then what can I say + + align:start position:0% +independent columns then what can I say + + + align:start position:0% +independent columns then what can I say +about this matrix it's invertible + + align:start position:0% +about this matrix it's invertible + + + align:start position:0% +about this matrix it's invertible +Gauss's plan works if a has independent + + align:start position:0% +Gauss's plan works if a has independent + + + align:start position:0% +Gauss's plan works if a has independent +columns then this would be a linear + + align:start position:0% +columns then this would be a linear + + + align:start position:0% +columns then this would be a linear +algebra step then this will be + + align:start position:0% +algebra step then this will be + + + align:start position:0% +algebra step then this will be +invertible you see the importance of + + align:start position:0% +invertible you see the importance of + + + align:start position:0% +invertible you see the importance of +that step if a has independent columns + + align:start position:0% +that step if a has independent columns + + + align:start position:0% +that step if a has independent columns +that means it has no null space only X + + align:start position:0% +that means it has no null space only X + + + align:start position:0% +that means it has no null space only X +equal zero is in the null space two + + align:start position:0% +equal zero is in the null space two + + + align:start position:0% +equal zero is in the null space two +independent columns but only two so not + + align:start position:0% +independent columns but only two so not + + + align:start position:0% +independent columns but only two so not +enough to solve systems but independent + + align:start position:0% +enough to solve systems but independent + + + align:start position:0% +enough to solve systems but independent +then you're okay this matrix is + + align:start position:0% +then you're okay this matrix is + + + align:start position:0% +then you're okay this matrix is +invertible you can do what Gauss tells + + align:start position:0% +invertible you can do what Gauss tells + + + align:start position:0% +invertible you can do what Gauss tells +you but we're prepared now we have to + + align:start position:0% +you but we're prepared now we have to + + + align:start position:0% +you but we're prepared now we have to +think okay so that what do I really want + + align:start position:0% +think okay so that what do I really want + + + align:start position:0% +think okay so that what do I really want +to do I want to connect this Gauss's + + align:start position:0% +to do I want to connect this Gauss's + + + align:start position:0% +to do I want to connect this Gauss's +solution to the pseudo inverse because + + align:start position:0% +solution to the pseudo inverse because + + + align:start position:0% +solution to the pseudo inverse because +I'm claiming they both give the same + + align:start position:0% +I'm claiming they both give the same + + + align:start position:0% +I'm claiming they both give the same +result the pseudo inverse yeah the + + align:start position:0% +result the pseudo inverse yeah the + + + align:start position:0% +result the pseudo inverse yeah the +pseudo inverse will apply but we have we + + align:start position:0% +pseudo inverse will apply but we have we + + + align:start position:0% +pseudo inverse will apply but we have we +have like something this a is not + + align:start position:0% +have like something this a is not + + + align:start position:0% +have like something this a is not +invertible just keep keep remembering + + align:start position:0% +invertible just keep keep remembering + + + align:start position:0% +invertible just keep keep remembering +this matrix it's not invertible but it's + + align:start position:0% +this matrix it's not invertible but it's + + + align:start position:0% +this matrix it's not invertible but it's +it has got independent columns what am i + + align:start position:0% +it has got independent columns what am i + + + align:start position:0% +it has got independent columns what am i +saying they're just just going back to + + align:start position:0% +saying they're just just going back to + + + align:start position:0% +saying they're just just going back to +the picture + + align:start position:0% + + + + align:start position:0% + +if if a has is a matrix with independent + + align:start position:0% +if if a has is a matrix with independent + + + align:start position:0% +if if a has is a matrix with independent +columns what space disappears in this + + align:start position:0% +columns what space disappears in this + + + align:start position:0% +columns what space disappears in this +picture the null space goes away so the + + align:start position:0% +picture the null space goes away so the + + + align:start position:0% +picture the null space goes away so the +picture is simpler but it's still the + + align:start position:0% +picture is simpler but it's still the + + + align:start position:0% +picture is simpler but it's still the +null space of a of a transpose this is + + align:start position:0% +null space of a of a transpose this is + + + align:start position:0% +null space of a of a transpose this is +still pretty big because I only had two + + align:start position:0% +still pretty big because I only had two + + + align:start position:0% +still pretty big because I only had two +columns and a whole lot of rows and + + align:start position:0% +columns and a whole lot of rows and + + + align:start position:0% +columns and a whole lot of rows and +that's gonna be reflected here + + align:start position:0% +that's gonna be reflected here + + + align:start position:0% +that's gonna be reflected here +so what what am I trying to say I'm + + align:start position:0% +so what what am I trying to say I'm + + + align:start position:0% +so what what am I trying to say I'm +trying to say that this answer is the + + align:start position:0% +trying to say that this answer is the + + + align:start position:0% +trying to say that this answer is the +same as the pseudo-inverse answer do we + + align:start position:0% +same as the pseudo-inverse answer do we + + + align:start position:0% +same as the pseudo-inverse answer do we +could possibly even check that point let + + align:start position:0% +could possibly even check that point let + + + align:start position:0% +could possibly even check that point let +me write it down first + + align:start position:0% +me write it down first + + + align:start position:0% +me write it down first +I claim that the answer a plus B is the + + align:start position:0% +I claim that the answer a plus B is the + + + align:start position:0% +I claim that the answer a plus B is the +same as the answer coming from here a + + align:start position:0% +same as the answer coming from here a + + + align:start position:0% +same as the answer coming from here a +transpose a inverse a transpose B when I + + align:start position:0% +transpose a inverse a transpose B when I + + + align:start position:0% +transpose a inverse a transpose B when I +guess the null space is zero the rank is + + align:start position:0% +guess the null space is zero the rank is + + + align:start position:0% +guess the null space is zero the rank is +all of em whatever you like to say I + + align:start position:0% +all of em whatever you like to say I + + + align:start position:0% +all of em whatever you like to say I +believe that that that method one this + + align:start position:0% +believe that that that method one this + + + align:start position:0% +believe that that that method one this +to it in one quick formula so remember + + align:start position:0% +to it in one quick formula so remember + + + align:start position:0% +to it in one quick formula so remember +that this was V Sigma plus u transpose + + align:start position:0% +that this was V Sigma plus u transpose + + + align:start position:0% +that this was V Sigma plus u transpose +right that's what a a transpose was that + + align:start position:0% +right that's what a a transpose was that + + + align:start position:0% +right that's what a a transpose was that +this should agree with this I I believe + + align:start position:0% +this should agree with this I I believe + + + align:start position:0% +this should agree with this I I believe +those are the same when the null space + + align:start position:0% +those are the same when the null space + + + align:start position:0% +those are the same when the null space +isn't in the picture so the fact that + + align:start position:0% +isn't in the picture so the fact that + + + align:start position:0% +isn't in the picture so the fact that +the null space is just a zero vector + + align:start position:0% +the null space is just a zero vector + + + align:start position:0% +the null space is just a zero vector +means that this in this inverse does + + align:start position:0% +means that this in this inverse does + + + align:start position:0% +means that this in this inverse does +exist so this inverse exists but but a a + + align:start position:0% +exist so this inverse exists but but a a + + + align:start position:0% +exist so this inverse exists but but a a +transpose is not invertible + + align:start position:0% +transpose is not invertible + + + align:start position:0% +transpose is not invertible +right no wait no inverse because a a + + align:start position:0% +right no wait no inverse because a a + + + align:start position:0% +right no wait no inverse because a a +transpose would be coming with a + + align:start position:0% +transpose would be coming with a + + + align:start position:0% +transpose would be coming with a +transpose all this is a null space of a + + align:start position:0% +transpose all this is a null space of a + + + align:start position:0% +transpose all this is a null space of a +transpose so a transpose is not + + align:start position:0% +transpose so a transpose is not + + + align:start position:0% +transpose so a transpose is not +invertible but but a transpose a is + + align:start position:0% +invertible but but a transpose a is + + + align:start position:0% +invertible but but a transpose a is +invertible could you how would you check + + align:start position:0% +invertible could you how would you check + + + align:start position:0% +invertible could you how would you check +that you see when i'm it's taken like + + align:start position:0% +that you see when i'm it's taken like + + + align:start position:0% +that you see when i'm it's taken like +pretty much the whole hour to get a + + align:start position:0% +pretty much the whole hour to get a + + + align:start position:0% +pretty much the whole hour to get a +picture of the geometry of the + + align:start position:0% +picture of the geometry of the + + + align:start position:0% +picture of the geometry of the +pseudo-inverse so this is the pseudo + + align:start position:0% +pseudo-inverse so this is the pseudo + + + align:start position:0% +pseudo-inverse so this is the pseudo +inverse and this is that matrix there + + align:start position:0% +inverse and this is that matrix there + + + align:start position:0% +inverse and this is that matrix there +what you know it's really doing its best + + align:start position:0% +what you know it's really doing its best + + + align:start position:0% +what you know it's really doing its best +to be the inverse in fact everybody here + + align:start position:0% +to be the inverse in fact everybody here + + + align:start position:0% +to be the inverse in fact everybody here +is just like doing their best to be the + + align:start position:0% +is just like doing their best to be the + + + align:start position:0% +is just like doing their best to be the +inverse now how well is this how close + + align:start position:0% +inverse now how well is this how close + + + align:start position:0% +inverse now how well is this how close +is that to being the inverse can I just + + align:start position:0% +is that to being the inverse can I just + + + align:start position:0% +is that to being the inverse can I just +ask you about that and then I'll make + + align:start position:0% +ask you about that and then I'll make + + + align:start position:0% +ask you about that and then I'll make +this connection and then we're out of + + align:start position:0% +this connection and then we're out of + + + align:start position:0% +this connection and then we're out of +time how close is that to being the + + align:start position:0% +time how close is that to being the + + + align:start position:0% +time how close is that to being the +inverse of a suppose I multiply that by + + align:start position:0% +inverse of a suppose I multiply that by + + + align:start position:0% +inverse of a suppose I multiply that by +a what do I get so so just notice if I + + align:start position:0% +a what do I get so so just notice if I + + + align:start position:0% +a what do I get so so just notice if I +multiply that by a what do I get + + align:start position:0% +multiply that by a what do I get + + + align:start position:0% +multiply that by a what do I get +I get yeah I get I terrific but don't be + + align:start position:0% +I get yeah I get I terrific but don't be + + + align:start position:0% +I get yeah I get I terrific but don't be +deceived to thinking that this is the + + align:start position:0% +deceived to thinking that this is the + + + align:start position:0% +deceived to thinking that this is the +inverse of a it only it worked on the + + align:start position:0% +inverse of a it only it worked on the + + + align:start position:0% +inverse of a it only it worked on the +left side but it's not going to be good + + align:start position:0% +left side but it's not going to be good + + + align:start position:0% +left side but it's not going to be good +on the right-hand side so if I try if I + + align:start position:0% +on the right-hand side so if I try if I + + + align:start position:0% +on the right-hand side so if I try if I +multiply a by this guy in that direction + + align:start position:0% +multiply a by this guy in that direction + + + align:start position:0% +multiply a by this guy in that direction +I'll get like as close to the identity + + align:start position:0% +I'll get like as close to the identity + + + align:start position:0% +I'll get like as close to the identity +as I can come but I won't get the + + align:start position:0% +as I can come but I won't get the + + + align:start position:0% +as I can come but I won't get the +identity that way so this is this a + + align:start position:0% +identity that way so this is this a + + + align:start position:0% +identity that way so this is this a +little box to say + + align:start position:0% +little box to say + + + align:start position:0% +little box to say +so what's the point of making I'm + + align:start position:0% +so what's the point of making I'm + + + align:start position:0% +so what's the point of making I'm +claiming that this is the pseudo-inverse + + align:start position:0% +claiming that this is the pseudo-inverse + + + align:start position:0% +claiming that this is the pseudo-inverse +whatever whatever these spaces the rain + + align:start position:0% +whatever whatever these spaces the rain + + + align:start position:0% +whatever whatever these spaces the rain +could be tiny just just one this works + + align:start position:0% +could be tiny just just one this works + + + align:start position:0% +could be tiny just just one this works +when the rank is in this I needed + + align:start position:0% +when the rank is in this I needed + + + align:start position:0% +when the rank is in this I needed +independent columns so when the rank is + + align:start position:0% +independent columns so when the rank is + + + align:start position:0% +independent columns so when the rank is +in so this is rank equal and that that + + align:start position:0% +in so this is rank equal and that that + + + align:start position:0% +in so this is rank equal and that that +Gauss worked then I can get a one then + + align:start position:0% +Gauss worked then I can get a one then + + + align:start position:0% +Gauss worked then I can get a one then +it's a one-sided inverse but it's not a + + align:start position:0% +it's a one-sided inverse but it's not a + + + align:start position:0% +it's a one-sided inverse but it's not a +two-sided inverse I can't do that but my + + align:start position:0% +two-sided inverse I can't do that but my + + + align:start position:0% +two-sided inverse I can't do that but my +matrix there I could find a one-sided + + align:start position:0% +matrix there I could find a one-sided + + + align:start position:0% +matrix there I could find a one-sided +inverse to get the 2 by 2 identity but I + + align:start position:0% +inverse to get the 2 by 2 identity but I + + + align:start position:0% +inverse to get the 2 by 2 identity but I +could never + + align:start position:0% +could never + + + align:start position:0% +could never +multiply that by some matrix and get the + + align:start position:0% +multiply that by some matrix and get the + + + align:start position:0% +multiply that by some matrix and get the +N by n identity those two pathetic + + align:start position:0% +N by n identity those two pathetic + + + align:start position:0% +N by n identity those two pathetic +columns okay + + align:start position:0% +columns okay + + + align:start position:0% +columns okay +maybe you feel like just checking this + + align:start position:0% +maybe you feel like just checking this + + + align:start position:0% +maybe you feel like just checking this +just takes patience what do I mean by + + align:start position:0% +just takes patience what do I mean by + + + align:start position:0% +just takes patience what do I mean by +checking it I mean stick in the pseudo + + align:start position:0% +checking it I mean stick in the pseudo + + + align:start position:0% +checking it I mean stick in the pseudo +the the SVD just put in the SVD and + + align:start position:0% +the the SVD just put in the SVD and + + + align:start position:0% +the the SVD just put in the SVD and +cancel like crazy and I think that'll + + align:start position:0% +cancel like crazy and I think that'll + + + align:start position:0% +cancel like crazy and I think that'll +pop out do you like believe me cuz it's + + align:start position:0% +pop out do you like believe me cuz it's + + + align:start position:0% +pop out do you like believe me cuz it's +gonna be a little painful 3 you know you + + align:start position:0% +gonna be a little painful 3 you know you + + + align:start position:0% +gonna be a little painful 3 you know you +say my V transpose all transposed and + + align:start position:0% +say my V transpose all transposed and + + + align:start position:0% +say my V transpose all transposed and +then something there and suddenly there + + align:start position:0% +then something there and suddenly there + + + align:start position:0% +then something there and suddenly there +I've got 9 matrices multiplying away but + + align:start position:0% +I've got 9 matrices multiplying away but + + + align:start position:0% +I've got 9 matrices multiplying away but +it's gonna like how all sorts of things + + align:start position:0% +it's gonna like how all sorts of things + + + align:start position:0% +it's gonna like how all sorts of things +will produce the identity and in the end + + align:start position:0% +will produce the identity and in the end + + + align:start position:0% +will produce the identity and in the end +that's what I'll have right right yep so + + align:start position:0% +that's what I'll have right right yep so + + + align:start position:0% +that's what I'll have right right yep so +that's this is the this is the it's a + + align:start position:0% +that's this is the this is the it's a + + + align:start position:0% +that's this is the this is the it's a +one-sided true inverse where the SVD + + align:start position:0% +one-sided true inverse where the SVD + + + align:start position:0% +one-sided true inverse where the SVD +this formula is prepared to have neither + + align:start position:0% +this formula is prepared to have neither + + + align:start position:0% +this formula is prepared to have neither +side invertible it's still we know what + + align:start position:0% +side invertible it's still we know what + + + align:start position:0% +side invertible it's still we know what +Sigma plus means anyway so under the + + align:start position:0% +Sigma plus means anyway so under the + + + align:start position:0% +Sigma plus means anyway so under the +assumption of independent columns Gauss + + align:start position:0% +assumption of independent columns Gauss + + + align:start position:0% +assumption of independent columns Gauss +works and gives the same answer as their + + align:start position:0% +works and gives the same answer as their + + + align:start position:0% +works and gives the same answer as their +pseudo inverse + + align:start position:0% + + + + align:start position:0% + +okay three minutes + + align:start position:0% +okay three minutes + + + align:start position:0% +okay three minutes +that's hardly time but this being a + + align:start position:0% +that's hardly time but this being a + + + align:start position:0% +that's hardly time but this being a +mighty I feel I should use it oh my god + + align:start position:0% +mighty I feel I should use it oh my god + + + align:start position:0% +mighty I feel I should use it oh my god +number three so what's number three + + align:start position:0% +number three so what's number three + + + align:start position:0% +number three so what's number three +about number three is is a is a as the + + align:start position:0% +about number three is is a is a as the + + + align:start position:0% +about number three is is a is a as the +same requirement as number two the same + + align:start position:0% +same requirement as number two the same + + + align:start position:0% +same requirement as number two the same +requirement of no null space but it says + + align:start position:0% +requirement of no null space but it says + + + align:start position:0% +requirement of no null space but it says +if I could get orthogonal columns first + + align:start position:0% +if I could get orthogonal columns first + + + align:start position:0% +if I could get orthogonal columns first +then this problem would be easy so + + align:start position:0% +then this problem would be easy so + + + align:start position:0% +then this problem would be easy so +everybody knows that gram-schmidt is a + + align:start position:0% +everybody knows that gram-schmidt is a + + + align:start position:0% +everybody knows that gram-schmidt is a +way boring way to get from from from + + align:start position:0% +way boring way to get from from from + + + align:start position:0% +way boring way to get from from from +these two columns to get two orthogonal + + align:start position:0% +these two columns to get two orthogonal + + + align:start position:0% +these two columns to get two orthogonal +columns actually the whole idea of + + align:start position:0% +columns actually the whole idea of + + + align:start position:0% +columns actually the whole idea of +gram-schmidt is already there for + + align:start position:0% +gram-schmidt is already there for + + + align:start position:0% +gram-schmidt is already there for +two-by-two so with so I have two minutes + + align:start position:0% +two-by-two so with so I have two minutes + + + align:start position:0% +two-by-two so with so I have two minutes +and we can do it let's see let's do + + align:start position:0% +and we can do it let's see let's do + + + align:start position:0% +and we can do it let's see let's do +gram-schmidt on these two columns column + + align:start position:0% +gram-schmidt on these two columns column + + + align:start position:0% +gram-schmidt on these two columns column +column a column column you accountant I + + align:start position:0% +column a column column you accountant I + + + align:start position:0% +column a column column you accountant I +don't want to use U and V column y&z + + align:start position:0% +don't want to use U and V column y&z + + + align:start position:0% +don't want to use U and V column y&z +okay suppose I want to orthogonalize + + align:start position:0% +okay suppose I want to orthogonalize + + + align:start position:0% +okay suppose I want to orthogonalize +those guys what's the gram-schmidt idea + + align:start position:0% +those guys what's the gram-schmidt idea + + + align:start position:0% +those guys what's the gram-schmidt idea +i take why it's perfectly good no + + align:start position:0% +i take why it's perfectly good no + + + align:start position:0% +i take why it's perfectly good no +problem with y there's the y vector + + align:start position:0% +problem with y there's the y vector + + + align:start position:0% +problem with y there's the y vector +they're all ones then this guy is not + + align:start position:0% +they're all ones then this guy is not + + + align:start position:0% +they're all ones then this guy is not +orthogonal probably to that it'll go off + + align:start position:0% +orthogonal probably to that it'll go off + + + align:start position:0% +orthogonal probably to that it'll go off +and some this in this direction with an + + align:start position:0% +and some this in this direction with an + + + align:start position:0% +and some this in this direction with an +angle that's not ninety degrees so what + + align:start position:0% +angle that's not ninety degrees so what + + + align:start position:0% +angle that's not ninety degrees so what +do i do i want to get orthogonal vectors + + align:start position:0% +do i do i want to get orthogonal vectors + + + align:start position:0% +do i do i want to get orthogonal vectors +I'm okay with this first guy but the + + align:start position:0% +I'm okay with this first guy but the + + + align:start position:0% +I'm okay with this first guy but the +second guy isn't orthogonal to the first + + align:start position:0% +second guy isn't orthogonal to the first + + + align:start position:0% +second guy isn't orthogonal to the first +so what do I do + + align:start position:0% +so what do I do + + + align:start position:0% +so what do I do +how do I in this picture how do I come + + align:start position:0% +how do I in this picture how do I come + + + align:start position:0% +how do I in this picture how do I come +up with a vector orthogonal to Y project + + align:start position:0% +up with a vector orthogonal to Y project + + + align:start position:0% +up with a vector orthogonal to Y project +I could I take this Z and I take its + + align:start position:0% +I could I take this Z and I take its + + + align:start position:0% +I could I take this Z and I take its +projection so Z has a little piece + + align:start position:0% +projection so Z has a little piece + + + align:start position:0% +projection so Z has a little piece +that Z vector has a little big piece + + align:start position:0% +that Z vector has a little big piece + + + align:start position:0% +that Z vector has a little big piece +already in the direction of what Y which + + align:start position:0% +already in the direction of what Y which + + + align:start position:0% +already in the direction of what Y which +I don't want and a piece orthogonal to + + align:start position:0% +I don't want and a piece orthogonal to + + + align:start position:0% +I don't want and a piece orthogonal to +it that's my other piece that's my other + + align:start position:0% +it that's my other piece that's my other + + + align:start position:0% +it that's my other piece that's my other +piece so here's why and here's the the + + align:start position:0% +piece so here's why and here's the the + + + align:start position:0% +piece so here's why and here's the the +this is that is Z minus the minus a + + align:start position:0% +this is that is Z minus the minus a + + + align:start position:0% +this is that is Z minus the minus a +projection let me just say whatever yeah + + align:start position:0% +projection let me just say whatever yeah + + + align:start position:0% +projection let me just say whatever yeah +I don't know if I even drew that picture + + align:start position:0% +I don't know if I even drew that picture + + + align:start position:0% +I don't know if I even drew that picture +right probably I didn't anyway whatever + + align:start position:0% +right probably I didn't anyway whatever + + + align:start position:0% +right probably I didn't anyway whatever +the the gram-schmidt idea is just + + align:start position:0% +the the gram-schmidt idea is just + + + align:start position:0% +the the gram-schmidt idea is just +orthogonalize in the natural way oh I'll + + align:start position:0% +orthogonalize in the natural way oh I'll + + + align:start position:0% +orthogonalize in the natural way oh I'll +come back to that at the beginning of + + align:start position:0% +come back to that at the beginning of + + + align:start position:0% +come back to that at the beginning of +next time and say a word about the + + align:start position:0% +next time and say a word about the + + + align:start position:0% +next time and say a word about the +fourth way but but so this least squares + + align:start position:0% +fourth way but but so this least squares + + + align:start position:0% +fourth way but but so this least squares +is is not deep learning it's what people + + align:start position:0% +is is not deep learning it's what people + + + align:start position:0% +is is not deep learning it's what people +did a century ago and continue to do for + + align:start position:0% +did a century ago and continue to do for + + + align:start position:0% +did a century ago and continue to do for +good reason okay and I'll send out that + + align:start position:0% +good reason okay and I'll send out that + + + align:start position:0% +good reason okay and I'll send out that +announcement about the class and you + + align:start position:0% +announcement about the class and you + + + align:start position:0% +announcement about the class and you +know the homework and you know the new + + align:start position:0% +know the homework and you know the new + + + align:start position:0% +know the homework and you know the new +due date is Friday good thank you \ No newline at end of file diff --git a/_CUXbDB0bUU.txt b/_CUXbDB0bUU.txt new file mode 100644 index 0000000000000000000000000000000000000000..dba14bc367c56de26bdb3ffbbb9f444257bc5656 --- /dev/null +++ b/_CUXbDB0bUU.txt @@ -0,0 +1,1659 @@ +align:start position:0% + +what is the purpose of the corporation + + align:start position:0% +what is the purpose of the corporation + + + align:start position:0% +what is the purpose of the corporation +this is one of the most controversial + + align:start position:0% +this is one of the most controversial + + + align:start position:0% +this is one of the most controversial +and perhaps one of the most important + + align:start position:0% +and perhaps one of the most important + + + align:start position:0% +and perhaps one of the most important +questions that we need to address in + + align:start position:0% +questions that we need to address in + + + align:start position:0% +questions that we need to address in +this course and that you will need to + + align:start position:0% +this course and that you will need to + + + align:start position:0% +this course and that you will need to +address as the Next Generation Workforce + + align:start position:0% +address as the Next Generation Workforce + + + align:start position:0% +address as the Next Generation Workforce +leaders why is this the case well + + align:start position:0% +leaders why is this the case well + + + align:start position:0% +leaders why is this the case well +because American CEOs have answered this + + align:start position:0% +because American CEOs have answered this + + + align:start position:0% +because American CEOs have answered this +in two different ways from the 1940s + + align:start position:0% +in two different ways from the 1940s + + + align:start position:0% +in two different ways from the 1940s +through the 70s and 80s and into the + + align:start position:0% +through the 70s and 80s and into the + + + align:start position:0% +through the 70s and 80s and into the +1990s there was a broad view of the + + align:start position:0% +1990s there was a broad view of the + + + align:start position:0% +1990s there was a broad view of the +corporation that is now narrowed down to + + align:start position:0% +corporation that is now narrowed down to + + + align:start position:0% +corporation that is now narrowed down to +focus on maximizing shareholder value in + + align:start position:0% +focus on maximizing shareholder value in + + + align:start position:0% +focus on maximizing shareholder value in +the short run here's a quote from the + + align:start position:0% +the short run here's a quote from the + + + align:start position:0% +the short run here's a quote from the +CEO of Sonesta hotels Roger sonen Bel he + + align:start position:0% +CEO of Sonesta hotels Roger sonen Bel he + + + align:start position:0% +CEO of Sonesta hotels Roger sonen Bel he +says social responsibility and expanding + + align:start position:0% +says social responsibility and expanding + + + align:start position:0% +says social responsibility and expanding +profitability are not at odds with one + + align:start position:0% +profitability are not at odds with one + + + align:start position:0% +profitability are not at odds with one +another quite the contrary they're two + + align:start position:0% +another quite the contrary they're two + + + align:start position:0% +another quite the contrary they're two +faces of the same coin that view was + + align:start position:0% +faces of the same coin that view was + + + align:start position:0% +faces of the same coin that view was +shared by a lot of CEOs of his era best + + align:start position:0% +shared by a lot of CEOs of his era best + + + align:start position:0% +shared by a lot of CEOs of his era best +Illustrated perhaps by graduates of this + + align:start position:0% +Illustrated perhaps by graduates of this + + + align:start position:0% +Illustrated perhaps by graduates of this +important institution called the Harvard + + align:start position:0% +important institution called the Harvard + + + align:start position:0% +important institution called the Harvard +Business School the class of + + align:start position:0% +Business School the class of + + + align:start position:0% +Business School the class of +1949 is known for producing an enormous + + align:start position:0% +1949 is known for producing an enormous + + + align:start position:0% +1949 is known for producing an enormous +number of CEOs that spread across the + + align:start position:0% +number of CEOs that spread across the + + + align:start position:0% +number of CEOs that spread across the +economy over the next decade or two many + + align:start position:0% +economy over the next decade or two many + + + align:start position:0% +economy over the next decade or two many +of them had been veterans of World War + + align:start position:0% +of them had been veterans of World War + + + align:start position:0% +of them had been veterans of World War +II in fact 90% went to the Harvard + + align:start position:0% +II in fact 90% went to the Harvard + + + align:start position:0% +II in fact 90% went to the Harvard +Business School on the GI Bill many of + + align:start position:0% +Business School on the GI Bill many of + + + align:start position:0% +Business School on the GI Bill many of +them were firsttime college students in + + align:start position:0% +them were firsttime college students in + + + align:start position:0% +them were firsttime college students in +their families many of them grew up + + align:start position:0% +their families many of them grew up + + + align:start position:0% +their families many of them grew up +during the Depression and they were + + align:start position:0% +during the Depression and they were + + + align:start position:0% +during the Depression and they were +imprinted by the hardships of that time + + align:start position:0% +imprinted by the hardships of that time + + + align:start position:0% +imprinted by the hardships of that time +as well as a commitment to community + + align:start position:0% +as well as a commitment to community + + + align:start position:0% +as well as a commitment to community +service that was embedded in them during + + align:start position:0% +service that was embedded in them during + + + align:start position:0% +service that was embedded in them during +World War II so they had a particular + + align:start position:0% +World War II so they had a particular + + + align:start position:0% +World War II so they had a particular +view of their + + align:start position:0% +view of their + + + align:start position:0% +view of their +responsibility let's start with an + + align:start position:0% +responsibility let's start with an + + + align:start position:0% +responsibility let's start with an +example from one of the best known + + align:start position:0% +example from one of the best known + + + align:start position:0% +example from one of the best known +companies of the 1950s through the 80s + + align:start position:0% +companies of the 1950s through the 80s + + + align:start position:0% +companies of the 1950s through the 80s +Xerox one of the companies that was a + + align:start position:0% +Xerox one of the companies that was a + + + align:start position:0% +Xerox one of the companies that was a +Pioneer High technology company LED in + + align:start position:0% +Pioneer High technology company LED in + + + align:start position:0% +Pioneer High technology company LED in +the development of Office Products and + + align:start position:0% +the development of Office Products and + + + align:start position:0% +the development of Office Products and +it was led from 1968 to 1982 by Peter + + align:start position:0% +it was led from 1968 to 1982 by Peter + + + align:start position:0% +it was led from 1968 to 1982 by Peter +mccullock one of those graduates of + + align:start position:0% +mccullock one of those graduates of + + + align:start position:0% +mccullock one of those graduates of +Harvard Business School class of 1949 + + align:start position:0% +Harvard Business School class of 1949 + + + align:start position:0% +Harvard Business School class of 1949 +Peter mccullock uh graduated and went to + + align:start position:0% +Peter mccullock uh graduated and went to + + + align:start position:0% +Peter mccullock uh graduated and went to +work at Xerox worked his way up through + + align:start position:0% +work at Xerox worked his way up through + + + align:start position:0% +work at Xerox worked his way up through +various managerial capacities became CEO + + align:start position:0% +various managerial capacities became CEO + + + align:start position:0% +various managerial capacities became CEO +in + + align:start position:0% +in + + + align:start position:0% +in +1968 Xerox was located in Rochester New + + align:start position:0% +1968 Xerox was located in Rochester New + + + align:start position:0% +1968 Xerox was located in Rochester New +York where they had manufacturing + + align:start position:0% +York where they had manufacturing + + + align:start position:0% +York where they had manufacturing +operations + + align:start position:0% +operations + + + align:start position:0% +operations +and mccullock believed very strongly + + align:start position:0% +and mccullock believed very strongly + + + align:start position:0% +and mccullock believed very strongly +that the role of the CEO was to be a + + align:start position:0% +that the role of the CEO was to be a + + + align:start position:0% +that the role of the CEO was to be a +good corporate citizen in the community + + align:start position:0% +good corporate citizen in the community + + + align:start position:0% +good corporate citizen in the community +he worked very hard to improve education + + align:start position:0% +he worked very hard to improve education + + + align:start position:0% +he worked very hard to improve education +to build strong community colleges which + + align:start position:0% +to build strong community colleges which + + + align:start position:0% +to build strong community colleges which +then provided a very competent Workforce + + align:start position:0% +then provided a very competent Workforce + + + align:start position:0% +then provided a very competent Workforce +for his organization and for others in + + align:start position:0% +for his organization and for others in + + + align:start position:0% +for his organization and for others in +the region he worked on local and + + align:start position:0% +the region he worked on local and + + + align:start position:0% +the region he worked on local and +National politics he worked closely with + + align:start position:0% +National politics he worked closely with + + + align:start position:0% +National politics he worked closely with +the labor union that represented the + + align:start position:0% +the labor union that represented the + + + align:start position:0% +the labor union that represented the +manufacturing employees at Xerox they + + align:start position:0% +manufacturing employees at Xerox they + + + align:start position:0% +manufacturing employees at Xerox they +were among the first to develop for + + align:start position:0% +were among the first to develop for + + + align:start position:0% +were among the first to develop for +example quality of working life programs + + align:start position:0% +example quality of working life programs + + + align:start position:0% +example quality of working life programs +and quality Circle improvements to + + align:start position:0% +and quality Circle improvements to + + + align:start position:0% +and quality Circle improvements to +improve productivity and to compete with + + align:start position:0% +improve productivity and to compete with + + + align:start position:0% +improve productivity and to compete with +growing International competition in the + + align:start position:0% +growing International competition in the + + + align:start position:0% +growing International competition in the +1970s and 1980s and in particular he + + align:start position:0% +1970s and 1980s and in particular he + + + align:start position:0% +1970s and 1980s and in particular he +believed very strongly at developing + + align:start position:0% +believed very strongly at developing + + + align:start position:0% +believed very strongly at developing +Talent from within the organization and + + align:start position:0% +Talent from within the organization and + + + align:start position:0% +Talent from within the organization and +particularly led the way for developing + + align:start position:0% +particularly led the way for developing + + + align:start position:0% +particularly led the way for developing +Talent among women and among minorities + + align:start position:0% +Talent among women and among minorities + + + align:start position:0% +Talent among women and among minorities +within zerox so it's not an accident + + align:start position:0% +within zerox so it's not an accident + + + align:start position:0% +within zerox so it's not an accident +that uh in 2002 and became the CEO of + + align:start position:0% +that uh in 2002 and became the CEO of + + + align:start position:0% +that uh in 2002 and became the CEO of +Xerox one of the first women to rise to + + align:start position:0% +Xerox one of the first women to rise to + + + align:start position:0% +Xerox one of the first women to rise to +that level of authority in American + + align:start position:0% +that level of authority in American + + + align:start position:0% +that level of authority in American +industry and it's not surprising then in + + align:start position:0% +industry and it's not surprising then in + + + align:start position:0% +industry and it's not surprising then in +2012 that when Anne retired the first + + align:start position:0% +2012 that when Anne retired the first + + + align:start position:0% +2012 that when Anne retired the first +African-American CEO of a very large + + align:start position:0% +African-American CEO of a very large + + + align:start position:0% +African-American CEO of a very large +Fortune 100 company Ursula Burns + + align:start position:0% +Fortune 100 company Ursula Burns + + + align:start position:0% +Fortune 100 company Ursula Burns +succeeded her and the culture carried + + align:start position:0% +succeeded her and the culture carried + + + align:start position:0% +succeeded her and the culture carried +forward the same view of corporate + + align:start position:0% +forward the same view of corporate + + + align:start position:0% +forward the same view of corporate +social responsibility can be seen in the + + align:start position:0% +social responsibility can be seen in the + + + align:start position:0% +social responsibility can be seen in the +words of these CEOs as was the case with + + align:start position:0% +words of these CEOs as was the case with + + + align:start position:0% +words of these CEOs as was the case with +Peter mccullock so if you look on + + align:start position:0% +Peter mccullock so if you look on + + + align:start position:0% +Peter mccullock so if you look on +xerox's social responsibility report on + + align:start position:0% +xerox's social responsibility report on + + + align:start position:0% +xerox's social responsibility report on +the web you'll find currently the + + align:start position:0% +the web you'll find currently the + + + align:start position:0% +the web you'll find currently the +current the same words that mirror what + + align:start position:0% +current the same words that mirror what + + + align:start position:0% +current the same words that mirror what +mccullock stood for quote since our + + align:start position:0% +mccullock stood for quote since our + + + align:start position:0% +mccullock stood for quote since our +earliest days Xerox has embarked on a + + align:start position:0% +earliest days Xerox has embarked on a + + + align:start position:0% +earliest days Xerox has embarked on a +never-ending journey to demonstrate that + + align:start position:0% +never-ending journey to demonstrate that + + + align:start position:0% +never-ending journey to demonstrate that +good business and good citizenship are + + align:start position:0% +good business and good citizenship are + + + align:start position:0% +good business and good citizenship are +not only compatible but are synergistic + + align:start position:0% +not only compatible but are synergistic + + + align:start position:0% +not only compatible but are synergistic +their report then goes on to talk about + + align:start position:0% +their report then goes on to talk about + + + align:start position:0% +their report then goes on to talk about +customer satisfaction Innovation via + + align:start position:0% +customer satisfaction Innovation via + + + align:start position:0% +customer satisfaction Innovation via +patents Community + + align:start position:0% +patents Community + + + align:start position:0% +patents Community +participation avoidance of Workforce + + align:start position:0% +participation avoidance of Workforce + + + align:start position:0% +participation avoidance of Workforce +injuries and so on employee + + align:start position:0% +injuries and so on employee + + + align:start position:0% +injuries and so on employee +participation in Community Affairs all + + align:start position:0% +participation in Community Affairs all + + + align:start position:0% +participation in Community Affairs all +as part of what they believe are the + + align:start position:0% +as part of what they believe are the + + + align:start position:0% +as part of what they believe are the +responsibilities of the modern + + align:start position:0% +responsibilities of the modern + + + align:start position:0% +responsibilities of the modern +Corporation this was the dominant view + + align:start position:0% +Corporation this was the dominant view + + + align:start position:0% +Corporation this was the dominant view +not only of Xerox during this time but + + align:start position:0% +not only of Xerox during this time but + + + align:start position:0% +not only of Xerox during this time but +also of other corporations best + + align:start position:0% +also of other corporations best + + + align:start position:0% +also of other corporations best +illustrated by the statements of the + + align:start position:0% +illustrated by the statements of the + + + align:start position:0% +illustrated by the statements of the +Business Roundtable the largest + + align:start position:0% +Business Roundtable the largest + + + align:start position:0% +Business Roundtable the largest +corporate Association of Executives from + + align:start position:0% +corporate Association of Executives from + + + align:start position:0% +corporate Association of Executives from +the 200 largest companies in the United + + align:start position:0% +the 200 largest companies in the United + + + align:start position:0% +the 200 largest companies in the United +States and as late as 1990 The Business + + align:start position:0% +States and as late as 1990 The Business + + + align:start position:0% +States and as late as 1990 The Business +Roundtable made the following public + + align:start position:0% +Roundtable made the following public + + + align:start position:0% +Roundtable made the following public +statement corporations are chartered to + + align:start position:0% +statement corporations are chartered to + + + align:start position:0% +statement corporations are chartered to +serve their shareholders and society as + + align:start position:0% +serve their shareholders and society as + + + align:start position:0% +serve their shareholders and society as +a whole the interests of shareholders + + align:start position:0% +a whole the interests of shareholders + + + align:start position:0% +a whole the interests of shareholders +are primarily measured of course by + + align:start position:0% +are primarily measured of course by + + + align:start position:0% +are primarily measured of course by +economic returns over time the other + + align:start position:0% +economic returns over time the other + + + align:start position:0% +economic returns over time the other +stakeholders in the corporation are its + + align:start position:0% +stakeholders in the corporation are its + + + align:start position:0% +stakeholders in the corporation are its +employees its customers its suppliers + + align:start position:0% +employees its customers its suppliers + + + align:start position:0% +employees its customers its suppliers +its creditors its communities where the + + align:start position:0% +its creditors its communities where the + + + align:start position:0% +its creditors its communities where the +corporation does its business and + + align:start position:0% +corporation does its business and + + + align:start position:0% +corporation does its business and +society as a whole and all of these are + + align:start position:0% +society as a whole and all of these are + + + align:start position:0% +society as a whole and all of these are +vital to the long-term economic + + align:start position:0% +vital to the long-term economic + + + align:start position:0% +vital to the long-term economic +performance of the + + align:start position:0% +performance of the + + + align:start position:0% +performance of the +corporation that's the view up till + + align:start position:0% +corporation that's the view up till + + + align:start position:0% +corporation that's the view up till +around the mid + + align:start position:0% +around the mid + + + align:start position:0% +around the mid +1990s by this time business is convinced + + align:start position:0% +1990s by this time business is convinced + + + align:start position:0% +1990s by this time business is convinced +that it should focus on shareholder + + align:start position:0% +that it should focus on shareholder + + + align:start position:0% +that it should focus on shareholder +value and so the business Round Table + + align:start position:0% +value and so the business Round Table + + + align:start position:0% +value and so the business Round Table +says in our view the Paramount duty of + + align:start position:0% +says in our view the Paramount duty of + + + align:start position:0% +says in our view the Paramount duty of +management and the board of directors is + + align:start position:0% +management and the board of directors is + + + align:start position:0% +management and the board of directors is +to the corporation stockholders the + + align:start position:0% +to the corporation stockholders the + + + align:start position:0% +to the corporation stockholders the +interests of other stakeholders are + + align:start position:0% +interests of other stakeholders are + + + align:start position:0% +interests of other stakeholders are +relevant only as derivative of the duty + + align:start position:0% +relevant only as derivative of the duty + + + align:start position:0% +relevant only as derivative of the duty +to stockholders the notion that the + + align:start position:0% +to stockholders the notion that the + + + align:start position:0% +to stockholders the notion that the +board of directors must somehow balance + + align:start position:0% +board of directors must somehow balance + + + align:start position:0% +board of directors must somehow balance +all of these other stakeholder interests + + align:start position:0% +all of these other stakeholder interests + + + align:start position:0% +all of these other stakeholder interests +fundamentally + + align:start position:0% +fundamentally + + + align:start position:0% +fundamentally +misconstrues the role of the directors + + align:start position:0% +misconstrues the role of the directors + + + align:start position:0% +misconstrues the role of the directors +and the responsibility of the + + align:start position:0% +and the responsibility of the + + + align:start position:0% +and the responsibility of the +corporation well this is a big change + + align:start position:0% +corporation well this is a big change + + + align:start position:0% +corporation well this is a big change +what caused this change well there was a + + align:start position:0% +what caused this change well there was a + + + align:start position:0% +what caused this change well there was a +revolution in ideas about the + + align:start position:0% +revolution in ideas about the + + + align:start position:0% +revolution in ideas about the +corporation that came largely from the + + align:start position:0% +corporation that came largely from the + + + align:start position:0% +corporation that came largely from the +academic literature of the time the + + align:start position:0% +academic literature of the time the + + + align:start position:0% +academic literature of the time the +leading fin s professors of the time + + align:start position:0% +leading fin s professors of the time + + + align:start position:0% +leading fin s professors of the time +fiser black and Bob Merton at MIT and + + align:start position:0% +fiser black and Bob Merton at MIT and + + + align:start position:0% +fiser black and Bob Merton at MIT and +their colleague Myron scholes at the + + align:start position:0% +their colleague Myron scholes at the + + + align:start position:0% +their colleague Myron scholes at the +University of Chicago had developed a + + align:start position:0% +University of Chicago had developed a + + + align:start position:0% +University of Chicago had developed a +formula for better ways of pricing + + align:start position:0% +formula for better ways of pricing + + + align:start position:0% +formula for better ways of pricing +options that is shareholder stock so + + align:start position:0% +options that is shareholder stock so + + + align:start position:0% +options that is shareholder stock so +that you could use stock options to + + align:start position:0% +that you could use stock options to + + + align:start position:0% +that you could use stock options to +compensate for CEOs their formula made + + align:start position:0% +compensate for CEOs their formula made + + + align:start position:0% +compensate for CEOs their formula made +it easier to use these processes and + + align:start position:0% +it easier to use these processes and + + + align:start position:0% +it easier to use these processes and +then colleagues at the Harvard Business + + align:start position:0% +then colleagues at the Harvard Business + + + align:start position:0% +then colleagues at the Harvard Business +School published a number of papers + + align:start position:0% +School published a number of papers + + + align:start position:0% +School published a number of papers +saying we ought to tie shareholder value + + align:start position:0% +saying we ought to tie shareholder value + + + align:start position:0% +saying we ought to tie shareholder value +to CEO compensation through the use of + + align:start position:0% +to CEO compensation through the use of + + + align:start position:0% +to CEO compensation through the use of +stock options and you saw the the role + + align:start position:0% +stock options and you saw the the role + + + align:start position:0% +stock options and you saw the the role +of stock options grow you saw the CEO + + align:start position:0% +of stock options grow you saw the CEO + + + align:start position:0% +of stock options grow you saw the CEO +compensation grow from what used to be + + align:start position:0% +compensation grow from what used to be + + + align:start position:0% +compensation grow from what used to be +about a ratio of 30 to1 that is the CEO + + align:start position:0% +about a ratio of 30 to1 that is the CEO + + + align:start position:0% +about a ratio of 30 to1 that is the CEO +earned about 30 times the average + + align:start position:0% +earned about 30 times the average + + + align:start position:0% +earned about 30 times the average +employee in The Firm to today where it's + + align:start position:0% +employee in The Firm to today where it's + + + align:start position:0% +employee in The Firm to today where it's +well over 300 to one well what was the + + align:start position:0% +well over 300 to one well what was the + + + align:start position:0% +well over 300 to one well what was the +consequence of all of this one of the + + align:start position:0% +consequence of all of this one of the + + + align:start position:0% +consequence of all of this one of the +examples that uh we could turn to to is + + align:start position:0% +examples that uh we could turn to to is + + + align:start position:0% +examples that uh we could turn to to is +another venerable company Stanley Tools + + align:start position:0% +another venerable company Stanley Tools + + + align:start position:0% +another venerable company Stanley Tools +a company that was a household term + + align:start position:0% +a company that was a household term + + + align:start position:0% +a company that was a household term +because of every toolbox in America had + + align:start position:0% +because of every toolbox in America had + + + align:start position:0% +because of every toolbox in America had +good wrenches and other tools made by + + align:start position:0% +good wrenches and other tools made by + + + align:start position:0% +good wrenches and other tools made by +the Stanley Corporation in Connecticut + + align:start position:0% +the Stanley Corporation in Connecticut + + + align:start position:0% +the Stanley Corporation in Connecticut +it was a very socially responsible + + align:start position:0% +it was a very socially responsible + + + align:start position:0% +it was a very socially responsible +company until the board of directors got + + align:start position:0% +company until the board of directors got + + + align:start position:0% +company until the board of directors got +taken over and someone said let's really + + align:start position:0% +taken over and someone said let's really + + + align:start position:0% +taken over and someone said let's really +focus on shareholder value and so new + + align:start position:0% +focus on shareholder value and so new + + + align:start position:0% +focus on shareholder value and so new +CEO was brought in place and started to + + align:start position:0% +CEO was brought in place and started to + + + align:start position:0% +CEO was brought in place and started to +lay people off not as a last resort in + + align:start position:0% +lay people off not as a last resort in + + + align:start position:0% +lay people off not as a last resort in +economic NE because of economic + + align:start position:0% +economic NE because of economic + + + align:start position:0% +economic NE because of economic +necessity but as a preemptive step to + + align:start position:0% +necessity but as a preemptive step to + + + align:start position:0% +necessity but as a preemptive step to +try to boost shareholder value more and + + align:start position:0% +try to boost shareholder value more and + + + align:start position:0% +try to boost shareholder value more and +more companies did that and in fact that + + align:start position:0% +more companies did that and in fact that + + + align:start position:0% +more companies did that and in fact that +led New York Times Reporter Lou uch + + align:start position:0% +led New York Times Reporter Lou uch + + + align:start position:0% +led New York Times Reporter Lou uch +chatel to write a very well-known book + + align:start position:0% +chatel to write a very well-known book + + + align:start position:0% +chatel to write a very well-known book +called The disposable American basically + + align:start position:0% +called The disposable American basically + + + align:start position:0% +called The disposable American basically +chronicling how American corporations + + align:start position:0% +chronicling how American corporations + + + align:start position:0% +chronicling how American corporations +changed their behavior over time did it + + align:start position:0% +changed their behavior over time did it + + + align:start position:0% +changed their behavior over time did it +really benefit shareholders all that + + align:start position:0% +really benefit shareholders all that + + + align:start position:0% +really benefit shareholders all that +much well if you look at the data the + + align:start position:0% +much well if you look at the data the + + + align:start position:0% +much well if you look at the data the +data show that shareholders got about + + align:start position:0% +data show that shareholders got about + + + align:start position:0% +data show that shareholders got about +the same rate of return about 7% in the + + align:start position:0% +the same rate of return about 7% in the + + + align:start position:0% +the same rate of return about 7% in the +old uh stakeholder era as they were + + align:start position:0% +old uh stakeholder era as they were + + + align:start position:0% +old uh stakeholder era as they were +getting in the shareholder era if you + + align:start position:0% +getting in the shareholder era if you + + + align:start position:0% +getting in the shareholder era if you +adjust for some of this restructuring in + + align:start position:0% +adjust for some of this restructuring in + + + align:start position:0% +adjust for some of this restructuring in +fact their rate of return goes down a + + align:start position:0% +fact their rate of return goes down a + + + align:start position:0% +fact their rate of return goes down a +little bit from the previous uh time + + align:start position:0% +little bit from the previous uh time + + + align:start position:0% +little bit from the previous uh time +period so we've imposed a lot of costs + + align:start position:0% +period so we've imposed a lot of costs + + + align:start position:0% +period so we've imposed a lot of costs +on society but have we really benefited + + align:start position:0% +on society but have we really benefited + + + align:start position:0% +on society but have we really benefited +the shareholders as the theory might + + align:start position:0% +the shareholders as the theory might + + + align:start position:0% +the shareholders as the theory might +suggest that's a question that you will + + align:start position:0% +suggest that's a question that you will + + + align:start position:0% +suggest that's a question that you will +have to answer the era of maximizing + + align:start position:0% +have to answer the era of maximizing + + + align:start position:0% +have to answer the era of maximizing +shareholder value in the short short run + + align:start position:0% +shareholder value in the short short run + + + align:start position:0% +shareholder value in the short short run +is still with us does this work for the + + align:start position:0% +is still with us does this work for the + + + align:start position:0% +is still with us does this work for the +future does it work for your generation + + align:start position:0% +future does it work for your generation + + + align:start position:0% +future does it work for your generation +that's a question that you will need to + + align:start position:0% +that's a question that you will need to + + + align:start position:0% +that's a question that you will need to +address as you shape the work the + + align:start position:0% +address as you shape the work the + + + align:start position:0% +address as you shape the work the +workforce and the corporation of the + + align:start position:0% +workforce and the corporation of the + + + align:start position:0% +workforce and the corporation of the +future \ No newline at end of file diff --git a/_XTuXlXav78.txt b/_XTuXlXav78.txt new file mode 100644 index 0000000000000000000000000000000000000000..95aa83dc676092b1ac1ffab64d31d71bb2c7f02a --- /dev/null +++ b/_XTuXlXav78.txt @@ -0,0 +1,3446 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So +today, we are going + +to talk about the midget +and parasol channels. + +I will begin by reminding you +of what these two channels are + +that I very briefly +talked about before. + +Namely, if you look at the +Golgi stain of cross sections + +of the retina, when you look +at just the ganglion cells, + +it was discovered +initially by the inventors, + +if you will, of the +Golgi stain, namely, + +Golgi himself and Cajal. + +Cajal did this, initially. + +And then, subsequently, a +fellow whose name is down here, + +Polyak, has used the same +technique to study the retina. + +And what he discovered +was-- not Polyak initially, + +but Cajal initially +discovered, and then was + +verified by Polyak using +these anatomical techniques, + +namely, the Golgi +stain-- that there's + +one class of cells that have +very small dendritic arbors, + +as you can see here, +and another set that + +has much, much larger arbors. + +Now, once this was +discovered, subsequently when + +it became possible to +record from individual cells + +and to study their +receptive fields + +and their basic organization, +and also to look + +at them from a +different point of view, + +it was, first of +all, shown that these + +are two very distinct +classes of cells + +in terms of the dendritic +arbors they create. + +And as I mentioned +to you before, + +these cells are +called parasol cells + +because the dendritic arbors +look like an umbrella. + +And at comparable +eccentricities, + +the midget cells are three +times smaller in diameter + +than are the so-called +parasol cells. + +And then I showed you +some data the last time + +indicating that these +two types of cells + +conduct at different velocities +to the central nervous system, + +with these bigger cells +having bigger axons conducting + +significantly faster +than the midget cells, + +and that you get a +distribution when you record + +from all the axons in the +retinal geniculate pathway + +that they form separate +populations because, initially, + +the argument was that +maybe this is just + +a continuous +population of cells. + +But it turns out +these are indeed + +two very distinct classes +on the anatomical level + +as well as the conduction +velocity level. + +Then when it became possible +to record from single neurons + +and to study their +receptive fields, + +it was shown-- I +showed you this picture + +before as well-- +that you have, first + +of all, center-surround +organization as discovered + +by Kuffler; and secondly, that +the midget and parasol cells + +are very different in size as +far as the receptive fields + +are concerned as well +as the dendritic arbors; + +and that the midget +cells in central retina + +receive an input from +just a single cone, + +whereas the parasol cells +got a multiple input. + +And another distinction +that was, at that time, made + +is that the neuronal +responses are + +such that midget cells respond +in a much more sustained + +fashion when you +activate the center + +mechanism than do +the parasol cells. + +So these respond much +more transiently. + +So this, then, were +initial cues as to what + +might be involved as to why +we have these two systems. + +And there were all +kinds of hypotheses. + +And then, eventually, +in the '60s and '70s + +and especially in the '80s and +'90s, all kinds of experiments + +were carried out to +try to establish just + +why these two separate +systems have evolved. + +So now, when the anatomical +work was further progressing, + +it was found, as I have +mentioned also the last time + +to you, that each cone in +the retina-- certainly true + +for the red and the +green cones, which + +would be equivalent +to the midget system-- + +gives rise to an ON and +an OFF bipolar cell. + +Those are the ones we +discussed the last time. + +What I did not +discuss the last time, + +and I'm not going to +discuss today either + +but will the next time we +talk about color perception, + +is that the blue +cones-- how many of you + +remember what is the frequency +of blue cones in the retina? + +AUDIENCE: 1 in 8. + +PROFESSOR: 1 in 8. + +Very good. + +Excellent. + +So that being the case, that +already makes them different + +because the numerosity's +so much lower. + +And then people have done +all kinds of recordings, + +and to this day, +it's not quite clear + +what the connection +or pattern is. + +But as I said, next time, +we will talk about it + +in some detail when +we talk about color. + +But here, don't get frightened, +we will discuss this + +the next time. + +But at any rate, we +have the blue cones. + +And when we talk +about color opponency + +that I will explain +the next time, + +we think of the opponency +to blue being yellow, + +and the opponency +to red being green. + +And so the assumption +here was made + +that the connections +in this case, + +somehow, must take place +to create color opponency. + +And since we have only three +kinds of cones in the retina, + +in the primate-- red, +green, and blue-- + +the opponency here +must, somehow, + +involve both the +red and green cones. + +So that's the complication that +we will discuss the next time. + +And so the assumption +was made that we + +have some so-called yellow/blue +cells and blue/yellow cells. + +And so I just want +to keep you puzzled + +as to what this +means, especially + +what it means with respect +to how we can see colors. + +And that's what we will +talk about the next time. + +So now, here we have, +by contrast-- and we + +go back here-- here, this +is, then, the midget system. + +And I showed you +the two extremes, + +which are very clear, +and in between, which + +would be somehow +creating the blue system. + +So that's the midget system +with very small receptive fields + +and very small cells. + +Now, by contrast, when you look +at the parasol system, what + +you see here is, as indicated +by the picture I showed you + +just a minute ago, is that the +receptive fields are bigger. + +The ganglion cell's +a lot bigger. + +And the dendritic arbors +are much more extensive. + +Now, that means, by the +way-- I shouldn't even say + +"by the way"-- that +means, very importantly, + +that the ON and OFF bipolar +cells that connect with the ON + +and OFF cells of the parasol +system are also much bigger + +and have much more extensive +arbors, dendritic arbors, + +because they sample many +cells instead of just one. + +But overall, what this +means is that when + +you look at the bipolar +cells in the retina, + +there are about three +times as many bipolar cells + +than there are photoreceptors. + +Now, if you think +about this-- somebody + +remembered the last +time-- that in the retina, + +we have about 50 +million cones, and we + +have about 120 to 150 rods. + +And so, then, if you think +about the fact, at least, + +for the cone system, we have +three times as many bipolar + +cells. + +This only applies fully +to the cone system. + +That still means that we +have 150 million bipolar + +cells in the retina. + +So it's absolutely +incredible, then, + +this tiny little thing that +you have in your head, which + +is less than an +inch in diameter, + +you have these millions and +millions and millions of cells. + +Amazing. + +So this is then the arrangement +for the parasol system. + +And now, we can +progress and make + +another point about how +clever the wiring became + +in the course of evolution. + +The cleverness here +is that, as you know, + +we only have a single layer +of photoreceptors, which, + +outside the fovea, has +a mix of rods and cones. + +But then if you look at the +receptive fields of ganglion + +cells, what you find is that +they have overlapping receptive + +fields for many +of the attributes. + +So you have overlapping +for ON and OFF, of course. + +And that's obvious +from the wiring. + +But you also have +overlap for the midget + +and the parasol cells. + +And lastly, there's an +overlap-- even if you just + +look at the rod +input-- which results + +in realizing that the +receptive fields become larger + +during dark adaptation by virtue +of the connections of the rod + +photoreceptors to the rod +bipolars than to the A, + +to amacrine cells, which then +connect with the same ganglion + +cells as do the cones. + +So this is, then, an +incredibly clever arrangement + +which enables you to see +things extremely well. + +And it's an incredible +feat of wiring + +that accomplish this +incredible arrangement. + +So now, another important +thing to consider, in addition + +to what I've said so +far about the midget + +and the parasol +cells, is that they + +have distribution over space. + +If you look at it from, say, +from the center of the eye, + +meaning the fovea, +going to the periphery, + +the ratio of midget and parasol +cells changes dramatically. + +In the center +here, in the fovea, + +you have a huge difference +in number of cells. + +But as you get to the periphery, +these two types of cells + +eventually become +equally numerous. + +Now, to show this +in relationship + +to the lateral +geniculate nucleus-- + +again, to repeat, in the fovea, +you have an 8 to 1 ratio; + +in the periphery, they +have 1 to 1 ratio. + +And this is directly reflected +in the lateral geniculate + +nucleus. + +Everything I've shown you +so far about the geniculate + +was a six-layered structure. + +But those six layers +exist only to about + +an 18-degree eccentricity +from the fovea. + +And after that, the +lateral geniculate nucleus + +becomes a four-layered +structure. + +And as done here in +a schematic fashion, + +the four layers for +the left and right eyes + +are pretty much +equal in numerosity. + +And that creates, +then, the 1 to 1 ratio. + +So that makes one think, +why do we have this shift? + +There must be something very +important in central vision + +for which the midget +system is good for. + +And in peripheral retina, +the parasol system + +becomes more important. + +So we are going to +pay attention to that + +as we examine what the functions +are of these two systems. + +So how do we go +about finding out + +the functions of +these two systems? + +Well, there are several methods. + +The first one I'm +going to tell you about + +is to record from individual +neurons-- say, in the cortex-- + +and determine what +kinds of inputs + +they get from the midget +and the parasol cells. + +So to do that, you first want +to look at the exact projections + +of the retinal +ganglion cells again. + +Just to remind you, here's the +lateral geniculate nucleus, + +again, in the region where +there are six layers. + +I already showed you +this picture before. + +And I told you that the +parvocellular layers project + +to 4C alpha; the magnocellular +layers to 4C beta; + +and those other cells, which +we'll talk about eventually, + +its lateral layers project to +the upper parts of the cortex. + +So now, we have a +good idea that even + +if the inputs to the +visual cortex-- meaning, + +in this case, of course, +the V1-- the two systems are + +separate in the input +layers, in 4C alpha and beta. + +And then the question +comes up, well, + +what happens when you look at +cells above and below the input + +layers? + +Do they converge? + +Or what's going on? + +So that's the kind of +questions we're going to ask. + +And we are going to +look at this more + +carefully here to find +out just how do you + +do an experiment like that. + +Well, one thing you can do here, +you can use a reversible agent + +that you can inject either +in the parvocellular + +or magnocellular layers +of the geniculate. + +And if you do that, if in +the parvocellular layers, + +this would be a blocking agent. + +Xylocaine is something +that's used frequently. + +There are several other agents. + +And so if you inject +that substance in here, + +you render the cells in the +geniculate unresponsive. + +It's to serve the same idea +as what we talked about + +with APB in the last time, +except this is not quite as + +neat because it's +not a pure chemical + +treatment like you did with APB. + +Secondly, you can do it in the +magnocellular layers as well + +and block that region. + +Now, if you do this +kind of experiment, + +let's first talk about +what happens in area of V1. + +Now, this is a very difficult +and complicated experiment. + +Sometimes, you can spend days +recording from a single animal + +because, first of all, +what you have to do + +is you have to put in electrodes +into the lateral geniculate + +nucleus, which is way down, +preferably into both regions, + +but there are many experiments +just to one or the other. + +And then put an +electrode into V1. + +Now, the next important +task, of course, + +is that you've got to record +from V1 in the region to which + +these cells or +these cells project. + +So to find that overlap +in the receptive fields + +that you need to do when +you record here, here, + +and here is that you have +to take many, many electrode + +penetrations until, finally, +you have an overlap. + +And once you have +that overlap, you + +can be sure that when you +inactivate this region + +by injecting the +Xylocaine, you can + +assess what the +responses are in the V1 + +before, during, and +after the injection. + +And most importantly, before +and during, naturally. + +So let's look at that. + +This has been done +studying many cells + +to get an overview +of what's going on. + +And I'm going to +show you, initially, + +just one example of +a cell to give you + +a feel for what that's like. + +So here we have +the cell respond. + +What you do is you +take a bar of light + +and move it across the +receptive field-- brrp, + +brrp-- for each edge. + +So those are the two +cumulative responses. + +[INAUDIBLE] + +That's the normal. + +Now, you inject into the +parvocellular portions + +of the geniculate. + +And lo and behold, the +cell keeps responding. + +Then you inject into +the magno portions. + +And then lo and behold, the +cell still keeps responding. + +But when you inject +into both-- bango! + +There's no response. + +So that means that +this particular cell + +gets a convergent input from +the midget and the parasol cells + +as they pass through the +lateral geniculate nucleus. + +Now, if one then does +a systematic study + +and then records from many +cells, what has been found here + +is that some cells do +get an exclusive input + +from the midget cells. + +Some get an exclusive input +from the parasol cells. + +And some are just like the one +I've shown you here-- namely, + +they get a convergent input. + +So that tells us, then, what +the very, very basic nature is + +of the input to the visual +cortex, you, to some degree, + +keep separate the two systems. + +And to some degree, +you also have + +a condition where +they are united. + +So that's what +happens in area V1. + +So now, the next thing +you are going to ask + +is, well, what happens +in other cortical areas? + +So here, then, I'm showing +you the same method picture. + +But now, you have +recording in V4 and MT, + +doing the similar +kinds of injections + +that I just described in the +lateral geniculate nucleus. + +So when one does this, +some interesting results + +had been obtained. + +And as always, before +this kind of experiment + +that actually tested +this question, + +there were, of +course, hypotheses. + +Some people +hypothesized that area + +of V4, which had +at one time been + +proclaimed to be a +color area-- and we'll + +come back to that shortly-- +it was claimed, therefore, + +that this area gets input +only from the midget system. + +And this area-- since it +has motion-selective cells, + +if you remember-- only gets +input from the parasol cells. + +So, therefore, we can +now have the acid test, + +thanks to some +remarkable work that + +had been done, much +of it by John Maunsell + +over at Harvard, +who had actually + +worked here at MIT before then. + +And he did an +experiment like that. + +And here's an example of a +single cell recording from V4. + +This is a magno block, and +this is the parvo block. + +This is before the block, +and this is after the block. + +So what you can see +here, this cell, again, + +response to a bar +moving across-- brrp, + +brrp-- like that. + +Here are the two +responses shown here as + +to how they come across +the receptive field. + +And you can see a vigorous +response after you do this + +and before you inject +Xylocaine into the geniculate + +to block, in this +case, the magno system; + +and in this case, +the parvo system. + +This is backwards from the +way I usually presented. + +I usually like to +put parvo first. + +Preference-- it's the bias. + +At any rate, you +can see what happens + +is dramatic for this particular +cell after you injected, + +you blocked the magno system. + +The cell-- we said has +spontaneous activity-- + +but it no longer +responds to the edges. + +By contrast, when +you do a parvo block, + +you only get a small effect. + +There is a reduction for +this particular cell, + +but it's still responding. + +So that is the example of +a recording in area of V4. + +Now, let us go and ask the +question, what about MT? + +Now, here's an example. + +Same arrangement-- magno first, +parvo second, before the block, + +after the block. + +In this case, in +MT, you get a cell + +that totally stopped +responding after magno block + +to this moving stimulus. + +And here, what you see +is after parvo block, + +the response continues. + +So now, this is just two cells. + +Now, to be sure that these +two cells are generally + +representative of these +observations, what you need + +to do is to collect this kind +of information from many cells, + +and then come up with a +qualitative statement. + +So what you can do is +you can, for each cell, + +when you do this +experiment, you can't + +determine how much the cell +fired here to the stimulus + +and how much it fired here. + +And then you can get a +ratio of that response. + +You can turn it into, like, +a percentage or maybe just + +to score them as 0 to 1 number. + +And then if you do that +for a whole bunch of cells, + +what you find is shown here. + +This is a bunch of cells in V4. + +This is a bunch of cells in MT. + +And what you can see here +is that in V4, first of all, + +you have a medium degree +of blockage, nothing major, + +but some blockage. + +But most importantly, +you get blockage + +both for parvocellular and +magnocellular inactivation. + +By contrast, in +MT, what you find + +is that when you block +magnocellular geniculate, + +most of the cells are +dramatically affected. + +Only a few cells are blocked +as a result of a parvocellular + +block. + +So the outcome of this is +that the hypothesis pertaining + +to MT, that it gets mostly an +input from the parasol system, + +is correct. + +But the idea that V4 +gets an input only + +from the midget system +is obviously incorrect, + +showing that it gets +an input from both. + +So to then summarize +the wiring diagram here, + +what you have here is +the eye, of course. + +And then you have the +midget and parasol cells + +that project, respectively, +to the parvocellular + +and magnocellular layers of +the lateral geniculate nucleus, + +then they go off to the cortex. + +And if you remember, +in the cortex, + +they terminated +4C alpha and beta. + +And then, also, as I told +you, up here, you already + +have many cells above and +below the input layers + +that get a convergent input from +the midget and parasol cells. + +So what happens then, in terms +of the projections to higher + +cortical areas-- to talk +about V2, for example-- + +you get some cells +which are purely + +driven by the midget +system, some cells purely + +driven by the parasol, and many +cells that are driven by both. + +So V2 becomes very +complicated because they + +have different subdivisions. + +Maybe in V2-- we talked +about it a little bit-- + +that may be receiving +different input from area of V1 + +in terms of whether +they are driven + +by the midget or +the parasol cells. + +Now, most notably, when +from V2 and from V1, + +you look at the +projections to area MT, + +the middle temporal +area, what you find + +is that this is +heavily dominated + +by the input from +the parasol cells. + +Then if you go beyond +that, this continues + +to the parietal lobe from MT. + +But then, when you +go from V2 to V4, + +then temporal, then the +frontal lobe, what you + +find that there's +a mix of inputs + +from both of these systems. + +So it highlights the fact +that, indeed, these things + +are quite complicated. + +And so we need to now +turn to a different method + +to try to ferret out beyond just +establishing the connections + +as to what on earth these +two systems are for. + +And needless to say, hypotheses +were rampant about this. + +And what I'm going +to do now, I'm + +going to tell you about +how one can go about + +and how many investigators have +gone about trying to determine + +what the functions are of +these two systems in processing + +visual information. + +So how do you do that? + +Well, the way you +do that is you can + +use what is called +lesion studies. + +What you can do is +you can selectively + +block either the +parvocellular or magnocellular + +systems at the level of +lateral geniculate nucleus + +because, by lucky happenstance, +the parvocellular layer is + +getting input from midget, +and the magnocellular layer is + +from the from the parasol cells. + +So you can make lesions, then. + +How do you make lesions? + +There are variety of +ways of making lesions. + +That's a huge field. + +It applies not only to vision, +to many, many other areas, + +to try to make carefully +selective lesions + +in various parts of the brain. + +Now, it's not easy to do +that in the geniculate. + +So what you have to +do is, again, you + +go in to the lateral geniculate +nucleus with a microelectrode. + +Once you do that-- +you already know + +the layout of the +geniculate-- you + +can find out where the +receptive fields are located, + +and you can +determine whether you + +are recording from the +parvocellular or magnocellular + +layers. + +You're going to adjust +the depth of the electrode + +to be either in the +parvocellular or magnocellular + +layers. + +And once you have established +the receptive field location + +and were certain about in +what parts of the geniculate + +you are recording, you can +then proceed to make a lesion. + +Now, there are a number +of ways of making lesions. + +One of them is +called heat lesions. + +You should take a +metal microelectrode. + +You take it down +there, and then you + +pass some current to make +the tip of the electrode hot, + +you can affect, as you know, +maybe a millimeter area + +or something like that in the +lateral geniculate nucleus. + +I'm talking about +small, small areas. + +Another alternative that you +can use is to inject a chemical. + +One of those commonly used +is called Ibotenic acid, + +which is a very nice attribute, +that when it causes a lesion, + +the borders are nicely +clearly defined. + +So no matter how you +do this, then once it + +is done in a monkey, then you +can study a monkey for months + +on end to see what +the vision is, + +of how the vision is affected. + +And then after you've done +that, you then process the brain + +and look at the lateral +geniculate nucleus + +to see what was the size +and location of the lesion. + +Now then, in some cases, it's +"Oh, my god, you did both. + +Nyah, nyah, nyah." + +You screwed up. + +So months and months of +work goes down the toilet. + +But in some cases, +you get a good effect. + +And that, eventually, +if you do it + +several times on +several monkeys can + +result in a solid publication. + +So that is the basic process +for making the lesions. + +Now, let me then +move on and broach + +the next important +topic-- namely, + +what are you going to study? + +So what you have to study since +you want to have an open mind + +and you don't want to say, "oh, +yeah, everything in the brain + +does color" or +something like that, + +and so instead of +just studying color, + +you have to study +many other aspects. + +So I'm going to tell you +about several kinds of tests + +that have the newest. + +And I will explain +each of those to you. + +But first, I will list them. + +The behavioral task that +is used-- very important-- + +is that you've got to be able +to confine the crucial stimulus + +either to the area +that you had blocked + +or the area that is intact. + +So one way to do that, +which is the easiest way, + +is to use a detection task. + +We already talked +about that briefly. + +The monkey first fixates. + +That confines his +looking to that location. + +And then you can present +a stimulus like this. + +And if he makes a +saccade to it, he + +gets a drop of apple +juice for a reward. + +Now, that is a procedure. + +And then, of course, +our next trial, + +it appears someplace else. + +On each trial, it's in +different locations. + +And on some trials, you +can present the stimulus + +in the area that +had been blocked. + +You get it from by +magnocellular or parvocellular + +lesions or infusions +or in an intact area. + +And that, then, enables +you to compare performance + +in regions where the monkey's +performance is normal + +because he's intact and in those +regions where he lacks either + +an input from the magnocellular +or from the parvocellular + +layers of the lateral +geniculate nucleus, + +meaning from the midget +and parasol cells. + +So now, another +task which is used + +to be able to carry out a +more thorough examination + +of visual capacities +is his discrimination. + +In which case, +after fixation, you + +have a whole bunch +of stimuli coming on. + +This is very effective +for studying color. + +And in this case, this +discrimination task often + +is called the so-called +oddities task. + +That's an easy way +to remember it. + +"Oddity" because this is odd. + +All the others, the distractors, +if you will, are the same. + +Only one stimulus is different. + +And, of course, the monkey +has to make a direct saccade + +to this stimulus to get a drop +of apple juice for reward. + +So that would be a so-called +discrimination task. + +So these are the two basic +tasks that can be used. + +And now, we can proceed and ask +the question of what exactly, + +what kinds of visual +capacities should be studied? + +So let me just say one +more thing, by the way. + +The way this is +done in a laboratory + +is that you have a performance +monitor, so-called, + +where the computer puts a square +around each of the dots that + +will have appeared-- +in this case, + +this should be +discrimination-- or where + +they will appear singly +in the detection task. + +And if the monkey +makes a saccade that + +lends the saccadic eye movement, +which you are recording, + +into the square area +there, then automatically + +a drop of apple +juice is discharged. + +But if he were to make a +similar saccade to here, + +he will not get +rewarded because this + +is the only correct position. + +And on each trial, that's +going to be someplace else. + +Everybody understands +the method? + +It's fairly straightforward. + +So now, we can move on +and look at an example + +of the kinds of lesions +that this can create. + +Here is a lateral +geniculate nucleus again, + +the six-layered portion. + +And you can see this area +here, that this is a lesion. + +There are no cells +functional here, + +which affects only the +parvocellular layers. + +You see here the two +magnocellular layers + +are normal. + +So this is the lesion +area which affects + +a few degrees of visual +angle-- in this case, + +in the lower part +of the visual field. + +Now, here we have +a magno lesion. + +If you just look +at this quickly, + +you say, what lesion +are you talking about? + +But if you look closely, +can you see this here? + +There are no cells here. + +So this is the region where both +layers, magnocellular layers + +that get the input +from the parasol cells, + +had been blocked. + +So that is the block there. + +So this is, then, an example +of a successful lesion. + +And once you do these +kinds of experiments-- + +some of these experiments +can take a couple of years, + +maybe longer-- you end up +having some monkeys who + +have neat lesions like +this, then it's a control. + +Let me just add +that, which I'm not + +going to show any pictures of. + +But you can also make, +on purpose, a lesion + +where you block both of +them-- both the magno + +and the parvocellular layers. + +You just block out a portion +of the lateral geniculate + +completely. + +Now, that's an +important control. + +For all kinds of experiments, +controls are essential. + +Now, let me tell you-- this +is available in the published + +material that you have +been asked to read-- + +that when you block +both magno and parvo, + +maybe a quarter of the +lateral geniculate nucleus, + +whenever you present stimuli in +the area that has a topographic + +correspondence to +the lesion's region, + +the monkey cannot see a thing. + +He cannot perform any +of those tasks at all. + +So clearly, whatever +effect one gets here + +with these selective +lesions can then + +be ascribed-- if you see +deficit after this one + +or deficit after that one-- +can be ascribed to what + +the midget and the +parasol cell systems do. + +So that, then, is the procedure. + +And now, we can move on and +list the perceptual functions + +that one wants to test. + +Now, think about it for +a minute, just quickly. + +What kinds of +functions would I want + +to test if I'm running +this experiment? + +How can we break down +the multitude of things + +that we have to process +into some basic functions? + +Well, first of all, +very important function, + +even though it may +have now [INAUDIBLE] + +is called contrast sensitivity. + +Because everything +you look at, the light + +reflects just about from +everything that you look at, + +and so the contrast +of the stimuli that's + +on a white sheet of paper +or a gray sheet of paper + +or when you look at +photographs is highly varied. + +And the question +is, how well can you + +see the different +levels of contrast? + +Another one, of course, +that's obvious is color. + +How well can you process +color information? + +And then another one is pattern. + +We often talk about +basic patterns. + +And the one I'm going +to tell you about mostly + +would be checkerboards +or something like that. + +Then we talk about texture. + +Most of the things that +we encounter in the world + +are textured. + +And so it's important for us +to be able to see texture. + +Then, of course, +shape, that's obvious. + +Then stereopsis. + +We will talk about stereopsis +in much more detail in a bit. + +What stereopsis involves, as +I've mentioned to you already, + +are the difference of the +input in the two eyes. + +And that difference is called +disparity, which the brain then + +interprets as depth. + +Another one, very important +because you often just see + +things appearing quickly +in very brief times, + +is to study flicker. + +And yet another one +is to study motion + +because that's so +central to our existence. + +And then to study brightness. + +And one thing I +haven't mentioned yet + +is scotopic vision. + +How well can you see on +the photopic and scotopic + +conditions? + +So those are, then, +the procedures. + +And so let us now look at the +first one of these-- contrast + +sensitivity. + +This has been +extensively studied, + +hundreds and hundreds of +papers, many of them in humans. + +And most commonly in these +papers, what they did + +was they used +sinusoidal gratings. + +And the way you do that, +then, in similar experiments + +as a detection experiment, you +present sinusoidal gratings + +with spatial frequency and whose +contrast you systematically + +vary. + +And when you do +that, you get what + +is called a contrast +sensitivity function. + +And so the most common one +that you read in many papers + +is plotted this way. + +This is spatial +frequency low, high. + +And this is contrast. + +Low, high. + +And then if you do that, then +you systematically studied + +this in humans, +interestingly enough, + +you get a function +like that-- meaning + +that in between levels +of spatial frequency, + +you see the best. + +And extreme levels, you +don't see quite as well. + +So one could use sinusoidal +gratings in animals. + +But sinusoidal gratings +aren't essential. + +What you can do instead is you +can present a checkerboard. + +And so here's an example, +same procedure as before. + +The monkey sees this and +makes a saccade to it. + +It gets you water. + +And then you vary +the spatial frequency + +and the contrast of it. + +So here is one. + +You can hardly see that +because the contrast is low. + +So now, to see this +overall, here's an example. + +Here, we vary the contrast. + +And here, we vary the +spatial frequency. + +And if you look at that, you +can see that in this region, + +depending on how far back +you are, this region, + +you can see the best. + +Here, it will be less so. + +And here, of course, it +drops off dramatically, + +just like that curve +I have drawn there. + +So this, then, enables one to +generate a so-called "contrast + +sensitivity" +function in a monkey + +in those regions of the +visual field that are intact + +and in those regions +of visual field + +in which you have either +magnocellular or parvocellular + +lesion that selectively +blocks the parasol + +and the midget systems. + +So that's the experiment, +then, for just studying + +contrast sensitivity. + +And if you do that, this is +the kind of result you get. + +This is the monkey's +normal performance. + +In this case, of four +spatial frequency levels. + +And you go up and +down with contrast, + +just like that +curve I drew there. + +So this is your contrast +sensitivity function. + +And it shows that +under normal conditions + +and after magnocellular lesion +that blocks the parasol system, + +there is no effect, meaning that +the parasol system doesn't seem + +to be too important for +contrast sensitivity. + +By contrast, there's +a huge effect, + +especially at high +spatial frequencies, + +after a parvocellular lesion +that blocks the midget system. + +So that, in essence +then, is what + +happens with +contrast sensitivity. + +Now, let us move on and say, +well, what about color vision? + +So how do you do +the color vision? + +I already told you that before. + +What you do is you +present, in this case, + +eight stimuli, one of which +is different from the others, + +and just have red +and green ones. + +This is the odd one. + +The monkey makes +a saccade to it. + +He gets a drop of apple +juice for a reward. + +Now, if you want to be +systematic about it, + +you can vary the degree +of color contrast. + +But the effect is so +dramatic that it was not + +necessary to do that. + +So let me show you +what the effect was. + +Here, we have a monkey's +normal performance + +when the test element +is blue, red, and green. + +This happens after a +parvocellular lesion, + +meaning when you block +the midget system, + +the monkey cannot +see colors at all. + +Just a total loss. + +Whereas, after +magnocellular lesion, + +his performance is +indistinguishable from normal. + +So this, then, +establishes the fact + +that color vision is controlled +by the midget system. + +Now, the fact that this +is the case perhaps + +is not that surprising +because I told you + +that when you look at the +cells in the midget system + +in central vision, +that most of them + +get an input from +just-- at least, + +the red and green ones-- get +an input from a single cone. + +So just looking at the +receptive field organization + +tells you that that +system is likely to be + +very important for +color processing. + +So that, then, is +confirmed by this kind + +behavioral experiment. + +So now, let us look at +brightness perception. + +Now, how is that different +from contrast sensitivity? + +It's different because, +in this case, what to do + +then is you use a +discrimination task like this. + +And I think most of you +can tell that this one is + +brighter than the others. + +Purposefully, I made +that a small difference, + +so you can appreciate the +fact that on each trial, + +we can vary the difference +between the distractors + +and the target. + +And you can generate +a curve seeing + +how much brightness +difference do + +you need to be able to perceive +a brightness difference. + +So if you do that +kind of experiment, + +one is in for a big surprise. + +This shows here what happens +after a parvocellular lesion. + +And this shows here what happens +after a magnocellular lesion. + +So when you block +the midget system, + +the performance is unaffected +as is the case with a magno + +lesion, meaning that +if you, obviously, + +that both the midget system +and the parasol system process + +information about brightness, +at least, at these low spatial + +frequencies that we have +used that I just showed you. + +So now, the other surprise +was that, then, the question + +became, well, what +if you do this not + +under photopic conditions and +do under scotopic conditions? + +And again, there's +no effect, meaning + +that the unique +inputs from the rods + +and the unique +inputs from the cones + +must go into both +of the systems. + +Now, the reason +that was surprising + +is because a couple of +papers have been published, + +maybe about 15 to 20 years ago, +that claimed that the rods feed + +selectively into +the parasol system, + +not into the midget system. + +So this totally disprove that. + +And then subsequently, careful +anatomical experiments also + +established that both the +small and the large cells, + +magno ganglion cells, +receive convergent input + +from the rods and the +cones as I had diagrammed + +to you in the previous session. + +So then, let's go on and look at +pattern and texture perception. + +In this case, let me show you +the kind of experiment that's + +done. + +This is when you +look at patterns. + +One way to do it, go back +to those same checkerboards, + +but make them high +contrast and have one + +at a different spatial +frequency than the others. + +And then you can +systematically vary the degree + +of spatial frequency +difference between the targets + +and the distractors. + +So that would be +the method that is + +used to study this kind +of pattern perception. + +The other one is to +look at textures. + +And in this case, those +of you in the back + +probably can't see this. + +But those of you up front, can +you see this little area here, + +where the diagonal +lines are reversed? + +So what happens is, first, you +just present this whole thing. + +And then you present the reverse +patterns and the surround. + +And when you do +that, the monkey has + +to make a saccade +to that location + +and will get a +drop of apple juice + +again for that performance. + +And then on each trial, +this appears somewhere else + +in one of the four to eight +locations in the display. + +So that's the procedure. + +And then if you do +this, you, again, + +luckily get a very dramatic +effect, apparently. + +Here it is. + +We have here normal performance. + +Here's a parvocellular +lesion, magnocellular lesion. + +This is texture, +and this is pattern. + +Pattern tasks was, overall, +much more difficult + +than the texture +one in this case. + +Well, what you see here +that is really dramatic + +is that when you block +the midget system, + +there's a tremendous loss in +your ability to see patterns + +and in your ability +to see textures. + +So fine vision for +detail seems to be + +central for the processing +of the midget system. + +So that, then, is +the effect that one + +gets with texture +and with pattern. + +So now, let's move on and +talk about stereoscopic depth + +perception. + +It's a topic we +are going to look + +at in more detail +in a later session. + +Let me now introduce +this, first of all, + +by telling you that stereoscopic +depth perception resulted + +predominately by +virtue of the fact + +that the eye is +moving to the front + +so that there was a +major binocular overlap. + +And if you talk about a monkey, +for example, or even many, + +many animals that do have +stereoscopic vision, here's + +an example of looking at a tree +when just about the only cue + +you have here would be based on +stereopsis because all of them + +are equally dark. + +Which branch is in +front of which one? + +And it's very hard to tell. + +If your monkey will jump from +this branch to this branch, + +if he can't tell where they +are relative to each other, + +the monkey is going to +fall down and drop dread. + +So it is very +important for monkeys + +to have a highly functional +stereoscopic system, which + +they do. + +And so, how do we study this? + +Well, the way we +study this is to use + +what is called a +random-dot stereogram. + +Random-dot stereograms +were created + +once computers became a reality +many, many years back by Bela + +Julesz. + +And he came up with +the idea that if you + +use this kinds of +random-dot stereograms, + +there's no other depth cue. + +So, in other words, +you can study + +just the stereoscopic depth +perception aspect of it. + +Now, why is this? + +Because what you do here is +you look at this two displays, + +you present this to the left +eye and this to the right eye. + +The way this is +done is that you use + +what is called a stereoscope. + +I bet you most of you +have seen a stereoscope. + +Everybody see a stereoscope? + +No? + +So a stereoscope +used to be something + +that was extremely popular +starting in the 19th century. + +They created these handheld +devices with the two lenses + +that you look through. + +And then they created a camera +that had two lenses in it + +at the same distance, +roughly, as your two eyes. + +And so it took a +picture, thereby, + +creating two pieces, +one by each lens. + +And then, what you +did, since the two have + +a slightly different perspective +of what you're looking at, + +then the photographs are +put into the stereoscope + +to look at. + +These two images are fused then. + +Looks like a single image. + +And due to their +very disparities, + +you see real depth. + +It's really dramatic. + +And when we talk about +stereoscopic depth perception, + +I'm going to actually bring +some stereoscopes here + +and some examples so you can +see exactly what that is like. + +But at any rate, in this +case, what you can do + +is you can take a little +area here just like before. + +And you can take the +dots in this area. + +You move them a little bit +this way, a few pixels. + +And you move this a +bit this way, that way. + +And then if it's a +square area, you're + +going to see a +square sticking out. + +And the monkey will then +make a saccade to that. + +But with one eye, he +cannot do anything. + +He can't see a thing because +these random-dot stereograms + +only give you information +about disparity. + +So if you do that, +you're going to have + +the monkey make a +saccade to these. + +You can vary the +degree of disparity. + +And when you do that, +what you find is, + +quite dramatically, is that +after a parvo lesion, when + +you block the midget system, +there's a tremendous loss. + +The monkey +essentially, especially + +at smaller disparities, +has totally + +lost his ability to use +stereoscopic depth information. + +So there is no deficit, however, +after a magnocellular lesion. + +So therefore, you can say safely +that, especially at smaller + +disparities, what you have +is the midget system that + +performs this remarkable task +of seeing things in depth + +by virtue of disparity +in the two eyes produced + +by stereoscopic vision. + +So that's really a +very dramatic effect. + +Then the next thing we can +look at is motion perception. + +Again, this can be +done in various ways, + +but I will just show +you an example of it. + +So the monkey first fixates. + +Again, use random-dot +stereograms here. + +And then you set in motion +a small square area. + +Ready? + +I hope. + +There we go. + +Or you can do the high +spatial frequency like that. + +And then, of course, on +each trial, that appears + +someplace else. + +And you can vary +the velocity or you + +can vary the contrast +of the display + +and see how the monkey +performs in the intact portions + +of visual field +and how it performs + +in those portions of the +visual field that are blocked + +either for the midget system +or for the parasol system. + +Clear? + +So let's think about +it for a minute. + +What do you think +you're going to get? + +Here we go. + +Here we are-- motion detection. + +This is a parvo lesion. + +This is a magno lesion. + +And so what you get is +a dramatic deficit, not + +an all-amount deficit, +but a dramatic deficit + +in seeing motion +after the magno lesion + +but not after parvo lesion. + +So this says that, +indeed, the parasol system + +plays a very important role +in motion perception, not + +an exclusive role. + +There is still some +performance there + +at very, very low contrast here. + +And there's a big effect +at very high contrast, + +and monkey does better. + +So we can conclude +that the parasol system + +is very important for +motion perception. + +So now, the next thing we +can look at is flicker. + +And in this case, when +you study flicker, + +instead of using a +monitor, people used LEDs. + +Now, why do you think that is? + +Why don't they +just use monitors? + +Well, I mean, the +reason for that + +is very straightforward, +actually. + +When you use a +regular monitor, what + +is the frequency of a monitor? + +It's the same as the frequency +of the alternating current + +that you have, that +shine the lights up here. + +But what is that in +the United States? + +60 hertz. + +And so that's what happens +on a regular monitor. + +And every 1 over 60 hertz +is you shift the image. + +In Europe, the frequency +is actually 50 hertz. + +So at any rate, because +of that, there's + +a rather limited +range over which + +you can vary the ON and OFF +activity of a flickering spot. + +So if you use any of +this, however, you + +can use it in a huge, +huge range of small steps. + +So, therefore, this +is what the display + +looks like that people +use to study this. + +First, the monkey fixates here. + +And then one of these LEDs +will start flickering. + +And I'll show you +the flickering, which + +is not perfect here +on this monitor, + +but it will give you a sense. + +Everybody see that flicker? + +Now, the mean flicker +value of that location + +is the same as the yellow +lights that you see there. + +So if it flickers +at a high rate, + +you can't tell that it's +flickering because it's + +beyond the ability of +the eye to resolve it, + +and then you can't make a +saccade to that location. + +So if you look at that, what you +find here, after parvo lesion + +and after magno lesion, +you get a gigantic deficit + +after magno lesion. + +And that fits with what I +told you in the beginning-- + +namely, that the +midget cells respond + +in a fairly sustained fashion +when the stimulus comes on. + +Whereas, the parasol +cells respond transiently, + +which makes them much more +readily available for motion + +and for flicker. + +So those, then, are +the major arrangements + +that we see with these +various experiments. + +And so we can summarize what +happens after parvocellular + +and magnocellular lesion +and say what happens here. + +So this one here is when +you block the midget system. + +This is where you block +the parasol system. + +And here are all the various +test that had been used. + +And you can see that +for the parasol system, + +the major deficit arises in +motion perception and flicker + +perception. + +So those two are very +important in the processing + +of the parasol system. + +Whereas, for the +midget system, you + +get lots of deficits in color +vision, texture perception, + +and fine pattern perception, +fine shape perception, + +in contrast sensitivity, +and in stereopsis. + +So this, then, gives you a sense +of what these two systems are + +important for in processing +visual information. + +And so, what you can do next +is to summarize what I just + +told you-- namely, that +the midget system is + +important for color, texture, +fine form, and fine stereo. + +The parasol system is +important for fast flicker + +and fast, low contrast motion. + +Both systems are capable of +doing brightness; coarse form; + +coarse stereo; slow +flicker; slow, high contrast + +motion; and scotopic vision. + +So it is not a +simple arrangement. + +It's a complex arrangement. + +There is overlap in what +both systems can do. + +So now, the big +question comes up. + +Why was it so important to +create both of these systems? + +Well, the number of +schemes that have evolved, + +certainly, the +motion is obvious. + +But one thing one +can come up with is + +a scheme of this sort that +has been proposed-- namely, + +that what happened as a result +of these two systems emerging, + +your ability to process +information has been extended. + +And for the midget system, +you expanded the ability + +to see up to high +spatial frequencies-- + +very, very important attribute. + +And I should add, also +for the midget system, + +it became possible +for you to see color. + +Whereas, when you come +to the parasol system, + +it expanded the +range of your ability + +to process information +in the temporal domain-- + +your ability to see very +fast motion, to see flicker. + +Now, let me add here that's +a very important attribute, + +by the way, for animals as +well as humans because one + +of the common things +that has emerged + +in the course of evolution +is what is called camouflage. + +I think I may have +mentioned that once before. + +That is that when +you or an animal, + +and the coloring of you, +which is done in thousands + +of animals, is made similar +to the background, then + +it's very difficult for you +to see that particular animal. + +So it has an +excellent camouflage. + +However, as soon as this +animal begins to move, + +the ability to camouflage +itself disappears. + +And animals have to move. + +And that's because +the parasol system + +is extremely +sensitive to motion. + +And so whenever an +animal begins to move, + +even though it has +excellent camouflage, + +it is predominantly +the parasol system + +that will destroy the +camouflage effect. + +I'm not saying +this is necessarily + +the only hypothesis, but +this is one hypothesis + +that had been advanced to try +to account for how sensible it + +is to have these two systems. + +Now, of course, +you could ask, how + +come this couldn't be just +done in one system-- all of it? + +Well, there are several +reasons for that-- + +is that to combine a +situation where you have + +a sustained response and a +transient response into one + +is next to impossible. + +And to have cells that +are highly sensitive, + +or the parasol cells, you need +to have a convergent input + +from several photoreceptors. + +But as soon as +you have that, you + +lose your ability +to see fine detail. + +So these requirements +to do this and this + +are antagonistic to each other. + +And it's not possible to +do that in a single cell + +at the retinal level. + +So it was decided, inasmuch +as they should decide, + +that it will be +best just to create + +two separate systems however +complicated that might be. + +So that, then, brings me +to the overall summary + +of what I had covered today. + +First of all, I +told you-- that's + +the obvious part-- are two +major channels that originate + +in the retina are the +midget and the parasol. + +I should add here that there +are many other channels + +in the retina, +but the cells that + +do that-- and we'll +talk about some of those + +later-- are much less numerous. + +The overwhelming majority +of cells in the retina + +are either midget and parasol. + +Then in central retina, +the receptive field center + +of the midget cells +and parvocellular cells + +is comprised of +just a single cone. + +The midget cells and the +parvocellular cells-- + +meaning that the midget projects +to the parvocellular layers. + +And I told you before that +the midget cells of the retina + +have receptive fields which are +quite similar to those, almost + +identical to those that you +see in the parvocellular + +layers of the lateral +geniculate nucleus. + +Then the parasol cells have +much larger receptive fields + +than do the midget cells. + +The cone input is mixed both +in the center and the surround. + +And that is the reason why this +system, the parasol system, + +cannot tell you +anything about color, + +but it is very sensitive and can +tell you about any change that + +occurs out there over time, +irrespective of the kind + +of color it has. + +Now, the midget and parasol cell +ratio from center to periphery + +changes from 8 to 1 to 1 to 1. + +Now, I should +reiterate that in that + +it is very important +for us to be + +sensitive to motion +in the periphery. + +That's if an animal is +threatened by some predator, + +it is highly desirable +to be able to very + +sensitive to any motion. + +And because of that, +you have a higher number + +of parasol cells in the +periphery than in the center. + +And so the ratio changes to +become equal in the periphery. + +Now, the midget +and parasol systems + +converge on some cells in V1. + +And the example, +the prime example, + +I've shown you when +they were separately + +blocked at the level the +geniculate, that the cell + +I showed you was one that did +receive a convergent input. + +But many other cells +receive single input. + +V4 receives inputs from both the +midget and the parasol cells. + +So it's not an area that only +deals with color, obviously. + +And what it will deal with, +we'll describe in more detail + +later. + +The major input to MT is +from the parasol cells. + +And that, often, MT +and MST have often + +been called the motion areas. + +But they also play +important role, by the way, + +in depth perception, +as we shall see. + +And then the midget +system extends the range + +of vision in the wavelength and +high spatial frequency domains. + +The parasol system +extends the range + +of vision in the high +frequency domain. + +And in the scheme +that I showed you + +is what leads to this +particular conclusion. + +So that, then, is the essence +of what I wanted to cover today. + +And I am now certainly +open to any questions + +that you might have about these +two fascinating systems that + +have evolved in the +retina over the millions + +and millions of +years of evolution. + +Well, I was so clear that +there are questions, huh? + +Well, I hope that +you sort of gotten + +a sense of what it is like to +do these kinds of experiments + +and how luckily, at least, in +some cases, these experiments + +can lead to nice discoveries +as to the workings + +of the visual system. + +Now, last time when we +talked about the APB, we did + +have a "magic bullet." + +This approach here is +not as neat, really, + +because you have to make +lesions rather than specifically + +affecting certain +neurotransmitters. + +And that could not be done +because the neurotransmitters + +for the midget and the +parasol cells are similar. + +So you can't use that +kind of procedure + +that we were able to use +miraculously for the ON and OFF + +channels. + +So that, in essence, is what +we are going to cover today. + +Did everybody sign? + +Any one of you not sign +the attendance sheet? + +If not, please come +up here and sign it. + +And then let me just say +again that next time, + +we are going to talk about +color-- another fascinating + +topic. + +And we are also going to +talk about visual adaptation. + +And if you can, if you +get a chance to do so, + +please try to read the +preparatory material which + +should make it easier +for you to not only + +comprehend but, +especially, to be + +able to memorize these facts. + +And the memorization is +a very important part + +of learning things +in any course. + +And it will, of +course, be essential + +when you get to the stage +of having to take the exams. + +Well, thank you so much. \ No newline at end of file diff --git a/aEd4FFeBV6U.txt b/aEd4FFeBV6U.txt new file mode 100644 index 0000000000000000000000000000000000000000..29509ad5e2e9c72fbf972c1af4a506b4abdc25d8 --- /dev/null +++ b/aEd4FFeBV6U.txt @@ -0,0 +1,819 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +now we're ready to look at Fornell + + align:start position:0% +now we're ready to look at Fornell + + + align:start position:0% +now we're ready to look at Fornell +diffraction from circular apertures the + + align:start position:0% +diffraction from circular apertures the + + + align:start position:0% +diffraction from circular apertures the +set up is again the same as before but + + align:start position:0% +set up is again the same as before but + + + align:start position:0% +set up is again the same as before but +let me go over it again here we have a + + align:start position:0% +let me go over it again here we have a + + + align:start position:0% +let me go over it again here we have a +helium-neon laser beam from the laser + + align:start position:0% +helium-neon laser beam from the laser + + + align:start position:0% +helium-neon laser beam from the laser +gets reflected by this mirror then gets + + align:start position:0% +gets reflected by this mirror then gets + + + align:start position:0% +gets reflected by this mirror then gets +reflected again by this mirror into this + + align:start position:0% +reflected again by this mirror into this + + + align:start position:0% +reflected again by this mirror into this +lens this is a short focal length lens + + align:start position:0% +lens this is a short focal length lens + + + align:start position:0% +lens this is a short focal length lens +which is focused into a pinhole an + + align:start position:0% +which is focused into a pinhole an + + + align:start position:0% +which is focused into a pinhole an +adjustable pinhole and the light from + + align:start position:0% +adjustable pinhole and the light from + + + align:start position:0% +adjustable pinhole and the light from +the pinhole is then is a spherical wave + + align:start position:0% +the pinhole is then is a spherical wave + + + align:start position:0% +the pinhole is then is a spherical wave +you can see it here on the card this is + + align:start position:0% +you can see it here on the card this is + + + align:start position:0% +you can see it here on the card this is +vertical wave and then we let it hit the + + align:start position:0% +vertical wave and then we let it hit the + + + align:start position:0% +vertical wave and then we let it hit the +screen now we're ready to look at + + align:start position:0% +screen now we're ready to look at + + + align:start position:0% +screen now we're ready to look at +Fornell diffraction from apertures we + + align:start position:0% +Fornell diffraction from apertures we + + + align:start position:0% +Fornell diffraction from apertures we +have two apertures for you and I'm going + + align:start position:0% +have two apertures for you and I'm going + + + align:start position:0% +have two apertures for you and I'm going +to place the first one in the in the + + align:start position:0% +to place the first one in the in the + + + align:start position:0% +to place the first one in the in the +beam so now if we can look at the screen + + align:start position:0% +beam so now if we can look at the screen + + + align:start position:0% +beam so now if we can look at the screen +while I'm adjusting + + align:start position:0% + + + + align:start position:0% + +the aperture now here we are it's a + + align:start position:0% +the aperture now here we are it's a + + + align:start position:0% +the aperture now here we are it's a +fixed aperture it's a thousand microns + + align:start position:0% +fixed aperture it's a thousand microns + + + align:start position:0% +fixed aperture it's a thousand microns +in diameter and as we can see we see the + + align:start position:0% +in diameter and as we can see we see the + + + align:start position:0% +in diameter and as we can see we see the +same kind of fernell diffraction pattern + + align:start position:0% +same kind of fernell diffraction pattern + + + align:start position:0% +same kind of fernell diffraction pattern +as we saw with the with the slit look we + + align:start position:0% +as we saw with the with the slit look we + + + align:start position:0% +as we saw with the with the slit look we +see lots of fringes they get finer and + + align:start position:0% +see lots of fringes they get finer and + + + align:start position:0% +see lots of fringes they get finer and +finer as you approach the center and + + align:start position:0% +finer as you approach the center and + + + align:start position:0% +finer as you approach the center and +also the contrast is less and less as + + align:start position:0% +also the contrast is less and less as + + + align:start position:0% +also the contrast is less and less as +you approach the center but what I'm + + align:start position:0% +you approach the center but what I'm + + + align:start position:0% +you approach the center but what I'm +going to do now instead of keeping the + + align:start position:0% +going to do now instead of keeping the + + + align:start position:0% +going to do now instead of keeping the +distance fixed what I'm going to do is + + align:start position:0% +distance fixed what I'm going to do is + + + align:start position:0% +distance fixed what I'm going to do is +vary the distance between the aperture + + align:start position:0% +vary the distance between the aperture + + + align:start position:0% +vary the distance between the aperture +and the the and the light or the + + align:start position:0% +and the the and the light or the + + + align:start position:0% +and the the and the light or the +aperture from the pinhole and I would + + align:start position:0% +aperture from the pinhole and I would + + + align:start position:0% +aperture from the pinhole and I would +like you to watch what what happens so + + align:start position:0% +like you to watch what what happens so + + + align:start position:0% +like you to watch what what happens so +now I'm going to move the pin hole at + + align:start position:0% +now I'm going to move the pin hole at + + + align:start position:0% +now I'm going to move the pin hole at +the aperture very close to the to the + + align:start position:0% +the aperture very close to the to the + + + align:start position:0% +the aperture very close to the to the +pinhole and then I move away and then + + align:start position:0% +pinhole and then I move away and then + + + align:start position:0% +pinhole and then I move away and then +you can see first you see lots of + + align:start position:0% +you can see first you see lots of + + + align:start position:0% +you can see first you see lots of +fringes and as I move away you see fewer + + align:start position:0% +fringes and as I move away you see fewer + + + align:start position:0% +fringes and as I move away you see fewer +and fewer fringes and if you look in the + + align:start position:0% +and fewer fringes and if you look in the + + + align:start position:0% +and fewer fringes and if you look in the +centre hope you can see that is a white + + align:start position:0% +centre hope you can see that is a white + + + align:start position:0% +centre hope you can see that is a white +spot in the centre now we have a dark + + align:start position:0% +spot in the centre now we have a dark + + + align:start position:0% +spot in the centre now we have a dark +spot in the centre and then now we're + + align:start position:0% +spot in the centre and then now we're + + + align:start position:0% +spot in the centre and then now we're +getting fewer and fewer fringes until we + + align:start position:0% +getting fewer and fewer fringes until we + + + align:start position:0% +getting fewer and fewer fringes until we +have only only two or three now let me + + align:start position:0% +have only only two or three now let me + + + align:start position:0% +have only only two or three now let me +go back towards the pinhole or towards + + align:start position:0% +go back towards the pinhole or towards + + + align:start position:0% +go back towards the pinhole or towards +the lens see the increase in the number + + align:start position:0% +the lens see the increase in the number + + + align:start position:0% +the lens see the increase in the number +of fringes now this is again this is + + align:start position:0% +of fringes now this is again this is + + + align:start position:0% +of fringes now this is again this is +very interesting and I'm going to leave + + align:start position:0% +very interesting and I'm going to leave + + + align:start position:0% +very interesting and I'm going to leave +it to you to figure out here we are very + + align:start position:0% +it to you to figure out here we are very + + + align:start position:0% +it to you to figure out here we are very +close to the lens and then we move away + + align:start position:0% +close to the lens and then we move away + + + align:start position:0% +close to the lens and then we move away +and the lens all right now what I'm + + align:start position:0% +and the lens all right now what I'm + + + align:start position:0% +and the lens all right now what I'm +going to do I'm going to move to the + + align:start position:0% +going to do I'm going to move to the + + + align:start position:0% +going to do I'm going to move to the +second the second aperture which is 400 + + align:start position:0% +second the second aperture which is 400 + + + align:start position:0% +second the second aperture which is 400 +microns in in diameter and here we are + + align:start position:0% +microns in in diameter and here we are + + + align:start position:0% +microns in in diameter and here we are +let me let me again pick it up there we + + align:start position:0% +let me let me again pick it up there we + + + align:start position:0% +let me let me again pick it up there we +are now this looks diffraction pattern + + align:start position:0% +are now this looks diffraction pattern + + + align:start position:0% +are now this looks diffraction pattern +looks slightly different and again I + + align:start position:0% +looks slightly different and again I + + + align:start position:0% +looks slightly different and again I +want you to to explain what's going on + + align:start position:0% +want you to to explain what's going on + + + align:start position:0% +want you to to explain what's going on +here again now I'm going to move the + + align:start position:0% +here again now I'm going to move the + + + align:start position:0% +here again now I'm going to move the +this new aperture 400 micron diameter + + align:start position:0% +this new aperture 400 micron diameter + + + align:start position:0% +this new aperture 400 micron diameter +aperture as close as possible to the + + align:start position:0% +aperture as close as possible to the + + + align:start position:0% +aperture as close as possible to the +lens you can see one ring inside and + + align:start position:0% +lens you can see one ring inside and + + + align:start position:0% +lens you can see one ring inside and +then now you see the bright dot in the + + align:start position:0% +then now you see the bright dot in the + + + align:start position:0% +then now you see the bright dot in the +middle then the bright dot becomes a + + align:start position:0% +middle then the bright dot becomes a + + + align:start position:0% +middle then the bright dot becomes a +dark spot in the middle and now we get + + align:start position:0% +dark spot in the middle and now we get + + + align:start position:0% +dark spot in the middle and now we get +the white dot in the brighter dot in the + + align:start position:0% +the white dot in the brighter dot in the + + + align:start position:0% +the white dot in the brighter dot in the +in the middle and here it's almost + + align:start position:0% +in the middle and here it's almost + + + align:start position:0% +in the middle and here it's almost +beginning to look like from half a + + align:start position:0% +beginning to look like from half a + + + align:start position:0% +beginning to look like from half a +diffraction so here let me move towards + + align:start position:0% +diffraction so here let me move towards + + + align:start position:0% +diffraction so here let me move towards +the lens towards the focus of the lens I + + align:start position:0% +the lens towards the focus of the lens I + + + align:start position:0% +the lens towards the focus of the lens I +mean and see how the that changes and as + + align:start position:0% +mean and see how the that changes and as + + + align:start position:0% +mean and see how the that changes and as +we move away that changes again + + align:start position:0% + + + + align:start position:0% + +so let me hold it over here let you look + + align:start position:0% +so let me hold it over here let you look + + + align:start position:0% +so let me hold it over here let you look +at it and I hope you'll be able to + + align:start position:0% +at it and I hope you'll be able to + + + align:start position:0% +at it and I hope you'll be able to +figure all this out remember the the + + align:start position:0% +figure all this out remember the the + + + align:start position:0% +figure all this out remember the the +diameter of this aperture is 400 microns + + align:start position:0% +diameter of this aperture is 400 microns + + + align:start position:0% +diameter of this aperture is 400 microns +and in the previous one it was a + + align:start position:0% +and in the previous one it was a + + + align:start position:0% +and in the previous one it was a +thousand thousand microns and again the + + align:start position:0% +thousand thousand microns and again the + + + align:start position:0% +thousand thousand microns and again the +light is a is a say it was being focused + + align:start position:0% +light is a is a say it was being focused + + + align:start position:0% +light is a is a say it was being focused +by Y lens onto a small pinhole and then + + align:start position:0% +by Y lens onto a small pinhole and then + + + align:start position:0% +by Y lens onto a small pinhole and then +we had a diverging beam that is + + align:start position:0% +we had a diverging beam that is + + + align:start position:0% +we had a diverging beam that is +impinging on on these two on these two + + align:start position:0% +impinging on on these two on these two + + + align:start position:0% +impinging on on these two on these two +apertures so in summary we've seen a + + align:start position:0% +apertures so in summary we've seen a + + + align:start position:0% +apertures so in summary we've seen a +variety of diffraction patterns we've + + align:start position:0% +variety of diffraction patterns we've + + + align:start position:0% +variety of diffraction patterns we've +seen one dimensional front Hoffer + + align:start position:0% +seen one dimensional front Hoffer + + + align:start position:0% +seen one dimensional front Hoffer +diffraction pattern and also we've seen + + align:start position:0% +diffraction pattern and also we've seen + + + align:start position:0% +diffraction pattern and also we've seen +two dimensional front half a diffraction + + align:start position:0% +two dimensional front half a diffraction + + + align:start position:0% +two dimensional front half a diffraction +patterns and finally we looked at + + align:start position:0% +patterns and finally we looked at + + + align:start position:0% +patterns and finally we looked at +fernell diffraction associated with with + + align:start position:0% +fernell diffraction associated with with + + + align:start position:0% +fernell diffraction associated with with +a slit or an adjustable slit and also + + align:start position:0% +a slit or an adjustable slit and also + + + align:start position:0% +a slit or an adjustable slit and also +with with apertures and then we saw how + + align:start position:0% +with with apertures and then we saw how + + + align:start position:0% +with with apertures and then we saw how +the diffraction pattern changes as we + + align:start position:0% +the diffraction pattern changes as we + + + align:start position:0% +the diffraction pattern changes as we +move the aperture closer and closer to + + align:start position:0% +move the aperture closer and closer to + + + align:start position:0% +move the aperture closer and closer to +the focus of the lens \ No newline at end of file diff --git a/al2lzKq4o5E.txt b/al2lzKq4o5E.txt new file mode 100644 index 0000000000000000000000000000000000000000..b4cbca182849fbd7fef33980d834500a8362fbf7 --- /dev/null +++ b/al2lzKq4o5E.txt @@ -0,0 +1,1827 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I'd like us to do some basic + + align:start position:0% +I'd like us to do some basic + + + align:start position:0% +I'd like us to do some basic +manipulation of some power series that + + align:start position:0% +manipulation of some power series that + + + align:start position:0% +manipulation of some power series that +you saw in the lecture so I have four + + align:start position:0% +you saw in the lecture so I have four + + + align:start position:0% +you saw in the lecture so I have four +problems here and what I'd like us to do + + align:start position:0% +problems here and what I'd like us to do + + + align:start position:0% +problems here and what I'd like us to do +is figure figure out what function each + + align:start position:0% +is figure figure out what function each + + + align:start position:0% +is figure figure out what function each +of these series represents now you can + + align:start position:0% +of these series represents now you can + + + align:start position:0% +of these series represents now you can +assume that the X values that we are + + align:start position:0% +assume that the X values that we are + + + align:start position:0% +assume that the X values that we are +going to insert into this function are + + align:start position:0% +going to insert into this function are + + + align:start position:0% +going to insert into this function are +only X values that that let the sums + + align:start position:0% +only X values that that let the sums + + + align:start position:0% +only X values that that let the sums +converge so you don't have to worry + + align:start position:0% +converge so you don't have to worry + + + align:start position:0% +converge so you don't have to worry +about anything to do with convergence of + + align:start position:0% +about anything to do with convergence of + + + align:start position:0% +about anything to do with convergence of +these sums just assume the sums converge + + align:start position:0% +these sums just assume the sums converge + + + align:start position:0% +these sums just assume the sums converge +that we've picked good X values okay and + + align:start position:0% +that we've picked good X values okay and + + + align:start position:0% +that we've picked good X values okay and +what I'd like you to have in the end for + + align:start position:0% +what I'd like you to have in the end for + + + align:start position:0% +what I'd like you to have in the end for +a b c and d is something like this sum + + align:start position:0% +a b c and d is something like this sum + + + align:start position:0% +a b c and d is something like this sum +is equal to a specific function it + + align:start position:0% +is equal to a specific function it + + + align:start position:0% +is equal to a specific function it +should not include a sum anymore so why + + align:start position:0% +should not include a sum anymore so why + + + align:start position:0% +should not include a sum anymore so why +don't you work on those for a bit pause + + align:start position:0% +don't you work on those for a bit pause + + + align:start position:0% +don't you work on those for a bit pause +the video and when you're done restart + + align:start position:0% +the video and when you're done restart + + + align:start position:0% +the video and when you're done restart +the video and I'll come back and show + + align:start position:0% +the video and I'll come back and show + + + align:start position:0% +the video and I'll come back and show +you how I work with + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% + + + + align:start position:0% + +all right welcome back well hopefully + + align:start position:0% +all right welcome back well hopefully + + + align:start position:0% +all right welcome back well hopefully +these were a little bit fun for you I + + align:start position:0% +these were a little bit fun for you I + + + align:start position:0% +these were a little bit fun for you I +always like them the first time I saw + + align:start position:0% +always like them the first time I saw + + + align:start position:0% +always like them the first time I saw +them to to see how one could manipulate + + align:start position:0% +them to to see how one could manipulate + + + align:start position:0% +them to to see how one could manipulate +these these series um so again what + + align:start position:0% +these these series um so again what + + + align:start position:0% +these these series um so again what +we're trying to do is figure out what + + align:start position:0% +we're trying to do is figure out what + + + align:start position:0% +we're trying to do is figure out what +function these series are represent + + align:start position:0% +function these series are represent + + + align:start position:0% +function these series are represent +we're assuming convergence and we're + + align:start position:0% +we're assuming convergence and we're + + + align:start position:0% +we're assuming convergence and we're +going to try and manipulate them to look + + align:start position:0% +going to try and manipulate them to look + + + align:start position:0% +going to try and manipulate them to look +like things we already know so I'm going + + align:start position:0% +like things we already know so I'm going + + + align:start position:0% +like things we already know so I'm going +to start I'm just going to go straight + + align:start position:0% +to start I'm just going to go straight + + + align:start position:0% +to start I'm just going to go straight +through a b c and d and I'm going to + + align:start position:0% +through a b c and d and I'm going to + + + align:start position:0% +through a b c and d and I'm going to +rewrite the problem each time because I + + align:start position:0% +rewrite the problem each time because I + + + align:start position:0% +rewrite the problem each time because I +don't want to keep coming back so a we + + align:start position:0% +don't want to keep coming back so a we + + + align:start position:0% +don't want to keep coming back so a we +had the sum Nal 0 To + + align:start position:0% +had the sum Nal 0 To + + + align:start position:0% +had the sum Nal 0 To +infinity x n + 2 over n + + align:start position:0% +infinity x n + 2 over n + + + align:start position:0% +infinity x n + 2 over n +factorial well this looks very close to + + align:start position:0% +factorial well this looks very close to + + + align:start position:0% +factorial well this looks very close to +something we know it looks a lot like + + align:start position:0% +something we know it looks a lot like + + + align:start position:0% +something we know it looks a lot like +the one the function e to the X the + + align:start position:0% +the one the function e to the X the + + + align:start position:0% +the one the function e to the X the +difference is that e to the X just has a + + align:start position:0% +difference is that e to the X just has a + + + align:start position:0% +difference is that e to the X just has a +power x to the N but the good news is + + align:start position:0% +power x to the N but the good news is + + + align:start position:0% +power x to the N but the good news is +that I am really I'm really close to + + align:start position:0% +that I am really I'm really close to + + + align:start position:0% +that I am really I'm really close to +that what I really have in the numerator + + align:start position:0% +that what I really have in the numerator + + + align:start position:0% +that what I really have in the numerator +is X to the N time x^2 + + align:start position:0% +is X to the N time x^2 + + + align:start position:0% +is X to the N time x^2 +because this x the n + 2 I can write as + + align:start position:0% +because this x the n + 2 I can write as + + + align:start position:0% +because this x the n + 2 I can write as +X the n * x^2 so every term has an X squ + + align:start position:0% +X the n * x^2 so every term has an X squ + + + align:start position:0% +X the n * x^2 so every term has an X squ +so as was mentioned in the lecture you + + align:start position:0% +so as was mentioned in the lecture you + + + align:start position:0% +so as was mentioned in the lecture you +can treat this really like pols in some + + align:start position:0% +can treat this really like pols in some + + + align:start position:0% +can treat this really like pols in some +way you can Factor this out so I can + + align:start position:0% +way you can Factor this out so I can + + + align:start position:0% +way you can Factor this out so I can +rewrite this as well I'll rewrite it in + + align:start position:0% +rewrite this as well I'll rewrite it in + + + align:start position:0% +rewrite this as well I'll rewrite it in +two + + align:start position:0% +two + + + align:start position:0% +two +steps 0 to Infinity of + + align:start position:0% +steps 0 to Infinity of + + + align:start position:0% +steps 0 to Infinity of +x^2 x to the N Over N factorial so x^2 * + + align:start position:0% +x^2 x to the N Over N factorial so x^2 * + + + align:start position:0% +x^2 x to the N Over N factorial so x^2 * +x n gives me the x n + 2 right + + align:start position:0% +x n gives me the x n + 2 right + + + align:start position:0% +x n gives me the x n + 2 right +but I can actually now because this + + align:start position:0% +but I can actually now because this + + + align:start position:0% +but I can actually now because this +belongs to every sum I can pull that all + + align:start position:0% +belongs to every sum I can pull that all + + + align:start position:0% +belongs to every sum I can pull that all +the way out in front right and if I pull + + align:start position:0% +the way out in front right and if I pull + + + align:start position:0% +the way out in front right and if I pull +that all the way out in front if I move + + align:start position:0% +that all the way out in front if I move + + + align:start position:0% +that all the way out in front if I move +this out to the front I have an x squ + + align:start position:0% +this out to the front I have an x squ + + + align:start position:0% +this out to the front I have an x squ +times this sum well what is the sum the + + align:start position:0% +times this sum well what is the sum the + + + align:start position:0% +times this sum well what is the sum the +sum is e to the X it's Nal 0 to Infinity + + align:start position:0% +sum is e to the X it's Nal 0 to Infinity + + + align:start position:0% +sum is e to the X it's Nal 0 to Infinity +of x to the N Over N factorial that's + + align:start position:0% +of x to the N Over N factorial that's + + + align:start position:0% +of x to the N Over N factorial that's +just e to the X so this function is X2 e + + align:start position:0% +just e to the X so this function is X2 e + + + align:start position:0% +just e to the X so this function is X2 e +to the X that's what a is if you were + + align:start position:0% +to the X that's what a is if you were + + + align:start position:0% +to the X that's what a is if you were +worried about it you could write e to + + align:start position:0% +worried about it you could write e to + + + align:start position:0% +worried about it you could write e to +the X as its series and then you can + + align:start position:0% +the X as its series and then you can + + + align:start position:0% +the X as its series and then you can +multiply through by x s and see if + + align:start position:0% +multiply through by x s and see if + + + align:start position:0% +multiply through by x s and see if +that's what you get but you'll see that + + align:start position:0% +that's what you get but you'll see that + + + align:start position:0% +that's what you get but you'll see that +is indeed how this problem + + align:start position:0% +is indeed how this problem + + + align:start position:0% +is indeed how this problem +works okay let's look at + + align:start position:0% +works okay let's look at + + + align:start position:0% +works okay let's look at +B okay + + align:start position:0% +B okay + + + align:start position:0% +B okay +B is equal to the + + align:start position:0% +B is equal to the + + + align:start position:0% +B is equal to the +sum it's a weird summation sign sorry + + align:start position:0% +sum it's a weird summation sign sorry + + + align:start position:0% +sum it's a weird summation sign sorry +about that b is equal to the sum Nal 2 + + align:start position:0% +about that b is equal to the sum Nal 2 + + + align:start position:0% +about that b is equal to the sum Nal 2 +to infinity x to the N that's what we + + align:start position:0% +to infinity x to the N that's what we + + + align:start position:0% +to infinity x to the N that's what we +wanted to look at well this looks very + + align:start position:0% +wanted to look at well this looks very + + + align:start position:0% +wanted to look at well this looks very +close to the geometric series but it's + + align:start position:0% +close to the geometric series but it's + + + align:start position:0% +close to the geometric series but it's +missing some terms right the geometric + + align:start position:0% +missing some terms right the geometric + + + align:start position:0% +missing some terms right the geometric +Series starts at n equals 0 to Infinity + + align:start position:0% +Series starts at n equals 0 to Infinity + + + align:start position:0% +Series starts at n equals 0 to Infinity +but the point I want to make here is + + align:start position:0% +but the point I want to make here is + + + align:start position:0% +but the point I want to make here is +that I can rewrite this as the geometric + + align:start position:0% +that I can rewrite this as the geometric + + + align:start position:0% +that I can rewrite this as the geometric +series and then I can take away what + + align:start position:0% +series and then I can take away what + + + align:start position:0% +series and then I can take away what +I've added in okay so these do not agree + + align:start position:0% +I've added in okay so these do not agree + + + align:start position:0% +I've added in okay so these do not agree +right now this equal sign is not true + + align:start position:0% +right now this equal sign is not true + + + align:start position:0% +right now this equal sign is not true +yet but what do I notice I notice this + + align:start position:0% +yet but what do I notice I notice this + + + align:start position:0% +yet but what do I notice I notice this +one has two more terms at the beginning + + align:start position:0% +one has two more terms at the beginning + + + align:start position:0% +one has two more terms at the beginning +than this one has what are those terms + + align:start position:0% +than this one has what are those terms + + + align:start position:0% +than this one has what are those terms +those are when n equals 0 and when n + + align:start position:0% +those are when n equals 0 and when n + + + align:start position:0% +those are when n equals 0 and when n +equals 1 right there's no n equal 0 or n + + align:start position:0% +equals 1 right there's no n equal 0 or n + + + align:start position:0% +equals 1 right there's no n equal 0 or n +equals 1 here the formulas are exactly + + align:start position:0% +equals 1 here the formulas are exactly + + + align:start position:0% +equals 1 here the formulas are exactly +the same right x to the n x the N they + + align:start position:0% +the same right x to the n x the N they + + + align:start position:0% +the same right x to the n x the N they +both go to Infinity but one starting at + + align:start position:0% +both go to Infinity but one starting at + + + align:start position:0% +both go to Infinity but one starting at +n equals 2 and one starting at n equals + + align:start position:0% +n equals 2 and one starting at n equals + + + align:start position:0% +n equals 2 and one starting at n equals +0 again I'm want to remind you why did I + + align:start position:0% +0 again I'm want to remind you why did I + + + align:start position:0% +0 again I'm want to remind you why did I +bother to write this thing at all is + + align:start position:0% +bother to write this thing at all is + + + align:start position:0% +bother to write this thing at all is +because this is a function we + + align:start position:0% +because this is a function we + + + align:start position:0% +because this is a function we +know but this equal sign is not true + + align:start position:0% +know but this equal sign is not true + + + align:start position:0% +know but this equal sign is not true +right now right I have to get rid of the + + align:start position:0% +right now right I have to get rid of the + + + align:start position:0% +right now right I have to get rid of the +extra stuff I added what did I add I + + align:start position:0% +extra stuff I added what did I add I + + + align:start position:0% +extra stuff I added what did I add I +added let me let me get this as a sum + + align:start position:0% +added let me let me get this as a sum + + + align:start position:0% +added let me let me get this as a sum +what did I add on I added on X to the 0o + + align:start position:0% +what did I add on I added on X to the 0o + + + align:start position:0% +what did I add on I added on X to the 0o +and X to the 1 so now I guess I should + + align:start position:0% +and X to the 1 so now I guess I should + + + align:start position:0% +and X to the 1 so now I guess I should +have written subtract here right I + + align:start position:0% +have written subtract here right I + + + align:start position:0% +have written subtract here right I +should + + align:start position:0% +should + + + align:start position:0% +should +subtract x to the 0 and I should + + align:start position:0% +subtract x to the 0 and I should + + + align:start position:0% +subtract x to the 0 and I should +subtract x to the 1 I've already said it + + align:start position:0% +subtract x to the 1 I've already said it + + + align:start position:0% +subtract x to the 1 I've already said it +once but I'm going to just to make sure + + align:start position:0% +once but I'm going to just to make sure + + + align:start position:0% +once but I'm going to just to make sure +everybody follows say it one more + + align:start position:0% +everybody follows say it one more + + + align:start position:0% +everybody follows say it one more +time I now I've taken the summation I + + align:start position:0% +time I now I've taken the summation I + + + align:start position:0% +time I now I've taken the summation I +started with which went from n equal 2 + + align:start position:0% +started with which went from n equal 2 + + + align:start position:0% +started with which went from n equal 2 +to + + align:start position:0% +to + + + align:start position:0% +to +Infinity I added two more terms to the + + align:start position:0% +Infinity I added two more terms to the + + + align:start position:0% +Infinity I added two more terms to the +sum I made it go from zero to Infinity + + align:start position:0% +sum I made it go from zero to Infinity + + + align:start position:0% +sum I made it go from zero to Infinity +so to keep equality I subtracted off the + + align:start position:0% +so to keep equality I subtracted off the + + + align:start position:0% +so to keep equality I subtracted off the +two things I added in I subtracted off x + + align:start position:0% +two things I added in I subtracted off x + + + align:start position:0% +two things I added in I subtracted off x +to the 0o and x to the + + align:start position:0% +to the 0o and x to the + + + align:start position:0% +to the 0o and x to the +1st so now what was the point of this + + align:start position:0% +1st so now what was the point of this + + + align:start position:0% +1st so now what was the point of this +part of the exercise well the point is + + align:start position:0% +part of the exercise well the point is + + + align:start position:0% +part of the exercise well the point is +that I know what this sum is that's the + + align:start position:0% +that I know what this sum is that's the + + + align:start position:0% +that I know what this sum is that's the +geometric series that's one over one - + + align:start position:0% + + + + align:start position:0% + +x this x to the 0 it's -1 x to the 1st - + + align:start position:0% +x this x to the 0 it's -1 x to the 1st - + + + align:start position:0% +x this x to the 0 it's -1 x to the 1st - +x so this I broke up into something I + + align:start position:0% +x so this I broke up into something I + + + align:start position:0% +x so this I broke up into something I +knew + + align:start position:0% +knew + + + align:start position:0% +knew +as a as a power series and then other + + align:start position:0% +as a as a power series and then other + + + align:start position:0% +as a as a power series and then other +pieces that I uh had added in to make it + + align:start position:0% +pieces that I uh had added in to make it + + + align:start position:0% +pieces that I uh had added in to make it +look like something I knew I had to + + align:start position:0% +look like something I knew I had to + + + align:start position:0% +look like something I knew I had to +subtract those off so that's the idea of + + align:start position:0% +subtract those off so that's the idea of + + + align:start position:0% +subtract those off so that's the idea of +that one if you wanted to go on and and + + align:start position:0% +that one if you wanted to go on and and + + + align:start position:0% +that one if you wanted to go on and and +simplify further you could do that but + + align:start position:0% +simplify further you could do that but + + + align:start position:0% +simplify further you could do that but +I'm willing to leave it just as is + + align:start position:0% +I'm willing to leave it just as is + + + align:start position:0% +I'm willing to leave it just as is +because the idea was really this part up + + align:start position:0% +because the idea was really this part up + + + align:start position:0% +because the idea was really this part up +here and then translating it down to + + align:start position:0% +here and then translating it down to + + + align:start position:0% +here and then translating it down to +this all right let me write C + + align:start position:0% +this all right let me write C + + + align:start position:0% +this all right let me write C +again the sum and equals 0 To + + align:start position:0% +again the sum and equals 0 To + + + align:start position:0% +again the sum and equals 0 To +infinity x the n/ N + + align:start position:0% +infinity x the n/ N + + + align:start position:0% +infinity x the n/ N +factorial plus X the N okay so was the + + align:start position:0% +factorial plus X the N okay so was the + + + align:start position:0% +factorial plus X the N okay so was the +sum n equal 0 To infinity x the N Over N + + align:start position:0% +sum n equal 0 To infinity x the N Over N + + + align:start position:0% +sum n equal 0 To infinity x the N Over N +factorial plus x to the n and the point + + align:start position:0% +factorial plus x to the n and the point + + + align:start position:0% +factorial plus x to the n and the point +to recognize here is again as as + + align:start position:0% +to recognize here is again as as + + + align:start position:0% +to recognize here is again as as +Professor jarrison mentioned you you're + + align:start position:0% +Professor jarrison mentioned you you're + + + align:start position:0% +Professor jarrison mentioned you you're +really treating these almost like + + align:start position:0% +really treating these almost like + + + align:start position:0% +really treating these almost like +polinomial so you're taking a series and + + align:start position:0% +polinomial so you're taking a series and + + + align:start position:0% +polinomial so you're taking a series and +you're adding these terms up but really + + align:start position:0% +you're adding these terms up but really + + + align:start position:0% +you're adding these terms up but really +what you can think about this is the two + + align:start position:0% +what you can think about this is the two + + + align:start position:0% +what you can think about this is the two +separate series added up and so this is + + align:start position:0% +separate series added up and so this is + + + align:start position:0% +separate series added up and so this is +the sum from any 0 to Infinity of X the + + align:start position:0% +the sum from any 0 to Infinity of X the + + + align:start position:0% +the sum from any 0 to Infinity of X the +n n factorial which we know plus the sum + + align:start position:0% +n n factorial which we know plus the sum + + + align:start position:0% +n n factorial which we know plus the sum +from Nal 0 to Infinity of of X the N + + align:start position:0% +from Nal 0 to Infinity of of X the N + + + align:start position:0% +from Nal 0 to Infinity of of X the N +which we know the first one is just e to + + align:start position:0% +which we know the first one is just e to + + + align:start position:0% +which we know the first one is just e to +the X and the second one we've been + + align:start position:0% +the X and the second one we've been + + + align:start position:0% +the X and the second one we've been +dealing a lot with these already + + align:start position:0% +dealing a lot with these already + + + align:start position:0% +dealing a lot with these already +today is just one over 1 minus X so the + + align:start position:0% +today is just one over 1 minus X so the + + + align:start position:0% +today is just one over 1 minus X so the +point I want to make is if you have this + + align:start position:0% +point I want to make is if you have this + + + align:start position:0% +point I want to make is if you have this +convergent series you can split it up + + align:start position:0% +convergent series you can split it up + + + align:start position:0% +convergent series you can split it up +into to it two pieces over the sum and + + align:start position:0% +into to it two pieces over the sum and + + + align:start position:0% +into to it two pieces over the sum and +these two are both convergent we know + + align:start position:0% +these two are both convergent we know + + + align:start position:0% +these two are both convergent we know +separately and so we can write what they + + align:start position:0% +separately and so we can write what they + + + align:start position:0% +separately and so we can write what they +are X the n/ N factorial from 0 to + + align:start position:0% +are X the n/ N factorial from 0 to + + + align:start position:0% +are X the n/ N factorial from 0 to +Infinity is e x x to the N from n equals + + align:start position:0% +Infinity is e x x to the N from n equals + + + align:start position:0% +Infinity is e x x to the N from n equals +0 to Infinity is 1 over 1 - + + align:start position:0% +0 to Infinity is 1 over 1 - + + + align:start position:0% +0 to Infinity is 1 over 1 - +x so now we just have one + + align:start position:0% +x so now we just have one + + + align:start position:0% +x so now we just have one +more let me write that one D was + + align:start position:0% +more let me write that one D was + + + align:start position:0% +more let me write that one D was +summation n = -1 to infinity x the n + + + align:start position:0% +summation n = -1 to infinity x the n + + + + align:start position:0% +summation n = -1 to infinity x the n + +one all right this was not meant to + + align:start position:0% +one all right this was not meant to + + + align:start position:0% +one all right this was not meant to +scare you but it was meant to test your + + align:start position:0% +scare you but it was meant to test your + + + align:start position:0% +scare you but it was meant to test your +understanding of Sigma notation so the + + align:start position:0% +understanding of Sigma notation so the + + + align:start position:0% +understanding of Sigma notation so the +problem is we're starting at Nal minus + + align:start position:0% +problem is we're starting at Nal minus + + + align:start position:0% +problem is we're starting at Nal minus +one but X is starting the exponent on X + + align:start position:0% +one but X is starting the exponent on X + + + align:start position:0% +one but X is starting the exponent on X +is at n plus one so I want to write it + + align:start position:0% +is at n plus one so I want to write it + + + align:start position:0% +is at n plus one so I want to write it +in some form that I know well let's try + + align:start position:0% +in some form that I know well let's try + + + align:start position:0% +in some form that I know well let's try +and get the subscript to be zero so what + + align:start position:0% +and get the subscript to be zero so what + + + align:start position:0% +and get the subscript to be zero so what +I'm going to do is I'm going to make + + align:start position:0% +I'm going to do is I'm going to make + + + align:start position:0% +I'm going to do is I'm going to make +change the name of the subscript I'm + + align:start position:0% +change the name of the subscript I'm + + + align:start position:0% +change the name of the subscript I'm +going to let it be m equals 0 to + + align:start position:0% +going to let it be m equals 0 to + + + align:start position:0% +going to let it be m equals 0 to +Infinity okay and I want M to count up + + align:start position:0% +Infinity okay and I want M to count up + + + align:start position:0% +Infinity okay and I want M to count up +the by one just the way n counts up so + + align:start position:0% +the by one just the way n counts up so + + + align:start position:0% +the by one just the way n counts up so +notice what I did when m equals 0 nal1 + + align:start position:0% +notice what I did when m equals 0 nal1 + + + align:start position:0% +notice what I did when m equals 0 nal1 +that's what we've set up as the first + + align:start position:0% +that's what we've set up as the first + + + align:start position:0% +that's what we've set up as the first +term that means n + 1 is equal to zero + + align:start position:0% +term that means n + 1 is equal to zero + + + align:start position:0% +term that means n + 1 is equal to zero +when m equals z and since I'm going up + + align:start position:0% +when m equals z and since I'm going up + + + align:start position:0% +when m equals z and since I'm going up +by one every time in my in my summation + + align:start position:0% +by one every time in my in my summation + + + align:start position:0% +by one every time in my in my summation +my iteration here that means that for + + align:start position:0% +my iteration here that means that for + + + align:start position:0% +my iteration here that means that for +every M I have I just have to take n + + + align:start position:0% +every M I have I just have to take n + + + + align:start position:0% +every M I have I just have to take n + +one to figure out what M is so I should + + align:start position:0% +one to figure out what M is so I should + + + align:start position:0% +one to figure out what M is so I should +have said it the other way for every N I + + align:start position:0% +have said it the other way for every N I + + + align:start position:0% +have said it the other way for every N I +have I just have to add one to get M + + align:start position:0% +have I just have to add one to get M + + + align:start position:0% +have I just have to add one to get M +okay so here if I start at one I start + + align:start position:0% +okay so here if I start at one I start + + + align:start position:0% +okay so here if I start at one I start +here at zero the next term here is zero + + align:start position:0% +here at zero the next term here is zero + + + align:start position:0% +here at zero the next term here is zero +n equals 0 but the next term here is m + + align:start position:0% +n equals 0 but the next term here is m + + + align:start position:0% +n equals 0 but the next term here is m +equals 1 the next term here would be n + + align:start position:0% +equals 1 the next term here would be n + + + align:start position:0% +equals 1 the next term here would be n +equals uh one and the next term here + + align:start position:0% +equals uh one and the next term here + + + align:start position:0% +equals uh one and the next term here +would be m equals 2 so they're just off + + align:start position:0% +would be m equals 2 so they're just off + + + align:start position:0% +would be m equals 2 so they're just off +by one but they're still catching every + + align:start position:0% +by one but they're still catching every + + + align:start position:0% +by one but they're still catching every +index now I don't have to change what's + + align:start position:0% +index now I don't have to change what's + + + align:start position:0% +index now I don't have to change what's +up here because Infinity if I add one to + + align:start position:0% +up here because Infinity if I add one to + + + align:start position:0% +up here because Infinity if I add one to +it I still am I'm still going off to + + align:start position:0% +it I still am I'm still going off to + + + align:start position:0% +it I still am I'm still going off to +Infinity so I don't have to change + + align:start position:0% +Infinity so I don't have to change + + + align:start position:0% +Infinity so I don't have to change +what's up here but I do want to write + + align:start position:0% +what's up here but I do want to write + + + align:start position:0% +what's up here but I do want to write +the formula or the formula I have in on + + align:start position:0% +the formula or the formula I have in on + + + align:start position:0% +the formula or the formula I have in on +inside the sum in terms of M + + align:start position:0% +inside the sum in terms of M + + + align:start position:0% +inside the sum in terms of M +but I've already got it because I know m + + align:start position:0% +but I've already got it because I know m + + + align:start position:0% +but I've already got it because I know m +is always equal to n+ one so I can + + align:start position:0% +is always equal to n+ one so I can + + + align:start position:0% +is always equal to n+ one so I can +replace this n plus one by an + + align:start position:0% +replace this n plus one by an + + + align:start position:0% +replace this n plus one by an +m and now we know what that one is right + + align:start position:0% +m and now we know what that one is right + + + align:start position:0% +m and now we know what that one is right +m equals 0 to Infinity of x to the m + + align:start position:0% +m equals 0 to Infinity of x to the m + + + align:start position:0% +m equals 0 to Infinity of x to the m +that's our geometric Series so it + + align:start position:0% +that's our geometric Series so it + + + align:start position:0% +that's our geometric Series so it +actually even though I wrote it in kind + + align:start position:0% +actually even though I wrote it in kind + + + align:start position:0% +actually even though I wrote it in kind +of a funny way it was actually just + + align:start position:0% +of a funny way it was actually just + + + align:start position:0% +of a funny way it was actually just +still the geometric series I just moved + + align:start position:0% +still the geometric series I just moved + + + align:start position:0% +still the geometric series I just moved +the indices a little bit to make sure we + + align:start position:0% +the indices a little bit to make sure we + + + align:start position:0% +the indices a little bit to make sure we +could play with those so the idea here + + align:start position:0% +could play with those so the idea here + + + align:start position:0% +could play with those so the idea here +the whole point of this exercise just to + + align:start position:0% +the whole point of this exercise just to + + + align:start position:0% +the whole point of this exercise just to +recognize how you can manipulate these + + align:start position:0% +recognize how you can manipulate these + + + align:start position:0% +recognize how you can manipulate these +series a little bit so that if they're + + align:start position:0% +series a little bit so that if they're + + + align:start position:0% +series a little bit so that if they're +in a form that looks kind of like one of + + align:start position:0% +in a form that looks kind of like one of + + + align:start position:0% +in a form that looks kind of like one of +the functions you know you can you can + + align:start position:0% +the functions you know you can you can + + + align:start position:0% +the functions you know you can you can +see if it actually is you know a product + + align:start position:0% +see if it actually is you know a product + + + align:start position:0% +see if it actually is you know a product +of something with the function you know + + align:start position:0% +of something with the function you know + + + align:start position:0% +of something with the function you know +or the sum of two functions you know or + + align:start position:0% +or the sum of two functions you know or + + + align:start position:0% +or the sum of two functions you know or +maybe one of the functions you know as a + + align:start position:0% +maybe one of the functions you know as a + + + align:start position:0% +maybe one of the functions you know as a +power series and then you have to drop + + align:start position:0% +power series and then you have to drop + + + align:start position:0% +power series and then you have to drop +off a couple terms so they each sort of + + align:start position:0% +off a couple terms so they each sort of + + + align:start position:0% +off a couple terms so they each sort of +demonstrate a different idea of how you + + align:start position:0% +demonstrate a different idea of how you + + + align:start position:0% +demonstrate a different idea of how you +can manipulate these convergent power + + align:start position:0% +can manipulate these convergent power + + + align:start position:0% +can manipulate these convergent power +series based on functions you already + + align:start position:0% +series based on functions you already + + + align:start position:0% +series based on functions you already +know so I'll stop there \ No newline at end of file diff --git a/ayrdDJPAD5M.txt b/ayrdDJPAD5M.txt new file mode 100644 index 0000000000000000000000000000000000000000..d42158a690c9e85f3cc65fc52a38d55093602838 --- /dev/null +++ b/ayrdDJPAD5M.txt @@ -0,0 +1,2099 @@ +align:start position:0% + +here we are in Libra office and you'll + + align:start position:0% +here we are in Libra office and you'll + + + align:start position:0% +here we are in Libra office and you'll +see that we have all the data we + + align:start position:0% +see that we have all the data we + + + align:start position:0% +see that we have all the data we +discussed in the previous videos loaded + + align:start position:0% +discussed in the previous videos loaded + + + align:start position:0% +discussed in the previous videos loaded +into the spreadsheet here let's take a + + align:start position:0% +into the spreadsheet here let's take a + + + align:start position:0% +into the spreadsheet here let's take a +minute to familiarize ourselves with how + + align:start position:0% +minute to familiarize ourselves with how + + + align:start position:0% +minute to familiarize ourselves with how +the data is setup so here we see we've + + align:start position:0% +the data is setup so here we see we've + + + align:start position:0% +the data is setup so here we see we've +got the number of surgical teams per + + align:start position:0% +got the number of surgical teams per + + + align:start position:0% +got the number of surgical teams per +department per day and which we've got + + align:start position:0% +department per day and which we've got + + + align:start position:0% +department per day and which we've got +it listed by Department all five of them + + align:start position:0% +it listed by Department all five of them + + + align:start position:0% +it listed by Department all five of them +are here and by day of the week Monday + + align:start position:0% +are here and by day of the week Monday + + + align:start position:0% +are here and by day of the week Monday +Tuesday Wednesday Thursday and Friday + + align:start position:0% +Tuesday Wednesday Thursday and Friday + + + align:start position:0% +Tuesday Wednesday Thursday and Friday +remember for all departments we have the + + align:start position:0% +remember for all departments we have the + + + align:start position:0% +remember for all departments we have the +same number of teams in per day except + + align:start position:0% +same number of teams in per day except + + + align:start position:0% +same number of teams in per day except +for oral surgery because the oral + + align:start position:0% +for oral surgery because the oral + + + align:start position:0% +for oral surgery because the oral +surgeon is only present on Tuesdays and + + align:start position:0% +surgeon is only present on Tuesdays and + + + align:start position:0% +surgeon is only present on Tuesdays and +Thursdays scrolling across we see that + + align:start position:0% +Thursdays scrolling across we see that + + + align:start position:0% +Thursdays scrolling across we see that +for all five departments again we've got + + align:start position:0% +for all five departments again we've got + + + align:start position:0% +for all five departments again we've got +the minimum number of operating rooms + + align:start position:0% +the minimum number of operating rooms + + + align:start position:0% +the minimum number of operating rooms +that each one requires each day this is + + align:start position:0% +that each one requires each day this is + + + align:start position:0% +that each one requires each day this is +simply zero as we keep going we see the + + align:start position:0% +simply zero as we keep going we see the + + + align:start position:0% +simply zero as we keep going we see the +maximum number of operating rooms that + + align:start position:0% +maximum number of operating rooms that + + + align:start position:0% +maximum number of operating rooms that +each department requires each day going + + align:start position:0% +each department requires each day going + + + align:start position:0% +each department requires each day going +down to the next set of data we've got + + align:start position:0% +down to the next set of data we've got + + + align:start position:0% +down to the next set of data we've got +the weekly Department requirements we've + + align:start position:0% +the weekly Department requirements we've + + + align:start position:0% +the weekly Department requirements we've +got the minimum and maximum number of + + align:start position:0% +got the minimum and maximum number of + + + align:start position:0% +got the minimum and maximum number of +operating rooms that each department + + align:start position:0% +operating rooms that each department + + + align:start position:0% +operating rooms that each department +requires each week we also have the + + align:start position:0% +requires each week we also have the + + + align:start position:0% +requires each week we also have the +weekly targets this is data because it + + align:start position:0% +weekly targets this is data because it + + + align:start position:0% +weekly targets this is data because it +is set by the department's before the + + align:start position:0% +is set by the department's before the + + + align:start position:0% +is set by the department's before the +operating room manager has a chance to + + align:start position:0% +operating room manager has a chance to + + + align:start position:0% +operating room manager has a chance to +schedule the operating rooms so this is + + align:start position:0% +schedule the operating rooms so this is + + + align:start position:0% +schedule the operating rooms so this is +our problem data and now let's go down + + align:start position:0% +our problem data and now let's go down + + + align:start position:0% +our problem data and now let's go down +to our decision variables all right so + + align:start position:0% +to our decision variables all right so + + + align:start position:0% +to our decision variables all right so +here are decision variables you see that + + align:start position:0% +here are decision variables you see that + + + align:start position:0% +here are decision variables you see that +we've set up a decision variable for + + align:start position:0% +we've set up a decision variable for + + + align:start position:0% +we've set up a decision variable for +each department and for each day of the + + align:start position:0% +each department and for each day of the + + + align:start position:0% +each department and for each day of the +week right now they're simply set to 0 + + align:start position:0% +week right now they're simply set to 0 + + + align:start position:0% +week right now they're simply set to 0 +but we've colored them yellow so they'll + + align:start position:0% +but we've colored them yellow so they'll + + + align:start position:0% +but we've colored them yellow so they'll +be easy to see let's now set up a column + + align:start position:0% +be easy to see let's now set up a column + + + align:start position:0% +be easy to see let's now set up a column +for weekly totals let's put that here + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so let's fill this in the weekly total + + align:start position:0% +so let's fill this in the weekly total + + + align:start position:0% +so let's fill this in the weekly total +for ophthalmology should just be the sum + + align:start position:0% +for ophthalmology should just be the sum + + + align:start position:0% +for ophthalmology should just be the sum +of all of the number of operating rooms + + align:start position:0% +of all of the number of operating rooms + + + align:start position:0% +of all of the number of operating rooms +assigned to ophthalmology from Monday + + align:start position:0% +assigned to ophthalmology from Monday + + + align:start position:0% +assigned to ophthalmology from Monday +through Friday so that's this entire row + + align:start position:0% + + + + align:start position:0% + +just like that and we can drag this + + align:start position:0% +just like that and we can drag this + + + align:start position:0% +just like that and we can drag this +formula down for every department okay + + align:start position:0% +formula down for every department okay + + + align:start position:0% +formula down for every department okay +so now if you actually go through each + + align:start position:0% +so now if you actually go through each + + + align:start position:0% +so now if you actually go through each +one of these you can see up in the + + align:start position:0% +one of these you can see up in the + + + align:start position:0% +one of these you can see up in the +formula tab that we've got the formula + + align:start position:0% +formula tab that we've got the formula + + + align:start position:0% +formula tab that we've got the formula +for the weekly totals here so let's get + + align:start position:0% +for the weekly totals here so let's get + + + align:start position:0% +for the weekly totals here so let's get +started by putting in our objectives at + + align:start position:0% +started by putting in our objectives at + + + align:start position:0% +started by putting in our objectives at +our constraints so down here I've set up + + align:start position:0% +our constraints so down here I've set up + + + align:start position:0% +our constraints so down here I've set up +a box for the objective but I haven't + + align:start position:0% +a box for the objective but I haven't + + + align:start position:0% +a box for the objective but I haven't +yet put in a formula for it so let's + + align:start position:0% +yet put in a formula for it so let's + + + align:start position:0% +yet put in a formula for it so let's +remind ourselves what the objective is + + align:start position:0% +remind ourselves what the objective is + + + align:start position:0% +remind ourselves what the objective is +here the objective is to maximize the + + align:start position:0% +here the objective is to maximize the + + + align:start position:0% +here the objective is to maximize the +percent of target allocation hours that + + align:start position:0% +percent of target allocation hours that + + + align:start position:0% +percent of target allocation hours that +each department is actually allocated so + + align:start position:0% +each department is actually allocated so + + + align:start position:0% +each department is actually allocated so +how can we calculate that our decision + + align:start position:0% +how can we calculate that our decision + + + align:start position:0% +how can we calculate that our decision +variables up here represent the number + + align:start position:0% +variables up here represent the number + + + align:start position:0% +variables up here represent the number +of operating room hours that each + + align:start position:0% +of operating room hours that each + + + align:start position:0% +of operating room hours that each +department is assigned on each day we + + align:start position:0% +department is assigned on each day we + + + align:start position:0% +department is assigned on each day we +calculated the total over here as the + + align:start position:0% +calculated the total over here as the + + + align:start position:0% +calculated the total over here as the +number of operating rooms that a + + align:start position:0% +number of operating rooms that a + + + align:start position:0% +number of operating rooms that a +department is assigned over the course + + align:start position:0% +department is assigned over the course + + + align:start position:0% +department is assigned over the course +of the week to turn that into hours we + + align:start position:0% +of the week to turn that into hours we + + + align:start position:0% +of the week to turn that into hours we +need to multiply it by 8 because + + align:start position:0% +need to multiply it by 8 because + + + align:start position:0% +need to multiply it by 8 because +operating rooms are staffed for 8 hours + + align:start position:0% +operating rooms are staffed for 8 hours + + + align:start position:0% +operating rooms are staffed for 8 hours +so let's create a column that turns this + + align:start position:0% +so let's create a column that turns this + + + align:start position:0% +so let's create a column that turns this +into hours we'll put it over here and + + align:start position:0% +into hours we'll put it over here and + + + align:start position:0% +into hours we'll put it over here and +we'll call it weekly hours ok and this + + align:start position:0% +we'll call it weekly hours ok and this + + + align:start position:0% +we'll call it weekly hours ok and this +will just be equal to 8 times the weekly + + align:start position:0% +will just be equal to 8 times the weekly + + + align:start position:0% +will just be equal to 8 times the weekly +totals great and we'll do this for all + + align:start position:0% +totals great and we'll do this for all + + + align:start position:0% +totals great and we'll do this for all +departments here this time I'll actually + + align:start position:0% +departments here this time I'll actually + + + align:start position:0% +departments here this time I'll actually +write it out + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +great so now we've got the weekly hours + + align:start position:0% +great so now we've got the weekly hours + + + align:start position:0% +great so now we've got the weekly hours +here but to calculate what fraction of + + align:start position:0% +here but to calculate what fraction of + + + align:start position:0% +here but to calculate what fraction of +the weekly target we've got to divide it + + align:start position:0% +the weekly target we've got to divide it + + + align:start position:0% +the weekly target we've got to divide it +by the total weekly target and the total + + align:start position:0% +by the total weekly target and the total + + + align:start position:0% +by the total weekly target and the total +weekly target we see is up here + + align:start position:0% +weekly target we see is up here + + + align:start position:0% +weekly target we see is up here +so let's set this up for every + + align:start position:0% +so let's set this up for every + + + align:start position:0% +so let's set this up for every +department in a column called percent of + + align:start position:0% +department in a column called percent of + + + align:start position:0% +department in a column called percent of +target okay so this will just be equal + + align:start position:0% +target okay so this will just be equal + + + align:start position:0% +target okay so this will just be equal +to the weekly number of hours divided by + + align:start position:0% +to the weekly number of hours divided by + + + align:start position:0% +to the weekly number of hours divided by +the weekly target okay so we'll just set + + align:start position:0% +the weekly target okay so we'll just set + + + align:start position:0% +the weekly target okay so we'll just set +that up for each department whoops + + align:start position:0% + + + + align:start position:0% + +certainly there are faster ways of doing + + align:start position:0% +certainly there are faster ways of doing + + + align:start position:0% +certainly there are faster ways of doing +this but I don't want to speed ahead if + + align:start position:0% +this but I don't want to speed ahead if + + + align:start position:0% +this but I don't want to speed ahead if +you guys aren't yet LibreOffice wizards + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so we've got the percent of + + align:start position:0% +all right so we've got the percent of + + + align:start position:0% +all right so we've got the percent of +target reached for every department so + + align:start position:0% +target reached for every department so + + + align:start position:0% +target reached for every department so +our objective we can go back to it now + + align:start position:0% +our objective we can go back to it now + + + align:start position:0% +our objective we can go back to it now +it'll just be the sum of all of these + + align:start position:0% +it'll just be the sum of all of these + + + align:start position:0% +it'll just be the sum of all of these +percent of targets so let's add that in + + align:start position:0% +percent of targets so let's add that in + + + align:start position:0% +percent of targets so let's add that in +equals sum and then we'll add in all of + + align:start position:0% +equals sum and then we'll add in all of + + + align:start position:0% +equals sum and then we'll add in all of +these percent of targets great so right + + align:start position:0% +these percent of targets great so right + + + align:start position:0% +these percent of targets great so right +now of course we haven't solved the + + align:start position:0% +now of course we haven't solved the + + + align:start position:0% +now of course we haven't solved the +problem yet so we've just got zero on + + align:start position:0% +problem yet so we've just got zero on + + + align:start position:0% +problem yet so we've just got zero on +our objective but before we go ahead and + + align:start position:0% +our objective but before we go ahead and + + + align:start position:0% +our objective but before we go ahead and +solve it we need to add in our + + align:start position:0% +solve it we need to add in our + + + align:start position:0% +solve it we need to add in our +constraints so down here in green we + + align:start position:0% +constraints so down here in green we + + + align:start position:0% +constraints so down here in green we +have a list of all the constraints we + + align:start position:0% +have a list of all the constraints we + + + align:start position:0% +have a list of all the constraints we +outlined in the previous videos let's + + align:start position:0% +outlined in the previous videos let's + + + align:start position:0% +outlined in the previous videos let's +review them quickly so the first one is + + align:start position:0% +review them quickly so the first one is + + + align:start position:0% +review them quickly so the first one is +just that the number of operating rooms + + align:start position:0% +just that the number of operating rooms + + + align:start position:0% +just that the number of operating rooms +assigned each day is integer we can't + + align:start position:0% +assigned each day is integer we can't + + + align:start position:0% +assigned each day is integer we can't +assign Ophthalmology three quarters of + + align:start position:0% +assign Ophthalmology three quarters of + + + align:start position:0% +assign Ophthalmology three quarters of +an operating room on Thursday or general + + align:start position:0% +an operating room on Thursday or general + + + align:start position:0% +an operating room on Thursday or general +surgery 6.5 operating rooms on Monday we + + align:start position:0% +surgery 6.5 operating rooms on Monday we + + + align:start position:0% +surgery 6.5 operating rooms on Monday we +need to make sure that these take + + align:start position:0% +need to make sure that these take + + + align:start position:0% +need to make sure that these take +integer values the next constraint is + + align:start position:0% +integer values the next constraint is + + + align:start position:0% +integer values the next constraint is +just that the total number of operating + + align:start position:0% +just that the total number of operating + + + align:start position:0% +just that the total number of operating +rooms each day has to be less than or + + align:start position:0% +rooms each day has to be less than or + + + align:start position:0% +rooms each day has to be less than or +equal to 10 so while we're here let's + + align:start position:0% +equal to 10 so while we're here let's + + + align:start position:0% +equal to 10 so while we're here let's +just add in a line underneath our + + align:start position:0% +just add in a line underneath our + + + align:start position:0% +just add in a line underneath our +decision variables which calculates the + + align:start position:0% +decision variables which calculates the + + + align:start position:0% +decision variables which calculates the +total number of operating rooms each day + + align:start position:0% +total number of operating rooms each day + + + align:start position:0% +total number of operating rooms each day +go over here we'll call it total number + + align:start position:0% +go over here we'll call it total number + + + align:start position:0% +go over here we'll call it total number +of operating rooms each day and this + + align:start position:0% +of operating rooms each day and this + + + align:start position:0% +of operating rooms each day and this +will just take the sum over all the + + align:start position:0% +will just take the sum over all the + + + align:start position:0% +will just take the sum over all the +operating rooms we assign on Monday just + + align:start position:0% +operating rooms we assign on Monday just + + + align:start position:0% +operating rooms we assign on Monday just +like that + + align:start position:0% +like that + + + align:start position:0% +like that +great and let's drag this formula across + + align:start position:0% +great and let's drag this formula across + + + align:start position:0% +great and let's drag this formula across +to use it for the entire week + + align:start position:0% + + + + align:start position:0% + +ok so now we've got that set up so we'll + + align:start position:0% +ok so now we've got that set up so we'll + + + align:start position:0% +ok so now we've got that set up so we'll +be able to do the second constraint the + + align:start position:0% +be able to do the second constraint the + + + align:start position:0% +be able to do the second constraint the +third set of constraints is the upper + + align:start position:0% +third set of constraints is the upper + + + align:start position:0% +third set of constraints is the upper +bound that is the upper bound on the + + align:start position:0% +bound that is the upper bound on the + + + align:start position:0% +bound that is the upper bound on the +number of surgical teams that are + + align:start position:0% +number of surgical teams that are + + + align:start position:0% +number of surgical teams that are +available each day we also have an upper + + align:start position:0% +available each day we also have an upper + + + align:start position:0% +available each day we also have an upper +bound on the daily Department operating + + align:start position:0% +bound on the daily Department operating + + + align:start position:0% +bound on the daily Department operating +room requirement and a lower bound on + + align:start position:0% +room requirement and a lower bound on + + + align:start position:0% +room requirement and a lower bound on +the daily Department operating room + + align:start position:0% +the daily Department operating room + + + align:start position:0% +the daily Department operating room +requirement similarly we have an upper + + align:start position:0% +requirement similarly we have an upper + + + align:start position:0% +requirement similarly we have an upper +bound and a lower bound on the weekly + + align:start position:0% +bound and a lower bound on the weekly + + + align:start position:0% +bound and a lower bound on the weekly +Department operating room requirements + + align:start position:0% +Department operating room requirements + + + align:start position:0% +Department operating room requirements +our last set of constraints has to do + + align:start position:0% +our last set of constraints has to do + + + align:start position:0% +our last set of constraints has to do +with departmental targets we want to + + align:start position:0% +with departmental targets we want to + + + align:start position:0% +with departmental targets we want to +make sure we don't give any department + + align:start position:0% +make sure we don't give any department + + + align:start position:0% +make sure we don't give any department +more operating room hours than they + + align:start position:0% +more operating room hours than they + + + align:start position:0% +more operating room hours than they +actually want so that means we want to + + align:start position:0% +actually want so that means we want to + + + align:start position:0% +actually want so that means we want to +make sure that the number of hours given + + align:start position:0% +make sure that the number of hours given + + + align:start position:0% +make sure that the number of hours given +to each department is less than or equal + + align:start position:0% +to each department is less than or equal + + + align:start position:0% +to each department is less than or equal +to the target and number that they asked + + align:start position:0% +to the target and number that they asked + + + align:start position:0% +to the target and number that they asked +for all right so let's go ahead and add + + align:start position:0% +for all right so let's go ahead and add + + + align:start position:0% +for all right so let's go ahead and add +these constraints into the solver so + + align:start position:0% +these constraints into the solver so + + + align:start position:0% +these constraints into the solver so +we'll start by putting our cursor on the + + align:start position:0% +we'll start by putting our cursor on the + + + align:start position:0% +we'll start by putting our cursor on the +objective function and going up to the + + align:start position:0% +objective function and going up to the + + + align:start position:0% +objective function and going up to the +Tools menu and here we select solar ok + + align:start position:0% +Tools menu and here we select solar ok + + + align:start position:0% +Tools menu and here we select solar ok +so because we started our cursor on the + + align:start position:0% +so because we started our cursor on the + + + align:start position:0% +so because we started our cursor on the +objective function so it comes up + + align:start position:0% +objective function so it comes up + + + align:start position:0% +objective function so it comes up +properly with the target cell already + + align:start position:0% +properly with the target cell already + + + align:start position:0% +properly with the target cell already +labeled we do want a maximum so we keep + + align:start position:0% +labeled we do want a maximum so we keep + + + align:start position:0% +labeled we do want a maximum so we keep +that the way it is and then here where + + align:start position:0% +that the way it is and then here where + + + align:start position:0% +that the way it is and then here where +it says by changing cells we put in our + + align:start position:0% +it says by changing cells we put in our + + + align:start position:0% +it says by changing cells we put in our +decision variables so we just select + + align:start position:0% +decision variables so we just select + + + align:start position:0% +decision variables so we just select +them all like this all right now before + + align:start position:0% +them all like this all right now before + + + align:start position:0% +them all like this all right now before +we start putting in our constraints I + + align:start position:0% +we start putting in our constraints I + + + align:start position:0% +we start putting in our constraints I +want to remind you to go into options + + align:start position:0% +want to remind you to go into options + + + align:start position:0% +want to remind you to go into options +and you'll need to change this from D + + align:start position:0% +and you'll need to change this from D + + + align:start position:0% +and you'll need to change this from D +EPS evolutionary algorithm to + + align:start position:0% +EPS evolutionary algorithm to + + + align:start position:0% +EPS evolutionary algorithm to +libreoffice linear solver ok so you + + align:start position:0% +libreoffice linear solver ok so you + + + align:start position:0% +libreoffice linear solver ok so you +notice that the settings you can choose + + align:start position:0% +notice that the settings you can choose + + + align:start position:0% +notice that the settings you can choose +to assume variables are integer and + + align:start position:0% +to assume variables are integer and + + + align:start position:0% +to assume variables are integer and +assume variables are non-negative + + align:start position:0% +assume variables are non-negative + + + align:start position:0% +assume variables are non-negative +we'll do that here in fact this takes + + align:start position:0% +we'll do that here in fact this takes + + + align:start position:0% +we'll do that here in fact this takes +care of our first constraint which was + + align:start position:0% +care of our first constraint which was + + + align:start position:0% +care of our first constraint which was +to assume that the variables are integer + + align:start position:0% + + + + align:start position:0% + +okay so we've got this set up now let's + + align:start position:0% +okay so we've got this set up now let's + + + align:start position:0% +okay so we've got this set up now let's +put in the rest of our constraints okay + + align:start position:0% +put in the rest of our constraints okay + + + align:start position:0% +put in the rest of our constraints okay +so we've already taken care of this + + align:start position:0% +so we've already taken care of this + + + align:start position:0% +so we've already taken care of this +first constraint that the daily number + + align:start position:0% +first constraint that the daily number + + + align:start position:0% +first constraint that the daily number +of operating rooms assigned is integer + + align:start position:0% +of operating rooms assigned is integer + + + align:start position:0% +of operating rooms assigned is integer +and we've taken care of that with our + + align:start position:0% +and we've taken care of that with our + + + align:start position:0% +and we've taken care of that with our +options so we'll go down to the next one + + align:start position:0% +options so we'll go down to the next one + + + align:start position:0% +options so we'll go down to the next one +the total number of operating rooms each + + align:start position:0% +the total number of operating rooms each + + + align:start position:0% +the total number of operating rooms each +day remember that we can't assign more + + align:start position:0% +day remember that we can't assign more + + + align:start position:0% +day remember that we can't assign more +than 10 so we'll select this whole row + + align:start position:0% +than 10 so we'll select this whole row + + + align:start position:0% +than 10 so we'll select this whole row +which has the total number of operating + + align:start position:0% +which has the total number of operating + + + align:start position:0% +which has the total number of operating +rooms assigned each day and we'll say + + align:start position:0% +rooms assigned each day and we'll say + + + align:start position:0% +rooms assigned each day and we'll say +that each element in this row has to be + + align:start position:0% +that each element in this row has to be + + + align:start position:0% +that each element in this row has to be +less than or equal to 10 great so onto + + align:start position:0% +less than or equal to 10 great so onto + + + align:start position:0% +less than or equal to 10 great so onto +the upper bound of surgical teams per + + align:start position:0% +the upper bound of surgical teams per + + + align:start position:0% +the upper bound of surgical teams per +day let's select our decision variables + + align:start position:0% +day let's select our decision variables + + + align:start position:0% +day let's select our decision variables +all of them at once okay and then we'll + + align:start position:0% +all of them at once okay and then we'll + + + align:start position:0% +all of them at once okay and then we'll +need to scroll up to our dia + + align:start position:0% + + + + align:start position:0% + +you'll notice here I'm inputting all + + align:start position:0% +you'll notice here I'm inputting all + + + align:start position:0% +you'll notice here I'm inputting all +these constraints all at once we're + + align:start position:0% +these constraints all at once we're + + + align:start position:0% +these constraints all at once we're +actually putting in 25 different + + align:start position:0% +actually putting in 25 different + + + align:start position:0% +actually putting in 25 different +constraints one for each day of the week + + align:start position:0% +constraints one for each day of the week + + + align:start position:0% +constraints one for each day of the week +and one for each surgical team and we're + + align:start position:0% +and one for each surgical team and we're + + + align:start position:0% +and one for each surgical team and we're +just putting them in with a single line + + align:start position:0% +just putting them in with a single line + + + align:start position:0% +just putting them in with a single line +by saying that all our decision + + align:start position:0% +by saying that all our decision + + + align:start position:0% +by saying that all our decision +variables need to be less than or equal + + align:start position:0% +variables need to be less than or equal + + + align:start position:0% +variables need to be less than or equal +to this box of constraints just like + + align:start position:0% +to this box of constraints just like + + + align:start position:0% +to this box of constraints just like +that okay so our next set of constraints + + align:start position:0% +that okay so our next set of constraints + + + align:start position:0% +that okay so our next set of constraints +is on the upper bound and lower bound of + + align:start position:0% +is on the upper bound and lower bound of + + + align:start position:0% +is on the upper bound and lower bound of +the daily Department of our requirements + + align:start position:0% +the daily Department of our requirements + + + align:start position:0% +the daily Department of our requirements +so we'll put in our decision variables + + align:start position:0% +so we'll put in our decision variables + + + align:start position:0% +so we'll put in our decision variables +again scroll down to those and let's say + + align:start position:0% +again scroll down to those and let's say + + + align:start position:0% +again scroll down to those and let's say +that these are less than or equal to + + align:start position:0% + + + + align:start position:0% + +sometimes we've got to move the solver + + align:start position:0% +sometimes we've got to move the solver + + + align:start position:0% +sometimes we've got to move the solver +around the maximum number of ORS per day + + align:start position:0% +around the maximum number of ORS per day + + + align:start position:0% +around the maximum number of ORS per day +per department okay and we'll do that + + align:start position:0% +per department okay and we'll do that + + + align:start position:0% +per department okay and we'll do that +again for the lower bound + + align:start position:0% + + + + align:start position:0% + +this time we need to change the operator + + align:start position:0% +this time we need to change the operator + + + align:start position:0% +this time we need to change the operator +to greater than greater than + + align:start position:0% + + + + align:start position:0% + +the minimum number of operating rooms + + align:start position:0% +the minimum number of operating rooms + + + align:start position:0% +the minimum number of operating rooms +per department per day you see here that + + align:start position:0% +per department per day you see here that + + + align:start position:0% +per department per day you see here that +we've got zeros in for the minimum + + align:start position:0% +we've got zeros in for the minimum + + + align:start position:0% +we've got zeros in for the minimum +number of operating rooms per day but + + align:start position:0% +number of operating rooms per day but + + + align:start position:0% +number of operating rooms per day but +you could conceivably expect that one + + align:start position:0% +you could conceivably expect that one + + + align:start position:0% +you could conceivably expect that one +department might actually want a minimum + + align:start position:0% +department might actually want a minimum + + + align:start position:0% +department might actually want a minimum +number of operating rooms per day for + + align:start position:0% +number of operating rooms per day for + + + align:start position:0% +number of operating rooms per day for +example general surgery which we see + + align:start position:0% +example general surgery which we see + + + align:start position:0% +example general surgery which we see +here has a weekly target of 189 hours + + align:start position:0% +here has a weekly target of 189 hours + + + align:start position:0% +here has a weekly target of 189 hours +might actually want to have more than + + align:start position:0% +might actually want to have more than + + + align:start position:0% +might actually want to have more than +zero operating rooms per day they might + + align:start position:0% +zero operating rooms per day they might + + + align:start position:0% +zero operating rooms per day they might +want to guarantee they've got at least + + align:start position:0% +want to guarantee they've got at least + + + align:start position:0% +want to guarantee they've got at least +one what experiment with changing some + + align:start position:0% +one what experiment with changing some + + + align:start position:0% +one what experiment with changing some +of these numbers after we solve the + + align:start position:0% +of these numbers after we solve the + + + align:start position:0% +of these numbers after we solve the +initial problem for now let's get our + + align:start position:0% +initial problem for now let's get our + + + align:start position:0% +initial problem for now let's get our +remaining constraints in the next ones + + align:start position:0% +remaining constraints in the next ones + + + align:start position:0% +remaining constraints in the next ones +we have are the weekly department or our + + align:start position:0% +we have are the weekly department or our + + + align:start position:0% +we have are the weekly department or our +requirements the upper bound and the + + align:start position:0% +requirements the upper bound and the + + + align:start position:0% +requirements the upper bound and the +lower bound so let's just scroll down + + align:start position:0% +lower bound so let's just scroll down + + + align:start position:0% +lower bound so let's just scroll down +here in the solver to give ourselves a + + align:start position:0% +here in the solver to give ourselves a + + + align:start position:0% +here in the solver to give ourselves a +few more rows okay so here we'll put in + + align:start position:0% +few more rows okay so here we'll put in + + + align:start position:0% +few more rows okay so here we'll put in +our weekly totals good thing we've + + align:start position:0% +our weekly totals good thing we've + + + align:start position:0% +our weekly totals good thing we've +already got this set up okay so weekly + + align:start position:0% +already got this set up okay so weekly + + + align:start position:0% +already got this set up okay so weekly +totals this will have to be less than + + align:start position:0% +totals this will have to be less than + + + align:start position:0% +totals this will have to be less than +the maximum required by any department + + align:start position:0% +the maximum required by any department + + + align:start position:0% +the maximum required by any department +in a given week so in the value column + + align:start position:0% +in a given week so in the value column + + + align:start position:0% +in a given week so in the value column +we go over here and we put in the + + align:start position:0% +we go over here and we put in the + + + align:start position:0% +we go over here and we put in the +maximum required each week we'll do the + + align:start position:0% +maximum required each week we'll do the + + + align:start position:0% +maximum required each week we'll do the +same for the lower bound again changing + + align:start position:0% +same for the lower bound again changing + + + align:start position:0% +same for the lower bound again changing +the operator to a greater than or equal + + align:start position:0% +the operator to a greater than or equal + + + align:start position:0% +the operator to a greater than or equal +to sign + + align:start position:0% + + + + align:start position:0% + +okay and we're on to our very last set + + align:start position:0% +okay and we're on to our very last set + + + align:start position:0% +okay and we're on to our very last set +of constraints which is the departmental + + align:start position:0% +of constraints which is the departmental + + + align:start position:0% +of constraints which is the departmental +targets down here so remember we can't + + align:start position:0% +targets down here so remember we can't + + + align:start position:0% +targets down here so remember we can't +assign a department more hours than they + + align:start position:0% +assign a department more hours than they + + + align:start position:0% +assign a department more hours than they +actually wanted to have because + + align:start position:0% +actually wanted to have because + + + align:start position:0% +actually wanted to have because +operating room time is so expensive so + + align:start position:0% +operating room time is so expensive so + + + align:start position:0% +operating room time is so expensive so +we'll select there the weekly number of + + align:start position:0% +we'll select there the weekly number of + + + align:start position:0% +we'll select there the weekly number of +hours which we already have a column set + + align:start position:0% +hours which we already have a column set + + + align:start position:0% +hours which we already have a column set +up to calculate so we'll put this in + + align:start position:0% +up to calculate so we'll put this in + + + align:start position:0% +up to calculate so we'll put this in +here that the weekly number of hours + + align:start position:0% +here that the weekly number of hours + + + align:start position:0% +here that the weekly number of hours +must be less than or equal to the target + + align:start position:0% +must be less than or equal to the target + + + align:start position:0% +must be less than or equal to the target +allocation hours so scroll back up here + + align:start position:0% +allocation hours so scroll back up here + + + align:start position:0% +allocation hours so scroll back up here +to the target allocation hours okay + + align:start position:0% +to the target allocation hours okay + + + align:start position:0% +to the target allocation hours okay +great now we've got all our constraints + + align:start position:0% +great now we've got all our constraints + + + align:start position:0% +great now we've got all our constraints +in and we're ready to go so let's hit + + align:start position:0% +in and we're ready to go so let's hit + + + align:start position:0% +in and we're ready to go so let's hit +solve it may take a few seconds up to a + + align:start position:0% +solve it may take a few seconds up to a + + + align:start position:0% +solve it may take a few seconds up to a +hundred in the next video we'll look at + + align:start position:0% +hundred in the next video we'll look at + + + align:start position:0% +hundred in the next video we'll look at +the results that we get and interpret + + align:start position:0% +the results that we get and interpret + + + align:start position:0% +the results that we get and interpret +them we'll also see how they change if + + align:start position:0% +them we'll also see how they change if + + + align:start position:0% +them we'll also see how they change if +we experiment with changing some of the + + align:start position:0% +we experiment with changing some of the + + + align:start position:0% +we experiment with changing some of the +numbers in the problem \ No newline at end of file diff --git a/bHvMYZvZp7Y.txt b/bHvMYZvZp7Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..553165391567aaee5651e44f372d3b4d3f3d28f3 --- /dev/null +++ b/bHvMYZvZp7Y.txt @@ -0,0 +1,1435 @@ +align:start position:0% + +so we've seen that partial orders are a + + align:start position:0% +so we've seen that partial orders are a + + + align:start position:0% +so we've seen that partial orders are a +set of axioms that capture + + align:start position:0% +set of axioms that capture + + + align:start position:0% +set of axioms that capture +the positive path relation + + align:start position:0% +the positive path relation + + + align:start position:0% +the positive path relation +or the + + align:start position:0% +or the + + + align:start position:0% +or the +uh arbitrary path relation in directed + + align:start position:0% +uh arbitrary path relation in directed + + + align:start position:0% +uh arbitrary path relation in directed +acyclic graphs or dags but there's still + + align:start position:0% +acyclic graphs or dags but there's still + + + align:start position:0% +acyclic graphs or dags but there's still +another way to understand these axioms + + align:start position:0% +another way to understand these axioms + + + align:start position:0% +another way to understand these axioms +that gives a kind of representation + + align:start position:0% +that gives a kind of representation + + + align:start position:0% +that gives a kind of representation +theorem for the kinds of for a kind of + + align:start position:0% +theorem for the kinds of for a kind of + + + align:start position:0% +theorem for the kinds of for a kind of +mathematical objects that are partial + + align:start position:0% +mathematical objects that are partial + + + align:start position:0% +mathematical objects that are partial +orders and that every partial order + + align:start position:0% +orders and that every partial order + + + align:start position:0% +orders and that every partial order +looks like + + align:start position:0% +looks like + + + align:start position:0% +looks like +so let's look at that example i'm + + align:start position:0% +so let's look at that example i'm + + + align:start position:0% +so let's look at that example i'm +interested in the proper subset relation + + align:start position:0% +interested in the proper subset relation + + + align:start position:0% +interested in the proper subset relation +a is a proper subset of b + + align:start position:0% +a is a proper subset of b + + + align:start position:0% +a is a proper subset of b +which you remember means that b has + + align:start position:0% +which you remember means that b has + + + align:start position:0% +which you remember means that b has +everything in it that a has and + + align:start position:0% +everything in it that a has and + + + align:start position:0% +everything in it that a has and +something extra so in particular since b + + align:start position:0% +something extra so in particular since b + + + align:start position:0% +something extra so in particular since b +has something extra b is not a subset of + + align:start position:0% +has something extra b is not a subset of + + + align:start position:0% +has something extra b is not a subset of +a certainly not a proper subset of a + + align:start position:0% +a certainly not a proper subset of a + + + align:start position:0% +a certainly not a proper subset of a +so let's look at an example of that here + + align:start position:0% +so let's look at an example of that here + + + align:start position:0% +so let's look at an example of that here +are seven sets + + align:start position:0% +are seven sets + + + align:start position:0% +are seven sets +and the arrows indicate the proper + + align:start position:0% +and the arrows indicate the proper + + + align:start position:0% +and the arrows indicate the proper +subset relation or more precisely the + + align:start position:0% +subset relation or more precisely the + + + align:start position:0% +subset relation or more precisely the +positive path relation + + align:start position:0% +positive path relation + + + align:start position:0% +positive path relation +in this + + align:start position:0% +in this + + + align:start position:0% +in this +graph represents the proper subset + + align:start position:0% +graph represents the proper subset + + + align:start position:0% +graph represents the proper subset +relation where arrows are understood + + align:start position:0% +relation where arrows are understood + + + align:start position:0% +relation where arrows are understood +where edges are understood to be + + align:start position:0% +where edges are understood to be + + + align:start position:0% +where edges are understood to be +pointing upwards so i've left out the uh + + align:start position:0% +pointing upwards so i've left out the uh + + + align:start position:0% +pointing upwards so i've left out the uh +the arrow heads this is also known as a + + align:start position:0% +the arrow heads this is also known as a + + + align:start position:0% +the arrow heads this is also known as a +hassa diagram + + align:start position:0% +hassa diagram + + + align:start position:0% +hassa diagram +where the height is an indication of + + align:start position:0% +where the height is an indication of + + + align:start position:0% +where the height is an indication of +what you of which way the arrows go so + + align:start position:0% +what you of which way the arrows go so + + + align:start position:0% +what you of which way the arrows go so +if arrows are pointing up this is + + align:start position:0% +if arrows are pointing up this is + + + align:start position:0% +if arrows are pointing up this is +telling me that for example this set of + + align:start position:0% +telling me that for example this set of + + + align:start position:0% +telling me that for example this set of +two elements one and five because + + align:start position:0% +two elements one and five because + + + align:start position:0% +two elements one and five because +there's a path up to the top set the top + + align:start position:0% +there's a path up to the top set the top + + + align:start position:0% +there's a path up to the top set the top +set has everything that this lower set + + align:start position:0% +set has everything that this lower set + + + align:start position:0% +set has everything that this lower set +has namely the top set has one and five + + align:start position:0% +has namely the top set has one and five + + + align:start position:0% +has namely the top set has one and five +and it's got extra stuff + + align:start position:0% +and it's got extra stuff + + + align:start position:0% +and it's got extra stuff +one the set consisting of just one is a + + align:start position:0% +one the set consisting of just one is a + + + align:start position:0% +one the set consisting of just one is a +proper subset of one and five because + + align:start position:0% +proper subset of one and five because + + + align:start position:0% +proper subset of one and five because +the set has one in it but it has an + + align:start position:0% +the set has one in it but it has an + + + align:start position:0% +the set has one in it but it has an +extra thing five and also there's a path + + align:start position:0% +extra thing five and also there's a path + + + align:start position:0% +extra thing five and also there's a path +from one up to one two five ten because + + align:start position:0% +from one up to one two five ten because + + + align:start position:0% +from one up to one two five ten because +1 2 5 10 has a 1 in it and extra stuff + + align:start position:0% +1 2 5 10 has a 1 in it and extra stuff + + + align:start position:0% +1 2 5 10 has a 1 in it and extra stuff +so that's what the picture is + + align:start position:0% +so that's what the picture is + + + align:start position:0% +so that's what the picture is +illustrating the proper subset relation + + align:start position:0% +illustrating the proper subset relation + + + align:start position:0% +illustrating the proper subset relation +on this particular collection of seven + + align:start position:0% +on this particular collection of seven + + + align:start position:0% +on this particular collection of seven +sets + + align:start position:0% +sets + + + align:start position:0% +sets +now let's look at a very similar example + + align:start position:0% +now let's look at a very similar example + + + align:start position:0% +now let's look at a very similar example +of the proper divides relation on some + + align:start position:0% +of the proper divides relation on some + + + align:start position:0% +of the proper divides relation on some +numbers so proper divides means a + + align:start position:0% +numbers so proper divides means a + + + align:start position:0% +numbers so proper divides means a +properly divides b if a divides b and + + align:start position:0% +properly divides b if a divides b and + + + align:start position:0% +properly divides b if a divides b and +it's not equal to b and i'm interested + + align:start position:0% +it's not equal to b and i'm interested + + + align:start position:0% +it's not equal to b and i'm interested +in the proper divides relation on this + + align:start position:0% +in the proper divides relation on this + + + align:start position:0% +in the proper divides relation on this +set of seven numbers 1 2 3 5 10 15 and + + align:start position:0% +set of seven numbers 1 2 3 5 10 15 and + + + align:start position:0% +set of seven numbers 1 2 3 5 10 15 and +30. and + + align:start position:0% +30. and + + + align:start position:0% +30. and +now there's a path from 5 to 30 because + + align:start position:0% +now there's a path from 5 to 30 because + + + align:start position:0% +now there's a path from 5 to 30 because +5 is a divisor of 30 and it's not equal + + align:start position:0% +5 is a divisor of 30 and it's not equal + + + align:start position:0% +5 is a divisor of 30 and it's not equal +to 30 it's a proper divisor of 30. and + + align:start position:0% +to 30 it's a proper divisor of 30. and + + + align:start position:0% +to 30 it's a proper divisor of 30. and +of course the point of this picture is + + align:start position:0% +of course the point of this picture is + + + align:start position:0% +of course the point of this picture is +to show that the proper divides relation + + align:start position:0% +to show that the proper divides relation + + + align:start position:0% +to show that the proper divides relation +on these seven numbers has exactly the + + align:start position:0% +on these seven numbers has exactly the + + + align:start position:0% +on these seven numbers has exactly the +same shape as the proper subset relation + + align:start position:0% +same shape as the proper subset relation + + + align:start position:0% +same shape as the proper subset relation +on those + + align:start position:0% +on those + + + align:start position:0% +on those +seven sets + + align:start position:0% +seven sets + + + align:start position:0% +seven sets +so there's the seven sets and their + + align:start position:0% +so there's the seven sets and their + + + align:start position:0% +so there's the seven sets and their +proper subset relation shown by the + + align:start position:0% +proper subset relation shown by the + + + align:start position:0% +proper subset relation shown by the +picture followed by the proper divides + + align:start position:0% +picture followed by the proper divides + + + align:start position:0% +picture followed by the proper divides +relation on this set of seven numbers + + align:start position:0% +relation on this set of seven numbers + + + align:start position:0% +relation on this set of seven numbers +and + + align:start position:0% +and + + + align:start position:0% +and +the precise notion or sense in which + + align:start position:0% +the precise notion or sense in which + + + align:start position:0% +the precise notion or sense in which +these things have the same shape + + align:start position:0% +these things have the same shape + + + align:start position:0% +these things have the same shape +obviously they can be drawn and one + + align:start position:0% +obviously they can be drawn and one + + + align:start position:0% +obviously they can be drawn and one +superimposed on the other but abstractly + + align:start position:0% +superimposed on the other but abstractly + + + align:start position:0% +superimposed on the other but abstractly +what we care about with partial orders + + align:start position:0% +what we care about with partial orders + + + align:start position:0% +what we care about with partial orders +and digraphs in general is + + align:start position:0% +and digraphs in general is + + + align:start position:0% +and digraphs in general is +when + + align:start position:0% +when + + + align:start position:0% +when +things are isomorphic + + align:start position:0% +things are isomorphic + + + align:start position:0% +things are isomorphic +is the technical name for the same shape + + align:start position:0% +is the technical name for the same shape + + + align:start position:0% +is the technical name for the same shape +and isomorphic means that all we care + + align:start position:0% +and isomorphic means that all we care + + + align:start position:0% +and isomorphic means that all we care +about are the connections + + align:start position:0% +about are the connections + + + align:start position:0% +about are the connections +uh between + + align:start position:0% +uh between + + + align:start position:0% +uh between +corresponding vertices two graphs where + + align:start position:0% +corresponding vertices two graphs where + + + align:start position:0% +corresponding vertices two graphs where +the vertices correspond in a way that + + align:start position:0% +the vertices correspond in a way that + + + align:start position:0% +the vertices correspond in a way that +where there's a connection from between + + align:start position:0% +where there's a connection from between + + + align:start position:0% +where there's a connection from between +two vertices there's also a connection + + align:start position:0% +two vertices there's also a connection + + + align:start position:0% +two vertices there's also a connection +between the corresponding vertices or + + align:start position:0% +between the corresponding vertices or + + + align:start position:0% +between the corresponding vertices or +isomorphic and the precise definition of + + align:start position:0% +isomorphic and the precise definition of + + + align:start position:0% +isomorphic and the precise definition of +isomorphic is that isomorphic when + + align:start position:0% +isomorphic is that isomorphic when + + + align:start position:0% +isomorphic is that isomorphic when +there's an edge preserving matching + + align:start position:0% +there's an edge preserving matching + + + align:start position:0% +there's an edge preserving matching +between their vertices matching means + + align:start position:0% +between their vertices matching means + + + align:start position:0% +between their vertices matching means +bijection and the formal definition is + + align:start position:0% +bijection and the formal definition is + + + align:start position:0% +bijection and the formal definition is +g1 is isomorphic to g2 if and only if + + align:start position:0% +g1 is isomorphic to g2 if and only if + + + align:start position:0% +g1 is isomorphic to g2 if and only if +there's a bijection from v1 the vertices + + align:start position:0% +there's a bijection from v1 the vertices + + + align:start position:0% +there's a bijection from v1 the vertices +of g1 to v2 the vertices of g2 with the + + align:start position:0% +of g1 to v2 the vertices of g2 with the + + + align:start position:0% +of g1 to v2 the vertices of g2 with the +property that if there's an edge between + + align:start position:0% +property that if there's an edge between + + + align:start position:0% +property that if there's an edge between +two vertices u and v + + align:start position:0% +two vertices u and v + + + align:start position:0% +two vertices u and v +in the first graph then there's an edge + + align:start position:0% +in the first graph then there's an edge + + + align:start position:0% +in the first graph then there's an edge +between the corresponding two vertices f + + align:start position:0% +between the corresponding two vertices f + + + align:start position:0% +between the corresponding two vertices f +of u and f of v in the second graph and + + align:start position:0% +of u and f of v in the second graph and + + + align:start position:0% +of u and f of v in the second graph and +that's an if and only if relation + + align:start position:0% +that's an if and only if relation + + + align:start position:0% +that's an if and only if relation +there's an edge between f of u and f of + + align:start position:0% +there's an edge between f of u and f of + + + align:start position:0% +there's an edge between f of u and f of +v if and only if there's an edge between + + align:start position:0% +v if and only if there's an edge between + + + align:start position:0% +v if and only if there's an edge between +u and v in the original graph that's the + + align:start position:0% +u and v in the original graph that's the + + + align:start position:0% +u and v in the original graph that's the +official definition of isomorphism for + + align:start position:0% +official definition of isomorphism for + + + align:start position:0% +official definition of isomorphism for +digraphs + + align:start position:0% +digraphs + + + align:start position:0% +digraphs +and the theorem that we illustrated with + + align:start position:0% +and the theorem that we illustrated with + + + align:start position:0% +and the theorem that we illustrated with +that example of proper divides and + + align:start position:0% +that example of proper divides and + + + align:start position:0% +that example of proper divides and +a proper subset is that in fact + + align:start position:0% +a proper subset is that in fact + + + align:start position:0% +a proper subset is that in fact +every strict partial order + + align:start position:0% +every strict partial order + + + align:start position:0% +every strict partial order +is isomorphic to some collection of + + align:start position:0% +is isomorphic to some collection of + + + align:start position:0% +is isomorphic to some collection of +subsets + + align:start position:0% +subsets + + + align:start position:0% +subsets +partially ordered by less than so this + + align:start position:0% +partially ordered by less than so this + + + align:start position:0% +partially ordered by less than so this +is a kind of a representation theorem if + + align:start position:0% +is a kind of a representation theorem if + + + align:start position:0% +is a kind of a representation theorem if +you want to know + + align:start position:0% +you want to know + + + align:start position:0% +you want to know +what kinds of things are + + align:start position:0% +what kinds of things are + + + align:start position:0% +what kinds of things are +partial orders the answer is that a + + align:start position:0% +partial orders the answer is that a + + + align:start position:0% +partial orders the answer is that a +strict partial order is something that + + align:start position:0% +strict partial order is something that + + + align:start position:0% +strict partial order is something that +looks like a bunch of sets under + + align:start position:0% +looks like a bunch of sets under + + + align:start position:0% +looks like a bunch of sets under +containment it's isomorphic to a bunch + + align:start position:0% +containment it's isomorphic to a bunch + + + align:start position:0% +containment it's isomorphic to a bunch +of sets under containment + + align:start position:0% +of sets under containment + + + align:start position:0% +of sets under containment +and the proof actually of this is is + + align:start position:0% +and the proof actually of this is is + + + align:start position:0% +and the proof actually of this is is +quite straightforward what i'm going to + + align:start position:0% +quite straightforward what i'm going to + + + align:start position:0% +quite straightforward what i'm going to +do to to find an isomorphism is you give + + align:start position:0% +do to to find an isomorphism is you give + + + align:start position:0% +do to to find an isomorphism is you give +me your arbitrary + + align:start position:0% +me your arbitrary + + + align:start position:0% +me your arbitrary +partial strict partial order r + + align:start position:0% +partial strict partial order r + + + align:start position:0% +partial strict partial order r +and i'm going to map an element a in the + + align:start position:0% +and i'm going to map an element a in the + + + align:start position:0% +and i'm going to map an element a in the +domain of r to the set of all of the + + align:start position:0% +domain of r to the set of all of the + + + align:start position:0% +domain of r to the set of all of the +elements that are quote below it that is + + align:start position:0% +elements that are quote below it that is + + + align:start position:0% +elements that are quote below it that is +all of the elements that are related to + + align:start position:0% +all of the elements that are related to + + + align:start position:0% +all of the elements that are related to +r so a is going to map to the set of b's + + align:start position:0% +r so a is going to map to the set of b's + + + align:start position:0% +r so a is going to map to the set of b's +such that b r a or b is equal to a and + + align:start position:0% +such that b r a or b is equal to a and + + + align:start position:0% +such that b r a or b is equal to a and +that is added for a technical condition + + align:start position:0% +that is added for a technical condition + + + align:start position:0% +that is added for a technical condition +remember r is strict so a is not related + + align:start position:0% +remember r is strict so a is not related + + + align:start position:0% +remember r is strict so a is not related +to a under r but i want it to be in the + + align:start position:0% +to a under r but i want it to be in the + + + align:start position:0% +to a under r but i want it to be in the +set that that a maps to so i'm throwing + + align:start position:0% +set that that a maps to so i'm throwing + + + align:start position:0% +set that that a maps to so i'm throwing +that in another way to say this is that + + align:start position:0% +that in another way to say this is that + + + align:start position:0% +that in another way to say this is that +the mapping f of a is equal to r inverse + + align:start position:0% +the mapping f of a is equal to r inverse + + + align:start position:0% +the mapping f of a is equal to r inverse +of a union a and let's just illustrate + + align:start position:0% +of a union a and let's just illustrate + + + align:start position:0% +of a union a and let's just illustrate +that + + align:start position:0% +that + + + align:start position:0% +that +by the example of the how do you turn + + align:start position:0% +by the example of the how do you turn + + + align:start position:0% +by the example of the how do you turn +the divides relation into the subset + + align:start position:0% +the divides relation into the subset + + + align:start position:0% +the divides relation into the subset +relation well the smallest element in + + align:start position:0% +relation well the smallest element in + + + align:start position:0% +relation well the smallest element in +the divides proper divides example was + + align:start position:0% +the divides proper divides example was + + + align:start position:0% +the divides proper divides example was +this the number one and i'm going to map + + align:start position:0% +this the number one and i'm going to map + + + align:start position:0% +this the number one and i'm going to map +it to the set consisting of one which is + + align:start position:0% +it to the set consisting of one which is + + + align:start position:0% +it to the set consisting of one which is +all of the elements that properly divide + + align:start position:0% +all of the elements that properly divide + + + align:start position:0% +all of the elements that properly divide +one along with one and then i'm going to + + align:start position:0% +one along with one and then i'm going to + + + align:start position:0% +one along with one and then i'm going to +map the number three to all of the + + align:start position:0% +map the number three to all of the + + + align:start position:0% +map the number three to all of the +elements that properly divide three + + align:start position:0% +elements that properly divide three + + + align:start position:0% +elements that properly divide three +along with three and that is one and + + align:start position:0% +along with three and that is one and + + + align:start position:0% +along with three and that is one and +three five maps to one and five two maps + + align:start position:0% +three five maps to one and five two maps + + + align:start position:0% +three five maps to one and five two maps +to one and two + + align:start position:0% +to one and two + + + align:start position:0% +to one and two +and at the next level i'm going to map + + align:start position:0% +and at the next level i'm going to map + + + align:start position:0% +and at the next level i'm going to map +15 to all of the numbers that properly + + align:start position:0% +15 to all of the numbers that properly + + + align:start position:0% +15 to all of the numbers that properly +divide 15 along with 15 so + + align:start position:0% +divide 15 along with 15 so + + + align:start position:0% +divide 15 along with 15 so +1 3 + + align:start position:0% +1 3 + + + align:start position:0% +1 3 +5 and 15 are what the + + align:start position:0% +5 and 15 are what the + + + align:start position:0% +5 and 15 are what the +number 15 maps to that's a set and + + align:start position:0% +number 15 maps to that's a set and + + + align:start position:0% +number 15 maps to that's a set and +likewise 10 maps to 1 2 5 15 and 30 maps + + align:start position:0% +likewise 10 maps to 1 2 5 15 and 30 maps + + + align:start position:0% +likewise 10 maps to 1 2 5 15 and 30 maps +to all of the numbers that are below it + + align:start position:0% +to all of the numbers that are below it + + + align:start position:0% +to all of the numbers that are below it +including itself and this is the general + + align:start position:0% +including itself and this is the general + + + align:start position:0% +including itself and this is the general +illustration of the way that you take an + + align:start position:0% +illustration of the way that you take an + + + align:start position:0% +illustration of the way that you take an +arbitrary strict partial order and map + + align:start position:0% +arbitrary strict partial order and map + + + align:start position:0% +arbitrary strict partial order and map +elements into sets which are basically + + align:start position:0% +elements into sets which are basically + + + align:start position:0% +elements into sets which are basically +their inverse images under the relation + + align:start position:0% +their inverse images under the relation + + + align:start position:0% +their inverse images under the relation +and the sets have exactly the same + + align:start position:0% +and the sets have exactly the same + + + align:start position:0% +and the sets have exactly the same +structure under proper containment + + align:start position:0% +structure under proper containment + + + align:start position:0% +structure under proper containment +as + + align:start position:0% +as + + + align:start position:0% +as +the relation so this is again a + + align:start position:0% +the relation so this is again a + + + align:start position:0% +the relation so this is again a +representation theorem that tells us + + align:start position:0% +representation theorem that tells us + + + align:start position:0% +representation theorem that tells us +that if we want to understand partial + + align:start position:0% +that if we want to understand partial + + + align:start position:0% +that if we want to understand partial +orders they are doing nothing more than + + align:start position:0% +orders they are doing nothing more than + + + align:start position:0% +orders they are doing nothing more than +talking about relations with the same + + align:start position:0% +talking about relations with the same + + + align:start position:0% +talking about relations with the same +structure as the proper + + align:start position:0% +structure as the proper + + + align:start position:0% +structure as the proper +subset relation on some collection of + + align:start position:0% +subset relation on some collection of + + + align:start position:0% +subset relation on some collection of +sets \ No newline at end of file diff --git a/bd-mavr5YlA.txt b/bd-mavr5YlA.txt new file mode 100644 index 0000000000000000000000000000000000000000..8251a97634f7a2ecc72cffa751343573eb230c6e --- /dev/null +++ b/bd-mavr5YlA.txt @@ -0,0 +1,13963 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so it's my pleasure to introduce + + align:start position:0% +so it's my pleasure to introduce + + + align:start position:0% +so it's my pleasure to introduce +professor simone amar singh he as our + + align:start position:0% +professor simone amar singh he as our + + + align:start position:0% +professor simone amar singh he as our +guest lecturer today so saman amar singh + + align:start position:0% +guest lecturer today so saman amar singh + + + align:start position:0% +guest lecturer today so saman amar singh +he is a professor in the EECS department + + align:start position:0% +he is a professor in the EECS department + + + align:start position:0% +he is a professor in the EECS department +at MIT and he's also the associate + + align:start position:0% +at MIT and he's also the associate + + + align:start position:0% +at MIT and he's also the associate +department head he's an expert in + + align:start position:0% +department head he's an expert in + + + align:start position:0% +department head he's an expert in +compilers domain-specific languages and + + align:start position:0% +compilers domain-specific languages and + + + align:start position:0% +compilers domain-specific languages and +auto-tuning in fact he was the designer + + align:start position:0% +auto-tuning in fact he was the designer + + + align:start position:0% +auto-tuning in fact he was the designer +of the open tuner framework that you've + + align:start position:0% +of the open tuner framework that you've + + + align:start position:0% +of the open tuner framework that you've +been using for your homework assignments + + align:start position:0% +been using for your homework assignments + + + align:start position:0% +been using for your homework assignments +so today saman is going to talk about + + align:start position:0% +so today saman is going to talk about + + + align:start position:0% +so today saman is going to talk about +some of his recent work on + + align:start position:0% +some of his recent work on + + + align:start position:0% +some of his recent work on +domain-specific languages and also on + + align:start position:0% +domain-specific languages and also on + + + align:start position:0% +domain-specific languages and also on +auto tuning so let's give some on + + align:start position:0% +auto tuning so let's give some on + + + align:start position:0% +auto tuning so let's give some on +immersing thank you ok so I used to take + + align:start position:0% +immersing thank you ok so I used to take + + + align:start position:0% +immersing thank you ok so I used to take +this class for many many years + + align:start position:0% +this class for many many years + + + align:start position:0% +this class for many many years +unfortunately now I am administrator so + + align:start position:0% +unfortunately now I am administrator so + + + align:start position:0% +unfortunately now I am administrator so +I don't I + + align:start position:0% +I don't I + + + align:start position:0% +I don't I +Julian and and Charles get to have the + + align:start position:0% +Julian and and Charles get to have the + + + align:start position:0% +Julian and and Charles get to have the +fun teaching the class hopefully you + + align:start position:0% +fun teaching the class hopefully you + + + align:start position:0% +fun teaching the class hopefully you +guys enjoy I know you're starting you're + + align:start position:0% +guys enjoy I know you're starting you're + + + align:start position:0% +guys enjoy I know you're starting you're +done project 1 2 & 3 in going into + + align:start position:0% +done project 1 2 & 3 in going into + + + align:start position:0% +done project 1 2 & 3 in going into +project 4 yeah project 4 is really fun + + align:start position:0% +project 4 yeah project 4 is really fun + + + align:start position:0% +project 4 yeah project 4 is really fun +and yeah it will look big and and + + align:start position:0% +and yeah it will look big and and + + + align:start position:0% +and yeah it will look big and and +daunting but that then you'll enjoy it + + align:start position:0% +daunting but that then you'll enjoy it + + + align:start position:0% +daunting but that then you'll enjoy it +and especially all the amount of time + + align:start position:0% +and especially all the amount of time + + + align:start position:0% +and especially all the amount of time +people spend working on it so so I think + + align:start position:0% +people spend working on it so so I think + + + align:start position:0% +people spend working on it so so I think +I'm making you scarier more than + + align:start position:0% +I'm making you scarier more than + + + align:start position:0% +I'm making you scarier more than +anything so ok so let's get into the + + align:start position:0% +anything so ok so let's get into the + + + align:start position:0% +anything so ok so let's get into the +talk today so I'm going to talk to you + + align:start position:0% +talk today so I'm going to talk to you + + + align:start position:0% +talk today so I'm going to talk to you +about domain-specific language it's a + + align:start position:0% +about domain-specific language it's a + + + align:start position:0% +about domain-specific language it's a +little bit about auto-tuning how it + + align:start position:0% +little bit about auto-tuning how it + + + align:start position:0% +little bit about auto-tuning how it +leaves sort of tuning so why is + + align:start position:0% +leaves sort of tuning so why is + + + align:start position:0% +leaves sort of tuning so why is +domain-specific languages so VI all used + + align:start position:0% +domain-specific languages so VI all used + + + align:start position:0% +domain-specific languages so VI all used +to general purpose languages that we use + + align:start position:0% +to general purpose languages that we use + + + align:start position:0% +to general purpose languages that we use +all the day all day and those languages + + align:start position:0% +all the day all day and those languages + + + align:start position:0% +all the day all day and those languages +are set up to capture a very large sort + + align:start position:0% +are set up to capture a very large sort + + + align:start position:0% +are set up to capture a very large sort +of what people might want to do in + + align:start position:0% +of what people might want to do in + + + align:start position:0% +of what people might want to do in +programming however lot of times there + + align:start position:0% +programming however lot of times there + + + align:start position:0% +programming however lot of times there +are specific area specific domains + + align:start position:0% +are specific area specific domains + + + align:start position:0% +are specific area specific domains +either some area in that you won't + + align:start position:0% +either some area in that you won't + + + align:start position:0% +either some area in that you won't +implement or the certain patterns you + + align:start position:0% +implement or the certain patterns you + + + align:start position:0% +implement or the certain patterns you +won't implement code that has lot of + + align:start position:0% +won't implement code that has lot of + + + align:start position:0% +won't implement code that has lot of +interesting properties that in a + + align:start position:0% +interesting properties that in a + + + align:start position:0% +interesting properties that in a +general-purpose language it's very hard + + align:start position:0% +general-purpose language it's very hard + + + align:start position:0% +general-purpose language it's very hard +to describe and a lot of times it's + + align:start position:0% +to describe and a lot of times it's + + + align:start position:0% +to describe and a lot of times it's +basically very hard especially from + + align:start position:0% +basically very hard especially from + + + align:start position:0% +basically very hard especially from +compiler point of view to take advantage + + align:start position:0% +compiler point of view to take advantage + + + align:start position:0% +compiler point of view to take advantage +because it has to work for everybody so + + align:start position:0% +because it has to work for everybody so + + + align:start position:0% +because it has to work for everybody so +domain-specific language basically is + + align:start position:0% +domain-specific language basically is + + + align:start position:0% +domain-specific language basically is +has this lot of engineering benefits + + align:start position:0% +has this lot of engineering benefits + + + align:start position:0% +has this lot of engineering benefits +because if we know that you are what you + + align:start position:0% +because if we know that you are what you + + + align:start position:0% +because if we know that you are what you +are building has a certain shape certain + + align:start position:0% +are building has a certain shape certain + + + align:start position:0% +are building has a certain shape certain +set of properties if the language + + align:start position:0% +set of properties if the language + + + align:start position:0% +set of properties if the language +capture this and if you are building on + + align:start position:0% +capture this and if you are building on + + + align:start position:0% +capture this and if you are building on +that it could be much easier to build it + + align:start position:0% +that it could be much easier to build it + + + align:start position:0% +that it could be much easier to build it +should be had a lot of clarity it's very + + align:start position:0% +should be had a lot of clarity it's very + + + align:start position:0% +should be had a lot of clarity it's very +easy to maintain that kind of things + + align:start position:0% +easy to maintain that kind of things + + + align:start position:0% +easy to maintain that kind of things +very easy to test and also the other + + align:start position:0% +very easy to test and also the other + + + align:start position:0% +very easy to test and also the other +thing is it's very easy to understand + + align:start position:0% +thing is it's very easy to understand + + + align:start position:0% +thing is it's very easy to understand +because the domain is very clear it's + + align:start position:0% +because the domain is very clear it's + + + align:start position:0% +because the domain is very clear it's +described if you can't build a library + + align:start position:0% +described if you can't build a library + + + align:start position:0% +described if you can't build a library +but somebody can go and do weird things + + align:start position:0% +but somebody can go and do weird things + + + align:start position:0% +but somebody can go and do weird things +in libraries if additional is if it is + + align:start position:0% +in libraries if additional is if it is + + + align:start position:0% +in libraries if additional is if it is +built into the language it's set in + + align:start position:0% +built into the language it's set in + + + align:start position:0% +built into the language it's set in +stone you can't go and say I'm going to + + align:start position:0% +stone you can't go and say I'm going to + + + align:start position:0% +stone you can't go and say I'm going to +change something here let me do some + + align:start position:0% +change something here let me do some + + + align:start position:0% +change something here let me do some +weird thing here it's it's built into + + align:start position:0% +weird thing here it's it's built into + + + align:start position:0% +weird thing here it's it's built into +the language so it's in stress there it + + align:start position:0% +the language so it's in stress there it + + + align:start position:0% +the language so it's in stress there it +makes it much easier for program + + align:start position:0% +makes it much easier for program + + + align:start position:0% +makes it much easier for program +multiplied but for my point of view the + + align:start position:0% +multiplied but for my point of view the + + + align:start position:0% +multiplied but for my point of view the +domain-specific language I really like + + align:start position:0% +domain-specific language I really like + + + align:start position:0% +domain-specific language I really like +are the languages where I know I can + + align:start position:0% +are the languages where I know I can + + + align:start position:0% +are the languages where I know I can +take advantage of knowledge of the + + align:start position:0% +take advantage of knowledge of the + + + align:start position:0% +take advantage of knowledge of the +domain experts to get really good + + align:start position:0% +domain experts to get really good + + + align:start position:0% +domain experts to get really good +performance so lot of times domain + + align:start position:0% +performance so lot of times domain + + + align:start position:0% +performance so lot of times domain +experts are high in this domain I can do + + align:start position:0% +experts are high in this domain I can do + + + align:start position:0% +experts are high in this domain I can do +okay if there's some linear algebra you + + align:start position:0% +okay if there's some linear algebra you + + + align:start position:0% +okay if there's some linear algebra you +know this kind of algebra that I can do + + align:start position:0% +know this kind of algebra that I can do + + + align:start position:0% +know this kind of algebra that I can do +to simplify the expression that algebra + + align:start position:0% +to simplify the expression that algebra + + + align:start position:0% +to simplify the expression that algebra +might only work on that dumb it's very + + align:start position:0% +might only work on that dumb it's very + + + align:start position:0% +might only work on that dumb it's very +hard to put some complex algebra into a + + align:start position:0% +hard to put some complex algebra into a + + + align:start position:0% +hard to put some complex algebra into a +in to press c plus plus so c but in that + + align:start position:0% +in to press c plus plus so c but in that + + + align:start position:0% +in to press c plus plus so c but in that +domain i can say hi can code it up so + + align:start position:0% +domain i can say hi can code it up so + + + align:start position:0% +domain i can say hi can code it up so +you can write any expression that i can + + align:start position:0% +you can write any expression that i can + + + align:start position:0% +you can write any expression that i can +simplify it and also there are a lot of + + align:start position:0% +simplify it and also there are a lot of + + + align:start position:0% +simplify it and also there are a lot of +idioms in each domain so some domain + + align:start position:0% +idioms in each domain so some domain + + + align:start position:0% +idioms in each domain so some domain +might say okay look i am going to + + align:start position:0% +might say okay look i am going to + + + align:start position:0% +might say okay look i am going to +represent a graph that i'm going to talk + + align:start position:0% +represent a graph that i'm going to talk + + + align:start position:0% +represent a graph that i'm going to talk +about in the normal free plus plus you + + align:start position:0% +about in the normal free plus plus you + + + align:start position:0% +about in the normal free plus plus you +put a bunch of classes you do this very + + align:start position:0% +put a bunch of classes you do this very + + + align:start position:0% +put a bunch of classes you do this very +complicated things it's the idiom is + + align:start position:0% +complicated things it's the idiom is + + + align:start position:0% +complicated things it's the idiom is +hidden in there first of all the c++ + + align:start position:0% +hidden in there first of all the c++ + + + align:start position:0% +hidden in there first of all the c++ +doesn't know that i had to look for + + align:start position:0% +doesn't know that i had to look for + + + align:start position:0% +doesn't know that i had to look for +graphs but even if you are look for + + align:start position:0% +graphs but even if you are look for + + + align:start position:0% +graphs but even if you are look for +graphs it's if you can try graphs in + + align:start position:0% +graphs it's if you can try graphs in + + + align:start position:0% +graphs it's if you can try graphs in +hundreds of millions of ways but if the + + align:start position:0% +hundreds of millions of ways but if the + + + align:start position:0% +hundreds of millions of ways but if the +if it is a first class support in the + + align:start position:0% +if it is a first class support in the + + + align:start position:0% +if it is a first class support in the +language i don't have to work heroically + + align:start position:0% +language i don't have to work heroically + + + align:start position:0% +language i don't have to work heroically +to extract that it's there i can easily + + align:start position:0% +to extract that it's there i can easily + + + align:start position:0% +to extract that it's there i can easily +see that so most of my compiler can be + + align:start position:0% +see that so most of my compiler can be + + + align:start position:0% +see that so most of my compiler can be +doing useful things in there and most of + + align:start position:0% +doing useful things in there and most of + + + align:start position:0% +doing useful things in there and most of +the time the other thing is if you build + + align:start position:0% +the time the other thing is if you build + + + align:start position:0% +the time the other thing is if you build +a domain-specific language right you can + + align:start position:0% +a domain-specific language right you can + + + align:start position:0% +a domain-specific language right you can +leave + + align:start position:0% +leave + + + align:start position:0% +leave +the complex the lower-level decision to + + align:start position:0% +the complex the lower-level decision to + + + align:start position:0% +the complex the lower-level decision to +the compiler in a few C++ you might be + + align:start position:0% +the compiler in a few C++ you might be + + + align:start position:0% +the compiler in a few C++ you might be +tempted to say yeah I know some of two + + align:start position:0% +tempted to say yeah I know some of two + + + align:start position:0% +tempted to say yeah I know some of two +minuses and let me do something here let + + align:start position:0% +minuses and let me do something here let + + + align:start position:0% +minuses and let me do something here let +me do some of the optimizations here so + + align:start position:0% +me do some of the optimizations here so + + + align:start position:0% +me do some of the optimizations here so +I have been working on optimization my + + align:start position:0% +I have been working on optimization my + + + align:start position:0% +I have been working on optimization my +all my life and lot of times when you + + align:start position:0% +all my life and lot of times when you + + + align:start position:0% +all my life and lot of times when you +write a compiled optimization fast you + + align:start position:0% +write a compiled optimization fast you + + + align:start position:0% +write a compiled optimization fast you +spent half of for more than half of your + + align:start position:0% +spent half of for more than half of your + + + align:start position:0% +spent half of for more than half of your +time undoing the crazy optimization the + + align:start position:0% +time undoing the crazy optimization the + + + align:start position:0% +time undoing the crazy optimization the +programmer did like you guys already so + + align:start position:0% +programmer did like you guys already so + + + align:start position:0% +programmer did like you guys already so +this you think you know better you go do + + align:start position:0% +this you think you know better you go do + + + align:start position:0% +this you think you know better you go do +something and that might work well then + + align:start position:0% +something and that might work well then + + + align:start position:0% +something and that might work well then +but believe me that code survives 20 + + align:start position:0% +but believe me that code survives 20 + + + align:start position:0% +but believe me that code survives 20 +years later and 20 years later that + + align:start position:0% +years later and 20 years later that + + + align:start position:0% +years later and 20 years later that +looks like a really stupid thing to do + + align:start position:0% +looks like a really stupid thing to do + + + align:start position:0% +looks like a really stupid thing to do +and then you look at and say okay now I + + align:start position:0% +and then you look at and say okay now I + + + align:start position:0% +and then you look at and say okay now I +had to undo everything in the compiler + + align:start position:0% +had to undo everything in the compiler + + + align:start position:0% +had to undo everything in the compiler +to do the right thing in the current + + align:start position:0% +to do the right thing in the current + + + align:start position:0% +to do the right thing in the current +architecture and because of that if you + + align:start position:0% +architecture and because of that if you + + + align:start position:0% +architecture and because of that if you +capture the right level I will let the + + align:start position:0% +capture the right level I will let the + + + align:start position:0% +capture the right level I will let the +compiler do that do the work in here and + + align:start position:0% +compiler do that do the work in here and + + + align:start position:0% +compiler do that do the work in here and +then as the architectures keep maturing + + align:start position:0% +then as the architectures keep maturing + + + align:start position:0% +then as the architectures keep maturing +as the problems keep changing I don't + + align:start position:0% +as the problems keep changing I don't + + + align:start position:0% +as the problems keep changing I don't +have to worry I don't have to undo these + + align:start position:0% +have to worry I don't have to undo these + + + align:start position:0% +have to worry I don't have to undo these +parts in here + + align:start position:0% +parts in here + + + align:start position:0% +parts in here +so so again I'm coming to the + + align:start position:0% +so so again I'm coming to the + + + align:start position:0% +so so again I'm coming to the +performance engineering class and + + align:start position:0% +performance engineering class and + + + align:start position:0% +performance engineering class and +telling you guys leave the performance + + align:start position:0% +telling you guys leave the performance + + + align:start position:0% +telling you guys leave the performance +to the compiler but that's nice thing + + align:start position:0% +to the compiler but that's nice thing + + + align:start position:0% +to the compiler but that's nice thing +that if the compiler can do the most of + + align:start position:0% +that if the compiler can do the most of + + + align:start position:0% +that if the compiler can do the most of +your work much nicer job so don't doubt + + align:start position:0% +your work much nicer job so don't doubt + + + align:start position:0% +your work much nicer job so don't doubt +the compiler so I'm going to talk about + + align:start position:0% +the compiler so I'm going to talk about + + + align:start position:0% +the compiler so I'm going to talk about +three parts in here one is three + + align:start position:0% +three parts in here one is three + + + align:start position:0% +three parts in here one is three +different programming languages in here + + align:start position:0% +different programming languages in here + + + align:start position:0% +different programming languages in here +domain-specific languages graffiti light + + align:start position:0% +domain-specific languages graffiti light + + + align:start position:0% +domain-specific languages graffiti light +and then open tuna which is not just in + + align:start position:0% +and then open tuna which is not just in + + + align:start position:0% +and then open tuna which is not just in +the language but a framework in here and + + align:start position:0% +the language but a framework in here and + + + align:start position:0% +the language but a framework in here and +between graph it and halide you will see + + align:start position:0% +between graph it and halide you will see + + + align:start position:0% +between graph it and halide you will see +some patterns and then we will see + + align:start position:0% +some patterns and then we will see + + + align:start position:0% +some patterns and then we will see +whether you you found the pattern that + + align:start position:0% +whether you you found the pattern that + + + align:start position:0% +whether you you found the pattern that +we are working on anything so gravity + + align:start position:0% +we are working on anything so gravity + + + align:start position:0% +we are working on anything so gravity +cells product that I work with Julian so + + align:start position:0% +cells product that I work with Julian so + + + align:start position:0% +cells product that I work with Julian so +if you have any questions of graffiti + + align:start position:0% +if you have any questions of graffiti + + + align:start position:0% +if you have any questions of graffiti +after today you can definitely gratitude + + align:start position:0% +after today you can definitely gratitude + + + align:start position:0% +after today you can definitely gratitude +and he knows probably more about graphs + + align:start position:0% +and he knows probably more about graphs + + + align:start position:0% +and he knows probably more about graphs +and graph it the mobile graph than + + align:start position:0% +and graph it the mobile graph than + + + align:start position:0% +and graph it the mobile graph than +probably anybody in this planet so so he + + align:start position:0% +probably anybody in this planet so so he + + + align:start position:0% +probably anybody in this planet so so he +sees a good resource to talk about + + align:start position:0% +sees a good resource to talk about + + + align:start position:0% +sees a good resource to talk about +graphs so talking about graphs graphs + + align:start position:0% +graphs so talking about graphs graphs + + + align:start position:0% +graphs so talking about graphs graphs +everywhere so if you go to something + + align:start position:0% +everywhere so if you go to something + + + align:start position:0% +everywhere so if you go to something +like Google and do some search the + + align:start position:0% +like Google and do some search the + + + align:start position:0% +like Google and do some search the +Google has represented the entire + + align:start position:0% +Google has represented the entire + + + align:start position:0% +Google has represented the entire +knowledge on the Internet is a big graph + + align:start position:0% +knowledge on the Internet is a big graph + + + align:start position:0% +knowledge on the Internet is a big graph +that you + + align:start position:0% +that you + + + align:start position:0% +that you +graph processing behind you that is how + + align:start position:0% +graph processing behind you that is how + + + align:start position:0% +graph processing behind you that is how +what guides your search in there oh if + + align:start position:0% +what guides your search in there oh if + + + align:start position:0% +what guides your search in there oh if +you go again mapped or something like + + align:start position:0% +you go again mapped or something like + + + align:start position:0% +you go again mapped or something like +Luba it will find your direction the + + align:start position:0% +Luba it will find your direction the + + + align:start position:0% +Luba it will find your direction the +entire road network is a graph and it's + + align:start position:0% +entire road network is a graph and it's + + + align:start position:0% +entire road network is a graph and it's +trying to find things like short as part + + align:start position:0% +trying to find things like short as part + + + align:start position:0% +trying to find things like short as part +in this graph or to give you the map and + + align:start position:0% +in this graph or to give you the map and + + + align:start position:0% +in this graph or to give you the map and +if you go to a recommendation engine to + + align:start position:0% +if you go to a recommendation engine to + + + align:start position:0% +if you go to a recommendation engine to +get a recommendation for a movie if you + + align:start position:0% +get a recommendation for a movie if you + + + align:start position:0% +get a recommendation for a movie if you +get a really cool movie you like that's + + align:start position:0% +get a really cool movie you like that's + + + align:start position:0% +get a really cool movie you like that's +because there's a huge graph between + + align:start position:0% +because there's a huge graph between + + + align:start position:0% +because there's a huge graph between +everybody who's watched movie they watch + + align:start position:0% +everybody who's watched movie they watch + + + align:start position:0% +everybody who's watched movie they watch +and they are likings to those movies and + + align:start position:0% +and they are likings to those movies and + + + align:start position:0% +and they are likings to those movies and +and they are looking and comparing you + + align:start position:0% +and they are looking and comparing you + + + align:start position:0% +and they are looking and comparing you +to them and recommending that that's all + + align:start position:0% +to them and recommending that that's all + + + align:start position:0% +to them and recommending that that's all +can be moved as graphs in here and even + + align:start position:0% +can be moved as graphs in here and even + + + align:start position:0% +can be moved as graphs in here and even +if you go to a ATM and try to do a + + align:start position:0% +if you go to a ATM and try to do a + + + align:start position:0% +if you go to a ATM and try to do a +transaction there's a very fast graph + + align:start position:0% +transaction there's a very fast graph + + + align:start position:0% +transaction there's a very fast graph +analysis back to say is this a + + align:start position:0% +analysis back to say is this a + + + align:start position:0% +analysis back to say is this a +fraudulent transaction or not so if most + + align:start position:0% +fraudulent transaction or not so if most + + + align:start position:0% +fraudulent transaction or not so if most +of the transactions people have done all + + align:start position:0% +of the transactions people have done all + + + align:start position:0% +of the transactions people have done all +the connectivities in the back in there + + align:start position:0% +the connectivities in the back in there + + + align:start position:0% +the connectivities in the back in there +by before the time that actually the + + align:start position:0% +by before the time that actually the + + + align:start position:0% +by before the time that actually the +money pops out of your ATM machine it + + align:start position:0% +money pops out of your ATM machine it + + + align:start position:0% +money pops out of your ATM machine it +tests that bunch of graph processes to + + align:start position:0% +tests that bunch of graph processes to + + + align:start position:0% +tests that bunch of graph processes to +understand okay this seems like a good + + align:start position:0% +understand okay this seems like a good + + + align:start position:0% +understand okay this seems like a good +transaction so I will actually give you + + align:start position:0% +transaction so I will actually give you + + + align:start position:0% +transaction so I will actually give you +the money sometimes you say you get this + + align:start position:0% +the money sometimes you say you get this + + + align:start position:0% +the money sometimes you say you get this +other messages that means that the graph + + align:start position:0% +other messages that means that the graph + + + align:start position:0% +other messages that means that the graph +processing decided there might be some + + align:start position:0% +processing decided there might be some + + + align:start position:0% +processing decided there might be some +weird thing going on there so lot of + + align:start position:0% +weird thing going on there so lot of + + + align:start position:0% +weird thing going on there so lot of +these things that some of them like maps + + align:start position:0% +these things that some of them like maps + + + align:start position:0% +these things that some of them like maps +and graphs has Maps and these + + align:start position:0% +and graphs has Maps and these + + + align:start position:0% +and graphs has Maps and these +transactions have very fine latency + + align:start position:0% +transactions have very fine latency + + + align:start position:0% +transactions have very fine latency +thing in that you have to get this thing + + align:start position:0% +thing in that you have to get this thing + + + align:start position:0% +thing in that you have to get this thing +done right you have to get to directions + + align:start position:0% +done right you have to get to directions + + + align:start position:0% +done right you have to get to directions +especially if you take a wrong turn + + align:start position:0% +especially if you take a wrong turn + + + align:start position:0% +especially if you take a wrong turn +you didn't get the next set of + + align:start position:0% +you didn't get the next set of + + + align:start position:0% +you didn't get the next set of +directions done very fast before you go + + align:start position:0% +directions done very fast before you go + + + align:start position:0% +directions done very fast before you go +eat some Rosten bad via traffic so you + + align:start position:0% +eat some Rosten bad via traffic so you + + + align:start position:0% +eat some Rosten bad via traffic so you +these things have to work for and other + + align:start position:0% +these things have to work for and other + + + align:start position:0% +these things have to work for and other +things like recommendations and Google + + align:start position:0% +things like recommendations and Google + + + align:start position:0% +things like recommendations and Google +search is huge graph they build the + + align:start position:0% +search is huge graph they build the + + + align:start position:0% +search is huge graph they build the +entire web oh then all the + + align:start position:0% +entire web oh then all the + + + align:start position:0% +entire web oh then all the +recommendations are to do huge amount of + + align:start position:0% +recommendations are to do huge amount of + + + align:start position:0% +recommendations are to do huge amount of +processing so performance matters a lot + + align:start position:0% +processing so performance matters a lot + + + align:start position:0% +processing so performance matters a lot +in these gap legations so let me dive + + align:start position:0% +in these gap legations so let me dive + + + align:start position:0% +in these gap legations so let me dive +down little bit deeper into show what + + align:start position:0% +down little bit deeper into show what + + + align:start position:0% +down little bit deeper into show what +graphs means what draw processing means + + align:start position:0% +graphs means what draw processing means + + + align:start position:0% +graphs means what draw processing means +so one of the very well-known graph + + align:start position:0% +so one of the very well-known graph + + + align:start position:0% +so one of the very well-known graph +algorithms is called + + align:start position:0% +algorithms is called + + + align:start position:0% +algorithms is called +pagerank anybody knows history of pager + + align:start position:0% +pagerank anybody knows history of pager + + + align:start position:0% +pagerank anybody knows history of pager +how many have heard of PageRank okay + + align:start position:0% +how many have heard of PageRank okay + + + align:start position:0% +how many have heard of PageRank okay +what does page stand in PageRank Larry + + align:start position:0% +what does page stand in PageRank Larry + + + align:start position:0% +what does page stand in PageRank Larry +Page so so the first algorithm Google + + align:start position:0% +Page so so the first algorithm Google + + + align:start position:0% +Page so so the first algorithm Google +did I don't think this anywhere near + + align:start position:0% +did I don't think this anywhere near + + + align:start position:0% +did I don't think this anywhere near +Google at this point was this algorithm + + align:start position:0% +Google at this point was this algorithm + + + align:start position:0% +Google at this point was this algorithm +PageRank so it did track these pages but + + align:start position:0% +PageRank so it did track these pages but + + + align:start position:0% +PageRank so it did track these pages but +it was developed by Larry Page so you so + + align:start position:0% +it was developed by Larry Page so you so + + + align:start position:0% +it was developed by Larry Page so you so +depends on either either pitch web pages + + align:start position:0% +depends on either either pitch web pages + + + align:start position:0% +depends on either either pitch web pages +or Larry Page we don't know but people + + align:start position:0% +or Larry Page we don't know but people + + + align:start position:0% +or Larry Page we don't know but people +thinks Larry Page in spades right so in + + align:start position:0% +thinks Larry Page in spades right so in + + + align:start position:0% +thinks Larry Page in spades right so in +our graph in here + + align:start position:0% +our graph in here + + + align:start position:0% +our graph in here +so this graph algorithm what it does is + + align:start position:0% +so this graph algorithm what it does is + + + align:start position:0% +so this graph algorithm what it does is +it strange to some iterations either + + align:start position:0% +it strange to some iterations either + + + align:start position:0% +it strange to some iterations either +smacks it onto some convergence in here + + align:start position:0% +smacks it onto some convergence in here + + + align:start position:0% +smacks it onto some convergence in here +so what it first do is it will go around + + align:start position:0% +so what it first do is it will go around + + + align:start position:0% +so what it first do is it will go around +look at all its neighbors and calculate + + align:start position:0% +look at all its neighbors and calculate + + + align:start position:0% +look at all its neighbors and calculate +basically a rank new rank out of all my + + align:start position:0% +basically a rank new rank out of all my + + + align:start position:0% +basically a rank new rank out of all my +neighbors so that means what is how good + + align:start position:0% +neighbors so that means what is how good + + + align:start position:0% +neighbors so that means what is how good +are my neighbors what's their rank and + + align:start position:0% +are my neighbors what's their rank and + + + align:start position:0% +are my neighbors what's their rank and +and what's their contribution to me so + + align:start position:0% +and what's their contribution to me so + + + align:start position:0% +and what's their contribution to me so +if beans being known to a good person + + align:start position:0% +if beans being known to a good person + + + align:start position:0% +if beans being known to a good person +and having a connection to a very + + align:start position:0% +and having a connection to a very + + + align:start position:0% +and having a connection to a very +well-known in this case of a webpage + + align:start position:0% +well-known in this case of a webpage + + + align:start position:0% +well-known in this case of a webpage +means my I am highly ranked so I'm more + + align:start position:0% +means my I am highly ranked so I'm more + + + align:start position:0% +means my I am highly ranked so I'm more +influential because I have closer to + + align:start position:0% +influential because I have closer to + + + align:start position:0% +influential because I have closer to +something in there so what it does is + + align:start position:0% +something in there so what it does is + + + align:start position:0% +something in there so what it does is +basically it will go it's not calculate + + align:start position:0% +basically it will go it's not calculate + + + align:start position:0% +basically it will go it's not calculate +some value and propagate to all the + + align:start position:0% +some value and propagate to all the + + + align:start position:0% +some value and propagate to all the +neighbors and aggregate in this so + + align:start position:0% +neighbors and aggregate in this so + + + align:start position:0% +neighbors and aggregate in this so +entire graph participating in that and + + align:start position:0% +entire graph participating in that and + + + align:start position:0% +entire graph participating in that and +then what happens is each node will go + + align:start position:0% +then what happens is each node will go + + + align:start position:0% +then what happens is each node will go +about calculating its new rank in there + + align:start position:0% +about calculating its new rank in there + + + align:start position:0% +about calculating its new rank in there +from looking at all rang it gets + + align:start position:0% +from looking at all rang it gets + + + align:start position:0% +from looking at all rang it gets +modified a little bit for towards an ill + + align:start position:0% +modified a little bit for towards an ill + + + align:start position:0% +modified a little bit for towards an ill +rank and then this swap all ranks and + + align:start position:0% +rank and then this swap all ranks and + + + align:start position:0% +rank and then this swap all ranks and +new ranks so this is the two + + align:start position:0% +new ranks so this is the two + + + align:start position:0% +new ranks so this is the two +computations that you iterate over that + + align:start position:0% +computations that you iterate over that + + + align:start position:0% +computations that you iterate over that +and you have to do for the entire graph + + align:start position:0% +and you have to do for the entire graph + + + align:start position:0% +and you have to do for the entire graph +in here so of course you can run this + + align:start position:0% +in here so of course you can run this + + + align:start position:0% +in here so of course you can run this +this will not very very slow if you run + + align:start position:0% +this will not very very slow if you run + + + align:start position:0% +this will not very very slow if you run +this so if you want to get performance + + align:start position:0% +this so if you want to get performance + + + align:start position:0% +this so if you want to get performance +you're right this piece of code so this + + align:start position:0% +you're right this piece of code so this + + + align:start position:0% +you're right this piece of code so this +piece of code basically is huge and it + + align:start position:0% +piece of code basically is huge and it + + + align:start position:0% +piece of code basically is huge and it +runs 23 23 times faster than the what's + + align:start position:0% +runs 23 23 times faster than the what's + + + align:start position:0% +runs 23 23 times faster than the what's +in the previous graph in here on a to + + align:start position:0% +in the previous graph in here on a to + + + align:start position:0% +in the previous graph in here on a to +elko machine it basically had + + align:start position:0% +elko machine it basically had + + + align:start position:0% +elko machine it basically had +multi-threaded so it get parallel + + align:start position:0% +multi-threaded so it get parallel + + + align:start position:0% +multi-threaded so it get parallel +performance it is load balance because + + align:start position:0% +performance it is load balance because + + + align:start position:0% +performance it is load balance because +as you know graphs vary in balance so + + align:start position:0% +as you know graphs vary in balance so + + + align:start position:0% +as you know graphs vary in balance so +you get load balance if you have + + align:start position:0% +you get load balance if you have + + + align:start position:0% +you get load balance if you have +non-uniform memory access machines + + align:start position:0% +non-uniform memory access machines + + + align:start position:0% +non-uniform memory access machines +things like multiple socket machines + + align:start position:0% +things like multiple socket machines + + + align:start position:0% +things like multiple socket machines +it will take advantage of that it + + align:start position:0% +it will take advantage of that it + + + align:start position:0% +it will take advantage of that it +advantage of caches lot of things + + align:start position:0% +advantage of caches lot of things + + + align:start position:0% +advantage of caches lot of things +happening in in this piece of code but + + align:start position:0% +happening in in this piece of code but + + + align:start position:0% +happening in in this piece of code but +of course you know this is hard to write + + align:start position:0% +of course you know this is hard to write + + + align:start position:0% +of course you know this is hard to write +this piece of code but also worse you + + align:start position:0% +this piece of code but also worse you + + + align:start position:0% +this piece of code but also worse you +might not know what to do what the right + + align:start position:0% +might not know what to do what the right + + + align:start position:0% +might not know what to do what the right +optimizer you might only internet you + + align:start position:0% +optimizer you might only internet you + + + align:start position:0% +optimizer you might only internet you +might don't try many things and this is + + align:start position:0% +might don't try many things and this is + + + align:start position:0% +might don't try many things and this is +very hard every time you change + + align:start position:0% +very hard every time you change + + + align:start position:0% +very hard every time you change +something if you say I want to do + + align:start position:0% +something if you say I want to do + + + align:start position:0% +something if you say I want to do +something a little bit different that I + + align:start position:0% +something a little bit different that I + + + align:start position:0% +something a little bit different that I +have to write a very complicated piece + + align:start position:0% +have to write a very complicated piece + + + align:start position:0% +have to write a very complicated piece +of code get it alright get everything + + align:start position:0% +of code get it alright get everything + + + align:start position:0% +of code get it alright get everything +working before I test him here so this + + align:start position:0% +working before I test him here so this + + + align:start position:0% +working before I test him here so this +is why we can use a DSL for this one so + + align:start position:0% +is why we can use a DSL for this one so + + + align:start position:0% +is why we can use a DSL for this one so +let me go little bit talk about graph + + align:start position:0% +let me go little bit talk about graph + + + align:start position:0% +let me go little bit talk about graph +algorithms and say this seems like a new + + align:start position:0% +algorithms and say this seems like a new + + + align:start position:0% +algorithms and say this seems like a new +set of me so what do people do with + + align:start position:0% +set of me so what do people do with + + + align:start position:0% +set of me so what do people do with +graphs so when they say graph algorithm + + align:start position:0% +graphs so when they say graph algorithm + + + align:start position:0% +graphs so when they say graph algorithm +so I'm going to go a little bit deep + + align:start position:0% +so I'm going to go a little bit deep + + + align:start position:0% +so I'm going to go a little bit deep +down to show you what type of things + + align:start position:0% +down to show you what type of things + + + align:start position:0% +down to show you what type of things +represent these graphs this one class of + + align:start position:0% +represent these graphs this one class of + + + align:start position:0% +represent these graphs this one class of +graph algorithms that are called + + align:start position:0% +graph algorithms that are called + + + align:start position:0% +graph algorithms that are called +topology driven algorithms that means + + align:start position:0% +topology driven algorithms that means + + + align:start position:0% +topology driven algorithms that means +the entire graph participates in the + + align:start position:0% +the entire graph participates in the + + + align:start position:0% +the entire graph participates in the +computation for example Google search + + align:start position:0% +computation for example Google search + + + align:start position:0% +computation for example Google search +before you do Google search it will do a + + align:start position:0% +before you do Google search it will do a + + + align:start position:0% +before you do Google search it will do a +do a entire basically collection of all + + align:start position:0% +do a entire basically collection of all + + + align:start position:0% +do a entire basically collection of all +the web web links it will build this an + + align:start position:0% +the web web links it will build this an + + + align:start position:0% +the web web links it will build this an +huge graph and do huge amount of + + align:start position:0% +huge graph and do huge amount of + + + align:start position:0% +huge graph and do huge amount of +processing to basically able to do the + + align:start position:0% +processing to basically able to do the + + + align:start position:0% +processing to basically able to do the +search in here recommendation engine so + + align:start position:0% +search in here recommendation engine so + + + align:start position:0% +search in here recommendation engine so +every probably few weeks or whatever it + + align:start position:0% +every probably few weeks or whatever it + + + align:start position:0% +every probably few weeks or whatever it +is it will collect all everybody's + + align:start position:0% +is it will collect all everybody's + + + align:start position:0% +is it will collect all everybody's +recommendations have this huge data and + + align:start position:0% +recommendations have this huge data and + + + align:start position:0% +recommendations have this huge data and +you're going to process that and do this + + align:start position:0% +you're going to process that and do this + + + align:start position:0% +you're going to process that and do this +recommendation so this is applying for + + align:start position:0% +recommendation so this is applying for + + + align:start position:0% +recommendation so this is applying for +the entire graphs and sometimes billions + + align:start position:0% +the entire graphs and sometimes billions + + + align:start position:0% +the entire graphs and sometimes billions +of trillions of known had to go into + + align:start position:0% +of trillions of known had to go into + + + align:start position:0% +of trillions of known had to go into +this computation another set of + + align:start position:0% +this computation another set of + + + align:start position:0% +this computation another set of +algorithms called data-driven algorithms + + align:start position:0% +algorithms called data-driven algorithms + + + align:start position:0% +algorithms called data-driven algorithms +so what that means is you start with + + align:start position:0% +so what that means is you start with + + + align:start position:0% +so what that means is you start with +certain nodes and then you keep going to + + align:start position:0% +certain nodes and then you keep going to + + + align:start position:0% +certain nodes and then you keep going to +its neighbors and its neighbors + + align:start position:0% +its neighbors and its neighbors + + + align:start position:0% +its neighbors and its neighbors +processing data in here as we do that + + align:start position:0% + + + + align:start position:0% + +the kind of algorithms that fit in this + + align:start position:0% +the kind of algorithms that fit in this + + + align:start position:0% +the kind of algorithms that fit in this +category are things like if you have a + + align:start position:0% +category are things like if you have a + + + align:start position:0% +category are things like if you have a +map if you have to find a shortest path + + align:start position:0% +map if you have to find a shortest path + + + align:start position:0% +map if you have to find a shortest path +that means I have probably two parts I + + align:start position:0% +that means I have probably two parts I + + + align:start position:0% +that means I have probably two parts I +don't have to get him from direction + + align:start position:0% +don't have to get him from direction + + + align:start position:0% +don't have to get him from direction +from here + + align:start position:0% +from here + + + align:start position:0% +from here +to Boston I don't have to figure go + + align:start position:0% +to Boston I don't have to figure go + + + align:start position:0% +to Boston I don't have to figure go +through New York nodes in New York I + + align:start position:0% +through New York nodes in New York I + + + align:start position:0% +through New York nodes in New York I +just have to go through my neighbors + + align:start position:0% +just have to go through my neighbors + + + align:start position:0% +just have to go through my neighbors +connected in via so I am I am basically + + align:start position:0% +connected in via so I am I am basically + + + align:start position:0% +connected in via so I am I am basically +operating on a certain area with some + + align:start position:0% +operating on a certain area with some + + + align:start position:0% +operating on a certain area with some +connections and and processing that + + align:start position:0% +connections and and processing that + + + align:start position:0% +connections and and processing that +there so these are data driven + + align:start position:0% +there so these are data driven + + + align:start position:0% +there so these are data driven +algorithms so so I might have huge graph + + align:start position:0% +algorithms so so I might have huge graph + + + align:start position:0% +algorithms so so I might have huge graph +but my computation might only work on a + + align:start position:0% +but my computation might only work on a + + + align:start position:0% +but my computation might only work on a +small region or a small part of the + + align:start position:0% +small region or a small part of the + + + align:start position:0% +small region or a small part of the +graph in these algorithms so when you're + + align:start position:0% +graph in these algorithms so when you're + + + align:start position:0% +graph in these algorithms so when you're +traversing through a graph doing that + + align:start position:0% +traversing through a graph doing that + + + align:start position:0% +traversing through a graph doing that +there are multiple ways of doing graphed + + align:start position:0% +there are multiple ways of doing graphed + + + align:start position:0% +there are multiple ways of doing graphed +reversals and this is why optimizations + + align:start position:0% +reversals and this is why optimizations + + + align:start position:0% +reversals and this is why optimizations +hard because there are many different + + align:start position:0% +hard because there are many different + + + align:start position:0% +hard because there are many different +ways of doing things and each has + + align:start position:0% +ways of doing things and each has + + + align:start position:0% +ways of doing things and each has +different set of outcomes you can get so + + align:start position:0% +different set of outcomes you can get so + + + align:start position:0% +different set of outcomes you can get so +assume lot of graph algorithms I need to + + align:start position:0% +assume lot of graph algorithms I need to + + + align:start position:0% +assume lot of graph algorithms I need to +get something from my neighbors okay one + + align:start position:0% +get something from my neighbors okay one + + + align:start position:0% +get something from my neighbors okay one +way to get something my neighbors is I + + align:start position:0% +way to get something my neighbors is I + + + align:start position:0% +way to get something my neighbors is I +can calculate what the neighbor all my + + align:start position:0% +can calculate what the neighbor all my + + + align:start position:0% +can calculate what the neighbor all my +neighbors might want and give it to all + + align:start position:0% +neighbors might want and give it to all + + + align:start position:0% +neighbors might want and give it to all +the neighbors and in there oh I can go + + align:start position:0% +the neighbors and in there oh I can go + + + align:start position:0% +the neighbors and in there oh I can go +change all the neighbors to update my + + align:start position:0% +change all the neighbors to update my + + + align:start position:0% +change all the neighbors to update my +values so what do you think okay you + + align:start position:0% +values so what do you think okay you + + + align:start position:0% +values so what do you think okay you +have done some programming in here what + + align:start position:0% +have done some programming in here what + + + align:start position:0% +have done some programming in here what +do you think about this is this a good + + align:start position:0% +do you think about this is this a good + + + align:start position:0% +do you think about this is this a good +way so if I won't update everybody I + + align:start position:0% +way so if I won't update everybody I + + + align:start position:0% +way so if I won't update everybody I +will calculate why what I won't do and + + align:start position:0% +will calculate why what I won't do and + + + align:start position:0% +will calculate why what I won't do and +I'll go change everybody all my + + align:start position:0% +I'll go change everybody all my + + + align:start position:0% +I'll go change everybody all my +neighbors not as parallel as it could be + + align:start position:0% +neighbors not as parallel as it could be + + + align:start position:0% +neighbors not as parallel as it could be +I think you are getting to a point but + + align:start position:0% +I think you are getting to a point but + + + align:start position:0% +I think you are getting to a point but +why it's not that parallel + + align:start position:0% + + + + align:start position:0% + +the neighbors - what + + align:start position:0% + + + + align:start position:0% + +yeah but okay that's a very good price + + align:start position:0% +yeah but okay that's a very good price + + + align:start position:0% +yeah but okay that's a very good price +so if you are doing a data-driven if I + + align:start position:0% +so if you are doing a data-driven if I + + + align:start position:0% +so if you are doing a data-driven if I +am doing that's not good but if + + align:start position:0% +am doing that's not good but if + + + align:start position:0% +am doing that's not good but if +everybody is doing that to their + + align:start position:0% +everybody is doing that to their + + + align:start position:0% +everybody is doing that to their +neighbor so then I have a parallelism so + + align:start position:0% +neighbor so then I have a parallelism so + + + align:start position:0% +neighbor so then I have a parallelism so +everybody might say you updated your + + align:start position:0% +everybody might say you updated your + + + align:start position:0% +everybody might say you updated your +neighbor you are updating you everybody + + align:start position:0% +neighbor you are updating you everybody + + + align:start position:0% +neighbor you are updating you everybody +is updating their neighbors so now + + align:start position:0% +is updating their neighbors so now + + + align:start position:0% +is updating their neighbors so now +there's another problem showing up + + align:start position:0% +there's another problem showing up + + + align:start position:0% +there's another problem showing up +what's the problem if everybody try to + + align:start position:0% +what's the problem if everybody try to + + + align:start position:0% +what's the problem if everybody try to +update their neighbors back there that's + + align:start position:0% +update their neighbors back there that's + + + align:start position:0% +update their neighbors back there that's +a race in there because everybody's gone + + align:start position:0% +a race in there because everybody's gone + + + align:start position:0% +a race in there because everybody's gone +right in there so if you want to get + + align:start position:0% +right in there so if you want to get + + + align:start position:0% +right in there so if you want to get +this actually right you have a bunch of + + align:start position:0% +this actually right you have a bunch of + + + align:start position:0% +this actually right you have a bunch of +issues here you want to basically do + + align:start position:0% +issues here you want to basically do + + + align:start position:0% +issues here you want to basically do +atomic updates because you need to lock + + align:start position:0% +atomic updates because you need to lock + + + align:start position:0% +atomic updates because you need to lock +that thing so it has to be like + + align:start position:0% +that thing so it has to be like + + + align:start position:0% +that thing so it has to be like +atomically updated in here and this is + + align:start position:0% +atomically updated in here and this is + + + align:start position:0% +atomically updated in here and this is +nice but I don't have to Travis anything + + align:start position:0% +nice but I don't have to Travis anything + + + align:start position:0% +nice but I don't have to Travis anything +because everybody I need to update I + + align:start position:0% +because everybody I need to update I + + + align:start position:0% +because everybody I need to update I +actually go and go and update him yeah + + align:start position:0% +actually go and go and update him yeah + + + align:start position:0% +actually go and go and update him yeah +that's that's nice way to do that + + align:start position:0% +that's that's nice way to do that + + + align:start position:0% +that's that's nice way to do that +especially if it is not a global thing + + align:start position:0% +especially if it is not a global thing + + + align:start position:0% +especially if it is not a global thing +so if I'm propagating I will update my + + align:start position:0% +so if I'm propagating I will update my + + + align:start position:0% +so if I'm propagating I will update my +neighbor's and-and-and-and-and and I can + + align:start position:0% +neighbor's and-and-and-and-and and I can + + + align:start position:0% +neighbor's and-and-and-and-and and I can +propagate that down another way to do + + align:start position:0% +propagate that down another way to do + + + align:start position:0% +propagate that down another way to do +that is pull schedule that means if I + + align:start position:0% +that is pull schedule that means if I + + + align:start position:0% +that is pull schedule that means if I +everybody look at ask their neighbors + + align:start position:0% +everybody look at ask their neighbors + + + align:start position:0% +everybody look at ask their neighbors +okay do you have what do you have to + + align:start position:0% +okay do you have what do you have to + + + align:start position:0% +okay do you have what do you have to +give it to me and I flicked everything + + align:start position:0% +give it to me and I flicked everything + + + align:start position:0% +give it to me and I flicked everything +from my neighbors and I update myself so + + align:start position:0% +from my neighbors and I update myself so + + + align:start position:0% +from my neighbors and I update myself so +is there a race condition now how many + + align:start position:0% +is there a race condition now how many + + + align:start position:0% +is there a race condition now how many +people say there's a race how many + + align:start position:0% +people say there's a race how many + + + align:start position:0% +people say there's a race how many +people think there's no race so what + + align:start position:0% +people think there's no race so what + + + align:start position:0% +people think there's no race so what +happens is I am reading from all the + + align:start position:0% +happens is I am reading from all the + + + align:start position:0% +happens is I am reading from all the +neighbors everybody is reading from the + + align:start position:0% +neighbors everybody is reading from the + + + align:start position:0% +neighbors everybody is reading from the +neighbors but I am only updating myself + + align:start position:0% +neighbors but I am only updating myself + + + align:start position:0% +neighbors but I am only updating myself +so because of that I'm the only one + + align:start position:0% +so because of that I'm the only one + + + align:start position:0% +so because of that I'm the only one +who's writing me so I don't have a race + + align:start position:0% +who's writing me so I don't have a race + + + align:start position:0% +who's writing me so I don't have a race +so it's very nice you don't have race + + align:start position:0% +so it's very nice you don't have race + + + align:start position:0% +so it's very nice you don't have race +but I might if I'm doing a data-driven + + align:start position:0% +but I might if I'm doing a data-driven + + + align:start position:0% +but I might if I'm doing a data-driven +transformation I might not know that I + + align:start position:0% +transformation I might not know that I + + + align:start position:0% +transformation I might not know that I +need to get updated because the update + + align:start position:0% +need to get updated because the update + + + align:start position:0% +need to get updated because the update +comes from that person and and and and + + align:start position:0% +comes from that person and and and and + + + align:start position:0% +comes from that person and and and and +that means I might be tasking oh do you + + align:start position:0% +that means I might be tasking oh do you + + + align:start position:0% +that means I might be tasking oh do you +have anything to say you might say no so + + align:start position:0% +have anything to say you might say no so + + + align:start position:0% +have anything to say you might say no so +in that sense I might basically doing + + align:start position:0% +in that sense I might basically doing + + + align:start position:0% +in that sense I might basically doing +lot of extra computation than necessary + + align:start position:0% +lot of extra computation than necessary + + + align:start position:0% +lot of extra computation than necessary +because I might not know that I have a + + align:start position:0% +because I might not know that I have a + + + align:start position:0% +because I might not know that I have a +data I need to get but I had asked you + + align:start position:0% +data I need to get but I had asked you + + + align:start position:0% +data I need to get but I had asked you +whether I should I should do this but I + + align:start position:0% +whether I should I should do this but I + + + align:start position:0% +whether I should I should do this but I +don't have any any any basically need to + + align:start position:0% +don't have any any any basically need to + + + align:start position:0% +don't have any any any basically need to +do any synchronization another + + align:start position:0% +do any synchronization another + + + align:start position:0% +do any synchronization another +interesting thing is I can take this + + align:start position:0% +interesting thing is I can take this + + + align:start position:0% +interesting thing is I can take this +graph and I can basically punch in the + + align:start position:0% +graph and I can basically punch in the + + + align:start position:0% +graph and I can basically punch in the +graph once I partition the graph I can + + align:start position:0% +graph once I partition the graph I can + + + align:start position:0% +graph once I partition the graph I can +basically say okay this Co get this + + align:start position:0% +basically say okay this Co get this + + + align:start position:0% +basically say okay this Co get this +graph please go get this graph + + align:start position:0% +graph please go get this graph + + + align:start position:0% +graph please go get this graph +oh this process are not discreet this + + align:start position:0% +oh this process are not discreet this + + + align:start position:0% +oh this process are not discreet this +graph what's the advantage of + + align:start position:0% +graph what's the advantage of + + + align:start position:0% +graph what's the advantage of +partitioning a graph why do I want to + + align:start position:0% +partitioning a graph why do I want to + + + align:start position:0% +partitioning a graph why do I want to +partition a graph large graph into small + + align:start position:0% +partition a graph large graph into small + + + align:start position:0% +partition a graph large graph into small +pieces of course you can't do a good + + align:start position:0% +pieces of course you can't do a good + + + align:start position:0% +pieces of course you can't do a good +partition you can't do arbitral + + align:start position:0% +partition you can't do arbitral + + + align:start position:0% +partition you can't do arbitral +partition so what happens if I do a good + + align:start position:0% +partition so what happens if I do a good + + + align:start position:0% +partition so what happens if I do a good +partitioning I don't tell the word + + align:start position:0% +partitioning I don't tell the word + + + align:start position:0% +partitioning I don't tell the word +because then then the answer comes out + + align:start position:0% +because then then the answer comes out + + + align:start position:0% +because then then the answer comes out +in there okay let me see anybody else + + align:start position:0% +in there okay let me see anybody else + + + align:start position:0% +in there okay let me see anybody else +you have asked anybody else want to + + align:start position:0% +you have asked anybody else want to + + + align:start position:0% +you have asked anybody else want to +answer come on you have taken it + + align:start position:0% +answer come on you have taken it + + + align:start position:0% +answer come on you have taken it +what happened if I take apart and and + + align:start position:0% +what happened if I take apart and and + + + align:start position:0% +what happened if I take apart and and +find two different groups and separate + + align:start position:0% +find two different groups and separate + + + align:start position:0% +find two different groups and separate +them and give this one to one and this + + align:start position:0% +them and give this one to one and this + + + align:start position:0% +them and give this one to one and this +one to another what what do I get I get + + align:start position:0% +one to another what what do I get I get + + + align:start position:0% +one to another what what do I get I get +parallelism also but other thing if I + + align:start position:0% +parallelism also but other thing if I + + + align:start position:0% +parallelism also but other thing if I +have a lot of connected things going to + + align:start position:0% +have a lot of connected things going to + + + align:start position:0% +have a lot of connected things going to +you these connected things go into that + + align:start position:0% +you these connected things go into that + + + align:start position:0% +you these connected things go into that +person what are the what else I can I + + align:start position:0% +person what are the what else I can I + + + align:start position:0% +person what are the what else I can I +get locality + + align:start position:0% +get locality + + + align:start position:0% +get locality +have you heard did you do locality in + + align:start position:0% +have you heard did you do locality in + + + align:start position:0% +have you heard did you do locality in +the class so that means the partition + + align:start position:0% +the class so that means the partition + + + align:start position:0% +the class so that means the partition +means my the thing I am working I am + + align:start position:0% +means my the thing I am working I am + + + align:start position:0% +means my the thing I am working I am +only working on a small amount and that + + align:start position:0% +only working on a small amount and that + + + align:start position:0% +only working on a small amount and that +might if you are lucky fit in my cache + + align:start position:0% +might if you are lucky fit in my cache + + + align:start position:0% +might if you are lucky fit in my cache +and it will be very nice that + + align:start position:0% +and it will be very nice that + + + align:start position:0% +and it will be very nice that +everybody's has to go to every know + + align:start position:0% +everybody's has to go to every know + + + align:start position:0% +everybody's has to go to every know +every node in here so so if I partition + + align:start position:0% +every node in here so so if I partition + + + align:start position:0% +every node in here so so if I partition +is properly I will get good locality in + + align:start position:0% +is properly I will get good locality in + + + align:start position:0% +is properly I will get good locality in +here it's actually written there oops + + align:start position:0% +here it's actually written there oops + + + align:start position:0% +here it's actually written there oops +okay so my answer was in there so in + + align:start position:0% +okay so my answer was in there so in + + + align:start position:0% +okay so my answer was in there so in +locality but of course now I might have + + align:start position:0% +locality but of course now I might have + + + align:start position:0% +locality but of course now I might have +a little bit extra overhead because now + + align:start position:0% +a little bit extra overhead because now + + + align:start position:0% +a little bit extra overhead because now +I might have to replicate some some + + align:start position:0% +I might have to replicate some some + + + align:start position:0% +I might have to replicate some some +nodes stuff like that because it's in + + align:start position:0% +nodes stuff like that because it's in + + + align:start position:0% +nodes stuff like that because it's in +both sides and India so another + + align:start position:0% +both sides and India so another + + + align:start position:0% +both sides and India so another +interesting in properties of graphs is + + align:start position:0% +interesting in properties of graphs is + + + align:start position:0% +interesting in properties of graphs is +when you look at data structures until + + align:start position:0% +when you look at data structures until + + + align:start position:0% +when you look at data structures until +now things like array is the size mantis + + align:start position:0% +now things like array is the size mantis + + + align:start position:0% +now things like array is the size mantis +is represent about array it fits the + + align:start position:0% +is represent about array it fits the + + + align:start position:0% +is represent about array it fits the +cache and stuff like that graphs there + + align:start position:0% +cache and stuff like that graphs there + + + align:start position:0% +cache and stuff like that graphs there +are some other properties of the graphs + + align:start position:0% +are some other properties of the graphs + + + align:start position:0% +are some other properties of the graphs +in here so if you go to social networks + + align:start position:0% +in here so if you go to social networks + + + align:start position:0% +in here so if you go to social networks +social network is a graph what's the + + align:start position:0% +social network is a graph what's the + + + align:start position:0% +social network is a graph what's the +interesting property and social networks + + align:start position:0% +interesting property and social networks + + + align:start position:0% +interesting property and social networks +use you have observed + + align:start position:0% + + + + align:start position:0% + +connectedness there are people like me + + align:start position:0% +connectedness there are people like me + + + align:start position:0% +connectedness there are people like me +that probably had 20 friends in there + + align:start position:0% +that probably had 20 friends in there + + + align:start position:0% +that probably had 20 friends in there +and has a very little number of + + align:start position:0% +and has a very little number of + + + align:start position:0% +and has a very little number of +connections and then there are + + align:start position:0% +connections and then there are + + + align:start position:0% +connections and then there are +celebrities who have millions of + + align:start position:0% +celebrities who have millions of + + + align:start position:0% +celebrities who have millions of +connections in here so the interesting + + align:start position:0% +connections in here so the interesting + + + align:start position:0% +connections in here so the interesting +thing is if you look at a social network + + align:start position:0% +thing is if you look at a social network + + + align:start position:0% +thing is if you look at a social network +graph you have this relationship called + + align:start position:0% +graph you have this relationship called + + + align:start position:0% +graph you have this relationship called +power law relationship that means + + align:start position:0% +power law relationship that means + + + align:start position:0% +power law relationship that means +there's exponential code there are some + + align:start position:0% +there's exponential code there are some + + + align:start position:0% +there's exponential code there are some +people here like very non well-known + + align:start position:0% +people here like very non well-known + + + align:start position:0% +people here like very non well-known +celebrities that that might have + + align:start position:0% +celebrities that that might have + + + align:start position:0% +celebrities that that might have +millions and millions of users in here + + align:start position:0% +millions and millions of users in here + + + align:start position:0% +millions and millions of users in here +connector connections in the neighbors + + align:start position:0% +connector connections in the neighbors + + + align:start position:0% +connector connections in the neighbors +so like so whatever it is in that node + + align:start position:0% +so like so whatever it is in that node + + + align:start position:0% +so like so whatever it is in that node +and there are people like me sitting + + align:start position:0% +and there are people like me sitting + + + align:start position:0% +and there are people like me sitting +here that has very little people + + align:start position:0% +here that has very little people + + + align:start position:0% +here that has very little people +connected to the rest of the world so + + align:start position:0% +connected to the rest of the world so + + + align:start position:0% +connected to the rest of the world so +this is normally people have observed + + align:start position:0% +this is normally people have observed + + + align:start position:0% +this is normally people have observed +this big social networks type graphs you + + align:start position:0% +this big social networks type graphs you + + + align:start position:0% +this big social networks type graphs you +have this kind of exponential + + align:start position:0% +have this kind of exponential + + + align:start position:0% +have this kind of exponential +relationship in here so web has + + align:start position:0% +relationship in here so web has + + + align:start position:0% +relationship in here so web has +exponential relationship a social + + align:start position:0% +exponential relationship a social + + + align:start position:0% +exponential relationship a social +network has this kind of relationship in + + align:start position:0% +network has this kind of relationship in + + + align:start position:0% +network has this kind of relationship in +there + + align:start position:0% +there + + + align:start position:0% +there +so those things you have to do very + + align:start position:0% +so those things you have to do very + + + align:start position:0% +so those things you have to do very +interesting thing when you process these + + align:start position:0% +interesting thing when you process these + + + align:start position:0% +interesting thing when you process these +graphs because there are certain + + align:start position:0% +graphs because there are certain + + + align:start position:0% +graphs because there are certain +connections that matter certain nodes + + align:start position:0% +connections that matter certain nodes + + + align:start position:0% +connections that matter certain nodes +that matter a lot as a big impact than + + align:start position:0% +that matter a lot as a big impact than + + + align:start position:0% +that matter a lot as a big impact than +other nodes then there are other graphs + + align:start position:0% +other nodes then there are other graphs + + + align:start position:0% +other nodes then there are other graphs +that are have a bounded degree + + align:start position:0% +that are have a bounded degree + + + align:start position:0% +that are have a bounded degree +distribution road networks the maximum + + align:start position:0% +distribution road networks the maximum + + + align:start position:0% +distribution road networks the maximum +connection probably you might have a + + align:start position:0% +connection probably you might have a + + + align:start position:0% +connection probably you might have a +intersection that has six roads coming + + align:start position:0% +intersection that has six roads coming + + + align:start position:0% +intersection that has six roads coming +together in there you don't have million + + align:start position:0% +together in there you don't have million + + + align:start position:0% +together in there you don't have million +roads connecting into one place anyway + + align:start position:0% +roads connecting into one place anyway + + + align:start position:0% +roads connecting into one place anyway +in there so that doesn't happen so this + + align:start position:0% +in there so that doesn't happen so this + + + align:start position:0% +in there so that doesn't happen so this +is lot more flatter lot more bounded + + align:start position:0% +is lot more flatter lot more bounded + + + align:start position:0% +is lot more flatter lot more bounded +degree distribution graphs in here they + + align:start position:0% +degree distribution graphs in here they + + + align:start position:0% +degree distribution graphs in here they +have lot of excellent locality near + + align:start position:0% +have lot of excellent locality near + + + align:start position:0% +have lot of excellent locality near +because of course all the crowds in in + + align:start position:0% +because of course all the crowds in in + + + align:start position:0% +because of course all the crowds in in +Cambridge might be connected but roads + + align:start position:0% +Cambridge might be connected but roads + + + align:start position:0% +Cambridge might be connected but roads +in Cambridge can be separated from roads + + align:start position:0% +in Cambridge can be separated from roads + + + align:start position:0% +in Cambridge can be separated from roads +in New York City so they are they are + + align:start position:0% +in New York City so they are they are + + + align:start position:0% +in New York City so they are they are +separate they are locality nice luck + + align:start position:0% +separate they are locality nice luck + + + align:start position:0% +separate they are locality nice luck +writing these kind of graphs so even if + + align:start position:0% +writing these kind of graphs so even if + + + align:start position:0% +writing these kind of graphs so even if +you say the graph is the same size the + + align:start position:0% +you say the graph is the same size the + + + align:start position:0% +you say the graph is the same size the +shape of the graph matters in + + align:start position:0% +shape of the graph matters in + + + align:start position:0% +shape of the graph matters in +computation a lot of times so what + + align:start position:0% +computation a lot of times so what + + + align:start position:0% +computation a lot of times so what +happens is now when you want to operate + + align:start position:0% +happens is now when you want to operate + + + align:start position:0% +happens is now when you want to operate +on this graph you have to look at three + + align:start position:0% +on this graph you have to look at three + + + align:start position:0% +on this graph you have to look at three +interesting properties one property is + + align:start position:0% +interesting properties one property is + + + align:start position:0% +interesting properties one property is +okay how much parallelism my algorithm + + align:start position:0% +okay how much parallelism my algorithm + + + align:start position:0% +okay how much parallelism my algorithm +what I trying to do to this graph is + + align:start position:0% +what I trying to do to this graph is + + + align:start position:0% +what I trying to do to this graph is +going to get it's like a Goldilocks type + + align:start position:0% +going to get it's like a Goldilocks type + + + align:start position:0% +going to get it's like a Goldilocks type +thing you don't want too much + + align:start position:0% +thing you don't want too much + + + align:start position:0% +thing you don't want too much +parallelism if you say I have algorithm + + align:start position:0% +parallelism if you say I have algorithm + + + align:start position:0% +parallelism if you say I have algorithm +that huge you want to parallelism if I + + align:start position:0% +that huge you want to parallelism if I + + + align:start position:0% +that huge you want to parallelism if I +can't take at + + align:start position:0% +can't take at + + + align:start position:0% +can't take at +is not useful so you need to get a + + align:start position:0% +is not useful so you need to get a + + + align:start position:0% +is not useful so you need to get a +parallel some good enough that I can + + align:start position:0% +parallel some good enough that I can + + + align:start position:0% +parallel some good enough that I can +actually use it then I really like to + + align:start position:0% +actually use it then I really like to + + + align:start position:0% +actually use it then I really like to +have locality because if I have locality + + align:start position:0% +have locality because if I have locality + + + align:start position:0% +have locality because if I have locality +if my caches will work everything will + + align:start position:0% +if my caches will work everything will + + + align:start position:0% +if my caches will work everything will +be nearby I can get runs things fast if + + align:start position:0% +be nearby I can get runs things fast if + + + align:start position:0% +be nearby I can get runs things fast if +I everytime I have to get something from + + align:start position:0% +I everytime I have to get something from + + + align:start position:0% +I everytime I have to get something from +main memory it can be very very slow so + + align:start position:0% +main memory it can be very very slow so + + + align:start position:0% +main memory it can be very very slow so +I want to get locality but interesting + + align:start position:0% +I want to get locality but interesting + + + align:start position:0% +I want to get locality but interesting +thing about graphs is to get localities + + align:start position:0% +thing about graphs is to get localities + + + align:start position:0% +thing about graphs is to get localities +and get some of these you might have do + + align:start position:0% +and get some of these you might have do + + + align:start position:0% +and get some of these you might have do +some extra work so if you saw that graph + + align:start position:0% +some extra work so if you saw that graph + + + align:start position:0% +some extra work so if you saw that graph +got divided into two different graphs I + + align:start position:0% +got divided into two different graphs I + + + align:start position:0% +got divided into two different graphs I +had extra nodes in here I might write + + align:start position:0% +had extra nodes in here I might write + + + align:start position:0% +had extra nodes in here I might write +some extra data structure so do some + + align:start position:0% +some extra data structure so do some + + + align:start position:0% +some extra data structure so do some +extra computation so I might have to do + + align:start position:0% +extra computation so I might have to do + + + align:start position:0% +extra computation so I might have to do +some extra work in here so in certain + + align:start position:0% +some extra work in here so in certain + + + align:start position:0% +some extra work in here so in certain +things I might not be that work + + align:start position:0% +things I might not be that work + + + align:start position:0% +things I might not be that work +efficient so I might I might get really + + align:start position:0% +efficient so I might I might get really + + + align:start position:0% +efficient so I might I might get really +good parallelism locality but I am doing + + align:start position:0% +good parallelism locality but I am doing + + + align:start position:0% +good parallelism locality but I am doing +too much work so for example if I want + + align:start position:0% +too much work so for example if I want + + + align:start position:0% +too much work so for example if I want +to assume I want to find one nodes + + align:start position:0% +to assume I want to find one nodes + + + align:start position:0% +to assume I want to find one nodes +neighbor very where to get good parents + + align:start position:0% +neighbor very where to get good parents + + + align:start position:0% +neighbor very where to get good parents +my everybody finds their neighbor ok but + + align:start position:0% +my everybody finds their neighbor ok but + + + align:start position:0% +my everybody finds their neighbor ok but +that's not efficient I mean most of the + + align:start position:0% +that's not efficient I mean most of the + + + align:start position:0% +that's not efficient I mean most of the +computation not useful so so there you + + align:start position:0% +computation not useful so so there you + + + align:start position:0% +computation not useful so so there you +can do things that you are doing extra + + align:start position:0% +can do things that you are doing extra + + + align:start position:0% +can do things that you are doing extra +work than necessary then that can get + + align:start position:0% +work than necessary then that can get + + + align:start position:0% +work than necessary then that can get +much faster other things but but but you + + align:start position:0% +much faster other things but but but you + + + align:start position:0% +much faster other things but but but you +have to be careful on doing that so you + + align:start position:0% +have to be careful on doing that so you + + + align:start position:0% +have to be careful on doing that so you +have this balance in there so certain + + align:start position:0% +have this balance in there so certain + + + align:start position:0% +have this balance in there so certain +algorithms will fit in different place + + align:start position:0% +algorithms will fit in different place + + + align:start position:0% +algorithms will fit in different place +in here in this trade-off space so push + + align:start position:0% +in here in this trade-off space so push + + + align:start position:0% +in here in this trade-off space so push +out with them will fit in here so for + + align:start position:0% +out with them will fit in here so for + + + align:start position:0% +out with them will fit in here so for +example if you go to something like a + + align:start position:0% +example if you go to something like a + + + align:start position:0% +example if you go to something like a +pull algorithm what you might find is + + align:start position:0% +pull algorithm what you might find is + + + align:start position:0% +pull algorithm what you might find is +you are doing less work efficient + + align:start position:0% +you are doing less work efficient + + + align:start position:0% +you are doing less work efficient +because you might do a little bit more + + align:start position:0% +because you might do a little bit more + + + align:start position:0% +because you might do a little bit more +work but it might be better in locality + + align:start position:0% +work but it might be better in locality + + + align:start position:0% +work but it might be better in locality +and and parallelism because you don't + + align:start position:0% +and and parallelism because you don't + + + align:start position:0% +and and parallelism because you don't +have do locks in here and then you do + + align:start position:0% +have do locks in here and then you do + + + align:start position:0% +have do locks in here and then you do +something like partitioning it gets + + align:start position:0% +something like partitioning it gets + + + align:start position:0% +something like partitioning it gets +really good locality in partitioning but + + align:start position:0% +really good locality in partitioning but + + + align:start position:0% +really good locality in partitioning but +you are doing extra work and also + + align:start position:0% +you are doing extra work and also + + + align:start position:0% +you are doing extra work and also +because when you're partying you might + + align:start position:0% +because when you're partying you might + + + align:start position:0% +because when you're partying you might +limit your parallelism in here so you + + align:start position:0% +limit your parallelism in here so you + + + align:start position:0% +limit your parallelism in here so you +might less parallelism but you get + + align:start position:0% +might less parallelism but you get + + + align:start position:0% +might less parallelism but you get +really good locality so all this is + + align:start position:0% +really good locality so all this is + + + align:start position:0% +really good locality so all this is +basically a large trade off space in + + align:start position:0% +basically a large trade off space in + + + align:start position:0% +basically a large trade off space in +here and then if when you keep adding + + align:start position:0% +here and then if when you keep adding + + + align:start position:0% +here and then if when you keep adding +more and more things you can do it fits + + align:start position:0% +more and more things you can do it fits + + + align:start position:0% +more and more things you can do it fits +into this this big trade of space so how + + align:start position:0% +into this this big trade of space so how + + + align:start position:0% +into this this big trade of space so how +do you decide what to go on the trade + + align:start position:0% +do you decide what to go on the trade + + + align:start position:0% +do you decide what to go on the trade +off space is a very important thing + + align:start position:0% +off space is a very important thing + + + align:start position:0% +off space is a very important thing +decision so it depends on the graphs if + + align:start position:0% +decision so it depends on the graphs if + + + align:start position:0% +decision so it depends on the graphs if +you have power log graph so you might + + align:start position:0% +you have power log graph so you might + + + align:start position:0% +you have power log graph so you might +want to do something if you have a + + align:start position:0% +want to do something if you have a + + + align:start position:0% +want to do something if you have a +more limited distributed graph you want + + align:start position:0% +more limited distributed graph you want + + + align:start position:0% +more limited distributed graph you want +do something else + + align:start position:0% +do something else + + + align:start position:0% +do something else +and the power of graph sometimes you + + align:start position:0% +and the power of graph sometimes you + + + align:start position:0% +and the power of graph sometimes you +might do something different for the + + align:start position:0% +might do something different for the + + + align:start position:0% +might do something different for the +high connected edges versus others you + + align:start position:0% +high connected edges versus others you + + + align:start position:0% +high connected edges versus others you +might don't even differentiate between + + align:start position:0% +might don't even differentiate between + + + align:start position:0% +might don't even differentiate between +that it depends algorithm so if you are + + align:start position:0% +that it depends algorithm so if you are + + + align:start position:0% +that it depends algorithm so if you are +doing will be sitting all the nodes + + align:start position:0% +doing will be sitting all the nodes + + + align:start position:0% +doing will be sitting all the nodes +versus a data-driven algorithm you might + + align:start position:0% +versus a data-driven algorithm you might + + + align:start position:0% +versus a data-driven algorithm you might +do something different it also different + + align:start position:0% +do something different it also different + + + align:start position:0% +do something different it also different +hardware you're running so for example + + align:start position:0% +hardware you're running so for example + + + align:start position:0% +hardware you're running so for example +if you are doing a Google search + + align:start position:0% +if you are doing a Google search + + + align:start position:0% +if you are doing a Google search +basically indexing you are running + + align:start position:0% +basically indexing you are running + + + align:start position:0% +basically indexing you are running +algorithm that has to operate of the + + align:start position:0% +algorithm that has to operate of the + + + align:start position:0% +algorithm that has to operate of the +entire graph in here and the graph is a + + align:start position:0% +entire graph in here and the graph is a + + + align:start position:0% +entire graph in here and the graph is a +power-law graphs in there and you're + + align:start position:0% +power-law graphs in there and you're + + + align:start position:0% +power-law graphs in there and you're +running on a cluster so the right thing + + align:start position:0% +running on a cluster so the right thing + + + align:start position:0% +running on a cluster so the right thing +might be something like a pull schedule + + align:start position:0% +might be something like a pull schedule + + + align:start position:0% +might be something like a pull schedule +with some partitioning and something + + align:start position:0% +with some partitioning and something + + + align:start position:0% +with some partitioning and something +like a vertex parallel or some kind of a + + align:start position:0% +like a vertex parallel or some kind of a + + + align:start position:0% +like a vertex parallel or some kind of a +parallelism scheme in here might give + + align:start position:0% +parallelism scheme in here might give + + + align:start position:0% +parallelism scheme in here might give +you the best performance but in the + + align:start position:0% +you the best performance but in the + + + align:start position:0% +you the best performance but in the +other side of the Google if you are + + align:start position:0% +other side of the Google if you are + + + align:start position:0% +other side of the Google if you are +trying to do a map and if you're trying + + align:start position:0% +trying to do a map and if you're trying + + + align:start position:0% +trying to do a map and if you're trying +to give you directions you have a very + + align:start position:0% +to give you directions you have a very + + + align:start position:0% +to give you directions you have a very +different type of a graph you are doing + + align:start position:0% +different type of a graph you are doing + + + align:start position:0% +different type of a graph you are doing +a data-driven algorithm in that graph + + align:start position:0% +a data-driven algorithm in that graph + + + align:start position:0% +a data-driven algorithm in that graph +and you might be running on a single + + align:start position:0% +and you might be running on a single + + + align:start position:0% +and you might be running on a single +machine because unity do direction fast + + align:start position:0% +machine because unity do direction fast + + + align:start position:0% +machine because unity do direction fast +for each individual time you might have + + align:start position:0% +for each individual time you might have + + + align:start position:0% +for each individual time you might have +a very different type of algorithm + + align:start position:0% +a very different type of algorithm + + + align:start position:0% +a very different type of algorithm +yonder on this graph the push out with a + + align:start position:0% +yonder on this graph the push out with a + + + align:start position:0% +yonder on this graph the push out with a +mean vertex parallel in the perhaps some + + align:start position:0% +mean vertex parallel in the perhaps some + + + align:start position:0% +mean vertex parallel in the perhaps some +combination in there and of course if + + align:start position:0% +combination in there and of course if + + + align:start position:0% +combination in there and of course if +you get a bad algorithm a bad set of way + + align:start position:0% +you get a bad algorithm a bad set of way + + + align:start position:0% +you get a bad algorithm a bad set of way +of doing it you can be very bad you can + + align:start position:0% +of doing it you can be very bad you can + + + align:start position:0% +of doing it you can be very bad you can +get hundreds of thousand times slower + + align:start position:0% +get hundreds of thousand times slower + + + align:start position:0% +get hundreds of thousand times slower +than the best you can achieve so it + + align:start position:0% +than the best you can achieve so it + + + align:start position:0% +than the best you can achieve so it +matters to find the right thing right + + align:start position:0% +matters to find the right thing right + + + align:start position:0% +matters to find the right thing right +way of doing thing so this is a graph it + + align:start position:0% +way of doing thing so this is a graph it + + + align:start position:0% +way of doing thing so this is a graph it +came in graphic as a domain-specific + + align:start position:0% +came in graphic as a domain-specific + + + align:start position:0% +came in graphic as a domain-specific +language base could be developed and one + + align:start position:0% +language base could be developed and one + + + align:start position:0% +language base could be developed and one +thing Rafa did was he said okay look the + + align:start position:0% +thing Rafa did was he said okay look the + + + align:start position:0% +thing Rafa did was he said okay look the +algorithm is mostly constant but how you + + align:start position:0% +algorithm is mostly constant but how you + + + align:start position:0% +algorithm is mostly constant but how you +process the how you go about it is very + + align:start position:0% +process the how you go about it is very + + + align:start position:0% +process the how you go about it is very +different so we won't separate these + + align:start position:0% +different so we won't separate these + + + align:start position:0% +different so we won't separate these +things so first thing we did was come up + + align:start position:0% +things so first thing we did was come up + + + align:start position:0% +things so first thing we did was come up +with algorithm is what do you want to + + align:start position:0% +with algorithm is what do you want to + + + align:start position:0% +with algorithm is what do you want to +compute it's very high level it don't + + align:start position:0% +compute it's very high level it don't + + + align:start position:0% +compute it's very high level it don't +tell you how we are computing that + + align:start position:0% +tell you how we are computing that + + + align:start position:0% +tell you how we are computing that +saying this is my algorithm I am going + + align:start position:0% +saying this is my algorithm I am going + + + align:start position:0% +saying this is my algorithm I am going +to process these nodes in this is the + + align:start position:0% +to process these nodes in this is the + + + align:start position:0% +to process these nodes in this is the +computation I want to do in there + + align:start position:0% +computation I want to do in there + + + align:start position:0% +computation I want to do in there +and you separate it with optimization of + + align:start position:0% +and you separate it with optimization of + + + align:start position:0% +and you separate it with optimization of +schedule how to compute so it's a okay + + align:start position:0% +schedule how to compute so it's a okay + + + align:start position:0% +schedule how to compute so it's a okay +to do this algorithm you have to do a + + align:start position:0% +to do this algorithm you have to do a + + + align:start position:0% +to do this algorithm you have to do a +push schedule do this + + align:start position:0% +push schedule do this + + + align:start position:0% +push schedule do this +which separately and the nice thing is + + align:start position:0% +which separately and the nice thing is + + + align:start position:0% +which separately and the nice thing is +that is now deeper if the graph change + + align:start position:0% +that is now deeper if the graph change + + + align:start position:0% +that is now deeper if the graph change +or the is the machine change I can I can + + align:start position:0% +or the is the machine change I can I can + + + align:start position:0% +or the is the machine change I can I can +give you a different schedule in here so + + align:start position:0% +give you a different schedule in here so + + + align:start position:0% +give you a different schedule in here so +let me show you some examples first look + + align:start position:0% +let me show you some examples first look + + + align:start position:0% +let me show you some examples first look +at algorithm in here so we show three + + align:start position:0% +at algorithm in here so we show three + + + align:start position:0% +at algorithm in here so we show three +different types of things you won't do + + align:start position:0% +different types of things you won't do + + + align:start position:0% +different types of things you won't do +so you want to do the entire graph in + + align:start position:0% +so you want to do the entire graph in + + + align:start position:0% +so you want to do the entire graph in +here and have the data driven oh I might + + align:start position:0% +here and have the data driven oh I might + + + align:start position:0% +here and have the data driven oh I might +want to just were operating on the + + align:start position:0% +want to just were operating on the + + + align:start position:0% +want to just were operating on the +vertices in here so this one we happy + + align:start position:0% +vertices in here so this one we happy + + + align:start position:0% +vertices in here so this one we happy +the the language provide a very simple + + align:start position:0% +the the language provide a very simple + + + align:start position:0% +the the language provide a very simple +way of doing that like media this + + align:start position:0% +way of doing that like media this + + + align:start position:0% +way of doing that like media this +function saying if there are edges all + + align:start position:0% +function saying if there are edges all + + + align:start position:0% +function saying if there are edges all +the edges of the graph apply you can + + align:start position:0% +the edges of the graph apply you can + + + align:start position:0% +the edges of the graph apply you can +give a function that function takes the + + align:start position:0% +give a function that function takes the + + + align:start position:0% +give a function that function takes the +basically nodes and the edges basically + + align:start position:0% +basically nodes and the edges basically + + + align:start position:0% +basically nodes and the edges basically +it will basically carry out this + + align:start position:0% +it will basically carry out this + + + align:start position:0% +it will basically carry out this +computation very simple way of doing + + align:start position:0% +computation very simple way of doing + + + align:start position:0% +computation very simple way of doing +that so this is the representation so + + align:start position:0% +that so this is the representation so + + + align:start position:0% +that so this is the representation so +the nice thing the simplicity of + + align:start position:0% +the nice thing the simplicity of + + + align:start position:0% +the nice thing the simplicity of +programming now if I write it in C if + + align:start position:0% +programming now if I write it in C if + + + align:start position:0% +programming now if I write it in C if +you look like a big blob of ugly code in + + align:start position:0% +you look like a big blob of ugly code in + + + align:start position:0% +you look like a big blob of ugly code in +the domain-specific language all you're + + align:start position:0% +the domain-specific language all you're + + + align:start position:0% +the domain-specific language all you're +right is this makes life very simple oh + + align:start position:0% +right is this makes life very simple oh + + + align:start position:0% +right is this makes life very simple oh +if you're a data driven language I have + + align:start position:0% +if you're a data driven language I have + + + align:start position:0% +if you're a data driven language I have +to say okay I start with this set of + + align:start position:0% +to say okay I start with this set of + + + align:start position:0% +to say okay I start with this set of +vertices to compute him here and here + + align:start position:0% +vertices to compute him here and here + + + align:start position:0% +vertices to compute him here and here +are the vertices I'm going to in here + + align:start position:0% +are the vertices I'm going to in here + + + align:start position:0% +are the vertices I'm going to in here +the vertex sent here and then I do some + + align:start position:0% +the vertex sent here and then I do some + + + align:start position:0% +the vertex sent here and then I do some +filtering because I might not go visit + + align:start position:0% +filtering because I might not go visit + + + align:start position:0% +filtering because I might not go visit +everybody there are some filtering of + + align:start position:0% +everybody there are some filtering of + + + align:start position:0% +everybody there are some filtering of +what you can do and then once you figure + + align:start position:0% +what you can do and then once you figure + + + align:start position:0% +what you can do and then once you figure +out exactly the things you are computing + + align:start position:0% +out exactly the things you are computing + + + align:start position:0% +out exactly the things you are computing +gets a function to go and apply to that + + align:start position:0% +gets a function to go and apply to that + + + align:start position:0% +gets a function to go and apply to that +so I can give you some very nice way of + + align:start position:0% +so I can give you some very nice way of + + + align:start position:0% +so I can give you some very nice way of +basically subsets in my graph with + + align:start position:0% +basically subsets in my graph with + + + align:start position:0% +basically subsets in my graph with +certain properties see like those things + + align:start position:0% +certain properties see like those things + + + align:start position:0% +certain properties see like those things +and now go compute there and if you're + + align:start position:0% +and now go compute there and if you're + + + align:start position:0% +and now go compute there and if you're +only doing 40 sees say okay a for each + + align:start position:0% +only doing 40 sees say okay a for each + + + align:start position:0% +only doing 40 sees say okay a for each +vertices again I can filter saying this + + align:start position:0% +vertices again I can filter saying this + + + align:start position:0% +vertices again I can filter saying this +subset or something go to that + + align:start position:0% +subset or something go to that + + + align:start position:0% +subset or something go to that +computation so language-wise is very + + align:start position:0% +computation so language-wise is very + + + align:start position:0% +computation so language-wise is very +simple this is what all you have to do + + align:start position:0% +simple this is what all you have to do + + + align:start position:0% +simple this is what all you have to do +now if you look at page rank page rank + + align:start position:0% +now if you look at page rank page rank + + + align:start position:0% +now if you look at page rank page rank +has two interesting update functions + + align:start position:0% +has two interesting update functions + + + align:start position:0% +has two interesting update functions +what is one is updating going looking at + + align:start position:0% +what is one is updating going looking at + + + align:start position:0% +what is one is updating going looking at +edges so what it says is new rank I get + + align:start position:0% +edges so what it says is new rank I get + + + align:start position:0% +edges so what it says is new rank I get +the destination edge and it get updated + + align:start position:0% +the destination edge and it get updated + + + align:start position:0% +the destination edge and it get updated +using all the sausages in here this is + + align:start position:0% +using all the sausages in here this is + + + align:start position:0% +using all the sausages in here this is +the update function very simple update + + align:start position:0% +the update function very simple update + + + align:start position:0% +the update function very simple update +function and then once you do that for + + align:start position:0% +function and then once you do that for + + + align:start position:0% +function and then once you do that for +each basically vertex I go I do internal + + align:start position:0% +each basically vertex I go I do internal + + + align:start position:0% +each basically vertex I go I do internal +update I give these two functions and + + align:start position:0% +update I give these two functions and + + + align:start position:0% +update I give these two functions and +put them together into into driver and + + align:start position:0% +put them together into into driver and + + + align:start position:0% +put them together into into driver and +the driver says from this function from + + align:start position:0% +the driver says from this function from + + + align:start position:0% +the driver says from this function from +this function and I'm done okay so + + align:start position:0% +this function and I'm done okay so + + + align:start position:0% +this function and I'm done okay so +I can write this chord at higher level + + align:start position:0% +I can write this chord at higher level + + + align:start position:0% +I can write this chord at higher level +much simpler much nice a much more + + align:start position:0% +much simpler much nice a much more + + + align:start position:0% +much simpler much nice a much more +elegant way okay it's much easier to + + align:start position:0% +elegant way okay it's much easier to + + + align:start position:0% +elegant way okay it's much easier to +understand easier than even the simple + + align:start position:0% +understand easier than even the simple + + + align:start position:0% +understand easier than even the simple +C++ code to understand what's going on + + align:start position:0% +C++ code to understand what's going on + + + align:start position:0% +C++ code to understand what's going on +if you write it in this way so this is + + align:start position:0% +if you write it in this way so this is + + + align:start position:0% +if you write it in this way so this is +the first advantage of for + + align:start position:0% +the first advantage of for + + + align:start position:0% +the first advantage of for +domain-specific language I can do this + + align:start position:0% +domain-specific language I can do this + + + align:start position:0% +domain-specific language I can do this +then the next thing you can do is now I + + align:start position:0% +then the next thing you can do is now I + + + align:start position:0% +then the next thing you can do is now I +can come up with the schedule so + + align:start position:0% +can come up with the schedule so + + + align:start position:0% +can come up with the schedule so +schedule should be easy to use and it + + align:start position:0% +schedule should be easy to use and it + + + align:start position:0% +schedule should be easy to use and it +should be powerful enough I should be + + align:start position:0% +should be powerful enough I should be + + + align:start position:0% +should be powerful enough I should be +able to get the best speed a possible + + align:start position:0% +able to get the best speed a possible + + + align:start position:0% +able to get the best speed a possible +because I can tell you all the crazy + + align:start position:0% +because I can tell you all the crazy + + + align:start position:0% +because I can tell you all the crazy +things I can do to the code so here's my + + align:start position:0% +things I can do to the code so here's my + + + align:start position:0% +things I can do to the code so here's my +program here for page drag and so what I + + align:start position:0% +program here for page drag and so what I + + + align:start position:0% +program here for page drag and so what I +can do is for this algorithm I can + + align:start position:0% +can do is for this algorithm I can + + + align:start position:0% +can do is for this algorithm I can +provide this schedule in here + + align:start position:0% +provide this schedule in here + + + align:start position:0% +provide this schedule in here +and this schedule basically says okay + + align:start position:0% +and this schedule basically says okay + + + align:start position:0% +and this schedule basically says okay +look at this guy s1 I marked it in there + + align:start position:0% +look at this guy s1 I marked it in there + + + align:start position:0% +look at this guy s1 I marked it in there +in the file in there for s1 I do I want + + align:start position:0% +in the file in there for s1 I do I want + + + align:start position:0% +in the file in there for s1 I do I want +to do sparse push type computation this + + align:start position:0% +to do sparse push type computation this + + + align:start position:0% +to do sparse push type computation this +is how I want to process this one and + + align:start position:0% +is how I want to process this one and + + + align:start position:0% +is how I want to process this one and +then by looking at that I can generate a + + align:start position:0% +then by looking at that I can generate a + + + align:start position:0% +then by looking at that I can generate a +pseudo code that looks like this that + + align:start position:0% +pseudo code that looks like this that + + + align:start position:0% +pseudo code that looks like this that +basically first go through the source + + align:start position:0% +basically first go through the source + + + align:start position:0% +basically first go through the source +nodes because I am doing push from + + align:start position:0% +nodes because I am doing push from + + + align:start position:0% +nodes because I am doing push from +source to destination and then I'm going + + align:start position:0% +source to destination and then I'm going + + + align:start position:0% +source to destination and then I'm going +through all the destination nodes of + + align:start position:0% +through all the destination nodes of + + + align:start position:0% +through all the destination nodes of +that source and I'm going to actually go + + align:start position:0% +that source and I'm going to actually go + + + align:start position:0% +that source and I'm going to actually go +up update them so I can do this this + + align:start position:0% +up update them so I can do this this + + + align:start position:0% +up update them so I can do this this +very simple updating you know but this + + align:start position:0% +very simple updating you know but this + + + align:start position:0% +very simple updating you know but this +might not do get that performance I say + + align:start position:0% +might not do get that performance I say + + + align:start position:0% +might not do get that performance I say +ah I want to do this in parallel a + + align:start position:0% +ah I want to do this in parallel a + + + align:start position:0% +ah I want to do this in parallel a +parallelism I won't run this parallel + + align:start position:0% +parallelism I won't run this parallel + + + align:start position:0% +parallelism I won't run this parallel +and then when I do that it will + + align:start position:0% +and then when I do that it will + + + align:start position:0% +and then when I do that it will +automatically generate say now I will + + align:start position:0% +automatically generate say now I will + + + align:start position:0% +automatically generate say now I will +make this two parallel and now I can't + + align:start position:0% +make this two parallel and now I can't + + + align:start position:0% +make this two parallel and now I can't +do a simple update I have two atomic add + + align:start position:0% +do a simple update I have two atomic add + + + align:start position:0% +do a simple update I have two atomic add +so here's my atomic add operation so the + + align:start position:0% +so here's my atomic add operation so the + + + align:start position:0% +so here's my atomic add operation so the +graph in here then you might think is + + align:start position:0% +graph in here then you might think is + + + align:start position:0% +graph in here then you might think is +that mm do I want to do the push can I + + align:start position:0% +that mm do I want to do the push can I + + + align:start position:0% +that mm do I want to do the push can I +do a pull so if I do a do a pull chain + + align:start position:0% +do a pull so if I do a do a pull chain + + + align:start position:0% +do a pull so if I do a do a pull chain +it will basically switch the know in + + align:start position:0% +it will basically switch the know in + + + align:start position:0% +it will basically switch the know in +here now I am going from destination to + + align:start position:0% +here now I am going from destination to + + + align:start position:0% +here now I am going from destination to +source I change the order in there and + + align:start position:0% +source I change the order in there and + + + align:start position:0% +source I change the order in there and +now I don't have to do that to make + + align:start position:0% +now I don't have to do that to make + + + align:start position:0% +now I don't have to do that to make +update because I am pulling everything + + align:start position:0% +update because I am pulling everything + + + align:start position:0% +update because I am pulling everything +to my know that updating and then of + + align:start position:0% +to my know that updating and then of + + + align:start position:0% +to my know that updating and then of +course if you want to do some kind of + + align:start position:0% +course if you want to do some kind of + + + align:start position:0% +course if you want to do some kind of +partitioning I can also say partitioning + + align:start position:0% +partitioning I can also say partitioning + + + align:start position:0% +partitioning I can also say partitioning +its now it appeared a subgraph in here + + align:start position:0% +its now it appeared a subgraph in here + + + align:start position:0% +its now it appeared a subgraph in here +and for the subgraph I am doing this + + align:start position:0% +and for the subgraph I am doing this + + + align:start position:0% +and for the subgraph I am doing this +partition so I can keep changing all + + align:start position:0% +partition so I can keep changing all + + + align:start position:0% +partition so I can keep changing all +these things look I didn't touch this my + + align:start position:0% +these things look I didn't touch this my + + + align:start position:0% +these things look I didn't touch this my +algorithm still says same I'm changing + + align:start position:0% +algorithm still says same I'm changing + + + align:start position:0% +algorithm still says same I'm changing +my my scheduling I can play with the + + align:start position:0% +my my scheduling I can play with the + + + align:start position:0% +my my scheduling I can play with the +schedule nice thing about that is now if + + align:start position:0% +schedule nice thing about that is now if + + + align:start position:0% +schedule nice thing about that is now if +you keep playing in the schedule + + align:start position:0% +you keep playing in the schedule + + + align:start position:0% +you keep playing in the schedule +here's the kind of performance like the + + align:start position:0% +here's the kind of performance like the + + + align:start position:0% +here's the kind of performance like the +first guy was sequential pretty bad + + align:start position:0% +first guy was sequential pretty bad + + + align:start position:0% +first guy was sequential pretty bad +performance the next guy just paralyzed + + align:start position:0% +performance the next guy just paralyzed + + + align:start position:0% +performance the next guy just paralyzed +in here I got some performance in in + + align:start position:0% +in here I got some performance in in + + + align:start position:0% +in here I got some performance in in +here but but it had all the + + align:start position:0% +here but but it had all the + + + align:start position:0% +here but but it had all the +synchronization so I changed the order + + align:start position:0% +synchronization so I changed the order + + + align:start position:0% +synchronization so I changed the order +of execution and I got another even + + align:start position:0% +of execution and I got another even + + + align:start position:0% +of execution and I got another even +better performance and now I partitioned + + align:start position:0% +better performance and now I partitioned + + + align:start position:0% +better performance and now I partitioned +got motor performance so this is the + + align:start position:0% +got motor performance so this is the + + + align:start position:0% +got motor performance so this is the +four order of the in doing that but of + + align:start position:0% +four order of the in doing that but of + + + align:start position:0% +four order of the in doing that but of +course you can play with many many + + align:start position:0% +course you can play with many many + + + align:start position:0% +course you can play with many many +different combinations and what graph it + + align:start position:0% +different combinations and what graph it + + + align:start position:0% +different combinations and what graph it +has is huge number of different + + align:start position:0% +has is huge number of different + + + align:start position:0% +has is huge number of different +combinations you can play with so there + + align:start position:0% +combinations you can play with so there + + + align:start position:0% +combinations you can play with so there +are a lot of different optimizations you + + align:start position:0% +are a lot of different optimizations you + + + align:start position:0% +are a lot of different optimizations you +can do Direction optimisation push-pull + + align:start position:0% +can do Direction optimisation push-pull + + + align:start position:0% +can do Direction optimisation push-pull +doing this path then different + + align:start position:0% +doing this path then different + + + align:start position:0% +doing this path then different +paralyzation cache new optimization and + + align:start position:0% +paralyzation cache new optimization and + + + align:start position:0% +paralyzation cache new optimization and +also data layout things like structures + + align:start position:0% +also data layout things like structures + + + align:start position:0% +also data layout things like structures +of arrays array of structure layout + + align:start position:0% +of arrays array of structure layout + + + align:start position:0% +of arrays array of structure layout +additional data structures that simplify + + align:start position:0% +additional data structures that simplify + + + align:start position:0% +additional data structures that simplify +computed all these things I can specify + + align:start position:0% +computed all these things I can specify + + + align:start position:0% +computed all these things I can specify +in here and then you can play with it's + + align:start position:0% +in here and then you can play with it's + + + align:start position:0% +in here and then you can play with it's +not clear which one means it depends on + + align:start position:0% +not clear which one means it depends on + + + align:start position:0% +not clear which one means it depends on +the algorithm depending on the graph + + align:start position:0% +the algorithm depending on the graph + + + align:start position:0% +the algorithm depending on the graph +shape graph size different machine you + + align:start position:0% +shape graph size different machine you + + + align:start position:0% +shape graph size different machine you +run so most of the time if you are a + + align:start position:0% +run so most of the time if you are a + + + align:start position:0% +run so most of the time if you are a +performance engineer you will be trying + + align:start position:0% +performance engineer you will be trying + + + align:start position:0% +performance engineer you will be trying +different things and look at the + + align:start position:0% +different things and look at the + + + align:start position:0% +different things and look at the +performance and say hey this doesn't get + + align:start position:0% +performance and say hey this doesn't get + + + align:start position:0% +performance and say hey this doesn't get +good cache behavior okay let me try + + align:start position:0% +good cache behavior okay let me try + + + align:start position:0% +good cache behavior okay let me try +differently so you won't iterate and + + align:start position:0% +differently so you won't iterate and + + + align:start position:0% +differently so you won't iterate and +these iterations you won't do fast and + + align:start position:0% +these iterations you won't do fast and + + + align:start position:0% +these iterations you won't do fast and +this will do that so let me tell you a + + align:start position:0% +this will do that so let me tell you a + + + align:start position:0% +this will do that so let me tell you a +little bit of results so this is a I had + + align:start position:0% +little bit of results so this is a I had + + + align:start position:0% +little bit of results so this is a I had +explained this is a little bit of a + + align:start position:0% +explained this is a little bit of a + + + align:start position:0% +explained this is a little bit of a +complicated graphic so what we looked at + + align:start position:0% +complicated graphic so what we looked at + + + align:start position:0% +complicated graphic so what we looked at +was run against bunch of different + + align:start position:0% +was run against bunch of different + + + align:start position:0% +was run against bunch of different +benchmarks a bunch of different + + align:start position:0% +benchmarks a bunch of different + + + align:start position:0% +benchmarks a bunch of different +frameworks that do graphs so what this + + align:start position:0% +frameworks that do graphs so what this + + + align:start position:0% +frameworks that do graphs so what this +says is here's a program PageRank + + align:start position:0% +says is here's a program PageRank + + + align:start position:0% +says is here's a program PageRank +run on a graph life journal graph in + + align:start position:0% +run on a graph life journal graph in + + + align:start position:0% +run on a graph life journal graph in +here one means it ran the fastest this + + align:start position:0% +here one means it ran the fastest this + + + align:start position:0% +here one means it ran the fastest this +ran about 8% slower this around 50% + + align:start position:0% +ran about 8% slower this around 50% + + + align:start position:0% +ran about 8% slower this around 50% +slower this ran 3x slower and 8x slower + + align:start position:0% +slower this ran 3x slower and 8x slower + + + align:start position:0% +slower this ran 3x slower and 8x slower +for that tough the interesting thing is + + align:start position:0% +for that tough the interesting thing is + + + align:start position:0% +for that tough the interesting thing is +as you add more different graphs if the + + align:start position:0% +as you add more different graphs if the + + + align:start position:0% +as you add more different graphs if the +performance changes so in fact even + + align:start position:0% +performance changes so in fact even + + + align:start position:0% +performance changes so in fact even +though we're and fastest for this rod + + align:start position:0% +though we're and fastest for this rod + + + align:start position:0% +though we're and fastest for this rod +graph it's a very different type of + + align:start position:0% +graph it's a very different type of + + + align:start position:0% +graph it's a very different type of +graph this framework R and provide the + + align:start position:0% +graph this framework R and provide the + + + align:start position:0% +graph this framework R and provide the +got the fastest result because the graph + + align:start position:0% +got the fastest result because the graph + + + align:start position:0% +got the fastest result because the graph +is different so it might be doing + + align:start position:0% +is different so it might be doing + + + align:start position:0% +is different so it might be doing +something that's better + + align:start position:0% +something that's better + + + align:start position:0% +something that's better +the interesting thing is since we have + + align:start position:0% +the interesting thing is since we have + + + align:start position:0% +the interesting thing is since we have +because most of other frameworks will + + align:start position:0% +because most of other frameworks will + + + align:start position:0% +because most of other frameworks will +have couple of built-in things they try + + align:start position:0% +have couple of built-in things they try + + + align:start position:0% +have couple of built-in things they try +they don't do give + + align:start position:0% +they don't do give + + + align:start position:0% +they don't do give +all this ability to try all these + + align:start position:0% +all this ability to try all these + + + align:start position:0% +all this ability to try all these +optimize and they say ha I know this + + align:start position:0% +optimize and they say ha I know this + + + align:start position:0% +optimize and they say ha I know this +this is really good I will do that + + align:start position:0% +this is really good I will do that + + + align:start position:0% +this is really good I will do that +it works for certain things not for + + align:start position:0% +it works for certain things not for + + + align:start position:0% +it works for certain things not for +everybody and so if you look at the + + align:start position:0% +everybody and so if you look at the + + + align:start position:0% +everybody and so if you look at the +entire different bread facade connected + + align:start position:0% +entire different bread facade connected + + + align:start position:0% +entire different bread facade connected +components shortest path algorithms what + + align:start position:0% +components shortest path algorithms what + + + align:start position:0% +components shortest path algorithms what +you find is is some frameworks are good + + align:start position:0% +you find is is some frameworks are good + + + align:start position:0% +you find is is some frameworks are good +sometimes they might be really bad in + + align:start position:0% +sometimes they might be really bad in + + + align:start position:0% +sometimes they might be really bad in +other times to either some algorithms + + align:start position:0% +other times to either some algorithms + + + align:start position:0% +other times to either some algorithms +from some type of data they can be + + align:start position:0% +from some type of data they can be + + + align:start position:0% +from some type of data they can be +really bad so this this algorithm was + + align:start position:0% +really bad so this this algorithm was + + + align:start position:0% +really bad so this this algorithm was +really kind of good at this data set but + + align:start position:0% +really kind of good at this data set but + + + align:start position:0% +really kind of good at this data set but +really bad than this data and really + + align:start position:0% +really bad than this data and really + + + align:start position:0% +really bad than this data and really +kind of not good in this algorithm we + + align:start position:0% +kind of not good in this algorithm we + + + align:start position:0% +kind of not good in this algorithm we +are most of the time good all the time + + align:start position:0% +are most of the time good all the time + + + align:start position:0% +are most of the time good all the time +the reason is we don't make decisions in + + align:start position:0% +the reason is we don't make decisions in + + + align:start position:0% +the reason is we don't make decisions in +in graph it what it will do is it will + + align:start position:0% +in graph it what it will do is it will + + + align:start position:0% +in graph it what it will do is it will +give you this ability to kind try + + align:start position:0% +give you this ability to kind try + + + align:start position:0% +give you this ability to kind try +different things and depending on the + + align:start position:0% +different things and depending on the + + + align:start position:0% +different things and depending on the +graph depending on the algorithm some + + align:start position:0% +graph depending on the algorithm some + + + align:start position:0% +graph depending on the algorithm some +optimizations might work better than the + + align:start position:0% +optimizations might work better than the + + + align:start position:0% +optimizations might work better than the +other this is what exactly what you guys + + align:start position:0% +other this is what exactly what you guys + + + align:start position:0% +other this is what exactly what you guys +have been doing in the class you are + + align:start position:0% +have been doing in the class you are + + + align:start position:0% +have been doing in the class you are +trying different optimizations by hand + + align:start position:0% +trying different optimizations by hand + + + align:start position:0% +trying different optimizations by hand +and the difference is every time you + + align:start position:0% +and the difference is every time you + + + align:start position:0% +and the difference is every time you +thought about optimizing you had to go + + align:start position:0% +thought about optimizing you had to go + + + align:start position:0% +thought about optimizing you had to go +change the entire program to make that + + align:start position:0% +change the entire program to make that + + + align:start position:0% +change the entire program to make that +work here you just change the scheduling + + align:start position:0% +work here you just change the scheduling + + + align:start position:0% +work here you just change the scheduling +language one write + + align:start position:0% +language one write + + + align:start position:0% +language one write +free compile run measure and you can do + + align:start position:0% +free compile run measure and you can do + + + align:start position:0% +free compile run measure and you can do +this fast any questions so far before I + + align:start position:0% +this fast any questions so far before I + + + align:start position:0% +this fast any questions so far before I +switch gears + + align:start position:0% + + + + align:start position:0% + +okay so I'm gonna switch to another + + align:start position:0% +okay so I'm gonna switch to another + + + align:start position:0% +okay so I'm gonna switch to another +domain-specific language you will find + + align:start position:0% +domain-specific language you will find + + + align:start position:0% +domain-specific language you will find +lot of similarity lot of parallels I + + align:start position:0% +lot of similarity lot of parallels I + + + align:start position:0% +lot of similarity lot of parallels I +mean near this was intentional I could + + align:start position:0% +mean near this was intentional I could + + + align:start position:0% +mean near this was intentional I could +have talked on many different + + align:start position:0% +have talked on many different + + + align:start position:0% +have talked on many different +domain-specific languages but I too took + + align:start position:0% +domain-specific languages but I too took + + + align:start position:0% +domain-specific languages but I too took +another one that you almost has kind of + + align:start position:0% +another one that you almost has kind of + + + align:start position:0% +another one that you almost has kind of +a mirror similarities of what's going on + + align:start position:0% +a mirror similarities of what's going on + + + align:start position:0% +a mirror similarities of what's going on +and you will see a pattern in team + + align:start position:0% +and you will see a pattern in team + + + align:start position:0% +and you will see a pattern in team +hopefully and after this I'll ask you + + align:start position:0% +hopefully and after this I'll ask you + + + align:start position:0% +hopefully and after this I'll ask you +what the patterns are this language is + + align:start position:0% +what the patterns are this language is + + + align:start position:0% +what the patterns are this language is +halide it was originally developed for + + align:start position:0% +halide it was originally developed for + + + align:start position:0% +halide it was originally developed for +image processing and it's focuses the + + align:start position:0% +image processing and it's focuses the + + + align:start position:0% +image processing and it's focuses the +grass focus on this past graph data + + align:start position:0% +grass focus on this past graph data + + + align:start position:0% +grass focus on this past graph data +structures here lights focused on + + align:start position:0% +structures here lights focused on + + + align:start position:0% +structures here lights focused on +because images are dense regular + + align:start position:0% +because images are dense regular + + + align:start position:0% +because images are dense regular +structures you do regular computation on + + align:start position:0% +structures you do regular computation on + + + align:start position:0% +structures you do regular computation on +the images and you process this thing + + align:start position:0% +the images and you process this thing + + + align:start position:0% +the images and you process this thing +and you have very complex pipeline like + + align:start position:0% +and you have very complex pipeline like + + + align:start position:0% +and you have very complex pipeline like +for example camera pipeline do many very + + align:start position:0% +for example camera pipeline do many very + + + align:start position:0% +for example camera pipeline do many very +complex algorithms to the image before + + align:start position:0% +complex algorithms to the image before + + + align:start position:0% +complex algorithms to the image before +you get from the bits coming out of your + + align:start position:0% +you get from the bits coming out of your + + + align:start position:0% +you get from the bits coming out of your +CCD to the the beautiful picture you see + + align:start position:0% +CCD to the the beautiful picture you see + + + align:start position:0% +CCD to the the beautiful picture you see +in Facebook and the primary coil of + + align:start position:0% +in Facebook and the primary coil of + + + align:start position:0% +in Facebook and the primary coil of +ferrite was you own match and exceed the + + align:start position:0% +ferrite was you own match and exceed the + + + align:start position:0% +ferrite was you own match and exceed the +hand optimize performance basically this + + align:start position:0% +hand optimize performance basically this + + + align:start position:0% +hand optimize performance basically this +was the pop art you wanna do and we want + + align:start position:0% +was the pop art you wanna do and we want + + + align:start position:0% +was the pop art you wanna do and we want +to reduce the road amount of programming + + align:start position:0% +to reduce the road amount of programming + + + align:start position:0% +to reduce the road amount of programming +that normally a performance engineer has + + align:start position:0% +that normally a performance engineer has + + + align:start position:0% +that normally a performance engineer has +to do to achieve this thing and we won't + + align:start position:0% +to do to achieve this thing and we won't + + + align:start position:0% +to do to achieve this thing and we won't +also increase the portability ability to + + align:start position:0% +also increase the portability ability to + + + align:start position:0% +also increase the portability ability to +take that program from different machine + + align:start position:0% +take that program from different machine + + + align:start position:0% +take that program from different machine +to difference so let me give you example + + align:start position:0% +to difference so let me give you example + + + align:start position:0% +to difference so let me give you example +here's a three by three blur example so + + align:start position:0% +here's a three by three blur example so + + + align:start position:0% +here's a three by three blur example so +what this does is this steal two loops + + align:start position:0% +what this does is this steal two loops + + + align:start position:0% +what this does is this steal two loops +go in the x-direction and do a blur in + + align:start position:0% +go in the x-direction and do a blur in + + + align:start position:0% +go in the x-direction and do a blur in +in in extreme direction get to get the + + align:start position:0% +in in extreme direction get to get the + + + align:start position:0% +in in extreme direction get to get the +average the three values next to each + + align:start position:0% +average the three values next to each + + + align:start position:0% +average the three values next to each +other and then it will go the result of + + align:start position:0% +other and then it will go the result of + + + align:start position:0% +other and then it will go the result of +that do it in my direction and average + + align:start position:0% +that do it in my direction and average + + + align:start position:0% +that do it in my direction and average +that okay very simple filter that you + + align:start position:0% +that okay very simple filter that you + + + align:start position:0% +that okay very simple filter that you +might want to do for image you can run + + align:start position:0% +might want to do for image you can run + + + align:start position:0% +might want to do for image you can run +this this is a valid C code but if you + + align:start position:0% +this this is a valid C code but if you + + + align:start position:0% +this this is a valid C code but if you +want to get performance you want to + + align:start position:0% +want to get performance you want to + + + align:start position:0% +want to get performance you want to +generate this guy this thing on the + + align:start position:0% +generate this guy this thing on the + + + align:start position:0% +generate this guy this thing on the +other hand Rand about 11 times faster + + align:start position:0% +other hand Rand about 11 times faster + + + align:start position:0% +other hand Rand about 11 times faster +than this one this has done tile it has + + align:start position:0% +than this one this has done tile it has + + + align:start position:0% +than this one this has done tile it has +fused multiple loops it has vectorize it + + align:start position:0% +fused multiple loops it has vectorize it + + + align:start position:0% +fused multiple loops it has vectorize it +has multi-threaded it turns into + + align:start position:0% +has multi-threaded it turns into + + + align:start position:0% +has multi-threaded it turns into +something + + align:start position:0% +something + + + align:start position:0% +something +and computation I'll get a little bit + + align:start position:0% +and computation I'll get a little bit + + + align:start position:0% +and computation I'll get a little bit +later and in basic needs a new roof line + + align:start position:0% +later and in basic needs a new roof line + + + align:start position:0% +later and in basic needs a new roof line +optimum performance that means it's + + align:start position:0% +optimum performance that means it's + + + align:start position:0% +optimum performance that means it's +using the machine resources to this max + + align:start position:0% +using the machine resources to this max + + + align:start position:0% +using the machine resources to this max +because this has bunch of floating-point + + align:start position:0% +because this has bunch of floating-point + + + align:start position:0% +because this has bunch of floating-point +operations + + align:start position:0% +operations + + + align:start position:0% +operations +so it's it's basically floating-point + + align:start position:0% +so it's it's basically floating-point + + + align:start position:0% +so it's it's basically floating-point +unit is running at the max performance + + align:start position:0% +unit is running at the max performance + + + align:start position:0% +unit is running at the max performance +so so that's nothing much else you could + + align:start position:0% +so so that's nothing much else you could + + + align:start position:0% +so so that's nothing much else you could +do to this one but you're right this + + align:start position:0% +do to this one but you're right this + + + align:start position:0% +do to this one but you're right this +thing and this is not that easy so this + + align:start position:0% +thing and this is not that easy so this + + + align:start position:0% +thing and this is not that easy so this +project started some time ago with one + + align:start position:0% +project started some time ago with one + + + align:start position:0% +project started some time ago with one +of my the person who did it going to he + + align:start position:0% +of my the person who did it going to he + + + align:start position:0% +of my the person who did it going to he +went to Adobe and they had this thing + + align:start position:0% +went to Adobe and they had this thing + + + align:start position:0% +went to Adobe and they had this thing +called a local laplacian filter in + + align:start position:0% +called a local laplacian filter in + + + align:start position:0% +called a local laplacian filter in +Camera Raw and Lightroom and Photoshop + + align:start position:0% +Camera Raw and Lightroom and Photoshop + + + align:start position:0% +Camera Raw and Lightroom and Photoshop +projects in here the reference + + align:start position:0% +projects in here the reference + + + align:start position:0% +projects in here the reference +implementation was about three hundred + + align:start position:0% +implementation was about three hundred + + + align:start position:0% +implementation was about three hundred +lines of code but implementation that + + align:start position:0% +lines of code but implementation that + + + align:start position:0% +lines of code but implementation that +they use was about thousand five hundred + + align:start position:0% +they use was about thousand five hundred + + + align:start position:0% +they use was about thousand five hundred +lines of code it took three months of + + align:start position:0% +lines of code it took three months of + + + align:start position:0% +lines of code it took three months of +one of their best engineers to get to + + align:start position:0% +one of their best engineers to get to + + + align:start position:0% +one of their best engineers to get to +that performance but it made sense + + align:start position:0% +that performance but it made sense + + + align:start position:0% +that performance but it made sense +because that give me I was able to get + + align:start position:0% +because that give me I was able to get + + + align:start position:0% +because that give me I was able to get +10x faster bite by trial and error for + + align:start position:0% +10x faster bite by trial and error for + + + align:start position:0% +10x faster bite by trial and error for +this piece of code it's a non-trivial + + align:start position:0% +this piece of code it's a non-trivial + + + align:start position:0% +this piece of code it's a non-trivial +piece of coding here and who could do + + align:start position:0% +piece of coding here and who could do + + + align:start position:0% +piece of coding here and who could do +that so the student Jonathan who's not + + align:start position:0% +that so the student Jonathan who's not + + + align:start position:0% +that so the student Jonathan who's not +professor at Berkeley he basically in + + align:start position:0% +professor at Berkeley he basically in + + + align:start position:0% +professor at Berkeley he basically in +one day in sixty line of a halide he was + + align:start position:0% +one day in sixty line of a halide he was + + + align:start position:0% +one day in sixty line of a halide he was +able to beat 2x of Adobe code name some + + align:start position:0% +able to beat 2x of Adobe code name some + + + align:start position:0% +able to beat 2x of Adobe code name some +sense then those days didn't generate + + align:start position:0% +sense then those days didn't generate + + + align:start position:0% +sense then those days didn't generate +any code for GPUs because they decided + + align:start position:0% +any code for GPUs because they decided + + + align:start position:0% +any code for GPUs because they decided +GPUs are change too fast and they can't + + align:start position:0% +GPUs are change too fast and they can't + + + align:start position:0% +GPUs are change too fast and they can't +keep up updating for GPUs in every + + align:start position:0% +keep up updating for GPUs in every + + + align:start position:0% +keep up updating for GPUs in every +generation then they because they + + align:start position:0% +generation then they because they + + + align:start position:0% +generation then they because they +because of that they were not the Adobe + + align:start position:0% +because of that they were not the Adobe + + + align:start position:0% +because of that they were not the Adobe +applications for not using GPU so I had + + align:start position:0% +applications for not using GPU so I had + + + align:start position:0% +applications for not using GPU so I had +Photoshop it's not going to use a GP + + align:start position:0% +Photoshop it's not going to use a GP + + + align:start position:0% +Photoshop it's not going to use a GP +when you imagine has a GPU so Jonathan + + align:start position:0% +when you imagine has a GPU so Jonathan + + + align:start position:0% +when you imagine has a GPU so Jonathan +still had some time left in the day so + + align:start position:0% +still had some time left in the day so + + + align:start position:0% +still had some time left in the day so +he said okay let me try to write on GPUs + + align:start position:0% +he said okay let me try to write on GPUs + + + align:start position:0% +he said okay let me try to write on GPUs +so he just basically the same code he + + align:start position:0% +so he just basically the same code he + + + align:start position:0% +so he just basically the same code he +changed GPUs and got + + align:start position:0% +changed GPUs and got + + + align:start position:0% +changed GPUs and got +9x faster faster than the faster player + + align:start position:0% +9x faster faster than the faster player + + + align:start position:0% +9x faster faster than the faster player +I will Adobe had ever had for this piece + + align:start position:0% +I will Adobe had ever had for this piece + + + align:start position:0% +I will Adobe had ever had for this piece +of thought so how do you do it again the + + align:start position:0% +of thought so how do you do it again the + + + align:start position:0% +of thought so how do you do it again the +key principle here is decoupling + + align:start position:0% +key principle here is decoupling + + + align:start position:0% +key principle here is decoupling +algorithm from schedule so algorithm + + align:start position:0% +algorithm from schedule so algorithm + + + align:start position:0% +algorithm from schedule so algorithm +again is what is computed and algorithm + + align:start position:0% +again is what is computed and algorithm + + + align:start position:0% +again is what is computed and algorithm +define the pipeline of very simple pure + + align:start position:0% +define the pipeline of very simple pure + + + align:start position:0% +define the pipeline of very simple pure +functions operating that in their + + align:start position:0% +functions operating that in their + + + align:start position:0% +functions operating that in their +execution order parallel sub all those + + align:start position:0% +execution order parallel sub all those + + + align:start position:0% +execution order parallel sub all those +things is left for the schedule the + + align:start position:0% +things is left for the schedule the + + + align:start position:0% +things is left for the schedule the +pipeline of halide just looks like this + + align:start position:0% +pipeline of halide just looks like this + + + align:start position:0% +pipeline of halide just looks like this +for the blur filter it says ok get the + + align:start position:0% +for the blur filter it says ok get the + + + align:start position:0% +for the blur filter it says ok get the +image in X dimension and and do it in + + align:start position:0% +image in X dimension and and do it in + + + align:start position:0% +image in X dimension and and do it in +the Y dimension that's all and the image + + align:start position:0% +the Y dimension that's all and the image + + + align:start position:0% +the Y dimension that's all and the image +size is because its operating on enter + + align:start position:0% +size is because its operating on enter + + + align:start position:0% +size is because its operating on enter +image you don't have loops in here + + align:start position:0% +image you don't have loops in here + + + align:start position:0% +image you don't have loops in here +that's all you are saying there then + + align:start position:0% +that's all you are saying there then + + + align:start position:0% +that's all you are saying there then +you'll copy the schedule again the same + + align:start position:0% +you'll copy the schedule again the same + + + align:start position:0% +you'll copy the schedule again the same +way when and where it's computed it to + + align:start position:0% +way when and where it's computed it to + + + align:start position:0% +way when and where it's computed it to +be simple that that you need to be able + + align:start position:0% +be simple that that you need to be able + + + align:start position:0% +be simple that that you need to be able +to say that and it has been powerful you + + align:start position:0% +to say that and it has been powerful you + + + align:start position:0% +to say that and it has been powerful you +need to be able to get the hand + + align:start position:0% +need to be able to get the hand + + + align:start position:0% +need to be able to get the hand +optimized performance or better by doing + + align:start position:0% +optimized performance or better by doing + + + align:start position:0% +optimized performance or better by doing +this something looks a little bit + + align:start position:0% +this something looks a little bit + + + align:start position:0% +this something looks a little bit +familiar because it's all these things a + + align:start position:0% +familiar because it's all these things a + + + align:start position:0% +familiar because it's all these things a +lot of work do you do performance kind + + align:start position:0% +lot of work do you do performance kind + + + align:start position:0% +lot of work do you do performance kind +of fit into these this genre you need to + + align:start position:0% +of fit into these this genre you need to + + + align:start position:0% +of fit into these this genre you need to +do a trade off between locality + + align:start position:0% +do a trade off between locality + + + align:start position:0% +do a trade off between locality +parallelism and redundant work that's + + align:start position:0% +parallelism and redundant work that's + + + align:start position:0% +parallelism and redundant work that's +what you look for in here so so let's + + align:start position:0% +what you look for in here so so let's + + + align:start position:0% +what you look for in here so so let's +look at the three things you need to do + + align:start position:0% +look at the three things you need to do + + + align:start position:0% +look at the three things you need to do +first you need to get parallelism + + align:start position:0% +first you need to get parallelism + + + align:start position:0% +first you need to get parallelism +parallelism is you need to keep the + + align:start position:0% +parallelism is you need to keep the + + + align:start position:0% +parallelism is you need to keep the +multi-core and vector units happy and + + align:start position:0% +multi-core and vector units happy and + + + align:start position:0% +multi-core and vector units happy and +probably the GPU BC but if you have too + + align:start position:0% +probably the GPU BC but if you have too + + + align:start position:0% +probably the GPU BC but if you have too +much parallelism it's not going to help + + align:start position:0% +much parallelism it's not going to help + + + align:start position:0% +much parallelism it's not going to help +you I means nobody is going to take + + align:start position:0% +you I means nobody is going to take + + + align:start position:0% +you I means nobody is going to take +advantage to pan parallelism so let's + + align:start position:0% +advantage to pan parallelism so let's + + + align:start position:0% +advantage to pan parallelism so let's +look at a piece of code in here so + + align:start position:0% +look at a piece of code in here so + + + align:start position:0% +look at a piece of code in here so +assume I have go and say I'm gonna run + + align:start position:0% +assume I have go and say I'm gonna run + + + align:start position:0% +assume I have go and say I'm gonna run +all these things parallel and all these + + align:start position:0% +all these things parallel and all these + + + align:start position:0% +all these things parallel and all these +things parallel afterwards if you have + + align:start position:0% +things parallel afterwards if you have + + + align:start position:0% +things parallel afterwards if you have +three cores great I got a lot more + + align:start position:0% +three cores great I got a lot more + + + align:start position:0% +three cores great I got a lot more +parallelism I got six times parallelism + + align:start position:0% +parallelism I got six times parallelism + + + align:start position:0% +parallelism I got six times parallelism +for are nobody's going to use that it's + + align:start position:0% +for are nobody's going to use that it's + + + align:start position:0% +for are nobody's going to use that it's +not that useful to get six times pedals + + align:start position:0% +not that useful to get six times pedals + + + align:start position:0% +not that useful to get six times pedals +I mean here on the other hand if you run + + align:start position:0% +I mean here on the other hand if you run + + + align:start position:0% +I mean here on the other hand if you run +like this one at a time you have + + align:start position:0% +like this one at a time you have + + + align:start position:0% +like this one at a time you have +parallelism of fun that's not that good + + align:start position:0% +parallelism of fun that's not that good + + + align:start position:0% +parallelism of fun that's not that good +because you are going to not be use the + + align:start position:0% +because you are going to not be use the + + + align:start position:0% +because you are going to not be use the +machine so what you really want is + + align:start position:0% +machine so what you really want is + + + align:start position:0% +machine so what you really want is +something basic + + align:start position:0% +something basic + + + align:start position:0% +something basic +it's done that actually do parallel sums + + align:start position:0% +it's done that actually do parallel sums + + + align:start position:0% +it's done that actually do parallel sums +of three might be the best way of + + align:start position:0% +of three might be the best way of + + + align:start position:0% +of three might be the best way of +running that machine to get to the get + + align:start position:0% +running that machine to get to the get + + + align:start position:0% +running that machine to get to the get +best performance you don't want too much + + align:start position:0% +best performance you don't want too much + + + align:start position:0% +best performance you don't want too much +you don't know + + align:start position:0% +you don't know + + + align:start position:0% +you don't know +too little you wanna get the exact right + + align:start position:0% +too little you wanna get the exact right + + + align:start position:0% +too little you wanna get the exact right +thing the next interesting thing you + + align:start position:0% +thing the next interesting thing you + + + align:start position:0% +thing the next interesting thing you +need to guess is locality normally when + + align:start position:0% +need to guess is locality normally when + + + align:start position:0% +need to guess is locality normally when +you image do image processing what you + + align:start position:0% +you image do image processing what you + + + align:start position:0% +you image do image processing what you +do is you do change everything in the + + align:start position:0% +do is you do change everything in the + + + align:start position:0% +do is you do change everything in the +image in one filter then the next + + align:start position:0% +image in one filter then the next + + + align:start position:0% +image in one filter then the next +filters go ahead and change everything + + align:start position:0% +filters go ahead and change everything + + + align:start position:0% +filters go ahead and change everything +in the image so what happens if I if one + + align:start position:0% +in the image so what happens if I if one + + + align:start position:0% +in the image so what happens if I if one +filter onto the entire image and the + + align:start position:0% +filter onto the entire image and the + + + align:start position:0% +filter onto the entire image and the +next filter come and start right into + + align:start position:0% +next filter come and start right into + + + align:start position:0% +next filter come and start right into +the entire image what happens basically + + align:start position:0% +the entire image what happens basically + + + align:start position:0% +the entire image what happens basically +is that good + + align:start position:0% +is that good + + + align:start position:0% +is that good +I give then time I'd say you do my first + + align:start position:0% +I give then time I'd say you do my first + + + align:start position:0% +I give then time I'd say you do my first +color correction and I will do some kind + + align:start position:0% +color correction and I will do some kind + + + align:start position:0% +color correction and I will do some kind +of chromatic aberration correction + + align:start position:0% +of chromatic aberration correction + + + align:start position:0% +of chromatic aberration correction +afterwards so what happens if you do + + align:start position:0% +afterwards so what happens if you do + + + align:start position:0% +afterwards so what happens if you do +something like that entire image process + + align:start position:0% +something like that entire image process + + + align:start position:0% +something like that entire image process +one filter then the next filter takes + + align:start position:0% +one filter then the next filter takes + + + align:start position:0% +one filter then the next filter takes +the image and process the entire you + + align:start position:0% +the image and process the entire you + + + align:start position:0% +the image and process the entire you +whatever multi megapixel image oh you + + align:start position:0% +whatever multi megapixel image oh you + + + align:start position:0% +whatever multi megapixel image oh you +know you're not change okay back there + + align:start position:0% +know you're not change okay back there + + + align:start position:0% +know you're not change okay back there +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +access the cache because if the images + + align:start position:0% +access the cache because if the images + + + align:start position:0% +access the cache because if the images +are large it doesn't fit in the cache + + align:start position:0% +are large it doesn't fit in the cache + + + align:start position:0% +are large it doesn't fit in the cache +it's not that great to do this this you + + align:start position:0% +it's not that great to do this this you + + + align:start position:0% +it's not that great to do this this you +won't get things in the cache in here so + + align:start position:0% +won't get things in the cache in here so + + + align:start position:0% +won't get things in the cache in here so +assume I go like this processing the + + align:start position:0% +assume I go like this processing the + + + align:start position:0% +assume I go like this processing the +entire first row before you go to the + + align:start position:0% +entire first row before you go to the + + + align:start position:0% +entire first row before you go to the +second row so what happens now here is + + align:start position:0% +second row so what happens now here is + + + align:start position:0% +second row so what happens now here is +we need to start touch this one I need + + align:start position:0% +we need to start touch this one I need + + + align:start position:0% +we need to start touch this one I need +to read these two values and those two + + align:start position:0% +to read these two values and those two + + + align:start position:0% +to read these two values and those two +are the last time I read them was where + + align:start position:0% +are the last time I read them was where + + + align:start position:0% +are the last time I read them was where +before I started so I stretch them I + + align:start position:0% +before I started so I stretch them I + + + align:start position:0% +before I started so I stretch them I +went through all the image and I come + + align:start position:0% +went through all the image and I come + + + align:start position:0% +went through all the image and I come +back to that this distance by the time I + + align:start position:0% +back to that this distance by the time I + + + align:start position:0% +back to that this distance by the time I +reach here I might these two might be + + align:start position:0% +reach here I might these two might be + + + align:start position:0% +reach here I might these two might be +out of the cache and when I go back + + align:start position:0% +out of the cache and when I go back + + + align:start position:0% +out of the cache and when I go back +there oops it's not in the cache I have + + align:start position:0% +there oops it's not in the cache I have + + + align:start position:0% +there oops it's not in the cache I have +a problem in that so the other way right + + align:start position:0% +a problem in that so the other way right + + + align:start position:0% +a problem in that so the other way right +way to do that might be on it this way + + align:start position:0% +way to do that might be on it this way + + + align:start position:0% +way to do that might be on it this way +you fire on it like this basically what + + align:start position:0% +you fire on it like this basically what + + + align:start position:0% +you fire on it like this basically what +happens is as you run when I touch this + + align:start position:0% +happens is as you run when I touch this + + + align:start position:0% +happens is as you run when I touch this +I won't have I want to get these three + + align:start position:0% +I won't have I want to get these three + + + align:start position:0% +I won't have I want to get these three +to run this thing last time I read this + + align:start position:0% +to run this thing last time I read this + + + align:start position:0% +to run this thing last time I read this +one was just before the in the previous + + align:start position:0% +one was just before the in the previous + + + align:start position:0% +one was just before the in the previous +iteration so to get to that I just + + align:start position:0% +iteration so to get to that I just + + + align:start position:0% +iteration so to get to that I just +touched it so the next guy uses it next + + align:start position:0% +touched it so the next guy uses it next + + + align:start position:0% +touched it so the next guy uses it next +guy and after after I go through that my + + align:start position:0% +guy and after after I go through that my + + + align:start position:0% +guy and after after I go through that my +window I will never touch that dang it I + + align:start position:0% +window I will never touch that dang it I + + + align:start position:0% +window I will never touch that dang it I +have a really good luck editing here so + + align:start position:0% +have a really good luck editing here so + + + align:start position:0% +have a really good luck editing here so +I won't operate it that way so I want to + + align:start position:0% +I won't operate it that way so I want to + + + align:start position:0% +I won't operate it that way so I want to +get good locality in here so redundant + + align:start position:0% +get good locality in here so redundant + + + align:start position:0% +get good locality in here so redundant +work is very interesting things + + align:start position:0% +work is very interesting things + + + align:start position:0% +work is very interesting things +sometimes if you want to get both + + align:start position:0% +sometimes if you want to get both + + + align:start position:0% +sometimes if you want to get both +locality and parallelism you might have + + align:start position:0% +locality and parallelism you might have + + + align:start position:0% +locality and parallelism you might have +to do some extra work a little bit of + + align:start position:0% +to do some extra work a little bit of + + + align:start position:0% +to do some extra work a little bit of +extra work so assume in this one I have + + align:start position:0% +extra work so assume in this one I have + + + align:start position:0% +extra work so assume in this one I have +to process these elements parallel if I + + align:start position:0% +to process these elements parallel if I + + + align:start position:0% +to process these elements parallel if I +want to run run these three because + + align:start position:0% +want to run run these three because + + + align:start position:0% +want to run run these three because +these three needs all these four + + align:start position:0% +these three needs all these four + + + align:start position:0% +these three needs all these four +elements in the list we need these four + + align:start position:0% +elements in the list we need these four + + + align:start position:0% +elements in the list we need these four +if I want to run these two parallel in + + align:start position:0% +if I want to run these two parallel in + + + align:start position:0% +if I want to run these two parallel in +two different course it might be better + + align:start position:0% +two different course it might be better + + + align:start position:0% +two different course it might be better +if both calculates these two values + + align:start position:0% +if both calculates these two values + + + align:start position:0% +if both calculates these two values +because I don't have to synchronize and + + align:start position:0% +because I don't have to synchronize and + + + align:start position:0% +because I don't have to synchronize and +stuff like I can say the left guy + + align:start position:0% +stuff like I can say the left guy + + + align:start position:0% +stuff like I can say the left guy +calculate four values and then I can do + + align:start position:0% +calculate four values and then I can do + + + align:start position:0% +calculate four values and then I can do +the three the right guy calculate the + + align:start position:0% +the three the right guy calculate the + + + align:start position:0% +the three the right guy calculate the +four values and then I can do the three + + align:start position:0% +four values and then I can do the three + + + align:start position:0% +four values and then I can do the three +I can do that thoroughly but now the + + align:start position:0% +I can do that thoroughly but now the + + + align:start position:0% +I can do that thoroughly but now the +middle two guys these to get calculated + + align:start position:0% +middle two guys these to get calculated + + + align:start position:0% +middle two guys these to get calculated +twice because both needs it and so what + + align:start position:0% +twice because both needs it and so what + + + align:start position:0% +twice because both needs it and so what +did that means is oops you can't keep + + align:start position:0% +did that means is oops you can't keep + + + align:start position:0% +did that means is oops you can't keep +that so you sometimes to do everything I + + align:start position:0% +that so you sometimes to do everything I + + + align:start position:0% +that so you sometimes to do everything I +might have to some redundant way so the + + align:start position:0% +might have to some redundant way so the + + + align:start position:0% +might have to some redundant way so the +look at that is I can put this into this + + align:start position:0% +look at that is I can put this into this + + + align:start position:0% +look at that is I can put this into this +scheduling framework + + align:start position:0% +scheduling framework + + + align:start position:0% +scheduling framework +I can make Matt by computation bandwidth + + align:start position:0% +I can make Matt by computation bandwidth + + + align:start position:0% +I can make Matt by computation bandwidth +that means cause interleaving with + + align:start position:0% +that means cause interleaving with + + + align:start position:0% +that means cause interleaving with +Lowell operator that means I finish + + align:start position:0% +Lowell operator that means I finish + + + align:start position:0% +Lowell operator that means I finish +everything before I go back again yeah + + align:start position:0% +everything before I go back again yeah + + + align:start position:0% +everything before I go back again yeah +between two things if I run two things I + + align:start position:0% +between two things if I run two things I + + + align:start position:0% +between two things if I run two things I +finish this one before I go to the next + + align:start position:0% +finish this one before I go to the next + + + align:start position:0% +finish this one before I go to the next +one + + align:start position:0% +one + + + align:start position:0% +one +fine interleaving means I process one + + align:start position:0% +fine interleaving means I process one + + + align:start position:0% +fine interleaving means I process one +element one that I go back and back and + + align:start position:0% +element one that I go back and back and + + + align:start position:0% +element one that I go back and back and +forth in here that's my two two options + + align:start position:0% +forth in here that's my two two options + + + align:start position:0% +forth in here that's my two two options +here other side is storage granularity + + align:start position:0% +here other side is storage granularity + + + align:start position:0% +here other side is storage granularity +what that means is storage generate very + + align:start position:0% +what that means is storage generate very + + + align:start position:0% +what that means is storage generate very +lower means I calculate something I + + align:start position:0% +lower means I calculate something I + + + align:start position:0% +lower means I calculate something I +don't remember next time I want it I + + align:start position:0% +don't remember next time I want it I + + + align:start position:0% +don't remember next time I want it I +recalculate it again very high strength + + align:start position:0% +recalculate it again very high strength + + + align:start position:0% +recalculate it again very high strength +generally means once I calculate I will + + align:start position:0% +generally means once I calculate I will + + + align:start position:0% +generally means once I calculate I will +remember it forever anytime you need + + align:start position:0% +remember it forever anytime you need + + + align:start position:0% +remember it forever anytime you need +that value I have it back for you so so + + align:start position:0% +that value I have it back for you so so + + + align:start position:0% +that value I have it back for you so so +that means I had to get it to you from + + align:start position:0% +that means I had to get it to you from + + + align:start position:0% +that means I had to get it to you from +anyway I calculated stroke and low means + + align:start position:0% +anyway I calculated stroke and low means + + + align:start position:0% +anyway I calculated stroke and low means +my process I calculate I use I throw it + + align:start position:0% +my process I calculate I use I throw it + + + align:start position:0% +my process I calculate I use I throw it +out if I need anybody else want it they + + align:start position:0% +out if I need anybody else want it they + + + align:start position:0% +out if I need anybody else want it they +are recalculate again so now you can + + align:start position:0% +are recalculate again so now you can + + + align:start position:0% +are recalculate again so now you can +have many different computations in + + align:start position:0% +have many different computations in + + + align:start position:0% +have many different computations in +different places of the space in here + + align:start position:0% +different places of the space in here + + + align:start position:0% +different places of the space in here +so if you want to compute somewhere here + + align:start position:0% +so if you want to compute somewhere here + + + align:start position:0% +so if you want to compute somewhere here +this is the schedule schedule in + + align:start position:0% +this is the schedule schedule in + + + align:start position:0% +this is the schedule schedule in +language that means I run this one and I + + align:start position:0% +language that means I run this one and I + + + align:start position:0% +language that means I run this one and I +run this one I have no redundant + + align:start position:0% +run this one I have no redundant + + + align:start position:0% +run this one I have no redundant +computation very cost gain interleaving + + align:start position:0% +computation very cost gain interleaving + + + align:start position:0% +computation very cost gain interleaving +okay that means I run the entire thing + + align:start position:0% +okay that means I run the entire thing + + + align:start position:0% +okay that means I run the entire thing +and done the next entire thing you can + + align:start position:0% +and done the next entire thing you can + + + align:start position:0% +and done the next entire thing you can +go very fine kerosene here I'll + + align:start position:0% +go very fine kerosene here I'll + + + align:start position:0% +go very fine kerosene here I'll +calculate this one and I'll calculate + + align:start position:0% +calculate this one and I'll calculate + + + align:start position:0% +calculate this one and I'll calculate +these three again these three again so + + align:start position:0% +these three again these three again so + + + align:start position:0% +these three again these three again so +the everything is calculated multiple + + align:start position:0% +the everything is calculated multiple + + + align:start position:0% +the everything is calculated multiple +times when you need it I recalculate + + align:start position:0% +times when you need it I recalculate + + + align:start position:0% +times when you need it I recalculate +every time I need something I don't + + align:start position:0% +every time I need something I don't + + + align:start position:0% +every time I need something I don't +store anything in here so it's good I + + align:start position:0% +store anything in here so it's good I + + + align:start position:0% +store anything in here so it's good I +have lot of locality but I am doing lot + + align:start position:0% +have lot of locality but I am doing lot + + + align:start position:0% +have lot of locality but I am doing lot +of recomputation and then here you have + + align:start position:0% +of recomputation and then here you have + + + align:start position:0% +of recomputation and then here you have +something like a sliding window + + align:start position:0% +something like a sliding window + + + align:start position:0% +something like a sliding window +basically you you are not recalculating + + align:start position:0% +basically you you are not recalculating + + + align:start position:0% +basically you you are not recalculating +anything but you are sliding in there + + align:start position:0% +anything but you are sliding in there + + + align:start position:0% +anything but you are sliding in there +you have little bit less parallelism and + + align:start position:0% +you have little bit less parallelism and + + + align:start position:0% +you have little bit less parallelism and +then you can't capture this entire + + align:start position:0% +then you can't capture this entire + + + align:start position:0% +then you can't capture this entire +spectrum in between in here and and you + + align:start position:0% +spectrum in between in here and and you + + + align:start position:0% +spectrum in between in here and and you +can get different levels of fusion of + + align:start position:0% +can get different levels of fusion of + + + align:start position:0% +can get different levels of fusion of +these tiles and you can calculate so I + + align:start position:0% +these tiles and you can calculate so I + + + align:start position:0% +these tiles and you can calculate so I +don't help recalculate everything I + + align:start position:0% +don't help recalculate everything I + + + align:start position:0% +don't help recalculate everything I +carefully calculate few things in here + + align:start position:0% +carefully calculate few things in here + + + align:start position:0% +carefully calculate few things in here +these to get recalculated + + align:start position:0% + + + + align:start position:0% + +and then you can I'll go to this fast in + + align:start position:0% +and then you can I'll go to this fast in + + + align:start position:0% +and then you can I'll go to this fast in +some sense you can these all these + + align:start position:0% +some sense you can these all these + + + align:start position:0% +some sense you can these all these +operations so here's interesting thing + + align:start position:0% +operations so here's interesting thing + + + align:start position:0% +operations so here's interesting thing +so here's I'm showing you different + + align:start position:0% +so here's I'm showing you different + + + align:start position:0% +so here's I'm showing you different +schedules at different points in here so + + align:start position:0% +schedules at different points in here so + + + align:start position:0% +schedules at different points in here so +I'm going to run this game this is on + + align:start position:0% +I'm going to run this game this is on + + + align:start position:0% +I'm going to run this game this is on +time so what it says is this is two in + + align:start position:0% +time so what it says is this is two in + + + align:start position:0% +time so what it says is this is two in +the you're going through the first same + + align:start position:0% +the you're going through the first same + + + align:start position:0% +the you're going through the first same +put ink in the middle one kind output in + + align:start position:0% +put ink in the middle one kind output in + + + align:start position:0% +put ink in the middle one kind output in +here so this is all locality lot of + + align:start position:0% +here so this is all locality lot of + + + align:start position:0% +here so this is all locality lot of +redundant work good Patterson locality + + align:start position:0% +redundant work good Patterson locality + + + align:start position:0% +redundant work good Patterson locality +all parents have not good look at it + + align:start position:0% +all parents have not good look at it + + + align:start position:0% +all parents have not good look at it +here's some kind of intermediate things + + align:start position:0% +here's some kind of intermediate things + + + align:start position:0% +here's some kind of intermediate things +so what it shows is these are no good a + + align:start position:0% +so what it shows is these are no good a + + + align:start position:0% +so what it shows is these are no good a +good balance between locality file some + + align:start position:0% +good balance between locality file some + + + align:start position:0% +good balance between locality file some +redundant work seem to do really well + + align:start position:0% +redundant work seem to do really well + + + align:start position:0% +redundant work seem to do really well +this can finish the fastest so what you + + align:start position:0% +this can finish the fastest so what you + + + align:start position:0% +this can finish the fastest so what you +do is to write different schedules for + + align:start position:0% +do is to write different schedules for + + + align:start position:0% +do is to write different schedules for +these things and then you keep running + + align:start position:0% +these things and then you keep running + + + align:start position:0% +these things and then you keep running +and we figured out what schedule works + + align:start position:0% +and we figured out what schedule works + + + align:start position:0% +and we figured out what schedule works +so this is kind of trial and error part + + align:start position:0% +so this is kind of trial and error part + + + align:start position:0% +so this is kind of trial and error part +you're dear to do in here + + align:start position:0% + + + + align:start position:0% + +so if you look at what's going on in + + align:start position:0% +so if you look at what's going on in + + + align:start position:0% +so if you look at what's going on in +here what you see here is the some + + align:start position:0% +here what you see here is the some + + + align:start position:0% +here what you see here is the some +example is bilateral filter computation + + align:start position:0% +example is bilateral filter computation + + + align:start position:0% +example is bilateral filter computation +here what it says the original is about + + align:start position:0% +here what it says the original is about + + + align:start position:0% +here what it says the original is about +102 lines of C++ code and you found + + align:start position:0% +102 lines of C++ code and you found + + + align:start position:0% +102 lines of C++ code and you found +something with good parallelism in here + + align:start position:0% +something with good parallelism in here + + + align:start position:0% +something with good parallelism in here +but we could write it inside two lights + + align:start position:0% +but we could write it inside two lights + + + align:start position:0% +but we could write it inside two lights +of halide in here and we were able to + + align:start position:0% +of halide in here and we were able to + + + align:start position:0% +of halide in here and we were able to +get about 6 s fast so they'd CPU but the + + align:start position:0% +get about 6 s fast so they'd CPU but the + + + align:start position:0% +get about 6 s fast so they'd CPU but the +best algorithm was somebody hand wrote + + align:start position:0% +best algorithm was somebody hand wrote + + + align:start position:0% +best algorithm was somebody hand wrote +for the paper on GPUs and what it did + + align:start position:0% +for the paper on GPUs and what it did + + + align:start position:0% +for the paper on GPUs and what it did +was it gave up some parallels of a much + + align:start position:0% +was it gave up some parallels of a much + + + align:start position:0% +was it gave up some parallels of a much +better locality and if you give us some + + align:start position:0% +better locality and if you give us some + + + align:start position:0% +better locality and if you give us some +panels a much better locality because we + + align:start position:0% +panels a much better locality because we + + + align:start position:0% +panels a much better locality because we +can optimize in that we got faster than + + align:start position:0% +can optimize in that we got faster than + + + align:start position:0% +can optimize in that we got faster than +their handwritten added with them so so + + align:start position:0% +their handwritten added with them so so + + + align:start position:0% +their handwritten added with them so so +we can change something + + align:start position:0% +we can change something + + + align:start position:0% +we can change something +yes again another algorithm that is + + align:start position:0% +yes again another algorithm that is + + + align:start position:0% +yes again another algorithm that is +doing segmenting in here and it was + + align:start position:0% +doing segmenting in here and it was + + + align:start position:0% +doing segmenting in here and it was +written in MATLAB and MATLAB is a lot + + align:start position:0% +written in MATLAB and MATLAB is a lot + + + align:start position:0% +written in MATLAB and MATLAB is a lot +less lines of code of course but in + + align:start position:0% +less lines of code of course but in + + + align:start position:0% +less lines of code of course but in +halide it's a little bit more line + + align:start position:0% +halide it's a little bit more line + + + align:start position:0% +halide it's a little bit more line +because you're not just calling library + + align:start position:0% +because you're not just calling library + + + align:start position:0% +because you're not just calling library +functions and halide was 70 times faster + + align:start position:0% +functions and halide was 70 times faster + + + align:start position:0% +functions and halide was 70 times faster +and if you write into GPU versus matlab + + align:start position:0% +and if you write into GPU versus matlab + + + align:start position:0% +and if you write into GPU versus matlab +it's about one hundred and a thousand + + align:start position:0% +it's about one hundred and a thousand + + + align:start position:0% +it's about one hundred and a thousand +times faster it's not because you are + + align:start position:0% +times faster it's not because you are + + + align:start position:0% +times faster it's not because you are +running bad matlab loops in fact what + + align:start position:0% +running bad matlab loops in fact what + + + align:start position:0% +running bad matlab loops in fact what +matlab did was it called very well hand + + align:start position:0% +matlab did was it called very well hand + + + align:start position:0% +matlab did was it called very well hand +optimized libraries but the problem with + + align:start position:0% +optimized libraries but the problem with + + + align:start position:0% +optimized libraries but the problem with +calling libraries there's no locality I + + align:start position:0% +calling libraries there's no locality I + + + align:start position:0% +calling libraries there's no locality I +call it really fast library for first + + align:start position:0% +call it really fast library for first + + + align:start position:0% +call it really fast library for first +routine it runs it really fast and then + + align:start position:0% +routine it runs it really fast and then + + + align:start position:0% +routine it runs it really fast and then +you call the next routine that has to + + align:start position:0% +you call the next routine that has to + + + align:start position:0% +you call the next routine that has to +taught the entire image again and now my + + align:start position:0% +taught the entire image again and now my + + + align:start position:0% +taught the entire image again and now my +image is completely off the cache so + + align:start position:0% +image is completely off the cache so + + + align:start position:0% +image is completely off the cache so +what happens is between this very fast + + align:start position:0% +what happens is between this very fast + + + align:start position:0% +what happens is between this very fast +libraries you're bringing the image from + + align:start position:0% +libraries you're bringing the image from + + + align:start position:0% +libraries you're bringing the image from +cache and and when you have something + + align:start position:0% +cache and and when you have something + + + align:start position:0% +cache and and when you have something +like a library you can fuse library + + align:start position:0% +like a library you can fuse library + + + align:start position:0% +like a library you can fuse library +functions together in halide we can fuse + + align:start position:0% +functions together in halide we can fuse + + + align:start position:0% +functions together in halide we can fuse +them together and say who I take this + + align:start position:0% +them together and say who I take this + + + align:start position:0% +them together and say who I take this +line of the image and I will do + + align:start position:0% +line of the image and I will do + + + align:start position:0% +line of the image and I will do +everything on that before I move to the + + align:start position:0% +everything on that before I move to the + + + align:start position:0% +everything on that before I move to the +next thing + + align:start position:0% +next thing + + + align:start position:0% +next thing +so I can do much faster no I my feeling + + align:start position:0% +so I can do much faster no I my feeling + + + align:start position:0% +so I can do much faster no I my feeling +is each function probably MATLAB was + + align:start position:0% +is each function probably MATLAB was + + + align:start position:0% +is each function probably MATLAB was +faster because they have a handwritten + + align:start position:0% +faster because they have a handwritten + + + align:start position:0% +faster because they have a handwritten +really fast thing but the copying of + + align:start position:0% +really fast thing but the copying of + + + align:start position:0% +really fast thing but the copying of +data from carrying from cache the cache + + align:start position:0% +data from carrying from cache the cache + + + align:start position:0% +data from carrying from cache the cache +effects was really slowing it down so + + align:start position:0% +effects was really slowing it down so + + + align:start position:0% +effects was really slowing it down so +here's the thing that we showed before + + align:start position:0% +here's the thing that we showed before + + + align:start position:0% +here's the thing that we showed before +this is a very complicated algorithm + + align:start position:0% +this is a very complicated algorithm + + + align:start position:0% +this is a very complicated algorithm +it's it's it's what you call a pyramidal + + align:start position:0% +it's it's it's what you call a pyramidal + + + align:start position:0% +it's it's it's what you call a pyramidal +algorithm so what it does is you take a + + align:start position:0% +algorithm so what it does is you take a + + + align:start position:0% +algorithm so what it does is you take a +medium here and you divide it into bunch + + align:start position:0% +medium here and you divide it into bunch + + + align:start position:0% +medium here and you divide it into bunch +of blocks in here in each level of + + align:start position:0% +of blocks in here in each level of + + + align:start position:0% +of blocks in here in each level of +pyramid and you do some computation do + + align:start position:0% +pyramid and you do some computation do + + + align:start position:0% +pyramid and you do some computation do +some lookup and do some up sampling in + + align:start position:0% +some lookup and do some up sampling in + + + align:start position:0% +some lookup and do some up sampling in +here you do some addition computation + + align:start position:0% +here you do some addition computation + + + align:start position:0% +here you do some addition computation +and compute that and then you come + + align:start position:0% +and compute that and then you come + + + align:start position:0% +and compute that and then you come +create more and more small and small + + align:start position:0% +create more and more small and small + + + align:start position:0% +create more and more small and small +images in here you do you basically make + + align:start position:0% +images in here you do you basically make + + + align:start position:0% +images in here you do you basically make +pyramid in here and so to do this right + + align:start position:0% +pyramid in here and so to do this right + + + align:start position:0% +pyramid in here and so to do this right +it's not that simple what that means in + + align:start position:0% +it's not that simple what that means in + + + align:start position:0% +it's not that simple what that means in +each of this level there are different + + align:start position:0% +each of this level there are different + + + align:start position:0% +each of this level there are different +balances you want to be if you have lot + + align:start position:0% +balances you want to be if you have lot + + + align:start position:0% +balances you want to be if you have lot +of data parallelism is not that + + align:start position:0% +of data parallelism is not that + + + align:start position:0% +of data parallelism is not that +important at that point because you have + + align:start position:0% +important at that point because you have + + + align:start position:0% +important at that point because you have +parallelism anyways you publish focus a + + align:start position:0% +parallelism anyways you publish focus a + + + align:start position:0% +parallelism anyways you publish focus a +lot more on locality but when you get to + + align:start position:0% +lot more on locality but when you get to + + + align:start position:0% +lot more on locality but when you get to +this smaller amount I think parallels a + + align:start position:0% +this smaller amount I think parallels a + + + align:start position:0% +this smaller amount I think parallels a +matter so so you have to come up with + + align:start position:0% +matter so so you have to come up with + + + align:start position:0% +matter so so you have to come up with +very interesting balances between those + + align:start position:0% +very interesting balances between those + + + align:start position:0% +very interesting balances between those +so many many things things to you at + + align:start position:0% +so many many things things to you at + + + align:start position:0% +so many many things things to you at +every level there's no three things + + align:start position:0% +every level there's no three things + + + align:start position:0% +every level there's no three things +there's hundreds of different levels so + + align:start position:0% +there's hundreds of different levels so + + + align:start position:0% +there's hundreds of different levels so +nice thing about here is you can play + + align:start position:0% +nice thing about here is you can play + + + align:start position:0% +nice thing about here is you can play +with all these things you can you can + + align:start position:0% +with all these things you can you can + + + align:start position:0% +with all these things you can you can +play with all these all these different + + align:start position:0% +play with all these all these different + + + align:start position:0% +play with all these all these different +concepts and and figure out which + + align:start position:0% +concepts and and figure out which + + + align:start position:0% +concepts and and figure out which +actually give you the fastest + + align:start position:0% +actually give you the fastest + + + align:start position:0% +actually give you the fastest +performance in that so little bit of I + + align:start position:0% +performance in that so little bit of I + + + align:start position:0% +performance in that so little bit of I +would say bragging rights in here for + + align:start position:0% +would say bragging rights in here for + + + align:start position:0% +would say bragging rights in here for +Hill he lied he lied left MIT about I + + align:start position:0% +Hill he lied he lied left MIT about I + + + align:start position:0% +Hill he lied he lied left MIT about I +think six years ago and right now it's + + align:start position:0% +think six years ago and right now it's + + + align:start position:0% +think six years ago and right now it's +every I in Google so it's on Android + + align:start position:0% +every I in Google so it's on Android + + + align:start position:0% +every I in Google so it's on Android +phones and it started to Google glass + + align:start position:0% +phones and it started to Google glass + + + align:start position:0% +phones and it started to Google glass +doesn't exist anymore but in that and in + + align:start position:0% +doesn't exist anymore but in that and in + + + align:start position:0% +doesn't exist anymore but in that and in +fact any old images all the videos + + align:start position:0% +fact any old images all the videos + + + align:start position:0% +fact any old images all the videos +uploaded to YouTube right now they do + + align:start position:0% +uploaded to YouTube right now they do + + + align:start position:0% +uploaded to YouTube right now they do +front end processing and that processing + + align:start position:0% +front end processing and that processing + + + align:start position:0% +front end processing and that processing +pipeline is written in halide and they + + align:start position:0% +pipeline is written in halide and they + + + align:start position:0% +pipeline is written in halide and they +switch to halide because hey light code + + align:start position:0% +switch to halide because hey light code + + + align:start position:0% +switch to halide because hey light code +was about I think four or five percent + + align:start position:0% +was about I think four or five percent + + + align:start position:0% +was about I think four or five percent +faster than the previous version and + + align:start position:0% +faster than the previous version and + + + align:start position:0% +faster than the previous version and +four five percent faster for Google was + + align:start position:0% +four five percent faster for Google was + + + align:start position:0% +four five percent faster for Google was +multi-million dollar say for them + + align:start position:0% +multi-million dollar say for them + + + align:start position:0% +multi-million dollar say for them +because there's so many videos get + + align:start position:0% +because there's so many videos get + + + align:start position:0% +because there's so many videos get +downloaded from that so recently there's + + align:start position:0% +downloaded from that so recently there's + + + align:start position:0% +downloaded from that so recently there's +a Photoshop announcement that saying + + align:start position:0% +a Photoshop announcement that saying + + + align:start position:0% +a Photoshop announcement that saying +they have a iOS version of Photoshop + + align:start position:0% +they have a iOS version of Photoshop + + + align:start position:0% +they have a iOS version of Photoshop +from Adobe they just announced it I + + align:start position:0% +from Adobe they just announced it I + + + align:start position:0% +from Adobe they just announced it I +don't think it's even out it and then + + align:start position:0% +don't think it's even out it and then + + + align:start position:0% +don't think it's even out it and then +entire Photoshop filters are written in + + align:start position:0% +entire Photoshop filters are written in + + + align:start position:0% +entire Photoshop filters are written in +this new version using halide + + align:start position:0% + + + + align:start position:0% + +Karl come released this processor called + + align:start position:0% +Karl come released this processor called + + + align:start position:0% +Karl come released this processor called +a Snapdragon image processor so that + + align:start position:0% +a Snapdragon image processor so that + + + align:start position:0% +a Snapdragon image processor so that +they build that processor to do image + + align:start position:0% +they build that processor to do image + + + align:start position:0% +they build that processor to do image +processing in there and the programming + + align:start position:0% +processing in there and the programming + + + align:start position:0% +processing in there and the programming +language to program that processor is + + align:start position:0% +language to program that processor is + + + align:start position:0% +language to program that processor is +basically halide so you write the code + + align:start position:0% +basically halide so you write the code + + + align:start position:0% +basically halide so you write the code +in halide so that is the kind of the + + align:start position:0% +in halide so that is the kind of the + + + align:start position:0% +in halide so that is the kind of the +assembly level that that makes it + + align:start position:0% +assembly level that that makes it + + + align:start position:0% +assembly level that that makes it +available for this in India and also + + align:start position:0% +available for this in India and also + + + align:start position:0% +available for this in India and also +Intel is using that so so there's lot of + + align:start position:0% +Intel is using that so so there's lot of + + + align:start position:0% +Intel is using that so so there's lot of +use of this system at this point which + + align:start position:0% +use of this system at this point which + + + align:start position:0% +use of this system at this point which +is really fun to see academic project + + align:start position:0% +is really fun to see academic project + + + align:start position:0% +is really fun to see academic project +get into a point it's very heavy to use + + align:start position:0% +get into a point it's very heavy to use + + + align:start position:0% +get into a point it's very heavy to use +and part of that is because it's very + + align:start position:0% +and part of that is because it's very + + + align:start position:0% +and part of that is because it's very +useful because people realize they need + + align:start position:0% +useful because people realize they need + + + align:start position:0% +useful because people realize they need +to optimize these code because cameras + + align:start position:0% +to optimize these code because cameras + + + align:start position:0% +to optimize these code because cameras +and stuff performance matter and instead + + align:start position:0% +and stuff performance matter and instead + + + align:start position:0% +and stuff performance matter and instead +of having some poor engineer spending + + align:start position:0% +of having some poor engineer spending + + + align:start position:0% +of having some poor engineer spending +months in the corner just trying out aid + + align:start position:0% +months in the corner just trying out aid + + + align:start position:0% +months in the corner just trying out aid +those things you can try the same things + + align:start position:0% +those things you can try the same things + + + align:start position:0% +those things you can try the same things +and lot more by do it faster ok so let + + align:start position:0% +and lot more by do it faster ok so let + + + align:start position:0% +and lot more by do it faster ok so let +me ask you questions so now between + + align:start position:0% +me ask you questions so now between + + + align:start position:0% +me ask you questions so now between +halite and graph it what did you find + + align:start position:0% + + + + align:start position:0% + +the bunch of similarities I want to + + align:start position:0% +the bunch of similarities I want to + + + align:start position:0% +the bunch of similarities I want to +figure out are there any interesting + + align:start position:0% +figure out are there any interesting + + + align:start position:0% +figure out are there any interesting +interesting similarities you guys found + + align:start position:0% +interesting similarities you guys found + + + align:start position:0% +interesting similarities you guys found +between these two projects + + align:start position:0% + + + + align:start position:0% + +so part of that is also a lot of times + + align:start position:0% +so part of that is also a lot of times + + + align:start position:0% +so part of that is also a lot of times +compilers are kind of black box we know + + align:start position:0% +compilers are kind of black box we know + + + align:start position:0% +compilers are kind of black box we know +everything just feed us we will give you + + align:start position:0% +everything just feed us we will give you + + + align:start position:0% +everything just feed us we will give you +the really fast code and the problem is + + align:start position:0% +the really fast code and the problem is + + + align:start position:0% +the really fast code and the problem is +they're never the fastest so so if you + + align:start position:0% +they're never the fastest so so if you + + + align:start position:0% +they're never the fastest so so if you +really care about performance you get + + align:start position:0% +really care about performance you get + + + align:start position:0% +really care about performance you get +90% then you get really frustrated now + + align:start position:0% +90% then you get really frustrated now + + + align:start position:0% +90% then you get really frustrated now +what do I do + + align:start position:0% +what do I do + + + align:start position:0% +what do I do +but these this was okay I am NOT going + + align:start position:0% +but these this was okay I am NOT going + + + align:start position:0% +but these this was okay I am NOT going +to you are better yet what to do but I + + align:start position:0% +to you are better yet what to do but I + + + align:start position:0% +to you are better yet what to do but I +will make you the life simpler so we + + align:start position:0% +will make you the life simpler so we + + + align:start position:0% +will make you the life simpler so we +still want the performance engineer it's + + align:start position:0% +still want the performance engineer it's + + + align:start position:0% +still want the performance engineer it's +not the the person who just don't + + align:start position:0% +not the the person who just don't + + + align:start position:0% +not the the person who just don't +understand performance feed you get fast + + align:start position:0% +understand performance feed you get fast + + + align:start position:0% +understand performance feed you get fast +code we need to perform but we won't + + align:start position:0% +code we need to perform but we won't + + + align:start position:0% +code we need to perform but we won't +make performance engineers life easier + + align:start position:0% +make performance engineers life easier + + + align:start position:0% +make performance engineers life easier +so so both of them said okay we need + + align:start position:0% +so so both of them said okay we need + + + align:start position:0% +so so both of them said okay we need +performance engineers we can automate it + + align:start position:0% +performance engineers we can automate it + + + align:start position:0% +performance engineers we can automate it +we don't know how to automate all these + + align:start position:0% +we don't know how to automate all these + + + align:start position:0% +we don't know how to automate all these +things that's too much complexity but we + + align:start position:0% +things that's too much complexity but we + + + align:start position:0% +things that's too much complexity but we +will let you performance engineer + + align:start position:0% +will let you performance engineer + + + align:start position:0% +will let you performance engineer +explain but to do but you'll make you + + align:start position:0% +explain but to do but you'll make you + + + align:start position:0% +explain but to do but you'll make you +like very simple what else + + align:start position:0% +like very simple what else + + + align:start position:0% +like very simple what else +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +do + + align:start position:0% +do + + + align:start position:0% +do +which is like pretty different yeah + + align:start position:0% +which is like pretty different yeah + + + align:start position:0% +which is like pretty different yeah +because I wouldn't say it you can do a + + align:start position:0% +because I wouldn't say it you can do a + + + align:start position:0% +because I wouldn't say it you can do a +lot of domain-specific of demand + + align:start position:0% +lot of domain-specific of demand + + + align:start position:0% +lot of domain-specific of demand +solution so algorithmic optimization is + + align:start position:0% +solution so algorithmic optimization is + + + align:start position:0% +solution so algorithmic optimization is +one level higher you can see I have a + + align:start position:0% +one level higher you can see I have a + + + align:start position:0% +one level higher you can see I have a +better algorithm so okay I don't want to + + align:start position:0% +better algorithm so okay I don't want to + + + align:start position:0% +better algorithm so okay I don't want to +do a quick search I can do insertion + + align:start position:0% +do a quick search I can do insertion + + + align:start position:0% +do a quick search I can do insertion +search because cook sortie insertion + + align:start position:0% +search because cook sortie insertion + + + align:start position:0% +search because cook sortie insertion +sort might be faster for certain class + + align:start position:0% +sort might be faster for certain class + + + align:start position:0% +sort might be faster for certain class +in there so that is level change we + + align:start position:0% +in there so that is level change we + + + align:start position:0% +in there so that is level change we +don't do Oh words that I can say like + + align:start position:0% +don't do Oh words that I can say like + + + align:start position:0% +don't do Oh words that I can say like +this happens in lot of thinner machine + + align:start position:0% +this happens in lot of thinner machine + + + align:start position:0% +this happens in lot of thinner machine +learning yeah if I just drop a number + + align:start position:0% +learning yeah if I just drop a number + + + align:start position:0% +learning yeah if I just drop a number +here I am okay I don't have to get the + + align:start position:0% +here I am okay I don't have to get the + + + align:start position:0% +here I am okay I don't have to get the +computer exactly right away I don't + + align:start position:0% +computer exactly right away I don't + + + align:start position:0% +computer exactly right away I don't +calculate everything if I calculate for + + align:start position:0% +calculate everything if I calculate for + + + align:start position:0% +calculate everything if I calculate for +10 people it's good enough so that kind + + align:start position:0% +10 people it's good enough so that kind + + + align:start position:0% +10 people it's good enough so that kind +of changes are you can't do because + + align:start position:0% +of changes are you can't do because + + + align:start position:0% +of changes are you can't do because +that's very contextual like for example + + align:start position:0% +that's very contextual like for example + + + align:start position:0% +that's very contextual like for example +a lot of time if we are doing things + + align:start position:0% +a lot of time if we are doing things + + + align:start position:0% +a lot of time if we are doing things +like machine learning there's no right + + align:start position:0% +like machine learning there's no right + + + align:start position:0% +like machine learning there's no right +answer you need to have a good answer + + align:start position:0% +answer you need to have a good answer + + + align:start position:0% +answer you need to have a good answer +so sometimes good means you can not do + + align:start position:0% +so sometimes good means you can not do + + + align:start position:0% +so sometimes good means you can not do +certain things and you need to find what + + align:start position:0% +certain things and you need to find what + + + align:start position:0% +certain things and you need to find what +things you shouldn't you cannot do that + + align:start position:0% +things you shouldn't you cannot do that + + + align:start position:0% +things you shouldn't you cannot do that +you get a huge benefit but you don't + + align:start position:0% +you get a huge benefit but you don't + + + align:start position:0% +you get a huge benefit but you don't +lose that much that level you can't do + + align:start position:0% +lose that much that level you can't do + + + align:start position:0% +lose that much that level you can't do +that that's the next level of part is + + align:start position:0% +that that's the next level of part is + + + align:start position:0% +that that's the next level of part is +saying okay how do you do that how do + + align:start position:0% +saying okay how do you do that how do + + + align:start position:0% +saying okay how do you do that how do +will somebody say okay look I can train + + align:start position:0% +will somebody say okay look I can train + + + align:start position:0% +will somebody say okay look I can train +it for 10 iteration 110 is good enough I + + align:start position:0% +it for 10 iteration 110 is good enough I + + + align:start position:0% +it for 10 iteration 110 is good enough I +can't if your code is written to Train + + align:start position:0% +can't if your code is written to Train + + + align:start position:0% +can't if your code is written to Train +400 iteration I can't tell you a 10 is + + align:start position:0% +400 iteration I can't tell you a 10 is + + + align:start position:0% +400 iteration I can't tell you a 10 is +good enough that is decision that has to + + align:start position:0% +good enough that is decision that has to + + + align:start position:0% +good enough that is decision that has to +be lot higher level then I can make so + + align:start position:0% +be lot higher level then I can make so + + + align:start position:0% +be lot higher level then I can make so +that said that there's an interesting + + align:start position:0% +that said that there's an interesting + + + align:start position:0% +that said that there's an interesting +level that can still existing in top of + + align:start position:0% +level that can still existing in top of + + + align:start position:0% +level that can still existing in top of +that which which we can't automate that + + align:start position:0% +that which which we can't automate that + + + align:start position:0% +that which which we can't automate that +easily but we might be able to make + + align:start position:0% +easily but we might be able to make + + + align:start position:0% +easily but we might be able to make +still a language like a scheduled + + align:start position:0% +still a language like a scheduled + + + align:start position:0% +still a language like a scheduled +language give you that option that says + + align:start position:0% +language give you that option that says + + + align:start position:0% +language give you that option that says +cool option ting you say like try some + + align:start position:0% +cool option ting you say like try some + + + align:start position:0% +cool option ting you say like try some +of these things that actually will + + align:start position:0% +of these things that actually will + + + align:start position:0% +of these things that actually will +change algorithm but but within the + + align:start position:0% +change algorithm but but within the + + + align:start position:0% +change algorithm but but within the +algorithm that means I will still give + + align:start position:0% +algorithm that means I will still give + + + align:start position:0% +algorithm that means I will still give +you the same answer I will try different + + align:start position:0% +you the same answer I will try different + + + align:start position:0% +you the same answer I will try different +things + + align:start position:0% + + + + align:start position:0% + +any other things any other things you + + align:start position:0% +any other things any other things you + + + align:start position:0% +any other things any other things you +guys thought that was interesting how + + align:start position:0% +guys thought that was interesting how + + + align:start position:0% +guys thought that was interesting how +about from somewhere here what are the + + align:start position:0% +about from somewhere here what are the + + + align:start position:0% +about from somewhere here what are the +interesting things you found back there + + align:start position:0% + + + + align:start position:0% + +yes what they'd know a lot of trial and + + align:start position:0% +yes what they'd know a lot of trial and + + + align:start position:0% +yes what they'd know a lot of trial and +error I mean this is the modern computer + + align:start position:0% +error I mean this is the modern computer + + + align:start position:0% +error I mean this is the modern computer +systems everything is extremely + + align:start position:0% +systems everything is extremely + + + align:start position:0% +systems everything is extremely +complicated there's no right way of + + align:start position:0% +complicated there's no right way of + + + align:start position:0% +complicated there's no right way of +doing things when you look at this + + align:start position:0% +doing things when you look at this + + + align:start position:0% +doing things when you look at this +pretty large piece of code and there + + align:start position:0% +pretty large piece of code and there + + + align:start position:0% +pretty large piece of code and there +might be a lot of it there are caches + + align:start position:0% +might be a lot of it there are caches + + + align:start position:0% +might be a lot of it there are caches +perils locality lot of things that that + + align:start position:0% +perils locality lot of things that that + + + align:start position:0% +perils locality lot of things that that +can go right and so you might have to + + align:start position:0% +can go right and so you might have to + + + align:start position:0% +can go right and so you might have to +try out many things so if you know the + + align:start position:0% +try out many things so if you know the + + + align:start position:0% +try out many things so if you know the +answer if you come up with I know + + align:start position:0% +answer if you come up with I know + + + align:start position:0% +answer if you come up with I know +exactly every time on the right hand so + + align:start position:0% +exactly every time on the right hand so + + + align:start position:0% +exactly every time on the right hand so +that's amazing but even the best + + align:start position:0% +that's amazing but even the best + + + align:start position:0% +that's amazing but even the best +performance person might not be able to + + align:start position:0% +performance person might not be able to + + + align:start position:0% +performance person might not be able to +look at a piece of code as AHA I know + + align:start position:0% +look at a piece of code as AHA I know + + + align:start position:0% +look at a piece of code as AHA I know +your solution you do a lot of these kind + + align:start position:0% +your solution you do a lot of these kind + + + align:start position:0% +your solution you do a lot of these kind +of supports that and you probably have + + align:start position:0% +of supports that and you probably have + + + align:start position:0% +of supports that and you probably have +figured that one out for most of your + + align:start position:0% +figured that one out for most of your + + + align:start position:0% +figured that one out for most of your +projects it's not like you went as yeah + + align:start position:0% +projects it's not like you went as yeah + + + align:start position:0% +projects it's not like you went as yeah +I know what to do you probably did many + + align:start position:0% +I know what to do you probably did many + + + align:start position:0% +I know what to do you probably did many +different trials and and and I know from + + align:start position:0% +different trials and and and I know from + + + align:start position:0% +different trials and and and I know from +this lot of things you actually they + + align:start position:0% +this lot of things you actually they + + + align:start position:0% +this lot of things you actually they +have no impact or slow down the code + + align:start position:0% +have no impact or slow down the code + + + align:start position:0% +have no impact or slow down the code +then you say well that didn't work and + + align:start position:0% +then you say well that didn't work and + + + align:start position:0% +then you say well that didn't work and +and all if deafs you leave in your codes + + align:start position:0% +and all if deafs you leave in your codes + + + align:start position:0% +and all if deafs you leave in your codes +show us like all the crazy things you + + align:start position:0% +show us like all the crazy things you + + + align:start position:0% +show us like all the crazy things you +tried and nothing happened so so that's + + align:start position:0% +tried and nothing happened so so that's + + + align:start position:0% +tried and nothing happened so so that's +interesting thing what else + + align:start position:0% + + + + align:start position:0% + +anything else little bit differently + + align:start position:0% +anything else little bit differently + + + align:start position:0% +anything else little bit differently +that you say on this one + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so interesting questions are there any + + align:start position:0% +so interesting questions are there any + + + align:start position:0% +so interesting questions are there any +other domains that don't have something + + align:start position:0% +other domains that don't have something + + + align:start position:0% +other domains that don't have something +like this people are working on similar + + align:start position:0% +like this people are working on similar + + + align:start position:0% +like this people are working on similar +things to machine learning these days + + align:start position:0% +things to machine learning these days + + + align:start position:0% +things to machine learning these days +that seem to be the domain and then + + align:start position:0% +that seem to be the domain and then + + + align:start position:0% +that seem to be the domain and then +tensorflow and and all those people are + + align:start position:0% +tensorflow and and all those people are + + + align:start position:0% +tensorflow and and all those people are +trying to do to build systems like + + align:start position:0% +trying to do to build systems like + + + align:start position:0% +trying to do to build systems like +similar like frameworks that you can get + + align:start position:0% +similar like frameworks that you can get + + + align:start position:0% +similar like frameworks that you can get +bad I mean that's a very I think the way + + align:start position:0% +bad I mean that's a very I think the way + + + align:start position:0% +bad I mean that's a very I think the way +I have operated is I go talk to people + + align:start position:0% +I have operated is I go talk to people + + + align:start position:0% +I have operated is I go talk to people +and sometimes you find this poor + + align:start position:0% +and sometimes you find this poor + + + align:start position:0% +and sometimes you find this poor +graduate student or postdoc who want to + + align:start position:0% +graduate student or postdoc who want to + + + align:start position:0% +graduate student or postdoc who want to +do some research but spending all their + + align:start position:0% +do some research but spending all their + + + align:start position:0% +do some research but spending all their +time basically optimizing their piece of + + align:start position:0% +time basically optimizing their piece of + + + align:start position:0% +time basically optimizing their piece of +code because they can't get their + + align:start position:0% +code because they can't get their + + + align:start position:0% +code because they can't get their +performance and and that might be a good + + align:start position:0% +performance and and that might be a good + + + align:start position:0% +performance and and that might be a good +domain you find these people in physics + + align:start position:0% +domain you find these people in physics + + + align:start position:0% +domain you find these people in physics +you find these people in biology and I + + align:start position:0% +you find these people in biology and I + + + align:start position:0% +you find these people in biology and I +am actually talking about it but because + + align:start position:0% +am actually talking about it but because + + + align:start position:0% +am actually talking about it but because +for example in biology the art of this + + align:start position:0% +for example in biology the art of this + + + align:start position:0% +for example in biology the art of this +gene sequencing stuff is there are very + + align:start position:0% +gene sequencing stuff is there are very + + + align:start position:0% +gene sequencing stuff is there are very +similar things you have to do but they + + align:start position:0% +similar things you have to do but they + + + align:start position:0% +similar things you have to do but they +seem to be spending all this time + + align:start position:0% +seem to be spending all this time + + + align:start position:0% +seem to be spending all this time +writing the code and made in like code + + align:start position:0% +writing the code and made in like code + + + align:start position:0% +writing the code and made in like code +complexity okay can you do something in + + align:start position:0% +complexity okay can you do something in + + + align:start position:0% +complexity okay can you do something in +that I mean the key thing is this is a + + align:start position:0% +that I mean the key thing is this is a + + + align:start position:0% +that I mean the key thing is this is a +good way to nicely what MIT is there are + + align:start position:0% +good way to nicely what MIT is there are + + + align:start position:0% +good way to nicely what MIT is there are +good lot of very smart people in many + + align:start position:0% +good lot of very smart people in many + + + align:start position:0% +good lot of very smart people in many +different domains try to push the state + + align:start position:0% +different domains try to push the state + + + align:start position:0% +different domains try to push the state +of the art and who's spending all this + + align:start position:0% +of the art and who's spending all this + + + align:start position:0% +of the art and who's spending all this +time cursing in front of a computer + + align:start position:0% +time cursing in front of a computer + + + align:start position:0% +time cursing in front of a computer +program to get to to a point they want + + align:start position:0% +program to get to to a point they want + + + align:start position:0% +program to get to to a point they want +to do because not because they know that + + align:start position:0% +to do because not because they know that + + + align:start position:0% +to do because not because they know that +they don't know the algorithm because + + align:start position:0% +they don't know the algorithm because + + + align:start position:0% +they don't know the algorithm because +the amount of data they had to deal with + + align:start position:0% +the amount of data they had to deal with + + + align:start position:0% +the amount of data they had to deal with +astronomy I mean they get this multiple + + align:start position:0% +astronomy I mean they get this multiple + + + align:start position:0% +astronomy I mean they get this multiple +telescopes that deluge of data and and + + align:start position:0% +telescopes that deluge of data and and + + + align:start position:0% +telescopes that deluge of data and and +and most of them they know what they + + align:start position:0% +and most of them they know what they + + + align:start position:0% +and most of them they know what they +have to do they just have to can't write + + align:start position:0% +have to do they just have to can't write + + + align:start position:0% +have to do they just have to can't write +the program to do it fast enough so + + align:start position:0% +the program to do it fast enough so + + + align:start position:0% +the program to do it fast enough so +there might be domains like that if you + + align:start position:0% +there might be domains like that if you + + + align:start position:0% +there might be domains like that if you +look at that and and there might be + + align:start position:0% +look at that and and there might be + + + align:start position:0% +look at that and and there might be +domains from application and domains + + align:start position:0% +domains from application and domains + + + align:start position:0% +domains from application and domains +from patterns like sparse matrices or + + align:start position:0% +from patterns like sparse matrices or + + + align:start position:0% +from patterns like sparse matrices or +graphs or patterns it's more not only on + + align:start position:0% +graphs or patterns it's more not only on + + + align:start position:0% +graphs or patterns it's more not only on +a single application I mean if it works + + align:start position:0% +a single application I mean if it works + + + align:start position:0% +a single application I mean if it works +in multiple places there might be other + + align:start position:0% +in multiple places there might be other + + + align:start position:0% +in multiple places there might be other +patterns say this is if you want to do + + align:start position:0% +patterns say this is if you want to do + + + align:start position:0% +patterns say this is if you want to do +research which might be interesting pace + + align:start position:0% +research which might be interesting pace + + + align:start position:0% +research which might be interesting pace +of doing research and and and and and + + align:start position:0% +of doing research and and and and and + + + align:start position:0% +of doing research and and and and and +and I have spent my life finding + + align:start position:0% +and I have spent my life finding + + + align:start position:0% +and I have spent my life finding +different domains and then a bunch of + + align:start position:0% +different domains and then a bunch of + + + align:start position:0% +different domains and then a bunch of +people that that that spend their + + align:start position:0% +people that that that spend their + + + align:start position:0% +people that that that spend their +lifetime just had hacking things and and + + align:start position:0% +lifetime just had hacking things and and + + + align:start position:0% +lifetime just had hacking things and and +and and telling them ok let me see + + align:start position:0% +and and telling them ok let me see + + + align:start position:0% +and and telling them ok let me see +whether we can do some nice abstraction + + align:start position:0% + + + + align:start position:0% + +anything else that that you guys found + + align:start position:0% +anything else that that you guys found + + + align:start position:0% +anything else that that you guys found +that's interesting so + + align:start position:0% +that's interesting so + + + align:start position:0% +that's interesting so +to both of them what are what's the + + align:start position:0% +to both of them what are what's the + + + align:start position:0% +to both of them what are what's the +space that they operated on to optimize + + align:start position:0% +space that they operated on to optimize + + + align:start position:0% +space that they operated on to optimize +programs + + align:start position:0% + + + + align:start position:0% + +dunph Amanda what I'm saying is it's + + align:start position:0% +dunph Amanda what I'm saying is it's + + + align:start position:0% +dunph Amanda what I'm saying is it's +what are the things that you try to + + align:start position:0% +what are the things that you try to + + + align:start position:0% +what are the things that you try to +optimize that there so there's a nice + + align:start position:0% +optimize that there so there's a nice + + + align:start position:0% +optimize that there so there's a nice +space of three different things + + align:start position:0% +space of three different things + + + align:start position:0% +space of three different things +parallelism locality and and and + + align:start position:0% +parallelism locality and and and + + + align:start position:0% +parallelism locality and and and +redundant work + + align:start position:0% +redundant work + + + align:start position:0% +redundant work +my feeling is as you go as a performance + + align:start position:0% +my feeling is as you go as a performance + + + align:start position:0% +my feeling is as you go as a performance +engineer that's going to be your life if + + align:start position:0% +engineer that's going to be your life if + + + align:start position:0% +engineer that's going to be your life if +I had additional thing there might be + + align:start position:0% +I had additional thing there might be + + + align:start position:0% +I had additional thing there might be +algorithmic things that you completely + + align:start position:0% +algorithmic things that you completely + + + align:start position:0% +algorithmic things that you completely +get rid of work but most of the time we + + align:start position:0% +get rid of work but most of the time we + + + align:start position:0% +get rid of work but most of the time we +all of you will be different performance + + align:start position:0% +all of you will be different performance + + + align:start position:0% +all of you will be different performance +we'll be working on some kind of a + + align:start position:0% +we'll be working on some kind of a + + + align:start position:0% +we'll be working on some kind of a +multi-core vector GPU type unit so you + + align:start position:0% +multi-core vector GPU type unit so you + + + align:start position:0% +multi-core vector GPU type unit so you +have to get parallelism so getting + + align:start position:0% +have to get parallelism so getting + + + align:start position:0% +have to get parallelism so getting +parallelism is important but then if you + + align:start position:0% +parallelism is important but then if you + + + align:start position:0% +parallelism is important but then if you +don't have locality it doesn't matter + + align:start position:0% +don't have locality it doesn't matter + + + align:start position:0% +don't have locality it doesn't matter +because most time you're waiting to get + + align:start position:0% +because most time you're waiting to get + + + align:start position:0% +because most time you're waiting to get +data from all the way from memory so you + + align:start position:0% +data from all the way from memory so you + + + align:start position:0% +data from all the way from memory so you +had to get good locality and then more + + align:start position:0% +had to get good locality and then more + + + align:start position:0% +had to get good locality and then more +lot of times you can do that really well + + align:start position:0% +lot of times you can do that really well + + + align:start position:0% +lot of times you can do that really well +if you do some extra computation but if + + align:start position:0% +if you do some extra computation but if + + + align:start position:0% +if you do some extra computation but if +you do too much extra things that's + + align:start position:0% +you do too much extra things that's + + + align:start position:0% +you do too much extra things that's +going to oh well that's not going to + + align:start position:0% +going to oh well that's not going to + + + align:start position:0% +going to oh well that's not going to +help you so it's all about playing in + + align:start position:0% +help you so it's all about playing in + + + align:start position:0% +help you so it's all about playing in +this you know you could a final project + + align:start position:0% +this you know you could a final project + + + align:start position:0% +this you know you could a final project +that's exactly what you're going to do + + align:start position:0% +that's exactly what you're going to do + + + align:start position:0% +that's exactly what you're going to do +you might say I if I can do some extra + + align:start position:0% +you might say I if I can do some extra + + + align:start position:0% +you might say I if I can do some extra +work okay I can do this fast but oops + + align:start position:0% +work okay I can do this fast but oops + + + align:start position:0% +work okay I can do this fast but oops +now this extra pre-compute pass or + + align:start position:0% +now this extra pre-compute pass or + + + align:start position:0% +now this extra pre-compute pass or +whatever it's not I can't amortize the + + align:start position:0% +whatever it's not I can't amortize the + + + align:start position:0% +whatever it's not I can't amortize the +cost so these these three things that + + align:start position:0% +cost so these these three things that + + + align:start position:0% +cost so these these three things that +that you're trading over that so that's + + align:start position:0% +that you're trading over that so that's + + + align:start position:0% +that you're trading over that so that's +one interesting thing other thing is we + + align:start position:0% +one interesting thing other thing is we + + + align:start position:0% +one interesting thing other thing is we +made it available for the programmers to + + align:start position:0% +made it available for the programmers to + + + align:start position:0% +made it available for the programmers to +do this scheduling a language but can + + align:start position:0% +do this scheduling a language but can + + + align:start position:0% +do this scheduling a language but can +you make it can you think of a way to + + align:start position:0% +you make it can you think of a way to + + + align:start position:0% +you make it can you think of a way to +make it a little bit easier for + + align:start position:0% +make it a little bit easier for + + + align:start position:0% +make it a little bit easier for +programmers they're doing a schedule + + align:start position:0% +programmers they're doing a schedule + + + align:start position:0% +programmers they're doing a schedule +language what can I do + + align:start position:0% +language what can I do + + + align:start position:0% +language what can I do +what's the nice thing about scheduling + + align:start position:0% +what's the nice thing about scheduling + + + align:start position:0% +what's the nice thing about scheduling +languages it's very simple it has a very + + align:start position:0% +languages it's very simple it has a very + + + align:start position:0% +languages it's very simple it has a very +simple pattern + + align:start position:0% + + + + align:start position:0% + +yeah I mean that's the number of options + + align:start position:0% +yeah I mean that's the number of options + + + align:start position:0% +yeah I mean that's the number of options +it's not like you can write any program + + align:start position:0% +it's not like you can write any program + + + align:start position:0% +it's not like you can write any program +there's certain things you can do the in + + align:start position:0% +there's certain things you can do the in + + + align:start position:0% +there's certain things you can do the in +schedule so if you know that space he's + + align:start position:0% +schedule so if you know that space he's + + + align:start position:0% +schedule so if you know that space he's +sort of who's doing that smarty what + + align:start position:0% +sort of who's doing that smarty what + + + align:start position:0% +sort of who's doing that smarty what +else can we do with it test them all + + align:start position:0% +else can we do with it test them all + + + align:start position:0% +else can we do with it test them all +that's one approach there we can do auto + + align:start position:0% +that's one approach there we can do auto + + + align:start position:0% +that's one approach there we can do auto +tuning so that switching to the auto + + align:start position:0% +tuning so that switching to the auto + + + align:start position:0% +tuning so that switching to the auto +tuning part of this talk so performance + + align:start position:0% +tuning part of this talk so performance + + + align:start position:0% +tuning part of this talk so performance +engineering basically most of the time + + align:start position:0% +engineering basically most of the time + + + align:start position:0% +engineering basically most of the time +is finding right these crazy things like + + align:start position:0% +is finding right these crazy things like + + + align:start position:0% +is finding right these crazy things like +you start looking at I think probably a + + align:start position:0% +you start looking at I think probably a + + + align:start position:0% +you start looking at I think probably a +charge talk about this voodoo parameters + + align:start position:0% +charge talk about this voodoo parameters + + + align:start position:0% +charge talk about this voodoo parameters +like okay what's the right block size + + align:start position:0% +like okay what's the right block size + + + align:start position:0% +like okay what's the right block size +and it has a big impact finding that I + + align:start position:0% +and it has a big impact finding that I + + + align:start position:0% +and it has a big impact finding that I +knew a memory allocation particular to + + align:start position:0% +knew a memory allocation particular to + + + align:start position:0% +knew a memory allocation particular to +find the right strategy what right + + align:start position:0% +find the right strategy what right + + + align:start position:0% +find the right strategy what right +memory allocation through bunch of these + + align:start position:0% +memory allocation through bunch of these + + + align:start position:0% +memory allocation through bunch of these +things even GCC compiler there are I + + align:start position:0% +things even GCC compiler there are I + + + align:start position:0% +things even GCC compiler there are I +think about 400 different flags for GCC + + align:start position:0% +think about 400 different flags for GCC + + + align:start position:0% +think about 400 different flags for GCC +and you can actually get factor of for + + align:start position:0% +and you can actually get factor of for + + + align:start position:0% +and you can actually get factor of for +performance by having esoterically + + align:start position:0% +performance by having esoterically + + + align:start position:0% +performance by having esoterically +200 flags into GCC it's crazy and and + + align:start position:0% +200 flags into GCC it's crazy and and + + + align:start position:0% +200 flags into GCC it's crazy and and +that 200 Flags it's not the same for + + align:start position:0% +that 200 Flags it's not the same for + + + align:start position:0% +that 200 Flags it's not the same for +every program and of course some + + align:start position:0% +every program and of course some + + + align:start position:0% +every program and of course some +programs will crash in some place but + + align:start position:0% +programs will crash in some place but + + + align:start position:0% +programs will crash in some place but +most of the time it'll slow down the + + align:start position:0% +most of the time it'll slow down the + + + align:start position:0% +most of the time it'll slow down the +speed up so you can't just just give all + + align:start position:0% +speed up so you can't just just give all + + + align:start position:0% +speed up so you can't just just give all +the flags of GCC and not rotate on that + + align:start position:0% +the flags of GCC and not rotate on that + + + align:start position:0% +the flags of GCC and not rotate on that +and and you can get factor of 2 to 4 + + align:start position:0% +and and you can get factor of 2 to 4 + + + align:start position:0% +and and you can get factor of 2 to 4 +performance in there it's just crazy and + + align:start position:0% +performance in there it's just crazy and + + + align:start position:0% +performance in there it's just crazy and +then because you do weird things in + + align:start position:0% +then because you do weird things in + + + align:start position:0% +then because you do weird things in +there and oh I know 2 or 3 will only do + + align:start position:0% +there and oh I know 2 or 3 will only do + + + align:start position:0% +there and oh I know 2 or 3 will only do +certain amount so o 3 doesn't it's not + + align:start position:0% +certain amount so o 3 doesn't it's not + + + align:start position:0% +certain amount so o 3 doesn't it's not +always right if you can try all these + + align:start position:0% +always right if you can try all these + + + align:start position:0% +always right if you can try all these +things so you can't do that and schedule + + align:start position:0% +things so you can't do that and schedule + + + align:start position:0% +things so you can't do that and schedule +in halide schedule in graph it all these + + align:start position:0% +in halide schedule in graph it all these + + + align:start position:0% +in halide schedule in graph it all these +things can be auto-tune so before taught + + align:start position:0% +things can be auto-tune so before taught + + + align:start position:0% +things can be auto-tune so before taught +uni when you have a large search space + + align:start position:0% +uni when you have a large search space + + + align:start position:0% +uni when you have a large search space +what do we normally do the the thing + + align:start position:0% +what do we normally do the the thing + + + align:start position:0% +what do we normally do the the thing +that when we think we are smart what do + + align:start position:0% +that when we think we are smart what do + + + align:start position:0% +that when we think we are smart what do +you do is we build models we have model + + align:start position:0% +you do is we build models we have model + + + align:start position:0% +you do is we build models we have model +for a cache and say can we understand + + align:start position:0% +for a cache and say can we understand + + + align:start position:0% +for a cache and say can we understand +the cache we have all these nice models + + align:start position:0% +the cache we have all these nice models + + + align:start position:0% +the cache we have all these nice models +in here and using the model I can + + align:start position:0% +in here and using the model I can + + + align:start position:0% +in here and using the model I can +predict AHA this is the right block size + + align:start position:0% +predict AHA this is the right block size + + + align:start position:0% +predict AHA this is the right block size +so what's the problem when you try to do + + align:start position:0% +so what's the problem when you try to do + + + align:start position:0% +so what's the problem when you try to do +a model + + align:start position:0% + + + + align:start position:0% + +exactly because most of the time when + + align:start position:0% +exactly because most of the time when + + + align:start position:0% +exactly because most of the time when +you try to model you had abstract and + + align:start position:0% +you try to model you had abstract and + + + align:start position:0% +you try to model you had abstract and +most of them you want to abstract out + + align:start position:0% +most of them you want to abstract out + + + align:start position:0% +most of them you want to abstract out +might be the most important part of the + + align:start position:0% +might be the most important part of the + + + align:start position:0% +might be the most important part of the +darn thing that we didn't consider so we + + align:start position:0% +darn thing that we didn't consider so we + + + align:start position:0% +darn thing that we didn't consider so we +build a model for cash but oops I could + + align:start position:0% +build a model for cash but oops I could + + + align:start position:0% +build a model for cash but oops I could +didn't figure out pages with pages made + + align:start position:0% +didn't figure out pages with pages made + + + align:start position:0% +didn't figure out pages with pages made +a big difference so so there might be + + align:start position:0% +a big difference so so there might be + + + align:start position:0% +a big difference so so there might be +things in real life that matters that + + align:start position:0% +things in real life that matters that + + + align:start position:0% +things in real life that matters that +didn't fit into your model or you didn't + + align:start position:0% +didn't fit into your model or you didn't + + + align:start position:0% +didn't fit into your model or you didn't +know it need to be fit in the model if + + align:start position:0% +know it need to be fit in the model if + + + align:start position:0% +know it need to be fit in the model if +you try to put everything that's too + + align:start position:0% +you try to put everything that's too + + + align:start position:0% +you try to put everything that's too +complicated of a model so you abstract + + align:start position:0% +complicated of a model so you abstract + + + align:start position:0% +complicated of a model so you abstract +something out you can see I have optimal + + align:start position:0% +something out you can see I have optimal + + + align:start position:0% +something out you can see I have optimal +result for this model but that optimal + + align:start position:0% +result for this model but that optimal + + + align:start position:0% +result for this model but that optimal +result might be like way off then the + + align:start position:0% +result might be like way off then the + + + align:start position:0% +result might be like way off then the +simple result you can get because the + + align:start position:0% +simple result you can get because the + + + align:start position:0% +simple result you can get because the +thing that you didn't put into the model + + align:start position:0% +thing that you didn't put into the model + + + align:start position:0% +thing that you didn't put into the model +are the important ones so model doesn't + + align:start position:0% +are the important ones so model doesn't + + + align:start position:0% +are the important ones so model doesn't +really the next thing is what you do + + align:start position:0% +really the next thing is what you do + + + align:start position:0% +really the next thing is what you do +heuristic based thing this is we are + + align:start position:0% +heuristic based thing this is we are + + + align:start position:0% +heuristic based thing this is we are +like this all people like come and say I + + align:start position:0% +like this all people like come and say I + + + align:start position:0% +like this all people like come and say I +know how to do this you know to do this + + align:start position:0% +know how to do this you know to do this + + + align:start position:0% +know how to do this you know to do this +you need to do this thing this thing + + align:start position:0% +you need to do this thing this thing + + + align:start position:0% +you need to do this thing this thing +this thing you can come up with some + + align:start position:0% +this thing you can come up with some + + + align:start position:0% +this thing you can come up with some +kind of the the whole grandmother + + align:start position:0% +kind of the the whole grandmother + + + align:start position:0% +kind of the the whole grandmother +solution type thing there are certain + + align:start position:0% +solution type thing there are certain + + + align:start position:0% +solution type thing there are certain +things that will always work and you + + align:start position:0% +things that will always work and you + + + align:start position:0% +things that will always work and you +hard code them so you can say if the + + align:start position:0% +hard code them so you can say if the + + + align:start position:0% +hard code them so you can say if the +matrix dimension is more than thousand + + align:start position:0% +matrix dimension is more than thousand + + + align:start position:0% +matrix dimension is more than thousand +always good to block or some kind of + + align:start position:0% +always good to block or some kind of + + + align:start position:0% +always good to block or some kind of +rules like that + + align:start position:0% +rules like that + + + align:start position:0% +rules like that +these roads work most of the time but + + align:start position:0% +these roads work most of the time but + + + align:start position:0% +these roads work most of the time but +obviously there are access cousins in + + align:start position:0% +obviously there are access cousins in + + + align:start position:0% +obviously there are access cousins in +certain cases that rules much worse that + + align:start position:0% +certain cases that rules much worse that + + + align:start position:0% +certain cases that rules much worse that +rules might be set for a certain machine + + align:start position:0% +rules might be set for a certain machine + + + align:start position:0% +rules might be set for a certain machine +said knock he takes all those things + + align:start position:0% +said knock he takes all those things + + + align:start position:0% +said knock he takes all those things +I'll give you the story so GCC has this + + align:start position:0% + + + + align:start position:0% + +fast table saw routine so fast table + + align:start position:0% +fast table saw routine so fast table + + + align:start position:0% +fast table saw routine so fast table +road sort routine says saw to using a + + align:start position:0% +road sort routine says saw to using a + + + align:start position:0% +road sort routine says saw to using a +parallel quicksort and when the number + + align:start position:0% +parallel quicksort and when the number + + + align:start position:0% +parallel quicksort and when the number +616 switch to insertion sort it's hard + + align:start position:0% +616 switch to insertion sort it's hard + + + align:start position:0% +616 switch to insertion sort it's hard +coded in in GCC Wow some amazing person + + align:start position:0% +coded in in GCC Wow some amazing person + + + align:start position:0% +coded in in GCC Wow some amazing person +figure of 16 this amazing number has to + + align:start position:0% +figure of 16 this amazing number has to + + + align:start position:0% +figure of 16 this amazing number has to +switch from parallel quicksort to + + align:start position:0% +switch from parallel quicksort to + + + align:start position:0% +switch from parallel quicksort to +insertion sort so we are try to figure + + align:start position:0% +insertion sort so we are try to figure + + + align:start position:0% +insertion sort so we are try to figure +out what's the profoundness of this + + align:start position:0% +out what's the profoundness of this + + + align:start position:0% +out what's the profoundness of this +number the profoundness of this number + + align:start position:0% +number the profoundness of this number + + + align:start position:0% +number the profoundness of this number +is samara 1995 when this code was + + align:start position:0% +is samara 1995 when this code was + + + align:start position:0% +is samara 1995 when this code was +released in those machines that was the + + align:start position:0% +released in those machines that was the + + + align:start position:0% +released in those machines that was the +right number that that 16 + + align:start position:0% +right number that that 16 + + + align:start position:0% +right number that that 16 +was a really good number to switch from + + align:start position:0% +was a really good number to switch from + + + align:start position:0% +was a really good number to switch from +parallelism to doing that because the + + align:start position:0% +parallelism to doing that because the + + + align:start position:0% +parallelism to doing that because the +cache size stuff like that but that 16 + + align:start position:0% +cache size stuff like that but that 16 + + + align:start position:0% +cache size stuff like that but that 16 +survived from 1995 I think even today + + align:start position:0% +survived from 1995 I think even today + + + align:start position:0% +survived from 1995 I think even today +it's there the today that number should + + align:start position:0% +it's there the today that number should + + + align:start position:0% +it's there the today that number should +be like 500 but it's in that because + + align:start position:0% +be like 500 but it's in that because + + + align:start position:0% +be like 500 but it's in that because +somebody thought 16 is the right it's + + align:start position:0% +somebody thought 16 is the right it's + + + align:start position:0% +somebody thought 16 is the right it's +hard-coded in they didn't change so + + align:start position:0% +hard-coded in they didn't change so + + + align:start position:0% +hard-coded in they didn't change so +there are a lot of things in compilers + + align:start position:0% +there are a lot of things in compilers + + + align:start position:0% +there are a lot of things in compilers +code like that the date or the some + + align:start position:0% +code like that the date or the some + + + align:start position:0% +code like that the date or the some +programmer said I know what works here + + align:start position:0% +programmer said I know what works here + + + align:start position:0% +programmer said I know what works here +this fits in there you put it in that + + align:start position:0% +this fits in there you put it in that + + + align:start position:0% +this fits in there you put it in that +but there's no rhyme or reason because + + align:start position:0% +but there's no rhyme or reason because + + + align:start position:0% +but there's no rhyme or reason because +at that time they had reason but it + + align:start position:0% +at that time they had reason but it + + + align:start position:0% +at that time they had reason but it +doesn't scale so lot of these heuristics + + align:start position:0% +doesn't scale so lot of these heuristics + + + align:start position:0% +doesn't scale so lot of these heuristics +get out of focus very fast and there's + + align:start position:0% +get out of focus very fast and there's + + + align:start position:0% +get out of focus very fast and there's +no theory behind it to say you know how + + align:start position:0% +no theory behind it to say you know how + + + align:start position:0% +no theory behind it to say you know how +do you update you have to go ask me why + + align:start position:0% +do you update you have to go ask me why + + + align:start position:0% +do you update you have to go ask me why +did you put that I made this oh yeah + + align:start position:0% +did you put that I made this oh yeah + + + align:start position:0% +did you put that I made this oh yeah +because my machine has a 32 kilobytes of + + align:start position:0% +because my machine has a 32 kilobytes of + + + align:start position:0% +because my machine has a 32 kilobytes of +cache like oh okay that's the different + + align:start position:0% +cache like oh okay that's the different + + + align:start position:0% +cache like oh okay that's the different +machine what we have today so that's the + + align:start position:0% +machine what we have today so that's the + + + align:start position:0% +machine what we have today so that's the +problem other things you can do search + + align:start position:0% +problem other things you can do search + + + align:start position:0% +problem other things you can do search +you can say okay I will try every + + align:start position:0% +you can say okay I will try every + + + align:start position:0% +you can say okay I will try every +possible thing the problem here is + + align:start position:0% +possible thing the problem here is + + + align:start position:0% +possible thing the problem here is +sometimes my search base is 10 to the + + align:start position:0% +sometimes my search base is 10 to the + + + align:start position:0% +sometimes my search base is 10 to the +power 10 you don't have any enough + + align:start position:0% +power 10 you don't have any enough + + + align:start position:0% +power 10 you don't have any enough +seconds in your lifetime to do that so + + align:start position:0% +seconds in your lifetime to do that so + + + align:start position:0% +seconds in your lifetime to do that so +sorry to be too complicated and that's + + align:start position:0% +sorry to be too complicated and that's + + + align:start position:0% +sorry to be too complicated and that's +where the auto 2 unit comes in so ok + + align:start position:0% +where the auto 2 unit comes in so ok + + + align:start position:0% +where the auto 2 unit comes in so ok +actually I have a little bit more slices + + align:start position:0% +actually I have a little bit more slices + + + align:start position:0% +actually I have a little bit more slices +so motel model bed solution is you come + + align:start position:0% +so motel model bed solution is you come + + + align:start position:0% +so motel model bed solution is you come +up with this comprehensive model like a + + align:start position:0% +up with this comprehensive model like a + + + align:start position:0% +up with this comprehensive model like a +cache model or something like that and + + align:start position:0% +cache model or something like that and + + + align:start position:0% +cache model or something like that and +you do that and you can exactly sure + + align:start position:0% +you do that and you can exactly sure + + + align:start position:0% +you do that and you can exactly sure +what's right for the optimal solution in + + align:start position:0% +what's right for the optimal solution in + + + align:start position:0% +what's right for the optimal solution in +here but the problem is hard to build + + align:start position:0% +here but the problem is hard to build + + + align:start position:0% +here but the problem is hard to build +models cannot model everything and most + + align:start position:0% +models cannot model everything and most + + + align:start position:0% +models cannot model everything and most +of the time model will miss the most + + align:start position:0% +of the time model will miss the most + + + align:start position:0% +of the time model will miss the most +important thing here is my based things + + align:start position:0% +important thing here is my based things + + + align:start position:0% +important thing here is my based things +in the rule of the thumb kind of a + + align:start position:0% +in the rule of the thumb kind of a + + + align:start position:0% +in the rule of the thumb kind of a +solution that you come up and say it's + + align:start position:0% +solution that you come up and say it's + + + align:start position:0% +solution that you come up and say it's +hard core it in there and it's very + + align:start position:0% +hard core it in there and it's very + + + align:start position:0% +hard core it in there and it's very +simple and easy works most of the time + + align:start position:0% +simple and easy works most of the time + + + align:start position:0% +simple and easy works most of the time +if you get it right but the problem is + + align:start position:0% +if you get it right but the problem is + + + align:start position:0% +if you get it right but the problem is +too simplistic it doesn't scare it + + align:start position:0% +too simplistic it doesn't scare it + + + align:start position:0% +too simplistic it doesn't scare it +doesn't doesn't stand the test of time + + align:start position:0% +doesn't doesn't stand the test of time + + + align:start position:0% +doesn't doesn't stand the test of time +most of the time in here exhaustive + + align:start position:0% +most of the time in here exhaustive + + + align:start position:0% +most of the time in here exhaustive +search is great but the problem is + + align:start position:0% +search is great but the problem is + + + align:start position:0% +search is great but the problem is +just way too much possibility of + + align:start position:0% +just way too much possibility of + + + align:start position:0% +just way too much possibility of +searching in here too big of search + + align:start position:0% +searching in here too big of search + + + align:start position:0% +searching in here too big of search +space can do that + + align:start position:0% +space can do that + + + align:start position:0% +space can do that +so this is where you want to prune the + + align:start position:0% +so this is where you want to prune the + + + align:start position:0% +so this is where you want to prune the +search space and the pruning the best + + align:start position:0% +search space and the pruning the best + + + align:start position:0% +search space and the pruning the best +way to do that is basically use Auto + + align:start position:0% +way to do that is basically use Auto + + + align:start position:0% +way to do that is basically use Auto +tuning so what auto tuner you can do is + + align:start position:0% +tuning so what auto tuner you can do is + + + align:start position:0% +tuning so what auto tuner you can do is +you can define the space of acceptable + + align:start position:0% +you can define the space of acceptable + + + align:start position:0% +you can define the space of acceptable +values nicely choose a value at random + + align:start position:0% +values nicely choose a value at random + + + align:start position:0% +values nicely choose a value at random +that's what this system will to try it + + align:start position:0% +that's what this system will to try it + + + align:start position:0% +that's what this system will to try it +out there and even where the performance + + align:start position:0% +out there and even where the performance + + + align:start position:0% +out there and even where the performance +of that value went to n because n to n + + align:start position:0% +of that value went to n because n to n + + + align:start position:0% +of that value went to n because n to n +matters because if you try to predict + + align:start position:0% +matters because if you try to predict + + + align:start position:0% +matters because if you try to predict +the most of time it might not work and + + align:start position:0% +the most of time it might not work and + + + align:start position:0% +the most of time it might not work and +if satisfies the performance that that + + align:start position:0% +if satisfies the performance that that + + + align:start position:0% +if satisfies the performance that that +you need you are done otherwise choose a + + align:start position:0% +you need you are done otherwise choose a + + + align:start position:0% +you need you are done otherwise choose a +new value and iterate over this go to + + align:start position:0% +new value and iterate over this go to + + + align:start position:0% +new value and iterate over this go to +three in depth so this is the kind of + + align:start position:0% +three in depth so this is the kind of + + + align:start position:0% +three in depth so this is the kind of +thing and what you have to do is you + + align:start position:0% +thing and what you have to do is you + + + align:start position:0% +thing and what you have to do is you +need to have a system to figure out how + + align:start position:0% +need to have a system to figure out how + + + align:start position:0% +need to have a system to figure out how +to do is fast basically what space to + + align:start position:0% +to do is fast basically what space to + + + align:start position:0% +to do is fast basically what space to +basically do that when to basically + + align:start position:0% +basically do that when to basically + + + align:start position:0% +basically do that when to basically +thing you are done and how to go through + + align:start position:0% +thing you are done and how to go through + + + align:start position:0% +thing you are done and how to go through +the iterating through that so this is + + align:start position:0% +the iterating through that so this is + + + align:start position:0% +the iterating through that so this is +the kind of it's cartoonish way what + + align:start position:0% +the kind of it's cartoonish way what + + + align:start position:0% +the kind of it's cartoonish way what +happens is you give a value can it you + + align:start position:0% +happens is you give a value can it you + + + align:start position:0% +happens is you give a value can it you +compile the program you run it with a + + align:start position:0% +compile the program you run it with a + + + align:start position:0% +compile the program you run it with a +bunch of data you have to run into it + + align:start position:0% +bunch of data you have to run into it + + + align:start position:0% +bunch of data you have to run into it +but otherwise you all fitting you can't + + align:start position:0% +but otherwise you all fitting you can't + + + align:start position:0% +but otherwise you all fitting you can't +run it with one and you get the results + + align:start position:0% +run it with one and you get the results + + + align:start position:0% +run it with one and you get the results +and you get something like average and + + align:start position:0% +and you get something like average and + + + align:start position:0% +and you get something like average and +then if you go through this loop in here + + align:start position:0% +then if you go through this loop in here + + + align:start position:0% +then if you go through this loop in here +and what open tuna has done is come up + + align:start position:0% +and what open tuna has done is come up + + + align:start position:0% +and what open tuna has done is come up +with the ensemble of techniques so the + + align:start position:0% +with the ensemble of techniques so the + + + align:start position:0% +with the ensemble of techniques so the +idea there is when you're searching + + align:start position:0% +idea there is when you're searching + + + align:start position:0% +idea there is when you're searching +through a space you might be at the + + align:start position:0% +through a space you might be at the + + + align:start position:0% +through a space you might be at the +bottom of a hill of the space so what + + align:start position:0% +bottom of a hill of the space so what + + + align:start position:0% +bottom of a hill of the space so what +that means is there certain value if you + + align:start position:0% +that means is there certain value if you + + + align:start position:0% +that means is there certain value if you +keep improving value that you're getting + + align:start position:0% +keep improving value that you're getting + + + align:start position:0% +keep improving value that you're getting +it better and better and better and at + + align:start position:0% +it better and better and better and at + + + align:start position:0% +it better and better and better and at +that time something like a hill climber + + align:start position:0% + + + + align:start position:0% + +here you climb but something like Ned + + align:start position:0% +here you climb but something like Ned + + + align:start position:0% +here you climb but something like Ned +limine hill climber can actually give + + align:start position:0% +limine hill climber can actually give + + + align:start position:0% +limine hill climber can actually give +you the best performance you're getting + + align:start position:0% +you the best performance you're getting + + + align:start position:0% +you the best performance you're getting +very fast in this but me to arrive at + + align:start position:0% +very fast in this but me to arrive at + + + align:start position:0% +very fast in this but me to arrive at +the top of the hill for that parameters + + align:start position:0% +the top of the hill for that parameters + + + align:start position:0% +the top of the hill for that parameters +there's no place to go so that if you + + align:start position:0% +there's no place to go so that if you + + + align:start position:0% +there's no place to go so that if you +try to give try to he'll come it's not + + align:start position:0% +try to give try to he'll come it's not + + + align:start position:0% +try to give try to he'll come it's not +going to helpful so at that time what + + align:start position:0% +going to helpful so at that time what + + + align:start position:0% +going to helpful so at that time what +you want to do is do something like a + + align:start position:0% +you want to do is do something like a + + + align:start position:0% +you want to do is do something like a +random search in here so what this + + align:start position:0% +random search in here so what this + + + align:start position:0% +random search in here so what this +system do open to you know you do it it + + align:start position:0% +system do open to you know you do it it + + + align:start position:0% +system do open to you know you do it it +will basically test this request in + + align:start position:0% +will basically test this request in + + + align:start position:0% +will basically test this request in +there and and if something is doing very + + align:start position:0% +there and and if something is doing very + + + align:start position:0% +there and and if something is doing very +well + + align:start position:0% +well + + + align:start position:0% +well +it will give it more time if not what it + + align:start position:0% +it will give it more time if not what it + + + align:start position:0% +it will give it more time if not what it +will do is it will say ok look + + align:start position:0% +will do is it will say ok look + + + align:start position:0% +will do is it will say ok look +this technique is not working let's try + + align:start position:0% +this technique is not working let's try + + + align:start position:0% +this technique is not working let's try +something else it'll basically look at + + align:start position:0% +something else it'll basically look at + + + align:start position:0% +something else it'll basically look at +the timing here so so it do that this + + align:start position:0% +the timing here so so it do that this + + + align:start position:0% +the timing here so so it do that this +search much faster than otherwise you + + align:start position:0% +search much faster than otherwise you + + + align:start position:0% +search much faster than otherwise you +can do so I want to finish this by + + align:start position:0% +can do so I want to finish this by + + + align:start position:0% +can do so I want to finish this by +showing what you did for total + + align:start position:0% +showing what you did for total + + + align:start position:0% +showing what you did for total +infographic + + align:start position:0% +infographic + + + align:start position:0% +infographic +so you have algorithm and you have a + + align:start position:0% +so you have algorithm and you have a + + + align:start position:0% +so you have algorithm and you have a +schedule it's pain to write this + + align:start position:0% +schedule it's pain to write this + + + align:start position:0% +schedule it's pain to write this +schedule it's in fact there's a good + + align:start position:0% +schedule it's in fact there's a good + + + align:start position:0% +schedule it's in fact there's a good +interest in things like in in when you + + align:start position:0% +interest in things like in in when you + + + align:start position:0% +interest in things like in in when you +do halide we decided okay it should be + + align:start position:0% +do halide we decided okay it should be + + + align:start position:0% +do halide we decided okay it should be +similar to write the algorithm for + + align:start position:0% +similar to write the algorithm for + + + align:start position:0% +similar to write the algorithm for +halide and the schedule Google very fast + + align:start position:0% +halide and the schedule Google very fast + + + align:start position:0% +halide and the schedule Google very fast +realized many people won't use a light + + align:start position:0% +realized many people won't use a light + + + align:start position:0% +realized many people won't use a light +and they fats it's about two years they + + align:start position:0% +and they fats it's about two years they + + + align:start position:0% +and they fats it's about two years they +had about hundreds of programmers who + + align:start position:0% +had about hundreds of programmers who + + + align:start position:0% +had about hundreds of programmers who +can write the algorithm but they only + + align:start position:0% +can write the algorithm but they only + + + align:start position:0% +can write the algorithm but they only +had five people who could write the + + align:start position:0% +had five people who could write the + + + align:start position:0% +had five people who could write the +really good schedule to try to really + + align:start position:0% +really good schedule to try to really + + + align:start position:0% +really good schedule to try to really +good schedule you need to understand a + + align:start position:0% +good schedule you need to understand a + + + align:start position:0% +good schedule you need to understand a +little bit of the hell with them you + + align:start position:0% +little bit of the hell with them you + + + align:start position:0% +little bit of the hell with them you +know understand a little bit of the + + align:start position:0% +know understand a little bit of the + + + align:start position:0% +know understand a little bit of the +architecture a little bit of everything + + align:start position:0% +architecture a little bit of everything + + + align:start position:0% +architecture a little bit of everything +and it that's much harder for people to + + align:start position:0% +and it that's much harder for people to + + + align:start position:0% +and it that's much harder for people to +learn so getting the schedule right it's + + align:start position:0% +learn so getting the schedule right it's + + + align:start position:0% +learn so getting the schedule right it's +not that easy and same thing in here + + align:start position:0% +not that easy and same thing in here + + + align:start position:0% +not that easy and same thing in here +because you need to understand a lot + + align:start position:0% +because you need to understand a lot + + + align:start position:0% +because you need to understand a lot +unless you do kind of random you can + + align:start position:0% +unless you do kind of random you can + + + align:start position:0% +unless you do kind of random you can +search all like arbitrary but to do try + + align:start position:0% +search all like arbitrary but to do try + + + align:start position:0% +search all like arbitrary but to do try +you need to know a little bit more so + + align:start position:0% +you need to know a little bit more so + + + align:start position:0% +you need to know a little bit more so +what we can do is we can basically give + + align:start position:0% +what we can do is we can basically give + + + align:start position:0% +what we can do is we can basically give +some I'd imp idea about the graphs and + + align:start position:0% +some I'd imp idea about the graphs and + + + align:start position:0% +some I'd imp idea about the graphs and +some idea about the rhythm in there we + + align:start position:0% +some idea about the rhythm in there we + + + align:start position:0% +some idea about the rhythm in there we +can auto-tune these things in there and + + align:start position:0% +can auto-tune these things in there and + + + align:start position:0% +can auto-tune these things in there and +then generate the schedule and so what + + align:start position:0% +then generate the schedule and so what + + + align:start position:0% +then generate the schedule and so what +we found was to generate this schedule + + align:start position:0% +we found was to generate this schedule + + + align:start position:0% +we found was to generate this schedule +if you do exhaustive search it runs four + + align:start position:0% +if you do exhaustive search it runs four + + + align:start position:0% +if you do exhaustive search it runs four +days but in in if you see Maradona open + + align:start position:0% +days but in in if you see Maradona open + + + align:start position:0% +days but in in if you see Maradona open +to you know you can find a really good + + align:start position:0% +to you know you can find a really good + + + align:start position:0% +to you know you can find a really good +schedule for in less than two hours and + + align:start position:0% +schedule for in less than two hours and + + + align:start position:0% +schedule for in less than two hours and +in fact few cases p4 schedules that was + + align:start position:0% +in fact few cases p4 schedules that was + + + align:start position:0% +in fact few cases p4 schedules that was +better than what we thought was the best + + align:start position:0% +better than what we thought was the best + + + align:start position:0% +better than what we thought was the best +possible schedule because it was able to + + align:start position:0% +possible schedule because it was able to + + + align:start position:0% +possible schedule because it was able to +it was able to search much better than + + align:start position:0% +it was able to search much better than + + + align:start position:0% +it was able to search much better than +our intuition would say in here and fine + + align:start position:0% +our intuition would say in here and fine + + + align:start position:0% +our intuition would say in here and fine +and even if our intuition know it it has + + align:start position:0% +and even if our intuition know it it has + + + align:start position:0% +and even if our intuition know it it has +more time to try many different + + align:start position:0% +more time to try many different + + + align:start position:0% +more time to try many different +combinations and trying something in + + align:start position:0% +combinations and trying something in + + + align:start position:0% +combinations and trying something in +come something better in here so that's + + align:start position:0% +come something better in here so that's + + + align:start position:0% +come something better in here so that's +all I have today + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/bkJ7zVcBpaQ.txt b/bkJ7zVcBpaQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..7ebdcc2a3c1e07e14f8ed4ec3e8cb382e67a6db8 --- /dev/null +++ b/bkJ7zVcBpaQ.txt @@ -0,0 +1,83 @@ +align:start position:0% + +and we're + + align:start position:0% + + + + align:start position:0% + +back Cameron is on the + + align:start position:0% +back Cameron is on the + + + align:start position:0% +back Cameron is on the +field and he's trying the plane is up + + align:start position:0% +field and he's trying the plane is up + + + align:start position:0% +field and he's trying the plane is up +and the plane is up + + align:start position:0% +and the plane is up + + + align:start position:0% +and the plane is up +and plane is + + align:start position:0% + + + + align:start position:0% + +down and the plane is + + align:start position:0% + + + + align:start position:0% + +down we might learn in the post + + align:start position:0% + + + + align:start position:0% + +interview what uh has + + align:start position:0% +interview what uh has + + + align:start position:0% +interview what uh has +going on + + align:start position:0% + + + + align:start position:0% + +here okay and I think 25 is going + + align:start position:0% +here okay and I think 25 is going + + + align:start position:0% +here okay and I think 25 is going +now so who's up now try it again \ No newline at end of file diff --git a/cDw2dF6vWlQ.txt b/cDw2dF6vWlQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..fe2ad4f4cd9e69e5a7615650f62e022092613e09 --- /dev/null +++ b/cDw2dF6vWlQ.txt @@ -0,0 +1,379 @@ +align:start position:0% + +you know um when you look at uh what's + + align:start position:0% +you know um when you look at uh what's + + + align:start position:0% +you know um when you look at uh what's +happening in the world now uh you see + + align:start position:0% +happening in the world now uh you see + + + align:start position:0% +happening in the world now uh you see +that uh uh institutions like MIT Harvard + + align:start position:0% +that uh uh institutions like MIT Harvard + + + align:start position:0% +that uh uh institutions like MIT Harvard +Stanford uh berkele okay they are all + + align:start position:0% +Stanford uh berkele okay they are all + + + align:start position:0% +Stanford uh berkele okay they are all +producing digital content and uh sharing + + align:start position:0% +producing digital content and uh sharing + + + align:start position:0% +producing digital content and uh sharing +it with the world okay something that we + + align:start position:0% +it with the world okay something that we + + + align:start position:0% +it with the world okay something that we +started with open coare here at MIT in + + align:start position:0% +started with open coare here at MIT in + + + align:start position:0% +started with open coare here at MIT in +year + + align:start position:0% +year + + + align:start position:0% +year +2001 uh this is now part of the profile + + align:start position:0% +2001 uh this is now part of the profile + + + align:start position:0% +2001 uh this is now part of the profile +of uh a top university you do research + + align:start position:0% +of uh a top university you do research + + + align:start position:0% +of uh a top university you do research +you teach your students and you share + + align:start position:0% +you teach your students and you share + + + align:start position:0% +you teach your students and you share +your material with World okay what what + + align:start position:0% +your material with World okay what what + + + align:start position:0% +your material with World okay what what +I see also happening now is that not + + align:start position:0% +I see also happening now is that not + + + align:start position:0% +I see also happening now is that not +only do you share your digital + + align:start position:0% +only do you share your digital + + + align:start position:0% +only do you share your digital +educational content with the world but + + align:start position:0% +educational content with the world but + + + align:start position:0% +educational content with the world but +you bring it back on campus and use that + + align:start position:0% +you bring it back on campus and use that + + + align:start position:0% +you bring it back on campus and use that +digital content to transform your own + + align:start position:0% +digital content to transform your own + + + align:start position:0% +digital content to transform your own +residential classroom this is sort of + + align:start position:0% +residential classroom this is sort of + + + align:start position:0% +residential classroom this is sort of +the final uh piece of the the loop which + + align:start position:0% +the final uh piece of the the loop which + + + align:start position:0% +the final uh piece of the the loop which +I think MIT is very serious uh in uh in + + align:start position:0% +I think MIT is very serious uh in uh in + + + align:start position:0% +I think MIT is very serious uh in uh in +accomplishing yeah uh we have uh we + + align:start position:0% +accomplishing yeah uh we have uh we + + + align:start position:0% +accomplishing yeah uh we have uh we +produced something like 200 + + align:start position:0% +produced something like 200 + + + align:start position:0% +produced something like 200 +muks and they are all used virtually all + + align:start position:0% +muks and they are all used virtually all + + + align:start position:0% +muks and they are all used virtually all +of them are being used for residential + + align:start position:0% +of them are being used for residential + + + align:start position:0% +of them are being used for residential +education and uh so much so that 90% of + + align:start position:0% +education and uh so much so that 90% of + + + align:start position:0% +education and uh so much so that 90% of +undergraduate students uh take at least + + align:start position:0% +undergraduate students uh take at least + + + align:start position:0% +undergraduate students uh take at least +one course at MIT uh that that uh uses + + align:start position:0% +one course at MIT uh that that uh uses + + + align:start position:0% +one course at MIT uh that that uh uses +the the + + align:start position:0% +the the + + + align:start position:0% +the the +Mook open courseware is used widely by + + align:start position:0% +Mook open courseware is used widely by + + + align:start position:0% +Mook open courseware is used widely by +undergraduate students more so than most + + align:start position:0% +undergraduate students more so than most + + + align:start position:0% +undergraduate students more so than most +people + + align:start position:0% +people + + + align:start position:0% +people +realize uh there's not a I don't think + + align:start position:0% +realize uh there's not a I don't think + + + align:start position:0% +realize uh there's not a I don't think +I've ever run across an MIT + + align:start position:0% +I've ever run across an MIT + + + align:start position:0% +I've ever run across an MIT +undergraduate student who had not heard + + align:start position:0% +undergraduate student who had not heard + + + align:start position:0% +undergraduate student who had not heard +of open course whereare they use it sort + + align:start position:0% +of open course whereare they use it sort + + + align:start position:0% +of open course whereare they use it sort +of like like air you know it's uh they + + align:start position:0% +of like like air you know it's uh they + + + align:start position:0% +of like like air you know it's uh they +use it to to see if they want to take a + + align:start position:0% +use it to to see if they want to take a + + + align:start position:0% +use it to to see if they want to take a +certain course next semester they use it + + align:start position:0% +certain course next semester they use it + + + align:start position:0% +certain course next semester they use it +to catch up on their own course they use + + align:start position:0% +to catch up on their own course they use + + + align:start position:0% +to catch up on their own course they use +problem sets from you know several years + + align:start position:0% +problem sets from you know several years + + + align:start position:0% +problem sets from you know several years +ago just to brush up on their own study + + align:start position:0% +ago just to brush up on their own study + + + align:start position:0% +ago just to brush up on their own study +of the course that they're + + align:start position:0% +of the course that they're + + + align:start position:0% +of the course that they're +taking um and sometimes just to look at + + align:start position:0% +taking um and sometimes just to look at + + + align:start position:0% +taking um and sometimes just to look at +a course that they know they're not + + align:start position:0% +a course that they know they're not + + + align:start position:0% +a course that they know they're not +going to take because it's outside of + + align:start position:0% +going to take because it's outside of + + + align:start position:0% +going to take because it's outside of +their specialty but they're just curious + + align:start position:0% +their specialty but they're just curious + + + align:start position:0% +their specialty but they're just curious +about what uh what's being taught in + + align:start position:0% +about what uh what's being taught in + + + align:start position:0% +about what uh what's being taught in +that course \ No newline at end of file diff --git a/cT855rpX8bc.txt b/cT855rpX8bc.txt new file mode 100644 index 0000000000000000000000000000000000000000..38acd79fca562d00be4771a7dc0e1b9a6bacb4c2 --- /dev/null +++ b/cT855rpX8bc.txt @@ -0,0 +1,3960 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +JEFF GORE: Today, what we want +to do is focus more explicitly + +on bacterial chemotaxis. + +Of course, a +discussion that we had + +on Thursday about "Life +at Low Reynolds Numbers" + +is certainly very +relevant to this question + +of how bacteria are +maybe able to find food + +or what constraints +they're faced in trying + +to solve this problem. + +Today, we're going to +discuss in more depth + +this idea of the biased random +walk that runs and tumbles + +that we talked about on +Thursday, that allow bacteria + +to swim towards attractants +and away from repellents. + +But in particular, +there's something + +that is rather subtle about the +particular biased random walk + +that bacteria implement. + +Now, the way that you +might kind of naively + +imagine that this +thing would work + +is that you would just have +this tumbling frequency be + +a function of the concentration +of the attractant, for example. + +And that indeed would allow +you to swim or to execute + +a biased random walk +towards, say, food sources, + +towards attractants, +but it would not + +be effective over a very +wide range of concentrations. + +However, if you experimentally +ask, how well can bacteria + +swim towards +attractants, it turns out + +they can respond over +five orders of magnitude + +of concentration of these +attractants, which is really + +quite incredible, if you think +about the engineering challenge + +that these little one-micron +cells are able to overcome. + +And the basic way that +they do this is they + +implement what's essentially +equivalent to integral feedback + +in the context of engineering, +where it turns out + +that the steady-state tumbling +frequency, so the frequency + +of which they'd +execute one of these + +tumbles that randomizes their +motion, that displays what's + +known as perfect adaptation. + +It's not a function of the +concentration of-- if you have + +a constant concentration +of an attractant, + +then it's not a +function of that. + +Of course, changes in +concentrations it responds to, + +but somehow, E. coli and +many other microorganisms + +are able to implement this +very clever thing where + +the steady-state frequency +of tumbling, of changing + +direction, is somehow +not a function + +of the overall +attractant concentration. + +Now, that's already an +interesting, I think, + +phenomenon. + +And in some ways, +you can think of it + +as some kind of +robustness, because there + +is some way in which this +tumbling frequency is + +robust against constant changes +in the level of attractants. + +And it's that +aspect, I think, that + +makes this example both +rather subtle but also + +quite confusing, because +it's the phenomenon + +of perfect adaptation +that already + +has some aspects of +robustness, but it's + +this phenomenon of +perfect adaptation + +that is robust against changes +in concentrations of proteins, + +for example, the concentration +of the protein [? key ?] + +R that we're going +to talk about. + +So I think that this +is in some ways maybe + +the prettiest +example that we have + +of this principle +of robustness, but I + +think it's also in +some ways the most + +tricky to wrap your head around, +because it's sort of robustness + +of a robustness in some ways. + +All right. + +So our goal for today is +going to be to make sure + +that we understand the challenge +that E. coli are facing + +and then to try to understand +the genetic circuit + +that they use in order to +overcome this challenge. + +So what I'm going to do for +the next hour and 15 minutes + +is we're going to leave +this network up on the board + +so that any time that +you're confused about what + +is R, B, Z, Y, so +forth, you can kind of + +look up here and remind +yourself what this thing is. + +But hopefully, the +reading from last night + +will help you in +following what's going on. + +There are a fair number of +letters, I will admit it. + +So first, I just +want to make sure + +that we're all +kind of remembering + +the basic phenomenon +that we're trying + +to study, which is this idea of +consecutive runs and tumbles. + +So this random walk is really +composed of what you might call + +or what we do call runs, +where the bacteria goes sort + +of straight and +then tumbles, which + +they randomize their motion. + +So this is runs and tumbles, +where bacteria, they + +go semi-straight for of order +a second-- order one second-- + +and this is the run. + +Then, they have +this tumbling that + +might last about one second, +so a 0.1 second tumble, + +over which the motion is +sort of random in this axis + +of the orientation. + +And then, they kind of +go in a new direction + +and then tumble again and then +new direction and so forth. + +So it's runs +followed by tumbles. + +Now, the thing that +changes depending + +on whether the cells +are sensing that they're + +moving up or down, say, +an attractant gradient + +is the frequency of +those tumbles, i.e. + +how long are the runs? + +I said that they're +around one second, + +but this will vary depending +upon whether bacteria + +sense that things +are getting better + +or things are getting worse. + +Can somebody remind us how +the bacteria actually execute + +one of these tumble motions? + +Yes? + +AUDIENCE: They have this other +motors-- they have mini-motors + +in their flagella +and they usually + +all spin one way, which I +think is counterclockwise. + +JEFF GORE: That's right. + +I always have trouble-- +so the runs are indeed + +when these things are +rotating counterclockwise. + +AUDIENCE: Yeah. + +And one of them can +decide to switch + +and start turning clockwise. + +And what it does, it just +sort of-- I don't know. + +I just imagine it throws +the whole motor off. + +JEFF GORE: Exactly. + +And the flagella in the context +of-- so we have our E. coli. + +The velocity is of order, +say, 30 microns per second. + +Now, they have these +flagella that are actually + +distributed-- the motors +are actually distributed + +across the entire cell. + +So it's not just on the back. + +But then, these individual +filaments kind of + +come together towards +the back and then + +they have this corkscrew shape. + +When these things +are all rotating + +in the counterclockwise +direction, + +that corresponds to a run, +when there's directed motion. + +But then if one of +them goes clockwise, + +the bundle falls apart. + +And indeed, there are some +very nice movies online + +where you can see that when +they're going clockwise, + +you see that the flagella are +kind of doing crazy things + +and that causes this +thing to kind of tumble + +in a random orientation. + +So it randomizes its direction. + +Now, one thing that +we did not talk + +about in the context of this +low Reynolds number motion + +was the question of +how hard you would + +have to pull in +order to get a cell + +to go 30 microns per second. + +Now, remember, we're in the +low Reynolds number regime, + +where the force +you have to apply + +is in general proportional +to this velocity. + +And this thing is very +much not a sphere, + +but if it were a sphere, for +a sphere, the proportionality + +constant is this 6 pi eta +av, where a here is again + +the radius. + +Now, regardless of +the precise shape, + +you'll always get for the low +Reynolds regime something that + +looks vaguely like this, where +this is going to the longest + +linear dimension and this here +depends on the precise geometry + +of the object. + +And so just-- it's +useful to try to get + +a sense of order of magnitude. + +How large are these forces +that we're talking about? + +In particular, +how hard would you + +have to pull a cell +in order to get + +it to go 30 microns per second? + +Now, of course then, +there's a question. + +What's roughly the scale that +we should be thinking about? + +Right now, a newton is the scale +that's for macroscopic objects. + +So you'd say, OK, probably +not going to be up that large. + +Then, on the other +scale, we can think + +about the forces that +can be applied or exerted + +by individual molecular motors. + +Has anybody studied this at all? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Right, +order of picanewtons. + +So force for a +molecular motor is going + +to be of order picanewtons. + +Now, there's a +simple way to kind of + +get at why this might actually +be, because what is it + +that powers many of +these molecular motors? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Yeah, so +it's often-- you're + +thinking of maybe the motors +that operate in a membrane. + +And then, there might +be some difference + +in a gradient, so a +difference in concentration + +across that membrane +and that can actually + +power, for example, rotation. + +We're going to talk +a little bit more + +about this in the context +of the flagella motor, + +because this is one of only +a few known rotary motors. + +I'm just going to write this +down so that I don't forget + +to say something about it. + +But in this case-- + +AUDIENCE: ATP? + +JEFF GORE: ATP, right? + +So in many cases, what +happens is that you have, + +for example, kinesin or myosin. + +These are motors that walk along +some track and in many cases, + +each step corresponds to a +single ATP being hydrolyzed. + +And so given that, +there's some maximal force + +that you can imagine +such a motor applying. + +So for example-- and what +might it depend upon? + +AUDIENCE: The energy of +ATP hydrolysis [INAUDIBLE] + +JEFF GORE: Ah, very good. + +So we have delta G for say, ATP. + +And there's going to be +a length scale, right? + +And what's going to +be the relevant length + +scale in the case of, for +example, a motor like kinesin? + +AUDIENCE: The flagella, I guess? + +JEFF GORE: Well, kinesin is +not walking along the flagella, + +but in this case, kinesin is +walking along microtubules, + +for example. + +So you're right that +we need a length scale, + +because this is going to have +some units of say, picanewton + +nanometers-- oops, +that's an Nm-- + +and we want to get a picanewton +so we're going to need a length + +scale to divide by, right? + +AUDIENCE: So how long +you move each time? + +JEFF GORE: That's right. + +It's kind of the distance that +this thing's moving, right? + +So indeed, what happens +in the case of kinesin + +is that they take steps +with what are called "heads" + +but we can think of them +as "feet" if we want. + +So each step is in this +case eight nanometers. + +For example, delta L for kinesin +is equal to eight nanometers. + +You don't need to know +this, but just it's + +useful to have some +sense of scale. + +Now, of course, +delta G of ATP, this + +depends upon the concentrations +of the reactants, + +of the products, and so forth. + +But this thing might be of +order 100 picanewton nanometers. + +Now, depending on +conditions, maybe it's + +70, but of order here. + +And indeed, what +this tells us is + +that just based on what +we've said right now, even + +without building any fancy +microscopes to measure + +how much force these +things can apply, + +you can see that the maximum +force it could possibly apply + +would be something on the +order of delta G divided + +by the length that it's pulling. + +Otherwise, you could make +a perpetual motion machine. + +So this-- well, +maybe what we'll do + +if we want to make +our math simpler, + +we could say this is around 80. + +It's of order there. + +But the point is that this +is of order 10 picanewtons, + +so it's kind of +picanewton scale. + +All right. + +So given this, it's interesting +to ask, how hard would you + +have to pull? + +So how big is a kinesin model +going to be, this protein? + +AUDIENCE: About +eight nanometers. + +JEFF GORE: Yeah, right, +about eight nanometers. + +Of course, it's kind +of long, spindly things + +like my skinny legs, +right, but let's + +indeed going to be +around that scale, + +whereas the cell is one micron +wide, multiple microns long, so + +much, much larger. + +We'll draw a little-- +here's a kinesin in there. + +It's even smaller than that. + +Kinesin's small. + +Now, the question is, +how much force would you + +have to apply in order to +pull an E. coli at 30 microns + +a second? + +Force to pull E. +coli at the speed + +that it's actually +observed to go-- now, + +you're unlikely to be able to +do the calculation right here. + +It's actually a +simple calculation. + +We could do it in +a moment, but it's + +useful to just kind of imagine +what scale might it be. + +All right, this is a way of-- +we can go up as high as we want. + +You can continue it on and this +is all in units of picanewtons. + +Once again, it's +useful to make guesses + +about your intuition +on these things + +just so you have some +notion of where we might be. + +And of course, in this case, +nobody wants to guess anything, + +because they feel-- +all right, I'll + +give you 10 seconds just +to make your best guess. + +Somebody's forcing you to do it. + +In this case, it's me. + +No reason that you actually +should necessarily get this. + +Pulling through water. + +AUDIENCE: At 30 microns. + +JEFF GORE: At 30 +microns per second. + +AUDIENCE: Could you +give us the viscosity + +of water in picanewtons? + +JEFF GORE: Yeah, it's +10 to the minus nine + +in the units of picanewton +nanometer second something. + +AUDIENCE: Great. + +JEFF GORE: Right. + +Now, I've given you enough time. + +You should have just +been able-- now, + +I'm going to be disappointed +if you don't get it right. + +No. + +Let's just see where we are. + +Ready? + +Three, two, one. + +OK, so I'd say that we +have a bunch of-- I'd say + +the mean is kind of a C-D-ish. + +We got some A-B's. + +All right, so I'd say it's +somewhere in the sense of, + +yeah, maybe it's 100,000. + +So maybe if you had 100 of these +kinesins pulling you along, + +then you'd be able to go 30 +microns a second, although you + +have to be careful because +kinesin can't actually + +go that fast. + +But these are details, right? + +No, there's a +reasonable question. + +How hard would you have to pull. + +Of course, if we want, +we could actually just + +do the equations here, right? + +The force, it's around 20. + +In units of picanewton +nanometer seconds, + +I told you that the eta is +around 10 to the minus 9. + +All right. + +And the radius, what +radius do you want to use? + +AUDIENCE: A micron. + +JEFF GORE: A micron. + +So do we write a 1 here? + +Do we write what? + +10 to the 3 because +I already told you + +that this was in units where +everything is picanewtons + +nanometers seconds. + +And velocity, this +is again per second. + +So this is three times 10 to +the 4, because that's how many + +nanometers per second. + +And this gets us to around-- +that's 10 to the seven. + +We're going to have +to divide by 100, + +so this is 60 divided by 100-- +so less than a picanewton. + +So this is really +pretty surprising. + +And again, this is a reflection +of the wonders of low Reynolds + +numbers kind of behavior. + +So it's somewhere here. + +Yes? + +AUDIENCE: So since +there are many flagella, + +is it telling us-- +[INAUDIBLE] is it telling us + +that they're very inefficient +compared to the [INAUDIBLE] + +JEFF GORE: Yeah, it's +a good question, right? + +So I think there +are several ways. + +And this is one +aspect maybe of what + +we read about in the "Life +at Low Reynolds Numbers." + +The comparison was to a +Datsun in Saudi Arabia. + +Of course, I think that this +was written in the '70s where + +that meant something. + +But I think that a Datsun, I +guess, is a fuel efficient car? + +Well, that was my +inference from that. + +And Saudi Arabia has a +lot of oil, still true. + +And the saying was that it might +only be 1% efficient or so, + +right? + +But if you don't have to +apply very much force there, + +then maybe that's +not a disaster. + +The swimming speed +is not actually + +a super strong function +of the number of flagella + +that are there, as far +as my understanding. + +So I'm actually a little +bit-- there are cases + +where you do get somewhat +higher speed with more flagella, + +although I have to confess, +just from the geometry + +of the multiple flagella I find +totally mystifying, because I + +would've thought they +would get tangled up, + +because each of them goes in +and they form a corkscrew. + +I don't know. + +It just doesn't seem +that it should work. + +But it does, so I'm not going +to argue that it doesn't. + +AUDIENCE: Probably it has to do +with the low Reynolds number. + +So you imagine swimming, +sort of flying around. + +JEFF GORE: Yeah, no, +my concern is not even + +a matter of the low +Reynolds number or not. + +It's just a matter of +they're each spinning + +and then-- this is something +really I've never understood, + +so I typically avoid +talking about it. + +I don't know. + +I just feel like +there's something wrong. + +But in any case, you don't +need to pull very hard in order + +to get even a micron-size +object to go rather fast. + +Yes? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Oh, I'm +not aware of it. + +This thing can actually +go-- it's 10 microns long, + +so this thing is huge, actually. + +But I-- + +AUDIENCE: It's +probably just a repeat. + +Or even if it is +a repeat, you can + +[INAUDIBLE] I'd +just be surprised + +if it wasn't, since +it seems like that. + +JEFF GORE: Yeah, +so I don't know, + +but I'm not even sure if +that would necessarily + +address my concern, which +is it seems like they + +have to go through each other. + +But it's not true, so I don't +want to make the argument too + +strongly. + +Did you have a question? + +AUDIENCE: So I was just +thinking about this [INAUDIBLE] + +Might it be possible that +they, if they are all sync up + +their rotations, then it doesn't +matter how tangled they are? + +JEFF GORE: Yeah, no, +even-- even if they're all + +spinning at the exact +same rate, I still + +feel that they +should get tangled, + +but it's a feeling that +is apparently not true. + +So I don't want to-- + +AUDIENCE: But if they're always +tumbling, maybe the time to-- + +JEFF GORE: No, no, no, +wait-- so it's not-- no, + +the tumble is not due to +my supposed mechanism. + +They're spinning at +something like 100 hertz. + +The motors are spinning at +something like 100 hertz, + +right? + +So in principle, if they +were going to get tangled, + +they would've gotten tangled. + +AUDIENCE: Seems [INAUDIBLE] + +JEFF GORE: That's +right, that's right. + +I do want to just +come back and say + +one thing about this +question of a rotary motor, + +because it's a fascinating +question-- oh yes, go ahead. + +AUDIENCE: Sorry, I just +had a quick question. + +What was the units of eta again? + +JEFF GORE: Oh, +this is the thing. + +The units of eta, I +always just go back here + +and I say, OK, +well, it's the units + +of a force divided by unit of +an area-- or sorry, of a radius, + +unit of a velocity, and then +I have to plug everything in. + +And then, I have to find an +equation with a force other + +than this equation, because if +you put this equation back in, + +then you don't get anywhere. + +These are useful. + +So I always have to actually +figure it out fresh each time. + +So it turns out that these +are indeed rotary motors. + +And I think that this was +actually the first-- as far + +as I'm aware, it's the first +example of a rotary motor + +in biology that had +been demonstrated, + +which is a fascinating idea +because in human engineering, + +rotary motors are everywhere. + +Yet somehow, if you +look at living things, + +they don't seem to +have rotary motors. + +Now, anybody want to suggest +why rotary motors might be rare + +in biology, in life? + +AUDIENCE: Rotary is just +that it rotates, right, + +not in terms of a mechanism +[INAUDIBLE] because there's + +also [INAUDIBLE] + +JEFF GORE: Well, I guess I'm +thinking of something that + +can continuously rotate, right? + +It's true that if you look +at-- we have ball socket joints + +and I can rotate them a +little bit, but certainly, + +I can't go-- there +are limits, right? + +And this is a pretty +striking difference + +between human engineering +and biological engineering. + +Yeah? + +AUDIENCE: If you tried to +connect anything across this, + +it would be more [INAUDIBLE] + +JEFF GORE: That's right. + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: That's right. + +The problem is you +just can't have + +anything connected across it. + +Otherwise, you really +do get tangled, right? + +Now, the question +then is, well, why + +is it that it's possible +to do that here then? + +AUDIENCE: Because we're +at such a small scale + +that we're not thinking of +connecting anything else. + +We're individual +molecules, anyway. + +There's nothing that +can go through that. + +JEFF GORE: Yeah, +it's interesting. + +And this is how I think +about it that well, + +at the molecular scale, you +just have some rotary something + +and it doesn't +have to be attached + +via, say, covalent +bonds or whatnot. + +And you can then force +something to rotate. + +Of course, it's a little +bit funny because this issue + +about connecting across +this rotation, that + +should be a problem for +human engineering, as well, + +but somehow, we +do get around it. + +I guess what I would +say is I don't have + +any comments, except for this +was then quite a surprise when + +it was discovered that this was +a rotor motor, just because we + +had not seen any in other +macroscopic living things. + +So then, it was quite +exciting to see it + +in the case of the +flagellar motor. + +And in your book, +you'll see that there's + +a very nice kind of EM +reconstruction of this motor + +and you can see how +it's hinged and it's + +powered by proton gradients +that kind of cause this thing + +to rotate. + +It's really a beautiful, +amazing thing. + +Does anybody know any other +examples of rotary motors? + +That's right. + +The other really famous one +is the F0F1 ATP synthase, + +which is, again, something +that's across a membrane + +and has, once again, a really +beautiful structure where + +it has this circular thing +in the membrane that rotates, + +responds to, again, +a proton gradient, + +and then that drives +rotation of this other part + +of the protein, F1. + +And then, that makes ATP. + +And that motor is amazing +also because it's reversible, + +in that the cell can also +burn ATP and drive a proton + +gradient. + +And indeed, in some +single-molecule experiments, + +they've even done +something where + +they attached a little +magnetic particle onto this F1 + +and then rotated themselves. + +And they showed that they +could actually make ATP. + +The efficiency was maybe not +great, something like that, + +because they're rotating +a macroscopic magnet + +and then they're +making ATPs there. + +But it's a pretty +remarkable aspect + +of these molecular motors. + +Now in this class, +we're not going + +to say anything more +about molecular motors, + +but I just wanted to mention +a few things about them + +because they're really +fun, beautiful things + +and there are other +classes that are + +at MIT that may give you an +opportunity to think about them + +some more. + +Any question about +where we are now? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: The common motor? + +AUDIENCE: Yeah, [INAUDIBLE] + +JEFF GORE: Oh. + +Well, I'd say that the +other class of motors + +that are seen a +lot in the context + +of these molecular +motors are motors that + +travel along linear tracks. + +So there's kinesin that +walks along microtubules. + +There are various myosins +that walk on actin. + +And then, of course, +DNA and RNA polymerase, + +we don't normally +think of them as motors + +but indeed, they +take an energy fuel + +and then they have to +walk along the template + +as they make either +the DNA or the RNA. + +So I'd say there are many, many +examples of molecular motors + +that convert chemical +energy into mechanical force + +and motion, particularly +along one-dimensional tracks. + +So those, I think, are the +most well-studied examples. + +Now, one way to study +this run and tumble motion + +is, of course, to +actually apply a gradient + +and then watch the +cells as they swim it. + +And that has been done. + +A lot's been learned +from that kind of assay, + +but it turns out that there +are two other assays that maybe + +allowed for more +controlled analysis + +of this chemotaxis +kind of response. + +So let's just say-- so +studying chemotaxis. + +The most obvious thing +is to apply a gradient + +and then watch. + +And indeed, the +classic assays where + +you add a little pipette with +an attractant or a repellent + +and watch the bacteria +swim toward or away, + +that demonstrates there +is indeed chemotaxis. + +But it's a little bit +difficult to quantify + +that process in many cases. + +What are the assays that maybe +you've read about recently? + +In [? Yuri's ?] book, how is +it that they actually analyzed + +this perfect adaptation? + +Yes? + +AUDIENCE: So you can bind the +flagella on the slide and then + +[INAUDIBLE] + +JEFF GORE: So one thing +that you can do is you can-- + +I may put it here. + +All right. + +So you can kind of attach +the cell to a slide. + +And typically attach it +to the slide by what? + +This isn't it. + +And does it matter where you +attach the cell to the slide? + +AUDIENCE: By the flagella. + +JEFF GORE: Yeah, +so you typically + +have attach it via this +hook that's at the end, + +so by some part of the +flagella-- to the slide + +by the flagella, we'll say. + +Flagellum? + +Flagella-- whatever. + +And the nice thing there is that +as the cell is doing its thing + +and it's spinning either +clockwise or counterclockwise, + +you can directly visualize +that because the whole cell is + +moving. + +And the cell is both the +thing that is doing the work + +and processing the +signals and everything, + +but it's also your +marker for what the state + +of this little hook is, right? + +This is a wonderfully +quantitative assay where you + +can get high time resolution. + +It's easy to do +the image analysis. + +And then, how do you typically +get this cell to change its, + +for example, tumbling frequency? + +AUDIENCE: Put an attractant. + +JEFF GORE: Right, so you +can add an attractant. + +And indeed, I just wanted to +separate this a little bit, + +because you can-- even +without doing this-- + +this is kind of the next +order step-- you can just + +add an attractant and +mix, because you don't + +want the spatial patterns. + +But a nice thing here, +this is a gradient in space + +and then you can watch +the bacteria swim. + +But you can also have +the gradient in time. + +And the cells can't +tell the difference. + +The nice thing here is +that you can then just + +add the attractant, +mix, and then + +you just watch all the +cells as they're going. + +You don't need to try to +follow them or whatnot, + +but you can just look to see how +the tumbling frequency changes + +over time. + +And of course, you would +typically use this trick + +together with this in order to +study perfect adaptation and so + +forth. + +If you collect this sort of +data and you plot the tumbling + +frequency as a function of +time, what you might see + +is that it starts out +at one per second. + +Now, if at this time, +I add an attractant, + +does the tumbling +frequency go up or down? + +And we're going to +do a verbal answer. + +Ready? + +Three, two, one. + +AUDIENCE: Down. + +JEFF GORE: Down. + +And that makes sense +because the cells + +think that they're moving +up an attractant gradient. + +So over a very short time scale, +tumbling frequency goes down. + +But then, over a time +scale of minutes-- + +it might be 5, 10 minutes-- +that tumbling frequency + +goes back to where it started. + +I just want to-- +this varies, but this + +could be order of 10 minutes. + +AUDIENCE: Why is it so long? + +JEFF GORE: Yeah. + +AUDIENCE: 10 minutes +is a very long time. + +JEFF GORE: Yeah, it's +a long time scale. + +And here's a question. + +Is it because this +is the time that it + +takes to make new protein? + +New protein +synthesis, we'll say. + +AUDIENCE: You're asking +if that's the time + +or if that's the +reason why is it long? + +JEFF GORE: I'm saying is this +the explanation for why this + +is 10 minutes, +because the cell has + +to go make new protein +in order to do this? + +So the cell is presumably going +to be making some new proteins, + +but is this what +you would really + +describe as being the causative +agent of this thing taking 10, + +20 minutes? + +Ready? + +Three, two, one. + +All right. + +So I'd say most people are +agreeing that actually, + +yes, it is. + +The answer is no. + +This is not. + +It may be the case that the +cell is making new protein, + +but this is not what's +setting the time scale there. + +Is-- + +AUDIENCE: More [INAUDIBLE] + +JEFF GORE: Right. + +You agreed that that was the +answer, but you didn't-- well, + +so I would say there are several +ways you can think about this, + +but we're going to go through +the model that is supported + +by, I think, a fair amount +of experimental evidence. + +But the key feature there +is that in this model, + +it works even if all the +protein concentrations are + +constant over time. + +So everything that's +happening in this network + +is happening as a +result of changes + +of the states of the protein. + +So proteins are either getting +methylated or phosphorylated + +and these-- right. + +But then, of course, +it's the question of, + +why is it 10 minutes instead +of 10 seconds or a minute? + +AUDIENCE: You need a +[INAUDIBLE] in there + +that's on the order of minutes, +like 100 minutes, which + +is very slow. + +Is there-- + +JEFF GORE: Yeah, well, +their one question is, this + +is what is called +the adaptation time. + +Now, is this a robust +feature in this model + +or in the cells, +for that matter? + +We'll just add +verbal, yes or no. + +Ready? + +Three, two, one, + +AUDIENCE: No. + +JEFF GORE: No. + +Now, and what that +means is that indeed, + +different kind of +versions of this network + +will have different times. + +And there is data looking +at variation in this + +between different cells. + +And I guess I don't have +a clear feeling for what + +would be optimal, in the sense +of allowing optimal climbing up + +of an attractant gradient. + +This thing has to be much +longer than the typical times + +for a tumble. + +Otherwise, it's +not even-- well, we + +wouldn't have been able +to measure it, I guess. + +But I agree that it could +have been one minute + +and I wouldn't +have batted an eye, + +in the sense that I don't +have any feeling for why + +it had to have been +this or something else. + +But somebody who +actually studies this + +might be able to +give a better answer. + +All right. + +AUDIENCE: But I guess-- +sorry, just one last thing. + +My question is not +why it's 10 minutes. + +It's not an +evolutionary question, + +like why is it useful, right? + +It's just somehow, [INAUDIBLE] + +JEFF GORE: Yeah I +think that there + +are different ways +of looking at this + +and then depending on +how you look at it, + +you either feel +surprised or not. + +So it's a little-- +now on the other hand, + +if you had added +a repellent, then + +the tumbling frequency +would actually go up + +and then come back down. + +But the key, key +thing in this system + +that we want to focus +our attention on + +is the fact that it comes +back to where it started. + +So it's the fact that I can +draw this dashed line that + +is this perfect adaptation. + +And so what we want +to do is understand + +where this phenomenon +of perfect adaptation + +comes from and maybe why +it is robust to changes + +in, for example, the +concentrations of some + +of these proteins. + +Now, let's just +make sure that we're + +all on the same page in +terms of what was known + +about this chemotaxis network. + +And I think it's worth +mentioning, perhaps, here + +that the whole series of +studies of bacterial chemotaxis + +going back to Howard +Berg and company + +and then later, the +studies that in robustness + +that Uri Alon and Stan +Leibler and Naama Barkai did. + +I think they represent really +just a wonderfully beautiful + +exploration at the interface +between physics and biology. + +I think you could teach +an entire course just + +on bacterial chemotaxis and +you could hit pretty much + +all the major themes in +biophysics over the last 40 + +years. + +It's really amazing to me. + +I myself have not done +any work in the field, + +but from afar, I've really +just admired the beauty + +of all these studies. + +And because you go back +to Howard Berg and Purcell + +and they're thinking about +how simple physics can inform + +the challenges that +bacteria are facing + +and how cells are actually +able to do a biased random walk + +and get anywhere, limits on +sensing both concentrations + +and gradients-- and +then later, the studies + +that they're this +topic of robustness, + +it's really a +wonderful example where + +Naama Barkai, when she was +a postdoc at Stan Leibler, + +they had published a Nature +paper in maybe '97 basically + +saying, this idea of robustness +is really important in biology + +and in order to have a robust +response of perfect adaptation, + +a model has to have +these features. + +So there's no experiments +there, but their model + +was guided by +previous observations + +that people had made. + +And then, two years +later, Uri, when + +he was a postdoc in +Stan's lab again, + +did kind of the +experimental confirmation + +of the model, where +he went in and he + +controlled the +concentration of chi R + +and showed that thee key +predictions of the model, i.e. + +the perfect adaptation, would +be robust to the concentration + +but that the tumbling frequency +and the adaptation time, they + +would not be robust to +chi R concentrations. + +They would move +in a way predicted + +by the model and all that. + +It's really amazing that it +all kind of holds together, + +because in many cases, we do +the modeling kind of post facto, + +right? + +And then, it's kind of +explaining our results. + +But the case where a +model is really useful + +is when it makes new +predictions that get you + +to go make new measurements. + +And this is a +situation where there + +are an infinite number of +experiments that you could do, + +but only some of them +will actually provide you + +a deep insight into +the mechanisms that + +are going on in the system. + +And I think this was a real +case where the models made + +some really clear predictions +and that allowed, in this case, + +Uri to go and make the strains +that allowed him to test + +the predictions of the model. + +And I think it's really amazing +that it all kind of works. + +All right. + +Now, all of the letters +that you see up there, + +they're not actually-- well, +first of all, the letters + +are somehow real. + +This is the real names +of the protein components + +in the chemotaxis +network in E. coli + +and largely in other organisms. + +But in each case, there's a +chi that comes in front, right? + +So R corresponds to +chi R, for example. + +And then, there's +chi B, chi W, chi A. + +And these were all identified +by genetics, so then + +by researchers looking +for mutants that + +were defective in chemotaxis. + +I don't know what +happened to C, D, E, F, G, + +because it does seem like we got +the first part of the alphabet + +and the last part +of the alphabet. + +I don't know. + +All right. + +Now, the basic +idea in the system + +is that you have chi W/A that +we often here will refer to as X + +just for simplicity. + +Now, these are proteins +in the membrane, + +so they have a binding +kind of pocket outside + +that will allow binding of +attractants or repellents. + +There might be say, +five different kinds + +of these receptor +complexes that can sense, + +that bind at different rates, +different kinds of attractants, + +repellents, and then the +signal is somehow integrated. + +Now, this could be either an +attractant or a repellant. + +The distinction +between these two + +is that we get different +levels of methylation + +onto chi W. Now in +this lecture, we're + +only going to be talking +about the methylated state + +versus the unmethylated. + +But in reality, depending on +the receptor complex they have, + +they might have four or five +different methylation sites. + +And this ability to switch +between different methylation + +states is really at the +heart of the phenomenon + +of robust perfect adaptation. + +The base feature in it, though, +is that chi A can phosphorylate + +chi Y and chi Y will then +go and yield the output, + +which is in this case, +increased tumbling frequency. + +But there are lots of +other bells and whistles + +that you can see on here, right? + +So of course, it's not just +that this phosphorylated + +chi Y just kind of +comes off on its own, + +but rather it's +actually done by chi Z. + +So there's a +constant cycling here + +and again, there's a +constant cycling here + +where the methyl groups are +taken off and then put back on. + +So if you look at +this, you really + +do feel that it's +rather wasteful, + +because there's a huge number +of these futile cycles going on. + +Chi Y is always kind of +being phosphorylated and then + +dephosphorylated and this is all +going to be costly to the cell. + +So you can imagine +then the only reason + +it's there is because it's +doing something useful. + +Now, there was a +comment in the chapter + +about what is the rate +limiting step in all this. + +And can somebody +remember what it was? + +Yeah? + +AUDIENCE: Is it methylation? + +JEFF GORE: So methylation, +there is a sense + +that that is actually +the longest time scale, + +but I guess because +the methylation + +is what results in +this thing coming + +in the perfect adaptation +over this 10 minutes. + +I guess what I meant-- so yeah, +that is the longest time scale. + +But I guess what I was +thinking about in rate limiting + +is the sense of when +the cell finds itself + +in a new environment, +it changes its state + +over a much shorter time scale. + +So this thing I drew is +almost vertical, right? + +So this question is, if +the cell finds itself + +in a new environment suddenly +and then it just really + +wants to tumble-- so you find +yourself in a crappy bar, + +how long does it take +for you to get out? + +Now, what's going to +be rate limiting there? + +Yeah? + +AUDIENCE: Phospho-- +phosphorylation. + +JEFF GORE: +Phosphorylation, yeah, + +although it turns out that's +not the rate limiting step. + +And this actually comes back +a little bit to something + +that we talked about in +the first part of the class + +that in these +transcription networks, + +the characteristic +timescale is what? + +AUDIENCE: G. + +JEFF GORE: Right. + +So the characteristic timescale +in the case of transcription + +networks is the time +it takes for you + +to change concentrations of +proteins, which is kind of cell + +generation time or if you +have active degradation, + +you might be able to make it +faster, whereas all of this + +is happening rather +quickly, say, + +maybe 1/10 tenth of a second. + +And a lot of these kinds of +processes, binding, unbinding, + +and actually even +the interactions + +between the proteins +can take place + +even maybe faster than that. + +So the actual rate limiting step +for when the cell finds itself + +in a bad environment +for it to start tumbling + +is actually due to diffusion. + +And that's diffusion of what? + +AUDIENCE: Y protein. + +JEFF GORE: Yeah, diffusion of +the phosphorylated Y, right? + +And that's because we +have the cells here. + +They find themselves +in the bad environment. + +They rapidly bind the +repellent or they quickly + +phosphorylate chi +Y. But then, Y is + +going to be formed +at one of the poles, + +because actually, there's +actually clustering + +of these receptors at +the poles of a cell + +and incidentally, we're not +going to talk about that here, + +but I think there's strong +experimental and theoretical + +evidence that this actually +increases the sensitivity. + +And indeed, people have used +simple Ising type models + +to try to understand how the +coupling between the binding + +of repellents on what's +essentially almost + +like a crystalline +array of receptors + +can allow the array +to better than you + +build it to as an individual. + +We're not going to get into +that here, but in any case, + +there's receptors +at the poles-- I + +don't know if it's +both poles or one pole, + +but one of the +poles of the other-- + +and that's where chi +Y is phosphorylated. + +But then, you can see that +these flagella are distributed + +all around the cell. + +So you have to diffuse +from say, the pole + +to the site of +the flagella motor + +in order to cause it to go +clockwise and then cause + +a tumble. + +Yeah? + +AUDIENCE: So do you +need only one motor? + +JEFF GORE: Yeah, so +you actually only + +need one motor to +get the tumbling. + +And so then, you may not +have to diffuse all the way + +to the other end, but-- and of +course, diffusion is random. + +And we all know that 0.1 +seconds is around the time + +that it takes for a +protein-sized object + +to diffuse across the +volume of a bacterial cell. + +We did that calculation +a couple weeks ago. + +So 0.1 seconds is indeed-- +so the rate limiting step + +is indeed this step +right here, which + +is diffusion of chi Y, the +phosphorylated version of it. + +All right. + +Now, we may not get too +much into the models + +here, because you +did read about them. + +But I will just +kind of sketch out + +sort of what you might call +the fine-tuned model and then + +the key assumption that +goes into this robust model. + +Now, what both models +assume and indeed + +what was known +from previous work + +was that chi R is +present at small number. + +So chi R, there might be around +100 proteins in the cell. + +And what does this mean +about the activity of chi R? + +What is the other word for it? + +It doesn't actually +have to quite mean it, + +but what is it that-- how-- + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: What's that? + +AUDIENCE: [? High ?] saturation. + +JEFF GORE: So yeah, +something is high. + +And what is typically assumed is +that chi R acts at saturation, + +chi R. But what do we mean by +"saturation" in these models? + +AUDIENCE: Maximum. + +JEFF GORE: Right. + +Does it mean that +if we add more chi + +R than the rate of methylation, +it doesn't increase? + +And I should have put a +little methyl group here. + +There are multiple +things you might + +mean by "acts at saturation." + +And in the models that +you read about last night, + +is what it means that if we +increase the number of chi R + +that it doesn't change +the rate of methylation? + +Yes or no? + +Ready? + +Three, two, one. + +AUDIENCE: No. + +JEFF GORE: No. + +And what they mean is something +rather different, which + +is that if we plot or if +we calculate the change + +in the concentration +of the methylated X-- + +now, we're calling this +whole thing Xm, methylated X, + +and this is just X. +The assumption is + +that we have X is +being methylated + +at a rate that is-- there's +no Michaelis-Menten term. + +If we were to write this +as it not being saturated, + +what is it acting on? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Yeah, it's +not the methylated x. + +So indeed, if we +were to write this, + +we're assuming that this is +at saturation, as they say. + +But any time that you +see something like this, + +you have to ask, +well, what would + +be the alternative, right? + +And the alternative +would be to include + +a term that looks kind of like +just X over some K plus X, + +because R is acting +on the unmethylated X. + +We're not including that. + +What that means is that we're +assuming that this thing is + +saturated, that the +concentration of X to be acted + +on is significantly larger than +the Michaelis constant there. + +And of course, this is +related to the amount of R, + +because as we get +more and more R, + +then eventually, we'll +remove some of this X + +and then we'll get into +the non-saturated regime. + +So these two statements +are related, but not + +the same thing. + +Now, there's also some rate that +the phosphorylated version of B + +removes the methyl groups +and that's indeed just going + +to be this Michaelis constant. + +And this is going to be +for the fine-tuned model. + +The robust model +looks very similar, + +but this is the simplest kind +of manifestation of this model. + +Now, once we're +writing this down, + +it's useful to make +sure that we can + +keep track of what's +actually happening + +over the course of +perfect adaptation. + +So now, let's imagine first +that an attractant arrives. + +That's going to change +the activity of X. + +And when we say +"activity," what we mean + +is the rate that's it's going +to phosphorylate both B and Y. + +So let's just make sure +that we know this direction. + +So we add an attractant. + +We'll say "add." + +What does this do? + +Does it make activity +go up or down? + +I'll give you 15 +seconds to make sure + +that you kind of understand +the workings of this network. + +This is activity of X, +this complex X. All right. + +Do you need more time? + +All right. + +Let's see where we are. + +Ready? + +Three, two, one. + +All right. + +So we got a majority +of the group + +is saying that it +should go down. + +Well, let's just +follow the logic. + +So we imagine an +attractant binding. + +If the activity goes +down, that means + +that we get less of +the phosphorylated chi + +Y. That means we get less +propensity to tumbling, + +which means that we +keep on going further. + +All right, that +sounds reasonable. + +Any questions about that logic? + +Yes? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Right. + +So we haven't said +anything yet about BM. + +That's what going +to happen next. + +And that's actually +the slow time scale. + +So what we had in +here is that we + +were kind of at this +steady-state tumbling + +frequency of one per second. + +We add an attractant. + +The tumbling frequency goes down +because of what we just said. + +But now, there's going to +be this longer time scale + +process whereby we +get recovery, where + +we come back to this +steady-state tumbling + +frequency. + +And that's going to +involve action on chi B. + +All right. + +So what happens is that +the attractant causes less + +of the phosphorylated +chi Y. But it's also + +going to cause less of the +phosphorylated chi B. Now, that + +means that we're going +to-- and remember, + +the phosphorylated +chi B is what's + +removing the methyl groups. + +So if we have less +flux going to the left, + +but we have the +same-- at that moment, + +we don't have any change in +the flux going to the right. + +So chi R is still acting on the +same unmethylated X's that it + +was operating on before. + +So it's the same flux to the +right, less flux to the left. + +So there's a net accumulation of +the methylated receptor, which + +we are calling X. So the +key thing here is that-- + +and it's this +methylated receptor that + +has more activity. + +In this model, this +unmethylated version actually + +doesn't have any activity. + +So then, if we get more of the +methylated X, then over time, + +we get a buildup +of the methylated X + +and that causes the +activity to come back up. + +Now, of course, +there's a question + +of-- I just said that +it comes back up, + +but I didn't say +that it comes back up + +exactly to its original +tumbling frequency. + +I didn't say that it necessarily +displays perfect adaptation. + +And that's because +in this model, + +the perfect adaptation +arises as a result of what + +we call fine-tuning, +because it only + +happens if all of the +parameters are just so. + +In Uri's book, he describes +a typical condition + +where that would be the case. + +And the problem is +that you can always + +fine-tune for some +concentrations of everything, + +chi R or chi this, chi that. + +But then if the +concentrations change, + +then you're no longer +fine-tuned correctly. + +You were fine-tuned +for a different world + +and now you're not-- and +that's the definition of being + +fine-tuned is that +if things change, + +you're no longer fine-tuned. + +You're just finely +off-tune, right? + +So this is the problem +with the fine-tuned model + +is that you can get +it right for a given-- + +for given concentrations +of everything, + +you can always +find what numbers. + +This is VB and +then there's going + +to be-- you can talk about +the activities of XM given + +the previous attractant +concentration and so on and so + +forth, but it's not +going to be fine-tuned + +if you change +anything else, like + +if you change concentration +of R, for example. + +And I'm happy to +go through the math + +and so forth maybe after +class if anybody's curious, + +but it's really +precisely what Uri did, + +so maybe I won't +get into it now. + +But the question +then is, well, how + +is it that you might +change this model in order + +to make it robust? + +And the change is somehow +surprisingly simple, + +which is that what you want +is chi B, instead of just + +acting on any old +methylated X, you + +want it to act only on +the methylated X that + +is in sort of in what we +would call this active state, + +where it's actually +able to catalyze + +either of those reactions. + +So the notion is that if you +have this methylated X, then + +it's kind of over a +very fast time scale. + +It's switching between what +we call an "active" state + +and some inactive one. + +And it's really only +in the active versions + +that chi B is able to act on +and remove the methyl group. + +And this is on the one +hand a clever thing + +that allows you to implement +this integral feedback. + +On the other hand, it's a little +bit of like pulling a bunny out + +of a hat, because you feel +like, well, these things may + +be happening over +microsecond time scales. + +It's hard to know exactly-- +how would you actually + +experimentally confirm this +is precisely what's going on? + +And I think that here, it's a +little bit subtle because you + +could maybe show that indeed +the rate of this demethylation + +is proportional to +the activity here, + +but you don't +necessarily have access + +to all of the molecular +dynamics that are taking place + +over microsecond time scales. + +So I think that you can do +measurements that give you + +confidence that this is +maybe what's going on, + +but you can't quite +100% nail it because + +of the nature of these +molecular fluctuations. + +So the idea there +is that if we say + +that there's this +rapid shuttling + +between the so-called +"active" and "inactive" + +methylated guys-- so this +is indicating that it's + +what we call "active," able +to catalyze this and this-- + +then this ends up +being equivalent + +to integral feedback, +where you'll always + +get perfect adaptation. + +Yeah? + +AUDIENCE: When you +put [INAUDIBLE] + +JEFF GORE: So the idea is that +we imagine that we're this + +receptor X. It's chi W, chi A. +Now whether it's-- let's say + +it's bound to something. + +It still bound to an +attractant, right? + +The way that the attractant +influences its activity-- + +and it has to influence +its activity if it's + +going to do anything-- +what we assume + +is the way that it's doing +it is that it's changing + +the sort of fraction +of time that I'm + +in some active conformation +where I can actually do work, + +versus the inactive conformation +where I'm taking a break. + +So when you get the +attractant and you + +spend more of your time in +this active conformation + +where you're, in this case, +phosphorylating proteins, + +and that's sort of the +mechanism through which + +an attractant or a +repellent or whatnot + +actually transmits its signal. + +And indeed, it has +to do something. + +Nothing that we're +discussing would work at all + +if we don't allow the signal +to be transmitted somehow + +through this receptor. + +So there is this sense +that this activity + +has to be a function of +the things out there. + +And the assumption that goes +into the perfect adaptation + +is really that the +rate of demethylation + +is proportional to that +kind of active fraction. + +And then, you can argue about +how discrete these entities + +have to be in order for the +mechanism to work and so forth, + +but certainly, there +has to be some way + +that binding to an attractant +leads to what we decided + +was less activity. + +Yeah? + +AUDIENCE: Just a quick question. + +So what's the relationship +between activity + +and methylation? + +Was it [INAUDIBLE] + +JEFF GORE: So the idea is that +we're typically maybe assuming + +that the unmethylated +guy has no activity, + +so it doesn't do any of +this phosphorylation, + +whereas the methylated +guy has some activity. + +And you can characterize +it by some rate of activity + +or some fraction +of the time that it + +is in this active state +that is doing something. + +Now, the question-- +and indeed this + +ends up-- well, you can see +here that in this model, + +because you're directly +acting on the active XM, then + +the steady-state +activity you can + +get from just setting this equal +to zero and it's some number. + +But then, the +question is, how long + +does it take to come back +to that steady state? + +And that's where +we get differences + +as a function of +concentration of chi R, + +because what's +happening always is + +that we have some kind +of cycle here where + +chi B is removing +the methyl groups, + +groups chi R is +adding them back. + +So you can imagine that +if you have more chi + +R than a steady state, you get +more-- when you're moving right + +by a steady state, +you have to have + +the same moving to the left, +because at steady state, + +it's equal. + +So the more chi R you +have, the faster this thing + +is going around. + +And that means that the +more chi R that you have, + +the more rapidly that you'll +get this perfect adaptation. + +So the experiment that Uri +did that I think is very nice + +is he directly modulated +the amount of chi R + +and he looked at +this adaptation time. + +And he found this +kind of came down, + +whereas if you look at +the steady-state tumbling + +frequency, this came +up, whereas the degree + +of perfect adaptation, +say the ratio or the error + +in this thing, +perfect adaptation + +was always kind of correct, in +the sense it always came back + +to its original value. + +AUDIENCE: Sorry. + +You say the [INAUDIBLE] +it only phosphorylates + +chi B when an +attractant [INAUDIBLE] + +Y [INAUDIBLE] attractant. + +JEFF GORE: No. + +So the attractant +or repellent can + +be combined to +either the methylated + +or the non-methylated, right? + +AUDIENCE: But [INAUDIBLE] +only [INAUDIBLE] + +phosphorylation of +chi B when [INAUDIBLE] + +JEFF GORE: No. + +So you're talking +about-- oh, OK. + +So it's really that the +methylated state can + +phosphorylate either +chi B or chi Y, + +but this is regardless whether +an attractant is bound or not. + +The attractant will influence +the rate or the activity + +that this happens. + +And given this model, you can +see that you have more chi R, + +then at steady state, you're +going to have more activity. + +More activity corresponds +to more phosphorylated chi + +y and more tumbling, +so an increase + +in the tumbling frequency. + +Yes? + +AUDIENCE: I guess +it's not clear to me + +where the ligand concentration +actually come in. + +JEFF GORE: Where +which concentration? + +AUDIENCE: The ligand +concentration. + +JEFF GORE: Oh, OK, yeah. + +AUDIENCE: Because +that's what [INAUDIBLE] + +JEFF GORE: Yeah, right. + +Yeah, so the idea here +is that if we start out + +without any attractant-- +so first of all, + +so let's imagine +we're at steady state. + +There's no attractant +or little attractant + +now, where of course, the +fluxes to the left and the right + +are the same. + +So there's some +methylated, some not. + +AUDIENCE: No, but I agree the +mechanics of just in the actual + +to write an equation +for the ligands + +to come in like [INAUDIBLE]. + +JEFF GORE: Right. + +So the idea is that when +you bind an attractant, + +that's going to change the +activity of the methylated. + +So it's going to +change, for example, + +the fraction that are active. + +AUDIENCE: And +decreases the activity. + +JEFF GORE: And it decreases +the activity, right. + +AUDIENCE: And some +sort of signal-- + +JEFF GORE: Yeah, +there's some-- right. + +And of course, we haven't +specified what that function, + +but the idea is that it leads +to a rapid decrease in activity, + +which corresponds to a rapid +decrease in this fraction that + +are active XM star. + +Does that make sense? + +So the last thing I wanted +to do is say something + +about what this means +for individuality. + +In particular, let's +imagine that we + +have a clonal +population of bacteria. + +And the question +is, in what ways + +will they be similar +or different? + +So now, we can just +imagine an experiment + +where I take a population +of cells with exactly + +the same genetic code and I +go and I measure, for example, + +the tumbling frequency +across this population. + +So we can talk about-- we +measure f1, f2, f3, fn-- + +so these are the tumbling +frequencies across n cells. + +This is n we'll say +genetically identical cells. + +The question is, will we get +the same tumbling frequency + +or should these +things be the same? + +And if not, why not? + +So let's just do our +little votes, all right? + +We have should they be the same +or should they be different. + +All right. + +Do you understand the question? + +Let's vote. + +Ready? + +Three, two, one. + +All right. + +Well, OK, so at least +the majority of people + +are saying they +should be different. + +And why might that be, somebody? + +AUDIENCE: We might +have [INAUDIBLE] + +JEFF GORE: Right. + +For example, we +might have variation + +in the concentration +of chi R. Now, + +this variation is sort +of a natural result + +of just fluctuating +this or that, right? + +But it's a little bit similar +to the experiment Uri did, + +where he actually in +this case has actually + +put chi R under the control of +an inducible promoter, where + +he could just add IPDG +and drive expression + +and then just measure +the mean of these things + +across the population. + +But even if you try to have +everything be the same, + +you'll have some +variation, which + +we found for small numbers +of proteins could be large. + +So that variation +will transmit itself + +into variations in both +the adaptation time + +and the tumbling frequency. + +And this is indeed was +observed as early as 1976. + +So there's a paper +in Nature in 1976 + +by Jim Spudich and Dan Koshland. + +So Spudich went on +to study a number + +of these molecular motors. + +In particular, he studied +many of these myosins. + +But he wrote this classic paper +in '76 called "Non-genetic + +individuality, chance +in the single cell." + +What he did is they looked at +many different individual cells + +using a few of those techniques +that I told you about. + +And what they found is +that some of the cells + +seemed to be what they +called kind of "twitchy" + +and some of them seemed +to be more relaxed. + +So the twitchy cells are the +guys that had a larger tumbling + +frequency. + +So they wouldn't swim +as far as the others. + +So they'd swim just +a little bit and then + +they'd change their mind, swim +a little bit, change their mind, + +whereas other cells had +much longer kind of runs, + +even though they're all +nominally identical. + +Now, can somebody +say the time scale + +over which we would expect +that personality to persist? + +AUDIENCE: Cell generation time. + +JEFF GORE: Yeah, +cell generation time. + +And why is that? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Yeah, right. + +So if this is chi R, over time, +it's going to do something. + +And so the typical +autocorrelation time + +should be kind of the +cell generation time. + +So what we call the typical time +should be rather generational. + +So indeed, this is +the same as humans. + +We have a well-defined +personality + +and then we pass on some of +our personality to our kids. + +The typical time +scale is a generation. + +So I'm teaching you guys super +useful things in this class. + +I don't want anybody +saying anything else. + +But I think that this +is a neat example of how + +different cells can have +what you might describe + +as being somehow +different personalities, + +but it arises for a +very particular reason + +because this information +is being transmitted + +through this network. + +Now, despite the +fact that they all + +have different chi +R concentrations-- + +so they might have different +tumbling frequencies + +and so forth, but +they should all + +be able to display +this phenomenon + +of perfect adaptation. + +So what we then see is +that from the experiments + +and from some simple +models, you can + +get insight into how it +is that this phenomenon + +of perfect adaptation +might be robust to changes + +in the concentrations of +different things, particularly + +chi R in this case. + +And chi R is the +dominant source of error + +because it's present +in such small numbers. + +Now, in the last +two minutes or so, + +I just want to remind everybody +about the other context + +in which we studied +robustness, because it's + +a much simpler +example and it helps + +to clarify what we mean by it. + +Does anybody remember +the other context + +that we have talked +about robustness? + +AUDIENCE: [INAUDIBLE] + +JEFF GORE: Negative +autoregulation someone + +said, maybe? + +AUDIENCE: Yes. + +JEFF GORE: OK, good, all right. + +So if we have some +protein that is negatively + +autoregulating itself, +then this adds robustness. + +And this is because +we can say, all right, + +this is the degradation term, +alpha x, the production term. + +And the limit of being perfect, +sharp, negative autoregulation + +looks like this. + +So this is the +production/degradation. + +And here, this might be beta. + +This is a k. + +Then, what we can +talk about is how + +the steady-state concentration +of x here is going to be k. + +And this thing is robust to +variations in some things, + +but not other things. + +For example, it's robust +to changes in alpha. + +That changes the slope. + +It's robust to changes in +beta, because that just + +brings it up and down, but it's +not robust to changes in k. + +So I think that any time +that if you are confused + +about robustness, in particular +thinking about robustness + +in the context of +chemotaxis gets + +you confused because of perfect +adaptation being confusing, + +I think it's always good +to come back and think + +about this because this is the +most clear case where you can + +talk about-- this +is the robustness + +of the steady-state +concentration + +of some protein against +variations in alpha and beta, + +but not against k. + +So it reminds you that it's +not that this level of x + +is robust against +everything, but it's + +robust against some things. + +And you can make sense +of which things it + +should be robust against, +which things not. + +So with that, I think +we're going to quit. + +I just want to remind +everybody that none + +of the work that we're +talking about here + +in the context of chemotaxis +and the genetic network + +will appear on the +exam, but we may + +have a problem on low +Reynolds number flow, + +maybe something Stokes drag. + +Diffusion might +make an appearance. + +Good luck on the exam. + +I'll see you guys on Tuesday. \ No newline at end of file diff --git a/cqdUuREzGuo.txt b/cqdUuREzGuo.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d4d0d163e5a54b2fd3c45265ab552937458bf75 --- /dev/null +++ b/cqdUuREzGuo.txt @@ -0,0 +1,11723 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +let's continue our discussion of + + align:start position:0% +let's continue our discussion of + + + align:start position:0% +let's continue our discussion of +measurable sets + + align:start position:0% +measurable sets + + + align:start position:0% +measurable sets +um + + align:start position:0% +um + + + align:start position:0% +um +let me just briefly recall for you + + align:start position:0% +let me just briefly recall for you + + + align:start position:0% +let me just briefly recall for you +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the end of last time we discussed some + + align:start position:0% +the end of last time we discussed some + + + align:start position:0% +the end of last time we discussed some +general Notions uh + + align:start position:0% +general Notions uh + + + align:start position:0% +general Notions uh +some some + + align:start position:0% + + + + align:start position:0% + +special collections of subsets of R uh + + align:start position:0% +special collections of subsets of R uh + + + align:start position:0% +special collections of subsets of R uh +one of those being in algebra which is + + align:start position:0% +one of those being in algebra which is + + + align:start position:0% +one of those being in algebra which is +closed undertaking compliments and + + align:start position:0% +closed undertaking compliments and + + + align:start position:0% +closed undertaking compliments and +taking finite unions and then we set a + + align:start position:0% +taking finite unions and then we set a + + + align:start position:0% +taking finite unions and then we set a +collection of subsets of ours the sigma + + align:start position:0% +collection of subsets of ours the sigma + + + align:start position:0% +collection of subsets of ours the sigma +algebra if it's also closed under taking + + align:start position:0% +algebra if it's also closed under taking + + + align:start position:0% +algebra if it's also closed under taking +countable unions okay + + align:start position:0% +countable unions okay + + + align:start position:0% +countable unions okay +and not every algebra is a sigma algebra + + align:start position:0% +and not every algebra is a sigma algebra + + + align:start position:0% +and not every algebra is a sigma algebra +why did we bring all this up while we + + align:start position:0% +why did we bring all this up while we + + + align:start position:0% +why did we bring all this up while we +were in the middle of + + align:start position:0% +were in the middle of + + + align:start position:0% +were in the middle of +discussion the discussing lebeg + + align:start position:0% +discussion the discussing lebeg + + + align:start position:0% +discussion the discussing lebeg +measurable set so recall that we say e + + align:start position:0% +measurable set so recall that we say e + + + align:start position:0% +measurable set so recall that we say e +is lebeg + + align:start position:0% + + + + align:start position:0% + +measurable if + + align:start position:0% + + + + align:start position:0% + +for all subsets of R A the measure the + + align:start position:0% +for all subsets of R A the measure the + + + align:start position:0% +for all subsets of R A the measure the +outer measure of a + + align:start position:0% +outer measure of a + + + align:start position:0% +outer measure of a +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +the outer measure of a intersect e plus + + align:start position:0% +the outer measure of a intersect e plus + + + align:start position:0% +the outer measure of a intersect e plus +the outer measure of a intersect the + + align:start position:0% +the outer measure of a intersect the + + + align:start position:0% +the outer measure of a intersect the +complement + + align:start position:0% +complement + + + align:start position:0% +complement +okay + + align:start position:0% + + + + align:start position:0% + +so in some sense a measurable set is you + + align:start position:0% +so in some sense a measurable set is you + + + align:start position:0% +so in some sense a measurable set is you +know one that divides sets nicely with + + align:start position:0% +know one that divides sets nicely with + + + align:start position:0% +know one that divides sets nicely with +respect to Outer measure okay + + align:start position:0% +respect to Outer measure okay + + + align:start position:0% +respect to Outer measure okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and so + + align:start position:0% +and so + + + align:start position:0% +and so +and we denoted + + align:start position:0% +and we denoted + + + align:start position:0% +and we denoted +script M to be the set of all + + align:start position:0% +script M to be the set of all + + + align:start position:0% +script M to be the set of all +e + + align:start position:0% +e + + + align:start position:0% +e +such that + + align:start position:0% +such that + + + align:start position:0% +such that +e is uh lebeg measurable + + align:start position:0% +e is uh lebeg measurable + + + align:start position:0% +e is uh lebeg measurable +and I'm going to stop saying lebeg + + align:start position:0% +and I'm going to stop saying lebeg + + + align:start position:0% +and I'm going to stop saying lebeg +measurable and just say measurable uh + + align:start position:0% +measurable and just say measurable uh + + + align:start position:0% +measurable and just say measurable uh +from now on + + align:start position:0% +from now on + + + align:start position:0% +from now on +um + + align:start position:0% + + + + align:start position:0% + +and what we showed was last time we + + align:start position:0% +and what we showed was last time we + + + align:start position:0% +and what we showed was last time we +showed that M the set of measurable + + align:start position:0% +showed that M the set of measurable + + + align:start position:0% +showed that M the set of measurable +subsets of R do form an algebra so you + + align:start position:0% +subsets of R do form an algebra so you + + + align:start position:0% +subsets of R do form an algebra so you +know it follows from the definition that + + align:start position:0% +know it follows from the definition that + + + align:start position:0% +know it follows from the definition that +if e is measurable then e complement is + + align:start position:0% +if e is measurable then e complement is + + + align:start position:0% +if e is measurable then e complement is +Metro but but we also showed that if I + + align:start position:0% +Metro but but we also showed that if I + + + align:start position:0% +Metro but but we also showed that if I +take a finite Union of measurable sets + + align:start position:0% +take a finite Union of measurable sets + + + align:start position:0% +take a finite Union of measurable sets +then uh or a finite collection of + + align:start position:0% +then uh or a finite collection of + + + align:start position:0% +then uh or a finite collection of +measurable sets their Union is + + align:start position:0% +measurable sets their Union is + + + align:start position:0% +measurable sets their Union is +measurable okay and what we're going to + + align:start position:0% +measurable okay and what we're going to + + + align:start position:0% +measurable okay and what we're going to +do today is we're going to show that + + align:start position:0% +do today is we're going to show that + + + align:start position:0% +do today is we're going to show that +um the set the collection of measurable + + align:start position:0% +um the set the collection of measurable + + + align:start position:0% +um the set the collection of measurable +lebeg measurable subsets of R form a + + align:start position:0% +lebeg measurable subsets of R form a + + + align:start position:0% +lebeg measurable subsets of R form a +sigma algebra so they have this uh you + + align:start position:0% +sigma algebra so they have this uh you + + + align:start position:0% +sigma algebra so they have this uh you +know + + align:start position:0% +know + + + align:start position:0% +know +stronger property and also that + + align:start position:0% + + + + align:start position:0% + +so last time + + align:start position:0% +so last time + + + align:start position:0% +so last time +um + + align:start position:0% + + + + align:start position:0% + +so there's no way to write this in + + align:start position:0% + + + + align:start position:0% + +so maybe not a definition but notation + + align:start position:0% +so maybe not a definition but notation + + + align:start position:0% +so maybe not a definition but notation +that b is the + + align:start position:0% +that b is the + + + align:start position:0% +that b is the +Boreal Sigma algebra + + align:start position:0% + + + + align:start position:0% + +which is + + align:start position:0% +which is + + + align:start position:0% +which is +I'll recall + + align:start position:0% +I'll recall + + + align:start position:0% +I'll recall +you proved at the end of last time so we + + align:start position:0% +you proved at the end of last time so we + + + align:start position:0% +you proved at the end of last time so we +gave this as a an example of a sigma + + align:start position:0% +gave this as a an example of a sigma + + + align:start position:0% +gave this as a an example of a sigma +algebra this is the smallest + + align:start position:0% +algebra this is the smallest + + + align:start position:0% +algebra this is the smallest +Sigma algebra + + align:start position:0% + + + + align:start position:0% + +containing + + align:start position:0% + + + + align:start position:0% + +all open + + align:start position:0% +all open + + + align:start position:0% +all open +sets Okay so any other Sigma algebra + + align:start position:0% +sets Okay so any other Sigma algebra + + + align:start position:0% +sets Okay so any other Sigma algebra +that contains all open sets uh contains + + align:start position:0% +that contains all open sets uh contains + + + align:start position:0% +that contains all open sets uh contains +the sigma algebra b the borrel out Sigma + + align:start position:0% +the sigma algebra b the borrel out Sigma + + + align:start position:0% +the sigma algebra b the borrel out Sigma +algebra + + align:start position:0% +algebra + + + align:start position:0% +algebra +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +like I said our goal for this lecture is + + align:start position:0% +like I said our goal for this lecture is + + + align:start position:0% +like I said our goal for this lecture is +we're going to show that uh this + + align:start position:0% +we're going to show that uh this + + + align:start position:0% +we're going to show that uh this +collection of lebeg measurable sets is + + align:start position:0% +collection of lebeg measurable sets is + + + align:start position:0% +collection of lebeg measurable sets is +is a sigma algebra we're going to show + + align:start position:0% +is a sigma algebra we're going to show + + + align:start position:0% +is a sigma algebra we're going to show +it contains the barel sigma algebra and + + align:start position:0% +it contains the barel sigma algebra and + + + align:start position:0% +it contains the barel sigma algebra and +then + + align:start position:0% +then + + + align:start position:0% +then +um + + align:start position:0% +um + + + align:start position:0% +um +you know what is I mean I can even state + + align:start position:0% +you know what is I mean I can even state + + + align:start position:0% +you know what is I mean I can even state +it now + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +or at least I'll just say in words what + + align:start position:0% +or at least I'll just say in words what + + + align:start position:0% +or at least I'll just say in words what +is lebeg measure it's simply the lebeg + + align:start position:0% +is lebeg measure it's simply the lebeg + + + align:start position:0% +is lebeg measure it's simply the lebeg +measure of a measurable set will be + + align:start position:0% +measure of a measurable set will be + + + align:start position:0% +measure of a measurable set will be +um + + align:start position:0% +um + + + align:start position:0% +um +the outer measure of that set as long as + + align:start position:0% +the outer measure of that set as long as + + + align:start position:0% +the outer measure of that set as long as +it's lebeg measurable + + align:start position:0% +it's lebeg measurable + + + align:start position:0% +it's lebeg measurable +okay so let's show uh what we're going + + align:start position:0% +okay so let's show uh what we're going + + + align:start position:0% +okay so let's show uh what we're going +to do is we're going to show that m is a + + align:start position:0% +to do is we're going to show that m is a + + + align:start position:0% +to do is we're going to show that m is a +sigma algebra + + align:start position:0% +sigma algebra + + + align:start position:0% +sigma algebra +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +uh one kind of + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +you know + + align:start position:0% + + + + align:start position:0% + +preliminary uh remark that or lemi that + + align:start position:0% +preliminary uh remark that or lemi that + + + align:start position:0% +preliminary uh remark that or lemi that +we're going to prove is that so this + + align:start position:0% +we're going to prove is that so this + + + align:start position:0% +we're going to prove is that so this +condition three says that you need to + + align:start position:0% +condition three says that you need to + + + align:start position:0% +condition three says that you need to +prove that every accountable collection + + align:start position:0% +prove that every accountable collection + + + align:start position:0% +prove that every accountable collection +is closed under taking unions right to + + align:start position:0% +is closed under taking unions right to + + + align:start position:0% +is closed under taking unions right to +ensure that an algebra is a sigma + + align:start position:0% +ensure that an algebra is a sigma + + + align:start position:0% +ensure that an algebra is a sigma +algebra but in fact you don't have to + + align:start position:0% +algebra but in fact you don't have to + + + align:start position:0% +algebra but in fact you don't have to +check it for + + align:start position:0% +check it for + + + align:start position:0% +check it for +an arbitrary collection you really just + + align:start position:0% +an arbitrary collection you really just + + + align:start position:0% +an arbitrary collection you really just +need to check it only for a countable + + align:start position:0% +need to check it only for a countable + + + align:start position:0% +need to check it only for a countable +collection of disjoint subsets so that's + + align:start position:0% +collection of disjoint subsets so that's + + + align:start position:0% +collection of disjoint subsets so that's +kind of the the + + align:start position:0% +kind of the the + + + align:start position:0% +kind of the the +a Lemma that we'll use + + align:start position:0% + + + + align:start position:0% + +when we prove that the collection of + + align:start position:0% +when we prove that the collection of + + + align:start position:0% +when we prove that the collection of +lebeg measurable sets is the sigma + + align:start position:0% +lebeg measurable sets is the sigma + + + align:start position:0% +lebeg measurable sets is the sigma +algebra is the following so let so this + + align:start position:0% +algebra is the following so let so this + + + align:start position:0% +algebra is the following so let so this +is General this has nothing to do + + align:start position:0% +is General this has nothing to do + + + align:start position:0% +is General this has nothing to do +necessarily with the bag measure let a + + align:start position:0% +necessarily with the bag measure let a + + + align:start position:0% +necessarily with the bag measure let a +be + + align:start position:0% + + + + align:start position:0% + +in algebra + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% +in + + + align:start position:0% +in +so again n here is a natural number + + align:start position:0% + + + + align:start position:0% + +a collection of + + align:start position:0% + + + + align:start position:0% + +elements of a so these are each of these + + align:start position:0% +elements of a so these are each of these + + + align:start position:0% +elements of a so these are each of these +is a subset of r + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +a countable collection FN + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +elements of a + + align:start position:0% + + + + align:start position:0% + +that are + + align:start position:0% +that are + + + align:start position:0% +that are +disjoint + + align:start position:0% + + + + align:start position:0% + +so if I take F in and FM and N do not + + align:start position:0% +so if I take F in and FM and N do not + + + align:start position:0% +so if I take F in and FM and N do not +equal M does not equal m then their + + align:start position:0% +equal M does not equal m then their + + + align:start position:0% +equal M does not equal m then their +intersection is empty + + align:start position:0% +intersection is empty + + + align:start position:0% +intersection is empty +such that + + align:start position:0% + + + + align:start position:0% + +the union of the ens + + align:start position:0% +the union of the ens + + + align:start position:0% +the union of the ens +uh equals the Union + + align:start position:0% +uh equals the Union + + + align:start position:0% +uh equals the Union +of the FNS + + align:start position:0% +of the FNS + + + align:start position:0% +of the FNS +okay so what does this say this says if + + align:start position:0% +okay so what does this say this says if + + + align:start position:0% +okay so what does this say this says if +we have so if we want to verify um + + align:start position:0% +we have so if we want to verify um + + + align:start position:0% +we have so if we want to verify um +let me make this a remark then + + align:start position:0% + + + + align:start position:0% + +what is uh the conclusion of this + + align:start position:0% + + + + align:start position:0% + +we only need to check + + align:start position:0% +we only need to check + + + align:start position:0% +we only need to check +this third condition for being a sigma + + align:start position:0% +this third condition for being a sigma + + + align:start position:0% +this third condition for being a sigma +algebra that accountable collection is + + align:start position:0% +algebra that accountable collection is + + + align:start position:0% +algebra that accountable collection is +closed under taking unions + + align:start position:0% +closed under taking unions + + + align:start position:0% +closed under taking unions +uh condition three for Sigma algebra for + + align:start position:0% +uh condition three for Sigma algebra for + + + align:start position:0% +uh condition three for Sigma algebra for +uh + + align:start position:0% + + + + align:start position:0% + +disjoint + + align:start position:0% + + + + align:start position:0% + +collections of elements + + align:start position:0% +collections of elements + + + align:start position:0% +collections of elements +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right this follows immediately from + + align:start position:0% +all right this follows immediately from + + + align:start position:0% +all right this follows immediately from +this limo because if I have any + + align:start position:0% +this limo because if I have any + + + align:start position:0% +this limo because if I have any +arbitrary collection of elements of the + + align:start position:0% +arbitrary collection of elements of the + + + align:start position:0% +arbitrary collection of elements of the +algebra then their Union is equal to a + + align:start position:0% +algebra then their Union is equal to a + + + align:start position:0% +algebra then their Union is equal to a +union of elements of a + + align:start position:0% +union of elements of a + + + align:start position:0% +union of elements of a +where the union is now over elements + + align:start position:0% +where the union is now over elements + + + align:start position:0% +where the union is now over elements +that are disjoint from each other okay + + align:start position:0% +that are disjoint from each other okay + + + align:start position:0% +that are disjoint from each other okay +so this is the point I only need to + + align:start position:0% +so this is the point I only need to + + + align:start position:0% +so this is the point I only need to +check the condition for an algebra to be + + align:start position:0% +check the condition for an algebra to be + + + align:start position:0% +check the condition for an algebra to be +a sigma algebra by checking that + + align:start position:0% +a sigma algebra by checking that + + + align:start position:0% +a sigma algebra by checking that +accountable unions of disjoint sets uh + + align:start position:0% +accountable unions of disjoint sets uh + + + align:start position:0% +accountable unions of disjoint sets uh +remain in the algebra + + align:start position:0% +remain in the algebra + + + align:start position:0% +remain in the algebra +okay + + align:start position:0% + + + + align:start position:0% + +okay so the proof is not very hard + + align:start position:0% +okay so the proof is not very hard + + + align:start position:0% +okay so the proof is not very hard +um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let uh + + align:start position:0% +let uh + + + align:start position:0% +let uh +G let's let's call it something G in to + + align:start position:0% +G let's let's call it something G in to + + + align:start position:0% +G let's let's call it something G in to +be + + align:start position:0% +be + + + align:start position:0% +be +the union k equals 1 to n + + align:start position:0% +the union k equals 1 to n + + + align:start position:0% +the union k equals 1 to n +of f k or of e k sorry + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% + + + + align:start position:0% + +then you know these are growing because + + align:start position:0% +then you know these are growing because + + + align:start position:0% +then you know these are growing because +g n contains the first n uh eks and then + + align:start position:0% +g n contains the first n uh eks and then + + + align:start position:0% +g n contains the first n uh eks and then +n plus one I tack on another one so + + align:start position:0% +n plus one I tack on another one so + + + align:start position:0% +n plus one I tack on another one so +G1 is contained in G2 is contained in G3 + + align:start position:0% +G1 is contained in G2 is contained in G3 + + + align:start position:0% +G1 is contained in G2 is contained in G3 +and + + align:start position:0% +and + + + align:start position:0% +and +you know this is just + + align:start position:0% +you know this is just + + + align:start position:0% +you know this is just +kind of + + align:start position:0% + + + + align:start position:0% + +easy to check and I'll leave it to you + + align:start position:0% +easy to check and I'll leave it to you + + + align:start position:0% +easy to check and I'll leave it to you +that the union of the ens is equal to + + align:start position:0% +that the union of the ens is equal to + + + align:start position:0% +that the union of the ens is equal to +the union of the gns + + align:start position:0% +the union of the gns + + + align:start position:0% +the union of the gns +okay I mean the gns are really just you + + align:start position:0% +okay I mean the gns are really just you + + + align:start position:0% +okay I mean the gns are really just you +know unions of the eks finite unions of + + align:start position:0% +know unions of the eks finite unions of + + + align:start position:0% +know unions of the eks finite unions of +the E case + + align:start position:0% +the E case + + + align:start position:0% +the E case +so + + align:start position:0% +so + + + align:start position:0% +so +uh you know this is this is pretty clear + + align:start position:0% +uh you know this is this is pretty clear + + + align:start position:0% +uh you know this is this is pretty clear +all right + + align:start position:0% + + + + align:start position:0% + +all right I mean you know if you + + align:start position:0% +all right I mean you know if you + + + align:start position:0% +all right I mean you know if you +actually want to sit down and do the + + align:start position:0% +actually want to sit down and do the + + + align:start position:0% +actually want to sit down and do the +argument every element in G in is + + align:start position:0% +argument every element in G in is + + + align:start position:0% +argument every element in G in is +contained in uh + + align:start position:0% +contained in uh + + + align:start position:0% +contained in uh +E1 up to e and so every GN is contained + + align:start position:0% +E1 up to e and so every GN is contained + + + align:start position:0% +E1 up to e and so every GN is contained +in this Union and therefore the union of + + align:start position:0% +in this Union and therefore the union of + + + align:start position:0% +in this Union and therefore the union of +the gns is contained in this Union and + + align:start position:0% +the gns is contained in this Union and + + + align:start position:0% +the gns is contained in this Union and +then it's easy to go the other way + + align:start position:0% +then it's easy to go the other way + + + align:start position:0% +then it's easy to go the other way +around showing this Union is contained + + align:start position:0% +around showing this Union is contained + + + align:start position:0% +around showing this Union is contained +in this Union so that they're equal + + align:start position:0% +in this Union so that they're equal + + + align:start position:0% +in this Union so that they're equal +okay + + align:start position:0% + + + + align:start position:0% + +and now I take + + align:start position:0% + + + + align:start position:0% + +F1 to be G1 + + align:start position:0% +F1 to be G1 + + + align:start position:0% +F1 to be G1 +and F uh + + align:start position:0% +and F uh + + + align:start position:0% +and F uh +n plus 1 to be + + align:start position:0% +n plus 1 to be + + + align:start position:0% +n plus 1 to be +f n plus 1 take away F in + + align:start position:0% +f n plus 1 take away F in + + + align:start position:0% +f n plus 1 take away F in +for n bigger than or equal to one or I + + align:start position:0% +for n bigger than or equal to one or I + + + align:start position:0% +for n bigger than or equal to one or I +should say sorry about that that should + + align:start position:0% +should say sorry about that that should + + + align:start position:0% +should say sorry about that that should +be + + align:start position:0% + + + + align:start position:0% + +g n plus 1 take away g n + + align:start position:0% +g n plus 1 take away g n + + + align:start position:0% +g n plus 1 take away g n +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what is this I take the first set to + + align:start position:0% +so what is this I take the first set to + + + align:start position:0% +so what is this I take the first set to +be G1 and then F2 will be what's in G2 + + align:start position:0% +be G1 and then F2 will be what's in G2 + + + align:start position:0% +be G1 and then F2 will be what's in G2 +but not in G1 so then uh + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +you know what is this uh + + align:start position:0% + + + + align:start position:0% + +what do we get we get that the union of + + align:start position:0% +what do we get we get that the union of + + + align:start position:0% +what do we get we get that the union of +any finite + + align:start position:0% +any finite + + + align:start position:0% +any finite +guy is equal to + + align:start position:0% +guy is equal to + + + align:start position:0% +guy is equal to +um in fact + + align:start position:0% + + + + align:start position:0% + +okay so I mean this is this is pretty + + align:start position:0% +okay so I mean this is this is pretty + + + align:start position:0% +okay so I mean this is this is pretty +clear again because what what am I doing + + align:start position:0% +clear again because what what am I doing + + + align:start position:0% +clear again because what what am I doing +here G2 or F2 will be what's in G2 take + + align:start position:0% +here G2 or F2 will be what's in G2 take + + + align:start position:0% +here G2 or F2 will be what's in G2 take +away G1 what's in F3 it's whatever's in + + align:start position:0% +away G1 what's in F3 it's whatever's in + + + align:start position:0% +away G1 what's in F3 it's whatever's in +G3 take away G2 + + align:start position:0% +G3 take away G2 + + + align:start position:0% +G3 take away G2 +and their Union you know is going to be + + align:start position:0% +and their Union you know is going to be + + + align:start position:0% +and their Union you know is going to be +the same as over here because I'm + + align:start position:0% +the same as over here because I'm + + + align:start position:0% +the same as over here because I'm +including G1 and then and so on I hope + + align:start position:0% +including G1 and then and so on I hope + + + align:start position:0% +including G1 and then and so on I hope +this is clear + + align:start position:0% + + + + align:start position:0% + +uh and in fact I don't know why I'm + + align:start position:0% +uh and in fact I don't know why I'm + + + align:start position:0% +uh and in fact I don't know why I'm +writing in + + align:start position:0% + + + + align:start position:0% + +um we in fact get this Union is equal to + + align:start position:0% +um we in fact get this Union is equal to + + + align:start position:0% +um we in fact get this Union is equal to +this Union all right + + align:start position:0% +this Union all right + + + align:start position:0% +this Union all right +um and again I'm leaving some details + + align:start position:0% +um and again I'm leaving some details + + + align:start position:0% +um and again I'm leaving some details +out but you can you know check + + align:start position:0% +out but you can you know check + + + align:start position:0% +out but you can you know check +that this Union is contained in this + + align:start position:0% +that this Union is contained in this + + + align:start position:0% +that this Union is contained in this +Union and then this Union is contained + + align:start position:0% +Union and then this Union is contained + + + align:start position:0% +Union and then this Union is contained +in this Union all right very easily but + + align:start position:0% +in this Union all right very easily but + + + align:start position:0% +in this Union all right very easily but +I hope uh you know I hope the ideas is + + align:start position:0% +I hope uh you know I hope the ideas is + + + align:start position:0% +I hope uh you know I hope the ideas is +pretty clear okay + + align:start position:0% +pretty clear okay + + + align:start position:0% +pretty clear okay +because you're just you know at each + + align:start position:0% +because you're just you know at each + + + align:start position:0% +because you're just you know at each +stage you're taking whatever is in this + + align:start position:0% +stage you're taking whatever is in this + + + align:start position:0% +stage you're taking whatever is in this +set + + align:start position:0% +set + + + align:start position:0% +set +um cutting out what was uh + + align:start position:0% +um cutting out what was uh + + + align:start position:0% +um cutting out what was uh +you know appeared before it okay in the + + align:start position:0% +you know appeared before it okay in the + + + align:start position:0% +you know appeared before it okay in the +sets before + + align:start position:0% +sets before + + + align:start position:0% +sets before +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +um now let's go back back to measurable + + align:start position:0% +um now let's go back back to measurable + + + align:start position:0% +um now let's go back back to measurable +sets we're now going to show that + + align:start position:0% +sets we're now going to show that + + + align:start position:0% +sets we're now going to show that +um well almost we are + + align:start position:0% +um well almost we are + + + align:start position:0% +um well almost we are +going to prove that + + align:start position:0% +going to prove that + + + align:start position:0% +going to prove that +the collection of lebeg measurable sets + + align:start position:0% +the collection of lebeg measurable sets + + + align:start position:0% +the collection of lebeg measurable sets +is a sigma algebra + + align:start position:0% +is a sigma algebra + + + align:start position:0% +is a sigma algebra +first we need the following theorem + + align:start position:0% + + + + align:start position:0% + +which is the following + + align:start position:0% +which is the following + + + align:start position:0% +which is the following +um + + align:start position:0% +um + + + align:start position:0% +um +let a be a subset of R and this is + + align:start position:0% +let a be a subset of R and this is + + + align:start position:0% +let a be a subset of R and this is +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +the whole game as we'll see + + align:start position:0% +the whole game as we'll see + + + align:start position:0% +the whole game as we'll see +let a be a subset of r + + align:start position:0% +let a be a subset of r + + + align:start position:0% +let a be a subset of r +E1 up to e in uh + + align:start position:0% +E1 up to e in uh + + + align:start position:0% +E1 up to e in uh +the bag measurable + + align:start position:0% + + + + align:start position:0% + +and not just measurable but + + align:start position:0% + + + + align:start position:0% + +be + + align:start position:0% + + + + align:start position:0% + +disjoint + + align:start position:0% + + + + align:start position:0% + +measurable sets so I only have finitely + + align:start position:0% +measurable sets so I only have finitely + + + align:start position:0% +measurable sets so I only have finitely +many of them + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +the union of these + + align:start position:0% +the union of these + + + align:start position:0% +the union of these +guys + + align:start position:0% +guys + + + align:start position:0% +guys +is equal to + + align:start position:0% + + + + align:start position:0% + +sum k equals 1 to n of + + align:start position:0% +sum k equals 1 to n of + + + align:start position:0% +sum k equals 1 to n of +the outer measure of + + align:start position:0% + + + + align:start position:0% + +a intersect e k + + align:start position:0% +a intersect e k + + + align:start position:0% +a intersect e k +all right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +foreign + + align:start position:0% + + + + align:start position:0% + +you know this shouldn't come as too much + + align:start position:0% +you know this shouldn't come as too much + + + align:start position:0% +you know this shouldn't come as too much +of a surprise because + + align:start position:0% +of a surprise because + + + align:start position:0% +of a surprise because +this is very close this is kind of close + + align:start position:0% +this is very close this is kind of close + + + align:start position:0% +this is very close this is kind of close +to saying you know uh + + align:start position:0% +to saying you know uh + + + align:start position:0% +to saying you know uh +I should say + + align:start position:0% +I should say + + + align:start position:0% +I should say +um + + align:start position:0% +um + + + align:start position:0% +um +you know this is + + align:start position:0% +you know this is + + + align:start position:0% +you know this is +very true if say E1 say you just have + + align:start position:0% +very true if say E1 say you just have + + + align:start position:0% +very true if say E1 say you just have +two sets E1 is e and E2 is e complement + + align:start position:0% +two sets E1 is e and E2 is e complement + + + align:start position:0% +two sets E1 is e and E2 is e complement +right then that's just the definition of + + align:start position:0% +right then that's just the definition of + + + align:start position:0% +right then that's just the definition of +being measurable + + align:start position:0% +being measurable + + + align:start position:0% +being measurable +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +and you build up from that by using + + align:start position:0% +and you build up from that by using + + + align:start position:0% +and you build up from that by using +induction all right that's that's + + align:start position:0% +induction all right that's that's + + + align:start position:0% +induction all right that's that's +the basic argument again I'm sorry I + + align:start position:0% +the basic argument again I'm sorry I + + + align:start position:0% +the basic argument again I'm sorry I +keep moving away from the chalkboard + + align:start position:0% +keep moving away from the chalkboard + + + align:start position:0% +keep moving away from the chalkboard +because I'm used to + + align:start position:0% +because I'm used to + + + align:start position:0% +because I'm used to +lecturing to a classroom even though + + align:start position:0% +lecturing to a classroom even though + + + align:start position:0% +lecturing to a classroom even though +it's been + + align:start position:0% +it's been + + + align:start position:0% +it's been +months now since I've been in a + + align:start position:0% +months now since I've been in a + + + align:start position:0% +months now since I've been in a +classroom with students so + + align:start position:0% +classroom with students so + + + align:start position:0% +classroom with students so +and because I'm a freak of nature who + + align:start position:0% +and because I'm a freak of nature who + + + align:start position:0% +and because I'm a freak of nature who +rides with my left hand so I have to + + align:start position:0% +rides with my left hand so I have to + + + align:start position:0% +rides with my left hand so I have to +write and then + + align:start position:0% +write and then + + + align:start position:0% +write and then +do this kind of move but anyways so + + align:start position:0% +do this kind of move but anyways so + + + align:start position:0% +do this kind of move but anyways so +we're going to prove this by induction + + align:start position:0% + + + + align:start position:0% + +so the proof is by induction + + align:start position:0% + + + + align:start position:0% + +so n equals one that's just one set this + + align:start position:0% +so n equals one that's just one set this + + + align:start position:0% +so n equals one that's just one set this +is clear + + align:start position:0% + + + + align:start position:0% + +that's just a measure the outer measure + + align:start position:0% +that's just a measure the outer measure + + + align:start position:0% +that's just a measure the outer measure +of a intersect E1 is equal to the outer + + align:start position:0% +of a intersect E1 is equal to the outer + + + align:start position:0% +of a intersect E1 is equal to the outer +measure of a intersect E1 so that's fine + + align:start position:0% +measure of a intersect E1 so that's fine + + + align:start position:0% +measure of a intersect E1 so that's fine +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so I'm going to put a check there + + align:start position:0% +so I'm going to put a check there + + + align:start position:0% +so I'm going to put a check there +without writing anything down so now + + align:start position:0% +without writing anything down so now + + + align:start position:0% +without writing anything down so now +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +let's label this statement by star + + align:start position:0% +let's label this statement by star + + + align:start position:0% +let's label this statement by star +so now let's do the induction step + + align:start position:0% + + + + align:start position:0% + +duction + + align:start position:0% + + + + align:start position:0% + +step so suppose + + align:start position:0% + + + + align:start position:0% + +star holds + + align:start position:0% + + + + align:start position:0% + +for n equals m and what we now want to + + align:start position:0% +for n equals m and what we now want to + + + align:start position:0% +for n equals m and what we now want to +show meaning that if I have E1 up to E1 + + align:start position:0% +show meaning that if I have E1 up to E1 + + + align:start position:0% +show meaning that if I have E1 up to E1 +up to e m disjoint measurable sets Then + + align:start position:0% +up to e m disjoint measurable sets Then + + + align:start position:0% +up to e m disjoint measurable sets Then +star holds now I want to show that + + align:start position:0% +star holds now I want to show that + + + align:start position:0% +star holds now I want to show that +statement holds for M plus 1. + + align:start position:0% + + + + align:start position:0% + +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +let + + align:start position:0% + + + + align:start position:0% + +E1 up to + + align:start position:0% +E1 up to + + + align:start position:0% +E1 up to +the M plus one + + align:start position:0% +the M plus one + + + align:start position:0% +the M plus one +the measurable + + align:start position:0% +the measurable + + + align:start position:0% +the measurable +uh + + align:start position:0% +uh + + + align:start position:0% +uh +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +disjoint sets + + align:start position:0% +disjoint sets + + + align:start position:0% +disjoint sets +so each of them their pairwise disjoint + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +then since + + align:start position:0% + + + + align:start position:0% + +em plus one + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +um + + align:start position:0% +um + + + align:start position:0% +um +what do we have + + align:start position:0% + + + + align:start position:0% + +well first let me + + align:start position:0% +well first let me + + + align:start position:0% +well first let me +before I use that + + align:start position:0% +before I use that + + + align:start position:0% +before I use that +let me just note something since uh em + + align:start position:0% +let me just note something since uh em + + + align:start position:0% +let me just note something since uh em +plus one is just disjoint from E1 up to + + align:start position:0% +plus one is just disjoint from E1 up to + + + align:start position:0% +plus one is just disjoint from E1 up to +e m + + align:start position:0% +e m + + + align:start position:0% +e m +uh + + align:start position:0% + + + + align:start position:0% + +let a be a subset of R we want to verify + + align:start position:0% +let a be a subset of R we want to verify + + + align:start position:0% +let a be a subset of R we want to verify +star for a so uh I need to have an a uh + + align:start position:0% + + + + align:start position:0% + +so since + + align:start position:0% +so since + + + align:start position:0% +so since +the + + align:start position:0% +the + + + align:start position:0% +the +K intersect + + align:start position:0% +K intersect + + + align:start position:0% +K intersect +the M plus 1 equals the empty set + + align:start position:0% +the M plus 1 equals the empty set + + + align:start position:0% +the M plus 1 equals the empty set +for all k equals 1 to m + + align:start position:0% +for all k equals 1 to m + + + align:start position:0% +for all k equals 1 to m +we get that a intersect + + align:start position:0% +we get that a intersect + + + align:start position:0% +we get that a intersect +the sum or the union I'm sorry k equals + + align:start position:0% +the sum or the union I'm sorry k equals + + + align:start position:0% +the sum or the union I'm sorry k equals +one + + align:start position:0% +one + + + align:start position:0% +one +n Plus 1. + + align:start position:0% + + + + align:start position:0% + +what is this equal to + + align:start position:0% +what is this equal to + + + align:start position:0% +what is this equal to +um + + align:start position:0% +um + + + align:start position:0% +um +or + + align:start position:0% +or + + + align:start position:0% +or +then I intersect that with E M plus 1. + + align:start position:0% +then I intersect that with E M plus 1. + + + align:start position:0% +then I intersect that with E M plus 1. +this is simply equal to a intersect + + align:start position:0% +this is simply equal to a intersect + + + align:start position:0% +this is simply equal to a intersect +e n plus one right because + + align:start position:0% +e n plus one right because + + + align:start position:0% +e n plus one right because +uh E1 up to e m these are disjoints so + + align:start position:0% +uh E1 up to e m these are disjoints so + + + align:start position:0% +uh E1 up to e m these are disjoints so +when I transfer this through + + align:start position:0% +when I transfer this through + + + align:start position:0% +when I transfer this through +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +you know I can write this intersection + + align:start position:0% +you know I can write this intersection + + + align:start position:0% +you know I can write this intersection +by bringing this intersect each of these + + align:start position:0% +by bringing this intersect each of these + + + align:start position:0% +by bringing this intersect each of these +eks for k equals one to n plus one and + + align:start position:0% +eks for k equals one to n plus one and + + + align:start position:0% +eks for k equals one to n plus one and +then this is empty when K is not equal + + align:start position:0% +then this is empty when K is not equal + + + align:start position:0% +then this is empty when K is not equal +to M plus one so I just pick up e n plus + + align:start position:0% +to M plus one so I just pick up e n plus + + + align:start position:0% +to M plus one so I just pick up e n plus +one and and I get that there + + align:start position:0% +one and and I get that there + + + align:start position:0% +one and and I get that there +um + + align:start position:0% +um + + + align:start position:0% +um +but also if I look at + + align:start position:0% + + + + align:start position:0% + +intersect the complement + + align:start position:0% + + + + align:start position:0% + +what is this this is equal to now + + align:start position:0% +what is this this is equal to now + + + align:start position:0% +what is this this is equal to now +k e k for K going from 1 to M these are + + align:start position:0% +k e k for K going from 1 to M these are + + + align:start position:0% +k e k for K going from 1 to M these are +all contained in the complement of em uh + + align:start position:0% +all contained in the complement of em uh + + + align:start position:0% +all contained in the complement of em uh +plus one right because they're disjoint + + align:start position:0% +plus one right because they're disjoint + + + align:start position:0% +plus one right because they're disjoint +so this is equal to just a intersect uh + + align:start position:0% + + + + align:start position:0% + +Union a equals one to m + + align:start position:0% + + + + align:start position:0% + +e k + + align:start position:0% +e k + + + align:start position:0% +e k +all right + + align:start position:0% + + + + align:start position:0% + +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +got ahead of myself a minute ago but now + + align:start position:0% +got ahead of myself a minute ago but now + + + align:start position:0% +got ahead of myself a minute ago but now +we're at this stage + + align:start position:0% + + + + align:start position:0% + +since e n plus one + + align:start position:0% + + + + align:start position:0% + +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the + + align:start position:0% +the + + + align:start position:0% +the +measure of a intersect + + align:start position:0% +measure of a intersect + + + align:start position:0% +measure of a intersect +this Union okay equals one + + align:start position:0% +this Union okay equals one + + + align:start position:0% +this Union okay equals one +n plus one + + align:start position:0% +n plus one + + + align:start position:0% +n plus one +e k + + align:start position:0% +e k + + + align:start position:0% +e k +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +the outer measure of a intersect + + align:start position:0% + + + + align:start position:0% + +k equals one n plus one + + align:start position:0% +k equals one n plus one + + + align:start position:0% +k equals one n plus one +p k intersect + + align:start position:0% +p k intersect + + + align:start position:0% +p k intersect +e n plus 1 plus + + align:start position:0% +e n plus 1 plus + + + align:start position:0% +e n plus 1 plus +the outer measure of + + align:start position:0% + + + + align:start position:0% + +a intersect Union okay equals one + + align:start position:0% +a intersect Union okay equals one + + + align:start position:0% +a intersect Union okay equals one +n plus one + + align:start position:0% +n plus one + + + align:start position:0% +n plus one +uh Eve k + + align:start position:0% +uh Eve k + + + align:start position:0% +uh Eve k +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +em plus one + + align:start position:0% +em plus one + + + align:start position:0% +em plus one +complement + + align:start position:0% +complement + + + align:start position:0% +complement +okay just using that e and plus one is + + align:start position:0% +okay just using that e and plus one is + + + align:start position:0% +okay just using that e and plus one is +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +and now we plug in what these things are + + align:start position:0% +and now we plug in what these things are + + + align:start position:0% +and now we plug in what these things are +so this whole thing is equal to a + + align:start position:0% +so this whole thing is equal to a + + + align:start position:0% +so this whole thing is equal to a +intersect D M plus one + + align:start position:0% +intersect D M plus one + + + align:start position:0% +intersect D M plus one +so this is equal to the measure of a + + align:start position:0% +so this is equal to the measure of a + + + align:start position:0% +so this is equal to the measure of a +intersect em + + align:start position:0% +intersect em + + + align:start position:0% +intersect em +plus one + + align:start position:0% + + + + align:start position:0% + +and now this whole thing is equal to + + align:start position:0% + + + + align:start position:0% + +the measure of a intersect + + align:start position:0% +the measure of a intersect + + + align:start position:0% +the measure of a intersect +the union only going up to m + + align:start position:0% + + + + align:start position:0% + +and now this is where we use the + + align:start position:0% +and now this is where we use the + + + align:start position:0% +and now this is where we use the +induction hypothesis right because now + + align:start position:0% +induction hypothesis right because now + + + align:start position:0% +induction hypothesis right because now +we have a union of M disjoint measurable + + align:start position:0% +we have a union of M disjoint measurable + + + align:start position:0% +we have a union of M disjoint measurable +sets so this is equal to + + align:start position:0% +sets so this is equal to + + + align:start position:0% +sets so this is equal to +um + + align:start position:0% + + + + align:start position:0% + +plus sum from k equals 1 to m + + align:start position:0% + + + + align:start position:0% + +uh a intersect e k so this is by + + align:start position:0% +uh a intersect e k so this is by + + + align:start position:0% +uh a intersect e k so this is by +our induction hypothesis + + align:start position:0% + + + + align:start position:0% + +and this is you know combining these two + + align:start position:0% +and this is you know combining these two + + + align:start position:0% +and this is you know combining these two +terms is exactly what we want for n + + align:start position:0% +terms is exactly what we want for n + + + align:start position:0% +terms is exactly what we want for n +equals n plus one k equals one and plus + + align:start position:0% +equals n plus one k equals one and plus + + + align:start position:0% +equals n plus one k equals one and plus +one + + align:start position:0% +one + + + align:start position:0% +one +outer measure of a + + align:start position:0% +outer measure of a + + + align:start position:0% +outer measure of a +intersect e k + + align:start position:0% +intersect e k + + + align:start position:0% +intersect e k +all right + + align:start position:0% +all right + + + align:start position:0% +all right +and and that's the proof + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so now using this theorem + + align:start position:0% + + + + align:start position:0% + +and the Lima before it + + align:start position:0% + + + + align:start position:0% + +we will prove that the collection M of + + align:start position:0% +we will prove that the collection M of + + + align:start position:0% +we will prove that the collection M of +lebeg measurable sets is a sigma algebra + + align:start position:0% + + + + align:start position:0% + +we already know it's in algebra up to + + align:start position:0% +we already know it's in algebra up to + + + align:start position:0% +we already know it's in algebra up to +this point but we just need to verify + + align:start position:0% +this point but we just need to verify + + + align:start position:0% +this point but we just need to verify +it's a sigma algebra + + align:start position:0% + + + + align:start position:0% + +all right so what's the proof now again + + align:start position:0% +all right so what's the proof now again + + + align:start position:0% +all right so what's the proof now again +based on this remark here + + align:start position:0% + + + + align:start position:0% + +right we only need to verify that uh + + align:start position:0% +right we only need to verify that uh + + + align:start position:0% +right we only need to verify that uh +if I have accountable + + align:start position:0% +if I have accountable + + + align:start position:0% +if I have accountable +collection of disjoint of disjoint + + align:start position:0% +collection of disjoint of disjoint + + + align:start position:0% +collection of disjoint of disjoint +measurable sets then the union is + + align:start position:0% +measurable sets then the union is + + + align:start position:0% +measurable sets then the union is +measurable right I don't have to check + + align:start position:0% +measurable right I don't have to check + + + align:start position:0% +measurable right I don't have to check +it for every collection of measurable + + align:start position:0% +it for every collection of measurable + + + align:start position:0% +it for every collection of measurable +sets just disjoint measurable sets + + align:start position:0% +sets just disjoint measurable sets + + + align:start position:0% +sets just disjoint measurable sets +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we just need to check so + + align:start position:0% + + + + align:start position:0% + +we've already checked it's an algebra so + + align:start position:0% + + + + align:start position:0% + +bye dilemma the first thing we proved + + align:start position:0% +bye dilemma the first thing we proved + + + align:start position:0% +bye dilemma the first thing we proved +during this lecture + + align:start position:0% +during this lecture + + + align:start position:0% +during this lecture +uh + + align:start position:0% + + + + align:start position:0% + +we just + + align:start position:0% + + + + align:start position:0% + +need to show + + align:start position:0% +need to show + + + align:start position:0% +need to show +m is + + align:start position:0% + + + + align:start position:0% + +closed under + + align:start position:0% + + + + align:start position:0% + +taking + + align:start position:0% +taking + + + align:start position:0% +taking +accountable + + align:start position:0% +accountable + + + align:start position:0% +accountable +diss joints + + align:start position:0% + + + + align:start position:0% + +unions meaning if I have a countable + + align:start position:0% +unions meaning if I have a countable + + + align:start position:0% +unions meaning if I have a countable +collection of disjoint measurable sets I + + align:start position:0% +collection of disjoint measurable sets I + + + align:start position:0% +collection of disjoint measurable sets I +need to show the union is is measurable + + align:start position:0% +need to show the union is is measurable + + + align:start position:0% +need to show the union is is measurable +so + + align:start position:0% + + + + align:start position:0% + +but e sub n + + align:start position:0% +but e sub n + + + align:start position:0% +but e sub n +B + + align:start position:0% +B + + + align:start position:0% +B +a + + align:start position:0% + + + + align:start position:0% + +countable collection here N is a natural + + align:start position:0% +countable collection here N is a natural + + + align:start position:0% +countable collection here N is a natural +number of + + align:start position:0% + + + + align:start position:0% + +disjoint + + align:start position:0% +disjoint + + + align:start position:0% +disjoint +measurable sets + + align:start position:0% +measurable sets + + + align:start position:0% +measurable sets +okay so we need to verify the definition + + align:start position:0% +okay so we need to verify the definition + + + align:start position:0% +okay so we need to verify the definition +of of being measurable but remember uh + + align:start position:0% +of of being measurable but remember uh + + + align:start position:0% +of of being measurable but remember uh +that's just that reduces uh really to + + align:start position:0% +that's just that reduces uh really to + + + align:start position:0% +that's just that reduces uh really to +one inequality since one of those + + align:start position:0% +one inequality since one of those + + + align:start position:0% +one inequality since one of those +inequalities is + + align:start position:0% +inequalities is + + + align:start position:0% +inequalities is +um + + align:start position:0% +um + + + align:start position:0% +um +always clear + + align:start position:0% +always clear + + + align:start position:0% +always clear +so + + align:start position:0% + + + + align:start position:0% + +let a be a subset of r + + align:start position:0% +let a be a subset of r + + + align:start position:0% +let a be a subset of r +and let's denote e to be the Union + + align:start position:0% + + + + align:start position:0% + +so what do we need to show + + align:start position:0% +so what do we need to show + + + align:start position:0% +so what do we need to show +um + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +we want to show that + + align:start position:0% +we want to show that + + + align:start position:0% +we want to show that +the outer measure of a intersect e + + align:start position:0% +the outer measure of a intersect e + + + align:start position:0% +the outer measure of a intersect e +complement Plus + + align:start position:0% +complement Plus + + + align:start position:0% +complement Plus +the outer measure of a intersect e e + + align:start position:0% +the outer measure of a intersect e e + + + align:start position:0% +the outer measure of a intersect e e +here again is the union + + align:start position:0% +here again is the union + + + align:start position:0% +here again is the union +is equal to the outer measure of a but + + align:start position:0% +is equal to the outer measure of a but + + + align:start position:0% +is equal to the outer measure of a but +we always have uh the outer measure of a + + align:start position:0% +we always have uh the outer measure of a + + + align:start position:0% +we always have uh the outer measure of a +is less than or equal to this so we just + + align:start position:0% +is less than or equal to this so we just + + + align:start position:0% +is less than or equal to this so we just +need to show this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +let's do this uh + + align:start position:0% + + + + align:start position:0% + +let N be a natural number so + + align:start position:0% + + + + align:start position:0% + +so let N be a natural number + + align:start position:0% +so let N be a natural number + + + align:start position:0% +so let N be a natural number +by + + align:start position:0% +by + + + align:start position:0% +by +so since + + align:start position:0% + + + + align:start position:0% + +m is an algebra + + align:start position:0% + + + + align:start position:0% + +this a finite Union n equals one to + + align:start position:0% +this a finite Union n equals one to + + + align:start position:0% +this a finite Union n equals one to +capital N of e sub n + + align:start position:0% +capital N of e sub n + + + align:start position:0% +capital N of e sub n +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +if I want + + align:start position:0% +if I want + + + align:start position:0% +if I want +the outer measure of a + + align:start position:0% + + + + align:start position:0% + +this is + + align:start position:0% + + + + align:start position:0% + +equal to the outer measure of a + + align:start position:0% +equal to the outer measure of a + + + align:start position:0% +equal to the outer measure of a +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +n equals 1 to n + + align:start position:0% +n equals 1 to n + + + align:start position:0% +n equals 1 to n +e sub n + + align:start position:0% +e sub n + + + align:start position:0% +e sub n +plus the outer measure of + + align:start position:0% +plus the outer measure of + + + align:start position:0% +plus the outer measure of +a intersect + + align:start position:0% +a intersect + + + align:start position:0% +a intersect +uh + + align:start position:0% +uh + + + align:start position:0% +uh +n equals 1 to n + + align:start position:0% +n equals 1 to n + + + align:start position:0% +n equals 1 to n +e and complement + + align:start position:0% +e and complement + + + align:start position:0% +e and complement +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +um + + align:start position:0% +um + + + align:start position:0% +um +this finite Union + + align:start position:0% +this finite Union + + + align:start position:0% +this finite Union +is contained in e + + align:start position:0% +is contained in e + + + align:start position:0% +is contained in e +right e is the the total Union + + align:start position:0% +right e is the the total Union + + + align:start position:0% +right e is the the total Union +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +the complement of this finite Union + + align:start position:0% +the complement of this finite Union + + + align:start position:0% +the complement of this finite Union +contains the complement of e okay + + align:start position:0% +contains the complement of e okay + + + align:start position:0% +contains the complement of e okay +so + + align:start position:0% +so + + + align:start position:0% +so +this complement here contains the + + align:start position:0% +this complement here contains the + + + align:start position:0% +this complement here contains the +complement of e and therefore a + + align:start position:0% +complement of e and therefore a + + + align:start position:0% +complement of e and therefore a +intersect this + + align:start position:0% +intersect this + + + align:start position:0% +intersect this +is a bigger set than a intersect the + + align:start position:0% +is a bigger set than a intersect the + + + align:start position:0% +is a bigger set than a intersect the +complement of e so + + align:start position:0% +complement of e so + + + align:start position:0% +complement of e so +this is bigger than or equal to the + + align:start position:0% +this is bigger than or equal to the + + + align:start position:0% +this is bigger than or equal to the +outer measure of a intersect + + align:start position:0% +outer measure of a intersect + + + align:start position:0% +outer measure of a intersect +Union n equals 1 to n + + align:start position:0% +Union n equals 1 to n + + + align:start position:0% +Union n equals 1 to n +e n + + align:start position:0% +e n + + + align:start position:0% +e n +plus uh the outer measure of a intersect + + align:start position:0% +plus uh the outer measure of a intersect + + + align:start position:0% +plus uh the outer measure of a intersect +e complement again because this finite + + align:start position:0% +e complement again because this finite + + + align:start position:0% +e complement again because this finite +Union is contained in the whole Union so + + align:start position:0% +Union is contained in the whole Union so + + + align:start position:0% +Union is contained in the whole Union so +when I take complements that switches + + align:start position:0% +when I take complements that switches + + + align:start position:0% +when I take complements that switches +around what's contained in what so then + + align:start position:0% +around what's contained in what so then + + + align:start position:0% +around what's contained in what so then +I get a intersect e complement is + + align:start position:0% +I get a intersect e complement is + + + align:start position:0% +I get a intersect e complement is +contained in a intersect the complement + + align:start position:0% +contained in a intersect the complement + + + align:start position:0% +contained in a intersect the complement +of this finite Union + + align:start position:0% +of this finite Union + + + align:start position:0% +of this finite Union +okay + + align:start position:0% + + + + align:start position:0% + +all right and that's good so this has + + align:start position:0% +all right and that's good so this has + + + align:start position:0% +all right and that's good so this has +now appeared we wanted this to be + + align:start position:0% +now appeared we wanted this to be + + + align:start position:0% +now appeared we wanted this to be +smaller than the the measure of a here + + align:start position:0% +smaller than the the measure of a here + + + align:start position:0% +smaller than the the measure of a here +and now what do we have + + align:start position:0% +and now what do we have + + + align:start position:0% +and now what do we have +we have the outer measure of a with a + + align:start position:0% +we have the outer measure of a with a + + + align:start position:0% +we have the outer measure of a with a +finite uh the a finite Union of disjoint + + align:start position:0% +finite uh the a finite Union of disjoint + + + align:start position:0% +finite uh the a finite Union of disjoint +measurable sets and we can write this + + align:start position:0% +measurable sets and we can write this + + + align:start position:0% +measurable sets and we can write this +using the previous theorem as + + align:start position:0% +using the previous theorem as + + + align:start position:0% +using the previous theorem as +some from + + align:start position:0% +some from + + + align:start position:0% +some from +n equals 1 to capital n + + align:start position:0% + + + + align:start position:0% + +outer measure of a intersect + + align:start position:0% +outer measure of a intersect + + + align:start position:0% +outer measure of a intersect +e n Plus + + align:start position:0% + + + + align:start position:0% + +just keeping the second term + + align:start position:0% +just keeping the second term + + + align:start position:0% +just keeping the second term +okay now this holds for every n right n + + align:start position:0% +okay now this holds for every n right n + + + align:start position:0% +okay now this holds for every n right n +was arbitrary + + align:start position:0% + + + + align:start position:0% + +so I can let capital N Go to Infinity + + align:start position:0% +so I can let capital N Go to Infinity + + + align:start position:0% +so I can let capital N Go to Infinity +remember so I've shown that the outer + + align:start position:0% +remember so I've shown that the outer + + + align:start position:0% +remember so I've shown that the outer +measure of a + + align:start position:0% +measure of a + + + align:start position:0% +measure of a +is bigger than or equal to this quantity + + align:start position:0% +is bigger than or equal to this quantity + + + align:start position:0% +is bigger than or equal to this quantity +here so I can let N Go to Infinity to + + align:start position:0% +here so I can let N Go to Infinity to + + + align:start position:0% +here so I can let N Go to Infinity to +conclude that the outer measure of a is + + align:start position:0% +conclude that the outer measure of a is + + + align:start position:0% +conclude that the outer measure of a is +bigger than or equal to sum from n + + align:start position:0% +bigger than or equal to sum from n + + + align:start position:0% +bigger than or equal to sum from n +equals 1 to Infinity of + + align:start position:0% +equals 1 to Infinity of + + + align:start position:0% +equals 1 to Infinity of +the outer measure of a intersect + + align:start position:0% +the outer measure of a intersect + + + align:start position:0% +the outer measure of a intersect +e n + + align:start position:0% +e n + + + align:start position:0% +e n +Plus + + align:start position:0% + + + + align:start position:0% + +the outer measure of the a intersect the + + align:start position:0% +the outer measure of the a intersect the + + + align:start position:0% +the outer measure of the a intersect the +complement of the union now + + align:start position:0% +complement of the union now + + + align:start position:0% +complement of the union now +remember what we proved about outer + + align:start position:0% +remember what we proved about outer + + + align:start position:0% +remember what we proved about outer +measure that the sum of the outer + + align:start position:0% +measure that the sum of the outer + + + align:start position:0% +measure that the sum of the outer +measures is bigger than or equal to the + + align:start position:0% +measures is bigger than or equal to the + + + align:start position:0% +measures is bigger than or equal to the +outer measure of the Union so this thing + + align:start position:0% +outer measure of the Union so this thing + + + align:start position:0% +outer measure of the Union so this thing +is bigger than or equal to the outer + + align:start position:0% +is bigger than or equal to the outer + + + align:start position:0% +is bigger than or equal to the outer +measure of the Union + + align:start position:0% +measure of the Union + + + align:start position:0% +measure of the Union +overall n a + + align:start position:0% +overall n a + + + align:start position:0% +overall n a +intersect en + + align:start position:0% + + + + align:start position:0% + +plus a intersect + + align:start position:0% +plus a intersect + + + align:start position:0% +plus a intersect +the complement and this is just equal to + + align:start position:0% + + + + align:start position:0% + +plus the outer measure of + + align:start position:0% +plus the outer measure of + + + align:start position:0% +plus the outer measure of +a intersect + + align:start position:0% +a intersect + + + align:start position:0% +a intersect +e complement okay + + align:start position:0% + + + + align:start position:0% + +all right so we've shown + + align:start position:0% +all right so we've shown + + + align:start position:0% +all right so we've shown +um + + align:start position:0% +um + + + align:start position:0% +um +that + + align:start position:0% +that + + + align:start position:0% +that +the collection of all the vague + + align:start position:0% +the collection of all the vague + + + align:start position:0% +the collection of all the vague +measurable subsets of R form a sigma + + align:start position:0% +measurable subsets of R form a sigma + + + align:start position:0% +measurable subsets of R form a sigma +algebra + + align:start position:0% + + + + align:start position:0% + +so let me just um + + align:start position:0% +so let me just um + + + align:start position:0% +so let me just um +you know maybe I should have said this + + align:start position:0% +you know maybe I should have said this + + + align:start position:0% +you know maybe I should have said this +at the start but let me just pause here + + align:start position:0% +at the start but let me just pause here + + + align:start position:0% +at the start but let me just pause here +for a second and maybe you're wondering + + align:start position:0% +for a second and maybe you're wondering + + + align:start position:0% +for a second and maybe you're wondering +why all this Sigma algebra business + + align:start position:0% +why all this Sigma algebra business + + + align:start position:0% +why all this Sigma algebra business +anyways what like + + align:start position:0% +anyways what like + + + align:start position:0% +anyways what like +why have I imposed this condition am I + + align:start position:0% +why have I imposed this condition am I + + + align:start position:0% +why have I imposed this condition am I +just making this this definition up at + + align:start position:0% +just making this this definition up at + + + align:start position:0% +just making this this definition up at +the + + align:start position:0% +the + + + align:start position:0% +the +as I go along + + align:start position:0% + + + + align:start position:0% + +now remember what but it's kind of a + + align:start position:0% +now remember what but it's kind of a + + + align:start position:0% +now remember what but it's kind of a +condition that's forced upon us based on + + align:start position:0% +condition that's forced upon us based on + + + align:start position:0% +condition that's forced upon us based on +our expectations in in the following + + align:start position:0% +our expectations in in the following + + + align:start position:0% +our expectations in in the following +sense + + align:start position:0% +sense + + + align:start position:0% +sense +um + + align:start position:0% +um + + + align:start position:0% +um +you remember one of the properties that + + align:start position:0% +you remember one of the properties that + + + align:start position:0% +you remember one of the properties that +we wanted of lebeg measure or measure in + + align:start position:0% +we wanted of lebeg measure or measure in + + + align:start position:0% +we wanted of lebeg measure or measure in +general was that the measure of a + + align:start position:0% +general was that the measure of a + + + align:start position:0% +general was that the measure of a +countable Union of disjoint sets is + + align:start position:0% +countable Union of disjoint sets is + + + align:start position:0% +countable Union of disjoint sets is +equal to the sum of the measures right + + align:start position:0% +equal to the sum of the measures right + + + align:start position:0% +equal to the sum of the measures right +and + + align:start position:0% +and + + + align:start position:0% +and +you know + + align:start position:0% +you know + + + align:start position:0% +you know +I stated without proof but there is a + + align:start position:0% +I stated without proof but there is a + + + align:start position:0% +I stated without proof but there is a +proof in the textbook that you know this + + align:start position:0% +proof in the textbook that you know this + + + align:start position:0% +proof in the textbook that you know this +is not + + align:start position:0% +is not + + + align:start position:0% +is not +you cannot have a measure defined on + + align:start position:0% +you cannot have a measure defined on + + + align:start position:0% +you cannot have a measure defined on +every subset satisfying those properties + + align:start position:0% +every subset satisfying those properties + + + align:start position:0% +every subset satisfying those properties +that uh that we outlined so you have to + + align:start position:0% +that uh that we outlined so you have to + + + align:start position:0% +that uh that we outlined so you have to +have some collection of subsets on which + + align:start position:0% +have some collection of subsets on which + + + align:start position:0% +have some collection of subsets on which +uh you have these properties that the + + align:start position:0% +uh you have these properties that the + + + align:start position:0% +uh you have these properties that the +measure of an interval is the length of + + align:start position:0% +measure of an interval is the length of + + + align:start position:0% +measure of an interval is the length of +the interval + + align:start position:0% +the interval + + + align:start position:0% +the interval +and uh that's translation and variant + + align:start position:0% +and uh that's translation and variant + + + align:start position:0% +and uh that's translation and variant +and that the measure of the Union is the + + align:start position:0% +and that the measure of the Union is the + + + align:start position:0% +and that the measure of the Union is the +sum of the measures + + align:start position:0% +sum of the measures + + + align:start position:0% +sum of the measures +that last statement though hidden in + + align:start position:0% +that last statement though hidden in + + + align:start position:0% +that last statement though hidden in +there is kind of a hidden there's kind + + align:start position:0% +there is kind of a hidden there's kind + + + align:start position:0% +there is kind of a hidden there's kind +of a subtle assumption right that if you + + align:start position:0% +of a subtle assumption right that if you + + + align:start position:0% +of a subtle assumption right that if you +have a measure to find on some + + align:start position:0% +have a measure to find on some + + + align:start position:0% +have a measure to find on some +collection of subsets + + align:start position:0% +collection of subsets + + + align:start position:0% +collection of subsets +then that collection of subsets better + + align:start position:0% +then that collection of subsets better + + + align:start position:0% +then that collection of subsets better +be closed undertaking countable unions + + align:start position:0% +be closed undertaking countable unions + + + align:start position:0% +be closed undertaking countable unions +right if I'm to be able to make the + + align:start position:0% +right if I'm to be able to make the + + + align:start position:0% +right if I'm to be able to make the +statement that I want that the measure + + align:start position:0% +statement that I want that the measure + + + align:start position:0% +statement that I want that the measure +of a countable Union of disjoint sets is + + align:start position:0% +of a countable Union of disjoint sets is + + + align:start position:0% +of a countable Union of disjoint sets is +equal to the sum of the measures + + align:start position:0% +equal to the sum of the measures + + + align:start position:0% +equal to the sum of the measures +then that + + align:start position:0% +then that + + + align:start position:0% +then that +hidden in there is that my measure has + + align:start position:0% +hidden in there is that my measure has + + + align:start position:0% +hidden in there is that my measure has +to be defined for a countable Union of + + align:start position:0% +to be defined for a countable Union of + + + align:start position:0% +to be defined for a countable Union of +measurable sets and other in other words + + align:start position:0% +measurable sets and other in other words + + + align:start position:0% +measurable sets and other in other words +if I have a countable collection of + + align:start position:0% +if I have a countable collection of + + + align:start position:0% +if I have a countable collection of +measurable sets then for the statement I + + align:start position:0% +measurable sets then for the statement I + + + align:start position:0% +measurable sets then for the statement I +want to even make sense I should have + + align:start position:0% +want to even make sense I should have + + + align:start position:0% +want to even make sense I should have +that the union of this accountable + + align:start position:0% +that the union of this accountable + + + align:start position:0% +that the union of this accountable +collection of measurable sets is + + align:start position:0% +collection of measurable sets is + + + align:start position:0% +collection of measurable sets is +contained in the class of of sets that + + align:start position:0% +contained in the class of of sets that + + + align:start position:0% +contained in the class of of sets that +I'm measuring all right and so you know + + align:start position:0% +I'm measuring all right and so you know + + + align:start position:0% +I'm measuring all right and so you know +that's + + align:start position:0% +that's + + + align:start position:0% +that's +before you know we even discussed uh + + align:start position:0% +before you know we even discussed uh + + + align:start position:0% +before you know we even discussed uh +outer measure all that + + align:start position:0% +outer measure all that + + + align:start position:0% +outer measure all that +how you could maybe see coming that we + + align:start position:0% +how you could maybe see coming that we + + + align:start position:0% +how you could maybe see coming that we +would have some condition like you know + + align:start position:0% +would have some condition like you know + + + align:start position:0% +would have some condition like you know +the the class of sets that we're going + + align:start position:0% +the the class of sets that we're going + + + align:start position:0% +the the class of sets that we're going +to measure will be a sigma algebra or + + align:start position:0% +to measure will be a sigma algebra or + + + align:start position:0% +to measure will be a sigma algebra or +should be a sigma algebra it should be + + align:start position:0% +should be a sigma algebra it should be + + + align:start position:0% +should be a sigma algebra it should be +closed undertaking countable unions okay + + align:start position:0% +closed undertaking countable unions okay + + + align:start position:0% +closed undertaking countable unions okay +so maybe I was rambling but hopefully + + align:start position:0% +so maybe I was rambling but hopefully + + + align:start position:0% +so maybe I was rambling but hopefully +you got something out of that + + align:start position:0% + + + + align:start position:0% + +Okay so we've shown that the + + align:start position:0% + + + + align:start position:0% + +we've shown + + align:start position:0% +we've shown + + + align:start position:0% +we've shown +that the set + + align:start position:0% + + + + align:start position:0% + +of measurable sets is a sigma algebra + + align:start position:0% +of measurable sets is a sigma algebra + + + align:start position:0% +of measurable sets is a sigma algebra +now what I'm going to show is that it + + align:start position:0% +now what I'm going to show is that it + + + align:start position:0% +now what I'm going to show is that it +contains the Borel Sigma algebra so + + align:start position:0% +contains the Borel Sigma algebra so + + + align:start position:0% +contains the Borel Sigma algebra so +remember the burel sigma algebra is the + + align:start position:0% +remember the burel sigma algebra is the + + + align:start position:0% +remember the burel sigma algebra is the +smallest Sigma algebra + + align:start position:0% +smallest Sigma algebra + + + align:start position:0% +smallest Sigma algebra +that contains all open sets right + + align:start position:0% +that contains all open sets right + + + align:start position:0% +that contains all open sets right +if I have any other Sigma algebra + + align:start position:0% +if I have any other Sigma algebra + + + align:start position:0% +if I have any other Sigma algebra +containing open sets + + align:start position:0% +containing open sets + + + align:start position:0% +containing open sets +that contains all open sets then it must + + align:start position:0% +that contains all open sets then it must + + + align:start position:0% +that contains all open sets then it must +contain the Borel Sigma algebra because + + align:start position:0% +contain the Borel Sigma algebra because + + + align:start position:0% +contain the Borel Sigma algebra because +the Borel Sigma algebra is the smallest + + align:start position:0% + + + + align:start position:0% + +smallest and I should say Quantum I + + align:start position:0% +smallest and I should say Quantum I + + + align:start position:0% +smallest and I should say Quantum I +should quantify small the smallest + + align:start position:0% +should quantify small the smallest + + + align:start position:0% +should quantify small the smallest +meaning with respect to inclusion okay + + align:start position:0% +meaning with respect to inclusion okay + + + align:start position:0% +meaning with respect to inclusion okay +if there's any other uh + + align:start position:0% +if there's any other uh + + + align:start position:0% +if there's any other uh +you know if there's any other Sigma + + align:start position:0% +you know if there's any other Sigma + + + align:start position:0% +you know if there's any other Sigma +algebra that contains all open sets then + + align:start position:0% +algebra that contains all open sets then + + + align:start position:0% +algebra that contains all open sets then +the Borel Sigma algebra b is contained + + align:start position:0% +the Borel Sigma algebra b is contained + + + align:start position:0% +the Borel Sigma algebra b is contained +in that Sigma algebra okay + + align:start position:0% +in that Sigma algebra okay + + + align:start position:0% +in that Sigma algebra okay +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +but first let's + + align:start position:0% +but first let's + + + align:start position:0% +but first let's +prove kind of um + + align:start position:0% +prove kind of um + + + align:start position:0% +prove kind of um +a simpler case + + align:start position:0% +a simpler case + + + align:start position:0% +a simpler case +or what should + + align:start position:0% + + + + align:start position:0% + +so let me State this and then I'll + + align:start position:0% +so let me State this and then I'll + + + align:start position:0% +so let me State this and then I'll +explain for all A and R uh + + align:start position:0% +explain for all A and R uh + + + align:start position:0% +explain for all A and R uh +the open interval a to Infinity + + align:start position:0% + + + + align:start position:0% + +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you know in the end we want to be + + align:start position:0% +so you know in the end we want to be + + + align:start position:0% +so you know in the end we want to be +able to show so we already know m is the + + align:start position:0% +able to show so we already know m is the + + + align:start position:0% +able to show so we already know m is the +sigma algebra if we can then show that + + align:start position:0% +sigma algebra if we can then show that + + + align:start position:0% +sigma algebra if we can then show that +every open set is measurable then that + + align:start position:0% +every open set is measurable then that + + + align:start position:0% +every open set is measurable then that +means + + align:start position:0% +means + + + align:start position:0% +means +uh that m is the sigma algebra + + align:start position:0% +uh that m is the sigma algebra + + + align:start position:0% +uh that m is the sigma algebra +containing all open sets and therefore + + align:start position:0% +containing all open sets and therefore + + + align:start position:0% +containing all open sets and therefore +it must contain the Borel Sigma algebra + + align:start position:0% +it must contain the Borel Sigma algebra + + + align:start position:0% +it must contain the Borel Sigma algebra +which remember is the smallest Sigma + + align:start position:0% +which remember is the smallest Sigma + + + align:start position:0% +which remember is the smallest Sigma +algebra containing all open sets + + align:start position:0% +algebra containing all open sets + + + align:start position:0% +algebra containing all open sets +so to build up to showing that every + + align:start position:0% +so to build up to showing that every + + + align:start position:0% +so to build up to showing that every +open set is measurable let's start with + + align:start position:0% +open set is measurable let's start with + + + align:start position:0% +open set is measurable let's start with +you know + + align:start position:0% +you know + + + align:start position:0% +you know +a very simple type of open set you know + + align:start position:0% +a very simple type of open set you know + + + align:start position:0% +a very simple type of open set you know +a half open uh + + align:start position:0% + + + + align:start position:0% + +or half infinite open interval + + align:start position:0% +or half infinite open interval + + + align:start position:0% +or half infinite open interval +Okay so + + align:start position:0% + + + + align:start position:0% + +but a b a subset of r + + align:start position:0% +but a b a subset of r + + + align:start position:0% +but a b a subset of r +and let's write A1 to be + + align:start position:0% +and let's write A1 to be + + + align:start position:0% +and let's write A1 to be +a intersect + + align:start position:0% +a intersect + + + align:start position:0% +a intersect +a interfa a + + align:start position:0% +a interfa a + + + align:start position:0% +a interfa a +to infinity and A2 to be a + + align:start position:0% +to infinity and A2 to be a + + + align:start position:0% +to infinity and A2 to be a +intersect to complement which is just + + align:start position:0% +intersect to complement which is just + + + align:start position:0% +intersect to complement which is just +minus infinity to a + + align:start position:0% +minus infinity to a + + + align:start position:0% +minus infinity to a +closed + + align:start position:0% + + + + align:start position:0% + +so we want to what do we want to show + + align:start position:0% +so we want to what do we want to show + + + align:start position:0% +so we want to what do we want to show +to show that uh + + align:start position:0% +to show that uh + + + align:start position:0% +to show that uh +this set is measurable + + align:start position:0% +this set is measurable + + + align:start position:0% +this set is measurable +we want to show that + + align:start position:0% +we want to show that + + + align:start position:0% +we want to show that +the outer measure of a one plus the + + align:start position:0% +the outer measure of a one plus the + + + align:start position:0% +the outer measure of a one plus the +outer measure + + align:start position:0% +outer measure + + + align:start position:0% +outer measure +of A2 is less than or equal to + + align:start position:0% +of A2 is less than or equal to + + + align:start position:0% +of A2 is less than or equal to +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +right because A1 is a intersect the set + + align:start position:0% +right because A1 is a intersect the set + + + align:start position:0% +right because A1 is a intersect the set +a 2 is a intersect a complement of that + + align:start position:0% +a 2 is a intersect a complement of that + + + align:start position:0% +a 2 is a intersect a complement of that +set + + align:start position:0% +set + + + align:start position:0% +set +right now if the outer measure of a is + + align:start position:0% +right now if the outer measure of a is + + + align:start position:0% +right now if the outer measure of a is +infinite this holds uh regardless so uh + + align:start position:0% + + + + align:start position:0% + +the outer measure is infinite done + + align:start position:0% +the outer measure is infinite done + + + align:start position:0% +the outer measure is infinite done +so + + align:start position:0% +so + + + align:start position:0% +so +suppose + + align:start position:0% + + + + align:start position:0% + +the outer measure is finite + + align:start position:0% + + + + align:start position:0% + +so what we're going to do is we're going + + align:start position:0% +so what we're going to do is we're going + + + align:start position:0% +so what we're going to do is we're going +to show that this uh + + align:start position:0% +to show that this uh + + + align:start position:0% +to show that this uh +some on the left hand side is less than + + align:start position:0% +some on the left hand side is less than + + + align:start position:0% +some on the left hand side is less than +or equal to this plus Epsilon where + + align:start position:0% +or equal to this plus Epsilon where + + + align:start position:0% +or equal to this plus Epsilon where +Epsilon is arbitrary okay and then we + + align:start position:0% +Epsilon is arbitrary okay and then we + + + align:start position:0% +Epsilon is arbitrary okay and then we +can send Epsilon to zero to get the + + align:start position:0% +can send Epsilon to zero to get the + + + align:start position:0% +can send Epsilon to zero to get the +inequality + + align:start position:0% +inequality + + + align:start position:0% +inequality +all right and this everything will + + align:start position:0% +all right and this everything will + + + align:start position:0% +all right and this everything will +reduce to + + align:start position:0% +reduce to + + + align:start position:0% +reduce to +um you know what we've done with + + align:start position:0% +um you know what we've done with + + + align:start position:0% +um you know what we've done with +intervals as you'll as you know you'll + + align:start position:0% +intervals as you'll as you know you'll + + + align:start position:0% +intervals as you'll as you know you'll +now see so + + align:start position:0% + + + + align:start position:0% + +let I in + + align:start position:0% + + + + align:start position:0% + +be + + align:start position:0% + + + + align:start position:0% + +the collection of open intervals + + align:start position:0% + + + + align:start position:0% + +such that remember the outer measure of + + align:start position:0% +such that remember the outer measure of + + + align:start position:0% +such that remember the outer measure of +a is the infimum of the sum of lengths + + align:start position:0% +a is the infimum of the sum of lengths + + + align:start position:0% +a is the infimum of the sum of lengths +of intervals covering a so such that sum + + align:start position:0% +of intervals covering a so such that sum + + + align:start position:0% +of intervals covering a so such that sum +Over N length of i n + + align:start position:0% +Over N length of i n + + + align:start position:0% +Over N length of i n +is less than or equal to Outer measure + + align:start position:0% +is less than or equal to Outer measure + + + align:start position:0% +is less than or equal to Outer measure +of a + + align:start position:0% +of a + + + align:start position:0% +of a +Plus + + align:start position:0% +Plus + + + align:start position:0% +Plus +Epsilon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +Define j in + + align:start position:0% +Define j in + + + align:start position:0% +Define j in +to be + + align:start position:0% +to be + + + align:start position:0% +to be +i n intersect uh + + align:start position:0% +i n intersect uh + + + align:start position:0% +i n intersect uh +a infinity + + align:start position:0% +a infinity + + + align:start position:0% +a infinity +k n to be + + align:start position:0% +k n to be + + + align:start position:0% +k n to be +i n intersect the complement of a to + + align:start position:0% +i n intersect the complement of a to + + + align:start position:0% +i n intersect the complement of a to +Infinity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now the union of the J ends + + align:start position:0% +now the union of the J ends + + + align:start position:0% +now the union of the J ends +okay well first off let me say + + align:start position:0% + + + + align:start position:0% + +then each of these uh sets JN and K in + + align:start position:0% + + + + align:start position:0% + +are + + align:start position:0% + + + + align:start position:0% + +intervals + + align:start position:0% +intervals + + + align:start position:0% +intervals +they're the intersection of two + + align:start position:0% +they're the intersection of two + + + align:start position:0% +they're the intersection of two +intervals + + align:start position:0% +intervals + + + align:start position:0% +intervals +you know one one open and one uh + + align:start position:0% +you know one one open and one uh + + + align:start position:0% +you know one one open and one uh +open and the other closed + + align:start position:0% +open and the other closed + + + align:start position:0% +open and the other closed +or empty + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now the union of the ions covers a + + align:start position:0% +now the union of the ions covers a + + + align:start position:0% +now the union of the ions covers a +so if I take the unions of the JNS this + + align:start position:0% +so if I take the unions of the JNS this + + + align:start position:0% +so if I take the unions of the JNS this +will cover a intersect a infinity + + align:start position:0% + + + + align:start position:0% + +then A1 + + align:start position:0% +then A1 + + + align:start position:0% +then A1 +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is contained in the Union + + align:start position:0% +is contained in the Union + + + align:start position:0% +is contained in the Union +of the J ends and similarly A2 is + + align:start position:0% +of the J ends and similarly A2 is + + + align:start position:0% +of the J ends and similarly A2 is +contained in the Union + + align:start position:0% +contained in the Union + + + align:start position:0% +contained in the Union +of the kns + + align:start position:0% + + + + align:start position:0% + +and one more thing + + align:start position:0% +and one more thing + + + align:start position:0% +and one more thing +now + + align:start position:0% +now + + + align:start position:0% +now +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i n is an interval and it's simple to + + align:start position:0% +i n is an interval and it's simple to + + + align:start position:0% +i n is an interval and it's simple to +check since uh + + align:start position:0% +check since uh + + + align:start position:0% +check since uh +the + + align:start position:0% +the + + + align:start position:0% +the +you know just based on this being a + + align:start position:0% +you know just based on this being a + + + align:start position:0% +you know just based on this being a +finite interval that + + align:start position:0% +finite interval that + + + align:start position:0% +finite interval that +if I take the length of + + align:start position:0% +if I take the length of + + + align:start position:0% +if I take the length of +I in this is equal to the length of j n + + align:start position:0% +I in this is equal to the length of j n + + + align:start position:0% +I in this is equal to the length of j n +plus the length + + align:start position:0% +plus the length + + + align:start position:0% +plus the length +of kn + + align:start position:0% +of kn + + + align:start position:0% +of kn +okay so I take each eye in and I split + + align:start position:0% +okay so I take each eye in and I split + + + align:start position:0% +okay so I take each eye in and I split +it up into two sub intervals okay they + + align:start position:0% +it up into two sub intervals okay they + + + align:start position:0% +it up into two sub intervals okay they +may not they're not going to be open + + align:start position:0% +may not they're not going to be open + + + align:start position:0% +may not they're not going to be open +intervals necessarily this will be an + + align:start position:0% +intervals necessarily this will be an + + + align:start position:0% +intervals necessarily this will be an +open interval this one not necessarily + + align:start position:0% +open interval this one not necessarily + + + align:start position:0% +open interval this one not necessarily +um + + align:start position:0% +um + + + align:start position:0% +um +but the sum of the links of these two + + align:start position:0% +but the sum of the links of these two + + + align:start position:0% +but the sum of the links of these two +intervals will add up to the length of + + align:start position:0% +intervals will add up to the length of + + + align:start position:0% +intervals will add up to the length of +the interval i n + + align:start position:0% +the interval i n + + + align:start position:0% +the interval i n +okay that's clear + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +there's uh + + align:start position:0% +there's uh + + + align:start position:0% +there's uh +if you'd like + + align:start position:0% + + + + align:start position:0% + +Jay and + + align:start position:0% +Jay and + + + align:start position:0% +Jay and +and + + align:start position:0% + + + + align:start position:0% + +kn + + align:start position:0% +kn + + + align:start position:0% +kn +will be + + align:start position:0% +will be + + + align:start position:0% +will be +you know including that + + align:start position:0% + + + + align:start position:0% + +okay and now + + align:start position:0% +okay and now + + + align:start position:0% +okay and now +we're almost home free + + align:start position:0% +we're almost home free + + + align:start position:0% +we're almost home free +so A1 is contained in this Union A2 is + + align:start position:0% +so A1 is contained in this Union A2 is + + + align:start position:0% +so A1 is contained in this Union A2 is +contained in this Union so if I look at + + align:start position:0% +contained in this Union so if I look at + + + align:start position:0% +contained in this Union so if I look at +the measure of A1 + + align:start position:0% +the measure of A1 + + + align:start position:0% +the measure of A1 +plus the measure of A2 + + align:start position:0% + + + + align:start position:0% + +the measure of A1 contained since it's + + align:start position:0% +the measure of A1 contained since it's + + + align:start position:0% +the measure of A1 contained since it's +contained in this Union + + align:start position:0% +contained in this Union + + + align:start position:0% +contained in this Union +is going to be less than or equal to the + + align:start position:0% +is going to be less than or equal to the + + + align:start position:0% +is going to be less than or equal to the +sum of the outer measures + + align:start position:0% + + + + align:start position:0% + +of JNS + + align:start position:0% +of JNS + + + align:start position:0% +of JNS +and + + align:start position:0% +and + + + align:start position:0% +and +the measure of A2 again is contained in + + align:start position:0% +the measure of A2 again is contained in + + + align:start position:0% +the measure of A2 again is contained in +K in the union of the KN so that's + + align:start position:0% +K in the union of the KN so that's + + + align:start position:0% +K in the union of the KN so that's +less than or equal to the sum of the + + align:start position:0% +less than or equal to the sum of the + + + align:start position:0% +less than or equal to the sum of the +measures of the kns + + align:start position:0% +measures of the kns + + + align:start position:0% +measures of the kns +and now bringing these two and together + + align:start position:0% +and now bringing these two and together + + + align:start position:0% +and now bringing these two and together +in one sum over n and using the fact + + align:start position:0% +in one sum over n and using the fact + + + align:start position:0% +in one sum over n and using the fact +that this is equal to + + align:start position:0% + + + + align:start position:0% + +so the outer measure of an interval is + + align:start position:0% +so the outer measure of an interval is + + + align:start position:0% +so the outer measure of an interval is +equal to its length + + align:start position:0% +equal to its length + + + align:start position:0% +equal to its length +which we proved last time + + align:start position:0% + + + + align:start position:0% + +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +some length of the ion and remember how + + align:start position:0% +some length of the ion and remember how + + + align:start position:0% +some length of the ion and remember how +did we choose the i n we chose this ion + + align:start position:0% +did we choose the i n we chose this ion + + + align:start position:0% +did we choose the i n we chose this ion +so that the length sum of the lengths of + + align:start position:0% +so that the length sum of the lengths of + + + align:start position:0% +so that the length sum of the lengths of +the i n is less than or equal to the + + align:start position:0% +the i n is less than or equal to the + + + align:start position:0% +the i n is less than or equal to the +outer measure of a plus Epsilon + + align:start position:0% + + + + align:start position:0% + +so I should have + + align:start position:0% +so I should have + + + align:start position:0% +so I should have +added here + + align:start position:0% +added here + + + align:start position:0% +added here +let Epsilon be positive sorry about that + + align:start position:0% +let Epsilon be positive sorry about that + + + align:start position:0% +let Epsilon be positive sorry about that +um + + align:start position:0% +um + + + align:start position:0% +um +okay so I've shown + + align:start position:0% + + + + align:start position:0% + +that for + + align:start position:0% +that for + + + align:start position:0% +that for +arbitrary Epsilon positive this number + + align:start position:0% +arbitrary Epsilon positive this number + + + align:start position:0% +arbitrary Epsilon positive this number +over here is less than or equal to + + align:start position:0% +over here is less than or equal to + + + align:start position:0% +over here is less than or equal to +still haven't finished sorry + + align:start position:0% +still haven't finished sorry + + + align:start position:0% +still haven't finished sorry +I'm getting ahead of myself + + align:start position:0% +I'm getting ahead of myself + + + align:start position:0% +I'm getting ahead of myself +that's what happens when you get excited + + align:start position:0% +that's what happens when you get excited + + + align:start position:0% +that's what happens when you get excited +so and this is less than or equal to the + + align:start position:0% +so and this is less than or equal to the + + + align:start position:0% +so and this is less than or equal to the +outer measure of a + + align:start position:0% +outer measure of a + + + align:start position:0% +outer measure of a +plus Epsilon + + align:start position:0% +plus Epsilon + + + align:start position:0% +plus Epsilon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we've shown that for arbitrary + + align:start position:0% +so we've shown that for arbitrary + + + align:start position:0% +so we've shown that for arbitrary +Epsilon positive this number is less + + align:start position:0% +Epsilon positive this number is less + + + align:start position:0% +Epsilon positive this number is less +than or equal to this number plus + + align:start position:0% +than or equal to this number plus + + + align:start position:0% +than or equal to this number plus +Epsilon so I can send Epsilon to zero + + align:start position:0% +Epsilon so I can send Epsilon to zero + + + align:start position:0% +Epsilon so I can send Epsilon to zero +to get that the outer measure + + align:start position:0% +to get that the outer measure + + + align:start position:0% +to get that the outer measure +of A1 Plus the outer measure + + align:start position:0% +of A1 Plus the outer measure + + + align:start position:0% +of A1 Plus the outer measure +of A2 + + align:start position:0% +of A2 + + + align:start position:0% +of A2 +is less than or equal to the outer + + align:start position:0% +is less than or equal to the outer + + + align:start position:0% +is less than or equal to the outer +measure of a which remember that's what + + align:start position:0% +measure of a which remember that's what + + + align:start position:0% +measure of a which remember that's what +we wanted to show + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +so we've shown that you know these open + + align:start position:0% +so we've shown that you know these open + + + align:start position:0% +so we've shown that you know these open +intervals from a to Infinity are are + + align:start position:0% +intervals from a to Infinity are are + + + align:start position:0% +intervals from a to Infinity are are +measurable it's now not + + align:start position:0% + + + + align:start position:0% + +a long trip to saying that every + + align:start position:0% + + + + align:start position:0% + +open set + + align:start position:0% +open set + + + align:start position:0% +open set +is the big measurable + + align:start position:0% + + + + align:start position:0% + +so theorem + + align:start position:0% + + + + align:start position:0% + +every open set is + + align:start position:0% +every open set is + + + align:start position:0% +every open set is +the bag measurable + + align:start position:0% + + + + align:start position:0% + +and thus + + align:start position:0% +and thus + + + align:start position:0% +and thus +the Borel Sigma algebra which is the + + align:start position:0% +the Borel Sigma algebra which is the + + + align:start position:0% +the Borel Sigma algebra which is the +smallest Sigma algebra containing all + + align:start position:0% +smallest Sigma algebra containing all + + + align:start position:0% +smallest Sigma algebra containing all +open sets is contained in the sigma + + align:start position:0% +open sets is contained in the sigma + + + align:start position:0% +open sets is contained in the sigma +algebra of measurable sets + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so we've shown these types of intervals + + align:start position:0% +so we've shown these types of intervals + + + align:start position:0% +so we've shown these types of intervals +are open + + align:start position:0% +are open + + + align:start position:0% +are open +let's show finite open intervals are are + + align:start position:0% +let's show finite open intervals are are + + + align:start position:0% +let's show finite open intervals are are +also uh I mean we've shown these types + + align:start position:0% +also uh I mean we've shown these types + + + align:start position:0% +also uh I mean we've shown these types +of open intervals are measurable let's + + align:start position:0% +of open intervals are measurable let's + + + align:start position:0% +of open intervals are measurable let's +now show that uh + + align:start position:0% +now show that uh + + + align:start position:0% +now show that uh +you know finite open set or finite open + + align:start position:0% +you know finite open set or finite open + + + align:start position:0% +you know finite open set or finite open +intervals are measurable so + + align:start position:0% +intervals are measurable so + + + align:start position:0% +intervals are measurable so +um + + align:start position:0% + + + + align:start position:0% + +now we have four + + align:start position:0% + + + + align:start position:0% + +all B and r + + align:start position:0% +all B and r + + + align:start position:0% +all B and r +that + + align:start position:0% + + + + align:start position:0% + +minus infinity to B this is equal to + + align:start position:0% +minus infinity to B this is equal to + + + align:start position:0% +minus infinity to B this is equal to +the union n equals 1 to Infinity of what + + align:start position:0% +the union n equals 1 to Infinity of what + + + align:start position:0% +the union n equals 1 to Infinity of what +of + + align:start position:0% + + + + align:start position:0% + +these the union of these half + + align:start position:0% +these the union of these half + + + align:start position:0% +these the union of these half +closed intervals + + align:start position:0% +closed intervals + + + align:start position:0% +closed intervals +which + + align:start position:0% + + + + align:start position:0% + +you know we can write as + + align:start position:0% +you know we can write as + + + align:start position:0% +you know we can write as +the complement of + + align:start position:0% +the complement of + + + align:start position:0% +the complement of +these types of open intervals right + + align:start position:0% +these types of open intervals right + + + align:start position:0% +these types of open intervals right +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% +um + + + align:start position:0% +um +we just showed that these types of + + align:start position:0% +we just showed that these types of + + + align:start position:0% +we just showed that these types of +intervals are open I mean these types of + + align:start position:0% +intervals are open I mean these types of + + + align:start position:0% +intervals are open I mean these types of +open intervals are measurable therefore + + align:start position:0% +open intervals are measurable therefore + + + align:start position:0% +open intervals are measurable therefore +their complement is measurable and the + + align:start position:0% +their complement is measurable and the + + + align:start position:0% +their complement is measurable and the +collection of measurable sets is the + + align:start position:0% +collection of measurable sets is the + + + align:start position:0% +collection of measurable sets is the +sigma algebra so accountable unions are + + align:start position:0% +sigma algebra so accountable unions are + + + align:start position:0% +sigma algebra so accountable unions are +also measurable so + + align:start position:0% + + + + align:start position:0% + +uh we conclude that this guy is + + align:start position:0% +uh we conclude that this guy is + + + align:start position:0% +uh we conclude that this guy is +measurable + + align:start position:0% + + + + align:start position:0% + +and therefore remember we you know for + + align:start position:0% +and therefore remember we you know for + + + align:start position:0% +and therefore remember we you know for +an algebra + + align:start position:0% + + + + align:start position:0% + +it's closed under or for Sigma algebra + + align:start position:0% +it's closed under or for Sigma algebra + + + align:start position:0% +it's closed under or for Sigma algebra +it's closed undertaking compliments and + + align:start position:0% +it's closed undertaking compliments and + + + align:start position:0% +it's closed undertaking compliments and +taking accountable unions but by De + + align:start position:0% +taking accountable unions but by De + + + align:start position:0% +taking accountable unions but by De +Morgan's uh + + align:start position:0% +Morgan's uh + + + align:start position:0% +Morgan's uh +uh laws that means it's also closed + + align:start position:0% +uh laws that means it's also closed + + + align:start position:0% +uh laws that means it's also closed +undertaking intersections uh we conclude + + align:start position:0% +undertaking intersections uh we conclude + + + align:start position:0% +undertaking intersections uh we conclude +that for all + + align:start position:0% +that for all + + + align:start position:0% +that for all +a b and R any finite Union I mean any + + align:start position:0% +a b and R any finite Union I mean any + + + align:start position:0% +a b and R any finite Union I mean any +finite open interval a b which is equal + + align:start position:0% +finite open interval a b which is equal + + + align:start position:0% +finite open interval a b which is equal +to + + align:start position:0% +to + + + align:start position:0% +to +minus infinity to B intersect + + align:start position:0% +minus infinity to B intersect + + + align:start position:0% +minus infinity to B intersect +a to Infinity + + align:start position:0% +a to Infinity + + + align:start position:0% +a to Infinity +uh this is measurable by what we just + + align:start position:0% +uh this is measurable by what we just + + + align:start position:0% +uh this is measurable by what we just +proved this is measurable by the theorem + + align:start position:0% +proved this is measurable by the theorem + + + align:start position:0% +proved this is measurable by the theorem +we proved before and sigma algebra are + + align:start position:0% +we proved before and sigma algebra are + + + align:start position:0% +we proved before and sigma algebra are +also closed under taking countable + + align:start position:0% +also closed under taking countable + + + align:start position:0% +also closed under taking countable +unions this is just a finite Union so + + align:start position:0% +unions this is just a finite Union so + + + align:start position:0% +unions this is just a finite Union so +this is also measurable + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +uh + + align:start position:0% + + + + align:start position:0% + +maybe you covered this in 100b maybe you + + align:start position:0% +maybe you covered this in 100b maybe you + + + align:start position:0% +maybe you covered this in 100b maybe you +didn't it's going to appear on + + align:start position:0% +didn't it's going to appear on + + + align:start position:0% +didn't it's going to appear on +assignment but I'll underline what I'm + + align:start position:0% +assignment but I'll underline what I'm + + + align:start position:0% +assignment but I'll underline what I'm +what's going to be on the assignment but + + align:start position:0% +what's going to be on the assignment but + + + align:start position:0% +what's going to be on the assignment but +since every + + align:start position:0% +since every + + + align:start position:0% +since every +open subset + + align:start position:0% +open subset + + + align:start position:0% +open subset +of r + + align:start position:0% +of r + + + align:start position:0% +of r +is a + + align:start position:0% + + + + align:start position:0% + +countable Union + + align:start position:0% +countable Union + + + align:start position:0% +countable Union +of in fact disjoint + + align:start position:0% + + + + align:start position:0% + +open intervals + + align:start position:0% +open intervals + + + align:start position:0% +open intervals +open intervals meaning could be a finite + + align:start position:0% +open intervals meaning could be a finite + + + align:start position:0% +open intervals meaning could be a finite +one it could be one like that it could + + align:start position:0% +one it could be one like that it could + + + align:start position:0% +one it could be one like that it could +be one like we wrote over there where + + align:start position:0% +be one like we wrote over there where + + + align:start position:0% +be one like we wrote over there where +it's a to Infinity + + align:start position:0% +it's a to Infinity + + + align:start position:0% +it's a to Infinity +but every open subset can be written as + + align:start position:0% +but every open subset can be written as + + + align:start position:0% +but every open subset can be written as +a countable Union of disjoint open + + align:start position:0% +a countable Union of disjoint open + + + align:start position:0% +a countable Union of disjoint open +intervals and since open intervals we've + + align:start position:0% +intervals and since open intervals we've + + + align:start position:0% +intervals and since open intervals we've +now concluded are always measurable + + align:start position:0% +now concluded are always measurable + + + align:start position:0% +now concluded are always measurable +uh that means their Union is measurable + + align:start position:0% + + + + align:start position:0% + +we conclude that every open set is + + align:start position:0% +we conclude that every open set is + + + align:start position:0% +we conclude that every open set is +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +Okay so + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +we now have a collection that we've set + + align:start position:0% +we now have a collection that we've set + + + align:start position:0% +we now have a collection that we've set +our measurable sets they form a sigma + + align:start position:0% +our measurable sets they form a sigma + + + align:start position:0% +our measurable sets they form a sigma +algebra they contain + + align:start position:0% +algebra they contain + + + align:start position:0% +algebra they contain +the borrel sigma algebra which consists + + align:start position:0% +the borrel sigma algebra which consists + + + align:start position:0% +the borrel sigma algebra which consists +of all which contains all open sets + + align:start position:0% +of all which contains all open sets + + + align:start position:0% +of all which contains all open sets +um + + align:start position:0% + + + + align:start position:0% + +so now we Define the big measure + + align:start position:0% +so now we Define the big measure + + + align:start position:0% +so now we Define the big measure +if e is a measurable set + + align:start position:0% + + + + align:start position:0% + +a little bag + + align:start position:0% + + + + align:start position:0% + +measure + + align:start position:0% + + + + align:start position:0% + +of E + + align:start position:0% +of E + + + align:start position:0% +of E +is denoted by m of e and it's just + + align:start position:0% + + + + align:start position:0% + +given by the outer measure of E + + align:start position:0% +given by the outer measure of E + + + align:start position:0% +given by the outer measure of E +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +um you know like I said when we first + + align:start position:0% +um you know like I said when we first + + + align:start position:0% +um you know like I said when we first +started all this business + + align:start position:0% +started all this business + + + align:start position:0% +started all this business +um + + align:start position:0% +um + + + align:start position:0% +um +lebeg measure is simply outer measure + + align:start position:0% +lebeg measure is simply outer measure + + + align:start position:0% +lebeg measure is simply outer measure +restricted to a nice collection of or to + + align:start position:0% +restricted to a nice collection of or to + + + align:start position:0% +restricted to a nice collection of or to +a collection of + + align:start position:0% +a collection of + + + align:start position:0% +a collection of +well-behaved sets okay and that's you + + align:start position:0% +well-behaved sets okay and that's you + + + align:start position:0% +well-behaved sets okay and that's you +know you see that here is that the big + + align:start position:0% +know you see that here is that the big + + + align:start position:0% +know you see that here is that the big +measure is nothing but outer measure + + align:start position:0% +measure is nothing but outer measure + + + align:start position:0% +measure is nothing but outer measure +restricted to those sets which we call + + align:start position:0% +restricted to those sets which we call + + + align:start position:0% +restricted to those sets which we call +measurable and measurable meant that + + align:start position:0% +measurable and measurable meant that + + + align:start position:0% +measurable and measurable meant that +they had this property that they kind of + + align:start position:0% +they had this property that they kind of + + + align:start position:0% +they had this property that they kind of +split sets uh you know evenly with + + align:start position:0% +split sets uh you know evenly with + + + align:start position:0% +split sets uh you know evenly with +respect to Outer measure + + align:start position:0% +respect to Outer measure + + + align:start position:0% +respect to Outer measure +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +Okay so + + align:start position:0% + + + + align:start position:0% + +immediately we kind of get a few simple + + align:start position:0% +immediately we kind of get a few simple + + + align:start position:0% +immediately we kind of get a few simple +things + + align:start position:0% +things + + + align:start position:0% +things +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +if + + align:start position:0% + + + + align:start position:0% + +A and B are measurable + + align:start position:0% +A and B are measurable + + + align:start position:0% +A and B are measurable +and a is contained in b + + align:start position:0% +and a is contained in b + + + align:start position:0% +and a is contained in b +then the measure of a + + align:start position:0% +then the measure of a + + + align:start position:0% +then the measure of a +is less than or equal to the measure of + + align:start position:0% +is less than or equal to the measure of + + + align:start position:0% +is less than or equal to the measure of +B why is this again because outer + + align:start position:0% +B why is this again because outer + + + align:start position:0% +B why is this again because outer +measure satisfies that right + + align:start position:0% +measure satisfies that right + + + align:start position:0% +measure satisfies that right +M of a is just the outer measure of a + + align:start position:0% +M of a is just the outer measure of a + + + align:start position:0% +M of a is just the outer measure of a +and that's less than or equal to the + + align:start position:0% +and that's less than or equal to the + + + align:start position:0% +and that's less than or equal to the +outer measure of B which is by + + align:start position:0% +outer measure of B which is by + + + align:start position:0% +outer measure of B which is by +definition the measure of B so you know + + align:start position:0% +definition the measure of B so you know + + + align:start position:0% +definition the measure of B so you know +the point is is that lebeg measure + + align:start position:0% +the point is is that lebeg measure + + + align:start position:0% +the point is is that lebeg measure +inherits many properties from Outer + + align:start position:0% +inherits many properties from Outer + + + align:start position:0% +inherits many properties from Outer +measure in particular we have this and + + align:start position:0% +measure in particular we have this and + + + align:start position:0% +measure in particular we have this and +then we also have + + align:start position:0% +then we also have + + + align:start position:0% +then we also have +since we know + + align:start position:0% +since we know + + + align:start position:0% +since we know +uh + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let me + + align:start position:0% +let me + + + align:start position:0% +let me +make one more + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +every interval + + align:start position:0% + + + + align:start position:0% + +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +let's let's state it this way + + align:start position:0% + + + + align:start position:0% + +if I is + + align:start position:0% +if I is + + + align:start position:0% +if I is +an interval + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +eye is measurable + + align:start position:0% +eye is measurable + + + align:start position:0% +eye is measurable +and + + align:start position:0% +and + + + align:start position:0% +and +the measure of I + + align:start position:0% +the measure of I + + + align:start position:0% +the measure of I +equals the length of I + + align:start position:0% +equals the length of I + + + align:start position:0% +equals the length of I +all right so we've shown all open + + align:start position:0% +all right so we've shown all open + + + align:start position:0% +all right so we've shown all open +intervals are you know + + align:start position:0% +intervals are you know + + + align:start position:0% +intervals are you know +uh measurable right that's what we did a + + align:start position:0% +uh measurable right that's what we did a + + + align:start position:0% +uh measurable right that's what we did a +minute ago when we showed um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so first off let me not get ahead of + + align:start position:0% +so first off let me not get ahead of + + + align:start position:0% +so first off let me not get ahead of +myself if I've shown that every eye is + + align:start position:0% +myself if I've shown that every eye is + + + align:start position:0% +myself if I've shown that every eye is +measurable then since lebeg measure is + + align:start position:0% +measurable then since lebeg measure is + + + align:start position:0% +measurable then since lebeg measure is +just a restriction of outer measure and + + align:start position:0% +just a restriction of outer measure and + + + align:start position:0% +just a restriction of outer measure and +outer in the outer measure of an + + align:start position:0% +outer in the outer measure of an + + + align:start position:0% +outer in the outer measure of an +interval is the length of the interval + + align:start position:0% +interval is the length of the interval + + + align:start position:0% +interval is the length of the interval +this is immediate right so I just need + + align:start position:0% +this is immediate right so I just need + + + align:start position:0% +this is immediate right so I just need +to verify that every interval + + align:start position:0% +to verify that every interval + + + align:start position:0% +to verify that every interval +right is measurable + + align:start position:0% +right is measurable + + + align:start position:0% +right is measurable +now we've shown every open interval is + + align:start position:0% +now we've shown every open interval is + + + align:start position:0% +now we've shown every open interval is +measurable but you know from there it's + + align:start position:0% +measurable but you know from there it's + + + align:start position:0% +measurable but you know from there it's +not uh + + align:start position:0% +not uh + + + align:start position:0% +not uh +you know it's not difficult to to get + + align:start position:0% +you know it's not difficult to to get + + + align:start position:0% +you know it's not difficult to to get +that every interval is measurable so + + align:start position:0% +that every interval is measurable so + + + align:start position:0% +that every interval is measurable so +um for example + + align:start position:0% + + + + align:start position:0% + +if I take a closed and bounded interval + + align:start position:0% +if I take a closed and bounded interval + + + align:start position:0% +if I take a closed and bounded interval +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +what does this equal to + + align:start position:0% +what does this equal to + + + align:start position:0% +what does this equal to +this is equal to B Infinity complement + + align:start position:0% +this is equal to B Infinity complement + + + align:start position:0% +this is equal to B Infinity complement +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +minus infinity a complement + + align:start position:0% +minus infinity a complement + + + align:start position:0% +minus infinity a complement +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so B Infinity complement gives me B to + + align:start position:0% +so B Infinity complement gives me B to + + + align:start position:0% +so B Infinity complement gives me B to +Infinity including B right + + align:start position:0% +Infinity including B right + + + align:start position:0% +Infinity including B right +the complement of minus infinity to a is + + align:start position:0% +the complement of minus infinity to a is + + + align:start position:0% +the complement of minus infinity to a is +a to Infinity including a and their + + align:start position:0% +a to Infinity including a and their + + + align:start position:0% +a to Infinity including a and their +intersection gives me a b now open + + align:start position:0% +intersection gives me a b now open + + + align:start position:0% +intersection gives me a b now open +intervals are measurable therefore the + + align:start position:0% +intervals are measurable therefore the + + + align:start position:0% +intervals are measurable therefore the +complement is measurable so each of + + align:start position:0% +complement is measurable so each of + + + align:start position:0% +complement is measurable so each of +these things is measurable and therefore + + align:start position:0% +these things is measurable and therefore + + + align:start position:0% +these things is measurable and therefore +their intersection is measurable so + + align:start position:0% +their intersection is measurable so + + + align:start position:0% +their intersection is measurable so +that's measurable + + align:start position:0% +that's measurable + + + align:start position:0% +that's measurable +okay and it's the same game with uh you + + align:start position:0% +okay and it's the same game with uh you + + + align:start position:0% +okay and it's the same game with uh you +know if I take away one of these guys + + align:start position:0% +know if I take away one of these guys + + + align:start position:0% +know if I take away one of these guys +all right + + align:start position:0% +all right + + + align:start position:0% +all right +except now + + align:start position:0% +except now + + + align:start position:0% +except now +um you know we would + + align:start position:0% +um you know we would + + + align:start position:0% +um you know we would +use kind of a trick like that so let me + + align:start position:0% +use kind of a trick like that so let me + + + align:start position:0% +use kind of a trick like that so let me +do one of them + + align:start position:0% +do one of them + + + align:start position:0% +do one of them +um + + align:start position:0% +um + + + align:start position:0% +um +let's say we look at + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +B + + align:start position:0% + + + + align:start position:0% + +well I mean I don't think we even have + + align:start position:0% +well I mean I don't think we even have + + + align:start position:0% +well I mean I don't think we even have +to do anything like that let's say I I + + align:start position:0% +to do anything like that let's say I I + + + align:start position:0% +to do anything like that let's say I I +look at something like this + + align:start position:0% +look at something like this + + + align:start position:0% +look at something like this +um + + align:start position:0% +um + + + align:start position:0% +um +this is equal to + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% +B + + + align:start position:0% +B +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +um + + align:start position:0% + + + + align:start position:0% + +complement okay so a half open interval + + align:start position:0% +complement okay so a half open interval + + + align:start position:0% +complement okay so a half open interval +including a not including B is equal to + + align:start position:0% +including a not including B is equal to + + + align:start position:0% +including a not including B is equal to +minus infinity B intersect minus + + align:start position:0% +minus infinity B intersect minus + + + align:start position:0% +minus infinity B intersect minus +infinity a complement right because then + + align:start position:0% +infinity a complement right because then + + + align:start position:0% +infinity a complement right because then +this gives me a to Infinity including a + + align:start position:0% +this gives me a to Infinity including a + + + align:start position:0% +this gives me a to Infinity including a +and this is measurable this is + + align:start position:0% +and this is measurable this is + + + align:start position:0% +and this is measurable this is +measurable the complement's measurable + + align:start position:0% +measurable the complement's measurable + + + align:start position:0% +measurable the complement's measurable +and therefore the intersection is + + align:start position:0% +and therefore the intersection is + + + align:start position:0% +and therefore the intersection is +measurable so this is + + align:start position:0% +measurable so this is + + + align:start position:0% +measurable so this is +measurable and + + align:start position:0% +measurable and + + + align:start position:0% +measurable and +those are the only two examples I'm + + align:start position:0% +those are the only two examples I'm + + + align:start position:0% +those are the only two examples I'm +going to do you can and + + align:start position:0% +going to do you can and + + + align:start position:0% +going to do you can and +basically by taking the complements of + + align:start position:0% +basically by taking the complements of + + + align:start position:0% +basically by taking the complements of +these you get the other types of + + align:start position:0% +these you get the other types of + + + align:start position:0% +these you get the other types of +intervals all right + + align:start position:0% +intervals all right + + + align:start position:0% +intervals all right +so + + align:start position:0% +so + + + align:start position:0% +so +you know this is a good one because this + + align:start position:0% +you know this is a good one because this + + + align:start position:0% +you know this is a good one because this +is one of the properties remember that + + align:start position:0% +is one of the properties remember that + + + align:start position:0% +is one of the properties remember that +we wanted + + align:start position:0% + + + + align:start position:0% + +of measure you know we at least wanted + + align:start position:0% +of measure you know we at least wanted + + + align:start position:0% +of measure you know we at least wanted +to be able to measure intervals and we + + align:start position:0% +to be able to measure intervals and we + + + align:start position:0% +to be able to measure intervals and we +wanted the measure of an interval or at + + align:start position:0% +wanted the measure of an interval or at + + + align:start position:0% +wanted the measure of an interval or at +least a la bag measure of an interval to + + align:start position:0% +least a la bag measure of an interval to + + + align:start position:0% +least a la bag measure of an interval to +be the length of that interval + + align:start position:0% +be the length of that interval + + + align:start position:0% +be the length of that interval +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now uh + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +let's verify that other condition that + + align:start position:0% +let's verify that other condition that + + + align:start position:0% +let's verify that other condition that +we wanted that uh + + align:start position:0% +we wanted that uh + + + align:start position:0% +we wanted that uh +the measure of a countable disjoint + + align:start position:0% +the measure of a countable disjoint + + + align:start position:0% +the measure of a countable disjoint +Union is the sum of the measures + + align:start position:0% +Union is the sum of the measures + + + align:start position:0% +Union is the sum of the measures +so + + align:start position:0% + + + + align:start position:0% + +suppose uh + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +is a countable collection + + align:start position:0% + + + + align:start position:0% + +of disjoint + + align:start position:0% + + + + align:start position:0% + +measurable sets + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the lebeg measure of the Union + + align:start position:0% +the lebeg measure of the Union + + + align:start position:0% +the lebeg measure of the Union +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +the sum of + + align:start position:0% + + + + align:start position:0% + +the label measure of the sets okay + + align:start position:0% +the label measure of the sets okay + + + align:start position:0% +the label measure of the sets okay +now this you know we don't get uh we + + align:start position:0% +now this you know we don't get uh we + + + align:start position:0% +now this you know we don't get uh we +have one of the inequalities here or we + + align:start position:0% +have one of the inequalities here or we + + + align:start position:0% +have one of the inequalities here or we +always have this as less than or equal + + align:start position:0% +always have this as less than or equal + + + align:start position:0% +always have this as less than or equal +to this uh simply because that follows + + align:start position:0% +to this uh simply because that follows + + + align:start position:0% +to this uh simply because that follows +from Outer measure remember outer + + align:start position:0% +from Outer measure remember outer + + + align:start position:0% +from Outer measure remember outer +measure satisfied this with an + + align:start position:0% +measure satisfied this with an + + + align:start position:0% +measure satisfied this with an +inequality there with M star and M Star + + align:start position:0% +inequality there with M star and M Star + + + align:start position:0% +inequality there with M star and M Star +okay but not equality + + align:start position:0% +okay but not equality + + + align:start position:0% +okay but not equality +specializing to these well-behaved sets + + align:start position:0% +specializing to these well-behaved sets + + + align:start position:0% +specializing to these well-behaved sets +gives us equality as we'll see + + align:start position:0% +gives us equality as we'll see + + + align:start position:0% +gives us equality as we'll see +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% + + + + align:start position:0% + +uh let me just reiterate that we do have + + align:start position:0% +uh let me just reiterate that we do have + + + align:start position:0% +uh let me just reiterate that we do have +one and we'll prove this by showing one + + align:start position:0% +one and we'll prove this by showing one + + + align:start position:0% +one and we'll prove this by showing one +is less than or equal to the other and + + align:start position:0% +is less than or equal to the other and + + + align:start position:0% +is less than or equal to the other and +vice versa we always have this is less + + align:start position:0% +vice versa we always have this is less + + + align:start position:0% +vice versa we always have this is less +than or equal to this + + align:start position:0% +than or equal to this + + + align:start position:0% +than or equal to this +um because of outer measure + + align:start position:0% +um because of outer measure + + + align:start position:0% +um because of outer measure +um + + align:start position:0% + + + + align:start position:0% + +so first off + + align:start position:0% + + + + align:start position:0% + +we know that we have + + align:start position:0% + + + + align:start position:0% + +this accountable Union is measurable + + align:start position:0% +this accountable Union is measurable + + + align:start position:0% +this accountable Union is measurable +because m is a Sigma algebra we showed + + align:start position:0% +because m is a Sigma algebra we showed + + + align:start position:0% +because m is a Sigma algebra we showed +that already + + align:start position:0% +that already + + + align:start position:0% +that already +and therefore the measure of the Union + + align:start position:0% + + + + align:start position:0% + +is by definition equal to + + align:start position:0% + + + + align:start position:0% + +the outer measure of the Union Which is + + align:start position:0% +the outer measure of the Union Which is + + + align:start position:0% +the outer measure of the Union Which is +less than or equal to the sum of + + align:start position:0% +less than or equal to the sum of + + + align:start position:0% +less than or equal to the sum of +the outer measures + + align:start position:0% +the outer measures + + + align:start position:0% +the outer measures +of the ens and remember these are all + + align:start position:0% +of the ens and remember these are all + + + align:start position:0% +of the ens and remember these are all +measurable so this is by definition the + + align:start position:0% +measurable so this is by definition the + + + align:start position:0% +measurable so this is by definition the +outer measure is the measure + + align:start position:0% + + + + align:start position:0% + +okay so this is what I meant by we + + align:start position:0% +okay so this is what I meant by we + + + align:start position:0% +okay so this is what I meant by we +always have one inequality one we + + align:start position:0% +always have one inequality one we + + + align:start position:0% +always have one inequality one we +already have one side of this inequality + + align:start position:0% +already have one side of this inequality + + + align:start position:0% +already have one side of this inequality +uh + + align:start position:0% +uh + + + align:start position:0% +uh +from Outer measure + + align:start position:0% +from Outer measure + + + align:start position:0% +from Outer measure +so now we just need to show + + align:start position:0% +so now we just need to show + + + align:start position:0% +so now we just need to show +the opposite inequality + + align:start position:0% + + + + align:start position:0% + +we now show uh sum and measure of e n + + align:start position:0% +we now show uh sum and measure of e n + + + align:start position:0% +we now show uh sum and measure of e n +is less than or equal to + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +foreign + + align:start position:0% + + + + align:start position:0% + +how do we show this + + align:start position:0% +how do we show this + + + align:start position:0% +how do we show this +uh + + align:start position:0% + + + + align:start position:0% + +it can be a natural number + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +what is the + + align:start position:0% +what is the + + + align:start position:0% +what is the +measure of + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +of finite + + align:start position:0% +of finite + + + align:start position:0% +of finite +Union of + + align:start position:0% + + + + align:start position:0% + +these guys well you know I'm right I can + + align:start position:0% +these guys well you know I'm right I can + + + align:start position:0% +these guys well you know I'm right I can +write this also as the measure so this + + align:start position:0% +write this also as the measure so this + + + align:start position:0% +write this also as the measure so this +is uh measurable and therefore I can + + align:start position:0% +is uh measurable and therefore I can + + + align:start position:0% +is uh measurable and therefore I can +write this as in fact R intersect this + + align:start position:0% +write this as in fact R intersect this + + + align:start position:0% +write this as in fact R intersect this +is kind of a stupid way to write it + + align:start position:0% +is kind of a stupid way to write it + + + align:start position:0% +is kind of a stupid way to write it +but I'm just doing it this way so that + + align:start position:0% +but I'm just doing it this way so that + + + align:start position:0% +but I'm just doing it this way so that +it looks like something we've already + + align:start position:0% +it looks like something we've already + + + align:start position:0% +it looks like something we've already +proven right you know earlier we proved + + align:start position:0% +proven right you know earlier we proved + + + align:start position:0% +proven right you know earlier we proved +that + + align:start position:0% +that + + + align:start position:0% +that +for measurable sets disjoint measurable + + align:start position:0% +for measurable sets disjoint measurable + + + align:start position:0% +for measurable sets disjoint measurable +sets + + align:start position:0% +sets + + + align:start position:0% +sets +the outer measure of a set intersect a + + align:start position:0% +the outer measure of a set intersect a + + + align:start position:0% +the outer measure of a set intersect a +finite Union of disjoint measurable sets + + align:start position:0% +finite Union of disjoint measurable sets + + + align:start position:0% +finite Union of disjoint measurable sets +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +um + + align:start position:0% +um + + + align:start position:0% +um +the sum of + + align:start position:0% +the sum of + + + align:start position:0% +the sum of +these measures + + align:start position:0% + + + + align:start position:0% + +so and this is + + align:start position:0% +so and this is + + + align:start position:0% +so and this is +equal to e sub n and the outer measure + + align:start position:0% +equal to e sub n and the outer measure + + + align:start position:0% +equal to e sub n and the outer measure +of a measurable set is by definition + + align:start position:0% +of a measurable set is by definition + + + align:start position:0% +of a measurable set is by definition +again the measure of the set so this is + + align:start position:0% +again the measure of the set so this is + + + align:start position:0% +again the measure of the set so this is +equal to n equals one two + + align:start position:0% +equal to n equals one two + + + align:start position:0% +equal to n equals one two +e sub n + + align:start position:0% +e sub n + + + align:start position:0% +e sub n +okay so what we've shown is that in fact + + align:start position:0% +okay so what we've shown is that in fact + + + align:start position:0% +okay so what we've shown is that in fact +for a finite disjoint Union the measure + + align:start position:0% +for a finite disjoint Union the measure + + + align:start position:0% +for a finite disjoint Union the measure +is equal to the sum of the measures I + + align:start position:0% +is equal to the sum of the measures I + + + align:start position:0% +is equal to the sum of the measures I +mean we already did prove that except + + align:start position:0% +mean we already did prove that except + + + align:start position:0% +mean we already did prove that except +with an a there + + align:start position:0% +with an a there + + + align:start position:0% +with an a there +um + + align:start position:0% +um + + + align:start position:0% +um +but this gives us the opposite + + align:start position:0% +but this gives us the opposite + + + align:start position:0% +but this gives us the opposite +inequality once we realize + + align:start position:0% + + + + align:start position:0% + +that we have this sum + + align:start position:0% + + + + align:start position:0% + +which is equal to the measure of + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +Which is less than or equal to the + + align:start position:0% +Which is less than or equal to the + + + align:start position:0% +Which is less than or equal to the +measure of the big total Union + + align:start position:0% + + + + align:start position:0% + +right because this set is contained in + + align:start position:0% +right because this set is contained in + + + align:start position:0% +right because this set is contained in +the in this set right so what I have is + + align:start position:0% +the in this set right so what I have is + + + align:start position:0% +the in this set right so what I have is +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +n was arbitrary I have that that thing + + align:start position:0% +n was arbitrary I have that that thing + + + align:start position:0% +n was arbitrary I have that that thing +on the left hand side is less than + + align:start position:0% +on the left hand side is less than + + + align:start position:0% +on the left hand side is less than +or equal to this thing on the right hand + + align:start position:0% +or equal to this thing on the right hand + + + align:start position:0% +or equal to this thing on the right hand +side + + align:start position:0% +side + + + align:start position:0% +side +okay + + align:start position:0% +okay + + + align:start position:0% +okay +for arbitrary in so now I let N Go to + + align:start position:0% +for arbitrary in so now I let N Go to + + + align:start position:0% +for arbitrary in so now I let N Go to +Infinity + + align:start position:0% + + + + align:start position:0% + +to conclude that + + align:start position:0% + + + + align:start position:0% + +as desired + + align:start position:0% + + + + align:start position:0% + +okay so this is you know that other + + align:start position:0% +okay so this is you know that other + + + align:start position:0% +okay so this is you know that other +property that we wanted that the the + + align:start position:0% +property that we wanted that the the + + + align:start position:0% +property that we wanted that the the +measure of + + align:start position:0% + + + + align:start position:0% + +of a disjoint Union is the sum of the + + align:start position:0% +of a disjoint Union is the sum of the + + + align:start position:0% +of a disjoint Union is the sum of the +measures + + align:start position:0% +measures + + + align:start position:0% +measures +now there was that last property we + + align:start position:0% +now there was that last property we + + + align:start position:0% +now there was that last property we +wanted that um + + align:start position:0% +wanted that um + + + align:start position:0% +wanted that um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +measure is translation and variant + + align:start position:0% +measure is translation and variant + + + align:start position:0% +measure is translation and variant +that'll be uh in the assignment so so + + align:start position:0% +that'll be uh in the assignment so so + + + align:start position:0% +that'll be uh in the assignment so so +let me state it here + + align:start position:0% + + + + align:start position:0% + +so what you'll prove in the assignment + + align:start position:0% +so what you'll prove in the assignment + + + align:start position:0% +so what you'll prove in the assignment +is + + align:start position:0% +is + + + align:start position:0% +is +if e is a measurable set + + align:start position:0% +if e is a measurable set + + + align:start position:0% +if e is a measurable set +and X is in r + + align:start position:0% +and X is in r + + + align:start position:0% +and X is in r +then the shift of this set x e plus X + + align:start position:0% +then the shift of this set x e plus X + + + align:start position:0% +then the shift of this set x e plus X +which is you know the set of all y plus + + align:start position:0% +which is you know the set of all y plus + + + align:start position:0% +which is you know the set of all y plus +X + + align:start position:0% +X + + + align:start position:0% +X +such that Y is an e + + align:start position:0% + + + + align:start position:0% + +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +and + + align:start position:0% + + + + align:start position:0% + +measure e of E equals the measure of E + + align:start position:0% +measure e of E equals the measure of E + + + align:start position:0% +measure e of E equals the measure of E +plus X Okay so + + align:start position:0% +plus X Okay so + + + align:start position:0% +plus X Okay so +this will be in the + + align:start position:0% + + + + align:start position:0% + +next assignment + + align:start position:0% + + + + align:start position:0% + +which will be assignment I think four + + align:start position:0% + + + + align:start position:0% + +which is the third property that we + + align:start position:0% +which is the third property that we + + + align:start position:0% +which is the third property that we +desired Okay so + + align:start position:0% +desired Okay so + + + align:start position:0% +desired Okay so +uh lebeg measure which is just outer + + align:start position:0% +uh lebeg measure which is just outer + + + align:start position:0% +uh lebeg measure which is just outer +measure restricted to a class of + + align:start position:0% +measure restricted to a class of + + + align:start position:0% +measure restricted to a class of +measurable subsets which is a sigma + + align:start position:0% +measurable subsets which is a sigma + + + align:start position:0% +measurable subsets which is a sigma +algebra + + align:start position:0% +algebra + + + align:start position:0% +algebra +satisfies the three you know + + align:start position:0% +satisfies the three you know + + + align:start position:0% +satisfies the three you know +kind of major things we wanted of a + + align:start position:0% +kind of major things we wanted of a + + + align:start position:0% +kind of major things we wanted of a +measure you know unfortunately the + + align:start position:0% +measure you know unfortunately the + + + align:start position:0% +measure you know unfortunately the +measure is not defined on all subsets + + align:start position:0% +measure is not defined on all subsets + + + align:start position:0% +measure is not defined on all subsets +but you know it's defined on a + + align:start position:0% +but you know it's defined on a + + + align:start position:0% +but you know it's defined on a +large class of of + + align:start position:0% +large class of of + + + align:start position:0% +large class of of +a very rich class of subsets of real + + align:start position:0% +a very rich class of subsets of real + + + align:start position:0% +a very rich class of subsets of real +numbers because it contains open sets + + align:start position:0% +numbers because it contains open sets + + + align:start position:0% +numbers because it contains open sets +closed sets and like I said you know + + align:start position:0% +closed sets and like I said you know + + + align:start position:0% +closed sets and like I said you know +Sigma algebras are + + align:start position:0% +Sigma algebras are + + + align:start position:0% +Sigma algebras are +closed undertaking countable + + align:start position:0% +closed undertaking countable + + + align:start position:0% +closed undertaking countable +intersections and compliments so you + + align:start position:0% +intersections and compliments so you + + + align:start position:0% +intersections and compliments so you +could take a collection of open sets and + + align:start position:0% +could take a collection of open sets and + + + align:start position:0% +could take a collection of open sets and +take its intersection which is not + + align:start position:0% +take its intersection which is not + + + align:start position:0% +take its intersection which is not +necessarily an open set + + align:start position:0% +necessarily an open set + + + align:start position:0% +necessarily an open set +uh + + align:start position:0% +uh + + + align:start position:0% +uh +but that would be in the sigma algebra + + align:start position:0% +but that would be in the sigma algebra + + + align:start position:0% +but that would be in the sigma algebra +and then you could take accountable + + align:start position:0% +and then you could take accountable + + + align:start position:0% +and then you could take accountable +Union of those types of sets and still + + align:start position:0% +Union of those types of sets and still + + + align:start position:0% +Union of those types of sets and still +remain in the sigma algebra and then you + + align:start position:0% +remain in the sigma algebra and then you + + + align:start position:0% +remain in the sigma algebra and then you +could take complements of those types of + + align:start position:0% +could take complements of those types of + + + align:start position:0% +could take complements of those types of +sets + + align:start position:0% +sets + + + align:start position:0% +sets +and stay in the sigma algebra so like + + align:start position:0% +and stay in the sigma algebra so like + + + align:start position:0% +and stay in the sigma algebra so like +you know my instructor said if you can + + align:start position:0% +you know my instructor said if you can + + + align:start position:0% +you know my instructor said if you can +write down the set chances are it's + + align:start position:0% +write down the set chances are it's + + + align:start position:0% +write down the set chances are it's +measurable + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so One Last Theorem will prove + + align:start position:0% + + + + align:start position:0% + +about measure and then we'll call it a + + align:start position:0% +about measure and then we'll call it a + + + align:start position:0% +about measure and then we'll call it a +day + + align:start position:0% +day + + + align:start position:0% +day +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and call it for you know the theory of + + align:start position:0% +and call it for you know the theory of + + + align:start position:0% +and call it for you know the theory of +measure by itself + + align:start position:0% +measure by itself + + + align:start position:0% +measure by itself +then we'll move on to measurable + + align:start position:0% +then we'll move on to measurable + + + align:start position:0% +then we'll move on to measurable +functions + + align:start position:0% +functions + + + align:start position:0% +functions +um + + align:start position:0% +um + + + align:start position:0% +um +and then lebeg integration of measurable + + align:start position:0% +and then lebeg integration of measurable + + + align:start position:0% +and then lebeg integration of measurable +functions + + align:start position:0% +functions + + + align:start position:0% +functions +um + + align:start position:0% +um + + + align:start position:0% +um +is the following if you like continuity + + align:start position:0% + + + + align:start position:0% + +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +measure + + align:start position:0% +measure + + + align:start position:0% +measure +which is the following so suppose + + align:start position:0% + + + + align:start position:0% + +e k + + align:start position:0% +e k + + + align:start position:0% +e k +is a + + align:start position:0% + + + + align:start position:0% + +collection + + align:start position:0% + + + + align:start position:0% + +of measurable sets + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% + + + + align:start position:0% + +E1 is contained in E2 is contained in E3 + + align:start position:0% +E1 is contained in E2 is contained in E3 + + + align:start position:0% +E1 is contained in E2 is contained in E3 +and so on + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +the measure of + + align:start position:0% + + + + align:start position:0% + +a equals 1 to Infinity + + align:start position:0% +a equals 1 to Infinity + + + align:start position:0% +a equals 1 to Infinity +of e k + + align:start position:0% +of e k + + + align:start position:0% +of e k +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +limit as n goes to Infinity but the + + align:start position:0% +limit as n goes to Infinity but the + + + align:start position:0% +limit as n goes to Infinity but the +measure of + + align:start position:0% +measure of + + + align:start position:0% +measure of +k equals one k equals n + + align:start position:0% +k equals one k equals n + + + align:start position:0% +k equals one k equals n +of e k + + align:start position:0% +of e k + + + align:start position:0% +of e k +which equals + + align:start position:0% + + + + align:start position:0% + +limit as n goes to Infinity of the + + align:start position:0% +limit as n goes to Infinity of the + + + align:start position:0% +limit as n goes to Infinity of the +measure of + + align:start position:0% +measure of + + + align:start position:0% +measure of +e n + + align:start position:0% +e n + + + align:start position:0% +e n +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know I just need to show this is + + align:start position:0% +you know I just need to show this is + + + align:start position:0% +you know I just need to show this is +equal to this and that's what I'll show + + align:start position:0% +equal to this and that's what I'll show + + + align:start position:0% +equal to this and that's what I'll show +is that this is equal to this + + align:start position:0% +is that this is equal to this + + + align:start position:0% +is that this is equal to this +um the fact that this is equal to this + + align:start position:0% +um the fact that this is equal to this + + + align:start position:0% +um the fact that this is equal to this +follows from the you know the assumption + + align:start position:0% +follows from the you know the assumption + + + align:start position:0% +follows from the you know the assumption +that they're nested right E1 is + + align:start position:0% +that they're nested right E1 is + + + align:start position:0% +that they're nested right E1 is +contained in E2 is contained in up to e + + align:start position:0% +contained in E2 is contained in up to e + + + align:start position:0% +contained in E2 is contained in up to e +n so the union is equal to e n + + align:start position:0% +n so the union is equal to e n + + + align:start position:0% +n so the union is equal to e n +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +I'm just going to show that these two + + align:start position:0% +I'm just going to show that these two + + + align:start position:0% +I'm just going to show that these two +things underlined in yellow are equal to + + align:start position:0% +things underlined in yellow are equal to + + + align:start position:0% +things underlined in yellow are equal to +each other and then the fact that this + + align:start position:0% +each other and then the fact that this + + + align:start position:0% +each other and then the fact that this +is equal to that is just follows from + + align:start position:0% +is equal to that is just follows from + + + align:start position:0% +is equal to that is just follows from +this assumption here + + align:start position:0% +this assumption here + + + align:start position:0% +this assumption here +okay + + align:start position:0% + + + + align:start position:0% + +all right so for the proof + + align:start position:0% + + + + align:start position:0% + +I'm going to do this trick again where + + align:start position:0% +I'm going to do this trick again where + + + align:start position:0% +I'm going to do this trick again where +we're going to write kind of the Union + + align:start position:0% +we're going to write kind of the Union + + + align:start position:0% +we're going to write kind of the Union +this this countable Union as uh + + align:start position:0% +this this countable Union as uh + + + align:start position:0% +this this countable Union as uh +a union of disjoint + + align:start position:0% +a union of disjoint + + + align:start position:0% +a union of disjoint +sets + + align:start position:0% +sets + + + align:start position:0% +sets +so we let f + + align:start position:0% +so we let f + + + align:start position:0% +so we let f +1 equal to B E1 + + align:start position:0% +1 equal to B E1 + + + align:start position:0% +1 equal to B E1 +F K plus 1 equal to + + align:start position:0% +F K plus 1 equal to + + + align:start position:0% +F K plus 1 equal to +e k plus one take away e k + + align:start position:0% +e k plus one take away e k + + + align:start position:0% +e k plus one take away e k +for + + align:start position:0% +for + + + align:start position:0% +for +K bigger than or equal to one + + align:start position:0% + + + + align:start position:0% + +um and let me just mark this is equal to + + align:start position:0% +um and let me just mark this is equal to + + + align:start position:0% +um and let me just mark this is equal to +e k plus 1 intersect + + align:start position:0% +e k plus 1 intersect + + + align:start position:0% +e k plus 1 intersect +EK complement since they're nested right + + align:start position:0% +EK complement since they're nested right + + + align:start position:0% +EK complement since they're nested right +since E1 is contained in E2 is contained + + align:start position:0% +since E1 is contained in E2 is contained + + + align:start position:0% +since E1 is contained in E2 is contained +and so on all right + + align:start position:0% +and so on all right + + + align:start position:0% +and so on all right +and note that since the eks are + + align:start position:0% +and note that since the eks are + + + align:start position:0% +and note that since the eks are +measurable this is measurable this is + + align:start position:0% +measurable this is measurable this is + + + align:start position:0% +measurable this is measurable this is +measurable it's complement is measurable + + align:start position:0% +measurable it's complement is measurable + + + align:start position:0% +measurable it's complement is measurable +the intersection is measurable so each + + align:start position:0% +the intersection is measurable so each + + + align:start position:0% +the intersection is measurable so each +of these are measurable + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +FK is + + align:start position:0% +FK is + + + align:start position:0% +FK is +a + + align:start position:0% +a + + + align:start position:0% +a +disjoint + + align:start position:0% + + + + align:start position:0% + +collection of + + align:start position:0% + + + + align:start position:0% + +measurable sets + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +we're all in and if I look at the union + + align:start position:0% +we're all in and if I look at the union + + + align:start position:0% +we're all in and if I look at the union +k equals 1 to n of + + align:start position:0% +k equals 1 to n of + + + align:start position:0% +k equals 1 to n of +FK so how am I building you know these + + align:start position:0% +FK so how am I building you know these + + + align:start position:0% +FK so how am I building you know these +guys I take F1 to be E1 F2 is going to + + align:start position:0% +guys I take F1 to be E1 F2 is going to + + + align:start position:0% +guys I take F1 to be E1 F2 is going to +be E2 take away whatever was already + + align:start position:0% +be E2 take away whatever was already + + + align:start position:0% +be E2 take away whatever was already +covered and E was already contained in + + align:start position:0% +covered and E was already contained in + + + align:start position:0% +covered and E was already contained in +E1 E3 is I mean F3 is whatever E3 is + + align:start position:0% +E1 E3 is I mean F3 is whatever E3 is + + + align:start position:0% +E1 E3 is I mean F3 is whatever E3 is +take away everything that was already + + align:start position:0% +take away everything that was already + + + align:start position:0% +take away everything that was already +appearing in E2 so you can check that + + align:start position:0% +appearing in E2 so you can check that + + + align:start position:0% +appearing in E2 so you can check that +the union from k equals 1 to n of f k + + align:start position:0% +the union from k equals 1 to n of f k + + + align:start position:0% +the union from k equals 1 to n of f k +is equal to e n + + align:start position:0% + + + + align:start position:0% + +all right and you know that's + + align:start position:0% +all right and you know that's + + + align:start position:0% +all right and you know that's +and therefore uh + + align:start position:0% + + + + align:start position:0% + +you know also + + align:start position:0% +you know also + + + align:start position:0% +you know also +that the Union + + align:start position:0% + + + + align:start position:0% + +is equal to + + align:start position:0% + + + + align:start position:0% + +this Union + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and now we conclude that if I take the + + align:start position:0% +and now we conclude that if I take the + + + align:start position:0% +and now we conclude that if I take the +measure of + + align:start position:0% +measure of + + + align:start position:0% +measure of +k equals 1 to Infinity + + align:start position:0% +k equals 1 to Infinity + + + align:start position:0% +k equals 1 to Infinity +V K this is equal to + + align:start position:0% +V K this is equal to + + + align:start position:0% +V K this is equal to +um + + align:start position:0% +um + + + align:start position:0% +um +you know this is equal to + + align:start position:0% +you know this is equal to + + + align:start position:0% +you know this is equal to +this Union here which is a union of + + align:start position:0% +this Union here which is a union of + + + align:start position:0% +this Union here which is a union of +disjoint a measurable set so this is + + align:start position:0% +disjoint a measurable set so this is + + + align:start position:0% +disjoint a measurable set so this is +equal to the sum k equals one to + + align:start position:0% +equal to the sum k equals one to + + + align:start position:0% +equal to the sum k equals one to +Infinity of the measure of f sub k + + align:start position:0% +Infinity of the measure of f sub k + + + align:start position:0% +Infinity of the measure of f sub k +which is equal to the Limit as n goes to + + align:start position:0% +which is equal to the Limit as n goes to + + + align:start position:0% +which is equal to the Limit as n goes to +Infinity + + align:start position:0% +Infinity + + + align:start position:0% +Infinity +k equals 1 to n measure of + + align:start position:0% +k equals 1 to n measure of + + + align:start position:0% +k equals 1 to n measure of +S Sub K and again this is a + + align:start position:0% +S Sub K and again this is a + + + align:start position:0% +S Sub K and again this is a +if you like + + align:start position:0% +if you like + + + align:start position:0% +if you like +I can rewrite this as + + align:start position:0% +I can rewrite this as + + + align:start position:0% +I can rewrite this as +limit as n goes to Infinity this finite + + align:start position:0% +limit as n goes to Infinity this finite + + + align:start position:0% +limit as n goes to Infinity this finite +sum of measures of these disjoint sets + + align:start position:0% +sum of measures of these disjoint sets + + + align:start position:0% +sum of measures of these disjoint sets +as a measure of k equals 1 to n + + align:start position:0% +as a measure of k equals 1 to n + + + align:start position:0% +as a measure of k equals 1 to n +of f k which equals + + align:start position:0% +of f k which equals + + + align:start position:0% +of f k which equals +um + + align:start position:0% + + + + align:start position:0% + +as we noted right here where where we're + + align:start position:0% +as we noted right here where where we're + + + align:start position:0% +as we noted right here where where we're +there + + align:start position:0% +there + + + align:start position:0% +there +is equal to the measure of + + align:start position:0% +is equal to the measure of + + + align:start position:0% +is equal to the measure of +Ian + + align:start position:0% +Ian + + + align:start position:0% +Ian +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so that takes care of the definition of + + align:start position:0% +so that takes care of the definition of + + + align:start position:0% +so that takes care of the definition of +lebeg measure next time we will Define + + align:start position:0% +lebeg measure next time we will Define + + + align:start position:0% +lebeg measure next time we will Define +lebeg measurable functions + + align:start position:0% +lebeg measurable functions + + + align:start position:0% +lebeg measurable functions +um + + align:start position:0% + + + + align:start position:0% + +which + + align:start position:0% +which + + + align:start position:0% +which +you know + + align:start position:0% + + + + align:start position:0% + +in some sense are + + align:start position:0% +in some sense are + + + align:start position:0% +in some sense are +in a certain sense so + + align:start position:0% +in a certain sense so + + + align:start position:0% +in a certain sense so +with respect to integration the analog + + align:start position:0% +with respect to integration the analog + + + align:start position:0% +with respect to integration the analog +of continuous functions so continuous + + align:start position:0% +of continuous functions so continuous + + + align:start position:0% +of continuous functions so continuous +functions + + align:start position:0% +functions + + + align:start position:0% +functions +have the property that if I have an open + + align:start position:0% +have the property that if I have an open + + + align:start position:0% +have the property that if I have an open +Set uh in the target + + align:start position:0% +Set uh in the target + + + align:start position:0% +Set uh in the target +or in the range so not the range but in + + align:start position:0% +or in the range so not the range but in + + + align:start position:0% +or in the range so not the range but in +the Target so if f is a function going + + align:start position:0% +the Target so if f is a function going + + + align:start position:0% +the Target so if f is a function going +from X to Y if I have an open set in y + + align:start position:0% +from X to Y if I have an open set in y + + + align:start position:0% +from X to Y if I have an open set in y +then the inverse image of that open set + + align:start position:0% +then the inverse image of that open set + + + align:start position:0% +then the inverse image of that open set +is an open set in x + + align:start position:0% +is an open set in x + + + align:start position:0% +is an open set in x +measurable functions will + + align:start position:0% +measurable functions will + + + align:start position:0% +measurable functions will +be similar to that except now with + + align:start position:0% +be similar to that except now with + + + align:start position:0% +be similar to that except now with +measurable sets but not quite uh we're + + align:start position:0% +measurable sets but not quite uh we're + + + align:start position:0% +measurable sets but not quite uh we're +not going to ask that they take lebeg + + align:start position:0% +not going to ask that they take lebeg + + + align:start position:0% +not going to ask that they take lebeg +measurable sets to lebeg measurable sets + + align:start position:0% +measurable sets to lebeg measurable sets + + + align:start position:0% +measurable sets to lebeg measurable sets +but uh borrel measurable sets to the + + align:start position:0% +but uh borrel measurable sets to the + + + align:start position:0% +but uh borrel measurable sets to the +inverse image should be a lebeg uh + + align:start position:0% +inverse image should be a lebeg uh + + + align:start position:0% +inverse image should be a lebeg uh +measurable set + + align:start position:0% +measurable set + + + align:start position:0% +measurable set +all right we'll uh we'll stop there \ No newline at end of file diff --git a/ctP2eqCROLc.txt b/ctP2eqCROLc.txt new file mode 100644 index 0000000000000000000000000000000000000000..8001740a57e11153e4b21739e7c2ecc88240bb51 --- /dev/null +++ b/ctP2eqCROLc.txt @@ -0,0 +1,403 @@ +align:start position:0% + +prosciutto Cocteau illa for nacho + + align:start position:0% +prosciutto Cocteau illa for nacho + + + align:start position:0% +prosciutto Cocteau illa for nacho +gorgonzola broccoli a spinachy-- + + align:start position:0% + + + + align:start position:0% + +questa è una fecha de salami ill + + align:start position:0% +questa è una fecha de salami ill + + + align:start position:0% +questa è una fecha de salami ill +prosciutto crudo + + align:start position:0% + + + + align:start position:0% + +la mozzarella la melanzana in pepperoni + + align:start position:0% +la mozzarella la melanzana in pepperoni + + + align:start position:0% +la mozzarella la melanzana in pepperoni +pepperoni Rosso red and in pepperoni + + align:start position:0% +pepperoni Rosso red and in pepperoni + + + align:start position:0% +pepperoni Rosso red and in pepperoni +Charlo yellow la Sukeena + + align:start position:0% +Charlo yellow la Sukeena + + + align:start position:0% +Charlo yellow la Sukeena +or look to Kino + + align:start position:0% +or look to Kino + + + align:start position:0% +or look to Kino +both are good these are our old friends + + align:start position:0% +both are good these are our old friends + + + align:start position:0% +both are good these are our old friends +Aldo Coppola and peperoncino no you + + align:start position:0% +Aldo Coppola and peperoncino no you + + + align:start position:0% +Aldo Coppola and peperoncino no you +Geneva la chuga chuga basilica lorry + + align:start position:0% +Geneva la chuga chuga basilica lorry + + + align:start position:0% +Geneva la chuga chuga basilica lorry +gana el sol salt la passata D Pomodoro + + align:start position:0% + + + + align:start position:0% + +Lacroix + + align:start position:0% +Lacroix + + + align:start position:0% +Lacroix +that's water in be carbonate Oh + + align:start position:0% + + + + align:start position:0% + +so do L little Easton tener la laa la + + align:start position:0% +so do L little Easton tener la laa la + + + align:start position:0% +so do L little Easton tener la laa la +pagina oggi siamo ill for no purpose in + + align:start position:0% +pagina oggi siamo ill for no purpose in + + + align:start position:0% +pagina oggi siamo ill for no purpose in +our la pizza + + align:start position:0% +our la pizza + + + align:start position:0% +our la pizza +mmm who's Yama who ke4 Nellie stove Phil + + align:start position:0% +mmm who's Yama who ke4 Nellie stove Phil + + + align:start position:0% +mmm who's Yama who ke4 Nellie stove Phil +couch in our live will direct the + + align:start position:0% +couch in our live will direct the + + + align:start position:0% +couch in our live will direct the +vegetable side once again because of a + + align:start position:0% +vegetable side once again because of a + + + align:start position:0% +vegetable side once again because of a +lotion a quick pizza usually you would + + align:start position:0% +lotion a quick pizza usually you would + + + align:start position:0% +lotion a quick pizza usually you would +have to start to eat pizza many hours in + + align:start position:0% +have to start to eat pizza many hours in + + + align:start position:0% +have to start to eat pizza many hours in +advance because we use East and then you + + align:start position:0% +advance because we use East and then you + + + align:start position:0% +advance because we use East and then you +have to wait for the dough rise for 1 + + align:start position:0% +have to wait for the dough rise for 1 + + + align:start position:0% +have to wait for the dough rise for 1 +hour + + align:start position:0% +hour + + + align:start position:0% +hour +we don't have time to clear classes the + + align:start position:0% +we don't have time to clear classes the + + + align:start position:0% +we don't have time to clear classes the +afternoon so we will make usual we're + + align:start position:0% +afternoon so we will make usual we're + + + align:start position:0% +afternoon so we will make usual we're +going to need once the dough is ready we + + align:start position:0% +going to need once the dough is ready we + + + align:start position:0% +going to need once the dough is ready we +will prepare our and we have different + + align:start position:0% +will prepare our and we have different + + + align:start position:0% +will prepare our and we have different +choices of toppings based on your tastes + + align:start position:0% +choices of toppings based on your tastes + + + align:start position:0% +choices of toppings based on your tastes +last time I asked you what did you like + + align:start position:0% +last time I asked you what did you like + + + align:start position:0% +last time I asked you what did you like +you like well here we have some of our + + align:start position:0% +you like well here we have some of our + + + align:start position:0% +you like well here we have some of our +old favorites + + align:start position:0% +old favorites + + + align:start position:0% +old favorites +we know each of them right now what is + + align:start position:0% +we know each of them right now what is + + + align:start position:0% +we know each of them right now what is +this well you will use it on the + + align:start position:0% +this well you will use it on the + + + align:start position:0% +this well you will use it on the +singular this is you know speaker + + align:start position:0% +singular this is you know speaker + + + align:start position:0% +singular this is you know speaker +pictures yeah yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +so we don't have more than one thing we + + align:start position:0% +so we don't have more than one thing we + + + align:start position:0% +so we don't have more than one thing we +had more we'd say + + align:start position:0% + + + + align:start position:0% + +and crudo cotton it's cooked + + align:start position:0% +and crudo cotton it's cooked + + + align:start position:0% +and crudo cotton it's cooked +crudo rock very much not a pizza every + + align:start position:0% +crudo rock very much not a pizza every + + + align:start position:0% +crudo rock very much not a pizza every +movie some young some of the battles + + align:start position:0% +movie some young some of the battles + + + align:start position:0% +movie some young some of the battles +sweeper mainly three four days like I'm + + align:start position:0% +sweeper mainly three four days like I'm + + + align:start position:0% +sweeper mainly three four days like I'm +just late into different groups anybody + + align:start position:0% +just late into different groups anybody + + + align:start position:0% +just late into different groups anybody +have a chance to prepare the little low + + align:start position:0% +have a chance to prepare the little low + + + align:start position:0% +have a chance to prepare the little low +dose but the first group will start with + + align:start position:0% +dose but the first group will start with + + + align:start position:0% +dose but the first group will start with +the dough and the second group will + + align:start position:0% +the dough and the second group will + + + align:start position:0% +the dough and the second group will +start by washing and cooking the + + align:start position:0% +start by washing and cooking the + + + align:start position:0% +start by washing and cooking the +vegetables because we want to cook them + + align:start position:0% +vegetables because we want to cook them + + + align:start position:0% +vegetables because we want to cook them +a little bit \ No newline at end of file diff --git a/dEsFEK4vnV4.txt b/dEsFEK4vnV4.txt new file mode 100644 index 0000000000000000000000000000000000000000..d525ce6c1689333e9f15acfc890b3b342cd30fde --- /dev/null +++ b/dEsFEK4vnV4.txt @@ -0,0 +1,4835 @@ +align:start position:0% + +so now we start on a a unit of about a + + align:start position:0% +so now we start on a a unit of about a + + + align:start position:0% +so now we start on a a unit of about a +half a dozen lectures on probability + + align:start position:0% +half a dozen lectures on probability + + + align:start position:0% +half a dozen lectures on probability +Theory which most students have been + + align:start position:0% +Theory which most students have been + + + align:start position:0% +Theory which most students have been +exposed to to some degree in high school + + align:start position:0% +exposed to to some degree in high school + + + align:start position:0% +exposed to to some degree in high school +we'll be taking a more thorough and uh + + align:start position:0% +we'll be taking a more thorough and uh + + + align:start position:0% +we'll be taking a more thorough and uh +theoretical look uh at the subject in + + align:start position:0% +theoretical look uh at the subject in + + + align:start position:0% +theoretical look uh at the subject in +our six + + align:start position:0% +our six + + + align:start position:0% +our six +lectures but before we begin let's give + + align:start position:0% +lectures but before we begin let's give + + + align:start position:0% +lectures but before we begin let's give +a little pitch for the significance of + + align:start position:0% +a little pitch for the significance of + + + align:start position:0% +a little pitch for the significance of +it there's been extensive debate Among + + align:start position:0% +it there's been extensive debate Among + + + align:start position:0% +it there's been extensive debate Among +The Faculty that uh probability Theory + + align:start position:0% +The Faculty that uh probability Theory + + + align:start position:0% +The Faculty that uh probability Theory +belongs right up there with physics and + + align:start position:0% +belongs right up there with physics and + + + align:start position:0% +belongs right up there with physics and +chemistry and math as something that + + align:start position:0% +chemistry and math as something that + + + align:start position:0% +chemistry and math as something that +should be fundamental requirement for + + align:start position:0% +should be fundamental requirement for + + + align:start position:0% +should be fundamental requirement for +all students to know it plays an + + align:start position:0% +all students to know it plays an + + + align:start position:0% +all students to know it plays an +absolutely fundamental role in the hard + + align:start position:0% +absolutely fundamental role in the hard + + + align:start position:0% +absolutely fundamental role in the hard +Sciences in the social sciences and an + + align:start position:0% +Sciences in the social sciences and an + + + align:start position:0% +Sciences in the social sciences and an +engineering um that uh pervades all + + align:start position:0% +engineering um that uh pervades all + + + align:start position:0% +engineering um that uh pervades all +those subjects and it's hard to imagine + + align:start position:0% +those subjects and it's hard to imagine + + + align:start position:0% +those subjects and it's hard to imagine +uh somebody legitimately being called + + align:start position:0% +uh somebody legitimately being called + + + align:start position:0% +uh somebody legitimately being called +fully educated if they don't understand + + align:start position:0% +fully educated if they don't understand + + + align:start position:0% +fully educated if they don't understand +the basics of probability Theory now + + align:start position:0% +the basics of probability Theory now + + + align:start position:0% +the basics of probability Theory now +historically probability Theory starts + + align:start position:0% +historically probability Theory starts + + + align:start position:0% +historically probability Theory starts +off in a somewhat disreputable way in + + align:start position:0% +off in a somewhat disreputable way in + + + align:start position:0% +off in a somewhat disreputable way in +the 16th and early 17th centuries or + + align:start position:0% +the 16th and early 17th centuries or + + + align:start position:0% +the 16th and early 17th centuries or +17th and early 18th centuries + + align:start position:0% +17th and early 18th centuries + + + align:start position:0% +17th and early 18th centuries +um uh with the analysis of gambling uh + + align:start position:0% +um uh with the analysis of gambling uh + + + align:start position:0% +um uh with the analysis of gambling uh +and but then it goes on to be the basis + + align:start position:0% +and but then it goes on to be the basis + + + align:start position:0% +and but then it goes on to be the basis +for uh the insurance industry and + + align:start position:0% +for uh the insurance industry and + + + align:start position:0% +for uh the insurance industry and +underwriting uh predicting life + + align:start position:0% +underwriting uh predicting life + + + align:start position:0% +underwriting uh predicting life +expectancy so that you could understand + + align:start position:0% +expectancy so that you could understand + + + align:start position:0% +expectancy so that you could understand +what kind of premiums to charge and then + + align:start position:0% +what kind of premiums to charge and then + + + align:start position:0% +what kind of premiums to charge and then +it goes on to uh allow uh the + + align:start position:0% +it goes on to uh allow uh the + + + align:start position:0% +it goes on to uh allow uh the +interpretation of noisy data with errors + + align:start position:0% +interpretation of noisy data with errors + + + align:start position:0% +interpretation of noisy data with errors +in it and the degree to which it + + align:start position:0% +in it and the degree to which it + + + align:start position:0% +in it and the degree to which it +confirms scientific and social science + + align:start position:0% +confirms scientific and social science + + + align:start position:0% +confirms scientific and social science +hypothesis but true to the historical + + align:start position:0% +hypothesis but true to the historical + + + align:start position:0% +hypothesis but true to the historical +basis let's begin + + align:start position:0% +basis let's begin + + + align:start position:0% +basis let's begin +with uh an example from gambling uh that + + align:start position:0% +with uh an example from gambling uh that + + + align:start position:0% +with uh an example from gambling uh that +illustrates the first idea of + + align:start position:0% +illustrates the first idea of + + + align:start position:0% +illustrates the first idea of +probability and then we're going to be + + align:start position:0% +probability and then we're going to be + + + align:start position:0% +probability and then we're going to be +working up to a methodology for + + align:start position:0% +working up to a methodology for + + + align:start position:0% +working up to a methodology for +inventing probability models called the + + align:start position:0% +inventing probability models called the + + + align:start position:0% +inventing probability models called the +tree model so let's begin with uh an + + align:start position:0% +tree model so let's begin with uh an + + + align:start position:0% +tree model so let's begin with uh an +example from poker and I'd like to ask a + + align:start position:0% +example from poker and I'd like to ask a + + + align:start position:0% +example from poker and I'd like to ask a +question if I deal a hand of five cards + + align:start position:0% +question if I deal a hand of five cards + + + align:start position:0% +question if I deal a hand of five cards +in poker what's the probability of + + align:start position:0% +in poker what's the probability of + + + align:start position:0% +in poker what's the probability of +getting exactly Two Jacks so there are + + align:start position:0% +getting exactly Two Jacks so there are + + + align:start position:0% +getting exactly Two Jacks so there are +13 ranks and there are four kinds of + + align:start position:0% +13 ranks and there are four kinds of + + + align:start position:0% +13 ranks and there are four kinds of +jacks spad hearts diamonds clubs what's + + align:start position:0% +jacks spad hearts diamonds clubs what's + + + align:start position:0% +jacks spad hearts diamonds clubs what's +the probability that among my five cards + + align:start position:0% +the probability that among my five cards + + + align:start position:0% +the probability that among my five cards +I'm going to get two of them well that's + + align:start position:0% +I'm going to get two of them well that's + + + align:start position:0% +I'm going to get two of them well that's +really a counting problem because I'm + + align:start position:0% +really a counting problem because I'm + + + align:start position:0% +really a counting problem because I'm +going to ask first of all how many + + align:start position:0% +going to ask first of all how many + + + align:start position:0% +going to ask first of all how many +possible Five Card hands are there we + + align:start position:0% +possible Five Card hands are there we + + + align:start position:0% +possible Five Card hands are there we +can think of these as the outcomes of a + + align:start position:0% +can think of these as the outcomes of a + + + align:start position:0% +can think of these as the outcomes of a +random experiment of just picking five + + align:start position:0% +random experiment of just picking five + + + align:start position:0% +random experiment of just picking five +cards and there are 52 choose five five + + align:start position:0% +cards and there are 52 choose five five + + + align:start position:0% +cards and there are 52 choose five five +card hands in a 52 card deck then there + + align:start position:0% +card hands in a 52 card deck then there + + + align:start position:0% +card hands in a 52 card deck then there +are four choose two ways of picking the + + align:start position:0% +are four choose two ways of picking the + + + align:start position:0% +are four choose two ways of picking the +suits for the Two Jacks that we have and + + align:start position:0% +suits for the Two Jacks that we have and + + + align:start position:0% +suits for the Two Jacks that we have and +so the total number of hand hands that + + align:start position:0% +so the total number of hand hands that + + + align:start position:0% +so the total number of hand hands that +have two Jacks is simply 4 choose two + + align:start position:0% +have two Jacks is simply 4 choose two + + + align:start position:0% +have two Jacks is simply 4 choose two +time 52 minus 4 the remaining 48 cards + + align:start position:0% +time 52 minus 4 the remaining 48 cards + + + align:start position:0% +time 52 minus 4 the remaining 48 cards +choose the remaining three cards in the + + align:start position:0% +choose the remaining three cards in the + + + align:start position:0% +choose the remaining three cards in the +Five Card hand um and then what we would + + align:start position:0% +Five Card hand um and then what we would + + + align:start position:0% +Five Card hand um and then what we would +say is that the probability of Two Jacks + + align:start position:0% +say is that the probability of Two Jacks + + + align:start position:0% +say is that the probability of Two Jacks +is basically the number of hands with + + align:start position:0% +is basically the number of hands with + + + align:start position:0% +is basically the number of hands with +Two Jacks divided by the total number of + + align:start position:0% +Two Jacks divided by the total number of + + + align:start position:0% +Two Jacks divided by the total number of +hands turns out to be about + + align:start position:0% +hands turns out to be about + + + align:start position:0% +hands turns out to be about +004 and under this interpretation + + align:start position:0% +004 and under this interpretation + + + align:start position:0% +004 and under this interpretation +basically what we're thinking of + + align:start position:0% +basically what we're thinking of + + + align:start position:0% +basically what we're thinking of +probability is telling us is what + + align:start position:0% +probability is telling us is what + + + align:start position:0% +probability is telling us is what +fraction of the time uh do I get what I + + align:start position:0% +fraction of the time uh do I get what I + + + align:start position:0% +fraction of the time uh do I get what I +want what's the fraction of the time + + align:start position:0% +want what's the fraction of the time + + + align:start position:0% +want what's the fraction of the time +that I quote win if winning consists of + + align:start position:0% +that I quote win if winning consists of + + + align:start position:0% +that I quote win if winning consists of +getting a pair of Jacks and by Symmetry + + align:start position:0% +getting a pair of Jacks and by Symmetry + + + align:start position:0% +getting a pair of Jacks and by Symmetry +and and the fact that we think of one + + align:start position:0% +and and the fact that we think of one + + + align:start position:0% +and and the fact that we think of one +hand is as likely to come up as another + + align:start position:0% +hand is as likely to come up as another + + + align:start position:0% +hand is as likely to come up as another +this fraction of hands that equal two + + align:start position:0% +this fraction of hands that equal two + + + align:start position:0% +this fraction of hands that equal two +Jack it makes sense to think of that as + + align:start position:0% +Jack it makes sense to think of that as + + + align:start position:0% +Jack it makes sense to think of that as +that's the probability that we'll get + + align:start position:0% +that's the probability that we'll get + + + align:start position:0% +that's the probability that we'll get +that hand if we think of all the hands + + align:start position:0% +that hand if we think of all the hands + + + align:start position:0% +that hand if we think of all the hands +as being equally likely we yank one out + + align:start position:0% +as being equally likely we yank one out + + + align:start position:0% +as being equally likely we yank one out +of the deck the fraction of time that we + + align:start position:0% +of the deck the fraction of time that we + + + align:start position:0% +of the deck the fraction of time that we +would expect to get to Jack is this + + align:start position:0% +would expect to get to Jack is this + + + align:start position:0% +would expect to get to Jack is this +number about + + align:start position:0% + + + + align:start position:0% + +004 so the general setup of probability + + align:start position:0% +004 so the general setup of probability + + + align:start position:0% +004 so the general setup of probability +the first idea based on this + + align:start position:0% +the first idea based on this + + + align:start position:0% +the first idea based on this +illustration with a pair of jacks is + + align:start position:0% +illustration with a pair of jacks is + + + align:start position:0% +illustration with a pair of jacks is +that we abstractly we have some set of + + align:start position:0% +that we abstractly we have some set of + + + align:start position:0% +that we abstractly we have some set of +we have some random experiment that's + + align:start position:0% +we have some random experiment that's + + + align:start position:0% +we have some random experiment that's +capable of producing outcomes these are + + align:start position:0% +capable of producing outcomes these are + + + align:start position:0% +capable of producing outcomes these are +mathematical black boxes called + + align:start position:0% +mathematical black boxes called + + + align:start position:0% +mathematical black boxes called +outcomes now a certain set of the + + align:start position:0% +outcomes now a certain set of the + + + align:start position:0% +outcomes now a certain set of the +outcomes we will think of as an event + + align:start position:0% +outcomes we will think of as an event + + + align:start position:0% +outcomes we will think of as an event +that we're interested in whether or not + + align:start position:0% +that we're interested in whether or not + + + align:start position:0% +that we're interested in whether or not +it happens we could think of it as the + + align:start position:0% +it happens we could think of it as the + + + align:start position:0% +it happens we could think of it as the +event of getting to jacks or the event + + align:start position:0% +event of getting to jacks or the event + + + align:start position:0% +event of getting to jacks or the event +of winning some game then we Define the + + align:start position:0% +of winning some game then we Define the + + + align:start position:0% +of winning some game then we Define the +probability of an event as simply the + + align:start position:0% +probability of an event as simply the + + + align:start position:0% +probability of an event as simply the +fraction of the outcomes in the event + + align:start position:0% +fraction of the outcomes in the event + + + align:start position:0% +fraction of the outcomes in the event +divided by the total number of outcomes + + align:start position:0% +divided by the total number of outcomes + + + align:start position:0% +divided by the total number of outcomes +among all the outcomes what fraction of + + align:start position:0% +among all the outcomes what fraction of + + + align:start position:0% +among all the outcomes what fraction of +outcomes are in the event and we Define + + align:start position:0% +outcomes are in the event and we Define + + + align:start position:0% +outcomes are in the event and we Define +that to be the probability of the event + + align:start position:0% +that to be the probability of the event + + + align:start position:0% +that to be the probability of the event +that's the first naive idea about + + align:start position:0% +that's the first naive idea about + + + align:start position:0% +that's the first naive idea about +probability Theory and it applies to a + + align:start position:0% +probability Theory and it applies to a + + + align:start position:0% +probability Theory and it applies to a +lot of cases but not always so now let's + + align:start position:0% +lot of cases but not always so now let's + + + align:start position:0% +lot of cases but not always so now let's +begin with an example which illustrates + + align:start position:0% +begin with an example which illustrates + + + align:start position:0% +begin with an example which illustrates +why this first idea needs to be refined + + align:start position:0% +why this first idea needs to be refined + + + align:start position:0% +why this first idea needs to be refined +and it doesn't really give us the kind + + align:start position:0% +and it doesn't really give us the kind + + + align:start position:0% +and it doesn't really give us the kind +of theory of probability that we like so + + align:start position:0% +of theory of probability that we like so + + + align:start position:0% +of theory of probability that we like so +let's turn to a a game that was really + + align:start position:0% +let's turn to a a game that was really + + + align:start position:0% +let's turn to a a game that was really +famous in the 1970s an enormously + + align:start position:0% +famous in the 1970s an enormously + + + align:start position:0% +famous in the 1970s an enormously +popular TV game hosted by a man named + + align:start position:0% +popular TV game hosted by a man named + + + align:start position:0% +popular TV game hosted by a man named +Monty Hall the actual name of the TV + + align:start position:0% +Monty Hall the actual name of the TV + + + align:start position:0% +Monty Hall the actual name of the TV +show was called Let's Make a Deal uh but + + align:start position:0% +show was called Let's Make a Deal uh but + + + align:start position:0% +show was called Let's Make a Deal uh but +we'll refer to it as the Monty Hall game + + align:start position:0% +we'll refer to it as the Monty Hall game + + + align:start position:0% +we'll refer to it as the Monty Hall game +and the way that this Let's Make a Deal + + align:start position:0% +and the way that this Let's Make a Deal + + + align:start position:0% +and the way that this Let's Make a Deal +show worked was roughly that there were + + align:start position:0% +show worked was roughly that there were + + + align:start position:0% +show worked was roughly that there were +three doors this is an actual picture of + + align:start position:0% +three doors this is an actual picture of + + + align:start position:0% +three doors this is an actual picture of +the stage set door one door two door + + align:start position:0% +the stage set door one door two door + + + align:start position:0% +the stage set door one door two door +three uh and by the way this uh game + + align:start position:0% +three uh and by the way this uh game + + + align:start position:0% +three uh and by the way this uh game +show still has a fan base there's a + + align:start position:0% +show still has a fan base there's a + + + align:start position:0% +show still has a fan base there's a +website for it that you can look at and + + align:start position:0% +website for it that you can look at and + + + align:start position:0% +website for it that you can look at and +even 40 years later people are still + + align:start position:0% +even 40 years later people are still + + + align:start position:0% +even 40 years later people are still +caught up in the Dynamics of the game so + + align:start position:0% +caught up in the Dynamics of the game so + + + align:start position:0% +caught up in the Dynamics of the game so +there are these three doors and the idea + + align:start position:0% +there are these three doors and the idea + + + align:start position:0% +there are these three doors and the idea +is that behind the doors they're going + + align:start position:0% +is that behind the doors they're going + + + align:start position:0% +is that behind the doors they're going +to have a prize behind one of them and + + align:start position:0% +to have a prize behind one of them and + + + align:start position:0% +to have a prize behind one of them and +some kind of booby prize often a goat + + align:start position:0% +some kind of booby prize often a goat + + + align:start position:0% +some kind of booby prize often a goat +held by a beautiful woman holding a goat + + align:start position:0% +held by a beautiful woman holding a goat + + + align:start position:0% +held by a beautiful woman holding a goat +on a leash just to keep things visually + + align:start position:0% +on a leash just to keep things visually + + + align:start position:0% +on a leash just to keep things visually +interesting uh and that's what you got + + align:start position:0% +interesting uh and that's what you got + + + align:start position:0% +interesting uh and that's what you got +if you lost and the contestants were + + align:start position:0% +if you lost and the contestants were + + + align:start position:0% +if you lost and the contestants were +going to somehow or other pick a door uh + + align:start position:0% +going to somehow or other pick a door uh + + + align:start position:0% +going to somehow or other pick a door uh +and hope that the prize was behind it + + align:start position:0% +and hope that the prize was behind it + + + align:start position:0% +and hope that the prize was behind it +there's the picture of the staff there's + + align:start position:0% +there's the picture of the staff there's + + + align:start position:0% +there's the picture of the staff there's +Monty Hall and his and the woman who was + + align:start position:0% +Monty Hall and his and the woman who was + + + align:start position:0% +Monty Hall and his and the woman who was +his assistant Carol Merill her job was + + align:start position:0% +his assistant Carol Merill her job was + + + align:start position:0% +his assistant Carol Merill her job was +to pick doors to open and show them to + + align:start position:0% +to pick doors to open and show them to + + + align:start position:0% +to pick doors to open and show them to +contestants to see what was behind them + + align:start position:0% +contestants to see what was behind them + + + align:start position:0% +contestants to see what was behind them +okay so here are the rules for the Monty + + align:start position:0% +okay so here are the rules for the Monty + + + align:start position:0% +okay so here are the rules for the Monty +Hall game the actual quiz show had more + + align:start position:0% +Hall game the actual quiz show had more + + + align:start position:0% +Hall game the actual quiz show had more +flexible rules but but for Simplicity + + align:start position:0% +flexible rules but but for Simplicity + + + align:start position:0% +flexible rules but but for Simplicity +we're we're going to define a nice uh + + align:start position:0% +we're we're going to define a nice uh + + + align:start position:0% +we're we're going to define a nice uh +simple precise and fixed set of rules + + align:start position:0% +simple precise and fixed set of rules + + + align:start position:0% +simple precise and fixed set of rules +the rules are that behind the three + + align:start position:0% +the rules are that behind the three + + + align:start position:0% +the rules are that behind the three +doors two of the doors are going to have + + align:start position:0% +doors two of the doors are going to have + + + align:start position:0% +doors two of the doors are going to have +goats and one of the doors is going to + + align:start position:0% +goats and one of the doors is going to + + + align:start position:0% +goats and one of the doors is going to +have a prize behind it often the prize + + align:start position:0% +have a prize behind it often the prize + + + align:start position:0% +have a prize behind it often the prize +is something like an automobile + + align:start position:0% +is something like an automobile + + + align:start position:0% +is something like an automobile +something really desirable so we can + + align:start position:0% +something really desirable so we can + + + align:start position:0% +something really desirable so we can +assume that the the uh the staff on + + align:start position:0% +assume that the the uh the staff on + + + align:start position:0% +assume that the the uh the staff on +purpose will uh place the prize at + + align:start position:0% +purpose will uh place the prize at + + + align:start position:0% +purpose will uh place the prize at +random behind the three doors because + + align:start position:0% +random behind the three doors because + + + align:start position:0% +random behind the three doors because +they don't want anybody to have a guess + + align:start position:0% +they don't want anybody to have a guess + + + align:start position:0% +they don't want anybody to have a guess +that some doors are more likely than + + align:start position:0% +that some doors are more likely than + + + align:start position:0% +that some doors are more likely than +others to have the prize and they're not + + align:start position:0% +others to have the prize and they're not + + + align:start position:0% +others to have the prize and they're not +allowed to cheat that is once they've + + align:start position:0% +allowed to cheat that is once they've + + + align:start position:0% +allowed to cheat that is once they've +decided which door is going to have the + + align:start position:0% +decided which door is going to have the + + + align:start position:0% +decided which door is going to have the +prize it's supposed to stay there + + align:start position:0% +prize it's supposed to stay there + + + align:start position:0% +prize it's supposed to stay there +throughout the game they can't move it + + align:start position:0% +throughout the game they can't move it + + + align:start position:0% +throughout the game they can't move it +in response to the what which door that + + align:start position:0% +in response to the what which door that + + + align:start position:0% +in response to the what which door that +the contestants pick that would be + + align:start position:0% +the contestants pick that would be + + + align:start position:0% +the contestants pick that would be +cheating okay next the contestant is + + align:start position:0% +cheating okay next the contestant is + + + align:start position:0% +cheating okay next the contestant is +given opportunity to pick one of the + + align:start position:0% +given opportunity to pick one of the + + + align:start position:0% +given opportunity to pick one of the +doors they're all closed and it's hard + + align:start position:0% +doors they're all closed and it's hard + + + align:start position:0% +doors they're all closed and it's hard +to understand how the contestant would + + align:start position:0% +to understand how the contestant would + + + align:start position:0% +to understand how the contestant would +make a choice but if the contestant was + + align:start position:0% +make a choice but if the contestant was + + + align:start position:0% +make a choice but if the contestant was +worried about the uh the staff trying to + + align:start position:0% +worried about the uh the staff trying to + + + align:start position:0% +worried about the uh the staff trying to +out guess him on where to put the goat + + align:start position:0% +out guess him on where to put the goat + + + align:start position:0% +out guess him on where to put the goat +uh and where to put the prize the + + align:start position:0% +uh and where to put the prize the + + + align:start position:0% +uh and where to put the prize the +contestant should just pick all the + + align:start position:0% +contestant should just pick all the + + + align:start position:0% +contestant should just pick all the +doors with equally like with equally + + align:start position:0% +doors with equally like with equally + + + align:start position:0% +doors with equally like with equally +likelihood then he can't be beaten by + + align:start position:0% +likelihood then he can't be beaten by + + + align:start position:0% +likelihood then he can't be beaten by +their trying to out guess him he could + + align:start position:0% +their trying to out guess him he could + + + align:start position:0% +their trying to out guess him he could +only be beaten by if they cheated him by + + align:start position:0% +only be beaten by if they cheated him by + + + align:start position:0% +only be beaten by if they cheated him by +moving the goat after he picked or + + align:start position:0% +moving the goat after he picked or + + + align:start position:0% +moving the goat after he picked or +moving the prize after he + + align:start position:0% +moving the prize after he + + + align:start position:0% +moving the prize after he +picked at this point once the contestant + + align:start position:0% +picked at this point once the contestant + + + align:start position:0% +picked at this point once the contestant +has picked a door let's say he picks + + align:start position:0% +has picked a door let's say he picks + + + align:start position:0% +has picked a door let's say he picks +door two then Monty instructs Carl to + + align:start position:0% +door two then Monty instructs Carl to + + + align:start position:0% +door two then Monty instructs Carl to +open a door with a goat behind it so + + align:start position:0% +open a door with a goat behind it so + + + align:start position:0% +open a door with a goat behind it so +he's going to choose an unpick door if + + align:start position:0% +he's going to choose an unpick door if + + + align:start position:0% +he's going to choose an unpick door if +the if the contestant has picked door + + align:start position:0% +the if the contestant has picked door + + + align:start position:0% +the if the contestant has picked door +two that means the door one and door + + align:start position:0% +two that means the door one and door + + + align:start position:0% +two that means the door one and door +three are unpicked doors and Monty tells + + align:start position:0% +three are unpicked doors and Monty tells + + + align:start position:0% +three are unpicked doors and Monty tells +Carol open either door one or door + + align:start position:0% +Carol open either door one or door + + + align:start position:0% +Carol open either door one or door +three whichever one or or perhaps both + + align:start position:0% +three whichever one or or perhaps both + + + align:start position:0% +three whichever one or or perhaps both +have a goat behind them and so Carol is + + align:start position:0% +have a goat behind them and so Carol is + + + align:start position:0% +have a goat behind them and so Carol is +going to open one of those doors and + + align:start position:0% +going to open one of those doors and + + + align:start position:0% +going to open one of those doors and +show a goat and everybody knows that + + align:start position:0% +show a goat and everybody knows that + + + align:start position:0% +show a goat and everybody knows that +they're going to see a goat because + + align:start position:0% +they're going to see a goat because + + + align:start position:0% +they're going to see a goat because +that's the way the game works and then + + align:start position:0% +that's the way the game works and then + + + align:start position:0% +that's the way the game works and then +at this point when the contestant has + + align:start position:0% +at this point when the contestant has + + + align:start position:0% +at this point when the contestant has +seen that there's a door that has a goat + + align:start position:0% +seen that there's a door that has a goat + + + align:start position:0% +seen that there's a door that has a goat +behind it and they're sitting on on a + + align:start position:0% +behind it and they're sitting on on a + + + align:start position:0% +behind it and they're sitting on on a +picked door and there's another unopened + + align:start position:0% +picked door and there's another unopened + + + align:start position:0% +picked door and there's another unopened +door that hasn't been picked the the + + align:start position:0% +door that hasn't been picked the the + + + align:start position:0% +door that hasn't been picked the the +contestant's job is to decide whether to + + align:start position:0% +contestant's job is to decide whether to + + + align:start position:0% +contestant's job is to decide whether to +stick with the door that they originally + + align:start position:0% +stick with the door that they originally + + + align:start position:0% +stick with the door that they originally +picked or switch to the other unopened + + align:start position:0% +picked or switch to the other unopened + + + align:start position:0% +picked or switch to the other unopened +door so if they pick door two and Carol + + align:start position:0% +door so if they pick door two and Carol + + + align:start position:0% +door so if they pick door two and Carol +opened door three they could stick with + + align:start position:0% +opened door three they could stick with + + + align:start position:0% +opened door three they could stick with +door two or they could switch to the + + align:start position:0% +door two or they could switch to the + + + align:start position:0% +door two or they could switch to the +closed door one and hope that maybe one + + align:start position:0% +closed door one and hope that maybe one + + + align:start position:0% +closed door one and hope that maybe one +has the prize behind it those are the + + align:start position:0% +has the prize behind it those are the + + + align:start position:0% +has the prize behind it those are the +rules of the game now um the game got a + + align:start position:0% +rules of the game now um the game got a + + + align:start position:0% +rules of the game now um the game got a +lot of prominence uh in a uh magazine + + align:start position:0% +lot of prominence uh in a uh magazine + + + align:start position:0% +lot of prominence uh in a uh magazine +column written by a woman named Marilyn + + align:start position:0% +column written by a woman named Marilyn + + + align:start position:0% +column written by a woman named Marilyn +vent the name of the uh magazine column + + align:start position:0% +vent the name of the uh magazine column + + + align:start position:0% +vent the name of the uh magazine column +is called ask Marilyn and she uh + + align:start position:0% +is called ask Marilyn and she uh + + + align:start position:0% +is called ask Marilyn and she uh +advertises herself as having the highest + + align:start position:0% +advertises herself as having the highest + + + align:start position:0% +advertises herself as having the highest +recorded IQ of all time some IQ of 200 + + align:start position:0% +recorded IQ of all time some IQ of 200 + + + align:start position:0% +recorded IQ of all time some IQ of 200 +and so she uh uh runs a popular science + + align:start position:0% +and so she uh uh runs a popular science + + + align:start position:0% +and so she uh uh runs a popular science +and math uh uh column with various kinds + + align:start position:0% +and math uh uh column with various kinds + + + align:start position:0% +and math uh uh column with various kinds +of puzzles and she took up the analysis + + align:start position:0% +of puzzles and she took up the analysis + + + align:start position:0% +of puzzles and she took up the analysis +of the Monte whole statistics and came + + align:start position:0% +of the Monte whole statistics and came + + + align:start position:0% +of the Monte whole statistics and came +to a conclusion uh and the conclusion + + align:start position:0% +to a conclusion uh and the conclusion + + + align:start position:0% +to a conclusion uh and the conclusion +caused a firestorm of response letters + + align:start position:0% +caused a firestorm of response letters + + + align:start position:0% +caused a firestorm of response letters +from all sorts of readers even quite s + + align:start position:0% +from all sorts of readers even quite s + + + align:start position:0% +from all sorts of readers even quite s +sophisticated uh PhD mathematicians who + + align:start position:0% +sophisticated uh PhD mathematicians who + + + align:start position:0% +sophisticated uh PhD mathematicians who +were arguing with her with her + + align:start position:0% +were arguing with her with her + + + align:start position:0% +were arguing with her with her +conclusion about the way the game worked + + align:start position:0% +conclusion about the way the game worked + + + align:start position:0% +conclusion about the way the game worked +and the probability of winning according + + align:start position:0% +and the probability of winning according + + + align:start position:0% +and the probability of winning according +to how the contestant behaved the debate + + align:start position:0% +to how the contestant behaved the debate + + + align:start position:0% +to how the contestant behaved the debate +basically came down to these two + + align:start position:0% +basically came down to these two + + + align:start position:0% +basically came down to these two +positions position one said that + + align:start position:0% +positions position one said that + + + align:start position:0% +positions position one said that +sticking and switching were equally good + + align:start position:0% +sticking and switching were equally good + + + align:start position:0% +sticking and switching were equally good +it really didn't matter what the + + align:start position:0% +it really didn't matter what the + + + align:start position:0% +it really didn't matter what the +contestant did whether they stuck with + + align:start position:0% +contestant did whether they stuck with + + + align:start position:0% +contestant did whether they stuck with +the door that they originally picked or + + align:start position:0% +the door that they originally picked or + + + align:start position:0% +the door that they originally picked or +switched to the unpicked door after the + + align:start position:0% +switched to the unpicked door after the + + + align:start position:0% +switched to the unpicked door after the +third door had been opened uh and that + + align:start position:0% +third door had been opened uh and that + + + align:start position:0% +third door had been opened uh and that +their likelihood of finding the prize + + align:start position:0% +their likelihood of finding the prize + + + align:start position:0% +their likelihood of finding the prize +was the same uh and the other argument + + align:start position:0% +was the same uh and the other argument + + + align:start position:0% +was the same uh and the other argument +very emphatically said switching is much + + align:start position:0% +very emphatically said switching is much + + + align:start position:0% +very emphatically said switching is much +better you should really switch no + + align:start position:0% +better you should really switch no + + + align:start position:0% +better you should really switch no +matter what and how can we resolve this + + align:start position:0% +matter what and how can we resolve this + + + align:start position:0% +matter what and how can we resolve this +question well the general method that + + align:start position:0% +question well the general method that + + + align:start position:0% +question well the general method that +we're proposing for dealing with + + align:start position:0% +we're proposing for dealing with + + + align:start position:0% +we're proposing for dealing with +problems like this where we're really + + align:start position:0% +problems like this where we're really + + + align:start position:0% +problems like this where we're really +trying to figure out what is the proper + + align:start position:0% +trying to figure out what is the proper + + + align:start position:0% +trying to figure out what is the proper +probability model is to draw a tree that + + align:start position:0% +probability model is to draw a tree that + + + align:start position:0% +probability model is to draw a tree that +shows step by step the progress of the + + align:start position:0% +shows step by step the progress of the + + + align:start position:0% +shows step by step the progress of the +uh process or experiment that's going to + + align:start position:0% +uh process or experiment that's going to + + + align:start position:0% +uh process or experiment that's going to +yield a random output and uh try to + + align:start position:0% +yield a random output and uh try to + + + align:start position:0% +yield a random output and uh try to +assign probabilities to each of the + + align:start position:0% +assign probabilities to each of the + + + align:start position:0% +assign probabilities to each of the +branches of the tree as you go and use + + align:start position:0% +branches of the tree as you go and use + + + align:start position:0% +branches of the tree as you go and use +that as a guide for how to assign + + align:start position:0% +that as a guide for how to assign + + + align:start position:0% +that as a guide for how to assign +probabilities to outcomes so let's begin + + align:start position:0% +probabilities to outcomes so let's begin + + + align:start position:0% +probabilities to outcomes so let's begin +first of all by finding out what the + + align:start position:0% +first of all by finding out what the + + + align:start position:0% +first of all by finding out what the +outcomes are so um and we're going to be + + align:start position:0% +outcomes are so um and we're going to be + + + align:start position:0% +outcomes are so um and we're going to be +analyzing the switch strategy so just + + align:start position:0% +analyzing the switch strategy so just + + + align:start position:0% +analyzing the switch strategy so just +for definiteness let's suppose that the + + align:start position:0% +for definiteness let's suppose that the + + + align:start position:0% +for definiteness let's suppose that the +contestant uh adopts the strategy that + + align:start position:0% +contestant uh adopts the strategy that + + + align:start position:0% +contestant uh adopts the strategy that +they pick a door Carol opens a door then + + align:start position:0% +they pick a door Carol opens a door then + + + align:start position:0% +they pick a door Carol opens a door then +shows a goat and they're going to switch + + align:start position:0% +shows a goat and they're going to switch + + + align:start position:0% +shows a goat and they're going to switch +to the non-oat closed door that they did + + align:start position:0% +to the non-oat closed door that they did + + + align:start position:0% +to the non-oat closed door that they did +not originally pick they're going to + + align:start position:0% +not originally pick they're going to + + + align:start position:0% +not originally pick they're going to +switch to the other door that they can + + align:start position:0% +switch to the other door that they can + + + align:start position:0% +switch to the other door that they can +switch to and we're going to ask about + + align:start position:0% +switch to and we're going to ask about + + + align:start position:0% +switch to and we're going to ask about +what are the outcomes and consequences + + align:start position:0% +what are the outcomes and consequences + + + align:start position:0% +what are the outcomes and consequences +of winning or losing if you adopt that + + align:start position:0% +of winning or losing if you adopt that + + + align:start position:0% +of winning or losing if you adopt that +strategy + + align:start position:0% +strategy + + + align:start position:0% +strategy +well the tree of possibilities goes like + + align:start position:0% +well the tree of possibilities goes like + + + align:start position:0% +well the tree of possibilities goes like +this the first step in this process that + + align:start position:0% +this the first step in this process that + + + align:start position:0% +this the first step in this process that +we've described is that the staff picks + + align:start position:0% +we've described is that the staff picks + + + align:start position:0% +we've described is that the staff picks +a prize location to a door to put the + + align:start position:0% +a prize location to a door to put the + + + align:start position:0% +a prize location to a door to put the +prize behind and so there are three + + align:start position:0% +prize behind and so there are three + + + align:start position:0% +prize behind and so there are three +possibilities they could put the prize + + align:start position:0% +possibilities they could put the prize + + + align:start position:0% +possibilities they could put the prize +behind door one door two and door three + + align:start position:0% +behind door one door two and door three + + + align:start position:0% +behind door one door two and door three +okay well let's examine the possibility + + align:start position:0% +okay well let's examine the possibility + + + align:start position:0% +okay well let's examine the possibility +that they put the prize behind door one + + align:start position:0% +that they put the prize behind door one + + + align:start position:0% +that they put the prize behind door one +so the next stage is they pick a door + + align:start position:0% +so the next stage is they pick a door + + + align:start position:0% +so the next stage is they pick a door +and if they pick um uh uh if the priz is + + align:start position:0% +and if they pick um uh uh if the priz is + + + align:start position:0% +and if they pick um uh uh if the priz is +behind and they pick a door again there + + align:start position:0% +behind and they pick a door again there + + + align:start position:0% +behind and they pick a door again there +are three possible doors uh that the + + align:start position:0% +are three possible doors uh that the + + + align:start position:0% +are three possible doors uh that the +contestant might pick contestant has no + + align:start position:0% +contestant might pick contestant has no + + + align:start position:0% +contestant might pick contestant has no +idea where the prize is and so the + + align:start position:0% +idea where the prize is and so the + + + align:start position:0% +idea where the prize is and so the +contestant can choose either door one or + + align:start position:0% +contestant can choose either door one or + + + align:start position:0% +contestant can choose either door one or +door two or door + + align:start position:0% +door two or door + + + align:start position:0% +door two or door +three at that point the third event in + + align:start position:0% +three at that point the third event in + + + align:start position:0% +three at that point the third event in +this random process or experiment is + + align:start position:0% +this random process or experiment is + + + align:start position:0% +this random process or experiment is +that Carol opens a door that has a goat + + align:start position:0% +that Carol opens a door that has a goat + + + align:start position:0% +that Carol opens a door that has a goat +behind it so let's examine that POS + + align:start position:0% +behind it so let's examine that POS + + + align:start position:0% +behind it so let's examine that POS +those possibilities so one possibility + + align:start position:0% +those possibilities so one possibility + + + align:start position:0% +those possibilities so one possibility +is that the prize is behind one and the + + align:start position:0% +is that the prize is behind one and the + + + align:start position:0% +is that the prize is behind one and the +contestant picks door one initially well + + align:start position:0% +contestant picks door one initially well + + + align:start position:0% +contestant picks door one initially well +that means that Carol can open either + + align:start position:0% +that means that Carol can open either + + + align:start position:0% +that means that Carol can open either +door two or door three in that + + align:start position:0% +door two or door three in that + + + align:start position:0% +door two or door three in that +circumstance uh because both of them + + align:start position:0% +circumstance uh because both of them + + + align:start position:0% +circumstance uh because both of them +have goats behind them on the other hand + + align:start position:0% +have goats behind them on the other hand + + + align:start position:0% +have goats behind them on the other hand +if the prize is at one and the + + align:start position:0% +if the prize is at one and the + + + align:start position:0% +if the prize is at one and the +contestant picks door two then Carol the + + align:start position:0% +contestant picks door two then Carol the + + + align:start position:0% +contestant picks door two then Carol the +two closed doors have one has the prize + + align:start position:0% +two closed doors have one has the prize + + + align:start position:0% +two closed doors have one has the prize +one and the other doesn't have the prize + + align:start position:0% +one and the other doesn't have the prize + + + align:start position:0% +one and the other doesn't have the prize +three Carol has to open door three + + align:start position:0% +three Carol has to open door three + + + align:start position:0% +three Carol has to open door three +likewise if the contestant picks door + + align:start position:0% +likewise if the contestant picks door + + + align:start position:0% +likewise if the contestant picks door +three when the prize is behind door one + + align:start position:0% +three when the prize is behind door one + + + align:start position:0% +three when the prize is behind door one +Carol has to open door two so these uh + + align:start position:0% +Carol has to open door two so these uh + + + align:start position:0% +Carol has to open door two so these uh +BR here she's got a two-way Branch she + + align:start position:0% +BR here she's got a two-way Branch she + + + align:start position:0% +BR here she's got a two-way Branch she +can choose to open either of the two + + align:start position:0% +can choose to open either of the two + + + align:start position:0% +can choose to open either of the two +goat doors two or three here there's + + align:start position:0% +goat doors two or three here there's + + + align:start position:0% +goat doors two or three here there's +only one unopened door with a goat she's + + align:start position:0% +only one unopened door with a goat she's + + + align:start position:0% +only one unopened door with a goat she's +got to open three there too okay and + + align:start position:0% +got to open three there too okay and + + + align:start position:0% +got to open three there too okay and +that describes the outcomes of the + + align:start position:0% +that describes the outcomes of the + + + align:start position:0% +that describes the outcomes of the +experiment that's the the process of the + + align:start position:0% +experiment that's the the process of the + + + align:start position:0% +experiment that's the the process of the +experiment and these nodes at the end + + align:start position:0% +experiment and these nodes at the end + + + align:start position:0% +experiment and these nodes at the end +these leaves of the tree describe the + + align:start position:0% +these leaves of the tree describe the + + + align:start position:0% +these leaves of the tree describe the +final outcomes on this + + align:start position:0% +final outcomes on this + + + align:start position:0% +final outcomes on this +Branch now if you look at the + + align:start position:0% +Branch now if you look at the + + + align:start position:0% +Branch now if you look at the +classification of these outcomes + + align:start position:0% +classification of these outcomes + + + align:start position:0% +classification of these outcomes +according to winning and losing well + + align:start position:0% +according to winning and losing well + + + align:start position:0% +according to winning and losing well +we're looking at the switch strategy so + + align:start position:0% +we're looking at the switch strategy so + + + align:start position:0% +we're looking at the switch strategy so +if the prize was behind one and the + + align:start position:0% +if the prize was behind one and the + + + align:start position:0% +if the prize was behind one and the +contestant picked door one initially + + align:start position:0% +contestant picked door one initially + + + align:start position:0% +contestant picked door one initially +then their strategy is to switch and + + align:start position:0% +then their strategy is to switch and + + + align:start position:0% +then their strategy is to switch and +they're going to switch away from the + + align:start position:0% +they're going to switch away from the + + + align:start position:0% +they're going to switch away from the +prize door so whichever door Carol + + align:start position:0% +prize door so whichever door Carol + + + align:start position:0% +prize door so whichever door Carol +opened to reveal the goat two or three + + align:start position:0% +opened to reveal the goat two or three + + + align:start position:0% +opened to reveal the goat two or three +the contestant is going to switch to the + + align:start position:0% +the contestant is going to switch to the + + + align:start position:0% +the contestant is going to switch to the +other one and they're going to lose so + + align:start position:0% +other one and they're going to lose so + + + align:start position:0% +other one and they're going to lose so +both both of these outcomes count as + + align:start position:0% +both both of these outcomes count as + + + align:start position:0% +both both of these outcomes count as +losses for the contestant on the other + + align:start position:0% +losses for the contestant on the other + + + align:start position:0% +losses for the contestant on the other +hand if the contestant picked uh if the + + align:start position:0% +hand if the contestant picked uh if the + + + align:start position:0% +hand if the contestant picked uh if the +prize was behind door one and the + + align:start position:0% +prize was behind door one and the + + + align:start position:0% +prize was behind door one and the +contestant picked door two then Carol + + align:start position:0% +contestant picked door two then Carol + + + align:start position:0% +contestant picked door two then Carol +opens the non prize door three and the + + align:start position:0% +opens the non prize door three and the + + + align:start position:0% +opens the non prize door three and the +contestant switches from two the only + + align:start position:0% +contestant switches from two the only + + + align:start position:0% +contestant switches from two the only +choice they have is to switch to one the + + align:start position:0% +choice they have is to switch to one the + + + align:start position:0% +choice they have is to switch to one the +prize door they win and this other case + + align:start position:0% +prize door they win and this other case + + + align:start position:0% +prize door they win and this other case +is symmetric and that summarizes the + + align:start position:0% +is symmetric and that summarizes the + + + align:start position:0% +is symmetric and that summarizes the +wins and losses in this branch of the + + align:start position:0% +wins and losses in this branch of the + + + align:start position:0% +wins and losses in this branch of the +tree now of course the rest of the tree + + align:start position:0% +tree now of course the rest of the tree + + + align:start position:0% +tree now of course the rest of the tree +is symmetric and so we don't need to + + align:start position:0% +is symmetric and so we don't need to + + + align:start position:0% +is symmetric and so we don't need to +talk it through again this is just + + align:start position:0% +talk it through again this is just + + + align:start position:0% +talk it through again this is just +simply the case where the priz is behind + + align:start position:0% +simply the case where the priz is behind + + + align:start position:0% +simply the case where the priz is behind +two the contestant has the same choices + + align:start position:0% +two the contestant has the same choices + + + align:start position:0% +two the contestant has the same choices +and Maryland has the same choices of + + align:start position:0% +and Maryland has the same choices of + + + align:start position:0% +and Maryland has the same choices of +which unopen door to uh to choose and + + align:start position:0% +which unopen door to uh to choose and + + + align:start position:0% +which unopen door to uh to choose and +likewise if the priz is behind three so + + align:start position:0% +likewise if the priz is behind three so + + + align:start position:0% +likewise if the priz is behind three so +if we look at this tree the tree is + + align:start position:0% +if we look at this tree the tree is + + + align:start position:0% +if we look at this tree the tree is +telling us that this is an experiment + + align:start position:0% +telling us that this is an experiment + + + align:start position:0% +telling us that this is an experiment +where which we think of as having 12 + + align:start position:0% +where which we think of as having 12 + + + align:start position:0% +where which we think of as having 12 +outcomes three in each of these ma four + + align:start position:0% +outcomes three in each of these ma four + + + align:start position:0% +outcomes three in each of these ma four +in each of these major branches so there + + align:start position:0% +in each of these major branches so there + + + align:start position:0% +in each of these major branches so there +are 12 outcomes of this random + + align:start position:0% +are 12 outcomes of this random + + + align:start position:0% +are 12 outcomes of this random +experiment of which um + + align:start position:0% +experiment of which um + + + align:start position:0% +experiment of which um +are losses and six are wins for the + + align:start position:0% +are losses and six are wins for the + + + align:start position:0% +are losses and six are wins for the +contestant and so we discover that + + align:start position:0% +contestant and so we discover that + + + align:start position:0% +contestant and so we discover that +there's six wins and six losses now the + + align:start position:0% +there's six wins and six losses now the + + + align:start position:0% +there's six wins and six losses now the +way that this game works if you think + + align:start position:0% +way that this game works if you think + + + align:start position:0% +way that this game works if you think +about it if the switching strategy + + align:start position:0% +about it if the switching strategy + + + align:start position:0% +about it if the switching strategy +wins that means that the sticking + + align:start position:0% +wins that means that the sticking + + + align:start position:0% +wins that means that the sticking +strategy would have lost because if + + align:start position:0% +strategy would have lost because if + + + align:start position:0% +strategy would have lost because if +switching wins it meant that you switch + + align:start position:0% +switching wins it meant that you switch + + + align:start position:0% +switching wins it meant that you switch +to the door that had the prize and so if + + align:start position:0% +to the door that had the prize and so if + + + align:start position:0% +to the door that had the prize and so if +you hadn't switched you must have been + + align:start position:0% +you hadn't switched you must have been + + + align:start position:0% +you hadn't switched you must have been +at a door that didn't have the prize and + + align:start position:0% +at a door that didn't have the prize and + + + align:start position:0% +at a door that didn't have the prize and +likewise if switching uh loses then uh + + align:start position:0% +likewise if switching uh loses then uh + + + align:start position:0% +likewise if switching uh loses then uh +you must have switched from the door + + align:start position:0% +you must have switched from the door + + + align:start position:0% +you must have switched from the door +with the prize to a door that didn't + + align:start position:0% +with the prize to a door that didn't + + + align:start position:0% +with the prize to a door that didn't +have the prize switching and that means + + align:start position:0% +have the prize switching and that means + + + align:start position:0% +have the prize switching and that means +if you'd stuck you would have won so + + align:start position:0% +if you'd stuck you would have won so + + + align:start position:0% +if you'd stuck you would have won so +what we can say is that really analyzing + + align:start position:0% +what we can say is that really analyzing + + + align:start position:0% +what we can say is that really analyzing +the switch strategy enables us to + + align:start position:0% +the switch strategy enables us to + + + align:start position:0% +the switch strategy enables us to +analyze the stick strategy + + align:start position:0% +analyze the stick strategy + + + align:start position:0% +analyze the stick strategy +simultaneously because you win by + + align:start position:0% +simultaneously because you win by + + + align:start position:0% +simultaneously because you win by +sticking if and only if you lose by + + align:start position:0% +sticking if and only if you lose by + + + align:start position:0% +sticking if and only if you lose by +switching now this simplification + + align:start position:0% +switching now this simplification + + + align:start position:0% +switching now this simplification +doesn't hold when there's more than + + align:start position:0% +doesn't hold when there's more than + + + align:start position:0% +doesn't hold when there's more than +three doors uh and that's another + + align:start position:0% +three doors uh and that's another + + + align:start position:0% +three doors uh and that's another +exercise but for now it it's telling us + + align:start position:0% +exercise but for now it it's telling us + + + align:start position:0% +exercise but for now it it's telling us +that if we analyze the switch strategy + + align:start position:0% +that if we analyze the switch strategy + + + align:start position:0% +that if we analyze the switch strategy +we also understand the stick the stick + + align:start position:0% +we also understand the stick the stick + + + align:start position:0% +we also understand the stick the stick +strategy and of course that means that + + align:start position:0% +strategy and of course that means that + + + align:start position:0% +strategy and of course that means that +if you uh use the stick strategy then + + align:start position:0% +if you uh use the stick strategy then + + + align:start position:0% +if you uh use the stick strategy then +the six wins become losses and the six + + align:start position:0% +the six wins become losses and the six + + + align:start position:0% +the six wins become losses and the six +losses become wins and again um there + + align:start position:0% +losses become wins and again um there + + + align:start position:0% +losses become wins and again um there +are six ways to lose and six ways to win + + align:start position:0% +are six ways to lose and six ways to win + + + align:start position:0% +are six ways to lose and six ways to win +so the first false conclusion from this + + align:start position:0% +so the first false conclusion from this + + + align:start position:0% +so the first false conclusion from this +is by reasoning about it as though they + + align:start position:0% +is by reasoning about it as though they + + + align:start position:0% +is by reasoning about it as though they +were poker hands and the false + + align:start position:0% +were poker hands and the false + + + align:start position:0% +were poker hands and the false +conclusion says look sticking and + + align:start position:0% +conclusion says look sticking and + + + align:start position:0% +conclusion says look sticking and +switching win with the same number of + + align:start position:0% +switching win with the same number of + + + align:start position:0% +switching win with the same number of +outcomes and lose with the same out + + align:start position:0% +outcomes and lose with the same out + + + align:start position:0% +outcomes and lose with the same out +number of outcomes so it really doesn't + + align:start position:0% +number of outcomes so it really doesn't + + + align:start position:0% +number of outcomes so it really doesn't +matter whether you stick or switch + + align:start position:0% +matter whether you stick or switch + + + align:start position:0% +matter whether you stick or switch +because the probability of winning in + + align:start position:0% +because the probability of winning in + + + align:start position:0% +because the probability of winning in +both cases is half the outcome 6 out of + + align:start position:0% +both cases is half the outcome 6 out of + + + align:start position:0% +both cases is half the outcome 6 out of +12 the probability doesn't matter that + + align:start position:0% +12 the probability doesn't matter that + + + align:start position:0% +12 the probability doesn't matter that +makes no difference whether you stick or + + align:start position:0% +makes no difference whether you stick or + + + align:start position:0% +makes no difference whether you stick or +switch and that's + + align:start position:0% +switch and that's + + + align:start position:0% +switch and that's +wrong and we will uh see + + align:start position:0% +wrong and we will uh see + + + align:start position:0% +wrong and we will uh see +why + + align:start position:0% +why + + + align:start position:0% +why +soon the other false argument is that we + + align:start position:0% +soon the other false argument is that we + + + align:start position:0% +soon the other false argument is that we +think about what happens after Carol has + + align:start position:0% +think about what happens after Carol has + + + align:start position:0% +think about what happens after Carol has +opened a door so where are we the + + align:start position:0% +opened a door so where are we the + + + align:start position:0% +opened a door so where are we the +contestant has picked a door has no idea + + align:start position:0% +contestant has picked a door has no idea + + + align:start position:0% +contestant has picked a door has no idea +where the goat or the prize is Carol + + align:start position:0% +where the goat or the prize is Carol + + + align:start position:0% +where the goat or the prize is Carol +opens a door and shows the contestant a + + align:start position:0% +opens a door and shows the contestant a + + + align:start position:0% +opens a door and shows the contestant a +goat what's left well there's two closed + + align:start position:0% +goat what's left well there's two closed + + + align:start position:0% +goat what's left well there's two closed +doors left one is the door with the + + align:start position:0% +doors left one is the door with the + + + align:start position:0% +doors left one is the door with the +prize and the other is the door without + + align:start position:0% +prize and the other is the door without + + + align:start position:0% +prize and the other is the door without +the prize that has a goat behind it and + + align:start position:0% +the prize that has a goat behind it and + + + align:start position:0% +the prize that has a goat behind it and +there's by symmetry of the doors the + + align:start position:0% +there's by symmetry of the doors the + + + align:start position:0% +there's by symmetry of the doors the +contestant has no idea what's behind the + + align:start position:0% +contestant has no idea what's behind the + + + align:start position:0% +contestant has no idea what's behind the +door that he picked or the remaining + + align:start position:0% +door that he picked or the remaining + + + align:start position:0% +door that he picked or the remaining +unopened door they're equally likely to + + align:start position:0% +unopened door they're equally likely to + + + align:start position:0% +unopened door they're equally likely to +contain the prize and so the argument is + + align:start position:0% +contain the prize and so the argument is + + + align:start position:0% +contain the prize and so the argument is +again that whether you stick or switch + + align:start position:0% +again that whether you stick or switch + + + align:start position:0% +again that whether you stick or switch +between those two doors uh that haven't + + align:start position:0% +between those two doors uh that haven't + + + align:start position:0% +between those two doors uh that haven't +yet been opened it doesn't really matter + + align:start position:0% +yet been opened it doesn't really matter + + + align:start position:0% +yet been opened it doesn't really matter +and so again the stick strategy and the + + align:start position:0% +and so again the stick strategy and the + + + align:start position:0% +and so again the stick strategy and the +switch strategy each win with the same + + align:start position:0% +switch strategy each win with the same + + + align:start position:0% +switch strategy each win with the same +50/50 probability and that's wrong + + align:start position:0% +50/50 probability and that's wrong + + + align:start position:0% +50/50 probability and that's wrong +too what's wrong well let's go back and + + align:start position:0% +too what's wrong well let's go back and + + + align:start position:0% +too what's wrong well let's go back and +look at this tree a little bit more + + align:start position:0% +look at this tree a little bit more + + + align:start position:0% +look at this tree a little bit more +carefully to understand what's going on + + align:start position:0% +carefully to understand what's going on + + + align:start position:0% +carefully to understand what's going on +and the first thing to notice about the + + align:start position:0% +and the first thing to notice about the + + + align:start position:0% +and the first thing to notice about the +tree is that it's not all that the + + align:start position:0% +tree is that it's not all that the + + + align:start position:0% +tree is that it's not all that the +structure of the tree leading to the + + align:start position:0% +structure of the tree leading to the + + + align:start position:0% +structure of the tree leading to the +leaves is not the same here's a leaf + + align:start position:0% +leaves is not the same here's a leaf + + + align:start position:0% +leaves is not the same here's a leaf +that has degree one uh sorry here's a + + align:start position:0% +that has degree one uh sorry here's a + + + align:start position:0% +that has degree one uh sorry here's a +here's a leaf that has degree two one + + align:start position:0% +here's a leaf that has degree two one + + + align:start position:0% +here's a leaf that has degree two one +way to get in and only one way out and + + align:start position:0% +way to get in and only one way out and + + + align:start position:0% +way to get in and only one way out and +here's a leaf that has degree three one + + align:start position:0% +here's a leaf that has degree three one + + + align:start position:0% +here's a leaf that has degree three one +way in and two ways out if we think of + + align:start position:0% +way in and two ways out if we think of + + + align:start position:0% +way in and two ways out if we think of +going from the root to the leaf and so + + align:start position:0% +going from the root to the leaf and so + + + align:start position:0% +going from the root to the leaf and so +it's not clear that these branches these + + align:start position:0% +it's not clear that these branches these + + + align:start position:0% +it's not clear that these branches these +leaves should be treated the same way + + align:start position:0% +leaves should be treated the same way + + + align:start position:0% +leaves should be treated the same way +well let's think about it more carefully + + align:start position:0% +well let's think about it more carefully + + + align:start position:0% +well let's think about it more carefully +about how are we going to assign + + align:start position:0% +about how are we going to assign + + + align:start position:0% +about how are we going to assign +probabilities to the various steps of + + align:start position:0% +probabilities to the various steps of + + + align:start position:0% +probabilities to the various steps of +the experiment well what we're going to + + align:start position:0% +the experiment well what we're going to + + + align:start position:0% +the experiment well what we're going to +assume for Simplicity is that the staff + + align:start position:0% +assume for Simplicity is that the staff + + + align:start position:0% +assume for Simplicity is that the staff +uh chooses a door at random to place the + + align:start position:0% +uh chooses a door at random to place the + + + align:start position:0% +uh chooses a door at random to place the +prize so that means that each of these + + align:start position:0% +prize so that means that each of these + + + align:start position:0% +prize so that means that each of these +branches occurs with probability 1/3 a + + align:start position:0% +branches occurs with probability 1/3 a + + + align:start position:0% +branches occurs with probability 1/3 a +third of the time they put the prize + + align:start position:0% +third of the time they put the prize + + + align:start position:0% +third of the time they put the prize +behind door one a third behind door two + + align:start position:0% +behind door one a third behind door two + + + align:start position:0% +behind door one a third behind door two +and a third behind door three okay let's + + align:start position:0% +and a third behind door three okay let's + + + align:start position:0% +and a third behind door three okay let's +continue exploring the branch where they + + align:start position:0% +continue exploring the branch where they + + + align:start position:0% +continue exploring the branch where they +put the prize behind door one at that + + align:start position:0% +put the prize behind door one at that + + + align:start position:0% +put the prize behind door one at that +point the contestant is going to pick a + + align:start position:0% +point the contestant is going to pick a + + + align:start position:0% +point the contestant is going to pick a +door and they can pick either door one + + align:start position:0% +door and they can pick either door one + + + align:start position:0% +door and they can pick either door one +two or three and absent any knowledge um + + align:start position:0% +two or three and absent any knowledge um + + + align:start position:0% +two or three and absent any knowledge um +uh and and also to be sure that they + + align:start position:0% +uh and and also to be sure that they + + + align:start position:0% +uh and and also to be sure that they +can't be out guessed by the staff + + align:start position:0% +can't be out guessed by the staff + + + align:start position:0% +can't be out guessed by the staff +realizing that they mostly prefer door + + align:start position:0% +realizing that they mostly prefer door + + + align:start position:0% +realizing that they mostly prefer door +one so they uh so if they're going to + + align:start position:0% +one so they uh so if they're going to + + + align:start position:0% +one so they uh so if they're going to +switch they'll put the prize behind door + + align:start position:0% +switch they'll put the prize behind door + + + align:start position:0% +switch they'll put the prize behind door +one to fool the contestant the + + align:start position:0% +one to fool the contestant the + + + align:start position:0% +one to fool the contestant the +contestant's protection is pick a door + + align:start position:0% +contestant's protection is pick a door + + + align:start position:0% +contestant's protection is pick a door +at random to have + + align:start position:0% +at random to have + + + align:start position:0% +at random to have +uh choose uh door one a third of the + + align:start position:0% +uh choose uh door one a third of the + + + align:start position:0% +uh choose uh door one a third of the +time and door two a third of the time + + align:start position:0% +time and door two a third of the time + + + align:start position:0% +time and door two a third of the time +and door three at a third time in a + + align:start position:0% +and door three at a third time in a + + + align:start position:0% +and door three at a third time in a +completely unpredictable way and so the + + align:start position:0% +completely unpredictable way and so the + + + align:start position:0% +completely unpredictable way and so the +contestant is going to choose each of + + align:start position:0% +contestant is going to choose each of + + + align:start position:0% +contestant is going to choose each of +those possible doors as their first + + align:start position:0% +those possible doors as their first + + + align:start position:0% +those possible doors as their first +choice with probability a third now what + + align:start position:0% +choice with probability a third now what + + + align:start position:0% +choice with probability a third now what +happens next well the next thing that + + align:start position:0% +happens next well the next thing that + + + align:start position:0% +happens next well the next thing that +happens is that Carol opens a door now + + align:start position:0% +happens is that Carol opens a door now + + + align:start position:0% +happens is that Carol opens a door now +this is the case where Carol has a + + align:start position:0% +this is the case where Carol has a + + + align:start position:0% +this is the case where Carol has a +choice the priz is behind one and the + + align:start position:0% +choice the priz is behind one and the + + + align:start position:0% +choice the priz is behind one and the +contestant happen to pick door one that + + align:start position:0% +contestant happen to pick door one that + + + align:start position:0% +contestant happen to pick door one that +means doors two and three both have + + align:start position:0% +means doors two and three both have + + + align:start position:0% +means doors two and three both have +goats and again for Simplicity let's + + align:start position:0% +goats and again for Simplicity let's + + + align:start position:0% +goats and again for Simplicity let's +assume that Carol when she has a choice + + align:start position:0% +assume that Carol when she has a choice + + + align:start position:0% +assume that Carol when she has a choice +she can open either door two or door + + align:start position:0% +she can open either door two or door + + + align:start position:0% +she can open either door two or door +three here does them with equal + + align:start position:0% +three here does them with equal + + + align:start position:0% +three here does them with equal +probability so we're going to assign + + align:start position:0% +probability so we're going to assign + + + align:start position:0% +probability so we're going to assign +probability a half to her opening door + + align:start position:0% +probability a half to her opening door + + + align:start position:0% +probability a half to her opening door +to uh when she has the choice between + + align:start position:0% +to uh when she has the choice between + + + align:start position:0% +to uh when she has the choice between +two or three and probability a half that + + align:start position:0% +two or three and probability a half that + + + align:start position:0% +two or three and probability a half that +she'll Open Door three and by the way we + + align:start position:0% +she'll Open Door three and by the way we + + + align:start position:0% +she'll Open Door three and by the way we +saw that those were losing outcomes for + + align:start position:0% +saw that those were losing outcomes for + + + align:start position:0% +saw that those were losing outcomes for +the contestant but here things are a + + align:start position:0% +the contestant but here things are a + + + align:start position:0% +the contestant but here things are a +little different if the contestant has + + align:start position:0% +little different if the contestant has + + + align:start position:0% +little different if the contestant has +chose if the prize is behind door one + + align:start position:0% +chose if the prize is behind door one + + + align:start position:0% +chose if the prize is behind door one +and the contestant has chosen door two + + align:start position:0% +and the contestant has chosen door two + + + align:start position:0% +and the contestant has chosen door two +Carol has no choice but to open the only + + align:start position:0% +Carol has no choice but to open the only + + + align:start position:0% +Carol has no choice but to open the only +other unchosen door with the goat behind + + align:start position:0% +other unchosen door with the goat behind + + + align:start position:0% +other unchosen door with the goat behind +it namely door three so we could say + + align:start position:0% +it namely door three so we could say + + + align:start position:0% +it namely door three so we could say +that this Choice really is probability + + align:start position:0% +that this Choice really is probability + + + align:start position:0% +that this Choice really is probability +one um and + + align:start position:0% +one um and + + + align:start position:0% +one um and +uh I got a little bit ahead of myself + + align:start position:0% +uh I got a little bit ahead of myself + + + align:start position:0% +uh I got a little bit ahead of myself +here but having filled in the + + align:start position:0% +here but having filled in the + + + align:start position:0% +here but having filled in the +probabilities on these edges what we + + align:start position:0% +probabilities on these edges what we + + + align:start position:0% +probabilities on these edges what we +figured out is that the probability of + + align:start position:0% +figured out is that the probability of + + + align:start position:0% +figured out is that the probability of +this topmost branch of losing is we said + + align:start position:0% +this topmost branch of losing is we said + + + align:start position:0% +this topmost branch of losing is we said +well a third of the time you go here and + + align:start position:0% +well a third of the time you go here and + + + align:start position:0% +well a third of the time you go here and +a third of that third you go here and + + align:start position:0% +a third of that third you go here and + + + align:start position:0% +a third of that third you go here and +half of that time you go to this vertex + + align:start position:0% +half of that time you go to this vertex + + + align:start position:0% +half of that time you go to this vertex +so it's a third of a third of and half + + align:start position:0% +so it's a third of a third of and half + + + align:start position:0% +so it's a third of a third of and half +of that or a weight of 1/8th and by + + align:start position:0% +of that or a weight of 1/8th and by + + + align:start position:0% +of that or a weight of 1/8th and by +symmetry this gets weight 1/18th but + + align:start position:0% +symmetry this gets weight 1/18th but + + + align:start position:0% +symmetry this gets weight 1/18th but +this way a third of the time the prize + + align:start position:0% +this way a third of the time the prize + + + align:start position:0% +this way a third of the time the prize +is behind door one a third of the time + + align:start position:0% +is behind door one a third of the time + + + align:start position:0% +is behind door one a third of the time +the contestant picks door two and after + + align:start position:0% +the contestant picks door two and after + + + align:start position:0% +the contestant picks door two and after +that Carol is forced to open door three + + align:start position:0% +that Carol is forced to open door three + + + align:start position:0% +that Carol is forced to open door three +so this branch occurs with certainty + + align:start position:0% +so this branch occurs with certainty + + + align:start position:0% +so this branch occurs with certainty +it's with probability one which means + + align:start position:0% +it's with probability one which means + + + align:start position:0% +it's with probability one which means +that we wind up at this Leaf a third of + + align:start position:0% +that we wind up at this Leaf a third of + + + align:start position:0% +that we wind up at this Leaf a third of +a third of the time for sure and its + + align:start position:0% +a third of the time for sure and its + + + align:start position:0% +a third of the time for sure and its +weight is 1 + + align:start position:0% +weight is 1 + + + align:start position:0% +weight is 1 +nth and of course by symmetry the + + align:start position:0% +nth and of course by symmetry the + + + align:start position:0% +nth and of course by symmetry the +similar weights get assigned to the + + align:start position:0% +similar weights get assigned to the + + + align:start position:0% +similar weights get assigned to the +winning and the losing so what we've + + align:start position:0% +winning and the losing so what we've + + + align:start position:0% +winning and the losing so what we've +concluded is that although there are six + + align:start position:0% +concluded is that although there are six + + + align:start position:0% +concluded is that although there are six +wins the weight of the wins is 6 9ths + + align:start position:0% +wins the weight of the wins is 6 9ths + + + align:start position:0% +wins the weight of the wins is 6 9ths +because their e wor worth 1 nth of the + + align:start position:0% +because their e wor worth 1 nth of the + + + align:start position:0% +because their e wor worth 1 nth of the +time and that winning will occur 2third + + align:start position:0% +time and that winning will occur 2third + + + align:start position:0% +time and that winning will occur 2third +of the time likewise there are six + + align:start position:0% +of the time likewise there are six + + + align:start position:0% +of the time likewise there are six +losses but there each only will occur an + + align:start position:0% +losses but there each only will occur an + + + align:start position:0% +losses but there each only will occur an +18th of the time and so we lose onethird + + align:start position:0% +18th of the time and so we lose onethird + + + align:start position:0% +18th of the time and so we lose onethird +of the time by the switch strategy the + + align:start position:0% +of the time by the switch strategy the + + + align:start position:0% +of the time by the switch strategy the +summary then is that the probability of + + align:start position:0% +summary then is that the probability of + + + align:start position:0% +summary then is that the probability of +winning if you switch is 2/3 and by the + + align:start position:0% +winning if you switch is 2/3 and by the + + + align:start position:0% +winning if you switch is 2/3 and by the +remark that you uh uh win with switching + + align:start position:0% +remark that you uh uh win with switching + + + align:start position:0% +remark that you uh uh win with switching +if and only if you lose with sticking it + + align:start position:0% +if and only if you lose with sticking it + + + align:start position:0% +if and only if you lose with sticking it +follows that you lose by sticking two of + + align:start position:0% +follows that you lose by sticking two of + + + align:start position:0% +follows that you lose by sticking two of +the time uh and so sticking is really a + + align:start position:0% +the time uh and so sticking is really a + + + align:start position:0% +the time uh and so sticking is really a +bad strategy and switching is the + + align:start position:0% +bad strategy and switching is the + + + align:start position:0% +bad strategy and switching is the +dominant way to go now we've in class uh + + align:start position:0% +dominant way to go now we've in class uh + + + align:start position:0% +dominant way to go now we've in class uh +we back up this theoretical analysis + + align:start position:0% +we back up this theoretical analysis + + + align:start position:0% +we back up this theoretical analysis +it's very logical but the question is is + + align:start position:0% +it's very logical but the question is is + + + align:start position:0% +it's very logical but the question is is +it true uh and you can do statistical + + align:start position:0% +it true uh and you can do statistical + + + align:start position:0% +it true uh and you can do statistical +experiments and have students pick doors + + align:start position:0% +experiments and have students pick doors + + + align:start position:0% +experiments and have students pick doors +and goats and prizes and sure enough uh + + align:start position:0% +and goats and prizes and sure enough uh + + + align:start position:0% +and goats and prizes and sure enough uh +it turns out that roughly two-thirds of + + align:start position:0% +it turns out that roughly two-thirds of + + + align:start position:0% +it turns out that roughly two-thirds of +the time and closer and closer to 2/3 + + align:start position:0% +the time and closer and closer to 2/3 + + + align:start position:0% +the time and closer and closer to 2/3 +the more times you play the game um the + + align:start position:0% +the more times you play the game um the + + + align:start position:0% +the more times you play the game um the +switching strategy wins 2third of the + + align:start position:0% +switching strategy wins 2third of the + + + align:start position:0% +switching strategy wins 2third of the +time so the second key idea in + + align:start position:0% +time so the second key idea in + + + align:start position:0% +time so the second key idea in +probability theory is that the outcomes + + align:start position:0% +probability theory is that the outcomes + + + align:start position:0% +probability theory is that the outcomes +may have differing probabilities they + + align:start position:0% +may have differing probabilities they + + + align:start position:0% +may have differing probabilities they +may have differing weights unlike the + + align:start position:0% +may have differing weights unlike the + + + align:start position:0% +may have differing weights unlike the +poker hand case when we look more + + align:start position:0% +poker hand case when we look more + + + align:start position:0% +poker hand case when we look more +closely at an exp random experiment with + + align:start position:0% +closely at an exp random experiment with + + + align:start position:0% +closely at an exp random experiment with +different outcomes we will agree that + + align:start position:0% +different outcomes we will agree that + + + align:start position:0% +different outcomes we will agree that +for various kinds of reasons of symmetry + + align:start position:0% +for various kinds of reasons of symmetry + + + align:start position:0% +for various kinds of reasons of symmetry +or logic and so on that it makes sense + + align:start position:0% +or logic and so on that it makes sense + + + align:start position:0% +or logic and so on that it makes sense +to assign different probability weights + + align:start position:0% +to assign different probability weights + + + align:start position:0% +to assign different probability weights +to the different outcomes it's not the + + align:start position:0% +to the different outcomes it's not the + + + align:start position:0% +to the different outcomes it's not the +case that the outcomes have uniform + + align:start position:0% +case that the outcomes have uniform + + + align:start position:0% +case that the outcomes have uniform +probability that they're all equally + + align:start position:0% +probability that they're all equally + + + align:start position:0% +probability that they're all equally +likely so to summarize um uh what + + align:start position:0% +likely so to summarize um uh what + + + align:start position:0% +likely so to summarize um uh what +happens especially well this example + + align:start position:0% +happens especially well this example + + + align:start position:0% +happens especially well this example +illustrates the confusion about a + + align:start position:0% +illustrates the confusion about a + + + align:start position:0% +illustrates the confusion about a +probability theory that was engendered + + align:start position:0% +probability theory that was engendered + + + align:start position:0% +probability theory that was engendered +to even some serious experts but in + + align:start position:0% +to even some serious experts but in + + + align:start position:0% +to even some serious experts but in +general intuition is very important as + + align:start position:0% +general intuition is very important as + + + align:start position:0% +general intuition is very important as +in any subject but it's also dangerous + + align:start position:0% +in any subject but it's also dangerous + + + align:start position:0% +in any subject but it's also dangerous +in probability Theory particularly for + + align:start position:0% +in probability Theory particularly for + + + align:start position:0% +in probability Theory particularly for +beginners who aren't experienced about + + align:start position:0% +beginners who aren't experienced about + + + align:start position:0% +beginners who aren't experienced about +some of these traps that you can fall + + align:start position:0% +some of these traps that you can fall + + + align:start position:0% +some of these traps that you can fall +into and so our proposal is that you be + + align:start position:0% +into and so our proposal is that you be + + + align:start position:0% +into and so our proposal is that you be +very wary of intuitive arguments they're + + align:start position:0% +very wary of intuitive arguments they're + + + align:start position:0% +very wary of intuitive arguments they're +valuable but you need another + + align:start position:0% +valuable but you need another + + + align:start position:0% +valuable but you need another +disciplined way to check them and we + + align:start position:0% +disciplined way to check them and we + + + align:start position:0% +disciplined way to check them and we +propose that you stick with what we call + + align:start position:0% +propose that you stick with what we call + + + align:start position:0% +propose that you stick with what we call +the four-part method when you're trying + + align:start position:0% +the four-part method when you're trying + + + align:start position:0% +the four-part method when you're trying +to devise a probability model for some + + align:start position:0% +to devise a probability model for some + + + align:start position:0% +to devise a probability model for some +random experiment so the the steps are + + align:start position:0% +random experiment so the the steps are + + + align:start position:0% +random experiment so the the steps are +first that you try to identify the + + align:start position:0% +first that you try to identify the + + + align:start position:0% +first that you try to identify the +outcomes of the random experiment and + + align:start position:0% +outcomes of the random experiment and + + + align:start position:0% +outcomes of the random experiment and +this is where the tree structure comes + + align:start position:0% +this is where the tree structure comes + + + align:start position:0% +this is where the tree structure comes +up if you try to model a step by Step at + + align:start position:0% +up if you try to model a step by Step at + + + align:start position:0% +up if you try to model a step by Step at +each stage of the tree what the possible + + align:start position:0% +each stage of the tree what the possible + + + align:start position:0% +each stage of the tree what the possible +substeps are in the overall process that + + align:start position:0% +substeps are in the overall process that + + + align:start position:0% +substeps are in the overall process that +yields the random outcome that's where + + align:start position:0% +yields the random outcome that's where + + + align:start position:0% +yields the random outcome that's where +the tree comes in as we Illustrated with + + align:start position:0% +the tree comes in as we Illustrated with + + + align:start position:0% +the tree comes in as we Illustrated with +Monty Hall uh the next thing to do is + + align:start position:0% +Monty Hall uh the next thing to do is + + + align:start position:0% +Monty Hall uh the next thing to do is +among the outcomes identify the ones + + align:start position:0% +among the outcomes identify the ones + + + align:start position:0% +among the outcomes identify the ones +that you considered to be the winning + + align:start position:0% +that you considered to be the winning + + + align:start position:0% +that you considered to be the winning +events or the or the winning outcomes or + + align:start position:0% +events or the or the winning outcomes or + + + align:start position:0% +events or the or the winning outcomes or +the or the outcomes in the event that + + align:start position:0% +the or the outcomes in the event that + + + align:start position:0% +the or the outcomes in the event that +you are concerned about whether or not + + align:start position:0% +you are concerned about whether or not + + + align:start position:0% +you are concerned about whether or not +it happens getting to Jacks uh picking + + align:start position:0% +it happens getting to Jacks uh picking + + + align:start position:0% +it happens getting to Jacks uh picking +the door with the prize so you need to + + align:start position:0% +the door with the prize so you need to + + + align:start position:0% +the door with the prize so you need to +identify the target event whose + + align:start position:0% +identify the target event whose + + + align:start position:0% +identify the target event whose +probability you're interested in we + + align:start position:0% +probability you're interested in we + + + align:start position:0% +probability you're interested in we +could call it the winning event the + + align:start position:0% +could call it the winning event the + + + align:start position:0% +could call it the winning event the +probability of winning the third key + + align:start position:0% +probability of winning the third key + + + align:start position:0% +probability of winning the third key +step is to try to use the tree and logic + + align:start position:0% +step is to try to use the tree and logic + + + align:start position:0% +step is to try to use the tree and logic +of it to assign probabilities to the + + align:start position:0% +of it to assign probabilities to the + + + align:start position:0% +of it to assign probabilities to the +outcomes uh and the fourth step then is + + align:start position:0% +outcomes uh and the fourth step then is + + + align:start position:0% +outcomes uh and the fourth step then is +simply to compute the probability of the + + align:start position:0% +simply to compute the probability of the + + + align:start position:0% +simply to compute the probability of the +event which you do in a very + + align:start position:0% +event which you do in a very + + + align:start position:0% +event which you do in a very +straightforward Way by basically adding + + align:start position:0% +straightforward Way by basically adding + + + align:start position:0% +straightforward Way by basically adding +up the probabilities of each of the + + align:start position:0% +up the probabilities of each of the + + + align:start position:0% +up the probabilities of each of the +outcomes in the event that is the + + align:start position:0% +outcomes in the event that is the + + + align:start position:0% +outcomes in the event that is the +four-step method now this Monty Hall + + align:start position:0% +four-step method now this Monty Hall + + + align:start position:0% +four-step method now this Monty Hall +tree that we came up with was um very + + align:start position:0% +tree that we came up with was um very + + + align:start position:0% +tree that we came up with was um very +literal and uh wildly unnecessarily + + align:start position:0% +literal and uh wildly unnecessarily + + + align:start position:0% +literal and uh wildly unnecessarily +complicated so let's take another look + + align:start position:0% +complicated so let's take another look + + + align:start position:0% +complicated so let's take another look +at that and a simpler argument that will + + align:start position:0% +at that and a simpler argument that will + + + align:start position:0% +at that and a simpler argument that will +lead us to the same conclusion about how + + align:start position:0% +lead us to the same conclusion about how + + + align:start position:0% +lead us to the same conclusion about how +the Monty hle game works and we'll do + + align:start position:0% +the Monty hle game works and we'll do + + + align:start position:0% +the Monty hle game works and we'll do +that in the next video \ No newline at end of file diff --git a/dSviy9E6Pz0.txt b/dSviy9E6Pz0.txt new file mode 100644 index 0000000000000000000000000000000000000000..e371d599b472f96c184f73103145a2ea1532e518 --- /dev/null +++ b/dSviy9E6Pz0.txt @@ -0,0 +1,3870 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK. + +Just to review where we are, +we've been talking about + +source coding as one of the +two major parts of digital + +communication. + +Remember, you take sources, +you turn them into bits. + +Then you take bits and you +transmit them over channels. + +And that sums up the +whole course. + +This is the part where you +transmit over channels. + +This is the part where you +process the sources. + +We're concentrating now on the +source side of things. + +Partly because by concentrating +on the source + +side of things, we will build +up the machinery we need to + +look at the channel +side of things. + +The channel side is really more +interesting, I think. + +Although there's been a great +deal of work on both of them. + +They're both important. + +And we said that we could +separate source coding into + +three pieces. + +If you start out with a waveform +source, the typical + +thing to do, and almost the only +thing to do, is to turn + +those waveforms into sequences +of numbers. + +Those sequences might +be samples. + +They might be numbers +in an expansion. + +They might be whatever. + +But the first thing you almost +always do is turn waveforms + +into a sequence of numbers. + +Because waveforms are just too +complicated to deal with. + +The next thing we do with +a sequence of numbers is + +quantize them. + +After we quantize them +we wind up with a + +finite set of symbols. + +And the next thing +we do is, we take + +that sequence of symbols. + +And -- + +and what we do at that point +is to do data compression. + +So that we try to represent +those symbols with as small as + +possible a number of binary +digits per source symbol. + +We want to do that in such +a way that we can receive + +it the other end. + +So let's review a little bit +about what we've done in the + +last couple of lectures. + +We talked about the +Kraft inequality. + +And the Kraft inequality, you +remember, says that the + +lengths of the codewords in any +prefix-free code have to + +satisfy this funny +inequality here. + +And this funny inequality, in +some sense, says if you want + +to make one codeword short, by +making that one codeword + +short, it eats up a large +part of this fraction. + +Since this sum has to be less +than or equal to 1. + +If, for example, you make l sub +1 equal to 1, then that + +uses up a half of this +sum right there. + +And all the other codewords +have to be much longer. + +So what this is saying, +essentially, and we proved it, + +and we did a bunch of things +with it, and your homework you + +worked with it, we have +shown that that + +inequality has to hold. + +The next thing we did is, given +a set of probabilities + +on a source, for example, p1 +up to p sub m, by this time + +you should feel very comfortable +in realizing that + +what you call these symbols +doesn't make any difference + +whatsoever as far +as any matter of + +encoding sources is concerned. + +The first thing you can do, if +you like to, is take whatever + +name somebody has given to a set +of symbols, replace them + +with your own symbols, and the +easiest set of symbols to use + +is the integers 1 to m. + +And that's what we +will usually do. + +So, given this set of +probabilities, and they have + +to add up to 1, the Huffman +algorithm is this ingenious + +algorithm, very, very, clever, +which constructs a prefix-free + +code of minimum expected +length. + +And that minimum expected length +is just defined as the + +sum over i, of p sub +i times l sub i. + +And the trick in the algorithm +is to find that set of l sub + +i's that satisfy this inequality +but minimize this + +expected value. + +Next thing we started to talk +about was a discrete + +memoryless source. + +A discrete memoryless source +is really a toy source. + +It's a toy source where you +assume that each letter in the + +sequence is independent, and +equally independent, and + +identically distributed. + +In other words, every +letter is the same. + +Every letter is independent +of every other letter. + +That's more appropriate for a +gambling game than it is for + +real sources. + +But, on the other hand, by +understanding this problem, + +we're starting to see that we +understand the whole problem + +of source coding. + +So we'll get on with +that as we go. + +But, anyway, when we have a +discrete memoryless source, + +what we found -- first we +defined the entropy of such a + +source as h of x, which is the +sum over i of minus p sub i, + +of logarithm of p sub i. + +And that was just something that +came out of trying to do + +this optimization not the way +that Huffman did it but the + +way that Shannon did it. + +Namely, Shannon looked at this +optimization in terms of + +dealing with entropy and +things like that. + +Huffman dealt with it in terms +of finding the optimal code. + +One of the very surprising +things is that the way Huffman + +looked at it, in terms of +entropy, is the way this + +really valuable, even though +it doesn't come up with an + +optimal code. + +I mean, here was poor Huffman, +who generated this beautiful + +algorithm, which is +extraordinarily simple, which + +solved what looked like +a hard problem. + +But yet, as far as information +theory is concerned, he used + +that algorithm, sure. + +But as far as all the +generalizations are concerned, + +it has almost nothing +to do with anything. + +But, anyway, when you look at +this entropy, what comes out + +of it is the fact that the +entropy of the source is less + +than or equal to the minimum +number of bits per source + +symbol that you can come up with +in a prefix-free code, + +which is less than +h of x plus 1. + +And the way we did that was just +to try to look at this + +minimization. + +And by looking at the +minimization, we usually + +showed it had to be greater +than or equal to H of x. + +And by looking at any code +which satisfied this + +inequality with any +set of length -- + +well, after we looked at this, +this said that what we really + +wanted to do was to make the +length of each codeword minus + +log of p sub i. + +That's not an integer. + +So the thing we did to get this +inequality is said, OK, + +if it's not an integer, we'll +raise it up the next value. + +Make it an integer. + +And as soon as we do that, the +Kraft inequality is satisfied. + +And you can generate a code +with that set of lengths. + +So that's where you get +these two bounds. + +This bound here is usually +very, very weak. + +Can anybody suggest the almost +unique example where this is + +almost tight? + +It's a simplistic sample +you can think of. + +It's a binary source. + +And what binary source has the +property that this is almost + +equal to this? + +Anybody out there? + +AUDIENCE: [UNINTELLIGIBLE] + +PROFESSOR: Make it almost +probability 0 + +and probability 1. + +You can't quite do that because +as soon as you make + +the probability of the 0, 0, +then you don't have to + +represent it. + +And you just know that it's +a sequence of all 1's. + +So you're all done. + +And you don't need any +bits to represent it. + +But if there's just some very +tiny epsilon probability of a + +0 and a big probability of a 1, +then the entropy is almost + +equal to 0. + +And this 1 here is needed +because l bar min is 1. + +You can't make it any +smaller than that. + +So, that's where that +comes from. + +Let's talk about entropy +just a little bit. + +If we have an alphabet which +has size m, which is the + +symbol we'll usually use +for the alphabet, x. + +And the probability that +x equals i, is p sub i. + +In other words, again, we're +using this convention so we're + +going to call the symbols the +integers 1 to capital M. Then + +the entropy is equal to this. + +And a nice way of representing +this is that the entropy is + +equal to the expected value +of minus the logarithm. + +Logarithms are always to the +base 2, in this course. + +When we want natural logarithms +we'll write ln, in + +other words it's log +to the base 2. + +So it's log to the base +2 of the probability + +of the symbol x. + +We call this the log pmf +random variable. + +We started out with x being +a chance variable. + +I mean, we happen to have +turned it into a random + +variable because we've +given it numbers. + +But that's irrelevant. + +We really want to think of +it as a chance variable. + +But now this quantity is a +numerical function of the + +symbol which comes out +of the source. + +And, therefore, this +quantity is a + +well-defined random variable. + +And we call it the log +pmf random variable. + +Some people call it +self-information. + +We'll find out why later. + +I don't particularly +like that word. + +One, because what we're dealing +with here has nothing + +to do with information. + +Probably the thought that this +all has something to do with + +information, namely, that +information theory has + +something to do with +information, probably held up + +the field for about +five years. + +Because everyone tried to figure +out, what does this + +have to do with information. + +And, of course, it had nothing +to do with information. + +It really only had +to do with data. + +And with probabilities of +various things in the data. + +So, anyway. + +Some people call it +self-information and + +we'll see why later. + +But this is the quantity +we're interested in. + +And we call it log pmf, +we sort of forget + +about the minus sign. + +It's not good to forget +about the minus sign, + +but I always do it. + +So I sort of expect other +people to do it, too. + +One of the properties of entropy +is, it has to be + +greater than or equal to 0. + +Why is it greater than +or equal to 0? + +Well, because these +probabilities here have to be + +less than or equal to 1. + +And the logarithm of something +less than or + +equal to 1 is negative. + +And therefore minus the +logarithm has to be greater + +than or equal to 0. + +This entropy is also less than +or equal to log M, log capital + +M. I'm not going to +prove that here. + +It's proven in the notes, it's +a trivial thing to do. + +Or maybe it's proven in one +of the problems, I forget. + +But, anyway, you can do it using +the inequality log of x + +is less than or equal +to x minus 1. + +Just like all inequalities +can be proven with that + +inequality. + +So there's a quality here +if x is equiprobable. + +Which is pretty clear, because +if all of these probabilities + +are equal to 1 over M, and you +take the expected value of + +logarithm of M, you get +logarithm of M. So there's + +nothing very surprising here. + +Now, the next thing -- and +here's where what we're going + +to do is, on one hand very +simple, and on the other hand + +very confusing. + +After you get the picture of +it, it becomes very simple. + +Before that, it all looks +rather strange. + +If you have two independent +chance variables, say x and y, + +then the choice where the sample +value of the chance + +variable x, and the choice of +the sample value y, together + +that's a pair of sample values +which we can view as one + +sample value. + +In other words, we can view xy +as a chance variable all in + +its own right. + +This isn't the sequence x, +followed by y, where you can + +think of it that way. + +But we want to think +of this here as a + +chance variable itself. + +Which takes on different +values. + +And the values it takes on are +pairs of sample values, 1 from + +x, 1 from ensemble y, and xy +takes on the sample value of + +little xy with the probability +p of x times p of y. + +As we move one with this course, +we'll become much less + +careful about putting these +subscripts down, which talk + +about random variables. + +And the arguments which talk +about sample values of those + +random variables. + +I want to keep doing it for a +while because most courses in + +probability, even 6.041, which +is the first course in + +probability, almost deliberately +fudges the + +difference between sample values +and random variables. + +And most people who work +with probability do + +this all the time. + +And you never know when you're +talking about a random + +variable and when you're talking +about a sample value + +of a random variable. + +And that's convenient for +getting insight about thing. + +And you do it for a while and +then pretty soon you wonder, + +what the heck is going on. + +Because you have no idea what's +a random variable any + +more, and what's a sample +value of it. + +So, this entropy, H, of the +chance variable, xy, is then + +expected value of minus the +logarithm of the probability + +of the chance variable, xy. + +Mainly, when you take the +expected value, you're taking + +the expected value of +a random variable. + +And for the random variable +here, in the chance variables, + +xy and here. + +This is the expected value of +minus the logarithm of p of x + +times the probability p of x. + +Which is the expected value. + +Since they're independent of +each other it's the sum. + +And that gives you H of x y is +equal to H of x plus H of y. + +This is really the reason why +you're interested in these + +chance variables which are +logarithms of probabilities. + +Because when you have +independent chance variables + +then you have the situation that +probabilities multiply + +and therefore log probabilities +add. + +All of the major theorems in +probability theory, in + +particular the law of large +numbers, which is the most + +important result in probability, +simple though it + +might be, that's the key to +everything in probability. + +That particular result talks +about sums of random variables + +and not about products +of random variables. + +So that's why Shannon did +everything in terms + +of these log PMF. + +And we will soon be doing +everything in + +terms of log PMF also. + +So now let's get back to +discrete memoryless sources. + +If you now have a block of n +chance variables, x1 to xn, + +and they're all IID, again we +can do this whole block as one + +big monster chance variable. + +If each one of these takes on +m possible values, then this + +monster chance variable +can take on m to + +the n possible values. + +Namely, each possible string +of symbols, each possible + +string of n symbols where each +one is a choice from the + +integers 1 to capital M. So +we're talking about tuples of + +numbers now. + +And those are the values that +this particular chance + +variable, x sub n, takes on. + +So it takes on these +probabilities, takes on these + +values with the probability p +of x n is the product from i + +equals 1 to n, of the individual +probabilities. + +In other words, again, when you +have independent chance + +variables, the probabilities +multiply. + +Which is all I'm saying here. + +So the chance variable x sub +n has the entropy H of x n, + +which is the expected value of +minus the logarithm of that + +probability. + +Which is the expected value of +minus the logarithm of the + +product of probabilities, which +is the expected value of + +the sum of minus the log of the +probabilities, which is n + +times H of x. + +If you compare this with the +previous slide, you'll see I + +haven't said anything new. + +This argument and this +argument are + +really exactly the same. + +All I did was do it for two +chance variables first. + +And then observe. + +But it generalizes, +to an arbitrary + +number of chance variables. + +You can say that it generalizes +to an infinite + +number of chance +variables also. + +And in some sense it does. + +And I would advise you +not to go there. + +Because you just get tangled up +with a lot of mathematics + +that you don't need. + +So the next thing is, how +do we fix the variable + +prefix-free codes and what +do we gain by it? + +So the thing we're going to do +now, instead of trying to + +compress one symbol at a time +from the source, we're going + +to segment the source into +blocks of n symbols each. + +And after we segment it into +blocks of n symbols each, + +we're going to encode the +block of n symbols. + +Now, what's new there? + +Nothing whatsoever is new. + +A block of n symbols is just +a chance variable. + +We know how to do optimal +encoding of chance variables. + +Namely, we use the Huffman +algorithm. + +You can do that here +on these n blocks. + +We also have this nice theorem, +which says that the + +entropy -- well, first the +entropy of x n as n times the + +entropy of x. + +So, in other words, when you +have independent identically + +distributed chance variables, +this entropy is just n times + +this entropy. + +But the important thing +is this result + +of doing the encoding. + +Which is the same result +we had before. + +Namely, this is the result of +what happens when you take a + +set -- when you take an +alphabet, and the alphabet can + +be anything whatsoever. + +And you encode that alphabet in +an optimal way, according + +to the probabilities of each +symbol within the alphabet. + +And the result that you get is +the entropy of this big chance + +variable x sub n is less than +or equal to the minimum -- + +well, it's less than or equal +to the expected value of the + +length of a code, whatever +code you have. + +But when you put the minimum on +here, this is less than the + +entropy of the chance variable +x super n plus 1. + +That's the same theorem +that we proved before. + +There's nothing new here. + +Now, if you divide this by n, +this by n, and this by n, you + +still have a valid inequality. + +When you divide this by +n, what do you get? + +You get H of x. + +When you divide this by n, +by definition L bar -- + +what we mean is the number of +bits per source symbol. + +We have n source symbols here. + +So when we divide by n, we get +the number of bits per source + +symbol in this monster symbol. + +So l min is equal to this. + +When we divide this +by n, we get this. + +When we divide this by +n, we get H of x. + +And now the whole reason for +doing this is, this silly + +little 1 here, which we're +trying very hard to think of + +as being negligible or +unimportant, has suddenly + +become 1 over n. + +And by making n big enough, +this truly is unimportant. + +If you're thinking in terms of +encoding a binary source, this + +1 here is very important. + +In other words, when you're +trying to encode a binary + +source, if you're encoding one +letter at a time, there's + +nothing you can do. + +You're absolutely stuck. + +Because if both of those +letters have non-zero + +probabilities, and you want a +uniquely decodable code, and + +you want to find codewords for +each of those two symbols, the + +best you can do is to have +an expected length of 1. + +Namely, you need 1 to encode 1, +and you need 0 to encode 0. + +And there's nothing else, +there's no freedom at + +all that you have. + +So you say, OK, in that +situation, I really have to go + +to longer blocks. + +And when I go to longer +blocks, I + +can get this resolved. + +And I know how to do it. + +I use Huffman's algorithm +or whatever. + +So, suddenly, I can start to +get the expected number of + +bits per source symbol. + +Down as close to h of x +as I want to make it. + +And I can't make +it any smaller. + +Which says that H of x now has +a very clear interpretation, + +at least for prefix-free codes, +of being the number of + +bits you need for encoding +prefix-free codes when you + +allow the possibility +of encoding them + +a block at a time. + +We're going to find later today +that the significance of + +this is far greater +than that, even. + +Because why use prefix-free +codes, we could use any old + +kind of code. + +When we study the Lempel-Ziv +codes tomorrow, we'll find out + +they aren't prefix-free +codes at all. + +They're really variable length +of variable length codes. + +So they aren't fixed +to variable length. + +And they do some pretty fancy +and tricky things. + +But they're still limited +to this same inequality. + +You can never beat the +entropy bound. + +If you want something to be +uniquely decodable, you're + +stuck with this bound. + +And we'll see why in a very +straightforward way, later. + +It's a very straightforward way +which I can guarantee all + +of you are going to look at it +and say, yes, that's obvious. + +And tomorrow you will look at it +and say, I don't understand + +that at all. + +And the next day you'll +look at it again and + +say, well, of course. + +And the day after that you'll +say, I don't understand that. + +And you'll go back and forth +like that for about two weeks. + +Don't be frustrated, because +it is simple. + +But at the same time it's +very sophisticated. + +So, let's now review the weak +law of large numbers. + +I usually just call it the +law of large numbers. + +I bridle a little bit when +people call it weak because, + +in fact it's the centerpiece +of probability theory. + +But there is this other thing +called the strong law of large + +numbers, which mathematicians +love because it lets them look + +at all kinds of mathematical +minutiae. + +It's also important, +I shouldn't + +play it down too much. + +And there are places where +you truly need it. + +For what we'll be doing, we +don't need it at all. + +And the weak law of large +numbers does in fact hold in + +many places where the strong +law doesn't hold. + +So if you know what the strong +law, is temporarily forget it + +for the for the rest +of the term. + +And just focus on +the weak law. + +And the weak law is not +terribly complicated. + +We have a sequence of +random variables. + +And each of them has +a mean y bar. + +And each of them has a variance +sigma sub y squared. + +And let's assume that they're +independent and identically + +distributed for the +time being. + +Just to avoid worrying +about anything. + +If we look at the sum of those +random variables, namely a is + +equal to y1 up to y sub n. + +Then the expected value of a is +the expected value of this + +plus the expected valuable +of y2, and so forth. + +So the expected value of +a is n times y bar. + +And I think in one of the +homework problems, you found + +the variance of a. + +And the variance of a, well, the +easiest thing to do is to + +reduce this to its +fluctuation. + +Reduce all of these to +their fluctuation. + +Then look at the variance of the +fluctuation, which is just + +the expected value +of this squared. + +Which is the expected value of +this squared plus the expected + +value of this squared, +and so forth. + +So the variance of a is n times +sigma sub y squared. + +I want all of you know that. + +That's sort of day two of +a probability course. + +As soon as you start talking +about random variables, that's + +one of the key things +that you do. + +One of the most important +things you do. + +The thing that we're interested +in here is more the + +sample average of y1 +up to y sub n. + +And the sample average, +by definition, is the + +sum divided by n. + +So in other words, the thing +that you're interested in here + +is to add all of these +random variables up. + +Take one over n times it. + +Which is a thing we +do all the time. + +I mean, we sum up a lot of +events, we divide by n, and we + +hope by doing that to get some +sort of typical value. + +And, usually there is some sort +of typical value that + +arises from that. + +What the law of large numbers +says is that there in fact is + +a typical value that arises. + +So this sample value is +a over n, which is the + +sum divided by n. + +And we call that the +sample average. + +The mean of the sample average +is just the mean of a, which + +is n times y bar, +divided by n. + +So the mean of the sample +average is y bar itself. + +The variance of the sample +variance, -- + +the variance of the sample +average, OK, that's, -- + +I'm talking too fast. + +The sample average here, you +would like to think of it as + +something which is known +and specific, like + +the expected value. + +It, in fact, is a +random variable. + +It changes with different +sample values. + +It can change from almost +nothing to very large + +quantities. + +And what we're interested in +saying is that most of the + +time, it's close to the +expected value. + +And that's what we're +aiming at here. + +And that's what the law +of large numbers says. + +The sample average here, the +variance of this, is now equal + +to the variance of a divided +by n squared. + +In other words, we're trying to +take the expected value of + +this quantity squared. + +So there's a 1 over n squared +that comes in here. + +When you take the 1 over n +squared here, this variance + +then becomes sigma -- + +I don't know why I +have the n there. + +Just take that n out, +if you will. + +I don't have my red +pen with me. + +And so it's the variance +of the random variable + +y, divided by n. + +In other words, the limit as n +goes to infinity of the of the + +variance of the sum is +equal to infinity. + +And the variance of the sample +average as n goes to infinity + +is equal to 0. + +And that's because of this 1 +over n squared effect here. + +When you add up a lot of +independent random variables, + +what you wind up with is the +sample average has a variance, + +which is going to 0. + +And the sum has a variance which +is going to infinity. + +That's important. + +Aside from all of the theorems +you've ever heard, this is + +sort of the gross, simple-minded +thing which you + +always ought to keep foremost +in your mind. + +This is what's happening +in probability theory. + +When you talk about sample +averages, this variance is + +getting small. + +Let's look at a picture +of this. + +Let's look at the distribution +function + +of this random variable. + +The sample average as +a random variable. + +And what we're finding here +is that this distribution + +function, if we look at it for +some modest value of n, we get + +something which looks like +this upper curve here. + +Which is then the lower +curve here. + +It's spread out more, so it +has a larger variance. + +Namely, the sample average +has a larger variance. + +When you make n bigger, what's +happening to the variance? + +The variance is getting +smaller. + +The variance is getting smaller +by a factor of 1/2. + +So this quantity is supposed +to have a variance which is + +equal to 1/2 of the +variance of this. + +How you find a variance +in a distribution + +function is your problem. + +But you know that if something +has a small variance, it's + +very closely tucked +in around this. + +In other words, as the variance +goes to 0, and the + +mean is y bar, you have a +distribution function which + +approaches a unit step. + +And all that just comes from +this very, very simple + +argument that says, when you +have a sum of IID random + +variables and you take the +sample average of it, namely, + +you divide by n, the +variance goes to 0. + +Which says, no matter how you +look at it, you wind up with + +something that looks +like a unit step. + +Now, the Chebyshev inequality, +which is one of the simpler + +inequalities in probability +theory, and I don't prove it + +because it's something +you've all seen. + +I don't know of any course in +probability which avoids the + +Chebyshev inequality. + +And what it says is, for any +epsilon greater than 0, the + +probability that the difference +between the sample + +average and the true mean, the +probability that that quantity + +and magnitude is greater than +or equal to epsilon, is less + +than or equal to sigma +sub y squared divided + +by n epsilon squared. + +Oh, incidentally that thing that +was called sigma sub n + +before was really +sigma squared. + +That's mainly the +variance of y. + +I hope it's right +in the notes. + +Might not be. + +It is? + +Good. + +So, that's what this +inequality says. + +There's an easy way to derive +this on the fly. + +Namely, if you're wondering what +all these constants are + +here, here's a way to do it. + +What we're looking at, in this +curve here, is we're trying to + +say, how much probability is +there outside of these plus + +and minus epsilon limits. + +And the Chebyshev inequality +says there can't be too much + +probability out here. + +And there can't be too much +probability out here. + +So, one way to get at this is +to say, OK, suppose I have + +some given probability +out here. + +And some given probability +out here. + +And suppose I want to minimize +the variance of a random + +variable which has that much +probability out here and that + +much probability out here. + +How do I do it? + +Well, the variance deals with +the square of how far you were + +away from the mean. + +So if I want to have a certain +amount of probability out + +here, I minimize my variance by +making this come straight, + +come up here with a little step, +then go across here. + +Go up here. + +And then, oops. + +Go up here. + +I wish I had my red pencil. + +Does anybody have a red pen? + +That will write on this stuff? + +Yes? + +No? + +Oh, great. + +Thank you. + +I will return it. + +So what we want is something +which goes over here. + +Comes up here. + +Goes across here. + +Goes up here. + +Goes across here, and +goes up again. + +That's the smallest you +can make the variance. + +It's squeezing everything +in as far as it + +can be squeezed in. + +Namely, everything out +here gets squeezed + +in to y minus epsilon. + +Everything in here gets +squeezed into 0. + +And everything out here gets +squeezed into epsilon. + +OK, calculate the +variance there. + +And that satisfies +the Chebyshev + +inequality with equality. + +So that's all the Chebyshev +inequality is. + +And it's a loose inequality +usually, because usually these + +curves look very nice. + +Usually this looks like a +Gaussian distribution + +function, and the central limit +theorem says that we + +don't need the central limit +theorem here, and we don't + +want the central limit theorem +here, because this thing is an + +inequality that says, life can't +be any worse than this. + +And all the central limit +theorem is, is an + +approximation. + +And then we have to worry +about when it's a good + +approximation and when it's +not a good approximation. + +So this says, when we carry it +one piece further, it's for + +any epsilon and delta +greater than 0. + +If we make n large enough -- +in other words, substitute + +delta for this. + +And then, when you make n small +enough, this quantity is + +smaller than delta. + +And that says that the +probability that s and y + +differ by more than epsilon is +less than or equal to delta + +when we make n big enough. + +So it says, you can make this +as small as you want. + +You can make this as +small as you want. + +And all you need to do +is make a sequence + +which is long enough. + +Now, the thing which is +mystifying about the law of + +large numbers is, you +need both the + +epsilon and the delta. + +You can't get rid of +either of them. + +In other words, you +can't say -- + +you can't reduce this to 0. + +Because it won't +make any sense. + +In other words, this +curve here tends to + +spread out on its tails. + +And therefore, there's always a +probability of error there. + +You can't move epsilon into 0 +because, for no finite end, do + +you really get a step +function here. + +So you need some wiggle +room on both end. + +You need wiggle room here, and +you need wiggle room here. + +And once you recognize that you +need those two pieces of + +wiggle room. + +Namely, you cannot talk about +the probability that this is + +equal to y bar, because +that's usually 0. + +And you cannot talk about +reducing this to 0 either. + +So both of those are needed. + +Why did I go through +all of this? + +Well, partly because +it's important. + +But partly because I want to +talk about something which is + +called the asymptotic +equipartition property. + +And because of those long words +you believe this has to + +be very complicated. + +I hope to convince you that +what the asymptotic + +equipartition property is, is +simply the week law of large + +numbers applied to +the log pmf. + +Because that, in fact, +is all it is. + +But it says some unusual +and fascinating things. + +So let's suppose that x1, x2, +and so forth is the output + +from a discrete memoryless +source. + +Look at the log pmf +of each of these. + +Namely, they each have the same +distribution function. + +So w of f x is going to be equal +to minus the logarithm + +of p sub x of x, for each of +these chance variables. + +w of x maps source symbols +into real numbers. + +So there's a random variable, +capital W of x sub j, which is + +a random variable. + +We have a random variable for +each one of these symbols to + +come out of the source. + +So, for each one of these +symbols, there's this log pmf + +random variable, which takes +on different values. + +So the expected value of this +log pmf, for the j'th symbol + +out of the source is the sum +of p sub x of x, namely the + +probability that the source +takes on the value x, times + +minus the logarithm +of p sub x. + +And that's just the entropy. + +So, the strange feeling about +this log pmf random variable + +is its expected value +is entropy. + +And w of x1, w of x2, and so +forth, are a sequence of IID + +random variables, each one of +them which has a mean, which + +is the entropy. + +So it's just exactly the +situation we had before. + +Instead of y bar, we have +the entropy of x. + +And instead of the random +variable y sub j, we have this + +random variable w of x sub j, +which is defined by the symbol + +in an alphabet. + +And just to review this, but +it's what we said before, if + +capital X1, this little x1, +namely, if little x1 is the + +sample value for the chance +variable x1 and if x2 is a + +sample value for the chance +variable X2, then the outcome + +for w of x1 plus w of x2 -- + +very hard to keep all these +little letters and capital + +letters straight. + +Is w of x1 plus w of x2 is minus +the logarithm of the + +probability of x1 minus the +logarithm of the probability + +of x2, which is minus the +logarithm of the product, + +which is minus the logarithm of +the joint probability of x1 + +and x2, which is the random +variable w of x1 x2. + +So the sum here is the random +variable corresponding to log + +pmf of the joint outputs +x1 and x2. + +So w of x1 x2 is the log pmf of +the event, but this joint + +chance variable takes +on the value x1 x2. + +And the random variable x1 x2 +is the sum of x1 and x2. + +So, what have I done here? + +I said this at the end of the +last slide, and you won't + +believe me. + +So, again this is one of these +things where tomorrow you + +won't believe me. + +And you'll have to go back +and look at that. + +But, anyway, x1 x2 is +a chance variable. + +And probabilities multiply in +log pmf's add, which is what + +we've been saying for a +couple of days now. + +So. + +If I look at the sum of n of +these random variables, the + +sum of these log probabilities +is the sum of the log of + +pmf's, which is minus the +logarithm of the probability + +of the entire sequence. + +That's just saying the same +thing we said before, for two + +random variables. + +The sample average of a log +pmf's is the sum of the w's + +divided by n, which is minus +the logarithm of the + +probability divided by n. + +The weak law of large numbers +applies, and the probability + +that this sample average minus +the expected value of w of x + +is greater than or equal to +epsilon is less than or equal + +to this quantity here. + +This quantity is minus the +logarithm of the probability + +of x sub n, divided by n, minus +H of x, greater than or + +equal to epsilon. + +So this is the thing that +we really want. + +I'm going to spend a few +slides trying to + +say what this means. + +But let's try to just look +at it now, and see + +what it must mean. + +It says that with high +probability, this quantity is + +almost the same as +this quantity. + +It says that with high +probability, the thing which + +comes out of the source is going +to have a probability, a + +log probability, divided by n, +which is close to the entropy. + +It says in some sense that with +high probability, the + +probability of what +comes out of the + +source is almost a constant. + +And that's amazing. + +That's what you'll wake up in +the morning and say, I don't + +believe that. + +But it's true. + +But you have to be careful +to interpret it right. + +So, we're going to define +the typical set. + +Namely, this is the typical set +of x's, which come out of + +the source. + +Namely, the typical +set of blocks of n + +symbols out of the source. + +And when you talk about a +typical set, you want + +something which includes most +of the probability. + +So what I'm going to include in +this typical set is all of + +these things that we talked +about before. + +Namely, we showed that the +probability that this quantity + +is greater than or equal to +epsilon is very small. + +So, with high probability what +comes out of the source + +satisfies this inequality +here. + +So I can write down the +distribution function of this + +random variable here. + +It's just this w -- + +this is a random variable w. + +I'm looking at the distribution +of that random + +variable w. + +And this quantity in here is +the probability of this + +typical set. + +In other words, when I draw this +distribution function for + +this combined random variable, +I've defined this typical set + +to be all the sequences which +lie between this point and + +this point. + +Namely, this is H +minus epsilon. + +And this is H plus epsilon, +moving H out here. + +So these are all the sequences +which satisfy + +this inequality here. + +So that's what I mean +by the typical set. + +It's all things which are +clustered around H in this + +distribution function. + +And as n approaches infinity, +this typical set approaches + +probability 1. + +In the same way that the +law of large numbers + +behaves that way. + +The probability that x sub n +is in this typical set is + +greater than or equal to 1 minus +sigma squared divided by + +n epsilon squared. + +Let's try to express that in +a bunch of other ways. + +If you're getting lost, +please ask questions. + +But I hope to come back to this +in a little bit, after we + +finish a little more +of the story. + +So, another way of expressing +this typical set -- let me + +look at that as the +typical set. + +If I take this inequality here +and I rewrite this, namely, + +this is the set of x's for +which this is less than + +epsilon plus H of x +and greater than + +H of x minus epsilon. + +So that's what I've +expressed here. + +It's the set of x's for which +n times H of x minus epsilon + +is less than this logarithm of +probability is great less than + +n times H of x plus epsilon. + +Namely, I'm looking at this +range of epsilon around H, + +which is this and this. + +If I write it again, if I +exponentiate all of this, it's + +the set of x's for which 2 to +the minus n, H of x, plus + +epsilon, that's this term +exponentiated, is less than + +this is less than this +term exponentiated. + +And what's going on here +is, I've taken care of + +the minus sign also. + +And if you can follow that in +your head, you're a better + +person than I am. + +But, anyway, it works. + +And if you fiddle around with +that, you'll see that that's + +what it is. + +So this typical set is a bound +on the probabilities of all + +these typical sequences. + +The typical sequences all are +enclosed in this range of + +probabilities. + +So the typical elements are +approximately equiprobable, in + +this strange sense above. + +Why do I say this is +a strange sense? + +Well, as n gets large, +what happens here? + +This is 2 to the minus +n times H of x. + +Which is the important +part of this. + +This epsilon here is +multiplied by n. + +And we're trying to say, as n +gets very, very big, we can + +make epsilon very, very small. + +But we really can't make n times +epsilon very negligible. + +But the point is, the important +thing here is, 2 to + +the minus n times H of x. + +So, in some sense, this +is close to 2 to the + +minus n H of x. + +In what sense is it true? + +Well, it's true in that sense. + +Where that, in fact is, +a valid inequality. + +Namely in terms of +sample averages, + +these things are close. + +When I do the exponentiation and +get rid of the n and all + +that stuff, they aren't +very close. + +But saying this sort of thing is +sort of like saying that 10 + +to the minus 23 is approximately +equal to 10 to + +the minus 25. + +And they're approximately equal +because they're both + +very, very small. + +And that's the kind of thing +that's going on here. + +And you're trying to distinguish +10 to the minus 23 + +and 10 to the minus 25 from 10 +to the minus 60th and from 10 + +to the minus three. + +So that's the kind of +approximations we're using. + +Namely, we're using +approximations on a log scale, + +instead of approximations +of ordinary numbers. + +But, still it's convenient to +think of these typical x's, + +typical sequences, as being +sequences which are + +constrained in probability +in this way. + +And this is the thing which +is easy to work with. + +The atypical set of strings, +namely, the compliment to this + +set, the thing we know about +that is the entire set doesn't + +have much probability. + +Namely, if you fix epsilon and +you let n get bigger and + +bigger, this atypical set +becomes totally negligible. + +And you can ignore it. + +So let's plow ahead. + +Stop for an example pretty +soon, but -- + +If I have a sequence which is +in the typical set, we then + +know that its probability is +greater than 2 to the minus n + +times H of x plus epsilon. + +That's what we said before. + +And, therefore, when I use +this inequality, the + +probability of x to the n, for +something in the typical set, + +is greater than this +quantity here. + +In other words, this is +greater than that. + +For everything in +a typical set. + +So now I'm heading over things +in a typical set. + +So I need to include the +number of things + +in a typical set. + +So what I have is this sum. + +And what is this sum? + +This is the probability +of the typical set. + +Because I'm adding overall +elements in the typical set. + +And it's greater than or equal +to the number of elements in a + +typical set times these +small probabilities. + +If I turn this around, it says +that the number of elements in + +a typical set is less +than 2 to the n + +times H of x plus epsilon. + +For any epsilon, no matter how +small I want to make it. + +Which says that the elements +in a typical set have + +probabilities which are about 2 +to the minus n times H of x. + +And the number of them is +approximately 2 to the + +n times H of x. + +In other words, what it says is +that this typical set is a + +bunch of essentially uniform +probabilities. + +So what I've done is to take +this very complicated source. + +And when I look at these very +humongous chance variables, + +which are very large sequences +out of the source, what I find + +is that there's a bunch of +things which collectively have + +zilch probability. + +There's a bunch of other things +which all have equal + +probability. + +And a number of them is +enough to add up to y. + +So I have turned this source, +when I look at it over a long + +enough sequence, into a source +of equiprobable events. + +And each of those events has +this probability here. + +Now, we know how to encode +equiprobable events. + +And that's the whole +point of this. + +So, this is less than +or equal to that. + +On the other side, we know that +1 minus delta is less + +than or equal to this +probability of a typical set. + +And this is less than the +number of elements in a + +typical set times 2 to the minus +n h of x minus epsilon. + +This is an upper +bound on this. + +This is less than this. + +So I just add all these things +up and I get this bound. + +So it says, the size of the +typical set is greater than 1 + +minus delta, times +this quantity. + +In other words, this is a pretty +exact sort of thing. + +If you don't mind dealing +with this 2 to the n + +epsilon factor here. + +If you agree that that's +negligible in some strange + +sense, the all of this +makes good sense. + +And if it is negligible, let me +start talking about source + +coding, which is why +this all works out. + +So the summary is that the +probability of the complement + +of the typical set +is essentially 0. + +The number of elements in a +typical set is approximately 2 + +to the n times h of x. + +I'm getting rid of all the +deltas and epsilons here, to + +get sort of the broad view +of what's important here. + +Each of the elements in a +typical set has probability 2 + +to the minus n times H of x. + +So I've turned a source +into a source of + +equiprobable elements. + +And there are 2 to the n +times h of x of them. + +Let's do an example of this. + +It's an example that you'll work +on more in the homework + +and do it a little +more cleanly. + +Let's look at a binary discrete +memoryless source, + +where the probability that x is +equal to 1 is p, which is + +less than 1/2. + +And the probability of 0 +is greater than 1/2. + +So, this is what you get when +you have a biased coin. + +And the biased coin has a +1 on one side and a 0 + +on the other side. + +And it's more likely to +come up 0's than 1's. + +I always used to wonder how +to make a biased coin. + +And I can give you a little +experiment which shows you you + +can make a biased coin. + +I mean, a biased is a little +round thing which is flat on + +the top and bottom. + +Suppose instead of that you +make a triangular coin. + +And instead of making it flat on +top and bottom, you turn it + +into a tetrahedron. + +So in fact, what this is now is +a coin which is built up on + +one side into a very +massive thing. + +And is flat on the other side. + +Since it's a tetrahedron +and it's an equilateral + +tetrahedron, the probability of +1 is going to be 1/4, and + +the probability of 0 +is going to be 3/4. + +So you can make biased coins. + +So when you get into +coin-tossing games with + +people, watch the coin +that they're using. + +It probably won't be a +tetrahedron, but anyway. + +So the entropy here, the log pmf +random variable, takes on + +the value of minus log +p with probability p. + +And it takes on the value minus +log 1 minus p, with + +probability 1 minus p. + +This is a probability of a 1. + +This is a probability of a 0. + +So, the entropy is +equal to this. + +Used to be that in information +theory courses, people would + +almost memorize what this +curve looked like. + +And they'd draw pictures +of it. + +There were famous curves +of this function, + +which looks like this. + +0, 1, 1. + +Turns out, that's not all that +important a distribution. + +It's a nice example +to talk about. + +The typical set, t epsilon n, +is the set of strings with + +about p n1's and about 1 +minus p times n 0's. + +In other words, that's the +typical thing to happen. + +And it's the typical thing in +terms of this law of large + +numbers here. + +Because you get 1's with +probability p. + +And therefore in a long +sequence, you're going to get + +about pn 1's and +1 minus p 0's. + +The probability of a typical +string is, if you get a string + +with this many 1's and +this many 0's, it's + +probability is p. + +Namely, the probability of a 1 +times the number of 1's you + +get, which is pn. + +Times the probability +of a 0, times the + +number of 0's you get. + +And if you look at what this +is, if you take p up in the + +exponent and 1 minus the p up in +the exponent, this becomes + +2 to the minus n times h of x, +just like what it should be. + +So these typical strings, with +about pn 1's and 1 minus pn + +0's, are in fact typical +in the sense we've + +been talking about. + +The number of n strings with pn +1's is n factorial divided + +by pn factorial divided by n +times 1 minus p factorial. + +I mean I hope you learned that +a long time ago, but you + +should learn it in probability +anyway. + +It's just very simple +combinatorics. + +So you have that many +different strings. + +So what I'm trying to get across +here is, there are a + +bunch of different things +going on here. + +We can talk about the random +variable which is the number + +of 1's that occur in +this long sequence. + +And with high probability, the +number of 1's that occur is + +close to pn. + +But if pn 1's occur, there's +still an awful lot of + +randomness left. + +Because we have to worry about +where those pn 1's appear. + +And those are the sequences +we're talking about. + +So, there are this many +sequences, all of which have + +that many 1's in them. + +And there's a similar number of +sequences for all similar + +numbers of 1's. + +Namely, if you take pn plus 1 +and pn plus 2, pn minus 1, pn + +minus 2, you get similar +numbers here. + +So those are the typical +sequences. + +Now, the important thing to +observe here is that you + +really have 2 to the n binary +strings altogether. + +And what this result is saying +is that collectively those + +don't make any difference. + +The law of large numbers says, +OK, there's just a humongous + +number of strings. + +You get the largest number +strings which have about half + +1's and half 0's. + +But their probability +is zilch. + +So the thing which is probable +is getting pn 1's + +and 1 minus pn 0's. + +Now, we have this typical set. + +What is the most likely sequence +of all, in this + +experiment? + +How do I maximize the +probability of + +a particular sequence? + +The probability of the sequence +is p to the i times 1 + +minus p to the n minus i. + +And 1 minus p is the +probability of 0. + +And p is the probability +of a 1. + +How do I choose i to +maximize this? + +Yeah? + +AUDIENCE: [UNINTELLIGIBLE] +all 0's. + +PROFESSOR: You make +them all 0's. + +So the most likely sequence +is all 0's. + +But that's not a typical +sequence. + +Why isn't it a typical +sequence? + +Because we chose to define +typical sequence in a + +different way. + +Namely is only one of those, and +there are only n of them + +with only a single one. + +So, in other words, what's going +on is that we have an + +enormous number of sequences +which have around half + +1's and half 0's. + +But they don't have +any probability. + +And collectively they don't +have any probability. + +We have a very small number of +sequences which have a very + +large number of 0's. + +But there aren't enough of those +to make any difference. + +And, therefore, the things that +make a difference are + +these typical things which +have about np 1's + +and 1 minus pn 0's. + +And that all sounds +very strange. + +But if I phrase this a different +way, you would all + +say that's exactly the way +you ought to do things. + +Because, in fact, when we look +at very, very long sequences, + +you know with extraordinarily +high probability what's going + +to come out of the source is +something with about pn 1's + +and about 1 minus +p times n 0's. + +So that's the likely set of +things to have happen. + +And it's just that there +are an enormous + +number of those things. + +There are this many of them. + +So, here what we're dealing with +is a balance between the + +number of elements of a +particular type, and the + +probability of them. + +And it turns out that this +number and its probability + +balance out to say that usually +what you get is about + +pn 1's and 1 minus +p times n 0's. + +Which is what the law of large +numbers said to begin with. + +All we're doing is interpreting +that here. + +But the thing that you see from +this example is, all of + +these things with exactly pn 1's +in them, assuming that pn + +is an integer, are +all equiprobable. + +They're all exactly +equiprobable. + +So what we're doing when we're +talking about this typical + +set, is first throwing out all +the things which have to many + +1's are or too few +1's in them. + +We're keeping only the ones +which are typical in the sense + +that they obey the law +of large numbers. + +And in this case, they obey the +law of large numbers for + +log pmf's also. + +And then all of those things +are about equally probable. + +So the idea in source coding +is, one of the ways to deal + +with source coding is, you want +to assign codewords to + +only these typical things. + +Now, maybe you might want to +assign codewords to something + +like all 0's also. + +Because it hardly +costs anything. + +And a Huffman code would +certainly do that. + +But it's not very important +whether you do or not. + +The important thing is, you +assign codewords to all of + +these typical sequences. + +So let's go back to +fixed-to-fixed + +length source codes. + +We talked a little bit about +fixed-to-fixed length source + +codes before. + +Do you remember what we did +with fixed-to-fixed length + +source codes before? + +We said we have an alphabet +of size m. + +We want something which +is uniquely decodable. + +And since we want something +which is uniquely decodable, + +we have to provide codewords +for everything. + +And, therefore, if we want to +choose a block length of n, + +we've got to generate m +to the n codewords. + +Here we say, wow, maybe we +don't have to provide + +codewords for everything. + +Maybe we're willing to tolerate +a certain small + +probability that the whole +thing fails and + +falls on its face. + +Now, does that make any sense? + +Well, view things the +following way. + +We said, when we started out +all of this, that we were + +going to look at prefix-free +codes. + +Where some codewords had a +longer length and some + +codewords had a shorter +length. + +And we were thinking of encoding +either single letters + +at a time, or a small block +of letters at a time. + +So think of encoding, say, +10 letters at a time. + +And think of doing this for +10 to the 20th letters. + +So you have the source here +which is pumping out letters + +at a regular rate. + +You're blocking them into +n letters at a time. + +You're encoding in a +prefix-free code. + +Out comes something. + +What comes is not coming +out at a regular right. + +What is coming out, sometimes +you get a lot of bits out. + +Sometimes a small number +of bits out. + +So, in other words, if you want +to send things over a + +channel, you need a buffer +there to save things. + +If, in fact, we decide that the +expected number of bits + +per source letter is, say, five +bits per source letter, + +then we expect over a very long +time to be producing five + +bits per source letter. + +And if we turn our channel on +for one year, to transmit all + +of these things, what's going +to happen is this very + +unlikely sequence occurs. + +Which in fact requires not one +year to transmit, but two + +years to transmit. + +In fact, what do we do if it +takes one year and five + +minutes to transmit instead +of one year? + +Well, we've got a failure. + +Somehow or other, the network +is going to fail us. + +I mean we all know that networks +fail all the time + +despite what engineers say. + +I mean, all of us who use +networks know that they do + +crazy things. + +And one of those crazy things +is that unusual things + +sometimes happen. + +So, we develop this very nice +theory of prefix-free codes. + +But prefix-free codes, +in fact, fail also. + +And they fail also because +buffers overflow. + +In other words, we are counting +on encoding things + +with a certain number of +bits per source symbol. + +And if these unusual things +occur, and we have too many + +bits per source symbol, +then we fail. + +So the idea that we're trying +to get at now is that + +prefix-free codes and +fixed-to-fixed length source + +codes which only encode +typical things. + +In fact, are sort of the same +if you look at them over a + +very, very large sequence +length. + +In other words, if you look at +a prefix-free code which is + +dealing with blocks of 10 +letters, and you look at a + +fixed-to-fixed length code which +is only dealing with + +typical things but is looking at +a length of 10 to the 20th, + +then over that length of 10 to +the 20th, your variable length + +code is going to have a bunch of +things which are about the + +length they ought to be. + +And a bunch of other +things which are + +extraordinarily long. + +The bunch of things which are +extraordinarily long are + +extraordinarily unpopular, but +there are an extraordinarily + +large number of them. + +Just like with a fixed-to-fixed +length code, + +you are going to fail. + +And you're going to fail on +an extraordinary number of + +different sequences. + +But, collectively, that set of +sequences don't have any + +probability. + +So the point that I'm trying to +get across is that, really, + +these two situations come +together when we look very + +long lengths. + +Namely, prefix-free codes are +just a way of generating codes + +that work for typical sequences +and over a very + +large, long period of time, will +generate about the right + +number of symbols. + +And that's what I'm trying +to get at here. + +Or what I'm trying to get +at in the next slide. + +So the fixed-to-fixed length +source code, I'm going to pick + +some epsilon and some delta. + +Namely, that epsilon and delta +which appeared in the law of + +large numbers. + +I'm going to make n as big as +I have to make it for that + +epsilon and that delta. + +And calculate how large it +has to be, but we won't. + +Then I'm going to assign fixed +length codewords to each + +sequence in the typical set. + +Now, am I going to really build + +something which does this? + +Of course not. + +I mean, I'm talking about +truly humongous lengths. + +So, this is really a conceptual +tool to understand + +what's going on. + +It's not something we're +going to implement. + +So I'm going to assign +codewords to all + +these typical elements. + +And then what I find is that +since the typical set, since + +the number of elements in it is +less than 2 to the n times + +H of x plus epsilon, if I choose +L bar, namely, the + +number of bits I'm going to use +for encoding these things, + +it's going to have to be H of +x plus epsilon in length. + +Because I need to provide +codewords for + +each of these things. + +And it needs to be an extra 1 +over n because of this integer + +constraint that we've been +dealing with all along, which + +doesn't make any difference. + +So if I choose L bar, that big, +in other words, if I make + +it just a little bit bigger +than the entropy, the + +probability of failure +is going to be less + +than or equal to delta. + +And I can make delta -- and I +can make the probability of + +failure as small as I want. + +So I can make this epsilon here +which is the extra bits + +per source symbol as +small as I want. + +So it says I can come as close +to the entropy bound in doing + +this, and come as close to +unique decodability as I want + +in doing this. + +And I have a fixed-to-fixed +length code, which after one + +year is going to stop. + +And I can turn my decoder off. + +I can turn my encoder off. + +I can go buy a new encoder +and a new decoder, which + +presumably works a little +bit better. + +And there isn't any problem +about when to turn it off. + +Because I know I can +turn it off. + +Because everything will +have come in by then. + +Here's a more interesting +story. + +Suppose I choose the number of +bits per source symbol that + +I'm going to use to be less than +or equal to the entropy + +minus 2 epsilon. + +Why 2 epsilon? + +Well, just wait a second. + +I mean, 2 epsilon is small +and epsilon is small. + +But I want to compare with this +other epsilon and my law + +of large numbers. + +And I'm going to pick +n large enough. + +The number of typical sequences, +we said before, was + +greater than 1 minus delta times +2 to the n times h of x + +minus epsilon. + +I'm going to make this epsilon +the same as that epsilon, + +which is why I wanted this +to be 2 epsilon. + +So my typical set is this big +when I choose n large enough. + +And this says that most +of the typical set + +can't be assigned codewords. + +In other words, this number +here is humongously larger + +then 2 to the l bar, which is in +the order of 2 to the nh of + +x minus 2 epsilon n. + +So the fraction of typical +elements that I can provide + +codewords for, between this and +this, I can only provide + +codewords for a fraction +2 to the minus + +epsilon n of the codewords. + +We have this big sea of +codewords, which are all + +essentially equally likely. + +And I can't provide codewords +for even a + +small fraction of them. + +So the probability of failure is +going to be 1 minus delta. + +The 1 minus delta's the +probability that I get + +something atypical. + +Plus, well, minus in this case, +2 to the minus epsilon + +n, which is the probability that +I can't encode a typical + +codeword that comes out. + +And this quantity goes to 1. + +So this says that if I'm willing +to use a number of + +bits bigger than the entropy, I +can succeed with probability + +very close to 1. + +And if I want to use a smaller +number of bits, I fail with + +probability 1. + +Which is the same as saying that +I'm using a prefix-free + +code, I'm going to run out of +buffer space eventually if I + +run long enough. + +If I have something that +I'm encoding -- + +well, just erase that. + +I'll say it more carefully +later. + +I do want to talk a little bit +about this Kraft inequality + +for unique decodability. + +You remember we proved the +Kraft inequality for + +prefix-free codes. + +I now want to talk about the +Kraft inequality for uniquely + +decodable codes. + +And you might think that I've +done all of this development + +of the AEP, the asymptotic +equipartition property. + +Incidentally, you now know where +those words come from. + +It's asymptotic because this +result is valid asymptotically + +as n goes to infinity. + +It's equipartition because +everything is equally likely. + +And its property, because +it's a property. + +So it's the asymptotic +equipartition property. + +And I didn't do it so I could +prove the Kraft inequality. + +It's just that that's an extra +bonus that we get. + +And by understanding why the +Kraft inequality has to hold + +for uniquely decodable codes, if +is one application for AEP + +which lets you see a little +bit about how to use it. + +OK, so the argument is an +argument by contradiction. + +Suppose you generate a set +of lengths for codewords. + +And you want this -- yeah? + +And the thing you would like to +do is to assign codewords + +of these lengths. + +And what we want to do is to +set this equal to some + +quantity b. + +In other words, suppose we beat +the Kraft inequality. + +Suppose we can make the lengths +even shorter than + +Kraft says we can make them. + +I mean, he was only a graduate +student, so we've got to be + +able to beat his inequality +somehow. + +So we're going to try to +make this equal to b. + +We're going to assume that +b is greater than 1. + +And then what we're going to +do is to show that we get a + +contradiction here. + +And this same argument can +work whether we have a + +discrete memoryless source or +a source with memory, or + +anything else. + +It can work with blocks, it can +work with variable length + +to variable length codes. + +It's all essentially +the same argument. + +So what I want to do is to +get a contradiction. + +I'm going to choose a discrete +memoryless source. + +And I'm going to make the +probabilities equal to 1 over + +b times 2 to the minus li. + +In other words, I can generate +a discrete memoryless source + +for talking about it with +any probabilities I + +want to give it. + +So I'm going to generate one +with these probabilities. + +So the lengths are going to +be equal to minus log of + +b times p sub i. + +Which says that the expected +length of the codewords is + +equal to the sum of p sub i l +sub i, which is equal to the + +entropy minus the +logarithm of b. + +Which means I can get an +expected length which is a + +little bit less than +the entropy. + +So now what I'm going to do is +to consider strings of n + +source letters. + +I'm going to make these string +very, very long. + +When I concatenate all these +codewords, I'm going to wind + +up with a length that's less +than n times H of x minus b + +over 2, minus log b over 2 +with high probability. + +And as a fixed-length code of +this length it's going to have + +a low failure probability. + +And, therefore, what this says +is I can, using this + +remarkable code with unique +decodability, and generating + +very long strings from it, I +can generate a fixed-length + +code which has a low failure +probability. + +And I just showed you +in the last slide + +that I can't do that. + +The probability of failure with +such a code has to be + +essentially 1. + +So that's a contradiction that +says you can't have these + +unique decodable codes. + +If you didn't get that in what +I said, don't be surprised. + +Because all I'm trying to do is +to steer you towards how to + +look at the section in the +notes that does that. + +It was a little too fast +and a little too late. + +But, anyway, that is the Kraft +inequality for unique + +decodability. + +OK, thanks. \ No newline at end of file diff --git a/eCaXlAaN2uE.txt b/eCaXlAaN2uE.txt new file mode 100644 index 0000000000000000000000000000000000000000..2cfe19a04c4caaf0fc4efb14e57ff1def0ef4beb --- /dev/null +++ b/eCaXlAaN2uE.txt @@ -0,0 +1,2095 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: I hope you're +all recovered from the quiz. + +Our apologies for +hard questions, + +but it's just the first quiz. + +We have a lot more fun +things to do in 006. + +So today's lecture today's +lecture is a light lecture, + +I would even call it a +recreational mathematics + +lecture. + +And so, thanks for coming. + +I'll make it worth +your while, all right? + +So we're going to talk +about irrationals. + +The motivation behind +this is really that every + +once in awhile we are going +to have a situation where + +we want to compute with numbers +that are much longer than 64 + +bits, which is really the word +length in standard computer + +these days. + +It used to be 8 bits +back in the day. + +For most of my adult +life it was 32 bits. + +And recently Intel and AMD +have gone to 64-bit processors. + +But 64 bits ain't +near enough if you + +want to do what's called high +precision computation, you want + +to find precisely the +weight of a neutrino, + +if you're a physicist, +for example. + +And that, you're talking +about literally a hundred + +decimal digits, +which is obviously + +much more than 64 bits. + +And that's just one example. + +So what happens if you want to +compute the square root of 2 + +to a million digits, or +pi to 10 million digits? + +How do you do that +on a computer? + +So that's what we're going +to do for this module, which + +is a short module on numerics. + +We'll have a lecture today +and another one on Tuesday + +telling you about techniques +that use, among other things, + +Newton's method to compute +irrational numbers, as one + +example, to arbitrary precision +And for your problem set + +you are you going to look at +different application that + +corresponds to encryption, +RSA encryption, + +where you have to +work with primes. + +These are now integers, +but you work with primes + +that are thousands of +bits long, so again, + +much more than 64 bits. + +And so you have to +think about how you're + +going to multiply numbers +that are thousands of bits + +long, how you're going to divide +numbers that are thousands + +of bits long, and that's really +the purpose of this module. + +So let's start off by +talking about irrationals. + +And Pythagoras, whom I'm +sure you've all heard of + +is credited with the discovery +that a square's diagonal + +and its side are +incommensurable. + +So you can't really express +the ratio as a rational number, + +as a ratio of integers. + +Now it turns out that the +Babylonians and the Indians + +knew this way before +Pythagoras, but he + +gets credit for the +Pythagoras theorem. + +And there's also a +Greek philosopher, + +in fact, maybe he was first +a philosopher and then + +a mathematician, and he +the espoused a philosophy + +that, I guess, is called +Pythagorean mysticism, that + +said that all is number, so +the world is about numbers. + +And he worshipped numbers, his +followers worshipped numbers. + +And the problem here was +that he didn't really + +like the square root of 2 +because he couldn't express it + +as a number, of what he thought +of as a number, which was 1, 2, + +3, et cetera, integers, +whole numbers. + +So he called this +ratio speechless, + +something that he +really couldn't explain. + +And irrationals were +actually considered a threat + +to the mystics because +they couldn't really + +explain what square +root of 2 was. + +They'd try and measure +it, and they would come up + +with the right answer because +the next time around it + +would be a little bit +different If they did things + +a little more precisely, +or not so precisely. + +And it bothered them no end. + +And so they tried to find +patterns in irrationals + +because they considered +them a threat. + +And they obviously +didn't find patterns, + +but imagine if we could +actually find patterns. + +I mean, that would +be a really big deal, + +it would be better than p equals +np, if you know what I mean. + +If you don't it doesn't matter. + +So that's another of motivation +for high precision arithmetic. + +Let's try and find +patterns in irrationals + +if you go to millions +and trillions of digits, + +maybe it's just a matter of time +before we discover that there's + +no such thing as +irrational numbers. + +Who knows? + +So let's do that for the +rest of this lecture. + +Let's try and +figure out how we're + +going to compute irrational +numbers, or things + +like square root of 2, +to arbitrary precision. + +So we can go play around, +and we'll give you some code, + +and you can play with it. + +So if you look at +square root of 2-- + +I'll just put this up +here-- so it's 1.414, + +you probably all know that. + +Then it's 213,562,373,095,048 +et cetera. + +I mean, I don't see +a pattern there. + +I see a zero, a +couple of zeroes here. + +It's hard to imagine-- +you'd probably + +want to think of a computer +program that generates + +square root of 2, and then +maybe a different computer + +program that's +looking for patterns. + +So let's not worry about +the square root of 2. + +I want to digress a little bit. + +I did say this was a bit of +a recreational mathematics + +lecture. + +And let's talk about something +completely different, + +which are Catalan numbers. + +So these are really my +favorite numbers in the world. + +And people like primes, some +people like irrationals, + +I like Catalan numbers. + +Catalan numbers are-- they +show up all over the place. + +How many of you know +what Catalan numbers are? + +Oh good. + +Excellent. + +So Catalan numbers have +a recursive definition. + +You can think of them as +representing the cardinality + +of the set p of balanced +parentheses strings. + +And we're going to +recursively define + +these strings as follows. + +We're going to have +lambda belonging + +to p where lambda +is the empty string. + +And that's rule one. + +Rule two is if alpha +and beta belong + +to p then I'm going to put +a paren, open paren, alpha, + +close paren, and then beta. + +And that belongs to p. + +So you iteratively or +recursively apply this rule + +over and over, and +you start getting + +strings that are balanced. + +So this is balanced. + +Now that's not +balanced, this is not + +balanced, and so +on and so forth. + +Obviously things +get more complicated + +in terms of the parentheses +if when you have more brackets + +or parentheses. + +And so, the nice thing +about this definition + +is that you can get every +non-empty balanced paren + +string, via rule two, from +a unique alpha, beta pair. + +So as an example, +suppose you want + +to generate the string +that looks like this-- + +So that's a little more +complicated than the strings + +that we have looked +at so far-- then you + +obtain that by having alpha +be this simple string. + +And then you put the brackets +around that, and then + +your beta corresponds to this. + +So now alpha and beta +were previously generated, + +so if you applied rule +two to the empty string, + +with alpha being +the empty string + +and beta being the empty string, +then you get this thing here. + +And obviously you could +get beta by setting + +alpha to be the empty string and +beta to be this string that you + +just generated, and +so on and so forth. + +So you just keep going and the +strings get longer and longer. + +The cardinality of the set +gets bigger and bigger. + +And those of the +Catalan numbers. + +OK + +And so, this is a +non-trivial question, + +which is I'd like to +enumerate the Catalan numbers, + +and compute, and get +an analytical form + +for the cardinality of the set. + +And that's really what +the Catalan number is. + +It's a cardinality of the set. + +And so cn is the number of +balanced parentheses strings + +with exactly n pairs +of parentheses. + +And I have c0 equals 1, +which is my base case. + +And that's just setting-- +it's an empty string. + +I'm going to say that +empty string is a string, + +and that's just setting +up the base case. + +And now I want an +equation for cn plus 1. + +And I need to use +the fact that I + +can get cn plus 1, a +particular strain that belongs + +to this set, where I have n plus +1 parenthesis in a unique way + +from a string I've previously +generated that was part + +of either the set that +had n parentheses-- + +or it was combined using +strings, where alpha was + +in some set that was +maybe generated awhile + +back with a small +n, or something + +significantly smaller than +n, and another thing that + +was generated, beta, +that was generated later, + +or maybe at the same +time, et cetera. + +So can someone tell me what an +equation would be for cn plus 1 + +based on the cis +that are less than n? + +So what about c1? + +Maybe I'll ask-- what about c1? + +What's c1? + +1. + +c1 is 1 because all I have +is this string, that's + +the only balanced string. + +Now I have c0 and c1. + +What's an equation for +c2 in terms of numbers. + +I want a number for +c2 based on c0 and c1. + +Someone? + +Yeah. + +AUDIENCE: C0 plus c1. + +PROFESSOR: c0 plus c1? + +No, not quite right. + +How many strings do I have? + +c0 plus c1. + +Yeah, actually you're right. + +Well, the number is right +but the equation is wrong. + +It's not quite that. + +You get a-- Yup. + +AUDIENCE: So when something +like c-- c1 times c1 plus c1. + +PROFESSOR: c1 times c1 plus c1? + +AUDIENCE: Yeah. + +PROFESSOR: I think +you want to use a c0. + +AUDIENCE: OK. c0. + +PROFESSOR: c0 Well, that's +not quite right either. + +Someone else. + +Yeah. + +OK. + +You. + +AUDIENCE: c0 times c1 +plus c1 [INAUDIBLE]. + +PROFESSOR: c0 +times c1-- c2 would + +be c0 times c1 plus c1 times c0. + +OK. + +And if you're setting the +alpha-- So here's the thing, + +you set the alpha, and +you choose the alpha, + +and then you choose the beta. + +And there's a couple +of different ways + +that you could choose the alpha. + +You could choose +the alpha from-- you + +could make it a +string that's empty, + +or you could make +it the one string + +that you've generated +so far, which + +is the standard simple +string, the non-empty, + +the non-trivial balanced string. + +And you could do that in +a couple different ways + +with alpha. + +And that's why you have +two terms over there. + +So the number, in terms of +all of the equations I got, + +they all came out +to be the same. + +It's 2, and that's correct. + +But this is the equation for it. + +And so now, tell me +what a general equation + +is for cn plus 1 +based on what we've + +learned so far for +the c2 equation? + +Yeah, back to you. + +AUDIENCE: So c0 times +cn plus c1 times cn + +minus 1 all the way to +cn times [INAUDIBLE]. + +PROFESSOR: Perfect. + +Good. + +That deserves a cushion. + +That wasn't me, it was you. + +And put it right +there, breadbasket. + +So cn plus 1 equals sigma, +so you give me a summation, + +k equals 0 through n, +ck, cn minus k where + +n is greater than or equal to 0. + +And you can figure this out, +it's not particularly important + +as to exactly why this is true. + +You can think about it offline. + +But the interesting thing is +that this is a generator of, + +obviously, and it's +going to give you + +a nice looking set of numbers. + +And I came in early and wrote +that the Catalan in numbers + +up on the board going from +c0, c1, c2, et cetera, just + +in case-- just in case you ever +see these numbers in real life, + +or when you're writing +computer programs. + +Or you're driving on the road, +the next time you see a license + +plate 4862, turn around and +tell your mom or dad, hey, + +that's the Catalan number. + +And maybe she'll be impressed. + +This, of course, +you're not going + +to see on a license +plate, but you can always + +make up a bumper +sticker or something, + +and you can have +the c17 as being + +a bumper sticker on your car. + +I mean, that's the kind +of thing that I'd do. + +Anyway, so it's just in +case you see these numbers-- + +we might come back to this a +little bit later in the class, + +but-- + +AUDIENCE: 42 is on that list. + +PROFESSOR: 42 is on that list. + +Yeah, it has to be. + +42 is on every list. + +42 is the answer +to every question. + +I am glad you guys didn't +put 42 down in the answer + +to every quiz question. + +It doesn't quite work +all the time, all right, + +but most of the time +42 is a good answer. + +Most of the time. + +OK good. + +So let's get down to business. + +So we talked about Catalan +numbers as a digression. + +If you see them you'll +recognize them, I think. + +Let's talk about how +we could compute. + +Let's go back to +irrationals and talk + +about how we could +compute square root of 2 + +and other things to +arbitrary precision. + +So what I want to do is to +talk about Newton's method. + +And Newton's method is +something you probably + +learned about in middle +school, high school. + +And let's say you +have a function + +y equals f of x where +this is x and that's + +y, the coordinate axes. + +And we want to try and find +the root of fx equals 0 + +through successive +approximation. + +For example, we might have f +of x equals x squared minus a. + +And if a is 2 then you're +trying to use Newton's method + +to find the root, +and you're going + +to end up trying to compute +square root of 2 or plus + +minus square root +of 2, in this case. + +But you can go for +a particular root, + +and you're try and +converge to that. + +So the way Newton's method +works is it tries, geometrically + +speaking, it tries +to find tangents-- + +and a different color +chalk would be useful here + +but I don't seem to see +one-- So what would happen + +is, let's say you +are sitting out here, + +and it's successive +approximation method, + +so this would give you x of i. + +And now you want to +compute x of i plus 1. + +And what you're going +to do is draw a tangent, + +like so, and find the +intercept onto the x-axis, + +the x-intercept. + +And that is going to +be your xi plus 1. + +And you have to write an +equation for that tangent. + +And this is, I guess, +trying to figure + +out how much of middle school +math or high school math + +that you remember. + +What is the equation +for that tangent? + +Anybody? + +The equation for that tangent? + +What do you do in order +to compute that tangent? + +Give me a name. + +AUDIENCE: Derivative? + +PROFESSOR: Derivative. + +Thank you. + +So what's the equation +for that tangent? + +y equals-- Someone? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: It's a good +think your middle school, + +high school teachers +aren't here. + +Not you. + +You already got a cushion. + +Someone else. + +Someone else. + +All right. + +I'll start giving +you some hints here. + +f of xi plus-- plus-- + +ALL: f prime. + +PROFESSOR: f prime xi. + +Thank you. + +Thank you. + +All right. + +You get a cushion. + +I'm getting them. + +Whatever it takes. + +Here you go. + +Yeah. + +That was left-handed, +by the way. + +I'm actually +right-handed, as you know. + +So what do we have here? + +So we have f prime xi. + +Now come on, let's +finish it, finish it. + +AUDIENCE: Times i minus xi. + +PROFESSOR: Times xi is xi. + +Thank you. + +OK. + +So now I get it. + +You thought this was +too simple a question. + +You guys were insulted +by the question. + +So that's why you didn't tell +me what it was At least, that's + +what I'm going to pretend +to make myself feel better. + +So y equals f of +xi plus f prime xi, + +which is the derivative +of f evaluated at xi times + +x minus xi, that's the +equation for the line. + +And that's essentially +what we have + +to do to compute things +like square root of 2, which + +is iteratively applied +Newton's method. + +The only problem is this +is all good in theory + +that we can do-- take that +equation turn it into xi + +plus 1 equals xi minus f of +xi divided by f prime of xi. + +And if you end up doing f of x +equals x squared minus a, then + +you have xi plus 1 +equals xi minus xi + +squared minus a divided by 2xi, +which is the derivative of x + +squared minus a evaluated at xi. + +And finally you get +this equation, xi + +plus a divided by +xi divided by 2. + +So it's fairly straightforward. + +xi plus 1 equals xi plus a +divided by xi divided by 2. + +And if you look +at this, remember + +that a is typically +a small number. + +I mean, it's two, in +this case, if you're + +computing square root of 2. + +it may even be an +integer, maybe a fraction. + +But you have to do +a division here. + +And remember that since +we want to compute things + +to millions of digits, +potentially, these numbers, + +the xi numbers, are going +to have millions of digits. + +And so if you end up +running this Newton method + +on a equals 2, then +if I simulate what + +happens without worrying +about the implementation, + +and this is what you'll get. + +You have x0-- you start with x0 +equals 1 with a bunch of zeros. + +xi equals 1.5 with a +bunch of zeros, et cetera. + +And then, x2 equals +1.41666 et cetera. + +That goes on. + +And we're not talking +about fractions here, + +we're talking about +floating point numbers that + +are integers with a certain +amount of precision. + +So you've decided that +you want to compute this + +to d digits of precision +where d may be a million. + +And so, really, here you would +have a representation that's + +a million digits +long that where, + +basically, everything is zero, +and here everything but one + +is 0, or maybe a couple +if you count the 1 here. + +And here you have +all these sixes here, + +and so on and so forth. + +And you keep going, and you +get x2 equals 1.414215686. + +And I want to write +one more because I + +want to point out +something that's important. + +1.414213562. + +And what's nice about +this, if you go compare it + +with what you have +up there, is that you + +have quadratic convergence +using the Newton's method. + +And what do I mean by that? + +Well, quadratic convergence +is a nice property. + +It's much better than +linear convergence. + +Linear convergence +would mean that you + +get an extra digit of +precision for every iteration. + +So in this case, actually, +a quadratic is better. + +Usually we think of +quadratic algorithms, + +and we are going to throw up. + +But linear algorithms +is what we like. + +But in this case it's +actually a good thing. + +You have this extended this +quadratic rate of convergence + +where the number of +digits that are correct + +doubles with every +iteration, as you can see. + +So here you have-- you +start with, roughly, + +if you rounded this +up you would get 5. + +So you're saying that that's +one digit of precision + +in terms of the decimal. + +And then, now you're +talking about 41421356, + +so that's 1, 2, +3, 4, 5, 6, 7, 8, + +so that's eight digits of +precision here, four here, + +and so on and so forth. + +So that's nice. + +That's why the Newton's +method is actually + +used in practice because the +number of digits doubles. + +This is a precision. + +So now you don't get too +scared about calculating things + +that are a million because +you kind of go and say, whoa, + +I mean, that's not +so bad, that's only + +a logarithmic number +of integrations. + +And it's not like you have to +run for a million iterations. + +You go 2, 4, 8, 16, and now +that exponential helps you, + +the geometric series helps you. + +So that's the nice thing +about the Newton's method. + +Haven't quite told +you how we are + +going to compute the +most important thing here + +with respect to a divided by xi. + +So this is just additions. + +You can imagine that if +you have long numbers + +you'd end up doing addition +fairly straightforwardly + +because you only have to +worry about one carry, + +and so you go off. + +And I'm sure you've +added up numbers + +that are in tens, if not +hundreds, of digits long + +but I'm guessing +you haven't manually + +multiplied numbers that are +hundreds of digits long. + +And if you have +I'd be impressed, + +though I won't +believe your result. + +But that's something that is +kind of a painful thing to do. + +And so that's why +we need computers. + +And that's multiplication +and-- has anybody + +divided a hundred-digit number +by another 50-digit number? + +No. + +So you need computers. + +So we've got to be able +to do that division there, + +a divided by xi, +using computers. + +And so that's really the purpose +of this and the next lecture + +If you're only going +to do a high precision + +multiplication here. + +And try see what an algorithm +would be for high precision + +multiplication because +what we're going to do + +is, essentially, take the +reciprocal of one over xi + +and then multiply that by a. + +And we need-- division is going +to require multiplication. + +You don't really +see a multiplication + +there other than +a times 1 over xi. + +And you can say, well, do we +really need multiplication? + +Well, the answer is +the division algorithm + +that is used in practice in +most division algorithms have + +multiplication as a subroutine. + +So we're going to have to +figure out high precision + +multiplication first-- +It's a little bit easier + +than division-- and use it as +a subroutine for high precision + +division, which +we'll do next time. + +So now we're sort of back +in 006 land, if you will. + +We have a problem that is +high precision multiplication, + +and we want to find +an algorithm for it. + +And there's the +vanilla algorithm + +that is going to take +certain amounts of time, + +asymptotically +speaking, and then there + +is better and better algorithms. + +As you can imagine, +multiplication + +is just such a +fundamental operation + +that people have +looked at trying + +to reduce the complexity of +high precision multiplication. + +So if you have n bits-- So +what is the standard algorithm + +for multiplication take if +you have n bits of precision? + +AUDIENCE: N squared. + +PROFESSOR: n squared. + +But you can do better. + +And the people are work on it. + +You can do fast +Fourier transforms. + +We won't quite do that here. + +If you take 6.046 you'll +probably learn about that. + +But we'll do a +couple of algorithms + +that are better than the +order n squared method, + +and we'll do one of those today. + +So the way they're going +to work with integers-- + +one little point that I need to +make before we move ahead here + +is, generally, we going to +say, for the purposes of 006, + +that we know the digits of +precision up front because we + +want d digits of precision, +maybe it's 42, maybe it's 125. + +In the case of our problem +set in RSA we going to have it + +1,024-bit numbers, maybe 2,048. + +So we know d beforehand. + +And so what we want +is an integer, which + +is 10 raised to d times the +square root of 2, a floor, + +and which is essentially the +same as that, 2 times 10 raised + +to 2 d. + +So we're going to treat +these as integers, + +so we don't want to worry +about decimal points + +and things like that. + +All of these things are +going to be integers. + +And there's no problem here. + +We can still use +Newton's method. + +It just works on integers. + +And let's take a +look at how we would + +apply Newton's method +in standard form. + +And we won't to +really get to the part + +where we're going to go from +division to multiplication + +today, as I said, +we're just going + +to look at how you can +multiply two numbers. + +So I didn't mean +to say that we're + +going to look at +Newton's method. + +We're going to look at high +precision multiplication, + +and then, eventually, +we're going + +to use that to build +Newton's method + +which requires the division. + +So I have two n-digit +numbers, and the radix + +could be-- the base +could be 2, 10. + +Normally, it doesn't +really matter. + +0 less than x, less than +y, strictly less than r + +raised to n. + +That's standard for the ranges. + +And what I have +here is-- the way + +I'm going to do this is use +our favorite strategy, which + +is divide and conquer, because +I have n, which is large, + +need to break things +down, break it into n + +by two-digit multiplications. + +And when, finally, +I break things down, + +I get down to 64 bits, I +just run one instruction + +on my computer to multiply +the 64-bit numbers. + +And the standard machines, you +would get 128 bits of result + +back when you multiply +64-bit numbers. + +So in some sense +you only go down-- + +you don't go down to 1 +bit, you go down to 64 + +and your machine does the rest. + +So what we have here +is you set x to be x1 + +where x1 is the high half, r +raised to n over 2 plus x0. + +So x1 is the more significant +half and x0 is the low half. + +And the same thing for y. + +y1, whoops, r raised +to n over 2 plus y0. + +Now the ranges change. + +x0 and x1 are smaller, so that's +what you have for x0 and x1. + +Same thing for y0 and y1. + +So that's a fairly +straightforward decomposition + +of this multiplication +operation. + +And again, if you do things +in a straightforward way + +you will create a recursive +multiply, as I'll write here. + +And what you do is you say +let z0 equal x0 times y0, + +z two equals x2 times +y2, and-- I missed z1, + +but z1 equals x0, y1 plus x1 y0. + +And I have, overall, +z equals y equals + +x1 y1 times r raised to n +plus x0 y1 plus x1 y0 times + +r raised to n over +2 plus x0 y0 zero. + +And this part here was +z0, this part here was z1, + +and this part here was z2. + +And if you look at, it you need +four multiplies, 1, 2, 3, 4. + +And you need four +multiplies of n + +by two-- n by two-digit numbers. + +And by now, after you have +prepared for quiz two, + +I will just say that it would +take theta n square time + +because you're +recursive equation + +is tn equals 4t of n over 2 plus +the linear time that you take + +for addition. + +So this is tn equals 4t +of n over 2 plus theta n. + +And you're assuming +that the additions here + +take linear time. + +So that's how you get your +theta n square algorithm. + +And we're not happy with that. + +We'd like to do better. + +And so how do you do better? + +Well, there's many +ways of doing better. + +The simplest way off fairly, +substantially lowering + +the complexity is +due to a gentleman + +by the name of Karatsuba. + +This is one of +those things where + +if you were born +early enough you + +get your name on an algorithm. + +And what happens here is, using +the z's that I have out there, + +you essentially say, look, +I know z0 equals x0 and y0, + +I'm going to go +ahead and multiply. + +z2 equals x2 and y2, +go ahead and do that. + +And now I'm going to write +z1 as x0 plus x1 times y0 + +plus y1 minus z0 minus z2. + +So you're actually +computing z0 and z2 first, + +and then using +them to compute z1. + +So someone tell me why +this is interesting? + +And just take it all the way to +the complexity of an algorithm. + +Explain to me why +this is interesting + +and why Karatsuba's algorithm +has-- I'll give it away-- + +a lower complexity +than theta n square? + +But tell me what it is. + +Someone? + +Someone other than you. + +Someone way at the back. + +Yup. + +Out there. + +AUDIENCE: It's n to +the log base 2 of 3. + +PROFESSOR: n raised to-- + +AUDIENCE: Log base 2-- + +PROFESSOR: --log base 2 of 3. + +That's exactly right. + +And now, why did you get that? + +Explain to me how you got there. + +AUDIENCE: If you're +using three products-- + +PROFESSOR: That's right. + +So first insight +is that we're only + +doing three +multiplications here. + +Additions are easy. + +And we're doing three +multiplications as opposed + +to four. + +So tell me how that +equation changed, of tn. + +tn equals-- + +AUDIENCE: 3 [INAUDIBLE]. + +PROFESSOR: 3 times t of +n over 2 plus theta n + +because you're doing three +multiplications rather than + +four. + +Multiplications are the +complicated operation. + +Divisions are even +more complicated, + +but additions are easy, and you +could do those in linear time + +for n-digit numbers. + +And so, if you do that and +then you go off and you say, + +well, that tells +us that tn equals + +theta of n raised to log two +of three, which is, by the way, + +theta of n raised to +1.58, roughly speaking. + +And I do not want to compute +that to arbitrary precision, + +though I could. + +But that goes on and on. + +Why don't you grab +this after you're done. + +But that just goes on and on. + +1.58 is a rough approximation. + +That's an irrational +number too, assuming + +you think that +irrational numbers exist. + +That's an irrational number. + +So good, that's +really all I had. + +By the way, it's 1.58490625. + +I really should have +written that down. + +1.58-- in the context +of this lecture + +I think it's +important that we get + +at least a few +digits a precision. + +Now you can imagine that you +could do it better than this. + +And it turns out that-- +we'll talk a little bit + +about this next time-- But you +can imagine breaking this up + +into not n over two chunks, +but n over three chunks. + +Why don't I just break +up x into the top third, + +the middle third, and +then the bottom third, + +and then try and see +if I can get away + +with fewer than eight +multiplications? + +Because the original +thing would have + +taken eight, and if I +can do less than eight, + +maybe I can reduce +that 1.58 number. + +So that's a little +bit of a preview + +for what we'll do next time. + +But what I'd like +to do is do a demo. + +And I want you to run +that-- it's out there so + +blank that out for a second. + +What I'd like to do is really +look at a different problem + +than square root of 2, and +show you a demo of code + +that Victor wrote that computes +this particular quantity that, + +you would argue, is irrational, +to arbitrary digits. + +Though we'll probably only go +up to about a thousand today. + +And if we just look at-- root +2 is kind of boring, right? + +It's been around for a while. + +Let's go back and remember +high school geometry. + +So I think your +high school teachers + +would like this lecture. + +Nice little review. + +So what is that about? + +That's supposed to be a circle, +I think, as you've forgotten. + +That's supposed to be a circle. + +And the circle here is +a really big circle. + +It's a trillion units long. + +I'm into big numbers +today, big numbers. + +And the center of the +circle is c, c for center. + +That is what's called a radius, +in case you'd forgotten. + +And that's b. + +And this is also a +radius, and that's a. + +And what I'm going +to do is I'm going-- + +I want to make a drop a little, +I guess, perpendicular down, + +which is one unit high. + +So the way that +this is structured + +is that this is one unit +high, this obviously + +is-- someone tell +me what that is, CB. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Half a trillion. + +That's half a trillion. + +And obviously, CA +is half a trillion. + +And if I call this +D, somebody who + +remembers high school or +middle school geometry + +give me an equation for AD. + +And that's definitely +worth a cushion. + +so what's an +equation for AD guys? + +Yeah. + +Go ahead. + +AUDIENCE: The radius, +half-trillion minus the square + +root of-- + +PROFESSOR: Square +root of-- Yeah? + +AUDIENCE: Minus the square root +of [INAUDIBLE] square minus 1? + +PROFESSOR: Perfect, perfect. + +OK good. + +So AD equals AC +minus CD, and that + +is going to be half a +trillion-- that is 500 billion, + +a little bit less +than bailout money, + +but it's close-- 500 thousand +minus square root of 500-- + +this, when you start +squaring this, of course, + +is not even real, +real big money. + +But 500 thousand +squared minus 1. + +So forget the +square root of two. + +You can put the screen down. + +So is it on, the projector? + +AUDIENCE: It's on, it +just needs a [INAUDIBLE]. + +PROFESSOR: OK. + +You can turn that on. + +AUDIENCE: Rolling. + +PROFESSOR: So what +we're going to do + +is, I'm just going to +show you the digits + +of this crazy quantity being +computed to tens of thousands + +of digits. + +And you argue that this +is it something clearly + +that isn't a perfect square. + +You took a perfect square, +subtracted 1 from it, + +and so you have an +irrational quantity + +that is going to go on and on. + +And let's see what that +number-- what it looks like. + +OK? + +Get out of the way. + +I hope you can +see from the back. + +AUDIENCE: Oh man, really? + +PROFESSOR: Looking pretty good +so far, looking pretty good. + +AUDIENCE: That's crazy. + +PROFESSOR: Somebody see +the numbers somewhere else? + +Have you see these +numbers before? + +Like 20 minutes ago, like +right in front of you? + +OK All right. + +So I think that's a +good place to stop. + +If you want an +explanation for this + +I think you can go +to section tomorrow. + +I'm going to use a some +attendance tomorrow. + +All right. + +Happy to answer questions +about the rest of the lecture, + +and thanks for coming. \ No newline at end of file diff --git a/eQxzotQiuhQ.txt b/eQxzotQiuhQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..289a02aa660ed24bd0c94496e97e095815bfce45 --- 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hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu this content has been + + align:start position:0% +ocw.mit.edu this content has been + + + align:start position:0% +ocw.mit.edu this content has been +removed du to copyright restrictions see + + align:start position:0% +removed du to copyright restrictions see + + + align:start position:0% +removed du to copyright restrictions see +the readings and viewings page for + + align:start position:0% +the readings and viewings page for + + + align:start position:0% +the readings and viewings page for +information about this material + + align:start position:0% +information about this material + + + align:start position:0% +information about this material +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that zigzag dance I think we missed at + + align:start position:0% +that zigzag dance I think we missed at + + + align:start position:0% +that zigzag dance I think we missed at +the very beginning of the film at least + + align:start position:0% +the very beginning of the film at least + + + align:start position:0% +the very beginning of the film at least +the audio wasn't working yet it just but + + align:start position:0% +the audio wasn't working yet it just but + + + align:start position:0% +the audio wasn't working yet it just but +you saw it later with the movement the + + align:start position:0% +you saw it later with the movement the + + + align:start position:0% +you saw it later with the movement the +male makes it's a fixed action pattern + + align:start position:0% +male makes it's a fixed action pattern + + + align:start position:0% +male makes it's a fixed action pattern +he makes in order to lead a female + + align:start position:0% +he makes in order to lead a female + + + align:start position:0% +he makes in order to lead a female +usually a female he is picked out from a + + align:start position:0% +usually a female he is picked out from a + + + align:start position:0% +usually a female he is picked out from a +group to his + + align:start position:0% + + + + align:start position:0% + +nest uh and it's when the female sees + + align:start position:0% +nest uh and it's when the female sees + + + align:start position:0% +nest uh and it's when the female sees +that if she's ready lay eggs she is + + align:start position:0% +that if she's ready lay eggs she is + + + align:start position:0% +that if she's ready lay eggs she is +induced to follow him the cause of her + + align:start position:0% +induced to follow him the cause of her + + + align:start position:0% +induced to follow him the cause of her +behavior is the sight of his + + align:start position:0% + + + + align:start position:0% + +behavior so you saw an example of the + + align:start position:0% +behavior so you saw an example of the + + + align:start position:0% +behavior so you saw an example of the +use of dummy + + align:start position:0% +use of dummy + + + align:start position:0% +use of dummy +stimula with the females of different + + align:start position:0% +stimula with the females of different + + + align:start position:0% +stimula with the females of different +the models of females of different + + align:start position:0% + + + + align:start position:0% + +shapes and you saw their analysis of the + + align:start position:0% +shapes and you saw their analysis of the + + + align:start position:0% +shapes and you saw their analysis of the +purpose they were looking for why that's + + align:start position:0% +purpose they were looking for why that's + + + align:start position:0% +purpose they were looking for why that's +adaptive in the fairly obvious reason + + align:start position:0% +adaptive in the fairly obvious reason + + + align:start position:0% +adaptive in the fairly obvious reason +was the larger females more larger + + align:start position:0% +was the larger females more larger + + + align:start position:0% +was the larger females more larger +swollen belly and so + + align:start position:0% +swollen belly and so + + + align:start position:0% +swollen belly and so +forth have more eggs so it benefits the + + align:start position:0% +forth have more eggs so it benefits the + + + align:start position:0% +forth have more eggs so it benefits the +male to choose such a female because + + align:start position:0% +male to choose such a female because + + + align:start position:0% +male to choose such a female because +then he can inseminate larger numbers + + align:start position:0% +then he can inseminate larger numbers + + + align:start position:0% +then he can inseminate larger numbers +and should result in Greater number of + + align:start position:0% + + + + align:start position:0% + +Offspring and by the way the purpose + + align:start position:0% +Offspring and by the way the purpose + + + align:start position:0% +Offspring and by the way the purpose +I mean if if the animal was conscious if + + align:start position:0% +I mean if if the animal was conscious if + + + align:start position:0% +I mean if if the animal was conscious if +you're dealing with humans and you say + + align:start position:0% +you're dealing with humans and you say + + + align:start position:0% +you're dealing with humans and you say +well if you want to know the purpose of + + align:start position:0% +well if you want to know the purpose of + + + align:start position:0% +well if you want to know the purpose of +something just ask the + + align:start position:0% +something just ask the + + + align:start position:0% +something just ask the +person but doesn't + + align:start position:0% +person but doesn't + + + align:start position:0% +person but doesn't +work you don't have to be aware of the + + align:start position:0% +work you don't have to be aware of the + + + align:start position:0% +work you don't have to be aware of the +purpose purpose is the evolutionary + + align:start position:0% +purpose purpose is the evolutionary + + + align:start position:0% +purpose purpose is the evolutionary +purpose it's what's evolved and you + + align:start position:0% +purpose it's what's evolved and you + + + align:start position:0% +purpose it's what's evolved and you +don't have to be aware of it all in fact + + align:start position:0% +don't have to be aware of it all in fact + + + align:start position:0% +don't have to be aware of it all in fact +you may give totally different reasons + + align:start position:0% +you may give totally different reasons + + + align:start position:0% +you may give totally different reasons +you would give approximate + + align:start position:0% +you would give approximate + + + align:start position:0% +you would give approximate +reasons but not the reasons where the + + align:start position:0% +reasons but not the reasons where the + + + align:start position:0% +reasons but not the reasons where the +whole uh Behavior pattern + + align:start position:0% +whole uh Behavior pattern + + + align:start position:0% +whole uh Behavior pattern +evolved and then you saw the study of + + align:start position:0% +evolved and then you saw the study of + + + align:start position:0% +evolved and then you saw the study of +development where they buried the + + align:start position:0% +development where they buried the + + + align:start position:0% +development where they buried the +orphan orphans and the naturally reared + + align:start position:0% +orphan orphans and the naturally reared + + + align:start position:0% +orphan orphans and the naturally reared +fish and uh how they differed in their + + align:start position:0% +fish and uh how they differed in their + + + align:start position:0% +fish and uh how they differed in their +anti-predator behavior their escape + + align:start position:0% +anti-predator behavior their escape + + + align:start position:0% +anti-predator behavior their escape +Behavior apparently the early experience + + align:start position:0% +Behavior apparently the early experience + + + align:start position:0% +Behavior apparently the early experience +plays an important role in shaping their + + align:start position:0% +plays an important role in shaping their + + + align:start position:0% +plays an important role in shaping their +later responses so it's their patterns + + align:start position:0% +later responses so it's their patterns + + + align:start position:0% +later responses so it's their patterns +of escape from a attacking fish is not + + align:start position:0% +of escape from a attacking fish is not + + + align:start position:0% +of escape from a attacking fish is not +totally unlearned it has a learn + + align:start position:0% +totally unlearned it has a learn + + + align:start position:0% +totally unlearned it has a learn +component as + + align:start position:0% + + + + align:start position:0% + +well and you learn the answers to these + + align:start position:0% +well and you learn the answers to these + + + align:start position:0% +well and you learn the answers to these +from that film also uh by looking at the + + align:start position:0% +from that film also uh by looking at the + + + align:start position:0% +from that film also uh by looking at the +fish that have evolved in isolation from + + align:start position:0% +fish that have evolved in isolation from + + + align:start position:0% +fish that have evolved in isolation from +each other for long enough they were + + align:start position:0% +each other for long enough they were + + + align:start position:0% +each other for long enough they were +able to see differences that have + + align:start position:0% +able to see differences that have + + + align:start position:0% +able to see differences that have +evolved with that because of + + align:start position:0% +evolved with that because of + + + align:start position:0% +evolved with that because of +different in one case some of the + + align:start position:0% +different in one case some of the + + + align:start position:0% +different in one case some of the +sticklebacks were initially ocean going + + align:start position:0% +sticklebacks were initially ocean going + + + align:start position:0% +sticklebacks were initially ocean going +and then they became isolated in the + + align:start position:0% +and then they became isolated in the + + + align:start position:0% +and then they became isolated in the +smaller uh Lake that became freshwater + + align:start position:0% +smaller uh Lake that became freshwater + + + align:start position:0% +smaller uh Lake that became freshwater +lake and you learn why the male sticker + + align:start position:0% +lake and you learn why the male sticker + + + align:start position:0% +lake and you learn why the male sticker +back fish drives the female away because + + align:start position:0% +back fish drives the female away because + + + align:start position:0% +back fish drives the female away because +she's + + align:start position:0% + + + + align:start position:0% + +cannibalistic the behavior of these + + align:start position:0% +cannibalistic the behavior of these + + + align:start position:0% +cannibalistic the behavior of these +animals of course evolves involves the + + align:start position:0% +animals of course evolves involves the + + + align:start position:0% +animals of course evolves involves the +behavior of both male and female an + + align:start position:0% +behavior of both male and female an + + + align:start position:0% +behavior of both male and female an +individual female can benefit by + + align:start position:0% +individual female can benefit by + + + align:start position:0% +individual female can benefit by +cannibalizing eggs because most the eggs + + align:start position:0% +cannibalizing eggs because most the eggs + + + align:start position:0% +cannibalizing eggs because most the eggs +she will be eating aren't hers and if + + align:start position:0% +she will be eating aren't hers and if + + + align:start position:0% +she will be eating aren't hers and if +she now can lay a lot more eggs she has + + align:start position:0% +she now can lay a lot more eggs she has + + + align:start position:0% +she now can lay a lot more eggs she has +a greater + + align:start position:0% +a greater + + + align:start position:0% +a greater +chance of reproducing or reproducing a + + align:start position:0% +chance of reproducing or reproducing a + + + align:start position:0% +chance of reproducing or reproducing a +larger number of + + align:start position:0% +larger number of + + + align:start position:0% +larger number of +individuals but of course that's not in + + align:start position:0% +individuals but of course that's not in + + + align:start position:0% +individuals but of course that's not in +the male's favor he wants to preserve + + align:start position:0% +the male's favor he wants to preserve + + + align:start position:0% +the male's favor he wants to preserve +those eggs that he is uh inseminated and + + align:start position:0% +those eggs that he is uh inseminated and + + + align:start position:0% +those eggs that he is uh inseminated and +he is the one in charge the safety of + + align:start position:0% +he is the one in charge the safety of + + + align:start position:0% +he is the one in charge the safety of +those eggs until they + + align:start position:0% +those eggs until they + + + align:start position:0% +those eggs until they +hatch the female PL in this word sorry + + align:start position:0% +hatch the female PL in this word sorry + + + align:start position:0% +hatch the female PL in this word sorry +so uh what does the male eat what does + + align:start position:0% +so uh what does the male eat what does + + + align:start position:0% +so uh what does the male eat what does +the male eat he doesn't eat + + align:start position:0% +the male eat he doesn't eat + + + align:start position:0% +the male eat he doesn't eat +eggs you know they eat very + + align:start position:0% +eggs you know they eat very + + + align:start position:0% +eggs you know they eat very +small organisms in vegetation but I'm + + align:start position:0% +small organisms in vegetation but I'm + + + align:start position:0% +small organisms in vegetation but I'm +not sure of the details there's plenty + + align:start position:0% +not sure of the details there's plenty + + + align:start position:0% +not sure of the details there's plenty +online about sticklebacks that would be + + align:start position:0% +online about sticklebacks that would be + + + align:start position:0% +online about sticklebacks that would be +a pretty easy thing if you want details + + align:start position:0% +a pretty easy thing if you want details + + + align:start position:0% +a pretty easy thing if you want details +okay so next time we'll be talking about + + align:start position:0% +okay so next time we'll be talking about + + + align:start position:0% +okay so next time we'll be talking about +tinbergens studies of birds Kitty weight + + align:start position:0% +tinbergens studies of birds Kitty weight + + + align:start position:0% +tinbergens studies of birds Kitty weight +gulls \ No newline at end of file diff --git a/evxReCLA-fU.txt b/evxReCLA-fU.txt new file mode 100644 index 0000000000000000000000000000000000000000..af2e7ff97c9cc033122f2caaef959054f35e5d01 --- /dev/null +++ b/evxReCLA-fU.txt @@ -0,0 +1,2819 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +what I'd like us to do is answer uh some + + align:start position:0% +what I'd like us to do is answer uh some + + + align:start position:0% +what I'd like us to do is answer uh some +questions I've posed here in really long + + align:start position:0% +questions I've posed here in really long + + + align:start position:0% +questions I've posed here in really long +problem so let me let me take us through + + align:start position:0% +problem so let me let me take us through + + + align:start position:0% +problem so let me let me take us through +it so we're going to consider a position + + align:start position:0% +it so we're going to consider a position + + + align:start position:0% +it so we're going to consider a position +Vector that's described by uh X oft yft + + align:start position:0% +Vector that's described by uh X oft yft + + + align:start position:0% +Vector that's described by uh X oft yft +t zero I want to have it in three space + + align:start position:0% +t zero I want to have it in three space + + + align:start position:0% +t zero I want to have it in three space +so I can take a cross product later um + + align:start position:0% +so I can take a cross product later um + + + align:start position:0% +so I can take a cross product later um +and then we're going to suppose that it + + align:start position:0% +and then we're going to suppose that it + + + align:start position:0% +and then we're going to suppose that it +actually has constant length and that + + align:start position:0% +actually has constant length and that + + + align:start position:0% +actually has constant length and that +when I look at the acceleration vector + + align:start position:0% +when I look at the acceleration vector + + + align:start position:0% +when I look at the acceleration vector +at T it's actually equal to a constant + + align:start position:0% +at T it's actually equal to a constant + + + align:start position:0% +at T it's actually equal to a constant +times times R of T where the constant is + + align:start position:0% +times times R of T where the constant is + + + align:start position:0% +times times R of T where the constant is +not zero okay so I can these are the two + + align:start position:0% +not zero okay so I can these are the two + + + align:start position:0% +not zero okay so I can these are the two +things I know about this position Vector + + align:start position:0% +things I know about this position Vector + + + align:start position:0% +things I know about this position Vector +it has constant length for all T it's it + + align:start position:0% +it has constant length for all T it's it + + + align:start position:0% +it has constant length for all T it's it +has constant length and the acceleration + + align:start position:0% +has constant length and the acceleration + + + align:start position:0% +has constant length and the acceleration +is always equal to some some constant + + align:start position:0% +is always equal to some some constant + + + align:start position:0% +is always equal to some some constant +times the position okay that's what I'm + + align:start position:0% +times the position okay that's what I'm + + + align:start position:0% +times the position okay that's what I'm +giving you and now I want you to use + + align:start position:0% +giving you and now I want you to use + + + align:start position:0% +giving you and now I want you to use +those things + + align:start position:0% +those things + + + align:start position:0% +those things +and vector differentiation to show that + + align:start position:0% +and vector differentiation to show that + + + align:start position:0% +and vector differentiation to show that +R do V is equal to Zer where V is the + + align:start position:0% +R do V is equal to Zer where V is the + + + align:start position:0% +R do V is equal to Zer where V is the +velocity and then to show that R cross V + + align:start position:0% +velocity and then to show that R cross V + + + align:start position:0% +velocity and then to show that R cross V +is constant so you're going to have to + + align:start position:0% +is constant so you're going to have to + + + align:start position:0% +is constant so you're going to have to +figure out essentially the thing you + + align:start position:0% +figure out essentially the thing you + + + align:start position:0% +figure out essentially the thing you +have to figure out is what relationship + + align:start position:0% +have to figure out is what relationship + + + align:start position:0% +have to figure out is what relationship +do you want to differentiate to to show + + align:start position:0% +do you want to differentiate to to show + + + align:start position:0% +do you want to differentiate to to show +these two things okay that's the hard + + align:start position:0% +these two things okay that's the hard + + + align:start position:0% +these two things okay that's the hard +part of this problem and then I want to + + align:start position:0% +part of this problem and then I want to + + + align:start position:0% +part of this problem and then I want to +see if you can give an example of such + + align:start position:0% +see if you can give an example of such + + + align:start position:0% +see if you can give an example of such +an R so if you can give an example of a + + align:start position:0% +an R so if you can give an example of a + + + align:start position:0% +an R so if you can give an example of a +position Vector that has these + + align:start position:0% +position Vector that has these + + + align:start position:0% +position Vector that has these +properties and maybe if you're having a + + align:start position:0% +properties and maybe if you're having a + + + align:start position:0% +properties and maybe if you're having a +a hard time the first thing for you to + + align:start position:0% +a hard time the first thing for you to + + + align:start position:0% +a hard time the first thing for you to +do might be to think about this and to + + align:start position:0% +do might be to think about this and to + + + align:start position:0% +do might be to think about this and to +see if you can figure out an example of + + align:start position:0% +see if you can figure out an example of + + + align:start position:0% +see if you can figure out an example of +that and then see kind of how things + + align:start position:0% +that and then see kind of how things + + + align:start position:0% +that and then see kind of how things +work together in that example that may + + align:start position:0% +work together in that example that may + + + align:start position:0% +work together in that example that may +actually prove helpful um so why don't + + align:start position:0% +actually prove helpful um so why don't + + + align:start position:0% +actually prove helpful um so why don't +you work on this problem pause the video + + align:start position:0% +you work on this problem pause the video + + + align:start position:0% +you work on this problem pause the video +and then when you're feeling good about + + align:start position:0% +and then when you're feeling good about + + + align:start position:0% +and then when you're feeling good about +your answer you can you can bring the + + align:start position:0% +your answer you can you can bring the + + + align:start position:0% +your answer you can you can bring the +video back up and I'll show you how I do + + align:start position:0% +video back up and I'll show you how I do + + + align:start position:0% +video back up and I'll show you how I do +it + + align:start position:0% + + + + align:start position:0% + +okay welcome back so there is a lot to + + align:start position:0% +okay welcome back so there is a lot to + + + align:start position:0% +okay welcome back so there is a lot to +do in this problem but let me just + + align:start position:0% +do in this problem but let me just + + + align:start position:0% +do in this problem but let me just +remind you what the framework is we have + + align:start position:0% +remind you what the framework is we have + + + align:start position:0% +remind you what the framework is we have +a position vector and we know two things + + align:start position:0% +a position vector and we know two things + + + align:start position:0% +a position vector and we know two things +about it we know that it has constant + + align:start position:0% +about it we know that it has constant + + + align:start position:0% +about it we know that it has constant +length and we know that the acceleration + + align:start position:0% +length and we know that the acceleration + + + align:start position:0% +length and we know that the acceleration +is always equal to some constant times + + align:start position:0% +is always equal to some constant times + + + align:start position:0% +is always equal to some constant times +the position I didn't give you the + + align:start position:0% +the position I didn't give you the + + + align:start position:0% +the position I didn't give you the +constant but we know it's always equal + + align:start position:0% +constant but we know it's always equal + + + align:start position:0% +constant but we know it's always equal +to some constant times the position and + + align:start position:0% +to some constant times the position and + + + align:start position:0% +to some constant times the position and +then we wanted to show two things using + + align:start position:0% +then we wanted to show two things using + + + align:start position:0% +then we wanted to show two things using +vector differentiation we wanted to show + + align:start position:0% +vector differentiation we wanted to show + + + align:start position:0% +vector differentiation we wanted to show +that R.V was zero and we wanted to show + + align:start position:0% +that R.V was zero and we wanted to show + + + align:start position:0% +that R.V was zero and we wanted to show +that R cross V was + + align:start position:0% +that R cross V was + + + align:start position:0% +that R cross V was +constant and uh and then we want to talk + + align:start position:0% +constant and uh and then we want to talk + + + align:start position:0% +constant and uh and then we want to talk +about what is an example so let's start + + align:start position:0% +about what is an example so let's start + + + align:start position:0% +about what is an example so let's start +off and see if we can figure out how to + + align:start position:0% +off and see if we can figure out how to + + + align:start position:0% +off and see if we can figure out how to +show that R.V is equal to zero and you + + align:start position:0% +show that R.V is equal to zero and you + + + align:start position:0% +show that R.V is equal to zero and you +know as you're thinking about this + + align:start position:0% +know as you're thinking about this + + + align:start position:0% +know as you're thinking about this +problem something something that you + + align:start position:0% +problem something something that you + + + align:start position:0% +problem something something that you +want to remember as you're thinking + + align:start position:0% +want to remember as you're thinking + + + align:start position:0% +want to remember as you're thinking +about this is well what are the things + + align:start position:0% +about this is well what are the things + + + align:start position:0% +about this is well what are the things +that I know I know that that R.R is is + + align:start position:0% +that I know I know that that R.R is is + + + align:start position:0% +that I know I know that that R.R is is +constant so I'm going to write that down + + align:start position:0% +constant so I'm going to write that down + + + align:start position:0% +constant so I'm going to write that down +r. R I'm not going to say is equal to C + + align:start position:0% +r. R I'm not going to say is equal to C + + + align:start position:0% +r. R I'm not going to say is equal to C +because that's a different constant so + + align:start position:0% +because that's a different constant so + + + align:start position:0% +because that's a different constant so +I'll just let me just call it C1 okay + + align:start position:0% +I'll just let me just call it C1 okay + + + align:start position:0% +I'll just let me just call it C1 okay +that's a different constant than my C + + align:start position:0% +that's a different constant than my C + + + align:start position:0% +that's a different constant than my C +maybe okay I know that r. R is some + + align:start position:0% +maybe okay I know that r. R is some + + + align:start position:0% +maybe okay I know that r. R is some +constant and I want to show something + + align:start position:0% +constant and I want to show something + + + align:start position:0% +constant and I want to show something +about + + align:start position:0% +about + + + align:start position:0% +about +R.V + + align:start position:0% +R.V + + + align:start position:0% +R.V +right so if I'm looking at this and I I + + align:start position:0% +right so if I'm looking at this and I I + + + align:start position:0% +right so if I'm looking at this and I I +say well I know this thing here so it's + + align:start position:0% +say well I know this thing here so it's + + + align:start position:0% +say well I know this thing here so it's +the only dotproduct relationship that I + + align:start position:0% +the only dotproduct relationship that I + + + align:start position:0% +the only dotproduct relationship that I +have because right now I I know a + + align:start position:0% +have because right now I I know a + + + align:start position:0% +have because right now I I know a +relationship uh between A and R and I + + align:start position:0% +relationship uh between A and R and I + + + align:start position:0% +relationship uh between A and R and I +know R has constant length since that's + + align:start position:0% +know R has constant length since that's + + + align:start position:0% +know R has constant length since that's +all I gave you if I want to look at a + + align:start position:0% +all I gave you if I want to look at a + + + align:start position:0% +all I gave you if I want to look at a +DOT product this is the relationship I + + align:start position:0% +DOT product this is the relationship I + + + align:start position:0% +DOT product this is the relationship I +know the constant length thing and so I + + align:start position:0% +know the constant length thing and so I + + + align:start position:0% +know the constant length thing and so I +know I somehow have to use this one to + + align:start position:0% +know I somehow have to use this one to + + + align:start position:0% +know I somehow have to use this one to +figure out something about R.V okay well + + align:start position:0% +figure out something about R.V okay well + + + align:start position:0% +figure out something about R.V okay well +what's the point that we should realize + + align:start position:0% +what's the point that we should realize + + + align:start position:0% +what's the point that we should realize +what is v v is is DDT of R right so I + + align:start position:0% +what is v v is is DDT of R right so I + + + align:start position:0% +what is v v is is DDT of R right so I +could take the derivative if I could + + align:start position:0% +could take the derivative if I could + + + align:start position:0% +could take the derivative if I could +take the derivative of just one of these + + align:start position:0% +take the derivative of just one of these + + + align:start position:0% +take the derivative of just one of these +things then I would get R.V down here + + align:start position:0% +things then I would get R.V down here + + + align:start position:0% +things then I would get R.V down here +right DD if I took DDT of just one of + + align:start position:0% +right DD if I took DDT of just one of + + + align:start position:0% +right DD if I took DDT of just one of +these I would get the + + align:start position:0% +these I would get the + + + align:start position:0% +these I would get the +R.V and DDT of this is zero but I can't + + align:start position:0% +R.V and DDT of this is zero but I can't + + + align:start position:0% +R.V and DDT of this is zero but I can't +do that right because if I take DDT of + + align:start position:0% +do that right because if I take DDT of + + + align:start position:0% +do that right because if I take DDT of +this whole thing I'm going to end up + + align:start position:0% +this whole thing I'm going to end up + + + align:start position:0% +this whole thing I'm going to end up +having to differentiate this R once and + + align:start position:0% +having to differentiate this R once and + + + align:start position:0% +having to differentiate this R once and +leave this alone and then I'm going to + + align:start position:0% +leave this alone and then I'm going to + + + align:start position:0% +leave this alone and then I'm going to +have to differentiate this R and leave + + align:start position:0% +have to differentiate this R and leave + + + align:start position:0% +have to differentiate this R and leave +this alone but if you heard what I was + + align:start position:0% +this alone but if you heard what I was + + + align:start position:0% +this alone but if you heard what I was +just saying maybe you see that that's + + align:start position:0% +just saying maybe you see that that's + + + align:start position:0% +just saying maybe you see that that's +actually still going to be okay so let's + + align:start position:0% +actually still going to be okay so let's + + + align:start position:0% +actually still going to be okay so let's +look at what happens I mean this is all + + align:start position:0% +look at what happens I mean this is all + + + align:start position:0% +look at what happens I mean this is all +really I have to work with so I'm going + + align:start position:0% +really I have to work with so I'm going + + + align:start position:0% +really I have to work with so I'm going +to explore let's look at what happens + + align:start position:0% +to explore let's look at what happens + + + align:start position:0% +to explore let's look at what happens +when I take + + align:start position:0% +when I take + + + align:start position:0% +when I take +DDT of + + align:start position:0% +DDT of + + + align:start position:0% +DDT of +R.R and I'm going to leave start leaving + + align:start position:0% +R.R and I'm going to leave start leaving + + + align:start position:0% +R.R and I'm going to leave start leaving +off the hats here because I'm going to + + align:start position:0% +off the hats here because I'm going to + + + align:start position:0% +off the hats here because I'm going to +leave them off somewhere so we're just + + align:start position:0% +leave them off somewhere so we're just + + + align:start position:0% +leave them off somewhere so we're just +leave them off now and and then I won't + + align:start position:0% +leave them off now and and then I won't + + + align:start position:0% +leave them off now and and then I won't +I won't leave some off and put some on + + align:start position:0% +I won't leave some off and put some on + + + align:start position:0% +I won't leave some off and put some on +so from here on out I'm just going to + + align:start position:0% +so from here on out I'm just going to + + + align:start position:0% +so from here on out I'm just going to +write r v and a without the hats but but + + align:start position:0% +write r v and a without the hats but but + + + align:start position:0% +write r v and a without the hats but but +they're + + align:start position:0% +they're + + + align:start position:0% +they're +vectors okay so DDT of r. R well I have + + align:start position:0% +vectors okay so DDT of r. R well I have + + + align:start position:0% +vectors okay so DDT of r. R well I have +to take DDT of R and then I dot that + + align:start position:0% +to take DDT of R and then I dot that + + + align:start position:0% +to take DDT of R and then I dot that +with + + align:start position:0% +with + + + align:start position:0% +with +r and then I take R dotted with uh sorry + + align:start position:0% +r and then I take R dotted with uh sorry + + + align:start position:0% +r and then I take R dotted with uh sorry +DDT of R DDT of R + + align:start position:0% +DDT of R DDT of R + + + align:start position:0% +DDT of R DDT of R +right well what do I get here DDT of r + + align:start position:0% +right well what do I get here DDT of r + + + align:start position:0% +right well what do I get here DDT of r +said was V so that's v. + + align:start position:0% +said was V so that's v. + + + align:start position:0% +said was V so that's v. +R and what do I get here this is R do oh + + align:start position:0% +R and what do I get here this is R do oh + + + align:start position:0% +R and what do I get here this is R do oh +there's DDT of R again so I get + + align:start position:0% +there's DDT of R again so I get + + + align:start position:0% +there's DDT of R again so I get +R.V now the great thing about the dot + + align:start position:0% +R.V now the great thing about the dot + + + align:start position:0% +R.V now the great thing about the dot +product is that if I switch the order of + + align:start position:0% +product is that if I switch the order of + + + align:start position:0% +product is that if I switch the order of +these two it's still the same thing so I + + align:start position:0% +these two it's still the same thing so I + + + align:start position:0% +these two it's still the same thing so I +can just write this as uh well I'll + + align:start position:0% +can just write this as uh well I'll + + + align:start position:0% +can just write this as uh well I'll +switch the order of this one so they + + align:start position:0% +switch the order of this one so they + + + align:start position:0% +switch the order of this one so they +both look like + + align:start position:0% +both look like + + + align:start position:0% +both look like +R.V plus + + align:start position:0% +R.V plus + + + align:start position:0% +R.V plus +R.V and that means I get two + + align:start position:0% +R.V and that means I get two + + + align:start position:0% +R.V and that means I get two +R.V right so so DDT of r r. R is + + align:start position:0% +R.V right so so DDT of r r. R is + + + align:start position:0% +R.V right so so DDT of r r. R is +actually two of R dotted with v the + + align:start position:0% +actually two of R dotted with v the + + + align:start position:0% +actually two of R dotted with v the +position dotted with the velocity now + + align:start position:0% +position dotted with the velocity now + + + align:start position:0% +position dotted with the velocity now +why is this going to help me because + + align:start position:0% +why is this going to help me because + + + align:start position:0% +why is this going to help me because +what do I know about this quantity + + align:start position:0% +what do I know about this quantity + + + align:start position:0% +what do I know about this quantity +R.R I know it's constant right so what + + align:start position:0% +R.R I know it's constant right so what + + + align:start position:0% +R.R I know it's constant right so what +is DDT of a constant DDT of a constant + + align:start position:0% +is DDT of a constant DDT of a constant + + + align:start position:0% +is DDT of a constant DDT of a constant +zero so I actually started off with + + align:start position:0% +zero so I actually started off with + + + align:start position:0% +zero so I actually started off with +knowing this was zero so if I go through + + align:start position:0% +knowing this was zero so if I go through + + + align:start position:0% +knowing this was zero so if I go through +the whole chain I see Zero is equal to + + align:start position:0% +the whole chain I see Zero is equal to + + + align:start position:0% +the whole chain I see Zero is equal to +let me put the zero down here again Zer + + align:start position:0% +let me put the zero down here again Zer + + + align:start position:0% +let me put the zero down here again Zer +is equal to 2 R.V and so R.V I know is + + align:start position:0% +is equal to 2 R.V and so R.V I know is + + + align:start position:0% +is equal to 2 R.V and so R.V I know is +equal to zero what does that mean + + align:start position:0% +equal to zero what does that mean + + + align:start position:0% +equal to zero what does that mean +geometrically that means r and v are + + align:start position:0% +geometrically that means r and v are + + + align:start position:0% +geometrically that means r and v are +orthogonal and where is V going to sit + + align:start position:0% +orthogonal and where is V going to sit + + + align:start position:0% +orthogonal and where is V going to sit +well if I come back over to how I + + align:start position:0% +well if I come back over to how I + + + align:start position:0% +well if I come back over to how I +described + + align:start position:0% +described + + + align:start position:0% +described +r r is in the XY plane right the Z + + align:start position:0% +r r is in the XY plane right the Z + + + align:start position:0% +r r is in the XY plane right the Z +component is zero so if I if I + + align:start position:0% +component is zero so if I if I + + + align:start position:0% +component is zero so if I if I +differentiate if I take DDT of R I'm + + align:start position:0% +differentiate if I take DDT of R I'm + + + align:start position:0% +differentiate if I take DDT of R I'm +going to have the derivative of the of + + align:start position:0% +going to have the derivative of the of + + + align:start position:0% +going to have the derivative of the of +the function of of X as a function of T + + align:start position:0% +the function of of X as a function of T + + + align:start position:0% +the function of of X as a function of T +and then whatever Y is as a function of + + align:start position:0% +and then whatever Y is as a function of + + + align:start position:0% +and then whatever Y is as a function of +t i take that derivative and this is + + align:start position:0% +t i take that derivative and this is + + + align:start position:0% +t i take that derivative and this is +still zero so V is going to sit in the + + align:start position:0% +still zero so V is going to sit in the + + + align:start position:0% +still zero so V is going to sit in the +XY plane and based on what we know so + + align:start position:0% +XY plane and based on what we know so + + + align:start position:0% +XY plane and based on what we know so +far we know it's actually orthogonal to + + align:start position:0% +far we know it's actually orthogonal to + + + align:start position:0% +far we know it's actually orthogonal to +R so they make a 90° angle at all times + + align:start position:0% +R so they make a 90° angle at all times + + + align:start position:0% +R so they make a 90° angle at all times +T okay and how did we do that again I + + align:start position:0% +T okay and how did we do that again I + + + align:start position:0% +T okay and how did we do that again I +just want to remind you we knew one do + + align:start position:0% +just want to remind you we knew one do + + + align:start position:0% +just want to remind you we knew one do +product relationship that was r. R was a + + align:start position:0% +product relationship that was r. R was a + + + align:start position:0% +product relationship that was r. R was a +constant so we differentiated that and + + align:start position:0% +constant so we differentiated that and + + + align:start position:0% +constant so we differentiated that and +tried to see what happened and that the + + align:start position:0% +tried to see what happened and that the + + + align:start position:0% +tried to see what happened and that the +main point at the end of it was that + + align:start position:0% +main point at the end of it was that + + + align:start position:0% +main point at the end of it was that +when I had a v.r I could rewrite it as + + align:start position:0% +when I had a v.r I could rewrite it as + + + align:start position:0% +when I had a v.r I could rewrite it as +an R.V and so I just end up with two of + + align:start position:0% +an R.V and so I just end up with two of + + + align:start position:0% +an R.V and so I just end up with two of +something that I want to know about so + + align:start position:0% +something that I want to know about so + + + align:start position:0% +something that I want to know about so +that's the main idea of the first part + + align:start position:0% +that's the main idea of the first part + + + align:start position:0% +that's the main idea of the first part +now the second part was I asked you to + + align:start position:0% +now the second part was I asked you to + + + align:start position:0% +now the second part was I asked you to +figure out something over here we wanted + + align:start position:0% +figure out something over here we wanted + + + align:start position:0% +figure out something over here we wanted +to know that R cross V is constant okay + + align:start position:0% +to know that R cross V is constant okay + + + align:start position:0% +to know that R cross V is constant okay +so in in T it's always the same all + + align:start position:0% +so in in T it's always the same all + + + align:start position:0% +so in in T it's always the same all +right so let's think about if I want to + + align:start position:0% +right so let's think about if I want to + + + align:start position:0% +right so let's think about if I want to +show that for every T something is + + align:start position:0% +show that for every T something is + + + align:start position:0% +show that for every T something is +constant I could show actually I've sort + + align:start position:0% +constant I could show actually I've sort + + + align:start position:0% +constant I could show actually I've sort +of seen it already I could show that its + + align:start position:0% +of seen it already I could show that its + + + align:start position:0% +of seen it already I could show that its +derivative is zero okay so if our cross + + align:start position:0% +derivative is zero okay so if our cross + + + align:start position:0% +derivative is zero okay so if our cross +V is constant or if it's derivative is + + align:start position:0% +V is constant or if it's derivative is + + + align:start position:0% +V is constant or if it's derivative is +zero I should say then R cross V was + + align:start position:0% +zero I should say then R cross V was + + + align:start position:0% +zero I should say then R cross V was +constant right if it's derivative is + + align:start position:0% +constant right if it's derivative is + + + align:start position:0% +constant right if it's derivative is +zero for all T then R cross V is + + align:start position:0% +zero for all T then R cross V is + + + align:start position:0% +zero for all T then R cross V is +constant right so that's really what we + + align:start position:0% +constant right so that's really what we + + + align:start position:0% +constant right so that's really what we +want to exploit here so let's look + + align:start position:0% +want to exploit here so let's look + + + align:start position:0% +want to exploit here so let's look +at the idea so we want to again let me + + align:start position:0% +at the idea so we want to again let me + + + align:start position:0% +at the idea so we want to again let me +write it down show R cross V is + + align:start position:0% +write it down show R cross V is + + + align:start position:0% +write it down show R cross V is +constant and the strategy we're going to + + align:start position:0% +constant and the strategy we're going to + + + align:start position:0% +constant and the strategy we're going to +use + + align:start position:0% +use + + + align:start position:0% +use +is to do this we're going to + + align:start position:0% +is to do this we're going to + + + align:start position:0% +is to do this we're going to +show that + + align:start position:0% +show that + + + align:start position:0% +show that +DDT of R cross V is equal to zero right + + align:start position:0% +DDT of R cross V is equal to zero right + + + align:start position:0% +DDT of R cross V is equal to zero right +if we can show that then this means that + + align:start position:0% +if we can show that then this means that + + + align:start position:0% +if we can show that then this means that +for all T it's the same it's not + + align:start position:0% +for all T it's the same it's not + + + align:start position:0% +for all T it's the same it's not +changing in t right so for all t r cross + + align:start position:0% +changing in t right so for all t r cross + + + align:start position:0% +changing in t right so for all t r cross +V is going to be the same so R cross V + + align:start position:0% +V is going to be the same so R cross V + + + align:start position:0% +V is going to be the same so R cross V +is going to be constant so the + + align:start position:0% +is going to be constant so the + + + align:start position:0% +is going to be constant so the +difference between the two problems was + + align:start position:0% +difference between the two problems was + + + align:start position:0% +difference between the two problems was +in the first problem you didn't quite + + align:start position:0% +in the first problem you didn't quite + + + align:start position:0% +in the first problem you didn't quite +know maybe what expression you needed to + + align:start position:0% +know maybe what expression you needed to + + + align:start position:0% +know maybe what expression you needed to +differentiate to find what you were + + align:start position:0% +differentiate to find what you were + + + align:start position:0% +differentiate to find what you were +looking for here we know what we need to + + align:start position:0% +looking for here we know what we need to + + + align:start position:0% +looking for here we know what we need to +differentiate but we have to make sure + + align:start position:0% +differentiate but we have to make sure + + + align:start position:0% +differentiate but we have to make sure +we understand to show this is constant + + align:start position:0% +we understand to show this is constant + + + align:start position:0% +we understand to show this is constant +when we differentiate we should get zero + + align:start position:0% +when we differentiate we should get zero + + + align:start position:0% +when we differentiate we should get zero +okay so that's that's sort of slight + + align:start position:0% +okay so that's that's sort of slight + + + align:start position:0% +okay so that's that's sort of slight +different type of of problem I'm asking + + align:start position:0% +different type of of problem I'm asking + + + align:start position:0% +different type of of problem I'm asking +you maybe from the other side here so + + align:start position:0% +you maybe from the other side here so + + + align:start position:0% +you maybe from the other side here so +let's now let's just see what we get on + + align:start position:0% +let's now let's just see what we get on + + + align:start position:0% +let's now let's just see what we get on +the left hand side so what's DDT of R + + align:start position:0% +the left hand side so what's DDT of R + + + align:start position:0% +the left hand side so what's DDT of R +cross V well DDT of R is V right so we + + align:start position:0% +cross V well DDT of R is V right so we + + + align:start position:0% +cross V well DDT of R is V right so we +get V cross V for the first term so we + + align:start position:0% +get V cross V for the first term so we + + + align:start position:0% +get V cross V for the first term so we +take DDT of R we get V we leave this V + + align:start position:0% +take DDT of R we get V we leave this V + + + align:start position:0% +take DDT of R we get V we leave this V +alone and then we add to that uh R cross + + align:start position:0% +alone and then we add to that uh R cross + + + align:start position:0% +alone and then we add to that uh R cross +DDT of V what's DDT of V that's a + + align:start position:0% +DDT of V what's DDT of V that's a + + + align:start position:0% +DDT of V what's DDT of V that's a +right now let's take a look at this well + + align:start position:0% +right now let's take a look at this well + + + align:start position:0% +right now let's take a look at this well +V cross v v is pointing in the same + + align:start position:0% +V cross v v is pointing in the same + + + align:start position:0% +V cross v v is pointing in the same +direction as itself so when you try and + + align:start position:0% +direction as itself so when you try and + + + align:start position:0% +direction as itself so when you try and +take a cross product of that you know + + align:start position:0% +take a cross product of that you know + + + align:start position:0% +take a cross product of that you know +that the length of your vector should be + + align:start position:0% +that the length of your vector should be + + + align:start position:0% +that the length of your vector should be +the area of the parallelogram formed by + + align:start position:0% +the area of the parallelogram formed by + + + align:start position:0% +the area of the parallelogram formed by +these two vectors but V and it's is + + align:start position:0% +these two vectors but V and it's is + + + align:start position:0% +these two vectors but V and it's is +pointing in the same direction as itself + + align:start position:0% +pointing in the same direction as itself + + + align:start position:0% +pointing in the same direction as itself +so there's no area there that's a + + align:start position:0% +so there's no area there that's a + + + align:start position:0% +so there's no area there that's a +geometric interpretation of why this + + align:start position:0% +geometric interpretation of why this + + + align:start position:0% +geometric interpretation of why this +thing should be zero another reason is + + align:start position:0% +thing should be zero another reason is + + + align:start position:0% +thing should be zero another reason is +remember that uh that your V cross V is + + align:start position:0% +remember that uh that your V cross V is + + + align:start position:0% +remember that uh that your V cross V is +going to include a s Theta term where + + align:start position:0% +going to include a s Theta term where + + + align:start position:0% +going to include a s Theta term where +Theta is the angle between the two + + align:start position:0% +Theta is the angle between the two + + + align:start position:0% +Theta is the angle between the two +vectors right that's another formula you + + align:start position:0% +vectors right that's another formula you + + + align:start position:0% +vectors right that's another formula you +have and so when you look at the angle + + align:start position:0% +have and so when you look at the angle + + + align:start position:0% +have and so when you look at the angle +between this vector and itself it's zero + + align:start position:0% +between this vector and itself it's zero + + + align:start position:0% +between this vector and itself it's zero +and S 0 is z so this is in fact zero + + align:start position:0% +and S 0 is z so this is in fact zero + + + align:start position:0% +and S 0 is z so this is in fact zero +that part so if this is zero then we get + + align:start position:0% +that part so if this is zero then we get + + + align:start position:0% +that part so if this is zero then we get +what we want well I only gave you one + + align:start position:0% +what we want well I only gave you one + + + align:start position:0% +what we want well I only gave you one +other bit of information in the problem + + align:start position:0% +other bit of information in the problem + + + align:start position:0% +other bit of information in the problem +and if you remember it was that a is + + align:start position:0% +and if you remember it was that a is + + + align:start position:0% +and if you remember it was that a is +always equal to a constant time R so I + + align:start position:0% +always equal to a constant time R so I + + + align:start position:0% +always equal to a constant time R so I +can rewrite this right hand side as R + + align:start position:0% +can rewrite this right hand side as R + + + align:start position:0% +can rewrite this right hand side as R +cross a constant time R and because of + + align:start position:0% +cross a constant time R and because of + + + align:start position:0% +cross a constant time R and because of +this because of properties of these + + align:start position:0% +this because of properties of these + + + align:start position:0% +this because of properties of these +cross products I can pull out the + + align:start position:0% +cross products I can pull out the + + + align:start position:0% +cross products I can pull out the +constant or I can actually I guess I + + align:start position:0% +constant or I can actually I guess I + + + align:start position:0% +constant or I can actually I guess I +don't need to pull it out to talk about + + align:start position:0% +don't need to pull it out to talk about + + + align:start position:0% +don't need to pull it out to talk about +it but it's nicer if I pull it out and + + align:start position:0% +it but it's nicer if I pull it out and + + + align:start position:0% +it but it's nicer if I pull it out and +look at what I have here and I have the + + align:start position:0% +look at what I have here and I have the + + + align:start position:0% +look at what I have here and I have the +exact same situation as V cross V so I + + align:start position:0% +exact same situation as V cross V so I + + + align:start position:0% +exact same situation as V cross V so I +mean this was still pointing in the same + + align:start position:0% +mean this was still pointing in the same + + + align:start position:0% +mean this was still pointing in the same +direction constant times R and R Still + + align:start position:0% +direction constant times R and R Still + + + align:start position:0% +direction constant times R and R Still +Point in the same direction as as as if + + align:start position:0% +Point in the same direction as as as if + + + align:start position:0% +Point in the same direction as as as if +I were to compare R and R so I didn't + + align:start position:0% +I were to compare R and R so I didn't + + + align:start position:0% +I were to compare R and R so I didn't +have to pull out the constant but then + + align:start position:0% +have to pull out the constant but then + + + align:start position:0% +have to pull out the constant but then +right here it's very easy to see that + + align:start position:0% +right here it's very easy to see that + + + align:start position:0% +right here it's very easy to see that +this is also zero so I had Z plus this + + align:start position:0% +this is also zero so I had Z plus this + + + align:start position:0% +this is also zero so I had Z plus this +so I get zero so I've shown through this + + align:start position:0% +so I get zero so I've shown through this + + + align:start position:0% +so I get zero so I've shown through this +process maybe I should have written + + align:start position:0% +process maybe I should have written + + + align:start position:0% +process maybe I should have written +equal signs here + + align:start position:0% +equal signs here + + + align:start position:0% +equal signs here +that DDT of R cross V is actually equal + + align:start position:0% +that DDT of R cross V is actually equal + + + align:start position:0% +that DDT of R cross V is actually equal +to zero and so you see that that this + + align:start position:0% +to zero and so you see that that this + + + align:start position:0% +to zero and so you see that that this +this cross product between r and v which + + align:start position:0% +this cross product between r and v which + + + align:start position:0% +this cross product between r and v which +we know are orthogonals sitting in the + + align:start position:0% +we know are orthogonals sitting in the + + + align:start position:0% +we know are orthogonals sitting in the +XY plane that it's always the same it's + + align:start position:0% +XY plane that it's always the same it's + + + align:start position:0% +XY plane that it's always the same it's +always the same vector and now I asked + + align:start position:0% +always the same vector and now I asked + + + align:start position:0% +always the same vector and now I asked +you to give an example and maybe you + + align:start position:0% +you to give an example and maybe you + + + align:start position:0% +you to give an example and maybe you +thought of an example first and then + + align:start position:0% +thought of an example first and then + + + align:start position:0% +thought of an example first and then +thought of how it worked and so the + + align:start position:0% +thought of how it worked and so the + + + align:start position:0% +thought of how it worked and so the +easiest example is if you let R of t + + align:start position:0% +easiest example is if you let R of t + + + align:start position:0% +easiest example is if you let R of t +equal cosine T sin T so the easiest + + align:start position:0% +equal cosine T sin T so the easiest + + + align:start position:0% +equal cosine T sin T so the easiest +example + + align:start position:0% + + + + align:start position:0% + +there are others + + align:start position:0% +there are others + + + align:start position:0% +there are others +obviously is if you let R of t equal + + align:start position:0% +obviously is if you let R of t equal + + + align:start position:0% +obviously is if you let R of t equal +cosine T sin T comma zero sorry I wasn't + + align:start position:0% +cosine T sin T comma zero sorry I wasn't + + + align:start position:0% +cosine T sin T comma zero sorry I wasn't +I was thinking about it in in three + + align:start position:0% +I was thinking about it in in three + + + align:start position:0% +I was thinking about it in in three +space right and in fact if I were to + + align:start position:0% +space right and in fact if I were to + + + align:start position:0% +space right and in fact if I were to +scale this it would still work I could + + align:start position:0% +scale this it would still work I could + + + align:start position:0% +scale this it would still work I could +put any constant in front this carves + + align:start position:0% +put any constant in front this carves + + + align:start position:0% +put any constant in front this carves +out if I let T go between zero and 2 pi + + align:start position:0% +out if I let T go between zero and 2 pi + + + align:start position:0% +out if I let T go between zero and 2 pi +or even minus infinity to Infinity I'm + + align:start position:0% +or even minus infinity to Infinity I'm + + + align:start position:0% +or even minus infinity to Infinity I'm +just carving out vectors that are uh + + align:start position:0% +just carving out vectors that are uh + + + align:start position:0% +just carving out vectors that are uh +that are the position Vector is always + + align:start position:0% +that are the position Vector is always + + + align:start position:0% +that are the position Vector is always +on the unit circle in this case right if + + align:start position:0% +on the unit circle in this case right if + + + align:start position:0% +on the unit circle in this case right if +I put a constant in front it's on + + align:start position:0% +I put a constant in front it's on + + + align:start position:0% +I put a constant in front it's on +another Circle so for whatever values of + + align:start position:0% +another Circle so for whatever values of + + + align:start position:0% +another Circle so for whatever values of +T I'm letting myself vary over it's + + align:start position:0% +T I'm letting myself vary over it's + + + align:start position:0% +T I'm letting myself vary over it's +going to be all the vectors are going to + + align:start position:0% +going to be all the vectors are going to + + + align:start position:0% +going to be all the vectors are going to +lie on some part of of a circle okay and + + align:start position:0% +lie on some part of of a circle okay and + + + align:start position:0% +lie on some part of of a circle okay and +so this is maybe the easi example maybe + + align:start position:0% +so this is maybe the easi example maybe + + + align:start position:0% +so this is maybe the easi example maybe +you want to calculate just to give + + align:start position:0% +you want to calculate just to give + + + align:start position:0% +you want to calculate just to give +yourself some practice what V of T is + + align:start position:0% +yourself some practice what V of T is + + + align:start position:0% +yourself some practice what V of T is +and what a of T actually is what these + + align:start position:0% +and what a of T actually is what these + + + align:start position:0% +and what a of T actually is what these +two quantities actually are and then + + align:start position:0% +two quantities actually are and then + + + align:start position:0% +two quantities actually are and then +look at what happens what happens with r + + align:start position:0% +look at what happens what happens with r + + + align:start position:0% +look at what happens what happens with r +and v and see y R.V is equal to zero + + align:start position:0% +and v and see y R.V is equal to zero + + + align:start position:0% +and v and see y R.V is equal to zero +what you should see I'll try and give + + align:start position:0% +what you should see I'll try and give + + + align:start position:0% +what you should see I'll try and give +you a a a picture of it geometrically + + align:start position:0% +you a a a picture of it geometrically + + + align:start position:0% +you a a a picture of it geometrically +what you should + + align:start position:0% +what you should + + + align:start position:0% +what you should +see is that you know if this is I'm + + align:start position:0% +see is that you know if this is I'm + + + align:start position:0% +see is that you know if this is I'm +going to try and we'll see if I can do + + align:start position:0% +going to try and we'll see if I can do + + + align:start position:0% +going to try and we'll see if I can do +this effectively a two-dimensional + + align:start position:0% +this effectively a two-dimensional + + + align:start position:0% +this effectively a two-dimensional +drawing in three space if this is the r + + align:start position:0% +drawing in three space if this is the r + + + align:start position:0% +drawing in three space if this is the r +I'm looking at that V has to be coming + + align:start position:0% +I'm looking at that V has to be coming + + + align:start position:0% +I'm looking at that V has to be coming +in this way out this way so there's R + + align:start position:0% +in this way out this way so there's R + + + align:start position:0% +in this way out this way so there's R +and there's V and this angle because I'm + + align:start position:0% +and there's V and this angle because I'm + + + align:start position:0% +and there's V and this angle because I'm +trying to squash what was a circle I + + align:start position:0% +trying to squash what was a circle I + + + align:start position:0% +trying to squash what was a circle I +guess I'll look from above first my + + align:start position:0% +guess I'll look from above first my + + + align:start position:0% +guess I'll look from above first my +picture is from above is looking like + + align:start position:0% +picture is from above is looking like + + + align:start position:0% +picture is from above is looking like +something like this there's R and + + align:start position:0% +something like this there's R and + + + align:start position:0% +something like this there's R and +there's V and that's a right angle right + + align:start position:0% +there's V and that's a right angle right + + + align:start position:0% +there's V and that's a right angle right +so if I look from this from coming down + + align:start position:0% +so if I look from this from coming down + + + align:start position:0% +so if I look from this from coming down +onto the XY plane here's a position + + align:start position:0% +onto the XY plane here's a position + + + align:start position:0% +onto the XY plane here's a position +Vector here's its velocity they're + + align:start position:0% +Vector here's its velocity they're + + + align:start position:0% +Vector here's its velocity they're +orthogonal and as I move all the way + + align:start position:0% +orthogonal and as I move all the way + + + align:start position:0% +orthogonal and as I move all the way +around the circle that position vector + + align:start position:0% +around the circle that position vector + + + align:start position:0% +around the circle that position vector +and the velocity are going to keep that + + align:start position:0% +and the velocity are going to keep that + + + align:start position:0% +and the velocity are going to keep that +relationship when I look at this I'm + + align:start position:0% +relationship when I look at this I'm + + + align:start position:0% +relationship when I look at this I'm +trying to kind of insert in the z-axis + + align:start position:0% +trying to kind of insert in the z-axis + + + align:start position:0% +trying to kind of insert in the z-axis +here when I look at this if I look at + + align:start position:0% +here when I look at this if I look at + + + align:start position:0% +here when I look at this if I look at +what is the cross product of these two + + align:start position:0% +what is the cross product of these two + + + align:start position:0% +what is the cross product of these two +vectors well it's always going to point + + align:start position:0% +vectors well it's always going to point + + + align:start position:0% +vectors well it's always going to point +in the Z Direction it's going to point + + align:start position:0% +in the Z Direction it's going to point + + + align:start position:0% +in the Z Direction it's going to point +straight in the Z direction from here + + align:start position:0% +straight in the Z direction from here + + + align:start position:0% +straight in the Z direction from here +because it's orthogonal to both of these + + align:start position:0% +because it's orthogonal to both of these + + + align:start position:0% +because it's orthogonal to both of these +it's going to point straight in the Z + + align:start position:0% +it's going to point straight in the Z + + + align:start position:0% +it's going to point straight in the Z +Direction and when I show that I know R + + align:start position:0% +Direction and when I show that I know R + + + align:start position:0% +Direction and when I show that I know R +is constant length I can then see V is + + align:start position:0% +is constant length I can then see V is + + + align:start position:0% +is constant length I can then see V is +constant length from the example I have + + align:start position:0% +constant length from the example I have + + + align:start position:0% +constant length from the example I have +here and as I rotate I'm going to this + + align:start position:0% +here and as I rotate I'm going to this + + + align:start position:0% +here and as I rotate I'm going to this +is constant length Okay so this is where + + align:start position:0% +is constant length Okay so this is where + + + align:start position:0% +is constant length Okay so this is where +uh the sort of picture of what we were + + align:start position:0% +uh the sort of picture of what we were + + + align:start position:0% +uh the sort of picture of what we were +actually describing very much more + + align:start position:0% +actually describing very much more + + + align:start position:0% +actually describing very much more +generally in the first part of this so + + align:start position:0% +generally in the first part of this so + + + align:start position:0% +generally in the first part of this so +the main point that I that I want us to + + align:start position:0% +the main point that I that I want us to + + + align:start position:0% +the main point that I that I want us to +see in this problem is that when we want + + align:start position:0% +see in this problem is that when we want + + + align:start position:0% +see in this problem is that when we want +to find information about relationships + + align:start position:0% +to find information about relationships + + + align:start position:0% +to find information about relationships +between r or r v and a this position and + + align:start position:0% +between r or r v and a this position and + + + align:start position:0% +between r or r v and a this position and +velocity and + + align:start position:0% +velocity and + + + align:start position:0% +velocity and +acceleration what we can do is + + align:start position:0% +acceleration what we can do is + + + align:start position:0% +acceleration what we can do is +differentiate these Vector fields we saw + + align:start position:0% +differentiate these Vector fields we saw + + + align:start position:0% +differentiate these Vector fields we saw +an example when you were looking at I + + align:start position:0% +an example when you were looking at I + + + align:start position:0% +an example when you were looking at I +think uh kep Kepler's second law you saw + + align:start position:0% +think uh kep Kepler's second law you saw + + + align:start position:0% +think uh kep Kepler's second law you saw +this in lecture um but I just want to + + align:start position:0% +this in lecture um but I just want to + + + align:start position:0% +this in lecture um but I just want to +show you that you can you can use this + + align:start position:0% +show you that you can you can use this + + + align:start position:0% +show you that you can you can use this +if you don't necessarily know uh + + align:start position:0% +if you don't necessarily know uh + + + align:start position:0% +if you don't necessarily know uh +explicitly things about a a position + + align:start position:0% +explicitly things about a a position + + + align:start position:0% +explicitly things about a a position +Vector you can still find out things + + align:start position:0% +Vector you can still find out things + + + align:start position:0% +Vector you can still find out things +about its relationship if you're given + + align:start position:0% +about its relationship if you're given + + + align:start position:0% +about its relationship if you're given +if you're given some information you + + align:start position:0% +if you're given some information you + + + align:start position:0% +if you're given some information you +don't actually have to have a formula to + + align:start position:0% +don't actually have to have a formula to + + + align:start position:0% +don't actually have to have a formula to +find out some information about these + + align:start position:0% +find out some information about these + + + align:start position:0% +find out some information about these +relationships so I think that's where + + align:start position:0% +relationships so I think that's where + + + align:start position:0% +relationships so I think that's where +I'll stop \ No newline at end of file diff --git a/fLKNjWXk71s.txt b/fLKNjWXk71s.txt new file mode 100644 index 0000000000000000000000000000000000000000..e5936ca02dc06e40ccd843e175694e8b3e11f344 --- /dev/null +++ b/fLKNjWXk71s.txt @@ -0,0 +1,5139 @@ +align:start position:0% + +instead of saying analyze this + + align:start position:0% +instead of saying analyze this + + + align:start position:0% +instead of saying analyze this +theoretical problem I said analyze your + + align:start position:0% +theoretical problem I said analyze your + + + align:start position:0% +theoretical problem I said analyze your +toenails tell me how much arsenic and + + align:start position:0% +toenails tell me how much arsenic and + + + align:start position:0% +toenails tell me how much arsenic and +gold you've got in your body all we + + align:start position:0% +gold you've got in your body all we + + + align:start position:0% +gold you've got in your body all we +study at MIT is the natural world and + + align:start position:0% +study at MIT is the natural world and + + + align:start position:0% +study at MIT is the natural world and +things we make out of it so everything + + align:start position:0% +things we make out of it so everything + + + align:start position:0% +things we make out of it so everything +is reducible to practice everything can + + align:start position:0% +is reducible to practice everything can + + + align:start position:0% +is reducible to practice everything can +be real if you put in the effort today + + align:start position:0% +be real if you put in the effort today + + + align:start position:0% +be real if you put in the effort today +in the podcast we're talking about + + align:start position:0% +in the podcast we're talking about + + + align:start position:0% +in the podcast we're talking about +ionizing radiation and nuclear + + align:start position:0% +ionizing radiation and nuclear + + + align:start position:0% +ionizing radiation and nuclear +engineering how do you make these things + + align:start position:0% +engineering how do you make these things + + + align:start position:0% +engineering how do you make these things +real and tangible matter is a form of + + align:start position:0% +real and tangible matter is a form of + + + align:start position:0% +real and tangible matter is a form of +energy and once that clicked everything + + align:start position:0% +energy and once that clicked everything + + + align:start position:0% +energy and once that clicked everything +seemed to make sense radioactive decay + + align:start position:0% +seemed to make sense radioactive decay + + + align:start position:0% +seemed to make sense radioactive decay +nuclear reactions all these things I + + align:start position:0% +nuclear reactions all these things I + + + align:start position:0% +nuclear reactions all these things I +remember that aha moment in this class + + align:start position:0% +remember that aha moment in this class + + + align:start position:0% +remember that aha moment in this class +that I teach as a second year student + + align:start position:0% +that I teach as a second year student + + + align:start position:0% +that I teach as a second year student +back in 2002 and it's those kind of + + align:start position:0% +back in 2002 and it's those kind of + + + align:start position:0% +back in 2002 and it's those kind of +moments that made me want to stay in it + + align:start position:0% +moments that made me want to stay in it + + + align:start position:0% +moments that made me want to stay in it +because I feel like wow I really know + + align:start position:0% +because I feel like wow I really know + + + align:start position:0% +because I feel like wow I really know +this field now welcome to choc radio a + + align:start position:0% +this field now welcome to choc radio a + + + align:start position:0% +this field now welcome to choc radio a +podcast about inspired teaching at MIT + + align:start position:0% +podcast about inspired teaching at MIT + + + align:start position:0% +podcast about inspired teaching at MIT +I'm your host Sarah Hansen from MIT + + align:start position:0% +I'm your host Sarah Hansen from MIT + + + align:start position:0% +I'm your host Sarah Hansen from MIT +OpenCourseWare the nuclear engineering + + align:start position:0% +OpenCourseWare the nuclear engineering + + + align:start position:0% +OpenCourseWare the nuclear engineering +and ionizing radiation course at MIT + + align:start position:0% +and ionizing radiation course at MIT + + + align:start position:0% +and ionizing radiation course at MIT +take students from understanding basic + + align:start position:0% +take students from understanding basic + + + align:start position:0% +take students from understanding basic +physics to grappling with the core + + align:start position:0% +physics to grappling with the core + + + align:start position:0% +physics to grappling with the core +concepts of Einstein's e equals + + align:start position:0% +concepts of Einstein's e equals + + + align:start position:0% +concepts of Einstein's e equals +mc-squared in this episode we're going + + align:start position:0% +mc-squared in this episode we're going + + + align:start position:0% +mc-squared in this episode we're going +to delve into how this is possible and + + align:start position:0% +to delve into how this is possible and + + + align:start position:0% +to delve into how this is possible and +what it takes to make a class that's not + + align:start position:0% +what it takes to make a class that's not + + + align:start position:0% +what it takes to make a class that's not +only hands-on but also capable of + + align:start position:0% +only hands-on but also capable of + + + align:start position:0% +only hands-on but also capable of +evolving daily my guest is one of the + + align:start position:0% +evolving daily my guest is one of the + + + align:start position:0% +evolving daily my guest is one of the +main people that makes this happen + + align:start position:0% +main people that makes this happen + + + align:start position:0% +main people that makes this happen +professor Mike short this course is all + + align:start position:0% +professor Mike short this course is all + + + align:start position:0% +professor Mike short this course is all +about radiation both it's its origins + + align:start position:0% +about radiation both it's its origins + + + align:start position:0% +about radiation both it's its origins +and its uses so this is the first course + + align:start position:0% +and its uses so this is the first course + + + align:start position:0% +and its uses so this is the first course +on it's intro to everything nuclear that + + align:start position:0% +on it's intro to everything nuclear that + + + align:start position:0% +on it's intro to everything nuclear that +any student at MIT would take and a lot + + align:start position:0% +any student at MIT would take and a lot + + + align:start position:0% +any student at MIT would take and a lot +of times for students it's their first + + align:start position:0% +of times for students it's their first + + + align:start position:0% +of times for students it's their first +modern physics course the physics + + align:start position:0% +modern physics course the physics + + + align:start position:0% +modern physics course the physics +courses that first year students take + + align:start position:0% +courses that first year students take + + + align:start position:0% +courses that first year students take +are often things that we've known for + + align:start position:0% +are often things that we've known for + + + align:start position:0% +are often things that we've known for +100 to 300 years and the field of + + align:start position:0% +100 to 300 years and the field of + + + align:start position:0% +100 to 300 years and the field of +nuclear physics is still evolving we're + + align:start position:0% +nuclear physics is still evolving we're + + + align:start position:0% +nuclear physics is still evolving we're +still using nuclear radiation spectra to + + align:start position:0% +still using nuclear radiation spectra to + + + align:start position:0% +still using nuclear radiation spectra to +detect the presence of water on Mars or + + align:start position:0% +detect the presence of water on Mars or + + + align:start position:0% +detect the presence of water on Mars or +the moon we're still confirming our + + align:start position:0% +the moon we're still confirming our + + + align:start position:0% +the moon we're still confirming our +knowledge of which particles do and + + align:start position:0% +knowledge of which particles do and + + + align:start position:0% +knowledge of which particles do and +don't exist in Y so this is also intro + + align:start position:0% +don't exist in Y so this is also intro + + + align:start position:0% +don't exist in Y so this is also intro +to modern physics so nuclear science and + + align:start position:0% +to modern physics so nuclear science and + + + align:start position:0% +to modern physics so nuclear science and +radiation in particular are emotionally + + align:start position:0% +radiation in particular are emotionally + + + align:start position:0% +radiation in particular are emotionally +charged top + + align:start position:0% +charged top + + + align:start position:0% +charged top +you know you you read on the internet + + align:start position:0% +you know you you read on the internet + + + align:start position:0% +you know you you read on the internet +claims like cell phones cause cancer + + align:start position:0% +claims like cell phones cause cancer + + + align:start position:0% +claims like cell phones cause cancer +things like that how are you preparing + + align:start position:0% +things like that how are you preparing + + + align:start position:0% +things like that how are you preparing +students to debunk pseudoscience and to + + align:start position:0% +students to debunk pseudoscience and to + + + align:start position:0% +students to debunk pseudoscience and to +really serve the public we actually + + align:start position:0% +really serve the public we actually + + + align:start position:0% +really serve the public we actually +spend two weeks at the end of the class + + align:start position:0% +spend two weeks at the end of the class + + + align:start position:0% +spend two weeks at the end of the class +looking at studies that are false or + + align:start position:0% +looking at studies that are false or + + + align:start position:0% +looking at studies that are false or +have exaggerated claims and teaching + + align:start position:0% +have exaggerated claims and teaching + + + align:start position:0% +have exaggerated claims and teaching +students what to look for so the first + + align:start position:0% +students what to look for so the first + + + align:start position:0% +students what to look for so the first +11 weeks of the class we teach the + + align:start position:0% +11 weeks of the class we teach the + + + align:start position:0% +11 weeks of the class we teach the +students the fundamentals of nuclear + + align:start position:0% +students the fundamentals of nuclear + + + align:start position:0% +students the fundamentals of nuclear +science and then we turn to published + + align:start position:0% +science and then we turn to published + + + align:start position:0% +science and then we turn to published +articles and blogs and other things in + + align:start position:0% +articles and blogs and other things in + + + align:start position:0% +articles and blogs and other things in +the field and we debunk myths like cell + + align:start position:0% +the field and we debunk myths like cell + + + align:start position:0% +the field and we debunk myths like cell +phones cause cancer due to ionizing + + align:start position:0% +phones cause cancer due to ionizing + + + align:start position:0% +phones cause cancer due to ionizing +radiation cellphones don't emit ionizing + + align:start position:0% +radiation cellphones don't emit ionizing + + + align:start position:0% +radiation cellphones don't emit ionizing +radiation we debunk myths like the + + align:start position:0% +radiation we debunk myths like the + + + align:start position:0% +radiation we debunk myths like the +tiniest little bit of irradiation can + + align:start position:0% +tiniest little bit of irradiation can + + + align:start position:0% +tiniest little bit of irradiation can +harm you when in truth we don't have the + + align:start position:0% +harm you when in truth we don't have the + + + align:start position:0% +harm you when in truth we don't have the +data for that but a lot of a lot of + + align:start position:0% +data for that but a lot of a lot of + + + align:start position:0% +data for that but a lot of a lot of +misinformation in radiation and nuclear + + align:start position:0% +misinformation in radiation and nuclear + + + align:start position:0% +misinformation in radiation and nuclear +science is incorporated into culture + + align:start position:0% +science is incorporated into culture + + + align:start position:0% +science is incorporated into culture +into our sort of collective + + align:start position:0% +into our sort of collective + + + align:start position:0% +into our sort of collective +consciousness and even in what's called + + align:start position:0% +consciousness and even in what's called + + + align:start position:0% +consciousness and even in what's called +the linear no-threshold model which says + + align:start position:0% +the linear no-threshold model which says + + + align:start position:0% +the linear no-threshold model which says +every little bit of radiation does harm + + align:start position:0% +every little bit of radiation does harm + + + align:start position:0% +every little bit of radiation does harm +we don't know that to be true or false + + align:start position:0% +we don't know that to be true or false + + + align:start position:0% +we don't know that to be true or false +and it's a good thing we don't because + + align:start position:0% +and it's a good thing we don't because + + + align:start position:0% +and it's a good thing we don't because +we would need to have exposed tens of + + align:start position:0% +we would need to have exposed tens of + + + align:start position:0% +we would need to have exposed tens of +millions of people to low levels of + + align:start position:0% +millions of people to low levels of + + + align:start position:0% +millions of people to low levels of +radiation in a controlled study which is + + align:start position:0% +radiation in a controlled study which is + + + align:start position:0% +radiation in a controlled study which is +not something I think is ethically + + align:start position:0% +not something I think is ethically + + + align:start position:0% +not something I think is ethically +correct to do it's also not ethically + + align:start position:0% +correct to do it's also not ethically + + + align:start position:0% +correct to do it's also not ethically +correct to say that all radiation causes + + align:start position:0% +correct to say that all radiation causes + + + align:start position:0% +correct to say that all radiation causes +harm because we don't know and I want + + align:start position:0% +harm because we don't know and I want + + + align:start position:0% +harm because we don't know and I want +students to both recognize false science + + align:start position:0% +students to both recognize false science + + + align:start position:0% +students to both recognize false science +in the field and recognize when we don't + + align:start position:0% +in the field and recognize when we don't + + + align:start position:0% +in the field and recognize when we don't +know enough information to say something + + align:start position:0% +know enough information to say something + + + align:start position:0% +know enough information to say something +confidently and be comfortable with that + + align:start position:0% +confidently and be comfortable with that + + + align:start position:0% +confidently and be comfortable with that +lack of knowledge it means there's + + align:start position:0% +lack of knowledge it means there's + + + align:start position:0% +lack of knowledge it means there's +something new to explore but it's if you + + align:start position:0% +something new to explore but it's if you + + + align:start position:0% +something new to explore but it's if you +don't have something to conclude don't + + align:start position:0% +don't have something to conclude don't + + + align:start position:0% +don't have something to conclude don't +draw a conclusion mm-hmm how does this + + align:start position:0% +draw a conclusion mm-hmm how does this + + + align:start position:0% +draw a conclusion mm-hmm how does this +connect to the irradiated fruit party + + align:start position:0% +connect to the irradiated fruit party + + + align:start position:0% +connect to the irradiated fruit party +that you have in the class what what is + + align:start position:0% +that you have in the class what what is + + + align:start position:0% +that you have in the class what what is +that yeah the last day of class we often + + align:start position:0% +that yeah the last day of class we often + + + align:start position:0% +that yeah the last day of class we often +have an irradiated fruit party where I + + align:start position:0% +have an irradiated fruit party where I + + + align:start position:0% +have an irradiated fruit party where I +bring in fruit that could only be + + align:start position:0% +bring in fruit that could only be + + + align:start position:0% +bring in fruit that could only be +brought into the US because it's + + align:start position:0% +brought into the US because it's + + + align:start position:0% +brought into the US because it's +irradiated so there are many fruits that + + align:start position:0% +irradiated so there are many fruits that + + + align:start position:0% +irradiated so there are many fruits that +are there are many different types of + + align:start position:0% +are there are many different types of + + + align:start position:0% +are there are many different types of +produce including fruits that are + + align:start position:0% +produce including fruits that are + + + align:start position:0% +produce including fruits that are +irradiated and it's the only known way + + align:start position:0% +irradiated and it's the only known way + + + align:start position:0% +irradiated and it's the only known way +to kill all of the insect viral and + + align:start position:0% +to kill all of the insect viral and + + + align:start position:0% +to kill all of the insect viral and +bacterial pathogens that can wreak havoc + + align:start position:0% +bacterial pathogens that can wreak havoc + + + align:start position:0% +bacterial pathogens that can wreak havoc +on either people or on our crops an + + align:start position:0% +on either people or on our crops an + + + align:start position:0% +on either people or on our crops an +interesting point of information Hawaii + + align:start position:0% +interesting point of information Hawaii + + + align:start position:0% +interesting point of information Hawaii +and Puerto Rico + + align:start position:0% +and Puerto Rico + + + align:start position:0% +and Puerto Rico +despite being part of the u.s. our + + align:start position:0% +despite being part of the u.s. our + + + align:start position:0% +despite being part of the u.s. our +agriculturally distinct in areas and you + + align:start position:0% +agriculturally distinct in areas and you + + + align:start position:0% +agriculturally distinct in areas and you +are not allowed to simply import produce + + align:start position:0% +are not allowed to simply import produce + + + align:start position:0% +are not allowed to simply import produce +from those I had an Apple confiscated + + align:start position:0% +from those I had an Apple confiscated + + + align:start position:0% +from those I had an Apple confiscated +from the airport Puerto Rico + + align:start position:0% +from the airport Puerto Rico + + + align:start position:0% +from the airport Puerto Rico +what I learned that to be the case + + align:start position:0% +what I learned that to be the case + + + align:start position:0% +what I learned that to be the case +however if you were radiate foods like + + align:start position:0% +however if you were radiate foods like + + + align:start position:0% +however if you were radiate foods like +this is why we can get a lot of + + align:start position:0% +this is why we can get a lot of + + + align:start position:0% +this is why we can get a lot of +pineapples from Costa Rica we've started + + align:start position:0% +pineapples from Costa Rica we've started + + + align:start position:0% +pineapples from Costa Rica we've started +getting mangosteens in from Thailand + + align:start position:0% +getting mangosteens in from Thailand + + + align:start position:0% +getting mangosteens in from Thailand +where I didn't know what that fruit was + + align:start position:0% +where I didn't know what that fruit was + + + align:start position:0% +where I didn't know what that fruit was +until a few years ago and now you can + + align:start position:0% +until a few years ago and now you can + + + align:start position:0% +until a few years ago and now you can +find them at H bar in Cambridge a lot of + + align:start position:0% +find them at H bar in Cambridge a lot of + + + align:start position:0% +find them at H bar in Cambridge a lot of +this is because we can kill the pests + + align:start position:0% +this is because we can kill the pests + + + align:start position:0% +this is because we can kill the pests +and it doesn't harm the food it doesn't + + align:start position:0% +and it doesn't harm the food it doesn't + + + align:start position:0% +and it doesn't harm the food it doesn't +make the food radioactive but a lot of + + align:start position:0% +make the food radioactive but a lot of + + + align:start position:0% +make the food radioactive but a lot of +us is to personalize the science so when + + align:start position:0% +us is to personalize the science so when + + + align:start position:0% +us is to personalize the science so when +students eat food that they may or may + + align:start position:0% +students eat food that they may or may + + + align:start position:0% +students eat food that they may or may +not known of been irradiated they taste + + align:start position:0% +not known of been irradiated they taste + + + align:start position:0% +not known of been irradiated they taste +good they seem safe and it's one of + + align:start position:0% +good they seem safe and it's one of + + + align:start position:0% +good they seem safe and it's one of +those things where once it's + + align:start position:0% +those things where once it's + + + align:start position:0% +those things where once it's +personalized it's not as scary when you + + align:start position:0% +personalized it's not as scary when you + + + align:start position:0% +personalized it's not as scary when you +learn the knowledge and then you see it + + align:start position:0% +learn the knowledge and then you see it + + + align:start position:0% +learn the knowledge and then you see it +for yourselves it becomes a lot more + + align:start position:0% +for yourselves it becomes a lot more + + + align:start position:0% +for yourselves it becomes a lot more +acceptable yeah learning through + + align:start position:0% +acceptable yeah learning through + + + align:start position:0% +acceptable yeah learning through +experience is very powerful what does it + + align:start position:0% +experience is very powerful what does it + + + align:start position:0% +experience is very powerful what does it +mean to you for students to develop + + align:start position:0% +mean to you for students to develop + + + align:start position:0% +mean to you for students to develop +fluency in this field it's important to + + align:start position:0% +fluency in this field it's important to + + + align:start position:0% +fluency in this field it's important to +be fluent in this field because a + + align:start position:0% +be fluent in this field because a + + + align:start position:0% +be fluent in this field because a +cursory knowledge of radiation science + + align:start position:0% +cursory knowledge of radiation science + + + align:start position:0% +cursory knowledge of radiation science +is not enough I'd say there are a lot of + + align:start position:0% +is not enough I'd say there are a lot of + + + align:start position:0% +is not enough I'd say there are a lot of +self-proclaimed experts I'll call them + + align:start position:0% +self-proclaimed experts I'll call them + + + align:start position:0% +self-proclaimed experts I'll call them +armchair PhDs who have learned a bit of + + align:start position:0% +armchair PhDs who have learned a bit of + + + align:start position:0% +armchair PhDs who have learned a bit of +genuine knowledge but then extrapolate + + align:start position:0% +genuine knowledge but then extrapolate + + + align:start position:0% +genuine knowledge but then extrapolate +it too far and that combined with all + + align:start position:0% +it too far and that combined with all + + + align:start position:0% +it too far and that combined with all +the things we've heard in pop culture + + align:start position:0% +the things we've heard in pop culture + + + align:start position:0% +the things we've heard in pop culture +unfortunately sometimes from celebrities + + align:start position:0% +unfortunately sometimes from celebrities + + + align:start position:0% +unfortunately sometimes from celebrities +spouting falsehoods about radiation or + + align:start position:0% +spouting falsehoods about radiation or + + + align:start position:0% +spouting falsehoods about radiation or +vaccines or other things that they don't + + align:start position:0% +vaccines or other things that they don't + + + align:start position:0% +vaccines or other things that they don't +understand people listen to other people + + align:start position:0% +understand people listen to other people + + + align:start position:0% +understand people listen to other people +and people listen to role models and + + align:start position:0% +and people listen to role models and + + + align:start position:0% +and people listen to role models and +folks that they look up to but it's + + align:start position:0% +folks that they look up to but it's + + + align:start position:0% +folks that they look up to but it's +important to be fluent and well grounded + + align:start position:0% +important to be fluent and well grounded + + + align:start position:0% +important to be fluent and well grounded +in the fundamentals so that you can sort + + align:start position:0% +in the fundamentals so that you can sort + + + align:start position:0% +in the fundamentals so that you can sort +out fact from fiction and I want every + + align:start position:0% +out fact from fiction and I want every + + + align:start position:0% +out fact from fiction and I want every +student that leaves my class to be able + + align:start position:0% +student that leaves my class to be able + + + align:start position:0% +student that leaves my class to be able +to recognize something that's incorrect + + align:start position:0% +to recognize something that's incorrect + + + align:start position:0% +to recognize something that's incorrect +even if it's told to them by a celebrity + + align:start position:0% +even if it's told to them by a celebrity + + + align:start position:0% +even if it's told to them by a celebrity +an expert a parent a friend anyone that + + align:start position:0% +an expert a parent a friend anyone that + + + align:start position:0% +an expert a parent a friend anyone that +they know what the reality is and it + + align:start position:0% +they know what the reality is and it + + + align:start position:0% +they know what the reality is and it +shouldn't depend on the source it comes + + align:start position:0% +shouldn't depend on the source it comes + + + align:start position:0% +shouldn't depend on the source it comes +from they should be able to tell whether + + align:start position:0% +from they should be able to tell whether + + + align:start position:0% +from they should be able to tell whether +it's real or not and verify if the + + align:start position:0% +it's real or not and verify if the + + + align:start position:0% +it's real or not and verify if the +source is genuine mm-hmm and how do you + + align:start position:0% +source is genuine mm-hmm and how do you + + + align:start position:0% +source is genuine mm-hmm and how do you +help students develop this fluency so it + + align:start position:0% +help students develop this fluency so it + + + align:start position:0% +help students develop this fluency so it +starts off with the fundamentals of + + align:start position:0% +starts off with the fundamentals of + + + align:start position:0% +starts off with the fundamentals of +radiation science so like any class we + + align:start position:0% +radiation science so like any class we + + + align:start position:0% +radiation science so like any class we +teach all the fundamentals from + + align:start position:0% +teach all the fundamentals from + + + align:start position:0% +teach all the fundamentals from +well-established theory but along the + + align:start position:0% +well-established theory but along the + + + align:start position:0% +well-established theory but along the +way every week we have labs and personal + + align:start position:0% +way every week we have labs and personal + + + align:start position:0% +way every week we have labs and personal +as + + align:start position:0% +as + + + align:start position:0% +as +like for example the first day of class + + align:start position:0% +like for example the first day of class + + + align:start position:0% +like for example the first day of class +I asked students to bring in their + + align:start position:0% +I asked students to bring in their + + + align:start position:0% +I asked students to bring in their +toenail clippings and they usually say + + align:start position:0% +toenail clippings and they usually say + + + align:start position:0% +toenail clippings and they usually say +that's disgusting what are we doing and + + align:start position:0% +that's disgusting what are we doing and + + + align:start position:0% +that's disgusting what are we doing and +I said you'll see we're gonna put them + + align:start position:0% +I said you'll see we're gonna put them + + + align:start position:0% +I said you'll see we're gonna put them +in the reactor and we irradiated air + + align:start position:0% +in the reactor and we irradiated air + + + align:start position:0% +in the reactor and we irradiated air +toenail clippings and because to some + + align:start position:0% +toenail clippings and because to some + + + align:start position:0% +toenail clippings and because to some +degree you are what you eat some of the + + align:start position:0% +degree you are what you eat some of the + + + align:start position:0% +degree you are what you eat some of the +elements which we eat and we don't want + + align:start position:0% +elements which we eat and we don't want + + + align:start position:0% +elements which we eat and we don't want +to things like arsenic or selenium or + + align:start position:0% +to things like arsenic or selenium or + + + align:start position:0% +to things like arsenic or selenium or +chromium some of which can be good in + + align:start position:0% +chromium some of which can be good in + + + align:start position:0% +chromium some of which can be good in +small amounts that and large amounts + + align:start position:0% +small amounts that and large amounts + + + align:start position:0% +small amounts that and large amounts +others like arsenic I'm not sure if + + align:start position:0% +others like arsenic I'm not sure if + + + align:start position:0% +others like arsenic I'm not sure if +there's a good use of it get + + align:start position:0% +there's a good use of it get + + + align:start position:0% +there's a good use of it get +incorporated into our toenails so we + + align:start position:0% +incorporated into our toenails so we + + + align:start position:0% +incorporated into our toenails so we +activate those toenails by putting them + + align:start position:0% +activate those toenails by putting them + + + align:start position:0% +activate those toenails by putting them +in the reactor they absorb neutrons and + + align:start position:0% +in the reactor they absorb neutrons and + + + align:start position:0% +in the reactor they absorb neutrons and +give off characteristic gamma rays + + align:start position:0% +give off characteristic gamma rays + + + align:start position:0% +give off characteristic gamma rays +giving away how many atoms of arsenic + + align:start position:0% +giving away how many atoms of arsenic + + + align:start position:0% +giving away how many atoms of arsenic +and selenium and such are incorporated + + align:start position:0% +and selenium and such are incorporated + + + align:start position:0% +and selenium and such are incorporated +into the toenails with striking + + align:start position:0% +into the toenails with striking + + + align:start position:0% +into the toenails with striking +precision and so we're able to tell + + align:start position:0% +precision and so we're able to tell + + + align:start position:0% +precision and so we're able to tell +where students come from based on + + align:start position:0% +where students come from based on + + + align:start position:0% +where students come from based on +analysis of their toenails we had one + + align:start position:0% +analysis of their toenails we had one + + + align:start position:0% +analysis of their toenails we had one +student who had a lot of gold in their + + align:start position:0% +student who had a lot of gold in their + + + align:start position:0% +student who had a lot of gold in their +toenails and I said I thought I asked + + align:start position:0% +toenails and I said I thought I asked + + + align:start position:0% +toenails and I said I thought I asked +you guys to you know clean these off + + align:start position:0% +you guys to you know clean these off + + + align:start position:0% +you guys to you know clean these off +remove any polish and the student said + + align:start position:0% +remove any polish and the student said + + + align:start position:0% +remove any polish and the student said +yeah I did but I live near a gold mining + + align:start position:0% +yeah I did but I live near a gold mining + + + align:start position:0% +yeah I did but I live near a gold mining +town and it's in the water wow that's so + + align:start position:0% +town and it's in the water wow that's so + + + align:start position:0% +town and it's in the water wow that's so +interesting so that's what I mean by + + align:start position:0% +interesting so that's what I mean by + + + align:start position:0% +interesting so that's what I mean by +personal is they discover things about + + align:start position:0% +personal is they discover things about + + + align:start position:0% +personal is they discover things about +themselves through nuclear science and + + align:start position:0% +themselves through nuclear science and + + + align:start position:0% +themselves through nuclear science and +the problem sets instead of saying + + align:start position:0% +the problem sets instead of saying + + + align:start position:0% +the problem sets instead of saying +analyze this theoretical problem I said + + align:start position:0% +analyze this theoretical problem I said + + + align:start position:0% +analyze this theoretical problem I said +analyze your toenails tell me how much + + align:start position:0% +analyze your toenails tell me how much + + + align:start position:0% +analyze your toenails tell me how much +arsenic and gold you've got in your body + + align:start position:0% +arsenic and gold you've got in your body + + + align:start position:0% +arsenic and gold you've got in your body +right right so in the course you make a + + align:start position:0% +right right so in the course you make a + + + align:start position:0% +right right so in the course you make a +point of saying that the method of + + align:start position:0% +point of saying that the method of + + + align:start position:0% +point of saying that the method of +instruction is often context first + + align:start position:0% +instruction is often context first + + + align:start position:0% +instruction is often context first +Theory second and then context again how + + align:start position:0% +Theory second and then context again how + + + align:start position:0% +Theory second and then context again how +does that relate to that method of + + align:start position:0% +does that relate to that method of + + + align:start position:0% +does that relate to that method of +instruction this is an example of that + + align:start position:0% +instruction this is an example of that + + + align:start position:0% +instruction this is an example of that +method of instruction I like to start by + + align:start position:0% +method of instruction I like to start by + + + align:start position:0% +method of instruction I like to start by +opening knowledge gaps rather than + + align:start position:0% +opening knowledge gaps rather than + + + align:start position:0% +opening knowledge gaps rather than +spouting theory at someone it doesn't + + align:start position:0% +spouting theory at someone it doesn't + + + align:start position:0% +spouting theory at someone it doesn't +usually stick if I just say here are + + align:start position:0% +usually stick if I just say here are + + + align:start position:0% +usually stick if I just say here are +some facts learn them it's usually in + + align:start position:0% +some facts learn them it's usually in + + + align:start position:0% +some facts learn them it's usually in +one ear out the other if they're + + align:start position:0% +one ear out the other if they're + + + align:start position:0% +one ear out the other if they're +listening at all but when you show + + align:start position:0% +listening at all but when you show + + + align:start position:0% +listening at all but when you show +someone something surprising they're + + align:start position:0% +someone something surprising they're + + + align:start position:0% +someone something surprising they're +fully engaged they're all this + + align:start position:0% +fully engaged they're all this + + + align:start position:0% +fully engaged they're all this +multi-sensory engaged they're they're + + align:start position:0% +multi-sensory engaged they're they're + + + align:start position:0% +multi-sensory engaged they're they're +listening in a lot of cases they're + + align:start position:0% +listening in a lot of cases they're + + + align:start position:0% +listening in a lot of cases they're +touching in some cases even smelling + + align:start position:0% +touching in some cases even smelling + + + align:start position:0% +touching in some cases even smelling +taste is the sense that we don't tend to + + align:start position:0% +taste is the sense that we don't tend to + + + align:start position:0% +taste is the sense that we don't tend to +engage in nuclear science with good + + align:start position:0% +engage in nuclear science with good + + + align:start position:0% +engage in nuclear science with good +reason but you can sense and feel and + + align:start position:0% +reason but you can sense and feel and + + + align:start position:0% +reason but you can sense and feel and +hear a lot of things in nuclear science + + align:start position:0% +hear a lot of things in nuclear science + + + align:start position:0% +hear a lot of things in nuclear science +like yesterday I was you know with one + + align:start position:0% +like yesterday I was you know with one + + + align:start position:0% +like yesterday I was you know with one +of my graduate students we were looking + + align:start position:0% +of my graduate students we were looking + + + align:start position:0% +of my graduate students we were looking +at some highly irradiated materials of a + + align:start position:0% +at some highly irradiated materials of a + + + align:start position:0% +at some highly irradiated materials of a +reactor and + + align:start position:0% +reactor and + + + align:start position:0% +reactor and +Idaho and we heard this little faint + + align:start position:0% +Idaho and we heard this little faint + + + align:start position:0% +Idaho and we heard this little faint +buzzing noise in the Geiger counter and + + align:start position:0% +buzzing noise in the Geiger counter and + + + align:start position:0% +buzzing noise in the Geiger counter and +if you put your ear up to the Geiger + + align:start position:0% +if you put your ear up to the Geiger + + + align:start position:0% +if you put your ear up to the Geiger +counter near the radiation source you + + align:start position:0% +counter near the radiation source you + + + align:start position:0% +counter near the radiation source you +can hear tiny electrical discharges so + + align:start position:0% +can hear tiny electrical discharges so + + + align:start position:0% +can hear tiny electrical discharges so +you could hear the detector working and + + align:start position:0% +you could hear the detector working and + + + align:start position:0% +you could hear the detector working and +then I want the student to say why is + + align:start position:0% +then I want the student to say why is + + + align:start position:0% +then I want the student to say why is +that why does why do I hear this fuzzy + + align:start position:0% +that why does why do I hear this fuzzy + + + align:start position:0% +that why does why do I hear this fuzzy +noise near the detector when it's + + align:start position:0% +noise near the detector when it's + + + align:start position:0% +noise near the detector when it's +working then when you explain why + + align:start position:0% +working then when you explain why + + + align:start position:0% +working then when you explain why +students tend to remember mm-hmm not too + + align:start position:0% +students tend to remember mm-hmm not too + + + align:start position:0% +students tend to remember mm-hmm not too +many people learn well by being lectured + + align:start position:0% +many people learn well by being lectured + + + align:start position:0% +many people learn well by being lectured +at but everyone learns well by opening + + align:start position:0% +at but everyone learns well by opening + + + align:start position:0% +at but everyone learns well by opening +knowledge gaps and you're effectively + + align:start position:0% +knowledge gaps and you're effectively + + + align:start position:0% +knowledge gaps and you're effectively +pulling the information in rather than + + align:start position:0% +pulling the information in rather than + + + align:start position:0% +pulling the information in rather than +us pushing it to the students something + + align:start position:0% +us pushing it to the students something + + + align:start position:0% +us pushing it to the students something +I learned from a mentor here is you + + align:start position:0% +I learned from a mentor here is you + + + align:start position:0% +I learned from a mentor here is you +can't push a string you want knowledge + + align:start position:0% +can't push a string you want knowledge + + + align:start position:0% +can't push a string you want knowledge +into a student's brain they've got to + + align:start position:0% +into a student's brain they've got to + + + align:start position:0% +into a student's brain they've got to +pull it you can't push it you made a + + align:start position:0% +pull it you can't push it you made a + + + align:start position:0% +pull it you can't push it you made a +choice in this iteration of the course + + align:start position:0% +choice in this iteration of the course + + + align:start position:0% +choice in this iteration of the course +to offer students the ability to do + + align:start position:0% +to offer students the ability to do + + + align:start position:0% +to offer students the ability to do +analytical homework or take home + + align:start position:0% +analytical homework or take home + + + align:start position:0% +analytical homework or take home +hands-on labs how did that work out what + + align:start position:0% +hands-on labs how did that work out what + + + align:start position:0% +hands-on labs how did that work out what +did that look like in practice + + align:start position:0% +did that look like in practice + + + align:start position:0% +did that look like in practice +interestingly I spent all this time + + align:start position:0% +interestingly I spent all this time + + + align:start position:0% +interestingly I spent all this time +making these optional labs + + align:start position:0% +making these optional labs + + + align:start position:0% +making these optional labs +nobody did them so the next couple of + + align:start position:0% +nobody did them so the next couple of + + + align:start position:0% +nobody did them so the next couple of +years I simply made everything mandatory + + align:start position:0% +years I simply made everything mandatory + + + align:start position:0% +years I simply made everything mandatory +the students said they love the + + align:start position:0% +the students said they love the + + + align:start position:0% +the students said they love the +flexibility they're really psyched that + + align:start position:0% +flexibility they're really psyched that + + + align:start position:0% +flexibility they're really psyched that +I put in all this time to do the labs + + align:start position:0% +I put in all this time to do the labs + + + align:start position:0% +I put in all this time to do the labs +but it wasn't for a grade so they didn't + + align:start position:0% +but it wasn't for a grade so they didn't + + + align:start position:0% +but it wasn't for a grade so they didn't +do it and so that's what I learned if + + align:start position:0% +do it and so that's what I learned if + + + align:start position:0% +do it and so that's what I learned if +it's not graded it's not gonna get done + + align:start position:0% +it's not graded it's not gonna get done + + + align:start position:0% +it's not graded it's not gonna get done +so I made all the labs mandatory cut out + + align:start position:0% +so I made all the labs mandatory cut out + + + align:start position:0% +so I made all the labs mandatory cut out +a little bit of the analytics in favor + + align:start position:0% +a little bit of the analytics in favor + + + align:start position:0% +a little bit of the analytics in favor +of adding context before and after the + + align:start position:0% +of adding context before and after the + + + align:start position:0% +of adding context before and after the +theory and retention went up grades went + + align:start position:0% +theory and retention went up grades went + + + align:start position:0% +theory and retention went up grades went +up on average and the course evaluations + + align:start position:0% +up on average and the course evaluations + + + align:start position:0% +up on average and the course evaluations +went up too + + align:start position:0% +went up too + + + align:start position:0% +went up too +so anything numerical we can get + + align:start position:0% +so anything numerical we can get + + + align:start position:0% +so anything numerical we can get +improved and in my subjective opinion so + + align:start position:0% +improved and in my subjective opinion so + + + align:start position:0% +improved and in my subjective opinion so +did the students knowledge of what's + + align:start position:0% +did the students knowledge of what's + + + align:start position:0% +did the students knowledge of what's +happening and that I get from my + + align:start position:0% +happening and that I get from my + + + align:start position:0% +happening and that I get from my +colleagues because I track these + + align:start position:0% +colleagues because I track these + + + align:start position:0% +colleagues because I track these +students as they progress through MIT + + align:start position:0% +students as they progress through MIT + + + align:start position:0% +students as they progress through MIT +through our department and my colleagues + + align:start position:0% +through our department and my colleagues + + + align:start position:0% +through our department and my colleagues +who teach further on courses the more + + align:start position:0% +who teach further on courses the more + + + align:start position:0% +who teach further on courses the more +advanced ones can tell me whether or not + + align:start position:0% +advanced ones can tell me whether or not + + + align:start position:0% +advanced ones can tell me whether or not +the students really know the + + align:start position:0% +the students really know the + + + align:start position:0% +the students really know the +fundamentals that they're depending on + + align:start position:0% +fundamentals that they're depending on + + + align:start position:0% +fundamentals that they're depending on +so far things have been getting better + + align:start position:0% +so far things have been getting better + + + align:start position:0% +so far things have been getting better +that it requires planning and it also + + align:start position:0% +that it requires planning and it also + + + align:start position:0% +that it requires planning and it also +requires a lot of thinking where I'll + + align:start position:0% +requires a lot of thinking where I'll + + + align:start position:0% +requires a lot of thinking where I'll +look through my syllabus and I have an + + align:start position:0% +look through my syllabus and I have an + + + align:start position:0% +look through my syllabus and I have an +empty column where the user doesn't + + align:start position:0% +empty column where the user doesn't + + + align:start position:0% +empty column where the user doesn't +exist in most syllabi which is what is + + align:start position:0% +exist in most syllabi which is what is + + + align:start position:0% +exist in most syllabi which is what is +this week's hands-on instruction and I + + align:start position:0% +this week's hands-on instruction and I + + + align:start position:0% +this week's hands-on instruction and I +try to make sure that's full so another + + align:start position:0% +try to make sure that's full so another + + + align:start position:0% +try to make sure that's full so another +example is if you want to know do you + + align:start position:0% +example is if you want to know do you + + + align:start position:0% +example is if you want to know do you +have real diamond rings when we get to + + align:start position:0% +have real diamond rings when we get to + + + align:start position:0% +have real diamond rings when we get to +reading electron spectra and carat + + align:start position:0% +reading electron spectra and carat + + + align:start position:0% +reading electron spectra and carat +mystic x-ray spectra I could either give + + align:start position:0% +mystic x-ray spectra I could either give + + + align:start position:0% +mystic x-ray spectra I could either give +them a problem from theory which is + + align:start position:0% +them a problem from theory which is + + + align:start position:0% +them a problem from theory which is +boring or I can run some standard for + + align:start position:0% +boring or I can run some standard for + + + align:start position:0% +boring or I can run some standard for +them where you they know what to expect + + align:start position:0% +them where you they know what to expect + + + align:start position:0% +them where you they know what to expect +or I can say that's a nice diamond ring + + align:start position:0% +or I can say that's a nice diamond ring + + + align:start position:0% +or I can say that's a nice diamond ring +you want to know if it's real and the + + align:start position:0% +you want to know if it's real and the + + + align:start position:0% +you want to know if it's real and the +student unbearably says absolutely I + + align:start position:0% +student unbearably says absolutely I + + + align:start position:0% +student unbearably says absolutely I +want to know if it's real so we have the + + align:start position:0% +want to know if it's real so we have the + + + align:start position:0% +want to know if it's real so we have the +student take the controls of the + + align:start position:0% +student take the controls of the + + + align:start position:0% +student take the controls of the +electron microscope and analyze it to + + align:start position:0% +electron microscope and analyze it to + + + align:start position:0% +electron microscope and analyze it to +see does that diamond emit zirconium + + align:start position:0% +see does that diamond emit zirconium + + + align:start position:0% +see does that diamond emit zirconium +x-rays because if it is it's cubic + + align:start position:0% +x-rays because if it is it's cubic + + + align:start position:0% +x-rays because if it is it's cubic +zirconia if it emits silicon x-rays it's + + align:start position:0% +zirconia if it emits silicon x-rays it's + + + align:start position:0% +zirconia if it emits silicon x-rays it's +moissanite or silicon carbide my + + align:start position:0% +moissanite or silicon carbide my + + + align:start position:0% +moissanite or silicon carbide my +favorite one was this day happened to + + align:start position:0% +favorite one was this day happened to + + + align:start position:0% +favorite one was this day happened to +fall on parents weekend so I asked the + + align:start position:0% +fall on parents weekend so I asked the + + + align:start position:0% +fall on parents weekend so I asked the +students does anybody have a diamond + + align:start position:0% +students does anybody have a diamond + + + align:start position:0% +students does anybody have a diamond +ring and one of the students mother said + + align:start position:0% +ring and one of the students mother said + + + align:start position:0% +ring and one of the students mother said +oh yeah let's check my engagement ring + + align:start position:0% +oh yeah let's check my engagement ring + + + align:start position:0% +oh yeah let's check my engagement ring +and her husband was just oh god what's + + align:start position:0% +and her husband was just oh god what's + + + align:start position:0% +and her husband was just oh god what's +gonna happen what's gonna happen he + + align:start position:0% +gonna happen what's gonna happen he + + + align:start position:0% +gonna happen what's gonna happen he +thinks he bought a genuine ring turned + + align:start position:0% +thinks he bought a genuine ring turned + + + align:start position:0% +thinks he bought a genuine ring turned +out to be real okay + + align:start position:0% +out to be real okay + + + align:start position:0% +out to be real okay +we had the mic can you tell us about the + + align:start position:0% +we had the mic can you tell us about the + + + align:start position:0% +we had the mic can you tell us about the +radioactive scavenger hunt sure I + + align:start position:0% +radioactive scavenger hunt sure I + + + align:start position:0% +radioactive scavenger hunt sure I +challenged the students to find the most + + align:start position:0% +challenged the students to find the most + + + align:start position:0% +challenged the students to find the most +radioactive place in Boston and each of + + align:start position:0% +radioactive place in Boston and each of + + + align:start position:0% +radioactive place in Boston and each of +them had to go in teams of two and pick + + align:start position:0% +them had to go in teams of two and pick + + + align:start position:0% +them had to go in teams of two and pick +a place that they thought would be + + align:start position:0% +a place that they thought would be + + + align:start position:0% +a place that they thought would be +radioactive based on what we've learned + + align:start position:0% +radioactive based on what we've learned + + + align:start position:0% +radioactive based on what we've learned +about where you find radiation so + + align:start position:0% +about where you find radiation so + + + align:start position:0% +about where you find radiation so +radiation a lot of it comes from space + + align:start position:0% +radiation a lot of it comes from space + + + align:start position:0% +radiation a lot of it comes from space +from cosmic protons that hit the + + align:start position:0% +from cosmic protons that hit the + + + align:start position:0% +from cosmic protons that hit the +atmosphere so some students thought I'll + + align:start position:0% +atmosphere so some students thought I'll + + + align:start position:0% +atmosphere so some students thought I'll +go to the top of the tallest building + + align:start position:0% +go to the top of the tallest building + + + align:start position:0% +go to the top of the tallest building +and I'll probably get more radiation + + align:start position:0% +and I'll probably get more radiation + + + align:start position:0% +and I'll probably get more radiation +others had read about radon underground + + align:start position:0% +others had read about radon underground + + + align:start position:0% +others had read about radon underground +because there are isotopes of radium and + + align:start position:0% +because there are isotopes of radium and + + + align:start position:0% +because there are isotopes of radium and +meeting radon gas and so they thought + + align:start position:0% +meeting radon gas and so they thought + + + align:start position:0% +meeting radon gas and so they thought +we'll go down into the subway get as low + + align:start position:0% +we'll go down into the subway get as low + + + align:start position:0% +we'll go down into the subway get as low +as we can go other students looked at + + align:start position:0% +as we can go other students looked at + + + align:start position:0% +as we can go other students looked at +the relative amount of radiation and + + align:start position:0% +the relative amount of radiation and + + + align:start position:0% +the relative amount of radiation and +different building materials like wood + + align:start position:0% +different building materials like wood + + + align:start position:0% +different building materials like wood +clay marble granite and they went to the + + align:start position:0% +clay marble granite and they went to the + + + align:start position:0% +clay marble granite and they went to the +most granite dense locations they could + + align:start position:0% +most granite dense locations they could + + + align:start position:0% +most granite dense locations they could +find or the ones with the most marble + + align:start position:0% +find or the ones with the most marble + + + align:start position:0% +find or the ones with the most marble +and those are the students that won + + align:start position:0% +and those are the students that won + + + align:start position:0% +and those are the students that won +there were places in Boston that have + + align:start position:0% +there were places in Boston that have + + + align:start position:0% +there were places in Boston that have +six times the normal radiation + + align:start position:0% +six times the normal radiation + + + align:start position:0% +six times the normal radiation +background simply because they're made + + align:start position:0% +background simply because they're made + + + align:start position:0% +background simply because they're made +out of marble or granite these include + + align:start position:0% +out of marble or granite these include + + + align:start position:0% +out of marble or granite these include +things like the state house and some + + align:start position:0% +things like the state house and some + + + align:start position:0% +things like the state house and some +fancy fountains around town did not know + + align:start position:0% +fancy fountains around town did not know + + + align:start position:0% +fancy fountains around town did not know +about the fountains but they just + + align:start position:0% +about the fountains but they just + + + align:start position:0% +about the fountains but they just +thought let's find giant chunks of stone + + align:start position:0% +thought let's find giant chunks of stone + + + align:start position:0% +thought let's find giant chunks of stone +and they were right + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the hands-on experiences that might + + align:start position:0% +the hands-on experiences that might + + + align:start position:0% +the hands-on experiences that might +creates for students of his course are + + align:start position:0% +creates for students of his course are + + + align:start position:0% +creates for students of his course are +pretty unique he told me that when he + + align:start position:0% +pretty unique he told me that when he + + + align:start position:0% +pretty unique he told me that when he +took this course as an undergraduate + + align:start position:0% +took this course as an undergraduate + + + align:start position:0% +took this course as an undergraduate +student at MIT + + align:start position:0% +student at MIT + + + align:start position:0% +student at MIT +it wasn't typically hands-on so I wanted + + align:start position:0% +it wasn't typically hands-on so I wanted + + + align:start position:0% +it wasn't typically hands-on so I wanted +to know what it's like to teach in a way + + align:start position:0% +to know what it's like to teach in a way + + + align:start position:0% +to know what it's like to teach in a way +that's so different from his own + + align:start position:0% +that's so different from his own + + + align:start position:0% +that's so different from his own +personal experience what does it take to + + align:start position:0% +personal experience what does it take to + + + align:start position:0% +personal experience what does it take to +create such fascinating labs and lessons + + align:start position:0% +create such fascinating labs and lessons + + + align:start position:0% +create such fascinating labs and lessons +without a clear model from one's own + + align:start position:0% +without a clear model from one's own + + + align:start position:0% +without a clear model from one's own +educational background its natural I + + align:start position:0% +educational background its natural I + + + align:start position:0% +educational background its natural I +teach the way that I learn because I + + align:start position:0% +teach the way that I learn because I + + + align:start position:0% +teach the way that I learn because I +thought back on all my experiences and I + + align:start position:0% +thought back on all my experiences and I + + + align:start position:0% +thought back on all my experiences and I +thought from which courses did I really + + align:start position:0% +thought from which courses did I really + + + align:start position:0% +thought from which courses did I really +remember a lot and these were things + + align:start position:0% +remember a lot and these were things + + + align:start position:0% +remember a lot and these were things +like hands-on blacksmithing or + + align:start position:0% +like hands-on blacksmithing or + + + align:start position:0% +like hands-on blacksmithing or +laboratory courses we did have a lab + + align:start position:0% +laboratory courses we did have a lab + + + align:start position:0% +laboratory courses we did have a lab +class where we counted a lot of + + align:start position:0% +class where we counted a lot of + + + align:start position:0% +class where we counted a lot of +radiation and I remember those labs very + + align:start position:0% +radiation and I remember those labs very + + + align:start position:0% +radiation and I remember those labs very +well and then I think back to my + + align:start position:0% +well and then I think back to my + + + align:start position:0% +well and then I think back to my +neutronics problem sets + + align:start position:0% +neutronics problem sets + + + align:start position:0% +neutronics problem sets +I remember the theory okay but I don't + + align:start position:0% +I remember the theory okay but I don't + + + align:start position:0% +I remember the theory okay but I don't +remember very many visual instances of + + align:start position:0% +remember very many visual instances of + + + align:start position:0% +remember very many visual instances of +that class it just kind of happened my + + align:start position:0% +that class it just kind of happened my + + + align:start position:0% +that class it just kind of happened my +knowledge just may be in there somewhere + + align:start position:0% +knowledge just may be in there somewhere + + + align:start position:0% +knowledge just may be in there somewhere +I don't know but I know where I was when + + align:start position:0% +I don't know but I know where I was when + + + align:start position:0% +I don't know but I know where I was when +I did most of the hands-on exercises and + + align:start position:0% +I did most of the hands-on exercises and + + + align:start position:0% +I did most of the hands-on exercises and +in the end you can make anything + + align:start position:0% +in the end you can make anything + + + align:start position:0% +in the end you can make anything +hands-on even neutronics that I + + align:start position:0% +hands-on even neutronics that I + + + align:start position:0% +hands-on even neutronics that I +mentioned so I what some point went + + align:start position:0% +mentioned so I what some point went + + + align:start position:0% +mentioned so I what some point went +skulking around places I oughtn't like + + align:start position:0% +skulking around places I oughtn't like + + + align:start position:0% +skulking around places I oughtn't like +around in the reactor once I got access + + align:start position:0% +around in the reactor once I got access + + + align:start position:0% +around in the reactor once I got access +and found an 8-foot pile of graphite + + align:start position:0% +and found an 8-foot pile of graphite + + + align:start position:0% +and found an 8-foot pile of graphite +that was behind a bunch of equipment it + + align:start position:0% +that was behind a bunch of equipment it + + + align:start position:0% +that was behind a bunch of equipment it +wasn't hidden it was just covered with + + align:start position:0% +wasn't hidden it was just covered with + + + align:start position:0% +wasn't hidden it was just covered with +junk and I asked what's that they just + + align:start position:0% +junk and I asked what's that they just + + + align:start position:0% +junk and I asked what's that they just +said oh that's our subcritical graphite + + align:start position:0% +said oh that's our subcritical graphite + + + align:start position:0% +said oh that's our subcritical graphite +reactor pile you know we're gonna get + + align:start position:0% +reactor pile you know we're gonna get + + + align:start position:0% +reactor pile you know we're gonna get +rid of that next year so I sounded the + + align:start position:0% +rid of that next year so I sounded the + + + align:start position:0% +rid of that next year so I sounded the +alarm and said it cannot get rid of this + + align:start position:0% +alarm and said it cannot get rid of this + + + align:start position:0% +alarm and said it cannot get rid of this +graphite pile and then our neutronics + + align:start position:0% +graphite pile and then our neutronics + + + align:start position:0% +graphite pile and then our neutronics +professor's been forging cored Smith + + align:start position:0% +professor's been forging cored Smith + + + align:start position:0% +professor's been forging cored Smith +said yeah you're right we can't so they + + align:start position:0% +said yeah you're right we can't so they + + + align:start position:0% +said yeah you're right we can't so they +spent a whole winter restoring it with a + + align:start position:0% +spent a whole winter restoring it with a + + + align:start position:0% +spent a whole winter restoring it with a +couple of students and now it's one of + + align:start position:0% +couple of students and now it's one of + + + align:start position:0% +couple of students and now it's one of +the central labs in my class and in + + align:start position:0% +the central labs in my class and in + + + align:start position:0% +the central labs in my class and in +their class so we've taken the most + + align:start position:0% +their class so we've taken the most + + + align:start position:0% +their class so we've taken the most +Theory heavy dry and boring class and + + align:start position:0% +Theory heavy dry and boring class and + + + align:start position:0% +Theory heavy dry and boring class and +turned it experimental because you can + + align:start position:0% +turned it experimental because you can + + + align:start position:0% +turned it experimental because you can +you're only studying the natural world + + align:start position:0% +you're only studying the natural world + + + align:start position:0% +you're only studying the natural world +right all we study at MIT is the natural + + align:start position:0% +right all we study at MIT is the natural + + + align:start position:0% +right all we study at MIT is the natural +world and things we make out of it so + + align:start position:0% +world and things we make out of it so + + + align:start position:0% +world and things we make out of it so +everything is reducible to practice + + align:start position:0% +everything is reducible to practice + + + align:start position:0% +everything is reducible to practice +everything can be real if you put in the + + align:start position:0% +everything can be real if you put in the + + + align:start position:0% +everything can be real if you put in the +ever + + align:start position:0% +ever + + + align:start position:0% +ever +part of what's so special about this + + align:start position:0% +part of what's so special about this + + + align:start position:0% +part of what's so special about this +class is the dedication that Mike and + + align:start position:0% +class is the dedication that Mike and + + + align:start position:0% +class is the dedication that Mike and +his colleagues have to constantly + + align:start position:0% +his colleagues have to constantly + + + align:start position:0% +his colleagues have to constantly +improving it through real-time student + + align:start position:0% +improving it through real-time student + + + align:start position:0% +improving it through real-time student +feedback and I don't mean fixing pieces + + align:start position:0% +feedback and I don't mean fixing pieces + + + align:start position:0% +feedback and I don't mean fixing pieces +to implement for the next semester I'm + + align:start position:0% +to implement for the next semester I'm + + + align:start position:0% +to implement for the next semester I'm +talking about next-day transformations + + align:start position:0% +talking about next-day transformations + + + align:start position:0% +talking about next-day transformations +of class procedures to accomplish this + + align:start position:0% +of class procedures to accomplish this + + + align:start position:0% +of class procedures to accomplish this +Mike created the aptly titled rants page + + align:start position:0% +Mike created the aptly titled rants page + + + align:start position:0% +Mike created the aptly titled rants page +the rant page is an anonymous simple PHP + + align:start position:0% +the rant page is an anonymous simple PHP + + + align:start position:0% +the rant page is an anonymous simple PHP +comment form that I wrote where I want + + align:start position:0% +comment form that I wrote where I want + + + align:start position:0% +comment form that I wrote where I want +students to tell me things that they + + align:start position:0% +students to tell me things that they + + + align:start position:0% +students to tell me things that they +want changed because I I try my best to + + align:start position:0% +want changed because I I try my best to + + + align:start position:0% +want changed because I I try my best to +collect in-person feedback from the + + align:start position:0% +collect in-person feedback from the + + + align:start position:0% +collect in-person feedback from the +students most want both one-on-one and + + align:start position:0% +students most want both one-on-one and + + + align:start position:0% +students most want both one-on-one and +in-class but some students don't feel + + align:start position:0% +in-class but some students don't feel + + + align:start position:0% +in-class but some students don't feel +comfortable telling a professor I don't + + align:start position:0% +comfortable telling a professor I don't + + + align:start position:0% +comfortable telling a professor I don't +like what you're doing so I give them a + + align:start position:0% +like what you're doing so I give them a + + + align:start position:0% +like what you're doing so I give them a +place to do so completely anonymously + + align:start position:0% +place to do so completely anonymously + + + align:start position:0% +place to do so completely anonymously +they could ended up being twenty lines + + align:start position:0% +they could ended up being twenty lines + + + align:start position:0% +they could ended up being twenty lines +of code wasn't hard and what I started + + align:start position:0% +of code wasn't hard and what I started + + + align:start position:0% +of code wasn't hard and what I started +getting was real-time feedback about I + + align:start position:0% +getting was real-time feedback about I + + + align:start position:0% +getting was real-time feedback about I +can't read your writing so then I know + + align:start position:0% +can't read your writing so then I know + + + align:start position:0% +can't read your writing so then I know +to slow it down or I really wish you + + align:start position:0% +to slow it down or I really wish you + + + align:start position:0% +to slow it down or I really wish you +wouldn't slow the class down for this + + align:start position:0% +wouldn't slow the class down for this + + + align:start position:0% +wouldn't slow the class down for this +one students incessant questions so I + + align:start position:0% +one students incessant questions so I + + + align:start position:0% +one students incessant questions so I +know to limit each student to a few + + align:start position:0% +know to limit each student to a few + + + align:start position:0% +know to limit each student to a few +questions if it gets to be too much and + + align:start position:0% +questions if it gets to be too much and + + + align:start position:0% +questions if it gets to be too much and +I would address them in class to say + + align:start position:0% +I would address them in class to say + + + align:start position:0% +I would address them in class to say +it's safe to address this because it's + + align:start position:0% +it's safe to address this because it's + + + align:start position:0% +it's safe to address this because it's +anonymous I have literally no way of + + align:start position:0% +anonymous I have literally no way of + + + align:start position:0% +anonymous I have literally no way of +knowing but if one person wrote it + + align:start position:0% +knowing but if one person wrote it + + + align:start position:0% +knowing but if one person wrote it +probably a lot of you are thinking it + + align:start position:0% +probably a lot of you are thinking it + + + align:start position:0% +probably a lot of you are thinking it +and the students responded positively to + + align:start position:0% +and the students responded positively to + + + align:start position:0% +and the students responded positively to +say wow it was really nice to know that + + align:start position:0% +say wow it was really nice to know that + + + align:start position:0% +say wow it was really nice to know that +we'd make a suggestion at 2:00 in the + + align:start position:0% +we'd make a suggestion at 2:00 in the + + + align:start position:0% +we'd make a suggestion at 2:00 in the +morning and then by 10:00 in the morning + + align:start position:0% +morning and then by 10:00 in the morning + + + align:start position:0% +morning and then by 10:00 in the morning +it would be addressed the class would + + align:start position:0% +it would be addressed the class would + + + align:start position:0% +it would be addressed the class would +change in real-time and they knew they + + align:start position:0% +change in real-time and they knew they + + + align:start position:0% +change in real-time and they knew they +had the power to shape their own + + align:start position:0% +had the power to shape their own + + + align:start position:0% +had the power to shape their own +learning + + align:start position:0% +learning + + + align:start position:0% +learning +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +with all the buzz around this course we + + align:start position:0% +with all the buzz around this course we + + + align:start position:0% +with all the buzz around this course we +had a ton of great questions come in + + align:start position:0% +had a ton of great questions come in + + + align:start position:0% +had a ton of great questions come in +from educators and students alike so we + + align:start position:0% +from educators and students alike so we + + + align:start position:0% +from educators and students alike so we +picked out some of our favorites and + + align:start position:0% +picked out some of our favorites and + + + align:start position:0% +picked out some of our favorites and +posed them to Mike number one what math + + align:start position:0% +posed them to Mike number one what math + + + align:start position:0% +posed them to Mike number one what math +do I need to understand this field + + align:start position:0% +do I need to understand this field + + + align:start position:0% +do I need to understand this field +that's a good question + + align:start position:0% +that's a good question + + + align:start position:0% +that's a good question +depends on how deeply you want to + + align:start position:0% +depends on how deeply you want to + + + align:start position:0% +depends on how deeply you want to +understand the field if you want to pass + + align:start position:0% +understand the field if you want to pass + + + align:start position:0% +understand the field if you want to pass +my class if you want to get an A in my + + align:start position:0% +my class if you want to get an A in my + + + align:start position:0% +my class if you want to get an A in my +class you don't really need much math + + align:start position:0% +class you don't really need much math + + + align:start position:0% +class you don't really need much math +beyond single variable calculus and even + + align:start position:0% +beyond single variable calculus and even + + + align:start position:0% +beyond single variable calculus and even +then it's not very much I think we use + + align:start position:0% +then it's not very much I think we use + + + align:start position:0% +then it's not very much I think we use +we have one or two lectures with + + align:start position:0% +we have one or two lectures with + + + align:start position:0% +we have one or two lectures with +integrals and a few lectures with + + align:start position:0% +integrals and a few lectures with + + + align:start position:0% +integrals and a few lectures with +differential equations but linear + + align:start position:0% +differential equations but linear + + + align:start position:0% +differential equations but linear +first-order things that you solve in + + align:start position:0% +first-order things that you solve in + + + align:start position:0% +first-order things that you solve in +calculus one number two when you were a + + align:start position:0% +calculus one number two when you were a + + + align:start position:0% +calculus one number two when you were a +student how did you deal with courses + + align:start position:0% +student how did you deal with courses + + + align:start position:0% +student how did you deal with courses +that didn't seem interesting to you but + + align:start position:0% +that didn't seem interesting to you but + + + align:start position:0% +that didn't seem interesting to you but +that you had to study that's a good + + align:start position:0% +that you had to study that's a good + + + align:start position:0% +that you had to study that's a good +question I have a few answers to that so + + align:start position:0% +question I have a few answers to that so + + + align:start position:0% +question I have a few answers to that so +for courses that didn't seem interesting + + align:start position:0% +for courses that didn't seem interesting + + + align:start position:0% +for courses that didn't seem interesting +that I had to study if I knew why I had + + align:start position:0% +that I had to study if I knew why I had + + + align:start position:0% +that I had to study if I knew why I had +to study it there was at least a + + align:start position:0% +to study it there was at least a + + + align:start position:0% +to study it there was at least a +practical reason to to do well for + + align:start position:0% +practical reason to to do well for + + + align:start position:0% +practical reason to to do well for +example from you it was neutronics + + align:start position:0% +example from you it was neutronics + + + align:start position:0% +example from you it was neutronics +Neutron transport is one of the things + + align:start position:0% +Neutron transport is one of the things + + + align:start position:0% +Neutron transport is one of the things +that makes nuclear engineers what they + + align:start position:0% +that makes nuclear engineers what they + + + align:start position:0% +that makes nuclear engineers what they +are I found it to be dry and not very + + align:start position:0% +are I found it to be dry and not very + + + align:start position:0% +are I found it to be dry and not very +real-world because I knew I was never + + align:start position:0% +real-world because I knew I was never + + + align:start position:0% +real-world because I knew I was never +going to be a reactor designer but I + + align:start position:0% +going to be a reactor designer but I + + + align:start position:0% +going to be a reactor designer but I +felt I would need to understand Neutron + + align:start position:0% +felt I would need to understand Neutron + + + align:start position:0% +felt I would need to understand Neutron +transport and power levels in order to + + align:start position:0% +transport and power levels in order to + + + align:start position:0% +transport and power levels in order to +be an effective nuclear material + + align:start position:0% +be an effective nuclear material + + + align:start position:0% +be an effective nuclear material +scientist luckily I was right for the + + align:start position:0% +scientist luckily I was right for the + + + align:start position:0% +scientist luckily I was right for the +classes which I just had to take because + + align:start position:0% +classes which I just had to take because + + + align:start position:0% +classes which I just had to take because +they were requirements and I had no + + align:start position:0% +they were requirements and I had no + + + align:start position:0% +they were requirements and I had no +reason to want to take them I got a + + align:start position:0% +reason to want to take them I got a + + + align:start position:0% +reason to want to take them I got a +little sneaky I ended up double majoring + + align:start position:0% +little sneaky I ended up double majoring + + + align:start position:0% +little sneaky I ended up double majoring +with material science and wrote a + + align:start position:0% +with material science and wrote a + + + align:start position:0% +with material science and wrote a +petition to get out of this one medical + + align:start position:0% +petition to get out of this one medical + + + align:start position:0% +petition to get out of this one medical +imaging class and replace it with 12 + + align:start position:0% +imaging class and replace it with 12 + + + align:start position:0% +imaging class and replace it with 12 +others in order to make a second major + + align:start position:0% +others in order to make a second major + + + align:start position:0% +others in order to make a second major +and that petition was approved so I + + align:start position:0% +and that petition was approved so I + + + align:start position:0% +and that petition was approved so I +actually did get to simply drop a + + align:start position:0% +actually did get to simply drop a + + + align:start position:0% +actually did get to simply drop a +departmental requirement by articulating + + align:start position:0% +departmental requirement by articulating + + + align:start position:0% +departmental requirement by articulating +why I wanted to study something else and + + align:start position:0% +why I wanted to study something else and + + + align:start position:0% +why I wanted to study something else and +not all students realize that they can + + align:start position:0% +not all students realize that they can + + + align:start position:0% +not all students realize that they can +do this but they can do this with a very + + align:start position:0% +do this but they can do this with a very + + + align:start position:0% +do this but they can do this with a very +good intellectual justification rules + + align:start position:0% +good intellectual justification rules + + + align:start position:0% +good intellectual justification rules +can be bent or broken okay number three + + align:start position:0% +can be bent or broken okay number three + + + align:start position:0% +can be bent or broken okay number three +why can't we just send nuclear waste to + + align:start position:0% +why can't we just send nuclear waste to + + + align:start position:0% +why can't we just send nuclear waste to +space we could just send nuclear waste + + align:start position:0% +space we could just send nuclear waste + + + align:start position:0% +space we could just send nuclear waste +to space and get it out of + + align:start position:0% +to space and get it out of + + + align:start position:0% +to space and get it out of +our hair it would be expensive it costs + + align:start position:0% +our hair it would be expensive it costs + + + align:start position:0% +our hair it would be expensive it costs +a lot of money per gram to get something + + align:start position:0% +a lot of money per gram to get something + + + align:start position:0% +a lot of money per gram to get something +off the planet + + align:start position:0% +off the planet + + + align:start position:0% +off the planet +someone has to agree to pay for it and + + align:start position:0% +someone has to agree to pay for it and + + + align:start position:0% +someone has to agree to pay for it and +what worries me most is what if one of + + align:start position:0% +what worries me most is what if one of + + + align:start position:0% +what worries me most is what if one of +those missions goes wrong what if you're + + align:start position:0% +those missions goes wrong what if you're + + + align:start position:0% +those missions goes wrong what if you're +launching a rocket full of the world's + + align:start position:0% +launching a rocket full of the world's + + + align:start position:0% +launching a rocket full of the world's +worst nuclear waste and something goes + + align:start position:0% +worst nuclear waste and something goes + + + align:start position:0% +worst nuclear waste and something goes +wrong at the launch and then it comes + + align:start position:0% +wrong at the launch and then it comes + + + align:start position:0% +wrong at the launch and then it comes +back down along with a rocket explosion + + align:start position:0% +back down along with a rocket explosion + + + align:start position:0% +back down along with a rocket explosion +then you have contaminated the planet so + + align:start position:0% +then you have contaminated the planet so + + + align:start position:0% +then you have contaminated the planet so +I personally believe in containing + + align:start position:0% +I personally believe in containing + + + align:start position:0% +I personally believe in containing +nuclear waste where we can see it rather + + align:start position:0% +nuclear waste where we can see it rather + + + align:start position:0% +nuclear waste where we can see it rather +than blasting it off into space and + + align:start position:0% +than blasting it off into space and + + + align:start position:0% +than blasting it off into space and +contaminating space unless we know where + + align:start position:0% +contaminating space unless we know where + + + align:start position:0% +contaminating space unless we know where +it's going and that nothing will go + + align:start position:0% +it's going and that nothing will go + + + align:start position:0% +it's going and that nothing will go +wrong as a lot of folks are worried + + align:start position:0% +wrong as a lot of folks are worried + + + align:start position:0% +wrong as a lot of folks are worried +about the dangers of radiation how are + + align:start position:0% +about the dangers of radiation how are + + + align:start position:0% +about the dangers of radiation how are +we gonna deal with nuclear waste and I + + align:start position:0% +we gonna deal with nuclear waste and I + + + align:start position:0% +we gonna deal with nuclear waste and I +don't fear nuclear waste but I've got a + + align:start position:0% +don't fear nuclear waste but I've got a + + + align:start position:0% +don't fear nuclear waste but I've got a +healthy respect for it and that whatever + + align:start position:0% +healthy respect for it and that whatever + + + align:start position:0% +healthy respect for it and that whatever +we do with it has to have the lowest + + align:start position:0% +we do with it has to have the lowest + + + align:start position:0% +we do with it has to have the lowest +probability of getting out and + + align:start position:0% +probability of getting out and + + + align:start position:0% +probability of getting out and +contaminating anything I think is a + + align:start position:0% +contaminating anything I think is a + + + align:start position:0% +contaminating anything I think is a +necessary thing to make in order to make + + align:start position:0% +necessary thing to make in order to make + + + align:start position:0% +necessary thing to make in order to make +nuclear power so if we want to make + + align:start position:0% +nuclear power so if we want to make + + + align:start position:0% +nuclear power so if we want to make +almost unlimited carbon free power we're + + align:start position:0% +almost unlimited carbon free power we're + + + align:start position:0% +almost unlimited carbon free power we're +going to make waste in the process + + align:start position:0% +going to make waste in the process + + + align:start position:0% +going to make waste in the process +you can't fight thermodynamics you're + + align:start position:0% +you can't fight thermodynamics you're + + + align:start position:0% +you can't fight thermodynamics you're +always going to have some waste of + + align:start position:0% +always going to have some waste of + + + align:start position:0% +always going to have some waste of +energy or something else but then what + + align:start position:0% +energy or something else but then what + + + align:start position:0% +energy or something else but then what +you do with it has to be very carefully + + align:start position:0% +you do with it has to be very carefully + + + align:start position:0% +you do with it has to be very carefully +considered and it sounds simple to blast + + align:start position:0% +considered and it sounds simple to blast + + + align:start position:0% +considered and it sounds simple to blast +it into space but then you have to think + + align:start position:0% +it into space but then you have to think + + + align:start position:0% +it into space but then you have to think +what could go wrong and who could I hurt + + align:start position:0% +what could go wrong and who could I hurt + + + align:start position:0% +what could go wrong and who could I hurt +if it goes wrong number four what do you + + align:start position:0% +if it goes wrong number four what do you + + + align:start position:0% +if it goes wrong number four what do you +think about the cultural and political + + align:start position:0% +think about the cultural and political + + + align:start position:0% +think about the cultural and political +idea against nuclear power to me the + + align:start position:0% +idea against nuclear power to me the + + + align:start position:0% +idea against nuclear power to me the +current cultural and political idea + + align:start position:0% +current cultural and political idea + + + align:start position:0% +current cultural and political idea +against nuclear power is not grounded in + + align:start position:0% +against nuclear power is not grounded in + + + align:start position:0% +against nuclear power is not grounded in +fact it's grounded in emotion and I've + + align:start position:0% +fact it's grounded in emotion and I've + + + align:start position:0% +fact it's grounded in emotion and I've +talked with a lot of folks who either + + align:start position:0% +talked with a lot of folks who either + + + align:start position:0% +talked with a lot of folks who either +know very little or very much about the + + align:start position:0% +know very little or very much about the + + + align:start position:0% +know very little or very much about the +physics and engineering of nuclear power + + align:start position:0% +physics and engineering of nuclear power + + + align:start position:0% +physics and engineering of nuclear power +but I find more often than not it's an + + align:start position:0% +but I find more often than not it's an + + + align:start position:0% +but I find more often than not it's an +issue designed to rally a base strangely + + align:start position:0% +issue designed to rally a base strangely + + + align:start position:0% +issue designed to rally a base strangely +I've never really understood this so + + align:start position:0% +I've never really understood this so + + + align:start position:0% +I've never really understood this so +many environmentalists are against + + align:start position:0% +many environmentalists are against + + + align:start position:0% +many environmentalists are against +nuclear power and I'm an + + align:start position:0% +nuclear power and I'm an + + + align:start position:0% +nuclear power and I'm an +environmentalist - which is why I'm for + + align:start position:0% +environmentalist - which is why I'm for + + + align:start position:0% +environmentalist - which is why I'm for +nuclear power so I find the anti-nuclear + + align:start position:0% +nuclear power so I find the anti-nuclear + + + align:start position:0% +nuclear power so I find the anti-nuclear +sentiment to be so strongly democratic + + align:start position:0% +sentiment to be so strongly democratic + + + align:start position:0% +sentiment to be so strongly democratic +and the pro-nuclear sentiment to be so + + align:start position:0% +and the pro-nuclear sentiment to be so + + + align:start position:0% +and the pro-nuclear sentiment to be so +strongly Republican neither of which is + + align:start position:0% +strongly Republican neither of which is + + + align:start position:0% +strongly Republican neither of which is +for reasons which I'm willing to accept + + align:start position:0% +for reasons which I'm willing to accept + + + align:start position:0% +for reasons which I'm willing to accept +they seem to be more about political + + align:start position:0% +they seem to be more about political + + + align:start position:0% +they seem to be more about political +tribalism than fact + + align:start position:0% +tribalism than fact + + + align:start position:0% +tribalism than fact +and it's interesting now that for the + + align:start position:0% +and it's interesting now that for the + + + align:start position:0% +and it's interesting now that for the +first time since we've had Chernobyl + + align:start position:0% +first time since we've had Chernobyl + + + align:start position:0% +first time since we've had Chernobyl +disasters and such more and more + + align:start position:0% +disasters and such more and more + + + align:start position:0% +disasters and such more and more +environmentalists are coming out in + + align:start position:0% +environmentalists are coming out in + + + align:start position:0% +environmentalists are coming out in +favor of nuclear power not because + + align:start position:0% +favor of nuclear power not because + + + align:start position:0% +favor of nuclear power not because +they're in favor of radiation and waste + + align:start position:0% +they're in favor of radiation and waste + + + align:start position:0% +they're in favor of radiation and waste +and such but the goal is to prevent + + align:start position:0% +and such but the goal is to prevent + + + align:start position:0% +and such but the goal is to prevent +climate change I would much sooner take + + align:start position:0% +climate change I would much sooner take + + + align:start position:0% +climate change I would much sooner take +a risk of something going wrong with + + align:start position:0% +a risk of something going wrong with + + + align:start position:0% +a risk of something going wrong with +nuclear power then definitely lose the + + align:start position:0% +nuclear power then definitely lose the + + + align:start position:0% +nuclear power then definitely lose the +battle to climate change everything to + + align:start position:0% +battle to climate change everything to + + + align:start position:0% +battle to climate change everything to +me comes out to minimizing risk to human + + align:start position:0% +me comes out to minimizing risk to human + + + align:start position:0% +me comes out to minimizing risk to human +life and maximizing quality of life so + + align:start position:0% +life and maximizing quality of life so + + + align:start position:0% +life and maximizing quality of life so +to me the risk of nuclear power is that + + align:start position:0% +to me the risk of nuclear power is that + + + align:start position:0% +to me the risk of nuclear power is that +if we can go all carbon free for energy + + align:start position:0% +if we can go all carbon free for energy + + + align:start position:0% +if we can go all carbon free for energy +we can reverse climate change if we + + align:start position:0% +we can reverse climate change if we + + + align:start position:0% +we can reverse climate change if we +refrain of using nuclear power for fear + + align:start position:0% +refrain of using nuclear power for fear + + + align:start position:0% +refrain of using nuclear power for fear +of the wastes getting out or the risk or + + align:start position:0% +of the wastes getting out or the risk or + + + align:start position:0% +of the wastes getting out or the risk or +the weapons then we're automatically + + align:start position:0% +the weapons then we're automatically + + + align:start position:0% +the weapons then we're automatically +losing the war and we're going to have + + align:start position:0% +losing the war and we're going to have + + + align:start position:0% +losing the war and we're going to have +an uninhabitable planet anyway and we + + align:start position:0% +an uninhabitable planet anyway and we + + + align:start position:0% +an uninhabitable planet anyway and we +can't get off this planet yet and then + + align:start position:0% +can't get off this planet yet and then + + + align:start position:0% +can't get off this planet yet and then +we'll go like then the same mistakes + + align:start position:0% +we'll go like then the same mistakes + + + align:start position:0% +we'll go like then the same mistakes +there's a good here for example I came + + align:start position:0% +there's a good here for example I came + + + align:start position:0% +there's a good here for example I came +into this department wanting to study + + align:start position:0% +into this department wanting to study + + + align:start position:0% +into this department wanting to study +fusion felt it wasn't ready yet so I + + align:start position:0% +fusion felt it wasn't ready yet so I + + + align:start position:0% +fusion felt it wasn't ready yet so I +spent a lot of my time on fission + + align:start position:0% +spent a lot of my time on fission + + + align:start position:0% +spent a lot of my time on fission +thinking this is going to be the bridge + + align:start position:0% +thinking this is going to be the bridge + + + align:start position:0% +thinking this is going to be the bridge +to fusion because fusion promises more + + align:start position:0% +to fusion because fusion promises more + + + align:start position:0% +to fusion because fusion promises more +carbon free power with far less + + align:start position:0% +carbon free power with far less + + + align:start position:0% +carbon free power with far less +radioactive voice but not none and I'm + + align:start position:0% +radioactive voice but not none and I'm + + + align:start position:0% +radioactive voice but not none and I'm +willing to accept the sum so it's not to + + align:start position:0% +willing to accept the sum so it's not to + + + align:start position:0% +willing to accept the sum so it's not to +lose the climate change battle which is + + align:start position:0% +lose the climate change battle which is + + + align:start position:0% +lose the climate change battle which is +already at our doorstep I do worry that + + align:start position:0% +already at our doorstep I do worry that + + + align:start position:0% +already at our doorstep I do worry that +many environmentalists lose sight of the + + align:start position:0% +many environmentalists lose sight of the + + + align:start position:0% +many environmentalists lose sight of the +real goal which is protecting the planet + + align:start position:0% +real goal which is protecting the planet + + + align:start position:0% +real goal which is protecting the planet +and to me protecting the plane that + + align:start position:0% +and to me protecting the plane that + + + align:start position:0% +and to me protecting the plane that +doesn't mean do no harm it means do as + + align:start position:0% +doesn't mean do no harm it means do as + + + align:start position:0% +doesn't mean do no harm it means do as +little harm as possible while preserving + + align:start position:0% +little harm as possible while preserving + + + align:start position:0% +little harm as possible while preserving +our quality of life + + align:start position:0% +our quality of life + + + align:start position:0% +our quality of life +number five while learning occasionally + + align:start position:0% +number five while learning occasionally + + + align:start position:0% +number five while learning occasionally +you'll have these moments where all of + + align:start position:0% +you'll have these moments where all of + + + align:start position:0% +you'll have these moments where all of +the sudden that dot suddenly connect and + + align:start position:0% +the sudden that dot suddenly connect and + + + align:start position:0% +the sudden that dot suddenly connect and +a previously challenging topic becomes + + align:start position:0% +a previously challenging topic becomes + + + align:start position:0% +a previously challenging topic becomes +seemingly perfectly clear to you could + + align:start position:0% +seemingly perfectly clear to you could + + + align:start position:0% +seemingly perfectly clear to you could +you share with us one of your brain + + align:start position:0% +you share with us one of your brain + + + align:start position:0% +you share with us one of your brain +blasts let's see for me it's the same + + align:start position:0% +blasts let's see for me it's the same + + + align:start position:0% +blasts let's see for me it's the same +one that most students get at about the + + align:start position:0% +one that most students get at about the + + + align:start position:0% +one that most students get at about the +one month mark in my class and that's + + align:start position:0% +one month mark in my class and that's + + + align:start position:0% +one month mark in my class and that's +energy is matter that equals mc-squared + + align:start position:0% +energy is matter that equals mc-squared + + + align:start position:0% +energy is matter that equals mc-squared +you see it on shirts all over MIT it's + + align:start position:0% +you see it on shirts all over MIT it's + + + align:start position:0% +you see it on shirts all over MIT it's +probably the one equation that everyone + + align:start position:0% +probably the one equation that everyone + + + align:start position:0% +probably the one equation that everyone +in America knows but not a lot of people + + align:start position:0% +in America knows but not a lot of people + + + align:start position:0% +in America knows but not a lot of people +really understand it that the conversion + + align:start position:0% +really understand it that the conversion + + + align:start position:0% +really understand it that the conversion +of + + align:start position:0% +of + + + align:start position:0% +of +into energy through ionizing radiation + + align:start position:0% +into energy through ionizing radiation + + + align:start position:0% +into energy through ionizing radiation +is the movement of energy from one form + + align:start position:0% +is the movement of energy from one form + + + align:start position:0% +is the movement of energy from one form +to another + + align:start position:0% +to another + + + align:start position:0% +to another +matter is a form of energy and once that + + align:start position:0% +matter is a form of energy and once that + + + align:start position:0% +matter is a form of energy and once that +clicked everything seemed to make sense + + align:start position:0% +clicked everything seemed to make sense + + + align:start position:0% +clicked everything seemed to make sense +radioactive decay nuclear reactions all + + align:start position:0% +radioactive decay nuclear reactions all + + + align:start position:0% +radioactive decay nuclear reactions all +these things I remember that aha moment + + align:start position:0% +these things I remember that aha moment + + + align:start position:0% +these things I remember that aha moment +in this class that I teach as a + + align:start position:0% +in this class that I teach as a + + + align:start position:0% +in this class that I teach as a +second-year student back in 2002 and + + align:start position:0% +second-year student back in 2002 and + + + align:start position:0% +second-year student back in 2002 and +it's those kind of moments that maybe + + align:start position:0% +it's those kind of moments that maybe + + + align:start position:0% +it's those kind of moments that maybe +want to stay in it today I feel like + + align:start position:0% +want to stay in it today I feel like + + + align:start position:0% +want to stay in it today I feel like +well I really know this field now if + + align:start position:0% +well I really know this field now if + + + align:start position:0% +well I really know this field now if +you're interested in learning more about + + align:start position:0% +you're interested in learning more about + + + align:start position:0% +you're interested in learning more about +ionizing radiation we've got all of + + align:start position:0% +ionizing radiation we've got all of + + + align:start position:0% +ionizing radiation we've got all of +Mike's course materials on our site you + + align:start position:0% +Mike's course materials on our site you + + + align:start position:0% +Mike's course materials on our site you +can find us at ocw.mit.edu + + align:start position:0% +can find us at ocw.mit.edu + + + align:start position:0% +can find us at ocw.mit.edu +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in his OCW course page made especially + + align:start position:0% +in his OCW course page made especially + + + align:start position:0% +in his OCW course page made especially +for educators you can find all sorts of + + align:start position:0% +for educators you can find all sorts of + + + align:start position:0% +for educators you can find all sorts of +different instructor insights on our + + align:start position:0% +different instructor insights on our + + + align:start position:0% +different instructor insights on our +educator portal at ocw.mit.edu slash + + align:start position:0% +educator portal at ocw.mit.edu slash + + + align:start position:0% +educator portal at ocw.mit.edu slash +educator until next time I'm Sarah + + align:start position:0% +educator until next time I'm Sarah + + + align:start position:0% +educator until next time I'm Sarah +Hansen from MIT OpenCourseWare \ No newline at end of file diff --git a/gXj4irGhxuo.txt b/gXj4irGhxuo.txt new file mode 100644 index 0000000000000000000000000000000000000000..66851b86645fa3f979a41d81881dee9603846b90 --- /dev/null +++ b/gXj4irGhxuo.txt @@ -0,0 +1,2059 @@ +align:start position:0% + +today we continue with scattering and we + + align:start position:0% +today we continue with scattering and we + + + align:start position:0% +today we continue with scattering and we +begin by reviewing what were the main + + align:start position:0% +begin by reviewing what were the main + + + align:start position:0% +begin by reviewing what were the main +ideas that have already been explored + + align:start position:0% +ideas that have already been explored + + + align:start position:0% +ideas that have already been explored +and here they are I've summarized the + + align:start position:0% +and here they are I've summarized the + + + align:start position:0% +and here they are I've summarized the +main results on the blackboard and we + + align:start position:0% +main results on the blackboard and we + + + align:start position:0% +main results on the blackboard and we +begin with an expansion of our solutions + + align:start position:0% +begin with an expansion of our solutions + + + align:start position:0% +begin with an expansion of our solutions +for the case of central potentials these + + align:start position:0% +for the case of central potentials these + + + align:start position:0% +for the case of central potentials these +side effects represents a solution away + + align:start position:0% +side effects represents a solution away + + + align:start position:0% +side effects represents a solution away +from the scattering Center the + + align:start position:0% +from the scattering Center the + + + align:start position:0% +from the scattering Center the +scattering Center is this region where + + align:start position:0% +scattering Center is this region where + + + align:start position:0% +scattering Center is this region where +there is a potential than the particles + + align:start position:0% +there is a potential than the particles + + + align:start position:0% +there is a potential than the particles +feel and this solution that we've + + align:start position:0% +feel and this solution that we've + + + align:start position:0% +feel and this solution that we've +written on top is a solution written for + + align:start position:0% +written on top is a solution written for + + + align:start position:0% +written on top is a solution written for +spherically symmetric potentials in the + + align:start position:0% +spherically symmetric potentials in the + + + align:start position:0% +spherically symmetric potentials in the +case that the potential is zero that is + + align:start position:0% +case that the potential is zero that is + + + align:start position:0% +case that the potential is zero that is +that solution is valid away from the + + align:start position:0% +that solution is valid away from the + + + align:start position:0% +that solution is valid away from the +potential we constructed it with the + + align:start position:0% +potential we constructed it with the + + + align:start position:0% +potential we constructed it with the +free particle solutions the JL and the + + align:start position:0% +free particle solutions the JL and the + + + align:start position:0% +free particle solutions the JL and the +NL of K are of the spherical shrugging + + align:start position:0% +NL of K are of the spherical shrugging + + + align:start position:0% +NL of K are of the spherical shrugging +or radial Schrodinger equation in + + align:start position:0% +or radial Schrodinger equation in + + + align:start position:0% +or radial Schrodinger equation in +particular we identify these objects + + align:start position:0% +particular we identify these objects + + + align:start position:0% +particular we identify these objects +called phase shifts that we discussed in + + align:start position:0% +called phase shifts that we discussed in + + + align:start position:0% +called phase shifts that we discussed in +the process of scattering with spherical + + align:start position:0% +the process of scattering with spherical + + + align:start position:0% +the process of scattering with spherical +waves and the result is that the way we + + align:start position:0% +waves and the result is that the way we + + + align:start position:0% +waves and the result is that the way we +introduce the phase shifts the tangent + + align:start position:0% +introduce the phase shifts the tangent + + + align:start position:0% +introduce the phase shifts the tangent +of the phase shift is determined by the + + align:start position:0% +of the phase shift is determined by the + + + align:start position:0% +of the phase shift is determined by the +ratio of these two coefficients BL over + + align:start position:0% +ratio of these two coefficients BL over + + + align:start position:0% +ratio of these two coefficients BL over +a L so there's a phase shift for every + + align:start position:0% +a L so there's a phase shift for every + + + align:start position:0% +a L so there's a phase shift for every +value of L beginning from L equal zero + + align:start position:0% +value of L beginning from L equal zero + + + align:start position:0% +value of L beginning from L equal zero +then we have that given that relation + + align:start position:0% +then we have that given that relation + + + align:start position:0% +then we have that given that relation +the solution above when you use the + + align:start position:0% +the solution above when you use the + + + align:start position:0% +the solution above when you use the +synthetic expansions for jl + NL takes + + align:start position:0% +synthetic expansions for jl + NL takes + + + align:start position:0% +synthetic expansions for jl + NL takes +that form with a sine of kr minus L PI + + align:start position:0% +that form with a sine of kr minus L PI + + + align:start position:0% +that form with a sine of kr minus L PI +over 2 plus a phase shift which is + + align:start position:0% +over 2 plus a phase shift which is + + + align:start position:0% +over 2 plus a phase shift which is +another way where you can read the phase + + align:start position:0% +another way where you can read the phase + + + align:start position:0% +another way where you can read the phase +shift of your solution we're going to + + align:start position:0% +shift of your solution we're going to + + + align:start position:0% +shift of your solution we're going to +focus today for a little while and + + align:start position:0% +focus today for a little while and + + + align:start position:0% +focus today for a little while and +understanding the physics of the phase + + align:start position:0% +understanding the physics of the phase + + + align:start position:0% +understanding the physics of the phase +shifts on how you find the + + align:start position:0% +shifts on how you find the + + + align:start position:0% +shifts on how you find the +but supposing you find the phase shifts + + align:start position:0% +but supposing you find the phase shifts + + + align:start position:0% +but supposing you find the phase shifts +and that was the derivation that was + + align:start position:0% +and that was the derivation that was + + + align:start position:0% +and that was the derivation that was +very non-trivial that with it + + align:start position:0% +very non-trivial that with it + + + align:start position:0% +very non-trivial that with it +last time we find what this scattering + + align:start position:0% +last time we find what this scattering + + + align:start position:0% +last time we find what this scattering +amplitude is in terms of the phase shift + + align:start position:0% +amplitude is in terms of the phase shift + + + align:start position:0% +amplitude is in terms of the phase shift +so this was our main hard work + + align:start position:0% +so this was our main hard work + + + align:start position:0% +so this was our main hard work +establishing that formula once you have + + align:start position:0% +establishing that formula once you have + + + align:start position:0% +establishing that formula once you have +that formula that f of K in preliminary + + align:start position:0% +that formula that f of K in preliminary + + + align:start position:0% +that formula that f of K in preliminary +work was shown to represent the + + align:start position:0% +work was shown to represent the + + + align:start position:0% +work was shown to represent the +scattering solution far away from the + + align:start position:0% +scattering solution far away from the + + + align:start position:0% +scattering solution far away from the +source far away from the source will + + align:start position:0% +source far away from the source will + + + align:start position:0% +source far away from the source will +have the incoming wave and the outgoing + + align:start position:0% +have the incoming wave and the outgoing + + + align:start position:0% +have the incoming wave and the outgoing +spherical wave modulated by FK of theta + + align:start position:0% +spherical wave modulated by FK of theta + + + align:start position:0% +spherical wave modulated by FK of theta +now in general you can have an FK of + + align:start position:0% +now in general you can have an FK of + + + align:start position:0% +now in general you can have an FK of +theta and Phi + + align:start position:0% +theta and Phi + + + align:start position:0% +theta and Phi +but then the phase shift method is not + + align:start position:0% +but then the phase shift method is not + + + align:start position:0% +but then the phase shift method is not +quite suitable for that for that we will + + align:start position:0% +quite suitable for that for that we will + + + align:start position:0% +quite suitable for that for that we will +discuss some other methods today that + + align:start position:0% +discuss some other methods today that + + + align:start position:0% +discuss some other methods today that +can allow us to do that so once you have + + align:start position:0% +can allow us to do that so once you have + + + align:start position:0% +can allow us to do that so once you have +this F of K you know the wave far away + + align:start position:0% +this F of K you know the wave far away + + + align:start position:0% +this F of K you know the wave far away +you know how it contributes to the cross + + align:start position:0% +you know how it contributes to the cross + + + align:start position:0% +you know how it contributes to the cross +section and you know how the phase + + align:start position:0% +section and you know how the phase + + + align:start position:0% +section and you know how the phase +shifts each phase shift contributes to + + align:start position:0% +shifts each phase shift contributes to + + + align:start position:0% +shifts each phase shift contributes to +the total cross section which is given + + align:start position:0% +the total cross section which is given + + + align:start position:0% +the total cross section which is given +here so this were our main results so + + align:start position:0% +here so this were our main results so + + + align:start position:0% +here so this were our main results so +let's leave this results here and + + align:start position:0% +let's leave this results here and + + + align:start position:0% +let's leave this results here and +discuss your general computation of + + align:start position:0% +discuss your general computation of + + + align:start position:0% +discuss your general computation of +aphasia if you're given a problem maybe + + align:start position:0% +aphasia if you're given a problem maybe + + + align:start position:0% +aphasia if you're given a problem maybe +like the problems in the pset and you + + align:start position:0% +like the problems in the pset and you + + + align:start position:0% +like the problems in the pset and you +need to find the phase shift so where do + + align:start position:0% +need to find the phase shift so where do + + + align:start position:0% +need to find the phase shift so where do +you begin there's nothing in there that + + align:start position:0% +you begin there's nothing in there that + + + align:start position:0% +you begin there's nothing in there that +seems to say okay this is the way you're + + align:start position:0% +seems to say okay this is the way you're + + + align:start position:0% +seems to say okay this is the way you're +going to find the phase shift so let's + + align:start position:0% +going to find the phase shift so let's + + + align:start position:0% +going to find the phase shift so let's +do this general computation of the + + align:start position:0% +do this general computation of the + + + align:start position:0% +do this general computation of the +fascia + + align:start position:0% + + + + align:start position:0% + +patient of the face shifts so I think + + align:start position:0% +patient of the face shifts so I think + + + align:start position:0% +patient of the face shifts so I think +you all know and there's some clear + + align:start position:0% +you all know and there's some clear + + + align:start position:0% +you all know and there's some clear +intuition if you want to figure out the + + align:start position:0% +intuition if you want to figure out the + + + align:start position:0% +intuition if you want to figure out the +phase shift at some point you have to + + align:start position:0% +phase shift at some point you have to + + + align:start position:0% +phase shift at some point you have to +look at this region are less than a + + align:start position:0% +look at this region are less than a + + + align:start position:0% +look at this region are less than a +where the potential is because after all + + align:start position:0% +where the potential is because after all + + + align:start position:0% +where the potential is because after all +the phase shift depends on the potential + + align:start position:0% +the phase shift depends on the potential + + + align:start position:0% +the phase shift depends on the potential +so that's unavoidable you have to get + + align:start position:0% +so that's unavoidable you have to get + + + align:start position:0% +so that's unavoidable you have to get +dirty with that potential and solve it + + align:start position:0% +dirty with that potential and solve it + + + align:start position:0% +dirty with that potential and solve it +so what is the equation that you have to + + align:start position:0% +so what is the equation that you have to + + + align:start position:0% +so what is the equation that you have to +solve it's the radial Schrodinger + + align:start position:0% +solve it's the radial Schrodinger + + + align:start position:0% +solve it's the radial Schrodinger +equation so you have to solve you set + + align:start position:0% +equation so you have to solve you set + + + align:start position:0% +equation so you have to solve you set +energy in the Schrodinger equation equal + + align:start position:0% +energy in the Schrodinger equation equal + + + align:start position:0% +energy in the Schrodinger equation equal +h squared K squared over 2m because + + align:start position:0% +h squared K squared over 2m because + + + align:start position:0% +h squared K squared over 2m because +we're using K from the beginning to + + align:start position:0% +we're using K from the beginning to + + + align:start position:0% +we're using K from the beginning to +represent the energy of the this state + + align:start position:0% +represent the energy of the this state + + + align:start position:0% +represent the energy of the this state +so energy is gonna be that and the + + align:start position:0% +so energy is gonna be that and the + + + align:start position:0% +so energy is gonna be that and the +radial Schrodinger equation is minus h + + align:start position:0% +radial Schrodinger equation is minus h + + + align:start position:0% +radial Schrodinger equation is minus h +squared over 2m the second V R squared + + align:start position:0% +squared over 2m the second V R squared + + + align:start position:0% +squared over 2m the second V R squared +plus the potential finally the potential + + align:start position:0% +plus the potential finally the potential + + + align:start position:0% +plus the potential finally the potential +shows up that's you have to solve that + + align:start position:0% +shows up that's you have to solve that + + + align:start position:0% +shows up that's you have to solve that +plus the potential centrifugal barrier H + + align:start position:0% +plus the potential centrifugal barrier H + + + align:start position:0% +plus the potential centrifugal barrier H +squared L times L plus 1 over 2m R + + align:start position:0% +squared L times L plus 1 over 2m R + + + align:start position:0% +squared L times L plus 1 over 2m R +squared all that acting on a solution U + + align:start position:0% +squared all that acting on a solution U + + + align:start position:0% +squared all that acting on a solution U +sub L I'll put the K as well of R equal + + align:start position:0% +sub L I'll put the K as well of R equal + + + align:start position:0% +sub L I'll put the K as well of R equal +the energy which is H squared K squared + + align:start position:0% +the energy which is H squared K squared + + + align:start position:0% +the energy which is H squared K squared +over 2m u L K of R so this step cannot + + align:start position:0% +over 2m u L K of R so this step cannot + + + align:start position:0% +over 2m u L K of R so this step cannot +be avoided you have to solve it you have + + align:start position:0% +be avoided you have to solve it you have + + + align:start position:0% +be avoided you have to solve it you have +to solve these equations + + align:start position:0% + + + + align:start position:0% + +so you solve this for R less than a this + + align:start position:0% +so you solve this for R less than a this + + + align:start position:0% +so you solve this for R less than a this +or R less than a you have some hints of + + align:start position:0% +or R less than a you have some hints of + + + align:start position:0% +or R less than a you have some hints of +what you're going to encounter because + + align:start position:0% +what you're going to encounter because + + + align:start position:0% +what you're going to encounter because +you know from solving radial equations + + align:start position:0% +you know from solving radial equations + + + align:start position:0% +you know from solving radial equations +that ul behaves like R to the L plus 1 + + align:start position:0% +that ul behaves like R to the L plus 1 + + + align:start position:0% +that ul behaves like R to the L plus 1 +as R goes to 0 + + align:start position:0% +as R goes to 0 + + + align:start position:0% +as R goes to 0 +that's a boundary condition for the elf + + align:start position:0% +that's a boundary condition for the elf + + + align:start position:0% +that's a boundary condition for the elf +wave and well with that you're supposed + + align:start position:0% +wave and well with that you're supposed + + + align:start position:0% +wave and well with that you're supposed +to solve for this ul okay + + align:start position:0% +to solve for this ul okay + + + align:start position:0% +to solve for this ul okay +so you solve for this ul and so what + + align:start position:0% +so you solve for this ul and so what + + + align:start position:0% +so you solve for this ul and so what +where are the phase shifts you're done + + align:start position:0% +where are the phase shifts you're done + + + align:start position:0% +where are the phase shifts you're done +with it and you need to know where are + + align:start position:0% +with it and you need to know where are + + + align:start position:0% +with it and you need to know where are +the phases well remember our notation is + + align:start position:0% +the phases well remember our notation is + + + align:start position:0% +the phases well remember our notation is +that we have a radial function L of K of + + align:start position:0% +that we have a radial function L of K of + + + align:start position:0% +that we have a radial function L of K of +R in the radial equation you know that + + align:start position:0% +R in the radial equation you know that + + + align:start position:0% +R in the radial equation you know that +the radial part of the solution of the + + align:start position:0% +the radial part of the solution of the + + + align:start position:0% +the radial part of the solution of the +Schrodinger equation + + align:start position:0% +Schrodinger equation + + + align:start position:0% +Schrodinger equation +it's a the full solution is a radial + + align:start position:0% +it's a the full solution is a radial + + + align:start position:0% +it's a the full solution is a radial +part times R why LM in this case why L 0 + + align:start position:0% +part times R why LM in this case why L 0 + + + align:start position:0% +part times R why LM in this case why L 0 +but this radial thing is you LK of R + + align:start position:0% +but this radial thing is you LK of R + + + align:start position:0% +but this radial thing is you LK of R +over R that is presumably something you + + align:start position:0% +over R that is presumably something you + + + align:start position:0% +over R that is presumably something you +still remember that the radial solution + + align:start position:0% +still remember that the radial solution + + + align:start position:0% +still remember that the radial solution +was you over R okay so you've solved it + + align:start position:0% +was you over R okay so you've solved it + + + align:start position:0% +was you over R okay so you've solved it +you got this quantity and you say + + align:start position:0% +you got this quantity and you say + + + align:start position:0% +you got this quantity and you say +alright what do I do next + + align:start position:0% +alright what do I do next + + + align:start position:0% +alright what do I do next +well but you have to do next is to match + + align:start position:0% +well but you have to do next is to match + + + align:start position:0% +well but you have to do next is to match +to this solutions that lie outside there + + align:start position:0% +to this solutions that lie outside there + + + align:start position:0% +to this solutions that lie outside there +is this solutions that hold for our + + align:start position:0% +is this solutions that hold for our + + + align:start position:0% +is this solutions that hold for our +greater than a where the potential is 0 + + align:start position:0% +greater than a where the potential is 0 + + + align:start position:0% +greater than a where the potential is 0 +so those have to be matched to this + + align:start position:0% +so those have to be matched to this + + + align:start position:0% +so those have to be matched to this +solution so let me draw a little diagram + + align:start position:0% +solution so let me draw a little diagram + + + align:start position:0% +solution so let me draw a little diagram +yeah we have diagram for our and here is + + align:start position:0% +yeah we have diagram for our and here is + + + align:start position:0% +yeah we have diagram for our and here is +a in this region the solution is our LK + + align:start position:0% +a in this region the solution is our LK + + + align:start position:0% +a in this region the solution is our LK +of our at the solution and the solution + + align:start position:0% +of our at the solution and the solution + + + align:start position:0% +of our at the solution and the solution +here this is for the elf partial wave + + align:start position:0% +here this is for the elf partial wave + + + align:start position:0% +here this is for the elf partial wave +the solution outside is the elf partial + + align:start position:0% +the solution outside is the elf partial + + + align:start position:0% +the solution outside is the elf partial +wave that I've written there so the + + align:start position:0% +wave that I've written there so the + + + align:start position:0% +wave that I've written there so the +solution here is some al j L of K R plus + + align:start position:0% +solution here is some al j L of K R plus + + + align:start position:0% +solution here is some al j L of K R plus +BL n L of K R so this one you've + + align:start position:0% +BL n L of K R so this one you've + + + align:start position:0% +BL n L of K R so this one you've +determined already you did solve the + + align:start position:0% +determined already you did solve the + + + align:start position:0% +determined already you did solve the +Schrodinger equation we cannot help you + + align:start position:0% +Schrodinger equation we cannot help you + + + align:start position:0% +Schrodinger equation we cannot help you +now depends of what potential you have + + align:start position:0% +now depends of what potential you have + + + align:start position:0% +now depends of what potential you have +you have to solve it each time but you + + align:start position:0% +you have to solve it each time but you + + + align:start position:0% +you have to solve it each time but you +now have the solution up to a but you + + align:start position:0% +now have the solution up to a but you + + + align:start position:0% +now have the solution up to a but you +know the general form of the solution + + align:start position:0% +know the general form of the solution + + + align:start position:0% +know the general form of the solution +for our greater than a and these two + + align:start position:0% +for our greater than a and these two + + + align:start position:0% +for our greater than a and these two +have to match here there might be cases + + align:start position:0% +have to match here there might be cases + + + align:start position:0% +have to match here there might be cases +in which there is a delta function + + align:start position:0% +in which there is a delta function + + + align:start position:0% +in which there is a delta function +precisely here like in the pset in which + + align:start position:0% +precisely here like in the pset in which + + + align:start position:0% +precisely here like in the pset in which +case you know that with a delta function + + align:start position:0% +case you know that with a delta function + + + align:start position:0% +case you know that with a delta function +the derivatives have to match in a funny + + align:start position:0% +the derivatives have to match in a funny + + + align:start position:0% +the derivatives have to match in a funny +way there's a discontinuity in the + + align:start position:0% +way there's a discontinuity in the + + + align:start position:0% +way there's a discontinuity in the +derivatives and the wave functions do + + align:start position:0% +derivatives and the wave functions do + + + align:start position:0% +derivatives and the wave functions do +have to match so let's assume that there + + align:start position:0% +have to match so let's assume that there + + + align:start position:0% +have to match so let's assume that there +in general that there's no delta + + align:start position:0% +in general that there's no delta + + + align:start position:0% +in general that there's no delta +function there and let's do that case if + + align:start position:0% +function there and let's do that case if + + + align:start position:0% +function there and let's do that case if +you had a delta function you could do a + + align:start position:0% +you had a delta function you could do a + + + align:start position:0% +you had a delta function you could do a +similar case and the way to do this is + + align:start position:0% +similar case and the way to do this is + + + align:start position:0% +similar case and the way to do this is +actually to match the wave functions and + + align:start position:0% +actually to match the wave functions and + + + align:start position:0% +actually to match the wave functions and +the derivatives so matching are equal a + + align:start position:0% +the derivatives so matching are equal a + + + align:start position:0% +the derivatives so matching are equal a +so you must have are LK of a is equal to + + align:start position:0% +so you must have are LK of a is equal to + + + align:start position:0% +so you must have are LK of a is equal to +a LJ + + align:start position:0% +a LJ + + + align:start position:0% +a LJ +l of ka + BL ml of ka the derivatives + + align:start position:0% +l of ka + BL ml of ka the derivatives + + + align:start position:0% +l of ka + BL ml of ka the derivatives +must also match let me use primes to + + align:start position:0% +must also match let me use primes to + + + align:start position:0% +must also match let me use primes to +indicate the riveted with respect to the + + align:start position:0% +indicate the riveted with respect to the + + + align:start position:0% +indicate the riveted with respect to the +argument + + align:start position:0% +argument + + + align:start position:0% +argument +most people use that for primes so the + + align:start position:0% +most people use that for primes so the + + + align:start position:0% +most people use that for primes so the +derivative of this one to be our L K a + + align:start position:0% +derivative of this one to be our L K a + + + align:start position:0% +derivative of this one to be our L K a +prime so that means the derivative of + + align:start position:0% +prime so that means the derivative of + + + align:start position:0% +prime so that means the derivative of +this function of our evaluated at a and + + align:start position:0% +this function of our evaluated at a and + + + align:start position:0% +this function of our evaluated at a and +it's a if the furniture with respect to + + align:start position:0% +it's a if the furniture with respect to + + + align:start position:0% +it's a if the furniture with respect to +a in order to get the unit's not to + + align:start position:0% +a in order to get the unit's not to + + + align:start position:0% +a in order to get the unit's not to +change you can multiply by an a I have + + align:start position:0% +change you can multiply by an a I have + + + align:start position:0% +change you can multiply by an a I have +to multiply them by an a on the right + + align:start position:0% +to multiply them by an a on the right + + + align:start position:0% +to multiply them by an a on the right +hand side when I take the derivative now + + align:start position:0% +hand side when I take the derivative now + + + align:start position:0% +hand side when I take the derivative now +when I take the derivative here with + + align:start position:0% +when I take the derivative here with + + + align:start position:0% +when I take the derivative here with +respect to R I think the derivative of J + + align:start position:0% +respect to R I think the derivative of J + + + align:start position:0% +respect to R I think the derivative of J +with respect to the argument and then + + align:start position:0% +with respect to the argument and then + + + align:start position:0% +with respect to the argument and then +the derivative of the argument with + + align:start position:0% +the derivative of the argument with + + + align:start position:0% +the derivative of the argument with +respect to R that picks out the K out + + align:start position:0% +respect to R that picks out the K out + + + align:start position:0% +respect to R that picks out the K out +since I put an A I get the ke ke times + + align:start position:0% +since I put an A I get the ke ke times + + + align:start position:0% +since I put an A I get the ke ke times +al J prime L at K a the derivative of J + + align:start position:0% +al J prime L at K a the derivative of J + + + align:start position:0% +al J prime L at K a the derivative of J +with respect to the argument evaluated + + align:start position:0% +with respect to the argument evaluated + + + align:start position:0% +with respect to the argument evaluated +at K a plus b l and prime L ok so here + + align:start position:0% +at K a plus b l and prime L ok so here + + + align:start position:0% +at K a plus b l and prime L ok so here +it is I've matched the function and the + + align:start position:0% +it is I've matched the function and the + + + align:start position:0% +it is I've matched the function and the +derivatives so I'm giving you an + + align:start position:0% +derivatives so I'm giving you an + + + align:start position:0% +derivatives so I'm giving you an +algorithm to do it anytime and all times + + align:start position:0% +algorithm to do it anytime and all times + + + align:start position:0% +algorithm to do it anytime and all times +at this point the right thing to do is + + align:start position:0% +at this point the right thing to do is + + + align:start position:0% +at this point the right thing to do is +to divide the equations because that + + align:start position:0% +to divide the equations because that + + + align:start position:0% +to divide the equations because that +gets rid of a lot of things that we are + + align:start position:0% +gets rid of a lot of things that we are + + + align:start position:0% +gets rid of a lot of things that we are +not interested in we were not interested + + align:start position:0% +not interested in we were not interested + + + align:start position:0% +not interested in we were not interested +in anything except the phase shift + + align:start position:0% +in anything except the phase shift + + + align:start position:0% +in anything except the phase shift +that's all we want + + align:start position:0% +that's all we want + + + align:start position:0% +that's all we want +the phase shift so how are we gonna get + + align:start position:0% +the phase shift so how are we gonna get + + + align:start position:0% +the phase shift so how are we gonna get +the phase shift well the phase shift + + align:start position:0% +the phase shift well the phase shift + + + align:start position:0% +the phase shift well the phase shift +comes from BL over a L so let + + align:start position:0% +comes from BL over a L so let + + + align:start position:0% +comes from BL over a L so let +form the ratio here so I'll form the + + align:start position:0% +form the ratio here so I'll form the + + + align:start position:0% +form the ratio here so I'll form the +ratio a are LK Prime at a / r lk at a + + align:start position:0% + + + + align:start position:0% + +and then I have K a that's still there + + align:start position:0% +and then I have K a that's still there + + + align:start position:0% +and then I have K a that's still there +and then let me divide I'm gonna divide + + align:start position:0% +and then let me divide I'm gonna divide + + + align:start position:0% +and then let me divide I'm gonna divide +these two things but then I can divide + + align:start position:0% +these two things but then I can divide + + + align:start position:0% +these two things but then I can divide +the numerator and the denominator by al + + align:start position:0% +the numerator and the denominator by al + + + align:start position:0% +the numerator and the denominator by al +so here I'll have the ratio of JL prime + + align:start position:0% +so here I'll have the ratio of JL prime + + + align:start position:0% +so here I'll have the ratio of JL prime +K ay plus BL over al and prime L of ka + + align:start position:0% + + + + align:start position:0% + +over the equation came out to do and + + align:start position:0% +over the equation came out to do and + + + align:start position:0% +over the equation came out to do and +balance but I don't know it's not so bad + + align:start position:0% +balance but I don't know it's not so bad + + + align:start position:0% +balance but I don't know it's not so bad +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +numerator and here you get JL of ka plus + + align:start position:0% +numerator and here you get JL of ka plus + + + align:start position:0% +numerator and here you get JL of ka plus +BL over al NL of ka but this is nothing + + align:start position:0% +BL over al NL of ka but this is nothing + + + align:start position:0% +BL over al NL of ka but this is nothing +but K a and the ratio J L prime at K a + + align:start position:0% +but K a and the ratio J L prime at K a + + + align:start position:0% +but K a and the ratio J L prime at K a +minus tan Delta K the Delta L that's + + align:start position:0% +minus tan Delta K the Delta L that's + + + align:start position:0% +minus tan Delta K the Delta L that's +what the ratio BL over al is and prime L + + align:start position:0% +what the ratio BL over al is and prime L + + + align:start position:0% +what the ratio BL over al is and prime L +of ka / j l of ka - times delta elf ada + + align:start position:0% +of ka / j l of ka - times delta elf ada + + + align:start position:0% +of ka / j l of ka - times delta elf ada +not a this energy and + + align:start position:0% +not a this energy and + + + align:start position:0% +not a this energy and +of K okay that's it actually we've + + align:start position:0% +of K okay that's it actually we've + + + align:start position:0% +of K okay that's it actually we've +solved the problem why because this + + align:start position:0% +solved the problem why because this + + + align:start position:0% +solved the problem why because this +number is supposed to be known because + + align:start position:0% +number is supposed to be known because + + + align:start position:0% +number is supposed to be known because +you have solved the equation you did + + align:start position:0% +you have solved the equation you did + + + align:start position:0% +you have solved the equation you did +solve the equation is sharing the + + align:start position:0% +solve the equation is sharing the + + + align:start position:0% +solve the equation is sharing the +equation from R equals zero to R equal a + + align:start position:0% +equation from R equals zero to R equal a + + + align:start position:0% +equation from R equals zero to R equal a +it's completely solved so that number is + + align:start position:0% +it's completely solved so that number is + + + align:start position:0% +it's completely solved so that number is +now the Bessel functions spherical + + align:start position:0% +now the Bessel functions spherical + + + align:start position:0% +now the Bessel functions spherical +vessels are known and all you need to + + align:start position:0% +vessels are known and all you need to + + + align:start position:0% +vessels are known and all you need to +find this tangent Delta and that + + align:start position:0% +find this tangent Delta and that + + + align:start position:0% +find this tangent Delta and that +equation determines it should I write + + align:start position:0% +equation determines it should I write + + + align:start position:0% +equation determines it should I write +the formula for tangent Delta okay let's + + align:start position:0% +the formula for tangent Delta okay let's + + + align:start position:0% +the formula for tangent Delta okay let's +write let's write it yeah okay one + + align:start position:0% +write let's write it yeah okay one + + + align:start position:0% +write let's write it yeah okay one +minute to write it it's just solving + + align:start position:0% +minute to write it it's just solving + + + align:start position:0% +minute to write it it's just solving +from here tan Delta of L is equal J + + align:start position:0% +from here tan Delta of L is equal J + + + align:start position:0% +from here tan Delta of L is equal J +prime L at k a- r l prime at a over k RL + + align:start position:0% +prime L at k a- r l prime at a over k RL + + + align:start position:0% +prime L at k a- r l prime at a over k RL +of a jl k a over n l prime at k a- r l + + align:start position:0% +of a jl k a over n l prime at k a- r l + + + align:start position:0% +of a jl k a over n l prime at k a- r l +prime of a over k r LF a that same + + align:start position:0% +prime of a over k r LF a that same + + + align:start position:0% +prime of a over k r LF a that same +constant n L of K a so that's solving + + align:start position:0% +constant n L of K a so that's solving + + + align:start position:0% +constant n L of K a so that's solving +for tangent Delta from this side equal + + align:start position:0% +for tangent Delta from this side equal + + + align:start position:0% +for tangent Delta from this side equal +to this side + + align:start position:0% + + + + align:start position:0% + +this shows that in principle once you + + align:start position:0% +this shows that in principle once you + + + align:start position:0% +this shows that in principle once you +have the solution from zero to a you + + align:start position:0% +have the solution from zero to a you + + + align:start position:0% +have the solution from zero to a you +have solved the problem of the phase + + align:start position:0% +have solved the problem of the phase + + + align:start position:0% +have solved the problem of the phase +shift you know the phase shifts it's a + + align:start position:0% +shift you know the phase shifts it's a + + + align:start position:0% +shift you know the phase shifts it's a +matter of just calculating them no might + + align:start position:0% +matter of just calculating them no might + + + align:start position:0% +matter of just calculating them no might +be a little messy and but if if your + + align:start position:0% +be a little messy and but if if your + + + align:start position:0% +be a little messy and but if if your +calculation is important and this is a + + align:start position:0% +calculation is important and this is a + + + align:start position:0% +calculation is important and this is a +problem you really want to solve you + + align:start position:0% +problem you really want to solve you + + + align:start position:0% +problem you really want to solve you +will be willing to look at the spherical + + align:start position:0% +will be willing to look at the spherical + + + align:start position:0% +will be willing to look at the spherical +Bessel functions which in fact their + + align:start position:0% +Bessel functions which in fact their + + + align:start position:0% +Bessel functions which in fact their +power trigonometric functions times + + align:start position:0% +power trigonometric functions times + + + align:start position:0% +power trigonometric functions times +powers are not as difficult as the + + align:start position:0% +powers are not as difficult as the + + + align:start position:0% +powers are not as difficult as the +ordinary Bessel functions so these are + + align:start position:0% +ordinary Bessel functions so these are + + + align:start position:0% +ordinary Bessel functions so these are +easy to work with and and these things + + align:start position:0% +easy to work with and and these things + + + align:start position:0% +easy to work with and and these things +are many times done numerically for a + + align:start position:0% +are many times done numerically for a + + + align:start position:0% +are many times done numerically for a +given potential you calculate the first + + align:start position:0% +given potential you calculate the first + + + align:start position:0% +given potential you calculate the first +ten phase shift and you get a solution + + align:start position:0% +ten phase shift and you get a solution + + + align:start position:0% +ten phase shift and you get a solution +that is very accurate so there's a lot + + align:start position:0% +that is very accurate so there's a lot + + + align:start position:0% +that is very accurate so there's a lot +of power in this formulation so you have + + align:start position:0% +of power in this formulation so you have + + + align:start position:0% +of power in this formulation so you have +a solution you have the phase shifts \ No newline at end of file diff --git a/gqBK3LVdyRw.txt b/gqBK3LVdyRw.txt new file mode 100644 index 0000000000000000000000000000000000000000..ba9d20efff0cdb8999c232588c2b42328e2b1271 --- /dev/null +++ b/gqBK3LVdyRw.txt @@ -0,0 +1,2416 @@ +align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +good morning claudo good morning thank + + align:start position:0% +good morning claudo good morning thank + + + align:start position:0% +good morning claudo good morning thank +you again for coming it's uh always a + + align:start position:0% +you again for coming it's uh always a + + + align:start position:0% +you again for coming it's uh always a +pleasure to show you the the factory to + + align:start position:0% +pleasure to show you the the factory to + + + align:start position:0% +pleasure to show you the the factory to +you um so before the main purpose that I + + align:start position:0% +you um so before the main purpose that I + + + align:start position:0% +you um so before the main purpose that I +show you the value stream the factory + + align:start position:0% +show you the value stream the factory + + + align:start position:0% +show you the value stream the factory +the product flow but before that let me + + align:start position:0% +the product flow but before that let me + + + align:start position:0% +the product flow but before that let me +uh I'm going to give you a little uh + + align:start position:0% +uh I'm going to give you a little uh + + + align:start position:0% +uh I'm going to give you a little uh +preview of who we are Wonder yeah + + align:start position:0% +preview of who we are Wonder yeah + + + align:start position:0% +preview of who we are Wonder yeah +everybody knows New Balance tell us + + align:start position:0% +everybody knows New Balance tell us + + + align:start position:0% +everybody knows New Balance tell us +about your journey to specifically about + + align:start position:0% +about your journey to specifically about + + + align:start position:0% +about your journey to specifically about +you know the lawence factory um the + + align:start position:0% +you know the lawence factory um the + + + align:start position:0% +you know the lawence factory um the +factory specifically is divided in you + + align:start position:0% +factory specifically is divided in you + + + align:start position:0% +factory specifically is divided in you +have standing here you got to your left + + align:start position:0% +have standing here you got to your left + + + align:start position:0% +have standing here you got to your left +side the portion that we call the cut + + align:start position:0% +side the portion that we call the cut + + + align:start position:0% +side the portion that we call the cut +through Stitch this is the made in + + align:start position:0% +through Stitch this is the made in + + + align:start position:0% +through Stitch this is the made in +America shoes that we cut from C from + + align:start position:0% +America shoes that we cut from C from + + + align:start position:0% +America shoes that we cut from C from +scratch and be packed here and to your + + align:start position:0% +scratch and be packed here and to your + + + align:start position:0% +scratch and be packed here and to your +right my right side is the we call the + + align:start position:0% +right my right side is the we call the + + + align:start position:0% +right my right side is the we call the +sourced upper world uh we get the so and + + align:start position:0% +sourced upper world uh we get the so and + + + align:start position:0% +sourced upper world uh we get the so and +the um and the upper from Asia and we + + align:start position:0% +the um and the upper from Asia and we + + + align:start position:0% +the um and the upper from Asia and we +just put it together now are you the + + align:start position:0% +just put it together now are you the + + + align:start position:0% +just put it together now are you the +only shoe company that actually + + align:start position:0% +only shoe company that actually + + + align:start position:0% +only shoe company that actually +manufactures shoes in the US I + + align:start position:0% +manufactures shoes in the US I + + + align:start position:0% +manufactures shoes in the US I +understand as it is that's what's behind + + align:start position:0% +understand as it is that's what's behind + + + align:start position:0% +understand as it is that's what's behind +me here that's you know and that's what + + align:start position:0% +me here that's you know and that's what + + + align:start position:0% +me here that's you know and that's what +our competitive Advantage great you know + + align:start position:0% +our competitive Advantage great you know + + + align:start position:0% +our competitive Advantage great you know +uh turnaround shoes in two or three days + + align:start position:0% +uh turnaround shoes in two or three days + + + align:start position:0% +uh turnaround shoes in two or three days +two or three days yeah we can get it + + align:start position:0% +two or three days yeah we can get it + + + align:start position:0% +two or three days yeah we can get it +into the in the customer we'll see that + + align:start position:0% +into the in the customer we'll see that + + + align:start position:0% +into the in the customer we'll see that +how you do that when we go through the + + align:start position:0% +how you do that when we go through the + + + align:start position:0% +how you do that when we go through the +value stre Absolutely I'll show that um + + align:start position:0% +value stre Absolutely I'll show that um + + + align:start position:0% +value stre Absolutely I'll show that um +so some statistics we uh pack 5200 pair + + align:start position:0% +so some statistics we uh pack 5200 pair + + + align:start position:0% +so some statistics we uh pack 5200 pair +a day and ship 50200 pair a day we are + + align:start position:0% +a day and ship 50200 pair a day we are + + + align:start position:0% +a day and ship 50200 pair a day we are + + align:start position:0% + + + align:start position:0% +Associates + + align:start position:0% +Associates + + + align:start position:0% +Associates +um which I'm going to show you when we + + align:start position:0% +um which I'm going to show you when we + + + align:start position:0% +um which I'm going to show you when we +go through operation the value stream + + align:start position:0% +go through operation the value stream + + + align:start position:0% +go through operation the value stream +which uh is a group operations uh + + align:start position:0% +which uh is a group operations uh + + + align:start position:0% +which uh is a group operations uh +putting a strategically in a Cell you + + align:start position:0% +putting a strategically in a Cell you + + + align:start position:0% +putting a strategically in a Cell you +shape to make a product um that has + + align:start position:0% +shape to make a product um that has + + + align:start position:0% +shape to make a product um that has +there's some history behind it and and + + align:start position:0% +there's some history behind it and and + + + align:start position:0% +there's some history behind it and and +it's very interesting what you see here + + align:start position:0% +it's very interesting what you see here + + + align:start position:0% +it's very interesting what you see here +is a of three and a half four years of + + align:start position:0% +is a of three and a half four years of + + + align:start position:0% +is a of three and a half four years of +lean transformation uh three and a half + + align:start position:0% +lean transformation uh three and a half + + + align:start position:0% +lean transformation uh three and a half +years ago we decided to work with the + + align:start position:0% +years ago we decided to work with the + + + align:start position:0% +years ago we decided to work with the +toota production uh company uh to about + + align:start position:0% +toota production uh company uh to about + + + align:start position:0% +toota production uh company uh to about +their to their production system which + + align:start position:0% +their to their production system which + + + align:start position:0% +their to their production system which +is uh lean is another name for it not so + + align:start position:0% +is uh lean is another name for it not so + + + align:start position:0% +is uh lean is another name for it not so +long four years ago it used to take us + + align:start position:0% +long four years ago it used to take us + + + align:start position:0% +long four years ago it used to take us +eight days to make a pair of shoes eight + + align:start position:0% +eight days to make a pair of shoes eight + + + align:start position:0% +eight days to make a pair of shoes eight +days from start to finish from start to + + align:start position:0% +days from start to finish from start to + + + align:start position:0% +days from start to finish from start to +finish anyway it didn't you weren't + + align:start position:0% +finish anyway it didn't you weren't + + + align:start position:0% +finish anyway it didn't you weren't +working on that shoe the whole time but + + align:start position:0% +working on that shoe the whole time but + + + align:start position:0% +working on that shoe the whole time but +start to finish that's a good question + + align:start position:0% +start to finish that's a good question + + + align:start position:0% +start to finish that's a good question +because what we call the value added + + align:start position:0% +because what we call the value added + + + align:start position:0% +because what we call the value added +work which was was only 23 minutes so + + align:start position:0% +work which was was only 23 minutes so + + + align:start position:0% +work which was was only 23 minutes so +the shoe was floating in the factory for + + align:start position:0% +the shoe was floating in the factory for + + + align:start position:0% +the shoe was floating in the factory for +8 days with only Associates uh touching + + align:start position:0% +8 days with only Associates uh touching + + + align:start position:0% +8 days with only Associates uh touching +the shoe adding value to the shoe for 23 + + align:start position:0% +the shoe adding value to the shoe for 23 + + + align:start position:0% +the shoe adding value to the shoe for 23 +minutes um when R transformation after + + align:start position:0% +minutes um when R transformation after + + + align:start position:0% +minutes um when R transformation after +three and a half years we went from + + align:start position:0% +three and a half years we went from + + + align:start position:0% +three and a half years we went from +eight days to right now it take us + + align:start position:0% +eight days to right now it take us + + + align:start position:0% +eight days to right now it take us +between two and three hours in it value + + align:start position:0% +between two and three hours in it value + + + align:start position:0% +between two and three hours in it value +stream to produce a pair of shoes so + + align:start position:0% +stream to produce a pair of shoes so + + + align:start position:0% +stream to produce a pair of shoes so +that's a 98% reduction it's still about + + align:start position:0% +that's a 98% reduction it's still about + + + align:start position:0% +that's a 98% reduction it's still about +23 minutes of value added time yes + + align:start position:0% +23 minutes of value added time yes + + + align:start position:0% +23 minutes of value added time yes +absolutely so so there's actually still + + align:start position:0% +absolutely so so there's actually still + + + align:start position:0% +absolutely so so there's actually still +some room for poten for improvement once + + align:start position:0% +some room for poten for improvement once + + + align:start position:0% +some room for poten for improvement once +you s l it canes part of your DNA it + + align:start position:0% +you s l it canes part of your DNA it + + + align:start position:0% +you s l it canes part of your DNA it +never stop you see supervisors and uh + + align:start position:0% +never stop you see supervisors and uh + + + align:start position:0% +never stop you see supervisors and uh +flow coordinators which are our team + + align:start position:0% +flow coordinators which are our team + + + align:start position:0% +flow coordinators which are our team +leaders always with a watch looking at + + align:start position:0% +leaders always with a watch looking at + + + align:start position:0% +leaders always with a watch looking at +uh the site teing cycle time C there + + align:start position:0% +uh the site teing cycle time C there + + + align:start position:0% +uh the site teing cycle time C there +opportunity to to + + align:start position:0% + + + + align:start position:0% + +improve so so we there are other + + align:start position:0% +improve so so we there are other + + + align:start position:0% +improve so so we there are other +statistics we reduce we were used to be + + align:start position:0% +statistics we reduce we were used to be + + + align:start position:0% +statistics we reduce we were used to be +in two + + align:start position:0% +in two + + + align:start position:0% +in two +floors uh right now we are in one we + + align:start position:0% +floors uh right now we are in one we + + + align:start position:0% +floors uh right now we are in one we +empty like a quarter uh I think it's + + align:start position:0% +empty like a quarter uh I think it's + + + align:start position:0% +empty like a quarter uh I think it's +like um close to 2500 square ft of floor + + align:start position:0% +like um close to 2500 square ft of floor + + + align:start position:0% +like um close to 2500 square ft of floor +um the beginning of a value stream that + + align:start position:0% +um the beginning of a value stream that + + + align:start position:0% +um the beginning of a value stream that +in those days were not called value + + align:start position:0% +in those days were not called value + + + align:start position:0% +in those days were not called value +stream was like straight lines uh used + + align:start position:0% +stream was like straight lines uh used + + + align:start position:0% +stream was like straight lines uh used +to be in this the first floor the + + align:start position:0% +to be in this the first floor the + + + align:start position:0% +to be in this the first floor the +beginning and the end on the second + + align:start position:0% +beginning and the end on the second + + + align:start position:0% +beginning and the end on the second +floor not too much communication no can + + align:start position:0% +floor not too much communication no can + + + align:start position:0% +floor not too much communication no can +see the whole value exactly and I'll + + align:start position:0% +see the whole value exactly and I'll + + + align:start position:0% +see the whole value exactly and I'll +show you later is the from a management + + align:start position:0% +show you later is the from a management + + + align:start position:0% +show you later is the from a management +point of view the ability to have a a + + align:start position:0% +point of view the ability to have a a + + + align:start position:0% +point of view the ability to have a a +value stream where the beginning and the + + align:start position:0% +value stream where the beginning and the + + + align:start position:0% +value stream where the beginning and the +end meet it's extremely powerful um so + + align:start position:0% +end meet it's extremely powerful um so + + + align:start position:0% +end meet it's extremely powerful um so +square foot I think it's close to 30% r + + align:start position:0% +square foot I think it's close to 30% r + + + align:start position:0% +square foot I think it's close to 30% r +ution Al working process I said + + align:start position:0% +ution Al working process I said + + + align:start position:0% +ution Al working process I said +98% + + align:start position:0% +98% + + + align:start position:0% +98% +um so this it's incredible so how how do + + align:start position:0% +um so this it's incredible so how how do + + + align:start position:0% +um so this it's incredible so how how do +we do that um part of Lan there are two + + align:start position:0% +we do that um part of Lan there are two + + + align:start position:0% +we do that um part of Lan there are two +basic concepts um T time which is flow + + align:start position:0% +basic concepts um T time which is flow + + + align:start position:0% +basic concepts um T time which is flow +that based on our uh capacity the value + + align:start position:0% +that based on our uh capacity the value + + + align:start position:0% +that based on our uh capacity the value +stream and availability is a tag time of + + align:start position:0% +stream and availability is a tag time of + + + align:start position:0% +stream and availability is a tag time of +25 22 and a half seconds which means + + align:start position:0% +25 22 and a half seconds which means + + + align:start position:0% +25 22 and a half seconds which means +that it's a frequency T time is a + + align:start position:0% +that it's a frequency T time is a + + + align:start position:0% +that it's a frequency T time is a +frequency of delivery so at the end of + + align:start position:0% +frequency of delivery so at the end of + + + align:start position:0% +frequency of delivery so at the end of +the line you will see shoe leaving every + + align:start position:0% +the line you will see shoe leaving every + + + align:start position:0% +the line you will see shoe leaving every +22 and pair shoes every 45 absolutely so + + align:start position:0% +22 and pair shoes every 45 absolutely so + + + align:start position:0% +22 and pair shoes every 45 absolutely so +that's the concept of the T time and + + align:start position:0% +that's the concept of the T time and + + + align:start position:0% +that's the concept of the T time and +flow and the other cons of waste we + + align:start position:0% +flow and the other cons of waste we + + + align:start position:0% +flow and the other cons of waste we +become uh actually we have a course we + + align:start position:0% +become uh actually we have a course we + + + align:start position:0% +become uh actually we have a course we +call uh waste uh detectives we we put + + align:start position:0% +call uh waste uh detectives we we put + + + align:start position:0% +call uh waste uh detectives we we put +our soures to Andi way so what is the + + align:start position:0% +our soures to Andi way so what is the + + + align:start position:0% +our soures to Andi way so what is the +way from in in the is every associate a + + align:start position:0% +way from in in the is every associate a + + + align:start position:0% +way from in in the is every associate a +waste detective yes that's where they + + align:start position:0% +waste detective yes that's where they + + + align:start position:0% +waste detective yes that's where they +are everyone here becomes a was take so + + align:start position:0% +are everyone here becomes a was take so + + + align:start position:0% +are everyone here becomes a was take so +I'll um I have a post very interesting + + align:start position:0% +I'll um I have a post very interesting + + + align:start position:0% +I'll um I have a post very interesting +that I like to use for tours and also + + align:start position:0% +that I like to use for tours and also + + + align:start position:0% +that I like to use for tours and also +for educational purposes where in the L + + align:start position:0% +for educational purposes where in the L + + + align:start position:0% +for educational purposes where in the L +World they are like the deadly waste and + + align:start position:0% +World they are like the deadly waste and + + + align:start position:0% +World they are like the deadly waste and +they are go through you over production + + align:start position:0% +they are go through you over production + + + align:start position:0% +they are go through you over production +we produce a head waiting and it's very + + align:start position:0% +we produce a head waiting and it's very + + + align:start position:0% +we produce a head waiting and it's very +interesting there are some uh + + align:start position:0% +interesting there are some uh + + + align:start position:0% +interesting there are some uh +interesting pictures with associate + + align:start position:0% +interesting pictures with associate + + + align:start position:0% +interesting pictures with associate +participating in them are the examples + + align:start position:0% +participating in them are the examples + + + align:start position:0% +participating in them are the examples +Transportation over processing so just + + align:start position:0% +Transportation over processing so just + + + align:start position:0% +Transportation over processing so just +on the waiting for example 8 days 23 + + align:start position:0% +on the waiting for example 8 days 23 + + + align:start position:0% +on the waiting for example 8 days 23 +minutes of value added there was a lot + + align:start position:0% +minutes of value added there was a lot + + + align:start position:0% +minutes of value added there was a lot +of waiting lot lot of you know yes and + + align:start position:0% +of waiting lot lot of you know yes and + + + align:start position:0% +of waiting lot lot of you know yes and +it used to be normal now is uh in + + align:start position:0% +it used to be normal now is uh in + + + align:start position:0% +it used to be normal now is uh in +transportation you had two floors before + + align:start position:0% +transportation you had two floors before + + + align:start position:0% +transportation you had two floors before +absolutely okay um over processing this + + align:start position:0% +absolutely okay um over processing this + + + align:start position:0% +absolutely okay um over processing this +is this is interesting ways that people + + align:start position:0% +is this is interesting ways that people + + + align:start position:0% +is this is interesting ways that people +don't sometimes have to understand in + + align:start position:0% +don't sometimes have to understand in + + + align:start position:0% +don't sometimes have to understand in +this particular uh case this shoe to it + + align:start position:0% +this particular uh case this shoe to it + + + align:start position:0% +this particular uh case this shoe to it +needs a row stitching at the bottom now + + align:start position:0% +needs a row stitching at the bottom now + + + align:start position:0% +needs a row stitching at the bottom now +they put two people might think well Two + + align:start position:0% +they put two people might think well Two + + + align:start position:0% +they put two people might think well Two +Is Better Than One no it's not the shoe + + align:start position:0% +Is Better Than One no it's not the shoe + + + align:start position:0% +Is Better Than One no it's not the shoe +needs one but sometime we tend to a two + + align:start position:0% +needs one but sometime we tend to a two + + + align:start position:0% +needs one but sometime we tend to a two +like maybe three C of pain when two was + + align:start position:0% +like maybe three C of pain when two was + + + align:start position:0% +like maybe three C of pain when two was +enough so we're look into that yeah um + + align:start position:0% +enough so we're look into that yeah um + + + align:start position:0% +enough so we're look into that yeah um +excess inventory y way I mean + + align:start position:0% +excess inventory y way I mean + + + align:start position:0% +excess inventory y way I mean +interesting asset seems to be in the + + align:start position:0% +interesting asset seems to be in the + + + align:start position:0% +interesting asset seems to be in the +balance sheet seems to be an asset but + + align:start position:0% +balance sheet seems to be an asset but + + + align:start position:0% +balance sheet seems to be an asset but +we see this as soon as we start the + + align:start position:0% +we see this as soon as we start the + + + align:start position:0% +we see this as soon as we start the +value stream walk absolutely this + + align:start position:0% +value stream walk absolutely this + + + align:start position:0% +value stream walk absolutely this +actually this is the first part The + + align:start position:0% +actually this is the first part The + + + align:start position:0% +actually this is the first part The +Cutting department and necessary motion + + align:start position:0% +Cutting department and necessary motion + + + align:start position:0% +Cutting department and necessary motion +safety has a lot to do with here here + + align:start position:0% +safety has a lot to do with here here + + + align:start position:0% +safety has a lot to do with here here +you have an associate placing is shoe + + align:start position:0% +you have an associate placing is shoe + + + align:start position:0% +you have an associate placing is shoe +and over + + align:start position:0% +and over + + + align:start position:0% +and over +stretching very different from getting + + align:start position:0% +stretching very different from getting + + + align:start position:0% +stretching very different from getting +closest to you know associate um and + + align:start position:0% +closest to you know associate um and + + + align:start position:0% +closest to you know associate um and +defects and we you know we added in a + + align:start position:0% +defects and we you know we added in a + + + align:start position:0% +defects and we you know we added in a +which is UN use associate creativity + + align:start position:0% +which is UN use associate creativity + + + align:start position:0% +which is UN use associate creativity +wonderful uh it's wonderful so when what + + align:start position:0% +wonderful uh it's wonderful so when what + + + align:start position:0% +wonderful uh it's wonderful so when what +we' all been training here is is that as + + align:start position:0% +we' all been training here is is that as + + + align:start position:0% +we' all been training here is is that as +we walk the floor we do analysis we are + + align:start position:0% +we walk the floor we do analysis we are + + + align:start position:0% +we walk the floor we do analysis we are +trying to identify this waste if we see + + align:start position:0% +trying to identify this waste if we see + + + align:start position:0% +trying to identify this waste if we see +somebody over stretching is motion we + + align:start position:0% +somebody over stretching is motion we + + + align:start position:0% +somebody over stretching is motion we +see somebody waiting so whenever we see + + align:start position:0% +see somebody waiting so whenever we see + + + align:start position:0% +see somebody waiting so whenever we see +these way we put together a continuous + + align:start position:0% +these way we put together a continuous + + + align:start position:0% +these way we put together a continuous +Improvement activity call you know theen + + align:start position:0% +Improvement activity call you know theen + + + align:start position:0% +Improvement activity call you know theen +activity so the whole goal is reduce + + align:start position:0% +activity so the whole goal is reduce + + + align:start position:0% +activity so the whole goal is reduce +waste improve flow reduce waste improve + + align:start position:0% +waste improve flow reduce waste improve + + + align:start position:0% +waste improve flow reduce waste improve +flow I want to see your value stream can + + align:start position:0% +flow I want to see your value stream can + + + align:start position:0% +flow I want to see your value stream can +we get started let's start it absolutely + + align:start position:0% +we get started let's start it absolutely + + + align:start position:0% +we get started let's start it absolutely +wonderful this this is uh the beginning + + align:start position:0% +wonderful this this is uh the beginning + + + align:start position:0% +wonderful this this is uh the beginning +of the value + + align:start position:0% +of the value + + + align:start position:0% +of the value +stream so this is the front end of your + + align:start position:0% +stream so this is the front end of your + + + align:start position:0% +stream so this is the front end of your +value stream here this is a front end of + + align:start position:0% +value stream here this is a front end of + + + align:start position:0% +value stream here this is a front end of +the value stream and you you don't call + + align:start position:0% +the value stream and you you don't call + + + align:start position:0% +the value stream and you you don't call +this the department you call the value + + align:start position:0% +this the department you call the value + + + align:start position:0% +this the department you call the value +stream value stream and the definition + + align:start position:0% +stream value stream and the definition + + + align:start position:0% +stream value stream and the definition +is value stream is a series of + + align:start position:0% +is value stream is a series of + + + align:start position:0% +is value stream is a series of +operations uh put in sequence we call it + + align:start position:0% +operations uh put in sequence we call it + + + align:start position:0% +operations uh put in sequence we call it +a cell to make a particular product okay + + align:start position:0% +a cell to make a particular product okay + + + align:start position:0% +a cell to make a particular product okay +uh not had to be one product be two + + align:start position:0% +uh not had to be one product be two + + + align:start position:0% +uh not had to be one product be two +product three product but there is some + + align:start position:0% +product three product but there is some + + + align:start position:0% +product three product but there is some +uh similar operations and then you can + + align:start position:0% +uh similar operations and then you can + + + align:start position:0% +uh similar operations and then you can +connect them okay now in in a little bit + + align:start position:0% +connect them okay now in in a little bit + + + align:start position:0% +connect them okay now in in a little bit +bigger sense your value stream goes all + + align:start position:0% +bigger sense your value stream goes all + + + align:start position:0% +bigger sense your value stream goes all +the way back to your + + align:start position:0% +the way back to your + + + align:start position:0% +the way back to your +suppliers and you know eventually out to + + align:start position:0% +suppliers and you know eventually out to + + + align:start position:0% +suppliers and you know eventually out to +your stores and so on but we're looking + + align:start position:0% +your stores and so on but we're looking + + + align:start position:0% +your stores and so on but we're looking +just at the value stream absolutely + + align:start position:0% +just at the value stream absolutely + + + align:start position:0% +just at the value stream absolutely +starting with what's coming from the + + align:start position:0% +starting with what's coming from the + + + align:start position:0% +starting with what's coming from the +suppliers and maybe at the end we'll see + + align:start position:0% +suppliers and maybe at the end we'll see + + + align:start position:0% +suppliers and maybe at the end we'll see +what's going out to your stores correct + + align:start position:0% +what's going out to your stores correct + + + align:start position:0% +what's going out to your stores correct +and as as a concept of value stream is + + align:start position:0% +and as as a concept of value stream is + + + align:start position:0% +and as as a concept of value stream is +used within a sell in manufacturing the + + align:start position:0% +used within a sell in manufacturing the + + + align:start position:0% +used within a sell in manufacturing the +concept true for the whole Corporation + + align:start position:0% +concept true for the whole Corporation + + + align:start position:0% +concept true for the whole Corporation +where where are let say a purchasing + + align:start position:0% +where where are let say a purchasing + + + align:start position:0% +where where are let say a purchasing +department will be a department part of + + align:start position:0% +department will be a department part of + + + align:start position:0% +department will be a department part of +the the whole Corporation body so you're + + align:start position:0% +the the whole Corporation body so you're + + + align:start position:0% +the the whole Corporation body so you're +correct yeah so so what you see here is + + align:start position:0% +correct yeah so so what you see here is + + + align:start position:0% +correct yeah so so what you see here is +the cutting that's the first uh the + + align:start position:0% +the cutting that's the first uh the + + + align:start position:0% +the cutting that's the first uh the +first operation and basically materials + + align:start position:0% +first operation and basically materials + + + align:start position:0% +first operation and basically materials +coming from our suppliers uh they come + + align:start position:0% +coming from our suppliers uh they come + + + align:start position:0% +coming from our suppliers uh they come +in EN rolls they go to the consolidation + + align:start position:0% +in EN rolls they go to the consolidation + + + align:start position:0% +in EN rolls they go to the consolidation +Center and then pull based on the demand + + align:start position:0% +Center and then pull based on the demand + + + align:start position:0% +Center and then pull based on the demand +okay uh the production schedule so this + + align:start position:0% +okay uh the production schedule so this + + + align:start position:0% +okay uh the production schedule so this +value PS based on its demand exactly + + align:start position:0% +value PS based on its demand exactly + + + align:start position:0% +value PS based on its demand exactly +exactly and the materials are uh layered + + align:start position:0% +exactly and the materials are uh layered + + + align:start position:0% +exactly and the materials are uh layered +in and we build what is call a web okay + + align:start position:0% +in and we build what is call a web okay + + + align:start position:0% +in and we build what is call a web okay +basically a web + + align:start position:0% +basically a web + + + align:start position:0% +basically a web +serious exactly how much is it given to + + align:start position:0% +serious exactly how much is it given to + + + align:start position:0% +serious exactly how much is it given to +the cutter is based we have a computer + + align:start position:0% +the cutter is based we have a computer + + + align:start position:0% +the cutter is based we have a computer +system that based on the schedule number + + align:start position:0% +system that based on the schedule number + + + align:start position:0% +system that based on the schedule number +of pairs the size and the width um we'll + + align:start position:0% +of pairs the size and the width um we'll + + + align:start position:0% +of pairs the size and the width um we'll +tell how many pairs we need and then how + + align:start position:0% +tell how many pairs we need and then how + + + align:start position:0% +tell how many pairs we need and then how +much you know um quare footage okay get + + align:start position:0% +much you know um quare footage okay get + + + align:start position:0% +much you know um quare footage okay get +to the + + align:start position:0% +to the + + + align:start position:0% +to the +cut basically how how frequently do you + + align:start position:0% +cut basically how how frequently do you + + + align:start position:0% +cut basically how how frequently do you +make that + + align:start position:0% +make that + + + align:start position:0% +make that +calculation well it's work quar like + + align:start position:0% +calculation well it's work quar like + + + align:start position:0% +calculation well it's work quar like +daily daily daily daily and right now + + align:start position:0% +daily daily daily daily and right now + + + align:start position:0% +daily daily daily daily and right now +with the different materials uh every uh + + align:start position:0% +with the different materials uh every uh + + + align:start position:0% +with the different materials uh every uh +daily calcul we deliver four to 5 hours + + align:start position:0% +daily calcul we deliver four to 5 hours + + + align:start position:0% +daily calcul we deliver four to 5 hours +worth of material like adjus in time + + align:start position:0% +worth of material like adjus in time + + + align:start position:0% +worth of material like adjus in time +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +absolutely so the + + align:start position:0% +absolutely so the + + + align:start position:0% +absolutely so the +cutter will pick out a scet d which is + + align:start position:0% +cutter will pick out a scet d which is + + + align:start position:0% +cutter will pick out a scet d which is +um has the shape of the part okay have + + align:start position:0% +um has the shape of the part okay have + + + align:start position:0% +um has the shape of the part okay have +hydraulic machine and place a Dy on the + + align:start position:0% +hydraulic machine and place a Dy on the + + + align:start position:0% +hydraulic machine and place a Dy on the +material uh the placement of the dice is + + align:start position:0% +material uh the placement of the dice is + + + align:start position:0% +material uh the placement of the dice is +called nesting mes okay and it's it's + + align:start position:0% +called nesting mes okay and it's it's + + + align:start position:0% +called nesting mes okay and it's it's +minimize waste I guess exactly it's like + + align:start position:0% +minimize waste I guess exactly it's like + + + align:start position:0% +minimize waste I guess exactly it's like +a puzzle uh cars may take from 3 mon to + + align:start position:0% +a puzzle uh cars may take from 3 mon to + + + align:start position:0% +a puzzle uh cars may take from 3 mon to +six month to get good at it um not only + + align:start position:0% +six month to get good at it um not only + + + align:start position:0% +six month to get good at it um not only +to understand where the die goes but + + align:start position:0% +to understand where the die goes but + + + align:start position:0% +to understand where the die goes but +also make it with + + align:start position:0% +also make it with + + + align:start position:0% +also make it with +speed because talk about speed let let + + align:start position:0% +speed because talk about speed let let + + + align:start position:0% +speed because talk about speed let let +me talk a bit concept concept which is a + + align:start position:0% +me talk a bit concept concept which is a + + + align:start position:0% +me talk a bit concept concept which is a +concept of tag time okay in the Le in + + align:start position:0% +concept of tag time okay in the Le in + + + align:start position:0% +concept of tag time okay in the Le in +the lean world you the goal is to flow + + align:start position:0% +the lean world you the goal is to flow + + + align:start position:0% +the lean world you the goal is to flow +and to reduce waste flow and to reduce + + align:start position:0% +and to reduce waste flow and to reduce + + + align:start position:0% +and to reduce waste flow and to reduce +waste uh based on the demand and this + + align:start position:0% +waste uh based on the demand and this + + + align:start position:0% +waste uh based on the demand and this +value stream which is 50 case today a + + align:start position:0% +value stream which is 50 case today a + + + align:start position:0% +value stream which is 50 case today a +case being + + align:start position:0% +case being + + + align:start position:0% +case being +and the available time per day 600 PA a + + align:start position:0% +and the available time per day 600 PA a + + + align:start position:0% +and the available time per day 600 PA a +day that this value this value + + align:start position:0% +day that this value this value + + + align:start position:0% +day that this value this value +specifically and 7 and a half hours in a + + align:start position:0% +specifically and 7 and a half hours in a + + + align:start position:0% +specifically and 7 and a half hours in a +shift the the the frequency of output is + + align:start position:0% +shift the the the frequency of output is + + + align:start position:0% +shift the the the frequency of output is +20 22 seconds you can first sh that + + align:start position:0% +20 22 seconds you can first sh that + + + align:start position:0% +20 22 seconds you can first sh that +frequency is called T time okay T + + align:start position:0% +frequency is called T time okay T + + + align:start position:0% +frequency is called T time okay T +time now although I just mentioned that + + align:start position:0% +time now although I just mentioned that + + + align:start position:0% +time now although I just mentioned that +the frequency is 20 2 and half seconds + + align:start position:0% +the frequency is 20 2 and half seconds + + + align:start position:0% +the frequency is 20 2 and half seconds +per + + align:start position:0% +per + + + align:start position:0% +per +Sho at this stage because of the uh + + align:start position:0% +Sho at this stage because of the uh + + + align:start position:0% +Sho at this stage because of the uh +characteristics of the operation + + align:start position:0% +characteristics of the operation + + + align:start position:0% +characteristics of the operation +we are not flowing one shoe at a time we + + align:start position:0% +we are not flowing one shoe at a time we + + + align:start position:0% +we are not flowing one shoe at a time we +are still in a bad World okay but a + + align:start position:0% +are still in a bad World okay but a + + + align:start position:0% +are still in a bad World okay but a +small bat small batches in the p in the + + align:start position:0% +small bat small batches in the p in the + + + align:start position:0% +small bat small batches in the p in the +past as I said before when we were our + + align:start position:0% +past as I said before when we were our + + + align:start position:0% +past as I said before when we were our +lead time was 8 Days um in a equivalent + + align:start position:0% +lead time was 8 Days um in a equivalent + + + align:start position:0% +lead time was 8 Days um in a equivalent +value stream we will have close to 400 + + align:start position:0% +value stream we will have close to 400 + + + align:start position:0% +value stream we will have close to 400 +cases of weip okay now when a lead time + + align:start position:0% +cases of weip okay now when a lead time + + + align:start position:0% +cases of weip okay now when a lead time +of 3 hours our working process is 20 25 + + align:start position:0% +of 3 hours our working process is 20 25 + + + align:start position:0% +of 3 hours our working process is 20 25 +cases okay that's a reduction of 98% so + + align:start position:0% +cases okay that's a reduction of 98% so + + + align:start position:0% +cases okay that's a reduction of 98% so +I see a little green thing on the floor + + align:start position:0% +I see a little green thing on the floor + + + align:start position:0% +I see a little green thing on the floor +that visual control says cutting rip + + align:start position:0% +that visual control says cutting rip + + + align:start position:0% +that visual control says cutting rip +seven cases maximum absolutely Absolut + + align:start position:0% +seven cases maximum absolutely Absolut + + + align:start position:0% +seven cases maximum absolutely Absolut +that's all the space you got so the + + align:start position:0% +that's all the space you got so the + + + align:start position:0% +that's all the space you got so the +Cutters will cut the individual + + align:start position:0% +Cutters will cut the individual + + + align:start position:0% +Cutters will cut the individual +Parts based on the material and they + + align:start position:0% +Parts based on the material and they + + + align:start position:0% +Parts based on the material and they +will be placing the parts on the on the + + align:start position:0% +will be placing the parts on the on the + + + align:start position:0% +will be placing the parts on the on the +bins okay when they finish the hour so + + align:start position:0% +bins okay when they finish the hour so + + + align:start position:0% +bins okay when they finish the hour so +here the the unit of uh of flow you can + + align:start position:0% +here the the unit of uh of flow you can + + + align:start position:0% +here the the unit of uh of flow you can +call it an hour could be between six and + + align:start position:0% +call it an hour could be between six and + + + align:start position:0% +call it an hour could be between six and +seven cases depending on this style okay + + align:start position:0% +seven cases depending on this style okay + + + align:start position:0% +seven cases depending on this style okay +so while we're here I I see a BM hanging + + align:start position:0% +so while we're here I I see a BM hanging + + + align:start position:0% +so while we're here I I see a BM hanging +up there so I want to just ask you about + + align:start position:0% +up there so I want to just ask you about + + + align:start position:0% +up there so I want to just ask you about +5S 5S that's actually that's uh it's + + align:start position:0% +5S 5S that's actually that's uh it's + + + align:start position:0% +5S 5S that's actually that's uh it's +very typical 5S is the um is a system + + align:start position:0% +very typical 5S is the um is a system + + + align:start position:0% +very typical 5S is the um is a system +that um or organization you know it's 5s + + align:start position:0% +that um or organization you know it's 5s + + + align:start position:0% +that um or organization you know it's 5s +for sore setting order shine + + align:start position:0% +for sore setting order shine + + + align:start position:0% +for sore setting order shine +standardized and such thing and uh it's + + align:start position:0% +standardized and such thing and uh it's + + + align:start position:0% +standardized and such thing and uh it's +much more than just cleaning um once you + + align:start position:0% +much more than just cleaning um once you + + + align:start position:0% +much more than just cleaning um once you +understand the 5S there are economics in + + align:start position:0% +understand the 5S there are economics in + + + align:start position:0% +understand the 5S there are economics in +place and there is a very key location + + align:start position:0% +place and there is a very key location + + + align:start position:0% +place and there is a very key location +of parts and this is the first system we + + align:start position:0% +of parts and this is the first system we + + + align:start position:0% +of parts and this is the first system we +implemented like 5 years ago I was going + + align:start position:0% +implemented like 5 years ago I was going + + + align:start position:0% +implemented like 5 years ago I was going +to ask you it's hard for you almost to + + align:start position:0% +to ask you it's hard for you almost to + + + align:start position:0% +to ask you it's hard for you almost to +imagine a place where it wouldn't natur + + align:start position:0% +imagine a place where it wouldn't natur + + + align:start position:0% +imagine a place where it wouldn't natur +be 5S but you had to start with 5S you + + align:start position:0% +be 5S but you had to start with 5S you + + + align:start position:0% +be 5S but you had to start with 5S you +said with the 5 + + align:start position:0% +said with the 5 + + + align:start position:0% +said with the 5 +because one of the I think the mistakes + + align:start position:0% +because one of the I think the mistakes + + + align:start position:0% +because one of the I think the mistakes +is thinking that 5S is just a cleaning + + align:start position:0% +is thinking that 5S is just a cleaning + + + align:start position:0% +is thinking that 5S is just a cleaning +so everybody understands cleaning and so + + align:start position:0% +so everybody understands cleaning and so + + + align:start position:0% +so everybody understands cleaning and so +might to clean and when you start a new + + align:start position:0% +might to clean and when you start a new + + + align:start position:0% +might to clean and when you start a new +process you can get so many gains by + + align:start position:0% +process you can get so many gains by + + + align:start position:0% +process you can get so many gains by +just cleaning it looks good there's much + + align:start position:0% +just cleaning it looks good there's much + + + align:start position:0% +just cleaning it looks good there's much +more to it but the broom in that place + + align:start position:0% +more to it but the broom in that place + + + align:start position:0% +more to it but the broom in that place +with the label say broom that's me it + + align:start position:0% +with the label say broom that's me it + + + align:start position:0% +with the label say broom that's me it +becomes part of your organizing yourself + + align:start position:0% +becomes part of your organizing yourself + + + align:start position:0% +becomes part of your organizing yourself +absolutely and it's part it goes deeper + + align:start position:0% +absolutely and it's part it goes deeper + + + align:start position:0% +absolutely and it's part it goes deeper +I think + + align:start position:0% +I think + + + align:start position:0% +I think +that five is good actually a reflection + + align:start position:0% +that five is good actually a reflection + + + align:start position:0% +that five is good actually a reflection +of leadership if you cannot get an + + align:start position:0% +of leadership if you cannot get an + + + align:start position:0% +of leadership if you cannot get an +organized workplace and + + align:start position:0% +organized workplace and + + + align:start position:0% +organized workplace and +clean you your chances of flowing + + align:start position:0% +clean you your chances of flowing + + + align:start position:0% +clean you your chances of flowing +product and meting the attack time are + + align:start position:0% +product and meting the attack time are + + + align:start position:0% +product and meting the attack time are +very slim so it has to do with the disab + + align:start position:0% +very slim so it has to do with the disab + + + align:start position:0% +very slim so it has to do with the disab +it's much bit deeper than that than just + + align:start position:0% +it's much bit deeper than that than just + + + align:start position:0% +it's much bit deeper than that than just +a cleaning uhhuh okay \ No newline at end of file diff --git a/hZ3bVZPUVAU.txt b/hZ3bVZPUVAU.txt new file mode 100644 index 0000000000000000000000000000000000000000..a1b48483282e2cb23ec9d6c6c3d96ed42fd77434 --- /dev/null +++ b/hZ3bVZPUVAU.txt @@ -0,0 +1,307 @@ +align:start position:0% + +so when you're teaching students to + + align:start position:0% +so when you're teaching students to + + + align:start position:0% +so when you're teaching students to +communicate orally effectively giving + + align:start position:0% +communicate orally effectively giving + + + align:start position:0% +communicate orally effectively giving +them a real living large audience ups + + align:start position:0% +them a real living large audience ups + + + align:start position:0% +them a real living large audience ups +their game considerably obviously like + + align:start position:0% +their game considerably obviously like + + + align:start position:0% +their game considerably obviously like +nobody wants to do a bad job in front of + + align:start position:0% +nobody wants to do a bad job in front of + + + align:start position:0% +nobody wants to do a bad job in front of +their peers in front of a group and + + align:start position:0% +their peers in front of a group and + + + align:start position:0% +their peers in front of a group and +obviously that's important because it + + align:start position:0% +obviously that's important because it + + + align:start position:0% +obviously that's important because it +replicates the kind of talks that + + align:start position:0% +replicates the kind of talks that + + + align:start position:0% +replicates the kind of talks that +they're likely to be giving say at + + align:start position:0% +they're likely to be giving say at + + + align:start position:0% +they're likely to be giving say at +conferences however it may not be wise + + align:start position:0% +conferences however it may not be wise + + + align:start position:0% +conferences however it may not be wise +to throw them in the deep end right away + + align:start position:0% +to throw them in the deep end right away + + + align:start position:0% +to throw them in the deep end right away +and a lot of times in classes that do + + align:start position:0% +and a lot of times in classes that do + + + align:start position:0% +and a lot of times in classes that do +have an oral communication component + + align:start position:0% +have an oral communication component + + + align:start position:0% +have an oral communication component +that's what happens you know somebody + + align:start position:0% +that's what happens you know somebody + + + align:start position:0% +that's what happens you know somebody +isn't necessarily an experienced speaker + + align:start position:0% +isn't necessarily an experienced speaker + + + align:start position:0% +isn't necessarily an experienced speaker +and their first experience of it is an + + align:start position:0% +and their first experience of it is an + + + align:start position:0% +and their first experience of it is an +end of the semester presentation and + + align:start position:0% +end of the semester presentation and + + + align:start position:0% +end of the semester presentation and +that's very very difficult for a lot of + + align:start position:0% +that's very very difficult for a lot of + + + align:start position:0% +that's very very difficult for a lot of +students so what I think has worked + + align:start position:0% +students so what I think has worked + + + align:start position:0% +students so what I think has worked +really well in this class is giving them + + align:start position:0% +really well in this class is giving them + + + align:start position:0% +really well in this class is giving them +that practice over and over again in a + + align:start position:0% +that practice over and over again in a + + + align:start position:0% +that practice over and over again in a +slightly safer setting where it's just a + + align:start position:0% +slightly safer setting where it's just a + + + align:start position:0% +slightly safer setting where it's just a +couple of people where the you know when + + align:start position:0% +couple of people where the you know when + + + align:start position:0% +couple of people where the you know when +you when they give the original practice + + align:start position:0% +you when they give the original practice + + + align:start position:0% +you when they give the original practice +oral presentation it's not even graded + + align:start position:0% +oral presentation it's not even graded + + + align:start position:0% +oral presentation it's not even graded +so it's safe to fail and that sense of + + align:start position:0% +so it's safe to fail and that sense of + + + align:start position:0% +so it's safe to fail and that sense of +safety in that sense of really building + + align:start position:0% +safety in that sense of really building + + + align:start position:0% +safety in that sense of really building +up stage by stage your skills is what + + align:start position:0% +up stage by stage your skills is what + + + align:start position:0% +up stage by stage your skills is what +gives them the confidence to be skilled + + align:start position:0% +gives them the confidence to be skilled + + + align:start position:0% +gives them the confidence to be skilled +communicators by the end of the semester + + align:start position:0% +communicators by the end of the semester + + + align:start position:0% +communicators by the end of the semester +you know by the time they finish 8:13 + + align:start position:0% +you know by the time they finish 8:13 + + + align:start position:0% +you know by the time they finish 8:13 +there is nobody in the class who doesn't + + align:start position:0% +there is nobody in the class who doesn't + + + align:start position:0% +there is nobody in the class who doesn't +understand what they need to do to make + + align:start position:0% +understand what they need to do to make + + + align:start position:0% +understand what they need to do to make +their presentation work and that makes + + align:start position:0% +their presentation work and that makes + + + align:start position:0% +their presentation work and that makes +it you know the moment of going into the + + align:start position:0% +it you know the moment of going into the + + + align:start position:0% +it you know the moment of going into the +you know the conference room or the or + + align:start position:0% +you know the conference room or the or + + + align:start position:0% +you know the conference room or the or +the classroom and standing up in front + + align:start position:0% +the classroom and standing up in front + + + align:start position:0% +the classroom and standing up in front +of their peers that makes it possible + + align:start position:0% +of their peers that makes it possible + + + align:start position:0% +of their peers that makes it possible +that makes it maybe even fun \ No newline at end of file diff --git a/iOilZsS_cnM.txt b/iOilZsS_cnM.txt new file mode 100644 index 0000000000000000000000000000000000000000..ef73ef946cf7bd1308883eab89a28e6bc4094c95 --- /dev/null +++ b/iOilZsS_cnM.txt @@ -0,0 +1,3727 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to this + +lecture on non-linear finite +element analysis. + +In the previous lectures, I +introduced you to non-linear + +finite element analysis, to +the solution methods that + +we're using in non-linear finite +element analysis, using + +primarily physical concepts. + +We are now ready to discuss the +mathematical basis of the + +procedures that we're using +to obtain solutions. + +Of course, this material is very +complex, and there is a + +lot we could discuss. + +But let us have a go at it. + +We have a body that undergoes +large displacements, large + +rotations, and large strains. + +So therefore, we consider +the body to + +undergo very large motions. + +We will use a Lagrangian +description of the + +motion of the body. + +Here, on this viewgraph, I have +prepared schematically + +the body that we +are looking at. + +Here the body is in its +configuration at time zero. + +Notice that the area is, the +surface area of the body is + +described as 0 A, the volume +is described as 0 V, the 0 + +being a left superscript. + +I should point out, at this +point, that you will be + +encountering now a lot of +superscripts and subscripts, + +and that actually makes the +discussion somewhat difficult. + +And for that reason, I like to +take now, on this viewgraph, + +just a minute to explain to you +why we have a particular + +superscript, a particular +subscript, in that particular + +location, and what +it means to us. + +So, a left superscript here, as +shown on A and V, means at + +time indicated by that, at the +time indicated by that + +superscript. + +So here we have 0 A, 0 V once +again, area at time 0, + +volume at time 0. + +A particular point here, point +P, has the coordinates 0 X 1, + +0 X 2, 0 X 3. + +Now, notice that these upper +0s here correspond to the + +time, as I just pointed out, +whereas 1, 2, and 3, of + +course, correspond to +the coordinate axis. + +This is a particular +material particle. + +This material particle will move +with the body from time 0 + +to time t as shown on +this viewgraph. + +Of course, at this particular +time now, the surface area of + +the body has become t A, +t now meaning surface + +area at time t. + +And the volume of the body +is t V. Notice that the + +coordinates of this material +particle now are t x + +1, t x 2, t x 3. + +We will assume, later on in our +actual solution, that the + +solution up to time t is known, +in other words, that + +the area, the volume, in fact, +the stresses, the strains, at + +time t are known. + +And that we will want to march +ahead one time increment, to + +time, t plus delta t. + +Notice the volume of the body, +now, is given by t plus delta + +t V. The surface area is given +by t plus delta t A. The + +coordinates of the material +particle have now become t + +plus delta t x 1, t plus delta t +x 2, and t plus delta t x 3. + +Well, there's one very +important point. + +And that important point is that +we are considering that + +the Cartesian coordinate axis +in which the motion of the + +body is measured remains +stationary. + +You should always keep +that in mind. + +In other words, here we have the +Cartesian axis, x 1, x 2, + +x 3, and those remain +stationary, whereas the body + +moves through those axes, +through the, well, system of + +axes, And we want to, of course, +solve for that motion. + +With the particle motion +described by the coordinates + +that I just mentioned, we can +now define the following + +quantities down here. + +We can say that t x i, the +coordinates at time t of the + +material particle, are +equal to 0 x i-- + +both of those quantities, of +course, we know already now + +what they are-- + +plus t u i. + +t u i are just the displacements +from + +time 0 to time t. + +Similarly for the situation +from time 0 to time + +t plus delta t. + +Notice that these are now the +displacements from time 0 to + +time t plus delta t. + +And we can, of course, talk +also about the incremental + +displacements. + +The incremental displacements +from time t plus delta t, or + +rather from time t, I should +say, to time t plus delta t. + +And those incremental +displacements + +are given by u i. + +Of course, the lower right +subscript always + +refers to the axis. + +In other words, i goes from +one to two to three. + +For the u's and for the x's. + +Well, I mentioned already that +the Cartesian axes are + +stationary. + +And I have prepared this +viewgraph to point it out once + +more very strongly. + +The unit distances along the +xi-axis are the same for 0 x + +i, t x i, and t plus +delta t x i. + +That is also a very +important point. + +Let's look at this very +simple example. + +Here we have an x 2- axis, +and we have the x + +1-axis along here. + +Notice the units along this axis +are 1, 2, 3, and so on. + +The material particle +has initially the + +coordinates, 2, say. + +Of course, then, this being +the length of 0 x 1. + +This particle, at time 0, moves +to time t by t u 1, the + +way we just said it earlier. + +And of course, the sum of +these two quantities is + +equal to t x 1. + +Notice that t x 1 is measured +along the same axis, with the + +same unit distances, as 0 x 1. + +And therefore, for this reason, +we now use just x 1 + +here, without the left +superscript, to denote the + +coordinate axis. + +By the way, in my book, the +textbook for this video + +course, I have frequently +put here, a t or 0. + +I feel now, it is better, +actually, to drop that + +superscript, because this +description, the way I just + +explained it to you, I think, +is even better. + +Well, let us talk now, +then, about the + +principle of virtual work. + +And now, we want to look at the +principle of virtual work + +applied to time t +plus delta t. + +The reason being, of course, +that we want to solve for the + +static and kinematic variables +at time t plus delta t. + +We assume that we know +the solution from + +time 0 to time t. + +We discussed in the previous + +lectures already the principle. + +I'd like to now just review it +once more, because it's just + +of utmost importance to very +well grasp, understand what + +the principle says, and +how we apply it then. + +Here we have now the +Cauchy stresses. + +I defined the Cauchy stresses +earlier as the + +force per unit area. + +The i j, of course, mean +coordinate axis, i and j. + +In three dimensional analysis, +going from 1 to 3. + +t plus delta t means the +Cauchy stress at time + +t plus delta t. + +These are the real stresses +that we want to solve for. + +Here we have virtual strains. + +These are infinitesimally small +strains, referred to the + +configuration at time +t plus delta t. + +This t plus delta t means a +reference to the configuration + +at time t plus delta t. + +And here we have, of course, +the t plus delta t d V, + +because we're integrating over +that volume which, of course, + +is unknown in the incremental +solution. + +This is the internet virtual +work, which must be equal to + +the external virtual work. + +Here is again, the script R. And +this script R, at time t + +plus delta t, is defined down +here in the viewgraph. + +We're integrating over the +volume, at time t plus delta + +t, the body forces. + +And these are the real body +forces, of forces per unit + +volume at time t plus delta t, +multiplied by the virtual + +displacements, delta u i. + +And the integration, of course, +goes over the volume + +at time t plus delta t. + +We're adding to this part the +surface forces, forces per + +unit area, at time t plus delta +t, multiplied by the + +virtual displacements +on the surface. + +This capital S stands for "on +the surface." And this product + +is integrated over the total +surface of the body at time t + +plus delta t. + +We assume that we know this part +once we have imposed a + +virtual displacement. + +And therefore, we can calculate +the right-hand side. + +Corresponding to that virtual +displacement we + +obtain virtual strains. + +And therefore, we can +calculate also + +the left-hand side. + +And once again, the principle of +virtual work says, that the + +left-hand side, the internal +virtual work, must be equal to + +the right-hand side, the +external virtual work, for any + +arbitrary virtual displacements +that satisfy the + +displacement boundary +conditions. + +Of course, remember, as I +pointed out earlier, in an + +earlier lecture, that the +virtual strains must + +correspond to the virtual +displacements. + +And here we have the virtual +strains, once again. + +On the viewgraph we saw this +stress, and I call it the + +Cauchy stress. + +Here, you have it spelled +out once more. + +It's the force per unit area +at time t plus delta t. + +We also talked about the +virtual strains. + +And the virtual strains here, +this was the quantity R, + +defined as shown on the +right-hand side. + +Let me once again point strongly +out that we are + +differentiating here, with +respect to the coordinates, at + +time t plus delta t. + +Of course, the j and +the i coordinate. + +And also, please recognize that +this strain is really the + +infinitesimal strain tensor +that you are very well + +familiar with in infinitesimal +analysis, in infinitesimal + +displacement analysis, I should +say, except for one + +difference that we're using +here, the unknown coordinates + +at time t plus delta t. + +And that is spelled out down +here, that we are using a + +variation in the small strains +referred to the configuration, + +at time t plus delta t. + +So really, if you are familiar +with the principle of virtual + +work, as applied in +infinitesimal displacement + +analysis, then you recognize +that the principle of virtual + +work now applied to large +deformation analysis, large + +displacement analysis, is quite +the same, except that we + +are applying it to the current +geometry, the current + +configuration of the body. + +In my textbook, actually, I have +a little note, a footnote + +that you might also look at, +in the beginning of Chapter + +Six, where I discuss this +principle of virtual work, + +that one way to look at it is +that you see a body and, you + +see the body in front of +yourself moving through the + +stationary coordinate frame-- + +once again, the Cartesian +coordinate frame is + +stationary. + +You see it move, you see the +body move through that + +coordinate frame. + +And there is somebody standing, +taking a picture. + +And that picture is taken +at time t plus delta t. + +And now you have a picture. + +And you apply the principle +of virtual work to that + +particular configuration +which has been + +captured in that picture. + +That's perhaps one way to look +at it, at least one way that I + +like to look at it. + +In order to solve, or to work +with the principal of virtual + +work, you need to rewrite the +principal, really, because we + +cannot integrate over an unknown +volume, and we cannot + +directly work with increments +in the Cauchy stresses. + +The volume t plus delta t, +remember, is unknown. + +And the reason why we cannot +directly work, or simply work + +with increments in Cauchy +stresses is because a Cauchy + +stress is always referred to the +current geometry, current + +configuration. + +So if we talk about the Cauchy +stress at time t, then it's + +the force per unit +area at time t. + +And the Cauchy stress at time +t plus delta t is the force + +per unit area at time +t plus delta t. + +Now you can't add a quantity +that is referred to time t to + +a quality that is referred to +time t plus delta t, because + +the areas, the reference +areas, have changed. + +And we have to somehow take +care of that in our + +formulation. + +And for that reason, we +introduce these two new + +quantities. + +The t 0 s is the 2nd +Piola-Kirchhoff stress tensor. + +And the t 0 epsilon is the +Green-Lagrange strain tensor. + +We introduce these quantities +because these are well known + +quantities. + +If you were to look into +continuum mechanics texts, + +they have been described +in many, many books. + +And they are well known +for some time. + +But we have extracted, +basically, this information + +from the continuum mechanics +literature, because it's a + +convenient, these are convenient +stress and strain + +measures to work with in +large deformation, + +finite element analysis. + +So, this is the stress +and that is the + +strain we will be using. + +And let me say the +following now. + +This t here, the upper t, means +stress at time t, in the + +configuration at time t. + +This lower 0 means that the +stress is referred to the + +configuration at time 0. + +Similarly for the Green-Lagrange +strain. + +Upper left, the configuration in +which the strain, or stress + +measure is measured, and the +lower subscript means, to + +which the configuration, +to which the + +measure is referred to. + +So this is something to keep +in mind, because we will be + +encountering this quite a bit. + +Here is the definition of the +stress tensor, t 0 s i j. + +Once again, the stress in +configuration t, referred to + +the configuration at time 0. + +i j, of course, being the +Cartesian coordinate + +components. + +Here we have the mass +density ratio. + +The mass density at time 0, in +configuration 0, if you like. + +The mass density at time t, in +configuration at time t. + +And here we have a new quantity, +which is actually + +the inverse of the deformation +gradient. + +This is a component +of the inverse of + +the deformation gradient. + +We will talk about this quantity +quite a bit just now. + +Here we have the +Cauchy stress. + +And here we have another +component such as that one. + +This is the 2nd Piola-Kirchhoff +stress. + +Once again, I will talk about +this piece of information + +quite a bit just now. + +The Green-Lagrange strain tensor +is defined as shown + +here, t 0 epsilon i j, i j, of +course, being the components + +into the Cartesian coordinate +axes, 1/2 t 0 u i comma j plus + +t zero u j comma i plus t 0 u k +comma i times t zero u k j. + +Notice that here we would select +a particular i and j, + +say i equals 1, j equals 2. + +You would substitute those i and +j numbers in here, so to + +say, and here as well. + +And notice that this k then, +would actually run over all + +possibilities. + +k going from 1, then +to 2, then to 3. + +In other words, there is a +summation involved here. + +By the way, similarly, we have +a summation involved here, + +because m and n would run over +all the possibilities. + +I will talk just now a little +bit more about it. + +But let's first now look at how +this particular piece of + +information here is defined. + +It's defined as a partial of 0 +x i with respect to t x m. + +Notice that this coordinate, +of course, is given, is + +assumed to be given. + +And that one here is also +now assumed to be given. + +Notice, of course, that t x +m is equal to 0 x m plus a + +displacement that +has occurred. + +Notice that this differentiation +here is + +defined as given here, partial +t u i with respect to the + +original coordinates. + +So, this lower 0 here, this +lower 0 here refers to the + +fact that we're differentiating +with respect + +to the original coordinates. + +This upper t here means that +we are differentiating the + +displacement at time t. + +Notice, of course, that i and +j are dummy indices here. + +So, in fact, this one here +is what I'm considering. + +But at the same time, I'm +considering that one, if I + +just switch around i and j. + +So these are the definitions +of these two quantities. + +And I mentioned briefly already +that we are summing in + +these definitions. + +For example, t s 1 1 would be +calculated from the formulas + +that I gave you as 0 +rho over t rho-- + +this, of course, is a scalar-- + +times this product here. + +What do we do here? + +We are selecting the +1 as that 1 here. + +That 1 here refers to that 1. + +And then we are letting these +components here, these + +components here, and that one +here, run over all the + +possibilities. + +Notice, here we have 1 2. + +That is this 1 here, +and that 1, 2. + +And here we have +3, 3 3, and 3. + +So in other words, these +first two are fixed. + +These first two here are fixed, +this 1 and that 1. + +They correspond to this +1, to these two 1s. + +But the other components vary +over all the possibilities, + +namely, 1, to 2, to 3. + +This is here the summation +convention, which is + +abundantly used in continuum +mechanics. + +And you might be very well +familiar with it. + +Using this 2nd Piola-Kirchhoff +stress and Green-Lagrange + +strain tensors-- + +and that is really the important +point now-- we can + +rewrite the basic equation of +the principle of virtual work + +in the form given here. + +Here on the left-hand side, we +have the Cauchy stresses times + +the variations on the +infinitesimal strains, or the + +small, infinitesimally virtual +small strains. + +We integrate this product +over the current volume. + +And we mentioned already that +we cannot deal with this + +integration very well. + +Well, we now rewrite, we can +rewrite this integral as shown + +here, 2nd Piola-Kirchhoff +stresses times variations in + +the Green-Lagrange strains. + +And we integrate this, we are +integrating this product over + +the original volume +of the body. + +And that is the clue. + +We know this volume. + +We asked in general, +increment analysis. + +We would not know this volume +if, for example, we only have + +calculated the response +up to t minus delta t. + +So, if we know this volume we +can directly deal with this + +integration. + +And we will see also that since +these stress components + +are always referred to the same +volume, the same area, we + +can also incrementally decompose +these stresses. + +And the same holds +for the strains. + +Notice this relation, of course, +holds for all times, + +delta t, 2 delta t, +t, t plus delta t. + +The way we talked about the +principal of virtual work just + +now, we really had, on the +left-hand side here, + +t plus delta t. + +Well, you would just exchange +this t, that t, and that t, + +and that t here, to +a t plus delta t. + +And similarly, of course, on the +right-hand side as well. + +I chose at the preparation of +the viewgraph to simply call + +it t, because after all, this +equation holds anyways, for + +any of those particular times. + +To develop, then, the +incremental finite element + +equations, we use the +principle of virtual + +work in this form. + +If we assume that at, that the +response has been calculated + +from time 0 to time t, we apply +the principle of virtual + +work at time t plus delta t. + +We integrate, now, over +a known volume, + +as I pointed out. + +And, we can directly decompose +the stresses at time t plus + +delta t, and the Green-Lagrange +strains at time + +t plus delta t as shown +in these equations. + +Now, notice that here we have +the stress at time t plus + +delta t referred to the +configuration at time 0 being + +equal to the stress at time t +referred to the configuration + +at time 0 plus an incremental +that is also + +referred to time 0. + +And this is what we +would like to see. + +Similarly for the Green-Lagrange +strain. + +These two items make if for us +possible to work very well + +with the principle of virtual +work in this particular form. + +Before developing, however, +the incremental continuum + +mechanics equations, I'd like +to discuss with you now some + +important kinematic +relationships that we use in + +general non-linear analysis. + +The 2nd Piola-Kirchhoff stress +and Green-Lagrange strains + +have some very interesting, +properties that I think I'd + +like to share with you +in a discussion. + +To explain some of these +properties, we want to + +introduce the deformation +gradient tensor. + +The deformation gradient tensor +is actually something + +very, very basic in continuum +mechanics. + +And so, let us spend a little +bit of time on this tensor, to + +get also a bit of a physical +feel for what it means, what + +it stands for, and what +can we do with it. + +The tensor captures the +straining of the body and the + +rotation of the body. + +And, as I mentioned, it is +really a very fundamental + +quantity used in continuum +mechanics. + +The definition of +the deformation + +gradient is as follows. + +Here, we have t 0 x being equal +to a matrix, a large + +matrix, which, of course, is +written in a Cartesian + +coordinate system. + +And notice what we're doing in +the elements of that matrix. + +We take the partial of t x +1 with respect to 0 x 1. + +In other words, we're taking the +coordinates at time t and + +differentiate them with respect +to the original + +coordinates. + +Here, the 1 component with +respect to the 1 component. + +Here, the t x 1 with respect +to the 0 x 2. + +And, t x 1 with respect +to 0 x 3. + +Like that, we get a three +by three matrix. + +Using indicial notation, we can +simply say that an element + +of that matrix, t 0 X i j, +capital X, because the matrix + +is defined as the capital t 0 X, +being equal partial of t X + +i with respect to 0 x j. + +Of course, i j are +those i j's here. + +And, you will also find in the +textbook the following + +notation here, t 0 x i j. + +Notice, when I have a comma +here, we denote the + +differentiation by that comma, +and we use a little x. + +That is different from using +the capital X here, with no + +comma, because that capital X +simply denotes a component of, + +let's go up here once more, +the t 0 x of that matrix. + +So this is a mathematical +definition, really, of the + +deformation gradient. + +And notice that in order to +calculate the elements of this + +matrix, of course what you need +to be given is this t x + +1, t x 2, t x 3, as a function +of 0 x 1, 0 x 2, and 0 x 3. + +If you are given the deformation +field, t x i as a + +function of the 0 x j's, then +you can calculate directly the + +components of the three +by three matrix. + +Another way to write the +deformation gradient is via + +this equation. + +t 0 x can be written +as 0 del, del 0. + +This here is a gradient +operator. + +Let's look down here. + +We have defined it here. + +Times t x, or this gradient +operator operates, I should + +say, on t x capital T. This +capital T means transposed. + +And this t x capital T +is given right here. + +Notice what we're listing in +this vector here now, in this + +row vector, are simply the +coordinates at time t, t x 1, + +t x 2, t x 3. + +Notice that there is +a transpose here. + +That transpose is simply +introduced to make sure that + +this right-hand side is equal to +what we have defined on the + +previous viewgraph this to be. + +If you leave out that capital +T, you would not quite get + +what we actually have defined +on the previous viewgraph. + +So that's why we put that +capital T in there. + +It would be a nice exercise +for you to just actually + +substitute from here into there, +plug into there, and + +write out the three by three +matrix, to make sure that you + +actually get what's given here +on the left-hand side the way + +we defined it on the +previous viewgraph. + +The deformation gradient, as I +briefly mentioned, describes + +the deformations, the rotations, +and stretches of + +the material fibers. + +Let's look at some +examples now. + +For example, if we have d 0 x +here, that is the material + +fiber in its original +configuration. + +Of course, that original +configuration is going to be + +deformed, moved through the +stationary coordinate system. + +That fiber moves into +this situation here. + +It becomes d t x. + +The deformation gradient gives +us this element as a function + +of that element, as given +in this equation. + +In other words, d t x is equal +to t 0 x times d 0 x. + +If you know this piece of +information, and you have + +calculated the deformation +gradient, you + +directly get d t x. + +That's what the deformation +gradient does for us. + +Well, an example. + +It's always nice to look at some +examples to demonstrate + +what we mean by these +theoretical formulas. + +And here we have a very +simple example. + +It's a one dimensional +deformation. + +We start off with this piece +of material, a rectangular + +piece of material. + +And that piece of material is +stretched out from time 0 to + +time t into this red +configuration. + +Quite a bit of stretching, but +the motion is simple because + +it's a uni-axial motion. + +Notice, the original length of +this piece of material is 1, + +and this side here +moves out 0.5. + +Of course, the material +particles here will move. + +For example, a particle that was +originally here, the black + +little lines there, will move +over to the right, and it + +becomes this red little line. + +This black line moves over +to become that red line. + +Notice the displacement of this +black line is given by + +this blue arrow here. + +This black line moves over to +there, and the displacement is + +given by that blue arrow. + +If we know the displacements of +all these particles here, + +we know the deformation field. + +Vice versa, if the deformation +field is given, and now we + +look at this equation here, we +know the displacements of all + +of the particles along. + +And t x 1 is equal to 0 x +1 for this particular + +deformation field plus +0.5 0 x 1 squared. + +Let's look at what this means. + +It tells that if I plug in a +particular coordinate on the + +right-hand side of a material +particle in its original + +configuration, then I'm going to +get the final coordinate of + +that same material particle, +that same material particle. + +Well, the deformation gradient +is defined via this + +relationship, and it's +therefore given + +as 1 plus 0 x 1. + +Notice, we have only motion in +one direction, so we only + +calculate this one component. + +Let's consider, quite +physically, a material + +particle initially at +x 1 equals 0.8. + +In other words, x 1 is +this direction, 0 x + +1 is equal to 0.8. + +Remember, x 1 just gives us +the coordinate direction. + +We now put a 0 on it to signify +that 0.8 is the + +position of the particle +initially. + +That particle moves with the +deformation field that I've + +been given to this point here, +and t x 1 is then 1.120. + +The same can, of course, be +repeated for an adjacent + +material particle. + +In other words, let us look +now at a material particle + +that is just a little bit to the +right-hand side, namely 0 + +x 1 being 0.850, slightly to +the right-hand side of the + +other material particle +that we looked at. + +This material particle, with the +deformation field that we + +have been prescribing, moves +to t x 1, this number here. + +We can now compute t 0 x 1 1, +the element of the deformation + +gradient as this difference +here. + +And the numbers are +plugged in here. + +And we obtain 1.82. + +Of course this is an estimate, +because we did not take a + +differential. + +If we actually calculate the +deformation gradient the way + +it's being defined, we get 1.80, +which is quite close to + +the estimate here. + +The reason for that difference, +of course, is that + +0 x 1, for this particle, is not +close enough, close enough + +to the earlier particle, +the other particle that + +we also looked at. + +In other words, 0.850 is not +close enough to 0.8, in order + +to get a very close relationship +here between + +these two numbers. + +Let's look at another +example, a two + +dimensional deformation example. + +Here now, we have as the +original configuration, this + +black body here, black outline +shown, in the coordinate + +system x 1 X 2. + +Once again, remember the +coordinate system is + +stationary. + +And let us look at two +material fibers, this + +one and that one. + +This one does not carry a hat. + +That one carries a hat. + +So these are two different +material fibers. + +These fibers move to here +from time 0 to time t. + +This fiber, d 0 x +becomes d t x. + +That fiber, d 0 x hat, +becomes d t x hat. + +In other words, of course, this +here in red shown, is the + +configuration at time t. + +Now, notice that these fibers +here have particular + +coordinates, 0 x 1, 0 x 2. + +You can think of these +coordinates to be at the + +beginning of that fiber. + +Of course, these are +differential fibers. + +They are very, very small. + +These coordinates move +over to t x 1, t x 2. + +In other words, the particle +from here moves to here and + +takes on these coordinates. + +We also, say, know, +that the whole-- + +I mean we also know, the whole +deformation field. + +And therefore we can directly +calculate the deformation + +gradient, the way I explained +it, by taking the + +differentiation of the current +coordinates with respect to + +the original coordinates. + +And those differentiations +give us these elements. + +If we do so, we have the +relationships between the d 0 + +x and d t x given +right down here. + +Notice, d 0 x has these +components in the x 1 x 2 + +coordinate frame. + +And you can see, for example, +this 0.866, the component in + +the x 1 direction, this +0.5 is the component + +into the x 2 direction. + +If we multiply this +out, we get d t x. + +And d t x, shown here, has +no component into the x 2 + +direction, but has a component +of 0.75 long + +into the x 1 direction. + +What this tells us, is that if +we know the motion of the body + +from time 0 to time t, and +particularly at time t, and if + +we have calculated the +deformation gradient the way + +we have defined it, then we can +relate how the original + +fibers, or the fibers in the +original configuration will + +rotate and stretch. + +And that relationship is given +via the deformation gradient, + +as surely shown here +quite physically. + +Because this fiber, originally +here, has rotated into a new + +position, and has, in this +particular case, been + +compressed. + +So, this relationship tells us +how the fiber has moved, + +rotated, and compressed. + +It does not tell us how +much the movement was. + +That is not given by +this relationship. + +That we have already, because +we have to have that + +information to calculate +t 0 x. + +But what this information, this +equation gives us, is how + +much the fiber has rotated and +compressed, or stretched. + +Well, let's look at another +fiber, the one that we had on + +the earlier viewgraph. + +Here, another fiber. + +And if we recognize, of course, +that for that material + +particle here, the same material +particle still, we + +still have the same deformation +gradient. + +We can take this fiber, or +rather the vectorial + +representation of that fiber, +as given here, multiply this + +out, and we directly find out +what has happened to that + +infinitesimal fiber in the +motion that we're considering. + +Notice, in this particular case, +the components of this + +fiber are 0 in this direction, +1.5 into that direction. + +And it has moved to here, and +has taken on components 1 and + +1 into each of the coordinate +directions. + +The deformation gradient is +very useful for various + +measures, computations +that we perform in + +finite element analysis. + +And one such computation +is to calculate the + +mass density ratios. + +In other words, we have to +assess how the mass density of + +the body, as it moves through +the space, changes. + +Let us look at how we do that. + +Here we have our stationary +coordinate + +system, x 1, x 2, x 3. + +And in that stationary +coordinate system, I'd like to + +focus our attention onto a +differential volume, a very + +small volume. + +I call that 0 d V curl. + +A curl is there because it is a +specific volume that we now + +want to look at. + +Notice that the volume that +I'm talking about here is + +spanned out by the +differential. + +Differential is d 0 x curl +1, 2 and 3 not shown. + +But this is the infinitesimal +volume at time 0. + +Now, in the motion from time +0 to time t, of course this + +volume will change. + +And at time t, it +looks like this. + +Notice that these + +differentials here have changed. + +We show just one, d 0 x curl +one, has gone over into d t x + +curl 1, the t now +denoting time t. + +And this is the volume obtained +from, that can be + +calculated from these +vectors shown here. + +In fact, this is how we +calculate this volume, and can + +therefore relate, also, +the mass densities. + +Let us look at some of +the basic equations. + +First of all, we can say that +the mass in this volume, this + +differential volume that we have +focused our attention on, + +and that I have given a curl +for that reason, that that + +mass must be preserved. + +And this means that this +relationship must hold. + +Volume times mass density at +time t must be equal to volume + +times mass density at time 0. + +We can show, then, that this +relationship holds. + +And I will talk about that just +now it a little bit more. + +And these two relationships, +then, clearly give us that + +this is how the mass +density changes. + +In other words, the mass density +at time t can directly + +be calculated from the mass +density at time 0 and the + +determinant of the deformation +gradient tensor. + +Notice, in three dimensional +analysis, this is a three by + +three matrix. + +And you would have to calculate +this matrix, at the + +particular point that you're +focusing your attention on, + +and take the determinant +of that matrix. + +Let us look at this relationship +here, because + +that is a very basic +relationship. + +It tells how the volume, the +differential volumes change as + +a function of time. + +And to show you how we arrive +at this relationship, I've + +just compiled here a +few viewgraphs to + +give you the proof. + +Initially, we can say that d 0 +x curl 1 is given via this + +relationship. + +Notice, this is the length +of this vector, simply. + +And, notice that I had aligned +this vector with the x 1 + +coordinate axis, therefore +these 0s. + +Similar, d 0 x curl 2 was +aligned with the x 2 + +coordinate axis, and therefore +these two 0s. + +And the length of the +vector is d s 2. + +d x curl 3 is given similarly, +but aligned, this vector is + +aligned in the 3 direction, and +the length was given as, + +is given as d s 3. + +Hence, by simple calculation, +of course, we find directly + +that the volume, the +differential volume that in + +the original configuration, is +given via this equation. + +But, if we now recognize that +we can express d t x curl i + +via this relationship here, and +that is nothing else than + +applying the deformation +gradient tensor the way we + +already talked about. + +We looked already at examples +where we put in a particular + +fiber, original configuration, +and calculated how this fiber + +stretched, deformed from +time 0 to time t. + +I just gave you some examples. + +And we use that information now, +here, to express the d t + +x curl i in terms +of d 0 x curl i. + +Of course, for i +equals 1, 2, 3. + +And now we use here a formula +that you must have encountered + +some time ago, in your studies +of mathematics. + +If you look at your old math +books, I'm sure you can + +extract that formula, which +simply says that the volume + +given, spanned by these vectors, +is given via this + +product here, as a cross product +of these two vectors, + +and the dot product of the +resulting two vectors. + +This, of course, gives you a +vector here, and you dot this + +vector with this vector, and you +get, directly, a number, + +which is the volume +of interest. + +However, if we now multiply +this out here, you find, + +directly, that this +is the answer. + +In other words, the deformation +gradient comes in + +right there. + +The determinant of +the deformation + +gradient comes in here. + +Of course, it comes in here +because you would substitute + +from here into there. + +And once again, since this +product here is nothing else + +than the original volume, +we're home. + +We have proven that d t V curl +is equal to the determinant of + +t 0 x times 0 d V curl, the +determinate of the deformation + +gradient in this relationship +between the + +differential volumes. + +It's really an interesting +proof, and maybe you want to + +think a little bit more about +it, and even go through this + +arithmetic here, to really +reinforce the understanding of + +what we are doing here. + +Let's look at a simple example +to just exemplify once again + +what we just talked about. + +Here we have a little example. + +A piece of material 1 long, +that in its original + +configuration is 1 long, +I should say. + +We are stretching that +piece of material up + +to time t, as shown. + +We assume uniform stretching. + +We assume plain strain +conditions. + +In other words, the strain +through the thickness is equal + +to 0 here, in this +particular case. + +And the deformation field is +assumed to be as shown here. + +Then, with the deformation field +given, clearly we can + +calculate this deformation +gradient. + +Here, this component is simply +obtained by differentiating t + +x 1 with respect to 0 x 1. + +If you do so, you get a 1 here +plus 0.25, giving you a 1.25. + +Because there is no shearing +in the material, and no + +rotation, these off diagonal +terms are 0. + +And, because there is no +stretching through this + +direction, and through the +thickness direction, we have + +1s right there. + +To take the determinant of this +matrix is rather simple. + +You just take the product of +the diagonal terms, and you + +directly obtain 1.25 for +its determinant. + +Now, let us plug this +into our formula. + +And here we have the result +of that formula. + +It tells us 0 rho is equal to +1.25 t rho for any particle, + +right here, because this +relationship is independent of + +the 0 x 1 component. + +Well, of course, this is also +a result of the uniform + +stretching. + +Notice that this makes +physical sense. + +If we have taken a piece +of material up here-- + +once more let us look at it-- + +that does not shrink here, +that does not stretch or + +shrink in this normal direction +as well, then surely + +the mass density has to decrease +as we stretch it. + +And in fact, this is being shown +right down here, t rho + +is equal to 0 rho +divided by 1.25. + +So, the result makes sense. + +We use also the inverse +deformation gradient. + +And here, on this viewgraph, +I've just summarized a few + +equations regarding this inverse +deformation gradient. + +Here, we now look at the +equation, where on the + +left-hand side we have the +material fiber at time 0, and + +on the right-hand side is the +material fiber at time t. + +In other words, d 0 x on the +left-hand side, and d t x on + +the right-hand side. + +The inverse deformation gradient +stands right here. + +Mathematically, we can show that +the inverse deformation + +gradient is nothing else +than t 0 x inverse. + +Of course, notice that 0 t +x would be calculated by + +differentiating the original +coordinates with respect to + +the coordinates at time t. + +However, we can also calculate +this matrix directly by taking + +this matrix here, where we +differentiate the coordinates + +at time t with respect to the +original coordinates. + +And then, having obtained this +matrix, calculated this + +matrix, we simply invert it. + +Well the proof that indeed +holds is given + +down here in green. + +We simply take the top equation +and substitute for d + +t x, as shown here, our +relationship that we had + +already earlier. + +And, if we then, well, look at +this equation, we can put + +brackets around here. + +And since d 0 x is equal to d +0 x for any material fiber, + +this must be the identity +matrix, which already + +completes the proof. + +An important theorem in +continuum mechanics is the + +polar decomposition theorem, +which tells that the + +deformation gradient, t 0 x, can +always be decomposed into + +a rotation matrix and +a stretch matrix. + +The rotation matrix is an +orthogonal matrix, of course, + +meaning that R, transposed R, +is the identity matrix. + +And the stretch matrix is +a symmetric matrix. + +This can always be +done for any x. + +And the proof, actually, is +given in the textbook. + +Please look at your study guide, +where I indicate where + +you can find the proof +in the textbook. + +And it might be quite good to +actually go through that proof + +in some detail, so as to +reinforce your understanding + +of what this theorem +really tells. + +The important point, once again, +is that we can always + +write the x matrix into this +form as R times u. + +And to give you an example of +what this means, let's look at + +this one here. + +Here we have, in the coordinate +frame x 1 x 2, a + +piece of material +3 long 2 wide. + +This is the original +configuration of the material. + +And that material moves +from time 0 to + +time t, as shown here. + +First it moves, it is being +stretched into the x 1 + +direction and into the x 2 +direction to take on the + +configuration shown in red. + +And then it rotates to take on +the configuration in green. + +And that, indeed, is the +configuration at time t. + +Let us calculate the x matrix +corresponding to that + +configuration, and see how +it would be decomposed + +into R times u. + +Well, we have done +that down here. + +Notice, this is the +x matrix, t 0 x. + +These are the components +of that matrix. + +And here we have the R matrix, +t 0 R. And here we + +have the t 0 u. + +In other words, this is the +rotation matrix, and this is + +the stretch matrix. + +Notice this stretch matrix +is indeed symmetric. + +Let's look at the components in +the stretch matrix a little + +bit closer. + +1.33 is nothing else than 4 +divided by 3, in other words, + +the stretching into +the x 1 direction. + +1.5, down here, is nothing else +than the stretching into + +x 2 direction, namely +2 goes over into 3. + +3 divided by 2, 1.5. + +Notice that these off diagonal +elements are 0, the reason + +being that there has been no +shearing from the original + +configuration to the +red configuration. + +The rotation matrix really +expresses mathematically the + +movement of this red piece of +material into the green + +configuration. + +Notice that the entries in +this rotation matrix are + +nothing else than cosines +and sines of + +this 30-degree rotation. + +For example, here you have +the cosine of 30 degrees. + +This is the sine +of 30 degrees. + +In fact, it's the rotation of +this material fiber right + +there, from here into there. + +Well, this is the rotation +matrix and stretch matrix for + +this example. + +And we could easily construct +other examples. + +In fact, you find in the +textbook some more examples + +that you might want to study +regarding this particular + +phenomenon. + +Using the deformation gradient, +we can describe, we + +can define a Cauchy-Green +deformation tensor. + +There is a right Cauchy-Green +deformation tensor. + +There is also a left +Cauchy-Green deformation + +tensor which, however, +we will not be using. + +So, when I talk about the +Cauchy-Green deformation + +tensor, I really mean the right + +Cauchy-Green deformation tensor. + +And it's defined +as shown here. + +We take the deformation +gradient, transposed, times + +the deformation gradient. + +Now, notice the deformation +gradient is always a three by + +three matrix, in a three +dimensional coordinate space. + +However, it can be +a non-symmetric + +or symmetric matrix. + +Generally, it is a non-symmetric +matrix. + +It would be a symmetric matrix +if there has been no rotation + +points on it. + +But, in general, it's +non-symmetric. + +Notice that this non-symmetric +matrix, multiplied here, as + +shown by the non-symmetric +matrix transposed, makes c + +symmetric, a very important +information. + +Well, indeed, if we substitute +for x here, we find that c is + +nothing else than +t 0 u squared. + +In other words, the stretch +matrix squared, since R is + +orthogonal. + +R goes in here. + +But R transposed R, of course, +is the identity matrix. + +And therefore c is +simply u squared. + +Notice that t 0 c is independent +of the rotation, + +via this equation here, and +therefore we say that c is + +invariant under a rigid +body rotation. + +In other words, a rigid body +rotation of a material fiber + +does not enter into +the elements of c. + +Let's look at an example. + +Two dimensional motion, the +original configuration for the + +piece of material that I like +to consider is shown here. + +It moves from time 0 to time t, +to the red configuration. + +And then, in the increment of +time delta t to that green + +configuration. + +But this movement over time +delta t is simply a rigid body + +motion of 90 degrees. + +Well, we can calculate t 0 +x corresponding to this + +configuration. + +Here it's done. + +And, by the formula that I gave +you, you get directly t 0 + +c by taking x transposed +times x. + +You get this matrix here. + +Well, now we can also +calculate t 0 x. + +How do we obtain, by the +way, this matrix? + +There is a subtle point. + +You obtain this matrix simply by +pre-multiplying this matrix + +by a rotation matrix +corresponding to this + +90-degree rotation. + +This is the answer. + +And if we now take this matrix, +transposed by the + +matrix itself, in other words +this product x transpose x, we + +get the c matrix. + +And we notice that the c +matrices are the same for both + +of these configurations. + +In other words, this simply +exemplifies that the rigid + +body rotation from red to green +here did not enter into + +the elements of the c. + +They did not change from time +t to time t plus delta t. + +We use this c matrix to define +a strain measure, the + +Green-Lagrange strain measure. + +It's, of course, a strain +measure that is very well + +known, described in many, +many textbooks. + +And it is, however, very useful +for finite element + +analysis, as I briefly pointed +out already earlier. + +This is the definition of the +Green-Lagrange strain tensor. + +Notice, this here is a three +by three matrix. + +And we are taking this three +by three matrix. + +We subtract the identity +matrix. + +The identity matrix, of course, +being just 1s on the + +diagonal, and 0s on all the +off diagonal elements. + +And there is a 1/2 here that +gives us the definition of the + +Green-Lagrange strain tensor. + +There are a number of very +interesting properties that + +this strain tensor displays. + +And I've listed them here. + +We can see that this strain +tensor is symmetric. + +We can see that this strain +tensor does not change from + +time t to time t plus delta t if +the only motion from time t + +to time t plus delta t was +a rigid body motion. + +And we can see directly that +the Green-Lagrange strain + +tensor is 0 if, from time 0 to +time t, the only motion was a + +rigid body motion. + +One can prove these particular +items, these statements, and I + +would like to encourage +you to do so. + +While you are doing it, I +will do the same here. + +And then we share our +experiences regarding these + +proofs just afterwards. + +Well, here I am giving now to +you some information regarding + +these proofs. + +t 0 epsilon is symmetric because +t 0 c is symmetric. + +And remember, we take here a +symmetric matrix from which we + +subtract a symmetric matrix, and +clearly, the result must + +be a symmetric matrix. + +A very simple proof really. + +Regarding the second item that I +mentioned earlier, for rigid + +body motion, we know that from +time t to time t plus delta t, + +we have that x at time t plus +delta t can be written as R + +times t 0 x. + +In other words, here I'm talking +about the deformation + +gradient at time t plus delta +t, and here about the + +deformation gradient +at time t. + +And they are related merely +by a rotation matrix. + +Now, if you substitute from here +into this equation, but + +apply the time t plus delta t, +you obtain, of course, as we + +saw actually on the earlier +example, that this c matrix + +does not change. + +And therefore, also the +Green-Lagrange stain tensor + +does not change. + +In fact, all of this information +was really + +addressed in the earlier +examples that we discussed. + +Also, for rigid body motion, we +have that the c matrix is + +simply the identity matrix, +because remember, the c + +matrix, Cauchy-Green deformation +tensor, does not + +change with rigid +body rotation. + +It is equal to the +identity matrix. + +And if you then takes this c +matrix and substitute right up + +there, on the top, you get that +the Green-Lagrange strain + +tensor is 0. + +So, 3 properties, really, that +we want to keep in mind + +regarding the Green-Lagrange +strain tensor when we + +later on use it. + +Another definition of the +Green-Lagrange strain tensor + +is given on this viewgraph. + +In fact, this right-hand side +that I'm showing here is + +simply obtained by substituting, +for the + +deformation gradient, the +identity matrix plus the + +deformation while the +displacement derivatives, with + +respect to the coordinates. + +In other words, what you want +to do, basically, is to + +substitute for t 0 x, in +terms of displacements. + +And if you go through and write +all the information out, + +you end up that the t 0 epsilon +i j component of the + +Green-Lagrange strain +tensor is given by + +this equation here. + +Notice that we have here i, j, +the same subscript that you + +see here, too. + +Of course, we're differentiating +with respect + +to the j component here. + +Here we have j, i, and +here k, i k,j. + +We're summing over k here. + +Notice also, that this part +here is non-linear in the + +displacements. + +This part is non-linear in the +displacements because these + +are, so to say, quadratic +terms. + +This here, this part, is linear +in displacements. + +From time to time, students +approach me and say to me, + +well, you must have neglected +something in the definition, + +or in this Green-Lagrange +strain tensor. + +Because you're only going +up to quadratic terms. + +you must have neglected cubic +terms, and high order terms. + +Well, the answer there is, we +have really neglected nothing. + +The point is, that we have +defined this tensor to be + +given by this equation. + +Of course, my earlier definition +was in terms of + +deformation gradients, +in terms of + +the deformation gradient. + +Now we actually have here +substituted displacements. + +But it's still a definition. + +This is, in fact, +the same tensor. + +The same components here would +be calculated using the + +earlier definition than +this one here. + +Same thing. + +And, as I say, it holds for any +deformation, any amount of + +straining and stretching. + +Let's look at one example, a +very simple example, where we + +have a simple four-node +element that + +we are pulling out. + +Originally, it it is in the +black configuration. + +It goes over into the +red configuration. + +If we calculate t 0 epsilon 1 1 +from the formula that I just + +showed you, you get +these two terms. + +This here is the engineering +strain term that we are very + +well familiar with. + +And this is here the non-linear +term, because it's + +a quadratic term. + +Non-linear in the displacement, +of course. + +If we plot this information, +as shown here on the graph, + +notice we're showing here t +delta over L, the original + +length, where t delta +is the displacement. + +And we have plotting here the +epsilon 1 1 component. + +Actually, we should +have said here-- + +let me make this correction +right now here-- + +we should have had, really +have had here a + +t 0 epsilon 1 1. + +The t 0 was missing there. + +Well, if we plot, in other +words, this component here as + +a function of these elements +here, of the t delta over 0 L, + +we get this red line, +the red line. + +Notice the non-linearality +in that strain. + +The engineering strain, which +is only the first term here, + +gives us a straight line. + +Notice that this strain here +increases quite rapidly as you + +pull out, and it decreases in +magnitude here, with this + +curvature, as you push in. + +So there's no symmetry in the +strain when you extend or + +compress a piece of material. + +In the engineering strain +component, of course, we see a + +symmetry, because we have +a straight line. + +Let us look at another example +to calculate once the + +Green-Lagrange strain. + +Here, we have the original +configuration + +of a four-node element. + +And that four-node element, +shown black here, goes over + +into this configuration at time +t, stretched into two + +directions, and then, at time t +plus delta t, it has rotated + +by 45 degrees. + +The deformation gradient +corresponding to time t is + +shown here. + +The Cauchy-Green deformation +tensor shown here. + +Notice no off diagonal +elements. + +Because the piece of material, +the four-node element-- you + +may think of this as a four-node +element, of course-- + +has simply been stretched +and compressed. + +There's no shearing. + +Therefore, we have +0 terms here. + +And, if we calculate the +Green-Lagrange strain tensor, + +we get this answer. + +Once again, no shearing +components in + +this tensor as well. + +If we now do the same for the +configuration at time t plus + +delta t, the green +configuration, we obtain this + +deformation gradient, this +Cauchy-Green deformation + +tensor, and this is a +Green-Lagrange strain tensor. + +Where we notice that the +Cauchy-Green deformation + +tensor has not changed, and +the Green-Lagrange strain + +tensor has also not changed. + +And this is what, of course, +we have proven already + +earlier, that from time t to +time t plus delta t, the + +Green-Lagrange strain tensor +and the Cauchy-Green + +deformation tensor, both +of those do not change. + +However for rigid body motion, +the x tensor, the deformation + +gradient, does change, look at +here, because this deformation + +gradient is affected +by the rotation. + +Let's look at another example, +because all these examples + +really enrich our understanding +of what these + +kinematic quantities stand for, +and what they give us. + +Here, we look at the example of +a simple shear deformation. + +Originally, the element that we +are looking at was in this + +configuration. + +And, it is sheared over. + +You can think of this top line +being simply moved over + +horizontally into the +red configuration. + +Notice that the original +length here is 1. + +This length is also 1. + +Notice that the movement +over is t delta. + +And we calculate +the deformation + +gradient once again. + +The deformation gradient now +being given by via these + +components. + +Let's try to explain these +components a bit. + +Well, this here is really the +differentiation of t x 1 with + +respect to 0 x 1. + +Now, t x 1 has not changed, +and therefore, this is 1. + +t x 1 is equal to 0 x 1 +in other words, and + +therefore, this is 1. + +Notice that the same holds also +for partial t x 2 with + +respect to 0 x 2. + +Notice that this element here +stands for partial t x 1 with + +respect to 0 x 2. + +And there, we look at partial +t x 1, a change into this + +direction as we walk that +direction, and that gives us + +this t delta, t delta over +this length here. + +In other words, this element +is nothing else than this + +length divided by that length. + +And it's, of course, the same +for any material particle over + +this domain. + +Because all of these material +particles have + +been sheared over. + +Well, if you now take x +transposed times x, you get + +this matrix here. + +And you identify directly +these terms, if we then + +calculate by the formula given, +the Green-Lagrange + +strain, this is the result. + +Notice that here we have now +shearing components. + +And notice also one very +interesting phenomena, a + +component appearing here. + +This is an interesting +component, because it is + +really an enormous strain +component in this direction. + +And now there's an epsilon 1, 1, +epsilon 2, 2, I should have + +said, component, an epsilon 2, +2 component that is non-zero + +in this particular case, + +In a material non-linear-only +formulation, where we only + +include infinitesimal +displacements, in other words, + +this part, of course, +would be 0. + +And that is also signified +by the square term. + +In other words, if indeed the +motion is small in this + +direction, then this would +become 0, at least + +approximately 0 when compared +to these terms, and it means + +that the Green-Lagrange strain +tensor reduces to the + +infinitesimal strain tensor that +we are so familiar with. + +The 2nd Piola-Kirchhoff stress +tensor and the Green-Lagrange + +strain tensors are energetically +conjugate. + +This is a very important +statement. + +And this is the reason why we +are working with these two + +tensors, the 2nd Piola-Kirchhoff +stress tensor + +and the Green-Lagrange +strain tensor. + +In fact, what is happening here, +is that this product + +here, which is the virtual work +at time t per current + +volume, per unit current volume, +that this here is + +given, of course, by the Cauchy +stress times the small, + +or the virtual, infinitesimal +strain, is defined this way. + +And here, we have the virtual +work at time t per unit + +original volume. + +And that is given by the 2nd +Piola-Kirchhoff stress times + +the variation in the +Green-Lagrange strain. + +We already had, earlier, that +the integration of this over + +the current volume is equal +to the integration of this + +quantity over the +original volume. + +Well, this is here once more, +something to be kept in mind. + +But the important point is that +the energy, that these + +two quantities are energetically +conjugate, and + +this is expressed via +this product here. + +Let's look at the 2nd +Piola-Kirchhoff + +stress tensor now. + +The 2nd Piola-Kirchhoff stress +tensor in indicial notation is + +defined as shown here. + +And we had already that + +definition early on a viewgraph. + +In matrix notation, we can +directly say this is the way + +you can also write it. + +Notice that the entries in this +three by three matrix-- + +I'm always thinking about three +components, or rather, + +three dimensional coordinate +space-- + +the entries here are nothing +else than those elements. + +The entries of this matrix, +of course, are + +those elements here. + +And similarly here, this is +the scalar that we talked + +about earlier already. + +If we solve from here for Cauchy +stresses, we directly + +obtain these two equations. + +Notice that in this matrix +notation now, we have the + +deformation gradient. + +Whereas in the earlier equation +that we looked at + +here, we had the inverse +deformation gradient. + +Well, these are relations that +we want to keep in mind, and + +that we will be referring to +quiet abundantly later on. + +Let us look at some properties +of the 2nd Piola-Kirchhoff + +stress tensor. + +First of all, t 0 +s is symmetric. + +While that can be seen directly +by looking at the + +definition, you might want to +prove it to yourself with a + +small example as well. + +t 0 s is invariant under +a rigid body motion, + +translation, and/or rotation. + +Hence, t 0 s only +changes when the + +material is actually deformed. + +This is a very important +statement, important fact, I + +should say, and we want to look +at an example just now. + +t 0 s has no direct physical +interpretation. + +Well, if you look at some +books, you'll see some + +pictures regarding t 0 s, +sorry, regarding the 2nd + +Piola-Kirchhoff stress tensor. + +In fact, I have some pictures +in my book, + +in an example there. + +But, these pictures are quite +far fetched, and they really + +don't give as deep a physical +insight as one would like to + +have with a stress measure. + +I personally like to now take +almost the attitude of saying, + +well, I accept that there is +no real strong physical + +interpretation of this +stress measure. + +It is used because it's +a convenient stress + +measure to deal with. + +We would not, in an engineering +analysis, really + +print it out in a computer +program. + +As I said earlier, we would, +of course, want to have the + +Cauchy stress as the stress +measure with which we want to + +design our structure. + +I look at it as a measure that +is convenient to work with in + +the engineering analysis. + +It's interesting, of course, +from a theoretical point of + +view to look at the elements and +to see how large they are, + +how small they are, when +compared to the Cauchy stress, + +the real physical stress that +we're interested in. + +But, we don't really need to +look for a strong physical + +interpretation. + +I know we are engineers. + +Engineers like to see pictures, +like to understand + +physically what's happening. + +And I can assure you that I've +tried myself quite hard to get + +physical interpretation of this +definition, of this 2nd + +Piola-Kirchhoff stress tensor. + +But, I have not arrived with +many good results. + +The best I could do is given +in my textbook, in the book + +that you are using +as a textbook. + +Let's look at an example here. + +The example of a four-node +element being stretched and + +rotated as shown here, and then +rotated as shown here. + +Notice that from time t, shown +as the red configuration, to + +time t plus delta t, we have +only a rigid body motion, a + +rotation of 60 degrees. + +Of course, the material would +be subjected to some Cauchy + +stresses, and Cauchy stresses +in this configuration and + +Cauchy stresses in this +configuration. + +Let us see how the Cauchy +stresses, and how the 2nd + +Piola-Kirchhoff stresses evolve +during this motion. + +And on this viewgraph here, +we have summarized that + +information. + +At time t the deformation +gradient is as shown here. + +The Cauchy stresses, +say, are like this. + +Of course, we would have to +introduce the material law, et + +cetera, et cetera. + +Let us assume that the Cauchy +stresses are like that. + +And then, given the Cauchy +stresses, the deformation + +gradient, we calculate the 2nd +Piola-Kirchhoff stress tensor. + +Let's say that this is now, +has now been calculated. + +And we do the same at +time t plus delta t. + +We know that there has, of +course, been additional motion + +from time t to time t plus +delta t, which means that + +these elements here +will change. + +And you should now be in a +position to calculate this + +tensor, because you know there +is only a rigid body motion + +that is being applied. + +And then, knowing this tensor, +we can directly also calculate + +the 2nd Piola-Kirchhoff +stress tensor. + +And we can calculate the +Cauchy stress tensor. + +So we can really calculate +all of these. + +And what do we see? + +This is the really +important point. + +We see that the 2nd +Piola-Kirchhoff stress tensor + +has not changed from time t +to time t plus delta t. + +This is the important +information + +that I mentioned earlier. + +However, the Cauchy +stress tensor, + +of course, has changed. + +The Cauchy stress tensor +has changed. + +One can, of course, prove that +the 2nd Piola-Kirchhoff stress + +tensor does not change when the +material is only subjected + +to a rigid body motion. + +And such proof is actually +given in the textbook. + +But this is a simple +application, and it + +exemplifies to you what I +mean by that statement. + +It's an important statement that +you should keep in mind + +as we go along with our further +discussion of the + +mathematical basis +of non-linear + +finite element analysis. + +This brings us then to the +end of this lecture. + +I have tried to give you some +of the mathematical bases, + +some of the ingredients, rather, +that we are using in + +finite element analysis. + +We have discussed stress and +strain measures that we will + +be encountering further +in the next lectures. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/iR1nRg-jm1o.txt b/iR1nRg-jm1o.txt new file mode 100644 index 0000000000000000000000000000000000000000..6347116c4df19fdb9f515a371bdeac3820ca776f --- /dev/null +++ b/iR1nRg-jm1o.txt @@ -0,0 +1,859 @@ +align:start position:0% + +in this video we are going to look at + + align:start position:0% +in this video we are going to look at + + + align:start position:0% +in this video we are going to look at +scales this first plot shows the average + + align:start position:0% +scales this first plot shows the average + + + align:start position:0% +scales this first plot shows the average +height of a 21 year old male and + + align:start position:0% +height of a 21 year old male and + + + align:start position:0% +height of a 21 year old male and +centimeters the x-axis is time starting + + align:start position:0% +centimeters the x-axis is time starting + + + align:start position:0% +centimeters the x-axis is time starting +in 1871 and ending in 1975 each person + + align:start position:0% +in 1871 and ending in 1975 each person + + + align:start position:0% +in 1871 and ending in 1975 each person +represents the height at a different + + align:start position:0% +represents the height at a different + + + align:start position:0% +represents the height at a different +point in time and the points are evenly + + align:start position:0% +point in time and the points are evenly + + + align:start position:0% +point in time and the points are evenly +spaced in time so the x-axis is okay the + + align:start position:0% +spaced in time so the x-axis is okay the + + + align:start position:0% +spaced in time so the x-axis is okay the +y-axis ranges from just under 160 to 180 + + align:start position:0% +y-axis ranges from just under 160 to 180 + + + align:start position:0% +y-axis ranges from just under 160 to 180 +centimeters which isn't inherently bad + + align:start position:0% +centimeters which isn't inherently bad + + + align:start position:0% +centimeters which isn't inherently bad +but does overstate the change the real + + align:start position:0% +but does overstate the change the real + + + align:start position:0% +but does overstate the change the real +problem is the bars and it was accurate + + align:start position:0% +problem is the bars and it was accurate + + + align:start position:0% +problem is the bars and it was accurate +we would only really see the hints of a + + align:start position:0% +we would only really see the hints of a + + + align:start position:0% +we would only really see the hints of a +man but instead we see their whole + + align:start position:0% +man but instead we see their whole + + + align:start position:0% +man but instead we see their whole +bodies making it seems that people have + + align:start position:0% +bodies making it seems that people have + + + align:start position:0% +bodies making it seems that people have +not only doubled in height but they've + + align:start position:0% +not only doubled in height but they've + + + align:start position:0% +not only doubled in height but they've +also doubled in wins this next plot also + + align:start position:0% +also doubled in wins this next plot also + + + align:start position:0% +also doubled in wins this next plot also +has issues of scale the total range of + + align:start position:0% +has issues of scale the total range of + + + align:start position:0% +has issues of scale the total range of +the plot is 8% to 10% + + align:start position:0% +the plot is 8% to 10% + + + align:start position:0% +the plot is 8% to 10% +although all the numbers fall in the + + align:start position:0% +although all the numbers fall in the + + + align:start position:0% +although all the numbers fall in the +range of 8.6% 29.2% + + align:start position:0% +range of 8.6% 29.2% + + + align:start position:0% +range of 8.6% 29.2% +if we plotted the y-axis on a 0 to 10 + + align:start position:0% +if we plotted the y-axis on a 0 to 10 + + + align:start position:0% +if we plotted the y-axis on a 0 to 10 +percent scale the conclusion would be + + align:start position:0% +percent scale the conclusion would be + + + align:start position:0% +percent scale the conclusion would be +that nothing is really changing at all + + align:start position:0% +that nothing is really changing at all + + + align:start position:0% +that nothing is really changing at all +the last point in a shot is at the wrong + + align:start position:0% +the last point in a shot is at the wrong + + + align:start position:0% +the last point in a shot is at the wrong +height and the size of America's makes + + align:start position:0% +height and the size of America's makes + + + align:start position:0% +height and the size of America's makes +the relative locations has a distinguish + + align:start position:0% +the relative locations has a distinguish + + + align:start position:0% +the relative locations has a distinguish +also notice that the gap between nine + + align:start position:0% +also notice that the gap between nine + + + align:start position:0% +also notice that the gap between nine +point nine point zero percent and the + + align:start position:0% +point nine point zero percent and the + + + align:start position:0% +point nine point zero percent and the +eight point nine percent mark is on the + + align:start position:0% +eight point nine percent mark is on the + + + align:start position:0% +eight point nine percent mark is on the +far left side and at eight point nine + + align:start position:0% +far left side and at eight point nine + + + align:start position:0% +far left side and at eight point nine +percent in eight point eight percent + + align:start position:0% +percent in eight point eight percent + + + align:start position:0% +percent in eight point eight percent +magaz have a different gap this plot + + align:start position:0% +magaz have a different gap this plot + + + align:start position:0% +magaz have a different gap this plot +shows the relative breakdown of teachers + + align:start position:0% +shows the relative breakdown of teachers + + + align:start position:0% +shows the relative breakdown of teachers +by race and a certain teaching program + + align:start position:0% +by race and a certain teaching program + + + align:start position:0% +by race and a certain teaching program +the caucasian bar is truncated which is + + align:start position:0% +the caucasian bar is truncated which is + + + align:start position:0% +the caucasian bar is truncated which is +a risky choice but could be appropriate + + align:start position:0% +a risky choice but could be appropriate + + + align:start position:0% +a risky choice but could be appropriate +in some situations a much bigger problem + + align:start position:0% +in some situations a much bigger problem + + + align:start position:0% +in some situations a much bigger problem +is that the scale of each blue bar is + + align:start position:0% +is that the scale of each blue bar is + + + align:start position:0% +is that the scale of each blue bar is +entirely different + + align:start position:0% +entirely different + + + align:start position:0% +entirely different +for example the Native American bar is + + align:start position:0% +for example the Native American bar is + + + align:start position:0% +for example the Native American bar is +about a third of the length of African + + align:start position:0% +about a third of the length of African + + + align:start position:0% +about a third of the length of African +American Bar but there are more than 10 + + align:start position:0% +American Bar but there are more than 10 + + + align:start position:0% +American Bar but there are more than 10 +times as many african-americans in this + + align:start position:0% +times as many african-americans in this + + + align:start position:0% +times as many african-americans in this +program as Native Americans in fact + + align:start position:0% +program as Native Americans in fact + + + align:start position:0% +program as Native Americans in fact +visually this plot is completely + + align:start position:0% +visually this plot is completely + + + align:start position:0% +visually this plot is completely +meaningless the only useful thing about + + align:start position:0% +meaningless the only useful thing about + + + align:start position:0% +meaningless the only useful thing about +it is the numbers but even there there + + align:start position:0% +it is the numbers but even there there + + + align:start position:0% +it is the numbers but even there there +is a bit of confusion as Native + + align:start position:0% +is a bit of confusion as Native + + + align:start position:0% +is a bit of confusion as Native +Americans are given to one decimal place + + align:start position:0% +Americans are given to one decimal place + + + align:start position:0% +Americans are given to one decimal place +but the episode which when combined with + + align:start position:0% +but the episode which when combined with + + + align:start position:0% +but the episode which when combined with +the confusing scales cast + + align:start position:0% +the confusing scales cast + + + align:start position:0% +the confusing scales cast +doubt on the correctness of an embassy + + align:start position:0% + + + + align:start position:0% + +here is a before or after of a same data + + align:start position:0% +here is a before or after of a same data + + + align:start position:0% +here is a before or after of a same data +on the left receive US military + + align:start position:0% +on the left receive US military + + + align:start position:0% +on the left receive US military +experience in a right axis and troop + + align:start position:0% +experience in a right axis and troop + + + align:start position:0% +experience in a right axis and troop +count on the left axis both the line and + + align:start position:0% +count on the left axis both the line and + + + align:start position:0% +count on the left axis both the line and +Bob Watts are individually okay but the + + align:start position:0% +Bob Watts are individually okay but the + + + align:start position:0% +Bob Watts are individually okay but the +combination is misleading because we + + align:start position:0% +combination is misleading because we + + + align:start position:0% +combination is misleading because we +have mixed two units dollars and people + + align:start position:0% +have mixed two units dollars and people + + + align:start position:0% +have mixed two units dollars and people +there is a false impression of some sort + + align:start position:0% +there is a false impression of some sort + + + align:start position:0% +there is a false impression of some sort +of crossover point in 1995 that does not + + align:start position:0% +of crossover point in 1995 that does not + + + align:start position:0% +of crossover point in 1995 that does not +exist on the right is the same data + + align:start position:0% +exist on the right is the same data + + + align:start position:0% +exist on the right is the same data +presented in a different way + + align:start position:0% +presented in a different way + + + align:start position:0% +presented in a different way +we now have troops on the x-axis and + + align:start position:0% +we now have troops on the x-axis and + + + align:start position:0% +we now have troops on the x-axis and +dollars on the y-axis the line moves + + align:start position:0% +dollars on the y-axis the line moves + + + align:start position:0% +dollars on the y-axis the line moves +through time now allowing us to see win + + align:start position:0% +through time now allowing us to see win + + + align:start position:0% +through time now allowing us to see win +moments of change occurred such as + + align:start position:0% +moments of change occurred such as + + + align:start position:0% +moments of change occurred such as +decreases in troop count through the 90s + + align:start position:0% +decreases in troop count through the 90s + + + align:start position:0% +decreases in troop count through the 90s +at the end of the Cold War the increase + + align:start position:0% +at the end of the Cold War the increase + + + align:start position:0% +at the end of the Cold War the increase +in spending of a 2000 s and a recent + + align:start position:0% +in spending of a 2000 s and a recent + + + align:start position:0% +in spending of a 2000 s and a recent +decreases in military spending + + align:start position:0% +decreases in military spending + + + align:start position:0% +decreases in military spending +the final visualization I want to show + + align:start position:0% +the final visualization I want to show + + + align:start position:0% +the final visualization I want to show +you today is all about the different + + align:start position:0% +you today is all about the different + + + align:start position:0% +you today is all about the different +types of household the US Census Bureau + + align:start position:0% +types of household the US Census Bureau + + + align:start position:0% +types of household the US Census Bureau +periodically determines how many + + align:start position:0% +periodically determines how many + + + align:start position:0% +periodically determines how many +households a cup comprised for example + + align:start position:0% +households a cup comprised for example + + + align:start position:0% +households a cup comprised for example +of married couples with and without + + align:start position:0% +of married couples with and without + + + align:start position:0% +of married couples with and without +children people living alone and so on + + align:start position:0% +children people living alone and so on + + + align:start position:0% +children people living alone and so on +first of all I'm not saying this as a + + align:start position:0% +first of all I'm not saying this as a + + + align:start position:0% +first of all I'm not saying this as a +bad visualization in fact if we are + + align:start position:0% +bad visualization in fact if we are + + + align:start position:0% +bad visualization in fact if we are +interested in the relative share of each + + align:start position:0% +interested in the relative share of each + + + align:start position:0% +interested in the relative share of each +type of household in a particular year + + align:start position:0% +type of household in a particular year + + + align:start position:0% +type of household in a particular year +it's actually pretty good + + align:start position:0% +it's actually pretty good + + + align:start position:0% +it's actually pretty good +however if what we interested in is the + + align:start position:0% +however if what we interested in is the + + + align:start position:0% +however if what we interested in is the +rates of change across the years this is + + align:start position:0% +rates of change across the years this is + + + align:start position:0% +rates of change across the years this is +next to useless the key problem is that + + align:start position:0% +next to useless the key problem is that + + + align:start position:0% +next to useless the key problem is that +the x axis is completely off the gap + + align:start position:0% +the x axis is completely off the gap + + + align:start position:0% +the x axis is completely off the gap +between the first two columns as ten + + align:start position:0% +between the first two columns as ten + + + align:start position:0% +between the first two columns as ten +years but the gap between the last two + + align:start position:0% +years but the gap between the last two + + + align:start position:0% +years but the gap between the last two +columns is only two years meaning that + + align:start position:0% +columns is only two years meaning that + + + align:start position:0% +columns is only two years meaning that +the rates are hard to read from this if + + align:start position:0% +the rates are hard to read from this if + + + align:start position:0% +the rates are hard to read from this if +we are not interested in the rates of + + align:start position:0% +we are not interested in the rates of + + + align:start position:0% +we are not interested in the rates of +changes but just want to compare two + + align:start position:0% +changes but just want to compare two + + + align:start position:0% +changes but just want to compare two +years at a time it's not bad but it's + + align:start position:0% +years at a time it's not bad but it's + + + align:start position:0% +years at a time it's not bad but it's +not easy either try comparing 1970 + + align:start position:0% +not easy either try comparing 1970 + + + align:start position:0% +not easy either try comparing 1970 +married without children to 2010 married + + align:start position:0% +married without children to 2010 married + + + align:start position:0% +married without children to 2010 married +without children without looking at the + + align:start position:0% +without children without looking at the + + + align:start position:0% +without children without looking at the +numbers can you tell if it is grown or + + align:start position:0% +numbers can you tell if it is grown or + + + align:start position:0% +numbers can you tell if it is grown or +shrunk finally and more generally this + + align:start position:0% +shrunk finally and more generally this + + + align:start position:0% +shrunk finally and more generally this +chart shows relative numbers if you look + + align:start position:0% +chart shows relative numbers if you look + + + align:start position:0% +chart shows relative numbers if you look +at absolute numbers we might find the + + align:start position:0% +at absolute numbers we might find the + + + align:start position:0% +at absolute numbers we might find the +total number of couples married with + + align:start position:0% +total number of couples married with + + + align:start position:0% +total number of couples married with +children is actually constant for a + + align:start position:0% +children is actually constant for a + + + align:start position:0% +children is actually constant for a +number of other households in Korea + + align:start position:0% +number of other households in Korea + + + align:start position:0% +number of other households in Korea +we are now going to change into our to + + align:start position:0% +we are now going to change into our to + + + align:start position:0% +we are now going to change into our to +try plotting this data as a line chat + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/iZKAtzK5WXM.txt b/iZKAtzK5WXM.txt new file mode 100644 index 0000000000000000000000000000000000000000..8cf05d5c4398235b601dd22cf11c93d8690cc446 --- /dev/null +++ b/iZKAtzK5WXM.txt @@ -0,0 +1,4930 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So today +is going to be + +our last pass at bound states. + +So starting next week or +actually starting next lecture, + +we're going to +look at scattering. + +Scattering's going to be great. + +But we need to close +out bound states. + +So today's topic +is the finite well, + +finite the potential well. + +We've sort of +sketched this when we + +looked at qualitative structure +of wave functions of energy + +eigenstates. + +But we're going to +solve the system today. + +So good. + +So the system we're +interested in is going to be-- + +The system we're +interested in is + +going to be a system +with a finite depth + +and a finite width. + +And I'll go into detail and +give you parameters in a bit. + +But first I want +to just think about + +how do we find energy +eigenfunctions of a potential + +of this form, v of x, which +is piecewise constant. + +So first off, is this is a +terribly realistic potential? + +Will you ever in the +real world find a system + +that has a potential which +is piecewise constant? + +Probably not. + +It's discontinuous. + +Right? + +So it's rather unphysical. + +But it's a very +useful toy model. + +So for example, if you take +a couple of capacitor plates, + +then you can induce a situation +where the electric field + +is nonzero in between +the capacitor plates + +and zero outside of +the capacitor plates. + +Right. + +So at a superficial level, +this looks discontinuous. + +It looks like the +electric field is-- + +But actually, you know +that microscopically there + +are a bunch of +charges, and everything + +is nice and continuous +except for the behavior + +right at the charges. + +So but it's reasonable +to model this + +as a step function +for an electric field. + +So this is going to +be an idealization, + +but it's going to be a +very useful idealization, + +the constant potential. + +OK. + +So what's the equation? + +What are we trying to do? + +We want to find the energy +eigenstates for this + +because we want to study +the time evolution. + +And the easiest way to solve +the Schrodinger equation, + +the time evolution equation, +is to expand an energy + +eigenstates. + +So the equation we want to solve +is energy eigenvalue times phi + +e of x is equal to minus +h bar squared on 2m phi + +e phi prime plus v of x. + +And I'm going to put it in +the form we've been using. + +Phi prime prime e of x +is equal to 2m upon h bar + +squared v of x minus e. + +OK. + +So this is the +form that I'm going + +to use today to solve for the +energy eigenvalue equations. + +e is some constant. + +Do you expect the allowed +energies to be arbitrary? + +No. + +They should be discrete. + +Yeah, exactly. + +So we expect that there should +be discrete lowest energy + +state, some number +of bound states. + +And then, eventually, +if the energy + +is greater than the +potential everywhere, + +the energies will be continuous. + +Any energy will be allowed +above the potential. + +So we'll have a continuum of +states above the potential. + +And we'll have a discrete +set of bound states-- + +Probably, it's reasonable +to expect some finite number + +of bound states +just by intuition. + +--from the infinite well. + +So we expect to have a finite +number of discrete energies + +and then a continuous set +of energies above zero. + +So if this is the asymptotic +value potential of zero. + +OK. + +And this is intuition +gained from our study + +of qualitative structure +of energy eigenfunctions. + +So we are going to talk +today about the bound states. + +And in recitation, +leaders should + +discuss the continuum +above zero energy. + +OK. + +So to solve for the actual +energy eigenfunctions + +and the energy eigenvalues, +what we need to do + +is we need to +solve this equation + +subject to some +boundary conditions. + +And the boundary conditions +we're going to want to solve + +are going to be finite. + +So it's normalizable infinity. + +The solution should +be vanishing far away. + +And the wave function +should be everywhere smooth. + +Well, at least it +should be continuous. + +So let's talk about what +exactly boundary conditions we + +want to impose. + +And so in particular, +we're going + +to want to solve for the energy +eigenfunctions in the regions + +where the potential is constant +and then patch together + +solutions at these boundaries. + +We know how to solve for +the energy eigenfunctions + +when the potential is constant. + +What are the energy +eigenfunctions? + +Yeah. + +Suppose I have a potential, +which is constant. + +v is equal to 0. + +What are the energy +eigenfunctions + +of this potential? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Yeah, e to the ikx. + +Yeah. + +Now, what if I +happen to tell you-- + +So we're at h bar +squared k squared upon 2m + +is equal to the energy. + +Suppose I happen to tell you +that here's the potential. + +And I want to find the +solution in this region + +where the energy is here +less than the potential. + +What are the solutions? + +That's a second order +differential equation. + +There should be two solutions. + +What are the solutions to that +differential equation when + +the energy is less +than the potential? + +AUDIENCE: Decaying and growing. + +PROFESSOR: Decaying and +growing exponentials. + +Exactly. e to the plus alpha +x and e to the minus alpha x. + +And the reason is +these are sinusoidal, + +and these have the +opposite concavity. + +They are growing and +dying exponentials. + +Cool? + +OK. + +So we've studied that. + +Yeah? + +AUDIENCE: Shouldn't +that be a phi e of x? + +PROFESSOR: Sorry. + +Oh, oh, yes, indeed. + +Sorry. + +Thank you. + +Phi e of x. + +It's early, and I'm still +working on the coffee. + +It won't take long. + +Good. + +So we know how to solve the +energy eigenvalue equation + +in all these regions where +the potential is constant. + +So our job is going to be to +find a solution where we patch + +them together at +these interfaces. + +We patch them together. + +And what condition +should we impose? + +So the basic condition +is going to be + +continuity of the wave +functions phi e of x. + +And so what are the +conditions that we need? + +Well, if v of x-- + +Here's the way I like +to think about this. + +Suppose v of x is continuous. + +So if the potential +is continuous, then + +what can you say? + +You can say that phi prime prime +is a continuous function times + +phi of x. + +So very roughly, if +we look at a region + +where phi isn't varying +very much, so if we + +have a potential that's +varying in some way, then + +phi prime prime, in a +region where it's not + +varying much compared to its +value as a function of x, + +does something +smooth because it's + +varying with the potential. + +And so phi prime, +which is just going + +to be the integral of this-- + +The integral of +a smooth function + +is again a smooth function. + +--and phi, the integral +of that function + +is also going to be a +nice, smooth function. + +OK? + +I've drawn it badly, but-- + +So the key thing here is that +if the potential is continuous, + +then the energy eigenfunction +has a second derivative, which + +is also continuous. + +That means its first +derivative is continuous. + +So that means the function +itself is continuous. + +Everyone agree with this? + +Questions? + +So in regions where the +potential's continuous, + +the wave function and its +first two derivatives all + +have to be continuous. + +On the other hand, suppose +the potential has a step. + +v of x has a step discontinuity. + +OK. + +So the potential +does one of those. + +So what does that tell +you about phi prime prime? + +It's a function of x. + +So for example, let's +look at that first step. + +Suppose the potential is that +first step down by some amount. + +Then phi prime prime is going +to decrease precipitously + +at some point. + +And the actual amount +that it decreases + +depends on the value of +phi because the change + +in the potential time is +the actual value of phi. + +And if that's true of +phi prime prime what can + +you say of phi prime? + +So this is discontinuous. + +Phi prime of x, +however, is the integral + +of this discontinuous function. + +And what does it do? + +Well, it's linearly +increasing in this region + +because its derivative +is constant. + +And here, it's linearly +increasing less. + +So it's not differentiably +smooth, but it's continuous. + +And then let's look at the +actual function phi of x. + +OK. + +What is it doing? + +Well, it's quadratic. + +And then here it's quadratic +a little less afterwards. + +But that still +continuous because it's + +the integral of a +continuous function. + +Everyone we cool with that? + +So even when we have a step +discontinuity in our potential, + +we still have that +our derivative + +and the value of the +function are continuous. + +Yeah? + +However, imagine the potential +has this delta function. + +Let's just really push it. + +What happens if our potential +has a delta function + +singularity? + +Really badly discontinuous. + +Then what can you say about phi +prime prime as a function of x? + +So it has a delta +function, right? + +So the phi prime prime has to +look like something relatively + +slowly varying, and then +a step delta function. + +So what does that tell you +about the derivative of the wave + +function? + +It's got a step function. + +Exactly. + +Because it's the integral of +this, and the integral is 0, 1. + +Whoops. + +I missed. + +So this is a delta. + +This is a step. + +And then the wave +function itself + +is, well, it's the integral +of a step, so it's continuous. + +Sorry. + +It's certainly not +differentiable. + +Its derivative is discontinuous. + +Well, it's differentiable +but its derivative's + +not supposed to be. + +It is not continuous, indeed. + +So this is continuous. + +So we've learned something +nice, that unless our potential + +is so stupid as to have +delta functions, which + +sounds fairly unphysical-- + +We'll come back to that +later in today's lecture. + +--unless our potential +has delta functions, + +the wave function and its first +derivative must be smooth. + +Yeah. + +This is just from the +energy eigenvalue equation. + +Now, we actually argued this +from the well definedness + +and the finiteness +of the expectation + +value of the momentum +earlier in the semester. + +But I wanted to give +you this argument for it + +because it's going to +play a useful role. + +And it also tells us that if +we do have a delta function + +singularity in the +potential, then the upshot + +is that the wave function +is going to be continuous, + +but its first +derivative will not. + +Its first derivative will +jump at the wave function. + +And that means that +the wave function-- + +Let me draw this +slightly differently. + +--the wave function +will have a kink. + +Its derivative will +not be continuous. + +OK. + +So anywhere where we +have a delta function + +in the potential, we will have +a kink in the wave function + +where the first derivative +is discontinuous. + +Cool? + +Yeah. + +AUDIENCE: What does +that mean as far + +as the expectation +value of the momentum? + +PROFESSOR: Ah, that's +an excellent question. + +So what do you expect to +happen at such a point? + +AUDIENCE: Well, your +momentum blows up. + +PROFESSOR: Yeah, exactly. + +So we're going to +have some pathologies + +with expectation +values in the momentum. + +Let's come back to that when we +talk about the delta function + +potential, which should +be at the end of today. + +Hold that question in +the back of your head. + +It's a good question. + +Other questions? + +OK. + +So what we're going to do now +is we're going to use, you know, + +math to find the +energy eigenfunctions + +and eigenvalues for the +finite well potential, i.e. + +we're going to solve +this equation contingent + +on the boundary +conditions that the wave + +function and its derivative +are smooth everywhere. + +And in particular, they must +be smooth here and here. + +I mean they've got to +be smooth everywhere. + +We know what the +solution is inside here. + +We know what the +solution is in here. + +All we have to worry about is +what happens at the interface. + +And we're going to use +smoothness of the wave function + +and its derivative to +impose conditions that + +allow us to match +across that step. + +Everyone cool with that? + +OK. + +So let's do it. + +By the way, just +a quick side note. + +Let me give you a definition. + +I've used this +phrase many times, + +but I haven't given +you a definition of it. + +So I've used the +phrase, bound state. + +And its opposite is +called a scattering state. + +So here's what I mean +by a bound state. + +Intuitively, a +bound state, if you + +think about this +classically, imagine + +I have a potential well. + +And I have a marble, +and I let go from here. + +This marble is bound. + +Right? + +It's never getting +out of the well. + +It's stuck. + +Yeah? + +And so I would call +that a bound marble. + +On the other hand, a marble +that I give a huge kick to, + +big velocity so +that it can get out, + +well then it's not bound +to this potential well. + +So I'll call that a scattering +state just to give it a name. + +And next lecture we'll see why +we call it a scattering state. + +The important thing is +that bound configurations + +of a classical +potential are things + +basically in a well +that are stuck. + +OK. + +So the quantum version of that +statement is the following. + +Suppose I take this +potential, and I + +treat it quantum mechanically, +and I consider a state + +with total energy like this. + +Well, among other +things, the total energy + +is less than the value of +the potential asymptotically + +far away. + +So what is the form +of a wave function + +in this region with this energy? + +Exponential, right? + +It's e to the +minus some alpha x, + +where alpha squared is roughly +the difference, alpha x. + +And out here it's going to +be e to the plus alpha x. + +And that's for normalizability. + +We want to have a single +particle in this state. + +So what that tells us is that +the wave function falls off + +in these classically disallowed +regions exponentially. + +And so the probability +of measuring the particle + +at an arbitrarily far +position goes to zero. + +And it goes to zero +exponentially rapidly. + +Cool? + +So I will call a bound state, a +quantum bound state, an energy + +eigenstate, such that +the probability falls off + +exponentially as we go far +away from wherever we think + +is an interesting point, +like the bottom of the well. + +Cool? + +A bound state is +just a state which + +is exponentially localized. + +If you put it there, +it will stay there. + +Yeah. + +And it's important that +when I say a bound state + +I'm talking about +energy eigenstates. + +And the reason is this. + +Bound state equals +energy eigenstate. + +The reason is that, +consider by contrast + +a free particle, +so a free particle + +with constant potential. + +What are the wave functions? + +What are the energy +eigenfunctions? + +Well, they're plane waves. + +Right. + +So are these bound states? + +No. + +Good. + +OK. + +On the other hand, +I claimed that I + +can build a wave packet, a +perfectly reasonable wave + +packet, which is a Gaussian. + +OK. + +This is some wave +function, psi of x times 0. + +It's a Gaussian. + +It's nice and narrow. + +Is that a bound state? + +Well, it's localized +at this moment in time. + +But will it remain, and in +particular its probability + +distribution, which +is this thing norm + +squared is localized in space-- + +Sorry. + +This was zero. + +--it's localized in space. + +The probability of +it being out here + +is not just +exponentially small, it's + +Gaussian so it's e to +the minus x squared. + +It's really not out here. + +But what happens if I let go? + +What happens if I look +at the system at time t? + +It's going to spread out. + +It's going to disperse. + +We're going to talk about +that in more detail later. + +So it's going to spread out. + +And eventually, it will get +out arbitrarily far away + +with whatever probably you like. + +So the probability distribution +is not time invariant. + +That is to say it's +not a stationary state. + +It's not an energy eigenstate. + +Saying something is bound +means that it never gets away. + +So bound states are +specifically energy eigenstates + +that are strictly +localized, that fall off + +at least exponentially as +we go away from the origin. + +Cool? + +It's just terminology, what +I mean by a bound state. + +Questions? + +OK. + +So let's talk about +the finite well. + +So I need to give you +definitions of the parameters. + +Let's draw this more precisely. + +Here's my well. + +Asymptotically, the +potential is zero. + +The potential depth, I'm +going to call minus v naught. + +OK. + +And I'm going to center +the well around zero. + +And I'll call the +sides minus l and l. + +And I want to find bound +states of this potential, + +just like we found bound states +of the harmonic oscillator, + +i.e. + +states with energy e, +which is less than zero. + +So these are going to give +us bound states because we're + +going to have exponential +fall offs far away. + +So a couple of things to note. + +The first is on, +I think, problem + +set three or four you +showed that if you + +have a potential, +which is symmetric, + +which is even, under x goes +to minus x, then every energy + +eigenfunction, or at least +every bound state energy + +eigenfunction, every energy +eigenfunction can be written + +as phi e symmetric or +phi e anti-symmetric. + +So it's either even or odd. + +It's either even or odd under +the exchange of x to minus x. + +So when our potential +is symmetric, + +the wave function or the +energy eigenfunctions + +are either symmetric +or anti-symmetric. + +OK. + +So we want to solve for +the actual eigenfunctions. + +So we want to solve +that equation. + +And we have this +nice simple fact + +that we know the +solutions in this region. + +We know the general +solution in this region. + +We know the general +solution in this region. + +So I'm going to call these +regions one, two, and three, + +just to give them a name. + +So in region one-- + +That's actually sort of stupid. + +Let's call this inside, +left, and right. + +Good. + +OK. + +So let's look at this equation. + +We have two cases. + +If the energy is greater than +the potential in some region, + +then this is of the +form phi prime prime + +is equal to energy +greater than potential. + +This is a negative number. + +And so this is a +minus k squared phi. + +And we get exponentials. + +And if, on the other hand, +e is less than v of x, then + +phi prime prime is equal +to plus alpha squared phi. + +I should say oscillator. + +And in particular here, I want +the k squared is equal to 2m + +upon h bar squared. + +It's just the +coefficient v minus e. + +And alpha squared is equal to +2m over h bar squared e minus v. + +OK. + +So let's apply that here. + +So in this region, we're +going to get oscillations + +because we're in a classically +allowed region, where + +the energy is greater +than the potential. + +So we'll get +oscillatory solutions. + +And the salient value +of k inside, is k + +is equal to the square root +of 2m over h bar squared times + +v minus e. + +So that's minus v naught. + +What did I do? + +I did. + +It's e minus v. I thank you. + +Yes. + +And I want the other one to +be l so it'd be minus v. Good. + +Good. + +Excellent. + +So root 2 over h bar squared. + +And now we have e +minus v naught, which + +is the actual value of +e, which is negative. + +Right? + +But minus v naught +or plus v naught + +is positive and +greater in magnitude. + +So this is a nice +positive number, + +and k is the square root of it. + +This is controlling +how rapidly the wave + +function oscillates +in this region. + +Similarly, out here we +have alpha is equal to-- + +Well, here the +potential is zero. + +So it's particularly easy. + +Alpha is equal to +the square root of 2m + +upon h bar squared of-- + +Now z minus e is zero minus +e, which is a negative number. + +So we can just write +e absolute value. + +So we can write the general +solution of this eigenfunction, + +of this eigenvalue equation, +as phi e of x is equal to-- + +Let's break it up into +inside and outside. + +Well, inside we know, since it's +constant with this value of k, + +we get superpositions of +oscillatory solutions. + +It' a second-order +difference equation. + +There are two solutions and +two integration constants. + +So first we have a cosine +of kx plus b sine kx. + +This is inside. + +And then on the left +we have a combination + +of exponentially growing and +exponentially decreasing. + +So the exponentially +growing is e to the alpha x + +plus de the minus alpha x. + +And on the right, +similarly by symmetry, + +we have some combination of e-- + +But I don't want to call +it the energy, so I'll + +call it the curly e. + +--to the alpha x plus +fe to the minus alpha x. + +OK. + +So that's the general solution. + +We solve the problem as a +superposition of the two + +oscillatory solutions +or a superposition + +of the two exponentially +growing and damped solutions + +or exponentially +growing and collapsing + +functions on the left and right. + +Questions? + +So a couple of things +to note at this point. + +So the first is we have +boundary conditions to impose. + +We have boundary conditions +at these two interfaces. + +But we also have boundary +conditions off in infinity. + +What are the boundary +conditions at infinity? + +Yeah, exactly. + +It should vanish. + +So we want the system +to be normalizable. + +So normalizable is +going to say that phi + +goes to zero at minus infinity. + +Phi of x goes to minus infinity +goes to zero, which it equals. + +And phi of x goes to plus +infinity should also be zero. + +OK. + +And then we're +also going to have + +the conditions at +the left boundary, + +and we're going +to have conditions + +at the right boundary. + +[LAUGHTER] + +All right. + +So what are the boundary +condition at the left boundary + +condition? + +So first off, what are +the boundary conditions + +we want to impose at the +left and right boundaries? + +AUDIENCE: Continuous. + +PROFESSOR: Continuous, +and the derivative + +should be continuous. + +Exactly. + +So we have that phi is +continuous, and phi prime-- + +Good god. + +--phi prime is continuous. + +Similarly, phi continuous, +phi prime continuous. + +OK. + +Do we have enough +boundary conditions + +to specify our function? + +So we have now for +our solution, we + +have six undetermined +coefficients. + +And we have six +boundary conditions. + +So that looks good. + +Are they all independent? + +Ponder that one. + +So in particular, let's +start with the normalizable. + +So in order for phi to go to +zero at minus infinity deep + +out on the left, +what should be true? + +Yeah, d goes to zero. + +Oops, equals zero. + +And on the right? + +Yeah, that curly +e equals 0, which + +is nice so I don't ever +have to write it again. + +So that's zero. + +And that's zero. + +OK. + +That's good. + +We can take advantage +though of something nice. + +We know that the +wave function has + +to be either symmetric +or anti-symmetric. + +Right? + +So we can exploit +that and say, look, + +the wave function is going to +be different from our boundary + +conditions, but +it's a true fact, + +and we can take advantage of it. + +We can use the +parody of the well. + +I can never-- + +So we can use the +parody of the potential + +to say that the system is either +symmetric or anti-symmetric. + +And these are often +said as even or odd + +because the function +will be, as a function + +of x, either even or odd. + +You either pick up a +minus sign or a plus sign + +under taking x to minus x. + +So if the system is +even, what can we + +say about these coefficients? + +What must be true +of b, for example? + +AUDIENCE: It's zero. + +PROFESSOR: Yeah. + +So b equals 0. + +And what else? + +AUDIENCE: It equals f. + +PROFESSOR: This equals f. + +Yeah, good. + +OK. + +This equals f. + +And if the system +is anti-symmetric, + +then a equal to 0. + +And we see that c +is equal to minus f. + +Yeah? + +So that's a useful +simplification. + +So it's easy to see that we +could do this either way. + +We could do either +symmetric or anti-symmetric. + +I'm going to, for +simplicity in lecture, + +focus on the even case. + +b is equal to 0, and +c is equal to minus f. + +Sorry, c is equal to f. + +So plus c. + +So now we're +specifically working + +with the even solutions. + +And on your problem set, +you'll repeat this calculation + +for the odd functions. + +So we're going to focus +on the even solutions. + +And now what we have +to do is we have + +to impose the boundary +conditions for phi and phi + +prime. + +So that's easy enough. + +We have the function. + +All we have to do is impose +that the values are the same. + +So for example, let's focus on +the left boundary conditions. + +Sorry. + +Let's focus on the +right because I + +don't want to deal +with that minus sign. + +So let's focus on the +right boundary conditions. + +So this is x is equal to plus l. + +So when x is equal to +plus l, what must be true? + +Phi and phi prime +must be continuous. + +So what's phi? + +So phi is equal to-- + +Well, from inside, +it's a cosine of kl. + +Yeah. + +And b is gone because we're only +looking at the even functions. + +On the right, however, it's +equal to c e to the minus alpha + +l because we're evaluating +at the right boundary. + +Yeah? + +OK. + +So this is cool. + +It allows us to determine +c in terms of a. + +And if we solve that +equation for c in terms of a, + +we'll get an +eigenfunction, phi even, + +with one overall +normalization coefficient, a. + +And then we can fix +that to whatever + +it has to be so that +everything integrates to one. + +Yeah? + +So that seems fine. + +It seems like we can +solve for c in terms of a. + +c is equal to-- + +This is weight. + +Well, OK. + +So c is equal to a cosine +e to the plus alpha l. + +On the other hand, we also have +a condition on the derivative. + +And the condition +on the derivative + +is that phi prime is continuous. + +And the derivative of +this, well that's easy. + +It's the derivative of cosine. + +So this is going +to be minus sine. + +But we pull out a factor +of k, because we're + +taking derivative +with respect to x. + +Minus k is sine of kx. + +Evaluate it out, sine of kl, l. + +And this is going +to be equal to minus + +alpha c e to the minus alpha l. + +AUDIENCE: You forgot an a. + +PROFESSOR: Oh, yes. + +There should be an a. + +Thank you. + +OK. + +So but now we've got +a problem because this + +says that c is equal to minus +a times k over alpha sine + +of kl times e to the alpha l. + +And that's bad +because c can't be + +equal to two different +numbers at the same time. + +There's a certain monogamy +of mathematical equations. + +It just doesn't work. + +So how do we deal with this? + +Well, let's think about +what these equations would + +have meant. + +Forget this one for +the moment, and just + +focus on that first expression. + +I'm going to rewrite +this slightly. + +a cosine of kl. + +OK. + +So what does this +expression say? + +Well, it seems like +it's just saying + +if we fix c to be equal to this +value, for fixed value of kappa + +l and alpha, then +there's a solution. + +However, what is k? + +What are k and alpha. + +k and alpha are +functions of the energy. + +So it would seem from +this point of view, + +like for any value +of the energy, + +we get a solution +to this equation. + +Everyone see that? + +But we know that can't +possibly be right + +because we expect the +solutions to be discrete. + +We don't expect +any value of energy + +to lead to a solution of the +energy eigenvalue equation. + +There should be only +discrete set of energies. + +Yeah? + +AUDIENCE: Did you +pick up an extra minus + +sign in the expression for c? + +PROFESSOR: You do. + +Thank you. + +The sign's cancel. + +Yes, excellent. + +I've never written this +equation in my life. + +So thank you. + +Yes, extra minus sign. + +So what's going on here? + +Well, what we see is +that we've written down + +the general form +of the solution. + +Here were imposing that we've +already imposed the condition + +that we're normalizable +at infinity. + +Here, we're imposing +the continuity condition + +on the right. + +And if we impose just +the continuity condition + +for the wave function, +we can find a solution. + +Similarly, if we impose only +the continuity condition + +for the derivative, +we can find a solution + +for arbitrary values +of the energy. + +But in order to find +a solution where + +the wave function and its +derivative are both continuous, + +it can't be true that the energy +takes just any value because it + +would tell you that c +takes two different values. + +Right? + +So there's a +consistency condition. + +For what values of energy or +equivalently, for what values + +of k and alpha are these +two expressions equal + +to the same thing? + +Cool? + +So we can get that +by saying, look + +we want both of these +equations to be true. + +And this is easy. + +I can take this equation and +divide it by this equation. + +And I will lose +my coefficients c. + +I will lose my coefficients a. + +What do we get? + +On the right hand side, we get-- + +And I'm going to put a +minus sign on everything. + +So minus, minus, minus. + +So if we take this equation and +we divide it by this equation, + +on the right hand +side, we get alpha, + +because the c +exponential drops off. + +And on this side, we lose the a. + +We get a k. + +And then we get sine over +cosine of kl, also known + +as tangent of kl. + +Here we have a kl. + +Here we have a k. + +These are all +dimensionful things. + +Let's multiply +everything by an l. + +And this is nice +and dimensionless. + +Both sides are dimensionless. + +So we get this condition. + +This is the +consistency condition, + +such that both the wave +function and its derivative + +can be continuous at +the right boundary. + +OK? + +And this is a pretty +nontrivial condition. + +It says, given a value +of k, you can always + +determine the value of alpha, +such as this equation as true. + +But remember that k and +alpha are both known + +functions of the energy. + +So this is really an equation, a +complicated, nonlinear equation + +for the energy. + +So this is equal to a horrible +expression, a condition, badly + +nonlinear, in fact, +transcendental condition + +on the energy. + +And where's it coming from? + +It's coming from normalizability +and continuity everywhere. + +And a useful thing +to check, and I + +invite you to do +this on your own, + +is to check that the boundary +conditions at the left wall + +give the same expression. + +Yeah. + +AUDIENCE: For our final +form of that equation, + +is there a reason that we prefer +to multiply both sides by l + +than divide both sides by k? + +PROFESSOR: Yeah. + +And it'll be little more +obvious in a second. + +But here's the reason. + +So let's divide through by l. + +This is the form that we got. + +What are the units? + +What are the dimensions +of this expression? + +k is a wave number, so it +has units of 1 upon length. + +Right? + +And that's good because that's +1 upon length times the length, + +and you'd better have something +dimensionless inside a tangent. + +But it seems there are two +things to say about this. + +The first is it seems like l +is playing an independent role + +from k in this equation. + +But this is dimensionless. + +These are both dimensionful +units of 1 over length. + +So we can make the entire +expression dimensionless + +and make it clear that k and l +don't have an independent life. + +The dimensionless quantity, +kl, times the tangent + +of that dimensionless +quantity is + +equal to this +dimensionless quantity. + +So the reason that this +is preferable is twofold. + +First off, it makes it +sort of obvious that k + +and l, you can't vary them +independently in this sense. + +But the second is that it makes +it nice and dimensionless. + +And you'll always, +whenever possible, + +want to put things in +dimensionless form. + +I mean it's just +multiplying by l. + +So it's obviously +not all that deep. + +But it's a convenient bit +of multiplication by l. + +Other questions? + +OK. + +So where are we? + +So I'd like to find the +solutions of this equation. + +So again, just to-- + +Let me write this slightly +differently where k squared is + +equal to 2m upon h +bar squared v0 plus e. + +And alpha squared is equal +to 2m upon h bar squared e, + +the positive value of e. + +So this is a really complicated +expression as a function of e. + +So I'd like to solve for the +actual energy eigenvalues. + +I want to know what are the +energy eigenvalues of the bound + +states of the finite potential +well, as a function of l, + +for example. + +Sadly, I can't +solve this equation. + +It's a transcendental equation. + +It's a sort of canonically +hard problem to solve. + +You can't write down a closed +from expression for it. + +However, there are a bunch +of ways to easily solve it. + +One is take your +convenient nearby laptop. + +Open up Mathematica, and ask it +to numerically find solutions + +to this. + +And you can do this. + +It's a good exercise. + +I will encourage you to +do so on your problem set. + +And in fact, on +the problem set, it + +asks you to do a calculation. + +And it encourages you +do it using Mathematica. + +Let me rephrase the +statement in the problem set. + +It would be crazy for you to +try to do it only by hand. + +You should do it by +hand and on computer + +because they're both easy. + +And you can check +against each other. + +They make different +things obvious. + +This should be your default is +to also check on Mathematica. + +The second thing we can do is we +can get a qualitative solution + +of this equation +just graphically. + +And since this is such a useful +technique, not just here, + +but throughout physics +to graphically solve + +transcendental +equations, I'm going + +to walk through it a little bit. + +So this is going to be +the graphical solution. + +And we can extract, +it turns out, + +an awful lot of the +physics of these energy + +eigenstates and their +energies through + +this graphical technique. + +So the first thing +is I write this + +in nice, dimensionless form. + +And let me give those +dimensionless variables a name. + +Let me call kl is equal to +z, just define a parameter z. + +And alpha l is a parameter y. + +And I want to note that z +squared plus y squared is + +equal to a constant, which +is, I will call if you just + +plug these guys out, kl +squared plus al squared. + +That's easy. + +Kl squared is this +guy times l squared. + +Al squared is this +guy times l squared. + +And so the e and +the minus e cancel + +when we add them together. + +So we just get 2mv0 over h +bar squared times l squared. + +So 2m upon h bar +squared l squared v0. + +And I'm going to call +this r naught in something + +of a pathological +abusive notation. + +OK. + +So this is our expression. + +And I actually want to +call this r0 squared. + +I know. + +I know. + +It's awful. + +But the reason I +want to do this is + +that this is the +equation for a circle. + +Yeah? + +And a circle has a radius. + +The thing that goes +over here is r squared. + +OK. + +So at this point, you're +thinking like, come on, circle. + +So let's plot it. + +So how are we going to +solve this equation? + +Here's what I want to solve. + +I have now two equations +relating z and y. + +We have that from this equation +z tangent z is equal to y. + +And from this equation we +have that z squared plus y + +squared is a +constant r0 squared. + +Where r0 squared depends on +the potential and the width + +in a very specific way, on +the depth of the potential + +and the width in a +very specific way. + +So we want to find-- + +Bless you. + +--simultaneously, we want to +find simultaneous solutions + +of these two equations. + +Yeah? + +So that's relatively easy. + +So here's y, and here's z. + +So this equation has solutions. + +Any time that y +plus z squared is + +equal to r0 squared, that means +any time we have a circle. + +So solutions for fixed +values of r0 lie on circles. + +Oh, I really should have +drawn this under here. + +Sorry. + +y and z. + +So those are the circles. + +Notice that I'm only focusing +on y and z, both positive. + +Why? + +Not yz, but W-H-Y . + +Why am I focusing +on the variables y + +and z being positive? + +Because we started out defining +them in terms of k and l, + +which were both positive, +and alpha and l, + +which were both positive. + +Can we find solutions +to this equation + +that have x and y negative? + +Sure. + +But they don't mean anything in +terms of our original problem. + +So to map onto solutions +of our original problem, + +we want to focus on the +positive values of y and z. + +Cool? + +OK. + +So that's this one. + +The solutions lie on circles. + +So given a value of y, you +can find a solution of z. + +But we want to also find a +solution of this equation. + +And this equation is a little +more entertaining to plot. + +Here's y. + +Here's z. + +So what does z tangent z do? + +Oh, shoot. + +I want to plot y vertical. + +Otherwise, it's going +to a giant pain. + +Happily, this plot +can be left identical. + +Let's plot y vertically. + +So the reason I want +to plot y vertically + +is that this is z tangent z. + +So first off, what does +tangent z look like? + +Yeah. + +This is awesome. + +Yeah, it looks like this. + +Yes, exactly. + +So tangent is sine over cosine. + +Sine is zero, and cosine is one. + +So it does this, as +you go to a value + +where the argument, let's +call the argument z. + +So if we just plot tangent-- + +OK. + +So when z is equal to pi over +2, then the denominator cosine + +vanishes, and that diverges. + +Oops. + +OK. + +So here's pi over 2. + +Here's pi. + +Whoops. + +Pi, pi over 2, and here's +3pi over 2, and so on. + +Now, we're only interested +in the first quadrant. + +So I'm just ignore down here. + +OK. + +So this is pi over 2. + +This is pi, 3pi over 2. + +OK. + +But this is not what +we're interested in. + +We're not interested +in tangent of z. + +We're interested in z tangent z. + +And what does z +tangent z look like? + +Well, it's basically the same. + +Right? + +z tangent z, it has an +extra factor of zero here + +and remains extra +small at the beginning. + +But it still curves +off roughly like this. + +And z is just nice +and linear, nice + +and regular throughout this. + +So it doesn't change +the fact that we + +have a divergence at pi over 2. + +And it doesn't change the fact +that it vanishes again at pi + +and becomes positive again. + +It just changes the +shape of the curve. + +And in fact, the way it +changes the shape of the curve + +is this becomes a little +fatter around the bottom. + +It's just a little more round. + +And when we get out +to large values of z, + +it's going to have a +more pronounced effect + +because that slope +is, at every example + +where it crosses z, that +slope is getting larger + +because the coefficient +of z is getting larger. + +OK. + +So it's just going to +get more and more sharp. + +But anyway, with all +that said, here's 0. + +Here's pi. + +Here's pi over 2. + +Here's pi. + +Here's 3pi over 2. + +The second plot we want +to plot, y is z tangent z. + +We know how to plot this. + +Cool? + +And what we want to find +are simultaneous solutions + +of this, values of y and z, for +which this equation is solved + +and this equation is solved +for the same value of y and z. + +This is a graphical solution. + +So let's combine them together. + +And the combined +plots look like this. + +First we have pi over 2. + +So let's plot the tangents. + +And then we have these circles +for various values of r. + +So for a particular +value of r, for example, + +suppose this is the value of r. + +This is r0. + +So how many +solutions do we have? + +One. + +One set of common +points where at y and z + +solve both equations. + +So we immediately learn +something really lovely. + +What happens to the +radius of that circle + +as I make the well deeper? + +Yeah, as I make the well +deeper, that means v0 gets + +larger and larger magnitude, +the radius gets larger. + +So does the circle. + +So if I make the well deeper, +I make this the circle larger. + +Will I still have a solution? + +Yeah, I'll still +have a solution. + +But check this out. + +Now, I'll have a new solution. + +And you can even see the +critical value of the depth + +and the width of the well. + +In order to have exactly a +new bound state appearing, + +what must the value of r0 be? + +Well, it's got to be that value, +such that r0 squared is pi. + +Yeah? + +And similarly, let me ask +you the following question. + +As I make the well deeper +and deeper and deeper, + +holding the width, and make it +deeper and deeper and deeper, + +does the number of states +increase or decrease? + +It increases. + +If you make it +deeper and deeper, + +the radius of that circle is +getting bigger and bigger. + +There are more points where this +circle intersects this point. + +So here's another one. + +We've got one here, one here, +one here, three solutions. + +And the number of +solutions just goes. + +Every time we click +over a new point + +by increasing the radius of the +circle, we get a new solution. + +We get another bound state. + +But here's the thing that +I really want to focus on. + +Let's make the well +less and less deep. + +Let's make it shallower +and shallower. + +At what depth do we lose +that first bound state? + +We never do. + +Right? + +There is no circle +so small that it + +doesn't intersect this curve. + +In a 1D, finite well potential, +there is always at least one + +bound state. + +There are never +zero bound states. + +This will turn out not to be +true in three dimensions, which + +is kind of interesting. + +But it's true in one +dimension that we always + +have at least one bound state. + +And in fact, you +can decorate this. + +You can use this and +fancy it up a bit + +to argue that in +any potential in 1D, + +there's always at +least one bound state + +unless the potential +is constant, + +I mean any potential that varies +and goes to zero infinity. + +Yeah? + +And so we still don't +have any numbers. + +But we know an awful lot about +the qualitative structure + +of the set of energy eigenvalues +of the spectrum of the energy. + +Questions? + +Yeah? + +AUDIENCE: So what +happens if r is bigger + +than pi or y is bigger than +pi and you get two solutions? + +PROFESSOR: Great. + +So when we have two solutions, +what does that mean? + +Well, you've got to bound +states, two different energies. + +Right? + +It's a good question. + +Every solution here corresponds +to some particular value of y + +and some particular value of z. + +But those values +of y and z are just + +telling you what +k and alpha are. + +And so that's +determining the energy. + +So a different +value of k is going + +to give you a different +value of the energy. + +So we can just eyeball +this in particular. + +Let's look at alpha. + +Alpha is just e. + +Alpha squared is just e. + +Yes? + +So here's a quick question. + +If alpha is just e, +and alpha l is y-- + +So this is our y value. + +y is roughly alpha, +the width, which + +means it's roughly the +energy square root. + +So this value, +the vertical value + +of each of these intersection +points on a given circle + +corresponds to the +square root of the energy + +times some coefficients. + +So which state has the +largest value of the energy? + +Absolute value, which +state is most deeply + +bound on this circle? + +Yeah, the first one. + +Right? + +Because it's got the +largest value of alpha. + +So this is nice. + +We see that the +first state always + +has a higher value of alpha +than the second state, + +which always has a higher value +of alpha than the third state. + +And every time we +add a new state, + +we make the depth of these +guys the binding energy + +of the already existing states. + +We make it just a +little bit deeper. + +We make them a little +more tightly bound. + +And only eventually +then do we get + +a new bound state appearing. + +And what's the energy +of that new bound state + +when it appears? + +Zero energy. + +It's appearing +just at threshold. + +OK. + +So we'll explore that in more +detail in the problem set. + +But for now, let me +leave it at that. + +Questions? + +Other questions? + +Yeah. + +AUDIENCE: You said that +this can be generalized + +to any nonconstant +function that you'd like. + +So there's always going to +be at least one bound state. + +What about, like +with delta function? + +PROFESSOR: Excellent question. + +What about the delta function? + +We're going to come back to +that in just a few minutes. + +It's a very good question. + +So the question is, look, +if any potential that + +goes to zero infinity +and wiggles inside, + +if any potential like that +in 1D has a bound state, what + +about the delta function? + +We briefly talked about that. + +So we're going to come back +to that in just a few minutes. + +But it's a pressing question. + +OK. + +Other questions? + +Yes. + +AUDIENCE: So the energy is +zero, but that's not possible. + +PROFESSOR: Thank you. + +OK. + +Good. + +So let me talk about that +in a little more detail. + +So I wasn't going to +go into this, but-- + +So when new bound states appear, +so let's consider a point where + +our r0 is, let's say, +it's just the right value + +so that r0 is equal to pi. + +OK. + +And we see that we're just about +to develop a new bound state. + +So let's think about what +that bound state looks like. + +So this is the new bound state. + +And I'm going to put +this in parentheses + +because it's got bound state. + +And we say at threshold. + +OK. + +At threshold, i.e. + +at the energy is roughly +zero, and r0 is equal to pi. + +So this is really what we mean. + +This new state, +when r0 is pi and we + +have a solution on +that second branch. + +Cool? + +So what does this wave +function look like? + +What does it look +like when you have + +a wave function +that just appeared? + +It's just barely bound. + +Well, first off, what +does it mean to be bound? + +Let's just step back +and remember for now. + +What does it mean +to be a bound state? + +It means you're an +energy eigenfunction + +and you're localized. + +Your wave function +falls off at infinity. + +Now, if it falls +off at infinity, + +do these guys fall +off at infinity? + +These wave functions, +sure, they fall + +of with an exponential damping. + +And in particular, let's +look at the right hand + +side of the well. + +This new bound state is +appearing just at zero energy. + +So out here, what is +the wave function? + +It's e to the minus alpha x. + +But what's alpha? + +Zero, right? + +There it is, zero. + +So this is e to the minus alpha +x where alpha is equal to 0. + +This is constant. + +So what does the wave +function look like? + +Well, the wave function, +again over the same domain-- + +Here's 0, l. + +And here's the value zero. + +We know that in this +domain it's oscillatory, + +and in this domain, +it's constant. + +And actually, since we know that +it's the first excited state, + +we know that it does this. + +So if we make the well +ever so slightly deeper, + +ever so slightly +deeper, which means + +making the radius of the +circle ever so slightly larger, + +we will get a nonzero value +for the alpha of this solution. + +Right? + +It'll be just tiny. + +But it'll be nonzero. + +So we make the well just +a little tiny bit deeper. + +We get something. + +OK, good. + +So what's going to happen +to the wave function? + +Well, instead of going flat. + +This is going to curve. + +It's got a little more energy. + +There's a little more curvature. + +So it curves just a +little tiny bit more. + +And then it matches onto a very +gradually decaying exponential. + +OK. + +So what's happening as we take +this bound state, the second + +bound state, and we make the +well a little more shallow? + +We make the well a +little more shallow. + +It's a little less +curved inside. + +And the evanescent tails, +the exponential tails + +become longer and longer +and longer and broader + +until they go off to infinity, +until they're infinitely wide. + +And is that +normalizable anymore? + +No, that's not normalizable. + +So the state really +isn't strictly localized + +at that point. + +It's not really a +normalizable state. + +And just when the state +ceases to be normalizable, + +it disappears. + +We make the well +just a little deeper, + +and there's no +state there at all. + +OK. + +So this tells you +a very nice thing. + +It's a good bit of intuition +that when states are appearing + +or disappearing, when states +are at threshold as you + +vary the depth, those threshold +bound states have exceedingly + +long evanescent tails, and +they're just barely bound. + +OK? + +This turns out to have all +sorts of useful consequences, + +but let me move on. + +Did that answer your question? + +Good. + +Yeah? + +AUDIENCE: So in this case, +the radius, as you say, + +is proportional to the length. + +Right? + +But also we have intuition +that as we increase + +the length of the +well, the energy's + +going to keep increasing-- + +PROFESSOR: Fantastic. + +OK. + +So what's up with that? + +Right. + +So the question is this. + +We already have intuition that +is if we take a finite well + +and we make it a +little bit wider, + +the ground state +energy should decrease. + +The energy of the ground state +should get deeper and deeper, + +or the magnitude +should increase, + +another way to say it. + +Right? + +That was our intuition. + +So let's check if that's true. + +What happens if I +take the ground state + +some value of the +radius, and then I + +make the well a +little bit wider. + +Well, if I make the +well a little bit wider, + +what happens to r0, the +radius of the circle? + +Well, if I double the length +of the well, the width + +of the well, then +it will double r0, + +and it will double the +radius of the circle. + +So if I make it +wider, r0 gets bigger, + +and we go to a bigger circle. + +And what happened to the +energy of this state? + +Yeah, it got deeper +and deeper and deeper. + +And meanwhile, as +we make it wider, + +as we make the well wider, the +circle is getting bigger again. + +And we're going to get +more and more states. + +So as we make the well wider, +holding the depth fixed, + +we get more and more states. + +As we make the well deeper, +holding the width fixed, + +we get more and more states. + +And so how do you trade off? + +If I make it twice +as wide, how much-- + +So here's a good question. + +Suppose I take a well, +and it has n states. + +Suppose I then make +it twice as wide. + +What must I do to the +energy so that it still + +has the same states +with the same energies? + +AUDIENCE: Divide it by 4. + +PROFESSOR: Yep, exactly. + +I've got to divide it by 4. + +Because I've doubled +the length, that + +means the radius +has gone up by four. + +But I get exactly +the same solutions + +if I just bring this out. + +Well, that's almost true. + +So if I put a +factor of 1/4 here, + +that's almost true, except for +the value of y is unchanged, + +but the alpha hasn't changed. + +Sorry. + +The alpha has changed +because there's an l. + +So y is fixed. + +But alpha's changed +because of the l. + +So the reason that it's +useful to write things + +in these dimensionless forms is +that you can see the play off + +of the various different +dimensionful parameters + +in changing the answer. + +Other questions. + +OK. + +So a couple of comments. + +So the first is let's +just check to make sure + +that this makes sense. + +We have already +solved this problem. + +We solved this +problem a while ago, + +but we solved it in +a particular limit. + +We solved it in the limit that +the potential one's arbitrarily + +deep. + +Right? + +So when the potential +one's are arbitrarily deep, + +holding the width fixed, +that was the infinite well. + +That was the first +problem we solved. + +So let's make sure that we +recover this in that limit. + +So what happens as we make +the well arbitrarily deep, + +holding the length fixed +or the width fixed. + +So if we make this +arbitrarily deep, + +v0 is getting arbitrarily large. + +That means r0 is getting-- + +We've got a huge circle. + +So what do these +solutions look like when + +we have a huge circle. + +Let me not do that here. + +Let me do that here. + +So if we make the +potential nice and deep, + +Let's think about what +that plot looks like. + +So again, that first plot looks +identical with the tangents. + +So on and so forth. + +And what I want to do is +I want to dot, dot, dot. + +OK. + +So this is way up there. + +So these guys are basically +vertical lines at this point. + +So for very, very large values +of y, and in particular, + +for very large values that are +of order the gigantically deep + +radius r0, what does +the circle look like? + +So what does the second equation +look like, the second curve? + +Well, again it's circles. + +But now it's a gigantic circle. + +Yeah, exactly. + +If it's a gigantic circle, +it's basically flat. + +It's not exactly flat, +but it's almost flat. + +It's a circle. + +So what are the values? + +And here's the key question. + +What are the values of-- + +Did do that right? + +Yeah, OK. + +Good. + +So what are the values of the +curve, where we get a solution? + +The values now of +z, are just exactly + +on these vertical lines, +on the separatrices. + +The value of z is at pi over 2. + +and 3pi over 2. + +And then another one at 5pi +over 2, and so on and so forth. + +Right? + +So what we find is that +the allowed values of z-- + +Sorry. + +kl, yes, good. + +--allowed values of z are +equal to 2n plus 1 over pi. + +Whoops 2n plus 1 +over 2 times pi. + +So let's just check that. + +So n is 0. + +That's 0 1/2 pi. + +n is 1. + +That's 3/2 pi. + +Good. + +So these are the +values of z, which + +says that kl is equal to 2n plus +1 upon 2 pi or k is equal to 2n + +plus 1 over 2l, which is +the width of this well + +because it's from +minus l to l pi. + +So is this the correct answer +for the infinite square well? + +Are these the +allowed values of k + +inside the well for the +infinite square well? + +Almost. + +Instead of 2n plus 1, it +should just be n plus 1. + +We seem to be missing about +half of the energy eigenvalues. + +AUDIENCE: That's +only the even ones. + +PROFESSOR: Yeah, thank you. + +This is only the even ones. + +We started out saying, oh, look. + +Let's look only +at the even ones. + +Where do you think the +odd ones are going to be? + +Ah, well the odd ones, +so this should be k even. + +So what about k odd? + +Well, we know the +answer already-- + +Whoops. + +Odd, that's an odd spelling. + +--should be equal to 2n +over 2l plus 2 over 2l. + +Whoops. + +2 capital L, pi. + +OK. + +This is our guess +just from matching on + +to the infinite square well. + +So what does that mean? + +Well, that means it should +be this one and this one. + +So when you go through this +exercise on your problem + +set and you find the +solutions for the odd, + +and you repeat this analysis +for the odd ground states. + +What should you expect? + +Well, you should +expect to find this. + +And what do you +think the curves are + +that you're going to use +int he graphical solution + +to do your +transcendental equation? + +Yeah, it's really +tempting to say, look. + +It's just going to be +something shifted, like this. + +OK. + +So these are going to be the odd +question mark, question mark. + +OK. + +So you'll check whether that's +correct intuition or not + +on your problem set. + +OK. + +Questions? + +Yeah? + +AUDIENCE: What about the lower +end of these states, where + +it won't have gone +off high enough? + +Is that [INAUDIBLE]? + +PROFESSOR: Excellent. + +So that's a really +good question. + +How to say it? + +What we've done here to +make this an infinite well-- + +So the question, let me +just repeat the question. + +The question is, look, what +about all the other states? + +OK, it's true that +r0 as gigantic. + +But eventually, we'll go +to a large enough z, where + +it's the circle coming +down over here too. + +So what's up with that? + +What are those states? + +Where are they? + +What do they mean in terms +if the infinite square well? + +Well, first off, what are +the energies of those states? + +AUDIENCE: Very low. + +PROFESSOR: They're +very low in magnitude, + +which means they're close +to what in absolute value? + +AUDIENCE: Zero. + +PROFESSOR: Zero. + +They're close to zero. + +So they're at the top +of the finite well. + +These are the states bound at +the top of the finite well. + +These are the states bound at +the bottom the finite well. + +But how many states are bound +at the top of the finite well + +when we take the limit that +the well goes infinitely deep? + +Yeah, none of them. + +Right? + +So when we make the +well infinitely deep, + +what we're saying +is, pay no attention + +to the top of the well. + +Look only at the +bottom of the well. + +And if it's really deep, it's +a pretty good approximation. + +So that's what we're doing here. + +We're saying, look. + +Pay no attention. + +There is no top of the well. + +There's just the bottom. + +And look at the +energy eigenvalues. + +Does that make sense? + +So what we're saying is if +you have a preposterously + +deep well, the energies +of a preposterously + +deep well should be +a good approximation + +to the low-lying energies +of an infinitely deep well. + +Because it's way up there, +what difference can it make? + +And that's what we're +seeing work out. + +Did that answer your question? + +AUDIENCE: Wait. + +I might have this backward. + +But when it says the high +energy instead of looking right + +at the top of the well-- + +PROFESSOR: Yeah. + +OK, good. + +So this is an important +bit of intuition. + +So when we say this +is the energy zero, + +and the potential has +a minimum at minus v0, + +and we're measuring the +energies relative to zero, + +then the states at the +top of the potential well + +are the states with +energy close to zero. + +And the states at the +bottom of the potential + +well are those states with +the energy of order v0. + +cool? + +And what are the energies +of all these states? + +They're order of v0. + +Right? + +Because this is-- + +Are they exactly v0? + +No, because this isn't linear. + +It's actually a circle. + +So there's going +to be a correction, + +and the correction is +going to be quadratic. + +If you work out that +correction, it's correct. + +The depth above the +bottom of the potential + +is correct for the energy of +the corresponding infinite well + +problem. + +I'll leave that to +you as an exercise. + +Other questions? + +OK. + +So there's another +limit of this system + +that's fun to think about. + +So this was the +infinite well limit. + +What I want to do is I +want to take advantage + +of the observation we made +a second ago that as we make + +the well deeper, +we get more states. + +As we make the well more +narrow, we get fewer states. + +To trade that off, consider +the following limit. + +I want to take a potential +well, which has a ground state. + +What does the ground +state look like? + +So the ground state wave +function is going to be-- + +So here's zero. + +And here's +exponentially growing. + +Here's exponentially decreasing. + +And if it's a ground state, how +many nodes will it have inside? + +How many nodes will +the ground state have? + +AUDIENCE: Zero. + +PROFESSOR: Zero. + +Good. + +OK. + +So the ground state will +look something like this. + +We more conventionally +draw it like this. + +But just for fun, I'm going +to draw it in this fashion. + +In particular, it +has some slope here. + +And it has some slope here. + +Oh, shoot. + +Did I? + +Yes, I did. + +Dammit. + +I just erased the one thing +that I wanted to hold onto. + +OK. + +So there's my wave function. + +It has some +particular slope here. + +It has some +particular slope here. + +And this is the ground +state wave function, + +with some energy. + +I don't know. + +I'll call it this. + +Now, what I want to +do is we've already + +shown that as we make the well +more and more shallow and more + +and more narrow, the +energy of the ground state + +gets closer and closer to zero. + +But there remains +always a bound state. + +There is always at +least one bound state. + +We proved that. + +Proved, as a physicist would. + +So I want to do that. + +I want to take this seriously. + +But here's the limit +I want to consider. + +Consider the limit that we +make the potential v goes + +to infinity, v0, while +making l go to zero. + +So what I want to do is I +want to take this thing, + +and I want to make it +deeper and deeper, but more + +and more narrow. + +If I do this +repeatedly, eventually I + +will get a delta function. + +And I will get a +delta function if I + +hold the area of this guy fixed. + +Yeah? + +So if I do so, holding the +area under this plot fixed, + +I will get a delta function. + +Everyone cool with that? + +So let's think, though, +quickly about what's + +going to happen to the +ground state wave function. + +So as I make the potential, +let's take this wave function, + +and let's look at this +version of the potential. + +So as I make the +potential deeper, + +what happens to the rate +of the oscillation inside + +or to the curvature inside? + +It increases. + +Right? + +So the system is oscillating +more, it changes more rapidly, + +because phi double +dot or phi double + +prime is equal to v minus e phi. + +It oscillates more rapidly. + +So to make it deeper, +the system tends + +to oscillate more rapidly. + +However, as we make +it more narrow, + +the system doesn't have +as far to oscillate. + +So it oscillates +more rapidly, but it + +doesn't oscillate as far. + +So what's going to happen? + +Well, as we make it more +and more narrow and deeper + +and deeper, we again have +the wave function coming in. + +And now it oscillates +very rapidly. + +Let's do it again. + +The wave function comes in, +and it oscillates very rapidly. + +And the it evanescent tail out. + +And now as we have a delta +function, exponential damping, + +it oscillates extremely rapidly +over an arbitrarily short + +distance and gives +us the kink that we + +knew at the very beginning +we should expect when + +the potential is +a delta function. + +Right? + +From our qualitative +structure of the wave function + +at the very beginning +we saw that when + +we have a delta +function potential, + +we should see a kink +in the wave function. + +Because again, if we have phi +prime prime is delta function + +discontinuous, phi prime +is the integral of this. + +This is a step, and +phi is continuous. + +And so here we have +a step function. + +We get a discontinuity +in the second derivative. + +Here we have a delta +function in the potential, + +and we get a discontinuity +in the first derivative + +if we get a kink in +the wave function. + +Yeah? + +AUDIENCE: Would we +get a jump there? + +PROFESSOR: Sorry. + +Say again. + +For e1? + +AUDIENCE: Yeah. + +Would we get a jump? + +PROFESSOR: Very good question. + +So let me do this +more seriously. + +Let's do this more carefully. + +So the question is, for +the first excited state, + +do we get a jump? + +Do we get a discontinuity? + +What do we get for the +first excited state? + +Right? + +So let's talk about +that in detail. + +It's a very good question. + +Example v is equal to +minus v0 delta of x. + +Now, here I want to just +warn you of something. + +This is totally standard +notation for these problems, + +but you should be +careful about dimensions. + +What are the dimensions of +v0, the parameter of v0? + +It's tempting to say energy. + +That's an energy. + +That's an energy. + +But wait. + +What are the dimensions +of the delta function? + +AUDIENCE: Length. + +PROFESSOR: Whatever +length right? + +Because we know that +delta of alpha x + +is equal to 1 over +norm alpha delta of x. + +So if I write delta +of x, which is always + +a slightly ballsy thing to +do because this should really + +be dimensionless, but if +I write delta of x, then + +this has units of 1 +over length, which + +means this must have units +of length times energy. + +OK. + +Just a little warning, +when you check your answers + +on a problem, you +always want to make sure + +that they're +dimensionally consistent. + +And so it will be +important to make sure + +that you use the +energy times the length + +for the dimensions +of that beast. + +So my question here is, +is there a bound state? + +So for this example, +for this potential, + +the delta function +potential bound state, which + +again is this guy, is +there a bound state? + +So again, we just ran +through the intuition + +where we made the potential +deep and deeper and deeper, + +v0 divided by epsilon +over width epsilon. + +So v0, in order for +this to be an energy + +has to be an energy +times a length + +because we're going to +divide it by length. + +So this is going to +give us a delta function + +potential in the limit. + +We have an intuition +that we should + +get a bound state with a kink. + +But let's check that intuition. + +We want to actually +solve this problem. + +So we'll do the same +thing we did before. + +We now write the general +solution in the places + +where the potential is +constant, which is on the left + +and on the right. + +And then we want to impose +appropriate boundary conditions + +at the interface and at +infinity, where these are going + +to be normalizable, and this +is whatever the right boundary + +conditions are. + +So we are going to have to +derive the appropriate boundary + +conditions. + +So let's just do that quickly. + +So phi with definite +e is equal to a-- + +So in this region +in the left, it's + +either growing or +decreasing exponential. + +So ae to the alpha x plus +be to the minus alpha x. + +And this is x less than 0. + +And ce to the alpha x +plus de to the minus + +alpha x for x greater than 0. + +So first off, let's +hit normalizability. + +What must be true +for normalizability? + +Yeah, they'd better be +converging to zero here + +and converging to zero here, +which means that c had better + +vanish and b had better vanish. + +OK. + +So those guys are gone +from normalizability. + +And meanwhile, if +this is symmetric, + +what is going to be true +of the ground state? + +It's going to be symmetric. + +So a must be equal to d. + +Great. + +So a is now just some overall +normalization constant, + +which we can fix +from normalization. + +So it looks like this +should be the solution. + +We have an exponential. + +We have an exponential. + +But there's one more +boundary condition to fix. + +We have to satisfy +some matching. + +We have to satisfy the +boundary conditions + +at the delta function. + +So what are those? + +What are those +matching conditions? + +So we can get that from the +energy eigenvalue equation, + +which says that +phi prime prime is + +equal to h bar squared upon 2m. + +Sorry. + +Get your dimensions right. + +So it's 2m over h bar +squared v minus e. + +In this case, v is equal +to minus v0 delta function. + +That's very strange. + +So minus 2m over h bar squared +v0 delta of x minus e-- + +I pulled out the minus. + +--so plus e phi. + +So this must be +true at every point. + +This of course, is +zero everywhere, + +except for at the origin. + +So what we want to do +is we want to turn this + +into a boundary condition. + +And we know what the +boundary condition is. + +If v is a delta function, that +means that phi prime prime + +is also a delta +function or proportional + +to a delta function. + +That means that phi +prime is a step function. + +And how did I get that? + +I got that by integrating +phi prime prime. + +You integrate a delta function, +you get a step function. + +Well, that's cool. + +How do we figure out what +step function discontinuity + +gives us? + +Let's integrate. + +Let's integrate right +across the delta function + +and figure out what +the discontinuity is. + +So let's take this +equation, integrate it + +from minus epsilon +to epsilon, where + +epsilon is a very small number. + +And that's epsilon to epsilon. + +So what is this going +to give us on the left? + +Well, integral of +a total derivative + +is just the value of the +thing at a value to the point. + +So this is going to be +phi prime at epsilon + +minus phi prime +and minus epsilon. + +What does that mean? + +The difference +between the derivative + +just after the origin and +just before the origin. + +This is the discontinuity +for very small epsilon. + +This is the discontinuity +of the derivative + +at the origin at +the delta function. + +And we already expected it +to have a step discontinuity. + +And there it is. + +And how big is it? + +Well on the right +hand side we have + +2m minus 2m upon h bar squared. + +And we're going +to get two terms. + +We get a term from +integrating the first term. + +But over this narrow +window, around, + +let's say epsilon was here, over +this narrow window we can treat + +the wave function as being +more or less constant. + +But in any case, +it's continuous. + +And this is a delta function. + +So we know what we get from the +integral of the delta function. + +We just get the value v0 +phi at the delta function. + +Phi of the zero at the +delta functions, so phi 0. + +We get a second term, which +is plus the energy integrated + +against phi. + +The energy's a constant. + +And phi is continuous. + +So this, whatever else +you can say about it, + +is roughly the +constant value of phi + +at the origin times the +energy times the width, which + +is epsilon. + +So plus-order epsilon terms. + +Everyone cool with that? + +So now what I'm +going to do is I'm + +going to take the limit +as epsilon goes to zero. + +So I'm just going to take +that the discontinuity just + +across zero. + +So this is going to give +me, of this gives me + +the change in the +slope at the origin. + +OK. + +The derivative just +after the origin + +minus the derivative just +before the origin is equal to-- + +These order epsilon +terms go away. + +--minus 2m upon h +bar squared v0 phi. + +So that's my continuity. + +That's the condition +for continuity + +of the derivative and +appropriate discontinuity + +of the first derivative +at the origin. + +And so this, when we +plug-in these values + +of this form for +the wave function, + +when we take a derivative, +all we're going to do + +is we're going to +pick up an alpha. + +And so when we work +all of this out-- + +I'm not going to go +through the algebra. + +You're going to go through +it on the problem set. + +--when we take this condition, +when we impose this condition + +with this wave +function, it gives us + +a very specific value for alpha. + +This is only solvable +if alpha is equal to mv0 + +upon h bar squared. + +Good. + +So let's just check the units. + +So this is momentum times +length, momentum times length. + +This is mass. + +This is an energy +times a length. + +So this has overall units +of, p squared over m, + +overall units of 1 upon +length, which is what we wan. + +So that's good. + +So we get alpha is +equal to mv0 upon h bar. + +And that gives us the +form of the potential. + +And it also tells us that the +energy, plugging this back in, + +is equal to minus h bar +squared alpha squared upon 2m, + +which we could then +plug-in the value of alpha + +and solve for v0. + +So what we found is that +there is a single bound state + +of the delta function +potential, which + +we could have gotten by +just taking this limit. + +It's a fun way to +rederive the same result. + +It's a nice check on +your understanding. + +So we find that there's +a single bound state + +of the delta function potential. + +Now, what about an +odd bound state? + +We assumed at an important +point that this was even. + +What if I assume +that it was odd? + +One node, what if we had +assumed that it was odd? + +What would be true +of the wave function? + +Well for odd, this would be +a, and this would be minus a. + +So the value of the wave +function at the origin is what? + +Zero. + +So that tells us the value +of the wave function is zero. + +What's the discontinuity? + +Zero. + +So it's as if +there's no potential + +because it has a zero right +at the delta function. + +Yeah? + +But that means that this wave +function, an odd wave function, + +doesn't notice the delta +function potential. + +So is there a bound state? + +No. + +So how many bound +states are there? + +Always exactly one for the +single isolated delta function. + +On your problem +set, you're going + +to use the result of the +single isolated delta function, + +and more broadly you're +going to derive the results + +for two delta functions. + +So you might say, why +two delta functions? + +And the answer is, +the two delta function + +problem, which +involves no math-- + +Right? + +It's a totally straightforward, +simple problem. + +You can all do it right +now on a piece of paper. + +The two delta +function problem is + +going to turn out to +be an awesome model + +for the binding of atoms. + +And we're going to use it as +intuition on your problem set + +to explain how quantum +mechanical effects can lead + +to an attractive force +between two atoms. + +See you next time. + +[APPLAUSE] \ No newline at end of file diff --git a/idNIKTaBEaI.txt b/idNIKTaBEaI.txt new file mode 100644 index 0000000000000000000000000000000000000000..160c82f34c49ccb7d9994af70825c819b963fd03 --- /dev/null +++ b/idNIKTaBEaI.txt @@ -0,0 +1,1195 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I'd like us to work on the following + + align:start position:0% +I'd like us to work on the following + + + align:start position:0% +I'd like us to work on the following +problem that has to do with Tangent + + align:start position:0% +problem that has to do with Tangent + + + align:start position:0% +problem that has to do with Tangent +planes and + + align:start position:0% +planes and + + + align:start position:0% +planes and +approximations so we know that a + + align:start position:0% +approximations so we know that a + + + align:start position:0% +approximations so we know that a +rectangle we'll say a rectangle has + + align:start position:0% +rectangle we'll say a rectangle has + + + align:start position:0% +rectangle we'll say a rectangle has +sides X and Y and we know that to find + + align:start position:0% +sides X and Y and we know that to find + + + align:start position:0% +sides X and Y and we know that to find +the area of the rectangle then we just + + align:start position:0% +the area of the rectangle then we just + + + align:start position:0% +the area of the rectangle then we just +take x * Y and I would like us to + + align:start position:0% +take x * Y and I would like us to + + + align:start position:0% +take x * Y and I would like us to +approximate the area for xal to 2.1 and + + align:start position:0% +approximate the area for xal to 2.1 and + + + align:start position:0% +approximate the area for xal to 2.1 and +y equal 2.8 and obviously with this type + + align:start position:0% +y equal 2.8 and obviously with this type + + + align:start position:0% +y equal 2.8 and obviously with this type +of equation it's not hard to just + + align:start position:0% +of equation it's not hard to just + + + align:start position:0% +of equation it's not hard to just +compute this but I'd like us to use the + + align:start position:0% +compute this but I'd like us to use the + + + align:start position:0% +compute this but I'd like us to use the +tangent plane approximation to determine + + align:start position:0% +tangent plane approximation to determine + + + align:start position:0% +tangent plane approximation to determine +the value and then we'll compare it to + + align:start position:0% +the value and then we'll compare it to + + + align:start position:0% +the value and then we'll compare it to +the actual value um just to give us an + + align:start position:0% +the actual value um just to give us an + + + align:start position:0% +the actual value um just to give us an +idea of how we can use the tangent plane + + align:start position:0% +idea of how we can use the tangent plane + + + align:start position:0% +idea of how we can use the tangent plane +to approximate things and obviously I'd + + align:start position:0% +to approximate things and obviously I'd + + + align:start position:0% +to approximate things and obviously I'd +like to do this near xal 2 and y equal 3 + + align:start position:0% +like to do this near xal 2 and y equal 3 + + + align:start position:0% +like to do this near xal 2 and y equal 3 +so when you're doing your tangent plane + + align:start position:0% +so when you're doing your tangent plane + + + align:start position:0% +so when you're doing your tangent plane +approximation do the approximation at + + align:start position:0% +approximation do the approximation at + + + align:start position:0% +approximation do the approximation at +xal 2 and yal 3 and then when you're + + align:start position:0% +xal 2 and yal 3 and then when you're + + + align:start position:0% +xal 2 and yal 3 and then when you're +done with that I would like you to an to + + align:start position:0% +done with that I would like you to an to + + + align:start position:0% +done with that I would like you to an to +answer this question so near x equal 2 + + align:start position:0% +answer this question so near x equal 2 + + + align:start position:0% +answer this question so near x equal 2 +and Y equals 3 which has a greater + + align:start position:0% +and Y equals 3 which has a greater + + + align:start position:0% +and Y equals 3 which has a greater +effect a change in X or an equal change + + align:start position:0% +effect a change in X or an equal change + + + align:start position:0% +effect a change in X or an equal change +in y so if I if I change by X in the + + align:start position:0% +in y so if I if I change by X in the + + + align:start position:0% +in y so if I if I change by X in the +same value as I change by Y which will + + align:start position:0% +same value as I change by Y which will + + + align:start position:0% +same value as I change by Y which will +have the greater + + align:start position:0% +have the greater + + + align:start position:0% +have the greater +impact so why don't you pause the tape + + align:start position:0% +impact so why don't you pause the tape + + + align:start position:0% +impact so why don't you pause the tape +work on the problems and when you're + + align:start position:0% +work on the problems and when you're + + + align:start position:0% +work on the problems and when you're +ready to see how I do them bring it back + + align:start position:0% +ready to see how I do them bring it back + + + align:start position:0% +ready to see how I do them bring it back +up and I'll come back and show you + + align:start position:0% + + + + align:start position:0% + +okay welcome back so we're going to work + + align:start position:0% +okay welcome back so we're going to work + + + align:start position:0% +okay welcome back so we're going to work +on this problem and as I mentioned the + + align:start position:0% +on this problem and as I mentioned the + + + align:start position:0% +on this problem and as I mentioned the +first thing we want to do is do a + + align:start position:0% +first thing we want to do is do a + + + align:start position:0% +first thing we want to do is do a +tangent plane approximation near xal 2 + + align:start position:0% +tangent plane approximation near xal 2 + + + align:start position:0% +tangent plane approximation near xal 2 +and yal 3 so let me write down what + + align:start position:0% +and yal 3 so let me write down what + + + align:start position:0% +and yal 3 so let me write down what +we're going to need in order to do that + + align:start position:0% +we're going to need in order to do that + + + align:start position:0% +we're going to need in order to do that +first we'll remind ourselves that in + + align:start position:0% +first we'll remind ourselves that in + + + align:start position:0% +first we'll remind ourselves that in +this case what I'm going to approximate + + align:start position:0% +this case what I'm going to approximate + + + align:start position:0% +this case what I'm going to approximate +is is the the area function for a + + align:start position:0% +is is the the area function for a + + + align:start position:0% +is is the the area function for a +rectangle which is a of X Y is equal to + + align:start position:0% +rectangle which is a of X Y is equal to + + + align:start position:0% +rectangle which is a of X Y is equal to +x * y so so that's the that's the + + align:start position:0% +x * y so so that's the that's the + + + align:start position:0% +x * y so so that's the that's the +function I'm going to be approximating + + align:start position:0% +function I'm going to be approximating + + + align:start position:0% +function I'm going to be approximating +and now the the actual approximation the + + align:start position:0% +and now the the actual approximation the + + + align:start position:0% +and now the the actual approximation the +tangent plane approximation has the + + align:start position:0% +tangent plane approximation has the + + + align:start position:0% +tangent plane approximation has the +following form so we know a ofx y is + + align:start position:0% +following form so we know a ofx y is + + + align:start position:0% +following form so we know a ofx y is +approximately well it's going to be the + + align:start position:0% +approximately well it's going to be the + + + align:start position:0% +approximately well it's going to be the +area evaluated at the point I'm + + align:start position:0% +area evaluated at the point I'm + + + align:start position:0% +area evaluated at the point I'm +interested in which we said was 2 comma + + align:start position:0% +interested in which we said was 2 comma + + + align:start position:0% +interested in which we said was 2 comma +3 right + + align:start position:0% +3 right + + + align:start position:0% +3 right +plus the X derivative of area evaluated + + align:start position:0% +plus the X derivative of area evaluated + + + align:start position:0% +plus the X derivative of area evaluated +at 2A 3 times the change in X and the + + align:start position:0% +at 2A 3 times the change in X and the + + + align:start position:0% +at 2A 3 times the change in X and the +change in X is where X is now versus + + align:start position:0% +change in X is where X is now versus + + + align:start position:0% +change in X is where X is now versus +where we started which is at xal 2 and + + align:start position:0% +where we started which is at xal 2 and + + + align:start position:0% +where we started which is at xal 2 and +then the same thing in terms of Y so you + + align:start position:0% +then the same thing in terms of Y so you + + + align:start position:0% +then the same thing in terms of Y so you +do the Y derivative evaluated at 2 comma + + align:start position:0% +do the Y derivative evaluated at 2 comma + + + align:start position:0% +do the Y derivative evaluated at 2 comma +3 and then you do the change in + + align:start position:0% +3 and then you do the change in + + + align:start position:0% +3 and then you do the change in +y and since we started at yal 3 the + + align:start position:0% +y and since we started at yal 3 the + + + align:start position:0% +y and since we started at yal 3 the +change in y is Yus 3 okay so now we + + align:start position:0% +change in y is Yus 3 okay so now we + + + align:start position:0% +change in y is Yus 3 okay so now we +obviously need to fill in three + + align:start position:0% +obviously need to fill in three + + + align:start position:0% +obviously need to fill in three +quantities here the three things we need + + align:start position:0% +quantities here the three things we need + + + align:start position:0% +quantities here the three things we need +to evaluate area evaluated at 23 it's X + + align:start position:0% +to evaluate area evaluated at 23 it's X + + + align:start position:0% +to evaluate area evaluated at 23 it's X +derivative evaluated at 23 and it's y + + align:start position:0% +derivative evaluated at 23 and it's y + + + align:start position:0% +derivative evaluated at 23 and it's y +derivative evaluated at 23 so so let me + + align:start position:0% +derivative evaluated at 23 so so let me + + + align:start position:0% +derivative evaluated at 23 so so let me +just point out what we have area + + align:start position:0% +just point out what we have area + + + align:start position:0% +just point out what we have area +evaluated at + + align:start position:0% +evaluated at + + + align:start position:0% +evaluated at +23 well that's just 2 * 3 which we can + + align:start position:0% +23 well that's just 2 * 3 which we can + + + align:start position:0% +23 well that's just 2 * 3 which we can +do so that's six that's pretty easy now + + align:start position:0% +do so that's six that's pretty easy now + + + align:start position:0% +do so that's six that's pretty easy now +a subx so the derivative of the area + + align:start position:0% +a subx so the derivative of the area + + + align:start position:0% +a subx so the derivative of the area +function with respect to X the + + align:start position:0% +function with respect to X the + + + align:start position:0% +function with respect to X the +derivative of the area function with + + align:start position:0% +derivative of the area function with + + + align:start position:0% +derivative of the area function with +respect to X is just y y in that case we + + align:start position:0% +respect to X is just y y in that case we + + + align:start position:0% +respect to X is just y y in that case we +treat as a constant we take this + + align:start position:0% +treat as a constant we take this + + + align:start position:0% +treat as a constant we take this +derivative we just get y back and so a + + align:start position:0% +derivative we just get y back and so a + + + align:start position:0% +derivative we just get y back and so a +subx evaluated at 23 is going to be Y + + align:start position:0% +subx evaluated at 23 is going to be Y + + + align:start position:0% +subx evaluated at 23 is going to be Y +which y here is three so we get a sub X + + align:start position:0% +which y here is three so we get a sub X + + + align:start position:0% +which y here is three so we get a sub X +is equal to 3 at 23 in a similar vein we + + align:start position:0% +is equal to 3 at 23 in a similar vein we + + + align:start position:0% +is equal to 3 at 23 in a similar vein we +can immediately look and see that a sub + + align:start position:0% +can immediately look and see that a sub + + + align:start position:0% +can immediately look and see that a sub +y evaluated at 23 is going to be two and + + align:start position:0% +y evaluated at 23 is going to be two and + + + align:start position:0% +y evaluated at 23 is going to be two and +the reason for that of course is if we + + align:start position:0% +the reason for that of course is if we + + + align:start position:0% +the reason for that of course is if we +look back here the derivative of a with + + align:start position:0% +look back here the derivative of a with + + + align:start position:0% +look back here the derivative of a with +respect to Y is X so evaluating it at 23 + + align:start position:0% +respect to Y is X so evaluating it at 23 + + + align:start position:0% +respect to Y is X so evaluating it at 23 +gives us two okay so now we just have to + + align:start position:0% +gives us two okay so now we just have to + + + align:start position:0% +gives us two okay so now we just have to +fill everything in so my tangent plane + + align:start position:0% +fill everything in so my tangent plane + + + align:start position:0% +fill everything in so my tangent plane +approximation now says I get 6 Plus 3 * + + align:start position:0% +approximation now says I get 6 Plus 3 * + + + align:start position:0% +approximation now says I get 6 Plus 3 * +x - 2 + 2 * y - 3 and what I wanted was + + align:start position:0% +x - 2 + 2 * y - 3 and what I wanted was + + + align:start position:0% +x - 2 + 2 * y - 3 and what I wanted was +the area at 2.1 comma + + align:start position:0% +the area at 2.1 comma + + + align:start position:0% +the area at 2.1 comma +2.8 so if I fill in uh those values for + + align:start position:0% +2.8 so if I fill in uh those values for + + + align:start position:0% +2.8 so if I fill in uh those values for +X and Y so 2.1 is X and 2.8 is y if I + + align:start position:0% +X and Y so 2.1 is X and 2.8 is y if I + + + align:start position:0% +X and Y so 2.1 is X and 2.8 is y if I +fill those in I get that this this is + + align:start position:0% +fill those in I get that this this is + + + align:start position:0% +fill those in I get that this this is +equal to well I keep writing + + align:start position:0% +equal to well I keep writing + + + align:start position:0% +equal to well I keep writing +approximately just to be safe is 6 + 3 * + + align:start position:0% +approximately just to be safe is 6 + 3 * + + + align:start position:0% +approximately just to be safe is 6 + 3 * +well 2.1 - 2 gives me a 0.1 there + + align:start position:0% +well 2.1 - 2 gives me a 0.1 there + + + align:start position:0% +well 2.1 - 2 gives me a 0.1 there +there and 2 * 2.8 - 3 gives me a.2 there + + align:start position:0% +there and 2 * 2.8 - 3 gives me a.2 there + + + align:start position:0% +there and 2 * 2.8 - 3 gives me a.2 there +so I get a.4 I get a positive3 so + + align:start position:0% +so I get a.4 I get a positive3 so + + + align:start position:0% +so I get a.4 I get a positive3 so +together this is + + align:start position:0% +together this is + + + align:start position:0% +together this is +A.1 6 -.1 gives me + + align:start position:0% +A.1 6 -.1 gives me + + + align:start position:0% +A.1 6 -.1 gives me +5.9 so the area based on the + + align:start position:0% +5.9 so the area based on the + + + align:start position:0% +5.9 so the area based on the +approximation is 5.9 square units and in + + align:start position:0% + + + + align:start position:0% + +actuality if you multiply it out I think + + align:start position:0% +actuality if you multiply it out I think + + + align:start position:0% +actuality if you multiply it out I think +you get something like + + align:start position:0% +you get something like + + + align:start position:0% +you get something like +5.88 so the Pro imation is is very good + + align:start position:0% +5.88 so the Pro imation is is very good + + + align:start position:0% +5.88 so the Pro imation is is very good +right we're close to 23 and that that is + + align:start position:0% +right we're close to 23 and that that is + + + align:start position:0% +right we're close to 23 and that that is +one of the reasons we can know it's + + align:start position:0% +one of the reasons we can know it's + + + align:start position:0% +one of the reasons we can know it's +going to be very it should be very good + + align:start position:0% +going to be very it should be very good + + + align:start position:0% +going to be very it should be very good +it should be pretty good okay now I just + + align:start position:0% +it should be pretty good okay now I just + + + align:start position:0% +it should be pretty good okay now I just +have to answer the second part of the + + align:start position:0% +have to answer the second part of the + + + align:start position:0% +have to answer the second part of the +question so let me remind us what the + + align:start position:0% +question so let me remind us what the + + + align:start position:0% +question so let me remind us what the +second part was it was near x equal 2 + + align:start position:0% +second part was it was near x equal 2 + + + align:start position:0% +second part was it was near x equal 2 +and y equal 3 which has a greater effect + + align:start position:0% +and y equal 3 which has a greater effect + + + align:start position:0% +and y equal 3 which has a greater effect +a change in X or an equal change in y + + align:start position:0% +a change in X or an equal change in y + + + align:start position:0% +a change in X or an equal change in y +and to do that it's really easiest to + + align:start position:0% +and to do that it's really easiest to + + + align:start position:0% +and to do that it's really easiest to +come back and look at maybe this line + + align:start position:0% +come back and look at maybe this line + + + align:start position:0% +come back and look at maybe this line +I'll underline this line right here + + align:start position:0% +I'll underline this line right here + + + align:start position:0% +I'll underline this line right here +actually I'll box it + + align:start position:0% +actually I'll box it + + + align:start position:0% +actually I'll box it +okay this value will represent the + + align:start position:0% +okay this value will represent the + + + align:start position:0% +okay this value will represent the +change in X so we started at two and we + + align:start position:0% +change in X so we started at two and we + + + align:start position:0% +change in X so we started at two and we +go somewhere and that'll represent the + + align:start position:0% +go somewhere and that'll represent the + + + align:start position:0% +go somewhere and that'll represent the +change in X this value represents the + + align:start position:0% +change in X this value represents the + + + align:start position:0% +change in X this value represents the +change in y so if we look at which has a + + align:start position:0% +change in y so if we look at which has a + + + align:start position:0% +change in y so if we look at which has a +greater impact near 2 three if my change + + align:start position:0% +greater impact near 2 three if my change + + + align:start position:0% +greater impact near 2 three if my change +in X and my change in y are equal then + + align:start position:0% +in X and my change in y are equal then + + + align:start position:0% +in X and my change in y are equal then +obviously this term has a bigger impact + + align:start position:0% +obviously this term has a bigger impact + + + align:start position:0% +obviously this term has a bigger impact +because there's a three the coefficient + + align:start position:0% +because there's a three the coefficient + + + align:start position:0% +because there's a three the coefficient +here is three and the coefficient here + + align:start position:0% +here is three and the coefficient here + + + align:start position:0% +here is three and the coefficient here +is two and so the point is changes in X + + align:start position:0% +is two and so the point is changes in X + + + align:start position:0% +is two and so the point is changes in X +will have a larger will have a greater + + align:start position:0% +will have a larger will have a greater + + + align:start position:0% +will have a larger will have a greater +effect than changes in y and what this + + align:start position:0% +effect than changes in y and what this + + + align:start position:0% +effect than changes in y and what this +corresponds to pictorially is if we make + + align:start position:0% +corresponds to pictorially is if we make + + + align:start position:0% +corresponds to pictorially is if we make +a slice where we keep y constant and we + + align:start position:0% +a slice where we keep y constant and we + + + align:start position:0% +a slice where we keep y constant and we +look at the curve in that uh in the XZ + + align:start position:0% +look at the curve in that uh in the XZ + + + align:start position:0% +look at the curve in that uh in the XZ +plane that corresponds to the fact that + + align:start position:0% +plane that corresponds to the fact that + + + align:start position:0% +plane that corresponds to the fact that +the derivative in the XZ plane of this + + align:start position:0% +the derivative in the XZ plane of this + + + align:start position:0% +the derivative in the XZ plane of this +of the curve there uh is more sign is + + align:start position:0% +of the curve there uh is more sign is + + + align:start position:0% +of the curve there uh is more sign is +more significant the curve there has a + + align:start position:0% +more significant the curve there has a + + + align:start position:0% +more significant the curve there has a +steeper derivative than if I kept the X + + align:start position:0% +steeper derivative than if I kept the X + + + align:start position:0% +steeper derivative than if I kept the X +the x value fixed and I looked in the YZ + + align:start position:0% +the x value fixed and I looked in the YZ + + + align:start position:0% +the x value fixed and I looked in the YZ +plane and I looked the curve there so + + align:start position:0% +plane and I looked the curve there so + + + align:start position:0% +plane and I looked the curve there so +that's the the sort of one-dimensional + + align:start position:0% +that's the the sort of one-dimensional + + + align:start position:0% +that's the the sort of one-dimensional +picture is that the the derivative of a + + align:start position:0% +picture is that the the derivative of a + + + align:start position:0% +picture is that the the derivative of a +curve in the X Direction keeping y fixed + + align:start position:0% +curve in the X Direction keeping y fixed + + + align:start position:0% +curve in the X Direction keeping y fixed +is steeper than the derivative of the + + align:start position:0% +is steeper than the derivative of the + + + align:start position:0% +is steeper than the derivative of the +curve in the y direction keeping X fixed + + align:start position:0% +curve in the y direction keeping X fixed + + + align:start position:0% +curve in the y direction keeping X fixed +so maybe hopefully that wasn't more + + align:start position:0% +so maybe hopefully that wasn't more + + + align:start position:0% +so maybe hopefully that wasn't more +confusing than it should have been from + + align:start position:0% +confusing than it should have been from + + + align:start position:0% +confusing than it should have been from +here you can see it right away but + + align:start position:0% +here you can see it right away but + + + align:start position:0% +here you can see it right away but +that's sort of the the picture of it as + + align:start position:0% +that's sort of the the picture of it as + + + align:start position:0% +that's sort of the the picture of it as +well so I think that's where I'll stop \ No newline at end of file diff --git a/j8ZGpRo8jd4.txt b/j8ZGpRo8jd4.txt new file mode 100644 index 0000000000000000000000000000000000000000..0e40abff52dc3e6d633fda7b2b1fd6be3f65ebe6 --- /dev/null +++ b/j8ZGpRo8jd4.txt @@ -0,0 +1,14939 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so I get to do the the + + align:start position:0% +ocw.mit.edu okay so I get to do the the + + + align:start position:0% +ocw.mit.edu okay so I get to do the the +introduction Spiel for today's class um + + align:start position:0% +introduction Spiel for today's class um + + + align:start position:0% +introduction Spiel for today's class um +and going to start by just saying what + + align:start position:0% +and going to start by just saying what + + + align:start position:0% +and going to start by just saying what +we're doing in class today so you've got + + align:start position:0% +we're doing in class today so you've got + + + align:start position:0% +we're doing in class today so you've got +sort of a framework of what we're doing + + align:start position:0% +sort of a framework of what we're doing + + + align:start position:0% +sort of a framework of what we're doing +because we're doing a whole lot of + + align:start position:0% +because we're doing a whole lot of + + + align:start position:0% +because we're doing a whole lot of +things and we're going to be jumping + + align:start position:0% +things and we're going to be jumping + + + align:start position:0% +things and we're going to be jumping +between speakers and workshops and + + align:start position:0% +between speakers and workshops and + + + align:start position:0% +between speakers and workshops and +lectures and in class workor so we + + align:start position:0% +lectures and in class workor so we + + + align:start position:0% +lectures and in class workor so we +actually have a lot of stuff to try and + + align:start position:0% +actually have a lot of stuff to try and + + + align:start position:0% +actually have a lot of stuff to try and +get through today to get you guys + + align:start position:0% +get through today to get you guys + + + align:start position:0% +get through today to get you guys +started on Project one um so we're going + + align:start position:0% +started on Project one um so we're going + + + align:start position:0% +started on Project one um so we're going +to introduce project one and that's + + align:start position:0% +to introduce project one and that's + + + align:start position:0% +to introduce project one and that's +actually what my brief lecture is going + + align:start position:0% +actually what my brief lecture is going + + + align:start position:0% +actually what my brief lecture is going +to be after I get done with the Clash + + align:start position:0% +to be after I get done with the Clash + + + align:start position:0% +to be after I get done with the Clash +Spiel um we're going to hear lectures on + + align:start position:0% +Spiel um we're going to hear lectures on + + + align:start position:0% +Spiel um we're going to hear lectures on +how to do brainstorming and then we'll + + align:start position:0% +how to do brainstorming and then we'll + + + align:start position:0% +how to do brainstorming and then we'll +ask you to brainstorm we're going to Le + + align:start position:0% +ask you to brainstorm we're going to Le + + + align:start position:0% +ask you to brainstorm we're going to Le +on prototyping and then I'm going to + + align:start position:0% +on prototyping and then I'm going to + + + align:start position:0% +on prototyping and then I'm going to +give a more pointed lecture on what we + + align:start position:0% +give a more pointed lecture on what we + + + align:start position:0% +give a more pointed lecture on what we +mean by low Fidelity prototype which is + + align:start position:0% +mean by low Fidelity prototype which is + + + align:start position:0% +mean by low Fidelity prototype which is +what project one calls for and we are + + align:start position:0% +what project one calls for and we are + + + align:start position:0% +what project one calls for and we are +going to do all those bits of in-class + + align:start position:0% +going to do all those bits of in-class + + + align:start position:0% +going to do all those bits of in-class +work hopefully scattered along the + + align:start position:0% +work hopefully scattered along the + + + align:start position:0% +work hopefully scattered along the +way okay so moving on to introducing + + align:start position:0% +way okay so moving on to introducing + + + align:start position:0% +way okay so moving on to introducing +project one so that you've got and the + + align:start position:0% +project one so that you've got and the + + + align:start position:0% +project one so that you've got and the +reason we're introducing project one + + align:start position:0% +reason we're introducing project one + + + align:start position:0% +reason we're introducing project one +before we give the supporting lectures + + align:start position:0% +before we give the supporting lectures + + + align:start position:0% +before we give the supporting lectures +is so you've got something to frame + + align:start position:0% +is so you've got something to frame + + + align:start position:0% +is so you've got something to frame +you're going to be hearing lectures + + align:start position:0% +you're going to be hearing lectures + + + align:start position:0% +you're going to be hearing lectures +about prototyping and brainstorming + + align:start position:0% +about prototyping and brainstorming + + + align:start position:0% +about prototyping and brainstorming +which we want you to do project one we + + align:start position:0% +which we want you to do project one we + + + align:start position:0% +which we want you to do project one we +want I want you to be thinking about the + + align:start position:0% +want I want you to be thinking about the + + + align:start position:0% +want I want you to be thinking about the +project as we give you the lecture so + + align:start position:0% +project as we give you the lecture so + + + align:start position:0% +project as we give you the lecture so +you can try and figure out how you're + + align:start position:0% +you can try and figure out how you're + + + align:start position:0% +you can try and figure out how you're +going to be applying that information to + + align:start position:0% +going to be applying that information to + + + align:start position:0% +going to be applying that information to +the thing we're going to be asking you + + align:start position:0% +the thing we're going to be asking you + + + align:start position:0% +the thing we're going to be asking you +to doing okay so the overall goal is and + + align:start position:0% +to doing okay so the overall goal is and + + + align:start position:0% +to doing okay so the overall goal is and +I have to actually stand back I can + + align:start position:0% +I have to actually stand back I can + + + align:start position:0% +I have to actually stand back I can +either see my notes or I can see the + + align:start position:0% +either see my notes or I can see the + + + align:start position:0% +either see my notes or I can see the +slides but I can't see both um so + + align:start position:0% +slides but I can't see both um so + + + align:start position:0% +slides but I can't see both um so +demonstrate a working mechanic via a low + + align:start position:0% +demonstrate a working mechanic via a low + + + align:start position:0% +demonstrate a working mechanic via a low +Fidelity paper prototype to serve as the + + align:start position:0% +Fidelity paper prototype to serve as the + + + align:start position:0% +Fidelity paper prototype to serve as the +Prototype for a digital game while + + align:start position:0% +Prototype for a digital game while + + + align:start position:0% +Prototype for a digital game while +tracking and understanding how your game + + align:start position:0% +tracking and understanding how your game + + + align:start position:0% +tracking and understanding how your game +design changes over time um any words + + align:start position:0% +design changes over time um any words + + + align:start position:0% +design changes over time um any words +there you didn't understand because + + align:start position:0% +there you didn't understand because + + + align:start position:0% +there you didn't understand because +we've got a lot of jargon actually up + + align:start position:0% +we've got a lot of jargon actually up + + + align:start position:0% +we've got a lot of jargon actually up +there a lot of game design jargon up + + align:start position:0% + + + + align:start position:0% + +there okay what exactly is a mechanic a + + align:start position:0% +there okay what exactly is a mechanic a + + + align:start position:0% +there okay what exactly is a mechanic a +mechanic that's actually a really good + + align:start position:0% +mechanic that's actually a really good + + + align:start position:0% +mechanic that's actually a really good +question um a mechanic is usually a key + + align:start position:0% +question um a mechanic is usually a key + + + align:start position:0% +question um a mechanic is usually a key +chunk of a game by which the player + + align:start position:0% +chunk of a game by which the player + + + align:start position:0% +chunk of a game by which the player +takes actions in the game or the game + + align:start position:0% +takes actions in the game or the game + + + align:start position:0% +takes actions in the game or the game +takes actions so if you're playing a + + align:start position:0% +takes actions so if you're playing a + + + align:start position:0% +takes actions so if you're playing a +platforming if you're playing like a + + align:start position:0% +platforming if you're playing like a + + + align:start position:0% +platforming if you're playing like a +basic platforming digital game um one of + + align:start position:0% +basic platforming digital game um one of + + + align:start position:0% +basic platforming digital game um one of +your basic mechanics is your character + + align:start position:0% +your basic mechanics is your character + + + align:start position:0% +your basic mechanics is your character +can jump and that's what your character + + align:start position:0% +can jump and that's what your character + + + align:start position:0% +can jump and that's what your character +often uses to solve a lot of problems a + + align:start position:0% +often uses to solve a lot of problems a + + + align:start position:0% +often uses to solve a lot of problems a +very common mechanic in games is + + align:start position:0% +very common mechanic in games is + + + align:start position:0% +very common mechanic in games is +shooting so a mechanic is basically an + + align:start position:0% +shooting so a mechanic is basically an + + + align:start position:0% +shooting so a mechanic is basically an +in-game action it's a game design term + + align:start position:0% +in-game action it's a game design term + + + align:start position:0% +in-game action it's a game design term +for for that any other + + align:start position:0% + + + + align:start position:0% + +questions okay then so um we're hoping + + align:start position:0% +questions okay then so um we're hoping + + + align:start position:0% +questions okay then so um we're hoping +that this project will teach you to do + + align:start position:0% +that this project will teach you to do + + + align:start position:0% +that this project will teach you to do +prototyping which is a skill we will + + align:start position:0% +prototyping which is a skill we will + + + align:start position:0% +prototyping which is a skill we will +hope you will use again in projects + + align:start position:0% +hope you will use again in projects + + + align:start position:0% +hope you will use again in projects +three and four and we expect you to and + + align:start position:0% +three and four and we expect you to and + + + align:start position:0% +three and four and we expect you to and +we're also going to introduce our very + + align:start position:0% +we're also going to introduce our very + + + align:start position:0% +we're also going to introduce our very +very first project management tool which + + align:start position:0% +very first project management tool which + + + align:start position:0% +very first project management tool which +is the design change log which is + + align:start position:0% +is the design change log which is + + + align:start position:0% +is the design change log which is +hopefully a reasonably quick and concise + + align:start position:0% +hopefully a reasonably quick and concise + + + align:start position:0% +hopefully a reasonably quick and concise +way to record the changes your team + + align:start position:0% +way to record the changes your team + + + align:start position:0% +way to record the changes your team +makes to your design as your design + + align:start position:0% +makes to your design as your design + + + align:start position:0% +makes to your design as your design +evolves and helps you keep a kind of a + + align:start position:0% +evolves and helps you keep a kind of a + + + align:start position:0% +evolves and helps you keep a kind of a +group memory of what you've done so you + + align:start position:0% +group memory of what you've done so you + + + align:start position:0% +group memory of what you've done so you +don't end up doing the same things + + align:start position:0% +don't end up doing the same things + + + align:start position:0% +don't end up doing the same things +again um but that's not actually all + + align:start position:0% +again um but that's not actually all + + + align:start position:0% +again um but that's not actually all +we're hoping to do that's just the + + align:start position:0% +we're hoping to do that's just the + + + align:start position:0% +we're hoping to do that's just the +official goals we're also using it to + + align:start position:0% +official goals we're also using it to + + + align:start position:0% +official goals we're also using it to +give you a small group experience + + align:start position:0% +give you a small group experience + + + align:start position:0% +give you a small group experience +working in teams on a creative project + + align:start position:0% +working in teams on a creative project + + + align:start position:0% +working in teams on a creative project +um the size this is this is the first + + align:start position:0% +um the size this is this is the first + + + align:start position:0% +um the size this is this is the first +and last time you'll be in nice small + + align:start position:0% +and last time you'll be in nice small + + + align:start position:0% +and last time you'll be in nice small +tight teams of three people project two + + align:start position:0% +tight teams of three people project two + + + align:start position:0% +tight teams of three people project two +we we boost you all the way up to six + + align:start position:0% +we we boost you all the way up to six + + + align:start position:0% +we we boost you all the way up to six +people and by the end we're going to be + + align:start position:0% +people and by the end we're going to be + + + align:start position:0% +people and by the end we're going to be +an eight person teams and you're going + + align:start position:0% +an eight person teams and you're going + + + align:start position:0% +an eight person teams and you're going +to get to see just how more complex it + + align:start position:0% +to get to see just how more complex it + + + align:start position:0% +to get to see just how more complex it +gets working with bigger and bigger + + align:start position:0% +gets working with bigger and bigger + + + align:start position:0% +gets working with bigger and bigger +groups but we're going to start un ni + + align:start position:0% +groups but we're going to start un ni + + + align:start position:0% +groups but we're going to start un ni +and we're going to start you small for + + align:start position:0% +and we're going to start you small for + + + align:start position:0% +and we're going to start you small for +your first project so you get a chance + + align:start position:0% +your first project so you get a chance + + + align:start position:0% +your first project so you get a chance +to learn how to + + align:start position:0% +to learn how to + + + align:start position:0% +to learn how to +communicate um we're going to teach + + align:start position:0% +communicate um we're going to teach + + + align:start position:0% +communicate um we're going to teach +brainstorming we're going to expect you + + align:start position:0% +brainstorming we're going to expect you + + + align:start position:0% +brainstorming we're going to expect you +to brainstorm again for projects three + + align:start position:0% +to brainstorm again for projects three + + + align:start position:0% +to brainstorm again for projects three +and four although we're not going to + + align:start position:0% +and four although we're not going to + + + align:start position:0% +and four although we're not going to +formally tell you where to do it or when + + align:start position:0% +formally tell you where to do it or when + + + align:start position:0% +formally tell you where to do it or when +to do it we're just going to expect you + + align:start position:0% +to do it we're just going to expect you + + + align:start position:0% +to do it we're just going to expect you +when you your groups to start going over + + align:start position:0% +when you your groups to start going over + + + align:start position:0% +when you your groups to start going over +ideas to use the techniques we've taught + + align:start position:0% +ideas to use the techniques we've taught + + + align:start position:0% +ideas to use the techniques we've taught +you in this project to do that on your + + align:start position:0% +you in this project to do that on your + + + align:start position:0% +you in this project to do that on your +own um we're also going to teach you and + + align:start position:0% +own um we're also going to teach you and + + + align:start position:0% +own um we're also going to teach you and +I think the most important thing here is + + align:start position:0% +I think the most important thing here is + + + align:start position:0% +I think the most important thing here is +working fast you got one week to do this + + align:start position:0% +working fast you got one week to do this + + + align:start position:0% +working fast you got one week to do this +project your final project the final + + align:start position:0% +project your final project the final + + + align:start position:0% +project your final project the final +version and the project reports on this + + align:start position:0% +version and the project reports on this + + + align:start position:0% +version and the project reports on this +are due next Monday you're going to get + + align:start position:0% +are due next Monday you're going to get + + + align:start position:0% +are due next Monday you're going to get +some time in class but unfortunately we + + align:start position:0% +some time in class but unfortunately we + + + align:start position:0% +some time in class but unfortunately we +have a lot to say to teach you + + align:start position:0% +have a lot to say to teach you + + + align:start position:0% +have a lot to say to teach you +everything you want to do with this + + align:start position:0% +everything you want to do with this + + + align:start position:0% +everything you want to do with this +class so you're not going to get all of + + align:start position:0% +class so you're not going to get all of + + + align:start position:0% +class so you're not going to get all of +class you're get a small portion of + + align:start position:0% +class you're get a small portion of + + + align:start position:0% +class you're get a small portion of +class Monday and Wednesday and we're + + align:start position:0% +class Monday and Wednesday and we're + + + align:start position:0% +class Monday and Wednesday and we're +going to expect to be able to play + + align:start position:0% +going to expect to be able to play + + + align:start position:0% +going to expect to be able to play +something on Wednesday in class when we + + align:start position:0% +something on Wednesday in class when we + + + align:start position:0% +something on Wednesday in class when we +looking hopefully you'll be running play + + align:start position:0% +looking hopefully you'll be running play + + + align:start position:0% +looking hopefully you'll be running play +tests we expect you have something + + align:start position:0% +tests we expect you have something + + + align:start position:0% +tests we expect you have something +working so you're going to have to learn + + align:start position:0% +working so you're going to have to learn + + + align:start position:0% +working so you're going to have to learn +how to work fast how do you get those + + align:start position:0% +how to work fast how do you get those + + + align:start position:0% +how to work fast how do you get those +ideas out of your head onto paper and + + align:start position:0% +ideas out of your head onto paper and + + + align:start position:0% +ideas out of your head onto paper and +usable + + align:start position:0% +usable + + + align:start position:0% +usable +quickly and finally um the prototypes + + align:start position:0% +quickly and finally um the prototypes + + + align:start position:0% +quickly and finally um the prototypes +you're Ching here are going to move on + + align:start position:0% +you're Ching here are going to move on + + + align:start position:0% +you're Ching here are going to move on +to project two probably about half of + + align:start position:0% +to project two probably about half of + + + align:start position:0% +to project two probably about half of +them um your team sizes are going to be + + align:start position:0% +them um your team sizes are going to be + + + align:start position:0% +them um your team sizes are going to be +shrinking so we'll be doing fewer of + + align:start position:0% +shrinking so we'll be doing fewer of + + + align:start position:0% +shrinking so we'll be doing fewer of +them um we the instructors are going to + + align:start position:0% +them um we the instructors are going to + + + align:start position:0% +them um we the instructors are going to +take a look at the prototypes as they + + align:start position:0% +take a look at the prototypes as they + + + align:start position:0% +take a look at the prototypes as they +come in both during the presentations + + align:start position:0% +come in both during the presentations + + + align:start position:0% +come in both during the presentations +and during the playable U play testing + + align:start position:0% +and during the playable U play testing + + + align:start position:0% +and during the playable U play testing +sessions and we're going to decide which + + align:start position:0% +sessions and we're going to decide which + + + align:start position:0% +sessions and we're going to decide which +of those projects we think really do + + align:start position:0% +of those projects we think really do + + + align:start position:0% +of those projects we think really do +have the potential to go on to be + + align:start position:0% +have the potential to go on to be + + + align:start position:0% +have the potential to go on to be +project to if your prototype isn't + + align:start position:0% +project to if your prototype isn't + + + align:start position:0% +project to if your prototype isn't +chosen to go on that doesn't mean it's + + align:start position:0% +chosen to go on that doesn't mean it's + + + align:start position:0% +chosen to go on that doesn't mean it's +not a good prototype um we may choose to + + align:start position:0% +not a good prototype um we may choose to + + + align:start position:0% +not a good prototype um we may choose to +exclude things because we think the + + align:start position:0% +exclude things because we think the + + + align:start position:0% +exclude things because we think the +scope is too big for a two-e project um + + align:start position:0% +scope is too big for a two-e project um + + + align:start position:0% +scope is too big for a two-e project um +we think it's a little too complicated + + align:start position:0% +we think it's a little too complicated + + + align:start position:0% +we think it's a little too complicated +to try and communicate the ideas we may + + align:start position:0% +to try and communicate the ideas we may + + + align:start position:0% +to try and communicate the ideas we may +also think that um + + align:start position:0% +also think that um + + + align:start position:0% +also think that um +um there are other projects that sort of + + align:start position:0% +um there are other projects that sort of + + + align:start position:0% +um there are other projects that sort of +nailed the requirements better so your + + align:start position:0% +nailed the requirements better so your + + + align:start position:0% +nailed the requirements better so your +project your prototype hasn't failed if + + align:start position:0% +project your prototype hasn't failed if + + + align:start position:0% +project your prototype hasn't failed if +it doesn't move on it's just that there + + align:start position:0% +it doesn't move on it's just that there + + + align:start position:0% +it doesn't move on it's just that there +were other ones that we think fit all + + align:start position:0% +were other ones that we think fit all + + + align:start position:0% +were other ones that we think fit all +the constraints better um and all the + + align:start position:0% +the constraints better um and all the + + + align:start position:0% +the constraints better um and all the +prototypes are important to + + align:start position:0% +prototypes are important to + + + align:start position:0% +prototypes are important to +do all right um so that's + + align:start position:0% +do all right um so that's + + + align:start position:0% +do all right um so that's +that okay um so the breakdown of the + + align:start position:0% +that okay um so the breakdown of the + + + align:start position:0% +that okay um so the breakdown of the +project is um today we'll be forming + + align:start position:0% +project is um today we'll be forming + + + align:start position:0% +project is um today we'll be forming +teams doing brainstorming and getting + + align:start position:0% +teams doing brainstorming and getting + + + align:start position:0% +teams doing brainstorming and getting +started working on things um we will do + + align:start position:0% +started working on things um we will do + + + align:start position:0% +started working on things um we will do +the first formal play testing session um + + align:start position:0% +the first formal play testing session um + + + align:start position:0% +the first formal play testing session um +on + + align:start position:0% +on + + + align:start position:0% +on +Wednesday Monday everything gets turned + + align:start position:0% +Wednesday Monday everything gets turned + + + align:start position:0% +Wednesday Monday everything gets turned +in and including your change + + align:start position:0% +in and including your change + + + align:start position:0% +in and including your change +log and a presentation the vision + + align:start position:0% +log and a presentation the vision + + + align:start position:0% +log and a presentation the vision +document we will be making in class so + + align:start position:0% +document we will be making in class so + + + align:start position:0% +document we will be making in class so +don't worry about that because we'll be + + align:start position:0% +don't worry about that because we'll be + + + align:start position:0% +don't worry about that because we'll be +explaining what a vision document is and + + align:start position:0% +explaining what a vision document is and + + + align:start position:0% +explaining what a vision document is and +how you make one um in class so don't + + align:start position:0% +how you make one um in class so don't + + + align:start position:0% +how you make one um in class so don't +worry too much about that that + + align:start position:0% +worry too much about that that + + + align:start position:0% +worry too much about that that +particular that + + align:start position:0% +particular that + + + align:start position:0% +particular that +requirement + + align:start position:0% +requirement + + + align:start position:0% +requirement +um the presentation the one minute pitch + + align:start position:0% +um the presentation the one minute pitch + + + align:start position:0% +um the presentation the one minute pitch +will be one of the things that helps + + align:start position:0% +will be one of the things that helps + + + align:start position:0% +will be one of the things that helps +sell your classmates on joining your + + align:start position:0% +sell your classmates on joining your + + + align:start position:0% +sell your classmates on joining your +team and will be one of the things that + + align:start position:0% +team and will be one of the things that + + + align:start position:0% +team and will be one of the things that +we use to decide whether or not we think + + align:start position:0% +we use to decide whether or not we think + + + align:start position:0% +we use to decide whether or not we think +you guys have a good enough core idea + + align:start position:0% +you guys have a good enough core idea + + + align:start position:0% +you guys have a good enough core idea +and enough core excitement to move that + + align:start position:0% +and enough core excitement to move that + + + align:start position:0% +and enough core excitement to move that +prototype forward so um it's actually + + align:start position:0% +prototype forward so um it's actually + + + align:start position:0% +prototype forward so um it's actually +pretty important and remember it needs + + align:start position:0% +pretty important and remember it needs + + + align:start position:0% +pretty important and remember it needs +to be one minute we're going to have + + align:start position:0% +to be one minute we're going to have + + + align:start position:0% +to be one minute we're going to have +like 10 groups up + + align:start position:0% +like 10 groups up + + + align:start position:0% +like 10 groups up +pitching so it's going to have to be + + align:start position:0% +pitching so it's going to have to be + + + align:start position:0% +pitching so it's going to have to be +fast + + align:start position:0% + + + + align:start position:0% + +um finally design change logs um which + + align:start position:0% +um finally design change logs um which + + + align:start position:0% +um finally design change logs um which +some of you may never have heard about + + align:start position:0% +some of you may never have heard about + + + align:start position:0% +some of you may never have heard about +whoa oh no my slide it isn't there oh + + align:start position:0% +whoa oh no my slide it isn't there oh + + + align:start position:0% +whoa oh no my slide it isn't there oh +because that screen's been because this + + align:start position:0% +because that screen's been because this + + + align:start position:0% +because that screen's been because this +one isn't aha oh boy let me let me + + align:start position:0% +one isn't aha oh boy let me let me + + + align:start position:0% +one isn't aha oh boy let me let me +restart this this + + align:start position:0% +restart this this + + + align:start position:0% +restart this this +presentation so who here has used a + + align:start position:0% +presentation so who here has used a + + + align:start position:0% +presentation so who here has used a +design change log before because if + + align:start position:0% +design change log before because if + + + align:start position:0% +design change log before because if +you've taken 608 I know you have all + + align:start position:0% +you've taken 608 I know you have all + + + align:start position:0% +you've taken 608 I know you have all +right so those are your experts if you + + align:start position:0% +right so those are your experts if you + + + align:start position:0% +right so those are your experts if you +have one of those people on your team + + align:start position:0% +have one of those people on your team + + + align:start position:0% +have one of those people on your team +you're in good shape talk to them um but + + align:start position:0% +you're in good shape talk to them um but + + + align:start position:0% +you're in good shape talk to them um but +essentially what a design change log is + + align:start position:0% +essentially what a design change log is + + + align:start position:0% +essentially what a design change log is +it's it's actually really simple it's + + align:start position:0% +it's it's actually really simple it's + + + align:start position:0% +it's it's actually really simple it's +three table it's a column it's a it's a + + align:start position:0% +three table it's a column it's a it's a + + + align:start position:0% +three table it's a column it's a it's a +table three row three columns you got a + + align:start position:0% +table three row three columns you got a + + + align:start position:0% +table three row three columns you got a +date you've got some action you made on + + align:start position:0% +date you've got some action you made on + + + align:start position:0% +date you've got some action you made on +your design to change it in some way and + + align:start position:0% +your design to change it in some way and + + + align:start position:0% +your design to change it in some way and +then you've got the reason why you made + + align:start position:0% +then you've got the reason why you made + + + align:start position:0% +then you've got the reason why you made +the change and every time you make a + + align:start position:0% +the change and every time you make a + + + align:start position:0% +the change and every time you make a +significant change to your to your + + align:start position:0% +significant change to your to your + + + align:start position:0% +significant change to your to your +project and or and or every day you work + + align:start position:0% +project and or and or every day you work + + + align:start position:0% +project and or and or every day you work +on your project you make another entry + + align:start position:0% +on your project you make another entry + + + align:start position:0% +on your project you make another entry +so you can so that your team and the + + align:start position:0% +so you can so that your team and the + + + align:start position:0% +so you can so that your team and the +people working on it and the people + + align:start position:0% +people working on it and the people + + + align:start position:0% +people working on it and the people +looking at your project to see where it + + align:start position:0% +looking at your project to see where it + + + align:start position:0% +looking at your project to see where it +is now can see why you made the + + align:start position:0% +is now can see why you made the + + + align:start position:0% +is now can see why you made the +decisions you made and what decisions + + align:start position:0% +decisions you made and what decisions + + + align:start position:0% +decisions you made and what decisions +you made what features you dropped what + + align:start position:0% +you made what features you dropped what + + + align:start position:0% +you made what features you dropped what +features you added what problems you + + align:start position:0% +features you added what problems you + + + align:start position:0% +features you added what problems you +were trying to solve when you made those + + align:start position:0% +were trying to solve when you made those + + + align:start position:0% +were trying to solve when you made those +changes um yeah I was probably anyway so + + align:start position:0% +changes um yeah I was probably anyway so + + + align:start position:0% +changes um yeah I was probably anyway so +that is in fact a design change log + + align:start position:0% +that is in fact a design change log + + + align:start position:0% +that is in fact a design change log +there's an example of one at the bottom + + align:start position:0% +there's an example of one at the bottom + + + align:start position:0% +there's an example of one at the bottom +of the problem one handout of the of the + + align:start position:0% +of the problem one handout of the of the + + + align:start position:0% +of the problem one handout of the of the +uh there's an example of one at the + + align:start position:0% +uh there's an example of one at the + + + align:start position:0% +uh there's an example of one at the +project one hand out um so you can see + + align:start position:0% +project one hand out um so you can see + + + align:start position:0% +project one hand out um so you can see +an example there are there any + + align:start position:0% + + + + align:start position:0% + +questions hearing no + + align:start position:0% +questions hearing no + + + align:start position:0% +questions hearing no +takers I hand you over to Philip for + + align:start position:0% +takers I hand you over to Philip for + + + align:start position:0% +takers I hand you over to Philip for +brainstorming + + align:start position:0% +brainstorming + + + align:start position:0% +brainstorming +okay all right let's talk about + + align:start position:0% +okay all right let's talk about + + + align:start position:0% +okay all right let's talk about +brainstorming how many of you have done + + align:start position:0% +brainstorming how many of you have done + + + align:start position:0% +brainstorming how many of you have done +brainstorming in any class high school + + align:start position:0% +brainstorming in any class high school + + + align:start position:0% +brainstorming in any class high school +before high school wow okay all right + + align:start position:0% +before high school wow okay all right + + + align:start position:0% +before high school wow okay all right +okay so it's it's it's it's a term that + + align:start position:0% +okay so it's it's it's it's a term that + + + align:start position:0% +okay so it's it's it's it's a term that +gets bandied around a lot let me see + + align:start position:0% +gets bandied around a lot let me see + + + align:start position:0% +gets bandied around a lot let me see +awesome um however there is a problem + + align:start position:0% +awesome um however there is a problem + + + align:start position:0% +awesome um however there is a problem +with brainstorming in that a lot of + + align:start position:0% +with brainstorming in that a lot of + + + align:start position:0% +with brainstorming in that a lot of +people have practiced it without + + align:start position:0% +people have practiced it without + + + align:start position:0% +people have practiced it without +actually knowing why certain things are + + align:start position:0% +actually knowing why certain things are + + + align:start position:0% +actually knowing why certain things are +done in a certain way and as a result of + + align:start position:0% +done in a certain way and as a result of + + + align:start position:0% +done in a certain way and as a result of +that may actually be doing it + + align:start position:0% +that may actually be doing it + + + align:start position:0% +that may actually be doing it +incorrectly we have an excerpt of an + + align:start position:0% +incorrectly we have an excerpt of an + + + align:start position:0% +incorrectly we have an excerpt of an +article uh sorry um a chapter from a + + align:start position:0% +article uh sorry um a chapter from a + + + align:start position:0% +article uh sorry um a chapter from a +book called applying imagination which + + align:start position:0% +book called applying imagination which + + + align:start position:0% +book called applying imagination which +is written by Alex Osborne who is the + + align:start position:0% +is written by Alex Osborne who is the + + + align:start position:0% +is written by Alex Osborne who is the +guy who actually came up with the term + + align:start position:0% +guy who actually came up with the term + + + align:start position:0% +guy who actually came up with the term +brainstorming and the practice of it he + + align:start position:0% +brainstorming and the practice of it he + + + align:start position:0% +brainstorming and the practice of it he +worked in advertising and he uh you know + + align:start position:0% +worked in advertising and he uh you know + + + align:start position:0% +worked in advertising and he uh you know +he he has lamented uh since he wrote + + align:start position:0% +he he has lamented uh since he wrote + + + align:start position:0% +he he has lamented uh since he wrote +that book that a lot of people kind of + + align:start position:0% +that book that a lot of people kind of + + + align:start position:0% +that book that a lot of people kind of +like liked the output of brainstorming + + align:start position:0% +like liked the output of brainstorming + + + align:start position:0% +like liked the output of brainstorming +but didn't really understand the + + align:start position:0% +but didn't really understand the + + + align:start position:0% +but didn't really understand the +practice of it so I'm going to try to S + + align:start position:0% +practice of it so I'm going to try to S + + + align:start position:0% +practice of it so I'm going to try to S +of start from first principes so that + + align:start position:0% +of start from first principes so that + + + align:start position:0% +of start from first principes so that +you understand why brainstorming is and + + align:start position:0% +you understand why brainstorming is and + + + align:start position:0% +you understand why brainstorming is and +how it's supposed to be working and then + + align:start position:0% +how it's supposed to be working and then + + + align:start position:0% +how it's supposed to be working and then +hopefully you can sort of like get the + + align:start position:0% +hopefully you can sort of like get the + + + align:start position:0% +hopefully you can sort of like get the +the benefits of it without maybe say + + align:start position:0% +the benefits of it without maybe say + + + align:start position:0% +the benefits of it without maybe say +overstating its uh it its power um now + + align:start position:0% +overstating its uh it its power um now + + + align:start position:0% +overstating its uh it its power um now +the main reason why we're doing brain + + align:start position:0% +the main reason why we're doing brain + + + align:start position:0% +the main reason why we're doing brain +storing in groups you will hear people + + align:start position:0% +storing in groups you will hear people + + + align:start position:0% +storing in groups you will hear people +out there in the game industry saying + + align:start position:0% +out there in the game industry saying + + + align:start position:0% +out there in the game industry saying +that brainstorming is not necessarily + + align:start position:0% +that brainstorming is not necessarily + + + align:start position:0% +that brainstorming is not necessarily +always the best way to be able to come + + align:start position:0% +always the best way to be able to come + + + align:start position:0% +always the best way to be able to come +up with an idea for a game um however in + + align:start position:0% +up with an idea for a game um however in + + + align:start position:0% +up with an idea for a game um however in +this class in particular and in a lot of + + align:start position:0% +this class in particular and in a lot of + + + align:start position:0% +this class in particular and in a lot of +video game design outside of this class + + align:start position:0% +video game design outside of this class + + + align:start position:0% +video game design outside of this class +game design is coordinated creative + + align:start position:0% +game design is coordinated creative + + + align:start position:0% +game design is coordinated creative +collaboration with involving different + + align:start position:0% +collaboration with involving different + + + align:start position:0% +collaboration with involving different +skilled workers and if you're going to + + align:start position:0% +skilled workers and if you're going to + + + align:start position:0% +skilled workers and if you're going to +this going to be the first time that + + align:start position:0% +this going to be the first time that + + + align:start position:0% +this going to be the first time that +you're going to to work with a team you + + align:start position:0% +you're going to to work with a team you + + + align:start position:0% +you're going to to work with a team you +need to sort of understand who are the + + align:start position:0% +need to sort of understand who are the + + + align:start position:0% +need to sort of understand who are the +people who you might be working with + + align:start position:0% +people who you might be working with + + + align:start position:0% +people who you might be working with +brainstorming if nothing else can be a + + align:start position:0% +brainstorming if nothing else can be a + + + align:start position:0% +brainstorming if nothing else can be a +really really good way to just be able + + align:start position:0% +really really good way to just be able + + + align:start position:0% +really really good way to just be able +to get a sense of who it is that you're + + align:start position:0% +to get a sense of who it is that you're + + + align:start position:0% +to get a sense of who it is that you're +going to be working with and when we + + align:start position:0% +going to be working with and when we + + + align:start position:0% +going to be working with and when we +start forming up teams uh you're not + + align:start position:0% +start forming up teams uh you're not + + + align:start position:0% +start forming up teams uh you're not +going to necessarily be able to choose + + align:start position:0% +going to necessarily be able to choose + + + align:start position:0% +going to necessarily be able to choose +who who you're brainstorming with so you + + align:start position:0% +who who you're brainstorming with so you + + + align:start position:0% +who who you're brainstorming with so you +want to be able to get a quick read of + + align:start position:0% +want to be able to get a quick read of + + + align:start position:0% +want to be able to get a quick read of +uh of their ideas and what their + + align:start position:0% +uh of their ideas and what their + + + align:start position:0% +uh of their ideas and what their +interest are and maybe decide hey this + + align:start position:0% +interest are and maybe decide hey this + + + align:start position:0% +interest are and maybe decide hey this +is a person that I'm going to do project + + align:start position:0% +is a person that I'm going to do project + + + align:start position:0% +is a person that I'm going to do project +one with later on however there are very + + align:start position:0% +one with later on however there are very + + + align:start position:0% +one with later on however there are very +strong social pressures of being + + align:start position:0% +strong social pressures of being + + + align:start position:0% +strong social pressures of being +imaginative in a collaborative + + align:start position:0% +imaginative in a collaborative + + + align:start position:0% +imaginative in a collaborative +environment uh you know especially here + + align:start position:0% +environment uh you know especially here + + + align:start position:0% +environment uh you know especially here +in MIT uh there are a lot of there's a + + align:start position:0% +in MIT uh there are a lot of there's a + + + align:start position:0% +in MIT uh there are a lot of there's a +lot of pressure to sort of like hold + + align:start position:0% +lot of pressure to sort of like hold + + + align:start position:0% +lot of pressure to sort of like hold +back your ideas or maybe not say what + + align:start position:0% +back your ideas or maybe not say what + + + align:start position:0% +back your ideas or maybe not say what +what what what's coming into your mind + + align:start position:0% +what what what's coming into your mind + + + align:start position:0% +what what what's coming into your mind +because you think you know that's kind + + align:start position:0% +because you think you know that's kind + + + align:start position:0% +because you think you know that's kind +of dumb you know other people are going + + align:start position:0% +of dumb you know other people are going + + + align:start position:0% +of dumb you know other people are going +to think that I'm stupid or anything + + align:start position:0% +to think that I'm stupid or anything + + + align:start position:0% +to think that I'm stupid or anything +like that and brainstorming has certain + + align:start position:0% +like that and brainstorming has certain + + + align:start position:0% +like that and brainstorming has certain +practices to be able to get you pass + + align:start position:0% +practices to be able to get you pass + + + align:start position:0% +practices to be able to get you pass +that so there are four principles of + + align:start position:0% +that so there are four principles of + + + align:start position:0% +that so there are four principles of +brainstorming this is high Templar just + + align:start position:0% +brainstorming this is high Templar just + + + align:start position:0% +brainstorming this is high Templar just +doing this thing um uh he was uh this + + align:start position:0% +doing this thing um uh he was uh this + + + align:start position:0% +doing this thing um uh he was uh this +was this was the four principles laid + + align:start position:0% +was this was the four principles laid + + + align:start position:0% +was this was the four principles laid +out by Alex Osborne and he was + + align:start position:0% +out by Alex Osborne and he was + + + align:start position:0% +out by Alex Osborne and he was +advertising uh man at bbdo which is a + + align:start position:0% +advertising uh man at bbdo which is a + + + align:start position:0% +advertising uh man at bbdo which is a +very very large advertising agency um + + align:start position:0% +very very large advertising agency um + + + align:start position:0% +very very large advertising agency um +and there are certain similarities in ad + + align:start position:0% +and there are certain similarities in ad + + + align:start position:0% +and there are certain similarities in ad +marketing and video game design right + + align:start position:0% +marketing and video game design right + + + align:start position:0% +marketing and video game design right +you can produce ads you can produce + + align:start position:0% +you can produce ads you can produce + + + align:start position:0% +you can produce ads you can produce +marketing you can produce games without + + align:start position:0% +marketing you can produce games without + + + align:start position:0% +marketing you can produce games without +necessarily saying yes we solved the + + align:start position:0% +necessarily saying yes we solved the + + + align:start position:0% +necessarily saying yes we solved the +problem uh there's a lot of different + + align:start position:0% +problem uh there's a lot of different + + + align:start position:0% +problem uh there's a lot of different +solutions for exactly the same problem + + align:start position:0% +solutions for exactly the same problem + + + align:start position:0% +solutions for exactly the same problem +and advertising is trying to get people + + align:start position:0% +and advertising is trying to get people + + + align:start position:0% +and advertising is trying to get people +to pay attention to the ad and maybe buy + + align:start position:0% +to pay attention to the ad and maybe buy + + + align:start position:0% +to pay attention to the ad and maybe buy +stuff uh in video games it's you know + + align:start position:0% +stuff uh in video games it's you know + + + align:start position:0% +stuff uh in video games it's you know +trying to create an entertaining + + align:start position:0% +trying to create an entertaining + + + align:start position:0% +trying to create an entertaining +experience for somebody else millions of + + align:start position:0% +experience for somebody else millions of + + + align:start position:0% +experience for somebody else millions of +ways to be able to accomplish that so + + align:start position:0% +ways to be able to accomplish that so + + + align:start position:0% +ways to be able to accomplish that so +we're not looking for like here's a + + align:start position:0% +we're not looking for like here's a + + + align:start position:0% +we're not looking for like here's a +engineering solution to engineering + + align:start position:0% +engineering solution to engineering + + + align:start position:0% +engineering solution to engineering +problem where there you know if the if + + align:start position:0% +problem where there you know if the if + + + align:start position:0% +problem where there you know if the if +if the thing doesn't explode you know + + align:start position:0% +if the thing doesn't explode you know + + + align:start position:0% +if the thing doesn't explode you know +you've done a good job that's a sort of + + align:start position:0% +you've done a good job that's a sort of + + + align:start position:0% +you've done a good job that's a sort of +like very easy metric to be able to + + align:start position:0% +like very easy metric to be able to + + + align:start position:0% +like very easy metric to be able to +measure success for for games for + + align:start position:0% +measure success for for games for + + + align:start position:0% +measure success for for games for +advertising not so + + align:start position:0% +advertising not so + + + align:start position:0% +advertising not so +easy so here's the first principle no + + align:start position:0% +easy so here's the first principle no + + + align:start position:0% +easy so here's the first principle no +criticism how many of you been in a + + align:start position:0% +criticism how many of you been in a + + + align:start position:0% +criticism how many of you been in a +brainstorm session where like you set + + align:start position:0% +brainstorm session where like you set + + + align:start position:0% +brainstorm session where like you set +your idea and then somebody said + + align:start position:0% +your idea and then somebody said + + + align:start position:0% +your idea and then somebody said +oh okay all right I see some hands go up + + align:start position:0% +oh okay all right I see some hands go up + + + align:start position:0% +oh okay all right I see some hands go up +all right okay so this is the most + + align:start position:0% +all right okay so this is the most + + + align:start position:0% +all right okay so this is the most +important rule of a brainstorm session + + align:start position:0% +important rule of a brainstorm session + + + align:start position:0% +important rule of a brainstorm session +if you do not stick to this rule if + + align:start position:0% +if you do not stick to this rule if + + + align:start position:0% +if you do not stick to this rule if +everybody around the group doesn't stick + + align:start position:0% +everybody around the group doesn't stick + + + align:start position:0% +everybody around the group doesn't stick +to this rule you can ruin the entire + + align:start position:0% +to this rule you can ruin the entire + + + align:start position:0% +to this rule you can ruin the entire +session the whole session can just + + align:start position:0% +session the whole session can just + + + align:start position:0% +session the whole session can just +become worthless uh basically you can + + align:start position:0% +become worthless uh basically you can + + + align:start position:0% +become worthless uh basically you can +give positive feedback it says like you + + align:start position:0% +give positive feedback it says like you + + + align:start position:0% +give positive feedback it says like you +know thanks for the idea um you know WR + + align:start position:0% +know thanks for the idea um you know WR + + + align:start position:0% +know thanks for the idea um you know WR +just simply writing it down is positive + + align:start position:0% +just simply writing it down is positive + + + align:start position:0% +just simply writing it down is positive +feedback of we've received your idea but + + align:start position:0% +feedback of we've received your idea but + + + align:start position:0% +feedback of we've received your idea but +you want to to uh hold back on sort of + + align:start position:0% +you want to to uh hold back on sort of + + + align:start position:0% +you want to to uh hold back on sort of +adverse judgment or any kind of negative + + align:start position:0% +adverse judgment or any kind of negative + + + align:start position:0% +adverse judgment or any kind of negative +reinfor ment uh you can share that after + + align:start position:0% +reinfor ment uh you can share that after + + + align:start position:0% +reinfor ment uh you can share that after +the brainstorm session you just don't + + align:start position:0% +the brainstorm session you just don't + + + align:start position:0% +the brainstorm session you just don't +want to do that during the brainstorm + + align:start position:0% +want to do that during the brainstorm + + + align:start position:0% +want to do that during the brainstorm +session because it inhibits the process + + align:start position:0% +session because it inhibits the process + + + align:start position:0% +session because it inhibits the process +of creating new ideas um again that's a + + align:start position:0% +of creating new ideas um again that's a + + + align:start position:0% +of creating new ideas um again that's a +sort of like professional shame and it's + + align:start position:0% +sort of like professional shame and it's + + + align:start position:0% +sort of like professional shame and it's +uh especially in a place here like MIT + + align:start position:0% +uh especially in a place here like MIT + + + align:start position:0% +uh especially in a place here like MIT +but also if you go out into the + + align:start position:0% +but also if you go out into the + + + align:start position:0% +but also if you go out into the +corporate world this idea of you don't + + align:start position:0% +corporate world this idea of you don't + + + align:start position:0% +corporate world this idea of you don't +want to look bad and then you can't have + + align:start position:0% +want to look bad and then you can't have + + + align:start position:0% +want to look bad and then you can't have +that in your head to have a proper + + align:start position:0% +that in your head to have a proper + + + align:start position:0% +that in your head to have a proper +brainstorming session if you're worried + + align:start position:0% +brainstorming session if you're worried + + + align:start position:0% +brainstorming session if you're worried +about how your ideas are going to be + + align:start position:0% +about how your ideas are going to be + + + align:start position:0% +about how your ideas are going to be +taken then you're not actually + + align:start position:0% +taken then you're not actually + + + align:start position:0% +taken then you're not actually +generating ideas at the speed that you + + align:start position:0% +generating ideas at the speed that you + + + align:start position:0% +generating ideas at the speed that you +need to be uh so you need to be able to + + align:start position:0% +need to be uh so you need to be able to + + + align:start position:0% +need to be uh so you need to be able to +let your entire group know that we now + + align:start position:0% +let your entire group know that we now + + + align:start position:0% +let your entire group know that we now +have total freedom to explore all + + align:start position:0% +have total freedom to explore all + + + align:start position:0% +have total freedom to explore all +territories whatever idea you generate + + align:start position:0% +territories whatever idea you generate + + + align:start position:0% +territories whatever idea you generate +we're going to write down and then we'll + + align:start position:0% +we're going to write down and then we'll + + + align:start position:0% +we're going to write down and then we'll +figure out which are the good ideas + + align:start position:0% +figure out which are the good ideas + + + align:start position:0% +figure out which are the good ideas +after we've generated all of these + + align:start position:0% +after we've generated all of these + + + align:start position:0% +after we've generated all of these +ideas secondly you kind of want to be + + align:start position:0% +ideas secondly you kind of want to be + + + align:start position:0% +ideas secondly you kind of want to be +free whealing um typically know the the + + align:start position:0% +free whealing um typically know the the + + + align:start position:0% +free whealing um typically know the the +crazier the idea you know the better + + align:start position:0% +crazier the idea you know the better + + + align:start position:0% +crazier the idea you know the better +it's easier to be able to teame down a + + align:start position:0% +it's easier to be able to teame down a + + + align:start position:0% +it's easier to be able to teame down a +crazy idea than to sort of take a fairly + + align:start position:0% +crazy idea than to sort of take a fairly + + + align:start position:0% +crazy idea than to sort of take a fairly +you know unambitious idea and scale it + + align:start position:0% +you know unambitious idea and scale it + + + align:start position:0% +you know unambitious idea and scale it +up um so typically uh you will get your + + align:start position:0% +up um so typically uh you will get your + + + align:start position:0% +up um so typically uh you will get your +best ideas from some sort of pipe dream + + align:start position:0% +best ideas from some sort of pipe dream + + + align:start position:0% +best ideas from some sort of pipe dream +or blue moon idea something that's out + + align:start position:0% +or blue moon idea something that's out + + + align:start position:0% +or blue moon idea something that's out +of scope something that's unfeasible and + + align:start position:0% +of scope something that's unfeasible and + + + align:start position:0% +of scope something that's unfeasible and +then you sort of scale it down into the + + align:start position:0% +then you sort of scale it down into the + + + align:start position:0% +then you sort of scale it down into the +thing that is actually feasible so go + + align:start position:0% +thing that is actually feasible so go + + + align:start position:0% +thing that is actually feasible so go +ahead and shoot for the moon shoot for + + align:start position:0% +ahead and shoot for the moon shoot for + + + align:start position:0% +ahead and shoot for the moon shoot for +the game that you can't possibly develop + + align:start position:0% +the game that you can't possibly develop + + + align:start position:0% +the game that you can't possibly develop +uh in the next week or in the next + + align:start position:0% +uh in the next week or in the next + + + align:start position:0% +uh in the next week or in the next +couple of weeks uh and then after the + + align:start position:0% +couple of weeks uh and then after the + + + align:start position:0% +couple of weeks uh and then after the +brainstorming session figure out how + + align:start position:0% +brainstorming session figure out how + + + align:start position:0% +brainstorming session figure out how +you're going to like pair to how how + + align:start position:0% +you're going to like pair to how how + + + align:start position:0% +you're going to like pair to how how +you're going to pair down that idea into + + align:start position:0% +you're going to pair down that idea into + + + align:start position:0% +you're going to pair down that idea into +something that you can do in a week or + + align:start position:0% +something that you can do in a week or + + + align:start position:0% +something that you can do in a week or +in two weeks um + + align:start position:0% +in two weeks um + + + align:start position:0% +in two weeks um +now it it you can expand on simple ideas + + align:start position:0% +now it it you can expand on simple ideas + + + align:start position:0% +now it it you can expand on simple ideas +and I'll talk a little bit about some + + align:start position:0% +and I'll talk a little bit about some + + + align:start position:0% +and I'll talk a little bit about some +strategies on doing that uh but uh + + align:start position:0% +strategies on doing that uh but uh + + + align:start position:0% +strategies on doing that uh but uh +usually reworking a wild idea to become + + align:start position:0% +usually reworking a wild idea to become + + + align:start position:0% +usually reworking a wild idea to become +feasible there usually a nugget there uh + + align:start position:0% +feasible there usually a nugget there uh + + + align:start position:0% +feasible there usually a nugget there uh +that's a lot easier to identify when you + + align:start position:0% +that's a lot easier to identify when you + + + align:start position:0% +that's a lot easier to identify when you +start big and then shrink + + align:start position:0% +start big and then shrink + + + align:start position:0% +start big and then shrink +down what are you going for you're + + align:start position:0% +down what are you going for you're + + + align:start position:0% +down what are you going for you're +trying to come up with as many ideas as + + align:start position:0% +trying to come up with as many ideas as + + + align:start position:0% +trying to come up with as many ideas as +possible quantity uh the greater number + + align:start position:0% +possible quantity uh the greater number + + + align:start position:0% +possible quantity uh the greater number +of ideas the more likelihood you that + + align:start position:0% +of ideas the more likelihood you that + + + align:start position:0% +of ideas the more likelihood you that +some of those ideas are actually going + + align:start position:0% +some of those ideas are actually going + + + align:start position:0% +some of those ideas are actually going +to be useful um you are not actually + + align:start position:0% +to be useful um you are not actually + + + align:start position:0% +to be useful um you are not actually +trying to solve the problem in + + align:start position:0% +trying to solve the problem in + + + align:start position:0% +trying to solve the problem in +brainstorming say you know if this if + + align:start position:0% +brainstorming say you know if this if + + + align:start position:0% +brainstorming say you know if this if +the problem that we're asking you to + + align:start position:0% +the problem that we're asking you to + + + align:start position:0% +the problem that we're asking you to +solve is create something playable in a + + align:start position:0% +solve is create something playable in a + + + align:start position:0% +solve is create something playable in a +week we're not asking you to solve that + + align:start position:0% +week we're not asking you to solve that + + + align:start position:0% +week we're not asking you to solve that +problem during the brainstorm session + + align:start position:0% +problem during the brainstorm session + + + align:start position:0% +problem during the brainstorm session +that comes after the brainstorm session + + align:start position:0% +that comes after the brainstorm session + + + align:start position:0% +that comes after the brainstorm session +that comes with things like prototyping + + align:start position:0% +that comes with things like prototyping + + + align:start position:0% +that comes with things like prototyping +which we'll get to later today so the + + align:start position:0% +which we'll get to later today so the + + + align:start position:0% +which we'll get to later today so the +more it's a same now that's a simple + + align:start position:0% +more it's a same now that's a simple + + + align:start position:0% +more it's a same now that's a simple +metric that you can use to gauge the + + align:start position:0% +metric that you can use to gauge the + + + align:start position:0% +metric that you can use to gauge the +success of a brainstorm such how many + + align:start position:0% +success of a brainstorm such how many + + + align:start position:0% +success of a brainstorm such how many +ideas that you generate and what pace + + align:start position:0% +ideas that you generate and what pace + + + align:start position:0% +ideas that you generate and what pace +that are you generating them at again + + align:start position:0% +that are you generating them at again + + + align:start position:0% +that are you generating them at again +that's why you don't want to be judging + + align:start position:0% +that's why you don't want to be judging + + + align:start position:0% +that's why you don't want to be judging +ideas while they're being generated all + + align:start position:0% +ideas while they're being generated all + + + align:start position:0% +ideas while they're being generated all +ideas should be included nothing is + + align:start position:0% +ideas should be included nothing is + + + align:start position:0% +ideas should be included nothing is +excluded and you you're going to need to + + align:start position:0% +excluded and you you're going to need to + + + align:start position:0% +excluded and you you're going to need to +reinforce that within the group of + + align:start position:0% +reinforce that within the group of + + + align:start position:0% +reinforce that within the group of +people that you're brainstorming with + + align:start position:0% +people that you're brainstorming with + + + align:start position:0% +people that you're brainstorming with +there's somebody who's actually got a + + align:start position:0% +there's somebody who's actually got a + + + align:start position:0% +there's somebody who's actually got a +job to specifically do that but you've + + align:start position:0% +job to specifically do that but you've + + + align:start position:0% +job to specifically do that but you've +got to help with + + align:start position:0% + + + + align:start position:0% + +that and uh you can build on ideas you + + align:start position:0% +that and uh you can build on ideas you + + + align:start position:0% +that and uh you can build on ideas you +can you can refer back to ideas that + + align:start position:0% +can you can refer back to ideas that + + + align:start position:0% +can you can refer back to ideas that +that have already been mentioned Tak a + + align:start position:0% +that have already been mentioned Tak a + + + align:start position:0% +that have already been mentioned Tak a +notes of and then combine them with your + + align:start position:0% +notes of and then combine them with your + + + align:start position:0% +notes of and then combine them with your +own idea or even have ideas that other + + align:start position:0% +own idea or even have ideas that other + + + align:start position:0% +own idea or even have ideas that other +people have come up with uh to be able + + align:start position:0% +people have come up with uh to be able + + + align:start position:0% +people have come up with uh to be able +to come up with with something sort of + + align:start position:0% +to come up with with something sort of + + + align:start position:0% +to come up with with something sort of +synthetically U more complex uh great + + align:start position:0% +synthetically U more complex uh great + + + align:start position:0% +synthetically U more complex uh great +ideas are often generated when desperate + + align:start position:0% +ideas are often generated when desperate + + + align:start position:0% +ideas are often generated when desperate +ideas are combined you know Lego plus + + align:start position:0% +ideas are combined you know Lego plus + + + align:start position:0% +ideas are combined you know Lego plus +Star Wars equals Lego Star + + align:start position:0% +Star Wars equals Lego Star + + + align:start position:0% +Star Wars equals Lego Star +Wars which is awesome you know marvel + + align:start position:0% +Wars which is awesome you know marvel + + + align:start position:0% +Wars which is awesome you know marvel +plus + + align:start position:0% +plus + + + align:start position:0% +plus +Capcom Marvel versus ccom okay great + + align:start position:0% +Capcom Marvel versus ccom okay great + + + align:start position:0% +Capcom Marvel versus ccom okay great +ideas there um and often that's actually + + align:start position:0% +ideas there um and often that's actually + + + align:start position:0% +ideas there um and often that's actually +where a lot of your really good ideas + + align:start position:0% +where a lot of your really good ideas + + + align:start position:0% +where a lot of your really good ideas +are going to come from because you're + + align:start position:0% +are going to come from because you're + + + align:start position:0% +are going to come from because you're +going to come up with a whole bunch of + + align:start position:0% +going to come up with a whole bunch of + + + align:start position:0% +going to come up with a whole bunch of +really mundane things that basically + + align:start position:0% +really mundane things that basically + + + align:start position:0% +really mundane things that basically +refer back to games that you've already + + align:start position:0% +refer back to games that you've already + + + align:start position:0% +refer back to games that you've already +played or things that or ideas that a + + align:start position:0% +played or things that or ideas that a + + + align:start position:0% +played or things that or ideas that a +lot of people have encountered but maybe + + align:start position:0% +lot of people have encountered but maybe + + + align:start position:0% +lot of people have encountered but maybe +not encountered together in the same + + align:start position:0% +not encountered together in the same + + + align:start position:0% +not encountered together in the same +context so this is how you how you're + + align:start position:0% +context so this is how you how you're + + + align:start position:0% +context so this is how you how you're +going to do it you're going to try start + + align:start position:0% +going to do it you're going to try start + + + align:start position:0% +going to do it you're going to try start +off with a really really try to create a + + align:start position:0% +off with a really really try to create a + + + align:start position:0% +off with a really really try to create a +little you know casual Spirit we this is + + align:start position:0% +little you know casual Spirit we this is + + + align:start position:0% +little you know casual Spirit we this is +not like a really straight L formal + + align:start position:0% +not like a really straight L formal + + + align:start position:0% +not like a really straight L formal +Affair throughout your start with giving + + align:start position:0% +Affair throughout your start with giving + + + align:start position:0% +Affair throughout your start with giving +your worst idea the worst idea that you + + align:start position:0% +your worst idea the worst idea that you + + + align:start position:0% +your worst idea the worst idea that you +can possibly think of the the the most + + align:start position:0% +can possibly think of the the the most + + + align:start position:0% +can possibly think of the the the most +useless uh terrible you know if you have + + align:start position:0% +useless uh terrible you know if you have + + + align:start position:0% +useless uh terrible you know if you have +to do offensive sure but you know uh uh + + align:start position:0% +to do offensive sure but you know uh uh + + + align:start position:0% +to do offensive sure but you know uh uh +usually that's just an idea that you + + align:start position:0% +usually that's just an idea that you + + + align:start position:0% +usually that's just an idea that you +know is dumb just tell people that you + + align:start position:0% +know is dumb just tell people that you + + + align:start position:0% +know is dumb just tell people that you +know everyone put it down write it down + + align:start position:0% +know everyone put it down write it down + + + align:start position:0% +know everyone put it down write it down +um while someone is speaking don't + + align:start position:0% +um while someone is speaking don't + + + align:start position:0% +um while someone is speaking don't +interrupt them uh but do designate a + + align:start position:0% +interrupt them uh but do designate a + + + align:start position:0% +interrupt them uh but do designate a +facilitator at the beginning of the + + align:start position:0% +facilitator at the beginning of the + + + align:start position:0% +facilitator at the beginning of the +session and it's going to be that + + align:start position:0% +session and it's going to be that + + + align:start position:0% +session and it's going to be that +person's job to keep things moving so so + + align:start position:0% +person's job to keep things moving so so + + + align:start position:0% +person's job to keep things moving so so +uh you don't really need to explain so + + align:start position:0% +uh you don't really need to explain so + + + align:start position:0% +uh you don't really need to explain so +much because again you're not trying to + + align:start position:0% +much because again you're not trying to + + + align:start position:0% +much because again you're not trying to +solve the problem here you're just + + align:start position:0% +solve the problem here you're just + + + align:start position:0% +solve the problem here you're just +trying to be able to get enough ideas + + align:start position:0% +trying to be able to get enough ideas + + + align:start position:0% +trying to be able to get enough ideas +out so that whoever's performing the + + align:start position:0% +out so that whoever's performing the + + + align:start position:0% +out so that whoever's performing the +role of the secretary can write it + + align:start position:0% +role of the secretary can write it + + + align:start position:0% +role of the secretary can write it +down and um and again be before you + + align:start position:0% +down and um and again be before you + + + align:start position:0% +down and um and again be before you +start the entire session make sure + + align:start position:0% +start the entire session make sure + + + align:start position:0% +start the entire session make sure +everybody understands this process you + + align:start position:0% +everybody understands this process you + + + align:start position:0% +everybody understands this process you +know uh if there's somebody who walked + + align:start position:0% +know uh if there's somebody who walked + + + align:start position:0% +know uh if there's somebody who walked +in late in a class or something and is + + align:start position:0% +in late in a class or something and is + + + align:start position:0% +in late in a class or something and is +just joining your team make sure they + + align:start position:0% +just joining your team make sure they + + + align:start position:0% +just joining your team make sure they +understand all of these rules the these + + align:start position:0% +understand all of these rules the these + + + align:start position:0% +understand all of these rules the these +four rules that that I went through and + + align:start position:0% +four rules that that I went through and + + + align:start position:0% +four rules that that I went through and +write down everything + + align:start position:0% +write down everything + + + align:start position:0% +write down everything +um now don't just write down the title + + align:start position:0% +um now don't just write down the title + + + align:start position:0% +um now don't just write down the title +of the idea you know um Turtle Tower + + align:start position:0% +of the idea you know um Turtle Tower + + + align:start position:0% +of the idea you know um Turtle Tower +Defense I don't know uh you know that's + + align:start position:0% +Defense I don't know uh you know that's + + + align:start position:0% +Defense I don't know uh you know that's +that's that's those are three easy words + + align:start position:0% +that's that's those are three easy words + + + align:start position:0% +that's that's those are three easy words +to write down but might be difficult for + + align:start position:0% +to write down but might be difficult for + + + align:start position:0% +to write down but might be difficult for +you to then remember exactly what that + + align:start position:0% +you to then remember exactly what that + + + align:start position:0% +you to then remember exactly what that +idea were they like anthropomorphic + + align:start position:0% +idea were they like anthropomorphic + + + align:start position:0% +idea were they like anthropomorphic +Turtles are the turtles the towers are + + align:start position:0% +Turtles are the turtles the towers are + + + align:start position:0% +Turtles are the turtles the towers are +the turtles marching into Towers you + + align:start position:0% +the turtles marching into Towers you + + + align:start position:0% +the turtles marching into Towers you +know it's like what was that again let + + align:start position:0% +know it's like what was that again let + + + align:start position:0% +know it's like what was that again let +whoever's taking down notes take a + + align:start position:0% +whoever's taking down notes take a + + + align:start position:0% +whoever's taking down notes take a +little bit more information maybe like a + + align:start position:0% +little bit more information maybe like a + + + align:start position:0% +little bit more information maybe like a +line of of information just so that when + + align:start position:0% +line of of information just so that when + + + align:start position:0% +line of of information just so that when +you come back to that idea you don't + + align:start position:0% +you come back to that idea you don't + + + align:start position:0% +you come back to that idea you don't +look at a title say that looks like a + + align:start position:0% +look at a title say that looks like a + + + align:start position:0% +look at a title say that looks like a +that what was that idea again you know + + align:start position:0% +that what was that idea again you know + + + align:start position:0% +that what was that idea again you know +does anybody remember what this idea was + + align:start position:0% +does anybody remember what this idea was + + + align:start position:0% +does anybody remember what this idea was +that you just take the time to be able + + align:start position:0% +that you just take the time to be able + + + align:start position:0% +that you just take the time to be able +to write things + + align:start position:0% +to write things + + + align:start position:0% +to write things +down now this is more General uh today + + align:start position:0% +down now this is more General uh today + + + align:start position:0% +down now this is more General uh today +we're asking you very specifically to + + align:start position:0% +we're asking you very specifically to + + + align:start position:0% +we're asking you very specifically to +brainstorm about the game that you're + + align:start position:0% +brainstorm about the game that you're + + + align:start position:0% +brainstorm about the game that you're +going to be prototyping for uh for + + align:start position:0% +going to be prototyping for uh for + + + align:start position:0% +going to be prototyping for uh for +project one uh but in general you can + + align:start position:0% +project one uh but in general you can + + + align:start position:0% +project one uh but in general you can +apply brainstorming to a bunch of + + align:start position:0% +apply brainstorming to a bunch of + + + align:start position:0% +apply brainstorming to a bunch of +different ideas even in the middle of a + + align:start position:0% +different ideas even in the middle of a + + + align:start position:0% +different ideas even in the middle of a +pro project project one or later or to + + align:start position:0% +pro project project one or later or to + + + align:start position:0% +pro project project one or later or to +other domains but it's very very + + align:start position:0% +other domains but it's very very + + + align:start position:0% +other domains but it's very very +important to be able to know what kinds + + align:start position:0% +important to be able to know what kinds + + + align:start position:0% +important to be able to know what kinds +of problems are good for brainstorming + + align:start position:0% +of problems are good for brainstorming + + + align:start position:0% +of problems are good for brainstorming +and what kind of problems are terrible + + align:start position:0% +and what kind of problems are terrible + + + align:start position:0% +and what kind of problems are terrible +for brainstorming um you need to be able + + align:start position:0% +for brainstorming um you need to be able + + + align:start position:0% +for brainstorming um you need to be able +to uh find a problem that is very + + align:start position:0% +to uh find a problem that is very + + + align:start position:0% +to uh find a problem that is very +clearly defined the problem should be + + align:start position:0% +clearly defined the problem should be + + + align:start position:0% +clearly defined the problem should be +simple if you've got a problem that's + + align:start position:0% +simple if you've got a problem that's + + + align:start position:0% +simple if you've got a problem that's +really really complex with uh uh you + + align:start position:0% +really really complex with uh uh you + + + align:start position:0% +really really complex with uh uh you +know lots of very different uh um + + align:start position:0% +know lots of very different uh um + + + align:start position:0% +know lots of very different uh um +opposing factors that you have to be + + align:start position:0% +opposing factors that you have to be + + + align:start position:0% +opposing factors that you have to be +taking take into account to optimize + + align:start position:0% +taking take into account to optimize + + + align:start position:0% +taking take into account to optimize +something you can try to divide that + + align:start position:0% +something you can try to divide that + + + align:start position:0% +something you can try to divide that +into complex uh those complex problems + + align:start position:0% +into complex uh those complex problems + + + align:start position:0% +into complex uh those complex problems +into Sub Sub sub divisions where each + + align:start position:0% +into Sub Sub sub divisions where each + + + align:start position:0% +into Sub Sub sub divisions where each +one of those subdivisions could have a + + align:start position:0% +one of those subdivisions could have a + + + align:start position:0% +one of those subdivisions could have a +uh separate answer or you could try to + + align:start position:0% +uh separate answer or you could try to + + + align:start position:0% +uh separate answer or you could try to +use a different problem solving strategy + + align:start position:0% +use a different problem solving strategy + + + align:start position:0% +use a different problem solving strategy +entirely you don't necessarily need to + + align:start position:0% +entirely you don't necessarily need to + + + align:start position:0% +entirely you don't necessarily need to +apply brainstorming to everything you + + align:start position:0% +apply brainstorming to everything you + + + align:start position:0% +apply brainstorming to everything you +should be able to articulate the problem + + align:start position:0% +should be able to articulate the problem + + + align:start position:0% +should be able to articulate the problem +simply and clearly um but just because I + + align:start position:0% +simply and clearly um but just because I + + + align:start position:0% +simply and clearly um but just because I +can articulate the problem doesn't + + align:start position:0% +can articulate the problem doesn't + + + align:start position:0% +can articulate the problem doesn't +necessarily mean that it's uh it's it's + + align:start position:0% +necessarily mean that it's uh it's it's + + + align:start position:0% +necessarily mean that it's uh it's it's +appropriate for for brainstorming + + align:start position:0% +appropriate for for brainstorming + + + align:start position:0% +appropriate for for brainstorming +Osborne for instance gives you example + + align:start position:0% +Osborne for instance gives you example + + + align:start position:0% +Osborne for instance gives you example +of get married that's your problem right + + align:start position:0% +of get married that's your problem right + + + align:start position:0% +of get married that's your problem right +okay and then you're trying to solve + + align:start position:0% +okay and then you're trying to solve + + + align:start position:0% +okay and then you're trying to solve +that brainstorming is a really terrible + + align:start position:0% +that brainstorming is a really terrible + + + align:start position:0% +that brainstorming is a really terrible +technique for + + align:start position:0% +technique for + + + align:start position:0% +technique for +that here are all the ways that you can + + align:start position:0% +that here are all the ways that you can + + + align:start position:0% +that here are all the ways that you can +get married it's like that doesn't help + + align:start position:0% +get married it's like that doesn't help + + + align:start position:0% +get married it's like that doesn't help +um you know uh uh maybe that doesn't + + align:start position:0% +um you know uh uh maybe that doesn't + + + align:start position:0% +um you know uh uh maybe that doesn't +identify the problem in in the first + + align:start position:0% +identify the problem in in the first + + + align:start position:0% +identify the problem in in the first +place it's a complex problem that's a + + align:start position:0% +place it's a complex problem that's a + + + align:start position:0% +place it's a complex problem that's a +little bit too large you know what's + + align:start position:0% +little bit too large you know what's + + + align:start position:0% +little bit too large you know what's +your game going to be about or what is + + align:start position:0% +your game going to be about or what is + + + align:start position:0% +your game going to be about or what is +your player going to do 80% of the time + + align:start position:0% +your player going to do 80% of the time + + + align:start position:0% +your player going to do 80% of the time +you know what's that one action that + + align:start position:0% +you know what's that one action that + + + align:start position:0% +you know what's that one action that +your that your player is going to do 80% + + align:start position:0% +your that your player is going to do 80% + + + align:start position:0% +your that your player is going to do 80% +you know where is our game set you know + + align:start position:0% +you know where is our game set you know + + + align:start position:0% +you know where is our game set you know +who is our main character these are sort + + align:start position:0% +who is our main character these are sort + + + align:start position:0% +who is our main character these are sort +of well well articulated Pro problems + + align:start position:0% +of well well articulated Pro problems + + + align:start position:0% +of well well articulated Pro problems +that brainstorming does work + + align:start position:0% +that brainstorming does work + + + align:start position:0% +that brainstorming does work +for now responsibilities again I said + + align:start position:0% +for now responsibilities again I said + + + align:start position:0% +for now responsibilities again I said +designate someone to be a facilitator + + align:start position:0% +designate someone to be a facilitator + + + align:start position:0% +designate someone to be a facilitator +and this person's job is to be uh to + + align:start position:0% +and this person's job is to be uh to + + + align:start position:0% +and this person's job is to be uh to +basically keep this whole session moving + + align:start position:0% +basically keep this whole session moving + + + align:start position:0% +basically keep this whole session moving +uh we don't like to use the word leader + + align:start position:0% +uh we don't like to use the word leader + + + align:start position:0% +uh we don't like to use the word leader +uh because you are not your job is not + + align:start position:0% +uh because you are not your job is not + + + align:start position:0% +uh because you are not your job is not +to be the head of the brainstorming + + align:start position:0% +to be the head of the brainstorming + + + align:start position:0% +to be the head of the brainstorming +session your job is to facilitate it + + align:start position:0% +session your job is to facilitate it + + + align:start position:0% +session your job is to facilitate it +there is to sort of be the clerical uh + + align:start position:0% +there is to sort of be the clerical uh + + + align:start position:0% +there is to sort of be the clerical uh +equivalent of moving the + + align:start position:0% +equivalent of moving the + + + align:start position:0% +equivalent of moving the +process along um so you need to + + align:start position:0% +process along um so you need to + + + align:start position:0% +process along um so you need to +understand the problem and then you know + + align:start position:0% +understand the problem and then you know + + + align:start position:0% +understand the problem and then you know +make sure that everybody around the the + + align:start position:0% +make sure that everybody around the the + + + align:start position:0% +make sure that everybody around the the +the the the brainstorm group also + + align:start position:0% +the the the brainstorm group also + + + align:start position:0% +the the the brainstorm group also +understands this problem um and then + + align:start position:0% +understands this problem um and then + + + align:start position:0% +understands this problem um and then +when the session actually goes every + + align:start position:0% +when the session actually goes every + + + align:start position:0% +when the session actually goes every +time you you sort of sense that there's + + align:start position:0% +time you you sort of sense that there's + + + align:start position:0% +time you you sort of sense that there's +some criticism coming out you say all + + align:start position:0% +some criticism coming out you say all + + + align:start position:0% +some criticism coming out you say all +right we'll put that aside move on to + + align:start position:0% +right we'll put that aside move on to + + + align:start position:0% +right we'll put that aside move on to +the next idea try to like diffuse any + + align:start position:0% +the next idea try to like diffuse any + + + align:start position:0% +the next idea try to like diffuse any +criticism When You See It Coming uh and + + align:start position:0% +criticism When You See It Coming uh and + + + align:start position:0% +criticism When You See It Coming uh and +encourage people who aren't speaking up + + align:start position:0% +encourage people who aren't speaking up + + + align:start position:0% +encourage people who aren't speaking up +to speak up you know just simply it's + + align:start position:0% +to speak up you know just simply it's + + + align:start position:0% +to speak up you know just simply it's +like you know uh what's on your what's + + align:start position:0% +like you know uh what's on your what's + + + align:start position:0% +like you know uh what's on your what's +on your mind or you know call out + + align:start position:0% +on your mind or you know call out + + + align:start position:0% +on your mind or you know call out +someone's name and just say you know you + + align:start position:0% +someone's name and just say you know you + + + align:start position:0% +someone's name and just say you know you +know uh you know any of these things + + align:start position:0% +know uh you know any of these things + + + align:start position:0% +know uh you know any of these things +give you any ideas try to sort of call + + align:start position:0% +give you any ideas try to sort of call + + + align:start position:0% +give you any ideas try to sort of call +out those people who aren't already very + + align:start position:0% +out those people who aren't already very + + + align:start position:0% +out those people who aren't already very +much involved in the process to try to + + align:start position:0% +much involved in the process to try to + + + align:start position:0% +much involved in the process to try to +get them into the process because the + + align:start position:0% +get them into the process because the + + + align:start position:0% +get them into the process because the +more people riff off each other the more + + align:start position:0% +more people riff off each other the more + + + align:start position:0% +more people riff off each other the more +um ideas you're going to be able to + + align:start position:0% +um ideas you're going to be able to + + + align:start position:0% +um ideas you're going to be able to +generate encourage people to join ideas + + align:start position:0% +generate encourage people to join ideas + + + align:start position:0% +generate encourage people to join ideas +together sometimes you just do that + + align:start position:0% +together sometimes you just do that + + + align:start position:0% +together sometimes you just do that +yourself just like look at two random + + align:start position:0% +yourself just like look at two random + + + align:start position:0% +yourself just like look at two random +things that you wrot down and just try + + align:start position:0% +things that you wrot down and just try + + + align:start position:0% +things that you wrot down and just try +to like slam them together just to get + + align:start position:0% +to like slam them together just to get + + + align:start position:0% +to like slam them together just to get +the process started and maybe other + + align:start position:0% +the process started and maybe other + + + align:start position:0% +the process started and maybe other +people will do more logical compositions + + align:start position:0% +people will do more logical compositions + + + align:start position:0% +people will do more logical compositions +um make sure that no voices are lost in + + align:start position:0% +um make sure that no voices are lost in + + + align:start position:0% +um make sure that no voices are lost in +this + + align:start position:0% +this + + + align:start position:0% +this +process it's not your job to identify + + align:start position:0% +process it's not your job to identify + + + align:start position:0% +process it's not your job to identify +it's not the facilitator's job by the + + align:start position:0% +it's not the facilitator's job by the + + + align:start position:0% +it's not the facilitator's job by the +way to identify what's the best solution + + align:start position:0% +way to identify what's the best solution + + + align:start position:0% +way to identify what's the best solution +on the board or on the computer when + + align:start position:0% +on the board or on the computer when + + + align:start position:0% +on the board or on the computer when +you're taking down these ideas uh that's + + align:start position:0% +you're taking down these ideas uh that's + + + align:start position:0% +you're taking down these ideas uh that's +not the pro that that that that that may + + align:start position:0% +not the pro that that that that that may + + + align:start position:0% +not the pro that that that that that may +not actually be the job of brainstorming + + align:start position:0% +not actually be the job of brainstorming + + + align:start position:0% +not actually be the job of brainstorming +at all that's actually a problem that + + align:start position:0% +at all that's actually a problem that + + + align:start position:0% +at all that's actually a problem that +you come to later when you see the whole + + align:start position:0% +you come to later when you see the whole + + + align:start position:0% +you come to later when you see the whole +pile of ideas that you generated and now + + align:start position:0% +pile of ideas that you generated and now + + + align:start position:0% +pile of ideas that you generated and now +you figure out what it is that you're + + align:start position:0% +you figure out what it is that you're + + + align:start position:0% +you figure out what it is that you're +going to choose for say project + + align:start position:0% +going to choose for say project + + + align:start position:0% +going to choose for say project +one now there's a second person who's + + align:start position:0% +one now there's a second person who's + + + align:start position:0% +one now there's a second person who's +involved this is person who either has a + + align:start position:0% +involved this is person who either has a + + + align:start position:0% +involved this is person who either has a +giant posted pad or a chalkboard or a + + align:start position:0% +giant posted pad or a chalkboard or a + + + align:start position:0% +giant posted pad or a chalkboard or a +computer usually connected to a + + align:start position:0% +computer usually connected to a + + + align:start position:0% +computer usually connected to a +projector uh and that person is a + + align:start position:0% +projector uh and that person is a + + + align:start position:0% +projector uh and that person is a +secretary whose basic basic job is to + + align:start position:0% +secretary whose basic basic job is to + + + align:start position:0% +secretary whose basic basic job is to +record every single idea in a way that + + align:start position:0% +record every single idea in a way that + + + align:start position:0% +record every single idea in a way that +everybody around the group can actually + + align:start position:0% +everybody around the group can actually + + + align:start position:0% +everybody around the group can actually +see those ideas um you don't want to + + align:start position:0% +see those ideas um you don't want to + + + align:start position:0% +see those ideas um you don't want to +just work on your own personal top on + + align:start position:0% +just work on your own personal top on + + + align:start position:0% +just work on your own personal top on +your own screen where no one else can + + align:start position:0% +your own screen where no one else can + + + align:start position:0% +your own screen where no one else can +see it because then then other people + + align:start position:0% +see it because then then other people + + + align:start position:0% +see it because then then other people +can't say look at ideas that have been + + align:start position:0% +can't say look at ideas that have been + + + align:start position:0% +can't say look at ideas that have been +mentioned before and combine them so + + align:start position:0% +mentioned before and combine them so + + + align:start position:0% +mentioned before and combine them so +make sure that you're writing things up + + align:start position:0% +make sure that you're writing things up + + + align:start position:0% +make sure that you're writing things up +on somewhere where everyone can see + + align:start position:0% +on somewhere where everyone can see + + + align:start position:0% +on somewhere where everyone can see +we've got some giant Post-it pads right + + align:start position:0% +we've got some giant Post-it pads right + + + align:start position:0% +we've got some giant Post-it pads right +here um and uh you can grab them and + + align:start position:0% +here um and uh you can grab them and + + + align:start position:0% +here um and uh you can grab them and +we've got some markers uhti stick them + + align:start position:0% +we've got some markers uhti stick them + + + align:start position:0% +we've got some markers uhti stick them +up on the wall and and write on them so + + align:start position:0% +up on the wall and and write on them so + + + align:start position:0% +up on the wall and and write on them so +you want to try to re just write down + + align:start position:0% +you want to try to re just write down + + + align:start position:0% +you want to try to re just write down +just report on what people are saying + + align:start position:0% +just report on what people are saying + + + align:start position:0% +just report on what people are saying +don't don't try to be editorial about it + + align:start position:0% +don't don't try to be editorial about it + + + align:start position:0% +don't don't try to be editorial about it +don't say good idea idea that's not your + + align:start position:0% +don't say good idea idea that's not your + + + align:start position:0% +don't say good idea idea that's not your +job either um you do want to keep an eye + + align:start position:0% +job either um you do want to keep an eye + + + align:start position:0% +job either um you do want to keep an eye +on the time especially because we're + + align:start position:0% +on the time especially because we're + + + align:start position:0% +on the time especially because we're +doing this in class and time will run + + align:start position:0% +doing this in class and time will run + + + align:start position:0% +doing this in class and time will run +out so uh so make sure that you actually + + align:start position:0% +out so uh so make sure that you actually + + + align:start position:0% +out so uh so make sure that you actually +have enough time to uh get down to those + + align:start position:0% +have enough time to uh get down to those + + + align:start position:0% +have enough time to uh get down to those +last couple of ideas before we we go + + align:start position:0% +last couple of ideas before we we go + + + align:start position:0% +last couple of ideas before we we go +into our next part of our class which I + + align:start position:0% +into our next part of our class which I + + + align:start position:0% +into our next part of our class which I +think is + + align:start position:0% +think is + + + align:start position:0% +think is +prototyping um the secretary can + + align:start position:0% +prototyping um the secretary can + + + align:start position:0% +prototyping um the secretary can +participate in the brainstorming it's + + align:start position:0% +participate in the brainstorming it's + + + align:start position:0% +participate in the brainstorming it's +sometimes a little bit tough uh it's + + align:start position:0% +sometimes a little bit tough uh it's + + + align:start position:0% +sometimes a little bit tough uh it's +tough to write down and listen to what + + align:start position:0% +tough to write down and listen to what + + + align:start position:0% +tough to write down and listen to what +other people are saying while trying to + + align:start position:0% +other people are saying while trying to + + + align:start position:0% +other people are saying while trying to +generate your own ideas so what you + + align:start position:0% +generate your own ideas so what you + + + align:start position:0% +generate your own ideas so what you +might want to do is split up your + + align:start position:0% +might want to do is split up your + + + align:start position:0% +might want to do is split up your +brainstorming session into basically two + + align:start position:0% +brainstorming session into basically two + + + align:start position:0% +brainstorming session into basically two +halves how much time are we giving them + + align:start position:0% +halves how much time are we giving them + + + align:start position:0% +halves how much time are we giving them +for brainstorming 30 30 minutes so split + + align:start position:0% +for brainstorming 30 30 minutes so split + + + align:start position:0% +for brainstorming 30 30 minutes so split +it into like two 15 minute chunks and um + + align:start position:0% +it into like two 15 minute chunks and um + + + align:start position:0% +it into like two 15 minute chunks and um +either the facilitator and the circuitry + + align:start position:0% +either the facilitator and the circuitry + + + align:start position:0% +either the facilitator and the circuitry +can switch or just get two other people + + align:start position:0% +can switch or just get two other people + + + align:start position:0% +can switch or just get two other people +to be patry and facilitator so the + + align:start position:0% +to be patry and facilitator so the + + + align:start position:0% +to be patry and facilitator so the +people who were facilitator and Petry + + align:start position:0% +people who were facilitator and Petry + + + align:start position:0% +people who were facilitator and Petry +can sit down and you know generate their + + align:start position:0% +can sit down and you know generate their + + + align:start position:0% +can sit down and you know generate their +and have the space to generate their own + + align:start position:0% +and have the space to generate their own + + + align:start position:0% +and have the space to generate their own +ideas while someone else is taking notes + + align:start position:0% +ideas while someone else is taking notes + + + align:start position:0% +ideas while someone else is taking notes +and making sure the process is running + + align:start position:0% +and making sure the process is running + + + align:start position:0% +and making sure the process is running +so so that's what we're asking you to do + + align:start position:0% +so so that's what we're asking you to do + + + align:start position:0% +so so that's what we're asking you to do +any questions about + + align:start position:0% + + + + align:start position:0% + +brainstorming or anything else I've + + align:start position:0% +brainstorming or anything else I've + + + align:start position:0% +brainstorming or anything else I've +said Is there a limit or a minimum + + align:start position:0% +said Is there a limit or a minimum + + + align:start position:0% +said Is there a limit or a minimum +number of ideas that we have to come up + + align:start position:0% +number of ideas that we have to come up + + + align:start position:0% +number of ideas that we have to come up +with is there a minimum idea of ideas uh + + align:start position:0% +with is there a minimum idea of ideas uh + + + align:start position:0% +with is there a minimum idea of ideas uh +no there is you you you don't have to + + align:start position:0% +no there is you you you don't have to + + + align:start position:0% +no there is you you you don't have to +say in fact don't um that's probably + + align:start position:0% +say in fact don't um that's probably + + + align:start position:0% +say in fact don't um that's probably +counterproductive don't say oh we have + + align:start position:0% +counterproductive don't say oh we have + + + align:start position:0% +counterproductive don't say oh we have +to hit at least 30 you know 30 ideas and + + align:start position:0% +to hit at least 30 you know 30 ideas and + + + align:start position:0% +to hit at least 30 you know 30 ideas and +we're done because that implies that + + align:start position:0% +we're done because that implies that + + + align:start position:0% +we're done because that implies that +once you're over 30 you can stop you + + align:start position:0% +once you're over 30 you can stop you + + + align:start position:0% +once you're over 30 you can stop you +don't want to stop you want to keep + + align:start position:0% +don't want to stop you want to keep + + + align:start position:0% +don't want to stop you want to keep +generating ideas until you run out of + + align:start position:0% +generating ideas until you run out of + + + align:start position:0% +generating ideas until you run out of +time and if it takes you you know um 30 + + align:start position:0% +time and if it takes you you know um 30 + + + align:start position:0% +time and if it takes you you know um 30 +minutes to come up with two ideas know + + align:start position:0% +minutes to come up with two ideas know + + + align:start position:0% +minutes to come up with two ideas know +that's fine that's the group that's + + align:start position:0% +that's fine that's the group that's + + + align:start position:0% +that's fine that's the group that's +that's that that's what your group was + + align:start position:0% +that's that that's what your group was + + + align:start position:0% +that's that that's what your group was +able to come up with uh generally you + + align:start position:0% +able to come up with uh generally you + + + align:start position:0% +able to come up with uh generally you +want to be generating like a lot uh uh + + align:start position:0% +want to be generating like a lot uh uh + + + align:start position:0% +want to be generating like a lot uh uh +you know several dozen ideas uh uh in a + + align:start position:0% +you know several dozen ideas uh uh in a + + + align:start position:0% +you know several dozen ideas uh uh in a +30 minute session we're going to ask you + + align:start position:0% +30 minute session we're going to ask you + + + align:start position:0% +30 minute session we're going to ask you +to form groups of six people grab the + + align:start position:0% +to form groups of six people grab the + + + align:start position:0% +to form groups of six people grab the +people who are nearest you um these + + align:start position:0% +people who are nearest you um these + + + align:start position:0% +people who are nearest you um these +groups of six six are going to like do + + align:start position:0% +groups of six six are going to like do + + + align:start position:0% +groups of six six are going to like do +us a favor and everybody stand up as you + + align:start position:0% +us a favor and everybody stand up as you + + + align:start position:0% +us a favor and everybody stand up as you +form groups sit + + align:start position:0% +form groups sit + + + align:start position:0% +form groups sit +down you've got three minutes to form + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +groups so we just finished the + + align:start position:0% +groups so we just finished the + + + align:start position:0% +groups so we just finished the +brainstorming session and I'd like to + + align:start position:0% +brainstorming session and I'd like to + + + align:start position:0% +brainstorming session and I'd like to +get some people's impression about like + + align:start position:0% +get some people's impression about like + + + align:start position:0% +get some people's impression about like +what worked did you like uh like have + + align:start position:0% +what worked did you like uh like have + + + align:start position:0% +what worked did you like uh like have +some time do you need like uh some time + + align:start position:0% +some time do you need like uh some time + + + align:start position:0% +some time do you need like uh some time +to get started people kind of feel it + + align:start position:0% +to get started people kind of feel it + + + align:start position:0% +to get started people kind of feel it +went a little slowly at the beginning + + align:start position:0% +went a little slowly at the beginning + + + align:start position:0% +went a little slowly at the beginning +and then picked up or died off + + align:start position:0% +and then picked up or died off + + + align:start position:0% +and then picked up or died off +halfway what were some of your thoughts + + align:start position:0% +halfway what were some of your thoughts + + + align:start position:0% +halfway what were some of your thoughts +yeah I think like sessions were + + align:start position:0% + + + + align:start position:0% + +like okay + + align:start position:0% +like okay + + + align:start position:0% +like okay +out okay all right so so like sort of + + align:start position:0% +out okay all right so so like sort of + + + align:start position:0% +out okay all right so so like sort of +like uh breaking up even further into + + align:start position:0% +like uh breaking up even further into + + + align:start position:0% +like uh breaking up even further into +smaller chunks and then yeah okay sure + + align:start position:0% +smaller chunks and then yeah okay sure + + + align:start position:0% +smaller chunks and then yeah okay sure +that's a good + + align:start position:0% +that's a good + + + align:start position:0% +that's a good +idea how about the the note takers or + + align:start position:0% +idea how about the the note takers or + + + align:start position:0% +idea how about the the note takers or +the facilitators yeah I think starting + + align:start position:0% +the facilitators yeah I think starting + + + align:start position:0% +the facilitators yeah I think starting +with words and themes helped us get just + + align:start position:0% +with words and themes helped us get just + + + align:start position:0% +with words and themes helped us get just +basic concepts out there and then start + + align:start position:0% +basic concepts out there and then start + + + align:start position:0% +basic concepts out there and then start +combining them rather than jumping into + + align:start position:0% +combining them rather than jumping into + + + align:start position:0% +combining them rather than jumping into +game ideas right and one of the reasons + + align:start position:0% +game ideas right and one of the reasons + + + align:start position:0% +game ideas right and one of the reasons +why we did that will also give you an + + align:start position:0% +why we did that will also give you an + + + align:start position:0% +why we did that will also give you an +idea of what's a theme versus what's a + + align:start position:0% +idea of what's a theme versus what's a + + + align:start position:0% +idea of what's a theme versus what's a +mechanic right yeah I think it's like + + align:start position:0% +mechanic right yeah I think it's like + + + align:start position:0% +mechanic right yeah I think it's like +hard to avoid the scenario of someone + + align:start position:0% +hard to avoid the scenario of someone + + + align:start position:0% +hard to avoid the scenario of someone +wri idea and then everyone's like oh + + align:start position:0% +wri idea and then everyone's like oh + + + align:start position:0% +wri idea and then everyone's like oh +that's cool let's let's like talk more + + align:start position:0% +that's cool let's let's like talk more + + + align:start position:0% +that's cool let's let's like talk more +about that thing instead of just + + align:start position:0% +about that thing instead of just + + + align:start position:0% +about that thing instead of just +throwing out completely different ideas + + align:start position:0% +throwing out completely different ideas + + + align:start position:0% +throwing out completely different ideas +right Al so switching to a different + + align:start position:0% +right Al so switching to a different + + + align:start position:0% +right Al so switching to a different +idea right well you know that's not + + align:start position:0% +idea right well you know that's not + + + align:start position:0% +idea right well you know that's not +necessarily a failure of a process + + align:start position:0% +necessarily a failure of a process + + + align:start position:0% +necessarily a failure of a process +either but you're right we're trying to + + align:start position:0% +either but you're right we're trying to + + + align:start position:0% +either but you're right we're trying to +generate quantity and instead people are + + align:start position:0% +generate quantity and instead people are + + + align:start position:0% +generate quantity and instead people are +trying to improve the quality of the + + align:start position:0% +trying to improve the quality of the + + + align:start position:0% +trying to improve the quality of the +idea uh so yeah but still that's you + + align:start position:0% +idea uh so yeah but still that's you + + + align:start position:0% +idea uh so yeah but still that's you +know that's a happy problem to have + + align:start position:0% +know that's a happy problem to have + + + align:start position:0% +know that's a happy problem to have +right it's it's a good point yeah I + + align:start position:0% +right it's it's a good point yeah I + + + align:start position:0% +right it's it's a good point yeah I +think for our team jokes uh had uh + + align:start position:0% +think for our team jokes uh had uh + + + align:start position:0% +think for our team jokes uh had uh +helped us a lot sure at first situation + + align:start position:0% +helped us a lot sure at first situation + + + align:start position:0% +helped us a lot sure at first situation +was more tense and then after one or two + + align:start position:0% +was more tense and then after one or two + + + align:start position:0% +was more tense and then after one or two +stupid ideas everyone became more casual + + align:start position:0% +stupid ideas everyone became more casual + + + align:start position:0% +stupid ideas everyone became more casual +and starting uh saying more ideas and + + align:start position:0% +and starting uh saying more ideas and + + + align:start position:0% +and starting uh saying more ideas and +that's why the throwing out the bad + + align:start position:0% +that's why the throwing out the bad + + + align:start position:0% +that's why the throwing out the bad +ideas part helps as well it helps you + + align:start position:0% +ideas part helps as well it helps you + + + align:start position:0% +ideas part helps as well it helps you +get into that mood of the you know we + + align:start position:0% +get into that mood of the you know we + + + align:start position:0% +get into that mood of the you know we +can be silly now um something that might + + align:start position:0% +can be silly now um something that might + + + align:start position:0% +can be silly now um something that might +help with the Switching gears uh problem + + align:start position:0% +help with the Switching gears uh problem + + + align:start position:0% +help with the Switching gears uh problem +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +the the the act of writing it down to + + align:start position:0% +the the the act of writing it down to + + + align:start position:0% +the the the act of writing it down to +begin with of course is you know sort of + + align:start position:0% +begin with of course is you know sort of + + + align:start position:0% +begin with of course is you know sort of +says the idea is on record and just to + + align:start position:0% +says the idea is on record and just to + + + align:start position:0% +says the idea is on record and just to +make it say like you know let's you can + + align:start position:0% +make it say like you know let's you can + + + align:start position:0% +make it say like you know let's you can +always say let's get back to that later + + align:start position:0% +always say let's get back to that later + + + align:start position:0% +always say let's get back to that later +uh because you will get back to it later + + align:start position:0% +uh because you will get back to it later + + + align:start position:0% +uh because you will get back to it later +anyway uh and there'll be time for that + + align:start position:0% +anyway uh and there'll be time for that + + + align:start position:0% +anyway uh and there'll be time for that +discussion doesn't always work but it's + + align:start position:0% +discussion doesn't always work but it's + + + align:start position:0% +discussion doesn't always work but it's +worth a + + align:start position:0% +worth a + + + align:start position:0% +worth a +shot cool okay uh let's talk a little + + align:start position:0% +shot cool okay uh let's talk a little + + + align:start position:0% +shot cool okay uh let's talk a little +bit uh again about project one just as a + + align:start position:0% +bit uh again about project one just as a + + + align:start position:0% +bit uh again about project one just as a +reminder there is a theme for project + + align:start position:0% +reminder there is a theme for project + + + align:start position:0% +reminder there is a theme for project +one and that's planning for Randomness + + align:start position:0% +one and that's planning for Randomness + + + align:start position:0% +one and that's planning for Randomness +you generated a lot of ideas we didn't + + align:start position:0% +you generated a lot of ideas we didn't + + + align:start position:0% +you generated a lot of ideas we didn't +do a uh we we we didn't really + + align:start position:0% +do a uh we we we didn't really + + + align:start position:0% +do a uh we we we didn't really +overemphasize that constraint right at + + align:start position:0% +overemphasize that constraint right at + + + align:start position:0% +overemphasize that constraint right at +the right at the beginning of the + + align:start position:0% +the right at the beginning of the + + + align:start position:0% +the right at the beginning of the +brainstorm session because we wanted you + + align:start position:0% +brainstorm session because we wanted you + + + align:start position:0% +brainstorm session because we wanted you +to generate tons and tons of ideas but + + align:start position:0% +to generate tons and tons of ideas but + + + align:start position:0% +to generate tons and tons of ideas but +now now you should be looking at that + + align:start position:0% +now now you should be looking at that + + + align:start position:0% +now now you should be looking at that +theme and thinking and the ideas that + + align:start position:0% +theme and thinking and the ideas that + + + align:start position:0% +theme and thinking and the ideas that +you've generated and figuring out which + + align:start position:0% +you've generated and figuring out which + + + align:start position:0% +you've generated and figuring out which +ones of those kind of match that theme + + align:start position:0% +ones of those kind of match that theme + + + align:start position:0% +ones of those kind of match that theme +um there now that that's sort of like + + align:start position:0% +um there now that that's sort of like + + + align:start position:0% +um there now that that's sort of like +the overall constraint the overall + + align:start position:0% +the overall constraint the overall + + + align:start position:0% +the overall constraint the overall +constraint of what we want the players + + align:start position:0% +constraint of what we want the players + + + align:start position:0% +constraint of what we want the players +to be doing is planning for Randomness + + align:start position:0% +to be doing is planning for Randomness + + + align:start position:0% +to be doing is planning for Randomness +but you know is it in space is it you + + align:start position:0% +but you know is it in space is it you + + + align:start position:0% +but you know is it in space is it you +know uh some sort of like dice rolling + + align:start position:0% +know uh some sort of like dice rolling + + + align:start position:0% +know uh some sort of like dice rolling +mechanic is it some sort of race + + align:start position:0% +mechanic is it some sort of race + + + align:start position:0% +mechanic is it some sort of race +mechanic or uh just a branching de Tre + + align:start position:0% +mechanic or uh just a branching de Tre + + + align:start position:0% +mechanic or uh just a branching de Tre +or something like that you know that + + align:start position:0% +or something like that you know that + + + align:start position:0% +or something like that you know that +comes into themes and mechanics uh so + + align:start position:0% +comes into themes and mechanics uh so + + + align:start position:0% +comes into themes and mechanics uh so +you want to be identifying that as well + + align:start position:0% +you want to be identifying that as well + + + align:start position:0% +you want to be identifying that as well +as as part of project uh of pro project + + align:start position:0% +as as part of project uh of pro project + + + align:start position:0% +as as part of project uh of pro project +one so what we're going to be asking you + + align:start position:0% +one so what we're going to be asking you + + + align:start position:0% +one so what we're going to be asking you +right now is that from your + + align:start position:0% +right now is that from your + + + align:start position:0% +right now is that from your +brainstorming group we want you to split + + align:start position:0% +brainstorming group we want you to split + + + align:start position:0% +brainstorming group we want you to split +into two groups that's your prototyping + + align:start position:0% +into two groups that's your prototyping + + + align:start position:0% +into two groups that's your prototyping +group for project one you only have to + + align:start position:0% +group for project one you only have to + + + align:start position:0% +group for project one you only have to +work with this group for one week you + + align:start position:0% +work with this group for one week you + + + align:start position:0% +work with this group for one week you +know you know this is this this is not a + + align:start position:0% +know you know this is this this is not a + + + align:start position:0% +know you know this is this this is not a +long-term commitment uh and uh we there + + align:start position:0% +long-term commitment uh and uh we there + + + align:start position:0% +long-term commitment uh and uh we there +were eight brainstorming groups so + + align:start position:0% +were eight brainstorming groups so + + + align:start position:0% +were eight brainstorming groups so +basically we're looking for 16 teams uh + + align:start position:0% +basically we're looking for 16 teams uh + + + align:start position:0% +basically we're looking for 16 teams uh +and so we're encouraging everyone to to + + align:start position:0% +and so we're encouraging everyone to to + + + align:start position:0% +and so we're encouraging everyone to to +to be in groups of three uh not only + + align:start position:0% +to be in groups of three uh not only + + + align:start position:0% +to be in groups of three uh not only +does that uh uh mean that you know we we + + align:start position:0% +does that uh uh mean that you know we we + + + align:start position:0% +does that uh uh mean that you know we we +will get the right number of groups it + + align:start position:0% +will get the right number of groups it + + + align:start position:0% +will get the right number of groups it +also means that if somebody Falls sick + + align:start position:0% +also means that if somebody Falls sick + + + align:start position:0% +also means that if somebody Falls sick +in the next week you know your team + + align:start position:0% +in the next week you know your team + + + align:start position:0% +in the next week you know your team +still has you know at least two people + + align:start position:0% +still has you know at least two people + + + align:start position:0% +still has you know at least two people +to work on it um so for each group of + + align:start position:0% +to work on it um so for each group of + + + align:start position:0% +to work on it um so for each group of +three F first of all you figure out who + + align:start position:0% +three F first of all you figure out who + + + align:start position:0% +three F first of all you figure out who +you're going to work with and then you + + align:start position:0% +you're going to work with and then you + + + align:start position:0% +you're going to work with and then you +choose one one item from your list one + + align:start position:0% +choose one one item from your list one + + + align:start position:0% +choose one one item from your list one +of these ideas from your list keeping in + + align:start position:0% +of these ideas from your list keeping in + + + align:start position:0% +of these ideas from your list keeping in +mind those constraints that I I just + + align:start position:0% +mind those constraints that I I just + + + align:start position:0% +mind those constraints that I I just +mentioned and uh we will be using that + + align:start position:0% +mentioned and uh we will be using that + + + align:start position:0% +mentioned and uh we will be using that +idea for the upcoming prototyping + + align:start position:0% +idea for the upcoming prototyping + + + align:start position:0% +idea for the upcoming prototyping +Workshop which I will be leading so once + + align:start position:0% +Workshop which I will be leading so once + + + align:start position:0% +Workshop which I will be leading so once +you know what your idea is you know who + + align:start position:0% +you know what your idea is you know who + + + align:start position:0% +you know what your idea is you know who +you're working with I will go into the + + align:start position:0% +you're working with I will go into the + + + align:start position:0% +you're working with I will go into the +prototyping Workshop to tell you what + + align:start position:0% +prototyping Workshop to tell you what + + + align:start position:0% +prototyping Workshop to tell you what +you do next um and the goal will be to + + align:start position:0% +you do next um and the goal will be to + + + align:start position:0% +you do next um and the goal will be to +then test that idea through the process + + align:start position:0% +then test that idea through the process + + + align:start position:0% +then test that idea through the process +of of prototyping and if it doesn't work + + align:start position:0% +of of prototyping and if it doesn't work + + + align:start position:0% +of of prototyping and if it doesn't work +you're free to choose a different theme + + align:start position:0% +you're free to choose a different theme + + + align:start position:0% +you're free to choose a different theme +but you still have to stick with your + + align:start position:0% +but you still have to stick with your + + + align:start position:0% +but you still have to stick with your +theme okay you stick with your team you + + align:start position:0% +theme okay you stick with your team you + + + align:start position:0% +theme okay you stick with your team you +can choose a different theme just to be + + align:start position:0% +can choose a different theme just to be + + + align:start position:0% +can choose a different theme just to be +clear all right uh we have 10 10 10 10 + + align:start position:0% +clear all right uh we have 10 10 10 10 + + + align:start position:0% +clear all right uh we have 10 10 10 10 +minutes to figure out who you want to + + align:start position:0% +minutes to figure out who you want to + + + align:start position:0% +minutes to figure out who you want to +work with and what's your like initial + + align:start position:0% +work with and what's your like initial + + + align:start position:0% +work with and what's your like initial +idea that you want to work with so go + + align:start position:0% +idea that you want to work with so go + + + align:start position:0% +idea that you want to work with so go +for + + align:start position:0% + + + + align:start position:0% + +it and yours your team was six + + align:start position:0% +it and yours your team was six + + + align:start position:0% +it and yours your team was six +right cool she used a computer + + align:start position:0% +right cool she used a computer + + + align:start position:0% +right cool she used a computer +controlled so it was really voice + + align:start position:0% +controlled so it was really voice + + + align:start position:0% +controlled so it was really voice +activated just didn't + + align:start position:0% +activated just didn't + + + align:start position:0% +activated just didn't +work + + align:start position:0% +work + + + align:start position:0% +work +aame and he made sure he he got + + align:start position:0% +aame and he made sure he he got + + + align:start position:0% +aame and he made sure he he got +how many of you have seen me give this + + align:start position:0% +how many of you have seen me give this + + + align:start position:0% +how many of you have seen me give this +presentation before okay how many of you + + align:start position:0% +presentation before okay how many of you + + + align:start position:0% +presentation before okay how many of you +are thinking does Philip give this + + align:start position:0% +are thinking does Philip give this + + + align:start position:0% +are thinking does Philip give this +presentation every + + align:start position:0% +presentation every + + + align:start position:0% +presentation every +class correct arino I + + align:start position:0% +class correct arino I + + + align:start position:0% +class correct arino I +do um so I apologize to everyone who's + + align:start position:0% +do um so I apologize to everyone who's + + + align:start position:0% +do um so I apologize to everyone who's +seen this presentation maybe there's one + + align:start position:0% +seen this presentation maybe there's one + + + align:start position:0% +seen this presentation maybe there's one +or two little points in here that you + + align:start position:0% +or two little points in here that you + + + align:start position:0% +or two little points in here that you +might not have seen before but for the + + align:start position:0% +might not have seen before but for the + + + align:start position:0% +might not have seen before but for the +most part it is the same uh because it + + align:start position:0% +most part it is the same uh because it + + + align:start position:0% +most part it is the same uh because it +is the fundamental skill that we try to + + align:start position:0% +is the fundamental skill that we try to + + + align:start position:0% +is the fundamental skill that we try to +teach in every single game design class + + align:start position:0% +teach in every single game design class + + + align:start position:0% +teach in every single game design class +uh because it is basically the the the + + align:start position:0% +uh because it is basically the the the + + + align:start position:0% +uh because it is basically the the the +first skill that you're going to need to + + align:start position:0% +first skill that you're going to need to + + + align:start position:0% +first skill that you're going to need to +be able to figure out when an idea Works + + align:start position:0% +be able to figure out when an idea Works + + + align:start position:0% +be able to figure out when an idea Works +um how many of you have made prototypes + + align:start position:0% +um how many of you have made prototypes + + + align:start position:0% +um how many of you have made prototypes +in any field say engineering software + + align:start position:0% +in any field say engineering software + + + align:start position:0% +in any field say engineering software +whatever all right why do you make a + + align:start position:0% + + + + align:start position:0% + +prototype because it's cheaper because + + align:start position:0% +prototype because it's cheaper because + + + align:start position:0% +prototype because it's cheaper because +it's cheaper than than making a real + + align:start position:0% +it's cheaper than than making a real + + + align:start position:0% +it's cheaper than than making a real +thing sure I thought I saw some hands up + + align:start position:0% +thing sure I thought I saw some hands up + + + align:start position:0% +thing sure I thought I saw some hands up +there yeah so faster than making a whole + + align:start position:0% +there yeah so faster than making a whole + + + align:start position:0% +there yeah so faster than making a whole +thing it's faster than making a whole + + align:start position:0% +thing it's faster than making a whole + + + align:start position:0% +thing it's faster than making a whole +thing yeah but that kind of goes hand in + + align:start position:0% +thing yeah but that kind of goes hand in + + + align:start position:0% +thing yeah but that kind of goes hand in +hand too right time time time Timeless + + align:start position:0% +hand too right time time time Timeless + + + align:start position:0% +hand too right time time time Timeless +money making drastic changes is a lot + + align:start position:0% +money making drastic changes is a lot + + + align:start position:0% +money making drastic changes is a lot +cheaper on paper than the system ah okay + + align:start position:0% +cheaper on paper than the system ah okay + + + align:start position:0% +cheaper on paper than the system ah okay +all right you can sort of like figure + + align:start position:0% +all right you can sort of like figure + + + align:start position:0% +all right you can sort of like figure +out what's broken and then you know and + + align:start position:0% +out what's broken and then you know and + + + align:start position:0% +out what's broken and then you know and +then make changes shows a proof of + + align:start position:0% +then make changes shows a proof of + + + align:start position:0% +then make changes shows a proof of +concept it shows a proof of concept to + + align:start position:0% +concept it shows a proof of concept to + + + align:start position:0% +concept it shows a proof of concept to +you can show it to other people um you + + align:start position:0% +you can show it to other people um you + + + align:start position:0% +you can show it to other people um you +know not not just prove it to yourself + + align:start position:0% +know not not just prove it to yourself + + + align:start position:0% +know not not just prove it to yourself +right um it's a lot easier to um + + align:start position:0% +right um it's a lot easier to um + + + align:start position:0% +right um it's a lot easier to um +experiment and make changes if necessary + + align:start position:0% +experiment and make changes if necessary + + + align:start position:0% +experiment and make changes if necessary +when you're not committed to something + + align:start position:0% +when you're not committed to something + + + align:start position:0% +when you're not committed to something +that you a lot all right you can try a + + align:start position:0% +that you a lot all right you can try a + + + align:start position:0% +that you a lot all right you can try a +lot of different ideas right you know + + align:start position:0% +lot of different ideas right you know + + + align:start position:0% +lot of different ideas right you know +it's like I'm not quite sure which way I + + align:start position:0% +it's like I'm not quite sure which way I + + + align:start position:0% +it's like I'm not quite sure which way I +want to go so I'm going to try a lot of + + align:start position:0% +want to go so I'm going to try a lot of + + + align:start position:0% +want to go so I'm going to try a lot of +different alterntive + + align:start position:0% +different alterntive + + + align:start position:0% +different alterntive +helps you + + align:start position:0% + + + + align:start position:0% + +realize catch the big problems that are + + align:start position:0% +realize catch the big problems that are + + + align:start position:0% +realize catch the big problems that are +going to break your design + + align:start position:0% +going to break your design + + + align:start position:0% +going to break your design +yeah move from 2D to 3D to move from 2D + + align:start position:0% +yeah move from 2D to 3D to move from 2D + + + align:start position:0% +yeah move from 2D to 3D to move from 2D +to 3D you you make a 2d prototype before + + align:start position:0% +to 3D you you make a 2d prototype before + + + align:start position:0% +to 3D you you make a 2d prototype before +sort of like taking it into a more + + align:start position:0% +sort of like taking it into a more + + + align:start position:0% +sort of like taking it into a more +complex uh design all of those are + + align:start position:0% +complex uh design all of those are + + + align:start position:0% +complex uh design all of those are +absolutely true um you know this is the + + align:start position:0% +absolutely true um you know this is the + + + align:start position:0% +absolutely true um you know this is the +general sense of why you want to do a + + align:start position:0% +general sense of why you want to do a + + + align:start position:0% +general sense of why you want to do a +prototype at all right is to you know + + align:start position:0% +prototype at all right is to you know + + + align:start position:0% +prototype at all right is to you know +get feedback from other people uh and + + align:start position:0% +get feedback from other people uh and + + + align:start position:0% +get feedback from other people uh and +you get it early you get it cheap and of + + align:start position:0% +you get it early you get it cheap and of + + + align:start position:0% +you get it early you get it cheap and of +course it well we we we we talked about + + align:start position:0% +course it well we we we we talked about + + + align:start position:0% +course it well we we we we talked about +making changes early on in process + + align:start position:0% +making changes early on in process + + + align:start position:0% +making changes early on in process +usually cost less money because you + + align:start position:0% +usually cost less money because you + + + align:start position:0% +usually cost less money because you +haven't committed anything uh you + + align:start position:0% +haven't committed anything uh you + + + align:start position:0% +haven't committed anything uh you +haven't invested a whole lot of + + align:start position:0% +haven't invested a whole lot of + + + align:start position:0% +haven't invested a whole lot of +resources in something just to have to + + align:start position:0% +resources in something just to have to + + + align:start position:0% +resources in something just to have to +change it again um you if you're not + + align:start position:0% +change it again um you if you're not + + + align:start position:0% +change it again um you if you're not +quite sure which direction you want your + + align:start position:0% +quite sure which direction you want your + + + align:start position:0% +quite sure which direction you want your +design to go uh you want to be able to + + align:start position:0% +design to go uh you want to be able to + + + align:start position:0% +design to go uh you want to be able to +have lots of different ideas on on the + + align:start position:0% +have lots of different ideas on on the + + + align:start position:0% +have lots of different ideas on on the +table and actually see how all of them + + align:start position:0% +table and actually see how all of them + + + align:start position:0% +table and actually see how all of them +work in one way or another uh we talked + + align:start position:0% +work in one way or another uh we talked + + + align:start position:0% +work in one way or another uh we talked +about how easy it is to be able to + + align:start position:0% +about how easy it is to be able to + + + align:start position:0% +about how easy it is to be able to +change your ideas when you're + + align:start position:0% +change your ideas when you're + + + align:start position:0% +change your ideas when you're +prototyping but also + + align:start position:0% +prototyping but also + + + align:start position:0% +prototyping but also +um it's easier to discard a prototype + + align:start position:0% +um it's easier to discard a prototype + + + align:start position:0% +um it's easier to discard a prototype +it's easier to just say well that was a + + align:start position:0% +it's easier to just say well that was a + + + align:start position:0% +it's easier to just say well that was a +bad idea you know uh because you haven't + + align:start position:0% +bad idea you know uh because you haven't + + + align:start position:0% +bad idea you know uh because you haven't +really spent all that much time on it + + align:start position:0% +really spent all that much time on it + + + align:start position:0% +really spent all that much time on it +and in many ways that's something you're + + align:start position:0% +and in many ways that's something you're + + + align:start position:0% +and in many ways that's something you're +going to need to do in game design a lot + + align:start position:0% +going to need to do in game design a lot + + + align:start position:0% +going to need to do in game design a lot +you're going to you're going to pursue + + align:start position:0% +you're going to you're going to pursue + + + align:start position:0% +you're going to you're going to pursue +some of these ideas some of these ideas + + align:start position:0% +some of these ideas some of these ideas + + + align:start position:0% +some of these ideas some of these ideas +that you've already been discussing and + + align:start position:0% +that you've already been discussing and + + + align:start position:0% +that you've already been discussing and +you're going to start prototyping it + + align:start position:0% +you're going to start prototyping it + + + align:start position:0% +you're going to start prototyping it +today and then you're going to say well + + align:start position:0% +today and then you're going to say well + + + align:start position:0% +today and then you're going to say well +that was a bad idea and shove the whole + + align:start position:0% +that was a bad idea and shove the whole + + + align:start position:0% +that was a bad idea and shove the whole +thing off the table into a trash can + + align:start position:0% +thing off the table into a trash can + + + align:start position:0% +thing off the table into a trash can +somewhere uh and start a fresh because + + align:start position:0% +somewhere uh and start a fresh because + + + align:start position:0% +somewhere uh and start a fresh because +you've spent what an hour designing this + + align:start position:0% +you've spent what an hour designing this + + + align:start position:0% +you've spent what an hour designing this +thing uh it's not it's it's not going to + + align:start position:0% +thing uh it's not it's it's not going to + + + align:start position:0% +thing uh it's not it's it's not going to +be a whole lot of time and then you can + + align:start position:0% +be a whole lot of time and then you can + + + align:start position:0% +be a whole lot of time and then you can +uh you you can learn from that process + + align:start position:0% +uh you you can learn from that process + + + align:start position:0% +uh you you can learn from that process +and and and and build something new so + + align:start position:0% +and and and and build something new so + + + align:start position:0% +and and and and build something new so +um so it's a very good mindset to be + + align:start position:0% +um so it's a very good mindset to be + + + align:start position:0% +um so it's a very good mindset to be +able to have in early iterations that + + align:start position:0% +able to have in early iterations that + + + align:start position:0% +able to have in early iterations that +this thing that you're making is it's + + align:start position:0% +this thing that you're making is it's + + + align:start position:0% +this thing that you're making is it's +meant to be informative it's it's meant + + align:start position:0% +meant to be informative it's it's meant + + + align:start position:0% +meant to be informative it's it's meant +to teach you something about this + + align:start position:0% +to teach you something about this + + + align:start position:0% +to teach you something about this +project that that that you're working on + + align:start position:0% +project that that that you're working on + + + align:start position:0% +project that that that you're working on +but it's also meant to be disposable uh + + align:start position:0% +but it's also meant to be disposable uh + + + align:start position:0% +but it's also meant to be disposable uh +it's something that you do not have to + + align:start position:0% +it's something that you do not have to + + + align:start position:0% +it's something that you do not have to +make look good or you don't have to make + + align:start position:0% +make look good or you don't have to make + + + align:start position:0% +make look good or you don't have to make +it last uh you don't have to make it + + align:start position:0% +it last uh you don't have to make it + + + align:start position:0% +it last uh you don't have to make it +perfect you just you're just trying to + + align:start position:0% +perfect you just you're just trying to + + + align:start position:0% +perfect you just you're just trying to +learn something through the process of + + align:start position:0% +learn something through the process of + + + align:start position:0% +learn something through the process of +prototyping now when you're making games + + align:start position:0% +prototyping now when you're making games + + + align:start position:0% +prototyping now when you're making games +this is what you're trying to to figure + + align:start position:0% +this is what you're trying to to figure + + + align:start position:0% +this is what you're trying to to figure +out you're trying to find the fun we've + + align:start position:0% +out you're trying to find the fun we've + + + align:start position:0% +out you're trying to find the fun we've +talked about games being a series of + + align:start position:0% +talked about games being a series of + + + align:start position:0% +talked about games being a series of +interesting choices um and when you're + + align:start position:0% +interesting choices um and when you're + + + align:start position:0% +interesting choices um and when you're +prototyping uh what what you're trying + + align:start position:0% +prototyping uh what what you're trying + + + align:start position:0% +prototyping uh what what you're trying +to do is they trying to identify what + + align:start position:0% +to do is they trying to identify what + + + align:start position:0% +to do is they trying to identify what +are those few game mechanics that are + + align:start position:0% +are those few game mechanics that are + + + align:start position:0% +are those few game mechanics that are +going to be able to sustain the interest + + align:start position:0% +going to be able to sustain the interest + + + align:start position:0% +going to be able to sustain the interest +of your players over a significant + + align:start position:0% +of your players over a significant + + + align:start position:0% +of your players over a significant +amount of time um so the nice thing + + align:start position:0% +amount of time um so the nice thing + + + align:start position:0% +amount of time um so the nice thing +about prototyping when you're you know + + align:start position:0% +about prototyping when you're you know + + + align:start position:0% +about prototyping when you're you know +say trying to design a computer game + + align:start position:0% +say trying to design a computer game + + + align:start position:0% +say trying to design a computer game +using paper materials or something is + + align:start position:0% +using paper materials or something is + + + align:start position:0% +using paper materials or something is +that you have to define those mechanics + + align:start position:0% +that you have to define those mechanics + + + align:start position:0% +that you have to define those mechanics +down to the very purest form um so for + + align:start position:0% +down to the very purest form um so for + + + align:start position:0% +down to the very purest form um so for +instance I could say oh this is going to + + align:start position:0% +instance I could say oh this is going to + + + align:start position:0% +instance I could say oh this is going to +be a game about space aliens and you're + + align:start position:0% +be a game about space aliens and you're + + + align:start position:0% +be a game about space aliens and you're +going to run around shooting um you know + + align:start position:0% +going to run around shooting um you know + + + align:start position:0% +going to run around shooting um you know +different kinds of weapons and + + align:start position:0% +different kinds of weapons and + + + align:start position:0% +different kinds of weapons and +occasionally throwing grenades and + + align:start position:0% +occasionally throwing grenades and + + + align:start position:0% +occasionally throwing grenades and +taking cover and you get to fly ships + + align:start position:0% +taking cover and you get to fly ships + + + align:start position:0% +taking cover and you get to fly ships +and drive things around and it's a but + + align:start position:0% +and drive things around and it's a but + + + align:start position:0% +and drive things around and it's a but +what you know I can do when I'm + + align:start position:0% +what you know I can do when I'm + + + align:start position:0% +what you know I can do when I'm +prototyping is that all right uh I'm + + align:start position:0% +prototyping is that all right uh I'm + + + align:start position:0% +prototyping is that all right uh I'm +going to you know make a game where you + + align:start position:0% +going to you know make a game where you + + + align:start position:0% +going to you know make a game where you +come out take a few pot shots go + + align:start position:0% +come out take a few pot shots go + + + align:start position:0% +come out take a few pot shots go +undercover wait for your shoes to + + align:start position:0% +undercover wait for your shoes to + + + align:start position:0% +undercover wait for your shoes to +recharge throw a grenade wait for shoes + + align:start position:0% +recharge throw a grenade wait for shoes + + + align:start position:0% +recharge throw a grenade wait for shoes +to recharge come on and take a few pot + + align:start position:0% +to recharge come on and take a few pot + + + align:start position:0% +to recharge come on and take a few pot +pot shots that's basically what game + + align:start position:0% +pot shots that's basically what game + + + align:start position:0% +pot shots that's basically what game +that's basically Halo um that's a thing + + align:start position:0% +that's basically Halo um that's a thing + + + align:start position:0% +that's basically Halo um that's a thing +that you do every 20 seconds in Halo all + + align:start position:0% +that you do every 20 seconds in Halo all + + + align:start position:0% +that you do every 20 seconds in Halo all +the time and that's really uh the thing + + align:start position:0% +the time and that's really uh the thing + + + align:start position:0% +the time and that's really uh the thing +that they have to nail and get + + align:start position:0% +that they have to nail and get + + + align:start position:0% +that they have to nail and get +absolutely right um so if you right + + align:start position:0% +absolutely right um so if you right + + + align:start position:0% +absolutely right um so if you right +making a prototype you can identify oh + + align:start position:0% +making a prototype you can identify oh + + + align:start position:0% +making a prototype you can identify oh +this core little Loop is the thing + + align:start position:0% +this core little Loop is the thing + + + align:start position:0% +this core little Loop is the thing +that's interesting and if we can + + align:start position:0% +that's interesting and if we can + + + align:start position:0% +that's interesting and if we can +actually get it right and tuned + + align:start position:0% +actually get it right and tuned + + + align:start position:0% +actually get it right and tuned +perfectly in a digital game then we know + + align:start position:0% +perfectly in a digital game then we know + + + align:start position:0% +perfectly in a digital game then we know +players are going to do this over and + + align:start position:0% +players are going to do this over and + + + align:start position:0% +players are going to do this over and +over and over again and it's going to + + align:start position:0% +over and over again and it's going to + + + align:start position:0% +over and over again and it's going to +feel good so you're trying to find that + + align:start position:0% +feel good so you're trying to find that + + + align:start position:0% +feel good so you're trying to find that +fun so you're going to focus on the + + align:start position:0% +fun so you're going to focus on the + + + align:start position:0% +fun so you're going to focus on the +small handful of choices that a player + + align:start position:0% +small handful of choices that a player + + + align:start position:0% +small handful of choices that a player +must make in order to play your + + align:start position:0% +must make in order to play your + + + align:start position:0% +must make in order to play your +prototype uh and you model a system with + + align:start position:0% +prototype uh and you model a system with + + + align:start position:0% +prototype uh and you model a system with +a few basic rules that creates + + align:start position:0% +a few basic rules that creates + + + align:start position:0% +a few basic rules that creates +interesting choices for the player um + + align:start position:0% +interesting choices for the player um + + + align:start position:0% +interesting choices for the player um +always ask a question about your game + + align:start position:0% +always ask a question about your game + + + align:start position:0% +always ask a question about your game +make sure it's falsifiable anyone heard + + align:start position:0% +make sure it's falsifiable anyone heard + + + align:start position:0% +make sure it's falsifiable anyone heard +that term + + align:start position:0% +that term + + + align:start position:0% +that term +falsifiable + + align:start position:0% +falsifiable + + + align:start position:0% +falsifiable +falsifiable hypothesis + + align:start position:0% +falsifiable hypothesis + + + align:start position:0% +falsifiable hypothesis +no yeah what's that mean basically it + + align:start position:0% +no yeah what's that mean basically it + + + align:start position:0% +no yeah what's that mean basically it +means some kind + + align:start position:0% +means some kind + + + align:start position:0% +means some kind +of opinion that can be proven yeah you + + align:start position:0% +of opinion that can be proven yeah you + + + align:start position:0% +of opinion that can be proven yeah you +could say well you know you said um same + + align:start position:0% +could say well you know you said um same + + + align:start position:0% +could say well you know you said um same +say say the the question is that we + + align:start position:0% +say say the the question is that we + + + align:start position:0% +say say the the question is that we +think the players are going to enjoy + + align:start position:0% +think the players are going to enjoy + + + align:start position:0% +think the players are going to enjoy +making these kinds of decisions and the + + align:start position:0% +making these kinds of decisions and the + + + align:start position:0% +making these kinds of decisions and the +answer could be no they don't + + align:start position:0% +answer could be no they don't + + + align:start position:0% +answer could be no they don't +you want that information um it could be + + align:start position:0% +you want that information um it could be + + + align:start position:0% +you want that information um it could be +something like you know this particular + + align:start position:0% +something like you know this particular + + + align:start position:0% +something like you know this particular +design is going to save time right you + + align:start position:0% +design is going to save time right you + + + align:start position:0% +design is going to save time right you +know it's going to be less of less of a + + align:start position:0% +know it's going to be less of less of a + + + align:start position:0% +know it's going to be less of less of a +cognitive load or it's going to be + + align:start position:0% +cognitive load or it's going to be + + + align:start position:0% +cognitive load or it's going to be +easier for players to understand and it + + align:start position:0% +easier for players to understand and it + + + align:start position:0% +easier for players to understand and it +should be that that kind of question + + align:start position:0% +should be that that kind of question + + + align:start position:0% +should be that that kind of question +that you that you ask when you're making + + align:start position:0% +that you that you ask when you're making + + + align:start position:0% +that you that you ask when you're making +a prototype your prototype should be + + align:start position:0% +a prototype your prototype should be + + + align:start position:0% +a prototype your prototype should be +able to be designed in a way where you + + align:start position:0% +able to be designed in a way where you + + + align:start position:0% +able to be designed in a way where you +can play sit someone in front of it play + + align:start position:0% +can play sit someone in front of it play + + + align:start position:0% +can play sit someone in front of it play +through it and then tell you yes or no + + align:start position:0% +through it and then tell you yes or no + + + align:start position:0% +through it and then tell you yes or no +was that hypothesis true or not now + + align:start position:0% +was that hypothesis true or not now + + + align:start position:0% +was that hypothesis true or not now +physical prototype in paper prototyping + + align:start position:0% +physical prototype in paper prototyping + + + align:start position:0% +physical prototype in paper prototyping +doesn't give you insight into everything + + align:start position:0% +doesn't give you insight into everything + + + align:start position:0% +doesn't give you insight into everything +that you can make achieve in a digital + + align:start position:0% +that you can make achieve in a digital + + + align:start position:0% +that you can make achieve in a digital +game it doesn't say for instance tell + + align:start position:0% +game it doesn't say for instance tell + + + align:start position:0% +game it doesn't say for instance tell +you terribly much about the sensory + + align:start position:0% +you terribly much about the sensory + + + align:start position:0% +you terribly much about the sensory +experience of playing that game or how + + align:start position:0% +experience of playing that game or how + + + align:start position:0% +experience of playing that game or how +feasible a certain feature is going to + + align:start position:0% +feasible a certain feature is going to + + + align:start position:0% +feasible a certain feature is going to +be so you don't discover everything + + align:start position:0% +be so you don't discover everything + + + align:start position:0% +be so you don't discover everything +through making a + + align:start position:0% +through making a + + + align:start position:0% +through making a +prototype um but you do get a lot now + + align:start position:0% +prototype um but you do get a lot now + + + align:start position:0% +prototype um but you do get a lot now +the other thing that we that a few + + align:start position:0% +the other thing that we that a few + + + align:start position:0% +the other thing that we that a few +people alluded to is to be is to build + + align:start position:0% +people alluded to is to be is to build + + + align:start position:0% +people alluded to is to be is to build +the ability for your prototype to um + + align:start position:0% +the ability for your prototype to um + + + align:start position:0% +the ability for your prototype to um +communicate to other people especially + + align:start position:0% +communicate to other people especially + + + align:start position:0% +communicate to other people especially +other people on your team uh so imagine + + align:start position:0% +other people on your team uh so imagine + + + align:start position:0% +other people on your team uh so imagine +getting into a room full of developers + + align:start position:0% +getting into a room full of developers + + + align:start position:0% +getting into a room full of developers +all of you are game developers uh and + + align:start position:0% +all of you are game developers uh and + + + align:start position:0% +all of you are game developers uh and +you don't know what's in each other's + + align:start position:0% +you don't know what's in each other's + + + align:start position:0% +you don't know what's in each other's +heads right now you you you maybe have + + align:start position:0% +heads right now you you you maybe have + + + align:start position:0% +heads right now you you you maybe have +narrow have come down to a certain uh uh + + align:start position:0% +narrow have come down to a certain uh uh + + + align:start position:0% +narrow have come down to a certain uh uh +theme and all of you have different + + align:start position:0% +theme and all of you have different + + + align:start position:0% +theme and all of you have different +versions of that game floating in your + + align:start position:0% +versions of that game floating in your + + + align:start position:0% +versions of that game floating in your +head somewhere um now if you want to be + + align:start position:0% +head somewhere um now if you want to be + + + align:start position:0% +head somewhere um now if you want to be +able to sort of explain that to somebody + + align:start position:0% +able to sort of explain that to somebody + + + align:start position:0% +able to sort of explain that to somebody +else it can be near to impossible to + + align:start position:0% +else it can be near to impossible to + + + align:start position:0% +else it can be near to impossible to +communicate that you can try doing it + + align:start position:0% +communicate that you can try doing it + + + align:start position:0% +communicate that you can try doing it +verbally you can try writing it down but + + align:start position:0% +verbally you can try writing it down but + + + align:start position:0% +verbally you can try writing it down but +it's all of those methods don't really + + align:start position:0% +it's all of those methods don't really + + + align:start position:0% +it's all of those methods don't really +compare very well to something you can + + align:start position:0% +compare very well to something you can + + + align:start position:0% +compare very well to something you can +actually set somebody in front and play + + align:start position:0% +actually set somebody in front and play + + + align:start position:0% +actually set somebody in front and play +so yeah what you're trying to do is + + align:start position:0% +so yeah what you're trying to do is + + + align:start position:0% +so yeah what you're trying to do is +you're trying to give your own team to + + align:start position:0% +you're trying to give your own team to + + + align:start position:0% +you're trying to give your own team to +start with something solid to work from + + align:start position:0% +start with something solid to work from + + + align:start position:0% +start with something solid to work from +it may not necessarily be it will almost + + align:start position:0% +it may not necessarily be it will almost + + + align:start position:0% +it may not necessarily be it will almost +certainly not be the idea that you're + + align:start position:0% +certainly not be the idea that you're + + + align:start position:0% +certainly not be the idea that you're +going to end up implementing in the long + + align:start position:0% +going to end up implementing in the long + + + align:start position:0% +going to end up implementing in the long +run but you're going to start creating + + align:start position:0% +run but you're going to start creating + + + align:start position:0% +run but you're going to start creating +some sort of framework for you to then + + align:start position:0% +some sort of framework for you to then + + + align:start position:0% +some sort of framework for you to then +say well I didn't like that I should + + align:start position:0% +say well I didn't like that I should + + + align:start position:0% +say well I didn't like that I should +change that or I really like that and + + align:start position:0% +change that or I really like that and + + + align:start position:0% +change that or I really like that and +and and and and and we should try to + + align:start position:0% +and and and and and we should try to + + + align:start position:0% +and and and and and we should try to +polish that uh uh a little bit uh so + + align:start position:0% +polish that uh uh a little bit uh so + + + align:start position:0% +polish that uh uh a little bit uh so +it's a communication tool and um all any + + align:start position:0% +it's a communication tool and um all any + + + align:start position:0% +it's a communication tool and um all any +kind of game design definitely uh + + align:start position:0% +kind of game design definitely uh + + + align:start position:0% +kind of game design definitely uh +benefits tremendously from early stages + + align:start position:0% +benefits tremendously from early stages + + + align:start position:0% +benefits tremendously from early stages +of a physical prototype uh because it + + align:start position:0% +of a physical prototype uh because it + + + align:start position:0% +of a physical prototype uh because it +allow it forces you to think through how + + align:start position:0% +allow it forces you to think through how + + + align:start position:0% +allow it forces you to think through how +your game is going to work uh every + + align:start position:0% +your game is going to work uh every + + + align:start position:0% +your game is going to work uh every +little detail about how your rules work + + align:start position:0% +little detail about how your rules work + + + align:start position:0% +little detail about how your rules work +at at least maybe not how your game + + align:start position:0% +at at least maybe not how your game + + + align:start position:0% +at at least maybe not how your game +looks maybe not what your input + + align:start position:0% +looks maybe not what your input + + + align:start position:0% +looks maybe not what your input +mechanism is but certainly what are the + + align:start position:0% +mechanism is but certainly what are the + + + align:start position:0% +mechanism is but certainly what are the +decisions that you're asking for your + + align:start position:0% +decisions that you're asking for your + + + align:start position:0% +decisions that you're asking for your +player and what are the consequences of + + align:start position:0% +player and what are the consequences of + + + align:start position:0% +player and what are the consequences of +those decisions um you have to Define + + align:start position:0% +those decisions um you have to Define + + + align:start position:0% +those decisions um you have to Define +them you have to write them down in + + align:start position:0% +them you have to write them down in + + + align:start position:0% +them you have to write them down in +rules uh that your players as well as + + align:start position:0% +rules uh that your players as well as + + + align:start position:0% +rules uh that your players as well as +your design team actually understand uh + + align:start position:0% +your design team actually understand uh + + + align:start position:0% +your design team actually understand uh +and then they're going to try it out and + + align:start position:0% +and then they're going to try it out and + + + align:start position:0% +and then they're going to try it out and +you're going to see all kinds of + + align:start position:0% +you're going to see all kinds of + + + align:start position:0% +you're going to see all kinds of +emerging little Dynamics pop up when all + + align:start position:0% +emerging little Dynamics pop up when all + + + align:start position:0% +emerging little Dynamics pop up when all +of these rules are put to together that + + align:start position:0% +of these rules are put to together that + + + align:start position:0% +of these rules are put to together that +you didn't anticipate and could be + + align:start position:0% +you didn't anticipate and could be + + + align:start position:0% +you didn't anticipate and could be +really cool or could completely break + + align:start position:0% +really cool or could completely break + + + align:start position:0% +really cool or could completely break +your game and you want to find that + + align:start position:0% + + + + align:start position:0% + +out um I talked about bringing in + + align:start position:0% +out um I talked about bringing in + + + align:start position:0% +out um I talked about bringing in +testers and uh and as we keep harping on + + align:start position:0% +testers and uh and as we keep harping on + + + align:start position:0% +testers and uh and as we keep harping on +on this class and again every single + + align:start position:0% +on this class and again every single + + + align:start position:0% +on this class and again every single +class that I teach testing is incredible + + align:start position:0% +class that I teach testing is incredible + + + align:start position:0% +class that I teach testing is incredible +important uh but the nice thing about + + align:start position:0% +important uh but the nice thing about + + + align:start position:0% +important uh but the nice thing about +paper prototyping is that you don't + + align:start position:0% +paper prototyping is that you don't + + + align:start position:0% +paper prototyping is that you don't +really need special skills you need + + align:start position:0% +really need special skills you need + + + align:start position:0% +really need special skills you need +third grade arts and craft skills really + + align:start position:0% +third grade arts and craft skills really + + + align:start position:0% +third grade arts and craft skills really +um maybe you know MIT math sure uh but + + align:start position:0% +um maybe you know MIT math sure uh but + + + align:start position:0% +um maybe you know MIT math sure uh but +but actual you know we're talking about + + align:start position:0% +but actual you know we're talking about + + + align:start position:0% +but actual you know we're talking about +using markers and scissors and + + align:start position:0% +using markers and scissors and + + + align:start position:0% +using markers and scissors and +kindergarten counters and dice um and + + align:start position:0% +kindergarten counters and dice um and + + + align:start position:0% +kindergarten counters and dice um and +the nice thing about it is that if your + + align:start position:0% +the nice thing about it is that if your + + + align:start position:0% +the nice thing about it is that if your +team gets larger and larger everyone can + + align:start position:0% +team gets larger and larger everyone can + + + align:start position:0% +team gets larger and larger everyone can +still contribute to the paper prototype + + align:start position:0% +still contribute to the paper prototype + + + align:start position:0% +still contribute to the paper prototype +it could be an artist it could be a + + align:start position:0% +it could be an artist it could be a + + + align:start position:0% +it could be an artist it could be a +designer a producer a quer a QA test + + align:start position:0% +designer a producer a quer a QA test + + + align:start position:0% +designer a producer a quer a QA test +even you know someone that you've just + + align:start position:0% +even you know someone that you've just + + + align:start position:0% +even you know someone that you've just +brought in for a day to play your game + + align:start position:0% +brought in for a day to play your game + + + align:start position:0% +brought in for a day to play your game +can all contribute to this uh to the + + align:start position:0% +can all contribute to this uh to the + + + align:start position:0% +can all contribute to this uh to the +design of your game because it can give + + align:start position:0% +design of your game because it can give + + + align:start position:0% +design of your game because it can give +you feedback of well what if instead of + + align:start position:0% +you feedback of well what if instead of + + + align:start position:0% +you feedback of well what if instead of +rolling this dice I roll that dice or + + align:start position:0% +rolling this dice I roll that dice or + + + align:start position:0% +rolling this dice I roll that dice or +what if the grid was a little bit bigger + + align:start position:0% +what if the grid was a little bit bigger + + + align:start position:0% +what if the grid was a little bit bigger +you know what if my pieces were a little + + align:start position:0% +you know what if my pieces were a little + + + align:start position:0% +you know what if my pieces were a little +bit larger and took up more space for + + align:start position:0% +bit larger and took up more space for + + + align:start position:0% +bit larger and took up more space for +instance um a paper prototype itself is + + align:start position:0% +instance um a paper prototype itself is + + + align:start position:0% +instance um a paper prototype itself is +not just interactive in its play but + + align:start position:0% +not just interactive in its play but + + + align:start position:0% +not just interactive in its play but +it's interactive in the design you can + + align:start position:0% +it's interactive in the design you can + + + align:start position:0% +it's interactive in the design you can +just like open up the hood of your uh + + align:start position:0% +just like open up the hood of your uh + + + align:start position:0% +just like open up the hood of your uh +paper pro pro protype and change a rule + + align:start position:0% +paper pro pro protype and change a rule + + + align:start position:0% +paper pro pro protype and change a rule +try doing that to uh do not do that when + + align:start position:0% +try doing that to uh do not do that when + + + align:start position:0% +try doing that to uh do not do that when +you're working with code in the middle + + align:start position:0% +you're working with code in the middle + + + align:start position:0% +you're working with code in the middle +of a play test do not change your code + + align:start position:0% +of a play test do not change your code + + + align:start position:0% +of a play test do not change your code +for God's sake um but you can do that + + align:start position:0% +for God's sake um but you can do that + + + align:start position:0% +for God's sake um but you can do that +with a paper prototype and in many times + + align:start position:0% +with a paper prototype and in many times + + + align:start position:0% +with a paper prototype and in many times +uh you might want to do that in the + + align:start position:0% +uh you might want to do that in the + + + align:start position:0% +uh you might want to do that in the +middle of a test it's like here you you + + align:start position:0% +middle of a test it's like here you you + + + align:start position:0% +middle of a test it's like here you you +you're playing a game you know 10 + + align:start position:0% +you're playing a game you know 10 + + + align:start position:0% +you're playing a game you know 10 +minutes into the game it's like oh my + + align:start position:0% +minutes into the game it's like oh my + + + align:start position:0% +minutes into the game it's like oh my +God this game is hurtling downhill into + + align:start position:0% +God this game is hurtling downhill into + + + align:start position:0% +God this game is hurtling downhill into +a pit uh and you and you can see it and + + align:start position:0% +a pit uh and you and you can see it and + + + align:start position:0% +a pit uh and you and you can see it and +the player see sees it and you know + + align:start position:0% +the player see sees it and you know + + + align:start position:0% +the player see sees it and you know +there is a problem you can just change a + + align:start position:0% +there is a problem you can just change a + + + align:start position:0% +there is a problem you can just change a +rule and just says what if we did this + + align:start position:0% +rule and just says what if we did this + + + align:start position:0% +rule and just says what if we did this +instead you know mid game even and then + + align:start position:0% +instead you know mid game even and then + + + align:start position:0% +instead you know mid game even and then +try it out says oh that seemed to maybe + + align:start position:0% +try it out says oh that seemed to maybe + + + align:start position:0% +try it out says oh that seemed to maybe +address the problem then start the game + + align:start position:0% +address the problem then start the game + + + align:start position:0% +address the problem then start the game +from the beginning and and see if it + + align:start position:0% +from the beginning and and see if it + + + align:start position:0% +from the beginning and and see if it +actually did uh but you can't do that + + align:start position:0% +actually did uh but you can't do that + + + align:start position:0% +actually did uh but you can't do that +with a paper prototype um paper + + align:start position:0% +with a paper prototype um paper + + + align:start position:0% +with a paper prototype um paper +prototypes in particular are very good + + align:start position:0% +prototypes in particular are very good + + + align:start position:0% +prototypes in particular are very good +at revealing usability problems the + + align:start position:0% +at revealing usability problems the + + + align:start position:0% +at revealing usability problems the +simple issue of a player has a decision + + align:start position:0% +simple issue of a player has a decision + + + align:start position:0% +simple issue of a player has a decision +knows what he or she wants to do and has + + align:start position:0% +knows what he or she wants to do and has + + + align:start position:0% +knows what he or she wants to do and has +no idea how to actually execute that you + + align:start position:0% +no idea how to actually execute that you + + + align:start position:0% +no idea how to actually execute that you +know you know it's like uh does that + + align:start position:0% +know you know it's like uh does that + + + align:start position:0% +know you know it's like uh does that +mean I roll first and then move or do I + + align:start position:0% +mean I roll first and then move or do I + + + align:start position:0% +mean I roll first and then move or do I +move first and roll which piece do I + + align:start position:0% +move first and roll which piece do I + + + align:start position:0% +move first and roll which piece do I +move you know uh things like things like + + align:start position:0% +move you know uh things like things like + + + align:start position:0% +move you know uh things like things like +that um paper prototypes are very very + + align:start position:0% +that um paper prototypes are very very + + + align:start position:0% +that um paper prototypes are very very +good it's sort of just laying that bear + + align:start position:0% +good it's sort of just laying that bear + + + align:start position:0% +good it's sort of just laying that bear +your your your team will see where those + + align:start position:0% +your your your team will see where those + + + align:start position:0% +your your your team will see where those +problems are as soon as somebody who's + + align:start position:0% +problems are as soon as somebody who's + + + align:start position:0% +problems are as soon as somebody who's +not part of your team sits down and + + align:start position:0% +not part of your team sits down and + + + align:start position:0% +not part of your team sits down and +tries to play + + align:start position:0% +tries to play + + + align:start position:0% +tries to play +it + + align:start position:0% +it + + + align:start position:0% +it +um let's see uh now players do tend to + + align:start position:0% +um let's see uh now players do tend to + + + align:start position:0% +um let's see uh now players do tend to +uh more readily give criticism when they + + align:start position:0% +uh more readily give criticism when they + + + align:start position:0% +uh more readily give criticism when they +see something that's very clear + + align:start position:0% +see something that's very clear + + + align:start position:0% +see something that's very clear +incomplete very clearly something that + + align:start position:0% +incomplete very clearly something that + + + align:start position:0% +incomplete very clearly something that +you're still working on and if you've + + align:start position:0% +you're still working on and if you've + + + align:start position:0% +you're still working on and if you've +got a handdrawn cardboard paper + + align:start position:0% +got a handdrawn cardboard paper + + + align:start position:0% +got a handdrawn cardboard paper +prototype in front of them they know + + align:start position:0% +prototype in front of them they know + + + align:start position:0% +prototype in front of them they know +you're right at the beginning of this + + align:start position:0% +you're right at the beginning of this + + + align:start position:0% +you're right at the beginning of this +project you know they they know that + + align:start position:0% +project you know they they know that + + + align:start position:0% +project you know they they know that +they can tell you something about I + + align:start position:0% +they can tell you something about I + + + align:start position:0% +they can tell you something about I +really don't like how this character + + align:start position:0% +really don't like how this character + + + align:start position:0% +really don't like how this character +looks and it's like that's fine we spent + + align:start position:0% +looks and it's like that's fine we spent + + + align:start position:0% +looks and it's like that's fine we spent +two minutes drawing that character you + + align:start position:0% +two minutes drawing that character you + + + align:start position:0% +two minutes drawing that character you +know we can completely redo that um and + + align:start position:0% +know we can completely redo that um and + + + align:start position:0% +know we can completely redo that um and +they'll tell you that uh if if it feels + + align:start position:0% +they'll tell you that uh if if it feels + + + align:start position:0% +they'll tell you that uh if if it feels +like like you haven't spend a whole lot + + align:start position:0% +like like you haven't spend a whole lot + + + align:start position:0% +like like you haven't spend a whole lot +of + + align:start position:0% +of + + + align:start position:0% +of +time in it and it's that's a useful + + align:start position:0% +time in it and it's that's a useful + + + align:start position:0% +time in it and it's that's a useful +trick by the way if you're doing say the + + align:start position:0% +trick by the way if you're doing say the + + + align:start position:0% +trick by the way if you're doing say the +digit version of your games later on it + + align:start position:0% +digit version of your games later on it + + + align:start position:0% +digit version of your games later on it +can actually be easier to get feedback + + align:start position:0% +can actually be easier to get feedback + + + align:start position:0% +can actually be easier to get feedback +if you like deliberately insert some + + align:start position:0% +if you like deliberately insert some + + + align:start position:0% +if you like deliberately insert some +things that look incomplete uh you know + + align:start position:0% +things that look incomplete uh you know + + + align:start position:0% +things that look incomplete uh you know +a giant box that says placeholder right + + align:start position:0% +a giant box that says placeholder right + + + align:start position:0% +a giant box that says placeholder right +there uh while you're getting while + + align:start position:0% +there uh while you're getting while + + + align:start position:0% +there uh while you're getting while +you're doing your testing just to get a + + align:start position:0% +you're doing your testing just to get a + + + align:start position:0% +you're doing your testing just to get a +little bit more feedback from your uh + + align:start position:0% +little bit more feedback from your uh + + + align:start position:0% +little bit more feedback from your uh +testers so they feel okay you're still + + align:start position:0% +testers so they feel okay you're still + + + align:start position:0% +testers so they feel okay you're still +working on this I can tell you that + + align:start position:0% +working on this I can tell you that + + + align:start position:0% +working on this I can tell you that +character looks you know looks terrible + + align:start position:0% +character looks you know looks terrible + + + align:start position:0% +character looks you know looks terrible +and it's like we spent three days on it + + align:start position:0% +and it's like we spent three days on it + + + align:start position:0% +and it's like we spent three days on it +but you don't say that you don't say + + align:start position:0% +but you don't say that you don't say + + + align:start position:0% +but you don't say that you don't say +that in front of them because you want + + align:start position:0% +that in front of them because you want + + + align:start position:0% +that in front of them because you want +that feedback um but when they give you + + align:start position:0% +that feedback um but when they give you + + + align:start position:0% +that feedback um but when they give you +feedback uh you take everything that + + align:start position:0% +feedback uh you take everything that + + + align:start position:0% +feedback uh you take everything that +they're telling you with a grain of salt + + align:start position:0% +they're telling you with a grain of salt + + + align:start position:0% +they're telling you with a grain of salt +because uh in the paper prototype is + + align:start position:0% +because uh in the paper prototype is + + + align:start position:0% +because uh in the paper prototype is +very very easy for a tester says I don't + + align:start position:0% +very very easy for a tester says I don't + + + align:start position:0% +very very easy for a tester says I don't +like pieces that are this color I want + + align:start position:0% +like pieces that are this color I want + + + align:start position:0% +like pieces that are this color I want +pieces that are that color and it's okay + + align:start position:0% +pieces that are that color and it's okay + + + align:start position:0% +pieces that are that color and it's okay +you know you could just make the + + align:start position:0% +you know you could just make the + + + align:start position:0% +you know you could just make the +substitution uh but what you could you + + align:start position:0% +substitution uh but what you could you + + + align:start position:0% +substitution uh but what you could you +should do is you should s of think back + + align:start position:0% +should do is you should s of think back + + + align:start position:0% +should do is you should s of think back +a little bit and try to figure out why + + align:start position:0% +a little bit and try to figure out why + + + align:start position:0% +a little bit and try to figure out why +they're giving you this piece of + + align:start position:0% +they're giving you this piece of + + + align:start position:0% +they're giving you this piece of +feedback you know they may have a + + align:start position:0% +feedback you know they may have a + + + align:start position:0% +feedback you know they may have a +personal preference and they think this + + align:start position:0% +personal preference and they think this + + + align:start position:0% +personal preference and they think this +is the way how it should be executed but + + align:start position:0% +is the way how it should be executed but + + + align:start position:0% +is the way how it should be executed but +probably what they're saying is they + + align:start position:0% +probably what they're saying is they + + + align:start position:0% +probably what they're saying is they +have a pro some sort of actual problem + + align:start position:0% +have a pro some sort of actual problem + + + align:start position:0% +have a pro some sort of actual problem +with your game and that's the only + + align:start position:0% +with your game and that's the only + + + align:start position:0% +with your game and that's the only +solution that they can think of so for + + align:start position:0% +solution that they can think of so for + + + align:start position:0% +solution that they can think of so for +instance uh you know why does this + + align:start position:0% +instance uh you know why does this + + + align:start position:0% +instance uh you know why does this +person want to change the color of the + + align:start position:0% +person want to change the color of the + + + align:start position:0% +person want to change the color of the +pieces that they're moving around is it + + align:start position:0% +pieces that they're moving around is it + + + align:start position:0% +pieces that they're moving around is it +because they are having trouble telling + + align:start position:0% +because they are having trouble telling + + + align:start position:0% +because they are having trouble telling +the pieces apart that may be the real + + align:start position:0% +the pieces apart that may be the real + + + align:start position:0% +the pieces apart that may be the real +problem and the solution may not be + + align:start position:0% +problem and the solution may not be + + + align:start position:0% +problem and the solution may not be +change the pieces to a different color + + align:start position:0% +change the pieces to a different color + + + align:start position:0% +change the pieces to a different color +maybe like you know change the piece + + align:start position:0% +maybe like you know change the piece + + + align:start position:0% +maybe like you know change the piece +into a completely different shape you + + align:start position:0% +into a completely different shape you + + + align:start position:0% +into a completely different shape you +know uh stick a little sticker on them + + align:start position:0% +know uh stick a little sticker on them + + + align:start position:0% +know uh stick a little sticker on them +uh on a computer is going to be uh + + align:start position:0% +uh on a computer is going to be uh + + + align:start position:0% +uh on a computer is going to be uh +different kinds of solutions vet every + + align:start position:0% +different kinds of solutions vet every + + + align:start position:0% +different kinds of solutions vet every +little bit of information that comes + + align:start position:0% +little bit of information that comes + + + align:start position:0% +little bit of information that comes +into you people can make suggestions on + + align:start position:0% +into you people can make suggestions on + + + align:start position:0% +into you people can make suggestions on +how you're going to change your design + + align:start position:0% +how you're going to change your design + + + align:start position:0% +how you're going to change your design +uh but it's up to the team to actually + + align:start position:0% +uh but it's up to the team to actually + + + align:start position:0% +uh but it's up to the team to actually +provide some sort of unified Direction + + align:start position:0% +provide some sort of unified Direction + + + align:start position:0% +provide some sort of unified Direction +on where you want the game to go so the + + align:start position:0% +on where you want the game to go so the + + + align:start position:0% +on where you want the game to go so the +the feedback is avable the solutions + + align:start position:0% +the feedback is avable the solutions + + + align:start position:0% +the feedback is avable the solutions +they're providing um may not be the + + align:start position:0% +they're providing um may not be the + + + align:start position:0% +they're providing um may not be the +solutions you want to use any question + + align:start position:0% +solutions you want to use any question + + + align:start position:0% +solutions you want to use any question +so far about why we're doing + + align:start position:0% + + + + align:start position:0% + +prototyping no + + align:start position:0% +prototyping no + + + align:start position:0% +prototyping no +okay we we have more questions later so + + align:start position:0% +okay we we have more questions later so + + + align:start position:0% +okay we we have more questions later so +here are the kinds of tools that you're + + align:start position:0% +here are the kinds of tools that you're + + + align:start position:0% +here are the kinds of tools that you're +going to be using very large sheets of + + align:start position:0% +going to be using very large sheets of + + + align:start position:0% +going to be using very large sheets of +paper um this is probably the smallest + + align:start position:0% +paper um this is probably the smallest + + + align:start position:0% +paper um this is probably the smallest +sheet of paper well we're going to be + + align:start position:0% +sheet of paper well we're going to be + + + align:start position:0% +sheet of paper well we're going to be +using index cards as well but this is uh + + align:start position:0% +using index cards as well but this is uh + + + align:start position:0% +using index cards as well but this is uh +a lot of you have seen this before in my + + align:start position:0% +a lot of you have seen this before in my + + + align:start position:0% +a lot of you have seen this before in my +other classes as well this is a square + + align:start position:0% +other classes as well this is a square + + + align:start position:0% +other classes as well this is a square +grid on one side hex grid on another uh + + align:start position:0% +grid on one side hex grid on another uh + + + align:start position:0% +grid on one side hex grid on another uh +for spatial games you can use this but + + align:start position:0% +for spatial games you can use this but + + + align:start position:0% +for spatial games you can use this but +sometimes it's much better to start with + + align:start position:0% +sometimes it's much better to start with + + + align:start position:0% +sometimes it's much better to start with +a blank sheet of paper so don't don't + + align:start position:0% +a blank sheet of paper so don't don't + + + align:start position:0% +a blank sheet of paper so don't don't +don't immediately start designing grid + + align:start position:0% +don't immediately start designing grid + + + align:start position:0% +don't immediately start designing grid +games just because we happen to have she + + align:start position:0% +games just because we happen to have she + + + align:start position:0% +games just because we happen to have she +sheets of grided paper um but we do want + + align:start position:0% +sheets of grided paper um but we do want + + + align:start position:0% +sheets of grided paper um but we do want +them to be large uh so that everyone + + align:start position:0% +them to be large uh so that everyone + + + align:start position:0% +them to be large uh so that everyone +around the team can actually see what + + align:start position:0% +around the team can actually see what + + + align:start position:0% +around the team can actually see what +you're working on at the same time as + + align:start position:0% +you're working on at the same time as + + + align:start position:0% +you're working on at the same time as +well as as the people playing the play + + align:start position:0% +well as as the people playing the play + + + align:start position:0% +well as as the people playing the play +playing the game if you're going to be + + align:start position:0% +playing the game if you're going to be + + + align:start position:0% +playing the game if you're going to be +designing something like a uh iPad game + + align:start position:0% +designing something like a uh iPad game + + + align:start position:0% +designing something like a uh iPad game +or something like that don't use + + align:start position:0% +or something like that don't use + + + align:start position:0% +or something like that don't use +something that's literally the size of + + align:start position:0% +something that's literally the size of + + + align:start position:0% +something that's literally the size of +the iPad use something a little bit + + align:start position:0% +the iPad use something a little bit + + + align:start position:0% +the iPad use something a little bit +larger so that everyone around the table + + align:start position:0% +larger so that everyone around the table + + + align:start position:0% +larger so that everyone around the table +can see what the tester is doing while + + align:start position:0% +can see what the tester is doing while + + + align:start position:0% +can see what the tester is doing while +they're testing your your your prototype + + align:start position:0% +they're testing your your your prototype + + + align:start position:0% +they're testing your your your prototype +um you we use index cards uh for a lot + + align:start position:0% +um you we use index cards uh for a lot + + + align:start position:0% +um you we use index cards uh for a lot +of different things uh writing down + + align:start position:0% +of different things uh writing down + + + align:start position:0% +of different things uh writing down +rules you can shuffle them and use them + + align:start position:0% +rules you can shuffle them and use them + + + align:start position:0% +rules you can shuffle them and use them +as playing cards uh you can record data + + align:start position:0% +as playing cards uh you can record data + + + align:start position:0% +as playing cards uh you can record data +on on them you know they're very + + align:start position:0% +on on them you know they're very + + + align:start position:0% +on on them you know they're very +disposable very re more accurately very + + align:start position:0% +disposable very re more accurately very + + + align:start position:0% +disposable very re more accurately very +recyclable please please recycle any + + align:start position:0% +recyclable please please recycle any + + + align:start position:0% +recyclable please please recycle any +paper + + align:start position:0% +paper + + + align:start position:0% +paper +material uh dice of course um they can + + align:start position:0% +material uh dice of course um they can + + + align:start position:0% +material uh dice of course um they can +be tokens they can be used to help keep + + align:start position:0% +be tokens they can be used to help keep + + + align:start position:0% +be tokens they can be used to help keep +track of stats but something that I've + + align:start position:0% +track of stats but something that I've + + + align:start position:0% +track of stats but something that I've +seen a lot that students like to use a + + align:start position:0% +seen a lot that students like to use a + + + align:start position:0% +seen a lot that students like to use a +lot is like they use two 10-sided dice + + align:start position:0% +lot is like they use two 10-sided dice + + + align:start position:0% +lot is like they use two 10-sided dice +to keep track of a number between one to + + align:start position:0% +to keep track of a number between one to + + + align:start position:0% +to keep track of a number between one to +one you know 0 to 99 um that's a really + + align:start position:0% +one you know 0 to 99 um that's a really + + + align:start position:0% +one you know 0 to 99 um that's a really +bad idea one brush of the hand and and + + align:start position:0% +bad idea one brush of the hand and and + + + align:start position:0% +bad idea one brush of the hand and and +and and that variable is gone right um + + align:start position:0% +and and that variable is gone right um + + + align:start position:0% +and and that variable is gone right um +You can swap the tens and and and the + + align:start position:0% +You can swap the tens and and and the + + + align:start position:0% +You can swap the tens and and and the +ones really easily it's like was that 91 + + align:start position:0% +ones really easily it's like was that 91 + + + align:start position:0% +ones really easily it's like was that 91 +or 19 I can't remember um so if you want + + align:start position:0% +or 19 I can't remember um so if you want + + + align:start position:0% +or 19 I can't remember um so if you want +to record variables just grab an index + + align:start position:0% +to record variables just grab an index + + + align:start position:0% +to record variables just grab an index +card and just write down the variable + + align:start position:0% +card and just write down the variable + + + align:start position:0% +card and just write down the variable +when whenever the variable changes cross + + align:start position:0% +when whenever the variable changes cross + + + align:start position:0% +when whenever the variable changes cross +it out write a new variable um this much + + align:start position:0% +it out write a new variable um this much + + + align:start position:0% +it out write a new variable um this much +better for you for you to use dice + + align:start position:0% +better for you for you to use dice + + + align:start position:0% +better for you for you to use dice +either as actual randomizers or you can + + align:start position:0% +either as actual randomizers or you can + + + align:start position:0% +either as actual randomizers or you can +use them sometimes as tokens that move + + align:start position:0% +use them sometimes as tokens that move + + + align:start position:0% +use them sometimes as tokens that move +around on on the + + align:start position:0% +around on on the + + + align:start position:0% +around on on the +board uh let's see what + + align:start position:0% +board uh let's see what + + + align:start position:0% +board uh let's see what +else uh game bits pieces from other + + align:start position:0% +else uh game bits pieces from other + + + align:start position:0% +else uh game bits pieces from other +games uh are wonderful but sometimes a + + align:start position:0% +games uh are wonderful but sometimes a + + + align:start position:0% +games uh are wonderful but sometimes a +little irritating because if you took + + align:start position:0% +little irritating because if you took + + + align:start position:0% +little irritating because if you took +them out of a game box then you have to + + align:start position:0% +them out of a game box then you have to + + + align:start position:0% +them out of a game box then you have to +put them back into the game box + + align:start position:0% +put them back into the game box + + + align:start position:0% +put them back into the game box +otherwise you've just ruined your copy + + align:start position:0% +otherwise you've just ruined your copy + + + align:start position:0% +otherwise you've just ruined your copy +of the game so I like using disposable + + align:start position:0% +of the game so I like using disposable + + + align:start position:0% +of the game so I like using disposable +kindergarten counters a lot because I + + align:start position:0% +kindergarten counters a lot because I + + + align:start position:0% +kindergarten counters a lot because I +don't really care about returning + + align:start position:0% +don't really care about returning + + + align:start position:0% +don't really care about returning +exactly the same number I took out um so + + align:start position:0% +exactly the same number I took out um so + + + align:start position:0% +exactly the same number I took out um so +and there's usually less assumption + + align:start position:0% +and there's usually less assumption + + + align:start position:0% +and there's usually less assumption +about what a kindergarten counter is + + align:start position:0% +about what a kindergarten counter is + + + align:start position:0% +about what a kindergarten counter is +supposed to be you know is it a number + + align:start position:0% +supposed to be you know is it a number + + + align:start position:0% +supposed to be you know is it a number +is it a person whereas if you use game + + align:start position:0% +is it a person whereas if you use game + + + align:start position:0% +is it a person whereas if you use game +bits you know that's kind of person + + align:start position:0% +bits you know that's kind of person + + + align:start position:0% +bits you know that's kind of person +shaped meeple shaped um Post-it glue and + + align:start position:0% +shaped meeple shaped um Post-it glue and + + + align:start position:0% +shaped meeple shaped um Post-it glue and +notepads oh I don't think we actually + + align:start position:0% +notepads oh I don't think we actually + + + align:start position:0% +notepads oh I don't think we actually +have any Post-it glue right now um but + + align:start position:0% +have any Post-it glue right now um but + + + align:start position:0% +have any Post-it glue right now um but +they're basically um glue sticks that + + align:start position:0% +they're basically um glue sticks that + + + align:start position:0% +they're basically um glue sticks that +don't stick uh permanently so so you you + + align:start position:0% +don't stick uh permanently so so you you + + + align:start position:0% +don't stick uh permanently so so you you +wipe you you you put them on an index + + align:start position:0% +wipe you you you put them on an index + + + align:start position:0% +wipe you you you put them on an index +card or a piece of paper and suddenly + + align:start position:0% +card or a piece of paper and suddenly + + + align:start position:0% +card or a piece of paper and suddenly +becomes a posted um but what we do have + + align:start position:0% +becomes a posted um but what we do have + + + align:start position:0% +becomes a posted um but what we do have +are a lot of posted notepads both big + + align:start position:0% +are a lot of posted notepads both big + + + align:start position:0% +are a lot of posted notepads both big +ones and small ones and these are useful + + align:start position:0% +ones and small ones and these are useful + + + align:start position:0% +ones and small ones and these are useful +for you to sort of like simulate + + align:start position:0% +for you to sort of like simulate + + + align:start position:0% +for you to sort of like simulate +displays for instance or variables and + + align:start position:0% +displays for instance or variables and + + + align:start position:0% +displays for instance or variables and +information that a player supposed to + + align:start position:0% +information that a player supposed to + + + align:start position:0% +information that a player supposed to +have and you don't want it to go flying + + align:start position:0% +have and you don't want it to go flying + + + align:start position:0% +have and you don't want it to go flying +off if somebody + + align:start position:0% +off if somebody + + + align:start position:0% +off if somebody +sneezes um of course or right I have a + + align:start position:0% +sneezes um of course or right I have a + + + align:start position:0% +sneezes um of course or right I have a +picture of some Kindergarten counters up + + align:start position:0% +picture of some Kindergarten counters up + + + align:start position:0% +picture of some Kindergarten counters up +there um pencils pens markers scissors + + align:start position:0% +there um pencils pens markers scissors + + + align:start position:0% +there um pencils pens markers scissors +tape just to be able to hold things + + align:start position:0% +tape just to be able to hold things + + + align:start position:0% +tape just to be able to hold things +together write down + + align:start position:0% +together write down + + + align:start position:0% +together write down +information um something else about + + align:start position:0% +information um something else about + + + align:start position:0% +information um something else about +about kindergarten counters we have a + + align:start position:0% +about kindergarten counters we have a + + + align:start position:0% +about kindergarten counters we have a +particular kind of kindergarten counter + + align:start position:0% +particular kind of kindergarten counter + + + align:start position:0% +particular kind of kindergarten counter +which is interlocking + + align:start position:0% +which is interlocking + + + align:start position:0% +which is interlocking +Cube do you take it + + align:start position:0% + + + + align:start position:0% + +out well if it's possible that we took + + align:start position:0% +out well if it's possible that we took + + + align:start position:0% +out well if it's possible that we took +them out because they're very + + align:start position:0% +them out because they're very + + + align:start position:0% +them out because they're very +problematic because once I give you + + align:start position:0% +problematic because once I give you + + + align:start position:0% +problematic because once I give you +interlocking cubes you make games about + + align:start position:0% +interlocking cubes you make games about + + + align:start position:0% +interlocking cubes you make games about +interlocking cubes uh it's like handing + + align:start position:0% +interlocking cubes uh it's like handing + + + align:start position:0% +interlocking cubes uh it's like handing +people leg like Legos and then the first + + align:start position:0% +people leg like Legos and then the first + + + align:start position:0% +people leg like Legos and then the first +thing everyone thinks of is Let's Make a + + align:start position:0% +thing everyone thinks of is Let's Make a + + + align:start position:0% +thing everyone thinks of is Let's Make a +game where you put things together and + + align:start position:0% +game where you put things together and + + + align:start position:0% +game where you put things together and +assemble them it's like stack counters + + align:start position:0% +assemble them it's like stack counters + + + align:start position:0% +assemble them it's like stack counters +stacking counters so you games + + align:start position:0% +stacking counters so you games + + + align:start position:0% +stacking counters so you games +stacking yeah the pieces that you end up + + align:start position:0% +stacking yeah the pieces that you end up + + + align:start position:0% +stacking yeah the pieces that you end up +prototyping with sometimes ends up + + align:start position:0% +prototyping with sometimes ends up + + + align:start position:0% +prototyping with sometimes ends up +shaping the the direction of your game + + align:start position:0% +shaping the the direction of your game + + + align:start position:0% +shaping the the direction of your game +uh and in sometimes if you are dealing + + align:start position:0% +uh and in sometimes if you are dealing + + + align:start position:0% +uh and in sometimes if you are dealing +with a designer's block you know that + + align:start position:0% +with a designer's block you know that + + + align:start position:0% +with a designer's block you know that +can be helpful that gives you a path to + + align:start position:0% +can be helpful that gives you a path to + + + align:start position:0% +can be helpful that gives you a path to +follow but in many ways that's a + + align:start position:0% +follow but in many ways that's a + + + align:start position:0% +follow but in many ways that's a +distraction uh you you start becoming + + align:start position:0% +distraction uh you you start becoming + + + align:start position:0% +distraction uh you you start becoming +constrained by your tools instead of the + + align:start position:0% +constrained by your tools instead of the + + + align:start position:0% +constrained by your tools instead of the +idea that you're trying to work with so + + align:start position:0% +idea that you're trying to work with so + + + align:start position:0% +idea that you're trying to work with so +uh if we manage to get get rid of the + + align:start position:0% +uh if we manage to get get rid of the + + + align:start position:0% +uh if we manage to get get rid of the +interlocking cubes that's awesome but if + + align:start position:0% +interlocking cubes that's awesome but if + + + align:start position:0% +interlocking cubes that's awesome but if +they're still in there by by all means + + align:start position:0% +they're still in there by by all means + + + align:start position:0% +they're still in there by by all means +use them but don't try to make don't + + align:start position:0% +use them but don't try to make don't + + + align:start position:0% +use them but don't try to make don't +don't automatically assume you have to + + align:start position:0% +don't automatically assume you have to + + + align:start position:0% +don't automatically assume you have to +make a game about about interlocking + + align:start position:0% +make a game about about interlocking + + + align:start position:0% +make a game about about interlocking +cubes now don't forget to keep a record + + align:start position:0% +cubes now don't forget to keep a record + + + align:start position:0% +cubes now don't forget to keep a record +of um of everything including all of the + + align:start position:0% +of um of everything including all of the + + + align:start position:0% +of um of everything including all of the +notes that you that you've had use your + + align:start position:0% +notes that you that you've had use your + + + align:start position:0% +notes that you that you've had use your +phone camera during the session um at + + align:start position:0% +phone camera during the session um at + + + align:start position:0% +phone camera during the session um at +the end of your project make sure that + + align:start position:0% +the end of your project make sure that + + + align:start position:0% +the end of your project make sure that +you you try to get them scanned or + + align:start position:0% +you you try to get them scanned or + + + align:start position:0% +you you try to get them scanned or +photocopied uh in some way there are a + + align:start position:0% +photocopied uh in some way there are a + + + align:start position:0% +photocopied uh in some way there are a +lot of uh photocopy machines around + + align:start position:0% +lot of uh photocopy machines around + + + align:start position:0% +lot of uh photocopy machines around +campus now there are actually scanners + + align:start position:0% +campus now there are actually scanners + + + align:start position:0% +campus now there are actually scanners +and you just put the all materials on + + align:start position:0% +and you just put the all materials on + + + align:start position:0% +and you just put the all materials on +top and then instead of generating a + + align:start position:0% +top and then instead of generating a + + + align:start position:0% +top and then instead of generating a +copy you can have them email a color + + align:start position:0% +copy you can have them email a color + + + align:start position:0% +copy you can have them email a color +scan to your to your email account those + + align:start position:0% +scan to your to your email account those + + + align:start position:0% +scan to your to your email account those +things are really useful for your final + + align:start position:0% +things are really useful for your final + + + align:start position:0% +things are really useful for your final +assignment okay so those are the + + align:start position:0% + + + + align:start position:0% + +tools who are the people sitting around + + align:start position:0% +tools who are the people sitting around + + + align:start position:0% +tools who are the people sitting around +the table um when you are doing when + + align:start position:0% +the table um when you are doing when + + + align:start position:0% +the table um when you are doing when +you've actually made a prototype then + + align:start position:0% +you've actually made a prototype then + + + align:start position:0% +you've actually made a prototype then +you know uh what happens is I I guess I + + align:start position:0% +you know uh what happens is I I guess I + + + align:start position:0% +you know uh what happens is I I guess I +got some of my slides mixed up uh this + + align:start position:0% +got some of my slides mixed up uh this + + + align:start position:0% +got some of my slides mixed up uh this +usually happens at the end of the of + + align:start position:0% +usually happens at the end of the of + + + align:start position:0% +usually happens at the end of the of +having designed a workable prototype is + + align:start position:0% +having designed a workable prototype is + + + align:start position:0% +having designed a workable prototype is +that there's going to be a bunch of + + align:start position:0% +that there's going to be a bunch of + + + align:start position:0% +that there's going to be a bunch of +people sitting around the table and each + + align:start position:0% +people sitting around the table and each + + + align:start position:0% +people sitting around the table and each +person has a different role that's of + + align:start position:0% +person has a different role that's of + + + align:start position:0% +person has a different role that's of +course the person who's actually going + + align:start position:0% +course the person who's actually going + + + align:start position:0% +course the person who's actually going +to be playing the game preferably + + align:start position:0% +to be playing the game preferably + + + align:start position:0% +to be playing the game preferably +somebody from a different team or + + align:start position:0% +somebody from a different team or + + + align:start position:0% +somebody from a different team or +somebody who's even outside of this + + align:start position:0% +somebody who's even outside of this + + + align:start position:0% +somebody who's even outside of this +class it could be one of us instructors + + align:start position:0% +class it could be one of us instructors + + + align:start position:0% +class it could be one of us instructors +for instance it could be one of the ocw + + align:start position:0% +for instance it could be one of the ocw + + + align:start position:0% +for instance it could be one of the ocw +people um and somebody in your team is + + align:start position:0% +people um and somebody in your team is + + + align:start position:0% +people um and somebody in your team is +going to be a facilitator this is the + + align:start position:0% +going to be a facilitator this is the + + + align:start position:0% +going to be a facilitator this is the +person who's going to present the rules + + align:start position:0% +person who's going to present the rules + + + align:start position:0% +person who's going to present the rules +to the person who's going to play you + + align:start position:0% +to the person who's going to play you + + + align:start position:0% +to the person who's going to play you +know tell them that where looking for + + align:start position:0% +know tell them that where looking for + + + align:start position:0% +know tell them that where looking for +your feedback make them comfortable you + + align:start position:0% +your feedback make them comfortable you + + + align:start position:0% +your feedback make them comfortable you +know make sure that they understand what + + align:start position:0% +know make sure that they understand what + + + align:start position:0% +know make sure that they understand what +they're supposed to be doing um and + + align:start position:0% +they're supposed to be doing um and + + + align:start position:0% +they're supposed to be doing um and +basically making sure that the session + + align:start position:0% +basically making sure that the session + + + align:start position:0% +basically making sure that the session +runs uh according to script that person + + align:start position:0% +runs uh according to script that person + + + align:start position:0% +runs uh according to script that person +or somebody else can also be the + + align:start position:0% +or somebody else can also be the + + + align:start position:0% +or somebody else can also be the +computer and this is the person who is + + align:start position:0% +computer and this is the person who is + + + align:start position:0% +computer and this is the person who is +actually making the Prototype work + + align:start position:0% +actually making the Prototype work + + + align:start position:0% +actually making the Prototype work +updating + + align:start position:0% +updating + + + align:start position:0% +updating +variables uh moving the positions of + + align:start position:0% +variables uh moving the positions of + + + align:start position:0% +variables uh moving the positions of +pieces on the board revealing new + + align:start position:0% +pieces on the board revealing new + + + align:start position:0% +pieces on the board revealing new +dialogue boxes or you know get basically + + align:start position:0% +dialogue boxes or you know get basically + + + align:start position:0% +dialogue boxes or you know get basically +making the board respond to what what + + align:start position:0% +making the board respond to what what + + + align:start position:0% +making the board respond to what what +the player decides to + + align:start position:0% +the player decides to + + + align:start position:0% +the player decides to +do and uh the computer is uh trying to + + align:start position:0% +do and uh the computer is uh trying to + + + align:start position:0% +do and uh the computer is uh trying to +do you know all the computation that + + align:start position:0% +do you know all the computation that + + + align:start position:0% +do you know all the computation that +your actual computer will do if you're + + align:start position:0% +your actual computer will do if you're + + + align:start position:0% +your actual computer will do if you're +making a digital game uh the computer + + align:start position:0% +making a digital game uh the computer + + + align:start position:0% +making a digital game uh the computer +should not do anything that a real + + align:start position:0% +should not do anything that a real + + + align:start position:0% +should not do anything that a real +computer wouldn't so for instance if + + align:start position:0% +computer wouldn't so for instance if + + + align:start position:0% +computer wouldn't so for instance if +somebody doesn't understand a rule the + + align:start position:0% +somebody doesn't understand a rule the + + + align:start position:0% +somebody doesn't understand a rule the +computer person shouldn't be + + align:start position:0% +computer person shouldn't be + + + align:start position:0% +computer person shouldn't be +correcting uh the the player the + + align:start position:0% +correcting uh the the player the + + + align:start position:0% +correcting uh the the player the +facilitator C but sometimes what I find + + align:start position:0% +facilitator C but sometimes what I find + + + align:start position:0% +facilitator C but sometimes what I find +is really interesting is that somebody + + align:start position:0% +is really interesting is that somebody + + + align:start position:0% +is really interesting is that somebody +thinks a rule Works differently I let + + align:start position:0% +thinks a rule Works differently I let + + + align:start position:0% +thinks a rule Works differently I let +them play through it + + align:start position:0% +them play through it + + + align:start position:0% +them play through it +and that that becomes like a different + + align:start position:0% +and that that becomes like a different + + + align:start position:0% +and that that becomes like a different +iteration of of the game and sometimes + + align:start position:0% +iteration of of the game and sometimes + + + align:start position:0% +iteration of of the game and sometimes +it turns out to be better um then you + + align:start position:0% +it turns out to be better um then you + + + align:start position:0% +it turns out to be better um then you +can run through the the the the + + align:start position:0% +can run through the the the the + + + align:start position:0% +can run through the the the the +iteration with with the corrected rule + + align:start position:0% +iteration with with the corrected rule + + + align:start position:0% +iteration with with the corrected rule +yeah so the person the computer does + + align:start position:0% +yeah so the person the computer does + + + align:start position:0% +yeah so the person the computer does +have to make a choice at that + + align:start position:0% + + + + align:start position:0% + +point + + align:start position:0% + + + + align:start position:0% + +yes something that doesn't work and the + + align:start position:0% +yes something that doesn't work and the + + + align:start position:0% +yes something that doesn't work and the +computer and a person playing the + + align:start position:0% +computer and a person playing the + + + align:start position:0% +computer and a person playing the +computer says nothing happens you know + + align:start position:0% +computer says nothing happens you know + + + align:start position:0% +computer says nothing happens you know +it's like you can do that right it's + + align:start position:0% +it's like you can do that right it's + + + align:start position:0% +it's like you can do that right it's +like if the person really doesn't + + align:start position:0% +like if the person really doesn't + + + align:start position:0% +like if the person really doesn't +Undernet rule but if the person like if + + align:start position:0% +Undernet rule but if the person like if + + + align:start position:0% +Undernet rule but if the person like if +you notice say this person is clearly + + align:start position:0% +you notice say this person is clearly + + + align:start position:0% +you notice say this person is clearly +playing a really suboptimal strategy you + + align:start position:0% +playing a really suboptimal strategy you + + + align:start position:0% +playing a really suboptimal strategy you +know just respond like a computer will + + align:start position:0% +know just respond like a computer will + + + align:start position:0% +know just respond like a computer will +you know lead them to that loose + + align:start position:0% +you know lead them to that loose + + + align:start position:0% +you know lead them to that loose +condition or whatever it is that that + + align:start position:0% +condition or whatever it is that that + + + align:start position:0% +condition or whatever it is that that +that that happens because because in + + align:start position:0% +that that happens because because in + + + align:start position:0% +that that happens because because in +many ways that's how an actual player is + + align:start position:0% +many ways that's how an actual player is + + + align:start position:0% +many ways that's how an actual player is +going to learn how to play your game in + + align:start position:0% +going to learn how to play your game in + + + align:start position:0% +going to learn how to play your game in +the long run they're going to make a lot + + align:start position:0% +the long run they're going to make a lot + + + align:start position:0% +the long run they're going to make a lot +of bad decisions the computer's going to + + align:start position:0% +of bad decisions the computer's going to + + + align:start position:0% +of bad decisions the computer's going to +respond and then they're going to learn + + align:start position:0% +respond and then they're going to learn + + + align:start position:0% +respond and then they're going to learn +from the mistakes that they made and + + align:start position:0% +from the mistakes that they made and + + + align:start position:0% +from the mistakes that they made and +then try it uh try it differently + + align:start position:0% +then try it uh try it differently + + + align:start position:0% +then try it uh try it differently +let's see um something else that the + + align:start position:0% +let's see um something else that the + + + align:start position:0% +let's see um something else that the +facilitator can do while the game is + + align:start position:0% +facilitator can do while the game is + + + align:start position:0% +facilitator can do while the game is +going on say the player is actually + + align:start position:0% +going on say the player is actually + + + align:start position:0% +going on say the player is actually +playing is to encourage the player to + + align:start position:0% +playing is to encourage the player to + + + align:start position:0% +playing is to encourage the player to +read to think aloud um so the person is + + align:start position:0% +read to think aloud um so the person is + + + align:start position:0% +read to think aloud um so the person is +the the person that youve brought in to + + align:start position:0% +the the person that youve brought in to + + + align:start position:0% +the the person that youve brought in to +play your game is trying to understand + + align:start position:0% +play your game is trying to understand + + + align:start position:0% +play your game is trying to understand +your game and they're just like sitting + + align:start position:0% +your game and they're just like sitting + + + align:start position:0% +your game and they're just like sitting +there in silence looking at bored and + + align:start position:0% +there in silence looking at bored and + + + align:start position:0% +there in silence looking at bored and +you don't know if they're bored confused + + align:start position:0% +you don't know if they're bored confused + + + align:start position:0% +you don't know if they're bored confused +or really into it so you ask them you + + align:start position:0% +or really into it so you ask them you + + + align:start position:0% +or really into it so you ask them you +know what are you thinking now right and + + align:start position:0% +know what are you thinking now right and + + + align:start position:0% +know what are you thinking now right and +if they're saying like what what are all + + align:start position:0% +if they're saying like what what are all + + + align:start position:0% +if they're saying like what what are all +these pieces all right then you know + + align:start position:0% +these pieces all right then you know + + + align:start position:0% +these pieces all right then you know +that they're confused facilitator can + + align:start position:0% +that they're confused facilitator can + + + align:start position:0% +that they're confused facilitator can +help you know can say all right let's + + align:start position:0% +help you know can say all right let's + + + align:start position:0% +help you know can say all right let's +let's start let's start again and I'll + + align:start position:0% +let's start let's start again and I'll + + + align:start position:0% +let's start let's start again and I'll +explain what all these pieces are it + + align:start position:0% +explain what all these pieces are it + + + align:start position:0% +explain what all these pieces are it +could be I've got like five different + + align:start position:0% +could be I've got like five different + + + align:start position:0% +could be I've got like five different +strategies and I'm trying to figure out + + align:start position:0% +strategies and I'm trying to figure out + + + align:start position:0% +strategies and I'm trying to figure out +which you know I'm thinking maybe if I + + align:start position:0% +which you know I'm thinking maybe if I + + + align:start position:0% +which you know I'm thinking maybe if I +move this here move this that okay that + + align:start position:0% +move this here move this that okay that + + + align:start position:0% +move this here move this that okay that +person's into it right the person is + + align:start position:0% +person's into it right the person is + + + align:start position:0% +person's into it right the person is +really thinking hard about this + + align:start position:0% +really thinking hard about this + + + align:start position:0% +really thinking hard about this +problem everybody else in your team + + align:start position:0% +problem everybody else in your team + + + align:start position:0% +problem everybody else in your team +watching that board and this is the + + align:start position:0% +watching that board and this is the + + + align:start position:0% +watching that board and this is the +reason why we have a big board is an + + align:start position:0% +reason why we have a big board is an + + + align:start position:0% +reason why we have a big board is an +observer you want to be able to see + + align:start position:0% +observer you want to be able to see + + + align:start position:0% +observer you want to be able to see +what's going on in your game you want to + + align:start position:0% +what's going on in your game you want to + + + align:start position:0% +what's going on in your game you want to +be be able to write down information in + + align:start position:0% +be be able to write down information in + + + align:start position:0% +be be able to write down information in +a notebook or on your laptop uh and try + + align:start position:0% +a notebook or on your laptop uh and try + + + align:start position:0% +a notebook or on your laptop uh and try +to record whatever information most + + align:start position:0% +to record whatever information most + + + align:start position:0% +to record whatever information most +importantly look at the face of the + + align:start position:0% +importantly look at the face of the + + + align:start position:0% +importantly look at the face of the +person who's playing the game see you + + align:start position:0% +person who's playing the game see you + + + align:start position:0% +person who's playing the game see you +know again that helps identify whether + + align:start position:0% +know again that helps identify whether + + + align:start position:0% +know again that helps identify whether +they're confused or whether you know + + align:start position:0% +they're confused or whether you know + + + align:start position:0% +they're confused or whether you know +they're really into it they're trying to + + align:start position:0% +they're really into it they're trying to + + + align:start position:0% +they're really into it they're trying to +make a tough decision or they're just + + align:start position:0% +make a tough decision or they're just + + + align:start position:0% +make a tough decision or they're just +bored + + align:start position:0% +bored + + + align:start position:0% +bored +um don't offer help to the user + + align:start position:0% +um don't offer help to the user + + + align:start position:0% +um don't offer help to the user +especially if you're on a development + + align:start position:0% +especially if you're on a development + + + align:start position:0% +especially if you're on a development +team and you know all about this game + + align:start position:0% +team and you know all about this game + + + align:start position:0% +team and you know all about this game +you know it can be a real temptation to + + align:start position:0% +you know it can be a real temptation to + + + align:start position:0% +you know it can be a real temptation to +you basically just tell the user this is + + align:start position:0% +you basically just tell the user this is + + + align:start position:0% +you basically just tell the user this is +what you want to do don't do that sit on + + align:start position:0% +what you want to do don't do that sit on + + + align:start position:0% +what you want to do don't do that sit on +your hands bite your tongue um it can be + + align:start position:0% +your hands bite your tongue um it can be + + + align:start position:0% +your hands bite your tongue um it can be +hard to take notes when you're sitting + + align:start position:0% +hard to take notes when you're sitting + + + align:start position:0% +hard to take notes when you're sitting +on your hands but you know uh take + + align:start position:0% +on your hands but you know uh take + + + align:start position:0% +on your hands but you know uh take +notes uh and uh the the person who's do + + align:start position:0% +notes uh and uh the the person who's do + + + align:start position:0% +notes uh and uh the the person who's do +who's being the computer and being the + + align:start position:0% +who's being the computer and being the + + + align:start position:0% +who's being the computer and being the +facilitator really doesn't have the + + align:start position:0% +facilitator really doesn't have the + + + align:start position:0% +facilitator really doesn't have the +bandwidth they that those people do not + + align:start position:0% +bandwidth they that those people do not + + + align:start position:0% +bandwidth they that those people do not +have the bandwidth to take notes so you + + align:start position:0% +have the bandwidth to take notes so you + + + align:start position:0% +have the bandwidth to take notes so you +so someone has to be officially + + align:start position:0% +so someone has to be officially + + + align:start position:0% +so someone has to be officially +designated with a job of actually taking + + align:start position:0% +designated with a job of actually taking + + + align:start position:0% +designated with a job of actually taking +notes and observing + + align:start position:0% +notes and observing + + + align:start position:0% +notes and observing +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +what we're going to be doing is a wizard + + align:start position:0% +what we're going to be doing is a wizard + + + align:start position:0% +what we're going to be doing is a wizard +of us test for your games and that is + + align:start position:0% +of us test for your games and that is + + + align:start position:0% +of us test for your games and that is +someone's playing the computer uh it's + + align:start position:0% +someone's playing the computer uh it's + + + align:start position:0% +someone's playing the computer uh it's +very constrainted in terms of + + align:start position:0% +very constrainted in terms of + + + align:start position:0% +very constrainted in terms of +communication between the computer and + + align:start position:0% +communication between the computer and + + + align:start position:0% +communication between the computer and +the person who's testing your game uh + + align:start position:0% +the person who's testing your game uh + + + align:start position:0% +the person who's testing your game uh +the rules are usually pretty rigid uh + + align:start position:0% +the rules are usually pretty rigid uh + + + align:start position:0% +the rules are usually pretty rigid uh +and the nice thing about it is that you + + align:start position:0% +and the nice thing about it is that you + + + align:start position:0% +and the nice thing about it is that you +can do a pretty deep uh analysis uh of + + align:start position:0% +can do a pretty deep uh analysis uh of + + + align:start position:0% +can do a pretty deep uh analysis uh of +your game you can you can you can make a + + align:start position:0% +your game you can you can you can make a + + + align:start position:0% +your game you can you can you can make a +game that sort of goes through multiple + + align:start position:0% +game that sort of goes through multiple + + + align:start position:0% +game that sort of goes through multiple +decisions into sort of long-term + + align:start position:0% +decisions into sort of long-term + + + align:start position:0% +decisions into sort of long-term +consequences that's not necessarily what + + align:start position:0% +consequences that's not necessarily what + + + align:start position:0% +consequences that's not necessarily what +we're asking you to do for project one + + align:start position:0% +we're asking you to do for project one + + + align:start position:0% +we're asking you to do for project one +I'm just telling you this because you + + align:start position:0% +I'm just telling you this because you + + + align:start position:0% +I'm just telling you this because you +might want to do this for project two + + align:start position:0% +might want to do this for project two + + + align:start position:0% +might want to do this for project two +three or four um you a wizard of us test + + align:start position:0% +three or four um you a wizard of us test + + + align:start position:0% +three or four um you a wizard of us test +allows you to really do a deep dive into + + align:start position:0% +allows you to really do a deep dive into + + + align:start position:0% +allows you to really do a deep dive into +how a particular feature works for + + align:start position:0% +how a particular feature works for + + + align:start position:0% +how a particular feature works for +instance uh and um since the H it's a + + align:start position:0% +instance uh and um since the H it's a + + + align:start position:0% +instance uh and um since the H it's a +human simulating the backend s + + align:start position:0% +human simulating the backend s + + + align:start position:0% +human simulating the backend s +simulating the Computing uh you can be + + align:start position:0% +simulating the Computing uh you can be + + + align:start position:0% +simulating the Computing uh you can be +very high fidelity uh at very little + + align:start position:0% +very high fidelity uh at very little + + + align:start position:0% +very high fidelity uh at very little +cost that's not again we're asking you + + align:start position:0% +cost that's not again we're asking you + + + align:start position:0% +cost that's not again we're asking you +to do for project one we're asking you + + align:start position:0% +to do for project one we're asking you + + + align:start position:0% +to do for project one we're asking you +to do a low Fidelity prototype and we'll + + align:start position:0% +to do a low Fidelity prototype and we'll + + + align:start position:0% +to do a low Fidelity prototype and we'll +go in a little bit more detail about + + align:start position:0% +go in a little bit more detail about + + + align:start position:0% +go in a little bit more detail about +what that is very important don't let + + align:start position:0% +what that is very important don't let + + + align:start position:0% +what that is very important don't let +the player know what the computer is + + align:start position:0% +the player know what the computer is + + + align:start position:0% +the player know what the computer is +thinking the computer only displays + + align:start position:0% +thinking the computer only displays + + + align:start position:0% +thinking the computer only displays +information you do not reveal what how + + align:start position:0% +information you do not reveal what how + + + align:start position:0% +information you do not reveal what how +the computer is coming to those uh + + align:start position:0% +the computer is coming to those uh + + + align:start position:0% +the computer is coming to those uh +conclusions there are a couple of other + + align:start position:0% +conclusions there are a couple of other + + + align:start position:0% +conclusions there are a couple of other +kinds of prototypes that you could + + align:start position:0% +kinds of prototypes that you could + + + align:start position:0% +kinds of prototypes that you could +design I'm going to run through them + + align:start position:0% +design I'm going to run through them + + + align:start position:0% +design I'm going to run through them +very quickly because that's not what + + align:start position:0% +very quickly because that's not what + + + align:start position:0% +very quickly because that's not what +happens in this + + align:start position:0% +happens in this + + + align:start position:0% +happens in this +class player versus player you know what + + align:start position:0% +class player versus player you know what + + + align:start position:0% +class player versus player you know what +you'd expect in a board game or a card + + align:start position:0% +you'd expect in a board game or a card + + + align:start position:0% +you'd expect in a board game or a card +game situation we have a class just for + + align:start position:0% +game situation we have a class just for + + + align:start position:0% +game situation we have a class just for +that + + align:start position:0% +that + + + align:start position:0% +that +and uh you can make Cooperative games + + align:start position:0% +and uh you can make Cooperative games + + + align:start position:0% +and uh you can make Cooperative games +competitive games you can make games + + align:start position:0% +competitive games you can make games + + + align:start position:0% +competitive games you can make games +where everybody has the same role a + + align:start position:0% +where everybody has the same role a + + + align:start position:0% +where everybody has the same role a +symmetric game or asymmetric game where + + align:start position:0% +symmetric game or asymmetric game where + + + align:start position:0% +symmetric game or asymmetric game where +everyone has different roles the problem + + align:start position:0% +everyone has different roles the problem + + + align:start position:0% +everyone has different roles the problem +about that is that there's a lot of + + align:start position:0% +about that is that there's a lot of + + + align:start position:0% +about that is that there's a lot of +loose communication happening between + + align:start position:0% +loose communication happening between + + + align:start position:0% +loose communication happening between +the people who are actually playing your + + align:start position:0% +the people who are actually playing your + + + align:start position:0% +the people who are actually playing your +game and they made a sign on a house + + align:start position:0% +game and they made a sign on a house + + + align:start position:0% +game and they made a sign on a house +rule that was totally not what you + + align:start position:0% +rule that was totally not what you + + + align:start position:0% +rule that was totally not what you +intended or designed as developers um + + align:start position:0% +intended or designed as developers um + + + align:start position:0% +intended or designed as developers um +and that turns out to be the rule that + + align:start position:0% +and that turns out to be the rule that + + + align:start position:0% +and that turns out to be the rule that +they'll end up playing with again what I + + align:start position:0% +they'll end up playing with again what I + + + align:start position:0% +they'll end up playing with again what I +like to do is I like to see them play + + align:start position:0% +like to do is I like to see them play + + + align:start position:0% +like to do is I like to see them play +through that rule then I at the end of + + align:start position:0% +through that rule then I at the end of + + + align:start position:0% +through that rule then I at the end of +the game I correct them and I have them + + align:start position:0% +the game I correct them and I have them + + + align:start position:0% +the game I correct them and I have them +play through the rule that I originally + + align:start position:0% +play through the rule that I originally + + + align:start position:0% +play through the rule that I originally +designed because sometimes the rule that + + align:start position:0% +designed because sometimes the rule that + + + align:start position:0% +designed because sometimes the rule that +they came up with is better the + + align:start position:0% +they came up with is better the + + + align:start position:0% +they came up with is better the +facilitator again helps to explain the + + align:start position:0% +facilitator again helps to explain the + + + align:start position:0% +facilitator again helps to explain the +rules at the beginning of the game and + + align:start position:0% +rules at the beginning of the game and + + + align:start position:0% +rules at the beginning of the game and +then you kind of just watch after that + + align:start position:0% +then you kind of just watch after that + + + align:start position:0% +then you kind of just watch after that +it's hard to get consistent results + + align:start position:0% +it's hard to get consistent results + + + align:start position:0% +it's hard to get consistent results +across tests when you're doing a + + align:start position:0% +across tests when you're doing a + + + align:start position:0% +across tests when you're doing a +multiplayer game because it's very hard + + align:start position:0% +multiplayer game because it's very hard + + + align:start position:0% +multiplayer game because it's very hard +to sort of duplicate exactly the same + + align:start position:0% +to sort of duplicate exactly the same + + + align:start position:0% +to sort of duplicate exactly the same +situation whereas you can do that on The + + align:start position:0% +situation whereas you can do that on The + + + align:start position:0% +situation whereas you can do that on The +Wizard of O test pretty easily but but + + align:start position:0% +Wizard of O test pretty easily but but + + + align:start position:0% +Wizard of O test pretty easily but but +if you're making a multiplayer game you + + align:start position:0% +if you're making a multiplayer game you + + + align:start position:0% +if you're making a multiplayer game you +have to do a multiplayer test so this + + align:start position:0% +have to do a multiplayer test so this + + + align:start position:0% +have to do a multiplayer test so this +might actually happen actually are we + + align:start position:0% +might actually happen actually are we + + + align:start position:0% +might actually happen actually are we +saying that you can only do single + + align:start position:0% +saying that you can only do single + + + align:start position:0% +saying that you can only do single +player games this semester + + align:start position:0% +player games this semester + + + align:start position:0% +player games this semester +or uh I'm not quite sure what the the + + align:start position:0% +or uh I'm not quite sure what the the + + + align:start position:0% +or uh I'm not quite sure what the the +the constraint + + align:start position:0% +the constraint + + + align:start position:0% +the constraint +is + + align:start position:0% +is + + + align:start position:0% +is +um you can also do live action not for + + align:start position:0% +um you can also do live action not for + + + align:start position:0% +um you can also do live action not for +today but uh I actually enjoy this uh + + align:start position:0% +today but uh I actually enjoy this uh + + + align:start position:0% +today but uh I actually enjoy this uh +where you actually have predetermined + + align:start position:0% +where you actually have predetermined + + + align:start position:0% +where you actually have predetermined +rules that are explained between the + + align:start position:0% +rules that are explained between the + + + align:start position:0% +rules that are explained between the +game and then you just let real human + + align:start position:0% +game and then you just let real human + + + align:start position:0% +game and then you just let real human +beings walk around and do stuff uh it's + + align:start position:0% +beings walk around and do stuff uh it's + + + align:start position:0% +beings walk around and do stuff uh it's +the problem with this is there a very + + align:start position:0% +the problem with this is there a very + + + align:start position:0% +the problem with this is there a very +limited communication between people who + + align:start position:0% +limited communication between people who + + + align:start position:0% +limited communication between people who +are playing a game or even the people + + align:start position:0% +are playing a game or even the people + + + align:start position:0% +are playing a game or even the people +who are Modera who are running + + align:start position:0% +who are Modera who are running + + + align:start position:0% +who are Modera who are running +the game because everyone's kind of + + align:start position:0% +the game because everyone's kind of + + + align:start position:0% +the game because everyone's kind of +physically spread out uh but it can be + + align:start position:0% +physically spread out uh but it can be + + + align:start position:0% +physically spread out uh but it can be +fun for it can be really useful for a + + align:start position:0% +fun for it can be really useful for a + + + align:start position:0% +fun for it can be really useful for a +game if your game is really about a + + align:start position:0% +game if your game is really about a + + + align:start position:0% +game if your game is really about a +human being walking through a space you + + align:start position:0% +human being walking through a space you + + + align:start position:0% +human being walking through a space you +know such like a stealth game or + + align:start position:0% +know such like a stealth game or + + + align:start position:0% +know such like a stealth game or +something like that yes there's actually + + align:start position:0% +something like that yes there's actually + + + align:start position:0% +something like that yes there's actually +a person in that U-Haul + + align:start position:0% + + + + align:start position:0% + +box all right so when you're actually + + align:start position:0% +box all right so when you're actually + + + align:start position:0% +box all right so when you're actually +making your prototype here are the + + align:start position:0% +making your prototype here are the + + + align:start position:0% +making your prototype here are the +things that you have to make sure uh you + + align:start position:0% +things that you have to make sure uh you + + + align:start position:0% +things that you have to make sure uh you +do for every single prototype keep it + + align:start position:0% +do for every single prototype keep it + + + align:start position:0% +do for every single prototype keep it +handdrawing because hand drawing is fast + + align:start position:0% +handdrawing because hand drawing is fast + + + align:start position:0% +handdrawing because hand drawing is fast +uh you want to keep it really really + + align:start position:0% +uh you want to keep it really really + + + align:start position:0% +uh you want to keep it really really +sketchy and look really sketchy and + + align:start position:0% +sketchy and look really sketchy and + + + align:start position:0% +sketchy and look really sketchy and +rough again because that actually gets + + align:start position:0% +rough again because that actually gets + + + align:start position:0% +rough again because that actually gets +you feedback from the people who are + + align:start position:0% +you feedback from the people who are + + + align:start position:0% +you feedback from the people who are +testing if you make it look too pretty + + align:start position:0% +testing if you make it look too pretty + + + align:start position:0% +testing if you make it look too pretty +people are going to hesitate on + + align:start position:0% +people are going to hesitate on + + + align:start position:0% +people are going to hesitate on +commenting on how your game looks for + + align:start position:0% +commenting on how your game looks for + + + align:start position:0% +commenting on how your game looks for +instance uh they may actually hesitate + + align:start position:0% +instance uh they may actually hesitate + + + align:start position:0% +instance uh they may actually hesitate +and commenting how your game works uh + + align:start position:0% +and commenting how your game works uh + + + align:start position:0% +and commenting how your game works uh +even though you may not even though that + + align:start position:0% +even though you may not even though that + + + align:start position:0% +even though you may not even though that +may not be the prettiest part of the + + align:start position:0% +may not be the prettiest part of the + + + align:start position:0% +may not be the prettiest part of the +game because they can tell you spent a + + align:start position:0% +game because they can tell you spent a + + + align:start position:0% +game because they can tell you spent a +lot of time on this game again you want + + align:start position:0% +lot of time on this game again you want + + + align:start position:0% +lot of time on this game again you want +it to be big everyone needs to be able + + align:start position:0% +it to be big everyone needs to be able + + + align:start position:0% +it to be big everyone needs to be able +to see what's going on during testing + + align:start position:0% +to see what's going on during testing + + + align:start position:0% +to see what's going on during testing +and just use one dark color if you can + + align:start position:0% +and just use one dark color if you can + + + align:start position:0% +and just use one dark color if you can +uh for your inks for your markers uh it + + align:start position:0% +uh for your inks for your markers uh it + + + align:start position:0% +uh for your inks for your markers uh it +need needs to be dark high contrast you + + align:start position:0% +need needs to be dark high contrast you + + + align:start position:0% +need needs to be dark high contrast you +know so that everyone can read it easily + + align:start position:0% +know so that everyone can read it easily + + + align:start position:0% +know so that everyone can read it easily +uh you can use different color cards for + + align:start position:0% +uh you can use different color cards for + + + align:start position:0% +uh you can use different color cards for +instance for uh to be able to tell this + + align:start position:0% +instance for uh to be able to tell this + + + align:start position:0% +instance for uh to be able to tell this +card is a different kind of card from + + align:start position:0% +card is a different kind of card from + + + align:start position:0% +card is a different kind of card from +that card uh but don't use like multiple + + align:start position:0% +that card uh but don't use like multiple + + + align:start position:0% +that card uh but don't use like multiple +colors on the same card that's just like + + align:start position:0% +colors on the same card that's just like + + + align:start position:0% +colors on the same card that's just like +not worth the effort and again it gives + + align:start position:0% +not worth the effort and again it gives + + + align:start position:0% +not worth the effort and again it gives +people the impression that you spent a + + align:start position:0% +people the impression that you spent a + + + align:start position:0% +people the impression that you spent a +lot of time on this prototype and even + + align:start position:0% +lot of time on this prototype and even + + + align:start position:0% +lot of time on this prototype and even +if you have you don't want to give them + + align:start position:0% +if you have you don't want to give them + + + align:start position:0% +if you have you don't want to give them +that that that + + align:start position:0% +that that that + + + align:start position:0% +that that that +impression you write your rules on the + + align:start position:0% +impression you write your rules on the + + + align:start position:0% +impression you write your rules on the +cards so keep track of your rules + + align:start position:0% +cards so keep track of your rules + + + align:start position:0% +cards so keep track of your rules +eventually you're going to end up like + + align:start position:0% +eventually you're going to end up like + + + align:start position:0% +eventually you're going to end up like +typing it down on your laptop because + + align:start position:0% +typing it down on your laptop because + + + align:start position:0% +typing it down on your laptop because +that will make it easier for you to turn + + align:start position:0% +that will make it easier for you to turn + + + align:start position:0% +that will make it easier for you to turn +in your work for project one uh but + + align:start position:0% +in your work for project one uh but + + + align:start position:0% +in your work for project one uh but +while you're working on a prototype try + + align:start position:0% +while you're working on a prototype try + + + align:start position:0% +while you're working on a prototype try +writing your rules on the cards instead + + align:start position:0% +writing your rules on the cards instead + + + align:start position:0% +writing your rules on the cards instead +because that allows you to do things + + align:start position:0% +because that allows you to do things + + + align:start position:0% +because that allows you to do things +like rearrange the the the steps in + + align:start position:0% +like rearrange the the the steps in + + + align:start position:0% +like rearrange the the the steps in +which uh certain rules operate allows + + align:start position:0% +which uh certain rules operate allows + + + align:start position:0% +which uh certain rules operate allows +you to change out the rule really easily + + align:start position:0% +you to change out the rule really easily + + + align:start position:0% +you to change out the rule really easily +while you know while keeping the old + + align:start position:0% +while you know while keeping the old + + + align:start position:0% +while you know while keeping the old +rule around and you can just swap things + + align:start position:0% +rule around and you can just swap things + + + align:start position:0% +rule around and you can just swap things +in and can try things differently every + + align:start position:0% +in and can try things differently every + + + align:start position:0% +in and can try things differently every +time you change a rule change the + + align:start position:0% +time you change a rule change the + + + align:start position:0% +time you change a rule change the +current you know if you're changing a + + align:start position:0% +current you know if you're changing a + + + align:start position:0% +current you know if you're changing a +number of your of rules instead of + + align:start position:0% +number of your of rules instead of + + + align:start position:0% +number of your of rules instead of +taking say take three steps every turn + + align:start position:0% +taking say take three steps every turn + + + align:start position:0% +taking say take three steps every turn +you say take two steps every turn just + + align:start position:0% +you say take two steps every turn just + + + align:start position:0% +you say take two steps every turn just +cross out the three and write two in + + align:start position:0% +cross out the three and write two in + + + align:start position:0% +cross out the three and write two in +there uh periodically take photos with + + align:start position:0% +there uh periodically take photos with + + + align:start position:0% +there uh periodically take photos with +your phone cameras uh and always try to + + align:start position:0% +your phone cameras uh and always try to + + + align:start position:0% +your phone cameras uh and always try to +simplify always try to like get down to + + align:start position:0% +simplify always try to like get down to + + + align:start position:0% +simplify always try to like get down to +the smallest set of rules that is + + align:start position:0% +the smallest set of rules that is + + + align:start position:0% +the smallest set of rules that is +necessary for you to test your idea part + + align:start position:0% +necessary for you to test your idea part + + + align:start position:0% +necessary for you to test your idea part +of that is just a speed up testing + + align:start position:0% +of that is just a speed up testing + + + align:start position:0% +of that is just a speed up testing +you're going to test with within your + + align:start position:0% +you're going to test with within your + + + align:start position:0% +you're going to test with within your +team first just to be able to see + + align:start position:0% +team first just to be able to see + + + align:start position:0% +team first just to be able to see +whether this basic mechanism works and + + align:start position:0% +whether this basic mechanism works and + + + align:start position:0% +whether this basic mechanism works and +eventually you're going to end up + + align:start position:0% +eventually you're going to end up + + + align:start position:0% +eventually you're going to end up +testing with each other and uh you the + + align:start position:0% +testing with each other and uh you the + + + align:start position:0% +testing with each other and uh you the +the the simpler your rules the less time + + align:start position:0% +the the simpler your rules the less time + + + align:start position:0% +the the simpler your rules the less time +it is to be able to start a new play + + align:start position:0% +it is to be able to start a new play + + + align:start position:0% +it is to be able to start a new play +test because there's less for you to + + align:start position:0% +test because there's less for you to + + + align:start position:0% +test because there's less for you to +explain to somebody else who's about + + align:start position:0% +explain to somebody else who's about + + + align:start position:0% +explain to somebody else who's about +who's who's never seen your game before + + align:start position:0% +who's who's never seen your game before + + + align:start position:0% +who's who's never seen your game before +so try to get get your rules to be as + + align:start position:0% +so try to get get your rules to be as + + + align:start position:0% +so try to get get your rules to be as +simple as + + align:start position:0% + + + + align:start position:0% + +possible also if you have too many rules + + align:start position:0% +possible also if you have too many rules + + + align:start position:0% +possible also if you have too many rules +and something breaks in your game it's + + align:start position:0% +and something breaks in your game it's + + + align:start position:0% +and something breaks in your game it's +sometimes harder to figure out which + + align:start position:0% +sometimes harder to figure out which + + + align:start position:0% +sometimes harder to figure out which +rule was was a culprit uh if you have + + align:start position:0% +rule was was a culprit uh if you have + + + align:start position:0% +rule was was a culprit uh if you have +few rules it's usually more obvious for + + align:start position:0% +few rules it's usually more obvious for + + + align:start position:0% +few rules it's usually more obvious for +you to spot + + align:start position:0% +you to spot + + + align:start position:0% +you to spot +now we talked about iterative design a + + align:start position:0% +now we talked about iterative design a + + + align:start position:0% +now we talked about iterative design a +lot and this is basically the loop that + + align:start position:0% +lot and this is basically the loop that + + + align:start position:0% +lot and this is basically the loop that +we're using while we are paper + + align:start position:0% +we're using while we are paper + + + align:start position:0% +we're using while we are paper +prototyping you start with a question a + + align:start position:0% +prototyping you start with a question a + + + align:start position:0% +prototyping you start with a question a +falsifiable question a yes no question + + align:start position:0% +falsifiable question a yes no question + + + align:start position:0% +falsifiable question a yes no question +uh and you know what does what is this + + align:start position:0% +uh and you know what does what is this + + + align:start position:0% +uh and you know what does what is this +prototype going to achieve maybe in this + + align:start position:0% +prototype going to achieve maybe in this + + + align:start position:0% +prototype going to achieve maybe in this +particular case it's going to be um does + + align:start position:0% +particular case it's going to be um does + + + align:start position:0% +particular case it's going to be um does +this theme that we picked actually have + + align:start position:0% +this theme that we picked actually have + + + align:start position:0% +this theme that we picked actually have +Randomness in it that you can plan for + + align:start position:0% +Randomness in it that you can plan for + + + align:start position:0% +Randomness in it that you can plan for +or is it or is the randomness So Random + + align:start position:0% +or is it or is the randomness So Random + + + align:start position:0% +or is it or is the randomness So Random +to the point where you can't plan for it + + align:start position:0% +to the point where you can't plan for it + + + align:start position:0% +to the point where you can't plan for it +or is it really just very deterministic + + align:start position:0% +or is it really just very deterministic + + + align:start position:0% +or is it really just very deterministic +and then when you play the game you can + + align:start position:0% +and then when you play the game you can + + + align:start position:0% +and then when you play the game you can +really tell you know yeah here's the + + align:start position:0% +really tell you know yeah here's the + + + align:start position:0% +really tell you know yeah here's the +optimal + + align:start position:0% +optimal + + + align:start position:0% +optimal +solution um you can look at XM exatic + + align:start position:0% +solution um you can look at XM exatic + + + align:start position:0% +solution um you can look at XM exatic +design anyone heard of this term mechi + + align:start position:0% +design anyone heard of this term mechi + + + align:start position:0% +design anyone heard of this term mechi +in particular uses this a + + align:start position:0% +in particular uses this a + + + align:start position:0% +in particular uses this a +lot um which is basically you establish + + align:start position:0% +lot um which is basically you establish + + + align:start position:0% +lot um which is basically you establish +axioms which are things that you are + + align:start position:0% +axioms which are things that you are + + + align:start position:0% +axioms which are things that you are +taking to be true a baseline uh that + + align:start position:0% +taking to be true a baseline uh that + + + align:start position:0% +taking to be true a baseline uh that +need to be fulfilled by any workable + + align:start position:0% +need to be fulfilled by any workable + + + align:start position:0% +need to be fulfilled by any workable +design so it could be uh we assume that + + align:start position:0% +design so it could be uh we assume that + + + align:start position:0% +design so it could be uh we assume that +this game needs to have a + + align:start position:0% +this game needs to have a + + + align:start position:0% +this game needs to have a +random some sort of random condition + + align:start position:0% +random some sort of random condition + + + align:start position:0% +random some sort of random condition +that's generated uh uh uh that that + + align:start position:0% +that's generated uh uh uh that that + + + align:start position:0% +that's generated uh uh uh that that +changes during the game and we need to + + align:start position:0% +changes during the game and we need to + + + align:start position:0% +changes during the game and we need to +be the player to + + align:start position:0% +be the player to + + + align:start position:0% +be the player to +identify that this number is changing + + align:start position:0% +identify that this number is changing + + + align:start position:0% +identify that this number is changing +and anticipate how where that number + + align:start position:0% +and anticipate how where that number + + + align:start position:0% +and anticipate how where that number +might end up going and if your prototype + + align:start position:0% +might end up going and if your prototype + + + align:start position:0% +might end up going and if your prototype +fulfills both of them then you know that + + align:start position:0% +fulfills both of them then you know that + + + align:start position:0% +fulfills both of them then you know that +prototype worked you can build a lot of + + align:start position:0% +prototype worked you can build a lot of + + + align:start position:0% +prototype worked you can build a lot of +different prototypes that fulfill those + + align:start position:0% +different prototypes that fulfill those + + + align:start position:0% +different prototypes that fulfill those +same to conditions that's another way to + + align:start position:0% +same to conditions that's another way to + + + align:start position:0% +same to conditions that's another way to +sort of start with a + + align:start position:0% +sort of start with a + + + align:start position:0% +sort of start with a +question and um then you actually start + + align:start position:0% +question and um then you actually start + + + align:start position:0% +question and um then you actually start +designing grabbing those pieces of paper + + align:start position:0% +designing grabbing those pieces of paper + + + align:start position:0% +designing grabbing those pieces of paper +writing out uh uh writing out your rules + + align:start position:0% +writing out uh uh writing out your rules + + + align:start position:0% +writing out uh uh writing out your rules +on cards brainstorming you know what + + align:start position:0% +on cards brainstorming you know what + + + align:start position:0% +on cards brainstorming you know what +your game's all about but you want to do + + align:start position:0% +your game's all about but you want to do + + + align:start position:0% +your game's all about but you want to do +this as quickly as possible the less + + align:start position:0% +this as quickly as possible the less + + + align:start position:0% +this as quickly as possible the less +time you can spend talking about this + + align:start position:0% +time you can spend talking about this + + + align:start position:0% +time you can spend talking about this +the more different kinds of ideas you're + + align:start position:0% +the more different kinds of ideas you're + + + align:start position:0% +the more different kinds of ideas you're +going to be able to run through and + + align:start position:0% +going to be able to run through and + + + align:start position:0% +going to be able to run through and +that's what we're trying to go to to to + + align:start position:0% +that's what we're trying to go to to to + + + align:start position:0% +that's what we're trying to go to to to +do during a prototyping process if + + align:start position:0% +do during a prototyping process if + + + align:start position:0% +do during a prototyping process if +you're ever in a situation where where + + align:start position:0% +you're ever in a situation where where + + + align:start position:0% +you're ever in a situation where where +you've got two different options you + + align:start position:0% +you've got two different options you + + + align:start position:0% +you've got two different options you +know this might be better or this might + + align:start position:0% +know this might be better or this might + + + align:start position:0% +know this might be better or this might +be better you're not quite sure it's + + align:start position:0% +be better you're not quite sure it's + + + align:start position:0% +be better you're not quite sure it's +faster to you it's usually faster than + + align:start position:0% +faster to you it's usually faster than + + + align:start position:0% +faster to you it's usually faster than +paper prototyping to just start making + + align:start position:0% +paper prototyping to just start making + + + align:start position:0% +paper prototyping to just start making +both prototypes you know all right you + + align:start position:0% +both prototypes you know all right you + + + align:start position:0% +both prototypes you know all right you +do this version you do this version + + align:start position:0% +do this version you do this version + + + align:start position:0% +do this version you do this version +generate the cards play through both of + + align:start position:0% +generate the cards play through both of + + + align:start position:0% +generate the cards play through both of +them and you get like actual evidence + + align:start position:0% +them and you get like actual evidence + + + align:start position:0% +them and you get like actual evidence +actual play testing evidence on which + + align:start position:0% +actual play testing evidence on which + + + align:start position:0% +actual play testing evidence on which +idea seems to work + + align:start position:0% +idea seems to work + + + align:start position:0% +idea seems to work +better um after you design you play + + align:start position:0% +better um after you design you play + + + align:start position:0% +better um after you design you play +through it you know first within your + + align:start position:0% +through it you know first within your + + + align:start position:0% +through it you know first within your +team and then you grab somebody from + + align:start position:0% +team and then you grab somebody from + + + align:start position:0% +team and then you grab somebody from +some from some other team or one of the + + align:start position:0% +some from some other team or one of the + + + align:start position:0% +some from some other team or one of the +instructors and will'll sit down and + + align:start position:0% +instructors and will'll sit down and + + + align:start position:0% +instructors and will'll sit down and +we'll and we'll play a game to see where + + align:start position:0% +we'll and we'll play a game to see where + + + align:start position:0% +we'll and we'll play a game to see where +are the strength in this design where + + align:start position:0% +are the strength in this design where + + + align:start position:0% +are the strength in this design where +the weaknesses whatever you design + + align:start position:0% +the weaknesses whatever you design + + + align:start position:0% +the weaknesses whatever you design +within an hour is going to be clunky and + + align:start position:0% +within an hour is going to be clunky and + + + align:start position:0% +within an hour is going to be clunky and +broken and really really you know not + + align:start position:0% +broken and really really you know not + + + align:start position:0% +broken and really really you know not +quite where you want to be that's fine + + align:start position:0% +quite where you want to be that's fine + + + align:start position:0% +quite where you want to be that's fine +go do a play test with that expectation + + align:start position:0% +go do a play test with that expectation + + + align:start position:0% +go do a play test with that expectation +that they going to be problems uh and + + align:start position:0% +that they going to be problems uh and + + + align:start position:0% +that they going to be problems uh and +you'll get a lot more information out of + + align:start position:0% +you'll get a lot more information out of + + + align:start position:0% +you'll get a lot more information out of +that play test then you will working on + + align:start position:0% +that play test then you will working on + + + align:start position:0% +that play test then you will working on +your + + align:start position:0% +your + + + align:start position:0% +your +own and then you use that information to + + align:start position:0% +own and then you use that information to + + + align:start position:0% +own and then you use that information to +revise your design make changes and then + + align:start position:0% +revise your design make changes and then + + + align:start position:0% +revise your design make changes and then +you repeat this entire process again + + align:start position:0% +you repeat this entire process again + + + align:start position:0% +you repeat this entire process again +either you amplify on the strengths uh + + align:start position:0% +either you amplify on the strengths uh + + + align:start position:0% +either you amplify on the strengths uh +you figure out what your weaknesses are + + align:start position:0% +you figure out what your weaknesses are + + + align:start position:0% +you figure out what your weaknesses are +and you make great and you make big + + align:start position:0% +and you make great and you make big + + + align:start position:0% +and you make great and you make big +changes so you repeat that and here are + + align:start position:0% +changes so you repeat that and here are + + + align:start position:0% +changes so you repeat that and here are +a couple of Tricks uh that can work + + align:start position:0% +a couple of Tricks uh that can work + + + align:start position:0% +a couple of Tricks uh that can work +sometimes if you have trouble figuring + + align:start position:0% +sometimes if you have trouble figuring + + + align:start position:0% +sometimes if you have trouble figuring +out what sort of changes to make in your + + align:start position:0% +out what sort of changes to make in your + + + align:start position:0% +out what sort of changes to make in your +design uh killing a rule just like + + align:start position:0% +design uh killing a rule just like + + + align:start position:0% +design uh killing a rule just like +taking a rule out sometimes fixes + + align:start position:0% +taking a rule out sometimes fixes + + + align:start position:0% +taking a rule out sometimes fixes +problems more than trying to fix a rule + + align:start position:0% +problems more than trying to fix a rule + + + align:start position:0% +problems more than trying to fix a rule +itself you know a certain thing is + + align:start position:0% +itself you know a certain thing is + + + align:start position:0% +itself you know a certain thing is +bogging down the game certain thing is + + align:start position:0% +bogging down the game certain thing is + + + align:start position:0% +bogging down the game certain thing is +too confusing uh just does the game work + + align:start position:0% +too confusing uh just does the game work + + + align:start position:0% +too confusing uh just does the game work +if you just take that rule out sometimes + + align:start position:0% +if you just take that rule out sometimes + + + align:start position:0% +if you just take that rule out sometimes +it does um you can make a resource + + align:start position:0% +it does um you can make a resource + + + align:start position:0% +it does um you can make a resource +that's limited unlimited or make a + + align:start position:0% +that's limited unlimited or make a + + + align:start position:0% +that's limited unlimited or make a +unlimited resource limited limited + + align:start position:0% +unlimited resource limited limited + + + align:start position:0% +unlimited resource limited limited +health unlimited health limited + + align:start position:0% +health unlimited health limited + + + align:start position:0% +health unlimited health limited +ammunition + + align:start position:0% +ammunition + + + align:start position:0% +ammunition +uh money um player interference is more + + align:start position:0% +uh money um player interference is more + + + align:start position:0% +uh money um player interference is more +for multiplayer games where sometimes if + + align:start position:0% +for multiplayer games where sometimes if + + + align:start position:0% +for multiplayer games where sometimes if +you if everybody is is playing their own + + align:start position:0% +you if everybody is is playing their own + + + align:start position:0% +you if everybody is is playing their own +little solo game and they're not + + align:start position:0% +little solo game and they're not + + + align:start position:0% +little solo game and they're not +interacting with each other you come up + + align:start position:0% +interacting with each other you come up + + + align:start position:0% +interacting with each other you come up +with ways to mess up each other's plans + + align:start position:0% +with ways to mess up each other's plans + + + align:start position:0% +with ways to mess up each other's plans +that doesn't always apply with M with + + align:start position:0% +that doesn't always apply with M with + + + align:start position:0% +that doesn't always apply with M with +with single player games but uh if + + align:start position:0% +with single player games but uh if + + + align:start position:0% +with single player games but uh if +you've ever played a game like a role + + align:start position:0% +you've ever played a game like a role + + + align:start position:0% +you've ever played a game like a role +playing game where you where you can + + align:start position:0% +playing game where you where you can + + + align:start position:0% +playing game where you where you can +delay the uh an an enemy has anyone seen + + align:start position:0% +delay the uh an an enemy has anyone seen + + + align:start position:0% +delay the uh an an enemy has anyone seen +one one of those where you can like cast + + align:start position:0% +one one of those where you can like cast + + + align:start position:0% +one one of those where you can like cast +slow or something on on a enemy and they + + align:start position:0% +slow or something on on a enemy and they + + + align:start position:0% +slow or something on on a enemy and they +kind attack you for another turn or + + align:start position:0% +kind attack you for another turn or + + + align:start position:0% +kind attack you for another turn or +something that's player interference + + align:start position:0% +something that's player interference + + + align:start position:0% +something that's player interference +right only the player that you're + + align:start position:0% +right only the player that you're + + + align:start position:0% +right only the player that you're +interfering with happens to be the + + align:start position:0% +interfering with happens to be the + + + align:start position:0% +interfering with happens to be the +computer um and what can you do to + + align:start position:0% +computer um and what can you do to + + + align:start position:0% +computer um and what can you do to +basically get into somebody else's plan + + align:start position:0% +basically get into somebody else's plan + + + align:start position:0% +basically get into somebody else's plan +and change it and the computer can have + + align:start position:0% +and change it and the computer can have + + + align:start position:0% +and change it and the computer can have +those rules + + align:start position:0% +those rules + + + align:start position:0% +those rules +too um mess with the play order mess + + align:start position:0% +too um mess with the play order mess + + + align:start position:0% +too um mess with the play order mess +with the order of your rules you know + + align:start position:0% +with the order of your rules you know + + + align:start position:0% +with the order of your rules you know +just try rearranging the order of rules + + align:start position:0% +just try rearranging the order of rules + + + align:start position:0% +just try rearranging the order of rules +and some sometimes by grouping things + + align:start position:0% +and some sometimes by grouping things + + + align:start position:0% +and some sometimes by grouping things +into sort of logical chunks it can make + + align:start position:0% +into sort of logical chunks it can make + + + align:start position:0% +into sort of logical chunks it can make +the EAS the game easier to understand + + align:start position:0% +the EAS the game easier to understand + + + align:start position:0% +the EAS the game easier to understand +instead of saying first you decide + + align:start position:0% +instead of saying first you decide + + + align:start position:0% +instead of saying first you decide +whether you're going to do this then you + + align:start position:0% +whether you're going to do this then you + + + align:start position:0% +whether you're going to do this then you +decide that whether you're going to do + + align:start position:0% +decide that whether you're going to do + + + align:start position:0% +decide that whether you're going to do +this then you're going to decide where + + align:start position:0% +this then you're going to decide where + + + align:start position:0% +this then you're going to decide where +to do this maybe just say make two of + + align:start position:0% +to do this maybe just say make two of + + + align:start position:0% +to do this maybe just say make two of +these three decisions right you know and + + align:start position:0% +these three decisions right you know and + + + align:start position:0% +these three decisions right you know and +uh and and every turn you get two of + + align:start position:0% +uh and and every turn you get two of + + + align:start position:0% +uh and and every turn you get two of +these three make them in any order you + + align:start position:0% +these three make them in any order you + + + align:start position:0% +these three make them in any order you +want that that's a way that you method + + align:start position:0% +want that that's a way that you method + + + align:start position:0% +want that that's a way that you method +play order if you're going to change + + align:start position:0% +play order if you're going to change + + + align:start position:0% +play order if you're going to change +variables either multiply or divide them + + align:start position:0% +variables either multiply or divide them + + + align:start position:0% +variables either multiply or divide them +by two there is not enough granular + + align:start position:0% +by two there is not enough granular + + + align:start position:0% +by two there is not enough granular +granularity in the prototypes that + + align:start position:0% +granularity in the prototypes that + + + align:start position:0% +granularity in the prototypes that +you're making to to today to do like a + + align:start position:0% +you're making to to today to do like a + + + align:start position:0% +you're making to to today to do like a +10% change in a certain variable and + + align:start position:0% +10% change in a certain variable and + + + align:start position:0% +10% change in a certain variable and +then be ble to detect whether that + + align:start position:0% +then be ble to detect whether that + + + align:start position:0% +then be ble to detect whether that +change was the right change or not + + align:start position:0% +change was the right change or not + + + align:start position:0% +change was the right change or not +that's not going to uh be obvious enough + + align:start position:0% +that's not going to uh be obvious enough + + + align:start position:0% +that's not going to uh be obvious enough +do like big multiples by of two of three + + align:start position:0% +do like big multiples by of two of three + + + align:start position:0% +do like big multiples by of two of three +to be able to see whether that's the + + align:start position:0% +to be able to see whether that's the + + + align:start position:0% +to be able to see whether that's the +change that's necessary you can tune + + align:start position:0% +change that's necessary you can tune + + + align:start position:0% +change that's necessary you can tune +things later uh when you are preparing + + align:start position:0% +things later uh when you are preparing + + + align:start position:0% +things later uh when you are preparing +the project for uh the play test on + + align:start position:0% +the project for uh the play test on + + + align:start position:0% +the project for uh the play test on +Wednesday for instance but when you're + + align:start position:0% +Wednesday for instance but when you're + + + align:start position:0% +Wednesday for instance but when you're +in this class do things by by by big + + align:start position:0% +in this class do things by by by big + + + align:start position:0% +in this class do things by by by big +multiples um if you're game's really + + align:start position:0% +multiples um if you're game's really + + + align:start position:0% +multiples um if you're game's really +really really kind of getting bed down + + align:start position:0% +really really kind of getting bed down + + + align:start position:0% +really really kind of getting bed down +and taking too long to play uh try to + + align:start position:0% +and taking too long to play uh try to + + + align:start position:0% +and taking too long to play uh try to +get down to the core set of rules the + + align:start position:0% +get down to the core set of rules the + + + align:start position:0% +get down to the core set of rules the +minimum set of rules that's necessarily + + align:start position:0% +minimum set of rules that's necessarily + + + align:start position:0% +minimum set of rules that's necessarily +even just for your game to work uh just + + align:start position:0% +even just for your game to work uh just + + + align:start position:0% +even just for your game to work uh just +for the game to run at all try to figure + + align:start position:0% +for the game to run at all try to figure + + + align:start position:0% +for the game to run at all try to figure +out what that core is uh the the minimum + + align:start position:0% +out what that core is uh the the minimum + + + align:start position:0% +out what that core is uh the the minimum +set of rules and then add in each rule + + align:start position:0% +set of rules and then add in each rule + + + align:start position:0% +set of rules and then add in each rule +one by one reconstruct your your your + + align:start position:0% +one by one reconstruct your your your + + + align:start position:0% +one by one reconstruct your your your +your game that's one way to identify + + align:start position:0% +your game that's one way to identify + + + align:start position:0% +your game that's one way to identify +where the main problems are in your game + + align:start position:0% +where the main problems are in your game + + + align:start position:0% +where the main problems are in your game +because as you add the the problematic + + align:start position:0% +because as you add the the problematic + + + align:start position:0% +because as you add the the problematic +rule things start to + + align:start position:0% +rule things start to + + + align:start position:0% +rule things start to +break uh and finally be willing to just + + align:start position:0% +break uh and finally be willing to just + + + align:start position:0% +break uh and finally be willing to just +throw away everything that you generate + + align:start position:0% +throw away everything that you generate + + + align:start position:0% +throw away everything that you generate +in the next hour okay every anything + + align:start position:0% +in the next hour okay every anything + + + align:start position:0% +in the next hour okay every anything +that that you make in the next hour + + align:start position:0% +that that you make in the next hour + + + align:start position:0% +that that you make in the next hour +might in fact just be terrible and + + align:start position:0% +might in fact just be terrible and + + + align:start position:0% +might in fact just be terrible and +you're going to learn that and that's + + align:start position:0% +you're going to learn that and that's + + + align:start position:0% +you're going to learn that and that's +fine that's why we make prototypes so + + align:start position:0% +fine that's why we make prototypes so + + + align:start position:0% +fine that's why we make prototypes so +that they can be disposable that's why + + align:start position:0% +that they can be disposable that's why + + + align:start position:0% +that they can be disposable that's why +that that's how I started this talk so + + align:start position:0% +that that's how I started this talk so + + + align:start position:0% +that that's how I started this talk so +any questions before we actually start + + align:start position:0% +any questions before we actually start + + + align:start position:0% +any questions before we actually start +making + + align:start position:0% + + + + align:start position:0% + +stuff coming up with rules you're going + + align:start position:0% +stuff coming up with rules you're going + + + align:start position:0% +stuff coming up with rules you're going +to grab pieces and create some sort of + + align:start position:0% +to grab pieces and create some sort of + + + align:start position:0% +to grab pieces and create some sort of +uh play surface or cards that people are + + align:start position:0% +uh play surface or cards that people are + + + align:start position:0% +uh play surface or cards that people are +going to play with you don't need to put + + align:start position:0% +going to play with you don't need to put + + + align:start position:0% +going to play with you don't need to put +anything on the + + align:start position:0% +anything on the + + + align:start position:0% +anything on the +board um and uh before everybody runs + + align:start position:0% +board um and uh before everybody runs + + + align:start position:0% +board um and uh before everybody runs +down and grabs things I guess we're + + align:start position:0% +down and grabs things I guess we're + + + align:start position:0% +down and grabs things I guess we're +going to go back and remind people what + + align:start position:0% +going to go back and remind people what + + + align:start position:0% +going to go back and remind people what +a low Fidelity um prototype + + align:start position:0% + + + + align:start position:0% + +is terrible as long as you're aware of + + align:start position:0% +is terrible as long as you're aware of + + + align:start position:0% +is terrible as long as you're aware of +it I thought I replaced it with the + + align:start position:0% +it I thought I replaced it with the + + + align:start position:0% +it I thought I replaced it with the +stack counters I guess + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +all right so we just have a couple more + + align:start position:0% +all right so we just have a couple more + + + align:start position:0% +all right so we just have a couple more +minutes left to class um couple things + + align:start position:0% +minutes left to class um couple things + + + align:start position:0% +minutes left to class um couple things +to remember before you leave take + + align:start position:0% +to remember before you leave take + + + align:start position:0% +to remember before you leave take +pictures of all your brainstorming notes + + align:start position:0% +pictures of all your brainstorming notes + + + align:start position:0% +pictures of all your brainstorming notes +and keep your your notes with you so + + align:start position:0% +and keep your your notes with you so + + + align:start position:0% +and keep your your notes with you so +take them away with you uh make sure + + align:start position:0% +take them away with you uh make sure + + + align:start position:0% +take them away with you uh make sure +everyone on your team can access those + + align:start position:0% +everyone on your team can access those + + + align:start position:0% +everyone on your team can access those +notes make sure you know the email + + align:start position:0% +notes make sure you know the email + + + align:start position:0% +notes make sure you know the email +addresses of the people you're on the on + + align:start position:0% +addresses of the people you're on the on + + + align:start position:0% +addresses of the people you're on the on +you're on your team with so you can talk + + align:start position:0% +you're on your team with so you can talk + + + align:start position:0% +you're on your team with so you can talk +to them again and before you leave the + + align:start position:0% +to them again and before you leave the + + + align:start position:0% +to them again and before you leave the +classroom today + + align:start position:0% +classroom today + + + align:start position:0% +classroom today +start up a document and enter your your + + align:start position:0% +start up a document and enter your your + + + align:start position:0% +start up a document and enter your your +change log so put in what you designed + + align:start position:0% +change log so put in what you designed + + + align:start position:0% +change log so put in what you designed +today and what problems you found by the + + align:start position:0% +today and what problems you found by the + + + align:start position:0% +today and what problems you found by the +end of the + + align:start position:0% +end of the + + + align:start position:0% +end of the +day so I'm going to repeat that one last + + align:start position:0% +day so I'm going to repeat that one last + + + align:start position:0% +day so I'm going to repeat that one last +time before you leave class + + align:start position:0% +time before you leave class + + + align:start position:0% +time before you leave class +today start up a document open up and + + align:start position:0% +today start up a document open up and + + + align:start position:0% +today start up a document open up and +start up your new design change log put + + align:start position:0% +start up your new design change log put + + + align:start position:0% +start up your new design change log put +the date put what you did today so a + + align:start position:0% +the date put what you did today so a + + + align:start position:0% +the date put what you did today so a +brief two two or three sentence + + align:start position:0% +brief two two or three sentence + + + align:start position:0% +brief two two or three sentence +description of what you design today and + + align:start position:0% +description of what you design today and + + + align:start position:0% +description of what you design today and +what are the problems you're facing now + + align:start position:0% +what are the problems you're facing now + + + align:start position:0% +what are the problems you're facing now +that'll be important to you both for + + align:start position:0% +that'll be important to you both for + + + align:start position:0% +that'll be important to you both for +when you start when you meet as as a + + align:start position:0% +when you start when you meet as as a + + + align:start position:0% +when you start when you meet as as a +team again to remember what you did but + + align:start position:0% +team again to remember what you did but + + + align:start position:0% +team again to remember what you did but +also later on to have a full history of + + align:start position:0% +also later on to have a full history of + + + align:start position:0% +also later on to have a full history of +everything that you've done + + align:start position:0% +everything that you've done + + + align:start position:0% +everything that you've done +okay um one more thing yes one more + + align:start position:0% +okay um one more thing yes one more + + + align:start position:0% +okay um one more thing yes one more +thing tomor wnes rather we are G to have + + align:start position:0% +thing tomor wnes rather we are G to have + + + align:start position:0% +thing tomor wnes rather we are G to have +play t be play tting all the protypes + + align:start position:0% +play t be play tting all the protypes + + + align:start position:0% +play t be play tting all the protypes +need for Wednesday + + align:start position:0% +need for Wednesday + + + align:start position:0% +need for Wednesday +and then we're starting Wednesday's + + align:start position:0% +and then we're starting Wednesday's + + + align:start position:0% +and then we're starting Wednesday's +class off with discussions about the + + align:start position:0% +class off with discussions about the + + + align:start position:0% +class off with discussions about the +game engine tutorial so bring your + + align:start position:0% +game engine tutorial so bring your + + + align:start position:0% +game engine tutorial so bring your +problems bring your questions about the + + align:start position:0% +problems bring your questions about the + + + align:start position:0% +problems bring your questions about the +engines that you were assigned and we'll + + align:start position:0% +engines that you were assigned and we'll + + + align:start position:0% +engines that you were assigned and we'll +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +them see you Wednesday \ No newline at end of file diff --git a/jPDAPmx4pXE.txt b/jPDAPmx4pXE.txt new file mode 100644 index 0000000000000000000000000000000000000000..9d6bf649e1bc0e4c0884386fe8da0f715afeb7de --- /dev/null +++ b/jPDAPmx4pXE.txt @@ -0,0 +1,3177 @@ +[MUSIC PLAYING - "JESU, JOY OF +MAN'S DESIRING" BY JOHANN + +SEBASTIAN BACH] + +PROFESSOR: Well, up 'til now, I +suppose, we've been learning + +about a lot of techniques for +organizing big programs, + +symbolic manipulation a bit, +some of the technology that + +you use for establishing +languages, one in terms of + +another, which is used for +organizing very large + +programs. In fact, the nicest +programs I know look more like + +a pile of languages than like +a decomposition of a problem + +into parts. + +Well, I suppose at this point, +there are still, however, a + +few mysteries about how this +sort of stuff works. + +And so what we'd like to do now +is diverge from the plan + +of telling you how to organize +big programs, and rather tell + +you something about the +mechanisms by which these + +things can be made to work. + +The main reason for this is +demystification, if you will, + +that we have a lot of mysteries +left, like exactly + +how it is the case that a +program is controlled, how a + +computer knows what the next +thing to do is, or + +something like that. + +And what I'd like to do now is +make that clear to you, that + +even if you've never played +with a physical computer + +before, the mechanism is really +very simple, and that + +you can understand it completely +with no trouble. + +So I'd like to start by +imagining that we-- + +well, the way we're going to do +this, by the way, is we're + +going to take some very simple +Lisp programs, very simple + +Lisp programs, and transform +them into hardware. + +I'm not going to worry about +some intermediate step of + +going through some existing +computer machine language and + +then showing you how that +computer works, because that's + +not as illuminating. + +So what I'm really going to +show you is how a piece of + +machinery can be built to do a +job that you have written down + +as a program. + +That program is, in fact, a +description of a machine. + +We're going to start with a very +simple program, proceed + +to show you some simple +mechanisms, proceed to a few + +more complicated programs, and +then later show you a not very + +complicated program, how the +evaluator transforms into a + +piece of hardware. + +And of course at that point, +you have made the universal + +transition and can execute any +program imaginable with a + +piece of well-defined +hardware. + +Well, let's start up now, give +you a real concrete feeling + +for this sort of thing. + +Let's start with a very +simple program. + +Here's Euclid's algorithm. + +It's actually a little +bit more modern + +than Euclid's algorithm. + +Euclid's algorithm for computing +the greatest common + +divisor of two numbers was +invented 350 BC, I think. + +It's the oldest known +algorithm. + +But here we're going to talk +about GCD of A and B, the + +Greatest Common Divisor or two +numbers, A and B. And the + +algorithm is extremely simple. + +If B is 0, then the result is +going to be A. Otherwise, the + +result is the GCD of B and the +remainder when A is divided by + +B. + +So this we have here is a very +simple iterative process. + +This a simple recursive +procedure, recursively defined + +procedure, recursive definition, +which yields an + +iterative process. + +And the way it works is that +every step, it determines + +whether B was zero. + +And if B is 0, we got the answer +in A. Otherwise, we + +make another step where A is +the old B, and B is the + +remainder of the old A divided +by the old B. Very simple. + +Now this, I've already told you +some of the mechanism by + +just saying it that way. + +I set it in time. + +I said there are certain steps, +and that, in fact, one + +of the things you can see here +is that one of the reasons why + +this is iterative is nothing is +needed of the last step to + +get the answer. + +All of the information that's +needed to run this algorithm + +is in A and B. It has two +well-defined state variables. + +So I'm going to define a machine +for you that can + +compute you GCDs. + +Now let's see. + +Every computer that's ever +been made that's a + +single-process computer, as +opposed to a multiprocessor of + +some sort, is made according +to the same plan. + +The plan is the computer has two +parts, a part called the + +datapaths, and a part called +the controller. + +The datapaths correspond to a +calculator that you might + +have. It contains certain +registers that remember + +things, and you've all +used calculators. + +It has some buttons on +it and some lights. + +And so by pushing the various +buttons, you can cause + +operations to happen inside +there among the registers, and + +some of the results +to be displayed. + +That's completely mechanical. + +You could imagine that box has +no intelligence in it. + +Now it might be very impressive +that it can produce + +the sine of a number, but that +at least is apparently + +possibly mechanical. + +At least, I could open that +up in the same way I'm + +about to open GCD. + +So this may have a whole +computer inside of it, but + +that's not interesting. + +Addition is certainly simple. + +That can be done without +any further mechanism. + +Now also, if we were to look +at the other half, the + +controller, that's a part +that's dumb, too. + +It pushes the buttons. + +It pushes them according to the +sequence, which is written + +down on a piece of paper, +and observes the lights. + +And every so often, it comes to +a place in a sequence that + +says, if light A is on, +do this sequence. + +Otherwise, do that sequence. + +And thereby, there's no +complexity there either. + +Well, let's just draw that and +see what we feel about that. + +So for computing GCDs, what I +want you to think about is + +that there are these +registers. + +A register is a place where I +store a number, in this case. + +And this one's called a. + +And then there's another +one for storing b. + +Now we have to see what things +we can do with these + +registers, and they're not +entirely obvious what you can + +do with them. + +Well, we have to see +what things we + +need to do with them. + +We're looking at the problem +we're trying to solve. + +One of the important things +for designing a computer, + +which I think most designers +don't do, is you study the + +problem you want to solve and +then use what you learn from + +studying the problem you want +to solve to put in the + +mechanisms needed to solve +it in the computer you're + +building, no more no less. + +Now it may be that the problem +you're trying to solve is + +everybody's problem, in which +case you have to build in a + +universal interpreter +of some language. + +But you shouldn't put any more +in than required to build the + +universal interpreter +of some language. + +We'll worry about that +in a second. + +OK, going back to +here, let's see. + +What do we have to +be able to do? + +Well, somehow, we have to be +able to get B into A. We have + +to be able to get the old value +of B into the value of + +A. So we have to have some path +by which stuff can flow, + +whatever this information +is, from b to a. + +I'm going to draw that with by +an arrow saying that it is + +possible to move the contents +of b into a, replacing the + +value of a. + +And there's a little button +here which you push which + +allows that to happen. + +That's what the little +x is here. + +Now it's also the case that I +have to be able to compute the + +remainder of a and b. + +Now that may be a complicated +mess. + +On the other hand, I'm going +to make it a small box. + +If we have to, we may open up +that box and look inside and + +see what it is. + +So here, I'm going to have a +little box, which I'm going to + +draw this way, which we'll +call the remainder. + +And it's going to take in a. + +That's going to take in b. + +And it's going to put out +something, the remainder of a + +divided by b. + +Another thing we have to see +here is that we have to be + +able to test whether +b is equal to 0. + +Well, that means somebody's +got to be looking at-- + +a thing that's looking +at the value of b. + +I have a light bulb here which +lights up if b equals 0. + +That's its job. + +And finally, I suppose, because +of the fact that we + +want the new value of a to be +the old value of b, and + +simultaneously the new value of +b to be something I've done + +with a, and if I plan to make +my machine such that + +everything happens one at a +time, one motion at a time, + +and I can't put two numbers in +a register, then I have to + +have another place to put one +while I'm interchanging. + +OK? + +I can't interchange the two +things in my hands, unless I + +either put two in one hand and +then pull it back the other + +way, or unless I put one down, +pick it up, and put the other + +one, like that, unless I'm a +juggler, which I'm not, as you + +can see, in which case I have a + +possibility of timing errors. + +In fact, much of the type of +computer design people do + +involves timing errors, of some +potential timing errors, + +which I don't much like. + +So for that reason, I have to +have a place to put the second + +one of them down. + +So I have a place called t, +which is a register just for + +temporary, t, with +a button on it. + +And then I'll take the result of +that, since I have to take + +that and put into b, over here, +we'll take the result of + +that and go like this, +and a button here. + +So that's the datapaths +of a GCD machine. + +Now what's the controller? + +Controller's a very +simple thing, too. + +The machine has a state. + +The way I like to visualize that +is that I've got a maze. + +And the maze has a +bunch of places + +connected by directed arrows. + +And what I have is a marble, +which represents the state of + +the controller. + +The marble rolls around +in the maze. + +Of course, this analogy breaks +down for energy reasons. + +I sometimes have to pump the +marble up to the top, because + +it's going to otherwise be a +perpetual motion machine. + +But not worrying about +that, this is + +not a physical analogy. + +This marble rolls around. + +And every time it rolls around +certain bumpers, like in a + +pinball machine, it pushes +one of these buttons. + +And every so often, it comes +to a place, which is a + +division, where it has +to make a choice. + +And there's a flap, which +is controlled by this. + +So that's a really mechanical +way of thinking about it. + +Of course, controllers these +days, are not built that way + +in real computers. + +They're built with +a little bit of + +ROM and a state register. + +But there was a time, like the +DEC PDP-6, where that's how + +you built the controller +of a machine. + +There was a bit that ran around +the delay line, and it + +triggered things +as it went by. + +And it would come back +to the beginning and + +get fed round again. + +And of course, there were all +sorts of great bugs you could + +have like two bits going +around, two marbles. + +And then the machine has +lost its marbles. + +That happens, too. + +Oh, well. + +So anyway, for this machine, +what I have + +to do is the following. + +I'm going to start +my maze here. + +And the first thing I've got +to do, in a notation which + +many of you are familiar with, +is b equal to zero, a test. + +And there's a possibility, +either yes, in + +which case I'm done. + +Otherwise, if no, then +I'm going have to + +roll over some bumpers. + +I'm going to do it in +the following order. + +I want to do this interchange +game. + +Now first, since I need both a +and b, but then the first-- + +and this is not necessary-- + +I want to collect this. + +This is the thing that's +going to go into b. + +So I'm going to say, take this, +which depends upon both + +a and b, and put the remainder +into here. + +So I'm going to push this button +first. Then, I'm going + +to transfer b to a, push that +button, and then I transfer + +the temporary into b, +push that button. + +So a very sequential machine, +it's very inefficient. + +But that's fine right now. + +We're going to name the buttons, +t gets remainder. + +a gets b. + +And b gets t. + +And then I'm going to go around +here and it's to go + +back to start. + +And if you look, what +are we seeing here? + +We're seeing the various-- + +what I really have is some sort +of mechanical connection, + +where t gets r controls +this thing. + +And I have here that a gets b +controls this fellow over + +here, and this fellow +over here. + +Boy, that's absolutely +pessimal, + +the inverse of optimal. + +Every line heads across every +other line the way I drew it. + +I suppose this goes +here, b gets t. + +Now I'd like to run +this machine. + +But before I run the machine, +I want to write down a + +description of this controller, +just so you can + +see that these things, of +course, as usual, can be + +written down in some nice +language, so that we don't + +have to always draw these +diagrams. One of the problems + +with diagrams is that they +take up a lot of space. + +And for a machine this small, +it takes two blackboards. + +For a machine that's the +evaluator machine, I have + +trouble putting it into +this room, even though + +it isn't very big. + +So I'm going to make a little +language for this that's just + +a description of that, +saying define a + +machine we'll call GCD. + +Of course, once we have +something like this, we have a + +simulator for it. + +And the reason why we want to +build a language in this form, + +is because all of a sudden +we can manipulate these + +expressions that I'm +writing down. + +And then of course I can write +things that can algebraically + +manipulate these things, +simulate them, all that sort + +of things that I might want to +do, perhaps transform them as + +a layout, who knows. + +Once I have a nice +representation of registers, + +it has certain registers, which +we can call A, B, and T. + +And there's a controller. + +Actually, a better language, +which would be more explicit, + +would be one which named +every button also and + +said what it did. + +Like, this button causes the +contents of T to go to the + +contents of B. Well I don't want +to do that, because it's + +actually harder to read +to do that, and it + +takes up more space. + +So I'm going to have that in +the instructions written in + +the controller. + +It's going to be implicit +what the operations are. + +They can be deduced by reading +these and collecting together + +all the different things +that can be done. + +Well, let's just look at +what these things are. + +There's a little loop that we +go around which says branch, + +this is the representation of +the little flap that decides + +which way you go here, if 0 +fetch of B, the contents of B, + +and if the contents of +B is 0, then go to a + +place called done. + +Now, one thing you're seeing +here, this looks very much + +like a traditional computer +language. + +And what you're seeing here +is things like labels that + +represent places in a sequence +written down as a sequence. + +The reason why they're needed +is because over here, I've + +written something with loops. + +But if I'm writing English text, +or something like that, + +it's hard to refer to a place. + +I don't have arrows. + +Arrows are represented by giving +names to the places + +where the arrows terminate, and +then referring to them by + +those names. + +Now this is just an encoding. + +There's nothing magical about +things like that. + +Next thing we're going to do is +we're going to say, how do + +we do T gets R? + +Oh, that's easy enough, +assign. + +We assign to T the remainder. + +Assign is the name +of the button. + +That's the button-pusher. + +Assign to T the remainder, and +here's the representation of + +the operation, when we divide +the fetch of A by the fetch of + +B. + +And we're also going to assign +to A the fetch of B, assign to + +B the result of getting the +contents of T. And now I have + +to refer to the beginning +here. + +I see, why don't I call that +loop like I have here? + +So that's that reference +to that arrow. + +And when we're done, +we're done. + +We go to here, which is +the end of the thing. + +So here's just a written +representation of this + +fragment of machinery that +we've drawn here. + +Now the next thing I'd like +to do is run this. + +I want us to feel it running. + +Never done this before, +you got to do it once. + +So let's take a particular +problem. + +Suppose we want to compute +the GCD of a equals 30 + +and b equals 42. + +I have no idea what +that is right now. + +But a 30 and b is 42. + +So that's how I start +this thing up. + +Well, what's the first +thing I do? + +I say is B equal to 0, no. + +Then assign to T the remainder +of the fetch of A and the + +fetch of B. Well the remainder +of 30 when divided by + +42 is itself 30. + +Push that button. + +Now the marble has +rolled to here. + +A gets B. That pushes +this button. + +So 42 moves into here. + +B gets C. Push that button. + +The 30 goes here. + +Let met just interchange them. + +Now let's see, go back +to the beginning. + +B 0, no. + +T gets the remainder. + +I suppose the remainder when +dividing 42 by 30 is 12. + +I push that one. + +Next thing I do is allow the +30 to go to here, push this + +one, allow the 12 +to go to here. + +Go around this thing. + +Is that done? + +No. + +How about-- + +so now I have to find out the +remainder of 30 divided by 12. + +And I believe that's 6. + +So 6 goes here on this +button push. + +Then the next thing I push +is this one, which the + +12 goes into here. + +Then I push this button. + +The 6 gets into here. + +Is 6 equal to 0? + +No. + +OK. + +So then at that point, the next +thing to do is divide it. + +Ooh, this has got a +remainder of 0. + +Looks like we're almost done. + +Move the 6 over here next. + +0 over here. + +Is the answer 0? + +Yes. + +B is 0, therefore the +answer is in A. + +The answer is 6. + +And indeed that's right, because +if we look at the + +original problem, what we have +is 30 is 2 times 3 times 5, + +and 42 is 2 times 3 times 7. + +So the greatest common divisor +is 2 times 3, which is 6. + +Now normally, we write one other +little line here, just + +to make it a little bit clearer, +which is that we + +leave in a connection saying +that this light is the guy + +that that flap looks at. + +Of course, any real machine +has a lot more complicated + +things in it than what +I've just shown you. + +Let's look for a second at +the first still store. + +Wow. + +Well you see, for example, one +thing we might want to do is + +worry about the operations +that are of IO form. + +And we may have to collect +something from the outside. + +So a state machine that we might +have, the controller may + +have to, for example, get a +value from something and put + +register a to load it up. + +I have to master load up +register b with another value. + +And then later, when I'm done, +I might want to print the + +answer out. + +And of course, that might be +either simple or complicated. + +I'm writing, assuming print +is very simple, and + +read is very simple. + +But in fact, in the real +world, those are very + +complicated operations, usually +much, much larger and + +more complicated than the thing +you're doing as your + +problem you're trying +to solve. + +On the other hand, I can +remember a time when, I + +remember using IBM 7090 computer +of sorts, where + +things like read and write of +a single object, a single + +number, a number, is a primitive +operation of the IO + +controller. + +OK? + +And so we have that kind +of thing in there. + +And in such a machine, well, +what are we really doing? + +We're just saying that there's +a source over here called + +"read," which is an operation +which always has a value. + +We have to think about this as +always having a value which + +can be gated into either +register a or b. + +And print is some sort of thing +which when you gate it + +appropriately, when you push the +button on it, will cause a + +print of the value that's +currently in register a. + +Nothing very exciting. + +So that's one sort of thing you +might want to have. But + +these are also other +things that are + +a little bit worrisome. + +Like I've used here some +complicated mechanisms. + +What you see here +is remainder. + +What is that? + +That may not be so obvious +how to compute. + +It may be something which when +you open it up, you get a + +whole machine. + +OK? + +In fact, that's true. + +For example, if I write down the +program for remainder, the + +simplest program for it is +by repeated subtraction. + +Because of course, division +can be done by repeated + +subtraction of numbers, +of integers. + +So the remainder of N divided by +D is nothing more than if N + +is less than D, then the result +is N. Otherwise, it's + +the remainder when we subtract +D from N with respect to D, + +when divided by D. Gee, +this looks just + +like the GCD program. + +Of course, it's not a very nice +way to do remainders. + +You'd really want to use +something like binary notation + +and shift and things like that +in a practical computer. + +But the point of that is that +if I open this thing up, I + +might find inside of +it a computer. + +Oh, we know how to do that. + +We just made one. + +And it could be another +thing just like this. + +On the other hand, we might want +to make a more efficient + +or better-structured machine, +or maybe make use of some of + +the registers more than once, +or some horrible mess like + +that that hardware designers +like to do, and + +for very good reasons. + +So for example, here's a machine +that you see, which + +you're not supposed to +be able to read. + +It's a little bit complicated. + +But what it is is the +integration of the remainder + +into the GCD machine. + +And it takes, in fact, +no more registers. + +There are three registers +in the datapaths. + +OK? + +But now there's a subtractor. + +There are two things +that are tested. + +Is b equal to 0, or +is t less than b? + +And then the controller, which +you see over here, is not much + +more complicated. + +But it has two loops in it, one +of which is the main one + +for doing the GCD, and one of +which is the subtraction loop + +for doing the remainder +sub-operation. + +And there are ways, of course, +of, if you think about it, + +taking the remainder program. + +If I take remainder, as you see +over there, as a lambda + +expression, substitute it in for +remainder over here in the + +GCD program, then do some +simplification by substituting + +a and b for remainder +in there, then I + +can unwind this loop. + +And I can get this piece of +machinery by basically, a + +little bit of algebraic +simplification on the lambda + +expressions. + +So I suppose you've seen +your first very + +simple machines now. + +Are there any questions? + +Good. + +This looks easy, doesn't it? + +Thank you. + +I suppose, take a break. + +[MUSIC PLAYING - "JESU, JOY OF +MAN'S DESIRING" BY JOHANN + +SEBASTIAN BACH] + +PROFESSOR: Well, let's see. + +Now you know how to make an +iterative procedure, or a + +procedure that yields +an iterative + +process, turn into a machine. + +I suppose the next thing we +want to do is worry about + +things that reveal recursive +processes. + +So let's play with a simple +factorial procedure. + +We define factorial of N to be +if n is 1, the result is 1, + +using 1 right now to decrease +the amount of work I have to + +do to simulate it, else it's +times N factorial N minus 1. + +And what's different with this +program, as you know, is that + +after I've computed factorial +of N minus 1 here, I have to + +do something to the result. + +I have to multiply it by N. + +So the only way I can visualize +what this machine is + +doing, because of the fact-- + +think of it this way, that I +have a machine out here which + +somehow needs a factorial +machine in order to compute + +its answer. + +But this machine, the outer +machine, has to exist before + +and after the factorial machine, +which is inside. + +Whereas in the iterative case, +the outer machine doesn't need + +to exist after the inner machine +is running, because + +you never need to go +back to the outer + +machine to do anything. + +So here we have a problem where +we have a machine which + +has the same machine +inside of it, an + +infinitely large machine. + +And it's got other things +inside of it, like a + +multiplier, which takes some +inputs, and there's a minus 1 + +box, and things like that. + +You can imagine that's +what it looks like. + +But the important thing is that +here I have something + +that happens before and after, +in the outer machine, the + +execution of the +inner machine. + +So this machine has +to have a life. + +It has to exist on both times +sides of this machine. + +So somehow, I have to have a +place to store the things that + +this thing needs to run. + +Infinite objects don't exist +in the real world. + +What we have to do is arrange +an illusion that we have an + +infinite object, we +have an infinite + +amount of hardware somewhere. + +Now of course, illusion's +all that really matters. + +If we can arrange that every +time you look at some infinite + +object, the part of it that +you look at is there, then + +it's as infinite as +you need it to be. + +And of course, one of the things +we might want to do, + +just look at this thing over +here, is the organization that + +we've had so far involves having +a part of the machine, + +which is the controller, which +sits right over here, which is + +perfectly finite and +very simple. + +We have some datapaths, +which consist of + +registers and operators. + +And what I propose to do here is +decompose the machine into + +two parts, such that there is a +part which is fundamentally + +finite, and some part where a +certain amount of infinite + +stuff can be kept. + +On the other hand this is very +simple and really isn't + +infinite, but it's +just very large. + +But it's so simple that it could +be cheaply reproduced in + +such large amounts, we call it +memory, that we can make a + +structure called a stack out of +it which will allow us to, + +in fact, simulate the existence +of an infinite + +machine which is made +out of a recursive + +nest of many machines. + +And the way it's going to work +is that we're going to store + +in this place called the stack +the information required after + +the inner machine runs to resume +the operation of the + +outer machine. + +So it will remember the +important things about the + +life of the outer machine that +will be needed for this + +computation. + +Since, of course, these machines +are nested in a + +recursive manner, then in fact +the stack will only be + +accessed in a manner which is +the last thing that goes in is + +the first thing that +comes out. + +So we'll only need to access +some little part + +of this stack memory. + +OK, well, let's do it. + +I'm going to build you a +datapath now, and I'm going to + +write the controller. + +And then we're going +to execute this to + +see how you do it. + +So the factorial machine +isn't so bad. + +It's going to have a register +called the value, where the + +answer is going to be stored, +and a registered called N, + +which is where the number I'm +taking factorial will be + +stored, factorial of. + +And it will be necessary in some +instances to connect VAL + +to N. + +In fact, one nice case of this +is if I just said over here, + +N, because that would be +right for N equal 1N. + +And I could just move +the answer over + +there if that's important. + +I'm not worried about +that right now. + +And there are things I have +to be able to do. + +Like I have to be able to, as +we see here, multiply N by + +something in VAL, because +VAL is the result + +of computing factorial. + +And I have to put the result +back into VAL. + +So here we can see that the +result of computing a + +factorial is N times the result + +of computing a factorial. + +VAL will be the representation +of the answer + +of the inner factorial. + +And so I'm going to have to have +a multiplier here, which + +is going to sample the value of +N and the value of VAL and + +put the result back into +VAL like that. + +I'm also going to have to be +able to see if N is 1. + +So I need a light bulb. + +And I suppose the other thing +I'm going to need to have is a + +way of decrementing N. So I'm +going to have a decrementer, + +which takes N and is going to +put back the result into N. + +That's pretty much what +I need in my machine. + +Now, there's a little +bit else I need. + +It's a little bit more +complicated, because I'm also + +going to need a way to store, to +save away, the things that + +are going to be needed for +resuming the computation of a + +factorial after I've done +a sub-factorial. + +What's that? + +One thing I need is N. + +So I'm going to build here +a thing called a stack. + +The stack is a bunch of stuff +that I'm going to write in + +sequentially. + +I don't how long it is. + +The longer it is, the better +my illusion of infinity. + +And I'm going to have to have a +way of getting stuff out of + +N and into the stack +and vice versa. + +So I'm going to need a +connection like this, which is + +two-way, whereby I can save +the value of N and then + +restore it some other time +through that connection. + +This is the stack. + +I also need a way of remembering +where I was in the + +computation of factorial +in the outer program. + +Now in the case of +this machine, it + +isn't very much a problem. + +Factorial always returns, has to +go back to the place where + +we multiply by N, except for the +last time, when it has to + +return to whatever needs +the factorial or + +go to done or stop. + +However, in general, I'm going +to have to remember where I + +have been, because I might have +computed factorial from + +somewhere else. + +I have to go back to that place +and continue there. + +So I'm going to have to have +some way of taking the place + +where the marble is in the +finite state controller, the + +state of the controller, +and storing that in + +the stack as well. + +And I'm going to have to have +ways of restoring that back to + +the state of the-- the marble. + +So I have to have something that +moves the marble to the + +right place. + +Well, we're going to have a +place which is the marble now. + +And it's called the continue +register, called continue, + +which is the place to +put the marble next + +time I go to continue. + +That's what that's for. + +And so there's got to be some +path from that into the + +controller. + +I also have to have some way of +saving that on the stack. + +And I have to have some way +of setting that up to have + +various constants, a certain +fixed number of constants. + +And that's very easy +to arrange. + +So let's have some +constants here. + +We'll call this one +after-fact. + +And that's a constant which +we'll get into the continue + +register, and also another +one called fact-done. + +So this is the machine +I want to build. + +That's its datapaths, at least. +And it mixes a little + +with the controller here, +because of the fact that I + +have to remember where +I was and restore + +myself to that place. + +But let's write the program +now which represents the + +controller. + +I'm not going to write the +define machine thing and the + +register list, because that's +not very interesting. + +I'm just going to write down the +sequence of instructions + +that constitute the +controller. + +So we have assign, to set +up, continue to done. + +We have a loop which says branch +if equal 1 fetch N, if + +N is 1, then go to the base +step of the induction, the + +simple case. + +Otherwise, I have to remember +the things that are necessary + +to perform a sub-factorial. + +I'm going to go over here, +and I have to perform a + +sub-factorial. + +So I have to remember what's +needed after I will + +be done with that. + +See, I'm about to do +something terrible. + +I'm about to change the value of +N. But this guy has to know + +the old value of N. But +in order to make the + +sub-factorial work, I have to +change the value of N. So I + +have to remember +the old value. + +And I also have to remember +where I've been. + +So I save up continue. + +And this is an instruction +that says, put + +something in the stack. + +Save the contents of the +continuation register, which + +in this case is done, because +later I'm going to change + +that, too, because I +need to go back to + +after-fact, as well. + +We'll see that. + +We save N, because I'm going +to need that for later. + +Assign to N the decrement of +fetch N. Assign continue, + +we're going to look at this now, +to after, we'll call it. + +That's a good name for this, a +little bit easier and shorter, + +and fits in here. + +Now look what I'm doing here. + +I'm saying, if the answer +is 1, I'm done. + +I'm going to have to just +get the answer. + +Otherwise, I'm going to save the +continuation, save N, make + +N one less than N, remember +I'm going to come back to + +someplace else, and +go back and start + +doing another factorial. + +However, I've got a different +machine [? in me ?] now. + +N is 1, and continue +is something else. + +N is N minus 1. + +Now after I'm done with +that, I can go there. + +I will restore the old value of +N, which is the opposite of + +this save over here. + +I will restore the +continuation. + +I will then go to here. + +I will assign to the VAL +register the product + +of N and fetch VAL. + +VAL fetch product assign. + +And then I will be done. + +I will have my answer to the +sub-factorial in VAL. + +At that point, I'm going to +return by going to the place + +where the continuation +is pointing. + +That says, go to +fetch continue. + +And then I have finally +a base step, which is + +the immediate answer. + +Assign to VAL fetch N, and +go to fetch continue. + +And then I'm done. + +Now let's see how this executes +on a very simple + +case, because then we'll see +the use of this stack to do + +the job we need. + +This is statically what it's +doing, but we have look + +dynamically at this. + +So let's see. + +First thing we do is +continue gets done. + +The way that happened +is I pushed this. + +Let's call that done +the way I have it. + +I push that button. + +Done goes into there. + +Now I also have to set +this thing up to + +have an initial value. + +Let's consider a factorial +of three, a simple case. + +And we're going to start +out with our stack + +growing over here. + +Stacks have their own little +internal state saying where + +they are, where the next place +I'm going to write is. + +So now we say, is N 1? + +The answer is no. + +So now I'm going to save +continue, bang. + +Now that done goes in here. + +And this moves to here, the next +place I'm going to write. + +Save N 3. + +OK? + +Assign to N the decrement +of N. That means + +I've pushed this button. + +This becomes 2. + +Assign to continue aft. + +So I've pushed that button. + +Aft goes in here. + +OK, now go to loop, bang, +so up to here. + +Is N 1? + +No. + +So I have to save continue. + +What's continue? + +Continue is aft. + +Push this button. + +So this moves to here. + +I have to save N. +N is over here. + +I got to 2. + +Push that button. + +So a 2 gets written there. + +And then this thing +moves down here. + +OK, save N. Assign N to +the decrement of N. + +This becomes a 1. + +Assign continue to aft. + +A-F-T gets written +there again. + +Go to loop. + +Is N equal to 1? + +Oh, yes, the answer is 1. + +OK, go to base step. + +Assign to VAL fetch of N. Bang, +1 gets put in there. + +Go to fetch continue. + +So we look in continue. + +Basically, I'm pushing a button +over here that goes to + +the controller. + +The continue becomes aft, and +all of a sudden, the program's + +running here. + +I now have to restore the outer +version of factorial. + +So we go here. + +We say, restore N. So restore +N means take the contents + +that's here. + +Push this button, and it goes +into here, 2, and the + +pointer moves up. + +Restore continue, pretty easy. + +Go push this button. + +And then aft gets written +in here again. + +That means this thing +moves up. + +I've gotten rid of something +else on my stack. + +Right, then I go to here, which +says, assign to VAL the + +product of N an VAL. + +So I push this button +over here, bang. + +2 times 1 gives me a 2, +get written there. + +Go to fetch continue. + +Continue is aft. + +I go to aft. + +Aft says restore N. Do your +restore N, means I take the + +value over here, which is 3, +push this up to here, and move + +it into here, N. Now it's +pushing that button. + +The next thing I do is +restore continue. + +Continue is now going +to become done. + +So this moves up here when +I push this button. + +Done may or may be there +anymore, I'm not interested, + +but it certainly is here. + +Next thing I do is assign to VAL +the product of the fetch + +of N and the fetch of VAL. + +That's pushing this button +over here, bang. + +2 times 3 is 6. + +So I get a 6 over here. + +And go to fetch continue, +whoops, I go to + +done, and I'm done. + +And my answer is 6, as you can +see in the VAL register. + +And in fact, the stack +is in the state it + +originally was in. + +Now there's a bit of discipline +in using these + +things like stacks that we +have to be careful of. + +And we'll see that in +the next segment. + +But first I want to ask +if there are any + +questions for this. + +Are there any questions? + +Yes, Ron. + +AUDIENCE: What happens when you +roll off the end of the + +stack with-- + +PROFESSOR: What do you +mean, roll off of? + +AUDIENCE: Well, the +largest number-- + +a larger starting point of N +requires more memory, correct? + +PROFESSOR: Oh, yes. + +Well, I need to have a +long enough stack. + +You say, what if I violate +my illusion? + +AUDIENCE: Yes. + +PROFESSOR: Well, then the +magic doesn't work. + +The truth of the matter is that +every machine is finite. + +And for a procedure like this, +there's a limit to the number + +of sub-factorials +I could have. + +Remember when we were doing the +y-operator a while ago, we + +pointed out that there was a +sequence of exponentiation + +procedures, each of which was +a little better than the + +previous one. + +Well, we're now seeing +how we implement that + +mathematical idea. + +The limiting process is only +so good as as far as + +you take the limit. + +If you think about it, +what am I using here? + +I'm using about two pieces of +memory for every recursion of + +this process. + +If we try to compute factorial +of 10,000, that's + +not a lot of memory. + +On the other hand, it's +an awful big number. + +So the question is, is that a +valuable thing in this case. + +But it really turns out not to +be a terrible limit, because + +memory is el cheapo, and people +are pretty expensive. + +OK, thank you, let's +take a break. + +[MUSIC PLAYING - "JESU, JOY OF +MAN'S DESIRING" BY JOHANN + +SEBASTIAN BACH] + +PROFESSOR: Well, let's see. + +What I've shown you now is how +to do a simple iterative + +process and a simple +recursive process. + +I just want to summarize the +design of simple machines for + +specific applications by showing +you a little bit more + +complicated design, that of +a thing that does doubly + +recursive Fibonacci, because +it will indicate to us, and + +we'll understand, a bit about +the conventions required for + +making stacks operate +correctly. + +So let's see. + +I'm just going to write down, +first of all, the program I'm + +going to translate. + +I need a Fibonacci procedure, +it's very simple, which says, + +if N is less than 2, the result +is N, otherwise it's + +the sum of Fib of N minus +1 and Fib of N minus 2. + +That's the plan I have here. + +And we're just going +to write down the + +controller for such a machine. + +We're going to assume that there +are registers, N, which + +holds the number we're taking +Fibonacci of, VAL, which is + +where the answer is going to get +put, and continue, which + +is the thing that's linked to +the controller, like before. + +But I'm not going to draw +another physical datapath, + +because it's pretty much +the same as the + +last one you've seen. + +And of course, one of the most +amazing things about + +computation is that after a +while, you build up a little + +more features and a few more +features, and all of the + +sudden, you've got everything +you need. + +So it's remarkable that it just +gets there so fast. I + +don't need much more to make +a universal computer. + +But in any case, let's look +at the controller for the + +Fibonacci thing. + +First thing I want to do is +start the thing up by assign + +to continue a place called done, +called Fib-done here. + +So that means that somewhere +over here, I'm going to have a + +label, Fib-done, which is the +place where I go when I want + +the machine to stop. + +That's what that is. + +And I'm going to +make up a loop. + +It's a place I'm going to go +to in order to start up + +computing a Fib. + +Whatever is in N at this point, +Fibonacci will be + +computed of, and we will return +to the place specified + +by continue. + +So what you're going to see +here at this place, what I + +want here is the contract that +says, I'm going to write this + +with a comment syntax, the +contract is N contains arg, + +the argument. + +Continue is the recipient. + +And that's where it is. + +At this point, if I ever go to +this place, I'm expecting this + +to be true, the argument for +computing the Fibonacci. + +Now the next thing I want +to do is to branch. + +And if N is less than 2-- + +by the way, I'm using what +looks like Lisp syntax. + +This is not Lisp. + +This does not run. + +What I'm writing here does not +run as a simple Lisp program. + +This is a representation +of another language. + +The reason I'm using the syntax +of parentheses and so + +on is because I tend to use +a Lisp system to write an + +interpreter for this which +allows me to simulate the + +machine I'm trying to build. + +I don't want to confuse +this to think that + +this is Lisp code. + +It's just I'm using a lot +of the pieces of Lisp. + +I'm embedding a language in +Lisp, using Lisp as pieces to + +make my process of making +my simulator easy. + +So I'm inheriting from Lisp +all of its properties. + +Fetch of N 2, I want +to go to a place + +called immediate answer. + +It's the base step. + +Now, that's somewhere over +here, just above done. + +And we'll see it later. + +Now, in the general case, which +is the part I'm going to + +write down now, let's +just do it. + +Well, first of all, I'm +going to have to + +call Fibonacci twice. + +In each case-- + +well, in one case at least, I'm +going to have to know what + +to do to come back and +do the next one. + +I have to remember, have I done +the first Fib, or have I + +done the second one? + +Do I have to come back to the +place where I do the second + +Fib, or do I have to come +back to the place + +where I do the add? + +In the first case, over the +first Fibonacci, I'm going to + +need the value of N for +computing for the second one. + +So I have to store some +of these things up. + +So first I'm going +to save continue. + +That's who needs the answer. + +And the reason I'm doing that is +because I'm about to assign + +continue to the place +which is the place I + +want to go to after. + +Let's call it Fib-N-minus-1, +big long name, + +classic Lisp name. + +Because I'm going to compute +the first Fib of N minus 1, + +and then after that, I +want to come back and + +do something else. + +That's the place I want to go +to after I've done the first + +Fibonacci calculation. + +And I want to do a save of N, +because I'm going to need it + +later, after that. + +Now I'm going to, at this point, +get ready to do the + +Fibonacci of N minus 1. + +So assign to N the difference +of the fetch of N and 1. + +Now I'm ready to go back +to doing the Fib loop. + +Have I satisfied my contract? + +And the answer is yes. + +N contains N minus 1, which +is what I need. + +Continue contains a place I want +to go to when I'm done + +with calculating N minus 1. + +So I've satisfied +the contract. + +And therefore, I can write +down here a label, + +after-Fib-N-minus-1. + +Now what am I going +to do here? + +Here's a place where I now +have to get ready to do + +Fib of N minus 2. + +But in order to do a Fib of N +minus 2, look, I don't know. + +I've clobbered my N over here. + +And presumably my N is counted +down all the way to 1 or 0 or + +something at this point. + +So I don't know what the value +of N in the N register is. + +I want the value of N that was +on the stack that I saved over + +here so that could restore +it over here. + +I saved up the value of N, which +is this value of N at + +this point, so that I could +restore it after computing Fib + +of N minus 1, so that I could +count that down to N minus 2 + +and then compute Fib +of N minus 2. + +So let's restore that. + +Restore of N. + +Now I'm about to do something +which is superstitious, and we + +will remove it shortly. + +I am about to finish the +sequence of doing the + +subroutine call, if you will. + +I'm going to say, well, I also +saved up the continuation, + +since I'm going to +restore it now. + +But actually, I don't have +to, because I'm not + +going to need it. + +We'll fix that in a second. + +So we'll do a restore of +continue, which is what I + +would in general need to do. + +And we're just going to see +what you would call in the + +compiler world a peephole +optimization, which says, + +whoops, you didn't +have to do that. + +OK, so the next thing I see +here is that I have to get + +ready now to do Fibonacci +of N minus 2. + +But I don't have to +save N anymore. + +The reason why I don't have to +save N anymore is because I + +don't need N after I've done Fib +of N minus 2, because the + +next thing I do is add. + +So I'm just going to set +up my N that way. + +Assign N minus difference +of fetch N and 2. + +Now I have to finish the +setup for calling + +Fibonacci of N minus 2. + +Well, I have to save up continue +and assign continue, + +continue, to the place which is +after Fib N 2, that place + +over here somewhere. + +However, I've got to +be very careful. + +The old value, the value of Fib +of N minus 1, I'm going to + +need later. + +The value of Fibonacci of N +minus 1, I'm going to need. + +And I can't clobber it, because +I'm going to have to + +add it to the value of +Fib of N minus 2. + +That's in the value register, +so I'm going to save it. + +So I have to save this right +now, save up VAL. + +And now I can go off to my +subroutine, go to Fib loop. + +Now before I go any further +and finish this program, I + +just want to look at this +segment so far and see, oh + +yes, there's a sequence of +instructions here, if you + +will, that I can do +something about. + +Here I have a restore of +continue, a save of continue, + +and then an assign of continue, +with no other + +references to continue +in between. + +The restore followed +by the save + +leaves the stack unchanged. + +The only difference is that I +set the continue register to a + +value, which is the value +that was on the stack. + +Since I now clobber that value, +as in it was never + +referenced, these instructions +are unnecessary. + +So we will remove these. + +But I couldn't have seen +that unless I had + +written them down. + +Was that really true? + +Well, I don't know. + +OK, so we've now gone +off to compute + +Fibonacci of N minus 2. + +So after that, what are +we going to do? + +Well, I suppose the first +thing we have to do-- + +we've got two things. + +We've got a thing in +the value register + +which is now valuable. + +We also have a thing on the +stack that can be restored + +into the value register. + +And what I have to be careful +with now is I want to shuffle + +this right so I can +do the multiply. + +Now there are various +conventions I might use, but + +I'm going to be very picky and +say, I'm only going to restore + +into a register I've +saved from. + +If that's the case, I have +to do a shuffle here. + +It's the same problem with how +many hands I have. So I'm + +going to assign to N, because +I'm not going to need N + +anymore, N is useless, the +current value of VAL, which + +was the value of Fib +of N minus 2. + +And I'm going to restore +the value register now. + +This restore matches this +save. And if you're very + +careful and examine very +carefully what goes on, + +restores and saves are +always matched. + +Now there's an outstanding save, +of course, that we have + +to get rid of soon. + +And so I restored the +value register. + +Now I restore the continue one, +which matches this one, + +dot, dot, dot, dot, dot, dot, +dot, down to here, restoring + +that continuation. + +That continuation is a +continuation of Fib of N, + +which is the problem I was +trying to solve, a major + +problem I'm trying to solve. + +So that's the guy I have to go +back to who wants Fib of N. I + +saved them all the way up here +when I realized N was + +not less than 2. + +And so I had to do a complicated +operation. + +Now I've got everything +I need to do it. + +So I'm going to restore that, +assign to VAL the sum of fetch + +VAL and fetch of N, and +go to continue. + +So now I've returned from +computing Fibonacci of N, the + +general case. + +Now what's left is we have to +fix up a few details, like + +there's the base case of this +induction, immediate answer, + +which is nothing more than +assign to VAL fetch of N, + +because N was less than 2, and +therefore, the answer is N in + +our original program, and +return continue-- + +bobble, bobble almost-- + +and finally Fib done. + +So that's a fairly complicated +program. + +And the reason I wanted you see +to that is because I want + +you to see the particular +flavors of stack discipline + +that I was obeying. + +It was first of all, I don't +want to take anything that I'm + +not going to need later. + +I was being very careful. + +And it's very important. + +And there are all sorts of other +disciplines people make + +with frames and things like that +of some sort, where you + +save all sorts of junk you're +not going to need later and + +restore it because, in some +sense, it's easier to do that. + +That's going to lead to various +disasters, which we'll + +see a little later. + +It's crucial to say exactly +what you're + +going to need later. + +It's an important idea. + +And the responsibility of that +is whoever saves something is + +the guy who restores it, +because he needs it. + +And in such discipline, you +can see what things are + +unnecessary, operations +that are unimportant. + +Now, one other thing I want to +tell you about that's very + +simple is that, of course, the +picture you see is not the + +whole picture. + +Supposing I had systems that +had things like other + +operations, CAR, CDR, cons, +building a vector and + +referencing the nth element of +it, or things like that. + +Well, at this level of detail, +whatever it is, we can + +conceptualize those +as primitive + +operations in the datapath. + +In other words, we could say +that some machine that, for + +example, has the append machine, +which has to do cons + +of the CAR of x with the append +of the CDR of x and y, + +well, gee, that's exactly +the same as + +the factorial structure. + +Well, it's got about +the same structure. + +And what do we have? + +We have some sort of things in +it which may be registers, x + +and y, and then x has to somehow +move to y sometimes, x + +has to get the value of y. + +And then we may have +to be able to do + +something which is a cons. + +I don't remember if I need to +like this is in this system, + +but cons is sort of like +subtract or add or something. + +It combines two things, +producing a thing which is the + +cons, which we may then +think goes into there. + +And then maybe a thing called +the CAR, which will produce-- + +I can get the CAR +or something. + +And maybe I can get the CDR +of something, and so on. + +But we shouldn't be too afraid +of saying things this way, + +because the worst that could +happen is if we open up cons, + +what we're going to find +is some machine. + +And cons may in fact overlap +with CAR and CDR, and it + +always does, in the same way +that plus and minus overlap, + +and really the same business. + +Cons, CAR, and CDR are going to +overlap, and we're going to + +find a little controller, a +little datapath, which may + +have some registers in it, +some stuff like that. + +And maybe inside it, there may +also be an infinite part, a + +part that's semi-infinite or +something, which is a lot of + +very uniform stuff, which +we'll call memory. + +And I wouldn't be so horrified +if that were the way it works. + +In fact, it does, and we'll +talk about that later. + +So are there any questions? + +Gee, what an unquestioning +audience. + +Suppose I tell you a horrible +pile of lies. + +OK. + +Well, thank you. + +Let's take our break. + +[MUSIC PLAYING - "JESU, JOY OF +MAN'S DESIRING" BY JOHANN + +SEBASTIAN BACH] \ No newline at end of file diff --git a/k0vA0aTcUZA.txt b/k0vA0aTcUZA.txt new file mode 100644 index 0000000000000000000000000000000000000000..41259a89101696c1f13d327e0bba439b535a19c6 --- /dev/null +++ b/k0vA0aTcUZA.txt @@ -0,0 +1,13467 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT opencourseware continue to + + align:start position:0% +will help MIT opencourseware continue to + + + align:start position:0% +will help MIT opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all right well it's time to start + + align:start position:0% +all right well it's time to start + + + align:start position:0% +all right well it's time to start +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so last time we were talking about e + + align:start position:0% +so last time we were talking about e + + + align:start position:0% +so last time we were talking about e +plus e minus to Jets + + align:start position:0% + + + + align:start position:0% + +particular e plus e minus the digest and + + align:start position:0% +particular e plus e minus the digest and + + + align:start position:0% +particular e plus e minus the digest and +we were talking about we talked about + + align:start position:0% +we were talking about we talked about + + + align:start position:0% +we were talking about we talked about +factorization and how to derive it + + align:start position:0% +factorization and how to derive it + + + align:start position:0% +factorization and how to derive it +and I've schematically written the + + align:start position:0% +and I've schematically written the + + + align:start position:0% +and I've schematically written the +result here last time we had a more + + align:start position:0% +result here last time we had a more + + + align:start position:0% +result here last time we had a more +definite formula with all the arguments + + align:start position:0% +definite formula with all the arguments + + + align:start position:0% +definite formula with all the arguments +made explicit so there were hard + + align:start position:0% +made explicit so there were hard + + + align:start position:0% +made explicit so there were hard +functions + + align:start position:0% +functions + + + align:start position:0% +functions +jet functions and the soft function + + align:start position:0% +jet functions and the soft function + + + align:start position:0% +jet functions and the soft function +and we could either think about + + align:start position:0% +and we could either think about + + + align:start position:0% +and we could either think about +measuring invariant masses into + + align:start position:0% +measuring invariant masses into + + + align:start position:0% +measuring invariant masses into +hemispheres and constraining them to be + + align:start position:0% +hemispheres and constraining them to be + + + align:start position:0% +hemispheres and constraining them to be +small to know we have die Jets or + + align:start position:0% +small to know we have die Jets or + + + align:start position:0% +small to know we have die Jets or +measuring kind of the sum of the two + + align:start position:0% +measuring kind of the sum of the two + + + align:start position:0% +measuring kind of the sum of the two +which we called which is effectively the + + align:start position:0% +which we called which is effectively the + + + align:start position:0% +which we called which is effectively the +thrust and then we get a slightly + + align:start position:0% +thrust and then we get a slightly + + + align:start position:0% +thrust and then we get a slightly +simpler formula because we can project + + align:start position:0% +simpler formula because we can project + + + align:start position:0% +simpler formula because we can project +these guys down onto guys that only have + + align:start position:0% +these guys down onto guys that only have + + + align:start position:0% +these guys down onto guys that only have +are functions of one variable but either + + align:start position:0% +are functions of one variable but either + + + align:start position:0% +are functions of one variable but either +way in either case we have a + + align:start position:0% +way in either case we have a + + + align:start position:0% +way in either case we have a +factorization theorem that separates the + + align:start position:0% +factorization theorem that separates the + + + align:start position:0% +factorization theorem that separates the +degrees of freedom and kind of the + + align:start position:0% +degrees of freedom and kind of the + + + align:start position:0% +degrees of freedom and kind of the +pictures that we have + + align:start position:0% + + + + align:start position:0% + +these kind of scales in the problem + + align:start position:0% +these kind of scales in the problem + + + align:start position:0% +these kind of scales in the problem +so this is from your chat you hired + + align:start position:0% +so this is from your chat you hired + + + align:start position:0% +so this is from your chat you hired +and be soft + + align:start position:0% + + + + align:start position:0% + +and we can use this factorization + + align:start position:0% +and we can use this factorization + + + align:start position:0% +and we can use this factorization +theorem to separate those scales into + + align:start position:0% +theorem to separate those scales into + + + align:start position:0% +theorem to separate those scales into +these functions and then we can use I + + align:start position:0% +these functions and then we can use I + + + align:start position:0% +these functions and then we can use I +started talking about using + + align:start position:0% +started talking about using + + + align:start position:0% +started talking about using +renormalization group equations in order + + align:start position:0% +renormalization group equations in order + + + align:start position:0% +renormalization group equations in order +to sum the logs between these scales + + align:start position:0% + + + + align:start position:0% + +and I want to just finish up that + + align:start position:0% +and I want to just finish up that + + + align:start position:0% +and I want to just finish up that +discussion + + align:start position:0% +discussion + + + align:start position:0% +discussion +so for the Wilson coefficient of the + + align:start position:0% +so for the Wilson coefficient of the + + + align:start position:0% +so for the Wilson coefficient of the +operator or for the for that matter for + + align:start position:0% +operator or for the for that matter for + + + align:start position:0% +operator or for the for that matter for +the hard function which is the square of + + align:start position:0% +the hard function which is the square of + + + align:start position:0% +the hard function which is the square of +the Wilson coefficient you have a very + + align:start position:0% +the Wilson coefficient you have a very + + + align:start position:0% +the Wilson coefficient you have a very +simple renormalization group equation + + align:start position:0% +simple renormalization group equation + + + align:start position:0% +simple renormalization group equation +and that's because momentum conservation + + align:start position:0% +and that's because momentum conservation + + + align:start position:0% +and that's because momentum conservation +is enough to fix all the + + align:start position:0% +is enough to fix all the + + + align:start position:0% +is enough to fix all the +all the variables that label collinear + + align:start position:0% +all the variables that label collinear + + + align:start position:0% +all the variables that label collinear +Fields so you just really just have this + + align:start position:0% +Fields so you just really just have this + + + align:start position:0% +Fields so you just really just have this +overall Q which is the center of mass + + align:start position:0% +overall Q which is the center of mass + + + align:start position:0% +overall Q which is the center of mass +energy and that's the only variable but + + align:start position:0% +energy and that's the only variable but + + + align:start position:0% +energy and that's the only variable but +it's fixed by kinematics so there's no + + align:start position:0% +it's fixed by kinematics so there's no + + + align:start position:0% +it's fixed by kinematics so there's no +convolutions + + align:start position:0% +convolutions + + + align:start position:0% +convolutions +in the case of these things called jet + + align:start position:0% +in the case of these things called jet + + + align:start position:0% +in the case of these things called jet +functions which we talked a little bit + + align:start position:0% +functions which we talked a little bit + + + align:start position:0% +functions which we talked a little bit +about last time you end up with a + + align:start position:0% +about last time you end up with a + + + align:start position:0% +about last time you end up with a +something like the altire Parisi where + + align:start position:0% +something like the altire Parisi where + + + align:start position:0% +something like the altire Parisi where +there's an integral + + align:start position:0% +there's an integral + + + align:start position:0% +there's an integral +it's a little bit different in the sense + + align:start position:0% +it's a little bit different in the sense + + + align:start position:0% +it's a little bit different in the sense +that we actually know it's structure to + + align:start position:0% +that we actually know it's structure to + + + align:start position:0% +that we actually know it's structure to +all orders and perturbation Theory it + + align:start position:0% +all orders and perturbation Theory it + + + align:start position:0% +all orders and perturbation Theory it +has this structure so it only has a very + + align:start position:0% +has this structure so it only has a very + + + align:start position:0% +has this structure so it only has a very +particular dependence on S has to scale + + align:start position:0% +particular dependence on S has to scale + + + align:start position:0% +particular dependence on S has to scale +like one over s so one thing that scales + + align:start position:0% +like one over s so one thing that scales + + + align:start position:0% +like one over s so one thing that scales +like one over s is a Delta function + + align:start position:0% +like one over s is a Delta function + + + align:start position:0% +like one over s is a Delta function +or a plus function and basically there's + + align:start position:0% +or a plus function and basically there's + + + align:start position:0% +or a plus function and basically there's +only this single type of plus function + + align:start position:0% +only this single type of plus function + + + align:start position:0% +only this single type of plus function +that can show up and that's the analog + + align:start position:0% +that can show up and that's the analog + + + align:start position:0% +that can show up and that's the analog +actually of something that happened to + + align:start position:0% +actually of something that happened to + + + align:start position:0% +actually of something that happened to +this guy where we said there was only a + + align:start position:0% +this guy where we said there was only a + + + align:start position:0% +this guy where we said there was only a +possibility of a single logarithm + + align:start position:0% +possibility of a single logarithm + + + align:start position:0% +possibility of a single logarithm +showing up + + align:start position:0% +showing up + + + align:start position:0% +showing up +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is how far we got + + align:start position:0% +so this is how far we got + + + align:start position:0% +so this is how far we got +whenever you have something whenever you + + align:start position:0% +whenever you have something whenever you + + + align:start position:0% +whenever you have something whenever you +have + + align:start position:0% +have + + + align:start position:0% +have +equations where you have convolutions + + align:start position:0% +equations where you have convolutions + + + align:start position:0% +equations where you have convolutions +like this what you should do is for your + + align:start position:0% +like this what you should do is for your + + + align:start position:0% +like this what you should do is for your +transform + + align:start position:0% +transform + + + align:start position:0% +transform +because if Euphoria transform something + + align:start position:0% +because if Euphoria transform something + + + align:start position:0% +because if Euphoria transform something +that's a convolution it becomes a + + align:start position:0% +that's a convolution it becomes a + + + align:start position:0% +that's a convolution it becomes a +product + + align:start position:0% + + + + align:start position:0% + +so before we transform and in order to + + align:start position:0% +so before we transform and in order to + + + align:start position:0% +so before we transform and in order to +be careful about + + align:start position:0% + + + + align:start position:0% + +convergence of our Fourier transform we + + align:start position:0% +convergence of our Fourier transform we + + + align:start position:0% +convergence of our Fourier transform we +give it a small imaginary part + + align:start position:0% +give it a small imaginary part + + + align:start position:0% +give it a small imaginary part +and we Define a position space an almost + + align:start position:0% +and we Define a position space an almost + + + align:start position:0% +and we Define a position space an almost +dimension + + align:start position:0% + + + + align:start position:0% + +has been almost mentioned up there that + + align:start position:0% +has been almost mentioned up there that + + + align:start position:0% +has been almost mentioned up there that +depend on S but now for a transformed + + align:start position:0% +depend on S but now for a transformed + + + align:start position:0% +depend on S but now for a transformed +and likewise we Define a position space + + align:start position:0% +and likewise we Define a position space + + + align:start position:0% +and likewise we Define a position space +jet function + + align:start position:0% +jet function + + + align:start position:0% +jet function +and why + + align:start position:0% + + + + align:start position:0% + +and then this formula here which is a + + align:start position:0% +and then this formula here which is a + + + align:start position:0% +and then this formula here which is a +convolution if you use if you use these + + align:start position:0% +convolution if you use if you use these + + + align:start position:0% +convolution if you use if you use these +in the inverse transforms you you arrive + + align:start position:0% +in the inverse transforms you you arrive + + + align:start position:0% +in the inverse transforms you you arrive +at a very simple formula for + + align:start position:0% +at a very simple formula for + + + align:start position:0% +at a very simple formula for +position space + + align:start position:0% + + + + align:start position:0% + +gamma J + + align:start position:0% + + + + align:start position:0% + +so the Fourier transform of a Delta + + align:start position:0% +so the Fourier transform of a Delta + + + align:start position:0% +so the Fourier transform of a Delta +function is just the identity so there's + + align:start position:0% +function is just the identity so there's + + + align:start position:0% +function is just the identity so there's +this term here + + align:start position:0% +this term here + + + align:start position:0% +this term here +comes that term there + + align:start position:0% +comes that term there + + + align:start position:0% +comes that term there +the Fourier transform of a plus function + + align:start position:0% +the Fourier transform of a plus function + + + align:start position:0% +the Fourier transform of a plus function +is actually a logarithm + + align:start position:0% +is actually a logarithm + + + align:start position:0% +is actually a logarithm +and in order to get that result you do + + align:start position:0% +and in order to get that result you do + + + align:start position:0% +and in order to get that result you do +need to + + align:start position:0% +need to + + + align:start position:0% +need to +have this convergence + + align:start position:0% +have this convergence + + + align:start position:0% +have this convergence +this little I zero in there + + align:start position:0% +this little I zero in there + + + align:start position:0% +this little I zero in there +so in general + + align:start position:0% +so in general + + + align:start position:0% +so in general +if you have there's a general kind of + + align:start position:0% +if you have there's a general kind of + + + align:start position:0% +if you have there's a general kind of +relation between + + align:start position:0% + + + + align:start position:0% + +logs in + + align:start position:0% + + + + align:start position:0% + +plus functions like that and in four a + + align:start position:0% +plus functions like that and in four a + + + align:start position:0% +plus functions like that and in four a +space + + align:start position:0% +space + + + align:start position:0% +space +the kind of highest logarithm you get is + + align:start position:0% +the kind of highest logarithm you get is + + + align:start position:0% +the kind of highest logarithm you get is +L to the K plus 1. + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +these logs here you're basically if you + + align:start position:0% +these logs here you're basically if you + + + align:start position:0% +these logs here you're basically if you +think about counting them you should + + align:start position:0% +think about counting them you should + + + align:start position:0% +think about counting them you should +count this one over S as an extra log + + align:start position:0% +count this one over S as an extra log + + + align:start position:0% +count this one over S as an extra log +and in Fourier space that becomes + + align:start position:0% +and in Fourier space that becomes + + + align:start position:0% +and in Fourier space that becomes +explicit you really just get a log to + + align:start position:0% +explicit you really just get a log to + + + align:start position:0% +explicit you really just get a log to +the K plus one + + align:start position:0% + + + + align:start position:0% + +all right but this formula here + + align:start position:0% +all right but this formula here + + + align:start position:0% +all right but this formula here +is something that again is a this kind + + align:start position:0% +is something that again is a this kind + + + align:start position:0% +is something that again is a this kind +of multiplicative form so what happens + + align:start position:0% +of multiplicative form so what happens + + + align:start position:0% +of multiplicative form so what happens +to the anomalous dimension + + align:start position:0% +to the anomalous dimension + + + align:start position:0% +to the anomalous dimension +in the Fourier spaces that it has a + + align:start position:0% +in the Fourier spaces that it has a + + + align:start position:0% +in the Fourier spaces that it has a +multiplicative form + + align:start position:0% +multiplicative form + + + align:start position:0% +multiplicative form +all right so we have + + align:start position:0% +all right so we have + + + align:start position:0% +all right so we have +u d by D mu + + align:start position:0% +u d by D mu + + + align:start position:0% +u d by D mu +J + + align:start position:0% +J + + + align:start position:0% +J +you know + + align:start position:0% +you know + + + align:start position:0% +you know +is simply gamma J + + align:start position:0% + + + + align:start position:0% + +a common Mew + + align:start position:0% + + + + align:start position:0% + +so it's no more difficult than this one + + align:start position:0% +so it's no more difficult than this one + + + align:start position:0% +so it's no more difficult than this one +formula up here + + align:start position:0% +formula up here + + + align:start position:0% +formula up here +just have to find the right space which + + align:start position:0% +just have to find the right space which + + + align:start position:0% +just have to find the right space which +is 40 space + + align:start position:0% +is 40 space + + + align:start position:0% +is 40 space +so then we can make an all order + + align:start position:0% +so then we can make an all order + + + align:start position:0% +so then we can make an all order +solution of that formula given that we + + align:start position:0% +solution of that formula given that we + + + align:start position:0% +solution of that formula given that we +know this + + align:start position:0% +know this + + + align:start position:0% +know this +we can just plug in this and integrate + + align:start position:0% +we can just plug in this and integrate + + + align:start position:0% +we can just plug in this and integrate +we've done this a few times now + + align:start position:0% + + + + align:start position:0% + +let me just do it formally by not doing + + align:start position:0% +let me just do it formally by not doing + + + align:start position:0% +let me just do it formally by not doing +the integrals but writing them out in a + + align:start position:0% +the integrals but writing them out in a + + + align:start position:0% +the integrals but writing them out in a +way that you could do them + + align:start position:0% +way that you could do them + + + align:start position:0% +way that you could do them +to show you what the all orders solution + + align:start position:0% +to show you what the all orders solution + + + align:start position:0% +to show you what the all orders solution +would look like + + align:start position:0% + + + + align:start position:0% + +so you can write the the solution using + + align:start position:0% +so you can write the the solution using + + + align:start position:0% +so you can write the the solution using +this fact + + align:start position:0% +this fact + + + align:start position:0% +this fact +and + + align:start position:0% +and + + + align:start position:0% +and +using this fact + + align:start position:0% + + + + align:start position:0% + +so we have to use that fact to convert + + align:start position:0% +so we have to use that fact to convert + + + align:start position:0% +so we have to use that fact to convert +this logarithm here into + + align:start position:0% +this logarithm here into + + + align:start position:0% +this logarithm here into +something that is just in terms of + + align:start position:0% +something that is just in terms of + + + align:start position:0% +something that is just in terms of +Alphas + + align:start position:0% + + + + align:start position:0% + +but using those two facts we can do the + + align:start position:0% +but using those two facts we can do the + + + align:start position:0% +but using those two facts we can do the +same kind of things that we've done + + align:start position:0% +same kind of things that we've done + + + align:start position:0% +same kind of things that we've done +before and write the all order solution + + align:start position:0% +before and write the all order solution + + + align:start position:0% +before and write the all order solution +in the following way + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +piece and then the cusp piece comes with + + align:start position:0% +piece and then the cusp piece comes with + + + align:start position:0% +piece and then the cusp piece comes with +two integrals because + + align:start position:0% +two integrals because + + + align:start position:0% +two integrals because +it had a logarithm and we turned one of + + align:start position:0% +it had a logarithm and we turned one of + + + align:start position:0% +it had a logarithm and we turned one of +the logarithms into an integral as well + + align:start position:0% + + + + align:start position:0% + +hopefully I've gotten all my twos right + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +something similar when we were talking + + align:start position:0% +something similar when we were talking + + + align:start position:0% +something similar when we were talking +about the running of the Wilson co-fit + + align:start position:0% +about the running of the Wilson co-fit + + + align:start position:0% +about the running of the Wilson co-fit +of the sea because it also had this kind + + align:start position:0% +of the sea because it also had this kind + + + align:start position:0% +of the sea because it also had this kind +of form with just a logarithm in a + + align:start position:0% +of form with just a logarithm in a + + + align:start position:0% +of form with just a logarithm in a +constant term and it's + + align:start position:0% +constant term and it's + + + align:start position:0% +constant term and it's +a similar thing here so this is an Euler + + align:start position:0% +a similar thing here so this is an Euler + + + align:start position:0% +a similar thing here so this is an Euler +solution for the running of the jet + + align:start position:0% +solution for the running of the jet + + + align:start position:0% +solution for the running of the jet +function of course we don't know these + + align:start position:0% +function of course we don't know these + + + align:start position:0% +function of course we don't know these +functions to all orders we only know + + align:start position:0% +functions to all orders we only know + + + align:start position:0% +functions to all orders we only know +them to some up to some given order + + align:start position:0% +them to some up to some given order + + + align:start position:0% +them to some up to some given order +and so you plug those whatever order you + + align:start position:0% +and so you plug those whatever order you + + + align:start position:0% +and so you plug those whatever order you +want to work you plug it into this + + align:start position:0% +want to work you plug it into this + + + align:start position:0% +want to work you plug it into this +formula and then you can do this + + align:start position:0% +formula and then you can do this + + + align:start position:0% +formula and then you can do this +integral and then you figure out these + + align:start position:0% +integral and then you figure out these + + + align:start position:0% +integral and then you figure out these +factors here + + align:start position:0% +factors here + + + align:start position:0% +factors here +and those factors are summing the logs + + align:start position:0% +and those factors are summing the logs + + + align:start position:0% +and those factors are summing the logs +in the case of the jet function + + align:start position:0% +in the case of the jet function + + + align:start position:0% +in the case of the jet function +uh what you would the way that you can + + align:start position:0% +uh what you would the way that you can + + + align:start position:0% +uh what you would the way that you can +think about this picture is that you + + align:start position:0% +think about this picture is that you + + + align:start position:0% +think about this picture is that you +want to you have to put the the guys in + + align:start position:0% +want to you have to put the the guys in + + + align:start position:0% +want to you have to put the the guys in +the factorizations here I'm at a common + + align:start position:0% +the factorizations here I'm at a common + + + align:start position:0% +the factorizations here I'm at a common +scale + + align:start position:0% +scale + + + align:start position:0% +scale +and so + + align:start position:0% +and so + + + align:start position:0% +and so +one way of thinking about it is as + + align:start position:0% +one way of thinking about it is as + + + align:start position:0% +one way of thinking about it is as +follows + + align:start position:0% +follows + + + align:start position:0% +follows +let's take our hard function and do + + align:start position:0% +let's take our hard function and do + + + align:start position:0% +let's take our hard function and do +perturbation Theory at U equals mu h + + align:start position:0% +perturbation Theory at U equals mu h + + + align:start position:0% +perturbation Theory at U equals mu h +and then we'll sum logs down to say the + + align:start position:0% +and then we'll sum logs down to say the + + + align:start position:0% +and then we'll sum logs down to say the +soft scale that's one way of doing it + + align:start position:0% +soft scale that's one way of doing it + + + align:start position:0% +soft scale that's one way of doing it +and we'll do perturbation theory for the + + align:start position:0% +and we'll do perturbation theory for the + + + align:start position:0% +and we'll do perturbation theory for the +jet function + + align:start position:0% +jet function + + + align:start position:0% +jet function +at a scale mu equals mule J and then + + align:start position:0% +at a scale mu equals mule J and then + + + align:start position:0% +at a scale mu equals mule J and then +we'll use this randomization group here + + align:start position:0% +we'll use this randomization group here + + + align:start position:0% +we'll use this randomization group here +and just say gamma J + + align:start position:0% + + + + align:start position:0% + +to run this guy down to the soft scale + + align:start position:0% +to run this guy down to the soft scale + + + align:start position:0% +to run this guy down to the soft scale +in that kind of scenario you wouldn't + + align:start position:0% +in that kind of scenario you wouldn't + + + align:start position:0% +in that kind of scenario you wouldn't +have to run the soft function + + align:start position:0% +have to run the soft function + + + align:start position:0% +have to run the soft function +this is like a top-down kind of picture + + align:start position:0% +this is like a top-down kind of picture + + + align:start position:0% +this is like a top-down kind of picture +where you're just running the objects at + + align:start position:0% +where you're just running the objects at + + + align:start position:0% +where you're just running the objects at +the higher scales down to the lowest + + align:start position:0% +the higher scales down to the lowest + + + align:start position:0% +the higher scales down to the lowest +scale that's one way of doing it you + + align:start position:0% +scale that's one way of doing it you + + + align:start position:0% +scale that's one way of doing it you +could also do it in an equivalent way + + align:start position:0% +could also do it in an equivalent way + + + align:start position:0% +could also do it in an equivalent way +where you run the soft function for + + align:start position:0% +where you run the soft function for + + + align:start position:0% +where you run the soft function for +example up to the jet scale and you + + align:start position:0% +example up to the jet scale and you + + + align:start position:0% +example up to the jet scale and you +don't run the jet function and that'll + + align:start position:0% +don't run the jet function and that'll + + + align:start position:0% +don't run the jet function and that'll +give you actually the same + + align:start position:0% +give you actually the same + + + align:start position:0% +give you actually the same +the same result + + align:start position:0% + + + + align:start position:0% + +but in the way I what I with the + + align:start position:0% +but in the way I what I with the + + + align:start position:0% +but in the way I what I with the +information I presented you this is the + + align:start position:0% +information I presented you this is the + + + align:start position:0% +information I presented you this is the +way that you would think about doing the + + align:start position:0% +way that you would think about doing the + + + align:start position:0% +way that you would think about doing the +renormalization group and that would sum + + align:start position:0% +renormalization group and that would sum + + + align:start position:0% +renormalization group and that would sum +up logarithms in the cross section + + align:start position:0% +up logarithms in the cross section + + + align:start position:0% +up logarithms in the cross section +and it's very easy if you write it in + + align:start position:0% +and it's very easy if you write it in + + + align:start position:0% +and it's very easy if you write it in +position space to see what type of + + align:start position:0% +position space to see what type of + + + align:start position:0% +position space to see what type of +logarithms you're signing up + + align:start position:0% + + + + align:start position:0% + +so in position space if we go back to a + + align:start position:0% +so in position space if we go back to a + + + align:start position:0% +so in position space if we go back to a +formula like the one at the top + + align:start position:0% +formula like the one at the top + + + align:start position:0% +formula like the one at the top +basically what happens is that in + + align:start position:0% +basically what happens is that in + + + align:start position:0% +basically what happens is that in +position space you again have a product + + align:start position:0% +position space you again have a product + + + align:start position:0% +position space you again have a product +so these convolutions here + + align:start position:0% +so these convolutions here + + + align:start position:0% +so these convolutions here +right which were also of this form + + align:start position:0% +right which were also of this form + + + align:start position:0% +right which were also of this form +if you for a transform then you end up + + align:start position:0% +if you for a transform then you end up + + + align:start position:0% +if you for a transform then you end up +with a product D Sigma d + + align:start position:0% +with a product D Sigma d + + + align:start position:0% +with a product D Sigma d +so schematically + + align:start position:0% +so schematically + + + align:start position:0% +so schematically +D Sigma d y + + align:start position:0% +D Sigma d y + + + align:start position:0% +D Sigma d y +for say where Y is the 4-H transform to + + align:start position:0% +for say where Y is the 4-H transform to + + + align:start position:0% +for say where Y is the 4-H transform to +a Thrust + + align:start position:0% +a Thrust + + + align:start position:0% +a Thrust +would just be h + + align:start position:0% +would just be h + + + align:start position:0% +would just be h +times J in position space + + align:start position:0% +times J in position space + + + align:start position:0% +times J in position space +a soft function in position space as + + align:start position:0% +a soft function in position space as + + + align:start position:0% +a soft function in position space as +well + + align:start position:0% +well + + + align:start position:0% +well +and there's + + align:start position:0% + + + + align:start position:0% + +Q somewhere but it would be very simple + + align:start position:0% +Q somewhere but it would be very simple + + + align:start position:0% +Q somewhere but it would be very simple +formula which just has a product + + align:start position:0% +formula which just has a product + + + align:start position:0% +formula which just has a product +and so you can figure out what logs + + align:start position:0% +and so you can figure out what logs + + + align:start position:0% +and so you can figure out what logs +you're summing + + align:start position:0% +you're summing + + + align:start position:0% +you're summing +the logs that you're summing again just + + align:start position:0% +the logs that you're summing again just + + + align:start position:0% +the logs that you're summing again just +as we talked about before are simplest + + align:start position:0% +as we talked about before are simplest + + + align:start position:0% +as we talked about before are simplest +to describe in in when you take the log + + align:start position:0% +to describe in in when you take the log + + + align:start position:0% +to describe in in when you take the log +because you're really summing logs in an + + align:start position:0% +because you're really summing logs in an + + + align:start position:0% +because you're really summing logs in an +exponent + + align:start position:0% +exponent + + + align:start position:0% +exponent +so if we talk about + + align:start position:0% +so if we talk about + + + align:start position:0% +so if we talk about +the log of D Sigma d y + + align:start position:0% + + + + align:start position:0% + +then we can enumerate the types of logs + + align:start position:0% +then we can enumerate the types of logs + + + align:start position:0% +then we can enumerate the types of logs +that one sums as follows + + align:start position:0% + + + + align:start position:0% + +so these are the leading logs + + align:start position:0% +so these are the leading logs + + + align:start position:0% +so these are the leading logs +next leading log and this is + + align:start position:0% +next leading log and this is + + + align:start position:0% +next leading log and this is +next the next leading log just like + + align:start position:0% +next the next leading log just like + + + align:start position:0% +next the next leading log just like +before okay when we were talking about + + align:start position:0% +before okay when we were talking about + + + align:start position:0% +before okay when we were talking about +enumerating the logs we talked about + + align:start position:0% +enumerating the logs we talked about + + + align:start position:0% +enumerating the logs we talked about +before an example where we're + + align:start position:0% +before an example where we're + + + align:start position:0% +before an example where we're +enumerating logs in the Wilson + + align:start position:0% +enumerating logs in the Wilson + + + align:start position:0% +enumerating logs in the Wilson +coefficient C now we're doing it for a + + align:start position:0% +coefficient C now we're doing it for a + + + align:start position:0% +coefficient C now we're doing it for a +full cross section but because in + + align:start position:0% +full cross section but because in + + + align:start position:0% +full cross section but because in +position space the cross section is + + align:start position:0% +position space the cross section is + + + align:start position:0% +position space the cross section is +simply product of objects + + align:start position:0% +simply product of objects + + + align:start position:0% +simply product of objects +it's it's you could think about just if + + align:start position:0% +it's it's you could think about just if + + + align:start position:0% +it's it's you could think about just if +you take the logarithm they kind of + + align:start position:0% +you take the logarithm they kind of + + + align:start position:0% +you take the logarithm they kind of +split apart and + + align:start position:0% +split apart and + + + align:start position:0% +split apart and +it's very simple to enumerate what + + align:start position:0% +it's very simple to enumerate what + + + align:start position:0% +it's very simple to enumerate what +corresponds to the things that you would + + align:start position:0% +corresponds to the things that you would + + + align:start position:0% +corresponds to the things that you would +get by putting in anomalous Dimensions + + align:start position:0% +get by putting in anomalous Dimensions + + + align:start position:0% +get by putting in anomalous Dimensions +at a given order so if you use the + + align:start position:0% +at a given order so if you use the + + + align:start position:0% +at a given order so if you use the +leading log anomalous dimension + + align:start position:0% +leading log anomalous dimension + + + align:start position:0% +leading log anomalous dimension +just the one Loop cusp and you get these + + align:start position:0% +just the one Loop cusp and you get these + + + align:start position:0% +just the one Loop cusp and you get these +terms + + align:start position:0% +terms + + + align:start position:0% +terms +you get the higher terms from the + + align:start position:0% +you get the higher terms from the + + + align:start position:0% +you get the higher terms from the +running of the coupling + + align:start position:0% +running of the coupling + + + align:start position:0% +running of the coupling +if you put in the next leading log terms + + align:start position:0% +if you put in the next leading log terms + + + align:start position:0% +if you put in the next leading log terms +then you get those terms + + align:start position:0% +then you get those terms + + + align:start position:0% +then you get those terms +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so you supplement that + + align:start position:0% +and so you supplement that + + + align:start position:0% +and so you supplement that +resubmation + + align:start position:0% +resubmation + + + align:start position:0% +resubmation +which comes from this K and this Omega + + align:start position:0% +which comes from this K and this Omega + + + align:start position:0% +which comes from this K and this Omega +in general you supplement that with sort + + align:start position:0% +in general you supplement that with sort + + + align:start position:0% +in general you supplement that with sort +of fixed order calculations of the H and + + align:start position:0% +of fixed order calculations of the H and + + + align:start position:0% +of fixed order calculations of the H and +the J and the s + + align:start position:0% +the J and the s + + + align:start position:0% +the J and the s +and that gives you a complete + + align:start position:0% +and that gives you a complete + + + align:start position:0% +and that gives you a complete +cross-section at some order + + align:start position:0% +cross-section at some order + + + align:start position:0% +cross-section at some order +some perturbation Theory + + align:start position:0% + + + + align:start position:0% + +so you could do that also in momentum + + align:start position:0% +so you could do that also in momentum + + + align:start position:0% +so you could do that also in momentum +space and you could write out the + + align:start position:0% +space and you could write out the + + + align:start position:0% +space and you could write out the +formula in momentum space just because + + align:start position:0% +formula in momentum space just because + + + align:start position:0% +formula in momentum space just because +after all that's what you want in the + + align:start position:0% +after all that's what you want in the + + + align:start position:0% +after all that's what you want in the +end + + align:start position:0% + + + + align:start position:0% + +position space is just really + + align:start position:0% +position space is just really + + + align:start position:0% +position space is just really +a nice way of deriving the results but + + align:start position:0% +a nice way of deriving the results but + + + align:start position:0% +a nice way of deriving the results but +then you + + align:start position:0% +then you + + + align:start position:0% +then you +eventually put back into momentum space + + align:start position:0% + + + + align:start position:0% + +in some way or another + + align:start position:0% +in some way or another + + + align:start position:0% +in some way or another +because that's where the data is + + align:start position:0% + + + + align:start position:0% + +and let me just show you what the + + align:start position:0% +and let me just show you what the + + + align:start position:0% +and let me just show you what the +formula would look like + + align:start position:0% +formula would look like + + + align:start position:0% +formula would look like +just so you get a kind of + + align:start position:0% +just so you get a kind of + + + align:start position:0% +just so you get a kind of +picture with all the + + align:start position:0% +picture with all the + + + align:start position:0% +picture with all the +arguments + + align:start position:0% +arguments + + + align:start position:0% +arguments +so if I were to Fourier transform the + + align:start position:0% +so if I were to Fourier transform the + + + align:start position:0% +so if I were to Fourier transform the +resump formula which so I hear I didn't + + align:start position:0% +resump formula which so I hear I didn't + + + align:start position:0% +resump formula which so I hear I didn't +even I didn't write the resubmation in + + align:start position:0% +even I didn't write the resubmation in + + + align:start position:0% +even I didn't write the resubmation in +right I didn't write in + + align:start position:0% +right I didn't write in + + + align:start position:0% +right I didn't write in +the evolution factors that correspond to + + align:start position:0% +the evolution factors that correspond to + + + align:start position:0% +the evolution factors that correspond to +to this so let me do that but let me do + + align:start position:0% +to this so let me do that but let me do + + + align:start position:0% +to this so let me do that but let me do +it in momentum space so + + align:start position:0% + + + + align:start position:0% + +I guess I made + + align:start position:0% +I guess I made + + + align:start position:0% +I guess I made +a slightly different Choice here wow + + align:start position:0% + + + + align:start position:0% + +so I'm doing it for the thrust case + + align:start position:0% + + + + align:start position:0% + +these convolutions just mean integrals + + align:start position:0% +these convolutions just mean integrals + + + align:start position:0% +these convolutions just mean integrals +over the variables that are like this S + + align:start position:0% +over the variables that are like this S + + + align:start position:0% +over the variables that are like this S +Prime for example + + align:start position:0% +Prime for example + + + align:start position:0% +Prime for example +so this is S Prime integral + + align:start position:0% + + + + align:start position:0% + +and this is an L Prime integral + + align:start position:0% + + + + align:start position:0% + +okay so there's three integrals in this + + align:start position:0% +okay so there's three integrals in this + + + align:start position:0% +okay so there's three integrals in this +formula + + align:start position:0% +formula + + + align:start position:0% +formula +I guess this is It's Kind of a Funny + + align:start position:0% +I guess this is It's Kind of a Funny + + + align:start position:0% +I guess this is It's Kind of a Funny +notation but + + align:start position:0% +notation but + + + align:start position:0% +notation but +written integral instead of writing + + align:start position:0% +written integral instead of writing + + + align:start position:0% +written integral instead of writing +these tensor signs + + align:start position:0% +these tensor signs + + + align:start position:0% +these tensor signs +that would have been probably more clear + + align:start position:0% + + + + align:start position:0% + +do that + + align:start position:0% + + + + align:start position:0% + +okay so there's the formula in momentum + + align:start position:0% +okay so there's the formula in momentum + + + align:start position:0% +okay so there's the formula in momentum +space + + align:start position:0% + + + + align:start position:0% + +and it's doing what I said + + align:start position:0% +and it's doing what I said + + + align:start position:0% +and it's doing what I said +this Factor here + + align:start position:0% +this Factor here + + + align:start position:0% +this Factor here +is running a hard function + + align:start position:0% +is running a hard function + + + align:start position:0% +is running a hard function +down to the soft scale + + align:start position:0% +down to the soft scale + + + align:start position:0% +down to the soft scale +and this other Factor + + align:start position:0% +and this other Factor + + + align:start position:0% +and this other Factor +here + + align:start position:0% +here + + + align:start position:0% +here +is running from the jet scale + + align:start position:0% +is running from the jet scale + + + align:start position:0% +is running from the jet scale +to the soft scale and I didn't have to + + align:start position:0% +to the soft scale and I didn't have to + + + align:start position:0% +to the soft scale and I didn't have to +run the soft function + + align:start position:0% +run the soft function + + + align:start position:0% +run the soft function +I've written in here that I evaluate + + align:start position:0% +I've written in here that I evaluate + + + align:start position:0% +I've written in here that I evaluate +this guy at the soft scale + + align:start position:0% +this guy at the soft scale + + + align:start position:0% +this guy at the soft scale +and this guy here remember is the + + align:start position:0% +and this guy here remember is the + + + align:start position:0% +and this guy here remember is the +non-perturbative guy + + align:start position:0% +non-perturbative guy + + + align:start position:0% +non-perturbative guy +which we also talked about a little last + + align:start position:0% +which we also talked about a little last + + + align:start position:0% +which we also talked about a little last +time + + align:start position:0% +time + + + align:start position:0% +time +okay so that's kind of the basic + + align:start position:0% +okay so that's kind of the basic + + + align:start position:0% +okay so that's kind of the basic +structure these use as usual are summing + + align:start position:0% +structure these use as usual are summing + + + align:start position:0% +structure these use as usual are summing +the logarithms and then you put fixed + + align:start position:0% +the logarithms and then you put fixed + + + align:start position:0% +the logarithms and then you put fixed +order + + align:start position:0% + + + + align:start position:0% + +results in for this guy + + align:start position:0% +results in for this guy + + + align:start position:0% +results in for this guy +for that guy and for + + align:start position:0% +for that guy and for + + + align:start position:0% +for that guy and for +this guy here + + align:start position:0% +this guy here + + + align:start position:0% +this guy here +I'm in doing so you get the resend + + align:start position:0% +I'm in doing so you get the resend + + + align:start position:0% +I'm in doing so you get the resend +result + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so this fact that I could have done the + + align:start position:0% +so this fact that I could have done the + + + align:start position:0% +so this fact that I could have done the +running differently that I could have + + align:start position:0% +running differently that I could have + + + align:start position:0% +running differently that I could have +run the soft function is a kind of + + align:start position:0% +run the soft function is a kind of + + + align:start position:0% +run the soft function is a kind of +consistency + + align:start position:0% +consistency + + + align:start position:0% +consistency +so + + align:start position:0% + + + + align:start position:0% + +there are other ways of doing the RG + + align:start position:0% +there are other ways of doing the RG + + + align:start position:0% +there are other ways of doing the RG +and they all lead to the same answer + + align:start position:0% +and they all lead to the same answer + + + align:start position:0% +and they all lead to the same answer +and when I say the same answer I really + + align:start position:0% +and when I say the same answer I really + + + align:start position:0% +and when I say the same answer I really +mean the same precisely exactly the same + + align:start position:0% +mean the same precisely exactly the same + + + align:start position:0% +mean the same precisely exactly the same +number + + align:start position:0% + + + + align:start position:0% + +so I really mean the same not just sort + + align:start position:0% +so I really mean the same not just sort + + + align:start position:0% +so I really mean the same not just sort +of approximately the same but exactly + + align:start position:0% +of approximately the same but exactly + + + align:start position:0% +of approximately the same but exactly +the same + + align:start position:0% +the same + + + align:start position:0% +the same +and the other ways of doing the rge are + + align:start position:0% +and the other ways of doing the rge are + + + align:start position:0% +and the other ways of doing the rge are +the basic idea of why there are more + + align:start position:0% +the basic idea of why there are more + + + align:start position:0% +the basic idea of why there are more +more than one way is again this fact + + align:start position:0% +more than one way is again this fact + + + align:start position:0% +more than one way is again this fact +that if I do coefficient renormalization + + align:start position:0% +that if I do coefficient renormalization + + + align:start position:0% +that if I do coefficient renormalization +that that's the inverse of doing Opera + + align:start position:0% +that that's the inverse of doing Opera + + + align:start position:0% +that that's the inverse of doing Opera +operator or normalization so there's two + + align:start position:0% +operator or normalization so there's two + + + align:start position:0% +operator or normalization so there's two +ways of thinking about doing the running + + align:start position:0% +ways of thinking about doing the running + + + align:start position:0% +ways of thinking about doing the running +you run the operators or you run the + + align:start position:0% +you run the operators or you run the + + + align:start position:0% +you run the operators or you run the +coefficients + + align:start position:0% + + + + align:start position:0% + +okay in this picture it's a little bit + + align:start position:0% +okay in this picture it's a little bit + + + align:start position:0% +okay in this picture it's a little bit +more complicated because we have three + + align:start position:0% +more complicated because we have three + + + align:start position:0% +more complicated because we have three +scales + + align:start position:0% +scales + + + align:start position:0% +scales +but when I'm running the hard function I + + align:start position:0% +but when I'm running the hard function I + + + align:start position:0% +but when I'm running the hard function I +equivalently could have run both the jet + + align:start position:0% +equivalently could have run both the jet + + + align:start position:0% +equivalently could have run both the jet +and the soft function and not run the + + align:start position:0% +and the soft function and not run the + + + align:start position:0% +and the soft function and not run the +hard function + + align:start position:0% +hard function + + + align:start position:0% +hard function +so let me maybe give one other way of + + align:start position:0% +so let me maybe give one other way of + + + align:start position:0% +so let me maybe give one other way of +doing this + + align:start position:0% +doing this + + + align:start position:0% +doing this +to show you so I could have run the hard + + align:start position:0% +to show you so I could have run the hard + + + align:start position:0% +to show you so I could have run the hard +function + + align:start position:0% +function + + + align:start position:0% +function +say just down to the jet scale + + align:start position:0% +say just down to the jet scale + + + align:start position:0% +say just down to the jet scale +and then instead of running the jet + + align:start position:0% +and then instead of running the jet + + + align:start position:0% +and then instead of running the jet +function I could have run the soft + + align:start position:0% +function I could have run the soft + + + align:start position:0% +function I could have run the soft +function + + align:start position:0% +function + + + align:start position:0% +function +up to the jet scale that would be + + align:start position:0% +up to the jet scale that would be + + + align:start position:0% +up to the jet scale that would be +another way of doing the RG + + align:start position:0% +another way of doing the RG + + + align:start position:0% +another way of doing the RG +and that would lead + + align:start position:0% +and that would lead + + + align:start position:0% +and that would lead +to an equivalent picture there's more + + align:start position:0% +to an equivalent picture there's more + + + align:start position:0% +to an equivalent picture there's more +than that more than two because + + align:start position:0% +than that more than two because + + + align:start position:0% +than that more than two because +there's three scales in this there's + + align:start position:0% +there's three scales in this there's + + + align:start position:0% +there's three scales in this there's +more than two natural things there's + + align:start position:0% +more than two natural things there's + + + align:start position:0% +more than two natural things there's +sort of three possible natural things + + align:start position:0% +sort of three possible natural things + + + align:start position:0% +sort of three possible natural things +where you would run to either this scale + + align:start position:0% +where you would run to either this scale + + + align:start position:0% +where you would run to either this scale +to scare the scale + + align:start position:0% +to scare the scale + + + align:start position:0% +to scare the scale +but at the base of it it all has to do + + align:start position:0% +but at the base of it it all has to do + + + align:start position:0% +but at the base of it it all has to do +with this equivalence that we talked + + align:start position:0% +with this equivalence that we talked + + + align:start position:0% +with this equivalence that we talked +about in simpler scenarios earlier + + align:start position:0% + + + + align:start position:0% + +and you can write this also as a + + align:start position:0% +and you can write this also as a + + + align:start position:0% +and you can write this also as a +relation between an almost Dimension so + + align:start position:0% +relation between an almost Dimension so + + + align:start position:0% +relation between an almost Dimension so +it implies non-trivial things about the + + align:start position:0% +it implies non-trivial things about the + + + align:start position:0% +it implies non-trivial things about the +formula that have to be true in order + + align:start position:0% +formula that have to be true in order + + + align:start position:0% +formula that have to be true in order +for this to work + + align:start position:0% +for this to work + + + align:start position:0% +for this to work +so for example + + align:start position:0% + + + + align:start position:0% + +it implies that the coefficients of the + + align:start position:0% +it implies that the coefficients of the + + + align:start position:0% +it implies that the coefficients of the +cuspin almost dimension in the various + + align:start position:0% +cuspin almost dimension in the various + + + align:start position:0% +cuspin almost dimension in the various +renormalization groups would be in a + + align:start position:0% +renormalization groups would be in a + + + align:start position:0% +renormalization groups would be in a +certain way that they would be related + + align:start position:0% +certain way that they would be related + + + align:start position:0% +certain way that they would be related +and even in the non-cuspend almost + + align:start position:0% +and even in the non-cuspend almost + + + align:start position:0% +and even in the non-cuspend almost +Dimensions which is this formula there's + + align:start position:0% +Dimensions which is this formula there's + + + align:start position:0% +Dimensions which is this formula there's +a relation between the jet hard and soft + + align:start position:0% +a relation between the jet hard and soft + + + align:start position:0% +a relation between the jet hard and soft +and almost dimensions + + align:start position:0% +and almost dimensions + + + align:start position:0% +and almost dimensions +okay that's needed + + align:start position:0% +okay that's needed + + + align:start position:0% +okay that's needed +this is kind of an expression of of this + + align:start position:0% +this is kind of an expression of of this + + + align:start position:0% +this is kind of an expression of of this +fact that you can do the reynoldization + + align:start position:0% +fact that you can do the reynoldization + + + align:start position:0% +fact that you can do the reynoldization +group by running different objects + + align:start position:0% +group by running different objects + + + align:start position:0% +group by running different objects +so you can derive this formula by just + + align:start position:0% +so you can derive this formula by just + + + align:start position:0% +so you can derive this formula by just +saying mu d by D mu of the cross section + + align:start position:0% +saying mu d by D mu of the cross section + + + align:start position:0% +saying mu d by D mu of the cross section +is zero + + align:start position:0% +is zero + + + align:start position:0% +is zero +and going through it if you were to + + align:start position:0% +and going through it if you were to + + + align:start position:0% +and going through it if you were to +allow + + align:start position:0% +allow + + + align:start position:0% +allow +then then you would find form it was + + align:start position:0% +then then you would find form it was + + + align:start position:0% +then then you would find form it was +like this one + + align:start position:0% +like this one + + + align:start position:0% +like this one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so questions + + align:start position:0% + + + + align:start position:0% + +so I kind of + + align:start position:0% +so I kind of + + + align:start position:0% +so I kind of +went quick because most of the concepts + + align:start position:0% +went quick because most of the concepts + + + align:start position:0% +went quick because most of the concepts +here are things that we've seen before + + align:start position:0% +here are things that we've seen before + + + align:start position:0% +here are things that we've seen before +in simpler guises + + align:start position:0% + + + + align:start position:0% + +the new complication is really that we + + align:start position:0% +the new complication is really that we + + + align:start position:0% +the new complication is really that we +have this dependence on a variable which + + align:start position:0% +have this dependence on a variable which + + + align:start position:0% +have this dependence on a variable which +ended up being y but by going to Fourier + + align:start position:0% +ended up being y but by going to Fourier + + + align:start position:0% +ended up being y but by going to Fourier +space it looked just like a simple + + align:start position:0% +space it looked just like a simple + + + align:start position:0% +space it looked just like a simple +product again and why it behaved kind of + + align:start position:0% +product again and why it behaved kind of + + + align:start position:0% +product again and why it behaved kind of +like a simple kinematic variable the end + + align:start position:0% +like a simple kinematic variable the end + + + align:start position:0% +like a simple kinematic variable the end +of the day we want a Fourier transform + + align:start position:0% +of the day we want a Fourier transform + + + align:start position:0% +of the day we want a Fourier transform +back but + + align:start position:0% +back but + + + align:start position:0% +back but +we have a space where things look + + align:start position:0% +we have a space where things look + + + align:start position:0% +we have a space where things look +familiar + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so that that Z plus C minus the die Jets + + align:start position:0% +so that that Z plus C minus the die Jets + + + align:start position:0% +so that that Z plus C minus the die Jets +and that's the last SCT one example I'm + + align:start position:0% +and that's the last SCT one example I'm + + + align:start position:0% +and that's the last SCT one example I'm +going to do for a while I'm now going to + + align:start position:0% +going to do for a while I'm now going to + + + align:start position:0% +going to do for a while I'm now going to +turn to doing sct2 and we'll spend some + + align:start position:0% +turn to doing sct2 and we'll spend some + + + align:start position:0% +turn to doing sct2 and we'll spend some +time talking about sct2 + + align:start position:0% + + + + align:start position:0% + +so in sct2 instead of having Ultra Soft + + align:start position:0% +so in sct2 instead of having Ultra Soft + + + align:start position:0% +so in sct2 instead of having Ultra Soft +interactions with collinear particles we + + align:start position:0% +interactions with collinear particles we + + + align:start position:0% +interactions with collinear particles we +have soft interactions with cleaner + + align:start position:0% +have soft interactions with cleaner + + + align:start position:0% +have soft interactions with cleaner +particles + + align:start position:0% + + + + align:start position:0% + +and so we have to + + align:start position:0% +and so we have to + + + align:start position:0% +and so we have to +call how that's going to work + + align:start position:0% +call how that's going to work + + + align:start position:0% +call how that's going to work +so if we take a soft particle + + align:start position:0% + + + + align:start position:0% + +consider a soft particle + + align:start position:0% +consider a soft particle + + + align:start position:0% +consider a soft particle +interacting with some collinear particle + + align:start position:0% +interacting with some collinear particle + + + align:start position:0% +interacting with some collinear particle +and ask what do we get out + + align:start position:0% + + + + align:start position:0% + +so if we just ask about momentum + + align:start position:0% +so if we just ask about momentum + + + align:start position:0% +so if we just ask about momentum +conservation we call this Q + + align:start position:0% +conservation we call this Q + + + align:start position:0% +conservation we call this Q +and Q is equal to Q soft plus Q + + align:start position:0% +and Q is equal to Q soft plus Q + + + align:start position:0% +and Q is equal to Q soft plus Q +collinear + + align:start position:0% +collinear + + + align:start position:0% +collinear +and since we know the scaling of these + + align:start position:0% +and since we know the scaling of these + + + align:start position:0% +and since we know the scaling of these +two we know the scaling of Q + + align:start position:0% +two we know the scaling of Q + + + align:start position:0% +two we know the scaling of Q +it's just given by whatever the larger + + align:start position:0% +it's just given by whatever the larger + + + align:start position:0% +it's just given by whatever the larger +of the scalings is + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +soft and collinear both have the same so + + align:start position:0% +soft and collinear both have the same so + + + align:start position:0% +soft and collinear both have the same so +let me remind you the scalings this guy + + align:start position:0% +let me remind you the scalings this guy + + + align:start position:0% +let me remind you the scalings this guy +was Q Lambda Lambda Lambda and this guy + + align:start position:0% +was Q Lambda Lambda Lambda and this guy + + + align:start position:0% +was Q Lambda Lambda Lambda and this guy +was Q Lambda squared one Lambda + + align:start position:0% +was Q Lambda squared one Lambda + + + align:start position:0% +was Q Lambda squared one Lambda +so the difference between Ultra Soft and + + align:start position:0% +so the difference between Ultra Soft and + + + align:start position:0% +so the difference between Ultra Soft and +cleaner and soft and cleaner is that + + align:start position:0% +cleaner and soft and cleaner is that + + + align:start position:0% +cleaner and soft and cleaner is that +soft and cleaner have the same size of + + align:start position:0% +soft and cleaner have the same size of + + + align:start position:0% +soft and cleaner have the same size of +perp momenta + + align:start position:0% +perp momenta + + + align:start position:0% +perp momenta +so the perp momento are just the water + + align:start position:0% +so the perp momento are just the water + + + align:start position:0% +so the perp momento are just the water +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +obviously in the minus momenta the one + + align:start position:0% +obviously in the minus momenta the one + + + align:start position:0% +obviously in the minus momenta the one +wins so the minus momentum of order one + + align:start position:0% +wins so the minus momentum of order one + + + align:start position:0% +wins so the minus momentum of order one +and in the plus momentum it's the soft + + align:start position:0% +and in the plus momentum it's the soft + + + align:start position:0% +and in the plus momentum it's the soft +that wins because it's bigger than the + + align:start position:0% +that wins because it's bigger than the + + + align:start position:0% +that wins because it's bigger than the +collinear so this is what Orlando + + align:start position:0% +collinear so this is what Orlando + + + align:start position:0% +collinear so this is what Orlando +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's actually much different than + + align:start position:0% +and that's actually much different than + + + align:start position:0% +and that's actually much different than +what we found when we added Ultra Soft + + align:start position:0% +what we found when we added Ultra Soft + + + align:start position:0% +what we found when we added Ultra Soft +and cleaner + + align:start position:0% +and cleaner + + + align:start position:0% +and cleaner +because when we added Ultra Soft and + + align:start position:0% +because when we added Ultra Soft and + + + align:start position:0% +because when we added Ultra Soft and +cleaner we got back linear + + align:start position:0% +cleaner we got back linear + + + align:start position:0% +cleaner we got back linear +here we're not getting back linear this + + align:start position:0% +here we're not getting back linear this + + + align:start position:0% +here we're not getting back linear this +is actually off shell + + align:start position:0% +is actually off shell + + + align:start position:0% +is actually off shell +from the perspective of our low energy + + align:start position:0% +from the perspective of our low energy + + + align:start position:0% +from the perspective of our low energy +modes + + align:start position:0% + + + + align:start position:0% + +because Q squared the biggest part of Q + + align:start position:0% +because Q squared the biggest part of Q + + + align:start position:0% +because Q squared the biggest part of Q +squared would be 1 times Lambda Q + + align:start position:0% +squared would be 1 times Lambda Q + + + align:start position:0% +squared would be 1 times Lambda Q +squareds of order Lambda + + align:start position:0% +squareds of order Lambda + + + align:start position:0% +squareds of order Lambda +which is much bigger than Lambda squared + + align:start position:0% + + + + align:start position:0% + +so adding a soft and a clinical particle + + align:start position:0% +so adding a soft and a clinical particle + + + align:start position:0% +so adding a soft and a clinical particle +in sct2 immediately gives you something + + align:start position:0% +in sct2 immediately gives you something + + + align:start position:0% +in sct2 immediately gives you something +off shell + + align:start position:0% +off shell + + + align:start position:0% +off shell +that's going to make some things easier + + align:start position:0% +that's going to make some things easier + + + align:start position:0% +that's going to make some things easier +and some things more complicated + + align:start position:0% +and some things more complicated + + + align:start position:0% +and some things more complicated +mostly it's going to make things a + + align:start position:0% +mostly it's going to make things a + + + align:start position:0% +mostly it's going to make things a +little more complicated but + + align:start position:0% + + + + align:start position:0% + +at least at the start it'll look easier + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +you can think about this from our mode + + align:start position:0% +you can think about this from our mode + + + align:start position:0% +you can think about this from our mode +picture + + align:start position:0% + + + + align:start position:0% + +where we had collineers that lived sauce + + align:start position:0% +where we had collineers that lived sauce + + + align:start position:0% +where we had collineers that lived sauce +that lived here and said cleaners that + + align:start position:0% +that lived here and said cleaners that + + + align:start position:0% +that lived here and said cleaners that +lived there + + align:start position:0% +lived there + + + align:start position:0% +lived there +in order for them to interact they have + + align:start position:0% +in order for them to interact they have + + + align:start position:0% +in order for them to interact they have +to sort of go up to a common a place + + align:start position:0% +to sort of go up to a common a place + + + align:start position:0% +to sort of go up to a common a place +where we can have a common momentum and + + align:start position:0% +where we can have a common momentum and + + + align:start position:0% +where we can have a common momentum and +that's a higher hyperbola + + align:start position:0% +that's a higher hyperbola + + + align:start position:0% +that's a higher hyperbola +like this it's not all the way up to the + + align:start position:0% +like this it's not all the way up to the + + + align:start position:0% +like this it's not all the way up to the +hard scale which is up here + + align:start position:0% + + + + align:start position:0% + +was hard + + align:start position:0% +was hard + + + align:start position:0% +was hard +but there's kind of an intermediate + + align:start position:0% +but there's kind of an intermediate + + + align:start position:0% +but there's kind of an intermediate +scale that comes in + + align:start position:0% +scale that comes in + + + align:start position:0% +scale that comes in +which is the scale of this Q squared + + align:start position:0% +which is the scale of this Q squared + + + align:start position:0% +which is the scale of this Q squared +Q squared + + align:start position:0% +Q squared + + + align:start position:0% +Q squared +what are the Q squared there and + + align:start position:0% +what are the Q squared there and + + + align:start position:0% +what are the Q squared there and +sometimes this is called a hard + + align:start position:0% +sometimes this is called a hard + + + align:start position:0% +sometimes this is called a hard +collinear scale + + align:start position:0% +collinear scale + + + align:start position:0% +collinear scale +this is kind of this would be called a + + align:start position:0% +this is kind of this would be called a + + + align:start position:0% +this is kind of this would be called a +hard collinear mode HC + + align:start position:0% + + + + align:start position:0% + +and you can even write down if you + + align:start position:0% +and you can even write down if you + + + align:start position:0% +and you can even write down if you +wanted an on-shell degree of freedom for + + align:start position:0% +wanted an on-shell degree of freedom for + + + align:start position:0% +wanted an on-shell degree of freedom for +this hard linear mode + + align:start position:0% + + + + align:start position:0% + +so an onshell version of it you could + + align:start position:0% +so an onshell version of it you could + + + align:start position:0% +so an onshell version of it you could +think of it as a mode in theory + + align:start position:0% +think of it as a mode in theory + + + align:start position:0% +think of it as a mode in theory +an onshell version of it would have a + + align:start position:0% +an onshell version of it would have a + + + align:start position:0% +an onshell version of it would have a +scaling that's Q one Lambda root Lambda + + align:start position:0% + + + + align:start position:0% + +so you could think about one way of + + align:start position:0% +so you could think about one way of + + + align:start position:0% +so you could think about one way of +approaching it which we'll take we'll + + align:start position:0% +approaching it which we'll take we'll + + + align:start position:0% +approaching it which we'll take we'll +take the this attitude in a minute one + + align:start position:0% +take the this attitude in a minute one + + + align:start position:0% +take the this attitude in a minute one +way of approaching this problem would be + + align:start position:0% +way of approaching this problem would be + + + align:start position:0% +way of approaching this problem would be +to sort of first think about doing some + + align:start position:0% +to sort of first think about doing some + + + align:start position:0% +to sort of first think about doing some +matching onto a theory with this hard + + align:start position:0% +matching onto a theory with this hard + + + align:start position:0% +matching onto a theory with this hard +linear mode and then trying to match + + align:start position:0% +linear mode and then trying to match + + + align:start position:0% +linear mode and then trying to match +down onto a theory that just has the + + align:start position:0% +down onto a theory that just has the + + + align:start position:0% +down onto a theory that just has the +clear and the soft mode + + align:start position:0% +clear and the soft mode + + + align:start position:0% +clear and the soft mode +and we'll exploit that a little later + + align:start position:0% +and we'll exploit that a little later + + + align:start position:0% +and we'll exploit that a little later +but first let me do a different thing + + align:start position:0% +but first let me do a different thing + + + align:start position:0% +but first let me do a different thing +and just ignore this dashed line + + align:start position:0% +and just ignore this dashed line + + + align:start position:0% +and just ignore this dashed line +and just think about matching directly + + align:start position:0% +and just think about matching directly + + + align:start position:0% +and just think about matching directly +from this hard from the qcd onto the + + align:start position:0% +from this hard from the qcd onto the + + + align:start position:0% +from this hard from the qcd onto the +sket2 which just has these two degrees + + align:start position:0% +sket2 which just has these two degrees + + + align:start position:0% +sket2 which just has these two degrees +of freedom + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +so what's going to happen is that we're + + align:start position:0% +so what's going to happen is that we're + + + align:start position:0% +so what's going to happen is that we're +going to have to integrate out more + + align:start position:0% +going to have to integrate out more + + + align:start position:0% +going to have to integrate out more +things because + + align:start position:0% +things because + + + align:start position:0% +things because +any type of interactions that we write + + align:start position:0% +any type of interactions that we write + + + align:start position:0% +any type of interactions that we write +down are basically giving us something + + align:start position:0% +down are basically giving us something + + + align:start position:0% +down are basically giving us something +off shell so let's do an example of this + + align:start position:0% +off shell so let's do an example of this + + + align:start position:0% +off shell so let's do an example of this +so we'll do an example of a heavy + + align:start position:0% +so we'll do an example of a heavy + + + align:start position:0% +so we'll do an example of a heavy +Delight + + align:start position:0% +Delight + + + align:start position:0% +Delight +current + + align:start position:0% +current + + + align:start position:0% +current +but now + + align:start position:0% +but now + + + align:start position:0% +but now +it won't be an sct2 current but rather + + align:start position:0% +it won't be an sct2 current but rather + + + align:start position:0% +it won't be an sct2 current but rather +an sct-1 + + align:start position:0% + + + + align:start position:0% + +so I just want to have one soft particle + + align:start position:0% +so I just want to have one soft particle + + + align:start position:0% +so I just want to have one soft particle +and one linear particle + + align:start position:0% +and one linear particle + + + align:start position:0% +and one linear particle +as possible example but now this is soft + + align:start position:0% +as possible example but now this is soft + + + align:start position:0% +as possible example but now this is soft +and this is clinier + + align:start position:0% +and this is clinier + + + align:start position:0% +and this is clinier +not Ultra Soft and clinier + + align:start position:0% + + + + align:start position:0% + +all right so we have some current + + align:start position:0% +all right so we have some current + + + align:start position:0% +all right so we have some current +I'm just going to label the lines with + + align:start position:0% +I'm just going to label the lines with + + + align:start position:0% +I'm just going to label the lines with +c's and S's + + align:start position:0% +c's and S's + + + align:start position:0% +c's and S's +so imagine that you attached a soft glue + + align:start position:0% +so imagine that you attached a soft glue + + + align:start position:0% +so imagine that you attached a soft glue +on + + align:start position:0% +on + + + align:start position:0% +on +here + + align:start position:0% +here + + + align:start position:0% +here +that would give you something that's off + + align:start position:0% +that would give you something that's off + + + align:start position:0% +that would give you something that's off +shell + + align:start position:0% +shell + + + align:start position:0% +shell +so this line here is off shell + + align:start position:0% +so this line here is off shell + + + align:start position:0% +so this line here is off shell +and likewise on this side if this is + + align:start position:0% +and likewise on this side if this is + + + align:start position:0% +and likewise on this side if this is +soft coming in + + align:start position:0% +soft coming in + + + align:start position:0% +soft coming in +let you attach something collinear here + + align:start position:0% +let you attach something collinear here + + + align:start position:0% +let you attach something collinear here +then this is off shell + + align:start position:0% +then this is off shell + + + align:start position:0% +then this is off shell +before when we had this picture and we + + align:start position:0% +before when we had this picture and we + + + align:start position:0% +before when we had this picture and we +were doing it for sct1 + + align:start position:0% +were doing it for sct1 + + + align:start position:0% +were doing it for sct1 +one set of attachments would still lead + + align:start position:0% +one set of attachments would still lead + + + align:start position:0% +one set of attachments would still lead +to on shell in particular on this side + + align:start position:0% +to on shell in particular on this side + + + align:start position:0% +to on shell in particular on this side +and this side we got something off shell + + align:start position:0% +and this side we got something off shell + + + align:start position:0% +and this side we got something off shell +we integrated it out and we got a Wilson + + align:start position:0% +we integrated it out and we got a Wilson + + + align:start position:0% +we integrated it out and we got a Wilson +line + + align:start position:0% +line + + + align:start position:0% +line +right + + align:start position:0% +right + + + align:start position:0% +right +here it's a little more complicated + + align:start position:0% +here it's a little more complicated + + + align:start position:0% +here it's a little more complicated +because you attach + + align:start position:0% +because you attach + + + align:start position:0% +because you attach +alternate modes on either side and you + + align:start position:0% +alternate modes on either side and you + + + align:start position:0% +alternate modes on either side and you +get something off shell and you just + + align:start position:0% +get something off shell and you just + + + align:start position:0% +get something off shell and you just +have to integrate out this pink line all + + align:start position:0% +have to integrate out this pink line all + + + align:start position:0% +have to integrate out this pink line all +at once + + align:start position:0% + + + + align:start position:0% + +and that's going to give you another + + align:start position:0% +and that's going to give you another + + + align:start position:0% +and that's going to give you another +type of Wilson line + + align:start position:0% +type of Wilson line + + + align:start position:0% +type of Wilson line +so we'll get + + align:start position:0% +so we'll get + + + align:start position:0% +so we'll get +in this in this calculation we're going + + align:start position:0% +in this in this calculation we're going + + + align:start position:0% +in this in this calculation we're going +to get w + + align:start position:0% +to get w + + + align:start position:0% +to get w +that's built of the clinier modes + + align:start position:0% +that's built of the clinier modes + + + align:start position:0% +that's built of the clinier modes +and another type of Wilson line + + align:start position:0% + + + + align:start position:0% + +from the soft nodes + + align:start position:0% + + + + align:start position:0% + +let's call it SN + + align:start position:0% +let's call it SN + + + align:start position:0% +let's call it SN +so how do you build up a Wilson line + + align:start position:0% +so how do you build up a Wilson line + + + align:start position:0% +so how do you build up a Wilson line +well this first of all think about + + align:start position:0% +well this first of all think about + + + align:start position:0% +well this first of all think about +attaching more gluons onto this line + + align:start position:0% +attaching more gluons onto this line + + + align:start position:0% +attaching more gluons onto this line +right that's kind of the analog of what + + align:start position:0% +right that's kind of the analog of what + + + align:start position:0% +right that's kind of the analog of what +we did before + + align:start position:0% +we did before + + + align:start position:0% +we did before +so just + + align:start position:0% + + + + align:start position:0% + +hatch more soft gluons here + + align:start position:0% +hatch more soft gluons here + + + align:start position:0% +hatch more soft gluons here +more cleaner gluons here + + align:start position:0% +more cleaner gluons here + + + align:start position:0% +more cleaner gluons here +this is my this might be the first thing + + align:start position:0% +this is my this might be the first thing + + + align:start position:0% +this is my this might be the first thing +you would try just adding those guys up + + align:start position:0% +you would try just adding those guys up + + + align:start position:0% +you would try just adding those guys up +and that means you have a whole line of + + align:start position:0% +and that means you have a whole line of + + + align:start position:0% +and that means you have a whole line of +things that it's off shell and you just + + align:start position:0% +things that it's off shell and you just + + + align:start position:0% +things that it's off shell and you just +calculate these diagrams + + align:start position:0% + + + + align:start position:0% + +and if you do that calculation + + align:start position:0% +and if you do that calculation + + + align:start position:0% +and if you do that calculation +it will give you Wilson lines + + align:start position:0% +it will give you Wilson lines + + + align:start position:0% +it will give you Wilson lines +and what it'll give is something that + + align:start position:0% +and what it'll give is something that + + + align:start position:0% +and what it'll give is something that +looks like this + + align:start position:0% + + + + align:start position:0% + +where SN dagger is a function of + + align:start position:0% +where SN dagger is a function of + + + align:start position:0% +where SN dagger is a function of +the N dot as component + + align:start position:0% +the N dot as component + + + align:start position:0% +the N dot as component +W is a function of say the M Bar Dot + + align:start position:0% +W is a function of say the M Bar Dot + + + align:start position:0% +W is a function of say the M Bar Dot +AC component so the Wilson lines along + + align:start position:0% +AC component so the Wilson lines along + + + align:start position:0% +AC component so the Wilson lines along +in some Direction + + align:start position:0% + + + + align:start position:0% + +and it did + + align:start position:0% +and it did + + + align:start position:0% +and it did +it looks like this + + align:start position:0% +it looks like this + + + align:start position:0% +it looks like this +see let's just pass + + align:start position:0% +see let's just pass + + + align:start position:0% +see let's just pass +now + + align:start position:0% +now + + + align:start position:0% +now +there's something wrong with this it's + + align:start position:0% +there's something wrong with this it's + + + align:start position:0% +there's something wrong with this it's +not quite the right answer + + align:start position:0% +not quite the right answer + + + align:start position:0% +not quite the right answer +the reason that the Wilson lines are the + + align:start position:0% +the reason that the Wilson lines are the + + + align:start position:0% +the reason that the Wilson lines are the +way they are is because I got the + + align:start position:0% +way they are is because I got the + + + align:start position:0% +way they are is because I got the +collinear ones from integrating out them + + align:start position:0% +collinear ones from integrating out them + + + align:start position:0% +collinear ones from integrating out them +out from the next to the heavy Quark + + align:start position:0% +out from the next to the heavy Quark + + + align:start position:0% +out from the next to the heavy Quark +which is the soft particle so that's why + + align:start position:0% +which is the soft particle so that's why + + + align:start position:0% +which is the soft particle so that's why +W sits next to h s dagger sits next to C + + align:start position:0% +W sits next to h s dagger sits next to C + + + align:start position:0% +W sits next to h s dagger sits next to C +because of the same thing on the on the + + align:start position:0% +because of the same thing on the on the + + + align:start position:0% +because of the same thing on the on the +cleaner side but if I wanted to make + + align:start position:0% +cleaner side but if I wanted to make + + + align:start position:0% +cleaner side but if I wanted to make +them into a gauge invariant thing I want + + align:start position:0% +them into a gauge invariant thing I want + + + align:start position:0% +them into a gauge invariant thing I want +the W to sit next to the C and the S + + align:start position:0% +the W to sit next to the C and the S + + + align:start position:0% +the W to sit next to the C and the S +dagger to sit next to the h + + align:start position:0% +dagger to sit next to the h + + + align:start position:0% +dagger to sit next to the h +that would be the analog of what we had + + align:start position:0% +that would be the analog of what we had + + + align:start position:0% +that would be the analog of what we had +in sct1 and that's not what we got if + + align:start position:0% +in sct1 and that's not what we got if + + + align:start position:0% +in sct1 and that's not what we got if +this was QED then that would be fine + + align:start position:0% +this was QED then that would be fine + + + align:start position:0% +this was QED then that would be fine +because this and this I could just + + align:start position:0% +because this and this I could just + + + align:start position:0% +because this and this I could just +commute them as long as this + + align:start position:0% +commute them as long as this + + + align:start position:0% +commute them as long as this +but I can always do that I can just push + + align:start position:0% +but I can always do that I can just push + + + align:start position:0% +but I can always do that I can just push +this guy through that guy but in qcd I + + align:start position:0% +this guy through that guy but in qcd I + + + align:start position:0% +this guy through that guy but in qcd I +can't because these guys have color + + align:start position:0% +can't because these guys have color + + + align:start position:0% +can't because these guys have color +matrices and they don't commute with + + align:start position:0% +matrices and they don't commute with + + + align:start position:0% +matrices and they don't commute with +each other + + align:start position:0% +each other + + + align:start position:0% +each other +so that means that this isn't quite the + + align:start position:0% +so that means that this isn't quite the + + + align:start position:0% +so that means that this isn't quite the +whole story here + + align:start position:0% +whole story here + + + align:start position:0% +whole story here +some diagrams that we missed + + align:start position:0% + + + + align:start position:0% + +so there must be some diagrams that are + + align:start position:0% +so there must be some diagrams that are + + + align:start position:0% +so there must be some diagrams that are +non-abelian that we missed + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +and what what are those diagrams + + align:start position:0% + + + + align:start position:0% + +so these are diagrams that involve + + align:start position:0% +so these are diagrams that involve + + + align:start position:0% +so these are diagrams that involve +triple gluon and three four Glon + + align:start position:0% +triple gluon and three four Glon + + + align:start position:0% +triple gluon and three four Glon +vertices + + align:start position:0% + + + + align:start position:0% + +and what these guys do it turns out is + + align:start position:0% +and what these guys do it turns out is + + + align:start position:0% +and what these guys do it turns out is +they do one thing in this calculation + + align:start position:0% +they do one thing in this calculation + + + align:start position:0% +they do one thing in this calculation +they really just flip the order of the W + + align:start position:0% +they really just flip the order of the W + + + align:start position:0% +they really just flip the order of the W +and the s + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +why do we have to consider those + + align:start position:0% +why do we have to consider those + + + align:start position:0% +why do we have to consider those +diagrams + + align:start position:0% + + + + align:start position:0% + +so think about + + align:start position:0% + + + + align:start position:0% + +instead of attaching gluons to quarks + + align:start position:0% +instead of attaching gluons to quarks + + + align:start position:0% +instead of attaching gluons to quarks +attach glance to gluons + + align:start position:0% +attach glance to gluons + + + align:start position:0% +attach glance to gluons +so say we have + + align:start position:0% + + + + align:start position:0% + +soft + + align:start position:0% +soft + + + align:start position:0% +soft +cleaner and we attach them to each other + + align:start position:0% +cleaner and we attach them to each other + + + align:start position:0% +cleaner and we attach them to each other +but to it through a three gluon vertex + + align:start position:0% +but to it through a three gluon vertex + + + align:start position:0% +but to it through a three gluon vertex +then this guy's off shell if that + + align:start position:0% +then this guy's off shell if that + + + align:start position:0% +then this guy's off shell if that +offshore guy attaches to this guy then + + align:start position:0% +offshore guy attaches to this guy then + + + align:start position:0% +offshore guy attaches to this guy then +it's off shell + + align:start position:0% +it's off shell + + + align:start position:0% +it's off shell +and if you integrate out diagrams like + + align:start position:0% +and if you integrate out diagrams like + + + align:start position:0% +and if you integrate out diagrams like +this that's going to change our result + + align:start position:0% +this that's going to change our result + + + align:start position:0% +this that's going to change our result +over there was + + align:start position:0% +over there was + + + align:start position:0% +over there was +like if you go to the same order on the + + align:start position:0% +like if you go to the same order on the + + + align:start position:0% +like if you go to the same order on the +other side + + align:start position:0% +other side + + + align:start position:0% +other side +exactly analogous thing + + align:start position:0% + + + + align:start position:0% + +okay so these are also things that you + + align:start position:0% +okay so these are also things that you + + + align:start position:0% +okay so these are also things that you +have to integrate out you have to + + align:start position:0% +have to integrate out you have to + + + align:start position:0% +have to integrate out you have to +integrate all these pink things out + + align:start position:0% +integrate all these pink things out + + + align:start position:0% +integrate all these pink things out +and if you do that then it does what I + + align:start position:0% +and if you do that then it does what I + + + align:start position:0% +and if you do that then it does what I +said + + align:start position:0% + + + + align:start position:0% + +do that tall orders + + align:start position:0% +do that tall orders + + + align:start position:0% +do that tall orders +but you can do with a + + align:start position:0% +but you can do with a + + + align:start position:0% +but you can do with a +auxiliary lagrangian type approach + + align:start position:0% + + + + align:start position:0% + +obviously you're not going to start + + align:start position:0% +obviously you're not going to start + + + align:start position:0% +obviously you're not going to start +calculating diagram installers but + + align:start position:0% +calculating diagram installers but + + + align:start position:0% +calculating diagram installers but +there's some tricks to doing it + + align:start position:0% +there's some tricks to doing it + + + align:start position:0% +there's some tricks to doing it +then you get + + align:start position:0% +then you get + + + align:start position:0% +then you get +them in the right order + + align:start position:0% + + + + align:start position:0% + +it's easy to check for example that at + + align:start position:0% +it's easy to check for example that at + + + align:start position:0% +it's easy to check for example that at +the order of two gluons that this guy + + align:start position:0% +the order of two gluons that this guy + + + align:start position:0% +the order of two gluons that this guy +does exactly what you want + + align:start position:0% +does exactly what you want + + + align:start position:0% +does exactly what you want +so this is then a cleaner gauge and + + align:start position:0% +so this is then a cleaner gauge and + + + align:start position:0% +so this is then a cleaner gauge and +variant + + align:start position:0% +variant + + + align:start position:0% +variant +object + + align:start position:0% +object + + + align:start position:0% +object +and this is then something that's soft + + align:start position:0% +and this is then something that's soft + + + align:start position:0% +and this is then something that's soft +agendarian + + align:start position:0% +agendarian + + + align:start position:0% +agendarian +and that's kind of nice that's what + + align:start position:0% +and that's kind of nice that's what + + + align:start position:0% +and that's kind of nice that's what +you're hoping that's what you're + + align:start position:0% +you're hoping that's what you're + + + align:start position:0% +you're hoping that's what you're +expecting + + align:start position:0% + + + + align:start position:0% + +um you want to add one more glue and + + align:start position:0% +um you want to add one more glue and + + + align:start position:0% +um you want to add one more glue and +wear I want to stick like a collinear + + align:start position:0% +wear I want to stick like a collinear + + + align:start position:0% +wear I want to stick like a collinear +right in between some softs + + align:start position:0% +right in between some softs + + + align:start position:0% +right in between some softs +yeah you mean like + + align:start position:0% +yeah you mean like + + + align:start position:0% +yeah you mean like +on here + + align:start position:0% +on here + + + align:start position:0% +on here +I got well yeah essentially being over + + align:start position:0% +I got well yeah essentially being over + + + align:start position:0% +I got well yeah essentially being over +on that diagram over there like no no + + align:start position:0% +on that diagram over there like no no + + + align:start position:0% +on that diagram over there like no no +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah it's the same thing I think so if + + align:start position:0% +yeah it's the same thing I think so if + + + align:start position:0% +yeah it's the same thing I think so if +you add this guy here then I think it's + + align:start position:0% +you add this guy here then I think it's + + + align:start position:0% +you add this guy here then I think it's +power suppressed because + + align:start position:0% +power suppressed because + + + align:start position:0% +power suppressed because +you it ends up being a power suppressed + + align:start position:0% +you it ends up being a power suppressed + + + align:start position:0% +you it ends up being a power suppressed +term that you don't need if I remember + + align:start position:0% +term that you don't need if I remember + + + align:start position:0% +term that you don't need if I remember +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +yeah this guy's power suppressed + + align:start position:0% + + + + align:start position:0% + +um no + + align:start position:0% +um no + + + align:start position:0% +um no +no you just you just you can think of + + align:start position:0% +no you just you just you can think of + + + align:start position:0% +no you just you just you can think of +this as a full Theory diagram right + + align:start position:0% +this as a full Theory diagram right + + + align:start position:0% +this as a full Theory diagram right +where this guy's off shell and you + + align:start position:0% +where this guy's off shell and you + + + align:start position:0% +where this guy's off shell and you +haven't changed kind of how he's off + + align:start position:0% +haven't changed kind of how he's off + + + align:start position:0% +haven't changed kind of how he's off +shell you just change the value of the + + align:start position:0% +shell you just change the value of the + + + align:start position:0% +shell you just change the value of the +momentum but one thing you've done is + + align:start position:0% +momentum but one thing you've done is + + + align:start position:0% +momentum but one thing you've done is +you've sort of doubled the number of + + align:start position:0% +you've sort of doubled the number of + + + align:start position:0% +you've sort of doubled the number of +hard propagators so if I remember + + align:start position:0% +hard propagators so if I remember + + + align:start position:0% +hard propagators so if I remember +correctly I think this guy + + align:start position:0% +correctly I think this guy + + + align:start position:0% +correctly I think this guy +just gives you something off shell + + align:start position:0% +just gives you something off shell + + + align:start position:0% +just gives you something off shell +pretty pretty confident I mean something + + align:start position:0% +pretty pretty confident I mean something + + + align:start position:0% +pretty pretty confident I mean something +that's power suppressed in Lambda + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so this is how soft collinear + + align:start position:0% +so this is how soft collinear + + + align:start position:0% +so this is how soft collinear +factorization works So Soft linear + + align:start position:0% +factorization works So Soft linear + + + align:start position:0% +factorization works So Soft linear +factorization if you think about it from + + align:start position:0% +factorization if you think about it from + + + align:start position:0% +factorization if you think about it from +the point of view of going from qcd to + + align:start position:0% +the point of view of going from qcd to + + + align:start position:0% +the point of view of going from qcd to +sct2 it's just you integrate out these + + align:start position:0% +sct2 it's just you integrate out these + + + align:start position:0% +sct2 it's just you integrate out these +pink lines as usual and you end up some + + align:start position:0% +pink lines as usual and you end up some + + + align:start position:0% +pink lines as usual and you end up some +with something that's where things are + + align:start position:0% +with something that's where things are + + + align:start position:0% +with something that's where things are +splitting apart and the reason that it's + + align:start position:0% +splitting apart and the reason that it's + + + align:start position:0% +splitting apart and the reason that it's +happening is because the op these lines + + align:start position:0% +happening is because the op these lines + + + align:start position:0% +happening is because the op these lines +are off shell that are where you would + + align:start position:0% +are off shell that are where you would + + + align:start position:0% +are off shell that are where you would +try to interact have interactions and so + + align:start position:0% +try to interact have interactions and so + + + align:start position:0% +try to interact have interactions and so +your your theory is kind of forced apart + + align:start position:0% +your your theory is kind of forced apart + + + align:start position:0% +your your theory is kind of forced apart +by the fact that these things can't + + align:start position:0% +by the fact that these things can't + + + align:start position:0% +by the fact that these things can't +interact in an on-shell way so it's + + align:start position:0% +interact in an on-shell way so it's + + + align:start position:0% +interact in an on-shell way so it's +different than sct1 + + align:start position:0% +different than sct1 + + + align:start position:0% +different than sct1 +in that in that sense + + align:start position:0% +in that in that sense + + + align:start position:0% +in that in that sense +so this is kind of cumbersome as you can + + align:start position:0% +so this is kind of cumbersome as you can + + + align:start position:0% +so this is kind of cumbersome as you can +see if you wanted to kind of think about + + align:start position:0% +see if you wanted to kind of think about + + + align:start position:0% +see if you wanted to kind of think about +doing it arbitrarily because it seems + + align:start position:0% +doing it arbitrarily because it seems + + + align:start position:0% +doing it arbitrarily because it seems +like you just have to calculate diagrams + + align:start position:0% +like you just have to calculate diagrams + + + align:start position:0% +like you just have to calculate diagrams +and who wants to calculate infinite + + align:start position:0% +and who wants to calculate infinite + + + align:start position:0% +and who wants to calculate infinite +classes of diagrams for arbitrarily + + align:start position:0% +classes of diagrams for arbitrarily + + + align:start position:0% +classes of diagrams for arbitrarily +complicated scenarios right + + align:start position:0% +complicated scenarios right + + + align:start position:0% +complicated scenarios right +maybe in this case we can do it but + + align:start position:0% +maybe in this case we can do it but + + + align:start position:0% +maybe in this case we can do it but +actually even in this case we have to + + align:start position:0% +actually even in this case we have to + + + align:start position:0% +actually even in this case we have to +resort to some tricks to do it to all + + align:start position:0% +resort to some tricks to do it to all + + + align:start position:0% +resort to some tricks to do it to all +learners + + align:start position:0% +learners + + + align:start position:0% +learners +and more complicated scenarios it would + + align:start position:0% +and more complicated scenarios it would + + + align:start position:0% +and more complicated scenarios it would +just get even more and more cumbersome + + align:start position:0% +just get even more and more cumbersome + + + align:start position:0% +just get even more and more cumbersome +so we'd like to have a a trick that's + + align:start position:0% +so we'd like to have a a trick that's + + + align:start position:0% +so we'd like to have a a trick that's +kind of generic where we could get the + + align:start position:0% +kind of generic where we could get the + + + align:start position:0% +kind of generic where we could get the +same answer and the way that we can do + + align:start position:0% +same answer and the way that we can do + + + align:start position:0% +same answer and the way that we can do +that is by using + + align:start position:0% +that is by using + + + align:start position:0% +that is by using +this dashed line up in the picture + + align:start position:0% +this dashed line up in the picture + + + align:start position:0% +this dashed line up in the picture +think about formulating rather than + + align:start position:0% +think about formulating rather than + + + align:start position:0% +think about formulating rather than +directly this sct2 formulate first in + + align:start position:0% +directly this sct2 formulate first in + + + align:start position:0% +directly this sct2 formulate first in +sct1 and then we'll match that sct-1 + + align:start position:0% +sct1 and then we'll match that sct-1 + + + align:start position:0% +sct1 and then we'll match that sct-1 +onto s on to qcd + + align:start position:0% +onto s on to qcd + + + align:start position:0% +onto s on to qcd +so + + align:start position:0% + + + + align:start position:0% + +another + + align:start position:0% +another + + + align:start position:0% +another +in some ways better method + + align:start position:0% + + + + align:start position:0% + +is to do + + align:start position:0% +is to do + + + align:start position:0% +is to do +qcd + + align:start position:0% +qcd + + + align:start position:0% +qcd +let's get one + + align:start position:0% +let's get one + + + align:start position:0% +let's get one +and then let's get one to step two + + align:start position:0% + + + + align:start position:0% + +three steps + + align:start position:0% + + + + align:start position:0% + +so we're gonna + + align:start position:0% +so we're gonna + + + align:start position:0% +so we're gonna +first use a scat wand that doesn't have + + align:start position:0% +first use a scat wand that doesn't have + + + align:start position:0% +first use a scat wand that doesn't have +the linear mode just has the soft mode + + align:start position:0% +the linear mode just has the soft mode + + + align:start position:0% +the linear mode just has the soft mode +and the hard cleaner mode + + align:start position:0% +and the hard cleaner mode + + + align:start position:0% +and the hard cleaner mode +so it has what I called HC in the + + align:start position:0% +so it has what I called HC in the + + + align:start position:0% +so it has what I called HC in the +picture and S + + align:start position:0% +picture and S + + + align:start position:0% +picture and S +okay so that would be a mode that has P + + align:start position:0% +okay so that would be a mode that has P + + + align:start position:0% +okay so that would be a mode that has P +Squared + + align:start position:0% +Squared + + + align:start position:0% +Squared +in this picture of order say + + align:start position:0% +in this picture of order say + + + align:start position:0% +in this picture of order say +let's call it Lambda squared + + align:start position:0% + + + + align:start position:0% + +so if I say that this is + + align:start position:0% + + + + align:start position:0% + +where some Lambda squared then you'd + + align:start position:0% +where some Lambda squared then you'd + + + align:start position:0% +where some Lambda squared then you'd +have the soft mode that has P Squared + + align:start position:0% +have the soft mode that has P Squared + + + align:start position:0% +have the soft mode that has P Squared +about a lot of squared and this hard + + align:start position:0% +about a lot of squared and this hard + + + align:start position:0% +about a lot of squared and this hard +cleaner mode that has P Squared of order + + align:start position:0% +cleaner mode that has P Squared of order + + + align:start position:0% +cleaner mode that has P Squared of order +Q Lambda and that's exactly an sct1 + + align:start position:0% +Q Lambda and that's exactly an sct1 + + + align:start position:0% +Q Lambda and that's exactly an sct1 +type situation where we were calling the + + align:start position:0% +type situation where we were calling the + + + align:start position:0% +type situation where we were calling the +C and us + + align:start position:0% + + + + align:start position:0% + +so that's kind of Step One + + align:start position:0% +so that's kind of Step One + + + align:start position:0% +so that's kind of Step One +step two is to factorize that theory + + align:start position:0% +step two is to factorize that theory + + + align:start position:0% +step two is to factorize that theory +which we know how to do + + align:start position:0% + + + + align:start position:0% + +in particular the ultra the sort of the + + align:start position:0% +in particular the ultra the sort of the + + + align:start position:0% +in particular the ultra the sort of the +Ultra Soft + + align:start position:0% +Ultra Soft + + + align:start position:0% +Ultra Soft +which is soft + + align:start position:0% +which is soft + + + align:start position:0% +which is soft +can be factorized with a field + + align:start position:0% +can be factorized with a field + + + align:start position:0% +can be factorized with a field +redefinition + + align:start position:0% + + + + align:start position:0% + +so this has the advantage that that this + + align:start position:0% +so this has the advantage that that this + + + align:start position:0% +so this has the advantage that that this +first stage we're still we still have a + + align:start position:0% +first stage we're still we still have a + + + align:start position:0% +first stage we're still we still have a +lot locality that protects us and helps + + align:start position:0% +lot locality that protects us and helps + + + align:start position:0% +lot locality that protects us and helps +us to understand the theory we then + + align:start position:0% +us to understand the theory we then + + + align:start position:0% +us to understand the theory we then +factorize and then in the third step + + align:start position:0% +factorize and then in the third step + + + align:start position:0% +factorize and then in the third step +we match sct1 onto sct2 + + align:start position:0% + + + + align:start position:0% + +and then we are just having we're + + align:start position:0% +and then we are just having we're + + + align:start position:0% +and then we are just having we're +getting rid of these hard linear modes + + align:start position:0% +getting rid of these hard linear modes + + + align:start position:0% +getting rid of these hard linear modes +matching them onto some linear modes + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +we still have our soft nodes + + align:start position:0% + + + + align:start position:0% + +so we think that the linear modes + + align:start position:0% +so we think that the linear modes + + + align:start position:0% +so we think that the linear modes +contain the hard cleaner modes contain + + align:start position:0% +contain the hard cleaner modes contain + + + align:start position:0% +contain the hard cleaner modes contain +the cleaner modes in the first stage but + + align:start position:0% +the cleaner modes in the first stage but + + + align:start position:0% +the cleaner modes in the first stage but +they also contain some other stuff which + + align:start position:0% +they also contain some other stuff which + + + align:start position:0% +they also contain some other stuff which +is unwanted baggage + + align:start position:0% +is unwanted baggage + + + align:start position:0% +is unwanted baggage +that we have to get rid of and that's + + align:start position:0% +that we have to get rid of and that's + + + align:start position:0% +that we have to get rid of and that's +why we have this second stage + + align:start position:0% +why we have this second stage + + + align:start position:0% +why we have this second stage +of matching + + align:start position:0% +of matching + + + align:start position:0% +of matching +but you can really think of it in the + + align:start position:0% +but you can really think of it in the + + + align:start position:0% +but you can really think of it in the +picture as doing first the matching we + + align:start position:0% +picture as doing first the matching we + + + align:start position:0% +picture as doing first the matching we +integrate out the hard scale but you + + align:start position:0% +integrate out the hard scale but you + + + align:start position:0% +integrate out the hard scale but you +contain in your effective Theory this + + align:start position:0% +contain in your effective Theory this + + + align:start position:0% +contain in your effective Theory this +scale Associated to the dashed line + + align:start position:0% +scale Associated to the dashed line + + + align:start position:0% +scale Associated to the dashed line +and then in the second stage you + + align:start position:0% +and then in the second stage you + + + align:start position:0% +and then in the second stage you +integrate out the dashed line + + align:start position:0% +integrate out the dashed line + + + align:start position:0% +integrate out the dashed line +and that gets YouTuber + + align:start position:0% +and that gets YouTuber + + + align:start position:0% +and that gets YouTuber +final thing you want which is just low + + align:start position:0% +final thing you want which is just low + + + align:start position:0% +final thing you want which is just low +energy modes on this line here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +one thing this does is give a simple + + align:start position:0% +one thing this does is give a simple + + + align:start position:0% +one thing this does is give a simple +procedure + + align:start position:0% +procedure + + + align:start position:0% +procedure +of constructing sct2 operators + + align:start position:0% +of constructing sct2 operators + + + align:start position:0% +of constructing sct2 operators +even though there's more non-locality in + + align:start position:0% +even though there's more non-locality in + + + align:start position:0% +even though there's more non-locality in +sct2 than there was in sct1 + + align:start position:0% + + + + align:start position:0% + +because there's non-locality because you + + align:start position:0% +because there's non-locality because you + + + align:start position:0% +because there's non-locality because you +don't just have this one scale that + + align:start position:0% +don't just have this one scale that + + + align:start position:0% +don't just have this one scale that +could cause non-locality you even have + + align:start position:0% +could cause non-locality you even have + + + align:start position:0% +could cause non-locality you even have +this smaller scale that's causing + + align:start position:0% +this smaller scale that's causing + + + align:start position:0% +this smaller scale that's causing +non-locality + + align:start position:0% +non-locality + + + align:start position:0% +non-locality +and that's that's explicit in the in the + + align:start position:0% +and that's that's explicit in the in the + + + align:start position:0% +and that's that's explicit in the in the +soft Wilson line the thing that's sort + + align:start position:0% +soft Wilson line the thing that's sort + + + align:start position:0% +soft Wilson line the thing that's sort +of giving the soft Wilson mind + + align:start position:0% +of giving the soft Wilson mind + + + align:start position:0% +of giving the soft Wilson mind +well the things that are producing the + + align:start position:0% +well the things that are producing the + + + align:start position:0% +well the things that are producing the +Wilson lines are really modes at this + + align:start position:0% +Wilson lines are really modes at this + + + align:start position:0% +Wilson lines are really modes at this +scale + + align:start position:0% + + + + align:start position:0% + +okay so it's more non-local + + align:start position:0% +okay so it's more non-local + + + align:start position:0% +okay so it's more non-local +one way of saying it's more non-local is + + align:start position:0% +one way of saying it's more non-local is + + + align:start position:0% +one way of saying it's more non-local is +simply that there'll be one over L + + align:start position:0% +simply that there'll be one over L + + + align:start position:0% +simply that there'll be one over L +pluses as well as one over L minuses + + align:start position:0% +pluses as well as one over L minuses + + + align:start position:0% +pluses as well as one over L minuses +that's another way of saying why it's + + align:start position:0% +that's another way of saying why it's + + + align:start position:0% +that's another way of saying why it's +more non-local + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +let's just do an example of something + + align:start position:0% +let's just do an example of something + + + align:start position:0% +let's just do an example of something +that makes it look trivial + + align:start position:0% +that makes it look trivial + + + align:start position:0% +that makes it look trivial +so let's say we wanted to do this + + align:start position:0% +so let's say we wanted to do this + + + align:start position:0% +so let's say we wanted to do this +calculation this way + + align:start position:0% +calculation this way + + + align:start position:0% +calculation this way +so then in step one we would simply + + align:start position:0% +so then in step one we would simply + + + align:start position:0% +so then in step one we would simply +write down the current in sct1 + + align:start position:0% + + + + align:start position:0% + +we would integrate out the offshell pink + + align:start position:0% +we would integrate out the offshell pink + + + align:start position:0% +we would integrate out the offshell pink +lines but there'd only be lines on one + + align:start position:0% +lines but there'd only be lines on one + + + align:start position:0% +lines but there'd only be lines on one +side and we get this + + align:start position:0% + + + + align:start position:0% + +which is our sct1 result for the heavy + + align:start position:0% +which is our sct1 result for the heavy + + + align:start position:0% +which is our sct1 result for the heavy +light crap + + align:start position:0% +light crap + + + align:start position:0% +light crap +then in step two we would do the field + + align:start position:0% +then in step two we would do the field + + + align:start position:0% +then in step two we would do the field +redefinition + + align:start position:0% + + + + align:start position:0% + +in order to factorize this Theory + + align:start position:0% + + + + align:start position:0% + +and we get that result + + align:start position:0% +and we get that result + + + align:start position:0% +and we get that result +and in step three + + align:start position:0% +and in step three + + + align:start position:0% +and in step three +in order to match this result onto a + + align:start position:0% +in order to match this result onto a + + + align:start position:0% +in order to match this result onto a +current in scc2 + + align:start position:0% + + + + align:start position:0% + +it's really simply a renaming here + + align:start position:0% + + + + align:start position:0% + +so why is this step so easy + + align:start position:0% +so why is this step so easy + + + align:start position:0% +so why is this step so easy +it looks completely trivial + + align:start position:0% +it looks completely trivial + + + align:start position:0% +it looks completely trivial +the reason that this step is so easy is + + align:start position:0% +the reason that this step is so easy is + + + align:start position:0% +the reason that this step is so easy is +that any tea product any time order + + align:start position:0% +that any tea product any time order + + + align:start position:0% +that any tea product any time order +product that you write down here will + + align:start position:0% +product that you write down here will + + + align:start position:0% +product that you write down here will +have a correspondence in this other case + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so when so if it's really that simple + + align:start position:0% +so when so if it's really that simple + + + align:start position:0% +so when so if it's really that simple +then you can see the advantages of this + + align:start position:0% +then you can see the advantages of this + + + align:start position:0% +then you can see the advantages of this +procedure + + align:start position:0% +procedure + + + align:start position:0% +procedure +it's not always that simple + + align:start position:0% + + + + align:start position:0% + +and let me present as a kind of theorem + + align:start position:0% +and let me present as a kind of theorem + + + align:start position:0% +and let me present as a kind of theorem +or just a bit of a statement + + align:start position:0% +or just a bit of a statement + + + align:start position:0% +or just a bit of a statement +why when it will be this simple and when + + align:start position:0% +why when it will be this simple and when + + + align:start position:0% +why when it will be this simple and when +it will not be this simple + + align:start position:0% + + + + align:start position:0% + +so basically you have to know when will + + align:start position:0% +so basically you have to know when will + + + align:start position:0% +so basically you have to know when will +the tea products between these two + + align:start position:0% +the tea products between these two + + + align:start position:0% +the tea products between these two +theories match up + + align:start position:0% +theories match up + + + align:start position:0% +theories match up +and the tea products will match up in + + align:start position:0% +and the tea products will match up in + + + align:start position:0% +and the tea products will match up in +the under the following circumstances + + align:start position:0% + + + + align:start position:0% + +or they won't match up under the + + align:start position:0% +or they won't match up under the + + + align:start position:0% +or they won't match up under the +following circumstances + + align:start position:0% + + + + align:start position:0% + +so if in this get one Theory + + align:start position:0% +so if in this get one Theory + + + align:start position:0% +so if in this get one Theory +you had time under products with greater + + align:start position:0% +you had time under products with greater + + + align:start position:0% +you had time under products with greater +than or equal to two + + align:start position:0% +than or equal to two + + + align:start position:0% +than or equal to two +operators that had soft and Colonial + + align:start position:0% +operators that had soft and Colonial + + + align:start position:0% +operators that had soft and Colonial +fields + + align:start position:0% + + + + align:start position:0% + +then you can generate some non-trivial + + align:start position:0% +then you can generate some non-trivial + + + align:start position:0% +then you can generate some non-trivial +matching + + align:start position:0% + + + + align:start position:0% + +so I think that's best illustrated by an + + align:start position:0% +so I think that's best illustrated by an + + + align:start position:0% +so I think that's best illustrated by an +example again so in this particular + + align:start position:0% +example again so in this particular + + + align:start position:0% +example again so in this particular +example up here we only had one operator + + align:start position:0% +example up here we only had one operator + + + align:start position:0% +example up here we only had one operator +that had both soft and cleaner Fields + + align:start position:0% +that had both soft and cleaner Fields + + + align:start position:0% +that had both soft and cleaner Fields +this external current + + align:start position:0% +this external current + + + align:start position:0% +this external current +and then we had lagrangians but they + + align:start position:0% +and then we had lagrangians but they + + + align:start position:0% +and then we had lagrangians but they +were totally decoupled after we made + + align:start position:0% +were totally decoupled after we made + + + align:start position:0% +were totally decoupled after we made +this filter definition the l0 lagrangian + + align:start position:0% +this filter definition the l0 lagrangian + + + align:start position:0% +this filter definition the l0 lagrangian +so they don't count as something that's + + align:start position:0% +so they don't count as something that's + + + align:start position:0% +so they don't count as something that's +mixing soft and cleaner fields we just + + align:start position:0% +mixing soft and cleaner fields we just + + + align:start position:0% +mixing soft and cleaner fields we just +had this operator + + align:start position:0% +had this operator + + + align:start position:0% +had this operator +but if you had two of these operators + + align:start position:0% +but if you had two of these operators + + + align:start position:0% +but if you had two of these operators +and you wanted to go through the same + + align:start position:0% +and you wanted to go through the same + + + align:start position:0% +and you wanted to go through the same +procedure then then you could get + + align:start position:0% +procedure then then you could get + + + align:start position:0% +procedure then then you could get +something non-trivial so let's imagine + + align:start position:0% +something non-trivial so let's imagine + + + align:start position:0% +something non-trivial so let's imagine +that scenario + + align:start position:0% + + + + align:start position:0% + +we had two operators + + align:start position:0% + + + + align:start position:0% + +think of having + + align:start position:0% + + + + align:start position:0% + +in this get one + + align:start position:0% +in this get one + + + align:start position:0% +in this get one +two interactions that are like this + + align:start position:0% +two interactions that are like this + + + align:start position:0% +two interactions that are like this +then we could string them together + + align:start position:0% +then we could string them together + + + align:start position:0% +then we could string them together +as follows + + align:start position:0% + + + + align:start position:0% + +so this is a tea product between two + + align:start position:0% +so this is a tea product between two + + + align:start position:0% +so this is a tea product between two +different interactions that both had + + align:start position:0% +different interactions that both had + + + align:start position:0% +different interactions that both had +soft and cleaning I'm just taking two of + + align:start position:0% +soft and cleaning I'm just taking two of + + + align:start position:0% +soft and cleaning I'm just taking two of +these guys putting them together and if + + align:start position:0% +these guys putting them together and if + + + align:start position:0% +these guys putting them together and if +you look at the off shellness of this + + align:start position:0% +you look at the off shellness of this + + + align:start position:0% +you look at the off shellness of this +line here + + align:start position:0% +line here + + + align:start position:0% +line here +then P Squared is of water in our + + align:start position:0% +then P Squared is of water in our + + + align:start position:0% +then P Squared is of water in our +accounting it's like it's a K plus times + + align:start position:0% +accounting it's like it's a K plus times + + + align:start position:0% +accounting it's like it's a K plus times +a q minus + + align:start position:0% +a q minus + + + align:start position:0% +a q minus +which is a q times a + + align:start position:0% + + + + align:start position:0% + +lot of the times a q + + align:start position:0% +lot of the times a q + + + align:start position:0% +lot of the times a q +so it's really something that lives at + + align:start position:0% +so it's really something that lives at + + + align:start position:0% +so it's really something that lives at +that Hard linear scale + + align:start position:0% +that Hard linear scale + + + align:start position:0% +that Hard linear scale +okay + + align:start position:0% + + + + align:start position:0% + +but you need two time two terms in the + + align:start position:0% +but you need two time two terms in the + + + align:start position:0% +but you need two time two terms in the +time order product that in order for the + + align:start position:0% +time order product that in order for the + + + align:start position:0% +time order product that in order for the +really to be a propagator like this that + + align:start position:0% +really to be a propagator like this that + + + align:start position:0% +really to be a propagator like this that +you're integrating out so this guy here + + align:start position:0% +you're integrating out so this guy here + + + align:start position:0% +you're integrating out so this guy here +will match onto something + + align:start position:0% +will match onto something + + + align:start position:0% +will match onto something +when you do this match and + + align:start position:0% +when you do this match and + + + align:start position:0% +when you do this match and +where you have sort of two soft fields + + align:start position:0% +where you have sort of two soft fields + + + align:start position:0% +where you have sort of two soft fields +and two cleaner fields + + align:start position:0% +and two cleaner fields + + + align:start position:0% +and two cleaner fields +like that + + align:start position:0% +like that + + + align:start position:0% +like that +because this guy here really is + + align:start position:0% +because this guy here really is + + + align:start position:0% +because this guy here really is +something that you would want to + + align:start position:0% +something that you would want to + + + align:start position:0% +something that you would want to +integrate out + + align:start position:0% +integrate out + + + align:start position:0% +integrate out +at that kind of dashed line it's a + + align:start position:0% +at that kind of dashed line it's a + + + align:start position:0% +at that kind of dashed line it's a +really it's an offshell hard cleaner + + align:start position:0% +really it's an offshell hard cleaner + + + align:start position:0% +really it's an offshell hard cleaner +mode + + align:start position:0% + + + + align:start position:0% + +but if you didn't have two tea products + + align:start position:0% +but if you didn't have two tea products + + + align:start position:0% +but if you didn't have two tea products +then you just effectively what happens + + align:start position:0% +then you just effectively what happens + + + align:start position:0% +then you just effectively what happens +is when you change the external + + align:start position:0% +is when you change the external + + + align:start position:0% +is when you change the external +kinematics in order to do the matching + + align:start position:0% +kinematics in order to do the matching + + + align:start position:0% +kinematics in order to do the matching +all the what were called hard collinear + + align:start position:0% +all the what were called hard collinear + + + align:start position:0% +all the what were called hard collinear +lines become collinear lines and then + + align:start position:0% +lines become collinear lines and then + + + align:start position:0% +lines become collinear lines and then +the matching is Trivial as it was up + + align:start position:0% +the matching is Trivial as it was up + + + align:start position:0% +the matching is Trivial as it was up +here + + align:start position:0% +here + + + align:start position:0% +here +but if you're in a situation like this + + align:start position:0% +but if you're in a situation like this + + + align:start position:0% +but if you're in a situation like this +then there is a line that you by + + align:start position:0% +then there is a line that you by + + + align:start position:0% +then there is a line that you by +changing these the scaling of these + + align:start position:0% +changing these the scaling of these + + + align:start position:0% +changing these the scaling of these +external guys it doesn't change the + + align:start position:0% +external guys it doesn't change the + + + align:start position:0% +external guys it doesn't change the +scaling of that internal line + + align:start position:0% +scaling of that internal line + + + align:start position:0% +scaling of that internal line +and then you get some non-trivial Wilson + + align:start position:0% +and then you get some non-trivial Wilson + + + align:start position:0% +and then you get some non-trivial Wilson +coefficient + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so let's call these HC + + align:start position:0% +so let's call these HC + + + align:start position:0% +so let's call these HC +yeah and so + + align:start position:0% +yeah and so + + + align:start position:0% +yeah and so +I I start by I I start by doing it + + align:start position:0% +I I start by I I start by doing it + + + align:start position:0% +I I start by I I start by doing it +calling them HC right + + align:start position:0% +calling them HC right + + + align:start position:0% +calling them HC right +and then what I want to do when I + + align:start position:0% +and then what I want to do when I + + + align:start position:0% +and then what I want to do when I +calculate this diagram to do the + + align:start position:0% +calculate this diagram to do the + + + align:start position:0% +calculate this diagram to do the +matching is I want to assign them + + align:start position:0% +matching is I want to assign them + + + align:start position:0% +matching is I want to assign them +a different scaling I want to Define + + align:start position:0% +a different scaling I want to Define + + + align:start position:0% +a different scaling I want to Define +them to be C instead of h c + + align:start position:0% +them to be C instead of h c + + + align:start position:0% +them to be C instead of h c +so I start out thinking of them as HC + + align:start position:0% +so I start out thinking of them as HC + + + align:start position:0% +so I start out thinking of them as HC +that's what I do in Step One + + align:start position:0% +that's what I do in Step One + + + align:start position:0% +that's what I do in Step One +I do the field I can do a field of a + + align:start position:0% +I do the field I can do a field of a + + + align:start position:0% +I do the field I can do a field of a +definition it doesn't matter + + align:start position:0% +definition it doesn't matter + + + align:start position:0% +definition it doesn't matter +but now I want to match from sct1 onto + + align:start position:0% +but now I want to match from sct1 onto + + + align:start position:0% +but now I want to match from sct1 onto +two so therefore what I do is I take my + + align:start position:0% +two so therefore what I do is I take my + + + align:start position:0% +two so therefore what I do is I take my +full Theory + + align:start position:0% +full Theory + + + align:start position:0% +full Theory +which is sct1 + + align:start position:0% +which is sct1 + + + align:start position:0% +which is sct1 +and I evaluate it with fields that have + + align:start position:0% +and I evaluate it with fields that have + + + align:start position:0% +and I evaluate it with fields that have +that don't have the right power counting + + align:start position:0% +that don't have the right power counting + + + align:start position:0% +that don't have the right power counting +for that theory and then I do a Taylor + + align:start position:0% +for that theory and then I do a Taylor + + + align:start position:0% +for that theory and then I do a Taylor +series expansion of all the diagrams so + + align:start position:0% +series expansion of all the diagrams so + + + align:start position:0% +series expansion of all the diagrams so +that's this I change my I change my + + align:start position:0% +that's this I change my I change my + + + align:start position:0% +that's this I change my I change my +external fields and I call them C + + align:start position:0% +external fields and I call them C + + + align:start position:0% +external fields and I call them C +instead of HC + + align:start position:0% +instead of HC + + + align:start position:0% +instead of HC +ultrasound so Ultra software really + + align:start position:0% +ultrasound so Ultra software really + + + align:start position:0% +ultrasound so Ultra software really +means and now I make them these soft but + + align:start position:0% +means and now I make them these soft but + + + align:start position:0% +means and now I make them these soft but +soft and Ultra Soft I just that's just + + align:start position:0% +soft and Ultra Soft I just that's just + + + align:start position:0% +soft and Ultra Soft I just that's just +really at renaming + + align:start position:0% +really at renaming + + + align:start position:0% +really at renaming +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +Ultra Soft is equal soft + + align:start position:0% +Ultra Soft is equal soft + + + align:start position:0% +Ultra Soft is equal soft +sorry maybe this makes it clearer Ultra + + align:start position:0% +sorry maybe this makes it clearer Ultra + + + align:start position:0% +sorry maybe this makes it clearer Ultra +Soft and soft are just two different + + align:start position:0% +Soft and soft are just two different + + + align:start position:0% +Soft and soft are just two different +names for the same thing + + align:start position:0% +names for the same thing + + + align:start position:0% +names for the same thing +but HC and C aren't because HC really + + align:start position:0% +but HC and C aren't because HC really + + + align:start position:0% +but HC and C aren't because HC really +lived on the hopper hyperbola I just put + + align:start position:0% +lived on the hopper hyperbola I just put + + + align:start position:0% +lived on the hopper hyperbola I just put +it I put the external particles onto the + + align:start position:0% +it I put the external particles onto the + + + align:start position:0% +it I put the external particles onto the +lower hyperbola but I'm frozen in here + + align:start position:0% +lower hyperbola but I'm frozen in here + + + align:start position:0% +lower hyperbola but I'm frozen in here +with one particle that stays in the + + align:start position:0% +with one particle that stays in the + + + align:start position:0% +with one particle that stays in the +upper hyperbola and therefore has to be + + align:start position:0% +upper hyperbola and therefore has to be + + + align:start position:0% +upper hyperbola and therefore has to be +integrated out + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the kind of thing that you would get + + align:start position:0% +so the kind of thing that you would get + + + align:start position:0% +so the kind of thing that you would get +by doing that + + align:start position:0% + + + + align:start position:0% + +is that you would get + + align:start position:0% + + + + align:start position:0% + +convolutions + + align:start position:0% +convolutions + + + align:start position:0% +convolutions +with some Wilson coefficient + + align:start position:0% + + + + align:start position:0% + +in this case there's sort of + + align:start position:0% + + + + align:start position:0% + +let me just say + + align:start position:0% +let me just say + + + align:start position:0% +let me just say +it depends on some P minuses + + align:start position:0% + + + + align:start position:0% + +E1 this is B2 + + align:start position:0% +E1 this is B2 + + + align:start position:0% +E1 this is B2 +and then there's in my example over + + align:start position:0% +and then there's in my example over + + + align:start position:0% +and then there's in my example over +there I guess I had some + + align:start position:0% +there I guess I had some + + + align:start position:0% +there I guess I had some +had some heavy quarks + + align:start position:0% + + + + align:start position:0% + +okay there's some direct structures but + + align:start position:0% + + + + align:start position:0% + +so it would be something like this where + + align:start position:0% +so it would be something like this where + + + align:start position:0% +so it would be something like this where +you'd get some function whatever it is + + align:start position:0% +you'd get some function whatever it is + + + align:start position:0% +you'd get some function whatever it is +that's coming exactly from integrating + + align:start position:0% +that's coming exactly from integrating + + + align:start position:0% +that's coming exactly from integrating +out the purple stuff so this is the + + align:start position:0% +out the purple stuff so this is the + + + align:start position:0% +out the purple stuff so this is the +Wilson coefficient + + align:start position:0% +Wilson coefficient + + + align:start position:0% +Wilson coefficient +and usually you would call these things + + align:start position:0% +and usually you would call these things + + + align:start position:0% +and usually you would call these things +kind of jet functions because + + align:start position:0% +kind of jet functions because + + + align:start position:0% +kind of jet functions because +they have they look like jet functions + + align:start position:0% + + + + align:start position:0% + +but this comes from + + align:start position:0% + + + + align:start position:0% + +it's got y nodes that got integrated out + + align:start position:0% +it's got y nodes that got integrated out + + + align:start position:0% +it's got y nodes that got integrated out +so the difference between this + + align:start position:0% +so the difference between this + + + align:start position:0% +so the difference between this +and sort of set one matching where + + align:start position:0% +and sort of set one matching where + + + align:start position:0% +and sort of set one matching where +you're integrating with the hard scale + + align:start position:0% +you're integrating with the hard scale + + + align:start position:0% +you're integrating with the hard scale +is you're already getting sensitivity + + align:start position:0% +is you're already getting sensitivity + + + align:start position:0% +is you're already getting sensitivity +here to the plus momentum of the soft + + align:start position:0% +here to the plus momentum of the soft + + + align:start position:0% +here to the plus momentum of the soft +it's kind of one difference + + align:start position:0% + + + + align:start position:0% + +okay so this is a general procedure for + + align:start position:0% +okay so this is a general procedure for + + + align:start position:0% +okay so this is a general procedure for +constructing sct2 + + align:start position:0% + + + + align:start position:0% + +see how much I want to say so let's say + + align:start position:0% +see how much I want to say so let's say + + + align:start position:0% +see how much I want to say so let's say +a few words about power Counting + + align:start position:0% +a few words about power Counting + + + align:start position:0% +a few words about power Counting +so if you take some tea product of terms + + align:start position:0% +so if you take some tea product of terms + + + align:start position:0% +so if you take some tea product of terms +in sct1 + + align:start position:0% +in sct1 + + + align:start position:0% +in sct1 +that will scale like some power of + + align:start position:0% +that will scale like some power of + + + align:start position:0% +that will scale like some power of +Lambda to the 2K + + align:start position:0% +Lambda to the 2K + + + align:start position:0% +Lambda to the 2K +okay so ins get one + + align:start position:0% +okay so ins get one + + + align:start position:0% +okay so ins get one +you have to be a little bit careful + + align:start position:0% +you have to be a little bit careful + + + align:start position:0% +you have to be a little bit careful +about power counting when you do this + + align:start position:0% +about power counting when you do this + + + align:start position:0% +about power counting when you do this +procedure so in sket one you could just + + align:start position:0% +procedure so in sket one you could just + + + align:start position:0% +procedure so in sket one you could just +assign some power let's call it Lambda + + align:start position:0% +assign some power let's call it Lambda + + + align:start position:0% +assign some power let's call it Lambda +to the 2K + + align:start position:0% +to the 2K + + + align:start position:0% +to the 2K +and when you do a matching onto operator + + align:start position:0% +and when you do a matching onto operator + + + align:start position:0% +and when you do a matching onto operator +and sket2 + + align:start position:0% +and sket2 + + + align:start position:0% +and sket2 +what you're generically going to find is + + align:start position:0% +what you're generically going to find is + + + align:start position:0% +what you're generically going to find is +that you'll get + + align:start position:0% +that you'll get + + + align:start position:0% +that you'll get +there'll be a relation between the power + + align:start position:0% +there'll be a relation between the power + + + align:start position:0% +there'll be a relation between the power +counting here and the power counting + + align:start position:0% +counting here and the power counting + + + align:start position:0% +counting here and the power counting +there which is good + + align:start position:0% +there which is good + + + align:start position:0% +there which is good +but there's also sort of one kind of + + align:start position:0% +but there's also sort of one kind of + + + align:start position:0% +but there's also sort of one kind of +thing to be aware of + + align:start position:0% + + + + align:start position:0% + +so if I Define + + align:start position:0% +so if I Define + + + align:start position:0% +so if I Define +ETA to be the power counting parameter + + align:start position:0% +ETA to be the power counting parameter + + + align:start position:0% +ETA to be the power counting parameter +for sct2 just to give it a different + + align:start position:0% +for sct2 just to give it a different + + + align:start position:0% +for sct2 just to give it a different +name so I can talk about the + + align:start position:0% +name so I can talk about the + + + align:start position:0% +name so I can talk about the +correspondence then basically Ada is + + align:start position:0% +correspondence then basically Ada is + + + align:start position:0% +correspondence then basically Ada is +like Lambda squared + + align:start position:0% +like Lambda squared + + + align:start position:0% +like Lambda squared +and that + + align:start position:0% +and that + + + align:start position:0% +and that +um + + align:start position:0% + + + + align:start position:0% + +well that just follows from this formula + + align:start position:0% +well that just follows from this formula + + + align:start position:0% +well that just follows from this formula +that they're if you want to identify + + align:start position:0% +that they're if you want to identify + + + align:start position:0% +that they're if you want to identify +Lambda squared is Lambda over Q for the + + align:start position:0% +Lambda squared is Lambda over Q for the + + + align:start position:0% +Lambda squared is Lambda over Q for the +collinear modes then + + align:start position:0% +collinear modes then + + + align:start position:0% +collinear modes then +this would be the right way of doing it + + align:start position:0% +this would be the right way of doing it + + + align:start position:0% +this would be the right way of doing it +Lambo little Lambda would be square root + + align:start position:0% +Lambo little Lambda would be square root + + + align:start position:0% +Lambo little Lambda would be square root +of Lambda over q but in sct1 for the + + align:start position:0% +of Lambda over q but in sct1 for the + + + align:start position:0% +of Lambda over q but in sct1 for the +cleaner modes you'd say there's some + + align:start position:0% +cleaner modes you'd say there's some + + + align:start position:0% +cleaner modes you'd say there's some +parameter Ada which is just Lambda over + + align:start position:0% +parameter Ada which is just Lambda over + + + align:start position:0% +parameter Ada which is just Lambda over +Q + + align:start position:0% +Q + + + align:start position:0% +Q +okay so basically it looks like you just + + align:start position:0% +okay so basically it looks like you just + + + align:start position:0% +okay so basically it looks like you just +take 2K and go over to K because you + + align:start position:0% +take 2K and go over to K because you + + + align:start position:0% +take 2K and go over to K because you +just change the definition of what + + align:start position:0% +just change the definition of what + + + align:start position:0% +just change the definition of what +you're calling the parameter but there's + + align:start position:0% +you're calling the parameter but there's + + + align:start position:0% +you're calling the parameter but there's +also this plus e + + align:start position:0% +also this plus e + + + align:start position:0% +also this plus e +that means it can you can get additional + + align:start position:0% +that means it can you can get additional + + + align:start position:0% +that means it can you can get additional +suppression + + align:start position:0% +suppression + + + align:start position:0% +suppression +and that plus e comes about from the + + align:start position:0% +and that plus e comes about from the + + + align:start position:0% +and that plus e comes about from the +fact that you also change the power + + align:start position:0% +fact that you also change the power + + + align:start position:0% +fact that you also change the power +counting for your external Fields when + + align:start position:0% +counting for your external Fields when + + + align:start position:0% +counting for your external Fields when +you do this procedure so something that + + align:start position:0% +you do this procedure so something that + + + align:start position:0% +you do this procedure so something that +was scaling like Lambda and the hard + + align:start position:0% +was scaling like Lambda and the hard + + + align:start position:0% +was scaling like Lambda and the hard +linear Theory might become Lambda + + align:start position:0% +linear Theory might become Lambda + + + align:start position:0% +linear Theory might become Lambda +squared I.E ETA + + align:start position:0% +squared I.E ETA + + + align:start position:0% +squared I.E ETA +in the sct2 theory + + align:start position:0% + + + + align:start position:0% + +so this e which is greater than zero + + align:start position:0% + + + + align:start position:0% + +changing the power counting of external + + align:start position:0% +changing the power counting of external + + + align:start position:0% +changing the power counting of external +fields + + align:start position:0% + + + + align:start position:0% + +Magic + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +this is one example is just having an + + align:start position:0% +this is one example is just having an + + + align:start position:0% +this is one example is just having an +external cleaner Quark or external + + align:start position:0% +external cleaner Quark or external + + + align:start position:0% +external cleaner Quark or external +cleaner purple glue on for example where + + align:start position:0% +cleaner purple glue on for example where + + + align:start position:0% +cleaner purple glue on for example where +you'd have C + + align:start position:0% +you'd have C + + + align:start position:0% +you'd have C +of order Lambda and sct1 and it becomes + + align:start position:0% +of order Lambda and sct1 and it becomes + + + align:start position:0% +of order Lambda and sct1 and it becomes +a border Ada and sct2 which is Lambda + + align:start position:0% +a border Ada and sct2 which is Lambda + + + align:start position:0% +a border Ada and sct2 which is Lambda +squared so that's an extra power of lam + + align:start position:0% +squared so that's an extra power of lam + + + align:start position:0% +squared so that's an extra power of lam +those extra factors of the power + + align:start position:0% +those extra factors of the power + + + align:start position:0% +those extra factors of the power +counting parameter + + align:start position:0% +counting parameter + + + align:start position:0% +counting parameter +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +what do we learn if we put all these + + align:start position:0% +what do we learn if we put all these + + + align:start position:0% +what do we learn if we put all these +things together + + align:start position:0% +things together + + + align:start position:0% +things together +well one thing + + align:start position:0% +well one thing + + + align:start position:0% +well one thing +since SCT since the soft and the cleaner + + align:start position:0% +since SCT since the soft and the cleaner + + + align:start position:0% +since SCT since the soft and the cleaner +Fields don't talk to each other when you + + align:start position:0% +Fields don't talk to each other when you + + + align:start position:0% +Fields don't talk to each other when you +write down lagrangians for them they're + + align:start position:0% +write down lagrangians for them they're + + + align:start position:0% +write down lagrangians for them they're +totally decoupled right from the start + + align:start position:0% +totally decoupled right from the start + + + align:start position:0% +totally decoupled right from the start +and so there's actually no + + align:start position:0% + + + + align:start position:0% + +mixed soft collinear lagrangian at + + align:start position:0% +mixed soft collinear lagrangian at + + + align:start position:0% +mixed soft collinear lagrangian at +leading order + + align:start position:0% + + + + align:start position:0% + +and so all the meat of this theory is + + align:start position:0% +and so all the meat of this theory is + + + align:start position:0% +and so all the meat of this theory is +coming about when you integrate out + + align:start position:0% +coming about when you integrate out + + + align:start position:0% +coming about when you integrate out +these offshore nodes and you construct + + align:start position:0% +these offshore nodes and you construct + + + align:start position:0% +these offshore nodes and you construct +the external operators + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +let's say a little bit more about power + + align:start position:0% +let's say a little bit more about power + + + align:start position:0% +let's say a little bit more about power +Counting + + align:start position:0% +Counting + + + align:start position:0% +Counting +so there's no mix-off cleaner lagrangea + + align:start position:0% +so there's no mix-off cleaner lagrangea + + + align:start position:0% +so there's no mix-off cleaner lagrangea +leading order and you can have + + align:start position:0% +leading order and you can have + + + align:start position:0% +leading order and you can have +you can get mixed things at sublitting + + align:start position:0% +you can get mixed things at sublitting + + + align:start position:0% +you can get mixed things at sublitting +litter + + align:start position:0% + + + + align:start position:0% + +so in that way it's like sct1 after the + + align:start position:0% +so in that way it's like sct1 after the + + + align:start position:0% +so in that way it's like sct1 after the +field redefinition + + align:start position:0% + + + + align:start position:0% + +but here there's no analog if you just + + align:start position:0% +but here there's no analog if you just + + + align:start position:0% +but here there's no analog if you just +want to go directly to sct2 there + + align:start position:0% +want to go directly to sct2 there + + + align:start position:0% +want to go directly to sct2 there +wouldn't be an analog of the filter + + align:start position:0% +wouldn't be an analog of the filter + + + align:start position:0% +wouldn't be an analog of the filter +definition + + align:start position:0% + + + + align:start position:0% + +all the Wilson lines are coming from + + align:start position:0% +all the Wilson lines are coming from + + + align:start position:0% +all the Wilson lines are coming from +integrating off-shell particles + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +in order to speed up a little + + align:start position:0% +in order to speed up a little + + + align:start position:0% +in order to speed up a little +I'm going to skip over one thing which I + + align:start position:0% +I'm going to skip over one thing which I + + + align:start position:0% +I'm going to skip over one thing which I +don't think I need so you can write down + + align:start position:0% +don't think I need so you can write down + + + align:start position:0% +don't think I need so you can write down +power counting formulas like we did in + + align:start position:0% +power counting formulas like we did in + + + align:start position:0% +power counting formulas like we did in +Kyle perturbation Theory maybe I'll just + + align:start position:0% +Kyle perturbation Theory maybe I'll just + + + align:start position:0% +Kyle perturbation Theory maybe I'll just +write those formulas down + + align:start position:0% +write those formulas down + + + align:start position:0% +write those formulas down +so + + align:start position:0% +so + + + align:start position:0% +so +in general + + align:start position:0% + + + + align:start position:0% + +in Kyle perturbation Theory we had a + + align:start position:0% +in Kyle perturbation Theory we had a + + + align:start position:0% +in Kyle perturbation Theory we had a +formula that said if we want to figure + + align:start position:0% +formula that said if we want to figure + + + align:start position:0% +formula that said if we want to figure +out the power counting of Any Given + + align:start position:0% +out the power counting of Any Given + + + align:start position:0% +out the power counting of Any Given +diagram we can have a counting for that + + align:start position:0% +diagram we can have a counting for that + + + align:start position:0% +diagram we can have a counting for that +diagram and we know how what size it is + + align:start position:0% +diagram and we know how what size it is + + + align:start position:0% +diagram and we know how what size it is +and there's analogous formulas like that + + align:start position:0% +and there's analogous formulas like that + + + align:start position:0% +and there's analogous formulas like that +in both sct1 and sct2 + + align:start position:0% +in both sct1 and sct2 + + + align:start position:0% +in both sct1 and sct2 +so + + align:start position:0% +so + + + align:start position:0% +so +in fct1 it's pretty simple you say you + + align:start position:0% +in fct1 it's pretty simple you say you + + + align:start position:0% +in fct1 it's pretty simple you say you +have something that's ordered Lambda to + + align:start position:0% +have something that's ordered Lambda to + + + align:start position:0% +have something that's ordered Lambda to +the delta + + align:start position:0% +the delta + + + align:start position:0% +the delta +then Delta the formula for it is the + + align:start position:0% +then Delta the formula for it is the + + + align:start position:0% +then Delta the formula for it is the +follows + + align:start position:0% + + + + align:start position:0% + +this is very analogous to what we talked + + align:start position:0% +this is very analogous to what we talked + + + align:start position:0% +this is very analogous to what we talked +about for cloud protonation Theory + + align:start position:0% + + + + align:start position:0% + +so these guys here + + align:start position:0% +so these guys here + + + align:start position:0% +so these guys here +are vertices that are purely Ultra Soft + + align:start position:0% + + + + align:start position:0% + +and if you have purely ultrasoft + + align:start position:0% +and if you have purely ultrasoft + + + align:start position:0% +and if you have purely ultrasoft +vertices you're subtracting eight + + align:start position:0% +vertices you're subtracting eight + + + align:start position:0% +vertices you're subtracting eight +because the measure of the Ultra Soft + + align:start position:0% +because the measure of the Ultra Soft + + + align:start position:0% +because the measure of the Ultra Soft +particles is eight + + align:start position:0% +particles is eight + + + align:start position:0% +particles is eight +I'm not deriving this for you I could + + align:start position:0% +I'm not deriving this for you I could + + + align:start position:0% +I'm not deriving this for you I could +but + + align:start position:0% +but + + + align:start position:0% +but +um I think it's fairly intuitive so if + + align:start position:0% +um I think it's fairly intuitive so if + + + align:start position:0% +um I think it's fairly intuitive so if +you think about the lowest order Cut + + align:start position:0% +you think about the lowest order Cut + + + align:start position:0% +you think about the lowest order Cut +lagrangian + + align:start position:0% +lagrangian + + + align:start position:0% +lagrangian +so sidebar ID slash PSI for ultrasofts + + align:start position:0% +so sidebar ID slash PSI for ultrasofts + + + align:start position:0% +so sidebar ID slash PSI for ultrasofts +this would already be something that's + + align:start position:0% +this would already be something that's + + + align:start position:0% +this would already be something that's +Lambda to the eight + + align:start position:0% +Lambda to the eight + + + align:start position:0% +Lambda to the eight +and this is then leading order so you + + align:start position:0% +and this is then leading order so you + + + align:start position:0% +and this is then leading order so you +subtract eight + + align:start position:0% +subtract eight + + + align:start position:0% +subtract eight +in the clip and this guy here is the + + align:start position:0% +in the clip and this guy here is the + + + align:start position:0% +in the clip and this guy here is the +rest this is sort of anything mixed + + align:start position:0% +rest this is sort of anything mixed + + + align:start position:0% +rest this is sort of anything mixed +or purely collinear + + align:start position:0% + + + + align:start position:0% + +and then for that guy you subtract four + + align:start position:0% +and then for that guy you subtract four + + + align:start position:0% +and then for that guy you subtract four +because as soon as you have at least one + + align:start position:0% +because as soon as you have at least one + + + align:start position:0% +because as soon as you have at least one +linear particle then you have to use the + + align:start position:0% +linear particle then you have to use the + + + align:start position:0% +linear particle then you have to use the +clinier measure + + align:start position:0% +clinier measure + + + align:start position:0% +clinier measure +and so here some operator like c bar + + align:start position:0% +and so here some operator like c bar + + + align:start position:0% +and so here some operator like c bar +and Dot DC was order allowed into the + + align:start position:0% +and Dot DC was order allowed into the + + + align:start position:0% +and Dot DC was order allowed into the +floor so you subtract four and that's + + align:start position:0% +floor so you subtract four and that's + + + align:start position:0% +floor so you subtract four and that's +leading order + + align:start position:0% +leading order + + + align:start position:0% +leading order +and so what this formula allows you to + + align:start position:0% +and so what this formula allows you to + + + align:start position:0% +and so what this formula allows you to +do is is really just you do power + + align:start position:0% +do is is really just you do power + + + align:start position:0% +do is is really just you do power +counting entirely in terms of vertices + + align:start position:0% +counting entirely in terms of vertices + + + align:start position:0% +counting entirely in terms of vertices +you never have to power count measures + + align:start position:0% +you never have to power count measures + + + align:start position:0% +you never have to power count measures +for Loops or power count propagators you + + align:start position:0% +for Loops or power count propagators you + + + align:start position:0% +for Loops or power count propagators you +just count vertices + + align:start position:0% +just count vertices + + + align:start position:0% +just count vertices +so if you want to know how how big a + + align:start position:0% +so if you want to know how how big a + + + align:start position:0% +so if you want to know how how big a +time under product is and it's a time + + align:start position:0% +time under product is and it's a time + + + align:start position:0% +time under product is and it's a time +order product of an L3 + + align:start position:0% +order product of an L3 + + + align:start position:0% +order product of an L3 +with an L2 + + align:start position:0% +with an L2 + + + align:start position:0% +with an L2 +with this kind of setup + + align:start position:0% +with this kind of setup + + + align:start position:0% +with this kind of setup +this will be basically you countless as + + align:start position:0% +this will be basically you countless as + + + align:start position:0% +this will be basically you countless as +Lambda 5. + + align:start position:0% + + + + align:start position:0% + +and you could even even get the sort of + + align:start position:0% +and you could even even get the sort of + + + align:start position:0% +and you could even even get the sort of +absolute size right taking to count the + + align:start position:0% +absolute size right taking to count the + + + align:start position:0% +absolute size right taking to count the +scaling of external particles + + align:start position:0% +scaling of external particles + + + align:start position:0% +scaling of external particles +and that's what this sort of constant + + align:start position:0% +and that's what this sort of constant + + + align:start position:0% +and that's what this sort of constant +prefactor does + + align:start position:0% + + + + align:start position:0% + +U is equal to one + + align:start position:0% +U is equal to one + + + align:start position:0% +U is equal to one +only for Pure pure Ultra Soft + + align:start position:0% + + + + align:start position:0% + +otherwise it's zero + + align:start position:0% + + + + align:start position:0% + +okay so there's formulas like this and + + align:start position:0% +okay so there's formulas like this and + + + align:start position:0% +okay so there's formulas like this and +there's an analogous one in sct2 which + + align:start position:0% +there's an analogous one in sct2 which + + + align:start position:0% +there's an analogous one in sct2 which +is a little more complicated + + align:start position:0% +is a little more complicated + + + align:start position:0% +is a little more complicated +but it allows you just to have a power + + align:start position:0% +but it allows you just to have a power + + + align:start position:0% +but it allows you just to have a power +counting where you can just power count + + align:start position:0% +counting where you can just power count + + + align:start position:0% +counting where you can just power count +lagrangians or operators + + align:start position:0% + + + + align:start position:0% + +go on + + align:start position:0% + + + + align:start position:0% + +without having to worry about kind of + + align:start position:0% +without having to worry about kind of + + + align:start position:0% +without having to worry about kind of +what propagators are do I have in this + + align:start position:0% +what propagators are do I have in this + + + align:start position:0% +what propagators are do I have in this +time of the product what Loops do I have + + align:start position:0% +time of the product what Loops do I have + + + align:start position:0% +time of the product what Loops do I have +you never have to ask those questions + + align:start position:0% +you never have to ask those questions + + + align:start position:0% +you never have to ask those questions +you're so power counting at vertices + + align:start position:0% +you're so power counting at vertices + + + align:start position:0% +you're so power counting at vertices +that makes things + + align:start position:0% +that makes things + + + align:start position:0% +that makes things +quite easy + + align:start position:0% +quite easy + + + align:start position:0% +quite easy +questions yeah + + align:start position:0% + + + + align:start position:0% + +that's right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so I want to do a couple of examples in + + align:start position:0% +so I want to do a couple of examples in + + + align:start position:0% +so I want to do a couple of examples in +sct2 + + align:start position:0% + + + + align:start position:0% + +so let's do an example + + align:start position:0% +so let's do an example + + + align:start position:0% +so let's do an example +Let's do an example + + align:start position:0% +Let's do an example + + + align:start position:0% +Let's do an example +which is in some ways simple and + + align:start position:0% + + + + align:start position:0% + +exclusive analog of our dis example and + + align:start position:0% +exclusive analog of our dis example and + + + align:start position:0% +exclusive analog of our dis example and +it's called the photon Pion form factor + + align:start position:0% +it's called the photon Pion form factor + + + align:start position:0% +it's called the photon Pion form factor +so it's exclusive there's a there's it's + + align:start position:0% +so it's exclusive there's a there's it's + + + align:start position:0% +so it's exclusive there's a there's it's +clearly exclusive there's a Pion + + align:start position:0% +clearly exclusive there's a Pion + + + align:start position:0% +clearly exclusive there's a Pion +and really that all that's going to come + + align:start position:0% +and really that all that's going to come + + + align:start position:0% +and really that all that's going to come +in here is kind of hard clinical + + align:start position:0% +in here is kind of hard clinical + + + align:start position:0% +in here is kind of hard clinical +factorization + + align:start position:0% +factorization + + + align:start position:0% +factorization +so it's simple in the way that + + align:start position:0% +so it's simple in the way that + + + align:start position:0% +so it's simple in the way that +that actually is not really exploiting + + align:start position:0% +that actually is not really exploiting + + + align:start position:0% +that actually is not really exploiting +the full complications of sct2 + + align:start position:0% +the full complications of sct2 + + + align:start position:0% +the full complications of sct2 +it's really just another example where + + align:start position:0% +it's really just another example where + + + align:start position:0% +it's really just another example where +we have hard modes factoring from linear + + align:start position:0% +we have hard modes factoring from linear + + + align:start position:0% +we have hard modes factoring from linear +modes but they're clearly sct2 modes + + align:start position:0% +modes but they're clearly sct2 modes + + + align:start position:0% +modes but they're clearly sct2 modes +because they're going to be modes for + + align:start position:0% +because they're going to be modes for + + + align:start position:0% +because they're going to be modes for +this Pion + + align:start position:0% +this Pion + + + align:start position:0% +this Pion +so we're going to use again in this for + + align:start position:0% +so we're going to use again in this for + + + align:start position:0% +so we're going to use again in this for +this calculation a bright frame + + align:start position:0% +this calculation a bright frame + + + align:start position:0% +this calculation a bright frame +um which you'll see I guess when I write + + align:start position:0% +um which you'll see I guess when I write + + + align:start position:0% +um which you'll see I guess when I write +down some momenta so + + align:start position:0% +down some momenta so + + + align:start position:0% +down some momenta so +what would you write down for this + + align:start position:0% +what would you write down for this + + + align:start position:0% +what would you write down for this +process in qcd first of all + + align:start position:0% +process in qcd first of all + + + align:start position:0% +process in qcd first of all +so you'd say I have a pi zero + + align:start position:0% +so you'd say I have a pi zero + + + align:start position:0% +so you'd say I have a pi zero +has some momentum P pi + + align:start position:0% +has some momentum P pi + + + align:start position:0% +has some momentum P pi +I have some current which I can take it + + align:start position:0% +I have some current which I can take it + + + align:start position:0% +I have some current which I can take it +zero and I want to make a transition + + align:start position:0% +zero and I want to make a transition + + + align:start position:0% +zero and I want to make a transition +from the pi zero to a single photon + + align:start position:0% + + + + align:start position:0% + +so you could write that as follows + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +I can always replace the photon by + + align:start position:0% +I can always replace the photon by + + + align:start position:0% +I can always replace the photon by +current + + align:start position:0% + + + + align:start position:0% + +and then I can parametrize that Matrix + + align:start position:0% +and then I can parametrize that Matrix + + + align:start position:0% +and then I can parametrize that Matrix +element like a form factor + + align:start position:0% + + + + align:start position:0% + +and if we go through things like parity + + align:start position:0% +and if we go through things like parity + + + align:start position:0% +and if we go through things like parity +charge conjugation and stuff like that + + align:start position:0% +charge conjugation and stuff like that + + + align:start position:0% +charge conjugation and stuff like that +time reversal + + align:start position:0% +time reversal + + + align:start position:0% +time reversal +if we find out that it's there's one + + align:start position:0% +if we find out that it's there's one + + + align:start position:0% +if we find out that it's there's one +real form factor and there's an Epsilon + + align:start position:0% +real form factor and there's an Epsilon + + + align:start position:0% +real form factor and there's an Epsilon +symbol + + align:start position:0% +symbol + + + align:start position:0% +symbol +in this guy it has to be linear in the + + align:start position:0% +in this guy it has to be linear in the + + + align:start position:0% +in this guy it has to be linear in the +polarization Vector that was already + + align:start position:0% +polarization Vector that was already + + + align:start position:0% +polarization Vector that was already +true here + + align:start position:0% +true here + + + align:start position:0% +true here +and there's sort of one way of getting + + align:start position:0% +and there's sort of one way of getting + + + align:start position:0% +and there's sort of one way of getting +the indices to work out which is with + + align:start position:0% +the indices to work out which is with + + + align:start position:0% +the indices to work out which is with +this Epsilon + + align:start position:0% +this Epsilon + + + align:start position:0% +this Epsilon +so what you're really after when you in + + align:start position:0% +so what you're really after when you in + + + align:start position:0% +so what you're really after when you in +this process would be sort of some + + align:start position:0% +this process would be sort of some + + + align:start position:0% +this process would be sort of some +understanding of this form factor that's + + align:start position:0% +understanding of this form factor that's + + + align:start position:0% +understanding of this form factor that's +the one piece of non-perturbative + + align:start position:0% +the one piece of non-perturbative + + + align:start position:0% +the one piece of non-perturbative +information everything else lorenscent + + align:start position:0% +information everything else lorenscent + + + align:start position:0% +information everything else lorenscent +variance is enough to tell you about + + align:start position:0% +variance is enough to tell you about + + + align:start position:0% +variance is enough to tell you about +so we'd like to see if there's a + + align:start position:0% +so we'd like to see if there's a + + + align:start position:0% +so we'd like to see if there's a +factorization theorem for that + + align:start position:0% +factorization theorem for that + + + align:start position:0% +factorization theorem for that +form factor + + align:start position:0% + + + + align:start position:0% + +if we take the limit where Q squared is + + align:start position:0% +if we take the limit where Q squared is + + + align:start position:0% +if we take the limit where Q squared is +large + + align:start position:0% + + + + align:start position:0% + +okay so we have an electromagnetic + + align:start position:0% +okay so we have an electromagnetic + + + align:start position:0% +okay so we have an electromagnetic +current + + align:start position:0% + + + + align:start position:0% + +and think about it as up and down quarks + + align:start position:0% +and think about it as up and down quarks + + + align:start position:0% +and think about it as up and down quarks +a Pion + + align:start position:0% + + + + align:start position:0% + +e so there's some Matrix + + align:start position:0% +e so there's some Matrix + + + align:start position:0% +e so there's some Matrix +in the two by two space which is the + + align:start position:0% +in the two by two space which is the + + + align:start position:0% +in the two by two space which is the +charge + + align:start position:0% +charge + + + align:start position:0% +charge +which you can write just + + align:start position:0% +which you can write just + + + align:start position:0% +which you can write just +two-thirds minus a third + + align:start position:0% +two-thirds minus a third + + + align:start position:0% +two-thirds minus a third +that or if you wanted to write in terms + + align:start position:0% +that or if you wanted to write in terms + + + align:start position:0% +that or if you wanted to write in terms +of poly matrices you could write it as + + align:start position:0% +of poly matrices you could write it as + + + align:start position:0% +of poly matrices you could write it as +identity over six + + align:start position:0% + + + + align:start position:0% + +three for + + align:start position:0% +three for + + + align:start position:0% +three for +isospin polymatrix over two + + align:start position:0% +isospin polymatrix over two + + + align:start position:0% +isospin polymatrix over two +okay so some charge Matrix is going to + + align:start position:0% +okay so some charge Matrix is going to + + + align:start position:0% +okay so some charge Matrix is going to +show up + + align:start position:0% +show up + + + align:start position:0% +show up +what happens if we expand for Q squared + + align:start position:0% +what happens if we expand for Q squared + + + align:start position:0% +what happens if we expand for Q squared +much greater than Lambda qcd squared + + align:start position:0% +much greater than Lambda qcd squared + + + align:start position:0% +much greater than Lambda qcd squared +in this formula over here this form + + align:start position:0% +in this formula over here this form + + + align:start position:0% +in this formula over here this form +factor knows about Lambda qcd and it + + align:start position:0% +factor knows about Lambda qcd and it + + + align:start position:0% +factor knows about Lambda qcd and it +knows about Q squared and we haven't + + align:start position:0% +knows about Q squared and we haven't + + + align:start position:0% +knows about Q squared and we haven't +expanded + + align:start position:0% +expanded + + + align:start position:0% +expanded +so what what happens if we do expand can + + align:start position:0% +so what what happens if we do expand can + + + align:start position:0% +so what what happens if we do expand can +we simplify that form factor + + align:start position:0% +we simplify that form factor + + + align:start position:0% +we simplify that form factor +and it does + + align:start position:0% +and it does + + + align:start position:0% +and it does +so I'm going to do this in the bright + + align:start position:0% +so I'm going to do this in the bright + + + align:start position:0% +so I'm going to do this in the bright +frame again + + align:start position:0% + + + + align:start position:0% + +and that effectively means I'm taking + + align:start position:0% +and that effectively means I'm taking + + + align:start position:0% +and that effectively means I'm taking +the momentum + + align:start position:0% +the momentum + + + align:start position:0% +the momentum +that corresponds to this the offshell + + align:start position:0% +that corresponds to this the offshell + + + align:start position:0% +that corresponds to this the offshell +photon as + + align:start position:0% +photon as + + + align:start position:0% +photon as +same form as we did before for our + + align:start position:0% +same form as we did before for our + + + align:start position:0% +same form as we did before for our +calculation in dis + + align:start position:0% + + + + align:start position:0% + +purely in the z z coordinate + + align:start position:0% + + + + align:start position:0% + +the momentum of the photon it's a + + align:start position:0% +the momentum of the photon it's a + + + align:start position:0% +the momentum of the photon it's a +non-shell thing so I can just write it + + align:start position:0% +non-shell thing so I can just write it + + + align:start position:0% +non-shell thing so I can just write it +as e of the photon say times a light + + align:start position:0% +as e of the photon say times a light + + + align:start position:0% +as e of the photon say times a light +like vector then P gamma squared will be + + align:start position:0% +like vector then P gamma squared will be + + + align:start position:0% +like vector then P gamma squared will be +zero as we want it to be + + align:start position:0% +zero as we want it to be + + + align:start position:0% +zero as we want it to be +and if I pick this kinematics then P Pi + + align:start position:0% +and if I pick this kinematics then P Pi + + + align:start position:0% +and if I pick this kinematics then P Pi +is just + + align:start position:0% +is just + + + align:start position:0% +is just +p plus b gamma + + align:start position:0% + + + + align:start position:0% + +so that would be pi + + align:start position:0% +so that would be pi + + + align:start position:0% +so that would be pi +foreign + + align:start position:0% + + + + align:start position:0% + +diagrams + + align:start position:0% +diagrams + + + align:start position:0% +diagrams +what am I talking about + + align:start position:0% +what am I talking about + + + align:start position:0% +what am I talking about +I'm talking about making making a + + align:start position:0% +I'm talking about making making a + + + align:start position:0% +I'm talking about making making a +transition + + align:start position:0% +transition + + + align:start position:0% +transition +with a + + align:start position:0% +with a + + + align:start position:0% +with a +off-shell Photon through a diagram like + + align:start position:0% +off-shell Photon through a diagram like + + + align:start position:0% +off-shell Photon through a diagram like +this one to apply zero + + align:start position:0% +this one to apply zero + + + align:start position:0% +this one to apply zero +or the plus the cross graph + + align:start position:0% + + + + align:start position:0% + +and with this set up with this + + align:start position:0% +and with this set up with this + + + align:start position:0% +and with this set up with this +kinematics this intermediate line here + + align:start position:0% +kinematics this intermediate line here + + + align:start position:0% +kinematics this intermediate line here +if we go through the scaling it's going + + align:start position:0% +if we go through the scaling it's going + + + align:start position:0% +if we go through the scaling it's going +to be hard + + align:start position:0% +to be hard + + + align:start position:0% +to be hard +so these guys with this kinematics uh we + + align:start position:0% +so these guys with this kinematics uh we + + + align:start position:0% +so these guys with this kinematics uh we +make the Pion collinear + + align:start position:0% +make the Pion collinear + + + align:start position:0% +make the Pion collinear +in order to see that you could impose + + align:start position:0% +in order to see that you could impose + + + align:start position:0% +in order to see that you could impose +pi squared equals m pi squared + + align:start position:0% +pi squared equals m pi squared + + + align:start position:0% +pi squared equals m pi squared +right this is never going to be made + + align:start position:0% +right this is never going to be made + + + align:start position:0% +right this is never going to be made +small but e is going to have to be tuned + + align:start position:0% +small but e is going to have to be tuned + + + align:start position:0% +small but e is going to have to be tuned +to be basically Q of Q over two so this + + align:start position:0% +to be basically Q of Q over two so this + + + align:start position:0% +to be basically Q of Q over two so this +thing is going to become if you impose + + align:start position:0% +thing is going to become if you impose + + + align:start position:0% +thing is going to become if you impose +this condition + + align:start position:0% +this condition + + + align:start position:0% +this condition +and like M pi squared over + + align:start position:0% +and like M pi squared over + + + align:start position:0% +and like M pi squared over +2q + + align:start position:0% +2q + + + align:start position:0% +2q +and then you find out that the piant is + + align:start position:0% +and then you find out that the piant is + + + align:start position:0% +and then you find out that the piant is +collinear + + align:start position:0% +collinear + + + align:start position:0% +collinear +so the pione is collinear + + align:start position:0% +so the pione is collinear + + + align:start position:0% +so the pione is collinear +the photon is a photon this line here is + + align:start position:0% +the photon is a photon this line here is + + + align:start position:0% +the photon is a photon this line here is +hard + + align:start position:0% +hard + + + align:start position:0% +hard +and so we want to integrate out the hard + + align:start position:0% +and so we want to integrate out the hard + + + align:start position:0% +and so we want to integrate out the hard +line and match the sky + + align:start position:0% +line and match the sky + + + align:start position:0% +line and match the sky +in the effective Theory onto + + align:start position:0% +in the effective Theory onto + + + align:start position:0% +in the effective Theory onto +some effective Theory operators that + + align:start position:0% +some effective Theory operators that + + + align:start position:0% +some effective Theory operators that +would look like this + + align:start position:0% + + + + align:start position:0% + +guy's pink + + align:start position:0% + + + + align:start position:0% + +okay so we just have to write down what + + align:start position:0% +okay so we just have to write down what + + + align:start position:0% +okay so we just have to write down what +type of effective Theory offers that + + align:start position:0% +type of effective Theory offers that + + + align:start position:0% +type of effective Theory offers that +could be and again it's an effective + + align:start position:0% +could be and again it's an effective + + + align:start position:0% +could be and again it's an effective +Theory operator with two Quark fields so + + align:start position:0% +Theory operator with two Quark fields so + + + align:start position:0% +Theory operator with two Quark fields so +it's very much like what we did before + + align:start position:0% +it's very much like what we did before + + + align:start position:0% +it's very much like what we did before +so + + align:start position:0% + + + + align:start position:0% + +I'm not going to be going through all + + align:start position:0% +I'm not going to be going through all + + + align:start position:0% +I'm not going to be going through all +the indices that I have to go through in + + align:start position:0% +the indices that I have to go through in + + + align:start position:0% +the indices that I have to go through in +order to keep track of you know charge + + align:start position:0% +order to keep track of you know charge + + + align:start position:0% +order to keep track of you know charge +conjugation and all those things I'll + + align:start position:0% +conjugation and all those things I'll + + + align:start position:0% +conjugation and all those things I'll +just write down the right answers for + + align:start position:0% +just write down the right answers for + + + align:start position:0% +just write down the right answers for +the part + + align:start position:0% +the part + + + align:start position:0% +the part +so + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +like this + + align:start position:0% +like this + + + align:start position:0% +like this +so after doing hard cleaner + + align:start position:0% +so after doing hard cleaner + + + align:start position:0% +so after doing hard cleaner +factorization there's again operators + + align:start position:0% +factorization there's again operators + + + align:start position:0% +factorization there's again operators +which is two quarks some hard Wilson + + align:start position:0% +which is two quarks some hard Wilson + + + align:start position:0% +which is two quarks some hard Wilson +coefficient which is this pink thing + + align:start position:0% +coefficient which is this pink thing + + + align:start position:0% +coefficient which is this pink thing +out the pink line + + align:start position:0% +out the pink line + + + align:start position:0% +out the pink line +that sits in the middle + + align:start position:0% +that sits in the middle + + + align:start position:0% +that sits in the middle +this obeys current conservation + + align:start position:0% +this obeys current conservation + + + align:start position:0% +this obeys current conservation +it dimensional analysis fixes this one + + align:start position:0% +it dimensional analysis fixes this one + + + align:start position:0% +it dimensional analysis fixes this one +over Q + + align:start position:0% +over Q + + + align:start position:0% +over Q +charge conjugation + + align:start position:0% +charge conjugation + + + align:start position:0% +charge conjugation +actually also provides constraints on + + align:start position:0% +actually also provides constraints on + + + align:start position:0% +actually also provides constraints on +the Wilson coefficient so + + align:start position:0% +the Wilson coefficient so + + + align:start position:0% +the Wilson coefficient so +just like it did in dis + + align:start position:0% +just like it did in dis + + + align:start position:0% +just like it did in dis +s so charge conjugation tells us that + + align:start position:0% + + + + align:start position:0% + +there's a relation between flipping + + align:start position:0% +there's a relation between flipping + + + align:start position:0% +there's a relation between flipping +signs + + align:start position:0% +signs + + + align:start position:0% +signs +if we go through + + align:start position:0% +if we go through + + + align:start position:0% +if we go through +so we just impose on this operator all + + align:start position:0% +so we just impose on this operator all + + + align:start position:0% +so we just impose on this operator all +the symmetries and things that we can + + align:start position:0% +the symmetries and things that we can + + + align:start position:0% +the symmetries and things that we can +think of and see what it says about the + + align:start position:0% +think of and see what it says about the + + + align:start position:0% +think of and see what it says about the +operator think about this writing the + + align:start position:0% +operator think about this writing the + + + align:start position:0% +operator think about this writing the +operator down based on this picture + + align:start position:0% +operator down based on this picture + + + align:start position:0% +operator down based on this picture +without ever calculating any diagrams + + align:start position:0% +without ever calculating any diagrams + + + align:start position:0% +without ever calculating any diagrams +just knowing what you're after + + align:start position:0% +just knowing what you're after + + + align:start position:0% +just knowing what you're after +and then imposing on it all the + + align:start position:0% +and then imposing on it all the + + + align:start position:0% +and then imposing on it all the +symmetries that should be conserved + + align:start position:0% + + + + align:start position:0% + +so one is dimensional analysis that gave + + align:start position:0% +so one is dimensional analysis that gave + + + align:start position:0% +so one is dimensional analysis that gave +the queue current conservation that's + + align:start position:0% +the queue current conservation that's + + + align:start position:0% +the queue current conservation that's +partly responsible for the Epsilon + + align:start position:0% +partly responsible for the Epsilon + + + align:start position:0% +partly responsible for the Epsilon +you should also look at parity + + align:start position:0% + + + + align:start position:0% + +go through flavor + + align:start position:0% +go through flavor + + + align:start position:0% +go through flavor +and + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +has this structure + + align:start position:0% +has this structure + + + align:start position:0% +has this structure +so I'm constant that I threw in here + + align:start position:0% + + + + align:start position:0% + +and you actually know from the Flavor + + align:start position:0% +and you actually know from the Flavor + + + align:start position:0% +and you actually know from the Flavor +that has got two photons right + + align:start position:0% +that has got two photons right + + + align:start position:0% +that has got two photons right +and I'm not ever adding any more photons + + align:start position:0% +and I'm not ever adding any more photons + + + align:start position:0% +and I'm not ever adding any more photons +so that means there's two factors of Q + + align:start position:0% +so that means there's two factors of Q + + + align:start position:0% +so that means there's two factors of Q +hat + + align:start position:0% +hat + + + align:start position:0% +hat +so there's a q hat squared + + align:start position:0% +so there's a q hat squared + + + align:start position:0% +so there's a q hat squared +which I can stick inside this gamma + + align:start position:0% +which I can stick inside this gamma + + + align:start position:0% +which I can stick inside this gamma +and it has to be a color singlet + + align:start position:0% + + + + align:start position:0% + +because it's going to have to have a + + align:start position:0% +because it's going to have to have a + + + align:start position:0% +because it's going to have to have a +non-trivial matrix element with a pi + + align:start position:0% +non-trivial matrix element with a pi + + + align:start position:0% +non-trivial matrix element with a pi +zero which is a color singlet + + align:start position:0% + + + + align:start position:0% + +and since it has to be so there's no ta + + align:start position:0% +and since it has to be so there's no ta + + + align:start position:0% +and since it has to be so there's no ta +inside the gamma + + align:start position:0% + + + + align:start position:0% + +there would be nothing for the index a + + align:start position:0% +there would be nothing for the index a + + + align:start position:0% +there would be nothing for the index a +to contract with + + align:start position:0% +to contract with + + + align:start position:0% +to contract with +and since it's a color singlet that + + align:start position:0% +and since it's a color singlet that + + + align:start position:0% +and since it's a color singlet that +means if you were to think about soft + + align:start position:0% +means if you were to think about soft + + + align:start position:0% +means if you were to think about soft +interactions here they would just cancel + + align:start position:0% +interactions here they would just cancel + + + align:start position:0% +interactions here they would just cancel +right if I were to make + + align:start position:0% +right if I were to make + + + align:start position:0% +right if I were to make +if I were to think about putting in soft + + align:start position:0% +if I were to think about putting in soft + + + align:start position:0% +if I were to think about putting in soft +interactions and integrating them out + + align:start position:0% +interactions and integrating them out + + + align:start position:0% +interactions and integrating them out +I'd get an S tag or s that would cancel + + align:start position:0% +I'd get an S tag or s that would cancel + + + align:start position:0% +I'd get an S tag or s that would cancel +out + + align:start position:0% +out + + + align:start position:0% +out +so that's the sense in which this is a + + align:start position:0% +so that's the sense in which this is a + + + align:start position:0% +so that's the sense in which this is a +simple example + + align:start position:0% + + + + align:start position:0% + +okay so then we would have a formula + + align:start position:0% +okay so then we would have a formula + + + align:start position:0% +okay so then we would have a formula +where we could equate the effective + + align:start position:0% +where we could equate the effective + + + align:start position:0% +where we could equate the effective +Theory result with the full Theory + + align:start position:0% +Theory result with the full Theory + + + align:start position:0% +Theory result with the full Theory +result + + align:start position:0% + + + + align:start position:0% + +so we can equate Matrix elements + + align:start position:0% + + + + align:start position:0% + +in which this example is different than + + align:start position:0% +in which this example is different than + + + align:start position:0% +in which this example is different than +deep inelastic scattering we're really + + align:start position:0% +deep inelastic scattering we're really + + + align:start position:0% +deep inelastic scattering we're really +doing a matching at the amplitude level + + align:start position:0% +doing a matching at the amplitude level + + + align:start position:0% +doing a matching at the amplitude level +so we're getting remember the form + + align:start position:0% +so we're getting remember the form + + + align:start position:0% +so we're getting remember the form +factor was a parameterization of the + + align:start position:0% +factor was a parameterization of the + + + align:start position:0% +factor was a parameterization of the +amplitude + + align:start position:0% + + + + align:start position:0% + +and if we do that + + align:start position:0% + + + + align:start position:0% + +if you like if you think about the two + + align:start position:0% +if you like if you think about the two + + + align:start position:0% +if you like if you think about the two +currents that we had + + align:start position:0% +currents that we had + + + align:start position:0% +currents that we had +we've integrated them out now thinking + + align:start position:0% +we've integrated them out now thinking + + + align:start position:0% +we've integrated them out now thinking +about just this operator here the Matrix + + align:start position:0% +about just this operator here the Matrix + + + align:start position:0% +about just this operator here the Matrix +element Pi zero to vacuum that we had + + align:start position:0% +element Pi zero to vacuum that we had + + + align:start position:0% +element Pi zero to vacuum that we had +defining this thing which had two + + align:start position:0% +defining this thing which had two + + + align:start position:0% +defining this thing which had two +currents just becomes the Matrix element + + align:start position:0% +currents just becomes the Matrix element + + + align:start position:0% +currents just becomes the Matrix element +of that operator + + align:start position:0% + + + + align:start position:0% + +again like our dis example we form the + + align:start position:0% +again like our dis example we form the + + + align:start position:0% +again like our dis example we form the +sum and difference of the momenta + + align:start position:0% + + + + align:start position:0% + +plus which is + + align:start position:0% +plus which is + + + align:start position:0% +plus which is +P dagger + + align:start position:0% +P dagger + + + align:start position:0% +P dagger +p + + align:start position:0% +p + + + align:start position:0% +p +and one of these guys just gives the + + align:start position:0% +and one of these guys just gives the + + + align:start position:0% +and one of these guys just gives the +total momentum + + align:start position:0% +total momentum + + + align:start position:0% +total momentum +the minus + + align:start position:0% +the minus + + + align:start position:0% +the minus +our second conventions + + align:start position:0% +our second conventions + + + align:start position:0% +our second conventions +so that gets fixed + + align:start position:0% + + + + align:start position:0% + +which in this case it just gets fixed to + + align:start position:0% + + + + align:start position:0% + +which is + + align:start position:0% +which is + + + align:start position:0% +which is +Q + + align:start position:0% + + + + align:start position:0% + +so if you like you've inserted the + + align:start position:0% +so if you like you've inserted the + + + align:start position:0% +so if you like you've inserted the +operator here + + align:start position:0% + + + + align:start position:0% + +on cleaner lines + + align:start position:0% +on cleaner lines + + + align:start position:0% +on cleaner lines +and then you have a matrix element with + + align:start position:0% +and then you have a matrix element with + + + align:start position:0% +and then you have a matrix element with +the pi zero + + align:start position:0% +the pi zero + + + align:start position:0% +the pi zero +and then you have gluons + + align:start position:0% + + + + align:start position:0% + +but you know that whatever momentum + + align:start position:0% +but you know that whatever momentum + + + align:start position:0% +but you know that whatever momentum +comes in has to be the momentum of the + + align:start position:0% +comes in has to be the momentum of the + + + align:start position:0% +comes in has to be the momentum of the +ion and that's the one momentum + + align:start position:0% +ion and that's the one momentum + + + align:start position:0% +ion and that's the one momentum +constraint + + align:start position:0% + + + + align:start position:0% + +so that means that the answer just + + align:start position:0% +so that means that the answer just + + + align:start position:0% +so that means that the answer just +involves + + align:start position:0% +involves + + + align:start position:0% +involves +one convolution again + + align:start position:0% + + + + align:start position:0% + +just the one that's unconstrained + + align:start position:0% + + + + align:start position:0% + +so there's a Wilson coefficient that + + align:start position:0% +so there's a Wilson coefficient that + + + align:start position:0% +so there's a Wilson coefficient that +depends on the other unconstrained guy + + align:start position:0% +depends on the other unconstrained guy + + + align:start position:0% +depends on the other unconstrained guy +which is p plus + + align:start position:0% +which is p plus + + + align:start position:0% +which is p plus +and then there's the Matrix element + + align:start position:0% + + + + align:start position:0% + +where I can write in a Delta function + + align:start position:0% +where I can write in a Delta function + + + align:start position:0% +where I can write in a Delta function +without p plus the usual kind of way + + align:start position:0% +without p plus the usual kind of way + + + align:start position:0% +without p plus the usual kind of way +that we've done + + align:start position:0% + + + + align:start position:0% + +but here it's a little different kind of + + align:start position:0% +but here it's a little different kind of + + + align:start position:0% +but here it's a little different kind of +Matrix element than the one we saw in + + align:start position:0% +Matrix element than the one we saw in + + + align:start position:0% +Matrix element than the one we saw in +dis because it's not forward it's vacuum + + align:start position:0% +dis because it's not forward it's vacuum + + + align:start position:0% +dis because it's not forward it's vacuum +to Pi zero + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +but it's actually the same operator that + + align:start position:0% +but it's actually the same operator that + + + align:start position:0% +but it's actually the same operator that +we were talking about in uh + + align:start position:0% +we were talking about in uh + + + align:start position:0% +we were talking about in uh +Eis effect + + align:start position:0% +Eis effect + + + align:start position:0% +Eis effect +the bilinear operator of a two + + align:start position:0% +the bilinear operator of a two + + + align:start position:0% +the bilinear operator of a two +clinical fields + + align:start position:0% +clinical fields + + + align:start position:0% +clinical fields +cleaner quarks dress with Wilson lines + + align:start position:0% + + + + align:start position:0% + +so one can go through a similar type of + + align:start position:0% +so one can go through a similar type of + + + align:start position:0% +so one can go through a similar type of +Matrix element analysis for this + + align:start position:0% +Matrix element analysis for this + + + align:start position:0% +Matrix element analysis for this +operator and it gives something that's + + align:start position:0% +operator and it gives something that's + + + align:start position:0% +operator and it gives something that's +called the light cone wave function + + align:start position:0% +called the light cone wave function + + + align:start position:0% +called the light cone wave function +so let me Define that for you + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +this Matrix element + + align:start position:0% + + + + align:start position:0% + +can be written in terms of an object + + align:start position:0% +can be written in terms of an object + + + align:start position:0% +can be written in terms of an object +that has a dimensionless variable + + align:start position:0% + + + + align:start position:0% + +it's kind of an analog of the part-time + + align:start position:0% +it's kind of an analog of the part-time + + + align:start position:0% +it's kind of an analog of the part-time +distribution function but for this + + align:start position:0% +distribution function but for this + + + align:start position:0% +distribution function but for this +Matrix element that we're dealing with + + align:start position:0% +Matrix element that we're dealing with + + + align:start position:0% +Matrix element that we're dealing with +here which is vacuum to Pion + + align:start position:0% + + + + align:start position:0% + +so this has some similarity to the + + align:start position:0% +so this has some similarity to the + + + align:start position:0% +so this has some similarity to the +formula we had in dis there's a Delta + + align:start position:0% +formula we had in dis there's a Delta + + + align:start position:0% +formula we had in dis there's a Delta +function there there's a Delta function + + align:start position:0% +function there there's a Delta function + + + align:start position:0% +function there there's a Delta function +here + + align:start position:0% +here + + + align:start position:0% +here +'s a dimensionless variable Z + + align:start position:0% +'s a dimensionless variable Z + + + align:start position:0% +'s a dimensionless variable Z +dimensionless variable Z there + + align:start position:0% +dimensionless variable Z there + + + align:start position:0% +dimensionless variable Z there +and this is a non-privative function + + align:start position:0% + + + + align:start position:0% + +so this is a what's called a light cone + + align:start position:0% +so this is a what's called a light cone + + + align:start position:0% +so this is a what's called a light cone +distribution function for the pione + + align:start position:0% + + + + align:start position:0% + +so generically when you have an + + align:start position:0% +so generically when you have an + + + align:start position:0% +so generically when you have an +exclusive process and you're producing + + align:start position:0% +exclusive process and you're producing + + + align:start position:0% +exclusive process and you're producing +some hadron that's very energetic like a + + align:start position:0% +some hadron that's very energetic like a + + + align:start position:0% +some hadron that's very energetic like a +Pion this is the type of thing that's + + align:start position:0% +Pion this is the type of thing that's + + + align:start position:0% +Pion this is the type of thing that's +going to show up one of these light cone + + align:start position:0% +going to show up one of these light cone + + + align:start position:0% +going to show up one of these light cone +distribution functions + + align:start position:0% + + + + align:start position:0% + +so this example a photon to pione is in + + align:start position:0% +so this example a photon to pione is in + + + align:start position:0% +so this example a photon to pione is in +some sense a very very simple exclusive + + align:start position:0% +some sense a very very simple exclusive + + + align:start position:0% +some sense a very very simple exclusive +process + + align:start position:0% + + + + align:start position:0% + +the simplest one in some sense + + align:start position:0% +the simplest one in some sense + + + align:start position:0% +the simplest one in some sense +okay so we could take this formula plug + + align:start position:0% +okay so we could take this formula plug + + + align:start position:0% +okay so we could take this formula plug +it back in there and then we'd have a + + align:start position:0% +it back in there and then we'd have a + + + align:start position:0% +it back in there and then we'd have a +factorization theorem + + align:start position:0% +factorization theorem + + + align:start position:0% +factorization theorem +and I think that you can imagine what + + align:start position:0% +and I think that you can imagine what + + + align:start position:0% +and I think that you can imagine what +that would look like I could write it + + align:start position:0% +that would look like I could write it + + + align:start position:0% +that would look like I could write it +instead of an integral over W as an + + align:start position:0% +instead of an integral over W as an + + + align:start position:0% +instead of an integral over W as an +integral over Z + + align:start position:0% +integral over Z + + + align:start position:0% +integral over Z +and that would be the factorization + + align:start position:0% +and that would be the factorization + + + align:start position:0% +and that would be the factorization +theorem involving this + + align:start position:0% +theorem involving this + + + align:start position:0% +theorem involving this +5 pi + + align:start position:0% +5 pi + + + align:start position:0% +5 pi +so + + align:start position:0% + + + + align:start position:0% + +yeah that's right so you should think of + + align:start position:0% +yeah that's right so you should think of + + + align:start position:0% +yeah that's right so you should think of +the Z + + align:start position:0% +the Z + + + align:start position:0% +the Z +as like so the way to think about the Z + + align:start position:0% +as like so the way to think about the Z + + + align:start position:0% +as like so the way to think about the Z +is as follows so think about like when + + align:start position:0% +is as follows so think about like when + + + align:start position:0% +is as follows so think about like when +you initially produced these guys here + + align:start position:0% +you initially produced these guys here + + + align:start position:0% +you initially produced these guys here +think about all the momentum going this + + align:start position:0% +think about all the momentum going this + + + align:start position:0% +think about all the momentum going this +way + + align:start position:0% +way + + + align:start position:0% +way +when you initially produce them from + + align:start position:0% +when you initially produce them from + + + align:start position:0% +when you initially produce them from +this hard interact from it after you've + + align:start position:0% +this hard interact from it after you've + + + align:start position:0% +this hard interact from it after you've +integrated out the hard interactions you + + align:start position:0% +integrated out the hard interactions you + + + align:start position:0% +integrated out the hard interactions you +had Z and one minus Z is the possible + + align:start position:0% +had Z and one minus Z is the possible + + + align:start position:0% +had Z and one minus Z is the possible +split of the quarks fields in the + + align:start position:0% +split of the quarks fields in the + + + align:start position:0% +split of the quarks fields in the +operator + + align:start position:0% +operator + + + align:start position:0% +operator +so the one of these guys carries Z + + align:start position:0% +so the one of these guys carries Z + + + align:start position:0% +so the one of these guys carries Z +effectively what this 2z minus 1 is + + align:start position:0% +effectively what this 2z minus 1 is + + + align:start position:0% +effectively what this 2z minus 1 is +doing is one of these guys is carrying Z + + align:start position:0% +doing is one of these guys is carrying Z + + + align:start position:0% +doing is one of these guys is carrying Z +and one of them's carrying one minus Z + + align:start position:0% +and one of them's carrying one minus Z + + + align:start position:0% +and one of them's carrying one minus Z +okay the sum of these is one and that's + + align:start position:0% +okay the sum of these is one and that's + + + align:start position:0% +okay the sum of these is one and that's +the analog of the statement that the + + align:start position:0% +the analog of the statement that the + + + align:start position:0% +the analog of the statement that the +whole total momentum should be the pi + + align:start position:0% +whole total momentum should be the pi + + + align:start position:0% +whole total momentum should be the pi +zero momentum but you don't know how to + + align:start position:0% +zero momentum but you don't know how to + + + align:start position:0% +zero momentum but you don't know how to +split how much goes into each one of + + align:start position:0% +split how much goes into each one of + + + align:start position:0% +split how much goes into each one of +those + + align:start position:0% +those + + + align:start position:0% +those +and what the wave function is it's kind + + align:start position:0% +and what the wave function is it's kind + + + align:start position:0% +and what the wave function is it's kind +of all the linear interactions + + align:start position:0% +of all the linear interactions + + + align:start position:0% +of all the linear interactions +that subsequently rearrange this thing + + align:start position:0% +that subsequently rearrange this thing + + + align:start position:0% +that subsequently rearrange this thing +before you sort of annihilate it with + + align:start position:0% +before you sort of annihilate it with + + + align:start position:0% +before you sort of annihilate it with +the state so I mean this all these + + align:start position:0% +the state so I mean this all these + + + align:start position:0% +the state so I mean this all these +things are like dressing up the Pion + + align:start position:0% +things are like dressing up the Pion + + + align:start position:0% +things are like dressing up the Pion +State you know they're producing the pi + + align:start position:0% +State you know they're producing the pi + + + align:start position:0% +State you know they're producing the pi +on pole so this is like five pi + + align:start position:0% +on pole so this is like five pi + + + align:start position:0% +on pole so this is like five pi +and so + + align:start position:0% +and so + + + align:start position:0% +and so +what you have is an operator that + + align:start position:0% +what you have is an operator that + + + align:start position:0% +what you have is an operator that +depends on z a wave function that + + align:start position:0% +depends on z a wave function that + + + align:start position:0% +depends on z a wave function that +depends on Z so this is a Wilson + + align:start position:0% +depends on Z so this is a Wilson + + + align:start position:0% +depends on Z so this is a Wilson +coefficient that depends on Z and your + + align:start position:0% +coefficient that depends on Z and your + + + align:start position:0% +coefficient that depends on Z and your +final factorization theorem is exactly + + align:start position:0% +final factorization theorem is exactly + + + align:start position:0% +final factorization theorem is exactly +of that + + align:start position:0% +of that + + + align:start position:0% +of that +type that instead of + + align:start position:0% + + + + align:start position:0% + +an integral of Z + + align:start position:0% + + + + align:start position:0% + +which also can depend on + + align:start position:0% +which also can depend on + + + align:start position:0% +which also can depend on +Mew + + align:start position:0% +Mew + + + align:start position:0% +Mew +and then + + align:start position:0% +and then + + + align:start position:0% +and then +five fives + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +universal yeah it's Universal + + align:start position:0% +universal yeah it's Universal + + + align:start position:0% +universal yeah it's Universal +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +yeah + + align:start position:0% + + + + align:start position:0% + +so as long as you can Factor it so that + + align:start position:0% +so as long as you can Factor it so that + + + align:start position:0% +so as long as you can Factor it so that +it's these fields + + align:start position:0% +it's these fields + + + align:start position:0% +it's these fields +and that pione then you have this Matrix + + align:start position:0% +and that pione then you have this Matrix + + + align:start position:0% +and that pione then you have this Matrix +element and you get this guy + + align:start position:0% + + + + align:start position:0% + +so people try to measure things about + + align:start position:0% +so people try to measure things about + + + align:start position:0% +so people try to measure things about +this guy at its moments + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +one thing that happens here has to do + + align:start position:0% +one thing that happens here has to do + + + align:start position:0% +one thing that happens here has to do +with this integral over Z which + + align:start position:0% +with this integral over Z which + + + align:start position:0% +with this integral over Z which +uh is kind of an there's still this is + + align:start position:0% +uh is kind of an there's still this is + + + align:start position:0% +uh is kind of an there's still this is +kind of in some sense an unsolved + + align:start position:0% +kind of in some sense an unsolved + + + align:start position:0% +kind of in some sense an unsolved +problem in SCT so I have to mention it + + align:start position:0% +problem in SCT so I have to mention it + + + align:start position:0% +problem in SCT so I have to mention it +so when you do this integral you could + + align:start position:0% +so when you do this integral you could + + + align:start position:0% +so when you do this integral you could +ask what does this C of Z look like + + align:start position:0% +ask what does this C of Z look like + + + align:start position:0% +ask what does this C of Z look like +and it turns out that c of Z + + align:start position:0% +and it turns out that c of Z + + + align:start position:0% +and it turns out that c of Z +will have in it terms that go like 1 + + align:start position:0% +will have in it terms that go like 1 + + + align:start position:0% +will have in it terms that go like 1 +over Z + + align:start position:0% +over Z + + + align:start position:0% +over Z +and so you get integrals that look like + + align:start position:0% +and so you get integrals that look like + + + align:start position:0% +and so you get integrals that look like +DZ + + align:start position:0% +DZ + + + align:start position:0% +DZ +over Z of 5 Pi of Z so say at lowest + + align:start position:0% +over Z of 5 Pi of Z so say at lowest + + + align:start position:0% +over Z of 5 Pi of Z so say at lowest +order this integral would show up + + align:start position:0% +order this integral would show up + + + align:start position:0% +order this integral would show up +and it turns out that for this Matrix + + align:start position:0% +and it turns out that for this Matrix + + + align:start position:0% +and it turns out that for this Matrix +element here you don't get anything + + align:start position:0% +element here you don't get anything + + + align:start position:0% +element here you don't get anything +worse than that you never get 1 over Z + + align:start position:0% +worse than that you never get 1 over Z + + + align:start position:0% +worse than that you never get 1 over Z +squared and this integral here because + + align:start position:0% +squared and this integral here because + + + align:start position:0% +squared and this integral here because +of properties of this 5 pi is finite + + align:start position:0% +of properties of this 5 pi is finite + + + align:start position:0% +of properties of this 5 pi is finite +there's no problems + + align:start position:0% +there's no problems + + + align:start position:0% +there's no problems +but there are examples known in the + + align:start position:0% +but there are examples known in the + + + align:start position:0% +but there are examples known in the +literature where that's not the case + + align:start position:0% +literature where that's not the case + + + align:start position:0% +literature where that's not the case +where you actually get one over Z + + align:start position:0% +where you actually get one over Z + + + align:start position:0% +where you actually get one over Z +squared + + align:start position:0% +squared + + + align:start position:0% +squared +and people have some understanding of + + align:start position:0% +and people have some understanding of + + + align:start position:0% +and people have some understanding of +the physics that's happening in those + + align:start position:0% +the physics that's happening in those + + + align:start position:0% +the physics that's happening in those +cases but it but there's not a complete + + align:start position:0% +cases but it but there's not a complete + + + align:start position:0% +cases but it but there's not a complete +understanding of how factorization works + + align:start position:0% +understanding of how factorization works + + + align:start position:0% +understanding of how factorization works +in those cases + + align:start position:0% +in those cases + + + align:start position:0% +in those cases +okay so it's not that doesn't happen in + + align:start position:0% +okay so it's not that doesn't happen in + + + align:start position:0% +okay so it's not that doesn't happen in +this example but there are other + + align:start position:0% +this example but there are other + + + align:start position:0% +this example but there are other +examples of exclusive processes that + + align:start position:0% +examples of exclusive processes that + + + align:start position:0% +examples of exclusive processes that +would lead to one over Z squared and + + align:start position:0% +would lead to one over Z squared and + + + align:start position:0% +would lead to one over Z squared and +then this integral is not well defined + + align:start position:0% + + + + align:start position:0% + +and people kind of understand that + + align:start position:0% +and people kind of understand that + + + align:start position:0% +and people kind of understand that +there's a cutoff that's coming in and + + align:start position:0% +there's a cutoff that's coming in and + + + align:start position:0% +there's a cutoff that's coming in and +they understand that that cut off + + align:start position:0% +they understand that that cut off + + + align:start position:0% +they understand that that cut off +actually has to do with some rapidity + + align:start position:0% +actually has to do with some rapidity + + + align:start position:0% +actually has to do with some rapidity +but how to explicitly write down the + + align:start position:0% +but how to explicitly write down the + + + align:start position:0% +but how to explicitly write down the +analog factorization theorem that + + align:start position:0% +analog factorization theorem that + + + align:start position:0% +analog factorization theorem that +involves those cutoffs and has a + + align:start position:0% +involves those cutoffs and has a + + + align:start position:0% +involves those cutoffs and has a +mineralization group is an unsolved + + align:start position:0% +mineralization group is an unsolved + + + align:start position:0% +mineralization group is an unsolved +problem + + align:start position:0% +problem + + + align:start position:0% +problem +unsolved sket2 problem + + align:start position:0% +unsolved sket2 problem + + + align:start position:0% +unsolved sket2 problem +okay but for the example we did + + align:start position:0% +okay but for the example we did + + + align:start position:0% +okay but for the example we did +everything's kosher and beautiful + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +I think what I'll do next time since + + align:start position:0% +I think what I'll do next time since + + + align:start position:0% +I think what I'll do next time since +we're out of time I'm not going to start + + align:start position:0% +we're out of time I'm not going to start + + + align:start position:0% +we're out of time I'm not going to start +my second example now so next time we'll + + align:start position:0% +my second example now so next time we'll + + + align:start position:0% +my second example now so next time we'll +do an example that does involve soft + + align:start position:0% +do an example that does involve soft + + + align:start position:0% +do an example that does involve soft +fields both soft and cleaner fields and + + align:start position:0% +fields both soft and cleaner fields and + + + align:start position:0% +fields both soft and cleaner fields and +sct2 + + align:start position:0% +sct2 + + + align:start position:0% +sct2 +um + + align:start position:0% +um + + + align:start position:0% +um +that's where we're going + + align:start position:0% +that's where we're going + + + align:start position:0% +that's where we're going +but we'll leave that to next time \ No newline at end of file diff --git a/kAeDRfk6A9w.txt b/kAeDRfk6A9w.txt new file mode 100644 index 0000000000000000000000000000000000000000..65e3bc39287887b3410e3eb412e4eac6b19e1c7d --- /dev/null +++ b/kAeDRfk6A9w.txt @@ -0,0 +1,18919 @@ +align:start position:0% + +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +today we are going to talk about the + + align:start position:0% +today we are going to talk about the + + + align:start position:0% +today we are going to talk about the +evolution of water resources management + + align:start position:0% +evolution of water resources management + + + align:start position:0% +evolution of water resources management +and at the end of the class you will be + + align:start position:0% +and at the end of the class you will be + + + align:start position:0% +and at the end of the class you will be +uh you will be able to + + align:start position:0% +uh you will be able to + + + align:start position:0% +uh you will be able to +describe paradigm shift and evolution of + + align:start position:0% +describe paradigm shift and evolution of + + + align:start position:0% +describe paradigm shift and evolution of +water resources management in in general + + align:start position:0% +water resources management in in general + + + align:start position:0% +water resources management in in general +but also you can critically evaluate the + + align:start position:0% +but also you can critically evaluate the + + + align:start position:0% +but also you can critically evaluate the +importance of + + align:start position:0% +importance of + + + align:start position:0% +importance of +iwrm for water diplomacy + + align:start position:0% +iwrm for water diplomacy + + + align:start position:0% +iwrm for water diplomacy +and also water energy food nexus and its + + align:start position:0% +and also water energy food nexus and its + + + align:start position:0% +and also water energy food nexus and its +relation with um water diplomacy and + + align:start position:0% +relation with um water diplomacy and + + + align:start position:0% +relation with um water diplomacy and +also importance of water diplomacy for + + align:start position:0% +also importance of water diplomacy for + + + align:start position:0% +also importance of water diplomacy for +acid being sustainable development goals + + align:start position:0% +acid being sustainable development goals + + + align:start position:0% +acid being sustainable development goals +today's talk is regarding + + align:start position:0% +today's talk is regarding + + + align:start position:0% +today's talk is regarding +a new process um recently a process of + + align:start position:0% +a new process um recently a process of + + + align:start position:0% +a new process um recently a process of +water resources management and + + align:start position:0% +water resources management and + + + align:start position:0% +water resources management and +sustainable + + align:start position:0% +sustainable + + + align:start position:0% +sustainable +development goals and its relation with + + align:start position:0% +development goals and its relation with + + + align:start position:0% +development goals and its relation with +water diplomacy + + align:start position:0% + + + + align:start position:0% + +uh in this figure i try to summarize uh + + align:start position:0% +uh in this figure i try to summarize uh + + + align:start position:0% +uh in this figure i try to summarize uh +from taken from this references + + align:start position:0% +from taken from this references + + + align:start position:0% +from taken from this references +uh how the water resource management has + + align:start position:0% +uh how the water resource management has + + + align:start position:0% +uh how the water resource management has +evolved throughout the time it has four + + align:start position:0% +evolved throughout the time it has four + + + align:start position:0% +evolved throughout the time it has four +metrics you can see that from the + + align:start position:0% +metrics you can see that from the + + + align:start position:0% +metrics you can see that from the +centralized management to this + + align:start position:0% +centralized management to this + + + align:start position:0% +centralized management to this +decentralized management + + align:start position:0% +decentralized management + + + align:start position:0% +decentralized management +uh in the vertical axis + + align:start position:0% +uh in the vertical axis + + + align:start position:0% +uh in the vertical axis +and from centralized management it means + + align:start position:0% +and from centralized management it means + + + align:start position:0% +and from centralized management it means +a centralized form of + + align:start position:0% +a centralized form of + + + align:start position:0% +a centralized form of +governance where + + align:start position:0% +governance where + + + align:start position:0% +governance where +stakeholder engagement and participation + + align:start position:0% +stakeholder engagement and participation + + + align:start position:0% +stakeholder engagement and participation +is uh the possibility of + + align:start position:0% +is uh the possibility of + + + align:start position:0% +is uh the possibility of +stakeholder engagement is very low but + + align:start position:0% +stakeholder engagement is very low but + + + align:start position:0% +stakeholder engagement is very low but +when it moves to the + + align:start position:0% +when it moves to the + + + align:start position:0% +when it moves to the +decentralized form of governance it can + + align:start position:0% +decentralized form of governance it can + + + align:start position:0% +decentralized form of governance it can +include stakeholder engagement from + + align:start position:0% +include stakeholder engagement from + + + align:start position:0% +include stakeholder engagement from +local peoples and local + + align:start position:0% +local peoples and local + + + align:start position:0% +local peoples and local +participations and in the + + align:start position:0% +participations and in the + + + align:start position:0% +participations and in the +horizontal axis you can see from the + + align:start position:0% +horizontal axis you can see from the + + + align:start position:0% +horizontal axis you can see from the +supply side + + align:start position:0% +supply side + + + align:start position:0% +supply side +management to the demand side management + + align:start position:0% +management to the demand side management + + + align:start position:0% +management to the demand side management +in the + + align:start position:0% +in the + + + align:start position:0% +in the +left + + align:start position:0% +left + + + align:start position:0% +left +um upper corner + + align:start position:0% +um upper corner + + + align:start position:0% +um upper corner +this is the traditional + + align:start position:0% +this is the traditional + + + align:start position:0% +this is the traditional +development of water resources + + align:start position:0% +development of water resources + + + align:start position:0% +development of water resources +management not only water resources + + align:start position:0% +management not only water resources + + + align:start position:0% +management not only water resources +management any development started from + + align:start position:0% +management any development started from + + + align:start position:0% +management any development started from +this side so it's highly centralized and + + align:start position:0% +this side so it's highly centralized and + + + align:start position:0% +this side so it's highly centralized and +uh supply side + + align:start position:0% +uh supply side + + + align:start position:0% +uh supply side +approach so + + align:start position:0% +approach so + + + align:start position:0% +approach so +this is the first development pattern of + + align:start position:0% +this is the first development pattern of + + + align:start position:0% +this is the first development pattern of +water resources so for example in this + + align:start position:0% +water resources so for example in this + + + align:start position:0% +water resources so for example in this +case + + align:start position:0% +case + + + align:start position:0% +case +only um + + align:start position:0% +only um + + + align:start position:0% +only um +option is to invest + + align:start position:0% +option is to invest + + + align:start position:0% +option is to invest +uh how to create dams + + align:start position:0% +uh how to create dams + + + align:start position:0% +uh how to create dams +construction + + align:start position:0% +construction + + + align:start position:0% +construction +preservers so this is the only + + align:start position:0% +preservers so this is the only + + + align:start position:0% +preservers so this is the only +consideration for for the water + + align:start position:0% +consideration for for the water + + + align:start position:0% +consideration for for the water +resources management and it's considered + + align:start position:0% +resources management and it's considered + + + align:start position:0% +resources management and it's considered +only engineering based approach and it's + + align:start position:0% +only engineering based approach and it's + + + align:start position:0% +only engineering based approach and it's +very technocratic approach without + + align:start position:0% +very technocratic approach without + + + align:start position:0% +very technocratic approach without +considering societal aspects or + + align:start position:0% +considering societal aspects or + + + align:start position:0% +considering societal aspects or +economic aspects mainly how to make the + + align:start position:0% +economic aspects mainly how to make the + + + align:start position:0% +economic aspects mainly how to make the +development and how the development + + align:start position:0% +development and how the development + + + align:start position:0% +development and how the development +patterns start and how the engineering + + align:start position:0% +patterns start and how the engineering + + + align:start position:0% +patterns start and how the engineering +structures can can + + align:start position:0% +structures can can + + + align:start position:0% +structures can can +can help to um make the + + align:start position:0% +can help to um make the + + + align:start position:0% +can help to um make the +development effective so this is the + + align:start position:0% +development effective so this is the + + + align:start position:0% +development effective so this is the +only only consideration in this phase + + align:start position:0% +only only consideration in this phase + + + align:start position:0% +only only consideration in this phase +and um + + align:start position:0% +and um + + + align:start position:0% +and um +then so this is the + + align:start position:0% +then so this is the + + + align:start position:0% +then so this is the +position of a + + align:start position:0% +position of a + + + align:start position:0% +position of a +in the left left hand side upper + + align:start position:0% +in the left left hand side upper + + + align:start position:0% +in the left left hand side upper +corner and but slowly + + align:start position:0% +corner and but slowly + + + align:start position:0% +corner and but slowly +it moves from a to b and in that case + + align:start position:0% +it moves from a to b and in that case + + + align:start position:0% +it moves from a to b and in that case +the um + + align:start position:0% +the um + + + align:start position:0% +the um +from investment oriented decision it + + align:start position:0% +from investment oriented decision it + + + align:start position:0% +from investment oriented decision it +moves it takes consideration of the + + align:start position:0% +moves it takes consideration of the + + + align:start position:0% +moves it takes consideration of the +societal issues slowly + + align:start position:0% +societal issues slowly + + + align:start position:0% +societal issues slowly +and then + + align:start position:0% +and then + + + align:start position:0% +and then +so initial um + + align:start position:0% +so initial um + + + align:start position:0% +so initial um +management paradigm considers mainly + + align:start position:0% +management paradigm considers mainly + + + align:start position:0% +management paradigm considers mainly +engineers hydrologists and technocrats + + align:start position:0% +engineers hydrologists and technocrats + + + align:start position:0% +engineers hydrologists and technocrats +but slowly they can understand that that + + align:start position:0% +but slowly they can understand that that + + + align:start position:0% +but slowly they can understand that that +this may create this can create + + align:start position:0% +this may create this can create + + + align:start position:0% +this may create this can create +consequences to the society and they can + + align:start position:0% +consequences to the society and they can + + + align:start position:0% +consequences to the society and they can +try to understand the demand of the + + align:start position:0% +try to understand the demand of the + + + align:start position:0% +try to understand the demand of the +local + + align:start position:0% +local + + + align:start position:0% +local +people + + align:start position:0% +people + + + align:start position:0% +people +slowly and so they try to incorporate + + align:start position:0% +slowly and so they try to incorporate + + + align:start position:0% +slowly and so they try to incorporate +the + + align:start position:0% +the + + + align:start position:0% +the +uh they try to um uh realize that water + + align:start position:0% +uh they try to um uh realize that water + + + align:start position:0% +uh they try to um uh realize that water +is not only the + + align:start position:0% +is not only the + + + align:start position:0% +is not only the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +what are what is not only the um + + align:start position:0% +what are what is not only the um + + + align:start position:0% +what are what is not only the um +development pattern or supply side + + align:start position:0% +development pattern or supply side + + + align:start position:0% +development pattern or supply side +management it needs to consider also + + align:start position:0% +management it needs to consider also + + + align:start position:0% +management it needs to consider also +societal and um economic aspect and thus + + align:start position:0% +societal and um economic aspect and thus + + + align:start position:0% +societal and um economic aspect and thus +the demand side options um started and + + align:start position:0% +the demand side options um started and + + + align:start position:0% +the demand side options um started and +demand side management started and then + + align:start position:0% +demand side management started and then + + + align:start position:0% +demand side management started and then +slowly it moves to the sea and in that + + align:start position:0% +slowly it moves to the sea and in that + + + align:start position:0% +slowly it moves to the sea and in that +case institutional reformation start or + + align:start position:0% +case institutional reformation start or + + + align:start position:0% +case institutional reformation start or +for example decentralized form of + + align:start position:0% +for example decentralized form of + + + align:start position:0% +for example decentralized form of +governance institution + + align:start position:0% +governance institution + + + align:start position:0% +governance institution +and um yeah so um the + + align:start position:0% +and um yeah so um the + + + align:start position:0% +and um yeah so um the +from + + align:start position:0% +from + + + align:start position:0% +from +um uh engineering based structure of the + + align:start position:0% +um uh engineering based structure of the + + + align:start position:0% +um uh engineering based structure of the +management paradigms + + align:start position:0% +management paradigms + + + align:start position:0% +management paradigms +shift shift towards um + + align:start position:0% + + + + align:start position:0% + +different + + align:start position:0% +different + + + align:start position:0% +different +disciplinary bodies in the management + + align:start position:0% +disciplinary bodies in the management + + + align:start position:0% +disciplinary bodies in the management +body but also + + align:start position:0% +body but also + + + align:start position:0% +body but also +local engagement can also um + + align:start position:0% +local engagement can also um + + + align:start position:0% +local engagement can also um +um taken place so this is the overall + + align:start position:0% +um taken place so this is the overall + + + align:start position:0% +um taken place so this is the overall +broader um evolution of the water + + align:start position:0% +broader um evolution of the water + + + align:start position:0% +broader um evolution of the water +resources + + align:start position:0% +resources + + + align:start position:0% +resources +management happens internationally and + + align:start position:0% +management happens internationally and + + + align:start position:0% +management happens internationally and +also many + + align:start position:0% +also many + + + align:start position:0% +also many +countries so here i can give an example + + align:start position:0% +countries so here i can give an example + + + align:start position:0% +countries so here i can give an example +how it happens in + + align:start position:0% +how it happens in + + + align:start position:0% +how it happens in +bangladesh because i know + + align:start position:0% +bangladesh because i know + + + align:start position:0% +bangladesh because i know +this um + + align:start position:0% +this um + + + align:start position:0% +this um +uh the context of bangladesh water + + align:start position:0% +uh the context of bangladesh water + + + align:start position:0% +uh the context of bangladesh water +resources management how it happens + + align:start position:0% +resources management how it happens + + + align:start position:0% +resources management how it happens +throughout the + + align:start position:0% +throughout the + + + align:start position:0% +throughout the +time so i can also explain + + align:start position:0% +time so i can also explain + + + align:start position:0% +time so i can also explain +the graph that i have shown and what + + align:start position:0% +the graph that i have shown and what + + + align:start position:0% +the graph that i have shown and what +happens practically in bangladesh case + + align:start position:0% +happens practically in bangladesh case + + + align:start position:0% +happens practically in bangladesh case +so um + + align:start position:0% +so um + + + align:start position:0% +so um +before 1947 + + align:start position:0% +before 1947 + + + align:start position:0% +before 1947 +bangladesh was a part of the british + + align:start position:0% +bangladesh was a part of the british + + + align:start position:0% +bangladesh was a part of the british +colony + + align:start position:0% +colony + + + align:start position:0% +colony +and um during that time there was no + + align:start position:0% +and um during that time there was no + + + align:start position:0% +and um during that time there was no +embankment to protect + + align:start position:0% +embankment to protect + + + align:start position:0% +embankment to protect +flooding in bangladesh so + + align:start position:0% +flooding in bangladesh so + + + align:start position:0% +flooding in bangladesh so +um + + align:start position:0% +um + + + align:start position:0% +um +in that time + + align:start position:0% +in that time + + + align:start position:0% +in that time +local people manage the embankment + + align:start position:0% +local people manage the embankment + + + align:start position:0% +local people manage the embankment +during the um + + align:start position:0% +during the um + + + align:start position:0% +during the um +dry season to um + + align:start position:0% +dry season to um + + + align:start position:0% +dry season to um +grow the + + align:start position:0% +grow the + + + align:start position:0% +grow the +crops and in that case landlords + + align:start position:0% +crops and in that case landlords + + + align:start position:0% +crops and in that case landlords +the + + align:start position:0% +the + + + align:start position:0% +the +british empire provide um + + align:start position:0% +british empire provide um + + + align:start position:0% +british empire provide um +ownership to the landlord to manage + + align:start position:0% +ownership to the landlord to manage + + + align:start position:0% +ownership to the landlord to manage +a specific area of land and through + + align:start position:0% +a specific area of land and through + + + align:start position:0% +a specific area of land and through +engaging local farmers + + align:start position:0% +engaging local farmers + + + align:start position:0% +engaging local farmers +the landlords um + + align:start position:0% +the landlords um + + + align:start position:0% +the landlords um +was was responsible for + + align:start position:0% +was was responsible for + + + align:start position:0% +was was responsible for +managing flood protection embankments + + align:start position:0% +managing flood protection embankments + + + align:start position:0% +managing flood protection embankments +only during the + + align:start position:0% +only during the + + + align:start position:0% +only during the +um dry season for growing crops + + align:start position:0% +um dry season for growing crops + + + align:start position:0% +um dry season for growing crops +but during rainy season that embankment + + align:start position:0% +but during rainy season that embankment + + + align:start position:0% +but during rainy season that embankment +was um + + align:start position:0% +was um + + + align:start position:0% +was um +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +vanished because of the um rainfall and + + align:start position:0% +vanished because of the um rainfall and + + + align:start position:0% +vanished because of the um rainfall and +the river water could enter into the + + align:start position:0% +the river water could enter into the + + + align:start position:0% +the river water could enter into the +flood plain and it helps sedimentation + + align:start position:0% +flood plain and it helps sedimentation + + + align:start position:0% +flood plain and it helps sedimentation +and it it increases the uh yeah so land + + align:start position:0% +and it it increases the uh yeah so land + + + align:start position:0% +and it it increases the uh yeah so land +formation + + align:start position:0% +formation + + + align:start position:0% +formation +was happening during that time because + + align:start position:0% +was happening during that time because + + + align:start position:0% +was happening during that time because +sediment could + + align:start position:0% +sediment could + + + align:start position:0% +sediment could +come into the uh flood plain + + align:start position:0% +come into the uh flood plain + + + align:start position:0% +come into the uh flood plain +and so this is kind of um natural + + align:start position:0% +and so this is kind of um natural + + + align:start position:0% +and so this is kind of um natural +process was maintained during that + + align:start position:0% +process was maintained during that + + + align:start position:0% +process was maintained during that +period but after 1947 the british colony + + align:start position:0% +period but after 1947 the british colony + + + align:start position:0% +period but after 1947 the british colony +ended and there is no institution like + + align:start position:0% +ended and there is no institution like + + + align:start position:0% +ended and there is no institution like +the + + align:start position:0% +the + + + align:start position:0% +the +landlord management + + align:start position:0% +landlord management + + + align:start position:0% +landlord management +territory was not there and + + align:start position:0% +territory was not there and + + + align:start position:0% +territory was not there and +since then um + + align:start position:0% +since then um + + + align:start position:0% +since then um +this + + align:start position:0% +this + + + align:start position:0% +this +part of land was was part of indian + + align:start position:0% +part of land was was part of indian + + + align:start position:0% +part of land was was part of indian +um state so um + + align:start position:0% +um state so um + + + align:start position:0% +um state so um +it was um + + align:start position:0% +it was um + + + align:start position:0% +it was um +so india and pakistan was divided and + + align:start position:0% +so india and pakistan was divided and + + + align:start position:0% +so india and pakistan was divided and +bangladesh was part of the east pakistan + + align:start position:0% +bangladesh was part of the east pakistan + + + align:start position:0% +bangladesh was part of the east pakistan +during that time + + align:start position:0% +during that time + + + align:start position:0% +during that time +and + + align:start position:0% +and + + + align:start position:0% +and +so during that time there was no + + align:start position:0% +so during that time there was no + + + align:start position:0% +so during that time there was no +responsible authority to managing the + + align:start position:0% +responsible authority to managing the + + + align:start position:0% +responsible authority to managing the +embankment or flood plain + + align:start position:0% +embankment or flood plain + + + align:start position:0% +embankment or flood plain +and + + align:start position:0% +and + + + align:start position:0% +and +during that time in 1954 and 55 there + + align:start position:0% +during that time in 1954 and 55 there + + + align:start position:0% +during that time in 1954 and 55 there +was a + + align:start position:0% +was a + + + align:start position:0% +was a +major flood events + + align:start position:0% +major flood events + + + align:start position:0% +major flood events +and after that flood events + + align:start position:0% +and after that flood events + + + align:start position:0% +and after that flood events +flood + + align:start position:0% +flood + + + align:start position:0% +flood +protection embankments was um + + align:start position:0% +protection embankments was um + + + align:start position:0% +protection embankments was um +constructed in 1960s + + align:start position:0% +constructed in 1960s + + + align:start position:0% +constructed in 1960s +and you see the during that + + align:start position:0% +and you see the during that + + + align:start position:0% +and you see the during that +pre-order heavy engineering works + + align:start position:0% +pre-order heavy engineering works + + + align:start position:0% +pre-order heavy engineering works +started + + align:start position:0% +started + + + align:start position:0% +started +and and in that case the embankment + + align:start position:0% +and and in that case the embankment + + + align:start position:0% +and and in that case the embankment +protect the flooding + + align:start position:0% +protect the flooding + + + align:start position:0% +protect the flooding +uh from the um + + align:start position:0% +uh from the um + + + align:start position:0% +uh from the um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +river but also um um + + align:start position:0% +river but also um um + + + align:start position:0% +river but also um um +it it it helps initially the + + align:start position:0% +it it it helps initially the + + + align:start position:0% +it it it helps initially the +agricultural uh production highly + + align:start position:0% +agricultural uh production highly + + + align:start position:0% +agricultural uh production highly +uh but slowly after few years + + align:start position:0% +uh but slowly after few years + + + align:start position:0% +uh but slowly after few years +uh you know + + align:start position:0% +uh you know + + + align:start position:0% +uh you know +this is um this uh this + + align:start position:0% +this is um this uh this + + + align:start position:0% +this is um this uh this +river um carries huge amount of sediment + + align:start position:0% +river um carries huge amount of sediment + + + align:start position:0% +river um carries huge amount of sediment +and that's sediment + + align:start position:0% +and that's sediment + + + align:start position:0% +and that's sediment +deposited in the flood plain and that + + align:start position:0% +deposited in the flood plain and that + + + align:start position:0% +deposited in the flood plain and that +makes the land formation in the flood + + align:start position:0% +makes the land formation in the flood + + + align:start position:0% +makes the land formation in the flood +plain but due to the embankment this + + align:start position:0% +plain but due to the embankment this + + + align:start position:0% +plain but due to the embankment this +process was um was not taken place due + + align:start position:0% +process was um was not taken place due + + + align:start position:0% +process was um was not taken place due +to the construction of the embankment + + align:start position:0% +to the construction of the embankment + + + align:start position:0% +to the construction of the embankment +and then the um + + align:start position:0% +and then the um + + + align:start position:0% +and then the um +sedimentation was happening in the river + + align:start position:0% +sedimentation was happening in the river + + + align:start position:0% +sedimentation was happening in the river +fed a riverbed instead of the floodplain + + align:start position:0% +fed a riverbed instead of the floodplain + + + align:start position:0% +fed a riverbed instead of the floodplain +so the floodplain ah the land formation + + align:start position:0% +so the floodplain ah the land formation + + + align:start position:0% +so the floodplain ah the land formation +was not happening in the flood plain but + + align:start position:0% +was not happening in the flood plain but + + + align:start position:0% +was not happening in the flood plain but +those um sedimentation um + + align:start position:0% +those um sedimentation um + + + align:start position:0% +those um sedimentation um +was + + align:start position:0% +was + + + align:start position:0% +was +those sediment was deposited in the + + align:start position:0% +those sediment was deposited in the + + + align:start position:0% +those sediment was deposited in the +riverbed and that increased the riverbed + + align:start position:0% +riverbed and that increased the riverbed + + + align:start position:0% +riverbed and that increased the riverbed +and it reduces the navigability at the + + align:start position:0% +and it reduces the navigability at the + + + align:start position:0% +and it reduces the navigability at the +same time + + align:start position:0% +same time + + + align:start position:0% +same time +the internal water logging started so in + + align:start position:0% +the internal water logging started so in + + + align:start position:0% +the internal water logging started so in +1980s this whole area of floodplain + + align:start position:0% +1980s this whole area of floodplain + + + align:start position:0% +1980s this whole area of floodplain +becomes waterlogged and permanent + + align:start position:0% +becomes waterlogged and permanent + + + align:start position:0% +becomes waterlogged and permanent +flooding was + + align:start position:0% +flooding was + + + align:start position:0% +flooding was +happening because of this construction + + align:start position:0% +happening because of this construction + + + align:start position:0% +happening because of this construction +of uh embankment so you see how the + + align:start position:0% +of uh embankment so you see how the + + + align:start position:0% +of uh embankment so you see how the +consequence started from the supply side + + align:start position:0% +consequence started from the supply side + + + align:start position:0% +consequence started from the supply side +approach um without considering without + + align:start position:0% +approach um without considering without + + + align:start position:0% +approach um without considering without +uh considering only the narrow focus of + + align:start position:0% +uh considering only the narrow focus of + + + align:start position:0% +uh considering only the narrow focus of +the supply side + + align:start position:0% +the supply side + + + align:start position:0% +the supply side +process so initially it helps in + + align:start position:0% +process so initially it helps in + + + align:start position:0% +process so initially it helps in +improving the agricultural production + + align:start position:0% +improving the agricultural production + + + align:start position:0% +improving the agricultural production +but + + align:start position:0% +but + + + align:start position:0% +but +in the long run it it created + + align:start position:0% +in the long run it it created + + + align:start position:0% +in the long run it it created +a disaster to the local + + align:start position:0% +a disaster to the local + + + align:start position:0% +a disaster to the local +people so local people understood this + + align:start position:0% +people so local people understood this + + + align:start position:0% +people so local people understood this +process + + align:start position:0% +process + + + align:start position:0% +process +and they + + align:start position:0% +and they + + + align:start position:0% +and they +really understood the + + align:start position:0% +really understood the + + + align:start position:0% +really understood the +what is happening there so + + align:start position:0% +what is happening there so + + + align:start position:0% +what is happening there so +going against against the + + align:start position:0% +going against against the + + + align:start position:0% +going against against the +government they try to cut the + + align:start position:0% +government they try to cut the + + + align:start position:0% +government they try to cut the +embankment and + + align:start position:0% +embankment and + + + align:start position:0% +embankment and +bring the river water inside the flood + + align:start position:0% +bring the river water inside the flood + + + align:start position:0% +bring the river water inside the flood +plain and this process they call this is + + align:start position:0% +plain and this process they call this is + + + align:start position:0% +plain and this process they call this is +tidal river management in 1990s + + align:start position:0% +tidal river management in 1990s + + + align:start position:0% +tidal river management in 1990s +so they try to implement this + + align:start position:0% +so they try to implement this + + + align:start position:0% +so they try to implement this +process going against uh government + + align:start position:0% +process going against uh government + + + align:start position:0% +process going against uh government +process and they try to implement + + align:start position:0% +process and they try to implement + + + align:start position:0% +process and they try to implement +locally + + align:start position:0% +locally + + + align:start position:0% +locally +with self-organizing + + align:start position:0% +with self-organizing + + + align:start position:0% +with self-organizing +capacity and that they implemented in + + align:start position:0% +capacity and that they implemented in + + + align:start position:0% +capacity and that they implemented in +one + + align:start position:0% +one + + + align:start position:0% +one +flood plain and they were successful and + + align:start position:0% +flood plain and they were successful and + + + align:start position:0% +flood plain and they were successful and +they um after uh + + align:start position:0% +they um after uh + + + align:start position:0% +they um after uh +two years they were able to um see the + + align:start position:0% +two years they were able to um see the + + + align:start position:0% +two years they were able to um see the +major impact like um navigability of uh + + align:start position:0% +major impact like um navigability of uh + + + align:start position:0% +major impact like um navigability of uh +in the riverbed um + + align:start position:0% +in the riverbed um + + + align:start position:0% +in the riverbed um +um + + align:start position:0% +um + + + align:start position:0% +um +is increased and also um + + align:start position:0% +is increased and also um + + + align:start position:0% +is increased and also um +the flood plain the sedimentation was + + align:start position:0% +the flood plain the sedimentation was + + + align:start position:0% +the flood plain the sedimentation was +happening in the flood plain so um then + + align:start position:0% +happening in the flood plain so um then + + + align:start position:0% +happening in the flood plain so um then +the + + align:start position:0% +the + + + align:start position:0% +the +government could also see the positive + + align:start position:0% +government could also see the positive + + + align:start position:0% +government could also see the positive +benefits so then they try to + + align:start position:0% +benefits so then they try to + + + align:start position:0% +benefits so then they try to +institutionalize this approach in the + + align:start position:0% +institutionalize this approach in the + + + align:start position:0% +institutionalize this approach in the +in the + + align:start position:0% +in the + + + align:start position:0% +in the +government approach so how you can see + + align:start position:0% +government approach so how you can see + + + align:start position:0% +government approach so how you can see +how the transformation or evolution + + align:start position:0% +how the transformation or evolution + + + align:start position:0% +how the transformation or evolution +happened in in this + + align:start position:0% +happened in in this + + + align:start position:0% +happened in in this +context uh similar explanation that i + + align:start position:0% +context uh similar explanation that i + + + align:start position:0% +context uh similar explanation that i +just gave in the in the + + align:start position:0% +just gave in the in the + + + align:start position:0% +just gave in the in the +previous slide + + align:start position:0% +previous slide + + + align:start position:0% +previous slide +just to show how how the evolution was + + align:start position:0% +just to show how how the evolution was + + + align:start position:0% +just to show how how the evolution was +uh happening + + align:start position:0% +uh happening + + + align:start position:0% +uh happening +i uh also try to explain uh how + + align:start position:0% +i uh also try to explain uh how + + + align:start position:0% +i uh also try to explain uh how +paradigm shift in um water resources + + align:start position:0% +paradigm shift in um water resources + + + align:start position:0% +paradigm shift in um water resources +management um happened through the + + align:start position:0% +management um happened through the + + + align:start position:0% +management um happened through the +literature provided by claudia paul + + align:start position:0% +literature provided by claudia paul + + + align:start position:0% +literature provided by claudia paul +boson um she's one of the + + align:start position:0% +boson um she's one of the + + + align:start position:0% +boson um she's one of the +um yeah + + align:start position:0% +um yeah + + + align:start position:0% +um yeah +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +experts on adaptive water resource + + align:start position:0% +experts on adaptive water resource + + + align:start position:0% +experts on adaptive water resource +management or integrated water resources + + align:start position:0% +management or integrated water resources + + + 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position:0% +and let's not worry about state and +local government and uh + + align:start position:0% +local government and uh + + + align:start position:0% +local government and uh +let's do it at a scale that turns around + + align:start position:0% +let's do it at a scale that turns around + + + align:start position:0% +let's do it at a scale that turns around +the lagging region because smaller scale + + align:start position:0% +the lagging region because smaller scale + + + align:start position:0% +the lagging region because smaller scale +efforts to turn around lagging regions + + align:start position:0% +efforts to turn around lagging regions + + + align:start position:0% +efforts to turn around lagging regions +don't work + + align:start position:0% +don't work + + + align:start position:0% +don't work +so + + align:start position:0% +so + + + align:start position:0% +so +the way to understand this the tva story + + align:start position:0% +the way to understand this the tva story + + + align:start position:0% +the way to understand this the tva story +and there are many books + + align:start position:0% +and there are many books + + + align:start position:0% +and there are many books +written about tva + + align:start position:0% +written about tva + + + align:start position:0% +written about tva +sort of longing for + + align:start position:0% +sort of longing for + + + align:start position:0% +sort of longing for +a regional publicly managed + + align:start position:0% +a regional publicly managed + + + align:start position:0% +a regional publicly managed +massive infrastructure + + align:start position:0% + + + + align:start position:0% + +project + + align:start position:0% +project + + + align:start position:0% +project +that would uh stimulate the economy in a + + align:start position:0% +that would uh stimulate the economy in a + + + align:start position:0% +that would uh stimulate the economy in a +way that wouldn't happen otherwise + + align:start position:0% +way that wouldn't happen otherwise + + + align:start position:0% +way that wouldn't happen otherwise +yeah yeah so um + + align:start position:0% +yeah yeah so um + + + align:start position:0% +yeah yeah so um +yeah also in the iwrm + + align:start position:0% +yeah also in the iwrm + + + align:start position:0% +yeah also in the iwrm +literacy uh globally this um + + align:start position:0% +literacy uh globally this um + + + align:start position:0% +literacy uh globally this um +tba approach is highly acknowledged and + + align:start position:0% +tba approach is highly acknowledged and + + + align:start position:0% +tba approach is highly acknowledged and +uh it says that the tbl like approach um + + align:start position:0% +uh it says that the tbl like approach um + + + align:start position:0% +uh it says that the tbl like approach um +mushroomed all over the world for um + + align:start position:0% +mushroomed all over the world for um + + + align:start 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regional development plan +through incorporating for example um + + align:start position:0% +through incorporating for example um + + + align:start position:0% +through incorporating for example um +power generation flood control + + align:start position:0% +power generation flood control + + + align:start position:0% +power generation flood control +and how this integration happens um and + + align:start position:0% +and how this integration happens um and + + + align:start position:0% +and how this integration happens um and +also the concept + + align:start position:0% +also the concept + + + align:start position:0% +also the concept +integration of multiple sectors + + align:start position:0% +integration of multiple sectors + + + align:start position:0% +integration of multiple sectors +uh in the iwrm also uh camp uh from this + + align:start position:0% +uh in the iwrm also uh camp uh from this + + + align:start position:0% +uh in the iwrm also uh camp uh from this +tv like approach that is um uh mentioned + + align:start position:0% +tv like approach that is um uh mentioned + + + align:start position:0% +tv like approach that is um uh mentioned +in the iwrm literature + + align:start position:0% + + + + align:start position:0% + +yeah so uh before going to + + align:start position:0% +yeah so uh before going to + + + align:start position:0% +yeah so uh before going to +principles maybe we can um + + align:start position:0% +principles maybe we can um + + + align:start position:0% +principles maybe we can um +have a + + align:start position:0% +have a + + + align:start position:0% +have a +participatory discussion here um why + + align:start position:0% +participatory discussion here um why + + + align:start position:0% +participatory discussion here um why +iwrm is important for water diplomacy in + + align:start position:0% +iwrm is important for water diplomacy in + + + align:start position:0% +iwrm is important for water diplomacy in +your + + align:start position:0% +your + + + align:start position:0% +your +opinion i i wanted to make it a breakout + + align:start position:0% +opinion i i wanted to make it a breakout + + + align:start position:0% +opinion i i wanted to make it a breakout +group but as we are only + + align:start position:0% +group but as we are only + + + align:start position:0% +group but as we are only +five people so maybe we can + + align:start position:0% +five people so maybe we can + + + align:start position:0% +five people so maybe we can +discuss why in your opinion also there + + align:start position:0% +discuss why in your opinion also there + + + align:start position:0% +discuss why in your opinion also there +was a memo question on this so maybe we + + align:start position:0% +was a memo question on this so maybe we + + + align:start position:0% +was a memo question on this so maybe we +can discuss here + + align:start position:0% +can discuss here + + + align:start position:0% +can discuss here +discuss here why iwrm is important for + + align:start position:0% +discuss here why iwrm is important for + + + align:start position:0% +discuss here why iwrm is important for +water diplomacy + + align:start position:0% + + + + align:start position:0% + +well i guess first do you think it is + + align:start position:0% +well i guess first do you think it is + + + align:start position:0% +well i guess first do you think it is +what what is it about + + align:start position:0% +what what is it about + + + align:start position:0% +what what is it about +integrated + + align:start position:0% +integrated + + + align:start position:0% +integrated +management of water resources + + align:start position:0% +management of water resources + + + align:start position:0% +management of water resources +that makes it an important + + align:start position:0% +that makes it an important + + + align:start position:0% +that makes it an important +element + + align:start position:0% +element + + + align:start position:0% +element +of + + align:start position:0% +of + + + align:start position:0% +of +dealing with transboundary waters + + align:start position:0% + + + + align:start position:0% + +this is a little bit of low-hanging + + align:start position:0% +this is a little bit of low-hanging + + + align:start position:0% +this is a little bit of low-hanging +fruit but one of the readings observed + + align:start position:0% +fruit but one of the readings observed + + + align:start position:0% +fruit but one of the readings observed +that it's the dominant paradigm for + + align:start position:0% +that it's the dominant paradigm for + + + align:start position:0% +that it's the dominant paradigm for +water management globally + + align:start position:0% +water management globally + + + align:start position:0% +water management globally +so it sort of + + align:start position:0% +so it sort of + + + align:start position:0% +so it sort of +is therefore + + align:start position:0% +is therefore + + + align:start position:0% +is therefore +important to diplomacy but i think one + + align:start position:0% +important to diplomacy but i think one + + + align:start position:0% +important to diplomacy but i think one +of the other things that + + align:start position:0% +of the other things that + + + align:start position:0% +of the other things that +stood out to me and i wrote a little bit + + align:start position:0% +stood out to me and i wrote a little bit + + + align:start position:0% +stood out to me and i wrote a little bit +about this in my in my memo is just + + align:start position:0% +about this in my in my memo is just + + + align:start position:0% +about this in my in my memo is just +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +efforts to move beyond diplomatic silos + + align:start position:0% +efforts to move beyond diplomatic silos + + + align:start position:0% +efforts to move beyond diplomatic silos +um there's there was an example in the + + align:start position:0% +um there's there was an example in the + + + align:start position:0% +um there's there was an example in the +loop at all piece that like really stood + + align:start position:0% +loop at all piece that like really stood + + + align:start position:0% +loop at all piece that like really stood +out to me about biofuels and how like + + align:start position:0% +out to me about biofuels and how like + + + align:start position:0% +out to me about biofuels and how like +the development of biofuels + + align:start position:0% +the development of biofuels + + + align:start position:0% +the development of biofuels +sort of subsequently catalyzed or + + align:start position:0% +sort of subsequently catalyzed or + + + align:start position:0% +sort of subsequently catalyzed or +exacerbated existing problems with water + + align:start position:0% +exacerbated existing problems with water + + + align:start position:0% +exacerbated existing problems with water +and food scarcity so the need for like a + + align:start position:0% +and food scarcity so the need for like a + + + align:start position:0% +and food scarcity so the need for like a +more integration a more integrated + + align:start position:0% +more integration a more integrated + + + align:start position:0% +more integration a more integrated +management approach felt + + align:start position:0% +management approach felt + + + align:start position:0% +management approach felt +sort of urgent and necessary as we as we + + align:start position:0% +sort of urgent and necessary as we as we + + + align:start position:0% +sort of urgent and necessary as we as we +move towards perhaps greater scarcity in + + align:start position:0% +move towards perhaps greater scarcity in + + + align:start position:0% +move towards perhaps greater scarcity in +certain water systems + + align:start position:0% +certain water systems + + + align:start position:0% +certain water systems +but how would that work or theoretically + + align:start position:0% +but how would that work or theoretically + + + align:start position:0% +but how would that work or theoretically +how might that work + + align:start position:0% +how might that work + + + align:start position:0% +how might that work +in context in which + + align:start position:0% +in context in which + + + align:start position:0% +in context in which +we do have siloed + + align:start position:0% +we do have siloed + + + align:start position:0% +we do have siloed +entities responsible for things like + + align:start position:0% +entities responsible for things like + + + align:start position:0% +entities responsible for things like +water + + align:start position:0% +water + + + align:start position:0% +water +and if you say + + align:start position:0% +and if you say + + + align:start position:0% +and if you say +well integrated + + align:start position:0% +well integrated + + + align:start position:0% +well integrated +management is the key + + align:start position:0% +management is the key + + + align:start position:0% +management is the key +to managing water in the future so that + + align:start position:0% +to managing water in the future so that + + + align:start position:0% +to managing water in the future so that +you can connect + + align:start position:0% +you can connect + + + align:start position:0% +you can connect +water with energy with food with land + + align:start position:0% +water with energy with food with land + + + align:start position:0% +water with energy with food with land +but that's not how those + + align:start position:0% +but that's not how those + + + align:start position:0% +but that's not how those +entities are set up + + align:start position:0% +entities are set up + + + align:start position:0% +entities are set up +right yeah is it aren't we basically + + align:start position:0% +right yeah is it aren't we basically + + + align:start position:0% +right yeah is it aren't we basically +setting + + align:start position:0% +setting + + + align:start position:0% +setting +up + + align:start position:0% + + + + align:start position:0% + +to setting up systems to fail + + align:start position:0% +to setting up systems to fail + + + align:start position:0% +to setting up systems to fail +if we say that they have to be + + align:start position:0% +if we say that they have to be + + + align:start position:0% +if we say that they have to be +integrated in order to do water + + align:start position:0% +integrated in order to do water + + + align:start position:0% +integrated in order to do water +management when we know that they're not + + align:start position:0% +management when we know that they're not + + + align:start position:0% +management when we know that they're not +therefore what are we hoping for + + align:start position:0% +therefore what are we hoping for + + + align:start position:0% +therefore what are we hoping for +that is a good question + + align:start position:0% +that is a good question + + + align:start position:0% +that is a good question +i don't know if i have an immediate + + align:start position:0% +i don't know if i have an immediate + + + align:start position:0% +i don't know if i have an immediate +answer i'll think about that though well + + align:start position:0% +answer i'll think about that though well + + + align:start position:0% +answer i'll think about that though well +i'm not sure there's a right answer yes + + align:start position:0% +i'm not sure there's a right answer yes + + + align:start position:0% +i'm not sure there's a right answer yes +uh it seems to me that + + align:start position:0% + + + + align:start position:0% + +from a from a planning perspective urban + + align:start position:0% +from a from a planning perspective urban + + + align:start position:0% +from a from a planning perspective urban +regional planning perspective not a + + align:start position:0% +regional planning perspective not a + + + align:start position:0% +regional planning perspective not a +water perspective + + align:start position:0% +water perspective + + + align:start position:0% +water perspective +there's always an argument for centuries + + align:start position:0% +there's always an argument for centuries + + + align:start position:0% +there's always an argument for centuries +that the way to plan cities effectively + + align:start position:0% +that the way to plan cities effectively + + + align:start position:0% +that the way to plan cities effectively +is to start with a clean + + align:start position:0% +is to start with a clean + + + align:start position:0% +is to start with a clean +empty area + + align:start position:0% +empty area + + + align:start position:0% +empty area +and have a designer make a comprehensive + + align:start position:0% +and have a designer make a comprehensive + + + align:start position:0% +and have a designer make a comprehensive +integrated plan + + align:start position:0% +integrated plan + + + align:start position:0% +integrated plan +so that the land is used efficiently so + + align:start position:0% +so that the land is used efficiently so + + + align:start position:0% +so that the land is used efficiently so +that all the uses are appropriately laid + + align:start position:0% +that all the uses are appropriately laid + + + align:start position:0% +that all the uses are appropriately laid +out and + + align:start position:0% +out and + + + align:start position:0% +out and +separate from each other when that's + + align:start position:0% +separate from each other when that's + + + align:start position:0% +separate from each other when that's +appropriate + + align:start position:0% +appropriate + + + align:start position:0% +appropriate +and that um you don't have to + + align:start position:0% +and that um you don't have to + + + align:start position:0% +and that um you don't have to +have holes in the plan + + align:start position:0% +have holes in the plan + + + align:start position:0% +have holes in the plan +where there's private ownership or other + + align:start position:0% +where there's private ownership or other + + + align:start position:0% +where there's private ownership or other +things that happen and you don't have to + + align:start position:0% +things that happen and you don't have to + + + align:start position:0% +things that happen and you don't have to +worry over time because you just started + + align:start position:0% +worry over time because you just started + + + align:start position:0% +worry over time because you just started +building in one corner and by the time + + align:start position:0% +building in one corner and by the time + + + align:start position:0% +building in one corner and by the time +it was done it was just a giant + + align:start position:0% +it was done it was just a giant + + + align:start position:0% +it was done it was just a giant +pattern that's uh of uncontrolled + + align:start position:0% +pattern that's uh of uncontrolled + + + align:start position:0% +pattern that's uh of uncontrolled +development the idea has always been + + align:start position:0% +development the idea has always been + + + align:start position:0% +development the idea has always been +you should plan whole cities in a + + align:start position:0% +you should plan whole cities in a + + + align:start position:0% +you should plan whole cities in a +comprehensive way to me + + align:start position:0% +comprehensive way to me + + + align:start position:0% +comprehensive way to me +iwrm has some of the same resonance okay + + align:start position:0% +iwrm has some of the same resonance okay + + + align:start position:0% +iwrm has some of the same resonance okay +now we know in real life there are very + + align:start position:0% +now we know in real life there are very + + + align:start position:0% +now we know in real life there are very +very few + + align:start position:0% +very few + + + align:start position:0% +very few +planned cities where the whole city was + + align:start position:0% +planned cities where the whole city was + + + align:start position:0% +planned cities where the whole city was +laid out + + align:start position:0% +laid out + + + align:start position:0% +laid out +and + + align:start position:0% +and + + + align:start position:0% +and +all of its evolution was guided by or + + align:start position:0% +all of its evolution was guided by or + + + align:start position:0% +all of its evolution was guided by or +controlled by the original plan + + align:start position:0% +controlled by the original plan + + + align:start position:0% +controlled by the original plan +and + + align:start position:0% +and + + + align:start position:0% +and +it's very hard to have in a democratic + + align:start position:0% +it's very hard to have in a democratic + + + align:start position:0% +it's very hard to have in a democratic +context and one in which there's private + + align:start position:0% +context and one in which there's private + + + align:start position:0% +context and one in which there's private +land ownership + + align:start position:0% +land ownership + + + align:start position:0% +land ownership +continuity + + align:start position:0% +continuity + + + align:start position:0% +continuity +with a single plan + + align:start position:0% +with a single plan + + + align:start position:0% +with a single plan +and even in some parts of the world + + align:start position:0% +and even in some parts of the world + + + align:start position:0% +and even in some parts of the world +where historically there were efforts to + + align:start position:0% +where historically there were efforts to + + + align:start position:0% +where historically there were efforts to +plan + + align:start position:0% +plan + + + align:start position:0% +plan +whole new capitals whole new cities + + align:start position:0% +whole new capitals whole new cities + + + align:start position:0% +whole new capitals whole new cities +where they brought in a famous architect + + align:start position:0% +where they brought in a famous architect + + + align:start position:0% +where they brought in a famous architect +who made a beautiful plan for the whole + + align:start position:0% +who made a beautiful plan for the whole + + + align:start position:0% +who made a beautiful plan for the whole +place + + align:start position:0% +place + + + align:start position:0% +place +over decades + + align:start position:0% +over decades + + + align:start position:0% +over decades +the place changes from what the original + + align:start position:0% +the place changes from what the original + + + align:start position:0% +the place changes from what the original +design was + + align:start position:0% +design was + + + align:start position:0% +design was +for all kinds of reasons not the least + + align:start position:0% +for all kinds of reasons not the least + + + align:start position:0% +for all kinds of reasons not the least +of which people want to have choice + + align:start position:0% +of which people want to have choice + + + align:start position:0% +of which people want to have choice +about what things are going to be look + + align:start position:0% +about what things are going to be look + + + align:start position:0% +about what things are going to be look +like and what it can do with what their + + align:start position:0% +like and what it can do with what their + + + align:start position:0% +like and what it can do with what their +land is and what say they have in a + + align:start position:0% +land is and what say they have in a + + + align:start position:0% +land is and what say they have in a +democratic context + + align:start position:0% +democratic context + + + align:start position:0% +democratic context +so + + align:start position:0% +so + + + align:start position:0% +so +just for purposes of of uh + + align:start position:0% +just for purposes of of uh + + + align:start position:0% +just for purposes of of uh +pursuing further the question that i + + align:start position:0% +pursuing further the question that i + + + align:start position:0% +pursuing further the question that i +asked you gemma is + + align:start position:0% +asked you gemma is + + + align:start position:0% +asked you gemma is +um do you imagine that people in a + + align:start position:0% +um do you imagine that people in a + + + align:start position:0% +um do you imagine that people in a +democratic context + + align:start position:0% +democratic context + + + align:start position:0% +democratic context +can live in in and work and build in a + + align:start position:0% +can live in in and work and build in a + + + align:start position:0% +can live in in and work and build in a +way that's comprehensive + + align:start position:0% +way that's comprehensive + + + align:start position:0% +way that's comprehensive +integrated and planned + + align:start position:0% +integrated and planned + + + align:start position:0% +integrated and planned +when all the forces of democracy + + align:start position:0% +when all the forces of democracy + + + align:start position:0% +when all the forces of democracy +privatization + + align:start position:0% +privatization + + + align:start position:0% +privatization +individuality and all the unexpected + + align:start position:0% +individuality and all the unexpected + + + align:start position:0% +individuality and all the unexpected +things that happen + + align:start position:0% +things that happen + + + align:start position:0% +things that happen +or organically + + align:start position:0% +or organically + + + align:start position:0% +or organically +pull in the opposite direction + + align:start position:0% + + + + align:start position:0% + +i mean i think i have to say yes but + + align:start position:0% +i mean i think i have to say yes but + + + align:start position:0% +i mean i think i have to say yes but +that's sort of my prerogative as a first + + align:start position:0% +that's sort of my prerogative as a first + + + align:start position:0% +that's sort of my prerogative as a first +semester urban planning student like if + + align:start position:0% +semester urban planning student like if + + + align:start position:0% +semester urban planning student like if +you i've already given up on the field + + align:start position:0% +you i've already given up on the field + + + align:start position:0% +you i've already given up on the field +then it may be too late for me + + align:start position:0% +then it may be too late for me + + + align:start position:0% +then it may be too late for me +um + + align:start position:0% + + + + align:start position:0% + +i think that + + align:start position:0% + + + + align:start position:0% + +some healthy skepticism isn't uncalled + + align:start position:0% +some healthy skepticism isn't uncalled + + + align:start position:0% +some healthy skepticism isn't uncalled +for i guess i mean it's + + align:start position:0% +for i guess i mean it's + + + align:start position:0% +for i guess i mean it's +i don't know i guess it's + + align:start position:0% +i don't know i guess it's + + + align:start position:0% +i don't know i guess it's +what is sort of resonant about iwrm and + + align:start position:0% +what is sort of resonant about iwrm and + + + align:start position:0% +what is sort of resonant about iwrm and +like the water nexus approach and like + + align:start position:0% +like the water nexus approach and like + + + align:start position:0% +like the water nexus approach and like +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +science policy interfaces more broadly + + align:start position:0% +science policy interfaces more broadly + + + align:start position:0% +science policy interfaces more broadly +is the + + align:start position:0% +is the + + + align:start position:0% +is the +kind of potential to reimagine existing + + align:start position:0% +kind of potential to reimagine existing + + + align:start position:0% +kind of potential to reimagine existing +diplomatic regimes but i don't know + + align:start position:0% +diplomatic regimes but i don't know + + + align:start position:0% +diplomatic regimes but i don't know +whether that actually will work in + + align:start position:0% +whether that actually will work in + + + align:start position:0% +whether that actually will work in +practice + + align:start position:0% +practice + + + align:start position:0% +practice +so maybe it's just an intellectual + + align:start position:0% +so maybe it's just an intellectual + + + align:start position:0% +so maybe it's just an intellectual +exercise but i think it's a useful + + align:start position:0% +exercise but i think it's a useful + + + align:start position:0% +exercise but i think it's a useful +intellectual exercise + + align:start position:0% +intellectual exercise + + + align:start position:0% +intellectual exercise +well it's only useful if it inspires + + align:start position:0% +well it's only useful if it inspires + + + align:start position:0% +well it's only useful if it inspires +something in practice that can be done + + align:start position:0% +something in practice that can be done + + + align:start position:0% +something in practice that can be done +right it's not useful + + align:start position:0% +right it's not useful + + + align:start position:0% +right it's not useful +if it alludes to something in theory + + align:start position:0% +if it alludes to something in theory + + + align:start position:0% +if it alludes to something in theory +that can't be done in practice and + + align:start position:0% +that can't be done in practice and + + + align:start position:0% +that can't be done in practice and +everybody's just thwarted + + align:start position:0% +everybody's just thwarted + + + align:start position:0% +everybody's just thwarted +and can't achieve what they're supposed + + align:start position:0% +and can't achieve what they're supposed + + + align:start position:0% +and can't achieve what they're supposed +to or the ideal + + align:start position:0% +to or the ideal + + + align:start position:0% +to or the ideal +and + + align:start position:0% +and + + + align:start position:0% +and +just to come to to loop back around + + align:start position:0% +just to come to to loop back around + + + align:start position:0% +just to come to to loop back around +again to urban planning nobody in urban + + align:start position:0% +again to urban planning nobody in urban + + + align:start position:0% +again to urban planning nobody in urban +planning teaches about comprehensive + + align:start position:0% +planning teaches about comprehensive + + + align:start position:0% +planning teaches about comprehensive +planned cities anymore except as a + + align:start position:0% +planned cities anymore except as a + + + align:start position:0% +planned cities anymore except as a +intriguing historical artifact + + align:start position:0% +intriguing historical artifact + + + align:start position:0% +intriguing historical artifact +nobody would imagine + + align:start position:0% +nobody would imagine + + + align:start position:0% +nobody would imagine +that you would build a place according + + align:start position:0% +that you would build a place according + + + align:start position:0% +that you would build a place according +to a plan at time one and expect at time + + align:start position:0% +to a plan at time one and expect at time + + + align:start position:0% +to a plan at time one and expect at time +two a decade two decades a century later + + align:start position:0% +two a decade two decades a century later + + + align:start position:0% +two a decade two decades a century later +that the place is going to have anything + + align:start position:0% +that the place is going to have anything + + + align:start position:0% +that the place is going to have anything +to do with what that original plan was + + align:start position:0% +to do with what that original plan was + + + align:start position:0% +to do with what that original plan was +and yet they still think there's + + align:start position:0% +and yet they still think there's + + + align:start position:0% +and yet they still think there's +planning going on + + align:start position:0% + + + + align:start position:0% + +the plan the planning + + align:start position:0% +the plan the planning + + + align:start position:0% +the plan the planning +is about the process of + + align:start position:0% +is about the process of + + + align:start position:0% +is about the process of +is but the process of adaptation + + align:start position:0% +is but the process of adaptation + + + align:start position:0% +is but the process of adaptation +yeah the planning is to create the + + align:start position:0% +yeah the planning is to create the + + + align:start position:0% +yeah the planning is to create the +institutions to be able to modify + + align:start position:0% +institutions to be able to modify + + + align:start position:0% +institutions to be able to modify +what you're doing collectively + + align:start position:0% +what you're doing collectively + + + align:start position:0% +what you're doing collectively +so it's it's still planning + + align:start position:0% +so it's it's still planning + + + align:start position:0% +so it's it's still planning +it's not planning it to achieve a + + align:start position:0% +it's not planning it to achieve a + + + align:start position:0% +it's not planning it to achieve a +pre-ordained comprehensive idea + + align:start position:0% +pre-ordained comprehensive idea + + + align:start position:0% +pre-ordained comprehensive idea +and i would argue in the water realm + + align:start position:0% +and i would argue in the water realm + + + align:start position:0% +and i would argue in the water realm +we ought to be worried about iwrm as an + + align:start position:0% +we ought to be worried about iwrm as an + + + align:start position:0% +we ought to be worried about iwrm as an +ideal + + align:start position:0% +ideal + + + align:start position:0% +ideal +because it presumes there are + + align:start position:0% +because it presumes there are + + + align:start position:0% +because it presumes there are +institutions with the authority + + align:start position:0% +institutions with the authority + + + align:start position:0% +institutions with the authority +the power with the knowledge + + align:start position:0% +the power with the knowledge + + + align:start position:0% +the power with the knowledge +to integrate across + + align:start position:0% +to integrate across + + + align:start position:0% +to integrate across +all of these multiple dimensions in + + align:start position:0% +all of these multiple dimensions in + + + align:start position:0% +all of these multiple dimensions in +spite of the fact that we have created + + align:start position:0% +spite of the fact that we have created + + + align:start position:0% +spite of the fact that we have created +the silos that you alluded to + + align:start position:0% +the silos that you alluded to + + + align:start position:0% +the silos that you alluded to +and that there are contending interests + + align:start position:0% +and that there are contending interests + + + align:start position:0% +and that there are contending interests +trying to pursue and maximize different + + align:start position:0% +trying to pursue and maximize different + + + align:start position:0% +trying to pursue and maximize different +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +for from their standpoint that are good + + align:start position:0% +for from their standpoint that are good + + + align:start position:0% +for from their standpoint that are good +from their standpoint + + align:start position:0% + + + + align:start position:0% + +so for the reasons i worry about + + align:start position:0% +so for the reasons i worry about + + + align:start position:0% +so for the reasons i worry about +comprehensive planning i worry about + + align:start position:0% +comprehensive planning i worry about + + + align:start position:0% +comprehensive planning i worry about +iwrm + + align:start position:0% +iwrm + + + align:start position:0% +iwrm +so any other thoughts + + align:start position:0% +so any other thoughts + + + align:start position:0% +so any other thoughts +regarding iworm + + align:start position:0% + + + + align:start position:0% + +i think something related to what we + + align:start position:0% +i think something related to what we + + + align:start position:0% +i think something related to what we +were just talking about is like the + + align:start position:0% +were just talking about is like the + + + align:start position:0% +were just talking about is like the +interesting fact that in some ways the + + align:start position:0% +interesting fact that in some ways the + + + align:start position:0% +interesting fact that in some ways the +iwrm is like very broad but then in + + align:start position:0% +iwrm is like very broad but then in + + + align:start position:0% +iwrm is like very broad but then in +other ways a lot of people criticize it + + align:start position:0% +other ways a lot of people criticize it + + + align:start position:0% +other ways a lot of people criticize it +for not being broad enough + + align:start position:0% +for not being broad enough + + + align:start position:0% +for not being broad enough +um saying that like the adaptive water + + align:start position:0% +um saying that like the adaptive water + + + align:start position:0% +um saying that like the adaptive water +management system like needs to replace + + align:start position:0% +management system like needs to replace + + + align:start position:0% +management system like needs to replace +or augment the iwrm because that um is + + align:start position:0% +or augment the iwrm because that um is + + + align:start position:0% +or augment the iwrm because that um is +moving toward + + align:start position:0% +moving toward + + + align:start position:0% +moving toward +that like can we not only create water + + align:start position:0% +that like can we not only create water + + + align:start position:0% +that like can we not only create water +management but can we make sure that + + align:start position:0% +management but can we make sure that + + + align:start position:0% +management but can we make sure that +this water management system is also + + align:start position:0% +this water management system is also + + + align:start position:0% +this water management system is also +going to be adaptable to the future + + align:start position:0% +going to be adaptable to the future + + + align:start position:0% +going to be adaptable to the future +because we have to assume that it's not + + align:start position:0% +because we have to assume that it's not + + + align:start position:0% +because we have to assume that it's not +constant when we look at these extreme + + align:start position:0% +constant when we look at these extreme + + + align:start position:0% +constant when we look at these extreme +weather patterns or + + align:start position:0% +weather patterns or + + + align:start position:0% +weather patterns or +um like changes in the nature of a + + align:start position:0% +um like changes in the nature of a + + + align:start position:0% +um like changes in the nature of a +conflict some of these iwrm + + align:start position:0% +conflict some of these iwrm + + + align:start position:0% +conflict some of these iwrm +um like + + align:start position:0% +um like + + + align:start position:0% +um like +management scenarios are just not + + align:start position:0% +management scenarios are just not + + + align:start position:0% +management scenarios are just not +like actively trying to adapt and become + + align:start position:0% +like actively trying to adapt and become + + + align:start position:0% +like actively trying to adapt and become +better to adjust to these changes so in + + align:start position:0% +better to adjust to these changes so in + + + align:start position:0% +better to adjust to these changes so in +a lot of ways people are saying like oh + + align:start position:0% +a lot of ways people are saying like oh + + + align:start position:0% +a lot of ways people are saying like oh +the iwrm is not enough like what about + + align:start position:0% +the iwrm is not enough like what about + + + align:start position:0% +the iwrm is not enough like what about +the nexus what about this like adaptive + + align:start position:0% +the nexus what about this like adaptive + + + align:start position:0% +the nexus what about this like adaptive +water management system and so like in + + align:start position:0% +water management system and so like in + + + align:start position:0% +water management system and so like in +my memo i talked a lot about how um i + + align:start position:0% +my memo i talked a lot about how um i + + + align:start position:0% +my memo i talked a lot about how um i +think one of the readings tried to + + align:start position:0% +think one of the readings tried to + + + align:start position:0% +think one of the readings tried to +analyze whether or not like you could + + align:start position:0% +analyze whether or not like you could + + + align:start position:0% +analyze whether or not like you could +replace the iwrm and i thought it was + + align:start position:0% +replace the iwrm and i thought it was + + + align:start position:0% +replace the iwrm and i thought it was +really interesting that they touched on + + align:start position:0% +really interesting that they touched on + + + align:start position:0% +really interesting that they touched on +like the social value of the iwrm like + + align:start position:0% +like the social value of the iwrm like + + + align:start position:0% +like the social value of the iwrm like +it's taken a long time to be adopted + + align:start position:0% +it's taken a long time to be adopted + + + align:start position:0% +it's taken a long time to be adopted +because + + align:start position:0% +because + + + align:start position:0% +because +like a lot of the water policy + + align:start position:0% +like a lot of the water policy + + + align:start position:0% +like a lot of the water policy +water diplomacy sector is like + + align:start position:0% +water diplomacy sector is like + + + align:start position:0% +water diplomacy sector is like +if well-respected water diplomats use a + + align:start position:0% +if well-respected water diplomats use a + + + align:start position:0% +if well-respected water diplomats use a +certain water management system then + + align:start position:0% +certain water management system then + + + align:start position:0% +certain water management system then +like it's more likely to be somewhere + + align:start position:0% +like it's more likely to be somewhere + + + align:start position:0% +like it's more likely to be somewhere +else not just + + align:start position:0% +else not just + + + align:start position:0% +else not just +i guess like how some business models or + + align:start position:0% +i guess like how some business models or + + + align:start position:0% +i guess like how some business models or +other like sectors might transfer a + + align:start position:0% +other like sectors might transfer a + + + align:start position:0% +other like sectors might transfer a +certain system so i just think that the + + align:start position:0% +certain system so i just think that the + + + align:start position:0% +certain system so i just think that the +the iwrms + + align:start position:0% +the iwrms + + + align:start position:0% +the iwrms +value the fact that it is water centric + + align:start position:0% +value the fact that it is water centric + + + align:start position:0% +value the fact that it is water centric +is like i think very + + align:start position:0% +is like i think very + + + align:start position:0% +is like i think very +like a strength of the iwrm and then the + + align:start position:0% +like a strength of the iwrm and then the + + + align:start position:0% +like a strength of the iwrm and then the +fact that in the nexus water is um not + + align:start position:0% +fact that in the nexus water is um not + + + align:start position:0% +fact that in the nexus water is um not +considered more valuable or important + + align:start position:0% +considered more valuable or important + + + align:start position:0% +considered more valuable or important +than these other + + align:start position:0% +than these other + + + align:start position:0% +than these other +like sectors that you're considering in + + align:start position:0% +like sectors that you're considering in + + + align:start position:0% +like sectors that you're considering in +the nexus whether or not it's like the + + align:start position:0% +the nexus whether or not it's like the + + + align:start position:0% +the nexus whether or not it's like the +food water energy nexus where like every + + align:start position:0% +food water energy nexus where like every + + + align:start position:0% +food water energy nexus where like every +sector needs to be treated equally i + + align:start position:0% +sector needs to be treated equally i + + + align:start position:0% +sector needs to be treated equally i +think like the fact that the iwrm puts + + align:start position:0% +think like the fact that the iwrm puts + + + align:start position:0% +think like the fact that the iwrm puts +the water + + align:start position:0% +the water + + + align:start position:0% +the water +like + + align:start position:0% +like + + + align:start position:0% +like +as the most important entity even though + + align:start position:0% +as the most important entity even though + + + align:start position:0% +as the most important entity even though +it is maybe creating some boundaries + + align:start position:0% +it is maybe creating some boundaries + + + align:start position:0% +it is maybe creating some boundaries +that the nexus wants to like get rid of + + align:start position:0% +that the nexus wants to like get rid of + + + align:start position:0% +that the nexus wants to like get rid of +i think is still really valuable because + + align:start position:0% +i think is still really valuable because + + + align:start position:0% +i think is still really valuable because +if you like + + align:start position:0% +if you like + + + align:start position:0% +if you like +get too broad it's hard to make any + + align:start position:0% +get too broad it's hard to make any + + + align:start position:0% +get too broad it's hard to make any +progress + + align:start position:0% +progress + + + align:start position:0% +progress +but maybe i've misinterpreted + + align:start position:0% +but maybe i've misinterpreted + + + align:start position:0% +but maybe i've misinterpreted +i don't know it seems like the future + + align:start position:0% +i don't know it seems like the future + + + align:start position:0% +i don't know it seems like the future +needs to be like more understanding and + + align:start position:0% +needs to be like more understanding and + + + align:start position:0% +needs to be like more understanding and +expansive and multi-centric but also + + align:start position:0% +expansive and multi-centric but also + + + align:start position:0% +expansive and multi-centric but also +like + + align:start position:0% +like + + + align:start position:0% +like +how do we make progress if we can't get + + align:start position:0% +how do we make progress if we can't get + + + align:start position:0% +how do we make progress if we can't get +all those people to sit at the table and + + align:start position:0% +all those people to sit at the table and + + + align:start position:0% +all those people to sit at the table and +make an agreement in any regard + + align:start position:0% + + + + align:start position:0% + +yeah i think uh in terms of um + + align:start position:0% +yeah i think uh in terms of um + + + align:start position:0% +yeah i think uh in terms of um +theoretical aspect of course the iwrm is + + align:start position:0% +theoretical aspect of course the iwrm is + + + align:start position:0% +theoretical aspect of course the iwrm is +very interesting and but in terms of + + align:start position:0% +very interesting and but in terms of + + + align:start position:0% +very interesting and but in terms of +practice um this is the main limitations + + align:start position:0% +practice um this is the main limitations + + + align:start position:0% +practice um this is the main limitations +that to + + align:start position:0% +that to + + + align:start position:0% +that to +uh implement this theoretical framework + + align:start position:0% +uh implement this theoretical framework + + + align:start position:0% +uh implement this theoretical framework +in practice this is highly + + align:start position:0% +in practice this is highly + + + align:start position:0% +in practice this is highly +criticized and + + align:start position:0% +criticized and + + + align:start position:0% +criticized and +this um implementation + + align:start position:0% +this um implementation + + + align:start position:0% +this um implementation +um through um + + align:start position:0% + + + + align:start position:0% + +actual uh following the actual process + + align:start position:0% +actual uh following the actual process + + + align:start position:0% +actual uh following the actual process +of the framework i i haven't done + + align:start position:0% +of the framework i i haven't done + + + align:start position:0% +of the framework i i haven't done +uh i haven't seen any um + + align:start position:0% +uh i haven't seen any um + + + align:start position:0% +uh i haven't seen any um +studies that really went through the + + align:start position:0% +studies that really went through the + + + align:start position:0% +studies that really went through the +iwrm implementation + + align:start position:0% +iwrm implementation + + + align:start position:0% +iwrm implementation +so that is the main challenging thing + + align:start position:0% +so that is the main challenging thing + + + align:start position:0% +so that is the main challenging thing +that the implementation of iwrm + + align:start position:0% +that the implementation of iwrm + + + align:start position:0% +that the implementation of iwrm +is + + align:start position:0% +is + + + align:start position:0% +is +is very difficult and is + + align:start position:0% +is very difficult and is + + + align:start position:0% +is very difficult and is +is one of the + + align:start position:0% +is one of the + + + align:start position:0% +is one of the +um + + align:start position:0% +um + + + align:start position:0% +um +unachieved goal of the iwrm that's the + + align:start position:0% +unachieved goal of the iwrm that's the + + + align:start position:0% +unachieved goal of the iwrm that's the +main + + align:start position:0% +main + + + align:start position:0% +main +criticism but in terms of the + + align:start position:0% +criticism but in terms of the + + + align:start position:0% +criticism but in terms of the +uh theoretical contribution that has + + align:start position:0% +uh theoretical contribution that has + + + align:start position:0% +uh theoretical contribution that has +been done is i think is + + align:start position:0% +been done is i think is + + + align:start position:0% +been done is i think is +highly valuable at the broader level + + align:start position:0% +highly valuable at the broader level + + + align:start position:0% +highly valuable at the broader level +but for implementing uh it needs kind of + + align:start position:0% +but for implementing uh it needs kind of + + + align:start position:0% +but for implementing uh it needs kind of +um yeah + + align:start position:0% +um yeah + + + align:start position:0% +um yeah +some kind of um implementation oriented + + align:start position:0% +some kind of um implementation oriented + + + align:start position:0% +some kind of um implementation oriented +approach + + align:start position:0% +approach + + + align:start position:0% +approach +that's how i i see + + align:start position:0% +that's how i i see + + + align:start position:0% +that's how i i see +so yeah + + align:start position:0% +so yeah + + + align:start position:0% +so yeah +any thought at all in practice i mean i + + align:start position:0% +any thought at all in practice i mean i + + + align:start position:0% +any thought at all in practice i mean i +guess i mean + + align:start position:0% +guess i mean + + + align:start position:0% +guess i mean +in practice i guess you would hope + + align:start position:0% +in practice i guess you would hope + + + align:start position:0% +in practice i guess you would hope +that negotiators would + + align:start position:0% +that negotiators would + + + align:start position:0% +that negotiators would +would have enough or be able to bring + + align:start position:0% +would have enough or be able to bring + + + align:start position:0% +would have enough or be able to bring +enough i mean this is obviously very + + align:start position:0% +enough i mean this is obviously very + + + align:start position:0% +enough i mean this is obviously very +dependent on on what the kind of + + align:start position:0% +dependent on on what the kind of + + + align:start position:0% +dependent on on what the kind of +initiating circumstances are of any + + align:start position:0% +initiating circumstances are of any + + + align:start position:0% +initiating circumstances are of any +negotiation but have enough flexibility + + align:start position:0% +negotiation but have enough flexibility + + + align:start position:0% +negotiation but have enough flexibility +to + + align:start position:0% +to + + + align:start position:0% +to +to draw upon kind of various + + align:start position:0% +to draw upon kind of various + + + align:start position:0% +to draw upon kind of various +frameworks + + align:start position:0% +frameworks + + + align:start position:0% +frameworks +as they + + align:start position:0% +as they + + + align:start position:0% +as they +as needed as as beneficial to + + align:start position:0% +as needed as as beneficial to + + + align:start position:0% +as needed as as beneficial to +a specific dispute whether or not you + + align:start position:0% +a specific dispute whether or not you + + + align:start position:0% +a specific dispute whether or not you +know they call it iwrm + + align:start position:0% +know they call it iwrm + + + align:start position:0% +know they call it iwrm +um + + align:start position:0% +um + + + align:start position:0% +um +or not + + align:start position:0% + + + + align:start position:0% + +you know the limitations of the iwrm + + align:start position:0% +you know the limitations of the iwrm + + + align:start position:0% +you know the limitations of the iwrm +whether it's in terms of scale or in + + align:start position:0% +whether it's in terms of scale or in + + + align:start position:0% +whether it's in terms of scale or in +terms of of kind of what's not included + + align:start position:0% +terms of of kind of what's not included + + + align:start position:0% +terms of of kind of what's not included +because of its water centric focus like + + align:start position:0% +because of its water centric focus like + + + align:start position:0% +because of its water centric focus like +can be supplemented by drawing off some + + align:start position:0% +can be supplemented by drawing off some + + + align:start position:0% +can be supplemented by drawing off some +of the other nexus + + align:start position:0% +of the other nexus + + + align:start position:0% +of the other nexus +some of the next approaches as you know + + align:start position:0% +some of the next approaches as you know + + + align:start position:0% +some of the next approaches as you know +the other others have said already that + + align:start position:0% +the other others have said already that + + + align:start position:0% +the other others have said already that +if you are kind of in the process of + + align:start position:0% +if you are kind of in the process of + + + align:start position:0% +if you are kind of in the process of +negotiating a dispute you + + align:start position:0% +negotiating a dispute you + + + align:start position:0% +negotiating a dispute you +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +ideally should be able to kind of + + align:start position:0% +ideally should be able to kind of + + + align:start position:0% +ideally should be able to kind of +pick and choose to an extent and not not + + align:start position:0% +pick and choose to an extent and not not + + + align:start position:0% +pick and choose to an extent and not not +be totally didactic about about how you + + align:start position:0% +be totally didactic about about how you + + + align:start position:0% +be totally didactic about about how you +apply these frameworks + + align:start position:0% +apply these frameworks + + + align:start position:0% +apply these frameworks +i mean i guess i + + align:start position:0% +i mean i guess i + + + align:start position:0% +i mean i guess i +i don't know how you analyze it then if + + align:start position:0% +i don't know how you analyze it then if + + + align:start position:0% +i don't know how you analyze it then if +you're looking at it so holistically but + + align:start position:0% +you're looking at it so holistically but + + + align:start position:0% +you're looking at it so holistically but +it's hard for me to imagine + + align:start position:0% +it's hard for me to imagine + + + align:start position:0% +it's hard for me to imagine +any any one framework being able to + + align:start position:0% +any any one framework being able to + + + align:start position:0% +any any one framework being able to +fully encompass kind of + + align:start position:0% +fully encompass kind of + + + align:start position:0% +fully encompass kind of +all the possibilities of of a water + + align:start position:0% +all the possibilities of of a water + + + align:start position:0% +all the possibilities of of a water +dispute + + align:start position:0% +dispute + + + align:start position:0% +dispute +i think starting with a dispute + + align:start position:0% +i think starting with a dispute + + + align:start position:0% +i think starting with a dispute +is um + + align:start position:0% +is um + + + align:start position:0% +is um +going to get you into a corner you don't + + align:start position:0% +going to get you into a corner you don't + + + align:start position:0% +going to get you into a corner you don't +need to be in + + align:start position:0% +need to be in + + + align:start position:0% +need to be in +start with the fact that you need to + + align:start position:0% +start with the fact that you need to + + + align:start position:0% +start with the fact that you need to +manage water + + align:start position:0% +manage water + + + align:start position:0% +manage water +there's not a dispute you just you have + + align:start position:0% +there's not a dispute you just you have + + + align:start position:0% +there's not a dispute you just you have +water and you have competing demands and + + align:start position:0% +water and you have competing demands and + + + align:start position:0% +water and you have competing demands and +you have competing interests and you + + align:start position:0% +you have competing interests and you + + + align:start position:0% +you have competing interests and you +have to manage the water + + align:start position:0% +have to manage the water + + + align:start position:0% +have to manage the water +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what would be a good way + + align:start position:0% +what would be a good way + + + align:start position:0% +what would be a good way +to manage the water + + align:start position:0% + + + + align:start position:0% + +to involve + + align:start position:0% +to involve + + + align:start position:0% +to involve +entities + + align:start position:0% +entities + + + align:start 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+engage +the stakeholders affected by + + align:start position:0% +the stakeholders affected by + + + align:start position:0% +the stakeholders affected by +the decisions so there's support for + + align:start position:0% +the decisions so there's support for + + + align:start position:0% +the decisions so there's support for +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +the decision is to go ahead with + + align:start position:0% +the decision is to go ahead with + + + align:start position:0% +the decision is to go ahead with +would it make more sense to look just + + align:start position:0% +would it make more sense to look just + + + align:start position:0% +would it make more sense to look just +narrowly at the water that you have + + align:start position:0% +narrowly at the water that you have + + + align:start position:0% +narrowly at the water that you have +responsibility for because you're within + + align:start position:0% +responsibility for because you're within + + + align:start position:0% +responsibility for because you're within +a political boundary or would it make + + align:start position:0% +a political boundary or would it make + + + align:start position:0% +a political boundary or would it make +more sense to look at the water system + + align:start position:0% +more sense to look at the water system + + + align:start position:0% +more sense to look at the water system +moving underground or above ground that + + align:start position:0% +moving underground or above ground that + + + align:start position:0% +moving underground or above ground that +affects the water that you have + + align:start position:0% +affects the water that you have + + + align:start position:0% +affects the water that you have +responsibility for + + align:start position:0% +responsibility for + + + align:start position:0% +responsibility for +because the answers to those three kinds + + align:start position:0% +because the answers to those three kinds + + + align:start position:0% +because the answers to those three kinds +of questions + + align:start position:0% +of questions + + + align:start position:0% +of questions +almost always lead + + align:start position:0% +almost always lead + + + align:start position:0% +almost always lead +to people saying + + align:start position:0% +to people saying + + + align:start position:0% +to people saying +broader + + align:start position:0% +broader + + + align:start position:0% +broader +linked more comprehensive more + + align:start position:0% +linked more comprehensive more + + + align:start position:0% +linked more comprehensive more +participatory + + align:start position:0% +participatory + + + align:start position:0% +participatory +more completely engaged because it it + + align:start position:0% +more completely engaged because it it + + + align:start position:0% +more completely engaged because it it +seems like a better way to manage water + + align:start position:0% +seems like a better way to manage water + + + align:start position:0% +seems like a better way to manage water +now + + align:start position:0% +now + + + align:start position:0% +now +assume there's a dispute + + align:start position:0% +assume there's a dispute + + + align:start position:0% +assume there's a dispute +within that water management system + + align:start position:0% +within that water management system + + + align:start position:0% +within that water management system +how would you expect it to be resolved + + align:start position:0% +how would you expect it to be resolved + + + align:start position:0% +how would you expect it to be resolved +well if you had + + align:start position:0% +well if you had + + + align:start position:0% +well if you had +pulled in + + align:start position:0% +pulled in + + + align:start position:0% +pulled in +all of those actors + + align:start position:0% +all of those actors + + + align:start position:0% +all of those actors +and all of those interests and all of + + align:start position:0% +and all of those interests and all of + + + align:start position:0% +and all of those interests and all of +that knowledge and all of that authority + + align:start position:0% +that knowledge and all of that authority + + + align:start position:0% +that knowledge and all of that authority +to manage the water + + align:start position:0% +to manage the water + + + align:start position:0% +to manage the water +and there was a dispute within that + + align:start position:0% +and there was a dispute within that + + + align:start position:0% +and there was a dispute within that +you'd probably have to engage + + align:start position:0% +you'd probably have to engage + + + align:start position:0% +you'd probably have to engage +all of those same elements in sorting + + align:start position:0% +all of those same elements in sorting + + + align:start position:0% +all of those same elements in sorting +out a dispute + + align:start position:0% +out a dispute + + + align:start position:0% +out a dispute +that emerged it would be hard to + + align:start position:0% +that emerged it would be hard to + + + align:start position:0% +that emerged it would be hard to +to say oh there's a dispute now all of + + align:start position:0% +to say oh there's a dispute now all of + + + align:start position:0% +to say oh there's a dispute now all of +you were involved in the planning of + + align:start position:0% +you were involved in the planning of + + + align:start position:0% +you were involved in the planning of +this and the management of this go away + + align:start position:0% +this and the management of this go away + + + align:start position:0% +this and the management of this go away +and the three of us will solve this + + align:start position:0% +and the three of us will solve this + + + align:start position:0% +and the three of us will solve this +it's not going to happen + + align:start position:0% +it's not going to happen + + + align:start position:0% +it's not going to happen +so iwrm isn't a dispute resolution + + align:start position:0% +so iwrm isn't a dispute resolution + + + align:start position:0% +so iwrm isn't a dispute resolution +mechanism + + align:start position:0% +mechanism + + + align:start position:0% +mechanism +iwrm is an approach to water management + + align:start position:0% +iwrm is an approach to water management + + + align:start position:0% +iwrm is an approach to water management +and when disputes come up it's all + + align:start position:0% +and when disputes come up it's all + + + align:start position:0% +and when disputes come up it's all +tangled up + + align:start position:0% +tangled up + + + align:start position:0% +tangled up +in the dispute resolution + + align:start position:0% +in the dispute resolution + + + align:start position:0% +in the dispute resolution +process + + align:start position:0% +process + + + align:start position:0% +process +because + + align:start position:0% +because + + + align:start position:0% +because +of what it took to do + + align:start position:0% +of what it took to do + + + align:start position:0% +of what it took to do +iwrm as the planning as as the + + align:start position:0% +iwrm as the planning as as the + + + align:start position:0% +iwrm as the planning as as the +management scheme + + align:start position:0% +management scheme + + + align:start position:0% +management scheme +it's never it was never meant to be a + + align:start position:0% +it's never it was never meant to be a + + + align:start position:0% +it's never it was never meant to be a +dispute resolution + + align:start position:0% +dispute resolution + + + align:start position:0% +dispute resolution +strategy or mechanism + + align:start position:0% +strategy or mechanism + + + align:start position:0% +strategy or mechanism +but it's tangled up + + align:start position:0% +but it's tangled up + + + align:start position:0% +but it's tangled up +with efforts at dispute resolution + + align:start position:0% +with efforts at dispute resolution + + + align:start position:0% +with efforts at dispute resolution +because it's kind of hard to shrink + + align:start position:0% +because it's kind of hard to shrink + + + align:start position:0% +because it's kind of hard to shrink +any of the dimensions the parties the + + align:start position:0% +any of the dimensions the parties the + + + align:start position:0% +any of the dimensions the parties the +interest the scope of the problem the + + align:start position:0% +interest the scope of the problem the + + + align:start position:0% +interest the scope of the problem the +institutional powers + + align:start position:0% +institutional powers + + + align:start position:0% +institutional powers +for purposes of resolving a dispute + + align:start position:0% +for purposes of resolving a dispute + + + align:start position:0% +for purposes of resolving a dispute +that's come up within + + align:start position:0% +that's come up within + + + align:start position:0% +that's come up within +the iwrm process + + align:start position:0% +the iwrm process + + + align:start position:0% +the iwrm process +are there models i mean could you could + + align:start position:0% +are there models i mean could you could + + + align:start position:0% +are there models i mean could you could +you differentiate and say and say the + + align:start position:0% +you differentiate and say and say the + + + align:start position:0% +you differentiate and say and say the +um + + align:start position:0% +um + + + align:start position:0% +um +you know the initial as you said any + + align:start position:0% +you know the initial as you said any + + + align:start position:0% +you know the initial as you said any +any you know anyone who thinks through + + align:start position:0% +any you know anyone who thinks through + + + align:start position:0% +any you know anyone who thinks through +the three questions you asked is gonna + + align:start position:0% +the three questions you asked is gonna + + + align:start position:0% +the three questions you asked is gonna +move out and say you know broader more + + align:start position:0% +move out and say you know broader more + + + align:start position:0% +move out and say you know broader more +inclusive greater scope for this could + + align:start position:0% +inclusive greater scope for this could + + + align:start position:0% +inclusive greater scope for this could +you differentiate and say + + align:start position:0% +you differentiate and say + + + align:start position:0% +you differentiate and say +okay the initial water management + + align:start position:0% +okay the initial water management + + + align:start position:0% +okay the initial water management +uh considered like um you know + + align:start position:0% +uh considered like um you know + + + align:start position:0% +uh considered like um you know +negotiations will will um kind of + + align:start position:0% +negotiations will will um kind of + + + align:start position:0% +negotiations will will um kind of +exist on this macro level and + + align:start position:0% +exist on this macro level and + + + align:start position:0% +exist on this macro level and +incorporate kind of many different kind + + align:start position:0% +incorporate kind of many different kind + + + align:start position:0% +incorporate kind of many different kind +of facets of of of the economy and and + + align:start position:0% +of facets of of of the economy and and + + + align:start position:0% +of facets of of of the economy and and +and kind of secondary tertiary effects + + align:start position:0% +and kind of secondary tertiary effects + + + align:start position:0% +and kind of secondary tertiary effects +of water management but then you say + + align:start position:0% +of water management but then you say + + + align:start position:0% +of water management but then you say +after that + + align:start position:0% +after that + + + align:start position:0% +after that +you basically incorporate dispute + + align:start position:0% +you basically incorporate dispute + + + align:start position:0% +you basically incorporate dispute +resolution processes that are hyper + + align:start position:0% +resolution processes that are hyper + + + align:start position:0% +resolution processes that are hyper +local that that are specific to to kind + + align:start position:0% +local that that are specific to to kind + + + align:start position:0% +local that that are specific to to kind +of the area where the where the + + align:start position:0% +of the area where the where the + + + align:start position:0% +of the area where the where the +resolution or where the dispute is + + align:start position:0% +resolution or where the dispute is + + + align:start position:0% +resolution or where the dispute is +taking place and don't require + + align:start position:0% +taking place and don't require + + + align:start position:0% +taking place and don't require +you know completely remapping all of the + + align:start position:0% +you know completely remapping all of the + + + align:start position:0% +you know completely remapping all of the +old terrain + + align:start position:0% +old terrain + + + align:start position:0% +old terrain +that historically that's what the law + + align:start position:0% +that historically that's what the law + + + align:start position:0% +that historically that's what the law +and regulation + + align:start position:0% +and regulation + + + align:start position:0% +and regulation +have in fact done + + align:start position:0% +have in fact done + + + align:start position:0% +have in fact done +right we have a + + align:start position:0% +right we have a + + + align:start position:0% +right we have a +system of water rights + + align:start position:0% +system of water rights + + + align:start position:0% +system of water rights +that has nothing to do + + align:start position:0% +that has nothing to do + + + align:start position:0% +that has nothing to do +with iwrm i'll just take california or + + align:start position:0% +with iwrm i'll just take california or + + + align:start position:0% +with iwrm i'll just take california or +take western united states iwrm + + align:start position:0% +take western united states iwrm + + + align:start position:0% +take western united states iwrm +you would plan that water in a certain + + align:start position:0% +you would plan that water in a certain + + + align:start position:0% +you would plan that water in a certain +way but you can't + + align:start position:0% +way but you can't + + + align:start position:0% +way but you can't +in a system + + align:start position:0% +in a system + + + align:start position:0% +in a system +that's defined + + align:start position:0% +that's defined + + + align:start position:0% +that's defined +senior water rights + + align:start position:0% +senior water rights + + + align:start position:0% +senior water rights +where people who got there first got the + + align:start position:0% +where people who got there first got the + + + align:start position:0% +where people who got there first got the +water and then nobody can tell them what + + align:start position:0% +water and then nobody can tell them what + + + align:start position:0% +water and then nobody can tell them what +to do with it and they can waste it they + + align:start position:0% +to do with it and they can waste it they + + + align:start position:0% +to do with it and they can waste it they +can do anything they want it's + + align:start position:0% +can do anything they want it's + + + align:start position:0% +can do anything they want it's +completely contrary to the ideas of iwrm + + align:start position:0% +completely contrary to the ideas of iwrm + + + align:start position:0% +completely contrary to the ideas of iwrm +and + + align:start position:0% +and + + + align:start position:0% +and +until relatively recently the whole + + align:start position:0% +until relatively recently the whole + + + align:start position:0% +until relatively recently the whole +water law + + align:start position:0% +water law + + + align:start position:0% +water law +around the world is not connected to + + align:start position:0% +around the world is not connected to + + + align:start position:0% +around the world is not connected to +water management + + align:start position:0% +water management + + + align:start position:0% +water management +the rules of water law come down almost + + align:start position:0% +the rules of water law come down almost + + + align:start position:0% +the rules of water law come down almost +in the way aaron you're describing it + + align:start position:0% +in the way aaron you're describing it + + + align:start position:0% +in the way aaron you're describing it +just how how can i localize this and + + align:start position:0% +just how how can i localize this and + + + align:start position:0% +just how how can i localize this and +situate it in the way we deal with other + + align:start position:0% +situate it in the way we deal with other + + + align:start position:0% +situate it in the way we deal with other +property rights + + align:start position:0% +property rights + + + align:start position:0% +property rights +and that's how we'll handle the dispute + + align:start position:0% +and that's how we'll handle the dispute + + + align:start position:0% +and that's how we'll handle the dispute +but it doesn't it doesn't fit + + align:start position:0% +but it doesn't it doesn't fit + + + align:start position:0% +but it doesn't it doesn't fit +with what we imagine is the broader + + align:start position:0% +with what we imagine is the broader + + + align:start position:0% +with what we imagine is the broader +scope and the need to take account of + + align:start position:0% +scope and the need to take account of + + + align:start position:0% +scope and the need to take account of +more interest and the desire to look at + + align:start position:0% +more interest and the desire to look at + + + align:start position:0% +more interest and the desire to look at +the interconnectedness of things and the + + align:start position:0% +the interconnectedness of things and the + + + align:start position:0% +the interconnectedness of things and the +need to look ahead not back at who had + + align:start position:0% +need to look ahead not back at who had + + + align:start position:0% +need to look ahead not back at who had +what rights but forward in terms of who + + align:start position:0% +what rights but forward in terms of who + + + align:start position:0% +what rights but forward in terms of who +has what needs + + align:start position:0% +has what needs + + + align:start position:0% +has what needs +and yet we're stuck with it + + align:start position:0% +and yet we're stuck with it + + + align:start position:0% +and yet we're stuck with it +so + + align:start position:0% +so + + + align:start position:0% +so +again iwrm + + align:start position:0% +again iwrm + + + align:start position:0% +again iwrm +is a water management approach + + align:start position:0% +is a water management approach + + + align:start position:0% +is a water management approach +it's it's easy to see how it evolved + + align:start position:0% +it's it's easy to see how it evolved + + + align:start position:0% +it's it's easy to see how it evolved +and it seems perfectly logical + + align:start position:0% +and it seems perfectly logical + + + align:start position:0% +and it seems perfectly logical +and it doesn't + + align:start position:0% +and it doesn't + + + align:start position:0% +and it doesn't +it doesn't offer an obvious or easy way + + align:start position:0% +it doesn't offer an obvious or easy way + + + align:start position:0% +it doesn't offer an obvious or easy way +of handling disputes over water within + + align:start position:0% +of handling disputes over water within + + + align:start position:0% +of handling disputes over water within +systems that are managed by iwrm + + align:start position:0% +systems that are managed by iwrm + + + align:start position:0% +systems that are managed by iwrm +and if you just try to solve this water + + align:start position:0% +and if you just try to solve this water + + + align:start position:0% +and if you just try to solve this water +dispute in a purely legal fashion that + + align:start position:0% +dispute in a purely legal fashion that + + + align:start position:0% +dispute in a purely legal fashion that +determines who has what senior rights + + align:start position:0% +determines who has what senior rights + + + align:start position:0% +determines who has what senior rights +and hey that's it it's property + + align:start position:0% +and hey that's it it's property + + + align:start position:0% +and hey that's it it's property +but that doesn't take account of water + + align:start position:0% +but that doesn't take account of water + + + align:start position:0% +but that doesn't take account of water +as a shared + + align:start position:0% +as a shared + + + align:start position:0% +as a shared +human resource or as a human right + + align:start position:0% +human resource or as a human right + + + align:start position:0% +human resource or as a human right +and now how do we solve disputes over + + align:start position:0% +and now how do we solve disputes over + + + align:start position:0% +and now how do we solve disputes over +the allocation of water we can't use + + align:start position:0% +the allocation of water we can't use + + + align:start position:0% +the allocation of water we can't use +the property rights law + + align:start position:0% +the property rights law + + + align:start position:0% +the property rights law +we need something else + + align:start position:0% +we need something else + + + align:start position:0% +we need something else +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah that makes sense + + align:start position:0% + + + + align:start position:0% + +and mitch how do you react to what i + + align:start position:0% +and mitch how do you react to what i + + + align:start position:0% +and mitch how do you react to what i +just said + + align:start position:0% +just said + + + align:start position:0% +just said +yeah i i um so in terms of a relation + + align:start position:0% +yeah i i um so in terms of a relation + + + align:start position:0% +yeah i i um so in terms of a relation +with iwrm and water diplomacy i see that + + align:start position:0% +with iwrm and water diplomacy i see that + + + align:start position:0% +with iwrm and water diplomacy i see that +um iwrm says um + + align:start position:0% +um iwrm says um + + + align:start position:0% +um iwrm says um +according to iworm principle or + + align:start position:0% +according to iworm principle or + + + align:start position:0% +according to iworm principle or +dimensions um water should be managed in + + align:start position:0% +dimensions um water should be managed in + + + align:start position:0% +dimensions um water should be managed in +a + + align:start position:0% +a + + + align:start position:0% +a +transboundary or watershed + + align:start position:0% +transboundary or watershed + + + align:start position:0% +transboundary or watershed +or ecological boundary + + align:start position:0% +or ecological boundary + + + align:start position:0% +or ecological boundary +so in that case i can see the + + align:start position:0% +so in that case i can see the + + + align:start position:0% +so in that case i can see the +relation with the + + align:start position:0% +relation with the + + + align:start 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boundary of +um + + align:start position:0% +um + + + align:start position:0% +um +ecological boundary with the political + + align:start position:0% +ecological boundary with the political + + + align:start position:0% +ecological boundary with the political +boundary and it can immediately creates + + align:start position:0% +boundary and it can immediately creates + + + align:start position:0% +boundary and it can immediately creates +institutional mismatch and that can be + + align:start position:0% +institutional mismatch and that can be + + + align:start position:0% +institutional mismatch and that can be +managed through uh diplo water diplomacy + + align:start position:0% +managed through uh diplo water diplomacy + + + align:start position:0% +managed through uh diplo water diplomacy +uh + + align:start position:0% +uh + + + align:start position:0% +uh +approach so that's how i can see + + align:start position:0% +approach so that's how i can see + + + align:start position:0% +approach so that's how i can see +a relation with iowa so i can see auto + + align:start position:0% +a relation with iowa so i can see auto + + + align:start position:0% +a relation with iowa so i can see auto +diplomacy can be useful + + align:start position:0% +diplomacy can be useful + + + align:start position:0% +diplomacy can be useful +for the + + align:start position:0% +for the + + + align:start position:0% +for the +um difficulties that have iwrm + + align:start position:0% +um difficulties that have iwrm + + + align:start position:0% +um difficulties that have iwrm +implementation can be somehow um + + align:start position:0% +implementation can be somehow um + + + align:start position:0% +implementation can be somehow um +implemented uh through incorporating + + align:start position:0% +implemented uh through incorporating + + + align:start position:0% +implemented uh through incorporating +water diplomacy approach that's that's + + align:start position:0% +water diplomacy approach that's that's + + + align:start position:0% +water diplomacy approach that's that's +how i feel um + + align:start position:0% +how i feel um + + + align:start position:0% +how i feel um +uh the relation of iwrm and other + + align:start position:0% +uh the relation of iwrm and other + + + align:start position:0% +uh the relation of iwrm and other +diplomacy + + align:start position:0% +diplomacy + + + align:start position:0% +diplomacy +do you want to go to your next slide and + + align:start position:0% +do you want to go to your next slide and + + + align:start position:0% +do you want to go to your next slide and +look at the + + align:start position:0% +look at the + + + align:start position:0% +look at the +principles of iwrm explicitly in light + + align:start position:0% +principles of iwrm explicitly in light + + + align:start position:0% +principles of iwrm explicitly in light +of the general discussion we've had yeah + + align:start position:0% +of the general discussion we've had yeah + + + align:start position:0% +of the general discussion we've had yeah +yeah + + align:start position:0% + + + + align:start position:0% + +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +these are just a historical perspective + + align:start position:0% +these are just a historical perspective + + + align:start position:0% +these are just a historical perspective +of iwrm so according to um + + align:start position:0% +of iwrm so according to um + + + align:start position:0% +of iwrm so according to um +so it has started from the even + + align:start position:0% +so it has started from the even + + + align:start position:0% +so it has started from the even +conference on water in mart del plata in + + align:start position:0% +conference on water in mart del plata in + + + align:start position:0% +conference on water in mart del plata in +1977 then in 1992 um + + align:start position:0% +1977 then in 1992 um + + + align:start position:0% +1977 then in 1992 um +dublin conference uh this is the main + + align:start position:0% +dublin conference uh this is the main + + + align:start position:0% +dublin conference uh this is the main +building block for developing the iwrm + + align:start position:0% +building block for developing the iwrm + + + align:start position:0% +building block for developing the iwrm +um + + align:start position:0% +um + + + align:start position:0% +um +principles and in in this conference + + align:start position:0% +principles and in in this conference + + + align:start position:0% +principles and in in this conference +these four principles has been + + align:start position:0% +these four principles has been + + + align:start position:0% +these four principles has been +considered so the principle number one + + align:start position:0% +considered so the principle number one + + + align:start position:0% +considered so the principle number one +is the + + align:start position:0% +is the + + + align:start position:0% +is the +freshwater is finite and + + align:start position:0% +freshwater is finite and + + + align:start position:0% +freshwater is finite and +vulnerable resources + + align:start position:0% +vulnerable resources + + + align:start position:0% +vulnerable resources +essential to sustain life + + align:start position:0% +essential to sustain life + + + align:start position:0% +essential to sustain life +development and the environment so here + + align:start position:0% +development and the environment so here + + + align:start position:0% +development and the environment so here +you can compare + + align:start position:0% +you can compare + + + align:start position:0% +you can compare +the uh thinking of the water diplomacy + + align:start position:0% +the uh thinking of the water diplomacy + + + align:start position:0% +the uh thinking of the water diplomacy +so + + align:start position:0% +so + + + align:start position:0% +so +it's completely um + + align:start position:0% +it's completely um + + + align:start position:0% +it's completely um +opposite of the thinking of the dublin + + align:start position:0% +opposite of the thinking of the dublin + + + align:start position:0% +opposite of the thinking of the dublin +principle where outer diplomacy + + align:start position:0% +principle where outer diplomacy + + + align:start position:0% +principle where outer diplomacy +framework + + align:start position:0% +framework + + + align:start position:0% +framework +considered water is the flexible + + align:start position:0% +considered water is the flexible + + + align:start position:0% +considered water is the flexible +resource instead of + + align:start position:0% +resource instead of + + + align:start position:0% +resource instead of +finite and vulnerable + + align:start position:0% +finite and vulnerable + + + align:start position:0% +finite and vulnerable +resource so how + + align:start position:0% +resource 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of +principle number two + + align:start position:0% +principle number two + + + align:start position:0% +principle number two +water diplomacy and management should be + + align:start position:0% +water diplomacy and management should be + + + align:start position:0% +water diplomacy and management should be +based on a participatory approach + + align:start position:0% +based on a participatory approach + + + align:start position:0% +based on a participatory approach +involving users planners and + + align:start position:0% +involving users planners and + + + align:start position:0% +involving users planners and +policy makers at all levels + + align:start position:0% +policy makers at all levels + + + align:start position:0% +policy makers at all levels +and another important principle is the + + align:start position:0% +and another important principle is the + + + align:start position:0% +and another important principle is the +women should be a part of the + + align:start 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+thinking of it as an economic good + + + align:start position:0% +thinking of it as an economic good +is not helpful + + align:start position:0% +is not helpful + + + align:start position:0% +is not helpful +and some of you know i i'm working on + + align:start position:0% +and some of you know i i'm working on + + + align:start position:0% +and some of you know i i'm working on +the problem of water shutoffs + + align:start position:0% +the problem of water shutoffs + + + align:start position:0% +the problem of water shutoffs +in american cities + + align:start position:0% +in american cities + + + align:start position:0% +in american cities +where people who can't pay their bill + + align:start position:0% +where people who can't pay their bill + + + align:start position:0% +where people who can't pay their bill +for their water for a month or two + + align:start position:0% +for their water for a month or two + + + align:start position:0% +for their water for a month or two +have their water shut off + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +they can't pay their bill because + + align:start position:0% +they can't pay their bill because + + + align:start position:0% +they can't pay their bill because +they're out of work and + + align:start position:0% +they're out of work and + + + align:start position:0% +they're out of work and +telling them they have to pay their bill + + align:start position:0% +telling them they have to pay their bill + + + align:start position:0% +telling them they have to pay their bill +isn't going to make it possible for them + + align:start position:0% +isn't going to make it possible for them + + + align:start position:0% +isn't going to make it possible for them +to pay their bill + + align:start position:0% +to pay their bill + + + align:start position:0% +to pay their bill +and then the next thing that the water + + align:start position:0% +and then the next thing that the water + + + align:start position:0% +and then the next thing that the water +department does is it calls the family + + align:start position:0% +department does is it calls the family + + + align:start position:0% +department does is it calls the family +services department and says take the + + align:start position:0% +services department and says take the + + + align:start position:0% +services department and says take the +children out of that home there's no + + align:start position:0% +children out of that home there's no + + + align:start position:0% +children out of that home there's no +water there it's that's not hygienic + + align:start position:0% +water there it's that's not hygienic + + + align:start position:0% +water there it's that's not hygienic +so their kids are taken away + + align:start position:0% +so their kids are taken away + + + align:start position:0% +so their kids are taken away +they still can't pay the bill + + align:start position:0% + + + + align:start position:0% + +and then the next thing that happens is + + align:start position:0% +and then the next thing that happens is + + + align:start position:0% +and then the next thing that happens is +the city puts + + align:start position:0% +the city puts + + + align:start position:0% +the city puts +sells the lien + + align:start position:0% +sells the lien + + + align:start position:0% +sells the lien +it's a economic instrument + + align:start position:0% +it's a economic instrument + + + align:start position:0% +it's a economic instrument +on the on the debt + + align:start position:0% +on the on the debt + + + align:start position:0% +on the on the debt +because the city needs money to pay to + + align:start position:0% +because the city needs money to pay to + + + align:start position:0% +because the city needs money to pay to +maintain the water system and if people + + align:start position:0% +maintain the water system and if people + + + align:start position:0% +maintain the water system and if people +don't pay their bills it doesn't have + + align:start position:0% +don't pay their bills it doesn't have + + + align:start position:0% +don't pay their bills it doesn't have +the money it can't maintain the system + + align:start position:0% +the money it can't maintain the system + + + align:start position:0% +the money it can't maintain the system +so it sells the debt + + align:start position:0% +so it sells the debt + + + align:start position:0% +so it sells the debt +to private money lenders + + align:start position:0% +to private money lenders + + + align:start position:0% +to private money lenders +who then + + align:start position:0% +who then + + + align:start position:0% +who then +come after the person on a daily basis + + align:start position:0% +come after the person on a daily basis + + + align:start position:0% +come after the person on a daily basis +and saying not only do you owe us the + + align:start position:0% +and saying not only do you owe us the + + + align:start position:0% +and saying not only do you owe us the +900 from the last four months now the + + align:start position:0% +900 from the last four months now the + + + align:start position:0% +900 from the last four months now the +interest rate and we've just increased + + align:start position:0% +interest rate and we've just increased + + + align:start position:0% +interest rate and we've just increased +it to 10 interest + + align:start position:0% +it to 10 interest + + + align:start position:0% +it to 10 interest +they can't pay the debt they can't pay + + align:start position:0% +they can't pay the debt they can't pay + + + align:start position:0% +they can't pay the debt they can't pay +the interest + + align:start position:0% +the interest + + + align:start position:0% +the interest +and then after a year the city says + + align:start position:0% +and then after a year the city says + + + align:start position:0% +and then after a year the city says +we're going to sell your house + + align:start position:0% +we're going to sell your house + + + align:start position:0% +we're going to sell your house +to recoup the + + align:start position:0% +to recoup the + + + align:start position:0% +to recoup the +mounting debt + + align:start position:0% + + + + align:start position:0% + +we have all kinds of + + align:start position:0% +we have all kinds of + + + align:start position:0% +we have all kinds of +cities in the united states where the + + align:start position:0% +cities in the united states where the + + + align:start position:0% +cities in the united states where the +water authority sells liens + + align:start position:0% +water authority sells liens + + + align:start position:0% +water authority sells liens +and forecloses on homes all because + + align:start position:0% +and forecloses on homes all because + + + align:start position:0% +and forecloses on homes all because 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is + + align:start position:0% +pay your bill because the presumption is + + + align:start position:0% +pay your bill because the presumption is +you'll die + + align:start position:0% + + + + align:start position:0% + +but we don't have comparable laws that + + align:start position:0% +but we don't have comparable laws that + + + align:start position:0% +but we don't have comparable laws that +say you can't shut off people's water + + align:start position:0% +say you can't shut off people's water + + + align:start position:0% +say you can't shut off people's water +now during covid + + align:start position:0% +now during covid + + + align:start position:0% +now during covid +very interestingly + + align:start position:0% +very interestingly + + + align:start position:0% +very interestingly +we have had a moratorium on water + + align:start position:0% +we have had a moratorium on water + + + align:start position:0% +we have had a moratorium on water +shutoffs in some cities + + align:start position:0% +shutoffs in some cities + + + align:start position:0% +shutoffs in some cities +because now the presumption is people + + align:start position:0% +because now the presumption is people + + + align:start position:0% +because now the presumption is people +have a good excuse for being unable to + + align:start position:0% +have a good excuse for being unable to + + + align:start position:0% +have a good excuse for being unable to +pay their bills but before somehow they + + align:start position:0% +pay their bills but before somehow they + + + align:start position:0% +pay their bills but before somehow they +didn't have an excuse like they lost + + align:start position:0% +didn't have an excuse like they lost + + + align:start position:0% +didn't have an excuse like they lost +their job + + align:start position:0% +their job + + + align:start position:0% +their job +this is all a function of thinking of + + align:start position:0% +this is all a function of thinking of + + + align:start position:0% +this is all a function of thinking of +water as an economic good + + align:start position:0% +water as an economic good + + + align:start position:0% +water as an economic good +what if we said + + align:start position:0% +what if we said + + + align:start position:0% +what if we said +every residential property gets a + + align:start position:0% +every residential property gets a + + + align:start position:0% +every residential property gets a +certain minimum amount of water that you + + align:start position:0% +certain minimum amount of water that you + + + align:start position:0% +certain minimum amount of water that you +need to stay alive it doesn't cost + + align:start position:0% +need to stay alive it doesn't cost + + + align:start position:0% +need to stay alive it doesn't cost +anything + + align:start position:0% +anything + + + align:start position:0% +anything +and then + + align:start position:0% +and then + + + align:start position:0% +and then +all the water above that + + align:start position:0% +all the water above that + + + align:start position:0% +all the water above that +you pay a price relative to your ability + + align:start position:0% +you pay a price relative to your ability + + + align:start position:0% +you pay a price relative to your ability +to pay + + align:start position:0% + + + + align:start position:0% + +well we never had in the united states a + + align:start position:0% +well we never had in the united states a + + + align:start position:0% +well we never had in the united states a +system of water fees based on ability to + + align:start position:0% +system of water fees based on ability to + + + align:start position:0% +system of water fees based on ability to +pay + + align:start position:0% +pay + + + align:start position:0% +pay +until last year when philadelphia passed + + align:start position:0% +until last year when philadelphia passed + + + align:start position:0% +until last year when philadelphia passed +the first municipal law + + align:start position:0% +the first municipal law + + + align:start position:0% +the first municipal law +saying that they wanted to move in a + + align:start position:0% +saying that they wanted to move in a + + + align:start position:0% +saying that they wanted to move in a +different direction + + align:start position:0% +different direction + + + align:start position:0% +different direction +and have people pay + + align:start position:0% +and have people pay + + + align:start position:0% +and have people pay +for some portion of their water relative + + align:start position:0% +for some portion of their water relative + + + align:start position:0% +for some portion of their water relative +to their ability to pay and you can + + align:start position:0% +to their ability to pay and you can + + + align:start position:0% +to their ability to pay and you can +imagine the legal battle that's now + + align:start position:0% +imagine the legal battle that's now + + + align:start position:0% +imagine the legal battle that's now +ongoing about whether that's okay or not + + align:start position:0% +ongoing about whether that's okay or not + + + align:start position:0% +ongoing about whether that's okay or not +but all of that + + align:start position:0% +but all of that + + + align:start position:0% +but all of that +is stems from the idea that water is a + + align:start position:0% +is stems from the idea that water is a + + + align:start position:0% +is stems from the idea that water is a +commodity + + align:start position:0% +commodity + + + align:start position:0% +commodity +and we should have to buy and sell it + + align:start position:0% +and we should have to buy and sell it + + + align:start position:0% +and we should have to buy and sell it +in australia + + align:start position:0% +in australia + + + align:start position:0% +in australia +when it + + align:start position:0% +when it + + + align:start position:0% +when it +saw that it was running out of water + + align:start position:0% +saw that it was running out of water + + + align:start position:0% +saw that it was running out of water +fresh water and had all terrible forest + + align:start position:0% +fresh water and had all terrible forest + + + align:start position:0% +fresh water and had all terrible forest +fires and other difficulties + + align:start position:0% +fires and other difficulties + + + align:start position:0% +fires and other difficulties +bought + + align:start position:0% +bought + + + align:start position:0% +bought +as a government + + align:start position:0% +as a government + + + align:start position:0% +as a government +all the water rights in one state + + align:start position:0% +all the water rights in one state + + + align:start position:0% +all the water rights in one state +back from the owners + + align:start position:0% +back from the owners + + + align:start position:0% +back from the owners +at a + + align:start position:0% +at a + + + align:start position:0% +at a +prevailing price per + + align:start position:0% +prevailing price per + + + align:start position:0% +prevailing price per +hectare + + align:start position:0% +hectare + + + align:start position:0% +hectare +and then + + align:start position:0% +and then + + + align:start position:0% +and then +it paid back the money by selling back + + align:start position:0% +it paid back the money by selling back + + + align:start position:0% +it paid back the money by selling back +the water rights but on a different + + align:start position:0% +the water rights but on a different + + + align:start position:0% +the water rights but on a different +basis to people + + align:start position:0% +basis to people + + + align:start position:0% +basis to people +to try to have greater equity + + align:start position:0% +to try to have greater equity + + + align:start position:0% +to try to have greater equity +in the availability of water + + align:start position:0% +in the availability of water + + + align:start position:0% +in the availability of water +so it built a whole system + + align:start position:0% +so it built a whole system + + + align:start position:0% +so it built a whole system +based on + + align:start position:0% +based on + + + align:start position:0% +based on +water as an economic + + align:start position:0% +water as an economic + + + align:start position:0% +water as an economic +good + + align:start position:0% +good + + + align:start position:0% +good +in order to address a common need + + align:start position:0% +in order to address a common need + + + align:start position:0% +in order to address a common need +where if we thought of water as a + + align:start position:0% +where if we thought of water as a + + + align:start position:0% +where if we thought of water as a +natural resource and as a common + + align:start position:0% +natural resource and as a common + + + align:start position:0% +natural resource and as a common +resource + + align:start position:0% +resource + + + align:start position:0% +resource +pricing wouldn't be the focus + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and we've tried to make a market out of + + align:start position:0% +and we've tried to make a market out of + + + align:start position:0% +and we've tried to make a market out of +everything in the in the western + + align:start position:0% +everything in the in the western + + + align:start position:0% +everything in the in the western +capitalist countries + + align:start position:0% +capitalist countries + + + align:start position:0% +capitalist countries +and so now we have problems of water + + align:start position:0% +and so now we have problems of water + + + align:start position:0% +and so now we have problems of water +being unavailable + + align:start position:0% +being unavailable + + + align:start position:0% +being unavailable +to different groups of people + + align:start position:0% +to different groups of people + + + align:start position:0% +to different groups of people +and i i worry that iwrm is about + + align:start position:0% +and i i worry that iwrm is about + + + align:start position:0% +and i i worry that iwrm is about +maximizing + + align:start position:0% +maximizing + + + align:start position:0% +maximizing +water as an economic good + + align:start position:0% +water as an economic good + + + align:start position:0% +water as an economic good +that's one of the seven principles or + + align:start position:0% +that's one of the seven principles or + + + align:start position:0% +that's one of the seven principles or +whatever that you had listed + + align:start position:0% +whatever that you had listed + + + align:start position:0% +whatever that you had listed +what water's an economic good + + align:start position:0% +what water's an economic good + + + align:start position:0% +what water's an economic good +um and + + align:start position:0% +um and + + + align:start position:0% +um and +there are several of the principles i + + align:start position:0% +there are several of the principles i + + + align:start position:0% +there are several of the principles i +understand completely where they came + + align:start position:0% +understand completely where they came + + + align:start position:0% +understand completely where they came +from + + align:start position:0% +from + + + align:start position:0% +from +but when i look in practice + + align:start position:0% +but when i look in practice + + + align:start position:0% +but when i look in practice +the problem is we have under investment + + align:start position:0% +the problem is we have under investment + + + align:start position:0% +the problem is we have under investment +in the capital + + align:start position:0% +in the capital + + + align:start position:0% +in the capital +improvements necessary to get water to + + align:start position:0% +improvements necessary to get water to + + + align:start position:0% +improvements necessary to get water to +people that need it + + align:start position:0% +people that need it + + + align:start position:0% +people that need it +and there's not a way to solve that + + align:start position:0% +and there's not a way to solve that + + + align:start position:0% +and there's not a way to solve that +through integrated water resource + + align:start position:0% +through integrated water resource + + + align:start position:0% +through integrated water resource +management that's a political + + align:start position:0% +management that's a political + + + align:start position:0% +management that's a political +ethical moral + + align:start position:0% +ethical moral + + + align:start position:0% +ethical moral +decision + + align:start position:0% +decision + + + align:start position:0% +decision +so + + align:start position:0% +so + + + align:start position:0% +so +a lot of the conflicts some of which + + align:start position:0% +a lot of the conflicts some of which + + + align:start position:0% +a lot of the conflicts some of which +don't rise to the level of a formal + + align:start position:0% +don't rise to the level of a formal + + + align:start position:0% +don't rise to the level of a formal +conflict because the poor the + + align:start position:0% +conflict because the poor the + + + align:start position:0% +conflict because the poor the +disadvantaged the marginalized don't + + align:start position:0% +disadvantaged the marginalized don't + + + align:start position:0% +disadvantaged the marginalized don't +have the political clout to make it a + + align:start position:0% +have the political clout to make it a + + + align:start position:0% +have the political clout to make it a +fight + + align:start position:0% +fight + + + align:start position:0% +fight +but in fact there's a conflict + + align:start position:0% +but in fact there's a conflict + + + align:start position:0% +but in fact there's a conflict +with very large numbers of people in + + align:start position:0% +with very large numbers of people in + + + align:start position:0% +with very large numbers of people in +different parts of the world unable to + + align:start position:0% +different parts of the world unable to + + + align:start position:0% +different parts of the world unable to +get adequate water because there's no + + align:start position:0% +get adequate water because there's no + + + align:start position:0% +get adequate water because there's no +way to pay the capital cost + + align:start position:0% +way to pay the capital cost + + + align:start position:0% +way to pay the capital cost +to build the desalination plant to build + + align:start position:0% +to build the desalination plant to build + + + align:start position:0% +to build the desalination plant to build +the water movement system to get water + + align:start position:0% +the water movement system to get water + + + align:start position:0% +the water movement system to get water +from one place to another + + align:start position:0% +from one place to another + + + align:start position:0% +from one place to another +so that's what i worry about iwrm + + align:start position:0% +so that's what i worry about iwrm + + + align:start position:0% +so that's what i worry about iwrm +causing + + align:start position:0% +causing + + + align:start position:0% +causing +conflict and not providing a pathway to + + align:start position:0% +conflict and not providing a pathway to + + + align:start position:0% +conflict and not providing a pathway to +resolution of conflicts given some of + + align:start position:0% +resolution of conflicts given some of + + + align:start position:0% +resolution of conflicts given some of +the principles it includes + + align:start position:0% +the principles it includes + + + align:start position:0% +the principles it includes +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +i i i had i had a different perspective + + align:start position:0% +i i i had i had a different perspective + + + align:start position:0% +i i i had i had a different perspective +to what you just said for example if + + align:start position:0% +to what you just said for example if + + + align:start position:0% +to what you just said for example if +um if a poor person in my country + + align:start position:0% +um if a poor person in my country + + + align:start position:0% +um if a poor person in my country +uh doesn't have access to clean water um + + align:start position:0% +uh doesn't have access to clean water um + + + align:start position:0% +uh doesn't have access to clean water um +he he's like installing a hand pump or + + align:start position:0% +he he's like installing a hand pump or + + + align:start position:0% +he he's like installing a hand pump or +something at the cost of thousand + + align:start position:0% +something at the cost of thousand + + + align:start position:0% +something at the cost of thousand +dollars or something it's an additional + + align:start position:0% +dollars or something it's an additional + + + align:start position:0% +dollars or something it's an additional +burden to his daily income + + align:start position:0% +burden to his daily income + + + align:start position:0% +burden to his daily income +uh what if the state state would have + + align:start position:0% +uh what if the state state would have + + + align:start position:0% +uh what if the state state would have +provided him a water supply network with + + align:start position:0% +provided him a water supply network with + + + align:start position:0% +provided him a water supply network with +a certain pricing and + + align:start position:0% +a certain pricing and + + + align:start position:0% +a certain pricing and +the state had ensured that that water + + align:start position:0% +the state had ensured that that water + + + align:start position:0% +the state had ensured that that water +was clean enough to drink like for + + align:start position:0% +was clean enough to drink like for + + + align:start position:0% +was clean enough to drink like for +example i i in pakistan can't drink + + align:start position:0% +example i i in pakistan can't drink + + + align:start position:0% +example i i in pakistan can't drink +water turkey from tap i'm not sure about + + align:start position:0% +water turkey from tap i'm not sure about + + + align:start position:0% +water turkey from tap i'm not sure about +drinking water directly from the tap but + + align:start position:0% +drinking water directly from the tap but + + + align:start position:0% +drinking water directly from the tap but +here in my + + align:start position:0% +here in my + + + align:start position:0% +here in my +residence in ithaca + + align:start position:0% +residence in ithaca + + + align:start position:0% +residence in ithaca +i drink water directly from tap + + align:start position:0% +i drink water directly from tap + + + align:start position:0% +i drink water directly from tap +so + + align:start position:0% +so + + + align:start position:0% +so +by this i'm saving money from the + + align:start position:0% +by this i'm saving money from the + + + align:start position:0% +by this i'm saving money from the +bottled water + + align:start position:0% +bottled water + + + align:start position:0% +bottled water +and then i'm saving money for installing + + align:start position:0% +and then i'm saving money for installing + + + align:start position:0% +and then i'm saving money for installing +my own boring system or pumping system + + align:start position:0% +my own boring system or pumping system + + + align:start position:0% +my own boring system or pumping system +so if the state provided me with clean + + align:start position:0% +so if the state provided me with clean + + + align:start position:0% +so if the state provided me with clean +water with certain price in which they + + align:start position:0% +water with certain price in which they + + + align:start position:0% +water with certain price in which they +are entering the infrastructure which is + + align:start position:0% +are entering the infrastructure which is + + + align:start position:0% +are entering the infrastructure which is +lesser than the amount which i am + + align:start position:0% +lesser than the amount which i am + + + align:start position:0% +lesser than the amount which i am +spending back home on bottled water and + + align:start position:0% +spending back home on bottled water and + + + align:start position:0% +spending back home on bottled water and +boring + + align:start position:0% +boring + + + align:start position:0% +boring +water + + align:start position:0% +water + + + align:start position:0% +water +costs like + + align:start position:0% +costs like + + + align:start position:0% +costs like +do well or something like that then + + align:start position:0% +do well or something like that then + + + align:start position:0% +do well or something like that then +would you don't you think that the + + align:start position:0% +would you don't you think that the + + + align:start position:0% +would you don't you think that the +approach would be most better the + + align:start position:0% +approach would be most better the + + + align:start position:0% +approach would be most better the +pricing water pricing approach would be + + align:start position:0% +pricing water pricing approach would be + + + align:start position:0% +pricing water pricing approach would be +better in this scenario + + align:start position:0% + + + + align:start position:0% + +um you're paying rent in ithaca + + align:start position:0% +um you're paying rent in ithaca + + + align:start position:0% +um you're paying rent in ithaca +that includes water cost + + align:start position:0% + + + + align:start position:0% + +and if you lived in flint michigan + + align:start position:0% +and if you lived in flint michigan + + + align:start position:0% +and if you lived in flint michigan +you would be paying + + align:start position:0% + + + + align:start position:0% + +not that much different rent + + align:start position:0% +not that much different rent + + + align:start position:0% +not that much different rent +but you couldn't drink the water from + + align:start position:0% +but you couldn't drink the water from + + + align:start position:0% +but you couldn't drink the water from +the top + + align:start position:0% +the top + + + align:start position:0% +the top +because it's been + + align:start position:0% +because it's been + + + align:start position:0% +because it's been +allowed to become contaminated + + align:start position:0% +allowed to become contaminated + + + align:start position:0% +allowed to become contaminated +and the city doesn't have the resources + + align:start position:0% +and the city doesn't have the resources + + + align:start position:0% +and the city doesn't have the resources +to rebuild the whole + + align:start position:0% +to rebuild the whole + + + align:start position:0% +to rebuild the whole +system so we've pushed on to individuals + + align:start position:0% +system so we've pushed on to individuals + + + align:start position:0% +system so we've pushed on to individuals +the cost of getting water in some cities + + align:start position:0% +the cost of getting water in some cities + + + align:start position:0% +the cost of getting water in some cities +whether we've allowed the water to + + align:start position:0% +whether we've allowed the water to + + + align:start position:0% +whether we've allowed the water to +become contaminated + + align:start position:0% +become contaminated + + + align:start position:0% +become contaminated +maintaining clean water + + align:start position:0% +maintaining clean water + + + align:start position:0% +maintaining clean water +is a i would argue a common cost + + align:start position:0% +is a i would argue a common cost + + + align:start position:0% +is a i would argue a common cost +not an individualized cost + + align:start position:0% +not an individualized cost + + + align:start position:0% +not an individualized cost +while you can go buy water in bottles + + align:start position:0% + + + + align:start position:0% + +we still expect the availability of + + align:start position:0% +we still expect the availability of + + + align:start position:0% +we still expect the availability of +clean water from the tap + + align:start position:0% +clean water from the tap + + + align:start position:0% +clean water from the tap +drinkable water that won't kill you + + align:start position:0% +drinkable water that won't kill you + + + align:start position:0% +drinkable water that won't kill you +to be a common cost + + align:start position:0% +to be a common cost + + + align:start position:0% +to be a common cost +if it's a common cost then we should + + align:start position:0% +if it's a common cost then we should + + + align:start position:0% +if it's a common cost then we should +collect taxes from everybody in a + + align:start position:0% +collect taxes from everybody in a + + + align:start position:0% +collect taxes from everybody in a +progressive way + + align:start position:0% +progressive way + + + align:start position:0% +progressive way +and take care of building the things + + align:start position:0% +and take care of building the things + + + align:start position:0% +and take care of building the things +that are common like + + align:start position:0% +that are common like + + + align:start position:0% +that are common like +clean water system + + align:start position:0% +clean water system + + + align:start position:0% +clean water system +so i know i i heard the comparison + + align:start position:0% +so i know i i heard the comparison + + + align:start position:0% +so i know i i heard the comparison +you're making + + align:start position:0% +you're making + + + align:start position:0% +you're making +but i would argue both in pakistan and + + align:start position:0% +but i would argue both in pakistan and + + + align:start position:0% +but i would argue both in pakistan and +in the united states + + align:start position:0% +in the united states + + + align:start position:0% +in the united states +that the responsibility of local + + align:start position:0% +that the responsibility of local + + + align:start position:0% +that the responsibility of local +government should be + + align:start position:0% +government should be + + + align:start position:0% +government should be +to provide + + align:start position:0% +to provide + + + align:start position:0% +to provide +drinkable water for people + + align:start position:0% +drinkable water for people + + + align:start position:0% +drinkable water for people +as a capital cost that's a collective + + align:start position:0% +as a capital cost that's a collective + + + align:start position:0% +as a capital cost that's a collective +cost + + align:start position:0% +cost + + + align:start position:0% +cost +and whether that cost is paid for from + + align:start position:0% +and whether that cost is paid for from + + + align:start position:0% +and whether that cost is paid for from +taxes which could be collected in a + + align:start position:0% +taxes which could be collected in a + + + align:start position:0% +taxes which could be collected in a +progressive way + + align:start position:0% +progressive way + + + align:start position:0% +progressive way +or fees + + align:start position:0% +or fees + + + align:start position:0% +or fees +which typically are not collected in a + + align:start position:0% +which typically are not collected in a + + + align:start position:0% +which typically are not collected in a +progressive way + + align:start position:0% +progressive way + + + align:start position:0% +progressive way +they don't look at ability to pay + + align:start position:0% +they don't look at ability to pay + + + align:start position:0% +they don't look at ability to pay +i think we can have that debate about + + align:start position:0% +i think we can have that debate about + + + align:start position:0% +i think we can have that debate about +what's the fair way to collect the money + + align:start position:0% +what's the fair way to collect the money + + + align:start position:0% +what's the fair way to collect the money +but once the money is collected it + + align:start position:0% +but once the money is collected it + + + align:start position:0% +but once the money is collected it +should be used to get everybody a + + align:start position:0% +should be used to get everybody a + + + align:start position:0% +should be used to get everybody a +minimum amount of clean water that + + align:start position:0% +minimum amount of clean water that + + + align:start position:0% +minimum amount of clean water that +that's my argument + + align:start position:0% + + + + align:start position:0% + +yeah and i and i think that also fits + + align:start position:0% +yeah and i and i think that also fits + + + align:start position:0% +yeah and i and i think that also fits +with the iwrm principle like social + + align:start position:0% +with the iwrm principle like social + + + align:start position:0% +with the iwrm principle like social +equity and + + align:start position:0% +equity and + + + align:start position:0% +equity and +uh yeah so + + align:start position:0% +uh yeah so + + + align:start position:0% +uh yeah so +and and to add to your point that uh i + + align:start position:0% +and and to add to your point that uh i + + + align:start position:0% +and and to add to your point that uh i +mean it is a iwrm is a collective + + align:start position:0% +mean it is a iwrm is a collective + + + align:start position:0% +mean it is a iwrm is a collective +approach it's not about governments only + + align:start position:0% +approach it's not about governments only + + + align:start position:0% +approach it's not about governments only +it's about people also society societal + + align:start position:0% +it's about people also society societal + + + align:start position:0% +it's about people also society societal +education for example if you're doing + + align:start position:0% +education for example if you're doing + + + align:start position:0% +education for example if you're doing +you just said use the word contamination + + align:start position:0% +you just said use the word contamination + + + align:start position:0% +you just said use the word contamination +who is doing contamination we are doing + + align:start position:0% +who is doing contamination we are doing + + + align:start position:0% +who is doing contamination we are doing +contamination we are uh mixing several + + align:start position:0% +contamination we are uh mixing several + + + align:start position:0% +contamination we are uh mixing several +water with water we are doing water + + align:start position:0% +water with water we are doing water + + + align:start position:0% +water with water we are doing water +thefts we are doing hole to the main + + align:start position:0% +thefts we are doing hole to the main + + + align:start position:0% +thefts we are doing hole to the main +water supply line to get more water for + + align:start position:0% +water supply line to get more water for + + + align:start position:0% +water supply line to get more water for +ourselves that is + + align:start position:0% +ourselves that is + + + align:start position:0% +ourselves that is +something related to + + align:start position:0% +something related to + + + align:start position:0% +something related to +the societal education + + align:start position:0% +the societal education + + + align:start position:0% +the societal education +if we do not educate people that + + align:start position:0% +if we do not educate people that + + + align:start position:0% +if we do not educate people that +water should be treated as a precious + + align:start position:0% +water should be treated as a precious + + + align:start position:0% +water should be treated as a precious +resource that it should not be + + align:start position:0% +resource that it should not be + + + align:start position:0% +resource that it should not be +contaminated it's like it's like a joint + + align:start position:0% +contaminated it's like it's like a joint + + + align:start position:0% +contaminated it's like it's like a joint +responsibility not the responsibility of + + align:start position:0% +responsibility not the responsibility of + + + align:start position:0% +responsibility not the responsibility of +government only + + align:start position:0% +government only + + + align:start position:0% +government only +i agree i agree + + align:start position:0% +i agree i agree + + + align:start position:0% +i agree i agree +um + + align:start position:0% +um + + + align:start position:0% +um +you'll have to excuse me i'm trying + + align:start position:0% +you'll have to excuse me i'm trying + + + align:start position:0% +you'll have to excuse me i'm trying +desperately + + align:start position:0% +desperately + + + align:start position:0% +desperately +to get the folks planning glasgow + + align:start position:0% +to get the folks planning glasgow + + + align:start position:0% +to get the folks planning glasgow +to + + align:start position:0% +to + + + align:start position:0% +to +approach the problem in a different way + + align:start position:0% +approach the problem in a different way + + + align:start position:0% +approach the problem in a different way +than they did in paris + + align:start position:0% +than they did in paris + + + align:start position:0% +than they did in paris +and uh they have chosen this hour + + align:start position:0% +and uh they have chosen this hour + + + align:start position:0% +and uh they have chosen this hour +uh at least i have a chance to talk to + + align:start position:0% +uh at least i have a chance to talk to + + + align:start position:0% +uh at least i have a chance to talk to +them + + align:start position:0% +them + + + align:start position:0% +them +i'm not making any progress this is the + + align:start position:0% +i'm not making any progress this is the + + + align:start position:0% +i'm not making any progress this is the +third try uh but i i feel obliged + + align:start position:0% +third try uh but i i feel obliged + + + align:start position:0% +third try uh but i i feel obliged +uh if they just meet in glasgow and do + + align:start position:0% +uh if they just meet in glasgow and do + + + align:start position:0% +uh if they just meet in glasgow and do +again what they did in paris + + align:start position:0% +again what they did in paris + + + align:start position:0% +again what they did in paris +we're doomed + + align:start position:0% +we're doomed + + + align:start position:0% +we're doomed +and there has to be a different + + align:start position:0% +and there has to be a different + + + align:start position:0% +and there has to be a different +discussion + + align:start position:0% +discussion + + + align:start position:0% +discussion +and um there's a group of us who are + + align:start position:0% +and um there's a group of us who are + + + align:start position:0% +and um there's a group of us who are +trying to promote a different global + + align:start position:0% +trying to promote a different global + + + align:start position:0% +trying to promote a different global +discussion on this question + + align:start position:0% +discussion on this question + + + align:start position:0% +discussion on this question +so i'm i'm going to disappear but the + + align:start position:0% +so i'm i'm going to disappear but the + + + align:start position:0% +so i'm i'm going to disappear but the +the conversation + + align:start position:0% +the conversation + + + align:start position:0% +the conversation +about iwrm + + align:start position:0% +about iwrm + + + align:start position:0% +about iwrm +is important because you need each of + + align:start position:0% +is important because you need each of + + + align:start position:0% +is important because you need each of +you + + align:start position:0% +you + + + align:start position:0% +you +needs to formulate + + align:start position:0% +needs to formulate + + + align:start position:0% +needs to formulate +to take a stand to formulate an idea + + align:start position:0% +to take a stand to formulate an idea + + + align:start position:0% +to take a stand to formulate an idea +of + + align:start position:0% +of + + + align:start position:0% +of +how you think water should be managed + + align:start position:0% +how you think water should be managed + + + align:start position:0% +how you think water should be managed +and how you think disputes over the + + align:start position:0% +and how you think disputes over the + + + align:start position:0% +and how you think disputes over the +management of water should be resolved + + align:start position:0% +management of water should be resolved + + + align:start position:0% +management of water should be resolved +and i don't think + + align:start position:0% +and i don't think + + + align:start position:0% +and i don't think +either animash or eye + + align:start position:0% +either animash or eye + + + align:start position:0% +either animash or eye +thinks we know all the answers and i + + align:start position:0% +thinks we know all the answers and i + + + align:start position:0% +thinks we know all the answers and i +don't think there's only one solution + + align:start position:0% +don't think there's only one solution + + + align:start position:0% +don't think there's only one solution +for all places at all times + + align:start position:0% +for all places at all times + + + align:start position:0% +for all places at all times +but we need to be thinking + + align:start position:0% +but we need to be thinking + + + align:start position:0% +but we need to be thinking +prescriptively + + align:start position:0% +prescriptively + + + align:start position:0% +prescriptively +and if the best language we could say is + + align:start position:0% +and if the best language we could say is + + + align:start position:0% +and if the best language we could say is +uh + + align:start position:0% + + + + align:start position:0% + +social needs are important + + align:start position:0% +social needs are important + + + align:start position:0% +social needs are important +common good should be taken into account + + align:start position:0% +common good should be taken into account + + + align:start position:0% +common good should be taken into account +water should be managed in a + + align:start position:0% +water should be managed in a + + + align:start position:0% +water should be managed in a +comprehensive fashion + + align:start position:0% +comprehensive fashion + + + align:start position:0% +comprehensive fashion +look at the linkage between water and + + align:start position:0% +look at the linkage between water and + + + align:start position:0% +look at the linkage between water and +everything i don't think that + + align:start position:0% +everything i don't think that + + + align:start position:0% +everything i don't think that +inspires action + + align:start position:0% +inspires action + + + align:start position:0% +inspires action +or policy i think it's too vague + + align:start position:0% +or policy i think it's too vague + + + align:start position:0% +or policy i think it's too vague +so i'm pushing you to think + + align:start position:0% +so i'm pushing you to think + + + align:start position:0% +so i'm pushing you to think +in more + + align:start position:0% +in more + + + align:start position:0% +in more +explicit prescriptive terms and then to + + align:start position:0% +explicit prescriptive terms and then to + + + align:start position:0% +explicit prescriptive terms and then to +be able to argue for it for that view + + align:start position:0% +be able to argue for it for that view + + + align:start position:0% +be able to argue for it for that view +before you leave can you just tell me + + align:start position:0% +before you leave can you just tell me + + + align:start position:0% +before you leave can you just tell me +the questions you are going to address + + align:start position:0% +the questions you are going to address + + + align:start position:0% +the questions you are going to address +in this meeting + + align:start position:0% +in this meeting + + + align:start position:0% +in this meeting +yes what should be done before the + + align:start position:0% +yes what should be done before the + + + align:start position:0% +yes what should be done before the +meeting + + align:start position:0% +meeting + + + align:start position:0% +meeting +by the people who will be coming to the + + align:start position:0% +by the people who will be coming to the + + + align:start position:0% +by the people who will be coming to the +meeting + + align:start position:0% +meeting + + + align:start position:0% +meeting +while they can still formulate new + + align:start position:0% +while they can still formulate new + + + align:start position:0% +while they can still formulate new +policy choices because once you're at + + align:start position:0% +policy choices because once you're at + + + align:start position:0% +policy choices because once you're at +the meeting + + align:start position:0% +the meeting + + + align:start position:0% +the meeting +all you do is argue about the text + + align:start position:0% +all you do is argue about the text + + + align:start position:0% +all you do is argue about the text +that's been sent out and every 197 + + align:start position:0% +that's been sent out and every 197 + + + align:start position:0% +that's been sent out and every 197 +delegations have been sent there with + + align:start position:0% +delegations have been sent there with + + + align:start position:0% +delegations have been sent there with +very explicit instructions by their + + align:start position:0% +very explicit instructions by their + + + align:start position:0% +very explicit instructions by their +country there's no problem solving that + + align:start position:0% +country there's no problem solving that + + + align:start position:0% +country there's no problem solving that +can happen at the meeting + + align:start position:0% +can happen at the meeting + + + align:start position:0% +can happen at the meeting +but before the meeting everyone is busy + + align:start position:0% +but before the meeting everyone is busy + + + align:start position:0% +but before the meeting everyone is busy +figuring out what they want + + align:start position:0% +figuring out what they want + + + align:start position:0% +figuring out what they want +everybody else to do + + align:start position:0% +everybody else to do + + + align:start position:0% +everybody else to do +there's no joint + + align:start position:0% +there's no joint + + + align:start position:0% +there's no joint +planning beforehand that and because it + + align:start position:0% +planning beforehand that and because it + + + align:start position:0% +planning beforehand that and because it +can't be done in an official way if it's + + align:start position:0% +can't be done in an official way if it's + + + align:start position:0% +can't be done in an official way if it's +done an official way then everybody's + + align:start position:0% +done an official way then everybody's + + + align:start position:0% +done an official way then everybody's +there reading the script from their + + align:start position:0% +there reading the script from their + + + align:start position:0% +there reading the script from their +country saying everybody else is + + align:start position:0% +country saying everybody else is + + + align:start position:0% +country saying everybody else is +responsible this is a problem that's a + + align:start position:0% +responsible this is a problem that's a + + + align:start position:0% +responsible this is a problem that's a +problem + + align:start position:0% +problem + + + align:start position:0% +problem +nothing can happen so we're trying to + + align:start position:0% +nothing can happen so we're trying to + + + align:start position:0% +nothing can happen so we're trying to +get a different kind of conversation + + align:start position:0% +get a different kind of conversation + + + align:start position:0% +get a different kind of conversation +amongst a substantial number + + align:start position:0% +amongst a substantial number + + + align:start position:0% +amongst a substantial number +of the + + align:start position:0% +of the + + + align:start position:0% +of the +people who will be at the conference + + align:start position:0% +people who will be at the conference + + + align:start position:0% +people who will be at the conference +representing their countries into + + align:start position:0% +representing their countries into + + + align:start position:0% +representing their countries into +conversations between now and the summer + + align:start position:0% +conversations between now and the summer + + + align:start position:0% +conversations between now and the summer +not in their official capacity just + + align:start position:0% +not in their official capacity just + + + align:start position:0% +not in their official capacity just +in terms of problem solving and not just + + align:start position:0% +in terms of problem solving and not just + + + align:start position:0% +in terms of problem solving and not just +technical the others as well + + align:start position:0% +technical the others as well + + + align:start position:0% +technical the others as well +but people said well how would you + + align:start position:0% +but people said well how would you + + + align:start position:0% +but people said well how would you +decide who participates + + align:start position:0% +decide who participates + + + align:start position:0% +decide who participates +and my argument is it doesn't matter + + align:start position:0% +and my argument is it doesn't matter + + + align:start position:0% +and my argument is it doesn't matter +they're not going to decide anything + + align:start position:0% +they're not going to decide anything + + + align:start position:0% +they're not going to decide anything +they're just going to put forward good + + align:start position:0% +they're just going to put forward good + + + align:start position:0% +they're just going to put forward good +proposals let's just have a diverse + + align:start position:0% +proposals let's just have a diverse + + + align:start position:0% +proposals let's just have a diverse +group that wants to put forward + + align:start position:0% +group that wants to put forward + + + align:start position:0% +group that wants to put forward +proposals in the collective interest + + align:start position:0% +proposals in the collective interest + + + align:start position:0% +proposals in the collective interest +well where would you have it + + align:start position:0% +well where would you have it + + + align:start position:0% +well where would you have it +when would you have it i said it doesn't + + align:start position:0% +when would you have it i said it doesn't + + + align:start position:0% +when would you have it i said it doesn't +matter we do it online we just need to + + align:start position:0% +matter we do it online we just need to + + + align:start position:0% +matter we do it online we just need to +start work on new proposals of a + + align:start position:0% +start work on new proposals of a + + + align:start position:0% +start work on new proposals of a +different kind and the question that i'm + + align:start position:0% +different kind and the question that i'm + + + align:start position:0% +different kind and the question that i'm +saying that the proposal should be about + + align:start position:0% +saying that the proposal should be about + + + align:start position:0% +saying that the proposal should be about +what help does your country need to get + + align:start position:0% +what help does your country need to get + + + align:start position:0% +what help does your country need to get +to net zero by 2030 not what's your + + align:start position:0% +to net zero by 2030 not what's your + + + align:start position:0% +to net zero by 2030 not what's your +responsibility for cutting stuff + + align:start position:0% +responsibility for cutting stuff + + + align:start position:0% +responsibility for cutting stuff +what help + + align:start position:0% +what help + + + align:start position:0% +what help +do you say you won't need to get to net + + align:start position:0% +do you say you won't need to get to net + + + align:start position:0% +do you say you won't need to get to net +zero by 2030 + + align:start position:0% +zero by 2030 + + + align:start position:0% +zero by 2030 +and collect that and look at the + + align:start position:0% +and collect that and look at the + + + align:start position:0% +and collect that and look at the +differences amongst what countries say + + align:start position:0% +differences amongst what countries say + + + align:start position:0% +differences amongst what countries say +they want to need and then figure out + + align:start position:0% +they want to need and then figure out + + + align:start position:0% +they want to need and then figure out +how different countries can help each + + align:start position:0% +how different countries can help each + + + align:start position:0% +how different countries can help each +other + + align:start position:0% +other + + + align:start position:0% +other +work toward that as the goal + + align:start position:0% +work toward that as the goal + + + align:start position:0% +work toward that as the goal +2030 net zero that's what we have to aim + + align:start position:0% +2030 net zero that's what we have to aim + + + align:start position:0% +2030 net zero that's what we have to aim +for + + align:start position:0% +for + + + align:start position:0% +for +but now all we have is how much of the + + align:start position:0% +but now all we have is how much of the + + + align:start position:0% +but now all we have is how much of the +over + + align:start position:0% +over + + + align:start position:0% +over +run + + align:start position:0% +run + + + align:start position:0% +run +will you agree to accept no matter what + + align:start position:0% +will you agree to accept no matter what + + + align:start position:0% +will you agree to accept no matter what +it costs you + + align:start position:0% +it costs you + + + align:start position:0% +it costs you +and the answer is you can't make me do + + align:start position:0% +and the answer is you can't make me do + + + align:start position:0% +and the answer is you can't make me do +it + + align:start position:0% +it + + + align:start position:0% +it +that's paris + + align:start position:0% +that's paris + + + align:start position:0% +that's paris +and we're gonna get it again in glasgow + + align:start position:0% +and we're gonna get it again in glasgow + + + align:start position:0% +and we're gonna get it again in glasgow +so that's that's what i'm the + + align:start position:0% +so that's that's what i'm the + + + align:start position:0% +so that's that's what i'm the +conversation i'm trying to promote + + align:start position:0% +conversation i'm trying to promote + + + align:start position:0% +conversation i'm trying to promote +forgive me yeah i will see you all next + + align:start position:0% +forgive me yeah i will see you all next + + + align:start position:0% +forgive me yeah i will see you all next +week + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +we wanted to say something uh + + align:start position:0% +we wanted to say something uh + + + align:start position:0% +we wanted to say something uh +maybe quickly because we only have + + align:start position:0% +maybe quickly because we only have + + + align:start position:0% +maybe quickly because we only have +i haven't been + + align:start position:0% +i haven't been + + + align:start position:0% +i haven't been +there + + align:start position:0% +there + + + align:start position:0% +there +i agree with the with larry's argument + + align:start position:0% +i agree with the with larry's argument + + + align:start position:0% +i agree with the with larry's argument +that there should be a minimum + + align:start position:0% +that there should be a minimum + + + align:start position:0% +that there should be a minimum +amount of water for every household or + + align:start position:0% +amount of water for every household or + + + align:start position:0% +amount of water for every household or +every person instead of + + align:start position:0% +every person instead of + + + align:start position:0% +every person instead of +putting them extreme pressure + + align:start position:0% +putting them extreme pressure + + + align:start position:0% +putting them extreme pressure +uh through the capitalist system this is + + align:start position:0% +uh through the capitalist system this is + + + align:start position:0% +uh through the capitalist system this is +a completely agree but at the same time + + align:start position:0% + + + + align:start position:0% + +in my country i've seen and probably + + align:start position:0% +in my country i've seen and probably + + + align:start position:0% +in my country i've seen and probably +have seen also that + + align:start position:0% +have seen also that + + + align:start position:0% +have seen also that +when something is free + + align:start position:0% +when something is free + + + align:start position:0% +when something is free +or whatever the amount that is when + + align:start position:0% +or whatever the amount that is when + + + align:start position:0% +or whatever the amount that is when +something is free + + align:start position:0% +something is free + + + align:start position:0% +something is free +most of the people and that has that is + + align:start position:0% +most of the people and that has that is + + + align:start position:0% +most of the people and that has that is +i've seen from my observation and i'm + + align:start position:0% +i've seen from my observation and i'm + + + align:start position:0% +i've seen from my observation and i'm +sure that the research if anyone + + align:start position:0% +sure that the research if anyone + + + align:start position:0% +sure that the research if anyone +does it would + + align:start position:0% +does it would + + + align:start position:0% +does it would +give the similar data + + align:start position:0% +give the similar data + + + align:start position:0% +give the similar data +that when something is free there is a + + align:start position:0% +that when something is free there is a + + + align:start position:0% +that when something is free there is a +tendency to waste + + align:start position:0% +tendency to waste + + + align:start position:0% +tendency to waste +and + + align:start position:0% + + + + align:start position:0% + +in bangladesh or in a in developing + + align:start position:0% +in bangladesh or in a in developing + + + align:start position:0% +in bangladesh or in a in developing +country a huge number of people + + align:start position:0% +country a huge number of people + + + align:start position:0% +country a huge number of people +they would be not that rich to afford it + + align:start position:0% +they would be not that rich to afford it + + + align:start position:0% +they would be not that rich to afford it +so the government would be giving them + + align:start position:0% +so the government would be giving them + + + align:start position:0% +so the government would be giving them +a massive amount of water in total + + align:start position:0% +a massive amount of water in total + + + align:start position:0% +a massive amount of water in total +and and if everybody + + align:start position:0% +and and if everybody + + + align:start position:0% +and and if everybody +wastes just a little or the majority of + + align:start position:0% +wastes just a little or the majority of + + + align:start position:0% +wastes just a little or the majority of +the people waste just a little that's a + + align:start position:0% +the people waste just a little that's a + + + align:start position:0% +the people waste just a little that's a +huge amount of water being wasted yes + + align:start position:0% +huge amount of water being wasted yes + + + align:start position:0% +huge amount of water being wasted yes +because it's free and just because it's + + align:start position:0% +because it's free and just because it's + + + align:start position:0% +because it's free and just because it's +free people do not evaluate that much so + + align:start position:0% +free people do not evaluate that much so + + + align:start position:0% +free people do not evaluate that much so +i was thinking that how do we + + align:start position:0% +i was thinking that how do we + + + align:start position:0% +i was thinking that how do we +make a mechanism to stop that is there + + align:start position:0% +make a mechanism to stop that is there + + + align:start position:0% +make a mechanism to stop that is there +any mechanism at all so + + align:start position:0% +any mechanism at all so + + + align:start position:0% +any mechanism at all so +that was my question + + align:start position:0% +that was my question + + + align:start position:0% +that was my question +yeah i think the uh in terms of iwrm + + align:start position:0% +yeah i think the uh in terms of iwrm + + + align:start position:0% +yeah i think the uh in terms of iwrm +principle the mechanism is there so + + align:start position:0% +principle the mechanism is there so + + + align:start position:0% +principle the mechanism is there so +uh we need to um + + align:start position:0% +uh we need to um + + + align:start position:0% +uh we need to um +place a price on the water and + + align:start position:0% +place a price on the water and + + + align:start position:0% +place a price on the water and +yeah one equity basis the price + + align:start position:0% +yeah one equity basis the price + + + align:start position:0% +yeah one equity basis the price +could be + + align:start position:0% +could be + + + align:start position:0% +could be +different for different um + + align:start position:0% +different for different um + + + align:start position:0% +different for different um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh group of people and that that can + + align:start position:0% +uh group of people and that that can + + + align:start position:0% +uh group of people and that that can +help efficiency of water use and this + + align:start position:0% +help efficiency of water use and this + + + align:start position:0% +help efficiency of water use and this +that is kind of demand side management + + align:start position:0% +that is kind of demand side management + + + align:start 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align:start position:0% +can also affect +implementation of um iwrms because if + + align:start position:0% +implementation of um iwrms because if + + + align:start position:0% +implementation of um iwrms because if +you + + align:start position:0% +you + + + align:start position:0% +you +promote um + + align:start position:0% +promote um + + + align:start position:0% +promote um +upstream order development projects for + + align:start position:0% +upstream order development projects for + + + align:start position:0% +upstream order development projects for +hydroelectricity then + + align:start position:0% +hydroelectricity then + + + align:start position:0% +hydroelectricity then +this can affect a relationship + + align:start position:0% +this can affect a relationship + + + align:start position:0% +this can affect a relationship +with them + + align:start position:0% +with them + + + align:start position:0% +with them +with the downstream + + align:start position:0% +with the downstream + + + align:start position:0% +with the downstream +countries so this kind of synergies and + + align:start position:0% +countries so this kind of synergies and + + + align:start position:0% +countries so this kind of synergies and +trade-offs are very important and that + + align:start position:0% +trade-offs are very important and that + + + align:start position:0% +trade-offs are very important and that +can be um reduced or that can be + + align:start position:0% +can be um reduced or that can be + + + align:start position:0% +can be um reduced or that can be +resolved through our diplomacy approach + + align:start position:0% +resolved through our diplomacy approach + + + align:start position:0% +resolved through our diplomacy approach +broadly so that's how i can see the link + + align:start position:0% +broadly so that's how i can see the link + + + align:start position:0% +broadly so that's how i can see the link +between the this disease and and um + + align:start position:0% +between the this disease and and um + + + align:start position:0% +between the this disease and and um +and what are diplomacy aspect in in + + align:start position:0% +and what are diplomacy aspect in in + + + align:start position:0% +and what are diplomacy aspect in in +general so + + align:start position:0% +general so + + + align:start position:0% +general so +that's that's um we wanted to um discuss + + align:start position:0% +that's that's um we wanted to um discuss + + + align:start position:0% +that's that's um we wanted to um discuss +today classes so first we already + + align:start position:0% +today classes so first we already + + + align:start position:0% +today classes so first we already +discussed the + + align:start position:0% +discussed the + + + align:start position:0% +discussed the +evolution of water resources management + + align:start position:0% +evolution of water resources management + + + align:start position:0% +evolution of water resources management +uh how it came from the supply side + + align:start position:0% +uh how it came from the supply side + + + align:start position:0% +uh how it came from the supply side +approach to the um + + align:start position:0% +approach to the um + + + align:start position:0% +approach to the um +demand and um decentralized approach + + align:start position:0% +demand and um decentralized approach + + + align:start position:0% +demand and um decentralized approach +with an example but then we already + + align:start position:0% +with an example but then we already + + + align:start position:0% +with an example but then we already +discussed + + align:start position:0% +discussed + + + align:start position:0% +discussed +uh iwrm and its importance um in the + + align:start position:0% +uh iwrm and its importance um in the + + + align:start position:0% +uh iwrm and its importance um in the +um international water resource + + align:start position:0% +um international water resource + + + align:start position:0% +um international water resource +management aspect and its + + align:start position:0% +management aspect and its + + + align:start position:0% +management aspect and its +relation with the water diplomacy but + + align:start position:0% +relation with the water diplomacy but + + + align:start position:0% +relation with the water diplomacy but +also we discussed um + + align:start position:0% +also we discussed um + + + align:start position:0% +also we discussed um +water energy food nexus and sustainable + + align:start position:0% +water energy food nexus and sustainable + + + align:start position:0% +water energy food nexus and sustainable +development goals and its + + align:start position:0% +development goals and its + + + align:start position:0% +development goals and its +relation with water diplomacy + + align:start position:0% +relation with water diplomacy + + + align:start position:0% +relation with water diplomacy +yes so the next class will be the week + + align:start position:0% +yes so the next class will be the week + + + align:start position:0% +yes so the next class will be the week +after and in that class we will play a + + align:start position:0% +after and in that class we will play a + + + align:start position:0% +after and in that class we will play a +role play simulation + + align:start position:0% +role play simulation + + + align:start position:0% +role play simulation +practically how we can resolve + + align:start position:0% +practically how we can resolve + + + align:start position:0% +practically how we can resolve +water conflicts + + align:start position:0% +water conflicts + + + align:start position:0% +water conflicts +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we'll play the game endopotomia river + + align:start position:0% +we'll play the game endopotomia river + + + align:start position:0% +we'll play the game endopotomia river +basin management and for the role plus + + align:start position:0% +basin management and for the role plus + + + align:start position:0% +basin management and for the role plus +simulation uh we will need 9 players + + align:start position:0% +simulation uh we will need 9 players + + + align:start position:0% +simulation uh we will need 9 players +but we have 6 players + + align:start position:0% +but we have 6 players + + + align:start position:0% +but we have 6 players +so + + align:start position:0% +so + + + align:start position:0% +so +do you know is there any of your friend + + align:start position:0% +do you know is there any of your friend + + + align:start position:0% +do you know is there any of your friend +could be interested in the role place + + align:start position:0% +could be interested in the role place + + + align:start position:0% +could be interested in the role place +simulation um if if you don't find i + + align:start position:0% +simulation um if if you don't find i + + + align:start position:0% +simulation um if if you don't find i +will try to find three other players but + + align:start position:0% +will try to find three other players but + + + align:start position:0% +will try to find three other players but +yeah if you have + + align:start position:0% +yeah if you have + + + align:start position:0% +yeah if you have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yeah interesting um + + align:start position:0% +yeah interesting um + + + align:start position:0% +yeah interesting um +uh colleagues that are + + align:start position:0% +uh colleagues that are + + + align:start position:0% +uh colleagues that are +highly interested to the to understand + + align:start position:0% +highly interested to the to understand + + + align:start position:0% +highly interested to the to understand +the role play game you can + + align:start position:0% +the role play game you can + + + align:start position:0% +the role play game you can +let me know yeah + + align:start position:0% +let me know yeah + + + align:start position:0% +let me know yeah +so another um + + align:start position:0% + + + + align:start position:0% + +notice our announcement is that + + align:start position:0% +notice our announcement is that + + + align:start position:0% +notice our announcement is that +next week um larry and me are going to + + align:start position:0% +next week um larry and me are going to + + + align:start position:0% +next week um larry and me are going to +talk on transboundary water resources + + align:start position:0% +talk on transboundary water resources + + + align:start position:0% +talk on transboundary water resources +management larry will discuss mainly the + + align:start position:0% +management larry will discuss mainly the + + + align:start position:0% +management larry will discuss mainly the +theoretical aspect and i will describe + + align:start position:0% +theoretical aspect and i will describe + + + align:start position:0% +theoretical aspect and i will describe +the um + + align:start position:0% +the um + + + align:start position:0% +the um +uh brahmaputra riverbasin case so if you + + align:start position:0% +uh brahmaputra riverbasin case so if you + + + align:start position:0% +uh brahmaputra riverbasin case so if you +are interested you + + align:start position:0% +are interested you + + + align:start position:0% +are interested you +you can + + align:start position:0% +you can + + + align:start position:0% +you can +join in this event i can share the link + + align:start position:0% +join in this event i can share the link + + + align:start position:0% +join in this event i can share the link +for the registration it's the um + + align:start position:0% +for the registration it's the um + + + align:start position:0% +for the registration it's the um +eu time so it's the european time + + align:start position:0% +eu time so it's the european time + + + align:start position:0% +eu time so it's the european time +so + + align:start position:0% +so + + + align:start position:0% +so +in + + align:start position:0% +in + + + align:start position:0% +in +u.s time is could be 11 11 a.m or yeah + + align:start position:0% +u.s time is could be 11 11 a.m or yeah + + + align:start position:0% +u.s time is could be 11 11 a.m or yeah +so if you are interested you you feel + + align:start position:0% +so if you are interested you you feel + + + align:start position:0% +so if you are interested you you feel +free to join this in this event + + align:start position:0% +free to join this in this event + + + align:start position:0% +free to join this in this event +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +another announcement sorry i wanted to + + align:start position:0% +another announcement sorry i wanted to + + + align:start position:0% +another announcement sorry i wanted to +put in the put it in here + + align:start position:0% +put in the put it in here + + + align:start position:0% +put in the put it in here +there is a discussion paper on + + align:start position:0% +there is a discussion paper on + + + align:start position:0% +there is a discussion paper on +water energy and food nexus + + align:start position:0% +water energy and food nexus + + + align:start position:0% +water energy and food nexus +and um + + align:start position:0% +and um + + + align:start position:0% +and um +there is a discussion series is um + + align:start position:0% +there is a discussion series is um + + + align:start position:0% +there is a discussion series is um +taking place by one of our + + align:start position:0% +taking place by one of our + + + align:start position:0% +taking place by one of our +colleague who is the editor of the + + align:start position:0% +colleague who is the editor of the + + + align:start position:0% +colleague who is the editor of the +journal + + align:start position:0% +journal + + + align:start position:0% +journal +water um hydrological sciences + + align:start position:0% +water um hydrological sciences + + + align:start position:0% +water um hydrological sciences +journal + + align:start position:0% +journal + + + align:start position:0% +journal +and in that discussion paper there is a + + align:start position:0% +and in that discussion paper there is a + + + align:start position:0% +and in that discussion paper there is a +topic on water energy and food nexus and + + align:start position:0% +topic on water energy and food nexus and + + + align:start position:0% +topic on water energy and food nexus and +if you are interested and if you feel um + + align:start position:0% +if you are interested and if you feel um + + + align:start position:0% +if you are interested and if you feel um +is fit in your area of interest + + align:start position:0% +is fit in your area of interest + + + align:start position:0% +is fit in your area of interest +there is a paper on water quality and + + align:start position:0% +there is a paper on water quality and + + + align:start position:0% +there is a paper on water quality and +water energy food nexus + + align:start position:0% +water energy food nexus + + + align:start position:0% +water energy food nexus +and if you can criticize or um + + align:start position:0% +and if you can criticize or um + + + align:start position:0% +and if you can criticize or um +comment on that paper that can also be + + align:start position:0% +comment on that paper that can also be + + + align:start position:0% +comment on that paper that can also be +published um if this is a + + align:start position:0% +published um if this is a + + + align:start position:0% +published um if this is a +concise and + + align:start position:0% +concise and + + + align:start position:0% +concise and +and um yeah in a written in a scientific + + align:start position:0% +and um yeah in a written in a scientific + + + align:start position:0% +and um yeah in a written in a scientific +way so i can share that link if you are + + align:start position:0% +way so i can share that link if you are + + + align:start position:0% +way so i can share that link if you are +interested in participating this kind of + + align:start position:0% +interested in participating this kind of + + + align:start position:0% +interested in participating this kind of +um + + align:start position:0% +um + + + align:start position:0% +um +writing + + align:start position:0% +writing + + + align:start position:0% +writing +you can let me know i i have the link + + align:start position:0% +you can let me know i i have the link + + + align:start position:0% +you can let me know i i have the link +with the editor of that + + align:start position:0% +with the editor of that + + + align:start position:0% +with the editor of that +journal so i can share with you um if + + align:start position:0% +journal so i can share with you um if + + + align:start position:0% +journal so i can share with you um if +you are interested so the write-up + + align:start position:0% +you are interested so the write-up + + + align:start position:0% +you are interested so the write-up +should be one or two page + + align:start position:0% +should be one or two page + + + align:start position:0% +should be one or two page +but it should be written in a scientific + + align:start position:0% +but it should be written in a scientific + + + align:start position:0% +but it should be written in a scientific +way + + align:start position:0% +way + + + align:start position:0% +way +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so i i will share those two links and + + align:start position:0% +so i i will share those two links and + + + align:start position:0% +so i i will share those two links and +also i will share the + + align:start position:0% +also i will share the + + + align:start position:0% +also i will share the +role place simulation um + + align:start position:0% +role place simulation um + + + align:start position:0% +role place simulation um +uh what the general instruction but also + + align:start position:0% +uh what the general instruction but also + + + align:start position:0% +uh what the general instruction but also +confidential instruction for his player + + align:start position:0% +confidential instruction for his player + + + align:start position:0% +confidential instruction for his player +i i'll share with you in next few days + + align:start position:0% +i i'll share with you in next few days + + + align:start position:0% +i i'll share with you in next few days +so + + align:start position:0% +so + + + align:start position:0% +so +bye \ No newline at end of file diff --git a/kUtvTc_d_q0.txt b/kUtvTc_d_q0.txt new file mode 100644 index 0000000000000000000000000000000000000000..9725fb6ed47cbc65d126943b1508bfb5e1b35810 --- /dev/null +++ b/kUtvTc_d_q0.txt @@ -0,0 +1,12187 @@ +align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +jerry + + align:start position:0% +jerry + + + align:start position:0% +jerry +started the ablation studies the visual + + align:start position:0% +started the ablation studies the visual + + + align:start position:0% +started the ablation studies the visual +system and the reason why he didn't he's + + align:start position:0% +system and the reason why he didn't he's + + + align:start position:0% +system and the reason why he didn't he's +not gonna i'm not taking it you know + + align:start position:0% +not gonna i'm not taking it you know + + + align:start position:0% +not gonna i'm not taking it you know +picking up where he left off is because + + align:start position:0% +picking up where he left off is because + + + align:start position:0% +picking up where he left off is because +jerry's really the specialist in this in + + align:start position:0% +jerry's really the specialist in this in + + + align:start position:0% +jerry's really the specialist in this in +fact you'll see in our textbook that his + + align:start position:0% +fact you'll see in our textbook that his + + + align:start position:0% +fact you'll see in our textbook that his +work is cited his 1969 paper is cited + + align:start position:0% +work is cited his 1969 paper is cited + + + align:start position:0% +work is cited his 1969 paper is cited +for some of the ablation that he did to + + align:start position:0% +for some of the ablation that he did to + + + align:start position:0% +for some of the ablation that he did to +the superior click of this it's classic + + align:start position:0% +the superior click of this it's classic + + + align:start position:0% +the superior click of this it's classic +work so + + align:start position:0% +work so + + + align:start position:0% +work so +um he really is the one to talk about + + align:start position:0% +um he really is the one to talk about + + + align:start position:0% +um he really is the one to talk about +that not only that i don't do lesion + + align:start position:0% +that not only that i don't do lesion + + + align:start position:0% +that not only that i don't do lesion +studies so another good reason for me + + align:start position:0% +studies so another good reason for me + + + align:start position:0% +studies so another good reason for me +not to so + + align:start position:0% +not to so + + + align:start position:0% +not to so +i am an electrophysiologist and i work + + align:start position:0% +i am an electrophysiologist and i work + + + align:start position:0% +i am an electrophysiologist and i work +mainly in the hippocampus but + + align:start position:0% +mainly in the hippocampus but + + + align:start position:0% +mainly in the hippocampus but +hopefully that'll transfer to the retina + + align:start position:0% +hopefully that'll transfer to the retina + + + align:start position:0% +hopefully that'll transfer to the retina +nicely for today so + + align:start position:0% +nicely for today so + + + align:start position:0% +nicely for today so +this is today's topic + + align:start position:0% +this is today's topic + + + align:start position:0% +this is today's topic +and + + align:start position:0% + + + + align:start position:0% + +what jerry had this kind of very large + + align:start position:0% +what jerry had this kind of very large + + + align:start position:0% +what jerry had this kind of very large +outline with lots of slides so we're + + align:start position:0% +outline with lots of slides so we're + + + align:start position:0% +outline with lots of slides so we're +probably only going to talk about the + + align:start position:0% +probably only going to talk about the + + + align:start position:0% +probably only going to talk about the +retina and maybe get to talk about the + + align:start position:0% +retina and maybe get to talk about the + + + align:start position:0% +retina and maybe get to talk about the +different cell types the ganglion cell + + align:start position:0% +different cell types the ganglion cell + + + align:start position:0% +different cell types the ganglion cell +types and + + align:start position:0% +types and + + + align:start position:0% +types and +i don't know if everybody's done the + + align:start position:0% +i don't know if everybody's done the + + + align:start position:0% +i don't know if everybody's done the +reading or whatnot but i'll try and + + align:start position:0% +reading or whatnot but i'll try and + + + align:start position:0% +reading or whatnot but i'll try and +introduce you just starting with the eye + + align:start position:0% +introduce you just starting with the eye + + + align:start position:0% +introduce you just starting with the eye +and then moving down to the retina and + + align:start position:0% +and then moving down to the retina and + + + align:start position:0% +and then moving down to the retina and +then looking at the retina inside + + align:start position:0% +then looking at the retina inside + + + align:start position:0% +then looking at the retina inside +so + + align:start position:0% +so + + + align:start position:0% +so +we'll probably tackle these first two + + align:start position:0% +we'll probably tackle these first two + + + align:start position:0% +we'll probably tackle these first two +things so we'll start with the + + align:start position:0% +things so we'll start with the + + + align:start position:0% +things so we'll start with the +vertebrate retina + + align:start position:0% +vertebrate retina + + + align:start position:0% +vertebrate retina +so + + align:start position:0% +so + + + align:start position:0% +so +there's a lot of information here on + + align:start position:0% +there's a lot of information here on + + + align:start position:0% +there's a lot of information here on +this slide and we're going to be going + + align:start position:0% +this slide and we're going to be going + + + align:start position:0% +this slide and we're going to be going +through it one by one so don't get too + + align:start position:0% +through it one by one so don't get too + + + align:start position:0% +through it one by one so don't get too +overwhelmed right here we're first gonna + + align:start position:0% +overwhelmed right here we're first gonna + + + align:start position:0% +overwhelmed right here we're first gonna +be talking about the different cell + + align:start position:0% +be talking about the different cell + + + align:start position:0% +be talking about the different cell +types i'm just gonna introduce you + + align:start position:0% +types i'm just gonna introduce you + + + align:start position:0% +types i'm just gonna introduce you +without telling you too much about them + + align:start position:0% +without telling you too much about them + + + align:start position:0% +without telling you too much about them +and then i'm gonna tell you about what + + align:start position:0% +and then i'm gonna tell you about what + + + align:start position:0% +and then i'm gonna tell you about what +is the really interesting cells in the + + align:start position:0% +is the really interesting cells in the + + + align:start position:0% +is the really interesting cells in the +retina which is the photoreceptors which + + align:start position:0% +retina which is the photoreceptors which + + + align:start position:0% +retina which is the photoreceptors which +is the kind of the input end of the + + align:start position:0% +is the kind of the input end of the + + + align:start position:0% +is the kind of the input end of the +retina and the retinal ganglion cells + + align:start position:0% +retina and the retinal ganglion cells + + + align:start position:0% +retina and the retinal ganglion cells +which is several levels back a minimum + + align:start position:0% +which is several levels back a minimum + + + align:start position:0% +which is several levels back a minimum +of two synapses back and that that's the + + align:start position:0% +of two synapses back and that that's the + + + align:start position:0% +of two synapses back and that that's the +output end of the retina so those are + + align:start position:0% +output end of the retina so those are + + + align:start position:0% +output end of the retina so those are +the interesting phenomena we're going to + + align:start position:0% +the interesting phenomena we're going to + + + align:start position:0% +the interesting phenomena we're going to +look hey what do the photoreceptors do + + align:start position:0% +look hey what do the photoreceptors do + + + align:start position:0% +look hey what do the photoreceptors do +what do the retinal ganglion cells do + + align:start position:0% +what do the retinal ganglion cells do + + + align:start position:0% +what do the retinal ganglion cells do +and then once we know what the input + + align:start position:0% +and then once we know what the input + + + align:start position:0% +and then once we know what the input +output transformation is we're going to + + align:start position:0% +output transformation is we're going to + + + align:start position:0% +output transformation is we're going to +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +electrophysiological studies in the mud + + align:start position:0% +electrophysiological studies in the mud + + + align:start position:0% +electrophysiological studies in the mud +puppy and i'll tell you what mud puppy + + align:start position:0% +puppy and i'll tell you what mud puppy + + + align:start position:0% +puppy and i'll tell you what mud puppy +is if you don't know soon talk about + + align:start position:0% +is if you don't know soon talk about + + + align:start position:0% +is if you don't know soon talk about +electrophysiology that does that + + align:start position:0% +electrophysiology that does that + + + align:start position:0% +electrophysiology that does that +transform in between input and output so + + align:start position:0% +transform in between input and output so + + + align:start position:0% +transform in between input and output so +let's get started with cell types + + align:start position:0% +let's get started with cell types + + + align:start position:0% +let's get started with cell types +um + + align:start position:0% +um + + + align:start position:0% +um +where is the retina this is the eye + + align:start position:0% +where is the retina this is the eye + + + align:start position:0% +where is the retina this is the eye +right here we'll start with this + + align:start position:0% +right here we'll start with this + + + align:start position:0% +right here we'll start with this +the retina is right here it's this thin + + align:start position:0% +the retina is right here it's this thin + + + align:start position:0% +the retina is right here it's this thin +layer it's just a couple hundred microns + + align:start position:0% +layer it's just a couple hundred microns + + + align:start position:0% +layer it's just a couple hundred microns +thick + + align:start position:0% +thick + + + align:start position:0% +thick +that's really small that's like a razor + + align:start position:0% +that's really small that's like a razor + + + align:start position:0% +that's really small that's like a razor +blade really really small and there's + + align:start position:0% +blade really really small and there's + + + align:start position:0% +blade really really small and there's +all these cells we're going to learn + + align:start position:0% +all these cells we're going to learn + + + align:start position:0% +all these cells we're going to learn +about today and they're just in this + + align:start position:0% +about today and they're just in this + + + align:start position:0% +about today and they're just in this +very very small + + align:start position:0% +very very small + + + align:start position:0% +very very small +piece of tissue so plan to keep in mind + + align:start position:0% +piece of tissue so plan to keep in mind + + + align:start position:0% +piece of tissue so plan to keep in mind +uh just i guess i'll give you some + + align:start position:0% +uh just i guess i'll give you some + + + align:start position:0% +uh just i guess i'll give you some +basics here the cornea is this this + + align:start position:0% +basics here the cornea is this this + + + align:start position:0% +basics here the cornea is this this +thing that does most of the refraction + + align:start position:0% +thing that does most of the refraction + + + align:start position:0% +thing that does most of the refraction +refraction focusing the rays of light + + align:start position:0% +refraction focusing the rays of light + + + align:start position:0% +refraction focusing the rays of light +onto the back visual plane of the eye + + align:start position:0% +onto the back visual plane of the eye + + + align:start position:0% +onto the back visual plane of the eye +and the lens also which is um can be + + align:start position:0% +and the lens also which is um can be + + + align:start position:0% +and the lens also which is um can be +adapted with these ciliary muscles um it + + align:start position:0% +adapted with these ciliary muscles um it + + + align:start position:0% +adapted with these ciliary muscles um it +also does some work in focusing too but + + align:start position:0% +also does some work in focusing too but + + + align:start position:0% +also does some work in focusing too but +the retina is this back plane right here + + align:start position:0% +the retina is this back plane right here + + + align:start position:0% +the retina is this back plane right here +and you can see the optic nerve exiting + + align:start position:0% +and you can see the optic nerve exiting + + + align:start position:0% +and you can see the optic nerve exiting +the retina and this optic nerve are + + align:start position:0% +the retina and this optic nerve are + + + align:start position:0% +the retina and this optic nerve are +considered central nervous system unlike + + align:start position:0% +considered central nervous system unlike + + + align:start position:0% +considered central nervous system unlike +uh you know sensory receptors like touch + + align:start position:0% +uh you know sensory receptors like touch + + + align:start position:0% +uh you know sensory receptors like touch +receptors or uh like + + align:start position:0% +receptors or uh like + + + align:start position:0% +receptors or uh like +in the year uh + + align:start position:0% +in the year uh + + + align:start position:0% +in the year uh +the the cochlea those are peripherals so + + align:start position:0% +the the cochlea those are peripherals so + + + align:start position:0% +the the cochlea those are peripherals so +this is central nervous system + + align:start position:0% +this is central nervous system + + + align:start position:0% +this is central nervous system +so there's five cell types going to be + + align:start position:0% +so there's five cell types going to be + + + align:start position:0% +so there's five cell types going to be +talking about today + + align:start position:0% +talking about today + + + align:start position:0% +talking about today +and here they're kind of roughly in + + align:start position:0% +and here they're kind of roughly in + + + align:start position:0% +and here they're kind of roughly in +order uh from input to output + + align:start position:0% +order uh from input to output + + + align:start position:0% +order uh from input to output +photoreceptors horizontal cells bipolar + + align:start position:0% +photoreceptors horizontal cells bipolar + + + align:start position:0% +photoreceptors horizontal cells bipolar +cells endocrine cells and lastly retinal + + align:start position:0% +cells endocrine cells and lastly retinal + + + align:start position:0% +cells endocrine cells and lastly retinal +ganglion cells + + align:start position:0% +ganglion cells + + + align:start position:0% +ganglion cells +so + + align:start position:0% +so + + + align:start position:0% +so +here's a picture again this is about as + + align:start position:0% +here's a picture again this is about as + + + align:start position:0% +here's a picture again this is about as +thick as a razor blade and + + align:start position:0% +thick as a razor blade and + + + align:start position:0% +thick as a razor blade and +this is um so + + align:start position:0% +this is um so + + + align:start position:0% +this is um so +the first thing i don't know if i have a + + align:start position:0% +the first thing i don't know if i have a + + + align:start position:0% +the first thing i don't know if i have a +better slide of this no i don't okay + + align:start position:0% +better slide of this no i don't okay + + + align:start position:0% +better slide of this no i don't okay +well we'll see this more later but the + + align:start position:0% +well we'll see this more later but the + + + align:start position:0% +well we'll see this more later but the +retina has this kind of inside out + + align:start position:0% +retina has this kind of inside out + + + align:start position:0% +retina has this kind of inside out +organization and that the photoreceptors + + align:start position:0% +organization and that the photoreceptors + + + align:start position:0% +organization and that the photoreceptors +what strongholds are is actually + + align:start position:0% +what strongholds are is actually + + + align:start position:0% +what strongholds are is actually +furthest back and what + + align:start position:0% +furthest back and what + + + align:start position:0% +furthest back and what +what is first is the ganglion cell so + + align:start position:0% +what is first is the ganglion cell so + + + align:start position:0% +what is first is the ganglion cell so +the light actually has to go like this + + align:start position:0% +the light actually has to go like this + + + align:start position:0% +the light actually has to go like this +and then the information is processed in + + align:start position:0% +and then the information is processed in + + + align:start position:0% +and then the information is processed in +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +inside the out fashion and then the + + align:start position:0% +inside the out fashion and then the + + + align:start position:0% +inside the out fashion and then the +ganglion cells all connect to that optic + + align:start position:0% +ganglion cells all connect to that optic + + + align:start position:0% +ganglion cells all connect to that optic +nerve and goes back so here are the + + align:start position:0% +nerve and goes back so here are the + + + align:start position:0% +nerve and goes back so here are the +different cell types of their initial + + align:start position:0% +different cell types of their initial + + + align:start position:0% +different cell types of their initial +letters we'll get into this more no need + + align:start position:0% +letters we'll get into this more no need + + + align:start position:0% +letters we'll get into this more no need +to worry about details right now so + + align:start position:0% +to worry about details right now so + + + align:start position:0% +to worry about details right now so +jerry health has this nice picture based + + align:start position:0% +jerry health has this nice picture based + + + align:start position:0% +jerry health has this nice picture based +on + + align:start position:0% +on + + + align:start position:0% +on +em a much finer + + align:start position:0% +em a much finer + + + align:start position:0% +em a much finer +electron micrograph look and you can see + + align:start position:0% +electron micrograph look and you can see + + + align:start position:0% +electron micrograph look and you can see +here synapses and how contacts are made + + align:start position:0% +here synapses and how contacts are made + + + align:start position:0% +here synapses and how contacts are made +h is like a horizontal cell these are + + align:start position:0% +h is like a horizontal cell these are + + + align:start position:0% +h is like a horizontal cell these are +the receptors again light is going this + + align:start position:0% +the receptors again light is going this + + + align:start position:0% +the receptors again light is going this +way + + align:start position:0% +way + + + align:start position:0% +way +i'm speeding up here because i'm going + + align:start position:0% +i'm speeding up here because i'm going + + + align:start position:0% +i'm speeding up here because i'm going +to slow down a lot and talk about each + + align:start position:0% +to slow down a lot and talk about each + + + align:start position:0% +to slow down a lot and talk about each +cell individually so + + align:start position:0% +cell individually so + + + align:start position:0% +cell individually so +yes + + align:start position:0% + + + + align:start position:0% + +sure + + align:start position:0% +sure + + + align:start position:0% +sure +sure so what i mean by inside out is + + align:start position:0% +sure so what i mean by inside out is + + + align:start position:0% +sure so what i mean by inside out is +that + + align:start position:0% +that + + + align:start position:0% +that +well think about this way if you're + + align:start position:0% +well think about this way if you're + + + align:start position:0% +well think about this way if you're +designing something like a video camera + + align:start position:0% +designing something like a video camera + + + align:start position:0% +designing something like a video camera +where you know where you're going to put + + align:start position:0% +where you know where you're going to put + + + align:start position:0% +where you know where you're going to put +the the ccd or something are you going + + align:start position:0% +the the ccd or something are you going + + + align:start position:0% +the the ccd or something are you going +to put that behind all the electronics + + align:start position:0% +to put that behind all the electronics + + + align:start position:0% +to put that behind all the electronics +and stuff or you know say you had made + + align:start position:0% +and stuff or you know say you had made + + + align:start position:0% +and stuff or you know say you had made +the electronics out of clear plastic or + + align:start position:0% +the electronics out of clear plastic or + + + align:start position:0% +the electronics out of clear plastic or +something still you'd worry about you + + align:start position:0% +something still you'd worry about you + + + align:start position:0% +something still you'd worry about you +know light getting bent and things like + + align:start position:0% +know light getting bent and things like + + + align:start position:0% +know light getting bent and things like +that it makes more sense to put the + + align:start position:0% +that it makes more sense to put the + + + align:start position:0% +that it makes more sense to put the +ccd's focal plane right out there right + + align:start position:0% +ccd's focal plane right out there right + + + align:start position:0% +ccd's focal plane right out there right +so you'd see it so that the light would + + align:start position:0% +so you'd see it so that the light would + + + align:start position:0% +so you'd see it so that the light would +be incident on that before it's incident + + align:start position:0% +be incident on that before it's incident + + + align:start position:0% +be incident on that before it's incident +on electronics and controls and things + + align:start position:0% +on electronics and controls and things + + + align:start position:0% +on electronics and controls and things +like that but here + + align:start position:0% +like that but here + + + align:start position:0% +like that but here +that's kind of reversed all the + + align:start position:0% +that's kind of reversed all the + + + align:start position:0% +that's kind of reversed all the +electronics and controls and processing + + align:start position:0% +electronics and controls and processing + + + align:start position:0% +electronics and controls and processing +stuff is here the light is coming from + + align:start position:0% +stuff is here the light is coming from + + + align:start position:0% +stuff is here the light is coming from +here into the retina and hitting the + + align:start position:0% +here into the retina and hitting the + + + align:start position:0% +here into the retina and hitting the +photoreceptors so what's what's + + align:start position:0% +photoreceptors so what's what's + + + align:start position:0% +photoreceptors so what's what's +interesting is then evolution has done + + align:start position:0% +interesting is then evolution has done + + + align:start position:0% +interesting is then evolution has done +some things and i didn't really want to + + align:start position:0% +some things and i didn't really want to + + + align:start position:0% +some things and i didn't really want to +get into this but i'll very briefly say + + align:start position:0% +get into this but i'll very briefly say + + + align:start position:0% +get into this but i'll very briefly say +to compensate for this one of these + + align:start position:0% +to compensate for this one of these + + + align:start position:0% +to compensate for this one of these +things is these cells all these right + + align:start position:0% +things is these cells all these right + + + align:start position:0% +things is these cells all these right +here are unmyelinated so that cells in + + align:start position:0% +here are unmyelinated so that cells in + + + align:start position:0% +here are unmyelinated so that cells in +their + + align:start position:0% +their + + + align:start position:0% +their +which are unmyelinated are cell bodies + + align:start position:0% +which are unmyelinated are cell bodies + + + align:start position:0% +which are unmyelinated are cell bodies +are by themselves clear um if you look + + align:start position:0% +are by themselves clear um if you look + + + align:start position:0% +are by themselves clear um if you look +in a microscope at cell culture say in + + align:start position:0% +in a microscope at cell culture say in + + + align:start position:0% +in a microscope at cell culture say in +our lab you'd see that + + align:start position:0% +our lab you'd see that + + + align:start position:0% +our lab you'd see that +so the myelin um coating can + + align:start position:0% +so the myelin um coating can + + + align:start position:0% +so the myelin um coating can +cause more of a diffraction of light + + align:start position:0% +cause more of a diffraction of light + + + align:start position:0% +cause more of a diffraction of light +another thing is behind the + + align:start position:0% +another thing is behind the + + + align:start position:0% +another thing is behind the +photoreceptors right here there's a + + align:start position:0% +photoreceptors right here there's a + + + align:start position:0% +photoreceptors right here there's a +pigment epithelium which is like this + + align:start position:0% +pigment epithelium which is like this + + + align:start position:0% +pigment epithelium which is like this +black layer and what it does is it + + align:start position:0% +black layer and what it does is it + + + align:start position:0% +black layer and what it does is it +absorbs anything that the photoreceptor + + align:start position:0% +absorbs anything that the photoreceptor + + + align:start position:0% +absorbs anything that the photoreceptor +does not absorb so you'll see later the + + align:start position:0% +does not absorb so you'll see later the + + + align:start position:0% +does not absorb so you'll see later the +photoreceptors are tuned to certain um + + align:start position:0% +photoreceptors are tuned to certain um + + + align:start position:0% +photoreceptors are tuned to certain um +colors of light say and tuned to certain + + align:start position:0% +colors of light say and tuned to certain + + + align:start position:0% +colors of light say and tuned to certain +frequencies of light i should say and + + align:start position:0% +frequencies of light i should say and + + + align:start position:0% +frequencies of light i should say and +that what's not absorbed you can imagine + + align:start position:0% +that what's not absorbed you can imagine + + + align:start position:0% +that what's not absorbed you can imagine +if you had a reflective surface it would + + align:start position:0% +if you had a reflective surface it would + + + align:start position:0% +if you had a reflective surface it would +go + + align:start position:0% +go + + + align:start position:0% +go +and then bounce back and that would + + align:start position:0% +and then bounce back and that would + + + align:start position:0% +and then bounce back and that would +cause some kind of interference in your + + align:start position:0% +cause some kind of interference in your + + + align:start position:0% +cause some kind of interference in your +sense it in your sensing so here there's + + align:start position:0% +sense it in your sensing so here there's + + + align:start position:0% +sense it in your sensing so here there's +like this black pigment epithelium so i + + align:start position:0% +like this black pigment epithelium so i + + + align:start position:0% +like this black pigment epithelium so i +don't know if that really answered your + + align:start position:0% +don't know if that really answered your + + + align:start position:0% +don't know if that really answered your +question that was an attempt + + align:start position:0% +question that was an attempt + + + align:start position:0% +question that was an attempt +um + + align:start position:0% +um + + + align:start position:0% +um +going to talk now about + + align:start position:0% +going to talk now about + + + align:start position:0% +going to talk now about +the phenomenology of the interesting + + align:start position:0% +the phenomenology of the interesting + + + align:start position:0% +the phenomenology of the interesting +stuff the photoreceptors how do they do + + align:start position:0% +stuff the photoreceptors how do they do + + + align:start position:0% +stuff the photoreceptors how do they do +their amazing job and what's the end + + align:start position:0% +their amazing job and what's the end + + + align:start position:0% +their amazing job and what's the end +part of the transform what are we + + align:start position:0% +part of the transform what are we + + + align:start position:0% +part of the transform what are we +getting out of the retina what are the + + align:start position:0% +getting out of the retina what are the + + + align:start position:0% +getting out of the retina what are the +retinal ganglion cells those output + + align:start position:0% +retinal ganglion cells those output + + + align:start position:0% +retinal ganglion cells those output +cells what do they send us what are they + + align:start position:0% +cells what do they send us what are they + + + align:start position:0% +cells what do they send us what are they +sending back to + + align:start position:0% +sending back to + + + align:start position:0% +sending back to +cortex and superior click list and all + + align:start position:0% +cortex and superior click list and all + + + align:start position:0% +cortex and superior click list and all +those interesting areas + + align:start position:0% +those interesting areas + + + align:start position:0% +those interesting areas +so we're going to start with the + + align:start position:0% +so we're going to start with the + + + align:start position:0% +so we're going to start with the +photoreceptors + + align:start position:0% +photoreceptors + + + align:start position:0% +photoreceptors +that this photoreceptor right there + + align:start position:0% +that this photoreceptor right there + + + align:start position:0% +that this photoreceptor right there +so here's a very nice i've you see this + + align:start position:0% +so here's a very nice i've you see this + + + align:start position:0% +so here's a very nice i've you see this +yeah you can see well um + + align:start position:0% +yeah you can see well um + + + align:start position:0% +yeah you can see well um +so i'm lucky to have some friends in + + align:start position:0% +so i'm lucky to have some friends in + + + align:start position:0% +so i'm lucky to have some friends in +vision science here who gave me these + + align:start position:0% +vision science here who gave me these + + + align:start position:0% +vision science here who gave me these +great photos this is a + + align:start position:0% +great photos this is a + + + align:start position:0% +great photos this is a +scanning electron microscope picture of + + align:start position:0% +scanning electron microscope picture of + + + align:start position:0% +scanning electron microscope picture of +rods and cones + + align:start position:0% +rods and cones + + + align:start position:0% +rods and cones +and you can see the rods these thin rods + + align:start position:0% +and you can see the rods these thin rods + + + align:start position:0% +and you can see the rods these thin rods +and the larger cones actually + + align:start position:0% +and the larger cones actually + + + align:start position:0% +and the larger cones actually +we'll get into a little bit about why + + align:start position:0% +we'll get into a little bit about why + + + align:start position:0% +we'll get into a little bit about why +why these here but i just want you to + + align:start position:0% +why these here but i just want you to + + + align:start position:0% +why these here but i just want you to +observe kind of the structure and how um + + align:start position:0% +observe kind of the structure and how um + + + align:start position:0% +observe kind of the structure and how um +how nice the organization is actually + + align:start position:0% +how nice the organization is actually + + + align:start position:0% +how nice the organization is actually +so + + align:start position:0% +so + + + align:start position:0% +so +why why this this rods and cone stuff so + + align:start position:0% +why why this this rods and cone stuff so + + + align:start position:0% +why why this this rods and cone stuff so +here's the question how do you design a + + align:start position:0% +here's the question how do you design a + + + align:start position:0% +here's the question how do you design a +visual system that can respond to high + + align:start position:0% +visual system that can respond to high + + + align:start position:0% +visual system that can respond to high +illumination levels during the daytime + + align:start position:0% +illumination levels during the daytime + + + align:start position:0% +illumination levels during the daytime +and low light levels at night and + + align:start position:0% +and low light levels at night and + + + align:start position:0% +and low light levels at night and +there's actually a few different things + + align:start position:0% +there's actually a few different things + + + align:start position:0% +there's actually a few different things +that are in the visual system + + align:start position:0% +that are in the visual system + + + align:start position:0% +that are in the visual system +to answer this question but there's one + + align:start position:0% +to answer this question but there's one + + + align:start position:0% +to answer this question but there's one +big one does anyone know what it is i + + align:start position:0% +big one does anyone know what it is i + + + align:start position:0% +big one does anyone know what it is i +kind of just gave it away on the last + + align:start position:0% +kind of just gave it away on the last + + + align:start position:0% +kind of just gave it away on the last +slide by my poor organization that + + align:start position:0% +slide by my poor organization that + + + align:start position:0% +slide by my poor organization that +slides + + align:start position:0% + + + + align:start position:0% + +mumbling mumbling yes + + align:start position:0% + + + + align:start position:0% + +you have two different kinds of + + align:start position:0% +you have two different kinds of + + + align:start position:0% +you have two different kinds of +photoreceptors that's exactly right so + + align:start position:0% +photoreceptors that's exactly right so + + + align:start position:0% +photoreceptors that's exactly right so +one is for scotopic vision which is the + + align:start position:0% +one is for scotopic vision which is the + + + align:start position:0% +one is for scotopic vision which is the +word that denotes low light vision + + align:start position:0% +word that denotes low light vision + + + align:start position:0% +word that denotes low light vision +that's rod dominated vision + + align:start position:0% +that's rod dominated vision + + + align:start position:0% +that's rod dominated vision +another one is for photopic which is + + align:start position:0% +another one is for photopic which is + + + align:start position:0% +another one is for photopic which is +highlight levels and that's cone + + align:start position:0% +highlight levels and that's cone + + + align:start position:0% +highlight levels and that's cone +dominated so let's get into a little bit + + align:start position:0% +dominated so let's get into a little bit + + + align:start position:0% +dominated so let's get into a little bit +more about these two luminance regimes + + align:start position:0% +more about these two luminance regimes + + + align:start position:0% +more about these two luminance regimes +and and the things associated by them so + + align:start position:0% +and and the things associated by them so + + + align:start position:0% +and and the things associated by them so +here is what you see with if you're just + + align:start position:0% +here is what you see with if you're just + + + align:start position:0% +here is what you see with if you're just +looking at cones and here's what you see + + align:start position:0% +looking at cones and here's what you see + + + align:start position:0% +looking at cones and here's what you see +if you're looking with rods and what's + + align:start position:0% +if you're looking with rods and what's + + + align:start position:0% +if you're looking with rods and what's +the big difference here between these + + align:start position:0% +the big difference here between these + + + align:start position:0% +the big difference here between these +pictures don't look at the textures look + + align:start position:0% +pictures don't look at the textures look + + + align:start position:0% +pictures don't look at the textures look +at the pictures what is the difference + + align:start position:0% +at the pictures what is the difference + + + align:start position:0% +at the pictures what is the difference +between this pneumatic + + align:start position:0% + + + + align:start position:0% + +right you see all the little spots here + + align:start position:0% +right you see all the little spots here + + + align:start position:0% +right you see all the little spots here +and here's the really the huge like wow + + align:start position:0% +and here's the really the huge like wow + + + align:start position:0% +and here's the really the huge like wow +look at this only one quanta is needed + + align:start position:0% +look at this only one quanta is needed + + + align:start position:0% +look at this only one quanta is needed +to stimulate a rod receptor so that + + align:start position:0% +to stimulate a rod receptor so that + + + align:start position:0% +to stimulate a rod receptor so that +that's amazing that one quanta can lead + + align:start position:0% +that's amazing that one quanta can lead + + + align:start position:0% +that's amazing that one quanta can lead +to + + align:start position:0% +to + + + align:start position:0% +to +as + + align:start position:0% +as + + + align:start position:0% +as +if you read in your textbook it'll + + align:start position:0% +if you read in your textbook it'll + + + align:start position:0% +if you read in your textbook it'll +explain a little bit more about how + + align:start position:0% +explain a little bit more about how + + + align:start position:0% +explain a little bit more about how +photoreceptors work but it can lead to + + align:start position:0% +photoreceptors work but it can lead to + + + align:start position:0% +photoreceptors work but it can lead to +this huge phosphorylation cascade that + + align:start position:0% +this huge phosphorylation cascade that + + + align:start position:0% +this huge phosphorylation cascade that +involves like + + align:start position:0% +involves like + + + align:start position:0% +involves like +thousands of cyclic gmp molecules and + + align:start position:0% +thousands of cyclic gmp molecules and + + + align:start position:0% +thousands of cyclic gmp molecules and +that's + + align:start position:0% +that's + + + align:start position:0% +that's +don't write that down it's not needed to + + align:start position:0% +don't write that down it's not needed to + + + align:start position:0% +don't write that down it's not needed to +know that but just + + align:start position:0% +know that but just + + + align:start position:0% +know that but just +if you're interested look in the book + + align:start position:0% +if you're interested look in the book + + + align:start position:0% +if you're interested look in the book +it's it's an amazing thing one quanta of + + align:start position:0% +it's it's an amazing thing one quanta of + + + align:start position:0% +it's it's an amazing thing one quanta of +light + + align:start position:0% +light + + + align:start position:0% +light +phosphorylating all those molecules so + + align:start position:0% +phosphorylating all those molecules so + + + align:start position:0% +phosphorylating all those molecules so +um + + align:start position:0% +um + + + align:start position:0% +um +okay what is the distribution of + + align:start position:0% +okay what is the distribution of + + + align:start position:0% +okay what is the distribution of +receptors in the eye why are receptors + + align:start position:0% +receptors in the eye why are receptors + + + align:start position:0% +receptors in the eye why are receptors +distributed this way and what does it + + align:start position:0% +distributed this way and what does it + + + align:start position:0% +distributed this way and what does it +imply about vision those are a lot of + + align:start position:0% +imply about vision those are a lot of + + + align:start position:0% +imply about vision those are a lot of +questions but + + align:start position:0% +questions but + + + align:start position:0% +questions but +there's two two main regions to the eye + + align:start position:0% +there's two two main regions to the eye + + + align:start position:0% +there's two two main regions to the eye +in this central portion which we call + + align:start position:0% +in this central portion which we call + + + align:start position:0% +in this central portion which we call +the phobia i don't know if everyone's + + align:start position:0% +the phobia i don't know if everyone's + + + align:start position:0% +the phobia i don't know if everyone's +familiar with that you can see that + + align:start position:0% +familiar with that you can see that + + + align:start position:0% +familiar with that you can see that +there's just cones these hexagonal tones + + align:start position:0% +there's just cones these hexagonal tones + + + align:start position:0% +there's just cones these hexagonal tones +there's no rods there and that's because + + align:start position:0% +there's no rods there and that's because + + + align:start position:0% +there's no rods there and that's because +these + + align:start position:0% +these + + + align:start position:0% +these +these you have this fine so in in the + + align:start position:0% +these you have this fine so in in the + + + align:start position:0% +these you have this fine so in in the +phobia when you fixate on something you + + align:start position:0% +phobia when you fixate on something you + + + align:start position:0% +phobia when you fixate on something you +have this fine uh high acuity color + + align:start position:0% +have this fine uh high acuity color + + + align:start position:0% +have this fine uh high acuity color +vision but here out in the periphery you + + align:start position:0% +vision but here out in the periphery you + + + align:start position:0% +vision but here out in the periphery you +have cones interspersed with rods too + + align:start position:0% +have cones interspersed with rods too + + + align:start position:0% +have cones interspersed with rods too +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so + + align:start position:0% +so + + + align:start position:0% +so +this this is another important point so + + align:start position:0% +this this is another important point so + + + align:start position:0% +this this is another important point so +here you have high color acuity now what + + align:start position:0% +here you have high color acuity now what + + + align:start position:0% +here you have high color acuity now what +do you think having this buys you what + + align:start position:0% +do you think having this buys you what + + + align:start position:0% +do you think having this buys you what +what is something you can tell me in + + align:start position:0% +what is something you can tell me in + + + align:start position:0% +what is something you can tell me in +terms of um so if i want to look at some + + align:start position:0% +terms of um so if i want to look at some + + + align:start position:0% +terms of um so if i want to look at some +fine color detail phobia is good but + + align:start position:0% +fine color detail phobia is good but + + + align:start position:0% +fine color detail phobia is good but +what what might this be good for + + align:start position:0% + + + + align:start position:0% + +contrast okay + + align:start position:0% +contrast okay + + + align:start position:0% +contrast okay +that's partially it + + align:start position:0% + + + + align:start position:0% + +anyone + + align:start position:0% +anyone + + + align:start position:0% +anyone +do + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +right so rods are for scottish vision + + align:start position:0% +right so rods are for scottish vision + + + align:start position:0% +right so rods are for scottish vision +right so that's like the low light level + + align:start position:0% +right so that's like the low light level + + + align:start position:0% +right so that's like the low light level +the night vision + + align:start position:0% +the night vision + + + align:start position:0% +the night vision +so have you ever noticed that when you + + align:start position:0% +so have you ever noticed that when you + + + align:start position:0% +so have you ever noticed that when you +like look out um like on a starry night + + align:start position:0% +like look out um like on a starry night + + + align:start position:0% +like look out um like on a starry night +or something if you're trying to see a + + align:start position:0% +or something if you're trying to see a + + + align:start position:0% +or something if you're trying to see a +star that's kind of dim have you noticed + + align:start position:0% +star that's kind of dim have you noticed + + + align:start position:0% +star that's kind of dim have you noticed +that it's not better to actually look + + align:start position:0% +that it's not better to actually look + + + align:start position:0% +that it's not better to actually look +right at it but just kind of go a little + + align:start position:0% +right at it but just kind of go a little + + + align:start position:0% +right at it but just kind of go a little +bit away like + + align:start position:0% +bit away like + + + align:start position:0% +bit away like +move your eyes a little bit away and you + + align:start position:0% +move your eyes a little bit away and you + + + align:start position:0% +move your eyes a little bit away and you +can see it kind of in a not quite + + align:start position:0% +can see it kind of in a not quite + + + align:start position:0% +can see it kind of in a not quite +peripheral but near the periphery + + align:start position:0% +peripheral but near the periphery + + + align:start position:0% +peripheral but near the periphery +now am i making it up yes one guy agrees + + align:start position:0% +now am i making it up yes one guy agrees + + + align:start position:0% +now am i making it up yes one guy agrees +with me good that's enough to go on in + + align:start position:0% +with me good that's enough to go on in + + + align:start position:0% +with me good that's enough to go on in +the next slide + + align:start position:0% +the next slide + + + align:start position:0% +the next slide +so + + align:start position:0% + + + + align:start position:0% + +what do these different cones and rods + + align:start position:0% +what do these different cones and rods + + + align:start position:0% +what do these different cones and rods +so + + align:start position:0% +so + + + align:start position:0% +so +these different photoreceptor types we + + align:start position:0% +these different photoreceptor types we + + + align:start position:0% +these different photoreceptor types we +distinguish them by the frequencies that + + align:start position:0% +distinguish them by the frequencies that + + + align:start position:0% +distinguish them by the frequencies that +they're tuned to so + + align:start position:0% +they're tuned to so + + + align:start position:0% +they're tuned to so +um you might hear me refer to these raw + + align:start position:0% +um you might hear me refer to these raw + + + align:start position:0% +um you might hear me refer to these raw +the cones as blue green and red but + + align:start position:0% +the cones as blue green and red but + + + align:start position:0% +the cones as blue green and red but +that's + + align:start position:0% +that's + + + align:start position:0% +that's +for obvious reasons you can see on this + + align:start position:0% +for obvious reasons you can see on this + + + align:start position:0% +for obvious reasons you can see on this +graph incorrect it's better to refuse + + align:start position:0% +graph incorrect it's better to refuse + + + align:start position:0% +graph incorrect it's better to refuse +refer to these as short wavelength + + align:start position:0% +refer to these as short wavelength + + + align:start position:0% +refer to these as short wavelength +medium wavelength and long you can see + + align:start position:0% +medium wavelength and long you can see + + + align:start position:0% +medium wavelength and long you can see +that somebody called this red it would + + align:start position:0% +that somebody called this red it would + + + align:start position:0% +that somebody called this red it would +be more really green yellow but um so + + align:start position:0% +be more really green yellow but um so + + + align:start position:0% +be more really green yellow but um so +here are the spectral + + align:start position:0% +here are the spectral + + + align:start position:0% +here are the spectral +sensitivities and there's a lot of if + + align:start position:0% +sensitivities and there's a lot of if + + + align:start position:0% +sensitivities and there's a lot of if +you take some of the vision classes here + + align:start position:0% +you take some of the vision classes here + + + align:start position:0% +you take some of the vision classes here +the the undergrad vision classes they'll + + align:start position:0% +the the undergrad vision classes they'll + + + align:start position:0% +the the undergrad vision classes they'll +tell you a little bit about um thinking + + align:start position:0% +tell you a little bit about um thinking + + + align:start position:0% +tell you a little bit about um thinking +about this from an engineering point of + + align:start position:0% +about this from an engineering point of + + + align:start position:0% +about this from an engineering point of +view you know why why are these two so + + align:start position:0% +view you know why why are these two so + + + align:start position:0% +view you know why why are these two so +close together and this one far apart + + align:start position:0% +close together and this one far apart + + + align:start position:0% +close together and this one far apart +what's the optimum way to design this + + align:start position:0% +what's the optimum way to design this + + + align:start position:0% +what's the optimum way to design this +and um i don't know i encourage you if + + align:start position:0% +and um i don't know i encourage you if + + + align:start position:0% +and um i don't know i encourage you if +you're interested in those kind of + + align:start position:0% +you're interested in those kind of + + + align:start position:0% +you're interested in those kind of +things to take those classes but you see + + align:start position:0% +things to take those classes but you see + + + align:start position:0% +things to take those classes but you see +the rods are kind of here + + align:start position:0% +the rods are kind of here + + + align:start position:0% +the rods are kind of here +uh in the middle + + align:start position:0% +uh in the middle + + + align:start position:0% +uh in the middle +so this is some recent work which is + + align:start position:0% +so this is some recent work which is + + + align:start position:0% +so this is some recent work which is +just absolutely um amazing neuroscience + + align:start position:0% +just absolutely um amazing neuroscience + + + align:start position:0% +just absolutely um amazing neuroscience +going on and these are the the first + + align:start position:0% +going on and these are the the first + + + align:start position:0% +going on and these are the the first +images um that were taken + + align:start position:0% +images um that were taken + + + align:start position:0% +images um that were taken +of + + align:start position:0% +of + + + align:start position:0% +of +the uh the human i guess i think it's + + align:start position:0% +the uh the human i guess i think it's + + + align:start position:0% +the uh the human i guess i think it's +the phobia i'm not i'm not sure so the + + align:start position:0% +the phobia i'm not i'm not sure so the + + + align:start position:0% +the phobia i'm not i'm not sure so the +phobia the phobial region just has cones + + align:start position:0% +phobia the phobial region just has cones + + + align:start position:0% +phobia the phobial region just has cones +but what's amazing about these images is + + align:start position:0% +but what's amazing about these images is + + + align:start position:0% +but what's amazing about these images is +you can distinguish the different cones + + align:start position:0% +you can distinguish the different cones + + + align:start position:0% +you can distinguish the different cones +the short ones are labeled blue the + + align:start position:0% +the short ones are labeled blue the + + + align:start position:0% +the short ones are labeled blue the +medium wavelength ones here are green + + align:start position:0% +medium wavelength ones here are green + + + align:start position:0% +medium wavelength ones here are green +and the long are red and the only thing + + align:start position:0% +and the long are red and the only thing + + + align:start position:0% +and the long are red and the only thing +that um + + align:start position:0% +that um + + + align:start position:0% +that um +what's stressed in this paper and the + + align:start position:0% +what's stressed in this paper and the + + + align:start position:0% +what's stressed in this paper and the +one thing to notice here which is + + align:start position:0% +one thing to notice here which is + + + align:start position:0% +one thing to notice here which is +interesting is that the blue cones are + + align:start position:0% +interesting is that the blue cones are + + + align:start position:0% +interesting is that the blue cones are +relatively less here and i'm not going + + align:start position:0% +relatively less here and i'm not going + + + align:start position:0% +relatively less here and i'm not going +to really explain why it's the one + + align:start position:0% +to really explain why it's the one + + + align:start position:0% +to really explain why it's the one +explanation that's been proposed has to + + align:start position:0% +explanation that's been proposed has to + + + align:start position:0% +explanation that's been proposed has to +do with chromatic aberration the fact + + align:start position:0% +do with chromatic aberration the fact + + + align:start position:0% +do with chromatic aberration the fact +that you can't focus all colors at the + + align:start position:0% +that you can't focus all colors at the + + + align:start position:0% +that you can't focus all colors at the +same time really no matter what kind of + + align:start position:0% +same time really no matter what kind of + + + align:start position:0% +same time really no matter what kind of +lens you have and that blue by itself + + align:start position:0% +lens you have and that blue by itself + + + align:start position:0% +lens you have and that blue by itself +the way the human visual system is + + align:start position:0% +the way the human visual system is + + + align:start position:0% +the way the human visual system is +designed blue is getting blurred anyways + + align:start position:0% +designed blue is getting blurred anyways + + + align:start position:0% +designed blue is getting blurred anyways +so evolution was like hey while blue's + + align:start position:0% +so evolution was like hey while blue's + + + align:start position:0% +so evolution was like hey while blue's +getting blurred i don't need to sample + + align:start position:0% +getting blurred i don't need to sample + + + align:start position:0% +getting blurred i don't need to sample +it as finely and that's why you have + + align:start position:0% +it as finely and that's why you have + + + align:start position:0% +it as finely and that's why you have +this kind of regular pattern of blue + + align:start position:0% +this kind of regular pattern of blue + + + align:start position:0% +this kind of regular pattern of blue +with reg relatively regular spacing + + align:start position:0% +with reg relatively regular spacing + + + align:start position:0% +with reg relatively regular spacing +whereas um red and green are just kind + + align:start position:0% +whereas um red and green are just kind + + + align:start position:0% +whereas um red and green are just kind +of look kind of random what's + + align:start position:0% +of look kind of random what's + + + align:start position:0% +of look kind of random what's +interesting is in this paper they only + + align:start position:0% +interesting is in this paper they only + + + align:start position:0% +interesting is in this paper they only +they have two two male subjects and the + + align:start position:0% +they have two two male subjects and the + + + align:start position:0% +they have two two male subjects and the +ratio of medium to long length cones + + align:start position:0% +ratio of medium to long length cones + + + align:start position:0% +ratio of medium to long length cones +between subjects differs by four to one + + align:start position:0% +between subjects differs by four to one + + + align:start position:0% +between subjects differs by four to one +so it's like this huge difference in + + align:start position:0% +so it's like this huge difference in + + + align:start position:0% +so it's like this huge difference in +what you but they both and both subjects + + align:start position:0% +what you but they both and both subjects + + + align:start position:0% +what you but they both and both subjects +reported normal color vision just a + + align:start position:0% +reported normal color vision just a + + + align:start position:0% +reported normal color vision just a +fun fact for you + + align:start position:0% +fun fact for you + + + align:start position:0% +fun fact for you +so + + align:start position:0% +so + + + align:start position:0% +so +the other kind of cell that we should + + align:start position:0% +the other kind of cell that we should + + + align:start position:0% +the other kind of cell that we should +talk a little bit about the + + align:start position:0% +talk a little bit about the + + + align:start position:0% +talk a little bit about the +phenomenology um + + align:start position:0% +phenomenology um + + + align:start position:0% +phenomenology um +and + + align:start position:0% +and + + + align:start position:0% +and +back to the receptor cell for a second + + align:start position:0% +back to the receptor cell for a second + + + align:start position:0% +back to the receptor cell for a second +the actual transduction cascade is not + + align:start position:0% +the actual transduction cascade is not + + + align:start position:0% +the actual transduction cascade is not +covered in this lecture because it's in + + align:start position:0% +covered in this lecture because it's in + + + align:start position:0% +covered in this lecture because it's in +the textbook so if you're interested in + + align:start position:0% +the textbook so if you're interested in + + + align:start position:0% +the textbook so if you're interested in +how the light signal becomes an + + align:start position:0% +how the light signal becomes an + + + align:start position:0% +how the light signal becomes an +electrical signal + + align:start position:0% +electrical signal + + + align:start position:0% +electrical signal +you know look there um + + align:start position:0% +you know look there um + + + align:start position:0% +you know look there um +so there's two basic types of retinal + + align:start position:0% +so there's two basic types of retinal + + + align:start position:0% +so there's two basic types of retinal +ganglion cells and one is an on center + + align:start position:0% +ganglion cells and one is an on center + + + align:start position:0% +ganglion cells and one is an on center +cell and the other is an off-center cell + + align:start position:0% +cell and the other is an off-center cell + + + align:start position:0% +cell and the other is an off-center cell +and we're going to be seeing something + + align:start position:0% +and we're going to be seeing something + + + align:start position:0% +and we're going to be seeing something +in a second to make this a little bit + + align:start position:0% +in a second to make this a little bit + + + align:start position:0% +in a second to make this a little bit +clearer but in the on center cell when + + align:start position:0% +clearer but in the on center cell when + + + align:start position:0% +clearer but in the on center cell when +this when a bright spot moves toward the + + align:start position:0% +this when a bright spot moves toward the + + + align:start position:0% +this when a bright spot moves toward the +center + + align:start position:0% +center + + + align:start position:0% +center +so there's there's photoreceptors in the + + align:start position:0% +so there's there's photoreceptors in the + + + align:start position:0% +so there's there's photoreceptors in the +center and then there's photoreceptors + + align:start position:0% +center and then there's photoreceptors + + + align:start position:0% +center and then there's photoreceptors +in the circular surround region and the + + align:start position:0% +in the circular surround region and the + + + align:start position:0% +in the circular surround region and the +retinal ganglion cell is pulling + + align:start position:0% +retinal ganglion cell is pulling + + + align:start position:0% +retinal ganglion cell is pulling +information from all of those + + align:start position:0% +information from all of those + + + align:start position:0% +information from all of those +and when the spot passes through this + + align:start position:0% +and when the spot passes through this + + + align:start position:0% +and when the spot passes through this +bright spot the on type cell fires + + align:start position:0% +bright spot the on type cell fires + + + align:start position:0% +bright spot the on type cell fires +and + + align:start position:0% +and + + + align:start position:0% +and +when this bright spot passes through + + align:start position:0% +when this bright spot passes through + + + align:start position:0% +when this bright spot passes through +with an off-type cell it's inhibited so + + align:start position:0% +with an off-type cell it's inhibited so + + + align:start position:0% +with an off-type cell it's inhibited so +the off-center cell or the off yeah off + + align:start position:0% +the off-center cell or the off yeah off + + + align:start position:0% +the off-center cell or the off yeah off +center cell prefers a dark patch on a + + align:start position:0% +center cell prefers a dark patch on a + + + align:start position:0% +center cell prefers a dark patch on a +light circle whereas this one prefers a + + align:start position:0% +light circle whereas this one prefers a + + + align:start position:0% +light circle whereas this one prefers a +light patch on the dark circle so + + align:start position:0% +light patch on the dark circle so + + + align:start position:0% +light patch on the dark circle so +retinal ganglion cells in action right + + align:start position:0% +retinal ganglion cells in action right + + + align:start position:0% +retinal ganglion cells in action right +so + + align:start position:0% +so + + + align:start position:0% +so +there's some classic movies um that i + + align:start position:0% +there's some classic movies um that i + + + align:start position:0% +there's some classic movies um that i +was able to acquire um of some of this + + align:start position:0% +was able to acquire um of some of this + + + align:start position:0% +was able to acquire um of some of this +some of this work and i guess one thing + + align:start position:0% +some of this work and i guess one thing + + + align:start position:0% +some of this work and i guess one thing +i should say just for those of you who + + align:start position:0% +i should say just for those of you who + + + align:start position:0% +i should say just for those of you who +look into this more these recordings are + + align:start position:0% +look into this more these recordings are + + + align:start position:0% +look into this more these recordings are +are not exactly from the retina but + + align:start position:0% +are not exactly from the retina but + + + align:start position:0% +are not exactly from the retina but +they're not exactly from retinal + + align:start position:0% +they're not exactly from retinal + + + align:start position:0% +they're not exactly from retinal +ganglion cells but they're from cells + + align:start position:0% +ganglion cells but they're from cells + + + align:start position:0% +ganglion cells but they're from cells +that display similar receptive field + + align:start position:0% +that display similar receptive field + + + align:start position:0% +that display similar receptive field +properties so when i use the word + + align:start position:0% +properties so when i use the word + + + align:start position:0% +properties so when i use the word +receptive field i mean something like + + align:start position:0% +receptive field i mean something like + + + align:start position:0% +receptive field i mean something like +bright spot on a dark patch or dark spot + + align:start position:0% +bright spot on a dark patch or dark spot + + + align:start position:0% +bright spot on a dark patch or dark spot +on a bright patch the the kind of the + + align:start position:0% +on a bright patch the the kind of the + + + align:start position:0% +on a bright patch the the kind of the +optimal stimulus there + + align:start position:0% +optimal stimulus there + + + align:start position:0% +optimal stimulus there +sure + + align:start position:0% +sure + + + align:start position:0% +sure +oh that's showing just denoting the time + + align:start position:0% +oh that's showing just denoting the time + + + align:start position:0% +oh that's showing just denoting the time +so when the spot hits the center the on + + align:start position:0% +so when the spot hits the center the on + + + align:start position:0% +so when the spot hits the center the on +type cell so this is time right here + + align:start position:0% +type cell so this is time right here + + + align:start position:0% +type cell so this is time right here +this is saying the direction of travel + + align:start position:0% +this is saying the direction of travel + + + align:start position:0% +this is saying the direction of travel +so here it's not in the center there it + + align:start position:0% +so here it's not in the center there it + + + align:start position:0% +so here it's not in the center there it +gets in the center there it leaves the + + align:start position:0% +gets in the center there it leaves the + + + align:start position:0% +gets in the center there it leaves the +center + + align:start position:0% +center + + + align:start position:0% +center +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the center of this circle right here + + align:start position:0% +the center of this circle right here + + + align:start position:0% +the center of this circle right here +which is the center of its receptive + + align:start position:0% +which is the center of its receptive + + + align:start position:0% +which is the center of its receptive +field so + + align:start position:0% +field so + + + align:start position:0% +field so +okay so we're going to look at some so + + align:start position:0% +okay so we're going to look at some so + + + align:start position:0% +okay so we're going to look at some so +with that small caveat i gave you about + + align:start position:0% +with that small caveat i gave you about + + + align:start position:0% +with that small caveat i gave you about +the movie don't worry about that we're + + align:start position:0% +the movie don't worry about that we're + + + align:start position:0% +the movie don't worry about that we're +going to look at how experimenters + + align:start position:0% +going to look at how experimenters + + + align:start position:0% +going to look at how experimenters +neuroscientists experimentally recording + + align:start position:0% +neuroscientists experimentally recording + + + align:start position:0% +neuroscientists experimentally recording +from um i think this is in cat but i'm + + align:start position:0% +from um i think this is in cat but i'm + + + align:start position:0% +from um i think this is in cat but i'm +not sure + + align:start position:0% +not sure + + + align:start position:0% +not sure +how they + + align:start position:0% +how they + + + align:start position:0% +how they +how they show that a cell truly is on + + align:start position:0% +how they show that a cell truly is on + + + align:start position:0% +how they show that a cell truly is on +center off surround versus off-center on + + align:start position:0% +center off surround versus off-center on + + + align:start position:0% +center off surround versus off-center on +surround + + align:start position:0% +surround + + + align:start position:0% +surround +so let's get to the movies + + align:start position:0% +so let's get to the movies + + + align:start position:0% +so let's get to the movies +it's gonna stay here + + align:start position:0% +it's gonna stay here + + + align:start position:0% +it's gonna stay here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +kind of blurry + + align:start position:0% +kind of blurry + + + align:start position:0% +kind of blurry +but you'll okay so what are you gonna be + + align:start position:0% +but you'll okay so what are you gonna be + + + align:start position:0% +but you'll okay so what are you gonna be +listening to so what you're hearing is + + align:start position:0% +listening to so what you're hearing is + + + align:start position:0% +listening to so what you're hearing is +they hooked up the amplifier that's okay + + align:start position:0% +they hooked up the amplifier that's okay + + + align:start position:0% +they hooked up the amplifier that's okay +electrode in the cell right recording + + align:start position:0% +electrode in the cell right recording + + + align:start position:0% +electrode in the cell right recording +from the cell hook to the amplifier up + + align:start position:0% +from the cell hook to the amplifier up + + + align:start position:0% +from the cell hook to the amplifier up +to a speaker you're going to be hearing + + align:start position:0% +to a speaker you're going to be hearing + + + align:start position:0% +to a speaker you're going to be hearing +action potentials like pop pop + + align:start position:0% +action potentials like pop pop + + + align:start position:0% +action potentials like pop pop +that's going to be action potentials + + align:start position:0% +that's going to be action potentials + + + align:start position:0% +that's going to be action potentials +what you're seeing is what the + + align:start position:0% +what you're seeing is what the + + + align:start position:0% +what you're seeing is what the +experimenter is moving around + + align:start position:0% +experimenter is moving around + + + align:start position:0% +experimenter is moving around +but the retina is being exposed to this + + align:start position:0% +but the retina is being exposed to this + + + align:start position:0% +but the retina is being exposed to this +this stimulus right here so you'll get + + align:start position:0% +this stimulus right here so you'll get + + + align:start position:0% +this stimulus right here so you'll get +it in a second + + align:start position:0% +it in a second + + + align:start position:0% +it in a second +here that that's the cell one cell + + align:start position:0% + + + + align:start position:0% + +bright spot kinda dark background + + align:start position:0% + + + + align:start position:0% + +so he's trying to find where is the + + align:start position:0% +so he's trying to find where is the + + + align:start position:0% +so he's trying to find where is the +maximal response right where is the uh + + align:start position:0% +maximal response right where is the uh + + + align:start position:0% +maximal response right where is the uh +did you see that + + align:start position:0% + + + + align:start position:0% + +so diffuse illumination over everything + + align:start position:0% +so diffuse illumination over everything + + + align:start position:0% +so diffuse illumination over everything +excites it a little bit but not a lot + + align:start position:0% +excites it a little bit but not a lot + + + align:start position:0% +excites it a little bit but not a lot +this is + + align:start position:0% +this is + + + align:start position:0% +this is +not as much as directly on its receptive + + align:start position:0% +not as much as directly on its receptive + + + align:start position:0% +not as much as directly on its receptive +field with the dark surround + + align:start position:0% +field with the dark surround + + + align:start position:0% +field with the dark surround +that's the that's like the optimal + + align:start position:0% +that's the that's like the optimal + + + align:start position:0% +that's the that's like the optimal +stimulus + + align:start position:0% +stimulus + + + align:start position:0% +stimulus +it's the circular uh + + align:start position:0% +it's the circular uh + + + align:start position:0% +it's the circular uh +center surround fields + + align:start position:0% +center surround fields + + + align:start position:0% +center surround fields +let me see if he does anything else + + align:start position:0% +let me see if he does anything else + + + align:start position:0% +let me see if he does anything else +interesting or if it's going to be oh + + align:start position:0% +interesting or if it's going to be oh + + + align:start position:0% +interesting or if it's going to be oh +that's good + + align:start position:0% + + + + align:start position:0% + +so that's like it's quiet all of a + + align:start position:0% +so that's like it's quiet all of a + + + align:start position:0% +so that's like it's quiet all of a +sudden because that darkness is so it's + + align:start position:0% +sudden because that darkness is so it's + + + align:start position:0% +sudden because that darkness is so it's +like the opposite of the uh the skin the + + align:start position:0% +like the opposite of the uh the skin the + + + align:start position:0% +like the opposite of the uh the skin the +bestie most is bright on black so black + + align:start position:0% +bestie most is bright on black so black + + + align:start position:0% +bestie most is bright on black so black +on bright is + + align:start position:0% +on bright is + + + align:start position:0% +on bright is +is the maxing condition + + align:start position:0% + + + + align:start position:0% + +okay this has been exciting for long + + align:start position:0% +okay this has been exciting for long + + + align:start position:0% +okay this has been exciting for long +enough + + align:start position:0% +enough + + + align:start position:0% +enough +so let's now go to off center + + align:start position:0% + + + + align:start position:0% + +okay it's not looking too happy + + align:start position:0% +okay it's not looking too happy + + + align:start position:0% +okay it's not looking too happy +what's up with that + + align:start position:0% + + + + align:start position:0% + +i can just open it again + + align:start position:0% + + + + align:start position:0% + +oh it's black + + align:start position:0% + + + + align:start position:0% + +i think this one takes a little longer + + align:start position:0% +i think this one takes a little longer + + + align:start position:0% +i think this one takes a little longer +for them to figure out what's going on + + align:start position:0% +for them to figure out what's going on + + + align:start position:0% +for them to figure out what's going on +here + + align:start position:0% + + + + align:start position:0% + +so fires when it goes away you can see + + align:start position:0% +so fires when it goes away you can see + + + align:start position:0% +so fires when it goes away you can see +that + + align:start position:0% + + + + align:start position:0% + +we're still trying to figure it out here + + align:start position:0% + + + + align:start position:0% + +so this is like the optimal stimulus + + align:start position:0% + + + + align:start position:0% + +now they're trying to find where the + + align:start position:0% +now they're trying to find where the + + + align:start position:0% +now they're trying to find where the +center truly is + + align:start position:0% + + + + align:start position:0% + +so background raven is just all dark it + + align:start position:0% +so background raven is just all dark it + + + align:start position:0% +so background raven is just all dark it +likes that but it likes this more + + align:start position:0% + + + + align:start position:0% + +i guess here they're just mapping their + + align:start position:0% +i guess here they're just mapping their + + + align:start position:0% +i guess here they're just mapping their +surround but this video isn't as good + + align:start position:0% +surround but this video isn't as good + + + align:start position:0% +surround but this video isn't as good +the first one is kind of the one to keep + + align:start position:0% +the first one is kind of the one to keep + + + align:start position:0% +the first one is kind of the one to keep +in your mind i guess this one isn't as + + align:start position:0% +in your mind i guess this one isn't as + + + align:start position:0% +in your mind i guess this one isn't as +impressive + + align:start position:0% +impressive + + + align:start position:0% +impressive +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +the question now um + + align:start position:0% +the question now um + + + align:start position:0% +the question now um +is how do we get from the photoreceptors + + align:start position:0% +is how do we get from the photoreceptors + + + align:start position:0% +is how do we get from the photoreceptors +to the retinal ganglion cells how do we + + align:start position:0% +to the retinal ganglion cells how do we + + + align:start position:0% +to the retinal ganglion cells how do we +get just from something that's light + + align:start position:0% +get just from something that's light + + + align:start position:0% +get just from something that's light +sensitive to actually the center + + align:start position:0% +sensitive to actually the center + + + align:start position:0% +sensitive to actually the center +surround + + align:start position:0% +surround + + + align:start position:0% +surround +the center surround fields this kind of + + align:start position:0% +the center surround fields this kind of + + + align:start position:0% +the center surround fields this kind of +opposition and what are the + + align:start position:0% +opposition and what are the + + + align:start position:0% +opposition and what are the +electrophysiological properties of all + + align:start position:0% +electrophysiological properties of all + + + align:start position:0% +electrophysiological properties of all +those cells in the middle horizontal + + align:start position:0% +those cells in the middle horizontal + + + align:start position:0% +those cells in the middle horizontal +bipolar how do they produce this + + align:start position:0% +bipolar how do they produce this + + + align:start position:0% +bipolar how do they produce this +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +so + + align:start position:0% +so + + + align:start position:0% +so +right so the part we're going to be + + align:start position:0% +right so the part we're going to be + + + align:start position:0% +right so the part we're going to be +interested in now again here's the + + align:start position:0% +interested in now again here's the + + + align:start position:0% +interested in now again here's the +photoreceptors back here inside out + + align:start position:0% +photoreceptors back here inside out + + + align:start position:0% +photoreceptors back here inside out +organization and here's the ganglion + + align:start position:0% +organization and here's the ganglion + + + align:start position:0% +organization and here's the ganglion +cells up here let me interested in this + + align:start position:0% +cells up here let me interested in this + + + align:start position:0% +cells up here let me interested in this +part in the middle here + + align:start position:0% +part in the middle here + + + align:start position:0% +part in the middle here +um + + align:start position:0% +um + + + align:start position:0% +um +another picture of that i guess + + align:start position:0% +another picture of that i guess + + + align:start position:0% +another picture of that i guess +so + + align:start position:0% +so + + + align:start position:0% +so +i actually didn't know about these until + + align:start position:0% +i actually didn't know about these until + + + align:start position:0% +i actually didn't know about these until +professor schneider told me that the + + align:start position:0% +professor schneider told me that the + + + align:start position:0% +professor schneider told me that the +classic studies the first recordings of + + align:start position:0% +classic studies the first recordings of + + + align:start position:0% +classic studies the first recordings of +all the different cells in the retina + + align:start position:0% +all the different cells in the retina + + + align:start position:0% +all the different cells in the retina +and seeing what they're doing kind of + + align:start position:0% +and seeing what they're doing kind of + + + align:start position:0% +and seeing what they're doing kind of +simultaneously was by + + align:start position:0% +simultaneously was by + + + align:start position:0% +simultaneously was by +woodland and dowling here and there are + + align:start position:0% +woodland and dowling here and there are + + + align:start position:0% +woodland and dowling here and there are +classical studies in the mud puppy does + + align:start position:0% +classical studies in the mud puppy does + + + align:start position:0% +classical studies in the mud puppy does +anybody know what a mud puppy is + + align:start position:0% +anybody know what a mud puppy is + + + align:start position:0% +anybody know what a mud puppy is +i didn't either my office made me what + + align:start position:0% +i didn't either my office made me what + + + align:start position:0% +i didn't either my office made me what +it was instantly and i was like whoa + + align:start position:0% +it was instantly and i was like whoa + + + align:start position:0% +it was instantly and i was like whoa +but this is the mud puppy so + + align:start position:0% +but this is the mud puppy so + + + align:start position:0% +but this is the mud puppy so +the mud puppy is like this + + align:start position:0% +the mud puppy is like this + + + align:start position:0% +the mud puppy is like this +salamander + + align:start position:0% +salamander + + + align:start position:0% +salamander +and it's got this crazy set of gills + + align:start position:0% +and it's got this crazy set of gills + + + align:start position:0% +and it's got this crazy set of gills +like that come out of it like that + + align:start position:0% +like that come out of it like that + + + align:start position:0% +like that come out of it like that +and here's the eye + + align:start position:0% +and here's the eye + + + align:start position:0% +and here's the eye +i think the reason it was chosen is the + + align:start position:0% +i think the reason it was chosen is the + + + align:start position:0% +i think the reason it was chosen is the +cells are large in its retina and + + align:start position:0% +cells are large in its retina and + + + align:start position:0% +cells are large in its retina and +can be easily this is before finer + + align:start position:0% +can be easily this is before finer + + + align:start position:0% +can be easily this is before finer +techniques such as patch plant + + align:start position:0% +techniques such as patch plant + + + align:start position:0% +techniques such as patch plant +electrophysiology were developed so + + align:start position:0% +electrophysiology were developed so + + + align:start position:0% +electrophysiology were developed so +large electrodes could easily be put in + + align:start position:0% +large electrodes could easily be put in + + + align:start position:0% +large electrodes could easily be put in +these cells + + align:start position:0% +these cells + + + align:start position:0% +these cells +so + + align:start position:0% +so + + + align:start position:0% +so +starting with the photoreceptors + + align:start position:0% +starting with the photoreceptors + + + align:start position:0% +starting with the photoreceptors +the main electrophysiological property + + align:start position:0% +the main electrophysiological property + + + align:start position:0% +the main electrophysiological property +to know about in the photoshop and i'll + + align:start position:0% +to know about in the photoshop and i'll + + + align:start position:0% +to know about in the photoshop and i'll +show you some current traces in a second + + align:start position:0% +show you some current traces in a second + + + align:start position:0% +show you some current traces in a second +so you can see this is that + + align:start position:0% +so you can see this is that + + + align:start position:0% +so you can see this is that +in response to light i mean you think + + align:start position:0% +in response to light i mean you think + + + align:start position:0% +in response to light i mean you think +that you know neurons when they get + + align:start position:0% +that you know neurons when they get + + + align:start position:0% +that you know neurons when they get +their stimulus they fire right but when + + align:start position:0% +their stimulus they fire right but when + + + align:start position:0% +their stimulus they fire right but when +the photoreceptors + + align:start position:0% +the photoreceptors + + + align:start position:0% +the photoreceptors +have light impinging on them + + align:start position:0% +have light impinging on them + + + align:start position:0% +have light impinging on them +they hyperpolarize they actually go more + + align:start position:0% +they hyperpolarize they actually go more + + + align:start position:0% +they hyperpolarize they actually go more +negative so is everybody familiar with + + align:start position:0% +negative so is everybody familiar with + + + align:start position:0% +negative so is everybody familiar with +those terms hyperpolarized is more + + align:start position:0% +those terms hyperpolarized is more + + + align:start position:0% +those terms hyperpolarized is more +negative depolarized is positive um + + align:start position:0% +negative depolarized is positive um + + + align:start position:0% +negative depolarized is positive um +that's just the electrophysiologist + + align:start position:0% +that's just the electrophysiologist + + + align:start position:0% +that's just the electrophysiologist +right + + align:start position:0% +right + + + align:start position:0% +right +convention there + + align:start position:0% +convention there + + + align:start position:0% +convention there +so + + align:start position:0% +so + + + align:start position:0% +so +um and hyperpolarizing means that the + + align:start position:0% +um and hyperpolarizing means that the + + + align:start position:0% +um and hyperpolarizing means that the +photoreceptors when they make their + + align:start position:0% +photoreceptors when they make their + + + align:start position:0% +photoreceptors when they make their +synapse with the next cell in the chain + + align:start position:0% +synapse with the next cell in the chain + + + align:start position:0% +synapse with the next cell in the chain +they're going to be they're going to be + + align:start position:0% +they're going to be they're going to be + + + align:start position:0% +they're going to be they're going to be +releasing less glutamate right because + + align:start position:0% +releasing less glutamate right because + + + align:start position:0% +releasing less glutamate right because +in their natural state they tend to be + + align:start position:0% +in their natural state they tend to be + + + align:start position:0% +in their natural state they tend to be +more polarized + + align:start position:0% +more polarized + + + align:start position:0% +more polarized +closer to firing firing means releasing + + align:start position:0% +closer to firing firing means releasing + + + align:start position:0% +closer to firing firing means releasing +glutamate so the only thing that's + + align:start position:0% +glutamate so the only thing that's + + + align:start position:0% +glutamate so the only thing that's +inverted is their response to light from + + align:start position:0% +inverted is their response to light from + + + align:start position:0% +inverted is their response to light from +what you might think they hyper polarize + + align:start position:0% +what you might think they hyper polarize + + + align:start position:0% +what you might think they hyper polarize +so + + align:start position:0% +so + + + align:start position:0% +so +another kind of interesting difference + + align:start position:0% +another kind of interesting difference + + + align:start position:0% +another kind of interesting difference +here is that the photoreceptors don't + + align:start position:0% +here is that the photoreceptors don't + + + align:start position:0% +here is that the photoreceptors don't +use action potentials they don't uh they + + align:start position:0% +use action potentials they don't uh they + + + align:start position:0% +use action potentials they don't uh they +don't fire they use these graded + + align:start position:0% +don't fire they use these graded + + + align:start position:0% +don't fire they use these graded +potentials they just slowly change their + + align:start position:0% +potentials they just slowly change their + + + align:start position:0% +potentials they just slowly change their +membrane to gradually more depolarize + + align:start position:0% +membrane to gradually more depolarize + + + align:start position:0% +membrane to gradually more depolarize +and then gradually more hyperpolarized + + align:start position:0% +and then gradually more hyperpolarized + + + align:start position:0% +and then gradually more hyperpolarized +as as they see light + + align:start position:0% +as as they see light + + + align:start position:0% +as as they see light +so + + align:start position:0% +so + + + align:start position:0% +so +this is a complex diagram we're going to + + align:start position:0% +this is a complex diagram we're going to + + + align:start position:0% +this is a complex diagram we're going to +go bit by bit here but this is just to + + align:start position:0% +go bit by bit here but this is just to + + + align:start position:0% +go bit by bit here but this is just to +show you that like look at the ganglion + + align:start position:0% +show you that like look at the ganglion + + + align:start position:0% +show you that like look at the ganglion +cells down here that's what we were + + align:start position:0% +cells down here that's what we were + + + align:start position:0% +cells down here that's what we were +listening to right those spikes you + + align:start position:0% +listening to right those spikes you + + + align:start position:0% +listening to right those spikes you +heard those blip flip lip that's like + + align:start position:0% +heard those blip flip lip that's like + + + align:start position:0% +heard those blip flip lip that's like +firing like spikes like this + + align:start position:0% +firing like spikes like this + + + align:start position:0% +firing like spikes like this +and here you can see there's no real + + align:start position:0% +and here you can see there's no real + + + align:start position:0% +and here you can see there's no real +spiking it's kind of just like + + align:start position:0% +spiking it's kind of just like + + + align:start position:0% +spiking it's kind of just like +woozy kind of going down and up you know + + align:start position:0% +woozy kind of going down and up you know + + + align:start position:0% +woozy kind of going down and up you know +so this is the graded potentials this is + + align:start position:0% +so this is the graded potentials this is + + + align:start position:0% +so this is the graded potentials this is +a very different regime this is analog + + align:start position:0% +a very different regime this is analog + + + align:start position:0% +a very different regime this is analog +this is very digital um to take an + + align:start position:0% +this is very digital um to take an + + + align:start position:0% +this is very digital um to take an +engineering perspective + + align:start position:0% +engineering perspective + + + align:start position:0% +engineering perspective +so + + align:start position:0% +so + + + align:start position:0% +so +so what we know about these now we know + + align:start position:0% +so what we know about these now we know + + + align:start position:0% +so what we know about these now we know +that they hyperpolarize in response to + + align:start position:0% +that they hyperpolarize in response to + + + align:start position:0% +that they hyperpolarize in response to +light and when they hyperpolarize that + + align:start position:0% +light and when they hyperpolarize that + + + align:start position:0% +light and when they hyperpolarize that +is when there's light there there's less + + align:start position:0% +is when there's light there there's less + + + align:start position:0% +is when there's light there there's less +glutamate okay how does this get us + + align:start position:0% +glutamate okay how does this get us + + + align:start position:0% +glutamate okay how does this get us +closer to center surround organization + + align:start position:0% +closer to center surround organization + + + align:start position:0% +closer to center surround organization +that's found down here in ganglion cells + + align:start position:0% +that's found down here in ganglion cells + + + align:start position:0% +that's found down here in ganglion cells +well the next kind of + + align:start position:0% +well the next kind of + + + align:start position:0% +well the next kind of +important cell in the chain is these + + align:start position:0% +important cell in the chain is these + + + align:start position:0% +important cell in the chain is these +bipolar cells which form a bridge + + align:start position:0% +bipolar cells which form a bridge + + + align:start position:0% +bipolar cells which form a bridge +literally between the photoreceptor and + + align:start position:0% +literally between the photoreceptor and + + + align:start position:0% +literally between the photoreceptor and +the retinal ganglion cell + + align:start position:0% +the retinal ganglion cell + + + align:start position:0% +the retinal ganglion cell +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +add to our little story of information + + align:start position:0% +add to our little story of information + + + align:start position:0% +add to our little story of information +here bipolars come in two major types um + + align:start position:0% +here bipolars come in two major types um + + + align:start position:0% +here bipolars come in two major types um +for the mo for the most part we should + + align:start position:0% +for the mo for the most part we should + + + align:start position:0% +for the mo for the most part we should +just say two major types there are some + + align:start position:0% +just say two major types there are some + + + align:start position:0% +just say two major types there are some +others too but they're not nearly as + + align:start position:0% +others too but they're not nearly as + + + align:start position:0% +others too but they're not nearly as +significant as these and they're either + + align:start position:0% +significant as these and they're either + + + align:start position:0% +significant as these and they're either +hyper polarizing or depolarizing + + align:start position:0% +hyper polarizing or depolarizing + + + align:start position:0% +hyper polarizing or depolarizing +so + + align:start position:0% +so + + + align:start position:0% +so +right so just let's look right now don't + + align:start position:0% +right so just let's look right now don't + + + align:start position:0% +right so just let's look right now don't +worry about the interpretation of that + + align:start position:0% +worry about the interpretation of that + + + align:start position:0% +worry about the interpretation of that +but look at this so + + align:start position:0% +but look at this so + + + align:start position:0% +but look at this so +here both photoreceptors are + + align:start position:0% +here both photoreceptors are + + + align:start position:0% +here both photoreceptors are +hyper-polarizing they're going going uh + + align:start position:0% +hyper-polarizing they're going going uh + + + align:start position:0% +hyper-polarizing they're going going uh +more negative and potential both of them + + align:start position:0% +more negative and potential both of them + + + align:start position:0% +more negative and potential both of them +are this one's not such a degree but + + align:start position:0% +are this one's not such a degree but + + + align:start position:0% +are this one's not such a degree but +look at these bipolar cells one of them + + align:start position:0% +look at these bipolar cells one of them + + + align:start position:0% +look at these bipolar cells one of them +is hyper polarizing in response to this + + align:start position:0% +is hyper polarizing in response to this + + + align:start position:0% +is hyper polarizing in response to this +hyperpolarization the other one is + + align:start position:0% +hyperpolarization the other one is + + + align:start position:0% +hyperpolarization the other one is +depolarizing so here you have two + + align:start position:0% +depolarizing so here you have two + + + align:start position:0% +depolarizing so here you have two +bipolar cell types either + + align:start position:0% +bipolar cell types either + + + align:start position:0% +bipolar cell types either +hyperpolarizing or depolar polarizing + + align:start position:0% +hyperpolarizing or depolar polarizing + + + align:start position:0% +hyperpolarizing or depolar polarizing +and we'll talk about what they do so um + + align:start position:0% +and we'll talk about what they do so um + + + align:start position:0% +and we'll talk about what they do so um +right okay so if you're using graded + + align:start position:0% +right okay so if you're using graded + + + align:start position:0% +right okay so if you're using graded +potentials this should be an obvious + + align:start position:0% +potentials this should be an obvious + + + align:start position:0% +potentials this should be an obvious +statement right here there's no action + + align:start position:0% +statement right here there's no action + + + align:start position:0% +statement right here there's no action +potentials actions of the synapse don't + + align:start position:0% +potentials actions of the synapse don't + + + align:start position:0% +potentials actions of the synapse don't +require action potentials um as i said + + align:start position:0% +require action potentials um as i said + + + align:start position:0% +require action potentials um as i said +it's a gradual change in the amount of + + align:start position:0% +it's a gradual change in the amount of + + + align:start position:0% +it's a gradual change in the amount of +neurotransmitter released so it's just + + align:start position:0% +neurotransmitter released so it's just + + + align:start position:0% +neurotransmitter released so it's just +another figure jerry gave me so i used + + align:start position:0% +another figure jerry gave me so i used + + + align:start position:0% +another figure jerry gave me so i used +it um you see in like there was the + + align:start position:0% +it um you see in like there was the + + + align:start position:0% +it um you see in like there was the +photoreceptor and the horizontal cells + + align:start position:0% +photoreceptor and the horizontal cells + + + align:start position:0% +photoreceptor and the horizontal cells +these slow graded + + align:start position:0% +these slow graded + + + align:start position:0% +these slow graded +bipolar cells excuse me these slow + + align:start position:0% +bipolar cells excuse me these slow + + + align:start position:0% +bipolar cells excuse me these slow +graded potentials but then by the time + + align:start position:0% +graded potentials but then by the time + + + align:start position:0% +graded potentials but then by the time +you reach + + align:start position:0% +you reach + + + align:start position:0% +you reach +ganglion cells and some cells that are + + align:start position:0% +ganglion cells and some cells that are + + + align:start position:0% +ganglion cells and some cells that are +right before them amicum cells action + + align:start position:0% +right before them amicum cells action + + + align:start position:0% +right before them amicum cells action +potential so we just want to make this + + align:start position:0% +potential so we just want to make this + + + align:start position:0% +potential so we just want to make this +difference really clear that you can + + align:start position:0% +difference really clear that you can + + + align:start position:0% +difference really clear that you can +look at this recording and see if you've + + align:start position:0% +look at this recording and see if you've + + + align:start position:0% +look at this recording and see if you've +got one of these um graded potential + + align:start position:0% +got one of these um graded potential + + + align:start position:0% +got one of these um graded potential +neurons or one of these action potential + + align:start position:0% +neurons or one of these action potential + + + align:start position:0% +neurons or one of these action potential +neurons + + align:start position:0% +neurons + + + align:start position:0% +neurons +so + + align:start position:0% +so + + + align:start position:0% +so +right so let's talk now about receptive + + align:start position:0% +right so let's talk now about receptive + + + align:start position:0% +right so let's talk now about receptive +fields so bipolar cells connect to + + align:start position:0% +fields so bipolar cells connect to + + + align:start position:0% +fields so bipolar cells connect to +multiple photoreceptors + + align:start position:0% +multiple photoreceptors + + + align:start position:0% +multiple photoreceptors +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +this this slide i guess is just to say + + align:start position:0% +this this slide i guess is just to say + + + align:start position:0% +this this slide i guess is just to say +that they have a circular receptive + + align:start position:0% +that they have a circular receptive + + + align:start position:0% +that they have a circular receptive +field so they're organized in terms of + + align:start position:0% +field so they're organized in terms of + + + align:start position:0% +field so they're organized in terms of +their connections such that they + + align:start position:0% +their connections such that they + + + align:start position:0% +their connections such that they +basically connect to a similar amount of + + align:start position:0% +basically connect to a similar amount of + + + align:start position:0% +basically connect to a similar amount of +photoreceptors in any direction from + + align:start position:0% +photoreceptors in any direction from + + + align:start position:0% +photoreceptors in any direction from +that cell right the photoreceptors you + + align:start position:0% +that cell right the photoreceptors you + + + align:start position:0% +that cell right the photoreceptors you +know um the ones the photoreceptors here + + align:start position:0% +know um the ones the photoreceptors here + + + align:start position:0% +know um the ones the photoreceptors here +are a little bit above this central area + + align:start position:0% +are a little bit above this central area + + + align:start position:0% +are a little bit above this central area +a little below so you imagine the + + align:start position:0% +a little below so you imagine the + + + align:start position:0% +a little below so you imagine the +bipolar cell is kind of in the middle of + + align:start position:0% +bipolar cell is kind of in the middle of + + + align:start position:0% +bipolar cell is kind of in the middle of +this receptive field + + align:start position:0% +this receptive field + + + align:start position:0% +this receptive field +so + + align:start position:0% +so + + + align:start position:0% +so +here's the experiment that we're going + + align:start position:0% +here's the experiment that we're going + + + align:start position:0% +here's the experiment that we're going +to show the results for in a second + + align:start position:0% +to show the results for in a second + + + align:start position:0% +to show the results for in a second +there's a spot of light the experimental + + align:start position:0% +there's a spot of light the experimental + + + align:start position:0% +there's a spot of light the experimental +moves + + align:start position:0% +moves + + + align:start position:0% +moves +and + + align:start position:0% +and + + + align:start position:0% +and +what is that okay oh there's + + align:start position:0% +what is that okay oh there's + + + align:start position:0% +what is that okay oh there's +what is this + + align:start position:0% +what is this + + + align:start position:0% +what is this +if there's an annulus flashed i'm not + + align:start position:0% +if there's an annulus flashed i'm not + + + align:start position:0% +if there's an annulus flashed i'm not +sure + + align:start position:0% +sure + + + align:start position:0% +sure +okay so let's just look at this right + + align:start position:0% +okay so let's just look at this right + + + align:start position:0% +okay so let's just look at this right +here + + align:start position:0% +here + + + align:start position:0% +here +right so there + + align:start position:0% +right so there + + + align:start position:0% +right so there +right so there's going to be just yeah + + align:start position:0% +right so there's going to be just yeah + + + align:start position:0% +right so there's going to be just yeah +this makes sense now so there's going to + + align:start position:0% +this makes sense now so there's going to + + + align:start position:0% +this makes sense now so there's going to +be + + align:start position:0% +be + + + align:start position:0% +be +in the receptive field first the first + + align:start position:0% +in the receptive field first the first + + + align:start position:0% +in the receptive field first the first +thing experimental does is places this + + align:start position:0% +thing experimental does is places this + + + align:start position:0% +thing experimental does is places this +annulus of bright light on a dark + + align:start position:0% +annulus of bright light on a dark + + + align:start position:0% +annulus of bright light on a dark +background and then what happens is the + + align:start position:0% +background and then what happens is the + + + align:start position:0% +background and then what happens is the +spotlight is just going to be moved + + align:start position:0% +spotlight is just going to be moved + + + align:start position:0% +spotlight is just going to be moved +across and you're going to see what + + align:start position:0% +across and you're going to see what + + + align:start position:0% +across and you're going to see what +happens when the bipolar cell that's + + align:start position:0% +happens when the bipolar cell that's + + + align:start position:0% +happens when the bipolar cell that's +hooked up to the photoreceptors that + + align:start position:0% +hooked up to the photoreceptors that + + + align:start position:0% +hooked up to the photoreceptors that +give it this input from these areas what + + align:start position:0% +give it this input from these areas what + + + align:start position:0% +give it this input from these areas what +it does + + align:start position:0% +it does + + + align:start position:0% +it does +so + + align:start position:0% +so + + + align:start position:0% +so +for if you do this experiment that exact + + align:start position:0% +for if you do this experiment that exact + + + align:start position:0% +for if you do this experiment that exact +experiment i showed you the bright spot + + align:start position:0% +experiment i showed you the bright spot + + + align:start position:0% +experiment i showed you the bright spot +of light through that that annulus and + + align:start position:0% +of light through that that annulus and + + + align:start position:0% +of light through that that annulus and +you can see here's + + align:start position:0% +you can see here's + + + align:start position:0% +you can see here's +dark bright and spots going to move + + align:start position:0% +dark bright and spots going to move + + + align:start position:0% +dark bright and spots going to move +across move across there's two types of + + align:start position:0% +across move across there's two types of + + + align:start position:0% +across move across there's two types of +bipolar cells and + + align:start position:0% +bipolar cells and + + + align:start position:0% +bipolar cells and +in the on-center bipolar cells it's + + align:start position:0% +in the on-center bipolar cells it's + + + align:start position:0% +in the on-center bipolar cells it's +gonna this spot is gonna cause a + + align:start position:0% +gonna this spot is gonna cause a + + + align:start position:0% +gonna this spot is gonna cause a +depolarization + + align:start position:0% +depolarization + + + align:start position:0% +depolarization +and we so we term + + align:start position:0% +and we so we term + + + align:start position:0% +and we so we term +we term this so + + align:start position:0% +we term this so + + + align:start position:0% +we term this so +there's multiple ways and this gets a + + align:start position:0% +there's multiple ways and this gets a + + + align:start position:0% +there's multiple ways and this gets a +little confusing to think about these + + align:start position:0% +little confusing to think about these + + + align:start position:0% +little confusing to think about these +but previously i've i've said that here + + align:start position:0% +but previously i've i've said that here + + + align:start position:0% +but previously i've i've said that here +if you have something like this a bright + + align:start position:0% +if you have something like this a bright + + + align:start position:0% +if you have something like this a bright +spot here + + align:start position:0% +spot here + + + align:start position:0% +spot here +that these depolarize so + + align:start position:0% +that these depolarize so + + + align:start position:0% +that these depolarize so +i'm going to confuse things even more + + align:start position:0% +i'm going to confuse things even more + + + align:start position:0% +i'm going to confuse things even more +here by saying the photoreceptor when it + + align:start position:0% +here by saying the photoreceptor when it + + + align:start position:0% +here by saying the photoreceptor when it +sees a bright spot what does it do + + align:start position:0% +sees a bright spot what does it do + + + align:start position:0% +sees a bright spot what does it do +right hyperpolarize and when it + + align:start position:0% +right hyperpolarize and when it + + + align:start position:0% +right hyperpolarize and when it +hyperpolarizes that means that the + + align:start position:0% +hyperpolarizes that means that the + + + align:start position:0% +hyperpolarizes that means that the +synapse what's happening more glutamate + + align:start position:0% +synapse what's happening more glutamate + + + align:start position:0% +synapse what's happening more glutamate +less glutamate + + align:start position:0% +less glutamate + + + align:start position:0% +less glutamate +less glutamate + + align:start position:0% +less glutamate + + + align:start position:0% +less glutamate +and the depolarizing bipolar is going to + + align:start position:0% +and the depolarizing bipolar is going to + + + align:start position:0% +and the depolarizing bipolar is going to +hyperpolarize or depolarize + + align:start position:0% +hyperpolarize or depolarize + + + align:start position:0% +hyperpolarize or depolarize +depolarize so less glutamate depolarizes + + align:start position:0% +depolarize so less glutamate depolarizes + + + align:start position:0% +depolarize so less glutamate depolarizes +which is the opposite of what we think + + align:start position:0% +which is the opposite of what we think + + + align:start position:0% +which is the opposite of what we think +in central synapses right i mean most + + align:start position:0% +in central synapses right i mean most + + + align:start position:0% +in central synapses right i mean most +central synapses more glutamate at depot + + align:start position:0% +central synapses more glutamate at depot + + + align:start position:0% +central synapses more glutamate at depot +right we go toward the action potential + + align:start position:0% +right we go toward the action potential + + + align:start position:0% +right we go toward the action potential +we go positive we depolarize so this is + + align:start position:0% +we go positive we depolarize so this is + + + align:start position:0% +we go positive we depolarize so this is +kind of like a strange cell and we term + + align:start position:0% +kind of like a strange cell and we term + + + align:start position:0% +kind of like a strange cell and we term +the cell either a depolarizing bipolar + + align:start position:0% +the cell either a depolarizing bipolar + + + align:start position:0% +the cell either a depolarizing bipolar +or an on center cell + + align:start position:0% +or an on center cell + + + align:start position:0% +or an on center cell +and then we say on center because when a + + align:start position:0% +and then we say on center because when a + + + align:start position:0% +and then we say on center because when a +bright spot of light is put there it + + align:start position:0% +bright spot of light is put there it + + + align:start position:0% +bright spot of light is put there it +depolarizes + + align:start position:0% + + + + align:start position:0% + +it takes a while to sink in just + + align:start position:0% +it takes a while to sink in just + + + align:start position:0% +it takes a while to sink in just +just deal with it so + + align:start position:0% +just deal with it so + + + align:start position:0% +just deal with it so +same thing + + align:start position:0% +same thing + + + align:start position:0% +same thing +same thing over a hyper-polarizing + + align:start position:0% +same thing over a hyper-polarizing + + + align:start position:0% +same thing over a hyper-polarizing +bipolar okay so we can have the bright + + align:start position:0% +bipolar okay so we can have the bright + + + align:start position:0% +bipolar okay so we can have the bright +spot of light less glutamate right + + align:start position:0% +spot of light less glutamate right + + + align:start position:0% +spot of light less glutamate right +bright spot of light less glutamate at + + align:start position:0% +bright spot of light less glutamate at + + + align:start position:0% +bright spot of light less glutamate at +the synapse + + align:start position:0% +the synapse + + + align:start position:0% +the synapse +and that leads to this type of cell + + align:start position:0% +and that leads to this type of cell + + + align:start position:0% +and that leads to this type of cell +because of it and why i mean why why do + + align:start position:0% +because of it and why i mean why why do + + + align:start position:0% +because of it and why i mean why why do +we have arbitrary these cells + + align:start position:0% +we have arbitrary these cells + + + align:start position:0% +we have arbitrary these cells +arbitrarily these different cell types + + align:start position:0% +arbitrarily these different cell types + + + align:start position:0% +arbitrarily these different cell types +it has to do with the channels the ion + + align:start position:0% +it has to do with the channels the ion + + + align:start position:0% +it has to do with the channels the ion +channels they're different channels that + + align:start position:0% +channels they're different channels that + + + align:start position:0% +channels they're different channels that +so they react differently in the + + align:start position:0% +so they react differently in the + + + align:start position:0% +so they react differently in the +presence of glutamate one one type of + + align:start position:0% +presence of glutamate one one type of + + + align:start position:0% +presence of glutamate one one type of +cell drives um drives the potential one + + align:start position:0% +cell drives um drives the potential one + + + align:start position:0% +cell drives um drives the potential one +way that is it say it opens channels + + align:start position:0% +way that is it say it opens channels + + + align:start position:0% +way that is it say it opens channels +right so in the presence of let's let's + + align:start position:0% +right so in the presence of let's let's + + + align:start position:0% +right so in the presence of let's let's +get it straight let's try and get it + + align:start position:0% +get it straight let's try and get it + + + align:start position:0% +get it straight let's try and get it +straight here so a bright spot of light + + align:start position:0% +straight here so a bright spot of light + + + align:start position:0% +straight here so a bright spot of light +um + + align:start position:0% +um + + + align:start position:0% +um +is going to be less glutamate right + + align:start position:0% +is going to be less glutamate right + + + align:start position:0% +is going to be less glutamate right +and that's going to cause this one to + + align:start position:0% +and that's going to cause this one to + + + align:start position:0% +and that's going to cause this one to +depolarize so we know that this kind of + + align:start position:0% +depolarize so we know that this kind of + + + align:start position:0% +depolarize so we know that this kind of +cell when it's exposed to glutamate it + + align:start position:0% +cell when it's exposed to glutamate it + + + align:start position:0% +cell when it's exposed to glutamate it +closes its channels it closes it and i + + align:start position:0% +closes its channels it closes it and i + + + align:start position:0% +closes its channels it closes it and i +don't know how much jerry's talked about + + align:start position:0% +don't know how much jerry's talked about + + + align:start position:0% +don't know how much jerry's talked about +this before but this is a meta in these + + align:start position:0% +this before but this is a meta in these + + + align:start position:0% +this before but this is a meta in these +cells it's metabotropic which means that + + align:start position:0% +cells it's metabotropic which means that + + + align:start position:0% +cells it's metabotropic which means that +the receptor is right is not next to the + + align:start position:0% +the receptor is right is not next to the + + + align:start position:0% +the receptor is right is not next to the +ion channel there's actually the + + align:start position:0% +ion channel there's actually the + + + align:start position:0% +ion channel there's actually the +receptor links on grabs onto the + + align:start position:0% +receptor links on grabs onto the + + + align:start position:0% +receptor links on grabs onto the +glutamate and then there's some + + align:start position:0% +glutamate and then there's some + + + align:start position:0% +glutamate and then there's some +intracellular processes that happen that + + align:start position:0% +intracellular processes that happen that + + + align:start position:0% +intracellular processes that happen that +force an ion channel kind of down the + + align:start position:0% +force an ion channel kind of down the + + + align:start position:0% +force an ion channel kind of down the +road to close um just a little bit + + align:start position:0% +road to close um just a little bit + + + align:start position:0% +road to close um just a little bit +farther from it on the membrane + + align:start position:0% +farther from it on the membrane + + + align:start position:0% +farther from it on the membrane +here what happens is the opposite + + align:start position:0% +here what happens is the opposite + + + align:start position:0% +here what happens is the opposite +glutamate links on and these are + + align:start position:0% +glutamate links on and these are + + + align:start position:0% +glutamate links on and these are +actually to fully confuse you these are + + align:start position:0% +actually to fully confuse you these are + + + align:start position:0% +actually to fully confuse you these are +ionotropic head don't worry about it + + align:start position:0% +ionotropic head don't worry about it + + + align:start position:0% +ionotropic head don't worry about it +doesn't matter + + align:start position:0% +doesn't matter + + + align:start position:0% +doesn't matter +links that glutamate links on right here + + align:start position:0% +links that glutamate links on right here + + + align:start position:0% +links that glutamate links on right here +and the ion channel opens causing + + align:start position:0% +and the ion channel opens causing + + + align:start position:0% +and the ion channel opens causing +causing sodium to rush sorry i should + + align:start position:0% +causing sodium to rush sorry i should + + + align:start position:0% +causing sodium to rush sorry i should +say in both cases when i say ion channel + + align:start position:0% +say in both cases when i say ion channel + + + align:start position:0% +say in both cases when i say ion channel +i mean sodium ion channel so if sodium + + align:start position:0% +i mean sodium ion channel so if sodium + + + align:start position:0% +i mean sodium ion channel so if sodium +goes in depolarizes so + + align:start position:0% +goes in depolarizes so + + + align:start position:0% +goes in depolarizes so +so here um it causes glutamate causes + + align:start position:0% +so here um it causes glutamate causes + + + align:start position:0% +so here um it causes glutamate causes +sodium to + + align:start position:0% +sodium to + + + align:start position:0% +sodium to +come in and will will depolarize the + + align:start position:0% +come in and will will depolarize the + + + align:start position:0% +come in and will will depolarize the +cell + + align:start position:0% +cell + + + align:start position:0% +cell +yes + + align:start position:0% + + + + align:start position:0% + +okay so let's let's get terminology here + + align:start position:0% +okay so let's let's get terminology here + + + align:start position:0% +okay so let's let's get terminology here +so on so photoreceptors are always the + + align:start position:0% +so on so photoreceptors are always the + + + align:start position:0% +so on so photoreceptors are always the +same they're depolarizing to light + + align:start position:0% +same they're depolarizing to light + + + align:start position:0% +same they're depolarizing to light +there's no on and off center arrangement + + align:start position:0% +there's no on and off center arrangement + + + align:start position:0% +there's no on and off center arrangement +because the photoreceptors are just the + + align:start position:0% +because the photoreceptors are just the + + + align:start position:0% +because the photoreceptors are just the +fine pixels of space they're the + + align:start position:0% +fine pixels of space they're the + + + align:start position:0% +fine pixels of space they're the +sampling guide they're the ones who are + + align:start position:0% +sampling guide they're the ones who are + + + align:start position:0% +sampling guide they're the ones who are +sampling the environment + + align:start position:0% +sampling the environment + + + align:start position:0% +sampling the environment +these are the first level of cells that + + align:start position:0% +these are the first level of cells that + + + align:start position:0% +these are the first level of cells that +are connected to multiple photoreceptors + + align:start position:0% +are connected to multiple photoreceptors + + + align:start position:0% +are connected to multiple photoreceptors +and integrate those samples and try and + + align:start position:0% +and integrate those samples and try and + + + align:start position:0% +and integrate those samples and try and +make some sense of it and that's that + + align:start position:0% +make some sense of it and that's that + + + align:start position:0% +make some sense of it and that's that +that is the first receptive field + + align:start position:0% +that is the first receptive field + + + align:start position:0% +that is the first receptive field +organization right i mean you can claim + + align:start position:0% +organization right i mean you can claim + + + align:start position:0% +organization right i mean you can claim +that photoreceptors have a receptive + + align:start position:0% +that photoreceptors have a receptive + + + align:start position:0% +that photoreceptors have a receptive +field but it's literally just is there + + align:start position:0% +field but it's literally just is there + + + align:start position:0% +field but it's literally just is there +light there or not i mean it is a + + align:start position:0% +light there or not i mean it is a + + + align:start position:0% +light there or not i mean it is a +receptive field but this is the first + + align:start position:0% +receptive field but this is the first + + + align:start position:0% +receptive field but this is the first +what we would call a higher level + + align:start position:0% +what we would call a higher level + + + align:start position:0% +what we would call a higher level +organization in a receptive field + + align:start position:0% +organization in a receptive field + + + align:start position:0% +organization in a receptive field +so + + align:start position:0% + + + + align:start position:0% + +i'm gonna move on + + align:start position:0% +i'm gonna move on + + + align:start position:0% +i'm gonna move on +um + + align:start position:0% +um + + + align:start position:0% +um +i'll see how far we get here oh we're + + align:start position:0% +i'll see how far we get here oh we're + + + align:start position:0% +i'll see how far we get here oh we're +gonna talk more about about bipolar so + + align:start position:0% +gonna talk more about about bipolar so + + + align:start position:0% +gonna talk more about about bipolar so +it's good + + align:start position:0% +it's good + + + align:start position:0% +it's good +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +as we kind of we saw this already in the + + align:start position:0% +as we kind of we saw this already in the + + + align:start position:0% +as we kind of we saw this already in the +retinal ganglion cells that there's this + + align:start position:0% +retinal ganglion cells that there's this + + + align:start position:0% +retinal ganglion cells that there's this +antagonistic effect by the surround so + + align:start position:0% +antagonistic effect by the surround so + + + align:start position:0% +antagonistic effect by the surround so +we in this previous slide we're just + + align:start position:0% +we in this previous slide we're just + + + align:start position:0% +we in this previous slide we're just +looking at one thing a bright spot of + + align:start position:0% +looking at one thing a bright spot of + + + align:start position:0% +looking at one thing a bright spot of +light in the center and what does it do + + align:start position:0% +light in the center and what does it do + + + align:start position:0% +light in the center and what does it do +what does it cause + + align:start position:0% +what does it cause + + + align:start position:0% +what does it cause +and here + + align:start position:0% +and here + + + align:start position:0% +and here +um + + align:start position:0% +um + + + align:start position:0% +um +i'm not having oh right here we're going + + align:start position:0% +i'm not having oh right here we're going + + + align:start position:0% +i'm not having oh right here we're going +to talk about the surround effect and + + align:start position:0% +to talk about the surround effect and + + + align:start position:0% +to talk about the surround effect and +i'm going to show you the experiment + + align:start position:0% +i'm going to show you the experiment + + + align:start position:0% +i'm going to show you the experiment +it's kind of hard to read from these + + align:start position:0% +it's kind of hard to read from these + + + align:start position:0% +it's kind of hard to read from these +slides what the experiment is so here's + + align:start position:0% +slides what the experiment is so here's + + + align:start position:0% +slides what the experiment is so here's +the experiment here + + align:start position:0% + + + + align:start position:0% + +everybody see that there's just + + align:start position:0% +everybody see that there's just + + + align:start position:0% +everybody see that there's just +a bright so it's a dark background and + + align:start position:0% +a bright so it's a dark background and + + + align:start position:0% +a bright so it's a dark background and +you just flash this bright annulus of + + align:start position:0% +you just flash this bright annulus of + + + align:start position:0% +you just flash this bright annulus of +light and again here's the this whole + + align:start position:0% +light and again here's the this whole + + + align:start position:0% +light and again here's the this whole +area is the receptive field of the + + align:start position:0% +area is the receptive field of the + + + align:start position:0% +area is the receptive field of the +photoreceptor so it's first dark and + + align:start position:0% +photoreceptor so it's first dark and + + + align:start position:0% +photoreceptor so it's first dark and +then just this right annulus is flashed + + align:start position:0% +then just this right annulus is flashed + + + align:start position:0% +then just this right annulus is flashed +okay so now let's look at the results so + + align:start position:0% +okay so now let's look at the results so + + + align:start position:0% +okay so now let's look at the results so +for the off center uh the hyper the one + + align:start position:0% +for the off center uh the hyper the one + + + align:start position:0% +for the off center uh the hyper the one +i've called um off center but it's the + + align:start position:0% +i've called um off center but it's the + + + align:start position:0% +i've called um off center but it's the +hyper polarizing bipolar + + align:start position:0% +hyper polarizing bipolar + + + align:start position:0% +hyper polarizing bipolar +um + + align:start position:0% +um + + + align:start position:0% +um +when we add the annulus in there + + align:start position:0% +when we add the annulus in there + + + align:start position:0% +when we add the annulus in there +it uh + + align:start position:0% +it uh + + + align:start position:0% +it uh +what happens here it depolarizes right + + align:start position:0% +what happens here it depolarizes right + + + align:start position:0% +what happens here it depolarizes right +that's right it depolarizes but beyond + + align:start position:0% +that's right it depolarizes but beyond + + + align:start position:0% +that's right it depolarizes but beyond +center when we add the bright annulus so + + align:start position:0% +center when we add the bright annulus so + + + align:start position:0% +center when we add the bright annulus so +it wants on center it wants light in the + + align:start position:0% +it wants on center it wants light in the + + + align:start position:0% +it wants on center it wants light in the +center we add the brightness on the + + align:start position:0% +center we add the brightness on the + + + align:start position:0% +center we add the brightness on the +outside + + align:start position:0% +outside + + + align:start position:0% +outside +we see + + align:start position:0% +we see + + + align:start position:0% +we see +that this does not it goes down it does + + align:start position:0% +that this does not it goes down it does + + + align:start position:0% +that this does not it goes down it does +not go closer to releasing more + + align:start position:0% +not go closer to releasing more + + + align:start position:0% +not go closer to releasing more +glutamate + + align:start position:0% +glutamate + + + align:start position:0% +glutamate +again when it goes up we're releasing + + align:start position:0% +again when it goes up we're releasing + + + align:start position:0% +again when it goes up we're releasing +more glutamate + + align:start position:0% +more glutamate + + + align:start position:0% +more glutamate +so basically + + align:start position:0% +so basically + + + align:start position:0% +so basically +the take-home message here is + + align:start position:0% +the take-home message here is + + + align:start position:0% +the take-home message here is +this right here sorry it just keeps + + align:start position:0% +this right here sorry it just keeps + + + align:start position:0% +this right here sorry it just keeps +flashing but okay imagine there's that + + align:start position:0% +flashing but okay imagine there's that + + + align:start position:0% +flashing but okay imagine there's that +bright thing again um that's the optimal + + align:start position:0% +bright thing again um that's the optimal + + + align:start position:0% +bright thing again um that's the optimal +stimulus for which type of cell on + + align:start position:0% +stimulus for which type of cell on + + + align:start position:0% +stimulus for which type of cell on +center off center + + align:start position:0% +center off center + + + align:start position:0% +center off center +off center right yeah that's right + + align:start position:0% +off center right yeah that's right + + + align:start position:0% +off center right yeah that's right +so + + align:start position:0% +so + + + align:start position:0% +so +because it's bright on the outside and + + align:start position:0% +because it's bright on the outside and + + + align:start position:0% +because it's bright on the outside and +dark on the inside + + align:start position:0% +dark on the inside + + + align:start position:0% +dark on the inside +so that's why this guy depolarizes and + + align:start position:0% +so that's why this guy depolarizes and + + + align:start position:0% +so that's why this guy depolarizes and +that's why this guy hyperpolarizes + + align:start position:0% +that's why this guy hyperpolarizes + + + align:start position:0% +that's why this guy hyperpolarizes +but it's sinking + + align:start position:0% + + + + align:start position:0% + +so we're going to backtrack for just a + + align:start position:0% +so we're going to backtrack for just a + + + align:start position:0% +so we're going to backtrack for just a +second um you might have noticed that in + + align:start position:0% +second um you might have noticed that in + + + align:start position:0% +second um you might have noticed that in +going from photoreceptors to bipolars i + + align:start position:0% +going from photoreceptors to bipolars i + + + align:start position:0% +going from photoreceptors to bipolars i +just kind of skipped over this + + align:start position:0% +just kind of skipped over this + + + align:start position:0% +just kind of skipped over this +cell right here the cell type the + + align:start position:0% +cell right here the cell type the + + + align:start position:0% +cell right here the cell type the +horizontal cells and + + align:start position:0% +horizontal cells and + + + align:start position:0% +horizontal cells and +horizontal cells are the ones that are + + align:start position:0% +horizontal cells are the ones that are + + + align:start position:0% +horizontal cells are the ones that are +responsible actually for creating that + + align:start position:0% +responsible actually for creating that + + + align:start position:0% +responsible actually for creating that +inhibitory surround you can see the + + align:start position:0% +inhibitory surround you can see the + + + align:start position:0% +inhibitory surround you can see the +bipolars even though they have kind of + + align:start position:0% +bipolars even though they have kind of + + + align:start position:0% +bipolars even though they have kind of +some dendritic branching here uh going + + align:start position:0% +some dendritic branching here uh going + + + align:start position:0% +some dendritic branching here uh going +over a few photoreceptors you can see + + align:start position:0% +over a few photoreceptors you can see + + + align:start position:0% +over a few photoreceptors you can see +that the horizontal cells have a much + + align:start position:0% +that the horizontal cells have a much + + + align:start position:0% +that the horizontal cells have a much +much more they're i mean they're + + align:start position:0% +much more they're i mean they're + + + align:start position:0% +much more they're i mean they're +horizontal they branch right okay and + + align:start position:0% +horizontal they branch right okay and + + + align:start position:0% +horizontal they branch right okay and +basically they're the ones that create + + align:start position:0% +basically they're the ones that create + + + align:start position:0% +basically they're the ones that create +the inhibitory surround + + align:start position:0% +the inhibitory surround + + + align:start position:0% +the inhibitory surround +and i'm not going to explain too much + + align:start position:0% +and i'm not going to explain too much + + + align:start position:0% +and i'm not going to explain too much +about the mechanism there and i don't + + align:start position:0% +about the mechanism there and i don't + + + align:start position:0% +about the mechanism there and i don't +know actually how much of it is fully + + align:start position:0% +know actually how much of it is fully + + + align:start position:0% +know actually how much of it is fully +known but it's it's these are inhibitory + + align:start position:0% +known but it's it's these are inhibitory + + + align:start position:0% +known but it's it's these are inhibitory +cells for the most part and they're the + + align:start position:0% +cells for the most part and they're the + + + align:start position:0% +cells for the most part and they're the +ones responsible for creating that + + align:start position:0% +ones responsible for creating that + + + align:start position:0% +ones responsible for creating that +inhibitory surround the uh + + align:start position:0% +inhibitory surround the uh + + + align:start position:0% +inhibitory surround the uh +on on center off surround or off center + + align:start position:0% +on on center off surround or off center + + + align:start position:0% +on on center off surround or off center +on surround + + align:start position:0% +on surround + + + align:start position:0% +on surround +okay + + align:start position:0% +okay + + + align:start position:0% +okay +before we get to the ganglion cells the + + align:start position:0% +before we get to the ganglion cells the + + + align:start position:0% +before we get to the ganglion cells the +next cell type is + + align:start position:0% +next cell type is + + + align:start position:0% +next cell type is +emicron cells + + align:start position:0% +emicron cells + + + align:start position:0% +emicron cells +so um + + align:start position:0% +so um + + + align:start position:0% +so um +right jerry slide here on center amicon + + align:start position:0% +right jerry slide here on center amicon + + + align:start position:0% +right jerry slide here on center amicon +cell so + + align:start position:0% +cell so + + + align:start position:0% +cell so +one question let's just back up for a + + align:start position:0% +one question let's just back up for a + + + align:start position:0% +one question let's just back up for a +second so one question you might be + + align:start position:0% +second so one question you might be + + + align:start position:0% +second so one question you might be +asking is + + align:start position:0% +asking is + + + align:start position:0% +asking is +well the bipolar cells have this + + align:start position:0% +well the bipolar cells have this + + + align:start position:0% +well the bipolar cells have this +you know center surround organization + + align:start position:0% +you know center surround organization + + + align:start position:0% +you know center surround organization +and when you show those videos of the + + align:start position:0% +and when you show those videos of the + + + align:start position:0% +and when you show those videos of the +retinal ganglion cells you know those + + align:start position:0% +retinal ganglion cells you know those + + + align:start position:0% +retinal ganglion cells you know those +ones they uh they just they also had you + + align:start position:0% +ones they uh they just they also had you + + + align:start position:0% +ones they uh they just they also had you +know basically center surround + + align:start position:0% +know basically center surround + + + align:start position:0% +know basically center surround +organization so + + align:start position:0% +organization so + + + align:start position:0% +organization so +what is all this i mean why don't we + + align:start position:0% +what is all this i mean why don't we + + + align:start position:0% +what is all this i mean why don't we +just have the bipolar cells going out to + + align:start position:0% +just have the bipolar cells going out to + + + align:start position:0% +just have the bipolar cells going out to +the brain i mean what is all this how do + + align:start position:0% +the brain i mean what is all this how do + + + align:start position:0% +the brain i mean what is all this how do +you need all this other machinery and + + align:start position:0% +you need all this other machinery and + + + align:start position:0% +you need all this other machinery and +the reason is that so i didn't show you + + align:start position:0% +the reason is that so i didn't show you + + + align:start position:0% +the reason is that so i didn't show you +fully in those movies the ganglion cell + + align:start position:0% +fully in those movies the ganglion cell + + + align:start position:0% +fully in those movies the ganglion cell +is actually more complex it adds in + + align:start position:0% +is actually more complex it adds in + + + align:start position:0% +is actually more complex it adds in +addition just this center surround thing + + align:start position:0% +addition just this center surround thing + + + align:start position:0% +addition just this center surround thing +it can add some temporal response + + align:start position:0% +it can add some temporal response + + + align:start position:0% +it can add some temporal response +properties and what what adds those is + + align:start position:0% +properties and what what adds those is + + + align:start position:0% +properties and what what adds those is +really these american cells and now + + align:start position:0% +really these american cells and now + + + align:start position:0% +really these american cells and now +we're going to enter into the digital + + align:start position:0% +we're going to enter into the digital + + + align:start position:0% +we're going to enter into the digital +domain the the gradient potentials are + + align:start position:0% +domain the the gradient potentials are + + + align:start position:0% +domain the the gradient potentials are +over we're now going to start talking + + align:start position:0% +over we're now going to start talking + + + align:start position:0% +over we're now going to start talking +more about action potentials so + + align:start position:0% + + + + align:start position:0% + +let's see here + + align:start position:0% +let's see here + + + align:start position:0% +let's see here +what's being done here + + align:start position:0% +what's being done here + + + align:start position:0% +what's being done here +is this is a + + align:start position:0% +is this is a + + + align:start position:0% +is this is a +very confusing diagram but i think that + + align:start position:0% +very confusing diagram but i think that + + + align:start position:0% +very confusing diagram but i think that +what's been done here is this spot is + + align:start position:0% +what's been done here is this spot is + + + align:start position:0% +what's been done here is this spot is +being moved across right here of this + + align:start position:0% +being moved across right here of this + + + align:start position:0% +being moved across right here of this +on-central anachronic cell on central + + align:start position:0% +on-central anachronic cell on central + + + align:start position:0% +on-central anachronic cell on central +means the optical stimulus is bright + + align:start position:0% +means the optical stimulus is bright + + + align:start position:0% +means the optical stimulus is bright +light at the center right okay so this + + align:start position:0% +light at the center right okay so this + + + align:start position:0% +light at the center right okay so this +is bright light moving toward the center + + align:start position:0% +is bright light moving toward the center + + + align:start position:0% +is bright light moving toward the center +and what you see here what these arrows + + align:start position:0% +and what you see here what these arrows + + + align:start position:0% +and what you see here what these arrows +indicate um look first just at this one + + align:start position:0% +indicate um look first just at this one + + + align:start position:0% +indicate um look first just at this one +graph is when we move in this direction + + align:start position:0% +graph is when we move in this direction + + + align:start position:0% +graph is when we move in this direction +well look at this during the time that + + align:start position:0% +well look at this during the time that + + + align:start position:0% +well look at this during the time that +it's over the middle area which you + + align:start position:0% +it's over the middle area which you + + + align:start position:0% +it's over the middle area which you +might say is this whole period right + + align:start position:0% +might say is this whole period right + + + align:start position:0% +might say is this whole period right +here like there's like this whole block + + align:start position:0% +here like there's like this whole block + + + align:start position:0% +here like there's like this whole block +right here + + align:start position:0% +right here + + + align:start position:0% +right here +well it's not that the responses is up + + align:start position:0% +well it's not that the responses is up + + + align:start position:0% +well it's not that the responses is up +the whole time it's not like an elevated + + align:start position:0% +the whole time it's not like an elevated + + + align:start position:0% +the whole time it's not like an elevated +response the entire time it's actually + + align:start position:0% +response the entire time it's actually + + + align:start position:0% +response the entire time it's actually +interestingly and super increase in + + align:start position:0% +interestingly and super increase in + + + align:start position:0% +interestingly and super increase in +response + + align:start position:0% +response + + + align:start position:0% +response +just as it enters the central part of + + align:start position:0% +just as it enters the central part of + + + align:start position:0% +just as it enters the central part of +the ah of the on uh center cell enters + + align:start position:0% +the ah of the on uh center cell enters + + + align:start position:0% +the ah of the on uh center cell enters +the central portion so it's like it's + + align:start position:0% +the central portion so it's like it's + + + align:start position:0% +the central portion so it's like it's +got this uh it's preference to fire + + align:start position:0% +got this uh it's preference to fire + + + align:start position:0% +got this uh it's preference to fire +right when it when it enters and you can + + align:start position:0% +right when it when it enters and you can + + + align:start position:0% +right when it when it enters and you can +see that the same you can prove this to + + align:start position:0% +see that the same you can prove this to + + + align:start position:0% +see that the same you can prove this to +yourself by doing the experiment taking + + align:start position:0% +yourself by doing the experiment taking + + + align:start position:0% +yourself by doing the experiment taking +the spot starting the spot on this side + + align:start position:0% +the spot starting the spot on this side + + + align:start position:0% +the spot starting the spot on this side +and going + + align:start position:0% +and going + + + align:start position:0% +and going +that way and that's what this + + align:start position:0% +that way and that's what this + + + align:start position:0% +that way and that's what this +unfortunately this is overlaid both + + align:start position:0% +unfortunately this is overlaid both + + + align:start position:0% +unfortunately this is overlaid both +directions but you can make out this + + align:start position:0% +directions but you can make out this + + + align:start position:0% +directions but you can make out this +trace is the same as this trace the one + + align:start position:0% +trace is the same as this trace the one + + + align:start position:0% +trace is the same as this trace the one +in this direction but you see the arrow + + align:start position:0% +in this direction but you see the arrow + + + align:start position:0% +in this direction but you see the arrow +going in that direction + + align:start position:0% +going in that direction + + + align:start position:0% +going in that direction +that direction + + align:start position:0% +that direction + + + align:start position:0% +that direction +that one you see a spike of the maximum + + align:start position:0% +that one you see a spike of the maximum + + + align:start position:0% +that one you see a spike of the maximum +response is right as it enters + + align:start position:0% +response is right as it enters + + + align:start position:0% +response is right as it enters +this uh this area so here you have this + + align:start position:0% +this uh this area so here you have this + + + align:start position:0% +this uh this area so here you have this +this beautiful + + align:start position:0% +this beautiful + + + align:start position:0% +this beautiful +temporal kind of characteristic + + align:start position:0% +temporal kind of characteristic + + + align:start position:0% +temporal kind of characteristic +so + + align:start position:0% +so + + + align:start position:0% +so +jerry's saying right here compare this + + align:start position:0% +jerry's saying right here compare this + + + align:start position:0% +jerry's saying right here compare this +with the receptor of the photoreceptor + + align:start position:0% +with the receptor of the photoreceptor + + + align:start position:0% +with the receptor of the photoreceptor +the horizontal cell the bipolar cell and + + align:start position:0% +the horizontal cell the bipolar cell and + + + align:start position:0% +the horizontal cell the bipolar cell and +what this shows is here the arrows going + + align:start position:0% +what this shows is here the arrows going + + + align:start position:0% +what this shows is here the arrows going +each way and the take home message here + + align:start position:0% +each way and the take home message here + + + align:start position:0% +each way and the take home message here +is look you put a spot oh this is kind + + align:start position:0% +is look you put a spot oh this is kind + + + align:start position:0% +is look you put a spot oh this is kind +of nice you see the photoreceptor + + align:start position:0% +of nice you see the photoreceptor + + + align:start position:0% +of nice you see the photoreceptor +why are these circles different sizes + + align:start position:0% +why are these circles different sizes + + + align:start position:0% +why are these circles different sizes +anyone + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +that's right it's got that huge + + align:start position:0% +that's right it's got that huge + + + align:start position:0% +that's right it's got that huge +dendritic arbitration whereas the + + align:start position:0% +dendritic arbitration whereas the + + + align:start position:0% +dendritic arbitration whereas the +photoreceptor hey it's just sticking out + + align:start position:0% +photoreceptor hey it's just sticking out + + + align:start position:0% +photoreceptor hey it's just sticking out +there looking at light right so it's got + + align:start position:0% +there looking at light right so it's got + + + align:start position:0% +there looking at light right so it's got +its one one little area so what this + + align:start position:0% +its one one little area so what this + + + align:start position:0% +its one one little area so what this +shows here is that look you go in one + + align:start position:0% +shows here is that look you go in one + + + align:start position:0% +shows here is that look you go in one +direction or the other direction the + + align:start position:0% +direction or the other direction the + + + align:start position:0% +direction or the other direction the +photoreceptor is gonna have the same + + align:start position:0% +photoreceptor is gonna have the same + + + align:start position:0% +photoreceptor is gonna have the same +neural response this is neural response + + align:start position:0% +neural response this is neural response + + + align:start position:0% +neural response this is neural response +right light comes in and it's going to + + align:start position:0% +right light comes in and it's going to + + + align:start position:0% +right light comes in and it's going to +depolarize + + align:start position:0% +depolarize + + + align:start position:0% +depolarize +hyper polarized okay hyper so it's going + + align:start position:0% +hyper polarized okay hyper so it's going + + + align:start position:0% +hyper polarized okay hyper so it's going +down right and then horizontal cell same + + align:start position:0% +down right and then horizontal cell same + + + align:start position:0% +down right and then horizontal cell same +thing bipolar cell same thing you see + + align:start position:0% +thing bipolar cell same thing you see + + + align:start position:0% +thing bipolar cell same thing you see +these kind of bumps here but it's + + align:start position:0% +these kind of bumps here but it's + + + align:start position:0% +these kind of bumps here but it's +basically the same response it's not + + align:start position:0% +basically the same response it's not + + + align:start position:0% +basically the same response it's not +nearly as peaked as this so the american + + align:start position:0% +nearly as peaked as this so the american + + + align:start position:0% +nearly as peaked as this so the american +cell adds this temporal complexity + + align:start position:0% + + + + align:start position:0% + +um so the so the on off organization + + align:start position:0% +um so the so the on off organization + + + align:start position:0% +um so the so the on off organization +starts at the level of the bipolar cell + + align:start position:0% +starts at the level of the bipolar cell + + + align:start position:0% +starts at the level of the bipolar cell +so no on the receptor and horizontal + + align:start position:0% +so no on the receptor and horizontal + + + align:start position:0% +so no on the receptor and horizontal +cell + + align:start position:0% + + + + align:start position:0% + +um actually you know i'm not too sure + + align:start position:0% +um actually you know i'm not too sure + + + align:start position:0% +um actually you know i'm not too sure +about the deceptive field of the + + align:start position:0% +about the deceptive field of the + + + align:start position:0% +about the deceptive field of the +horizontal cell you know let me let me + + align:start position:0% +horizontal cell you know let me let me + + + align:start position:0% +horizontal cell you know let me let me +backtrack on that i've not seen + + align:start position:0% +backtrack on that i've not seen + + + align:start position:0% +backtrack on that i've not seen +recordings of well there are probably + + align:start position:0% +recordings of well there are probably + + + align:start position:0% +recordings of well there are probably +some here let's look at it after words + + align:start position:0% +some here let's look at it after words + + + align:start position:0% +some here let's look at it after words +it's not terribly important but uh in + + align:start position:0% +it's not terribly important but uh in + + + align:start position:0% +it's not terribly important but uh in +your handout probably a few slides back + + align:start position:0% +your handout probably a few slides back + + + align:start position:0% +your handout probably a few slides back +there + + align:start position:0% +there + + + align:start position:0% +there +there's the summary and uh + + align:start position:0% +there's the summary and uh + + + align:start position:0% +there's the summary and uh +but that that doesn't have this exact + + align:start position:0% +but that that doesn't have this exact + + + align:start position:0% +but that that doesn't have this exact +experiment let's talk about this maybe + + align:start position:0% +experiment let's talk about this maybe + + + align:start position:0% +experiment let's talk about this maybe +offline because i'm not sure i haven't + + align:start position:0% +offline because i'm not sure i haven't + + + align:start position:0% +offline because i'm not sure i haven't +really seen good recordings of + + align:start position:0% +really seen good recordings of + + + align:start position:0% +really seen good recordings of +horizontal cells so right + + align:start position:0% +horizontal cells so right + + + align:start position:0% +horizontal cells so right +made that comparison so direction + + align:start position:0% +made that comparison so direction + + + align:start position:0% +made that comparison so direction +selectivity and ganglion's all right oh + + align:start position:0% +selectivity and ganglion's all right oh + + + align:start position:0% +selectivity and ganglion's all right oh +so jerry jerry wants to show you a model + + align:start position:0% +so jerry jerry wants to show you a model + + + align:start position:0% +so jerry jerry wants to show you a model +that's been proposed of how this might + + align:start position:0% +that's been proposed of how this might + + + align:start position:0% +that's been proposed of how this might +work + + align:start position:0% +work + + + align:start position:0% +work +so + + align:start position:0% +so + + + align:start position:0% +so +so again this direction selectivity + + align:start position:0% +so again this direction selectivity + + + align:start position:0% +so again this direction selectivity +which i showed you right now in an + + align:start position:0% +which i showed you right now in an + + + align:start position:0% +which i showed you right now in an +american cell is also found + + align:start position:0% +american cell is also found + + + align:start position:0% +american cell is also found +in certain ganglion cells + + align:start position:0% +in certain ganglion cells + + + align:start position:0% +in certain ganglion cells +she's asleep okay and certain ganglion + + align:start position:0% +she's asleep okay and certain ganglion + + + align:start position:0% +she's asleep okay and certain ganglion +cells but um so i want to show you how + + align:start position:0% +cells but um so i want to show you how + + + align:start position:0% +cells but um so i want to show you how +one model of this has been proposed how + + align:start position:0% +one model of this has been proposed how + + + align:start position:0% +one model of this has been proposed how +the american cell can lead to this + + align:start position:0% +the american cell can lead to this + + + align:start position:0% +the american cell can lead to this +directional selectivity and + + align:start position:0% +directional selectivity and + + + align:start position:0% +directional selectivity and +this is again one of these models with + + align:start position:0% +this is again one of these models with + + + align:start position:0% +this is again one of these models with +lots of synapses so let's just try and + + align:start position:0% +lots of synapses so let's just try and + + + align:start position:0% +lots of synapses so let's just try and +keep this simple so + + align:start position:0% +keep this simple so + + + align:start position:0% +keep this simple so +there's a preferred direction + + align:start position:0% +there's a preferred direction + + + align:start position:0% +there's a preferred direction +and a null direction so + + align:start position:0% +and a null direction so + + + align:start position:0% +and a null direction so +preferred direction we can imagine the + + align:start position:0% +preferred direction we can imagine the + + + align:start position:0% +preferred direction we can imagine the +spot moves this way so what would happen + + align:start position:0% +spot moves this way so what would happen + + + align:start position:0% +spot moves this way so what would happen +is + + align:start position:0% +is + + + align:start position:0% +is +this bipolar gets the spot let's just + + align:start position:0% +this bipolar gets the spot let's just + + + align:start position:0% +this bipolar gets the spot let's just +assume all the bipolars are on center to + + align:start position:0% +assume all the bipolars are on center to + + + align:start position:0% +assume all the bipolars are on center to +keep my life simple because + + align:start position:0% +keep my life simple because + + + align:start position:0% +keep my life simple because +yeah i think that's a valid assumption + + align:start position:0% +yeah i think that's a valid assumption + + + align:start position:0% +yeah i think that's a valid assumption +let's do that so this one fires right + + align:start position:0% +let's do that so this one fires right + + + align:start position:0% +let's do that so this one fires right +okay so what we're trying to do is get + + align:start position:0% +okay so what we're trying to do is get + + + align:start position:0% +okay so what we're trying to do is get +excite this this ganglion cell when + + align:start position:0% +excite this this ganglion cell when + + + align:start position:0% +excite this this ganglion cell when +something's moved this way and not + + align:start position:0% +something's moved this way and not + + + align:start position:0% +something's moved this way and not +excite it when it's moved this way so + + align:start position:0% +excite it when it's moved this way so + + + align:start position:0% +excite it when it's moved this way so +this one fires + + align:start position:0% +this one fires + + + align:start position:0% +this one fires +and what it does is it also it makes a + + align:start position:0% +and what it does is it also it makes a + + + align:start position:0% +and what it does is it also it makes a +synapse onto um + + align:start position:0% +synapse onto um + + + align:start position:0% +synapse onto um +this amacrine cell which + + align:start position:0% +this amacrine cell which + + + align:start position:0% +this amacrine cell which +why is this not like intensity right now + + align:start position:0% +why is this not like intensity right now + + + align:start position:0% +why is this not like intensity right now +which right okay so it makes synapse + + align:start position:0% +which right okay so it makes synapse + + + align:start position:0% +which right okay so it makes synapse +onto one of these american cells which + + align:start position:0% +onto one of these american cells which + + + align:start position:0% +onto one of these american cells which +also synapses onto + + align:start position:0% + + + + align:start position:0% + +onto the ganglion cell + + align:start position:0% +onto the ganglion cell + + + align:start position:0% +onto the ganglion cell +and + + align:start position:0% +and + + + align:start position:0% +and +you can see that if you + + align:start position:0% +you can see that if you + + + align:start position:0% +you can see that if you +so first this fires then this fires but + + align:start position:0% +so first this fires then this fires but + + + align:start position:0% +so first this fires then this fires but +you can see by this one firing here it's + + align:start position:0% +you can see by this one firing here it's + + + align:start position:0% +you can see by this one firing here it's +also + + align:start position:0% +also + + + align:start position:0% +also +induced this neuron to fire down here + + align:start position:0% +induced this neuron to fire down here + + + align:start position:0% +induced this neuron to fire down here +right this + + align:start position:0% +right this + + + align:start position:0% +right this +this synapse is excitatory excites this + + align:start position:0% +this synapse is excitatory excites this + + + align:start position:0% +this synapse is excitatory excites this +one + + align:start position:0% +one + + + align:start position:0% +one +and this one's also excited + + align:start position:0% +and this one's also excited + + + align:start position:0% +and this one's also excited +simultaneously from the bipolar cell + + align:start position:0% +simultaneously from the bipolar cell + + + align:start position:0% +simultaneously from the bipolar cell +because we're moving the stimulus this + + align:start position:0% +because we're moving the stimulus this + + + align:start position:0% +because we're moving the stimulus this +way that bipolar cell excites the next + + align:start position:0% +way that bipolar cell excites the next + + + align:start position:0% +way that bipolar cell excites the next +um + + align:start position:0% +um + + + align:start position:0% +um +the next american cell and that + + align:start position:0% +the next american cell and that + + + align:start position:0% +the next american cell and that +that one makes it easier to fire because + + align:start position:0% +that one makes it easier to fire because + + + align:start position:0% +that one makes it easier to fire because +then the stimulus is also here so + + align:start position:0% +then the stimulus is also here so + + + align:start position:0% +then the stimulus is also here so +what's what's happening is that there's + + align:start position:0% +what's what's happening is that there's + + + align:start position:0% +what's what's happening is that there's +the kind of sequential + + align:start position:0% +the kind of sequential + + + align:start position:0% +the kind of sequential +excitation in this direction whereas if + + align:start position:0% +excitation in this direction whereas if + + + align:start position:0% +excitation in this direction whereas if +you move in this direction when this + + align:start position:0% +you move in this direction when this + + + align:start position:0% +you move in this direction when this +bipolar cell fires + + align:start position:0% +bipolar cell fires + + + align:start position:0% +bipolar cell fires +this synapse and you can see it's by the + + align:start position:0% +this synapse and you can see it's by the + + + align:start position:0% +this synapse and you can see it's by the +asymmetry of these um american cell + + align:start position:0% +asymmetry of these um american cell + + + align:start position:0% +asymmetry of these um american cell +synapses this one fires + + align:start position:0% +synapses this one fires + + + align:start position:0% +synapses this one fires +it makes it easier for this one to fire + + align:start position:0% +it makes it easier for this one to fire + + + align:start position:0% +it makes it easier for this one to fire +but + + align:start position:0% +but + + + align:start position:0% +but +um makes it easier for this one right + + align:start position:0% +um makes it easier for this one right + + + align:start position:0% +um makes it easier for this one right +but this one makes right makes an + + align:start position:0% +but this one makes right makes an + + + align:start position:0% +but this one makes right makes an +inhibitory synapse onto this emicron + + align:start position:0% +inhibitory synapse onto this emicron + + + align:start position:0% +inhibitory synapse onto this emicron +cell so this one's less likely to fire + + align:start position:0% +cell so this one's less likely to fire + + + align:start position:0% +cell so this one's less likely to fire +by the time the stimulus reaches this + + align:start position:0% +by the time the stimulus reaches this + + + align:start position:0% +by the time the stimulus reaches this +bipolar cell so all you need to observe + + align:start position:0% +bipolar cell so all you need to observe + + + align:start position:0% +bipolar cell so all you need to observe +here is that it's the asymmetry in these + + align:start position:0% +here is that it's the asymmetry in these + + + align:start position:0% +here is that it's the asymmetry in these +connections that make it easier for this + + align:start position:0% +connections that make it easier for this + + + align:start position:0% +connections that make it easier for this +direction than for that direction + + align:start position:0% +direction than for that direction + + + align:start position:0% +direction than for that direction +easier to excite this cell and it's + + align:start position:0% +easier to excite this cell and it's + + + align:start position:0% +easier to excite this cell and it's +really + + align:start position:0% +really + + + align:start position:0% +really +if you find this confusing the way to do + + align:start position:0% +if you find this confusing the way to do + + + align:start position:0% +if you find this confusing the way to do +this is think + + align:start position:0% +this is think + + + align:start position:0% +this is think +at time point one this gets excited time + + align:start position:0% +at time point one this gets excited time + + + align:start position:0% +at time point one this gets excited time +point two this gets excited time point + + align:start position:0% +point two this gets excited time point + + + align:start position:0% +point two this gets excited time point +three just gets excited and then just + + align:start position:0% +three just gets excited and then just + + + align:start position:0% +three just gets excited and then just +trace okay this is a plus connection + + align:start position:0% +trace okay this is a plus connection + + + align:start position:0% +trace okay this is a plus connection +that means this guy's easier to excite + + align:start position:0% +that means this guy's easier to excite + + + align:start position:0% +that means this guy's easier to excite +and well then he's also getting a + + align:start position:0% +and well then he's also getting a + + + align:start position:0% +and well then he's also getting a +connection from this because at time + + align:start position:0% +connection from this because at time + + + align:start position:0% +connection from this because at time +point two the stimulus is here and + + align:start position:0% +point two the stimulus is here and + + + align:start position:0% +point two the stimulus is here and +that's what's gonna prefer this + + align:start position:0% +that's what's gonna prefer this + + + align:start position:0% +that's what's gonna prefer this +direction so there's a way to kind of + + align:start position:0% +direction so there's a way to kind of + + + align:start position:0% +direction so there's a way to kind of +work through these diagrams synapse by + + align:start position:0% +work through these diagrams synapse by + + + align:start position:0% +work through these diagrams synapse by +synapse and think that the conduction + + align:start position:0% +synapse and think that the conduction + + + align:start position:0% +synapse and think that the conduction +time from one synapse to another is it's + + align:start position:0% +time from one synapse to another is it's + + + align:start position:0% +time from one synapse to another is it's +much shorter actually than the + + align:start position:0% +much shorter actually than the + + + align:start position:0% +much shorter actually than the +conduction time + + align:start position:0% +conduction time + + + align:start position:0% +conduction time +for most stimuli i would think going + + align:start position:0% +for most stimuli i would think going + + + align:start position:0% +for most stimuli i would think going +across so you can you can assume that + + align:start position:0% +across so you can you can assume that + + + align:start position:0% +across so you can you can assume that +even though it has to traverse the + + align:start position:0% +even though it has to traverse the + + + align:start position:0% +even though it has to traverse the +synapse it's already made it over there + + align:start position:0% +synapse it's already made it over there + + + align:start position:0% +synapse it's already made it over there +by the time that bipolar cell fires the + + align:start position:0% +by the time that bipolar cell fires the + + + align:start position:0% +by the time that bipolar cell fires the +next one in in there in the uh line + + align:start position:0% + + + + align:start position:0% + +was that clear should i go over that + + align:start position:0% +was that clear should i go over that + + + align:start position:0% +was that clear should i go over that +more + + align:start position:0% +more + + + align:start position:0% +more +i think i might even bundle that up more + + align:start position:0% +i think i might even bundle that up more + + + align:start position:0% +i think i might even bundle that up more +by going over more though okay let's + + align:start position:0% +by going over more though okay let's + + + align:start position:0% +by going over more though okay let's +keep moving so + + align:start position:0% +keep moving so + + + align:start position:0% +keep moving so +this type of model is i guess also been + + align:start position:0% +this type of model is i guess also been + + + align:start position:0% +this type of model is i guess also been +supported by some experimental studies + + align:start position:0% +supported by some experimental studies + + + align:start position:0% +supported by some experimental studies +um + + align:start position:0% +um + + + align:start position:0% +um +okay so this one's an easy one to + + align:start position:0% +okay so this one's an easy one to + + + align:start position:0% +okay so this one's an easy one to +explain the american cells are gabaergic + + align:start position:0% +explain the american cells are gabaergic + + + align:start position:0% +explain the american cells are gabaergic +cells that because they make those + + align:start position:0% +cells that because they make those + + + align:start position:0% +cells that because they make those +inhibitory connections right so the + + align:start position:0% +inhibitory connections right so the + + + align:start position:0% +inhibitory connections right so the +inhibitory neurotransmitter in the cns + + align:start position:0% +inhibitory neurotransmitter in the cns + + + align:start position:0% +inhibitory neurotransmitter in the cns +the primary one is gaba + + align:start position:0% + + + + align:start position:0% + +and so if you block if you use a blocker + + align:start position:0% +and so if you block if you use a blocker + + + align:start position:0% +and so if you block if you use a blocker +a gaba antagonist in the retina all the + + align:start position:0% +a gaba antagonist in the retina all the + + + align:start position:0% +a gaba antagonist in the retina all the +directional specificity goes away so + + align:start position:0% +directional specificity goes away so + + + align:start position:0% +directional specificity goes away so +this is a good argument for those + + align:start position:0% +this is a good argument for those + + + align:start position:0% +this is a good argument for those +immigrant cells um + + align:start position:0% +immigrant cells um + + + align:start position:0% +immigrant cells um +i don't know what i think this what what + + align:start position:0% +i don't know what i think this what what + + + align:start position:0% +i don't know what i think this what what +the summary of this here says that some + + align:start position:0% +the summary of this here says that some + + + align:start position:0% +the summary of this here says that some +people think that it might be happening + + align:start position:0% +people think that it might be happening + + + align:start position:0% +people think that it might be happening +even earlier like horizontals and + + align:start position:0% +even earlier like horizontals and + + + align:start position:0% +even earlier like horizontals and +bipolars that might be causing + + align:start position:0% +bipolars that might be causing + + + align:start position:0% +bipolars that might be causing +directional selectivity but + + align:start position:0% +directional selectivity but + + + align:start position:0% +directional selectivity but +the jury is still out on it + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +back to this you saw this diagram before + + align:start position:0% +back to this you saw this diagram before + + + align:start position:0% +back to this you saw this diagram before +this one i gave you before this is the + + align:start position:0% +this one i gave you before this is the + + + align:start position:0% +this one i gave you before this is the +straight on and off center response + + align:start position:0% +straight on and off center response + + + align:start position:0% +straight on and off center response +standard stuff and this is showing you + + align:start position:0% +standard stuff and this is showing you + + + align:start position:0% +standard stuff and this is showing you +that ganglion cells also because of this + + align:start position:0% +that ganglion cells also because of this + + + align:start position:0% +that ganglion cells also because of this +neat wiring with the american cells can + + align:start position:0% +neat wiring with the american cells can + + + align:start position:0% +neat wiring with the american cells can +have these transient + + align:start position:0% +have these transient + + + align:start position:0% +have these transient +responses so + + align:start position:0% +responses so + + + align:start position:0% +responses so +that + + align:start position:0% +that + + + align:start position:0% +that +they fire more right when the stimulus + + align:start position:0% +they fire more right when the stimulus + + + align:start position:0% +they fire more right when the stimulus +enters the central area then + + align:start position:0% +enters the central area then + + + align:start position:0% +enters the central area then +say like this where it fire where it's + + align:start position:0% +say like this where it fire where it's + + + align:start position:0% +say like this where it fire where it's +uniform firing when the stimulus is + + align:start position:0% +uniform firing when the stimulus is + + + align:start position:0% +uniform firing when the stimulus is +anywhere in that central area but here + + align:start position:0% +anywhere in that central area but here + + + align:start position:0% +anywhere in that central area but here +it's only on entrance it's a transient + + align:start position:0% +it's only on entrance it's a transient + + + align:start position:0% +it's only on entrance it's a transient +um response + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +direction selected still movie + + align:start position:0% + + + + align:start position:0% + +it's a time of mine + + align:start position:0% + + + + align:start position:0% + +i'll do it again + + align:start position:0% + + + + align:start position:0% + +let's play this here no not gonna happen + + align:start position:0% + + + + align:start position:0% + +does anybody notice that it only fires + + align:start position:0% +does anybody notice that it only fires + + + align:start position:0% +does anybody notice that it only fires +when you go in this direction not when + + align:start position:0% +when you go in this direction not when + + + align:start position:0% +when you go in this direction not when +you go in that direction + + align:start position:0% +you go in that direction + + + align:start position:0% +you go in that direction +so this is actually this light stick is + + align:start position:0% +so this is actually this light stick is + + + align:start position:0% +so this is actually this light stick is +way bigger than the receptive field so + + align:start position:0% +way bigger than the receptive field so + + + align:start position:0% +way bigger than the receptive field so +he's going to try and figure out what + + align:start position:0% +he's going to try and figure out what + + + align:start position:0% +he's going to try and figure out what +the receptive field is this is + + align:start position:0% +the receptive field is this is + + + align:start position:0% +the receptive field is this is +neuroscience and action + + align:start position:0% + + + + align:start position:0% + +folks neuroscience in action in like the + + align:start position:0% +folks neuroscience in action in like the + + + align:start position:0% +folks neuroscience in action in like the +60s though but still + + align:start position:0% + + + + align:start position:0% + +so you see it's much less when it goes + + align:start position:0% +so you see it's much less when it goes + + + align:start position:0% +so you see it's much less when it goes +the other way does everybody see that + + align:start position:0% +the other way does everybody see that + + + align:start position:0% +the other way does everybody see that +it's much much more in this direction + + align:start position:0% +it's much much more in this direction + + + align:start position:0% +it's much much more in this direction +oh he figured it out finally + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay you got it + + align:start position:0% +okay you got it + + + align:start position:0% +okay you got it +yay experimenter + + align:start position:0% + + + + align:start position:0% + +uh no no this this is like um + + align:start position:0% +uh no no this this is like um + + + align:start position:0% +uh no no this this is like um +anesthetized preparation i think + + align:start position:0% +anesthetized preparation i think + + + align:start position:0% +anesthetized preparation i think +actually i'm trying to think maybe maybe + + align:start position:0% +actually i'm trying to think maybe maybe + + + align:start position:0% +actually i'm trying to think maybe maybe +you know it could be like explant too + + align:start position:0% +you know it could be like explant too + + + align:start position:0% +you know it could be like explant too +i'm and this is no this is this might be + + align:start position:0% +i'm and this is no this is this might be + + + align:start position:0% +i'm and this is no this is this might be +monkey or cat no no this this is + + align:start position:0% +monkey or cat no no this this is + + + align:start position:0% +monkey or cat no no this this is +you know i wish i could give you the + + align:start position:0% +you know i wish i could give you the + + + align:start position:0% +you know i wish i could give you the +definitive answer it is + + align:start position:0% +definitive answer it is + + + align:start position:0% +definitive answer it is +i'm pretty sure this is single this is + + align:start position:0% +i'm pretty sure this is single this is + + + align:start position:0% +i'm pretty sure this is single this is +single cell responses though um what is + + align:start position:0% +single cell responses though um what is + + + align:start position:0% +single cell responses though um what is +he writing on he's writing on so + + align:start position:0% +he writing on he's writing on so + + + align:start position:0% +he writing on he's writing on so +basically the way + + align:start position:0% +basically the way + + + align:start position:0% +basically the way +if this is done in a nest sized cat it's + + align:start position:0% +if this is done in a nest sized cat it's + + + align:start position:0% +if this is done in a nest sized cat it's +put into a stereotactic hold which means + + align:start position:0% +put into a stereotactic hold which means + + + align:start position:0% +put into a stereotactic hold which means +it's basically immobilized and it's + + align:start position:0% +it's basically immobilized and it's + + + align:start position:0% +it's basically immobilized and it's +anesthetized so it's not going to really + + align:start position:0% +anesthetized so it's not going to really + + + align:start position:0% +anesthetized so it's not going to really +be moving too much anyways and they make + + align:start position:0% +be moving too much anyways and they make + + + align:start position:0% +be moving too much anyways and they make +a recording from from this area of + + align:start position:0% +a recording from from this area of + + + align:start position:0% +a recording from from this area of +retina basically the cat is just + + align:start position:0% +retina basically the cat is just + + + align:start position:0% +retina basically the cat is just +the eyelids are held open and it's going + + align:start position:0% +the eyelids are held open and it's going + + + align:start position:0% +the eyelids are held open and it's going +to be staring at a screen and the video + + align:start position:0% +to be staring at a screen and the video + + + align:start position:0% +to be staring at a screen and the video +camera is also focused on the same + + align:start position:0% +camera is also focused on the same + + + align:start position:0% +camera is also focused on the same +screen that the cat is staring at so + + align:start position:0% +screen that the cat is staring at so + + + align:start position:0% +screen that the cat is staring at so +that's we're seeing it from kind of the + + align:start position:0% +that's we're seeing it from kind of the + + + align:start position:0% +that's we're seeing it from kind of the +video camera sitting next to the cat or + + align:start position:0% +video camera sitting next to the cat or + + + align:start position:0% +video camera sitting next to the cat or +something + + align:start position:0% +something + + + align:start position:0% +something +something like that + + align:start position:0% + + + + align:start position:0% + +the crazy things they used to do okay um + + align:start position:0% +the crazy things they used to do okay um + + + align:start position:0% +the crazy things they used to do okay um +so + + align:start position:0% +so + + + align:start position:0% +so +this is kind of a nice general principle + + align:start position:0% +this is kind of a nice general principle + + + align:start position:0% +this is kind of a nice general principle +to to know about the retina and that the + + align:start position:0% +to to know about the retina and that the + + + align:start position:0% +to to know about the retina and that the +idea that these cells kind of form these + + align:start position:0% +idea that these cells kind of form these + + + align:start position:0% +idea that these cells kind of form these +two cascades and that each cascade + + align:start position:0% +two cascades and that each cascade + + + align:start position:0% +two cascades and that each cascade +contributes to specific + + align:start position:0% +contributes to specific + + + align:start position:0% +contributes to specific +electrophysiological properties specific + + align:start position:0% +electrophysiological properties specific + + + align:start position:0% +electrophysiological properties specific +receptive field properties + + align:start position:0% +receptive field properties + + + align:start position:0% +receptive field properties +that arise so you can explain the + + align:start position:0% +that arise so you can explain the + + + align:start position:0% +that arise so you can explain the +responses of the bipolar cells in terms + + align:start position:0% +responses of the bipolar cells in terms + + + align:start position:0% +responses of the bipolar cells in terms +of connections with the photoreceptors + + align:start position:0% +of connections with the photoreceptors + + + align:start position:0% +of connections with the photoreceptors +and the horizontal cells that is the + + align:start position:0% +and the horizontal cells that is the + + + align:start position:0% +and the horizontal cells that is the +photoreceptors here + + align:start position:0% +photoreceptors here + + + align:start position:0% +photoreceptors here +um + + align:start position:0% +um + + + align:start position:0% +um +uh making the center and the horizontal + + align:start position:0% +uh making the center and the horizontal + + + align:start position:0% +uh making the center and the horizontal +cells making this antagonistic surround + + align:start position:0% +cells making this antagonistic surround + + + align:start position:0% +cells making this antagonistic surround +remember the sound surround is always + + align:start position:0% +remember the sound surround is always + + + align:start position:0% +remember the sound surround is always +the opposite on versus off + + align:start position:0% +the opposite on versus off + + + align:start position:0% +the opposite on versus off +on + + align:start position:0% +on + + + align:start position:0% +on +and then you can do the similar kind of + + align:start position:0% +and then you can do the similar kind of + + + align:start position:0% +and then you can do the similar kind of +explanation with the ganglion cell + + align:start position:0% +explanation with the ganglion cell + + + align:start position:0% +explanation with the ganglion cell +responses and explain their properties + + align:start position:0% +responses and explain their properties + + + align:start position:0% +responses and explain their properties +in terms of connections with the + + align:start position:0% +in terms of connections with the + + + align:start position:0% +in terms of connections with the +bipolars and emicron and you should see + + align:start position:0% +bipolars and emicron and you should see + + + align:start position:0% +bipolars and emicron and you should see +the connections here horizontal and + + align:start position:0% +the connections here horizontal and + + + align:start position:0% +the connections here horizontal and +american cells arborize they branch + + align:start position:0% +american cells arborize they branch + + + align:start position:0% +american cells arborize they branch +dendritic trees and receptors and + + align:start position:0% +dendritic trees and receptors and + + + align:start position:0% +dendritic trees and receptors and +bipolar cells are like the direct kind + + align:start position:0% +bipolar cells are like the direct kind + + + align:start position:0% +bipolar cells are like the direct kind +of input coming right right down there + + align:start position:0% +of input coming right right down there + + + align:start position:0% +of input coming right right down there +but the american cells and horizontal + + align:start position:0% +but the american cells and horizontal + + + align:start position:0% +but the american cells and horizontal +cells are able to take in the inputs of + + align:start position:0% +cells are able to take in the inputs of + + + align:start position:0% +cells are able to take in the inputs of +multiple + + align:start position:0% +multiple + + + align:start position:0% +multiple +um + + align:start position:0% +um + + + align:start position:0% +um +multiple uh say bipolars or + + align:start position:0% +multiple uh say bipolars or + + + align:start position:0% +multiple uh say bipolars or +photoreceptors and then send them down + + align:start position:0% +photoreceptors and then send them down + + + align:start position:0% +photoreceptors and then send them down +to the next level which in this case is + + align:start position:0% +to the next level which in this case is + + + align:start position:0% +to the next level which in this case is +bipolar in this case is um + + align:start position:0% +bipolar in this case is um + + + align:start position:0% +bipolar in this case is um +ganglion cells and what the result is + + align:start position:0% +ganglion cells and what the result is + + + align:start position:0% +ganglion cells and what the result is +here is that hey you already have the + + align:start position:0% +here is that hey you already have the + + + align:start position:0% +here is that hey you already have the +center surround organization but what + + align:start position:0% +center surround organization but what + + + align:start position:0% +center surround organization but what +this basically does it makes it's um + + align:start position:0% +this basically does it makes it's um + + + align:start position:0% +this basically does it makes it's um +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +like a stronger definition i guess is + + align:start position:0% +like a stronger definition i guess is + + + align:start position:0% +like a stronger definition i guess is +another way of putting it it intensifies + + align:start position:0% +another way of putting it it intensifies + + + align:start position:0% +another way of putting it it intensifies +the center surround antagonist makes it + + align:start position:0% +the center surround antagonist makes it + + + align:start position:0% +the center surround antagonist makes it +even more pronounced and it also adds + + align:start position:0% +even more pronounced and it also adds + + + align:start position:0% +even more pronounced and it also adds +those temporal properties that we saw + + align:start position:0% +those temporal properties that we saw + + + align:start position:0% +those temporal properties that we saw +so oh + + align:start position:0% +so oh + + + align:start position:0% +so oh +and these cascades are referred to often + + align:start position:0% +and these cascades are referred to often + + + align:start position:0% +and these cascades are referred to often +as this this area here + + align:start position:0% +as this this area here + + + align:start position:0% +as this this area here +is the outer plexiform layer outer + + align:start position:0% +is the outer plexiform layer outer + + + align:start position:0% +is the outer plexiform layer outer +meaning closer to the light sensing and + + align:start position:0% +meaning closer to the light sensing and + + + align:start position:0% +meaning closer to the light sensing and +the inner plex formula here is this + + align:start position:0% +the inner plex formula here is this + + + align:start position:0% +the inner plex formula here is this +inner uh closer to the ganglion cells so + + align:start position:0% +inner uh closer to the ganglion cells so + + + align:start position:0% +inner uh closer to the ganglion cells so +you can the retina is actually separated + + align:start position:0% +you can the retina is actually separated + + + align:start position:0% +you can the retina is actually separated +that way and the natural question is + + align:start position:0% +that way and the natural question is + + + align:start position:0% +that way and the natural question is +well where do the bipolar cells fall + + align:start position:0% +well where do the bipolar cells fall + + + align:start position:0% +well where do the bipolar cells fall +they're in both + + align:start position:0% +they're in both + + + align:start position:0% +they're in both +so + + align:start position:0% + + + + align:start position:0% + +wow this really flew this time so + + align:start position:0% +wow this really flew this time so + + + align:start position:0% +wow this really flew this time so +this is kind of an interesting analysis + + align:start position:0% +this is kind of an interesting analysis + + + align:start position:0% +this is kind of an interesting analysis +jerry had in here + + align:start position:0% +jerry had in here + + + align:start position:0% +jerry had in here +but the greater the complexity of the + + align:start position:0% +but the greater the complexity of the + + + align:start position:0% +but the greater the complexity of the +ganglion cell responses the greater the + + align:start position:0% +ganglion cell responses the greater the + + + align:start position:0% +ganglion cell responses the greater the +ratio of amicryn cell synapses to + + align:start position:0% +ratio of amicryn cell synapses to + + + align:start position:0% +ratio of amicryn cell synapses to +bipolar cell synapses + + align:start position:0% +bipolar cell synapses + + + align:start position:0% +bipolar cell synapses +okay well + + align:start position:0% +okay well + + + align:start position:0% +okay well +what would you think i guess you all + + align:start position:0% +what would you think i guess you all + + + align:start position:0% +what would you think i guess you all +have the slide so i can't do this but + + align:start position:0% +have the slide so i can't do this but + + + align:start position:0% +have the slide so i can't do this but +what would you think do you think that + + align:start position:0% +what would you think do you think that + + + align:start position:0% +what would you think do you think that +you or a pigeon has more complex + + align:start position:0% +you or a pigeon has more complex + + + align:start position:0% +you or a pigeon has more complex +ganglion cell responses and hence the + + align:start position:0% +ganglion cell responses and hence the + + + align:start position:0% +ganglion cell responses and hence the +greater this ratio would be greater + + align:start position:0% +greater this ratio would be greater + + + align:start position:0% +greater this ratio would be greater +you or the pigeon + + align:start position:0% +you or the pigeon + + + align:start position:0% +you or the pigeon +come on + + align:start position:0% +come on + + + align:start position:0% +come on +can't bet against yourself + + align:start position:0% +can't bet against yourself + + + align:start position:0% +can't bet against yourself +it's the pigeon + + align:start position:0% +it's the pigeon + + + align:start position:0% +it's the pigeon +the pigeon has + + align:start position:0% +the pigeon has + + + align:start position:0% +the pigeon has +a lot more + + align:start position:0% +a lot more + + + align:start position:0% +a lot more +ten point so this is the ratio again + + align:start position:0% +ten point so this is the ratio again + + + align:start position:0% +ten point so this is the ratio again +of endocrine to bipolar synapses with + + align:start position:0% +of endocrine to bipolar synapses with + + + align:start position:0% +of endocrine to bipolar synapses with +gain cells there's much more that + + align:start position:0% +gain cells there's much more that + + + align:start position:0% +gain cells there's much more that +amicrine which you know that fine they + + align:start position:0% +amicrine which you know that fine they + + + align:start position:0% +amicrine which you know that fine they +intensify the receptive field and the + + align:start position:0% +intensify the receptive field and the + + + align:start position:0% +intensify the receptive field and the +center surround organization and they + + align:start position:0% +center surround organization and they + + + align:start position:0% +center surround organization and they +also add those temporal properties and + + align:start position:0% +also add those temporal properties and + + + align:start position:0% +also add those temporal properties and +well well this doesn't make sense we're + + align:start position:0% +well well this doesn't make sense we're + + + align:start position:0% +well well this doesn't make sense we're +smarter than pigeons we have better + + align:start position:0% +smarter than pigeons we have better + + + align:start position:0% +smarter than pigeons we have better +eyesight than pigeons it's true better + + align:start position:0% +eyesight than pigeons it's true better + + + align:start position:0% +eyesight than pigeons it's true better +eyesight + + align:start position:0% +eyesight + + + align:start position:0% +eyesight +what's up with this + + align:start position:0% +what's up with this + + + align:start position:0% +what's up with this +who's got a hypothesis + + align:start position:0% + + + + align:start position:0% + +that is the right answer speak up what + + align:start position:0% +that is the right answer speak up what + + + align:start position:0% +that is the right answer speak up what +is that + + align:start position:0% +is that + + + align:start position:0% +is that +speak speak out that i don't heard + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% + + + + align:start position:0% + +totally right so i mean pigeons don't + + align:start position:0% +totally right so i mean pigeons don't + + + align:start position:0% +totally right so i mean pigeons don't +have this complex um layering of v1 + + align:start position:0% +have this complex um layering of v1 + + + align:start position:0% +have this complex um layering of v1 +v2v34 and your jerry's going to go more + + align:start position:0% +v2v34 and your jerry's going to go more + + + align:start position:0% +v2v34 and your jerry's going to go more +into cortical vision later but we're + + align:start position:0% +into cortical vision later but we're + + + align:start position:0% +into cortical vision later but we're +going to see that we don't need to do + + align:start position:0% +going to see that we don't need to do + + + align:start position:0% +going to see that we don't need to do +that much in the retina we've got lots + + align:start position:0% +that much in the retina we've got lots + + + align:start position:0% +that much in the retina we've got lots +of other stuff so + + align:start position:0% +of other stuff so + + + align:start position:0% +of other stuff so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +let's try and + + align:start position:0% +let's try and + + + align:start position:0% +let's try and +try and do some of this maybe + + align:start position:0% +try and do some of this maybe + + + align:start position:0% +try and do some of this maybe +yeah i can go a few more minutes right + + align:start position:0% +yeah i can go a few more minutes right + + + align:start position:0% +yeah i can go a few more minutes right +okay so talk about these ganglion cell + + align:start position:0% +okay so talk about these ganglion cell + + + align:start position:0% +okay so talk about these ganglion cell +types + + align:start position:0% +types + + + align:start position:0% +types +and um + + align:start position:0% +and um + + + align:start position:0% +and um +this is just a picture showing a few + + align:start position:0% +this is just a picture showing a few + + + align:start position:0% +this is just a picture showing a few +different types of ganglion cells all i + + align:start position:0% +different types of ganglion cells all i + + + align:start position:0% +different types of ganglion cells all i +want you to take away from this is that + + align:start position:0% +want you to take away from this is that + + + align:start position:0% +want you to take away from this is that +there are many different types and many + + align:start position:0% +there are many different types and many + + + align:start position:0% +there are many different types and many +different dendritic arborizations + + align:start position:0% +different dendritic arborizations + + + align:start position:0% +different dendritic arborizations +normally the bigger ones have bigger + + align:start position:0% +normally the bigger ones have bigger + + + align:start position:0% +normally the bigger ones have bigger +receptive fields smaller ones smaller + + align:start position:0% +receptive fields smaller ones smaller + + + align:start position:0% +receptive fields smaller ones smaller +receptor fields + + align:start position:0% +receptor fields + + + align:start position:0% +receptor fields +and that these cell types um we find + + align:start position:0% +and that these cell types um we find + + + align:start position:0% +and that these cell types um we find +electrophysiological differences between + + align:start position:0% +electrophysiological differences between + + + align:start position:0% +electrophysiological differences between +the different ganglion cell types like + + align:start position:0% +the different ganglion cell types like + + + align:start position:0% +the different ganglion cell types like +say like the membrane resistance + + align:start position:0% +say like the membrane resistance + + + align:start position:0% +say like the membrane resistance +membrane capacitance the the way that + + align:start position:0% +membrane capacitance the the way that + + + align:start position:0% +membrane capacitance the the way that +they fire in response to different kinds + + align:start position:0% +they fire in response to different kinds + + + align:start position:0% +they fire in response to different kinds +of moving stimuli those are + + align:start position:0% +of moving stimuli those are + + + align:start position:0% +of moving stimuli those are +electrophysiological differences and the + + align:start position:0% +electrophysiological differences and the + + + align:start position:0% +electrophysiological differences and the +neat thing is that those correspond to + + align:start position:0% +neat thing is that those correspond to + + + align:start position:0% +neat thing is that those correspond to +the morphological differences morphology + + align:start position:0% +the morphological differences morphology + + + align:start position:0% +the morphological differences morphology +being this kind of stuff how big the + + align:start position:0% +being this kind of stuff how big the + + + align:start position:0% +being this kind of stuff how big the +cell is what does its arbor look like + + align:start position:0% +cell is what does its arbor look like + + + align:start position:0% +cell is what does its arbor look like +so i think jerry will explain probably a + + align:start position:0% +so i think jerry will explain probably a + + + align:start position:0% +so i think jerry will explain probably a +bit more about that but + + align:start position:0% +bit more about that but + + + align:start position:0% +bit more about that but +what i want to focus i guess here on is + + align:start position:0% +what i want to focus i guess here on is + + + align:start position:0% +what i want to focus i guess here on is +that um + + align:start position:0% +that um + + + align:start position:0% +that um +these y cells we're going to talk about + + align:start position:0% +these y cells we're going to talk about + + + align:start position:0% +these y cells we're going to talk about +for a second more + + align:start position:0% +for a second more + + + align:start position:0% +for a second more +and but their their distribution is very + + align:start position:0% +and but their their distribution is very + + + align:start position:0% +and but their their distribution is very +um seems very optimized in the retina + + align:start position:0% +um seems very optimized in the retina + + + align:start position:0% +um seems very optimized in the retina +this is a particular type of retinal + + align:start position:0% +this is a particular type of retinal + + + align:start position:0% +this is a particular type of retinal +ganglion cell and + + align:start position:0% +ganglion cell and + + + align:start position:0% +ganglion cell and +we + + align:start position:0% +we + + + align:start position:0% +we +that they they seem to perfectly cover + + align:start position:0% +that they they seem to perfectly cover + + + align:start position:0% +that they they seem to perfectly cover +the retina and + + align:start position:0% +the retina and + + + align:start position:0% +the retina and +get kind of respect of these boundaries + + align:start position:0% +get kind of respect of these boundaries + + + align:start position:0% +get kind of respect of these boundaries +so this + + align:start position:0% +so this + + + align:start position:0% +so this +without leaving holes which is kind of + + align:start position:0% +without leaving holes which is kind of + + + align:start position:0% +without leaving holes which is kind of +an interesting thing i'll show this in + + align:start position:0% +an interesting thing i'll show this in + + + align:start position:0% +an interesting thing i'll show this in +more detail in a second and this this + + align:start position:0% +more detail in a second and this this + + + align:start position:0% +more detail in a second and this this +appears to rise because of these + + align:start position:0% +appears to rise because of these + + + align:start position:0% +appears to rise because of these +competitive interactions um between the + + align:start position:0% +competitive interactions um between the + + + align:start position:0% +competitive interactions um between the +dendrites as in the developing uh + + align:start position:0% +dendrites as in the developing uh + + + align:start position:0% +dendrites as in the developing uh +animals so + + align:start position:0% +animals so + + + align:start position:0% +animals so +here's the so we're going to focus on + + align:start position:0% +here's the so we're going to focus on + + + align:start position:0% +here's the so we're going to focus on +these y type retinal ganglion cells + + align:start position:0% +these y type retinal ganglion cells + + + align:start position:0% +these y type retinal ganglion cells +there's on cells off cells you guys know + + align:start position:0% +there's on cells off cells you guys know + + + align:start position:0% +there's on cells off cells you guys know +about that right here just pictures of + + align:start position:0% +about that right here just pictures of + + + align:start position:0% +about that right here just pictures of +them so here's a neat experiment that + + align:start position:0% +them so here's a neat experiment that + + + align:start position:0% +them so here's a neat experiment that +was done it's kind of like theoretical + + align:start position:0% +was done it's kind of like theoretical + + + align:start position:0% +was done it's kind of like theoretical +and experimental neuroscience combined + + align:start position:0% +and experimental neuroscience combined + + + align:start position:0% +and experimental neuroscience combined +so they looked at the fields here they + + align:start position:0% +so they looked at the fields here they + + + align:start position:0% +so they looked at the fields here they +look at these the dendritic fields here + + align:start position:0% +look at these the dendritic fields here + + + align:start position:0% +look at these the dendritic fields here +and they just drew + + align:start position:0% +and they just drew + + + align:start position:0% +and they just drew +lines that would just you know link up + + align:start position:0% +lines that would just you know link up + + + align:start position:0% +lines that would just you know link up +all the dendrites so i hear the lines + + align:start position:0% +all the dendrites so i hear the lines + + + align:start position:0% +all the dendrites so i hear the lines +drawn in you can see there's like this + + align:start position:0% +drawn in you can see there's like this + + + align:start position:0% +drawn in you can see there's like this +little overlap good coverage of of the + + align:start position:0% +little overlap good coverage of of the + + + align:start position:0% +little overlap good coverage of of the +space by these dendritic arbors + + align:start position:0% +space by these dendritic arbors + + + align:start position:0% +space by these dendritic arbors +now what if they just took some kind of + + align:start position:0% +now what if they just took some kind of + + + align:start position:0% +now what if they just took some kind of +i don't know why they chose a particular + + align:start position:0% +i don't know why they chose a particular + + + align:start position:0% +i don't know why they chose a particular +radius but they say they put a dot where + + align:start position:0% +radius but they say they put a dot where + + + align:start position:0% +radius but they say they put a dot where +every cell body center was and then they + + align:start position:0% +every cell body center was and then they + + + align:start position:0% +every cell body center was and then they +took some radius out from that and just + + align:start position:0% +took some radius out from that and just + + + align:start position:0% +took some radius out from that and just +drew circles around well you get these + + align:start position:0% +drew circles around well you get these + + + align:start position:0% +drew circles around well you get these +gaps in here + + align:start position:0% +gaps in here + + + align:start position:0% +gaps in here +now say you took this right here and you + + align:start position:0% +now say you took this right here and you + + + align:start position:0% +now say you took this right here and you +just took the mirror image let's just + + align:start position:0% +just took the mirror image let's just + + + align:start position:0% +just took the mirror image let's just +say so we can keep this way is to keep + + align:start position:0% +say so we can keep this way is to keep + + + align:start position:0% +say so we can keep this way is to keep +the area the same i don't know this + + align:start position:0% +the area the same i don't know this + + + align:start position:0% +the area the same i don't know this +experiment actually + + align:start position:0% +experiment actually + + + align:start position:0% +experiment actually +i don't know if i would quite done this + + align:start position:0% +i don't know if i would quite done this + + + align:start position:0% +i don't know if i would quite done this +way but i think that this is kind of an + + align:start position:0% +way but i think that this is kind of an + + + align:start position:0% +way but i think that this is kind of an +older experiment it's all respected on + + align:start position:0% +older experiment it's all respected on + + + align:start position:0% +older experiment it's all respected on +those terms so here they just flipped + + align:start position:0% +those terms so here they just flipped + + + align:start position:0% +those terms so here they just flipped +along an axis + + align:start position:0% +along an axis + + + align:start position:0% +along an axis +like an axis like this they just went + + align:start position:0% +like an axis like this they just went + + + align:start position:0% +like an axis like this they just went +flipped around the dendritic fields you + + align:start position:0% +flipped around the dendritic fields you + + + align:start position:0% +flipped around the dendritic fields you +get these huge gaps so they take this to + + align:start position:0% +get these huge gaps so they take this to + + + align:start position:0% +get these huge gaps so they take this to +be evidence for competition between the + + align:start position:0% +be evidence for competition between the + + + align:start position:0% +be evidence for competition between the +dendrites that they had to um that there + + align:start position:0% +dendrites that they had to um that there + + + align:start position:0% +dendrites that they had to um that there +are these actual interactions where they + + align:start position:0% +are these actual interactions where they + + + align:start position:0% +are these actual interactions where they +they they went you know they were going + + align:start position:0% +they they went you know they were going + + + align:start position:0% +they they went you know they were going +out and then they met some neighbor you + + align:start position:0% +out and then they met some neighbor you + + + align:start position:0% +out and then they met some neighbor you +know from dendrites to mosul and said + + align:start position:0% +know from dendrites to mosul and said + + + align:start position:0% +know from dendrites to mosul and said +hey oh it's your space okay and they + + align:start position:0% +hey oh it's your space okay and they + + + align:start position:0% +hey oh it's your space okay and they +just backed off and they each kind of + + align:start position:0% +just backed off and they each kind of + + + align:start position:0% +just backed off and they each kind of +agreed to only um take up a certain + + align:start position:0% +agreed to only um take up a certain + + + align:start position:0% +agreed to only um take up a certain +amount of areas so that there's this + + align:start position:0% +amount of areas so that there's this + + + align:start position:0% +amount of areas so that there's this +actual cell to cell communication during + + align:start position:0% +actual cell to cell communication during + + + align:start position:0% +actual cell to cell communication during +the development process which is really + + align:start position:0% +the development process which is really + + + align:start position:0% +the development process which is really +interesting that random receptive fields + + align:start position:0% +interesting that random receptive fields + + + align:start position:0% +interesting that random receptive fields +placed around the cell body do not work + + align:start position:0% +placed around the cell body do not work + + + align:start position:0% +placed around the cell body do not work +these dendrites as crazy as this looks + + align:start position:0% +these dendrites as crazy as this looks + + + align:start position:0% +these dendrites as crazy as this looks +this is very very intentionally made for + + align:start position:0% +this is very very intentionally made for + + + align:start position:0% +this is very very intentionally made for +high coverage and no no spots no gaps in + + align:start position:0% +high coverage and no no spots no gaps in + + + align:start position:0% +high coverage and no no spots no gaps in +the coverage + + align:start position:0% +the coverage + + + align:start position:0% +the coverage +um + + align:start position:0% +um + + + align:start position:0% +um +let's do it let's do it okay so in the + + align:start position:0% +let's do it let's do it okay so in the + + + align:start position:0% +let's do it let's do it okay so in the +monkey and in us there are these two + + align:start position:0% +monkey and in us there are these two + + + align:start position:0% +monkey and in us there are these two +types of retinal ganglion cells parasol + + align:start position:0% +types of retinal ganglion cells parasol + + + align:start position:0% +types of retinal ganglion cells parasol +cells and cells + + align:start position:0% +cells and cells + + + align:start position:0% +cells and cells +i love that parasol cells are like an + + align:start position:0% +i love that parasol cells are like an + + + align:start position:0% +i love that parasol cells are like an +umbrella they have a big arbor they're + + align:start position:0% +umbrella they have a big arbor they're + + + align:start position:0% +umbrella they have a big arbor they're +huge the cells are like midgets + + align:start position:0% +huge the cells are like midgets + + + align:start position:0% +huge the cells are like midgets +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +the cells + + align:start position:0% +the cells + + + align:start position:0% +the cells +make up most of the retinal ganglion + + align:start position:0% +make up most of the retinal ganglion + + + align:start position:0% +make up most of the retinal ganglion +cells and so does does this sound + + align:start position:0% +cells and so does does this sound + + + align:start position:0% +cells and so does does this sound +familiar i think we talked about this + + align:start position:0% +familiar i think we talked about this + + + align:start position:0% +familiar i think we talked about this +before + + align:start position:0% +before + + + align:start position:0% +before +from the retina + + align:start position:0% +from the retina + + + align:start position:0% +from the retina +the optometer goes back to the lateral + + align:start position:0% +the optometer goes back to the lateral + + + align:start position:0% +the optometer goes back to the lateral +geniculate body in the thalamus i guess + + align:start position:0% +geniculate body in the thalamus i guess + + + align:start position:0% +geniculate body in the thalamus i guess +there right okay and then goes to visual + + align:start position:0% +there right okay and then goes to visual + + + align:start position:0% +there right okay and then goes to visual +cortex occipital right visual cortex so + + align:start position:0% +cortex occipital right visual cortex so + + + align:start position:0% +cortex occipital right visual cortex so +when i say lgn it's the lateral + + align:start position:0% +when i say lgn it's the lateral + + + align:start position:0% +when i say lgn it's the lateral +geniculate nucleus of the thalamus + + align:start position:0% +geniculate nucleus of the thalamus + + + align:start position:0% +geniculate nucleus of the thalamus +that's that's the next waste station + + align:start position:0% +that's that's the next waste station + + + align:start position:0% +that's that's the next waste station +that's where the synapse from the the + + align:start position:0% +that's where the synapse from the the + + + align:start position:0% +that's where the synapse from the the +rental ganglion cell synapse there and + + align:start position:0% +rental ganglion cell synapse there and + + + align:start position:0% +rental ganglion cell synapse there and +then those guys go back to v1 primary + + align:start position:0% +then those guys go back to v1 primary + + + align:start position:0% +then those guys go back to v1 primary +visual cortex and 80 of the cells these + + align:start position:0% +visual cortex and 80 of the cells these + + + align:start position:0% +visual cortex and 80 of the cells these + cells why because they're small + + align:start position:0% + cells why because they're small + + + align:start position:0% + cells why because they're small +and they have fine receptive fields fine + + align:start position:0% +and they have fine receptive fields fine + + + align:start position:0% +and they have fine receptive fields fine +color acuity here the parasol cells can + + align:start position:0% +color acuity here the parasol cells can + + + align:start position:0% +color acuity here the parasol cells can +convey information about movement + + align:start position:0% +convey information about movement + + + align:start position:0% +convey information about movement +because they've got huge receptive + + align:start position:0% +because they've got huge receptive + + + align:start position:0% +because they've got huge receptive +fields so when i go like this and the + + align:start position:0% +fields so when i go like this and the + + + align:start position:0% +fields so when i go like this and the +whole world is spinning here + + align:start position:0% +whole world is spinning here + + + align:start position:0% +whole world is spinning here +the paracel cells which have huge arbors + + align:start position:0% +the paracel cells which have huge arbors + + + align:start position:0% +the paracel cells which have huge arbors +can can track movement over larger + + align:start position:0% +can can track movement over larger + + + align:start position:0% +can can track movement over larger +distances in the cells but of + + align:start position:0% +distances in the cells but of + + + align:start position:0% +distances in the cells but of +course this fine acuity vision that + + align:start position:0% +course this fine acuity vision that + + + align:start position:0% +course this fine acuity vision that +seems to be dominant 80 + + align:start position:0% +seems to be dominant 80 + + + align:start position:0% +seems to be dominant 80 +of ganglion cells and lgn this is to + + align:start position:0% +of ganglion cells and lgn this is to + + + align:start position:0% +of ganglion cells and lgn this is to +show you some differences + + align:start position:0% +show you some differences + + + align:start position:0% +show you some differences +uh cells are small paracel cells + + align:start position:0% +uh cells are small paracel cells + + + align:start position:0% +uh cells are small paracel cells +are big i think that's the takeaway + + align:start position:0% +are big i think that's the takeaway + + + align:start position:0% +are big i think that's the takeaway +point right here on + + align:start position:0% +point right here on + + + align:start position:0% +point right here on +um + + align:start position:0% +um + + + align:start position:0% +um +what does this thing oh this is just + + align:start position:0% +what does this thing oh this is just + + + align:start position:0% +what does this thing oh this is just +showing from the fovea to the periphery + + align:start position:0% +showing from the fovea to the periphery + + + align:start position:0% +showing from the fovea to the periphery +uh the diameter of the dendritic fields + + align:start position:0% +uh the diameter of the dendritic fields + + + align:start position:0% +uh the diameter of the dendritic fields +and this shows that + + align:start position:0% +and this shows that + + + align:start position:0% +and this shows that +consistently the parasol cells are + + align:start position:0% +consistently the parasol cells are + + + align:start position:0% +consistently the parasol cells are +bigger they're about three times bigger + + align:start position:0% +bigger they're about three times bigger + + + align:start position:0% +bigger they're about three times bigger +as what this caption i think says + + align:start position:0% +as what this caption i think says + + + align:start position:0% +as what this caption i think says +um though you can see that in the + + align:start position:0% +um though you can see that in the + + + align:start position:0% +um though you can see that in the +periphery everybody gets bigger because + + align:start position:0% +periphery everybody gets bigger because + + + align:start position:0% +periphery everybody gets bigger because +phobia is where we want to be small when + + align:start position:0% +phobia is where we want to be small when + + + align:start position:0% +phobia is where we want to be small when +i have high visual acuity um because + + align:start position:0% +i have high visual acuity um because + + + align:start position:0% +i have high visual acuity um because +why that well because the photoreceptors + + align:start position:0% +why that well because the photoreceptors + + + align:start position:0% +why that well because the photoreceptors +in that area are more tightly + + align:start position:0% +in that area are more tightly + + + align:start position:0% +in that area are more tightly +concentrated just cones really tightly + + align:start position:0% +concentrated just cones really tightly + + + align:start position:0% +concentrated just cones really tightly +packed + + align:start position:0% +packed + + + align:start position:0% +packed +many more cones in the phobia than in + + align:start position:0% +many more cones in the phobia than in + + + align:start position:0% +many more cones in the phobia than in +the peripheries + + align:start position:0% +the peripheries + + + align:start position:0% +the peripheries +and the phobia is a much smaller area + + align:start position:0% +and the phobia is a much smaller area + + + align:start position:0% +and the phobia is a much smaller area +too + + align:start position:0% +too + + + align:start position:0% +too +this is just showing you again paracel + + align:start position:0% +this is just showing you again paracel + + + align:start position:0% +this is just showing you again paracel +system huge lots of photoreceptors + + align:start position:0% +system huge lots of photoreceptors + + + align:start position:0% +system huge lots of photoreceptors + system each ganglion cell has + + align:start position:0% + system each ganglion cell has + + + align:start position:0% + system each ganglion cell has +like a small number of inputs basically + + align:start position:0% +like a small number of inputs basically + + + align:start position:0% +like a small number of inputs basically +that's it i'm going to stop there \ No newline at end of file diff --git a/kZrb6ZIwJqg.txt b/kZrb6ZIwJqg.txt new file mode 100644 index 0000000000000000000000000000000000000000..e793987004b2f8098d9d23c5eba00c1a3dacae7f --- /dev/null +++ b/kZrb6ZIwJqg.txt @@ -0,0 +1,12963 @@ +align:start position:0% + +so today I'm going to talk about + + align:start position:0% +so today I'm going to talk about + + + align:start position:0% +so today I'm going to talk about +precision medicine and we don't really + + align:start position:0% +precision medicine and we don't really + + + align:start position:0% +precision medicine and we don't really +have a very precise idea of what + + align:start position:0% +have a very precise idea of what + + + align:start position:0% +have a very precise idea of what +precision medicine is and so I'm gonna + + align:start position:0% +precision medicine is and so I'm gonna + + + align:start position:0% +precision medicine is and so I'm gonna +start by talking about that a little bit + + align:start position:0% +start by talking about that a little bit + + + align:start position:0% +start by talking about that a little bit +David talked about disease subtyping and + + align:start position:0% +David talked about disease subtyping and + + + align:start position:0% +David talked about disease subtyping and +if you think about how how do you figure + + align:start position:0% +if you think about how how do you figure + + + align:start position:0% +if you think about how how do you figure +out what are the subtypes of a disease + + align:start position:0% +out what are the subtypes of a disease + + + align:start position:0% +out what are the subtypes of a disease +you do it by some kind of clustering on + + align:start position:0% +you do it by some kind of clustering on + + + align:start position:0% +you do it by some kind of clustering on +a bunch of different sorts of data and + + align:start position:0% +a bunch of different sorts of data and + + + align:start position:0% +a bunch of different sorts of data and +so we have data like demographics + + align:start position:0% +so we have data like demographics + + + align:start position:0% +so we have data like demographics +comorbidities vital signs medications + + align:start position:0% +comorbidities vital signs medications + + + align:start position:0% +comorbidities vital signs medications +procedures disease trajectories whatever + + align:start position:0% +procedures disease trajectories whatever + + + align:start position:0% +procedures disease trajectories whatever +those mean image similarities and today + + align:start position:0% +those mean image similarities and today + + + align:start position:0% +those mean image similarities and today +mostly I'm going to focus on genetics + + align:start position:0% +mostly I'm going to focus on genetics + + + align:start position:0% +mostly I'm going to focus on genetics +because this was the great hope of the + + align:start position:0% +because this was the great hope of the + + + align:start position:0% +because this was the great hope of the +human genome project that as we + + align:start position:0% +human genome project that as we + + + align:start position:0% +human genome project that as we +understood more about the genetic + + align:start position:0% +understood more about the genetic + + + align:start position:0% +understood more about the genetic +influences on disease it would help us + + align:start position:0% +influences on disease it would help us + + + align:start position:0% +influences on disease it would help us +create precise ways of dealing with + + align:start position:0% +create precise ways of dealing with + + + align:start position:0% +create precise ways of dealing with +various diseases and figuring out the + + align:start position:0% +various diseases and figuring out the + + + align:start position:0% +various diseases and figuring out the +right therapies for them and so on so I + + align:start position:0% +right therapies for them and so on so I + + + align:start position:0% +right therapies for them and so on so I +want to start by reviewing a little bit + + align:start position:0% +want to start by reviewing a little bit + + + align:start position:0% +want to start by reviewing a little bit +a study that was done by the National + + align:start position:0% +a study that was done by the National + + + align:start position:0% +a study that was done by the National +Research Council of the National + + align:start position:0% +Research Council of the National + + + align:start position:0% +Research Council of the National +Academies and it's called toward + + align:start position:0% +Academies and it's called toward + + + align:start position:0% +Academies and it's called toward +precision medicine this was fairly + + align:start position:0% +precision medicine this was fairly + + + align:start position:0% +precision medicine this was fairly +recent 2017 and they have some + + align:start position:0% +recent 2017 and they have some + + + align:start position:0% +recent 2017 and they have some +interesting observations so they start + + align:start position:0% +interesting observations so they start + + + align:start position:0% +interesting observations so they start +off and they say well why is this + + align:start position:0% +off and they say well why is this + + + align:start position:0% +off and they say well why is this +relevant now when it may not have been + + align:start position:0% +relevant now when it may not have been + + + align:start position:0% +relevant now when it may not have been +relevant before and of course the biggie + + align:start position:0% +relevant before and of course the biggie + + + align:start position:0% +relevant before and of course the biggie +is new capabilities to compile molecular + + align:start position:0% +is new capabilities to compile molecular + + + align:start position:0% +is new capabilities to compile molecular +data on patients on a scale that was + + align:start position:0% +data on patients on a scale that was + + + align:start position:0% +data on patients on a scale that was +unimaginable 20 years ago so people + + align:start position:0% +unimaginable 20 years ago so people + + + align:start position:0% +unimaginable 20 years ago so people +estimated that getting the first human + + align:start position:0% +estimated that getting the first human + + + align:start position:0% +estimated that getting the first human +genome cost about three billion dollars + + align:start position:0% +genome cost about three billion dollars + + + align:start position:0% +genome cost about three billion dollars +okay today getting a human genome costs + + align:start position:0% +okay today getting a human genome costs + + + align:start position:0% +okay today getting a human genome costs +less than a thousand dollars I have some + + align:start position:0% +less than a thousand dollars I have some + + + align:start position:0% +less than a thousand dollars I have some +figures later in the in the talk showing + + align:start position:0% +figures later in the in the talk showing + + + align:start position:0% +figures later in the in the talk showing +some of the ads that people are running + + align:start position:0% +some of the ads that people are running + + + align:start position:0% +some of the ads that people are running +increasing success in utilizing + + align:start position:0% +increasing success in utilizing + + + align:start position:0% +increasing success in utilizing +molecular information to improve + + align:start position:0% +molecular information to improve + + + align:start position:0% +molecular information to improve +diagnosis and treatment we'll talk about + + align:start position:0% +diagnosis and treatment we'll talk about + + + align:start position:0% +diagnosis and treatment we'll talk about +some of those advances in AI T so that + + align:start position:0% +some of those advances in AI T so that + + + align:start position:0% +some of those advances in AI T so that +we have bigger capabilities of dealing + + align:start position:0% +we have bigger capabilities of dealing + + + align:start position:0% +we have bigger capabilities of dealing +with so-called Big Data a perfect storm + + align:start position:0% +with so-called Big Data a perfect storm + + + align:start position:0% +with so-called Big Data a perfect storm +among stakeholders that has made them + + align:start position:0% +among stakeholders that has made them + + + align:start position:0% +among stakeholders that has made them +much more receptive to this kind of + + align:start position:0% +much more receptive to this kind of + + + align:start position:0% +much more receptive to this kind of +information so the fact that costs in + + align:start position:0% +information so the fact that costs in + + + align:start position:0% +information so the fact that costs in +the healthcare system in the u.s. keep + + align:start position:0% +the healthcare system in the u.s. keep + + + align:start position:0% +the healthcare system in the u.s. keep +rising and quality doesn't keep rising + + align:start position:0% +rising and quality doesn't keep rising + + + align:start position:0% +rising and quality doesn't keep rising +proportionately makes everybody + + align:start position:0% +proportionately makes everybody + + + align:start position:0% +proportionately makes everybody +desperate to come up with new ways of of + + align:start position:0% +desperate to come up with new ways of of + + + align:start position:0% +desperate to come up with new ways of of +dealing with this problem and so this + + align:start position:0% +dealing with this problem and so this + + + align:start position:0% +dealing with this problem and so this +looks like you know the next great hope + + align:start position:0% +looks like you know the next great hope + + + align:start position:0% +looks like you know the next great hope +for how to do it and shifting public + + align:start position:0% +for how to do it and shifting public + + + align:start position:0% +for how to do it and shifting public +attitudes toward molecular data so if + + align:start position:0% +attitudes toward molecular data so if + + + align:start position:0% +attitudes toward molecular data so if +how many of you have seen the movie + + align:start position:0% +how many of you have seen the movie + + + align:start position:0% +how many of you have seen the movie +Gattaca a few so you know that's a + + align:start position:0% +Gattaca a few so you know that's a + + + align:start position:0% +Gattaca a few so you know that's a +dystopian view of what happens when + + align:start position:0% +dystopian view of what happens when + + + align:start position:0% +dystopian view of what happens when +people are genotyped and can therefore + + align:start position:0% +people are genotyped and can therefore + + + align:start position:0% +people are genotyped and can therefore +be tracked by their genetics and it is + + align:start position:0% +be tracked by their genetics and it is + + + align:start position:0% +be tracked by their genetics and it is +true that there are horror stories that + + align:start position:0% +true that there are horror stories that + + + align:start position:0% +true that there are horror stories that +can happen but nevertheless people seem + + align:start position:0% +can happen but nevertheless people seem + + + align:start position:0% +can happen but nevertheless people seem +to be more relaxed today about allowing + + align:start position:0% +to be more relaxed today about allowing + + + align:start position:0% +to be more relaxed today about allowing +that kind of data to be collected and + + align:start position:0% +that kind of data to be collected and + + + align:start position:0% +that kind of data to be collected and +used because they see the potential + + align:start position:0% +used because they see the potential + + + align:start position:0% +used because they see the potential +benefits outweighing the costs not + + align:start position:0% +benefits outweighing the costs not + + + align:start position:0% +benefits outweighing the costs not +everybody but you know that's continues + + align:start position:0% +everybody but you know that's continues + + + align:start position:0% +everybody but you know that's continues +to be a serious issue so this report + + align:start position:0% +to be a serious issue so this report + + + align:start position:0% +to be a serious issue so this report +goes on and says you know let's think + + align:start position:0% +goes on and says you know let's think + + + align:start position:0% +goes on and says you know let's think +about how to integrate all kinds of + + align:start position:0% +about how to integrate all kinds of + + + align:start position:0% +about how to integrate all kinds of +different data about individuals and + + align:start position:0% +different data about individuals and + + + align:start position:0% +different data about individuals and +they start off and they say you know one + + align:start position:0% +they start off and they say you know one + + + align:start position:0% +they start off and they say you know one +good example of this has been Google + + align:start position:0% +good example of this has been Google + + + align:start position:0% +good example of this has been Google +Maps so Google Maps has a coordinate + + align:start position:0% +Maps so Google Maps has a coordinate + + + align:start position:0% +Maps so Google Maps has a coordinate +system which is basically longitude and + + align:start position:0% +system which is basically longitude and + + + align:start position:0% +system which is basically longitude and +latitude for every point on the earth + + align:start position:0% +latitude for every point on the earth + + + align:start position:0% +latitude for every point on the earth +and they can use that coordinate system + + align:start position:0% +and they can use that coordinate system + + + align:start position:0% +and they can use that coordinate system +in order to layer on top of each other + + align:start position:0% +in order to layer on top of each other + + + align:start position:0% +in order to layer on top of each other +information about postal codes built + + align:start position:0% +information about postal codes built + + + align:start position:0% +information about postal codes built +structure census tracts land use + + align:start position:0% +structure census tracts land use + + + align:start position:0% +structure census tracts land use +transportation everything okay and they + + align:start position:0% +transportation everything okay and they + + + align:start position:0% +transportation everything okay and they +said wow this is really cool if only we + + align:start position:0% +said wow this is really cool if only we + + + align:start position:0% +said wow this is really cool if only we +could do this in healthcare and so their + + align:start position:0% +could do this in healthcare and so their + + + align:start position:0% +could do this in healthcare and so their +vision is to try to do that in + + align:start position:0% +vision is to try to do that in + + + align:start position:0% +vision is to try to do that in +healthcare by saying well what + + align:start position:0% +healthcare by saying well what + + + align:start position:0% +healthcare by saying well what +corresponds to latitude and longitude is + + align:start position:0% +corresponds to latitude and longitude is + + + align:start position:0% +corresponds to latitude and longitude is +individual patients and these individual + + align:start position:0% +individual patients and these individual + + + align:start position:0% +individual patients and these individual +patients have various kinds of data + + align:start position:0% +patients have various kinds of data + + + align:start position:0% +patients have various kinds of data +about + + align:start position:0% +about + + + align:start position:0% +about +including their microbiome their + + align:start position:0% +including their microbiome their + + + align:start position:0% +including their microbiome their +epigenome their genome clinical signs + + align:start position:0% +epigenome their genome clinical signs + + + align:start position:0% +epigenome their genome clinical signs +and symptoms the expose on what are they + + align:start position:0% +and symptoms the expose on what are they + + + align:start position:0% +and symptoms the expose on what are they +exposed to and so there's been a real + + align:start position:0% +exposed to and so there's been a real + + + align:start position:0% +exposed to and so there's been a real +attempt to go out and create large + + align:start position:0% +attempt to go out and create large + + + align:start position:0% +attempt to go out and create large +collections of data that bring together + + align:start position:0% +collections of data that bring together + + + align:start position:0% +collections of data that bring together +all of this kind of information one of + + align:start position:0% +all of this kind of information one of + + + align:start position:0% +all of this kind of information one of +those that is notable is the Department + + align:start position:0% +those that is notable is the Department + + + align:start position:0% +those that is notable is the Department +of Health well NIH basically started a + + align:start position:0% +of Health well NIH basically started a + + + align:start position:0% +of Health well NIH basically started a +project about a year and a half ago + + align:start position:0% +project about a year and a half ago + + + align:start position:0% +project about a year and a half ago +called all of us sounds sort of menacing + + align:start position:0% +called all of us sounds sort of menacing + + + align:start position:0% +called all of us sounds sort of menacing +but it it's really a million of us and + + align:start position:0% +but it it's really a million of us and + + + align:start position:0% +but it it's really a million of us and +they have asked institutions around the + + align:start position:0% +they have asked institutions around the + + + align:start position:0% +they have asked institutions around the +United States to get volunteers to + + align:start position:0% +United States to get volunteers to + + + align:start position:0% +United States to get volunteers to +volunteer to provide their genetic + + align:start position:0% +volunteer to provide their genetic + + + align:start position:0% +volunteer to provide their genetic +information their clinical data where + + align:start position:0% +information their clinical data where + + + align:start position:0% +information their clinical data where +they live where they commute things like + + align:start position:0% +they live where they commute things like + + + align:start position:0% +they live where they commute things like +that so that they can get environmental + + align:start position:0% +that so that they can get environmental + + + align:start position:0% +that so that they can get environmental +data about them and then it's meant to + + align:start position:0% +data about them and then it's meant to + + + align:start position:0% +data about them and then it's meant to +be an ongoing collection of data about a + + align:start position:0% +be an ongoing collection of data about a + + + align:start position:0% +be an ongoing collection of data about a +million people who are supposed to be a + + align:start position:0% +million people who are supposed to be a + + + align:start position:0% +million people who are supposed to be a +representative sample of the United + + align:start position:0% +representative sample of the United + + + align:start position:0% +representative sample of the United +States so you'll see in some of the + + align:start position:0% +States so you'll see in some of the + + + align:start position:0% +States so you'll see in some of the +projects I talk about later today that + + align:start position:0% +projects I talk about later today that + + + align:start position:0% +projects I talk about later today that +many of the studies have been done in + + align:start position:0% +many of the studies have been done in + + + align:start position:0% +many of the studies have been done in +populations of European ancestry and so + + align:start position:0% +populations of European ancestry and so + + + align:start position:0% +populations of European ancestry and so +they may not apply to people of other + + align:start position:0% +they may not apply to people of other + + + align:start position:0% +they may not apply to people of other +ethnicities this is attempting to sample + + align:start position:0% +ethnicities this is attempting to sample + + + align:start position:0% +ethnicities this is attempting to sample +accurately so that the fraction of + + align:start position:0% +accurately so that the fraction of + + + align:start position:0% +accurately so that the fraction of +African Americans and Asians and + + align:start position:0% +African Americans and Asians and + + + align:start position:0% +African Americans and Asians and +Hispanics and so on corresponds to the + + align:start position:0% +Hispanics and so on corresponds to the + + + align:start position:0% +Hispanics and so on corresponds to the +sample in the United States population + + align:start position:0% +sample in the United States population + + + align:start position:0% +sample in the United States population +there's a long history how many of you + + align:start position:0% +there's a long history how many of you + + + align:start position:0% +there's a long history how many of you +have heard of the Framingham Heart Study + + align:start position:0% +have heard of the Framingham Heart Study + + + align:start position:0% +have heard of the Framingham Heart Study +a lot of people so Framingham in the + + align:start position:0% +a lot of people so Framingham in the + + + align:start position:0% +a lot of people so Framingham in the +1940s agreed to become the subject of a + + align:start position:0% +1940s agreed to become the subject of a + + + align:start position:0% +1940s agreed to become the subject of a +long term experiment I think it's now + + align:start position:0% +long term experiment I think it's now + + + align:start position:0% +long term experiment I think it's now +run by Boston University where every + + align:start position:0% +run by Boston University where every + + + align:start position:0% +run by Boston University where every +year or two they go out and they survey + + align:start position:0% +year or two they go out and they survey + + + align:start position:0% +year or two they go out and they survey +I can't remember the number of people + + align:start position:0% +I can't remember the number of people + + + align:start position:0% +I can't remember the number of people +that something started of something like + + align:start position:0% +that something started of something like + + + align:start position:0% +that something started of something like +50,000 people about their habits and + + align:start position:0% +50,000 people about their habits and + + + align:start position:0% +50,000 people about their habits and +whether they smoked and what their + + align:start position:0% +whether they smoked and what their + + + align:start position:0% +whether they smoked and what their +weight and height is and + + align:start position:0% +weight and height is and + + + align:start position:0% +weight and height is and +any clinical problems they've had + + align:start position:0% +any clinical problems they've had + + + align:start position:0% +any clinical problems they've had +surgical procedures etc and they've been + + align:start position:0% +surgical procedures etc and they've been + + + align:start position:0% +surgical procedures etc and they've been +collecting that database now over + + align:start position:0% +collecting that database now over + + + align:start position:0% +collecting that database now over +several generations of people that + + align:start position:0% +several generations of people that + + + align:start position:0% +several generations of people that +descend from those and they've started + + align:start position:0% +descend from those and they've started + + + align:start position:0% +descend from those and they've started +collecting genetic data as well so all + + align:start position:0% +collecting genetic data as well so all + + + align:start position:0% +collecting genetic data as well so all +of us is really doing this on a very + + align:start position:0% +of us is really doing this on a very + + + align:start position:0% +of us is really doing this on a very +large scale now the vision of these of + + align:start position:0% +large scale now the vision of these of + + + align:start position:0% +large scale now the vision of these of +this study was to say that we're going + + align:start position:0% +this study was to say that we're going + + + align:start position:0% +this study was to say that we're going +to build this information Commons which + + align:start position:0% +to build this information Commons which + + + align:start position:0% +to build this information Commons which +collects all this kind of information + + align:start position:0% +collects all this kind of information + + + align:start position:0% +collects all this kind of information +and then we're going to develop + + align:start position:0% +and then we're going to develop + + + align:start position:0% +and then we're going to develop +knowledge from that information or from + + align:start position:0% +knowledge from that information or from + + + align:start position:0% +knowledge from that information or from +that data and that knowledge will become + + align:start position:0% +that data and that knowledge will become + + + align:start position:0% +that data and that knowledge will become +the substrate on which biomedical + + align:start position:0% +the substrate on which biomedical + + + align:start position:0% +the substrate on which biomedical +research can rest so if we find + + align:start position:0% +research can rest so if we find + + + align:start position:0% +research can rest so if we find +significant associations then that + + align:start position:0% +significant associations then that + + + align:start position:0% +significant associations then that +suggests that one should do studies + + align:start position:0% +suggests that one should do studies + + + align:start position:0% +suggests that one should do studies +which will not necessarily be answered + + align:start position:0% +which will not necessarily be answered + + + align:start position:0% +which will not necessarily be answered +by the data that they've collected you + + align:start position:0% +by the data that they've collected you + + + align:start position:0% +by the data that they've collected you +may have to grow knockout mice or + + align:start position:0% +may have to grow knockout mice or + + + align:start position:0% +may have to grow knockout mice or +something in order to test whether an + + align:start position:0% +something in order to test whether an + + + align:start position:0% +something in order to test whether an +idea really works but this is a way of + + align:start position:0% +idea really works but this is a way of + + + align:start position:0% +idea really works but this is a way of +integrating all of that type of + + align:start position:0% +integrating all of that type of + + + align:start position:0% +integrating all of that type of +information and of course it can affect + + align:start position:0% +information and of course it can affect + + + align:start position:0% +information and of course it can affect +diagnosis treatment and health outcomes + + align:start position:0% +diagnosis treatment and health outcomes + + + align:start position:0% +diagnosis treatment and health outcomes +which are the holy grail for what you'd + + align:start position:0% +which are the holy grail for what you'd + + + align:start position:0% +which are the holy grail for what you'd +like to do in medicine now here's a + + align:start position:0% +like to do in medicine now here's a + + + align:start position:0% +like to do in medicine now here's a +here's an interesting problem so the + + align:start position:0% +here's an interesting problem so the + + + align:start position:0% +here's an interesting problem so the +focus notice was on taxonomy so Sam + + align:start position:0% +focus notice was on taxonomy so Sam + + + align:start position:0% +focus notice was on taxonomy so Sam +Johnson was a very famous 17th century + + align:start position:0% +Johnson was a very famous 17th century + + + align:start position:0% +Johnson was a very famous 17th century +British writer and he built + + align:start position:0% +British writer and he built + + + align:start position:0% +British writer and he built +encyclopedias and dictionaries and was a + + align:start position:0% +encyclopedias and dictionaries and was a + + + align:start position:0% +encyclopedias and dictionaries and was a +poet and a reviewer and a commentator + + align:start position:0% +poet and a reviewer and a commentator + + + align:start position:0% +poet and a reviewer and a commentator +and did all kinds of fancy things and + + align:start position:0% +and did all kinds of fancy things and + + + align:start position:0% +and did all kinds of fancy things and +one of his quotes as my diseases are an + + align:start position:0% +one of his quotes as my diseases are an + + + align:start position:0% +one of his quotes as my diseases are an +asthma and a dropsy and what is less + + align:start position:0% +asthma and a dropsy and what is less + + + align:start position:0% +asthma and a dropsy and what is less +curable 75 years old so that he was + + align:start position:0% +curable 75 years old so that he was + + + align:start position:0% +curable 75 years old so that he was +funny too now if you look up drop see in + + align:start position:0% +funny too now if you look up drop see in + + + align:start position:0% +funny too now if you look up drop see in +a dictionary + + align:start position:0% +a dictionary + + + align:start position:0% +a dictionary +how many of you have heard of dropsy a + + align:start position:0% +how many of you have heard of dropsy a + + + align:start position:0% +how many of you have heard of dropsy a +couple so how did you hear of it + + align:start position:0% + + + + align:start position:0% + +sorry from a novel yeah yeah I mean I + + align:start position:0% +sorry from a novel yeah yeah I mean I + + + align:start position:0% +sorry from a novel yeah yeah I mean I +learned about it by watching Masterpiece + + align:start position:0% +learned about it by watching Masterpiece + + + align:start position:0% +learned about it by watching Masterpiece +Theatre with 18th cent or 19th century + + align:start position:0% +Theatre with 18th cent or 19th century + + + align:start position:0% +Theatre with 18th cent or 19th century +people were you know the grandmother + + align:start position:0% +people were you know the grandmother + + + align:start position:0% +people were you know the grandmother +would take to her bed with the dropsy + + align:start position:0% +would take to her bed with the dropsy + + + align:start position:0% +would take to her bed with the dropsy +and it didn't turn out well typically + + align:start position:0% +and it didn't turn out well typically + + + align:start position:0% +and it didn't turn out well typically +but it took a long time for those people + + align:start position:0% +but it took a long time for those people + + + align:start position:0% +but it took a long time for those people +to die so dropsy is water sickness + + align:start position:0% +to die so dropsy is water sickness + + + align:start position:0% +to die so dropsy is water sickness +swelling edema etc it's actually not a + + align:start position:0% +swelling edema etc it's actually not a + + + align:start position:0% +swelling edema etc it's actually not a +disease it's a symptom of a whole bunch + + align:start position:0% +disease it's a symptom of a whole bunch + + + align:start position:0% +disease it's a symptom of a whole bunch +of diseases so it could be pulmonary + + align:start position:0% +of diseases so it could be pulmonary + + + align:start position:0% +of diseases so it could be pulmonary +disease heart failure kidney disease etc + + align:start position:0% +disease heart failure kidney disease etc + + + align:start position:0% +disease heart failure kidney disease etc +and it's interesting I look back on this + + align:start position:0% +and it's interesting I look back on this + + + align:start position:0% +and it's interesting I look back on this +I couldn't find that for putting + + align:start position:0% +I couldn't find that for putting + + + align:start position:0% +I couldn't find that for putting +together this lecture but at one point I + + align:start position:0% +together this lecture but at one point I + + + align:start position:0% +together this lecture but at one point I +did discover that the last time dropsy + + align:start position:0% +did discover that the last time dropsy + + + align:start position:0% +did discover that the last time dropsy +was listed as the cause of death of a + + align:start position:0% +was listed as the cause of death of a + + + align:start position:0% +was listed as the cause of death of a +patient in the United States was in 1949 + + align:start position:0% +patient in the United States was in 1949 + + + align:start position:0% +patient in the United States was in 1949 +so since then it's disappeared as a + + align:start position:0% +so since then it's disappeared as a + + + align:start position:0% +so since then it's disappeared as a +disease from the taxonomy and if you + + align:start position:0% +disease from the taxonomy and if you + + + align:start position:0% +disease from the taxonomy and if you +talk to pulmonary people they suspect + + align:start position:0% +talk to pulmonary people they suspect + + + align:start position:0% +talk to pulmonary people they suspect +that asthma which is still a disease in + + align:start position:0% +that asthma which is still a disease in + + + align:start position:0% +that asthma which is still a disease in +our current lexicon may be very much + + align:start position:0% +our current lexicon may be very much + + + align:start position:0% +our current lexicon may be very much +like dropsy it's not a disease it's a + + align:start position:0% +like dropsy it's not a disease it's a + + + align:start position:0% +like dropsy it's not a disease it's a +symptom of a whole bunch of underlying + + align:start position:0% +symptom of a whole bunch of underlying + + + align:start position:0% +symptom of a whole bunch of underlying +causes and the idea is that we need to + + align:start position:0% +causes and the idea is that we need to + + + align:start position:0% +causes and the idea is that we need to +get good enough and precise enough and + + align:start position:0% +get good enough and precise enough and + + + align:start position:0% +get good enough and precise enough and +being able to figure out what these are + + align:start position:0% +being able to figure out what these are + + + align:start position:0% +being able to figure out what these are +so I talked to my friends at Kohana at + + align:start position:0% +so I talked to my friends at Kohana at + + + align:start position:0% +so I talked to my friends at Kohana at +at Harvard a few weeks ago when I + + align:start position:0% +at Harvard a few weeks ago when I + + + align:start position:0% +at Harvard a few weeks ago when I +started preparing this lecture and he + + align:start position:0% +started preparing this lecture and he + + + align:start position:0% +started preparing this lecture and he +has the following idea and the example + + align:start position:0% +has the following idea and the example + + + align:start position:0% +has the following idea and the example +I'm going to show you is from him so he + + align:start position:0% +I'm going to show you is from him so he + + + align:start position:0% +I'm going to show you is from him so he +says well look we should have this + + align:start position:0% +says well look we should have this + + + align:start position:0% +says well look we should have this +precision medicine modality space which + + align:start position:0% +precision medicine modality space which + + + align:start position:0% +precision medicine modality space which +is this high dimensional space that + + align:start position:0% +is this high dimensional space that + + + align:start position:0% +is this high dimensional space that +contains all of that information that is + + align:start position:0% +contains all of that information that is + + + align:start position:0% +contains all of that information that is +in the in the NRC report and then what + + align:start position:0% +in the in the NRC report and then what + + + align:start position:0% +in the in the NRC report and then what +we do is in this high dimensional space + + align:start position:0% +we do is in this high dimensional space + + + align:start position:0% +we do is in this high dimensional space +if we're lucky we're going to find + + align:start position:0% +if we're lucky we're going to find + + + align:start position:0% +if we're lucky we're going to find +clusters of data + + align:start position:0% +clusters of data + + + align:start position:0% +clusters of data +so this always happens if you ever take + + align:start position:0% +so this always happens if you ever take + + + align:start position:0% +so this always happens if you ever take +a very high-dimensional data set and put + + align:start position:0% +a very high-dimensional data set and put + + + align:start position:0% +a very high-dimensional data set and put +it into it's very high dimensional + + align:start position:0% +it into it's very high dimensional + + + align:start position:0% +it into it's very high dimensional +representation space it's almost never + + align:start position:0% +representation space it's almost never + + + align:start position:0% +representation space it's almost never +the case that the data is scattered sort + + align:start position:0% +the case that the data is scattered sort + + + align:start position:0% +the case that the data is scattered sort +of uniformly through the space if that + + align:start position:0% +of uniformly through the space if that + + + align:start position:0% +of uniformly through the space if that +were true it wouldn't help us very much + + align:start position:0% +were true it wouldn't help us very much + + + align:start position:0% +were true it wouldn't help us very much +but generally it's not true and what you + + align:start position:0% +but generally it's not true and what you + + + align:start position:0% +but generally it's not true and what you +find is that the data tends to be on + + align:start position:0% +find is that the data tends to be on + + + align:start position:0% +find is that the data tends to be on +lower dimensional manifolds so it's in + + align:start position:0% +lower dimensional manifolds so it's in + + + align:start position:0% +lower dimensional manifolds so it's in +subsets of the space and so a lot of the + + align:start position:0% +subsets of the space and so a lot of the + + + align:start position:0% +subsets of the space and so a lot of the +trick in trying to analyze this kind of + + align:start position:0% +trick in trying to analyze this kind of + + + align:start position:0% +trick in trying to analyze this kind of +data is figuring out what those those + + align:start position:0% +data is figuring out what those those + + + align:start position:0% +data is figuring out what those those +lower dimensional manifolds look like + + align:start position:0% +lower dimensional manifolds look like + + + align:start position:0% +lower dimensional manifolds look like +and often you will find among a very + + align:start position:0% +and often you will find among a very + + + align:start position:0% +and often you will find among a very +large data set a cluster of patients + + align:start position:0% +large data set a cluster of patients + + + align:start position:0% +large data set a cluster of patients +like this and then Zacks approach is to + + align:start position:0% +like this and then Zacks approach is to + + + align:start position:0% +like this and then Zacks approach is to +say well if you're patient it's hard to + + align:start position:0% +say well if you're patient it's hard to + + + align:start position:0% +say well if you're patient it's hard to +represent three dimensions in two but if + + align:start position:0% +represent three dimensions in two but if + + + align:start position:0% +represent three dimensions in two but if +your patient falls somewhere in the + + align:start position:0% +your patient falls somewhere in the + + + align:start position:0% +your patient falls somewhere in the +middle of such a cluster then that + + align:start position:0% +middle of such a cluster then that + + + align:start position:0% +middle of such a cluster then that +probably means that they're kind of + + align:start position:0% +probably means that they're kind of + + + align:start position:0% +probably means that they're kind of +normal for that cluster whereas if they + + align:start position:0% +normal for that cluster whereas if they + + + align:start position:0% +normal for that cluster whereas if they +fall somewhere at the edge of such a + + align:start position:0% +fall somewhere at the edge of such a + + + align:start position:0% +fall somewhere at the edge of such a +cluster that probably means that there's + + align:start position:0% +cluster that probably means that there's + + + align:start position:0% +cluster that probably means that there's +something odd going on that is worth + + align:start position:0% +something odd going on that is worth + + + align:start position:0% +something odd going on that is worth +investigating + + align:start position:0% +investigating + + + align:start position:0% +investigating +because they're unusual so then he gave + + align:start position:0% +because they're unusual so then he gave + + + align:start position:0% +because they're unusual so then he gave +me an example of a patient of his and + + align:start position:0% +me an example of a patient of his and + + + align:start position:0% +me an example of a patient of his and +let me give you a minute to read this + + align:start position:0% + + + + align:start position:0% + +yeah the where does it say armamentarium + + align:start position:0% +yeah the where does it say armamentarium + + + align:start position:0% +yeah the where does it say armamentarium +oh yeah so an armamentarium historically + + align:start position:0% +oh yeah so an armamentarium historically + + + align:start position:0% +oh yeah so an armamentarium historically +is is the set of arms that are available + + align:start position:0% +is is the set of arms that are available + + + align:start position:0% +is is the set of arms that are available +to an army so this is the set of + + align:start position:0% +to an army so this is the set of + + + align:start position:0% +to an army so this is the set of +treatments that are available to a + + align:start position:0% +treatments that are available to a + + + align:start position:0% +treatments that are available to a +doctor well you probably know what + + align:start position:0% +doctor well you probably know what + + + align:start position:0% +doctor well you probably know what +antibiotics are and immunosuppressants + + align:start position:0% +antibiotics are and immunosuppressants + + + align:start position:0% +antibiotics are and immunosuppressants +you've probably heard of anyway it's a + + align:start position:0% +you've probably heard of anyway it's a + + + align:start position:0% +you've probably heard of anyway it's a +bunch of different therapies so this is + + align:start position:0% +bunch of different therapies so this is + + + align:start position:0% +bunch of different therapies so this is +what what's called a sick puppy it's a + + align:start position:0% +what what's called a sick puppy it's a + + + align:start position:0% +what what's called a sick puppy it's a +kid who is not doing well they started + + align:start position:0% +kid who is not doing well they started + + + align:start position:0% +kid who is not doing well they started +life at age three with ulcerative + + align:start position:0% +life at age three with ulcerative + + + align:start position:0% +life at age three with ulcerative +colitis which was well controlled by the + + align:start position:0% +colitis which was well controlled by the + + + align:start position:0% +colitis which was well controlled by the +kinds of medications that they normally + + align:start position:0% +kinds of medications that they normally + + + align:start position:0% +kinds of medications that they normally +give people with that disease and then + + align:start position:0% +give people with that disease and then + + + align:start position:0% +give people with that disease and then +all of a sudden ten years later he + + align:start position:0% +all of a sudden ten years later he + + + align:start position:0% +all of a sudden ten years later he +breaks out with this horrible abdominal + + align:start position:0% +breaks out with this horrible abdominal + + + align:start position:0% +breaks out with this horrible abdominal +pain and diarrhea and and blood in his + + align:start position:0% +pain and diarrhea and and blood in his + + + align:start position:0% +pain and diarrhea and and blood in his +in his stool and they try a bunch of + + align:start position:0% +in his stool and they try a bunch of + + + align:start position:0% +in his stool and they try a bunch of +stuff that they think about of work and + + align:start position:0% +stuff that they think about of work and + + + align:start position:0% +stuff that they think about of work and +it doesn't work okay so the kid was + + align:start position:0% +it doesn't work okay so the kid was + + + align:start position:0% +it doesn't work okay so the kid was +facing some fairly drastic options like + + align:start position:0% +facing some fairly drastic options like + + + align:start position:0% +facing some fairly drastic options like +cutting out the part of his colon that + + align:start position:0% +cutting out the part of his colon that + + + align:start position:0% +cutting out the part of his colon that +was inflamed so your colon is an + + align:start position:0% +was inflamed so your colon is an + + + align:start position:0% +was inflamed so your colon is an +important part of your digestive tract + + align:start position:0% +important part of your digestive tract + + + align:start position:0% +important part of your digestive tract +and so losing it is is not fun and would + + align:start position:0% +and so losing it is is not fun and would + + + align:start position:0% +and so losing it is is not fun and would +have bad consequences for the rest of + + align:start position:0% +have bad consequences for the rest of + + + align:start position:0% +have bad consequences for the rest of +his life but what they did is is they + + align:start position:0% +his life but what they did is is they + + + align:start position:0% +his life but what they did is is they +said well why is he not responding to + + align:start position:0% +said well why is he not responding to + + + align:start position:0% +said well why is he not responding to +any of these therapies and the + + align:start position:0% +any of these therapies and the + + + align:start position:0% +any of these therapies and the +difficulty you can imagine in that cloud + + align:start position:0% +difficulty you can imagine in that cloud + + + align:start position:0% +difficulty you can imagine in that cloud +of points picture is how do you figure + + align:start position:0% +of points picture is how do you figure + + + align:start position:0% +of points picture is how do you figure +out whether the person is an + + align:start position:0% +out whether the person is an + + + align:start position:0% +out whether the person is an +outlier or is in the middle of one of + + align:start position:0% +outlier or is in the middle of one of + + + align:start position:0% +outlier or is in the middle of one of +these clusters when it depends on a lot + + align:start position:0% +these clusters when it depends on a lot + + + align:start position:0% +these clusters when it depends on a lot +of things in this kid's case what it + + align:start position:0% +of things in this kid's case what it + + + align:start position:0% +of things in this kid's case what it +depended on most significantly was the + + align:start position:0% +depended on most significantly was the + + + align:start position:0% +depended on most significantly was the +last six months of his experience were + + align:start position:0% +last six months of his experience were + + + align:start position:0% +last six months of his experience were +before he was doing okay with the + + align:start position:0% +before he was doing okay with the + + + align:start position:0% +before he was doing okay with the +standard treatment so that cloud might + + align:start position:0% +standard treatment so that cloud might + + + align:start position:0% +standard treatment so that cloud might +have represented people with ulcerative + + align:start position:0% +have represented people with ulcerative + + + align:start position:0% +have represented people with ulcerative +colitis who are well controlled by the + + align:start position:0% +colitis who are well controlled by the + + + align:start position:0% +colitis who are well controlled by the +standard treatment and now all of a + + align:start position:0% +standard treatment and now all of a + + + align:start position:0% +standard treatment and now all of a +sudden he becomes an outlier so what + + align:start position:0% +sudden he becomes an outlier so what + + + align:start position:0% +sudden he becomes an outlier so what +happened in this case is they said well + + align:start position:0% +happened in this case is they said well + + + align:start position:0% +happened in this case is they said well +maybe there are different groups of + + align:start position:0% +maybe there are different groups of + + + align:start position:0% +maybe there are different groups of +ulcerative colitis patients so maybe + + align:start position:0% +ulcerative colitis patients so maybe + + + align:start position:0% +ulcerative colitis patients so maybe +there are ones who have a lifelong + + align:start position:0% +there are ones who have a lifelong + + + align:start position:0% +there are ones who have a lifelong +remission after treatment with a + + align:start position:0% +remission after treatment with a + + + align:start position:0% +remission after treatment with a +commonly used monoclonal antibody so + + align:start position:0% +commonly used monoclonal antibody so + + + align:start position:0% +commonly used monoclonal antibody so +that's the cluster the center of the + + align:start position:0% +that's the cluster the center of the + + + align:start position:0% +that's the cluster the center of the +cluster maybe there are people who have + + align:start position:0% +cluster maybe there are people who have + + + align:start position:0% +cluster maybe there are people who have +multi year remission but become + + align:start position:0% +multi year remission but become + + + align:start position:0% +multi year remission but become +refractory to these drugs and after + + align:start position:0% +refractory to these drugs and after + + + align:start position:0% +refractory to these drugs and after +other treatments they have to undergo a + + align:start position:0% +other treatments they have to undergo a + + + align:start position:0% +other treatments they have to undergo a +colectomy so that's the removal of the + + align:start position:0% +colectomy so that's the removal of the + + + align:start position:0% +colectomy so that's the removal of the +colon and then there are people who have + + align:start position:0% +colon and then there are people who have + + + align:start position:0% +colon and then there are people who have +initially a remission but then those + + align:start position:0% +initially a remission but then those + + + align:start position:0% +initially a remission but then those +standard therapy works so that's what + + align:start position:0% +standard therapy works so that's what + + + align:start position:0% +standard therapy works so that's what +this kid is is in this cluster so how do + + align:start position:0% +this kid is is in this cluster so how do + + + align:start position:0% +this kid is is in this cluster so how do +you treat this as a machine learning + + align:start position:0% +you treat this as a machine learning + + + align:start position:0% +you treat this as a machine learning +problem from the point of view of having + + align:start position:0% +problem from the point of view of having + + + align:start position:0% +problem from the point of view of having +lots of data about lots of different + + align:start position:0% +lots of data about lots of different + + + align:start position:0% +lots of data about lots of different +patients and the challenges of course + + align:start position:0% +patients and the challenges of course + + + align:start position:0% +patients and the challenges of course +include things like what's your distance + + align:start position:0% +include things like what's your distance + + + align:start position:0% +include things like what's your distance +function in doing the kind of clustering + + align:start position:0% +function in doing the kind of clustering + + + align:start position:0% +function in doing the kind of clustering +that people typically do how do you + + align:start position:0% +that people typically do how do you + + + align:start position:0% +that people typically do how do you +define what an outlier is because + + align:start position:0% +define what an outlier is because + + + align:start position:0% +define what an outlier is because +there's always a continuum where it just + + align:start position:0% +there's always a continuum where it just + + + align:start position:0% +there's always a continuum where it just +gets more and more diffuse what's the + + align:start position:0% +gets more and more diffuse what's the + + + align:start position:0% +gets more and more diffuse what's the +best representation for time varying + + align:start position:0% +best representation for time varying + + + align:start position:0% +best representation for time varying +data which is critical in this case + + align:start position:0% +data which is critical in this case + + + align:start position:0% +data which is critical in this case +what's the optimal waiting or + + align:start position:0% +what's the optimal waiting or + + + align:start position:0% +what's the optimal waiting or +normalization of dimensions so does + + align:start position:0% +normalization of dimensions so does + + + align:start position:0% +normalization of dimensions so does +every dimension in this very high + + align:start position:0% +every dimension in this very high + + + align:start position:0% +every dimension in this very high +dimensional space count the same or our + + align:start position:0% +dimensional space count the same or our + + + align:start position:0% +dimensional space count the same or our +differences along certain dimensions + + align:start position:0% +differences along certain dimensions + + + align:start position:0% +differences along certain dimensions +more important than those among others + + align:start position:0% +more important than those among others + + + align:start position:0% +more important than those among others +and does that in fact vary from problem + + align:start position:0% +and does that in fact vary from problem + + + align:start position:0% +and does that in fact vary from problem +to problem + + align:start position:0% +to problem + + + align:start position:0% +to problem +the answer is probably yes so how do we + + align:start position:0% +the answer is probably yes so how do we + + + align:start position:0% +the answer is probably yes so how do we +find the neighborhood for the patient + + align:start position:0% +find the neighborhood for the patient + + + align:start position:0% +find the neighborhood for the patient +well I'm going to give you some clues by + + align:start position:0% +well I'm going to give you some clues by + + + align:start position:0% +well I'm going to give you some clues by +starting with a shallow dive into + + align:start position:0% +starting with a shallow dive into + + + align:start position:0% +starting with a shallow dive into +genetics so if you've taken a molecular + + align:start position:0% +genetics so if you've taken a molecular + + + align:start position:0% +genetics so if you've taken a molecular +cell biology class this should not be + + align:start position:0% +cell biology class this should not be + + + align:start position:0% +cell biology class this should not be +news to you and I'm gonna run through it + + align:start position:0% +news to you and I'm gonna run through it + + + align:start position:0% +news to you and I'm gonna run through it +pretty quickly if you haven't then I + + align:start position:0% +pretty quickly if you haven't then I + + + align:start position:0% +pretty quickly if you haven't then I +hope at least you'll pick up some of the + + align:start position:0% +hope at least you'll pick up some of the + + + align:start position:0% +hope at least you'll pick up some of the +vocabulary so a wise biologist said + + align:start position:0% +vocabulary so a wise biologist said + + + align:start position:0% +vocabulary so a wise biologist said +biology is the science of exceptions + + align:start position:0% +biology is the science of exceptions + + + align:start position:0% +biology is the science of exceptions +there are almost no rules about 25 years + + align:start position:0% +there are almost no rules about 25 years + + + align:start position:0% +there are almost no rules about 25 years +ago the biology department here taught a + + align:start position:0% +ago the biology department here taught a + + + align:start position:0% +ago the biology department here taught a +special class for engineering faculty to + + align:start position:0% +special class for engineering faculty to + + + align:start position:0% +special class for engineering faculty to +try to explain to us what they were + + align:start position:0% +try to explain to us what they were + + + align:start position:0% +try to explain to us what they were +teaching in their introductory biology + + align:start position:0% +teaching in their introductory biology + + + align:start position:0% +teaching in their introductory biology +molecular biology classes and I remember + + align:start position:0% +molecular biology classes and I remember + + + align:start position:0% +molecular biology classes and I remember +I was sitting next to Gerry Sussman one + + align:start position:0% +I was sitting next to Gerry Sussman one + + + align:start position:0% +I was sitting next to Gerry Sussman one +of my colleagues and after we heard some + + align:start position:0% +of my colleagues and after we heard some + + + align:start position:0% +of my colleagues and after we heard some +lecture about the 47 ways that some + + align:start position:0% +lecture about the 47 ways that some + + + align:start position:0% +lecture about the 47 ways that some +theory doesn't apply in many many cases + + align:start position:0% +theory doesn't apply in many many cases + + + align:start position:0% +theory doesn't apply in many many cases +Gerry turns to me and he says you know + + align:start position:0% +Gerry turns to me and he says you know + + + align:start position:0% +Gerry turns to me and he says you know +the problem with this field is there are + + align:start position:0% +the problem with this field is there are + + + align:start position:0% +the problem with this field is there are +just too many damned exceptions there + + align:start position:0% +just too many damned exceptions there + + + align:start position:0% +just too many damned exceptions there +there are no theories it's it's all + + align:start position:0% +there are no theories it's it's all + + + align:start position:0% +there are no theories it's it's all +exceptions and so even biologists + + align:start position:0% +exceptions and so even biologists + + + align:start position:0% +exceptions and so even biologists +recognized this now people have observed + + align:start position:0% +recognized this now people have observed + + + align:start position:0% +recognized this now people have observed +for ever since human beings walked the + + align:start position:0% +for ever since human beings walked the + + + align:start position:0% +for ever since human beings walked the +earth that children tend to be similar + + align:start position:0% +earth that children tend to be similar + + + align:start position:0% +earth that children tend to be similar +to their parents in many ways and until + + align:start position:0% +to their parents in many ways and until + + + align:start position:0% +to their parents in many ways and until +Gregor Mendel this was a great mystery + + align:start position:0% +Gregor Mendel this was a great mystery + + + align:start position:0% +Gregor Mendel this was a great mystery +why is it that you were like your + + align:start position:0% +why is it that you were like your + + + align:start position:0% +why is it that you were like your +parents I mean you must have gotten + + align:start position:0% +parents I mean you must have gotten + + + align:start position:0% +parents I mean you must have gotten +something from them that sort of carries + + align:start position:0% +something from them that sort of carries + + + align:start position:0% +something from them that sort of carries +through and makes you similar to them so + + align:start position:0% +through and makes you similar to them so + + + align:start position:0% +through and makes you similar to them so +Mendel had this notion of having + + align:start position:0% +Mendel had this notion of having + + + align:start position:0% +Mendel had this notion of having +discrete factors of inheritance which he + + align:start position:0% +discrete factors of inheritance which he + + + align:start position:0% +discrete factors of inheritance which he +called genes he had no idea what these + + align:start position:0% +called genes he had no idea what these + + + align:start position:0% +called genes he had no idea what these +were but conceptually he knew that they + + align:start position:0% +were but conceptually he knew that they + + + align:start position:0% +were but conceptually he knew that they +must exist and then he did a bunch of + + align:start position:0% +must exist and then he did a bunch of + + + align:start position:0% +must exist and then he did a bunch of +experiments on P plans showing that peas + + align:start position:0% +experiments on P plans showing that peas + + + align:start position:0% +experiments on P plans showing that peas +that are wrinkled tend to have offspring + + align:start position:0% +that are wrinkled tend to have offspring + + + align:start position:0% +that are wrinkled tend to have offspring +peas that are also wrinkled + + align:start position:0% +peas that are also wrinkled + + + align:start position:0% +peas that are also wrinkled +and he worked out the genetics of what + + align:start position:0% +and he worked out the genetics of what + + + align:start position:0% +and he worked out the genetics of what +we now call Mendelian inheritance namely + + align:start position:0% +we now call Mendelian inheritance namely + + + align:start position:0% +we now call Mendelian inheritance namely +dominant versus recessive inheritance + + align:start position:0% +dominant versus recessive inheritance + + + align:start position:0% +dominant versus recessive inheritance +patterns then Johann Mishima sure came + + align:start position:0% +patterns then Johann Mishima sure came + + + align:start position:0% +patterns then Johann Mishima sure came +along some years later and he discovered + + align:start position:0% +along some years later and he discovered + + + align:start position:0% +along some years later and he discovered +a weird thing in cells called nucleon + + align:start position:0% +a weird thing in cells called nucleon + + + align:start position:0% +a weird thing in cells called nucleon +which is now known as DNA and in it but + + align:start position:0% +which is now known as DNA and in it but + + + align:start position:0% +which is now known as DNA and in it but +it wasn't until 1952 that Hershey and + + align:start position:0% +it wasn't until 1952 that Hershey and + + + align:start position:0% +it wasn't until 1952 that Hershey and +chase said hey it's DNA that is carrying + + align:start position:0% +chase said hey it's DNA that is carrying + + + align:start position:0% +chase said hey it's DNA that is carrying +this genetic information from generation + + align:start position:0% +this genetic information from generation + + + align:start position:0% +this genetic information from generation +to generation and then of course Watson + + align:start position:0% +to generation and then of course Watson + + + align:start position:0% +to generation and then of course Watson +Crick and Franklin the following year + + align:start position:0% +Crick and Franklin the following year + + + align:start position:0% +Crick and Franklin the following year +deciphered the structure of DNA that + + align:start position:0% +deciphered the structure of DNA that + + + align:start position:0% +deciphered the structure of DNA that +it's this double helix and then figured + + align:start position:0% +it's this double helix and then figured + + + align:start position:0% +it's this double helix and then figured +out what the mechanism must be that + + align:start position:0% +out what the mechanism must be that + + + align:start position:0% +out what the mechanism must be that +allows DNA to transmit this information + + align:start position:0% +allows DNA to transmit this information + + + align:start position:0% +allows DNA to transmit this information +so you have a double helix you match the + + align:start position:0% +so you have a double helix you match the + + + align:start position:0% +so you have a double helix you match the +four letters ACTG + + align:start position:0% +four letters ACTG + + + align:start position:0% +four letters ACTG +opposite each other and you can + + align:start position:0% +opposite each other and you can + + + align:start position:0% +opposite each other and you can +replicate this DNA by splitting it apart + + align:start position:0% +replicate this DNA by splitting it apart + + + align:start position:0% +replicate this DNA by splitting it apart +and growing another strand that is the + + align:start position:0% +and growing another strand that is the + + + align:start position:0% +and growing another strand that is the +complement of the first one now you have + + align:start position:0% +complement of the first one now you have + + + align:start position:0% +complement of the first one now you have +two and you can have children and pass + + align:start position:0% +two and you can have children and pass + + + align:start position:0% +two and you can have children and pass +on this information to them so that was + + align:start position:0% +on this information to them so that was + + + align:start position:0% +on this information to them so that was +a big deal so a gene is defined by the + + align:start position:0% +a big deal so a gene is defined by the + + + align:start position:0% +a big deal so a gene is defined by the +National Center for Biotechnology + + align:start position:0% +National Center for Biotechnology + + + align:start position:0% +National Center for Biotechnology +information as a fundamental physical + + align:start position:0% +information as a fundamental physical + + + align:start position:0% +information as a fundamental physical +and functional unit of heredity + + align:start position:0% +and functional unit of heredity + + + align:start position:0% +and functional unit of heredity +that's a DNA sequence located on a + + align:start position:0% +that's a DNA sequence located on a + + + align:start position:0% +that's a DNA sequence located on a +specific site on a chromosome which + + align:start position:0% +specific site on a chromosome which + + + align:start position:0% +specific site on a chromosome which +encodes a specific functional product + + align:start position:0% +encodes a specific functional product + + + align:start position:0% +encodes a specific functional product +namely RNA or a protein I'll come back + + align:start position:0% +namely RNA or a protein I'll come back + + + align:start position:0% +namely RNA or a protein I'll come back +to that in a minute remaining mysteries + + align:start position:0% +to that in a minute remaining mysteries + + + align:start position:0% +to that in a minute remaining mysteries +it's still very hard to figure out what + + align:start position:0% +it's still very hard to figure out what + + + align:start position:0% +it's still very hard to figure out what +parts of DNA code genes so you would + + align:start position:0% +parts of DNA code genes so you would + + + align:start position:0% +parts of DNA code genes so you would +think we might have solved this but we + + align:start position:0% +think we might have solved this but we + + + align:start position:0% +think we might have solved this but we +haven't quite and what does the rest + + align:start position:0% +haven't quite and what does the rest + + + align:start position:0% +haven't quite and what does the rest +which is the vast majority of the DNA do + + align:start position:0% +which is the vast majority of the DNA do + + + align:start position:0% +which is the vast majority of the DNA do +if it's not encoding genes + + align:start position:0% +if it's not encoding genes + + + align:start position:0% +if it's not encoding genes +and then how does the folding and the + + align:start position:0% +and then how does the folding and the + + + align:start position:0% +and then how does the folding and the +geometry the topology of this these + + align:start position:0% +geometry the topology of this these + + + align:start position:0% +geometry the topology of this these +structures influence their function so I + + align:start position:0% +structures influence their function so I + + + align:start position:0% +structures influence their function so I +went back and I read some of Francis + + align:start position:0% +went back and I read some of Francis + + + align:start position:0% +went back and I read some of Francis +Crick's work from the 1950s and it's + + align:start position:0% +Crick's work from the 1950s and it's + + + align:start position:0% +Crick's work from the 1950s and it's +very interesting that this hypothesis + + align:start position:0% +very interesting that this hypothesis + + + align:start position:0% +very interesting that this hypothesis +was considered controversial and + + align:start position:0% +was considered controversial and + + + align:start position:0% +was considered controversial and +tentative at the time so he said the + + align:start position:0% +tentative at the time so he said the + + + align:start position:0% +tentative at the time so he said the +specificity of a piece of nucleic acid + + align:start position:0% +specificity of a piece of nucleic acid + + + align:start position:0% +specificity of a piece of nucleic acid +is expressed solely by the sequence of + + align:start position:0% +is expressed solely by the sequence of + + + align:start position:0% +is expressed solely by the sequence of +its bases and this sequence is a simple + + align:start position:0% +its bases and this sequence is a simple + + + align:start position:0% +its bases and this sequence is a simple +code for the amino acid sequence of a + + align:start position:0% +code for the amino acid sequence of a + + + align:start position:0% +code for the amino acid sequence of a +particular protein and there were people + + align:start position:0% +particular protein and there were people + + + align:start position:0% +particular protein and there were people +arguing that he was just flat wrong that + + align:start position:0% +arguing that he was just flat wrong that + + + align:start position:0% +arguing that he was just flat wrong that +this was not true + + align:start position:0% +this was not true + + + align:start position:0% +this was not true +of course it turned out he was right and + + align:start position:0% +of course it turned out he was right and + + + align:start position:0% +of course it turned out he was right and +then the central dogma is the transfer + + align:start position:0% +then the central dogma is the transfer + + + align:start position:0% +then the central dogma is the transfer +of information from nucleic acid to + + align:start position:0% +of information from nucleic acid to + + + align:start position:0% +of information from nucleic acid to +nucleic acid or from nucleic acid to + + align:start position:0% +nucleic acid or from nucleic acid to + + + align:start position:0% +nucleic acid or from nucleic acid to +protein may be possible but transfer + + align:start position:0% +protein may be possible but transfer + + + align:start position:0% +protein may be possible but transfer +from protein to protein or from protein + + align:start position:0% +from protein to protein or from protein + + + align:start position:0% +from protein to protein or from protein +to nucleic acid is impossible and that's + + align:start position:0% +to nucleic acid is impossible and that's + + + align:start position:0% +to nucleic acid is impossible and that's +not quite true but it's it's a good + + align:start position:0% +not quite true but it's it's a good + + + align:start position:0% +not quite true but it's it's a good +first approximation so this is where + + align:start position:0% +first approximation so this is where + + + align:start position:0% +first approximation so this is where +things stood back about 60 years ago and + + align:start position:0% +things stood back about 60 years ago and + + + align:start position:0% +things stood back about 60 years ago and +then a few Nobel Prizes later we began + + align:start position:0% +then a few Nobel Prizes later we began + + + align:start position:0% +then a few Nobel Prizes later we began +to understand some of the mechanism of + + align:start position:0% +to understand some of the mechanism of + + + align:start position:0% +to understand some of the mechanism of +how this works and of course how it + + align:start position:0% +how this works and of course how it + + + align:start position:0% +how this works and of course how it +works is that you have DNA which is + + align:start position:0% +works is that you have DNA which is + + + align:start position:0% +works is that you have DNA which is +these four bases double stranded RNA + + align:start position:0% +these four bases double stranded RNA + + + align:start position:0% +these four bases double stranded RNA +gets produced in the process of + + align:start position:0% +gets produced in the process of + + + align:start position:0% +gets produced in the process of +transcription so this thing unfolds an + + align:start position:0% +transcription so this thing unfolds an + + + align:start position:0% +transcription so this thing unfolds an +RNA strand is built along the DNA and + + align:start position:0% +RNA strand is built along the DNA and + + + align:start position:0% +RNA strand is built along the DNA and +separates from the DNA creating a + + align:start position:0% +separates from the DNA creating a + + + align:start position:0% +separates from the DNA creating a +single-stranded RNA and then it goes and + + align:start position:0% +single-stranded RNA and then it goes and + + + align:start position:0% +single-stranded RNA and then it goes and +hooks up with the ribosome and the + + align:start position:0% +hooks up with the ribosome and the + + + align:start position:0% +hooks up with the ribosome and the +ribosome takes that RNA and takes the + + align:start position:0% +ribosome takes that RNA and takes the + + + align:start position:0% +ribosome takes that RNA and takes the +codes in triplets and each triplet + + align:start position:0% +codes in triplets and each triplet + + + align:start position:0% +codes in triplets and each triplet +stands for a particular amino acid which + + align:start position:0% +stands for a particular amino acid which + + + align:start position:0% +stands for a particular amino acid which +it then assembles in sequence and + + align:start position:0% +it then assembles in sequence and + + + align:start position:0% +it then assembles in sequence and +creates proteins which are sequences of + + align:start position:0% +creates proteins which are sequences of + + + align:start position:0% +creates proteins which are sequences of +amino acids now it's very complicated + + align:start position:0% +amino acids now it's very complicated + + + align:start position:0% +amino acids now it's very complicated +because because there's + + align:start position:0% +because because there's + + + align:start position:0% +because because there's +three-dimensionality and there's time + + align:start position:0% +three-dimensionality and there's time + + + align:start position:0% +three-dimensionality and there's time +involved and there are rate constants + + align:start position:0% +involved and there are rate constants + + + align:start position:0% +involved and there are rate constants +this is a chemistry after all so again a + + align:start position:0% +this is a chemistry after all so again a + + + align:start position:0% +this is a chemistry after all so again a +few more Nobel Prizes later we we have + + align:start position:0% +few more Nobel Prizes later we we have + + + align:start position:0% +few more Nobel Prizes later we we have +that transcription that process of + + align:start position:0% +that transcription that process of + + + align:start position:0% +that transcription that process of +turning DNA into RNA is regulated by + + align:start position:0% +turning DNA into RNA is regulated by + + + align:start position:0% +turning DNA into RNA is regulated by +promoter repressor and enhancer regions + + align:start position:0% +promoter repressor and enhancer regions + + + align:start position:0% +promoter repressor and enhancer regions +on the genome and that proteins mediate + + align:start position:0% +on the genome and that proteins mediate + + + align:start position:0% +on the genome and that proteins mediate +this process by binding to the DNA and + + align:start position:0% +this process by binding to the DNA and + + + align:start position:0% +this process by binding to the DNA and +causing the beginning of transcription + + align:start position:0% +causing the beginning of transcription + + + align:start position:0% +causing the beginning of transcription +or causing it to run faster or causing + + align:start position:0% +or causing it to run faster or causing + + + align:start position:0% +or causing it to run faster or causing +it to run slower or they interfere with + + align:start position:0% +it to run slower or they interfere with + + + align:start position:0% +it to run slower or they interfere with +it + + align:start position:0% +it + + + align:start position:0% +it +etc there are also these enhancers some + + align:start position:0% +etc there are also these enhancers some + + + align:start position:0% +etc there are also these enhancers some +of which are very far away from the + + align:start position:0% +of which are very far away from the + + + align:start position:0% +of which are very far away from the +coding region that make huge differences + + align:start position:0% +coding region that make huge differences + + + align:start position:0% +coding region that make huge differences +in how much of the RNA and therefore how + + align:start position:0% +in how much of the RNA and therefore how + + + align:start position:0% +in how much of the RNA and therefore how +much of the protein is made and the + + align:start position:0% +much of the protein is made and the + + + align:start position:0% +much of the protein is made and the +current understanding of that is that if + + align:start position:0% +current understanding of that is that if + + + align:start position:0% +current understanding of that is that if +here's the gene it may be that the + + align:start position:0% +here's the gene it may be that the + + + align:start position:0% +here's the gene it may be that the +strand of DNA loops around and the + + align:start position:0% +strand of DNA loops around and the + + + align:start position:0% +strand of DNA loops around and the +enhancer even though it's distant in + + align:start position:0% +enhancer even though it's distant in + + + align:start position:0% +enhancer even though it's distant in +genetic units is actually in close + + align:start position:0% +genetic units is actually in close + + + align:start position:0% +genetic units is actually in close +physical proximity and therefore can + + align:start position:0% +physical proximity and therefore can + + + align:start position:0% +physical proximity and therefore can +either I can encourage more of this + + align:start position:0% +either I can encourage more of this + + + align:start position:0% +either I can encourage more of this +transcription to take place by the way + + align:start position:0% +transcription to take place by the way + + + align:start position:0% +transcription to take place by the way +if you're interested in this stuff of + + align:start position:0% +if you're interested in this stuff of + + + align:start position:0% +if you're interested in this stuff of +course MIT teaches a lot of courses in + + align:start position:0% +course MIT teaches a lot of courses in + + + align:start position:0% +course MIT teaches a lot of courses in +how to do this + + align:start position:0% +how to do this + + + align:start position:0% +how to do this +Dave Gifford and Manolos callus both + + align:start position:0% +Dave Gifford and Manolos callus both + + + align:start position:0% +Dave Gifford and Manolos callus both +teach computational courses in how to + + align:start position:0% +teach computational courses in how to + + + align:start position:0% +teach computational courses in how to +apply computational methods to try to + + align:start position:0% +apply computational methods to try to + + + align:start position:0% +apply computational methods to try to +decipher this kind of activity so + + align:start position:0% +decipher this kind of activity so + + + align:start position:0% +decipher this kind of activity so +repressors prevent activator from + + align:start position:0% +repressors prevent activator from + + + align:start position:0% +repressors prevent activator from +binding or alters the activator in order + + align:start position:0% +binding or alters the activator in order + + + align:start position:0% +binding or alters the activator in order +to change the rate constants and so this + + align:start position:0% +to change the rate constants and so this + + + align:start position:0% +to change the rate constants and so this +is another mechanism now one of the + + align:start position:0% +is another mechanism now one of the + + + align:start position:0% +is another mechanism now one of the +problems is that if you look at the + + align:start position:0% +problems is that if you look at the + + + align:start position:0% +problems is that if you look at the +total amount of DNA in your in your + + align:start position:0% +total amount of DNA in your in your + + + align:start position:0% +total amount of DNA in your in your +genes in your cells only about one and a + + align:start position:0% +genes in your cells only about one and a + + + align:start position:0% +genes in your cells only about one and a +half percent are exons which are the + + align:start position:0% +half percent are exons which are the + + + align:start position:0% +half percent are exons which are the +parts that code for mRNA and eventually + + align:start position:0% +parts that code for mRNA and eventually + + + align:start position:0% +parts that code for mRNA and eventually +protein so the question is what is the + + align:start position:0% +protein so the question is what is the + + + align:start position:0% +protein so the question is what is the +other ninety eight and a half percent + + align:start position:0% +other ninety eight and a half percent + + + align:start position:0% +other ninety eight and a half percent +Duke + + align:start position:0% +Duke + + + align:start position:0% +Duke +there was this unfortunate tendency in + + align:start position:0% +there was this unfortunate tendency in + + + align:start position:0% +there was this unfortunate tendency in +the biology community to call that junk + + align:start position:0% +the biology community to call that junk + + + align:start position:0% +the biology community to call that junk +DNA which of course is a terrible notion + + align:start position:0% +DNA which of course is a terrible notion + + + align:start position:0% +DNA which of course is a terrible notion +because evolution would certainly have + + align:start position:0% +because evolution would certainly have + + + align:start position:0% +because evolution would certainly have +gotten rid of it if it was truly junk + + align:start position:0% +gotten rid of it if it was truly junk + + + align:start position:0% +gotten rid of it if it was truly junk +because we ourselves spend a lot of + + align:start position:0% +because we ourselves spend a lot of + + + align:start position:0% +because we ourselves spend a lot of +energy building this stuff and every + + align:start position:0% +energy building this stuff and every + + + align:start position:0% +energy building this stuff and every +time a cell divides it rebuilds all that + + align:start position:0% +time a cell divides it rebuilds all that + + + align:start position:0% +time a cell divides it rebuilds all that +so-called junk DNA so it can't possibly + + align:start position:0% +so-called junk DNA so it can't possibly + + + align:start position:0% +so-called junk DNA so it can't possibly +be junk but the question is what does it + + align:start position:0% +be junk but the question is what does it + + + align:start position:0% +be junk but the question is what does it +do and we don't really know for a lot of + + align:start position:0% +do and we don't really know for a lot of + + + align:start position:0% +do and we don't really know for a lot of +it + + align:start position:0% +it + + + align:start position:0% +it +so there are introns I'll show you a + + align:start position:0% +so there are introns I'll show you a + + + align:start position:0% +so there are introns I'll show you a +picture of their segments of the coding + + align:start position:0% +picture of their segments of the coding + + + align:start position:0% +picture of their segments of the coding +region that don't wind up as part of the + + align:start position:0% +region that don't wind up as part of the + + + align:start position:0% +region that don't wind up as part of the +RNA they're spliced out and we don't + + align:start position:0% +RNA they're spliced out and we don't + + + align:start position:0% +RNA they're spliced out and we don't +quite know why there are these + + align:start position:0% +quite know why there are these + + + align:start position:0% +quite know why there are these +regulatory sequences which is only about + + align:start position:0% +regulatory sequences which is only about + + + align:start position:0% +regulatory sequences which is only about +5% that are those promoters and + + align:start position:0% +5% that are those promoters and + + + align:start position:0% +5% that are those promoters and +repressors and and enhancers that I + + align:start position:0% +repressors and and enhancers that I + + + align:start position:0% +repressors and and enhancers that I +talked about and then there's a whole + + align:start position:0% +talked about and then there's a whole + + + align:start position:0% +talked about and then there's a whole +bunch of repetitive DNA that includes + + align:start position:0% +bunch of repetitive DNA that includes + + + align:start position:0% +bunch of repetitive DNA that includes +transpose xi slated sequences and mostly + + align:start position:0% +transpose xi slated sequences and mostly + + + align:start position:0% +transpose xi slated sequences and mostly +we don't understand what it all does ok + + align:start position:0% +we don't understand what it all does ok + + + align:start position:0% +we don't understand what it all does ok +hypotheses or things like well maybe + + align:start position:0% +hypotheses or things like well maybe + + + align:start position:0% +hypotheses or things like well maybe +it's a storehouse of potentially useful + + align:start position:0% +it's a storehouse of potentially useful + + + align:start position:0% +it's a storehouse of potentially useful +DNA so that if environmental conditions + + align:start position:0% +DNA so that if environmental conditions + + + align:start position:0% +DNA so that if environmental conditions +change a lot then the cell doesn't have + + align:start position:0% +change a lot then the cell doesn't have + + + align:start position:0% +change a lot then the cell doesn't have +to reinvent the stuff from scratch it + + align:start position:0% +to reinvent the stuff from scratch it + + + align:start position:0% +to reinvent the stuff from scratch it +saved it from previous times when in in + + align:start position:0% +saved it from previous times when in in + + + align:start position:0% +saved it from previous times when in in +evolution when that may have been useful + + align:start position:0% +evolution when that may have been useful + + + align:start position:0% +evolution when that may have been useful +but that's pretty much pure speculation + + align:start position:0% +but that's pretty much pure speculation + + + align:start position:0% +but that's pretty much pure speculation +at this point so just recently the + + align:start position:0% +at this point so just recently the + + + align:start position:0% +at this point so just recently the +Killian lecture was was given by Gerald + + align:start position:0% +Killian lecture was was given by Gerald + + + align:start position:0% +Killian lecture was was given by Gerald +Fink who's a geneticist here and his + + align:start position:0% +Fink who's a geneticist here and his + + + align:start position:0% +Fink who's a geneticist here and his +claim is that a gene is not any segment + + align:start position:0% +claim is that a gene is not any segment + + + align:start position:0% +claim is that a gene is not any segment +of DNA that produces RNA or a protein + + align:start position:0% +of DNA that produces RNA or a protein + + + align:start position:0% +of DNA that produces RNA or a protein +but it's any segment of DNA + + align:start position:0% +but it's any segment of DNA + + + align:start position:0% +but it's any segment of DNA +that is transcribed into RNA that has + + align:start position:0% +that is transcribed into RNA that has + + + align:start position:0% +that is transcribed into RNA that has +some function whatever it is not + + align:start position:0% +some function whatever it is not + + + align:start position:0% +some function whatever it is not +necessarily building proteins but just + + align:start position:0% +necessarily building proteins but just + + + align:start position:0% +necessarily building proteins but just +anything and I think that view is + + align:start position:0% +anything and I think that view is + + + align:start position:0% +anything and I think that view is +becoming accepted so I promised you a + + align:start position:0% +becoming accepted so I promised you a + + + align:start position:0% +becoming accepted so I promised you a +little bit of more complexity so when + + align:start position:0% +little bit of more complexity so when + + + align:start position:0% +little bit of more complexity so when +you look at your DNA in eukaryotes like + + align:start position:0% +you look at your DNA in eukaryotes like + + + align:start position:0% +you look at your DNA in eukaryotes like +us here's the promoter and then here is + + align:start position:0% +us here's the promoter and then here is + + + align:start position:0% +us here's the promoter and then here is +the sequence of the genome when this + + align:start position:0% +the sequence of the genome when this + + + align:start position:0% +the sequence of the genome when this +gets transcribed it gets transcribed + + align:start position:0% +gets transcribed it gets transcribed + + + align:start position:0% +gets transcribed it gets transcribed +into something called pre mRNA messenger + + align:start position:0% +into something called pre mRNA messenger + + + align:start position:0% +into something called pre mRNA messenger +RNA and then there's this process of + + align:start position:0% +RNA and then there's this process of + + + align:start position:0% +RNA and then there's this process of +alternative splicing that splices out + + align:start position:0% +alternative splicing that splices out + + + align:start position:0% +alternative splicing that splices out +the the introns and leaves only the + + align:start position:0% +the the introns and leaves only the + + + align:start position:0% +the the introns and leaves only the +exons but sometimes it doesn't leave all + + align:start position:0% +exons but sometimes it doesn't leave all + + + align:start position:0% +exons but sometimes it doesn't leave all +the exons that only leave some of them + + align:start position:0% +the exons that only leave some of them + + + align:start position:0% +the exons that only leave some of them +and so the same gene can under various + + align:start position:0% +and so the same gene can under various + + + align:start position:0% +and so the same gene can under various +circumstances produce different mRNA + + align:start position:0% +circumstances produce different mRNA + + + align:start position:0% +circumstances produce different mRNA +which then produces different proteins + + align:start position:0% +which then produces different proteins + + + align:start position:0% +which then produces different proteins +and again there's a lot of mysteries + + align:start position:0% +and again there's a lot of mysteries + + + align:start position:0% +and again there's a lot of mysteries +about exactly how all this works + + align:start position:0% +about exactly how all this works + + + align:start position:0% +about exactly how all this works +nevertheless that's the basic mechanism + + align:start position:0% +nevertheless that's the basic mechanism + + + align:start position:0% +nevertheless that's the basic mechanism +and then here I've just listed a few of + + align:start position:0% +and then here I've just listed a few of + + + align:start position:0% +and then here I've just listed a few of +the of the complexity problems so there + + align:start position:0% +the of the complexity problems so there + + + align:start position:0% +the of the complexity problems so there +are things like RNA can turn into DNA + + align:start position:0% +are things like RNA can turn into DNA + + + align:start position:0% +are things like RNA can turn into DNA +this is a trick that viruses use a lot + + align:start position:0% +this is a trick that viruses use a lot + + + align:start position:0% +this is a trick that viruses use a lot +they incorporate themselves into your + + align:start position:0% +they incorporate themselves into your + + + align:start position:0% +they incorporate themselves into your +cell create a DNA complement to the RNA + + align:start position:0% +cell create a DNA complement to the RNA + + + align:start position:0% +cell create a DNA complement to the RNA +and then use that to generate more + + align:start position:0% +and then use that to generate more + + + align:start position:0% +and then use that to generate more +viruses so this is very typical of a + + align:start position:0% +viruses so this is very typical of a + + + align:start position:0% +viruses so this is very typical of a +viral infection + + align:start position:0% +viral infection + + + align:start position:0% +viral infection +prions we don't also don't understand + + align:start position:0% +prions we don't also don't understand + + + align:start position:0% +prions we don't also don't understand +very well this is like mad cow disease + + align:start position:0% +very well this is like mad cow disease + + + align:start position:0% +very well this is like mad cow disease +where these proteins are able to cause + + align:start position:0% +where these proteins are able to cause + + + align:start position:0% +where these proteins are able to cause +changes in other proteins without going + + align:start position:0% +changes in other proteins without going + + + align:start position:0% +changes in other proteins without going +through the RNA DNA mediated mechanisms + + align:start position:0% +through the RNA DNA mediated mechanisms + + + align:start position:0% +through the RNA DNA mediated mechanisms +there are DNA modifying proteins the + + align:start position:0% +there are DNA modifying proteins the + + + align:start position:0% +there are DNA modifying proteins the +most important of which is the stuff + + align:start position:0% +most important of which is the stuff + + + align:start position:0% +most important of which is the stuff +involved in CRISPR cas9 + + align:start position:0% +involved in CRISPR cas9 + + + align:start position:0% +involved in CRISPR cas9 +which is this relatively new discovery + + align:start position:0% +which is this relatively new discovery + + + align:start position:0% +which is this relatively new discovery +about how bacteria are able to use a + + align:start position:0% +about how bacteria are able to use a + + + align:start position:0% +about how bacteria are able to use a +mechanism that they stole from viruses + + align:start position:0% +mechanism that they stole from viruses + + + align:start position:0% +mechanism that they stole from viruses +to edit the genetic complement of + + align:start position:0% +to edit the genetic complement of + + + align:start position:0% +to edit the genetic complement of +themselves and more importantly of other + + align:start position:0% +themselves and more importantly of other + + + align:start position:0% +themselves and more importantly of other +viruses that attack them + + align:start position:0% +viruses that attack them + + + align:start position:0% +viruses that attack them +so it's an antiviral defense mechanism + + align:start position:0% +so it's an antiviral defense mechanism + + + align:start position:0% +so it's an antiviral defense mechanism +and we're now figuring out how to use it + + align:start position:0% +and we're now figuring out how to use it + + + align:start position:0% +and we're now figuring out how to use it +to do gene editing you may have read + + align:start position:0% +to do gene editing you may have read + + + align:start position:0% +to do gene editing you may have read +about this Chinese guy who actually went + + align:start position:0% +about this Chinese guy who actually went + + + align:start position:0% +about this Chinese guy who actually went +out and edited the genome of a couple of + + align:start position:0% +out and edited the genome of a couple of + + + align:start position:0% +out and edited the genome of a couple of +girls who were born in China + + align:start position:0% +girls who were born in China + + + align:start position:0% +girls who were born in China +incorporating some I think resistance + + align:start position:0% +incorporating some I think resistance + + + align:start position:0% +incorporating some I think resistance +against HIV infections in their genome + + align:start position:0% +against HIV infections in their genome + + + align:start position:0% +against HIV infections in their genome +and of course this is probably way too + + align:start position:0% +and of course this is probably way too + + + align:start position:0% +and of course this is probably way too +early to do experiments on human beings + + align:start position:0% +early to do experiments on human beings + + + align:start position:0% +early to do experiments on human beings +because they haven't demonstrated that + + align:start position:0% +because they haven't demonstrated that + + + align:start position:0% +because they haven't demonstrated that +this is safe but maybe that'll become + + align:start position:0% +this is safe but maybe that'll become + + + align:start position:0% +this is safe but maybe that'll become +accepted George Church and at Harvard + + align:start position:0% +accepted George Church and at Harvard + + + align:start position:0% +accepted George Church and at Harvard +has been going around + + align:start position:0% +has been going around + + + align:start position:0% +has been going around +he likes to rattle people's chains and + + align:start position:0% +he likes to rattle people's chains and + + + align:start position:0% +he likes to rattle people's chains and +he's been going around saying well the + + align:start position:0% +he's been going around saying well the + + + align:start position:0% +he's been going around saying well the +guy didn't you know he was unethical and + + align:start position:0% +guy didn't you know he was unethical and + + + align:start position:0% +guy didn't you know he was unethical and +was a slob but what he's doing is a + + align:start position:0% +was a slob but what he's doing is a + + + align:start position:0% +was a slob but what he's doing is a +really great idea so we'll see where + + align:start position:0% +really great idea so we'll see where + + + align:start position:0% +really great idea so we'll see where +that goes okay and then there are these + + align:start position:0% +that goes okay and then there are these + + + align:start position:0% +that goes okay and then there are these +retrotransposons where pieces of DNA in + + align:start position:0% +retrotransposons where pieces of DNA in + + + align:start position:0% +retrotransposons where pieces of DNA in +Eukarya just pop out of some wherever + + align:start position:0% +Eukarya just pop out of some wherever + + + align:start position:0% +Eukarya just pop out of some wherever +they are and insert themselves in some + + align:start position:0% +they are and insert themselves in some + + + align:start position:0% +they are and insert themselves in some +other place in the genome and in plants + + align:start position:0% +other place in the genome and in plants + + + align:start position:0% +other place in the genome and in plants +this happens a lot so for example wheat + + align:start position:0% +this happens a lot so for example wheat + + + align:start position:0% +this happens a lot so for example wheat +seems to have a huge number of copies of + + align:start position:0% +seems to have a huge number of copies of + + + align:start position:0% +seems to have a huge number of copies of +DNA segments that maybe it had only one + + align:start position:0% +DNA segments that maybe it had only one + + + align:start position:0% +DNA segments that maybe it had only one +of but it's replicated using through + + align:start position:0% +of but it's replicated using through + + + align:start position:0% +of but it's replicated using through +this mechanism okay + + align:start position:0% +this mechanism okay + + + align:start position:0% +this mechanism okay +last bit of complexity so we have + + align:start position:0% +last bit of complexity so we have + + + align:start position:0% +last bit of complexity so we have +various kinds of RNA there's long + + align:start position:0% +various kinds of RNA there's long + + + align:start position:0% +various kinds of RNA there's long +non-coding RNA which seems to + + align:start position:0% +non-coding RNA which seems to + + + align:start position:0% +non-coding RNA which seems to +participate in gene regulation + + align:start position:0% +participate in gene regulation + + + align:start position:0% +participate in gene regulation +there's RNA interference that there are + + align:start position:0% +there's RNA interference that there are + + + align:start position:0% +there's RNA interference that there are +these these small RNA pieces that will + + align:start position:0% +these these small RNA pieces that will + + + align:start position:0% +these these small RNA pieces that will +actually latch on to the RNA produced by + + align:start position:0% +actually latch on to the RNA produced by + + + align:start position:0% +actually latch on to the RNA produced by +the stain + + align:start position:0% +the stain + + + align:start position:0% +the stain +genetic mechanism and prevent it from + + align:start position:0% +genetic mechanism and prevent it from + + + align:start position:0% +genetic mechanism and prevent it from +being translated into protein + + align:start position:0% +being translated into protein + + + align:start position:0% +being translated into protein +this was another Nobel Prize a few years + + align:start position:0% +this was another Nobel Prize a few years + + + align:start position:0% +this was another Nobel Prize a few years +ago almost everything in this field if + + align:start position:0% +ago almost everything in this field if + + + align:start position:0% +ago almost everything in this field if +you're first you get a Nobel Prize for + + align:start position:0% +you're first you get a Nobel Prize for + + + align:start position:0% +you're first you get a Nobel Prize for +it once the proteins are made they're + + align:start position:0% +it once the proteins are made they're + + + align:start position:0% +it once the proteins are made they're +degraded differentially so there are + + align:start position:0% +degraded differentially so there are + + + align:start position:0% +degraded differentially so there are +different mechanisms in the cell that + + align:start position:0% +different mechanisms in the cell that + + + align:start position:0% +different mechanisms in the cell that +destroy certain kinds of proteins much + + align:start position:0% +destroy certain kinds of proteins much + + + align:start position:0% +destroy certain kinds of proteins much +faster than others and so the production + + align:start position:0% +faster than others and so the production + + + align:start position:0% +faster than others and so the production +rate doesn't tell you how much is going + + align:start position:0% +rate doesn't tell you how much is going + + + align:start position:0% +rate doesn't tell you how much is going +to be there at any particular time + + align:start position:0% +to be there at any particular time + + + align:start position:0% +to be there at any particular time +and then there's this tertiary secondary + + align:start position:0% +and then there's this tertiary secondary + + + align:start position:0% +and then there's this tertiary secondary +and tertiary structure where there's + + align:start position:0% +and tertiary structure where there's + + + align:start position:0% +and tertiary structure where there's +actually what is it's like a mile of DNA + + align:start position:0% +actually what is it's like a mile of DNA + + + align:start position:0% +actually what is it's like a mile of DNA +in each of your cells so it wouldn't fit + + align:start position:0% +in each of your cells so it wouldn't fit + + + align:start position:0% +in each of your cells so it wouldn't fit +and so it gets wrapped up on on these + + align:start position:0% +and so it gets wrapped up on on these + + + align:start position:0% +and so it gets wrapped up on on these +Isetta lated histones to produce + + align:start position:0% +Isetta lated histones to produce + + + align:start position:0% +Isetta lated histones to produce +something called chromatin and again we + + align:start position:0% +something called chromatin and again we + + + align:start position:0% +something called chromatin and again we +don't quite understand how this all + + align:start position:0% +don't quite understand how this all + + + align:start position:0% +don't quite understand how this all +works because you'd think that if you + + align:start position:0% +works because you'd think that if you + + + align:start position:0% +works because you'd think that if you +wrap stuff up like this it would become + + align:start position:0% +wrap stuff up like this it would become + + + align:start position:0% +wrap stuff up like this it would become +inaccessible to Trent to transcription + + align:start position:0% +inaccessible to Trent to transcription + + + align:start position:0% +inaccessible to Trent to transcription +and therefore it's not clear how it gets + + align:start position:0% +and therefore it's not clear how it gets + + + align:start position:0% +and therefore it's not clear how it gets +expressed but somehow or other the cell + + align:start position:0% +expressed but somehow or other the cell + + + align:start position:0% +expressed but somehow or other the cell +is able to do that so there's a lot yet + + align:start position:0% +is able to do that so there's a lot yet + + + align:start position:0% +is able to do that so there's a lot yet +to learn in this area okay now the + + align:start position:0% +to learn in this area okay now the + + + align:start position:0% +to learn in this area okay now the +reason we're interested in all this is + + align:start position:0% +reason we're interested in all this is + + + align:start position:0% +reason we're interested in all this is +because if you plot Moore's Law for how + + align:start position:0% +because if you plot Moore's Law for how + + + align:start position:0% +because if you plot Moore's Law for how +quickly computers are becoming cheaper + + align:start position:0% +quickly computers are becoming cheaper + + + align:start position:0% +quickly computers are becoming cheaper +per performance and you plot the cost of + + align:start position:0% +per performance and you plot the cost of + + + align:start position:0% +per performance and you plot the cost of +gene sequencing it keeps going down and + + align:start position:0% +gene sequencing it keeps going down and + + + align:start position:0% +gene sequencing it keeps going down and +it goes down much faster even than + + align:start position:0% +it goes down much faster even than + + + align:start position:0% +it goes down much faster even than +Moore's law so this is pretty remarkable + + align:start position:0% +Moore's law so this is pretty remarkable + + + align:start position:0% +Moore's law so this is pretty remarkable +and it means that you know as I said + + align:start position:0% +and it means that you know as I said + + + align:start position:0% +and it means that you know as I said +that three billion dollar first genome + + align:start position:0% +that three billion dollar first genome + + + align:start position:0% +that three billion dollar first genome +now costs just a few hundred dollars in + + align:start position:0% +now costs just a few hundred dollars in + + + align:start position:0% +now costs just a few hundred dollars in +fact if you're just interested in the + + align:start position:0% +fact if you're just interested in the + + + align:start position:0% +fact if you're just interested in the +whole exome so only the two percent + + align:start position:0% +whole exome so only the two percent + + + align:start position:0% +whole exome so only the two percent +roughly of the gene that of the DNA that + + align:start position:0% +roughly of the gene that of the DNA that + + + align:start position:0% +roughly of the gene that of the DNA that +produces genetic coding you can now go + + align:start position:0% +produces genetic coding you can now go + + + align:start position:0% +produces genetic coding you can now go +to this company + + align:start position:0% +to this company + + + align:start position:0% +to this company +which I have nothing to do with I just + + align:start position:0% +which I have nothing to do with I just + + + align:start position:0% +which I have nothing to do with I just +pulled this off the web but you know for + + align:start position:0% +pulled this off the web but you know for + + + align:start position:0% +pulled this off the web but you know for +$299 they will give you 50 times + + align:start position:0% +$299 they will give you 50 times + + + align:start position:0% +$299 they will give you 50 times +coverage on on about six Giga bases and + + align:start position:0% +coverage on on about six Giga bases and + + + align:start position:0% +coverage on on about six Giga bases and +the four if you pay them an extra + + align:start position:0% +the four if you pay them an extra + + + align:start position:0% +the four if you pay them an extra +hundred dollars they'll do it at a + + align:start position:0% +hundred dollars they'll do it at a + + + align:start position:0% +hundred dollars they'll do it at a +hundred ex coverage so these techniques + + align:start position:0% +hundred ex coverage so these techniques + + + align:start position:0% +hundred ex coverage so these techniques +are very noisy and so it's important to + + align:start position:0% +are very noisy and so it's important to + + + align:start position:0% +are very noisy and so it's important to +get lots of replicates in order to + + align:start position:0% +get lots of replicates in order to + + + align:start position:0% +get lots of replicates in order to +reassemble what you think is going on a + + align:start position:0% +reassemble what you think is going on a + + + align:start position:0% +reassemble what you think is going on a +slightly more recent phenomenon is + + align:start position:0% +slightly more recent phenomenon is + + + align:start position:0% +slightly more recent phenomenon is +people say well not only can we sequence + + align:start position:0% +people say well not only can we sequence + + + align:start position:0% +people say well not only can we sequence +your DNA but we can sequence the RNA + + align:start position:0% +your DNA but we can sequence the RNA + + + align:start position:0% +your DNA but we can sequence the RNA +that got Tran transcribed from the DNA + + align:start position:0% +that got Tran transcribed from the DNA + + + align:start position:0% +that got Tran transcribed from the DNA +and in fact you can buy a kit for 360 + + align:start position:0% +and in fact you can buy a kit for 360 + + + align:start position:0% +and in fact you can buy a kit for 360 +dollars that will take the RNA from + + align:start position:0% +dollars that will take the RNA from + + + align:start position:0% +dollars that will take the RNA from +individual cells so these are like Pico + + align:start position:0% +individual cells so these are like Pico + + + align:start position:0% +individual cells so these are like Pico +liter amounts of of stuff and it will + + align:start position:0% +liter amounts of of stuff and it will + + + align:start position:0% +liter amounts of of stuff and it will +give you the RNA sequence for $360 for + + align:start position:0% +give you the RNA sequence for $360 for + + + align:start position:0% +give you the RNA sequence for $360 for +up to a hundred cells right so three + + align:start position:0% +up to a hundred cells right so three + + + align:start position:0% +up to a hundred cells right so three +bucks three and a half bucks per cell so + + align:start position:0% +bucks three and a half bucks per cell so + + + align:start position:0% +bucks three and a half bucks per cell so +people are very excited and there are + + align:start position:0% +people are very excited and there are + + + align:start position:0% +people are very excited and there are +now also companies that will sell you + + align:start position:0% +now also companies that will sell you + + + align:start position:0% +now also companies that will sell you +advanced analysis so they will correlate + + align:start position:0% +advanced analysis so they will correlate + + + align:start position:0% +advanced analysis so they will correlate +the data that you're getting with + + align:start position:0% +the data that you're getting with + + + align:start position:0% +the data that you're getting with +different databases and figure out + + align:start position:0% +different databases and figure out + + + align:start position:0% +different databases and figure out +whether this represents you know a + + align:start position:0% +whether this represents you know a + + + align:start position:0% +whether this represents you know a +dominant or a recessive or an excellent + + align:start position:0% +dominant or a recessive or an excellent + + + align:start position:0% +dominant or a recessive or an excellent +model if you have familial data and + + align:start position:0% +model if you have familial data and + + + align:start position:0% +model if you have familial data and +functional annotation of candidate genes + + align:start position:0% +functional annotation of candidate genes + + + align:start position:0% +functional annotation of candidate genes +etc and so for example starting about + + align:start position:0% +etc and so for example starting about + + + align:start position:0% +etc and so for example starting about +three years ago if you walk into the + + align:start position:0% +three years ago if you walk into the + + + align:start position:0% +three years ago if you walk into the +dana-farber with a newly diagnosed + + align:start position:0% +dana-farber with a newly diagnosed + + + align:start position:0% +dana-farber with a newly diagnosed +cancer a solid tumor cancer they will + + align:start position:0% +cancer a solid tumor cancer they will + + + align:start position:0% +cancer a solid tumor cancer they will +take a sample of that cancer send it off + + align:start position:0% +take a sample of that cancer send it off + + + align:start position:0% +take a sample of that cancer send it off +to companies like this or their own labs + + align:start position:0% +to companies like this or their own labs + + + align:start position:0% +to companies like this or their own labs +and do sequencing and do analysis and + + align:start position:0% +and do sequencing and do analysis and + + + align:start position:0% +and do sequencing and do analysis and +try to figure out exactly which damaged + + align:start position:0% +try to figure out exactly which damaged + + + align:start position:0% +try to figure out exactly which damaged +genes that you have maybe causing the + + align:start position:0% +genes that you have maybe causing the + + + align:start position:0% +genes that you have maybe causing the +cancer and maybe more importantly since + + align:start position:0% +cancer and maybe more importantly since + + + align:start position:0% +cancer and maybe more importantly since +it's still a pretty empirical field + + align:start position:0% +it's still a pretty empirical field + + + align:start position:0% +it's still a pretty empirical field +which unusual variants of your genes + + align:start position:0% +which unusual variants of your genes + + + align:start position:0% +which unusual variants of your genes +suggest that certain drugs are likely to + + align:start position:0% +suggest that certain drugs are likely to + + + align:start position:0% +suggest that certain drugs are likely to +be more effective in treating your + + align:start position:0% +be more effective in treating your + + + align:start position:0% +be more effective in treating your +cancer than other drugs so this has + + align:start position:0% +cancer than other drugs so this has + + + align:start position:0% +cancer than other drugs so this has +become completely routine in cancer care + + align:start position:0% +become completely routine in cancer care + + + align:start position:0% +become completely routine in cancer care +and and and in a few other domains okay + + align:start position:0% +and and and in a few other domains okay + + + align:start position:0% +and and and in a few other domains okay +so now I'm going to switch to a more + + align:start position:0% +so now I'm going to switch to a more + + + align:start position:0% +so now I'm going to switch to a more +technical set of material so if you want + + align:start position:0% +technical set of material so if you want + + + align:start position:0% +technical set of material so if you want +to characterize disease subtypes using + + align:start position:0% +to characterize disease subtypes using + + + align:start position:0% +to characterize disease subtypes using +gene expression arrays microarrays + + align:start position:0% +gene expression arrays microarrays + + + align:start position:0% +gene expression arrays microarrays +here's one way to do it and this is a + + align:start position:0% +here's one way to do it and this is a + + + align:start position:0% +here's one way to do it and this is a +famous paper by a Lozada + + align:start position:0% +famous paper by a Lozada + + + align:start position:0% +famous paper by a Lozada +it was essentially the first of this + + align:start position:0% +it was essentially the first of this + + + align:start position:0% +it was essentially the first of this +class of papers back in 2001 I think + + align:start position:0% +class of papers back in 2001 I think + + + align:start position:0% +class of papers back in 2001 I think +yeah 2001 and since then there have been + + align:start position:0% +yeah 2001 and since then there have been + + + align:start position:0% +yeah 2001 and since then there have been +probably tens or hundreds of thousands + + align:start position:0% +probably tens or hundreds of thousands + + + align:start position:0% +probably tens or hundreds of thousands +of other papers published doing similar + + align:start position:0% +of other papers published doing similar + + + align:start position:0% +of other papers published doing similar +kinds of analyses on other datasets so + + align:start position:0% +kinds of analyses on other datasets so + + + align:start position:0% +kinds of analyses on other datasets so +what they did is they said okay we're + + align:start position:0% +what they did is they said okay we're + + + align:start position:0% +what they did is they said okay we're +going to extract the the the coding RNA + + align:start position:0% +going to extract the the the coding RNA + + + align:start position:0% +going to extract the the the coding RNA +we're going to create complimentary DNA + + align:start position:0% +we're going to create complimentary DNA + + + align:start position:0% +we're going to create complimentary DNA +from it we're going to use a technique + + align:start position:0% +from it we're going to use a technique + + + align:start position:0% +from it we're going to use a technique +to amplify that because we're starting + + align:start position:0% +to amplify that because we're starting + + + align:start position:0% +to amplify that because we're starting +with teeny tiny quantities and then + + align:start position:0% +with teeny tiny quantities and then + + + align:start position:0% +with teeny tiny quantities and then +we're going to take a microarray which + + align:start position:0% +we're going to take a microarray which + + + align:start position:0% +we're going to take a microarray which +is either a like a glass slide with tens + + align:start position:0% +is either a like a glass slide with tens + + + align:start position:0% +is either a like a glass slide with tens +or hundreds of thousands of spotted bits + + align:start position:0% +or hundreds of thousands of spotted bits + + + align:start position:0% +or hundreds of thousands of spotted bits +of DNA on it or it's a silicon chip with + + align:start position:0% +of DNA on it or it's a silicon chip with + + + align:start position:0% +of DNA on it or it's a silicon chip with +wells that again have tens or hundreds + + align:start position:0% +wells that again have tens or hundreds + + + align:start position:0% +wells that again have tens or hundreds +of thousands of bits of DNA in it now + + align:start position:0% +of thousands of bits of DNA in it now + + + align:start position:0% +of thousands of bits of DNA in it now +where does that DNA come from initially + + align:start position:0% +where does that DNA come from initially + + + align:start position:0% +where does that DNA come from initially +it was just a random collection of + + align:start position:0% +it was just a random collection of + + + align:start position:0% +it was just a random collection of +pieces of genes from the genome then + + align:start position:0% +pieces of genes from the genome then + + + align:start position:0% +pieces of genes from the genome then +since then they've gotten somewhat more + + align:start position:0% +since then they've gotten somewhat more + + + align:start position:0% +since then they've gotten somewhat more +sophisticated but the idea is that I'm + + align:start position:0% +sophisticated but the idea is that I'm + + + align:start position:0% +sophisticated but the idea is that I'm +going to take the amplified cDNA I'm + + align:start position:0% +going to take the amplified cDNA I'm + + + align:start position:0% +going to take the amplified cDNA I'm +going to mark it with one of these + + align:start position:0% +going to mark it with one of these + + + align:start position:0% +going to mark it with one of these +jellyfish proteins that glows under + + align:start position:0% +jellyfish proteins that glows under + + + align:start position:0% +jellyfish proteins that glows under +light and then I'm going to flow it over + + align:start position:0% +light and then I'm going to flow it over + + + align:start position:0% +light and then I'm going to flow it over +this slide or over this well the set of + + align:start position:0% +this slide or over this well the set of + + + align:start position:0% +this slide or over this well the set of +wells + + align:start position:0% +wells + + + align:start position:0% +wells +and the complementary parts of the of + + align:start position:0% +and the complementary parts of the of + + + align:start position:0% +and the complementary parts of the of +the complimentary DNA will stick to the + + align:start position:0% +the complimentary DNA will stick to the + + + align:start position:0% +the complimentary DNA will stick to the +parts to the samples of DNA that are in + + align:start position:0% +parts to the samples of DNA that are in + + + align:start position:0% +parts to the samples of DNA that are in +this well okay stands to reason an + + align:start position:0% +this well okay stands to reason an + + + align:start position:0% +this well okay stands to reason an +alternative is that you take normal + + align:start position:0% +alternative is that you take normal + + + align:start position:0% +alternative is that you take normal +tissue as well as say the cancerous + + align:start position:0% +tissue as well as say the cancerous + + + align:start position:0% +tissue as well as say the cancerous +tissue you mark the normal tissue with + + align:start position:0% +tissue you mark the normal tissue with + + + align:start position:0% +tissue you mark the normal tissue with +green fluorescent jellyfish stuff and + + align:start position:0% +green fluorescent jellyfish stuff and + + + align:start position:0% +green fluorescent jellyfish stuff and +you mark the cancer with red and then + + align:start position:0% +you mark the cancer with red and then + + + align:start position:0% +you mark the cancer with red and then +you flow both of them in equal amounts + + align:start position:0% +you flow both of them in equal amounts + + + align:start position:0% +you flow both of them in equal amounts +over the array that lets you measure a + + align:start position:0% +over the array that lets you measure a + + + align:start position:0% +over the array that lets you measure a +ratio and you don't have as much of a + + align:start position:0% +ratio and you don't have as much of a + + + align:start position:0% +ratio and you don't have as much of a +calibration problem about trying to + + align:start position:0% +calibration problem about trying to + + + align:start position:0% +calibration problem about trying to +figure out the exact value and then you + + align:start position:0% +figure out the exact value and then you + + + align:start position:0% +figure out the exact value and then you +cluster these samples by nearness and + + align:start position:0% +cluster these samples by nearness and + + + align:start position:0% +cluster these samples by nearness and +expression space and you cluster the + + align:start position:0% +expression space and you cluster the + + + align:start position:0% +expression space and you cluster the +genes by expression similarity across + + align:start position:0% +genes by expression similarity across + + + align:start position:0% +genes by expression similarity across +samples so it used to be called by + + align:start position:0% +samples so it used to be called by + + + align:start position:0% +samples so it used to be called by +clustering and I'll talk in a few + + align:start position:0% +clustering and I'll talk in a few + + + align:start position:0% +clustering and I'll talk in a few +minutes about a particular technique for + + align:start position:0% +minutes about a particular technique for + + + align:start position:0% +minutes about a particular technique for +doing this so this is a typical + + align:start position:0% +doing this so this is a typical + + + align:start position:0% +doing this so this is a typical +microarray experiment the RNAs is turned + + align:start position:0% +microarray experiment the RNAs is turned + + + align:start position:0% +microarray experiment the RNAs is turned +into its complimentary DNA flowed over + + align:start position:0% +into its complimentary DNA flowed over + + + align:start position:0% +into its complimentary DNA flowed over +the microarray chip and you get out a + + align:start position:0% +the microarray chip and you get out a + + + align:start position:0% +the microarray chip and you get out a +bunch of spots that are to various + + align:start position:0% +bunch of spots that are to various + + + align:start position:0% +bunch of spots that are to various +degrees of green and red and then you + + align:start position:0% +degrees of green and red and then you + + + align:start position:0% +degrees of green and red and then you +calculate their ratio and then you do + + align:start position:0% +calculate their ratio and then you do + + + align:start position:0% +calculate their ratio and then you do +this by clustering and what you get is a + + align:start position:0% +this by clustering and what you get is a + + + align:start position:0% +this by clustering and what you get is a +hierarchical clustering of genes and a + + align:start position:0% +hierarchical clustering of genes and a + + + align:start position:0% +hierarchical clustering of genes and a +hierarchical clustering in their case of + + align:start position:0% +hierarchical clustering in their case of + + + align:start position:0% +hierarchical clustering in their case of +breast cancer biopsy specimens that + + align:start position:0% +breast cancer biopsy specimens that + + + align:start position:0% +breast cancer biopsy specimens that +express these genes in different ways + + align:start position:0% +express these genes in different ways + + + align:start position:0% +express these genes in different ways +okay so this was pretty revolutionary + + align:start position:0% +okay so this was pretty revolutionary + + + align:start position:0% +okay so this was pretty revolutionary +because the answers made sense so what + + align:start position:0% +because the answers made sense so what + + + align:start position:0% +because the answers made sense so what +they when they did this on 19 so lines + + align:start position:0% +they when they did this on 19 so lines + + + align:start position:0% +they when they did this on 19 so lines +and 65 breast tumor samples and a whole + + align:start position:0% +and 65 breast tumor samples and a whole + + + align:start position:0% +and 65 breast tumor samples and a whole +bunch of genes they came up with the + + align:start position:0% +bunch of genes they came up with the + + + align:start position:0% +bunch of genes they came up with the +clustering that said hmm it looks like + + align:start position:0% +clustering that said hmm it looks like + + + align:start position:0% +clustering that said hmm it looks like +there are some samples that have this + + align:start position:0% +there are some samples that have this + + + align:start position:0% +there are some samples that have this +endothelial cell cluster + + align:start position:0% +endothelial cell cluster + + + align:start position:0% +endothelial cell cluster +so it's a particular kind of problem and + + align:start position:0% +so it's a particular kind of problem and + + + align:start position:0% +so it's a particular kind of problem and +you could correlate it with with + + align:start position:0% +you could correlate it with with + + + align:start position:0% +you could correlate it with with +pathology from the tumor slides and + + align:start position:0% +pathology from the tumor slides and + + + align:start position:0% +pathology from the tumor slides and +different subclasses and then this is a + + align:start position:0% +different subclasses and then this is a + + + align:start position:0% +different subclasses and then this is a +very typical kind of heat map that you + + align:start position:0% +very typical kind of heat map that you + + + align:start position:0% +very typical kind of heat map that you +see in this type of study another study + + align:start position:0% +see in this type of study another study + + + align:start position:0% +see in this type of study another study +from sixty five breast carcinoma samples + + align:start position:0% +from sixty five breast carcinoma samples + + + align:start position:0% +from sixty five breast carcinoma samples +using the gene list that they curated + + align:start position:0% +using the gene list that they curated + + + align:start position:0% +using the gene list that they curated +before looks like it clusters the + + align:start position:0% +before looks like it clusters the + + + align:start position:0% +before looks like it clusters the +expression levels into these five + + align:start position:0% +expression levels into these five + + + align:start position:0% +expression levels into these five +clusters right it's a little hard to + + align:start position:0% +clusters right it's a little hard to + + + align:start position:0% +clusters right it's a little hard to +look at I mean when I stare at these + + align:start position:0% +look at I mean when I stare at these + + + align:start position:0% +look at I mean when I stare at these +it's not obvious to me why the + + align:start position:0% +it's not obvious to me why the + + + align:start position:0% +it's not obvious to me why the +mathematics came up with exactly those + + align:start position:0% +mathematics came up with exactly those + + + align:start position:0% +mathematics came up with exactly those +clusters rather than some others but you + + align:start position:0% +clusters rather than some others but you + + + align:start position:0% +clusters rather than some others but you +can see that there is some sense to it + + align:start position:0% +can see that there is some sense to it + + + align:start position:0% +can see that there is some sense to it +so here you see a lot of greens at this + + align:start position:0% +so here you see a lot of greens at this + + + align:start position:0% +so here you see a lot of greens at this +end of it and not very much at this end + + align:start position:0% +end of it and not very much at this end + + + align:start position:0% +end of it and not very much at this end +and vice versa so there is some + + align:start position:0% +and vice versa so there is some + + + align:start position:0% +and vice versa so there is some +difference between these clusters yeah + + align:start position:0% + + + + align:start position:0% + +yes so I'm going to talk in a minute + + align:start position:0% +yes so I'm going to talk in a minute + + + align:start position:0% +yes so I'm going to talk in a minute +about modern gene wide Association + + align:start position:0% +about modern gene wide Association + + + align:start position:0% +about modern gene wide Association +studies where basically you say I'm + + align:start position:0% +studies where basically you say I'm + + + align:start position:0% +studies where basically you say I'm +going to look at every gene known to man + + align:start position:0% +going to look at every gene known to man + + + align:start position:0% +going to look at every gene known to man +so they still have a list but the list + + align:start position:0% +so they still have a list but the list + + + align:start position:0% +so they still have a list but the list +is you know 20,000 or 25,000 it's + + align:start position:0% +is you know 20,000 or 25,000 it's + + + align:start position:0% +is you know 20,000 or 25,000 it's +whatever we know about and and that + + align:start position:0% +whatever we know about and and that + + + align:start position:0% +whatever we know about and and that +that's another way of doing it so what + + align:start position:0% +that's another way of doing it so what + + + align:start position:0% +that's another way of doing it so what +what was compelling about about this + + align:start position:0% +what was compelling about about this + + + align:start position:0% +what was compelling about about this +work this groups work is a later + + align:start position:0% +work this groups work is a later + + + align:start position:0% +work this groups work is a later +analysis showed that these five subtypes + + align:start position:0% +analysis showed that these five subtypes + + + align:start position:0% +analysis showed that these five subtypes +actually had different survival rates + + align:start position:0% +actually had different survival rates + + + align:start position:0% +actually had different survival rates +and at a P equal point oh one level of + + align:start position:0% +and at a P equal point oh one level of + + + align:start position:0% +and at a P equal point oh one level of +statistical significance you've seen + + align:start position:0% +statistical significance you've seen + + + align:start position:0% +statistical significance you've seen +these survival curves of course before + + align:start position:0% +these survival curves of course before + + + align:start position:0% +these survival curves of course before +from David's lecture but this is pretty + + align:start position:0% +from David's lecture but this is pretty + + + align:start position:0% +from David's lecture but this is pretty +pretty impressive that doing something + + align:start position:0% +pretty impressive that doing something + + + align:start position:0% +pretty impressive that doing something +that had nothing to do with the clinical + + align:start position:0% +that had nothing to do with the clinical + + + align:start position:0% +that had nothing to do with the clinical +condition of the patient this is purely + + align:start position:0% +condition of the patient this is purely + + + align:start position:0% +condition of the patient this is purely +based on their gene expression levels + + align:start position:0% +based on their gene expression levels + + + align:start position:0% +based on their gene expression levels +you were able to find clusters + + align:start position:0% +you were able to find clusters + + + align:start position:0% +you were able to find clusters +that actually behave differently + + align:start position:0% +that actually behave differently + + + align:start position:0% +that actually behave differently +clinically so some of them do better + + align:start position:0% +clinically so some of them do better + + + align:start position:0% +clinically so some of them do better +than others so this this paper and this + + align:start position:0% +than others so this this paper and this + + + align:start position:0% +than others so this this paper and this +set of this approach to work set off a + + align:start position:0% +set of this approach to work set off a + + + align:start position:0% +set of this approach to work set off a +huge set of additional work this was + + align:start position:0% +huge set of additional work this was + + + align:start position:0% +huge set of additional work this was +again back in the a lazada paper they + + align:start position:0% +again back in the a lazada paper they + + + align:start position:0% +again back in the a lazada paper they +did a similar relationship between 96 + + align:start position:0% +did a similar relationship between 96 + + + align:start position:0% +did a similar relationship between 96 +samples of normal and malignant + + align:start position:0% +samples of normal and malignant + + + align:start position:0% +samples of normal and malignant +lymphocytes and they get a similar + + align:start position:0% +lymphocytes and they get a similar + + + align:start position:0% +lymphocytes and they get a similar +result where the clusters that they + + align:start position:0% +result where the clusters that they + + + align:start position:0% +result where the clusters that they +identify here correspond to sort of well + + align:start position:0% +identify here correspond to sort of well + + + align:start position:0% +identify here correspond to sort of well +understood existing types of lymphoma so + + align:start position:0% +understood existing types of lymphoma so + + + align:start position:0% +understood existing types of lymphoma so +this is again gives you some confidence + + align:start position:0% +this is again gives you some confidence + + + align:start position:0% +this is again gives you some confidence +that what you're extracting from these + + align:start position:0% +that what you're extracting from these + + + align:start position:0% +that what you're extracting from these +genetic correlations is meaningful in + + align:start position:0% +genetic correlations is meaningful in + + + align:start position:0% +genetic correlations is meaningful in +the terms that people who deal with + + align:start position:0% +the terms that people who deal with + + + align:start position:0% +the terms that people who deal with +lymphomas think about about the topic + + align:start position:0% +lymphomas think about about the topic + + + align:start position:0% +lymphomas think about about the topic +but of course it can give you much more + + align:start position:0% +but of course it can give you much more + + + align:start position:0% +but of course it can give you much more +detail because people's intuitions may + + align:start position:0% +detail because people's intuitions may + + + align:start position:0% +detail because people's intuitions may +not be as effective as these large-scale + + align:start position:0% +not be as effective as these large-scale + + + align:start position:0% +not be as effective as these large-scale +data analyses so to get to your question + + align:start position:0% +data analyses so to get to your question + + + align:start position:0% +data analyses so to get to your question +about generalizing this I mean here's + + align:start position:0% +about generalizing this I mean here's + + + align:start position:0% +about generalizing this I mean here's +one way that I look at this if I list + + align:start position:0% +one way that I look at this if I list + + + align:start position:0% +one way that I look at this if I list +all the all the genes and I list all the + + align:start position:0% +all the all the genes and I list all the + + + align:start position:0% +all the all the genes and I list all the +phenotypes now we're a little more sure + + align:start position:0% +phenotypes now we're a little more sure + + + align:start position:0% +phenotypes now we're a little more sure +of what the genes are then of what the + + align:start position:0% +of what the genes are then of what the + + + align:start position:0% +of what the genes are then of what the +phenotypes are so that that's an + + align:start position:0% +phenotypes are so that that's an + + + align:start position:0% +phenotypes are so that that's an +interesting problem then I can do a + + align:start position:0% +interesting problem then I can do a + + + align:start position:0% +interesting problem then I can do a +bunch of analyses so you know what is a + + align:start position:0% +bunch of analyses so you know what is a + + + align:start position:0% +bunch of analyses so you know what is a +phenotype well it can be a diagnosed + + align:start position:0% +phenotype well it can be a diagnosed + + + align:start position:0% +phenotype well it can be a diagnosed +disease like breast cancer or it can be + + align:start position:0% +disease like breast cancer or it can be + + + align:start position:0% +disease like breast cancer or it can be +the type of lymphoma from the two + + align:start position:0% +the type of lymphoma from the two + + + align:start position:0% +the type of lymphoma from the two +examples I've just shown you it can also + + align:start position:0% +examples I've just shown you it can also + + + align:start position:0% +examples I've just shown you it can also +be a qualitative or a quantitative trait + + align:start position:0% +be a qualitative or a quantitative trait + + + align:start position:0% +be a qualitative or a quantitative trait +it could be your weight it could be your + + align:start position:0% +it could be your weight it could be your + + + align:start position:0% +it could be your weight it could be your +eye color it could be you know almost + + align:start position:0% +eye color it could be you know almost + + + align:start position:0% +eye color it could be you know almost +anything that is clinically known about + + align:start position:0% +anything that is clinically known about + + + align:start position:0% +anything that is clinically known about +you and it could even be behavior it + + align:start position:0% +you and it could even be behavior it + + + align:start position:0% +you and it could even be behavior it +could be things like + + align:start position:0% +could be things like + + + align:start position:0% +could be things like +you know how what is your daily output + + align:start position:0% +you know how what is your daily output + + + align:start position:0% +you know how what is your daily output +of Twitter posts right but that's a + + align:start position:0% +of Twitter posts right but that's a + + + align:start position:0% +of Twitter posts right but that's a +perfectly reasonable trait I don't know + + align:start position:0% +perfectly reasonable trait I don't know + + + align:start position:0% +perfectly reasonable trait I don't know +if it's genetically predictable but + + align:start position:0% +if it's genetically predictable but + + + align:start position:0% +if it's genetically predictable but +you'll see some surprising things there + + align:start position:0% +you'll see some surprising things there + + + align:start position:0% +you'll see some surprising things there +are so then how do you analyze this well + + align:start position:0% +are so then how do you analyze this well + + + align:start position:0% +are so then how do you analyze this well +if you start by looking at a particular + + align:start position:0% +if you start by looking at a particular + + + align:start position:0% +if you start by looking at a particular +phenotype and say what genes are + + align:start position:0% +phenotype and say what genes are + + + align:start position:0% +phenotype and say what genes are +associated with this then you're doing + + align:start position:0% +associated with this then you're doing + + + align:start position:0% +associated with this then you're doing +what's called a G wasps or a genome-wide + + align:start position:0% +what's called a G wasps or a genome-wide + + + align:start position:0% +what's called a G wasps or a genome-wide +Association study so you look for + + align:start position:0% +Association study so you look for + + + align:start position:0% +Association study so you look for +genetic differences that correspond to + + align:start position:0% +genetic differences that correspond to + + + align:start position:0% +genetic differences that correspond to +specific phenotypic differences and + + align:start position:0% +specific phenotypic differences and + + + align:start position:0% +specific phenotypic differences and +usually you're looking at things like + + align:start position:0% +usually you're looking at things like + + + align:start position:0% +usually you're looking at things like +single nucleotide polymorphisms so this + + align:start position:0% +single nucleotide polymorphisms so this + + + align:start position:0% +single nucleotide polymorphisms so this +is places where your genome differs from + + align:start position:0% +is places where your genome differs from + + + align:start position:0% +is places where your genome differs from +the reference genome the the most common + + align:start position:0% +the reference genome the the most common + + + align:start position:0% +the reference genome the the most common +genome in the human population + + align:start position:0% +genome in the human population + + + align:start position:0% +genome in the human population +at one particular locus so you have a + + align:start position:0% +at one particular locus so you have a + + + align:start position:0% +at one particular locus so you have a +see instead of a G or something one + + align:start position:0% +see instead of a G or something one + + + align:start position:0% +see instead of a G or something one +place in your genes copy number + + align:start position:0% +place in your genes copy number + + + align:start position:0% +place in your genes copy number +variations there's there are stretches + + align:start position:0% +variations there's there are stretches + + + align:start position:0% +variations there's there are stretches +of DNA that have repeats in them and the + + align:start position:0% +of DNA that have repeats in them and the + + + align:start position:0% +of DNA that have repeats in them and the +number of repeats is variable so one of + + align:start position:0% +number of repeats is variable so one of + + + align:start position:0% +number of repeats is variable so one of +the most famous ones of these is the one + + align:start position:0% +the most famous ones of these is the one + + + align:start position:0% +the most famous ones of these is the one +associated with Huntington's disease it + + align:start position:0% +associated with Huntington's disease it + + + align:start position:0% +associated with Huntington's disease it +turns out that if you have up to + + align:start position:0% +turns out that if you have up to + + + align:start position:0% +turns out that if you have up to +twenty-something repeats of a certain + + align:start position:0% +twenty-something repeats of a certain + + + align:start position:0% +twenty-something repeats of a certain +section of DNA you're perfectly healthy + + align:start position:0% +section of DNA you're perfectly healthy + + + align:start position:0% +section of DNA you're perfectly healthy +but if you're above 30-something then + + align:start position:0% +but if you're above 30-something then + + + align:start position:0% +but if you're above 30-something then +you're gonna die of Huntington's disease + + align:start position:0% +you're gonna die of Huntington's disease + + + align:start position:0% +you're gonna die of Huntington's disease +and again we don't quite understand + + align:start position:0% +and again we don't quite understand + + + align:start position:0% +and again we don't quite understand +these mechanisms but these are + + align:start position:0% +these mechanisms but these are + + + align:start position:0% +these mechanisms but these are +empirically known so copy number + + align:start position:0% +empirically known so copy number + + + align:start position:0% +empirically known so copy number +variations are important gene expression + + align:start position:0% +variations are important gene expression + + + align:start position:0% +variations are important gene expression +levels which I've talked about a minute + + align:start position:0% +levels which I've talked about a minute + + + align:start position:0% +levels which I've talked about a minute +ago but the trick here energy was-- is + + align:start position:0% +ago but the trick here energy was-- is + + + align:start position:0% +ago but the trick here energy was-- is +to look at a very wide set of genes + + align:start position:0% +to look at a very wide set of genes + + + align:start position:0% +to look at a very wide set of genes +rather than just a limited set of + + align:start position:0% +rather than just a limited set of + + + align:start position:0% +rather than just a limited set of +samples that you know you're interested + + align:start position:0% +samples that you know you're interested + + + align:start position:0% +samples that you know you're interested +in now the other approach is the + + align:start position:0% +in now the other approach is the + + + align:start position:0% +in now the other approach is the +opposite which is to say let's look at a + + align:start position:0% +opposite which is to say let's look at a + + + align:start position:0% +opposite which is to say let's look at a +particular gene and figure out what's it + + align:start position:0% +particular gene and figure out what's it + + + align:start position:0% +particular gene and figure out what's it +correlated with and so that's called a + + align:start position:0% +correlated with and so that's called a + + + align:start position:0% +correlated with and so that's called a +fee WAAS phenome wide Association study + + align:start position:0% +fee WAAS phenome wide Association study + + + align:start position:0% +fee WAAS phenome wide Association study +and now what you do + + align:start position:0% +and now what you do + + + align:start position:0% +and now what you do +as you list all the different phenotypes + + align:start position:0% +as you list all the different phenotypes + + + align:start position:0% +as you list all the different phenotypes +and you say well we can do the same kind + + align:start position:0% +and you say well we can do the same kind + + + align:start position:0% +and you say well we can do the same kind +of analysis to say which of them are + + align:start position:0% +of analysis to say which of them are + + + align:start position:0% +of analysis to say which of them are +disproportionately present in people who + + align:start position:0% +disproportionately present in people who + + + align:start position:0% +disproportionately present in people who +have that genetic variant so here's what + + align:start position:0% +have that genetic variant so here's what + + + align:start position:0% +have that genetic variant so here's what +a typical Gy looks like this is called a + + align:start position:0% +a typical Gy looks like this is called a + + + align:start position:0% +a typical Gy looks like this is called a +Manhattan plot which i think is pretty + + align:start position:0% +Manhattan plot which i think is pretty + + + align:start position:0% +Manhattan plot which i think is pretty +funny but it does kind of look like this + + align:start position:0% +funny but it does kind of look like this + + + align:start position:0% +funny but it does kind of look like this +guy line of Manhattan so this is all of + + align:start position:0% +guy line of Manhattan so this is all of + + + align:start position:0% +guy line of Manhattan so this is all of +your genes laid out in sequence along + + align:start position:0% +your genes laid out in sequence along + + + align:start position:0% +your genes laid out in sequence along +your chromosomes and you take a + + align:start position:0% +your chromosomes and you take a + + + align:start position:0% +your chromosomes and you take a +particular phenotype and you say what is + + align:start position:0% +particular phenotype and you say what is + + + align:start position:0% +particular phenotype and you say what is +the difference in the ratio of + + align:start position:0% +the difference in the ratio of + + + align:start position:0% +the difference in the ratio of +expression levels between people who + + align:start position:0% +expression levels between people who + + + align:start position:0% +expression levels between people who +have this disease and people who don't + + align:start position:0% +have this disease and people who don't + + + align:start position:0% +have this disease and people who don't +have this disease and something like + + align:start position:0% +have this disease and something like + + + align:start position:0% +have this disease and something like +this gene whatever it is clearly there's + + align:start position:0% +this gene whatever it is clearly there's + + + align:start position:0% +this gene whatever it is clearly there's +an enormous difference in its expression + + align:start position:0% +an enormous difference in its expression + + + align:start position:0% +an enormous difference in its expression +level and so you would be surprised if + + align:start position:0% +level and so you would be surprised if + + + align:start position:0% +level and so you would be surprised if +this gene didn't have something to do + + align:start position:0% +this gene didn't have something to do + + + align:start position:0% +this gene didn't have something to do +with the disease and similarly you can + + align:start position:0% +with the disease and similarly you can + + + align:start position:0% +with the disease and similarly you can +calculate sort of different significance + + align:start position:0% +calculate sort of different significance + + + align:start position:0% +calculate sort of different significance +levels you have to do something like a + + align:start position:0% +levels you have to do something like a + + + align:start position:0% +levels you have to do something like a +bonferroni correction because you're + + align:start position:0% +bonferroni correction because you're + + + align:start position:0% +bonferroni correction because you're +testing so many hypotheses + + align:start position:0% +testing so many hypotheses + + + align:start position:0% +testing so many hypotheses +simultaneously and so typically the top + + align:start position:0% +simultaneously and so typically the top + + + align:start position:0% +simultaneously and so typically the top +of these lines is the bonferroni + + align:start position:0% +of these lines is the bonferroni + + + align:start position:0% +of these lines is the bonferroni +correction the corrected threshold and + + align:start position:0% +correction the corrected threshold and + + + align:start position:0% +correction the corrected threshold and +then you say okay this guy this guy this + + align:start position:0% +then you say okay this guy this guy this + + + align:start position:0% +then you say okay this guy this guy this +guy this guy and this guy come above + + align:start position:0% +guy this guy and this guy come above + + + align:start position:0% +guy this guy and this guy come above +that threshold so these are good + + align:start position:0% +that threshold so these are good + + + align:start position:0% +that threshold so these are good +candidate genes to think that may be + + align:start position:0% +candidate genes to think that may be + + + align:start position:0% +candidate genes to think that may be +associated with this disease now can you + + align:start position:0% +associated with this disease now can you + + + align:start position:0% +associated with this disease now can you +go out and start treating people based + + align:start position:0% +go out and start treating people based + + + align:start position:0% +go out and start treating people based +on that well it's probably not a good + + align:start position:0% +on that well it's probably not a good + + + align:start position:0% +on that well it's probably not a good +idea because there are many reasons why + + align:start position:0% +idea because there are many reasons why + + + align:start position:0% +idea because there are many reasons why +this analysis might have failed all the + + align:start position:0% +this analysis might have failed all the + + + align:start position:0% +this analysis might have failed all the +lessons that you've heard about + + align:start position:0% +lessons that you've heard about + + + align:start position:0% +lessons that you've heard about +confounders come in very strongly here + + align:start position:0% +confounders come in very strongly here + + + align:start position:0% +confounders come in very strongly here +and so typically what biologists do is + + align:start position:0% +and so typically what biologists do is + + + align:start position:0% +and so typically what biologists do is +they do this kind of analysis they then + + align:start position:0% +they do this kind of analysis they then + + + align:start position:0% +they do this kind of analysis they then +create a strain of knockout mice who + + align:start position:0% +create a strain of knockout mice who + + + align:start position:0% +create a strain of knockout mice who +have some analog of whatever disease it + + align:start position:0% +have some analog of whatever disease it + + + align:start position:0% +have some analog of whatever disease it +is that you're studying and and they see + + align:start position:0% +is that you're studying and and they see + + + align:start position:0% +is that you're studying and and they see +whether in fact knocking out a certain + + align:start position:0% +whether in fact knocking out a certain + + + align:start position:0% +whether in fact knocking out a certain +gene + + align:start position:0% +gene + + + align:start position:0% +gene +like you know this guy cures or creates + + align:start position:0% +like you know this guy cures or creates + + + align:start position:0% +like you know this guy cures or creates +the disease that you're interested in in + + align:start position:0% +the disease that you're interested in in + + + align:start position:0% +the disease that you're interested in in +this mouse model and then you have a + + align:start position:0% +this mouse model and then you have a + + + align:start position:0% +this mouse model and then you have a +more mechanistic explanation for what + + align:start position:0% +more mechanistic explanation for what + + + align:start position:0% +more mechanistic explanation for what +the relationship might be okay so + + align:start position:0% +the relationship might be okay so + + + align:start position:0% +the relationship might be okay so +basically you're looking at the ratio of + + align:start position:0% +basically you're looking at the ratio of + + + align:start position:0% +basically you're looking at the ratio of +the odds of having the disease if you + + align:start position:0% +the odds of having the disease if you + + + align:start position:0% +the odds of having the disease if you +have the a snip or if you have a genetic + + align:start position:0% +have the a snip or if you have a genetic + + + align:start position:0% +have the a snip or if you have a genetic +variant to having the disease if you + + align:start position:0% +variant to having the disease if you + + + align:start position:0% +variant to having the disease if you +don't have the genetic variant yeah + + align:start position:0% + + + + align:start position:0% + +I'm curious there are specific + + align:start position:0% +I'm curious there are specific + + + align:start position:0% +I'm curious there are specific +computational techniques adapted to this + + align:start position:0% +computational techniques adapted to this + + + align:start position:0% +computational techniques adapted to this +scenario that allow you to sort of mind + + align:start position:0% +scenario that allow you to sort of mind + + + align:start position:0% +scenario that allow you to sort of mind +a bit more yeah so if you talk to the + + align:start position:0% +a bit more yeah so if you talk to the + + + align:start position:0% +a bit more yeah so if you talk to the +statisticians who are more expert at + + align:start position:0% +statisticians who are more expert at + + + align:start position:0% +statisticians who are more expert at +this than the computer scientists + + align:start position:0% +this than the computer scientists + + + align:start position:0% +this than the computer scientists +typically they will tell you that + + align:start position:0% +typically they will tell you that + + + align:start position:0% +typically they will tell you that +bonferroni is is a very conservative + + align:start position:0% +bonferroni is is a very conservative + + + align:start position:0% +bonferroni is is a very conservative +kind of correction and if you can impose + + align:start position:0% +kind of correction and if you can impose + + + align:start position:0% +kind of correction and if you can impose +some sort of structure on the set of + + align:start position:0% +some sort of structure on the set of + + + align:start position:0% +some sort of structure on the set of +genes that you're testing then you can + + align:start position:0% +genes that you're testing then you can + + + align:start position:0% +genes that you're testing then you can +cheat and you can say well you know + + align:start position:0% +cheat and you can say well you know + + + align:start position:0% +cheat and you can say well you know +these 75 genes actually are all part of + + align:start position:0% +these 75 genes actually are all part of + + + align:start position:0% +these 75 genes actually are all part of +the same mechanism and we're really + + align:start position:0% +the same mechanism and we're really + + + align:start position:0% +the same mechanism and we're really +testing the mechanism and not the + + align:start position:0% +testing the mechanism and not the + + + align:start position:0% +testing the mechanism and not the +individual gene and therefore instead of + + align:start position:0% +individual gene and therefore instead of + + + align:start position:0% +individual gene and therefore instead of +making a bonferroni correction for 75 of + + align:start position:0% +making a bonferroni correction for 75 of + + + align:start position:0% +making a bonferroni correction for 75 of +these guys we only have to do it for one + + align:start position:0% +these guys we only have to do it for one + + + align:start position:0% +these guys we only have to do it for one +and so you can reduce the bonferroni + + align:start position:0% +and so you can reduce the bonferroni + + + align:start position:0% +and so you can reduce the bonferroni +correction that way but people get + + align:start position:0% +correction that way but people get + + + align:start position:0% +correction that way but people get +nervous when you do that because you + + align:start position:0% +nervous when you do that because you + + + align:start position:0% +nervous when you do that because you +know your incentive as as a researcher + + align:start position:0% +know your incentive as as a researcher + + + align:start position:0% +know your incentive as as a researcher +is to show statistically significant + + align:start position:0% +is to show statistically significant + + + align:start position:0% +is to show statistically significant +results but that whole question of + + align:start position:0% +results but that whole question of + + + align:start position:0% +results but that whole question of +p-values keeps coming under under + + align:start position:0% +p-values keeps coming under under + + + align:start position:0% +p-values keeps coming under under +discussion so the the head of the + + align:start position:0% +discussion so the the head of the + + + align:start position:0% +discussion so the the head of the +American Statistical Association about + + align:start position:0% +American Statistical Association about + + + align:start position:0% +American Statistical Association about +15 years ago + + align:start position:0% +15 years ago + + + align:start position:0% +15 years ago +was a Stanford professor and he + + align:start position:0% +was a Stanford professor and he + + + align:start position:0% +was a Stanford professor and he +published what became a very notorious + + align:start position:0% + + + + align:start position:0% + +article saying you know we got it all + + align:start position:0% +article saying you know we got it all + + + align:start position:0% +article saying you know we got it all +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +statistical significance is not + + align:start position:0% +statistical significance is not + + + align:start position:0% +statistical significance is not +significance in the in the standard + + align:start position:0% +significance in the in the standard + + + align:start position:0% +significance in the in the standard +English sense of the word and so he + + align:start position:0% +English sense of the word and so he + + + align:start position:0% +English sense of the word and so he +called for various other ways and was + + align:start position:0% +called for various other ways and was + + + align:start position:0% +called for various other ways and was +more sympathetic to Bayesian kinds of + + align:start position:0% +more sympathetic to Bayesian kinds of + + + align:start position:0% +more sympathetic to Bayesian kinds of +reasoning and things like that so there + + align:start position:0% +reasoning and things like that so there + + + align:start position:0% +reasoning and things like that so there +may be some gradual movement to that but + + align:start position:0% +may be some gradual movement to that but + + + align:start position:0% +may be some gradual movement to that but +this is a huge can of worms to which we + + align:start position:0% +this is a huge can of worms to which we + + + align:start position:0% +this is a huge can of worms to which we +don't have a very good mechanistic + + align:start position:0% +don't have a very good mechanistic + + + align:start position:0% +don't have a very good mechanistic +answer okay all right so if you do these + + align:start position:0% +answer okay all right so if you do these + + + align:start position:0% +answer okay all right so if you do these +these G Wasa's and and this is the real + + align:start position:0% +these G Wasa's and and this is the real + + + align:start position:0% +these G Wasa's and and this is the real +problem with them is that most of what + + align:start position:0% +problem with them is that most of what + + + align:start position:0% +problem with them is that most of what +you see is down here so you have things + + align:start position:0% +you see is down here so you have things + + + align:start position:0% +you see is down here so you have things +with + + align:start position:0% +with + + + align:start position:0% +with +common variance but they have very small + + align:start position:0% +common variance but they have very small + + + align:start position:0% +common variance but they have very small +effect sizes when you look at what their + + align:start position:0% +effect sizes when you look at what their + + + align:start position:0% +effect sizes when you look at what their +effect is on a particular disease and so + + align:start position:0% +effect is on a particular disease and so + + + align:start position:0% +effect is on a particular disease and so +that seems at Kohana that i mentioned + + align:start position:0% +that seems at Kohana that i mentioned + + + align:start position:0% +that seems at Kohana that i mentioned +earlier has always been challenging + + align:start position:0% +earlier has always been challenging + + + align:start position:0% +earlier has always been challenging +people doing this kind of work saying + + align:start position:0% +people doing this kind of work saying + + + align:start position:0% +people doing this kind of work saying +look for example we did an odds we did a + + align:start position:0% +look for example we did an odds we did a + + + align:start position:0% +look for example we did an odds we did a +G wass with cat Leo who was a guest + + align:start position:0% +G wass with cat Leo who was a guest + + + align:start position:0% +G wass with cat Leo who was a guest +interviewee here when I was lecturing + + align:start position:0% +interviewee here when I was lecturing + + + align:start position:0% +interviewee here when I was lecturing +earlier in the semester + + align:start position:0% +earlier in the semester + + + align:start position:0% +earlier in the semester +she's a Rheumatologist and we did a + + align:start position:0% +she's a Rheumatologist and we did a + + + align:start position:0% +she's a Rheumatologist and we did a +genome-wide Association study we found a + + align:start position:0% +genome-wide Association study we found a + + + align:start position:0% +genome-wide Association study we found a +bunch of genes that had odds ratios of + + align:start position:0% +bunch of genes that had odds ratios of + + + align:start position:0% +bunch of genes that had odds ratios of +like one point one two one one point 2 + + align:start position:0% +like one point one two one one point 2 + + + align:start position:0% +like one point one two one one point 2 +to 1 and they're statistically + + align:start position:0% +to 1 and they're statistically + + + align:start position:0% +to 1 and they're statistically +significant because if you collect + + align:start position:0% +significant because if you collect + + + align:start position:0% +significant because if you collect +enough data everything is statistically + + align:start position:0% +enough data everything is statistically + + + align:start position:0% +enough data everything is statistically +significant ok + + align:start position:0% +significant ok + + + align:start position:0% +significant ok +but are they significant in the other + + align:start position:0% +but are they significant in the other + + + align:start position:0% +but are they significant in the other +sense of significance well so Zach's + + align:start position:0% +sense of significance well so Zach's + + + align:start position:0% +sense of significance well so Zach's +argument was that if you look at + + align:start position:0% +argument was that if you look at + + + align:start position:0% +argument was that if you look at +something like the odds ratio of lung + + align:start position:0% +something like the odds ratio of lung + + + align:start position:0% +something like the odds ratio of lung +cancer for people who do and don't smoke + + align:start position:0% +cancer for people who do and don't smoke + + + align:start position:0% +cancer for people who do and don't smoke +the odds ratio is 8 ok so when you + + align:start position:0% +the odds ratio is 8 ok so when you + + + align:start position:0% +the odds ratio is 8 ok so when you +compare 1.1 to 8 you should be ashamed + + align:start position:0% +compare 1.1 to 8 you should be ashamed + + + align:start position:0% +compare 1.1 to 8 you should be ashamed +here you're not doing very well in terms + + align:start position:0% +here you're not doing very well in terms + + + align:start position:0% +here you're not doing very well in terms +of elucidating what the effects really + + align:start position:0% +of elucidating what the effects really + + + align:start position:0% +of elucidating what the effects really +are and so Zach actually has argued very + + align:start position:0% +are and so Zach actually has argued very + + + align:start position:0% +are and so Zach actually has argued very +strongly that rather than focusing all + + align:start position:0% +strongly that rather than focusing all + + + align:start position:0% +strongly that rather than focusing all +our attention on these genetic factors + + align:start position:0% +our attention on these genetic factors + + + align:start position:0% +our attention on these genetic factors +that have very weak relationships we + + align:start position:0% +that have very weak relationships we + + + align:start position:0% +that have very weak relationships we +should instead focus more on clinical + + align:start position:0% +should instead focus more on clinical + + + align:start position:0% +should instead focus more on clinical +things that often have stronger + + align:start position:0% +things that often have stronger + + + align:start position:0% +things that often have stronger +predictive relationships and some + + align:start position:0% +predictive relationships and some + + + align:start position:0% +predictive relationships and some +combination of course is best now it is + + align:start position:0% +combination of course is best now it is + + + align:start position:0% +combination of course is best now it is +true that we know a whole bunch of + + align:start position:0% +true that we know a whole bunch of + + + align:start position:0% +true that we know a whole bunch of +highly penetrant Mendelian mutations so + + align:start position:0% +highly penetrant Mendelian mutations so + + + align:start position:0% +highly penetrant Mendelian mutations so +these are ones were you know one change + + align:start position:0% +these are ones were you know one change + + + align:start position:0% +these are ones were you know one change +in your genome and all of a sudden you + + align:start position:0% +in your genome and all of a sudden you + + + align:start position:0% +in your genome and all of a sudden you +have some terrible disease and I think + + align:start position:0% +have some terrible disease and I think + + + align:start position:0% +have some terrible disease and I think +when the genome project started in the + + align:start position:0% +when the genome project started in the + + + align:start position:0% +when the genome project started in the +1990s there was an expectation that we + + align:start position:0% +1990s there was an expectation that we + + + align:start position:0% +1990s there was an expectation that we +would find a whole bunch more things + + align:start position:0% +would find a whole bunch more things + + + align:start position:0% +would find a whole bunch more things +like that from knowing the genome + + align:start position:0% +like that from knowing the genome + + + align:start position:0% +like that from knowing the genome +and that expectation was dashed because + + align:start position:0% +and that expectation was dashed because + + + align:start position:0% +and that expectation was dashed because +what we discovered is that our + + align:start position:0% +what we discovered is that our + + + align:start position:0% +what we discovered is that our +predecessors were actually pretty good + + align:start position:0% +predecessors were actually pretty good + + + align:start position:0% +predecessors were actually pretty good +at recognizing those kinds of diseases + + align:start position:0% +at recognizing those kinds of diseases + + + align:start position:0% +at recognizing those kinds of diseases +you know from Mendel on with the + + align:start position:0% +you know from Mendel on with the + + + align:start position:0% +you know from Mendel on with the +wrinkled peas if you see a family in + + align:start position:0% +wrinkled peas if you see a family in + + + align:start position:0% +wrinkled peas if you see a family in +which there's a segregation pattern + + align:start position:0% +which there's a segregation pattern + + + align:start position:0% +which there's a segregation pattern +where you can see who has the disease + + align:start position:0% +where you can see who has the disease + + + align:start position:0% +where you can see who has the disease +and who doesn't and what their + + align:start position:0% +and who doesn't and what their + + + align:start position:0% +and who doesn't and what their +relationships are you can get a pretty + + align:start position:0% +relationships are you can get a pretty + + + align:start position:0% +relationships are you can get a pretty +good idea of what genes or what genetic + + align:start position:0% +good idea of what genes or what genetic + + + align:start position:0% +good idea of what genes or what genetic +variants are associated with that + + align:start position:0% +variants are associated with that + + + align:start position:0% +variants are associated with that +disease and it turns out we had found + + align:start position:0% +disease and it turns out we had found + + + align:start position:0% +disease and it turns out we had found +almost all of them and so there weren't + + align:start position:0% +almost all of them and so there weren't + + + align:start position:0% +almost all of them and so there weren't +a whole lot more that are highly + + align:start position:0% +a whole lot more that are highly + + + align:start position:0% +a whole lot more that are highly +penetrant Mendelian mutations and so + + align:start position:0% +penetrant Mendelian mutations and so + + + align:start position:0% +penetrant Mendelian mutations and so +what we had is mostly these common + + align:start position:0% +what we had is mostly these common + + + align:start position:0% +what we had is mostly these common +variants with small effects what's + + align:start position:0% +variants with small effects what's + + + align:start position:0% +variants with small effects what's +really interesting and worth working on + + align:start position:0% +really interesting and worth working on + + + align:start position:0% +really interesting and worth working on +is these rare variants with small + + align:start position:0% +is these rare variants with small + + + align:start position:0% +is these rare variants with small +effects so the things you know the + + align:start position:0% +effects so the things you know the + + + align:start position:0% +effects so the things you know the +mystery kid like the kid whose case I + + align:start position:0% +mystery kid like the kid whose case I + + + align:start position:0% +mystery kid like the kid whose case I +showed you probably have some + + align:start position:0% +showed you probably have some + + + align:start position:0% +showed you probably have some +interesting genetics that is quite + + align:start position:0% +interesting genetics that is quite + + + align:start position:0% +interesting genetics that is quite +uncommon and obviously for a long time + + align:start position:0% +uncommon and obviously for a long time + + + align:start position:0% +uncommon and obviously for a long time +had a small effect but then all of a + + align:start position:0% +had a small effect but then all of a + + + align:start position:0% +had a small effect but then all of a +sudden something happened and there is + + align:start position:0% +sudden something happened and there is + + + align:start position:0% +sudden something happened and there is +this whole field called unknown disease + + align:start position:0% +this whole field called unknown disease + + + align:start position:0% +this whole field called unknown disease +diagnosis that says you know what do you + + align:start position:0% +diagnosis that says you know what do you + + + align:start position:0% +diagnosis that says you know what do you +do when some weirdo walks in off the + + align:start position:0% +do when some weirdo walks in off the + + + align:start position:0% +do when some weirdo walks in off the +street and you have no idea what's going + + align:start position:0% +street and you have no idea what's going + + + align:start position:0% +street and you have no idea what's going +on and there are now companies so I was + + align:start position:0% +on and there are now companies so I was + + + align:start position:0% +on and there are now companies so I was +a judge in a challenge about four or + + align:start position:0% +a judge in a challenge about four or + + + align:start position:0% +a judge in a challenge about four or +five years ago where we took eight kids + + align:start position:0% +five years ago where we took eight kids + + + align:start position:0% +five years ago where we took eight kids +like this and we genotype them and we + + align:start position:0% +like this and we genotype them and we + + + align:start position:0% +like this and we genotype them and we +genotype their parents and their + + align:start position:0% +genotype their parents and their + + + align:start position:0% +genotype their parents and their +grandparents and their siblings and we + + align:start position:0% +grandparents and their siblings and we + + + align:start position:0% +grandparents and their siblings and we +took all their clinical data this was + + align:start position:0% +took all their clinical data this was + + + align:start position:0% +took all their clinical data this was +with the consent of their parents of + + align:start position:0% +with the consent of their parents of + + + align:start position:0% +with the consent of their parents of +course and we made it available as a + + align:start position:0% +course and we made it available as a + + + align:start position:0% +course and we made it available as a +contest and we had 20-something + + align:start position:0% +contest and we had 20-something + + + align:start position:0% +contest and we had 20-something +participants from around the world who + + align:start position:0% +participants from around the world who + + + align:start position:0% +participants from around the world who +tried to figure out something useful to + + align:start position:0% +tried to figure out something useful to + + + align:start position:0% +tried to figure out something useful to +say about these kids and you go through + + align:start position:0% +say about these kids and you go through + + + align:start position:0% +say about these kids and you go through +a pipeline and we did this in two rounds + + align:start position:0% +a pipeline and we did this in two rounds + + + align:start position:0% +a pipeline and we did this in two rounds +the first round the pipeline's all + + align:start position:0% +the first round the pipeline's all + + + align:start position:0% +the first round the pipeline's all +looked very + + align:start position:0% +looked very + + + align:start position:0% +looked very +and the second round a couple years + + align:start position:0% +and the second round a couple years + + + align:start position:0% +and the second round a couple years +later the pipeline's had pretty much + + align:start position:0% +later the pipeline's had pretty much + + + align:start position:0% +later the pipeline's had pretty much +converged and I see now that there's a + + align:start position:0% +converged and I see now that there's a + + + align:start position:0% +converged and I see now that there's a +company that did well in one of these + + align:start position:0% +company that did well in one of these + + + align:start position:0% +company that did well in one of these +challenges that now sells this as a + + align:start position:0% +challenges that now sells this as a + + + align:start position:0% +challenges that now sells this as a +service like I showed you before + + align:start position:0% +service like I showed you before + + + align:start position:0% +service like I showed you before +different company and so you send them + + align:start position:0% +different company and so you send them + + + align:start position:0% +different company and so you send them +the the gene the genetic makeup of some + + align:start position:0% +the the gene the genetic makeup of some + + + align:start position:0% +the the gene the genetic makeup of some +kid with weird condition and the genetic + + align:start position:0% +kid with weird condition and the genetic + + + align:start position:0% +kid with weird condition and the genetic +makeup of their family and it tries to + + align:start position:0% +makeup of their family and it tries to + + + align:start position:0% +makeup of their family and it tries to +guess which genes might be involved in + + align:start position:0% +guess which genes might be involved in + + + align:start position:0% +guess which genes might be involved in +the in causing the problem that this + + align:start position:0% +the in causing the problem that this + + + align:start position:0% +the in causing the problem that this +child has that's not the answer of + + align:start position:0% +child has that's not the answer of + + + align:start position:0% +child has that's not the answer of +course because that's just a sort of + + align:start position:0% +course because that's just a sort of + + + align:start position:0% +course because that's just a sort of +suspicion of a problem and then you have + + align:start position:0% +suspicion of a problem and then you have + + + align:start position:0% +suspicion of a problem and then you have +to go out and do real biological work to + + align:start position:0% +to go out and do real biological work to + + + align:start position:0% +to go out and do real biological work to +try to reproduce that scenario and see + + align:start position:0% +try to reproduce that scenario and see + + + align:start position:0% +try to reproduce that scenario and see +what the effects really are but at least + + align:start position:0% +what the effects really are but at least + + + align:start position:0% +what the effects really are but at least +in in a couple of cases out of those + + align:start position:0% +in in a couple of cases out of those + + + align:start position:0% +in in a couple of cases out of those +eight those hints have in fact led to a + + align:start position:0% +eight those hints have in fact led to a + + + align:start position:0% +eight those hints have in fact led to a +much better understanding of what caused + + align:start position:0% +much better understanding of what caused + + + align:start position:0% +much better understanding of what caused +the problems in these in these children + + align:start position:0% + + + + align:start position:0% + +that was fun by the way I I got my name + + align:start position:0% +that was fun by the way I I got my name + + + align:start position:0% +that was fun by the way I I got my name +as an author on one of these things that + + align:start position:0% +as an author on one of these things that + + + align:start position:0% +as an author on one of these things that +looks like a high-energy physics + + align:start position:0% +looks like a high-energy physics + + + align:start position:0% +looks like a high-energy physics +experiment it's the first two pages of + + align:start position:0% +experiment it's the first two pages of + + + align:start position:0% +experiment it's the first two pages of +the paper is just the list of authors so + + align:start position:0% +the paper is just the list of authors so + + + align:start position:0% +the paper is just the list of authors so +that's kind of interesting okay now + + align:start position:0% +that's kind of interesting okay now + + + align:start position:0% +that's kind of interesting okay now +here's a more recent study which is + + align:start position:0% +here's a more recent study which is + + + align:start position:0% +here's a more recent study which is +genome-wide Association of type two + + align:start position:0% +genome-wide Association of type two + + + align:start position:0% +genome-wide Association of type two +diabetes it's not quite gene wide + + align:start position:0% +diabetes it's not quite gene wide + + + align:start position:0% +diabetes it's not quite gene wide +because they didn't study every locus + + align:start position:0% +because they didn't study every locus + + + align:start position:0% +because they didn't study every locus +but they studied a hundred Llosa that + + align:start position:0% +but they studied a hundred Llosa that + + + align:start position:0% +but they studied a hundred Llosa that +have been associated with type 2 + + align:start position:0% +have been associated with type 2 + + + align:start position:0% +have been associated with type 2 +diabetes in previous studies so of + + align:start position:0% +diabetes in previous studies so of + + + align:start position:0% +diabetes in previous studies so of +course if you're not the first person + + align:start position:0% +course if you're not the first person + + + align:start position:0% +course if you're not the first person +doing this kind of work you can rely on + + align:start position:0% +doing this kind of work you can rely on + + + align:start position:0% +doing this kind of work you can rely on +the literature where other people have + + align:start position:0% +the literature where other people have + + + align:start position:0% +the literature where other people have +already come up with some interesting + + align:start position:0% +already come up with some interesting + + + align:start position:0% +already come up with some interesting +ideas so they wound up selecting 90 for + + align:start position:0% +ideas so they wound up selecting 90 for + + + align:start position:0% +ideas so they wound up selecting 90 for +type 2 diabetes associated variants so + + align:start position:0% +type 2 diabetes associated variants so + + + align:start position:0% +type 2 diabetes associated variants so +these are glycemic traits you know + + align:start position:0% +these are glycemic traits you know + + + align:start position:0% +these are glycemic traits you know +fasting insulin fasting glucose etc + + align:start position:0% +fasting insulin fasting glucose etc + + + align:start position:0% +fasting insulin fasting glucose etc +things about your body your body mass + + align:start position:0% +things about your body your body mass + + + align:start position:0% +things about your body your body mass +and + + align:start position:0% +and + + + align:start position:0% +and +height weight circumference etc lipid + + align:start position:0% +height weight circumference etc lipid + + + align:start position:0% +height weight circumference etc lipid +levels of various sorts associations + + align:start position:0% +levels of various sorts associations + + + align:start position:0% +levels of various sorts associations +with different diseases coronary artery + + align:start position:0% +with different diseases coronary artery + + + align:start position:0% +with different diseases coronary artery +disease renal function etc and let me + + align:start position:0% +disease renal function etc and let me + + + align:start position:0% +disease renal function etc and let me +come back to this so what they did is + + align:start position:0% +come back to this so what they did is + + + align:start position:0% +come back to this so what they did is +they said okay here's the way we're + + align:start position:0% +they said okay here's the way we're + + + align:start position:0% +they said okay here's the way we're +going to model this we have an + + align:start position:0% +going to model this we have an + + + align:start position:0% +going to model this we have an +association matrix that is 47 traits by + + align:start position:0% +association matrix that is 47 traits by + + + align:start position:0% +association matrix that is 47 traits by +94 genetic factors so we make a matrix + + align:start position:0% +94 genetic factors so we make a matrix + + + align:start position:0% +94 genetic factors so we make a matrix +out of that and then they did something + + align:start position:0% +out of that and then they did something + + + align:start position:0% +out of that and then they did something +funny so they doubled the traits the + + align:start position:0% +funny so they doubled the traits the + + + align:start position:0% +funny so they doubled the traits the +technology for matrix factorization is + + align:start position:0% +technology for matrix factorization is + + + align:start position:0% +technology for matrix factorization is +called non-negative matrix factorization + + align:start position:0% +called non-negative matrix factorization + + + align:start position:0% +called non-negative matrix factorization +and since many of those associations + + align:start position:0% +and since many of those associations + + + align:start position:0% +and since many of those associations +were negative what they did is for each + + align:start position:0% +were negative what they did is for each + + + align:start position:0% +were negative what they did is for each +trait that had both positive and + + align:start position:0% +trait that had both positive and + + + align:start position:0% +trait that had both positive and +negative values they duplicated the + + align:start position:0% +negative values they duplicated the + + + align:start position:0% +negative values they duplicated the +column they created one column that had + + align:start position:0% +column they created one column that had + + + align:start position:0% +column they created one column that had +positive associations and one column + + align:start position:0% +positive associations and one column + + + align:start position:0% +positive associations and one column +that had the negation of the negative + + align:start position:0% +that had the negation of the negative + + + align:start position:0% +that had the negation of the negative +associations with zeros everywhere else + + align:start position:0% +associations with zeros everywhere else + + + align:start position:0% +associations with zeros everywhere else +so that's how they dealt with that + + align:start position:0% +so that's how they dealt with that + + + align:start position:0% +so that's how they dealt with that +problem and then they said ok we're + + align:start position:0% +problem and then they said ok we're + + + align:start position:0% +problem and then they said ok we're +going to apply matrix factorization to + + align:start position:0% +going to apply matrix factorization to + + + align:start position:0% +going to apply matrix factorization to +factor X into two matrices W and H and I + + align:start position:0% +factor X into two matrices W and H and I + + + align:start position:0% +factor X into two matrices W and H and I +drew those here on the board so you have + + align:start position:0% +drew those here on the board so you have + + + align:start position:0% +drew those here on the board so you have +one matrix that well this is your + + align:start position:0% +one matrix that well this is your + + + align:start position:0% +one matrix that well this is your +original 47 by 94 matrix and the + + align:start position:0% +original 47 by 94 matrix and the + + + align:start position:0% +original 47 by 94 matrix and the +question is can you find two smaller + + align:start position:0% +question is can you find two smaller + + + align:start position:0% +question is can you find two smaller +matrices that are 47 by K and K by 94 + + align:start position:0% +matrices that are 47 by K and K by 94 + + + align:start position:0% +matrices that are 47 by K and K by 94 +that when you multiply these together + + align:start position:0% +that when you multiply these together + + + align:start position:0% +that when you multiply these together +you get back some close approximation to + + align:start position:0% +you get back some close approximation to + + + align:start position:0% +you get back some close approximation to +that matrix now if you've been looking + + align:start position:0% +that matrix now if you've been looking + + + align:start position:0% +that matrix now if you've been looking +at the literature there are all kinds of + + align:start position:0% +at the literature there are all kinds of + + + align:start position:0% +at the literature there are all kinds of +ideas like auto-encoders and and you + + align:start position:0% +ideas like auto-encoders and and you + + + align:start position:0% +ideas like auto-encoders and and you +know they all these are all basically + + align:start position:0% +know they all these are all basically + + + align:start position:0% +know they all these are all basically +the same underlying idea it's an + + align:start position:0% +the same underlying idea it's an + + + align:start position:0% +the same underlying idea it's an +unsupervised method that says can we + + align:start position:0% +unsupervised method that says can we + + + align:start position:0% +unsupervised method that says can we +find interesting patterns in the data by + + align:start position:0% +find interesting patterns in the data by + + + align:start position:0% +find interesting patterns in the data by +doing some kind of dimension reduction + + align:start position:0% +doing some kind of dimension reduction + + + align:start position:0% +doing some kind of dimension reduction +and this is one of those methods for + + align:start position:0% +and this is one of those methods for + + + align:start position:0% +and this is one of those methods for +doing dimension reduction so what's nice + + align:start position:0% +doing dimension reduction so what's nice + + + align:start position:0% +doing dimension reduction so what's nice +about this one is that when they get + + align:start position:0% +about this one is that when they get + + + align:start position:0% +about this one is that when they get +their W and H they + + align:start position:0% +their W and H they + + + align:start position:0% +their W and H they +predict X from that and then they know + + align:start position:0% +predict X from that and then they know + + + align:start position:0% +predict X from that and then they know +of course what the error is and they say + + align:start position:0% +of course what the error is and they say + + + align:start position:0% +of course what the error is and they say +well minimizing that error is our + + align:start position:0% +well minimizing that error is our + + + align:start position:0% +well minimizing that error is our +objective + + align:start position:0% +objective + + + align:start position:0% +objective +so that also lets them get it the + + align:start position:0% +so that also lets them get it the + + + align:start position:0% +so that also lets them get it the +question of what's the right K and + + align:start position:0% +question of what's the right K and + + + align:start position:0% +question of what's the right K and +that's an important problem because + + align:start position:0% +that's an important problem because + + + align:start position:0% +that's an important problem because +normally clustering methods like + + align:start position:0% +normally clustering methods like + + + align:start position:0% +normally clustering methods like +hierarchical clustering you have to + + align:start position:0% +hierarchical clustering you have to + + + align:start position:0% +hierarchical clustering you have to +specify what the number of clusters is + + align:start position:0% +specify what the number of clusters is + + + align:start position:0% +specify what the number of clusters is +that you're looking for and that's hard + + align:start position:0% +that you're looking for and that's hard + + + align:start position:0% +that you're looking for and that's hard +to do a priori whereas this technique + + align:start position:0% +to do a priori whereas this technique + + + align:start position:0% +to do a priori whereas this technique +can suggest at least which one fits the + + align:start position:0% +can suggest at least which one fits the + + + align:start position:0% +can suggest at least which one fits the +data best and so the loss function is + + align:start position:0% +data best and so the loss function is + + + align:start position:0% +data best and so the loss function is +some regularize del to distance between + + align:start position:0% +some regularize del to distance between + + + align:start position:0% +some regularize del to distance between +the reconstruction W times H and X and + + align:start position:0% +the reconstruction W times H and X and + + + align:start position:0% +the reconstruction W times H and X and +some penalty terms based on the size of + + align:start position:0% +some penalty terms based on the size of + + + align:start position:0% +some penalty terms based on the size of +W and H coupled by these relevance + + align:start position:0% +W and H coupled by these relevance + + + align:start position:0% +W and H coupled by these relevance +weights that you can look at the paper + + align:start position:0% +weights that you can look at the paper + + + align:start position:0% +weights that you can look at the paper +which I think I referred to in here and + + align:start position:0% +which I think I referred to in here and + + + align:start position:0% +which I think I referred to in here and +I asked you to read and then they do + + align:start position:0% +I asked you to read and then they do + + + align:start position:0% +I asked you to read and then they do +give sampling and a whole bunch of + + align:start position:0% +give sampling and a whole bunch of + + + align:start position:0% +give sampling and a whole bunch of +computational tricks to speed up the + + align:start position:0% +computational tricks to speed up the + + + align:start position:0% +computational tricks to speed up the +process so they got about 17,000 people + + align:start position:0% +process so they got about 17,000 people + + + align:start position:0% +process so they got about 17,000 people +from four different studies they're all + + align:start position:0% +from four different studies they're all + + + align:start position:0% +from four different studies they're all +of European ancestry so there's the + + align:start position:0% +of European ancestry so there's the + + + align:start position:0% +of European ancestry so there's the +usual generalization problem of how do + + align:start position:0% +usual generalization problem of how do + + + align:start position:0% +usual generalization problem of how do +you apply this to people from other + + align:start position:0% +you apply this to people from other + + + align:start position:0% +you apply this to people from other +parts of the world and they did + + align:start position:0% +parts of the world and they did + + + align:start position:0% +parts of the world and they did +individual analysis individual level + + align:start position:0% +individual analysis individual level + + + align:start position:0% +individual analysis individual level +analyses of all the individuals with + + align:start position:0% +analyses of all the individuals with + + + align:start position:0% +analyses of all the individuals with +type 2 diabetes from these and the + + align:start position:0% +type 2 diabetes from these and the + + + align:start position:0% +type 2 diabetes from these and the +results were that they found five + + align:start position:0% +results were that they found five + + + align:start position:0% +results were that they found five +subtypes again five which were present + + align:start position:0% +subtypes again five which were present + + + align:start position:0% +subtypes again five which were present +on eighty two point three percent of + + align:start position:0% +on eighty two point three percent of + + + align:start position:0% +on eighty two point three percent of +iterations so they by the way the total + + align:start position:0% +iterations so they by the way the total + + + align:start position:0% +iterations so they by the way the total +random aside there's a wonderful video + + align:start position:0% +random aside there's a wonderful video + + + align:start position:0% +random aside there's a wonderful video +at Caltech of the woman who just made + + align:start position:0% +at Caltech of the woman who just made + + + align:start position:0% +at Caltech of the woman who just made +the picture of the black hole shadow and + + align:start position:0% +the picture of the black hole shadow and + + + align:start position:0% +the picture of the black hole shadow and +she makes arguments very much like this + + align:start position:0% +she makes arguments very much like this + + + align:start position:0% +she makes arguments very much like this +you know we tried a whole bunch of + + align:start position:0% +you know we tried a whole bunch of + + + align:start position:0% +you know we tried a whole bunch of +different ways of coming up with this + + align:start position:0% +different ways of coming up with this + + + align:start position:0% +different ways of coming up with this +picture and what we decided was true is + + align:start position:0% +picture and what we decided was true is + + + align:start position:0% +picture and what we decided was true is +whatever showed up in almost all of the + + align:start position:0% +whatever showed up in almost all of the + + + align:start position:0% +whatever showed up in almost all of the +different methods of reconstructing it + + align:start position:0% +different methods of reconstructing it + + + align:start position:0% +different methods of reconstructing it +so the + + align:start position:0% +so the + + + align:start position:0% +so the +this kind of a similar argument and + + align:start position:0% +this kind of a similar argument and + + + align:start position:0% +this kind of a similar argument and +their interpretations medically or that + + align:start position:0% +their interpretations medically or that + + + align:start position:0% +their interpretations medically or that +one of them is involved with variations + + align:start position:0% +one of them is involved with variations + + + align:start position:0% +one of them is involved with variations +in in the beta cells so these are the + + align:start position:0% +in in the beta cells so these are the + + + align:start position:0% +in in the beta cells so these are the +cells in your pancreas that make insulin + + align:start position:0% +cells in your pancreas that make insulin + + + align:start position:0% +cells in your pancreas that make insulin +one of them is in variations in pro + + align:start position:0% +one of them is in variations in pro + + + align:start position:0% +one of them is in variations in pro +insulin which is a predecessor of + + align:start position:0% +insulin which is a predecessor of + + + align:start position:0% +insulin which is a predecessor of +insulin that is under different controls + + align:start position:0% +insulin that is under different controls + + + align:start position:0% +insulin that is under different controls +and then three others have to do with + + align:start position:0% +and then three others have to do with + + + align:start position:0% +and then three others have to do with +obesity bad things about your your lipid + + align:start position:0% +obesity bad things about your your lipid + + + align:start position:0% +obesity bad things about your your lipid +metabolism and then your liver function + + align:start position:0% +metabolism and then your liver function + + + align:start position:0% +metabolism and then your liver function +okay and if you look at their results + + align:start position:0% +okay and if you look at their results + + + align:start position:0% +okay and if you look at their results +the top spider diagrams so the way to + + align:start position:0% +the top spider diagrams so the way to + + + align:start position:0% +the top spider diagrams so the way to +interpret these is that the middle + + align:start position:0% +interpret these is that the middle + + + align:start position:0% +interpret these is that the middle +circle octagon the one in the very + + align:start position:0% +circle octagon the one in the very + + + align:start position:0% +circle octagon the one in the very +middle is the one with negative data the + + align:start position:0% +middle is the one with negative data the + + + align:start position:0% +middle is the one with negative data the +one in between that and the outside is + + align:start position:0% +one in between that and the outside is + + + align:start position:0% +one in between that and the outside is +with zero correlation and the outside + + align:start position:0% +with zero correlation and the outside + + + align:start position:0% +with zero correlation and the outside +one is with positive correlation and + + align:start position:0% +one is with positive correlation and + + + align:start position:0% +one is with positive correlation and +what you see is that different factors + + align:start position:0% +what you see is that different factors + + + align:start position:0% +what you see is that different factors +have different influences in these + + align:start position:0% +have different influences in these + + + align:start position:0% +have different influences in these +different clusters so these are the + + align:start position:0% +different clusters so these are the + + + align:start position:0% +different clusters so these are the +factors that are most informative and + + align:start position:0% +factors that are most informative and + + + align:start position:0% +factors that are most informative and +figuring out which cluster somebody + + align:start position:0% +figuring out which cluster somebody + + + align:start position:0% +figuring out which cluster somebody +belongs to and they indeed look + + align:start position:0% +belongs to and they indeed look + + + align:start position:0% +belongs to and they indeed look +considerably different I'm not going to + + align:start position:0% +considerably different I'm not going to + + + align:start position:0% +considerably different I'm not going to +have you read this but it'll be in the + + align:start position:0% +have you read this but it'll be in the + + + align:start position:0% +have you read this but it'll be in the +slides now one thing that's interesting + + align:start position:0% +slides now one thing that's interesting + + + align:start position:0% +slides now one thing that's interesting +and and again this won't be on the final + + align:start position:0% +and and again this won't be on the final + + + align:start position:0% +and and again this won't be on the final +exam but look at these numbers they're + + align:start position:0% +exam but look at these numbers they're + + + align:start position:0% +exam but look at these numbers they're +all tiny right some of them are hugely + + align:start position:0% +all tiny right some of them are hugely + + + align:start position:0% +all tiny right some of them are hugely +statistically significant so you know di + + align:start position:0% +statistically significant so you know di + + + align:start position:0% +statistically significant so you know di +whatever that is contributes point oh + + align:start position:0% +whatever that is contributes point oh + + + align:start position:0% +whatever that is contributes point oh +five units to having beta cell type of + + align:start position:0% +five units to having beta cell type of + + + align:start position:0% +five units to having beta cell type of +this disease at a p-value of six point + + align:start position:0% +this disease at a p-value of six point + + + align:start position:0% +this disease at a p-value of six point +six times ten to the minus thirty + + align:start position:0% +six times ten to the minus thirty + + + align:start position:0% +six times ten to the minus thirty +seventh so it's definitely there + + align:start position:0% +seventh so it's definitely there + + + align:start position:0% +seventh so it's definitely there +it's definitely in effect but it's not a + + align:start position:0% +it's definitely in effect but it's not a + + + align:start position:0% +it's definitely in effect but it's not a +very big effect and what strikes me in + + align:start position:0% +very big effect and what strikes me in + + + align:start position:0% +very big effect and what strikes me in +every time I look at studies like this + + align:start position:0% +every time I look at studies like this + + + align:start position:0% +every time I look at studies like this +is just how small those effects are + + align:start position:0% +is just how small those effects are + + + align:start position:0% +is just how small those effects are +whether you're predicting some output + + align:start position:0% +whether you're predicting some output + + + align:start position:0% +whether you're predicting some output +like the level of insulin and the + + align:start position:0% +like the level of insulin and the + + + align:start position:0% +like the level of insulin and the +patient or whether you're predicting + + align:start position:0% +patient or whether you're predicting + + + align:start position:0% +patient or whether you're predicting +something like a category membership as + + align:start position:0% +something like a category membership as + + + align:start position:0% +something like a category membership as +in this table okay so I said fee wass is + + align:start position:0% +in this table okay so I said fee wass is + + + align:start position:0% +in this table okay so I said fee wass is +a reverse G wass and the first paper + + align:start position:0% +a reverse G wass and the first paper + + + align:start position:0% +a reverse G wass and the first paper +that introduced the terminology was by + + align:start position:0% +that introduced the terminology was by + + + align:start position:0% +that introduced the terminology was by +Josh Denny and colleagues at Vanderbilt + + align:start position:0% +Josh Denny and colleagues at Vanderbilt + + + align:start position:0% +Josh Denny and colleagues at Vanderbilt +in 2010 and so they did not quite a + + align:start position:0% +in 2010 and so they did not quite a + + + align:start position:0% +in 2010 and so they did not quite a +phenom wide Association but they said + + align:start position:0% +phenom wide Association but they said + + + align:start position:0% +phenom wide Association but they said +we're gonna take 25,000 samples from the + + align:start position:0% +we're gonna take 25,000 samples from the + + + align:start position:0% +we're gonna take 25,000 samples from the +Vanderbilt biobank and we're gonna take + + align:start position:0% +Vanderbilt biobank and we're gonna take + + + align:start position:0% +Vanderbilt biobank and we're gonna take +the first six thousand European + + align:start position:0% +the first six thousand European + + + align:start position:0% +the first six thousand European +Americans with samples no other criteria + + align:start position:0% +Americans with samples no other criteria + + + align:start position:0% +Americans with samples no other criteria +for selection why you repeat an + + align:start position:0% +for selection why you repeat an + + + align:start position:0% +for selection why you repeat an +Americans because all the G wast data is + + align:start position:0% +Americans because all the G wast data is + + + align:start position:0% +Americans because all the G wast data is +about European Americans so they wanted + + align:start position:0% +about European Americans so they wanted + + + align:start position:0% +about European Americans so they wanted +to be able to compare to that and then + + align:start position:0% +to be able to compare to that and then + + + align:start position:0% +to be able to compare to that and then +they said let's pick not one snip but + + align:start position:0% +they said let's pick not one snip but + + + align:start position:0% +they said let's pick not one snip but +five different snips that were + + align:start position:0% +five different snips that were + + + align:start position:0% +five different snips that were +interested in so they picked these which + + align:start position:0% +interested in so they picked these which + + + align:start position:0% +interested in so they picked these which +are known to be associated with coronary + + align:start position:0% +are known to be associated with coronary + + + align:start position:0% +are known to be associated with coronary +artery disease and carotid artery + + align:start position:0% +artery disease and carotid artery + + + align:start position:0% +artery disease and carotid artery +stenosis atrial fibrillation multiple + + align:start position:0% +stenosis atrial fibrillation multiple + + + align:start position:0% +stenosis atrial fibrillation multiple +sclerosis and lupus rheumatoid arthritis + + align:start position:0% +sclerosis and lupus rheumatoid arthritis + + + align:start position:0% +sclerosis and lupus rheumatoid arthritis +and Crohn's disease so it's a nice grab + + align:start position:0% +and Crohn's disease so it's a nice grab + + + align:start position:0% +and Crohn's disease so it's a nice grab +bag of interesting disease associations + + align:start position:0% +bag of interesting disease associations + + + align:start position:0% +bag of interesting disease associations +and then the hard work they did was they + + align:start position:0% +and then the hard work they did was they + + + align:start position:0% +and then the hard work they did was they +went through the tens of thousands of + + align:start position:0% +went through the tens of thousands of + + + align:start position:0% +went through the tens of thousands of +different billing codes that were + + align:start position:0% +different billing codes that were + + + align:start position:0% +different billing codes that were +available and they by hand clustered + + align:start position:0% +available and they by hand clustered + + + align:start position:0% +available and they by hand clustered +them into seven hundred and forty-four + + align:start position:0% +them into seven hundred and forty-four + + + align:start position:0% +them into seven hundred and forty-four +case groups and said okay these are the + + align:start position:0% +case groups and said okay these are the + + + align:start position:0% +case groups and said okay these are the +phenotypes that were interested in okay + + align:start position:0% +phenotypes that were interested in okay + + + align:start position:0% +phenotypes that were interested in okay +and that data set by the way is still + + align:start position:0% +and that data set by the way is still + + + align:start position:0% +and that data set by the way is still +available and it's been used by a lot of + + align:start position:0% +available and it's been used by a lot of + + + align:start position:0% +available and it's been used by a lot of +other people because nobody wants to + + align:start position:0% +other people because nobody wants to + + + align:start position:0% +other people because nobody wants to +repeat that analysis so now what you see + + align:start position:0% +repeat that analysis so now what you see + + + align:start position:0% +repeat that analysis so now what you see +is something very similar to what you + + align:start position:0% +is something very similar to what you + + + align:start position:0% +is something very similar to what you +saw on G wasps except here what we have + + align:start position:0% +saw on G wasps except here what we have + + + align:start position:0% +saw on G wasps except here what we have +is the icd-9 code + + align:start position:0% +is the icd-9 code + + + align:start position:0% +is the icd-9 code +group I guess by the time this got + + align:start position:0% +group I guess by the time this got + + + align:start position:0% +group I guess by the time this got +published it was up to a thousand and + + align:start position:0% +published it was up to a thousand and + + + align:start position:0% +published it was up to a thousand and +these are the same kinds of odds ratios + + align:start position:0% +these are the same kinds of odds ratios + + + align:start position:0% +these are the same kinds of odds ratios +for for the genetic expression of those + + align:start position:0% +for for the genetic expression of those + + + align:start position:0% +for for the genetic expression of those +of those markers and what you find again + + align:start position:0% +of those markers and what you find again + + + align:start position:0% +of those markers and what you find again +is that this is the P equal point oh + + align:start position:0% +is that this is the P equal point oh + + + align:start position:0% +is that this is the P equal point oh +five that's the bonferroni corrected + + align:start position:0% +five that's the bonferroni corrected + + + align:start position:0% +five that's the bonferroni corrected +version and only multiple sclerosis + + align:start position:0% +version and only multiple sclerosis + + + align:start position:0% +version and only multiple sclerosis +comes up for this particular snip which + + align:start position:0% +comes up for this particular snip which + + + align:start position:0% +comes up for this particular snip which +was one of the ones that they expected + + align:start position:0% +was one of the ones that they expected + + + align:start position:0% +was one of the ones that they expected +to come up but they were interested to + + align:start position:0% +to come up but they were interested to + + + align:start position:0% +to come up but they were interested to +see what else lights up when you do this + + align:start position:0% +see what else lights up when you do this + + + align:start position:0% +see what else lights up when you do this +sort of analysis and what they + + align:start position:0% +sort of analysis and what they + + + align:start position:0% +sort of analysis and what they +discovered is that you know malignant + + align:start position:0% +discovered is that you know malignant + + + align:start position:0% +discovered is that you know malignant +neoplasm of the rectum benign digestive + + align:start position:0% +neoplasm of the rectum benign digestive + + + align:start position:0% +neoplasm of the rectum benign digestive +tract neoplasms so there's something + + align:start position:0% +tract neoplasms so there's something + + + align:start position:0% +tract neoplasms so there's something +going on about cancer that is somehow + + align:start position:0% +going on about cancer that is somehow + + + align:start position:0% +going on about cancer that is somehow +related to this single nucleotide + + align:start position:0% +related to this single nucleotide + + + align:start position:0% +related to this single nucleotide +polymorphism not at a statistically high + + align:start position:0% +polymorphism not at a statistically high + + + align:start position:0% +polymorphism not at a statistically high +enough level but it's still kind of + + align:start position:0% +enough level but it's still kind of + + + align:start position:0% +enough level but it's still kind of +intriguing that there may be some + + align:start position:0% +intriguing that there may be some + + + align:start position:0% +intriguing that there may be some +relationship there yeah yeah I don't + + align:start position:0% +relationship there yeah yeah I don't + + + align:start position:0% +relationship there yeah yeah I don't +believe that you can get their data + + align:start position:0% +believe that you can get their data + + + align:start position:0% +believe that you can get their data +unless you I think if I mean they're + + align:start position:0% +unless you I think if I mean they're + + + align:start position:0% +unless you I think if I mean they're +pretty good about collaborating with + + align:start position:0% +pretty good about collaborating with + + + align:start position:0% +pretty good about collaborating with +people so if if you're willing to you + + align:start position:0% +people so if if you're willing to you + + + align:start position:0% +people so if if you're willing to you +know become a volunteer employee at + + align:start position:0% +know become a volunteer employee at + + + align:start position:0% +know become a volunteer employee at +Vanderbilt they could probably take you + + align:start position:0% +Vanderbilt they could probably take you + + + align:start position:0% +Vanderbilt they could probably take you +but I just made that up + + align:start position:0% +but I just made that up + + + align:start position:0% +but I just made that up +but every hospital has very strong + + align:start position:0% +but every hospital has very strong + + + align:start position:0% +but every hospital has very strong +controls now what is available is the + + align:start position:0% +controls now what is available is the + + + align:start position:0% +controls now what is available is the +NCBI has geo the gene expression omnibus + + align:start position:0% +NCBI has geo the gene expression omnibus + + + align:start position:0% +NCBI has geo the gene expression omnibus +which has enormous amounts like like I + + align:start position:0% +which has enormous amounts like like I + + + align:start position:0% +which has enormous amounts like like I +think hundreds of billions of sample + + align:start position:0% +think hundreds of billions of sample + + + align:start position:0% +think hundreds of billions of sample +data but you don't often know exactly + + align:start position:0% +data but you don't often know exactly + + + align:start position:0% +data but you don't often know exactly +what the sample is from so it comes with + + align:start position:0% +what the sample is from so it comes with + + + align:start position:0% +what the sample is from so it comes with +an accession number and an English + + align:start position:0% +an accession number and an English + + + align:start position:0% +an accession number and an English +description of the of what kind of data + + align:start position:0% +description of the of what kind of data + + + align:start position:0% +description of the of what kind of data +it is and there are actually lots of + + align:start position:0% +it is and there are actually lots of + + + align:start position:0% +it is and there are actually lots of +papers where people have done natural + + align:start position:0% +papers where people have done natural + + + align:start position:0% +papers where people have done natural +language process + + align:start position:0% +language process + + + align:start position:0% +language process +on those English descriptions in order + + align:start position:0% +on those English descriptions in order + + + align:start position:0% +on those English descriptions in order +to try to figure out what kind of data + + align:start position:0% +to try to figure out what kind of data + + + align:start position:0% +to try to figure out what kind of data +this is and then they can make use of it + + align:start position:0% +this is and then they can make use of it + + + align:start position:0% +this is and then they can make use of it +so you can be clever and there's a ton + + align:start position:0% +so you can be clever and there's a ton + + + align:start position:0% +so you can be clever and there's a ton +of data out there but it's not well + + align:start position:0% +of data out there but it's not well + + + align:start position:0% +of data out there but it's not well +curated data now what's interesting is + + align:start position:0% +curated data now what's interesting is + + + align:start position:0% +curated data now what's interesting is +you don't always get what you expect so + + align:start position:0% +you don't always get what you expect so + + + align:start position:0% +you don't always get what you expect so +for example that snip was selected + + align:start position:0% +for example that snip was selected + + + align:start position:0% +for example that snip was selected +because it's thought to be associated + + align:start position:0% +because it's thought to be associated + + + align:start position:0% +because it's thought to be associated +with multiple sclerosis and lupus but in + + align:start position:0% +with multiple sclerosis and lupus but in + + + align:start position:0% +with multiple sclerosis and lupus but in +reality the association with lupus is + + align:start position:0% +reality the association with lupus is + + + align:start position:0% +reality the association with lupus is +not significant it's a p-value of 0.5 + + align:start position:0% +not significant it's a p-value of 0.5 + + + align:start position:0% +not significant it's a p-value of 0.5 +which is not very impressive the + + align:start position:0% +which is not very impressive the + + + align:start position:0% +which is not very impressive the +association with multiple sclerosis is + + align:start position:0% +association with multiple sclerosis is + + + align:start position:0% +association with multiple sclerosis is +significant and so they found in this + + align:start position:0% +significant and so they found in this + + + align:start position:0% +significant and so they found in this +particular study a couple of things that + + align:start position:0% +particular study a couple of things that + + + align:start position:0% +particular study a couple of things that +had been expected but didn't work out + + align:start position:0% +had been expected but didn't work out + + + align:start position:0% +had been expected but didn't work out +right + + align:start position:0% +right + + + align:start position:0% +right +so for example this snip which was + + align:start position:0% +so for example this snip which was + + + align:start position:0% +so for example this snip which was +associated with coronary artery disease + + align:start position:0% +associated with coronary artery disease + + + align:start position:0% +associated with coronary artery disease +and thought to be associated with this + + align:start position:0% +and thought to be associated with this + + + align:start position:0% +and thought to be associated with this +carotid plaque deposition in your + + align:start position:0% +carotid plaque deposition in your + + + align:start position:0% +carotid plaque deposition in your +carotid artery just isn't p-value of 0.8 + + align:start position:0% +carotid artery just isn't p-value of 0.8 + + + align:start position:0% +carotid artery just isn't p-value of 0.8 +e2 is not not impressive at all okay + + align:start position:0% +e2 is not not impressive at all okay + + + align:start position:0% +e2 is not not impressive at all okay +onward so that was done for snips now a + + align:start position:0% +onward so that was done for snips now a + + + align:start position:0% +onward so that was done for snips now a +very popular idea today is to look at + + align:start position:0% +very popular idea today is to look at + + + align:start position:0% +very popular idea today is to look at +expression levels partly because of + + align:start position:0% +expression levels partly because of + + + align:start position:0% +expression levels partly because of +those prices I showed you where you can + + align:start position:0% +those prices I showed you where you can + + + align:start position:0% +those prices I showed you where you can +very cheaply get expression levels from + + align:start position:0% +very cheaply get expression levels from + + + align:start position:0% +very cheaply get expression levels from +lots of samples and so there's this + + align:start position:0% +lots of samples and so there's this + + + align:start position:0% +lots of samples and so there's this +whole notion of expression quantitative + + align:start position:0% +whole notion of expression quantitative + + + align:start position:0% +whole notion of expression quantitative +trait loci or eqtls that says hey + + align:start position:0% +trait loci or eqtls that says hey + + + align:start position:0% +trait loci or eqtls that says hey +instead of working as hard as the + + align:start position:0% +instead of working as hard as the + + + align:start position:0% +instead of working as hard as the +Vanderbilt guys did to figure out these + + align:start position:0% +Vanderbilt guys did to figure out these + + + align:start position:0% +Vanderbilt guys did to figure out these +hundreds of categories of disease let's + + align:start position:0% +hundreds of categories of disease let's + + + align:start position:0% +hundreds of categories of disease let's +just take your gene expression levels + + align:start position:0% +just take your gene expression levels + + + align:start position:0% +just take your gene expression levels +and use those as defining the trait that + + align:start position:0% +and use those as defining the trait that + + + align:start position:0% +and use those as defining the trait that +we're interested in so now we're looking + + align:start position:0% +we're interested in so now we're looking + + + align:start position:0% +we're interested in so now we're looking +at the relationship between your genome + + align:start position:0% +at the relationship between your genome + + + align:start position:0% +at the relationship between your genome +and the expression levels and so you + + align:start position:0% +and the expression levels and so you + + + align:start position:0% +and the expression levels and so you +might say well that ought to be easy + + align:start position:0% +might say well that ought to be easy + + + align:start position:0% +might say well that ought to be easy +because if the gene is there it's going + + align:start position:0% +because if the gene is there it's going + + + align:start position:0% +because if the gene is there it's going +to get expressed but of course that's + + align:start position:0% +to get expressed but of course that's + + + align:start position:0% +to get expressed but of course that's +not telling you whether + + align:start position:0% +not telling you whether + + + align:start position:0% +not telling you whether +Gina's being activated or repressed or + + align:start position:0% +Gina's being activated or repressed or + + + align:start position:0% +Gina's being activated or repressed or +enhanced or whether any of these other + + align:start position:0% +enhanced or whether any of these other + + + align:start position:0% +enhanced or whether any of these other +complications that I talked about + + align:start position:0% +complications that I talked about + + + align:start position:0% +complications that I talked about +earlier are present and so this is an + + align:start position:0% +earlier are present and so this is an + + + align:start position:0% +earlier are present and so this is an +interesting empirical question and so + + align:start position:0% +interesting empirical question and so + + + align:start position:0% +interesting empirical question and so +people say well you know maybe a small + + align:start position:0% +people say well you know maybe a small + + + align:start position:0% +people say well you know maybe a small +genetic variation will cause different + + align:start position:0% +genetic variation will cause different + + + align:start position:0% +genetic variation will cause different +expression levels of some some RNA and + + align:start position:0% +expression levels of some some RNA and + + + align:start position:0% +expression levels of some some RNA and +we can measure these and then use those + + align:start position:0% +we can measure these and then use those + + + align:start position:0% +we can measure these and then use those +to do this kind of analysis so + + align:start position:0% +to do this kind of analysis so + + + align:start position:0% +to do this kind of analysis so +differential expression in different + + align:start position:0% +differential expression in different + + + align:start position:0% +differential expression in different +populations there's evidence that for + + align:start position:0% +populations there's evidence that for + + + align:start position:0% +populations there's evidence that for +example if you take 16 people of African + + align:start position:0% +example if you take 16 people of African + + + align:start position:0% +example if you take 16 people of African +descent than 17 percent of the genes in + + align:start position:0% +descent than 17 percent of the genes in + + + align:start position:0% +descent than 17 percent of the genes in +a small sample of 16 people differ in + + align:start position:0% +a small sample of 16 people differ in + + + align:start position:0% +a small sample of 16 people differ in +their expression level in among those + + align:start position:0% +their expression level in among those + + + align:start position:0% +their expression level in among those +individuals and similarly 26 percent in + + align:start position:0% +individuals and similarly 26 percent in + + + align:start position:0% +individuals and similarly 26 percent in +in this Asian population and 17 to 29 + + align:start position:0% +in this Asian population and 17 to 29 + + + align:start position:0% +in this Asian population and 17 to 29 +percent in a hapmap sample of course + + align:start position:0% +percent in a hapmap sample of course + + + align:start position:0% +percent in a hapmap sample of course +some of these differences may be because + + align:start position:0% +some of these differences may be because + + + align:start position:0% +some of these differences may be because +of confounders like environment + + align:start position:0% +of confounders like environment + + + align:start position:0% +of confounders like environment +different tissues limited correlation of + + align:start position:0% +different tissues limited correlation of + + + align:start position:0% +different tissues limited correlation of +these expression levels to disease + + align:start position:0% +these expression levels to disease + + + align:start position:0% +these expression levels to disease +phenotypes nevertheless this type of + + align:start position:0% +phenotypes nevertheless this type of + + + align:start position:0% +phenotypes nevertheless this type of +analysis has uncovered relationships + + align:start position:0% +analysis has uncovered relationships + + + align:start position:0% +analysis has uncovered relationships +between these eqtls and asthma and + + align:start position:0% +between these eqtls and asthma and + + + align:start position:0% +between these eqtls and asthma and +crohn's disease so I'll let you read the + + align:start position:0% +crohn's disease so I'll let you read the + + + align:start position:0% +crohn's disease so I'll let you read the +conclusion of one of these studies + + align:start position:0% + + + + align:start position:0% + +so this is saying what I said before + + align:start position:0% +so this is saying what I said before + + + align:start position:0% +so this is saying what I said before +that we we probably know all the + + align:start position:0% +that we we probably know all the + + + align:start position:0% +that we we probably know all the +Mendelian diseases so the diseases that + + align:start position:0% +Mendelian diseases so the diseases that + + + align:start position:0% +Mendelian diseases so the diseases that +were interested in understanding better + + align:start position:0% +were interested in understanding better + + + align:start position:0% +were interested in understanding better +today are the ones that are not + + align:start position:0% +today are the ones that are not + + + align:start position:0% +today are the ones that are not +Mendelian but there are some complicated + + align:start position:0% +Mendelian but there are some complicated + + + align:start position:0% +Mendelian but there are some complicated +combination of effects from different + + align:start position:0% +combination of effects from different + + + align:start position:0% +combination of effects from different +different genes and that makes it of + + align:start position:0% +different genes and that makes it of + + + align:start position:0% +different genes and that makes it of +course a much harder problem there's a + + align:start position:0% +course a much harder problem there's a + + + align:start position:0% +course a much harder problem there's a +an interesting recent paper + + align:start position:0% +an interesting recent paper + + + align:start position:0% +an interesting recent paper +well not that recent 2005 that uses + + align:start position:0% +well not that recent 2005 that uses + + + align:start position:0% +well not that recent 2005 that uses +Bayesian network technology to try to + + align:start position:0% +Bayesian network technology to try to + + + align:start position:0% +Bayesian network technology to try to +get at this and so they say well if you + + align:start position:0% +get at this and so they say well if you + + + align:start position:0% +get at this and so they say well if you +have some quantitative trait locus and + + align:start position:0% +have some quantitative trait locus and + + + align:start position:0% +have some quantitative trait locus and +you treat the RNA expression level as + + align:start position:0% +you treat the RNA expression level as + + + align:start position:0% +you treat the RNA expression level as +this expression quantitative trait locus + + align:start position:0% +this expression quantitative trait locus + + + align:start position:0% +this expression quantitative trait locus +and then you trait you take CS some + + align:start position:0% +and then you trait you take CS some + + + align:start position:0% +and then you trait you take CS some +complex trait which might be a disease + + align:start position:0% +complex trait which might be a disease + + + align:start position:0% +complex trait which might be a disease +or it might be a proclivity for + + align:start position:0% +or it might be a proclivity for + + + align:start position:0% +or it might be a proclivity for +something or it might be one of of Josh + + align:start position:0% +something or it might be one of of Josh + + + align:start position:0% +something or it might be one of of Josh +Denny's categories or whatever then + + align:start position:0% +Denny's categories or whatever then + + + align:start position:0% +Denny's categories or whatever then +there are a number of different Bayesian + + align:start position:0% +there are a number of different Bayesian + + + align:start position:0% +there are a number of different Bayesian +network style models that you can build + + align:start position:0% +network style models that you can build + + + align:start position:0% +network style models that you can build +so you can say ah the genetic variant + + align:start position:0% +so you can say ah the genetic variant + + + align:start position:0% +so you can say ah the genetic variant +causes a difference in gene expression + + align:start position:0% +causes a difference in gene expression + + + align:start position:0% +causes a difference in gene expression +which in turn causes the disease or you + + align:start position:0% +which in turn causes the disease or you + + + align:start position:0% +which in turn causes the disease or you +could say hmmm the genetic trait causes + + align:start position:0% +could say hmmm the genetic trait causes + + + align:start position:0% +could say hmmm the genetic trait causes +the disease which in turn causes the + + align:start position:0% +the disease which in turn causes the + + + align:start position:0% +the disease which in turn causes the +observable difference in gene expression + + align:start position:0% +observable difference in gene expression + + + align:start position:0% +observable difference in gene expression +or you can say that the the genetic + + align:start position:0% +or you can say that the the genetic + + + align:start position:0% +or you can say that the the genetic +variant causes both the expression level + + align:start position:0% +variant causes both the expression level + + + align:start position:0% +variant causes both the expression level +and the disease but they're not + + align:start position:0% +and the disease but they're not + + + align:start position:0% +and the disease but they're not +necessarily coupled so they may be + + align:start position:0% +necessarily coupled so they may be + + + align:start position:0% +necessarily coupled so they may be +conditionally independent given on the + + align:start position:0% +conditionally independent given on the + + + align:start position:0% +conditionally independent given on the +given the genetic variant or you can + + align:start position:0% +given the genetic variant or you can + + + align:start position:0% +given the genetic variant or you can +have more complex issues like you could + + align:start position:0% +have more complex issues like you could + + + align:start position:0% +have more complex issues like you could +have the gene causing changes in + + align:start position:0% +have the gene causing changes in + + + align:start position:0% +have the gene causing changes in +expression level of a whole bunch of + + align:start position:0% +expression level of a whole bunch of + + + align:start position:0% +expression level of a whole bunch of +different RNA which combined cause some + + align:start position:0% +different RNA which combined cause some + + + align:start position:0% +different RNA which combined cause some +disease or you can have different + + align:start position:0% +disease or you can have different + + + align:start position:0% +disease or you can have different +genetic changes all impacting the + + align:start position:0% +genetic changes all impacting the + + + align:start position:0% +genetic changes all impacting the +rushon of some RNA which causes the + + align:start position:0% +rushon of some RNA which causes the + + + align:start position:0% +rushon of some RNA which causes the +disease or just wait for it oops + + align:start position:0% + + + + align:start position:0% + +you can have models like this that say + + align:start position:0% +you can have models like this that say + + + align:start position:0% +you can have models like this that say +you know we have some environmental + + align:start position:0% +you know we have some environmental + + + align:start position:0% +you know we have some environmental +contributions and a bunch of different + + align:start position:0% +contributions and a bunch of different + + + align:start position:0% +contributions and a bunch of different +genes which affect the expression of a + + align:start position:0% +genes which affect the expression of a + + + align:start position:0% +genes which affect the expression of a +bunch of different eqtls + + align:start position:0% +bunch of different eqtls + + + align:start position:0% +bunch of different eqtls +which cause a bunch of clinical traits + + align:start position:0% +which cause a bunch of clinical traits + + + align:start position:0% +which cause a bunch of clinical traits +which cause changes in a bunch of + + align:start position:0% +which cause changes in a bunch of + + + align:start position:0% +which cause changes in a bunch of +reactive RNA which cause comorbidities + + align:start position:0% +reactive RNA which cause comorbidities + + + align:start position:0% +reactive RNA which cause comorbidities +right so the approach that that they + + align:start position:0% +right so the approach that that they + + + align:start position:0% +right so the approach that that they +take is to say well we can generate a + + align:start position:0% +take is to say well we can generate a + + + align:start position:0% +take is to say well we can generate a +large set of hypotheses like this and + + align:start position:0% +large set of hypotheses like this and + + + align:start position:0% +large set of hypotheses like this and +then just calculate the the likelihood + + align:start position:0% +then just calculate the the likelihood + + + align:start position:0% +then just calculate the the likelihood +of the data given each of these + + align:start position:0% +of the data given each of these + + + align:start position:0% +of the data given each of these +hypotheses and whichever one assigns the + + align:start position:0% +hypotheses and whichever one assigns the + + + align:start position:0% +hypotheses and whichever one assigns the +greatest likelihood to the data is most + + align:start position:0% +greatest likelihood to the data is most + + + align:start position:0% +greatest likelihood to the data is most +likely to be the one that's close to + + align:start position:0% +likely to be the one that's close to + + + align:start position:0% +likely to be the one that's close to +correct so let me just blast through the + + align:start position:0% +correct so let me just blast through the + + + align:start position:0% +correct so let me just blast through the +rest of this quickly scaling up genome + + align:start position:0% +rest of this quickly scaling up genome + + + align:start position:0% +rest of this quickly scaling up genome +phenome Association studies the UK + + align:start position:0% +phenome Association studies the UK + + + align:start position:0% +phenome Association studies the UK +biobank is sort of like this all of us + + align:start position:0% +biobank is sort of like this all of us + + + align:start position:0% +biobank is sort of like this all of us +project but they do make their data + + align:start position:0% +project but they do make their data + + + align:start position:0% +project but they do make their data +available all of us will also but it + + align:start position:0% +available all of us will also but it + + + align:start position:0% +available all of us will also but it +hasn't been collected yet UK biobank has + + align:start position:0% +hasn't been collected yet UK biobank has + + + align:start position:0% +hasn't been collected yet UK biobank has +about half a million de-identified + + align:start position:0% +about half a million de-identified + + + align:start position:0% +about half a million de-identified +individuals with full exome sequencing + + align:start position:0% +individuals with full exome sequencing + + + align:start position:0% +individuals with full exome sequencing +although they only have about 10% of + + align:start position:0% +although they only have about 10% of + + + align:start position:0% +although they only have about 10% of +what of what they want now and many of + + align:start position:0% +what of what they want now and many of + + + align:start position:0% +what of what they want now and many of +them will have worn 24-hour activity + + align:start position:0% +them will have worn 24-hour activity + + + align:start position:0% +them will have worn 24-hour activity +monitors so that we have behavioural + + align:start position:0% +monitors so that we have behavioural + + + align:start position:0% +monitors so that we have behavioural +data some of them have had repeat + + align:start position:0% +data some of them have had repeat + + + align:start position:0% +data some of them have had repeat +measurements they do online + + align:start position:0% +measurements they do online + + + align:start position:0% +measurements they do online +questionnaires about 1/5 of them will + + align:start position:0% +questionnaires about 1/5 of them will + + + align:start position:0% +questionnaires about 1/5 of them will +have imaging and it's linked to their + + align:start position:0% +have imaging and it's linked to their + + + align:start position:0% +have imaging and it's linked to their +electronic health record so we know if + + align:start position:0% +electronic health record so we know if + + + align:start position:0% +electronic health record so we know if +they died or if they had cancer or + + align:start position:0% +they died or if they had cancer or + + + align:start position:0% +they died or if they had cancer or +various Hospital episodes etc and + + align:start position:0% +various Hospital episodes etc and + + + align:start position:0% +various Hospital episodes etc and +there's an ongoing there's a website + + align:start position:0% +there's an ongoing there's a website + + + align:start position:0% +there's an ongoing there's a website +here which publishes the latest analyses + + align:start position:0% +here which publishes the latest analyses + + + align:start position:0% +here which publishes the latest analyses +and so you see on April 18th genetic + + align:start position:0% +and so you see on April 18th genetic + + + align:start position:0% +and so you see on April 18th genetic +variants + + align:start position:0% +variants + + + align:start position:0% +variants +that protect against obesity and type 2 + + align:start position:0% +that protect against obesity and type 2 + + + align:start position:0% +that protect against obesity and type 2 +diabetes discovered moderate meat-eaters + + align:start position:0% +diabetes discovered moderate meat-eaters + + + align:start position:0% +diabetes discovered moderate meat-eaters +are at risk of bowel cancer and research + + align:start position:0% +are at risk of bowel cancer and research + + + align:start position:0% +are at risk of bowel cancer and research +identifies genetic causes of poor sleep + + align:start position:0% +identifies genetic causes of poor sleep + + + align:start position:0% +identifies genetic causes of poor sleep +so this is all over the place but these + + align:start position:0% +so this is all over the place but these + + + align:start position:0% +so this is all over the place but these +are all the studies that are being done + + align:start position:0% +are all the studies that are being done + + + align:start position:0% +are all the studies that are being done +by this I'll skip this but there's a + + align:start position:0% +by this I'll skip this but there's a + + + align:start position:0% +by this I'll skip this but there's a +group here at MGH and the broad that is + + align:start position:0% +group here at MGH and the broad that is + + + align:start position:0% +group here at MGH and the broad that is +using this data to do large-scale + + align:start position:0% +using this data to do large-scale + + + align:start position:0% +using this data to do large-scale +many-many gene wide Association studies + + align:start position:0% +many-many gene wide Association studies + + + align:start position:0% +many-many gene wide Association studies +and one of the things that that I + + align:start position:0% +and one of the things that that I + + + align:start position:0% +and one of the things that that I +promised you which is interesting is + + align:start position:0% +promised you which is interesting is + + + align:start position:0% +promised you which is interesting is +from these studies they say well the + + align:start position:0% +from these studies they say well the + + + align:start position:0% +from these studies they say well the +heritability of height is pretty good + + align:start position:0% +heritability of height is pretty good + + + align:start position:0% +heritability of height is pretty good +it's about 0.46 with a p-value of 10 to + + align:start position:0% +it's about 0.46 with a p-value of 10 to + + + align:start position:0% +it's about 0.46 with a p-value of 10 to +the minus 109 so your height is + + align:start position:0% +the minus 109 so your height is + + + align:start position:0% +the minus 109 so your height is +definitely determined in large part by + + align:start position:0% +definitely determined in large part by + + + align:start position:0% +definitely determined in large part by +your parents ID but what's interesting + + align:start position:0% +your parents ID but what's interesting + + + align:start position:0% +your parents ID but what's interesting +is that whether you get a college degree + + align:start position:0% +is that whether you get a college degree + + + align:start position:0% +is that whether you get a college degree +or not is determined by whether your + + align:start position:0% +or not is determined by whether your + + + align:start position:0% +or not is determined by whether your +parents got a college degree or not this + + align:start position:0% +parents got a college degree or not this + + + align:start position:0% +parents got a college degree or not this +is probably not genetic okay or it's + + align:start position:0% +is probably not genetic okay or it's + + + align:start position:0% +is probably not genetic okay or it's +only partly genetic but it clearly has + + align:start position:0% +only partly genetic but it clearly has + + + align:start position:0% +only partly genetic but it clearly has +confounders from money and social status + + align:start position:0% +confounders from money and social status + + + align:start position:0% +confounders from money and social status +and various things like that and then + + align:start position:0% +and various things like that and then + + + align:start position:0% +and various things like that and then +what what I found the music is that even + + align:start position:0% +what what I found the music is that even + + + align:start position:0% +what what I found the music is that even +TV watching is partly hair inheritable + + align:start position:0% +TV watching is partly hair inheritable + + + align:start position:0% +TV watching is partly hair inheritable +from your genetics whom you fortunately + + align:start position:0% +from your genetics whom you fortunately + + + align:start position:0% +from your genetics whom you fortunately +my parents watch a lot of TV the last + + align:start position:0% +my parents watch a lot of TV the last + + + align:start position:0% +my parents watch a lot of TV the last +thing I wanted to mention but I'm not + + align:start position:0% +thing I wanted to mention but I'm not + + + align:start position:0% +thing I wanted to mention but I'm not +gonna have time to get into it is this + + align:start position:0% +gonna have time to get into it is this + + + align:start position:0% +gonna have time to get into it is this +notion of gene set enrichment analysis + + align:start position:0% +notion of gene set enrichment analysis + + + align:start position:0% +notion of gene set enrichment analysis +it's what I was saying before that genes + + align:start position:0% +it's what I was saying before that genes + + + align:start position:0% +it's what I was saying before that genes +typically don't act by themselves and so + + align:start position:0% +typically don't act by themselves and so + + + align:start position:0% +typically don't act by themselves and so +if you think back on high school biology + + align:start position:0% +if you think back on high school biology + + + align:start position:0% +if you think back on high school biology +you probably learned about the krebs + + align:start position:0% +you probably learned about the krebs + + + align:start position:0% +you probably learned about the krebs +cycle that powers cellular mechanisms so + + align:start position:0% +cycle that powers cellular mechanisms so + + + align:start position:0% +cycle that powers cellular mechanisms so +if you break any part of that cycle your + + align:start position:0% +if you break any part of that cycle your + + + align:start position:0% +if you break any part of that cycle your +cells don't get enough energy and so it + + align:start position:0% +cells don't get enough energy and so it + + + align:start position:0% +cells don't get enough energy and so it +stands to reason that if you want to + + align:start position:0% +stands to reason that if you want to + + + align:start position:0% +stands to reason that if you want to +understand that sort of metabolism you + + align:start position:0% +understand that sort of metabolism you + + + align:start position:0% +understand that sort of metabolism you +shouldn't be looking at an individual + + align:start position:0% +shouldn't be looking at an individual + + + align:start position:0% +shouldn't be looking at an individual +gene but you should be looking at all of + + align:start position:0% +gene but you should be looking at all of + + + align:start position:0% +gene but you should be looking at all of +the genes that are in + + align:start position:0% +the genes that are in + + + align:start position:0% +the genes that are in +in that process and so there have been + + align:start position:0% +in that process and so there have been + + + align:start position:0% +in that process and so there have been +many attempts to try to do this the + + align:start position:0% +many attempts to try to do this the + + + align:start position:0% +many attempts to try to do this the +Broad Institute here has a set of + + align:start position:0% +Broad Institute here has a set of + + + align:start position:0% +Broad Institute here has a set of +originally 1,300 biologically defined + + align:start position:0% +originally 1,300 biologically defined + + + align:start position:0% +originally 1,300 biologically defined +gene sets so these were ones that + + align:start position:0% +gene sets so these were ones that + + + align:start position:0% +gene sets so these were ones that +interacted with each other in + + align:start position:0% +interacted with each other in + + + align:start position:0% +interacted with each other in +controlling some important mechanism in + + align:start position:0% +controlling some important mechanism in + + + align:start position:0% +controlling some important mechanism in +the body they're now up to 18,000 for + + align:start position:0% +the body they're now up to 18,000 for + + + align:start position:0% +the body they're now up to 18,000 for +example genes involved in oxidative + + align:start position:0% +example genes involved in oxidative + + + align:start position:0% +example genes involved in oxidative +phosphorylation and muscle tissue show + + align:start position:0% +phosphorylation and muscle tissue show + + + align:start position:0% +phosphorylation and muscle tissue show +reduced expression in diabetics although + + align:start position:0% +reduced expression in diabetics although + + + align:start position:0% +reduced expression in diabetics although +the average decrease per gene is only + + align:start position:0% +the average decrease per gene is only + + + align:start position:0% +the average decrease per gene is only +20% so they have these sets and from + + align:start position:0% +20% so they have these sets and from + + + align:start position:0% +20% so they have these sets and from +those there's a very nice technique that + + align:start position:0% +those there's a very nice technique that + + + align:start position:0% +those there's a very nice technique that +is able to pull it's essentially a way + + align:start position:0% +is able to pull it's essentially a way + + + align:start position:0% +is able to pull it's essentially a way +of strengthening the gene wide + + align:start position:0% +of strengthening the gene wide + + + align:start position:0% +of strengthening the gene wide +associations by allowing you to + + align:start position:0% +associations by allowing you to + + + align:start position:0% +associations by allowing you to +associate them with these sets of genes + + align:start position:0% +associate them with these sets of genes + + + align:start position:0% +associate them with these sets of genes +and the approach that they take is quite + + align:start position:0% +and the approach that they take is quite + + + align:start position:0% +and the approach that they take is quite +clever they say if we take all the genes + + align:start position:0% +clever they say if we take all the genes + + + align:start position:0% +clever they say if we take all the genes +in the genes ette and we order them by + + align:start position:0% +in the genes ette and we order them by + + + align:start position:0% +in the genes ette and we order them by +their correlation with whatever trait + + align:start position:0% +their correlation with whatever trait + + + align:start position:0% +their correlation with whatever trait +were interested in then the genes that + + align:start position:0% +were interested in then the genes that + + + align:start position:0% +were interested in then the genes that +are closer to the beginning of that are + + align:start position:0% +are closer to the beginning of that are + + + align:start position:0% +are closer to the beginning of that are +more likely to be involved because + + align:start position:0% +more likely to be involved because + + + align:start position:0% +more likely to be involved because +they're the ones that are most strongly + + align:start position:0% +they're the ones that are most strongly + + + align:start position:0% +they're the ones that are most strongly +associated and so they have this random + + align:start position:0% +associated and so they have this random + + + align:start position:0% +associated and so they have this random +walk process that finds sort of the + + align:start position:0% +walk process that finds sort of the + + + align:start position:0% +walk process that finds sort of the +maximum place where you can say anything + + align:start position:0% +maximum place where you can say anything + + + align:start position:0% +maximum place where you can say anything +before that is likely to be associated + + align:start position:0% +before that is likely to be associated + + + align:start position:0% +before that is likely to be associated +with the disease that you're interested + + align:start position:0% +with the disease that you're interested + + + align:start position:0% +with the disease that you're interested +in and they've had a number of successes + + align:start position:0% +in and they've had a number of successes + + + align:start position:0% +in and they've had a number of successes +of showing enrichment in you know + + align:start position:0% +of showing enrichment in you know + + + align:start position:0% +of showing enrichment in you know +various diseases and various biological + + align:start position:0% +various diseases and various biological + + + align:start position:0% +various diseases and various biological +factors the last thing I want to say is + + align:start position:0% +factors the last thing I want to say is + + + align:start position:0% +factors the last thing I want to say is +a little bit disappointing I was really + + align:start position:0% +a little bit disappointing I was really + + + align:start position:0% +a little bit disappointing I was really +looking for the killer paper to talk + + align:start position:0% +looking for the killer paper to talk + + + align:start position:0% +looking for the killer paper to talk +about that uses some really + + align:start position:0% +about that uses some really + + + align:start position:0% +about that uses some really +sophisticated deep learning machine + + align:start position:0% +sophisticated deep learning machine + + + align:start position:0% +sophisticated deep learning machine +learning and as far as I can tell it + + align:start position:0% +learning and as far as I can tell it + + + align:start position:0% +learning and as far as I can tell it +doesn't exist yet so most of these + + align:start position:0% +doesn't exist yet so most of these + + + align:start position:0% +doesn't exist yet so most of these +methods are based on clustering + + align:start position:0% +methods are based on clustering + + + align:start position:0% +methods are based on clustering +techniques + + align:start position:0% +techniques + + + align:start position:0% +techniques +on clever ideas like the one for gene + + align:start position:0% +on clever ideas like the one for gene + + + align:start position:0% +on clever ideas like the one for gene +set enrichment analysis but they're not + + align:start position:0% +set enrichment analysis but they're not + + + align:start position:0% +set enrichment analysis but they're not +they're not neural network types of + + align:start position:0% +they're not neural network types of + + + align:start position:0% +they're not neural network types of +techniques they're not immensely + + align:start position:0% +techniques they're not immensely + + + align:start position:0% +techniques they're not immensely +sophisticated so what you see coming up + + align:start position:0% +sophisticated so what you see coming up + + + align:start position:0% +sophisticated so what you see coming up +is things like Bayesian networks and + + align:start position:0% +is things like Bayesian networks and + + + align:start position:0% +is things like Bayesian networks and +clustering and matrix factorization and + + align:start position:0% +clustering and matrix factorization and + + + align:start position:0% +clustering and matrix factorization and +so on which sort of sound like 10 15 20 + + align:start position:0% +so on which sort of sound like 10 15 20 + + + align:start position:0% +so on which sort of sound like 10 15 20 +year-old technologies and I haven't seen + + align:start position:0% +year-old technologies and I haven't seen + + + align:start position:0% +year-old technologies and I haven't seen +examples yet of the you know hot off the + + align:start position:0% +examples yet of the you know hot off the + + + align:start position:0% +examples yet of the you know hot off the +presses + + align:start position:0% +presses + + + align:start position:0% +presses +we built a eighty-three layer neural + + align:start position:0% +we built a eighty-three layer neural + + + align:start position:0% +we built a eighty-three layer neural +network that outperforms these these + + align:start position:0% +network that outperforms these these + + + align:start position:0% +network that outperforms these these +other methods I suspect that that's + + align:start position:0% +other methods I suspect that that's + + + align:start position:0% +other methods I suspect that that's +coming it just hasn't hasn't hit yet as + + align:start position:0% +coming it just hasn't hasn't hit yet as + + + align:start position:0% +coming it just hasn't hasn't hit yet as +far as I know if you know of such papers + + align:start position:0% +far as I know if you know of such papers + + + align:start position:0% +far as I know if you know of such papers +by all means looking you know alright + + align:start position:0% +by all means looking you know alright + + + align:start position:0% +by all means looking you know alright +thank you + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/krZI60lKPek.txt b/krZI60lKPek.txt new file mode 100644 index 0000000000000000000000000000000000000000..f35870f767f2e9b01d11c3432890774882fc6a71 --- /dev/null +++ b/krZI60lKPek.txt @@ -0,0 +1,5731 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +everyone today we are going to look at + + align:start position:0% +everyone today we are going to look at + + + align:start position:0% +everyone today we are going to look at +dynamic programming again so I think I + + align:start position:0% +dynamic programming again so I think I + + + align:start position:0% +dynamic programming again so I think I +have mentioned several times so you + + align:start position:0% +have mentioned several times so you + + + align:start position:0% +have mentioned several times so you +should all know it by heart now the + + align:start position:0% +should all know it by heart now the + + + align:start position:0% +should all know it by heart now the +dynamic programming its main idea is + + align:start position:0% + + + + align:start position:0% + +divided a problem into subproblems and + + align:start position:0% + + + + align:start position:0% + +we use the results of the problems + + align:start position:0% +we use the results of the problems + + + align:start position:0% +we use the results of the problems +you've already solved right and of + + align:start position:0% +you've already solved right and of + + + align:start position:0% +you've already solved right and of +course in 604 6 we always care about + + align:start position:0% +course in 604 6 we always care about + + + align:start position:0% +course in 604 6 we always care about +runtime so those are the two are our big + + align:start position:0% +runtime so those are the two are our big + + + align:start position:0% +runtime so those are the two are our big +themes for dynamic programming now let's + + align:start position:0% +themes for dynamic programming now let's + + + align:start position:0% +themes for dynamic programming now let's +start with a warm up example it's really + + align:start position:0% +start with a warm up example it's really + + + align:start position:0% +start with a warm up example it's really +simple let's say we have a grid there's + + align:start position:0% +simple let's say we have a grid there's + + + align:start position:0% +simple let's say we have a grid there's +a robot + + align:start position:0% +a robot + + + align:start position:0% +a robot +from say coordinate 1 1 and it wants to + + align:start position:0% +from say coordinate 1 1 and it wants to + + + align:start position:0% +from say coordinate 1 1 and it wants to +go to coordinate MN so at every step it + + align:start position:0% +go to coordinate MN so at every step it + + + align:start position:0% +go to coordinate MN so at every step it +can only either take a step up or take a + + align:start position:0% +can only either take a step up or take a + + + align:start position:0% +can only either take a step up or take a +step on the right so how many distinct + + align:start position:0% +step on the right so how many distinct + + + align:start position:0% +step on the right so how many distinct +paths are there for the robot to take + + align:start position:0% + + + + align:start position:0% + +is the question clear so we have a robot + + align:start position:0% +is the question clear so we have a robot + + + align:start position:0% +is the question clear so we have a robot +at coordinate 1 1 it wants to go to + + align:start position:0% +at coordinate 1 1 it wants to go to + + + align:start position:0% +at coordinate 1 1 it wants to go to +coordinate MN and it every step it can + + align:start position:0% +coordinate MN and it every step it can + + + align:start position:0% +coordinate MN and it every step it can +either take a step up or take a step to + + align:start position:0% +either take a step up or take a step to + + + align:start position:0% +either take a step up or take a step to +the right how many distinct paths are + + align:start position:0% +the right how many distinct paths are + + + align:start position:0% +the right how many distinct paths are +there that can take the robot to its + + align:start position:0% +there that can take the robot to its + + + align:start position:0% +there that can take the robot to its +destination any ideas how to solve that + + align:start position:0% + + + + align:start position:0% + +but problems as + + align:start position:0% + + + + align:start position:0% + +at some point yeah + + align:start position:0% + + + + align:start position:0% + +yeah yeah does that one get that so it's + + align:start position:0% +yeah yeah does that one get that so it's + + + align:start position:0% +yeah yeah does that one get that so it's +very simple I know I have only one way + + align:start position:0% +very simple I know I have only one way + + + align:start position:0% +very simple I know I have only one way +to get to this points why I need to go + + align:start position:0% +to get to this points why I need to go + + + align:start position:0% +to get to this points why I need to go +all the way right and only one way to + + align:start position:0% +all the way right and only one way to + + + align:start position:0% +all the way right and only one way to +get to these points I need to go all the + + align:start position:0% +get to these points I need to go all the + + + align:start position:0% +get to these points I need to go all the +way up so for all the intermediate nodes + + align:start position:0% +way up so for all the intermediate nodes + + + align:start position:0% +way up so for all the intermediate nodes +my number of choices are discarding just + + align:start position:0% +my number of choices are discarding just + + + align:start position:0% +my number of choices are discarding just +a number of distinct paths I can come + + align:start position:0% +a number of distinct paths I can come + + + align:start position:0% +a number of distinct paths I can come +from my left plus the number of distinct + + align:start position:0% +from my left plus the number of distinct + + + align:start position:0% +from my left plus the number of distinct +paths I can come from bottom and then I + + align:start position:0% +paths I can come from bottom and then I + + + align:start position:0% +paths I can come from bottom and then I +keep going for every node I'll just take + + align:start position:0% +keep going for every node I'll just take + + + align:start position:0% +keep going for every node I'll just take +a sum between like the two numbers on my + + align:start position:0% +a sum between like the two numbers on my + + + align:start position:0% +a sum between like the two numbers on my +left and on my bottom and go from there + + align:start position:0% +left and on my bottom and go from there + + + align:start position:0% +left and on my bottom and go from there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it's got clear + + align:start position:0% + + + + align:start position:0% + +so this example is very simple but it + + align:start position:0% +so this example is very simple but it + + + align:start position:0% +so this example is very simple but it +does illustrate the point of dynamic + + align:start position:0% +does illustrate the point of dynamic + + + align:start position:0% +does illustrate the point of dynamic +programming very well as you are use of + + align:start position:0% +programming very well as you are use of + + + align:start position:0% +programming very well as you are use of +subproblems and ask how many distinct + + align:start position:0% +subproblems and ask how many distinct + + + align:start position:0% +subproblems and ask how many distinct +paths can I come here and you reuse the + + align:start position:0% +paths can I come here and you reuse the + + + align:start position:0% +paths can I come here and you reuse the +result of for example this subproblem + + align:start position:0% +result of for example this subproblem + + + align:start position:0% +result of for example this subproblem +because you are using it to compute this + + align:start position:0% +because you are using it to compute this + + + align:start position:0% +because you are using it to compute this +number and that number if you don't do + + align:start position:0% +number and that number if you don't do + + + align:start position:0% +number and that number if you don't do +that if you don't memorize and reuse the + + align:start position:0% +that if you don't memorize and reuse the + + + align:start position:0% +that if you don't memorize and reuse the +results and while your runtime will be + + align:start position:0% +results and while your runtime will be + + + align:start position:0% +results and while your runtime will be +worse so what's the runtime of that + + align:start position:0% + + + + align:start position:0% + +let's pick up + + align:start position:0% + + + + align:start position:0% + +it's just an M times n right why because + + align:start position:0% +it's just an M times n right why because + + + align:start position:0% +it's just an M times n right why because +I have this many unique subproblems one + + align:start position:0% +I have this many unique subproblems one + + + align:start position:0% +I have this many unique subproblems one +at each point and and I'm just taking a + + align:start position:0% +at each point and and I'm just taking a + + + align:start position:0% +at each point and and I'm just taking a +sum of two numbers at each subproblem so + + align:start position:0% +sum of two numbers at each subproblem so + + + align:start position:0% +sum of two numbers at each subproblem so +it takes me constant time to solve to + + align:start position:0% +it takes me constant time to solve to + + + align:start position:0% +it takes me constant time to solve to +merge the results from my cell problems + + align:start position:0% +merge the results from my cell problems + + + align:start position:0% +merge the results from my cell problems +to get my problem so to analyze run time + + align:start position:0% +to get my problem so to analyze run time + + + align:start position:0% +to get my problem so to analyze run time +usually we ask a question how many + + align:start position:0% +usually we ask a question how many + + + align:start position:0% +usually we ask a question how many +unique problems do I have and what's the + + align:start position:0% +unique problems do I have and what's the + + + align:start position:0% +unique problems do I have and what's the +amount of merge work I have to do at + + align:start position:0% +amount of merge work I have to do at + + + align:start position:0% +amount of merge work I have to do at +every step that's the toy example + + align:start position:0% + + + + align:start position:0% + +let's look at some more complicated + + align:start position:0% +let's look at some more complicated + + + align:start position:0% +let's look at some more complicated +examples our first one is called make + + align:start position:0% +examples our first one is called make + + + align:start position:0% +examples our first one is called make +change as its name suggests we have a + + align:start position:0% +change as its name suggests we have a + + + align:start position:0% +change as its name suggests we have a +bunch of coins as one as to all the way + + align:start position:0% +bunch of coins as one as to all the way + + + align:start position:0% +bunch of coins as one as to all the way +to say SM so each coin has some values + + align:start position:0% +to say SM so each coin has some values + + + align:start position:0% +to say SM so each coin has some values +like 1 cent 5 cent 10 cent and then + + align:start position:0% +like 1 cent 5 cent 10 cent and then + + + align:start position:0% +like 1 cent 5 cent 10 cent and then +we're going to make it make change for a + + align:start position:0% +we're going to make it make change for a + + + align:start position:0% +we're going to make it make change for a +total of incense and ask what's the + + align:start position:0% +total of incense and ask what's the + + + align:start position:0% +total of incense and ask what's the +minimum number of coins + + align:start position:0% +minimum number of coins + + + align:start position:0% +minimum number of coins +do I need to make a change event and + + align:start position:0% +do I need to make a change event and + + + align:start position:0% +do I need to make a change event and +cents + + align:start position:0% + + + + align:start position:0% + +so to guarantee that we can always make + + align:start position:0% +so to guarantee that we can always make + + + align:start position:0% +so to guarantee that we can always make +this change will set as one to be 1 + + align:start position:0% +this change will set as one to be 1 + + + align:start position:0% +this change will set as one to be 1 +otherwise there is a chance that if the + + align:start position:0% +otherwise there is a chance that if the + + + align:start position:0% +otherwise there is a chance that if the +problem is solvable any ideas + + align:start position:0% +problem is solvable any ideas + + + align:start position:0% +problem is solvable any ideas +oh it's the problem clear go ahead + + align:start position:0% + + + + align:start position:0% + +what least these numbers they are input + + align:start position:0% +what least these numbers they are input + + + align:start position:0% +what least these numbers they are input +they are also inputs it could be one + + align:start position:0% +they are also inputs it could be one + + + align:start position:0% +they are also inputs it could be one +seven five seven ten cents or three + + align:start position:0% +seven five seven ten cents or three + + + align:start position:0% +seven five seven ten cents or three +cents seven cents though the smallest + + align:start position:0% +cents seven cents though the smallest + + + align:start position:0% +cents seven cents though the smallest +one is always one okay I need to find a + + align:start position:0% +one is always one okay I need to find a + + + align:start position:0% +one is always one okay I need to find a +combination of them for each of them I + + align:start position:0% +combination of them for each of them I + + + align:start position:0% +combination of them for each of them I +have infinite number of them so I can + + align:start position:0% +have infinite number of them so I can + + + align:start position:0% +have infinite number of them so I can +find two of these three of those five of + + align:start position:0% +find two of these three of those five of + + + align:start position:0% +find two of these three of those five of +that two such that their sum is n is the + + align:start position:0% +that two such that their sum is n is the + + + align:start position:0% +that two such that their sum is n is the +problem tree okay any ideas how to stop + + align:start position:0% +problem tree okay any ideas how to stop + + + align:start position:0% +problem tree okay any ideas how to stop +that + + align:start position:0% + + + + align:start position:0% + +let's just use naive or very + + align:start position:0% +let's just use naive or very + + + align:start position:0% +let's just use naive or very +straightforward algorithms + + align:start position:0% + + + + align:start position:0% + +god + + align:start position:0% + + + + align:start position:0% + +okay great yeah let's just do exhaustive + + align:start position:0% +okay great yeah let's just do exhaustive + + + align:start position:0% +okay great yeah let's just do exhaustive +search let's pick si if I pick this coin + + align:start position:0% +search let's pick si if I pick this coin + + + align:start position:0% +search let's pick si if I pick this coin +then my sub problem becomes n minus the + + align:start position:0% +then my sub problem becomes n minus the + + + align:start position:0% +then my sub problem becomes n minus the +coin value right and of course I use the + + align:start position:0% +coin value right and of course I use the + + + align:start position:0% +coin value right and of course I use the +one coin right that's a tie so then I + + align:start position:0% +one coin right that's a tie so then I + + + align:start position:0% +one coin right that's a tie so then I +take a mean of this for all the ice and + + align:start position:0% +take a mean of this for all the ice and + + + align:start position:0% +take a mean of this for all the ice and +that's the solution so far so good + + align:start position:0% + + + + align:start position:0% + +okay so what's the runtime of this + + align:start position:0% +okay so what's the runtime of this + + + align:start position:0% +okay so what's the runtime of this +algorithm + + align:start position:0% + + + + align:start position:0% + +it's not immediately obvious then we ask + + align:start position:0% +it's not immediately obvious then we ask + + + align:start position:0% +it's not immediately obvious then we ask +how many unique subproblems are there + + align:start position:0% +how many unique subproblems are there + + + align:start position:0% +how many unique subproblems are there +and how much work do I have to do to go + + align:start position:0% +and how much work do I have to do to go + + + align:start position:0% +and how much work do I have to do to go +from my subproblems to my original + + align:start position:0% +from my subproblems to my original + + + align:start position:0% +from my subproblems to my original +problem so how many subproblems are + + align:start position:0% +problem so how many subproblems are + + + align:start position:0% +problem so how many subproblems are +there + + align:start position:0% + + + + align:start position:0% + +so to be clear for this one we have to + + align:start position:0% +so to be clear for this one we have to + + + align:start position:0% +so to be clear for this one we have to +call this recursive core again right and + + align:start position:0% +call this recursive core again right and + + + align:start position:0% +call this recursive core again right and +- si probably - SJ + + align:start position:0% + + + + align:start position:0% + +and if you cannot compute how many + + align:start position:0% +and if you cannot compute how many + + + align:start position:0% +and if you cannot compute how many +subproblems are there let's just give a + + align:start position:0% +subproblems are there let's just give a + + + align:start position:0% +subproblems are there let's just give a +bound + + align:start position:0% + + + + align:start position:0% + +any ideas + + align:start position:0% + + + + align:start position:0% + +jump right + + align:start position:0% +jump right + + + align:start position:0% +jump right +I + + align:start position:0% + + + + align:start position:0% + +yeah correct so this may not be a very + + align:start position:0% +yeah correct so this may not be a very + + + align:start position:0% +yeah correct so this may not be a very +tight bound but we know we cannot have + + align:start position:0% +tight bound but we know we cannot have + + + align:start position:0% +tight bound but we know we cannot have +more than this number of subproblems + + align:start position:0% +more than this number of subproblems + + + align:start position:0% +more than this number of subproblems +right actually I don't need to even put + + align:start position:0% +right actually I don't need to even put + + + align:start position:0% +right actually I don't need to even put +the order there I know we can have no + + align:start position:0% +the order there I know we can have no + + + align:start position:0% +the order there I know we can have no +more than n subproblems they'll just + + align:start position:0% +more than n subproblems they'll just + + + align:start position:0% +more than n subproblems they'll just +make change of N and minus 1 and minus 2 + + align:start position:0% +make change of N and minus 1 and minus 2 + + + align:start position:0% +make change of N and minus 1 and minus 2 +all the way to them to make change 1 and + + align:start position:0% +all the way to them to make change 1 and + + + align:start position:0% +all the way to them to make change 1 and +actually this bound is pretty tight + + align:start position:0% +actually this bound is pretty tight + + + align:start position:0% +actually this bound is pretty tight +because we set our smallest coins 1 so + + align:start position:0% +because we set our smallest coins 1 so + + + align:start position:0% +because we set our smallest coins 1 so +we will make a recursive call to make + + align:start position:0% +we will make a recursive call to make + + + align:start position:0% +we will make a recursive call to make +change n minus 1 right if I pick the one + + align:start position:0% +change n minus 1 right if I pick the one + + + align:start position:0% +change n minus 1 right if I pick the one +coin a one-cent coin first and then from + + align:start position:0% +coin a one-cent coin first and then from + + + align:start position:0% +coin a one-cent coin first and then from +there I will pick a 1 cent coin again + + align:start position:0% +there I will pick a 1 cent coin again + + + align:start position:0% +there I will pick a 1 cent coin again +that gives me a subproblem but minus 2 + + align:start position:0% +that gives me a subproblem but minus 2 + + + align:start position:0% +that gives me a subproblem but minus 2 +so indeed I will encounter all the n + + align:start position:0% +so indeed I will encounter all the n + + + align:start position:0% +so indeed I will encounter all the n +subproblems right ok so having realized + + align:start position:0% +subproblems right ok so having realized + + + align:start position:0% +subproblems right ok so having realized +that how much work do I have to do to go + + align:start position:0% +that how much work do I have to do to go + + + align:start position:0% +that how much work do I have to do to go +from here to there + + align:start position:0% + + + + align:start position:0% + +Yeah right right because well I'm taking + + align:start position:0% +Yeah right right because well I'm taking + + + align:start position:0% +Yeah right right because well I'm taking +a mean of how many terms M terms so + + align:start position:0% +a mean of how many terms M terms so + + + align:start position:0% +a mean of how many terms M terms so +that's all run time + + align:start position:0% + + + + align:start position:0% + +any questions so far + + align:start position:0% + + + + align:start position:0% + +okay if not let me take a digression so + + align:start position:0% +okay if not let me take a digression so + + + align:start position:0% +okay if not let me take a digression so +make change this problem if you think + + align:start position:0% +make change this problem if you think + + + align:start position:0% +make change this problem if you think +about it it's very similar to knapsack + + align:start position:0% + + + + align:start position:0% + +as anyone not proud of this problem + + align:start position:0% +as anyone not proud of this problem + + + align:start position:0% +as anyone not proud of this problem +knapsack means you have a bunch of items + + align:start position:0% +knapsack means you have a bunch of items + + + align:start position:0% +knapsack means you have a bunch of items +you want to pack these into a bag and + + align:start position:0% +you want to pack these into a bag and + + + align:start position:0% +you want to pack these into a bag and +the bag has a certain size and you want + + align:start position:0% +the bag has a certain size and you want + + + align:start position:0% +the bag has a certain size and you want +to sew each item has a certain value and + + align:start position:0% +to sew each item has a certain value and + + + align:start position:0% +to sew each item has a certain value and +you want to pack the items that have the + + align:start position:0% +you want to pack the items that have the + + + align:start position:0% +you want to pack the items that have the +largest combined value into your bag so + + align:start position:0% + + + + align:start position:0% + +why is it why are they similar because + + align:start position:0% +why is it why are they similar because + + + align:start position:0% +why is it why are they similar because +if so in some sense n is our size we + + align:start position:0% +if so in some sense n is our size we + + + align:start position:0% +if so in some sense n is our size we +want to pick a bunch of coins to make + + align:start position:0% +want to pick a bunch of coins to make + + + align:start position:0% +want to pick a bunch of coins to make +the size N and each coin here actually + + align:start position:0% +the size N and each coin here actually + + + align:start position:0% +the size N and each coin here actually +has a negative value because we want to + + align:start position:0% +has a negative value because we want to + + + align:start position:0% +has a negative value because we want to +pick the minimum of it if you do that + + align:start position:0% +pick the minimum of it if you do that + + + align:start position:0% +pick the minimum of it if you do that +then this problem is exactly knapsack + + align:start position:0% +then this problem is exactly knapsack + + + align:start position:0% +then this problem is exactly knapsack +and knapsack is np-complete that means + + align:start position:0% +and knapsack is np-complete that means + + + align:start position:0% +and knapsack is np-complete that means +we don't know a polynomial solution to + + align:start position:0% +we don't know a polynomial solution to + + + align:start position:0% +we don't know a polynomial solution to +it yet however we just found one + + align:start position:0% +it yet however we just found one + + + align:start position:0% +it yet however we just found one +right this our input is and stuff and + + align:start position:0% +right this our input is and stuff and + + + align:start position:0% +right this our input is and stuff and +then our solution is polynomial 2m and + + align:start position:0% +then our solution is polynomial 2m and + + + align:start position:0% +then our solution is polynomial 2m and +polynomial to the N right if this is + + align:start position:0% +polynomial to the N right if this is + + + align:start position:0% +polynomial to the N right if this is +true then I have found a polynomial + + align:start position:0% +true then I have found a polynomial + + + align:start position:0% +true then I have found a polynomial +solution to one NP problem so P equals + + align:start position:0% +solution to one NP problem so P equals + + + align:start position:0% +solution to one NP problem so P equals +NP so we should all be getting Turing + + align:start position:0% +NP so we should all be getting Turing + + + align:start position:0% +NP so we should all be getting Turing +Award for that so clearly something is + + align:start position:0% +Award for that so clearly something is + + + align:start position:0% +Award for that so clearly something is +wrong + + align:start position:0% + + + + align:start position:0% + +no but there's nothing there's no + + align:start position:0% +no but there's nothing there's no + + + align:start position:0% +no but there's nothing there's no +problem with this solution right this + + align:start position:0% +problem with this solution right this + + + align:start position:0% +problem with this solution right this +covers all the cases and our analysis is + + align:start position:0% +covers all the cases and our analysis is + + + align:start position:0% +covers all the cases and our analysis is +definitely correct + + align:start position:0% + + + + align:start position:0% + +so yeah does anyone get what I'm asking + + align:start position:0% +so yeah does anyone get what I'm asking + + + align:start position:0% +so yeah does anyone get what I'm asking +so what's the contradiction here + + align:start position:0% + + + + align:start position:0% + +we'll probably discuss this later in + + align:start position:0% +we'll probably discuss this later in + + + align:start position:0% +we'll probably discuss this later in +later lectures when we get to complexity + + align:start position:0% +later lectures when we get to complexity + + + align:start position:0% +later lectures when we get to complexity +or reduction so but to give a short + + align:start position:0% +or reduction so but to give a short + + + align:start position:0% +or reduction so but to give a short +answer the problem is that when we say + + align:start position:0% +answer the problem is that when we say + + + align:start position:0% +answer the problem is that when we say +the input is n its size is not n so I + + align:start position:0% +the input is n its size is not n so I + + + align:start position:0% +the input is n its size is not n so I +only need log in this to represent this + + align:start position:0% +only need log in this to represent this + + + align:start position:0% +only need log in this to represent this +input right make sense + + align:start position:0% +input right make sense + + + align:start position:0% +input right make sense +therefore for log in length input my + + align:start position:0% +therefore for log in length input my + + + align:start position:0% +therefore for log in length input my +runtime is n that means my runtime is + + align:start position:0% +runtime is n that means my runtime is + + + align:start position:0% +runtime is n that means my runtime is +exponential it's not polynomial okay now + + align:start position:0% +exponential it's not polynomial okay now + + + align:start position:0% +exponential it's not polynomial okay now +that's end of the digression + + align:start position:0% + + + + align:start position:0% + +okay now let's look at another example + + align:start position:0% + + + + align:start position:0% + +this one is called rectangular blocks so + + align:start position:0% +this one is called rectangular blocks so + + + align:start position:0% +this one is called rectangular blocks so +in this problem we have a bunch of + + align:start position:0% +in this problem we have a bunch of + + + align:start position:0% +in this problem we have a bunch of +blocks say 1 2 all the way to N and each + + align:start position:0% +blocks say 1 2 all the way to N and each + + + align:start position:0% +blocks say 1 2 all the way to N and each +each of them has a length width and + + align:start position:0% +each of them has a length width and + + + align:start position:0% +each of them has a length width and +height so it's a three dimensional block + + align:start position:0% +height so it's a three dimensional block + + + align:start position:0% +height so it's a three dimensional block +so I want to put blocks stack them on + + align:start position:0% +so I want to put blocks stack them on + + + align:start position:0% +so I want to put blocks stack them on +top of each other to get a maximum + + align:start position:0% +top of each other to get a maximum + + + align:start position:0% +top of each other to get a maximum +height but in order for J could be put + + align:start position:0% +height but in order for J could be put + + + align:start position:0% +height but in order for J could be put +on top of them + + align:start position:0% +on top of them + + + align:start position:0% +on top of them +I require the length of J could be + + align:start position:0% +I require the length of J could be + + + align:start position:0% +I require the length of J could be +smaller than length of I and width of J + + align:start position:0% +smaller than length of I and width of J + + + align:start position:0% +smaller than length of I and width of J +is also smaller than with a pie so + + align:start position:0% +is also smaller than with a pie so + + + align:start position:0% +is also smaller than with a pie so +visually I just meant so this is a block + + align:start position:0% +visually I just meant so this is a block + + + align:start position:0% +visually I just meant so this is a block +I can put another block on there right + + align:start position:0% +I can put another block on there right + + + align:start position:0% +I can put another block on there right +they are smaller in width and length but + + align:start position:0% +they are smaller in width and length but + + + align:start position:0% +they are smaller in width and length but +I cannot put this guy on top of it + + align:start position:0% +I cannot put this guy on top of it + + + align:start position:0% +I cannot put this guy on top of it +because one of them one of its dimension + + align:start position:0% +because one of them one of its dimension + + + align:start position:0% +because one of them one of its dimension +is larger than the underlying block and + + align:start position:0% +is larger than the underlying block and + + + align:start position:0% +is larger than the underlying block and +to make things simple ah that's not + + align:start position:0% +to make things simple ah that's not + + + align:start position:0% +to make things simple ah that's not +allowed rotating so okay I can rotate it + + align:start position:0% +allowed rotating so okay I can rotate it + + + align:start position:0% +allowed rotating so okay I can rotate it +now it's still doesn't fit but you see + + align:start position:0% +now it's still doesn't fit but you see + + + align:start position:0% +now it's still doesn't fit but you see +the complication sorry that you allow + + align:start position:0% +the complication sorry that you allow + + + align:start position:0% +the complication sorry that you allow +rotate then there's more possibility so + + align:start position:0% +rotate then there's more possibility so + + + align:start position:0% +rotate then there's more possibility so +L and length and width are so one of + + align:start position:0% +L and length and width are so one of + + + align:start position:0% +L and length and width are so one of +them is north/south the other is + + align:start position:0% +them is north/south the other is + + + align:start position:0% +them is north/south the other is +east/west you cannot change that + + align:start position:0% + + + + align:start position:0% + +okay is the problem clear we want to + + align:start position:0% +okay is the problem clear we want to + + + align:start position:0% +okay is the problem clear we want to +stack one on one on top of each other to + + align:start position:0% +stack one on one on top of each other to + + + align:start position:0% +stack one on one on top of each other to +look at the maximum height + + align:start position:0% + + + + align:start position:0% + +any ideas again let's start from simple + + align:start position:0% +any ideas again let's start from simple + + + align:start position:0% +any ideas again let's start from simple +algorithm say let's just try everything + + align:start position:0% +algorithm say let's just try everything + + + align:start position:0% +algorithm say let's just try everything +out + + align:start position:0% + + + + align:start position:0% + +okay go ahead + + align:start position:0% + + + + align:start position:0% + +funny + + align:start position:0% +funny + + + align:start position:0% +funny +you're going too fast let's write the + + align:start position:0% +you're going too fast let's write the + + + align:start position:0% +you're going too fast let's write the +algorithm first so I want to solve my + + align:start position:0% +algorithm first so I want to solve my + + + align:start position:0% +algorithm first so I want to solve my +rectangle block problem say from 1 to N + + align:start position:0% +rectangle block problem say from 1 to N + + + align:start position:0% +rectangle block problem say from 1 to N +what are my subproblems + + align:start position:0% + + + + align:start position:0% + +okay that's true as one block + + align:start position:0% + + + + align:start position:0% + +so I get his height and then I have a + + align:start position:0% +so I get his height and then I have a + + + align:start position:0% +so I get his height and then I have a +sub problem what is the sub problem and + + align:start position:0% +sub problem what is the sub problem and + + + align:start position:0% +sub problem what is the sub problem and +then I'll take a max Y right so the + + align:start position:0% +then I'll take a max Y right so the + + + align:start position:0% +then I'll take a max Y right so the +difficulty here is ah this sub problem + + align:start position:0% +difficulty here is ah this sub problem + + + align:start position:0% +difficulty here is ah this sub problem +so Andrew right so Andrew said it's just + + align:start position:0% +so Andrew right so Andrew said it's just + + + align:start position:0% +so Andrew right so Andrew said it's just +everything except I is that a case go + + align:start position:0% +everything except I is that a case go + + + align:start position:0% +everything except I is that a case go +ahead + + align:start position:0% + + + + align:start position:0% + +right you get that yeah not only with we + + align:start position:0% +right you get that yeah not only with we + + + align:start position:0% +right you get that yeah not only with we +have to exclude I we also we also have + + align:start position:0% +have to exclude I we also we also have + + + align:start position:0% +have to exclude I we also we also have +to exclude everything longer or wider + + align:start position:0% +to exclude everything longer or wider + + + align:start position:0% +to exclude everything longer or wider +than I so that's actually a messy + + align:start position:0% +than I so that's actually a messy + + + align:start position:0% +than I so that's actually a messy +problem so let me define now this uh + + align:start position:0% +problem so let me define now this uh + + + align:start position:0% +problem so let me define now this uh +broad problem to be a compatible set of + + align:start position:0% + + + + align:start position:0% + +Li and Omega s sorry WI and let me + + align:start position:0% +Li and Omega s sorry WI and let me + + + align:start position:0% +Li and Omega s sorry WI and let me +define that to be the set of blocks + + align:start position:0% +define that to be the set of blocks + + + align:start position:0% +define that to be the set of blocks +where the length is smaller than the + + align:start position:0% +where the length is smaller than the + + + align:start position:0% +where the length is smaller than the +required length and therewith sorry it's + + align:start position:0% +required length and therewith sorry it's + + + align:start position:0% +required length and therewith sorry it's +also smaller than the required width so + + align:start position:0% +also smaller than the required width so + + + align:start position:0% +also smaller than the required width so +this should remind you of the weighted + + align:start position:0% +this should remind you of the weighted + + + align:start position:0% +this should remind you of the weighted +interval scheduling problem where we + + align:start position:0% +interval scheduling problem where we + + + align:start position:0% +interval scheduling problem where we +define a competitive compatible set once + + align:start position:0% +define a competitive compatible set once + + + align:start position:0% +define a competitive compatible set once +we have chosen some block + + align:start position:0% + + + + align:start position:0% + +question Optum up maximize h we want to + + align:start position:0% +question Optum up maximize h we want to + + + align:start position:0% +question Optum up maximize h we want to +get as high as possible I choose a block + + align:start position:0% +get as high as possible I choose a block + + + align:start position:0% +get as high as possible I choose a block +I get its height and then I find out the + + align:start position:0% +I get its height and then I find out the + + + align:start position:0% +I get its height and then I find out the +competitive remaining blocks and I want + + align:start position:0% +competitive remaining blocks and I want + + + align:start position:0% +competitive remaining blocks and I want +to stack them on top of it + + align:start position:0% +to stack them on top of it + + + align:start position:0% +to stack them on top of it +okay everyone agrees this problem this + + align:start position:0% +okay everyone agrees this problem this + + + align:start position:0% +okay everyone agrees this problem this +solution is correct okay then let's + + align:start position:0% +solution is correct okay then let's + + + align:start position:0% +solution is correct okay then let's +analyze this runtime + + align:start position:0% + + + + align:start position:0% + +so how do we analyze run time + + align:start position:0% + + + + align:start position:0% + +what's the first question I always ask + + align:start position:0% + + + + align:start position:0% + +yeah I not sure who said that but how + + align:start position:0% +yeah I not sure who said that but how + + + align:start position:0% +yeah I not sure who said that but how +many subproblems do we have + + align:start position:0% + + + + align:start position:0% + +at most an + + align:start position:0% + + + + align:start position:0% + +can you explain why is that case it's + + align:start position:0% +can you explain why is that case it's + + + align:start position:0% +can you explain why is that case it's +just a gas and if the compatibles + + align:start position:0% +just a gas and if the compatibles + + + align:start position:0% +just a gas and if the compatibles +nothing in the canal and will not be in + + align:start position:0% +nothing in the canal and will not be in + + + align:start position:0% +nothing in the canal and will not be in +the compatible + + align:start position:0% + + + + align:start position:0% + +okay that's very tricky I didn't get + + align:start position:0% +okay that's very tricky I didn't get + + + align:start position:0% +okay that's very tricky I didn't get +that can say I can like you to start + + align:start position:0% +that can say I can like you to start + + + align:start position:0% +that can say I can like you to start +with and then everything that's in the + + align:start position:0% +with and then everything that's in the + + + align:start position:0% +with and then everything that's in the +compatible set and won't be in the + + align:start position:0% +compatible set and won't be in the + + + align:start position:0% +compatible set and won't be in the +comparison + + align:start position:0% + + + + align:start position:0% + +okay I think I got what you said so if + + align:start position:0% +okay I think I got what you said so if + + + align:start position:0% +okay I think I got what you said so if +we think there are only n sub problems + + align:start position:0% +we think there are only n sub problems + + + align:start position:0% +we think there are only n sub problems +what are they they have to be compatible + + align:start position:0% +what are they they have to be compatible + + + align:start position:0% +what are they they have to be compatible +set L 1 w 1 then our 2 W 2 right these + + align:start position:0% +set L 1 w 1 then our 2 W 2 right these + + + align:start position:0% +set L 1 w 1 then our 2 W 2 right these +artists and unique subproblems you are + + align:start position:0% +artists and unique subproblems you are + + + align:start position:0% +artists and unique subproblems you are +thinking of thinking about right now is + + align:start position:0% +thinking of thinking about right now is + + + align:start position:0% +thinking of thinking about right now is +there any chance that I will get a + + align:start position:0% +there any chance that I will get a + + + align:start position:0% +there any chance that I will get a +compatible set like something like L 3 + + align:start position:0% +compatible set like something like L 3 + + + align:start position:0% +compatible set like something like L 3 +but W 5 right if I ever have this sub + + align:start position:0% +but W 5 right if I ever have this sub + + + align:start position:0% +but W 5 right if I ever have this sub +problem then well my number of + + align:start position:0% +problem then well my number of + + + align:start position:0% +problem then well my number of +subproblems are kind of exploding + + align:start position:0% + + + + align:start position:0% + +yeah I see many of you are saying no why + + align:start position:0% +yeah I see many of you are saying no why + + + align:start position:0% +yeah I see many of you are saying no why +not because if we have subproblems say + + align:start position:0% +not because if we have subproblems say + + + align:start position:0% +not because if we have subproblems say +compatible set of Li and WI and if we go + + align:start position:0% +compatible set of Li and WI and if we go + + + align:start position:0% +compatible set of Li and WI and if we go +from here and choose a next item choose + + align:start position:0% +from here and choose a next item choose + + + align:start position:0% +from here and choose a next item choose +the next block say T it's guaranteed + + align:start position:0% +the next block say T it's guaranteed + + + align:start position:0% +the next block say T it's guaranteed +that T has aa is shorter and narrower + + align:start position:0% +that T has aa is shorter and narrower + + + align:start position:0% +that T has aa is shorter and narrower +right that means our new subproblem or + + align:start position:0% +right that means our new subproblem or + + + align:start position:0% +right that means our new subproblem or +new compatible set becomes our new + + align:start position:0% +new compatible set becomes our new + + + align:start position:0% +new compatible set becomes our new +subproblem need to be compatible with T + + align:start position:0% +subproblem need to be compatible with T + + + align:start position:0% +subproblem need to be compatible with T +instead of I right so the only + + align:start position:0% +instead of I right so the only + + + align:start position:0% +instead of I right so the only +subproblems I can get are these ones + + align:start position:0% +subproblems I can get are these ones + + + align:start position:0% +subproblems I can get are these ones +like I cannot I cannot have one of these + + align:start position:0% +like I cannot I cannot have one of these + + + align:start position:0% +like I cannot I cannot have one of these +okay so subproblems are the number of + + align:start position:0% +okay so subproblems are the number of + + + align:start position:0% +okay so subproblems are the number of +subproblems are n and how much work do I + + align:start position:0% +subproblems are n and how much work do I + + + align:start position:0% +subproblems are n and how much work do I +have to do + + align:start position:0% + + + + align:start position:0% + +at each level + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +yeah yeah because I'm just taking the + + align:start position:0% +yeah yeah because I'm just taking the + + + align:start position:0% +yeah yeah because I'm just taking the +max right and there are n potential + + align:start position:0% +max right and there are n potential + + + align:start position:0% +max right and there are n potential +choices inside my max so runtime and + + align:start position:0% +choices inside my max so runtime and + + + align:start position:0% +choices inside my max so runtime and +square + + align:start position:0% + + + + align:start position:0% + +okay we're not fully done because there + + align:start position:0% +okay we're not fully done because there + + + align:start position:0% +okay we're not fully done because there +is an extra step when we are trying to + + align:start position:0% +is an extra step when we are trying to + + + align:start position:0% +is an extra step when we are trying to +do this we have to figure out what each + + align:start position:0% +do this we have to figure out what each + + + align:start position:0% +do this we have to figure out what each +of these are right because once I go + + align:start position:0% +of these are right because once I go + + + align:start position:0% +of these are right because once I go +into into this sub-problem I need to + + align:start position:0% +into into this sub-problem I need to + + + align:start position:0% +into into this sub-problem I need to +take a max on all the blocks that's in + + align:start position:0% +take a max on all the blocks that's in + + + align:start position:0% +take a max on all the blocks that's in +this set right I have to know what + + align:start position:0% +this set right I have to know what + + + align:start position:0% +this set right I have to know what +blocks are in that set is the heart + + align:start position:0% +blocks are in that set is the heart + + + align:start position:0% +blocks are in that set is the heart +so how would you do that + + align:start position:0% + + + + align:start position:0% + +okay so I check all of them + + align:start position:0% +okay so I check all of them + + + align:start position:0% +okay so I check all of them +that's over then I get I'm pretty sure + + align:start position:0% +that's over then I get I'm pretty sure + + + align:start position:0% +that's over then I get I'm pretty sure +you just been scanning + + align:start position:0% +you just been scanning + + + align:start position:0% +you just been scanning +scan the entire thing and pick out the + + align:start position:0% +scan the entire thing and pick out the + + + align:start position:0% +scan the entire thing and pick out the +compatible ones right but that's for + + align:start position:0% +compatible ones right but that's for + + + align:start position:0% +compatible ones right but that's for +this sub problem you have to do it for + + align:start position:0% +this sub problem you have to do it for + + + align:start position:0% +this sub problem you have to do it for +everyone + + align:start position:0% +everyone + + + align:start position:0% +everyone +oh there may be a better way so I think + + align:start position:0% +oh there may be a better way so I think + + + align:start position:0% +oh there may be a better way so I think +the previous tier is telling me there is + + align:start position:0% +the previous tier is telling me there is + + + align:start position:0% +the previous tier is telling me there is +a better way to do that so in order to + + align:start position:0% +a better way to do that so in order to + + + align:start position:0% +a better way to do that so in order to +find the entire compatible self he + + align:start position:0% +find the entire compatible self he + + + align:start position:0% +find the entire compatible self he +claims you can do it in and login but I + + align:start position:0% +claims you can do it in and login but I + + + align:start position:0% +claims you can do it in and login but I +haven't checked that so I'm not sure + + align:start position:0% +haven't checked that so I'm not sure + + + align:start position:0% +haven't checked that so I'm not sure +this is a folklore legend here yeah + + align:start position:0% +this is a folklore legend here yeah + + + align:start position:0% +this is a folklore legend here yeah +we'll double-check that offline but + + align:start position:0% +we'll double-check that offline but + + + align:start position:0% +we'll double-check that offline but +assuming if I if I don't have this then + + align:start position:0% +assuming if I if I don't have this then + + + align:start position:0% +assuming if I if I don't have this then +figure out all these sub problems we'll + + align:start position:0% +figure out all these sub problems we'll + + + align:start position:0% +figure out all these sub problems we'll +also take n square right then my total + + align:start position:0% +also take n square right then my total + + + align:start position:0% +also take n square right then my total +runtime is n square plus n square and + + align:start position:0% +runtime is n square plus n square and + + + align:start position:0% +runtime is n square plus n square and +still n square + + align:start position:0% + + + + align:start position:0% + +I started the ammonia solution + + align:start position:0% +I started the ammonia solution + + + align:start position:0% +I started the ammonia solution +keeping a sort of + + align:start position:0% + + + + align:start position:0% + +yeah I think it should be something + + align:start position:0% +yeah I think it should be something + + + align:start position:0% +yeah I think it should be something +along those line but yeah I haven't + + align:start position:0% +along those line but yeah I haven't + + + align:start position:0% +along those line but yeah I haven't +figure out whether you sort by length or + + align:start position:0% +figure out whether you sort by length or + + + align:start position:0% +figure out whether you sort by length or +you by width or you can only sort by one + + align:start position:0% +you by width or you can only sort by one + + + align:start position:0% +you by width or you can only sort by one +of them so after sorting say let's sort + + align:start position:0% +of them so after sorting say let's sort + + + align:start position:0% +of them so after sorting say let's sort +by length then after this after sorting + + align:start position:0% +by length then after this after sorting + + + align:start position:0% +by length then after this after sorting +I may get something like this right and + + align:start position:0% +I may get something like this right and + + + align:start position:0% +I may get something like this right and +if I am asking what's the compatible set + + align:start position:0% +if I am asking what's the compatible set + + + align:start position:0% +if I am asking what's the compatible set +of with this guy I still have to kick + + align:start position:0% +of with this guy I still have to kick + + + align:start position:0% +of with this guy I still have to kick +all of them out + + align:start position:0% + + + + align:start position:0% + +yeah so it's entirely not entirely clear + + align:start position:0% +yeah so it's entirely not entirely clear + + + align:start position:0% +yeah so it's entirely not entirely clear +to me how to do it but I think you can + + align:start position:0% +to me how to do it but I think you can + + + align:start position:0% +to me how to do it but I think you can +potentially consider having another say + + align:start position:0% +potentially consider having another say + + + align:start position:0% +potentially consider having another say +binary tree that's sorted by width and + + align:start position:0% +binary tree that's sorted by width and + + + align:start position:0% +binary tree that's sorted by width and +you can go in and just delete everything + + align:start position:0% +you can go in and just delete everything + + + align:start position:0% +you can go in and just delete everything +larger than a certain width so that's + + align:start position:0% +larger than a certain width so that's + + + align:start position:0% +larger than a certain width so that's +the yeah okay + + align:start position:0% + + + + align:start position:0% + +okay okay but constructing that graph + + align:start position:0% +okay okay but constructing that graph + + + align:start position:0% +okay okay but constructing that graph +already takes all 10 square correct + + align:start position:0% + + + + align:start position:0% + +okay let's move on I don't have time to + + align:start position:0% +okay let's move on I don't have time to + + + align:start position:0% +okay let's move on I don't have time to +figure this out no let's think about so + + align:start position:0% +figure this out no let's think about so + + + align:start position:0% +figure this out no let's think about so +this problem is remotely similar to + + align:start position:0% + + + + align:start position:0% + +interval scheduling weighted interval + + align:start position:0% +interval scheduling weighted interval + + + align:start position:0% +interval scheduling weighted interval +scheduling right in in a sense that it + + align:start position:0% +scheduling right in in a sense that it + + + align:start position:0% +scheduling right in in a sense that it +has some compatible set and in the very + + align:start position:0% +has some compatible set and in the very + + + align:start position:0% +has some compatible set and in the very +first lecture and recitation we have two + + align:start position:0% +first lecture and recitation we have two + + + align:start position:0% +first lecture and recitation we have two +algorithm for weighted interval + + align:start position:0% +algorithm for weighted interval + + + align:start position:0% +algorithm for weighted interval +scheduling and one of them is better + + align:start position:0% +scheduling and one of them is better + + + align:start position:0% +scheduling and one of them is better +than the other this one looks like the + + align:start position:0% +than the other this one looks like the + + + align:start position:0% +than the other this one looks like the +naive algorithm so does anyone remember + + align:start position:0% +naive algorithm so does anyone remember + + + align:start position:0% +naive algorithm so does anyone remember +what the better algorithm is for + + align:start position:0% +what the better algorithm is for + + + align:start position:0% +what the better algorithm is for +weighted interval scheduling + + align:start position:0% + + + + align:start position:0% + +instead of checking every one as my + + align:start position:0% +instead of checking every one as my + + + align:start position:0% +instead of checking every one as my +potential lowest one it really doesn't + + align:start position:0% +potential lowest one it really doesn't + + + align:start position:0% +potential lowest one it really doesn't +make sense to do that because for the + + align:start position:0% +make sense to do that because for the + + + align:start position:0% +make sense to do that because for the +very small ones I shouldn't put it put + + align:start position:0% +very small ones I shouldn't put it put + + + align:start position:0% +very small ones I shouldn't put it put +them as my bottom one I should only try + + align:start position:0% +them as my bottom one I should only try + + + align:start position:0% +them as my bottom one I should only try +I should try the larger ones first + + align:start position:0% + + + + align:start position:0% + +yep crap so just in the same line of + + align:start position:0% +yep crap so just in the same line of + + + align:start position:0% +yep crap so just in the same line of +thought as weighted interval scheduling + + align:start position:0% +thought as weighted interval scheduling + + + align:start position:0% +thought as weighted interval scheduling +let's first assault them but then his a + + align:start position:0% +let's first assault them but then his a + + + align:start position:0% +let's first assault them but then his a +little tricky because do I sort by + + align:start position:0% +little tricky because do I sort by + + + align:start position:0% +little tricky because do I sort by +length or width so I'm not sure yet but + + align:start position:0% +length or width so I'm not sure yet but + + + align:start position:0% +length or width so I'm not sure yet but +so let's just sort by length and then + + align:start position:0% +so let's just sort by length and then + + + align:start position:0% +so let's just sort by length and then +with so this means if they have the same + + align:start position:0% +with so this means if they have the same + + + align:start position:0% +with so this means if they have the same +length than our sort them by with so I + + align:start position:0% +length than our sort them by with so I + + + align:start position:0% +length than our sort them by with so I +can create a sorted list + + align:start position:0% +can create a sorted list + + + align:start position:0% +can create a sorted list +let me just assume that it's a in place + + align:start position:0% +let me just assume that it's a in place + + + align:start position:0% +let me just assume that it's a in place +sort and now I have the sorted list so + + align:start position:0% +sort and now I have the sorted list so + + + align:start position:0% +sort and now I have the sorted list so +once I have that so I should the + + align:start position:0% +once I have that so I should the + + + align:start position:0% +once I have that so I should the +question also the possible solutions I + + align:start position:0% +question also the possible solutions I + + + align:start position:0% +question also the possible solutions I +should consider is that whether or not + + align:start position:0% +should consider is that whether or not + + + align:start position:0% +should consider is that whether or not +or not I put my first block as the + + align:start position:0% +or not I put my first block as the + + + align:start position:0% +or not I put my first block as the +bottom one right it doesn't make sense + + align:start position:0% +bottom one right it doesn't make sense + + + align:start position:0% +bottom one right it doesn't make sense +for me to put those later ones down so + + align:start position:0% +for me to put those later ones down so + + + align:start position:0% +for me to put those later ones down so +my subproblem i sorry if my original + + align:start position:0% +my subproblem i sorry if my original + + + align:start position:0% +my subproblem i sorry if my original +problem becomes taking a max and whether + + align:start position:0% +problem becomes taking a max and whether + + + align:start position:0% +problem becomes taking a max and whether +or not i choose block 1 if I do then I + + align:start position:0% +or not i choose block 1 if I do then I + + + align:start position:0% +or not i choose block 1 if I do then I +get its weight a high story and my sub + + align:start position:0% +get its weight a high story and my sub + + + align:start position:0% +get its weight a high story and my sub +problem is + + align:start position:0% + + + + align:start position:0% + +the ones compatible with it + + align:start position:0% +the ones compatible with it + + + align:start position:0% +the ones compatible with it +correct + + align:start position:0% + + + + align:start position:0% + +if I do not choose it let my subproblem + + align:start position:0% +if I do not choose it let my subproblem + + + align:start position:0% +if I do not choose it let my subproblem +is what and reverse step from - all the + + align:start position:0% +is what and reverse step from - all the + + + align:start position:0% +is what and reverse step from - all the +way to it so why is this correct so I + + align:start position:0% +way to it so why is this correct so I + + + align:start position:0% +way to it so why is this correct so I +claim this cover all that covers all the + + align:start position:0% +claim this cover all that covers all the + + + align:start position:0% +claim this cover all that covers all the +cases like either h1 is chosen as the + + align:start position:0% +cases like either h1 is chosen as the + + + align:start position:0% +cases like either h1 is chosen as the +first bottom one or it's not it's not + + align:start position:0% +first bottom one or it's not it's not + + + align:start position:0% +first bottom one or it's not it's not +chosen at all it's impossible for h1 to + + align:start position:0% +chosen at all it's impossible for h1 to + + + align:start position:0% +chosen at all it's impossible for h1 to +be somewhere in the middle right because + + align:start position:0% +be somewhere in the middle right because + + + align:start position:0% +be somewhere in the middle right because +it has the longest largest length okay + + align:start position:0% + + + + align:start position:0% + +so how many subproblems do I have + + align:start position:0% + + + + align:start position:0% + +still n so there all of these compatible + + align:start position:0% +still n so there all of these compatible + + + align:start position:0% +still n so there all of these compatible +set of L 1 W 1 now 2 W 2 but looks like + + align:start position:0% +set of L 1 W 1 now 2 W 2 but looks like + + + align:start position:0% +set of L 1 W 1 now 2 W 2 but looks like +I do have some new sub problems right + + align:start position:0% +I do have some new sub problems right + + + align:start position:0% +I do have some new sub problems right +these do not exist before however there + + align:start position:0% +these do not exist before however there + + + align:start position:0% +these do not exist before however there +are only n of them right there just a + + align:start position:0% +are only n of them right there just a + + + align:start position:0% +are only n of them right there just a +suffix of the entire set right so I + + align:start position:0% +suffix of the entire set right so I + + + align:start position:0% +suffix of the entire set right so I +still have o of n subproblems under each + + align:start position:0% +still have o of n subproblems under each + + + align:start position:0% +still have o of n subproblems under each +step I'm doing constant amount of work + + align:start position:0% +step I'm doing constant amount of work + + + align:start position:0% +step I'm doing constant amount of work +there just two items so we found the + + align:start position:0% +there just two items so we found the + + + align:start position:0% +there just two items so we found the +order in solution I'll be done is it + + align:start position:0% +order in solution I'll be done is it + + + align:start position:0% +order in solution I'll be done is it +really + + align:start position:0% +really + + + align:start position:0% +really +order n ok nope yeah I still have to + + align:start position:0% +order n ok nope yeah I still have to + + + align:start position:0% +order n ok nope yeah I still have to +find all these seeds and first I + + align:start position:0% +find all these seeds and first I + + + align:start position:0% +find all these seeds and first I +actually have have a source step right + + align:start position:0% +actually have have a source step right + + + align:start position:0% +actually have have a source step right +that sort step is and login yeah then + + align:start position:0% +that sort step is and login yeah then + + + align:start position:0% +that sort step is and login yeah then +again what if we do it naively then it's + + align:start position:0% +again what if we do it naively then it's + + + align:start position:0% +again what if we do it naively then it's +again n square because I have to find + + align:start position:0% +again n square because I have to find + + + align:start position:0% +again n square because I have to find +this compatible set each of them but if + + align:start position:0% +this compatible set each of them but if + + + align:start position:0% +this compatible set each of them but if +there is analog in solution to find + + align:start position:0% +there is analog in solution to find + + + align:start position:0% +there is analog in solution to find +these compatible sets then my final + + align:start position:0% +these compatible sets then my final + + + align:start position:0% +these compatible sets then my final +runtime is n log N + + align:start position:0% + + + + align:start position:0% + +make sense + + align:start position:0% + + + + align:start position:0% + +any questions so far + + align:start position:0% + + + + align:start position:0% + +okay so now we actually have a choice so + + align:start position:0% +okay so now we actually have a choice so + + + align:start position:0% +okay so now we actually have a choice so +we can either go through another DP + + align:start position:0% +we can either go through another DP + + + align:start position:0% +we can either go through another DP +example I do have another one but then + + align:start position:0% +example I do have another one but then + + + align:start position:0% +example I do have another one but then +see one of the lecture suggested that it + + align:start position:0% +see one of the lecture suggested that it + + + align:start position:0% +see one of the lecture suggested that it +seems that many people have some trouble + + align:start position:0% +seems that many people have some trouble + + + align:start position:0% +seems that many people have some trouble +understanding yesterday's lecture on + + align:start position:0% +understanding yesterday's lecture on + + + align:start position:0% +understanding yesterday's lecture on +universal hashing and perfect hashing so + + align:start position:0% +universal hashing and perfect hashing so + + + align:start position:0% +universal hashing and perfect hashing so +we can also consider going through that + + align:start position:0% +we can also consider going through that + + + align:start position:0% +we can also consider going through that +well of course the third option is to + + align:start position:0% +well of course the third option is to + + + align:start position:0% +well of course the third option is to +just call it a day and so so let me just + + align:start position:0% +just call it a day and so so let me just + + + align:start position:0% +just call it a day and so so let me just +take a poll how many people prefer we go + + align:start position:0% +take a poll how many people prefer we go + + + align:start position:0% +take a poll how many people prefer we go +over the hash stuff okay how many people + + align:start position:0% +over the hash stuff okay how many people + + + align:start position:0% +over the hash stuff okay how many people +prefer another DP example okay sorry + + align:start position:0% +prefer another DP example okay sorry + + + align:start position:0% +prefer another DP example okay sorry +guys how many people just want to leave + + align:start position:0% +guys how many people just want to leave + + + align:start position:0% +guys how many people just want to leave +it's fine okay great that's it okay so + + align:start position:0% +it's fine okay great that's it okay so + + + align:start position:0% +it's fine okay great that's it okay so +so much for DP and we do have another + + align:start position:0% +so much for DP and we do have another + + + align:start position:0% +so much for DP and we do have another +example we are releasing recitation + + align:start position:0% +example we are releasing recitation + + + align:start position:0% +example we are releasing recitation +notes for those of you who are + + align:start position:0% +notes for those of you who are + + + align:start position:0% +notes for those of you who are +interested you can take a look so well + + align:start position:0% +interested you can take a look so well + + + align:start position:0% +interested you can take a look so well +you know you all know that we haven't go + + align:start position:0% +you know you all know that we haven't go + + + align:start position:0% +you know you all know that we haven't go +into DP in my lectures yet so this is + + align:start position:0% +into DP in my lectures yet so this is + + + align:start position:0% +into DP in my lectures yet so this is +really just a warm-up and to prepare you + + align:start position:0% +really just a warm-up and to prepare you + + + align:start position:0% +really just a warm-up and to prepare you +to go to the more advanced PP concepts + + align:start position:0% +to go to the more advanced PP concepts + + + align:start position:0% +to go to the more advanced PP concepts +and also DP will be covered in quiz 1 + + align:start position:0% +and also DP will be covered in quiz 1 + + + align:start position:0% +and also DP will be covered in quiz 1 +but the difficulty will be strictly + + align:start position:0% +but the difficulty will be strictly + + + align:start position:0% +but the difficulty will be strictly +easier than the examples we cover here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now let's review universal and perfect + + align:start position:0% +now let's review universal and perfect + + + align:start position:0% +now let's review universal and perfect +hashing so it's not like I have a better + + align:start position:0% +hashing so it's not like I have a better + + + align:start position:0% +hashing so it's not like I have a better +way to teach it on our advantage here is + + align:start position:0% +way to teach it on our advantage here is + + + align:start position:0% +way to teach it on our advantage here is +that we have fewer people so you can ask + + align:start position:0% +that we have fewer people so you can ask + + + align:start position:0% +that we have fewer people so you can ask +questions you have so let me start with + + align:start position:0% +questions you have so let me start with + + + align:start position:0% +questions you have so let me start with +the motivating example so why do we care + + align:start position:0% +the motivating example so why do we care + + + align:start position:0% +the motivating example so why do we care +about hash it's because we want to + + align:start position:0% +about hash it's because we want to + + + align:start position:0% +about hash it's because we want to +create a hash table of say M it has m + + align:start position:0% +create a hash table of say M it has m + + + align:start position:0% +create a hash table of say M it has m +things and we will receive input say K 0 + + align:start position:0% +things and we will receive input say K 0 + + + align:start position:0% +things and we will receive input say K 0 +K 1 all the way to can K n minus 1 and + + align:start position:0% +K 1 all the way to can K n minus 1 and + + + align:start position:0% +K 1 all the way to can K n minus 1 and +keys and we'll create a hash function to + + align:start position:0% +keys and we'll create a hash function to + + + align:start position:0% +keys and we'll create a hash function to +each of them to map them to one of the + + align:start position:0% +each of them to map them to one of the + + + align:start position:0% +each of them to map them to one of the +bins and the hope is that if if n is + + align:start position:0% +bins and the hope is that if if n is + + + align:start position:0% +bins and the hope is that if if n is +Theta M or in the other way and they see + + align:start position:0% +Theta M or in the other way and they see + + + align:start position:0% +Theta M or in the other way and they see +the N then each pin should contain a + + align:start position:0% +the N then each pin should contain a + + + align:start position:0% +the N then each pin should contain a +constant number of keys so to complete a + + align:start position:0% +constant number of keys so to complete a + + + align:start position:0% +constant number of keys so to complete a +picture all the keys are drawn from a + + align:start position:0% +picture all the keys are drawn from a + + + align:start position:0% +picture all the keys are drawn from a +universe that has size you and this you + + align:start position:0% +universe that has size you and this you + + + align:start position:0% +universe that has size you and this you +is usually pretty large let's say it's + + align:start position:0% +is usually pretty large let's say it's + + + align:start position:0% +is usually pretty large let's say it's +larger than M square it's larger mine + + align:start position:0% +larger than M square it's larger mine + + + align:start position:0% +larger than M square it's larger mine +than the square of my hash table size + + align:start position:0% + + + + align:start position:0% + +but let me first start with a negative + + align:start position:0% +but let me first start with a negative + + + align:start position:0% +but let me first start with a negative +result so if my hash function is + + align:start position:0% +result so if my hash function is + + + align:start position:0% +result so if my hash function is +deterministic then there always exists a + + align:start position:0% +deterministic then there always exists a + + + align:start position:0% +deterministic then there always exists a +series of input that all map to the same + + align:start position:0% +series of input that all map to the same + + + align:start position:0% +series of input that all map to the same +thing + + align:start position:0% + + + + align:start position:0% + +we call that worst case + + align:start position:0% + + + + align:start position:0% + +we don't we don't like the worst case + + align:start position:0% +we don't we don't like the worst case + + + align:start position:0% +we don't we don't like the worst case +why because in that case the Hajj is not + + align:start position:0% +why because in that case the Hajj is not + + + align:start position:0% +why because in that case the Hajj is not +doing anything we still have all of the + + align:start position:0% +doing anything we still have all of the + + + align:start position:0% +doing anything we still have all of the +items in the same list + + align:start position:0% + + + + align:start position:0% + +ah why is that why is that llama true + + align:start position:0% +ah why is that why is that llama true + + + align:start position:0% +ah why is that why is that llama true +because by a very simple teaching whole + + align:start position:0% +because by a very simple teaching whole + + + align:start position:0% +because by a very simple teaching whole +argument so imagine I insert all of the + + align:start position:0% +argument so imagine I insert all of the + + + align:start position:0% +argument so imagine I insert all of the +keys in the universe into my hash table + + align:start position:0% +keys in the universe into my hash table + + + align:start position:0% +keys in the universe into my hash table +I will never do that in practice it's + + align:start position:0% +I will never do that in practice it's + + + align:start position:0% +I will never do that in practice it's +just a thought experiment so by a simple + + align:start position:0% +just a thought experiment so by a simple + + + align:start position:0% +just a thought experiment so by a simple +pigeonhole argument if u is greater than + + align:start position:0% +pigeonhole argument if u is greater than + + + align:start position:0% +pigeonhole argument if u is greater than +M square then at least something will + + align:start position:0% +M square then at least something will + + + align:start position:0% +M square then at least something will +contain more than M elements right well + + align:start position:0% +contain more than M elements right well + + + align:start position:0% +contain more than M elements right well +if it just so happens that my input + + align:start position:0% +if it just so happens that my input + + + align:start position:0% +if it just so happens that my input +are these M keys then my hash will hash + + align:start position:0% +are these M keys then my hash will hash + + + align:start position:0% +are these M keys then my hash will hash +all of them to the same thing make sense + + align:start position:0% +all of them to the same thing make sense + + + align:start position:0% +all of them to the same thing make sense +so this is the problem we are trying to + + align:start position:0% +so this is the problem we are trying to + + + align:start position:0% +so this is the problem we are trying to +solve we don't want this worst case and + + align:start position:0% +solve we don't want this worst case and + + + align:start position:0% +solve we don't want this worst case and +did that say that if H is deterministic + + align:start position:0% +did that say that if H is deterministic + + + align:start position:0% +did that say that if H is deterministic +we cannot avoid that right they always + + align:start position:0% +we cannot avoid that right they always + + + align:start position:0% +we cannot avoid that right they always +exist the worst case so what's the + + align:start position:0% +exist the worst case so what's the + + + align:start position:0% +exist the worst case so what's the +solution then the solution is to + + align:start position:0% +solution then the solution is to + + + align:start position:0% +solution then the solution is to +randomize H + + align:start position:0% + + + + align:start position:0% + +however I can't really randomize H I so + + align:start position:0% +however I can't really randomize H I so + + + align:start position:0% +however I can't really randomize H I so +if H take some key if my hash function + + align:start position:0% +if H take some key if my hash function + + + align:start position:0% +if H take some key if my hash function +maps a key into a certain being well the + + align:start position:0% +maps a key into a certain being well the + + + align:start position:0% +maps a key into a certain being well the +next time I call this hash function it + + align:start position:0% +next time I call this hash function it + + + align:start position:0% +next time I call this hash function it +better give the same thing right + + align:start position:0% +better give the same thing right + + + align:start position:0% +better give the same thing right +otherwise I cannot find that item so H + + align:start position:0% +otherwise I cannot find that item so H + + + align:start position:0% +otherwise I cannot find that item so H +needs to be deterministic so now our + + align:start position:0% +needs to be deterministic so now our + + + align:start position:0% +needs to be deterministic so now our +only choice is to pick a random H make + + align:start position:0% +only choice is to pick a random H make + + + align:start position:0% +only choice is to pick a random H make +sense every hash function is + + align:start position:0% +sense every hash function is + + + align:start position:0% +sense every hash function is +deterministic but we will pick a random + + align:start position:0% +deterministic but we will pick a random + + + align:start position:0% +deterministic but we will pick a random +one from a family of hash functions so + + align:start position:0% +one from a family of hash functions so + + + align:start position:0% +one from a family of hash functions so +in some sense it is this is cheating why + + align:start position:0% +in some sense it is this is cheating why + + + align:start position:0% +in some sense it is this is cheating why +because all I'm saying is I will not + + align:start position:0% +because all I'm saying is I will not + + + align:start position:0% +because all I'm saying is I will not +choose a hash function beforehand our + + align:start position:0% +choose a hash function beforehand our + + + align:start position:0% +choose a hash function beforehand our +wait for the user to insert inputs if I + + align:start position:0% +wait for the user to insert inputs if I + + + align:start position:0% +wait for the user to insert inputs if I +have too many collisions I'll choose + + align:start position:0% +have too many collisions I'll choose + + + align:start position:0% +have too many collisions I'll choose +another one if I have too many + + align:start position:0% +another one if I have too many + + + align:start position:0% +another one if I have too many +collisions out with another one okay I + + align:start position:0% +collisions out with another one okay I + + + align:start position:0% +collisions out with another one okay I +think I forgot to mention one thing + + align:start position:0% +think I forgot to mention one thing + + + align:start position:0% +think I forgot to mention one thing +that's important so you may ask why + + align:start position:0% +that's important so you may ask why + + + align:start position:0% +that's important so you may ask why +twerk here why do I care about that + + align:start position:0% +twerk here why do I care about that + + + align:start position:0% +twerk here why do I care about that +worst case what's the chance of it's + + align:start position:0% +worst case what's the chance of it's + + + align:start position:0% +worst case what's the chance of it's +happening in practice it's very low but + + align:start position:0% +happening in practice it's very low but + + + align:start position:0% +happening in practice it's very low but +in algorithms we really don't we really + + align:start position:0% +in algorithms we really don't we really + + + align:start position:0% +in algorithms we really don't we really +don't like making assumptions input why + + align:start position:0% +don't like making assumptions input why + + + align:start position:0% +don't like making assumptions input why +because if you imagine you are running + + align:start position:0% +because if you imagine you are running + + + align:start position:0% +because if you imagine you are running +or say a website web server well your + + align:start position:0% +or say a website web server well your + + + align:start position:0% +or say a website web server well your +code has some hash table in it so if + + align:start position:0% +code has some hash table in it so if + + + align:start position:0% +code has some hash table in it so if +your competitor or someone who hates you + + align:start position:0% +your competitor or someone who hates you + + + align:start position:0% +your competitor or someone who hates you +wants to put you out of business + + align:start position:0% +wants to put you out of business + + + align:start position:0% +wants to put you out of business +and if he knows your hash function he + + align:start position:0% +and if he knows your hash function he + + + align:start position:0% +and if he knows your hash function he +can create a worst case input right that + + align:start position:0% +can create a worst case input right that + + + align:start position:0% +can create a worst case input right that +will make your website like infinitely + + align:start position:0% +will make your website like infinitely + + + align:start position:0% +will make your website like infinitely +slow so what we are saying here is I + + align:start position:0% +slow so what we are saying here is I + + + align:start position:0% +slow so what we are saying here is I +don't tell him what my what hash + + align:start position:0% +don't tell him what my what hash + + + align:start position:0% +don't tell him what my what hash +function I'll use I'll say I choose one + + align:start position:0% +function I'll use I'll say I choose one + + + align:start position:0% +function I'll use I'll say I choose one +if he figures out the wrong input the + + align:start position:0% +if he figures out the wrong input the + + + align:start position:0% +if he figures out the wrong input the +worst case input I'm going to change my + + align:start position:0% +worst case input I'm going to change my + + + align:start position:0% +worst case input I'm going to change my +hash function + + align:start position:0% +hash function + + + align:start position:0% +hash function +use another one okay make sense + + align:start position:0% + + + + align:start position:0% + +now the definition of universal hash + + align:start position:0% +now the definition of universal hash + + + align:start position:0% +now the definition of universal hash +function + + align:start position:0% + + + + align:start position:0% + +is that if I pick a random H from my + + align:start position:0% +is that if I pick a random H from my + + + align:start position:0% +is that if I pick a random H from my +universal hash function family the + + align:start position:0% +universal hash function family the + + + align:start position:0% +universal hash function family the +probability that any key I map to the + + align:start position:0% +probability that any key I map to the + + + align:start position:0% +probability that any key I map to the +same thing as any KJ should be less or + + align:start position:0% +same thing as any KJ should be less or + + + align:start position:0% +same thing as any KJ should be less or +equal than one over m where m is my hash + + align:start position:0% +equal than one over m where m is my hash + + + align:start position:0% +equal than one over m where m is my hash +table this is really the best you can + + align:start position:0% +table this is really the best you can + + + align:start position:0% +table this is really the best you can +get if H function is really evenly + + align:start position:0% +get if H function is really evenly + + + align:start position:0% +get if H function is really evenly +distributing things you should get this + + align:start position:0% +distributing things you should get this + + + align:start position:0% +distributing things you should get this +property so we have seen one universal + + align:start position:0% +property so we have seen one universal + + + align:start position:0% +property so we have seen one universal +hash function in the class I'll give + + align:start position:0% +hash function in the class I'll give + + + align:start position:0% +hash function in the class I'll give +just I'll just go over the other example + + align:start position:0% +just I'll just go over the other example + + + align:start position:0% +just I'll just go over the other example +which is a k plus P modulo P and then + + align:start position:0% +which is a k plus P modulo P and then + + + align:start position:0% +which is a k plus P modulo P and then +modulo n so P is a prime number that is + + align:start position:0% +modulo n so P is a prime number that is + + + align:start position:0% +modulo n so P is a prime number that is +greater than the universe size we will + + align:start position:0% +greater than the universe size we will + + + align:start position:0% +greater than the universe size we will +see why this is a universal hash + + align:start position:0% +see why this is a universal hash + + + align:start position:0% +see why this is a universal hash +function so to do that we just need to + + align:start position:0% +function so to do that we just need to + + + align:start position:0% +function so to do that we just need to +analyze the collision probability so if + + align:start position:0% +analyze the collision probability so if + + + align:start position:0% +analyze the collision probability so if +I have two key that k1 k1 and k2 then + + align:start position:0% +I have two key that k1 k1 and k2 then + + + align:start position:0% +I have two key that k1 k1 and k2 then +map to the same beam that means they + + align:start position:0% +map to the same beam that means they + + + align:start position:0% +map to the same beam that means they +must have this property right after + + align:start position:0% +must have this property right after + + + align:start position:0% +must have this property right after +taking a mod M their difference should + + align:start position:0% +taking a mod M their difference should + + + align:start position:0% +taking a mod M their difference should +be a multiple of M right because if this + + align:start position:0% +be a multiple of M right because if this + + + align:start position:0% +be a multiple of M right because if this +is true after I taking the modulo M they + + align:start position:0% +is true after I taking the modulo M they + + + align:start position:0% +is true after I taking the modulo M they +will map to the same B make sense now I + + align:start position:0% +will map to the same B make sense now I + + + align:start position:0% +will map to the same B make sense now I +can quickly write it as a time's the + + align:start position:0% +can quickly write it as a time's the + + + align:start position:0% +can quickly write it as a time's the +difference of the key equals a multiple + + align:start position:0% +difference of the key equals a multiple + + + align:start position:0% +difference of the key equals a multiple +of M mod P + + align:start position:0% +of M mod P + + + align:start position:0% +of M mod P +now k1 and k2 are not equal so they are + + align:start position:0% +now k1 and k2 are not equal so they are + + + align:start position:0% +now k1 and k2 are not equal so they are +nonzero and in this group we are based + + align:start position:0% +nonzero and in this group we are based + + + align:start position:0% +nonzero and in this group we are based +on some numbers degree we have an + + align:start position:0% +on some numbers degree we have an + + + align:start position:0% +on some numbers degree we have an +inverse element for it so if if this + + align:start position:0% +inverse element for it so if if this + + + align:start position:0% +inverse element for it so if if this +happens we'll call it a bad a how many + + align:start position:0% +happens we'll call it a bad a how many + + + align:start position:0% +happens we'll call it a bad a how many +bad days do I have so that's a bad one + + align:start position:0% +bad days do I have so that's a bad one + + + align:start position:0% +bad days do I have so that's a bad one +one of a will make this equation holds + + align:start position:0% +one of a will make this equation holds + + + align:start position:0% +one of a will make this equation holds +with I equals one another a make the + + align:start position:0% +with I equals one another a make the + + + align:start position:0% +with I equals one another a make the +equation holds by I with I equals two + + align:start position:0% +equation holds by I with I equals two + + + align:start position:0% +equation holds by I with I equals two +but how many such is do I have at most + + align:start position:0% +but how many such is do I have at most + + + align:start position:0% +but how many such is do I have at most +like because this equation can hold with + + align:start position:0% +like because this equation can hold with + + + align:start position:0% +like because this equation can hold with +M 2 M 3 M all the way to P over m floor + + align:start position:0% +M 2 M 3 M all the way to P over m floor + + + align:start position:0% +M 2 M 3 M all the way to P over m floor +M right this is the total number of + + align:start position:0% +M right this is the total number of + + + align:start position:0% +M right this is the total number of +possible ways this equation can hold so + + align:start position:0% +possible ways this equation can hold so + + + align:start position:0% +possible ways this equation can hold so +how many bad 8 the bad days do I have I + + align:start position:0% +how many bad 8 the bad days do I have I + + + align:start position:0% +how many bad 8 the bad days do I have I +have P over m over the total number of + + align:start position:0% +have P over m over the total number of + + + align:start position:0% +have P over m over the total number of +A's which is P minus 1 well yeah I + + align:start position:0% +A's which is P minus 1 well yeah I + + + align:start position:0% +A's which is P minus 1 well yeah I +forgot to mention that so a is from 1 to + + align:start position:0% +forgot to mention that so a is from 1 to + + + align:start position:0% +forgot to mention that so a is from 1 to +P minus 1 + + align:start position:0% + + + + align:start position:0% + +okay so I can always choose my pee to be + + align:start position:0% +okay so I can always choose my pee to be + + + align:start position:0% +okay so I can always choose my pee to be +not a multiple of em if I do that this + + align:start position:0% +not a multiple of em if I do that this + + + align:start position:0% +not a multiple of em if I do that this +floor so then P and P minus 1 do not + + align:start position:0% +floor so then P and P minus 1 do not + + + align:start position:0% +floor so then P and P minus 1 do not +cross the boundary of multiple m right + + align:start position:0% +cross the boundary of multiple m right + + + align:start position:0% +cross the boundary of multiple m right +then this is true and this is less than + + align:start position:0% + + + + align:start position:0% + +1 over m so this is a universal hash + + align:start position:0% +1 over m so this is a universal hash + + + align:start position:0% +1 over m so this is a universal hash +function family + + align:start position:0% + + + + align:start position:0% + +so what's the randomness here the + + align:start position:0% +so what's the randomness here the + + + align:start position:0% +so what's the randomness here the +randomness is is a our picker a to get + + align:start position:0% +randomness is is a our picker a to get + + + align:start position:0% +randomness is is a our picker a to get +my one of my hash and if it doesn't work + + align:start position:0% +my one of my hash and if it doesn't work + + + align:start position:0% +my one of my hash and if it doesn't work +now pick another day huh P is a prime + + align:start position:0% +now pick another day huh P is a prime + + + align:start position:0% +now pick another day huh P is a prime +number I choose yeah be our B is I think + + align:start position:0% +number I choose yeah be our B is I think + + + align:start position:0% +number I choose yeah be our B is I think +it's also a random number so yeah so + + align:start position:0% +it's also a random number so yeah so + + + align:start position:0% +it's also a random number so yeah so +actually it's not needed but I think + + align:start position:0% +actually it's not needed but I think + + + align:start position:0% +actually it's not needed but I think +there's some deep reason then they keep + + align:start position:0% +there's some deep reason then they keep + + + align:start position:0% +there's some deep reason then they keep +it in the hash function I'm not sure why + + align:start position:0% + + + + align:start position:0% + +now once we have that once we have + + align:start position:0% +now once we have that once we have + + + align:start position:0% +now once we have that once we have +universal hash people also want perfect + + align:start position:0% +universal hash people also want perfect + + + align:start position:0% +universal hash people also want perfect +hashing which means I want absolute + + align:start position:0% +hashing which means I want absolute + + + align:start position:0% +hashing which means I want absolute +absolutely zero creation so how do I do + + align:start position:0% +absolutely zero creation so how do I do + + + align:start position:0% +absolutely zero creation so how do I do +that let me first give a method one I'll + + align:start position:0% +that let me first give a method one I'll + + + align:start position:0% +that let me first give a method one I'll +just use any universal hash function but + + align:start position:0% +just use any universal hash function but + + + align:start position:0% +just use any universal hash function but +my choose I choose my m to be n square I + + align:start position:0% + + + + align:start position:0% + +claim this is a perfect hash function + + align:start position:0% +claim this is a perfect hash function + + + align:start position:0% +claim this is a perfect hash function +with certain probability why because I + + align:start position:0% +with certain probability why because I + + + align:start position:0% +with certain probability why because I +want to calculate probability no + + align:start position:0% +want to calculate probability no + + + align:start position:0% +want to calculate probability no +collision + + align:start position:0% + + + + align:start position:0% + +it's yeah one minus probability I do + + align:start position:0% +it's yeah one minus probability I do + + + align:start position:0% +it's yeah one minus probability I do +have a collision and I can use a Union + + align:start position:0% +have a collision and I can use a Union + + + align:start position:0% +have a collision and I can use a Union +bound that's the probability that any + + align:start position:0% +bound that's the probability that any + + + align:start position:0% +bound that's the probability that any +pair as a collision any pair of H x + + align:start position:0% +pair as a collision any pair of H x + + + align:start position:0% +pair as a collision any pair of H x +equals H y how many pairs do I have yeah + + align:start position:0% +equals H y how many pairs do I have yeah + + + align:start position:0% +equals H y how many pairs do I have yeah +n choose 2 which is this number right + + align:start position:0% +n choose 2 which is this number right + + + align:start position:0% +n choose 2 which is this number right +and based on so if it's a universal hash + + align:start position:0% +and based on so if it's a universal hash + + + align:start position:0% +and based on so if it's a universal hash +function then any collision any two + + align:start position:0% +function then any collision any two + + + align:start position:0% +function then any collision any two +colliding the probability is 1 over m + + align:start position:0% +colliding the probability is 1 over m + + + align:start position:0% +colliding the probability is 1 over m +right so I choose my M to be n square so + + align:start position:0% +right so I choose my M to be n square so + + + align:start position:0% +right so I choose my M to be n square so +this one is larger than 1/2 so what I'm + + align:start position:0% +this one is larger than 1/2 so what I'm + + + align:start position:0% +this one is larger than 1/2 so what I'm +saying so to get a perfect Hogg hash + + align:start position:0% +saying so to get a perfect Hogg hash + + + align:start position:0% +saying so to get a perfect Hogg hash +function I'll just use the simplest way + + align:start position:0% +function I'll just use the simplest way + + + align:start position:0% +function I'll just use the simplest way +I select the universal hash function + + align:start position:0% +I select the universal hash function + + + align:start position:0% +I select the universal hash function +with M equals n square I have a + + align:start position:0% +with M equals n square I have a + + + align:start position:0% +with M equals n square I have a +probability more than 1/2 to succeed or + + align:start position:0% +probability more than 1/2 to succeed or + + + align:start position:0% +probability more than 1/2 to succeed or +if I don't succeed I'll choose another + + align:start position:0% +if I don't succeed I'll choose another + + + align:start position:0% +if I don't succeed I'll choose another +one until I succeed + + align:start position:0% +one until I succeed + + + align:start position:0% +one until I succeed +so this is a randomized algorithm and we + + align:start position:0% +so this is a randomized algorithm and we + + + align:start position:0% +so this is a randomized algorithm and we +can make it a one-color up with them or + + align:start position:0% +can make it a one-color up with them or + + + align:start position:0% +can make it a one-color up with them or +Las Vegas algorithm so I can either say + + align:start position:0% +Las Vegas algorithm so I can either say + + + align:start position:0% +Las Vegas algorithm so I can either say +if I choose alpha log n times then + + align:start position:0% +if I choose alpha log n times then + + + align:start position:0% +if I choose alpha log n times then +what's the chance that none of my choice + + align:start position:0% +what's the chance that none of my choice + + + align:start position:0% +what's the chance that none of my choice +studies fights perfect hashing these + + align:start position:0% +studies fights perfect hashing these + + + align:start position:0% +studies fights perfect hashing these +probability is my failure probability is + + align:start position:0% +probability is my failure probability is + + + align:start position:0% +probability is my failure probability is +less than this + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +by each chance I have a half success + + align:start position:0% +by each chance I have a half success + + + align:start position:0% +by each chance I have a half success +rate and I try this many times what's + + align:start position:0% +rate and I try this many times what's + + + align:start position:0% +rate and I try this many times what's +the chances of all of them failing this + + align:start position:0% +the chances of all of them failing this + + + align:start position:0% +the chances of all of them failing this +is one over N raised to alpha + + align:start position:0% + + + + align:start position:0% + +right of course I can also say I'll keep + + align:start position:0% +right of course I can also say I'll keep + + + align:start position:0% +right of course I can also say I'll keep +trying until I succeed then I have a + + align:start position:0% +trying until I succeed then I have a + + + align:start position:0% +trying until I succeed then I have a +100% success rate + + align:start position:0% +100% success rate + + + align:start position:0% +100% success rate +but my run time could potentially go + + align:start position:0% +but my run time could potentially go + + + align:start position:0% +but my run time could potentially go +unbound it make sense okay + + align:start position:0% +unbound it make sense okay + + + align:start position:0% +unbound it make sense okay +this sounds like a perfect solution the + + align:start position:0% +this sounds like a perfect solution the + + + align:start position:0% +this sounds like a perfect solution the +only problem is that the space + + align:start position:0% +only problem is that the space + + + align:start position:0% +only problem is that the space +complexity of this method is n square + + align:start position:0% +complexity of this method is n square + + + align:start position:0% +complexity of this method is n square +because I choose my M hash table size to + + align:start position:0% +because I choose my M hash table size to + + + align:start position:0% +because I choose my M hash table size to +the N square so this is the only thing + + align:start position:0% +the N square so this is the only thing + + + align:start position:0% +the N square so this is the only thing +we don't want in this simple method + + align:start position:0% + + + + align:start position:0% + +our final goal is to have a perfect hash + + align:start position:0% +our final goal is to have a perfect hash + + + align:start position:0% +our final goal is to have a perfect hash +function that has space over then and + + align:start position:0% +function that has space over then and + + + align:start position:0% +function that has space over then and +also run time are some polynomial Union + + align:start position:0% +also run time are some polynomial Union + + + align:start position:0% +also run time are some polynomial Union +and failure probability arbitrarily + + align:start position:0% +and failure probability arbitrarily + + + align:start position:0% +and failure probability arbitrarily +small and the idea there is this + + align:start position:0% +small and the idea there is this + + + align:start position:0% +small and the idea there is this +two-level hashing so I choose a h1 first + + align:start position:0% +two-level hashing so I choose a h1 first + + + align:start position:0% +two-level hashing so I choose a h1 first +to hash my keys into into beings and for + + align:start position:0% +to hash my keys into into beings and for + + + align:start position:0% +to hash my keys into into beings and for +each pin say I get our 1 elements here + + align:start position:0% +each pin say I get our 1 elements here + + + align:start position:0% +each pin say I get our 1 elements here +our two elements here so on so forth + + align:start position:0% +our two elements here so on so forth + + + align:start position:0% +our two elements here so on so forth +I'll choose each of the pins to be a + + align:start position:0% +I'll choose each of the pins to be a + + + align:start position:0% +I'll choose each of the pins to be a +second level perfect hashing so we can + + align:start position:0% +second level perfect hashing so we can + + + align:start position:0% +second level perfect hashing so we can +use the method 1 to choose this small + + align:start position:0% +use the method 1 to choose this small + + + align:start position:0% +use the method 1 to choose this small +one right if I choose M 1 which is the + + align:start position:0% +one right if I choose M 1 which is the + + + align:start position:0% +one right if I choose M 1 which is the +hash table size of this guy to be l1 + + align:start position:0% +hash table size of this guy to be l1 + + + align:start position:0% +hash table size of this guy to be l1 +square then I know after our for login + + align:start position:0% +square then I know after our for login + + + align:start position:0% +square then I know after our for login +trial this one should be a perfect + + align:start position:0% +trial this one should be a perfect + + + align:start position:0% +trial this one should be a perfect +hashing right after after another half a + + align:start position:0% +hashing right after after another half a + + + align:start position:0% +hashing right after after another half a +login trial I should resolve all the + + align:start position:0% +login trial I should resolve all the + + + align:start position:0% +login trial I should resolve all the +conflicts in l2 to make it a perfect + + align:start position:0% +conflicts in l2 to make it a perfect + + + align:start position:0% +conflicts in l2 to make it a perfect +hashing make sense so after n log n + + align:start position:0% +hashing make sense so after n log n + + + align:start position:0% +hashing make sense so after n log n +trials I will make all of these I will + + align:start position:0% +trials I will make all of these I will + + + align:start position:0% +trials I will make all of these I will +resolve all the conflicts in my second + + align:start position:0% +resolve all the conflicts in my second + + + align:start position:0% +resolve all the conflicts in my second +level hashing questions + + align:start position:0% + + + + align:start position:0% + +let me think about that offline I am not + + align:start position:0% +let me think about that offline I am not + + + align:start position:0% +let me think about that offline I am not +sure about that + + align:start position:0% + + + + align:start position:0% + +okay so the only remaining problem is we + + align:start position:0% +okay so the only remaining problem is we + + + align:start position:0% +okay so the only remaining problem is we +need to figure out whether we achieve + + align:start position:0% +need to figure out whether we achieve + + + align:start position:0% +need to figure out whether we achieve +this space of n what is the space + + align:start position:0% +this space of n what is the space + + + align:start position:0% +this space of n what is the space +complexity of this algorithm is n plus + + align:start position:0% + + + + align:start position:0% + +Li square because each table each table + + align:start position:0% +Li square because each table each table + + + align:start position:0% +Li square because each table each table +size is the square of the elements in it + + align:start position:0% +size is the square of the elements in it + + + align:start position:0% +size is the square of the elements in it +and finally we have that markov + + align:start position:0% +and finally we have that markov + + + align:start position:0% +and finally we have that markov +inequality things something like that to + + align:start position:0% +inequality things something like that to + + + align:start position:0% +inequality things something like that to +prove this is this is the case with so + + align:start position:0% +prove this is this is the case with so + + + align:start position:0% +prove this is this is the case with so +my space is all then also with the + + align:start position:0% +my space is all then also with the + + + align:start position:0% +my space is all then also with the +probability of greater than 1/2 then I + + align:start position:0% +probability of greater than 1/2 then I + + + align:start position:0% +probability of greater than 1/2 then I +can keep going + + align:start position:0% +can keep going + + + align:start position:0% +can keep going +I'll try our for log n times on my first + + align:start position:0% +I'll try our for log n times on my first + + + align:start position:0% +I'll try our for log n times on my first +level hash function until my space is + + align:start position:0% +level hash function until my space is + + + align:start position:0% +level hash function until my space is +all then right once I get get to that + + align:start position:0% +all then right once I get get to that + + + align:start position:0% +all then right once I get get to that +point I'll try choosing universal hash + + align:start position:0% +point I'll try choosing universal hash + + + align:start position:0% +point I'll try choosing universal hash +functions for my smaller tables until I + + align:start position:0% +functions for my smaller tables until I + + + align:start position:0% +functions for my smaller tables until I +succeed ok + + align:start position:0% + + + + align:start position:0% + +that's it for hashing and DBT + + align:start position:0% + + + + align:start position:0% + +so it's mentioned that it's only study \ No newline at end of file diff --git a/lbqlj1g8gu0.txt b/lbqlj1g8gu0.txt new file mode 100644 index 0000000000000000000000000000000000000000..29c425ffd48e15dfe0f5eaa1e656ca42f2774537 --- /dev/null +++ b/lbqlj1g8gu0.txt @@ -0,0 +1,17451 @@ +align:start position:0% + +well good afternoon everyone or good + + align:start position:0% +well good afternoon everyone or good + + + align:start position:0% +well good afternoon everyone or good +morning or good evening no matter uh + + align:start position:0% +morning or good evening no matter uh + + + align:start position:0% +morning or good evening no matter uh +where you are in the world it's some + + align:start position:0% +where you are in the world it's some + + + align:start position:0% +where you are in the world it's some +time of the day or night and I'm + + align:start position:0% +time of the day or night and I'm + + + align:start position:0% +time of the day or night and I'm +delighted that we can use this time now + + align:start position:0% +delighted that we can use this time now + + + align:start position:0% +delighted that we can use this time now +to provide a wrap-up to the journey that + + align:start position:0% +to provide a wrap-up to the journey that + + + align:start position:0% +to provide a wrap-up to the journey that +we've been on for the last seven weeks + + align:start position:0% +we've been on for the last seven weeks + + + align:start position:0% +we've been on for the last seven weeks +we've covered a lot of ground we've + + align:start position:0% +we've covered a lot of ground we've + + + align:start position:0% +we've covered a lot of ground we've +looked at a lot of different issues that + + align:start position:0% +looked at a lot of different issues that + + + align:start position:0% +looked at a lot of different issues that +are so Central to our future to the + + align:start position:0% +are so Central to our future to the + + + align:start position:0% +are so Central to our future to the +future of work and today what we want to + + align:start position:0% +future of work and today what we want to + + + align:start position:0% +future of work and today what we want to +do is to try to take stock what did we + + align:start position:0% +do is to try to take stock what did we + + + align:start position:0% +do is to try to take stock what did we +learn where are we going how are we + + align:start position:0% +learn where are we going how are we + + + align:start position:0% +learn where are we going how are we +going to individually and then + + align:start position:0% +going to individually and then + + + align:start position:0% +going to individually and then +collectively make this a better + + align:start position:0% +collectively make this a better + + + align:start position:0% +collectively make this a better +workplace for the future for all concern + + align:start position:0% +workplace for the future for all concern + + + align:start position:0% +workplace for the future for all concern +so I'm really pleased that we can have + + align:start position:0% +so I'm really pleased that we can have + + + align:start position:0% +so I'm really pleased that we can have +this session in a very interactive way + + align:start position:0% +this session in a very interactive way + + + align:start position:0% +this session in a very interactive way +and as uh we indicated on the course + + align:start position:0% +and as uh we indicated on the course + + + align:start position:0% +and as uh we indicated on the course +materials you can post uh uh questions + + align:start position:0% +materials you can post uh uh questions + + + align:start position:0% +materials you can post uh uh questions +or comments as we go along some of you I + + align:start position:0% +or comments as we go along some of you I + + + align:start position:0% +or comments as we go along some of you I +know are already on Twitter there's the + + align:start position:0% +know are already on Twitter there's the + + + align:start position:0% +know are already on Twitter there's the +hashtag and I believe that's going to + + align:start position:0% +hashtag and I believe that's going to + + + align:start position:0% +hashtag and I believe that's going to +continue to show for you uh those of you + + align:start position:0% +continue to show for you uh those of you + + + align:start position:0% +continue to show for you uh those of you +who are comfortable using Twitter uh and + + align:start position:0% +who are comfortable using Twitter uh and + + + align:start position:0% +who are comfortable using Twitter uh and +one of our colleagues here in the + + align:start position:0% +one of our colleagues here in the + + + align:start position:0% +one of our colleagues here in the +classroom will uh convey your questions + + align:start position:0% +classroom will uh convey your questions + + + align:start position:0% +classroom will uh convey your questions +or comments you can also post uh on the + + align:start position:0% +or comments you can also post uh on the + + + align:start position:0% +or comments you can also post uh on the +discussion board where we put a heading + + align:start position:0% +discussion board where we put a heading + + + align:start position:0% +discussion board where we put a heading +uh for the live discussion so let's make + + align:start position:0% +uh for the live discussion so let's make + + + align:start position:0% +uh for the live discussion so let's make +this really an interactive uh session + + align:start position:0% +this really an interactive uh session + + + align:start position:0% +this really an interactive uh session +I'm joined here this afternoon by our + + align:start position:0% +I'm joined here this afternoon by our + + + align:start position:0% +I'm joined here this afternoon by our +MBA class that has been uh working with + + align:start position:0% +MBA class that has been uh working with + + + align:start position:0% +MBA class that has been uh working with +us throughout the semester uh as you + + align:start position:0% +us throughout the semester uh as you + + + align:start position:0% +us throughout the semester uh as you +know many of them served as expert + + align:start position:0% +know many of them served as expert + + + align:start position:0% +know many of them served as expert +facilitators for you so now they all + + align:start position:0% +facilitators for you so now they all + + + align:start position:0% +facilitators for you so now they all +have a certificate in mediation and and + + align:start position:0% +have a certificate in mediation and and + + + align:start position:0% +have a certificate in mediation and and +facilitation they're experienced and + + align:start position:0% +facilitation they're experienced and + + + align:start position:0% +facilitation they're experienced and +they're going to go out and and start + + align:start position:0% +they're going to go out and and start + + + align:start position:0% +they're going to go out and and start +doing this uh in the workplace of the + + align:start position:0% +doing this uh in the workplace of the + + + align:start position:0% +doing this uh in the workplace of the +future but uh we'll take questions and + + align:start position:0% +future but uh we'll take questions and + + + align:start position:0% +future but uh we'll take questions and +comments uh from our colleagues here + + align:start position:0% +comments uh from our colleagues here + + + align:start position:0% +comments uh from our colleagues here +because they've been following and + + align:start position:0% +because they've been following and + + + align:start position:0% +because they've been following and +working on the same issues as we've been + + align:start position:0% +working on the same issues as we've been + + + align:start position:0% +working on the same issues as we've been +going through this course so why don't + + align:start position:0% +going through this course so why don't + + + align:start position:0% +going through this course so why don't +we get started uh and let's see a little + + align:start position:0% +we get started uh and let's see a little + + + align:start position:0% +we get started uh and let's see a little +bit first who are we well I want to + + align:start position:0% +bit first who are we well I want to + + + align:start position:0% +bit first who are we well I want to +thank uh our partners this uh Enterprise + + align:start position:0% +thank uh our partners this uh Enterprise + + + align:start position:0% +thank uh our partners this uh Enterprise +is only possible because we have a lot + + align:start position:0% +is only possible because we have a lot + + + align:start position:0% +is only possible because we have a lot +of good organizations that are working + + align:start position:0% +of good organizations that are working + + + align:start position:0% +of good organizations that are working +together to make it possible starting + + align:start position:0% +together to make it possible starting + + + align:start position:0% +together to make it possible starting +with edx and mitx our platform and our + + align:start position:0% +with edx and mitx our platform and our + + + align:start position:0% +with edx and mitx our platform and our +delivery uh source and the team of uh of + + align:start position:0% +delivery uh source and the team of uh of + + + align:start position:0% +delivery uh source and the team of uh of +people working behind the scenes to uh + + align:start position:0% +people working behind the scenes to uh + + + align:start position:0% +people working behind the scenes to uh +do the videos with me and with our + + align:start position:0% +do the videos with me and with our + + + align:start position:0% +do the videos with me and with our +colleagues and to do the the editing and + + align:start position:0% +colleagues and to do the the editing and + + + align:start position:0% +colleagues and to do the the editing and +to put the materials on the the course + + align:start position:0% +to put the materials on the the course + + + align:start position:0% +to put the materials on the the course +site and all part of this process I'm + + align:start position:0% +site and all part of this process I'm + + + align:start position:0% +site and all part of this process I'm +very pleased that we have Partners at + + align:start position:0% +very pleased that we have Partners at + + + align:start position:0% +very pleased that we have Partners at +both Cornell University and the school + + align:start position:0% +both Cornell University and the school + + + align:start position:0% +both Cornell University and the school +of Labor and Industrial relations uh at + + align:start position:0% +of Labor and Industrial relations uh at + + + align:start position:0% +of Labor and Industrial relations uh at +and at uh Rutter's University and the + + align:start position:0% +and at uh Rutter's University and the + + + align:start position:0% +and at uh Rutter's University and the +School of Management and Labor Relations + + align:start position:0% +School of Management and Labor Relations + + + align:start position:0% +School of Management and Labor Relations +where courses have Tak classes have + + align:start position:0% +where courses have Tak classes have + + + align:start position:0% +where courses have Tak classes have +taken the course uh on their own campus + + align:start position:0% +taken the course uh on their own campus + + + align:start position:0% +taken the course uh on their own campus +and in fact we're going to uh draw on + + align:start position:0% +and in fact we're going to uh draw on + + + align:start position:0% +and in fact we're going to uh draw on +some of the material that uh were uh + + align:start position:0% +some of the material that uh were uh + + + align:start position:0% +some of the material that uh were uh +provided by students from uh those + + align:start position:0% +provided by students from uh those + + + align:start position:0% +provided by students from uh those +classes as we uh Move Along here this + + align:start position:0% +classes as we uh Move Along here this + + + align:start position:0% +classes as we uh Move Along here this +afternoon and then finally our our + + align:start position:0% +afternoon and then finally our our + + + align:start position:0% +afternoon and then finally our our +colleagues at the Hatachi Foundation uh + + align:start position:0% +colleagues at the Hatachi Foundation uh + + + align:start position:0% +colleagues at the Hatachi Foundation uh +you saw one video that uh uh Barbara + + align:start position:0% +you saw one video that uh uh Barbara + + + align:start position:0% +you saw one video that uh uh Barbara +Dyer helped to produce uh on + + align:start position:0% +Dyer helped to produce uh on + + + align:start position:0% +Dyer helped to produce uh on +entrepreneurship well the Hatachi + + align:start position:0% +entrepreneurship well the Hatachi + + + align:start position:0% +entrepreneurship well the Hatachi +Foundation is a partner with us + + align:start position:0% +Foundation is a partner with us + + + align:start position:0% +Foundation is a partner with us +throughout this course uh in providing + + align:start position:0% +throughout this course uh in providing + + + align:start position:0% +throughout this course uh in providing +materials and support as we go along so + + align:start position:0% +materials and support as we go along so + + + align:start position:0% +materials and support as we go along so +with the MIT School of Management with + + align:start position:0% +with the MIT School of Management with + + + align:start position:0% +with the MIT School of Management with +our Institute for work and employment + + align:start position:0% +our Institute for work and employment + + + align:start position:0% +our Institute for work and employment +research we have lots of organizations + + align:start position:0% +research we have lots of organizations + + + align:start position:0% +research we have lots of organizations +supporting um this Enterprise and then + + align:start position:0% +supporting um this Enterprise and then + + + align:start position:0% +supporting um this Enterprise and then +who are we well uh + + align:start position:0% +who are we well uh + + + align:start position:0% +who are we well uh +we are at at uh + + align:start position:0% +we are at at uh + + + align:start position:0% +we are at at uh +4,299 students in counting that number + + align:start position:0% +4,299 students in counting that number + + + align:start position:0% +4,299 students in counting that number +went up this morning so I suspect uh it + + align:start position:0% +went up this morning so I suspect uh it + + + align:start position:0% +went up this morning so I suspect uh it +may continue to grow as we as we go + + align:start position:0% +may continue to grow as we as we go + + + align:start position:0% +may continue to grow as we as we go +along and as we keep this material live + + align:start position:0% +along and as we keep this material live + + + align:start position:0% +along and as we keep this material live +uh on the the course site but uh it's a + + align:start position:0% +uh on the the course site but uh it's a + + + align:start position:0% +uh on the the course site but uh it's a +very very diverse class and that's what + + align:start position:0% +very very diverse class and that's what + + + align:start position:0% +very very diverse class and that's what +makes it really interesting 144 + + align:start position:0% +makes it really interesting 144 + + + align:start position:0% +makes it really interesting 144 +countries uh we have people uh uh wide + + align:start position:0% +countries uh we have people uh uh wide + + + align:start position:0% +countries uh we have people uh uh wide +uh distribution of educational + + align:start position:0% +uh distribution of educational + + + align:start position:0% +uh distribution of educational +backgrounds from high school some + + align:start position:0% +backgrounds from high school some + + + align:start position:0% +backgrounds from high school some +students in high school students + + align:start position:0% +students in high school students + + + align:start position:0% +students in high school students +graduated from High School in Technical + + align:start position:0% +graduated from High School in Technical + + + align:start position:0% +graduated from High School in Technical +and and vocational schools uh uh many + + align:start position:0% +and and vocational schools uh uh many + + + align:start position:0% +and and vocational schools uh uh many +who have gotten four-year degrees and a + + align:start position:0% +who have gotten four-year degrees and a + + + align:start position:0% +who have gotten four-year degrees and a +a large number with Advanced degrees so + + align:start position:0% +a large number with Advanced degrees so + + + align:start position:0% +a large number with Advanced degrees so +it's a it's a group that reflects the + + align:start position:0% +it's a it's a group that reflects the + + + align:start position:0% +it's a it's a group that reflects the +notion that education is important a + + align:start position:0% +notion that education is important a + + + align:start position:0% +notion that education is important a +theme that we beat uh uh over the head + + align:start position:0% +theme that we beat uh uh over the head + + + align:start position:0% +theme that we beat uh uh over the head +very hard uh throughout the course and + + align:start position:0% +very hard uh throughout the course and + + + align:start position:0% +very hard uh throughout the course and +we'll continue to talk about uh here + + align:start position:0% +we'll continue to talk about uh here + + + align:start position:0% +we'll continue to talk about uh here +this afternoon uh also a very + + align:start position:0% +this afternoon uh also a very + + + align:start position:0% +this afternoon uh also a very +interesting age distribution uh the + + align:start position:0% +interesting age distribution uh the + + + align:start position:0% +interesting age distribution uh the +median age is 31 but that uh if you look + + align:start position:0% +median age is 31 but that uh if you look + + + align:start position:0% +median age is 31 but that uh if you look +at this distribution you see that there + + align:start position:0% +at this distribution you see that there + + + align:start position:0% +at this distribution you see that there +are many younger people and then a a + + align:start position:0% +are many younger people and then a a + + + align:start position:0% +are many younger people and then a a +spattering of people uh more senior uh + + align:start position:0% +spattering of people uh more senior uh + + + align:start position:0% +spattering of people uh more senior uh +uh to age 31 all the way up to someone + + align:start position:0% +uh to age 31 all the way up to someone + + + align:start position:0% +uh to age 31 all the way up to someone +in their 90s so welcome uh to our senior + + align:start position:0% +in their 90s so welcome uh to our senior + + + align:start position:0% +in their 90s so welcome uh to our senior +citizens who are still interested in + + align:start position:0% +citizens who are still interested in + + + align:start position:0% +citizens who are still interested in +shaping the future of work I think + + align:start position:0% +shaping the future of work I think + + + align:start position:0% +shaping the future of work I think +that's fantastic so gender uh we have + + align:start position:0% +that's fantastic so gender uh we have + + + align:start position:0% +that's fantastic so gender uh we have +majority of males but a good uh + + align:start position:0% +majority of males but a good uh + + + align:start position:0% +majority of males but a good uh +distribution we have uh uh uh uh + + align:start position:0% +distribution we have uh uh uh uh + + + align:start position:0% +distribution we have uh uh uh uh +distribution also in terms of + + align:start position:0% +distribution also in terms of + + + align:start position:0% +distribution also in terms of +backgrounds and industries I don't put + + align:start position:0% +backgrounds and industries I don't put + + + align:start position:0% +backgrounds and industries I don't put +it on the slides here but we have people + + align:start position:0% +it on the slides here but we have people + + + align:start position:0% +it on the slides here but we have people +with experience in all different + + align:start position:0% +with experience in all different + + + align:start position:0% +with experience in all different +Industries and occupations we have + + align:start position:0% +Industries and occupations we have + + + align:start position:0% +Industries and occupations we have +people who are uh union members or have + + align:start position:0% +people who are uh union members or have + + + align:start position:0% +people who are uh union members or have +been union members about 18 or 19% uh + + align:start position:0% +been union members about 18 or 19% uh + + + align:start position:0% +been union members about 18 or 19% uh +that's a larger number than you find in + + align:start position:0% +that's a larger number than you find in + + + align:start position:0% +that's a larger number than you find in +the United States but then in in the + + align:start position:0% +the United States but then in in the + + + align:start position:0% +the United States but then in in the +distribution of the population but then + + align:start position:0% +distribution of the population but then + + + align:start position:0% +distribution of the population but then +uh around the world it's more reflective + + align:start position:0% +uh around the world it's more reflective + + + align:start position:0% +uh around the world it's more reflective +of the workforce as we find it and + + align:start position:0% +of the workforce as we find it and + + + align:start position:0% +of the workforce as we find it and +people of all different occupations + + align:start position:0% +people of all different occupations + + + align:start position:0% +people of all different occupations +levels from entry level to phds and + + align:start position:0% +levels from entry level to phds and + + + align:start position:0% +levels from entry level to phds and +advanced uh uh professionals people do + + align:start position:0% +advanced uh uh professionals people do + + + align:start position:0% +advanced uh uh professionals people do +working in the gig economy and people + + align:start position:0% +working in the gig economy and people + + + align:start position:0% +working in the gig economy and people +working in more standard settings so we + + align:start position:0% +working in more standard settings so we + + + align:start position:0% +working in more standard settings so we +uh learned a lot from each other and + + align:start position:0% +uh learned a lot from each other and + + + align:start position:0% +uh learned a lot from each other and +let's take a look at what some of the + + align:start position:0% +let's take a look at what some of the + + + align:start position:0% +let's take a look at what some of the +overriding lessons are I put three + + align:start position:0% +overriding lessons are I put three + + + align:start position:0% +overriding lessons are I put three +lessons here that reflect really the + + align:start position:0% +lessons here that reflect really the + + + align:start position:0% +lessons here that reflect really the +motivation for this course and that were + + align:start position:0% +motivation for this course and that were + + + align:start position:0% +motivation for this course and that were +emphasized throughout and I'll only use + + align:start position:0% +emphasized throughout and I'll only use + + + align:start position:0% +emphasized throughout and I'll only use +these to introduce uh where we're going + + align:start position:0% +these to introduce uh where we're going + + + align:start position:0% +these to introduce uh where we're going +to go but basically uh you put a lot of + + align:start position:0% +to go but basically uh you put a lot of + + + align:start position:0% +to go but basically uh you put a lot of +emphasis on this high high road low road + + align:start position:0% +emphasis on this high high road low road + + + align:start position:0% +emphasis on this high high road low road +distinction as we did in teaching uh + + align:start position:0% +distinction as we did in teaching uh + + + align:start position:0% +distinction as we did in teaching uh +this material that we know that there + + align:start position:0% +this material that we know that there + + + align:start position:0% +this material that we know that there +are choices that companies can make to + + align:start position:0% +are choices that companies can make to + + + align:start position:0% +are choices that companies can make to +create uh good organizations that are + + align:start position:0% +create uh good organizations that are + + + align:start position:0% +create uh good organizations that are +financially successful and that if they + + align:start position:0% +financially successful and that if they + + + align:start position:0% +financially successful and that if they +follow a set of well-defined practices + + align:start position:0% +follow a set of well-defined practices + + + align:start position:0% +follow a set of well-defined practices +that uh can also be good for their + + align:start position:0% +that uh can also be good for their + + + align:start position:0% +that uh can also be good for their +employees but not all firms compete that + + align:start position:0% +employees but not all firms compete that + + + align:start position:0% +employees but not all firms compete that +way not all firms are organized that way + + align:start position:0% +way not all firms are organized that way + + + align:start position:0% +way not all firms are organized that way +and so we emphasized and you emphasized + + align:start position:0% +and so we emphasized and you emphasized + + + align:start position:0% +and so we emphasized and you emphasized +the importance of trying to encourage + + align:start position:0% +the importance of trying to encourage + + + align:start position:0% +the importance of trying to encourage +more High Road firms as a key takeaway + + align:start position:0% +more High Road firms as a key takeaway + + + align:start position:0% +more High Road firms as a key takeaway +lesson uh from this course we also + + align:start position:0% +lesson uh from this course we also + + + align:start position:0% +lesson uh from this course we also +emphasize something that uh uh many + + align:start position:0% +emphasize something that uh uh many + + + align:start position:0% +emphasize something that uh uh many +found surprising the notion that we need + + align:start position:0% +found surprising the notion that we need + + + align:start position:0% +found surprising the notion that we need +to rebuild worker bargaining power + + align:start position:0% +to rebuild worker bargaining power + + + align:start position:0% +to rebuild worker bargaining power +particularly here in the United States + + align:start position:0% +particularly here in the United States + + + align:start position:0% +particularly here in the United States +but increasingly across the world and + + align:start position:0% +but increasingly across the world and + + + align:start position:0% +but increasingly across the world and +some of you reminded Us in the + + align:start position:0% +some of you reminded Us in the + + + align:start position:0% +some of you reminded Us in the +discussion forum as late as this + + align:start position:0% +discussion forum as late as this + + + align:start position:0% +discussion forum as late as this +afternoon that in some parts of the + + align:start position:0% +afternoon that in some parts of the + + + align:start position:0% +afternoon that in some parts of the +world workers don't have legal right to + + align:start position:0% +world workers don't have legal right to + + + align:start position:0% +world workers don't have legal right to +organize or a legal right to voice their + + align:start position:0% +organize or a legal right to voice their + + + align:start position:0% +organize or a legal right to voice their +concerns or that their their efforts are + + align:start position:0% +concerns or that their their efforts are + + + align:start position:0% +concerns or that their their efforts are +suppressed u in variety of ways and so + + align:start position:0% +suppressed u in variety of ways and so + + + align:start position:0% +suppressed u in variety of ways and so +we have to respect workers for their + + align:start position:0% +we have to respect workers for their + + + align:start position:0% +we have to respect workers for their +rights for the Dignity of work and the + + align:start position:0% +rights for the Dignity of work and the + + + align:start position:0% +rights for the Dignity of work and the +opportunity for uh expressing their + + align:start position:0% +opportunity for uh expressing their + + + align:start position:0% +opportunity for uh expressing their +concerns with power and with + + align:start position:0% +concerns with power and with + + + align:start position:0% +concerns with power and with +Effectiveness so that they can + + align:start position:0% +Effectiveness so that they can + + + align:start position:0% +Effectiveness so that they can +contribute both to their own + + align:start position:0% +contribute both to their own + + + align:start position:0% +contribute both to their own +improvements but also to the viability + + align:start position:0% +improvements but also to the viability + + + align:start position:0% +improvements but also to the viability +of their Enterprises and then finally + + align:start position:0% +of their Enterprises and then finally + + + align:start position:0% +of their Enterprises and then finally +this emphasis is on trying to get + + align:start position:0% +this emphasis is on trying to get + + + align:start position:0% +this emphasis is on trying to get +business and labor education and + + align:start position:0% +business and labor education and + + + align:start position:0% +business and labor education and +government working + + align:start position:0% + + + + align:start position:0% + +together we particularly feel it here in + + align:start position:0% +together we particularly feel it here in + + + align:start position:0% +together we particularly feel it here in +the United States at the moment with the + + align:start position:0% +the United States at the moment with the + + + align:start position:0% +the United States at the moment with the +rhic the unfortunate rhetoric in my + + align:start position:0% +rhic the unfortunate rhetoric in my + + + align:start position:0% +rhic the unfortunate rhetoric in my +personal view that is uh so active and + + align:start position:0% +personal view that is uh so active and + + + align:start position:0% +personal view that is uh so active and +and maybe even dominating our political + + align:start position:0% +and maybe even dominating our political + + + align:start position:0% +and maybe even dominating our political +campaign at the moment with people not + + align:start position:0% +campaign at the moment with people not + + + align:start position:0% +campaign at the moment with people not +respecting um each other's rights each + + align:start position:0% +respecting um each other's rights each + + + align:start position:0% +respecting um each other's rights each +each other's backgrounds each other's + + align:start position:0% +each other's backgrounds each other's + + + align:start position:0% +each other's backgrounds each other's +traditions and each other's preferences + + align:start position:0% +traditions and each other's preferences + + + align:start position:0% +traditions and each other's preferences +and I think we've got to find ways to + + align:start position:0% +and I think we've got to find ways to + + + align:start position:0% +and I think we've got to find ways to +get across these interest group lines to + + align:start position:0% +get across these interest group lines to + + + align:start position:0% +get across these interest group lines to +solve some of these problems so that's a + + align:start position:0% +solve some of these problems so that's a + + + align:start position:0% +solve some of these problems so that's a +bit of of an overview of what we've + + align:start position:0% +bit of of an overview of what we've + + + align:start position:0% +bit of of an overview of what we've +covered and and some of the major themes + + align:start position:0% +covered and and some of the major themes + + + align:start position:0% +covered and and some of the major themes +now let's dig a little bit deeper and + + align:start position:0% +now let's dig a little bit deeper and + + + align:start position:0% +now let's dig a little bit deeper and +let's start about with what do you want + + align:start position:0% +let's start about with what do you want + + + align:start position:0% +let's start about with what do you want +from work remember we started with a + + align:start position:0% +from work remember we started with a + + + align:start position:0% +from work remember we started with a +question right at the beginning of of + + align:start position:0% +question right at the beginning of of + + + align:start position:0% +question right at the beginning of of +the class what's the most important + + align:start position:0% +the class what's the most important + + + align:start position:0% +the class what's the most important +priority for you when you think about + + align:start position:0% +priority for you when you think about + + + align:start position:0% +priority for you when you think about +what you're looking for in your work and + + align:start position:0% +what you're looking for in your work and + + + align:start position:0% +what you're looking for in your work and +in your careers and the results are + + align:start position:0% +in your careers and the results are + + + align:start position:0% +in your careers and the results are +quite interesting and I think there are + + align:start position:0% +quite interesting and I think there are + + + align:start position:0% +quite interesting and I think there are +more Nuance than even this pie chart + + align:start position:0% +more Nuance than even this pie chart + + + align:start position:0% +more Nuance than even this pie chart +shows yes number one is getting a good + + align:start position:0% +shows yes number one is getting a good + + + align:start position:0% +shows yes number one is getting a good +balance between work and family life 26% + + align:start position:0% +balance between work and family life 26% + + + align:start position:0% +balance between work and family life 26% +of you uh rated that your top priority + + align:start position:0% +of you uh rated that your top priority + + + align:start position:0% +of you uh rated that your top priority +followed very closely by this + + align:start position:0% +followed very closely by this + + + align:start position:0% +followed very closely by this +interesting concern for having an impact + + align:start position:0% +interesting concern for having an impact + + + align:start position:0% +interesting concern for having an impact +for dealing with real problems + + align:start position:0% +for dealing with real problems + + + align:start position:0% +for dealing with real problems +significant problems in your Society and + + align:start position:0% +significant problems in your Society and + + + align:start position:0% +significant problems in your Society and +your your your your location your + + align:start position:0% +your your your your location your + + + align:start position:0% +your your your your location your +community you want to address the issues + + align:start position:0% +community you want to address the issues + + + align:start position:0% +community you want to address the issues +that are in front of us today maybe it's + + align:start position:0% +that are in front of us today maybe it's + + + align:start position:0% +that are in front of us today maybe it's +um dealing with climate change and + + align:start position:0% +um dealing with climate change and + + + align:start position:0% +um dealing with climate change and +saving the planet for yourselves and + + align:start position:0% +saving the planet for yourselves and + + + align:start position:0% +saving the planet for yourselves and +Next Generation other generations to + + align:start position:0% +Next Generation other generations to + + + align:start position:0% +Next Generation other generations to +follow maybe it's dealing with the + + align:start position:0% +follow maybe it's dealing with the + + + align:start position:0% +follow maybe it's dealing with the +poverty that we find in too Parts too + + align:start position:0% +poverty that we find in too Parts too + + + align:start position:0% +poverty that we find in too Parts too +many parts of our world maybe it's + + align:start position:0% +many parts of our world maybe it's + + + align:start position:0% +many parts of our world maybe it's +dealing with some of the Social + + align:start position:0% +dealing with some of the Social + + + align:start position:0% +dealing with some of the Social +Challenges and conflicts that we have in + + align:start position:0% +Challenges and conflicts that we have in + + + align:start position:0% +Challenges and conflicts that we have in +the war torn areas of the world but you + + align:start position:0% +the war torn areas of the world but you + + + align:start position:0% +the war torn areas of the world but you +want to make a difference and I think + + align:start position:0% +want to make a difference and I think + + + align:start position:0% +want to make a difference and I think +that is fantastic and yes you want a a + + align:start position:0% +that is fantastic and yes you want a a + + + align:start position:0% +that is fantastic and yes you want a a +good uh Financial uh return for your + + align:start position:0% +good uh Financial uh return for your + + + align:start position:0% +good uh Financial uh return for your +Investments and your contributions but + + align:start position:0% +Investments and your contributions but + + + align:start position:0% +Investments and your contributions but +notice these are mixed together and I + + align:start position:0% +notice these are mixed together and I + + + align:start position:0% +notice these are mixed together and I +think when we did the interviews when we + + align:start position:0% +think when we did the interviews when we + + + align:start position:0% +think when we did the interviews when we +did the uh exercise around asking how + + align:start position:0% +did the uh exercise around asking how + + + align:start position:0% +did the uh exercise around asking how +are your views similar or different than + + align:start position:0% +are your views similar or different than + + + align:start position:0% +are your views similar or different than +your parents the dominant thing that + + align:start position:0% +your parents the dominant thing that + + + align:start position:0% +your parents the dominant thing that +came through in your qualitative + + align:start position:0% +came through in your qualitative + + + align:start position:0% +came through in your qualitative +comments to me was that you want many of + + align:start position:0% +comments to me was that you want many of + + + align:start position:0% +comments to me was that you want many of +the same things as your parents + + align:start position:0% +the same things as your parents + + + align:start position:0% +the same things as your parents +respect Security in some sense Financial + + align:start position:0% +respect Security in some sense Financial + + + align:start position:0% +respect Security in some sense Financial +uh security but you also want more you + + align:start position:0% +uh security but you also want more you + + + align:start position:0% +uh security but you also want more you +you recognize you are perhaps more + + align:start position:0% +you recognize you are perhaps more + + + align:start position:0% +you recognize you are perhaps more +privileged than your parents or + + align:start position:0% +privileged than your parents or + + + align:start position:0% +privileged than your parents or +grandparents and that uh you are in a + + align:start position:0% +grandparents and that uh you are in a + + + align:start position:0% +grandparents and that uh you are in a +position where you can uh have a an + + align:start position:0% +position where you can uh have a an + + + align:start position:0% +position where you can uh have a an +opportunity + + align:start position:0% +opportunity + + + align:start position:0% +opportunity +to uh have a meaningful job make a + + align:start position:0% +to uh have a meaningful job make a + + + align:start position:0% +to uh have a meaningful job make a +meaningful contribution and really + + align:start position:0% +meaningful contribution and really + + + align:start position:0% +meaningful contribution and really +contribute to improving society and so I + + align:start position:0% +contribute to improving society and so I + + + align:start position:0% +contribute to improving society and so I +think there's more uh that you expect + + align:start position:0% +think there's more uh that you expect + + + align:start position:0% +think there's more uh that you expect +out of work than perhaps prior + + align:start position:0% +out of work than perhaps prior + + + align:start position:0% +out of work than perhaps prior +Generations here's just a couple of uh + + align:start position:0% +Generations here's just a couple of uh + + + align:start position:0% +Generations here's just a couple of uh +examples that I want to put a little bit + + align:start position:0% +examples that I want to put a little bit + + + align:start position:0% +examples that I want to put a little bit +more uh substance on that pie chart + + align:start position:0% +more uh substance on that pie chart + + + align:start position:0% +more uh substance on that pie chart +because I think it tells us something + + align:start position:0% +because I think it tells us something + + + align:start position:0% +because I think it tells us something +about uh the complexities of work today + + align:start position:0% +about uh the complexities of work today + + + align:start position:0% +about uh the complexities of work today +and of the workforce today and this uh + + align:start position:0% +and of the workforce today and this uh + + + align:start position:0% +and of the workforce today and this uh +is is one point that someone made and I + + align:start position:0% +is is one point that someone made and I + + + align:start position:0% +is is one point that someone made and I +think it summarizes that chart pretty + + align:start position:0% +think it summarizes that chart pretty + + + align:start position:0% +think it summarizes that chart pretty +nicely I dream of a well-balanced work + + align:start position:0% +nicely I dream of a well-balanced work + + + align:start position:0% +nicely I dream of a well-balanced work +and family environment where I can + + align:start position:0% +and family environment where I can + + + align:start position:0% +and family environment where I can +develop my skills and put them to + + align:start position:0% +develop my skills and put them to + + + align:start position:0% +develop my skills and put them to +service of my community as well as to + + align:start position:0% +service of my community as well as to + + + align:start position:0% +service of my community as well as to +get a wage that allows me to live + + align:start position:0% +get a wage that allows me to live + + + align:start position:0% +get a wage that allows me to live +decently and provide for my future + + align:start position:0% +decently and provide for my future + + + align:start position:0% +decently and provide for my future +Offspring so here we bring family and + + align:start position:0% +Offspring so here we bring family and + + + align:start position:0% +Offspring so here we bring family and +work together we bring commitment to U + + align:start position:0% +work together we bring commitment to U + + + align:start position:0% +work together we bring commitment to U +an important cause but an expectation + + align:start position:0% +an important cause but an expectation + + + align:start position:0% +an important cause but an expectation +that I can do this in a way that will uh + + align:start position:0% +that I can do this in a way that will uh + + + align:start position:0% +that I can do this in a way that will uh +uh take care of my family + + align:start position:0% +uh take care of my family + + + align:start position:0% +uh take care of my family +needs our MBA students here in the + + align:start position:0% +needs our MBA students here in the + + + align:start position:0% +needs our MBA students here in the +classroom had an assignment to go out + + align:start position:0% +classroom had an assignment to go out + + + align:start position:0% +classroom had an assignment to go out +and talk to uh other workers to + + align:start position:0% +and talk to uh other workers to + + + align:start position:0% +and talk to uh other workers to +interview them and do an A A an audio + + align:start position:0% +interview them and do an A A an audio + + + align:start position:0% +interview them and do an A A an audio +recording and we had we received some + + align:start position:0% +recording and we had we received some + + + align:start position:0% +recording and we had we received some +fantastic uh uh recordings and and + + align:start position:0% +fantastic uh uh recordings and and + + + align:start position:0% +fantastic uh uh recordings and and +stories from workers telling their own + + align:start position:0% +stories from workers telling their own + + + align:start position:0% +stories from workers telling their own +story about work and I just want to uh + + align:start position:0% +story about work and I just want to uh + + + align:start position:0% +story about work and I just want to uh +illustrate two of them that I think uh + + align:start position:0% +illustrate two of them that I think uh + + + align:start position:0% +illustrate two of them that I think uh +help bring home uh the complexity and + + align:start position:0% +help bring home uh the complexity and + + + align:start position:0% +help bring home uh the complexity and +the diversity that we find in work + + align:start position:0% +the diversity that we find in work + + + align:start position:0% +the diversity that we find in work +experiences and in our Workforce + + align:start position:0% +experiences and in our Workforce + + + align:start position:0% +experiences and in our Workforce +today this one says it's an immigrant + + align:start position:0% +today this one says it's an immigrant + + + align:start position:0% +today this one says it's an immigrant +from Ghana working in a temporary job in + + align:start position:0% +from Ghana working in a temporary job in + + + align:start position:0% +from Ghana working in a temporary job in +transportation and construction and uh + + align:start position:0% +transportation and construction and uh + + + align:start position:0% +transportation and construction and uh +Manufacturing Services and has had a + + align:start position:0% +Manufacturing Services and has had a + + + align:start position:0% +Manufacturing Services and has had a +variety of these kinds of jobs and what + + align:start position:0% +variety of these kinds of jobs and what + + + align:start position:0% +variety of these kinds of jobs and what +is what is his aspiration it's very + + align:start position:0% +is what is his aspiration it's very + + + align:start position:0% +is what is his aspiration it's very +basic and very simple for an immigrant + + align:start position:0% +basic and very simple for an immigrant + + + align:start position:0% +basic and very simple for an immigrant +he wants to finish school he wants to + + align:start position:0% +he wants to finish school he wants to + + + align:start position:0% +he wants to finish school he wants to +get a better job he wants to start a + + align:start position:0% +get a better job he wants to start a + + + align:start position:0% +get a better job he wants to start a +family and he wants to live comfortably + + align:start position:0% +family and he wants to live comfortably + + + align:start position:0% +family and he wants to live comfortably +that's the Immigrant story that builds + + align:start position:0% +that's the Immigrant story that builds + + + align:start position:0% +that's the Immigrant story that builds +so many countries around the world where + + align:start position:0% +so many countries around the world where + + + align:start position:0% +so many countries around the world where +people take the the risks of moving uh + + align:start position:0% +people take the the risks of moving uh + + + align:start position:0% +people take the the risks of moving uh +from their Homeland to somewhere else in + + align:start position:0% +from their Homeland to somewhere else in + + + align:start position:0% +from their Homeland to somewhere else in +search of a better life and it's our + + align:start position:0% +search of a better life and it's our + + + align:start position:0% +search of a better life and it's our +responsibility therefore to make sure + + align:start position:0% +responsibility therefore to make sure + + + align:start position:0% +responsibility therefore to make sure +that people who have that aspiration can + + align:start position:0% +that people who have that aspiration can + + + align:start position:0% +that people who have that aspiration can +actually realize it and we appreciate + + align:start position:0% +actually realize it and we appreciate + + + align:start position:0% +actually realize it and we appreciate +the value that they bring to our + + align:start position:0% +the value that they bring to our + + + align:start position:0% +the value that they bring to our +countries when they come I thought that + + align:start position:0% +countries when they come I thought that + + + align:start position:0% +countries when they come I thought that +was a very interesting comment and this + + align:start position:0% +was a very interesting comment and this + + + align:start position:0% +was a very interesting comment and this +is one this might be one of my most + + align:start position:0% +is one this might be one of my most + + + align:start position:0% +is one this might be one of my most +favorite ones it's from a 26-year-old + + align:start position:0% +favorite ones it's from a 26-year-old + + + align:start position:0% +favorite ones it's from a 26-year-old +college graduate who is an Uber driver + + align:start position:0% +college graduate who is an Uber driver + + + align:start position:0% +college graduate who is an Uber driver +at the moment and just I'll read this + + align:start position:0% +at the moment and just I'll read this + + + align:start position:0% +at the moment and just I'll read this +because it it illustrates the complexity + + align:start position:0% +because it it illustrates the complexity + + + align:start position:0% +because it it illustrates the complexity +of what's going on in this individual + + align:start position:0% +of what's going on in this individual + + + align:start position:0% +of what's going on in this individual +mind and in his life and trying to + + align:start position:0% +mind and in his life and trying to + + + align:start position:0% +mind and in his life and trying to +figure out where to go next and he's + + align:start position:0% +figure out where to go next and he's + + + align:start position:0% +figure out where to go next and he's +saying what am I looking for in the next + + align:start position:0% +saying what am I looking for in the next + + + align:start position:0% +saying what am I looking for in the next +job well I'm looking for a well-paying + + align:start position:0% +job well I'm looking for a well-paying + + + align:start position:0% +job well I'm looking for a well-paying +job over $15 an + + align:start position:0% +job over $15 an + + + align:start position:0% +job over $15 an +hour whether we consider that wellp paid + + align:start position:0% +hour whether we consider that wellp paid + + + align:start position:0% +hour whether we consider that wellp paid +or not is another question but that's + + align:start position:0% +or not is another question but that's + + + align:start position:0% +or not is another question but that's +what his aspiration is at the moment + + align:start position:0% +what his aspiration is at the moment + + + align:start position:0% +what his aspiration is at the moment +salary is definitely there but number + + align:start position:0% +salary is definitely there but number + + + align:start position:0% +salary is definitely there but number +one is the environment as long as I + + align:start position:0% +one is the environment as long as I + + + align:start position:0% +one is the environment as long as I +enjoy what I'm doing be able to live + + align:start position:0% +enjoy what I'm doing be able to live + + + align:start position:0% +enjoy what I'm doing be able to live +your life and enjoy what you are doing + + align:start position:0% +your life and enjoy what you are doing + + + align:start position:0% +your life and enjoy what you are doing +but now I'm finding that it's really + + align:start position:0% +but now I'm finding that it's really + + + align:start position:0% +but now I'm finding that it's really +hard to live off off one job I see lots + + align:start position:0% +hard to live off off one job I see lots + + + align:start position:0% +hard to live off off one job I see lots +of people having to work two jobs for me + + align:start position:0% +of people having to work two jobs for me + + + align:start position:0% +of people having to work two jobs for me +it's just to be able to support yourself + + align:start position:0% +it's just to be able to support yourself + + + align:start position:0% +it's just to be able to support yourself +and your family with one job seems to me + + align:start position:0% +and your family with one job seems to me + + + align:start position:0% +and your family with one job seems to me +that's a very very basic simple + + align:start position:0% +that's a very very basic simple + + + align:start position:0% +that's a very very basic simple +aspiration that if we can't deliver on + + align:start position:0% +aspiration that if we can't deliver on + + + align:start position:0% +aspiration that if we can't deliver on +that particular expectation there's + + align:start position:0% +that particular expectation there's + + + align:start position:0% +that particular expectation there's +something wrong with our work systems + + align:start position:0% +something wrong with our work systems + + + align:start position:0% +something wrong with our work systems +there's something wrong with our economy + + align:start position:0% +there's something wrong with our economy + + + align:start position:0% +there's something wrong with our economy +and there's something wrong with the way + + align:start position:0% +and there's something wrong with the way + + + align:start position:0% +and there's something wrong with the way +in which we are structuring uh work + + align:start position:0% +in which we are structuring uh work + + + align:start position:0% +in which we are structuring uh work +today + + align:start position:0% +today + + + align:start position:0% +today +if we can't really provide an + + align:start position:0% +if we can't really provide an + + + align:start position:0% +if we can't really provide an +opportunity to support yourself and your + + align:start position:0% +opportunity to support yourself and your + + + align:start position:0% +opportunity to support yourself and your +family with one job we've got a lot more + + align:start position:0% +family with one job we've got a lot more + + + align:start position:0% +family with one job we've got a lot more +work to do these were just a couple of + + align:start position:0% +work to do these were just a couple of + + + align:start position:0% +work to do these were just a couple of +the interviews that uh uh were uh came + + align:start position:0% +the interviews that uh uh were uh came + + + align:start position:0% +the interviews that uh uh were uh came +from our mbas but I want to turn to the + + align:start position:0% +from our mbas but I want to turn to the + + + align:start position:0% +from our mbas but I want to turn to the +people in the classroom and ask them + + align:start position:0% +people in the classroom and ask them + + + align:start position:0% +people in the classroom and ask them +just very quickly just give me a quick + + align:start position:0% +just very quickly just give me a quick + + + align:start position:0% +just very quickly just give me a quick +one minute or one sentence or two + + align:start position:0% +one minute or one sentence or two + + + align:start position:0% +one minute or one sentence or two +summary what surprised you when you talk + + align:start position:0% +summary what surprised you when you talk + + + align:start position:0% +summary what surprised you when you talk +to workers because encouraged the the + + align:start position:0% +to workers because encouraged the the + + + align:start position:0% +to workers because encouraged the the +students to go out talk to them + + align:start position:0% + + + + align:start position:0% + +talk going to start thank you I think + + align:start position:0% +talk going to start thank you I think + + + align:start position:0% +talk going to start thank you I think +for me it's it's reading this and + + align:start position:0% +for me it's it's reading this and + + + align:start position:0% +for me it's it's reading this and +comparing to what I had in my interview + + align:start position:0% +comparing to what I had in my interview + + + align:start position:0% +comparing to what I had in my interview +I actually interview uh someone who work + + align:start position:0% +I actually interview uh someone who work + + + align:start position:0% +I actually interview uh someone who work +at management consulting which is very + + align:start position:0% +at management consulting which is very + + + align:start position:0% +at management consulting which is very +high Prestige profession very well paid + + align:start position:0% +high Prestige profession very well paid + + + align:start position:0% +high Prestige profession very well paid +and the thing they complained was + + align:start position:0% +and the thing they complained was + + + align:start position:0% +and the thing they complained was +balance of between work and personal + + align:start position:0% +balance of between work and personal + + + align:start position:0% +balance of between work and personal +life working 100 hours a week and having + + align:start position:0% +life working 100 hours a week and having + + + align:start position:0% +life working 100 hours a week and having +to they did they wanted to quit just to + + align:start position:0% +to they did they wanted to quit just to + + + align:start position:0% +to they did they wanted to quit just to +have more time to spend doing the things + + align:start position:0% +have more time to spend doing the things + + + align:start position:0% +have more time to spend doing the things +they they liked and being with their + + align:start position:0% +they they liked and being with their + + + align:start position:0% +they they liked and being with their +families so it's like on both on the top + + align:start position:0% +families so it's like on both on the top + + + align:start position:0% +families so it's like on both on the top +and the bottom people are feeling the + + align:start position:0% +and the bottom people are feeling the + + + align:start position:0% +and the bottom people are feeling the +same need of like maybe they're + + align:start position:0% +same need of like maybe they're + + + align:start position:0% +same need of like maybe they're +overworking and like too much pressure + + align:start position:0% +overworking and like too much pressure + + + align:start position:0% +overworking and like too much pressure +on them + + align:start position:0% + + + + align:start position:0% + +here's what else did you + + align:start position:0% + + + + align:start position:0% + +so uh with the first uh citation we had + + align:start position:0% +so uh with the first uh citation we had + + + align:start position:0% +so uh with the first uh citation we had +up there I was interviewing a French uh + + align:start position:0% +up there I was interviewing a French uh + + + align:start position:0% +up there I was interviewing a French uh +retail worker and it was interesting to + + align:start position:0% +retail worker and it was interesting to + + + align:start position:0% +retail worker and it was interesting to +hear how that worker didn't want to use + + align:start position:0% +hear how that worker didn't want to use + + + align:start position:0% +hear how that worker didn't want to use +their nationality which could easily be + + align:start position:0% +their nationality which could easily be + + + align:start position:0% +their nationality which could easily be +associated with luxury products uh as + + align:start position:0% +associated with luxury products uh as + + + align:start position:0% +associated with luxury products uh as +their selling point so they were trying + + align:start position:0% +their selling point so they were trying + + + align:start position:0% +their selling point so they were trying +to kind of break out of it and they + + align:start position:0% +to kind of break out of it and they + + + align:start position:0% +to kind of break out of it and they +recognized the value but just + + align:start position:0% +recognized the value but just + + + align:start position:0% +recognized the value but just +interesting to hear how different + + align:start position:0% +interesting to hear how different + + + align:start position:0% +interesting to hear how different +backgrounds and nationalities can + + align:start position:0% +backgrounds and nationalities can + + + align:start position:0% +backgrounds and nationalities can +influence how you approach work how you + + align:start position:0% +influence how you approach work how you + + + align:start position:0% +influence how you approach work how you +succeed at work and how you want to be + + align:start position:0% +succeed at work and how you want to be + + + align:start position:0% +succeed at work and how you want to be +identified at work + + align:start position:0% + + + + align:start position:0% + +and the fact that this person was was a + + align:start position:0% +and the fact that this person was was a + + + align:start position:0% +and the fact that this person was was a +a wine salesman well we tend to think + + align:start position:0% +a wine salesman well we tend to think + + + align:start position:0% +a wine salesman well we tend to think +French wine my goodness but he wanted to + + align:start position:0% +French wine my goodness but he wanted to + + + align:start position:0% +French wine my goodness but he wanted to +demonstrate that he knew wine not + + align:start position:0% +demonstrate that he knew wine not + + + align:start position:0% +demonstrate that he knew wine not +because he was French and didn't want to + + align:start position:0% +because he was French and didn't want to + + + align:start position:0% +because he was French and didn't want to +use that as uh as a marketing device he + + align:start position:0% +use that as uh as a marketing device he + + + align:start position:0% +use that as uh as a marketing device he +wanted to demonstrate he really loves + + align:start position:0% +wanted to demonstrate he really loves + + + align:start position:0% +wanted to demonstrate he really loves +this uh Cuisine he loves to do it he + + align:start position:0% +this uh Cuisine he loves to do it he + + + align:start position:0% +this uh Cuisine he loves to do it he +loves to sell it and he wants to uh have + + align:start position:0% +loves to sell it and he wants to uh have + + + align:start position:0% +loves to sell it and he wants to uh have +an impact what + + align:start position:0% +an impact what + + + align:start position:0% +an impact what +else quo go ahead we lost the here we + + align:start position:0% +else quo go ahead we lost the here we + + + align:start position:0% +else quo go ahead we lost the here we +are + + align:start position:0% +are + + + align:start position:0% +are +go ahead um I interviewed uh someone who + + align:start position:0% +go ahead um I interviewed uh someone who + + + align:start position:0% +go ahead um I interviewed uh someone who +works with the state um of Massachusetts + + align:start position:0% +works with the state um of Massachusetts + + + align:start position:0% +works with the state um of Massachusetts +and on the theme of work balance um he + + align:start position:0% +and on the theme of work balance um he + + + align:start position:0% +and on the theme of work balance um he +said something interesting that even + + align:start position:0% +said something interesting that even + + + align:start position:0% +said something interesting that even +though a lot of times people think + + align:start position:0% +though a lot of times people think + + + align:start position:0% +though a lot of times people think +working in Government doesn't pay well + + align:start position:0% +working in Government doesn't pay well + + + align:start position:0% +working in Government doesn't pay well +their work balance actually comes into + + align:start position:0% +their work balance actually comes into + + + align:start position:0% +their work balance actually comes into +effect because they're not allowed to + + align:start position:0% +effect because they're not allowed to + + + align:start position:0% +effect because they're not allowed to +check the emails when they go home so in + + align:start position:0% +check the emails when they go home so in + + + align:start position:0% +check the emails when they go home so in +the private sector you may get a cell + + align:start position:0% +the private sector you may get a cell + + + align:start position:0% +the private sector you may get a cell +phone and a laptops and all that but + + align:start position:0% +phone and a laptops and all that but + + + align:start position:0% +phone and a laptops and all that but +somehow you expect it to be on 24/7 yeah + + align:start position:0% +somehow you expect it to be on 24/7 yeah + + + align:start position:0% +somehow you expect it to be on 24/7 yeah +so this technology can either be our + + align:start position:0% +so this technology can either be our + + + align:start position:0% +so this technology can either be our +Ally or our worst enemy and and they + + align:start position:0% +Ally or our worst enemy and and they + + + align:start position:0% +Ally or our worst enemy and and they +have a solution or a strategy for + + align:start position:0% +have a solution or a strategy for + + + align:start position:0% +have a solution or a strategy for +dealing with so that was very + + align:start position:0% +dealing with so that was very + + + align:start position:0% +dealing with so that was very +interesting good and yeah I interviewed + + align:start position:0% +interesting good and yeah I interviewed + + + align:start position:0% +interesting good and yeah I interviewed +a immigrant worker she was a woman from + + align:start position:0% +a immigrant worker she was a woman from + + + align:start position:0% +a immigrant worker she was a woman from +Bangladesh and working for last 10 years + + align:start position:0% +Bangladesh and working for last 10 years + + + align:start position:0% +Bangladesh and working for last 10 years +in us and uh that surprised me when I + + align:start position:0% +in us and uh that surprised me when I + + + align:start position:0% +in us and uh that surprised me when I +asked what is your uh wish she said that + + align:start position:0% +asked what is your uh wish she said that + + + align:start position:0% +asked what is your uh wish she said that +I want that I could save that amount of + + align:start position:0% +I want that I could save that amount of + + + align:start position:0% +I want that I could save that amount of +money that I can afford a two-bedroom + + align:start position:0% +money that I can afford a two-bedroom + + + align:start position:0% +money that I can afford a two-bedroom +house and I can keep my child myself and + + align:start position:0% +house and I can keep my child myself and + + + align:start position:0% +house and I can keep my child myself and +that was uh she was already doing two + + align:start position:0% +that was uh she was already doing two + + + align:start position:0% +that was uh she was already doing two +jobs and I really that make me think + + align:start position:0% +jobs and I really that make me think + + + align:start position:0% +jobs and I really that make me think +that that the price of the housing is so + + align:start position:0% +that that the price of the housing is so + + + align:start position:0% +that that the price of the housing is so +high and a person who is working + + align:start position:0% +high and a person who is working + + + align:start position:0% +high and a person who is working +full-time and he even for the extra time + + align:start position:0% +full-time and he even for the extra time + + + align:start position:0% +full-time and he even for the extra time +she was doing two job it's difficult for + + align:start position:0% +she was doing two job it's difficult for + + + align:start position:0% +she was doing two job it's difficult for +us uh for her to maintain uh Family Life + + align:start position:0% +us uh for her to maintain uh Family Life + + + align:start position:0% +us uh for her to maintain uh Family Life +along with the world yeah so here's + + align:start position:0% +along with the world yeah so here's + + + align:start position:0% +along with the world yeah so here's +someone who has a + + align:start position:0% +someone who has a + + + align:start position:0% +someone who has a +family resp set of responsibilities + + align:start position:0% +family resp set of responsibilities + + + align:start position:0% +family resp set of responsibilities +holding down two jobs just trying to uh + + align:start position:0% +holding down two jobs just trying to uh + + + align:start position:0% +holding down two jobs just trying to uh +to survive and get ahead uh another + + align:start position:0% +to survive and get ahead uh another + + + align:start position:0% +to survive and get ahead uh another +immigrant uh uh story that is uh very + + align:start position:0% +immigrant uh uh story that is uh very + + + align:start position:0% +immigrant uh uh story that is uh very +common for people who are trying to make + + align:start position:0% +common for people who are trying to make + + + align:start position:0% +common for people who are trying to make +it here anyone else want to offer + + align:start position:0% + + + + align:start position:0% + +yes uh for me my my interview is a pH + + align:start position:0% +yes uh for me my my interview is a pH + + + align:start position:0% +yes uh for me my my interview is a pH +student which is uh in the UA and uh he + + align:start position:0% +student which is uh in the UA and uh he + + + align:start position:0% +student which is uh in the UA and uh he +has three different kind of occupation + + align:start position:0% +has three different kind of occupation + + + align:start position:0% +has three different kind of occupation +for 12 years and uh what surprised me + + align:start position:0% +for 12 years and uh what surprised me + + + align:start position:0% +for 12 years and uh what surprised me +that I also uh mentioned to you the the + + align:start position:0% +that I also uh mentioned to you the the + + + align:start position:0% +that I also uh mentioned to you the the +labor union in the UA or the Arabic area + + align:start position:0% +labor union in the UA or the Arabic area + + + align:start position:0% +labor union in the UA or the Arabic area +most countries is illegal which uh is my + + align:start position:0% +most countries is illegal which uh is my + + + align:start position:0% +most countries is illegal which uh is my +first time to know that and previously I + + align:start position:0% +first time to know that and previously I + + + align:start position:0% +first time to know that and previously I +already heard the new that the the + + align:start position:0% +already heard the new that the the + + + align:start position:0% +already heard the new that the the +immigration label like from Pakistan + + align:start position:0% +immigration label like from Pakistan + + + align:start position:0% +immigration label like from Pakistan +from uh from India they got very low + + align:start position:0% +from uh from India they got very low + + + align:start position:0% +from uh from India they got very low +payment like uh it's about uh uh $200 us + + align:start position:0% +payment like uh it's about uh uh $200 us + + + align:start position:0% +payment like uh it's about uh uh $200 us +per month probably or even less and uh + + align:start position:0% +per month probably or even less and uh + + + align:start position:0% +per month probably or even less and uh +but before that I have no idea that + + align:start position:0% +but before that I have no idea that + + + align:start position:0% +but before that I have no idea that +there's no protection of this uh these + + align:start position:0% +there's no protection of this uh these + + + align:start position:0% +there's no protection of this uh these +labels and uh uh generally the the their + + align:start position:0% +labels and uh uh generally the the their + + + align:start position:0% +labels and uh uh generally the the their +visa is linked to the employer which + + align:start position:0% +visa is linked to the employer which + + + align:start position:0% +visa is linked to the employer which +means the employer can can easily misuse + + align:start position:0% +means the employer can can easily misuse + + + align:start position:0% +means the employer can can easily misuse +their right to force them to work + + align:start position:0% + + + + align:start position:0% + +hard particularly in the Middle East + + align:start position:0% +hard particularly in the Middle East + + + align:start position:0% +hard particularly in the Middle East +I've spent some time in Saudi Arabia + + align:start position:0% +I've spent some time in Saudi Arabia + + + align:start position:0% +I've spent some time in Saudi Arabia +trying to work with the minister of + + align:start position:0% +trying to work with the minister of + + + align:start position:0% +trying to work with the minister of +Labor in Saudi Arabia to change those + + align:start position:0% +Labor in Saudi Arabia to change those + + + align:start position:0% +Labor in Saudi Arabia to change those +and it's very difficult uh but here is a + + align:start position:0% +and it's very difficult uh but here is a + + + align:start position:0% +and it's very difficult uh but here is a +country where uh worker rights are very + + align:start position:0% +country where uh worker rights are very + + + align:start position:0% +country where uh worker rights are very +much suppressed and particularly the + + align:start position:0% +much suppressed and particularly the + + + align:start position:0% +much suppressed and particularly the +vast majority of the workforce in the + + align:start position:0% +vast majority of the workforce in the + + + align:start position:0% +vast majority of the workforce in the +private sector are immigrants from very + + align:start position:0% +private sector are immigrants from very + + + align:start position:0% +private sector are immigrants from very +low-income countries and they're tied to + + align:start position:0% +low-income countries and they're tied to + + + align:start position:0% +low-income countries and they're tied to +their employer so when we think about + + align:start position:0% +their employer so when we think about + + + align:start position:0% +their employer so when we think about +the workplace today and we think about + + align:start position:0% +the workplace today and we think about + + + align:start position:0% +the workplace today and we think about +our aspirations we generally tend to + + align:start position:0% +our aspirations we generally tend to + + + align:start position:0% +our aspirations we generally tend to +think about uh the fact that we have a + + align:start position:0% +think about uh the fact that we have a + + + align:start position:0% +think about uh the fact that we have a +free labor market we can move if things + + align:start position:0% +free labor market we can move if things + + + align:start position:0% +free labor market we can move if things +are are not satisfactory or we can raise + + align:start position:0% +are are not satisfactory or we can raise + + + align:start position:0% +are are not satisfactory or we can raise +our voice individually or collectively + + align:start position:0% +our voice individually or collectively + + + align:start position:0% +our voice individually or collectively +to try to change things but we have to + + align:start position:0% +to try to change things but we have to + + + align:start position:0% +to try to change things but we have to +understand that a very large number of + + align:start position:0% +understand that a very large number of + + + align:start position:0% +understand that a very large number of +people across the globe + + align:start position:0% +people across the globe + + + align:start position:0% +people across the globe +don't have those very very basic rights + + align:start position:0% +don't have those very very basic rights + + + align:start position:0% +don't have those very very basic rights +are what the international labor + + align:start position:0% +are what the international labor + + + align:start position:0% +are what the international labor +organization remember guy Ryder's um + + align:start position:0% +organization remember guy Ryder's um + + + align:start position:0% +organization remember guy Ryder's um +introduction to this course way back in + + align:start position:0% +introduction to this course way back in + + + align:start position:0% +introduction to this course way back in +the first uh first week the secretary + + align:start position:0% +the first uh first week the secretary + + + align:start position:0% +the first uh first week the secretary +the director general of the ILO in + + align:start position:0% +the director general of the ILO in + + + align:start position:0% +the director general of the ILO in +Geneva a core principle a core human + + align:start position:0% +Geneva a core principle a core human + + + align:start position:0% +Geneva a core principle a core human +right according to the international + + align:start position:0% +right according to the international + + + align:start position:0% +right according to the international +labor organization a part of the UN is + + align:start position:0% +labor organization a part of the UN is + + + align:start position:0% +labor organization a part of the UN is +freedom of Association Along with + + align:start position:0% +freedom of Association Along with + + + align:start position:0% +freedom of Association Along with +freedom from discrimination and from + + align:start position:0% +freedom from discrimination and from + + + align:start position:0% +freedom from discrimination and from +forc labor and child labor so those are + + align:start position:0% +forc labor and child labor so those are + + + align:start position:0% +forc labor and child labor so those are +some very very basic things that we + + align:start position:0% +some very very basic things that we + + + align:start position:0% +some very very basic things that we +expect in the world of work but not all + + align:start position:0% +expect in the world of work but not all + + + align:start position:0% +expect in the world of work but not all +people and in fact a very significant + + align:start position:0% +people and in fact a very significant + + + align:start position:0% +people and in fact a very significant +portion of the workforce across the + + align:start position:0% +portion of the workforce across the + + + align:start position:0% +portion of the workforce across the +globe don't have these basic rights so + + align:start position:0% +globe don't have these basic rights so + + + align:start position:0% +globe don't have these basic rights so +we have to re remember this as we think + + align:start position:0% +we have to re remember this as we think + + + align:start position:0% +we have to re remember this as we think +about where we are and how we advance + + align:start position:0% +about where we are and how we advance + + + align:start position:0% +about where we are and how we advance +from from the stage that we're at Shahid + + align:start position:0% +from from the stage that we're at Shahid + + + align:start position:0% +from from the stage that we're at Shahid +do you have a there's a there was a + + align:start position:0% +do you have a there's a there was a + + + align:start position:0% +do you have a there's a there was a +question on Twitter where uh someone + + align:start position:0% +question on Twitter where uh someone + + + align:start position:0% +question on Twitter where uh someone +asked do we have uh do you have an + + align:start position:0% +asked do we have uh do you have an + + + align:start position:0% +asked do we have uh do you have an +example of a government a country which + + align:start position:0% +example of a government a country which + + + align:start position:0% +example of a government a country which +is sort of facilitating uh some of that + + align:start position:0% +is sort of facilitating uh some of that + + + align:start position:0% +is sort of facilitating uh some of that +making sure that some of these uh Visa + + align:start position:0% +making sure that some of these uh Visa + + + align:start position:0% +making sure that some of these uh Visa +issues and S sort of things are not + + align:start position:0% +issues and S sort of things are not + + + align:start position:0% +issues and S sort of things are not +imposed on the people um on the workers + + align:start position:0% +imposed on the people um on the workers + + + align:start position:0% +imposed on the people um on the workers +we have some good examples of this there + + align:start position:0% +we have some good examples of this there + + + align:start position:0% +we have some good examples of this there +there are examples of of countries that + + align:start position:0% +there are examples of of countries that + + + align:start position:0% +there are examples of of countries that +are struggling with this and working on + + align:start position:0% +are struggling with this and working on + + + align:start position:0% +are struggling with this and working on +it uh one middle- inome country that is + + align:start position:0% +it uh one middle- inome country that is + + + align:start position:0% +it uh one middle- inome country that is +is actually quite Advanced uh is + + align:start position:0% +is actually quite Advanced uh is + + + align:start position:0% +is actually quite Advanced uh is +Singapore Singapore has uh a a lot of uh + + align:start position:0% +Singapore Singapore has uh a a lot of uh + + + align:start position:0% +Singapore Singapore has uh a a lot of uh +immigrant workers particular + + align:start position:0% +immigrant workers particular + + + align:start position:0% +immigrant workers particular +particularly in the domestic Service uh + + align:start position:0% +particularly in the domestic Service uh + + + align:start position:0% +particularly in the domestic Service uh +sector and they've had some scandals + + align:start position:0% +sector and they've had some scandals + + + align:start position:0% +sector and they've had some scandals +some terrible experiences but they have + + align:start position:0% +some terrible experiences but they have + + + align:start position:0% +some terrible experiences but they have +now uh imposed some very strong uh legal + + align:start position:0% +now uh imposed some very strong uh legal + + + align:start position:0% +now uh imposed some very strong uh legal +uh uh constraints and strong enforcement + + align:start position:0% +uh uh constraints and strong enforcement + + + align:start position:0% +uh uh constraints and strong enforcement +because it's the it's one thing to have + + align:start position:0% +because it's the it's one thing to have + + + align:start position:0% +because it's the it's one thing to have +a a law but it's another thing to try to + + align:start position:0% +a a law but it's another thing to try to + + + align:start position:0% +a a law but it's another thing to try to +enforce it and so Singapore is working + + align:start position:0% +enforce it and so Singapore is working + + + align:start position:0% +enforce it and so Singapore is working +uh to to to make progress in this uh + + align:start position:0% +uh to to to make progress in this uh + + + align:start position:0% +uh to to to make progress in this uh +Direction uh but I have to say in the in + + align:start position:0% +Direction uh but I have to say in the in + + + align:start position:0% +Direction uh but I have to say in the in +the Middle East some countries are doing + + align:start position:0% +the Middle East some countries are doing + + + align:start position:0% +the Middle East some countries are doing +a better job job but there is a long + + align:start position:0% +a better job job but there is a long + + + align:start position:0% +a better job job but there is a long +long way to go and that's where perhaps + + align:start position:0% +long way to go and that's where perhaps + + + align:start position:0% +long way to go and that's where perhaps +uh um uh the issue is most serious and + + align:start position:0% +uh um uh the issue is most serious and + + + align:start position:0% +uh um uh the issue is most serious and +and most profound because the benefits + + align:start position:0% +and most profound because the benefits + + + align:start position:0% +and most profound because the benefits +to migrant immigrant workers going from + + align:start position:0% +to migrant immigrant workers going from + + + align:start position:0% +to migrant immigrant workers going from +Pakistan or Bangladesh to the Middle + + align:start position:0% +Pakistan or Bangladesh to the Middle + + + align:start position:0% +Pakistan or Bangladesh to the Middle +East are quite substantial if they can + + align:start position:0% +East are quite substantial if they can + + + align:start position:0% +East are quite substantial if they can +stand the harsh conditions of the work + + align:start position:0% +stand the harsh conditions of the work + + + align:start position:0% +stand the harsh conditions of the work +and the the the Employers in the Middle + + align:start position:0% +and the the the Employers in the Middle + + + align:start position:0% +and the the the Employers in the Middle +East understand that there are real + + align:start position:0% +East understand that there are real + + + align:start position:0% +East understand that there are real +advantages uh for people coming to take + + align:start position:0% +advantages uh for people coming to take + + + align:start position:0% +advantages uh for people coming to take +that work and so therefore uh that just + + align:start position:0% +that work and so therefore uh that just + + + align:start position:0% +that work and so therefore uh that just +feeds into some of the more harsh harsh + + align:start position:0% +feeds into some of the more harsh harsh + + + align:start position:0% +feeds into some of the more harsh harsh +rules I think we will see change um + + align:start position:0% +rules I think we will see change um + + + align:start position:0% +rules I think we will see change um +those of you who have been reading the + + align:start position:0% +those of you who have been reading the + + + align:start position:0% +those of you who have been reading the +world news have just heard that Saudi + + align:start position:0% +world news have just heard that Saudi + + + align:start position:0% +world news have just heard that Saudi +Arabia is trying to move away from some + + align:start position:0% +Arabia is trying to move away from some + + + align:start position:0% +Arabia is trying to move away from some +of its dependence on the oil industry uh + + align:start position:0% +of its dependence on the oil industry uh + + + align:start position:0% +of its dependence on the oil industry uh +Saudi Arabia has also tried to introduce + + align:start position:0% +Saudi Arabia has also tried to introduce + + + align:start position:0% +Saudi Arabia has also tried to introduce +slowly uh at the the with the leadership + + align:start position:0% +slowly uh at the the with the leadership + + + align:start position:0% +slowly uh at the the with the leadership +of uh their minister of Labor a number + + align:start position:0% +of uh their minister of Labor a number + + + align:start position:0% +of uh their minister of Labor a number +of years ago uh more rights for women + + align:start position:0% +of years ago uh more rights for women + + + align:start position:0% +of years ago uh more rights for women +because women don't have many rights to + + align:start position:0% +because women don't have many rights to + + + align:start position:0% +because women don't have many rights to +drive a car or to work in U settings + + align:start position:0% +drive a car or to work in U settings + + + align:start position:0% +drive a car or to work in U settings +where men are present that is slowly + + align:start position:0% +where men are present that is slowly + + + align:start position:0% +where men are present that is slowly +changing that's going to take a long + + align:start position:0% +changing that's going to take a long + + + align:start position:0% +changing that's going to take a long +time but here again is a is an example + + align:start position:0% +time but here again is a is an example + + + align:start position:0% +time but here again is a is an example +of of a society that has a set of values + + align:start position:0% +of of a society that has a set of values + + + align:start position:0% +of of a society that has a set of values +historical values that are very + + align:start position:0% +historical values that are very + + + align:start position:0% +historical values that are very +important to their identity and their + + align:start position:0% +important to their identity and their + + + align:start position:0% +important to their identity and their +religion but uh as Outsiders we may have + + align:start position:0% +religion but uh as Outsiders we may have + + + align:start position:0% +religion but uh as Outsiders we may have +some questions about them we have to + + align:start position:0% +some questions about them we have to + + + align:start position:0% +some questions about them we have to +understand these countries in their own + + align:start position:0% +understand these countries in their own + + + align:start position:0% +understand these countries in their own +cultural context but I do believe there + + align:start position:0% +cultural context but I do believe there + + + align:start position:0% +cultural context but I do believe there +are some very basic core rights of work + + align:start position:0% +are some very basic core rights of work + + + align:start position:0% +are some very basic core rights of work +and that that have to be uh um uh + + align:start position:0% +and that that have to be uh um uh + + + align:start position:0% +and that that have to be uh um uh +respected regardless of where people + + align:start position:0% +respected regardless of where people + + + align:start position:0% +respected regardless of where people +work how they work who they are and who + + align:start position:0% +work how they work who they are and who + + + align:start position:0% +work how they work who they are and who +they work for so I think this is a is a + + align:start position:0% +they work for so I think this is a is a + + + align:start position:0% +they work for so I think this is a is a +campaign it's something that we can + + align:start position:0% +campaign it's something that we can + + + align:start position:0% +campaign it's something that we can +continue to work for so thank you for + + align:start position:0% +continue to work for so thank you for + + + align:start position:0% +continue to work for so thank you for +that question whoever uh posed it on + + align:start position:0% +that question whoever uh posed it on + + + align:start position:0% +that question whoever uh posed it on +Twitter okay let's move on this is u a + + align:start position:0% +Twitter okay let's move on this is u a + + + align:start position:0% +Twitter okay let's move on this is u a +good start we have an understanding uh a + + align:start position:0% +good start we have an understanding uh a + + + align:start position:0% +good start we have an understanding uh a +deeper understanding of what we are + + align:start position:0% +deeper understanding of what we are + + + align:start position:0% +deeper understanding of what we are +looking for from work and now a really + + align:start position:0% +looking for from work and now a really + + + align:start position:0% +looking for from work and now a really +good discussion of what people around + + align:start position:0% +good discussion of what people around + + + align:start position:0% +good discussion of what people around +the world are experiencing as as they + + align:start position:0% +the world are experiencing as as they + + + align:start position:0% +the world are experiencing as as they +try to improve their situation we paid + + align:start position:0% +try to improve their situation we paid + + + align:start position:0% +try to improve their situation we paid +special attention to history in this + + align:start position:0% +special attention to history in this + + + align:start position:0% +special attention to history in this +class and I want to thank uh one of the + + align:start position:0% +class and I want to thank uh one of the + + + align:start position:0% +class and I want to thank uh one of the +participants in the class for posting + + align:start position:0% +participants in the class for posting + + + align:start position:0% +participants in the class for posting +this uh great quote from Thomas + + align:start position:0% +this uh great quote from Thomas + + + align:start position:0% +this uh great quote from Thomas +Jefferson one of our most famous + + align:start position:0% +Jefferson one of our most famous + + + align:start position:0% +Jefferson one of our most famous +presidents the third president of the + + align:start position:0% +presidents the third president of the + + + align:start position:0% +presidents the third president of the +United States um uh and one of the + + align:start position:0% +United States um uh and one of the + + + align:start position:0% +United States um uh and one of the +authors of the Declaration of + + align:start position:0% +authors of the Declaration of + + + align:start position:0% +authors of the Declaration of +Independence for the United States so uh + + align:start position:0% +Independence for the United States so uh + + + align:start position:0% +Independence for the United States so uh +Jefferson said that history by + + align:start position:0% +Jefferson said that history by + + + align:start position:0% +Jefferson said that history by +appraising them of the past will enable + + align:start position:0% +appraising them of the past will enable + + + align:start position:0% +appraising them of the past will enable +them that is all of us to judge to be a + + align:start position:0% +them that is all of us to judge to be a + + + align:start position:0% +them that is all of us to judge to be a +judge of the future it will Avail us + + align:start position:0% +judge of the future it will Avail us + + + align:start position:0% +judge of the future it will Avail us +to learn from the experience of other + + align:start position:0% +to learn from the experience of other + + + align:start position:0% +to learn from the experience of other +times and other nations it will qualify + + align:start position:0% +times and other nations it will qualify + + + align:start position:0% +times and other nations it will qualify +us as judges of the actions and designs + + align:start position:0% +us as judges of the actions and designs + + + align:start position:0% +us as judges of the actions and designs +of men that's a very uh time-honored or + + align:start position:0% +of men that's a very uh time-honored or + + + align:start position:0% +of men that's a very uh time-honored or +unhonorable uh use of the word men but + + align:start position:0% +unhonorable uh use of the word men but + + + align:start position:0% +unhonorable uh use of the word men but +that's what the way he wrote and it'll + + align:start position:0% +that's what the way he wrote and it'll + + + align:start position:0% +that's what the way he wrote and it'll +enable us to know the itions of others + + align:start position:0% +enable us to know the itions of others + + + align:start position:0% +enable us to know the itions of others +even under every disguise it may not + + align:start position:0% +even under every disguise it may not + + + align:start position:0% +even under every disguise it may not +assume and knowing it to defeat its + + align:start position:0% +assume and knowing it to defeat its + + + align:start position:0% +assume and knowing it to defeat its +views Thomas Jefferson was a student of + + align:start position:0% +views Thomas Jefferson was a student of + + + align:start position:0% +views Thomas Jefferson was a student of +History Thomas Jefferson respected + + align:start position:0% +History Thomas Jefferson respected + + + align:start position:0% +History Thomas Jefferson respected +history we respect history in this class + + align:start position:0% +history we respect history in this class + + + align:start position:0% +history we respect history in this class +not to repeat it not to try to go back + + align:start position:0% +not to repeat it not to try to go back + + + align:start position:0% +not to repeat it not to try to go back +to the way things were but to learn from + + align:start position:0% +to the way things were but to learn from + + + align:start position:0% +to the way things were but to learn from +it so that we can lay a foundation uh + + align:start position:0% +it so that we can lay a foundation uh + + + align:start position:0% +it so that we can lay a foundation uh +for the future so we spent time here in + + align:start position:0% +for the future so we spent time here in + + + align:start position:0% +for the future so we spent time here in +the United States talking about this + + align:start position:0% +the United States talking about this + + + align:start position:0% +the United States talking about this +Foundation that was laid in the 1930s + + align:start position:0% +Foundation that was laid in the 1930s + + + align:start position:0% +Foundation that was laid in the 1930s +called the New Deal and we even + + align:start position:0% +called the New Deal and we even + + + align:start position:0% +called the New Deal and we even +celebrated some of the uh the people who + + align:start position:0% +celebrated some of the uh the people who + + + align:start position:0% +celebrated some of the uh the people who +helped to bring about it uh a professor + + align:start position:0% +helped to bring about it uh a professor + + + align:start position:0% +helped to bring about it uh a professor +from the University of Wisconsin whose + + align:start position:0% +from the University of Wisconsin whose + + + align:start position:0% +from the University of Wisconsin whose +ideas led to unemployment insurance and + + align:start position:0% +ideas led to unemployment insurance and + + + align:start position:0% +ideas led to unemployment insurance and +led to Social Security and led to the + + align:start position:0% +led to Social Security and led to the + + + align:start position:0% +led to Social Security and led to the +the passage of child labor and minimum + + align:start position:0% +the passage of child labor and minimum + + + align:start position:0% +the passage of child labor and minimum +wage legislation in that state and in + + align:start position:0% +wage legislation in that state and in + + + align:start position:0% +wage legislation in that state and in +other states before we got National + + align:start position:0% +other states before we got National + + + align:start position:0% +other states before we got National +legislation and to Francis Perkins the + + align:start position:0% +legislation and to Francis Perkins the + + + align:start position:0% +legislation and to Francis Perkins the +first woman who was a a member of a + + align:start position:0% +first woman who was a a member of a + + + align:start position:0% +first woman who was a a member of a +president's cabinet President Roosevelt + + align:start position:0% +president's cabinet President Roosevelt + + + align:start position:0% +president's cabinet President Roosevelt +asked her to to be the Secretary of + + align:start position:0% +asked her to to be the Secretary of + + + align:start position:0% +asked her to to be the Secretary of +State and Francis Perkins said to the + + align:start position:0% +State and Francis Perkins said to the + + + align:start position:0% +State and Francis Perkins said to the +president when he asked her are you sure + + align:start position:0% +president when he asked her are you sure + + + align:start position:0% +president when he asked her are you sure +you really want me because if you are + + align:start position:0% +you really want me because if you are + + + align:start position:0% +you really want me because if you are +going to put me in that office I'm going + + align:start position:0% +going to put me in that office I'm going + + + align:start position:0% +going to put me in that office I'm going +to bring my experience to bring about + + align:start position:0% +to bring my experience to bring about + + + align:start position:0% +to bring my experience to bring about +social security some minimum wage some + + align:start position:0% +social security some minimum wage some + + + align:start position:0% +social security some minimum wage some +basic rights of unemployment insurance + + align:start position:0% +basic rights of unemployment insurance + + + align:start position:0% +basic rights of unemployment insurance +to bear in uh at a national level + + align:start position:0% +to bear in uh at a national level + + + align:start position:0% +to bear in uh at a national level +Francis Perkins observed firsthand the + + align:start position:0% +Francis Perkins observed firsthand the + + + align:start position:0% +Francis Perkins observed firsthand the +terror of a factory fire called The + + align:start position:0% +terror of a factory fire called The + + + align:start position:0% +terror of a factory fire called The +Triangle shirt waste fire in New York + + align:start position:0% +Triangle shirt waste fire in New York + + + align:start position:0% +Triangle shirt waste fire in New York +City in u the early ier part of the + + align:start position:0% +City in u the early ier part of the + + + align:start position:0% +City in u the early ier part of the +century where over a 100 women died + + align:start position:0% +century where over a 100 women died + + + align:start position:0% +century where over a 100 women died +because the fire escapes were locked as + + align:start position:0% +because the fire escapes were locked as + + + align:start position:0% +because the fire escapes were locked as +the fire burned in that particular + + align:start position:0% +the fire burned in that particular + + + align:start position:0% +the fire burned in that particular +Factory and that imprinted + + align:start position:0% +Factory and that imprinted + + + align:start position:0% +Factory and that imprinted +her commitment to make a better place + + align:start position:0% +her commitment to make a better place + + + align:start position:0% +her commitment to make a better place +for work a more safe place to work and + + align:start position:0% +for work a more safe place to work and + + + align:start position:0% +for work a more safe place to work and +as a result of leadership and ideas and + + align:start position:0% +as a result of leadership and ideas and + + + align:start position:0% +as a result of leadership and ideas and +commitment and a change in politics in + + align:start position:0% +commitment and a change in politics in + + + align:start position:0% +commitment and a change in politics in +the 1930s we got the foundation of the + + align:start position:0% +the 1930s we got the foundation of the + + + align:start position:0% +the 1930s we got the foundation of the +Social Security the M retirement + + align:start position:0% +Social Security the M retirement + + + align:start position:0% +Social Security the M retirement +Security Act basically the unemployment + + align:start position:0% +Security Act basically the unemployment + + + align:start position:0% +Security Act basically the unemployment +insurance for the first time the ability + + align:start position:0% +insurance for the first time the ability + + + align:start position:0% +insurance for the first time the ability +to join a union and engage in collec a + + align:start position:0% +to join a union and engage in collec a + + + align:start position:0% +to join a union and engage in collec a +bargaining protected for the first time + + align:start position:0% +bargaining protected for the first time + + + align:start position:0% +bargaining protected for the first time +and a minimum wage uh and overtime rules + + align:start position:0% +and a minimum wage uh and overtime rules + + + align:start position:0% +and a minimum wage uh and overtime rules +for the first time that foundation in + + align:start position:0% +for the first time that foundation in + + + align:start position:0% +for the first time that foundation in +the United States and comparable + + align:start position:0% +the United States and comparable + + + align:start position:0% +the United States and comparable +legislation in other countries many in + + align:start position:0% +legislation in other countries many in + + + align:start position:0% +legislation in other countries many in +Europe before us some in Asia after us + + align:start position:0% +Europe before us some in Asia after us + + + align:start position:0% +Europe before us some in Asia after us +some still struggling to put these kinds + + align:start position:0% +some still struggling to put these kinds + + + align:start position:0% +some still struggling to put these kinds +of basic foundations and Floors on on + + align:start position:0% +of basic foundations and Floors on on + + + align:start position:0% +of basic foundations and Floors on on +their conditions of work but it was that + + align:start position:0% +their conditions of work but it was that + + + align:start position:0% +their conditions of work but it was that +Foundation that allowed us to then build + + align:start position:0% +Foundation that allowed us to then build + + + align:start position:0% +Foundation that allowed us to then build +what we talked about uh uh in several + + align:start position:0% +what we talked about uh uh in several + + + align:start position:0% +what we talked about uh uh in several +sessions as the social contract here in + + align:start position:0% +sessions as the social contract here in + + + align:start position:0% +sessions as the social contract here in +the United States and in in other other + + align:start position:0% +the United States and in in other other + + + align:start position:0% +the United States and in in other other +places and so the question then is we + + align:start position:0% +places and so the question then is we + + + align:start position:0% +places and so the question then is we +can we build on this yes this worked for + + align:start position:0% +can we build on this yes this worked for + + + align:start position:0% +can we build on this yes this worked for +many years and we'll look at that in + + align:start position:0% +many years and we'll look at that in + + + align:start position:0% +many years and we'll look at that in +just a moment just to refresh our minds + + align:start position:0% +just a moment just to refresh our minds + + + align:start position:0% +just a moment just to refresh our minds +but can we build a new Foundation if + + align:start position:0% +but can we build a new Foundation if + + + align:start position:0% +but can we build a new Foundation if +today's world has changed as + + align:start position:0% +today's world has changed as + + + align:start position:0% +today's world has changed as +dramatically as we have discussed it + + align:start position:0% +dramatically as we have discussed it + + + align:start position:0% +dramatically as we have discussed it +throughout this course then it behooves + + align:start position:0% +throughout this course then it behooves + + + align:start position:0% +throughout this course then it behooves +us to ask what's the New Foundation + + align:start position:0% +us to ask what's the New Foundation + + + align:start position:0% +us to ask what's the New Foundation +what's the new body of legislation that + + align:start position:0% +what's the new body of legislation that + + + align:start position:0% +what's the new body of legislation that +would lay the framework for us to + + align:start position:0% +would lay the framework for us to + + + align:start position:0% +would lay the framework for us to +advance and to deal with some of the + + align:start position:0% +advance and to deal with some of the + + + align:start position:0% +advance and to deal with some of the +issues we're going to uh talk about here + + align:start position:0% +issues we're going to uh talk about here + + + align:start position:0% +issues we're going to uh talk about here +in just a few minutes so let's adilia + + align:start position:0% +in just a few minutes so let's adilia + + + align:start position:0% +in just a few minutes so let's adilia +did you have a question or comment yeah + + align:start position:0% +did you have a question or comment yeah + + + align:start position:0% +did you have a question or comment yeah +just a comment that uh like U years + + align:start position:0% +just a comment that uh like U years + + + align:start position:0% +just a comment that uh like U years +decades ago like Francis Roos he said + + align:start position:0% +decades ago like Francis Roos he said + + + align:start position:0% +decades ago like Francis Roos he said +that in this country any who is uh who + + align:start position:0% +that in this country any who is uh who + + + align:start position:0% +that in this country any who is uh who +who is uh depending on its existence by + + align:start position:0% +who is uh depending on its existence by + + + align:start position:0% +who is uh depending on its existence by +paying less than the living wage should + + align:start position:0% +paying less than the living wage should + + + align:start position:0% +paying less than the living wage should +not have a right to be in us so and he + + align:start position:0% +not have a right to be in us so and he + + + align:start position:0% +not have a right to be in us so and he +said that by the by the living vage I + + align:start position:0% +said that by the by the living vage I + + + align:start position:0% +said that by the by the living vage I +don't mean that just just above + + align:start position:0% +don't mean that just just above + + + align:start position:0% +don't mean that just just above +existence like just more subsistent but + + align:start position:0% +existence like just more subsistent but + + + align:start position:0% +existence like just more subsistent but +but I mean that it should be a living w + + align:start position:0% +but I mean that it should be a living w + + + align:start position:0% +but I mean that it should be a living w +mean the decent wage so I mean perhaps + + align:start position:0% +mean the decent wage so I mean perhaps + + + align:start position:0% +mean the decent wage so I mean perhaps +in this course that's what we are trying + + align:start position:0% +in this course that's what we are trying + + + align:start position:0% +in this course that's what we are trying +to stress that there should be a decent + + align:start position:0% +to stress that there should be a decent + + + align:start position:0% +to stress that there should be a decent +living for the workers also yeah no + + align:start position:0% +living for the workers also yeah no + + + align:start position:0% +living for the workers also yeah no +absolutely was uh he was a strong + + align:start position:0% +absolutely was uh he was a strong + + + align:start position:0% +absolutely was uh he was a strong +advocate for worker rights for uh urging + + align:start position:0% +advocate for worker rights for uh urging + + + align:start position:0% +advocate for worker rights for uh urging +business to provide a a living wage and + + align:start position:0% +business to provide a a living wage and + + + align:start position:0% +business to provide a a living wage and +to get us out of the Great Depression of + + align:start position:0% +to get us out of the Great Depression of + + + align:start position:0% +to get us out of the Great Depression of +the 1930s and it was that kind of strong + + align:start position:0% +the 1930s and it was that kind of strong + + + align:start position:0% +the 1930s and it was that kind of strong +uh National leadership that helped to to + + align:start position:0% +uh National leadership that helped to to + + + align:start position:0% +uh National leadership that helped to to +make this possible so let's look at what + + align:start position:0% +make this possible so let's look at what + + + align:start position:0% +make this possible so let's look at what +happened we've talked about the social + + align:start position:0% +happened we've talked about the social + + + align:start position:0% +happened we've talked about the social +contract and if you look at this chart + + align:start position:0% +contract and if you look at this chart + + + align:start position:0% +contract and if you look at this chart +which we uh used at several points in + + align:start position:0% +which we uh used at several points in + + + align:start position:0% +which we uh used at several points in +the course it shows as you you've uh + + align:start position:0% +the course it shows as you you've uh + + + align:start position:0% +the course it shows as you you've uh +seen before that from the end of World + + align:start position:0% +seen before that from the end of World + + + align:start position:0% +seen before that from the end of World +War II up through the 1970s till about + + align:start position:0% +War II up through the 1970s till about + + + align:start position:0% +War II up through the 1970s till about +1980 wages and productivity moved + + align:start position:0% +1980 wages and productivity moved + + + align:start position:0% +1980 wages and productivity moved +together in tandem that is as the + + align:start position:0% +together in tandem that is as the + + + align:start position:0% +together in tandem that is as the +economy got stronger the institutions of + + align:start position:0% +economy got stronger the institutions of + + + align:start position:0% +economy got stronger the institutions of +collective bargaining the leadership of + + align:start position:0% +collective bargaining the leadership of + + + align:start position:0% +collective bargaining the leadership of +personnel management and human resource + + align:start position:0% +personnel management and human resource + + + align:start position:0% +personnel management and human resource +managers uh uh in our large corporations + + align:start position:0% +managers uh uh in our large corporations + + + align:start position:0% +managers uh uh in our large corporations +made sure that wages were moving up in + + align:start position:0% +made sure that wages were moving up in + + + align:start position:0% +made sure that wages were moving up in +in in tandem with productivity so + + align:start position:0% +in in tandem with productivity so + + + align:start position:0% +in in tandem with productivity so +workers shared by and large in the + + align:start position:0% +workers shared by and large in the + + + align:start position:0% +workers shared by and large in the +benefits of the economic growth but + + align:start position:0% +benefits of the economic growth but + + + align:start position:0% +benefits of the economic growth but +something happened as we all know uh in + + align:start position:0% +something happened as we all know uh in + + + align:start position:0% +something happened as we all know uh in +the the late 70s and the early 1980s to + + align:start position:0% +the the late 70s and the early 1980s to + + + align:start position:0% +the the late 70s and the early 1980s to +break this relationship and that's when + + align:start position:0% +break this relationship and that's when + + + align:start position:0% +break this relationship and that's when +you see wages flatlining and + + align:start position:0% +you see wages flatlining and + + + align:start position:0% +you see wages flatlining and +productivity continuing to grow and that + + align:start position:0% +productivity continuing to grow and that + + + align:start position:0% +productivity continuing to grow and that +uh my friends I think explains a lot of + + align:start position:0% +uh my friends I think explains a lot of + + + align:start position:0% +uh my friends I think explains a lot of +the frustrations that we are seeing here + + align:start position:0% +the frustrations that we are seeing here + + + align:start position:0% +the frustrations that we are seeing here +in the United States play out in our + + align:start position:0% +in the United States play out in our + + + align:start position:0% +in the United States play out in our +political debates today that workers + + align:start position:0% +political debates today that workers + + + align:start position:0% +political debates today that workers +today are saying we have not shared or + + align:start position:0% +today are saying we have not shared or + + + align:start position:0% +today are saying we have not shared or +we have been displaced and our income + + align:start position:0% +we have been displaced and our income + + + align:start position:0% +we have been displaced and our income +which uh came from good jobs maybe + + align:start position:0% +which uh came from good jobs maybe + + + align:start position:0% +which uh came from good jobs maybe +manufacturing jobs which have gone + + align:start position:0% +manufacturing jobs which have gone + + + align:start position:0% +manufacturing jobs which have gone +offshore or been outsourced domestically + + align:start position:0% +offshore or been outsourced domestically + + + align:start position:0% +offshore or been outsourced domestically +or whatever happened to them Changed by + + align:start position:0% +or whatever happened to them Changed by + + + align:start position:0% +or whatever happened to them Changed by +technology uh have not benefited from a + + align:start position:0% +technology uh have not benefited from a + + + align:start position:0% +technology uh have not benefited from a +lot of these changes and so we are now + + align:start position:0% +lot of these changes and so we are now + + + align:start position:0% +lot of these changes and so we are now +reaping the costs of uh not addressing + + align:start position:0% +reaping the costs of uh not addressing + + + align:start position:0% +reaping the costs of uh not addressing +these changes in the economy so that + + align:start position:0% +these changes in the economy so that + + + align:start position:0% +these changes in the economy so that +people could keep up um with this + + align:start position:0% +people could keep up um with this + + + align:start position:0% +people could keep up um with this +process and so one of the things that we + + align:start position:0% +process and so one of the things that we + + + align:start position:0% +process and so one of the things that we +did in the course is we asked all of you + + align:start position:0% +did in the course is we asked all of you + + + align:start position:0% +did in the course is we asked all of you +what do you think about this do you + + align:start position:0% +what do you think about this do you + + + align:start position:0% +what do you think about this do you +believe wages and productivity should go + + align:start position:0% +believe wages and productivity should go + + + align:start position:0% +believe wages and productivity should go +together and the vast majority over 80% + + align:start position:0% +together and the vast majority over 80% + + + align:start position:0% +together and the vast majority over 80% +of you said yes but you're worried about + + align:start position:0% +of you said yes but you're worried about + + + align:start position:0% +of you said yes but you're worried about +it you're also realistic you know that + + align:start position:0% +it you're also realistic you know that + + + align:start position:0% +it you're also realistic you know that +the world has changed you know that + + align:start position:0% +the world has changed you know that + + + align:start position:0% +the world has changed you know that +globalization is more uh dominant now + + align:start position:0% +globalization is more uh dominant now + + + align:start position:0% +globalization is more uh dominant now +you know that technology has eliminated + + align:start position:0% +you know that technology has eliminated + + + align:start position:0% +you know that technology has eliminated +a lot of routine jobs as we we covered + + align:start position:0% +a lot of routine jobs as we we covered + + + align:start position:0% +a lot of routine jobs as we we covered +it in in later sections of of the class + + align:start position:0% +it in in later sections of of the class + + + align:start position:0% +it in in later sections of of the class +and you've seen it in your own + + align:start position:0% +and you've seen it in your own + + + align:start position:0% +and you've seen it in your own +communities we know that that uh uh + + align:start position:0% +communities we know that that uh uh + + + align:start position:0% +communities we know that that uh uh +we're creating new forms of work that + + align:start position:0% +we're creating new forms of work that + + + align:start position:0% +we're creating new forms of work that +don't always provide some of the same + + align:start position:0% +don't always provide some of the same + + + align:start position:0% +don't always provide some of the same +supports and and benefits and so while + + align:start position:0% +supports and and benefits and so while + + + align:start position:0% +supports and and benefits and so while +you know that uh you would like to see + + align:start position:0% +you know that uh you would like to see + + + align:start position:0% +you know that uh you would like to see +this happen and these uh comments come + + align:start position:0% +this happen and these uh comments come + + + align:start position:0% +this happen and these uh comments come +again off the discussion board uh you're + + align:start position:0% +again off the discussion board uh you're + + + align:start position:0% +again off the discussion board uh you're +all worried about how we are how can we + + align:start position:0% +all worried about how we are how can we + + + align:start position:0% +all worried about how we are how can we +make this happen and I think the one on + + align:start position:0% +make this happen and I think the one on + + + align:start position:0% +make this happen and I think the one on +the left really captures uh the + + align:start position:0% +the left really captures uh the + + + align:start position:0% +the left really captures uh the +sentiment of the class uh uh as as well + + align:start position:0% +sentiment of the class uh uh as as well + + + align:start position:0% +sentiment of the class uh uh as as well +as any that I saw on the discussion + + align:start position:0% +as any that I saw on the discussion + + + align:start position:0% +as any that I saw on the discussion +board and it says I think it's important + + align:start position:0% +board and it says I think it's important + + + align:start position:0% +board and it says I think it's important +to maintain the productivity increases + + align:start position:0% +to maintain the productivity increases + + + align:start position:0% +to maintain the productivity increases +aligned with raising wages if we as a + + align:start position:0% +aligned with raising wages if we as a + + + align:start position:0% +aligned with raising wages if we as a +society continue to show only huge + + align:start position:0% +society continue to show only huge + + + align:start position:0% +society continue to show only huge +social and economic inequalities and + + align:start position:0% +social and economic inequalities and + + + align:start position:0% +social and economic inequalities and +that the rich get richer and the poor + + align:start position:0% +that the rich get richer and the poor + + + align:start position:0% +that the rich get richer and the poor +get poorer then we will not be able to + + align:start position:0% +get poorer then we will not be able to + + + align:start position:0% +get poorer then we will not be able to +have a successful and sustainable + + align:start position:0% +have a successful and sustainable + + + align:start position:0% +have a successful and sustainable +Society that's a powerful statement and + + align:start position:0% +Society that's a powerful statement and + + + align:start position:0% +Society that's a powerful statement and +if people really feel that way then + + align:start position:0% +if people really feel that way then + + + align:start position:0% +if people really feel that way then +eventually they are going to act to + + align:start position:0% +eventually they are going to act to + + + align:start position:0% +eventually they are going to act to +change this and it's our job to turn + + align:start position:0% +change this and it's our job to turn + + + align:start position:0% +change this and it's our job to turn +some of this anger and frustration into + + align:start position:0% +some of this anger and frustration into + + + align:start position:0% +some of this anger and frustration into +positive actions for dealing with this + + align:start position:0% +positive actions for dealing with this + + + align:start position:0% +positive actions for dealing with this +gap between economic progress for + + align:start position:0% +gap between economic progress for + + + align:start position:0% +gap between economic progress for +some but a lot of people left behind so + + align:start position:0% +some but a lot of people left behind so + + + align:start position:0% +some but a lot of people left behind so +how do we do it we have to go beyond + + align:start position:0% +how do we do it we have to go beyond + + + align:start position:0% +how do we do it we have to go beyond +just hoping that it changes or wishing + + align:start position:0% +just hoping that it changes or wishing + + + align:start position:0% +just hoping that it changes or wishing +that it changes or worrying that we + + align:start position:0% +that it changes or worrying that we + + + align:start position:0% +that it changes or worrying that we +can't change it um and we have to start + + align:start position:0% +can't change it um and we have to start + + + align:start position:0% +can't change it um and we have to start +to address some of the the the core + + align:start position:0% +to address some of the the the core + + + align:start position:0% +to address some of the the the core +causes of the change + + align:start position:0% +causes of the change + + + align:start position:0% +causes of the change +and we spent some time talking about is + + align:start position:0% +and we spent some time talking about is + + + align:start position:0% +and we spent some time talking about is +this inevitable and we started with the + + align:start position:0% +this inevitable and we started with the + + + align:start position:0% +this inevitable and we started with the +corporation what is the corporation for + + align:start position:0% +corporation what is the corporation for + + + align:start position:0% +corporation what is the corporation for +is the corporation simply an instrument + + align:start position:0% +is the corporation simply an instrument + + + align:start position:0% +is the corporation simply an instrument +to maximize shareholder value is the + + align:start position:0% +to maximize shareholder value is the + + + align:start position:0% +to maximize shareholder value is the +corporation expected to be held + + align:start position:0% +corporation expected to be held + + + align:start position:0% +corporation expected to be held +accountable for + + align:start position:0% +accountable for + + + align:start position:0% +accountable for +additional interests in society for + + align:start position:0% +additional interests in society for + + + align:start position:0% +additional interests in society for +employees for their communities well we + + align:start position:0% +employees for their communities well we + + + align:start position:0% +employees for their communities well we +heard from one of the most respected uh + + align:start position:0% +heard from one of the most respected uh + + + align:start position:0% +heard from one of the most respected uh +former CEOs and Business Leaders in the + + align:start position:0% +former CEOs and Business Leaders in the + + + align:start position:0% +former CEOs and Business Leaders in the +United States in fact glob + + align:start position:0% +United States in fact glob + + + align:start position:0% +United States in fact glob +of the last generation John Reed + + align:start position:0% +of the last generation John Reed + + + align:start position:0% +of the last generation John Reed +president and CEO of uh CEO of City Corp + + align:start position:0% +president and CEO of uh CEO of City Corp + + + align:start position:0% +president and CEO of uh CEO of City Corp +then went on to be president of the New + + align:start position:0% +then went on to be president of the New + + + align:start position:0% +then went on to be president of the New +York Stock Exchange and that interview + + align:start position:0% +York Stock Exchange and that interview + + + align:start position:0% +York Stock Exchange and that interview +that I did with John which I did a year + + align:start position:0% +that I did with John which I did a year + + + align:start position:0% +that I did with John which I did a year +ago I think that interview has been + + align:start position:0% +ago I think that interview has been + + + align:start position:0% +ago I think that interview has been +replayed by more business schools than + + align:start position:0% +replayed by more business schools than + + + align:start position:0% +replayed by more business schools than +anything else from this course because + + align:start position:0% +anything else from this course because + + + align:start position:0% +anything else from this course because +here's someone who is is so highly + + align:start position:0% +here's someone who is is so highly + + + align:start position:0% +here's someone who is is so highly +respected and has lived through the + + align:start position:0% +respected and has lived through the + + + align:start position:0% +respected and has lived through the +transition and John Reed's view + + align:start position:0% +transition and John Reed's view + + + align:start position:0% +transition and John Reed's view +reflected the views of most people + + align:start position:0% +reflected the views of most people + + + align:start position:0% +reflected the views of most people +people in uh in the online course and he + + align:start position:0% +people in uh in the online course and he + + + align:start position:0% +people in uh in the online course and he +basically said look a corporation yes + + align:start position:0% +basically said look a corporation yes + + + align:start position:0% +basically said look a corporation yes +has to has to achieve profits and + + align:start position:0% +has to has to achieve profits and + + + align:start position:0% +has to has to achieve profits and +shareholder value that's that's beyond + + align:start position:0% +shareholder value that's that's beyond + + + align:start position:0% +shareholder value that's that's beyond +questional but we also have to worry + + align:start position:0% +questional but we also have to worry + + + align:start position:0% +questional but we also have to worry +about the customers we have to worry + + align:start position:0% +about the customers we have to worry + + + align:start position:0% +about the customers we have to worry +about the employees and if we don't do + + align:start position:0% +about the employees and if we don't do + + + align:start position:0% +about the employees and if we don't do +that then in the long run organizations + + align:start position:0% +that then in the long run organizations + + + align:start position:0% +that then in the long run organizations +are going to face such a backlash and + + align:start position:0% +are going to face such a backlash and + + + align:start position:0% +are going to face such a backlash and +we're not going to prepare the labor + + align:start position:0% +we're not going to prepare the labor + + + align:start position:0% +we're not going to prepare the labor +force for the future because + + align:start position:0% +force for the future because + + + align:start position:0% +force for the future because +corporations are also training engines + + align:start position:0% +corporations are also training engines + + + align:start position:0% +corporations are also training engines +and he's very worried about the + + align:start position:0% +and he's very worried about the + + + align:start position:0% +and he's very worried about the +workforce and the training that's why he + + align:start position:0% +workforce and the training that's why he + + + align:start position:0% +workforce and the training that's why he +was so active in education both here at + + align:start position:0% +was so active in education both here at + + + align:start position:0% +was so active in education both here at +MIT as an officer of our Corporation but + + align:start position:0% +MIT as an officer of our Corporation but + + + align:start position:0% +MIT as an officer of our Corporation but +also I know in in his private uh uh uh + + align:start position:0% +also I know in in his private uh uh uh + + + align:start position:0% +also I know in in his private uh uh uh +work around the country and indeed + + align:start position:0% +work around the country and indeed + + + align:start position:0% +work around the country and indeed +around the globe and trying to advance + + align:start position:0% +around the globe and trying to advance + + + align:start position:0% +around the globe and trying to advance +particularly technical education + + align:start position:0% +particularly technical education + + + align:start position:0% +particularly technical education +Advanced science technology engineering + + align:start position:0% +Advanced science technology engineering + + + align:start position:0% +Advanced science technology engineering +and math education in our universities + + align:start position:0% +and math education in our universities + + + align:start position:0% +and math education in our universities +and in our high schools so here's the + + align:start position:0% +and in our high schools so here's the + + + align:start position:0% +and in our high schools so here's the +challenge if we recognize and most of + + align:start position:0% +challenge if we recognize and most of + + + align:start position:0% +challenge if we recognize and most of +you said we expect corporations to + + align:start position:0% +you said we expect corporations to + + + align:start position:0% +you said we expect corporations to +behave in ways that respond to + + align:start position:0% +behave in ways that respond to + + + align:start position:0% +behave in ways that respond to +shareholders and stake other + + align:start position:0% +shareholders and stake other + + + align:start position:0% +shareholders and stake other +stakeholders what do we do that's nice + + align:start position:0% +stakeholders what do we do that's nice + + + align:start position:0% +stakeholders what do we do that's nice +rhetoric but if all we do is complain + + align:start position:0% +rhetoric but if all we do is complain + + + align:start position:0% +rhetoric but if all we do is complain +about it or go out on the streets and + + align:start position:0% +about it or go out on the streets and + + + align:start position:0% +about it or go out on the streets and +hold up a a a sign or a picket sign I + + align:start position:0% +hold up a a a sign or a picket sign I + + + align:start position:0% +hold up a a a sign or a picket sign I +suppose that's a that's a statement but + + align:start position:0% +suppose that's a that's a statement but + + + align:start position:0% +suppose that's a that's a statement but +that's not going to get the job done so + + align:start position:0% +that's not going to get the job done so + + + align:start position:0% +that's not going to get the job done so +we spent a lot of time talking about + + align:start position:0% +we spent a lot of time talking about + + + align:start position:0% +we spent a lot of time talking about +what to do and we use lots of examples + + align:start position:0% +what to do and we use lots of examples + + + align:start position:0% +what to do and we use lots of examples +and here's just a few and you you've all + + align:start position:0% +and here's just a few and you you've all + + + align:start position:0% +and here's just a few and you you've all +heard about these uh throughout the + + align:start position:0% +heard about these uh throughout the + + + align:start position:0% +heard about these uh throughout the +course uh as Costco compared to Walmart + + align:start position:0% +course uh as Costco compared to Walmart + + + align:start position:0% +course uh as Costco compared to Walmart +Costco a retailer that uh does invest in + + align:start position:0% +Costco a retailer that uh does invest in + + + align:start position:0% +Costco a retailer that uh does invest in +its employees that does go the high road + + align:start position:0% +its employees that does go the high road + + + align:start position:0% +its employees that does go the high road +as we call it that says we're going to + + align:start position:0% +as we call it that says we're going to + + + align:start position:0% +as we call it that says we're going to +invest in our employees we're going to + + align:start position:0% +invest in our employees we're going to + + + align:start position:0% +invest in our employees we're going to +make them more productive than our + + align:start position:0% +make them more productive than our + + + align:start position:0% +make them more productive than our +competitors and by making them more + + align:start position:0% +competitors and by making them more + + + align:start position:0% +competitors and by making them more +productive we can afford to pay them a + + align:start position:0% +productive we can afford to pay them a + + + align:start position:0% +productive we can afford to pay them a +higher wage this is not charity this is + + align:start position:0% +higher wage this is not charity this is + + + align:start position:0% +higher wage this is not charity this is +the way we're going to do business this + + align:start position:0% +the way we're going to do business this + + + align:start position:0% +the way we're going to do business this +is way we're going to meet our customer + + align:start position:0% +is way we're going to meet our customer + + + align:start position:0% +is way we're going to meet our customer +customer needs and it's been very + + align:start position:0% +customer needs and it's been very + + + align:start position:0% +customer needs and it's been very +successful in in doing so financially + + align:start position:0% +successful in in doing so financially + + + align:start position:0% +successful in in doing so financially +and uh and it provides a high level of + + align:start position:0% +and uh and it provides a high level of + + + align:start position:0% +and uh and it provides a high level of +customer service and has a loyal + + align:start position:0% +customer service and has a loyal + + + align:start position:0% +customer service and has a loyal +customer base and also provides good + + align:start position:0% +customer base and also provides good + + + align:start position:0% +customer base and also provides good +jobs and we compared that with Walmart + + align:start position:0% +jobs and we compared that with Walmart + + + align:start position:0% +jobs and we compared that with Walmart +Walmart is a worldwide one of the the + + align:start position:0% +Walmart is a worldwide one of the the + + + align:start position:0% +Walmart is a worldwide one of the the +largest private employer uh in the world + + align:start position:0% +largest private employer uh in the world + + + align:start position:0% +largest private employer uh in the world +perhaps certainly here in in in North + + align:start position:0% +perhaps certainly here in in in North + + + align:start position:0% +perhaps certainly here in in in North +America it is and in many of the + + align:start position:0% +America it is and in many of the + + + align:start position:0% +America it is and in many of the +countries uh represented in this course + + align:start position:0% +countries uh represented in this course + + + align:start position:0% +countries uh represented in this course +and Walmart had do a lot of very good + + align:start position:0% +and Walmart had do a lot of very good + + + align:start position:0% +and Walmart had do a lot of very good +things for the environment Walmart was + + align:start position:0% +things for the environment Walmart was + + + align:start position:0% +things for the environment Walmart was +one of the first corporations to respond + + align:start position:0% +one of the first corporations to respond + + + align:start position:0% +one of the first corporations to respond +when we had this terrible um hurricane + + align:start position:0% +when we had this terrible um hurricane + + + align:start position:0% +when we had this terrible um hurricane +uh Katrina in New Orleans in 2005 and it + + align:start position:0% +uh Katrina in New Orleans in 2005 and it + + + align:start position:0% +uh Katrina in New Orleans in 2005 and it +sent before anybody asked it to do it uh + + align:start position:0% +sent before anybody asked it to do it uh + + + align:start position:0% +sent before anybody asked it to do it uh +trucks of water and support and and food + + align:start position:0% +trucks of water and support and and food + + + align:start position:0% +trucks of water and support and and food +to help uh the victims of that hurricane + + align:start position:0% +to help uh the victims of that hurricane + + + align:start position:0% +to help uh the victims of that hurricane +so Walmart does a lot of good things but + + align:start position:0% +so Walmart does a lot of good things but + + + align:start position:0% +so Walmart does a lot of good things but +Walmart also competes on the basis of + + align:start position:0% +Walmart also competes on the basis of + + + align:start position:0% +Walmart also competes on the basis of +just low prices and low wages and + + align:start position:0% +just low prices and low wages and + + + align:start position:0% +just low prices and low wages and +keeping unions out and in controlling + + align:start position:0% +keeping unions out and in controlling + + + align:start position:0% +keeping unions out and in controlling +the work force in ways that creates high + + align:start position:0% +the work force in ways that creates high + + + align:start position:0% +the work force in ways that creates high +levels of turnover not such good + + align:start position:0% +levels of turnover not such good + + + align:start position:0% +levels of turnover not such good +customer satisfaction and service but + + align:start position:0% +customer satisfaction and service but + + + align:start position:0% +customer satisfaction and service but +low prices and so here we have the two + + align:start position:0% +low prices and so here we have the two + + + align:start position:0% +low prices and so here we have the two +comparisons that allow us to say which + + align:start position:0% +comparisons that allow us to say which + + + align:start position:0% +comparisons that allow us to say which +one do we prefer could Walmart improve + + align:start position:0% +one do we prefer could Walmart improve + + + align:start position:0% +one do we prefer could Walmart improve +its organization and its performance on + + align:start position:0% +its organization and its performance on + + + align:start position:0% +its organization and its performance on +the employment side the same way it has + + align:start position:0% +the employment side the same way it has + + + align:start position:0% +the employment side the same way it has +demonstrated it can do on the + + align:start position:0% +demonstrated it can do on the + + + align:start position:0% +demonstrated it can do on the +environmental side or on the operations + + align:start position:0% +environmental side or on the operations + + + align:start position:0% +environmental side or on the operations +side where it is as good as any company + + align:start position:0% +side where it is as good as any company + + + align:start position:0% +side where it is as good as any company +in the world + + align:start position:0% +in the world + + + align:start position:0% +in the world +if it did perhaps we could have a high + + align:start position:0% +if it did perhaps we could have a high + + + align:start position:0% +if it did perhaps we could have a high +road retail industry but it holds + + align:start position:0% +road retail industry but it holds + + + align:start position:0% +road retail industry but it holds +everybody else down in the retail + + align:start position:0% +everybody else down in the retail + + + align:start position:0% +everybody else down in the retail +industry we used another example in + + align:start position:0% +industry we used another example in + + + align:start position:0% +industry we used another example in +retail a local one here um in the Boston + + align:start position:0% +retail a local one here um in the Boston + + + align:start position:0% +retail a local one here um in the Boston +and New England region one that uh our + + align:start position:0% +and New England region one that uh our + + + align:start position:0% +and New England region one that uh our +colleague xenop tan uh uh did a very + + align:start position:0% +colleague xenop tan uh uh did a very + + + align:start position:0% +colleague xenop tan uh uh did a very +good video on called Market Basket and + + align:start position:0% +good video on called Market Basket and + + + align:start position:0% +good video on called Market Basket and +this has now become kind of an icon for + + align:start position:0% +this has now become kind of an icon for + + + align:start position:0% +this has now become kind of an icon for +a high road retail firm a firm that + + align:start position:0% +a high road retail firm a firm that + + + align:start position:0% +a high road retail firm a firm that +where the employees the the the high + + align:start position:0% +where the employees the the the high + + + align:start position:0% +where the employees the the the high +level EX Ives the store managers the + + align:start position:0% +level EX Ives the store managers the + + + align:start position:0% +level EX Ives the store managers the +clerks the truck drivers the warehouse + + align:start position:0% +clerks the truck drivers the warehouse + + + align:start position:0% +clerks the truck drivers the warehouse +workers did an unprecedented thing + + align:start position:0% +workers did an unprecedented thing + + + align:start position:0% +workers did an unprecedented thing +something I've never seen in in all the + + align:start position:0% +something I've never seen in in all the + + + align:start position:0% +something I've never seen in in all the +years I've been working in this field I + + align:start position:0% +years I've been working in this field I + + + align:start position:0% +years I've been working in this field I +never saw a coalition like that come + + align:start position:0% +never saw a coalition like that come + + + align:start position:0% +never saw a coalition like that come +together to say we are going to stand up + + align:start position:0% +together to say we are going to stand up + + + align:start position:0% +together to say we are going to stand up +for a high road company and a high road + + align:start position:0% +for a high road company and a high road + + + align:start position:0% +for a high road company and a high road +CEO who is being fired by the board so + + align:start position:0% +CEO who is being fired by the board so + + + align:start position:0% +CEO who is being fired by the board so +that they can extract more money uh for + + align:start position:0% +that they can extract more money uh for + + + align:start position:0% +that they can extract more money uh for +the owners of the company and for six + + align:start position:0% +the owners of the company and for six + + + align:start position:0% +the owners of the company and for six +weeks they they rallied the + + align:start position:0% +weeks they they rallied the + + + align:start position:0% +weeks they they rallied the +employees they basically stopped the + + align:start position:0% +employees they basically stopped the + + + align:start position:0% +employees they basically stopped the +business from functioning they had the + + align:start position:0% +business from functioning they had the + + + align:start position:0% +business from functioning they had the +loyal support of their customers because + + align:start position:0% +loyal support of their customers because + + + align:start position:0% +loyal support of their customers because +their customers knew what was at stake + + align:start position:0% +their customers knew what was at stake + + + align:start position:0% +their customers knew what was at stake +for them because here's a company that + + align:start position:0% +for them because here's a company that + + + align:start position:0% +for them because here's a company that +has very low prices but great customer + + align:start position:0% +has very low prices but great customer + + + align:start position:0% +has very low prices but great customer +service great Community uh involvement + + align:start position:0% +service great Community uh involvement + + + align:start position:0% +service great Community uh involvement +in stores all over New England family + + align:start position:0% +in stores all over New England family + + + align:start position:0% +in stores all over New England family +relationships the people know each other + + align:start position:0% +relationships the people know each other + + + align:start position:0% +relationships the people know each other +when they shop and they know the + + align:start position:0% +when they shop and they know the + + + align:start position:0% +when they shop and they know the +employees the employees wear their + + align:start position:0% +employees the employees wear their + + + align:start position:0% +employees the employees wear their +tenure and in a little badge on their + + align:start position:0% +tenure and in a little badge on their + + + align:start position:0% +tenure and in a little badge on their +their shirt and this was all going to go + + align:start position:0% +their shirt and this was all going to go + + + align:start position:0% +their shirt and this was all going to go +away and and you saw how the community + + align:start position:0% +away and and you saw how the community + + + align:start position:0% +away and and you saw how the community +how the media how the employees came + + align:start position:0% +how the media how the employees came + + + align:start position:0% +how the media how the employees came +together to fight for good jobs and a + + align:start position:0% +together to fight for good jobs and a + + + align:start position:0% +together to fight for good jobs and a +good company and in the end the the + + align:start position:0% +good company and in the end the the + + + align:start position:0% +good company and in the end the the +board of directors relented and uh they + + align:start position:0% +board of directors relented and uh they + + + align:start position:0% +board of directors relented and uh they +reinstated the CEO that company now is + + align:start position:0% +reinstated the CEO that company now is + + + align:start position:0% +reinstated the CEO that company now is +not only successful financially it's + + align:start position:0% +not only successful financially it's + + + align:start position:0% +not only successful financially it's +expanded the the prices have remained + + align:start position:0% +expanded the the prices have remained + + + align:start position:0% +expanded the the prices have remained +low relative to their competitors and in + + align:start position:0% +low relative to their competitors and in + + + align:start position:0% +low relative to their competitors and in +fact uh uh if you want to go and see a + + align:start position:0% +fact uh uh if you want to go and see a + + + align:start position:0% +fact uh uh if you want to go and see a +movie this weekend that they're going to + + align:start position:0% +movie this weekend that they're going to + + + align:start position:0% +movie this weekend that they're going to +premere a documentary here in a local + + align:start position:0% +premere a documentary here in a local + + + align:start position:0% +premere a documentary here in a local +theater in Somerville which is just uh + + align:start position:0% +theater in Somerville which is just uh + + + align:start position:0% +theater in Somerville which is just uh +near us uh here off the MIT campus uh uh + + align:start position:0% +near us uh here off the MIT campus uh uh + + + align:start position:0% +near us uh here off the MIT campus uh uh +where it's called food fight but it + + align:start position:0% +where it's called food fight but it + + + align:start position:0% +where it's called food fight but it +basically tells the story of the people + + align:start position:0% +basically tells the story of the people + + + align:start position:0% +basically tells the story of the people +who were involved in that dispute it's a + + align:start position:0% +who were involved in that dispute it's a + + + align:start position:0% +who were involved in that dispute it's a +very powerful powerful video uh uh movie + + align:start position:0% +very powerful powerful video uh uh movie + + + align:start position:0% +very powerful powerful video uh uh movie +I've seen it I'm not I don't get any + + align:start position:0% +I've seen it I'm not I don't get any + + + align:start position:0% +I've seen it I'm not I don't get any +royalties on it so this isn't a + + align:start position:0% +royalties on it so this isn't a + + + align:start position:0% +royalties on it so this isn't a +commercial for it but it really is the + + align:start position:0% +commercial for it but it really is the + + + align:start position:0% +commercial for it but it really is the +best documentary of people who have put + + align:start position:0% +best documentary of people who have put + + + align:start position:0% +best documentary of people who have put +their lives and their jobs on the line + + align:start position:0% +their lives and their jobs on the line + + + align:start position:0% +their lives and their jobs on the line +for something they really believed in + + align:start position:0% +for something they really believed in + + + align:start position:0% +for something they really believed in +and it worked out in in uh in in uh uh + + align:start position:0% +and it worked out in in uh in in uh uh + + + align:start position:0% +and it worked out in in uh in in uh uh +good way for them but there are other + + align:start position:0% +good way for them but there are other + + + align:start position:0% +good way for them but there are other +examples Southwest Airlines we've used + + align:start position:0% +examples Southwest Airlines we've used + + + align:start position:0% +examples Southwest Airlines we've used +uh Kaiser Permanente highly unionized + + align:start position:0% +uh Kaiser Permanente highly unionized + + + align:start position:0% +uh Kaiser Permanente highly unionized +Southwest is highly unionized Labor + + align:start position:0% +Southwest is highly unionized Labor + + + align:start position:0% +Southwest is highly unionized Labor +Management Partnerships where they are + + align:start position:0% +Management Partnerships where they are + + + align:start position:0% +Management Partnerships where they are +working together to improve health care + + align:start position:0% +working together to improve health care + + + align:start position:0% +working together to improve health care +we know that the bundle of practices + + align:start position:0% +we know that the bundle of practices + + + align:start position:0% +we know that the bundle of practices +that are necessary to make this work + + align:start position:0% +that are necessary to make this work + + + align:start position:0% +that are necessary to make this work +move from good operation strategy that + + align:start position:0% +move from good operation strategy that + + + align:start position:0% +move from good operation strategy that +is you really need to manage your + + align:start position:0% +is you really need to manage your + + + align:start position:0% +is you really need to manage your +inventory you need to manage your + + align:start position:0% +inventory you need to manage your + + + align:start position:0% +inventory you need to manage your +operations you have to have good + + align:start position:0% +operations you have to have good + + + align:start position:0% +operations you have to have good +efficient uh practices if you're a + + align:start position:0% +efficient uh practices if you're a + + + align:start position:0% +efficient uh practices if you're a +manufacturer or if you're a service + + align:start position:0% +manufacturer or if you're a service + + + align:start position:0% +manufacturer or if you're a service +provider and that has to be matched with + + align:start position:0% +provider and that has to be matched with + + + align:start position:0% +provider and that has to be matched with +effective use of Technologies but also + + align:start position:0% +effective use of Technologies but also + + + align:start position:0% +effective use of Technologies but also +training of the workforce of respecting + + align:start position:0% +training of the workforce of respecting + + + align:start position:0% +training of the workforce of respecting +the workforce for asking the workforce + + align:start position:0% +the workforce for asking the workforce + + + align:start position:0% +the workforce for asking the workforce +for their engagement their ideas on how + + align:start position:0% +for their engagement their ideas on how + + + align:start position:0% +for their engagement their ideas on how +to improve operations over time for in + + align:start position:0% +to improve operations over time for in + + + align:start position:0% +to improve operations over time for in +including the the uh concerns for work + + align:start position:0% +including the the uh concerns for work + + + align:start position:0% +including the the uh concerns for work +and family and finding that balance that + + align:start position:0% +and family and finding that balance that + + + align:start position:0% +and family and finding that balance that +makes the most sense for the nature of + + align:start position:0% +makes the most sense for the nature of + + + align:start position:0% +makes the most sense for the nature of +the organization it means that you have + + align:start position:0% +the organization it means that you have + + + align:start position:0% +the organization it means that you have +to have a business strategy that + + align:start position:0% +to have a business strategy that + + + align:start position:0% +to have a business strategy that +supports Innovation and good customer + + align:start position:0% +supports Innovation and good customer + + + align:start position:0% +supports Innovation and good customer +service and values those kinds of of of + + align:start position:0% +service and values those kinds of of of + + + align:start position:0% +service and values those kinds of of of +features as a way of doing business The + + align:start position:0% +features as a way of doing business The + + + align:start position:0% +features as a way of doing business The +Way Southwest does does it they turn + + align:start position:0% +Way Southwest does does it they turn + + + align:start position:0% +Way Southwest does does it they turn +those planes around more quickly than + + align:start position:0% +those planes around more quickly than + + + align:start position:0% +those planes around more quickly than +anyone else when a plane lands from the + + align:start position:0% +anyone else when a plane lands from the + + + align:start position:0% +anyone else when a plane lands from the +time it lands to the time it takes off + + align:start position:0% +time it lands to the time it takes off + + + align:start position:0% +time it lands to the time it takes off +because people are working together in + + align:start position:0% +because people are working together in + + + align:start position:0% +because people are working together in +teams in very flexible ways and solving + + align:start position:0% +teams in very flexible ways and solving + + + align:start position:0% +teams in very flexible ways and solving +problems for each other and meeting + + align:start position:0% +problems for each other and meeting + + + align:start position:0% +problems for each other and meeting +customers needs and so that's the way in + + align:start position:0% +customers needs and so that's the way in + + + align:start position:0% +customers needs and so that's the way in +which we know one can build a company + + align:start position:0% +which we know one can build a company + + + align:start position:0% +which we know one can build a company +that works financially for the share + + align:start position:0% +that works financially for the share + + + align:start position:0% +that works financially for the share +owners share owners and the investors + + align:start position:0% +owners share owners and the investors + + + align:start position:0% +owners share owners and the investors +and also works for customers and can + + align:start position:0% +and also works for customers and can + + + align:start position:0% +and also works for customers and can +work for employees but it takes a lot of + + align:start position:0% +work for employees but it takes a lot of + + + align:start position:0% +work for employees but it takes a lot of +hard work and so one of the questions we + + align:start position:0% +hard work and so one of the questions we + + + align:start position:0% +hard work and so one of the questions we +always have is well why is it why is it + + align:start position:0% +always have is well why is it why is it + + + align:start position:0% +always have is well why is it why is it +that it's so hard to see that and is the + + align:start position:0% +that it's so hard to see that and is the + + + align:start position:0% +that it's so hard to see that and is the +privates uh or the public corporation + + align:start position:0% +privates uh or the public corporation + + + align:start position:0% +privates uh or the public corporation +the only way to do it some companies + + align:start position:0% +the only way to do it some companies + + + align:start position:0% +the only way to do it some companies +some organizations are turning to + + align:start position:0% +some organizations are turning to + + + align:start position:0% +some organizations are turning to +different organizational forms to make + + align:start position:0% +different organizational forms to make + + + align:start position:0% +different organizational forms to make +this happen and this is just a sampling + + align:start position:0% +this happen and this is just a sampling + + + align:start position:0% +this happen and this is just a sampling +and talked about these uh throughout the + + align:start position:0% +and talked about these uh throughout the + + + align:start position:0% +and talked about these uh throughout the +class uh at various points as well many + + align:start position:0% +class uh at various points as well many + + + align:start position:0% +class uh at various points as well many +of you know about Patagonia this uh + + align:start position:0% +of you know about Patagonia this uh + + + align:start position:0% +of you know about Patagonia this uh +clothing maker and in fact Patagonia + + align:start position:0% +clothing maker and in fact Patagonia + + + align:start position:0% +clothing maker and in fact Patagonia +I'll tell you a story that's going on + + align:start position:0% +I'll tell you a story that's going on + + + align:start position:0% +I'll tell you a story that's going on +right now here that uh in one of our + + align:start position:0% +right now here that uh in one of our + + + align:start position:0% +right now here that uh in one of our +communities uh North uh west of here + + align:start position:0% +communities uh North uh west of here + + + align:start position:0% +communities uh North uh west of here +called uh Lawrence Massachusetts an old + + align:start position:0% +called uh Lawrence Massachusetts an old + + + align:start position:0% +called uh Lawrence Massachusetts an old +textile industry uh town that is uh uh + + align:start position:0% +textile industry uh town that is uh uh + + + align:start position:0% +textile industry uh town that is uh uh +very highly uh populated by immigrants + + align:start position:0% +very highly uh populated by immigrants + + + align:start position:0% +very highly uh populated by immigrants +now uh Latinos uh largely and and uh + + align:start position:0% +now uh Latinos uh largely and and uh + + + align:start position:0% +now uh Latinos uh largely and and uh +people from various parts of of Latin + + align:start position:0% +people from various parts of of Latin + + + align:start position:0% +people from various parts of of Latin +and South America and there was a plant + + align:start position:0% +and South America and there was a plant + + + align:start position:0% +and South America and there was a plant +there that was privately owned it was + + align:start position:0% +there that was privately owned it was + + + align:start position:0% +there that was privately owned it was +called molden Mills and in the 1990 and + + align:start position:0% +called molden Mills and in the 1990 and + + + align:start position:0% +called molden Mills and in the 1990 and +it was owned + + align:start position:0% +it was owned + + + align:start position:0% +it was owned +by a fellow by the name of Aon + + align:start position:0% +by a fellow by the name of Aon + + + align:start position:0% +by a fellow by the name of Aon +fierstein who had a very good + + align:start position:0% +fierstein who had a very good + + + align:start position:0% +fierstein who had a very good +relationship with the workers with the + + align:start position:0% +relationship with the workers with the + + + align:start position:0% +relationship with the workers with the +community with the Union in that plant + + align:start position:0% +community with the Union in that plant + + + align:start position:0% +community with the Union in that plant +providing decent jobs and they had a + + align:start position:0% +providing decent jobs and they had a + + + align:start position:0% +providing decent jobs and they had a +terrible fire I think it was 1995 or + + align:start position:0% +terrible fire I think it was 1995 or + + + align:start position:0% +terrible fire I think it was 1995 or +1997 the plant burned down and Aaron Fen + + align:start position:0% +1997 the plant burned down and Aaron Fen + + + align:start position:0% +1997 the plant burned down and Aaron Fen +said we're going to rebuild it and by + + align:start position:0% +said we're going to rebuild it and by + + + align:start position:0% +said we're going to rebuild it and by +God while we're rebuilding it I'm going + + align:start position:0% +God while we're rebuilding it I'm going + + + align:start position:0% +God while we're rebuilding it I'm going +to make sure that the employees still + + align:start position:0% +to make sure that the employees still + + + align:start position:0% +to make sure that the employees still +get paid and this made national news and + + align:start position:0% +get paid and this made national news and + + + align:start position:0% +get paid and this made national news and +and he did it not for the publicity he + + align:start position:0% +and he did it not for the publicity he + + + align:start position:0% +and he did it not for the publicity he +did it because he wanted to hold on to + + align:start position:0% +did it because he wanted to hold on to + + + align:start position:0% +did it because he wanted to hold on to +that Workforce and he was committed to + + align:start position:0% +that Workforce and he was committed to + + + align:start position:0% +that Workforce and he was committed to +it and he knew that that that that + + align:start position:0% +it and he knew that that that that + + + align:start position:0% +it and he knew that that that that +Workforce had made his family very + + align:start position:0% +Workforce had made his family very + + + align:start position:0% +Workforce had made his family very +prosperous they rebuilt the plant made + + align:start position:0% +prosperous they rebuilt the plant made + + + align:start position:0% +prosperous they rebuilt the plant made +it more modern as succeeded over time + + align:start position:0% +it more modern as succeeded over time + + + align:start position:0% +it more modern as succeeded over time +when feierstein retired it then got + + align:start position:0% +when feierstein retired it then got + + + align:start position:0% +when feierstein retired it then got +bought by a private Equity Firm that + + align:start position:0% +bought by a private Equity Firm that + + + align:start position:0% +bought by a private Equity Firm that +private Equity Firm now wants to to + + align:start position:0% +private Equity Firm now wants to to + + + align:start position:0% +private Equity Firm now wants to to +close it down and move it uh to another + + align:start position:0% +close it down and move it uh to another + + + align:start position:0% +close it down and move it uh to another +part of the country or move it uh + + align:start position:0% +part of the country or move it uh + + + align:start position:0% +part of the country or move it uh +offshore and so the employees and their + + align:start position:0% +offshore and so the employees and their + + + align:start position:0% +offshore and so the employees and their +Union have turned to Patagonia because + + align:start position:0% +Union have turned to Patagonia because + + + align:start position:0% +Union have turned to Patagonia because +they make Po Tech and Patagonia is the + + align:start position:0% +they make Po Tech and Patagonia is the + + + align:start position:0% +they make Po Tech and Patagonia is the +big p is a big purchaser of polartech + + align:start position:0% +big p is a big purchaser of polartech + + + align:start position:0% +big p is a big purchaser of polartech +and said to Patagonia why don't you buy + + align:start position:0% +and said to Patagonia why don't you buy + + + align:start position:0% +and said to Patagonia why don't you buy +this plant why don't you buy this + + align:start position:0% +this plant why don't you buy this + + + align:start position:0% +this plant why don't you buy this +business and keep us going in a viable + + align:start position:0% +business and keep us going in a viable + + + align:start position:0% +business and keep us going in a viable +way so here's another case where some + + align:start position:0% +way so here's another case where some + + + align:start position:0% +way so here's another case where some +choice + + align:start position:0% +choice + + + align:start position:0% +choice +about how do we sustain decent Quality + + align:start position:0% +about how do we sustain decent Quality + + + align:start position:0% +about how do we sustain decent Quality +Employment with a very good business + + align:start position:0% +Employment with a very good business + + + align:start position:0% +Employment with a very good business +with a very good product that is serving + + align:start position:0% +with a very good product that is serving + + + align:start position:0% +with a very good product that is serving +lots of customers in very innovative + + align:start position:0% +lots of customers in very innovative + + + align:start position:0% +lots of customers in very innovative +ways uh in in in various kinds of + + align:start position:0% +ways uh in in in various kinds of + + + align:start position:0% +ways uh in in in various kinds of +sporting sport clothing uh can we find a + + align:start position:0% +sporting sport clothing uh can we find a + + + align:start position:0% +sporting sport clothing uh can we find a +way to sustain that business I don't + + align:start position:0% +way to sustain that business I don't + + + align:start position:0% +way to sustain that business I don't +know what the answer will be but it's + + align:start position:0% +know what the answer will be but it's + + + align:start position:0% +know what the answer will be but it's +playing out uh quietly at the moment uh + + align:start position:0% +playing out uh quietly at the moment uh + + + align:start position:0% +playing out uh quietly at the moment uh +about 40 Mi uh here from uh from here uh + + align:start position:0% +about 40 Mi uh here from uh from here uh + + + align:start position:0% +about 40 Mi uh here from uh from here uh +from the MIT campus we have other + + align:start position:0% +from the MIT campus we have other + + + align:start position:0% +from the MIT campus we have other +examples mandr it's a Spanish uh uh + + align:start position:0% +examples mandr it's a Spanish uh uh + + + align:start position:0% +examples mandr it's a Spanish uh uh +Cooperative that built over time uh to + + align:start position:0% +Cooperative that built over time uh to + + + align:start position:0% +Cooperative that built over time uh to +become a major industrial Enterprise in + + align:start position:0% +become a major industrial Enterprise in + + + align:start position:0% +become a major industrial Enterprise in +that part of the world and in fact has + + align:start position:0% +that part of the world and in fact has + + + align:start position:0% +that part of the world and in fact has +uh operations around the world including + + align:start position:0% +uh operations around the world including + + + align:start position:0% +uh operations around the world including +here in in the United States uh uh + + align:start position:0% +here in in the United States uh uh + + + align:start position:0% +here in in the United States uh uh +employee owned companies uh we used a + + align:start position:0% +employee owned companies uh we used a + + + align:start position:0% +employee owned companies uh we used a +couple of different Brewery examples and + + align:start position:0% +couple of different Brewery examples and + + + align:start position:0% +couple of different Brewery examples and +this one happens to be a local one + + align:start position:0% +this one happens to be a local one + + + align:start position:0% +this one happens to be a local one +Harpoon I put it up there because I tend + + align:start position:0% +Harpoon I put it up there because I tend + + + align:start position:0% +Harpoon I put it up there because I tend +to like their beer and uh and I like the + + align:start position:0% +to like their beer and uh and I like the + + + align:start position:0% +to like their beer and uh and I like the +fact that they are uh also employee + + align:start position:0% +fact that they are uh also employee + + + align:start position:0% +fact that they are uh also employee +owned but it's a it's a fine + + align:start position:0% +owned but it's a it's a fine + + + align:start position:0% +owned but it's a it's a fine +organization again this is not a + + align:start position:0% +organization again this is not a + + + align:start position:0% +organization again this is not a +commercial for their beer but if you + + align:start position:0% +commercial for their beer but if you + + + align:start position:0% +commercial for their beer but if you +ever have the opportunity I wouldn't + + align:start position:0% +ever have the opportunity I wouldn't + + + align:start position:0% +ever have the opportunity I wouldn't +discourage you from trying it so it uh + + align:start position:0% +discourage you from trying it so it uh + + + align:start position:0% +discourage you from trying it so it uh +it has uh it it's wellmade uh and then + + align:start position:0% +it has uh it it's wellmade uh and then + + + align:start position:0% +it has uh it it's wellmade uh and then +my favorite example uh uh people here + + align:start position:0% +my favorite example uh uh people here + + + align:start position:0% +my favorite example uh uh people here +are a little sick of hearing it about my + + align:start position:0% +are a little sick of hearing it about my + + + align:start position:0% +are a little sick of hearing it about my +Green Bay Packer football team but + + align:start position:0% +Green Bay Packer football team but + + + align:start position:0% +Green Bay Packer football team but +here's a little town Green Bay Wisconsin + + align:start position:0% +here's a little town Green Bay Wisconsin + + + align:start position:0% +here's a little town Green Bay Wisconsin +that supports uh a football team because + + align:start position:0% +that supports uh a football team because + + + align:start position:0% +that supports uh a football team because +the football team is owned by the + + align:start position:0% +the football team is owned by the + + + align:start position:0% +the football team is owned by the +community there's no way that that + + align:start position:0% +community there's no way that that + + + align:start position:0% +community there's no way that that +football team would have lasted from + + align:start position:0% +football team would have lasted from + + + align:start position:0% +football team would have lasted from +1927 when they were first formed and + + align:start position:0% +1927 when they were first formed and + + + align:start position:0% +1927 when they were first formed and +stayed in Green Bay up until today and + + align:start position:0% +stayed in Green Bay up until today and + + + align:start position:0% +stayed in Green Bay up until today and +will stay there forever because the + + align:start position:0% +will stay there forever because the + + + align:start position:0% +will stay there forever because the +community owns it and it can't be sold + + align:start position:0% +community owns it and it can't be sold + + + align:start position:0% +community owns it and it can't be sold +it can't be sold to some investor who + + align:start position:0% +it can't be sold to some investor who + + + align:start position:0% +it can't be sold to some investor who +wants to have a hobby because he or + + align:start position:0% +wants to have a hobby because he or + + + align:start position:0% +wants to have a hobby because he or +she's made um uh their fortunes and + + align:start position:0% +she's made um uh their fortunes and + + + align:start position:0% +she's made um uh their fortunes and +therefore they just want a football team + + align:start position:0% +therefore they just want a football team + + + align:start position:0% +therefore they just want a football team +this is something that builds community + + align:start position:0% +this is something that builds community + + + align:start position:0% +this is something that builds community +and the loyalty to that organization and + + align:start position:0% +and the loyalty to that organization and + + + align:start position:0% +and the loyalty to that organization and +to that football team carries on even + + align:start position:0% +to that football team carries on even + + + align:start position:0% +to that football team carries on even +for those of us who have moved away for + + align:start position:0% +for those of us who have moved away for + + + align:start position:0% +for those of us who have moved away for +many years so we can build these + + align:start position:0% +many years so we can build these + + + align:start position:0% +many years so we can build these +organizations we can use different kind + + align:start position:0% +organizations we can use different kind + + + align:start position:0% +organizations we can use different kind +of governance models we can use + + align:start position:0% +of governance models we can use + + + align:start position:0% +of governance models we can use +different kinds of business uh + + align:start position:0% +different kinds of business uh + + + align:start position:0% +different kinds of business uh +strategies but we have to respect the + + align:start position:0% +strategies but we have to respect the + + + align:start position:0% +strategies but we have to respect the +need to and respect the rights of + + align:start position:0% +need to and respect the rights of + + + align:start position:0% +need to and respect the rights of +employees respect the need to manage in + + align:start position:0% +employees respect the need to manage in + + + align:start position:0% +employees respect the need to manage in +a way that makes the organization + + align:start position:0% +a way that makes the organization + + + align:start position:0% +a way that makes the organization +successful as well as uh responsive to + + align:start position:0% +successful as well as uh responsive to + + + align:start position:0% +successful as well as uh responsive to +employee concerns and + + align:start position:0% +employee concerns and + + + align:start position:0% +employee concerns and +so you have strong views just as you had + + align:start position:0% +so you have strong views just as you had + + + align:start position:0% +so you have strong views just as you had +strong views about the corporation uh + + align:start position:0% +strong views about the corporation uh + + + align:start position:0% +strong views about the corporation uh +there was a lively debate on the + + align:start position:0% +there was a lively debate on the + + + align:start position:0% +there was a lively debate on the +discussion board about these high road + + align:start position:0% +discussion board about these high road + + + align:start position:0% +discussion board about these high road +firms and low road firms and you + + align:start position:0% +firms and low road firms and you + + + align:start position:0% +firms and low road firms and you +recognize as this quote recognizes that + + align:start position:0% +recognize as this quote recognizes that + + + align:start position:0% +recognize as this quote recognizes that +some firms have a natural Affinity to + + align:start position:0% +some firms have a natural Affinity to + + + align:start position:0% +some firms have a natural Affinity to +being a high road firm because it's + + align:start position:0% +being a high road firm because it's + + + align:start position:0% +being a high road firm because it's +consistent with their business strategy + + align:start position:0% +consistent with their business strategy + + + align:start position:0% +consistent with their business strategy +that is they say here that if you want + + align:start position:0% +that is they say here that if you want + + + align:start position:0% +that is they say here that if you want +to compete on the basis of innovation + + align:start position:0% +to compete on the basis of innovation + + + align:start position:0% +to compete on the basis of innovation +and it's part of the core business + + align:start position:0% +and it's part of the core business + + + align:start position:0% +and it's part of the core business +strategy then you're more likely to be a + + align:start position:0% +strategy then you're more likely to be a + + + align:start position:0% +strategy then you're more likely to be a +high road firm but what about firms that + + align:start position:0% +high road firm but what about firms that + + + align:start position:0% +high road firm but what about firms that +don't have that business strategy how + + align:start position:0% +don't have that business strategy how + + + align:start position:0% +don't have that business strategy how +are we going to get them to do it and + + align:start position:0% +are we going to get them to do it and + + + align:start position:0% +are we going to get them to do it and +how are we going to get more firms to + + align:start position:0% +how are we going to get more firms to + + + align:start position:0% +how are we going to get more firms to +compete on this basis well that's the + + align:start position:0% +compete on this basis well that's the + + + align:start position:0% +compete on this basis well that's the +big question the answer that comes here + + align:start position:0% +big question the answer that comes here + + + align:start position:0% +big question the answer that comes here +is it's only going to come uh if there's + + align:start position:0% +is it's only going to come uh if there's + + + align:start position:0% +is it's only going to come uh if there's +uh pressure from employees if employees + + align:start position:0% +uh pressure from employees if employees + + + align:start position:0% +uh pressure from employees if employees +themselves start to raise their voices + + align:start position:0% +themselves start to raise their voices + + + align:start position:0% +themselves start to raise their voices +in How to do this so I would ask you I + + align:start position:0% +in How to do this so I would ask you I + + + align:start position:0% +in How to do this so I would ask you I +would ask the people in this room if you + + align:start position:0% +would ask the people in this room if you + + + align:start position:0% +would ask the people in this room if you +were to move forward and try to move us + + align:start position:0% +were to move forward and try to move us + + + align:start position:0% +were to move forward and try to move us +to see high road firms spread more uh + + align:start position:0% +to see high road firms spread more uh + + + align:start position:0% +to see high road firms spread more uh +rapidly and more broadly AC across our + + align:start position:0% +rapidly and more broadly AC across our + + + align:start position:0% +rapidly and more broadly AC across our +Industries so that uh more people in our + + align:start position:0% +Industries so that uh more people in our + + + align:start position:0% +Industries so that uh more people in our +economy could benefit from these + + align:start position:0% +economy could benefit from these + + + align:start position:0% +economy could benefit from these +strategies what needs to be + + align:start position:0% + + + + align:start position:0% + +done and if you have ideas online put + + align:start position:0% +done and if you have ideas online put + + + align:start position:0% +done and if you have ideas online put +them on the discussion board send us + + align:start position:0% +them on the discussion board send us + + + align:start position:0% +them on the discussion board send us +your your comments on Twitter but this + + align:start position:0% +your your comments on Twitter but this + + + align:start position:0% +your your comments on Twitter but this +to me is the most challenging + + align:start position:0% +to me is the most challenging + + + align:start position:0% +to me is the most challenging +question as you think about your answer + + align:start position:0% +question as you think about your answer + + + align:start position:0% +question as you think about your answer +some of you recall that two weeks ago we + + align:start position:0% +some of you recall that two weeks ago we + + + align:start position:0% +some of you recall that two weeks ago we +were fortunate in enough to have the + + align:start position:0% +were fortunate in enough to have the + + + align:start position:0% +were fortunate in enough to have the +Secretary of Labor Tom Perez come and + + align:start position:0% +Secretary of Labor Tom Perez come and + + + align:start position:0% +Secretary of Labor Tom Perez come and +speak to our MIT uh Sloan school mbas + + align:start position:0% +speak to our MIT uh Sloan school mbas + + + align:start position:0% +speak to our MIT uh Sloan school mbas +and he posed that question and he + + align:start position:0% +and he posed that question and he + + + align:start position:0% +and he posed that question and he +challenged the Future Leaders in the MBA + + align:start position:0% +challenged the Future Leaders in the MBA + + + align:start position:0% +challenged the Future Leaders in the MBA +and in the Sloan Community to manage in + + align:start position:0% +and in the Sloan Community to manage in + + + align:start position:0% +and in the Sloan Community to manage in +the ways that we're talking about here + + align:start position:0% +the ways that we're talking about here + + + align:start position:0% +the ways that we're talking about here +but privately as we talked about it he + + align:start position:0% +but privately as we talked about it he + + + align:start position:0% +but privately as we talked about it he +too asked me and others what can he do + + align:start position:0% +too asked me and others what can he do + + + align:start position:0% +too asked me and others what can he do +what can we do to spread these kinds of + + align:start position:0% +what can we do to spread these kinds of + + + align:start position:0% +what can we do to spread these kinds of +practices more widely and and so I'm + + align:start position:0% +practices more widely and and so I'm + + + align:start position:0% +practices more widely and and so I'm +asking in you Leo I think there's one + + align:start position:0% +asking in you Leo I think there's one + + + align:start position:0% +asking in you Leo I think there's one +thing that the students said here with + + align:start position:0% +thing that the students said here with + + + align:start position:0% +thing that the students said here with +additional policies some policies are + + align:start position:0% +additional policies some policies are + + + align:start position:0% +additional policies some policies are +necessary not just giving worker voice + + align:start position:0% +necessary not just giving worker voice + + + align:start position:0% +necessary not just giving worker voice +and like stronger units but also even + + align:start position:0% +and like stronger units but also even + + + align:start position:0% +and like stronger units but also even +higher minimum wage if minimum wage + + align:start position:0% +higher minimum wage if minimum wage + + + align:start position:0% +higher minimum wage if minimum wage +minimum wage is higher and like in + + align:start position:0% +minimum wage is higher and like in + + + align:start position:0% +minimum wage is higher and like in +general salaries will be higher that put + + align:start position:0% +general salaries will be higher that put + + + align:start position:0% +general salaries will be higher that put +pressure on the companies to train the + + align:start position:0% +pressure on the companies to train the + + + align:start position:0% +pressure on the companies to train the +workers and have more productive workers + + align:start position:0% +workers and have more productive workers + + + align:start position:0% +workers and have more productive workers +because if you're going to have you're + + align:start position:0% +because if you're going to have you're + + + align:start position:0% +because if you're going to have you're +going to be forced to pay a better + + align:start position:0% +going to be forced to pay a better + + + align:start position:0% +going to be forced to pay a better +salary you're going to try to extract + + align:start position:0% +salary you're going to try to extract + + + align:start position:0% +salary you're going to try to extract +that value that you obain the only way + + align:start position:0% +that value that you obain the only way + + + align:start position:0% +that value that you obain the only way +you can do it is by training them more + + align:start position:0% +you can do it is by training them more + + + align:start position:0% +you can do it is by training them more +and having them uh like being better and + + align:start position:0% +and having them uh like being better and + + + align:start position:0% +and having them uh like being better and +you're also giving work and protection + + align:start position:0% +you're also giving work and protection + + + align:start position:0% +you're also giving work and protection +from being laid off so easily so that + + align:start position:0% +from being laid off so easily so that + + + align:start position:0% +from being laid off so easily so that +also commits the company a little bit + + align:start position:0% +also commits the company a little bit + + + align:start position:0% +also commits the company a little bit +more to their workers so in that sense + + align:start position:0% +more to their workers so in that sense + + + align:start position:0% +more to their workers so in that sense +you can create maybe a more yeah so so + + align:start position:0% +you can create maybe a more yeah so so + + + align:start position:0% +you can create maybe a more yeah so so +Leo is is is respect is is reflecting a + + align:start position:0% +Leo is is is respect is is reflecting a + + + align:start position:0% +Leo is is is respect is is reflecting a +view that many people hold that we've + + align:start position:0% +view that many people hold that we've + + + align:start position:0% +view that many people hold that we've +got to bring up the floor of the low + + align:start position:0% +got to bring up the floor of the low + + + align:start position:0% +got to bring up the floor of the low +road and we've got a higher minimum wage + + align:start position:0% +road and we've got a higher minimum wage + + + align:start position:0% +road and we've got a higher minimum wage +stronger enforcement of other labor + + align:start position:0% +stronger enforcement of other labor + + + align:start position:0% +stronger enforcement of other labor +standards perhaps uh that's going to + + align:start position:0% +standards perhaps uh that's going to + + + align:start position:0% +standards perhaps uh that's going to +create some incentives uh um you know + + align:start position:0% +create some incentives uh um you know + + + align:start position:0% +create some incentives uh um you know +Walmart did raise its its wages by a + + align:start position:0% +Walmart did raise its its wages by a + + + align:start position:0% +Walmart did raise its its wages by a +dollar an hour above the minimum wage in + + align:start position:0% +dollar an hour above the minimum wage in + + + align:start position:0% +dollar an hour above the minimum wage in +response to employee pressure now what + + align:start position:0% +response to employee pressure now what + + + align:start position:0% +response to employee pressure now what +that requires McDonald's to get the + + align:start position:0% +that requires McDonald's to get the + + + align:start position:0% +that requires McDonald's to get the +return on that increased wage is they've + + align:start position:0% +return on that increased wage is they've + + + align:start position:0% +return on that increased wage is they've +got to start to train people they've got + + align:start position:0% +got to start to train people they've got + + + align:start position:0% +got to start to train people they've got +to hold on to their employees more for a + + align:start position:0% +to hold on to their employees more for a + + + align:start position:0% +to hold on to their employees more for a +longer period of time whether they will + + align:start position:0% +longer period of time whether they will + + + align:start position:0% +longer period of time whether they will +do that or not I don't know but + + align:start position:0% +do that or not I don't know but + + + align:start position:0% +do that or not I don't know but +absolutely it sets in motion some of the + + align:start position:0% +absolutely it sets in motion some of the + + + align:start position:0% +absolutely it sets in motion some of the +Dynamics that create a stronger + + align:start position:0% +Dynamics that create a stronger + + + align:start position:0% +Dynamics that create a stronger +incentive great this is going back to + + align:start position:0% +incentive great this is going back to + + + align:start position:0% +incentive great this is going back to +stuff we've talked about since the + + align:start position:0% +stuff we've talked about since the + + + align:start position:0% +stuff we've talked about since the +beginning of the semester but I think + + align:start position:0% +beginning of the semester but I think + + + align:start position:0% +beginning of the semester but I think +getting the right investors on board if + + align:start position:0% +getting the right investors on board if + + + align:start position:0% +getting the right investors on board if +you need investors is critical and I + + align:start position:0% +you need investors is critical and I + + + align:start position:0% +you need investors is critical and I +think a lot of the entrepreneurial + + align:start position:0% +think a lot of the entrepreneurial + + + align:start position:0% +think a lot of the entrepreneurial +classes MIT where people talk about + + align:start position:0% +classes MIT where people talk about + + + align:start position:0% +classes MIT where people talk about +making sure if you're in an early stage + + align:start position:0% +making sure if you're in an early stage + + + align:start position:0% +making sure if you're in an early stage +startup you get investors that are + + align:start position:0% +startup you get investors that are + + + align:start position:0% +startup you get investors that are +aligned with what you want I think too + + align:start position:0% +aligned with what you want I think too + + + align:start position:0% +aligned with what you want I think too +often you that you see investors that + + align:start position:0% +often you that you see investors that + + + align:start position:0% +often you that you see investors that +push companies to try to scal really + + align:start position:0% +push companies to try to scal really + + + align:start position:0% +push companies to try to scal really +quickly Y and a lot of that + + align:start position:0% +quickly Y and a lot of that + + + align:start position:0% +quickly Y and a lot of that +necessitates sacrifices that this quote + + align:start position:0% +necessitates sacrifices that this quote + + + align:start position:0% +necessitates sacrifices that this quote +kind of talks about but I don't think + + align:start position:0% +kind of talks about but I don't think + + + align:start position:0% +kind of talks about but I don't think +you have that motivation unless you have + + align:start position:0% +you have that motivation unless you have + + + align:start position:0% +you have that motivation unless you have +someone else who kind of can give you + + align:start position:0% +someone else who kind of can give you + + + align:start position:0% +someone else who kind of can give you +that pressure and can TR to force you to + + align:start position:0% +that pressure and can TR to force you to + + + align:start position:0% +that pressure and can TR to force you to +take it so picking your investors is + + align:start position:0% +take it so picking your investors is + + + align:start position:0% +take it so picking your investors is +really important and uh in the one of + + align:start position:0% +really important and uh in the one of + + + align:start position:0% +really important and uh in the one of +the the videos that we did for the + + align:start position:0% +the the videos that we did for the + + + align:start position:0% +the the videos that we did for the +course Scott Stern one of our colleagues + + align:start position:0% +course Scott Stern one of our colleagues + + + align:start position:0% +course Scott Stern one of our colleagues +who teaches entrepreneurial strategy is + + align:start position:0% +who teaches entrepreneurial strategy is + + + align:start position:0% +who teaches entrepreneurial strategy is +is one of our our best people in this + + align:start position:0% +is one of our our best people in this + + + align:start position:0% +is one of our our best people in this +this field uh makes that point and in + + align:start position:0% +this field uh makes that point and in + + + align:start position:0% +this field uh makes that point and in +fact there'll be a slide that'll + + align:start position:0% +fact there'll be a slide that'll + + + align:start position:0% +fact there'll be a slide that'll +illustrate this uh just in a few minutes + + align:start position:0% +illustrate this uh just in a few minutes + + + align:start position:0% +illustrate this uh just in a few minutes +but absolutely picking uh your investors + + align:start position:0% +but absolutely picking uh your investors + + + align:start position:0% +but absolutely picking uh your investors +is really uh critical Ben I wonder how + + align:start position:0% +is really uh critical Ben I wonder how + + + align:start position:0% +is really uh critical Ben I wonder how +hard it is to change the momentum of + + align:start position:0% +hard it is to change the momentum of + + + align:start position:0% +hard it is to change the momentum of +something like Walmart was publicly + + align:start position:0% +something like Walmart was publicly + + + align:start position:0% +something like Walmart was publicly +traded but for example with Harpoon it + + align:start position:0% +traded but for example with Harpoon it + + + align:start position:0% +traded but for example with Harpoon it +had the option of being bought out and + + align:start position:0% +had the option of being bought out and + + + align:start position:0% +had the option of being bought out and +they consciously made a decision as as + + align:start position:0% +they consciously made a decision as as + + + align:start position:0% +they consciously made a decision as as +private privately held company to move + + align:start position:0% +private privately held company to move + + + align:start position:0% +private privately held company to move +towards that employee own so is it too + + align:start position:0% +towards that employee own so is it too + + + align:start position:0% +towards that employee own so is it too +hard to manipulate Walmart and should we + + align:start position:0% +hard to manipulate Walmart and should we + + + align:start position:0% +hard to manipulate Walmart and should we +just focus on um you know advancing the + + align:start position:0% +just focus on um you know advancing the + + + align:start position:0% +just focus on um you know advancing the +Costco and the market baskets and the + + align:start position:0% +Costco and the market baskets and the + + + align:start position:0% +Costco and the market baskets and the +the harpoons the Allagash of the world + + align:start position:0% +the harpoons the Allagash of the world + + + align:start position:0% +the harpoons the Allagash of the world +and you just kind of let + + align:start position:0% +and you just kind of let + + + align:start position:0% +and you just kind of let +Walmart you know sew or reap what it + + align:start position:0% +Walmart you know sew or reap what it + + + align:start position:0% +Walmart you know sew or reap what it +sews with it This legal labor practices + + align:start position:0% +sews with it This legal labor practices + + + align:start position:0% +sews with it This legal labor practices +well that's a good question I'm not sure + + align:start position:0% +well that's a good question I'm not sure + + + align:start position:0% +well that's a good question I'm not sure +that I have have the answer should we + + align:start position:0% +that I have have the answer should we + + + align:start position:0% +that I have have the answer should we +let Walmart alone because it's the + + align:start position:0% +let Walmart alone because it's the + + + align:start position:0% +let Walmart alone because it's the +toughest nut to crack in some ways uh or + + align:start position:0% +toughest nut to crack in some ways uh or + + + align:start position:0% +toughest nut to crack in some ways uh or +because it's the biggest it would have + + align:start position:0% +because it's the biggest it would have + + + align:start position:0% +because it's the biggest it would have +the biggest effect uh should we put + + align:start position:0% +the biggest effect uh should we put + + + align:start position:0% +the biggest effect uh should we put +resources there I do believe that you + + align:start position:0% +resources there I do believe that you + + + align:start position:0% +resources there I do believe that you +know it's uh uh a sign of uh you know + + align:start position:0% +know it's uh uh a sign of uh you know + + + align:start position:0% +know it's uh uh a sign of uh you know +some mental problems when you keep + + align:start position:0% +some mental problems when you keep + + + align:start position:0% +some mental problems when you keep +beating yourself head against the wall + + align:start position:0% +beating yourself head against the wall + + + align:start position:0% +beating yourself head against the wall +right and I think if you can't really + + align:start position:0% +right and I think if you can't really + + + align:start position:0% +right and I think if you can't really +change it then you have to go where you + + align:start position:0% +change it then you have to go where you + + + align:start position:0% +change it then you have to go where you +can really bring about change yes we + + align:start position:0% +can really bring about change yes we + + + align:start position:0% +can really bring about change yes we +should perhaps continue to uh put + + align:start position:0% +should perhaps continue to uh put + + + align:start position:0% +should perhaps continue to uh put +pressure on companies like Walmart but + + align:start position:0% +pressure on companies like Walmart but + + + align:start position:0% +pressure on companies like Walmart but +perhaps we have to go where the + + align:start position:0% +perhaps we have to go where the + + + align:start position:0% +perhaps we have to go where the +opportunities are and that's why courses + + align:start position:0% +opportunities are and that's why courses + + + align:start position:0% +opportunities are and that's why courses +like this educating the next generation + + align:start position:0% +like this educating the next generation + + + align:start position:0% +like this educating the next generation +of leaders is so I think important + + align:start position:0% +of leaders is so I think important + + + align:start position:0% +of leaders is so I think important +because we can make a difference and if + + align:start position:0% +because we can make a difference and if + + + align:start position:0% +because we can make a difference and if +if we can get people to think about the + + align:start position:0% +if we can get people to think about the + + + align:start position:0% +if we can get people to think about the +choices and know that they've got + + align:start position:0% +choices and know that they've got + + + align:start position:0% +choices and know that they've got +choices and recognize that there are + + align:start position:0% +choices and recognize that there are + + + align:start position:0% +choices and recognize that there are +some directions that they can take their + + align:start position:0% +some directions that they can take their + + + align:start position:0% +some directions that they can take their +company and as you go out into the the + + align:start position:0% +company and as you go out into the the + + + align:start position:0% +company and as you go out into the the +company companies that you will be + + align:start position:0% +company companies that you will be + + + align:start position:0% +company companies that you will be +employed in and the people uh in the + + align:start position:0% +employed in and the people uh in the + + + align:start position:0% +employed in and the people uh in the +online course go out and work in a + + align:start position:0% +online course go out and work in a + + + align:start position:0% +online course go out and work in a +variety of settings you can be raising + + align:start position:0% +variety of settings you can be raising + + + align:start position:0% +variety of settings you can be raising +these questions and in fact I'll tell + + align:start position:0% +these questions and in fact I'll tell + + + align:start position:0% +these questions and in fact I'll tell +you a secret there are some Sloan school + + align:start position:0% +you a secret there are some Sloan school + + + align:start position:0% +you a secret there are some Sloan school +graduates in some companies not to be + + align:start position:0% +graduates in some companies not to be + + + align:start position:0% +graduates in some companies not to be +mentioned but uh similar to what we were + + align:start position:0% +mentioned but uh similar to what we were + + + align:start position:0% +mentioned but uh similar to what we were +talking about here who are raising those + + align:start position:0% +talking about here who are raising those + + + align:start position:0% +talking about here who are raising those +questions today and bringing some of + + align:start position:0% +questions today and bringing some of + + + align:start position:0% +questions today and bringing some of +their Executives back to campus to see + + align:start position:0% +their Executives back to campus to see + + + align:start position:0% +their Executives back to campus to see +if they can learn more about what would + + align:start position:0% +if they can learn more about what would + + + align:start position:0% +if they can learn more about what would +it take is it possible to do it so I'm + + align:start position:0% +it take is it possible to do it so I'm + + + align:start position:0% +it take is it possible to do it so I'm +uh you know maybe an + + align:start position:0% +uh you know maybe an + + + align:start position:0% +uh you know maybe an +internal Optimist on this I'm not naive + + align:start position:0% +internal Optimist on this I'm not naive + + + align:start position:0% +internal Optimist on this I'm not naive +it's a big road to to to travel but I + + align:start position:0% +it's a big road to to to travel but I + + + align:start position:0% +it's a big road to to to travel but I +think we can make a difference and so I + + align:start position:0% +think we can make a difference and so I + + + align:start position:0% +think we can make a difference and so I +want to go where the opportunities are + + align:start position:0% +want to go where the opportunities are + + + align:start position:0% +want to go where the opportunities are +perhaps more than uh where the the + + align:start position:0% +perhaps more than uh where the the + + + align:start position:0% +perhaps more than uh where the the +resistance is is greatest well this is + + align:start position:0% +resistance is is greatest well this is + + + align:start position:0% +resistance is is greatest well this is +just uh one uh way of of proceeding we + + align:start position:0% +just uh one uh way of of proceeding we + + + align:start position:0% +just uh one uh way of of proceeding we +the high road strategies are really + + align:start position:0% +the high road strategies are really + + + align:start position:0% +the high road strategies are really +important there are opportunities for + + align:start position:0% +important there are opportunities for + + + align:start position:0% +important there are opportunities for +moving forward and you had the the folks + + align:start position:0% +moving forward and you had the the folks + + + align:start position:0% +moving forward and you had the the folks +in the online course have had the + + align:start position:0% +in the online course have had the + + + align:start position:0% +in the online course have had the +experience of testing this idea because + + align:start position:0% +experience of testing this idea because + + + align:start position:0% +experience of testing this idea because +one of the assignments was to go out and + + align:start position:0% +one of the assignments was to go out and + + + align:start position:0% +one of the assignments was to go out and +interview someone in an organization in + + align:start position:0% +interview someone in an organization in + + + align:start position:0% +interview someone in an organization in +an industry of interest uh to you and + + align:start position:0% +an industry of interest uh to you and + + + align:start position:0% +an industry of interest uh to you and +you ask them a series of questions that + + align:start position:0% +you ask them a series of questions that + + + align:start position:0% +you ask them a series of questions that +come from the research that's been done + + align:start position:0% +come from the research that's been done + + + align:start position:0% +come from the research that's been done +on what does it take to build a high + + align:start position:0% +on what does it take to build a high + + + align:start position:0% +on what does it take to build a high +road high performance work organization + + align:start position:0% +road high performance work organization + + + align:start position:0% +road high performance work organization +and what does it take to meet the + + align:start position:0% +and what does it take to meet the + + + align:start position:0% +and what does it take to meet the +aspirations of the workforce to be have + + align:start position:0% +aspirations of the workforce to be have + + + align:start position:0% +aspirations of the workforce to be have +satisfying work experience + + align:start position:0% +satisfying work experience + + + align:start position:0% +satisfying work experience +and that battery of questions uh uh then + + align:start position:0% +and that battery of questions uh uh then + + + align:start position:0% +and that battery of questions uh uh then +ended with a very simple question to uh + + align:start position:0% +ended with a very simple question to uh + + + align:start position:0% +ended with a very simple question to uh +to the student who was collecting the + + align:start position:0% +to the student who was collecting the + + + align:start position:0% +to the student who was collecting the +data on the basis of interview with an + + align:start position:0% +data on the basis of interview with an + + + align:start position:0% +data on the basis of interview with an +employee and said to the student if uh + + align:start position:0% +employee and said to the student if uh + + + align:start position:0% +employee and said to the student if uh +you were offered a job in this + + align:start position:0% +you were offered a job in this + + + align:start position:0% +you were offered a job in this +organization would you take it or not + + align:start position:0% +organization would you take it or not + + + align:start position:0% +organization would you take it or not +and the numbers the raw numbers were 60% + + align:start position:0% +and the numbers the raw numbers were 60% + + + align:start position:0% +and the numbers the raw numbers were 60% +said yes but 40% said no I didn't hear + + align:start position:0% +said yes but 40% said no I didn't hear + + + align:start position:0% +said yes but 40% said no I didn't hear +that this was the kind of organizational + + align:start position:0% +that this was the kind of organizational + + + align:start position:0% +that this was the kind of organizational +environment that would allow me to to + + align:start position:0% +environment that would allow me to to + + + align:start position:0% +environment that would allow me to to +use my skills or to be have a satisfying + + align:start position:0% +use my skills or to be have a satisfying + + + align:start position:0% +use my skills or to be have a satisfying +work experience that's a pretty + + align:start position:0% +work experience that's a pretty + + + align:start position:0% +work experience that's a pretty +remarkable distribution that 40% after + + align:start position:0% +remarkable distribution that 40% after + + + align:start position:0% +remarkable distribution that 40% after +hearing about an organization say no + + align:start position:0% +hearing about an organization say no + + + align:start position:0% +hearing about an organization say no +thank you I don't think I would take a + + align:start position:0% +thank you I don't think I would take a + + + align:start position:0% +thank you I don't think I would take a +job there I think we've got a lot of + + align:start position:0% +job there I think we've got a lot of + + + align:start position:0% +job there I think we've got a lot of +work to do but the good news in this is + + align:start position:0% +work to do but the good news in this is + + + align:start position:0% +work to do but the good news in this is +you do a little bit of statistical + + align:start position:0% +you do a little bit of statistical + + + align:start position:0% +you do a little bit of statistical +analysis and you ask uh do these high + + align:start position:0% +analysis and you ask uh do these high + + + align:start position:0% +analysis and you ask uh do these high +performance High Road characteristics + + align:start position:0% +performance High Road characteristics + + + align:start position:0% +performance High Road characteristics +and good job characteristics predict + + align:start position:0% +and good job characteristics predict + + + align:start position:0% +and good job characteristics predict +whether someone would take a job or not + + align:start position:0% +whether someone would take a job or not + + + align:start position:0% +whether someone would take a job or not +the good news for employers is that if + + align:start position:0% +the good news for employers is that if + + + align:start position:0% +the good news for employers is that if +you provide these kinds of opportunities + + align:start position:0% +you provide these kinds of opportunities + + + align:start position:0% +you provide these kinds of opportunities +and features on your in your workplace + + align:start position:0% +and features on your in your workplace + + + align:start position:0% +and features on your in your workplace +you have a 75% chance of attracting the + + align:start position:0% +you have a 75% chance of attracting the + + + align:start position:0% +you have a 75% chance of attracting the +talent that you need that people will + + align:start position:0% +talent that you need that people will + + + align:start position:0% +talent that you need that people will +accept a job it's not 60 it's now 75 + + align:start position:0% +accept a job it's not 60 it's now 75 + + + align:start position:0% +accept a job it's not 60 it's now 75 +that's a substantial change and so the + + align:start position:0% +that's a substantial change and so the + + + align:start position:0% +that's a substantial change and so the +good news is that firms can attract the + + align:start position:0% +good news is that firms can attract the + + + align:start position:0% +good news is that firms can attract the +kind of a talent and perhaps retain the + + align:start position:0% +kind of a talent and perhaps retain the + + + align:start position:0% +kind of a talent and perhaps retain the +kind of talent that they need to support + + align:start position:0% +kind of talent that they need to support + + + align:start position:0% +kind of talent that they need to support +a high performance organization if they + + align:start position:0% +a high performance organization if they + + + align:start position:0% +a high performance organization if they +uh invest and and engage in the right + + align:start position:0% +uh invest and and engage in the right + + + align:start position:0% +uh invest and and engage in the right +set of practices so that's another + + align:start position:0% +set of practices so that's another + + + align:start position:0% +set of practices so that's another +reason why I think we need to do more of + + align:start position:0% +reason why I think we need to do more of + + + align:start position:0% +reason why I think we need to do more of +this we need to keep asking about what's + + align:start position:0% +this we need to keep asking about what's + + + align:start position:0% +this we need to keep asking about what's +going on in in organizations uh there + + align:start position:0% +going on in in organizations uh there + + + align:start position:0% +going on in in organizations uh there +are a growing number of online platforms + + align:start position:0% +are a growing number of online platforms + + + align:start position:0% +are a growing number of online platforms +and various kinds of uh uh use of + + align:start position:0% +and various kinds of uh uh use of + + + align:start position:0% +and various kinds of uh uh use of +Information Technology that we'll talk + + align:start position:0% +Information Technology that we'll talk + + + align:start position:0% +Information Technology that we'll talk +about in just a moment that uh is + + align:start position:0% +about in just a moment that uh is + + + align:start position:0% +about in just a moment that uh is +providing more information on firms + + align:start position:0% +providing more information on firms + + + align:start position:0% +providing more information on firms +glass door is probably the best known + + align:start position:0% +glass door is probably the best known + + + align:start position:0% +glass door is probably the best known +where it collects employee uh ratings of + + align:start position:0% +where it collects employee uh ratings of + + + align:start position:0% +where it collects employee uh ratings of +their employer well we need to use that + + align:start position:0% +their employer well we need to use that + + + align:start position:0% +their employer well we need to use that +kind of data those those data to + + align:start position:0% +kind of data those those data to + + + align:start position:0% +kind of data those those data to +understand what is the difference + + align:start position:0% +understand what is the difference + + + align:start position:0% +understand what is the difference +between an attractive place to work and + + align:start position:0% +between an attractive place to work and + + + align:start position:0% +between an attractive place to work and +a less attractive place to work and then + + align:start position:0% +a less attractive place to work and then + + + align:start position:0% +a less attractive place to work and then +use our our our skills to move to where + + align:start position:0% +use our our our skills to move to where + + + align:start position:0% +use our our our skills to move to where +the good jobs are so that we discipline + + align:start position:0% +the good jobs are so that we discipline + + + align:start position:0% +the good jobs are so that we discipline +and again bring up uh the the Lower Road + + align:start position:0% +and again bring up uh the the Lower Road + + + align:start position:0% +and again bring up uh the the Lower Road +firm so I'm encouraged by the the good + + align:start position:0% +firm so I'm encouraged by the the good + + + align:start position:0% +firm so I'm encouraged by the the good +job survey exercise I hope uh people do + + align:start position:0% +job survey exercise I hope uh people do + + + align:start position:0% +job survey exercise I hope uh people do +that maybe informally don't have to go + + align:start position:0% +that maybe informally don't have to go + + + align:start position:0% +that maybe informally don't have to go +out and ask 25 questions every time but + + align:start position:0% +out and ask 25 questions every time but + + + align:start position:0% +out and ask 25 questions every time but +you can ask the key questions because + + align:start position:0% +you can ask the key questions because + + + align:start position:0% +you can ask the key questions because +you know what they are and you know what + + align:start position:0% +you know what they are and you know what + + + align:start position:0% +you know what they are and you know what +you're looking for and you know what's + + align:start position:0% +you're looking for and you know what's + + + align:start position:0% +you're looking for and you know what's +really + + align:start position:0% +really + + + align:start position:0% +really +important then we came to this question + + align:start position:0% +important then we came to this question + + + align:start position:0% +important then we came to this question +about well unions uh unions have this + + align:start position:0% +about well unions uh unions have this + + + align:start position:0% +about well unions uh unions have this +great phrase in the United States uh in + + align:start position:0% +great phrase in the United States uh in + + + align:start position:0% +great phrase in the United States uh in +the 20th century they say we're the + + align:start position:0% +the 20th century they say we're the + + + align:start position:0% +the 20th century they say we're the +organization that brought you the + + align:start position:0% +organization that brought you the + + + align:start position:0% +organization that brought you the +weekend and they're right they're the + + align:start position:0% +weekend and they're right they're the + + + align:start position:0% +weekend and they're right they're the +organization that really negotiated more + + align:start position:0% +organization that really negotiated more + + + align:start position:0% +organization that really negotiated more +time off how holiday pay vacation pay uh + + align:start position:0% +time off how holiday pay vacation pay uh + + + align:start position:0% +time off how holiday pay vacation pay uh +sick + + align:start position:0% +sick + + + align:start position:0% +sick +leave weekend overtime rates for uh + + align:start position:0% +leave weekend overtime rates for uh + + + align:start position:0% +leave weekend overtime rates for uh +working the the the unattractive hours + + align:start position:0% +working the the the unattractive hours + + + align:start position:0% +working the the the unattractive hours +or working more than 40 hours and so on + + align:start position:0% +or working more than 40 hours and so on + + + align:start position:0% +or working more than 40 hours and so on +and and so unions have a very long + + align:start position:0% +and and so unions have a very long + + + align:start position:0% +and and so unions have a very long +history in the United States and around + + align:start position:0% +history in the United States and around + + + align:start position:0% +history in the United States and around +the the world uh for improving wages + + align:start position:0% +the the world uh for improving wages + + + align:start position:0% +the the world uh for improving wages +hours in working conditions and helping + + align:start position:0% +hours in working conditions and helping + + + align:start position:0% +hours in working conditions and helping +to to lift up uh the standards in our + + align:start position:0% +to to lift up uh the standards in our + + + align:start position:0% +to to lift up uh the standards in our +economies but we all know that + + align:start position:0% +economies but we all know that + + + align:start position:0% +economies but we all know that +particularly here in the United States + + align:start position:0% +particularly here in the United States + + + align:start position:0% +particularly here in the United States +but many countries around the world + + align:start position:0% +but many countries around the world + + + align:start position:0% +but many countries around the world +unions are on the decline and in fact + + align:start position:0% +unions are on the decline and in fact + + + align:start position:0% +unions are on the decline and in fact +many people probably in the online + + align:start position:0% +many people probably in the online + + + align:start position:0% +many people probably in the online +course never even thought much about + + align:start position:0% +course never even thought much about + + + align:start position:0% +course never even thought much about +unions many of the people here at the + + align:start position:0% +unions many of the people here at the + + + align:start position:0% +unions many of the people here at the +Sloan school it's not on the front + + align:start position:0% +Sloan school it's not on the front + + + align:start position:0% +Sloan school it's not on the front +burner of their minds to think about + + align:start position:0% +burner of their minds to think about + + + align:start position:0% +burner of their minds to think about +unions as a force for economic + + align:start position:0% +unions as a force for economic + + + align:start position:0% +unions as a force for economic +advancement in our economy or in their + + align:start position:0% +advancement in our economy or in their + + + align:start position:0% +advancement in our economy or in their +particular work lives so we felt it was + + align:start position:0% +particular work lives so we felt it was + + + align:start position:0% +particular work lives so we felt it was +important to engage this question is + + align:start position:0% +important to engage this question is + + + align:start position:0% +important to engage this question is +there a future do we still need them and + + align:start position:0% +there a future do we still need them and + + + align:start position:0% +there a future do we still need them and +and the views were were quite diverse + + align:start position:0% +and the views were were quite diverse + + + align:start position:0% +and the views were were quite diverse +and a good discussion but I think + + align:start position:0% +and a good discussion but I think + + + align:start position:0% +and a good discussion but I think +there's a dominant view that well unions + + align:start position:0% +there's a dominant view that well unions + + + align:start position:0% +there's a dominant view that well unions +played an important role in the past in + + align:start position:0% +played an important role in the past in + + + align:start position:0% +played an important role in the past in +the way in which they function and they + + align:start position:0% +the way in which they function and they + + + align:start position:0% +the way in which they function and they +had some negative features as well they + + align:start position:0% +had some negative features as well they + + + align:start position:0% +had some negative features as well they +brought uh maybe too much rigidity and + + align:start position:0% +brought uh maybe too much rigidity and + + + align:start position:0% +brought uh maybe too much rigidity and +some some work rules that impeded + + align:start position:0% +some some work rules that impeded + + + align:start position:0% +some some work rules that impeded +productivity or and that continue to + + align:start position:0% +productivity or and that continue to + + + align:start position:0% +productivity or and that continue to +impede productivity in some cases they + + align:start position:0% +impede productivity in some cases they + + + align:start position:0% +impede productivity in some cases they +were resistant to change because people + + align:start position:0% +were resistant to change because people + + + align:start position:0% +were resistant to change because people +uh got uh uh used to the way in which + + align:start position:0% +uh got uh uh used to the way in which + + + align:start position:0% +uh got uh uh used to the way in which +they were working into the benefits and + + align:start position:0% +they were working into the benefits and + + + align:start position:0% +they were working into the benefits and +to their control over job opportunities + + align:start position:0% +to their control over job opportunities + + + align:start position:0% +to their control over job opportunities +and so on they restricted access to + + align:start position:0% +and so on they restricted access to + + + align:start position:0% +and so on they restricted access to +Union jobs in some cases to their + + align:start position:0% +Union jobs in some cases to their + + + align:start position:0% +Union jobs in some cases to their +relatives or people who looked like them + + align:start position:0% +relatives or people who looked like them + + + align:start position:0% +relatives or people who looked like them +and so uh there's a a history of + + align:start position:0% +and so uh there's a a history of + + + align:start position:0% +and so uh there's a a history of +discrimination in some unions that is + + align:start position:0% +discrimination in some unions that is + + + align:start position:0% +discrimination in some unions that is +not a very attractive part of the + + align:start position:0% +not a very attractive part of the + + + align:start position:0% +not a very attractive part of the +history of Labor either so unions have a + + align:start position:0% +history of Labor either so unions have a + + + align:start position:0% +history of Labor either so unions have a +positive and a negative historical uh uh + + align:start position:0% +positive and a negative historical uh uh + + + align:start position:0% +positive and a negative historical uh uh +uh set or historical record that uh we + + align:start position:0% +uh set or historical record that uh we + + + align:start position:0% +uh set or historical record that uh we +need to understand but the question is + + align:start position:0% +need to understand but the question is + + + align:start position:0% +need to understand but the question is +what will replace this void or fill this + + align:start position:0% +what will replace this void or fill this + + + align:start position:0% +what will replace this void or fill this +void that's now left in the United + + align:start position:0% +void that's now left in the United + + + align:start position:0% +void that's now left in the United +States and in some other countries as + + align:start position:0% +States and in some other countries as + + + align:start position:0% +States and in some other countries as +unions decline is there a a way to + + align:start position:0% +unions decline is there a a way to + + + align:start position:0% +unions decline is there a a way to +revise unions re rebuild them to create + + align:start position:0% +revise unions re rebuild them to create + + + align:start position:0% +revise unions re rebuild them to create +organizations or entities that advocate + + align:start position:0% +organizations or entities that advocate + + + align:start position:0% +organizations or entities that advocate +for workers in a modern way that was a a + + align:start position:0% +for workers in a modern way that was a a + + + align:start position:0% +for workers in a modern way that was a a +source of discussion it's a source of + + align:start position:0% +source of discussion it's a source of + + + align:start position:0% +source of discussion it's a source of +debate in uh this country and in many + + align:start position:0% +debate in uh this country and in many + + + align:start position:0% +debate in uh this country and in many +countries around the world and basically + + align:start position:0% +countries around the world and basically + + + align:start position:0% +countries around the world and basically +I think most people in the course have + + align:start position:0% +I think most people in the course have + + + align:start position:0% +I think most people in the course have +come to the conclusion that yes there is + + align:start position:0% +come to the conclusion that yes there is + + + align:start position:0% +come to the conclusion that yes there is +a role but it can't be just as I put it + + align:start position:0% +a role but it can't be just as I put it + + + align:start position:0% +a role but it can't be just as I put it +in in in in the textbook uh your father + + align:start position:0% +in in in in the textbook uh your father + + + align:start position:0% +in in in in the textbook uh your father +or your grandfather's Union because it + + align:start position:0% +or your grandfather's Union because it + + + align:start position:0% +or your grandfather's Union because it +was mostly a male-dominated labor + + align:start position:0% +was mostly a male-dominated labor + + + align:start position:0% +was mostly a male-dominated labor +movement it no longer by the way is + + align:start position:0% +movement it no longer by the way is + + + align:start position:0% +movement it no longer by the way is +we're now in the United States at about + + align:start position:0% +we're now in the United States at about + + + align:start position:0% +we're now in the United States at about +the uh uh just about 50% of union + + align:start position:0% +the uh uh just about 50% of union + + + align:start position:0% +the uh uh just about 50% of union +members are women um uh uh as well as + + align:start position:0% +members are women um uh uh as well as + + + align:start position:0% +members are women um uh uh as well as +men and so it's changed over time but + + align:start position:0% +men and so it's changed over time but + + + align:start position:0% +men and so it's changed over time but +that's kind of the history but there's + + align:start position:0% +that's kind of the history but there's + + + align:start position:0% +that's kind of the history but there's +there's a recognition that unions have + + align:start position:0% +there's a recognition that unions have + + + align:start position:0% +there's a recognition that unions have +to change uh there seems to be it says + + align:start position:0% +to change uh there seems to be it says + + + align:start position:0% +to change uh there seems to be it says +here a a conscious effort to revitalize + + align:start position:0% +here a a conscious effort to revitalize + + + align:start position:0% +here a a conscious effort to revitalize +the way that unions work in order to + + align:start position:0% +the way that unions work in order to + + + align:start position:0% +the way that unions work in order to +meet the needs of the most vulnerable + + align:start position:0% +meet the needs of the most vulnerable + + + align:start position:0% +meet the needs of the most vulnerable +workers in recent years particularly in + + align:start position:0% +workers in recent years particularly in + + + align:start position:0% +workers in recent years particularly in +a globalized world so we're seeing + + align:start position:0% +a globalized world so we're seeing + + + align:start position:0% +a globalized world so we're seeing +unions try to to work to deal with the + + align:start position:0% +unions try to to work to deal with the + + + align:start position:0% +unions try to to work to deal with the +terrible problems that have occurred for + + align:start position:0% +terrible problems that have occurred for + + + align:start position:0% +terrible problems that have occurred for +example in Bangladesh where uh the + + align:start position:0% +example in Bangladesh where uh the + + + align:start position:0% +example in Bangladesh where uh the +factory uh first a terrible factory fire + + align:start position:0% +factory uh first a terrible factory fire + + + align:start position:0% +factory uh first a terrible factory fire +that took over 100 workers lives + + align:start position:0% +that took over 100 workers lives + + + align:start position:0% +that took over 100 workers lives +and then the terrible Factory collapse + + align:start position:0% +and then the terrible Factory collapse + + + align:start position:0% +and then the terrible Factory collapse +that took over a thousand workers lives + + align:start position:0% +that took over a thousand workers lives + + + align:start position:0% +that took over a thousand workers lives +in Bangladesh where standards were were + + align:start position:0% +in Bangladesh where standards were were + + + align:start position:0% +in Bangladesh where standards were were +not being attended to and so out of that + + align:start position:0% +not being attended to and so out of that + + + align:start position:0% +not being attended to and so out of that +has come a global effort of unions from + + align:start position:0% +has come a global effort of unions from + + + align:start position:0% +has come a global effort of unions from +Europe and from around the world to say + + align:start position:0% +Europe and from around the world to say + + + align:start position:0% +Europe and from around the world to say +we need to work together with companies + + align:start position:0% +we need to work together with companies + + + align:start position:0% +we need to work together with companies +in something that's called the Accord + + align:start position:0% +in something that's called the Accord + + + align:start position:0% +in something that's called the Accord +that is a negotiated agreement for + + align:start position:0% +that is a negotiated agreement for + + + align:start position:0% +that is a negotiated agreement for +arbitration for safety Provisions for + + align:start position:0% +arbitration for safety Provisions for + + + align:start position:0% +arbitration for safety Provisions for +safety inspections and for workers to + + align:start position:0% +safety inspections and for workers to + + + align:start position:0% +safety inspections and for workers to +have a voice + + align:start position:0% +have a voice + + + align:start position:0% +have a voice +in that Society long way to go on that + + align:start position:0% +in that Society long way to go on that + + + align:start position:0% +in that Society long way to go on that +and in fact some American corporations + + align:start position:0% +and in fact some American corporations + + + align:start position:0% +and in fact some American corporations +say we want to address these issues but + + align:start position:0% +say we want to address these issues but + + + align:start position:0% +say we want to address these issues but +we don't want to include unions in that + + align:start position:0% +we don't want to include unions in that + + + align:start position:0% +we don't want to include unions in that +process so there's a parallel effort + + align:start position:0% +process so there's a parallel effort + + + align:start position:0% +process so there's a parallel effort +called the alliance in with firms like + + align:start position:0% +called the alliance in with firms like + + + align:start position:0% +called the alliance in with firms like +uh the Gap and Walmart and others from + + align:start position:0% +uh the Gap and Walmart and others from + + + align:start position:0% +uh the Gap and Walmart and others from +the US that are going it alone I don't + + align:start position:0% +the US that are going it alone I don't + + + align:start position:0% +the US that are going it alone I don't +know which way is the best I'm not an + + align:start position:0% +know which way is the best I'm not an + + + align:start position:0% +know which way is the best I'm not an +expert on Bangladesh I've only been + + align:start position:0% +expert on Bangladesh I've only been + + + align:start position:0% +expert on Bangladesh I've only been +there on one very very short visit so I + + align:start position:0% +there on one very very short visit so I + + + align:start position:0% +there on one very very short visit so I +wouldn't make a judgment of what the + + align:start position:0% +wouldn't make a judgment of what the + + + align:start position:0% +wouldn't make a judgment of what the +right strategy is but here we have + + align:start position:0% +right strategy is but here we have + + + align:start position:0% +right strategy is but here we have +efforts to try to do something about + + align:start position:0% +efforts to try to do something about + + + align:start position:0% +efforts to try to do something about +global labor standards by bringing about + + align:start position:0% +global labor standards by bringing about + + + align:start position:0% +global labor standards by bringing about +some Coalition of the local uh + + align:start position:0% +some Coalition of the local uh + + + align:start position:0% +some Coalition of the local uh +organizations the local unions to the + + align:start position:0% +organizations the local unions to the + + + align:start position:0% +organizations the local unions to the +extent that they exist International + + align:start position:0% +extent that they exist International + + + align:start position:0% +extent that they exist International +unions working with companies and with + + align:start position:0% +unions working with companies and with + + + align:start position:0% +unions working with companies and with +Brands to try to enforce standards in + + align:start position:0% +Brands to try to enforce standards in + + + align:start position:0% +Brands to try to enforce standards in +those factories we we talked about Nike + + align:start position:0% +those factories we we talked about Nike + + + align:start position:0% +those factories we we talked about Nike +in the course we talked about how they + + align:start position:0% +in the course we talked about how they + + + align:start position:0% +in the course we talked about how they +went through this process we talked + + align:start position:0% +went through this process we talked + + + align:start position:0% +went through this process we talked +about Apple's um struggles in China and + + align:start position:0% +about Apple's um struggles in China and + + + align:start position:0% +about Apple's um struggles in China and +the suicides and the terrible conditions + + align:start position:0% +the suicides and the terrible conditions + + + align:start position:0% +the suicides and the terrible conditions +in organizations like foxcon this is the + + align:start position:0% +in organizations like foxcon this is the + + + align:start position:0% +in organizations like foxcon this is the +front line of worker voice and + + align:start position:0% +front line of worker voice and + + + align:start position:0% +front line of worker voice and +representation where we have to invent + + align:start position:0% +representation where we have to invent + + + align:start position:0% +representation where we have to invent +new ways U to make things work we also + + align:start position:0% +new ways U to make things work we also + + + align:start position:0% +new ways U to make things work we also +talked about uh the role of Labor + + align:start position:0% +talked about uh the role of Labor + + + align:start position:0% +talked about uh the role of Labor +Management Partnerships uh we've been + + align:start position:0% +Management Partnerships uh we've been + + + align:start position:0% +Management Partnerships uh we've been +privileged to work with Kaiser + + align:start position:0% +privileged to work with Kaiser + + + align:start position:0% +privileged to work with Kaiser +Permanente for several decades now in + + align:start position:0% +Permanente for several decades now in + + + align:start position:0% +Permanente for several decades now in +helping to understand and study the + + align:start position:0% +helping to understand and study the + + + align:start position:0% +helping to understand and study the +Labor Management part parip they put in + + align:start position:0% +Labor Management part parip they put in + + + align:start position:0% +Labor Management part parip they put in +place and to work with them to improve + + align:start position:0% +place and to work with them to improve + + + align:start position:0% +place and to work with them to improve +it because all of these institutions are + + align:start position:0% +it because all of these institutions are + + + align:start position:0% +it because all of these institutions are +sort of fragile and there are always + + align:start position:0% +sort of fragile and there are always + + + align:start position:0% +sort of fragile and there are always +tensions that are involved but here's an + + align:start position:0% +tensions that are involved but here's an + + + align:start position:0% +tensions that are involved but here's an +organization that has worked with its + + align:start position:0% +organization that has worked with its + + + align:start position:0% +organization that has worked with its +unions in health care and on the front + + align:start position:0% +unions in health care and on the front + + + align:start position:0% +unions in health care and on the front +lines you now have 300 or + + align:start position:0% +lines you now have 300 or + + + align:start position:0% +lines you now have 300 or +3,500 what they call unit-based teams + + align:start position:0% +3,500 what they call unit-based teams + + + align:start position:0% +3,500 what they call unit-based teams +teams of employees doctors nurses + + align:start position:0% +teams of employees doctors nurses + + + align:start position:0% +teams of employees doctors nurses +technicians service employees people who + + align:start position:0% +technicians service employees people who + + + align:start position:0% +technicians service employees people who +uh uh the janitors in the organization + + align:start position:0% +uh uh the janitors in the organization + + + align:start position:0% +uh uh the janitors in the organization +work to say how can we improve + + align:start position:0% +work to say how can we improve + + + align:start position:0% +work to say how can we improve +operations how can we reduce injuries + + align:start position:0% +operations how can we reduce injuries + + + align:start position:0% +operations how can we reduce injuries +back injuries for the workforce how can + + align:start position:0% +back injuries for the workforce how can + + + align:start position:0% +back injuries for the workforce how can +we reduce the infections that we + + align:start position:0% +we reduce the infections that we + + + align:start position:0% +we reduce the infections that we +sometimes find in hospitals what are we + + align:start position:0% +sometimes find in hospitals what are we + + + align:start position:0% +sometimes find in hospitals what are we +doing to to uh change the operation to + + align:start position:0% +doing to to uh change the operation to + + + align:start position:0% +doing to to uh change the operation to +serve our customers to use technology to + + align:start position:0% +serve our customers to use technology to + + + align:start position:0% +serve our customers to use technology to +make sure that we're checking on our our + + align:start position:0% +make sure that we're checking on our our + + + align:start position:0% +make sure that we're checking on our our +our our clients or our patients out + + align:start position:0% +our our clients or our patients out + + + align:start position:0% +our our clients or our patients out +there and saying gee I've looked on the + + align:start position:0% +there and saying gee I've looked on the + + + align:start position:0% +there and saying gee I've looked on the +record and I noticed that you haven't + + align:start position:0% +record and I noticed that you haven't + + + align:start position:0% +record and I noticed that you haven't +been in uh to fill your prescriptions + + align:start position:0% +been in uh to fill your prescriptions + + + align:start position:0% +been in uh to fill your prescriptions +are you haven't come in for your uh + + align:start position:0% +are you haven't come in for your uh + + + align:start position:0% +are you haven't come in for your uh +scheduled appointments what's going on + + align:start position:0% +scheduled appointments what's going on + + + align:start position:0% +scheduled appointments what's going on +and how can we get + + align:start position:0% +and how can we get + + + align:start position:0% +and how can we get +um uh uh get those issues addressed more + + align:start position:0% +um uh uh get those issues addressed more + + + align:start position:0% +um uh uh get those issues addressed more +effectively working in teams together + + align:start position:0% +effectively working in teams together + + + align:start position:0% +effectively working in teams together +labor and management saying this is part + + align:start position:0% +labor and management saying this is part + + + align:start position:0% +labor and management saying this is part +of how we're going to create worldclass + + align:start position:0% +of how we're going to create worldclass + + + align:start position:0% +of how we're going to create worldclass +Health Care delivery and at the same + + align:start position:0% +Health Care delivery and at the same + + + align:start position:0% +Health Care delivery and at the same +time then have industry-leading wages + + align:start position:0% +time then have industry-leading wages + + + align:start position:0% +time then have industry-leading wages +and so there are ways to do this we've + + align:start position:0% +and so there are ways to do this we've + + + align:start position:0% +and so there are ways to do this we've +learned from organizations like Saturn + + align:start position:0% +learned from organizations like Saturn + + + align:start position:0% +learned from organizations like Saturn +that started that way but didn't get the + + align:start position:0% +that started that way but didn't get the + + + align:start position:0% +that started that way but didn't get the +kind of support we've learned from + + align:start position:0% +kind of support we've learned from + + + align:start position:0% +kind of support we've learned from +Kaiser we need more of those kinds of + + align:start position:0% +Kaiser we need more of those kinds of + + + align:start position:0% +Kaiser we need more of those kinds of +organizations according to to many of + + align:start position:0% +organizations according to to many of + + + align:start position:0% +organizations according to to many of +you but you're also thinking more + + align:start position:0% +you but you're also thinking more + + + align:start position:0% +you but you're also thinking more +creatively and there was a lively + + align:start position:0% +creatively and there was a lively + + + align:start position:0% +creatively and there was a lively +discussion I I couldn't uh pass putting + + align:start position:0% +discussion I I couldn't uh pass putting + + + align:start position:0% +discussion I I couldn't uh pass putting +uh this concept of a digital Union which + + align:start position:0% +uh this concept of a digital Union which + + + align:start position:0% +uh this concept of a digital Union which +came right off the discussion board uh + + align:start position:0% +came right off the discussion board uh + + + align:start position:0% +came right off the discussion board uh +of uh that uh created quite a a a set of + + align:start position:0% +of uh that uh created quite a a a set of + + + align:start position:0% +of uh that uh created quite a a a set of +comments over over the course of uh of + + align:start position:0% +comments over over the course of uh of + + + align:start position:0% +comments over over the course of uh of +the term and basically by digital unions + + align:start position:0% +the term and basically by digital unions + + + align:start position:0% +the term and basically by digital unions +they're really talking about ways to use + + align:start position:0% +they're really talking about ways to use + + + align:start position:0% +they're really talking about ways to use +information to use online platforms The + + align:start position:0% +information to use online platforms The + + + align:start position:0% +information to use online platforms The +Way businesses are using them to share + + align:start position:0% +Way businesses are using them to share + + + align:start position:0% +Way businesses are using them to share +information + + align:start position:0% +information + + + align:start position:0% +information +what where are the good jobs where are + + align:start position:0% +what where are the good jobs where are + + + align:start position:0% +what where are the good jobs where are +there not such good jobs how can we + + align:start position:0% +there not such good jobs how can we + + + align:start position:0% +there not such good jobs how can we +mobilize in China the way workers + + align:start position:0% +mobilize in China the way workers + + + align:start position:0% +mobilize in China the way workers +mobilized today is through their + + align:start position:0% +mobilized today is through their + + + align:start position:0% +mobilized today is through their +smartphones they don't have independent + + align:start position:0% +smartphones they don't have independent + + + align:start position:0% +smartphones they don't have independent +unions but they do have the technology + + align:start position:0% +unions but they do have the technology + + + align:start position:0% +unions but they do have the technology +and they use that to build their own + + align:start position:0% +and they use that to build their own + + + align:start position:0% +and they use that to build their own +network when they feel most grieved in + + align:start position:0% +network when they feel most grieved in + + + align:start position:0% +network when they feel most grieved in +the need to do something about it now + + align:start position:0% +the need to do something about it now + + + align:start position:0% +the need to do something about it now +they have to often do something in a in + + align:start position:0% +they have to often do something in a in + + + align:start position:0% +they have to often do something in a in +a in a pretty uh spontaneous way and + + align:start position:0% +a in a pretty uh spontaneous way and + + + align:start position:0% +a in a pretty uh spontaneous way and +sometimes in a in a in in a very strong + + align:start position:0% +sometimes in a in a in in a very strong + + + align:start position:0% +sometimes in a in a in in a very strong +resistance sometimes even in a violent + + align:start position:0% +resistance sometimes even in a violent + + + align:start position:0% +resistance sometimes even in a violent +way and sometimes even holding the the + + align:start position:0% +way and sometimes even holding the the + + + align:start position:0% +way and sometimes even holding the the +plant manager hostage uh in uh in uh his + + align:start position:0% +plant manager hostage uh in uh in uh his + + + align:start position:0% +plant manager hostage uh in uh in uh his +or her own uh facility until uh + + align:start position:0% +or her own uh facility until uh + + + align:start position:0% +or her own uh facility until uh +something can be negotiated but they're + + align:start position:0% +something can be negotiated but they're + + + align:start position:0% +something can be negotiated but they're +using technology to try to find new ways + + align:start position:0% +using technology to try to find new ways + + + align:start position:0% +using technology to try to find new ways +of of meeting worker needs then there + + align:start position:0% +of of meeting worker needs then there + + + align:start position:0% +of of meeting worker needs then there +are other organizations that we cited uh + + align:start position:0% +are other organizations that we cited uh + + + align:start position:0% +are other organizations that we cited uh +different kinds of of organizations that + + align:start position:0% +different kinds of of organizations that + + + align:start position:0% +different kinds of of organizations that +aren't even called unions some of them + + align:start position:0% +aren't even called unions some of them + + + align:start position:0% +aren't even called unions some of them +use the term but they're really outside + + align:start position:0% +use the term but they're really outside + + + align:start position:0% +use the term but they're really outside +of the traditional form of unions this + + align:start position:0% +of the traditional form of unions this + + + align:start position:0% +of the traditional form of unions this +one up in the upper leftand corner here + + align:start position:0% +one up in the upper leftand corner here + + + align:start position:0% +one up in the upper leftand corner here +restaurant Opportunity Center uh was + + align:start position:0% +restaurant Opportunity Center uh was + + + align:start position:0% +restaurant Opportunity Center uh was +cited uh in in the course a number of + + align:start position:0% +cited uh in in the course a number of + + + align:start position:0% +cited uh in in the course a number of +times but it's worth uh focusing on + + align:start position:0% +times but it's worth uh focusing on + + + align:start position:0% +times but it's worth uh focusing on +because it's a very interesting + + align:start position:0% +because it's a very interesting + + + align:start position:0% +because it's a very interesting +organization that came out of a tragedy + + align:start position:0% +organization that came out of a tragedy + + + align:start position:0% +organization that came out of a tragedy +it it it it was formed after our + + align:start position:0% +it it it it was formed after our + + + align:start position:0% +it it it it was formed after our +terrible uh experience in in uh + + align:start position:0% +terrible uh experience in in uh + + + align:start position:0% +terrible uh experience in in uh +September 11th uh uh when the Twin tire + + align:start position:0% +September 11th uh uh when the Twin tire + + + align:start position:0% +September 11th uh uh when the Twin tire +was in New York uh uh collapsed from a + + align:start position:0% +was in New York uh uh collapsed from a + + + align:start position:0% +was in New York uh uh collapsed from a +terrorist attack and uh out of that + + align:start position:0% +terrorist attack and uh out of that + + + align:start position:0% +terrorist attack and uh out of that +there was a restaurant called the + + align:start position:0% +there was a restaurant called the + + + align:start position:0% +there was a restaurant called the +windows on the world at the top that + + align:start position:0% +windows on the world at the top that + + + align:start position:0% +windows on the world at the top that +obviously collapsed with it and many uh + + align:start position:0% +obviously collapsed with it and many uh + + + align:start position:0% +obviously collapsed with it and many uh +employees died uh in that uh in that uh + + align:start position:0% +employees died uh in that uh in that uh + + + align:start position:0% +employees died uh in that uh in that uh +tragedy and so this organization was + + align:start position:0% +tragedy and so this organization was + + + align:start position:0% +tragedy and so this organization was +formed to try to deal with the families + + align:start position:0% +formed to try to deal with the families + + + align:start position:0% +formed to try to deal with the families +and to help people uh cope with with + + align:start position:0% +and to help people uh cope with with + + + align:start position:0% +and to help people uh cope with with +that terrible disaster and what it's + + align:start position:0% +that terrible disaster and what it's + + + align:start position:0% +that terrible disaster and what it's +evolved into is an organization that + + align:start position:0% +evolved into is an organization that + + + align:start position:0% +evolved into is an organization that +works to both improve job conditions for + + align:start position:0% +works to both improve job conditions for + + + align:start position:0% +works to both improve job conditions for +people in restaurants but also to + + align:start position:0% +people in restaurants but also to + + + align:start position:0% +people in restaurants but also to +publicize uh uh good practices for + + align:start position:0% +publicize uh uh good practices for + + + align:start position:0% +publicize uh uh good practices for +sustainable food and for food + + align:start position:0% +sustainable food and for food + + + align:start position:0% +sustainable food and for food +preparation and for um the way in which + + align:start position:0% +preparation and for um the way in which + + + align:start position:0% +preparation and for um the way in which +the workforce is treated the way in + + align:start position:0% +the workforce is treated the way in + + + align:start position:0% +the workforce is treated the way in +which the customers are treated they + + align:start position:0% +which the customers are treated they + + + align:start position:0% +which the customers are treated they +encourage customers to rate not only the + + align:start position:0% +encourage customers to rate not only the + + + align:start position:0% +encourage customers to rate not only the +quality of the food but also the quality + + align:start position:0% +quality of the food but also the quality + + + align:start position:0% +quality of the food but also the quality +of the working conditions to ask about + + align:start position:0% +of the working conditions to ask about + + + align:start position:0% +of the working conditions to ask about +it in the restaurants and they're + + align:start position:0% +it in the restaurants and they're + + + align:start position:0% +it in the restaurants and they're +working to stay outside of the + + align:start position:0% +working to stay outside of the + + + align:start position:0% +working to stay outside of the +traditions of Labor uh relations to find + + align:start position:0% +traditions of Labor uh relations to find + + + align:start position:0% +traditions of Labor uh relations to find +new ways to train employees to provide + + align:start position:0% +new ways to train employees to provide + + + align:start position:0% +new ways to train employees to provide +information on where good jobs are to + + align:start position:0% +information on where good jobs are to + + + align:start position:0% +information on where good jobs are to +make sure that they are taking care of + + align:start position:0% +make sure that they are taking care of + + + align:start position:0% +make sure that they are taking care of +the safety and health and providing more + + align:start position:0% +the safety and health and providing more + + + align:start position:0% +the safety and health and providing more +information and working with restaurant + + align:start position:0% +information and working with restaurant + + + align:start position:0% +information and working with restaurant +owners they are working with some of the + + align:start position:0% +owners they are working with some of the + + + align:start position:0% +owners they are working with some of the +most uh uh Innovative restaurant owners + + align:start position:0% +most uh uh Innovative restaurant owners + + + align:start position:0% +most uh uh Innovative restaurant owners +in New York and in San Francisco and in + + align:start position:0% +in New York and in San Francisco and in + + + align:start position:0% +in New York and in San Francisco and in +other country uh other cities in the + + align:start position:0% +other country uh other cities in the + + + align:start position:0% +other country uh other cities in the +United States to promote this as part of + + align:start position:0% +United States to promote this as part of + + + align:start position:0% +United States to promote this as part of +their good company good job strategy and + + align:start position:0% +their good company good job strategy and + + + align:start position:0% +their good company good job strategy and +so this is just another way in which uh + + align:start position:0% +so this is just another way in which uh + + + align:start position:0% +so this is just another way in which uh +Creative Minds young people in this case + + align:start position:0% +Creative Minds young people in this case + + + align:start position:0% +Creative Minds young people in this case +young people and immigrants working + + align:start position:0% +young people and immigrants working + + + align:start position:0% +young people and immigrants working +together largely to say we can find ways + + align:start position:0% +together largely to say we can find ways + + + align:start position:0% +together largely to say we can find ways +to do this in a modern fashion that is + + align:start position:0% +to do this in a modern fashion that is + + + align:start position:0% +to do this in a modern fashion that is +is responsive to both consumers to uh + + align:start position:0% +is responsive to both consumers to uh + + + align:start position:0% +is responsive to both consumers to uh +employees and to the businesses that + + align:start position:0% +employees and to the businesses that + + + align:start position:0% +employees and to the businesses that +operate so I think uh we're in an + + align:start position:0% +operate so I think uh we're in an + + + align:start position:0% +operate so I think uh we're in an +interesting time will these grow to be + + align:start position:0% +interesting time will these grow to be + + + align:start position:0% +interesting time will these grow to be +large enough to have an effect I don't + + align:start position:0% +large enough to have an effect I don't + + + align:start position:0% +large enough to have an effect I don't +know but I think it's really up to all + + align:start position:0% +know but I think it's really up to all + + + align:start position:0% +know but I think it's really up to all +of you all of you wherever you happen to + + align:start position:0% +of you all of you wherever you happen to + + + align:start position:0% +of you all of you wherever you happen to +be in the world to invent the kinds of + + align:start position:0% +be in the world to invent the kinds of + + + align:start position:0% +be in the world to invent the kinds of +organizations that work effectively for + + align:start position:0% +organizations that work effectively for + + + align:start position:0% +organizations that work effectively for +you in the kind of work settings that + + align:start position:0% +you in the kind of work settings that + + + align:start position:0% +you in the kind of work settings that +you find yourself today and out of that + + align:start position:0% +you find yourself today and out of that + + + align:start position:0% +you find yourself today and out of that +will come some models that will grow + + align:start position:0% +will come some models that will grow + + + align:start position:0% +will come some models that will grow +perhaps over time and have an + + align:start position:0% +perhaps over time and have an + + + align:start position:0% +perhaps over time and have an +effect well we didn't just talk about + + align:start position:0% +effect well we didn't just talk about + + + align:start position:0% +effect well we didn't just talk about +what others need to do we spent a good + + align:start position:0% +what others need to do we spent a good + + + align:start position:0% +what others need to do we spent a good +deal of time talking about what + + align:start position:0% +deal of time talking about what + + + align:start position:0% +deal of time talking about what +individuals need to do and we emphasize + + align:start position:0% +individuals need to do and we emphasize + + + align:start position:0% +individuals need to do and we emphasize +obviously education as as the + + align:start position:0% +obviously education as as the + + + align:start position:0% +obviously education as as the +Cornerstone as a necessary condition but + + align:start position:0% +Cornerstone as a necessary condition but + + + align:start position:0% +Cornerstone as a necessary condition but +you also emphasize the need to be + + align:start position:0% +you also emphasize the need to be + + + align:start position:0% +you also emphasize the need to be +proactive and engage in uh a career + + align:start position:0% +proactive and engage in uh a career + + + align:start position:0% +proactive and engage in uh a career +planning exercise and so uh one of the + + align:start position:0% +planning exercise and so uh one of the + + + align:start position:0% +planning exercise and so uh one of the +assignments was to fill out uh the + + align:start position:0% +assignments was to fill out uh the + + + align:start position:0% +assignments was to fill out uh the +online uh uh questionnaire provided by + + align:start position:0% +online uh uh questionnaire provided by + + + align:start position:0% +online uh uh questionnaire provided by +the Department of Labor and its uh + + align:start position:0% +the Department of Labor and its uh + + + align:start position:0% +the Department of Labor and its uh +vocational U um and career planning uh + + align:start position:0% +vocational U um and career planning uh + + + align:start position:0% +vocational U um and career planning uh +tool which is just a standard one it's + + align:start position:0% +tool which is just a standard one it's + + + align:start position:0% +tool which is just a standard one it's +not any better I don't think or any + + align:start position:0% +not any better I don't think or any + + + align:start position:0% +not any better I don't think or any +worse than what you find elsewhere the + + align:start position:0% +worse than what you find elsewhere the + + + align:start position:0% +worse than what you find elsewhere the +the advantage is it's free and that's + + align:start position:0% +the advantage is it's free and that's + + + align:start position:0% +the advantage is it's free and that's +why we used it because we didn't want to + + align:start position:0% +why we used it because we didn't want to + + + align:start position:0% +why we used it because we didn't want to +have to have people pay for it uh but it + + align:start position:0% +have to have people pay for it uh but it + + + align:start position:0% +have to have people pay for it uh but it +it it it was the starting point and out + + align:start position:0% +it it it was the starting point and out + + + align:start position:0% +it it it was the starting point and out +of that completing that it provides + + align:start position:0% +of that completing that it provides + + + align:start position:0% +of that completing that it provides +information on what one's aptitudes are + + align:start position:0% +information on what one's aptitudes are + + + align:start position:0% +information on what one's aptitudes are +what they might be good at what jobs and + + align:start position:0% +what they might be good at what jobs and + + + align:start position:0% +what they might be good at what jobs and +occupations match uh those aptitudes + + align:start position:0% +occupations match uh those aptitudes + + + align:start position:0% +occupations match uh those aptitudes +very well what levels of Education are + + align:start position:0% +very well what levels of Education are + + + align:start position:0% +very well what levels of Education are +needed to get to different um levels of + + align:start position:0% +needed to get to different um levels of + + + align:start position:0% +needed to get to different um levels of +of the occupational structure in that + + align:start position:0% +of the occupational structure in that + + + align:start position:0% +of the occupational structure in that +particular area and that provides uh an + + align:start position:0% +particular area and that provides uh an + + + align:start position:0% +particular area and that provides uh an +opportunity to say I can now make a + + align:start position:0% +opportunity to say I can now make a + + + align:start position:0% +opportunity to say I can now make a +roadmap for how to go from where I am to + + align:start position:0% +roadmap for how to go from where I am to + + + align:start position:0% +roadmap for how to go from where I am to +realizing what I want to do uh but we + + align:start position:0% +realizing what I want to do uh but we + + + align:start position:0% +realizing what I want to do uh but we +also ask people to go out and talk to + + align:start position:0% +also ask people to go out and talk to + + + align:start position:0% +also ask people to go out and talk to +people in those occupations to get a + + align:start position:0% +people in those occupations to get a + + + align:start position:0% +people in those occupations to get a +firsthand sense of it so that they have + + align:start position:0% +firsthand sense of it so that they have + + + align:start position:0% +firsthand sense of it so that they have +a a more personalized view of what is it + + align:start position:0% +a a more personalized view of what is it + + + align:start position:0% +a a more personalized view of what is it +that uh this job is really all about and + + align:start position:0% +that uh this job is really all about and + + + align:start position:0% +that uh this job is really all about and +I think when I read uh the responses + + align:start position:0% +I think when I read uh the responses + + + align:start position:0% +I think when I read uh the responses +that's where the learning really started + + align:start position:0% +that's where the learning really started + + + align:start position:0% +that's where the learning really started +to take place and so the ability to go + + align:start position:0% +to take place and so the ability to go + + + align:start position:0% +to take place and so the ability to go +out and engage with people and really + + align:start position:0% +out and engage with people and really + + + align:start position:0% +out and engage with people and really +learn from their experiences is so + + align:start position:0% +learn from their experiences is so + + + align:start position:0% +learn from their experiences is so +critical to making uh these career + + align:start position:0% +critical to making uh these career + + + align:start position:0% +critical to making uh these career +planning guides uh come to life and look + + align:start position:0% +planning guides uh come to life and look + + + align:start position:0% +planning guides uh come to life and look +at the interesting mix of jobs and + + align:start position:0% +at the interesting mix of jobs and + + + align:start position:0% +at the interesting mix of jobs and +occupations here I got to kick out this + + align:start position:0% +occupations here I got to kick out this + + + align:start position:0% +occupations here I got to kick out this +is only a sample I just took some of the + + align:start position:0% +is only a sample I just took some of the + + + align:start position:0% +is only a sample I just took some of the +the the kind of more interesting ones uh + + align:start position:0% +the the kind of more interesting ones uh + + + align:start position:0% +the the kind of more interesting ones uh +I guess they're all interesting but we + + align:start position:0% +I guess they're all interesting but we + + + align:start position:0% +I guess they're all interesting but we +have everything from engineers and HR + + align:start position:0% +have everything from engineers and HR + + + align:start position:0% +have everything from engineers and HR +managers and labor leaders and artists + + align:start position:0% +managers and labor leaders and artists + + + align:start position:0% +managers and labor leaders and artists +and futurists someone's going to going + + align:start position:0% +and futurists someone's going to going + + + align:start position:0% +and futurists someone's going to going +to is very interested in being a + + align:start position:0% +to is very interested in being a + + + align:start position:0% +to is very interested in being a +futurist H holoc cons ultan anyone know + + align:start position:0% +futurist H holoc cons ultan anyone know + + + align:start position:0% +futurist H holoc cons ultan anyone know +what holoc + + align:start position:0% +what holoc + + + align:start position:0% +what holoc +is probably + + align:start position:0% +is probably + + + align:start position:0% +is probably +not well holoc is uh basically uh + + align:start position:0% +not well holoc is uh basically uh + + + align:start position:0% +not well holoc is uh basically uh +organizational consultant who works to + + align:start position:0% +organizational consultant who works to + + + align:start position:0% +organizational consultant who works to +share power and and Authority throughout + + align:start position:0% +share power and and Authority throughout + + + align:start position:0% +share power and and Authority throughout +the organization and to try to reduce uh + + align:start position:0% +the organization and to try to reduce uh + + + align:start position:0% +the organization and to try to reduce uh +or even completely get rid of hierarchy + + align:start position:0% +or even completely get rid of hierarchy + + + align:start position:0% +or even completely get rid of hierarchy +it's very controversial not uh uh it has + + align:start position:0% +it's very controversial not uh uh it has + + + align:start position:0% +it's very controversial not uh uh it has +some very strong uh Advocates and has + + align:start position:0% +some very strong uh Advocates and has + + + align:start position:0% +some very strong uh Advocates and has +some very strong critics uh but here's + + align:start position:0% +some very strong critics uh but here's + + + align:start position:0% +some very strong critics uh but here's +someone who is really committed to it + + align:start position:0% +someone who is really committed to it + + + align:start position:0% +someone who is really committed to it +and is going to go out and wants to make + + align:start position:0% +and is going to go out and wants to make + + + align:start position:0% +and is going to go out and wants to make +a career of it and I I applaud that um + + align:start position:0% +a career of it and I I applaud that um + + + align:start position:0% +a career of it and I I applaud that um +that energy a sports agent + + align:start position:0% +that energy a sports agent + + + align:start position:0% +that energy a sports agent +psychometrician technical writers + + align:start position:0% +psychometrician technical writers + + + align:start position:0% +psychometrician technical writers +artists graphic artists so these are + + align:start position:0% +artists graphic artists so these are + + + align:start position:0% +artists graphic artists so these are +these are jobs these are all jobs that + + align:start position:0% +these are jobs these are all jobs that + + + align:start position:0% +these are jobs these are all jobs that +people will feel that they will find + + align:start position:0% +people will feel that they will find + + + align:start position:0% +people will feel that they will find +what they really want to do and I want + + align:start position:0% +what they really want to do and I want + + + align:start position:0% +what they really want to do and I want +you to keep these in mind when we think + + align:start position:0% +you to keep these in mind when we think + + + align:start position:0% +you to keep these in mind when we think +about in two slides down the road here H + + align:start position:0% +about in two slides down the road here H + + + align:start position:0% +about in two slides down the road here H +about the role of Technology because one + + align:start position:0% +about the role of Technology because one + + + align:start position:0% +about the role of Technology because one +of the big worries in this course that + + align:start position:0% +of the big worries in this course that + + + align:start position:0% +of the big worries in this course that +was voiced by so many people is what's + + align:start position:0% +was voiced by so many people is what's + + + align:start position:0% +was voiced by so many people is what's +going to happen to our jobs as + + align:start position:0% +going to happen to our jobs as + + + align:start position:0% +going to happen to our jobs as +technology comes along so I want to come + + align:start position:0% +technology comes along so I want to come + + + align:start position:0% +technology comes along so I want to come +to that in a moment but look at these + + align:start position:0% +to that in a moment but look at these + + + align:start position:0% +to that in a moment but look at these +are jobs that are not going to + + align:start position:0% +are jobs that are not going to + + + align:start position:0% +are jobs that are not going to +necessarily go away and not going to be + + align:start position:0% +necessarily go away and not going to be + + + align:start position:0% +necessarily go away and not going to be +taken over by robots or artificial + + align:start position:0% +taken over by robots or artificial + + + align:start position:0% +taken over by robots or artificial +intelligence in the near future they + + align:start position:0% +intelligence in the near future they + + + align:start position:0% +intelligence in the near future they +will be influenced by them for sure but + + align:start position:0% +will be influenced by them for sure but + + + align:start position:0% +will be influenced by them for sure but +uh we'll come to that in a moment what + + align:start position:0% +uh we'll come to that in a moment what + + + align:start position:0% +uh we'll come to that in a moment what +are some of the the the themes that uh + + align:start position:0% +are some of the the the themes that uh + + + align:start position:0% +are some of the the the themes that uh +came out in the career development + + align:start position:0% +came out in the career development + + + align:start position:0% +came out in the career development +planning process this is just a sampling + + align:start position:0% +planning process this is just a sampling + + + align:start position:0% +planning process this is just a sampling +from both this year and last year uh the + + align:start position:0% +from both this year and last year uh the + + + align:start position:0% +from both this year and last year uh the +themes were almost identical across the + + align:start position:0% +themes were almost identical across the + + + align:start position:0% +themes were almost identical across the +two years very strong emphasis on + + align:start position:0% +two years very strong emphasis on + + + align:start position:0% +two years very strong emphasis on +getting the credentials getting some + + align:start position:0% +getting the credentials getting some + + + align:start position:0% +getting the credentials getting some +stamp of approval that I've got the + + align:start position:0% +stamp of approval that I've got the + + + align:start position:0% +stamp of approval that I've got the +skills that I my customers can trust me + + align:start position:0% +skills that I my customers can trust me + + + align:start position:0% +skills that I my customers can trust me +to come in and do that work in my in + + align:start position:0% +to come in and do that work in my in + + + align:start position:0% +to come in and do that work in my in +someone's house or in community or in + + align:start position:0% +someone's house or in community or in + + + align:start position:0% +someone's house or in community or in +taking care of people in my family and + + align:start position:0% +taking care of people in my family and + + + align:start position:0% +taking care of people in my family and +so that's a growing uh uh recognition + + align:start position:0% +so that's a growing uh uh recognition + + + align:start position:0% +so that's a growing uh uh recognition +that that's important the importance on + + align:start position:0% +that that's important the importance on + + + align:start position:0% +that that's important the importance on +having networks and building these + + align:start position:0% +having networks and building these + + + align:start position:0% +having networks and building these +networks so that they know where the + + align:start position:0% +networks so that they know where the + + + align:start position:0% +networks so that they know where the +good opportunities are and have access + + align:start position:0% +good opportunities are and have access + + + align:start position:0% +good opportunities are and have access +to them emphasis on lifelong learning + + align:start position:0% +to them emphasis on lifelong learning + + + align:start position:0% +to them emphasis on lifelong learning +and emphasis on courses like this that + + align:start position:0% +and emphasis on courses like this that + + + align:start position:0% +and emphasis on courses like this that +we can use this online technology + + align:start position:0% +we can use this online technology + + + align:start position:0% +we can use this online technology +perhaps to augment the basic education + + align:start position:0% +perhaps to augment the basic education + + + align:start position:0% +perhaps to augment the basic education +over the the course of time to support + + align:start position:0% +over the the course of time to support + + + align:start position:0% +over the the course of time to support +the lifelong learning process and then + + align:start position:0% +the lifelong learning process and then + + + align:start position:0% +the lifelong learning process and then +recognition that people will have to + + align:start position:0% +recognition that people will have to + + + align:start position:0% +recognition that people will have to +keep their skills current because they + + align:start position:0% +keep their skills current because they + + + align:start position:0% +keep their skills current because they +will be changing careers and moving + + align:start position:0% +will be changing careers and moving + + + align:start position:0% +will be changing careers and moving +across occupations most likely uh over + + align:start position:0% +across occupations most likely uh over + + + align:start position:0% +across occupations most likely uh over +time and then finally this really + + align:start position:0% +time and then finally this really + + + align:start position:0% +time and then finally this really +important point that sometimes the + + align:start position:0% +important point that sometimes the + + + align:start position:0% +important point that sometimes the +career planning process uh doesn't pay + + align:start position:0% +career planning process uh doesn't pay + + + align:start position:0% +career planning process uh doesn't pay +enough attention to that we don't make + + align:start position:0% +enough attention to that we don't make + + + align:start position:0% +enough attention to that we don't make +these decisions in isolation we live in + + align:start position:0% +these decisions in isolation we live in + + + align:start position:0% +these decisions in isolation we live in +a community we live in a family we have + + align:start position:0% +a community we live in a family we have + + + align:start position:0% +a community we live in a family we have +Partners we have children and many uh + + align:start position:0% +Partners we have children and many uh + + + align:start position:0% +Partners we have children and many uh +many of us have children or other + + align:start position:0% +many of us have children or other + + + align:start position:0% +many of us have children or other +relatives who depend on us sometimes + + align:start position:0% +relatives who depend on us sometimes + + + align:start position:0% +relatives who depend on us sometimes +elderly parents who need to be cared for + + align:start position:0% +elderly parents who need to be cared for + + + align:start position:0% +elderly parents who need to be cared for +and so as we make these plans one of the + + align:start position:0% +and so as we make these plans one of the + + + align:start position:0% +and so as we make these plans one of the +the the requests in the planning + + align:start position:0% +the the requests in the planning + + + align:start position:0% +the the requests in the planning +exercise was don't just tell us what you + + align:start position:0% +exercise was don't just tell us what you + + + align:start position:0% +exercise was don't just tell us what you +want to do but make sure that you tell + + align:start position:0% +want to do but make sure that you tell + + + align:start position:0% +want to do but make sure that you tell +us how it will affect everyone else in + + align:start position:0% +us how it will affect everyone else in + + + align:start position:0% +us how it will affect everyone else in +your immediate uh family or social + + align:start position:0% +your immediate uh family or social + + + align:start position:0% +your immediate uh family or social +setting and so that's an important part + + align:start position:0% +setting and so that's an important part + + + align:start position:0% +setting and so that's an important part +of this career planning I think we can + + align:start position:0% +of this career planning I think we can + + + align:start position:0% +of this career planning I think we can +do this I don't believe that we should + + align:start position:0% +do this I don't believe that we should + + + align:start position:0% +do this I don't believe that we should +overdo career planning we can't predict + + align:start position:0% +overdo career planning we can't predict + + + align:start position:0% +overdo career planning we can't predict +the future completely and we shouldn't + + align:start position:0% +the future completely and we shouldn't + + + align:start position:0% +the future completely and we shouldn't +be so determined that there's only one + + align:start position:0% +be so determined that there's only one + + + align:start position:0% +be so determined that there's only one +course uh for the future but we should + + align:start position:0% +course uh for the future but we should + + + align:start position:0% +course uh for the future but we should +plan to be ready to take advantage of + + align:start position:0% +plan to be ready to take advantage of + + + align:start position:0% +plan to be ready to take advantage of +opportunities when they come along and + + align:start position:0% +opportunities when they come along and + + + align:start position:0% +opportunities when they come along and +know which directions we want to go in + + align:start position:0% +know which directions we want to go in + + + align:start position:0% +know which directions we want to go in +and not be afraid to take those steps + + align:start position:0% +and not be afraid to take those steps + + + align:start position:0% +and not be afraid to take those steps +when an opportunity is uh is is open to + + align:start position:0% +when an opportunity is uh is is open to + + + align:start position:0% +when an opportunity is uh is is open to +us so the career planning and the + + align:start position:0% +us so the career planning and the + + + align:start position:0% +us so the career planning and the +personal development uh plan process in + + align:start position:0% +personal development uh plan process in + + + align:start position:0% +personal development uh plan process in +this course was a vital part of what we + + align:start position:0% +this course was a vital part of what we + + + align:start position:0% +this course was a vital part of what we +did but then we come to this question + + align:start position:0% +did but then we come to this question + + + align:start position:0% +did but then we come to this question +and I this is a great frame I wish I + + align:start position:0% +and I this is a great frame I wish I + + + align:start position:0% +and I this is a great frame I wish I +could take t uh take credit for this + + align:start position:0% +could take t uh take credit for this + + + align:start position:0% +could take t uh take credit for this +will technology eat our jobs but I + + align:start position:0% +will technology eat our jobs but I + + + align:start position:0% +will technology eat our jobs but I +didn't uh invent that term I did a + + align:start position:0% +didn't uh invent that term I did a + + + align:start position:0% +didn't uh invent that term I did a +little bit of a of a Facebook uh chat + + align:start position:0% +little bit of a of a Facebook uh chat + + + align:start position:0% +little bit of a of a Facebook uh chat +with a uh very talented uh leader from + + align:start position:0% +with a uh very talented uh leader from + + + align:start position:0% +with a uh very talented uh leader from +Sama group uh her name is Layla Janna uh + + align:start position:0% +Sama group uh her name is Layla Janna uh + + + align:start position:0% +Sama group uh her name is Layla Janna uh +and she runs an organization that really + + align:start position:0% +and she runs an organization that really + + + align:start position:0% +and she runs an organization that really +works with very lowincome people all + + align:start position:0% +works with very lowincome people all + + + align:start position:0% +works with very lowincome people all +over the globe to try to help them to + + align:start position:0% +over the globe to try to help them to + + + align:start position:0% +over the globe to try to help them to +use technology to improve uh their + + align:start position:0% +use technology to improve uh their + + + align:start position:0% +use technology to improve uh their +livelihood and to gain access to better + + align:start position:0% +livelihood and to gain access to better + + + align:start position:0% +livelihood and to gain access to better +opportunities and so um uh she raised + + align:start position:0% +opportunities and so um uh she raised + + + align:start position:0% +opportunities and so um uh she raised +the question and we had this discussion + + align:start position:0% +the question and we had this discussion + + + align:start position:0% +the question and we had this discussion +will technology eat our jobs we took a + + align:start position:0% +will technology eat our jobs we took a + + + align:start position:0% +will technology eat our jobs we took a +pretty strong position on this and here + + align:start position:0% +pretty strong position on this and here + + + align:start position:0% +pretty strong position on this and here +we are at MIT and we have some of the + + align:start position:0% +we are at MIT and we have some of the + + + align:start position:0% +we are at MIT and we have some of the +people who are known for being some of + + align:start position:0% +people who are known for being some of + + + align:start position:0% +people who are known for being some of +the more pessimistic and we have some + + align:start position:0% +the more pessimistic and we have some + + + align:start position:0% +the more pessimistic and we have some +people who are known for being more + + align:start position:0% +people who are known for being more + + + align:start position:0% +people who are known for being more +optimistic we've got them all at MIT I + + align:start position:0% +optimistic we've got them all at MIT I + + + align:start position:0% +optimistic we've got them all at MIT I +always say that if you we have a + + align:start position:0% +always say that if you we have a + + + align:start position:0% +always say that if you we have a +thousand faculty members and On Any + + align:start position:0% +thousand faculty members and On Any + + + align:start position:0% +thousand faculty members and On Any +Given issue those 1,000 faculty members + + align:start position:0% +Given issue those 1,000 faculty members + + + align:start position:0% +Given issue those 1,000 faculty members +will have at least 3,000 points of view + + align:start position:0% +will have at least 3,000 points of view + + + align:start position:0% +will have at least 3,000 points of view +so and on this I think uh uh we we can + + align:start position:0% +so and on this I think uh uh we we can + + + align:start position:0% +so and on this I think uh uh we we can +see people all over the place because we + + align:start position:0% +see people all over the place because we + + + align:start position:0% +see people all over the place because we +don't really know the serious answer is + + align:start position:0% +don't really know the serious answer is + + + align:start position:0% +don't really know the serious answer is +we don't know how Rapid or how + + align:start position:0% +we don't know how Rapid or how + + + align:start position:0% +we don't know how Rapid or how +broadscale uh artificial intelligence + + align:start position:0% +broadscale uh artificial intelligence + + + align:start position:0% +broadscale uh artificial intelligence +machine learning and all of these other + + align:start position:0% +machine learning and all of these other + + + align:start position:0% +machine learning and all of these other +things are going to take over jobs but + + align:start position:0% +things are going to take over jobs but + + + align:start position:0% +things are going to take over jobs but +we know that if we don't do anything if + + align:start position:0% +we know that if we don't do anything if + + + align:start position:0% +we know that if we don't do anything if +we let it happen then we're at the risk + + align:start position:0% +we let it happen then we're at the risk + + + align:start position:0% +we let it happen then we're at the risk +of the worst scenario but if we use + + align:start position:0% +of the worst scenario but if we use + + + align:start position:0% +of the worst scenario but if we use +technology to + + align:start position:0% +technology to + + + align:start position:0% +technology to +augment work to augment and strengthen + + align:start position:0% +augment work to augment and strengthen + + + align:start position:0% +augment work to augment and strengthen +the role of human judgment then we might + + align:start position:0% +the role of human judgment then we might + + + align:start position:0% +the role of human judgment then we might +be able to have the best of both worlds + + align:start position:0% +be able to have the best of both worlds + + + align:start position:0% +be able to have the best of both worlds +and that's what even the the IBM Watson + + align:start position:0% +and that's what even the the IBM Watson + + + align:start position:0% +and that's what even the the IBM Watson +uh creators emphasized here at techn at + + align:start position:0% +uh creators emphasized here at techn at + + + align:start position:0% +uh creators emphasized here at techn at +at M in a technology day a couple of + + align:start position:0% +at M in a technology day a couple of + + + align:start position:0% +at M in a technology day a couple of +months ago and so we can do this we will + + align:start position:0% +months ago and so we can do this we will + + + align:start position:0% +months ago and so we can do this we will +have displacement there's no question + + align:start position:0% +have displacement there's no question + + + align:start position:0% +have displacement there's no question +that jobs are going to be displaced the + + align:start position:0% +that jobs are going to be displaced the + + + align:start position:0% +that jobs are going to be displaced the +question is are we going to be uh ahead + + align:start position:0% +question is are we going to be uh ahead + + + align:start position:0% +question is are we going to be uh ahead +of the curve and really work to make + + align:start position:0% +of the curve and really work to make + + + align:start position:0% +of the curve and really work to make +sure that we take care of those people + + align:start position:0% +sure that we take care of those people + + + align:start position:0% +sure that we take care of those people +who are displaced provide them + + align:start position:0% +who are displaced provide them + + + align:start position:0% +who are displaced provide them +opportunities to move to where the job + + align:start position:0% +opportunities to move to where the job + + + align:start position:0% +opportunities to move to where the job +the good jobs are make sure that they've + + align:start position:0% +the good jobs are make sure that they've + + + align:start position:0% +the good jobs are make sure that they've +got the skills build up over time so + + align:start position:0% +got the skills build up over time so + + + align:start position:0% +got the skills build up over time so +that they can make those changes and + + align:start position:0% +that they can make those changes and + + + align:start position:0% +that they can make those changes and +then get on with this process so I think + + align:start position:0% +then get on with this process so I think + + + align:start position:0% +then get on with this process so I think +we can uh use it I think we're going to + + align:start position:0% +we can uh use it I think we're going to + + + align:start position:0% +we can uh use it I think we're going to +see more of these worker centered apps + + align:start position:0% +see more of these worker centered apps + + + align:start position:0% +see more of these worker centered apps +that help us adapt to technology ol I + + align:start position:0% +that help us adapt to technology ol I + + + align:start position:0% +that help us adapt to technology ol I +used the example we had an interview + + align:start position:0% +used the example we had an interview + + + align:start position:0% +used the example we had an interview +with sherpashare the founders that use + + align:start position:0% +with sherpashare the founders that use + + + align:start position:0% +with sherpashare the founders that use +the Uber technology to share information + + align:start position:0% +the Uber technology to share information + + + align:start position:0% +the Uber technology to share information +with the drivers on what their real + + align:start position:0% +with the drivers on what their real + + + align:start position:0% +with the drivers on what their real +earnings are and now we're seeing + + align:start position:0% +earnings are and now we're seeing + + + align:start position:0% +earnings are and now we're seeing +drivers use that app in new creative + + align:start position:0% +drivers use that app in new creative + + + align:start position:0% +drivers use that app in new creative +ways and other uh competing apps are + + align:start position:0% +ways and other uh competing apps are + + + align:start position:0% +ways and other uh competing apps are +also out there even since we uh did that + + align:start position:0% +also out there even since we uh did that + + + align:start position:0% +also out there even since we uh did that +interview a couple of months ago so I'm + + align:start position:0% +interview a couple of months ago so I'm + + + align:start position:0% +interview a couple of months ago so I'm +excited about the use of technology to + + align:start position:0% +excited about the use of technology to + + + align:start position:0% +excited about the use of technology to +improve work but we've got to harness it + + align:start position:0% +improve work but we've got to harness it + + + align:start position:0% +improve work but we've got to harness it +we've got to be proactive if we're going + + align:start position:0% +we've got to be proactive if we're going + + + align:start position:0% +we've got to be proactive if we're going +to be successful and what about + + align:start position:0% +to be successful and what about + + + align:start position:0% +to be successful and what about +entrepreneurship and again there's a lot + + align:start position:0% +entrepreneurship and again there's a lot + + + align:start position:0% +entrepreneurship and again there's a lot +of hypee about entrepreneurship that all + + align:start position:0% +of hypee about entrepreneurship that all + + + align:start position:0% +of hypee about entrepreneurship that all +new jobs are created by startups well + + align:start position:0% +new jobs are created by startups well + + + align:start position:0% +new jobs are created by startups well +that's not quite true but a large number + + align:start position:0% +that's not quite true but a large number + + + align:start position:0% +that's not quite true but a large number +of new jobs are created by startups so + + align:start position:0% +of new jobs are created by startups so + + + align:start position:0% +of new jobs are created by startups so +the the the importance of startups the + + align:start position:0% +the the the importance of startups the + + + align:start position:0% +the the the importance of startups the +importance of Entrepreneurship is is is + + align:start position:0% +importance of Entrepreneurship is is is + + + align:start position:0% +importance of Entrepreneurship is is is +beyond question we've got to make sure + + align:start position:0% +beyond question we've got to make sure + + + align:start position:0% +beyond question we've got to make sure +that we have a healthy growth of new + + align:start position:0% +that we have a healthy growth of new + + + align:start position:0% +that we have a healthy growth of new +Enterprises but we've got to do this in + + align:start position:0% +Enterprises but we've got to do this in + + + align:start position:0% +Enterprises but we've got to do this in +a more inclusive way we've had terrible + + align:start position:0% +a more inclusive way we've had terrible + + + align:start position:0% +a more inclusive way we've had terrible +scandals and again I'm glad it's all + + align:start position:0% +scandals and again I'm glad it's all + + + align:start position:0% +scandals and again I'm glad it's all +over the news these days + + align:start position:0% +over the news these days + + + align:start position:0% +over the news these days +about how uh male-dominated Silicon + + align:start position:0% +about how uh male-dominated Silicon + + + align:start position:0% +about how uh male-dominated Silicon +Valley is with its startups and how + + align:start position:0% +Valley is with its startups and how + + + align:start position:0% +Valley is with its startups and how +difficult it is for women to move to + + align:start position:0% +difficult it is for women to move to + + + align:start position:0% +difficult it is for women to move to +higher levels of of leadership in that + + align:start position:0% +higher levels of of leadership in that + + + align:start position:0% +higher levels of of leadership in that +uh part of our U our growing sector of + + align:start position:0% +uh part of our U our growing sector of + + + align:start position:0% +uh part of our U our growing sector of +the economy and how difficult it is for + + align:start position:0% +the economy and how difficult it is for + + + align:start position:0% +the economy and how difficult it is for +women to get money from Venture + + align:start position:0% +women to get money from Venture + + + align:start position:0% +women to get money from Venture +capitalists well we've got to change + + align:start position:0% +capitalists well we've got to change + + + align:start position:0% +capitalists well we've got to change +that and build a more inclusive + + align:start position:0% +that and build a more inclusive + + + align:start position:0% +that and build a more inclusive +capitalism if we are going to be + + align:start position:0% +capitalism if we are going to be + + + align:start position:0% +capitalism if we are going to be +successful and in fact we know some + + align:start position:0% +successful and in fact we know some + + + align:start position:0% +successful and in fact we know some +things and so that's where the Hitachi + + align:start position:0% +things and so that's where the Hitachi + + + align:start position:0% +things and so that's where the Hitachi +Foundation has been so successful in + + align:start position:0% +Foundation has been so successful in + + + align:start position:0% +Foundation has been so successful in +building a program to help young + + align:start position:0% +building a program to help young + + + align:start position:0% +building a program to help young +entrepreneurs to find those investors to + + align:start position:0% +entrepreneurs to find those investors to + + + align:start position:0% +entrepreneurs to find those investors to +pick those investors as gray said + + align:start position:0% +pick those investors as gray said + + + align:start position:0% +pick those investors as gray said +earlier in in this session this + + align:start position:0% +earlier in in this session this + + + align:start position:0% +earlier in in this session this +afternoon to make sure that they pick + + align:start position:0% +afternoon to make sure that they pick + + + align:start position:0% +afternoon to make sure that they pick +investors that are supportive of uh + + align:start position:0% +investors that are supportive of uh + + + align:start position:0% +investors that are supportive of uh +growth opportunities we didn't use this + + align:start position:0% +growth opportunities we didn't use this + + + align:start position:0% +growth opportunities we didn't use this +little example but I like it because + + align:start position:0% +little example but I like it because + + + align:start position:0% +little example but I like it because +maybe I like the name called beep but + + align:start position:0% +maybe I like the name called beep but + + + align:start position:0% +maybe I like the name called beep but +beep is a is a + + align:start position:0% +beep is a is a + + + align:start position:0% +beep is a is a +online uh used car uh business started + + align:start position:0% +online uh used car uh business started + + + align:start position:0% +online uh used car uh business started +in San Francisco go spreading in other + + align:start position:0% +in San Francisco go spreading in other + + + align:start position:0% +in San Francisco go spreading in other +parts of of the country we used it in + + align:start position:0% +parts of of the country we used it in + + + align:start position:0% +parts of of the country we used it in +our our oncampus course as a case and so + + align:start position:0% +our our oncampus course as a case and so + + + align:start position:0% +our our oncampus course as a case and so +our students in the room here are + + align:start position:0% +our students in the room here are + + + align:start position:0% +our students in the room here are +familiar with it but basically beep + + align:start position:0% +familiar with it but basically beep + + + align:start position:0% +familiar with it but basically beep +faced this question who would you buy a + + align:start position:0% +faced this question who would you buy a + + + align:start position:0% +faced this question who would you buy a +used car from do you want to buy it from + + align:start position:0% +used car from do you want to buy it from + + + align:start position:0% +used car from do you want to buy it from +someone who is a full-time employee who + + align:start position:0% +someone who is a full-time employee who + + + align:start position:0% +someone who is a full-time employee who +who was signing off and certifying that + + align:start position:0% +who was signing off and certifying that + + + align:start position:0% +who was signing off and certifying that +this car has been inspected this car has + + align:start position:0% +this car has been inspected this car has + + + align:start position:0% +this car has been inspected this car has +been uh uh repaired this car is safe and + + align:start position:0% +been uh uh repaired this car is safe and + + + align:start position:0% +been uh uh repaired this car is safe and +this car is worth the price that is + + align:start position:0% +this car is worth the price that is + + + align:start position:0% +this car is worth the price that is +being asked or or do you want to buy it + + align:start position:0% +being asked or or do you want to buy it + + + align:start position:0% +being asked or or do you want to buy it +from someone who doesn't have that same + + align:start position:0% +from someone who doesn't have that same + + + align:start position:0% +from someone who doesn't have that same +kind of commitment is just hired as a + + align:start position:0% +kind of commitment is just hired as a + + + align:start position:0% +kind of commitment is just hired as a +contractor to go through the motions to + + align:start position:0% +contractor to go through the motions to + + + align:start position:0% +contractor to go through the motions to +do it and BP faced investors with + + align:start position:0% +do it and BP faced investors with + + + align:start position:0% +do it and BP faced investors with +debates about that and they went in the + + align:start position:0% +debates about that and they went in the + + + align:start position:0% +debates about that and they went in the +direction of hiring and cons and staying + + align:start position:0% +direction of hiring and cons and staying + + + align:start position:0% +direction of hiring and cons and staying +with a business strategy that says we + + align:start position:0% +with a business strategy that says we + + + align:start position:0% +with a business strategy that says we +think trust is so important and quality + + align:start position:0% +think trust is so important and quality + + + align:start position:0% +think trust is so important and quality +is so important that we're going to keep + + align:start position:0% +is so important that we're going to keep + + + align:start position:0% +is so important that we're going to keep +the full-time jobs with with decent + + align:start position:0% +the full-time jobs with with decent + + + align:start position:0% +the full-time jobs with with decent +wages and benefits now that's a choice + + align:start position:0% +wages and benefits now that's a choice + + + align:start position:0% +wages and benefits now that's a choice +that young firms also can make but I uh + + align:start position:0% +that young firms also can make but I uh + + + align:start position:0% +that young firms also can make but I uh +am under No Illusion of the pressures + + align:start position:0% +am under No Illusion of the pressures + + + align:start position:0% +am under No Illusion of the pressures +that startups face to conserve costs + + align:start position:0% +that startups face to conserve costs + + + align:start position:0% +that startups face to conserve costs +because they don't have much money and + + align:start position:0% +because they don't have much money and + + + align:start position:0% +because they don't have much money and +they don't have a lot of resources so + + align:start position:0% +they don't have a lot of resources so + + + align:start position:0% +they don't have a lot of resources so +it's very difficult but if we don't + + align:start position:0% +it's very difficult but if we don't + + + align:start position:0% +it's very difficult but if we don't +imprint good jobs right at the beginning + + align:start position:0% +imprint good jobs right at the beginning + + + align:start position:0% +imprint good jobs right at the beginning +it's going to be very hard to uh bring + + align:start position:0% +it's going to be very hard to uh bring + + + align:start position:0% +it's going to be very hard to uh bring +them in a little bit later so making + + align:start position:0% +them in a little bit later so making + + + align:start position:0% +them in a little bit later so making +sure that we worry about inclusive + + align:start position:0% +sure that we worry about inclusive + + + align:start position:0% +sure that we worry about inclusive +entrepreneurship and inclusive + + align:start position:0% +entrepreneurship and inclusive + + + align:start position:0% +entrepreneurship and inclusive +capitalism uh right from the beginning + + align:start position:0% +capitalism uh right from the beginning + + + align:start position:0% +capitalism uh right from the beginning +is very important + + align:start position:0% +is very important + + + align:start position:0% +is very important +AST I was just thinking uh you told talk + + align:start position:0% +AST I was just thinking uh you told talk + + + align:start position:0% +AST I was just thinking uh you told talk +about the US and the unions where you + + align:start position:0% +about the US and the unions where you + + + align:start position:0% +about the US and the unions where you +have declined maybe most one place where + + align:start position:0% +have declined maybe most one place where + + + align:start position:0% +have declined maybe most one place where +I feel that the us can help us in other + + align:start position:0% +I feel that the us can help us in other + + + align:start position:0% +I feel that the us can help us in other +parts of the world is about taking risk + + align:start position:0% +parts of the world is about taking risk + + + align:start position:0% +parts of the world is about taking risk +because here if you're an entrepreneur + + align:start position:0% +because here if you're an entrepreneur + + + align:start position:0% +because here if you're an entrepreneur +you go for it but you fail maybe because + + align:start position:0% +you go for it but you fail maybe because + + + align:start position:0% +you go for it but you fail maybe because +the technology wasn't such a good idea + + align:start position:0% +the technology wasn't such a good idea + + + align:start position:0% +the technology wasn't such a good idea +as you hoped for you have a legal system + + align:start position:0% +as you hoped for you have a legal system + + + align:start position:0% +as you hoped for you have a legal system +an + + align:start position:0% +an + + + align:start position:0% +an +environmental en social ecosystem that + + align:start position:0% +environmental en social ecosystem that + + + align:start position:0% +environmental en social ecosystem that +let you go for a new tribe I think in + + align:start position:0% +let you go for a new tribe I think in + + + align:start position:0% +let you go for a new tribe I think in +lots of other places in the world you've + + align:start position:0% +lots of other places in the world you've + + + align:start position:0% +lots of other places in the world you've +got two red lines on you and you're a + + align:start position:0% +got two red lines on you and you're a + + + align:start position:0% +got two red lines on you and you're a +loser in the family parties you are + + align:start position:0% +loser in the family parties you are + + + align:start position:0% +loser in the family parties you are +hidden away because you're a looser so I + + align:start position:0% +hidden away because you're a looser so I + + + align:start position:0% +hidden away because you're a looser so I +think there uh there is a lot of gain + + align:start position:0% +think there uh there is a lot of gain + + + align:start position:0% +think there uh there is a lot of gain +with technology but also with you in + + align:start position:0% +with technology but also with you in + + + align:start position:0% +with technology but also with you in +America that you can help us in the rest + + align:start position:0% +America that you can help us in the rest + + + align:start position:0% +America that you can help us in the rest +of the world to be more entrepreneurial + + align:start position:0% +of the world to be more entrepreneurial + + + align:start position:0% +of the world to be more entrepreneurial +and to try I think that's a very + + align:start position:0% +and to try I think that's a very + + + align:start position:0% +and to try I think that's a very +important point I'm glad you made it uh + + align:start position:0% +important point I'm glad you made it uh + + + align:start position:0% +important point I'm glad you made it uh +in the online course there's also an + + align:start position:0% +in the online course there's also an + + + align:start position:0% +in the online course there's also an +essay from one of our Sloan graduates + + align:start position:0% +essay from one of our Sloan graduates + + + align:start position:0% +essay from one of our Sloan graduates +from a number of years ago John Joy gr + + align:start position:0% +from a number of years ago John Joy gr + + + align:start position:0% +from a number of years ago John Joy gr +who's who's written about European + + align:start position:0% +who's who's written about European + + + align:start position:0% +who's who's written about European +entrepreneurship and he works on this in + + align:start position:0% +entrepreneurship and he works on this in + + + align:start position:0% +entrepreneurship and he works on this in +Europe and he's lamenting the fact that + + align:start position:0% +Europe and he's lamenting the fact that + + + align:start position:0% +Europe and he's lamenting the fact that +Europe is so slow to have that kind of + + align:start position:0% +Europe is so slow to have that kind of + + + align:start position:0% +Europe is so slow to have that kind of +infrastructure risk-taking and support + + align:start position:0% +infrastructure risk-taking and support + + + align:start position:0% +infrastructure risk-taking and support +for entrepreneurs and says we've got to + + align:start position:0% +for entrepreneurs and says we've got to + + + align:start position:0% +for entrepreneurs and says we've got to +really change that so he's reinforcing + + align:start position:0% +really change that so he's reinforcing + + + align:start position:0% +really change that so he's reinforcing +uh the important point that you made and + + align:start position:0% +uh the important point that you made and + + + align:start position:0% +uh the important point that you made and +I think it's worth uh uh worth paying + + align:start position:0% +I think it's worth uh uh worth paying + + + align:start position:0% +I think it's worth uh uh worth paying +attention to some of the strengths that + + align:start position:0% +attention to some of the strengths that + + + align:start position:0% +attention to some of the strengths that +we have here as as we move forward well + + align:start position:0% +we have here as as we move forward well + + + align:start position:0% +we have here as as we move forward well +you went through this very difficult + + align:start position:0% +you went through this very difficult + + + align:start position:0% +you went through this very difficult +challenging and and and for many of you + + align:start position:0% +challenging and and and for many of you + + + align:start position:0% +challenging and and and for many of you +rewarding experience of saying all right + + align:start position:0% +rewarding experience of saying all right + + + align:start position:0% +rewarding experience of saying all right +enough of this talk about it enough of + + align:start position:0% +enough of this talk about it enough of + + + align:start position:0% +enough of this talk about it enough of +this reading about it enough of the + + align:start position:0% +this reading about it enough of the + + + align:start position:0% +this reading about it enough of the +watching boring videos let's try to + + align:start position:0% +watching boring videos let's try to + + + align:start position:0% +watching boring videos let's try to +negotiate the Next Generation social + + align:start position:0% +negotiate the Next Generation social + + + align:start position:0% +negotiate the Next Generation social +contract and so I applaud the energy + + align:start position:0% +contract and so I applaud the energy + + + align:start position:0% +contract and so I applaud the energy +that you put into it uh those that + + align:start position:0% +that you put into it uh those that + + + align:start position:0% +that you put into it uh those that +participated and our our colleagues here + + align:start position:0% +participated and our our colleagues here + + + align:start position:0% +participated and our our colleagues here +on campus who helped to facilitate it + + align:start position:0% +on campus who helped to facilitate it + + + align:start position:0% +on campus who helped to facilitate it +and so I just want to share a little bit + + align:start position:0% +and so I just want to share a little bit + + + align:start position:0% +and so I just want to share a little bit +of of the settlements and and and what + + align:start position:0% +of of the settlements and and and what + + + align:start position:0% +of of the settlements and and and what +you you came away from that exercise + + align:start position:0% +you you came away from that exercise + + + align:start position:0% +you you came away from that exercise +with it's a difficult exercise to do uh + + align:start position:0% +with it's a difficult exercise to do uh + + + align:start position:0% +with it's a difficult exercise to do uh +it's challenging because of the + + align:start position:0% +it's challenging because of the + + + align:start position:0% +it's challenging because of the +differences in time zones and so on but + + align:start position:0% +differences in time zones and so on but + + + align:start position:0% +differences in time zones and so on but +I think it's worth uh doing perhaps + + align:start position:0% +I think it's worth uh doing perhaps + + + align:start position:0% +I think it's worth uh doing perhaps +maybe in some modified ways some of you + + align:start position:0% +maybe in some modified ways some of you + + + align:start position:0% +maybe in some modified ways some of you +made some good suggestions and look we + + align:start position:0% +made some good suggestions and look we + + + align:start position:0% +made some good suggestions and look we +again had a very broad distribution we + + align:start position:0% +again had a very broad distribution we + + + align:start position:0% +again had a very broad distribution we +had 44 countries uh uh uh participating + + align:start position:0% +had 44 countries uh uh uh participating + + + align:start position:0% +had 44 countries uh uh uh participating +in this experience a nice broad array + + align:start position:0% +in this experience a nice broad array + + + align:start position:0% +in this experience a nice broad array +and here's some of the priorities that + + align:start position:0% +and here's some of the priorities that + + + align:start position:0% +and here's some of the priorities that +you you chose to focus on and there were + + align:start position:0% +you you chose to focus on and there were + + + align:start position:0% +you you chose to focus on and there were +a set of as you recall Workforce + + align:start position:0% +a set of as you recall Workforce + + + align:start position:0% +a set of as you recall Workforce +Development compens ation fairness + + align:start position:0% +Development compens ation fairness + + + align:start position:0% +Development compens ation fairness +representation organizational + + align:start position:0% +representation organizational + + + align:start position:0% +representation organizational +performance family and community and + + align:start position:0% +performance family and community and + + + align:start position:0% +performance family and community and +basically not one of those dominated + + align:start position:0% +basically not one of those dominated + + + align:start position:0% +basically not one of those dominated +there was a good distribution of + + align:start position:0% +there was a good distribution of + + + align:start position:0% +there was a good distribution of +priorities everyone recognized the + + align:start position:0% +priorities everyone recognized the + + + align:start position:0% +priorities everyone recognized the +importance of all of these there was + + align:start position:0% +importance of all of these there was + + + align:start position:0% +importance of all of these there was +clearly a a higher preference for + + align:start position:0% +clearly a a higher preference for + + + align:start position:0% +clearly a a higher preference for +Workforce Development and a little bit + + align:start position:0% +Workforce Development and a little bit + + + align:start position:0% +Workforce Development and a little bit +more for fairness and and and + + align:start position:0% +more for fairness and and and + + + align:start position:0% +more for fairness and and and +non-discrimination but the varied + + align:start position:0% +non-discrimination but the varied + + + align:start position:0% +non-discrimination but the varied +interest said just what you said early + + align:start position:0% +interest said just what you said early + + + align:start position:0% +interest said just what you said early +on in the course about how important + + align:start position:0% +on in the course about how important + + + align:start position:0% +on in the course about how important +multiple things are to you in in the + + align:start position:0% +multiple things are to you in in the + + + align:start position:0% +multiple things are to you in in the +workplace and so lifelong learning + + align:start position:0% +workplace and so lifelong learning + + + align:start position:0% +workplace and so lifelong learning +dominated uh voice and representation + + align:start position:0% +dominated uh voice and representation + + + align:start position:0% +dominated uh voice and representation +the concern for productivity and + + align:start position:0% +the concern for productivity and + + + align:start position:0% +the concern for productivity and +flexibility in organizations uh + + align:start position:0% +flexibility in organizations uh + + + align:start position:0% +flexibility in organizations uh +dominated and work and family came + + align:start position:0% +dominated and work and family came + + + align:start position:0% +dominated and work and family came +through as well and these are just some + + align:start position:0% +through as well and these are just some + + + align:start position:0% +through as well and these are just some +numbers I'm not going to go through + + align:start position:0% +numbers I'm not going to go through + + + align:start position:0% +numbers I'm not going to go through +these they just reflect basically what I + + align:start position:0% +these they just reflect basically what I + + + align:start position:0% +these they just reflect basically what I +said uh a minute ago because we're + + align:start position:0% +said uh a minute ago because we're + + + align:start position:0% +said uh a minute ago because we're +running a little bit short on on time + + align:start position:0% +running a little bit short on on time + + + align:start position:0% +running a little bit short on on time +but let's look at what you uh agreed to + + align:start position:0% +but let's look at what you uh agreed to + + + align:start position:0% +but let's look at what you uh agreed to +well we had about + + align:start position:0% +well we had about + + + align:start position:0% +well we had about +157 uh agreements some of them were two- + + align:start position:0% +157 uh agreements some of them were two- + + + align:start position:0% +157 uh agreements some of them were two- +party some were three-party some were + + align:start position:0% +party some were three-party some were + + + align:start position:0% +party some were three-party some were +four-party but across those clusters + + align:start position:0% +four-party but across those clusters + + + align:start position:0% +four-party but across those clusters +what you did is you you embodied the + + align:start position:0% +what you did is you you embodied the + + + align:start position:0% +what you did is you you embodied the +knowledge of the high performance work + + align:start position:0% +knowledge of the high performance work + + + align:start position:0% +knowledge of the high performance work +organizations you said we can't just + + align:start position:0% +organizations you said we can't just + + + align:start position:0% +organizations you said we can't just +focus on training and many of your + + align:start position:0% +focus on training and many of your + + + align:start position:0% +focus on training and many of your +agreements had training combined with + + align:start position:0% +agreements had training combined with + + + align:start position:0% +agreements had training combined with +Performance training combined with + + align:start position:0% +Performance training combined with + + + align:start position:0% +Performance training combined with +compensation training provided combined + + align:start position:0% +compensation training provided combined + + + align:start position:0% +compensation training provided combined +with making sure it was inclusive some + + align:start position:0% +with making sure it was inclusive some + + + align:start position:0% +with making sure it was inclusive some +of the European examples said we're even + + align:start position:0% +of the European examples said we're even + + + align:start position:0% +of the European examples said we're even +going to find ways to bring it to the + + align:start position:0% +going to find ways to bring it to the + + + align:start position:0% +going to find ways to bring it to the +platform economy and see see if we can't + + align:start position:0% +platform economy and see see if we can't + + + align:start position:0% +platform economy and see see if we can't +bring some of our training experience + + align:start position:0% +bring some of our training experience + + + align:start position:0% +bring some of our training experience +and our our our represent models into + + align:start position:0% +and our our our represent models into + + + align:start position:0% +and our our our represent models into +that uh sphere and so a very strong + + align:start position:0% +that uh sphere and so a very strong + + + align:start position:0% +that uh sphere and so a very strong +emphasis on lifelong learning on Career + + align:start position:0% +emphasis on lifelong learning on Career + + + align:start position:0% +emphasis on lifelong learning on Career +planning uh the notion that people + + align:start position:0% +planning uh the notion that people + + + align:start position:0% +planning uh the notion that people +should have representation emphasis on + + align:start position:0% +should have representation emphasis on + + + align:start position:0% +should have representation emphasis on +Partnerships uh strong commitment to + + align:start position:0% +Partnerships uh strong commitment to + + + align:start position:0% +Partnerships uh strong commitment to +flexibility in organizations strong + + align:start position:0% +flexibility in organizations strong + + + align:start position:0% +flexibility in organizations strong +commitment to profit sharing that came + + align:start position:0% +commitment to profit sharing that came + + + align:start position:0% +commitment to profit sharing that came +through in in many of these um uh + + align:start position:0% +through in in many of these um uh + + + align:start position:0% +through in in many of these um uh +agreements as well and so I think you + + align:start position:0% +agreements as well and so I think you + + + align:start position:0% +agreements as well and so I think you +found ways to reach across interest + + align:start position:0% +found ways to reach across interest + + + align:start position:0% +found ways to reach across interest +group lines to find ways to find Common + + align:start position:0% +group lines to find ways to find Common + + + align:start position:0% +group lines to find ways to find Common +Ground now if you can do it in this + + align:start position:0% +Ground now if you can do it in this + + + align:start position:0% +Ground now if you can do it in this +exercise then perhaps why can't we do it + + align:start position:0% +exercise then perhaps why can't we do it + + + align:start position:0% +exercise then perhaps why can't we do it +in our broader societies I would urge + + align:start position:0% +in our broader societies I would urge + + + align:start position:0% +in our broader societies I would urge +everyone to take these same issues and + + align:start position:0% +everyone to take these same issues and + + + align:start position:0% +everyone to take these same issues and +move them uh to other settings so where + + align:start position:0% +move them uh to other settings so where + + + align:start position:0% +move them uh to other settings so where +did we end up well the last thing we + + align:start position:0% +did we end up well the last thing we + + + align:start position:0% +did we end up well the last thing we +asked is what are the the messages to + + align:start position:0% +asked is what are the the messages to + + + align:start position:0% +asked is what are the the messages to +the Next Generation leaders HR + + align:start position:0% +the Next Generation leaders HR + + + align:start position:0% +the Next Generation leaders HR +professionals labor Educators and + + align:start position:0% +professionals labor Educators and + + + align:start position:0% +professionals labor Educators and +government officials and our friends at + + align:start position:0% +government officials and our friends at + + + align:start position:0% +government officials and our friends at +Cornell help us out on the HR side so my + + align:start position:0% +Cornell help us out on the HR side so my + + + align:start position:0% +Cornell help us out on the HR side so my +good friend Lee Dyer who led that class + + align:start position:0% +good friend Lee Dyer who led that class + + + align:start position:0% +good friend Lee Dyer who led that class +and his students provided these next + + align:start position:0% +and his students provided these next + + + align:start position:0% +and his students provided these next +three slides on what do they see because + + align:start position:0% +three slides on what do they see because + + + align:start position:0% +three slides on what do they see because +they are moving into this profession so + + align:start position:0% +they are moving into this profession so + + + align:start position:0% +they are moving into this profession so +what is it that they see is important + + align:start position:0% +what is it that they see is important + + + align:start position:0% +what is it that they see is important +for the HR profession to attend to and + + align:start position:0% +for the HR profession to attend to and + + + align:start position:0% +for the HR profession to attend to and +they emphasized three themes + + align:start position:0% +they emphasized three themes + + + align:start position:0% +they emphasized three themes +globalization technology and + + align:start position:0% +globalization technology and + + + align:start position:0% +globalization technology and +demographics and on the basis of that + + align:start position:0% +demographics and on the basis of that + + + align:start position:0% +demographics and on the basis of that +came up with uh a set of slides on and + + align:start position:0% +came up with uh a set of slides on and + + + align:start position:0% +came up with uh a set of slides on and +points on what it means for recruit M + + align:start position:0% +points on what it means for recruit M + + + align:start position:0% +points on what it means for recruit M +that they have to recognize that there + + align:start position:0% +that they have to recognize that there + + + align:start position:0% +that they have to recognize that there +has to be a good fit between the + + align:start position:0% +has to be a good fit between the + + + align:start position:0% +has to be a good fit between the +competencies the organization needs and + + align:start position:0% +competencies the organization needs and + + + align:start position:0% +competencies the organization needs and +what employees need to bring they need + + align:start position:0% +what employees need to bring they need + + + align:start position:0% +what employees need to bring they need +to develop uh new sets of technical + + align:start position:0% +to develop uh new sets of technical + + + align:start position:0% +to develop uh new sets of technical +knowledge emphasizing the the uh the + + align:start position:0% +knowledge emphasizing the the uh the + + + align:start position:0% +knowledge emphasizing the the uh the +technical and stem skills but also + + align:start position:0% +technical and stem skills but also + + + align:start position:0% +technical and stem skills but also +combining that with problem solving and + + align:start position:0% +combining that with problem solving and + + + align:start position:0% +combining that with problem solving and +being able to work collaboratively in + + align:start position:0% +being able to work collaboratively in + + + align:start position:0% +being able to work collaboratively in +teams so they embodied the integration + + align:start position:0% +teams so they embodied the integration + + + align:start position:0% +teams so they embodied the integration +of technology and organizational skills + + align:start position:0% +of technology and organizational skills + + + align:start position:0% +of technology and organizational skills +and understanding the need to be + + align:start position:0% +and understanding the need to be + + + align:start position:0% +and understanding the need to be +responsive to people's differences in + + align:start position:0% +responsive to people's differences in + + + align:start position:0% +responsive to people's differences in +culture and backgrounds so I think on + + align:start position:0% +culture and backgrounds so I think on + + + align:start position:0% +culture and backgrounds so I think on +the recruitment side that's a really + + align:start position:0% +the recruitment side that's a really + + + align:start position:0% +the recruitment side that's a really +powerful set of of points on the + + align:start position:0% +powerful set of of points on the + + + align:start position:0% +powerful set of of points on the +globalization side they they saw the + + align:start position:0% +globalization side they they saw the + + + align:start position:0% +globalization side they they saw the +positives and the negatives that yes + + align:start position:0% +positives and the negatives that yes + + + align:start position:0% +positives and the negatives that yes +globalization creates an opportunity to + + align:start position:0% +globalization creates an opportunity to + + + align:start position:0% +globalization creates an opportunity to +compete for talent all across the world + + align:start position:0% +compete for talent all across the world + + + align:start position:0% +compete for talent all across the world +and it at the same time provides more + + align:start position:0% +and it at the same time provides more + + + align:start position:0% +and it at the same time provides more +diversity that we need to manage + + align:start position:0% +diversity that we need to manage + + + align:start position:0% +diversity that we need to manage +effectively but it also provides some + + align:start position:0% +effectively but it also provides some + + + align:start position:0% +effectively but it also provides some +low wage Havens and that's going to put + + align:start position:0% +low wage Havens and that's going to put + + + align:start position:0% +low wage Havens and that's going to put +pressure on our compensation structur so + + align:start position:0% +pressure on our compensation structur so + + + align:start position:0% +pressure on our compensation structur so +they were quite realistic in having to + + align:start position:0% +they were quite realistic in having to + + + align:start position:0% +they were quite realistic in having to +man AG the tensions of globalization and + + align:start position:0% +man AG the tensions of globalization and + + + align:start position:0% +man AG the tensions of globalization and +on + + align:start position:0% +on + + + align:start position:0% +on +technology it came back again to + + align:start position:0% +technology it came back again to + + + align:start position:0% +technology it came back again to +emphasize the complimentary nature that + + align:start position:0% +emphasize the complimentary nature that + + + align:start position:0% +emphasize the complimentary nature that +technology can play if they are + + align:start position:0% +technology can play if they are + + + align:start position:0% +technology can play if they are +proactive and if there's one message to + + align:start position:0% +proactive and if there's one message to + + + align:start position:0% +proactive and if there's one message to +the HR community in fact I delivered it + + align:start position:0% +the HR community in fact I delivered it + + + align:start position:0% +the HR community in fact I delivered it +this morning to a group of HR + + align:start position:0% +this morning to a group of HR + + + align:start position:0% +this morning to a group of HR +professionals and in in talking about + + align:start position:0% +professionals and in in talking about + + + align:start position:0% +professionals and in in talking about +these issues is that they have to get + + align:start position:0% +these issues is that they have to get + + + align:start position:0% +these issues is that they have to get +out in front of Technology they have to + + align:start position:0% +out in front of Technology they have to + + + align:start position:0% +out in front of Technology they have to +be part of the technology designers and + + align:start position:0% +be part of the technology designers and + + + align:start position:0% +be part of the technology designers and +enablers to make work really compliments + + align:start position:0% +enablers to make work really compliments + + + align:start position:0% +enablers to make work really compliments +to technology and I think that's an + + align:start position:0% +to technology and I think that's an + + + align:start position:0% +to technology and I think that's an +opportunity for the HR profession and + + align:start position:0% +opportunity for the HR profession and + + + align:start position:0% +opportunity for the HR profession and +then they commented as well on + + align:start position:0% +then they commented as well on + + + align:start position:0% +then they commented as well on +demographics uh along the lines that + + align:start position:0% +demographics uh along the lines that + + + align:start position:0% +demographics uh along the lines that +we've talked about for mentoring uh the + + align:start position:0% +we've talked about for mentoring uh the + + + align:start position:0% +we've talked about for mentoring uh the +Next Generation Workforce and so on so + + align:start position:0% +Next Generation Workforce and so on so + + + align:start position:0% +Next Generation Workforce and so on so +thank you to our our colleagues at + + align:start position:0% +thank you to our our colleagues at + + + align:start position:0% +thank you to our our colleagues at +Cornell for those inputs but you also + + align:start position:0% +Cornell for those inputs but you also + + + align:start position:0% +Cornell for those inputs but you also +raised in your own conversations issues + + align:start position:0% +raised in your own conversations issues + + + align:start position:0% +raised in your own conversations issues +around implications for worker advocates + + align:start position:0% +around implications for worker advocates + + + align:start position:0% +around implications for worker advocates +for U needing to listen to the workforce + + align:start position:0% +for U needing to listen to the workforce + + + align:start position:0% +for U needing to listen to the workforce +to learn from the workforce to build the + + align:start position:0% +to learn from the workforce to build the + + + align:start position:0% +to learn from the workforce to build the +new organizations not to be just + + align:start position:0% +new organizations not to be just + + + align:start position:0% +new organizations not to be just +captivated by the way in which we did + + align:start position:0% +captivated by the way in which we did + + + align:start position:0% +captivated by the way in which we did +things in the past to build on the + + align:start position:0% +things in the past to build on the + + + align:start position:0% +things in the past to build on the +strengths of the past but to look to the + + align:start position:0% +strengths of the past but to look to the + + + align:start position:0% +strengths of the past but to look to the +Future and particularly to use + + align:start position:0% +Future and particularly to use + + + align:start position:0% +Future and particularly to use +information Technologies as building new + + align:start position:0% +information Technologies as building new + + + align:start position:0% +information Technologies as building new +sources of power and for those of us in + + align:start position:0% +sources of power and for those of us in + + + align:start position:0% +sources of power and for those of us in +the education Community emphasizing + + align:start position:0% +the education Community emphasizing + + + align:start position:0% +the education Community emphasizing +we've got to be more creative in using + + align:start position:0% +we've got to be more creative in using + + + align:start position:0% +we've got to be more creative in using +all this technology online learning and + + align:start position:0% +all this technology online learning and + + + align:start position:0% +all this technology online learning and +uh uh other mechanisms to provide good + + align:start position:0% +uh uh other mechanisms to provide good + + + align:start position:0% +uh uh other mechanisms to provide good +guidance for the Next Generation + + align:start position:0% +guidance for the Next Generation + + + align:start position:0% +guidance for the Next Generation +Workforce and to provide opportunities + + align:start position:0% +Workforce and to provide opportunities + + + align:start position:0% +Workforce and to provide opportunities +for continuing to learn as we go along + + align:start position:0% +for continuing to learn as we go along + + + align:start position:0% +for continuing to learn as we go along +and then the toughest nut obviously is + + align:start position:0% +and then the toughest nut obviously is + + + align:start position:0% +and then the toughest nut obviously is +breaking the gridlock that we find in + + align:start position:0% +breaking the gridlock that we find in + + + align:start position:0% +breaking the gridlock that we find in +the United States and in some other + + align:start position:0% +the United States and in some other + + + align:start position:0% +the United States and in some other +countries over National politics and + + align:start position:0% +countries over National politics and + + + align:start position:0% +countries over National politics and +here we emphasize right from the + + align:start position:0% +here we emphasize right from the + + + align:start position:0% +here we emphasize right from the +beginning that the lessons always come + + align:start position:0% +beginning that the lessons always come + + + align:start position:0% +beginning that the lessons always come +from the local level first and so if we + + align:start position:0% +from the local level first and so if we + + + align:start position:0% +from the local level first and so if we +can build on the innovations that are + + align:start position:0% +can build on the innovations that are + + + align:start position:0% +can build on the innovations that are +happening that we've talked about + + align:start position:0% +happening that we've talked about + + + align:start position:0% +happening that we've talked about +throughout this course uh at the local + + align:start position:0% +throughout this course uh at the local + + + align:start position:0% +throughout this course uh at the local +level then maybe someday soon uh our + + align:start position:0% +level then maybe someday soon uh our + + + align:start position:0% +level then maybe someday soon uh our +national leaders will wake up and say + + align:start position:0% +national leaders will wake up and say + + + align:start position:0% +national leaders will wake up and say +maybe it's time for us to start working + + align:start position:0% +maybe it's time for us to start working + + + align:start position:0% +maybe it's time for us to start working +uh together so our bottom line message + + align:start position:0% +uh together so our bottom line message + + + align:start position:0% +uh together so our bottom line message +to the Next Generation Workforce to all + + align:start position:0% +to the Next Generation Workforce to all + + + align:start position:0% +to the Next Generation Workforce to all +of us and to all of you I guess I'm not + + align:start position:0% +of us and to all of you I guess I'm not + + + align:start position:0% +of us and to all of you I guess I'm not +the Next Generation Workforce but you + + align:start position:0% +the Next Generation Workforce but you + + + align:start position:0% +the Next Generation Workforce but you +are the Next Generation Workforce is + + align:start position:0% +are the Next Generation Workforce is + + + align:start position:0% +are the Next Generation Workforce is +education + + align:start position:0% +education + + + align:start position:0% +education +preschool formal schooling and lifelong + + align:start position:0% +preschool formal schooling and lifelong + + + align:start position:0% +preschool formal schooling and lifelong +learning education throughout one's life + + align:start position:0% +learning education throughout one's life + + + align:start position:0% +learning education throughout one's life +making sure you explore but don't become + + align:start position:0% +making sure you explore but don't become + + + align:start position:0% +making sure you explore but don't become +a victim of too tight a career plan but + + align:start position:0% +a victim of too tight a career plan but + + + align:start position:0% +a victim of too tight a career plan but +take opportunities when they are + + align:start position:0% +take opportunities when they are + + + align:start position:0% +take opportunities when they are +available keep those skills current work + + align:start position:0% +available keep those skills current work + + + align:start position:0% +available keep those skills current work +together keep your resume up to date and + + align:start position:0% +together keep your resume up to date and + + + align:start position:0% +together keep your resume up to date and +one foot in the external labor market to + + align:start position:0% +one foot in the external labor market to + + + align:start position:0% +one foot in the external labor market to +use that as a source of power and get + + align:start position:0% +use that as a source of power and get + + + align:start position:0% +use that as a source of power and get +involved and together if there's a + + align:start position:0% +involved and together if there's a + + + align:start position:0% +involved and together if there's a +bottom line here we can shape the future + + align:start position:0% +bottom line here we can shape the future + + + align:start position:0% +bottom line here we can shape the future +of work so where are we going once again + + align:start position:0% +of work so where are we going once again + + + align:start position:0% +of work so where are we going once again +we emphasize the high road importance + + align:start position:0% +we emphasize the high road importance + + + align:start position:0% +we emphasize the high road importance +rebuild bargaining power get the parties + + align:start position:0% +rebuild bargaining power get the parties + + + align:start position:0% +rebuild bargaining power get the parties +working together and then let me give + + align:start position:0% +working together and then let me give + + + align:start position:0% +working together and then let me give +you the real bottom line from two + + align:start position:0% +you the real bottom line from two + + + align:start position:0% +you the real bottom line from two +students uh from uh our discussion board + + align:start position:0% +students uh from uh our discussion board + + + align:start position:0% +students uh from uh our discussion board +and I'll just read these and end uh on + + align:start position:0% +and I'll just read these and end uh on + + + align:start position:0% +and I'll just read these and end uh on +this note and one said taking this + + align:start position:0% +this note and one said taking this + + + align:start position:0% +this note and one said taking this +course has given me hope that the future + + align:start position:0% +course has given me hope that the future + + + align:start position:0% +course has given me hope that the future +of work and the path I wish to take + + align:start position:0% +of work and the path I wish to take + + + align:start position:0% +of work and the path I wish to take +after college and the future of work + + align:start position:0% +after college and the future of work + + + align:start position:0% +after college and the future of work +depends on the mindset of individual + + align:start position:0% +depends on the mindset of individual + + + align:start position:0% +depends on the mindset of individual +workers of all of you if the workers are + + align:start position:0% +workers of all of you if the workers are + + + align:start position:0% +workers of all of you if the workers are +hardworking and have confidence the + + align:start position:0% +hardworking and have confidence the + + + align:start position:0% +hardworking and have confidence the +future of work will toil in their favor + + align:start position:0% +future of work will toil in their favor + + + align:start position:0% +future of work will toil in their favor +I think that's a beautiful phrase uh and + + align:start position:0% +I think that's a beautiful phrase uh and + + + align:start position:0% +I think that's a beautiful phrase uh and +and I appreciate uh the authors offering + + align:start position:0% +and I appreciate uh the authors offering + + + align:start position:0% +and I appreciate uh the authors offering +it and then uh uh one that came just + + align:start position:0% +it and then uh uh one that came just + + + align:start position:0% +it and then uh uh one that came just +today I I came away feeling a personal + + align:start position:0% +today I I came away feeling a personal + + + align:start position:0% +today I I came away feeling a personal +call to action to help shape the future + + align:start position:0% +call to action to help shape the future + + + align:start position:0% +call to action to help shape the future +of work myself that indeed the future of + + align:start position:0% +of work myself that indeed the future of + + + align:start position:0% +of work myself that indeed the future of +work is up to us we have to do we have + + align:start position:0% +work is up to us we have to do we have + + + align:start position:0% +work is up to us we have to do we have +we do have the power to shape the future + + align:start position:0% +we do have the power to shape the future + + + align:start position:0% +we do have the power to shape the future +of work by bringing together all of the + + align:start position:0% +of work by bringing together all of the + + + align:start position:0% +of work by bringing together all of the +stakeholders these are the bottom line + + align:start position:0% +stakeholders these are the bottom line + + + align:start position:0% +stakeholders these are the bottom line +messages of this course this is what we + + align:start position:0% +messages of this course this is what we + + + align:start position:0% +messages of this course this is what we +all put all this energy all you put all + + align:start position:0% +all put all this energy all you put all + + + align:start position:0% +all put all this energy all you put all +the energy you put into it in the online + + align:start position:0% +the energy you put into it in the online + + + align:start position:0% +the energy you put into it in the online +version and our friends here on campus + + align:start position:0% +version and our friends here on campus + + + align:start position:0% +version and our friends here on campus +and I think together we can shape the + + align:start position:0% +and I think together we can shape the + + + align:start position:0% +and I think together we can shape the +future of work so we just need to move + + align:start position:0% +future of work so we just need to move + + + align:start position:0% +future of work so we just need to move +forward we will put all of this material + + align:start position:0% +forward we will put all of this material + + + align:start position:0% +forward we will put all of this material +uh online it will stay online and you'll + + align:start position:0% +uh online it will stay online and you'll + + + align:start position:0% +uh online it will stay online and you'll +be encouraged to come back and use the + + align:start position:0% +be encouraged to come back and use the + + + align:start position:0% +be encouraged to come back and use the +material maybe use it in teaching others + + align:start position:0% +material maybe use it in teaching others + + + align:start position:0% +material maybe use it in teaching others +uh in the future so it'll stay on on the + + align:start position:0% +uh in the future so it'll stay on on the + + + align:start position:0% +uh in the future so it'll stay on on the +platform uh for anyone who wants to use + + align:start position:0% +platform uh for anyone who wants to use + + + align:start position:0% +platform uh for anyone who wants to use +it or anyone who wants to join uh and + + align:start position:0% +it or anyone who wants to join uh and + + + align:start position:0% +it or anyone who wants to join uh and +use it uh in the future we think that + + align:start position:0% +use it uh in the future we think that + + + align:start position:0% +use it uh in the future we think that +together if we use what we know about + + align:start position:0% +together if we use what we know about + + + align:start position:0% +together if we use what we know about +how work has uh uh been structured in + + align:start position:0% +how work has uh uh been structured in + + + align:start position:0% +how work has uh uh been structured in +the past on what work in the past What + + align:start position:0% +the past on what work in the past What + + + align:start position:0% +the past on what work in the past What +stopped working in the in uh more recent + + align:start position:0% +stopped working in the in uh more recent + + + align:start position:0% +stopped working in the in uh more recent +years why the world uh of work has to + + align:start position:0% +years why the world uh of work has to + + + align:start position:0% +years why the world uh of work has to +change to keep up with changes in + + align:start position:0% +change to keep up with changes in + + + align:start position:0% +change to keep up with changes in +technology and keep up with the people + + align:start position:0% +technology and keep up with the people + + + align:start position:0% +technology and keep up with the people +uh who are doing the work we can make a + + align:start position:0% +uh who are doing the work we can make a + + + align:start position:0% +uh who are doing the work we can make a +difference so I want to thank you all + + align:start position:0% +difference so I want to thank you all + + + align:start position:0% +difference so I want to thank you all +for the the many hours of of effort that + + align:start position:0% +for the the many hours of of effort that + + + align:start position:0% +for the the many hours of of effort that +you put into this course I want to thank + + align:start position:0% +you put into this course I want to thank + + + align:start position:0% +you put into this course I want to thank +you for taking an interest in improving + + align:start position:0% +you for taking an interest in improving + + + align:start position:0% +you for taking an interest in improving +the the future of work and I hope that + + align:start position:0% +the the future of work and I hope that + + + align:start position:0% +the the future of work and I hope that +together we'll all make a difference + + align:start position:0% +together we'll all make a difference + + + align:start position:0% +together we'll all make a difference +thank you very much + + align:start position:0% +thank you very much + + + align:start position:0% +thank you very much +[Applause] \ No newline at end of file diff --git a/llaa-iEYDLI.txt b/llaa-iEYDLI.txt new file mode 100644 index 0000000000000000000000000000000000000000..f9b7c35d5b4b84210c69f1efc94ac92bf1f75513 --- /dev/null +++ b/llaa-iEYDLI.txt @@ -0,0 +1,2867 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: -- that this is not +a quick clicker question, so + +you actually need to maybe write +something down to figure + +out the answer. + +So if you haven't clicked in +yet, or if you want to change + +your answer, keep in mind that +you might need to jot down, + +for example, a Lewis structure +before you can answer this + +question. + +-- and get in your final answer + +to the clicker question. + +For those of you just walking +in now, you might not have a + +chance to get all of the thought +process that you need + +in on this clicker question, +because it is based on a Lewis + +structure, so we will +go over it. + +But for those of you that have +been here for 30 seconds or + +longer, see if you can get +the right answer in here. + +All right, so OK, it looks +like we have a very mixed + +response in terms of +the answer to the + +clicker question today. + +Raise your hand if you didn't +have time to figure out the + +Lewis structure. + +OK, so that accounts +for some of you. + +Let's go over the correct +answer this question. + +So, who got the right answer -- + +31% of us. + +This is not the kind of +percentages we're looking for, + +so let's go over this. + +In class on Monday, we did go +over the geometries, and the + +geometries themselves are very +straightforward, once you know + +what the Lewis structure is, but +remember, you can't just + +always look at a molecule +and automatically + +know the Lewis structure. + +We actually need to think about +those valence electrons. + +So, here we're dealing with +selenium hydride, so s e h 2. + +I told you that there's 6 +valence electrons in selenium, + +so we have 6 there, plus 1 +for each of the hydrogen. + +So what we should have is +8 valence electrons + +in our Lewis structure. + +How many electrons do we need +to have full valence shells? + +STUDENT: [INAUDIBLE] + +PROFESSOR: 12, that's right. + +We need 8 plus 4 is 12 +for full shells. + +That means that we need 12 +minus 8, or 4 bonding + +electrons in our structure. + +So I tried to give you one that +you could draw pretty + +quickly, it just has +hydrogens in It. + +So we have s e h 2. + +We can do our 4 bonding +electrons. + +How many valence electrons +do we have left? + +STUDENT: [INAUDIBLE] + +PROFESSOR: 4, that's right. + +So, we need to fill our octet +for selenium, so 1, 2, 3, 4. + +So, this is our Lewis structure +here, hopefully you + +can see why it's not linear. + +If it were linear, which 32% of +you seem have thought, that + +would have meant that our Lewis +structure had no lone + +pairs in it, right, and +that's not the case. + +We have two lone pairs, so if +we thought about what the + +bonds were everywhere, +it would be 109 . + +5, but it's bent because we're +only looking at the bonds, + +we're not counting the Lewis +structures in naming our + +geometry, but they do +affect the angles. + +And it turns out that it's +actually less than 109 . + +5, because those lone pairs +are pushing the bonds even + +further away. + +So, does this make sense to +everyone if you think + +about it this way? + +Pretty much, okay. + +So, we'll try another clicker +question like this later. + +Some of these questions that +look very straightforward just + +naming the geometry, you have +to remember to do the first + +step before you jump in and +go ahead with a naming. + +So you'll got plenty of practice +with this on your + +problem-set if you +haven't already. + +All right. + +So before we start in with +today's notes, I do want to + +mention that this morning +the Nobel Prize in + +chemistry was announced. + +This is an exciting week in +science in general because we + +got to hear another +Nobel Prize every + +morning pretty much. + +So, let's settle down for a +second and start listening. + +All right. + +So, today we're going to be +talking about molecular + +orbital theory, but first I +wanted to just mention, in + +case some of you didn't hear +what the Nobel Prize was this + +morning, and this was in +chemistry, it went to three + +different chemists. + +Osamu Shimomura, who's a +Japanese chemist, and then + +Martin Chalfi who's at Columbia, +and Robert Chen + +who's at U. C. San Diego. + +The three of these chemists +split the Nobel Prize this + +morning for their discovery +and/or their application of + +using green fluorescent +protein, which + +is also called GFP. + +How many of you have heard +of GFP before? + +Oh, that's so great. + +OK. + +Many of you have heard of GFP. + +For some of you that haven't +I'll just say that it's a + +protein, it's 238 amino acids, +which means that it's about + +1,000, actually more than 1,000 +atoms in size, and this + +protein is fluorescent. + +The protein was first discovered +and first isolated + +from this jellyfish here. + +This was done by Shimomura, +and he did this in + +the 60's and 70's. + +He actually recognized and, of +course, many people recognized + +that this jellyfish was +fluorescent, and he isolated + +the actual protein, and +determined and proved that + +this protein was sufficient to +cause this fluorescence. + +So, in terms of thinking about +applications of why it's so + +exciting that you have this +fluorescent protein, other + +than it's always really fun +to look at things that are + +fluorescent, we can think about +in terms of biology why + +it's so exciting, you can +actually tag this protein to + +any other protein that you're +studying and now you have a + +visual handle on what's +going on. + +So, for example, if you were +interested in some protein + +involved in cancer, you +could tag it with GFP. + +You could watch where it +localizes in the cell, there + +are fluorescent assays you could +use to determine what + +other proteins it +interacts with. + +You could see, for example, +when it's expressed in a + +cancer cell, and where +it's expressed. + +There are all sorts of things +you can do once you can + +visualize something +with fluorescence. + +The reason it is so exciting +that it's a protein, and it's + +a protein, this is the structure +here, it's a ribbon + +structure so you can kind of see +what it looks like, it's + +made up of all natural +amino acids. + +So this means we can code for +it in DNA, you don't have to + +worry how am I going to +get into the cell. + +All you have to do is mutate +the DNA, which is very + +straightforward to do in +molecular biology, and now you + +can tag absolutely any protein +that you're interested in. + +So, as I said, this was first +discovered and isolated from + +the jellyfish. + +This was done by Shimomura -- +that was kind of the first + +step in this process of having +it become such a useful tool. + +And then, many years later, +not until 1994 did Martin + +Chalfi, at Columbia, show that +yes, I can, in fact, take the + +DNA and put it into a different +organism, and he put + +it into e coli, a bacteria. + +And what he could show was that +it could be expressed, + +this is a picture from his 1994 +science paper, in that e + +coli, and it is going +to fluoresce green. + +Now, the first application +tends to not be quite as + +exciting as, for example, all +the other organisms people + +have put it in since then -- +you can have flies, you see + +transgenic mice that are glowing +green with this GFP. + +Of course, that's not the useful +application for it, + +it's more of a proof of +principle, but it does show + +you that you can put it in for +studies in any organisms. + +And the field was really +pushed forward by the + +discoveries of Robert Chen at UC +San Diego, and what he did + +was he actually figured out how +it was that this protein + +fluoresced, what caused the +actual fluorescence. + +And once he did that, both he +and many other scientists, + +could then, once they understood +what caused the + +fluorescence, make little +changes to the actual protein, + +and tune what the properties +of that + +fluorescent protein were. + +So now, for example, there are +a whole range, just a whole + +rainbow of fluorescent proteins +that can be used. + +And I'm sure you can imagine +that if you want to label onw + +protein green and one red and +one yellow, now you can start + +looking at really complex +biological processes. + +So, it's pretty rare that +chemistry makes + +the every day news. + +So hopefully you'll all look +in the normal papers today, + +not just the scientific +journals, and get to read + +something about chemistry. + +It's always fun to see how its +described in The New York + +Times or in The Boston Globe. + +The other thing I wanted to +mention and I'm not sure if + +the exhibit's still there. + +But there was an exhibit of +jellyfish, I know at least + +until last year, at the Boston +Museum of Science, and all of + +you guys can get +in there free. + +And it's neat to see the glowing +jellyfish and think + +about the fluorescent protein +that's in them. + +So, I encourage you to do that +the next time you have some + +free time on your hands, maybe +at IAP or some time like that. + +All right, so let's move +into today's notes. + +Today we're talking about +molecular orbital theory. + +This is a shift, this is a new +topic that we're starting. + +So far we've exclusively been +using Lewis structures any + +time we've tried to describe +bonding within molecules. + +Lewis structures are really +useful, we use them all the + +time in chemistry. + +And they're useful because, +first of all, they're easy to + +depict, they're easy to draw -- +relatively easy once we get + +all the rules down. + +And also they're accurate +over 90% of the time. + +But they're not accurate all the +time in predicting bonding + +within molecules, and the reason +for this is because + +Lewis structures are +not, in fact, + +based on quantum mechanics. + +So, molecular orbital theory, on +the other hand, is based on + +quantum mechanics. + +And specifically, MO theory +is the quantum mechanical + +description of wave functions +within molecules. + +So, saying wave functions within +molecules might sound a + +little confusing, but remember +we spent a lot of time talking + +about wave functions within +atoms, and we know how to + +describe that, we know that a +wave function just means an + +atomic orbital. + +It's the same thing with +molecules -- a molecular wave + +function just means a +molecular orbital. + +So, we'll start today talking +about the two kinds of + +molecular orbitals, we can +talk about bonding or + +anti-bonding orbitals. + +Then we're going to actually +use MO theory to describe + +bonding within these molecules, +and we'll start + +with homonuclear diatomic +molecules. + +Diatomic mean it's di atomic, +it's made up of two atoms, and + +homonuclear means that those two +are the same atoms. Then + +at the end, we'll look at an +example with a heteronuclear + +diatomic molecules. + +So, again, the same thing, but +now two different atoms. + +So, I will point out, in terms +of MO theory, because it + +rigorously does take into +account quantum mechanics, it + +starts to become complicated +once we go + +beyond diatomic molecules. + +So we're going to limit in our +discussion in 511-1 for + +molecular orbital theory +to diatomic molecules. + +However, on Friday we will use a +different approach so we can + +talk about bonding within atoms +that have more than two + +atoms, molecules with +more than two atoms. + +All right, so one thing that I +first want to point out about + +MO theory that is a big +difference from Lewis + +structures, is that in MO theory +valence electrons are + +de-localized over the +entire molecule. + +So, when we talked about Lewis +structures, we actually + +assigned electrons to individual +atoms or to + +individual bonds. + +Whereas in molecular orbital +theory, what I'm telling you + +is instead we understand that +the electrons are spread all + +over the molecule, they're not +just associated with a single + +atom or a single bond. + +So specifically, what we do +associate them instead is + +within molecular orbitals, and +what we say is that they can + +be either in bonding or +anti-bonding orbitals. + +And again, I want to point out +that a molecular orbital, we + +can also call that +a wave function, + +they're the same thing. + +And these orbitals arise from +the combination of individual + +atomic orbital. + +So, if we have two atomic +orbitals coming together from + +two different atoms and they +combine, what we end up + +forming is a molecular +orbital. + +The reason that we can talk +about this is remember that + +we're talking about wave +functions, we're talking about + +waves, so we can have +constructive interference in + +which two different orbitals can +constructively interfere, + +we can also have destructive +interference. + +So, we'll start by taking +a look at constructive + +interference, and another way to +explain this is just to say + +again, molecular orbitals +are a linear + +combination of atomic orbitals. + +So, let's start our discussion +of a bonding orbital. + +Our simplest case that we can +look at would be if we had two + +1 s orbitals coming together. + +So let's say, for example, +in a hydrogen atom. + +So in hydrogen atom a, I'll +depict that here where the + +nucleus is this dot, and then +the circle is what I'm + +depicting as the +wave function. + +It makes sense to draw the wave +function as a circle, + +because we do know +that 1 s orbitals + +are spherically symmetric. + +So, we can say that a circle is +a good approximation for a + +1 s wave function. + +Similarly, with the second +hydrogen atom, we've got the + +nucleus in the middle, and the 1 +s b wave function around it. + +So these are atomic orbitals. + +What we're going to do in +forming a molecule is just + +bring these two orbitals close +together such that now we have + +their nucleus, the two nuclei, +at a distance apart that's + +equal to the bond length. + +And what we end up forming is +a molecular orbital, because + +as we bring these two atomic +orbitals close together, the + +part between them, that wave +function, constructively + +interferes such that in our +molecular orbital, we actually + +have a lot of wave function +in between the two nuclei. + +So we can go ahead and name our +molecular orbital, just + +like we know how to name +our atomic orbitals. + +And I'm going to name +this sigma 1 s. + +The 1 s just comes from the +fact that the molecular + +orbital is a combination of +two 1 s atomic orbitals. + +And the sigma tells us something +about the symmetry + +of this molecular orbital, +specifically that it's + +cylindrically symmetric +about the bond axis. + +So that is the bond axis -- it's +just the axis between the + +two nuclei. + +Sometimes it's also called +the internuclear axis. + +So any time you have two atoms +bonding, the bond axis is just + +the axis that they're +bonding along. + +Another thing I want to point +out about every sigma orbital + +that you see, and it will make +more sense when we contrast it + +with pi orbitals later. + +But in sigma orbitals, you have +no nodal planes along the + +bond axis, so if we had a nodal +plane here, we'd see an + +area where the wave function +was equal to zero. + +We don't see that. + +It will make more sense when we +can show you one where it + +does have that area. + +But keep in mind sigma orbitals +have no nodal planes + +along the bond axis. + +All right. + +So, let's look at this in +another way, sometimes it's + +hard to picture these +waves combining. + +So let's think of them a little +bit more by graphing + +the amplitude of the wave, and +seeing how we can have this + +constructive interference. + +So again, if we think of a graph +of the wave function, we + +had the wave function is at +its highest amplitude when + +it's lined up with the nucleus, +and then as we got + +further away from the nucleus, +the amplitude of the wave + +function ends up tapering off +until -- it never hits zero + +exactly, but it goes +down very low. + +So we can draw that for 1 s a, +we can also draw it for 1 s b, + +and what I'm saying for the +molecular wave function is + +that we have the interference +between the two, and we have a + +constructive interference, so +we end up adding these two + +wave functions together. + +So, we're talking about wave +functions and we know that + +means orbitals, but this is -- +probably the better way to + +think about is the physical + +interpretation of the wave function. + +So what is the wave function +squared going to be equal to? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Probability +density, yes. + +Probability density of finding +an electron within that + +molecule in some given volume. + +So let's think about that +instead, let's think about + +probability density. + +So if we're talking about +probability density that's the + +wave function squared. + +But now we're talking not about +an atomic wave function, + +we're talking about a molecular +wave function. + +So to talk about it's squared, +we're going to say it's sigma + +1 s squared. + +Oh, and actually before you skip +your page in the notes, I + +realized I should write out for +you what the addition is + +to start with. + +So, when we're combining two +waves, what we have is 1 s a + +that we're adding together +with 1 s for + +b, the second atom. + +And what we end up for +our molecular wave + +function is sigma 1 s. + +So this is what we call +our molecular orbital. + +All right, so that will now +allow you to turn the page, I + +think, and we can take a look +at the probability. + +So the probability again, +that's just the orbital + +squared, the wave function +squared. + +So when we write that out, we +just write sigma 1 s squared, + +or we can break it up into its +individual parts, there's no + +reason we can't do +that as well. + +So just to say that it's 1 s +squared plus 1 s b, all of + +that together squared. + +So if we write out every term +individually, what we end up + +with is essentially just the +probability density for the + +first atom, then the probability +density for the + +second atom, and then we have +this last term here, and this + +is what ends up being the +interference term. + +So in this case where we're +adding it together, this is + +going to be constructive +interference. + +So in this case the cross term +represents constructive + +interference between the two +1 s atomic wave functions. + +And this again is what +we're going to + +call a bonding orbital. + +So it can often make a lot more +sense if we think about + +things in terms of energy. + +We've been discussing energy +diagrams a lot in this class, + +it's a very good way to +visualize exactly + +what's going on. + +So, let's think of the energy +of interaction when we're + +comparing atomic orbitals to +molecular bonding orbitals. + +And what you find is when you +have a bonding orbital, the + +energy decreases compared +to the atomic orbitals. + +So you can see here in this +slide we have the atomic + +orbitals for the two hydrogen +atoms, each of them have one + +electron in them, hydrogen has +one electron in a 1 s orbital. + +So, if we look at the molecular +orbital, that's + +actually going to be lower in +energy than either of the two + +atomic orbitals. + +So it's going to be favorable +for the electrons instead to + +go to that lower energy +state and be within + +the molecular orbital. + +So, let's draw in our electrons +there, so we have + +our two electrons now in +the molecular orbital. + +So any time that you're drawing +these molecular + +orbital diagrams, you want to +keep in mind that the number + +of electrons that you have in +atomic orbitals, you need to + +add those together +and put that many + +electrons into your molecule. + +Right, we had one from each +atom, so that means we need a + +total of two in our +molecular orbital. + +And what you can see directly +from looking at this energy + +level diagram, is that the +molecule that we have is now + +more stable in the individual +atoms. That makes sense + +because we're lower in energy, +the electrons are + +now lower in energy. + +So that's the idea of a bonding +molecular orbital. + +Since we're talking about wave +functions, since we're talking + +about the properties of waves, +we don't only have + +constructive interference, we +can also imagine a case where + +we would have destructive +interference. + +Just like we see destructive +interference with water waves + +or with light waves, we can +also see destructive + +interference with orbitals. + +So, let's think about what +that would look like. + +So in this case we would have +1 s a and 1 s b, and instead + +we would subtract one from the +other, and what we would see + +is that instead of having +additional, more wave function + +in the middle here, we've +actually cancelled out the + +wave function and we +end up with a node. + +So we can also name this +orbital, and this orbital + +we're going to call +sigma 1 s star. + +So if we name this orbital, +this is an anti-bonding + +molecular orbital. + +So we had bonding and now +we're talking about + +anti-bonding. + +When we talk about anti-bonding, +essentially + +we're taking 1 s a and now we're +subtracting 1 s b, and + +what we end up with again is +sigma 1 s, and the important + +thing to remember is to +write this star here. + +So any time you see a +star that means an + +anti-bonding orbital. + +Again we can look at this in +terms of thinking about a + +picture this way, in terms of +drawing the wave function out + +on an axis. + +So we have 1 s a, and we're +drawing this as having a + +positive amplitude, but since +we have destructive + +interference we're going to +draw 1 s b as having the + +opposite sign, so we +have a plus and a + +minus in terms of signs. + +So that should make it very easy +to picture that this is + +being cancelled out +in the middle. + +If we overlay what the actual +molecular orbital is on top of + +it, what you see is that in +the center you end up + +cancelling out the wave +function entirely. + +So this is the 1 s star, sigma 1 +s star orbital, and what you + +have in the center here is a +node, right in the center + +between the two nuclei. + +So again if we look at this +in terms of its physical + +interpretation or probability +density, what we need to do is + +square the wave function. + +So if we square sigma 1 s star, +we flip the amplitude so + +it's all positive now, but again +we still have this node + +right in the middle. + +So if we talk about the +probability density and we + +write that in, it's going to be +sigma 1 s star squared, so + +now we're talking about +1 s a minus 1 s b, all + +of that being squared. + +And again, if we write out what +all the terms are, we + +again have 1 s a squared plus +1 s b squared, but now what + +we're doing is we're actually +subtracting the + +interference term. + +So if we're subtracting the +interference term, what we + +have here now is destructive +interference. + +So let's think about the energy +of interaction here. + +When we were talking about +constructive interference, we + +had more electron density +in between the 2 nuclei. + +So that lowered the energy +of the molecular orbital. + +So, bonding orbitals +are down here. + +But when we think about where +anti-bonding orbitals should + +be, it should be higher +in energy. + +It's increased compared to +the atomic orbitals. + +So we would label our +anti-bonding orbital higher in + +energy than our 1 s +atomic orbitals. + +So, let's think a little bit +about what this means. + +First of all, again to repeat, +any time we see the star, + +sigma 1 s star, that's an +anti-bonding orbital. + +When we talk about that, +basically what we're saying, + +and you can see that because of +that negative interference, + +we actually have less electron +density between the nuclei + +than we did when they were two +separate atoms. So you can see + +that this is non-bonding, +this is even worse than + +non-bonding, it's anti-bonding, +because we're + +actually getting rid of electron +density between the + +two nuclei. + +And we know that it's electron +density between the nuclei + +that holds two atoms +together in a bond. + +So what I want to point out is +that it creates an effect that + +is exactly opposite of a bond. + +You might have thought before +we started talking about + +molecular orbital theory that +non-bonding was the opposite + +of bonding, it's not, +anti-bonding is the opposite + +of bonding, and anti-bonding +is not non-bonding. + +We can see that if we just look +at this picture here. + +Here is bonding, and here +is non-bonding. + +Anti-bonding is even higher in +energy than non-bonding. + +And the other thing to point out +is that the energy that an + +anti-bonding orbital is raised +by, is the same amount as a + +bonding orbital is lowered by. + +So any time I draw these +molecular orbitals, I do my + +best, and I'm not always +perfect, yet trying to make + +this energy different exactly +the same for the anti-bonding + +orbital being raised, +versus the bonding + +orbital being lowered. + +So those should be raised and +lowered by the same energy. + +So now let's take a look +at some of -- is there + +a question up there? + +STUDENT: Why would two atoms +decide to [INAUDIBLE]. + +PROFESSOR: Well, they +don't want to. + +It's a higher energy +situation. + +So we'll start to look at +molecules and we'll see if we + +take two atoms and we fill in +our molecular orbital and it + +turns out that they have more +anti-bonding orbitals than + +bonding, that's -- a diatomic +molecule we'll never see. + +So it helps us predict, will we +see this, for example, h 2, + +which we're going to be about to +do, we'll see is stabilized + +because it has more bonding +than anti-bonding. + +So we'll predict, yes, +there's a bond here. + +That's a really good question. + +So, let's go ahead and do this +and take a look at some of the + +actual atoms that we can +think about and think + +about them in molecules. + +So our simplest case that we +started talking about was + +molecular hydrogen. + +I want to finish this discussion +by including the + +anti-bonding orbital, and this +is a tip for you when you're + +drawing your molecular orbital +diagrams, any time you draw a + +bonding orbital, there is +also an anti-bonding + +orbital that exists. + +It might not have any electrons +in it, but it still + +exists, so you need to draw +these into your molecular + +orbital diagram. + +So I wanted to make sure you +have a complete set for + +hydrogen in your notes. + +So let's take a look at this. + +Hydrogen, we can first draw +in our atomic electrons. + +So there's one electron +in each hydrogen atom. + +And then this means we'll have +a total of two electrons in + +our hydrogen molecule, so we +can fill both of those into + +the sigma 1 s orbital, +the bonding orbital. + +We don't have to put anything +into the anti-bonding orbital, + +so that's great. + +What we've seen is we have a net +lowering of energy of the + +molecule versus the +individual atoms. + +So let's draw the electron +configuration of hydrogen, the + +molecule, molecular hydrogen. + +What you saw, what we've done +a lot of is drawing the + +electron configurations for +different atoms, we can do the + +same thing for a molecule. + +So, if we take h 2, and we +want to draw the electron + +configuration, it's +very short. + +All it is sigma 1 s, and then +we have two electrons in it, + +so it's sigma 1 s squared. + +So this is our electron +configuration. + +Let's take a look at +another example. + +Let's draw the molecular +diagram for h e 2 now. + +So again, we can fill in our +atomic orbitals here, there's + +going to be two electrons in +each of our atomic orbitals. + +So now let's go ahead and fill +in our molecular orbitals. + +We need to fill in a total +of four electrons. + +So we have two electrons in +our bonding orbital, but + +because we use the same rules to +fill up molecular orbitals + +as we do atomic orbitals, so the +Pauli exclusion principle + +tells us we can't have more +than two electrons per + +orbital, so we have +to go up to our + +anti-bonding orbital here. + +So this means that we have two +of the electrons are lowered + +in energy, but two are +raised in energy. + +So would this be a stabilized +molecule then? + +STUDENT: [INAUDIBLE] + +PROFESSOR: No. + +So, compared to the atoms, it +should be somewhat the same + +energy, we shouldn't get any +extra stabilization from + +forming the molecule. + +So lets go ahead and write +what the electron + +configuration would +be of h e 2. + +And again, we're just filling in +the different orbitals, so + +we have sigma 1 s, that's going +to be squared, and now + +we have sigma 1 s +star squared. + +So we can compare the two +electron configurations, and + +we can actually think about -- +what we figure out from them, + +we see that two are lowered in +energy, two electrons are + +raised in energy, so we have no +net gain or no net loss in + +energy for h e 2. + +And there's actually a way that +we can make predictions + +here, and what I'll tell you +is molecular orbital theory + +predicts that h e 2 does not +exist because it's not + +stabilized in terms of +forming the molecule. + +The way that we can figure this +out is using something + +called bond order, and bond +order is equal to 1/2 times + +the number of bonding electrons, +minus the number of + +anti-bonding electrons. + +And the bond order you get out +will either be, for example, + +zero, which would mean that you +have no bond, or you could + +have 1, a single bond, 1 . + +5, a 1 and 1/2 bond, 2, a +double bond, and so on. + +So let's figure out the bond +order for our two molecules + +here that we figured out the +electron configuration for. + +So I guess we'll start +with helium 2. + +So the bond order is going to +be equal to 1/2, and then it + +will be 2 minus 2. + +So our bond order for h e 2 +is going to be equal to 0. + +So it has a 0 bond, there's +no bond in h e 2. + +Let's look for hydrogen. + +For hydrogen our bond order is +going to equal 1/2, 2 minus 0. + +So we would predict +a bond order of 1. + +What kind of a bond is +a bond order of 1? + +Yeah, we'd expect to see a +single bond in hydrogen. + +So what actually turns out the +reality is that h e 2 does + +exist, but it exists as the +weakest chemical bond known, + +and it wasn't, in fact, even +found to exist until 1993, so + +I can assure you this is not a +bond that you see very often + +in nature, and it is a +very, very weak bond. + +It only has a dissociation +energy of 0 . + +1 kilojoules per mole. + +So that should make sense, +because we saw no energy + +difference between the actual +atoms and the molecules. + +Molecular orbital theory, even +at this very basic level, + +allowed us to predict that no, +we're not going to see a true + +bond here, a strong bond. + +In contrast, the dissociation +energy of a bond for hydrogen, + +and molecular hydrogen is +everywhere around us, we see + +432 kilojoules per mole. + +All right, so we can now see a +little bit of what the power + +of molecular orbital theory is +in predicting what kind of + +bonds we're going to see in +molecules, or whether or not + +we'll see this bonding +occur at all. + +So let's look at another +example, let's take lithium 2 + +and see what we can +figure out here. + +In lithium 2, we have two atoms +of lithium, each have + +three electrons in them. + +So now we have to include both +the 1 s orbitals and also the + +2 s orbitals. + +So any time in a molecular +orbital diagram you draw in + +orbitals, you need to draw the + +corresponding molecular orbitals. + +So, this means we need to have +sigma 1 s, sigma 1 s star, and + +now sigma 2 s and +sigma 2 s star. + +Something I'll also point out +as you see these dashed line + +that tell you where the +individual molecular orbitals + +are arising from, as you get +to higher and higher atomic + +numbers of molecules that you're +making, it makes a lot + +more sense to look at a diagram +when you draw these + +dotted lines in, because +they can start to get + +a little bit confusing. + +So when you go ahead and draw +these on your problem-sets or + +on your exams, it's a good idea +to put these dashed lines + +in, both for you and for people +reading it to see + +exactly where your molecular +orbitals are coming from. + +So, this means we have a total +of six electrons that we need + +to put into molecular +orbitals. + +So again we just start filling +those up -- we have two in the + +1 s, two in the sigma 1 s star, +and then we have two in + +the sigma 2 s. + +So we should be able to also +calculate the bond order, just + +like we did for hydrogen +and helium. + +First we can do that by +knowing the electron + +configuration, we can write it +out just by going up the table + +here, up the energy levels. + +And you can go ahead and tell +me what you think the bond + +order is going to be +for this molecule. + +All right. + +Let's take 10 more +seconds on this. + +OK, good, we're back on +track a little bit + +with our clicker answers. + +So it's selection three or +one is the bond order. + +So let's switch back to our +class notes and look at what + +this means. + +So we know that it's 1, because +we have 1, 2, 3, 4 + +bonding, minus 2 anti-bonding, +and 1/2 of that is a bond + +order of 1. + +We would predict to see a single +bond between lithium, + +and it turns out that's +what we see. + +And so you have for a reference, +the dissociation + +energy of lithium 2 is 105 +kilojoules per mole. + +So let's keep moving along the +periodic table and keep + +applying our molecular +orbitals. + +For example now, with b e 2, +so beryllium 2 has four + +electrons in terms +of each atom. + +So you can start by filling +those in, and now we can fill + +in our molecular orbitals +as well. + +This means we need a total +of eight electrons in our + +molecular orbitals. + +So we have two in 1 s, two in +the sigma 1 s star, two in the + +sigma 2 s, and two in +the sigma 2 s star. + +So let's go ahead and figure +out the bonding order for + +beryllium here. + +So when we figure it out for +beryllium -- let's see if I + +wrote in your notes what +the actual -- electron + +configuration, OK that's already +in your notes for you. + +So let's go right to the bond +order for beryllium. + +So for the bond order we want +to take 1/2 of the total + +number of bonding electrons, so +that's going to be 4 minus + +anti-bonding is 4, so we end up +getting a bond order that's + +equal to 0. + +So what I want to point out with +this case in beryllium is + +that you don't have to use all +of the electrons to figure out + +the bond order, and in fact, +once you get to molecules that + +are from atoms with atomic +numbers of 8 or 10, you're not + +going to want to maybe +draw out the full + +molecular orbital diagram. + +So what I want to tell you is +we also always get the same + +bond order if we instead +only deal + +with the valence electrons. + +So let's just prove that to +ourselves and figure out the + +bond order just using +valence electrons. + +So this would mean the bond +order is equal to 1/2, and in + +terms of valence electrons, +how many bonding valence + +electrons do we have? + +STUDENT: [INAUDIBLE] + +PROFESSOR: All right, what +about anti-bonding? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Two. + +OK, good. + +So again, we're going to +see that we have a + +bonding order of 0. + +So we would not predict +to see a b e 2 bond. + +So what we see is a bond order +of 0, and again, the bond is + +very, very weak. + +Essentially we're not going +to see this, it's 9 + +kilojoules per mole. + +All right. + +So, so far we've looked only +at molecules that involve + +atoms that have only +s orbitals in them. + +I'm sure you're thinking well, +what do we do in the case of p + +orbitals, and, in fact, we +can do the same thing. + +Again, we're going to take the +linear combination of those p + +atomic orbitals and make what +are called pi or some more + +sigma molecular orbitals. + +So let's look at the first case +where we have either the + +2 p x or 2 p y type of orbitals +that we're combining. + +So they're the same shape, +this is the shape of the + +orbital or the shape of the wave +function, and we can call + +this either 2 p x a being +combined with 2 p x b, or we + +could say since it's the same +shape, it's 2 p y a being + +combined with 2 p y b. + +And in either case if we first +talk about constructive + +interference, what again we're +going to see is that where + +these two orbitals come +together, we're going to see + +increased wave function in +that area, so we saw + +constructive interference. + +So again, we can name these +molecular orbitals and these + +we're going to call -- also to +point out there is now a bond + +axis along this nodal plane, +which is something we didn't + +see before when we were +combining the s orbitals. + +So when we go ahead and name +these, we're going to call + +these pi orbitals. + +We'll call it either pi 2 p x, +if we're combining the x + +orbitals, or pi 2 p y. + +The reason that I wanted to +point out this nodal plane + +here is because this is why +it is called a pi orbital. + +Pi orbitals are a molecular +orbital that have a nodal + +plane through the bond axis. + +Remember this is our bond axis +here, and you can see there is + +this area where the wave +function is equal to zero all + +along that plane, that's +a nodal plane. + +So that's why these +are pi orbitals + +instead of sigma orbitals. + +So again, we can think about +the probability density in + +terms of squaring the +wave function. + +So now what it is that we're +squaring is if we're talking + +about x orbital, it's pi 2 p +x squared, and this is just + +equal to the 2 p x a plus the 2 +p x b all squared, or if we + +write out all of the terms we +have 2 p x a squared plus 2 p + +x b squared, and then this term +here, and again, this is + +our interference term. + +In this case is it constructive +or destructive + +interference? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Constructive +interference. + +We're seeing that the wave +function's adding together and + +giving us more wave function +in the center here. + +All right. + +So we see constructive +interference, of course, we + +can also see destructive +interference. + +So I changed the colors here +to show that these are 2 p + +orbitals with an opposite phase +or an opposite sign. + +So what happens when we add a 2 +p a and we subtract from it + +a 2 p x b, or the same with a 2 +p y a subtracting a 2 p y b, + +is that we're actually going +to cancel out the wave + +function in the center, so we +now have 2 nodal planes. + +So again, this is an +anti-bonding orbital, and what + +you see is that there is now +less electron density between + +the two nuclei than there was +when you had non-bonding. + +So we're going to call this the +sigma 2 p x star, or if + +we're talking about the 2 p y +orbitals we'll call this the + +pi 2 p x star, and the +pi 2 p y star. + +And the pi star orbitals result +from any time you have + +destructive interference from +2 p orbitals that are either + +the p x or the p y. + +So now we can move on to an +example where we do, in fact, + +have to use some p orbitals, +so this would be b 2. + +How many electrons +are in boron? + +Five. + +I see some hands going up. + +There's five electrons So what +you'll notice here is that I + +only filled in 3 electrons. + +What do these electrons +represent? + +STUDENT: Valence. + +PROFESSOR: Valence electrons. + +OK, sometimes you're going to +be asked to draw a molecular + +orbital diagram where you're +asked to include all + +electrons, and sometimes it +will specifically say only + +include valence electrons. + +That happens because of space +issues that you were asked to + +do that, because you can always +assume that all of the + +core orbitals are already +going to be filled. + +So, in this case, we're just +drawing the molecular orbital + +diagram for the valence +electrons, so we + +have three for each. + +And what we see here is now when +we're combining the p, we + +have our 2 p x and our 2 p y +orbitals that are lower in + +energy, and then our pi +anti-bonding orbitals that are + +higher in energy. + +You might be asking where the 2 +p z orbital is and we'll get + +to that soon once we need it. + +Let's just first fill in +this for the b 2 case. + +So we can start at the bottom, +two electrons in sigma 2 s, + +two electrons in +sigma 2 s star. + +Now we need to jump up to using +these pi orbitals, and + +what we're going to do is put +one electron into each of our + +pi 2 p x and 2 p y orbitals. + +So again you can see as we're +filling up our molecular + +orbitals, we're using the exact +same principle we used + +to fill up atomic orbitals. + +So let's think about what +the valence electron + +configuration is here. + +So now we're looking +at the case of b 2. + +And what we're looking at is a +valence electron molecular + +orbital diagram, so let's +just draw the electron + +configuration for the valence +orbitals, so that will be + +sigma 2 s 2, sigma 2 s star 2, +and now we start in with our + +pi 2 p x 1, and our +pi 2 p y 1. + +So this is our valence electron + +configuration for b 2. + +All right. + +So what would you expect the +bonding order for b 2 to be? + +Shout it out if you know. + +STUDENT: one. + +PROFESSOR: And I didn't write up +there but it is one, and we + +can see that it's 1, because +it's 1/2 of 2, 4 minus 2, so + +1/2 of 2, the bonding order is +going to be equal to one. + +So let's move on to another +example, let's talk about + +carbon here. + +Again, we're just talking about +the valence electrons. + +So carbon has four valence +electrons, so if we talk about + +c 2, again we're going to start +filling in our molecular + +orbitals, and now we're going +to have eight electrons to + +fill into our molecular +orbitals. + +So, we'll put two in the sigma +2 s, two in the sigma 2 s + +star, and now we're going to +fill one and one into each of + +our pi 2 p x and 2 p y, but we +still have two electrons left, + +so what we're going to do is +double up in terms of our 2 p + +x and our 2 p y. + +So let's think about what this +valence electron configuration + +is for c 2. + +And again, I want you to have +practiced drawing these out in + +the form -- you always need to +start with the sigma and then + +write the number +of the orbital. + +So, sigma 2 s has two electrons, +sigma 2 s star with + +two electrons, and now we have +sigma 2 p x -- how many + +electrons here? + +STUDENT: Two. + +PROFESSOR: Two. + +And sigma 2 p y, two +electrons here. + +Oh excuse me, pi 2 p y, thank +you -- pi 2 p x and pi 2 p y. + +So let's talk about what +the bonding order is + +going to be for c 2. + +So what's the bonding +order for c 2? + +STUDENT: Two. + +PROFESSOR: two? + +OK, so we have 2, 4, 6 minus 2, +so we have 1/2 of 6 minus + +2, so that's 1/2 half 4, so we +have a bonding order of two + +for carbon 2. + +So we would expect to see a +double bond for a c 2 where we + +would expect to see a -- double +bond for c 2 and a + +single bond for b 2. + +And that is, in fact, what we +can surmise if we look at the + +different dissociation energies +for the two bonds. + +So for b 2, which is a single +bond, that's 289 kilojoules + +per mole to break it, and it +takes us more energy to break + +this double bond for carbon, +which is 599 + +kilojoules per mole. + +So, in general what we see, +and this is always true if + +we're comparing the same atom, +and in general, if we're + +comparing different types of +molecules, but we know that a + +single bond is always weaker +than a double bond, which is + +weaker than a triple bond. + +And obviously, no bond is the +weakest of all is not bonding. + +All right. + +So let's look now at the case +where we do have 2 p z + +orbitals that we're +talking about. + +So again, what we're talking +about is the linear + +combination of atomic 2 p +orbitals, and now we're + +talking about 2 p z. + +So if we have constructive +interference between the two, + +what we're going to see is our +molecular orbital looks + +something like this. + +Do you predict that this will +be a sigma or a pi orbital? + +STUDENT: [INAUDIBLE] + +PROFESSOR: All right, I'm +hearing a little of both, but + +I'm very encouraged to +hear quite a few + +people saying sigma. + +This is, in fact, a sigma +2 p z orbital is what + +this orbital is called. + +The reason that it's sigma is +if you look at the bonding + +axis here, is that there +is no nodal plane + +along the bonding axis. + +Also, it is cylindrically +symmetric around the bonding + +axis, so this is how we know +that it's a sigma orbital. + +So some p orbitals form pi +molecular orbitals, and some + +form sigma p orbitals. + +Specifically, it's always the +z that forms the sigma + +orbital, and the reason is at +least at a minimum for this + +class we always define the +internuclear axis as the z + +axis, so this is always the z +axis, so it's always going to + +be the 2 p z's that are coming +together head-on. + +The reason that there is +increased electron density + +here is you can see that these +two orbitals come together and + +constructively interfere. + +We can also talk about +anti-bonding orbitals where we + +have destructive interference. + +So instead, these would be +canceling out wave functions + +between the two, so we would end +up with a nodal plane down + +the center. + +Would this be a sigma or a pi? + +It's still sigma. + +So even though we see a nodal +plane down the center, I just + +want to really point out that +it's only when we have a nodal + +plane in the internuclear or +the bond axis that we're + +calling that a pi orbital. + +So this is still a +sigma -- it's a + +sigma 2 p z star orbital. + +We have destructive +interference here. + +So now let's look at an example +where we talk about + +using these 2 p z orbitals, +so let's look at oxygen. + +So the first thing I want to +point out is that the 2 p z, + +the sigma 2 p z is even lower in +energy than the pi orbitals + +here, and the anti-bonding sigma +orbital is going to be + +higher in energy than the pi 2 +p orbitals that we have here. + +So in oxygen again, this is +just showing the valence + +electrons, so we end up having +six valence electrons from + +each oxygen atom. + +We can fill right up our table +just like we did before, but + +now we have included our +2 p z orbital here. + +So we have two electrons in +sigma 2 s, two in sigma 2 s + +star, in sigma 2 p z we have two +-- those are filled first, + +and now we're going to put +one into pi 2 p x, and + +one into pi 2 p y. + +So we can write out what the +electron configuration is + +here, and I think that I have +already written that out for + +you in your notes. + +What is the bond order of o 2? + +It's two. + +Oh excuse me, I didn't fill +in all of my electrons. + +All right. + +So we had a total +of 2, 4, 6, 8. + +So we had a total of 12. + +So we filled in four here -- +we need to keep going. + +All right, so I did this not at +all purposely, but this can + +point out for you that you need +to make sure that the + +number of electrons that you +have in your molecular orbital + +does match up with the total +number that you have in your + +atomic orbitals. + +So I did not do any counting up +here, you should make sure + +you do counting, I apologize. + +So we need to fill all the +way up to the pi 2 p x, + +and the pi 2 p y. + +All right, so the bonding order, +you're correct, should + +be 2, if we subtract the +number of bonding minus + +anti-bonding electrons +and take that in 1/2. + +And what I want to point out +that we just figured out for + +molecular orbital theory, is +that o 2 is a biradical, + +because remember, the definition +of a radical is + +when we have an unpaired +electron. + +You can see that we have two +unpaired electrons in this + +molecule here -- one in the pi +2 p x star, and one in the pi + +2 p y star orbital. + +This was something we could +not predict using Lewis + +structures, but we can predict +using MO theory that we have a + +radical species here. + +So that's a really important +type of an application that we + +can use MO theory for that we +weren't able to do with our + +Lewis structures. + +All right, I want to do one more +at homonuclear example + +here, and this is n 2. + +The first thing that I need to +point out is you can actually + +see an n 2 versus o 2 that we +flip-flopped the energy of the + +sigma and the pi 2 p orbitals. + +So this is a glitch, just like +sometimes we had glitches in + +filling up our atomic +orbitals. + +This is something that +you need to remember. + +And what you need to remember is +if the z is equal to eight + +or greater, such as oxygen being +the cut-off point, this + +sigma 2 p orbital is actually +lower in energy than the pi 2 + +p orbitals, the molecular +orbitals. + +But for anything 7 or +less, so what is the + +atomic number for nitrogen? + +STUDENT: Five. + +PROFESSOR: five -- there's five +valence electrons, but + +the atomic number is +actually seven. + +So z equals 7 -- this is the +cut-off where, in fact, the + +sigma orbital is going to be +higher in energy than the pi 2 + +p orbitals. + +This is something that you +just need to remember. + +I wrote it down your notes, if +you can put a big star next to + +it so you don't forget this. + +This is something you're going +to be responsible for in + +drawing out your molecular +orbitals. + +So let's fill it out in this +way, keeping in mind that + +we're going to fill out the +pi 2 p's before the sigma. + +So we have a total of 2, 4, 6, +8, 10 valence electrons, so + +I'll make sure I count to 10 +as we fill up our molecular + +orbitals here. + +We have two, then +we have four. + +Now we're going to start in +with that pi 2 p orbitals, + +which gives us 1 each, and then +two each in those, and + +then after that, we'll go up +to our sigma 2 p z orbital. + +So this is going to be our +molecular orbital diagram. + +And again, I've written for you, +but you can figure out + +what the electron configuration +is just by + +writing up in this order here. + +And what is the bond order +going to be n 2? + +STUDENT: [INAUDIBLE] + +PROFESSOR: It's going +to be three. + +So, you can go ahead and +calculate that, if you can't + +see that right away. + +So we'll end here, we'll +finish up with the + +heteronuclear example +on Friday. \ No newline at end of file diff --git a/lw5ka_lJFkU.txt b/lw5ka_lJFkU.txt new file mode 100644 index 0000000000000000000000000000000000000000..c8add45f2b20b74b355c8b8130f743a0847d2382 --- /dev/null +++ b/lw5ka_lJFkU.txt @@ -0,0 +1,2179 @@ +align:start position:0% + +so here it is connections for connection + + align:start position:0% + + + + align:start position:0% + +so we'll take a situation as follows + + align:start position:0% +so we'll take a situation as follows + + + align:start position:0% +so we'll take a situation as follows +here is the point of X equals a output + + align:start position:0% +here is the point of X equals a output + + + align:start position:0% +here is the point of X equals a output +just a here here is the x-axis and I + + align:start position:0% +just a here here is the x-axis and I + + + align:start position:0% +just a here here is the x-axis and I +will imagine that I have a linear + + align:start position:0% +will imagine that I have a linear + + + align:start position:0% +will imagine that I have a linear +potential so we have a linear potential + + align:start position:0% +potential so we have a linear potential + + + align:start position:0% +potential so we have a linear potential +here why do we imagine a linear + + align:start position:0% +here why do we imagine a linear + + + align:start position:0% +here why do we imagine a linear +potential it's because the thing we + + align:start position:0% +potential it's because the thing we + + + align:start position:0% +potential it's because the thing we +would really kind of want to think about + + align:start position:0% +would really kind of want to think about + + + align:start position:0% +would really kind of want to think about +he said what is called the turning point + + align:start position:0% +he said what is called the turning point + + + align:start position:0% +he said what is called the turning point +energy and a potential there's a turning + + align:start position:0% +energy and a potential there's a turning + + + align:start position:0% +energy and a potential there's a turning +point but it's clear that near enough to + + align:start position:0% +point but it's clear that near enough to + + + align:start position:0% +point but it's clear that near enough to +the turning point this is linear and the + + align:start position:0% +the turning point this is linear and the + + + align:start position:0% +the turning point this is linear and the +problem for the wkb approximation fails + + align:start position:0% +problem for the wkb approximation fails + + + align:start position:0% +problem for the wkb approximation fails +as we discuss is precisely in this + + align:start position:0% +as we discuss is precisely in this + + + align:start position:0% +as we discuss is precisely in this +region now I will make one claim that + + align:start position:0% +region now I will make one claim that + + + align:start position:0% +region now I will make one claim that +this is really what's going to connect + + align:start position:0% +this is really what's going to connect + + + align:start position:0% +this is really what's going to connect +here these two asymptotic expansions + + align:start position:0% +here these two asymptotic expansions + + + align:start position:0% +here these two asymptotic expansions +that we found here are in fact wkb + + align:start position:0% +that we found here are in fact wkb + + + align:start position:0% +that we found here are in fact wkb +approximation of our calculation so our + + align:start position:0% +approximation of our calculation so our + + + align:start position:0% +approximation of our calculation so our +whole procedure here is going to be + + align:start position:0% +whole procedure here is going to be + + + align:start position:0% +whole procedure here is going to be +assuming that we have a linear potential + + align:start position:0% +assuming that we have a linear potential + + + align:start position:0% +assuming that we have a linear potential +here and I will take the linear + + align:start position:0% +here and I will take the linear + + + align:start position:0% +here and I will take the linear +potential seriously so I will imagine it + + align:start position:0% +potential seriously so I will imagine it + + + align:start position:0% +potential seriously so I will imagine it +even goes forever and what we're going + + align:start position:0% +even goes forever and what we're going + + + align:start position:0% +even goes forever and what we're going +to do is find away from the turning + + align:start position:0% +to do is find away from the turning + + + align:start position:0% +to do is find away from the turning +point so the energy is going to be here + + align:start position:0% +point so the energy is going to be here + + + align:start position:0% +point so the energy is going to be here +here is V of X X V of X the energy and + + align:start position:0% +here is V of X X V of X the energy and + + + align:start position:0% +here is V of X X V of X the energy and +then we have this region + + align:start position:0% +then we have this region + + + align:start position:0% +then we have this region +which is a wkb region region and we have + + align:start position:0% +which is a wkb region region and we have + + + align:start position:0% +which is a wkb region region and we have +this region over here that is also a wkb + + align:start position:0% +this region over here that is also a wkb + + + align:start position:0% +this region over here that is also a wkb +region and the region in the middle is + + align:start position:0% +region and the region in the middle is + + + align:start position:0% +region and the region in the middle is +not a wkb region is a region where all + + align:start position:0% +not a wkb region is a region where all + + + align:start position:0% +not a wkb region is a region where all +solutions fail wkb solutions fail + + align:start position:0% +solutions fail wkb solutions fail + + + align:start position:0% +solutions fail wkb solutions fail +they're not valid in this region so + + align:start position:0% +they're not valid in this region so + + + align:start position:0% +they're not valid in this region so +let's assume we have here therefore a + + align:start position:0% +let's assume we have here therefore a + + + align:start position:0% +let's assume we have here therefore a +potential that is linear and therefore V + + align:start position:0% +potential that is linear and therefore V + + + align:start position:0% +potential that is linear and therefore V +of X minus e of X minus the energy is + + align:start position:0% +of X minus e of X minus the energy is + + + align:start position:0% +of X minus e of X minus the energy is +going to be a number times X minus a + + align:start position:0% +going to be a number times X minus a + + + align:start position:0% +going to be a number times X minus a +where G is a positive constant it has + + align:start position:0% +where G is a positive constant it has + + + align:start position:0% +where G is a positive constant it has +some units V minus E is a linear + + align:start position:0% +some units V minus E is a linear + + + align:start position:0% +some units V minus E is a linear +function that vanishes at x equals a so + + align:start position:0% +function that vanishes at x equals a so + + + align:start position:0% +function that vanishes at x equals a so +this is a nice description of the + + align:start position:0% +this is a nice description of the + + + align:start position:0% +this is a nice description of the +situation and then + + align:start position:0% + + + + align:start position:0% + +you could write a wkb solution so what + + align:start position:0% +you could write a wkb solution so what + + + align:start position:0% +you could write a wkb solution so what +is your wkb solution let's write the wkb + + align:start position:0% +is your wkb solution let's write the wkb + + + align:start position:0% +is your wkb solution let's write the wkb +solution sigh wkb on the right and then + + align:start position:0% +solution sigh wkb on the right and then + + + align:start position:0% +solution sigh wkb on the right and then +we'll write a wkb solution on the left + + align:start position:0% +we'll write a wkb solution on the left + + + align:start position:0% +we'll write a wkb solution on the left +the right and left so here is what we + + align:start position:0% +the right and left so here is what we + + + align:start position:0% +the right and left so here is what we +know typical wkb solution on the right + + align:start position:0% +know typical wkb solution on the right + + + align:start position:0% +know typical wkb solution on the right +that is a forbidden region square root + + align:start position:0% +that is a forbidden region square root + + + align:start position:0% +that is a forbidden region square root +of Kappa of X you would have a decrease + + align:start position:0% +of Kappa of X you would have a decrease + + + align:start position:0% +of Kappa of X you would have a decrease +in exponential e to the minus a to X + + align:start position:0% +in exponential e to the minus a to X + + + align:start position:0% +in exponential e to the minus a to X +Kappa of X prime VX prime and then you + + align:start position:0% +Kappa of X prime VX prime and then you + + + align:start position:0% +Kappa of X prime VX prime and then you +have B over square root of Kappa of X e + + align:start position:0% +have B over square root of Kappa of X e + + + align:start position:0% +have B over square root of Kappa of X e +to the a to X cap of X prime DX prime so + + align:start position:0% +to the a to X cap of X prime DX prime so + + + align:start position:0% +to the a to X cap of X prime DX prime so +this is what you've been told is + + align:start position:0% +this is what you've been told is + + + align:start position:0% +this is what you've been told is +supposed to be your wkb approximation + + align:start position:0% + + + + align:start position:0% + +decay in exponential a prefactor growing + + align:start position:0% +decay in exponential a prefactor growing + + + align:start position:0% +decay in exponential a prefactor growing +exponential a pre factor and cap of x is + + align:start position:0% +exponential a pre factor and cap of x is + + + align:start position:0% +exponential a pre factor and cap of x is +something that you know from this + + align:start position:0% +something that you know from this + + + align:start position:0% +something that you know from this +potential so this you would write for + + align:start position:0% +potential so this you would write for + + + align:start position:0% +potential so this you would write for +any potential on the right are on the + + align:start position:0% +any potential on the right are on the + + + align:start position:0% +any potential on the right are on the +left as well and here your Kappa of x + + align:start position:0% +left as well and here your Kappa of x + + + align:start position:0% +left as well and here your Kappa of x +squared is 2 m over H squared V of X + + align:start position:0% +squared is 2 m over H squared V of X + + + align:start position:0% +squared is 2 m over H squared V of X +minus E + + align:start position:0% + + + + align:start position:0% + +that's the physician of Kappa squared + + align:start position:0% +that's the physician of Kappa squared + + + align:start position:0% +that's the physician of Kappa squared +you're in the region where V is greater + + align:start position:0% +you're in the region where V is greater + + + align:start position:0% +you're in the region where V is greater +than E and therefore this is equal to 2m + + align:start position:0% +than E and therefore this is equal to 2m + + + align:start position:0% +than E and therefore this is equal to 2m +g over H squared X minus a so our next + + align:start position:0% +g over H squared X minus a so our next + + + align:start position:0% +g over H squared X minus a so our next +step is a little calculation we should + + align:start position:0% +step is a little calculation we should + + + align:start position:0% +step is a little calculation we should +simplify all this quantities here we + + align:start position:0% +simplify all this quantities here we + + + align:start position:0% +simplify all this quantities here we +should evaluate them because we have a + + align:start position:0% +should evaluate them because we have a + + + align:start position:0% +should evaluate them because we have a +Kappa you have a linear function we can + + align:start position:0% +Kappa you have a linear function we can + + + align:start position:0% +Kappa you have a linear function we can +do the integrals we can put what Kappa + + align:start position:0% +do the integrals we can put what Kappa + + + align:start position:0% +do the integrals we can put what Kappa +is so everything can be done here so if + + align:start position:0% +is so everything can be done here so if + + + align:start position:0% +is so everything can be done here so if +we do it what do we get + + align:start position:0% +we do it what do we get + + + align:start position:0% +we do it what do we get +so evaluate we get the following now I + + align:start position:0% +so evaluate we get the following now I + + + align:start position:0% +so evaluate we get the following now I +will introduce some notation to write + + align:start position:0% +will introduce some notation to write + + + align:start position:0% +will introduce some notation to write +this so first I'll write it side right + + align:start position:0% +this so first I'll write it side right + + + align:start position:0% +this so first I'll write it side right +of xwk be equal 1 over square root of 8 + + align:start position:0% +of xwk be equal 1 over square root of 8 + + + align:start position:0% +of xwk be equal 1 over square root of 8 +that's a symbol I haven't defined yet + + align:start position:0% +that's a symbol I haven't defined yet + + + align:start position:0% +that's a symbol I haven't defined yet +due to the 1/4 e to the minus 2/3 u to + + align:start position:0% +due to the 1/4 e to the minus 2/3 u to + + + align:start position:0% +due to the 1/4 e to the minus 2/3 u to +the three-halves plus b square root of 8 + + align:start position:0% +the three-halves plus b square root of 8 + + + align:start position:0% +the three-halves plus b square root of 8 +a 1 over u to the 1/4 into the + + align:start position:0% +a 1 over u to the 1/4 into the + + + align:start position:0% +a 1 over u to the 1/4 into the +two-thirds u to the three-halves okay + + align:start position:0% +two-thirds u to the three-halves okay + + + align:start position:0% +two-thirds u to the three-halves okay +that's what you get you recognize the a + + align:start position:0% +that's what you get you recognize the a + + + align:start position:0% +that's what you get you recognize the a +and the B's and here is what we need to + + align:start position:0% +and the B's and here is what we need to + + + align:start position:0% +and the B's and here is what we need to +introduce a couple of variables to make + + align:start position:0% +introduce a couple of variables to make + + + align:start position:0% +introduce a couple of variables to make +sure we we know what every symbol is and + + align:start position:0% +sure we we know what every symbol is and + + + align:start position:0% +sure we we know what every symbol is and +here they are you is 8x minus a and ADA + + align:start position:0% +here they are you is 8x minus a and ADA + + + align:start position:0% +here they are you is 8x minus a and ADA +is 2m g over H squared to the 1/3 + + align:start position:0% + + + + align:start position:0% + +just roughly K squared is proportional + + align:start position:0% +just roughly K squared is proportional + + + align:start position:0% +just roughly K squared is proportional +to you so K is proportional to u to the + + align:start position:0% +to you so K is proportional to u to the + + + align:start position:0% +to you so K is proportional to u to the +one-half and therefore square root of K + + align:start position:0% +one-half and therefore square root of K + + + align:start position:0% +one-half and therefore square root of K +gives you the U to the 1/4 the integrals + + align:start position:0% +gives you the U to the 1/4 the integrals + + + align:start position:0% +gives you the U to the 1/4 the integrals +also work that way and you see already + + align:start position:0% +also work that way and you see already + + + align:start position:0% +also work that way and you see already +here + + align:start position:0% +here + + + align:start position:0% +here +things that look like the airy function + + align:start position:0% +things that look like the airy function + + + align:start position:0% +things that look like the airy function +and that will become even clearer soon + + align:start position:0% +and that will become even clearer soon + + + align:start position:0% +and that will become even clearer soon +so this is our solution for the wkb + + align:start position:0% +so this is our solution for the wkb + + + align:start position:0% +so this is our solution for the wkb +expression on the right but let's do + + align:start position:0% +expression on the right but let's do + + + align:start position:0% +expression on the right but let's do +also the wkb expression on the left + + align:start position:0% + + + + align:start position:0% + +the wkb expression on the left would be + + align:start position:0% +the wkb expression on the left would be + + + align:start position:0% +the wkb expression on the left would be +another wave of this kind but with + + align:start position:0% +another wave of this kind but with + + + align:start position:0% +another wave of this kind but with +cosines or with Exponential's that we've + + align:start position:0% +cosines or with Exponential's that we've + + + align:start position:0% +cosines or with Exponential's that we've +done before so what did it used to look + + align:start position:0% +done before so what did it used to look + + + align:start position:0% +done before so what did it used to look +like it used to look like ke effects and + + align:start position:0% +like it used to look like ke effects and + + + align:start position:0% +like it used to look like ke effects and +integrals of plus minus I integrals of K + + align:start position:0% +integrals of plus minus I integrals of K + + + align:start position:0% +integrals of plus minus I integrals of K +of X prime the X prime that was the way + + align:start position:0% +of X prime the X prime that was the way + + + align:start position:0% +of X prime the X prime that was the way +the wkb solution look like I'm now + + align:start position:0% +the wkb solution look like I'm now + + + align:start position:0% +the wkb solution look like I'm now +trying to write this this expression for + + align:start position:0% +trying to write this this expression for + + + align:start position:0% +trying to write this this expression for +the wkb solution on the right now I want + + align:start position:0% +the wkb solution on the right now I want + + + align:start position:0% +the wkb solution on the right now I want +to make a remark that even though I'm + + align:start position:0% +to make a remark that even though I'm + + + align:start position:0% +to make a remark that even though I'm +using the linear potential in general if + + align:start position:0% +using the linear potential in general if + + + align:start position:0% +using the linear potential in general if +your potential even eventually becomes + + align:start position:0% +your potential even eventually becomes + + + align:start position:0% +your potential even eventually becomes +something different in this region and + + align:start position:0% +something different in this region and + + + align:start position:0% +something different in this region and +good so I'm moving away from the bad + + align:start position:0% +good so I'm moving away from the bad + + + align:start position:0% +good so I'm moving away from the bad +point sufficiently so that the wkb + + align:start position:0% +point sufficiently so that the wkb + + + align:start position:0% +point sufficiently so that the wkb +approximation is good but I don't want + + align:start position:0% +approximation is good but I don't want + + + align:start position:0% +approximation is good but I don't want +to move away so much so that the + + align:start position:0% +to move away so much so that the + + + align:start position:0% +to move away so much so that the +potential fails dramatically to be + + align:start position:0% +potential fails dramatically to be + + + align:start position:0% +potential fails dramatically to be +linear I have to straddle limited region + + align:start position:0% +linear I have to straddle limited region + + + align:start position:0% +linear I have to straddle limited region +in fact I don't want to go too far so + + align:start position:0% +in fact I don't want to go too far so + + + align:start position:0% +in fact I don't want to go too far so +this were your solutions before in a + + align:start position:0% +this were your solutions before in a + + + align:start position:0% +this were your solutions before in a +region where you're in the allowed + + align:start position:0% +region where you're in the allowed + + + align:start position:0% +region where you're in the allowed +classically allowed region now this form + + align:start position:0% +classically allowed region now this form + + + align:start position:0% +classically allowed region now this form +of the solutions will not be practical + + align:start position:0% +of the solutions will not be practical + + + align:start position:0% +of the solutions will not be practical +for us so I will write them instead with + + align:start position:0% +for us so I will write them instead with + + + align:start position:0% +for us so I will write them instead with +sines and cosines it will be better for + + align:start position:0% +sines and cosines it will be better for + + + align:start position:0% +sines and cosines it will be better for +us to bright it with sines and cosines + + align:start position:0% +us to bright it with sines and cosines + + + align:start position:0% +us to bright it with sines and cosines +so let me write it with science and + + align:start position:0% +so let me write it with science and + + + align:start position:0% +so let me write it with science and +sigh left now wkb of you or X sorry + + align:start position:0% +sigh left now wkb of you or X sorry + + + align:start position:0% +sigh left now wkb of you or X sorry +there's gonna be C over square root of K + + align:start position:0% +there's gonna be C over square root of K + + + align:start position:0% +there's gonna be C over square root of K +of X and I will write the cosine of + + align:start position:0% +of X and I will write the cosine of + + + align:start position:0% +of X and I will write the cosine of +integral from X to a you see I'm on the + + align:start position:0% +integral from X to a you see I'm on the + + + align:start position:0% +integral from X to a you see I'm on the +left so it's natural to write in the + + align:start position:0% +left so it's natural to write in the + + + align:start position:0% +left so it's natural to write in the +world from X to a on the other hand on + + align:start position:0% +world from X to a on the other hand on + + + align:start position:0% +world from X to a on the other hand on +the right was natural to write integral + + align:start position:0% +the right was natural to write integral + + + align:start position:0% +the right was natural to write integral +from a to X and that's what we did + + align:start position:0% +from a to X and that's what we did + + + align:start position:0% +from a to X and that's what we did +cosine from X to a and we'll have here K + + align:start position:0% +cosine from X to a and we'll have here K + + + align:start position:0% +cosine from X to a and we'll have here K +of X prime DX prime plus B over square + + align:start position:0% +of X prime DX prime plus B over square + + + align:start position:0% +of X prime DX prime plus B over square +root of K of X sine of X to a K of X + + align:start position:0% +root of K of X sine of X to a K of X + + + align:start position:0% +root of K of X sine of X to a K of X +prime DX Prime and you could say look + + align:start position:0% +prime DX Prime and you could say look + + + align:start position:0% +prime DX Prime and you could say look +that's good you just traded the + + align:start position:0% +that's good you just traded the + + + align:start position:0% +that's good you just traded the +Exponential's for science and closed + + align:start position:0% +Exponential's for science and closed + + + align:start position:0% +Exponential's for science and closed +signs and that's fine still for what + + align:start position:0% +signs and that's fine still for what + + + align:start position:0% +signs and that's fine still for what +we're gonna do later it's convenient to + + align:start position:0% +we're gonna do later it's convenient to + + + align:start position:0% +we're gonna do later it's convenient to +write our wkb approximation still in a + + align:start position:0% +write our wkb approximation still in a + + + align:start position:0% +write our wkb approximation still in a +little different way I can add a face + + align:start position:0% +little different way I can add a face + + + align:start position:0% +little different way I can add a face +here and a face there and that still is + + align:start position:0% +here and a face there and that still is + + + align:start position:0% +here and a face there and that still is +the most general solution because it + + align:start position:0% +the most general solution because it + + + align:start position:0% +the most general solution because it +involves sines and cosines and unless I + + align:start position:0% +involves sines and cosines and unless I + + + align:start position:0% +involves sines and cosines and unless I +would put a face that differs by PI over + + align:start position:0% +would put a face that differs by PI over + + + align:start position:0% +would put a face that differs by PI over +two and one becomes equal to the other + + align:start position:0% +two and one becomes equal to the other + + + align:start position:0% +two and one becomes equal to the other +now I'm gonna shift both by PI over four + + align:start position:0% +now I'm gonna shift both by PI over four + + + align:start position:0% +now I'm gonna shift both by PI over four +and therefore these are still different + + align:start position:0% +and therefore these are still different + + + align:start position:0% +and therefore these are still different +functions and it's convenient to do that + + align:start position:0% +functions and it's convenient to do that + + + align:start position:0% +functions and it's convenient to do that +so this is our answers for the wkb + + align:start position:0% +so this is our answers for the wkb + + + align:start position:0% +so this is our answers for the wkb +solution + + align:start position:0% + + + + align:start position:0% + +we have to do the same thing with it + + align:start position:0% +we have to do the same thing with it + + + align:start position:0% +we have to do the same thing with it +here in which we expand and evaluate in + + align:start position:0% +here in which we expand and evaluate in + + + align:start position:0% +here in which we expand and evaluate in +terms of you and ADA and this quantity + + align:start position:0% +terms of you and ADA and this quantity + + + align:start position:0% +terms of you and ADA and this quantity +so what do we get we get C over square + + align:start position:0% +so what do we get we get C over square + + + align:start position:0% +so what do we get we get C over square +root of 8 u to the 1/4 cosine 2/3 u to + + align:start position:0% +root of 8 u to the 1/4 cosine 2/3 u to + + + align:start position:0% +root of 8 u to the 1/4 cosine 2/3 u to +the three-halves minus PI over 4 plus V + + align:start position:0% +the three-halves minus PI over 4 plus V + + + align:start position:0% +the three-halves minus PI over 4 plus V +over square root of 8 u to the 1/4 sine + + align:start position:0% +over square root of 8 u to the 1/4 sine + + + align:start position:0% +over square root of 8 u to the 1/4 sine +of 2/3 u to the three-halves minus PI + + align:start position:0% +of 2/3 u to the three-halves minus PI + + + align:start position:0% +of 2/3 u to the three-halves minus PI +over 4 so this is our side left wkb of + + align:start position:0% +over 4 so this is our side left wkb of + + + align:start position:0% +over 4 so this is our side left wkb of +text + + align:start position:0% + + + + align:start position:0% + +okay were in good shape + + align:start position:0% +okay were in good shape + + + align:start position:0% +okay were in good shape +I'm gonna raise this up and and now you + + align:start position:0% +I'm gonna raise this up and and now you + + + align:start position:0% +I'm gonna raise this up and and now you +could say all right you've done the wkb + + align:start position:0% +could say all right you've done the wkb + + + align:start position:0% +could say all right you've done the wkb +thing but on the other hand how about + + align:start position:0% +thing but on the other hand how about + + + align:start position:0% +thing but on the other hand how about +the exact solution what is the exact + + align:start position:0% +the exact solution what is the exact + + + align:start position:0% +the exact solution what is the exact +solution to this problem if written the + + align:start position:0% +solution to this problem if written the + + + align:start position:0% +solution to this problem if written the +wkb approximation for the linear + + align:start position:0% +wkb approximation for the linear + + + align:start position:0% +wkb approximation for the linear +potential the wkb approximation for the + + align:start position:0% +potential the wkb approximation for the + + + align:start position:0% +potential the wkb approximation for the +linear potential now what is the exact + + align:start position:0% +linear potential now what is the exact + + + align:start position:0% +linear potential now what is the exact +solution for the problem well your + + align:start position:0% +solution for the problem well your + + + align:start position:0% +solution for the problem well your +Schrodinger equation is minus H squared + + align:start position:0% +Schrodinger equation is minus H squared + + + align:start position:0% +Schrodinger equation is minus H squared +over 2m side double dot of X plus V of X + + align:start position:0% +over 2m side double dot of X plus V of X + + + align:start position:0% +over 2m side double dot of X plus V of X +minus the energy on size is equal to + + align:start position:0% +minus the energy on size is equal to + + + align:start position:0% +minus the energy on size is equal to +zero + + align:start position:0% + + + + align:start position:0% + +well we've written this already a couple + + align:start position:0% +well we've written this already a couple + + + align:start position:0% +well we've written this already a couple +of times so this is minus H squared over + + align:start position:0% +of times so this is minus H squared over + + + align:start position:0% +of times so this is minus H squared over +2m side double dot plus G X minus a sigh + + align:start position:0% +2m side double dot plus G X minus a sigh + + + align:start position:0% +2m side double dot plus G X minus a sigh +equals 0 that is our V minus E and in + + align:start position:0% +equals 0 that is our V minus E and in + + + align:start position:0% +equals 0 that is our V minus E and in +terms of the u variable the differential + + align:start position:0% +terms of the u variable the differential + + + align:start position:0% +terms of the u variable the differential +equation of course becomes the second sy + + align:start position:0% +equation of course becomes the second sy + + + align:start position:0% +equation of course becomes the second sy +the U squared it will use I that's why + + align:start position:0% +the U squared it will use I that's why + + + align:start position:0% +the U squared it will use I that's why +the error function is relevant here we + + align:start position:0% +the error function is relevant here we + + + align:start position:0% +the error function is relevant here we +get back to that equation that is the + + align:start position:0% +get back to that equation that is the + + + align:start position:0% +get back to that equation that is the +equation in for the exact linear + + align:start position:0% +equation in for the exact linear + + + align:start position:0% +equation in for the exact linear +potential and those would be the exact + + align:start position:0% +potential and those would be the exact + + + align:start position:0% +potential and those would be the exact +solutions so our exact solutions are sy + + align:start position:0% +solutions so our exact solutions are sy + + + align:start position:0% +solutions so our exact solutions are sy +being some linear combination of the + + align:start position:0% +being some linear combination of the + + + align:start position:0% +being some linear combination of the +function and the other airy functions + + align:start position:0% + + + + align:start position:0% + +and now let's do one case first before + + align:start position:0% +and now let's do one case first before + + + align:start position:0% +and now let's do one case first before +we get into something that is more + + align:start position:0% +we get into something that is more + + + align:start position:0% +we get into something that is more +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +let's take psy to be the solution to be + + align:start position:0% +let's take psy to be the solution to be + + + align:start position:0% +let's take psy to be the solution to be +the airy function a I of you that's your + + align:start position:0% +the airy function a I of you that's your + + + align:start position:0% +the airy function a I of you that's your +solution now if that is your solution + + align:start position:0% +solution now if that is your solution + + + align:start position:0% +solution now if that is your solution +you would have this behavior the + + align:start position:0% +you would have this behavior the + + + align:start position:0% +you would have this behavior the +behavior with noted here for the + + align:start position:0% +behavior with noted here for the + + + align:start position:0% +behavior with noted here for the +solution + + align:start position:0% + + + + align:start position:0% + +and now you compare and you look at what + + align:start position:0% +and now you compare and you look at what + + + align:start position:0% +and now you compare and you look at what +you got you say all right I have a + + align:start position:0% +you got you say all right I have a + + + align:start position:0% +you got you say all right I have a +solution and I know how it looks + + align:start position:0% +solution and I know how it looks + + + align:start position:0% +solution and I know how it looks +rigorously how it looks to the right and + + align:start position:0% +rigorously how it looks to the right and + + + align:start position:0% +rigorously how it looks to the right and +to the left that's how it looks and this + + align:start position:0% +to the left that's how it looks and this + + + align:start position:0% +to the left that's how it looks and this +is the exact solution this is the wkb + + align:start position:0% +is the exact solution this is the wkb + + + align:start position:0% +is the exact solution this is the wkb +solution and I know how it looks to the + + align:start position:0% +solution and I know how it looks to the + + + align:start position:0% +solution and I know how it looks to the +right and how it looks to the left and I + + align:start position:0% +right and how it looks to the left and I + + + align:start position:0% +right and how it looks to the left and I +see the correspondence we see this term + + align:start position:0% +see the correspondence we see this term + + + align:start position:0% +see the correspondence we see this term +in yellow is a solution that is a + + align:start position:0% +in yellow is a solution that is a + + + align:start position:0% +in yellow is a solution that is a +decaying exponential and we see it here + + align:start position:0% + + + + align:start position:0% + +and we have the red term the + + align:start position:0% +and we have the red term the + + + align:start position:0% +and we have the red term the +oscillations and we see it also here so + + align:start position:0% +oscillations and we see it also here so + + + align:start position:0% +oscillations and we see it also here so +here is a connection condition in fact + + align:start position:0% +here is a connection condition in fact + + + align:start position:0% +here is a connection condition in fact +when you derive these are synthetic + + align:start position:0% +when you derive these are synthetic + + + align:start position:0% +when you derive these are synthetic +expansions you need a true connection + + align:start position:0% +expansions you need a true connection + + + align:start position:0% +expansions you need a true connection +condition because you connected a single + + align:start position:0% +condition because you connected a single + + + align:start position:0% +condition because you connected a single +function from the left and from the + + align:start position:0% +function from the left and from the + + + align:start position:0% +function from the left and from the +right here it was to the right here it + + align:start position:0% +right here it was to the right here it + + + align:start position:0% +right here it was to the right here it +was to the left and this is a connection + + align:start position:0% +was to the left and this is a connection + + + align:start position:0% +was to the left and this is a connection +form it'll be this is the same function + + align:start position:0% +form it'll be this is the same function + + + align:start position:0% +form it'll be this is the same function +so here we see that if we wrote the wkb + + align:start position:0% +so here we see that if we wrote the wkb + + + align:start position:0% +so here we see that if we wrote the wkb +solution and we were aiming at maybe + + align:start position:0% +solution and we were aiming at maybe + + + align:start position:0% +solution and we were aiming at maybe +this solution we would have that this + + align:start position:0% +this solution we would have that this + + + align:start position:0% +this solution we would have that this +term goes connects with this term and + + align:start position:0% +term goes connects with this term and + + + align:start position:0% +term goes connects with this term and +the coefficients differ by 1/2 that 1/2 + + align:start position:0% +the coefficients differ by 1/2 that 1/2 + + + align:start position:0% +the coefficients differ by 1/2 that 1/2 +has no other explanation than the + + align:start position:0% +has no other explanation than the + + + align:start position:0% +has no other explanation than the +asymptotic expansions there's the square + + align:start position:0% +asymptotic expansions there's the square + + + align:start position:0% +asymptotic expansions there's the square +root of pi these things and there's the + + align:start position:0% +root of pi these things and there's the + + + align:start position:0% +root of pi these things and there's the +two functions + + align:start position:0% +two functions + + + align:start position:0% +two functions +so if you put the 1/2 is there in the + + align:start position:0% +so if you put the 1/2 is there in the + + + align:start position:0% +so if you put the 1/2 is there in the +exponential so you could put a 1/2 here + + align:start position:0% +exponential so you could put a 1/2 here + + + align:start position:0% +exponential so you could put a 1/2 here +and 2a if you wish so you realize that + + align:start position:0% +and 2a if you wish so you realize that + + + align:start position:0% +and 2a if you wish so you realize that +in order to have a connection to a would + + align:start position:0% +in order to have a connection to a would + + + align:start position:0% +in order to have a connection to a would +be equal to see the two coefficients + + align:start position:0% +be equal to see the two coefficients + + + align:start position:0% +be equal to see the two coefficients +here are related in that way there's a + + align:start position:0% +here are related in that way there's a + + + align:start position:0% +here are related in that way there's a +number here and a number here it happens + + align:start position:0% +number here and a number here it happens + + + align:start position:0% +number here and a number here it happens +to be two a and C in this case so two a + + align:start position:0% +to be two a and C in this case so two a + + + align:start position:0% +to be two a and C in this case so two a +is equal to C so if we choose a equals 1 + + align:start position:0% +is equal to C so if we choose a equals 1 + + + align:start position:0% +is equal to C so if we choose a equals 1 +we would have C equal to so here is a + + align:start position:0% +we would have C equal to so here is a + + + align:start position:0% +we would have C equal to so here is a +matching condition therefore we have + + align:start position:0% +matching condition therefore we have + + + align:start position:0% +matching condition therefore we have +that a wkb solution that has the C + + align:start position:0% +that a wkb solution that has the C + + + align:start position:0% +that a wkb solution that has the C +factor with C equals 2 so it would be 2 + + align:start position:0% +factor with C equals 2 so it would be 2 + + + align:start position:0% +factor with C equals 2 so it would be 2 +over square root of K of X in here times + + align:start position:0% +over square root of K of X in here times + + + align:start position:0% +over square root of K of X in here times +cosine of this x over a K of X prime DX + + align:start position:0% +cosine of this x over a K of X prime DX + + + align:start position:0% +cosine of this x over a K of X prime DX +prime minus PI over 4 is connected we'll + + align:start position:0% +prime minus PI over 4 is connected we'll + + + align:start position:0% +prime minus PI over 4 is connected we'll +see more on that with 1 over square root + + align:start position:0% +see more on that with 1 over square root + + + align:start position:0% +see more on that with 1 over square root +of Kappa of X this solution with a + + align:start position:0% +of Kappa of X this solution with a + + + align:start position:0% +of Kappa of X this solution with a +equals to 1 what we have here e to the + + align:start position:0% +equals to 1 what we have here e to the + + + align:start position:0% +equals to 1 what we have here e to the +minus a over X Kappa of X prime DX prime + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +that is the first connection condition + + align:start position:0% +that is the first connection condition + + + align:start position:0% +that is the first connection condition +we will discuss it further in a couple + + align:start position:0% +we will discuss it further in a couple + + + align:start position:0% +we will discuss it further in a couple +of minutes but this is how you connect + + align:start position:0% +of minutes but this is how you connect + + + align:start position:0% +of minutes but this is how you connect +things a single solution of the + + align:start position:0% +things a single solution of the + + + align:start position:0% +things a single solution of the +differential equation looks like this + + align:start position:0% +differential equation looks like this + + + align:start position:0% +differential equation looks like this +term and like that term on the left and + + align:start position:0% +term and like that term on the left and + + + align:start position:0% +term and like that term on the left and +on the right here is your wkb solution + + align:start position:0% +on the right here is your wkb solution + + + align:start position:0% +on the right here is your wkb solution +this general solution looks like this + + align:start position:0% +this general solution looks like this + + + align:start position:0% +this general solution looks like this +term and if then should match to + + align:start position:0% +term and if then should match to + + + align:start position:0% +term and if then should match to +something that looks like that if you + + align:start position:0% +something that looks like that if you + + + align:start position:0% +something that looks like that if you +have the Aerie function so in general + + align:start position:0% +have the Aerie function so in general + + + align:start position:0% +have the Aerie function so in general +for not linear potentials this is the + + align:start position:0% +for not linear potentials this is the + + + align:start position:0% +for not linear potentials this is the +term that gives rise to that so we take + + align:start position:0% +term that gives rise to that so we take + + + align:start position:0% +term that gives rise to that so we take +that this term in general is matched to + + align:start position:0% +that this term in general is matched to + + + align:start position:0% +that this term in general is matched to +the top term in the blackboard here \ No newline at end of file diff --git a/mHonq7Gjjqg.txt b/mHonq7Gjjqg.txt new file mode 100644 index 0000000000000000000000000000000000000000..671fe2eee8c9c398602bb65ee41bca62c92bbc45 --- /dev/null +++ b/mHonq7Gjjqg.txt @@ -0,0 +1,755 @@ +align:start position:0% + +we will now go through a derivation of + + align:start position:0% +we will now go through a derivation of + + + align:start position:0% +we will now go through a derivation of +the law of total variance this + + align:start position:0% +the law of total variance this + + + align:start position:0% +the law of total variance this +particular derivation is not insightful + + align:start position:0% +particular derivation is not insightful + + + align:start position:0% +particular derivation is not insightful +it will not really give you any + + align:start position:0% +it will not really give you any + + + align:start position:0% +it will not really give you any +intuition as to why the law of total + + align:start position:0% +intuition as to why the law of total + + + align:start position:0% +intuition as to why the law of total +variance is correct on the other hand it + + align:start position:0% +variance is correct on the other hand it + + + align:start position:0% +variance is correct on the other hand it +involves some interesting manipulations + + align:start position:0% +involves some interesting manipulations + + + align:start position:0% +involves some interesting manipulations +that will be useful to be able to follow + + align:start position:0% +that will be useful to be able to follow + + + align:start position:0% +that will be useful to be able to follow +and understand the kinds of objects that + + align:start position:0% +and understand the kinds of objects that + + + align:start position:0% +and understand the kinds of objects that +are being moved around and why each step + + align:start position:0% +are being moved around and why each step + + + align:start position:0% +are being moved around and why each step +is valid our derivation relies on the + + align:start position:0% +is valid our derivation relies on the + + + align:start position:0% +is valid our derivation relies on the +standard formula that we have on how to + + align:start position:0% +standard formula that we have on how to + + + align:start position:0% +standard formula that we have on how to +calculate variances and our first step + + align:start position:0% +calculate variances and our first step + + + align:start position:0% +calculate variances and our first step +is to apply this formula to the + + align:start position:0% +is to apply this formula to the + + + align:start position:0% +is to apply this formula to the +conditional variance now the conditional + + align:start position:0% +conditional variance now the conditional + + + align:start position:0% +conditional variance now the conditional +variance is like an ordinary variance + + align:start position:0% +variance is like an ordinary variance + + + align:start position:0% +variance is like an ordinary variance +except that it is calculated in a + + align:start position:0% +except that it is calculated in a + + + align:start position:0% +except that it is calculated in a +conditional universe so we apply this + + align:start position:0% +conditional universe so we apply this + + + align:start position:0% +conditional universe so we apply this +formula except that the expectation of x + + align:start position:0% +formula except that the expectation of x + + + align:start position:0% +formula except that the expectation of x +squared is the expectation calculated in + + align:start position:0% +squared is the expectation calculated in + + + align:start position:0% +squared is the expectation calculated in +the conditional universe and similarly + + align:start position:0% +the conditional universe and similarly + + + align:start position:0% +the conditional universe and similarly +for the next term is the square of the + + align:start position:0% +for the next term is the square of the + + + align:start position:0% +for the next term is the square of the +expected value of x but it's the + + align:start position:0% +expected value of x but it's the + + + align:start position:0% +expected value of x but it's the +expected value of x as calculated in a + + align:start position:0% +expected value of x as calculated in a + + + align:start position:0% +expected value of x as calculated in a +conditional universe so this is an + + align:start position:0% +conditional universe so this is an + + + align:start position:0% +conditional universe so this is an +equality between numbers what does it + + align:start position:0% +equality between numbers what does it + + + align:start position:0% +equality between numbers what does it +translate to this has been defined as a + + align:start position:0% +translate to this has been defined as a + + + align:start position:0% +translate to this has been defined as a +random variable that takes this value + + align:start position:0% +random variable that takes this value + + + align:start position:0% +random variable that takes this value +when Capital y is equal to little Y what + + align:start position:0% +when Capital y is equal to little Y what + + + align:start position:0% +when Capital y is equal to little Y what +is the random variable that takes this + + align:start position:0% +is the random variable that takes this + + + align:start position:0% +is the random variable that takes this +value when Capital y is little Y well + + align:start position:0% +value when Capital y is little Y well + + + align:start position:0% +value when Capital y is little Y well +this random variable here is a random + + align:start position:0% +this random variable here is a random + + + align:start position:0% +this random variable here is a random +variable that takes this value when + + align:start position:0% +variable that takes this value when + + + align:start position:0% +variable that takes this value when +Capital y is equal to little Y and this + + align:start position:0% +Capital y is equal to little Y and this + + + align:start position:0% +Capital y is equal to little Y and this +random variable here is a random + + align:start position:0% +random variable here is a random + + + align:start position:0% +random variable here is a random +variable that takes this numerical value + + align:start position:0% +variable that takes this numerical value + + + align:start position:0% +variable that takes this numerical value +when Capital y is equal to little Y so + + align:start position:0% +when Capital y is equal to little Y so + + + align:start position:0% +when Capital y is equal to little Y so +to summarize this is the random variable + + align:start position:0% +to summarize this is the random variable + + + align:start position:0% +to summarize this is the random variable +that takes this numerical value when + + align:start position:0% +that takes this numerical value when + + + align:start position:0% +that takes this numerical value when +Capital y is equal to little Y and this + + align:start position:0% +Capital y is equal to little Y and this + + + align:start position:0% +Capital y is equal to little Y and this +is a random variable that takes this + + align:start position:0% +is a random variable that takes this + + + align:start position:0% +is a random variable that takes this +value when Capital y is equal to little + + align:start position:0% +value when Capital y is equal to little + + + align:start position:0% +value when Capital y is equal to little +Y + + align:start position:0% +Y + + + align:start position:0% +Y +this expression the left-hand side is + + align:start position:0% +this expression the left-hand side is + + + align:start position:0% +this expression the left-hand side is +equal to the right-hand side for all + + align:start position:0% +equal to the right-hand side for all + + + align:start position:0% +equal to the right-hand side for all +wise and therefore this random variable + + align:start position:0% +wise and therefore this random variable + + + align:start position:0% +wise and therefore this random variable +and that random variable always take the + + align:start position:0% +and that random variable always take the + + + align:start position:0% +and that random variable always take the +same numerical values no matter what Y + + align:start position:0% +same numerical values no matter what Y + + + align:start position:0% +same numerical values no matter what Y +happens to be so these are identical + + align:start position:0% +happens to be so these are identical + + + align:start position:0% +happens to be so these are identical +random variables and so we have this + + align:start position:0% +random variables and so we have this + + + align:start position:0% +random variables and so we have this +equality between random variables the + + align:start position:0% +equality between random variables the + + + align:start position:0% +equality between random variables the +next step as were working towards + + align:start position:0% +next step as were working towards + + + align:start position:0% +next step as were working towards +calculating this first term here in the + + align:start position:0% +calculating this first term here in the + + + align:start position:0% +calculating this first term here in the +law of total variance is to take the + + align:start position:0% +law of total variance is to take the + + + align:start position:0% +law of total variance is to take the +expectation of this expression what is + + align:start position:0% +expectation of this expression what is + + + align:start position:0% +expectation of this expression what is +it we take the expectation of the first + + align:start position:0% +it we take the expectation of the first + + + align:start position:0% +it we take the expectation of the first +term it's the expectation of a + + align:start position:0% +term it's the expectation of a + + + align:start position:0% +term it's the expectation of a +conditional expectation and according to + + align:start position:0% +conditional expectation and according to + + + align:start position:0% +conditional expectation and according to +the law of iterated expectations it is + + align:start position:0% +the law of iterated expectations it is + + + align:start position:0% +the law of iterated expectations it is +the same as the unconditional + + align:start position:0% +the same as the unconditional + + + align:start position:0% +the same as the unconditional +expectation and then we have the + + align:start position:0% +expectation and then we have the + + + align:start position:0% +expectation and then we have the +expected value of the next term + + align:start position:0% + + + + align:start position:0% + +next we want to make some progress + + align:start position:0% +next we want to make some progress + + + align:start position:0% +next we want to make some progress +towards calculating this second quantity + + align:start position:0% +towards calculating this second quantity + + + align:start position:0% +towards calculating this second quantity +in the law of total variance and the way + + align:start position:0% +in the law of total variance and the way + + + align:start position:0% +in the law of total variance and the way +to calculate it is to just apply this + + align:start position:0% +to calculate it is to just apply this + + + align:start position:0% +to calculate it is to just apply this +general property of variances to the + + align:start position:0% +general property of variances to the + + + align:start position:0% +general property of variances to the +special case where X gets replaced by + + align:start position:0% +special case where X gets replaced by + + + align:start position:0% +special case where X gets replaced by +the expected value of x given Y so the + + align:start position:0% +the expected value of x given Y so the + + + align:start position:0% +the expected value of x given Y so the +first term will be the expected value of + + align:start position:0% +first term will be the expected value of + + + align:start position:0% +first term will be the expected value of +our random variable squared our random + + align:start position:0% +our random variable squared our random + + + align:start position:0% +our random variable squared our random +variable is the expected value of x + + align:start position:0% +variable is the expected value of x + + + align:start position:0% +variable is the expected value of x +given Y and the second term involves the + + align:start position:0% +given Y and the second term involves the + + + align:start position:0% +given Y and the second term involves the +expected value of the random variable + + align:start position:0% +expected value of the random variable + + + align:start position:0% +expected value of the random variable +whose variance were considering so it's + + align:start position:0% +whose variance were considering so it's + + + align:start position:0% +whose variance were considering so it's +the expected value of this random + + align:start position:0% +the expected value of this random + + + align:start position:0% +the expected value of this random +variable so it's the expected value of + + align:start position:0% +variable so it's the expected value of + + + align:start position:0% +variable so it's the expected value of +the conditional expectation and + + align:start position:0% +the conditional expectation and + + + align:start position:0% +the conditional expectation and +everything gets squared what is this + + align:start position:0% +everything gets squared what is this + + + align:start position:0% +everything gets squared what is this +term by the law of iterated expectations + + align:start position:0% +term by the law of iterated expectations + + + align:start position:0% +term by the law of iterated expectations +the expected value of a conditional + + align:start position:0% +the expected value of a conditional + + + align:start position:0% +the expected value of a conditional +expectation is the same as the + + align:start position:0% +expectation is the same as the + + + align:start position:0% +expectation is the same as the +unconditional expectation so this last + + align:start position:0% +unconditional expectation so this last + + + align:start position:0% +unconditional expectation so this last +term here is of this form what we will + + align:start position:0% +term here is of this form what we will + + + align:start position:0% +term here is of this form what we will +do next is to take this expression here + + align:start position:0% +do next is to take this expression here + + + align:start position:0% +do next is to take this expression here +and that expression here and add them + + align:start position:0% +and that expression here and add them + + + align:start position:0% +and that expression here and add them +together when we add them we notice that + + align:start position:0% +together when we add them we notice that + + + align:start position:0% +together when we add them we notice that +this term and that term are the same so + + align:start position:0% +this term and that term are the same so + + + align:start position:0% +this term and that term are the same so +they cancel out and were left with the + + align:start position:0% +they cancel out and were left with the + + + align:start position:0% +they cancel out and were left with the +expected value of x squared minus the + + align:start position:0% +expected value of x squared minus the + + + align:start position:0% +expected value of x squared minus the +square of the expected value but we know + + align:start position:0% +square of the expected value but we know + + + align:start position:0% +square of the expected value but we know +that this is the same as the variance of + + align:start position:0% +that this is the same as the variance of + + + align:start position:0% +that this is the same as the variance of +X so we have proved that the sum of + + align:start position:0% +X so we have proved that the sum of + + + align:start position:0% +X so we have proved that the sum of +these two terms which are the two terms + + align:start position:0% +these two terms which are the two terms + + + align:start position:0% +these two terms which are the two terms +up here give us the variance of X \ No newline at end of file diff --git a/oRpERQA4Vik.txt b/oRpERQA4Vik.txt new file mode 100644 index 0000000000000000000000000000000000000000..d797c2cfdc53beb02fabcab727878c785cdd7f4a --- /dev/null +++ b/oRpERQA4Vik.txt @@ -0,0 +1,3067 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK. + +So who's going lecture? + +Good. + +Does everything makes sense? + +AUDIENCE: Mostly. + +PROFESSOR: That's good, because +we're going to do problems. + +AUDIENCE: Awesome. + +PROFESSOR: So, what I want +to talk about is, first, + +there's a subtlety in the +Rubik's cube problem, which I'm + +guessing nobody has seen yet, +but we're going to talk about + +it anyway, because otherwise +you'll trip on it while you're + +doing the problem. + +And then we're going to +talk about one or maybe two + +problems. + +And I'm excited about +the problem titled, + +"there's StarCraft +and counter strikes," + +so, let's hope we get to them. + +AUDIENCE: I'm curious, did you +write this week's problem set? + +Because there's some +Chinese in there. + +PROFESSOR: No. + +AUDIENCE: Oh, OK. + +PROFESSOR: No, +someone else wrote it. + +I suggested putting +that in there, though. + +AUDIENCE: You had an +awesome internship, right? + +[INAUDIBLE] + +AUDIENCE: Wait, did you make all +the AMD [INAUDIBLE] questions? + +PROFESSOR:Of course. + +That's my stuff. + +OK. + +So Rubik's cubes. + +Did everyone see a 2 +by 2 by 2 Rubik's cube? + +You guys are going +to lecture, right? + +You have one. + +Yeah. + +Did you guys see Eric's +2 by 2 by 2 Rubik's cube? + +It looks sort of like this. + +All right, so big +Rubik's cube has how many + +small cubelets in it? + +AUDIENCE: 80. + +AUDIENCE: 80. + +AUDIENCE: I like cubelets +better than cubies. + +Cubies is hard to say. + +PROFESSOR: Yeah, I +would say cubicles. + +So let's go for-- +let's try cubelets + +and see how this works. + +OK. + +So each cubelet has six +faces, but three faces + +are always facing inwards. + +They're always attached +to the center of the cube. + +So we don't care about them. + +We only care about +the other three faces. + +So if you have a +plastic Rubik's cube. + +Say this is a plastic-- +This is a plastic cube. + +Then you're going to have +eight plastic cubelets. + +Each cubelet has +three colored faces + +and three faces that +we don't care about. + +So how many total plastic +faces in a cubelet, sorry, + +plastic cube? + +AUDIENCE: Twenty-four. +[INAUDIBLE] + +PROFESSOR: All right. + +Now let's play with +an imaginary cube. + +And I call this +a wireframe cube, + +because I draw it like this. + +So, here pretend you have the +skeleton of a Rubik's cube, + +made out of wires or out +of wood or something. + +So it's basically a small sheet +of wood, small piece of wood, + +small sheet of wood, +so on and so forth. + +And so this doesn't +have any colors in it, + +but it's the right shape +and sort of the right look. + +So the way you would build +the configuration is, + +you take 24 plastic faces that +you get from a plastic cube, + +and you paste them one +by one onto the faces + +of a wireframe cube. + +And they claim that this +can build any configuration + +that you can think about. + +If you look at a cube, after +no matter how many moves + +you've done to it, +it's going to have + +some-- it's going to have +the faces somewhere, right? + +So you can take the +faces and face them + +where they belong +and there you go. + +You have a real cube +built out of a wireframe + +and plastic faces. + +How many wireframe +faces there are? + +Please don't get this wrong. + +AUDIENCE: Twenty-four. + +PROFESSOR: OK. + +AUDIENCE: There are +some configurations + +that aren't possible, right? + +PROFESSOR: OK. + +There are some configurations +that aren't possible, + +and that is very good news. + +We'll get to that later. + +Let's see how the code +talks about these faces. + +So suppose we have a cubelet +that has these faces. + +Front faces yellow, this face is +blue, and this face is orange. + +This facing code is called-- +so this yellow face here + +is called y o b. + +So y is yellow, that's +the yellow face, + +and is the yellow +facing the cubelet that + +has a yellow face, an orange +face, and a blue face. + +Fortunately, there +aren't two cubelets + +that have the same face +color, so this is good enough + +to distinguish +between all of them. + +Let's see if you guys +are paying attention. + +How would I call this face? + +AUDIENCE: o y b? + +PROFESSOR: Yeah. + +Either that or o b y, whichever +one the code happens to use. + +So the principal is, +these are the colors + +and the first one is the +face that you're pointing at. + +So there are 24 +plastic faces, so there + +are 24 names for +these plastic faces. + +Let's see how we name +the wireframe faces. + +If I take this face-- so +we don't have colors here, + +they're all the same. + +So instead we care +about their position. + +A cube has a front +and a back, right? + +This cubelet is on the +front somewhere, right? + +So I'm going to have front +somewhere in the name. + +It has an upper face +and a lower face. + +Is this going to +be upper or lower? + +AUDIENCE: Upper. + +PROFESSOR: And +the left or right? + +PROFESSOR: Right. + +PROFESSOR: OK. + +So front upper right, +which face am I looking at? + +AUDIENCE: The front. + +PROFESSOR: OK. + +f u r, fur. + +How about this space? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So far so good? + +Or it could be r u f, right? + +PROFESSOR: Or it could be r u f. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I really don't know +what it means, I'm behind. + +AUDIENCE: Ruff like a dog? + +It has fur. + +PROFESSOR: Oh, ruff ruff ruff. + +OK. + +That's not too bad. + +I was afraid of something worse. + +OK. + +That's cool. + +So a configuration +will take plastic faces + +and face them onto +the wireframe faces. + +So a configuration is going +to be an array of 24 elements. + +And the first element is going +to tell me which plastic face + +ends up in-- Let's say if +you are the second one, + +says which plastic +face ends up in r u f, + +and the third one, let's +assume it's the space. + +AUDIENCE: Ruff. + +PROFESSOR: Ruff. + +And there are 21 +more faces, right? + +So each face has +a number from zero + +to 23, because we're in Python, +so we like zero-based indexing. + +And 24 elements in the +array, 24 plastic faces. + +Which plastic face +goes into f u r? + +Assuming this cubelet here-- +see, I said cubicle anyway. + +This cubelet here goes here +in exactly this configuration. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah. + +So this face ends up here. + +And that's what it means that +the first element in the array + +is y o b. + +How about r u f? + +Who ends up in r u f? + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: B o y. + +PROFESSOR: And who +ends up in e r f? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: OK. + +So does everyone +understand configurations? + +Does this make sense? + +AUDIENCE: Yeah. + +I got lost somewhere in there. + +Can you explain the order +for f u r and [INAUDIBLE]? + +Like front upright? + +PROFESSOR: Oh. + +So do you mean-- so the +order of the letters. + +So there are two orderings here. + +One is the order of the +letters and there is an order. + +I think the code +uses clockwise order, + +but what really matters is the +first letter tells you which + +face you're talking about. + +AUDIENCE: So this is front face. + +PROFESSOR: Face, up face. + +AUDIENCE: What's up? + +What's front? + +PROFESSOR: So for this +cubelet, this is front, + +this is the right, this is up. + +This cubelet wold have a +front, an up, and a left. + +So now there are +24 faces and all + +of them get numbers from 0 23. + +And here we assume that +f u r is space zero, + +r u f is space 1, and +e r f is face 2, which + +is not quite [INAUDIBLE], but +you'll have the mapping there. + +OK. + +So a configuration is in +an array of 24 elements + +and it maps plastic faces +to wireframe faces, which + +brings us to, how many +configurations are there? + +AUDIENCE: You mean like +mapping 4 factorial? + +PROFESSOR: OK. + +So let's see what it does. + +We have 24 plastic faces. + +From 0 to 23. + +And they have to be +mapped to 24 positions. + +AUDIENCE: [INTERPOSING VOICES] + +AUDIENCE: There's six +colors, aren't there? + +AUDIENCE: Yeah. + +PROFESSOR: There are six colors, +but if this is also yellow, + +but there's a red here. + +This is a different face, +see, this is yellow, + +red, and there's +a green down here. + +Then this is the yellow face of +the yellow, green, red cubelet. + +So we care about the +individual faces. + +So yeah, your answer was right. + +I'm trying to explain +it to everyone else. + +But your answer is right. + +AUDIENCE: Well, wait. + +But you can't-- I mean, we +talk about some are impossible. + +Like, you're always gonna +have a grouping of y o b. + +That's never gonna change. + +PROFESSOR: Right. + +So some of these +aren't reachable, + +because you're not allowed +to break up the cube. + +AUDIENCE: Yeah. + +PROFESSOR: And that's OK. + +This is still how the +code represents them. + +So I'm asking if you had-- if +all these would be possible, + +how many would we get? + +And the answer is that +to map 24 plastic faces + +to 24 wireframe faces. + +So this mapping is called-- +anyone good with math? + +AUDIENCE: 1 to 1. + +AUDIENCE: Bijection. + +PROFESSOR: OK. + +So when you're taking-- OK. + +So when we have two sets and you +have a bijection between them + +or 1 to 1 mapping, that +function is also called? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: You probably +don't know the answer yet. + +You have to wait +until the end of 6042. + +So I'm trying to hint that +right now, if you remember + +the end of 6042, maybe the +answer is somewhere there. + +AUDIENCE: Blur?. + +AUDIENCE: Perfect. + +AUDIENCE: A perfect match + +AUDIENCE: Permut--. + +AUDIENCE: I totally learned +about that in middle school, + +I think. + +PROFESSOR: OK. + +So this is-- + +AUDIENCE: Permutations +and combinations. + +PROFESSOR: So this +is a permutation. + +AUDIENCE: Yeah. + +PROFESSOR: How many permutations +do you have out of 24 elements? + +AUDIENCE: Does that order +[? mean ?] [? matters ?] + +[INAUDIBLE] 24 [INAUDIBLE]. + +PROFESSOR: So this is a +lot of permutations, right? + +It's a good thing +that we're not going + +to explore most of +these configurations. + +So we said before, +that we're going + +to build a graph where the +vertices are configurations, + +and the edges are +moves that get us + +from one configuration +to another configuration. + +Can they afford to build +this graph first and then run + +BFS on it? + +Not going to work, right? + +We don't have +enough RAM for this. + +So instead we're going +to have to operate + +on an implicit graph +for presentation. + +Well, fortunately, BFS +doesn't want the whole graph. + +The way BFS works is +it has a list of nodes + +that it has to visit, and +when it visits a node, + +it wants to know its neighbors. + +And that's it. + +Yes? + +Everyone happy with it? + +So all they have +to do is, in order + +to build this implicit +graph representation, + +is we have to know +the start node, + +So BFS can start somewhere. + +And we have to be able +to give it a node, + +we have to be able to generate +all the neighbor nodes. + +So given the +configuration, we have + +to be able to generate +the configurations that + +would result by applying +most of that configuration. + +So what are the moves +that you can do with this? + +Suppose you have a cubelet. + +What are the possible moves? + +There aren't that many. + +We're interested in the +simplest kind of moves. + +AUDIENCE: [INAUDIBLE] + +AUDIENCE: Yeah, you +can make the right side + +go right, which is equivalent +to the left side going left. + +And then you can do [INAUDIBLE] +4, left [INAUDIBLE]. + +AUDIENCE: It's a nice number. + +PROFESSOR: OK. + +I think there are a few more, +so here's how I look at it. + +You can take the front +face, so these four, + +and do a clockwise +rotation, 90 degrees, + +or you can do a counterclockwise +rotation, 90 degrees. + +And you can do +that for each face. + +AUDIENCE: But doing a front +clockwise rotation is the same + +as doing a back counter +clockwise rotation, which + +is [? it-- ?] + +AUDIENCE: Yeah. + +PROFESSOR: Doing +a front clockwise, + +doing a back counterclockwise +is the same thing + +after you account +for symmetries. + +Yeah. + +AUDIENCE: Exactly. + +AUDIENCE: So it's six? + +PROFESSOR: Yep. + +So there's only six after +you account for symmetries. + +Let's play devil's +advocate and assume + +we don't account for symmetries. + +We're actually doing +the code, because I + +need to teach you something. + +So let's assume we don't apply. + +By the way, how +would you account + +for symmetries, easy way? + +Did anyone read the +comments in the code? + +OK. + +So would you account +for symmetries. + +AUDIENCE: Doesn't +it just happen? + +The permutation is +going to [INAUDIBLE]. + +AUDIENCE: Can you +just look at it, + +like, each space is neighboring +faces, and [INAUDIBLE]? + +PROFESSOR: So the way we do +it is we anchor one cubelet. + +So we have one cubelet that +is a plastic cubelet that + +is always going to go here. + +So three plastic +faces here are always + +going to go to three +wireframed faces here. + +And if you fix those +three faces then + +you don't have simple +symmetries anymore. + +All right? + +Three axes of symmetry, so +fixing three faces settles it. + +AUDIENCE: Wait, so then how +many moves are possible? + +12? + +AUDIENCE: No. + +But you only do +one thing, though. + +Now you don't do +counterclock-- you don't do. + +AUDIENCE: If one is +anchored, there's six left. + +AUDIENCE: Yeah. + +Yeah. + +You don't move the anchored one. + +AUDIENCE: Oh yeah, because +you can only [INAUDIBLE] two + +of the-- three of +the faces now, but. + +PROFESSOR: OK. + +So let's look at the left face. + +So you have a configuration. + +So you can move the +left face clockwise, + +left face counterclockwise. + +You can move the top +face clockwise, top face + +counterclockwise, +and a couple more. + +So what does a move look like? + +Someone said it before. + +So when you're doing a move, +what's going to happen is, + +a move doesn't +create plastic faces + +and it doesn't +destroy them, right? + +It just changes their +position on the wireframe. + +So if you have an initial +configuration that + +has plastic faces assigned +to wireframe faces, + +and you have a +final configuration, + +these plastic faces are +going to end up somewhere + +on the wireframe. + +And that's true for +all the plastic faces. + +So the plastic faces are +going to end up somewhere. + +Also, what's nice is if +we look at the wireframe, + +if I do a clockwise rotation +in the front, whatever + +plastic face was here +is going to end up here. + +Whatever plastic face was +here is going to end up here, + +so on and so forth. + +So it's a function of rotation +[INAUDIBLE] inside [INAUDIBLE]. + +Like the four faces that +correspond to each other, + +rotate. + +PROFESSOR: OK. + +That's some good-- that's +going deeper than want to go. + +I want to account for +something simpler. + +So my point is that +the arrows will always, + +if I do a right +clockwise rotation, + +the arrows will +always look the same. + +So the only thing that changes +is what's inside the array. + +But if you take one +configuration array + +and you move things +according to the way you're + +supposed to move them for +the front clockwise move, + +you're going to get +the right result. + +So what is this a +bunch of arrows called? + +What does it do? + +What does it do to the faces? + +What does it do to the +elements of the array? + +AUDIENCE: It moves +in different spots. + +PROFESSOR: OK, so +fancy math name? + +AUDIENCE: Shuffle. + +PROFESSOR: OK. + +So this is what I got before. + +This is how you +think of it, right? + +It's a shuffle, so fancy +math name for a shuttle. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: All right. + +AUDIENCE: Something +going on here. + +PROFESSOR: So then a move is a? + +AUDIENCE: Rotation +[? permutation?]. + +[INAUDIBLE] + +PROFESSOR: All right, so the +thing is-- the difficult part + +of the code is you +have two things that + +are represented by permutations. + +Configurations are +permutations of plastic faces + +onto the array, onto the +array of wireframes faces. + +And then a move is a +permutation of a configuration + +into another configuration. + +OK, so now if I want +to compute neighbors, + +I take-- we think +there are six moves, + +so I'm going to take six moves. + +I'm going to type out the +permutations, so 6 times + +24 numbers, and that's it. + +Now I can compute neighbors. + +Does that make sense? + +AUDIENCE: I think you +have all the permutations. + +PROFESSOR: So there +are six moves, right? + +AUDIENCE: Yeah, but +then it's right. + +Oh yeah-- + +PROFESSOR: If I take +a configuration, + +and I apply the +permutation for this move, + +I'm going to get a +new configuration, + +and that's its neighbor. + +So if I apply the +permutation for LC 4, + +left clockwise to +this configuration, + +I get the new configuration. + +So all I need to do is hard +code those configurations, + +and then I'm done. + +I can compute neighbors. + +But that's a lot of typing. + +I don't want to type as much. + +I want to reduce my +burden a little bit. + +And we can do that by noticing +that some moves are associated + +with some other moves. + +So, if I go left +clockwise move, that's + +the inverse of a left +counterclockwise move. + +So, if given the permutation, +I could compute its inverse, + +then I wouldn't have to +type as many permutations. + +Right? + +Why do I care about that? + +Did anyone take 6004? + +Remember? + +So at some lab, which +is the dreaded beta lab, + +you have to write the control +block for a processor, right? + +And that's a lot of zeros and +1's that you have to type. + +And if you get one wrong, +good luck to [INAUDIBLE]. + +[INTERPOSING VOICES] + +AUDIENCE: 18 wide and 64 tall. + +PROFESSOR: I know. + +AUDIENCE: Copy and paste like. + +AUDIENCE: Yeah, and copy paste. + +[INAUDIBLE] + +PROFESSOR: OK. + +Bad memory. + +Let's move on. + +Let's move on. + +So two good news, two +pieces of good news. + +One, some of these are +redundant in our case, two, + +we wrote everything for you, so +you don't have to write them, + +we're just teaching +you how we did them, + +because the inverse of +a permutation is cool + +and I think it's a +good concept to know. + +So let's look at how +a permutation looks + +like and compute its +inverse and then move on + +to other nice problems. + +OK so let's take a +presentation of five elements, + +not going to go to +24 on the board here. + +3, 5, 1, 2, 4. + +This is how permutations +look like in math mode. + +If you want to be +more explicit, you + +can add a row numbers above. + +And this is a bit more explicit +about what a permutation does. + +So permutation takes an input +list, let's say a b c d e. + +And for this is an output list, +according to the recipe that + +you see here . + +So this pretty much says, the +first element of the output + +is the third element +of the input. + +The second element of the +output is the fifth element + +in the input. + +Wait, this is the +wrong permutation. + +It doesn't look as pretty, so +I'm changing the permutation. + +The third element of the +output is the first element + +in the input. + +The fourth element of the +output is which letter? + +So which letter? + +AUDIENCE: Oh. [INAUDIBLE] + +PROFESSOR: And the fifth element +of the output is which letter? + +AUDIENCE: Did you mean +to get c instead of a? + +No. + +PROFESSOR: Yeah. + +That would make more +sense, wouldn't it? + +Thank you. + +OK. + +So if this is +permutation pi, then this + +is the effect of applying +pi to this original list. + +Now the inverse of a +permutation by minus 1 + +is another bunch of arrows, +and what I want to do + +is, if I take this, which +is the output of pi, + +and I run it through +these arrows, + +I want to get back a b c d e. + +So I want to undo +the effect of pi. + +OK. + +How do I compute this inverse? + +How do I compute pi +minus 1 given pi? + +AUDIENCE: Wait, you're +giving us the initial, + +when we start with c d a e b? + +PROFESSOR: You only +start with this. + +This doesn't matter at all. + +A different list would +get different results. + +So this is the permutation, +and I want pi to the minus 1. + +AUDIENCE: So you take the value. + +So you have 3 4 1 5 2. + +So the value at index +1 you put that index, + +that index has a value +of index 3, et cetera. + +AUDIENCE: So c would +go to position 1? + +AUDIENCE: Wait. + +PROFESSOR: OK. + +AUDIENCE: Is it true +that you can run pi, + +so the number of times it will +eventually equal pi inverse? + +PROFESSOR: Yes, but +that's complicated algebra + +to prove that. + +AUDIENCE: Not forget that. + +Just like make that +[INAUDIBLE] thing that you made + +and sort of flip it. + +PROFESSOR: OK. + +I like that. + +So 34152, 1 2 3 4 5. + +Except this doesn't +look very pretty, + +so I need to sort +them again, right? + +So 1 3, 2 5, 3 1, 4 2, 5 4. + +Right? + +Did you guys come +up with it now? + +Congrats. + +So this is good. + +This is how you +compute an inverse. + +Let's figure out why you +compute an inverse that way. + +Let's look at b. + +So b starts out at +position 2, right? + +And then pi of 5 equals 2, which +means that, after applying 5, + +b is going to go to position 5. + +So pi inverse has to +take b and put it where? + +Back to 2, right? + +Otherwise it's not +a good inverse. + +So pi inverse of 2. + +So the second +element in the output + +has to be which +element in the input? + +5, right? + +Otherwise, this wouldn't +undo the effect of pi. + +So if you write out our +permutation and split + +the index and the value, we +get the inverse permutation. + +So you can compute that with a +couple of lines of Python code. + +OK. + +So this lets us now compute +some of the permutations there. + +So we only have to type +up two, three, four, + +or something like that. + +It's a bit nicer +and you guys don't + +have to type up any, +because we gave them to you. + +Aren't we nice? + +All right. + +Any questions about +permutations or Rubik's cubes? + +AUDIENCE: Wait, so +to get high inverse + +based off those numbers, +you just-- well, + +it's the same thing. + +Wait, but 5 got flipped. + +Or you think the maybe if the +inverse of that matrix then? + +PROFESSOR: So you take these +two and you flip them, right? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: And then you keep +these bound, but you sort them. + +2 5, 3 1, 4, no-- 3 5 1 2 4. + +AUDIENCE: Oh they're still +based off the top row? + +AUDIENCE: Yeah. + +AUDIENCE: Oh, OK. + +AUDIENCE: Wait, how did +he get the second one? + +AUDIENCE: Based off the top row. + +PROFESSOR: So you sort this +one, but you keep the bonds, + +so 3 ends up here and it +gives it 1, 4 ends up here + +and it gives us 2. + +OK. + +So this make sense? + +Good. + +We're remembering +that, that's good. + +Now let's talk about a problem. + +So this is a Rubik's cube, +this is how it works. + +Hopefully we will remember +how to solve game. + +Let's try to solve +StarCraft Well, + +of course we're going to cheat. + +We're going to solve a +simpler version of StarCraft + +because it turns out you +can't really solve StarCraft + +with the computers +that we have now. + +So let's make a few +simplifying assumptions. + +Who play StarCraft, by the way? + +Two? + +OK. + +So you guys, please +pay attention + +to the simplifying +assumptions, because this + +isn't real StarCraft. + +It's a lot easier, so that we +can build a problem out of it. + +All right. + +So we're going to play +with a race called Zerg. + +And so the idea of StarCraft +is you build an army + +and then you take +this army and you + +destroy your opponent, +nice and simple. + +Good old violent games. + +So we're going to look at the +build order part of the game. + +So the build order is the +opening strategy and it takes + +care of the building process, +so it's the strategy that says, + +what are you going +to build and when, + +in order to come up with an +army as quickly as possible? + +So the main goal is to amass +an army quickly and then take + +that army and +destroy the opponent. + +And yes, I know, not +real life StarCraft, + +but let's go with it. + +OK, so these are the +rules in our toy StarCraft + +And the Zerg is started with a +building called the hatchery. + +And out of a hatchery-- +the currency of the game, + +by the way, is minerals. + +We'll write that +down as dollars. + +So out of a hatchery +you can build a drone + +by spending 50 minerals. + +You can build an +overlord by spending 100, + +or you can build a +Zergling by spending 50. + +All right, what do +each of these do? + +A drone harvests minerals +for you, so it's a worker. + +So, for every drone +that you have, + +you get eight minerals a second. + +So drone gets you eight +minerals a second. + +As Zergling is your +attack unit, so this + +is the guy that you want +to build in the end. + +So this destroys your opponents. + +I don't know how to make a +nice icon for that, so big + +smiley green. + +This makes it happy. + +All right. + +Overlords help you +control your units, + +so drones and +Zerglings are units. + +You can't build-- for every +eight units that you build, + +you have to have an overlord. + +Otherwise, you can't +build more units + +until you build overlords. + +So if you have eight drones, +you can't build a ninth on one + +you build an overlord. + +If you have eight drones +and these eight Zerglings, + +you have to build +a second overlord + +to be able to build more units. + +So one overlord can help +you control eight units. + +In order to build +a Zergling, which + +is what you want +to do in the end, + +because these are the attack +units, you need to spend $50, + +and you also need to +have one building called + +a spawning pool. + +You what? + +All right. + +So how do you build +that spawning pool? + +Drones can work for +you, but they can also + +transform into buildings. + +So a drone mutates into a +building, and after it mutates, + +it doesn't work for you +anymore, by the way, so no more + +minerals. + +So a drone can mutate into the +spawning pool for 200 minerals, + +I think. + +It can mutate into a hatchery. + +That's the same thing +that you have up here for, + +how much is it? + +$450. + +And it can mutate into +an evolution chamber + +that we'll talk +about soon, for $400. + +OK. + +Why do we care about having +more than one hatchery? + +One hatchery can build one unit +per second, no more than that. + +So once you have a lot +of drones and you're + +making a lot of money, you need +to have a lot of hatcheries + +so that you can spend the money. + +Our goal is not to amass money, +it's to build units, right? + +So money doesn't +help you, I'm going + +to spend it as fast as possible. + +OK. + +An evolution chamber +lets you build-- let's + +you upgrade research +to technologies. + +And these technologies +aren't like badges. + +Once you get them, +you keep them. + +So you can research +an attack upgrade + +and you can research +a defense upgrade. + +They're both 1,000 minerals, +but you only have to do it once. + +Why do I care about these? + +They decide how strong +your Zerglings are. + +So, given a Zergling, at +the beginning of the game, + +you don't have the +attack upgrade, + +and you don't have +a defense upgrade. + +So the Zerglings attack is 1. + +If you research +the attack upgrade, + +but you haven't researched +the defense one, + +their total power is 133. + +If you research the defense +upgrade, but not the attack + +upgrade, their +total power is 1.2. + +And after your research both of +them, their total power is 2. + +Again, oversimplifying. + +So, we have to build an army +that's as powerful as possible. + +So in the end you want to +have both of these researched. + +All right. + +Now there's one more +limitation, that is, + +you cannot control more than +200 of these units total, + +because even if you +have a lot of overlords, + +your brain isn't immensely huge, +so you can only control 200 + +units. + +So we want to build these 200 +units as fast as possible. + +And out of these +200 units, we want + +to have at least 150 Zerglings. + +If you build 200 +drones, you're not + +going to attack your +opponent with that, + +those aren't very useful. + +But you need some drones +in order to make money, + +so you need the balance. + +So the goal is to get to 200 +units as quickly as possible, + +and at least 150 Zergs. + +Yes? + +Evolution chamber. + +Easy, that's too much. + +OK. + +So how do we solve this? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So how +do we solve this? + +AUDIENCE: Watch the pros play. + +PROFESSOR: Well, they're going +to play real StarCraft this + +is toy StarCraft this is +six-level 6 StarCraft so it's + +not going to work. + +But there is a simple +strategy, because I + +haven't added one +last constraint. + +AUDIENCE: Lets me guess. + +PROFESSOR: No. + +It's going to be +harassing your enemy. + +But if you don't have to +harass your enemy intuitively + +and build your economy +first, so first + +build your drones +and hatcheries, + +and then pop out +Zerglings, right? + +So there's a greedy strategy. + +If you spend about an hour +with a sheet of paper, + +you can realize what +is the right order + +to build drones and +hatcheries and overlords, + +so that you get to a nice +big economy, and then, Bam! + +Build Zerglings. + +Once you get to 50 drones, +you start build Zerglings + +as fast as possible. + +So this is a greedy +strategy, you + +don't need to do a +lot of work for that. + +So we want to make +things more interesting. + +So in order to make +things more interesting, + +the game time goes in seconds. + +Everything that we had +here is in seconds. + +Every two minutes, so two +minutes, which is 120 seconds. + +So every two minutes +I want to assemble + +a small pack of +Zerglings and send them + +to the enemy to harass them. + +And the Antonio enemy +will defend themselves + +and they will +destroy my Zerglings, + +but they won't be able to +focus on the game very well. + +So I need to do this in order +to have a good chance to win. + +If I don't do this, my +strategy is invalid. + +AUDIENCE: Does the enemy, +does it do that to us as well? + +PROFESSOR: No. + +We're sending them facts. + +We are going to have a really +fast strategy, because we're + +computing the optimal +strategy, so they're not + +going to have time. + +They're going to +be fighting us off. + +OK, how many +Zerglings do I send? + +I have to send enough +Zerglings so that the attack + +power at minutes 2m is +6 times log 1 plus m. + +You knew there has to +be some mapping there. + +So the reason for this is, let's +look at the first two minutes. + +After two minutes, if we +haven't researched any upgrades, + +we need to send this +in six Zerglings. + +If we researched both +upgrades, we only + +need to send in three Zerglings. + +If we researched +one of the upgrades, + +we need to send +in five Zerglings. + +So this is the +total attack power, + +not the numbers are of +Zerglings that we need to send. + +AUDIENCE: And is minutes? + +PROFESSOR: Actually, +it's basically + +which attack wave you're +doing, so every two minutes. + +AUDIENCE: Oh, OK. + +So the first one +is m equals zero. + +PROFESSOR: And 1. + +That is not the one attacking +right in the beginning + +when we don't have Zerglings. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Equals 1, n equals 2, +n equals 3, so on and so forth. + +AUDIENCE: How did +you get that formula? + +OK. + +PROFESSOR: Is it +making your life hard? + +Would that be logged base +2, or is that log base 10? + +PROFESSOR: Sure, log base 2. + +Fine. + +OK, so how are we +going to solve this? + +Intuitively, how did +we solve all the game + +problems, all the +problems recently? + +What are we going to do? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So the +first thing we're + +going to build a graph, right? + +AUDIENCE: Yeah. + +PROFESSOR: So build a graph. + +The vertices are the +states of the game, + +so a vertex shows +me what state I'm in + +and an edge shows +possible moves that I do. + +So what I need to keep track +in the vertex, what's my state? + +AUDIENCE: How much money +you have, and how many units + +you have? + +And maybe how fast +you're making money? + +AUDIENCE: Oh, unless +the states, are + +states-- they're not movable? + +Oh, I guess they could be +moveable [INAUDIBLE] could + +do nothing, in the +next second, right? + +PROFESSOR: So you're saying +you need to keep track of time, + +too? + +AUDIENCE: I don't know. + +PROFESSOR: OK so maybe time. + +What else? + +AUDIENCE: Badge +[INAUDIBLE] thing. + +PROFESSOR: OK so upgrades. + +You said units, I'm +going to say buildings. + +AUDIENCE: Wait, is +Zergling is a building? + +PROFESSOR: A Zergling +is a unit, so- + +AUDIENCE: Overlords. + +PROFESSOR: Unit, unit, unit. + +Building, building, +building, upgrade, upgrade. + +So let's see how are we +going to keep track of them. + +That's a good point. + +We started looking at units, +we started looking at units. + +So how do I keep +track of my units? + +What I need to know? + +AUDIENCE: The number of +drones, overlords, servlings. + +PROFESSOR: Droids, drones, +overlords, Zerglings. + +OK. + +How about buildings? + +AUDIENCE: [INAUDIBLE] PHEC-- + +PROFESSOR: Almost. + +So I want to know the +number of hatcheries, + +because this is how +fast I can produce. + +But then how many spawning +pools am I going to build? + +Good. + +So that was StarCraft player 1. + +Once you have a spawning +pool, you can build Zerglings, + +there's no reason to +build more than one. + +So a spawning pool is +going to be like a badge. + +Once you build it, you +have it, you're done. + +So it's Boolean. + +AUDIENCE: Wait, what's +a spawning pool again? + +PROFESSOR: So a spawning +pool is something + +that you build off a drone +and once you have it, + +you can build Zerglings +from a hatchery. + +So that's all it does. + +AUDIENCE: Why would +you want two if you + +can build four Zerglings? + +PROFESSOR: So the spawning +pool doesn't build a Zergling. + +See, the hatchery +builds the Zerglings. + +So the spawning +pool is just there. + +You need to have it +to cross the edge. + +Otherwise you can't. + +AUDIENCE: OK. + +I understand. + +PROFESSOR: OK. + +So what else for buildings? + +Whether you have +it or not, right? + +OK. + +How about upgrades? + +[INAUDIBLE] a u, d u. + +PROFESSOR: So two +flags, a u, d u. + +Cool. + +So now we have the thorny +issues of money and time. + +Let's say that we're going to +have some sort of approximation + +that's going to allow us +to not keep track of money, + +because money is-- you +can have a lot of money, + +so that will give us +an explosion of states. + +So we're going to assume +that we're spending money + +as fast as possible, +because that's + +what you usually want to do. + +AUDIENCE: So should your +money always be zero then? + +PROFESSOR: Almost. + +It's very close to that. + +So you start off with no money. + +You accumulate +money, then you're + +going to issue some build +orders and build something. + +And your money's +going to drop, maybe + +to zero, maybe to almost zero. + +Then you wait to +accumulate more money, + +issue another build order. + +Wait to accumulate more money, +hopefully it goes faster now. + +Issue another build order. + +We're going to approximate +that every time we + +issue a build order, +so every time we + +tell our things to +build something, + +the money will drop to zero. + +So that doesn't mean you +can only build one thing + +and then your money +drops to zero. + +If you wait for a few +seconds and then you + +have two hatcheries and tell +both of them to build drones, + +you build two drones and +then your money goes to zero. + +So that means that if we +model our states carefully, + +we don't have to +keep track of money. + +AUDIENCE: You should +probably keep track of time. + +AUDIENCE: Actually +keep track of the rate + +you're gathering though, right? + +PROFESSOR: So what's the +rate that you're gathering? + +AUDIENCE: It's the number of-- + +AUDIENCE: Oh [INAUDIBLE] +drones, yeah. [INAUDIBLE], OK. + +PROFESSOR: So this +multiplied by 8%. + +AUDIENCE: So we should +keep track of time. + +PROFESSOR: OK. + +So how would we solve it +if we keep track of time? + +AUDIENCE: You multiply + +AUDIENCE: Can you do +that layer thing again? + +Where is that? + +PROFESSOR: So you're going +to have-- so what's a layer? + +AUDIENCE: Actually, never mind. + +AUDIENCE: I want to +know what a layer is. + +PROFESSOR: Sorry? + +AUDIENCE: I want to +know what a layer is. + +PROFESSOR: So last time we-- we +solved problems by saying that, + +so we had the graph of streets. + +We had a highway graph. + +And that was a 2D graph. + +And we made it into a +3D graph by adding time + +as a third dimension. + +So we had layers, +where each layer was, + +said that you're at +a point in the graph + +at a certain point in time. + +So there's a layer 4 +times 0, layer 4 time 1, + +so on and so forth. + +And you start at time 0 and +kept going up the graph. + +AUDIENCE: You have +a flag that says, + +I've just purchased something? + +Because that way then you'll +know that you've completely + +exhausted your-- that +maybe that will tell you + +that you can't buy +anything for awhile, right? + +Because if we're not +keeping track of money then + +we should know [INAUDIBLE]. + +PROFESSOR: OK. + +So that's a good point. + +So if I have-- so suppose here +I have to wait for five seconds + +to get enough +money to do a move. + +If I keep track of +time in my state and I + +have five things here. + +I also have to keep +track of money, right? + +I have to know how +much money I'm getting, + +so that I know where +I'm buying things. + +On the other hand, +in this case, if I + +keep track of both time +and money as states, + +I can implement a +precise strategy. + +I don't need this approximation. + +If I do that, then what +search algorithm would I use? + +So if I have time in states, +so each vertex in my note + +says that I get from some +states to some other state + +in one unit of time. + +What algorithm do I use +to search for my strategy? + +Yeah. + +Why do I use BFS? + +AUDIENCE: Because every +edge has the same weight. + +PROFESSOR: Every edge has +the same weight, right? + +So if we keep +track of time, then + +we-- we keep track of time, +we keep track of money, + +we use BFS, we have a solution. + +So. + +Let's try to not do +it, either of these. + +If I don't want to +keep track of time + +and I don't want to +keep track of money, + +what would an edge be? + +If I want to say that, hey, this +is a state and this is a state. + +What should be the +edge connecting them. + +AUDIENCE: What other +item you got is. + +AUDIENCE: Is that +after a second? + +PROFESSOR: So the +distance between these + +won't be a second, right? + +If I have to wait +for five seconds to + +accumulate enough to +issue this build order + +that would get me +the state then-- + +AUDIENCE: The time +you have to wait? + +PROFESSOR: So that's what +I would put on an edge. + +So this way I don't have +to keep track of money, + +I don't have to +keep track of time. + +So the graph is smaller. + +So I can look into +bigger graphs. + +If I do this, what +algorithm do I use? + +To find my strategy? + +AUDIENCE: [INAUDIBLE]. + +[INTERPOSING VOICES] + +PROFESSOR: So no time, no money. + +And [? extra ?]. + +So this looks +reasonably easy, right? + +I mean, if you want to get +from one state to another, + +you see what you'd +have to build, + +you see how much +it costs, and you + +see how much you have to wait +to accumulate those resources. + +Except there's one glitch. + +How do we deal with this? + +How do we make sure that we do +our attacks on time and how do + +we know that we're-- how +do we keep track of them? + +AUDIENCE: What is this +again representing? + +PROFESSOR: So this is +that every two minutes you + +have to have a +number of Zerglings + +that you're sending +to attack the enemy. + +And the number of Zerglings +that you need to have + +depends on the time and +it depends on the upgrades + +that you got. + +So how do we keep track of this? + +AUDIENCE: If the edges +are a function of time, + +then just know that at radius +120-- at radius 120 over 5, + +then you'd have to +send more Zerglings. + +PROFESSOR: So what if not all +the edges have the same weight. + +So let's look at how a graph +looks like for a little bit. + +So we're going to +have an initial state, + +say one hatchery and six +drones and one overlord. + +And we want to +build a new drone. + +Say we want to +build a new drone. + +A drone costs 50 minerals. + +We have six drones. + +Each drone gets us +eight minerals a second, + +so in one second we're +going to get 48 minerals. + +So bummer, we have to wait for +two seconds to build one drone. + +And now we're going to be in +the state of one hatchery, seven + +drones, one overlord. + +If you said we want to +build a hatchery-- then + +we're going to need to +accumulate 400 or 450. + +Oh, we have to accumulate 450, +using six drones, 48 minerals, + +so I guess nine seconds. + +So we're going to have +to wait for nine seconds + +to get that money. + +And then when we +build, we're going + +to spend the drone +building, because it's + +going to turn into a hatchery. + +And then we're going to end +up with two hatcheries, five + +drones, and one overlord. + +So edges have different weights. + +So I can't look at the radius +in terms of number of his edges. + +AUDIENCE: Everything +builds instantaneously. + +PROFESSOR: Yeah, sure. + +AUDIENCE: You could keep track +of just the total distance + +from whatever starting +build you are? + +AUDIENCE: Actually, +if the distance + +from the origin to where +you're at is a multiple of 120, + +then you should +have another state + +that you have to [INAUDIBLE]. + +AUDIENCE: Assuming you have any +drones left, hopefully you do. + +PROFESSOR: So that's modeling. + +One way of doing it is +sure, model every round + +of the attack as one, +every round of harassment + +is one there in the graph, +and we can do it that way. + +Is that what you're saying? + +So you can't-- once +you're at 120 seconds, + +you have to do an attack and +then you get to the next layer + +in the graph. + +AUDIENCE: That makes +a lot of sense. + +AUDIENCE: Of course that's +what we were thinking. + +PROFESSOR: How about +let's not do that. + +How about let's represent +it without layers? + +So that's good. + +You're getting closer +to the solution. + +It is much better than +representing every time. + +Write the number of +layers this time over 120, + +it's a huge improvement. + +Well, we can do it +without any-- we can do it + +without any time +notion whatsoever. + +Let's see, can I let +you think about it? + +Oh, I can let you think +about it for 30 seconds. + +So there's a key +insight here that-- + +AUDIENCE: Ooh. + +PROFESSOR: Yeah. + +AUDIENCE: [INAUDIBLE] but if +you figure how much time has + +elapsed, based on +the items we have + +and our starting state, right? + +Because if we have +two hatcheries + +and we started +with one hatchery, + +we know that at least +nine seconds has elapsed. + +PROFESSOR: Well, so I like the +first part of what you said, + +the second part is +too complicated. + +But we can know +what time we're at. + +Why? + +AUDIENCE: Because it takes +a certain amount of time + +to achieve everything, +each thing. + +AUDIENCE: Are we assuming +that we take the shortest + +path to get to each +state that we're at? + +PROFESSOR: So we're +using the extra. + +How does the extra work? + +You have a queue, +a priority queue. + +You extract a node, you +look at the neighbors. + +When you extract +the node, do you + +know the distance to that node? + +AUDIENCE: Can you explain? + +You ask? + +PROFESSOR: I'm asking. + +AUDIENCE: I know, but like +the node asks and says, + +how far away are you? + +PROFESSOR: So you need to keep +that in the priority queue. + +So the extra-- +the main invariant + +is that once you +pull out the node, + +you're not going to find any +shorter path to that node. + +So you already know +the shortest path. + +That how you sort the nodes +in the priority queue. + +So when we're at +a configuration-- + +Say we're at some +configuration here, + +two hatches, six drones, +and five Zerglings. + +We already know that, say +we're at time 119 seconds. + +If what I want to do next +is build another hatchery, + +then I have to wait, what, six +drones, same thing as before. + +I have to wait for +nine seconds, right? + +So the edge would +look like this. + +And then we're going to get +to three hatcheries, five + +drones, five Zerglings. + +This crosses a one, this crosses +a two-minute boundary, right? + +So when I cross +this boundary, I'd + +better have enough +Zerglings to do an attack. + +Do I have enough +Zerglings to do an attack? + +No. + +So is this a valid move? + +Is this the valid +edge in our graph? + +It's not. + +So when you're at a node, +you already know the time + +that you need to +get to that node, + +so when you generate +the neighbors, + +you can check for +each edge to see + +it crosses that 120 second game. + +Now let's assume it does. + +Let's see how this +works and this + +is the last thing we're doing. + +So suppose you have two +hatcheries, six drones, + +and eight Zerglings. + +And you're going to +build that same hatchery. + +So you're going to go +past this 120 second mark. + +What state are you +going to end up in? + +How many hatcheries? + +AUDIENCE: Three. + +PROFESSOR: OK. + +How many drones. + +AUDIENCE: Five. + +PROFESSOR: How many Zerglings. + +AUDIENCE: Two. + +PROFESSOR: Yes. + +So key elements, two +Zerglings, because this edge + +crosses the 120-second +harassment boundary, + +so you have to send +in six Zerglings + +and you're going to lose them. + +So we're taking advantage of +how the extra works to sort + +of generate our +edges on the fly. + +So we wouldn't be able +to regenerate this graph, + +even if we wanted to have to. + +We have to work with the +implicit representation + +and, as we learn the +distances to the nodes, + +the minimum distances, +we also learned the edges + +that we have coming +out of those nodes. + +AUDIENCE: So it's kinda of +like this graph that's growing + +and we're like as it +gets to a certain point + +we kill a bunch of paths +and then it keeps on going. + +PROFESSOR: Yeah. + +Doesn't this makes sense? + +So the good news is +that this is like we're + +training you to run +a 10-mile marathon, + +so you can run 50 +meters for the test. + +Let's still try to +get it, because I + +think it's a cool problem. \ No newline at end of file diff --git a/pA-AgV8wo0o.txt b/pA-AgV8wo0o.txt new file mode 100644 index 0000000000000000000000000000000000000000..079c4d0a1ac83362e062d032080f50c3ce5af8e6 --- /dev/null +++ b/pA-AgV8wo0o.txt @@ -0,0 +1,10475 @@ +align:start position:0% + +welcome to + + align:start position:0% +welcome to + + + align:start position:0% +welcome to +fintech shaping the future of the world + + align:start position:0% +fintech shaping the future of the world + + + align:start position:0% +fintech shaping the future of the world +of finance + + align:start position:0% +of finance + + + align:start position:0% +of finance +and happy spring it's may i thought + + align:start position:0% +and happy spring it's may i thought + + + align:start position:0% +and happy spring it's may i thought +what the heck you've got to be a little + + align:start position:0% +what the heck you've got to be a little + + + align:start position:0% +what the heck you've got to be a little +innovative try teaching from outdoors so + + align:start position:0% +innovative try teaching from outdoors so + + + align:start position:0% +innovative try teaching from outdoors so +this is + + align:start position:0% +this is + + + align:start position:0% +this is +not a virtual background if + + align:start position:0% +not a virtual background if + + + align:start position:0% +not a virtual background if +the if the sun is too much or + + align:start position:0% +the if the sun is too much or + + + align:start position:0% +the if the sun is too much or +the the birds are too much that's an + + align:start position:0% +the the birds are too much that's an + + + align:start position:0% +the the birds are too much that's an +additional thing romaine can give me + + align:start position:0% +additional thing romaine can give me + + + align:start position:0% +additional thing romaine can give me +advice on + + align:start position:0% +advice on + + + align:start position:0% +advice on +now today we're going to dive into + + align:start position:0% +now today we're going to dive into + + + align:start position:0% +now today we're going to dive into +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +and technology or would some call this + + align:start position:0% +and technology or would some call this + + + align:start position:0% +and technology or would some call this +little sector of fintech + + align:start position:0% +little sector of fintech + + + align:start position:0% +little sector of fintech +as insure tech but it's not so little + + align:start position:0% +as insure tech but it's not so little + + + align:start position:0% +as insure tech but it's not so little +and it's not just simply because + + align:start position:0% +and it's not just simply because + + + align:start position:0% +and it's not just simply because +the excitement is around payments and + + align:start position:0% +the excitement is around payments and + + + align:start position:0% +the excitement is around payments and +challenger banks and + + align:start position:0% +challenger banks and + + + align:start position:0% +challenger banks and +apps like robin hood and the capital + + align:start position:0% +apps like robin hood and the capital + + + align:start position:0% +apps like robin hood and the capital +markets and so forth that we leave in + + align:start position:0% +markets and so forth that we leave in + + + align:start position:0% +markets and so forth that we leave in +short tech to the end i also think in + + align:start position:0% +short tech to the end i also think in + + + align:start position:0% +short tech to the end i also think in +short tech is an interesting field that + + align:start position:0% +short tech is an interesting field that + + + align:start position:0% +short tech is an interesting field that +it brings + + align:start position:0% +it brings + + + align:start position:0% +it brings +all the pieces together in some way + + align:start position:0% +all the pieces together in some way + + + align:start position:0% +all the pieces together in some way +it brings together a part of finance + + align:start position:0% +it brings together a part of finance + + + align:start position:0% +it brings together a part of finance +that has + + align:start position:0% +that has + + + align:start position:0% +that has +big legacy incumbents in every country + + align:start position:0% +big legacy incumbents in every country + + + align:start position:0% +big legacy incumbents in every country +we're in + + align:start position:0% +we're in + + + align:start position:0% +we're in +there's this handful of life insurance + + align:start position:0% +there's this handful of life insurance + + + align:start position:0% +there's this handful of life insurance +companies and + + align:start position:0% +companies and + + + align:start position:0% +companies and +property and casualty insurance that's + + align:start position:0% +property and casualty insurance that's + + + align:start position:0% +property and casualty insurance that's +those + + align:start position:0% +those + + + align:start position:0% +those +that offer lines of insurance on our + + align:start position:0% +that offer lines of insurance on our + + + align:start position:0% +that offer lines of insurance on our +homes our autos and so forth + + align:start position:0% +homes our autos and so forth + + + align:start position:0% +homes our autos and so forth +health care insurers particularly in + + align:start position:0% +health care insurers particularly in + + + align:start position:0% +health care insurers particularly in +those countries that have + + align:start position:0% +those countries that have + + + align:start position:0% +those countries that have +uh like the u.s big + + align:start position:0% +uh like the u.s big + + + align:start position:0% +uh like the u.s big +open health care systems these insurance + + align:start position:0% +open health care systems these insurance + + + align:start position:0% +open health care systems these insurance +companies + + align:start position:0% +companies + + + align:start position:0% +companies +big legacy companies have tended to be a + + align:start position:0% +big legacy companies have tended to be a + + + align:start position:0% +big legacy companies have tended to be a +little behind the curve + + align:start position:0% +little behind the curve + + + align:start position:0% +little behind the curve +of technology compared to the wall + + align:start position:0% +of technology compared to the wall + + + align:start position:0% +of technology compared to the wall +street firms not a lot behind but a + + align:start position:0% +street firms not a lot behind but a + + + align:start position:0% +street firms not a lot behind but a +little behind + + align:start position:0% +little behind + + + align:start position:0% +little behind +and then the insure tech itself the + + align:start position:0% +and then the insure tech itself the + + + align:start position:0% +and then the insure tech itself the +fintech within insure + + align:start position:0% +fintech within insure + + + align:start position:0% +fintech within insure +assurance has done some really + + align:start position:0% +assurance has done some really + + + align:start position:0% +assurance has done some really +interesting things particularly around + + align:start position:0% +interesting things particularly around + + + align:start position:0% +interesting things particularly around +alternative data and we're going to dive + + align:start position:0% +alternative data and we're going to dive + + + align:start position:0% +alternative data and we're going to dive +into some of these + + align:start position:0% +into some of these + + + align:start position:0% +into some of these +uh opportunities and also + + align:start position:0% +uh opportunities and also + + + align:start position:0% +uh opportunities and also +uh they're they're a little bit uh + + align:start position:0% +uh they're they're a little bit uh + + + align:start position:0% +uh they're they're a little bit uh +new forms of alternative data it's not + + align:start position:0% +new forms of alternative data it's not + + + align:start position:0% +new forms of alternative data it's not +just about our credit rating + + align:start position:0% +just about our credit rating + + + align:start position:0% +just about our credit rating +it's about our driving it's about our + + align:start position:0% +it's about our driving it's about our + + + align:start position:0% +it's about our driving it's about our +homes + + align:start position:0% +homes + + + align:start position:0% +homes +it's about thinking about can we + + align:start position:0% +it's about thinking about can we + + + align:start position:0% +it's about thinking about can we +underwrite insurance risk + + align:start position:0% +underwrite insurance risk + + + align:start position:0% +underwrite insurance risk +related to how we live our lives + + align:start position:0% +related to how we live our lives + + + align:start position:0% +related to how we live our lives +how we drive our cars how small + + align:start position:0% +how we drive our cars how small + + + align:start position:0% +how we drive our cars how small +businesses + + align:start position:0% +businesses + + + align:start position:0% +businesses +are operated and whether there's more + + align:start position:0% +are operated and whether there's more + + + align:start position:0% +are operated and whether there's more +information + + align:start position:0% +information + + + align:start position:0% +information +that can be brought to bear or not just + + align:start position:0% +that can be brought to bear or not just + + + align:start position:0% +that can be brought to bear or not just +financial inclusion but the pricing and + + align:start position:0% +financial inclusion but the pricing and + + + align:start position:0% +financial inclusion but the pricing and +underwriting of risk + + align:start position:0% +underwriting of risk + + + align:start position:0% +underwriting of risk +of course we're going to see the same + + align:start position:0% +of course we're going to see the same + + + align:start position:0% +of course we're going to see the same +trends about artificial intelligence + + align:start position:0% +trends about artificial intelligence + + + align:start position:0% +trends about artificial intelligence +we're going to see some + + align:start position:0% +we're going to see some + + + align:start position:0% +we're going to see some +really important trends around user + + align:start position:0% +really important trends around user + + + align:start position:0% +really important trends around user +interfaces + + align:start position:0% +interfaces + + + align:start position:0% +interfaces +and one of the most interesting areas + + align:start position:0% +and one of the most interesting areas + + + align:start position:0% +and one of the most interesting areas +around user interfaces is what's called + + align:start position:0% +around user interfaces is what's called + + + align:start position:0% +around user interfaces is what's called +claims management + + align:start position:0% +claims management + + + align:start position:0% +claims management +an area that you know hopefully you + + align:start position:0% +an area that you know hopefully you + + + align:start position:0% +an area that you know hopefully you +don't have to think about too much but + + align:start position:0% +don't have to think about too much but + + + align:start position:0% +don't have to think about too much but +amongst this class of + + align:start position:0% +amongst this class of + + + align:start position:0% +amongst this class of +80 or more i'm sure that somebody's had + + align:start position:0% +80 or more i'm sure that somebody's had + + + align:start position:0% +80 or more i'm sure that somebody's had +a little fender bender had some scrape + + align:start position:0% +a little fender bender had some scrape + + + align:start position:0% +a little fender bender had some scrape +up on the roads + + align:start position:0% +up on the roads + + + align:start position:0% +up on the roads +and now that there are apps that you can + + align:start position:0% +and now that there are apps that you can + + + align:start position:0% +and now that there are apps that you can +just on your mobile phone + + align:start position:0% +just on your mobile phone + + + align:start position:0% +just on your mobile phone +take some quick photographs and put it + + align:start position:0% +take some quick photographs and put it + + + align:start position:0% +take some quick photographs and put it +right into the system + + align:start position:0% +right into the system + + + align:start position:0% +right into the system +claims management is changing quite a + + align:start position:0% +claims management is changing quite a + + + align:start position:0% +claims management is changing quite a +bit now + + align:start position:0% +bit now + + + align:start position:0% +bit now +as well and there's startups in this + + align:start position:0% +as well and there's startups in this + + + align:start position:0% +as well and there's startups in this +space that basically say we will get you + + align:start position:0% +space that basically say we will get you + + + align:start position:0% +space that basically say we will get you +better claims management + + align:start position:0% +better claims management + + + align:start position:0% +better claims management +faster smoother and a better user + + align:start position:0% +faster smoother and a better user + + + align:start position:0% +faster smoother and a better user +experience about claims management + + align:start position:0% +experience about claims management + + + align:start position:0% +experience about claims management +so with that i'm going to try to um + + align:start position:0% +so with that i'm going to try to um + + + align:start position:0% +so with that i'm going to try to um +upload the slides again if we can join + + align:start position:0% +upload the slides again if we can join + + + align:start position:0% +upload the slides again if we can join +sort of the community together uh sort + + align:start position:0% +sort of the community together uh sort + + + align:start position:0% +sort of the community together uh sort +of videos on + + align:start position:0% +of videos on + + + align:start position:0% +of videos on +uh please raise your hands actively + + align:start position:0% +uh please raise your hands actively + + + align:start position:0% +uh please raise your hands actively +romaine's gonna be watching + + align:start position:0% +romaine's gonna be watching + + + align:start position:0% +romaine's gonna be watching +uh for any blue hands up also + + align:start position:0% +uh for any blue hands up also + + + align:start position:0% +uh for any blue hands up also +in the chat and uh if the birds get to + + align:start position:0% +in the chat and uh if the birds get to + + + align:start position:0% +in the chat and uh if the birds get to +be too much just know that i'll go back + + align:start position:0% +be too much just know that i'll go back + + + align:start position:0% +be too much just know that i'll go back +in on + + align:start position:0% +in on + + + align:start position:0% +in on +inside on wednesday romaine how is it so + + align:start position:0% +inside on wednesday romaine how is it so + + + align:start position:0% +inside on wednesday romaine how is it so +far + + align:start position:0% +far + + + align:start position:0% +far +it's fine it's very nice don't worry all + + align:start position:0% +it's fine it's very nice don't worry all + + + align:start position:0% +it's fine it's very nice don't worry all +right + + align:start position:0% +right + + + align:start position:0% +right +all right he's he's assuring me that i + + align:start position:0% +all right he's he's assuring me that i + + + align:start position:0% +all right he's he's assuring me that i +can keep having a little bit of uh + + align:start position:0% +can keep having a little bit of uh + + + align:start position:0% +can keep having a little bit of uh +of in indulgence here uh + + align:start position:0% +of in indulgence here uh + + + align:start position:0% +of in indulgence here uh +in this uh beautiful outdoor setting and + + align:start position:0% +in this uh beautiful outdoor setting and + + + align:start position:0% +in this uh beautiful outdoor setting and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +what i'm gonna need to do is go to the + + align:start position:0% +what i'm gonna need to do is go to the + + + align:start position:0% +what i'm gonna need to do is go to the +share screens + + align:start position:0% +share screens + + + align:start position:0% +share screens +so we're going to talk a little bit + + align:start position:0% +so we're going to talk a little bit + + + align:start position:0% +so we're going to talk a little bit +we're going to start a little bit about + + align:start position:0% +we're going to start a little bit about + + + align:start position:0% +we're going to start a little bit about +the insurance value chain + + align:start position:0% +the insurance value chain + + + align:start position:0% +the insurance value chain +and the sector's landscape now and + + align:start position:0% +and the sector's landscape now and + + + align:start position:0% +and the sector's landscape now and +traditionally in business schools + + align:start position:0% +traditionally in business schools + + + align:start position:0% +traditionally in business schools +traditionally + + align:start position:0% +traditionally + + + align:start position:0% +traditionally +in worlds of finance and finance majors + + align:start position:0% +in worlds of finance and finance majors + + + align:start position:0% +in worlds of finance and finance majors +there's a lot of time spent on banking + + align:start position:0% +there's a lot of time spent on banking + + + align:start position:0% +there's a lot of time spent on banking +and on capital markets and there's + + align:start position:0% +and on capital markets and there's + + + align:start position:0% +and on capital markets and there's +some time but less time spent on + + align:start position:0% +some time but less time spent on + + + align:start position:0% +some time but less time spent on +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +and so i'm going to just lay the + + align:start position:0% +and so i'm going to just lay the + + + align:start position:0% +and so i'm going to just lay the +groundwork a little bit about insurance + + align:start position:0% +groundwork a little bit about insurance + + + align:start position:0% +groundwork a little bit about insurance +some of the challenges in the sector + + align:start position:0% +some of the challenges in the sector + + + align:start position:0% +some of the challenges in the sector +itself and then get into this field + + align:start position:0% +itself and then get into this field + + + align:start position:0% +itself and then get into this field +fintech and insurance or what a lot of + + align:start position:0% +fintech and insurance or what a lot of + + + align:start position:0% +fintech and insurance or what a lot of +people call insure tech + + align:start position:0% +people call insure tech + + + align:start position:0% +people call insure tech +opportunities business models and the + + align:start position:0% +opportunities business models and the + + + align:start position:0% +opportunities business models and the +startups so that's sort of the goal of + + align:start position:0% +startups so that's sort of the goal of + + + align:start position:0% +startups so that's sort of the goal of +the + + align:start position:0% +the + + + align:start position:0% +the +class the readings uh + + align:start position:0% +class the readings uh + + + align:start position:0% +class the readings uh +were really about this area of insure + + align:start position:0% +were really about this area of insure + + + align:start position:0% +were really about this area of insure +tech there was a + + align:start position:0% +tech there was a + + + align:start position:0% +tech there was a +a handful of them + + align:start position:0% +a handful of them + + + align:start position:0% +a handful of them +the bank of international sediment + + align:start position:0% +the bank of international sediment + + + align:start position:0% +the bank of international sediment +reading was really talking about some of + + align:start position:0% +reading was really talking about some of + + + align:start position:0% +reading was really talking about some of +the regulatory challenges and whether + + align:start position:0% +the regulatory challenges and whether + + + align:start position:0% +the regulatory challenges and whether +insure tech is will change some of the + + align:start position:0% +insure tech is will change some of the + + + align:start position:0% +insure tech is will change some of the +risks + + align:start position:0% +risks + + + align:start position:0% +risks +in terms of regulating this space + + align:start position:0% +in terms of regulating this space + + + align:start position:0% +in terms of regulating this space +and then a little reading about asia and + + align:start position:0% +and then a little reading about asia and + + + align:start position:0% +and then a little reading about asia and +if you've not had the opportunity to + + align:start position:0% +if you've not had the opportunity to + + + align:start position:0% +if you've not had the opportunity to +look at some of the readings because + + align:start position:0% +look at some of the readings because + + + align:start position:0% +look at some of the readings because +they were just put up last friday + + align:start position:0% +they were just put up last friday + + + align:start position:0% +they were just put up last friday +uh go back sort of dive in take a take a + + align:start position:0% +uh go back sort of dive in take a take a + + + align:start position:0% +uh go back sort of dive in take a take a +little look + + align:start position:0% +little look + + + align:start position:0% +little look +and again we'll see if there's anybody + + align:start position:0% +and again we'll see if there's anybody + + + align:start position:0% +and again we'll see if there's anybody +who wants to give a little few + + align:start position:0% +who wants to give a little few + + + align:start position:0% +who wants to give a little few +in this field but what opportunities in + + align:start position:0% +in this field but what opportunities in + + + align:start position:0% +in this field but what opportunities in +the current + + align:start position:0% +the current + + + align:start position:0% +the current +insurance sector or what are the pain + + align:start position:0% +insurance sector or what are the pain + + + align:start position:0% +insurance sector or what are the pain +points you think + + align:start position:0% +points you think + + + align:start position:0% +points you think +that you might want to highlight um + + align:start position:0% +that you might want to highlight um + + + align:start position:0% +that you might want to highlight um +and and again this is just to get a + + align:start position:0% +and and again this is just to get a + + + align:start position:0% +and and again this is just to get a +little conversation going so + + align:start position:0% +little conversation going so + + + align:start position:0% +little conversation going so +romaine okay + + align:start position:0% +romaine okay + + + align:start position:0% +romaine okay +here we go who will be our first + + align:start position:0% +here we go who will be our first + + + align:start position:0% +here we go who will be our first +volunteer for today + + align:start position:0% +volunteer for today + + + align:start position:0% +volunteer for today +has anybody ever had insurance and felt + + align:start position:0% +has anybody ever had insurance and felt + + + align:start position:0% +has anybody ever had insurance and felt +there was a little pain point michael + + align:start position:0% +there was a little pain point michael + + + align:start position:0% +there was a little pain point michael +i see a hand up as always michael is + + align:start position:0% +i see a hand up as always michael is + + + align:start position:0% +i see a hand up as always michael is +helping us out + + align:start position:0% +helping us out + + + align:start position:0% +helping us out +to get us started let's go ahead + + align:start position:0% +to get us started let's go ahead + + + align:start position:0% +to get us started let's go ahead +yeah um i think one of the + + align:start position:0% +yeah um i think one of the + + + align:start position:0% +yeah um i think one of the +kind of the obvious ones is just + + align:start position:0% +kind of the obvious ones is just + + + align:start position:0% +kind of the obvious ones is just +processing time it's just + + align:start position:0% +processing time it's just + + + align:start position:0% +processing time it's just +really kind of through each step of the + + align:start position:0% +really kind of through each step of the + + + align:start position:0% +really kind of through each step of the +process underwriting + + align:start position:0% +process underwriting + + + align:start position:0% +process underwriting +oh no processing completely measured + + align:start position:0% +oh no processing completely measured + + + align:start position:0% +oh no processing completely measured +it's just it just takes a long time so + + align:start position:0% +it's just it just takes a long time so + + + align:start position:0% +it's just it just takes a long time so +kind of there's definitely a lot of + + align:start position:0% +kind of there's definitely a lot of + + + align:start position:0% +kind of there's definitely a lot of +opportunities for automatic feedback or + + align:start position:0% +opportunities for automatic feedback or + + + align:start position:0% +opportunities for automatic feedback or +leveraging ai to really speed that up + + align:start position:0% +leveraging ai to really speed that up + + + align:start position:0% +leveraging ai to really speed that up +for consumers + + align:start position:0% +for consumers + + + align:start position:0% +for consumers +all right so so let's the the two sides + + align:start position:0% +all right so so let's the the two sides + + + align:start position:0% +all right so so let's the the two sides +of processing it's the front end + + align:start position:0% +of processing it's the front end + + + align:start position:0% +of processing it's the front end +when you're actually trying to get your + + align:start position:0% +when you're actually trying to get your + + + align:start position:0% +when you're actually trying to get your +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +when you're actually it's caught + + align:start position:0% +when you're actually it's caught + + + align:start position:0% +when you're actually it's caught +underwriting the insurance company is + + align:start position:0% +underwriting the insurance company is + + + align:start position:0% +underwriting the insurance company is +pricing and giving you availability of + + align:start position:0% +pricing and giving you availability of + + + align:start position:0% +pricing and giving you availability of +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +and whether it's life insurance where + + align:start position:0% +and whether it's life insurance where + + + align:start position:0% +and whether it's life insurance where +you might have to send in some medical + + align:start position:0% +you might have to send in some medical + + + align:start position:0% +you might have to send in some medical +tests and the like + + align:start position:0% +tests and the like + + + align:start position:0% +tests and the like +homeowners insurance renters insurance + + align:start position:0% +homeowners insurance renters insurance + + + align:start position:0% +homeowners insurance renters insurance +auto insurance where there's a process + + align:start position:0% +auto insurance where there's a process + + + align:start position:0% +auto insurance where there's a process +going on at the front end + + align:start position:0% +going on at the front end + + + align:start position:0% +going on at the front end +and then there's also the process if you + + align:start position:0% +and then there's also the process if you + + + align:start position:0% +and then there's also the process if you +have an accident + + align:start position:0% +have an accident + + + align:start position:0% +have an accident +insurance is this product that basically + + align:start position:0% +insurance is this product that basically + + + align:start position:0% +insurance is this product that basically +if you never hear from your insurance + + align:start position:0% +if you never hear from your insurance + + + align:start position:0% +if you never hear from your insurance +company and + + align:start position:0% +company and + + + align:start position:0% +company and +they never hear from you you've paid a + + align:start position:0% +they never hear from you you've paid a + + + align:start position:0% +they never hear from you you've paid a +premium + + align:start position:0% +premium + + + align:start position:0% +premium +to protect you against a risk but the + + align:start position:0% +to protect you against a risk but the + + + align:start position:0% +to protect you against a risk but the +risk has not + + align:start position:0% +risk has not + + + align:start position:0% +risk has not +generated a loss but then you have the + + align:start position:0% +generated a loss but then you have the + + + align:start position:0% +generated a loss but then you have the +accident + + align:start position:0% +accident + + + align:start position:0% +accident +then you have the problem then you have + + align:start position:0% +then you have the problem then you have + + + align:start position:0% +then you have the problem then you have +to send in a claim + + align:start position:0% +to send in a claim + + + align:start position:0% +to send in a claim +and that process and the back end the + + align:start position:0% +and that process and the back end the + + + align:start position:0% +and that process and the back end the +insurance companies want to protect + + align:start position:0% +insurance companies want to protect + + + align:start position:0% +insurance companies want to protect +against fraud + + align:start position:0% +against fraud + + + align:start position:0% +against fraud +they want to fulfill your claim but they + + align:start position:0% +they want to fulfill your claim but they + + + align:start position:0% +they want to fulfill your claim but they +want to protect against fraud + + align:start position:0% +want to protect against fraud + + + align:start position:0% +want to protect against fraud +and the claim adjustment process is a + + align:start position:0% +and the claim adjustment process is a + + + align:start position:0% +and the claim adjustment process is a +significant + + align:start position:0% +significant + + + align:start position:0% +significant +time and human and paper-based and + + align:start position:0% +time and human and paper-based and + + + align:start position:0% +time and human and paper-based and +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +legal based circumstance so + + align:start position:0% +legal based circumstance so + + + align:start position:0% +legal based circumstance so +michael you're right pain points at the + + align:start position:0% +michael you're right pain points at the + + + align:start position:0% +michael you're right pain points at the +front end particular pain points and the + + align:start position:0% +front end particular pain points and the + + + align:start position:0% +front end particular pain points and the +claims processing side + + align:start position:0% +claims processing side + + + align:start position:0% +claims processing side +um anything else you want to throw in + + align:start position:0% + + + + align:start position:0% + +um i guess uh oh we've got two other + + align:start position:0% +um i guess uh oh we've got two other + + + align:start position:0% +um i guess uh oh we've got two other +hands if you want i mean + + align:start position:0% +hands if you want i mean + + + align:start position:0% +hands if you want i mean +that's right um pass it off to somebody + + align:start position:0% +that's right um pass it off to somebody + + + align:start position:0% +that's right um pass it off to somebody +else + + align:start position:0% +else + + + align:start position:0% +else +alessandro yeah i think another big + + align:start position:0% +alessandro yeah i think another big + + + align:start position:0% +alessandro yeah i think another big +trend is gonna + + align:start position:0% +trend is gonna + + + align:start position:0% +trend is gonna +we're gonna see different type of + + align:start position:0% +we're gonna see different type of + + + align:start position:0% +we're gonna see different type of +insurances + + align:start position:0% +insurances + + + align:start position:0% +insurances +um come to life there is more and more + + align:start position:0% +um come to life there is more and more + + + align:start position:0% +um come to life there is more and more +risks + + align:start position:0% +risks + + + align:start position:0% +risks +are becoming quantifiable and this leads + + align:start position:0% +are becoming quantifiable and this leads + + + align:start position:0% +are becoming quantifiable and this leads +to a number of + + align:start position:0% +to a number of + + + align:start position:0% +to a number of +events or things we can get an insurance + + align:start position:0% +events or things we can get an insurance + + + align:start position:0% +events or things we can get an insurance +on so + + align:start position:0% +on so + + + align:start position:0% +on so +the selection of things on which we can + + align:start position:0% +the selection of things on which we can + + + align:start position:0% +the selection of things on which we can +get insured + + align:start position:0% +get insured + + + align:start position:0% +get insured +it's going to increase dramatically + + align:start position:0% +it's going to increase dramatically + + + align:start position:0% +it's going to increase dramatically +because the the quantifiable risks + + align:start position:0% +because the the quantifiable risks + + + align:start position:0% +because the the quantifiable risks +are getting bigger and bigger right and + + align:start position:0% +are getting bigger and bigger right and + + + align:start position:0% +are getting bigger and bigger right and +sometimes it's not just a new risk in + + align:start position:0% +sometimes it's not just a new risk in + + + align:start position:0% +sometimes it's not just a new risk in +society but it's as + + align:start position:0% +society but it's as + + + align:start position:0% +society but it's as +as alexandra saying the quantifiability + + align:start position:0% +as alexandra saying the quantifiability + + + align:start position:0% +as alexandra saying the quantifiability +of it so let's take auto insurance + + align:start position:0% +of it so let's take auto insurance + + + align:start position:0% +of it so let's take auto insurance +and a company that started a number of + + align:start position:0% +and a company that started a number of + + + align:start position:0% +and a company that started a number of +years ago called metro mile + + align:start position:0% +years ago called metro mile + + + align:start position:0% +years ago called metro mile +simple concept what if we charged + + align:start position:0% +simple concept what if we charged + + + align:start position:0% +simple concept what if we charged +insurance automobile insurance not + + align:start position:0% +insurance automobile insurance not + + + align:start position:0% +insurance automobile insurance not +by the month but maybe by the mile + + align:start position:0% +by the month but maybe by the mile + + + align:start position:0% +by the month but maybe by the mile +could we quantify that you've only + + align:start position:0% +could we quantify that you've only + + + align:start position:0% +could we quantify that you've only +driven a mile + + align:start position:0% +driven a mile + + + align:start position:0% +driven a mile +and that would be the insurance and if + + align:start position:0% +and that would be the insurance and if + + + align:start position:0% +and that would be the insurance and if +you're a heavy driver there's more + + align:start position:0% +you're a heavy driver there's more + + + align:start position:0% +you're a heavy driver there's more +and in fact what if the mile is out on + + align:start position:0% +and in fact what if the mile is out on + + + align:start position:0% +and in fact what if the mile is out on +the country roads + + align:start position:0% +the country roads + + + align:start position:0% +the country roads +or it's actually in the cities and where + + align:start position:0% +or it's actually in the cities and where + + + align:start position:0% +or it's actually in the cities and where +you're driving + + align:start position:0% +you're driving + + + align:start position:0% +you're driving +so quantifiability the analytics the + + align:start position:0% +so quantifiability the analytics the + + + align:start position:0% +so quantifiability the analytics the +computer capability + + align:start position:0% +computer capability + + + align:start position:0% +computer capability +but also the connections to all of us + + align:start position:0% +but also the connections to all of us + + + align:start position:0% +but also the connections to all of us +with sensors + + align:start position:0% +with sensors + + + align:start position:0% +with sensors +and the internet of things um + + align:start position:0% +and the internet of things um + + + align:start position:0% +and the internet of things um +so i've sort of given a little bit of a + + align:start position:0% +so i've sort of given a little bit of a + + + align:start position:0% +so i've sort of given a little bit of a +preview but there were some other hands + + align:start position:0% +preview but there were some other hands + + + align:start position:0% +preview but there were some other hands +up how have + + align:start position:0% +up how have + + + align:start position:0% +up how have +that which we've talked about all + + align:start position:0% +that which we've talked about all + + + align:start position:0% +that which we've talked about all +semester machine learning alternative + + align:start position:0% +semester machine learning alternative + + + align:start position:0% +semester machine learning alternative +data + + align:start position:0% +data + + + align:start position:0% +data +uh influence this but a new factor that + + align:start position:0% +uh influence this but a new factor that + + + align:start position:0% +uh influence this but a new factor that +we've really not talked much about + + align:start position:0% +we've really not talked much about + + + align:start position:0% +we've really not talked much about +in banking and challenger banks and + + align:start position:0% +in banking and challenger banks and + + + align:start position:0% +in banking and challenger banks and +payment systems + + align:start position:0% +payment systems + + + align:start position:0% +payment systems +is the internet of thing devices + + align:start position:0% +is the internet of thing devices + + + align:start position:0% +is the internet of thing devices +possibly changing + + align:start position:0% +possibly changing + + + align:start position:0% +possibly changing +the field of insurance + + align:start position:0% +the field of insurance + + + align:start position:0% +the field of insurance +danielle would you like to go + + align:start position:0% + + + + align:start position:0% + +sure um and also you just broke up there + + align:start position:0% +sure um and also you just broke up there + + + align:start position:0% +sure um and also you just broke up there +so if you lose me sorry about my + + align:start position:0% +so if you lose me sorry about my + + + align:start position:0% +so if you lose me sorry about my +internet connection + + align:start position:0% +internet connection + + + align:start position:0% +internet connection +um so there's an opportunity for + + align:start position:0% +um so there's an opportunity for + + + align:start position:0% +um so there's an opportunity for +the insurance landscape to be changed by + + align:start position:0% +the insurance landscape to be changed by + + + align:start position:0% +the insurance landscape to be changed by +alternative data in that companies can + + align:start position:0% +alternative data in that companies can + + + align:start position:0% +alternative data in that companies can +now + + align:start position:0% +now + + + align:start position:0% +now +inform their underwriting process with a + + align:start position:0% +inform their underwriting process with a + + + align:start position:0% +inform their underwriting process with a +lot more information a lot richer set of + + align:start position:0% +lot more information a lot richer set of + + + align:start position:0% +lot more information a lot richer set of +data than they previously had + + align:start position:0% +data than they previously had + + + align:start position:0% +data than they previously had +so whereas for health insurance or life + + align:start position:0% +so whereas for health insurance or life + + + align:start position:0% +so whereas for health insurance or life +insurance you might have had to fill out + + align:start position:0% +insurance you might have had to fill out + + + align:start position:0% +insurance you might have had to fill out +a survey + + align:start position:0% +a survey + + + align:start position:0% +a survey +people are varying degrees of honest on + + align:start position:0% +people are varying degrees of honest on + + + align:start position:0% +people are varying degrees of honest on +those kinds of surveys + + align:start position:0% +those kinds of surveys + + + align:start position:0% +those kinds of surveys +now we're suddenly generating an + + align:start position:0% +now we're suddenly generating an + + + align:start position:0% +now we're suddenly generating an +extremely accurate picture of ourselves + + align:start position:0% +extremely accurate picture of ourselves + + + align:start position:0% +extremely accurate picture of ourselves +almost passively by everything we do in + + align:start position:0% +almost passively by everything we do in + + + align:start position:0% +almost passively by everything we do in +the world and companies can access that + + align:start position:0% +the world and companies can access that + + + align:start position:0% +the world and companies can access that +information + + align:start position:0% +information + + + align:start position:0% +information +right or can they access it they still + + align:start position:0% +right or can they access it they still + + + align:start position:0% +right or can they access it they still +have to have a network + + align:start position:0% +have to have a network + + + align:start position:0% +have to have a network +and what's really interesting in this + + align:start position:0% +and what's really interesting in this + + + align:start position:0% +and what's really interesting in this +space is that just as we saw + + align:start position:0% +space is that just as we saw + + + align:start position:0% +space is that just as we saw +data aggregation an important feature + + align:start position:0% +data aggregation an important feature + + + align:start position:0% +data aggregation an important feature +uh in the payment space with companies + + align:start position:0% +uh in the payment space with companies + + + align:start position:0% +uh in the payment space with companies +like plaid and galileo and everything + + align:start position:0% +like plaid and galileo and everything + + + align:start position:0% +like plaid and galileo and everything +that they were + + align:start position:0% +that they were + + + align:start position:0% +that they were +they're right there collecting data + + align:start position:0% +they're right there collecting data + + + align:start position:0% +they're right there collecting data +between the banks and the payment + + align:start position:0% +between the banks and the payment + + + align:start position:0% +between the banks and the payment +systems + + align:start position:0% +systems + + + align:start position:0% +systems +and then uh hundreds or thousands of + + align:start position:0% +and then uh hundreds or thousands of + + + align:start position:0% +and then uh hundreds or thousands of +fintech startups that there were data + + align:start position:0% +fintech startups that there were data + + + align:start position:0% +fintech startups that there were data +aggregators in the middle + + align:start position:0% +aggregators in the middle + + + align:start position:0% +aggregators in the middle +there are data aggregators in this field + + align:start position:0% +there are data aggregators in this field + + + align:start position:0% +there are data aggregators in this field +as well to collect that data + + align:start position:0% +as well to collect that data + + + align:start position:0% +as well to collect that data +commercialize the data but maybe stand + + align:start position:0% +commercialize the data but maybe stand + + + align:start position:0% +commercialize the data but maybe stand +between + + align:start position:0% +between + + + align:start position:0% +between +our lives and all the sensors and data + + align:start position:0% +our lives and all the sensors and data + + + align:start position:0% +our lives and all the sensors and data +collection efforts and + + align:start position:0% +collection efforts and + + + align:start position:0% +collection efforts and +hundreds or thousands of startups on the + + align:start position:0% +hundreds or thousands of startups on the + + + align:start position:0% +hundreds or thousands of startups on the +other side as well + + align:start position:0% +other side as well + + + align:start position:0% +other side as well +um nikhil + + align:start position:0% + + + + align:start position:0% + +sure i think this is more specific to + + align:start position:0% +sure i think this is more specific to + + + align:start position:0% +sure i think this is more specific to +the health insurance side of things + + align:start position:0% +the health insurance side of things + + + align:start position:0% +the health insurance side of things +where a lot of times in health insurance + + align:start position:0% +where a lot of times in health insurance + + + align:start position:0% +where a lot of times in health insurance +claims 90 + + align:start position:0% +claims 90 + + + align:start position:0% +claims 90 +of claims are auto adjudicated and most + + align:start position:0% +of claims are auto adjudicated and most + + + align:start position:0% +of claims are auto adjudicated and most +of them are based on like statistical + + align:start position:0% +of them are based on like statistical + + + align:start position:0% +of them are based on like statistical +methods + + align:start position:0% +methods + + + align:start position:0% +methods +with the influx of ai like you can + + align:start position:0% +with the influx of ai like you can + + + align:start position:0% +with the influx of ai like you can +review claims that you weren't reviewing + + align:start position:0% +review claims that you weren't reviewing + + + align:start position:0% +review claims that you weren't reviewing +before + + align:start position:0% +before + + + align:start position:0% +before +and so you could potentially uncover + + align:start position:0% +and so you could potentially uncover + + + align:start position:0% +and so you could potentially uncover +more fraud waste and abuse than you were + + align:start position:0% +more fraud waste and abuse than you were + + + align:start position:0% +more fraud waste and abuse than you were +um so this is like a market that they + + align:start position:0% +um so this is like a market that they + + + align:start position:0% +um so this is like a market that they +haven't sized yet because they don't + + align:start position:0% +haven't sized yet because they don't + + + align:start position:0% +haven't sized yet because they don't +know how big + + align:start position:0% +know how big + + + align:start position:0% +know how big +fraud might be so i think there's a big + + align:start position:0% +fraud might be so i think there's a big + + + align:start position:0% +fraud might be so i think there's a big +trend there as well + + align:start position:0% +trend there as well + + + align:start position:0% +trend there as well +great great point and sometimes it's not + + align:start position:0% +great great point and sometimes it's not + + + align:start position:0% +great great point and sometimes it's not +truly artificial intelligence or machine + + align:start position:0% +truly artificial intelligence or machine + + + align:start position:0% +truly artificial intelligence or machine +learning it's just + + align:start position:0% +learning it's just + + + align:start position:0% +learning it's just +the remarkable ability to collect sort + + align:start position:0% +the remarkable ability to collect sort + + + align:start position:0% +the remarkable ability to collect sort +clean up the data standardize the data + + align:start position:0% +clean up the data standardize the data + + + align:start position:0% +clean up the data standardize the data +that might also have a bit of + + align:start position:0% +that might also have a bit of + + + align:start position:0% +that might also have a bit of +machine learning on top of it but it + + align:start position:0% +machine learning on top of it but it + + + align:start position:0% +machine learning on top of it but it +doesn't have to be the machine learning + + align:start position:0% +doesn't have to be the machine learning + + + align:start position:0% +doesn't have to be the machine learning +it's + + align:start position:0% +it's + + + align:start position:0% +it's +it's sort of this partnering up and then + + align:start position:0% +it's sort of this partnering up and then + + + align:start position:0% +it's sort of this partnering up and then +what are some of the challenges we're + + align:start position:0% +what are some of the challenges we're + + + align:start position:0% +what are some of the challenges we're +going to talk about some of the + + align:start position:0% +going to talk about some of the + + + align:start position:0% +going to talk about some of the +challenges for the startups trying to + + align:start position:0% +challenges for the startups trying to + + + align:start position:0% +challenges for the startups trying to +get in there + + align:start position:0% +get in there + + + align:start position:0% +get in there +capital regulation and + + align:start position:0% +capital regulation and + + + align:start position:0% +capital regulation and +does anybody have a view as to date to + + align:start position:0% +does anybody have a view as to date to + + + align:start position:0% +does anybody have a view as to date to +date why we haven't seen + + align:start position:0% +date why we haven't seen + + + align:start position:0% +date why we haven't seen +uh with some important exceptions but we + + align:start position:0% +uh with some important exceptions but we + + + align:start position:0% +uh with some important exceptions but we +haven't seen + + align:start position:0% +haven't seen + + + align:start position:0% +haven't seen +big tech firms getting engaged + + align:start position:0% +big tech firms getting engaged + + + align:start position:0% +big tech firms getting engaged +in the insurance field + + align:start position:0% + + + + align:start position:0% + +now there's some important exceptions + + align:start position:0% +now there's some important exceptions + + + align:start position:0% +now there's some important exceptions +we'll talk about in china by the way + + align:start position:0% +we'll talk about in china by the way + + + align:start position:0% +we'll talk about in china by the way +but um why we haven't seen + + align:start position:0% +but um why we haven't seen + + + align:start position:0% +but um why we haven't seen +amazon they're in the credit card space + + align:start position:0% +amazon they're in the credit card space + + + align:start position:0% +amazon they're in the credit card space +in apple in + + align:start position:0% +in apple in + + + align:start position:0% +in apple in +in payment space but why we haven't seen + + align:start position:0% +in payment space but why we haven't seen + + + align:start position:0% +in payment space but why we haven't seen +big big + + align:start position:0% +big big + + + align:start position:0% +big big +uh tech by and large lyra + + align:start position:0% +uh tech by and large lyra + + + align:start position:0% +uh tech by and large lyra +yeah um so i just think that it's mostly + + align:start position:0% +yeah um so i just think that it's mostly + + + align:start position:0% +yeah um so i just think that it's mostly +because there's + + align:start position:0% +because there's + + + align:start position:0% +because there's +a lot of barriers to entry namely like + + align:start position:0% +a lot of barriers to entry namely like + + + align:start position:0% +a lot of barriers to entry namely like +as you mentioned regulation and also + + align:start position:0% +as you mentioned regulation and also + + + align:start position:0% +as you mentioned regulation and also +lack of expertise which all of these + + align:start position:0% +lack of expertise which all of these + + + align:start position:0% +lack of expertise which all of these +insurance companies already have + + align:start position:0% +insurance companies already have + + + align:start position:0% +insurance companies already have +so i think it's also a regulation and + + align:start position:0% +so i think it's also a regulation and + + + align:start position:0% +so i think it's also a regulation and +high cost because of lack of expertise + + align:start position:0% +high cost because of lack of expertise + + + align:start position:0% +high cost because of lack of expertise +that prevents these big tech firms from + + align:start position:0% +that prevents these big tech firms from + + + align:start position:0% +that prevents these big tech firms from +entering into the insurance market all + + align:start position:0% +entering into the insurance market all + + + align:start position:0% +entering into the insurance market all +right so i think that's partly right but + + align:start position:0% +right so i think that's partly right but + + + align:start position:0% +right so i think that's partly right but +i'm also going to put out the question + + align:start position:0% +i'm also going to put out the question + + + align:start position:0% +i'm also going to put out the question +throughout the class and as your thought + + align:start position:0% +throughout the class and as your thought + + + align:start position:0% +throughout the class and as your thought +experience at the end + + align:start position:0% +experience at the end + + + align:start position:0% +experience at the end +is it just that we haven't gotten there + + align:start position:0% +is it just that we haven't gotten there + + + align:start position:0% +is it just that we haven't gotten there +yet is it possibility that + + align:start position:0% +yet is it possibility that + + + align:start position:0% +yet is it possibility that +that again big tech is about data + + align:start position:0% +that again big tech is about data + + + align:start position:0% +that again big tech is about data +networks and activities as the back of + + align:start position:0% +networks and activities as the back of + + + align:start position:0% +networks and activities as the back of +international settlement + + align:start position:0% +international settlement + + + align:start position:0% +international settlement +has written and so do they want to layer + + align:start position:0% +has written and so do they want to layer + + + align:start position:0% +has written and so do they want to layer +another activity + + align:start position:0% +another activity + + + align:start position:0% +another activity +upon that network upon that network + + align:start position:0% +upon that network upon that network + + + align:start position:0% +upon that network upon that network +we haven't quite seen it i said that + + align:start position:0% +we haven't quite seen it i said that + + + align:start position:0% +we haven't quite seen it i said that +with one important exception in china + + align:start position:0% +with one important exception in china + + + align:start position:0% +with one important exception in china +and china + + align:start position:0% +and china + + + align:start position:0% +and china +a number of years ago big tech + + align:start position:0% +a number of years ago big tech + + + align:start position:0% +a number of years ago big tech +alibaba attention + + align:start position:0% +alibaba attention + + + align:start position:0% +alibaba attention +as wechat partnered up with one of the + + align:start position:0% +as wechat partnered up with one of the + + + align:start position:0% +as wechat partnered up with one of the +largest insurance companies + + align:start position:0% +largest insurance companies + + + align:start position:0% +largest insurance companies +in china and the three of them started + + align:start position:0% +in china and the three of them started + + + align:start position:0% +in china and the three of them started +effectively and in short tech it's the + + align:start position:0% +effectively and in short tech it's the + + + align:start position:0% +effectively and in short tech it's the +world's largest + + align:start position:0% +world's largest + + + align:start position:0% +world's largest +insurtech if you we still call it that + + align:start position:0% +insurtech if you we still call it that + + + align:start position:0% +insurtech if you we still call it that +and it was an owned owned and operated + + align:start position:0% +and it was an owned owned and operated + + + align:start position:0% +and it was an owned owned and operated +by three + + align:start position:0% +by three + + + align:start position:0% +by three +big very big companies uh + + align:start position:0% +big very big companies uh + + + align:start position:0% +big very big companies uh +ping-ang was the insurance company and + + align:start position:0% +ping-ang was the insurance company and + + + align:start position:0% +ping-ang was the insurance company and +so it wasn't direct it was a joint + + align:start position:0% +so it wasn't direct it was a joint + + + align:start position:0% +so it wasn't direct it was a joint +venture + + align:start position:0% +venture + + + align:start position:0% +venture +but it's a question of will we see this + + align:start position:0% +but it's a question of will we see this + + + align:start position:0% +but it's a question of will we see this +coming into the future or not + + align:start position:0% +coming into the future or not + + + align:start position:0% +coming into the future or not +um so let's just sort of dive into the + + align:start position:0% +um so let's just sort of dive into the + + + align:start position:0% +um so let's just sort of dive into the +value chain + + align:start position:0% +value chain + + + align:start position:0% +value chain +you've got to design a product you've + + align:start position:0% +you've got to design a product you've + + + align:start position:0% +you've got to design a product you've +got to market it it goes all the way to + + align:start position:0% +got to market it it goes all the way to + + + align:start position:0% +got to market it it goes all the way to +claims management + + align:start position:0% +claims management + + + align:start position:0% +claims management +you can be in any one of these pieces uh + + align:start position:0% +you can be in any one of these pieces uh + + + align:start position:0% +you can be in any one of these pieces uh +this is just pulled from the federal + + align:start position:0% +this is just pulled from the federal + + + align:start position:0% +this is just pulled from the federal +insurance office of the u.s department + + align:start position:0% +insurance office of the u.s department + + + align:start position:0% +insurance office of the u.s department +of treasury from a report + + align:start position:0% +of treasury from a report + + + align:start position:0% +of treasury from a report +last year but each of these pieces + + align:start position:0% +last year but each of these pieces + + + align:start position:0% +last year but each of these pieces +might have a piece of competition and a + + align:start position:0% +might have a piece of competition and a + + + align:start position:0% +might have a piece of competition and a +pain point + + align:start position:0% +pain point + + + align:start position:0% +pain point +we talked a little bit about claims + + align:start position:0% +we talked a little bit about claims + + + align:start position:0% +we talked a little bit about claims +management that's claims management + + align:start position:0% +management that's claims management + + + align:start position:0% +management that's claims management +separates insurance from the banking + + align:start position:0% +separates insurance from the banking + + + align:start position:0% +separates insurance from the banking +fintech we've talked about but a lot of + + align:start position:0% +fintech we've talked about but a lot of + + + align:start position:0% +fintech we've talked about but a lot of +the + + align:start position:0% +the + + + align:start position:0% +the +underwriting and the front end designing + + align:start position:0% +underwriting and the front end designing + + + align:start position:0% +underwriting and the front end designing +a product + + align:start position:0% +a product + + + align:start position:0% +a product +and the marketing you'll see that an + + align:start position:0% +and the marketing you'll see that an + + + align:start position:0% +and the marketing you'll see that an +awful lot of disruption is going + + align:start position:0% +awful lot of disruption is going + + + align:start position:0% +awful lot of disruption is going +on at that front end marketing is sales + + align:start position:0% +on at that front end marketing is sales + + + align:start position:0% +on at that front end marketing is sales +it's brokerage it's bringing in the + + align:start position:0% +it's brokerage it's bringing in the + + + align:start position:0% +it's brokerage it's bringing in the +customer + + align:start position:0% +customer + + + align:start position:0% +customer +it's a better user interface a better + + align:start position:0% +it's a better user interface a better + + + align:start position:0% +it's a better user interface a better +user experience + + align:start position:0% +user experience + + + align:start position:0% +user experience +in the underwriting and rating side you + + align:start position:0% +in the underwriting and rating side you + + + align:start position:0% +in the underwriting and rating side you +can underwrite + + align:start position:0% +can underwrite + + + align:start position:0% +can underwrite +credit you can underwrite insurance it's + + align:start position:0% +credit you can underwrite insurance it's + + + align:start position:0% +credit you can underwrite insurance it's +basically + + align:start position:0% +basically + + + align:start position:0% +basically +how much insurance will i provide to + + align:start position:0% +how much insurance will i provide to + + + align:start position:0% +how much insurance will i provide to +whom at what price + + align:start position:0% +whom at what price + + + align:start position:0% +whom at what price +and and that underwriting process + + align:start position:0% +and and that underwriting process + + + align:start position:0% +and and that underwriting process +ultimately + + align:start position:0% +ultimately + + + align:start position:0% +ultimately +comes to administering the policy and + + align:start position:0% +comes to administering the policy and + + + align:start position:0% +comes to administering the policy and +then the claims management side of it + + align:start position:0% +then the claims management side of it + + + align:start position:0% +then the claims management side of it +so each of these pieces of the value + + align:start position:0% +so each of these pieces of the value + + + align:start position:0% +so each of these pieces of the value +chain might have + + align:start position:0% +chain might have + + + align:start position:0% +chain might have +pain points the front the front four of + + align:start position:0% +pain points the front the front four of + + + align:start position:0% +pain points the front the front four of +these + + align:start position:0% +these + + + align:start position:0% +these +designing products to policy + + align:start position:0% +designing products to policy + + + align:start position:0% +designing products to policy +administration actually has a lot of + + align:start position:0% +administration actually has a lot of + + + align:start position:0% +administration actually has a lot of +overlap with the banking + + align:start position:0% +overlap with the banking + + + align:start position:0% +overlap with the banking +sector um not identical + + align:start position:0% +sector um not identical + + + align:start position:0% +sector um not identical +important differences um so + + align:start position:0% +important differences um so + + + align:start position:0% +important differences um so +what's the sector look like i just list + + align:start position:0% +what's the sector look like i just list + + + align:start position:0% +what's the sector look like i just list +companies on these several next slides + + align:start position:0% +companies on these several next slides + + + align:start position:0% +companies on these several next slides +life insurance + + align:start position:0% +life insurance + + + align:start position:0% +life insurance +property and casualty what i want you to + + align:start position:0% +property and casualty what i want you to + + + align:start position:0% +property and casualty what i want you to +take out of is not particular names in + + align:start position:0% +take out of is not particular names in + + + align:start position:0% +take out of is not particular names in +your country whether it's + + align:start position:0% +your country whether it's + + + align:start position:0% +your country whether it's +china life or metlife or nippon life + + align:start position:0% +china life or metlife or nippon life + + + align:start position:0% +china life or metlife or nippon life +and and swiss life it's that + + align:start position:0% +and and swiss life it's that + + + align:start position:0% +and and swiss life it's that +if you look at when these companies were + + align:start position:0% +if you look at when these companies were + + + align:start position:0% +if you look at when these companies were +founded + + align:start position:0% +founded + + + align:start position:0% +founded +many are + + align:start position:0% +many are + + + align:start position:0% +many are +20th century but many are actually 19th + + align:start position:0% +20th century but many are actually 19th + + + align:start position:0% +20th century but many are actually 19th +century + + align:start position:0% +century + + + align:start position:0% +century +the the concentration and the survival + + align:start position:0% + + + + align:start position:0% + +the persistence of insurance companies + + align:start position:0% +the persistence of insurance companies + + + align:start position:0% +the persistence of insurance companies +is quite + + align:start position:0% +is quite + + + align:start position:0% +is quite +consistent around the globe they talk + + align:start position:0% +consistent around the globe they talk + + + align:start position:0% +consistent around the globe they talk +about the big five in china but in + + align:start position:0% +about the big five in china but in + + + align:start position:0% +about the big five in china but in +any country in any country there's a + + align:start position:0% +any country in any country there's a + + + align:start position:0% +any country in any country there's a +handful of insurance companies + + align:start position:0% +handful of insurance companies + + + align:start position:0% +handful of insurance companies +once you get to about the top 10 you're + + align:start position:0% +once you get to about the top 10 you're + + + align:start position:0% +once you get to about the top 10 you're +at 85 + + align:start position:0% +at 85 + + + align:start position:0% +at 85 +to 90 plus percent market share + + align:start position:0% +to 90 plus percent market share + + + align:start position:0% +to 90 plus percent market share +particularly in life insurance and + + align:start position:0% +particularly in life insurance and + + + align:start position:0% +particularly in life insurance and +property and casualty + + align:start position:0% +property and casualty + + + align:start position:0% +property and casualty +little less so in some other fields and + + align:start position:0% +little less so in some other fields and + + + align:start position:0% +little less so in some other fields and +there's of course health and managed + + align:start position:0% +there's of course health and managed + + + align:start position:0% +there's of course health and managed +care more a feature of the u.s health + + align:start position:0% +care more a feature of the u.s health + + + align:start position:0% +care more a feature of the u.s health +care system + + align:start position:0% +care system + + + align:start position:0% +care system +where it's private insurance and then + + align:start position:0% +where it's private insurance and then + + + align:start position:0% +where it's private insurance and then +big diversified companies + + align:start position:0% +big diversified companies + + + align:start position:0% +big diversified companies +uh across the globe diversified simply + + align:start position:0% +uh across the globe diversified simply + + + align:start position:0% +uh across the globe diversified simply +means that it's both in life + + align:start position:0% +means that it's both in life + + + align:start position:0% +means that it's both in life +and and property and casualty and the + + align:start position:0% +and and property and casualty and the + + + align:start position:0% +and and property and casualty and the +like so it's multi-line + + align:start position:0% +like so it's multi-line + + + align:start position:0% +like so it's multi-line +um but let's not forget there's also + + align:start position:0% +um but let's not forget there's also + + + align:start position:0% +um but let's not forget there's also +reinsurance and then + + align:start position:0% +reinsurance and then + + + align:start position:0% +reinsurance and then +brokers and the brokerage side is an + + align:start position:0% +brokers and the brokerage side is an + + + align:start position:0% +brokers and the brokerage side is an +area where + + align:start position:0% +area where + + + align:start position:0% +area where +disruptors have started to say well + + align:start position:0% +disruptors have started to say well + + + align:start position:0% +disruptors have started to say well +maybe we can broker insurance and by + + align:start position:0% +maybe we can broker insurance and by + + + align:start position:0% +maybe we can broker insurance and by +brokering insurance is basically + + align:start position:0% +brokering insurance is basically + + + align:start position:0% +brokering insurance is basically +making the sales making the marketing + + align:start position:0% +making the sales making the marketing + + + align:start position:0% +making the sales making the marketing +but not taking the risk onto your own + + align:start position:0% +but not taking the risk onto your own + + + align:start position:0% +but not taking the risk onto your own +balance sheet + + align:start position:0% +balance sheet + + + align:start position:0% +balance sheet +benefits administration software + + align:start position:0% +benefits administration software + + + align:start position:0% +benefits administration software +the only companies that are 21st century + + align:start position:0% +the only companies that are 21st century + + + align:start position:0% +the only companies that are 21st century +companies on this + + align:start position:0% +companies on this + + + align:start position:0% +companies on this +whole sort of review is in the software + + align:start position:0% +whole sort of review is in the software + + + align:start position:0% +whole sort of review is in the software +and services side of things + + align:start position:0% +and services side of things + + + align:start position:0% +and services side of things +so that's kind of my kind of you know + + align:start position:0% +so that's kind of my kind of you know + + + align:start position:0% +so that's kind of my kind of you know +overall point u.s insurance premiums + + align:start position:0% +overall point u.s insurance premiums + + + align:start position:0% +overall point u.s insurance premiums +just to give you a sense of scale of the + + align:start position:0% +just to give you a sense of scale of the + + + align:start position:0% +just to give you a sense of scale of the +market about one and a half + + align:start position:0% +market about one and a half + + + align:start position:0% +market about one and a half +trillion dollars a year we talk about + + align:start position:0% +trillion dollars a year we talk about + + + align:start position:0% +trillion dollars a year we talk about +the finance sector that's about + + align:start position:0% +the finance sector that's about + + + align:start position:0% +the finance sector that's about +seven and a half trillion in the u.s + + align:start position:0% +seven and a half trillion in the u.s + + + align:start position:0% +seven and a half trillion in the u.s +i'm sorry seven and a half percent seven + + align:start position:0% +i'm sorry seven and a half percent seven + + + align:start position:0% +i'm sorry seven and a half percent seven +and a half percent of gdp + + align:start position:0% +and a half percent of gdp + + + align:start position:0% +and a half percent of gdp +uh overstatement there which is about + + align:start position:0% +uh overstatement there which is about + + + align:start position:0% +uh overstatement there which is about +one half trillion + + align:start position:0% +one half trillion + + + align:start position:0% +one half trillion +this is consistent with that size these + + align:start position:0% +this is consistent with that size these + + + align:start position:0% +this is consistent with that size these +are the premiums being paid + + align:start position:0% +are the premiums being paid + + + align:start position:0% +are the premiums being paid +into uh direct premiums written + + align:start position:0% + + + + align:start position:0% + +the health and life side of things just + + align:start position:0% +the health and life side of things just + + + align:start position:0% +the health and life side of things just +to give you a little flavor and these + + align:start position:0% +to give you a little flavor and these + + + align:start position:0% +to give you a little flavor and these +will all be on canvas of course + + align:start position:0% +will all be on canvas of course + + + align:start position:0% +will all be on canvas of course +by and large a big part of the life and + + align:start position:0% +by and large a big part of the life and + + + align:start position:0% +by and large a big part of the life and +health side is so + + align:start position:0% +health side is so + + + align:start position:0% +health side is so +set savings products there's competition + + align:start position:0% +set savings products there's competition + + + align:start position:0% +set savings products there's competition +between + + align:start position:0% +between + + + align:start position:0% +between +life companies and banks + + align:start position:0% +life companies and banks + + + align:start position:0% +life companies and banks +live companies and investment management + + align:start position:0% +live companies and investment management + + + align:start position:0% +live companies and investment management +companies on the annuity side + + align:start position:0% +companies on the annuity side + + + align:start position:0% +companies on the annuity side +the disruption so to speak has been + + align:start position:0% +the disruption so to speak has been + + + align:start position:0% +the disruption so to speak has been +happening + + align:start position:0% +happening + + + align:start position:0% +happening +largely in property and casualty but to + + align:start position:0% +largely in property and casualty but to + + + align:start position:0% +largely in property and casualty but to +the extent that ensure tech starts to + + align:start position:0% +the extent that ensure tech starts to + + + align:start position:0% +the extent that ensure tech starts to +get into the space + + align:start position:0% +get into the space + + + align:start position:0% +get into the space +i think you will see more and more + + align:start position:0% +i think you will see more and more + + + align:start position:0% +i think you will see more and more +disruption in the savings product side + + align:start position:0% +disruption in the savings product side + + + align:start position:0% +disruption in the savings product side +as well + + align:start position:0% +as well + + + align:start position:0% +as well +the the companies like betterment and + + align:start position:0% +the the companies like betterment and + + + align:start position:0% +the the companies like betterment and +all those companies we talked about + + align:start position:0% +all those companies we talked about + + + align:start position:0% +all those companies we talked about +in the wealth management side or in + + align:start position:0% +in the wealth management side or in + + + align:start position:0% +in the wealth management side or in +wealthtech + + align:start position:0% +wealthtech + + + align:start position:0% +wealthtech +i think you will see starting to say + + align:start position:0% +i think you will see starting to say + + + align:start position:0% +i think you will see starting to say +wait maybe we can get into the annuity + + align:start position:0% +wait maybe we can get into the annuity + + + align:start position:0% +wait maybe we can get into the annuity +side as well the annuity + + align:start position:0% +side as well the annuity + + + align:start position:0% +side as well the annuity +and saving side of life insurance + + align:start position:0% +and saving side of life insurance + + + align:start position:0% +and saving side of life insurance +products + + align:start position:0% +products + + + align:start position:0% +products +property and casualty just a little + + align:start position:0% +property and casualty just a little + + + align:start position:0% +property and casualty just a little +breakdown here in the u.s + + align:start position:0% + + + + align:start position:0% + +and so now we turn to challenges pain + + align:start position:0% +and so now we turn to challenges pain + + + align:start position:0% +and so now we turn to challenges pain +points + + align:start position:0% +points + + + align:start position:0% +points +what do we have this is true of any + + align:start position:0% +what do we have this is true of any + + + align:start position:0% +what do we have this is true of any +incumbent company + + align:start position:0% +incumbent company + + + align:start position:0% +incumbent company +you could be a company that's been in + + align:start position:0% +you could be a company that's been in + + + align:start position:0% +you could be a company that's been in +business for a hundred plus years + + align:start position:0% +business for a hundred plus years + + + align:start position:0% +business for a hundred plus years +and you're you're sitting there going + + align:start position:0% +and you're you're sitting there going + + + align:start position:0% +and you're you're sitting there going +i'm + + align:start position:0% +i'm + + + align:start position:0% +i'm +selling through an agent or broker + + align:start position:0% +selling through an agent or broker + + + align:start position:0% +selling through an agent or broker +network + + align:start position:0% +network + + + align:start position:0% +network +and the agency and brokerage network + + align:start position:0% +and the agency and brokerage network + + + align:start position:0% +and the agency and brokerage network +here in the us + + align:start position:0% +here in the us + + + align:start position:0% +here in the us +takes a big chunk of fees + + align:start position:0% +takes a big chunk of fees + + + align:start position:0% +takes a big chunk of fees +i think on the property casually side + + align:start position:0% +i think on the property casually side + + + align:start position:0% +i think on the property casually side +we're probably + + align:start position:0% +we're probably + + + align:start position:0% +we're probably +in the 10 to 13 percent of of premiums + + align:start position:0% +in the 10 to 13 percent of of premiums + + + align:start position:0% +in the 10 to 13 percent of of premiums +on average + + align:start position:0% +on average + + + align:start position:0% +on average +but in some products it's much larger + + align:start position:0% +but in some products it's much larger + + + align:start position:0% +but in some products it's much larger +some a little + + align:start position:0% +some a little + + + align:start position:0% +some a little +smaller the life side the premiums + + align:start position:0% +smaller the life side the premiums + + + align:start position:0% +smaller the life side the premiums +i think are in high single digits to 10 + + align:start position:0% +i think are in high single digits to 10 + + + align:start position:0% +i think are in high single digits to 10 +on average + + align:start position:0% +on average + + + align:start position:0% +on average +and while i'm not sort of an expert of + + align:start position:0% +and while i'm not sort of an expert of + + + align:start position:0% +and while i'm not sort of an expert of +all the + + align:start position:0% +all the + + + align:start position:0% +all the +fee that's basically means if you pay a + + align:start position:0% +fee that's basically means if you pay a + + + align:start position:0% +fee that's basically means if you pay a +thousand dollars for your auto insurance + + align:start position:0% +thousand dollars for your auto insurance + + + align:start position:0% +thousand dollars for your auto insurance +100 plus dollars 120 dollars is being + + align:start position:0% +100 plus dollars 120 dollars is being + + + align:start position:0% +100 plus dollars 120 dollars is being +taken by those agents and brokers + + align:start position:0% +taken by those agents and brokers + + + align:start position:0% +taken by those agents and brokers +claims administration we talked about it + + align:start position:0% +claims administration we talked about it + + + align:start position:0% +claims administration we talked about it +very paper and human intensive + + align:start position:0% +very paper and human intensive + + + align:start position:0% +very paper and human intensive +litigation risk all abound um + + align:start position:0% +litigation risk all abound um + + + align:start position:0% +litigation risk all abound um +insurance companies are built up around + + align:start position:0% +insurance companies are built up around + + + align:start position:0% +insurance companies are built up around +this + + align:start position:0% +this + + + align:start position:0% +this +legacy tech just like in in in + + align:start position:0% +legacy tech just like in in in + + + align:start position:0% +legacy tech just like in in in +payments and in credit + + align:start position:0% + + + + align:start position:0% + +of every dollar a premium a big chunk is + + align:start position:0% +of every dollar a premium a big chunk is + + + align:start position:0% +of every dollar a premium a big chunk is +not only going to the agents + + align:start position:0% +not only going to the agents + + + align:start position:0% +not only going to the agents +and the brokers but a big chunk is of + + align:start position:0% +and the brokers but a big chunk is of + + + align:start position:0% +and the brokers but a big chunk is of +going of course to the whole + + align:start position:0% +going of course to the whole + + + align:start position:0% +going of course to the whole +claims processing and the whole value + + align:start position:0% +claims processing and the whole value + + + align:start position:0% +claims processing and the whole value +chain + + align:start position:0% +chain + + + align:start position:0% +chain +and because it's deeply regulated in + + align:start position:0% +and because it's deeply regulated in + + + align:start position:0% +and because it's deeply regulated in +many marketplaces you can't offer a new + + align:start position:0% +many marketplaces you can't offer a new + + + align:start position:0% +many marketplaces you can't offer a new +type of insurance without getting some + + align:start position:0% +type of insurance without getting some + + + align:start position:0% +type of insurance without getting some +official sector approval going through + + align:start position:0% +official sector approval going through + + + align:start position:0% +official sector approval going through +the product design phase + + align:start position:0% +the product design phase + + + align:start position:0% +the product design phase +often has legacy and time delays within + + align:start position:0% +often has legacy and time delays within + + + align:start position:0% +often has legacy and time delays within +it + + align:start position:0% +it + + + align:start position:0% +it +and of course just like the other fields + + align:start position:0% +and of course just like the other fields + + + align:start position:0% +and of course just like the other fields +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +whole sorts of questions about user + + align:start position:0% +whole sorts of questions about user + + + align:start position:0% +whole sorts of questions about user +interface and user experience + + align:start position:0% +interface and user experience + + + align:start position:0% +interface and user experience +all of these present challenges but they + + align:start position:0% +all of these present challenges but they + + + align:start position:0% +all of these present challenges but they +also present opportunities + + align:start position:0% +also present opportunities + + + align:start position:0% +also present opportunities +remain any questions not yet but let's + + align:start position:0% +remain any questions not yet but let's + + + align:start position:0% +remain any questions not yet but let's +wait perhaps a few seconds + + align:start position:0% +wait perhaps a few seconds + + + align:start position:0% +wait perhaps a few seconds +no i don't see any hands up all right + + align:start position:0% +no i don't see any hands up all right + + + align:start position:0% +no i don't see any hands up all right +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so insurance and insurance tech + + align:start position:0% +so insurance and insurance tech + + + align:start position:0% +so insurance and insurance tech +it you can sort of say i want to be + + align:start position:0% +it you can sort of say i want to be + + + align:start position:0% +it you can sort of say i want to be +involved in the pricing and underwriting + + align:start position:0% +involved in the pricing and underwriting + + + align:start position:0% +involved in the pricing and underwriting +the quotes the policy administration the + + align:start position:0% +the quotes the policy administration the + + + align:start position:0% +the quotes the policy administration the +claims management sort of four different + + align:start position:0% +claims management sort of four different + + + align:start position:0% +claims management sort of four different +sectors improving the + + align:start position:0% +sectors improving the + + + align:start position:0% +sectors improving the +customer engagement lowering operating + + align:start position:0% +customer engagement lowering operating + + + align:start position:0% +customer engagement lowering operating +costs + + align:start position:0% +costs + + + align:start position:0% +costs +look of course it always goes back to + + align:start position:0% +look of course it always goes back to + + + align:start position:0% +look of course it always goes back to +can you do something better + + align:start position:0% +can you do something better + + + align:start position:0% +can you do something better +quicker cheaper but as we talked about + + align:start position:0% +quicker cheaper but as we talked about + + + align:start position:0% +quicker cheaper but as we talked about +earlier it could be in product design + + align:start position:0% +earlier it could be in product design + + + align:start position:0% +earlier it could be in product design +as well it could be in in not just doing + + align:start position:0% +as well it could be in in not just doing + + + align:start position:0% +as well it could be in in not just doing +it cheaper in pricing but more + + align:start position:0% +it cheaper in pricing but more + + + align:start position:0% +it cheaper in pricing but more +availability + + align:start position:0% +availability + + + align:start position:0% +availability +and his metro mile is done really in + + align:start position:0% +and his metro mile is done really in + + + align:start position:0% +and his metro mile is done really in +using metrics to get to a new type of + + align:start position:0% +using metrics to get to a new type of + + + align:start position:0% +using metrics to get to a new type of +product + + align:start position:0% +product + + + align:start position:0% +product +itself and the quoting and issuing of + + align:start position:0% +itself and the quoting and issuing of + + + align:start position:0% +itself and the quoting and issuing of +products + + align:start position:0% +products + + + align:start position:0% +products +so uh what are some of the opportunities + + align:start position:0% +so uh what are some of the opportunities + + + align:start position:0% +so uh what are some of the opportunities +more specifically + + align:start position:0% +more specifically + + + align:start position:0% +more specifically +i think across financial technology + + align:start position:0% +i think across financial technology + + + align:start position:0% +i think across financial technology +it's about user interface and user + + align:start position:0% +it's about user interface and user + + + align:start position:0% +it's about user interface and user +experience + + align:start position:0% +experience + + + align:start position:0% +experience +so that could be in the sales side it + + align:start position:0% +so that could be in the sales side it + + + align:start position:0% +so that could be in the sales side it +can be in the account management + + align:start position:0% +can be in the account management + + + align:start position:0% +can be in the account management +digital and mobile phones but also in + + align:start position:0% +digital and mobile phones but also in + + + align:start position:0% +digital and mobile phones but also in +the conversational + + align:start position:0% +the conversational + + + align:start position:0% +the conversational +interface underwriting + + align:start position:0% +interface underwriting + + + align:start position:0% +interface underwriting +we've talked about it really not just + + align:start position:0% +we've talked about it really not just + + + align:start position:0% +we've talked about it really not just +the machine learning but the alternative + + align:start position:0% +the machine learning but the alternative + + + align:start position:0% +the machine learning but the alternative +data + + align:start position:0% +data + + + align:start position:0% +data +and then claims processing i think these + + align:start position:0% +and then claims processing i think these + + + align:start position:0% +and then claims processing i think these +are the big three + + align:start position:0% +are the big three + + + align:start position:0% +are the big three +they seem pretty simple once i say it + + align:start position:0% +they seem pretty simple once i say it + + + align:start position:0% +they seem pretty simple once i say it +but it's sort of like + + align:start position:0% +but it's sort of like + + + align:start position:0% +but it's sort of like +thinking about it and if you have a + + align:start position:0% +thinking about it and if you have a + + + align:start position:0% +thinking about it and if you have a +business model if you're going into this + + align:start position:0% +business model if you're going into this + + + align:start position:0% +business model if you're going into this +business + + align:start position:0% +business + + + align:start position:0% +business +or you're at prudential life insurance + + align:start position:0% +or you're at prudential life insurance + + + align:start position:0% +or you're at prudential life insurance +or nippon life it's sort of saying + + align:start position:0% +or nippon life it's sort of saying + + + align:start position:0% +or nippon life it's sort of saying +how can we use technology to enhance + + align:start position:0% +how can we use technology to enhance + + + align:start position:0% +how can we use technology to enhance +user experience + + align:start position:0% +user experience + + + align:start position:0% +user experience +how can we enhance basically the pricing + + align:start position:0% +how can we enhance basically the pricing + + + align:start position:0% +how can we enhance basically the pricing +and the availability of our product + + align:start position:0% +and the availability of our product + + + align:start position:0% +and the availability of our product +called underwriting + + align:start position:0% +called underwriting + + + align:start position:0% +called underwriting +how do we do the back end the first two + + align:start position:0% +how do we do the back end the first two + + + align:start position:0% +how do we do the back end the first two +user experience and underwriting very + + align:start position:0% +user experience and underwriting very + + + align:start position:0% +user experience and underwriting very +much true in banking tech + + align:start position:0% +much true in banking tech + + + align:start position:0% +much true in banking tech +claims processing somewhat unique here + + align:start position:0% +claims processing somewhat unique here + + + align:start position:0% +claims processing somewhat unique here +and it's about data capture + + align:start position:0% + + + + align:start position:0% + +now one part of the data capture + + align:start position:0% +now one part of the data capture + + + align:start position:0% +now one part of the data capture +and you can see it here drones the + + align:start position:0% +and you can see it here drones the + + + align:start position:0% +and you can see it here drones the +internet of things + + align:start position:0% +internet of things + + + align:start position:0% +internet of things +smartphones telematics wearables + + align:start position:0% + + + + align:start position:0% + +i i'm curious romaine you'll see if + + align:start position:0% +i i'm curious romaine you'll see if + + + align:start position:0% +i i'm curious romaine you'll see if +anyone will raise their hand + + align:start position:0% +anyone will raise their hand + + + align:start position:0% +anyone will raise their hand +is anybody actually taking insurance + + align:start position:0% +is anybody actually taking insurance + + + align:start position:0% +is anybody actually taking insurance +where the insurance company has said for + + align:start position:0% +where the insurance company has said for + + + align:start position:0% +where the insurance company has said for +your automobile + + align:start position:0% +your automobile + + + align:start position:0% +your automobile +we want to have access to your driving + + align:start position:0% +we want to have access to your driving + + + align:start position:0% +we want to have access to your driving +record directly + + align:start position:0% +record directly + + + align:start position:0% +record directly +through your car's telematics telematics + + align:start position:0% +through your car's telematics telematics + + + align:start position:0% +through your car's telematics telematics +is a word that didn't exist 30 and 50 + + align:start position:0% +is a word that didn't exist 30 and 50 + + + align:start position:0% +is a word that didn't exist 30 and 50 +years ago + + align:start position:0% +years ago + + + align:start position:0% +years ago +it's really or if it did exist it wasn't + + align:start position:0% +it's really or if it did exist it wasn't + + + align:start position:0% +it's really or if it did exist it wasn't +commonly used + + align:start position:0% +commonly used + + + align:start position:0% +commonly used +it's about all the information + + align:start position:0% +it's about all the information + + + align:start position:0% +it's about all the information +that your car is collecting + + align:start position:0% +that your car is collecting + + + align:start position:0% +that your car is collecting +on driving in the computers + + align:start position:0% +on driving in the computers + + + align:start position:0% +on driving in the computers +on board your your car + + align:start position:0% +on board your your car + + + align:start position:0% +on board your your car +and it's not just gps and it can sort of + + align:start position:0% +and it's not just gps and it can sort of + + + align:start position:0% +and it's not just gps and it can sort of +assess your driving + + align:start position:0% +assess your driving + + + align:start position:0% +assess your driving +smartphones as well can assess our + + align:start position:0% +smartphones as well can assess our + + + align:start position:0% +smartphones as well can assess our +driving + + align:start position:0% +driving + + + align:start position:0% +driving +because smartphones are not just + + align:start position:0% +because smartphones are not just + + + align:start position:0% +because smartphones are not just +locational devices + + align:start position:0% +locational devices + + + align:start position:0% +locational devices +but they can get all this the ups and + + align:start position:0% +but they can get all this the ups and + + + align:start position:0% +but they can get all this the ups and +downs + + align:start position:0% +downs + + + align:start position:0% +downs +of your driving what does that mean + + align:start position:0% +of your driving what does that mean + + + align:start position:0% +of your driving what does that mean +that between smartphones and the + + align:start position:0% +that between smartphones and the + + + align:start position:0% +that between smartphones and the +computers on our cars + + align:start position:0% + + + + align:start position:0% + +a product can be offered that says we + + align:start position:0% +a product can be offered that says we + + + align:start position:0% +a product can be offered that says we +know enough about your driving that we + + align:start position:0% +know enough about your driving that we + + + align:start position:0% +know enough about your driving that we +will give you + + align:start position:0% +will give you + + + align:start position:0% +will give you +fine-tuned pricing and underwriting + + align:start position:0% +fine-tuned pricing and underwriting + + + align:start position:0% +fine-tuned pricing and underwriting +yeah i had a question um around the + + align:start position:0% +yeah i had a question um around the + + + align:start position:0% +yeah i had a question um around the +around google's deal with ascension to + + align:start position:0% +around google's deal with ascension to + + + align:start position:0% +around google's deal with ascension to +store and analyze the medical records + + align:start position:0% +store and analyze the medical records + + + align:start position:0% +store and analyze the medical records +from their hospital network and i'm + + align:start position:0% +from their hospital network and i'm + + + align:start position:0% +from their hospital network and i'm +curious if you + + align:start position:0% +curious if you + + + align:start position:0% +curious if you +think that kind of entrance of big tech + + align:start position:0% +think that kind of entrance of big tech + + + align:start position:0% +think that kind of entrance of big tech +into the medical world is + + align:start position:0% +into the medical world is + + + align:start position:0% +into the medical world is +going to be more common and if that + + align:start position:0% +going to be more common and if that + + + align:start position:0% +going to be more common and if that +might be a potential avenue for + + align:start position:0% +might be a potential avenue for + + + align:start position:0% +might be a potential avenue for +those kinds of companies getting the + + align:start position:0% +those kinds of companies getting the + + + align:start position:0% +those kinds of companies getting the +insight into + + align:start position:0% +insight into + + + align:start position:0% +insight into +health data that they would need to make + + align:start position:0% +health data that they would need to make + + + align:start position:0% +health data that they would need to make +them confident to move into insurance + + align:start position:0% +them confident to move into insurance + + + align:start position:0% +them confident to move into insurance +i think uh you've landed upon one area + + align:start position:0% +i think uh you've landed upon one area + + + align:start position:0% +i think uh you've landed upon one area +that + + align:start position:0% +that + + + align:start position:0% +that +big tech can be very uh influential + + align:start position:0% +big tech can be very uh influential + + + align:start position:0% +big tech can be very uh influential +particularly the big ai companies like + + align:start position:0% +particularly the big ai companies like + + + align:start position:0% +particularly the big ai companies like +google + + align:start position:0% +google + + + align:start position:0% +google +and beidou and china to the extent + + align:start position:0% +and beidou and china to the extent + + + align:start position:0% +and beidou and china to the extent +and we'll see there are some startups + + align:start position:0% +and we'll see there are some startups + + + align:start position:0% +and we'll see there are some startups +that are entering this field because + + align:start position:0% +that are entering this field because + + + align:start position:0% +that are entering this field because +they're very good at + + align:start position:0% +they're very good at + + + align:start position:0% +they're very good at +data analytics and machine learning and + + align:start position:0% +data analytics and machine learning and + + + align:start position:0% +data analytics and machine learning and +to the extent that they can be data + + align:start position:0% +to the extent that they can be data + + + align:start position:0% +to the extent that they can be data +aggregators like + + align:start position:0% +aggregators like + + + align:start position:0% +aggregators like +google you're absolutely right i don't + + align:start position:0% +google you're absolutely right i don't + + + align:start position:0% +google you're absolutely right i don't +think it's just healthcare by the way + + align:start position:0% +think it's just healthcare by the way + + + align:start position:0% +think it's just healthcare by the way +but i think healthcare is a really + + align:start position:0% +but i think healthcare is a really + + + align:start position:0% +but i think healthcare is a really +important piece of it + + align:start position:0% +important piece of it + + + align:start position:0% +important piece of it +that many insurance companies healthcare + + align:start position:0% +that many insurance companies healthcare + + + align:start position:0% +that many insurance companies healthcare +management companies in the u.s + + align:start position:0% +management companies in the u.s + + + align:start position:0% +management companies in the u.s +have a tremendous amount of data and + + align:start position:0% +have a tremendous amount of data and + + + align:start position:0% +have a tremendous amount of data and +they want to make more sense of it + + align:start position:0% +they want to make more sense of it + + + align:start position:0% +they want to make more sense of it +and they want to with that data provide + + align:start position:0% +and they want to with that data provide + + + align:start position:0% +and they want to with that data provide +more fine-tuned insurance products but + + align:start position:0% +more fine-tuned insurance products but + + + align:start position:0% +more fine-tuned insurance products but +also help manage our health care system + + align:start position:0% +also help manage our health care system + + + align:start position:0% +also help manage our health care system +uh better so i think it is an avenue for + + align:start position:0% +uh better so i think it is an avenue for + + + align:start position:0% +uh better so i think it is an avenue for +certain big tech companies that are + + align:start position:0% +certain big tech companies that are + + + align:start position:0% +certain big tech companies that are +uh at the cutting edge of of data + + align:start position:0% +uh at the cutting edge of of data + + + align:start position:0% +uh at the cutting edge of of data +analytics and machine learning + + align:start position:0% +analytics and machine learning + + + align:start position:0% +analytics and machine learning +not for every uh big tech company but + + align:start position:0% +not for every uh big tech company but + + + align:start position:0% +not for every uh big tech company but +um for many i agree with that + + align:start position:0% +um for many i agree with that + + + align:start position:0% +um for many i agree with that +did anybody have an insurance product + + align:start position:0% +did anybody have an insurance product + + + align:start position:0% +did anybody have an insurance product +did anybody take out an auto insurance + + align:start position:0% +did anybody take out an auto insurance + + + align:start position:0% +did anybody take out an auto insurance +uh + + align:start position:0% + + + + align:start position:0% + +i think probably alessandro he had his + + align:start position:0% +i think probably alessandro he had his + + + align:start position:0% +i think probably alessandro he had his +hand up but + + align:start position:0% +hand up but + + + align:start position:0% +hand up but +probably for that question i had um this + + align:start position:0% +probably for that question i had um this + + + align:start position:0% +probably for that question i had um this +little + + align:start position:0% + + + + align:start position:0% + +chip or computer on board and um + + align:start position:0% +chip or computer on board and um + + + align:start position:0% +chip or computer on board and um +basically yeah it um traced everything + + align:start position:0% +basically yeah it um traced everything + + + align:start position:0% +basically yeah it um traced everything +that i did with the car like where + + align:start position:0% +that i did with the car like where + + + align:start position:0% +that i did with the car like where +i where i was how many miles i drove + + align:start position:0% +i where i was how many miles i drove + + + align:start position:0% +i where i was how many miles i drove +everything and actually it actually + + align:start position:0% +everything and actually it actually + + + align:start position:0% +everything and actually it actually +helped me to + + align:start position:0% +helped me to + + + align:start position:0% +helped me to +decrease the cost of insurance there you + + align:start position:0% +decrease the cost of insurance there you + + + align:start position:0% +decrease the cost of insurance there you +go there you go + + align:start position:0% +go there you go + + + align:start position:0% +go there you go +now some of the first telematics patents + + align:start position:0% +now some of the first telematics patents + + + align:start position:0% +now some of the first telematics patents +filed + + align:start position:0% +filed + + + align:start position:0% +filed +uh on telematics were in the late 1990s + + align:start position:0% + + + + align:start position:0% + +but what we found is it's really changed + + align:start position:0% +but what we found is it's really changed + + + align:start position:0% +but what we found is it's really changed +the field of auto insurance + + align:start position:0% +the field of auto insurance + + + align:start position:0% +the field of auto insurance +this little visualization about + + align:start position:0% +this little visualization about + + + align:start position:0% +this little visualization about +insurtech again from the department of + + align:start position:0% +insurtech again from the department of + + + align:start position:0% +insurtech again from the department of +treasury study last fall + + align:start position:0% +treasury study last fall + + + align:start position:0% +treasury study last fall +i think it's just a good place to to + + align:start position:0% +i think it's just a good place to to + + + align:start position:0% +i think it's just a good place to to +pause for a second + + align:start position:0% +pause for a second + + + align:start position:0% +pause for a second +we're not going to go through every box + + align:start position:0% +we're not going to go through every box + + + align:start position:0% +we're not going to go through every box +but whether it's + + align:start position:0% +but whether it's + + + align:start position:0% +but whether it's +sensors and telematics and this is a big + + align:start position:0% +sensors and telematics and this is a big + + + align:start position:0% +sensors and telematics and this is a big +piece + + align:start position:0% +piece + + + align:start position:0% +piece +of having those sensors and telematics + + align:start position:0% +of having those sensors and telematics + + + align:start position:0% +of having those sensors and telematics +there + + align:start position:0% +there + + + align:start position:0% +there +to lower alexandro's cost of insurance + + align:start position:0% +to lower alexandro's cost of insurance + + + align:start position:0% +to lower alexandro's cost of insurance +but also for claims management if the + + align:start position:0% +but also for claims management if the + + + align:start position:0% +but also for claims management if the +telematics and sensors are there + + align:start position:0% +telematics and sensors are there + + + align:start position:0% +telematics and sensors are there +upon an accident then you can lower a + + align:start position:0% +upon an accident then you can lower a + + + align:start position:0% +upon an accident then you can lower a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +the cost of claims management and the + + align:start position:0% +the cost of claims management and the + + + align:start position:0% +the cost of claims management and the +insurance companies + + align:start position:0% +insurance companies + + + align:start position:0% +insurance companies +can have confidence the accident + + align:start position:0% +can have confidence the accident + + + align:start position:0% +can have confidence the accident +actually happened + + align:start position:0% +actually happened + + + align:start position:0% +actually happened +potentially figure out who's at fought + + align:start position:0% + + + + align:start position:0% + +see right at that moment what's going on + + align:start position:0% +see right at that moment what's going on + + + align:start position:0% +see right at that moment what's going on +in that automobile + + align:start position:0% +in that automobile + + + align:start position:0% +in that automobile +visual computing literally downloading + + align:start position:0% +visual computing literally downloading + + + align:start position:0% +visual computing literally downloading +uploading + + align:start position:0% +uploading + + + align:start position:0% +uploading +photographs into the claims management + + align:start position:0% +photographs into the claims management + + + align:start position:0% +photographs into the claims management +process we've already talked about + + align:start position:0% +process we've already talked about + + + align:start position:0% +process we've already talked about +machine learning and ai but blockchain + + align:start position:0% +machine learning and ai but blockchain + + + align:start position:0% +machine learning and ai but blockchain +technology i want to touch upon + + align:start position:0% +technology i want to touch upon + + + align:start position:0% +technology i want to touch upon +of all the fields of blockchain + + align:start position:0% +of all the fields of blockchain + + + align:start position:0% +of all the fields of blockchain +technology + + align:start position:0% +technology + + + align:start position:0% +technology +that we generally have heard about and + + align:start position:0% +that we generally have heard about and + + + align:start position:0% +that we generally have heard about and +many of them are hype versus reality + + align:start position:0% +many of them are hype versus reality + + + align:start position:0% +many of them are hype versus reality +one field is whether with the use + + align:start position:0% +one field is whether with the use + + + align:start position:0% +one field is whether with the use +of blockchain technology that we can + + align:start position:0% +of blockchain technology that we can + + + align:start position:0% +of blockchain technology that we can +have an append only log + + align:start position:0% +have an append only log + + + align:start position:0% +have an append only log +that is tamper resistant whether there + + align:start position:0% +that is tamper resistant whether there + + + align:start position:0% +that is tamper resistant whether there +would be trust + + align:start position:0% +would be trust + + + align:start position:0% +would be trust +in a field of insurance called + + align:start position:0% +in a field of insurance called + + + align:start position:0% +in a field of insurance called +parametric insurance + + align:start position:0% +parametric insurance + + + align:start position:0% +parametric insurance +in essence if we had an automated + + align:start position:0% +in essence if we had an automated + + + align:start position:0% +in essence if we had an automated +smart contract that said + + align:start position:0% +smart contract that said + + + align:start position:0% +smart contract that said +that if this happens i get paid so + + align:start position:0% +that if this happens i get paid so + + + align:start position:0% +that if this happens i get paid so +what's the this + + align:start position:0% +what's the this + + + align:start position:0% +what's the this +one field that a group of students + + align:start position:0% +one field that a group of students + + + align:start position:0% +one field that a group of students +studied last + + align:start position:0% +studied last + + + align:start position:0% +studied last +year uh studying it on behalf of + + align:start position:0% +year uh studying it on behalf of + + + align:start position:0% +year uh studying it on behalf of +uh a group in asia was + + align:start position:0% +uh a group in asia was + + + align:start position:0% +uh a group in asia was +parametric insurance for + + align:start position:0% +parametric insurance for + + + align:start position:0% +parametric insurance for +airline delays if you could embed on + + align:start position:0% +airline delays if you could embed on + + + align:start position:0% +airline delays if you could embed on +a a tamper resistant + + align:start position:0% +a a tamper resistant + + + align:start position:0% +a a tamper resistant +ledger on that ledger you would embed + + align:start position:0% +ledger on that ledger you would embed + + + align:start position:0% +ledger on that ledger you would embed +smart contracts that says if the plane + + align:start position:0% +smart contracts that says if the plane + + + align:start position:0% +smart contracts that says if the plane +takes off more than a half hour late + + align:start position:0% +takes off more than a half hour late + + + align:start position:0% +takes off more than a half hour late +you automatically get paid a mobile app + + align:start position:0% + + + + align:start position:0% + +no trying to rely on the airlines + + align:start position:0% +no trying to rely on the airlines + + + align:start position:0% +no trying to rely on the airlines +whether they're accurately + + align:start position:0% +whether they're accurately + + + align:start position:0% +whether they're accurately +telling you or not that the plane took + + align:start position:0% +telling you or not that the plane took + + + align:start position:0% +telling you or not that the plane took +off late + + align:start position:0% +off late + + + align:start position:0% +off late +put it on a blockchain technology now + + align:start position:0% +put it on a blockchain technology now + + + align:start position:0% +put it on a blockchain technology now +maybe you could do it with a central + + align:start position:0% +maybe you could do it with a central + + + align:start position:0% +maybe you could do it with a central +database as well + + align:start position:0% +database as well + + + align:start position:0% +database as well +but there are many people looking to + + align:start position:0% +but there are many people looking to + + + align:start position:0% +but there are many people looking to +whether to use blockchain technology for + + align:start position:0% +whether to use blockchain technology for + + + align:start position:0% +whether to use blockchain technology for +parametric insurance but the sensors and + + align:start position:0% +parametric insurance but the sensors and + + + align:start position:0% +parametric insurance but the sensors and +telematics the visual computing the + + align:start position:0% +telematics the visual computing the + + + align:start position:0% +telematics the visual computing the +machine learning those are real + + align:start position:0% +machine learning those are real + + + align:start position:0% +machine learning those are real +the department of treasury sort of also + + align:start position:0% +the department of treasury sort of also + + + align:start position:0% +the department of treasury sort of also +put something on the + + align:start position:0% +put something on the + + + align:start position:0% +put something on the +on the edge in terms of blockchain + + align:start position:0% +on the edge in terms of blockchain + + + align:start position:0% +on the edge in terms of blockchain +technology + + align:start position:0% +technology + + + align:start position:0% +technology +challenges though abound for insure tech + + align:start position:0% +challenges though abound for insure tech + + + align:start position:0% +challenges though abound for insure tech +there's still the age-old challenge of + + align:start position:0% +there's still the age-old challenge of + + + align:start position:0% +there's still the age-old challenge of +funding and it's + + align:start position:0% +funding and it's + + + align:start position:0% +funding and it's +it's particularly true in insurance + + align:start position:0% +it's particularly true in insurance + + + align:start position:0% +it's particularly true in insurance +because if you take an insurance risk + + align:start position:0% +because if you take an insurance risk + + + align:start position:0% +because if you take an insurance risk +onto your balance sheet that's a + + align:start position:0% +onto your balance sheet that's a + + + align:start position:0% +onto your balance sheet that's a +liability of an insurance company that's + + align:start position:0% +liability of an insurance company that's + + + align:start position:0% +liability of an insurance company that's +a liability that + + align:start position:0% +a liability that + + + align:start position:0% +a liability that +in the future they have to pay out a + + align:start position:0% +in the future they have to pay out a + + + align:start position:0% +in the future they have to pay out a +claim + + align:start position:0% +claim + + + align:start position:0% +claim +on an accident a loss on your home + + align:start position:0% +on an accident a loss on your home + + + align:start position:0% +on an accident a loss on your home +or on your life so many companies + + align:start position:0% +or on your life so many companies + + + align:start position:0% +or on your life so many companies +are fighting challenges if they're + + align:start position:0% +are fighting challenges if they're + + + align:start position:0% +are fighting challenges if they're +startups how can they access capital + + align:start position:0% +startups how can they access capital + + + align:start position:0% +startups how can they access capital +now in the banking sector you can + + align:start position:0% +now in the banking sector you can + + + align:start position:0% +now in the banking sector you can +possibly do it through + + align:start position:0% +possibly do it through + + + align:start position:0% +possibly do it through +securitization you can basically say i'm + + align:start position:0% +securitization you can basically say i'm + + + align:start position:0% +securitization you can basically say i'm +not gonna + + align:start position:0% +not gonna + + + align:start position:0% +not gonna +i'm not gonna build my own balance sheet + + align:start position:0% +i'm not gonna build my own balance sheet + + + align:start position:0% +i'm not gonna build my own balance sheet +i'm gonna + + align:start position:0% +i'm gonna + + + align:start position:0% +i'm gonna +sort of rent a balance sheet i'm gonna + + align:start position:0% +sort of rent a balance sheet i'm gonna + + + align:start position:0% +sort of rent a balance sheet i'm gonna +lay it off similarly here + + align:start position:0% +lay it off similarly here + + + align:start position:0% +lay it off similarly here +you can lay off some risk in the + + align:start position:0% +you can lay off some risk in the + + + align:start position:0% +you can lay off some risk in the +reinsurance markets but it's not + + align:start position:0% +reinsurance markets but it's not + + + align:start position:0% +reinsurance markets but it's not +quite the same for these insured tech + + align:start position:0% +quite the same for these insured tech + + + align:start position:0% +quite the same for these insured tech +startups + + align:start position:0% +startups + + + align:start position:0% +startups +most challenger banks partner with + + align:start position:0% +most challenger banks partner with + + + align:start position:0% +most challenger banks partner with +some bank get a warehouse line of credit + + align:start position:0% +some bank get a warehouse line of credit + + + align:start position:0% +some bank get a warehouse line of credit +and possibly also then sell their loans + + align:start position:0% +and possibly also then sell their loans + + + align:start position:0% +and possibly also then sell their loans +after they're initiated here + + align:start position:0% +after they're initiated here + + + align:start position:0% +after they're initiated here +it's not as robust it's not as developed + + align:start position:0% +it's not as robust it's not as developed + + + align:start position:0% +it's not as robust it's not as developed +but again + + align:start position:0% +but again + + + align:start position:0% +but again +many insurance fintech startups + + align:start position:0% +many insurance fintech startups + + + align:start position:0% +many insurance fintech startups +are saying do i partner with a big + + align:start position:0% +are saying do i partner with a big + + + align:start position:0% +are saying do i partner with a big +dominant insurance company because i + + align:start position:0% +dominant insurance company because i + + + align:start position:0% +dominant insurance company because i +can't build my balance sheet + + align:start position:0% +can't build my balance sheet + + + align:start position:0% +can't build my balance sheet +as rapidly if you choose to be a carrier + + align:start position:0% +as rapidly if you choose to be a carrier + + + align:start position:0% +as rapidly if you choose to be a carrier +and a carrier is the term to say that + + align:start position:0% +and a carrier is the term to say that + + + align:start position:0% +and a carrier is the term to say that +you actually take the insurance onto + + align:start position:0% +you actually take the insurance onto + + + align:start position:0% +you actually take the insurance onto +your balance sheet you have the + + align:start position:0% +your balance sheet you have the + + + align:start position:0% +your balance sheet you have the +liability + + align:start position:0% +liability + + + align:start position:0% +liability +choose to be a carrier it's balance + + align:start position:0% +choose to be a carrier it's balance + + + align:start position:0% +choose to be a carrier it's balance +sheet intensive + + align:start position:0% +sheet intensive + + + align:start position:0% +sheet intensive +also just how do you fund your startup + + align:start position:0% +also just how do you fund your startup + + + align:start position:0% +also just how do you fund your startup +run rate loss because all the startups + + align:start position:0% +run rate loss because all the startups + + + align:start position:0% +run rate loss because all the startups +tend to have multiple years of building + + align:start position:0% +tend to have multiple years of building + + + align:start position:0% +tend to have multiple years of building +out + + align:start position:0% +out + + + align:start position:0% +out +a network and building the platform + + align:start position:0% +a network and building the platform + + + align:start position:0% +a network and building the platform +itself + + align:start position:0% +itself + + + align:start position:0% +itself +clearly the competitive landscape the + + align:start position:0% +clearly the competitive landscape the + + + align:start position:0% +clearly the competitive landscape the +regulatory frameworks + + align:start position:0% +regulatory frameworks + + + align:start position:0% +regulatory frameworks +the regulatory frameworks do you get + + align:start position:0% +the regulatory frameworks do you get + + + align:start position:0% +the regulatory frameworks do you get +licensed again + + align:start position:0% +licensed again + + + align:start position:0% +licensed again +similar to challenger banks remember we + + align:start position:0% +similar to challenger banks remember we + + + align:start position:0% +similar to challenger banks remember we +talked about there's neo banks + + align:start position:0% +talked about there's neo banks + + + align:start position:0% +talked about there's neo banks +and challenger banks which often people + + align:start position:0% +and challenger banks which often people + + + align:start position:0% +and challenger banks which often people +sort of say + + align:start position:0% +sort of say + + + align:start position:0% +sort of say +uh in in the same breath they're the + + align:start position:0% +uh in in the same breath they're the + + + align:start position:0% +uh in in the same breath they're the +same but more specifically a neobank is + + align:start position:0% +same but more specifically a neobank is + + + align:start position:0% +same but more specifically a neobank is +something doing a lot of banking + + align:start position:0% +something doing a lot of banking + + + align:start position:0% +something doing a lot of banking +functions that has not yet gotten a + + align:start position:0% +functions that has not yet gotten a + + + align:start position:0% +functions that has not yet gotten a +banking license + + align:start position:0% +banking license + + + align:start position:0% +banking license +similar here if you're thinking about + + align:start position:0% +similar here if you're thinking about + + + align:start position:0% +similar here if you're thinking about +starting + + align:start position:0% +starting + + + align:start position:0% +starting +an insurance fintech firm what type of + + align:start position:0% +an insurance fintech firm what type of + + + align:start position:0% +an insurance fintech firm what type of +licensing will you get will just be a + + align:start position:0% +licensing will you get will just be a + + + align:start position:0% +licensing will you get will just be a +brokerage licensing + + align:start position:0% +brokerage licensing + + + align:start position:0% +brokerage licensing +in various jurisdictions you have to + + align:start position:0% +in various jurisdictions you have to + + + align:start position:0% +in various jurisdictions you have to +register to be a broker or an agent + + align:start position:0% +register to be a broker or an agent + + + align:start position:0% +register to be a broker or an agent +or you actually registering to take + + align:start position:0% +or you actually registering to take + + + align:start position:0% +or you actually registering to take +lines onto your balance sheet and become + + align:start position:0% +lines onto your balance sheet and become + + + align:start position:0% +lines onto your balance sheet and become +a carrier + + align:start position:0% + + + + align:start position:0% + +and then of course user adoption + + align:start position:0% +and then of course user adoption + + + align:start position:0% +and then of course user adoption +and the use of data and in terms of the + + align:start position:0% +and the use of data and in terms of the + + + align:start position:0% +and the use of data and in terms of the +use of data + + align:start position:0% +use of data + + + align:start position:0% +use of data +there aren't quite the same laws it + + align:start position:0% +there aren't quite the same laws it + + + align:start position:0% +there aren't quite the same laws it +doesn't we we have the same conceptual + + align:start position:0% +doesn't we we have the same conceptual + + + align:start position:0% +doesn't we we have the same conceptual +framework that you have to be + + align:start position:0% +framework that you have to be + + + align:start position:0% +framework that you have to be +fair and unbiased but there aren't quite + + align:start position:0% +fair and unbiased but there aren't quite + + + align:start position:0% +fair and unbiased but there aren't quite +the same laws + + align:start position:0% +the same laws + + + align:start position:0% +the same laws +like the equal credit opportunity act + + align:start position:0% +like the equal credit opportunity act + + + align:start position:0% +like the equal credit opportunity act +here in the u.s + + align:start position:0% +here in the u.s + + + align:start position:0% +here in the u.s +and in terms of the use of data as we'll + + align:start position:0% +and in terms of the use of data as we'll + + + align:start position:0% +and in terms of the use of data as we'll +see in a minute + + align:start position:0% +see in a minute + + + align:start position:0% +see in a minute +if you sign a waiver and say you can use + + align:start position:0% +if you sign a waiver and say you can use + + + align:start position:0% +if you sign a waiver and say you can use +my driving record to give my insurance + + align:start position:0% +my driving record to give my insurance + + + align:start position:0% +my driving record to give my insurance +as alexandra did they can use that data + + align:start position:0% +as alexandra did they can use that data + + + align:start position:0% +as alexandra did they can use that data +also on the claims management side + + align:start position:0% +also on the claims management side + + + align:start position:0% +also on the claims management side +it's not just to lower the cost it's + + align:start position:0% +it's not just to lower the cost it's + + + align:start position:0% +it's not just to lower the cost it's +also to see + + align:start position:0% +also to see + + + align:start position:0% +also to see +if you call up and say i had an accident + + align:start position:0% +if you call up and say i had an accident + + + align:start position:0% +if you call up and say i had an accident +they look at the telematics and say + + align:start position:0% +they look at the telematics and say + + + align:start position:0% +they look at the telematics and say +did this really happen + + align:start position:0% + + + + align:start position:0% + +so the insurtech landscape we're not + + align:start position:0% +so the insurtech landscape we're not + + + align:start position:0% +so the insurtech landscape we're not +going to dive into this slide but it's + + align:start position:0% +going to dive into this slide but it's + + + align:start position:0% +going to dive into this slide but it's +just + + align:start position:0% +just + + + align:start position:0% +just +each of these pieces each of these + + align:start position:0% +each of these pieces each of these + + + align:start position:0% +each of these pieces each of these +pieces it might be that you're + + align:start position:0% +pieces it might be that you're + + + align:start position:0% +pieces it might be that you're +trying to go into the billing and + + align:start position:0% +trying to go into the billing and + + + align:start position:0% +trying to go into the billing and +payments + + align:start position:0% +payments + + + align:start position:0% +payments +which is sort of rudimentary sort of you + + align:start position:0% +which is sort of rudimentary sort of you + + + align:start position:0% +which is sort of rudimentary sort of you +could be going all the way + + align:start position:0% +could be going all the way + + + align:start position:0% +could be going all the way +to another area and say we're going to + + align:start position:0% +to another area and say we're going to + + + align:start position:0% +to another area and say we're going to +be the best + + align:start position:0% +be the best + + + align:start position:0% +be the best +data analytics on wearables and by mean + + align:start position:0% +data analytics on wearables and by mean + + + align:start position:0% +data analytics on wearables and by mean +wearables how many people have a fitbit + + align:start position:0% +wearables how many people have a fitbit + + + align:start position:0% +wearables how many people have a fitbit +does anybody want to talk about whether + + align:start position:0% +does anybody want to talk about whether + + + align:start position:0% +does anybody want to talk about whether +you've signed up for insurance + + align:start position:0% +you've signed up for insurance + + + align:start position:0% +you've signed up for insurance +uh that your insurance company can get + + align:start position:0% +uh that your insurance company can get + + + align:start position:0% +uh that your insurance company can get +your data + + align:start position:0% +your data + + + align:start position:0% +your data +off of your fitbit or off of your apple + + align:start position:0% +off of your fitbit or off of your apple + + + align:start position:0% +off of your fitbit or off of your apple +watch + + align:start position:0% +watch + + + align:start position:0% +watch +off your off you know what you're using + + align:start position:0% +off your off you know what you're using + + + align:start position:0% +off your off you know what you're using +for for exercise can lower your + + align:start position:0% +for for exercise can lower your + + + align:start position:0% +for for exercise can lower your +cost of insurance i'm going to pause + + align:start position:0% +cost of insurance i'm going to pause + + + align:start position:0% +cost of insurance i'm going to pause +remain + + align:start position:0% + + + + align:start position:0% + +i don't see any hands up ah lindsay go + + align:start position:0% +i don't see any hands up ah lindsay go + + + align:start position:0% +i don't see any hands up ah lindsay go +ahead + + align:start position:0% +ahead + + + align:start position:0% +ahead +well i didn't have like the agreement + + align:start position:0% +well i didn't have like the agreement + + + align:start position:0% +well i didn't have like the agreement +straight with the + + align:start position:0% +straight with the + + + align:start position:0% +straight with the +insurance but what i did have is that my + + align:start position:0% +insurance but what i did have is that my + + + align:start position:0% +insurance but what i did have is that my +former employer had a program where we + + align:start position:0% +former employer had a program where we + + + align:start position:0% +former employer had a program where we +would connect + + align:start position:0% +would connect + + + align:start position:0% +would connect +our tracking devices like for steps and + + align:start position:0% +our tracking devices like for steps and + + + align:start position:0% +our tracking devices like for steps and +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +uh with this program that like would + + align:start position:0% +uh with this program that like would + + + align:start position:0% +uh with this program that like would +give you kickbacks if you've got so many + + align:start position:0% +give you kickbacks if you've got so many + + + align:start position:0% +give you kickbacks if you've got so many +steps a day + + align:start position:0% +steps a day + + + align:start position:0% +steps a day +uh so like i'd get tons of gift cards + + align:start position:0% +uh so like i'd get tons of gift cards + + + align:start position:0% +uh so like i'd get tons of gift cards +because of all the steps i tracked in + + align:start position:0% +because of all the steps i tracked in + + + align:start position:0% +because of all the steps i tracked in +and that data i'm sure was going to the + + align:start position:0% +and that data i'm sure was going to the + + + align:start position:0% +and that data i'm sure was going to the +insurance company to lower the + + align:start position:0% +insurance company to lower the + + + align:start position:0% +insurance company to lower the +right so if you got to your 10 000 steps + + align:start position:0% +right so if you got to your 10 000 steps + + + align:start position:0% +right so if you got to your 10 000 steps +or maybe they gave you a premium for 5 + + align:start position:0% +or maybe they gave you a premium for 5 + + + align:start position:0% +or maybe they gave you a premium for 5 +000 steps + + align:start position:0% +000 steps + + + align:start position:0% +000 steps +you got uh some rewards + + align:start position:0% +you got uh some rewards + + + align:start position:0% +you got uh some rewards +now we we all know about rewards + + align:start position:0% +now we we all know about rewards + + + align:start position:0% +now we we all know about rewards +programs in + + align:start position:0% +programs in + + + align:start position:0% +programs in +credit cards and that's part of that + + align:start position:0% +credit cards and that's part of that + + + align:start position:0% +credit cards and that's part of that +two and three quarter percent + + align:start position:0% +two and three quarter percent + + + align:start position:0% +two and three quarter percent +interchange fees + + align:start position:0% +interchange fees + + + align:start position:0% +interchange fees +these rewards by your employer + + align:start position:0% +these rewards by your employer + + + align:start position:0% +these rewards by your employer +ultimately the economic incentives is + + align:start position:0% +ultimately the economic incentives is + + + align:start position:0% +ultimately the economic incentives is +the employer can have + + align:start position:0% +the employer can have + + + align:start position:0% +the employer can have +lower cost of health insurance that data + + align:start position:0% +lower cost of health insurance that data + + + align:start position:0% +lower cost of health insurance that data +through the intermediation of your + + align:start position:0% +through the intermediation of your + + + align:start position:0% +through the intermediation of your +employment contract + + align:start position:0% +employment contract + + + align:start position:0% +employment contract +was lowering health insurance costs for + + align:start position:0% +was lowering health insurance costs for + + + align:start position:0% +was lowering health insurance costs for +some group health insurance now + + align:start position:0% +some group health insurance now + + + align:start position:0% +some group health insurance now +i think your employer was also doing it + + align:start position:0% +i think your employer was also doing it + + + align:start position:0% +i think your employer was also doing it +because they know if you're a better + + align:start position:0% +because they know if you're a better + + + align:start position:0% +because they know if you're a better +health + + align:start position:0% +health + + + align:start position:0% +health +that you also have fewer days off you'll + + align:start position:0% +that you also have fewer days off you'll + + + align:start position:0% +that you also have fewer days off you'll +be you'll be + + align:start position:0% +be you'll be + + + align:start position:0% +be you'll be +hopefully a better employee so they're + + align:start position:0% +hopefully a better employee so they're + + + align:start position:0% +hopefully a better employee so they're +also lowering some of their + + align:start position:0% +also lowering some of their + + + align:start position:0% +also lowering some of their +their uh costs in terms of their direct + + align:start position:0% +their uh costs in terms of their direct + + + align:start position:0% +their uh costs in terms of their direct +costs + + align:start position:0% +costs + + + align:start position:0% +costs +but it also relates to health insurance + + align:start position:0% +but it also relates to health insurance + + + align:start position:0% +but it also relates to health insurance +so wearables trackables telematics + + align:start position:0% +so wearables trackables telematics + + + align:start position:0% +so wearables trackables telematics +and the internet of thing the internet + + align:start position:0% +and the internet of thing the internet + + + align:start position:0% +and the internet of thing the internet +of thing is a term + + align:start position:0% +of thing is a term + + + align:start position:0% +of thing is a term +is about sensors + + align:start position:0% +is about sensors + + + align:start position:0% +is about sensors +and it's about sensors and many items in + + align:start position:0% +and it's about sensors and many items in + + + align:start position:0% +and it's about sensors and many items in +our home as well + + align:start position:0% + + + + align:start position:0% + +if you have a home security system in + + align:start position:0% +if you have a home security system in + + + align:start position:0% +if you have a home security system in +the last + + align:start position:0% +the last + + + align:start position:0% +the last +five or ten years you've been able to + + align:start position:0% +five or ten years you've been able to + + + align:start position:0% +five or ten years you've been able to +tie that + + align:start position:0% +tie that + + + align:start position:0% +tie that +into more data now + + align:start position:0% +into more data now + + + align:start position:0% +into more data now +home security systems have for decades + + align:start position:0% +home security systems have for decades + + + align:start position:0% +home security systems have for decades +somehow had to communicate + + align:start position:0% +somehow had to communicate + + + align:start position:0% +somehow had to communicate +through a security company to law + + align:start position:0% +through a security company to law + + + align:start position:0% +through a security company to law +enforcement if the alarm went off + + align:start position:0% +enforcement if the alarm went off + + + align:start position:0% +enforcement if the alarm went off +but i'm talking about more fine-tuned + + align:start position:0% +but i'm talking about more fine-tuned + + + align:start position:0% +but i'm talking about more fine-tuned +monitoring + + align:start position:0% +monitoring + + + align:start position:0% +monitoring +and we all are aware even though that + + align:start position:0% +and we all are aware even though that + + + align:start position:0% +and we all are aware even though that +very few of us might have it + + align:start position:0% +very few of us might have it + + + align:start position:0% +very few of us might have it +that you can have apps on your phone + + align:start position:0% +that you can have apps on your phone + + + align:start position:0% +that you can have apps on your phone +that you could communicate with your + + align:start position:0% +that you could communicate with your + + + align:start position:0% +that you could communicate with your +home to turn + + align:start position:0% +home to turn + + + align:start position:0% +home to turn +on your heat or your air conditioning + + align:start position:0% +on your heat or your air conditioning + + + align:start position:0% +on your heat or your air conditioning +monitor your home home monitoring + + align:start position:0% +monitor your home home monitoring + + + align:start position:0% +monitor your home home monitoring +devices + + align:start position:0% +devices + + + align:start position:0% +devices +that makes all of us maybe more + + align:start position:0% +that makes all of us maybe more + + + align:start position:0% +that makes all of us maybe more +comfortable + + align:start position:0% +comfortable + + + align:start position:0% +comfortable +that our home is secure or even + + align:start position:0% +that our home is secure or even + + + align:start position:0% +that our home is secure or even +to have the communication from the home + + align:start position:0% +to have the communication from the home + + + align:start position:0% +to have the communication from the home +if for some reason + + align:start position:0% +if for some reason + + + align:start position:0% +if for some reason +there's a problem in the home and + + align:start position:0% +there's a problem in the home and + + + align:start position:0% +there's a problem in the home and +there's + + align:start position:0% +there's + + + align:start position:0% +there's +sensors on refrigerators there's sensors + + align:start position:0% +sensors on refrigerators there's sensors + + + align:start position:0% +sensors on refrigerators there's sensors +on hvac + + align:start position:0% +on hvac + + + align:start position:0% +on hvac +heating and ventilation systems there + + align:start position:0% +heating and ventilation systems there + + + align:start position:0% +heating and ventilation systems there +are sensors throughout houses + + align:start position:0% +are sensors throughout houses + + + align:start position:0% +are sensors throughout houses +the 2020s we're going to see this just + + align:start position:0% +the 2020s we're going to see this just + + + align:start position:0% +the 2020s we're going to see this just +absolutely mushroom in terms of sensors + + align:start position:0% +absolutely mushroom in terms of sensors + + + align:start position:0% +absolutely mushroom in terms of sensors +so what's that data do for the insurance + + align:start position:0% +so what's that data do for the insurance + + + align:start position:0% +so what's that data do for the insurance +field + + align:start position:0% +field + + + align:start position:0% +field +that's why i think in short tech and + + align:start position:0% +that's why i think in short tech and + + + align:start position:0% +that's why i think in short tech and +insurance and + + align:start position:0% +insurance and + + + align:start position:0% +insurance and +in fintech is such an exciting and + + align:start position:0% +in fintech is such an exciting and + + + align:start position:0% +in fintech is such an exciting and +interesting place + + align:start position:0% +interesting place + + + align:start position:0% +interesting place +because we are basically in a + + align:start position:0% +because we are basically in a + + + align:start position:0% +because we are basically in a +transformational time right now in terms + + align:start position:0% +transformational time right now in terms + + + align:start position:0% +transformational time right now in terms +of sensor technology + + align:start position:0% +of sensor technology + + + align:start position:0% +of sensor technology +and embedding sensors into our economies + + align:start position:0% +and embedding sensors into our economies + + + align:start position:0% +and embedding sensors into our economies +not because of insurance + + align:start position:0% +not because of insurance + + + align:start position:0% +not because of insurance +but because many + + align:start position:0% +but because many + + + align:start position:0% +but because many +users want to sort of monitor either + + align:start position:0% +users want to sort of monitor either + + + align:start position:0% +users want to sort of monitor either +their home their automobile they're + + align:start position:0% +their home their automobile they're + + + align:start position:0% +their home their automobile they're +wearable they're trackable + + align:start position:0% +wearable they're trackable + + + align:start position:0% +wearable they're trackable +and now with this this + + align:start position:0% +and now with this this + + + align:start position:0% +and now with this this +really challenging time around the + + align:start position:0% +really challenging time around the + + + align:start position:0% +really challenging time around the +corona virus crisis + + align:start position:0% +corona virus crisis + + + align:start position:0% +corona virus crisis +we're talking about contact tracing + + align:start position:0% +we're talking about contact tracing + + + align:start position:0% +we're talking about contact tracing +and all that contact tracing could also + + align:start position:0% +and all that contact tracing could also + + + align:start position:0% +and all that contact tracing could also +be fed in depending upon the + + align:start position:0% +be fed in depending upon the + + + align:start position:0% +be fed in depending upon the +jurisdiction but + + align:start position:0% +jurisdiction but + + + align:start position:0% +jurisdiction but +depending upon the regulation into + + align:start position:0% +depending upon the regulation into + + + align:start position:0% +depending upon the regulation into +health insurance rates life insurance + + align:start position:0% +health insurance rates life insurance + + + align:start position:0% +health insurance rates life insurance +rates + + align:start position:0% +rates + + + align:start position:0% +rates +or any form of insurance again largely + + align:start position:0% +or any form of insurance again largely + + + align:start position:0% +or any form of insurance again largely +dependent upon + + align:start position:0% +dependent upon + + + align:start position:0% +dependent upon +the various jurisdictions + + align:start position:0% +the various jurisdictions + + + align:start position:0% +the various jurisdictions +regulatory and legal frameworks + + align:start position:0% + + + + align:start position:0% + +so what are some of the possibilities + + align:start position:0% +so what are some of the possibilities + + + align:start position:0% +so what are some of the possibilities +you can become a licensed insurer + + align:start position:0% +you can become a licensed insurer + + + align:start position:0% +you can become a licensed insurer +that means actually committing balance + + align:start position:0% +that means actually committing balance + + + align:start position:0% +that means actually committing balance +sheet + + align:start position:0% +sheet + + + align:start position:0% +sheet +becoming licensed taking claims on as a + + align:start position:0% +becoming licensed taking claims on as a + + + align:start position:0% +becoming licensed taking claims on as a +liability + + align:start position:0% +liability + + + align:start position:0% +liability +managing the asset side as well you + + align:start position:0% +managing the asset side as well you + + + align:start position:0% +managing the asset side as well you +could be a managed general agent + + align:start position:0% +could be a managed general agent + + + align:start position:0% +could be a managed general agent +think broker this is just a term to say + + align:start position:0% +think broker this is just a term to say + + + align:start position:0% +think broker this is just a term to say +you could be managing agents or + + align:start position:0% +you could be managing agents or + + + align:start position:0% +you could be managing agents or +brokerage or sales + + align:start position:0% +brokerage or sales + + + align:start position:0% +brokerage or sales +those are kind of the two big divides + + align:start position:0% +those are kind of the two big divides + + + align:start position:0% +those are kind of the two big divides +but you could just be on the technology + + align:start position:0% +but you could just be on the technology + + + align:start position:0% +but you could just be on the technology +side or the data aggregation side these + + align:start position:0% +side or the data aggregation side these + + + align:start position:0% +side or the data aggregation side these +are the various models + + align:start position:0% +are the various models + + + align:start position:0% +are the various models +for insurtech some of this startups we + + align:start position:0% +for insurtech some of this startups we + + + align:start position:0% +for insurtech some of this startups we +won't go through each one of them but + + align:start position:0% +won't go through each one of them but + + + align:start position:0% +won't go through each one of them but +you're going to see + + align:start position:0% +you're going to see + + + align:start position:0% +you're going to see +a common thing in these lists is + + align:start position:0% +a common thing in these lists is + + + align:start position:0% +a common thing in these lists is +by and large all founded in the 20 teens + + align:start position:0% +by and large all founded in the 20 teens + + + align:start position:0% +by and large all founded in the 20 teens +so this is 5 or 10 years + + align:start position:0% +so this is 5 or 10 years + + + align:start position:0% +so this is 5 or 10 years +of dynamic change you're going to see + + align:start position:0% +of dynamic change you're going to see + + + align:start position:0% +of dynamic change you're going to see +heavy emphasis on homeowners and autos + + align:start position:0% +heavy emphasis on homeowners and autos + + + align:start position:0% +heavy emphasis on homeowners and autos +so it's in the consumer space very + + align:start position:0% +so it's in the consumer space very + + + align:start position:0% +so it's in the consumer space very +similar to + + align:start position:0% +similar to + + + align:start position:0% +similar to +credit you see a little bit moving into + + align:start position:0% +credit you see a little bit moving into + + + align:start position:0% +credit you see a little bit moving into +small business but not + + align:start position:0% +small business but not + + + align:start position:0% +small business but not +large commercial lines though bold + + align:start position:0% +large commercial lines though bold + + + align:start position:0% +large commercial lines though bold +penguin is a commercial insurance + + align:start position:0% +penguin is a commercial insurance + + + align:start position:0% +penguin is a commercial insurance +exchange a lot is on the front end and + + align:start position:0% +exchange a lot is on the front end and + + + align:start position:0% +exchange a lot is on the front end and +on the auto side you also get + + align:start position:0% +on the auto side you also get + + + align:start position:0% +on the auto side you also get +marketplace comparisons just like in the + + align:start position:0% +marketplace comparisons just like in the + + + align:start position:0% +marketplace comparisons just like in the +credit space + + align:start position:0% +credit space + + + align:start position:0% +credit space +it's basically expedia for auto + + align:start position:0% +it's basically expedia for auto + + + align:start position:0% +it's basically expedia for auto +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +so to speak you could say or expedia for + + align:start position:0% +so to speak you could say or expedia for + + + align:start position:0% +so to speak you could say or expedia for +fill in the blank insurance + + align:start position:0% +fill in the blank insurance + + + align:start position:0% +fill in the blank insurance +these are the marketplace comparisons + + align:start position:0% +these are the marketplace comparisons + + + align:start position:0% +these are the marketplace comparisons +like + + align:start position:0% +like + + + align:start position:0% +like +cover hound and and goji + + align:start position:0% +cover hound and and goji + + + align:start position:0% +cover hound and and goji +um but + + align:start position:0% +um but + + + align:start position:0% +um but +throughout you'll see home and auto + + align:start position:0% +throughout you'll see home and auto + + + align:start position:0% +throughout you'll see home and auto +small business is kind of the dominant + + align:start position:0% +small business is kind of the dominant + + + align:start position:0% +small business is kind of the dominant +how many + + align:start position:0% +how many + + + align:start position:0% +how many +has anybody uh use the product lemonade + + align:start position:0% +has anybody uh use the product lemonade + + + align:start position:0% +has anybody uh use the product lemonade +for renters insurance + + align:start position:0% + + + + align:start position:0% + +wow i don't see any hands up nobody + + align:start position:0% + + + + align:start position:0% + +so lemonade got into the field basically + + align:start position:0% +so lemonade got into the field basically + + + align:start position:0% +so lemonade got into the field basically +to say + + align:start position:0% +to say + + + align:start position:0% +to say +it's so many people particularly in the + + align:start position:0% +it's so many people particularly in the + + + align:start position:0% +it's so many people particularly in the +u.s + + align:start position:0% +u.s + + + align:start position:0% +u.s +or renting and we just want some + + align:start position:0% +or renting and we just want some + + + align:start position:0% +or renting and we just want some +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +for our our objects and our things in + + align:start position:0% +for our our objects and our things in + + + align:start position:0% +for our our objects and our things in +our homes and + + align:start position:0% +our homes and + + + align:start position:0% +our homes and +in case there's a problem or maybe the + + align:start position:0% +in case there's a problem or maybe the + + + align:start position:0% +in case there's a problem or maybe the +landlord says you have to have renter's + + align:start position:0% +landlord says you have to have renter's + + + align:start position:0% +landlord says you have to have renter's +insurance + + align:start position:0% + + + + align:start position:0% + +policy bizarre policy bazaar about 12 + + align:start position:0% +policy bizarre policy bazaar about 12 + + + align:start position:0% +policy bizarre policy bazaar about 12 +years old + + align:start position:0% +years old + + + align:start position:0% +years old +one of the largest marketplace + + align:start position:0% +one of the largest marketplace + + + align:start position:0% +one of the largest marketplace +comparison + + align:start position:0% +comparison + + + align:start position:0% +comparison +in india it's a remarkable platform + + align:start position:0% +in india it's a remarkable platform + + + align:start position:0% +in india it's a remarkable platform +again think broadly speaking expedia for + + align:start position:0% +again think broadly speaking expedia for + + + align:start position:0% +again think broadly speaking expedia for +health and life insurance + + align:start position:0% +health and life insurance + + + align:start position:0% +health and life insurance +you know where you can price compare + + align:start position:0% +you know where you can price compare + + + align:start position:0% +you know where you can price compare +policy bizarre + + align:start position:0% +policy bizarre + + + align:start position:0% +policy bizarre +uh of these various companies + + align:start position:0% +uh of these various companies + + + align:start position:0% +uh of these various companies +just pause a bit on root root uses + + align:start position:0% +just pause a bit on root root uses + + + align:start position:0% +just pause a bit on root root uses +telematics to price their products + + align:start position:0% +telematics to price their products + + + align:start position:0% +telematics to price their products +almost every one of the auto + + align:start position:0% +almost every one of the auto + + + align:start position:0% +almost every one of the auto +companies on here are using telematics + + align:start position:0% +companies on here are using telematics + + + align:start position:0% +companies on here are using telematics +and smartphones some of them started on + + align:start position:0% +and smartphones some of them started on + + + align:start position:0% +and smartphones some of them started on +telematics + + align:start position:0% +telematics + + + align:start position:0% +telematics +some started more on the smartphone side + + align:start position:0% +some started more on the smartphone side + + + align:start position:0% +some started more on the smartphone side +but the merger of those two + + align:start position:0% +but the merger of those two + + + align:start position:0% +but the merger of those two +tractable in the auto field is about + + align:start position:0% +tractable in the auto field is about + + + align:start position:0% +tractable in the auto field is about +claims management + + align:start position:0% +claims management + + + align:start position:0% +claims management +just solely sort of focusing there and i + + align:start position:0% +just solely sort of focusing there and i + + + align:start position:0% +just solely sort of focusing there and i +said i was going to mention about china + + align:start position:0% +said i was going to mention about china + + + align:start position:0% +said i was going to mention about china +the last on this list and i probably + + align:start position:0% +the last on this list and i probably + + + align:start position:0% +the last on this list and i probably +will mispronounce how to say + + align:start position:0% +will mispronounce how to say + + + align:start position:0% +will mispronounce how to say +it zong on um + + align:start position:0% +it zong on um + + + align:start position:0% +it zong on um +was formed by three very large companies + + align:start position:0% +was formed by three very large companies + + + align:start position:0% +was formed by three very large companies +online property and casualty in china + + align:start position:0% +online property and casualty in china + + + align:start position:0% +online property and casualty in china +it's gone public sense it's a very + + align:start position:0% +it's gone public sense it's a very + + + align:start position:0% +it's gone public sense it's a very +significant company in china + + align:start position:0% +significant company in china + + + align:start position:0% +significant company in china +it's the only online + + align:start position:0% +it's the only online + + + align:start position:0% +it's the only online +insurance company that got licensing in + + align:start position:0% +insurance company that got licensing in + + + align:start position:0% +insurance company that got licensing in +china + + align:start position:0% +china + + + align:start position:0% +china +so it chose to get licensing it had the + + align:start position:0% +so it chose to get licensing it had the + + + align:start position:0% +so it chose to get licensing it had the +backing of three very large companies + + align:start position:0% +backing of three very large companies + + + align:start position:0% +backing of three very large companies +seven years ago it got said licensing + + align:start position:0% +seven years ago it got said licensing + + + align:start position:0% +seven years ago it got said licensing +and it has a certain advantage that to + + align:start position:0% +and it has a certain advantage that to + + + align:start position:0% +and it has a certain advantage that to +my knowledge i don't think anybody + + align:start position:0% +my knowledge i don't think anybody + + + align:start position:0% +my knowledge i don't think anybody +else has been there so it gives you some + + align:start position:0% +else has been there so it gives you some + + + align:start position:0% +else has been there so it gives you some +of the smattering i'm + + align:start position:0% +of the smattering i'm + + + align:start position:0% +of the smattering i'm +to pause roving to see if there's any + + align:start position:0% +to pause roving to see if there's any + + + align:start position:0% +to pause roving to see if there's any +questions + + align:start position:0% + + + + align:start position:0% + +we good i think we're good gary + + align:start position:0% +we good i think we're good gary + + + align:start position:0% +we good i think we're good gary +healthcare healthcare fintech + + align:start position:0% +healthcare healthcare fintech + + + align:start position:0% +healthcare healthcare fintech +i'd still call it insure attacks some + + align:start position:0% +i'd still call it insure attacks some + + + align:start position:0% +i'd still call it insure attacks some +people can call it healthtech + + align:start position:0% +people can call it healthtech + + + align:start position:0% +people can call it healthtech +this is the insurance side and how + + align:start position:0% +this is the insurance side and how + + + align:start position:0% +this is the insurance side and how +technology is coming in to disrupt again + + align:start position:0% +technology is coming in to disrupt again + + + align:start position:0% +technology is coming in to disrupt again +you could be in + + align:start position:0% +you could be in + + + align:start position:0% +you could be in +any piece of this uh + + align:start position:0% +any piece of this uh + + + align:start position:0% +any piece of this uh +i borrow this chart from ft partners + + align:start position:0% +i borrow this chart from ft partners + + + align:start position:0% +i borrow this chart from ft partners +but you could be in any piece of this + + align:start position:0% +but you could be in any piece of this + + + align:start position:0% +but you could be in any piece of this +and and say i'm going to do the payment + + align:start position:0% +and and say i'm going to do the payment + + + align:start position:0% +and and say i'm going to do the payment +side i'm going to do the claims side i'm + + align:start position:0% +side i'm going to do the claims side i'm + + + align:start position:0% +side i'm going to do the claims side i'm +going to be in benefits management + + align:start position:0% +going to be in benefits management + + + align:start position:0% +going to be in benefits management +but any piece of this and so in the + + align:start position:0% +but any piece of this and so in the + + + align:start position:0% +but any piece of this and so in the +again most of these are in the us but + + align:start position:0% +again most of these are in the us but + + + align:start position:0% +again most of these are in the us but +not all + + align:start position:0% +not all + + + align:start position:0% +not all +just some of what we're seeing american + + align:start position:0% +just some of what we're seeing american + + + align:start position:0% +just some of what we're seeing american +well is about telehealth the very + + align:start position:0% +well is about telehealth the very + + + align:start position:0% +well is about telehealth the very +important thing now that we're + + align:start position:0% +important thing now that we're + + + align:start position:0% +important thing now that we're +in in a period of time that we can't + + align:start position:0% +in in a period of time that we can't + + + align:start position:0% +in in a period of time that we can't +visit our doctors + + align:start position:0% +visit our doctors + + + align:start position:0% +visit our doctors +in person again you'll see most not all + + align:start position:0% +in person again you'll see most not all + + + align:start position:0% +in person again you'll see most not all +of these + + align:start position:0% +of these + + + align:start position:0% +of these +are in the last 10 years clover + + align:start position:0% +are in the last 10 years clover + + + align:start position:0% +are in the last 10 years clover +which is a unicorn almost all of these + + align:start position:0% +which is a unicorn almost all of these + + + align:start position:0% +which is a unicorn almost all of these +not all of these are unicorns meaning + + align:start position:0% +not all of these are unicorns meaning + + + align:start position:0% +not all of these are unicorns meaning +worth over a billion dollars + + align:start position:0% +worth over a billion dollars + + + align:start position:0% +worth over a billion dollars +um clover is about + + align:start position:0% +um clover is about + + + align:start position:0% +um clover is about +taking our analytics about how we live + + align:start position:0% +taking our analytics about how we live + + + align:start position:0% +taking our analytics about how we live +our lives + + align:start position:0% +our lives + + + align:start position:0% +our lives +and trying to underwrite + + align:start position:0% +and trying to underwrite + + + align:start position:0% +and trying to underwrite +and lower the cost to us probably the + + align:start position:0% +and lower the cost to us probably the + + + align:start position:0% +and lower the cost to us probably the +largest ones are bright health + + align:start position:0% +largest ones are bright health + + + align:start position:0% +largest ones are bright health +which is selling cert a medicare + + align:start position:0% +which is selling cert a medicare + + + align:start position:0% +which is selling cert a medicare +advantage is in the u.s + + align:start position:0% +advantage is in the u.s + + + align:start position:0% +advantage is in the u.s +on top of medicare which is government + + align:start position:0% +on top of medicare which is government + + + align:start position:0% +on top of medicare which is government +provided + + align:start position:0% +provided + + + align:start position:0% +provided +you can you can have an augmented + + align:start position:0% +you can you can have an augmented + + + align:start position:0% +you can you can have an augmented +program on top + + align:start position:0% +program on top + + + align:start position:0% +program on top +called medicare advantage bright health + + align:start position:0% +called medicare advantage bright health + + + align:start position:0% +called medicare advantage bright health +clover gusto you'll see also there's a + + align:start position:0% +clover gusto you'll see also there's a + + + align:start position:0% +clover gusto you'll see also there's a +significant number of companies that + + align:start position:0% +significant number of companies that + + + align:start position:0% +significant number of companies that +have gotten into + + align:start position:0% +have gotten into + + + align:start position:0% +have gotten into +the benefit administration this is + + align:start position:0% +the benefit administration this is + + + align:start position:0% +the benefit administration this is +working with small businesses + + align:start position:0% +working with small businesses + + + align:start position:0% +working with small businesses +to administer their benefits zettafits + + align:start position:0% +to administer their benefits zettafits + + + align:start position:0% +to administer their benefits zettafits +that was + + align:start position:0% +that was + + + align:start position:0% +that was +formed in 2013 by 2015 we actually use + + align:start position:0% +formed in 2013 by 2015 we actually use + + + align:start position:0% +formed in 2013 by 2015 we actually use +benefits + + align:start position:0% +benefits + + + align:start position:0% +benefits +on an effort i was involved with was a + + align:start position:0% +on an effort i was involved with was a + + + align:start position:0% +on an effort i was involved with was a +cfo + + align:start position:0% +cfo + + + align:start position:0% +cfo +of the hillary clinton campaign it was a + + align:start position:0% +of the hillary clinton campaign it was a + + + align:start position:0% +of the hillary clinton campaign it was a +two-year-old startup and we decided to + + align:start position:0% +two-year-old startup and we decided to + + + align:start position:0% +two-year-old startup and we decided to +go with benefits because we could + + align:start position:0% +go with benefits because we could + + + align:start position:0% +go with benefits because we could +outsource to this vendor + + align:start position:0% + + + + align:start position:0% + +our benefits administration for our + + align:start position:0% +our benefits administration for our + + + align:start position:0% +our benefits administration for our +startup + + align:start position:0% + + + + align:start position:0% + +now that startup ultimately proved + + align:start position:0% +now that startup ultimately proved + + + align:start position:0% +now that startup ultimately proved +unsuccessful as you know + + align:start position:0% +unsuccessful as you know + + + align:start position:0% +unsuccessful as you know +but over the course of time 5 000 + + align:start position:0% +but over the course of time 5 000 + + + align:start position:0% +but over the course of time 5 000 +employees + + align:start position:0% +employees + + + align:start position:0% +employees +all that benefit administration the + + align:start position:0% +all that benefit administration the + + + align:start position:0% +all that benefit administration the +health care and so forth + + align:start position:0% +health care and so forth + + + align:start position:0% +health care and so forth +and so forth benefits + + align:start position:0% +and so forth benefits + + + align:start position:0% +and so forth benefits +health equities is in this field through + + align:start position:0% +health equities is in this field through + + + align:start position:0% +health equities is in this field through +health savings accounts + + align:start position:0% +health savings accounts + + + align:start position:0% +health savings accounts +health equities actually bought uh in + + align:start position:0% +health equities actually bought uh in + + + align:start position:0% +health equities actually bought uh in +the last two years a company called wage + + align:start position:0% +the last two years a company called wage + + + align:start position:0% +the last two years a company called wage +works that i was at + + align:start position:0% +works that i was at + + + align:start position:0% +works that i was at +i was when wage works was a start-up + + align:start position:0% +i was when wage works was a start-up + + + align:start position:0% +i was when wage works was a start-up +company + + align:start position:0% +company + + + align:start position:0% +company +i went on their board and managed + + align:start position:0% +i went on their board and managed + + + align:start position:0% +i went on their board and managed +the hiring of a cfo and helped wage work + + align:start position:0% +the hiring of a cfo and helped wage work + + + align:start position:0% +the hiring of a cfo and helped wage work +prepare to go public + + align:start position:0% +prepare to go public + + + align:start position:0% +prepare to go public +as a private company as a fintech years + + align:start position:0% +as a private company as a fintech years + + + align:start position:0% +as a private company as a fintech years +ago health club + + align:start position:0% +ago health club + + + align:start position:0% +ago health club +equities bought that company wage works + + align:start position:0% +equities bought that company wage works + + + align:start position:0% +equities bought that company wage works +gusto is very significant in this field + + align:start position:0% +gusto is very significant in this field + + + align:start position:0% +gusto is very significant in this field +as well so you have a sense + + align:start position:0% +as well so you have a sense + + + align:start position:0% +as well so you have a sense +it's the marrying of finance and health + + align:start position:0% +it's the marrying of finance and health + + + align:start position:0% +it's the marrying of finance and health +so it can be through the benefits and + + align:start position:0% +so it can be through the benefits and + + + align:start position:0% +so it can be through the benefits and +payroll administration side which is + + align:start position:0% +payroll administration side which is + + + align:start position:0% +payroll administration side which is +finance or it can be directly + + align:start position:0% +finance or it can be directly + + + align:start position:0% +finance or it can be directly +marketplace comparisons like go + + align:start position:0% +marketplace comparisons like go + + + align:start position:0% +marketplace comparisons like go +health which is similar to policy bazaar + + align:start position:0% +health which is similar to policy bazaar + + + align:start position:0% +health which is similar to policy bazaar +in india all of these little sub sectors + + align:start position:0% +in india all of these little sub sectors + + + align:start position:0% +in india all of these little sub sectors +and slices + + align:start position:0% + + + + align:start position:0% + +data related is sort of the last little + + align:start position:0% +data related is sort of the last little + + + align:start position:0% +data related is sort of the last little +slice + + align:start position:0% +slice + + + align:start position:0% +slice +and this goes to the earlier question + + align:start position:0% +and this goes to the earlier question + + + align:start position:0% +and this goes to the earlier question +about google and health care + + align:start position:0% +about google and health care + + + align:start position:0% +about google and health care +while we haven't seen big tech there i + + align:start position:0% +while we haven't seen big tech there i + + + align:start position:0% +while we haven't seen big tech there i +think that we're bound to + + align:start position:0% +think that we're bound to + + + align:start position:0% +think that we're bound to +because there's so many data analytic + + align:start position:0% +because there's so many data analytic + + + align:start position:0% +because there's so many data analytic +cambridge mobile + + align:start position:0% +cambridge mobile + + + align:start position:0% +cambridge mobile +telematics do not please don't confuse + + align:start position:0% +telematics do not please don't confuse + + + align:start position:0% +telematics do not please don't confuse +with cambridge analytica + + align:start position:0% +with cambridge analytica + + + align:start position:0% +with cambridge analytica +but cambridge mobi telematics you can + + align:start position:0% +but cambridge mobi telematics you can + + + align:start position:0% +but cambridge mobi telematics you can +see + + align:start position:0% +see + + + align:start position:0% +see +there are data aggregators that are + + align:start position:0% +there are data aggregators that are + + + align:start position:0% +there are data aggregators that are +collecting telematic data they're not + + align:start position:0% +collecting telematic data they're not + + + align:start position:0% +collecting telematic data they're not +alone + + align:start position:0% +alone + + + align:start position:0% +alone +and then with that data commercializing + + align:start position:0% +and then with that data commercializing + + + align:start position:0% +and then with that data commercializing +it to insurance companies + + align:start position:0% +it to insurance companies + + + align:start position:0% +it to insurance companies +big insurance companies as well as + + align:start position:0% +big insurance companies as well as + + + align:start position:0% +big insurance companies as well as +startups + + align:start position:0% +startups + + + align:start position:0% +startups +strong arm tech one of one of my + + align:start position:0% +strong arm tech one of one of my + + + align:start position:0% +strong arm tech one of one of my +favorites in this field + + align:start position:0% +favorites in this field + + + align:start position:0% +favorites in this field +they're selling a product that in + + align:start position:0% +they're selling a product that in + + + align:start position:0% +they're selling a product that in +factories + + align:start position:0% +factories + + + align:start position:0% +factories +if your factory workers will wear + + align:start position:0% +if your factory workers will wear + + + align:start position:0% +if your factory workers will wear +some wearable not a fitbit some of it's + + align:start position:0% +some wearable not a fitbit some of it's + + + align:start position:0% +some wearable not a fitbit some of it's +like + + align:start position:0% +like + + + align:start position:0% +like +around the mid mid uh + + align:start position:0% +around the mid mid uh + + + align:start position:0% +around the mid mid uh +chest range but if they'll + + align:start position:0% +chest range but if they'll + + + align:start position:0% +chest range but if they'll +wear a sensor you can lower the cost + + align:start position:0% +wear a sensor you can lower the cost + + + align:start position:0% +wear a sensor you can lower the cost +of workplace insurance you can also + + align:start position:0% +of workplace insurance you can also + + + align:start position:0% +of workplace insurance you can also +hopefully + + align:start position:0% +hopefully + + + align:start position:0% +hopefully +make the workplace safer so they're + + align:start position:0% +make the workplace safer so they're + + + align:start position:0% +make the workplace safer so they're +selling a safety device + + align:start position:0% +selling a safety device + + + align:start position:0% +selling a safety device +injury protection but it's about + + align:start position:0% +injury protection but it's about + + + align:start position:0% +injury protection but it's about +software + + align:start position:0% +software + + + align:start position:0% +software +and hardware because they're selling the + + align:start position:0% +and hardware because they're selling the + + + align:start position:0% +and hardware because they're selling the +wearables + + align:start position:0% +wearables + + + align:start position:0% +wearables +and it's called strong arm tech will it + + align:start position:0% +and it's called strong arm tech will it + + + align:start position:0% +and it's called strong arm tech will it +be successful it's been around nine + + align:start position:0% +be successful it's been around nine + + + align:start position:0% +be successful it's been around nine +years + + align:start position:0% +years + + + align:start position:0% +years +so what you're seeing in insurance tech + + align:start position:0% +so what you're seeing in insurance tech + + + align:start position:0% +so what you're seeing in insurance tech +which i think is so fascinating and + + align:start position:0% +which i think is so fascinating and + + + align:start position:0% +which i think is so fascinating and +potentially transformative is a whole + + align:start position:0% +potentially transformative is a whole + + + align:start position:0% +potentially transformative is a whole +world of + + align:start position:0% +world of + + + align:start position:0% +world of +sensors and collecting alternative data + + align:start position:0% +sensors and collecting alternative data + + + align:start position:0% +sensors and collecting alternative data +whether it's from our cars back to the + + align:start position:0% +whether it's from our cars back to the + + + align:start position:0% +whether it's from our cars back to the +telematics + + align:start position:0% +telematics + + + align:start position:0% +telematics +whether it's from our our + + align:start position:0% +whether it's from our our + + + align:start position:0% +whether it's from our our +watches or our wearables our fitbits + + align:start position:0% +watches or our wearables our fitbits + + + align:start position:0% +watches or our wearables our fitbits +from our smartphones from the sensors in + + align:start position:0% +from our smartphones from the sensors in + + + align:start position:0% +from our smartphones from the sensors in +our homes + + align:start position:0% +our homes + + + align:start position:0% +our homes +all that can sort of collect data a + + align:start position:0% +all that can sort of collect data a + + + align:start position:0% +all that can sort of collect data a +little bit of machine learning not + + align:start position:0% +little bit of machine learning not + + + align:start position:0% +little bit of machine learning not +always deep machine learning deep + + align:start position:0% +always deep machine learning deep + + + align:start position:0% +always deep machine learning deep +learning + + align:start position:0% +learning + + + align:start position:0% +learning +but some machine learning lower the + + align:start position:0% +but some machine learning lower the + + + align:start position:0% +but some machine learning lower the +costs + + align:start position:0% +costs + + + align:start position:0% +costs +broaden the inclusion potentially and + + align:start position:0% +broaden the inclusion potentially and + + + align:start position:0% +broaden the inclusion potentially and +then on the claims management side as + + align:start position:0% +then on the claims management side as + + + align:start position:0% +then on the claims management side as +well + + align:start position:0% +well + + + align:start position:0% +well +sensor technology collecting the data + + align:start position:0% +sensor technology collecting the data + + + align:start position:0% +sensor technology collecting the data +lowering the fraud + + align:start position:0% +lowering the fraud + + + align:start position:0% +lowering the fraud +and and the like there's one firm that + + align:start position:0% +and and the like there's one firm that + + + align:start position:0% +and and the like there's one firm that +brags that they have the shortest claim + + align:start position:0% +brags that they have the shortest claim + + + align:start position:0% +brags that they have the shortest claim +uh settlement period + + align:start position:0% +uh settlement period + + + align:start position:0% +uh settlement period +that an online app was able to get claim + + align:start position:0% +that an online app was able to get claim + + + align:start position:0% +that an online app was able to get claim +settlement down to + + align:start position:0% +settlement down to + + + align:start position:0% +settlement down to +less than minutes and i think there was + + align:start position:0% +less than minutes and i think there was + + + align:start position:0% +less than minutes and i think there was +one claim that was settled in seconds + + align:start position:0% +one claim that was settled in seconds + + + align:start position:0% +one claim that was settled in seconds +it was an automobile accident it was + + align:start position:0% +it was an automobile accident it was + + + align:start position:0% +it was an automobile accident it was +something they could do + + align:start position:0% +something they could do + + + align:start position:0% +something they could do +quite quickly technologically but i also + + align:start position:0% +quite quickly technologically but i also + + + align:start position:0% +quite quickly technologically but i also +think that it was a bit of a + + align:start position:0% +think that it was a bit of a + + + align:start position:0% +think that it was a bit of a +marketing thing that they wanted to say + + align:start position:0% +marketing thing that they wanted to say + + + align:start position:0% +marketing thing that they wanted to say +you could get claims management down to + + align:start position:0% +you could get claims management down to + + + align:start position:0% +you could get claims management down to +minutes + + align:start position:0% +minutes + + + align:start position:0% +minutes +um so that sort of is a little bit of + + align:start position:0% +um so that sort of is a little bit of + + + align:start position:0% +um so that sort of is a little bit of +review \ No newline at end of file diff --git a/po0oVE5Lhf0.txt b/po0oVE5Lhf0.txt new file mode 100644 index 0000000000000000000000000000000000000000..2fe57d574824c2510097adcafde8f52289940f9b --- /dev/null +++ b/po0oVE5Lhf0.txt @@ -0,0 +1,3483 @@ +align:start position:0% + +identity gives you a pair of glasses to + + align:start position:0% +identity gives you a pair of glasses to + + + align:start position:0% +identity gives you a pair of glasses to +see the world through you experience the + + align:start position:0% +see the world through you experience the + + + align:start position:0% +see the world through you experience the +world a certain way because of the + + align:start position:0% +world a certain way because of the + + + align:start position:0% +world a certain way because of the +multiplicity of your identities and the + + align:start position:0% +multiplicity of your identities and the + + + align:start position:0% +multiplicity of your identities and the +certain identities you have what it + + align:start position:0% +certain identities you have what it + + + align:start position:0% +certain identities you have what it +brings in science is if someone shows up + + align:start position:0% +brings in science is if someone shows up + + + align:start position:0% +brings in science is if someone shows up +has a pair of glasses at seal blue and + + align:start position:0% +has a pair of glasses at seal blue and + + + align:start position:0% +has a pair of glasses at seal blue and +then someone shows up and has a pair of + + align:start position:0% +then someone shows up and has a pair of + + + align:start position:0% +then someone shows up and has a pair of +glasses that see yellow suddenly we can + + align:start position:0% +glasses that see yellow suddenly we can + + + align:start position:0% +glasses that see yellow suddenly we can +see green + + align:start position:0% +see green + + + align:start position:0% +see green +today on Chalk radio moving toward a + + align:start position:0% +today on Chalk radio moving toward a + + + align:start position:0% +today on Chalk radio moving toward a +more diverse and Equitable field of + + align:start position:0% +more diverse and Equitable field of + + + align:start position:0% +more diverse and Equitable field of +science through Hands-On online + + align:start position:0% +science through Hands-On online + + + align:start position:0% +science through Hands-On online +education + + align:start position:0% +education + + + align:start position:0% +education +I'm Sarah Hansen for this episode I + + align:start position:0% +I'm Sarah Hansen for this episode I + + + align:start position:0% +I'm Sarah Hansen for this episode I +talked with two founders of an online + + align:start position:0% +talked with two founders of an online + + + align:start position:0% +talked with two founders of an online +MIT program that's seeking to make + + align:start position:0% +MIT program that's seeking to make + + + align:start position:0% +MIT program that's seeking to make +material science and engineering + + align:start position:0% +material science and engineering + + + align:start position:0% +material science and engineering +education accessible to students Beyond + + align:start position:0% +education accessible to students Beyond + + + align:start position:0% +education accessible to students Beyond +MIT + + align:start position:0% +MIT + + + align:start position:0% +MIT +the program is called micro or the + + align:start position:0% +the program is called micro or the + + + align:start position:0% +the program is called micro or the +materials Initiative for comprehensive + + align:start position:0% +materials Initiative for comprehensive + + + align:start position:0% +materials Initiative for comprehensive +research opportunity + + align:start position:0% +research opportunity + + + align:start position:0% +research opportunity +my guests were two of the program's + + align:start position:0% +my guests were two of the program's + + + align:start position:0% +my guests were two of the program's +creators Jessica sandland and Cecile + + align:start position:0% +creators Jessica sandland and Cecile + + + align:start position:0% +creators Jessica sandland and Cecile +chezo + + align:start position:0% +chezo + + + align:start position:0% +chezo +my name is Jessica sandland I am a + + align:start position:0% +my name is Jessica sandland I am a + + + align:start position:0% +my name is Jessica sandland I am a +lecturer in the department of Materials + + align:start position:0% +lecturer in the department of Materials + + + align:start position:0% +lecturer in the department of Materials +Science and Engineering I'm Cecile I + + align:start position:0% +Science and Engineering I'm Cecile I + + + align:start position:0% +Science and Engineering I'm Cecile I +used to be a graduate student at MIT I + + align:start position:0% +used to be a graduate student at MIT I + + + align:start position:0% +used to be a graduate student at MIT I +now graduated in May so I am a MIT PhD + + align:start position:0% + + + + align:start position:0% + +um shipping off to Chicago where I'll be + + align:start position:0% +um shipping off to Chicago where I'll be + + + align:start position:0% +um shipping off to Chicago where I'll be +starting as a faculty in Material + + align:start position:0% +starting as a faculty in Material + + + align:start position:0% +starting as a faculty in Material +Science and Engineering at Northwestern + + align:start position:0% +Science and Engineering at Northwestern + + + align:start position:0% +Science and Engineering at Northwestern +University + + align:start position:0% +University + + + align:start position:0% +University +Jessica and Cecile met while Cecile was + + align:start position:0% +Jessica and Cecile met while Cecile was + + + align:start position:0% +Jessica and Cecile met while Cecile was +the graduate student representative for + + align:start position:0% +the graduate student representative for + + + align:start position:0% +the graduate student representative for +the diversity equity and inclusion + + align:start position:0% +the diversity equity and inclusion + + + align:start position:0% +the diversity equity and inclusion +collaborative in the mechanical + + align:start position:0% +collaborative in the mechanical + + + align:start position:0% +collaborative in the mechanical +engineering Lab at MIT + + align:start position:0% +engineering Lab at MIT + + + align:start position:0% +engineering Lab at MIT +diversity equity and inclusion or Dei is + + align:start position:0% +diversity equity and inclusion or Dei is + + + align:start position:0% +diversity equity and inclusion or Dei is +at the core of micro's Mission to make + + align:start position:0% +at the core of micro's Mission to make + + + align:start position:0% +at the core of micro's Mission to make +Material Science more welcoming and + + align:start position:0% +Material Science more welcoming and + + + align:start position:0% +Material Science more welcoming and +accessible to minoritized undergraduate + + align:start position:0% +accessible to minoritized undergraduate + + + align:start position:0% +accessible to minoritized undergraduate +students + + align:start position:0% +students + + + align:start position:0% +students +but before we delve into the program's + + align:start position:0% +but before we delve into the program's + + + align:start position:0% +but before we delve into the program's +Mission let's first get clear on a + + align:start position:0% +Mission let's first get clear on a + + + align:start position:0% +Mission let's first get clear on a +pretty important term + + align:start position:0% +pretty important term + + + align:start position:0% +pretty important term +what is Material Science + + align:start position:0% +what is Material Science + + + align:start position:0% +what is Material Science +Material Science is the study of + + align:start position:0% +Material Science is the study of + + + align:start position:0% +Material Science is the study of +materials basically understanding the + + align:start position:0% +materials basically understanding the + + + align:start position:0% +materials basically understanding the +materials from the atomic scale all the + + align:start position:0% +materials from the atomic scale all the + + + align:start position:0% +materials from the atomic scale all the +way to the macro scale for instance if I + + align:start position:0% +way to the macro scale for instance if I + + + align:start position:0% +way to the macro scale for instance if I +have metal if I process metal a certain + + align:start position:0% +have metal if I process metal a certain + + + align:start position:0% +have metal if I process metal a certain +way like I cast it I can make certain + + align:start position:0% +way like I cast it I can make certain + + + align:start position:0% +way like I cast it I can make certain +types of objects like a pot for instance + + align:start position:0% +types of objects like a pot for instance + + + align:start position:0% +types of objects like a pot for instance +if you want a beautiful Le closet cast + + align:start position:0% +if you want a beautiful Le closet cast + + + align:start position:0% +if you want a beautiful Le closet cast +iron skillet kind of thing now if I + + align:start position:0% +iron skillet kind of thing now if I + + + align:start position:0% +iron skillet kind of thing now if I +shape it as a sheet I can make cans for + + align:start position:0% +shape it as a sheet I can make cans for + + + align:start position:0% +shape it as a sheet I can make cans for +Coca-Cola or different other sodas or + + align:start position:0% +Coca-Cola or different other sodas or + + + align:start position:0% +Coca-Cola or different other sodas or +that kind of stuff so that's the whole + + align:start position:0% +that kind of stuff so that's the whole + + + align:start position:0% +that kind of stuff so that's the whole +point of Material Science is really + + align:start position:0% +point of Material Science is really + + + align:start position:0% +point of Material Science is really +understanding the link between how do + + align:start position:0% +understanding the link between how do + + + align:start position:0% +understanding the link between how do +you make materials from the atomic scale + + align:start position:0% +you make materials from the atomic scale + + + align:start position:0% +you make materials from the atomic scale +as a way to a centimeter tons kilogram + + align:start position:0% +as a way to a centimeter tons kilogram + + + align:start position:0% +as a way to a centimeter tons kilogram +scales + + align:start position:0% +scales + + + align:start position:0% +scales +for large volume application and how is + + align:start position:0% +for large volume application and how is + + + align:start position:0% +for large volume application and how is +it affected at every step of the way + + align:start position:0% +it affected at every step of the way + + + align:start position:0% +it affected at every step of the way +it plays a role in so many different + + align:start position:0% +it plays a role in so many different + + + align:start position:0% +it plays a role in so many different +fields and it's so many different + + align:start position:0% +fields and it's so many different + + + align:start position:0% +fields and it's so many different +applications we have people in our + + align:start position:0% +applications we have people in our + + + align:start position:0% +applications we have people in our +department who are doing work in energy + + align:start position:0% +department who are doing work in energy + + + align:start position:0% +department who are doing work in energy +science they're looking at + + align:start position:0% +science they're looking at + + + align:start position:0% +science they're looking at +sustainability questions they're trying + + align:start position:0% +sustainability questions they're trying + + + align:start position:0% +sustainability questions they're trying +to figure out new ways of developing + + align:start position:0% +to figure out new ways of developing + + + align:start position:0% +to figure out new ways of developing +materials for novel medical devices and + + align:start position:0% +materials for novel medical devices and + + + align:start position:0% +materials for novel medical devices and +I think it just has such a reach for me + + align:start position:0% +I think it just has such a reach for me + + + align:start position:0% +I think it just has such a reach for me +that's maybe one of the most exciting + + align:start position:0% +that's maybe one of the most exciting + + + align:start position:0% +that's maybe one of the most exciting +things about Material Science is just + + align:start position:0% +things about Material Science is just + + + align:start position:0% +things about Material Science is just +how many different fields it really + + align:start position:0% +how many different fields it really + + + align:start position:0% +how many different fields it really +touches + + align:start position:0% +touches + + + align:start position:0% +touches +Material Science is a fairly new field + + align:start position:0% +Material Science is a fairly new field + + + align:start position:0% +Material Science is a fairly new field +that brings together different science + + align:start position:0% +that brings together different science + + + align:start position:0% +that brings together different science +specialties + + align:start position:0% +specialties + + + align:start position:0% +specialties +it didn't used to be its own discipline + + align:start position:0% +it didn't used to be its own discipline + + + align:start position:0% +it didn't used to be its own discipline +until like about the 50s 60s where + + align:start position:0% +until like about the 50s 60s where + + + align:start position:0% +until like about the 50s 60s where +people started talking about Material + + align:start position:0% +people started talking about Material + + + align:start position:0% +people started talking about Material +Science we're relatively young stem + + align:start position:0% +Science we're relatively young stem + + + align:start position:0% +Science we're relatively young stem +field that initiated from physics + + align:start position:0% +field that initiated from physics + + + align:start position:0% +field that initiated from physics +chemistry + + align:start position:0% +chemistry + + + align:start position:0% +chemistry +engineering altogether + + align:start position:0% +engineering altogether + + + align:start position:0% +engineering altogether +okay so Material Science is this + + align:start position:0% +okay so Material Science is this + + + align:start position:0% +okay so Material Science is this +relatively new field that incorporates + + align:start position:0% +relatively new field that incorporates + + + align:start position:0% +relatively new field that incorporates +all these different traditional stem + + align:start position:0% +all these different traditional stem + + + align:start position:0% +all these different traditional stem +Fields into the study of the materials + + align:start position:0% +Fields into the study of the materials + + + align:start position:0% +Fields into the study of the materials +we use every day + + align:start position:0% +we use every day + + + align:start position:0% +we use every day +so what is the materials Initiative for + + align:start position:0% +so what is the materials Initiative for + + + align:start position:0% +so what is the materials Initiative for +comprehensive research opportunity + + align:start position:0% +comprehensive research opportunity + + + align:start position:0% +comprehensive research opportunity +micro it's an online undergraduate + + align:start position:0% +micro it's an online undergraduate + + + align:start position:0% +micro it's an online undergraduate +research and learning program that is + + align:start position:0% +research and learning program that is + + + align:start position:0% +research and learning program that is +for students from minoritized background + + align:start position:0% +for students from minoritized background + + + align:start position:0% +for students from minoritized background +and that is focused on Material Science + + align:start position:0% +and that is focused on Material Science + + + align:start position:0% +and that is focused on Material Science +and Engineering + + align:start position:0% +and Engineering + + + align:start position:0% +and Engineering +the initial motivation for this is as I + + align:start position:0% +the initial motivation for this is as I + + + align:start position:0% +the initial motivation for this is as I +said earlier Material Science is a + + align:start position:0% +said earlier Material Science is a + + + align:start position:0% +said earlier Material Science is a +relatively young field + + align:start position:0% +relatively young field + + + align:start position:0% +relatively young field +we have a lot of diversity problems that + + align:start position:0% +we have a lot of diversity problems that + + + align:start position:0% +we have a lot of diversity problems that +a lot of stem Fields have but we have + + align:start position:0% +a lot of stem Fields have but we have + + + align:start position:0% +a lot of stem Fields have but we have +this added difficulty that it's actually + + align:start position:0% +this added difficulty that it's actually + + + align:start position:0% +this added difficulty that it's actually +not a topic in high school or in fact in + + align:start position:0% +not a topic in high school or in fact in + + + align:start position:0% +not a topic in high school or in fact in +the majority of undergraduate + + align:start position:0% +the majority of undergraduate + + + align:start position:0% +the majority of undergraduate +institutions you can't major in Material + + align:start position:0% +institutions you can't major in Material + + + align:start position:0% +institutions you can't major in Material +Science and Engineering the goal of this + + align:start position:0% +Science and Engineering the goal of this + + + align:start position:0% +Science and Engineering the goal of this +program was really to promote our field + + align:start position:0% +program was really to promote our field + + + align:start position:0% +program was really to promote our field +of Material Science and Engineering + + align:start position:0% +of Material Science and Engineering + + + align:start position:0% +of Material Science and Engineering +through a Hands-On + + align:start position:0% +through a Hands-On + + + align:start position:0% +through a Hands-On +research experience but it needed to be + + align:start position:0% +research experience but it needed to be + + + align:start position:0% +research experience but it needed to be +accessible I know it sounds a little + + align:start position:0% +accessible I know it sounds a little + + + align:start position:0% +accessible I know it sounds a little +paradoxical to talk about hands-on + + align:start position:0% +paradoxical to talk about hands-on + + + align:start position:0% +paradoxical to talk about hands-on +experience in an online program but this + + align:start position:0% +experience in an online program but this + + + align:start position:0% +experience in an online program but this +is the whole concept we were pursuing is + + align:start position:0% +is the whole concept we were pursuing is + + + align:start position:0% +is the whole concept we were pursuing is +like we've seen during the pandemic that + + align:start position:0% +like we've seen during the pandemic that + + + align:start position:0% +like we've seen during the pandemic that +people can do research remotely and can + + align:start position:0% +people can do research remotely and can + + + align:start position:0% +people can do research remotely and can +do very impactful research remotely + + align:start position:0% +do very impactful research remotely + + + align:start position:0% +do very impactful research remotely +I was curious to know more about how + + align:start position:0% +I was curious to know more about how + + + align:start position:0% +I was curious to know more about how +students do this Hands-On research + + align:start position:0% +students do this Hands-On research + + + align:start position:0% +students do this Hands-On research +remotely so Cecile gave me an example + + align:start position:0% +remotely so Cecile gave me an example + + + align:start position:0% +remotely so Cecile gave me an example +she told me about a participant in the + + align:start position:0% +she told me about a participant in the + + + align:start position:0% +she told me about a participant in the +micro program named Toby Toby is a + + align:start position:0% +micro program named Toby Toby is a + + + align:start position:0% +micro program named Toby Toby is a +mechanical engineering undergrad at the + + align:start position:0% +mechanical engineering undergrad at the + + + align:start position:0% +mechanical engineering undergrad at the +University of Maryland in Baltimore + + align:start position:0% +University of Maryland in Baltimore + + + align:start position:0% +University of Maryland in Baltimore +County he paired up with an MIT grad + + align:start position:0% +County he paired up with an MIT grad + + + align:start position:0% +County he paired up with an MIT grad +student named Richard + + align:start position:0% +student named Richard + + + align:start position:0% +student named Richard +Richard is Material Science student is + + align:start position:0% +Richard is Material Science student is + + + align:start position:0% +Richard is Material Science student is +looking at making batteries with very + + align:start position:0% +looking at making batteries with very + + + align:start position:0% +looking at making batteries with very +very high capacity based on + + align:start position:0% +very high capacity based on + + + align:start position:0% +very high capacity based on +nanomaterials + + align:start position:0% +nanomaterials + + + align:start position:0% +nanomaterials +and he's doing that in the lab he's + + align:start position:0% +and he's doing that in the lab he's + + + align:start position:0% +and he's doing that in the lab he's +making different batteries and trying to + + align:start position:0% +making different batteries and trying to + + + align:start position:0% +making different batteries and trying to +figure out how to make them + + align:start position:0% +figure out how to make them + + + align:start position:0% +figure out how to make them +manufacturable and in high capacity and + + align:start position:0% +manufacturable and in high capacity and + + + align:start position:0% +manufacturable and in high capacity and +what Toby does is he models use a finite + + align:start position:0% +what Toby does is he models use a finite + + + align:start position:0% +what Toby does is he models use a finite +element softwares that is called console + + align:start position:0% +element softwares that is called console + + + align:start position:0% +element softwares that is called console +it does it on his laptop remote in into + + align:start position:0% +it does it on his laptop remote in into + + + align:start position:0% +it does it on his laptop remote in into +a server we have in our lab + + align:start position:0% +a server we have in our lab + + + align:start position:0% +a server we have in our lab +to simulate what would be the final + + align:start position:0% +to simulate what would be the final + + + align:start position:0% +to simulate what would be the final +properties of a battery depending on the + + align:start position:0% +properties of a battery depending on the + + + align:start position:0% +properties of a battery depending on the +shape we give the size we give the + + align:start position:0% +shape we give the size we give the + + + align:start position:0% +shape we give the size we give the +material we give for it and how does + + align:start position:0% +material we give for it and how does + + + align:start position:0% +material we give for it and how does +that relate to how Richard can change + + align:start position:0% +that relate to how Richard can change + + + align:start position:0% +that relate to how Richard can change +this process and make the battery even + + align:start position:0% +this process and make the battery even + + + align:start position:0% +this process and make the battery even +better by taking information from that + + align:start position:0% +better by taking information from that + + + align:start position:0% +better by taking information from that +model that Toby is developing and + + align:start position:0% +model that Toby is developing and + + + align:start position:0% +model that Toby is developing and +understanding how different aspects + + align:start position:0% +understanding how different aspects + + + align:start position:0% +understanding how different aspects +materials in the battery size Etc can + + align:start position:0% +materials in the battery size Etc can + + + align:start position:0% +materials in the battery size Etc can +affect the final properties + + align:start position:0% +affect the final properties + + + align:start position:0% +affect the final properties +one of the core motivations for the + + align:start position:0% +one of the core motivations for the + + + align:start position:0% +one of the core motivations for the +micro program is to create opportunities + + align:start position:0% +micro program is to create opportunities + + + align:start position:0% +micro program is to create opportunities +for students who have historically been + + align:start position:0% +for students who have historically been + + + align:start position:0% +for students who have historically been +excluded from pursuing Material Science + + align:start position:0% +excluded from pursuing Material Science + + + align:start position:0% +excluded from pursuing Material Science +and Engineering as a career + + align:start position:0% +and Engineering as a career + + + align:start position:0% +and Engineering as a career +it was this idea of taking Material + + align:start position:0% +it was this idea of taking Material + + + align:start position:0% +it was this idea of taking Material +Science research involve undergraduate + + align:start position:0% +Science research involve undergraduate + + + align:start position:0% +Science research involve undergraduate +students who may not have a Material + + align:start position:0% +students who may not have a Material + + + align:start position:0% +students who may not have a Material +Science Program in their department and + + align:start position:0% +Science Program in their department and + + + align:start position:0% +Science Program in their department and +who are part of minoritized communities + + align:start position:0% +who are part of minoritized communities + + + align:start position:0% +who are part of minoritized communities +so they can learn about Material Science + + align:start position:0% +so they can learn about Material Science + + + align:start position:0% +so they can learn about Material Science +through the online courses we give them + + align:start position:0% +through the online courses we give them + + + align:start position:0% +through the online courses we give them +we don't look for research experience we + + align:start position:0% +we don't look for research experience we + + + align:start position:0% +we don't look for research experience we +look for research potential even if an + + align:start position:0% +look for research potential even if an + + + align:start position:0% +look for research potential even if an +undergrad has never done research before + + align:start position:0% +undergrad has never done research before + + + align:start position:0% +undergrad has never done research before +and that's important because in numerous + + align:start position:0% +and that's important because in numerous + + + align:start position:0% +and that's important because in numerous +undergraduates institutions you can't do + + align:start position:0% +undergraduates institutions you can't do + + + align:start position:0% +undergraduates institutions you can't do +research + + align:start position:0% +research + + + align:start position:0% +research +if they have interest in research and + + align:start position:0% +if they have interest in research and + + + align:start position:0% +if they have interest in research and +they explain to us why they're so + + align:start position:0% +they explain to us why they're so + + + align:start position:0% +they explain to us why they're so +interested in research even without + + align:start position:0% +interested in research even without + + + align:start position:0% +interested in research even without +prior research experience they should + + align:start position:0% +prior research experience they should + + + align:start position:0% +prior research experience they should +apply this is important for us the point + + align:start position:0% +apply this is important for us the point + + + align:start position:0% +apply this is important for us the point +is to reach people who may not have that + + align:start position:0% +is to reach people who may not have that + + + align:start position:0% +is to reach people who may not have that +opportunity otherwise + + align:start position:0% +opportunity otherwise + + + align:start position:0% +opportunity otherwise +part of what makes micro so special is + + align:start position:0% +part of what makes micro so special is + + + align:start position:0% +part of what makes micro so special is +its emphasis on demonstrating the power + + align:start position:0% +its emphasis on demonstrating the power + + + align:start position:0% +its emphasis on demonstrating the power +of diversity equity and inclusion in + + align:start position:0% +of diversity equity and inclusion in + + + align:start position:0% +of diversity equity and inclusion in +stem both Cecile and Jessica spoke about + + align:start position:0% +stem both Cecile and Jessica spoke about + + + align:start position:0% +stem both Cecile and Jessica spoke about +what it was like for them as women + + align:start position:0% +what it was like for them as women + + + align:start position:0% +what it was like for them as women +becoming Professionals in the field of + + align:start position:0% +becoming Professionals in the field of + + + align:start position:0% +becoming Professionals in the field of +Material Science it left them with an + + align:start position:0% +Material Science it left them with an + + + align:start position:0% +Material Science it left them with an +understanding of the value and + + align:start position:0% +understanding of the value and + + + align:start position:0% +understanding of the value and +importance of identity which informs + + align:start position:0% +importance of identity which informs + + + align:start position:0% +importance of identity which informs +their work at micro + + align:start position:0% +their work at micro + + + align:start position:0% +their work at micro +the way I usually describe it is + + align:start position:0% +the way I usually describe it is + + + align:start position:0% +the way I usually describe it is +identity regardless of it if it is a + + align:start position:0% +identity regardless of it if it is a + + + align:start position:0% +identity regardless of it if it is a +visible Identity or invisible identity + + align:start position:0% +visible Identity or invisible identity + + + align:start position:0% +visible Identity or invisible identity +what it gives you is it gives you a pair + + align:start position:0% +what it gives you is it gives you a pair + + + align:start position:0% +what it gives you is it gives you a pair +of glasses to see the world through + + align:start position:0% +of glasses to see the world through + + + align:start position:0% +of glasses to see the world through +you experience the world a certain way + + align:start position:0% +you experience the world a certain way + + + align:start position:0% +you experience the world a certain way +because of the multiplicity of your + + align:start position:0% +because of the multiplicity of your + + + align:start position:0% +because of the multiplicity of your +identities and in the certain identities + + align:start position:0% +identities and in the certain identities + + + align:start position:0% +identities and in the certain identities +you have + + align:start position:0% +you have + + + align:start position:0% +you have +what it brings in science is if someone + + align:start position:0% +what it brings in science is if someone + + + align:start position:0% +what it brings in science is if someone +shows up has a pair of glasses that see + + align:start position:0% +shows up has a pair of glasses that see + + + align:start position:0% +shows up has a pair of glasses that see +all blue and then someone shows up and + + align:start position:0% +all blue and then someone shows up and + + + align:start position:0% +all blue and then someone shows up and +has a pair of glasses that see yellow + + align:start position:0% +has a pair of glasses that see yellow + + + align:start position:0% +has a pair of glasses that see yellow +suddenly we can see green this is the + + align:start position:0% +suddenly we can see green this is the + + + align:start position:0% +suddenly we can see green this is the +power of diversity and Innovation and + + align:start position:0% +power of diversity and Innovation and + + + align:start position:0% +power of diversity and Innovation and +really understanding this and there is + + align:start position:0% +really understanding this and there is + + + align:start position:0% +really understanding this and there is +example historically of that to take the + + align:start position:0% +example historically of that to take the + + + align:start position:0% +example historically of that to take the +example of women in science for instance + + align:start position:0% +example of women in science for instance + + + align:start position:0% +example of women in science for instance +the increase of female representative in + + align:start position:0% +the increase of female representative in + + + align:start position:0% +the increase of female representative in +the medical field in the United States + + align:start position:0% +the medical field in the United States + + + align:start position:0% +the medical field in the United States +in the 80s and 90s + + align:start position:0% +in the 80s and 90s + + + align:start position:0% +in the 80s and 90s +shed new light on understanding disease + + align:start position:0% +shed new light on understanding disease + + + align:start position:0% +shed new light on understanding disease +and pathologies that affect women such + + align:start position:0% +and pathologies that affect women such + + + align:start position:0% +and pathologies that affect women such +as breast cancer or different heart + + align:start position:0% +as breast cancer or different heart + + + align:start position:0% +as breast cancer or different heart +diseases and there was this brand new + + align:start position:0% +diseases and there was this brand new + + + align:start position:0% +diseases and there was this brand new +wave of innovation that came because you + + align:start position:0% +wave of innovation that came because you + + + align:start position:0% +wave of innovation that came because you +had more diversity in your Workforce + + align:start position:0% +had more diversity in your Workforce + + + align:start position:0% +had more diversity in your Workforce +I came to MIT as an undergraduate for + + align:start position:0% +I came to MIT as an undergraduate for + + + align:start position:0% +I came to MIT as an undergraduate for +the first time in 1995. at the time as a + + align:start position:0% +the first time in 1995. at the time as a + + + align:start position:0% +the first time in 1995. at the time as a +woman in engineering + + align:start position:0% +woman in engineering + + + align:start position:0% +woman in engineering +it looked very different here + + align:start position:0% +it looked very different here + + + align:start position:0% +it looked very different here +but it was also very rapidly changing I + + align:start position:0% +but it was also very rapidly changing I + + + align:start position:0% +but it was also very rapidly changing I +understand yeah from a personal level + + align:start position:0% +understand yeah from a personal level + + + align:start position:0% +understand yeah from a personal level +what it means as an engineer + + align:start position:0% +what it means as an engineer + + + align:start position:0% +what it means as an engineer +to see these role models to see these + + align:start position:0% +to see these role models to see these + + + align:start position:0% +to see these role models to see these +people who are doing + + align:start position:0% +people who are doing + + + align:start position:0% +people who are doing +the best Material Science and + + align:start position:0% +the best Material Science and + + + align:start position:0% +the best Material Science and +Engineering work that is being done in + + align:start position:0% +Engineering work that is being done in + + + align:start position:0% +Engineering work that is being done in +the world and they look a little bit + + align:start position:0% +the world and they look a little bit + + + align:start position:0% +the world and they look a little bit +more like me than they used to back in + + align:start position:0% +more like me than they used to back in + + + align:start position:0% +more like me than they used to back in +1995. + + align:start position:0% +1995. + + + align:start position:0% +1995. +having experienced that Evolution I + + align:start position:0% +having experienced that Evolution I + + + align:start position:0% +having experienced that Evolution I +think I really appreciate the power of + + align:start position:0% +think I really appreciate the power of + + + align:start position:0% +think I really appreciate the power of +it in a very real way + + align:start position:0% +it in a very real way + + + align:start position:0% +it in a very real way +when we take the stern of understanding + + align:start position:0% +when we take the stern of understanding + + + align:start position:0% +when we take the stern of understanding +sustainability and understanding all + + align:start position:0% +sustainability and understanding all + + + align:start position:0% +sustainability and understanding all +those challenges our world is facing + + align:start position:0% +those challenges our world is facing + + + align:start position:0% +those challenges our world is facing +right now diversity of identity brings + + align:start position:0% +right now diversity of identity brings + + + align:start position:0% +right now diversity of identity brings +diversity of perspective + + align:start position:0% +diversity of perspective + + + align:start position:0% +diversity of perspective +an ergo faster more meaningful progress + + align:start position:0% +an ergo faster more meaningful progress + + + align:start position:0% +an ergo faster more meaningful progress +on the scientific level but also on the + + align:start position:0% +on the scientific level but also on the + + + align:start position:0% +on the scientific level but also on the +human and societal level + + align:start position:0% +human and societal level + + + align:start position:0% +human and societal level +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +while getting underrepresented students + + align:start position:0% +while getting underrepresented students + + + align:start position:0% +while getting underrepresented students +through the door here's an important + + align:start position:0% +through the door here's an important + + + align:start position:0% +through the door here's an important +step supporting these students to then + + align:start position:0% +step supporting these students to then + + + align:start position:0% +step supporting these students to then +succeed in their work is another + + align:start position:0% +succeed in their work is another + + + align:start position:0% +succeed in their work is another +critical component of the micro program + + align:start position:0% +critical component of the micro program + + + align:start position:0% +critical component of the micro program +one of the ways they achieve this is by + + align:start position:0% +one of the ways they achieve this is by + + + align:start position:0% +one of the ways they achieve this is by +providing Hands-On mentorship + + align:start position:0% +providing Hands-On mentorship + + + align:start position:0% +providing Hands-On mentorship +Cecile and program co-founder Max + + align:start position:0% +Cecile and program co-founder Max + + + align:start position:0% +Cecile and program co-founder Max +latewell were grad students when the + + align:start position:0% +latewell were grad students when the + + + align:start position:0% +latewell were grad students when the +program was first enacted + + align:start position:0% +program was first enacted + + + align:start position:0% +program was first enacted +Cecile and Max as graduate students I + + align:start position:0% +Cecile and Max as graduate students I + + + align:start position:0% +Cecile and Max as graduate students I +think were also really really essential + + align:start position:0% +think were also really really essential + + + align:start position:0% +think were also really really essential +to the success of this program in a way + + align:start position:0% +to the success of this program in a way + + + align:start position:0% +to the success of this program in a way +that I almost could not overstate there + + align:start position:0% +that I almost could not overstate there + + + align:start position:0% +that I almost could not overstate there +will be talk about sometimes as near + + align:start position:0% +will be talk about sometimes as near + + + align:start position:0% +will be talk about sometimes as near +peer mentors they are these very + + align:start position:0% +peer mentors they are these very + + + align:start position:0% +peer mentors they are these very +experienced graduate students who have + + align:start position:0% +experienced graduate students who have + + + align:start position:0% +experienced graduate students who have +been successfully working in this field + + align:start position:0% +been successfully working in this field + + + align:start position:0% +been successfully working in this field +for a number of years but they're not so + + align:start position:0% +for a number of years but they're not so + + + align:start position:0% +for a number of years but they're not so +far away from these undergraduates and + + align:start position:0% +far away from these undergraduates and + + + align:start position:0% +far away from these undergraduates and +their undergraduate experience they were + + align:start position:0% +their undergraduate experience they were + + + align:start position:0% +their undergraduate experience they were +able to provide advice they were able to + + align:start position:0% +able to provide advice they were able to + + + align:start position:0% +able to provide advice they were able to +help with Fellowship applications and + + align:start position:0% +help with Fellowship applications and + + + align:start position:0% +help with Fellowship applications and +graduate school applications and how do + + align:start position:0% +graduate school applications and how do + + + align:start position:0% +graduate school applications and how do +I write an abstract for this conference + + align:start position:0% +I write an abstract for this conference + + + align:start position:0% +I write an abstract for this conference +that I want to go to I think that the + + align:start position:0% +that I want to go to I think that the + + + align:start position:0% +that I want to go to I think that the +barrier for approaching Cecile or + + align:start position:0% +barrier for approaching Cecile or + + + align:start position:0% +barrier for approaching Cecile or +approaching Max for help was much lower + + align:start position:0% +approaching Max for help was much lower + + + align:start position:0% +approaching Max for help was much lower +than it is coming to maybe a faculty + + align:start position:0% +than it is coming to maybe a faculty + + + align:start position:0% +than it is coming to maybe a faculty +member and saying I need help with this + + align:start position:0% +member and saying I need help with this + + + align:start position:0% +member and saying I need help with this +problem I think that having that near + + align:start position:0% +problem I think that having that near + + + align:start position:0% +problem I think that having that near +peer mentorship opportunity was + + align:start position:0% +peer mentorship opportunity was + + + align:start position:0% +peer mentorship opportunity was +absolutely critical and Max and Cecile + + align:start position:0% +absolutely critical and Max and Cecile + + + align:start position:0% +absolutely critical and Max and Cecile +were just so engaged and so fundamental + + align:start position:0% +were just so engaged and so fundamental + + + align:start position:0% +were just so engaged and so fundamental +to the success of that program beyond + + align:start position:0% +to the success of that program beyond + + + align:start position:0% +to the success of that program beyond +the actual micro staff each one of these + + align:start position:0% +the actual micro staff each one of these + + + align:start position:0% +the actual micro staff each one of these +students had at least one and ideally + + align:start position:0% +students had at least one and ideally + + + align:start position:0% +students had at least one and ideally +really two research mentors + + align:start position:0% +really two research mentors + + + align:start position:0% +really two research mentors +also + + align:start position:0% +also + + + align:start position:0% +also +our program had additional components + + align:start position:0% +our program had additional components + + + align:start position:0% +our program had additional components +apart from the research and the material + + align:start position:0% +apart from the research and the material + + + align:start position:0% +apart from the research and the material +science curriculum there was a soft + + align:start position:0% +science curriculum there was a soft + + + align:start position:0% +science curriculum there was a soft +skill component where we organized + + align:start position:0% +skill component where we organized + + + align:start position:0% +skill component where we organized +Workshop + + align:start position:0% +Workshop + + + align:start position:0% +Workshop +for the students to learn how to write + + align:start position:0% +for the students to learn how to write + + + align:start position:0% +for the students to learn how to write +an abstract for instance how to define + + align:start position:0% +an abstract for instance how to define + + + align:start position:0% +an abstract for instance how to define +research questions also skills that are + + align:start position:0% +research questions also skills that are + + + align:start position:0% +research questions also skills that are +Beyond technical skill but are super + + align:start position:0% +Beyond technical skill but are super + + + align:start position:0% +Beyond technical skill but are super +important if you're thinking about a + + align:start position:0% +important if you're thinking about a + + + align:start position:0% +important if you're thinking about a +research career or even an academic like + + align:start position:0% +research career or even an academic like + + + align:start position:0% +research career or even an academic like +additional degrees in academics + + align:start position:0% +additional degrees in academics + + + align:start position:0% +additional degrees in academics +the other component was the mentoring + + align:start position:0% +the other component was the mentoring + + + align:start position:0% +the other component was the mentoring +component which is really + + align:start position:0% +component which is really + + + align:start position:0% +component which is really +teaching + + align:start position:0% +teaching + + + align:start position:0% +teaching +those research mentors on how to provide + + align:start position:0% +those research mentors on how to provide + + + align:start position:0% +those research mentors on how to provide +meaningful and inclusive mentoring for + + align:start position:0% +meaningful and inclusive mentoring for + + + align:start position:0% +meaningful and inclusive mentoring for +these students + + align:start position:0% +these students + + + align:start position:0% +these students +the inclusive mentoring training + + align:start position:0% +the inclusive mentoring training + + + align:start position:0% +the inclusive mentoring training +included a series of worksheets for + + align:start position:0% +included a series of worksheets for + + + align:start position:0% +included a series of worksheets for +mentors that instructed them in things + + align:start position:0% +mentors that instructed them in things + + + align:start position:0% +mentors that instructed them in things +like effective and inclusive + + align:start position:0% +like effective and inclusive + + + align:start position:0% +like effective and inclusive +Communication in a remote environment + + align:start position:0% +Communication in a remote environment + + + align:start position:0% +Communication in a remote environment +planning and managing and more we'll + + align:start position:0% +planning and managing and more we'll + + + align:start position:0% +planning and managing and more we'll +provide links to these worksheets in the + + align:start position:0% +provide links to these worksheets in the + + + align:start position:0% +provide links to these worksheets in the +show notes for this episode + + align:start position:0% +show notes for this episode + + + align:start position:0% +show notes for this episode +while micro certainly does benefit its + + align:start position:0% +while micro certainly does benefit its + + + align:start position:0% +while micro certainly does benefit its +student participants one of my favorite + + align:start position:0% +student participants one of my favorite + + + align:start position:0% +student participants one of my favorite +parts of the conversation was the + + align:start position:0% +parts of the conversation was the + + + align:start position:0% +parts of the conversation was the +importance that Jessica and Cecile put + + align:start position:0% +importance that Jessica and Cecile put + + + align:start position:0% +importance that Jessica and Cecile put +on how much the mentors and Labs + + align:start position:0% +on how much the mentors and Labs + + + align:start position:0% +on how much the mentors and Labs +actually benefited from the work these + + align:start position:0% +actually benefited from the work these + + + align:start position:0% +actually benefited from the work these +highly talented students produced + + align:start position:0% +highly talented students produced + + + align:start position:0% +highly talented students produced +one of the things that I would really + + align:start position:0% +one of the things that I would really + + + align:start position:0% +one of the things that I would really +like to point out is that these students + + align:start position:0% +like to point out is that these students + + + align:start position:0% +like to point out is that these students +are engaging in real impactful research + + align:start position:0% +are engaging in real impactful research + + + align:start position:0% +are engaging in real impactful research +they are doing science they are doing + + align:start position:0% +they are doing science they are doing + + + align:start position:0% +they are doing science they are doing +engineering we talked a lot earlier + + align:start position:0% +engineering we talked a lot earlier + + + align:start position:0% +engineering we talked a lot earlier +about the mentors and what the mentors + + align:start position:0% +about the mentors and what the mentors + + + align:start position:0% +about the mentors and what the mentors +have to offer the mentees but I really + + align:start position:0% +have to offer the mentees but I really + + + align:start position:0% +have to offer the mentees but I really +think it's also important to point out + + align:start position:0% +think it's also important to point out + + + align:start position:0% +think it's also important to point out +that these Laboratories are getting the + + align:start position:0% +that these Laboratories are getting the + + + align:start position:0% +that these Laboratories are getting the +work of these talented + + align:start position:0% +work of these talented + + + align:start position:0% +work of these talented +really enthusiastic students and they're + + align:start position:0% +really enthusiastic students and they're + + + align:start position:0% +really enthusiastic students and they're +bringing new ideas into their lab groups + + align:start position:0% +bringing new ideas into their lab groups + + + align:start position:0% +bringing new ideas into their lab groups +and they're taking initiative to try new + + align:start position:0% +and they're taking initiative to try new + + + align:start position:0% +and they're taking initiative to try new +things I think it's something that we + + align:start position:0% +things I think it's something that we + + + align:start position:0% +things I think it's something that we +hope is valuable to our micro students + + align:start position:0% +hope is valuable to our micro students + + + align:start position:0% +hope is valuable to our micro students +but it's also a really valuable thing + + align:start position:0% +but it's also a really valuable thing + + + align:start position:0% +but it's also a really valuable thing +for the lab groups as well + + align:start position:0% +for the lab groups as well + + + align:start position:0% +for the lab groups as well +my favorite example of this is + + align:start position:0% +my favorite example of this is + + + align:start position:0% +my favorite example of this is +Nick is a math major I don't think he + + align:start position:0% +Nick is a math major I don't think he + + + align:start position:0% +Nick is a math major I don't think he +had done research before Nick is from + + align:start position:0% +had done research before Nick is from + + + align:start position:0% +had done research before Nick is from +Grand Valley State University + + align:start position:0% +Grand Valley State University + + + align:start position:0% +Grand Valley State University +and you apply it as a math major in + + align:start position:0% +and you apply it as a math major in + + + align:start position:0% +and you apply it as a math major in +micro + + align:start position:0% +micro + + + align:start position:0% +micro +and he started doing research on a data + + align:start position:0% +and he started doing research on a data + + + align:start position:0% +and he started doing research on a data +analysis of some chemical + + align:start position:0% +analysis of some chemical + + + align:start position:0% +analysis of some chemical +characterization of protein + + align:start position:0% +characterization of protein + + + align:start position:0% +characterization of protein +Nick was like the way you're doing this + + align:start position:0% +Nick was like the way you're doing this + + + align:start position:0% +Nick was like the way you're doing this +there's a better way of doing it with + + align:start position:0% +there's a better way of doing it with + + + align:start position:0% +there's a better way of doing it with +math + + align:start position:0% +math + + + align:start position:0% +math +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you know like I don't understand why you + + align:start position:0% +you know like I don't understand why you + + + align:start position:0% +you know like I don't understand why you +guys are doing this this way there's a + + align:start position:0% +guys are doing this this way there's a + + + align:start position:0% +guys are doing this this way there's a +much better way of doing it there's this + + align:start position:0% +much better way of doing it there's this + + + align:start position:0% +much better way of doing it there's this +math method that's just gonna work just + + align:start position:0% +math method that's just gonna work just + + + align:start position:0% +math method that's just gonna work just +fine and he just came up with this + + align:start position:0% +fine and he just came up with this + + + align:start position:0% +fine and he just came up with this +algorithm that just goes through + + align:start position:0% +algorithm that just goes through + + + align:start position:0% +algorithm that just goes through +enormous volume of data to classify + + align:start position:0% +enormous volume of data to classify + + + align:start position:0% +enormous volume of data to classify +efficiency of markers on protein or + + align:start position:0% +efficiency of markers on protein or + + + align:start position:0% +efficiency of markers on protein or +something something that I personally do + + align:start position:0% +something something that I personally do + + + align:start position:0% +something something that I personally do +not fully understand + + align:start position:0% +not fully understand + + + align:start position:0% +not fully understand +what is so funny is then we talked to + + align:start position:0% +what is so funny is then we talked to + + + align:start position:0% +what is so funny is then we talked to +his grad student mentor and the + + align:start position:0% +his grad student mentor and the + + + align:start position:0% +his grad student mentor and the +professor of the lab group he was part + + align:start position:0% +professor of the lab group he was part + + + align:start position:0% +professor of the lab group he was part +of and they were like oh yeah Nick is + + align:start position:0% +of and they were like oh yeah Nick is + + + align:start position:0% +of and they were like oh yeah Nick is +great Nick just came up with this thing + + align:start position:0% +great Nick just came up with this thing + + + align:start position:0% +great Nick just came up with this thing +that we don't fully understand the math + + align:start position:0% +that we don't fully understand the math + + + align:start position:0% +that we don't fully understand the math +but it's fantastic it works out great + + align:start position:0% +but it's fantastic it works out great + + + align:start position:0% +but it's fantastic it works out great +Ergo yet another example of this like + + align:start position:0% +Ergo yet another example of this like + + + align:start position:0% +Ergo yet another example of this like +you come up with another pair of glasses + + align:start position:0% +you come up with another pair of glasses + + + align:start position:0% +you come up with another pair of glasses +and you look at this problem and you're + + align:start position:0% +and you look at this problem and you're + + + align:start position:0% +and you look at this problem and you're +like I have a solution for this that is + + align:start position:0% +like I have a solution for this that is + + + align:start position:0% +like I have a solution for this that is +so much simpler than what you've been + + align:start position:0% +so much simpler than what you've been + + + align:start position:0% +so much simpler than what you've been +doing for years + + align:start position:0% +doing for years + + + align:start position:0% +doing for years +one of the things we at ocw love about + + align:start position:0% +one of the things we at ocw love about + + + align:start position:0% +one of the things we at ocw love about +micro is how it harnesses the power of + + align:start position:0% +micro is how it harnesses the power of + + + align:start position:0% +micro is how it harnesses the power of +online learning to make Science + + align:start position:0% +online learning to make Science + + + align:start position:0% +online learning to make Science +Education more accessible and Equitable + + align:start position:0% +Education more accessible and Equitable + + + align:start position:0% +Education more accessible and Equitable +both Jessica and Cecile share this + + align:start position:0% +both Jessica and Cecile share this + + + align:start position:0% +both Jessica and Cecile share this +passion the reason I'm so interested in + + align:start position:0% +passion the reason I'm so interested in + + + align:start position:0% +passion the reason I'm so interested in +and passionate about online learning is + + align:start position:0% +and passionate about online learning is + + + align:start position:0% +and passionate about online learning is +that it has so much potential to + + align:start position:0% +that it has so much potential to + + + align:start position:0% +that it has so much potential to +increase access and it has so much + + align:start position:0% +increase access and it has so much + + + align:start position:0% +increase access and it has so much +potential to share what we do here at + + align:start position:0% +potential to share what we do here at + + + align:start position:0% +potential to share what we do here at +MIT more broadly I have been working in + + align:start position:0% +MIT more broadly I have been working in + + + align:start position:0% +MIT more broadly I have been working in +online learning at MIT now for like nine + + align:start position:0% +online learning at MIT now for like nine + + + align:start position:0% +online learning at MIT now for like nine +years almost a decade we do a lot of + + align:start position:0% +years almost a decade we do a lot of + + + align:start position:0% +years almost a decade we do a lot of +experiments and we have to do a lot of + + align:start position:0% +experiments and we have to do a lot of + + + align:start position:0% +experiments and we have to do a lot of +experiments because some things that + + align:start position:0% +experiments because some things that + + + align:start position:0% +experiments because some things that +sound like a good idea really aren't and + + align:start position:0% +sound like a good idea really aren't and + + + align:start position:0% +sound like a good idea really aren't and +some things some things that you don't + + align:start position:0% +some things some things that you don't + + + align:start position:0% +some things some things that you don't +think are going to work out can work out + + align:start position:0% +think are going to work out can work out + + + align:start position:0% +think are going to work out can work out +really really really well and if you + + align:start position:0% +really really really well and if you + + + align:start position:0% +really really really well and if you +don't try them you don't learn this was + + align:start position:0% +don't try them you don't learn this was + + + align:start position:0% +don't try them you don't learn this was +just one of those projects but I thought + + align:start position:0% +just one of those projects but I thought + + + align:start position:0% +just one of those projects but I thought +this could work really well and it does + + align:start position:0% +this could work really well and it does + + + align:start position:0% +this could work really well and it does +two things that I'm really really + + align:start position:0% +two things that I'm really really + + + align:start position:0% +two things that I'm really really +excited about this is a tangible + + align:start position:0% +excited about this is a tangible + + + align:start position:0% +excited about this is a tangible +opportunity to increase diversity in our + + align:start position:0% +opportunity to increase diversity in our + + + align:start position:0% +opportunity to increase diversity in our +field and this is a tangible way of + + align:start position:0% +field and this is a tangible way of + + + align:start position:0% +field and this is a tangible way of +exposing more people to Material Science + + align:start position:0% +exposing more people to Material Science + + + align:start position:0% +exposing more people to Material Science +and Engineering to me if I can use my + + align:start position:0% +and Engineering to me if I can use my + + + align:start position:0% +and Engineering to me if I can use my +online learning experience to do those + + align:start position:0% +online learning experience to do those + + + align:start position:0% +online learning experience to do those +things I want to do that because that's + + align:start position:0% +things I want to do that because that's + + + align:start position:0% +things I want to do that because that's +why I work in this field + + align:start position:0% +why I work in this field + + + align:start position:0% +why I work in this field +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +each student that participated in micro + + align:start position:0% +each student that participated in micro + + + align:start position:0% +each student that participated in micro +has written a brief description of their + + align:start position:0% +has written a brief description of their + + + align:start position:0% +has written a brief description of their +work within their MIT Labs if you're + + align:start position:0% +work within their MIT Labs if you're + + + align:start position:0% +work within their MIT Labs if you're +interested in seeing what research the + + align:start position:0% +interested in seeing what research the + + + align:start position:0% +interested in seeing what research the +participants did and learning more about + + align:start position:0% +participants did and learning more about + + + align:start position:0% +participants did and learning more about +what's possible in a remote setting you + + align:start position:0% +what's possible in a remote setting you + + + align:start position:0% +what's possible in a remote setting you +can check them out at + + align:start position:0% +can check them out at + + + align:start position:0% +can check them out at +micro.mit.edu you can also learn about + + align:start position:0% +micro.mit.edu you can also learn about + + + align:start position:0% +micro.mit.edu you can also learn about +how to become a participant in the + + align:start position:0% +how to become a participant in the + + + align:start position:0% +how to become a participant in the +program there as well + + align:start position:0% +program there as well + + + align:start position:0% +program there as well +you'll also find all of the micro + + align:start position:0% +you'll also find all of the micro + + + align:start position:0% +you'll also find all of the micro +Creative Commons licensed teaching + + align:start position:0% +Creative Commons licensed teaching + + + align:start position:0% +Creative Commons licensed teaching +materials on our website at + + align:start position:0% +materials on our website at + + + align:start position:0% +materials on our website at +ocw.mit.edu you can help others find + + align:start position:0% +ocw.mit.edu you can help others find + + + align:start position:0% +ocw.mit.edu you can help others find +these resources and this podcast by + + align:start position:0% +these resources and this podcast by + + + align:start position:0% +these resources and this podcast by +leaving us a rating and review until + + align:start position:0% +leaving us a rating and review until + + + align:start position:0% +leaving us a rating and review until +next time signing off from Cambridge + + align:start position:0% +next time signing off from Cambridge + + + align:start position:0% +next time signing off from Cambridge +Massachusetts I'm your host Sarah Hansen + + align:start position:0% +Massachusetts I'm your host Sarah Hansen + + + align:start position:0% +Massachusetts I'm your host Sarah Hansen +from MIT opencourseware + + align:start position:0% +from MIT opencourseware + + + align:start position:0% +from MIT opencourseware +MIT chalk radios producers include + + align:start position:0% +MIT chalk radios producers include + + + align:start position:0% +MIT chalk radios producers include +myself Brett patchy and Dave leshansky + + align:start position:0% +myself Brett patchy and Dave leshansky + + + align:start position:0% +myself Brett patchy and Dave leshansky +show notes for this episode were written + + align:start position:0% +show notes for this episode were written + + + align:start position:0% +show notes for this episode were written +by Peter Chipman the micro supplemental + + align:start position:0% +by Peter Chipman the micro supplemental + + + align:start position:0% +by Peter Chipman the micro supplemental +resource was built on opencourseware by + + align:start position:0% +resource was built on opencourseware by + + + align:start position:0% +resource was built on opencourseware by +Shiba nemat Nasser we're funded by MIT + + align:start position:0% +Shiba nemat Nasser we're funded by MIT + + + align:start position:0% +Shiba nemat Nasser we're funded by MIT +open learning and supporters like you + + align:start position:0% + + + + align:start position:0% + +open courseware will always be free and + + align:start position:0% +open courseware will always be free and + + + align:start position:0% +open courseware will always be free and +open for you to learn anytime anywhere + + align:start position:0% +open for you to learn anytime anywhere + + + align:start position:0% +open for you to learn anytime anywhere +millions of people learn with ocw + + align:start position:0% +millions of people learn with ocw + + + align:start position:0% +millions of people learn with ocw +resources each month and none of it + + align:start position:0% +resources each month and none of it + + + align:start position:0% +resources each month and none of it +would be possible without the generosity + + align:start position:0% +would be possible without the generosity + + + align:start position:0% +would be possible without the generosity +of ocw users who give back when they can + + align:start position:0% +of ocw users who give back when they can + + + align:start position:0% +of ocw users who give back when they can +we hope you'll consider making a + + align:start position:0% +we hope you'll consider making a + + + align:start position:0% +we hope you'll consider making a +donation to help power free and open + + align:start position:0% +donation to help power free and open + + + align:start position:0% +donation to help power free and open +resources from MIT for Learners like you \ No newline at end of file diff --git a/q38KAGAKORk.txt b/q38KAGAKORk.txt new file mode 100644 index 0000000000000000000000000000000000000000..af2bef415ceb6606ea27a3afefbb3b3aa699cc1a --- /dev/null +++ b/q38KAGAKORk.txt @@ -0,0 +1,6707 @@ +align:start position:0% + +so how did you become interested in + + align:start position:0% +so how did you become interested in + + + align:start position:0% +so how did you become interested in +computation structures well in the early + + align:start position:0% +computation structures well in the early + + + align:start position:0% +computation structures well in the early +70s I was a college student trying to + + align:start position:0% +70s I was a college student trying to + + + align:start position:0% +70s I was a college student trying to +earn my way through college and so I was + + align:start position:0% +earn my way through college and so I was + + + align:start position:0% +earn my way through college and so I was +the computer operator on the third shift + + align:start position:0% +the computer operator on the third shift + + + align:start position:0% +the computer operator on the third shift +for the campus computer and I was in the + + align:start position:0% +for the campus computer and I was in the + + + align:start position:0% +for the campus computer and I was in the +era in which you could only afford one + + align:start position:0% +era in which you could only afford one + + + align:start position:0% +era in which you could only afford one +and since watching the blinking lights + + align:start position:0% +and since watching the blinking lights + + + align:start position:0% +and since watching the blinking lights +was boring I pulled out the schematics + + align:start position:0% +was boring I pulled out the schematics + + + align:start position:0% +was boring I pulled out the schematics +for the computer I was running for the + + align:start position:0% +for the computer I was running for the + + + align:start position:0% +for the computer I was running for the +for the University and I started trying + + align:start position:0% +for the University and I started trying + + + align:start position:0% +for the University and I started trying +to figure out how the computer worked + + align:start position:0% +to figure out how the computer worked + + + align:start position:0% +to figure out how the computer worked +and ever since then it's been sort of a + + align:start position:0% +and ever since then it's been sort of a + + + align:start position:0% +and ever since then it's been sort of a +lifelong interest in figuring out how do + + align:start position:0% +lifelong interest in figuring out how do + + + align:start position:0% +lifelong interest in figuring out how do +they actually put together these + + align:start position:0% +they actually put together these + + + align:start position:0% +they actually put together these +components to make a machine that can do + + align:start position:0% +components to make a machine that can do + + + align:start position:0% +components to make a machine that can do +computation and that interest is coupled + + align:start position:0% +computation and that interest is coupled + + + align:start position:0% +computation and that interest is coupled +with your interest in teaching and + + align:start position:0% +with your interest in teaching and + + + align:start position:0% +with your interest in teaching and +learning and especially online education + + align:start position:0% +learning and especially online education + + + align:start position:0% +learning and especially online education +could you talk a little bit about where + + align:start position:0% +could you talk a little bit about where + + + align:start position:0% +could you talk a little bit about where +that interest comes from well you know I + + align:start position:0% +that interest comes from well you know I + + + align:start position:0% +that interest comes from well you know I +was always fascinated and very motivated + + align:start position:0% +was always fascinated and very motivated + + + align:start position:0% +was always fascinated and very motivated +by the great teachers I was could listen + + align:start position:0% +by the great teachers I was could listen + + + align:start position:0% +by the great teachers I was could listen +to and so you know everybody picks a + + align:start position:0% +to and so you know everybody picks a + + + align:start position:0% +to and so you know everybody picks a +model when they're a teenager or young + + align:start position:0% +model when they're a teenager or young + + + align:start position:0% +model when they're a teenager or young +adult they say I want to be like + + align:start position:0% +adult they say I want to be like + + + align:start position:0% +adult they say I want to be like +so-and-so + + align:start position:0% +so-and-so + + + align:start position:0% +so-and-so +well the so-and-so's I like to pick were + + align:start position:0% +well the so-and-so's I like to pick were + + + align:start position:0% +well the so-and-so's I like to pick were +the the excellent teachers I had so I + + align:start position:0% +the the excellent teachers I had so I + + + align:start position:0% +the the excellent teachers I had so I +said I'm gonna try to be the best + + align:start position:0% +said I'm gonna try to be the best + + + align:start position:0% +said I'm gonna try to be the best +teacher I can there's something very + + align:start position:0% +teacher I can there's something very + + + align:start position:0% +teacher I can there's something very +satisfying about teaching students and + + align:start position:0% +satisfying about teaching students and + + + align:start position:0% +satisfying about teaching students and +having them not and let's uh suddenly + + align:start position:0% +having them not and let's uh suddenly + + + align:start position:0% +having them not and let's uh suddenly +get it so so it's been sort of a a very + + align:start position:0% +get it so so it's been sort of a a very + + + align:start position:0% +get it so so it's been sort of a a very +fulfilling experience to teach and so + + align:start position:0% +fulfilling experience to teach and so + + + align:start position:0% +fulfilling experience to teach and so +that's sort of a virtuous cycle right + + align:start position:0% +that's sort of a virtuous cycle right + + + align:start position:0% +that's sort of a virtuous cycle right +you get good vibes from teaching and + + align:start position:0% +you get good vibes from teaching and + + + align:start position:0% +you get good vibes from teaching and +then you do it better next year and you + + align:start position:0% +then you do it better next year and you + + + align:start position:0% +then you do it better next year and you +get better vibes and so it's just for 40 + + align:start position:0% +get better vibes and so it's just for 40 + + + align:start position:0% +get better vibes and so it's just for 40 +years that's been a great it's been + + align:start position:0% +years that's been a great it's been + + + align:start position:0% +years that's been a great it's been +great what kind of background + + align:start position:0% +great what kind of background + + + align:start position:0% +great what kind of background +experiences to the students bring + + align:start position:0% +experiences to the students bring + + + align:start position:0% +experiences to the students bring +related to computation it's all over + + align:start position:0% +related to computation it's all over + + + align:start position:0% +related to computation it's all over +than that it's all over the map so some + + align:start position:0% +than that it's all over the map so some + + + align:start position:0% +than that it's all over the map so some +of them will come having you know + + align:start position:0% +of them will come having you know + + + align:start position:0% +of them will come having you know +programmed computers for a long time and + + align:start position:0% +programmed computers for a long time and + + + align:start position:0% +programmed computers for a long time and +maybe even know a little bit about how + + align:start position:0% +maybe even know a little bit about how + + + align:start position:0% +maybe even know a little bit about how +the computers are structured on the + + align:start position:0% +the computers are structured on the + + + align:start position:0% +the computers are structured on the +insides other 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or the you know the actual + + align:start position:0% +the OS or the you know the actual + + + align:start position:0% +the OS or the you know the actual +hardware inside and so they come with + + align:start position:0% +hardware inside and so they come with + + + align:start position:0% +hardware inside and so they come with +interest but no background at all so how + + align:start position:0% +interest but no background at all so how + + + align:start position:0% +interest but no background at all so how +do you structure a course to meet the + + align:start position:0% +do you structure a course to meet the + + + align:start position:0% +do you structure a course to meet the +needs of people with diverse backgrounds + + align:start position:0% +needs of people with diverse backgrounds + + + align:start position:0% +needs of people with diverse backgrounds +like that right so it's to handle really + + align:start position:0% +like that right so it's to handle really + + + align:start position:0% +like that right so it's to handle really +diverse backgrounds you have to have a + + align:start position:0% +diverse backgrounds you have to have a + + + align:start position:0% +diverse backgrounds you have to have a +huge range of materials so you need + + align:start position:0% +huge range of materials so you need + + + align:start position:0% +huge range of materials so you need +something that somebody who just I need + + align:start position:0% +something that somebody who just I need + + + align:start position:0% +something that somebody who just I need +to start at the beginning you need a + + align:start position:0% +to start at the beginning you need a + + + align:start position:0% +to start at the beginning you need a +beginning for them to start at and for + + align:start position:0% +beginning for them to start at and for + + + align:start position:0% +beginning for them to start at and for +somebody who sort of you know passed the + + align:start position:0% +somebody who sort of you know passed the + + + align:start position:0% +somebody who sort of you know passed the +first half of your material you need a + + align:start position:0% +first half of your material you need a + + + align:start position:0% +first half of your material you need a +second half which will engage their + + align:start position:0% +second half which will engage their + + + align:start position:0% +second half which will engage their +interests so I create a huge I think of + + align:start position:0% +interests so I create a huge I think of + + + align:start position:0% +interests so I create a huge I think of +it as a buffet there's lots of dishes + + align:start position:0% +it as a buffet there's lots of dishes + + + align:start position:0% +it as a buffet there's lots of dishes +and you can start at the beginning of + + align:start position:0% +and you can start at the beginning of + + + align:start position:0% +and you can start at the beginning of +the buffet and and sort of you know pick + + align:start position:0% +the buffet and and sort of you know pick + + + align:start position:0% +the buffet and and sort of you know pick +it up from scratch or you can say I I'm + + align:start position:0% +it up from scratch or you can say I I'm + + + align:start position:0% +it up from scratch or you can say I I'm +gonna skip the first couple courses and + + align:start position:0% +gonna skip the first couple courses and + + + align:start position:0% +gonna skip the first couple courses and +I'm ready to dive in you know sort of in + + align:start position:0% +I'm ready to dive in you know sort of in + + + align:start position:0% +I'm ready to dive in you know sort of in +the middle of the conversation somewhere + + align:start position:0% +the middle of the conversation somewhere + + + align:start position:0% +the middle of the conversation somewhere +so the I think the real key is having a + + align:start position:0% +so the I think the real key is having a + + + align:start position:0% +so the I think the real key is having a +huge selection of materials to draw from + + align:start position:0% +huge selection of materials to draw from + + + align:start position:0% +huge selection of materials to draw from +and that's I think one of the hallmarks + + align:start position:0% +and that's I think one of the hallmarks + + + align:start position:0% +and that's I think one of the hallmarks +of six double O four has been that you + + align:start position:0% +of six double O four has been that you + + + align:start position:0% +of six double O four has been that you +know we have every possible way of + + align:start position:0% +know we have every possible way of + + + align:start position:0% +know we have every possible way of +learning the materials so not only for + + align:start position:0% +learning the materials so not only for + + + align:start position:0% +learning the materials so not only for +different backgrounds but for different + + align:start position:0% +different backgrounds but for different + + + align:start position:0% +different backgrounds but for different +learning styles these are some students + + align:start position:0% +learning styles these are some students + + + align:start position:0% +learning styles these are some students +talk or listen some students want to + + align:start position:0% +talk or listen some students want to + + + align:start position:0% +talk or listen some students want to +read some students just want to work on + + align:start position:0% +read some students just want to work on + + + align:start position:0% +read some students just want to work on +piece sets and do just-in-time learning + + align:start position:0% +piece sets and do just-in-time learning + + + align:start position:0% +piece sets and do just-in-time learning +where they you know sort of say here's + + align:start position:0% +where they you know sort of say here's + + + align:start position:0% +where they you know sort of say here's +what I need to know now I'll go look at + + align:start position:0% +what I need to know now I'll go look at + + + align:start position:0% +what I need to know now I'll go look at +the material just find the worked + + align:start position:0% +the material just find the worked + + + align:start position:0% +the material just find the worked +example and if I don't understand the + + align:start position:0% +example and if I don't understand the + + + align:start position:0% +example and if I don't understand the +work example I'll go you know actually + + align:start position:0% +work example I'll go you know actually + + + align:start position:0% +work example I'll go you know actually +read the text so they're they actually + + align:start position:0% +read the text so they're they actually + + + align:start position:0% +read the text so they're they actually +only get to the beginning of the if you + + align:start position:0% +only get to the beginning of the if you + + + align:start position:0% +only get to the beginning of the if you +will the the introductory are though + + align:start position:0% +will the the introductory are though + + + align:start position:0% +will the the introductory are though +explanatory material only and as a last + + align:start position:0% +explanatory material only and as a last + + + align:start position:0% +explanatory material only and as a last +resort if they somehow didn't get pick + + align:start position:0% +resort if they somehow didn't get pick + + + align:start position:0% +resort if they somehow didn't get pick +it up from before so many different + + align:start position:0% +it up from before so many different + + + align:start position:0% +it up from before so many different +learning styles many different + + align:start position:0% +learning styles many different + + + align:start position:0% +learning styles many different +backgrounds how has the MITx residential + + align:start position:0% +backgrounds how has the MITx residential + + + align:start position:0% +backgrounds how has the MITx residential +platform + + align:start position:0% + + + + align:start position:0% + +enabled you to provide this buffet well + + align:start position:0% +enabled you to provide this buffet well + + + align:start position:0% +enabled you to provide this buffet well +one is easy it's a one-stop shop for all + + align:start position:0% +one is easy it's a one-stop shop for all + + + align:start position:0% +one is easy it's a one-stop shop for all +the different sorts of materials and the + + align:start position:0% +the different sorts of materials and the + + + align:start position:0% +the different sorts of materials and the +other is you know there's sort of an + + align:start position:0% +other is you know there's sort of an + + + align:start position:0% +other is you know there's sort of an +emerging best practice + + align:start position:0% +emerging best practice + + + align:start position:0% +emerging best practice +how to explain material to people for + + align:start position:0% +how to explain material to people for + + + align:start position:0% +how to explain material to people for +the first time so you know you want to + + align:start position:0% +the first time so you know you want to + + + align:start position:0% +the first time so you know you want to +do a short bytes sound bytes video bytes + + align:start position:0% +do a short bytes sound bytes video bytes + + + align:start position:0% +do a short bytes sound bytes video bytes +you know those short segments of + + align:start position:0% +you know those short segments of + + + align:start position:0% +you know those short segments of +learning where you introduce a single + + align:start position:0% +learning where you introduce a single + + + align:start position:0% +learning where you introduce a single +skill or a single 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gonna ask you some simple +questions not puzzlers they're just if + + align:start position:0% +questions not puzzlers they're just if + + + align:start position:0% +questions not puzzlers they're just if +you understood what I just don't you on + + align:start position:0% +you understood what I just don't you on + + + align:start position:0% +you understood what I just don't you on +the video then you can answer them and + + align:start position:0% +the video then you can answer them and + + + align:start position:0% +the video then you can answer them and +so that gives us students a chance to + + align:start position:0% +so that gives us students a chance to + + + align:start position:0% +so that gives us students a chance to +start the process of retrieval learning + + align:start position:0% +start the process of retrieval learning + + + align:start position:0% +start the process of retrieval learning +right where you keep coming back again + + align:start position:0% +right where you keep coming back again + + + align:start position:0% +right where you keep coming back again +and again and I'll ask you a similar + + align:start position:0% +and again and I'll ask you a similar + + + align:start position:0% +and again and I'll ask you a similar +sort of question you know two segments + + align:start position:0% +sort of question you know two segments + + + align:start position:0% +sort of question you know two segments +later and you know pretty soon you're + + align:start position:0% +later and you know pretty soon you're + + + align:start position:0% +later and you know pretty soon you're +pulling it out of your short term and + + align:start position:0% +pulling it out of your short term and + + + align:start position:0% +pulling it out of your short term and +then medium term and long term memories + + align:start position:0% +then medium term and long term memories + + + align:start position:0% +then medium term and long term memories +so the mitx + + align:start position:0% +so the mitx + + + align:start position:0% +so the mitx +platform works really well at letting + + align:start position:0% +platform works really well at letting + + + align:start position:0% +platform works really well at letting +you construct those sort of learning + + align:start position:0% +you construct those sort of learning + + + align:start position:0% +you construct those sort of learning +sequences and I think the students + + align:start position:0% +sequences and I think the students + + + align:start position:0% +sequences and I think the students +appreciate it everything's much more + + align:start position:0% +appreciate it everything's much more + + + align:start position:0% +appreciate it everything's much more +bite-sized you know we both know is you + + align:start position:0% +bite-sized you know we both know is you + + + align:start position:0% +bite-sized you know we both know is you +can imagine pushing play on a 50-minute + + align:start position:0% +can imagine pushing play on a 50-minute + + + align:start position:0% +can imagine pushing play on a 50-minute +video and you know long about minute + + align:start position:0% +video and you know long about minute + + + align:start position:0% +video and you know long about minute +while I'm gonna say 37 but I long about + + align:start position:0% +while I'm gonna say 37 but I long about + + + align:start position:0% +while I'm gonna say 37 but I long about +minute six you're gonna be okay maybe I + + align:start position:0% +minute six you're gonna be okay maybe I + + + align:start position:0% +minute six you're gonna be okay maybe I +should check my email while I'm + + align:start position:0% +should check my email while I'm + + + align:start position:0% +should check my email while I'm +listening to this okay it's it's you + + align:start position:0% +listening to this okay it's it's you + + + align:start position:0% +listening to this okay it's it's you +know keeping things short and sweet so + + align:start position:0% +know keeping things short and sweet so + + + align:start position:0% +know keeping things short and sweet so +you have a huge nose up now you have a + + align:start position:0% +you have a huge nose up now you have a + + + align:start position:0% +you have a huge nose up now you have a +bunch of short bytes + + align:start position:0% +bunch of short bytes + + + align:start position:0% +bunch of short bytes +now the MIT X platforms let you organize + + align:start position:0% +now the MIT X platforms let you organize + + + align:start position:0% +now the MIT X platforms let you organize +those with questions that let you sort + + align:start position:0% +those with questions that let you sort + + + align:start position:0% +those with questions that let you sort +of continue to test your learning so + + align:start position:0% +of continue to test your learning so + + + align:start position:0% +of continue to test your learning so +it's actually worked out to be a very + + align:start position:0% +it's actually worked out to be a very + + + align:start position:0% +it's actually worked out to be a very +nice way of making a fairly organized + + align:start position:0% +nice way of making a fairly organized + + + align:start position:0% +nice way of making a fairly organized +tour through the material that the + + align:start position:0% +tour through the material that the + + + align:start position:0% +tour through the material that the +students can start and stop and come + + align:start position:0% +students can start and stop and come + + + align:start position:0% +students can start and stop and come +back to right plus is asynchronous in + + align:start position:0% +back to right plus is asynchronous in + + + align:start position:0% +back to right plus is asynchronous in +other words they they get to choose + + align:start position:0% +other words they they get to choose + + + align:start 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handed a piece of chalk and be +told to teach you know unlike the + + align:start position:0% +told to teach you know unlike the + + + align:start position:0% +told to teach you know unlike the +teachers for your kids in elementary + + align:start position:0% +teachers for your kids in elementary + + + align:start position:0% +teachers for your kids in elementary +school who have actually gone through a + + align:start position:0% +school who have actually gone through a + + + align:start position:0% +school who have actually gone through a +program teaches them how to teach we're + + align:start position:0% +program teaches them how to teach we're + + + align:start position:0% +program teaches them how to teach we're +just said here at teach and so it's all + + align:start position:0% +just said here at teach and so it's all + + + align:start position:0% +just said here at teach and so it's all +anecdotal it's all trying to remember + + align:start position:0% +anecdotal it's all trying to remember + + + align:start position:0% +anecdotal it's all trying to remember +how people taught you finally we have + + align:start position:0% +how people taught you finally we have + + + align:start position:0% +how people taught you finally we have +you know the online courses are + + align:start position:0% +you know the online courses are + + + align:start position:0% +you know the online courses are +providing a real educational laboratory + + align:start position:0% +providing a real educational laboratory + + + align:start position:0% +providing a real educational laboratory +we're able to try out different + + align:start position:0% +we're able to try out different + + + align:start position:0% +we're able to try out different +techniques we're able to you know make + + align:start position:0% +techniques we're able to you know make + + + align:start position:0% +techniques we're able to you know make +fairly accurate assessments of how well + + align:start position:0% +fairly accurate assessments of how well + + + align:start position:0% +fairly accurate assessments of how well +did that just work you know whether it + + align:start position:0% +did that just work you know whether it + + + align:start position:0% +did that just work you know whether it +was an exercise or a video segment or a + + align:start position:0% +was an exercise or a video segment or a + + + align:start position:0% +was an exercise or a video segment or a +design problem and so we can actually + + align:start position:0% +design problem and so we can actually + + + align:start position:0% +design problem and so we can actually +you know do a/b tests within the same + + align:start position:0% +you know do a/b tests within the same + + + align:start position:0% +you know do a/b tests within the same +cadre so you know it's it's pretty neat + + align:start position:0% +cadre so you know it's it's pretty neat + + + align:start position:0% +cadre so you know it's it's pretty neat +having a lab I mean as a scientist and + + align:start position:0% +having a lab I mean as a scientist and + + + align:start position:0% +having a lab I mean as a scientist and +engineer you can say look III know about + + align:start position:0% +engineer you can say look III know about + + + align:start position:0% +engineer you can say look III know about +you know I heard high pot you know build + + align:start position:0% +you know I heard high pot you know build + + + align:start position:0% +you know I heard high pot you know build +hypothesis test it you know through a + + align:start position:0% +hypothesis test it you know through a + + + align:start position:0% +hypothesis test it you know through a +bunch of experiments we can really do + + align:start position:0% +bunch of experiments we can really do + + + align:start position:0% +bunch of experiments we can really do +the experiments with the MIT X platform + + align:start position:0% +the experiments with the MIT X platform + + + align:start position:0% +the experiments with the MIT X platform +and so that's been great yeah it's + + align:start position:0% +and so that's been great yeah it's + + + align:start position:0% +and so that's been great yeah it's +really exciting it is let's talk about + + align:start position:0% +really exciting it is let's talk about + + + align:start position:0% +really exciting it is let's talk about +learning in the classroom and teaching + + align:start position:0% +learning in the classroom and teaching + + + align:start position:0% +learning in the classroom and teaching +large lecture classes what strategies do + + align:start position:0% +large lecture classes what strategies do + + + align:start position:0% +large lecture classes what strategies do +you have for keeping students engaged + + align:start position:0% +you have for keeping students engaged + + + align:start position:0% +you have for keeping students engaged +well that's interesting because because + + align:start position:0% +well that's interesting because because + + + align:start position:0% +well that's interesting because because +we have so many different materials + + align:start position:0% +we have so many different materials + + + align:start position:0% +we have so many different materials +really the only students who come to + + align:start position:0% +really the only students who come to + + + align:start position:0% +really the only students who come to +lecture are the ones who you know for + + align:start position:0% +lecture are the ones who you know for + + + align:start position:0% +lecture are the ones who you know for +whom lecture is how they learn I was + + align:start position:0% +whom lecture is how they learn I was + + + align:start position:0% +whom lecture is how they learn I was +such a student so I just so the people + + align:start position:0% +such a student so I just so the people + + + align:start position:0% +such a student so I just so the people +who were there are not you know as a + + align:start position:0% +who were there are not you know as a + + + align:start position:0% +who were there are not you know as a +draft arm either so they're prepared to + + align:start position:0% +draft arm either so they're prepared to + + + align:start position:0% +draft arm either so they're prepared to +be somewhat engaged by a local + + align:start position:0% +be somewhat engaged by a local + + + align:start position:0% +be somewhat engaged by a local +presentation so I have a well-developed + + align:start position:0% +presentation so I have a well-developed + + + align:start position:0% +presentation so I have a well-developed +set of materials that I present in class + + align:start position:0% +set of materials that I present in class + + + align:start position:0% +set of materials that I present in class +that have sort of been debugged for + + align:start position:0% +that have sort of been debugged for + + + align:start position:0% +that have sort of been debugged for +having not too much or too little a + + align:start position:0% +having not too much or too little a + + + align:start position:0% +having not too much or too little a +progression that most people can follow + + align:start position:0% +progression that most people can follow + + + align:start position:0% +progression that most people can follow +and then I'm I'm you know happily when + + align:start position:0% +and then I'm I'm you know happily when + + + align:start position:0% +and then I'm I'm you know happily when +you teach for a while you start to get + + align:start position:0% +you teach for a while you start to get + + + align:start position:0% +you teach for a while you start to get +more relaxed and so this is a very + + align:start position:0% +more relaxed and so this is a very + + + align:start position:0% +more relaxed and so this is a very +relaxed sort of experience you know I + + align:start position:0% +relaxed sort of experience you know I + + + align:start position:0% +relaxed sort of experience you know I +tell jokes I tell stories from my career + + align:start position:0% +tell jokes I tell stories from my career + + + align:start position:0% +tell jokes I tell stories from my career +and it's interesting to me how you know + + align:start position:0% +and it's interesting to me how you know + + + align:start position:0% +and it's interesting to me how you know +when the piece students are making + + align:start position:0% +when the piece students are making + + + align:start position:0% +when the piece students are making +comments at the end of the semester and + + align:start position:0% +comments at the end of the semester and + + + align:start position:0% +comments at the end of the semester and +the evaluations many of them say well I + + align:start position:0% +the evaluations many of them say well I + + + align:start position:0% +the evaluations many of them say well I +really like the story so it's you know + + align:start position:0% +really like the story so it's you know + + + align:start position:0% +really like the story so it's you know +after boring you with technical details + + align:start position:0% +after boring you with technical details + + + align:start position:0% +after boring you with technical details +that's fun to say and then when I tried + + align:start position:0% +that's fun to say and then when I tried + + + align:start position:0% +that's fun to say and then when I tried +to use that you know the following thing + + align:start position:0% +to use that you know the following thing + + + align:start position:0% +to use that you know the following thing +happened and all of a sudden they're + + align:start position:0% +happened and all of a sudden they're + + + align:start position:0% +happened and all of a sudden they're +sort of picking up saying oh you know + + align:start position:0% +sort of picking up saying oh you know + + + align:start position:0% +sort of picking up saying oh you know +and I think it helps them remember the + + align:start position:0% +and I think it helps them remember the + + + align:start position:0% +and I think it helps them remember the +related good it does might not you think + + align:start position:0% +related good it does might not you think + + + align:start position:0% +related good it does might not you think +about what you remember from lectures is + + align:start position:0% +about what you remember from lectures is + + + align:start position:0% +about what you remember from lectures is +almost never a technical nugget it's a + + align:start position:0% +almost never a technical nugget it's a + + + align:start position:0% +almost never a technical nugget it's a +joke they told or an accident that + + align:start position:0% +joke they told or an accident that + + + align:start position:0% +joke they told or an accident that +happened or a mistake that was made and + + align:start position:0% +happened or a mistake that was made and + + + align:start position:0% +happened or a mistake that was made and +so it's paint if there's a concept + + align:start position:0% +so it's paint if there's a concept + + + align:start position:0% +so it's paint if there's a concept +called fluency mmm-hmm which is + + align:start position:0% +called fluency mmm-hmm which is + + + align:start position:0% +called fluency mmm-hmm which is +basically how smoothly things are going + + align:start position:0% +basically how smoothly things are going + + + align:start position:0% +basically how smoothly things are going +and and and everybody's nodding but not + + align:start position:0% +and and and everybody's nodding but not + + + align:start position:0% +and and and everybody's nodding but not +you know this or your mind is starting + + align:start position:0% +you know this or your mind is starting + + + align:start position:0% +you know this or your mind is starting +to drift because it's all so it's + + align:start position:0% +to drift because it's all so it's + + + align:start position:0% +to drift because it's all so it's +actually good to try to put a little + + align:start position:0% +actually good to try to put a little + + + align:start position:0% +actually good to try to put a little +disfluency into your lecture to actually + + align:start position:0% +disfluency into your lecture to actually + + + align:start position:0% +disfluency into your lecture to actually +have a you know you stopped and you tell + + align:start position:0% +have a you know you stopped and you tell + + + align:start position:0% +have a you know you stopped and you tell +a joke or you make a mistake or you drop + + align:start position:0% +a joke or you make a mistake or you drop + + + align:start position:0% +a joke or you make a mistake or you drop +the chalk and say darn and you look at + + align:start position:0% +the chalk and say darn and you look at + + + align:start position:0% +the chalk and say darn and you look at +the floor right or and here's what I + + align:start position:0% +the floor right or and here's what I + + + align:start position:0% +the floor right or and here's what I +like to do is you walk out from behind + + align:start position:0% +like to do is you walk out from behind + + + align:start position:0% +like to do is you walk out from behind +the lecture table or a lectern and you + + align:start position:0% +the lecture table or a lectern and you + + + align:start position:0% +the lecture table or a lectern and you +approach the audience and you can see + + align:start position:0% +approach the audience and you can see + + + align:start position:0% +approach the audience and you can see +them sort of going wait he's escaped so + + align:start position:0% +them sort of going wait he's escaped so + + + align:start position:0% +them sort of going wait he's escaped so +does anything that sort of switches up + + align:start position:0% +does anything that sort of switches up + + + align:start position:0% +does anything that sort of switches up +you know the sort of I'm just going + + align:start position:0% +you know the sort of I'm just going + + + align:start position:0% +you know the sort of I'm just going +with a flow here so you know making you + + align:start position:0% +with a flow here so you know making you + + + align:start position:0% +with a flow here so you know making you +know little flows that have things that + + align:start position:0% +know little flows that have things that + + + align:start position:0% +know little flows that have things that +change make a lot of difference and + + align:start position:0% +change make a lot of difference and + + + align:start position:0% +change make a lot of difference and +keeping people sort of engaged that's a + + align:start position:0% +keeping people sort of engaged that's a + + + align:start position:0% +keeping people sort of engaged that's a +great tip let's talk for a second about + + align:start position:0% +great tip let's talk for a second about + + + align:start position:0% +great tip let's talk for a second about +the teaching team I understand there's + + align:start position:0% +the teaching team I understand there's + + + align:start position:0% +the teaching team I understand there's +there are a fair number of people + + align:start position:0% +there are a fair number of people + + + align:start position:0% +there are a fair number of people +involved in developing and teaching this + + align:start position:0% +involved in developing and teaching this + + + align:start position:0% +involved in developing and teaching this +course you talk about that well we have + + align:start position:0% +course you talk about that well we have + + + align:start position:0% +course you talk about that well we have +a little cadre of people who are + + align:start position:0% +a little cadre of people who are + + + align:start position:0% +a little cadre of people who are +instructors I've been sort of a part of + + align:start position:0% +instructors I've been sort of a part of + + + align:start position:0% +instructors I've been sort of a part of +that cadre every semester for a very + + align:start position:0% +that cadre every semester for a very + + + align:start position:0% +that cadre every semester for a very +long time but we have other you know + + align:start position:0% +long time but we have other you know + + + align:start position:0% +long time but we have other you know +people who come in from the outside or + + align:start position:0% +people who come in from the outside or + + + align:start position:0% +people who come in from the outside or +in recent years the department is added + + align:start position:0% +in recent years the department is added + + + align:start position:0% +in recent years the department is added +election lecturer resources so there's + + align:start position:0% +election lecturer resources so there's + + + align:start position:0% +election lecturer resources so there's +another lecturer associated with it and + + align:start position:0% +another lecturer associated with it and + + + align:start position:0% +another lecturer associated with it and +then faculty come in so it's and they're + + align:start position:0% +then faculty come in so it's and they're + + + align:start position:0% +then faculty come in so it's and they're +you know they provide a little depth to + + align:start position:0% +you know they provide a little depth to + + + align:start position:0% +you know they provide a little depth to +the gene pool but then we have graduate + + align:start position:0% +the gene pool but then we have graduate + + + align:start position:0% +the gene pool but then we have graduate +TAS who teach recitations and we have + + align:start position:0% +TAS who teach recitations and we have + + + align:start position:0% +TAS who teach recitations and we have +student undergraduate TAS and then lab + + align:start position:0% +student undergraduate TAS and then lab + + + align:start position:0% +student undergraduate TAS and then lab +assistants so they're certain we have + + align:start position:0% +assistants so they're certain we have + + + align:start position:0% +assistants so they're certain we have +this whole hierarchy they've all taken + + align:start position:0% +this whole hierarchy they've all taken + + + align:start position:0% +this whole hierarchy they've all taken +the course almost they've all loved it + + align:start position:0% +the course almost they've all loved it + + + align:start position:0% +the course almost they've all loved it +so I mean this is sort of the material + + align:start position:0% +so I mean this is sort of the material + + + align:start position:0% +so I mean this is sort of the material +that people say oh this is really pretty + + align:start position:0% +that people say oh this is really pretty + + + align:start position:0% +that people say oh this is really pretty +neat you know I can't wait to tell the + + align:start position:0% +neat you know I can't wait to tell the + + + align:start position:0% +neat you know I can't wait to tell the +next person this works and so as they + + align:start position:0% +next person this works and so as they + + + align:start position:0% +next person this works and so as they +sit there and work with the students you + + align:start position:0% +sit there and work with the students you + + + align:start position:0% +sit there and work with the students you +know sort of like me there's an + + align:start position:0% +know sort of like me there's an + + + align:start position:0% +know sort of like me there's an +enthusiasm a sort of bubbles out yeah + + align:start position:0% +enthusiasm a sort of bubbles out yeah + + + align:start position:0% +enthusiasm a sort of bubbles out yeah +and the students actually you know I + + align:start position:0% +and the students actually you know I + + + align:start position:0% +and the students actually you know I +sort of listed things sort of well I was + + align:start position:0% +sort of listed things sort of well I was + + + align:start position:0% +sort of listed things sort of well I was +going to say top down and I'm not sugar + + align:start position:0% +going to say top down and I'm not sugar + + + align:start position:0% +going to say top down and I'm not sugar +lecturers are at the top but there are + + align:start position:0% +lecturers are at the top but there are + + + align:start position:0% +lecturers are at the top but there are +instructors are at the top but the + + align:start position:0% +instructors are at the top but the + + + align:start position:0% +instructors are at the top but the +students actually prefer the other thing + + align:start position:0% +students actually prefer the other thing + + + align:start position:0% +students actually prefer the other thing +which is they actually you know asking + + align:start position:0% +which is they actually you know asking + + + align:start position:0% +which is they actually you know asking +in LA it's very you know it's not very + + align:start position:0% +in LA it's very you know it's not very + + + align:start position:0% +in LA it's very you know it's not very +intimidating I think the students maybe + + align:start position:0% +intimidating I think the students maybe + + + align:start position:0% +intimidating I think the students maybe +they just took it last semester and so + + align:start position:0% +they just took it last semester and so + + + align:start position:0% +they just took it last semester and so +they have fresh in their minds what it + + align:start position:0% +they have fresh in their minds what it + + + align:start position:0% +they have fresh in their minds what it +is they needed to do in order to get + + align:start position:0% +is they needed to do in order to get + + + align:start position:0% +is they needed to do in order to get +whatever it is they're trying to get so + + align:start position:0% +whatever it is they're trying to get so + + + align:start position:0% +whatever it is they're trying to get so +and then you sort of work other chain up + + align:start position:0% +and then you sort of work other chain up + + + align:start position:0% +and then you sort of work other chain up +you know work up the hierarchy to + + align:start position:0% +you know work up the hierarchy to + + + align:start position:0% +you know work up the hierarchy to +you know get an answer if people below + + align:start position:0% +you know get an answer if people below + + + align:start position:0% +you know get an answer if people below +and that way you're only asking + + align:start position:0% +and that way you're only asking + + + align:start position:0% +and that way you're only asking +questions of the more intimidating + + align:start position:0% +questions of the more intimidating + + + align:start position:0% +questions of the more intimidating +people when you're pretty sure that no + + align:start position:0% +people when you're pretty sure that no + + + align:start position:0% +people when you're pretty sure that no +one else has the answer so it's really + + align:start position:0% +one else has the answer so it's really + + + align:start position:0% +one else has the answer so it's really +you know by the time the questions sort + + align:start position:0% +you know by the time the questions sort + + + align:start position:0% +you know by the time the questions sort +of get to me mostly no one is there no + + align:start position:0% +of get to me mostly no one is there no + + + align:start position:0% +of get to me mostly no one is there no +one is worried that they're a dumb + + align:start position:0% +one is worried that they're a dumb + + + align:start position:0% +one is worried that they're a dumb +question now I don't think we believe + + align:start position:0% +question now I don't think we believe + + + align:start position:0% +question now I don't think we believe +and dumb questions I'm Nikole questions + + align:start position:0% +and dumb questions I'm Nikole questions + + + align:start position:0% +and dumb questions I'm Nikole questions +are sort of interesting but I think the + + align:start position:0% +are sort of interesting but I think the + + + align:start position:0% +are sort of interesting but I think the +students look I asked 10 people none of + + align:start position:0% +students look I asked 10 people none of + + + align:start position:0% +students look I asked 10 people none of +us news and now we can ask you and we're + + align:start position:0% +us news and now we can ask you and we're + + + align:start position:0% +us news and now we can ask you and we're +I'm pretty confident that it's not + + align:start position:0% +I'm pretty confident that it's not + + + align:start position:0% +I'm pretty confident that it's not +wasn't an obvious thing that if I'd only + + align:start position:0% +wasn't an obvious thing that if I'd only + + + align:start position:0% +wasn't an obvious thing that if I'd only +read the assignment I would have known + + align:start position:0% +read the assignment I would have known + + + align:start position:0% +read the assignment I would have known +so that sort of range of sort of + + align:start position:0% +so that sort of range of sort of + + + align:start position:0% +so that sort of range of sort of +experience level and age you know at the + + align:start position:0% +experience level and age you know at the + + + align:start position:0% +experience level and age you know at the +high end of the experience level you can + + align:start position:0% +high end of the experience level you can + + + align:start position:0% +high end of the experience level you can +get an answer to any question at the + + align:start position:0% +get an answer to any question at the + + + align:start position:0% +get an answer to any question at the +beginning end of the experience level + + align:start position:0% +beginning end of the experience level + + + align:start position:0% +beginning end of the experience level +you're talking to somebody who was you + + align:start position:0% +you're talking to somebody who was you + + + align:start position:0% +you're talking to somebody who was you +know just had just you know months ago + + align:start position:0% +know just had just you know months ago + + + align:start position:0% +know just had just you know months ago +did what you're doing and so is know we + + align:start position:0% +did what you're doing and so is know we + + + align:start position:0% +did what you're doing and so is know we +can be you know I can ask you and we + + align:start position:0% +can be you know I can ask you and we + + + align:start position:0% +can be you know I can ask you and we +won't be embarrassed right right + + align:start position:0% +won't be embarrassed right right + + + align:start position:0% +won't be embarrassed right right +what's the role of the online fora in + + align:start position:0% +what's the role of the online fora in + + + align:start position:0% +what's the role of the online fora in +the course for helping students feel + + align:start position:0% +the course for helping students feel + + + align:start position:0% +the course for helping students feel +comfortable asking questions and how do + + align:start position:0% +comfortable asking questions and how do + + + align:start position:0% +comfortable asking questions and how do +you monitor it how do you run it + + align:start position:0% +you monitor it how do you run it + + + align:start position:0% +you monitor it how do you run it +productively this is something that + + align:start position:0% +productively this is something that + + + align:start position:0% +productively this is something that +educators sometimes struggle with well I + + align:start position:0% +educators sometimes struggle with well I + + + align:start position:0% +educators sometimes struggle with well I +mean it's to me it's a it's a wonderful + + align:start position:0% +mean it's to me it's a it's a wonderful + + + align:start position:0% +mean it's to me it's a it's a wonderful +asset for the first time I'm able to + + align:start position:0% +asset for the first time I'm able to + + + align:start position:0% +asset for the first time I'm able to +make a thoughtful answer to a question + + align:start position:0% +make a thoughtful answer to a question + + + align:start position:0% +make a thoughtful answer to a question +and have a hundred and eighty people + + align:start position:0% +and have a hundred and eighty people + + + align:start position:0% +and have a hundred and eighty people +look at the answer instead of one and + + align:start position:0% +look at the answer instead of one and + + + align:start position:0% +look at the answer instead of one and +then the next person has the same + + align:start position:0% +then the next person has the same + + + align:start position:0% +then the next person has the same +question you say well I just I think you + + align:start position:0% +question you say well I just I think you + + + align:start position:0% +question you say well I just I think you +know up with a large class you can't + + align:start position:0% +know up with a large class you can't + + + align:start position:0% +know up with a large class you can't +spend ten minutes for each of them you + + align:start position:0% +spend ten minutes for each of them you + + + align:start position:0% +spend ten minutes for each of them you +know 300 people so so it's a great place + + align:start position:0% +know 300 people so so it's a great place + + + align:start position:0% +know 300 people so so it's a great place +to ask questions I try to always give a + + align:start position:0% +to ask questions I try to always give a + + + align:start position:0% +to ask questions I try to always give a +thoughtful and respectful answer to each + + align:start position:0% +thoughtful and respectful answer to each + + + align:start position:0% +thoughtful and respectful answer to each +question so even if the question is sort + + align:start position:0% +question so even if the question is sort + + + align:start position:0% +question so even if the question is sort +of like whoa if you had done the reading + + align:start position:0% +of like whoa if you had done the reading + + + align:start position:0% +of like whoa if you had done the reading +you would have known I say well if you + + align:start position:0% +you would have known I say well if you + + + align:start position:0% +you would have known I say well if you +you know look back at the material you + + align:start position:0% +you know look back at the material you + + + align:start position:0% +you know look back at the material you +see it explains the following right you + + align:start position:0% +see it explains the following right you + + + align:start position:0% +see it explains the following right you +know try to make it not a little hint + + align:start position:0% +know try to make it not a little hint + + + align:start position:0% +know try to make it not a little hint +that maybe a little bit more preparation + + align:start position:0% +that maybe a little bit more preparation + + + align:start position:0% +that maybe a little bit more preparation +but but many of the questions are look I + + align:start position:0% +but but many of the questions are look I + + + align:start position:0% +but but many of the questions are look I +read the material I'm still not getting + + align:start position:0% +read the material I'm still not getting + + + align:start position:0% +read the material I'm still not getting +it I need an example + + align:start position:0% +it I need an example + + + align:start position:0% +it I need an example +and so the students I try to make + + align:start position:0% +and so the students I try to make + + + align:start position:0% +and so the students I try to make +students feel very comfortable asking + + align:start position:0% +students feel very comfortable asking + + + align:start position:0% +students feel very comfortable asking +this never there's nothing no cost they + + align:start position:0% +this never there's nothing no cost they + + + align:start position:0% +this never there's nothing no cost they +can ask anonymously so that removes some + + align:start position:0% +can ask anonymously so that removes some + + + align:start position:0% +can ask anonymously so that removes some +of the barrier okay and then I think + + align:start position:0% +of the barrier okay and then I think + + + align:start position:0% +of the barrier okay and then I think +this see the fall 2017 we had about 2500 + + align:start position:0% +this see the fall 2017 we had about 2500 + + + align:start position:0% +this see the fall 2017 we had about 2500 +contributions to the harm the average + + align:start position:0% +contributions to the harm the average + + + align:start position:0% +contributions to the harm the average +response time is about 20 minutes and so + + align:start position:0% +response time is about 20 minutes and so + + + align:start position:0% +response time is about 20 minutes and so +you say wait but students are asking + + align:start position:0% +you say wait but students are asking + + + align:start position:0% +you say wait but students are asking +questions at 3 a.m. yeah and how does + + align:start position:0% +questions at 3 a.m. yeah and how does + + + align:start position:0% +questions at 3 a.m. yeah and how does +that work and you know it turns out that + + align:start position:0% +that work and you know it turns out that + + + align:start position:0% +that work and you know it turns out that +we have you know TAS we act particularly + + align:start position:0% +we have you know TAS we act particularly + + + align:start position:0% +we have you know TAS we act particularly +good yes exactly + + align:start position:0% +good yes exactly + + + align:start position:0% +good yes exactly +3 a.m. they're just hitting their stride + + align:start position:0% +3 a.m. they're just hitting their stride + + + align:start position:0% +3 a.m. they're just hitting their stride +a lot of us who are involved in the core + + align:start position:0% +a lot of us who are involved in the core + + + align:start position:0% +a lot of us who are involved in the core +sort of have a we put the notification + + align:start position:0% +sort of have a we put the notification + + + align:start position:0% +sort of have a we put the notification +of postings on real-time and so we get + + align:start position:0% +of postings on real-time and so we get + + + align:start position:0% +of postings on real-time and so we get +an email right away and so often we can + + align:start position:0% +an email right away and so often we can + + + align:start position:0% +an email right away and so often we can +just type in an answer and it's okay and + + align:start position:0% +just type in an answer and it's okay and + + + align:start position:0% +just type in an answer and it's okay and +there I'm really I think the fast + + align:start position:0% +there I'm really I think the fast + + + align:start position:0% +there I'm really I think the fast +response time really reduces the + + align:start position:0% +response time really reduces the + + + align:start position:0% +response time really reduces the +frustration level of the students + + align:start position:0% +frustration level of the students + + + align:start position:0% +frustration level of the students +there's nothing like being stuck on + + align:start position:0% +there's nothing like being stuck on + + + align:start position:0% +there's nothing like being stuck on +something right and saying I wish I + + align:start position:0% +something right and saying I wish I + + + align:start position:0% +something right and saying I wish I +could ask somebody well for the first + + align:start position:0% +could ask somebody well for the first + + + align:start position:0% +could ask somebody well for the first +time you know it's 3:12 in the morning + + align:start position:0% +time you know it's 3:12 in the morning + + + align:start position:0% +time you know it's 3:12 in the morning +and you can say wait I can't ask and I + + align:start position:0% +and you can say wait I can't ask and I + + + align:start position:0% +and you can say wait I can't ask and I +can get an answer and the students + + align:start position:0% +can get an answer and the students + + + align:start position:0% +can get an answer and the students +really really appreciate that so it the + + align:start position:0% +really really appreciate that so it the + + + align:start position:0% +really really appreciate that so it the +forum has really I think changed to a + + align:start position:0% + + + + align:start position:0% + +level of frustration when they get stuck + + align:start position:0% +level of frustration when they get stuck + + + align:start position:0% +level of frustration when they get stuck +they you know is being stuck it's just a + + align:start position:0% +they you know is being stuck it's just a + + + align:start position:0% +they you know is being stuck it's just a +10-minute process not a two-day process + + align:start position:0% +10-minute process not a two-day process + + + align:start position:0% +10-minute process not a two-day process +right oh my god the next office hours + + align:start position:0% +right oh my god the next office hours + + + align:start position:0% +right oh my god the next office hours +are after the weekend when we do so and + + align:start position:0% +are after the weekend when we do so and + + + align:start position:0% +are after the weekend when we do so and +of course a lot of students are doing + + align:start position:0% +of course a lot of students are doing + + + align:start position:0% +of course a lot of students are doing +work outside of you know sort of 9 to 5 + + align:start position:0% +work outside of you know sort of 9 to 5 + + + align:start position:0% +work outside of you know sort of 9 to 5 +hours so so it's a way for the staff to + + align:start position:0% +hours so so it's a way for the staff to + + + align:start position:0% +hours so so it's a way for the staff to +be a 24/7 staff instead of just a + + align:start position:0% +be a 24/7 staff instead of just a + + + align:start position:0% +be a 24/7 staff instead of just a +nine-to-five 5 days a week staff um the + + align:start position:0% +nine-to-five 5 days a week staff um the + + + align:start position:0% +nine-to-five 5 days a week staff um the +staff like I mean the students work like + + align:start position:0% +staff like I mean the students work like + + + align:start position:0% +staff like I mean the students work like +that to mean listen most of the people + + align:start position:0% +that to mean listen most of the people + + + align:start position:0% +that to mean listen most of the people +who were helping on the forum or keeping + + align:start position:0% +who were helping on the forum or keeping + + + align:start position:0% +who were helping on the forum or keeping +the same schedule as the users at the + + align:start position:0% +the same schedule as the users at the + + + align:start position:0% +the same schedule as the users at the +forum so it's it's it's a good match ok + + align:start position:0% +forum so it's it's it's a good match ok + + + align:start position:0% +forum so it's it's it's a good match ok +let's talk for a minute about the lab + + align:start position:0% +let's talk for a minute about the lab + + + align:start position:0% +let's talk for a minute about the lab +experiences in the course so students + + align:start position:0% +experiences in the course so students + + + align:start position:0% +experiences in the course so students +get hands-on experience doing digital + + align:start position:0% +get hands-on experience doing digital + + + align:start position:0% +get hands-on experience doing digital +design yes could you talk about a few of + + align:start position:0% +design yes could you talk about a few of + + + align:start position:0% +design yes could you talk about a few of +those experiences and also does that + + align:start position:0% +those experiences and also does that + + + align:start position:0% +those experiences and also does that +take place here where we are right now + + align:start position:0% +take place here where we are right now + + + align:start position:0% +take place here where we are right now +well you can do it anywhere it's + + align:start position:0% +well you can do it anywhere it's + + + align:start position:0% +well you can do it anywhere it's +browser-based so there's no software to + + align:start position:0% +browser-based so there's no software to + + + align:start position:0% +browser-based so there's no software to +download you're just just on the web you + + align:start position:0% +download you're just just on the web you + + + align:start position:0% +download you're just just on the web you +go and so one of the things I enjoy + + align:start position:0% +go and so one of the things I enjoy + + + align:start position:0% +go and so one of the things I enjoy +doing is to build browser based computer + + align:start position:0% +doing is to build browser based computer + + + align:start position:0% +doing is to build browser based computer +aided design tools + + align:start position:0% +aided design tools + + + align:start position:0% +aided design tools +it turns out that they actually work + + align:start position:0% +it turns out that they actually work + + + align:start position:0% +it turns out that they actually work +really well the modern browser + + align:start position:0% +really well the modern browser + + + align:start position:0% +really well the modern browser +environments are quite capable as a you + + align:start position:0% +environments are quite capable as a you + + + align:start position:0% +environments are quite capable as a you +know as a programming environment yeah a + + align:start position:0% +know as a programming environment yeah a + + + align:start position:0% +know as a programming environment yeah a +few tricks but once you do it it works + + align:start position:0% +few tricks but once you do it it works + + + align:start position:0% +few tricks but once you do it it works +well so so they're reasonably high + + align:start position:0% +well so so they're reasonably high + + + align:start position:0% +well so so they're reasonably high +performing tools they can sit down and + + align:start position:0% +performing tools they can sit down and + + + align:start position:0% +performing tools they can sit down and +do much of the design work we do is sort + + align:start position:0% +do much of the design work we do is sort + + + align:start position:0% +do much of the design work we do is sort +of a design driven learning where we're + + align:start position:0% +of a design driven learning where we're + + + align:start position:0% +of a design driven learning where we're +actively trying to get them to build + + align:start position:0% +actively trying to get them to build + + + align:start position:0% +actively trying to get them to build +something that we've described and we + + align:start position:0% +something that we've described and we + + + align:start position:0% +something that we've described and we +may have even told them in quite some + + align:start position:0% +may have even told them in quite some + + + align:start position:0% +may have even told them in quite some +detail how it fits together but there's + + align:start position:0% +detail how it fits together but there's + + + align:start position:0% +detail how it fits together but there's +something about you know the old muscle + + align:start position:0% +something about you know the old muscle + + + align:start position:0% +something about you know the old muscle +memory bit about you know if you + + align:start position:0% +memory bit about you know if you + + + align:start position:0% +memory bit about you know if you +actually build it yourself you know drag + + align:start position:0% +actually build it yourself you know drag + + + align:start position:0% +actually build it yourself you know drag +the components on and wire them up + + align:start position:0% +the components on and wire them up + + + align:start position:0% +the components on and wire them up +you'll lack you know you'll you'll + + align:start position:0% +you'll lack you know you'll you'll + + + align:start position:0% +you'll lack you know you'll you'll +remember it much better or you'll ask + + align:start position:0% +remember it much better or you'll ask + + + align:start position:0% +remember it much better or you'll ask +you ask yourself wait does this go here + + align:start position:0% +you ask yourself wait does this go here + + + align:start position:0% +you ask yourself wait does this go here +or here and then you say then you look + + align:start position:0% +or here and then you say then you look + + + align:start position:0% +or here and then you say then you look +back and you're starting say I'm really + + align:start position:0% +back and you're starting say I'm really + + + align:start position:0% +back and you're starting say I'm really +looking at this diagnose the + + align:start position:0% +looking at this diagnose the + + + align:start position:0% +looking at this diagnose the +instructions for the first time with + + align:start position:0% +instructions for the first time with + + + align:start position:0% +instructions for the first time with +enough care to appreciate that oh I have + + align:start position:0% +enough care to appreciate that oh I have + + + align:start position:0% +enough care to appreciate that oh I have +to put it this way in order for it to + + align:start position:0% +to put it this way in order for it to + + + align:start position:0% +to put it this way in order for it to +work and so we're sort of you know hand + + align:start position:0% +work and so we're sort of you know hand + + + align:start position:0% +work and so we're sort of you know hand +and eye you know or engaged if not just + + align:start position:0% +and eye you know or engaged if not just + + + align:start position:0% +and eye you know or engaged if not just +a listening experience we were able to + + align:start position:0% +a listening experience we were able to + + + align:start position:0% +a listening experience we were able to +if you assemble something we rebuild + + align:start position:0% +if you assemble something we rebuild + + + align:start position:0% +if you assemble something we rebuild +test to see if it functions correctly + + align:start position:0% +test to see if it functions correctly + + + align:start position:0% +test to see if it functions correctly +and so you can tell right away whether + + align:start position:0% +and so you can tell right away whether + + + align:start position:0% +and so you can tell right away whether +you've screwed it up it's not like why + + align:start position:0% +you've screwed it up it's not like why + + + align:start position:0% +you've screwed it up it's not like why +turn it in and a week later long past + + align:start position:0% +turn it in and a week later long past + + + align:start position:0% +turn it in and a week later long past +when I've ceased to care I get back a + + align:start position:0% +when I've ceased to care I get back a + + + align:start position:0% +when I've ceased to care I get back a +red X and I say okay well dang so here + + align:start position:0% +red X and I say okay well dang so here + + + align:start position:0% +red X and I say okay well dang so here +they have to get it right in order to + + align:start position:0% +they have to get it right in order to + + + align:start position:0% +they have to get it right in order to +complete it but we tell them right away + + align:start position:0% +complete it but we tell them right away + + + align:start position:0% +complete it but we tell them right away +that it's not right and they keep + + align:start position:0% +that it's not right and they keep + + + align:start position:0% +that it's not right and they keep +working on it or they post on Piazza my + + align:start position:0% +working on it or they post on Piazza my + + + align:start position:0% +working on it or they post on Piazza my +circuit doesn't work we can the staff + + align:start position:0% +circuit doesn't work we can the staff + + + align:start position:0% +circuit doesn't work we can the staff +can pull it up remotely from the server + + align:start position:0% +can pull it up remotely from the server + + + align:start position:0% +can pull it up remotely from the server +and say + + align:start position:0% +and say + + + align:start position:0% +and say +here's where here's your mistake so the + + align:start position:0% +here's where here's your mistake so the + + + align:start position:0% +here's where here's your mistake so the +idea is that the students are actually + + align:start position:0% +idea is that the students are actually + + + align:start position:0% +idea is that the students are actually +being engineers this may be their one of + + align:start position:0% +being engineers this may be their one of + + + align:start position:0% +being engineers this may be their one of +the first actual you know build it + + align:start position:0% +the first actual you know build it + + + align:start position:0% +the first actual you know build it +experiences they have a good mind these + + align:start position:0% +experiences they have a good mind these + + + align:start position:0% +experiences they have a good mind these +are sophomores right so so it's a little + + align:start position:0% +are sophomores right so so it's a little + + + align:start position:0% +are sophomores right so so it's a little +bit of fun to you know say well this is + + align:start position:0% +bit of fun to you know say well this is + + + align:start position:0% +bit of fun to you know say well this is +sort of neat I I you know I've actually + + align:start position:0% +sort of neat I I you know I've actually + + + align:start position:0% +sort of neat I I you know I've actually +put together the circuit and debugged it + + align:start position:0% +put together the circuit and debugged it + + + align:start position:0% +put together the circuit and debugged it +I mean and so I had to say well what was + + align:start position:0% +I mean and so I had to say well what was + + + align:start position:0% +I mean and so I had to say well what was +wrong I got any the wrong thing what did + + align:start position:0% +wrong I got any the wrong thing what did + + + align:start position:0% +wrong I got any the wrong thing what did +I do wrong and then fix it so that's a + + align:start position:0% +I do wrong and then fix it so that's a + + + align:start position:0% +I do wrong and then fix it so that's a +very valuable experience so it's one + + align:start position:0% +very valuable experience so it's one + + + align:start position:0% +very valuable experience so it's one +thing it's like the late-night-tv + + align:start position:0% +thing it's like the late-night-tv + + + align:start position:0% +thing it's like the late-night-tv +salesman right when you watch them use + + align:start position:0% +salesman right when you watch them use + + + align:start position:0% +salesman right when you watch them use +it as so but you get the digit widget + + align:start position:0% +it as so but you get the digit widget + + + align:start position:0% +it as so but you get the digit widget +home and it doesn't work and so that's + + align:start position:0% +home and it doesn't work and so that's + + + align:start position:0% +home and it doesn't work and so that's +it I've seen it in lecture they've seen + + align:start position:0% +it I've seen it in lecture they've seen + + + align:start position:0% +it I've seen it in lecture they've seen +it on the videos they've seen it in + + align:start position:0% +it on the videos they've seen it in + + + align:start position:0% +it on the videos they've seen it in +worked examples and it's all extremely + + align:start position:0% +worked examples and it's all extremely + + + align:start position:0% +worked examples and it's all extremely +obvious that this is straightforward + + align:start position:0% +obvious that this is straightforward + + + align:start position:0% +obvious that this is straightforward +until you do it yourself and then you + + align:start position:0% +until you do it yourself and then you + + + align:start position:0% +until you do it yourself and then you +fill in all the pieces that you know you + + align:start position:0% +fill in all the pieces that you know you + + + align:start position:0% +fill in all the pieces that you know you +were just being oh how hard could that + + align:start position:0% +were just being oh how hard could that + + + align:start position:0% +were just being oh how hard could that +be oh now I know so they work hard at + + align:start position:0% +be oh now I know so they work hard at + + + align:start position:0% +be oh now I know so they work hard at +trying to fix that so but I think the + + align:start position:0% +trying to fix that so but I think the + + + align:start position:0% +trying to fix that so but I think the +whole idea of these virtual lab benches + + align:start position:0% +whole idea of these virtual lab benches + + + align:start position:0% +whole idea of these virtual lab benches +is is great as I said the execution + + align:start position:0% +is is great as I said the execution + + + align:start position:0% +is is great as I said the execution +environment and the graphics environment + + align:start position:0% +environment and the graphics environment + + + align:start position:0% +environment and the graphics environment +on the browser is first-rate it's very + + align:start position:0% +on the browser is first-rate it's very + + + align:start position:0% +on the browser is first-rate it's very +easy to build sophisticated tools that + + align:start position:0% +easy to build sophisticated tools that + + + align:start position:0% +easy to build sophisticated tools that +use you know reasonably complex + + align:start position:0% +use you know reasonably complex + + + align:start position:0% +use you know reasonably complex +calculations in the background and have + + align:start position:0% +calculations in the background and have + + + align:start position:0% +calculations in the background and have +a really great music interface and the + + align:start position:0% +a really great music interface and the + + + align:start position:0% +a really great music interface and the +browser is portable so you know 20 years + + align:start position:0% +browser is portable so you know 20 years + + + align:start position:0% +browser is portable so you know 20 years +ago I gave you software to download on + + align:start position:0% +ago I gave you software to download on + + + align:start position:0% +ago I gave you software to download on +your computer to do this stuff + + align:start position:0% +your computer to do this stuff + + + align:start position:0% +your computer to do this stuff +you know when mind that was everybody's + + align:start position:0% +you know when mind that was everybody's + + + align:start position:0% +you know when mind that was everybody's +environment was a little different oh + + align:start position:0% +environment was a little different oh + + + align:start position:0% +environment was a little different oh +you don't have the latest version of + + align:start position:0% +you don't have the latest version of + + + align:start position:0% +you don't have the latest version of +that library well you can't run this but + + align:start position:0% +that library well you can't run this but + + + align:start position:0% +that library well you can't run this but +if you update your library you can't run + + align:start position:0% +if you update your library you can't run + + + align:start position:0% +if you update your library you can't run +that and it was it was really a + + align:start position:0% +that and it was it was really a + + + align:start position:0% +that and it was it was really a +nightmare so you know packaging means + + align:start position:0% +nightmare so you know packaging means + + + align:start position:0% +nightmare so you know packaging means +packaging up these lab experiences in a + + align:start position:0% +packaging up these lab experiences in a + + + align:start position:0% +packaging up these lab experiences in a +way that they can be used by people + + align:start position:0% +way that they can be used by people + + + align:start position:0% +way that they can be used by people +around the world + + align:start position:0% +around the world + + + align:start position:0% +around the world +you know I so here I was I was writing + + align:start position:0% +you know I so here I was I was writing + + + align:start position:0% +you know I so here I was I was writing +on the Hong Kong subway and some young + + align:start position:0% +on the Hong Kong subway and some young + + + align:start position:0% +on the Hong Kong subway and some young +adult comes up to me and says I took + + align:start position:0% +adult comes up to me and says I took + + + align:start position:0% +adult comes up to me and says I took +your MITx course me and I really love + + align:start position:0% +your MITx course me and I really love + + + align:start position:0% +your MITx course me and I really love +doing the circuit stuff and I didn't + + align:start position:0% +doing the circuit stuff and I didn't + + + align:start position:0% +doing the circuit stuff and I didn't +have to down + + align:start position:0% +have to down + + + align:start position:0% +have to down +load anything and I'm sort of going wow + + align:start position:0% +load anything and I'm sort of going wow + + + align:start position:0% +load anything and I'm sort of going wow +I mean this is you know it is + + align:start position:0% +I mean this is you know it is + + + align:start position:0% +I mean this is you know it is +interesting to be stopped by people + + align:start position:0% +interesting to be stopped by people + + + align:start position:0% +interesting to be stopped by people +right and you know they start talking + + align:start position:0% +right and you know they start talking + + + align:start position:0% +right and you know they start talking +about how this was more than just a + + align:start position:0% +about how this was more than just a + + + align:start position:0% +about how this was more than just a +listening experience so these virtual + + align:start position:0% +listening experience so these virtual + + + align:start position:0% +listening experience so these virtual +labs are actually go from you know being + + align:start position:0% +labs are actually go from you know being + + + align:start position:0% +labs are actually go from you know being +something that I mean it takes courses + + align:start position:0% +something that I mean it takes courses + + + align:start position:0% +something that I mean it takes courses +from being a listening experience with + + align:start position:0% +from being a listening experience with + + + align:start position:0% +from being a listening experience with +maybe some pencil p-sets + + align:start position:0% +maybe some pencil p-sets + + + align:start position:0% +maybe some pencil p-sets +to you know your your your hands are + + align:start position:0% +to you know your your your hands are + + + align:start position:0% +to you know your your your hands are +active so you know hands on brain on + + align:start position:0% +active so you know hands on brain on + + + align:start position:0% +active so you know hands on brain on +right and what people reins turn on is + + align:start position:0% +right and what people reins turn on is + + + align:start position:0% +right and what people reins turn on is +amazing what they they they remember it + + align:start position:0% +amazing what they they they remember it + + + align:start position:0% +amazing what they they they remember it +right it so so what kind of challenges + + align:start position:0% +right it so so what kind of challenges + + + align:start position:0% +right it so so what kind of challenges +do students encounter when they're + + align:start position:0% +do students encounter when they're + + + align:start position:0% +do students encounter when they're +trying their hand at being engineers for + + align:start position:0% +trying their hand at being engineers for + + + align:start position:0% +trying their hand at being engineers for +the first time and is there anything + + align:start position:0% +the first time and is there anything + + + align:start position:0% +the first time and is there anything +that tends to pop up again and again um + + align:start position:0% +that tends to pop up again and again um + + + align:start position:0% +that tends to pop up again and again um +so I think you know a lot of this is + + align:start position:0% +so I think you know a lot of this is + + + align:start position:0% +so I think you know a lot of this is +sort of confidence so you know people + + align:start position:0% +sort of confidence so you know people + + + align:start position:0% +sort of confidence so you know people +sometimes the students come to me and + + align:start position:0% +sometimes the students come to me and + + + align:start position:0% +sometimes the students come to me and +say I want to make this work and I said + + align:start position:0% +say I want to make this work and I said + + + align:start position:0% +say I want to make this work and I said +okay your desire let's fix it and I go + + align:start position:0% +okay your desire let's fix it and I go + + + align:start position:0% +okay your desire let's fix it and I go +through and we you know I keep my hands + + align:start position:0% +through and we you know I keep my hands + + + align:start position:0% +through and we you know I keep my hands +in my pockets and let them do the fixing + + align:start position:0% +in my pockets and let them do the fixing + + + align:start position:0% +in my pockets and let them do the fixing +but I say have you thought about this if + + align:start position:0% +but I say have you thought about this if + + + align:start position:0% +but I say have you thought about this if +this works and that doesn't what does + + align:start position:0% +this works and that doesn't what does + + + align:start position:0% +this works and that doesn't what does +that tell you right and so a lot of + + align:start position:0% +that tell you right and so a lot of + + + align:start position:0% +that tell you right and so a lot of +students aren't very good at taking the + + align:start position:0% +students aren't very good at taking the + + + align:start position:0% +students aren't very good at taking the +information they do know and using it to + + align:start position:0% +information they do know and using it to + + + align:start position:0% +information they do know and using it to +deduce the next thing to try or the next + + align:start position:0% +deduce the next thing to try or the next + + + align:start position:0% +deduce the next thing to try or the next +thing to test and narrow down where the + + align:start position:0% +thing to test and narrow down where the + + + align:start position:0% +thing to test and narrow down where the +problem is so there's a real is of + + align:start position:0% +problem is so there's a real is of + + + align:start position:0% +problem is so there's a real is of +learning something you have to learn how + + align:start position:0% +learning something you have to learn how + + + align:start position:0% +learning something you have to learn how +to do is to be organized about how takes + + align:start position:0% +to do is to be organized about how takes + + + align:start position:0% +to do is to be organized about how takes +taking something that isn't working and + + align:start position:0% +taking something that isn't working and + + + align:start position:0% +taking something that isn't working and +a complicated thing so parts of it are + + align:start position:0% +a complicated thing so parts of it are + + + align:start position:0% +a complicated thing so parts of it are +working but something isn't and trying + + align:start position:0% +working but something isn't and trying + + + align:start position:0% +working but something isn't and trying +to work back from both ends to somewhere + + align:start position:0% +to work back from both ends to somewhere + + + align:start position:0% +to work back from both ends to somewhere +in the middle it doesn't work and so + + align:start position:0% +in the middle it doesn't work and so + + + align:start position:0% +in the middle it doesn't work and so +that's a skill that you have to practice + + align:start position:0% +that's a skill that you have to practice + + + align:start position:0% +that's a skill that you have to practice +for awhile and so I you know I try to + + align:start position:0% +for awhile and so I you know I try to + + + align:start position:0% +for awhile and so I you know I try to +help with that skill I have a lot of + + align:start position:0% +help with that skill I have a lot of + + + align:start position:0% +help with that skill I have a lot of +confidence that will work most students + + align:start position:0% +confidence that will work most students + + + align:start position:0% +confidence that will work most students +are pretty convinced that you know + + align:start position:0% +are pretty convinced that you know + + + align:start position:0% +are pretty convinced that you know +either the simulator is broken or is + + align:start position:0% +either the simulator is broken or is + + + align:start position:0% +either the simulator is broken or is +hopeless and so they're somewhat + + align:start position:0% +hopeless and so they're somewhat + + + align:start position:0% +hopeless and so they're somewhat +surprised to realize that there's a + + align:start position:0% +surprised to realize that there's a + + + align:start position:0% +surprised to realize that there's a +systematic way to make something that + + align:start position:0% +systematic way to make something that + + + align:start position:0% +systematic way to make something that +works + + align:start position:0% +works + + + align:start position:0% +works +once they was they are convinced that + + align:start position:0% +once they was they are convinced that + + + align:start position:0% +once they was they are convinced that +that's actually true they start getting + + align:start position:0% +that's actually true they start getting + + + align:start position:0% +that's actually true they start getting +more confident that it doesn't work now + + align:start position:0% +more confident that it doesn't work now + + + align:start position:0% +more confident that it doesn't work now +but I'll just work one up for ten + + align:start position:0% +but I'll just work one up for ten + + + align:start position:0% +but I'll just work one up for ten +minutes and I'm sure it will + + align:start position:0% +minutes and I'm sure it will + + + align:start position:0% +minutes and I'm sure it will +as opposed just saying oh the only thing + + align:start position:0% +as opposed just saying oh the only thing + + + align:start position:0% +as opposed just saying oh the only thing +I can do is to raise my hand and say + + align:start position:0% +I can do is to raise my hand and say + + + align:start position:0% +I can do is to raise my hand and say +could you help me because it isn't + + align:start position:0% +could you help me because it isn't + + + align:start position:0% +could you help me because it isn't +working + + align:start position:0% +working + + + align:start position:0% +working +so we try to get the students out of you + + align:start position:0% +so we try to get the students out of you + + + align:start position:0% +so we try to get the students out of you +know look your job is to actually make + + align:start position:0% +know look your job is to actually make + + + align:start position:0% +know look your job is to actually make +it work not to merely ask us to come + + align:start position:0% +it work not to merely ask us to come + + + align:start position:0% +it work not to merely ask us to come +over and watch us make it work and some + + align:start position:0% +over and watch us make it work and some + + + align:start position:0% +over and watch us make it work and some +students make that transition so it's + + align:start position:0% +students make that transition so it's + + + align:start position:0% +students make that transition so it's +the course so it seems like a learning + + align:start position:0% +the course so it seems like a learning + + + align:start position:0% +the course so it seems like a learning +goal in the course is not only learning + + align:start position:0% +goal in the course is not only learning + + + align:start position:0% +goal in the course is not only learning +the architecture of digital systems but + + align:start position:0% +the architecture of digital systems but + + + align:start position:0% +the architecture of digital systems but +also developing professional + + align:start position:0% +also developing professional + + + align:start position:0% +also developing professional +competencies in the sense of attitudes + + align:start position:0% +competencies in the sense of attitudes + + + align:start position:0% +competencies in the sense of attitudes +that engineers embrace and there's a + + align:start position:0% +that engineers embrace and there's a + + + align:start position:0% +that engineers embrace and there's a +bunch of processes that you have and the + + align:start position:0% +bunch of processes that you have and the + + + align:start position:0% +bunch of processes that you have and the +same thing is true of all learning + + align:start position:0% +same thing is true of all learning + + + align:start position:0% +same thing is true of all learning +you're learning how to learn is + + align:start position:0% +you're learning how to learn is + + + align:start position:0% +you're learning how to learn is +something that sophomores are still + + align:start position:0% +something that sophomores are still + + + align:start position:0% +something that sophomores are still +doing right and so this is probably the + + align:start position:0% +doing right and so this is probably the + + + align:start position:0% +doing right and so this is probably the +first time that they've been sort of + + align:start position:0% +first time that they've been sort of + + + align:start position:0% +first time that they've been sort of +thrown into the deep end we try to have + + align:start position:0% +thrown into the deep end we try to have + + + align:start position:0% +thrown into the deep end we try to have +lots of Life Guards standing by but + + align:start position:0% +lots of Life Guards standing by but + + + align:start position:0% +lots of Life Guards standing by but +we're prepared to do more than just you + + align:start position:0% +we're prepared to do more than just you + + + align:start position:0% +we're prepared to do more than just you +know check off on our clipboard sink or + + align:start position:0% +know check off on our clipboard sink or + + + align:start position:0% +know check off on our clipboard sink or +swim + + align:start position:0% +swim + + + align:start position:0% +swim +I mean we're you're not ready to dive in + + align:start position:0% +I mean we're you're not ready to dive in + + + align:start position:0% +I mean we're you're not ready to dive in +and say okay try this try that but + + align:start position:0% +and say okay try this try that but + + + align:start position:0% +and say okay try this try that but +actually pretty helpful to you know have + + align:start position:0% +actually pretty helpful to you know have + + + align:start position:0% +actually pretty helpful to you know have +an experience like this after your + + align:start position:0% +an experience like this after your + + + align:start position:0% +an experience like this after your +freshman year which has a lot of + + align:start position:0% +freshman year which has a lot of + + + align:start position:0% +freshman year which has a lot of +training wheels but before your + + align:start position:0% +training wheels but before your + + + align:start position:0% +training wheels but before your +upper-level classes where you know the + + align:start position:0% +upper-level classes where you know the + + + align:start position:0% +upper-level classes where you know the +training you know the help is a little + + align:start position:0% +training you know the help is a little + + + align:start position:0% +training you know the help is a little +thin I mean one of the great things + + align:start position:0% +thin I mean one of the great things + + + align:start position:0% +thin I mean one of the great things +about double-o forests that half the + + align:start position:0% +about double-o forests that half the + + + align:start position:0% +about double-o forests that half the +people on your hall have taken this + + align:start position:0% +people on your hall have taken this + + + align:start position:0% +people on your hall have taken this +course and so even though we have our + + align:start position:0% +course and so even though we have our + + + align:start position:0% +course and so even though we have our +course staff you can go down your hall + + align:start position:0% +course staff you can go down your hall + + + align:start position:0% +course staff you can go down your hall +and as I say every other person will say + + align:start position:0% +and as I say every other person will say + + + align:start position:0% +and as I say every other person will say +oh I took the course yeah I did + + align:start position:0% +oh I took the course yeah I did + + + align:start position:0% +oh I took the course yeah I did +so there's actually an enormous you know + + align:start position:0% +so there's actually an enormous you know + + + align:start position:0% +so there's actually an enormous you know +body of knowledge about the material and + + align:start position:0% +body of knowledge about the material and + + + align:start position:0% +body of knowledge about the material and +things like that so it's you know not + + align:start position:0% +things like that so it's you know not + + + align:start position:0% +things like that so it's you know not +many courses have that opportunity but + + align:start position:0% +many courses have that opportunity but + + + align:start position:0% +many courses have that opportunity but +we take great advantage of it so there's + + align:start position:0% +we take great advantage of it so there's + + + align:start position:0% +we take great advantage of it so there's +a lot of sort of you know hallway + + align:start position:0% +a lot of sort of you know hallway + + + align:start position:0% +a lot of sort of you know hallway +learning pure learning that happens + + align:start position:0% +learning pure learning that happens + + + align:start position:0% +learning pure learning that happens +outside of the sort of structured + + align:start position:0% +outside of the sort of structured + + + align:start position:0% +outside of the sort of structured +learning + + align:start position:0% +learning + + + align:start position:0% +learning +glass that's fascinating it kind of + + align:start position:0% +glass that's fascinating it kind of + + + align:start position:0% +glass that's fascinating it kind of +speaks to the importance of having + + align:start position:0% +speaks to the importance of having + + + align:start position:0% +speaks to the importance of having +common learning experiences at the + + align:start position:0% +common learning experiences at the + + + align:start position:0% +common learning experiences at the +undergraduate level just to facilitate + + align:start position:0% +undergraduate level just to facilitate + + + align:start position:0% +undergraduate level just to facilitate +that sort of like you said hallway + + align:start position:0% +that sort of like you said hallway + + + align:start position:0% +that sort of like you said hallway +learning it's really interesting well + + align:start position:0% +learning it's really interesting well + + + align:start position:0% +learning it's really interesting well +plus you know students often you know + + align:start position:0% +plus you know students often you know + + + align:start position:0% +plus you know students often you know +during the day it's hectic distracting + + align:start position:0% +during the day it's hectic distracting + + + align:start position:0% +during the day it's hectic distracting +to come to lecture they have lots of + + align:start position:0% +to come to lecture they have lots of + + + align:start position:0% +to come to lecture they have lots of +things in their minds so you know mostly + + align:start position:0% +things in their minds so you know mostly + + + align:start position:0% +things in their minds so you know mostly +it's being the quiet of the room then + + align:start position:0% +it's being the quiet of the room then + + + align:start position:0% +it's being the quiet of the room then +they probably intellectually really + + align:start position:0% +they probably intellectually really + + + align:start position:0% +they probably intellectually really +grapple with the material so first of + + align:start position:0% +grapple with the material so first of + + + align:start position:0% +grapple with the material so first of +all giving them things to grapple with + + align:start position:0% +all giving them things to grapple with + + + align:start position:0% +all giving them things to grapple with +is good but then making sure they're + + align:start position:0% +is good but then making sure they're + + + align:start position:0% +is good but then making sure they're +supported either through peers or + + align:start position:0% +supported either through peers or + + + align:start position:0% +supported either through peers or +through the Piazza forum when they're + + align:start position:0% +through the Piazza forum when they're + + + align:start position:0% +through the Piazza forum when they're +outside of the sort of structured help + + align:start position:0% +outside of the sort of structured help + + + align:start position:0% +outside of the sort of structured help +we provide + + align:start position:0% +we provide + + + align:start position:0% +we provide +it's really I think changed how the + + align:start position:0% +it's really I think changed how the + + + align:start position:0% +it's really I think changed how the +students consume the course and so it's + + align:start position:0% +students consume the course and so it's + + + align:start position:0% +students consume the course and so it's +you know you know the lecture attendance + + align:start position:0% +you know you know the lecture attendance + + + align:start position:0% +you know you know the lecture attendance +is modest but a lot of people being very + + align:start position:0% +is modest but a lot of people being very + + + align:start position:0% +is modest but a lot of people being very +well on the learning the material on the + + align:start position:0% +well on the learning the material on the + + + align:start position:0% +well on the learning the material on the +assessments right I mean I think that + + align:start position:0% +assessments right I mean I think that + + + align:start position:0% +assessments right I mean I think that +speaks to what you talked about earlier + + align:start position:0% +speaks to what you talked about earlier + + + align:start position:0% +speaks to what you talked about earlier +and that you offer a buffet of ways to + + align:start position:0% +and that you offer a buffet of ways to + + + align:start position:0% +and that you offer a buffet of ways to +learn and so people who come to the + + align:start position:0% +learn and so people who come to the + + + align:start position:0% +learn and so people who come to the +lectures are the people who learn best + + align:start position:0% +lectures are the people who learn best + + + align:start position:0% +lectures are the people who learn best +through that format + + align:start position:0% +through that format + + + align:start position:0% +through that format +right and some people I never see except + + align:start position:0% +right and some people I never see except + + + align:start position:0% +right and some people I never see except +occasionally they'll come out me and + + align:start position:0% +occasionally they'll come out me and + + + align:start position:0% +occasionally they'll come out me and +when I have lab hours they'll come by + + align:start position:0% +when I have lab hours they'll come by + + + align:start position:0% +when I have lab hours they'll come by +because they just want to chitchat right + + align:start position:0% +because they just want to chitchat right + + + align:start position:0% +because they just want to chitchat right +hey we have one of the activities you do + + align:start position:0% +hey we have one of the activities you do + + + align:start position:0% +hey we have one of the activities you do +after you do the design we have a + + align:start position:0% +after you do the design we have a + + + align:start position:0% +after you do the design we have a +checkoff so you have to come and sort of + + align:start position:0% +checkoff so you have to come and sort of + + + align:start position:0% +checkoff so you have to come and sort of +explain your design partly that's just + + align:start position:0% +explain your design partly that's just + + + align:start position:0% +explain your design partly that's just +to make sure that maybe you actually did + + align:start position:0% +to make sure that maybe you actually did + + + align:start position:0% +to make sure that maybe you actually did +the design instead of your friend down + + align:start position:0% +the design instead of your friend down + + + align:start position:0% +the design instead of your friend down +the hall and so at the very least we + + align:start position:0% +the hall and so at the very least we + + + align:start position:0% +the hall and so at the very least we +want them to understand the design that + + align:start position:0% +want them to understand the design that + + + align:start position:0% +want them to understand the design that +they claim they have done but for people + + align:start position:0% +they claim they have done but for people + + + align:start position:0% +they claim they have done but for people +who have worked hard on it as an + + align:start position:0% +who have worked hard on it as an + + + align:start position:0% +who have worked hard on it as an +operative to come by and show it off and + + align:start position:0% +operative to come by and show it off and + + + align:start position:0% +operative to come by and show it off and +so you know there is they're proud of + + align:start position:0% +so you know there is they're proud of + + + align:start position:0% +so you know there is they're proud of +their baby + + align:start position:0% +their baby + + + align:start position:0% +their baby +right I mean they particularly towards + + align:start position:0% +right I mean they particularly towards + + + align:start position:0% +right I mean they particularly towards +the end of the course when we have a + + align:start position:0% +the end of the course when we have a + + + align:start position:0% +the end of the course when we have a +fairly complex design project which is + + align:start position:0% +fairly complex design project which is + + + align:start position:0% +fairly complex design project which is +actually very hard to get very high + + align:start position:0% +actually very hard to get very high + + + align:start position:0% +actually very hard to get very high +marks on I mean you have to + + align:start position:0% +marks on I mean you have to + + + align:start position:0% +marks on I mean you have to +really good and so it's an amazing + + align:start position:0% +really good and so it's an amazing + + + align:start position:0% +really good and so it's an amazing +number of people who tackle that and + + align:start position:0% +number of people who tackle that and + + + align:start position:0% +number of people who tackle that and +they really they come in and say okay + + align:start position:0% +they really they come in and say okay + + + align:start position:0% +they really they come in and say okay +I'm stuck here give me some ideas what + + align:start position:0% +I'm stuck here give me some ideas what + + + align:start position:0% +I'm stuck here give me some ideas what +to try next and if you dare try to say + + align:start position:0% +to try next and if you dare try to say + + + align:start position:0% +to try next and if you dare try to say +well you know just do this you know + + align:start position:0% +well you know just do this you know + + + align:start position:0% +well you know just do this you know +they're I don't want the answer I want + + align:start position:0% +they're I don't want the answer I want + + + align:start position:0% +they're I don't want the answer I want +you to I'm having fun here so I'm gonna + + align:start position:0% +you to I'm having fun here so I'm gonna + + + align:start position:0% +you to I'm having fun here so I'm gonna +take away the fun part + + align:start position:0% +take away the fun part + + + align:start position:0% +take away the fun part +I want to puzzle out myself I just need + + align:start position:0% +I want to puzzle out myself I just need + + + align:start position:0% +I want to puzzle out myself I just need +some hints as to where my puzzle ershon + + align:start position:0% +some hints as to where my puzzle ershon + + + align:start position:0% +some hints as to where my puzzle ershon +should be focusing me so the fun is in + + align:start position:0% +should be focusing me so the fun is in + + + align:start position:0% +should be focusing me so the fun is in +the puzzle it is it is and they're doing + + align:start position:0% +the puzzle it is it is and they're doing + + + align:start position:0% +the puzzle it is it is and they're doing +of it so it and I think that's great + + align:start position:0% +of it so it and I think that's great + + + align:start position:0% +of it so it and I think that's great +because when students first come they + + align:start position:0% +because when students first come they + + + align:start position:0% +because when students first come they +tend to be focusing on the answers you + + align:start position:0% +tend to be focusing on the answers you + + + align:start position:0% +tend to be focusing on the answers you +know here you give me a bunch of + + align:start position:0% +know here you give me a bunch of + + + align:start position:0% +know here you give me a bunch of +worksheet full of questions so I looked + + align:start position:0% +worksheet full of questions so I looked + + + align:start position:0% +worksheet full of questions so I looked +at the answers I think I'm good to go I + + align:start position:0% +at the answers I think I'm good to go I + + + align:start position:0% +at the answers I think I'm good to go I +say no the worksheets aren't because we + + align:start position:0% +say no the worksheets aren't because we + + + align:start position:0% +say no the worksheets aren't because we +want you to know the answers to those + + align:start position:0% +want you to know the answers to those + + + align:start position:0% +want you to know the answers to those +questions the worksheets are helping you + + align:start position:0% +questions the worksheets are helping you + + + align:start position:0% +questions the worksheets are helping you +diagnose whether you understand things + + align:start position:0% +diagnose whether you understand things + + + align:start position:0% +diagnose whether you understand things +so the best thing you can happen to the + + align:start position:0% +so the best thing you can happen to the + + + align:start position:0% +so the best thing you can happen to the +worksheet is I don't know how to do this + + align:start position:0% +worksheet is I don't know how to do this + + + align:start position:0% +worksheet is I don't know how to do this +problem and so I should go figure out + + align:start position:0% +problem and so I should go figure out + + + align:start position:0% +problem and so I should go figure out +how to do it so it's you know if you're + + align:start position:0% +how to do it so it's you know if you're + + + align:start position:0% +how to do it so it's you know if you're +doing this self-paced mastery learning + + align:start position:0% +doing this self-paced mastery learning + + + align:start position:0% +doing this self-paced mastery learning +stick which is sort of how we try to + + align:start position:0% +stick which is sort of how we try to + + + align:start position:0% +stick which is sort of how we try to +help students you know become master the + + align:start position:0% +help students you know become master the + + + align:start position:0% +help students you know become master the +material at their own at their own pace + + align:start position:0% +material at their own at their own pace + + + align:start position:0% +material at their own at their own pace +you know whenever they want to so we + + align:start position:0% +you know whenever they want to so we + + + align:start position:0% +you know whenever they want to so we +have to provide a lot of self + + align:start position:0% +have to provide a lot of self + + + align:start position:0% +have to provide a lot of self +assessments they have to use them as + + align:start position:0% +assessments they have to use them as + + + align:start position:0% +assessments they have to use them as +assessments though they don't use them + + align:start position:0% +assessments though they don't use them + + + align:start position:0% +assessments though they don't use them +as assessments over there to say oh the + + align:start position:0% +as assessments over there to say oh the + + + align:start position:0% +as assessments over there to say oh the +answers three to this question and I + + align:start position:0% +answers three to this question and I + + + align:start position:0% +answers three to this question and I +hope they ask this one on the quiz + + align:start position:0% +hope they ask this one on the quiz + + + align:start position:0% +hope they ask this one on the quiz +they're not getting it so you know + + align:start position:0% +they're not getting it so you know + + + align:start position:0% +they're not getting it so you know +getting students to stop focusing on the + + align:start position:0% +getting students to stop focusing on the + + + align:start position:0% +getting students to stop focusing on the +answers and really focus on what or how + + align:start position:0% +answers and really focus on what or how + + + align:start position:0% +answers and really focus on what or how +do i tackle this sort of problem or you + + align:start position:0% +do i tackle this sort of problem or you + + + align:start position:0% +do i tackle this sort of problem or you +know of all the things i know how to do + + align:start position:0% +know of all the things i know how to do + + + align:start position:0% +know of all the things i know how to do +i first have to select the appropriate + + align:start position:0% +i first have to select the appropriate + + + align:start position:0% +i first have to select the appropriate +concept or skill and then i have to know + + align:start position:0% +concept or skill and then i have to know + + + align:start position:0% +concept or skill and then i have to know +how to apply it it's sort of neat to + + align:start position:0% +how to apply it it's sort of neat to + + + align:start position:0% +how to apply it it's sort of neat to +watch them make the transition from + + align:start position:0% +watch them make the transition from + + + align:start position:0% +watch them make the transition from +coming in and sort of answer focused to + + align:start position:0% +coming in and sort of answer focused to + + + align:start position:0% +coming in and sort of answer focused to +leaving sort of like okay you can ask me + + align:start position:0% +leaving sort of like okay you can ask me + + + align:start position:0% +leaving sort of like okay you can ask me +anything because i actually know how to + + align:start position:0% +anything because i actually know how to + + + align:start position:0% +anything because i actually know how to +do things I mean from scratch not not + + align:start position:0% +do things I mean from scratch not not + + + align:start position:0% +do things I mean from scratch not not +because I you know just you could pick + + align:start position:0% +because I you know just you could pick + + + align:start position:0% +because I you know just you could pick +something + + align:start position:0% +something + + + align:start position:0% +something +I can not only recognize the right + + align:start position:0% +I can not only recognize the right + + + align:start position:0% +I can not only recognize the right +answer when I see it I can actually make + + align:start position:0% +answer when I see it I can actually make + + + align:start position:0% +answer when I see it I can actually make +right answers right that's a very but + + align:start position:0% +right answers right that's a very but + + + align:start position:0% +right answers right that's a very but +people feel empowered when they can do + + align:start position:0% +people feel empowered when they can do + + + align:start position:0% +people feel empowered when they can do +that and so um let's talk a bit about + + align:start position:0% +that and so um let's talk a bit about + + + align:start position:0% +that and so um let's talk a bit about +the future it seems like the course is + + align:start position:0% +the future it seems like the course is + + + align:start position:0% +the future it seems like the course is +finely tuned already but do you have + + align:start position:0% +finely tuned already but do you have + + + align:start position:0% +finely tuned already but do you have +ideas for how you might tweak it in the + + align:start position:0% +ideas for how you might tweak it in the + + + align:start position:0% +ideas for how you might tweak it in the +future well so I'm retiring No so it's + + align:start position:0% +future well so I'm retiring No so it's + + + align:start position:0% +future well so I'm retiring No so it's +being turned over to our new team some + + align:start position:0% +being turned over to our new team some + + + align:start position:0% +being turned over to our new team some +of the people who were part of the + + align:start position:0% +of the people who were part of the + + + align:start position:0% +of the people who were part of the +teaching cadre earlier or taking it over + + align:start position:0% +teaching cadre earlier or taking it over + + + align:start position:0% +teaching cadre earlier or taking it over +they of course have their own strong + + align:start position:0% +they of course have their own strong + + + align:start position:0% +they of course have their own strong +opinions about better ways of doing + + align:start position:0% +opinions about better ways of doing + + + align:start position:0% +opinions about better ways of doing +things so I think that you know the + + align:start position:0% +things so I think that you know the + + + align:start position:0% +things so I think that you know the +basic structure the course will be the + + align:start position:0% +basic structure the course will be the + + + align:start position:0% +basic structure the course will be the +same the basic list of topics that will + + align:start position:0% +same the basic list of topics that will + + + align:start position:0% +same the basic list of topics that will +be taught but they have a different sort + + align:start position:0% +be taught but they have a different sort + + + align:start position:0% +be taught but they have a different sort +of design experience in mind + + align:start position:0% +of design experience in mind + + + align:start position:0% +of design experience in mind +so they'll find their own way it's + + align:start position:0% +so they'll find their own way it's + + + align:start position:0% +so they'll find their own way it's +interesting to me because I think until + + align:start position:0% +interesting to me because I think until + + + align:start position:0% +interesting to me because I think until +you've taught a 300 person course you + + align:start position:0% +you've taught a 300 person course you + + + align:start position:0% +you've taught a 300 person course you +may not appreciate how things which work + + align:start position:0% +may not appreciate how things which work + + + align:start position:0% +may not appreciate how things which work +really well with you know two students + + align:start position:0% +really well with you know two students + + + align:start position:0% +really well with you know two students +in your office there are 10 students and + + align:start position:0% +in your office there are 10 students and + + + align:start position:0% +in your office there are 10 students and +a rest you know recitation doesn't + + align:start position:0% +a rest you know recitation doesn't + + + align:start position:0% +a rest you know recitation doesn't +really work for 300 students you know + + align:start position:0% +really work for 300 students you know + + + align:start position:0% +really work for 300 students you know +you suddenly say well they'll ask a + + align:start position:0% +you suddenly say well they'll ask a + + + align:start position:0% +you suddenly say well they'll ask a +question if they have one so I don't + + align:start position:0% +question if they have one so I don't + + + align:start position:0% +question if they have one so I don't +need to be too specific it's sort of + + align:start position:0% +need to be too specific it's sort of + + + align:start position:0% +need to be too specific it's sort of +interesting to say whoa you know 300 + + align:start position:0% +interesting to say whoa you know 300 + + + align:start position:0% +interesting to say whoa you know 300 +questions that's a lot of questions and + + align:start position:0% +questions that's a lot of questions and + + + align:start position:0% +questions that's a lot of questions and +three of them from every student so you + + align:start position:0% +three of them from every student so you + + + align:start position:0% +three of them from every student so you +have a thousand questions this week and + + align:start position:0% +have a thousand questions this week and + + + align:start position:0% +have a thousand questions this week and +so you start learning how you know + + align:start position:0% +so you start learning how you know + + + align:start position:0% +so you start learning how you know +carefully the materials have to be + + align:start position:0% +carefully the materials have to be + + + align:start position:0% +carefully the materials have to be +prepared in one of the questions you + + align:start position:0% +prepared in one of the questions you + + + align:start position:0% +prepared in one of the questions you +sent me you talked about you know + + align:start position:0% +sent me you talked about you know + + + align:start position:0% +sent me you talked about you know +engineering the materials and a big + + align:start position:0% +engineering the materials and a big + + + align:start position:0% +engineering the materials and a big +class has a real issue with engineering + + align:start position:0% +class has a real issue with engineering + + + align:start position:0% +class has a real issue with engineering +materials that you know will help you + + align:start position:0% +materials that you know will help you + + + align:start position:0% +materials that you know will help you +know get students and do the things you + + align:start position:0% +know get students and do the things you + + + align:start position:0% +know get students and do the things you +want them to do but you can't leave them + + align:start position:0% +want them to do but you can't leave them + + + align:start position:0% +want them to do but you can't leave them +adrift because you only have so much + + align:start position:0% +adrift because you only have so much + + + align:start position:0% +adrift because you only have so much +capacity to pull them all back to shore + + align:start position:0% +capacity to pull them all back to shore + + + align:start position:0% +capacity to pull them all back to shore +and so you really have to you know put + + align:start position:0% +and so you really have to you know put + + + align:start position:0% +and so you really have to you know put +most of what they need into the + + align:start position:0% +most of what they need into the + + + align:start position:0% +most of what they need into the +materials right can you say more about + + align:start position:0% +materials right can you say more about + + + align:start position:0% +materials right can you say more about +engineering the materials to keep + + align:start position:0% +engineering the materials to keep + + + align:start position:0% +engineering the materials to keep +everyone afloat well so it's an + + align:start position:0% +everyone afloat well so it's an + + + align:start position:0% +everyone afloat well so it's an +iterative process I mean you know people + + align:start position:0% +iterative process I mean you know people + + + align:start position:0% +iterative process I mean you know people +say wow double-o forums like clockwork + + align:start position:0% +say wow double-o forums like clockwork + + + align:start position:0% +say wow double-o forums like clockwork +this is the best organized course I've + + align:start position:0% +this is the best organized course I've + + + align:start position:0% +this is the best organized course I've +ever had and I say well you know + + align:start position:0% +ever had and I say well you know + + + align:start position:0% +ever had and I say well you know +20 years ago you wouldn't have said that + + align:start position:0% +20 years ago you wouldn't have said that + + + align:start position:0% +20 years ago you wouldn't have said that +you know you know we've had our share of + + align:start position:0% +you know you know we've had our share of + + + align:start position:0% +you know you know we've had our share of +unfortunate assignments or undoable + + align:start position:0% +unfortunate assignments or undoable + + + align:start position:0% +unfortunate assignments or undoable +assignments or assignments that were you + + align:start position:0% +assignments or assignments that were you + + + align:start position:0% +assignments or assignments that were you +know that's too hard for some students + + align:start position:0% +know that's too hard for some students + + + align:start position:0% +know that's too hard for some students +are too easy for everybody and so you + + align:start position:0% +are too easy for everybody and so you + + + align:start position:0% +are too easy for everybody and so you +know yes we do that we we try to get + + align:start position:0% +know yes we do that we we try to get + + + align:start position:0% +know yes we do that we we try to get +student feedback the forum is actually + + align:start position:0% +student feedback the forum is actually + + + align:start position:0% +student feedback the forum is actually +great for that you get instant feedback + + align:start position:0% +great for that you get instant feedback + + + align:start position:0% +great for that you get instant feedback +on this and so if you're good you make + + align:start position:0% +on this and so if you're good you make + + + align:start position:0% +on this and so if you're good you make +notes you know I think I've taught this + + align:start position:0% +notes you know I think I've taught this + + + align:start position:0% +notes you know I think I've taught this +course well know 30-some esters and so + + align:start position:0% +course well know 30-some esters and so + + + align:start position:0% +course well know 30-some esters and so +that gives you a lot of opportunity to + + align:start position:0% +that gives you a lot of opportunity to + + + align:start position:0% +that gives you a lot of opportunity to +think you know reflect at the end of + + align:start position:0% +think you know reflect at the end of + + + align:start position:0% +think you know reflect at the end of +each semester about what went right what + + align:start position:0% +each semester about what went right what + + + align:start position:0% +each semester about what went right what +went wrong with a good staff there right + + align:start position:0% +went wrong with a good staff there right + + + align:start position:0% +went wrong with a good staff there right +usually on top of it you know oh we got + + align:start position:0% +usually on top of it you know oh we got + + + align:start position:0% +usually on top of it you know oh we got +to change this or you know I spent too + + align:start position:0% +to change this or you know I spent too + + + align:start position:0% +to change this or you know I spent too +much time helping students with this so + + align:start position:0% +much time helping students with this so + + + align:start position:0% +much time helping students with this so +putting down and even in real time will + + align:start position:0% +putting down and even in real time will + + + align:start position:0% +putting down and even in real time will +will add a paragraph to the assignment + + align:start position:0% +will add a paragraph to the assignment + + + align:start position:0% +will add a paragraph to the assignment +saying oh you know a little bit more + + align:start position:0% +saying oh you know a little bit more + + + align:start position:0% +saying oh you know a little bit more +explanation or a hint right so you know + + align:start position:0% +explanation or a hint right so you know + + + align:start position:0% +explanation or a hint right so you know +so a willingness to you know sort of and + + align:start position:0% +so a willingness to you know sort of and + + + align:start position:0% +so a willingness to you know sort of and +think of building the materials as a + + align:start position:0% +think of building the materials as a + + + align:start position:0% +think of building the materials as a +continuous process and after a while + + align:start position:0% +continuous process and after a while + + + align:start position:0% +continuous process and after a while +most what the potholes are filled in and + + align:start position:0% +most what the potholes are filled in and + + + align:start position:0% +most what the potholes are filled in and +the drive is pretty smooth right and and + + align:start position:0% +the drive is pretty smooth right and and + + + align:start position:0% +the drive is pretty smooth right and and +sometimes the you know the unexpected + + align:start position:0% +sometimes the you know the unexpected + + + align:start position:0% +sometimes the you know the unexpected +problem is actually you know a doorway + + align:start position:0% +problem is actually you know a doorway + + + align:start position:0% +problem is actually you know a doorway +actually into a whole new a whole new + + align:start position:0% +actually into a whole new a whole new + + + align:start position:0% +actually into a whole new a whole new +thing we've had some students said you + + align:start position:0% +thing we've had some students said you + + + align:start position:0% +thing we've had some students said you +know I thought about this and I tried + + align:start position:0% +know I thought about this and I tried + + + align:start position:0% +know I thought about this and I tried +doing it this way and I'm going whoa + + align:start position:0% +doing it this way and I'm going whoa + + + align:start position:0% +doing it this way and I'm going whoa +what a great insight that is and so we + + align:start position:0% +what a great insight that is and so we + + + align:start position:0% +what a great insight that is and so we +want all the students to have that + + align:start position:0% +want all the students to have that + + + align:start position:0% +want all the students to have that +opportunity so now we're going to figure + + align:start position:0% +opportunity so now we're going to figure + + + align:start position:0% +opportunity so now we're going to figure +out how to build that in to the into the + + align:start position:0% +out how to build that in to the into the + + + align:start position:0% +out how to build that in to the into the +into the design problem so that + + align:start position:0% +into the design problem so that + + + align:start position:0% +into the design problem so that +everybody says you know has an + + align:start position:0% +everybody says you know has an + + + align:start position:0% +everybody says you know has an +opportunity to go aha + + align:start position:0% +opportunity to go aha + + + align:start position:0% +opportunity to go aha +it was really neat that this you know + + align:start position:0% +it was really neat that this you know + + + align:start position:0% +it was really neat that this you know +students were able to come up with that + + align:start position:0% +students were able to come up with that + + + align:start position:0% +students were able to come up with that +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +but you know that gives you a viewpoint + + align:start position:0% +but you know that gives you a viewpoint + + + align:start position:0% +but you know that gives you a viewpoint +you know it it gives you an opportunity + + align:start position:0% +you know it it gives you an opportunity + + + align:start position:0% +you know it it gives you an opportunity +to understand how students are seeing + + align:start position:0% +to understand how students are seeing + + + align:start position:0% +to understand how students are seeing +what you're asking they misunderstood so + + align:start position:0% +what you're asking they misunderstood so + + + align:start position:0% +what you're asking they misunderstood so +they answered a different question and + + align:start position:0% +they answered a different question and + + + align:start position:0% +they answered a different question and +it turns out that different question was + + align:start position:0% +it turns out that different question was + + + align:start position:0% +it turns out that different question was +at least as interesting or maybe even + + align:start position:0% +at least as interesting or maybe even + + + align:start position:0% +at least as interesting or maybe even +better than the one you asked and so + + align:start position:0% +better than the one you asked and so + + + align:start position:0% +better than the one you asked and so +then you start you know this is one of + + align:start position:0% +then you start you know this is one of + + + align:start position:0% +then you start you know this is one of +these virtuous cycles right there + + align:start position:0% +these virtuous cycles right there + + + align:start position:0% +these virtuous cycles right there +there's slowly you build up stuff where + + align:start position:0% +there's slowly you build up stuff where + + + align:start position:0% +there's slowly you build up stuff where +you end up with questions that are + + align:start position:0% +you end up with questions that are + + + align:start position:0% +you end up with questions that are +really you know they don't look like + + align:start position:0% +really you know they don't look like + + + align:start position:0% +really you know they don't look like +there's much to them but there's been a + + align:start position:0% +there's much to them but there's been a + + + align:start position:0% +there's much to them but there's been a +lot of evolution behind asking it just + + align:start position:0% +lot of evolution behind asking it just + + + align:start position:0% +lot of evolution behind asking it just +this way + + align:start position:0% +this way + + + align:start position:0% +this way +just you know in in just this order so + + align:start position:0% +just you know in in just this order so + + + align:start position:0% +just you know in in just this order so +it's been fun to go through that + + align:start position:0% +it's been fun to go through that + + + align:start position:0% +it's been fun to go through that +experience and often surprising you at + + align:start position:0% +experience and often surprising you at + + + align:start position:0% +experience and often surprising you at +all I thought it was so clear \ No newline at end of file diff --git a/qZHseRxAWZ8.txt b/qZHseRxAWZ8.txt new file mode 100644 index 0000000000000000000000000000000000000000..858a185d34bfcf94462a5d7ab286c3462844a1de --- /dev/null +++ b/qZHseRxAWZ8.txt @@ -0,0 +1,2351 @@ +Okay, those are the formulas. +You will get all of those on + +the test, plus a couple more +that I will give you today. + +Those will be the basic +formulas of the Laplace + +transform. +If I think you need anything + +else, I'll give you other stuff, +too. + +So, I'm going to leave those on +the board all period. + +The basic test for today is to +see how Laplace transforms are + +used to solve linear +differential equations with + +constant coefficients. +Now, to do that, + +we're going to have to take the +Laplace transform of a + +derivative. +And, in order to make sense of + +that procedure, +we're going to have to ask, + +I apologize in advance, +but a slightly theoretical + +question, namely, +we have to have some guarantee + +in advance that the Laplace +transform is going to exist. + +Now, how could the Laplace +transform fail to exist? + +Can't I always calculate this? +And the answer is, + +no, you can't always calculate +it because this is an improper + +integral. +I'm integrating all the way up + +to infinity, and you know that +improper integrals don't always + +converge. +You know, if the integrand for + +example just didn't have the +exponential factor there, + +were simply t dt, +that it might look like it made + +sense, but that integral doesn't +converge. + +And, anyway, +it has no value. + +So, I need conditions in +advance, which guarantee that + +the Laplace transforms will +exist. + +Only under those circumstances +will the formulas make any + +sense. +Now, there is a standard + +condition that's in your book. +But, I didn't get a chance to + +talk about it last time. +So, I thought I'd better spent + +the first few minutes today +talking about the condition + +because it's what we're going to +need in order to be able to + +solve differential equations. +The condition that makes the + +Laplace transform definitely +exist for a function is that f + +of t shouldn't grow too +rapidly. + +It can grow rapidly. +It can grow because the e to + +the minus s t is +pulling it down, + +trying hard to pull it down to +zero to make the integral + +converge. +All we have to do is to + +guarantee that it doesn't grow +so rapidly that the e to the + +minus s t is powerless to pull +it down. + +Now, the condition is it's +what's called a growth + +condition. +These are very important in + +applications, +and unfortunately, + +it's always taught in 18.01, +but it's not always taught in + +high school calculus. +And, it's a question of how + +fast the function is allowed to +grow. + +And, the condition is +universally said this way, + +should be of exponential type. +So, what I'm defining is the + +phrase "exponential type." I'll +put it in quotation marks for + +that reason. +What does this mean? + +It's a condition, +a growth condition on a + +function, says how fast it can +get big. + +It says that f of t in +size, since f of t might get + +negatively very large, +and that would hurt, + +make the integral hard to +converge, not likely to + +converge, use the absolute +value. + +In other words, +I don't care if f of t is going + +up or going down very low. +Whichever way it goes, + +its size should not be bigger +than a rapidly growing + +exponential. +And, here's a rapidly growing + +exponential. +c is some positive constant, + +for some positive constant c +and some positive constant k. + +And, this should be true for +all values of t. + +All t greater than or equal to +zero. + +I don't have to worry about +negative values of t because the + +integral doesn't care about +them. + +I'm only doing the integration +as t runs from zero to infinity. + +In other words, +f of t could have been + +an extremely wild function, +sewn a lot of oats or whatever + +functions do for negative values +of t, and we don't care. + +It's only what's happening from +now from time zero onto + +infinity. +As long as it behaves now, + +from now on, +it's okay. + +All right, so, +the way it should behave is by + +being an exponential type. +Now, to try to give you some + +feeling for what this means, +these functions, + +for example, if k is 100, + +do you have any idea what the +plot of e to the 100t + +looks like? +It goes straight up. + +On every computer you try to +plot it on, e to the 100t + +goes like that +unless, of course, + +you make the scale t equals +zero to, over here, + +is one millionth. +Well, even that won't do. + +Okay, so these functions really +can grow quite rapidly. + +Let's take an example and see +what's of exponential type, + +and then perhaps even more +interestingly, + +what isn't. +The function sine t, + +is that of exponential type? +Well, sure. + +Its absolute value is always +less than or equal to one. + +So, it's also this paradigm. +If I take c equal to one, + +and what should I take k to be? +Zero. + +Take k to be zero, +c equals one, + +and in fact sine t +plays that condition. + +Here's one that's more +interesting, t to the n. + +Think of t to the 100th power. + +Is that smaller than some +exponential with maybe a + +constant out front? +Well, t to the 100th power + +goes straight up, +also. + +Well, we feel that if we make +the exponential big enough, + +maybe it will win out. +In fact, you don't have to make + +the exponential big. +k equals one is good + +enough. +In other words, + +I don't have to put absolute +value signs around the t to the + +n because I'm only +thinking about t as being a + +positive number, +anyway. + +I say that that's less than or +equal to some constant M, + +positive constant M times e to +the t will be good + +enough for some M and all t. +Now, why is that? + +Why is that? +The way to think of that, + +so, what this proves is that, +therefore, t to the n + +is of exponential type, +which we could have guessed + +because after all we were able +to calculate its Laplace + +transform. +Now, just because you can + +calculate the Laplace transform +doesn't mean it's of exponential + +type, but in practical matters, +it almost always does. + +So, t to the n is of +exponential type. + +How do you prove that? +Well, the weighted secret is to + +look at t to the n divided by e +to the t. + +In other words, +look at the quotient. + +What I'd like to argue is that +this is bounded by some number, + +capital M. +That's the question I'm asking. + +Now, why is this so? +Well, I think I can convince + +you of it without having to work +very hard. + +What does the graph of this +function look like? + +It starts here, +so I'm graphing this function, + +this ratio. +When t is equal to zero, + +its value is zero, +right, because of the + +numerator. +What happens as t goes to + +infinity? +What happens to this? + +What does it approach? +Zero. + +And, why? +By L'Hop. + +By L'Hopital's rule. +Just keep differentiating, + +reapply the rule over and over, +keep differentiating it n + +times, and finally you'll have +won the numerator down to t to + +the zero, +which isn't doing anything + +much. +And, the denominator, + +no matter how many times you +differentiate it, + +it's still t, +to the t all the time. + +So, by using Lopital's rule n +times, you change the top to one + +or n factorial, +actually; the bottom stays e to + +the t, +and the ratio clearly + +approaches zero, +and therefore, + +it approached zero to start +with. + +So, I don't know what this +function's doing in between. + +It's a positive function. +It's continuous because the top + +and bottom are continuous, +and the bottom is never zero. + +So, it's a continuous function +which starts out at zero and is + +positive, and as t goes to +infinity, it gets closer and + +closer to the t-axis, +again. + +Well, what does t to the n +do? + +It might wave around. +It doesn't actually. + +But, the point is, +because it's continuous, + +starts at zero, +ends at zero, + +it's bounded. +It has a maximum somewhere. + +And, that maximum is M. +So, it has a maximum. + +All you have to know is where +it starts, and where it ends up, + +and the fact that it's +continuous. + +That guarantees that it has a +maximum. + +So, it is less than some +maximum, and that shows that + +it's of exponential type. +Now, of course, + +before you get the idea that +everything's of exponential + +type, let's see what isn't. +I'll give you two functions + +that are not of exponential +type, for different reasons. + +One over t is not of +exponential type. + +Well, of course, +it's not defined that t equals + +zero. But, you know, + +it's okay for an integral not +to be defined at one point + +because you're measuring an +area, and when you measure an + +area, what happened to one point +doesn't really matter much. + +That's not the thing. +What's wrong with one over t is + +that the integral doesn't +converge at zero times one over + +t dt. +That integral, + +when t is near zero, +this is approximately equal to + +one, right? +If t is zero, + +this is one. +So, it's like the function, + +integral from zero to infinity +of one over t, + +near zero it's close to, + +it's like the integral from +zero to someplace of no + +importance, dt over t. + +But, this does not converge. +This is like log t, + +and log zero is minus infinity. +So, it doesn't converge. + +So, one over t is not +of exponential type. + +So, what's the Laplace +transform of one over t? + +It doesn't have a Laplace + +transform. +Well, what if I put t equals + +negative n? +What about t to the minus one? + +Well, that only works for + +positive integers, +not negative integers. + +Okay, so it's not of +exponential type. + +However, that's because it +never really gets started + +properly. +It's more fun to look at a + +function which is not of +exponential type because it + +grows too fast. +Now, what's a function that + +grows faster that it grows so +rapidly that you can't find any + +function e to the k t +which bounds it? + +A function which grows too +rapidly, a simple one is e to + +the t squared, +grows too rapidly to be of + +exponential type. +And, the argument is simple. + +No matter what you propose, +it's always, + +for the K, no matter how big a +number, use Avogadro's number, + +use anything you want. +Ultimately, this is going to be + +bigger than k t no matter how +big k is, no matter how big k + +is. +When is this going to happen? + +This will happen if t squared +is bigger than k t. + +In other words, +as soon as t becomes bigger + +than k, you might have to wait +quite a while for that to + +happen, but, as soon as t gets +bigger than 10 to the 10 to the + +23, +this e to the t squared will be + +bigger than e to the 10 to the +10 to the 23 times t. + +So, e to the t squared, + +it's a simple +function, a simple elementary + +function. +It grows so rapidly it doesn't + +have a Laplace transform. +Okay, so how are we going to + +solve differential equations if +e to the t squared? + +I won't give you any. +And, the reason I won't give + +you any: because I never saw one +occur in real life. + +Nature, like sines, +cosines, exponentials, + +are fine, I've never seen a +physical, you know, + +this is just my ignorance. +But, I've never seen a physical + +problem that involved a function +growing as rapidly as e to the t + +squared. +That may be just my ignorance. + +But, I do know the Laplace +transform won't be used to solve + +differential equations involving +such a function. + +How about e to the minus t +squared? + +That's different. +It looks almost the same, + +but e to the minus t squared +does this. + +It's very well-behaved. +That's the curve, + +of course, that you're all +afraid of. + +Don't panic. +Okay. + +So, I'd like to explain to you +now how differential equations, + +maybe I should save-- I'll tell +you what. + +We need more formulas. +So, I'll put them, + +why don't I save this board, +and instead, + +I'll describe to you the basic +way Laplace transforms are used + +to solve differential equations, +what are they called, + +a paradigm. +I'll show you the paradigm, + +and then we'll fill in the +holes so you have some overall + +view of how the procedure goes, +and then you'll understand + +where the various pieces fit +into it. + +I think you'll understand it +better that way. + +So, what do we do? +Start with the differential + +equation. +But, right away, + +there's a fundamental +difference between what the + +Laplace transform does, +and what we've been doing up + +until now, namely, +what you have to start with is + +not merely the differential +equation. + +Let's say we have linear with +constant coefficients. + +It's almost never used to solve +any other type of problem. + +And, let's take second order so +I don't have to do, + +because that's the kind we've +been working with all term. + +But, it's allowed to be +inhomogeneous, + +so, f of t. +Let's call the something else, + +another letter, +h of t. + +I'll want f of t for +the function I'm taking the + +Laplace transform of. +All right, now, + +the difference is that up to +now, you know techniques for + +solving this just as it stands. +The Laplace transform does not + +know how to solve this just +doesn't stands. + +The Laplace transform must have +an initial value problem. + +In other words, +you must supply from the + +beginning the initial conditions +that the y is to satisfy. + +Now, I don't want to say any +specific numbers, + +so I'll use generic numbers. +Well, but look, + +what do we do if we get a +problem and there are no initial + +conditions; does that mean we +can't use the Laplace transform? + +No, of course you can use it. +But, you will just have to + +assume the initial conditions +are on the numbers. + +You'll say it but the initial +conditions be y sub zero + +and y zero prime, +or whatever, + +a and b, whatever you want to +call it. + +And now, the answer, +then, will involve the a and + +the b or the y zero and the y +zero prime. + +But, you must, +at least, give lip service to + +the initial conditions, +whereas before we didn't have + +to do that. +Now, depending on your point of + +view, that's a grave defect, +or it is, so what? + +Let's adopt the so what point +of view. + +So, there's our problem. +It's an initial value problem. + +How is it solved by the Laplace +transform? + +Well, the idea is you take the +Laplace transform of this + +differential equation and the +initial conditions. + +So, I'm going to explain to you +how to do that. + +Not right now, +because we're going to need, + +first, the Laplace transform of +a derivative, + +the formula for that. +You don't know that yet. + +But when you do know it, +you will be able to take the + +Laplace transform of the initial +value problem. + +So, I'll put the little l here, +and what comes out is, + +well, y of t is the +solution to the original + +problem. +If y of t is the + +function which satisfies that +equation and these initial + +conditions, its Laplace +transform, let's call it capital + +Y, that's our standard notation, +but it's going to be of a new + +variable, s. +So, when I take the Laplace + +transform of the differential +equation with the initial + +conditions, what comes out is an +algebraic-- the emphasis is on + +algebraic: no derivatives, +no transcendental functions, + +nothing like that, +an algebraic equation, + +m Y of s. + +And, now what? +Well, now, in the domain of s, + +it's easy to solve this +algebraic equation. + +Not all algebraic equations are +easy to solve for the capital Y. + +But, the ones you will get will +always be, not because I am + +making life easy for you, +but that's the way the Laplace + +transform works. +So, you will solve it for Y. + +And, the answer will always +come out to be Y equals, + +Y of s equals some +rational function, + +some quotient of polynomials in +s, a polynomial in s divided by + +some other polynomial in s. + +And, now what? +Well, this is the Laplace + +transform of the answer. +This is the Laplace transform + +of the solution we are looking +for. + +So, the final step is to go +backwards by taking the inverse + +Laplace transform of this guy. +And, what will you get? + +Well, you will get y equals the +y of t that we are + +looking for. +It's really a wildly improbable + +procedure. +In other words, + +instead of going from here to +here, you have to imagine + +there's a mountain here. +And, the only way to get around + +it is to go, first, +here, and then cross the stream + +here, and then go back up, +and go back up. + +It looks like a senseless +procedure, what do they call it, + +going around Robin Hood's barn, +it was called when I was a, + +I don't know why it's called +that. + +But that's what we used to call +it; not Laplace transform. + +That was just a generic thing +when you had to do something + +like this. +But, the answer is that it's + +hard to go from here to here, +but trivial to go from here to + +here. +This solution step is the + +easiest step of all. +This is not very hard. + +It's easy, in fact. +This is easy and + +straightforward. +This is trivial, + +essentially, +yeah, trivial. + +But, this step is the hard +step. + +This is where you have to use +partial fractions, + +look up things in the table to +get back there so that most of + +the work of the procedure isn't +going from here to here. + +Going from here to there is a +breeze. + +Okay, now, in order to +implement this, + +what is it we have to do? +Well, the basic thing is I have + +to explain to you, +you already know at least a + +little bit, a reasonable amount +of technique for taking that + +step if you went to recitation +yesterday and practiced a little + +bit. +This part, I assure you, + +is nothing. +So, all I have to do now is + +explain to you how to take the +Laplace transform of the + +differential equation. +And, that really means, + +how do you take the Laplace +transform of a derivative? + +So, that's our problem. +What I want to form, + +in other words, +is a formula for the Laplace + +transform f prime of t. + +Now, in terms of what? +Well, since f is an arbitrary + +function, the only thing I could +hope for is somehow to express + +the Laplace transform of the +derivative in terms of the + +Laplace transform of the +original function. + +So, that's what I'm aiming for. +Okay, where are we going to + +start? +Well, starting is easy because + +we know nothing. +If you don't know anything, + +then there's no place to start +but the definition. + +Since I know nothing whatever +about the function f of t, + +and I want to +calculate the Laplace transform, + +I'd better start with the +definition. + +Whatever this is, +it's the integral from zero to + +infinity of e to the minus s t +times f prime of t dt. + +Now, what am I looking for? +I'm looking for somehow to + +transform this so that what +appears here is not + +f prime of t, which I'm +clueless about, but f of t + +because if this were f of t, +this expression would be the + +Laplace transform of f of t. + +And, I'm assuming I know that. +So, the question is how do I + +take this and somehow do +something clever to it that + +turns this into f of t +instead of f prime of t? + +Now, to first the question that + +way, I hope I would get 100% +response on what to do. + +But, I'll go for 1%. +So, what should I do? + +I want to change that, so that +instead of f prime of t, + +f of t +appears there instead. + +What should I do? +Integrate by parts, + +the most fundamental procedure +in advanced analysis. + +Everything important and +interesting depends on + +integration by parts. +And, when you consider that + +integration by parts is nothing +more than just the formula for + +the derivative of a product read +backwards, it's amazing. + +It never fails to amaze me, +but it's okay. + +That's what mathematics are so +great. + +Okay, so let's use integration +by parts. + +Integration by parts: +okay, so, we have to decide, + +of course, there's no doubt +that this is the factor we want + +to integrate, +which means we have to be + +willing to differentiate this +factor. + +But that will be okay because +it looks practically, + +like any exponential, +it looks practically the same + +after you've differentiated it. +So, let's do the work. + +First step is you don't do the +differentiation. + +You only do the integration. +So, the first step is e to the + +negative s t. +And, the integral of f prime of + +t is just f of t. + +And, that's to be evaluated +between the limits zero and + +infinity. +And then, minus, + +again, before you forget it, +put down that minus sign. + +The integral between the limits +of what you get by doing both + +operations, both the +differentiation and the + +integration. +So, the differentiation will be + +by using the chain rule. +Remember, I'm differentiating + +with respect to t. +The variable is t here, + +not s. +s is just a parameter. + +It's just a constant, +a variable constant, + +if you get my meaning. +That's not an oxymoron. + +A variable constant: +a parameter is a variable + +constant, variable because you +can manipulate the little slider + +and make a change its value, +right? + +That's why it's variable. +It's not a variable. + +It's variable, +if you get the distinction. + +Okay, well, I mean, +it becomes a variable + +[LAUGHTER]. +But right now, + +it's not a variable. +It's just sitting there in the + +integral. +All right, so, + +minus s, e to the negative s t, +f of t dt. + +Now, this part's easy. + +The interesting thing is this +expression. + +So, and the most interesting +thing is I have to evaluate it + +at infinity. +Now, of course, + +that means take the limit as +you go towards, + +as you let t goes to infinity. +Now, so what I'm interested in + +knowing is what's the limit of +that expression? + +I'll write it as f of t divided +by e to the s t. + +Remember, s is a positive + +number. +s t goes to infinity, + +and I want to know what the +limit of that is. + +Well, the limit is what it is. +But really, if that limit isn't + +zero, I'm in deep trouble since +the whole process is out of + +control. +What will make that limit zero? + +Well, that f of t +should not grow faster than e to + +the s t if s is a big +enough number. + +And now, that's just what will +happen if f of t is of + +exponential type. +It's for this step right here + +that is the most crucial place +at which we need to know that f + +of t is of exponential type. +So, that limit is zero since f + +of t is of exponential type, +in other words, + +that the value, +the absolute value of f of t, + +becomes less than, +let's say, put in the c if you + +want, but it's not very +important, c e to the k t + +efor all values of t. +And, therefore, + +this will go to zero as soon as +s becomes bigger than that k. + +In other words, + +if f of t isn't +growing any faster than e to the + +k t , +then as soon as s is a number, + +that parameter has the value +bigger than k, + +this ratio is going to go to +zero because the denominator + +will always be bigger than the +numerator, and getting bigger + +faster. +So, this goes to zero if s is + +bigger than k. +At the upper limit, + +therefore, this is zero. +Again, assuming that s is + +bigger than that k, +the k of the exponential type, + +how about at the lower limit? +We're used to seeing zero + +there, but we're not going to +get zero. + +If I plug in t equals zero, +this factor becomes one. + +And, what happens to that one? +f of zero. + +You mean, I'm going to have to +know what f of zero is before I + +can take the Laplace transform +of this derivative? + +The answer is yes, +and that's why you have to have + +an initial value problem. +You have to know in advance + +what the value of the function +that you are looking for is at + +zero because it enters into the +formula. + +I didn't make up these rules; +I'm just following them. + +So, what's the rest? +The two negatives cancel, + +and you get plus s. +It's just a parameter, + +so I can pull it out of the +integral. + +I'm integrating with respect to +t, and what's left is, + +well, what is left? +If I take out minus s, + +combine it there, +I get what's left is just the + +Laplace transform of the +function I started with. + +So, it's F of s. +And, that's the magic formula + +for the Laplace transform of the +derivative. + +So, it's worth putting up on +our little list. + +So, f prime of t, +assuming it's of exponential + +type, has as its Laplace +transform, well, + +what is it? +Let's put down the major part + +of it is s times whatever the +Laplace transform of the + +original function, +F of t, + +was. +So, I take the original Laplace + +transform. +When I multiply it by s, + +that corresponds to taking the +derivative. + +But there's also that little +extra piece. + +I must know the value of the +starting value of the function. + +This is the formula you'll used +to take a Laplace transform of + +the differential equation. +Now, but you see I'm not done + +yet because that will take care +of the term a y prime. + +But, I don't know what the +Laplace transform of the second + +derivative is. +Okay, so, we need a formula for + +the Laplace transform of a +second derivative as well as the + +first. +Now, the hack method is to say, + +secondary, all right. +I've got to do this. + +I'll second derivative here, +second derivative here, + +what do I do with that? +Ah-ha, I integrate by parts + +twice. +Yes, you can do that. + +But that's a hack method. +And, of course, + +I know you're too smart to do +that. + +What you would do instead is-- +How are we going to fill that + +in? +Well, a second derivative is + +also a first derivative. +A second derivative is the + +first derivative of the first +derivative. + +Okay, now, we'll just call this +glop, something. + +So, it's glop prime. +What is the formula for the + +Laplace transform of glop prime? +It is, well, + +I have my formula. +It is the glop prime. + +The formula for it is s times +the Laplace transform of glop, + +okay, glop. +Well, glop is f prime of t. + +I'm not done yet, + +minus glop evaluated at zero. +What's glop evaluated at zero? + +Well, f prime of zero. + +Now, I don't want the formula +in that form, + +but I have to have it in that +form because I know what the + +Laplace transform of f prime of +t is. + +I just calculated that. +So, this is equal to s times + +the Laplace transform of f prime +of t, which is s times F of s, + +capital F of s, +minus f of zero. + +All that bracket stuff + +corresponds to this guy. +And, don't forget the stuff + +that's tagging along, +minus f prime of zero. + +And now, put that all together. + +What is it going to be? +Well, there's the principal + +term which consists of s squared +multiplied by F of s. + +That's the main part of it. + +And, the rest is the sort of +fellow travelers. + +So, we have minus s times f of +zero, + +little term tagging along. +This is a constant times s. + +And then, we've got another +one, still another constant. + +So, what we have is to +calculate the Laplace transform + +of the second derivative, +I need to know both f of zero + +and f prime of zero, +exactly the initial + +conditions that the problem was +given for the initial value + +problem. +But, notice, + +there's a principal part of it. +That's the s squared F of s. + +That's the guts of it, + +so to speak. +The rest of it, + +you know, you might hope that +these two numbers are zero. + +It could happen, +and often it is made to happen + +and problems to simplify them. +And I case, you don't have to + +worry; they're not there. +But, if they are there, + +you must put them in or you get +the wrong answer. + +So, that's the list of +formulas. + +So, those formulas on the top +board and these two extra ones, + +those are the things you will +be working with on Friday. + +But I stress, +the Laplace transform won't be + +a big part of the exam. +The exam, of course, + +doesn't exist, +let's say a maximum of 20%, + +maybe 15. +I don't know, + +give or take a few points. +Yeah, what's a point or two? + +Okay, let's solve, +yeah, we have time. + +We have time to solve a +problem. + +Let's solve a problem. +See, I can't touch that. + +It's untouchable. +Okay, this, we've got to keep. + +Problem? Okay. + +Okay, now you know how to solve +this problem by operators. + +Let me just briefly remind you +of the basic steps. + +You have to do two separate +tasks. + +You have to first solve the +homogeneous equation, + +putting a zero there. +That's the first thing you + +learned to do. +That's easy. + +You could almost do that in +your head now. + +You get the characteristic +polynomial, get its roots, + +get the two functions, +e to the t and e to the + +negative t, +which are the solutions. + +You make up c1 times one, +and c2 times the other. + +That's the complementary +function that solves the + +homogeneous problem. +And then you have to find a + +particular solution. +Can you see what would happen + +if you try to find the +particular solution? + +The number here is negative +one, right? + +Negative one is a root of the +characteristic polynomial, + +so you've got to use that extra +formula. + +It's okay. +That's why I gave it to you. + +You've used the exponential +input theorem with the extra + +formula. +Then, you will get the + +particular solution. +And now, you have to make the + +general solution. +The particular solution plus + +the complementary function, +and now you are ready to put in + +the initial conditions. +At the very end, + +when you've got the whole +general solution, + +now you put in, +not before, you put in the + +initial conditions. +You have to calculate the + +derivative of that thing and +substitute this. + +You take it as it stands to +substitute this. + +You get a pair of simultaneous +equations for c1 and c2. + +You solve them: +answer. + +It's a rather elaborate +procedure, which has at least + +three or four separate steps, +all of which, + +of course, must be done +correctly. + +Now, the Laplace transform, +instead, feeds the entire + +problem into the Laplace +transform machine. + +You follow that little blue +pattern, and you come out with + +the answer. +So, let's do the Laplace + +transform way. +Okay, so, the first step is to + +say, if here's my unknown +function, y of t, + +it obeys this law, +and here are its starting + +values, a bit of its derivative. +What I'm going to take is the + +Laplace transform of this +equation. + +In other words, +I'll take the Laplace transform + +of this side, +and this side also. + +And, they must be equal because +if they were equal to start + +with, the Laplace transforms +also have to be equal. + +Okay, so let's take the Laplace +transform of this equation. + +Okay, first ID the Laplace +transform of the second + +derivative. +Okay, that's going to be, + +don't forget the principal +terms. + +There is some people who get so +hypnotized by this. + +I just know I'm going to forget +this. + +So, they read it. +Then they forget this. + +But that's everything. +That's the important part. + +Okay, so it's s times, +I'm calling the Laplace + +transform not capital F but +capital Y because my original + +function is called little y. +So, it's s squared Y. + +It's Y of s, +but I'm not going to put that, + +the of s in because it just +makes the thing look more + +complicated. +And now, before you forget, + +you have to put in the rest. +So, minus s times the value at + +zero, which is one, +minus the value of the + +derivative. +But, that's zero. + +So, this is not too hard a +problem. + +So, minus s minus zero, +so I don't have to put that + +in. +So, all this is the Laplace + +transform of y double prime. + +And now, minus the Laplace +transform of y, + +well, that's just capital Y. +What's that equal to? + +The Laplace transform of the +right-hand side. + +Okay, look up the formula. +It is e to the negative t, + +a is minus one, +so, it's one over s minus minus + +one; +so, it is s plus one. + +This is that. +Okay, the next thing we have to + +do is solve for Y. +That doesn't look too hard. + +Solve it for y. +Okay, the best thing to do is + +put s squared, +group all the Y terms together + +unless you're really quite a +good calculator. + +Maybe make one extra line out +of it. + +Yeah, definitely do this. +And then, the extra garbage I + +refer to as the garbage, +this stuff, and this stuff, + +the stuff, the linear +polynomials which are tagging + +along move to the right-hand +side because they don't involve + +capital Y. +So, this we will move to the + +other side. +And so, that's equal to (one + +over (s plus one)) plus s. + +Now, you have a basic choice. +About half the time, + +it's a good idea to combine +these terms. + +The other half of the time, +it's not a good idea to combine + +those terms. +So, how do we know whether to + +do it or not to do it? +Experience, which you will get + +by solving many, +many problems. + +Okay, I'm going to combine them +because I think it's a good + +thing to do here. +So, what is that? + +That's s squared plus s plus +one. + +So, it's s squared plus s plus +one divided by s plus one, + +okay? +I'm still not done because now + +we have to know, +what's Y? + +All right, now we have to +think. + +What we're going to do is get Y +in this form. + +But, I want it in the form in +which it's most suited for using + +partial fractions. +In other words, + +I want the denominator as +factored as I possibly can be. + +Okay, well, the numerator is +going to be just what it was. + +How should I write the +denominator? + +Well, the denominator is going +to have the factor s plus one + +in it from here. +But after I divide through, + +the other factor will be s +squared minus one, + +right? +But, s squared minus one is s + +minus one times s plus one. + +So, I have to divide this by s +squared minus one. + +Factored, it's this. +So, the end result is there are + +two of these and one of the +other. + +And now, it's ready to be used. +It's better to be a partial + +fraction. +So, the final step is to use a + +partial fraction's decomposition +on this so that you can + +calculate its inverse Laplace +transform. + +So, let's do that. +Okay, (s squared plus s plus + +one) divided by that thing, +(s plus one) squared times (s + +minus one) equals s plus + +one squared plus s +plus one plus s minus one. + +In the top will be constants, + +just constants. +Let's do it this way first, + +and I'll say at the very end, +something else. + +Maybe now. +Many of you are upset. + +Some of you are upset. +I know this for a fact because + +in high school, +or wherever you learned to do + +this before, there weren't two +terms here. + +There was just one term, +s plus one squared. + +If you do it that way, + +then it's all right. +Then, it's all right, + +but I don't recommend it. +In that case, + +the numerators will not be +constants. + +But, if you just have that, +then because this is a + +quadratic polynomial all by +itself. + +You've got to have a linear +polynomial, a s plus b + +in the top, see? + +So, you must have a s plus b +here, + +as I'm sure you remember if +that's the way you learned to do + +it. But, to do cover-up, + +the best way as much as +possible to separate out the + +terms. +If this were a cubic term, + +God forbid, s plus one cubed, + +then you'd have to have s plus +one cubed, + +s plus one squared. + +Okay, I won't give you anything +bigger than quadratic. + +[LAUGHTER] +You can trust me. + +Okay, now, what can we find by +the cover up method? + +Well, surely this. +Cover up the s minus one, + +put s equals one, +and I get three divided by two + +squared, four. +So, this is three quarters. + +Now, in this, + +you can always find the highest +power by cover-up because, + +cover it up, +put s equals negative one, + +and you get one minus one +plus one. + +So, one up there, +negative one here makes + +negative two here. +So, one over negative two. + +So, it's minus one half. + +Now, this you cannot determine + +by cover-up because you'd want +to cover-up just one of these s + +plus ones. +But then you can't put s equals + +negative one because +you get infinity. + +You get zero there, +makes infinity. + +So, this must be determined +some other way, + +either by undetermined +coefficients, + +or if you've just got one +thing, for heaven's sake, + +just make a substitution. +See, this is supposed to be + +true. +This is an algebraic identity, + +true for all values of the +variable, and therefore, + +it ought to be true when s +equals zero, + +for instance. +Why zero? + +Well, because I haven't used it +yet. + +I used negative one and +positive one, + +but I didn't use zero. +Okay, let's use zero. + +Put s equals zero. +What do we get? + +Well, on the left-hand side, +I get one divided by one + +squared, negative. +So, I get minus one on the left + +hand side equals, +what do I get on the right? + +Put s equals zero, +you get negative one half. + +Well, this is the number I'm + +trying to find. +So, let's write that simply as + +plus c, putting s equals zero. +s equals zero here gives me + +negative three quarters. + +Okay, what's c? +This is minus a half, + +minus three quarters, +is minus five quarters. + +Put it on the other side, + +minus one plus five quarters is +plus one quarter. + +So, c equals one quarter. + +And now, we are ready to do the + +final step. +Take the inverse Laplace + +transform. +You see what I said when I said + +that all the work is in this +last step? + +Just look how much of the work, +how much of the board is + +devoted to the first two steps, +and how much is going to be + +devoted to the last step? +Okay, so we get e to the + +inverse Laplace transform. +Well, the first term is the + +hardest. +Let's let that go for the + +moment. +So, I leave a space for it, + +and then we will have one +quarter. + +Well, one over s plus one is, + +that's just the exponential +formula. + +One over s plus one would be e +to the negative t,e to the minus + +one times t. +So, it's one quarter e to the + +minus one times t. + +And, how about the next thing +would be three quarters times, + +well, here it's negative one, +so that's e to the plus t. + +Notice how those signs work. + +And, that just leaves us the +Laplace transform of this thing. + +Now, you look at it and you +say, this Laplace transform + +happened in two steps. +I took something and I got, + +essentially, +one over s squared. + +And then, I changed s to s plus +one. + +All right, what gives one over +s squared? + +The Laplace transform of what +is one over s squared? + +t, you say to yourself, +one over s to some power is + +essentially some power of t. +And then, you look at the + +formula. +Notice at the top is one + +factorial, which is one, +of course. + +Okay, now, then how do I +convert this to one over s plus + +one squared? +That's the exponential shift + +formula. +If you know what the Laplace + +transform, so the first formula +in the middle of the board on + +the top, there, +if you know what, + +change s to s plus one, +corresponds to + +multiplying by e to the t. + +So, it is t times e to the +negative t. + +Sorry, that corresponds to +this. + +So, this is the exponential +shift formula. + +If t goes to one over s squared, +then t e to the + +minus t goes to one +over s plus one squared. + +Okay, but there's a constant + +out front. +So, it's minus one half t e to + +the negative t. + +Now, tell me, +what parts of this solution, + +oh boy, we're over time. +But, notice, + +this is what would have been +the particular solution, + +(y)p before, +and this is the stuff that + +occurs in the complementary +function, but already the + +appropriate constants have been +supplied for the coefficients. + +You don't have to calculate +them separately. + +They were built into the +method. + +Okay, good luck on Friday, +and see you there. \ No newline at end of file diff --git a/qeDewaJ4n24.txt b/qeDewaJ4n24.txt new file mode 100644 index 0000000000000000000000000000000000000000..d994a97e92c738112fde45fd24ee0edbc405eb95 --- /dev/null +++ b/qeDewaJ4n24.txt @@ -0,0 +1,11483 @@ +align:start position:0% + +Okay. So last time uh we uh we talked + + align:start position:0% +Okay. So last time uh we uh we talked + + + align:start position:0% +Okay. So last time uh we uh we talked +about + + align:start position:0% +about + + + align:start position:0% +about +um in particular we talked about two + + align:start position:0% +um in particular we talked about two + + + align:start position:0% +um in particular we talked about two +things. We talked about the cushy + + align:start position:0% +things. We talked about the cushy + + + align:start position:0% +things. We talked about the cushy +uh convergence here. + + align:start position:0% + + + + align:start position:0% + +So the cushy convergence theorem says + + align:start position:0% +So the cushy convergence theorem says + + + align:start position:0% +So the cushy convergence theorem says +that any any cushy sequence + + align:start position:0% + + + + align:start position:0% + +uh is convergent. + + align:start position:0% + + + + align:start position:0% + +Right? So this is one thing we talked + + align:start position:0% +Right? So this is one thing we talked + + + align:start position:0% +Right? So this is one thing we talked +quite a bit about last time. uh and we + + align:start position:0% +quite a bit about last time. uh and we + + + align:start position:0% +quite a bit about last time. uh and we +proved it but we proved it assuming + + align:start position:0% +proved it but we proved it assuming + + + align:start position:0% +proved it but we proved it assuming +another theorem. So we showed it the + + align:start position:0% +another theorem. So we showed it the + + + align:start position:0% +another theorem. So we showed it the +proof + + align:start position:0% + + + + align:start position:0% + +proof used + + align:start position:0% + + + + align:start position:0% + +the also bas + + align:start position:0% + + + + align:start position:0% + +now now + + align:start position:0% +now now + + + align:start position:0% +now now +the person bias theorem. So that's the + + align:start position:0% +the person bias theorem. So that's the + + + align:start position:0% +the person bias theorem. So that's the +following. + + align:start position:0% + + + + align:start position:0% + +So this is the following theorem + + align:start position:0% +So this is the following theorem + + + align:start position:0% +So this is the following theorem +that say that any bounded + + align:start position:0% +that say that any bounded + + + align:start position:0% +that say that any bounded +any bounded + + align:start position:0% + + + + align:start position:0% + +any bounded + + align:start position:0% +any bounded + + + align:start position:0% +any bounded +sequence + + align:start position:0% + + + + align:start position:0% + +A end has a convergent subsequence + + align:start position:0% + + + + align:start position:0% + +and let's call it a and k. Okay, that + + align:start position:0% +and let's call it a and k. Okay, that + + + align:start position:0% +and let's call it a and k. Okay, that +was the balsano vra theorem. So using + + align:start position:0% +was the balsano vra theorem. So using + + + align:start position:0% +was the balsano vra theorem. So using +this remember the cushi convergence + + align:start position:0% +this remember the cushi convergence + + + align:start position:0% +this remember the cushi convergence +theorem the proof then went like this + + align:start position:0% +theorem the proof then went like this + + + align:start position:0% +theorem the proof then went like this +that if you take a cushi sequence then + + align:start position:0% +that if you take a cushi sequence then + + + align:start position:0% +that if you take a cushi sequence then +it was easy to prove that it was bounded + + align:start position:0% +it was easy to prove that it was bounded + + + align:start position:0% +it was easy to prove that it was bounded +then you use the balsano vasium to say + + align:start position:0% +then you use the balsano vasium to say + + + align:start position:0% +then you use the balsano vasium to say +that now the sequence is bounded it's a + + align:start position:0% +that now the sequence is bounded it's a + + + align:start position:0% +that now the sequence is bounded it's a +sequence the sequence is bounded so it + + align:start position:0% +sequence the sequence is bounded so it + + + align:start position:0% +sequence the sequence is bounded so it +has a convergent subsequence so you have + + align:start position:0% +has a convergent subsequence so you have + + + align:start position:0% +has a convergent subsequence so you have +and the limit you would then want to + + align:start position:0% +and the limit you would then want to + + + align:start position:0% +and the limit you would then want to +prove that the limit is actually a limit + + align:start position:0% +prove that the limit is actually a limit + + + align:start position:0% +prove that the limit is actually a limit +That's for the whole sequence right + + align:start position:0% +That's for the whole sequence right + + + align:start position:0% +That's for the whole sequence right +that's what we did right + + align:start position:0% +that's what we did right + + + align:start position:0% +that's what we did right +now but we didn't prove the balsano vess + + align:start position:0% +now but we didn't prove the balsano vess + + + align:start position:0% +now but we didn't prove the balsano vess +theorem so let's try to pro prove it now + + align:start position:0% + + + + align:start position:0% + +so proof of the bzano vos + + align:start position:0% + + + + align:start position:0% + +so let me try to explain the idea + + align:start position:0% + + + + align:start position:0% + +So you have a sequence a n + + align:start position:0% +So you have a sequence a n + + + align:start position:0% +So you have a sequence a n +and a n is bounded. Let's just say it + + align:start position:0% +and a n is bounded. Let's just say it + + + align:start position:0% +and a n is bounded. Let's just say it +doesn't matter but let's say that a n + + align:start position:0% +doesn't matter but let's say that a n + + + align:start position:0% +doesn't matter but let's say that a n +lie in the interval from 0 to one. + + align:start position:0% +lie in the interval from 0 to one. + + + align:start position:0% +lie in the interval from 0 to one. +It could be any other bounded interval + + align:start position:0% +It could be any other bounded interval + + + align:start position:0% +It could be any other bounded interval +but but let's just say it's 0 to one. + + align:start position:0% +but but let's just say it's 0 to one. + + + align:start position:0% +but but let's just say it's 0 to one. +Then the idea is that you we want to + + align:start position:0% +Then the idea is that you we want to + + + align:start position:0% +Then the idea is that you we want to +prove that a n we want to so the idea is + + align:start position:0% +prove that a n we want to so the idea is + + + align:start position:0% +prove that a n we want to so the idea is +that we want to find + + align:start position:0% +that we want to find + + + align:start position:0% +that we want to find +want to find + + align:start position:0% + + + + align:start position:0% + +um a subsequence + + align:start position:0% + + + + align:start position:0% + +A and K + + align:start position:0% +A and K + + + align:start position:0% +A and K +and two other sequences. + + align:start position:0% + + + + align:start position:0% + +and two other sequences. + + align:start position:0% + + + + align:start position:0% + +A sorry B K and C K. And these two other + + align:start position:0% +A sorry B K and C K. And these two other + + + align:start position:0% +A sorry B K and C K. And these two other +sequences has a property that if you + + align:start position:0% +sequences has a property that if you + + + align:start position:0% +sequences has a property that if you +have here + + align:start position:0% +have here + + + align:start position:0% +have here +A and K then the B's lie below + + align:start position:0% +A and K then the B's lie below + + + align:start position:0% +A and K then the B's lie below +the they lie below the A and K and the + + align:start position:0% +the they lie below the A and K and the + + + align:start position:0% +the they lie below the A and K and the +C's + + align:start position:0% +C's + + + align:start position:0% +C's +lies above it. + + align:start position:0% +lies above it. + + + align:start position:0% +lies above it. +So, so the sequence the subsequence + + align:start position:0% +So, so the sequence the subsequence + + + align:start position:0% +So, so the sequence the subsequence +that we will find is going to be + + align:start position:0% +that we will find is going to be + + + align:start position:0% +that we will find is going to be +squeezed between two other sequences. + + align:start position:0% +squeezed between two other sequences. + + + align:start position:0% +squeezed between two other sequences. +So, so right. So, a and k + + align:start position:0% +So, so right. So, a and k + + + align:start position:0% +So, so right. So, a and k +is squeezed + + align:start position:0% + + + + align:start position:0% + +between two other sequences. + + align:start position:0% + + + + align:start position:0% + +And the thing about the other sequences + + align:start position:0% +And the thing about the other sequences + + + align:start position:0% +And the thing about the other sequences +is that they are much nicer + + align:start position:0% +is that they are much nicer + + + align:start position:0% +is that they are much nicer +because so why are they much nicer? The + + align:start position:0% +because so why are they much nicer? The + + + align:start position:0% +because so why are they much nicer? The +BKS + + align:start position:0% +BKS + + + align:start position:0% +BKS +are monotum + + align:start position:0% +are monotum + + + align:start position:0% +are monotum +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +and the CK + + align:start position:0% +and the CK + + + align:start position:0% +and the CK +are monotum decreasing. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, so you have that. So the picture is + + align:start position:0% +So, so you have that. So the picture is + + + align:start position:0% +So, so you have that. So the picture is +sort of that the that the bees the bees + + align:start position:0% +sort of that the that the bees the bees + + + align:start position:0% +sort of that the that the bees the bees +are always moving in this directions. + + align:start position:0% +are always moving in this directions. + + + align:start position:0% +are always moving in this directions. +The C's here this is the B's they you + + align:start position:0% +The C's here this is the B's they you + + + align:start position:0% +The C's here this is the B's they you +know as as K get larger they're moving + + align:start position:0% +know as as K get larger they're moving + + + align:start position:0% +know as as K get larger they're moving +to the right and the C case are moving + + align:start position:0% +to the right and the C case are moving + + + align:start position:0% +to the right and the C case are moving +to the left and these guys + + align:start position:0% +to the left and these guys + + + align:start position:0% +to the left and these guys +A and K + + align:start position:0% +A and K + + + align:start position:0% +A and K +they will be squeezed between these two + + align:start position:0% +they will be squeezed between these two + + + align:start position:0% +they will be squeezed between these two +right? So if you're looking at a later + + align:start position:0% +right? So if you're looking at a later + + + align:start position:0% +right? So if you're looking at a later +one right h so this is like one and now + + align:start position:0% +one right h so this is like one and now + + + align:start position:0% +one right h so this is like one and now +imagine that you take a later uh uh in + + align:start position:0% +imagine that you take a later uh uh in + + + align:start position:0% +imagine that you take a later uh uh in +the subsequence + + align:start position:0% +the subsequence + + + align:start position:0% +the subsequence +sorry let me indicate it here a n say l + + align:start position:0% +sorry let me indicate it here a n say l + + + align:start position:0% +sorry let me indicate it here a n say l +and l is now further out in the + + align:start position:0% +and l is now further out in the + + + align:start position:0% +and l is now further out in the +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +then this is going to be lying between b + + align:start position:0% +then this is going to be lying between b + + + align:start position:0% +then this is going to be lying between b +L and CL + + align:start position:0% +L and CL + + + align:start position:0% +L and CL +but these here this here will lie you + + align:start position:0% +but these here this here will lie you + + + align:start position:0% +but these here this here will lie you +know the B L because it's further out in + + align:start position:0% +know the B L because it's further out in + + + align:start position:0% +know the B L because it's further out in +subsequence it would lie to the right of + + align:start position:0% +subsequence it would lie to the right of + + + align:start position:0% +subsequence it would lie to the right of +the so here will be BK it would be BK + + align:start position:0% +the so here will be BK it would be BK + + + align:start position:0% +the so here will be BK it would be BK +would be to the left and CK would be to + + align:start position:0% +would be to the left and CK would be to + + + align:start position:0% +would be to the left and CK would be to +the right of this right so you see that + + align:start position:0% +the right of this right so you see that + + + align:start position:0% +the right of this right so you see that +these here are coming together they're + + align:start position:0% +these here are coming together they're + + + align:start position:0% +these here are coming together they're +coming together like this and the the + + align:start position:0% +coming together like this and the the + + + align:start position:0% +coming together like this and the the +the a no the the a the subsequent is + + align:start position:0% +the a no the the a the subsequent is + + + align:start position:0% +the a no the the a the subsequent is +going to be squeezed in smaller and + + align:start position:0% +going to be squeezed in smaller and + + + align:start position:0% +going to be squeezed in smaller and +smaller interval right and that's going + + align:start position:0% +smaller interval right and that's going + + + align:start position:0% +smaller interval right and that's going +to force it to converge right and the + + align:start position:0% +to force it to converge right and the + + + align:start position:0% +to force it to converge right and the +the point here is that because this here + + align:start position:0% +the point here is that because this here + + + align:start position:0% +the point here is that because this here +is increasing + + align:start position:0% +is increasing + + + align:start position:0% +is increasing +and they always lie between the ones + + align:start position:0% +and they always lie between the ones + + + align:start position:0% +and they always lie between the ones +that go below this automatically means + + align:start position:0% +that go below this automatically means + + + align:start position:0% +that go below this automatically means +that the B case will always be less than + + align:start position:0% +that the B case will always be less than + + + align:start position:0% +that the B case will always be less than +than the first + + align:start position:0% +than the first + + + align:start position:0% +than the first +C + + align:start position:0% +C + + + align:start position:0% +C +and and this C case will always be + + align:start position:0% +and and this C case will always be + + + align:start position:0% +and and this C case will always be +bigger than the first + + align:start position:0% +bigger than the first + + + align:start position:0% +bigger than the first +uh B and so this is a more a sequence + + align:start position:0% +uh B and so this is a more a sequence + + + align:start position:0% +uh B and so this is a more a sequence +that go up but it's bounded so it has a + + align:start position:0% +that go up but it's bounded so it has a + + + align:start position:0% +that go up but it's bounded so it has a +limit so BK + + align:start position:0% +limit so BK + + + align:start position:0% +limit so BK +is converging to something + + align:start position:0% +is converging to something + + + align:start position:0% +is converging to something +the CKS are going down but they're + + align:start position:0% +the CKS are going down but they're + + + align:start position:0% +the CKS are going down but they're +bounded from uniformly bounded from + + align:start position:0% +bounded from uniformly bounded from + + + align:start position:0% +bounded from uniformly bounded from +below so they will also be converging + + align:start position:0% +below so they will also be converging + + + align:start position:0% +below so they will also be converging +converging, + + align:start position:0% +converging, + + + align:start position:0% +converging, +right? But now they're coming closer + + align:start position:0% +right? But now they're coming closer + + + align:start position:0% +right? But now they're coming closer +together, right? They're coming closer + + align:start position:0% +together, right? They're coming closer + + + align:start position:0% +together, right? They're coming closer +and closer together. This is converging + + align:start position:0% +and closer together. This is converging + + + align:start position:0% +and closer together. This is converging +to that and this is converted to this. + + align:start position:0% +to that and this is converted to this. + + + align:start position:0% +to that and this is converted to this. +So that's going to imply that B is equal + + align:start position:0% +So that's going to imply that B is equal + + + align:start position:0% +So that's going to imply that B is equal +to C. + + align:start position:0% +to C. + + + align:start position:0% +to C. +Okay, that's the idea. Yeah, sorry. + + align:start position:0% + + + + align:start position:0% + +>> They they only they + + align:start position:0% +>> They they only they + + + align:start position:0% +>> They they only they +will uh they they will be uh they will + + align:start position:0% +will uh they they will be uh they will + + + align:start position:0% +will uh they they will be uh they will +have sorry the B + + align:start position:0% +have sorry the B + + + align:start position:0% +have sorry the B +K will be less or equal to B K + one and + + align:start position:0% +K will be less or equal to B K + one and + + + align:start position:0% +K will be less or equal to B K + one and +the C K + + align:start position:0% +the C K + + + align:start position:0% +the C K +will uh be uh big or equal to CK + one. + + align:start position:0% +will uh be uh big or equal to CK + one. + + + align:start position:0% +will uh be uh big or equal to CK + one. +>> So so it's not strict it's like + + align:start position:0% +>> So so it's not strict it's like + + + align:start position:0% +>> So so it's not strict it's like +inequality like this. + + align:start position:0% + + + + align:start position:0% + +>> Yeah that's right. But the thing is also + + align:start position:0% +>> Yeah that's right. But the thing is also + + + align:start position:0% +>> Yeah that's right. But the thing is also +that they are going to that the + + align:start position:0% +that they are going to that the + + + align:start position:0% +that they are going to that the +difference. So the CK is lying above the + + align:start position:0% +difference. So the CK is lying above the + + + align:start position:0% +difference. So the CK is lying above the +BK. Right? So this here is positive. + + align:start position:0% +BK. Right? So this here is positive. + + + align:start position:0% +BK. Right? So this here is positive. +This is + + align:start position:0% +This is + + + align:start position:0% +This is +and we prove that this here is bounded + + align:start position:0% +and we prove that this here is bounded + + + align:start position:0% +and we prove that this here is bounded +by two. It was actually going to be + + align:start position:0% +by two. It was actually going to be + + + align:start position:0% +by two. It was actually going to be +equal to we actually prove that this + + align:start position:0% +equal to we actually prove that this + + + align:start position:0% +equal to we actually prove that this +here is equal to um to one minus like + + align:start position:0% +here is equal to um to one minus like + + + align:start position:0% +here is equal to um to one minus like +this and you see this here goes to zero. + + align:start position:0% +this and you see this here goes to zero. + + + align:start position:0% +this and you see this here goes to zero. +So you're right that uh if they didn't + + align:start position:0% +So you're right that uh if they didn't + + + align:start position:0% +So you're right that uh if they didn't +come together we couldn't conclude + + align:start position:0% +come together we couldn't conclude + + + align:start position:0% +come together we couldn't conclude +things but they will come together this + + align:start position:0% +things but they will come together this + + + align:start position:0% +things but they will come together this +will guarantee. So how do we do this? + + align:start position:0% +will guarantee. So how do we do this? + + + align:start position:0% +will guarantee. So how do we do this? +That's the idea. How do we do this? + + align:start position:0% +That's the idea. How do we do this? + + + align:start position:0% +That's the idea. How do we do this? +Well, + + align:start position:0% +Well, + + + align:start position:0% +Well, +and again I'm just I'm just doing 0 to + + align:start position:0% +and again I'm just I'm just doing 0 to + + + align:start position:0% +and again I'm just I'm just doing 0 to +one, but it but the same argument work + + align:start position:0% +one, but it but the same argument work + + + align:start position:0% +one, but it but the same argument work +for any other interval. It's only like + + align:start position:0% +for any other interval. It's only like + + + align:start position:0% +for any other interval. It's only like +it will look it will look simpler if I + + align:start position:0% +it will look it will look simpler if I + + + align:start position:0% +it will look it will look simpler if I +do it from 0 to one. Uh but it's not + + align:start position:0% +do it from 0 to one. Uh but it's not + + + align:start position:0% +do it from 0 to one. Uh but it's not +there's nothing essential I'm using + + align:start position:0% +there's nothing essential I'm using + + + align:start position:0% +there's nothing essential I'm using +about. So here is your starting interval + + align:start position:0% +about. So here is your starting interval + + + align:start position:0% +about. So here is your starting interval +from 0 to one. + + align:start position:0% +from 0 to one. + + + align:start position:0% +from 0 to one. +We want to construct a subsequence and + + align:start position:0% +We want to construct a subsequence and + + + align:start position:0% +We want to construct a subsequence and +we want to not only what do we want to + + align:start position:0% +we want to not only what do we want to + + + align:start position:0% +we want to not only what do we want to +construct a subsequence but we also want + + align:start position:0% +construct a subsequence but we also want + + + align:start position:0% +construct a subsequence but we also want +to construct the sequence BK and the + + align:start position:0% +to construct the sequence BK and the + + + align:start position:0% +to construct the sequence BK and the +sequence CK right so let me find let me + + align:start position:0% +sequence CK right so let me find let me + + + align:start position:0% +sequence CK right so let me find let me +define B1 b1 is just going to be zero + + align:start position:0% +define B1 b1 is just going to be zero + + + align:start position:0% +define B1 b1 is just going to be zero +c1 is going to be one + + align:start position:0% +c1 is going to be one + + + align:start position:0% +c1 is going to be one +and then uh a n1 that's the subsequence + + align:start position:0% +and then uh a n1 that's the subsequence + + + align:start position:0% +and then uh a n1 that's the subsequence +the first element is subsequence I just + + align:start position:0% +the first element is subsequence I just + + + align:start position:0% +the first element is subsequence I just +take it to be the first element in + + align:start position:0% +take it to be the first element in + + + align:start position:0% +take it to be the first element in +sequence okay so now of course we have + + align:start position:0% +sequence okay so now of course we have + + + align:start position:0% +sequence okay so now of course we have +trivially that we have that b1 which is + + align:start position:0% +trivially that we have that b1 which is + + + align:start position:0% +trivially that we have that b1 which is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +this is lesser equal to a1 because it + + align:start position:0% +this is lesser equal to a1 because it + + + align:start position:0% +this is lesser equal to a1 because it +lie in this interval lesser or equal to + + align:start position:0% +lie in this interval lesser or equal to + + + align:start position:0% +lie in this interval lesser or equal to +c1 which is one Okay. + + align:start position:0% +c1 which is one Okay. + + + align:start position:0% +c1 which is one Okay. +Now then you divide it into two + + align:start position:0% +Now then you divide it into two + + + align:start position:0% +Now then you divide it into two +intervals here. So the second step is + + align:start position:0% +intervals here. So the second step is + + + align:start position:0% +intervals here. So the second step is +that you take the interval from 0 to + + align:start position:0% +that you take the interval from 0 to + + + align:start position:0% +that you take the interval from 0 to +one. + + align:start position:0% +one. + + + align:start position:0% +one. +You divide it into two halves. Right? So + + align:start position:0% +You divide it into two halves. Right? So + + + align:start position:0% +You divide it into two halves. Right? So +you have between zero and a half and a + + align:start position:0% +you have between zero and a half and a + + + align:start position:0% +you have between zero and a half and a +half and one. The whole sequence lie in + + align:start position:0% +half and one. The whole sequence lie in + + + align:start position:0% +half and one. The whole sequence lie in +this interval. + + align:start position:0% +this interval. + + + align:start position:0% +this interval. +So this means that there are either + + align:start position:0% +So this means that there are either + + + align:start position:0% +So this means that there are either +infinitely many here or infinitely many + + align:start position:0% +infinitely many here or infinitely many + + + align:start position:0% +infinitely many here or infinitely many +there. Right? Let's say that infinitely + + align:start position:0% +there. Right? Let's say that infinitely + + + align:start position:0% +there. Right? Let's say that infinitely +many of the a lie in this interval. + + align:start position:0% +many of the a lie in this interval. + + + align:start position:0% +many of the a lie in this interval. +Okay? So then we're going to + + align:start position:0% +Okay? So then we're going to + + + align:start position:0% +Okay? So then we're going to +forward we were going to just focus on + + align:start position:0% +forward we were going to just focus on + + + align:start position:0% +forward we were going to just focus on +this interval and on sub intervals of + + align:start position:0% +this interval and on sub intervals of + + + align:start position:0% +this interval and on sub intervals of +this. Okay. So the we need we have + + align:start position:0% +this. Okay. So the we need we have + + + align:start position:0% +this. Okay. So the we need we have +defined a1 + + align:start position:0% +defined a1 + + + align:start position:0% +defined a1 +a now we want to define and b1 and c1 + + align:start position:0% +a now we want to define and b1 and c1 + + + align:start position:0% +a now we want to define and b1 and c1 +then so now assume again assume + + align:start position:0% + + + + align:start position:0% + +that infinite many + + align:start position:0% + + + + align:start position:0% + +lie in this interval right so then we + + align:start position:0% +lie in this interval right so then we + + + align:start position:0% +lie in this interval right so then we +make um we a n2 the second element in a + + align:start position:0% +make um we a n2 the second element in a + + + align:start position:0% +make um we a n2 the second element in a +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +we let it be the next element after a1 + + align:start position:0% +we let it be the next element after a1 + + + align:start position:0% +we let it be the next element after a1 +that is in this smaller interval right + + align:start position:0% +that is in this smaller interval right + + + align:start position:0% +that is in this smaller interval right +so this here is the second element + + align:start position:0% + + + + align:start position:0% + +in the original sequence + + align:start position:0% +in the original sequence + + + align:start position:0% +in the original sequence +[Applause] + + align:start position:0% + + + + align:start position:0% + +that lies + + align:start position:0% +that lies + + + align:start position:0% +that lies +[Applause] + + align:start position:0% + + + + align:start position:0% + +in the interval from 0 to a half. + + align:start position:0% +in the interval from 0 to a half. + + + align:start position:0% +in the interval from 0 to a half. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +that's a n2, right? We don't want to + + align:start position:0% +that's a n2, right? We don't want to + + + align:start position:0% +that's a n2, right? We don't want to +have a1 again, right? We need another + + align:start position:0% +have a1 again, right? We need another + + + align:start position:0% +have a1 again, right? We need another +element because it's otherwise it's not + + align:start position:0% +element because it's otherwise it's not + + + align:start position:0% +element because it's otherwise it's not +going to be a subsequence. You can't + + align:start position:0% +going to be a subsequence. You can't + + + align:start position:0% +going to be a subsequence. You can't +pick a pick the A1 we already I mean it + + align:start position:0% +pick a pick the A1 we already I mean it + + + align:start position:0% +pick a pick the A1 we already I mean it +could be the same value but it's it will + + align:start position:0% +could be the same value but it's it will + + + align:start position:0% +could be the same value but it's it will +have to come from a different subscript. + + align:start position:0% +have to come from a different subscript. + + + align:start position:0% +have to come from a different subscript. +Okay. Now B2 + + align:start position:0% +Okay. Now B2 + + + align:start position:0% +Okay. Now B2 +is then just going to be the left end + + align:start position:0% +is then just going to be the left end + + + align:start position:0% +is then just going to be the left end +point of this interval. So this is again + + align:start position:0% +point of this interval. So this is again + + + align:start position:0% +point of this interval. So this is again +zero and C2 + + align:start position:0% +zero and C2 + + + align:start position:0% +zero and C2 +is going to be the right end point of + + align:start position:0% +is going to be the right end point of + + + align:start position:0% +is going to be the right end point of +this interval we're now focusing on. So + + align:start position:0% +this interval we're now focusing on. So + + + align:start position:0% +this interval we're now focusing on. So +that's a half. + + align:start position:0% + + + + align:start position:0% + +Now + + align:start position:0% +Now + + + align:start position:0% +Now +uh so now to the next. So now how do we + + align:start position:0% +uh so now to the next. So now how do we + + + align:start position:0% +uh so now to the next. So now how do we +construct the third element in the + + align:start position:0% +construct the third element in the + + + align:start position:0% +construct the third element in the +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +and the corresponding + + align:start position:0% +and the corresponding + + + align:start position:0% +and the corresponding +B's and C's. + + align:start position:0% +B's and C's. + + + align:start position:0% +B's and C's. +Okay. The thing is that and here you + + align:start position:0% +Okay. The thing is that and here you + + + align:start position:0% +Okay. The thing is that and here you +have to be a little bit careful because + + align:start position:0% +have to be a little bit careful because + + + align:start position:0% +have to be a little bit careful because +now we we we we + + align:start position:0% +now we we we we + + + align:start position:0% +now we we we we +assumed that there was infinitely many + + align:start position:0% +assumed that there was infinitely many + + + align:start position:0% +assumed that there was infinitely many +elements in the sequence that lie in + + align:start position:0% +elements in the sequence that lie in + + + align:start position:0% +elements in the sequence that lie in +this smaller interval. You are going to + + align:start position:0% +this smaller interval. You are going to + + + align:start position:0% +this smaller interval. You are going to +only from here on out you're going to + + align:start position:0% +only from here on out you're going to + + + align:start position:0% +only from here on out you're going to +only look at those infinitely many. + + align:start position:0% +only look at those infinitely many. + + + align:start position:0% +only look at those infinitely many. +You're not going to care about you know + + align:start position:0% +You're not going to care about you know + + + align:start position:0% +You're not going to care about you know +so this may be the fifth the seventh the + + align:start position:0% +so this may be the fifth the seventh the + + + align:start position:0% +so this may be the fifth the seventh the +15th element in the original sequence. + + align:start position:0% +15th element in the original sequence. + + + align:start position:0% +15th element in the original sequence. +You're not going to worry about what + + align:start position:0% +You're not going to worry about what + + + align:start position:0% +You're not going to worry about what +lies here, right? And so now you divide + + align:start position:0% +lies here, right? And so now you divide + + + align:start position:0% +lies here, right? And so now you divide +this one here into two halves. This + + align:start position:0% +this one here into two halves. This + + + align:start position:0% +this one here into two halves. This +interval between zero and a half, you + + align:start position:0% +interval between zero and a half, you + + + align:start position:0% +interval between zero and a half, you +divide it into two halves. + + align:start position:0% +divide it into two halves. + + + align:start position:0% +divide it into two halves. +And so so now imagine you have then the + + align:start position:0% +And so so now imagine you have then the + + + align:start position:0% +And so so now imagine you have then the +picture here. Here you have zero. Here + + align:start position:0% +picture here. Here you have zero. Here + + + align:start position:0% +picture here. Here you have zero. Here +you have uh a half. + + align:start position:0% +you have uh a half. + + + align:start position:0% +you have uh a half. +And then you divide it into this + + align:start position:0% +And then you divide it into this + + + align:start position:0% +And then you divide it into this +interval from zero to half. You divide + + align:start position:0% +interval from zero to half. You divide + + + align:start position:0% +interval from zero to half. You divide +it into + + align:start position:0% +it into + + + align:start position:0% +it into +two equally + + align:start position:0% +two equally + + + align:start position:0% +two equally +large intervals. So + + align:start position:0% +large intervals. So + + + align:start position:0% +large intervals. So +now + + align:start position:0% +now + + + align:start position:0% +now +we already we're just focusing on the + + align:start position:0% +we already we're just focusing on the + + + align:start position:0% +we already we're just focusing on the +infinitely many of the original sequence + + align:start position:0% +infinitely many of the original sequence + + + align:start position:0% +infinitely many of the original sequence +that lie here. But of those infinitely + + align:start position:0% +that lie here. But of those infinitely + + + align:start position:0% +that lie here. But of those infinitely +many either infinite many lie here or + + align:start position:0% +many either infinite many lie here or + + + align:start position:0% +many either infinite many lie here or +infinitely many lie there. Right? + + align:start position:0% +infinitely many lie there. Right? + + + align:start position:0% +infinitely many lie there. Right? +Let's say that that there's only + + align:start position:0% +Let's say that that there's only + + + align:start position:0% +Let's say that that there's only +finitely many here. Say but there are + + align:start position:0% +finitely many here. Say but there are + + + align:start position:0% +finitely many here. Say but there are +infinitely many here. Right? So if + + align:start position:0% +infinitely many here. Right? So if + + + align:start position:0% +infinitely many here. Right? So if +there's infinitely many in this interval + + align:start position:0% +there's infinitely many in this interval + + + align:start position:0% +there's infinitely many in this interval +here, then from here on out, you would + + align:start position:0% +here, then from here on out, you would + + + align:start position:0% +here, then from here on out, you would +only focus on those infinite many. And + + align:start position:0% +only focus on those infinite many. And + + + align:start position:0% +only focus on those infinite many. And +the next element would be right we know + + align:start position:0% +the next element would be right we know + + + align:start position:0% +the next element would be right we know +that uh right the next element would be + + align:start position:0% +that uh right the next element would be + + + align:start position:0% +that uh right the next element would be +the next element after the the one you + + align:start position:0% +the next element after the the one you + + + align:start position:0% +the next element after the the one you +pick to be the second element in the + + align:start position:0% +pick to be the second element in the + + + align:start position:0% +pick to be the second element in the +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +that would lie in this in this + + align:start position:0% +that would lie in this in this + + + align:start position:0% +that would lie in this in this +subsequence. Right? So we define a3 + + align:start position:0% +subsequence. Right? So we define a3 + + + align:start position:0% +subsequence. Right? So we define a3 +is now the next element. So a N3 + + align:start position:0% +is now the next element. So a N3 + + + align:start position:0% +is now the next element. So a N3 +this is now this element that lies in in + + align:start position:0% +this is now this element that lies in in + + + align:start position:0% +this is now this element that lies in in +in this interval here right and then B + + align:start position:0% +in this interval here right and then B + + + align:start position:0% +in this interval here right and then B +B3 is then going to be 1 / 4 and B uh + + align:start position:0% +B3 is then going to be 1 / 4 and B uh + + + align:start position:0% +B3 is then going to be 1 / 4 and B uh +sorry and C3 + + align:start position:0% +sorry and C3 + + + align:start position:0% +sorry and C3 +is going to be the right uh end point of + + align:start position:0% +is going to be the right uh end point of + + + align:start position:0% +is going to be the right uh end point of +this interval 1 over 4 one over two + + align:start position:0% +this interval 1 over 4 one over two + + + align:start position:0% +this interval 1 over 4 one over two +Right? + + align:start position:0% + + + + align:start position:0% + +And then you continue, right? Then you + + align:start position:0% +And then you continue, right? Then you + + + align:start position:0% +And then you continue, right? Then you +continue this way. So let me just make + + align:start position:0% +continue this way. So let me just make + + + align:start position:0% +continue this way. So let me just make +sure that it's totally clear. Let me + + align:start position:0% +sure that it's totally clear. Let me + + + align:start position:0% +sure that it's totally clear. Let me +just go over how how we did it. + + align:start position:0% +just go over how how we did it. + + + align:start position:0% +just go over how how we did it. +Right? So, so just because I want to be + + align:start position:0% +Right? So, so just because I want to be + + + align:start position:0% +Right? So, so just because I want to be +careful that you, you know, once you, so + + align:start position:0% +careful that you, you know, once you, so + + + align:start position:0% +careful that you, you know, once you, so +we started with the interval from 0 to + + align:start position:0% +we started with the interval from 0 to + + + align:start position:0% +we started with the interval from 0 to +one, the first element you just pick in + + align:start position:0% +one, the first element you just pick in + + + align:start position:0% +one, the first element you just pick in +the subsequence that was just the first + + align:start position:0% +the subsequence that was just the first + + + align:start position:0% +the subsequence that was just the first +element in the original sequence and the + + align:start position:0% +element in the original sequence and the + + + align:start position:0% +element in the original sequence and the +B1 was just the left endpoint here. So + + align:start position:0% +B1 was just the left endpoint here. So + + + align:start position:0% +B1 was just the left endpoint here. So +that was zero. C1 was the right endpoint + + align:start position:0% +that was zero. C1 was the right endpoint + + + align:start position:0% +that was zero. C1 was the right endpoint +that was one. + + align:start position:0% +that was one. + + + align:start position:0% +that was one. +Now you divide it into two and one of + + align:start position:0% +Now you divide it into two and one of + + + align:start position:0% +Now you divide it into two and one of +the two half potentially of course both + + align:start position:0% +the two half potentially of course both + + + align:start position:0% +the two half potentially of course both +of the two half could have infinite many + + align:start position:0% +of the two half could have infinite many + + + align:start position:0% +of the two half could have infinite many +elements in the original sequence. You + + align:start position:0% +elements in the original sequence. You + + + align:start position:0% +elements in the original sequence. You +just focus on one of the two half that + + align:start position:0% +just focus on one of the two half that + + + align:start position:0% +just focus on one of the two half that +have infinite elements, right? If + + align:start position:0% +have infinite elements, right? If + + + align:start position:0% +have infinite elements, right? If +they're both fine, but you just take one + + align:start position:0% +they're both fine, but you just take one + + + align:start position:0% +they're both fine, but you just take one +of them, right? + + align:start position:0% +of them, right? + + + align:start position:0% +of them, right? +And so from here on out, we're just + + align:start position:0% +And so from here on out, we're just + + + align:start position:0% +And so from here on out, we're just +going to focus on those infinitely many. + + align:start position:0% +going to focus on those infinitely many. + + + align:start position:0% +going to focus on those infinitely many. +And then you're going to pick the next + + align:start position:0% +And then you're going to pick the next + + + align:start position:0% +And then you're going to pick the next +one after the the A1 that lies in that + + align:start position:0% +one after the the A1 that lies in that + + + align:start position:0% +one after the the A1 that lies in that +interval you're focusing on. That's the + + align:start position:0% +interval you're focusing on. That's the + + + align:start position:0% +interval you're focusing on. That's the +second element in a subsequence. And the + + align:start position:0% +second element in a subsequence. And the + + + align:start position:0% +second element in a subsequence. And the +B's will always be the left end point of + + align:start position:0% +B's will always be the left end point of + + + align:start position:0% +B's will always be the left end point of +the interval. The C's will be the right + + align:start position:0% +the interval. The C's will be the right + + + align:start position:0% +the interval. The C's will be the right +end point of the interval. + + align:start position:0% +end point of the interval. + + + align:start position:0% +end point of the interval. +Then when you do the third element, then + + align:start position:0% +Then when you do the third element, then + + + align:start position:0% +Then when you do the third element, then +you have to remember that you were + + align:start position:0% +you have to remember that you were + + + align:start position:0% +you have to remember that you were +looking at infinitely many. And so now + + align:start position:0% +looking at infinitely many. And so now + + + align:start position:0% +looking at infinitely many. And so now +it's like you're looking at you divide + + align:start position:0% +it's like you're looking at you divide + + + align:start position:0% +it's like you're looking at you divide +this interval into two. + + align:start position:0% +this interval into two. + + + align:start position:0% +this interval into two. +And now either this one here or that one + + align:start position:0% +And now either this one here or that one + + + align:start position:0% +And now either this one here or that one +here has infinite many, right? and you + + align:start position:0% +here has infinite many, right? and you + + + align:start position:0% +here has infinite many, right? and you +pick whatever it is. I mean, I guess we + + align:start position:0% +pick whatever it is. I mean, I guess we + + + align:start position:0% +pick whatever it is. I mean, I guess we +we assumed it was this interval. + + align:start position:0% +we assumed it was this interval. + + + align:start position:0% +we assumed it was this interval. +And then the next element after the the + + align:start position:0% +And then the next element after the the + + + align:start position:0% +And then the next element after the the +two first you picked in the original + + align:start position:0% +two first you picked in the original + + + align:start position:0% +two first you picked in the original +sequence, the next element that lies in + + align:start position:0% +sequence, the next element that lies in + + + align:start position:0% +sequence, the next element that lies in +this that's going to be your third + + align:start position:0% +this that's going to be your third + + + align:start position:0% +this that's going to be your third +element of the sequence. And then still + + align:start position:0% +element of the sequence. And then still + + + align:start position:0% +element of the sequence. And then still +the B's will be then of this interval + + align:start position:0% +the B's will be then of this interval + + + align:start position:0% +the B's will be then of this interval +you're focusing on would be the left end + + align:start position:0% +you're focusing on would be the left end + + + align:start position:0% +you're focusing on would be the left end +point and the C the right end point. + + align:start position:0% +point and the C the right end point. + + + align:start position:0% +point and the C the right end point. +Right? If you do that, you see each time + + align:start position:0% +Right? If you do that, you see each time + + + align:start position:0% +Right? If you do that, you see each time +you're halfing it. So it means well it + + align:start position:0% +you're halfing it. So it means well it + + + align:start position:0% +you're halfing it. So it means well it +first of all it means that the that the + + align:start position:0% +first of all it means that the that the + + + align:start position:0% +first of all it means that the that the +bees are going to be increasing right + + align:start position:0% +bees are going to be increasing right + + + align:start position:0% +bees are going to be increasing right +because it's always right each time you + + align:start position:0% +because it's always right each time you + + + align:start position:0% +because it's always right each time you +divide into a half and it's always and + + align:start position:0% +divide into a half and it's always and + + + align:start position:0% +divide into a half and it's always and +but it's like the interval you focus on + + align:start position:0% +but it's like the interval you focus on + + + align:start position:0% +but it's like the interval you focus on +previously you divide into a half like + + align:start position:0% +previously you divide into a half like + + + align:start position:0% +previously you divide into a half like +this and then you either you pick either + + align:start position:0% +this and then you either you pick either + + + align:start position:0% +this and then you either you pick either +this point or that point right and this + + align:start position:0% +this point or that point right and this + + + align:start position:0% +this point or that point right and this +here was the previous one right so the + + align:start position:0% +here was the previous one right so the + + + align:start position:0% +here was the previous one right so the +bees will always be increasing + + align:start position:0% +bees will always be increasing + + + align:start position:0% +bees will always be increasing +Likewise, the C's will be a decreasing + + align:start position:0% +Likewise, the C's will be a decreasing + + + align:start position:0% +Likewise, the C's will be a decreasing +sequence. + + align:start position:0% +sequence. + + + align:start position:0% +sequence. +And you also see + + align:start position:0% +And you also see + + + align:start position:0% +And you also see +that the difference between CK say CK + + + align:start position:0% +that the difference between CK say CK + + + + align:start position:0% +that the difference between CK say CK + +1 minus B K + one that the difference + + align:start position:0% +1 minus B K + one that the difference + + + align:start position:0% +1 minus B K + one that the difference +here, right? But the difference is going + + align:start position:0% +here, right? But the difference is going + + + align:start position:0% +here, right? But the difference is going +to be like half of the length of the + + align:start position:0% +to be like half of the length of the + + + align:start position:0% +to be like half of the length of the +previous interval, right? So the + + align:start position:0% +previous interval, right? So the + + + align:start position:0% +previous interval, right? So the +difference here is going to be 1/2. it's + + align:start position:0% +difference here is going to be 1/2. it's + + + align:start position:0% +difference here is going to be 1/2. it's +actually going to be 12 + + align:start position:0% +actually going to be 12 + + + align:start position:0% +actually going to be 12 +uh and then B C + + align:start position:0% +uh and then B C + + + align:start position:0% +uh and then B C +minus BK. + + align:start position:0% +minus BK. + + + align:start position:0% +minus BK. +So you're getting this form right and so + + align:start position:0% +So you're getting this form right and so + + + align:start position:0% +So you're getting this form right and so +and now if you just use that you're + + align:start position:0% +and now if you just use that you're + + + align:start position:0% +and now if you just use that you're +starting with if you're just using that + + align:start position:0% +starting with if you're just using that + + + align:start position:0% +starting with if you're just using that +the aridium. So when so you get this + + align:start position:0% +the aridium. So when so you get this + + + align:start position:0% +the aridium. So when so you get this +recursive formula here + + align:start position:0% +recursive formula here + + + align:start position:0% +recursive formula here +and you also have that c uh 1 minus b1 + + align:start position:0% +and you also have that c uh 1 minus b1 + + + align:start position:0% +and you also have that c uh 1 minus b1 +this is the length of the original + + align:start position:0% +this is the length of the original + + + align:start position:0% +this is the length of the original +interval right because b1 was zero c1 + + align:start position:0% +interval right because b1 was zero c1 + + + align:start position:0% +interval right because b1 was zero c1 +was one so this is one + + align:start position:0% +was one so this is one + + + align:start position:0% +was one so this is one +and so you're just putting this in and + + align:start position:0% +and so you're just putting this in and + + + align:start position:0% +and so you're just putting this in and +so you get the formula that c k minus bk + + align:start position:0% +so you get the formula that c k minus bk + + + align:start position:0% +so you get the formula that c k minus bk +K is equal to 2 to the uh 1 minus K. + + align:start position:0% +K is equal to 2 to the uh 1 minus K. + + + align:start position:0% +K is equal to 2 to the uh 1 minus K. +So you're getting this formula here. + + align:start position:0% +So you're getting this formula here. + + + align:start position:0% +So you're getting this formula here. +This just come from this recursive + + align:start position:0% +This just come from this recursive + + + align:start position:0% +This just come from this recursive +formula and how this starts right. See + + align:start position:0% +formula and how this starts right. See + + + align:start position:0% +formula and how this starts right. See +this give you this. Okay. And so you see + + align:start position:0% +this give you this. Okay. And so you see + + + align:start position:0% +this give you this. Okay. And so you see +that the length of these interval + + align:start position:0% +that the length of these interval + + + align:start position:0% +that the length of these interval +becomes smaller and smaller. Again the + + align:start position:0% +becomes smaller and smaller. Again the + + + align:start position:0% +becomes smaller and smaller. Again the +sequence BK is increasing the CK is + + align:start position:0% +sequence BK is increasing the CK is + + + align:start position:0% +sequence BK is increasing the CK is +decreasing. So this means that this here + + align:start position:0% +decreasing. So this means that this here + + + align:start position:0% +decreasing. So this means that this here +is converging to some B. This here is + + align:start position:0% +is converging to some B. This here is + + + align:start position:0% +is converging to some B. This here is +converging to some C. And because the + + align:start position:0% +converging to some C. And because the + + + align:start position:0% +converging to some C. And because the +difference between these goes to zero. + + align:start position:0% +difference between these goes to zero. + + + align:start position:0% +difference between these goes to zero. +Then the B must be equal to C. + + align:start position:0% +Then the B must be equal to C. + + + align:start position:0% +Then the B must be equal to C. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +and and so this will prove that the + + align:start position:0% +and and so this will prove that the + + + align:start position:0% +and and so this will prove that the +limit that you construct because the the + + align:start position:0% +limit that you construct because the the + + + align:start position:0% +limit that you construct because the the +this is going to be squeezed + + align:start position:0% + + + + align:start position:0% + +you have this property that if you're + + align:start position:0% +you have this property that if you're + + + align:start position:0% +you have this property that if you're +looking at a k and even uh sorry a n k + + align:start position:0% +looking at a k and even uh sorry a n k + + + align:start position:0% +looking at a k and even uh sorry a n k +and even a uh n l + + align:start position:0% +and even a uh n l + + + align:start position:0% +and even a uh n l +that this thing here. This here will by + + align:start position:0% +that this thing here. This here will by + + + align:start position:0% +that this thing here. This here will by +construction will lie between these two + + align:start position:0% +construction will lie between these two + + + align:start position:0% +construction will lie between these two +but all the later ones will also lie in + + align:start position:0% +but all the later ones will also lie in + + + align:start position:0% +but all the later ones will also lie in +this interval. Right? So this here will + + align:start position:0% +this interval. Right? So this here will + + + align:start position:0% +this interval. Right? So this here will +also lie in this interval + + align:start position:0% +also lie in this interval + + + align:start position:0% +also lie in this interval +CK as long as L here is bigger equal to + + align:start position:0% +CK as long as L here is bigger equal to + + + align:start position:0% +CK as long as L here is bigger equal to +K. + + align:start position:0% +K. + + + align:start position:0% +K. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +And so you see that this thing here this + + align:start position:0% +And so you see that this thing here this + + + align:start position:0% +And so you see that this thing here this +thing here will because this here is + + align:start position:0% +thing here will because this here is + + + align:start position:0% +thing here will because this here is +converging + + align:start position:0% +converging + + + align:start position:0% +converging +to B and this is actually now we prove + + align:start position:0% +to B and this is actually now we prove + + + align:start position:0% +to B and this is actually now we prove +that this converts to the same number B. + + align:start position:0% +that this converts to the same number B. + + + align:start position:0% +that this converts to the same number B. +So this means that these guys here that + + align:start position:0% +So this means that these guys here that + + + align:start position:0% +So this means that these guys here that +is squeezed between these two other + + align:start position:0% +is squeezed between these two other + + + align:start position:0% +is squeezed between these two other +sequence will also converge + + align:start position:0% +sequence will also converge + + + align:start position:0% +sequence will also converge +to B. Okay. So that's a vol. + + align:start position:0% + + + + align:start position:0% + +Okay. Another key concept is um in this + + align:start position:0% +Okay. Another key concept is um in this + + + align:start position:0% +Okay. Another key concept is um in this +class is the concept of a series. + + align:start position:0% +class is the concept of a series. + + + align:start position:0% +class is the concept of a series. +Um + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +and so so this is the concept of a + + align:start position:0% +and so so this is the concept of a + + + align:start position:0% +and so so this is the concept of a +series. + + align:start position:0% + + + + align:start position:0% + +U and so a series is like as follows + + align:start position:0% +U and so a series is like as follows + + + align:start position:0% +U and so a series is like as follows +that suppose you have so let + + align:start position:0% +that suppose you have so let + + + align:start position:0% +that suppose you have so let +a n be a sequence + + align:start position:0% + + + + align:start position:0% + +from a sequence you can form another + + align:start position:0% +from a sequence you can form another + + + align:start position:0% +from a sequence you can form another +sequence and you can form another + + align:start position:0% +sequence and you can form another + + + align:start position:0% +sequence and you can form another +sequence the following way that s so we + + align:start position:0% +sequence the following way that s so we + + + align:start position:0% +sequence the following way that s so we +form + + align:start position:0% +form + + + align:start position:0% +form +another sequence + + align:start position:0% + + + + align:start position:0% + +And that is that uh s1 and we call this + + align:start position:0% +And that is that uh s1 and we call this + + + align:start position:0% +And that is that uh s1 and we call this +other sequence sn another sequence sn + + align:start position:0% +other sequence sn another sequence sn + + + align:start position:0% +other sequence sn another sequence sn +and uh and the sequence is defined as + + align:start position:0% +and uh and the sequence is defined as + + + align:start position:0% +and uh and the sequence is defined as +follows that s_ub_1 is a1 + + align:start position:0% +follows that s_ub_1 is a1 + + + align:start position:0% +follows that s_ub_1 is a1 +s_ub_2 is a1 + a2 + + align:start position:0% +s_ub_2 is a1 + a2 + + + align:start position:0% +s_ub_2 is a1 + a2 +s3 3 + + align:start position:0% +s3 3 + + + align:start position:0% +s3 3 +is uh a1 + a2 + a3. + + align:start position:0% +is uh a1 + a2 + a3. + + + align:start position:0% +is uh a1 + a2 + a3. +Um, S4 is where you summing the first + + align:start position:0% +Um, S4 is where you summing the first + + + align:start position:0% +Um, S4 is where you summing the first +four element in this in the original + + align:start position:0% +four element in this in the original + + + align:start position:0% +four element in this in the original +sequence + + align:start position:0% + + + + align:start position:0% + +and and then you write sorry this is + + align:start position:0% +and and then you write sorry this is + + + align:start position:0% +and and then you write sorry this is +first four element and then you write + + align:start position:0% +first four element and then you write + + + align:start position:0% +first four element and then you write +the nth element you write it just as a + + align:start position:0% +the nth element you write it just as a + + + align:start position:0% +the nth element you write it just as a +sum where I equals to one say to N of + + align:start position:0% +sum where I equals to one say to N of + + + align:start position:0% +sum where I equals to one say to N of +the AIS. + + align:start position:0% + + + + align:start position:0% + +So, so if you have a a sequence then you + + align:start position:0% +So, so if you have a a sequence then you + + + align:start position:0% +So, so if you have a a sequence then you +can form another sequence + + align:start position:0% +can form another sequence + + + align:start position:0% +can form another sequence +and this is this we denote by s and this + + align:start position:0% +and this is this we denote by s and this + + + align:start position:0% +and this is this we denote by s and this +here is this here is so we really so + + align:start position:0% +here is this here is so we really so + + + align:start position:0% +here is this here is so we really so +this here other sequence if a sequence + + align:start position:0% +this here other sequence if a sequence + + + align:start position:0% +this here other sequence if a sequence +is of this form then you call it a + + align:start position:0% +is of this form then you call it a + + + align:start position:0% +is of this form then you call it a +series so so uh so sn here so but sn is + + align:start position:0% +series so so uh so sn here so but sn is + + + align:start position:0% +series so so uh so sn here so but sn is +just a sequence this here is called is + + align:start position:0% +just a sequence this here is called is + + + align:start position:0% +just a sequence this here is called is +said to be + + align:start position:0% + + + + align:start position:0% + +a series. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now um let's let's go to the most so I'm + + align:start position:0% +Now um let's let's go to the most so I'm + + + align:start position:0% +Now um let's let's go to the most so I'm +sure m probably everybody have heard + + align:start position:0% +sure m probably everybody have heard + + + align:start position:0% +sure m probably everybody have heard +about that's a kind of one of the famous + + align:start position:0% +about that's a kind of one of the famous + + + align:start position:0% +about that's a kind of one of the famous +Greek paradoxes is this with I mean they + + align:start position:0% +Greek paradoxes is this with I mean they + + + align:start position:0% +Greek paradoxes is this with I mean they +have various different forms is this + + align:start position:0% +have various different forms is this + + + align:start position:0% +have various different forms is this +with one form of it is with Achilles and + + align:start position:0% +with one form of it is with Achilles and + + + align:start position:0% +with one form of it is with Achilles and +the turtle where the turtle is getting a + + align:start position:0% +the turtle where the turtle is getting a + + + align:start position:0% +the turtle where the turtle is getting a +head start of Achilles and the paradox + + align:start position:0% +head start of Achilles and the paradox + + + align:start position:0% +head start of Achilles and the paradox +is that because the turtle have a head + + align:start position:0% +is that because the turtle have a head + + + align:start position:0% +is that because the turtle have a head +start, then Achilles can never catch up + + align:start position:0% +start, then Achilles can never catch up + + + align:start position:0% +start, then Achilles can never catch up +with the turtle even though the turtle + + align:start position:0% +with the turtle even though the turtle + + + align:start position:0% +with the turtle even though the turtle +is moving incredibly slowly because in + + align:start position:0% +is moving incredibly slowly because in + + + align:start position:0% +is moving incredibly slowly because in +order to catch up with the turtle then + + align:start position:0% +order to catch up with the turtle then + + + align:start position:0% +order to catch up with the turtle then +Achilles first have have to go um half + + align:start position:0% +Achilles first have have to go um half + + + align:start position:0% +Achilles first have have to go um half +of the distance that the turtle have + + align:start position:0% +of the distance that the turtle have + + + align:start position:0% +of the distance that the turtle have +gone and then once you have done that he + + align:start position:0% +gone and then once you have done that he + + + align:start position:0% +gone and then once you have done that he +have to go half of the distance that he + + align:start position:0% +have to go half of the distance that he + + + align:start position:0% +have to go half of the distance that he +that the turtle now have traveled etc + + align:start position:0% +that the turtle now have traveled etc + + + align:start position:0% +that the turtle now have traveled etc +and so this go on infinitely long and + + align:start position:0% +and so this go on infinitely long and + + + align:start position:0% +and so this go on infinitely long and +Therefore, he can never catch up with + + align:start position:0% +Therefore, he can never catch up with + + + align:start position:0% +Therefore, he can never catch up with +the turtle. There's various other + + align:start position:0% +the turtle. There's various other + + + align:start position:0% +the turtle. There's various other +version of this, right? But that and + + align:start position:0% +version of this, right? But that and + + + align:start position:0% +version of this, right? But that and +that's exactly a series and like and + + align:start position:0% +that's exactly a series and like and + + + align:start position:0% +that's exactly a series and like and +this is also like the most important + + align:start position:0% +this is also like the most important + + + align:start position:0% +this is also like the most important +series is what's called the geometric + + align:start position:0% +series is what's called the geometric + + + align:start position:0% +series is what's called the geometric +series. + + align:start position:0% +series. + + + align:start position:0% +series. +So the geometric series. + + align:start position:0% +So the geometric series. + + + align:start position:0% +So the geometric series. +So this is a you know the most important + + align:start position:0% +So this is a you know the most important + + + align:start position:0% +So this is a you know the most important +uh series and it's the most important + + align:start position:0% +uh series and it's the most important + + + align:start position:0% +uh series and it's the most important +because it's kind of a non-trivial + + align:start position:0% +because it's kind of a non-trivial + + + align:start position:0% +because it's kind of a non-trivial +series that can be used to determine + + align:start position:0% +series that can be used to determine + + + align:start position:0% +series that can be used to determine +whether other series or whether these + + align:start position:0% +whether other series or whether these + + + align:start position:0% +whether other series or whether these +other for other sums whether these uh + + align:start position:0% +other for other sums whether these uh + + + align:start position:0% +other for other sums whether these uh +this sequence sn whether it converges or + + align:start position:0% +this sequence sn whether it converges or + + + align:start position:0% +this sequence sn whether it converges or +not. So the geometric series is the + + align:start position:0% +not. So the geometric series is the + + + align:start position:0% +not. So the geometric series is the +following that C you take some number C + + align:start position:0% +following that C you take some number C + + + align:start position:0% +following that C you take some number C +and then you are summing uh this number + + align:start position:0% +and then you are summing uh this number + + + align:start position:0% +and then you are summing uh this number +but to a power so you're looking at + + align:start position:0% +but to a power so you're looking at + + + align:start position:0% +but to a power so you're looking at +where you have some power say from zero + + align:start position:0% +where you have some power say from zero + + + align:start position:0% +where you have some power say from zero +to n + + align:start position:0% +to n + + + align:start position:0% +to n +right so this means that um so this is + + align:start position:0% +right so this means that um so this is + + + align:start position:0% +right so this means that um so this is +SN so it mean that s uh s zero uh this + + align:start position:0% +SN so it mean that s uh s zero uh this + + + align:start position:0% +SN so it mean that s uh s zero uh this +is just where you have + + align:start position:0% +is just where you have + + + align:start position:0% +is just where you have +where you have uh by C to the power zero + + align:start position:0% +where you have uh by C to the power zero + + + align:start position:0% +where you have uh by C to the power zero +by definition is one and s1 is then when + + align:start position:0% +by definition is one and s1 is then when + + + align:start position:0% +by definition is one and s1 is then when +you're summing + + align:start position:0% +you're summing + + + align:start position:0% +you're summing +c to the power z plus c to ^ 1. So + + align:start position:0% +c to the power z plus c to ^ 1. So + + + align:start position:0% +c to the power z plus c to ^ 1. So +that's just uh 1 + c and s_ub_2 is then + + align:start position:0% +that's just uh 1 + c and s_ub_2 is then + + + align:start position:0% +that's just uh 1 + c and s_ub_2 is then +uh s_ub_2 is then + + align:start position:0% +uh s_ub_2 is then + + + align:start position:0% +uh s_ub_2 is then +[Applause] + + align:start position:0% + + + + align:start position:0% + +s_2 is then uh c 0 + c1 + + align:start position:0% +s_2 is then uh c 0 + c1 + + + align:start position:0% +s_2 is then uh c 0 + c1 ++ c². So that's just 1 + uh c + uh c², + + align:start position:0% ++ c². So that's just 1 + uh c + uh c², + + + align:start position:0% ++ c². So that's just 1 + uh c + uh c², +right? Etc. + + align:start position:0% +right? Etc. + + + align:start position:0% +right? Etc. +So that's a geometric series where it's + + align:start position:0% +So that's a geometric series where it's + + + align:start position:0% +So that's a geometric series where it's +just a number and each time you multiply + + align:start position:0% +just a number and each time you multiply + + + align:start position:0% +just a number and each time you multiply +that number by itself the end time and + + align:start position:0% +that number by itself the end time and + + + align:start position:0% +that number by itself the end time and +then you're adding it to the previous. + + align:start position:0% +then you're adding it to the previous. + + + align:start position:0% +then you're adding it to the previous. +So that's the geometric series. Okay. + + align:start position:0% +So that's the geometric series. Okay. + + + align:start position:0% +So that's the geometric series. Okay. +And now and the reason why this is uh + + align:start position:0% +And now and the reason why this is uh + + + align:start position:0% +And now and the reason why this is uh +important is that this is very useful to + + align:start position:0% +important is that this is very useful to + + + align:start position:0% +important is that this is very useful to +determine whether other series are + + align:start position:0% +determine whether other series are + + + align:start position:0% +determine whether other series are +convergent or not because you can + + align:start position:0% +convergent or not because you can + + + align:start position:0% +convergent or not because you can +compare it. You can compare other series + + align:start position:0% +compare it. You can compare other series + + + align:start position:0% +compare it. You can compare other series +with the geometric series + + align:start position:0% +with the geometric series + + + align:start position:0% +with the geometric series +and the geometric series is easy to + + align:start position:0% +and the geometric series is easy to + + + align:start position:0% +and the geometric series is easy to +determine whether it's convergent or + + align:start position:0% +determine whether it's convergent or + + + align:start position:0% +determine whether it's convergent or +not. And so this is because of the + + align:start position:0% +not. And so this is because of the + + + align:start position:0% +not. And so this is because of the +following little calculation here. Let's + + align:start position:0% +following little calculation here. Let's + + + align:start position:0% +following little calculation here. Let's +suppose I'm looking at some summing here + + align:start position:0% +suppose I'm looking at some summing here + + + align:start position:0% +suppose I'm looking at some summing here +from zero to N of C to the power I + + align:start position:0% +from zero to N of C to the power I + + + align:start position:0% +from zero to N of C to the power I +and now I multiply this with C. Right? + + align:start position:0% +and now I multiply this with C. Right? + + + align:start position:0% +and now I multiply this with C. Right? +So then this here would just be where + + align:start position:0% +So then this here would just be where + + + align:start position:0% +So then this here would just be where +I'm summing here. You see if I multiply + + align:start position:0% +I'm summing here. You see if I multiply + + + align:start position:0% +I'm summing here. You see if I multiply +by C I can move that C inside and then + + align:start position:0% +by C I can move that C inside and then + + + align:start position:0% +by C I can move that C inside and then +the first time it's really right. So you + + align:start position:0% +the first time it's really right. So you + + + align:start position:0% +the first time it's really right. So you +can write this thing here. So let me + + align:start position:0% +can write this thing here. So let me + + + align:start position:0% +can write this thing here. So let me +just write it out. So this is C and then + + align:start position:0% +just write it out. So this is C and then + + + align:start position:0% +just write it out. So this is C and then +it's 1 + C + C 2 + CQ + + align:start position:0% +it's 1 + C + C 2 + CQ + + + align:start position:0% +it's 1 + C + C 2 + CQ +etc like that up to C uh N. + + align:start position:0% +etc like that up to C uh N. + + + align:start position:0% +etc like that up to C uh N. +And if you multiply by C then of course + + align:start position:0% +And if you multiply by C then of course + + + align:start position:0% +And if you multiply by C then of course +this is just C + C ^2 + C cub up to + + align:start position:0% +this is just C + C ^2 + C cub up to + + + align:start position:0% +this is just C + C ^2 + C cub up to +uh C to the N + one. Okay. + + align:start position:0% +uh C to the N + one. Okay. + + + align:start position:0% +uh C to the N + one. Okay. +And so this means that if you take this + + align:start position:0% +And so this means that if you take this + + + align:start position:0% +And so this means that if you take this +thing here, so if you take if you're + + align:start position:0% +thing here, so if you take if you're + + + align:start position:0% +thing here, so if you take if you're +looking at this sum from zero to n of CI + + align:start position:0% +looking at this sum from zero to n of CI + + + align:start position:0% +looking at this sum from zero to n of CI +and now you multiply by 1 minus C, + + align:start position:0% +and now you multiply by 1 minus C, + + + align:start position:0% +and now you multiply by 1 minus C, +right? Then this here is the same as + + align:start position:0% +right? Then this here is the same as + + + align:start position:0% +right? Then this here is the same as +this here is the same as + + align:start position:0% +this here is the same as + + + align:start position:0% +this here is the same as +just one times this. So let me just + + align:start position:0% +just one times this. So let me just + + + align:start position:0% +just one times this. So let me just +write it out. This is what this just + + align:start position:0% +write it out. This is what this just + + + align:start position:0% +write it out. This is what this just +give you the in original series. So this + + align:start position:0% +give you the in original series. So this + + + align:start position:0% +give you the in original series. So this +gives you this up to CN. That's when we + + align:start position:0% +gives you this up to CN. That's when we + + + align:start position:0% +gives you this up to CN. That's when we +multiply the one in when we multiply it + + align:start position:0% +multiply the one in when we multiply it + + + align:start position:0% +multiply the one in when we multiply it +by minus C then we get this thing here + + align:start position:0% +by minus C then we get this thing here + + + align:start position:0% +by minus C then we get this thing here +with a minus sign. So we're getting + + align:start position:0% +with a minus sign. So we're getting + + + align:start position:0% +with a minus sign. So we're getting +minus C. Um so I can write like this + + align:start position:0% + + + + align:start position:0% + +like that. + + align:start position:0% +like that. + + + align:start position:0% +like that. +But now you see that there's a lot of + + align:start position:0% +But now you see that there's a lot of + + + align:start position:0% +But now you see that there's a lot of +cancellation, right? This thing here + + align:start position:0% +cancellation, right? This thing here + + + align:start position:0% +cancellation, right? This thing here +cancel + + align:start position:0% +cancel + + + align:start position:0% +cancel +with this here. The next one would + + align:start position:0% +with this here. The next one would + + + align:start position:0% +with this here. The next one would +cancel with this. This here would cancel + + align:start position:0% +cancel with this. This here would cancel + + + align:start position:0% +cancel with this. This here would cancel +with the second last, right? And so you + + align:start position:0% +with the second last, right? And so you + + + align:start position:0% +with the second last, right? And so you +were only left with this one here and + + align:start position:0% +were only left with this one here and + + + align:start position:0% +were only left with this one here and +that one here. But the this one here + + align:start position:0% +that one here. But the this one here + + + align:start position:0% +that one here. But the this one here +comes in with a minus sign. So this is 1 + + align:start position:0% +comes in with a minus sign. So this is 1 + + + align:start position:0% +comes in with a minus sign. So this is 1 +minus c to the n + one. + + align:start position:0% +minus c to the n + one. + + + align:start position:0% +minus c to the n + one. +Okay. So we have this little formula + + align:start position:0% + + + + align:start position:0% + +have this little formula say that if you + + align:start position:0% +have this little formula say that if you + + + align:start position:0% +have this little formula say that if you +take uh if you take 1 minus c and you + + align:start position:0% +take uh if you take 1 minus c and you + + + align:start position:0% +take uh if you take 1 minus c and you +sum from i = z + + align:start position:0% +sum from i = z + + + align:start position:0% +sum from i = z +to n ci + + align:start position:0% +to n ci + + + align:start position:0% +to n ci +right this is what we did here then + + align:start position:0% +right this is what we did here then + + + align:start position:0% +right this is what we did here then +you're getting 1 - 1 - c to the n + one. + + align:start position:0% +you're getting 1 - 1 - c to the n + one. + + + align:start position:0% +you're getting 1 - 1 - c to the n + one. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now of course if c if c is one let's + + align:start position:0% +So now of course if c if c is one let's + + + align:start position:0% +So now of course if c if c is one let's +wait with figuring it out but assume + + align:start position:0% +wait with figuring it out but assume + + + align:start position:0% +wait with figuring it out but assume +that c here is not equal to one + + align:start position:0% +that c here is not equal to one + + + align:start position:0% +that c here is not equal to one +then I can write this here + + align:start position:0% +then I can write this here + + + align:start position:0% +then I can write this here +as that this sum here i = z to n ci I + + align:start position:0% +as that this sum here i = z to n ci I + + + align:start position:0% +as that this sum here i = z to n ci I +can just divide here by this here on + + align:start position:0% +can just divide here by this here on + + + align:start position:0% +can just divide here by this here on +both sides. So I get this thing here + + align:start position:0% +both sides. So I get this thing here + + + align:start position:0% +both sides. So I get this thing here +1 minus C. So I have this formula here + + align:start position:0% + + + + align:start position:0% + +assuming that C is not equal to one. So + + align:start position:0% +assuming that C is not equal to one. So + + + align:start position:0% +assuming that C is not equal to one. So +I can divide by 1 minus C. + + align:start position:0% +I can divide by 1 minus C. + + + align:start position:0% +I can divide by 1 minus C. +And now you see that um so now we can + + align:start position:0% +And now you see that um so now we can + + + align:start position:0% +And now you see that um so now we can +now from this here we can determine so + + align:start position:0% +now from this here we can determine so + + + align:start position:0% +now from this here we can determine so +we can prove a little theorem. + + align:start position:0% + + + + align:start position:0% + +So that the geometric series so this is + + align:start position:0% +So that the geometric series so this is + + + align:start position:0% +So that the geometric series so this is +geometric series convergence + + align:start position:0% + + + + align:start position:0% + +convergence. + + align:start position:0% +convergence. + + + align:start position:0% +convergence. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Remember that this this thing here. So a + + align:start position:0% +Remember that this this thing here. So a + + + align:start position:0% +Remember that this this thing here. So a +series here. So maybe I should just + + align:start position:0% +series here. So maybe I should just + + + align:start position:0% +series here. So maybe I should just +emphasize that over here. + + align:start position:0% + + + + align:start position:0% + +So if you write down a series, so again + + align:start position:0% +So if you write down a series, so again + + + align:start position:0% +So if you write down a series, so again +a series is always that you're starting + + align:start position:0% +a series is always that you're starting + + + align:start position:0% +a series is always that you're starting +with a sequence like this and then you + + align:start position:0% +with a sequence like this and then you + + + align:start position:0% +with a sequence like this and then you +form this other sequence sn where you're + + align:start position:0% +form this other sequence sn where you're + + + align:start position:0% +form this other sequence sn where you're +summing the first + + align:start position:0% +summing the first + + + align:start position:0% +summing the first +um the first n you know I guess in this + + align:start position:0% +um the first n you know I guess in this + + + align:start position:0% +um the first n you know I guess in this +case now I'm starting from zero so then + + align:start position:0% +case now I'm starting from zero so then + + + align:start position:0% +case now I'm starting from zero so then +it would be n plus one elements + + align:start position:0% +it would be n plus one elements + + + align:start position:0% +it would be n plus one elements +like this + + align:start position:0% +like this + + + align:start position:0% +like this +and and and and sometimes one also just + + align:start position:0% +and and and and sometimes one also just + + + align:start position:0% +and and and and sometimes one also just +write for the series one write it as + + align:start position:0% +write for the series one write it as + + + align:start position:0% +write for the series one write it as +as this where one + + align:start position:0% +as this where one + + + align:start position:0% +as this where one +uh one write like this here + + align:start position:0% +uh one write like this here + + + align:start position:0% +uh one write like this here +but uh but really what you're thinking + + align:start position:0% +but uh but really what you're thinking + + + align:start position:0% +but uh but really what you're thinking +about is this sequence here and so but + + align:start position:0% +about is this sequence here and so but + + + align:start position:0% +about is this sequence here and so but +you you sort of with a slight abuse of + + align:start position:0% +you you sort of with a slight abuse of + + + align:start position:0% +you you sort of with a slight abuse of +notation you write this here for a + + align:start position:0% +notation you write this here for a + + + align:start position:0% +notation you write this here for a +series but what you're thinking about is + + align:start position:0% +series but what you're thinking about is + + + align:start position:0% +series but what you're thinking about is +this sequence And so a series is + + align:start position:0% +this sequence And so a series is + + + align:start position:0% +this sequence And so a series is +convergent. + + align:start position:0% + + + + align:start position:0% + +It is convergent. + + align:start position:0% + + + + align:start position:0% + +Uh just means + + align:start position:0% +Uh just means + + + align:start position:0% +Uh just means +that the sequence + + align:start position:0% + + + + align:start position:0% + +sn is convergent. + + align:start position:0% + + + + align:start position:0% + +Okay. So it just means that that that + + align:start position:0% +Okay. So it just means that that that + + + align:start position:0% +Okay. So it just means that that that +this sequence sn is convergent + + align:start position:0% +this sequence sn is convergent + + + align:start position:0% +this sequence sn is convergent +and the and the and the sum and the + + align:start position:0% +and the and the and the sum and the + + + align:start position:0% +and the and the and the sum and the +limit + + align:start position:0% +limit + + + align:start position:0% +limit +of the sequence series + + align:start position:0% +of the sequence series + + + align:start position:0% +of the sequence series +this is just the limit + + align:start position:0% +this is just the limit + + + align:start position:0% +this is just the limit +um is the limit + + align:start position:0% + + + + align:start position:0% + +of the sn + + align:start position:0% + + + + align:start position:0% + +That's called that is usually denoted + + align:start position:0% + + + + align:start position:0% + +denoted + + align:start position:0% +denoted + + + align:start position:0% +denoted +by by by this uh by this infinite sum + + align:start position:0% +by by by this uh by this infinite sum + + + align:start position:0% +by by by this uh by this infinite sum +a sorry this was I + + align:start position:0% +a sorry this was I + + + align:start position:0% +a sorry this was I +ai like that right so so you see there's + + align:start position:0% +ai like that right so so you see there's + + + align:start position:0% +ai like that right so so you see there's +a little bit of abuse of notation + + align:start position:0% +a little bit of abuse of notation + + + align:start position:0% +a little bit of abuse of notation +that one one talk about a series and one + + align:start position:0% +that one one talk about a series and one + + + align:start position:0% +that one one talk about a series and one +typically write it like this. What one + + align:start position:0% +typically write it like this. What one + + + align:start position:0% +typically write it like this. What one +really mean is that one think about this + + align:start position:0% +really mean is that one think about this + + + align:start position:0% +really mean is that one think about this +sequence here and then if it's + + align:start position:0% +sequence here and then if it's + + + align:start position:0% +sequence here and then if it's +convergent this just means that these Sn + + align:start position:0% +convergent this just means that these Sn + + + align:start position:0% +convergent this just means that these Sn +converge + + align:start position:0% +converge + + + align:start position:0% +converge +and the limit the limit but the limit + + align:start position:0% +and the limit the limit but the limit + + + align:start position:0% +and the limit the limit but the limit +you would also write as this. So in a + + align:start position:0% +you would also write as this. So in a + + + align:start position:0% +you would also write as this. So in a +way this symbol here is used for two + + align:start position:0% +way this symbol here is used for two + + + align:start position:0% +way this symbol here is used for two +different things. it's used for the + + align:start position:0% +different things. it's used for the + + + align:start position:0% +different things. it's used for the +series and if the series is convergent + + align:start position:0% +series and if the series is convergent + + + align:start position:0% +series and if the series is convergent +it's also used for the limit. Okay, this + + align:start position:0% +it's also used for the limit. Okay, this + + + align:start position:0% +it's also used for the limit. Okay, this +is like standard. So, + + align:start position:0% +is like standard. So, + + + align:start position:0% +is like standard. So, +okay. So, now let's come back to the + + align:start position:0% +okay. So, now let's come back to the + + + align:start position:0% +okay. So, now let's come back to the +geometric series, right? So, again the + + align:start position:0% +geometric series, right? So, again the + + + align:start position:0% +geometric series, right? So, again the +geometric series were that you take some + + align:start position:0% +geometric series were that you take some + + + align:start position:0% +geometric series were that you take some +C + + align:start position:0% +C + + + align:start position:0% +C +and then you form this series here + + align:start position:0% +and then you form this series here + + + align:start position:0% +and then you form this series here +C I I = Z to infinity. It's it's of + + align:start position:0% +C I I = Z to infinity. It's it's of + + + align:start position:0% +C I I = Z to infinity. It's it's of +course important where you start. I mean + + align:start position:0% +course important where you start. I mean + + + align:start position:0% +course important where you start. I mean +it's the convergence is not important + + align:start position:0% +it's the convergence is not important + + + align:start position:0% +it's the convergence is not important +but the what the limit is depends on + + align:start position:0% +but the what the limit is depends on + + + align:start position:0% +but the what the limit is depends on +where you start. Okay. So so this is a + + align:start position:0% +where you start. Okay. So so this is a + + + align:start position:0% +where you start. Okay. So so this is a +geometric series and we have that if um + + align:start position:0% +geometric series and we have that if um + + + align:start position:0% +geometric series and we have that if um +if see here so we have now the following + + align:start position:0% +if see here so we have now the following + + + align:start position:0% +if see here so we have now the following +that um that the geometric series + + align:start position:0% + + + + align:start position:0% + +series + + align:start position:0% +series + + + align:start position:0% +series +is convergent + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +if C here in absolute value is less than + + align:start position:0% +if C here in absolute value is less than + + + align:start position:0% +if C here in absolute value is less than +one + + align:start position:0% +one + + + align:start position:0% +one +uh and uh and divergent otherwise + + align:start position:0% + + + + align:start position:0% + +if as the absolute value of C is bigger + + align:start position:0% +if as the absolute value of C is bigger + + + align:start position:0% +if as the absolute value of C is bigger +to one. + + align:start position:0% +to one. + + + align:start position:0% +to one. +Okay. So, so this is the claim that okay + + align:start position:0% +Okay. So, so this is the claim that okay + + + align:start position:0% +Okay. So, so this is the claim that okay +and so this is and and so this is a + + align:start position:0% +and so this is and and so this is a + + + align:start position:0% +and so this is and and so this is a +claim and and in fact um + + align:start position:0% +claim and and in fact um + + + align:start position:0% +claim and and in fact um +right and and in fact so one more thing + + align:start position:0% +right and and in fact so one more thing + + + align:start position:0% +right and and in fact so one more thing +is that that + + align:start position:0% + + + + align:start position:0% + +so moreover + + align:start position:0% + + + + align:start position:0% + +If uh if C + + align:start position:0% +If uh if C + + + align:start position:0% +If uh if C +is less than one then the limit so so so + + align:start position:0% +is less than one then the limit so so so + + + align:start position:0% +is less than one then the limit so so so +then the claim is that it's convergent + + align:start position:0% +then the claim is that it's convergent + + + align:start position:0% +then the claim is that it's convergent +then the limit + + align:start position:0% + + + + align:start position:0% + +is uh one one minus 2. This here has a + + align:start position:0% +is uh one one minus 2. This here has a + + + align:start position:0% +is uh one one minus 2. This here has a +limit and so we write this here as the + + align:start position:0% +limit and so we write this here as the + + + align:start position:0% +limit and so we write this here as the +this infin. + + align:start position:0% + + + + align:start position:0% + +Okay. Now let's just try to prove this. + + align:start position:0% +Okay. Now let's just try to prove this. + + + align:start position:0% +Okay. Now let's just try to prove this. +So let me first do and we have we almost + + align:start position:0% +So let me first do and we have we almost + + + align:start position:0% +So let me first do and we have we almost +there already. + + align:start position:0% +there already. + + + align:start position:0% +there already. +So the thing is + + align:start position:0% +So the thing is + + + align:start position:0% +So the thing is +that + + align:start position:0% + + + + align:start position:0% + +Right. So let's first look at the case + + align:start position:0% + + + + align:start position:0% + +uh assume + + align:start position:0% + + + + align:start position:0% + +C in absolute value it's less than + + align:start position:0% +C in absolute value it's less than + + + align:start position:0% +C in absolute value it's less than +strictly less than one. Well, then we + + align:start position:0% +strictly less than one. Well, then we + + + align:start position:0% +strictly less than one. Well, then we +have already proven that Sn is so sn + + align:start position:0% + + + + align:start position:0% + +I = 0 to N CI and we have already proven + + align:start position:0% +I = 0 to N CI and we have already proven + + + align:start position:0% +I = 0 to N CI and we have already proven +that this here is 1 minus CN + 1 over 1 + + align:start position:0% +that this here is 1 minus CN + 1 over 1 + + + align:start position:0% +that this here is 1 minus CN + 1 over 1 +- C right and this makes sense C is + + align:start position:0% +- C right and this makes sense C is + + + align:start position:0% +- C right and this makes sense C is +strictly norm is strictly less than one + + align:start position:0% +strictly norm is strictly less than one + + + align:start position:0% +strictly norm is strictly less than one +so in particular C is not one right so + + align:start position:0% +so in particular C is not one right so + + + align:start position:0% +so in particular C is not one right so +this here is is fine but now you see + + align:start position:0% +this here is is fine but now you see + + + align:start position:0% +this here is is fine but now you see +that If you take something with norm + + align:start position:0% +that If you take something with norm + + + align:start position:0% +that If you take something with norm +strictly less than one, then just + + align:start position:0% +strictly less than one, then just + + + align:start position:0% +strictly less than one, then just +because CN + one, the norm of this here, + + align:start position:0% +because CN + one, the norm of this here, + + + align:start position:0% +because CN + one, the norm of this here, +well, if you take a something and you + + align:start position:0% +well, if you take a something and you + + + align:start position:0% +well, if you take a something and you +multiply it by another, so so if you + + align:start position:0% +multiply it by another, so so if you + + + align:start position:0% +multiply it by another, so so if you +take two numbers a and b and you take + + align:start position:0% +take two numbers a and b and you take + + + align:start position:0% +take two numbers a and b and you take +the absolute value of the product, + + align:start position:0% +the absolute value of the product, + + + align:start position:0% +the absolute value of the product, +that's the same as the product of the + + align:start position:0% +that's the same as the product of the + + + align:start position:0% +that's the same as the product of the +absolute values, + + align:start position:0% +absolute values, + + + align:start position:0% +absolute values, +right? So, so this means that if you + + align:start position:0% +right? So, so this means that if you + + + align:start position:0% +right? So, so this means that if you +take C to the power n + one, so if you + + align:start position:0% +take C to the power n + one, so if you + + + align:start position:0% +take C to the power n + one, so if you +take C and you multiply it by self, n + + + align:start position:0% +take C and you multiply it by self, n + + + + align:start position:0% +take C and you multiply it by self, n + +one time, this is the same as the + + align:start position:0% +one time, this is the same as the + + + align:start position:0% +one time, this is the same as the +absolute value times to raised to the + + align:start position:0% +absolute value times to raised to the + + + align:start position:0% +absolute value times to raised to the +power n plus one, right? And so now you + + align:start position:0% +power n plus one, right? And so now you + + + align:start position:0% +power n plus one, right? And so now you +see that because this c has absolute + + align:start position:0% +see that because this c has absolute + + + align:start position:0% +see that because this c has absolute +value less than one, strictly less than + + align:start position:0% +value less than one, strictly less than + + + align:start position:0% +value less than one, strictly less than +one, then as n go to infinity, this here + + align:start position:0% +one, then as n go to infinity, this here + + + align:start position:0% +one, then as n go to infinity, this here +converts to zero. Right? So this means + + align:start position:0% +converts to zero. Right? So this means + + + align:start position:0% +converts to zero. Right? So this means +that as n go to infinity this thing here + + align:start position:0% +that as n go to infinity this thing here + + + align:start position:0% +that as n go to infinity this thing here +right converge this here goes to zero. + + align:start position:0% +right converge this here goes to zero. + + + align:start position:0% +right converge this here goes to zero. +So just by the algebraic rules for + + align:start position:0% +So just by the algebraic rules for + + + align:start position:0% +So just by the algebraic rules for +limits right this thing here is going to + + align:start position:0% +limits right this thing here is going to + + + align:start position:0% +limits right this thing here is going to +converge to one minus C over one like + + align:start position:0% +converge to one minus C over one like + + + align:start position:0% +converge to one minus C over one like +that right + + align:start position:0% + + + + align:start position:0% + +so you see that in the case where the + + align:start position:0% +so you see that in the case where the + + + align:start position:0% +so you see that in the case where the +where C in absolute value is strictly + + align:start position:0% +where C in absolute value is strictly + + + align:start position:0% +where C in absolute value is strictly +less than one then we have now proven + + align:start position:0% +less than one then we have now proven + + + align:start position:0% +less than one then we have now proven +that the geometric series is convergent + + align:start position:0% +that the geometric series is convergent + + + align:start position:0% +that the geometric series is convergent +and in fact we have even which is really + + align:start position:0% +and in fact we have even which is really + + + align:start position:0% +and in fact we have even which is really +nice and and sort of unusual for a + + align:start position:0% +nice and and sort of unusual for a + + + align:start position:0% +nice and and sort of unusual for a +series. I mean, usually you cannot + + align:start position:0% +series. I mean, usually you cannot + + + align:start position:0% +series. I mean, usually you cannot +actually determine what the limit is, + + align:start position:0% +actually determine what the limit is, + + + align:start position:0% +actually determine what the limit is, +but in this case, we could, right? But + + align:start position:0% +but in this case, we could, right? But + + + align:start position:0% +but in this case, we could, right? But +we still need to figure out why is it + + align:start position:0% +we still need to figure out why is it + + + align:start position:0% +we still need to figure out why is it +not convergent if C + + align:start position:0% +not convergent if C + + + align:start position:0% +not convergent if C +is um the absolute value of C is bigger + + align:start position:0% +is um the absolute value of C is bigger + + + align:start position:0% +is um the absolute value of C is bigger +or equal to one. + + align:start position:0% +or equal to one. + + + align:start position:0% +or equal to one. +And so here's an easy thing. + + align:start position:0% +And so here's an easy thing. + + + align:start position:0% +And so here's an easy thing. +I mean, but you could also kind of I + + align:start position:0% +I mean, but you could also kind of I + + + align:start position:0% +I mean, but you could also kind of I +mean, yeah. So, here's an easy thing + + align:start position:0% +mean, yeah. So, here's an easy thing + + + align:start position:0% +mean, yeah. So, here's an easy thing +that if you're looking at C, sorry, SN + + + align:start position:0% +that if you're looking at C, sorry, SN + + + + align:start position:0% +that if you're looking at C, sorry, SN + +1 minus SN, + + align:start position:0% +1 minus SN, + + + align:start position:0% +1 minus SN, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +Well, SN + one or SN say this here was + + align:start position:0% +Well, SN + one or SN say this here was + + + align:start position:0% +Well, SN + one or SN say this here was +just right. This here was just C to the + + align:start position:0% +just right. This here was just C to the + + + align:start position:0% +just right. This here was just C to the +power zero up to C to the power n S N + + + align:start position:0% +power zero up to C to the power n S N + + + + align:start position:0% +power zero up to C to the power n S N + +one + + align:start position:0% +one + + + align:start position:0% +one +is where you do the same stuff. You're + + align:start position:0% +is where you do the same stuff. You're + + + align:start position:0% +is where you do the same stuff. You're +adding these guys, + + align:start position:0% +adding these guys, + + + align:start position:0% +adding these guys, +but then you have to add one more, + + align:start position:0% +but then you have to add one more, + + + align:start position:0% +but then you have to add one more, +right? So this means that this + + align:start position:0% +right? So this means that this + + + align:start position:0% +right? So this means that this +difference here is really C to the N + + + align:start position:0% +difference here is really C to the N + + + + align:start position:0% +difference here is really C to the N + +one, right? + + align:start position:0% +one, right? + + + align:start position:0% +one, right? +But now I could look at the absolute + + align:start position:0% +But now I could look at the absolute + + + align:start position:0% +But now I could look at the absolute +value of this difference. + + align:start position:0% +value of this difference. + + + align:start position:0% +value of this difference. +This is this + + align:start position:0% +This is this + + + align:start position:0% +This is this +but this is the same again as C to the + + align:start position:0% +but this is the same again as C to the + + + align:start position:0% +but this is the same again as C to the +power n + one. + + align:start position:0% +power n + one. + + + align:start position:0% +power n + one. +But you see if C here is the absolute + + align:start position:0% +But you see if C here is the absolute + + + align:start position:0% +But you see if C here is the absolute +value is bigger equal to one then this + + align:start position:0% +value is bigger equal to one then this + + + align:start position:0% +value is bigger equal to one then this +thing here then this thing here so if + + align:start position:0% +thing here then this thing here so if + + + align:start position:0% +thing here then this thing here so if +the absolute value here is bigger equal + + align:start position:0% +the absolute value here is bigger equal + + + align:start position:0% +the absolute value here is bigger equal +to one then this thing here must be big + + align:start position:0% +to one then this thing here must be big + + + align:start position:0% +to one then this thing here must be big +or equal to one right remember that if a + + align:start position:0% +or equal to one right remember that if a + + + align:start position:0% +or equal to one right remember that if a +sequence is convergent if a sequence is + + align:start position:0% +sequence is convergent if a sequence is + + + align:start position:0% +sequence is convergent if a sequence is +convergent then it is a cushy sequence + + align:start position:0% +convergent then it is a cushy sequence + + + align:start position:0% +convergent then it is a cushy sequence +it's a cushy sequence that if you go + + align:start position:0% +it's a cushy sequence that if you go + + + align:start position:0% +it's a cushy sequence that if you go +sufficiently far out then from there on + + align:start position:0% +sufficiently far out then from there on + + + align:start position:0% +sufficiently far out then from there on +and out everything bunch very very close + + align:start position:0% +and out everything bunch very very close + + + align:start position:0% +and out everything bunch very very close +together but you see here not even two + + align:start position:0% +together but you see here not even two + + + align:start position:0% +together but you see here not even two +consecutive is bunching together because + + align:start position:0% +consecutive is bunching together because + + + align:start position:0% +consecutive is bunching together because +independent on how far out how large n + + align:start position:0% +independent on how far out how large n + + + align:start position:0% +independent on how far out how large n +is the difference is always at least one + + align:start position:0% +is the difference is always at least one + + + align:start position:0% +is the difference is always at least one +right so this is not even a cus I mean + + align:start position:0% +right so this is not even a cus I mean + + + align:start position:0% +right so this is not even a cus I mean +this well I mean it's actually + + align:start position:0% +this well I mean it's actually + + + align:start position:0% +this well I mean it's actually +equivalent of course but it's not a cus + + align:start position:0% +equivalent of course but it's not a cus + + + align:start position:0% +equivalent of course but it's not a cus +sequence it sort of failed like the most + + align:start position:0% +sequence it sort of failed like the most + + + align:start position:0% +sequence it sort of failed like the most +basic thing with consecutive ones + + align:start position:0% +basic thing with consecutive ones + + + align:start position:0% +basic thing with consecutive ones +does not even lie close together. So + + align:start position:0% +does not even lie close together. So + + + align:start position:0% +does not even lie close together. So +this proved this uh this theorem about + + align:start position:0% +this proved this uh this theorem about + + + align:start position:0% +this proved this uh this theorem about +the geometric convergence the geometric + + align:start position:0% +the geometric convergence the geometric + + + align:start position:0% +the geometric convergence the geometric +series convergence. + + align:start position:0% +series convergence. + + + align:start position:0% +series convergence. +Okay. So now so this is like + + align:start position:0% +Okay. So now so this is like + + + align:start position:0% +Okay. So now so this is like +the most important example of a + + align:start position:0% +the most important example of a + + + align:start position:0% +the most important example of a +sequence. Um + + align:start position:0% +sequence. Um + + + align:start position:0% +sequence. Um +maybe the second most important + + align:start position:0% +maybe the second most important + + + align:start position:0% +maybe the second most important +is what's called the harmonic series. + + align:start position:0% + + + + align:start position:0% + +So harmonic series + + align:start position:0% + + + + align:start position:0% + +and but the harmonic series is + + align:start position:0% +and but the harmonic series is + + + align:start position:0% +and but the harmonic series is +unfortunately not a series that is + + align:start position:0% +unfortunately not a series that is + + + align:start position:0% +unfortunately not a series that is +convergent. So the harmonic series is + + align:start position:0% +convergent. So the harmonic series is + + + align:start position:0% +convergent. So the harmonic series is +the following. So I again I'm writing it + + align:start position:0% +the following. So I again I'm writing it + + + align:start position:0% +the following. So I again I'm writing it +I'm using this abusive notation + + align:start position:0% +I'm using this abusive notation + + + align:start position:0% +I'm using this abusive notation +that I'm writing the series as like a + + align:start position:0% +that I'm writing the series as like a + + + align:start position:0% +that I'm writing the series as like a +infinite sum but this infinite sum you + + align:start position:0% +infinite sum but this infinite sum you + + + align:start position:0% +infinite sum but this infinite sum you +know but it's not a convergent series. + + align:start position:0% +know but it's not a convergent series. + + + align:start position:0% +know but it's not a convergent series. +So the infinite sum doesn't really make + + align:start position:0% +So the infinite sum doesn't really make + + + align:start position:0% +So the infinite sum doesn't really make +sense. So so this is the here I have to + + align:start position:0% +sense. So so this is the here I have to + + + align:start position:0% +sense. So so this is the here I have to +start because I'm dividing by n. So I'm + + align:start position:0% +start because I'm dividing by n. So I'm + + + align:start position:0% +start because I'm dividing by n. So I'm +starting by one with one. So this here + + align:start position:0% +starting by one with one. So this here + + + align:start position:0% +starting by one with one. So this here +is called the harmonic sh. + + align:start position:0% +is called the harmonic sh. + + + align:start position:0% +is called the harmonic sh. +Okay. and and um and there's there's + + align:start position:0% +Okay. and and um and there's there's + + + align:start position:0% +Okay. and and um and there's there's +various so for series + + align:start position:0% +various so for series + + + align:start position:0% +various so for series +and for series there's like a sort of + + align:start position:0% +and for series there's like a sort of + + + align:start position:0% +and for series there's like a sort of +bunch of things bunch of tests that are + + align:start position:0% +bunch of things bunch of tests that are + + + align:start position:0% +bunch of things bunch of tests that are +useful to determine whether a series is + + align:start position:0% +useful to determine whether a series is + + + align:start position:0% +useful to determine whether a series is +converging or not right and but there's + + align:start position:0% +converging or not right and but there's + + + align:start position:0% +converging or not right and but there's +but and and the ones and we'll talk + + align:start position:0% +but and and the ones and we'll talk + + + align:start position:0% +but and and the ones and we'll talk +about these tests I talk a little bit + + align:start position:0% +about these tests I talk a little bit + + + align:start position:0% +about these tests I talk a little bit +about later in this lecture I'll talk + + align:start position:0% +about later in this lecture I'll talk + + + align:start position:0% +about later in this lecture I'll talk +about some of the tests but not all of + + align:start position:0% +about some of the tests but not all of + + + align:start position:0% +about some of the tests but not all of +them and and we will later talk about + + align:start position:0% +them and and we will later talk about + + + align:start position:0% +them and and we will later talk about +more the test that is particular useful + + align:start position:0% +more the test that is particular useful + + + align:start position:0% +more the test that is particular useful +in this case it's what's called the + + align:start position:0% +in this case it's what's called the + + + align:start position:0% +in this case it's what's called the +integral test but I won't talk about + + align:start position:0% +integral test but I won't talk about + + + align:start position:0% +integral test but I won't talk about +that today + + align:start position:0% +that today + + + align:start position:0% +that today +um but instead I will show you a very + + align:start position:0% +um but instead I will show you a very + + + align:start position:0% +um but instead I will show you a very +simple proof of why this here + + align:start position:0% +simple proof of why this here + + + align:start position:0% +simple proof of why this here +is not convergent + + align:start position:0% + + + + align:start position:0% + +so uh so so here's a theorem + + align:start position:0% + + + + align:start position:0% + +The harmonic series + + align:start position:0% + + + + align:start position:0% + +is a divergence. It's not conver it's + + align:start position:0% +is a divergence. It's not conver it's + + + align:start position:0% +is a divergence. It's not conver it's +diverg. + + align:start position:0% + + + + align:start position:0% + +Okay. And so in fact what we will prove + + align:start position:0% +Okay. And so in fact what we will prove + + + align:start position:0% +Okay. And so in fact what we will prove +is the following + + align:start position:0% +is the following + + + align:start position:0% +is the following +that we will show that if you're looking + + align:start position:0% +that we will show that if you're looking + + + align:start position:0% +that we will show that if you're looking +at so n is an integer. If you're looking + + align:start position:0% +at so n is an integer. If you're looking + + + align:start position:0% +at so n is an integer. If you're looking +at at so this is this is like so this is + + align:start position:0% +at at so this is this is like so this is + + + align:start position:0% +at at so this is this is like so this is +like a right this is only some of the + + align:start position:0% +like a right this is only some of the + + + align:start position:0% +like a right this is only some of the +you know you only hit for this here you + + align:start position:0% +you know you only hit for this here you + + + align:start position:0% +you know you only hit for this here you +only hit some of the um element in the + + align:start position:0% +only hit some of the um element in the + + + align:start position:0% +only hit some of the um element in the +sequence right so this is where I'm + + align:start position:0% +sequence right so this is where I'm + + + align:start position:0% +sequence right so this is where I'm +summing again from i = 1 to 2 n to 2 to + + align:start position:0% +summing again from i = 1 to 2 n to 2 to + + + align:start position:0% +summing again from i = 1 to 2 n to 2 to +the n minus one n is an integer of 1 I + + align:start position:0% +the n minus one n is an integer of 1 I + + + align:start position:0% +the n minus one n is an integer of 1 I +right so I want to prove that these guys + + align:start position:0% +right so I want to prove that these guys + + + align:start position:0% +right so I want to prove that these guys +here + + align:start position:0% +here + + + align:start position:0% +here +if if the original sequence has been + + align:start position:0% +if if the original sequence has been + + + align:start position:0% +if if the original sequence has been +convergent then of course any + + align:start position:0% +convergent then of course any + + + align:start position:0% +convergent then of course any +subsequence would also be convergent and + + align:start position:0% +subsequence would also be convergent and + + + align:start position:0% +subsequence would also be convergent and +we're going to prove that this thing + + align:start position:0% +we're going to prove that this thing + + + align:start position:0% +we're going to prove that this thing +here is big or equal to n /2 so I claim + + align:start position:0% +here is big or equal to n /2 so I claim + + + align:start position:0% +here is big or equal to n /2 so I claim +that we have this so this is a claim + + align:start position:0% + + + + align:start position:0% + +that you have this But if you have this + + align:start position:0% +that you have this But if you have this + + + align:start position:0% +that you have this But if you have this +thing here, you see that then the se + + align:start position:0% +thing here, you see that then the se + + + align:start position:0% +thing here, you see that then the se +this subsequence here is unbounded. + + align:start position:0% +this subsequence here is unbounded. + + + align:start position:0% +this subsequence here is unbounded. +Right? So of course the original + + align:start position:0% +Right? So of course the original + + + align:start position:0% +Right? So of course the original +harmonic series is not convergent. + + align:start position:0% +harmonic series is not convergent. + + + align:start position:0% +harmonic series is not convergent. +Right? So let's try to prove this. And + + align:start position:0% +Right? So let's try to prove this. And + + + align:start position:0% +Right? So let's try to prove this. And +again you know this is not um this is + + align:start position:0% +again you know this is not um this is + + + align:start position:0% +again you know this is not um this is +just like a simple proof of that very + + align:start position:0% +just like a simple proof of that very + + + align:start position:0% +just like a simple proof of that very +simple minor proof that the harmonic + + align:start position:0% +simple minor proof that the harmonic + + + align:start position:0% +simple minor proof that the harmonic +series is divergent + + align:start position:0% +series is divergent + + + align:start position:0% +series is divergent +but but there are you know more + + align:start position:0% +but but there are you know more + + + align:start position:0% +but but there are you know more +you know once we learn about the + + align:start position:0% +you know once we learn about the + + + align:start position:0% +you know once we learn about the +integral test and so on there are other + + align:start position:0% +integral test and so on there are other + + + align:start position:0% +integral test and so on there are other +in a way better ways of doing it. + + align:start position:0% +in a way better ways of doing it. + + + align:start position:0% +in a way better ways of doing it. +So let me try to prove this. So I want + + align:start position:0% +So let me try to prove this. So I want + + + align:start position:0% +So let me try to prove this. So I want +to prove the claim + + align:start position:0% +to prove the claim + + + align:start position:0% +to prove the claim +prove of of the claim. + + align:start position:0% + + + + align:start position:0% + +So I'm going to prove it by so I just + + align:start position:0% +So I'm going to prove it by so I just + + + align:start position:0% +So I'm going to prove it by so I just +prove so so I want to establish this for + + align:start position:0% +prove so so I want to establish this for + + + align:start position:0% +prove so so I want to establish this for +all n and I'm going to prove it first + + align:start position:0% +all n and I'm going to prove it first + + + align:start position:0% +all n and I'm going to prove it first +when um when n + + align:start position:0% +when um when n + + + align:start position:0% +when um when n +is equal to one. Right? So let's show + + align:start position:0% +is equal to one. Right? So let's show + + + align:start position:0% +is equal to one. Right? So let's show +this for n equal to one. + + align:start position:0% +this for n equal to one. + + + align:start position:0% +this for n equal to one. +So for n= to one + + align:start position:0% +So for n= to one + + + align:start position:0% +So for n= to one +well then the claim here means that um + + align:start position:0% +well then the claim here means that um + + + align:start position:0% +well then the claim here means that um +right so 2 to the one that's two so this + + align:start position:0% +right so 2 to the one that's two so this + + + align:start position:0% +right so 2 to the one that's two so this +is this is s1 right right because two to + + align:start position:0% +is this is s1 right right because two to + + + align:start position:0% +is this is s1 right right because two to +the one is 2 minus one so this is one so + + align:start position:0% +the one is 2 minus one so this is one so + + + align:start position:0% +the one is 2 minus one so this is one so +I claim that so so I want to prove that + + align:start position:0% +I claim that so so I want to prove that + + + align:start position:0% +I claim that so so I want to prove that +s1 is bigger equal to a + + align:start position:0% +s1 is bigger equal to a + + + align:start position:0% +s1 is bigger equal to a +want to show + + align:start position:0% + + + + align:start position:0% + +but of course S1 here S1 is just one + + align:start position:0% +but of course S1 here S1 is just one + + + align:start position:0% +but of course S1 here S1 is just one +over one so it's actually that's + + align:start position:0% +over one so it's actually that's + + + align:start position:0% +over one so it's actually that's +definitely fine okay so this is so it's + + align:start position:0% +definitely fine okay so this is so it's + + + align:start position:0% +definitely fine okay so this is so it's +for so we we so so we want to prove the + + align:start position:0% +for so we we so so we want to prove the + + + align:start position:0% +for so we we so so we want to prove the +claim and the claim is okay so claim is + + align:start position:0% +claim and the claim is okay so claim is + + + align:start position:0% +claim and the claim is okay so claim is +okay + + align:start position:0% +okay + + + align:start position:0% +okay +for n = 1. Okay. So now I want to prove + + align:start position:0% +for n = 1. Okay. So now I want to prove + + + align:start position:0% +for n = 1. Okay. So now I want to prove +it. So I want to assume so assume + + align:start position:0% + + + + align:start position:0% + +the claim + + align:start position:0% + + + + align:start position:0% + +is correct + + align:start position:0% + + + + align:start position:0% + +for for N and we want to prove it for + + align:start position:0% +for for N and we want to prove it for + + + align:start position:0% +for for N and we want to prove it for +want to show it + + align:start position:0% + + + + align:start position:0% + +to show the claim + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +for the next one, right? And so I I have + + align:start position:0% +for the next one, right? And so I I have + + + align:start position:0% +for the next one, right? And so I I have +that. So we we have we assume + + align:start position:0% + + + + align:start position:0% + +that s2 n + + align:start position:0% +that s2 n + + + align:start position:0% +that s2 n +minus one that this is bigger than n /2 + + align:start position:0% +minus one that this is bigger than n /2 + + + align:start position:0% +minus one that this is bigger than n /2 +and then I want to look at uh s 2 n + 1 + + align:start position:0% +and then I want to look at uh s 2 n + 1 + + + align:start position:0% +and then I want to look at uh s 2 n + 1 +-1. Okay, how can I write this thing + + align:start position:0% +-1. Okay, how can I write this thing + + + align:start position:0% +-1. Okay, how can I write this thing +here? So I'm summing, right? This here + + align:start position:0% +here? So I'm summing, right? This here + + + align:start position:0% +here? So I'm summing, right? This here +is a sum of the one over I where I do it + + align:start position:0% +is a sum of the one over I where I do it + + + align:start position:0% +is a sum of the one over I where I do it +up to this thing here. But I can think + + align:start position:0% +up to this thing here. But I can think + + + align:start position:0% +up to this thing here. But I can think +about that as a sum of the one where I + + align:start position:0% +about that as a sum of the one where I + + + align:start position:0% +about that as a sum of the one where I +do up to this here + + align:start position:0% +do up to this here + + + align:start position:0% +do up to this here +and then then I have to sorry sum the + + align:start position:0% +and then then I have to sorry sum the + + + align:start position:0% +and then then I have to sorry sum the +rest also. So this is I = to 2 n to 2 n + + align:start position:0% +rest also. So this is I = to 2 n to 2 n + + + align:start position:0% +rest also. So this is I = to 2 n to 2 n ++ 1 + + align:start position:0% ++ 1 + + + align:start position:0% ++ 1 +2 n sorry + 1 - 1 + + align:start position:0% +2 n sorry + 1 - 1 + + + align:start position:0% +2 n sorry + 1 - 1 +like this of 1 / i right + + align:start position:0% + + + + align:start position:0% + +but now you see + + align:start position:0% +but now you see + + + align:start position:0% +but now you see +I want to bound it from below + + align:start position:0% +I want to bound it from below + + + align:start position:0% +I want to bound it from below +right so I + + align:start position:0% +right so I + + + align:start position:0% +right so I +So if you sort of continue this line + + align:start position:0% +So if you sort of continue this line + + + align:start position:0% +So if you sort of continue this line +then by assumption this thing here is + + align:start position:0% +then by assumption this thing here is + + + align:start position:0% +then by assumption this thing here is +bounded by n /2 right this thing here + + align:start position:0% +bounded by n /2 right this thing here + + + align:start position:0% +bounded by n /2 right this thing here +right I'm summing right I'm summing two + + align:start position:0% +right I'm summing right I'm summing two + + + align:start position:0% +right I'm summing right I'm summing two +n numbers right from here to here there + + align:start position:0% +n numbers right from here to here there + + + align:start position:0% +n numbers right from here to here there +are two n numbers + + align:start position:0% +are two n numbers + + + align:start position:0% +are two n numbers +right + + align:start position:0% +right + + + align:start position:0% +right +and uh and so it's two n numbers and if + + align:start position:0% +and uh and so it's two n numbers and if + + + align:start position:0% +and uh and so it's two n numbers and if +I take the smallest of those two + + align:start position:0% +I take the smallest of those two + + + align:start position:0% +I take the smallest of those two +numbers, right? If I take the smallest + + align:start position:0% +numbers, right? If I take the smallest + + + align:start position:0% +numbers, right? If I take the smallest +of these guys and I multiply by 2 n, + + align:start position:0% +of these guys and I multiply by 2 n, + + + align:start position:0% +of these guys and I multiply by 2 n, +then that's definitely a lower bound. So + + align:start position:0% +then that's definitely a lower bound. So + + + align:start position:0% +then that's definitely a lower bound. So +let's try to do this. So I say 2 n 2 to + + align:start position:0% +let's try to do this. So I say 2 n 2 to + + + align:start position:0% +let's try to do this. So I say 2 n 2 to +the n and then the smallest, but the + + align:start position:0% +the n and then the smallest, but the + + + align:start position:0% +the n and then the smallest, but the +smallest is the last one. So the + + align:start position:0% +smallest is the last one. So the + + + align:start position:0% +smallest is the last one. So the +smallest is 1 / 2 to the n + one + + align:start position:0% +smallest is 1 / 2 to the n + one + + + align:start position:0% +smallest is 1 / 2 to the n + one +minus one, right? + + align:start position:0% +minus one, right? + + + align:start position:0% +minus one, right? +But this thing here, right, is of course + + align:start position:0% +But this thing here, right, is of course + + + align:start position:0% +But this thing here, right, is of course +obviously bigger than so n / two. This + + align:start position:0% +obviously bigger than so n / two. This + + + align:start position:0% +obviously bigger than so n / two. This +thing here, well, this is 2 to the n. + + align:start position:0% +thing here, well, this is 2 to the n. + + + align:start position:0% +thing here, well, this is 2 to the n. +But this thing here, if I divide by a + + align:start position:0% +But this thing here, if I divide by a + + + align:start position:0% +But this thing here, if I divide by a +larger number, and the larger number is + + align:start position:0% +larger number, and the larger number is + + + align:start position:0% +larger number, and the larger number is +just this here, then I get something + + align:start position:0% +just this here, then I get something + + + align:start position:0% +just this here, then I get something +even smaller. So I would have 1 / 2 to + + align:start position:0% +even smaller. So I would have 1 / 2 to + + + align:start position:0% +even smaller. So I would have 1 / 2 to +the n + one, right? + + align:start position:0% +the n + one, right? + + + align:start position:0% +the n + one, right? +But now you see that this thing here + + align:start position:0% +But now you see that this thing here + + + align:start position:0% +But now you see that this thing here +cancel with these guys here. And so + + align:start position:0% +cancel with these guys here. And so + + + align:start position:0% +cancel with these guys here. And so +you're getting that this is n / 2 + a + + align:start position:0% +you're getting that this is n / 2 + a + + + align:start position:0% +you're getting that this is n / 2 + a +half. And so this is n + one / two. And + + align:start position:0% +half. And so this is n + one / two. And + + + align:start position:0% +half. And so this is n + one / two. And +that's exactly the claim for n + one. + + align:start position:0% +that's exactly the claim for n + one. + + + align:start position:0% +that's exactly the claim for n + one. +Right? So we proven that if it was true + + align:start position:0% +Right? So we proven that if it was true + + + align:start position:0% +Right? So we proven that if it was true +for n then it's also true for n + one. + + align:start position:0% +for n then it's also true for n + one. + + + align:start position:0% +for n then it's also true for n + one. +And we remember to check that the + + align:start position:0% +And we remember to check that the + + + align:start position:0% +And we remember to check that the +beginning was also okay. + + align:start position:0% +beginning was also okay. + + + align:start position:0% +beginning was also okay. +Okay, so that's the harmonic series. So + + align:start position:0% +Okay, so that's the harmonic series. So + + + align:start position:0% +Okay, so that's the harmonic series. So +you see that the harmonic series is + + align:start position:0% +you see that the harmonic series is + + + align:start position:0% +you see that the harmonic series is +divergent. + + align:start position:0% +divergent. + + + align:start position:0% +divergent. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +um the harmonic series is of course an + + align:start position:0% +um the harmonic series is of course an + + + align:start position:0% +um the harmonic series is of course an +example of something else. + + align:start position:0% +example of something else. + + + align:start position:0% +example of something else. +Namely that + + align:start position:0% +Namely that + + + align:start position:0% +Namely that +if you're looking at so when you're + + align:start position:0% +if you're looking at so when you're + + + align:start position:0% +if you're looking at so when you're +looking at a series + + align:start position:0% +looking at a series + + + align:start position:0% +looking at a series +the first thing you look at typically is + + align:start position:0% + + + + align:start position:0% + +Okay. So, + + align:start position:0% +Okay. So, + + + align:start position:0% +Okay. So, +let me just have a side here. So, + + align:start position:0% +let me just have a side here. So, + + + align:start position:0% +let me just have a side here. So, +if you give me a series, + + align:start position:0% +if you give me a series, + + + align:start position:0% +if you give me a series, +you know, it doesn't really matter where + + align:start position:0% +you know, it doesn't really matter where + + + align:start position:0% +you know, it doesn't really matter where +I mean it + + align:start position:0% +I mean it + + + align:start position:0% +I mean it +it doesn't matter very much where it's + + align:start position:0% +it doesn't matter very much where it's + + + align:start position:0% +it doesn't matter very much where it's +the for for whether a series is + + align:start position:0% +the for for whether a series is + + + align:start position:0% +the for for whether a series is +convergent. It doesn't matter where you + + align:start position:0% +convergent. It doesn't matter where you + + + align:start position:0% +convergent. It doesn't matter where you +start because this is just adding + + align:start position:0% +start because this is just adding + + + align:start position:0% +start because this is just adding +something to it. It will matter where + + align:start position:0% +something to it. It will matter where + + + align:start position:0% +something to it. It will matter where +you start for the limit but not whether + + align:start position:0% +you start for the limit but not whether + + + align:start position:0% +you start for the limit but not whether +or not the sequence series is + + align:start position:0% +or not the sequence series is + + + align:start position:0% +or not the sequence series is +converging. But if you give me a limit + + align:start position:0% +converging. But if you give me a limit + + + align:start position:0% +converging. But if you give me a limit +the first thing I always check is that + + align:start position:0% +the first thing I always check is that + + + align:start position:0% +the first thing I always check is that +this so first so so for a series + + align:start position:0% + + + + align:start position:0% + +always check + + align:start position:0% + + + + align:start position:0% + +if a n goes to zero or not. + + align:start position:0% + + + + align:start position:0% + +And why? Because if you give me a + + align:start position:0% +And why? Because if you give me a + + + align:start position:0% +And why? Because if you give me a +series, this the the the question about + + align:start position:0% +series, this the the the question about + + + align:start position:0% +series, this the the the question about +a series is always whether it's + + align:start position:0% +a series is always whether it's + + + align:start position:0% +a series is always whether it's +converging or not. Right? And again, + + align:start position:0% +converging or not. Right? And again, + + + align:start position:0% +converging or not. Right? And again, +just like we did, if you're looking at + + align:start position:0% +just like we did, if you're looking at + + + align:start position:0% +just like we did, if you're looking at +Sn + + align:start position:0% +Sn + + + align:start position:0% +Sn +say minus SN minus one, this is where + + align:start position:0% +say minus SN minus one, this is where + + + align:start position:0% +say minus SN minus one, this is where +I'm looking at two consecutive things, + + align:start position:0% +I'm looking at two consecutive things, + + + align:start position:0% +I'm looking at two consecutive things, +right? But if I'm looking at this + + align:start position:0% +right? But if I'm looking at this + + + align:start position:0% +right? But if I'm looking at this +difference here, the difference here, + + align:start position:0% +difference here, the difference here, + + + align:start position:0% +difference here, the difference here, +this is where I'm summing up to the a n + + align:start position:0% +this is where I'm summing up to the a n + + + align:start position:0% +this is where I'm summing up to the a n +minus one. Here I'm summing up to the a + + align:start position:0% +minus one. Here I'm summing up to the a + + + align:start position:0% +minus one. Here I'm summing up to the a +n. So the difference here is a n. And if + + align:start position:0% +n. So the difference here is a n. And if + + + align:start position:0% +n. So the difference here is a n. And if +the sequence just like we saw, if the + + align:start position:0% +the sequence just like we saw, if the + + + align:start position:0% +the sequence just like we saw, if the +sequence of the series sorry is + + align:start position:0% +sequence of the series sorry is + + + align:start position:0% +sequence of the series sorry is +convergent, it means that this sequence + + align:start position:0% +convergent, it means that this sequence + + + align:start position:0% +convergent, it means that this sequence +here is convergent. But it means that it + + align:start position:0% +here is convergent. But it means that it + + + align:start position:0% +here is convergent. But it means that it +has to be a cruise sequence that things + + align:start position:0% +has to be a cruise sequence that things + + + align:start position:0% +has to be a cruise sequence that things +have to bunch together. But that two + + align:start position:0% +have to bunch together. But that two + + + align:start position:0% +have to bunch together. But that two +consecutive bunchs together or not is + + align:start position:0% +consecutive bunchs together or not is + + + align:start position:0% +consecutive bunchs together or not is +determined whether a n goes to zero or + + align:start position:0% +determined whether a n goes to zero or + + + align:start position:0% +determined whether a n goes to zero or +not. So if a n does not go to zero, you + + align:start position:0% +not. So if a n does not go to zero, you + + + align:start position:0% +not. So if a n does not go to zero, you +already done, right? There's no reason + + align:start position:0% +already done, right? There's no reason + + + align:start position:0% +already done, right? There's no reason +to continue. It's already clear that + + align:start position:0% +to continue. It's already clear that + + + align:start position:0% +to continue. It's already clear that +this if a end does not go to zero, you + + align:start position:0% +this if a end does not go to zero, you + + + align:start position:0% +this if a end does not go to zero, you +can just say it it doesn't converge + + align:start position:0% +can just say it it doesn't converge + + + align:start position:0% +can just say it it doesn't converge +because a end doesn't go to zero. So + + align:start position:0% +because a end doesn't go to zero. So + + + align:start position:0% +because a end doesn't go to zero. So +there's no reason to start with any kind + + align:start position:0% +there's no reason to start with any kind + + + align:start position:0% +there's no reason to start with any kind +of test or anything any sort of uh good + + align:start position:0% +of test or anything any sort of uh good + + + align:start position:0% +of test or anything any sort of uh good +ideas. + + align:start position:0% + + + + align:start position:0% + +Um okay so so that was just a side + + align:start position:0% +Um okay so so that was just a side + + + align:start position:0% +Um okay so so that was just a side +remark. The other thing is that for the + + align:start position:0% +remark. The other thing is that for the + + + align:start position:0% +remark. The other thing is that for the +the harmonic series is uh you know so + + align:start position:0% +the harmonic series is uh you know so + + + align:start position:0% +the harmonic series is uh you know so +this of course failed this test + + align:start position:0% +this of course failed this test + + + align:start position:0% +this of course failed this test +but but it also is an example of + + align:start position:0% +but but it also is an example of + + + align:start position:0% +but but it also is an example of +something where you're taking a so + + align:start position:0% +something where you're taking a so + + + align:start position:0% +something where you're taking a so +suppose you take a so you have a + + align:start position:0% +suppose you take a so you have a + + + align:start position:0% +suppose you take a so you have a +sequence a n + + align:start position:0% +sequence a n + + + align:start position:0% +sequence a n +and and then you're forming the series + + align:start position:0% + + + + align:start position:0% + +this here. Now, if all of the a + + align:start position:0% + + + + align:start position:0% + +suppose that all of the a ends are non- + + align:start position:0% +suppose that all of the a ends are non- + + + align:start position:0% +suppose that all of the a ends are non- +negative, right? Then if you're looking + + align:start position:0% +negative, right? Then if you're looking + + + align:start position:0% +negative, right? Then if you're looking +at sn + + align:start position:0% +at sn + + + align:start position:0% +at sn ++ one, you can think about sn + one as + + align:start position:0% ++ one, you can think about sn + one as + + + align:start position:0% ++ one, you can think about sn + one as +where you're summing + + align:start position:0% +where you're summing + + + align:start position:0% +where you're summing +the first + + align:start position:0% +the first + + + align:start position:0% +the first +n elements and then you're adding + + align:start position:0% +n elements and then you're adding + + + align:start position:0% +n elements and then you're adding +the n plus one elements. Right? So this + + align:start position:0% +the n plus one elements. Right? So this + + + align:start position:0% +the n plus one elements. Right? So this +here you can think about as sn + + align:start position:0% +here you can think about as sn + + + align:start position:0% +here you can think about as sn +plus a n + one. And so of course if you + + align:start position:0% +plus a n + one. And so of course if you + + + align:start position:0% +plus a n + one. And so of course if you +have if all of these elements is non- + + align:start position:0% +have if all of these elements is non- + + + align:start position:0% +have if all of these elements is non- +negative this means that this here is + + align:start position:0% +negative this means that this here is + + + align:start position:0% +negative this means that this here is +non- negative. So this thing here is + + align:start position:0% +non- negative. So this thing here is + + + align:start position:0% +non- negative. So this thing here is +bigger than Sn. So you see that if all + + align:start position:0% +bigger than Sn. So you see that if all + + + align:start position:0% +bigger than Sn. So you see that if all +of the element a is non negative then + + align:start position:0% +of the element a is non negative then + + + align:start position:0% +of the element a is non negative then +this sequence sn is monotone. So in this + + align:start position:0% +this sequence sn is monotone. So in this + + + align:start position:0% +this sequence sn is monotone. So in this +case here if you have this this imply + + align:start position:0% +case here if you have this this imply + + + align:start position:0% +case here if you have this this imply +that this sn + + align:start position:0% +that this sn + + + align:start position:0% +that this sn +is mono increasing right. And so now to + + align:start position:0% +is mono increasing right. And so now to + + + align:start position:0% +is mono increasing right. And so now to +say whether this in if you have this to + + align:start position:0% +say whether this in if you have this to + + + align:start position:0% +say whether this in if you have this to +determine whether this series here is + + align:start position:0% +determine whether this series here is + + + align:start position:0% +determine whether this series here is +convergent or not it's just a matter of + + align:start position:0% +convergent or not it's just a matter of + + + align:start position:0% +convergent or not it's just a matter of +proving whether you know to determine + + align:start position:0% +proving whether you know to determine + + + align:start position:0% +proving whether you know to determine +whether this this + + align:start position:0% +whether this this + + + align:start position:0% +whether this this +sequence is bounded or not. Right? So + + align:start position:0% +sequence is bounded or not. Right? So + + + align:start position:0% +sequence is bounded or not. Right? So +you just need to find a bound. + + align:start position:0% + + + + align:start position:0% + +Okay. So this naturally leads to looking + + align:start position:0% +Okay. So this naturally leads to looking + + + align:start position:0% +Okay. So this naturally leads to looking +at what's called absolute convergence. + + align:start position:0% +at what's called absolute convergence. + + + align:start position:0% +at what's called absolute convergence. +So this is something stronger than + + align:start position:0% +So this is something stronger than + + + align:start position:0% +So this is something stronger than +convergence. + + align:start position:0% + + + + align:start position:0% + +And for many things for many although + + align:start position:0% +And for many things for many although + + + align:start position:0% +And for many things for many although +not all + + align:start position:0% +not all + + + align:start position:0% +not all +there's a particular test that deals + + align:start position:0% +there's a particular test that deals + + + align:start position:0% +there's a particular test that deals +with it with uh where you don't have + + align:start position:0% +with it with uh where you don't have + + + align:start position:0% +with it with uh where you don't have +both things or where you don't have the + + align:start position:0% +both things or where you don't have the + + + align:start position:0% +both things or where you don't have the +stronger property. So for many things + + align:start position:0% +stronger property. So for many things + + + align:start position:0% +stronger property. So for many things +you are you have absolute convergence. + + align:start position:0% +you are you have absolute convergence. + + + align:start position:0% +you are you have absolute convergence. +Um okay and um + + align:start position:0% +Um okay and um + + + align:start position:0% +Um okay and um +so let me try to so absolute conver. + + align:start position:0% + + + + align:start position:0% + +So again you have a um a series here. + + align:start position:0% + + + + align:start position:0% + +This series here is set to be absolute + + align:start position:0% +This series here is set to be absolute + + + align:start position:0% +This series here is set to be absolute +convergence or converge absolutely. So + + align:start position:0% +convergence or converge absolutely. So + + + align:start position:0% +convergence or converge absolutely. So +converge + + align:start position:0% + + + + align:start position:0% + +absolutely + + align:start position:0% + + + + align:start position:0% + +if if the co the series where you slap + + align:start position:0% +if if the co the series where you slap + + + align:start position:0% +if if the co the series where you slap +absolute values on them. If this thing + + align:start position:0% +absolute values on them. If this thing + + + align:start position:0% +absolute values on them. If this thing +here + + align:start position:0% +here + + + align:start position:0% +here +converge + + align:start position:0% + + + + align:start position:0% + +right? + + align:start position:0% + + + + align:start position:0% + +So if this so we say that this here + + align:start position:0% +So if this so we say that this here + + + align:start position:0% +So if this so we say that this here +converts absolutely if this here + + align:start position:0% +converts absolutely if this here + + + align:start position:0% +converts absolutely if this here +converge. Okay. Now + + align:start position:0% +converge. Okay. Now + + + align:start position:0% +converge. Okay. Now +uh so I claim that uh that absolute + + align:start position:0% +uh so I claim that uh that absolute + + + align:start position:0% +uh so I claim that uh that absolute +convergence is stronger than + + align:start position:0% +convergence is stronger than + + + align:start position:0% +convergence is stronger than +convergence. + + align:start position:0% + + + + align:start position:0% + +So, so absolute + + align:start position:0% + + + + align:start position:0% + +convergence + + align:start position:0% + + + + align:start position:0% + +implies + + align:start position:0% +implies + + + align:start position:0% +implies +uh convergence. + + align:start position:0% + + + + align:start position:0% + +This is a theorem. + + align:start position:0% + + + + align:start position:0% + +But it's not the other way around, + + align:start position:0% +But it's not the other way around, + + + align:start position:0% +But it's not the other way around, +right? So if you have what's called the + + align:start position:0% +right? So if you have what's called the + + + align:start position:0% +right? So if you have what's called the +So here an example + + align:start position:0% +So here an example + + + align:start position:0% +So here an example +and and we haven't yet proved that it's + + align:start position:0% +and and we haven't yet proved that it's + + + align:start position:0% +and and we haven't yet proved that it's +converging, but we'll do that in some + + align:start position:0% +converging, but we'll do that in some + + + align:start position:0% +converging, but we'll do that in some +later lecture. + + align:start position:0% + + + + align:start position:0% + +So um so here's an example. + + align:start position:0% +So um so here's an example. + + + align:start position:0% +So um so here's an example. +If you're looking at the series minus + + align:start position:0% +If you're looking at the series minus + + + align:start position:0% +If you're looking at the series minus +one to the power n / n n n n n n n n n n + + align:start position:0% +one to the power n / n n n n n n n n n n + + + align:start position:0% +one to the power n / n n n n n n n n n n +n n n n n n n n n n n n n n n n n n n n + + align:start position:0% +n n n n n n n n n n n n n n n n n n n n + + + align:start position:0% +n n n n n n n n n n n n n n n n n n n n +n n n n n n n n n n n = 1 to infinity. + + align:start position:0% +n n n n n n n n n n n = 1 to infinity. + + + align:start position:0% +n n n n n n n n n n n = 1 to infinity. +This here you see this is if if this + + align:start position:0% +This here you see this is if if this + + + align:start position:0% +This here you see this is if if this +hair just had been one then it had been + + align:start position:0% +hair just had been one then it had been + + + align:start position:0% +hair just had been one then it had been +the harmonic series. This here series is + + align:start position:0% +the harmonic series. This here series is + + + align:start position:0% +the harmonic series. This here series is +it's also kind of like a famous series. + + align:start position:0% +it's also kind of like a famous series. + + + align:start position:0% +it's also kind of like a famous series. +It's called the alternating + + align:start position:0% +It's called the alternating + + + align:start position:0% +It's called the alternating +alternating harmonic series. + + align:start position:0% + + + + align:start position:0% + +And it's alternating alternating mean + + align:start position:0% +And it's alternating alternating mean + + + align:start position:0% +And it's alternating alternating mean +that the sign of it is alternating + + align:start position:0% +that the sign of it is alternating + + + align:start position:0% +that the sign of it is alternating +right. So the sign of this a element it + + align:start position:0% +right. So the sign of this a element it + + + align:start position:0% +right. So the sign of this a element it +keep changing from guess in this case + + align:start position:0% +keep changing from guess in this case + + + align:start position:0% +keep changing from guess in this case +the first one is negative the next one + + align:start position:0% +the first one is negative the next one + + + align:start position:0% +the first one is negative the next one +is positive. So it go back and forth + + align:start position:0% +is positive. So it go back and forth + + + align:start position:0% +is positive. So it go back and forth +between uh uh back and forth uh around + + align:start position:0% +between uh uh back and forth uh around + + + align:start position:0% +between uh uh back and forth uh around +zero. to a harmonic series. + + align:start position:0% +zero. to a harmonic series. + + + align:start position:0% +zero. to a harmonic series. +And this series is convergent + + align:start position:0% + + + + align:start position:0% + +is convergent + + align:start position:0% + + + + align:start position:0% + +but not absolutely convergent. + + align:start position:0% + + + + align:start position:0% + +Why? Because the the if you slap + + align:start position:0% +Why? Because the the if you slap + + + align:start position:0% +Why? Because the the if you slap +absolute value sign you get the + + align:start position:0% +absolute value sign you get the + + + align:start position:0% +absolute value sign you get the +harmonics is and we already know that + + align:start position:0% +harmonics is and we already know that + + + align:start position:0% +harmonics is and we already know that +this is not convergent but not + + align:start position:0% +this is not convergent but not + + + align:start position:0% +this is not convergent but not +absolutely converted. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So this is the alternating harmonic + + align:start position:0% +So this is the alternating harmonic + + + align:start position:0% +So this is the alternating harmonic +series. Okay. Now let's try to prove + + align:start position:0% +series. Okay. Now let's try to prove + + + align:start position:0% +series. Okay. Now let's try to prove +that uh absolute convergence implies + + align:start position:0% +that uh absolute convergence implies + + + align:start position:0% +that uh absolute convergence implies +convergence. + + align:start position:0% + + + + align:start position:0% + +And so I'm going to look at so I take + + align:start position:0% +And so I'm going to look at so I take + + + align:start position:0% +And so I'm going to look at so I take +two series. So I have SN that's my + + align:start position:0% +two series. So I have SN that's my + + + align:start position:0% +two series. So I have SN that's my +original series a I = Z to N like that. + + align:start position:0% +original series a I = Z to N like that. + + + align:start position:0% +original series a I = Z to N like that. +And then I take the one where I slap + + align:start position:0% +And then I take the one where I slap + + + align:start position:0% +And then I take the one where I slap +absolute value sign and I denote it with + + align:start position:0% +absolute value sign and I denote it with + + + align:start position:0% +absolute value sign and I denote it with +a bar. + + align:start position:0% +a bar. + + + align:start position:0% +a bar. +So I = to zero 2 N of A. + + align:start position:0% +So I = to zero 2 N of A. + + + align:start position:0% +So I = to zero 2 N of A. +And then I make a little observation + + align:start position:0% +And then I make a little observation + + + align:start position:0% +And then I make a little observation +and the observation is + + align:start position:0% +and the observation is + + + align:start position:0% +and the observation is +that if I take + + align:start position:0% +that if I take + + + align:start position:0% +that if I take +if I'm looking at + + align:start position:0% +if I'm looking at + + + align:start position:0% +if I'm looking at +SN and SM + + align:start position:0% +SN and SM + + + align:start position:0% +SN and SM +so just think about at N here is larger + + align:start position:0% +so just think about at N here is larger + + + align:start position:0% +so just think about at N here is larger +than N. + + align:start position:0% +than N. + + + align:start position:0% +than N. +Then you can think about this thing here + + align:start position:0% +Then you can think about this thing here + + + align:start position:0% +Then you can think about this thing here +as this thing here is just where you're + + align:start position:0% +as this thing here is just where you're + + + align:start position:0% +as this thing here is just where you're +summing from m + one + + align:start position:0% + + + + align:start position:0% + +n up to a n right that's this difference + + align:start position:0% +n up to a n right that's this difference + + + align:start position:0% +n up to a n right that's this difference +right + + align:start position:0% +right + + + align:start position:0% +right +but if you take absolute value on this + + align:start position:0% +but if you take absolute value on this + + + align:start position:0% +but if you take absolute value on this +absolute value on that well that's a + + align:start position:0% +absolute value on that well that's a + + + align:start position:0% +absolute value on that well that's a +that's of of course less or equal to + + align:start position:0% +that's of of course less or equal to + + + align:start position:0% +that's of of course less or equal to +right where you're taking absolute value + + align:start position:0% +right where you're taking absolute value + + + align:start position:0% +right where you're taking absolute value +on each individual one + + align:start position:0% + + + + align:start position:0% + +like that. + + align:start position:0% +like that. + + + align:start position:0% +like that. +But this thing here is just this is just + + align:start position:0% +But this thing here is just this is just + + + align:start position:0% +But this thing here is just this is just +right this thing here is just for the + + align:start position:0% +right this thing here is just for the + + + align:start position:0% +right this thing here is just for the +the other series. this is it's the same + + align:start position:0% +the other series. this is it's the same + + + align:start position:0% +the other series. this is it's the same +sort of difference + + align:start position:0% + + + + align:start position:0% + +and and here actually I don't need to + + align:start position:0% +and and here actually I don't need to + + + align:start position:0% +and and here actually I don't need to +take absolute value but I could take + + align:start position:0% +take absolute value but I could take + + + align:start position:0% +take absolute value but I could take +absolute value but this is already non + + align:start position:0% +absolute value but this is already non + + + align:start position:0% +absolute value but this is already non +negative + + align:start position:0% +negative + + + align:start position:0% +negative +and so you see that so so you make this + + align:start position:0% +and so you see that so so you make this + + + align:start position:0% +and so you see that so so you make this +little observation but now we know that + + align:start position:0% +little observation but now we know that + + + align:start position:0% +little observation but now we know that +if it is absolutely convergent then this + + align:start position:0% +if it is absolutely convergent then this + + + align:start position:0% +if it is absolutely convergent then this +sequence here converge so this means + + align:start position:0% +sequence here converge so this means + + + align:start position:0% +sequence here converge so this means +that in particular it's equivalent to + + align:start position:0% +that in particular it's equivalent to + + + align:start position:0% +that in particular it's equivalent to +saying that it's a cushy sequence and so + + align:start position:0% +saying that it's a cushy sequence and so + + + align:start position:0% +saying that it's a cushy sequence and so +this means that things if you are + + align:start position:0% +this means that things if you are + + + align:start position:0% +this means that things if you are +sufficiently far out these things here + + align:start position:0% +sufficiently far out these things here + + + align:start position:0% +sufficiently far out these things here +have bunched together epsilon together + + align:start position:0% +have bunched together epsilon together + + + align:start position:0% +have bunched together epsilon together +if you are bigger than some capital n + + align:start position:0% +if you are bigger than some capital n + + + align:start position:0% +if you are bigger than some capital n +but now this inequality say that these + + align:start position:0% +but now this inequality say that these + + + align:start position:0% +but now this inequality say that these +things here bunch together so you see + + align:start position:0% +things here bunch together so you see + + + align:start position:0% +things here bunch together so you see +that that if this is convergent + + align:start position:0% +that that if this is convergent + + + align:start position:0% +that that if this is convergent +then it's a cy sequence but this means + + align:start position:0% +then it's a cy sequence but this means + + + align:start position:0% +then it's a cy sequence but this means +that this here is a cy sequence so it + + align:start position:0% +that this here is a cy sequence so it + + + align:start position:0% +that this here is a cy sequence so it +means that there are vision series was + + align:start position:0% +means that there are vision series was + + + align:start position:0% +means that there are vision series was +converged. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% +Okay. Um + + + align:start position:0% +Okay. Um +and so now let's look at one more + + align:start position:0% +and so now let's look at one more + + + align:start position:0% +and so now let's look at one more +example and then then we'll talk about + + align:start position:0% +example and then then we'll talk about + + + align:start position:0% +example and then then we'll talk about +some of the tests. + + align:start position:0% +some of the tests. + + + align:start position:0% +some of the tests. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +yeah. So let's look at so we we we saw + + align:start position:0% +yeah. So let's look at so we we we saw + + + align:start position:0% +yeah. So let's look at so we we we saw +that the harmonic series is divergent. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% + + + + align:start position:0% + +so we saw that the harmonic series is + + align:start position:0% +so we saw that the harmonic series is + + + align:start position:0% +so we saw that the harmonic series is +divergent + + align:start position:0% +divergent + + + align:start position:0% +divergent +but let's what about + + align:start position:0% + + + + align:start position:0% + +right I mean and what about so this is + + align:start position:0% +right I mean and what about so this is + + + align:start position:0% +right I mean and what about so this is +another thing you could do right so + + align:start position:0% +another thing you could do right so + + + align:start position:0% +another thing you could do right so +maybe the most important + + align:start position:0% +maybe the most important + + + align:start position:0% +maybe the most important +series is the geometric series after + + align:start position:0% +series is the geometric series after + + + align:start position:0% +series is the geometric series after +that you can debate a little bit which + + align:start position:0% +that you can debate a little bit which + + + align:start position:0% +that you can debate a little bit which +series is the most important and but + + align:start position:0% +series is the most important and but + + + align:start position:0% +series is the most important and but +these here is some other candidates for + + align:start position:0% +these here is some other candidates for + + + align:start position:0% +these here is some other candidates for +that. Um, so I'm looking at now the sum + + align:start position:0% +that. Um, so I'm looking at now the sum + + + align:start position:0% +that. Um, so I'm looking at now the sum +here n = 0 to infinity. + + align:start position:0% +here n = 0 to infinity. + + + align:start position:0% +here n = 0 to infinity. +Uh, and I'm looking at + + align:start position:0% +Uh, and I'm looking at + + + align:start position:0% +Uh, and I'm looking at +uh 1 / n squares. But you could do it + + align:start position:0% +uh 1 / n squares. But you could do it + + + align:start position:0% +uh 1 / n squares. But you could do it +more generally where you raise it to + + align:start position:0% +more generally where you raise it to + + + align:start position:0% +more generally where you raise it to +some power. Right? If that power was + + align:start position:0% +some power. Right? If that power was + + + align:start position:0% +some power. Right? If that power was +one, you got the alternating, you got + + align:start position:0% +one, you got the alternating, you got + + + align:start position:0% +one, you got the alternating, you got +the harmonic series. But I'm now I'm + + align:start position:0% +the harmonic series. But I'm now I'm + + + align:start position:0% +the harmonic series. But I'm now I'm +just looking at a specific power two. + + align:start position:0% +just looking at a specific power two. + + + align:start position:0% +just looking at a specific power two. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And so I claim that that this series + + align:start position:0% +And so I claim that that this series + + + align:start position:0% +And so I claim that that this series +here this here is um this here is um I + + align:start position:0% +here this here is um this here is um I + + + align:start position:0% +here this here is um this here is um I +mean this one doesn't really have a name + + align:start position:0% +mean this one doesn't really have a name + + + align:start position:0% +mean this one doesn't really have a name +but it is a key series. And so I claim + + align:start position:0% +but it is a key series. And so I claim + + + align:start position:0% +but it is a key series. And so I claim +that this here is convergence. So this + + align:start position:0% +that this here is convergence. So this + + + align:start position:0% +that this here is convergence. So this +is + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +You observe that the a n in this case + + align:start position:0% +You observe that the a n in this case + + + align:start position:0% +You observe that the a n in this case +this is just 1 / n^2 right and these + + align:start position:0% +this is just 1 / n^2 right and these + + + align:start position:0% +this is just 1 / n^2 right and these +here are non- negative. So all we need + + align:start position:0% +here are non- negative. So all we need + + + align:start position:0% +here are non- negative. So all we need +to do is so we just need to prove. So + + align:start position:0% +to do is so we just need to prove. So + + + align:start position:0% +to do is so we just need to prove. So +this is when the a ends are non negative + + align:start position:0% +this is when the a ends are non negative + + + align:start position:0% +this is when the a ends are non negative +all you need to prove is that that the + + align:start position:0% +all you need to prove is that that the + + + align:start position:0% +all you need to prove is that that the +sequence you just need to prove need to + + align:start position:0% +sequence you just need to prove need to + + + align:start position:0% +sequence you just need to prove need to +show + + align:start position:0% + + + + align:start position:0% + +that the SN which is where you're + + align:start position:0% +that the SN which is where you're + + + align:start position:0% +that the SN which is where you're +summing here + + align:start position:0% + + + + align:start position:0% + +I = uh you can't you shouldn't sum from + + align:start position:0% +I = uh you can't you shouldn't sum from + + + align:start position:0% +I = uh you can't you shouldn't sum from +zero sum from one I = to uh one to n + + align:start position:0% +zero sum from one I = to uh one to n + + + align:start position:0% +zero sum from one I = to uh one to n +that you will need to prove that these + + align:start position:0% +that you will need to prove that these + + + align:start position:0% +that you will need to prove that these +here are bounded + + align:start position:0% +here are bounded + + + align:start position:0% +here are bounded +and this is because the a + + align:start position:0% +and this is because the a + + + align:start position:0% +and this is because the a +ends are non negative. + + align:start position:0% + + + + align:start position:0% + +Okay. So now the idea here is that um I + + align:start position:0% +Okay. So now the idea here is that um I + + + align:start position:0% +Okay. So now the idea here is that um I +mean again this is not + + align:start position:0% +mean again this is not + + + align:start position:0% +mean again this is not +um this is not necessarily how I would + + align:start position:0% +um this is not necessarily how I would + + + align:start position:0% +um this is not necessarily how I would +do it but um if but this the advantage + + align:start position:0% +do it but um if but this the advantage + + + align:start position:0% +do it but um if but this the advantage +with this here is that it doesn't use + + align:start position:0% +with this here is that it doesn't use + + + align:start position:0% +with this here is that it doesn't use +anything fancy. I mean it's not like the + + align:start position:0% +anything fancy. I mean it's not like the + + + align:start position:0% +anything fancy. I mean it's not like the +the the way later on you would do it + + align:start position:0% +the the way later on you would do it + + + align:start position:0% +the the way later on you would do it +will you would use the integral test but + + align:start position:0% +will you would use the integral test but + + + align:start position:0% +will you would use the integral test but +we haven't talked about this integral + + align:start position:0% +we haven't talked about this integral + + + align:start position:0% +we haven't talked about this integral +test yet. So you can do it very simple + + align:start position:0% +test yet. So you can do it very simple + + + align:start position:0% +test yet. So you can do it very simple +mindedly. + + align:start position:0% +mindedly. + + + align:start position:0% +mindedly. +And so the claim here is that + + align:start position:0% +And so the claim here is that + + + align:start position:0% +And so the claim here is that +um that um that you want to compare. + + align:start position:0% +um that um that you want to compare. + + + align:start position:0% +um that um that you want to compare. +So we want to we want to make a + + align:start position:0% +So we want to we want to make a + + + align:start position:0% +So we want to we want to make a +following claim + + align:start position:0% +following claim + + + align:start position:0% +following claim +uh that um + + align:start position:0% +uh that um + + + align:start position:0% +uh that um +that um that if you're looking at s to + + align:start position:0% +that um that if you're looking at s to + + + align:start position:0% +that um that if you're looking at s to +the 2 n + one sorry f to the 2 n. So + + align:start position:0% +the 2 n + one sorry f to the 2 n. So + + + align:start position:0% +the 2 n + one sorry f to the 2 n. So +it's just similar to what we did before. + + align:start position:0% +it's just similar to what we did before. + + + align:start position:0% +it's just similar to what we did before. +If we want to prove we want to prove + + align:start position:0% +If we want to prove we want to prove + + + align:start position:0% +If we want to prove we want to prove +that this thing here uh for this uh + + align:start position:0% +that this thing here uh for this uh + + + align:start position:0% +that this thing here uh for this uh +series that this is less than the sum + + align:start position:0% +series that this is less than the sum + + + align:start position:0% +series that this is less than the sum +here from i uh equal to uh zero to n of + + align:start position:0% +here from i uh equal to uh zero to n of + + + align:start position:0% +here from i uh equal to uh zero to n of +12 to the power i. So we'll put n minus + + align:start position:0% +12 to the power i. So we'll put n minus + + + align:start position:0% +12 to the power i. So we'll put n minus +one. + + align:start position:0% +one. + + + align:start position:0% +one. +So we claim this thing here. + + align:start position:0% +So we claim this thing here. + + + align:start position:0% +So we claim this thing here. +Now you see that so we claim that we + + align:start position:0% +Now you see that so we claim that we + + + align:start position:0% +Now you see that so we claim that we +have this inequality for all in right + + align:start position:0% +have this inequality for all in right + + + align:start position:0% +have this inequality for all in right +but um this thing here we already know + + align:start position:0% +but um this thing here we already know + + + align:start position:0% +but um this thing here we already know +that this here is a geometric series + + align:start position:0% + + + + align:start position:0% + +series + + align:start position:0% +series + + + align:start position:0% +series +with C = to a half so it's convergent + + align:start position:0% + + + + align:start position:0% + +and you see this thing here is a subsequ + + align:start position:0% +and you see this thing here is a subsequ + + + align:start position:0% +and you see this thing here is a subsequ +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +but it's a subsequence because this here + + align:start position:0% +but it's a subsequence because this here + + + align:start position:0% +but it's a subsequence because this here +is convergent. This here is this here is + + align:start position:0% +is convergent. This here is this here is + + + align:start position:0% +is convergent. This here is this here is +yeah right this here is bounded by + + align:start position:0% +yeah right this here is bounded by + + + align:start position:0% +yeah right this here is bounded by +something fixed right so it means that + + align:start position:0% +something fixed right so it means that + + + align:start position:0% +something fixed right so it means that +this subsequence here is bounded + + align:start position:0% +this subsequence here is bounded + + + align:start position:0% +this subsequence here is bounded +but the original series was a mono + + align:start position:0% +but the original series was a mono + + + align:start position:0% +but the original series was a mono +increasing sequence. So if a subsequence + + align:start position:0% +increasing sequence. So if a subsequence + + + align:start position:0% +increasing sequence. So if a subsequence +is bounded then the original sequence is + + align:start position:0% +is bounded then the original sequence is + + + align:start position:0% +is bounded then the original sequence is +bounded and and so convergent right. So + + align:start position:0% +bounded and and so convergent right. So + + + align:start position:0% +bounded and and so convergent right. So +we just need to prove we just need to + + align:start position:0% +we just need to prove we just need to + + + align:start position:0% +we just need to prove we just need to +give a bound like this and the bound + + align:start position:0% +give a bound like this and the bound + + + align:start position:0% +give a bound like this and the bound +here you get is but we already + + align:start position:0% +here you get is but we already + + + align:start position:0% +here you get is but we already +determined that this here is less or + + align:start position:0% +determined that this here is less or + + + align:start position:0% +determined that this here is less or +equal to one over 1 minus c. C is a + + align:start position:0% +equal to one over 1 minus c. C is a + + + align:start position:0% +equal to one over 1 minus c. C is a +half. So this is like this. So this here + + align:start position:0% +half. So this is like this. So this here + + + align:start position:0% +half. So this is like this. So this here +is a half. So this whole thing here is + + align:start position:0% +is a half. So this whole thing here is + + + align:start position:0% +is a half. So this whole thing here is +two. + + align:start position:0% +two. + + + align:start position:0% +two. +So this here would be bounded by two. + + align:start position:0% +So this here would be bounded by two. + + + align:start position:0% +So this here would be bounded by two. +Right? Okay. So now we want to prove so + + align:start position:0% +Right? Okay. So now we want to prove so + + + align:start position:0% +Right? Okay. So now we want to prove so +we want to prove this claim here. So if + + align:start position:0% +we want to prove this claim here. So if + + + align:start position:0% +we want to prove this claim here. So if +we can prove this claim then we have + + align:start position:0% +we can prove this claim then we have + + + align:start position:0% +we can prove this claim then we have +that the series this series here is + + align:start position:0% +that the series this series here is + + + align:start position:0% +that the series this series here is +convergent. + + align:start position:0% +convergent. + + + align:start position:0% +convergent. +Okay. So now let's let's let's try to do + + align:start position:0% +Okay. So now let's let's let's try to do + + + align:start position:0% +Okay. So now let's let's let's try to do +that. So when + + align:start position:0% +that. So when + + + align:start position:0% +that. So when +n is equal to one so we we do it again + + align:start position:0% +n is equal to one so we we do it again + + + align:start position:0% +n is equal to one so we we do it again +in the same way. + + align:start position:0% +in the same way. + + + align:start position:0% +in the same way. +This is called by induction. We do it + + align:start position:0% +This is called by induction. We do it + + + align:start position:0% +This is called by induction. We do it +for first for + + align:start position:0% +for first for + + + align:start position:0% +for first for +for n = 1 for n = 1 it is a claim that s + + align:start position:0% +for n = 1 for n = 1 it is a claim that s + + + align:start position:0% +for n = 1 for n = 1 it is a claim that s +right if n is equal to one this is 2 + + align:start position:0% +right if n is equal to one this is 2 + + + align:start position:0% +right if n is equal to one this is 2 +minus one that's one so it's a claim + + align:start position:0% +minus one that's one so it's a claim + + + align:start position:0% +minus one that's one so it's a claim +that this thing here + + align:start position:0% +that this thing here + + + align:start position:0% +that this thing here +is uh is bigger equals is lesser equal + + align:start position:0% +is uh is bigger equals is lesser equal + + + align:start position:0% +is uh is bigger equals is lesser equal +to + + align:start position:0% +to + + + align:start position:0% +to +and now it's when n is equal to one it's + + align:start position:0% +and now it's when n is equal to one it's + + + align:start position:0% +and now it's when n is equal to one it's +just this is you're just summing over + + align:start position:0% +just this is you're just summing over + + + align:start position:0% +just this is you're just summing over +one thing. It's just one thing and it is + + align:start position:0% +one thing. It's just one thing and it is + + + align:start position:0% +one thing. It's just one thing and it is +a half to the power zero and that's one. + + align:start position:0% +a half to the power zero and that's one. + + + align:start position:0% +a half to the power zero and that's one. +So for n= 1, this is what we need to + + align:start position:0% +So for n= 1, this is what we need to + + + align:start position:0% +So for n= 1, this is what we need to +show. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +But now let's see + + align:start position:0% +But now let's see + + + align:start position:0% +But now let's see +for n equal to one. Well, this here is + + align:start position:0% +for n equal to one. Well, this here is + + + align:start position:0% +for n equal to one. Well, this here is +indeed one. So that's okay, right? + + align:start position:0% +indeed one. So that's okay, right? + + + align:start position:0% +indeed one. So that's okay, right? +So this is okay. + + align:start position:0% + + + + align:start position:0% + +So now assume + + align:start position:0% + + + + align:start position:0% + +assume that s ^ 2n -1 is bounded by this + + align:start position:0% +assume that s ^ 2n -1 is bounded by this + + + align:start position:0% +assume that s ^ 2n -1 is bounded by this +i = 0 to n -1 of 12 to the power i. + + align:start position:0% +i = 0 to n -1 of 12 to the power i. + + + align:start position:0% +i = 0 to n -1 of 12 to the power i. +Right? So assume this and we want to + + align:start position:0% +Right? So assume this and we want to + + + align:start position:0% +Right? So assume this and we want to +prove the same thing but for n + one. So + + align:start position:0% +prove the same thing but for n + one. So + + + align:start position:0% +prove the same thing but for n + one. So +want to show + + align:start position:0% + + + + align:start position:0% + +the same inequality + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +n + one. Okay. + + align:start position:0% + + + + align:start position:0% + +So let me do that. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So I'm looking at s 2 n + 1 -1. + + align:start position:0% +So I'm looking at s 2 n + 1 -1. + + + align:start position:0% +So I'm looking at s 2 n + 1 -1. +So s 2n + 1 - one I can write as where + + align:start position:0% +So s 2n + 1 - one I can write as where + + + align:start position:0% +So s 2n + 1 - one I can write as where +I'm summing the first 2 n minus one + + align:start position:0% +I'm summing the first 2 n minus one + + + align:start position:0% +I'm summing the first 2 n minus one +and then I'm I'm summing + + align:start position:0% +and then I'm I'm summing + + + align:start position:0% +and then I'm I'm summing +and then plus and then I'm what I'm + + align:start position:0% +and then plus and then I'm what I'm + + + align:start position:0% +and then plus and then I'm what I'm +summing from I equ= to 2 n to uh up to 2 + + align:start position:0% +summing from I equ= to 2 n to uh up to 2 + + + align:start position:0% +summing from I equ= to 2 n to uh up to 2 +n + 1 - one + + align:start position:0% +n + 1 - one + + + align:start position:0% +n + 1 - one +right and then it's 1 / i^ 2 + + align:start position:0% +right and then it's 1 / i^ 2 + + + align:start position:0% +right and then it's 1 / i^ 2 +now in this case remember before we + + align:start position:0% +now in this case remember before we + + + align:start position:0% +now in this case remember before we +wanted to prove that something was + + align:start position:0% +wanted to prove that something was + + + align:start position:0% +wanted to prove that something was +divergent + + align:start position:0% +divergent + + + align:start position:0% +divergent +So we wanted to give a lower bound. In + + align:start position:0% +So we wanted to give a lower bound. In + + + align:start position:0% +So we wanted to give a lower bound. In +this case we want to give a upper bound. + + align:start position:0% +this case we want to give a upper bound. + + + align:start position:0% +this case we want to give a upper bound. +So when we do this we think about what + + align:start position:0% +So when we do this we think about what + + + align:start position:0% +So when we do this we think about what +is the instead of what is the smallest + + align:start position:0% +is the instead of what is the smallest + + + align:start position:0% +is the instead of what is the smallest +we think about what is the largest of + + align:start position:0% +we think about what is the largest of + + + align:start position:0% +we think about what is the largest of +these numbers but that's the first one + + align:start position:0% +these numbers but that's the first one + + + align:start position:0% +these numbers but that's the first one +right and there are again just like + + align:start position:0% +right and there are again just like + + + align:start position:0% +right and there are again just like +before there are two n many of them. So + + align:start position:0% +before there are two n many of them. So + + + align:start position:0% +before there are two n many of them. So +this thing here is lesser equal to s2 n + + align:start position:0% +this thing here is lesser equal to s2 n + + + align:start position:0% +this thing here is lesser equal to s2 n +minus one. Sorry. Yeah, like this. And + + align:start position:0% +minus one. Sorry. Yeah, like this. And + + + align:start position:0% +minus one. Sorry. Yeah, like this. And +then there are two n many they're all + + align:start position:0% +then there are two n many they're all + + + align:start position:0% +then there are two n many they're all +non negative. And this is and the first + + align:start position:0% +non negative. And this is and the first + + + align:start position:0% +non negative. And this is and the first +one is the largest. + + align:start position:0% +one is the largest. + + + align:start position:0% +one is the largest. +So 1 / 2 n + + align:start position:0% +So 1 / 2 n + + + align:start position:0% +So 1 / 2 n +squared like this, right? + + align:start position:0% +squared like this, right? + + + align:start position:0% +squared like this, right? +And so you see that this thing here is + + align:start position:0% +And so you see that this thing here is + + + align:start position:0% +And so you see that this thing here is +so now we can fill in the assumption. We + + align:start position:0% +so now we can fill in the assumption. We + + + align:start position:0% +so now we can fill in the assumption. We +were assuming that this here was less + + align:start position:0% +were assuming that this here was less + + + align:start position:0% +were assuming that this here was less +than this. + + align:start position:0% +than this. + + + align:start position:0% +than this. +So this is the sum from + + align:start position:0% +So this is the sum from + + + align:start position:0% +So this is the sum from +i =0 to n -1 of 12 to the power i + + align:start position:0% + + + + align:start position:0% + +and uh the this thing here but the + + align:start position:0% +and uh the this thing here but the + + + align:start position:0% +and uh the this thing here but the +square kills that one and you're still + + align:start position:0% +square kills that one and you're still + + + align:start position:0% +square kills that one and you're still +left with one over 2n + + align:start position:0% +left with one over 2n + + + align:start position:0% +left with one over 2n +but you see this is of course exactly + + align:start position:0% +but you see this is of course exactly + + + align:start position:0% +but you see this is of course exactly +the next one in the series. So this is I + + align:start position:0% +the next one in the series. So this is I + + + align:start position:0% +the next one in the series. So this is I += 0 to N of a half to the power I like + + align:start position:0% += 0 to N of a half to the power I like + + + align:start position:0% += 0 to N of a half to the power I like +that right and that's indeed this is + + align:start position:0% +that right and that's indeed this is + + + align:start position:0% +that right and that's indeed this is +like the induction step right this is + + align:start position:0% +like the induction step right this is + + + align:start position:0% +like the induction step right this is +what's called the induction step so this + + align:start position:0% +what's called the induction step so this + + + align:start position:0% +what's called the induction step so this +is so it's true also so if it's true for + + align:start position:0% +is so it's true also so if it's true for + + + align:start position:0% +is so it's true also so if it's true for +n the claim then it's also true for n + + align:start position:0% +n the claim then it's also true for n + + + align:start position:0% +n the claim then it's also true for n +plus one + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now uh so now um let me I have just + + align:start position:0% +So now uh so now um let me I have just + + + align:start position:0% +So now uh so now um let me I have just +four minutes left. There's a little bit + + align:start position:0% +four minutes left. There's a little bit + + + align:start position:0% +four minutes left. There's a little bit +more uh in I already posted the lecture + + align:start position:0% +more uh in I already posted the lecture + + + align:start position:0% +more uh in I already posted the lecture +notes uh and um and there's a bit more + + align:start position:0% +notes uh and um and there's a bit more + + + align:start position:0% +notes uh and um and there's a bit more +here I want to talk about. + + align:start position:0% +here I want to talk about. + + + align:start position:0% +here I want to talk about. +So I want to talk about some of the + + align:start position:0% +So I want to talk about some of the + + + align:start position:0% +So I want to talk about some of the +tests but we we'll talk about that more + + align:start position:0% +tests but we we'll talk about that more + + + align:start position:0% +tests but we we'll talk about that more +next time also. So to determine + + align:start position:0% + + + + align:start position:0% + +whether another series + + align:start position:0% + + + + align:start position:0% + +a series is converging + + align:start position:0% +a series is converging + + + align:start position:0% +a series is converging +converge + + align:start position:0% +converge + + + align:start position:0% +converge +uh then + + align:start position:0% +uh then + + + align:start position:0% +uh then +there are a number of tests + + align:start position:0% + + + + align:start position:0% + +and then of the the key + + align:start position:0% +and then of the the key + + + align:start position:0% +and then of the the key +uh the key point is to use the right + + align:start position:0% +uh the key point is to use the right + + + align:start position:0% +uh the key point is to use the right +test. So uh I will just talk about so I + + align:start position:0% +test. So uh I will just talk about so I + + + align:start position:0% +test. So uh I will just talk about so I +just mentioned some of the tests but we + + align:start position:0% +just mentioned some of the tests but we + + + align:start position:0% +just mentioned some of the tests but we +won't anyway go through all of them you + + align:start position:0% +won't anyway go through all of them you + + + align:start position:0% +won't anyway go through all of them you +know so maybe I can't go through any of + + align:start position:0% +know so maybe I can't go through any of + + + align:start position:0% +know so maybe I can't go through any of +them. So there's a comparison test, + + align:start position:0% + + + + align:start position:0% + +there's a ratio test, + + align:start position:0% + + + + align:start position:0% + +there's root test, + + align:start position:0% + + + + align:start position:0% + +and there's also the one I talked about + + align:start position:0% +and there's also the one I talked about + + + align:start position:0% +and there's also the one I talked about +several times, the integral test. + + align:start position:0% + + + + align:start position:0% + +And then there's even one called the + + align:start position:0% +And then there's even one called the + + + align:start position:0% +And then there's even one called the +alternate series test. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay, now maybe I can just talk about + + align:start position:0% +Okay, now maybe I can just talk about + + + align:start position:0% +Okay, now maybe I can just talk about +the the comparison test. That's in a way + + align:start position:0% +the the comparison test. That's in a way + + + align:start position:0% +the the comparison test. That's in a way +the simplest of. + + align:start position:0% + + + + align:start position:0% + +And so the comparison test is + + align:start position:0% +And so the comparison test is + + + align:start position:0% +And so the comparison test is +that you're looking at two series. So + + align:start position:0% +that you're looking at two series. So + + + align:start position:0% +that you're looking at two series. So +you have these two series here + + align:start position:0% + + + + align:start position:0% + +and you have this other series here. + + align:start position:0% + + + + align:start position:0% + +And the comparison tests say that if you + + align:start position:0% +And the comparison tests say that if you + + + align:start position:0% +And the comparison tests say that if you +have a n bigger equal to zero less or + + align:start position:0% +have a n bigger equal to zero less or + + + align:start position:0% +have a n bigger equal to zero less or +equal to bn. So if you have this and + + align:start position:0% + + + + align:start position:0% + +and the B and this series here + + align:start position:0% +and the B and this series here + + + align:start position:0% +and the B and this series here +converge + + align:start position:0% + + + + align:start position:0% + +then then the corresponding thing with + + align:start position:0% +then then the corresponding thing with + + + align:start position:0% +then then the corresponding thing with +the A in + + align:start position:0% +the A in + + + align:start position:0% +the A in +will also converge. + + align:start position:0% + + + + align:start position:0% + +and and this this this is the simplest + + align:start position:0% +and and this this this is the simplest + + + align:start position:0% +and and this this this is the simplest +version of the comparison test and this + + align:start position:0% +version of the comparison test and this + + + align:start position:0% +version of the comparison test and this +is in a way used in two ways right so + + align:start position:0% +is in a way used in two ways right so + + + align:start position:0% +is in a way used in two ways right so +you often you have a series and maybe it + + align:start position:0% +you often you have a series and maybe it + + + align:start position:0% +you often you have a series and maybe it +could be a super complicated series + + align:start position:0% +could be a super complicated series + + + align:start position:0% +could be a super complicated series +and uh but you see some kind of path in + + align:start position:0% +and uh but you see some kind of path in + + + align:start position:0% +and uh but you see some kind of path in +and so you can compare it with a much + + align:start position:0% +and so you can compare it with a much + + + align:start position:0% +and so you can compare it with a much +simpler series that perhaps you already + + align:start position:0% +simpler series that perhaps you already + + + align:start position:0% +simpler series that perhaps you already +know whether it's converging right and + + align:start position:0% +know whether it's converging right and + + + align:start position:0% +know whether it's converging right and +so if you can compare it with something + + align:start position:0% +so if you can compare it with something + + + align:start position:0% +so if you can compare it with something +else and you know that that converge + + align:start position:0% +else and you know that that converge + + + align:start position:0% +else and you know that that converge +then you conclude that that that a end + + align:start position:0% +then you conclude that that that a end + + + align:start position:0% +then you conclude that that that a end +series is converging. It's also + + align:start position:0% +series is converging. It's also + + + align:start position:0% +series is converging. It's also +sometimes used that you want to + + align:start position:0% +sometimes used that you want to + + + align:start position:0% +sometimes used that you want to +determine whether this series here is + + align:start position:0% +determine whether this series here is + + + align:start position:0% +determine whether this series here is +converging but you can you actually you + + align:start position:0% +converging but you can you actually you + + + align:start position:0% +converging but you can you actually you +can easily kind of compare it with some + + align:start position:0% +can easily kind of compare it with some + + + align:start position:0% +can easily kind of compare it with some +other series where you have this + + align:start position:0% +other series where you have this + + + align:start position:0% +other series where you have this +relationship here and this one you + + align:start position:0% +relationship here and this one you + + + align:start position:0% +relationship here and this one you +already know is divergent right so it's + + align:start position:0% +already know is divergent right so it's + + + align:start position:0% +already know is divergent right so it's +used in both ways when it's used to both + + align:start position:0% +used in both ways when it's used to both + + + align:start position:0% +used in both ways when it's used to both +determine that a series is convergent + + align:start position:0% +determine that a series is convergent + + + align:start position:0% +determine that a series is convergent +and it's also used to determine that the + + align:start position:0% +and it's also used to determine that the + + + align:start position:0% +and it's also used to determine that the +series is divergent okay so there's a + + align:start position:0% +series is divergent okay so there's a + + + align:start position:0% +series is divergent okay so there's a +little bit more about test on the in the + + align:start position:0% +little bit more about test on the in the + + + align:start position:0% +little bit more about test on the in the +lecture notes. Um but we will anyway + + align:start position:0% +lecture notes. Um but we will anyway + + + align:start position:0% +lecture notes. Um but we will anyway +talk about it more next time. Yeah. + + align:start position:0% +talk about it more next time. Yeah. + + + align:start position:0% +talk about it more next time. Yeah. +>> Question about like the intuition of + + align:start position:0% +>> Question about like the intuition of + + + align:start position:0% +>> Question about like the intuition of +this like + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +Right. Right. Right. So so so that's + + align:start position:0% +Right. Right. Right. So so so that's + + + align:start position:0% +Right. Right. Right. So so so that's +right. So + + align:start position:0% +right. So + + + align:start position:0% +right. So +so so + + align:start position:0% +so so + + + align:start position:0% +so so +right. So that's so that sort of thing + + align:start position:0% +right. So that's so that sort of thing + + + align:start position:0% +right. So that's so that sort of thing +is I mean this last one show you that + + align:start position:0% +is I mean this last one show you that + + + align:start position:0% +is I mean this last one show you that +the geometric series is one that is that + + align:start position:0% +the geometric series is one that is that + + + align:start position:0% +the geometric series is one that is that +sort of come up often as a kind of + + align:start position:0% +sort of come up often as a kind of + + + align:start position:0% +sort of come up often as a kind of +comparison in a way when how you get it + + align:start position:0% +comparison in a way when how you get it + + + align:start position:0% +comparison in a way when how you get it +different for different people obviously + + align:start position:0% +different for different people obviously + + + align:start position:0% +different for different people obviously +you don't start with a claim you sort of + + align:start position:0% +you don't start with a claim you sort of + + + align:start position:0% +you don't start with a claim you sort of +looking at the first few things and you + + align:start position:0% +looking at the first few things and you + + + align:start position:0% +looking at the first few things and you +see a pattern basically but it's not I + + align:start position:0% +see a pattern basically but it's not I + + + align:start position:0% +see a pattern basically but it's not I +mean you know this is not the way you + + align:start position:0% +mean you know this is not the way you + + + align:start position:0% +mean you know this is not the way you +want to really you know later on you + + align:start position:0% +want to really you know later on you + + + align:start position:0% +want to really you know later on you +know I would never prove any kind of + + align:start position:0% +know I would never prove any kind of + + + align:start position:0% +know I would never prove any kind of +convergence like this you know there's a + + align:start position:0% +convergence like this you know there's a + + + align:start position:0% +convergence like this you know there's a +a there's a way of comparing it with the + + align:start position:0% +a there's a way of comparing it with the + + + align:start position:0% +a there's a way of comparing it with the +so the idea is let me just tell you but + + align:start position:0% +so the idea is let me just tell you but + + + align:start position:0% +so the idea is let me just tell you but +of course the lecture is over but but + + align:start position:0% +of course the lecture is over but but + + + align:start position:0% +of course the lecture is over but but +there is um so the integral test is that + + align:start position:0% +there is um so the integral test is that + + + align:start position:0% +there is um so the integral test is that +you're looking at so you're looking at a + + align:start position:0% +you're looking at so you're looking at a + + + align:start position:0% +you're looking at so you're looking at a +series and if you have a series of non- + + align:start position:0% +series and if you have a series of non- + + + align:start position:0% +series and if you have a series of non- +negative numbers you can think about + + align:start position:0% +negative numbers you can think about + + + align:start position:0% +negative numbers you can think about +that the series is like the area below. + + align:start position:0% +that the series is like the area below. + + + align:start position:0% +that the series is like the area below. +If this here is if this is think about + + align:start position:0% +If this here is if this is think about + + + align:start position:0% +If this here is if this is think about +this here as a1 and this is maybe a2 + + align:start position:0% +this here as a1 and this is maybe a2 + + + align:start position:0% +this here as a1 and this is maybe a2 +then you can think about the sum as the + + align:start position:0% +then you can think about the sum as the + + + align:start position:0% +then you can think about the sum as the +sum of the areas like this and so the + + align:start position:0% +sum of the areas like this and so the + + + align:start position:0% +sum of the areas like this and so the +integral of test is that you comparing + + align:start position:0% +integral of test is that you comparing + + + align:start position:0% +integral of test is that you comparing +it with some curve and the area that + + align:start position:0% +it with some curve and the area that + + + align:start position:0% +it with some curve and the area that +lies below it then it's like much more + + align:start position:0% +lies below it then it's like much more + + + align:start position:0% +lies below it then it's like much more +clear right the other one is like where + + align:start position:0% +clear right the other one is like where + + + align:start position:0% +clear right the other one is like where +you have to do it case by case right + + align:start position:0% +you have to do it case by case right + + + align:start position:0% +you have to do it case by case right +that's not you know here there's a kind + + align:start position:0% +that's not you know here there's a kind + + + align:start position:0% +that's not you know here there's a kind +of general idea So it's nice in this + + align:start position:0% +of general idea So it's nice in this + + + align:start position:0% +of general idea So it's nice in this +particular case. I'm not sure it's you + + align:start position:0% +particular case. I'm not sure it's you + + + align:start position:0% +particular case. I'm not sure it's you +know what I mean. I mean you had to look + + align:start position:0% +know what I mean. I mean you had to look + + + align:start position:0% +know what I mean. I mean you had to look +at the first few things and see if you + + align:start position:0% +at the first few things and see if you + + + align:start position:0% +at the first few things and see if you +see a pattern, right? And of course you + + align:start position:0% +see a pattern, right? And of course you + + + align:start position:0% +see a pattern, right? And of course you +don't start with a claim, right? That's + + align:start position:0% +don't start with a claim, right? That's + + + align:start position:0% +don't start with a claim, right? That's +like the end. When you when you actually + + align:start position:0% +like the end. When you when you actually + + + align:start position:0% +like the end. When you when you actually +have a claim, then you already know + + align:start position:0% +have a claim, then you already know + + + align:start position:0% +have a claim, then you already know +what's going on. \ No newline at end of file diff --git a/qgL0cA7GkJo.txt b/qgL0cA7GkJo.txt new file mode 100644 index 0000000000000000000000000000000000000000..195009e2683eb235d0f44b3d526ca81d8f8a0578 --- /dev/null +++ b/qgL0cA7GkJo.txt @@ -0,0 +1,10827 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +basic concepts of readability talking + + align:start position:0% +basic concepts of readability talking + + + align:start position:0% +basic concepts of readability talking +about how we can represent rich sets in + + align:start position:0% +about how we can represent rich sets in + + + align:start position:0% +about how we can represent rich sets in +continuous spaces in Savannah is going + + align:start position:0% +continuous spaces in Savannah is going + + + align:start position:0% +continuous spaces in Savannah is going +to take it over and talk about some + + align:start position:0% +to take it over and talk about some + + + align:start position:0% +to take it over and talk about some +applications in robust motion planning + + align:start position:0% +applications in robust motion planning + + + align:start position:0% +applications in robust motion planning +and then terraria is going to talk about + + align:start position:0% +and then terraria is going to talk about + + + align:start position:0% +and then terraria is going to talk about +how we can peel presets and focus on + + align:start position:0% +how we can peel presets and focus on + + + align:start position:0% +how we can peel presets and focus on +these two + + align:start position:0% +these two + + + align:start position:0% +these two +unclosed and cell phones ok so rich + + align:start position:0% +unclosed and cell phones ok so rich + + + align:start position:0% +unclosed and cell phones ok so rich +abili is a task of figuring out what + + align:start position:0% +abili is a task of figuring out what + + + align:start position:0% +abili is a task of figuring out what +states a dynamical system and possibly + + align:start position:0% +states a dynamical system and possibly + + + align:start position:0% +states a dynamical system and possibly +reach or B yet at a certain time so for + + align:start position:0% +reach or B yet at a certain time so for + + + align:start position:0% +reach or B yet at a certain time so for +example we have these two these two + + align:start position:0% +example we have these two these two + + + align:start position:0% +example we have these two these two +systems we have a finite state machine + + align:start position:0% +systems we have a finite state machine + + + align:start position:0% +systems we have a finite state machine +and discrete system and a continuous + + align:start position:0% +and discrete system and a continuous + + + align:start position:0% +and discrete system and a continuous +system and they started starting six + + align:start position:0% +system and they started starting six + + + align:start position:0% +system and they started starting six +then these are our actions with the + + align:start position:0% +then these are our actions with the + + + align:start position:0% +then these are our actions with the +movies or one factor we can be in either + + align:start position:0% +movies or one factor we can be in either + + + align:start position:0% +movies or one factor we can be in either +of these two states or we can be + + align:start position:0% +of these two states or we can be + + + align:start position:0% +of these two states or we can be +anywhere in this for two seconds three + + align:start position:0% +anywhere in this for two seconds three + + + align:start position:0% +anywhere in this for two seconds three +seconds and so on okay so this is what + + align:start position:0% +seconds and so on okay so this is what + + + align:start position:0% +seconds and so on okay so this is what +we typically yes the motivation for this + + align:start position:0% +we typically yes the motivation for this + + + align:start position:0% +we typically yes the motivation for this +one of the applications for reach + + align:start position:0% +one of the applications for reach + + + align:start position:0% +one of the applications for reach +ability is for verification verification + + align:start position:0% +ability is for verification verification + + + align:start position:0% +ability is for verification verification +is just attached to making sure that we + + align:start position:0% +is just attached to making sure that we + + + align:start position:0% +is just attached to making sure that we +are never gonna reach any bad States so + + align:start position:0% +are never gonna reach any bad States so + + + align:start position:0% +are never gonna reach any bad States so +for you let's say we have a microwave a + + align:start position:0% +for you let's say we have a microwave a + + + align:start position:0% +for you let's say we have a microwave a +bad state is the microwave been open and + + align:start position:0% +bad state is the microwave been open and + + + align:start position:0% +bad state is the microwave been open and +on we want to make sure that these five + + align:start position:0% +on we want to make sure that these five + + + align:start position:0% +on we want to make sure that these five +saves are never reaching so what we do + + align:start position:0% +saves are never reaching so what we do + + + align:start position:0% +saves are never reaching so what we do +is we compute reachable sets and we + + align:start position:0% +is we compute reachable sets and we + + + align:start position:0% +is we compute reachable sets and we +check for intersection like the back + + align:start position:0% +check for intersection like the back + + + align:start position:0% +check for intersection like the back +states to see my TV's on an open or like + + align:start position:0% +states to see my TV's on an open or like + + + align:start position:0% +states to see my TV's on an open or like +over here let's say we have these + + align:start position:0% +over here let's say we have these + + + align:start position:0% +over here let's say we have these +obstacles + + align:start position:0% +obstacles + + + align:start position:0% +obstacles +let's say we got a wall or some other + + align:start position:0% +let's say we got a wall or some other + + + align:start position:0% +let's say we got a wall or some other +obstacle burner + + align:start position:0% +obstacle burner + + + align:start position:0% +obstacle burner +we wanna this is bad right because we + + align:start position:0% +we wanna this is bad right because we + + + align:start position:0% +we wanna this is bad right because we +can reach this state and it's the same + + align:start position:0% +can reach this state and it's the same + + + align:start position:0% +can reach this state and it's the same +as over any questions so far + + align:start position:0% +as over any questions so far + + + align:start position:0% +as over any questions so far +feel free + + align:start position:0% + + + + align:start position:0% + +another motivation for each ability is + + align:start position:0% +another motivation for each ability is + + + align:start position:0% +another motivation for each ability is +for robots motor planning when I think + + align:start position:0% +for robots motor planning when I think + + + align:start position:0% +for robots motor planning when I think +more about and I have a video of this so + + align:start position:0% +more about and I have a video of this so + + + align:start position:0% +more about and I have a video of this so +but we can do with the regional it is + + align:start position:0% +but we can do with the regional it is + + + align:start position:0% +but we can do with the regional it is +stuff like this + + align:start position:0% + + + + align:start position:0% + +okay so this is done using flow tips + + align:start position:0% +okay so this is done using flow tips + + + align:start position:0% +okay so this is done using flow tips +which is rich sense really + + align:start position:0% +which is rich sense really + + + align:start position:0% +which is rich sense really +their art is going to talk more about + + align:start position:0% +their art is going to talk more about + + + align:start position:0% +their art is going to talk more about +this example + + align:start position:0% + + + + align:start position:0% + +okay so now before we talk more about + + align:start position:0% +okay so now before we talk more about + + + align:start position:0% +okay so now before we talk more about +this cool examples this is just + + align:start position:0% +this cool examples this is just + + + align:start position:0% +this cool examples this is just +formalized concepts this let's define + + align:start position:0% +formalized concepts this let's define + + + align:start position:0% +formalized concepts this let's define +some things so let's go back to the same + + align:start position:0% +some things so let's go back to the same + + + align:start position:0% +some things so let's go back to the same +system that we have state machine we + + align:start position:0% +system that we have state machine we + + + align:start position:0% +system that we have state machine we +have a finite set of states as a finite + + align:start position:0% +have a finite set of states as a finite + + + align:start position:0% +have a finite set of states as a finite +set of inputs u which in this case are + + align:start position:0% +set of inputs u which in this case are + + + align:start position:0% +set of inputs u which in this case are +Eastern North and the transition + + align:start position:0% +Eastern North and the transition + + + align:start position:0% +Eastern North and the transition +function and the state visit the trick + + align:start position:0% +function and the state visit the trick + + + align:start position:0% +function and the state visit the trick +is to keep things simple and we have a + + align:start position:0% +is to keep things simple and we have a + + + align:start position:0% +is to keep things simple and we have a +set of initial States x0 which I need + + align:start position:0% +set of initial States x0 which I need + + + align:start position:0% +set of initial States x0 which I need +labeled spring so the rich set is + + align:start position:0% +labeled spring so the rich set is + + + align:start position:0% +labeled spring so the rich set is +defined as the set of states that we can + + align:start position:0% +defined as the set of states that we can + + + align:start position:0% +defined as the set of states that we can +possibly be at time T so more formally + + align:start position:0% +possibly be at time T so more formally + + + align:start position:0% +possibly be at time T so more formally +there exists a sequence of T control + + align:start position:0% +there exists a sequence of T control + + + align:start position:0% +there exists a sequence of T control +inputs that will take us from this + + align:start position:0% +inputs that will take us from this + + + align:start position:0% +inputs that will take us from this +initial state to the corresponding + + align:start position:0% +initial state to the corresponding + + + align:start position:0% +initial state to the corresponding +region so let's say for example it at + + align:start position:0% +region so let's say for example it at + + + align:start position:0% +region so let's say for example it at +that state it's in the return at time 3 + + align:start position:0% +that state it's in the return at time 3 + + + align:start position:0% +that state it's in the return at time 3 +because there exists a sequence of three + + align:start position:0% +because there exists a sequence of three + + + align:start position:0% +because there exists a sequence of three +inputs in this case this is one such + + align:start position:0% +inputs in this case this is one such + + + align:start position:0% +inputs in this case this is one such +sequence there's two more that will take + + align:start position:0% +sequence there's two more that will take + + + align:start position:0% +sequence there's two more that will take +us from the initial state to that okay + + align:start position:0% + + + + align:start position:0% + +and then the reachable set reset + + align:start position:0% +and then the reachable set reset + + + align:start position:0% +and then the reachable set reset +reachable set is defined as the union of + + align:start position:0% +reachable set is defined as the union of + + + align:start position:0% +reachable set is defined as the union of +follow reach sets for time less than or + + align:start position:0% +follow reach sets for time less than or + + + align:start position:0% +follow reach sets for time less than or +equal to T so the reachable set at time + + align:start position:0% +equal to T so the reachable set at time + + + align:start position:0% +equal to T so the reachable set at time +0 is just the initial set of states and + + align:start position:0% +0 is just the initial set of states and + + + align:start position:0% +0 is just the initial set of states and +then what we have a so the reachable set + + align:start position:0% +then what we have a so the reachable set + + + align:start position:0% +then what we have a so the reachable set +is what we used to test for intersection + + align:start position:0% +is what we used to test for intersection + + + align:start position:0% +is what we used to test for intersection +with bad States because that's all the + + align:start position:0% +with bad States because that's all the + + + align:start position:0% +with bad States because that's all the +states that we can possibly reach at + + align:start position:0% +states that we can possibly reach at + + + align:start position:0% +states that we can possibly reach at +something from time 0 to time some time + + align:start position:0% + + + + align:start position:0% + +now as some of you may have figured out + + align:start position:0% +now as some of you may have figured out + + + align:start position:0% +now as some of you may have figured out +by now there's a simple way for some + + align:start position:0% +by now there's a simple way for some + + + align:start position:0% +by now there's a simple way for some +finite state machines that we can + + align:start position:0% +finite state machines that we can + + + align:start position:0% +finite state machines that we can +compute to reach 6 so for example let's + + align:start position:0% +compute to reach 6 so for example let's + + + align:start position:0% +compute to reach 6 so for example let's +say we wanted to reset at time T one way + + align:start position:0% +say we wanted to reset at time T one way + + + align:start position:0% +say we wanted to reset at time T one way +the easiest way we can do this is to + + align:start position:0% +the easiest way we can do this is to + + + align:start position:0% +the easiest way we can do this is to +break this up into time steps into + + align:start position:0% +break this up into time steps into + + + align:start position:0% +break this up into time steps into +single tanks X so instead of computing + + align:start position:0% +single tanks X so instead of computing + + + align:start position:0% +single tanks X so instead of computing +it straight for time to this first + + align:start position:0% +it straight for time to this first + + + align:start position:0% +it straight for time to this first +competed for time on and now we can use + + align:start position:0% +competed for time on and now we can use + + + align:start position:0% +competed for time on and now we can use +these two states as the study set of + + align:start position:0% +these two states as the study set of + + + align:start position:0% +these two states as the study set of +initial 6 and computer the reach set for + + align:start position:0% +initial 6 and computer the reach set for + + + align:start position:0% +initial 6 and computer the reach set for +one more time and that gives us this + + align:start position:0% +one more time and that gives us this + + + align:start position:0% +one more time and that gives us this +reachable recent + + align:start position:0% +reachable recent + + + align:start position:0% +reachable recent +any questions okay and the reason why + + align:start position:0% +any questions okay and the reason why + + + align:start position:0% +any questions okay and the reason why +this works is because three sets are + + align:start position:0% +this works is because three sets are + + + align:start position:0% +this works is because three sets are +semi groups and semigroups satisfy this + + align:start position:0% +semi groups and semigroups satisfy this + + + align:start position:0% +semi groups and semigroups satisfy this +equality so we can we can not just break + + align:start position:0% +equality so we can we can not just break + + + align:start position:0% +equality so we can we can not just break +it up in into single tank sets we can + + align:start position:0% +it up in into single tank sets we can + + + align:start position:0% +it up in into single tank sets we can +break it up into any two times yes okay + + align:start position:0% +break it up into any two times yes okay + + + align:start position:0% +break it up into any two times yes okay +so all of this was for finite state + + align:start position:0% +so all of this was for finite state + + + align:start position:0% +so all of this was for finite state +machines but for continuous systems + + align:start position:0% +machines but for continuous systems + + + align:start position:0% +machines but for continuous systems +things get a little more complicated + + align:start position:0% +things get a little more complicated + + + align:start position:0% +things get a little more complicated +it's a lot of the same concepts but we + + align:start position:0% +it's a lot of the same concepts but we + + + align:start position:0% +it's a lot of the same concepts but we +need to handle a very important issue + + align:start position:0% +need to handle a very important issue + + + align:start position:0% +need to handle a very important issue +and that is how to represent with sets + + align:start position:0% +and that is how to represent with sets + + + align:start position:0% +and that is how to represent with sets +or just sets regions in space for + + align:start position:0% +or just sets regions in space for + + + align:start position:0% +or just sets regions in space for +continuous systems because in a finite + + align:start position:0% +continuous systems because in a finite + + + align:start position:0% +continuous systems because in a finite +state machine we can just enumerate the + + align:start position:0% +state machine we can just enumerate the + + + align:start position:0% +state machine we can just enumerate the +list of states in the reach into each + + align:start position:0% +list of states in the reach into each + + + align:start position:0% +list of states in the reach into each +set of reachable set in a continuous + + align:start position:0% +set of reachable set in a continuous + + + align:start position:0% +set of reachable set in a continuous +system we need some other way we can't + + align:start position:0% +system we need some other way we can't + + + align:start position:0% +system we need some other way we can't +just say every is every point for which + + align:start position:0% +just say every is every point for which + + + align:start position:0% +just say every is every point for which +there exist a sequence of control inputs + + align:start position:0% +there exist a sequence of control inputs + + + align:start position:0% +there exist a sequence of control inputs +because there can be intervening + + align:start position:0% +because there can be intervening + + + align:start position:0% +because there can be intervening +infinitely many points so what we do we + + align:start position:0% +infinitely many points so what we do we + + + align:start position:0% +infinitely many points so what we do we +have two types of representations that + + align:start position:0% +have two types of representations that + + + align:start position:0% +have two types of representations that +we like one is convex polytopes + + align:start position:0% +we like one is convex polytopes + + + align:start position:0% +we like one is convex polytopes +that's just the generalization of a + + align:start position:0% +that's just the generalization of a + + + align:start position:0% +that's just the generalization of a +convex polygon into inspect in two + + align:start position:0% +convex polygon into inspect in two + + + align:start position:0% +convex polygon into inspect in two +dimensions and we have two basic ways + + align:start position:0% +dimensions and we have two basic ways + + + align:start position:0% +dimensions and we have two basic ways +that we can represent these comics + + align:start position:0% +that we can represent these comics + + + align:start position:0% +that we can represent these comics +polytopes what is with these sub + + align:start position:0% +polytopes what is with these sub + + + align:start position:0% +polytopes what is with these sub +pharisees like this ad the convex + + align:start position:0% +pharisees like this ad the convex + + + align:start position:0% +pharisees like this ad the convex +polytope is defined as the comic so in + + align:start position:0% +polytope is defined as the comic so in + + + align:start position:0% +polytope is defined as the comic so in +case someone is doesn't remember + + align:start position:0% +case someone is doesn't remember + + + align:start position:0% +case someone is doesn't remember +toys they say we have just suddenly some + + align:start position:0% +toys they say we have just suddenly some + + + align:start position:0% +toys they say we have just suddenly some +points the comics the convicts fall + + align:start position:0% +points the comics the convicts fall + + + align:start position:0% +points the comics the convicts fall +imagine you have a rubber band and + + align:start position:0% +imagine you have a rubber band and + + + align:start position:0% +imagine you have a rubber band and +you're gonna straighten up and America + + align:start position:0% +you're gonna straighten up and America + + + align:start position:0% +you're gonna straighten up and America +and what that's gonna do is this and the + + align:start position:0% +and what that's gonna do is this and the + + + align:start position:0% +and what that's gonna do is this and the +comics all is just the hilarium inside + + align:start position:0% +comics all is just the hilarium inside + + + align:start position:0% +comics all is just the hilarium inside +inside the robber okay and then another + + align:start position:0% +inside the robber okay and then another + + + align:start position:0% +inside the robber okay and then another +way we can represent convex polytope is + + align:start position:0% +way we can represent convex polytope is + + + align:start position:0% +way we can represent convex polytope is +with with set of inequalities so for + + align:start position:0% +with with set of inequalities so for + + + align:start position:0% +with with set of inequalities so for +example here we have four lines here's + + align:start position:0% +example here we have four lines here's + + + align:start position:0% +example here we have four lines here's +the equation for each time so let's say + + align:start position:0% +the equation for each time so let's say + + + align:start position:0% +the equation for each time so let's say +this red line we want anything below the + + align:start position:0% +this red line we want anything below the + + + align:start position:0% +this red line we want anything below the +red line this will then we want anything + + align:start position:0% +red line this will then we want anything + + + align:start position:0% +red line this will then we want anything +to the right so anything greater than + + align:start position:0% +to the right so anything greater than + + + align:start position:0% +to the right so anything greater than +and so on so this area is just the + + align:start position:0% +and so on so this area is just the + + + align:start position:0% +and so on so this area is just the +intersection of all these inequalities + + align:start position:0% +intersection of all these inequalities + + + align:start position:0% +intersection of all these inequalities +and each of these representations has + + align:start position:0% +and each of these representations has + + + align:start position:0% +and each of these representations has +and a planet and the planet over me okay + + align:start position:0% +and a planet and the planet over me okay + + + align:start position:0% +and a planet and the planet over me okay +very excited to taste for emptiness we + + align:start position:0% +very excited to taste for emptiness we + + + align:start position:0% +very excited to taste for emptiness we +perceive with our set of vertices is + + align:start position:0% +perceive with our set of vertices is + + + align:start position:0% +perceive with our set of vertices is +empty then our comics college of the + + align:start position:0% +empty then our comics college of the + + + align:start position:0% +empty then our comics college of the +columbia these inequalities is very + + align:start position:0% +columbia these inequalities is very + + + align:start position:0% +columbia these inequalities is very +useful for testing membership because + + align:start position:0% +useful for testing membership because + + + align:start position:0% +useful for testing membership because +for any question we can just plug it + + align:start position:0% +for any question we can just plug it + + + align:start position:0% +for any question we can just plug it +into every inequality and if it's for + + align:start position:0% +into every inequality and if it's for + + + align:start position:0% +into every inequality and if it's for +every inequality okay + + align:start position:0% +every inequality okay + + + align:start position:0% +every inequality okay +I'm connecting I'll just + + align:start position:0% + + + + align:start position:0% + +convexity means that any two points + + align:start position:0% +convexity means that any two points + + + align:start position:0% +convexity means that any two points +inside of our recent our region is + + align:start position:0% +inside of our recent our region is + + + align:start position:0% +inside of our recent our region is +slightly convex it before the line + + align:start position:0% +slightly convex it before the line + + + align:start position:0% +slightly convex it before the line +connecting the two points all the points + + align:start position:0% +connecting the two points all the points + + + align:start position:0% +connecting the two points all the points +in that line are gonna be in the region + + align:start position:0% +in that line are gonna be in the region + + + align:start position:0% +in that line are gonna be in the region +so here you can see that this is + + align:start position:0% +so here you can see that this is + + + align:start position:0% +so here you can see that this is +convection here this red area is outside + + align:start position:0% +convection here this red area is outside + + + align:start position:0% +convection here this red area is outside +the region so piece of a region is non + + align:start position:0% +the region so piece of a region is non + + + align:start position:0% +the region so piece of a region is non +convex and convexity is going to be + + align:start position:0% +convex and convexity is going to be + + + align:start position:0% +convex and convexity is going to be +important for the algorithms later on + + align:start position:0% +important for the algorithms later on + + + align:start position:0% +important for the algorithms later on +Gerardo okay other than convex polytopes + + align:start position:0% +Gerardo okay other than convex polytopes + + + align:start position:0% +Gerardo okay other than convex polytopes +we can also use elite sites to represent + + align:start position:0% +we can also use elite sites to represent + + + align:start position:0% +we can also use elite sites to represent +which sets so websites are just the + + align:start position:0% +which sets so websites are just the + + + align:start position:0% +which sets so websites are just the +extension of ellipses - and spaces in + + align:start position:0% +extension of ellipses - and spaces in + + + align:start position:0% +extension of ellipses - and spaces in +dimensions and a convex polygon is + + align:start position:0% +dimensions and a convex polygon is + + + align:start position:0% +dimensions and a convex polygon is +defined by this X is just following + + align:start position:0% +defined by this X is just following + + + align:start position:0% +defined by this X is just following +points inside the polygons inside the + + align:start position:0% +points inside the polygons inside the + + + align:start position:0% +points inside the polygons inside the +olives please the center and they just + + align:start position:0% +olives please the center and they just + + + align:start position:0% +olives please the center and they just +tells us about is how deform the + + align:start position:0% +tells us about is how deform the + + + align:start position:0% +tells us about is how deform the +ellipses any questions + + align:start position:0% + + + + align:start position:0% + +and one of the reasons why we like + + align:start position:0% +and one of the reasons why we like + + + align:start position:0% +and one of the reasons why we like +convex polytopes why we like ellipses + + align:start position:0% +convex polytopes why we like ellipses + + + align:start position:0% +convex polytopes why we like ellipses +the website is because of their closer + + align:start position:0% +the website is because of their closer + + + align:start position:0% +the website is because of their closer +under linear operators so let's say + + align:start position:0% +under linear operators so let's say + + + align:start position:0% +under linear operators so let's say +we've got P that is economic small equal + + align:start position:0% +we've got P that is economic small equal + + + align:start position:0% +we've got P that is economic small equal +or on their lips like then if we have a + + align:start position:0% +or on their lips like then if we have a + + + align:start position:0% +or on their lips like then if we have a +matrix a then a times P which is defined + + align:start position:0% +matrix a then a times P which is defined + + + align:start position:0% +matrix a then a times P which is defined +that way it is still gonna be a convex + + align:start position:0% +that way it is still gonna be a convex + + + align:start position:0% +that way it is still gonna be a convex +polytope or an ellipse Alicia so if we + + align:start position:0% +polytope or an ellipse Alicia so if we + + + align:start position:0% +polytope or an ellipse Alicia so if we +have something like this then this can + + align:start position:0% +have something like this then this can + + + align:start position:0% +have something like this then this can +maybe get deformed but it's still going + + align:start position:0% +maybe get deformed but it's still going + + + align:start position:0% +maybe get deformed but it's still going +to be coming from its college and the + + align:start position:0% +to be coming from its college and the + + + align:start position:0% +to be coming from its college and the +reason why this is nice is that if we + + align:start position:0% +reason why this is nice is that if we + + + align:start position:0% +reason why this is nice is that if we +have a linear system like this we find + + align:start position:0% +have a linear system like this we find + + + align:start position:0% +have a linear system like this we find +this way or this way and then if we + + align:start position:0% +this way or this way and then if we + + + align:start position:0% +this way or this way and then if we +start with basically if we start with a + + align:start position:0% +start with basically if we start with a + + + align:start position:0% +start with basically if we start with a +convex set of states then where our rich + + align:start position:0% +convex set of states then where our rich + + + align:start position:0% +convex set of states then where our rich +states are always gonna be complex + + align:start position:0% +states are always gonna be complex + + + align:start position:0% +states are always gonna be complex +because we're just multiplying by a and + + align:start position:0% +because we're just multiplying by a and + + + align:start position:0% +because we're just multiplying by a and +this is very nice to me this tells us + + align:start position:0% +this is very nice to me this tells us + + + align:start position:0% +this is very nice to me this tells us +that our representation is gonna be good + + align:start position:0% +that our representation is gonna be good + + + align:start position:0% +that our representation is gonna be good +because we can just use convex polytopes + + align:start position:0% +because we can just use convex polytopes + + + align:start position:0% +because we can just use convex polytopes +websites and take with us + + align:start position:0% + + + + align:start position:0% + +thank you sir + + align:start position:0% +thank you sir + + + align:start position:0% +thank you sir +okay so even though the rich sensory + + align:start position:0% +okay so even though the rich sensory + + + align:start position:0% +okay so even though the rich sensory +comics the reachable set might not be + + align:start position:0% +comics the reachable set might not be + + + align:start position:0% +comics the reachable set might not be +convex but it will always be a union of + + align:start position:0% +convex but it will always be a union of + + + align:start position:0% +convex but it will always be a union of +convex polytopes or loop slaves for + + align:start position:0% +convex polytopes or loop slaves for + + + align:start position:0% +convex polytopes or loop slaves for +example let's say in the previous + + align:start position:0% +example let's say in the previous + + + align:start position:0% +example let's say in the previous +example we started here then we after + + align:start position:0% +example we started here then we after + + + align:start position:0% +example we started here then we after +one tactic we work here so these are the + + align:start position:0% +one tactic we work here so these are the + + + align:start position:0% +one tactic we work here so these are the +things and then our reachable settings + + align:start position:0% +things and then our reachable settings + + + align:start position:0% +things and then our reachable settings +the union of both of them this is + + align:start position:0% +the union of both of them this is + + + align:start position:0% +the union of both of them this is +clearly not complex but it is a union of + + align:start position:0% +clearly not complex but it is a union of + + + align:start position:0% +clearly not complex but it is a union of +convex polytopes so we can represent + + align:start position:0% +convex polytopes so we can represent + + + align:start position:0% +convex polytopes so we can represent +everything with the okay any questions + + align:start position:0% +everything with the okay any questions + + + align:start position:0% +everything with the okay any questions +before we move on to + + align:start position:0% + + + + align:start position:0% + +okay so now that you have registered for + + align:start position:0% +okay so now that you have registered for + + + align:start position:0% +okay so now that you have registered for +Tricia volunteers and encounter puzzle + + align:start position:0% +Tricia volunteers and encounter puzzle + + + align:start position:0% +Tricia volunteers and encounter puzzle +pieces and + + align:start position:0% + + + + align:start position:0% + +there are + + align:start position:0% + + + + align:start position:0% + +you know the idea is still like more a + + align:start position:0% +you know the idea is still like more a + + + align:start position:0% +you know the idea is still like more a +glider or two to lots of obstacles + + align:start position:0% +glider or two to lots of obstacles + + + align:start position:0% +glider or two to lots of obstacles +percent of uncertainties and + + align:start position:0% +percent of uncertainties and + + + align:start position:0% +percent of uncertainties and +disturbances a robotic rationing the + + align:start position:0% +disturbances a robotic rationing the + + + align:start position:0% +disturbances a robotic rationing the +object + + align:start position:0% + + + + align:start position:0% + +and more importantly which ability is + + align:start position:0% +and more importantly which ability is + + + align:start position:0% +and more importantly which ability is +like use for verifying city boundaries + + align:start position:0% +like use for verifying city boundaries + + + align:start position:0% +like use for verifying city boundaries +for the state if it goes + + align:start position:0% +for the state if it goes + + + align:start position:0% +for the state if it goes +desperation away + + align:start position:0% +desperation away + + + align:start position:0% +desperation away +so the sections are going to work + + align:start position:0% +so the sections are going to work + + + align:start position:0% +so the sections are going to work +another one of evolution sevens robust + + align:start position:0% +another one of evolution sevens robust + + + align:start position:0% +another one of evolution sevens robust +worship time during + + align:start position:0% + + + + align:start position:0% + +so the goal of wooden party this + + align:start position:0% +so the goal of wooden party this + + + align:start position:0% +so the goal of wooden party this +required a set of control inputs that + + align:start position:0% +required a set of control inputs that + + + align:start position:0% +required a set of control inputs that +take you from the start state to the + + align:start position:0% +take you from the start state to the + + + align:start position:0% +take you from the start state to the +goal State + + align:start position:0% +goal State + + + align:start position:0% +goal State +so in this example without without + + align:start position:0% +so in this example without without + + + align:start position:0% +so in this example without without +colliding with the optional so here was + + align:start position:0% +colliding with the optional so here was + + + align:start position:0% +colliding with the optional so here was +like one possible path from the start + + align:start position:0% +like one possible path from the start + + + align:start position:0% +like one possible path from the start +state to the goal State + + align:start position:0% +state to the goal State + + + align:start position:0% +state to the goal State +so if this looks nice and it does not + + align:start position:0% +so if this looks nice and it does not + + + align:start position:0% +so if this looks nice and it does not +collide with any of you obstacles + + align:start position:0% + + + + align:start position:0% + +you might find it going businesses so + + align:start position:0% +you might find it going businesses so + + + align:start position:0% +you might find it going businesses so +this is because the part that you avoid + + align:start position:0% +this is because the part that you avoid + + + align:start position:0% +this is because the part that you avoid +an abuse preparedness but this does not + + align:start position:0% +an abuse preparedness but this does not + + + align:start position:0% +an abuse preparedness but this does not +take into account in certain areas in + + align:start position:0% +take into account in certain areas in + + + align:start position:0% +take into account in certain areas in +the environment and suddenly it's good + + align:start position:0% +the environment and suddenly it's good + + + align:start position:0% +the environment and suddenly it's good +so there are different kinds of a sudden + + align:start position:0% +so there are different kinds of a sudden + + + align:start position:0% +so there are different kinds of a sudden +it is one of them was involved with all + + align:start position:0% +it is one of them was involved with all + + + align:start position:0% +it is one of them was involved with all +the services when your + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +there are some randomness in the initial + + align:start position:0% +there are some randomness in the initial + + + align:start position:0% +there are some randomness in the initial +condition you are thinking of starting + + align:start position:0% +condition you are thinking of starting + + + align:start position:0% +condition you are thinking of starting +over at zero so there is randomization + + align:start position:0% +over at zero so there is randomization + + + align:start position:0% +over at zero so there is randomization +the goal of robust motion planning is to + + align:start position:0% +the goal of robust motion planning is to + + + align:start position:0% +the goal of robust motion planning is to +is to have some calories and some + + align:start position:0% +is to have some calories and some + + + align:start position:0% +is to have some calories and some +contracts for the system + + align:start position:0% +contracts for the system + + + align:start position:0% +contracts for the system +without even with the obstacles even in + + align:start position:0% +without even with the obstacles even in + + + align:start position:0% +without even with the obstacles even in +purses of these uncertainties so there + + align:start position:0% +purses of these uncertainties so there + + + align:start position:0% +purses of these uncertainties so there +was a problem let's look at some of the + + align:start position:0% +was a problem let's look at some of the + + + align:start position:0% +was a problem let's look at some of the +solutions that come out for solid + + align:start position:0% +solutions that come out for solid + + + align:start position:0% +solutions that come out for solid +the time line + + align:start position:0% +the time line + + + align:start position:0% +the time line +like all of them have core concept where + + align:start position:0% +like all of them have core concept where + + + align:start position:0% +like all of them have core concept where +they kind of use some representation to + + align:start position:0% +they kind of use some representation to + + + align:start position:0% +they kind of use some representation to +to to represent the lead sets the set of + + align:start position:0% +to to represent the lead sets the set of + + + align:start position:0% +to to represent the lead sets the set of +possible states of the system can be and + + align:start position:0% +possible states of the system can be and + + + align:start position:0% +possible states of the system can be and +then instead of searching for a single + + align:start position:0% +then instead of searching for a single + + + align:start position:0% +then instead of searching for a single +tragically policy research for these + + align:start position:0% +tragically policy research for these + + + align:start position:0% +tragically policy research for these +representations learning if you find + + align:start position:0% +representations learning if you find + + + align:start position:0% +representations learning if you find +ourselves representations that you know + + align:start position:0% +ourselves representations that you know + + + align:start position:0% +ourselves representations that you know +from the state budget you don't get any + + align:start position:0% +from the state budget you don't get any + + + align:start position:0% +from the state budget you don't get any +of the obstacles so it's a way of + + align:start position:0% +of the obstacles so it's a way of + + + align:start position:0% +of the obstacles so it's a way of +representing + + align:start position:0% +representing + + + align:start position:0% +representing +[Music] + + align:start position:0% + + + + align:start position:0% + +have a set of fools + + align:start position:0% + + + + align:start position:0% + +combination of all possible paths that + + align:start position:0% +combination of all possible paths that + + + align:start position:0% +combination of all possible paths that +we took you from any coordination state + + align:start position:0% +we took you from any coordination state + + + align:start position:0% +we took you from any coordination state +economies this is kind of producing all + + align:start position:0% +economies this is kind of producing all + + + align:start position:0% +economies this is kind of producing all +possible + + align:start position:0% +possible + + + align:start position:0% +possible +so you search for this produce to be a + + align:start position:0% +so you search for this produce to be a + + + align:start position:0% +so you search for this produce to be a +particle motion + + align:start position:0% + + + + align:start position:0% + +in 2006 I got + + align:start position:0% +in 2006 I got + + + align:start position:0% +in 2006 I got +well constraint that you can also + + align:start position:0% +well constraint that you can also + + + align:start position:0% +well constraint that you can also +reasonable compensation federal trials + + align:start position:0% +reasonable compensation federal trials + + + align:start position:0% +reasonable compensation federal trials +[Music] + + align:start position:0% + + + + align:start position:0% + +Astor takes to obesity followers for + + align:start position:0% +Astor takes to obesity followers for + + + align:start position:0% +Astor takes to obesity followers for +washing planning the files is also a + + align:start position:0% +washing planning the files is also a + + + align:start position:0% +washing planning the files is also a +similar concept to your cute + + align:start position:0% +similar concept to your cute + + + align:start position:0% +similar concept to your cute +it's kind of like psychic power so in + + align:start position:0% +it's kind of like psychic power so in + + + align:start position:0% +it's kind of like psychic power so in +the structure of the go to body has work + + align:start position:0% +the structure of the go to body has work + + + align:start position:0% +the structure of the go to body has work +which is adding these nude photos + + align:start position:0% +which is adding these nude photos + + + align:start position:0% +which is adding these nude photos +like in there are references for the + + align:start position:0% +like in there are references for the + + + align:start position:0% +like in there are references for the +other people + + align:start position:0% + + + + align:start position:0% + +so entirely of using punishment for + + align:start position:0% +so entirely of using punishment for + + + align:start position:0% +so entirely of using punishment for +every part + + align:start position:0% + + + + align:start position:0% + +for this for this part of the lecture + + align:start position:0% +for this for this part of the lecture + + + align:start position:0% +for this for this part of the lecture +we'll assume about four hours and let me + + align:start position:0% +we'll assume about four hours and let me + + + align:start position:0% +we'll assume about four hours and let me +see + + align:start position:0% + + + + align:start position:0% + +so it was like these photos + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so it's kind of something + + align:start position:0% +so it's kind of something + + + align:start position:0% +so it's kind of something +immediate paths are all if you have a + + align:start position:0% +immediate paths are all if you have a + + + align:start position:0% +immediate paths are all if you have a +very special meaning + + align:start position:0% +very special meaning + + + align:start position:0% +very special meaning +so I think Jared a little expensive + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +all right so so funnel is basically it's + + align:start position:0% +all right so so funnel is basically it's + + + align:start position:0% +all right so so funnel is basically it's +kind of like a reset around the certain + + align:start position:0% +kind of like a reset around the certain + + + align:start position:0% +kind of like a reset around the certain +points there's a way to do it is you + + align:start position:0% +points there's a way to do it is you + + + align:start position:0% +points there's a way to do it is you +have some nominal trajectory and then it + + align:start position:0% +have some nominal trajectory and then it + + + align:start position:0% +have some nominal trajectory and then it +were going that trajectory + + align:start position:0% +were going that trajectory + + + align:start position:0% +were going that trajectory +you can view of some kind of reach + + align:start position:0% +you can view of some kind of reach + + + align:start position:0% +you can view of some kind of reach +at that midpoint and so you blow it up + + align:start position:0% +at that midpoint and so you blow it up + + + align:start position:0% +at that midpoint and so you blow it up +and it becomes some kind of ellipsoid + + align:start position:0% +and it becomes some kind of ellipsoid + + + align:start position:0% +and it becomes some kind of ellipsoid +and as long as you're within that + + align:start position:0% +and as long as you're within that + + + align:start position:0% +and as long as you're within that +ellipsoid no matter what to search + + align:start position:0% +ellipsoid no matter what to search + + + align:start position:0% +ellipsoid no matter what to search +you're gonna go back to the words the + + align:start position:0% +you're gonna go back to the words the + + + align:start position:0% +you're gonna go back to the words the +nominal path and then so what join all + + align:start position:0% +nominal path and then so what join all + + + align:start position:0% +nominal path and then so what join all +of those websites over the trajectory + + align:start position:0% +of those websites over the trajectory + + + align:start position:0% +of those websites over the trajectory +didn't get a certain kind of model and + + align:start position:0% +didn't get a certain kind of model and + + + align:start position:0% +didn't get a certain kind of model and +as long as you're inside that final + + align:start position:0% +as long as you're inside that final + + + align:start position:0% +as long as you're inside that final +period of state on + + align:start position:0% +period of state on + + + align:start position:0% +period of state on +one of the + + align:start position:0% +one of the + + + align:start position:0% +one of the +with some disturbances for your estate + + align:start position:0% +with some disturbances for your estate + + + align:start position:0% +with some disturbances for your estate +so that the great + + align:start position:0% +so that the great + + + align:start position:0% +so that the great +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +as long as you're in the funnel so this + + align:start position:0% +as long as you're in the funnel so this + + + align:start position:0% +as long as you're in the funnel so this +considered + + align:start position:0% +considered + + + align:start position:0% +considered +or it's the dynamics with the control + + align:start position:0% +or it's the dynamics with the control + + + align:start position:0% +or it's the dynamics with the control +system + + align:start position:0% + + + + align:start position:0% + +if so + + align:start position:0% + + + + align:start position:0% + +and let me just quickly add so so my + + align:start position:0% +and let me just quickly add so so my + + + align:start position:0% +and let me just quickly add so so my +photo is absolutely right I just + + align:start position:0% +photo is absolutely right I just + + + align:start position:0% +photo is absolutely right I just +typically would use the same terminology + + align:start position:0% +typically would use the same terminology + + + align:start position:0% +typically would use the same terminology +use different terminology like each of + + align:start position:0% +use different terminology like each of + + + align:start position:0% +use different terminology like each of +the applications of glow trees has some + + align:start position:0% +the applications of glow trees has some + + + align:start position:0% +the applications of glow trees has some +variant which is definitely buy in the + + align:start position:0% +variant which is definitely buy in the + + + align:start position:0% +variant which is definitely buy in the +particular invariant on this one right + + align:start position:0% +particular invariant on this one right + + + align:start position:0% +particular invariant on this one right +is that if if you are in the photo if + + align:start position:0% +is that if if you are in the photo if + + + align:start position:0% +is that if if you are in the photo if +you applying our felt you are + + align:start position:0% +you applying our felt you are + + + align:start position:0% +you applying our felt you are +Hogan City done then you're guaranteed + + align:start position:0% +Hogan City done then you're guaranteed + + + align:start position:0% +Hogan City done then you're guaranteed +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +to be like + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +no that's not necessarily in general + + align:start position:0% +no that's not necessarily in general + + + align:start position:0% +no that's not necessarily in general +flow tube is simply a bundle of + + align:start position:0% +flow tube is simply a bundle of + + + align:start position:0% +flow tube is simply a bundle of +projectors which which capture some + + align:start position:0% +projectors which which capture some + + + align:start position:0% +projectors which which capture some +common feature and then maybe that they + + align:start position:0% +common feature and then maybe that they + + + align:start position:0% +common feature and then maybe that they +move to a limit cycle maybe that they + + align:start position:0% +move to a limit cycle maybe that they + + + align:start position:0% +move to a limit cycle maybe that they +stabilize to a point maybe that they + + align:start position:0% +stabilize to a point maybe that they + + + align:start position:0% +stabilize to a point maybe that they +moved to a goal maybe that they always + + align:start position:0% +moved to a goal maybe that they always + + + align:start position:0% +moved to a goal maybe that they always +maintain their state + + align:start position:0% +maintain their state + + + align:start position:0% +maintain their state +in a politic of this particular ability + + align:start position:0% +in a politic of this particular ability + + + align:start position:0% +in a politic of this particular ability +to do disturbance and stay within the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +this but instead of Christine + + align:start position:0% +this but instead of Christine + + + align:start position:0% +this but instead of Christine +very close to the trees so really the + + align:start position:0% +very close to the trees so really the + + + align:start position:0% +very close to the trees so really the +technology like to see make us one - so + + align:start position:0% +technology like to see make us one - so + + + align:start position:0% +technology like to see make us one - so +that's why disability with Ocean + + align:start position:0% +that's why disability with Ocean + + + align:start position:0% +that's why disability with Ocean +Sciences if you combine dynamite was fun + + align:start position:0% +Sciences if you combine dynamite was fun + + + align:start position:0% +Sciences if you combine dynamite was fun +it has its + + align:start position:0% +it has its + + + align:start position:0% +it has its +and it might happen with such a thing + + align:start position:0% +and it might happen with such a thing + + + align:start position:0% +and it might happen with such a thing +but they say more susceptible to to the + + align:start position:0% +but they say more susceptible to to the + + + align:start position:0% +but they say more susceptible to to the +disturbances so + + align:start position:0% + + + + align:start position:0% + +what's the start + + align:start position:0% +what's the start + + + align:start position:0% +what's the start +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it's so fun it's all about planning to + + align:start position:0% +it's so fun it's all about planning to + + + align:start position:0% +it's so fun it's all about planning to +assure that we know + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you + + align:start position:0% +you + + + align:start position:0% +you +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so one father would do online planning + + align:start position:0% +so one father would do online planning + + + align:start position:0% +so one father would do online planning +that you cannot do any expensive + + align:start position:0% +that you cannot do any expensive + + + align:start position:0% +that you cannot do any expensive +computation and all of these faraway + + align:start position:0% +computation and all of these faraway + + + align:start position:0% +computation and all of these faraway +places + + align:start position:0% +places + + + align:start position:0% +places +requested something about you + + align:start position:0% +requested something about you + + + align:start position:0% +requested something about you +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +complete follows on the flag but idea + + align:start position:0% +complete follows on the flag but idea + + + align:start position:0% +complete follows on the flag but idea +university like computer photos of + + align:start position:0% +university like computer photos of + + + align:start position:0% +university like computer photos of +possible state and state and we use this + + align:start position:0% +possible state and state and we use this + + + align:start position:0% +possible state and state and we use this +library + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so that these are the set of possible + + align:start position:0% +so that these are the set of possible + + + align:start position:0% +so that these are the set of possible +products from experience it and each + + align:start position:0% +products from experience it and each + + + align:start position:0% +products from experience it and each +possible trajectory computer + + align:start position:0% +possible trajectory computer + + + align:start position:0% +possible trajectory computer +the idea for that parent s to finally + + align:start position:0% +the idea for that parent s to finally + + + align:start position:0% +the idea for that parent s to finally +see both of these + + align:start position:0% +see both of these + + + align:start position:0% +see both of these +cause that beats you from starts to play + + align:start position:0% +cause that beats you from starts to play + + + align:start position:0% +cause that beats you from starts to play +video signals so important component of + + align:start position:0% +video signals so important component of + + + align:start position:0% +video signals so important component of +ideal situation compositor + + align:start position:0% + + + + align:start position:0% + +so so why plant and you're doing a + + align:start position:0% +so so why plant and you're doing a + + + align:start position:0% +so so why plant and you're doing a +forward search and with the father was + + align:start position:0% +forward search and with the father was + + + align:start position:0% +forward search and with the father was +why you spy was instead + + align:start position:0% +why you spy was instead + + + align:start position:0% +why you spy was instead +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +like I guess at the answer what + + align:start position:0% + + + + align:start position:0% + +why use funnels instead of parties well + + align:start position:0% +why use funnels instead of parties well + + + align:start position:0% +why use funnels instead of parties well +for why use funnels well as opposed to + + align:start position:0% +for why use funnels well as opposed to + + + align:start position:0% +for why use funnels well as opposed to +anything else + + align:start position:0% +anything else + + + align:start position:0% +anything else +I guess artistes you have like the + + align:start position:0% +I guess artistes you have like the + + + align:start position:0% +I guess artistes you have like the +classical example where you want to go + + align:start position:0% +classical example where you want to go + + + align:start position:0% +classical example where you want to go +through a very well if you want to go + + align:start position:0% +through a very well if you want to go + + + align:start position:0% +through a very well if you want to go +through a very narrow region well first + + align:start position:0% +through a very narrow region well first + + + align:start position:0% +through a very narrow region well first +of all I guess an artist started to have + + align:start position:0% +of all I guess an artist started to have + + + align:start position:0% +of all I guess an artist started to have +a hard time finding that narrow region + + align:start position:0% +a hard time finding that narrow region + + + align:start position:0% +a hard time finding that narrow region +because you need like a point and then + + align:start position:0% +because you need like a point and then + + + align:start position:0% +because you need like a point and then +our teeth by themselves don't for the + + align:start position:0% +our teeth by themselves don't for the + + + align:start position:0% +our teeth by themselves don't for the +account for for errors maybe some + + align:start position:0% +account for for errors maybe some + + + align:start position:0% +account for for errors maybe some +extension but funnels you can be sure + + align:start position:0% +extension but funnels you can be sure + + + align:start position:0% +extension but funnels you can be sure +that you're always in the same inside + + align:start position:0% +that you're always in the same inside + + + align:start position:0% +that you're always in the same inside +the phone so this forum was just to make + + align:start position:0% +the phone so this forum was just to make + + + align:start position:0% +the phone so this forum was just to make +sure + + align:start position:0% + + + + align:start position:0% + +do you honestly yeah I think you know + + align:start position:0% +do you honestly yeah I think you know + + + align:start position:0% +do you honestly yeah I think you know +what what he just said you know it's the + + align:start position:0% +what what he just said you know it's the + + + align:start position:0% +what what he just said you know it's the +point of the finals is that they provide + + align:start position:0% +point of the finals is that they provide + + + align:start position:0% +point of the finals is that they provide +a control policy the the actual + + align:start position:0% +a control policy the the actual + + + align:start position:0% +a control policy the the actual +reference trajectory that you have on + + align:start position:0% +reference trajectory that you have on + + + align:start position:0% +reference trajectory that you have on +the left is the motion planning of with + + align:start position:0% +the left is the motion planning of with + + + align:start position:0% +the left is the motion planning of with +the funnels you get a control policy + + align:start position:0% +the funnels you get a control policy + + + align:start position:0% +the funnels you get a control policy +because when you start executing the + + align:start position:0% +because when you start executing the + + + align:start position:0% +because when you start executing the +motion plan there's always going to be a + + align:start position:0% +motion plan there's always going to be a + + + align:start position:0% +motion plan there's always going to be a +disturbance so you want a control policy + + align:start position:0% +disturbance so you want a control policy + + + align:start position:0% +disturbance so you want a control policy +they can teach you on that + + align:start position:0% +they can teach you on that + + + align:start position:0% +they can teach you on that +you know there's all sorts of control + + align:start position:0% +you know there's all sorts of control + + + align:start position:0% +you know there's all sorts of control +policy use simply ie controllers they + + align:start position:0% +policy use simply ie controllers they + + + align:start position:0% +policy use simply ie controllers they +work in some cases funnels provide + + align:start position:0% +work in some cases funnels provide + + + align:start position:0% +work in some cases funnels provide +better guarantees with complex dynamics + + align:start position:0% + + + + align:start position:0% + +so today + + align:start position:0% + + + + align:start position:0% + +to find you + + align:start position:0% + + + + align:start position:0% + +sinners so you cannot always compose for + + align:start position:0% +sinners so you cannot always compose for + + + align:start position:0% +sinners so you cannot always compose for +house like some questions and the girls + + align:start position:0% +house like some questions and the girls + + + align:start position:0% +house like some questions and the girls +have + + align:start position:0% +have + + + align:start position:0% +have +so there's other things have other if + + align:start position:0% +so there's other things have other if + + + align:start position:0% +so there's other things have other if +I'm going from left to right so you have + + align:start position:0% +I'm going from left to right so you have + + + align:start position:0% +I'm going from left to right so you have +a situation + + align:start position:0% +a situation + + + align:start position:0% +a situation +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +smaller phone + + align:start position:0% +smaller phone + + + align:start position:0% +smaller phone +and + + align:start position:0% + + + + align:start position:0% + +so so what if I listen for the quality + + align:start position:0% +so so what if I listen for the quality + + + align:start position:0% +so so what if I listen for the quality +of stability so that bit of these + + align:start position:0% +of stability so that bit of these + + + align:start position:0% +of stability so that bit of these +combinations do you think that will be + + align:start position:0% +combinations do you think that will be + + + align:start position:0% +combinations do you think that will be +the composition + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +legal order likely that the plural is + + align:start position:0% +legal order likely that the plural is + + + align:start position:0% +legal order likely that the plural is +actual apartments where the consultant + + align:start position:0% +actual apartments where the consultant + + + align:start position:0% +actual apartments where the consultant +here at the very college + + align:start position:0% + + + + align:start position:0% + +yeah that's true so if your insightful + + align:start position:0% +yeah that's true so if your insightful + + + align:start position:0% +yeah that's true so if your insightful +follow-up but this guarantees that you + + align:start position:0% +follow-up but this guarantees that you + + + align:start position:0% +follow-up but this guarantees that you +will stay inside the cutoff but it could + + align:start position:0% +will stay inside the cutoff but it could + + + align:start position:0% +will stay inside the cutoff but it could +happen that you can + + align:start position:0% +happen that you can + + + align:start position:0% +happen that you can +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and after this they became going + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +after you to the First Folio studies and + + align:start position:0% +after you to the First Folio studies and + + + align:start position:0% +after you to the First Folio studies and +follow and we can do science accidents + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +the sweetness + + align:start position:0% +the sweetness + + + align:start position:0% +the sweetness +[Music] + + align:start position:0% + + + + align:start position:0% + +there's a lot of metadata + + align:start position:0% +there's a lot of metadata + + + align:start position:0% +there's a lot of metadata +so those online planning you don't have + + align:start position:0% +so those online planning you don't have + + + align:start position:0% +so those online planning you don't have +all the information + + align:start position:0% +all the information + + + align:start position:0% +all the information +[Music] + + align:start position:0% + + + + align:start position:0% + +but we still have the initial time + + align:start position:0% +but we still have the initial time + + + align:start position:0% +but we still have the initial time +policy protects you from yourself simple + + align:start position:0% +policy protects you from yourself simple + + + align:start position:0% +policy protects you from yourself simple +state + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and you also get the current state + + align:start position:0% +and you also get the current state + + + align:start position:0% +and you also get the current state +this is also such a concern immediately + + align:start position:0% +this is also such a concern immediately + + + align:start position:0% +this is also such a concern immediately +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and check your current so + + align:start position:0% +and check your current so + + + align:start position:0% +and check your current so +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so cynical exotoxins need to know any + + align:start position:0% +so cynical exotoxins need to know any + + + align:start position:0% +so cynical exotoxins need to know any +kind for us so many times you have all + + align:start position:0% +kind for us so many times you have all + + + align:start position:0% +kind for us so many times you have all +this nightmare + + align:start position:0% +this nightmare + + + align:start position:0% +this nightmare +funny was that that that has you fight + + align:start position:0% +funny was that that that has you fight + + + align:start position:0% +funny was that that that has you fight +us enough power that starts with my + + align:start position:0% +us enough power that starts with my + + + align:start position:0% +us enough power that starts with my +current location and any of the + + align:start position:0% +current location and any of the + + + align:start position:0% +current location and any of the +obstacles + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one on sequence and then again your pipe + + align:start position:0% +one on sequence and then again your pipe + + + align:start position:0% +one on sequence and then again your pipe +controls + + align:start position:0% +controls + + + align:start position:0% +controls +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +beautiful lights and alerts + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it's about you reach the goal so + + align:start position:0% +it's about you reach the goal so + + + align:start position:0% +it's about you reach the goal so +literally on a plan using final + + align:start position:0% +literally on a plan using final + + + align:start position:0% +literally on a plan using final +libraries + + align:start position:0% + + + + align:start position:0% + +can you say more about about the + + align:start position:0% +can you say more about about the + + + align:start position:0% +can you say more about about the +connotation of the frontal area + + align:start position:0% +connotation of the frontal area + + + align:start position:0% +connotation of the frontal area +so certainly generator says funnels + + align:start position:0% +so certainly generator says funnels + + + align:start position:0% +so certainly generator says funnels +which covered the complete sales pace + + align:start position:0% +which covered the complete sales pace + + + align:start position:0% +which covered the complete sales pace +yeah so other thing there's every + + align:start position:0% +yeah so other thing there's every + + + align:start position:0% +yeah so other thing there's every +possible in the future quite possible + + align:start position:0% +possible in the future quite possible + + + align:start position:0% +possible in the future quite possible +this time any point and so then you can + + align:start position:0% +this time any point and so then you can + + + align:start position:0% +this time any point and so then you can +make you don't know all this happen for + + align:start position:0% +make you don't know all this happen for + + + align:start position:0% +make you don't know all this happen for +every interesting + + align:start position:0% +every interesting + + + align:start position:0% +every interesting +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +if you're doing + + align:start position:0% +if you're doing + + + align:start position:0% +if you're doing +[Music] + + align:start position:0% + + + + align:start position:0% + +coalition + + align:start position:0% + + + + align:start position:0% + +what guarantees like that if it really + + align:start position:0% +what guarantees like that if it really + + + align:start position:0% +what guarantees like that if it really +isn't an online problem that you're not + + align:start position:0% +isn't an online problem that you're not + + + align:start position:0% +isn't an online problem that you're not +gonna run out of a funnel like that you + + align:start position:0% +gonna run out of a funnel like that you + + + align:start position:0% +gonna run out of a funnel like that you +reach a dead end but the adaptable + + align:start position:0% +reach a dead end but the adaptable + + + align:start position:0% +reach a dead end but the adaptable +enough to make a u-turn at all times you + + align:start position:0% +enough to make a u-turn at all times you + + + align:start position:0% +enough to make a u-turn at all times you +give it there's some like latency it + + align:start position:0% +give it there's some like latency it + + + align:start position:0% +give it there's some like latency it +does like perfectly timeless and there + + align:start position:0% +does like perfectly timeless and there + + + align:start position:0% +does like perfectly timeless and there +were buses that you'll always go find a + + align:start position:0% +were buses that you'll always go find a + + + align:start position:0% +were buses that you'll always go find a +path even if we have guarantees that + + align:start position:0% +path even if we have guarantees that + + + align:start position:0% +path even if we have guarantees that +you'll always stay within a funnel yeah + + align:start position:0% +you'll always stay within a funnel yeah + + + align:start position:0% +you'll always stay within a funnel yeah +just because these obstacles come out of + + align:start position:0% +just because these obstacles come out of + + + align:start position:0% +just because these obstacles come out of +nowhere same way that we don't have it + + align:start position:0% +nowhere same way that we don't have it + + + align:start position:0% +nowhere same way that we don't have it +guarantee the funnel a safe through the + + align:start position:0% +guarantee the funnel a safe through the + + + align:start position:0% +guarantee the funnel a safe through the +entire duration of our execution + + align:start position:0% +entire duration of our execution + + + align:start position:0% +entire duration of our execution +yes that's that's important point and I + + align:start position:0% +yes that's that's important point and I + + + align:start position:0% +yes that's that's important point and I +gotta tell you I think Amy + + align:start position:0% + + + + align:start position:0% + +even for robots I can't actually a + + align:start position:0% +even for robots I can't actually a + + + align:start position:0% +even for robots I can't actually a +better if they don't let skin would come + + align:start position:0% +better if they don't let skin would come + + + align:start position:0% +better if they don't let skin would come +back I mean I guess it looks like I do I + + align:start position:0% +back I mean I guess it looks like I do I + + + align:start position:0% +back I mean I guess it looks like I do I +couldn't I didn't say like what what + + align:start position:0% +couldn't I didn't say like what what + + + align:start position:0% +couldn't I didn't say like what what +guarantees do you need to have about + + align:start position:0% +guarantees do you need to have about + + + align:start position:0% +guarantees do you need to have about +like the obstacles it's an online setup + + align:start position:0% +like the obstacles it's an online setup + + + align:start position:0% +like the obstacles it's an online setup +maybe you have that engine + + align:start position:0% +maybe you have that engine + + + align:start position:0% +maybe you have that engine +like you can find a puncher can fight + + align:start position:0% +like you can find a puncher can fight + + + align:start position:0% +like you can find a puncher can fight +anything that was + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +well like if you're in some kind of + + align:start position:0% +well like if you're in some kind of + + + align:start position:0% +well like if you're in some kind of +Collider that can't sit like the + + align:start position:0% +Collider that can't sit like the + + + align:start position:0% +Collider that can't sit like the +quadratus stop go backwards some with + + align:start position:0% +quadratus stop go backwards some with + + + align:start position:0% +quadratus stop go backwards some with +that they don't have funnels that + + align:start position:0% +that they don't have funnels that + + + align:start position:0% +that they don't have funnels that +playing backwards but if you're in some + + align:start position:0% +playing backwards but if you're in some + + + align:start position:0% +playing backwards but if you're in some +kind of glider go straight to the wall + + align:start position:0% +kind of glider go straight to the wall + + + align:start position:0% +kind of glider go straight to the wall +there okay even humans that make errors + + align:start position:0% +there okay even humans that make errors + + + align:start position:0% +there okay even humans that make errors +there's like situation that humans can't + + align:start position:0% +there's like situation that humans can't + + + align:start position:0% +there's like situation that humans can't +that could get out of sort of your + + align:start position:0% +that could get out of sort of your + + + align:start position:0% +that could get out of sort of your +system is dynamically not going to be + + align:start position:0% +system is dynamically not going to be + + + align:start position:0% +system is dynamically not going to be +able to make up turn orchestrating + + align:start position:0% +able to make up turn orchestrating + + + align:start position:0% +able to make up turn orchestrating +something no matter how smart a penny + + align:start position:0% +something no matter how smart a penny + + + align:start position:0% +something no matter how smart a penny +algorithm is the matter here like + + align:start position:0% +algorithm is the matter here like + + + align:start position:0% +algorithm is the matter here like +there's a wallet there's stop there's + + align:start position:0% +there's a wallet there's stop there's + + + align:start position:0% +there's a wallet there's stop there's +obviously situation + + align:start position:0% +obviously situation + + + align:start position:0% +obviously situation +[Music] + + align:start position:0% + + + + align:start position:0% + +hopefully you're in a situation where + + align:start position:0% +hopefully you're in a situation where + + + align:start position:0% +hopefully you're in a situation where +you're not + + align:start position:0% + + + + align:start position:0% + +it's also that based on how far away + + align:start position:0% +it's also that based on how far away + + + align:start position:0% +it's also that based on how far away +your since we can see if your since + + align:start position:0% +your since we can see if your since + + + align:start position:0% +your since we can see if your since +you're gonna be seen five meters ahead + + align:start position:0% +you're gonna be seen five meters ahead + + + align:start position:0% +you're gonna be seen five meters ahead +and indigo five meters per second + + align:start position:0% +and indigo five meters per second + + + align:start position:0% +and indigo five meters per second +gonna happen take decisions but if your + + align:start position:0% +gonna happen take decisions but if your + + + align:start position:0% +gonna happen take decisions but if your +sensor has perfect make about the + + align:start position:0% +sensor has perfect make about the + + + align:start position:0% +sensor has perfect make about the +environment then what seems like Beamish + + align:start position:0% +environment then what seems like Beamish + + + align:start position:0% +environment then what seems like Beamish +the best paths may not actually smell + + align:start position:0% +the best paths may not actually smell + + + align:start position:0% +the best paths may not actually smell +them + + align:start position:0% + + + + align:start position:0% + +depends on Dianetics answers + + align:start position:0% +depends on Dianetics answers + + + align:start position:0% +depends on Dianetics answers +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +maybe + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah so I'm going to talk about how to + + align:start position:0% +yeah so I'm going to talk about how to + + + align:start position:0% +yeah so I'm going to talk about how to +actually compute them out of computer + + align:start position:0% +actually compute them out of computer + + + align:start position:0% +actually compute them out of computer +models generally I'm going to give it a + + align:start position:0% +models generally I'm going to give it a + + + align:start position:0% +models generally I'm going to give it a +sample of what each one is used word so + + align:start position:0% +sample of what each one is used word so + + + align:start position:0% +sample of what each one is used word so +we have a question before like power + + align:start position:0% +we have a question before like power + + + align:start position:0% +we have a question before like power +flow tubes and levels different flow + + align:start position:0% +flow tubes and levels different flow + + + align:start position:0% +flow tubes and levels different flow +tubes are so the easiest way they're + + align:start position:0% +tubes are so the easiest way they're + + + align:start position:0% +tubes are so the easiest way they're +both some kind of way to energy that + + align:start position:0% +both some kind of way to energy that + + + align:start position:0% +both some kind of way to energy that +into the robustness jeez so say you are + + align:start position:0% +into the robustness jeez so say you are + + + align:start position:0% +into the robustness jeez so say you are +here you want to be here + + align:start position:0% +here you want to be here + + + align:start position:0% +here you want to be here +we're both most planning algorithms you + + align:start position:0% +we're both most planning algorithms you + + + align:start position:0% +we're both most planning algorithms you +get some kind of hat from here to here + + align:start position:0% +get some kind of hat from here to here + + + align:start position:0% +get some kind of hat from here to here +but say there's some disturbance that + + align:start position:0% +but say there's some disturbance that + + + align:start position:0% +but say there's some disturbance that +pushes you down here or something you've + + align:start position:0% +pushes you down here or something you've + + + align:start position:0% +pushes you down here or something you've +done you don't know if you're going to + + align:start position:0% +done you don't know if you're going to + + + align:start position:0% +done you don't know if you're going to +be able to reach there or not but a + + align:start position:0% +be able to reach there or not but a + + + align:start position:0% +be able to reach there or not but a +float tube is is some kind of settlement + + align:start position:0% +float tube is is some kind of settlement + + + align:start position:0% +float tube is is some kind of settlement +entries that'll basically go from some + + align:start position:0% +entries that'll basically go from some + + + align:start position:0% +entries that'll basically go from some +initial states which are here to certain + + align:start position:0% +initial states which are here to certain + + + align:start position:0% +initial states which are here to certain +goals over here and if you're within + + align:start position:0% +goals over here and if you're within + + + align:start position:0% +goals over here and if you're within +this flow tube and you got pushed down + + align:start position:0% +this flow tube and you got pushed down + + + align:start position:0% +this flow tube and you got pushed down +in a different trajectory you know how + + align:start position:0% +in a different trajectory you know how + + + align:start position:0% +in a different trajectory you know how +to get from here to here anyway so you + + align:start position:0% +to get from here to here anyway so you + + + align:start position:0% +to get from here to here anyway so you +don't really care if you're pushed as + + align:start position:0% +don't really care if you're pushed as + + + align:start position:0% +don't really care if you're pushed as +long as it's still within here + + align:start position:0% +long as it's still within here + + + align:start position:0% +long as it's still within here +a funnel + + align:start position:0% +a funnel + + + align:start position:0% +a funnel +[Music] + + align:start position:0% + + + + align:start position:0% + +so funnel is say you compute some + + align:start position:0% +so funnel is say you compute some + + + align:start position:0% +so funnel is say you compute some +nominal trajectory around here using the + + align:start position:0% +nominal trajectory around here using the + + + align:start position:0% +nominal trajectory around here using the +system theory and stability theory you + + align:start position:0% +system theory and stability theory you + + + align:start position:0% +system theory and stability theory you +know that with your control inputs + + align:start position:0% +know that with your control inputs + + + align:start position:0% +know that with your control inputs +you're gonna stay at each of these + + align:start position:0% +you're gonna stay at each of these + + + align:start position:0% +you're gonna stay at each of these +points in a state with the key gear + + align:start position:0% +points in a state with the key gear + + + align:start position:0% +points in a state with the key gear +within these circles so if you can push + + align:start position:0% +within these circles so if you can push + + + align:start position:0% +within these circles so if you can push +down here you know you're going to be + + align:start position:0% +down here you know you're going to be + + + align:start position:0% +down here you know you're going to be +able to get back off your path and + + align:start position:0% +able to get back off your path and + + + align:start position:0% +able to get back off your path and +you're going to try to convert back to + + align:start position:0% +you're going to try to convert back to + + + align:start position:0% +you're going to try to convert back to +your nominal so you have some sort of + + align:start position:0% + + + + align:start position:0% + +I have a question how quickly there's a + + align:start position:0% +I have a question how quickly there's a + + + align:start position:0% +I have a question how quickly there's a +funnel it sort of relates to what Brian + + align:start position:0% +funnel it sort of relates to what Brian + + + align:start position:0% +funnel it sort of relates to what Brian +was saying is method in like these it is + + align:start position:0% +was saying is method in like these it is + + + align:start position:0% +was saying is method in like these it is +very well if you have a high dimensional + + align:start position:0% +very well if you have a high dimensional + + + align:start position:0% +very well if you have a high dimensional +space space there's a funnel + + align:start position:0% +space space there's a funnel + + + align:start position:0% +space space there's a funnel +poverty between there's a seven-point + + align:start position:0% +poverty between there's a seven-point + + + align:start position:0% +poverty between there's a seven-point +set of phones so to the crystal isn't + + align:start position:0% +set of phones so to the crystal isn't + + + align:start position:0% +set of phones so to the crystal isn't +about in the individual funnel but in + + align:start position:0% +about in the individual funnel but in + + + align:start position:0% +about in the individual funnel but in +the bigger + + align:start position:0% +the bigger + + + align:start position:0% +the bigger +right wiki jelly to send other photos + + align:start position:0% +right wiki jelly to send other photos + + + align:start position:0% +right wiki jelly to send other photos +does it depends how much time you want + + align:start position:0% +does it depends how much time you want + + + align:start position:0% +does it depends how much time you want +to put into it + + align:start position:0% +to put into it + + + align:start position:0% +to put into it +generally if like if you only compute + + align:start position:0% +generally if like if you only compute + + + align:start position:0% +generally if like if you only compute +two funnels one of them goes over here + + align:start position:0% +two funnels one of them goes over here + + + align:start position:0% +two funnels one of them goes over here +and one goes here and they're not going + + align:start position:0% +and one goes here and they're not going + + + align:start position:0% +and one goes here and they're not going +to covering the state space so it + + align:start position:0% +to covering the state space so it + + + align:start position:0% +to covering the state space so it +depends on how much computation you want + + align:start position:0% +depends on how much computation you want + + + align:start position:0% +depends on how much computation you want +to do offline previously so you set of + + align:start position:0% +to do offline previously so you set of + + + align:start position:0% +to do offline previously so you set of +constants here another one this right + + align:start position:0% +constants here another one this right + + + align:start position:0% +constants here another one this right +here on one this year + + align:start position:0% +here on one this year + + + align:start position:0% +here on one this year +and you have your big library of recipes + + align:start position:0% +and you have your big library of recipes + + + align:start position:0% +and you have your big library of recipes +I think I think they skip that paper + + align:start position:0% +I think I think they skip that paper + + + align:start position:0% +I think I think they skip that paper +injecting it is probably okay um + + align:start position:0% +injecting it is probably okay um + + + align:start position:0% +injecting it is probably okay um +yeah but I mean as far as computing + + align:start position:0% +yeah but I mean as far as computing + + + align:start position:0% +yeah but I mean as far as computing +where you're going to go if you compute + + align:start position:0% +where you're going to go if you compute + + + align:start position:0% +where you're going to go if you compute +that path set but yes you're right in + + align:start position:0% +that path set but yes you're right in + + + align:start position:0% +that path set but yes you're right in +the confidence so here's what I + + align:start position:0% +the confidence so here's what I + + + align:start position:0% +the confidence so here's what I +explained normally have your optimal + + align:start position:0% +explained normally have your optimal + + + align:start position:0% +explained normally have your optimal +trajectory but you get pushed off it you + + align:start position:0% +trajectory but you get pushed off it you + + + align:start position:0% +trajectory but you get pushed off it you +may not get back to the goal State but + + align:start position:0% +may not get back to the goal State but + + + align:start position:0% +may not get back to the goal State but +if you have a set of trajectories that + + align:start position:0% +if you have a set of trajectories that + + + align:start position:0% +if you have a set of trajectories that +go from some initial space to your goal + + align:start position:0% +go from some initial space to your goal + + + align:start position:0% +go from some initial space to your goal +state and you stay within that you know + + align:start position:0% +state and you stay within that you know + + + align:start position:0% +state and you stay within that you know +how to get your goal state you can't be + + align:start position:0% +how to get your goal state you can't be + + + align:start position:0% +how to get your goal state you can't be +a question again so some ways to + + align:start position:0% +a question again so some ways to + + + align:start position:0% +a question again so some ways to +approximate flew to you to use some kind + + align:start position:0% +approximate flew to you to use some kind + + + align:start position:0% +approximate flew to you to use some kind +of money to witches previously as long + + align:start position:0% +of money to witches previously as long + + + align:start position:0% +of money to witches previously as long +as a convex polytope you can take that + + align:start position:0% +as a convex polytope you can take that + + + align:start position:0% +as a convex polytope you can take that +cross sectional area and you can also + + align:start position:0% +cross sectional area and you can also + + + align:start position:0% +cross sectional area and you can also +use ellipsoids or rectangles as + + align:start position:0% +use ellipsoids or rectangles as + + + align:start position:0% +use ellipsoids or rectangles as +cross-sections an important point is you + + align:start position:0% +cross-sections an important point is you + + + align:start position:0% +cross-sections an important point is you +know that they're in our cross section + + align:start position:0% +know that they're in our cross section + + + align:start position:0% +know that they're in our cross section +approximations so as you see here you + + align:start position:0% +approximations so as you see here you + + + align:start position:0% +approximations so as you see here you +may this would be your actually flow to + + align:start position:0% +may this would be your actually flow to + + + align:start position:0% +may this would be your actually flow to +where your approximation has to be an + + align:start position:0% +where your approximation has to be an + + + align:start position:0% +where your approximation has to be an +inner one because that guarantees that + + align:start position:0% +inner one because that guarantees that + + + align:start position:0% +inner one because that guarantees that +you're within the flow too but it means + + align:start position:0% +you're within the flow too but it means + + + align:start position:0% +you're within the flow too but it means +you may also miss it with a how to do + + align:start position:0% +you may also miss it with a how to do + + + align:start position:0% +you may also miss it with a how to do +Jacobi selfish also if you want to + + align:start position:0% +Jacobi selfish also if you want to + + + align:start position:0% +Jacobi selfish also if you want to +a better approximation + + align:start position:0% + + + + align:start position:0% + +okay so we're a bust planning on you + + align:start position:0% +okay so we're a bust planning on you + + + align:start position:0% +okay so we're a bust planning on you +plan a trajectory from here here and + + align:start position:0% +plan a trajectory from here here and + + + align:start position:0% +plan a trajectory from here here and +that should be but then you get this sir + + align:start position:0% +that should be but then you get this sir + + + align:start position:0% +that should be but then you get this sir +you're still within the trajectory so + + align:start position:0% +you're still within the trajectory so + + + align:start position:0% +you're still within the trajectory so +you're still good but it's the work of + + align:start position:0% +you're still good but it's the work of + + + align:start position:0% +you're still good but it's the work of +my question Williams and Hoffman shows + + align:start position:0% +my question Williams and Hoffman shows + + + align:start position:0% +my question Williams and Hoffman shows +that so what do you do when you're + + align:start position:0% +that so what do you do when you're + + + align:start position:0% +that so what do you do when you're +actually outside of deal outside of the + + align:start position:0% +actually outside of deal outside of the + + + align:start position:0% +actually outside of deal outside of the +funnel now we knew is temporal plenty so + + align:start position:0% +funnel now we knew is temporal plenty so + + + align:start position:0% +funnel now we knew is temporal plenty so +using the algorithm that we previously + + align:start position:0% +using the algorithm that we previously + + + align:start position:0% +using the algorithm that we previously +learned in class you can take your goal + + align:start position:0% +learned in class you can take your goal + + + align:start position:0% +learned in class you can take your goal +state and move the timeline back to + + align:start position:0% +state and move the timeline back to + + + align:start position:0% +state and move the timeline back to +different times so here this is this + + align:start position:0% +different times so here this is this + + + align:start position:0% +different times so here this is this +flow tube is if you're here in a certain + + align:start position:0% +flow tube is if you're here in a certain + + + align:start position:0% +flow tube is if you're here in a certain +amount of time can you get some here and + + align:start position:0% +amount of time can you get some here and + + + align:start position:0% +amount of time can you get some here and +if you get it outside a bit then you + + align:start position:0% +if you get it outside a bit then you + + + align:start position:0% +if you get it outside a bit then you +can't do that anymore but you can just + + align:start position:0% +can't do that anymore but you can just + + + align:start position:0% +can't do that anymore but you can just +use our algorithm and route back the + + align:start position:0% +use our algorithm and route back the + + + align:start position:0% +use our algorithm and route back the +gold time and then when you move the + + align:start position:0% +gold time and then when you move the + + + align:start position:0% +gold time and then when you move the +whole time the whole funnel shifts is + + align:start position:0% +whole time the whole funnel shifts is + + + align:start position:0% +whole time the whole funnel shifts is +now your you can be over here and you + + align:start position:0% +now your you can be over here and you + + + align:start position:0% +now your you can be over here and you +don't care about getting here at this + + align:start position:0% +don't care about getting here at this + + + align:start position:0% +don't care about getting here at this +time you can get here at this time now + + align:start position:0% +time you can get here at this time now + + + align:start position:0% +time you can get here at this time now +so then you move over and now where you + + align:start position:0% +so then you move over and now where you + + + align:start position:0% +so then you move over and now where you +were you can get back to because you're + + align:start position:0% +were you can get back to because you're + + + align:start position:0% +were you can get back to because you're +now inside the loop again + + align:start position:0% + + + + align:start position:0% + +okay so one example is a humanoid + + align:start position:0% +okay so one example is a humanoid + + + align:start position:0% +okay so one example is a humanoid +footstep planning so this takes a + + align:start position:0% +footstep planning so this takes a + + + align:start position:0% +footstep planning so this takes a +complex system you have a bunch of + + align:start position:0% +complex system you have a bunch of + + + align:start position:0% +complex system you have a bunch of +different courses system you have like + + align:start position:0% +different courses system you have like + + + align:start position:0% +different courses system you have like +your center of mass dynamics you have + + align:start position:0% +your center of mass dynamics you have + + + align:start position:0% +your center of mass dynamics you have +their like that name that's what that + + align:start position:0% +their like that name that's what that + + + align:start position:0% +their like that name that's what that +handles and so what you're trying to do + + align:start position:0% +handles and so what you're trying to do + + + align:start position:0% +handles and so what you're trying to do +is plan your foot steps forward and + + align:start position:0% +is plan your foot steps forward and + + + align:start position:0% +is plan your foot steps forward and +through time see our original plan of + + align:start position:0% +through time see our original plan of + + + align:start position:0% +through time see our original plan of +where you want your foot steps to be for + + align:start position:0% +where you want your foot steps to be for + + + align:start position:0% +where you want your foot steps to be for +different parts so that there's discrete + + align:start position:0% +different parts so that there's discrete + + + align:start position:0% +different parts so that there's discrete +things that happen it really previously + + align:start position:0% +things that happen it really previously + + + align:start position:0% +things that happen it really previously +seen at a lecture so one thing that can + + align:start position:0% +seen at a lecture so one thing that can + + + align:start position:0% +seen at a lecture so one thing that can +happen is your left foot hits the ground + + align:start position:0% +happen is your left foot hits the ground + + + align:start position:0% +happen is your left foot hits the ground +and then your recklessness off your left + + align:start position:0% +and then your recklessness off your left + + + align:start position:0% +and then your recklessness off your left +foot looks very direct so you have a + + align:start position:0% +foot looks very direct so you have a + + + align:start position:0% +foot looks very direct so you have a +certain table temporal constraints on + + align:start position:0% +certain table temporal constraints on + + + align:start position:0% +certain table temporal constraints on +the system that you want a to your pipe + + align:start position:0% +the system that you want a to your pipe + + + align:start position:0% +the system that you want a to your pipe +and so as you start planning okay you + + align:start position:0% +and so as you start planning okay you + + + align:start position:0% +and so as you start planning okay you +have flow tubes to get you from one step + + align:start position:0% +have flow tubes to get you from one step + + + align:start position:0% +have flow tubes to get you from one step +to another step and that that guarantees + + align:start position:0% +to another step and that that guarantees + + + align:start position:0% +to another step and that that guarantees +that you're going to stay with them that + + align:start position:0% +that you're going to stay with them that + + + align:start position:0% +that you're going to stay with them that +was even if you get disturb you have to + + align:start position:0% +was even if you get disturb you have to + + + align:start position:0% +was even if you get disturb you have to +push + + align:start position:0% +push + + + align:start position:0% +push +get from one step to the other but then + + align:start position:0% +get from one step to the other but then + + + align:start position:0% +get from one step to the other but then +also with the thing that we saw in the + + align:start position:0% +also with the thing that we saw in the + + + align:start position:0% +also with the thing that we saw in the +previous slide you the timeline back and + + align:start position:0% +previous slide you the timeline back and + + + align:start position:0% +previous slide you the timeline back and +forth as long as you're within your + + align:start position:0% +forth as long as you're within your + + + align:start position:0% +forth as long as you're within your +temporal constraints and then today + + align:start position:0% +temporal constraints and then today + + + align:start position:0% +temporal constraints and then today +that's those workflow tubes for the feet + + align:start position:0% +that's those workflow tubes for the feet + + + align:start position:0% +that's those workflow tubes for the feet +and I will guarantee that your feet go + + align:start position:0% +and I will guarantee that your feet go + + + align:start position:0% +and I will guarantee that your feet go +off where they want to but you can + + align:start position:0% +off where they want to but you can + + + align:start position:0% +off where they want to but you can +decompose the system to also have flow + + align:start position:0% +decompose the system to also have flow + + + align:start position:0% +decompose the system to also have flow +tubes for the center of mass so the + + align:start position:0% +tubes for the center of mass so the + + + align:start position:0% +tubes for the center of mass so the +center of mass does is can be broken + + align:start position:0% +center of mass does is can be broken + + + align:start position:0% +center of mass does is can be broken +down separate flow tubes does that make + + align:start position:0% +down separate flow tubes does that make + + + align:start position:0% +down separate flow tubes does that make +sense + + align:start position:0% + + + + align:start position:0% + +so this is the humour necklace that my + + align:start position:0% +so this is the humour necklace that my + + + align:start position:0% +so this is the humour necklace that my +anger we stopped previously and now I + + align:start position:0% +anger we stopped previously and now I + + + align:start position:0% +anger we stopped previously and now I +understand how the feet are planned to + + align:start position:0% +understand how the feet are planned to + + + align:start position:0% +understand how the feet are planned to +go to each of the blocks let's see + + align:start position:0% + + + + align:start position:0% + +no question uh-huh you said you have a + + align:start position:0% +no question uh-huh you said you have a + + + align:start position:0% +no question uh-huh you said you have a +got a separate photo for the center of + + align:start position:0% +got a separate photo for the center of + + + align:start position:0% +got a separate photo for the center of +mass but aren't they believe is the same + + align:start position:0% +mass but aren't they believe is the same + + + align:start position:0% +mass but aren't they believe is the same +flow to burn a high-dimensional yes but + + align:start position:0% +flow to burn a high-dimensional yes but + + + align:start position:0% +flow to burn a high-dimensional yes but +that's that when you decoupler system + + align:start position:0% +that's that when you decoupler system + + + align:start position:0% +that's that when you decoupler system +any video flow tube for has a full + + align:start position:0% +any video flow tube for has a full + + + align:start position:0% +any video flow tube for has a full +system plenty high dimensional is it + + align:start position:0% +system plenty high dimensional is it + + + align:start position:0% +system plenty high dimensional is it +hard to read couple well it's still a + + align:start position:0% +hard to read couple well it's still a + + + align:start position:0% +hard to read couple well it's still a +here's the dynamics of the system so + + align:start position:0% +here's the dynamics of the system so + + + align:start position:0% +here's the dynamics of the system so +that you can a couple how you want how + + align:start position:0% +that you can a couple how you want how + + + align:start position:0% +that you can a couple how you want how +you want it to move and the basic + + align:start position:0% +you want it to move and the basic + + + align:start position:0% +you want it to move and the basic +constraints but eventually like as you + + align:start position:0% +constraints but eventually like as you + + + align:start position:0% +constraints but eventually like as you +said you can add analysis of it can I + + align:start position:0% +said you can add analysis of it can I + + + align:start position:0% +said you can add analysis of it can I +make a comment about that yeah there's a + + align:start position:0% +make a comment about that yeah there's a + + + align:start position:0% +make a comment about that yeah there's a +technique called feedback linearization + + align:start position:0% +technique called feedback linearization + + + align:start position:0% +technique called feedback linearization +that can be used to be compose a complex + + align:start position:0% +that can be used to be compose a complex + + + align:start position:0% +that can be used to be compose a complex +nonlinear dynamic system into a set of + + align:start position:0% +nonlinear dynamic system into a set of + + + align:start position:0% +nonlinear dynamic system into a set of +linear ones and that allows you to treat + + align:start position:0% +linear ones and that allows you to treat + + + align:start position:0% +linear ones and that allows you to treat +the center of mass and a separately + + align:start position:0% +the center of mass and a separately + + + align:start position:0% +the center of mass and a separately +control flow through computation in fact + + align:start position:0% +control flow through computation in fact + + + align:start position:0% +control flow through computation in fact +while guaranteeing a little axis this is + + align:start position:0% +while guaranteeing a little axis this is + + + align:start position:0% +while guaranteeing a little axis this is +work done by us + + align:start position:0% +work done by us + + + align:start position:0% +work done by us +actually + + align:start position:0% + + + + align:start position:0% + +this is a robot doing the same kind of + + align:start position:0% +this is a robot doing the same kind of + + + align:start position:0% +this is a robot doing the same kind of +lean on martyrs + + align:start position:0% + + + + align:start position:0% + +let's walk downstairs playing it's + + align:start position:0% +let's walk downstairs playing it's + + + align:start position:0% +let's walk downstairs playing it's +footsteps they're a pretty complicated + + align:start position:0% + + + + align:start position:0% + +stuff sir not exactly a path where if I + + align:start position:0% +stuff sir not exactly a path where if I + + + align:start position:0% +stuff sir not exactly a path where if I +walk moving them around as long as your + + align:start position:0% +walk moving them around as long as your + + + align:start position:0% +walk moving them around as long as your +monthly team gets where every year we'll + + align:start position:0% +monthly team gets where every year we'll + + + align:start position:0% +monthly team gets where every year we'll +say is + + align:start position:0% + + + + align:start position:0% + +awesome + + align:start position:0% + + + + align:start position:0% + +so that was a kind of communities and oh + + align:start position:0% +so that was a kind of communities and oh + + + align:start position:0% +so that was a kind of communities and oh +and another way that you can also + + align:start position:0% +and another way that you can also + + + align:start position:0% +and another way that you can also +compute proteins is by learning so you + + align:start position:0% +compute proteins is by learning so you + + + align:start position:0% +compute proteins is by learning so you +have some kind of example move through + + align:start position:0% +have some kind of example move through + + + align:start position:0% +have some kind of example move through +trajectories from one state to the other + + align:start position:0% +trajectories from one state to the other + + + align:start position:0% +trajectories from one state to the other +and you can estimate on floats based on + + align:start position:0% +and you can estimate on floats based on + + + align:start position:0% +and you can estimate on floats based on +where the charities are as long as you + + align:start position:0% + + + + align:start position:0% + +is the dynamics always linear because I + + align:start position:0% +is the dynamics always linear because I + + + align:start position:0% +is the dynamics always linear because I +thought like a pure and kind of the + + align:start position:0% +thought like a pure and kind of the + + + align:start position:0% +thought like a pure and kind of the +complex also mind you like it was a + + align:start position:0% +complex also mind you like it was a + + + align:start position:0% +complex also mind you like it was a +nonlinear dynamics and + + align:start position:0% +nonlinear dynamics and + + + align:start position:0% +nonlinear dynamics and +not be a pencil that shape well you can + + align:start position:0% +not be a pencil that shape well you can + + + align:start position:0% +not be a pencil that shape well you can +plan nonlinear systems to you but as far + + align:start position:0% +plan nonlinear systems to you but as far + + + align:start position:0% +plan nonlinear systems to you but as far +as I know + + align:start position:0% + + + + align:start position:0% + +so yeah the the polytopes family require + + align:start position:0% +so yeah the the polytopes family require + + + align:start position:0% +so yeah the the polytopes family require +many ization with the system and as a + + align:start position:0% +many ization with the system and as a + + + align:start position:0% +many ization with the system and as a +limit to the vehicle range of the + + align:start position:0% +limit to the vehicle range of the + + + align:start position:0% +limit to the vehicle range of the +linearization and that's you know that's + + align:start position:0% +linearization and that's you know that's + + + align:start position:0% +linearization and that's you know that's +massaged with me but it is the case that + + align:start position:0% +massaged with me but it is the case that + + + align:start position:0% +massaged with me but it is the case that +it's kind of the standard thing that you + + align:start position:0% +it's kind of the standard thing that you + + + align:start position:0% +it's kind of the standard thing that you +do without in your systems right which + + align:start position:0% +do without in your systems right which + + + align:start position:0% +do without in your systems right which +is piece of you're making the piecewise + + align:start position:0% +is piece of you're making the piecewise + + + align:start position:0% +is piece of you're making the piecewise +linear but you are you are linearizing + + align:start position:0% +linear but you are you are linearizing + + + align:start position:0% +linear but you are you are linearizing +than in every step and there's other + + align:start position:0% +than in every step and there's other + + + align:start position:0% +than in every step and there's other +techniques that people who developed + + align:start position:0% +techniques that people who developed + + + align:start position:0% +techniques that people who developed +with quote it was what you do require + + align:start position:0% +with quote it was what you do require + + + align:start position:0% +with quote it was what you do require +the info system + + align:start position:0% +the info system + + + align:start position:0% +the info system +right here at kendama proximation + + align:start position:0% + + + + align:start position:0% + +again so funnels goal is basically to + + align:start position:0% +again so funnels goal is basically to + + + align:start position:0% +again so funnels goal is basically to +binary guarantees your safety under a + + align:start position:0% +binary guarantees your safety under a + + + align:start position:0% +binary guarantees your safety under a +bounded uncertainty + + align:start position:0% +bounded uncertainty + + + align:start position:0% +bounded uncertainty +so there are regions of Finance and + + align:start position:0% +so there are regions of Finance and + + + align:start position:0% +so there are regions of Finance and +variants throughout all time during that + + align:start position:0% +variants throughout all time during that + + + align:start position:0% +variants throughout all time during that +trajectory and you define and set of + + align:start position:0% +trajectory and you define and set of + + + align:start position:0% +trajectory and you define and set of +practice there's a trade-off between + + align:start position:0% +practice there's a trade-off between + + + align:start position:0% +practice there's a trade-off between +computation time is guarantees so if + + align:start position:0% +computation time is guarantees so if + + + align:start position:0% +computation time is guarantees so if +your trajectory if you compute more + + align:start position:0% +your trajectory if you compute more + + + align:start position:0% +your trajectory if you compute more +notes that you're going to be able to + + align:start position:0% +notes that you're going to be able to + + + align:start position:0% +notes that you're going to be able to +fill in these little gaps between + + align:start position:0% +fill in these little gaps between + + + align:start position:0% +fill in these little gaps between +ellipsoids whereas if you lesson no + + align:start position:0% +ellipsoids whereas if you lesson no + + + align:start position:0% +ellipsoids whereas if you lesson no +one's gonna take less time to meet your + + align:start position:0% +one's gonna take less time to meet your + + + align:start position:0% +one's gonna take less time to meet your +lips would but it's also gonna + + align:start position:0% + + + + align:start position:0% + +and especially important when planning + + align:start position:0% +and especially important when planning + + + align:start position:0% +and especially important when planning +so if you're planning some kind of point + + align:start position:0% +so if you're planning some kind of point + + + align:start position:0% +so if you're planning some kind of point +cloud then some of what's making you + + align:start position:0% +cloud then some of what's making you + + + align:start position:0% +cloud then some of what's making you +right here where you want to live so it + + align:start position:0% +right here where you want to live so it + + + align:start position:0% +right here where you want to live so it +doesn't intersect together + + align:start position:0% +doesn't intersect together + + + align:start position:0% +doesn't intersect together +and you might think that's bad but + + align:start position:0% +and you might think that's bad but + + + align:start position:0% +and you might think that's bad but +actually it's + + align:start position:0% + + + + align:start position:0% + +yeah so an example is so glider which is + + align:start position:0% +yeah so an example is so glider which is + + + align:start position:0% +yeah so an example is so glider which is +given in the paper by on the US and so + + align:start position:0% +given in the paper by on the US and so + + + align:start position:0% +given in the paper by on the US and so +what you start doing is you create a + + align:start position:0% +what you start doing is you create a + + + align:start position:0% +what you start doing is you create a +your system your function and this is + + align:start position:0% +your system your function and this is + + + align:start position:0% +your system your function and this is +depending on your state time and W which + + align:start position:0% +depending on your state time and W which + + + align:start position:0% +depending on your state time and W which +is a some kind of bounded uncertainty + + align:start position:0% +is a some kind of bounded uncertainty + + + align:start position:0% +is a some kind of bounded uncertainty +and you choose the boundary certainty + + align:start position:0% +and you choose the boundary certainty + + + align:start position:0% +and you choose the boundary certainty +which means that um and choose some kind + + align:start position:0% +which means that um and choose some kind + + + align:start position:0% +which means that um and choose some kind +of reasonable estimate of how much can + + align:start position:0% +of reasonable estimate of how much can + + + align:start position:0% +of reasonable estimate of how much can +happen your system that you didn't + + align:start position:0% +happen your system that you didn't + + + align:start position:0% +happen your system that you didn't +account for so you started on your + + align:start position:0% +account for so you started on your + + + align:start position:0% +account for so you started on your +velocity can be different from what you + + align:start position:0% +velocity can be different from what you + + + align:start position:0% +velocity can be different from what you +want say your nominal velocities ten + + align:start position:0% +want say your nominal velocities ten + + + align:start position:0% +want say your nominal velocities ten +meters per second you can have some kind + + align:start position:0% +meters per second you can have some kind + + + align:start position:0% +meters per second you can have some kind +of drag or you have some inconsistency + + align:start position:0% +of drag or you have some inconsistency + + + align:start position:0% +of drag or you have some inconsistency +in your motors and so what you expect is + + align:start position:0% +in your motors and so what you expect is + + + align:start position:0% +in your motors and so what you expect is +that there's a plus or minus 0.5 meters + + align:start position:0% +that there's a plus or minus 0.5 meters + + + align:start position:0% +that there's a plus or minus 0.5 meters +per second to your nominal so when you + + align:start position:0% +per second to your nominal so when you + + + align:start position:0% +per second to your nominal so when you +start writing your equations this is + + align:start position:0% +start writing your equations this is + + + align:start position:0% +start writing your equations this is +what you expect your robot to do and + + align:start position:0% +what you expect your robot to do and + + + align:start position:0% +what you expect your robot to do and +then that can vary forward and backwards + + align:start position:0% +then that can vary forward and backwards + + + align:start position:0% +then that can vary forward and backwards +and up what your actual innocence but + + align:start position:0% +and up what your actual innocence but + + + align:start position:0% +and up what your actual innocence but +then you add some kind of wind on your + + align:start position:0% +then you add some kind of wind on your + + + align:start position:0% +then you add some kind of wind on your +system which some kind of cross + + align:start position:0% +system which some kind of cross + + + align:start position:0% +system which some kind of cross +sectionally yes president + + align:start position:0% + + + + align:start position:0% + +so what that ends up doing is pushing + + align:start position:0% +so what that ends up doing is pushing + + + align:start position:0% +so what that ends up doing is pushing +your system away prefer you want it to + + align:start position:0% +your system away prefer you want it to + + + align:start position:0% +your system away prefer you want it to +actually be so now you have some kind of + + align:start position:0% +actually be so now you have some kind of + + + align:start position:0% +actually be so now you have some kind of +some kind of velocity miss or any and + + align:start position:0% +some kind of velocity miss or any and + + + align:start position:0% +some kind of velocity miss or any and +you also have wind they can push you one + + align:start position:0% +you also have wind they can push you one + + + align:start position:0% +you also have wind they can push you one +way or the other so how do you deal with + + align:start position:0% +way or the other so how do you deal with + + + align:start position:0% +way or the other so how do you deal with +that well you start with your nominal + + align:start position:0% +that well you start with your nominal + + + align:start position:0% +that well you start with your nominal +trajectory that's a plane flying + + align:start position:0% +trajectory that's a plane flying + + + align:start position:0% +trajectory that's a plane flying +perfectly straight everything there's no + + align:start position:0% +perfectly straight everything there's no + + + align:start position:0% +perfectly straight everything there's no +uncertainty everything is deterministic + + align:start position:0% +uncertainty everything is deterministic + + + align:start position:0% +uncertainty everything is deterministic +and yeah it's like you wanted to so and + + align:start position:0% +and yeah it's like you wanted to so and + + + align:start position:0% +and yeah it's like you wanted to so and +then so right there the way he hits it + + align:start position:0% +then so right there the way he hits it + + + align:start position:0% +then so right there the way he hits it +so what do you do you have to have some + + align:start position:0% +so what do you do you have to have some + + + align:start position:0% +so what do you do you have to have some +kind of control as some kind of + + align:start position:0% +kind of control as some kind of + + + align:start position:0% +kind of control as some kind of +controller bringing back to your novel + + align:start position:0% +controller bringing back to your novel + + + align:start position:0% +controller bringing back to your novel +objectory and try to control you around + + align:start position:0% +objectory and try to control you around + + + align:start position:0% +objectory and try to control you around +the system so a standard way to do that + + align:start position:0% +the system so a standard way to do that + + + align:start position:0% +the system so a standard way to do that +is to make have a cost function and + + align:start position:0% +is to make have a cost function and + + + align:start position:0% +is to make have a cost function and +create your optimal trajectory and this + + align:start position:0% +create your optimal trajectory and this + + + align:start position:0% +create your optimal trajectory and this +is this cost function basically in kind + + align:start position:0% +is this cost function basically in kind + + + align:start position:0% +is this cost function basically in kind +of mirrors a QR controller and by + + align:start position:0% +of mirrors a QR controller and by + + + align:start position:0% +of mirrors a QR controller and by +solving all these equations which is a + + align:start position:0% +solving all these equations which is a + + + align:start position:0% +solving all these equations which is a +pretty standard process + + align:start position:0% +pretty standard process + + + align:start position:0% +pretty standard process +to do that you get a controller that + + align:start position:0% +to do that you get a controller that + + + align:start position:0% +to do that you get a controller that +tries to bring you back to your nominal + + align:start position:0% +tries to bring you back to your nominal + + + align:start position:0% +tries to bring you back to your nominal +trajectory and well you don't have any + + align:start position:0% +trajectory and well you don't have any + + + align:start position:0% +trajectory and well you don't have any +guarantees just with the controller you + + align:start position:0% +guarantees just with the controller you + + + align:start position:0% +guarantees just with the controller you +don't have any guarantees on how far you + + align:start position:0% +don't have any guarantees on how far you + + + align:start position:0% +don't have any guarantees on how far you +can push do you have any gears where + + align:start position:0% +can push do you have any gears where + + + align:start position:0% +can push do you have any gears where +you're gonna go and where your system + + align:start position:0% +you're gonna go and where your system + + + align:start position:0% +you're gonna go and where your system +can't push you so so when you compute + + align:start position:0% +can't push you so so when you compute + + + align:start position:0% +can't push you so so when you compute +the funnel what you do is you choose the + + align:start position:0% +the funnel what you do is you choose the + + + align:start position:0% +the funnel what you do is you choose the +option off function and I'll explain + + align:start position:0% +option off function and I'll explain + + + align:start position:0% +option off function and I'll explain +what that is in the next slide and you + + align:start position:0% +what that is in the next slide and you + + + align:start position:0% +what that is in the next slide and you +try to minimize the space around that + + align:start position:0% +try to minimize the space around that + + + align:start position:0% +try to minimize the space around that +function to trust to bring it back so + + align:start position:0% +function to trust to bring it back so + + + align:start position:0% +function to trust to bring it back so +what this is is so you have some kind of + + align:start position:0% +what this is is so you have some kind of + + + align:start position:0% +what this is is so you have some kind of +your initial state and this would be the + + align:start position:0% +your initial state and this would be the + + + align:start position:0% +your initial state and this would be the +initial state and the whole region what + + align:start position:0% +initial state and the whole region what + + + align:start position:0% +initial state and the whole region what +you're trying to do is minimize it + + align:start position:0% +you're trying to do is minimize it + + + align:start position:0% +you're trying to do is minimize it +around it does that make sense why you + + align:start position:0% +around it does that make sense why you + + + align:start position:0% +around it does that make sense why you +do that so your trajectory is basically + + align:start position:0% +do that so your trajectory is basically + + + align:start position:0% +do that so your trajectory is basically +going to go anywhere around here and + + align:start position:0% +going to go anywhere around here and + + + align:start position:0% +going to go anywhere around here and +what you're trying to do is find the + + align:start position:0% +what you're trying to do is find the + + + align:start position:0% +what you're trying to do is find the +region of space that minimizes that + + align:start position:0% +region of space that minimizes that + + + align:start position:0% +region of space that minimizes that +encompasses all over the places that + + align:start position:0% +encompasses all over the places that + + + align:start position:0% +encompasses all over the places that +your bigger system is going to get to + + align:start position:0% +your bigger system is going to get to + + + align:start position:0% +your bigger system is going to get to +so that's easy to do when you draw it + + align:start position:0% +so that's easy to do when you draw it + + + align:start position:0% +so that's easy to do when you draw it +out and you know exactly where your + + align:start position:0% +out and you know exactly where your + + + align:start position:0% +out and you know exactly where your +systems gonna get oh it's easy to just + + align:start position:0% +systems gonna get oh it's easy to just + + + align:start position:0% +systems gonna get oh it's easy to just +shrink your ball around it but how do + + align:start position:0% +shrink your ball around it but how do + + + align:start position:0% +shrink your ball around it but how do +you actually + + align:start position:0% + + + + align:start position:0% + +yeah okay so when you have that for each + + align:start position:0% +yeah okay so when you have that for each + + + align:start position:0% +yeah okay so when you have that for each +point in the trajectory you know that + + align:start position:0% +point in the trajectory you know that + + + align:start position:0% +point in the trajectory you know that +you're gonna stay with me here because + + align:start position:0% +you're gonna stay with me here because + + + align:start position:0% +you're gonna stay with me here because +you're gonna have some kind of for your + + align:start position:0% +you're gonna have some kind of for your + + + align:start position:0% +you're gonna have some kind of for your +nominal trajectory you're gonna have + + align:start position:0% +nominal trajectory you're gonna have + + + align:start position:0% +nominal trajectory you're gonna have +different places where your system a + + align:start position:0% +different places where your system a + + + align:start position:0% +different places where your system a +other given conditions and philosophy + + align:start position:0% +other given conditions and philosophy + + + align:start position:0% +other given conditions and philosophy +and and wind uncertainty we're going to + + align:start position:0% +and and wind uncertainty we're going to + + + align:start position:0% +and and wind uncertainty we're going to +go anywhere within that but as long as + + align:start position:0% +go anywhere within that but as long as + + + align:start position:0% +go anywhere within that but as long as +you know you're still in that ellipsoid + + align:start position:0% +you know you're still in that ellipsoid + + + align:start position:0% +you know you're still in that ellipsoid +then you're going to stay within those + + align:start position:0% +then you're going to stay within those + + + align:start position:0% +then you're going to stay within those +ellipsoids as you go down the path + + align:start position:0% +ellipsoids as you go down the path + + + align:start position:0% +ellipsoids as you go down the path +already okay so the reason they use the + + align:start position:0% +already okay so the reason they use the + + + align:start position:0% +already okay so the reason they use the +a banal functions is there's different + + align:start position:0% +a banal functions is there's different + + + align:start position:0% +a banal functions is there's different +ways to measure stability and so so + + align:start position:0% +ways to measure stability and so so + + + align:start position:0% +ways to measure stability and so so +there's different ways to measure + + align:start position:0% +there's different ways to measure + + + align:start position:0% +there's different ways to measure +instability in a nonlinear system so in + + align:start position:0% +instability in a nonlinear system so in + + + align:start position:0% +instability in a nonlinear system so in +a linear system you're either unstable + + align:start position:0% +a linear system you're either unstable + + + align:start position:0% +a linear system you're either unstable +or you're globally exponentially stable + + align:start position:0% +or you're globally exponentially stable + + + align:start position:0% +or you're globally exponentially stable +so you're going to converge back to here + + align:start position:0% +so you're going to converge back to here + + + align:start position:0% +so you're going to converge back to here +- whatever civility equilibrium when you + + align:start position:0% +- whatever civility equilibrium when you + + + align:start position:0% +- whatever civility equilibrium when you +have an exponential rate but there is + + align:start position:0% +have an exponential rate but there is + + + align:start position:0% +have an exponential rate but there is +also in nonlinear systems there's global + + align:start position:0% +also in nonlinear systems there's global + + + align:start position:0% +also in nonlinear systems there's global +exponential stability + + align:start position:0% +exponential stability + + + align:start position:0% +exponential stability +there's asymptotic stability and there's + + align:start position:0% +there's asymptotic stability and there's + + + align:start position:0% +there's asymptotic stability and there's +really + + align:start position:0% +really + + + align:start position:0% +really +sense of layout which is what we care + + align:start position:0% +sense of layout which is what we care + + + align:start position:0% +sense of layout which is what we care +about so the difference between that is + + align:start position:0% +about so the difference between that is + + + align:start position:0% +about so the difference between that is +this is phenomenal and globally + + align:start position:0% +this is phenomenal and globally + + + align:start position:0% +this is phenomenal and globally +exponentially stable means that no + + align:start position:0% +exponentially stable means that no + + + align:start position:0% +exponentially stable means that no +matter where you start anywhere on board + + align:start position:0% +matter where you start anywhere on board + + + align:start position:0% +matter where you start anywhere on board +you're going to be converging back to + + align:start position:0% +you're going to be converging back to + + + align:start position:0% +you're going to be converging back to +this equilibrium point at an exponential + + align:start position:0% +this equilibrium point at an exponential + + + align:start position:0% +this equilibrium point at an exponential +rate so that's the best scenario that's + + align:start position:0% +rate so that's the best scenario that's + + + align:start position:0% +rate so that's the best scenario that's +what you want asymptotic stability means + + align:start position:0% +what you want asymptotic stability means + + + align:start position:0% +what you want asymptotic stability means +that you're going to be going from + + align:start position:0% +that you're going to be going from + + + align:start position:0% +that you're going to be going from +somewhere on the board within a certain + + align:start position:0% +somewhere on the board within a certain + + + align:start position:0% +somewhere on the board within a certain +region back to its nominal trajectory + + align:start position:0% +region back to its nominal trajectory + + + align:start position:0% +region back to its nominal trajectory +but it doesn't have to be an exponential + + align:start position:0% +but it doesn't have to be an exponential + + + align:start position:0% +but it doesn't have to be an exponential +rate so you can do something like that + + align:start position:0% +rate so you can do something like that + + + align:start position:0% +rate so you can do something like that +as long as eventually you start + + align:start position:0% +as long as eventually you start + + + align:start position:0% +as long as eventually you start +converging back to them and then there's + + align:start position:0% +converging back to them and then there's + + + align:start position:0% +converging back to them and then there's +another stability in the sense of + + align:start position:0% +another stability in the sense of + + + align:start position:0% +another stability in the sense of +Lyapunov which is say you're here you're + + align:start position:0% +Lyapunov which is say you're here you're + + + align:start position:0% +Lyapunov which is say you're here you're +just going to be doing anything anything + + align:start position:0% +just going to be doing anything anything + + + align:start position:0% +just going to be doing anything anything +crazy as long as it stays within some + + align:start position:0% +crazy as long as it stays within some + + + align:start position:0% +crazy as long as it stays within some +certain thing which in the 1d case we + + align:start position:0% +certain thing which in the 1d case we + + + align:start position:0% +certain thing which in the 1d case we +saw was little ball going around it + + align:start position:0% +saw was little ball going around it + + + align:start position:0% +saw was little ball going around it +so imagine there's like a Falls for each + + align:start position:0% +so imagine there's like a Falls for each + + + align:start position:0% +so imagine there's like a Falls for each +of these and this is where your + + align:start position:0% +of these and this is where your + + + align:start position:0% +of these and this is where your +trajectory possibly go a lot of the + + align:start position:0% +trajectory possibly go a lot of the + + + align:start position:0% +trajectory possibly go a lot of the +states have been that eelinator system + + align:start position:0% +states have been that eelinator system + + + align:start position:0% +states have been that eelinator system +is stable in a sensible way out enough + + align:start position:0% +is stable in a sensible way out enough + + + align:start position:0% +is stable in a sensible way out enough +that makes sense cool all right + + align:start position:0% +that makes sense cool all right + + + align:start position:0% +that makes sense cool all right +so knowing this is that I just have a + + align:start position:0% +so knowing this is that I just have a + + + align:start position:0% +so knowing this is that I just have a +basic question so the we open our + + align:start position:0% +basic question so the we open our + + + align:start position:0% +basic question so the we open our +function is around a stable set point + + align:start position:0% +function is around a stable set point + + + align:start position:0% +function is around a stable set point +but the trajectory has zero velocity so + + align:start position:0% +but the trajectory has zero velocity so + + + align:start position:0% +but the trajectory has zero velocity so +what is the you know the point that it's + + align:start position:0% +what is the you know the point that it's + + + align:start position:0% +what is the you know the point that it's +stabilizing around you can stabilize + + align:start position:0% +stabilizing around you can stabilize + + + align:start position:0% +stabilizing around you can stabilize +around Internet + + align:start position:0% +around Internet + + + align:start position:0% +around Internet +which is also what the deal so you have + + align:start position:0% +which is also what the deal so you have + + + align:start position:0% +which is also what the deal so you have +your little point here and this is your + + align:start position:0% +your little point here and this is your + + + align:start position:0% +your little point here and this is your +accomplish fu some kind of skate and + + align:start position:0% +accomplish fu some kind of skate and + + + align:start position:0% +accomplish fu some kind of skate and +your win can knock you this way your + + align:start position:0% +your win can knock you this way your + + + align:start position:0% +your win can knock you this way your +velocity difference cannot you this way + + align:start position:0% +velocity difference cannot you this way + + + align:start position:0% +velocity difference cannot you this way +or this way but as long as you're still + + align:start position:0% +or this way but as long as you're still + + + align:start position:0% +or this way but as long as you're still +within that you got converge back to it + + align:start position:0% +within that you got converge back to it + + + align:start position:0% +within that you got converge back to it +and this is a so the value from the + + align:start position:0% +and this is a so the value from the + + + align:start position:0% +and this is a so the value from the +Abenaki function and these are the + + align:start position:0% +Abenaki function and these are the + + + align:start position:0% +Abenaki function and these are the +different states you can have an + + align:start position:0% +different states you can have an + + + align:start position:0% +different states you can have an +important thing to notice is the the + + align:start position:0% +important thing to notice is the the + + + align:start position:0% +important thing to notice is the the +derivative is negative definite or + + align:start position:0% +derivative is negative definite or + + + align:start position:0% +derivative is negative definite or +negative semi definite in this case and + + align:start position:0% +negative semi definite in this case and + + + align:start position:0% +negative semi definite in this case and +that means that basically you're you're + + align:start position:0% +that means that basically you're you're + + + align:start position:0% +that means that basically you're you're +all your trajectories no matter where + + align:start position:0% +all your trajectories no matter where + + + align:start position:0% +all your trajectories no matter where +you go they're going to be going down + + align:start position:0% +you go they're going to be going down + + + align:start position:0% +you go they're going to be going down +this cone and eventually they're going + + align:start position:0% +this cone and eventually they're going + + + align:start position:0% +this cone and eventually they're going +to go down to some value so that make + + align:start position:0% +to go down to some value so that make + + + align:start position:0% +to go down to some value so that make +sense us like brilliant it's not my your + + align:start position:0% +sense us like brilliant it's not my your + + + align:start position:0% +sense us like brilliant it's not my your +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +all right so once you know that it makes + + align:start position:0% +all right so once you know that it makes + + + align:start position:0% +all right so once you know that it makes +sense to use the autonomic functions as + + align:start position:0% +sense to use the autonomic functions as + + + align:start position:0% +sense to use the autonomic functions as +canvas for for computing close + + align:start position:0% + + + + align:start position:0% + +so so ellipsoid is actually defined by a + + align:start position:0% +so so ellipsoid is actually defined by a + + + align:start position:0% +so so ellipsoid is actually defined by a +quadratic the optimal function which + + align:start position:0% +quadratic the optimal function which + + + align:start position:0% +quadratic the optimal function which +down here relation is shown the the + + align:start position:0% +down here relation is shown the the + + + align:start position:0% +down here relation is shown the the +equation for an ellipsoid is my son be + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +so that was the equation for an ellipse + + align:start position:0% +so that was the equation for an ellipse + + + align:start position:0% +so that was the equation for an ellipse +with the April showed previously the + + align:start position:0% +with the April showed previously the + + + align:start position:0% +with the April showed previously the +quadratic damping our function has the + + align:start position:0% +quadratic damping our function has the + + + align:start position:0% +quadratic damping our function has the +same same structure where you have this + + align:start position:0% +same same structure where you have this + + + align:start position:0% +same same structure where you have this +being x2 live which is basically the + + align:start position:0% +being x2 live which is basically the + + + align:start position:0% +being x2 live which is basically the +error of your state so it so some kind + + align:start position:0% +error of your state so it so some kind + + + align:start position:0% +error of your state so it so some kind +of snap being the snake that you're + + align:start position:0% +of snap being the snake that you're + + + align:start position:0% +of snap being the snake that you're +actually in minus X here which is a + + align:start position:0% +actually in minus X here which is a + + + align:start position:0% +actually in minus X here which is a +nominal at the point that you want to + + align:start position:0% +nominal at the point that you want to + + + align:start position:0% +nominal at the point that you want to +reach so this defines the region around + + align:start position:0% +reach so this defines the region around + + + align:start position:0% +reach so this defines the region around +your a nominal point which would be + + align:start position:0% +your a nominal point which would be + + + align:start position:0% +your a nominal point which would be +somewhere in there and the ellipsoid is + + align:start position:0% +somewhere in there and the ellipsoid is + + + align:start position:0% +somewhere in there and the ellipsoid is +computed by doing that minimization that + + align:start position:0% +computed by doing that minimization that + + + align:start position:0% +computed by doing that minimization that +I showed and then you can figure out the + + align:start position:0% +I showed and then you can figure out the + + + align:start position:0% +I showed and then you can figure out the +region inside of it by solving that + + align:start position:0% +region inside of it by solving that + + + align:start position:0% +region inside of it by solving that +equation and if it is less than 1 I + + align:start position:0% +equation and if it is less than 1 I + + + align:start position:0% +equation and if it is less than 1 I +believe you're inside and those are all + + align:start position:0% +believe you're inside and those are all + + + align:start position:0% +believe you're inside and those are all +the red jobs we show the + + align:start position:0% +the red jobs we show the + + + align:start position:0% +the red jobs we show the +so that's used when computing + + align:start position:0% +so that's used when computing + + + align:start position:0% +so that's used when computing +trajectories you saw you solve for say + + align:start position:0% +trajectories you saw you solve for say + + + align:start position:0% +trajectories you saw you solve for say +that you're inside of my club you know + + align:start position:0% +that you're inside of my club you know + + + align:start position:0% +that you're inside of my club you know +which points you're going to hate inside + + align:start position:0% +which points you're going to hate inside + + + align:start position:0% +which points you're going to hate inside +of this looks like so in your planning + + align:start position:0% +of this looks like so in your planning + + + align:start position:0% +of this looks like so in your planning +you solve that equation for each of the + + align:start position:0% +you solve that equation for each of the + + + align:start position:0% +you solve that equation for each of the +ellipsoids and you know + + align:start position:0% + + + + align:start position:0% + +right so this is a video that I needed + + align:start position:0% +right so this is a video that I needed + + + align:start position:0% +right so this is a video that I needed +and this is using both photo libraries + + align:start position:0% +and this is using both photo libraries + + + align:start position:0% +and this is using both photo libraries +for collision avoidance this is showing + + align:start position:0% +for collision avoidance this is showing + + + align:start position:0% +for collision avoidance this is showing +for just one funnel the glider dynamics + + align:start position:0% +for just one funnel the glider dynamics + + + align:start position:0% +for just one funnel the glider dynamics +we're showing one of the three signs + + align:start position:0% +we're showing one of the three signs + + + align:start position:0% +we're showing one of the three signs +they were pretty simplified but so you + + align:start position:0% +they were pretty simplified but so you + + + align:start position:0% +they were pretty simplified but so you +see right there that there's objects and + + align:start position:0% +see right there that there's objects and + + + align:start position:0% +see right there that there's objects and +like plants a path around so the funnel + + align:start position:0% +like plants a path around so the funnel + + + align:start position:0% +like plants a path around so the funnel +this is one possible one right here I'm + + align:start position:0% +this is one possible one right here I'm + + + align:start position:0% +this is one possible one right here I'm +pretty sure they tell it where objects + + align:start position:0% +pretty sure they tell it where objects + + + align:start position:0% +pretty sure they tell it where objects +are even though they're not actually + + align:start position:0% +are even though they're not actually + + + align:start position:0% +are even though they're not actually +there and it finds that funnel being the + + align:start position:0% +there and it finds that funnel being the + + + align:start position:0% +there and it finds that funnel being the +one that I want and you see that + + align:start position:0% +one that I want and you see that + + + align:start position:0% +one that I want and you see that +throughout the entire path the glider + + align:start position:0% +throughout the entire path the glider + + + align:start position:0% +throughout the entire path the glider +will stay within the funnel + + align:start position:0% + + + + align:start position:0% + +and then when you're searching with the + + align:start position:0% +and then when you're searching with the + + + align:start position:0% +and then when you're searching with the +online planning algorithm we've shown + + align:start position:0% +online planning algorithm we've shown + + + align:start position:0% +online planning algorithm we've shown +previously it goes through all of these + + align:start position:0% +previously it goes through all of these + + + align:start position:0% +previously it goes through all of these +funnels and eventually finds the best + + align:start position:0% +funnels and eventually finds the best + + + align:start position:0% +funnels and eventually finds the best +safe one you won't always find a safe + + align:start position:0% +safe one you won't always find a safe + + + align:start position:0% +safe one you won't always find a safe +winners just in case you did but it + + align:start position:0% +winners just in case you did but it + + + align:start position:0% +winners just in case you did but it +finds the best one by around the patent + + align:start position:0% +finds the best one by around the patent + + + align:start position:0% +finds the best one by around the patent +so one way that it finds the best one is + + align:start position:0% +so one way that it finds the best one is + + + align:start position:0% +so one way that it finds the best one is +by finding all of so if you're playing a + + align:start position:0% +by finding all of so if you're playing a + + + align:start position:0% +by finding all of so if you're playing a +point cloud and you find all the points + + align:start position:0% +point cloud and you find all the points + + + align:start position:0% +point cloud and you find all the points +of the light with being the ellipsoid + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so here is a much different obstacles + + align:start position:0% +so here is a much different obstacles + + + align:start position:0% +so here is a much different obstacles +and secret there's some pretty dynamic + + align:start position:0% +and secret there's some pretty dynamic + + + align:start position:0% +and secret there's some pretty dynamic +movements which is + + align:start position:0% + + + + align:start position:0% + +so within that there's + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +is there a way to like get back to + + align:start position:0% +is there a way to like get back to + + + align:start position:0% +is there a way to like get back to +full screen + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +like a cone + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so with the online planning algorithm + + align:start position:0% +so with the online planning algorithm + + + align:start position:0% +so with the online planning algorithm +here's one of the possible paths you + + align:start position:0% +here's one of the possible paths you + + + align:start position:0% +here's one of the possible paths you +have to cut of trees and those were + + align:start position:0% +have to cut of trees and those were + + + align:start position:0% +have to cut of trees and those were +shows the previous little round thing + + align:start position:0% +shows the previous little round thing + + + align:start position:0% +shows the previous little round thing +like foxy tree living things use a + + align:start position:0% +like foxy tree living things use a + + + align:start position:0% +like foxy tree living things use a +sensor model you get out back and as + + align:start position:0% +sensor model you get out back and as + + + align:start position:0% +sensor model you get out back and as +you're going you plan your paths and the + + align:start position:0% +you're going you plan your paths and the + + + align:start position:0% +you're going you plan your paths and the +way that this works is every five meters + + align:start position:0% +way that this works is every five meters + + + align:start position:0% +way that this works is every five meters +you might have and then as you're + + align:start position:0% +you might have and then as you're + + + align:start position:0% +you might have and then as you're +climbing through it you get new sensor + + align:start position:0% +climbing through it you get new sensor + + + align:start position:0% +climbing through it you get new sensor +information and using the algorithm + + align:start position:0% + + + + align:start position:0% + +and that'll guarantee you that you're + + align:start position:0% +and that'll guarantee you that you're + + + align:start position:0% +and that'll guarantee you that you're +safe and when you're flying + + align:start position:0% +safe and when you're flying + + + align:start position:0% +safe and when you're flying +obviously you don't see the puzzles but + + align:start position:0% +obviously you don't see the puzzles but + + + align:start position:0% +obviously you don't see the puzzles but +right here you can see there's probably + + align:start position:0% +right here you can see there's probably + + + align:start position:0% +right here you can see there's probably +one funnel here and that another funnel + + align:start position:0% +one funnel here and that another funnel + + + align:start position:0% +one funnel here and that another funnel +it - this way you know that goes - here + + align:start position:0% +it - this way you know that goes - here + + + align:start position:0% +it - this way you know that goes - here +goes there and that's a full path and + + align:start position:0% +goes there and that's a full path and + + + align:start position:0% +goes there and that's a full path and +there's also a cool one as it shows that + + align:start position:0% +there's also a cool one as it shows that + + + align:start position:0% +there's also a cool one as it shows that +you go through the treaty and that's + + align:start position:0% +you go through the treaty and that's + + + align:start position:0% +you go through the treaty and that's +where one of the formals is rather than + + align:start position:0% +where one of the formals is rather than + + + align:start position:0% +where one of the formals is rather than +going around it's possibly you start + + align:start position:0% +going around it's possibly you start + + + align:start position:0% +going around it's possibly you start +computing you funnel where you start + + align:start position:0% +computing you funnel where you start + + + align:start position:0% +computing you funnel where you start +searching a new library here and you may + + align:start position:0% +searching a new library here and you may + + + align:start position:0% +searching a new library here and you may +not be able to make it up the way it's + + align:start position:0% +not be able to make it up the way it's + + + align:start position:0% +not be able to make it up the way it's +time given what speed you're going at + + align:start position:0% +time given what speed you're going at + + + align:start position:0% +time given what speed you're going at +does anyone have any questions + + align:start position:0% + + + + align:start position:0% + +and this is the online depending on + + align:start position:0% +and this is the online depending on + + + align:start position:0% +and this is the online depending on +saw before it now + + align:start position:0% + + + + align:start position:0% + +and some of the references the paper + + align:start position:0% +and some of the references the paper + + + align:start position:0% +and some of the references the paper +from the video that we just saw that's + + align:start position:0% +from the video that we just saw that's + + + align:start position:0% +from the video that we just saw that's +given Tyrion that also goes to the + + align:start position:0% +given Tyrion that also goes to the + + + align:start position:0% +given Tyrion that also goes to the +example for death + + align:start position:0% +example for death + + + align:start position:0% +example for death +Rizzoli was one of the original people + + align:start position:0% +Rizzoli was one of the original people + + + align:start position:0% +Rizzoli was one of the original people +that can get afloat to Hoffman Williams + + align:start position:0% +that can get afloat to Hoffman Williams + + + align:start position:0% +that can get afloat to Hoffman Williams +did a temporal mining for footsteps and + + align:start position:0% +did a temporal mining for footsteps and + + + align:start position:0% +did a temporal mining for footsteps and +become a humanoid system and I I did + + align:start position:0% +become a humanoid system and I I did + + + align:start position:0% +become a humanoid system and I I did +most of the of stuff on the quadcopter I + + align:start position:0% +most of the of stuff on the quadcopter I + + + align:start position:0% +most of the of stuff on the quadcopter I +did see that another run ended note that + + align:start position:0% +did see that another run ended note that + + + align:start position:0% +did see that another run ended note that +was a big thing in my personal research + + align:start position:0% +was a big thing in my personal research + + + align:start position:0% +was a big thing in my personal research +was that even though you may not be able + + align:start position:0% +was that even though you may not be able + + + align:start position:0% +was that even though you may not be able +to compute or that you may not find a + + align:start position:0% +to compute or that you may not find a + + + align:start position:0% +to compute or that you may not find a +funnel that necessarily those find a + + align:start position:0% +funnel that necessarily those find a + + + align:start position:0% +funnel that necessarily those find a +safe path you can shift that fall around + + align:start position:0% +safe path you can shift that fall around + + + align:start position:0% +safe path you can shift that fall around +it slightly up and down that as long as + + align:start position:0% +it slightly up and down that as long as + + + align:start position:0% +it slightly up and down that as long as +a person ellipsoid is still within and + + align:start position:0% +a person ellipsoid is still within and + + + align:start position:0% +a person ellipsoid is still within and +as long as your initial state still we + + align:start position:0% +as long as your initial state still we + + + align:start position:0% +as long as your initial state still we +did another ellipsoid and that's easy to + + align:start position:0% +did another ellipsoid and that's easy to + + + align:start position:0% +did another ellipsoid and that's easy to +do is you can just give it a simple + + align:start position:0% +do is you can just give it a simple + + + align:start position:0% +do is you can just give it a simple +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +seen the other and + + align:start position:0% +seen the other and + + + align:start position:0% +seen the other and +you transform this s-matrix then they'll + + align:start position:0% +you transform this s-matrix then they'll + + + align:start position:0% +you transform this s-matrix then they'll +transform your entire funnel shifted + + align:start position:0% +transform your entire funnel shifted + + + align:start position:0% +transform your entire funnel shifted +around + + align:start position:0% +around + + + align:start position:0% +around + find their best one home even + + align:start position:0% + find their best one home even + + + align:start position:0% + find their best one home even +though it making something if it was + + align:start position:0% +though it making something if it was + + + align:start position:0% +though it making something if it was +slightly shifted to the left you get + + align:start position:0% +slightly shifted to the left you get + + + align:start position:0% +slightly shifted to the left you get +enough you get distributing he's + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +the psych-up that funded by chance my + + align:start position:0% +the psych-up that funded by chance my + + + align:start position:0% +the psych-up that funded by chance my +straight there right yeah if if you want + + align:start position:0% +straight there right yeah if if you want + + + align:start position:0% +straight there right yeah if if you want +to give it some ridiculous wind like a + + align:start position:0% +to give it some ridiculous wind like a + + + align:start position:0% +to give it some ridiculous wind like a +thousand miles per hour that you're + + align:start position:0% +thousand miles per hour that you're + + + align:start position:0% +thousand miles per hour that you're +gonna huge funnels but that's under + + align:start position:0% +gonna huge funnels but that's under + + + align:start position:0% +gonna huge funnels but that's under +there's some kind of reasonable you know + + align:start position:0% +there's some kind of reasonable you know + + + align:start position:0% +there's some kind of reasonable you know +is this region + + align:start position:0% +is this region + + + align:start position:0% +is this region +worse or something there's minutes or so + + align:start position:0% +worse or something there's minutes or so + + + align:start position:0% +worse or something there's minutes or so +yeah that's basically what your downside + + align:start position:0% +yeah that's basically what your downside + + + align:start position:0% +yeah that's basically what your downside +so do you have any like any element in + + align:start position:0% +so do you have any like any element in + + + align:start position:0% +so do you have any like any element in +your mind that it's like not using + + align:start position:0% +your mind that it's like not using + + + align:start position:0% +your mind that it's like not using +offline so this like mostly we do the + + align:start position:0% +offline so this like mostly we do the + + + align:start position:0% +offline so this like mostly we do the +offline and online search but if you're + + align:start position:0% +offline and online search but if you're + + + align:start position:0% +offline and online search but if you're +like in a while Department + + align:start position:0% +like in a while Department + + + align:start position:0% +like in a while Department +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that I mean there are algorithms that + + align:start position:0% +that I mean there are algorithms that + + + align:start position:0% +that I mean there are algorithms that +we'll we'll just a basic controller will + + align:start position:0% +we'll we'll just a basic controller will + + + align:start position:0% +we'll we'll just a basic controller will +try to get you back to novel trajectory + + align:start position:0% +try to get you back to novel trajectory + + + align:start position:0% +try to get you back to novel trajectory +but there's nothing that I know of at + + align:start position:0% +but there's nothing that I know of at + + + align:start position:0% +but there's nothing that I know of at +least that would guarantee you safety + + align:start position:0% +least that would guarantee you safety + + + align:start position:0% +least that would guarantee you safety +and I'll give you an all-encompassing + + align:start position:0% +and I'll give you an all-encompassing + + + align:start position:0% +and I'll give you an all-encompassing +reagent like I look to you very funny + + align:start position:0% +reagent like I look to you very funny + + + align:start position:0% +reagent like I look to you very funny +because I took so to you find + + align:start position:0% +because I took so to you find + + + align:start position:0% +because I took so to you find +there's an infinite number of paths so + + align:start position:0% +there's an infinite number of paths so + + + align:start position:0% +there's an infinite number of paths so +getting from here to here with your + + align:start position:0% +getting from here to here with your + + + align:start position:0% +getting from here to here with your +system basically like every little mind + + align:start position:0% +system basically like every little mind + + + align:start position:0% +system basically like every little mind +you can change they have and that + + align:start position:0% +you can change they have and that + + + align:start position:0% +you can change they have and that +approximate and the funnels quality + + align:start position:0% +approximate and the funnels quality + + + align:start position:0% +approximate and the funnels quality +compute regions where they can go so I + + align:start position:0% +compute regions where they can go so I + + + align:start position:0% +compute regions where they can go so I +don't know this region but you'll be + + align:start position:0% +don't know this region but you'll be + + + align:start position:0% +don't know this region but you'll be +able to compute some trajectory and then + + align:start position:0% +able to compute some trajectory and then + + + align:start position:0% +able to compute some trajectory and then +like your controller will take their + + align:start position:0% +like your controller will take their + + + align:start position:0% +like your controller will take their +state error but it won't + + align:start position:0% + + + + align:start position:0% + +but with the funnels how do you compute + + align:start position:0% +but with the funnels how do you compute + + + align:start position:0% +but with the funnels how do you compute +your initial set of states or the + + align:start position:0% +your initial set of states or the + + + align:start position:0% +your initial set of states or the +allowed initial set of states you have + + align:start position:0% +allowed initial set of states you have + + + align:start position:0% +allowed initial set of states you have +these uncertainties like for the wind + + align:start position:0% +these uncertainties like for the wind + + + align:start position:0% +these uncertainties like for the wind +and velocity but what about you know the + + align:start position:0% +and velocity but what about you know the + + + align:start position:0% +and velocity but what about you know the +initial state is sort of before those + + align:start position:0% +initial state is sort of before those + + + align:start position:0% +initial state is sort of before those +disturbances happened but you probably + + align:start position:0% +disturbances happened but you probably + + + align:start position:0% +disturbances happened but you probably +want more than one initial State + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +or something you're done here that'd be + + align:start position:0% +or something you're done here that'd be + + + align:start position:0% +or something you're done here that'd be +good thanks + + align:start position:0% + + + + align:start position:0% + +so with the funnels to say younger of + + align:start position:0% +so with the funnels to say younger of + + + align:start position:0% +so with the funnels to say younger of +nominal trajectory again your lips + + align:start position:0% +nominal trajectory again your lips + + + align:start position:0% +nominal trajectory again your lips +around it so when your sister starts you + + align:start position:0% +around it so when your sister starts you + + + align:start position:0% +around it so when your sister starts you +have your initial state and your just + + align:start position:0% +have your initial state and your just + + + align:start position:0% +have your initial state and your just +rotates just is get me here at time t0 + + align:start position:0% +rotates just is get me here at time t0 + + + align:start position:0% +rotates just is get me here at time t0 +but over the time commuted you can go + + align:start position:0% +but over the time commuted you can go + + + align:start position:0% +but over the time commuted you can go +over here or + + align:start position:0% + + + + align:start position:0% + +but I just mean that you want to apply + + align:start position:0% +but I just mean that you want to apply + + + align:start position:0% +but I just mean that you want to apply +the the funnel multiple times and your + + align:start position:0% +the the funnel multiple times and your + + + align:start position:0% +the the funnel multiple times and your +initial state may not be exactly the + + align:start position:0% +initial state may not be exactly the + + + align:start position:0% +initial state may not be exactly the +same so it should be possible to use the + + align:start position:0% +same so it should be possible to use the + + + align:start position:0% +same so it should be possible to use the +same funnel you know even though the + + align:start position:0% +same funnel you know even though the + + + align:start position:0% +same funnel you know even though the +initial state is off by a little bit + + align:start position:0% +initial state is off by a little bit + + + align:start position:0% +initial state is off by a little bit +yeah okay so say the key chose this + + align:start position:0% +yeah okay so say the key chose this + + + align:start position:0% +yeah okay so say the key chose this +phone first and eventually like what + + align:start position:0% +phone first and eventually like what + + + align:start position:0% +phone first and eventually like what +actually happens is to do this push + + align:start position:0% +actually happens is to do this push + + + align:start position:0% +actually happens is to do this push +around and then you end up here instead + + align:start position:0% +around and then you end up here instead + + + align:start position:0% +around and then you end up here instead +of this nama one um as long as your next + + align:start position:0% +of this nama one um as long as your next + + + align:start position:0% +of this nama one um as long as your next +funnel Dickies plans so you can start a + + align:start position:0% +funnel Dickies plans so you can start a + + + align:start position:0% +funnel Dickies plans so you can start a +new funnel at any point in this + + align:start position:0% +new funnel at any point in this + + + align:start position:0% +new funnel at any point in this +trajectory as long as the next funnel is + + align:start position:0% +trajectory as long as the next funnel is + + + align:start position:0% +trajectory as long as the next funnel is +also as long as you have the + + align:start position:0% +also as long as you have the + + + align:start position:0% +also as long as you have the +intersection between and the next funnel + + align:start position:0% +intersection between and the next funnel + + + align:start position:0% +intersection between and the next funnel +and if you're in this region and you + + align:start position:0% +and if you're in this region and you + + + align:start position:0% +and if you're in this region and you +find the next one + + align:start position:0% +find the next one + + + align:start position:0% +find the next one +well what you do is you plan the next + + align:start position:0% +well what you do is you plan the next + + + align:start position:0% +well what you do is you plan the next +model with this original executor so as + + align:start position:0% +model with this original executor so as + + + align:start position:0% +model with this original executor so as +long as that's your next X 0 and then + + align:start position:0% +long as that's your next X 0 and then + + + align:start position:0% +long as that's your next X 0 and then +this will take on a new nominal + + align:start position:0% +this will take on a new nominal + + + align:start position:0% +this will take on a new nominal +trajectory I'm just just saying asking + + align:start position:0% +trajectory I'm just just saying asking + + + align:start position:0% +trajectory I'm just just saying asking +how do you like for the one all the way + + align:start position:0% +how do you like for the one all the way + + + align:start position:0% +how do you like for the one all the way +on the left that one yeah how do you + + align:start position:0% +on the left that one yeah how do you + + + align:start position:0% +on the left that one yeah how do you +define how it will be an initial region + + align:start position:0% +define how it will be an initial region + + + align:start position:0% +define how it will be an initial region +is okay so that one say if you if you + + align:start position:0% +is okay so that one say if you if you + + + align:start position:0% +is okay so that one say if you if you +start saying not moving or something and + + align:start position:0% +start saying not moving or something and + + + align:start position:0% +start saying not moving or something and +yet which is that we're asking preferred + + align:start position:0% +yet which is that we're asking preferred + + + align:start position:0% +yet which is that we're asking preferred +well I mean I'm saying that that you're + + align:start position:0% +well I mean I'm saying that that you're + + + align:start position:0% +well I mean I'm saying that that you're +using the lead uncertainty and me and + + align:start position:0% +using the lead uncertainty and me and + + + align:start position:0% +using the lead uncertainty and me and +that essentially defines how to make + + align:start position:0% +that essentially defines how to make + + + align:start position:0% +that essentially defines how to make +those those funnels are you may also + + align:start position:0% +those those funnels are you may also + + + align:start position:0% +those those funnels are you may also +define how big the first one is yes so + + align:start position:0% +define how big the first one is yes so + + + align:start position:0% +define how big the first one is yes so +what you're doing because what you want + + align:start position:0% +what you're doing because what you want + + + align:start position:0% +what you're doing because what you want +to do is use the funnel ones that have + + align:start position:0% +to do is use the funnel ones that have + + + align:start position:0% +to do is use the funnel ones that have +some funnel library and be able to use + + align:start position:0% +some funnel library and be able to use + + + align:start position:0% +some funnel library and be able to use +those throughout the whole time and so + + align:start position:0% +those throughout the whole time and so + + + align:start position:0% +those throughout the whole time and so +you don't want said so I guess what + + align:start position:0% +you don't want said so I guess what + + + align:start position:0% +you don't want said so I guess what +you're asking + + align:start position:0% +you're asking + + + align:start position:0% +you're asking +the first funnel you're gonna start at + + align:start position:0% +the first funnel you're gonna start at + + + align:start position:0% +the first funnel you're gonna start at +some initial space here would fill + + align:start position:0% +some initial space here would fill + + + align:start position:0% +some initial space here would fill +velocity stuff like that and so you're + + align:start position:0% +velocity stuff like that and so you're + + + align:start position:0% +velocity stuff like that and so you're +not having a certainty on the first + + align:start position:0% +not having a certainty on the first + + + align:start position:0% +not having a certainty on the first +thing you know where you start to see + + align:start position:0% +thing you know where you start to see + + + align:start position:0% +thing you know where you start to see +yeah I'm just asking you know + + align:start position:0% +yeah I'm just asking you know + + + align:start position:0% +yeah I'm just asking you know +independent of the the wind and stuff + + align:start position:0% +independent of the the wind and stuff + + + align:start position:0% +independent of the the wind and stuff +like that you might just be starting at + + align:start position:0% +like that you might just be starting at + + + align:start position:0% +like that you might just be starting at +a point other than what that nominal + + align:start position:0% +a point other than what that nominal + + + align:start position:0% +a point other than what that nominal +point is so you may want to define that + + align:start position:0% +point is so you may want to define that + + + align:start position:0% +point is so you may want to define that +initial funnel size by some other + + align:start position:0% +initial funnel size by some other + + + align:start position:0% +initial funnel size by some other +criteria besides we because their answer + + align:start position:0% +criteria besides we because their answer + + + align:start position:0% +criteria besides we because their answer +house where you are yeah I mean the + + align:start position:0% +house where you are yeah I mean the + + + align:start position:0% +house where you are yeah I mean the +sensor uncertainty but you know you just + + align:start position:0% +sensor uncertainty but you know you just + + + align:start position:0% +sensor uncertainty but you know you just +may happen to be + + align:start position:0% +may happen to be + + + align:start position:0% +may happen to be +you know if you're doing the glider + + align:start position:0% +you know if you're doing the glider + + + align:start position:0% +you know if you're doing the glider +experiment ten times you know you may + + align:start position:0% +experiment ten times you know you may + + + align:start position:0% +experiment ten times you know you may +not started from exactly the same + + align:start position:0% +not started from exactly the same + + + align:start position:0% +not started from exactly the same +position every time yeah well you should + + align:start position:0% +position every time yeah well you should + + + align:start position:0% +position every time yeah well you should +your your every time that you funnel you + + align:start position:0% +your your every time that you funnel you + + + align:start position:0% +your your every time that you funnel you +start at anomalous rejection of that in + + align:start position:0% +start at anomalous rejection of that in + + + align:start position:0% +start at anomalous rejection of that in +front so you know you're not gonna have + + align:start position:0% +front so you know you're not gonna have + + + align:start position:0% +front so you know you're not gonna have +this funnel and you're not you're never + + align:start position:0% +this funnel and you're not you're never + + + align:start position:0% +this funnel and you're not you're never +going to start over here on the first + + align:start position:0% +going to start over here on the first + + + align:start position:0% +going to start over here on the first +one you're always going to start at this + + align:start position:0% +one you're always going to start at this + + + align:start position:0% +one you're always going to start at this +point well I know the point of the + + align:start position:0% +point well I know the point of the + + + align:start position:0% +point well I know the point of the +funnel is so that you can reuse it + + align:start position:0% +funnel is so that you can reuse it + + + align:start position:0% +funnel is so that you can reuse it +without having to replan yeah you gave + + align:start position:0% +without having to replan yeah you gave + + + align:start position:0% +without having to replan yeah you gave +you can move the fumbles around you can + + align:start position:0% +you can move the fumbles around you can + + + align:start position:0% +you can move the fumbles around you can +move yeah yeah that was um so yeah so + + align:start position:0% +move yeah yeah that was um so yeah so + + + align:start position:0% +move yeah yeah that was um so yeah so +every time you start to follow if you + + align:start position:0% +every time you start to follow if you + + + align:start position:0% +every time you start to follow if you +start having to stop multi Factory but + + align:start position:0% +start having to stop multi Factory but + + + align:start position:0% +start having to stop multi Factory but +the next time you use the same model you + + align:start position:0% +the next time you use the same model you + + + align:start position:0% +the next time you use the same model you +could be over here and just ship them + + align:start position:0% +could be over here and just ship them + + + align:start position:0% +could be over here and just ship them +down to exactly the same point so the + + align:start position:0% +down to exactly the same point so the + + + align:start position:0% +down to exactly the same point so the +initial state is never going to be any + + align:start position:0% +initial state is never going to be any + + + align:start position:0% +initial state is never going to be any +where it's starting at zero is not going + + align:start position:0% +where it's starting at zero is not going + + + align:start position:0% +where it's starting at zero is not going +to be somewhere other than the nominal + + align:start position:0% +to be somewhere other than the nominal + + + align:start position:0% +to be somewhere other than the nominal +trajectory but that's one it could be + + align:start position:0% +trajectory but that's one it could be + + + align:start position:0% +trajectory but that's one it could be +over here and you just ship the whole + + align:start position:0% +over here and you just ship the whole + + + align:start position:0% +over here and you just ship the whole +whole round and as long as routine zero + + align:start position:0% +whole round and as long as routine zero + + + align:start position:0% +whole round and as long as routine zero +and as long as t0 in the boat + + align:start position:0% +and as long as t0 in the boat + + + align:start position:0% +and as long as t0 in the boat +[Music] + + align:start position:0% + + + + align:start position:0% + +you can also like turn it as long as we + + align:start position:0% +you can also like turn it as long as we + + + align:start position:0% +you can also like turn it as long as we +get + + align:start position:0% +get + + + align:start position:0% +get +with my business it seemed like this + + align:start position:0% +with my business it seemed like this + + + align:start position:0% +with my business it seemed like this +shifting of turning it's a pretty + + align:start position:0% +shifting of turning it's a pretty + + + align:start position:0% +shifting of turning it's a pretty +complex search problem in itself like is + + align:start position:0% +complex search problem in itself like is + + + align:start position:0% +complex search problem in itself like is +that that's a hard problem now that was + + align:start position:0% +that that's a hard problem now that was + + + align:start position:0% +that that's a hard problem now that was +actually the get rid of this somebody + + align:start position:0% +actually the get rid of this somebody + + + align:start position:0% +actually the get rid of this somebody +else I should have found the work very + + align:start position:0% +else I should have found the work very + + + align:start position:0% +else I should have found the work very +differently + + align:start position:0% + + + + align:start position:0% + +but yeah there's I mean there's a bunch + + align:start position:0% +but yeah there's I mean there's a bunch + + + align:start position:0% +but yeah there's I mean there's a bunch +of different ways to do it I did a + + align:start position:0% +of different ways to do it I did a + + + align:start position:0% +of different ways to do it I did a +pretty not very smart search where I + + align:start position:0% +pretty not very smart search where I + + + align:start position:0% +pretty not very smart search where I +just looked for the funnels the safest + + align:start position:0% +just looked for the funnels the safest + + + align:start position:0% +just looked for the funnels the safest +funnel being the one with the least + + align:start position:0% +funnel being the one with the least + + + align:start position:0% +funnel being the one with the least +number of points in the point dog within + + align:start position:0% +number of points in the point dog within + + + align:start position:0% +number of points in the point dog within +that entire funnel and then managing + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +but basically what I did was find the + + align:start position:0% +but basically what I did was find the + + + align:start position:0% +but basically what I did was find the +safest funnel and make there still was a + + align:start position:0% +safest funnel and make there still was a + + + align:start position:0% +safest funnel and make there still was a +collision collision within the safest + + align:start position:0% +collision collision within the safest + + + align:start position:0% +collision collision within the safest +funneled and I had made our minimization + + align:start position:0% +funneled and I had made our minimization + + + align:start position:0% +funneled and I had made our minimization +problem and as you shifted back and + + align:start position:0% +problem and as you shifted back and + + + align:start position:0% +problem and as you shifted back and +forth and there was a cost function so + + align:start position:0% +forth and there was a cost function so + + + align:start position:0% +forth and there was a cost function so +you're not doing an optimization of the + + align:start position:0% +you're not doing an optimization of the + + + align:start position:0% +you're not doing an optimization of the +online wedding yeah that was an input + + align:start position:0% +online wedding yeah that was an input + + + align:start position:0% +online wedding yeah that was an input +that was implemented in real time + + align:start position:0% +that was implemented in real time + + + align:start position:0% +that was implemented in real time +simulation but that wasn't implemented + + align:start position:0% +simulation but that wasn't implemented + + + align:start position:0% +simulation but that wasn't implemented +on the actual glider + + align:start position:0% +on the actual glider + + + align:start position:0% +on the actual glider +as a + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +and you also want I also made it so you + + align:start position:0% +and you also want I also made it so you + + + align:start position:0% +and you also want I also made it so you +minimize the amount that you've shifted + + align:start position:0% +minimize the amount that you've shifted + + + align:start position:0% +minimize the amount that you've shifted +to so you don't want to shift it + + align:start position:0% +to so you don't want to shift it + + + align:start position:0% +to so you don't want to shift it +completely somewhere else is you won't + + align:start position:0% +completely somewhere else is you won't + + + align:start position:0% +completely somewhere else is you won't +be in your path and you'll end up doing + + align:start position:0% +be in your path and you'll end up doing + + + align:start position:0% +be in your path and you'll end up doing +so dynamic it appears I think you'll be + + align:start position:0% +so dynamic it appears I think you'll be + + + align:start position:0% +so dynamic it appears I think you'll be +flying and then if you compute a funnel + + align:start position:0% +flying and then if you compute a funnel + + + align:start position:0% +flying and then if you compute a funnel +that's here that's kind of safe when you + + align:start position:0% +that's here that's kind of safe when you + + + align:start position:0% +that's here that's kind of safe when you +shift it all the way down to here your + + align:start position:0% +shift it all the way down to here your + + + align:start position:0% +shift it all the way down to here your +bladders gonna be doing something crazy + + align:start position:0% +bladders gonna be doing something crazy + + + align:start position:0% +bladders gonna be doing something crazy +that made oh I guess it would be Ken + + align:start position:0% +that made oh I guess it would be Ken + + + align:start position:0% +that made oh I guess it would be Ken +but I mean it might say for + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yes it is anybody being + + align:start position:0% +yes it is anybody being + + + align:start position:0% +yes it is anybody being +Castellon huh so um so you've given us + + align:start position:0% +Castellon huh so um so you've given us + + + align:start position:0% +Castellon huh so um so you've given us +models of bounded uncertainty in urinal + + align:start position:0% +models of bounded uncertainty in urinal + + + align:start position:0% +models of bounded uncertainty in urinal +dynamics so if you use probabilistic + + align:start position:0% +dynamics so if you use probabilistic + + + align:start position:0% +dynamics so if you use probabilistic +models then your phone will start + + align:start position:0% +models then your phone will start + + + align:start position:0% +models then your phone will start +looking like risk allocations is there + + align:start position:0% +looking like risk allocations is there + + + align:start position:0% +looking like risk allocations is there +and an interpretation of one + + align:start position:0% +and an interpretation of one + + + align:start position:0% +and an interpretation of one +[Music] + + align:start position:0% + + + + align:start position:0% + +talk a little bit about the interaction + + align:start position:0% +talk a little bit about the interaction + + + align:start position:0% +talk a little bit about the interaction +between the selection at the Thomas + + align:start position:0% +between the selection at the Thomas + + + align:start position:0% +between the selection at the Thomas +elections and the underlying type of + + align:start position:0% +elections and the underlying type of + + + align:start position:0% +elections and the underlying type of +matter so you know something that's + + align:start position:0% +matter so you know something that's + + + align:start position:0% +matter so you know something that's +planning the reference trajectory right + + align:start position:0% +planning the reference trajectory right + + + align:start position:0% +planning the reference trajectory right +that's separate from their flow to + + align:start position:0% +that's separate from their flow to + + + align:start position:0% +that's separate from their flow to +selection area very long selection and + + align:start position:0% +selection area very long selection and + + + align:start position:0% +selection area very long selection and +then you have this like the funnels or + + align:start position:0% +then you have this like the funnels or + + + align:start position:0% +then you have this like the funnels or +flow tubes that allow you to follow that + + align:start position:0% +flow tubes that allow you to follow that + + + align:start position:0% +flow tubes that allow you to follow that +that trajectory the list you can pull + + align:start position:0% +that trajectory the list you can pull + + + align:start position:0% +that trajectory the list you can pull +with or how do they interact like say if + + align:start position:0% +with or how do they interact like say if + + + align:start position:0% +with or how do they interact like say if +you have a bullet or don't have a safe + + align:start position:0% +you have a bullet or don't have a safe + + + align:start position:0% +you have a bullet or don't have a safe +for ^ v reference trajectory okay so + + align:start position:0% +for ^ v reference trajectory okay so + + + align:start position:0% +for ^ v reference trajectory okay so +it's you're asking basically difficulty + + align:start position:0% +it's you're asking basically difficulty + + + align:start position:0% +it's you're asking basically difficulty +planning with the library yeah kind of + + align:start position:0% +planning with the library yeah kind of + + + align:start position:0% +planning with the library yeah kind of +well because like I know like the the + + align:start position:0% +well because like I know like the the + + + align:start position:0% +well because like I know like the the +checkout planner that uses like the + + align:start position:0% +checkout planner that uses like the + + + align:start position:0% +checkout planner that uses like the +incremental half signer writes the path + + align:start position:0% +incremental half signer writes the path + + + align:start position:0% +incremental half signer writes the path +or something like that + + align:start position:0% +or something like that + + + align:start position:0% +or something like that +thank you that could is it are you + + align:start position:0% +thank you that could is it are you + + + align:start position:0% +thank you that could is it are you +fitting flow tube so the reference + + align:start position:0% +fitting flow tube so the reference + + + align:start position:0% +fitting flow tube so the reference +directly but you do that offline so you + + align:start position:0% +directly but you do that offline so you + + + align:start position:0% +directly but you do that offline so you +can keep they're good they're called + + align:start position:0% +can keep they're good they're called + + + align:start position:0% +can keep they're good they're called +like funnel libraries or usually learn + + align:start position:0% +like funnel libraries or usually learn + + + align:start position:0% +like funnel libraries or usually learn +trabecular libraries so here in + + align:start position:0% +trabecular libraries so here in + + + align:start position:0% +trabecular libraries so here in +computing a trajectory in real time for + + align:start position:0% +computing a trajectory in real time for + + + align:start position:0% +computing a trajectory in real time for +a fascinating dynamic system is going to + + align:start position:0% +a fascinating dynamic system is going to + + + align:start position:0% +a fascinating dynamic system is going to +be expensive and then + + align:start position:0% +be expensive and then + + + align:start position:0% +be expensive and then +in a puddle up top that can be more + + align:start position:0% +in a puddle up top that can be more + + + align:start position:0% +in a puddle up top that can be more +expensive so Allah or a lot of people do + + align:start position:0% +expensive so Allah or a lot of people do + + + align:start position:0% +expensive so Allah or a lot of people do +is they can keep the library offline for + + align:start position:0% +is they can keep the library offline for + + + align:start position:0% +is they can keep the library offline for +a trajectory and plan using that but on + + align:start position:0% +a trajectory and plan using that but on + + + align:start position:0% +a trajectory and plan using that but on +this morning you compute your trajectory + + align:start position:0% +this morning you compute your trajectory + + + align:start position:0% +this morning you compute your trajectory +compute the funnel around that + + align:start position:0% +compute the funnel around that + + + align:start position:0% +compute the funnel around that +trajectory offline and then search + + align:start position:0% +trajectory offline and then search + + + align:start position:0% +trajectory offline and then search +through the funnel live radio search + + align:start position:0% +through the funnel live radio search + + + align:start position:0% +through the funnel live radio search +through trajectories and then run a bit + + align:start position:0% +through trajectories and then run a bit + + + align:start position:0% +through trajectories and then run a bit +of fun around them you just search also + + align:start position:0% +of fun around them you just search also + + + align:start position:0% +of fun around them you just search also +a cool thing about models for sister + + align:start position:0% +a cool thing about models for sister + + + align:start position:0% +a cool thing about models for sister +countries is a lot of trajectories will + + align:start position:0% +countries is a lot of trajectories will + + + align:start position:0% +countries is a lot of trajectories will +be discretized for so you have your + + align:start position:0% +be discretized for so you have your + + + align:start position:0% +be discretized for so you have your +nodes and so say this is where your + + align:start position:0% +nodes and so say this is where your + + + align:start position:0% +nodes and so say this is where your +trajectory does and you have node points + + align:start position:0% +trajectory does and you have node points + + + align:start position:0% +trajectory does and you have node points +here and you're trying to fly it past a + + align:start position:0% +here and you're trying to fly it past a + + + align:start position:0% +here and you're trying to fly it past a +wall or something + + align:start position:0% +wall or something + + + align:start position:0% +wall or something +if your wall goes here your algorithm + + align:start position:0% +if your wall goes here your algorithm + + + align:start position:0% +if your wall goes here your algorithm +just going to search these points and + + align:start position:0% +just going to search these points and + + + align:start position:0% +just going to search these points and +it's gonna say okay roll and this is a + + align:start position:0% +it's gonna say okay roll and this is a + + + align:start position:0% +it's gonna say okay roll and this is a +safe path under the node points + + align:start position:0% +safe path under the node points + + + align:start position:0% +safe path under the node points +intersect with this walls to fly + + align:start position:0% + + + + align:start position:0% + +but a funnel since you have this return + + align:start position:0% +but a funnel since you have this return + + + align:start position:0% +but a funnel since you have this return +around it + + align:start position:0% +around it + + + align:start position:0% +around it +you made a batch of it on that + + align:start position:0% + + + + align:start position:0% + +when we search this the algorithm can + + align:start position:0% +when we search this the algorithm can + + + align:start position:0% +when we search this the algorithm can +see if it's a less than a greater than + + align:start position:0% +see if it's a less than a greater than + + + align:start position:0% +see if it's a less than a greater than +one you're going to find all these + + align:start position:0% +one you're going to find all these + + + align:start position:0% +one you're going to find all these +points in that region but I guess that + + align:start position:0% +points in that region but I guess that + + + align:start position:0% +points in that region but I guess that +depends on how well you want to + + align:start position:0% +depends on how well you want to + + + align:start position:0% +depends on how well you want to +discretize it if your trajectory there + + align:start position:0% +discretize it if your trajectory there + + + align:start position:0% +discretize it if your trajectory there +were two small points that you're not a + + align:start position:0% +were two small points that you're not a + + + align:start position:0% +were two small points that you're not a +fetish + + align:start position:0% + + + + align:start position:0% + +seems like you could like we're building + + align:start position:0% +seems like you could like we're building + + + align:start position:0% +seems like you could like we're building +a normal are key without punish truncate + + align:start position:0% +a normal are key without punish truncate + + + align:start position:0% +a normal are key without punish truncate +points did you say other illegal seems + + align:start position:0% +points did you say other illegal seems + + + align:start position:0% +points did you say other illegal seems +that if you're automatically adding on + + align:start position:0% +that if you're automatically adding on + + + align:start position:0% +that if you're automatically adding on +that funnel instead of generating an + + align:start position:0% +that funnel instead of generating an + + + align:start position:0% +that funnel instead of generating an +entire trajectory and I made a puddle + + align:start position:0% +entire trajectory and I made a puddle + + + align:start position:0% +entire trajectory and I made a puddle +you can save occasional time for some + + align:start position:0% +you can save occasional time for some + + + align:start position:0% +you can save occasional time for some +things like that do you know if that's + + align:start position:0% +things like that do you know if that's + + + align:start position:0% +things like that do you know if that's +done I do know that we come to you + + align:start position:0% +done I do know that we come to you + + + align:start position:0% +done I do know that we come to you +obviously would minimize computation + + align:start position:0% +obviously would minimize computation + + + align:start position:0% +obviously would minimize computation +time but it's not critical but also + + align:start position:0% +time but it's not critical but also + + + align:start position:0% +time but it's not critical but also +employed to do that all our flying so + + align:start position:0% +employed to do that all our flying so + + + align:start position:0% +employed to do that all our flying so +and you want to I don't think it's + + align:start position:0% + + + + align:start position:0% + +it takes like depending on how how many + + align:start position:0% +it takes like depending on how how many + + + align:start position:0% +it takes like depending on how how many +dimensional your state has yeah it's not + + align:start position:0% +dimensional your state has yeah it's not + + + align:start position:0% +dimensional your state has yeah it's not +like you're flying one of these things + + align:start position:0% +like you're flying one of these things + + + align:start position:0% +like you're flying one of these things +go crash + + align:start position:0% + + + + align:start position:0% + +[Applause] \ No newline at end of file diff --git a/quSdhgX3NB8.txt b/quSdhgX3NB8.txt new file mode 100644 index 0000000000000000000000000000000000000000..a2013b7ae08e0d44fc33adc39c48878fdc8a9c32 --- /dev/null +++ b/quSdhgX3NB8.txt @@ -0,0 +1,2907 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +uh with this lecture i'd like to + + align:start position:0% +uh with this lecture i'd like to + + + align:start position:0% +uh with this lecture i'd like to +introduce the major players of this + + align:start position:0% +introduce the major players of this + + + align:start position:0% +introduce the major players of this +class the particles + + align:start position:0% +class the particles + + + align:start position:0% +class the particles +fundamental fundamental particles + + align:start position:0% +fundamental fundamental particles + + + align:start position:0% +fundamental fundamental particles +but also some of the compound particles + + align:start position:0% +but also some of the compound particles + + + align:start position:0% +but also some of the compound particles +which play a role in the discussions + + align:start position:0% +which play a role in the discussions + + + align:start position:0% +which play a role in the discussions +we'll have over the next weeks + + align:start position:0% + + + + align:start position:0% + +for centuries people believed + + align:start position:0% +for centuries people believed + + + align:start position:0% +for centuries people believed +that atoms are + + align:start position:0% +that atoms are + + + align:start position:0% +that atoms are +the most fundamental constitutions of + + align:start position:0% +the most fundamental constitutions of + + + align:start position:0% +the most fundamental constitutions of +matter + + align:start position:0% +matter + + + align:start position:0% +matter +the name atom comes from the greek + + align:start position:0% +the name atom comes from the greek + + + align:start position:0% +the name atom comes from the greek +atomic which means + + align:start position:0% +atomic which means + + + align:start position:0% +atomic which means +not divisible but as you know today + + align:start position:0% +not divisible but as you know today + + + align:start position:0% +not divisible but as you know today +electrons and nuclei build an atom + + align:start position:0% + + + + align:start position:0% + +but even those nuclei are not + + align:start position:0% +but even those nuclei are not + + + align:start position:0% +but even those nuclei are not +fundamental particles + + align:start position:0% +fundamental particles + + + align:start position:0% +fundamental particles +as you see nicely here in this picture + + align:start position:0% +as you see nicely here in this picture + + + align:start position:0% +as you see nicely here in this picture +the nuclei is built off + + align:start position:0% +the nuclei is built off + + + align:start position:0% +the nuclei is built off +and can be built out of many neutrons + + align:start position:0% +and can be built out of many neutrons + + + align:start position:0% +and can be built out of many neutrons +and protons + + align:start position:0% +and protons + + + align:start position:0% +and protons +and even those protons and neutrons are + + align:start position:0% +and even those protons and neutrons are + + + align:start position:0% +and even those protons and neutrons are +not fundamental particles + + align:start position:0% +not fundamental particles + + + align:start position:0% +not fundamental particles +a proton for example is depicted here um + + align:start position:0% +a proton for example is depicted here um + + + align:start position:0% +a proton for example is depicted here um +has three components or three + + align:start position:0% +has three components or three + + + align:start position:0% +has three components or three +constituents um + + align:start position:0% +constituents um + + + align:start position:0% +constituents um +two up to up quarks and one down quark a + + align:start position:0% +two up to up quarks and one down quark a + + + align:start position:0% +two up to up quarks and one down quark a +neutron then + + align:start position:0% +neutron then + + + align:start position:0% +neutron then +is built out of one down quark and two + + align:start position:0% +is built out of one down quark and two + + + align:start position:0% +is built out of one down quark and two +up quarks + + align:start position:0% +up quarks + + + align:start position:0% +up quarks +um it is kind of important to understand + + align:start position:0% +um it is kind of important to understand + + + align:start position:0% +um it is kind of important to understand +and appreciate + + align:start position:0% +and appreciate + + + align:start position:0% +and appreciate +the size of those particles + + align:start position:0% +the size of those particles + + + align:start position:0% +the size of those particles +um specifically the difference in size + + align:start position:0% +um specifically the difference in size + + + align:start position:0% +um specifically the difference in size +comparing here an + + align:start position:0% +comparing here an + + + align:start position:0% +comparing here an +atom a typical atom of the size of 10 to + + align:start position:0% +atom a typical atom of the size of 10 to + + + align:start position:0% +atom a typical atom of the size of 10 to +the minus 10 meters + + align:start position:0% +the minus 10 meters + + + align:start position:0% +the minus 10 meters +and that compares to a nucleon which can + + align:start position:0% +and that compares to a nucleon which can + + + align:start position:0% +and that compares to a nucleon which can +be a few + + align:start position:0% +be a few + + + align:start position:0% +be a few +10 10 to the minus 15 meters + + align:start position:0% +10 10 to the minus 15 meters + + + align:start position:0% +10 10 to the minus 15 meters +when we talk about a proton typically + + align:start position:0% +when we talk about a proton typically + + + align:start position:0% +when we talk about a proton typically +like to use + + align:start position:0% +like to use + + + align:start position:0% +like to use +um units of femtometers which is 10 + + align:start position:0% +um units of femtometers which is 10 + + + align:start position:0% +um units of femtometers which is 10 +minus 10 to the minus 15 meters + + align:start position:0% +minus 10 to the minus 15 meters + + + align:start position:0% +minus 10 to the minus 15 meters +um the tremendous size different + + align:start position:0% +um the tremendous size different + + + align:start position:0% +um the tremendous size different +also explains the finding of the famous + + align:start position:0% +also explains the finding of the famous + + + align:start position:0% +also explains the finding of the famous +gold foil experiment + + align:start position:0% +gold foil experiment + + + align:start position:0% +gold foil experiment +which found that an atom basically is + + align:start position:0% +which found that an atom basically is + + + align:start position:0% +which found that an atom basically is +made out of + + align:start position:0% +made out of + + + align:start position:0% +made out of +nothingness empty space and a very dense + + align:start position:0% +nothingness empty space and a very dense + + + align:start position:0% +nothingness empty space and a very dense +charged core the nucleus so you see this + + align:start position:0% +charged core the nucleus so you see this + + + align:start position:0% +charged core the nucleus so you see this +very much in this picture and by + + align:start position:0% +very much in this picture and by + + + align:start position:0% +very much in this picture and by +comparing those order of magnitudes + + align:start position:0% +comparing those order of magnitudes + + + align:start position:0% +comparing those order of magnitudes +not shown in this picture here is a + + align:start position:0% +not shown in this picture here is a + + + align:start position:0% +not shown in this picture here is a +particle + + align:start position:0% +particle + + + align:start position:0% +particle +which doesn't really like to interact + + align:start position:0% +which doesn't really like to interact + + + align:start position:0% +which doesn't really like to interact +with anybody else + + align:start position:0% +with anybody else + + + align:start position:0% +with anybody else +or which the forces it's interacting + + align:start position:0% +or which the forces it's interacting + + + align:start position:0% +or which the forces it's interacting +with are so weak that it cannot be + + align:start position:0% +with are so weak that it cannot be + + + align:start position:0% +with are so weak that it cannot be +bound and that is certain neutrino a + + align:start position:0% +bound and that is certain neutrino a + + + align:start position:0% +bound and that is certain neutrino a +neutrino is not that different from an + + align:start position:0% +neutrino is not that different from an + + + align:start position:0% +neutrino is not that different from an +electron + + align:start position:0% +electron + + + align:start position:0% +electron +or from a quark it's just that the + + align:start position:0% +or from a quark it's just that the + + + align:start position:0% +or from a quark it's just that the +interactions + + align:start position:0% +interactions + + + align:start position:0% +interactions +it participates in um + + align:start position:0% +it participates in um + + + align:start position:0% +it participates in um +are only the weak force as we understand + + align:start position:0% +are only the weak force as we understand + + + align:start position:0% +are only the weak force as we understand +today + + align:start position:0% + + + + align:start position:0% + +um just to be clear when i talk about a + + align:start position:0% +um just to be clear when i talk about a + + + align:start position:0% +um just to be clear when i talk about a +fundamental particle i talk about a + + align:start position:0% +fundamental particle i talk about a + + + align:start position:0% +fundamental particle i talk about a +particle + + align:start position:0% +particle + + + align:start position:0% +particle +um which has no size it's + + align:start position:0% +um which has no size it's + + + align:start position:0% +um which has no size it's +infinitely infinitely small + + align:start position:0% +infinitely infinitely small + + + align:start position:0% +infinitely infinitely small +um it has no substructure meaning it + + align:start position:0% +um it has no substructure meaning it + + + align:start position:0% +um it has no substructure meaning it +cannot be broken up in constituents + + align:start position:0% +cannot be broken up in constituents + + + align:start position:0% +cannot be broken up in constituents +um and can also not be excited + + align:start position:0% +um and can also not be excited + + + align:start position:0% +um and can also not be excited +having said that this is our current + + align:start position:0% +having said that this is our current + + + align:start position:0% +having said that this is our current +understanding of nature + + align:start position:0% +understanding of nature + + + align:start position:0% +understanding of nature +and of those particles experimentally we + + align:start position:0% +and of those particles experimentally we + + + align:start position:0% +and of those particles experimentally we +can only probe + + align:start position:0% +can only probe + + + align:start position:0% +can only probe +those particles to a certain scale or + + align:start position:0% +those particles to a certain scale or + + + align:start position:0% +those particles to a certain scale or +size + + align:start position:0% +size + + + align:start position:0% +size +and we'll talk later about how precisely + + align:start position:0% +and we'll talk later about how precisely + + + align:start position:0% +and we'll talk later about how precisely +we actually do know that a quark is + + align:start position:0% +we actually do know that a quark is + + + align:start position:0% +we actually do know that a quark is +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +or an electron is fundamental + + align:start position:0% +or an electron is fundamental + + + align:start position:0% +or an electron is fundamental +in this discussion here in most of the + + align:start position:0% +in this discussion here in most of the + + + align:start position:0% +in this discussion here in most of the +lecture i'll talk about a standard model + + align:start position:0% +lecture i'll talk about a standard model + + + align:start position:0% +lecture i'll talk about a standard model +in particle physics + + align:start position:0% + + + + align:start position:0% + +it is a fact that our measurements + + align:start position:0% +it is a fact that our measurements + + + align:start position:0% +it is a fact that our measurements +and our experimental of findings are in + + align:start position:0% +and our experimental of findings are in + + + align:start position:0% +and our experimental of findings are in +uh fantastic agreement with this very + + align:start position:0% +uh fantastic agreement with this very + + + align:start position:0% +uh fantastic agreement with this very +predictive predictive + + align:start position:0% +predictive predictive + + + align:start position:0% +predictive predictive +theory um the only + + align:start position:0% +theory um the only + + + align:start position:0% +theory um the only +uh experimental deviation from this is + + align:start position:0% +uh experimental deviation from this is + + + align:start position:0% +uh experimental deviation from this is +the fact that we measure the mass of + + align:start position:0% +the fact that we measure the mass of + + + align:start position:0% +the fact that we measure the mass of +neutrinos to be non-zero + + align:start position:0% +neutrinos to be non-zero + + + align:start position:0% +neutrinos to be non-zero +um as a consequence you know you could + + align:start position:0% +um as a consequence you know you could + + + align:start position:0% +um as a consequence you know you could +say the standard model is broken or we + + align:start position:0% +say the standard model is broken or we + + + align:start position:0% +say the standard model is broken or we +found physics beyond the standard model + + align:start position:0% +found physics beyond the standard model + + + align:start position:0% +found physics beyond the standard model +but it is actually rather + + align:start position:0% +but it is actually rather + + + align:start position:0% +but it is actually rather +straightforward to extend the standard + + align:start position:0% +straightforward to extend the standard + + + align:start position:0% +straightforward to extend the standard +model to accommodate neutrino masses so + + align:start position:0% +model to accommodate neutrino masses so + + + align:start position:0% +model to accommodate neutrino masses so +we can + + align:start position:0% +we can + + + align:start position:0% +we can +you know just forget about this small + + align:start position:0% +you know just forget about this small + + + align:start position:0% +you know just forget about this small +fact and assume that the standard model + + align:start position:0% +fact and assume that the standard model + + + align:start position:0% +fact and assume that the standard model +described nature as we know it + + align:start position:0% +described nature as we know it + + + align:start position:0% +described nature as we know it +in the last week of this class we'll + + align:start position:0% +in the last week of this class we'll + + + align:start position:0% +in the last week of this class we'll +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +motivation why you think that the + + align:start position:0% +motivation why you think that the + + + align:start position:0% +motivation why you think that the +standard model in fact is not complete + + align:start position:0% +standard model in fact is not complete + + + align:start position:0% +standard model in fact is not complete +and one of the big drivers here is the + + align:start position:0% +and one of the big drivers here is the + + + align:start position:0% +and one of the big drivers here is the +fact that we cannot + + align:start position:0% +fact that we cannot + + + align:start position:0% +fact that we cannot +observe describe all of the observations + + align:start position:0% +observe describe all of the observations + + + align:start position:0% +observe describe all of the observations +in nature + + align:start position:0% +in nature + + + align:start position:0% +in nature +specifically the observation of dark + + align:start position:0% +specifically the observation of dark + + + align:start position:0% +specifically the observation of dark +matter + + align:start position:0% +matter + + + align:start position:0% +matter +with the standard model in multiple + + align:start position:0% +with the standard model in multiple + + + align:start position:0% +with the standard model in multiple +physics but that's for later day + + align:start position:0% + + + + align:start position:0% + +looking into some more detail the + + align:start position:0% +looking into some more detail the + + + align:start position:0% +looking into some more detail the +standard model has + + align:start position:0% +standard model has + + + align:start position:0% +standard model has +sets of particles some are particles + + align:start position:0% +sets of particles some are particles + + + align:start position:0% +sets of particles some are particles +which carry forces + + align:start position:0% +which carry forces + + + align:start position:0% +which carry forces +and some are metaparticles the ones who + + align:start position:0% +and some are metaparticles the ones who + + + align:start position:0% +and some are metaparticles the ones who +carry forces are all spin-one vertical + + align:start position:0% +carry forces are all spin-one vertical + + + align:start position:0% +carry forces are all spin-one vertical +particles and their bosons with that + + align:start position:0% +particles and their bosons with that + + + align:start position:0% +particles and their bosons with that +we have in the standard model describe + + align:start position:0% +we have in the standard model describe + + + align:start position:0% +we have in the standard model describe +three interactions the electromagnetic + + align:start position:0% +three interactions the electromagnetic + + + align:start position:0% +three interactions the electromagnetic +interactions which you all know from + + align:start position:0% +interactions which you all know from + + + align:start position:0% +interactions which you all know from +light electromagnetic phenomena + + align:start position:0% +light electromagnetic phenomena + + + align:start position:0% +light electromagnetic phenomena +chemistry you know the atoms behavior + + align:start position:0% +chemistry you know the atoms behavior + + + align:start position:0% +chemistry you know the atoms behavior +molecule + + align:start position:0% +molecule + + + align:start position:0% +molecule +is determined by electromagnetic + + align:start position:0% +is determined by electromagnetic + + + align:start position:0% +is determined by electromagnetic +interactions + + align:start position:0% +interactions + + + align:start position:0% +interactions +and then there's a strong interaction + + align:start position:0% +and then there's a strong interaction + + + align:start position:0% +and then there's a strong interaction +the name already tells you that it's + + align:start position:0% +the name already tells you that it's + + + align:start position:0% +the name already tells you that it's +strong it's very strong + + align:start position:0% +strong it's very strong + + + align:start position:0% +strong it's very strong +um the fourth carrier here is the gluon + + align:start position:0% +um the fourth carrier here is the gluon + + + align:start position:0% +um the fourth carrier here is the gluon +each clue + + align:start position:0% +each clue + + + align:start position:0% +each clue +the plunge there's eight and that + + align:start position:0% +the plunge there's eight and that + + + align:start position:0% +the plunge there's eight and that +differentiated + + align:start position:0% +differentiated + + + align:start position:0% +differentiated +differentiate by the so-called color + + align:start position:0% + + + + align:start position:0% + +which is an interesting effect + + align:start position:0% +which is an interesting effect + + + align:start position:0% +which is an interesting effect +and then there is the weak interaction + + align:start position:0% +and then there is the weak interaction + + + align:start position:0% +and then there is the weak interaction +um carried by the w boson and the z + + align:start position:0% +um carried by the w boson and the z + + + align:start position:0% +um carried by the w boson and the z +boson they are different they're on + + align:start position:0% +boson they are different they're on + + + align:start position:0% +boson they are different they're on +right because they carry a mass they are + + align:start position:0% +right because they carry a mass they are + + + align:start position:0% +right because they carry a mass they are +massive particles and they're actually + + align:start position:0% +massive particles and they're actually + + + align:start position:0% +massive particles and they're actually +quite heavy + + align:start position:0% +quite heavy + + + align:start position:0% +quite heavy +about 80 to 100 times as heavy + + align:start position:0% +about 80 to 100 times as heavy + + + align:start position:0% +about 80 to 100 times as heavy +as a proton + + align:start position:0% +as a proton + + + align:start position:0% +as a proton +um the weak interaction is responsible + + align:start position:0% +um the weak interaction is responsible + + + align:start position:0% +um the weak interaction is responsible +for neutron decays + + align:start position:0% +for neutron decays + + + align:start position:0% +for neutron decays +also responsible for the burning of the + + align:start position:0% +also responsible for the burning of the + + + align:start position:0% +also responsible for the burning of the +sun and in our nuclear physics part + + align:start position:0% +sun and in our nuclear physics part + + + align:start position:0% +sun and in our nuclear physics part +we'll talk + + align:start position:0% +we'll talk + + + align:start position:0% +we'll talk +in detail about what that all means the + + align:start position:0% +in detail about what that all means the + + + align:start position:0% +in detail about what that all means the +gravitational effects are not considered + + align:start position:0% +gravitational effects are not considered + + + align:start position:0% +gravitational effects are not considered +in the standard model they're very very + + align:start position:0% +in the standard model they're very very + + + align:start position:0% +in the standard model they're very very +weak + + align:start position:0% +weak + + + align:start position:0% +weak +compared to the strength of the other + + align:start position:0% +compared to the strength of the other + + + align:start position:0% +compared to the strength of the other +forces we'll discuss here + + align:start position:0% +forces we'll discuss here + + + align:start position:0% +forces we'll discuss here +but it's technically very difficult to + + align:start position:0% +but it's technically very difficult to + + + align:start position:0% +but it's technically very difficult to +actually accommodate + + align:start position:0% +actually accommodate + + + align:start position:0% +actually accommodate +gravity as part of a quantum field + + align:start position:0% +gravity as part of a quantum field + + + align:start position:0% +gravity as part of a quantum field +theory + + align:start position:0% +theory + + + align:start position:0% +theory +and therefore we can we will simply + + align:start position:0% +and therefore we can we will simply + + + align:start position:0% +and therefore we can we will simply +ignore this fact + + align:start position:0% +ignore this fact + + + align:start position:0% +ignore this fact +and that's yet another reason why you + + align:start position:0% +and that's yet another reason why you + + + align:start position:0% +and that's yet another reason why you +can consider the standard model to be + + align:start position:0% +can consider the standard model to be + + + align:start position:0% +can consider the standard model to be +incomplete as a + + align:start position:0% +incomplete as a + + + align:start position:0% +incomplete as a +model or theory describing nature + + align:start position:0% + + + + align:start position:0% + +the metaparticles themselves are all + + align:start position:0% +the metaparticles themselves are all + + + align:start position:0% +the metaparticles themselves are all +fermions they have spin half + + align:start position:0% +fermions they have spin half + + + align:start position:0% +fermions they have spin half +and they come in three different + + align:start position:0% +and they come in three different + + + align:start position:0% +and they come in three different +generations the only difference between + + align:start position:0% +generations the only difference between + + + align:start position:0% +generations the only difference between +one generation to the next is the fact + + align:start position:0% +one generation to the next is the fact + + + align:start position:0% +one generation to the next is the fact +that + + align:start position:0% +that + + + align:start position:0% +that +those particles have different mass + + align:start position:0% +those particles have different mass + + + align:start position:0% +those particles have different mass +in other words their coupling to the + + align:start position:0% +in other words their coupling to the + + + align:start position:0% +in other words their coupling to the +higgs field is different + + align:start position:0% +higgs field is different + + + align:start position:0% +higgs field is different +and that's the only difference between + + align:start position:0% +and that's the only difference between + + + align:start position:0% +and that's the only difference between +those particles there's consequences + + align:start position:0% +those particles there's consequences + + + align:start position:0% +those particles there's consequences +out of this for example heavier + + align:start position:0% +out of this for example heavier + + + align:start position:0% +out of this for example heavier +particles + + align:start position:0% +particles + + + align:start position:0% +particles +can decay into lighter particles + + align:start position:0% +can decay into lighter particles + + + align:start position:0% +can decay into lighter particles +we differentiate between the quarks and + + align:start position:0% +we differentiate between the quarks and + + + align:start position:0% +we differentiate between the quarks and +leptons quarks + + align:start position:0% +leptons quarks + + + align:start position:0% +leptons quarks +partake in the strong interactions where + + align:start position:0% +partake in the strong interactions where + + + align:start position:0% +partake in the strong interactions where +leptons are neutral + + align:start position:0% +leptons are neutral + + + align:start position:0% +leptons are neutral +in the strong interaction and then we + + align:start position:0% +in the strong interaction and then we + + + align:start position:0% +in the strong interaction and then we +have seen neutrinos already and + + align:start position:0% +have seen neutrinos already and + + + align:start position:0% +have seen neutrinos already and +electron type particles electron type + + align:start position:0% +electron type particles electron type + + + align:start position:0% +electron type particles electron type +particles + + align:start position:0% +particles + + + align:start position:0% +particles +the charged leptons they have electric + + align:start position:0% +the charged leptons they have electric + + + align:start position:0% +the charged leptons they have electric +charge so they + + align:start position:0% +charge so they + + + align:start position:0% +charge so they +coupled to photons by neutrinos don't + + align:start position:0% +coupled to photons by neutrinos don't + + + align:start position:0% +coupled to photons by neutrinos don't +i show you here again one of those + + align:start position:0% +i show you here again one of those + + + align:start position:0% +i show you here again one of those +striking differences + + align:start position:0% +striking differences + + + align:start position:0% +striking differences +an electron is 9 times 10 to the minus + + align:start position:0% +an electron is 9 times 10 to the minus + + + align:start position:0% +an electron is 9 times 10 to the minus +31 kilogram heavy + + align:start position:0% +31 kilogram heavy + + + align:start position:0% +31 kilogram heavy +we like to talk about units in a + + align:start position:0% +we like to talk about units in a + + + align:start position:0% +we like to talk about units in a +different class + + align:start position:0% +different class + + + align:start position:0% +different class +but that's 511 kev + + align:start position:0% +but that's 511 kev + + + align:start position:0% +but that's 511 kev +why the muon is about 200 times heavier + + align:start position:0% +why the muon is about 200 times heavier + + + align:start position:0% +why the muon is about 200 times heavier +and even heavier as a tower lepton + + align:start position:0% +and even heavier as a tower lepton + + + align:start position:0% +and even heavier as a tower lepton +as i said before that allows the tau + + align:start position:0% +as i said before that allows the tau + + + align:start position:0% +as i said before that allows the tau +lepton and also the muons to decay into + + align:start position:0% +lepton and also the muons to decay into + + + align:start position:0% +lepton and also the muons to decay into +lighter particles + + align:start position:0% +lighter particles + + + align:start position:0% +lighter particles +i will talk about this this and how how + + align:start position:0% +i will talk about this this and how how + + + align:start position:0% +i will talk about this this and how how +we can use those decays in order to + + align:start position:0% +we can use those decays in order to + + + align:start position:0% +we can use those decays in order to +learn about the standard modulator + + align:start position:0% +learn about the standard modulator + + + align:start position:0% +learn about the standard modulator +and then there is a higgs boson and + + align:start position:0% +and then there is a higgs boson and + + + align:start position:0% +and then there is a higgs boson and +again the higgs boson discovered in 2012 + + align:start position:0% +again the higgs boson discovered in 2012 + + + align:start position:0% +again the higgs boson discovered in 2012 +space plays a very special role in the + + align:start position:0% +space plays a very special role in the + + + align:start position:0% +space plays a very special role in the +in the standard mode + + align:start position:0% +in the standard mode + + + align:start position:0% +in the standard mode +we talked about the lagrange and the + + align:start position:0% +we talked about the lagrange and the + + + align:start position:0% +we talked about the lagrange and the +theory + + align:start position:0% +theory + + + align:start position:0% +theory +um which describes the standard model or + + align:start position:0% +um which describes the standard model or + + + align:start position:0% +um which describes the standard model or +which is you know the basic there's a + + align:start position:0% +which is you know the basic there's a + + + align:start position:0% +which is you know the basic there's a +theory itself + + align:start position:0% +theory itself + + + align:start position:0% +theory itself +later on in this theory we introduce a + + align:start position:0% +later on in this theory we introduce a + + + align:start position:0% +later on in this theory we introduce a +potential which is shown here this + + align:start position:0% + + + + align:start position:0% + +mexican head if you want potential and + + align:start position:0% +mexican head if you want potential and + + + align:start position:0% +mexican head if you want potential and +what you see here is that in this + + align:start position:0% +what you see here is that in this + + + align:start position:0% +what you see here is that in this +picture that the lowest energy state of + + align:start position:0% +picture that the lowest energy state of + + + align:start position:0% +picture that the lowest energy state of +this potential + + align:start position:0% +this potential + + + align:start position:0% +this potential +breaks a symmetry so it's away from the + + align:start position:0% +breaks a symmetry so it's away from the + + + align:start position:0% +breaks a symmetry so it's away from the +zero point + + align:start position:0% +zero point + + + align:start position:0% +zero point +and that symmetry breaking then gives + + align:start position:0% +and that symmetry breaking then gives + + + align:start position:0% +and that symmetry breaking then gives +mass to the w and the z boson which i + + align:start position:0% +mass to the w and the z boson which i + + + align:start position:0% +mass to the w and the z boson which i +was describing before + + align:start position:0% +was describing before + + + align:start position:0% +was describing before +and the coupling of metaparticles to the + + align:start position:0% +and the coupling of metaparticles to the + + + align:start position:0% +and the coupling of metaparticles to the +higgs field gives masses as particles + + align:start position:0% +higgs field gives masses as particles + + + align:start position:0% +higgs field gives masses as particles +all this on a later date i thought here + + align:start position:0% +all this on a later date i thought here + + + align:start position:0% +all this on a later date i thought here +i also give you how cern actually + + align:start position:0% +i also give you how cern actually + + + align:start position:0% +i also give you how cern actually +depicts + + align:start position:0% +depicts + + + align:start position:0% +depicts +um the higgs boson july 4th is a special + + align:start position:0% +um the higgs boson july 4th is a special + + + align:start position:0% +um the higgs boson july 4th is a special +day in the us but it's also a special + + align:start position:0% +day in the us but it's also a special + + + align:start position:0% +day in the us but it's also a special +day + + align:start position:0% +day + + + align:start position:0% +day +at cern because the higgs discovery has + + align:start position:0% +at cern because the higgs discovery has + + + align:start position:0% +at cern because the higgs discovery has +been announced on this day + + align:start position:0% +been announced on this day + + + align:start position:0% +been announced on this day +and at cern typically the menu is + + align:start position:0% +and at cern typically the menu is + + + align:start position:0% +and at cern typically the menu is +enriched on that day + + align:start position:0% +enriched on that day + + + align:start position:0% +enriched on that day +by the higgs borden itself in form of + + align:start position:0% +by the higgs borden itself in form of + + + align:start position:0% +by the higgs borden itself in form of +pizza + + align:start position:0% +pizza + + + align:start position:0% +pizza +which takes the shape of event displays + + align:start position:0% +which takes the shape of event displays + + + align:start position:0% +which takes the shape of event displays +displays of protein potent collisions + + align:start position:0% +displays of protein potent collisions + + + align:start position:0% +displays of protein potent collisions +into the higgs boson and then + + align:start position:0% +into the higgs boson and then + + + align:start position:0% +into the higgs boson and then +further decays we look at some of those + + align:start position:0% +further decays we look at some of those + + + align:start position:0% +further decays we look at some of those +event displays also later + + align:start position:0% +event displays also later + + + align:start position:0% +event displays also later +so that completes the elementary the + + align:start position:0% +so that completes the elementary the + + + align:start position:0% +so that completes the elementary the +fundamental particles of the standard + + align:start position:0% +fundamental particles of the standard + + + align:start position:0% +fundamental particles of the standard +model + + align:start position:0% +model + + + align:start position:0% +model +are particles which describe almost + + align:start position:0% +are particles which describe almost + + + align:start position:0% +are particles which describe almost +everything around us + + align:start position:0% +everything around us + + + align:start position:0% +everything around us +so we have seen the charge in neutral + + align:start position:0% +so we have seen the charge in neutral + + + align:start position:0% +so we have seen the charge in neutral +leptons we have seen the quarks + + align:start position:0% +leptons we have seen the quarks + + + align:start position:0% +leptons we have seen the quarks +we have seen the force carriers is a wz + + align:start position:0% +we have seen the force carriers is a wz + + + align:start position:0% +we have seen the force carriers is a wz +boson the proton and the blue one + + align:start position:0% +boson the proton and the blue one + + + align:start position:0% +boson the proton and the blue one +and the higgs boson which you know is + + align:start position:0% +and the higgs boson which you know is + + + align:start position:0% +and the higgs boson which you know is +kind of the + + align:start position:0% +kind of the + + + align:start position:0% +kind of the +very special particle holding this all + + align:start position:0% +very special particle holding this all + + + align:start position:0% +very special particle holding this all +together + + align:start position:0% + + + + align:start position:0% + +um an interesting point here is again + + align:start position:0% +um an interesting point here is again + + + align:start position:0% +um an interesting point here is again +looking a little bit at history + + align:start position:0% +looking a little bit at history + + + align:start position:0% +looking a little bit at history +and when those particles have been + + align:start position:0% +and when those particles have been + + + align:start position:0% +and when those particles have been +discovered + + align:start position:0% +discovered + + + align:start position:0% +discovered +and also when those particles have been + + align:start position:0% + + + + align:start position:0% + +explained um and i don't want to read + + align:start position:0% +explained um and i don't want to read + + + align:start position:0% +explained um and i don't want to read +this all to you um you'd see that you + + align:start position:0% +this all to you um you'd see that you + + + align:start position:0% +this all to you um you'd see that you +know the earliest discovery was the + + align:start position:0% +know the earliest discovery was the + + + align:start position:0% +know the earliest discovery was the +discovery by + + align:start position:0% +discovery by + + + align:start position:0% +discovery by +jj thompson of the electron and the + + align:start position:0% +jj thompson of the electron and the + + + align:start position:0% +jj thompson of the electron and the +latest + + align:start position:0% +latest + + + align:start position:0% +latest +the completion of the particles in the + + align:start position:0% +the completion of the particles in the + + + align:start position:0% +the completion of the particles in the +standard model + + align:start position:0% +standard model + + + align:start position:0% +standard model +the higgs boson in 2012. interesting for + + align:start position:0% +the higgs boson in 2012. interesting for + + + align:start position:0% +the higgs boson in 2012. interesting for +the higgs boson + + align:start position:0% +the higgs boson + + + align:start position:0% +the higgs boson +the time between the theoretical + + align:start position:0% +the time between the theoretical + + + align:start position:0% +the time between the theoretical +discovery by peter hicks + + align:start position:0% +discovery by peter hicks + + + align:start position:0% +discovery by peter hicks +in france was about 50 years before the + + align:start position:0% +in france was about 50 years before the + + + align:start position:0% +in france was about 50 years before the +experimental discovery + + align:start position:0% + + + + align:start position:0% + +but then there is also composite + + align:start position:0% +but then there is also composite + + + align:start position:0% +but then there is also composite +particles the things around you are all + + align:start position:0% +particles the things around you are all + + + align:start position:0% +particles the things around you are all +composite particles + + align:start position:0% +composite particles + + + align:start position:0% +composite particles +um here we can differentiate between + + align:start position:0% +um here we can differentiate between + + + align:start position:0% +um here we can differentiate between +mesons and baryons + + align:start position:0% +mesons and baryons + + + align:start position:0% +mesons and baryons +mesons are particles which are made out + + align:start position:0% +mesons are particles which are made out + + + align:start position:0% +mesons are particles which are made out +of quarks and anti-core pairs + + align:start position:0% +of quarks and anti-core pairs + + + align:start position:0% +of quarks and anti-core pairs +of the bound states and they are botonic + + align:start position:0% +of the bound states and they are botonic + + + align:start position:0% +of the bound states and they are botonic +because you add + + align:start position:0% +because you add + + + align:start position:0% +because you add +in half part two spin half particles + + align:start position:0% +in half part two spin half particles + + + align:start position:0% +in half part two spin half particles +together + + align:start position:0% +together + + + align:start position:0% +together +one example is a pion which is made out + + align:start position:0% +one example is a pion which is made out + + + align:start position:0% +one example is a pion which is made out +of up quarks and down quarks + + align:start position:0% +of up quarks and down quarks + + + align:start position:0% +of up quarks and down quarks +that can be charged in neutral ions + + align:start position:0% +that can be charged in neutral ions + + + align:start position:0% +that can be charged in neutral ions +and the the zoo of particle increases + + align:start position:0% +and the the zoo of particle increases + + + align:start position:0% +and the the zoo of particle increases +quite + + align:start position:0% +quite + + + align:start position:0% +quite +quickly uh if you then consider that + + align:start position:0% +quickly uh if you then consider that + + + align:start position:0% +quickly uh if you then consider that +it's not just up and down clocks making + + align:start position:0% +it's not just up and down clocks making + + + align:start position:0% +it's not just up and down clocks making +those particles but you could add + + align:start position:0% +those particles but you could add + + + align:start position:0% +those particles but you could add +strangeness to that meaning a strange + + align:start position:0% +strangeness to that meaning a strange + + + align:start position:0% +strangeness to that meaning a strange +quark and so you see here in this + + align:start position:0% +quark and so you see here in this + + + align:start position:0% +quark and so you see here in this +in this picture um + + align:start position:0% + + + + align:start position:0% + +the mesons the pions attas but also then + + align:start position:0% +the mesons the pions attas but also then + + + align:start position:0% +the mesons the pions attas but also then +neutrals and charged particles with + + align:start position:0% +neutrals and charged particles with + + + align:start position:0% +neutrals and charged particles with +different charges and then chaons which + + align:start position:0% +different charges and then chaons which + + + align:start position:0% +different charges and then chaons which +are particles which have + + align:start position:0% +are particles which have + + + align:start position:0% +are particles which have +one s-clock in addition to an up + + align:start position:0% +one s-clock in addition to an up + + + align:start position:0% +one s-clock in addition to an up +and then there's barions they're made + + align:start position:0% +and then there's barions they're made + + + align:start position:0% +and then there's barions they're made +out of three quarks we have already seen + + align:start position:0% +out of three quarks we have already seen + + + align:start position:0% +out of three quarks we have already seen +the proton and the neutron + + align:start position:0% +the proton and the neutron + + + align:start position:0% +the proton and the neutron +but also here you can see a different + + align:start position:0% +but also here you can see a different + + + align:start position:0% +but also here you can see a different +configuration + + align:start position:0% +configuration + + + align:start position:0% +configuration +we'll introduce a concept of isospin + + align:start position:0% +we'll introduce a concept of isospin + + + align:start position:0% +we'll introduce a concept of isospin +you can see here the proton and the + + align:start position:0% +you can see here the proton and the + + + align:start position:0% +you can see here the proton and the +neutron and then strangeness being added + + align:start position:0% +neutron and then strangeness being added + + + align:start position:0% +neutron and then strangeness being added +with one + + align:start position:0% +with one + + + align:start position:0% +with one +or two components of strategies and then + + align:start position:0% +or two components of strategies and then + + + align:start position:0% +or two components of strategies and then +there's this isospin component as well + + align:start position:0% +there's this isospin component as well + + + align:start position:0% +there's this isospin component as well +this situation becomes complex very very + + align:start position:0% +this situation becomes complex very very + + + align:start position:0% +this situation becomes complex very very +quickly but we'll look at this + + align:start position:0% +quickly but we'll look at this + + + align:start position:0% +quickly but we'll look at this +in more detail and then again + + align:start position:0% +in more detail and then again + + + align:start position:0% +in more detail and then again +putting those bound state together bound + + align:start position:0% +putting those bound state together bound + + + align:start position:0% +putting those bound state together bound +states of our protons and neutrons so + + align:start position:0% +states of our protons and neutrons so + + + align:start position:0% +states of our protons and neutrons so +the strong force + + align:start position:0% +the strong force + + + align:start position:0% +the strong force +gives us a rich table of nuclei or an + + align:start position:0% +gives us a rich table of nuclei or an + + + align:start position:0% +gives us a rich table of nuclei or an +isotope tape + + align:start position:0% +isotope tape + + + align:start position:0% +isotope tape +um here you can describe nuclei by the + + align:start position:0% +um here you can describe nuclei by the + + + align:start position:0% +um here you can describe nuclei by the +number of protons which is typically + + align:start position:0% +number of protons which is typically + + + align:start position:0% +number of protons which is typically +called z + + align:start position:0% +called z + + + align:start position:0% +called z +and the number of neutrons which is + + align:start position:0% +and the number of neutrons which is + + + align:start position:0% +and the number of neutrons which is +typically called n + + align:start position:0% +typically called n + + + align:start position:0% +typically called n +um the sum n plus z is the atomic mass + + align:start position:0% +um the sum n plus z is the atomic mass + + + align:start position:0% +um the sum n plus z is the atomic mass +now each proton and the neutron are + + align:start position:0% +now each proton and the neutron are + + + align:start position:0% +now each proton and the neutron are +about one gev heavy + + align:start position:0% +about one gev heavy + + + align:start position:0% +about one gev heavy +and then the atomic mass is simply the + + align:start position:0% +and then the atomic mass is simply the + + + align:start position:0% +and then the atomic mass is simply the +sum of them so you already know + + align:start position:0% +sum of them so you already know + + + align:start position:0% +sum of them so you already know +explicitly + + align:start position:0% +explicitly + + + align:start position:0% +explicitly +how heavy your isotope might be + + align:start position:0% +how heavy your isotope might be + + + align:start position:0% +how heavy your isotope might be +we'll talk about the fact that those + + align:start position:0% +we'll talk about the fact that those + + + align:start position:0% +we'll talk about the fact that those +masses are not quite + + align:start position:0% +masses are not quite + + + align:start position:0% +masses are not quite +the sum of the masses later because + + align:start position:0% +the sum of the masses later because + + + align:start position:0% +the sum of the masses later because +there's some binding energy involved + + align:start position:0% +there's some binding energy involved + + + align:start position:0% +there's some binding energy involved +and then isotopes can be stable or + + align:start position:0% +and then isotopes can be stable or + + + align:start position:0% +and then isotopes can be stable or +unstable they can decay in various + + align:start position:0% +unstable they can decay in various + + + align:start position:0% +unstable they can decay in various +processes + + align:start position:0% +processes + + + align:start position:0% +processes +you can combine them it's very + + align:start position:0% +you can combine them it's very + + + align:start position:0% +you can combine them it's very +interesting to understand and how + + align:start position:0% +interesting to understand and how + + + align:start position:0% +interesting to understand and how +they're actually being created + + align:start position:0% +they're actually being created + + + align:start position:0% +they're actually being created +in our solar system or the universe in + + align:start position:0% +in our solar system or the universe in + + + align:start position:0% +in our solar system or the universe in +general + + align:start position:0% +general + + + align:start position:0% +general +so with this i'd like to conclude this + + align:start position:0% +so with this i'd like to conclude this + + + align:start position:0% +so with this i'd like to conclude this +this part of the introduction so we have + + align:start position:0% +this part of the introduction so we have + + + align:start position:0% +this part of the introduction so we have +seen + + align:start position:0% +seen + + + align:start position:0% +seen +the major players of of this course with + + align:start position:0% +the major players of of this course with + + + align:start position:0% +the major players of of this course with +the fundamental particles but also the + + align:start position:0% +the fundamental particles but also the + + + align:start position:0% +the fundamental particles but also the +compound particles + + align:start position:0% +compound particles + + + align:start position:0% +compound particles +meson variants and nuclei + + align:start position:0% +meson variants and nuclei + + + align:start position:0% +meson variants and nuclei +and there's a few more points in the + + align:start position:0% +and there's a few more points in the + + + align:start position:0% +and there's a few more points in the +introduction before we then dive into + + align:start position:0% +introduction before we then dive into + + + align:start position:0% +introduction before we then dive into +a little bit more of this theoretical + + align:start position:0% +a little bit more of this theoretical + + + align:start position:0% +a little bit more of this theoretical +discussion \ No newline at end of file diff --git a/qubzQvNNaLI.txt b/qubzQvNNaLI.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4516cb98b043ad01696b2a4fafa6b5c68ea21fe --- /dev/null +++ b/qubzQvNNaLI.txt @@ -0,0 +1,3803 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation, or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK, I guess +we'll get started. + +So last time we talked about +hearing loss, and deafness, + +and cochlear implants. + +Any questions? + +So did anyone read the Sunday +New York Times yesterday? + +My email really lit up when this +front page article showed up + +and it was titled, "Ground +Shaking Noise Rocks NFL + +and Eardrums Take a Big Hit." + +So the reason my email lit +up is because my lab director + +is quoted. + +So it's a big deal to be quoted +in the Sunday Times, right? + +So this is talking +about the NFL games + +where they have a noise +meter down on the field + +and they encourage the fans +to make a lot of noise. + +And apparently at the Seattle +Seahawks recent game-- + +whatever-- the +crowd was recorded + +at making 136 decibel +noise in September. + +And so it says later on in +the article, "Fans accustomed + +to hollering may--" is that what +they do at the Seahawks games? + +"May scoff at the warnings +as nanny state silliness. + +But to auditory experts, +the danger is very real. + +People think it's cool +or funny, or whatever. + +But there is increasing--" +this is a quote "Increasing + +evidence that if your ears are +ringing, damage is happening, + +said M. Charles Liberman, a +professor of otology at Harvard + +Medical School, and the director +of a hearing research lab + +at the Massachusetts +Eye And Ear Infirmary." + +So he's a director +of the lab where + +we're going to have +a lab tour later. + +"There's something +irreversible going on, + +and it's only going to get +worse as you get older. + +Liberman's research shows that +even in the immediate effects + +of noise exposure after the +immediate effects subside-- + +the ringing, the muffling, +the feeling of pressure-- ears + +do not really recover." + +So noise damage in the news. + +I'll pass it around. + +All right. + +So yeah, question? + +AUDIENCE: I just have +a quick question. + +So when I'm down at the +T, it's extremely loud. + +Do you happen to know how +loud that is in decibels? + +PROFESSOR: I've never +measured it on the T. + +AUDIENCE: I had a +friend who tried. + +And the thing on his phone +wouldn't go high enough. + +PROFESSOR: Yes. + +And a lot of folks have +a sound level meter app. + +So how high was the maximum? + +AUDIENCE: The max was 100, +and it more than maxed out. + +PROFESSOR: Yeah. + +Well, so I wouldn't be +surprised if it's 110 dB + +on the T. Certain +in between stops + +runs are louder than others +as you know if you ride the T. + +So I think that +that's not so damaging + +that it would hurt your hearing. + +But if you were the conductor +or the driver on the train, + +you really have +to worry about it. + +On the other hand, +if you're the driver, + +you have to have good +hearing to respond + +to some kind of signals. + +So it's not like they can +just wear hearing protection. + +In this article +about NFL fans, they + +said in some games they hand +out those little foam ear + +plugs, which attenuate the +noise as much as 20 dB. + +So if you're listening to 120, +put the noise-- ear plug in + +and it goes down to 100. + +But it also said that some +people, like children, + +can't fit the foam ear +plugs in their ear canal. + +So it doesn't work for them. + +And some people, like +people who work on the T, + +need good hearing. + +So today, we're going +to move on and get back + +to the auditory brainstem. + +We had talked about the +auditory pathway that comes up + +from the cochlea through +the auditory nerve + +and into the cochlear +nucleus, which + +is the very lowest +level of the brainstem. + +And now we're going to +talk about some higher + +levels of the brainstem. + +And especially some +pathways that are + +called descending systems +and brainstem reflexes. + +So we'll define what +those two things are. + +We'll talk especially about +one descending system, which + +is a brainstem reflex called +the olivocochlear neurons. + +Their anatomy, their functions, +and their reflex pathway. + +And let me just stop and tie in +once again with hearing loss. + +These two brainstem +reflexes that I'm + +going to talk about +clearly protect the ear + +from damage due to +high-level sound. + +So that is certainly one of the +functions of the Olivocochlear + +neurons. + +And we'll see how +that takes place. + +The second brain stem +reflex that we'll talk about + +is the middle ear muscle reflex. + +There are two muscles +in your middle ear. + +When they contract, they +make your sense of hearing + +less sensitive. + +Why would you ever +want that to happen? + +Well again, these +muscles contract + +when you're in a high-level +sound environment, + +like at the NFL game. + +And one of their +functions is to reduce + +the sound getting +into your inner ear. + +So to prevent damage from +the high-level sound that + +might otherwise damage +your hair cells. + +So that's the subject +of today's talk. + +Now, what do I mean by reflexes +and descending systems? + +Well, this is a nice diagram +from Michael Slama, who + +shows in the solid lines +the pathways going up, + +which we've been talking about. + +And sometimes those pathways +are called ascending systems + +because they go up. + +So it says here in +red, the solid lines + +are ascending pathways. + +So by ascending, we mean from +a lower level up to a higher. + +And ultimately, to the highest +level in the neural pathway + +to the cortex. + +There are analogous +descending systems, + +which are shown here +in dashed lines. + +And I think you can +see some of them. + +For example, here's +auditory cortex. + +And there's some +dashed lines, which + +means cell bodies sitting +an auditory cortex that + +project their axons down and end +at the next lowest level, which + +is the auditory thalamus +or the medial geniculate. + +And so that would be an +example of a descending system + +because the information is +starting at the higher level + +and going down to a lower level. + +And at every junction +between nuclei + +you can find descending systems. + +And in the auditory pathway, +even at the lowest level, + +you have a descending +system that + +starts here in +the superior olive + +and goes all the way +out to the cochlea. + +And we talked about some +efferent nerve endings + +on the hair cells +and the nerve fibers. + +And that descending system is +called the olivocochlear system + +of neurons because it +starts out in the olive + +and goes to the cochlear. + +OK, so that's what +descending systems + +is, starting from higher levels +and going down to lower levels. + +Now, how does that work out +with brainstem reflexes? + +Well, we've said that +one of the functions + +of these olivocochlear +neurons would + +be they prevent the +cochlea from being + +damaged by high-level sounds. + +Well, when would you +activate that system? + +Well, obviously, when +you hear a loud sound. + +So the ascending pathway +has to come into the brain, + +synapse in the cochlear nucleus, +go up to the olivary complex, + +and then come back down to the +cochlear to prevent the damage. + +And so that little loop +that I just diagrammed + +could be called +a reflex pathway. + +So let's define +what a reflex is. + +What is a reflex? + +Anybody know? + +What does it mean +to act reflexively? + +AUDIENCE: Automatic reaction. + +PROFESSOR: Right. + +So an automatic response. + +And certainly, these +olivocochlear neurons + +turn on automatically. + +And sort of in between the +lines of that definition + +means that the reflex pathway +is operating down here + +in the automatic portion +of your auditory pathway + +in the brainstem. + +The part where you think +the auditory cortex + +or the other regions of cortex +doesn't have to get involved. + +You don't have to say, OK, +I'm in a loud environment. + +Should I respond +with this reflex? + +OK. + +Yeah, maybe I will. + +OK, respond. + +You don't have to +think about it. + +It's automatic +because it happens + +in the parts of the brain where +things happen automatically. + +What other things +happen in the brainstem? + +Well, control of breathing. + +You have the motor neurons +that come to your chest muscles + +and your diaphragm that +enable you to breathe. + +Those motor neurons are +located in the brainstem. + +And the control of respiration +is this brainstem function. + +It doesn't have to go +all the way to the cortex + +and have to think about it. + +Now, that's not to say that +reflexes, like the breathing + +reflex, you can +say, OK, I'm going + +to stop breathing for a minute. + +OK, I'm going to hold my breath. + +So you can, via +your higher centers, + +say I'm going to send +information down here. + +Maybe some of these +other descending pathways + +come down to the +olivocochlear neurons and say, + +I'm not going to do this +reflex for a moment. + +Of course, you eventually +have to start breathing again. + +But you can have higher center +control of these reflexes. + +It's not that the higher +centers aren't involved. + +OK, so another reflex would be +your patellar tendon reflex. + +The physician tests when you +go to your doctor's office. + +They hit your patellar +tendon with a little mallet + +and see that your leg contracts. + +And apparently, everyone +passes that test, right? + +You can't walk into +the doctor's office + +without having some +kind of reflex. + +But they're actually testing +for hyper-reflex in that case. + +And so some of these +reflexes can be in overdrive. + +And that's what the +physician is testing for. + +OK, so we are really +interested in what all + +these descending systems do. + +What do the descending +systems do in general? + +Well, it actually ends up being +a very hard issue to study. + +We know that those systems are +there, but what good are they? + +What do they do in +our sense of hearing? + +So the classic, old-fashioned +way of studying such a system + +would be to go in +and make a lesion + +and see how the animal's +behavior, the person's behavior + +changes, or do +some kind of test. + +But it turns out most of +these descending systems + +are intertwined with their +corresponding ascending + +pathway. + +So it's very difficult to go +in and make a cut or a burning + +lesion that just lesions one +of the descending pathways + +and not affect the +ascending pathway, which + +would complicate +the interpretation. + +The reason that some of +these systems-- for example, + +the olivocochlear +neurons-- are amenable + +and we know a lot +about them-- are + +amenable to experimentation-- +is we can selectively + +lesion and stimulate +them in isolation + +from the ascending systems. + +And let me show you a diagram +done of the olivocochlear + +system that illustrates that. + +So these are the olivocochlear +neurons, these stars here. + +There are two types. + +The red are the so-called +medial olivocochlear neurons + +because they're sitting +in the medial part + +of the superior olive. + +The green ones are so-called +lateral olivocochlear neurons + +because they're sitting +in the more lateral part + +the superior olive. + +And this diagram shows the cell +bodies of those olivocochlear + +neurons that are innovating +this cochlea-- sending axons out + +to this cochlea +on the right side. + +And that defines this cochlea +as the ipsilateral cochlea. + +Ipsi means the same. + +So that cochlea gets a name. + +That's the ipsilateral cochlear. + +And you can see that these +green lateral olivocochlear + +neurons are basically on +the same side of the brain + +stem as the cochlea +that they innervate. + +But these medial +olivocochlear neurons + +are distributed on both +sides of the brain. + +So there's a little bit +difference in anatomy. + +Now, these are a +little bit like neurons + +that we call motor neurons. + +Everybody knows what a +motor neuron is, right? + +It's going from the brain of the +spinal cord out to the muscle. + +That's why it's +called a motor neuron. + +And when it fires off, +it contracts the muscle + +that it's innervating. + +It turns out all the muscles +on the side of the body, + +let's say the +ipsilateral muscles, + +the motor neurons are located +on that same side of the brain. + +So right-side muscles are always +innervated by right-side motor + +neurons. + +So this anatomy is a little +bit different than the anatomy + +of motor neurons. + +Even though these +neurons are having + +an effect in the +cochlea, they're + +not innervating muscles. + +They're innervating +hair cells in this case. + +They do use the same +neurotransmitter as muscles. + +So the olivocochlear neurons +use the neurotransmitter + +acetylcholine. + +And so they would be +called cholinergic. + +OK, so they synthesize +the acetylcholine + +and their cell bodies +are transported down + +to the axons and +the nerve terminals. + +Out in the cochlea +use acetylcholine. + +They release it. + +Now, where do they +release it to? + +They release it +to their targets. + +And out in the periphery, these +Medial Olivocochlear Neurons, + +or the MOC neurons, target +the outer hair cells. + +And they release +acetylcholine directly + +onto the outer hair +cells via their synapses. + +The lateral +olivocochlear neurons + +come out to the periphery and +they release the acetylcholine + +in their synapses on +the auditory nerve fiber + +peripheral dendrites. + +OK, so the innervation +is very distinct. + +What are the auditory +nerve peripheral dendrites? + +Well, those are the ones +we've been talking about. + +We've been talking about +auditory nerve fibers. + +They start at the inner hair +cells for the most part. + +They send messages. + +That's what this +arrow is indicating. + +Send messages into the brain. + +When there's a sound, +the membranes move. + +The outer hair cells +are electromotile. + +The inner hair cells respond. + +They send messages, +synaptic messages, + +to their nerve fibers. + +The nerve fibers spike and they +send information to the brain + +through the cochlear nucleus. + +These efferent fibers +are sending messages + +the opposite way. + +They're starting in the brain +and going out to the cochlea. + +And out in the +cochlea, this arrow + +means that the information +is coming from the brain + +out to the outer hair cells or +the auditory nerve dendrites + +here. + +Is everybody clear about that? + +Now, the anatomy +works out so that you + +can do some pretty +interesting things. + +You can make a cut of this nerve +bundle, the olivocochlear nerve + +bundle. + +You can stimulate it. + +And right there underneath +where the word "brainstem" is, + +there's a great +place to make a cut + +or to electrically stimulate +and activate this system. + +Well, why don't we use sound +to stimulate the system? + +Well, it's a little messier. + +It's cleaner to +activate this bundle + +with electrical +stimulation because you + +can put your stimulating +electron right on it + +and only activate that system. + +So that's one big advantage. + +You can selectively activate +these olivocochlear neurons + +and then study, well, +what the heck do + +they do out in the cochlea? + +What changes do they have +when you activate them? + +And what changes happen +when you deactivate them + +and making a cut in the system? + +And de-efferent, if +you will, the cochlea. + +And as this list shows, there +are a number of functions. + +And if I had to pick one of +these, each of these functions + +has some experimental support. + +And I don't think I +would be able to pick + +which is the most important. + +Well, sure, if you're +at an NFL game, + +you are probably experiencing +a very high sound level. + +And so it becomes +important in that situation + +to protect the +cochlea from damage. + +So it depends on the situation. + +But we're going to +go through these. + +In turn, I think that +since I mentioned damage, + +and since I don't +have a slide on it, + +let me say how that +experimental evidence arises. + +It's a very simple +type of experiment. + +You take an animal. + +You put it in a high-level +sound environment + +comparable to an +NFL game, 120 dB. + +Take the animal out, +you study its cochleas. + +You can count the hair cells. + +You can measure the responses. + +The hearing has become +much less sensitive. + +Some of the hair cells +have been killed. + +OK, no big deal. + +We went over that last time. + +Take a second animal. + +And in that animal, cut this +olivocochlear bundle going out + +to, let's say, the +ipsilateral cochlea. + +The olivocochlear neurons +going to this other side, + +the contralateral cochlea, +leave that intact. + +OK, beautiful experiment +because within just one animal, + +you have one side's cochlea +has been de-efferented. + +You have cut off +these efferent fibers. + +The other side has a +normal innervation. + +Expose the animal to 120 dB SPL. + +Do the same response metrics. + +Test the responses +of the cochlea. + +Look at how many hair +cells have been killed. + +You find that there is a huge +difference in the two ears. + +Where the efference or +these olivocochlear neurons + +have been cut, there's +a lot of damage + +and a lot of loss +of sensitivity. + +On the intact side, +it has been protected. + +There is less damage +and better responses. + +It's more sensitive. + +So it's a very, very nice, +very elegant experiment + +that's been done many times. + +In probably both +of these systems, + +the medials and the laterals +provide such protection + +from damage. + +So we can say one +of the functions + +then is then protection. + +What do I mean by these +other functions-- shift + +the dynamic range +of hearing, reduce + +the effects of noise masking, +and reduce hearing sensitivity + +when paying attention +to visual tasks? + +OK, we're going to go +over those one by one. + +For the first one, the +experiment runs like this. + +You record from these afferent +auditory nerve fibers. + +And instead of cutting +these olivocochlear neurons, + +you stimulate them. + +You can put a stimulating +electrode right down there, + +right below the +word "brainstem," + +and activate this bundle. + +What happens to the +responses of the nerve fibers + +when you activate this +olivocochlear system? + +And that's what's shown here. + +And this experiment has +been done since the 1970s. + +This is an old experiment. + +This is the response +in terms of the firing + +rate from the auditory nerve. + +And in this case, a tone is on. + +So you're really driving +the auditory nerve fiber. + +So the firing rate is high. + +Then, during the +second black bar + +here, you stimulate the +olivocochlear neurons + +that are going out +to the cochlea. + +And look what happens +to the firing rate. + +It goes almost down to zero. + +When you turn that +stimulation off, + +the firing rate comes back +to about what it was before. + +There's been a huge +inhibition of firing rate + +in the auditory nerve. + +If you plot the firing rate as +a function of the tone burst + +level-- so now we're going +to do different tones + +at different levels. + +At low tone levels where the +fiber is firing spontaneously, + +there's hardly any effect. + +In mid-levels, like we +saw illustrated here, + +this is without stimulation. + +This is with stimulation. + +There's a huge decrease +in firing rate. + +And up at the +highest levels where + +the fiber has become +saturated-- saturation means + +that even though you're +increasing the tone burst, + +you're not increasing the fire +rate coming from the fiber-- + +there's very little effect +of this stimulation. + +How can that help us? + +We have a dynamic range +problem in hearing. + +Most auditory nerve fibers-- +forget about the stimulation + +right now. + +Look at the solid curve. + +The dynamic range of most +auditory nerve fibers + +has just 20 or 30 dB +before saturating. + +That means the fiber +goes up and it saturates. + +What happens when we +get to the NFL game + +or in the better case, +what happens when + +we're in a restaurant +or a bar and we want + +to listen to the speaker +across the table from us? + +Well, that's a pretty +high sound level, 80 dB. + +It's not damaging, +but it's high enough + +to saturate our +auditory nerve fibers. + +That means when the +added sound level + +of the person across the +table from you, their voice, + +adds to the +background, they're not + +going to change the firing rate +of your auditory nerve fibers. + +And the brain won't +know except by seeing + +the person's lips move +that there is speech. + +It's much better to +understand any kind of signals + +to be within this rising +function of the firing rate + +curve, not in the +saturated function where + +there's no change +in firing rate. + +OK, so how can the +olivocochlear system + +help us with this +dynamic range problem? + +Well, I've been emphasizing +the decrease of firing rates. + +But as you can see from +this curve with stimulation + +of the OC neurons, the effect +is to shift this function over. + +In this case, it's +about a 20 dB shift. + +And now, at 70 dB, you're in the +dynamic range of the function. + +And you're not saturated +anymore as you were before. + +So one of the +functions, we think then + +from this type of experiment, +is the MOC efference kick in, + +reflexively kick in when +you're in a high-level sound + +environment. + +And they shift the firing +rate functions over + +so you can now +understand a speaker's + +voice in a high-level +background. + +Now, there are +some other factors + +that change an increase of +dynamic range of hearing, which + +I don't think are +important to the course. + +But we have talked about +two-tone suppression. + +This certainly does +the same kind of thing. + +We're going to talk about +contraction of the middle ear + +muscles, which also helps you +with the dynamic range problem. + +So this is clearly then, +one important function + +of the olivocochlear neurons. + +That is, shifting dynamic range. + +Now, is there +experimental evidence + +besides what you +see here looking + +at firing rates of +auditory nerve fibers + +to suggest that the +olivocochlear system really + +does this? + +There is a little bit. + +That is, with animals +trained to detect changes + +in tones in a +background of noise, + +they do it a little +bit better when + +they have an intact +olivocochlear system. + +You can't do these +experiments in humans + +because it's very difficult +to turn this system off. + +We don't know a way of turning +it off or interrupting it. + +And people probably call this +system into play reflexively. + +So it's difficult to do these +kinds of experiments in humans. + +Now, there's another +important function + +of the olivocochlear +system, which is probably + +to reduce the effects +of noise masking. + +And we haven't talked too much +about masking in this course. + +I mean, two-tone suppression +is a kind of masking. + +Masking is where you're +listening to one sound + +and a second sound comes in +and interferes your ability + +to detect that very first sound. + +So I have a +demonstration, though, + +that I think will convince you +that masking is very important. + +And it runs like this. + +So the demonstration +is going to be + +you're listening to tone bursts, +which are the pink things here. + +And they're at 2,000 Hertz, +so it's going to be kind + +of a little bit above +our 1,000 standard + +middle-of-the-hearing-range +frequency. + +And it's going to give +you 10 tone bursts + +and they're each going +to be successively softer + +in sound level. + +And you're supposed to count +how many steps you can hear. + +And I think there +are 10 of them. + +We should be able to hear +all 10 with the way I + +have set the level. + +The second part +of the demo is now + +the signal is masked +with broadband noise. + +So the broadband noise +will come on first. + +Shh. + +And these tone pips will +be on top of that noise. + +And you're supposed to +count now how many tone + +pips you can hear with +the broadband noise. + +And I think there's a +little verbiage before this. + +Just ignore that. + +[AUDIO PLAYBACK] + +-Critical bands by masking. + +You will hear a 2,000 +Hertz tone in 10 decreasing + +steps of 5 decibels. + +Count how many +steps you can hear. + +Series are presented twice. + +[BEEPING] + +[END AUDIO PLAYBACK] + +PROFESSOR: OK, so could +everybody hear most of them? + +10? + +All 10? + +OK. + +Here's the masked. + +[AUDIO PLAYBACK] + +-Now the signal is masked +with broadband noise. + +[BEEPING] + +[END AUDIO PLAYBACK] + +PROFESSOR: OK, how many now? + +AUDIENCE: Five. + +PROFESSOR: Five? + +I mean, this is not a +bad illustration, right? + +When the pink tone bursts +get within the black noise, + +they're pretty +much disappearing. + +So clearly the noise +was an effective masker + +of the tone pip. + +Now, we had the example +earlier of the phenomenon + +called two-tone suppression. + +And that was measured in +an auditory nerve fiber. + +And everybody should be able +to draw an auditory nerve + +fiber tuning curve. + +On the x-axis, we +have the frequency + +of the sound in kilohertz. + +And the y-axis, we have +the sound pressure level + +for a response. + +An auditory nerve tuning curves, +at least those with high CFs, + +look like this. + +And the characteristic frequency +is the frequency right here. + +In two-tone suppression, +what we had is two tones. + +The first tone is +a probe tone, which + +is placed inside the nerve +fibers response area. + +And if you look at a +graph of firing rate-- + +so this is firing-- and +you turn that tone on, + +the firing rate is +going to go way up. + +Maybe 100 spikes per +second because it's + +within the response area. + +Now, the second tone, sometimes +called the suppressor, + +is put outside the response +area but close to it. + +OK, so here's the probe. + +This is the probe +tone, high firing rate. + +And now a little +bit later, we're + +going to turn on a second tone. + +And this is called +the suppressor. + +And I haven't drawn +this very well, + +but when the suppressor +goes on, the firing rate + +can come back down. + +This goes off first. + +And come back up. + +OK. + +So clearly, at least in the +discharges of auditory nerve + +fibers, you can have suppressors +outside the response areas + +that decrease the +response to probes. + +This probe tone is going to +be signaled by auditory nerve + +fibers close to that frequency. + +So many auditory nerve fibers +have CFs close to 2 kilohertz. + +This noise has energy +throughout the frequency range, + +if it's absolutely white noise. + +Some of its noise will be +within the response area, + +but some of it will be +in suppression areas. + +And these suppression +areas can be + +either side of the +excitatory area. + +And they can be big. + +And in some cases, they can +overrule the excitation, + +or at least decrease it. + +So some of the reason you +couldn't hear the tone when + +it was masked by +the noise is because + +of two-tone suppression. + +This is sometimes called +suppressive masking. + +There's another kind of masking +that's important-- it may + +be equally important-- and +it's called adaptive masking. + +And it comes from the +process called adaptation. + +Almost all sensory +systems have adaptation, + +which means that when +you turn a stimulus on, + +you get a vigorous response. + +And even though the stimulus +stays on, after a while + +the response dies +down a little bit. + +And that process is +called adaptation. + +So I've illustrated the +process of adaptation + +for auditory nerve fibers +in this next graph. + +Here's that pink +tone burst at 2,000 + +Hertz we were listening to. + +There's the auditory +nerve response to it. + +Right as the tone +burst goes on, there's + +going to be a vigorous +discharge, which + +die eyes down and +becomes a smaller-- still + +a discharge, but a +smaller discharge. + +And that process is +called adaptation. + +Where do you think +that process arises? + +OK, while you're +thinking about that, + +I'm going to draw a picture +of what's happening here. + +So you have the three +rows of outer hair cells. + +We have the inner hair cell. + +We have the auditory +nerve fiber. + +And we're recording here. + +And we're saying, +we turn the sound on + +and you get a whole +bunch of spikes + +from that single +auditory nerve fiber. + +But after a few milliseconds +or so, the response dies down. + +What experiment could you do? + +We don't know where +that process is arising. + +We can't explain it. + +What experiment would you do +to study where that comes from? + +Anybody? + +Here's the tone. + +Here's the response +from the nerve fiber. + +What do we need to +figure out where + +that adaptation is taking place? + +Well, how about recording +from somewhere else? + +What about recording +from the hair cell? + +OK, if you do that, the hair +cell doesn't fire spikes, + +but it has a receptor potential +in response to the sound. + +The receptor goes +on and stays on. + +OK, where is adaptation +taking place? + +Well, somewhere between the +hair cell and the nerve fiber. + +The hair cell doesn't adapt, +the nerve fiber does adapt. + +what could explain +adaptation then given that? + +Anybody? + +OK, what do we have here? + +We have a synaptic ribbon with +lots of synaptic vesicles. + +The tone goes on. + +You have a whole bunch +of synaptic vesicles. + +You release them because the +hair cell has depolarized. + +You have a burst of +auditory nerve firing. + +And you can make new +synaptic vesicles, right? + +Yeah, but it takes time. + +OK, so as time goes on, +you've released all of these + +or many of them. + +And you can make some new ones, +but maybe not quite as fast + +as you've released them. + +So you deplete your +synaptic vesicles. + +The hair cell's +still responding. + +There are fewer vesicles and +fewer neurotransmitter released + +to the nerve and so the +nerve firing dies out. + +So adaptation is often ascribed +to the diminished release + +of neurotransmitter. + +And so far, that's all +adaptation to a single tone. + +How does that explain masking? + +Well, if your nerve fiber +responded to the noise-- + +at the very beginning you +heard that noise come on-- shh. + +And then the tone came +on a little bit later. + +If the tone is high +in level, sure, it's + +going to still have some +synaptic vesicles to release. + +But if the tone is very +soft, the hair cell + +is not going to be able to +release synaptic vesicles + +because they've +already been released + +at the beginning of the noise. + +So adaptive masking is where +you have, to a certain extent, + +run out of hair cell +neurotransmitter. + +And there's none, or much +less, left to release. + +Clearly, adaptive masking +means that this fiber is also + +responding to the mask or +the noise in this case. + +So in adaptive masking +you have to have + +a stimulus that excites. + +The masker has to excite the +nerve fiber and the hair cell. + +And the probe-- probe +is always exciting it. + +So that is a second +explanation for masking. + +Now in this case, the +olivocochlear system + +can actually help you +with adaptive masking. + +How can it help you? + +Well, in this +case, if you also-- + +when you start to +hear this noise, + +you call that olivocochlear +system into play. + +And it acts. + +What does it act to do? + +It decreases the firing +of the auditory nerve. + +Then when you have +the tone come along, + +you have plenty of +neurotransmitter + +left in the hair cell because +you haven't released it all. + +And you have at least +some to be released + +in response to the tone. + +So in this case, +the third function + +then of the +olivocochlear system is + +to reduce the +effects of masking. + +And we should have +said back here + +when I listed the functions, +reduce the effects of noise + +masking, especially +adaptive noise masking. + +The kind where the masker +excites the fiber unlike + +suppressive masking where the +masker reduces the response. + +There are certainly important +and reliable studies + +where animals in which the +olivocochlear bundle has + +been cut have much more of a +problem with noise masking. + +They cannot detect signals that +are buried in a noise masker + +as well as animals with an +intact olivocochlear bundle. + +So clearly, that is +a viable function. + +Now finally, and this is pretty +important for our course here, + +there's been this fourth idea +of what the olivocochlear + +reflex could do. + +And it's always been a +little bit wishy-washy + +because there hasn't been really +good experimental evidence. + +Until this paper-- this +paper Delano et al, + +2007-- is the paper that we +have listed for reading today. + +And this paper clearly +shows that another function + +of the olivocochlear system is +when you're paying attention + +to something that +is not auditory, + +like a visual stimulus, +the olivocochlear system + +acts and reduces your +sense of hearing. + +You're not using hearing +for whatever task, + +so you desensitize your +hearing and you pay attention + +to the visual system. + +OK, so how is this +going to work? + +So this paper +trained chinchillas + +as the experimental animal. + +And the task was to pay +attention to lights. + +So let me get my +pointer here so I + +can point out a little better. + +So this is the task +in part A here. + +And this neutral cue is a +light that's straight ahead + +from the experimental animal. + +And that goes on and +says to the animal + +that the trial is starting. + +Then, that goes off and +one of two targets appears. + +Either a left target +or a right target. + +And these are little spots +of light to the animal's left + +or to the right. + +The task then is if the +left target went on, + +the animal goes and +presses the left lever. + +And if it does that correctly, +it gets a food reward. + +If the light went +on on the right, + +the right target +was illuminated, + +the right lever is +supposed to be pressed. + +And if the animal +does that correctly, + +then it gets a food reward. + +If it does nothing or if +it presses the wrong lever, + +it's punished by a timeout. + +And the animals +are food deprived, + +so they're motivated +to do this task. + +That's the visual task. + +Now, on top of that there's +some auditory stimuli presented. + +And they're not +relevant to the task. + +They're just ongoing +all the time. + +And here then in B are the +target and the neutral cue + +lights and the response period. + +And the auditory stimulus +going on all the time + +is a click or a tone burst. + +And it's just going +on all the time. + +And they're making +some recordings + +from the auditory system. + +And in this case, they're +making a recording + +from the round window +of the cochlea. + +And if you had a microscope, +you could see some little blips + +right here in response +to the clicks. + +And they're pretty big here. + +But as time goes on, +they get smaller. + +And that's plotted right here. + +The response they're +measuring is called the CAP, + +and that's the Compound +Action Potential. + +And if you are astute +here, the action potential + +is another word for +"spikes" or "impulses." + +But they're not measuring +from one single fiber, + +they're putting a big +electrode on the round window + +of the cochlear and they're +measuring the summed + +or compound action potential +from the whole auditory nerve. + +It's just a convenient +place to do it. + +You can do it in +an awake animal. + +You can do it in awake behaving +animal like we have here. + +When you turn on a click, almost +all the auditory nerve fibers + +fire synchronously and +you get a big response. + +Hardly have to do +any averaging at all. + +OK, so that's the response, +the compound action potential. + +And this graph plots the CAP +amplitude-- how big it is. + +Upward on the graph +is a big amplitude + +and lower is a +diminished amplitude. + +And right here at +zero-- they just + +call it zero because +that's sort of the baseline + +before the trial even starts. + +So in this first bar here +is the neutral OK cue. + +That's the thing in the middle +that says to the animal, + +the task is starting. + +And right away during +that neutral cue, + +these black dots show you that +the compound action potential + +is decreasing. + +Then, the neutral cue goes +off and the target-- one + +of the targets goes on. + +Either the left or right. + +And the compound action +potential further decreases. + +Then, the animal makes +its response here + +in this dashed line. + +OK, gets its food reward +and the CAP comes back up. + +OK, now how do we explain this? + +Well, the CAP is the +summed firing rate + +of many auditory nerve fibers. + +Instead of stimulation +of the OC neurons + +decreasing the firing rate, +essentially the animal + +itself has turned +on its OC neurons + +and the firing +rate has gone down. + +Or the summed response, in +this case, has gone down. + +The animal has said to +the olivocochlear system, + +I'm starting a visual task. + +I don't want to pay attention to +extraneous things, like sounds. + +So I'm going to +decrease my sensitivity + +in hearing by activating +these olivocochlear neurons. + +Now, pay attention to +the important targets, + +which are visual. + +Now, there are some other +symbols in here that are open. + +They're a little +bit harder to see. + +But there are some +CAP amplitudes + +from another trial of +these same animals. + +And for one reason or +another, the chinchillas + +didn't always do the task. + +Every now and then they would +just not pay attention to it. + +They wouldn't press the lever. + +They wouldn't respond at all. + +As if they were +sort of spaced out, + +thinking about something +else if you will. + +And in those cases, +which are timeout trials. + +Let's see, what +did they call them? + +Ah, omissions. + +This little symbol +right here is omissions. + +So it's an omission trial +where the animal didn't even + +do the task. + +In that case, the +olivocochlear system + +is apparently not +called into play at all. + +The animal is just +not doing the task. + +Now, the investigators were +very astute and they said, + +we're going to make +the task a little more + +difficult for the +animals and see + +if we get a bigger effect here. + +And the way to make +the task difficult + +is make the targets brief. + +So instead of the target going +on for a couple of seconds, + +the target went on for +just a half a second. + +And here's a trial with +just a half a second. + +And there was a big decrease +in the auditory response. + +If the target went +on for a long time, + +there was less of a decrease. + +And this is the effect plotted +as a function of target + +duration. + +Brief targets made +this job harder + +to do for the chinchillas. + +So this is clearly, +at least to me, + +some evidence that you call into +play the olivocochlear system + +when you're doing a visual task. + +So maybe as humans, we do this +when we're trying to read. + +We're concentrating on +the book, visual stimulus. + +And our neighbors +music is going on. + +It's not relevant +to what we're doing. + +Maybe we're listening +to it subconsciously, + +but we decrease the response +to that auditory stimulus + +because it's not +important to the task. + +So clearly then, +this is good evidence + +from this single study +for the last function + +for the olivocochlear +system, which + +is that you reduce your hearing +sensitivity when attending + +to visual or perhaps +other modality tasks. + +So these are the +four basic functions + +then for the +olivocochlear system. + +Now, before I leave the +olivocochlear system, + +let's do a little review here +on exactly how it's acting. + +So we said we're activating +these systems going out + +to the hair cells +and we're reducing + +the responses of the +auditory nerve fibers. + +Something I haven't told you +but was observed maybe 20 + +years after the phenomenon +was first discovered + +is the idea of which +of these systems + +is being used here +when we electrically + +stimulate the system +and activated it. + +It turns out that the +medial olivocochlear neurons + +have big, fat myelinated axons. + +And you can maybe appreciate +that from this drawing + +that these are very thick lines. + +The lateral olivocochlear +neurons have very thin axons. + +And one effect of that +besides how fast they conduct + +impulses is when you stimulate, +for example, at this position + +here in the brainstem, it takes +a huge amount of stimulating + +current to activate +very thin nerve + +fibers like the lateral +olivocochlear neurons. + +If you apply a huge +stimulating current here, + +the current spreads +to everywhere, + +including the +facial nerve, which + +causes the experimental +animal to twitch. + +So that's almost never done. + +More moderate levels +of stimulation current + +are applied here. + +And at those levels, the +predominant system activating + +is the medial +olivocochlear neurons. + +Those MOC neurons +send their fibers out + +to the outer hair cells. + +And we say when they +act on the outer hair + +cells, the responses of +the nerve fibers diminish. + +As we review, we should be +able to account for that. + +OK, we are stimulating +nerve fibers + +that go out to the +outer hair cells here. + +And we're recording +the responses + +from the auditory nerve +fibers right here. + +Of course, these +olivocochlear neurons + +are sending messages +out to the periphery. + +And the auditory nerve +fibers are sending messages + +into the brain. + +Somebody explain to me +what's happening here. + +What are we doing to the cochlea +to cause these responses to go + +down when we apply +this simulation? + +Anybody? + +We're affecting the +outer hair cells, right? + +What are the outer hair cells? + +The cochlea amplifier, right? + +It turns out that +releasing the acetylcholine + +on to the outer +hair cells decreases + +their electromotility. + +So in effect, it discusses the +gain of the cochlear amplifier. + +If the cochlea is +less amplified, + +the inner hair cell stereocilia +are going to be bent less. + +They're going to release +less neurotransmitter + +to the associated +auditory nerve fibers. + +And we're going to measure +less of a response. + +That is how the +olivocochlear neurons-- + +those that go to the +outer hair cells-- + +affect the responses of +the auditory nerve fiber. + +So this decrease +in firing rate then + +is a manifestation +of turning down + +the gain of the +cochlear amplifier. + +It was quite a mystery when +this innervation was first + +worked out before the +outer hair cells really + +were known to be the amplifier. + +How could stimulation of fibers +going to the outer hair cells + +give you decreases in +responses of fibers + +coming from the +inner hair cells? + +And now that the outer +hair cells are clearly + +associated with the cochlear +amplifier, it's clear. + +Now, what was the +loss of sensitivity + +when the outer hair cells +were completely gone + +or when their prestin +was knocked out? + +Anybody? + +What was the loss +of sensitivity? + +40 to 60 dB, right? + +So if you eliminated +the cochlear amplifier, + +we had a loss of 40 to 60 dB. + +What kind of effect do +we have from stimulation + +of the olivocochlear neurons? + +Well, the length of this arrow +when brought down to the x-axis + +shows you how much +sensitivity is lost. + +You could overcome +this by dialing + +in an increase of sound pressure +level to make up for it. + +You could titrate the effect +of decreasing the gain + +by increasing the +sound stimulus. + +And the width of that arrow, +the length of that arrow, + +is about 25 dB. + +So instead of eliminating +the cochlear amplifier, + +you just reduce its gain by the +action of these olivocochlear + +neurons. + +The effect is about 25 dB. + +Which is a fairly strong effect, +but you're not completely + +ridding the cochlea of +the cochlear amplifier. + +You're decreasing its gain. + +OK, so that's kind of a review +on outer hair cell function + +and how these olivocochlear +neurons affect the outer hair + +cells. + +So you really have a +controllable cochlear amplifier + +controlled by these +olivocochlear neurons, + +or efferent neurons, +or descending neurons + +coming from the brain +out to the cochlea. + +Any questions about that? + +OK. + +If there aren't, then I'll go +on to another reflex pathway. + +Maybe I actually do have one +more thing to talk about. + +Right. + +Let me just mention this +idea that this reflex pathway + +is kind of getting teased +out by current studies. + +And it can be a little +bit complicated, + +so let me show you +what people are working + +on now in the +olivocochlear reflex. + +Here, I think I've +flipped the slide on you + +so that this slide shows +the MOC neurons going + +to the left cochlea. + +OK. + +That's the ipsilateral cochlea. + +How do these MOC neurons +get their inputs? + +Where do they come from? + +OK. + +Well, the red and blue are +the olivocochlear neurons + +coming out to the cochlea and +the purple are their inputs. + +And all of the inputs have to, +of course, use the cochlea. + +To get this olivocochlear +neurons to fire in response + +to sound, you have to +activate the cochlea. + +You activate the auditory nerve. + +The auditory nerve goes into +the cochlea nucleus then. + +And that's where the +limits of our understanding + +are sort of-- we are +approaching the limits + +of our understanding. + +What are the cochlear +nucleus neurons + +that are the so-called MOC +reflex interneurons that + +are drawn in purple here? + +When we talked about +the cochlear nucleus, + +we identified a bunch of +different types of neurons. + +We had spherical +cells, globular cells. + +Both of those are +known as bushy cells. + +We had stellate cells. + +We had pyramidal cells. + +We had octopus cells. + +Which of those provide the +inputs for the MOC neurons? + +And that's assuming +a direct pathway, + +which I'll give you from some +other experimental evidence + +which I won't show you. + +At least one group +of cochlear nucleus + +neurons projects +to the MOC neurons. + +And how do I know that? + +Well, you can record +from the MOC neurons + +and turn a sound on. + +And in less than 5 milliseconds, +you can get a response. + +So there isn't enough time +for the reflex pathway + +to go up to the +auditory cortex, which + +takes about 4 or 5 synapses. + +And to go around there +and start coming down, + +that takes 10 or +20 milliseconds. + +You get a response +here very quickly. + +And so there isn't enough time, +except for cochlear nucleus + +to project directly there. + +So which of those cochlear +nucleus neurons do project? + +Well, we don't know +absolutely for sure. + +But it looks like +from lesion studies + +that probably the stellate +cells in the cochlear nucleus. + +And especially +the stellate cells + +in the part of the cochlear +nucleus called the PVCN. + +And I think we talked +about the ventral cochlear + +nucleus and the dorsal +cochlear nucleus + +as being the big main divisions. + +In the VCN, there's two +subdivisions, AVCN and PVCN. + +And the stellate cells +that seem to be-- the MOC + +reflex interneurons +are in the PVCN. + +How do we know that? + +You can make lesion studies in +various parts of the cochlear + +nucleus. + +If you lesion the DCN, this +reflex goes along fine. + +If you lesion the AVCN, +it goes along fine. + +In the PVCN, if you +make a lesion there, + +the reflex is interrupted. + +In the PVCN, there are a +number of types of neurons. + +The ones that seem to have the +right characteristics in terms + +of latency, sustainability +of response, + +tuning, are the stellate cells. + +So it's a little bit +of a squishy argument. + +Stellate cells seem to +project to the right way. + +So most of the evidence +is behind the idea + +that those particular +cochlear nucleus + +cells are the ones that are +the reflex interneurons. + +Now, another point of this slide +is that the MOC reflex pathway + +is consensually organize. + +So what does consensual mean? + +What does consensual in +terms of reflex mean? + +Not in terms of +consensual sex, in terms + +of reflexes or +brainstem organization. + +How does the detective in the +old 1950s black and white movie + +come to the victim +whose lying down + +and shine a flashlight +in the eye-- how does he + +decide that the +person is really dead? + +The pupil constricts if the +person's still alive, right? + +The brainstem is still working. + +It's a very quick test. + +You don't have to +have a stethoscope + +and listen to the heartbeat. + +You can be brain dead and +still have a heartbeat. + +But if you shine light +in a person's eye, + +the pupil constricts, right? + +So that is a brainstem reflects. + +The pupillary +constriction reflex. + +It turns out if you shine +light in the right eye, what + +happens to your left pupil? + +It constricts, right. + +So both pupils constrict from +just a stimulus in one eye. + +And that is called consensual. + +It means in agreement. + +The left and the right side do +the same thing in agreement. + +So most of these +brainstem reflexes + +are consensually organized. + +And it turns out +that you can look + +at the MOC reflex +in your left ear. + +And obviously, if you +put sound in there, + +that reflex is +going to take place. + +But you can also +elicit that reflex + +by sound in the right ear. + +For some reason, sound in either +ear can activate the reflex. + +Not quite as well, +labeling studies + +have shown that just +some of the MOC neurons + +are responsive to sound in +the ipsilateral cochlea. + +That is, the cochlea +that they project to. + +And about half as many +are responsive to sound + +in the other ear. + +The so-called +contralateral cochlea + +and the so-called +contra response, + +MOC neurons in red here. + +Labeling studies have +shown these contra + +response neurons are sitting +on the side of the brain + +as the cochlea that +they innervate. + +But the ipsi +response neurons are + +located on the opposite side +of the brain [INAUDIBLE]. + +And knowing those +response characteristics, + +then you can draw +the purple pathway + +that's necessary to drive them. + +These contra response neurons +respond to sound over here, + +so they must get +this purple arrow. + +These ipsi response neurons +are responsive to sound here, + +so they must get +this purple pathway. + +And it's kind of complicated, +but that's the kind of studies + +that people do now on +these brainstem reflexes. + +And I want to just +say one more thing. + +People are now working on where +the neurons go in the cochlea. + +So these are some tuning +curves from these MOC neurons. + +So they show sharp tuning +just like the auditory nerve. + +And where do they go? + +Well, they have a very nice +so-called tonotopic projection + +into the cochlea. + +That is, an MOC +neuron with a high CF + +goes and innervates at a +very basal cochlear location. + +and. + +An MOC neuron with a low CF +goes and innervates closer + +to the apex. + +And this black line +shows the mapping + +for auditory nerve fibers. + +Those are the ones coming +out of the cochlea. + +And the colored dots +show the mapping + +for the fibers going +back on to the cochlea. + +Everything, remember, +in the auditory system + +is tonotopically organized. + +So it's no surprise +that that would happen. + +But it opens up the idea +maybe that if you're + +interested in turning off +your sense of hearing just + +for low frequencies, you +could activate these fibers, + +go out to the cochlea +in just the apical part, + +and leave the basal part. + +Let's say you're very +interested in listening + +to high-frequency sounds. + +Leave the basal part intact. + +Or vice-versa. + +You could control the +cochlea in a frequency band + +by frequency band manner. + +The anatomical +substrate there is + +laid for that type +of manipulation. + +You don't have to shut down +the whole sense of hearing. + +OK, so let's move on +to the second system + +that I want to talk about. + +That is, the brainstem reflexes +associated with the stapedius + +and tenser tympani +middle-ear muscles. + +These are two muscles that +are in the middle ear. + +Remember the middle ear was +the part of the ear that + +starts at the eardrum +and ends at the cochlea? + +There are two +middle ear muscles. + +There's a tensor tympani. + +This is shaded in brown here. + +And there's the stapedius +shaded in red here. + +The stapedius tugs +on the stapes. + +And the tensor tympani +tugs on the malleus. + +But it gets its name +because when it contracts, + +it looks like-- if you're +looking at the eardrum + +through an otoscope, it looks +like the tympanic membrane gets + +really tense. + +It looks a little flaccid +before it contracts, + +and then it gets real tense. + +So it's a tensor tympani. + +And what happens when +those muscles contract? + +That's shown in this next slide. + +They reduce the +sound transmission + +through the middle ear. + +This is just simply a +graph on contraction + +of the stapedius muscle. + +This is during the contraction. + +This is the magnitude change. + +So it looks like sound doesn't +get through the middle ear + +anywhere near as +well as normally. + +And you have about a 25 dB +decrease in sensitivity. + +Simply what that means is +that usually the eardrum moves + +and these bones move and they +convey efficiently the sound + +into the inner ear. + +But if you tug on the +muscles and contract them, + +then the bones don't +vibrate as easily. + +And the sound doesn't +get into the inner ear. + +So this is again, like +the olivocochlear system, + +an inhibitory system in +that when it's activated + +it reduces your +sensitivity of hearing. + +Now, how are these +muscles controlled? + +Well, they're controlled by +neurons coming from the brain. + +But in the case of +muscles, of course, + +they're always on the +same side of the brain + +as the muscles they innervate. + +So the left stapedius muscle +is controlled by motor neurons + +on the left side of your brain. + +And the stapedius +muscle motor neurons + +run in the seventh +cranial nerve. + +And what's the +seventh cranial nerve? + +Anybody? + +We have the eighth cranial nerve +is auditory and vestibular. + +What's the seventh? + +Anybody? + +AUDIENCE: Facial. + +PROFESSOR: Facial, right. + +So the stapedius axons +go in that cranial nerve. + +The stapedius motor +neuron axons, should say. + +And for the tensor tympani, +it's the fifth cranial nerve. + +Tensor tympani. + +So some very +interesting experiments + +have been done in +people who have + +a compromise of their +seventh cranial nerve. + +Does anybody know +what Bell's palsy is? + +Does anybody know +what a palsy is? + +Palsy means your motor neurons +aren't working so well. + +So what happens? + +In Bell's palsy, the +seventh cranial nerve + +innervates facial musculature. + +So if you have a problem, +a cut seventh nerve + +or a Bell's palsy, which +is a viral infection + +of the seventh cranial +nerve on one side, one + +side of your facial features +droop because the muscles + +there, which ordinary keep +your muscles in good control + +of your face, they're +not working anymore. + +So a person with a Bell's palsy +has a droopy face on that side. + +The other side is fine because +the other seventh cranial + +nerve is working just fine. + +Or it usually is. + +It's very often the case +that it's unilateral. + +In Scandinavia where you can +do experiments on humans, + +or you could at least +do experiments on humans + +to a much greater extent than +in the United States, what + +some enterprising +researchers did was + +they took people who had +Bell's palsy and they said, + +well, you can go and +work in your ordinary job + +in the automobile factory +where it's really loud. + +They tested their hearing +before they went to work + +and they tested their hearing +at the end of the work day. + +They tested it in the left +ear and in the right ear. + +Let's say the right ear +was the palsied ear. + +And then, left ear, +which was normal, + +person came out at +the end of the workday + +and their hearing +was just right. + +In the palsied side, +at the end of the day + +they had a temporary +threshold shift. + +That means that if they're +hearing was down at 0 dB + +at the beginning of the +day, their thresholds + +were elevated at +the end of the day. + +And hopefully, it's temporary. + +That is, if you sleep all +night and things recover, + +you're back to +normal the next day. + +But what had happened-- this +is a beautiful experiment + +because it's +controlled-- left-right + +in the same individual. + +So whatever that person did-- +took drugs, or got infections, + +or whatever-- was +hopefully bilateral. + +It's a human, so you +can test very well + +thresholds of hearing. + +Presumably then, the +stapedius muscle, + +which was not working +on the palsied side, + +couldn't protect the +ear from the high levels + +of sound in the +work environment. + +And there was +damage-- hopefully, + +temporary-- to that +person's hearing. + +So clearly, the contraction +of these muscles, + +which makes sound not go +through the middle ear as well, + +is of beneficial effect. + +For example, they protect +the cochlea from damage. + +People who are at the NFL games +are having their middle ear + +muscles contract. + +Certainly, the stapedius. + +And probably the tensor tympani. + +They probably reduce the +effects of noise masking. + +So that is a little +twist here in terms + +of the spectrum of +where these muscles act. + +It turns out when the muscles +contract, both the stapedius + +and the tensor tympani, +they affect low frequencies + +to a much greater +extent than highs. + +For example, here you have +a reduction in transmission + +through the middle ear of 25 +dB at the lowest frequency + +and 0, or even actually, +improved transmission + +at the high frequencies. + +And if you've ever been in +a car and you accelerate + +to go on the highway, +you know the low rumbling + +of the sound of the car means +you have to turn the radio up + +when you want to enjoy your +music because the low rumbling + +of the car, these +low frequencies + +tend to mask the +interesting high frequencies + +or mid-frequencies of +the music that you're + +trying to listen +to on the radio. + +So low frequencies tend to mask +mid and highs very effectively. + +And so if you decrease +the transmission + +for the low +frequencies, you reduce + +the effects of noise masking. + +Especially by +low-frequency noises. + +Now finally, an +interesting thing + +that is clearly known for +the middle ear muscles + +is that they +contract just before + +and during when you speak. + +During you speak, OK? + +I don't know who wrote that. + +But anyway, when I speak, +I'm contracting my middle ear + +muscles. + +And the idea there is +perhaps when you're speaking, + +you don't want to +listen to yourself. + +And if you're speaking in +a loud voice, like 80 dB, + +I'm trying to project here. + +Or if I'm yelling at +some family members, + +I want to not decrease my +sense of hearing or damage it. + +So I contract my own +middle ear muscles + +to prevent self-stimulation. + +After I finish my +speaking or vocalization, + +my muscles then stop +their contraction, + +going back to normal. + +And then my sense of +hearing is very acute + +because it hasn't been damaged +by my own vocalization. + +And later on in +the course, when we + +talk about echolocation in bats. + +So bats send out +this pulse of sound, + +which is their vocalization. + +And they listen for an echo. + +The pulse of sound +can be 120 dB. + +They're really screaming because +their targets, the insects + +that they hunt, are +very, very small. + +And there's not much +physical surface + +for that to reflect off. + +So the reflecting +sound is very small. + +And so they maximize +that reflection + +by emitting a very +high-level acoustic pulse. + +And they don't want to damage +or desensitize their hearing + +because they're listening +to very soft reflections + +from the echoes. + +So bats clearly tense their +middle ear muscles right + +before they make this +echo-locating pulse. + +We don't know if that's the case +for the olivocochlear neurons. + +It just hasn't +been investigated. + +It's very hard to measure their +effects during vocalizations. + +But perhaps they do. + +Certainly, the middle +ear muscles do. + +OK, that's all I wanted to say +so we're sort of out of time. + +Any questions? + +And I want to make +one announcement + +about Wednesday's class. + +So in Wednesday's +class we're going + +to be talking about +sound localization, + +and listening to sounds that +differ in intraural timing + +and level difference. + +And so the usual +demonstrations that I play + +aren't going to work +very well because we + +want to manipulate +just one of those cues. + +So we're going to be +listening in headphones. + +So I have some great demos. + +So please, if you can, bring +some headphones or earbuds. + +And maybe download the demos +from the course website. + +I have a few players that I +can also circulate around. + +But if some people have +these demos on their laptops, + +that would be more convenient. + +OK? + +See you on Wednesday. \ No newline at end of file diff --git a/rCqMiPk1BJE.txt b/rCqMiPk1BJE.txt new file mode 100644 index 0000000000000000000000000000000000000000..af6b20d263462006886eabf9f53a8ba6bbc46ecc --- /dev/null +++ b/rCqMiPk1BJE.txt @@ -0,0 +1,6179 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +last time we began having a look at how + + align:start position:0% +last time we began having a look at how + + + align:start position:0% +last time we began having a look at how +languages are constructed remember the + + align:start position:0% +languages are constructed remember the + + + align:start position:0% +languages are constructed remember the +main point that an evaluator for Lisp + + align:start position:0% +main point that an evaluator for Lisp + + + align:start position:0% +main point that an evaluator for Lisp +say has two main elements there's eval + + align:start position:0% +say has two main elements there's eval + + + align:start position:0% +say has two main elements there's eval +and evals job is to take in an + + align:start position:0% +and evals job is to take in an + + + align:start position:0% +and evals job is to take in an +expression and an environment and turn + + align:start position:0% +expression and an environment and turn + + + align:start position:0% +expression and an environment and turn +that into a procedure and some arguments + + align:start position:0% +that into a procedure and some arguments + + + align:start position:0% +that into a procedure and some arguments +and pass that off to apply and apply + + align:start position:0% +and pass that off to apply and apply + + + align:start position:0% +and pass that off to apply and apply +takes the procedure in the arguments + + align:start position:0% +takes the procedure in the arguments + + + align:start position:0% +takes the procedure in the arguments +turns that back into in the general case + + align:start position:0% +turns that back into in the general case + + + align:start position:0% +turns that back into in the general case +another expression to be evaluated in + + align:start position:0% +another expression to be evaluated in + + + align:start position:0% +another expression to be evaluated in +another environment and passes that off + + align:start position:0% +another environment and passes that off + + + align:start position:0% +another environment and passes that off +to EDI which passes it to apply and + + align:start position:0% +to EDI which passes it to apply and + + + align:start position:0% +to EDI which passes it to apply and +there's this whole big circle where + + align:start position:0% +there's this whole big circle where + + + align:start position:0% +there's this whole big circle where +things go around and around and around + + align:start position:0% +things go around and around and around + + + align:start position:0% +things go around and around and around +until you get either to some very + + align:start position:0% +until you get either to some very + + + align:start position:0% +until you get either to some very +primitive data or to a primitive + + align:start position:0% +primitive data or to a primitive + + + align:start position:0% +primitive data or to a primitive +procedure see what the cycle has to do + + align:start position:0% +procedure see what the cycle has to do + + + align:start position:0% +procedure see what the cycle has to do +with is unwinding the means of + + align:start position:0% +with is unwinding the means of + + + align:start position:0% +with is unwinding the means of +combination and the means of abstraction + + align:start position:0% +combination and the means of abstraction + + + align:start position:0% +combination and the means of abstraction +in the language so for instance you have + + align:start position:0% +in the language so for instance you have + + + align:start position:0% +in the language so for instance you have +a procedure in Lisp a procedure is a + + align:start position:0% +a procedure in Lisp a procedure is a + + + align:start position:0% +a procedure in Lisp a procedure is a +general way of saying I want to be able + + align:start position:0% +general way of saying I want to be able + + + align:start position:0% +general way of saying I want to be able +to evaluate this expression for any + + align:start position:0% +to evaluate this expression for any + + + align:start position:0% +to evaluate this expression for any +value of the arguments and that's sort + + align:start position:0% +value of the arguments and that's sort + + + align:start position:0% +value of the arguments and that's sort +of what's going on here that's what + + align:start position:0% +of what's going on here that's what + + + align:start position:0% +of what's going on here that's what +apply does it says the general thing + + align:start position:0% +apply does it says the general thing + + + align:start position:0% +apply does it says the general thing +coming in with the arguments reduces to + + align:start position:0% +coming in with the arguments reduces to + + + align:start position:0% +coming in with the arguments reduces to +the expression that's the body and then + + align:start position:0% +the expression that's the body and then + + + align:start position:0% +the expression that's the body and then +if that's a compound expression or + + align:start position:0% +if that's a compound expression or + + + align:start position:0% +if that's a compound expression or +another procedure application the thing + + align:start position:0% +another procedure application the thing + + + align:start position:0% +another procedure application the thing +will go around and around the circle + + align:start position:0% +will go around and around the circle + + + align:start position:0% +will go around and around the circle +anyway that's sort of the basic + + align:start position:0% +anyway that's sort of the basic + + + align:start position:0% +anyway that's sort of the basic +structure of objects o1 cyou have the + + align:start position:0% +structure of objects o1 cyou have the + + + align:start position:0% +structure of objects o1 cyou have the +interpreter in your hands you have all + + align:start position:0% +interpreter in your hands you have all + + + align:start position:0% +interpreter in your hands you have all +this power to start playing with the + + align:start position:0% +this power to start playing with the + + + align:start position:0% +this power to start playing with the +language so you can make it dynamically + + align:start position:0% +language so you can make it dynamically + + + align:start position:0% +language so you can make it dynamically +scoped or you can put in normal order + + align:start position:0% +scoped or you can put in normal order + + + align:start position:0% +scoped or you can put in normal order +evaluation or you can add new forms to + + align:start position:0% +evaluation or you can add new forms to + + + align:start position:0% +evaluation or you can add new forms to +the language whatever you like or more + + align:start position:0% +the language whatever you like or more + + + align:start position:0% +the language whatever you like or more +generally there's this notion of + + align:start position:0% +generally there's this notion of + + + align:start position:0% +generally there's this notion of +metalinguistic abstraction which says + + align:start position:0% +metalinguistic abstraction which says + + + align:start position:0% +metalinguistic abstraction which says +that part of your perspective as an + + align:start position:0% +that part of your perspective as an + + + align:start position:0% +that part of your perspective as an +engineer as a software engineer but as + + align:start position:0% +engineer as a software engineer but as + + + align:start position:0% +engineer as a software engineer but as +an engineer in general is that you can + + align:start position:0% +an engineer in general is that you can + + + align:start position:0% +an engineer in general is that you can +gain control of complexity by inventing + + align:start position:0% +gain control of complexity by inventing + + + align:start position:0% +gain control of complexity by inventing +new languages sometimes let's see one + + align:start position:0% +new languages sometimes let's see one + + + align:start position:0% +new languages sometimes let's see one +way to think about computer programming + + align:start position:0% +way to think about computer programming + + + align:start position:0% +way to think about computer programming +is that it's only instant it only + + align:start position:0% +is that it's only instant it only + + + align:start position:0% +is that it's only instant it only +incidentally has to do with getting a + + align:start position:0% +incidentally has to do with getting a + + + align:start position:0% +incidentally has to do with getting a +computer to do something primarily what + + align:start position:0% +computer to do something primarily what + + + align:start position:0% +computer to do something primarily what +a computer program has to do with it's a + + align:start position:0% +a computer program has to do with it's a + + + align:start position:0% +a computer program has to do with it's a +way of expressing ideas + + align:start position:0% +way of expressing ideas + + + align:start position:0% +way of expressing ideas +way of communicating ideas and sometimes + + align:start position:0% +way of communicating ideas and sometimes + + + align:start position:0% +way of communicating ideas and sometimes +when you want to communicate new kinds + + align:start position:0% +when you want to communicate new kinds + + + align:start position:0% +when you want to communicate new kinds +of ideas you'd like to invent new modes + + align:start position:0% +of ideas you'd like to invent new modes + + + align:start position:0% +of ideas you'd like to invent new modes +of expressing that well today we're + + align:start position:0% +of expressing that well today we're + + + align:start position:0% +of expressing that well today we're +going to apply this framework to build a + + align:start position:0% +going to apply this framework to build a + + + align:start position:0% +going to apply this framework to build a +new language see once we have the basic + + align:start position:0% +new language see once we have the basic + + + align:start position:0% +new language see once we have the basic +idea of the interpreter you can pretty + + align:start position:0% +idea of the interpreter you can pretty + + + align:start position:0% +idea of the interpreter you can pretty +much go build any language that you like + + align:start position:0% +much go build any language that you like + + + align:start position:0% +much go build any language that you like +so for example we could go off and build + + align:start position:0% +so for example we could go off and build + + + align:start position:0% +so for example we could go off and build +Pascal and she would worry about syntax + + align:start position:0% +Pascal and she would worry about syntax + + + align:start position:0% +Pascal and she would worry about syntax +and parsing and various kinds of + + align:start position:0% +and parsing and various kinds of + + + align:start position:0% +and parsing and various kinds of +compiler optimizations and you know + + align:start position:0% +compiler optimizations and you know + + + align:start position:0% +compiler optimizations and you know +there are people who make honest livings + + align:start position:0% +there are people who make honest livings + + + align:start position:0% +there are people who make honest livings +doing that but at the at the level of + + align:start position:0% +doing that but at the at the level of + + + align:start position:0% +doing that but at the at the level of +abstraction that we're talking a Pascal + + align:start position:0% +abstraction that we're talking a Pascal + + + align:start position:0% +abstraction that we're talking a Pascal +interpreter would not look very + + align:start position:0% +interpreter would not look very + + + align:start position:0% +interpreter would not look very +different at all from what you saw Jerry + + align:start position:0% +different at all from what you saw Jerry + + + align:start position:0% +different at all from what you saw Jerry +do last time instead of that we'll spend + + align:start position:0% +do last time instead of that we'll spend + + + align:start position:0% +do last time instead of that we'll spend +today building a really different + + align:start position:0% +today building a really different + + + align:start position:0% +today building a really different +language straight a language that that + + align:start position:0% +language straight a language that that + + + align:start position:0% +language straight a language that that +encourages you to think about + + align:start position:0% +encourages you to think about + + + align:start position:0% +encourages you to think about +programming not in terms of procedures + + align:start position:0% +programming not in terms of procedures + + + align:start position:0% +programming not in terms of procedures +but in a really different way and the + + align:start position:0% +but in a really different way and the + + + align:start position:0% +but in a really different way and the +lecture today is going to be at at two + + align:start position:0% +lecture today is going to be at at two + + + align:start position:0% +lecture today is going to be at at two +levels simultaneously on the one hand + + align:start position:0% +levels simultaneously on the one hand + + + align:start position:0% +levels simultaneously on the one hand +I'm going to show you what this language + + align:start position:0% +I'm going to show you what this language + + + align:start position:0% +I'm going to show you what this language +looks like and on the other hand I'll + + align:start position:0% +looks like and on the other hand I'll + + + align:start position:0% +looks like and on the other hand I'll +show you how it's implemented and we'll + + align:start position:0% +show you how it's implemented and we'll + + + align:start position:0% +show you how it's implemented and we'll +build an implementation and Lisp and see + + align:start position:0% +build an implementation and Lisp and see + + + align:start position:0% +build an implementation and Lisp and see +how that works + + align:start position:0% +how that works + + + align:start position:0% +how that works +and you should be drawing lessons on two + + align:start position:0% +and you should be drawing lessons on two + + + align:start position:0% +and you should be drawing lessons on two +levels the first is is to realize just + + align:start position:0% +levels the first is is to realize just + + + align:start position:0% +levels the first is is to realize just +how different a language can be so if + + align:start position:0% +how different a language can be so if + + + align:start position:0% +how different a language can be so if +you think that the the jump from Fortran + + align:start position:0% +you think that the the jump from Fortran + + + align:start position:0% +you think that the the jump from Fortran +to Lisp is a big deal you haven't seen + + align:start position:0% +to Lisp is a big deal you haven't seen + + + align:start position:0% +to Lisp is a big deal you haven't seen +anything yet and secondly you'll see + + align:start position:0% +anything yet and secondly you'll see + + + align:start position:0% +anything yet and secondly you'll see +that even with such a very different + + align:start position:0% +that even with such a very different + + + align:start position:0% +that even with such a very different +language which will turn out to not have + + align:start position:0% +language which will turn out to not have + + + align:start position:0% +language which will turn out to not have +procedures at all and not talk about + + align:start position:0% +procedures at all and not talk about + + + align:start position:0% +procedures at all and not talk about +functions at all they'll still be this + + align:start position:0% +functions at all they'll still be this + + + align:start position:0% +functions at all they'll still be this +basic cycle of eval and apply that + + align:start position:0% +basic cycle of eval and apply that + + + align:start position:0% +basic cycle of eval and apply that +unwinds the the means of combination and + + align:start position:0% +unwinds the the means of combination and + + + align:start position:0% +unwinds the the means of combination and +the means of abstraction and then + + align:start position:0% +the means of abstraction and then + + + align:start position:0% +the means of abstraction and then +thirdly as kind of a minor but elegant + + align:start position:0% +thirdly as kind of a minor but elegant + + + align:start position:0% +thirdly as kind of a minor but elegant +technical point you see a nice use of + + align:start position:0% +technical point you see a nice use of + + + align:start position:0% +technical point you see a nice use of +streams to avoid backtracking + + align:start position:0% + + + + align:start position:0% + +okay well I said that this language is + + align:start position:0% +okay well I said that this language is + + + align:start position:0% +okay well I said that this language is +very different to explain that let's go + + align:start position:0% +very different to explain that let's go + + + align:start position:0% +very different to explain that let's go +back to the very first idea that we + + align:start position:0% +back to the very first idea that we + + + align:start position:0% +back to the very first idea that we +talked about in this course and that was + + align:start position:0% +talked about in this course and that was + + + align:start position:0% +talked about in this course and that was +the idea of the distinction between the + + align:start position:0% +the idea of the distinction between the + + + align:start position:0% +the idea of the distinction between the +declarative knowledge of mathematics the + + align:start position:0% +declarative knowledge of mathematics the + + + align:start position:0% +declarative knowledge of mathematics the +the definition of the square root as a + + align:start position:0% +the definition of the square root as a + + + align:start position:0% +the definition of the square root as a +mathematical truth and the idea that + + align:start position:0% +mathematical truth and the idea that + + + align:start position:0% +mathematical truth and the idea that +computer science talks about the how-to + + align:start position:0% +computer science talks about the how-to + + + align:start position:0% +computer science talks about the how-to +knowledge contrast that definition of + + align:start position:0% +knowledge contrast that definition of + + + align:start position:0% +knowledge contrast that definition of +square root with a program to compute a + + align:start position:0% +square root with a program to compute a + + + align:start position:0% +square root with a program to compute a +square it it's that's where we started + + align:start position:0% +square it it's that's where we started + + + align:start position:0% +square it it's that's where we started +off well wouldn't it be great if you + + align:start position:0% +off well wouldn't it be great if you + + + align:start position:0% +off well wouldn't it be great if you +could somehow bridge this gap and make a + + align:start position:0% +could somehow bridge this gap and make a + + + align:start position:0% +could somehow bridge this gap and make a +programming language which sort of did + + align:start position:0% +programming language which sort of did + + + align:start position:0% +programming language which sort of did +things but you talked about it in in + + align:start position:0% +things but you talked about it in in + + + align:start position:0% +things but you talked about it in in +terms of truth in declarative terms so + + align:start position:0% +terms of truth in declarative terms so + + + align:start position:0% +terms of truth in declarative terms so +there would be a programming language in + + align:start position:0% +there would be a programming language in + + + align:start position:0% +there would be a programming language in +which you specify facts right you tell + + align:start position:0% +which you specify facts right you tell + + + align:start position:0% +which you specify facts right you tell +it what is you say what is true and then + + align:start position:0% +it what is you say what is true and then + + + align:start position:0% +it what is you say what is true and then +when you want an answer somehow the + + align:start position:0% +when you want an answer somehow the + + + align:start position:0% +when you want an answer somehow the +language has built into it automatically + + align:start position:0% +language has built into it automatically + + + align:start position:0% +language has built into it automatically +general kinds of how-to knowledge so it + + align:start position:0% +general kinds of how-to knowledge so it + + + align:start position:0% +general kinds of how-to knowledge so it +can just take your facts and it can + + align:start position:0% +can just take your facts and it can + + + align:start position:0% +can just take your facts and it can +involve these methods on its own using + + align:start position:0% +involve these methods on its own using + + + align:start position:0% +involve these methods on its own using +the facts you gave it and maybe some + + align:start position:0% +the facts you gave it and maybe some + + + align:start position:0% +the facts you gave it and maybe some +general rules of logic so for instance I + + align:start position:0% +general rules of logic so for instance I + + + align:start position:0% +general rules of logic so for instance I +might go up to this program and start + + align:start position:0% +might go up to this program and start + + + align:start position:0% +might go up to this program and start +telling it some things so I might tell + + align:start position:0% +telling it some things so I might tell + + + align:start position:0% +telling it some things so I might tell +it that the that the son of that the son + + align:start position:0% +it that the that the son of that the son + + + align:start position:0% +it that the that the son of that the son +of Adam is able and I might tell it that + + align:start position:0% +of Adam is able and I might tell it that + + + align:start position:0% +of Adam is able and I might tell it that +the son of son of Adam is king and I + + align:start position:0% +the son of son of Adam is king and I + + + align:start position:0% +the son of son of Adam is king and I +might tell it that the son of Cain is + + align:start position:0% +might tell it that the son of Cain is + + + align:start position:0% +might tell it that the son of Cain is +Enoch and I might tell it that the son + + align:start position:0% +Enoch and I might tell it that the son + + + align:start position:0% +Enoch and I might tell it that the son +of + + align:start position:0% + + + + align:start position:0% + +Enoch is your ad and all through the + + align:start position:0% +Enoch is your ad and all through the + + + align:start position:0% +Enoch is your ad and all through the +rest of chapter whatever of Genesis + + align:start position:0% +rest of chapter whatever of Genesis + + + align:start position:0% +rest of chapter whatever of Genesis +which ends up ending in ADA by the way + + align:start position:0% +which ends up ending in ADA by the way + + + align:start position:0% +which ends up ending in ADA by the way +this shows the the genealogy of ADA from + + align:start position:0% +this shows the the genealogy of ADA from + + + align:start position:0% +this shows the the genealogy of ADA from +Cain anyway once you tell it these facts + + align:start position:0% +Cain anyway once you tell it these facts + + + align:start position:0% +Cain anyway once you tell it these facts +you might ask it Thanks you might go up + + align:start position:0% +you might ask it Thanks you might go up + + + align:start position:0% +you might ask it Thanks you might go up +to your language and say Oh who's the + + align:start position:0% +to your language and say Oh who's the + + + align:start position:0% +to your language and say Oh who's the +who's the son of the atom and you can + + align:start position:0% +who's the son of the atom and you can + + + align:start position:0% +who's the son of the atom and you can +very easily imagine having a little + + align:start position:0% +very easily imagine having a little + + + align:start position:0% +very easily imagine having a little +general-purpose search program which + + align:start position:0% +general-purpose search program which + + + align:start position:0% +general-purpose search program which +would be able to go through and response + + align:start position:0% +would be able to go through and response + + + align:start position:0% +would be able to go through and response +to that say oh yeah + + align:start position:0% +to that say oh yeah + + + align:start position:0% +to that say oh yeah +this there are two answers the son of + + align:start position:0% +this there are two answers the son of + + + align:start position:0% +this there are two answers the son of +Adam is Abel and the son of Adam is Cain + + align:start position:0% +Adam is Abel and the son of Adam is Cain + + + align:start position:0% +Adam is Abel and the son of Adam is Cain +or you might say based on the very same + + align:start position:0% +or you might say based on the very same + + + align:start position:0% +or you might say based on the very same +facts who is a Cain the son of and then + + align:start position:0% +facts who is a Cain the son of and then + + + align:start position:0% +facts who is a Cain the son of and then +you can imagine generating another + + align:start position:0% +you can imagine generating another + + + align:start position:0% +you can imagine generating another +slightly different search program which + + align:start position:0% +slightly different search program which + + + align:start position:0% +slightly different search program which +would be able to go through and and + + align:start position:0% +would be able to go through and and + + + align:start position:0% +would be able to go through and and +check for who's who is can't Cain and + + align:start position:0% +check for who's who is can't Cain and + + + align:start position:0% +check for who's who is can't Cain and +son of and come up with Adam or you + + align:start position:0% +son of and come up with Adam or you + + + align:start position:0% +son of and come up with Adam or you +might say what's what's the relationship + + align:start position:0% +might say what's what's the relationship + + + align:start position:0% +might say what's what's the relationship +between Cain and Enoch and again a minor + + align:start position:0% +between Cain and Enoch and again a minor + + + align:start position:0% +between Cain and Enoch and again a minor +variant on that search program you could + + align:start position:0% +variant on that search program you could + + + align:start position:0% +variant on that search program you could +figure out that it said son of but even + + align:start position:0% +figure out that it said son of but even + + + align:start position:0% +figure out that it said son of but even +here in this very simple example what + + align:start position:0% +here in this very simple example what + + + align:start position:0% +here in this very simple example what +you see is that a single fact see a + + align:start position:0% +you see is that a single fact see a + + + align:start position:0% +you see is that a single fact see a +single fact like the son of the atom is + + align:start position:0% +single fact like the son of the atom is + + + align:start position:0% +single fact like the son of the atom is +king can be used to answer different + + align:start position:0% +king can be used to answer different + + + align:start position:0% +king can be used to answer different +kinds of questions you can say who's the + + align:start position:0% +kinds of questions you can say who's the + + + align:start position:0% +kinds of questions you can say who's the +king in the son of or you can say who's + + align:start position:0% +king in the son of or you can say who's + + + align:start position:0% +king in the son of or you can say who's +the who's the son of the Adam or you can + + align:start position:0% +the who's the son of the Adam or you can + + + align:start position:0% +the who's the son of the Adam or you can +say what's the relation between Adam and + + align:start position:0% +say what's the relation between Adam and + + + align:start position:0% +say what's the relation between Adam and +Cain those are different questions being + + align:start position:0% +Cain those are different questions being + + + align:start position:0% +Cain those are different questions being +run by different traditional procedures + + align:start position:0% +run by different traditional procedures + + + align:start position:0% +run by different traditional procedures +all based on the same fact and that's + + align:start position:0% +all based on the same fact and that's + + + align:start position:0% +all based on the same fact and that's +going to be the essence of the power of + + align:start position:0% +going to be the essence of the power of + + + align:start position:0% +going to be the essence of the power of +this programming style that one piece of + + align:start position:0% +this programming style that one piece of + + + align:start position:0% +this programming style that one piece of +declarative knowledge can be used as the + + align:start position:0% +declarative knowledge can be used as the + + + align:start position:0% +declarative knowledge can be used as the +basis for a lot of different kinds of + + align:start position:0% +basis for a lot of different kinds of + + + align:start position:0% +basis for a lot of different kinds of +how-to knowledge as opposed to the kinds + + align:start position:0% +how-to knowledge as opposed to the kinds + + + align:start position:0% +how-to knowledge as opposed to the kinds +of procedures were writing where you + + align:start position:0% +of procedures were writing where you + + + align:start position:0% +of procedures were writing where you +sort of tell it what input you're giving + + align:start position:0% +sort of tell it what input you're giving + + + align:start position:0% +sort of tell it what input you're giving +in and what answer you want so for + + align:start position:0% +in and what answer you want so for + + + align:start position:0% +in and what answer you want so for +instance our square root program can + + align:start position:0% +instance our square root program can + + + align:start position:0% +instance our square root program can +perfectly well answer the question + + align:start position:0% +perfectly well answer the question + + + align:start position:0% +perfectly well answer the question +what's + + align:start position:0% +what's + + + align:start position:0% +what's +square root of 144 but in principle the + + align:start position:0% +square root of 144 but in principle the + + + align:start position:0% +square root of 144 but in principle the +mathematical definition of square root + + align:start position:0% +mathematical definition of square root + + + align:start position:0% +mathematical definition of square root +tells you other things like it could say + + align:start position:0% +tells you other things like it could say + + + align:start position:0% +tells you other things like it could say +what is what is 17 the square root of + + align:start position:0% +what is what is 17 the square root of + + + align:start position:0% +what is what is 17 the square root of +and that would be have to answered by a + + align:start position:0% +and that would be have to answered by a + + + align:start position:0% +and that would be have to answered by a +different program so the mathematical + + align:start position:0% +different program so the mathematical + + + align:start position:0% +different program so the mathematical +definition or the in general the the + + align:start position:0% +definition or the in general the the + + + align:start position:0% +definition or the in general the the +facts that you give it or somehow + + align:start position:0% +facts that you give it or somehow + + + align:start position:0% +facts that you give it or somehow +unbiased as to what what as to what the + + align:start position:0% +unbiased as to what what as to what the + + + align:start position:0% +unbiased as to what what as to what the +question is whereas the programs we tend + + align:start position:0% +question is whereas the programs we tend + + + align:start position:0% +question is whereas the programs we tend +to write specifically because they're + + align:start position:0% +to write specifically because they're + + + align:start position:0% +to write specifically because they're +how-to knowledge tend to be looking for + + align:start position:0% +how-to knowledge tend to be looking for + + + align:start position:0% +how-to knowledge tend to be looking for +a specific answer so that's going to be + + align:start position:0% +a specific answer so that's going to be + + + align:start position:0% +a specific answer so that's going to be +one characteristic of what we're talking + + align:start position:0% +one characteristic of what we're talking + + + align:start position:0% +one characteristic of what we're talking +about we can go on we can imagine that + + align:start position:0% +about we can go on we can imagine that + + + align:start position:0% +about we can go on we can imagine that +we've given our language some sort of + + align:start position:0% +we've given our language some sort of + + + align:start position:0% +we've given our language some sort of +facts now let's give it some rules of + + align:start position:0% +facts now let's give it some rules of + + + align:start position:0% +facts now let's give it some rules of +inference we can say for instance if the + + align:start position:0% +inference we can say for instance if the + + + align:start position:0% +inference we can say for instance if the +I'll make up some syntax here if the son + + align:start position:0% +I'll make up some syntax here if the son + + + align:start position:0% +I'll make up some syntax here if the son +of X is y I'll put question marks to + + align:start position:0% +of X is y I'll put question marks to + + + align:start position:0% +of X is y I'll put question marks to +indicate variables here if the son of X + + align:start position:0% +indicate variables here if the son of X + + + align:start position:0% +indicate variables here if the son of X +is y and the son of Y is Z then the + + align:start position:0% +is y and the son of Y is Z then the + + + align:start position:0% +is y and the son of Y is Z then the +grandson of X is Z so I can imagine + + align:start position:0% +grandson of X is Z so I can imagine + + + align:start position:0% +grandson of X is Z so I can imagine +telling telling my machine that rule and + + align:start position:0% +telling telling my machine that rule and + + + align:start position:0% +telling telling my machine that rule and +then being able to say for instance + + align:start position:0% +then being able to say for instance + + + align:start position:0% +then being able to say for instance +who's the grandson of Adam or whose ear + + align:start position:0% +who's the grandson of Adam or whose ear + + + align:start position:0% +who's the grandson of Adam or whose ear +odd the grandson of or deduce all + + align:start position:0% +odd the grandson of or deduce all + + + align:start position:0% +odd the grandson of or deduce all +grandson relationships you possibly can + + align:start position:0% +grandson relationships you possibly can + + + align:start position:0% +grandson relationships you possibly can +from this information and you can + + align:start position:0% +from this information and you can + + + align:start position:0% +from this information and you can +imagine somehow the language knowing how + + align:start position:0% +imagine somehow the language knowing how + + + align:start position:0% +imagine somehow the language knowing how +to do that automatically okay let me + + align:start position:0% +to do that automatically okay let me + + + align:start position:0% +to do that automatically okay let me +let me give you a maybe a little bit + + align:start position:0% +let me give you a maybe a little bit + + + align:start position:0% +let me give you a maybe a little bit +more concrete example here's a here's a + + align:start position:0% +more concrete example here's a here's a + + + align:start position:0% +more concrete example here's a here's a +procedure that merges two sorted lists + + align:start position:0% +procedure that merges two sorted lists + + + align:start position:0% +procedure that merges two sorted lists +so x and y are to say lists of numbers + + align:start position:0% +so x and y are to say lists of numbers + + + align:start position:0% +so x and y are to say lists of numbers +list of distinct numbers if you like + + align:start position:0% +list of distinct numbers if you like + + + align:start position:0% +list of distinct numbers if you like +that or that are in increasing order and + + align:start position:0% +that or that are in increasing order and + + + align:start position:0% +that or that are in increasing order and +what merge does is take two such lists + + align:start position:0% +what merge does is take two such lists + + + align:start position:0% +what merge does is take two such lists +and combine them into a list where + + align:start position:0% +and combine them into a list where + + + align:start position:0% +and combine them into a list where +everything is an increasing order and + + align:start position:0% +everything is an increasing order and + + + align:start position:0% +everything is an increasing order and +this is a pretty easy program that you + + align:start position:0% +this is a pretty easy program that you + + + align:start position:0% +this is a pretty easy program that you +ought to be able to write it says if x + + align:start position:0% +ought to be able to write it says if x + + + align:start position:0% +ought to be able to write it says if x +is empty the answer is y if y is empty + + align:start position:0% +is empty the answer is y if y is empty + + + align:start position:0% +is empty the answer is y if y is empty +the answer is x otherwise you compare + + align:start position:0% +the answer is x otherwise you compare + + + align:start position:0% +the answer is x otherwise you compare +the first two elements so you pick out + + align:start position:0% +the first two elements so you pick out + + + align:start position:0% +the first two elements so you pick out +the first thing in X and the first thing + + align:start position:0% +the first thing in X and the first thing + + + align:start position:0% +the first thing in X and the first thing +in Y and then depending on which one's + + align:start position:0% +in Y and then depending on which one's + + + align:start position:0% +in Y and then depending on which one's +left I'm on which which of those first + + align:start position:0% +left I'm on which which of those first + + + align:start position:0% +left I'm on which which of those first +elements is less you stick the lower one + + align:start position:0% +elements is less you stick the lower one + + + align:start position:0% +elements is less you stick the lower one +on to the result of recursively merging + + align:start position:0% +on to the result of recursively merging + + + align:start position:0% +on to the result of recursively merging +either chopping the first one or X or + + align:start position:0% +either chopping the first one or X or + + + align:start position:0% +either chopping the first one or X or +chopping the first one off Y that's a + + align:start position:0% +chopping the first one off Y that's a + + + align:start position:0% +chopping the first one off Y that's a +standard kind of program let's look at + + align:start position:0% +standard kind of program let's look at + + + align:start position:0% +standard kind of program let's look at +the the logic let's forget about the + + align:start position:0% +the the logic let's forget about the + + + align:start position:0% +the the logic let's forget about the +program and look at the logic on which + + align:start position:0% +program and look at the logic on which + + + align:start position:0% +program and look at the logic on which +that procedures based see there's some + + align:start position:0% +that procedures based see there's some + + + align:start position:0% +that procedures based see there's some +logic which says gee if we if the first + + align:start position:0% +logic which says gee if we if the first + + + align:start position:0% +logic which says gee if we if the first +one is less then we get the answer by + + align:start position:0% +one is less then we get the answer by + + + align:start position:0% +one is less then we get the answer by +sticking something on to the result of + + align:start position:0% +sticking something on to the result of + + + align:start position:0% +sticking something on to the result of +recursively merging the rest so let's + + align:start position:0% +recursively merging the rest so let's + + + align:start position:0% +recursively merging the rest so let's +try to be explicit about what that logic + + align:start position:0% +try to be explicit about what that logic + + + align:start position:0% +try to be explicit about what that logic +is that's making the program work + + align:start position:0% +is that's making the program work + + + align:start position:0% +is that's making the program work +alright so here's one piece here's the + + align:start position:0% +alright so here's one piece here's the + + + align:start position:0% +alright so here's one piece here's the +piece of the program which recursively + + align:start position:0% +piece of the program which recursively + + + align:start position:0% +piece of the program which recursively +chops down X if the first thing in X is + + align:start position:0% +chops down X if the first thing in X is + + + align:start position:0% +chops down X if the first thing in X is +smaller and if you want to be very + + align:start position:0% +smaller and if you want to be very + + + align:start position:0% +smaller and if you want to be very +explicit about what the logic is there + + align:start position:0% +explicit about what the logic is there + + + align:start position:0% +explicit about what the logic is there +what's really going on is is a deduction + + align:start position:0% +what's really going on is is a deduction + + + align:start position:0% +what's really going on is is a deduction +which says if you know that some list + + align:start position:0% +which says if you know that some list + + + align:start position:0% +which says if you know that some list +that we'll call cooter of x and y merge + + align:start position:0% +that we'll call cooter of x and y merge + + + align:start position:0% +that we'll call cooter of x and y merge +to form Z and you know that a is less + + align:start position:0% +to form Z and you know that a is less + + + align:start position:0% +to form Z and you know that a is less +than the first thing in Y then you know + + align:start position:0% +than the first thing in Y then you know + + + align:start position:0% +than the first thing in Y then you know +that if you put a onto the cooter of X + + align:start position:0% +that if you put a onto the cooter of X + + + align:start position:0% +that if you put a onto the cooter of X +then that result and Y merged to form a + + align:start position:0% +then that result and Y merged to form a + + + align:start position:0% +then that result and Y merged to form a +onto Z + + align:start position:0% +onto Z + + + align:start position:0% +onto Z +and what that is that's the underlying + + align:start position:0% +and what that is that's the underlying + + + align:start position:0% +and what that is that's the underlying +piece of logic I haven't written it as a + + align:start position:0% +piece of logic I haven't written it as a + + + align:start position:0% +piece of logic I haven't written it as a +program I wrote it as a sort of + + align:start position:0% +program I wrote it as a sort of + + + align:start position:0% +program I wrote it as a sort of +deduction that sits that's underneath + + align:start position:0% +deduction that sits that's underneath + + + align:start position:0% +deduction that sits that's underneath +this particular clause that says we can + + align:start position:0% +this particular clause that says we can + + + align:start position:0% +this particular clause that says we can +use the recursion there and then similar + + align:start position:0% +use the recursion there and then similar + + + align:start position:0% +use the recursion there and then similar +here's the other clause just to just to + + align:start position:0% +here's the other clause just to just to + + + align:start position:0% +here's the other clause just to just to +complete it the other clause is based on + + align:start position:0% +complete it the other clause is based on + + + align:start position:0% +complete it the other clause is based on +this piece of logic which is almost + + align:start position:0% +this piece of logic which is almost + + + align:start position:0% +this piece of logic which is almost +almost the same and I won't go through + + align:start position:0% +almost the same and I won't go through + + + align:start position:0% +almost the same and I won't go through +it and then there's the end cases we're + + align:start position:0% +it and then there's the end cases we're + + + align:start position:0% +it and then there's the end cases we're +sitting where we tested for null and + + align:start position:0% +sitting where we tested for null and + + + align:start position:0% +sitting where we tested for null and +that's based on the idea that for any X + + align:start position:0% +that's based on the idea that for any X + + + align:start position:0% +that's based on the idea that for any X +X and the empty list merged to form X or + + align:start position:0% +X and the empty list merged to form X or + + + align:start position:0% +X and the empty list merged to form X or +for any Y the empty list and Y merged to + + align:start position:0% +for any Y the empty list and Y merged to + + + align:start position:0% +for any Y the empty list and Y merged to +form Y okay so there's there's a piece + + align:start position:0% +form Y okay so there's there's a piece + + + align:start position:0% +form Y okay so there's there's a piece +of there's a piece of procedure and the + + align:start position:0% +of there's a piece of procedure and the + + + align:start position:0% +of there's a piece of procedure and the +logic on which it's based and notice a + + align:start position:0% +logic on which it's based and notice a + + + align:start position:0% +logic on which it's based and notice a +big difference the procedure looked like + + align:start position:0% +big difference the procedure looked like + + + align:start position:0% +big difference the procedure looked like +a procedure looked like this it said + + align:start position:0% +a procedure looked like this it said + + + align:start position:0% +a procedure looked like this it said +there was a box and all the all the + + align:start position:0% +there was a box and all the all the + + + align:start position:0% +there was a box and all the all the +things we've been doing have the + + align:start position:0% +things we've been doing have the + + + align:start position:0% +things we've been doing have the +characteristic we have boxes and things + + align:start position:0% +characteristic we have boxes and things + + + align:start position:0% +characteristic we have boxes and things +going in and things going out there was + + align:start position:0% +going in and things going out there was + + + align:start position:0% +going in and things going out there was +this box called merge and in came an x + + align:start position:0% +this box called merge and in came an x + + + align:start position:0% +this box called merge and in came an x +and y and out came an answer that's the + + align:start position:0% +and y and out came an answer that's the + + + align:start position:0% +and y and out came an answer that's the +character of the procedure that we wrote + + align:start position:0% + + + + align:start position:0% + +these rules don't look like that these + + align:start position:0% +these rules don't look like that these + + + align:start position:0% +these rules don't look like that these +rules talk about or relation there's + + align:start position:0% +rules talk about or relation there's + + + align:start position:0% +rules talk about or relation there's +some sort of relation then in those + + align:start position:0% +some sort of relation then in those + + + align:start position:0% +some sort of relation then in those +slides I called merge to form so I said + + align:start position:0% +slides I called merge to form so I said + + + align:start position:0% +slides I called merge to form so I said +x and y merge to form Z and somehow this + + align:start position:0% +x and y merge to form Z and somehow this + + + align:start position:0% +x and y merge to form Z and somehow this +this is not this is a function right the + + align:start position:0% +this is not this is a function right the + + + align:start position:0% +this is not this is a function right the +answer is a function of x and y and here + + align:start position:0% +answer is a function of x and y and here + + + align:start position:0% +answer is a function of x and y and here +what I have is a relation between three + + align:start position:0% +what I have is a relation between three + + + align:start position:0% +what I have is a relation between three +things and I'm not going to specify + + align:start position:0% +things and I'm not going to specify + + + align:start position:0% +things and I'm not going to specify +which is the input and which is the + + align:start position:0% +which is the input and which is the + + + align:start position:0% +which is the input and which is the +output and the reason I want to say that + + align:start position:0% +output and the reason I want to say that + + + align:start position:0% +output and the reason I want to say that +is because in principle we could use + + align:start position:0% +is because in principle we could use + + + align:start position:0% +is because in principle we could use +exactly the same logic rules to answer a + + align:start position:0% +exactly the same logic rules to answer a + + + align:start position:0% +exactly the same logic rules to answer a +lot of different questions so we could + + align:start position:0% +lot of different questions so we could + + + align:start position:0% +lot of different questions so we could +say for instance giving imagine giving + + align:start position:0% +say for instance giving imagine giving + + + align:start position:0% +say for instance giving imagine giving +our machine those rules of logic not the + + align:start position:0% +our machine those rules of logic not the + + + align:start position:0% +our machine those rules of logic not the +program the underlying rules of logic + + align:start position:0% +program the underlying rules of logic + + + align:start position:0% +program the underlying rules of logic +then it ought to be able to say we could + + align:start position:0% +then it ought to be able to say we could + + + align:start position:0% +then it ought to be able to say we could +ask it 137 and + + align:start position:0% +ask it 137 and + + + align:start position:0% +ask it 137 and +two four eight merge merge to form wat + + align:start position:0% +two four eight merge merge to form wat + + + align:start position:0% +two four eight merge merge to form wat +and that's a question it would it be + + align:start position:0% +and that's a question it would it be + + + align:start position:0% +and that's a question it would it be +able to answer that's exactly the the + + align:start position:0% +able to answer that's exactly the the + + + align:start position:0% +able to answer that's exactly the the +same question that our list procedure + + align:start position:0% +same question that our list procedure + + + align:start position:0% +same question that our list procedure +answered but the exact same rules should + + align:start position:0% +answered but the exact same rules should + + + align:start position:0% +answered but the exact same rules should +also be enough to be able to to answer a + + align:start position:0% +also be enough to be able to to answer a + + + align:start position:0% +also be enough to be able to to answer a +question like this 137 and wat merged to + + align:start position:0% +question like this 137 and wat merged to + + + align:start position:0% +question like this 137 and wat merged to +form one two three four seven eight the + + align:start position:0% +form one two three four seven eight the + + + align:start position:0% +form one two three four seven eight the +same rules of logic can answer this + + align:start position:0% +same rules of logic can answer this + + + align:start position:0% +same rules of logic can answer this +although the procedure we wrote can't + + align:start position:0% +although the procedure we wrote can't + + + align:start position:0% +although the procedure we wrote can't +answer that question or we might be able + + align:start position:0% +answer that question or we might be able + + + align:start position:0% +answer that question or we might be able +to say what you know what and what else + + align:start position:0% + + + + align:start position:0% + +merge to form as merge to form what and + + align:start position:0% +merge to form as merge to form what and + + + align:start position:0% +merge to form as merge to form what and +what else merged to form one two three + + align:start position:0% +what else merged to form one two three + + + align:start position:0% +what else merged to form one two three +four 78 and the things should be able to + + align:start position:0% +four 78 and the things should be able to + + + align:start position:0% +four 78 and the things should be able to +go through if it really can apply that + + align:start position:0% +go through if it really can apply that + + + align:start position:0% +go through if it really can apply that +logic and deduce all whatever it is two + + align:start position:0% +logic and deduce all whatever it is two + + + align:start position:0% +logic and deduce all whatever it is two +to the sixth answers to that question + + align:start position:0% + + + + align:start position:0% + +okay because it could be one and the + + align:start position:0% +okay because it could be one and the + + + align:start position:0% +okay because it could be one and the +rest or could be one two and the rest or + + align:start position:0% +rest or could be one two and the rest or + + + align:start position:0% +rest or could be one two and the rest or +it could be one and three and seven and + + align:start position:0% +it could be one and three and seven and + + + align:start position:0% +it could be one and three and seven and +the rest there's a whole bunch of the + + align:start position:0% +the rest there's a whole bunch of the + + + align:start position:0% +the rest there's a whole bunch of the +answers and in principle the logic is + + align:start position:0% +answers and in principle the logic is + + + align:start position:0% +answers and in principle the logic is +should be enough to deduce that so + + align:start position:0% +should be enough to deduce that so + + + align:start position:0% +should be enough to deduce that so +they're going to be two big differences + + align:start position:0% +they're going to be two big differences + + + align:start position:0% +they're going to be two big differences +in the kind of program we're going to + + align:start position:0% +in the kind of program we're going to + + + align:start position:0% +in the kind of program we're going to +look at and not only list but + + align:start position:0% +look at and not only list but + + + align:start position:0% +look at and not only list but +essentially all the programming you've + + align:start position:0% +essentially all the programming you've + + + align:start position:0% +essentially all the programming you've +probably done so far in in pretty much + + align:start position:0% +probably done so far in in pretty much + + + align:start position:0% +probably done so far in in pretty much +any language you can think of the first + + align:start position:0% +any language you can think of the first + + + align:start position:0% +any language you can think of the first +is we're not going to be computing + + align:start position:0% +is we're not going to be computing + + + align:start position:0% +is we're not going to be computing +functions right we're not going to be + + align:start position:0% +functions right we're not going to be + + + align:start position:0% +functions right we're not going to be +talking about about things that take + + align:start position:0% +talking about about things that take + + + align:start position:0% +talking about about things that take +input and output we're going to be + + align:start position:0% +input and output we're going to be + + + align:start position:0% +input and output we're going to be +talking about relations and that means + + align:start position:0% +talking about relations and that means + + + align:start position:0% +talking about relations and that means +in principle these relations don't have + + align:start position:0% +in principle these relations don't have + + + align:start position:0% +in principle these relations don't have +directionality so the the knowledge that + + align:start position:0% +directionality so the the knowledge that + + + align:start position:0% +directionality so the the knowledge that +you specified to answer this question + + align:start position:0% +you specified to answer this question + + + align:start position:0% +you specified to answer this question +should be the same that that same + + align:start position:0% +should be the same that that same + + + align:start position:0% +should be the same that that same +knowledge should also allow you to + + align:start position:0% +knowledge should also allow you to + + + align:start position:0% +knowledge should also allow you to +answer these other questions and + + align:start position:0% +answer these other questions and + + + align:start position:0% +answer these other questions and +conversely + + align:start position:0% + + + + align:start position:0% + +and the second issue the second issue is + + align:start position:0% +and the second issue the second issue is + + + align:start position:0% +and the second issue the second issue is +that since we're talking about relations + + align:start position:0% +that since we're talking about relations + + + align:start position:0% +that since we're talking about relations +these relations don't necessarily have + + align:start position:0% +these relations don't necessarily have + + + align:start position:0% +these relations don't necessarily have +one answer so that third question down + + align:start position:0% +one answer so that third question down + + + align:start position:0% +one answer so that third question down +there doesn't have a particular answer + + align:start position:0% +there doesn't have a particular answer + + + align:start position:0% +there doesn't have a particular answer +it has a whole bunch of answers it's + + align:start position:0% +it has a whole bunch of answers it's + + + align:start position:0% +it has a whole bunch of answers it's +well that's where we're going this style + + align:start position:0% +well that's where we're going this style + + + align:start position:0% +well that's where we're going this style +of programming by the way is called + + align:start position:0% +of programming by the way is called + + + align:start position:0% +of programming by the way is called +logic programming in kind of obvious + + align:start position:0% +logic programming in kind of obvious + + + align:start position:0% +logic programming in kind of obvious +reasons and people who do logic + + align:start position:0% +reasons and people who do logic + + + align:start position:0% +reasons and people who do logic +programming say that they have this + + align:start position:0% +programming say that they have this + + + align:start position:0% +programming say that they have this +little phrase they say the point of + + align:start position:0% +little phrase they say the point of + + + align:start position:0% +little phrase they say the point of +logic programming is that you use logic + + align:start position:0% +logic programming is that you use logic + + + align:start position:0% +logic programming is that you use logic +you use logic to express what is true + + align:start position:0% +you use logic to express what is true + + + align:start position:0% +you use logic to express what is true +you use logic to check whether something + + align:start position:0% +you use logic to check whether something + + + align:start position:0% +you use logic to check whether something +is true and you use logic to find out + + align:start position:0% +is true and you use logic to find out + + + align:start position:0% +is true and you use logic to find out +what is true the best-known logic + + align:start position:0% +what is true the best-known logic + + + align:start position:0% +what is true the best-known logic +programming language is you probably + + align:start position:0% +programming language is you probably + + + align:start position:0% +programming language is you probably +know it's called Prolog the language + + align:start position:0% +know it's called Prolog the language + + + align:start position:0% +know it's called Prolog the language +that we're going to we're going to + + align:start position:0% +that we're going to we're going to + + + align:start position:0% +that we're going to we're going to +implement this morning is was something + + align:start position:0% +implement this morning is was something + + + align:start position:0% +implement this morning is was something +we call the query language and it + + align:start position:0% +we call the query language and it + + + align:start position:0% +we call the query language and it +essentially has the essence of Prolog it + + align:start position:0% +essentially has the essence of Prolog it + + + align:start position:0% +essentially has the essence of Prolog it +can do about the same stuff although + + align:start position:0% +can do about the same stuff although + + + align:start position:0% +can do about the same stuff although +it's a lot slower because we're gonna + + align:start position:0% +it's a lot slower because we're gonna + + + align:start position:0% +it's a lot slower because we're gonna +implement it in Lisp right rather than + + align:start position:0% +implement it in Lisp right rather than + + + align:start position:0% +implement it in Lisp right rather than +building a particular compiler we're + + align:start position:0% +building a particular compiler we're + + + align:start position:0% +building a particular compiler we're +going interpreted on top of the Lisp + + align:start position:0% +going interpreted on top of the Lisp + + + align:start position:0% +going interpreted on top of the Lisp +interpreter but other than that it can + + align:start position:0% +interpreter but other than that it can + + + align:start position:0% +interpreter but other than that it can +do about the same stuff this Prolog it + + align:start position:0% +do about the same stuff this Prolog it + + + align:start position:0% +do about the same stuff this Prolog it +has about the same power and about the + + align:start position:0% +has about the same power and about the + + + align:start position:0% +has about the same power and about the +same limitations alright let's break for + + align:start position:0% +same limitations alright let's break for + + + align:start position:0% +same limitations alright let's break for +questions + + align:start position:0% + + + + align:start position:0% + +yes could you please repeat what the + + align:start position:0% +yes could you please repeat what the + + + align:start position:0% +yes could you please repeat what the +three things use logic programming to + + align:start position:0% +three things use logic programming to + + + align:start position:0% +three things use logic programming to +find in other words define what is true + + align:start position:0% +find in other words define what is true + + + align:start position:0% +find in other words define what is true +learn what is true right see the sort of + + align:start position:0% +learn what is true right see the sort of + + + align:start position:0% +learn what is true right see the sort of +a logic programming programmers little + + align:start position:0% +a logic programming programmers little + + + align:start position:0% +a logic programming programmers little +little catechism you use logic to to + + align:start position:0% +little catechism you use logic to to + + + align:start position:0% +little catechism you use logic to to +express what is true like these rules + + align:start position:0% +express what is true like these rules + + + align:start position:0% +express what is true like these rules +you use logic to to check whether + + align:start position:0% +you use logic to to check whether + + + align:start position:0% +you use logic to to check whether +something is true and that's the kind of + + align:start position:0% +something is true and that's the kind of + + + align:start position:0% +something is true and that's the kind of +question I didn't answer here I might + + align:start position:0% +question I didn't answer here I might + + + align:start position:0% +question I didn't answer here I might +say another question I could put down + + align:start position:0% +say another question I could put down + + + align:start position:0% +say another question I could put down +here is to say is it true that 137 and + + align:start position:0% +here is to say is it true that 137 and + + + align:start position:0% +here is to say is it true that 137 and +248 merged to form one to six ten and + + align:start position:0% +248 merged to form one to six ten and + + + align:start position:0% +248 merged to form one to six ten and +that same logic should be enough to to + + align:start position:0% +that same logic should be enough to to + + + align:start position:0% +that same logic should be enough to to +say to say no so I use logic to check + + align:start position:0% +say to say no so I use logic to check + + + align:start position:0% +say to say no so I use logic to check +what is true and then you also use logic + + align:start position:0% +what is true and then you also use logic + + + align:start position:0% +what is true and then you also use logic +to find out what's true + + align:start position:0% + + + + align:start position:0% + +alright let's break + + align:start position:0% +alright let's break + + + align:start position:0% +alright let's break +[Music] + + align:start position:0% + + + + align:start position:0% + +okay let's go ahead and take a look at + + align:start position:0% +okay let's go ahead and take a look at + + + align:start position:0% +okay let's go ahead and take a look at +this query language in operation the + + align:start position:0% +this query language in operation the + + + align:start position:0% +this query language in operation the +first thing you might notice when I put + + align:start position:0% +first thing you might notice when I put + + + align:start position:0% +first thing you might notice when I put +up that little biblical database is that + + align:start position:0% +up that little biblical database is that + + + align:start position:0% +up that little biblical database is that +it's nice to be able to ask this + + align:start position:0% +it's nice to be able to ask this + + + align:start position:0% +it's nice to be able to ask this +language questions in relation to some + + align:start position:0% +language questions in relation to some + + + align:start position:0% +language questions in relation to some +collection of facts so let's let's start + + align:start position:0% +collection of facts so let's let's start + + + align:start position:0% +collection of facts so let's let's start +often and make a little collection of + + align:start position:0% +often and make a little collection of + + + align:start position:0% +often and make a little collection of +facts this is a tiny fragment of one of + + align:start position:0% +facts this is a tiny fragment of one of + + + align:start position:0% +facts this is a tiny fragment of one of +our personnel records for a a boston + + align:start position:0% +our personnel records for a a boston + + + align:start position:0% +our personnel records for a a boston +high tech company and here's a piece of + + align:start position:0% +high tech company and here's a piece of + + + align:start position:0% +high tech company and here's a piece of +the personnel record of ben bitdiddle + + align:start position:0% +the personnel record of ben bitdiddle + + + align:start position:0% +the personnel record of ben bitdiddle +and ben ben bitdiddle is the is the + + align:start position:0% +and ben ben bitdiddle is the is the + + + align:start position:0% +and ben ben bitdiddle is the is the +computer wizard in this company + + align:start position:0% +computer wizard in this company + + + align:start position:0% +computer wizard in this company +he's the underpaid computer wizard in + + align:start position:0% +he's the underpaid computer wizard in + + + align:start position:0% +he's the underpaid computer wizard in +this company his supervisor is Oliver + + align:start position:0% +this company his supervisor is Oliver + + + align:start position:0% +this company his supervisor is Oliver +Warbucks and here's his address so the + + align:start position:0% +Warbucks and here's his address so the + + + align:start position:0% +Warbucks and here's his address so the +format is we're giving this information + + align:start position:0% +format is we're giving this information + + + align:start position:0% +format is we're giving this information +job salary supervisor address and there + + align:start position:0% +job salary supervisor address and there + + + align:start position:0% +job salary supervisor address and there +some other conventions computer here + + align:start position:0% +some other conventions computer here + + + align:start position:0% +some other conventions computer here +means that Ben works in the computer + + align:start position:0% +means that Ben works in the computer + + + align:start position:0% +means that Ben works in the computer +division and his position in the + + align:start position:0% +division and his position in the + + + align:start position:0% +division and his position in the +computer division is wizard there's + + align:start position:0% +computer division is wizard there's + + + align:start position:0% +computer division is wizard there's +somebody else élisa élisa p hacker is a + + align:start position:0% +somebody else élisa élisa p hacker is a + + + align:start position:0% +somebody else élisa élisa p hacker is a +computer programmer and she works for + + align:start position:0% +computer programmer and she works for + + + align:start position:0% +computer programmer and she works for +Ben + + align:start position:0% +Ben + + + align:start position:0% +Ben +and she lives in Cambridge yeah there's + + align:start position:0% +and she lives in Cambridge yeah there's + + + align:start position:0% +and she lives in Cambridge yeah there's +another programmer who works for being + + align:start position:0% +another programmer who works for being + + + align:start position:0% +another programmer who works for being +who's let me tweak it and there's a + + align:start position:0% +who's let me tweak it and there's a + + + align:start position:0% +who's let me tweak it and there's a +programmer trainee who's Lois reasoner + + align:start position:0% +programmer trainee who's Lois reasoner + + + align:start position:0% +programmer trainee who's Lois reasoner +and he works for ELISA and the big wheel + + align:start position:0% +and he works for ELISA and the big wheel + + + align:start position:0% +and he works for ELISA and the big wheel +of the company doesn't work for anybody + + align:start position:0% +of the company doesn't work for anybody + + + align:start position:0% +of the company doesn't work for anybody +right that's all over Warbucks anyway + + align:start position:0% +right that's all over Warbucks anyway + + + align:start position:0% +right that's all over Warbucks anyway +what we're gonna do is is ask questions + + align:start position:0% +what we're gonna do is is ask questions + + + align:start position:0% +what we're gonna do is is ask questions +about that little world and that'll + + align:start position:0% +about that little world and that'll + + + align:start position:0% +about that little world and that'll +that'll be a sample world that we were + + align:start position:0% +that'll be a sample world that we were + + + align:start position:0% +that'll be a sample world that we were +gonna do logic in let me just write up + + align:start position:0% +gonna do logic in let me just write up + + + align:start position:0% +gonna do logic in let me just write up +here for probably the last time what I + + align:start position:0% +here for probably the last time what I + + + align:start position:0% +here for probably the last time what I +said is the very most important thing + + align:start position:0% +said is the very most important thing + + + align:start position:0% +said is the very most important thing +you should get out of this course and + + align:start position:0% +you should get out of this course and + + + align:start position:0% +you should get out of this course and +that is when somebody tells you about a + + align:start position:0% +that is when somebody tells you about a + + + align:start position:0% +that is when somebody tells you about a +language you say fine what are the + + align:start position:0% +language you say fine what are the + + + align:start position:0% +language you say fine what are the +primitives what are the means of + + align:start position:0% +primitives what are the means of + + + align:start position:0% +primitives what are the means of +combination + + align:start position:0% + + + + align:start position:0% + +right how do you put the perimeters + + align:start position:0% +right how do you put the perimeters + + + align:start position:0% +right how do you put the perimeters +together and then how do you abstract + + align:start position:0% +together and then how do you abstract + + + align:start position:0% +together and then how do you abstract +them how do you abstract the compound + + align:start position:0% +them how do you abstract the compound + + + align:start position:0% +them how do you abstract the compound +pieces so you can use them as pieces to + + align:start position:0% +pieces so you can use them as pieces to + + + align:start position:0% +pieces so you can use them as pieces to +make something more complicated said + + align:start position:0% +make something more complicated said + + + align:start position:0% +make something more complicated said +there's a whole bunch of times already + + align:start position:0% +there's a whole bunch of times already + + + align:start position:0% +there's a whole bunch of times already +but it's worth saying again okay let's + + align:start position:0% +but it's worth saying again okay let's + + + align:start position:0% +but it's worth saying again okay let's +start the primitives well there's really + + align:start position:0% +start the primitives well there's really + + + align:start position:0% +start the primitives well there's really +only one primitive and the primitive in + + align:start position:0% +only one primitive and the primitive in + + + align:start position:0% +only one primitive and the primitive in +this language is called a query at a + + align:start position:0% +this language is called a query at a + + + align:start position:0% +this language is called a query at a +primitive query let's look at some + + align:start position:0% +primitive query let's look at some + + + align:start position:0% +primitive query let's look at some +primitive queries great job X who is a + + align:start position:0% +primitive queries great job X who is a + + + align:start position:0% +primitive queries great job X who is a +computer programmer or find every but + + align:start position:0% +computer programmer or find every but + + + align:start position:0% +computer programmer or find every but +find every fact in the database that + + align:start position:0% +find every fact in the database that + + + align:start position:0% +find every fact in the database that +matches job of X's computer programmer + + align:start position:0% +matches job of X's computer programmer + + + align:start position:0% +matches job of X's computer programmer +and you see a little syntax here things + + align:start position:0% +and you see a little syntax here things + + + align:start position:0% +and you see a little syntax here things +without question marks are meant to be + + align:start position:0% +without question marks are meant to be + + + align:start position:0% +without question marks are meant to be +literal question mark X means that's a + + align:start position:0% +literal question mark X means that's a + + + align:start position:0% +literal question mark X means that's a +variable and this thing will match for + + align:start position:0% +variable and this thing will match for + + + align:start position:0% +variable and this thing will match for +example the fact that Alisa P hacker is + + align:start position:0% +example the fact that Alisa P hacker is + + + align:start position:0% +example the fact that Alisa P hacker is +a computer programmer where X is Alisa P + + align:start position:0% +a computer programmer where X is Alisa P + + + align:start position:0% +a computer programmer where X is Alisa P +hacker we're more generally I could have + + align:start position:0% +hacker we're more generally I could have + + + align:start position:0% +hacker we're more generally I could have +something with two variables in it I + + align:start position:0% +something with two variables in it I + + + align:start position:0% +something with two variables in it I +could say the job of X is computer + + align:start position:0% +could say the job of X is computer + + + align:start position:0% +could say the job of X is computer +something in that will match computer + + align:start position:0% +something in that will match computer + + + align:start position:0% +something in that will match computer +wizard alright so there's something here + + align:start position:0% +wizard alright so there's something here + + + align:start position:0% +wizard alright so there's something here +type on that wizard or a type on that's + + align:start position:0% +type on that wizard or a type on that's + + + align:start position:0% +type on that wizard or a type on that's +programmer or X might match various + + align:start position:0% +programmer or X might match various + + + align:start position:0% +programmer or X might match various +certain things so there on our little + + align:start position:0% +certain things so there on our little + + + align:start position:0% +certain things so there on our little +example only three facts and that + + align:start position:0% +example only three facts and that + + + align:start position:0% +example only three facts and that +database that matched that query let's + + align:start position:0% +database that matched that query let's + + + align:start position:0% +database that matched that query let's +see just to show you some syntax the + + align:start position:0% +see just to show you some syntax the + + + align:start position:0% +see just to show you some syntax the +same query + + align:start position:0% + + + + align:start position:0% + +this query doesn't match the job of the + + align:start position:0% +this query doesn't match the job of the + + + align:start position:0% +this query doesn't match the job of the +ex great doesn't match Louis reason or + + align:start position:0% +ex great doesn't match Louis reason or + + + align:start position:0% +ex great doesn't match Louis reason or +the reason for that is when I write + + align:start position:0% +the reason for that is when I write + + + align:start position:0% +the reason for that is when I write +something here what I mean is that this + + align:start position:0% +something here what I mean is that this + + + align:start position:0% +something here what I mean is that this +is going to be a list of two symbols of + + align:start position:0% +is going to be a list of two symbols of + + + align:start position:0% +is going to be a list of two symbols of +which the first is the word computer and + + align:start position:0% +which the first is the word computer and + + + align:start position:0% +which the first is the word computer and +the second can be anything and Louis's + + align:start position:0% +the second can be anything and Louis's + + + align:start position:0% +the second can be anything and Louis's +job description here has three symbols + + align:start position:0% +job description here has three symbols + + + align:start position:0% +job description here has three symbols +so it doesn't match and just to show you + + align:start position:0% +so it doesn't match and just to show you + + + align:start position:0% +so it doesn't match and just to show you +a little bit of syntax the more general + + align:start position:0% +a little bit of syntax the more general + + + align:start position:0% +a little bit of syntax the more general +thing I might want to type is a thing + + align:start position:0% +thing I might want to type is a thing + + + align:start position:0% +thing I might want to type is a thing +with a dot here and this is just + + align:start position:0% +with a dot here and this is just + + + align:start position:0% +with a dot here and this is just +standard list notation for saying this + + align:start position:0% +standard list notation for saying this + + + align:start position:0% +standard list notation for saying this +is a list of which the first element is + + align:start position:0% +is a list of which the first element is + + + align:start position:0% +is a list of which the first element is +the word computers and the rest is + + align:start position:0% +the word computers and the rest is + + + align:start position:0% +the word computers and the rest is +something that I'll call type so this + + align:start position:0% +something that I'll call type so this + + + align:start position:0% +something that I'll call type so this +one would match Louis's job as computer + + align:start position:0% +one would match Louis's job as computer + + + align:start position:0% +one would match Louis's job as computer +programmer trainee and type here would + + align:start position:0% +programmer trainee and type here would + + + align:start position:0% +programmer trainee and type here would +be the coder of this love this list it + + align:start position:0% +be the coder of this love this list it + + + align:start position:0% +be the coder of this love this list it +would be the the list programmer trainee + + align:start position:0% +would be the the list programmer trainee + + + align:start position:0% +would be the the list programmer trainee +and that kind of dot processing is done + + align:start position:0% +and that kind of dot processing is done + + + align:start position:0% +and that kind of dot processing is done +automatically by the by the list reader + + align:start position:0% +automatically by the by the list reader + + + align:start position:0% +automatically by the by the list reader +ok well let's actually try this the idea + + align:start position:0% +ok well let's actually try this the idea + + + align:start position:0% +ok well let's actually try this the idea +is I'm going to type in queries in this + + align:start position:0% +is I'm going to type in queries in this + + + align:start position:0% +is I'm going to type in queries in this +language and answers will come out let's + + align:start position:0% +language and answers will come out let's + + + align:start position:0% +language and answers will come out let's +let's look at this I can go up and say + + align:start position:0% +let's look at this I can go up and say + + + align:start position:0% +let's look at this I can go up and say +gee who works in the computer division + + align:start position:0% +gee who works in the computer division + + + align:start position:0% +gee who works in the computer division +job of X is computer dot Y it doesn't + + align:start position:0% +job of X is computer dot Y it doesn't + + + align:start position:0% +job of X is computer dot Y it doesn't +matter what I call the dummy variables + + align:start position:0% +matter what I call the dummy variables + + + align:start position:0% +matter what I call the dummy variables +it says the answers to that and it's + + align:start position:0% +it says the answers to that and it's + + + align:start position:0% +it says the answers to that and it's +down for answers or I can go off and say + + align:start position:0% +down for answers or I can go off and say + + + align:start position:0% +down for answers or I can go off and say +tell me about everybody's supervisor so + + align:start position:0% +tell me about everybody's supervisor so + + + align:start position:0% +tell me about everybody's supervisor so +I'll put in the query the primitive + + align:start position:0% +I'll put in the query the primitive + + + align:start position:0% +I'll put in the query the primitive +query the supervisor of X is y + + align:start position:0% + + + + align:start position:0% + +they're there all the supervisor + + align:start position:0% +they're there all the supervisor + + + align:start position:0% +they're there all the supervisor +relationships I know or I could go type + + align:start position:0% +relationships I know or I could go type + + + align:start position:0% +relationships I know or I could go type +in who lives in Cambridge so I can say + + align:start position:0% +in who lives in Cambridge so I can say + + + align:start position:0% +in who lives in Cambridge so I can say +the address of X is Cambridge dot + + align:start position:0% +the address of X is Cambridge dot + + + align:start position:0% +the address of X is Cambridge dot +anything and only one person lives in + + align:start position:0% +anything and only one person lives in + + + align:start position:0% +anything and only one person lives in +Cambridge okay so those are primitive + + align:start position:0% +Cambridge okay so those are primitive + + + align:start position:0% +Cambridge okay so those are primitive +queries and you see what happens the + + align:start position:0% +queries and you see what happens the + + + align:start position:0% +queries and you see what happens the +basic interaction with the system is you + + align:start position:0% +basic interaction with the system is you + + + align:start position:0% +basic interaction with the system is you +type in a query and it types out all + + align:start position:0% +type in a query and it types out all + + + align:start position:0% +type in a query and it types out all +possible answers or another way to say + + align:start position:0% +possible answers or another way to say + + + align:start position:0% +possible answers or another way to say +that it finds out all the possible + + align:start position:0% +that it finds out all the possible + + + align:start position:0% +that it finds out all the possible +values of those variables x and y or T + + align:start position:0% +values of those variables x and y or T + + + align:start position:0% +values of those variables x and y or T +or whatever I called them and it types + + align:start position:0% +or whatever I called them and it types + + + align:start position:0% +or whatever I called them and it types +out all ways of taking that query and + + align:start position:0% +out all ways of taking that query and + + + align:start position:0% +out all ways of taking that query and +instantiating it remember that from the + + align:start position:0% +instantiating it remember that from the + + + align:start position:0% +instantiating it remember that from the +from the rule system lecture + + align:start position:0% +from the rule system lecture + + + align:start position:0% +from the rule system lecture +instantiates the query with all possible + + align:start position:0% +instantiates the query with all possible + + + align:start position:0% +instantiates the query with all possible +values for those variables and then + + align:start position:0% +values for those variables and then + + + align:start position:0% +values for those variables and then +types out all of them and there are a + + align:start position:0% +types out all of them and there are a + + + align:start position:0% +types out all of them and there are a +lot of ways you can arrange a logic + + align:start position:0% +lot of ways you can arrange a logic + + + align:start position:0% +lot of ways you can arrange a logic +language Prolog for instance to + + align:start position:0% +language Prolog for instance to + + + align:start position:0% +language Prolog for instance to +something slightly different rather than + + align:start position:0% +something slightly different rather than + + + align:start position:0% +something slightly different rather than +typing back your query Prolog would type + + align:start position:0% +typing back your query Prolog would type + + + align:start position:0% +typing back your query Prolog would type +out x equals this and y equals that or x + + align:start position:0% +out x equals this and y equals that or x + + + align:start position:0% +out x equals this and y equals that or x +equals this and y equals that and that's + + align:start position:0% +equals this and y equals that and that's + + + align:start position:0% +equals this and y equals that and that's +that's a very surface level thing and + + align:start position:0% +that's a very surface level thing and + + + align:start position:0% +that's a very surface level thing and +you can decide what you like okay all + + align:start position:0% +you can decide what you like okay all + + + align:start position:0% +you can decide what you like okay all +right so the primitives in this language + + align:start position:0% +right so the primitives in this language + + + align:start position:0% +right so the primitives in this language +only one write primitive query okay + + align:start position:0% +only one write primitive query okay + + + align:start position:0% +only one write primitive query okay +means a combination let's look at some + + align:start position:0% +means a combination let's look at some + + + align:start position:0% +means a combination let's look at some +compound queries in this language here's + + align:start position:0% +compound queries in this language here's + + + align:start position:0% +compound queries in this language here's +one this one says tell me all the people + + align:start position:0% +one this one says tell me all the people + + + align:start position:0% +one this one says tell me all the people +who work in the computer division tell + + align:start position:0% +who work in the computer division tell + + + align:start position:0% +who work in the computer division tell +me all the people who work in the + + align:start position:0% +me all the people who work in the + + + align:start position:0% +me all the people who work in the +computer division together with their + + align:start position:0% +computer division together with their + + + align:start position:0% +computer division together with their +supervisors the way I write that as a + + align:start position:0% +supervisors the way I write that as a + + + align:start position:0% +supervisors the way I write that as a +query is and and the job of X is + + align:start position:0% +query is and and the job of X is + + + align:start position:0% +query is and and the job of X is +computer something or other + + align:start position:0% +computer something or other + + + align:start position:0% +computer something or other +and job of X is computer dot Y and the + + align:start position:0% +and job of X is computer dot Y and the + + + align:start position:0% +and job of X is computer dot Y and the +supervisor of X is e all right tell me + + align:start position:0% +supervisor of X is e all right tell me + + + align:start position:0% +supervisor of X is e all right tell me +all the people in the computer division + + align:start position:0% +all the people in the computer division + + + align:start position:0% +all the people in the computer division +that's this together with their + + align:start position:0% +that's this together with their + + + align:start position:0% +that's this together with their +supervisors + + align:start position:0% +supervisors + + + align:start position:0% +supervisors +and notice in this query I have three + + align:start position:0% +and notice in this query I have three + + + align:start position:0% +and notice in this query I have three +variables XY XY and Z and this X is + + align:start position:0% +variables XY XY and Z and this X is + + + align:start position:0% +variables XY XY and Z and this X is +supposed to be the same as that X all + + align:start position:0% +supposed to be the same as that X all + + + align:start position:0% +supposed to be the same as that X all +right so X works in the computer + + align:start position:0% +right so X works in the computer + + + align:start position:0% +right so X works in the computer +division and the supervisor of X is Z ok + + align:start position:0% +division and the supervisor of X is Z ok + + + align:start position:0% +division and the supervisor of X is Z ok +let's try another one + + align:start position:0% +let's try another one + + + align:start position:0% +let's try another one +so one means of combination is and who + + align:start position:0% +so one means of combination is and who + + + align:start position:0% +so one means of combination is and who +are all the people who make more than + + align:start position:0% +are all the people who make more than + + + align:start position:0% +are all the people who make more than +$30,000 all right and the salary of some + + align:start position:0% +$30,000 all right and the salary of some + + + align:start position:0% +$30,000 all right and the salary of some +person P is some amount a and when I go + + align:start position:0% +person P is some amount a and when I go + + + align:start position:0% +person P is some amount a and when I go +and look at a a is greater than 30,000 + + align:start position:0% +and look at a a is greater than 30,000 + + + align:start position:0% +and look at a a is greater than 30,000 +and list value here is a little piece of + + align:start position:0% +and list value here is a little piece of + + + align:start position:0% +and list value here is a little piece of +interface that that interfaces the query + + align:start position:0% +interface that that interfaces the query + + + align:start position:0% +interface that that interfaces the query +language to the underlying Lisp but + + align:start position:0% +language to the underlying Lisp but + + + align:start position:0% +language to the underlying Lisp but +lists list value allows you to do is + + align:start position:0% +lists list value allows you to do is + + + align:start position:0% +lists list value allows you to do is +call any Lisp predicate inside this this + + align:start position:0% +call any Lisp predicate inside this this + + + align:start position:0% +call any Lisp predicate inside this this +inside a query so here I'm using the + + align:start position:0% +inside a query so here I'm using the + + + align:start position:0% +inside a query so here I'm using the +list predicate greater than so I say + + align:start position:0% +list predicate greater than so I say + + + align:start position:0% +list predicate greater than so I say +list value and I say and so all the + + align:start position:0% +list value and I say and so all the + + + align:start position:0% +list value and I say and so all the +people whose salary is greater than + + align:start position:0% +people whose salary is greater than + + + align:start position:0% +people whose salary is greater than +30,000 or here's a more complicated one + + align:start position:0% +30,000 or here's a more complicated one + + + align:start position:0% +30,000 or here's a more complicated one +tell me all the people who work in the + + align:start position:0% +tell me all the people who work in the + + + align:start position:0% +tell me all the people who work in the +computer division who do not have a + + align:start position:0% +computer division who do not have a + + + align:start position:0% +computer division who do not have a +supervisor who works in the computer + + align:start position:0% +supervisor who works in the computer + + + align:start position:0% +supervisor who works in the computer +division right and X works in the + + align:start position:0% +division right and X works in the + + + align:start position:0% +division right and X works in the +computer division the job of X is + + align:start position:0% +computer division the job of X is + + + align:start position:0% +computer division the job of X is +computer dot Y and it's not the case + + align:start position:0% +computer dot Y and it's not the case + + + align:start position:0% +computer dot Y and it's not the case +that both X has a supervisor Z and the + + align:start position:0% +that both X has a supervisor Z and the + + + align:start position:0% +that both X has a supervisor Z and the +job of Z is computer something-or-other + + align:start position:0% +job of Z is computer something-or-other + + + align:start position:0% +job of Z is computer something-or-other +right so again this X has got to be that + + align:start position:0% +right so again this X has got to be that + + + align:start position:0% +right so again this X has got to be that +X and this Z is going to be that's a and + + align:start position:0% +X and this Z is going to be that's a and + + + align:start position:0% +X and this Z is going to be that's a and +then you see another means of + + align:start position:0% +then you see another means of + + + align:start position:0% +then you see another means of +combination not + + align:start position:0% + + + + align:start position:0% + +all right all right well let's look at + + align:start position:0% +all right all right well let's look at + + + align:start position:0% +all right all right well let's look at +that it works the same way I can go up + + align:start position:0% +that it works the same way I can go up + + + align:start position:0% +that it works the same way I can go up +to the Machine and say and the job of X + + align:start position:0% +to the Machine and say and the job of X + + + align:start position:0% +to the Machine and say and the job of X +is computer dot Y and the supervisor of + + align:start position:0% + + + + align:start position:0% + +X is Z and I type that in like a query + + align:start position:0% +X is Z and I type that in like a query + + + align:start position:0% +X is Z and I type that in like a query +right and it what it types back what you + + align:start position:0% +right and it what it types back what you + + + align:start position:0% +right and it what it types back what you +see are the queries I typed it + + align:start position:0% +see are the queries I typed it + + + align:start position:0% +see are the queries I typed it +instantiated by all possible answers and + + align:start position:0% +instantiated by all possible answers and + + + align:start position:0% +instantiated by all possible answers and +then you see there a lot of the answers + + align:start position:0% +then you see there a lot of the answers + + + align:start position:0% +then you see there a lot of the answers +all right so the means of combination in + + align:start position:0% +all right so the means of combination in + + + align:start position:0% +all right so the means of combination in +this language and this why it's called a + + align:start position:0% +this language and this why it's called a + + + align:start position:0% +this language and this why it's called a +logic language are our logical + + align:start position:0% +logic language are our logical + + + align:start position:0% +logic language are our logical +operations needs of combinations are + + align:start position:0% +operations needs of combinations are + + + align:start position:0% +operations needs of combinations are +things like like and and not and there's + + align:start position:0% +things like like and and not and there's + + + align:start position:0% +things like like and and not and there's +one I didn't show you which is or and + + align:start position:0% +one I didn't show you which is or and + + + align:start position:0% +one I didn't show you which is or and +then I showed you list value which is a + + align:start position:0% +then I showed you list value which is a + + + align:start position:0% +then I showed you list value which is a +not logic of course but there's a little + + align:start position:0% +not logic of course but there's a little + + + align:start position:0% +not logic of course but there's a little +special hack to interface that to Lisp + + align:start position:0% +special hack to interface that to Lisp + + + align:start position:0% +special hack to interface that to Lisp +so you can get more power those are the + + align:start position:0% +so you can get more power those are the + + + align:start position:0% +so you can get more power those are the +means of combination + + align:start position:0% +means of combination + + + align:start position:0% +means of combination +okay the means of abstraction what we'd + + align:start position:0% +okay the means of abstraction what we'd + + + align:start position:0% +okay the means of abstraction what we'd +like to do let's go back and for a + + align:start position:0% +like to do let's go back and for a + + + align:start position:0% +like to do let's go back and for a +second look at that last slide we might + + align:start position:0% +second look at that last slide we might + + + align:start position:0% +second look at that last slide we might +like to take a very complicated thing + + align:start position:0% +like to take a very complicated thing + + + align:start position:0% +like to take a very complicated thing +the idea that someone works in a + + align:start position:0% +the idea that someone works in a + + + align:start position:0% +the idea that someone works in a +division but does not have a supervisor + + align:start position:0% +division but does not have a supervisor + + + align:start position:0% +division but does not have a supervisor +in the division and that's before name + + align:start position:0% +in the division and that's before name + + + align:start position:0% +in the division and that's before name +that well if someone works in a division + + align:start position:0% +that well if someone works in a division + + + align:start position:0% +that well if someone works in a division +and does not have a supervisor who works + + align:start position:0% +and does not have a supervisor who works + + + align:start position:0% +and does not have a supervisor who works +in that division that means that person + + align:start position:0% +in that division that means that person + + + align:start position:0% +in that division that means that person +is a big-shot + + align:start position:0% +is a big-shot + + + align:start position:0% +is a big-shot +so let's make a rule that somebody X is + + align:start position:0% +so let's make a rule that somebody X is + + + align:start position:0% +so let's make a rule that somebody X is +a big-shot in some department if X works + + align:start position:0% +a big-shot in some department if X works + + + align:start position:0% +a big-shot in some department if X works +in the department right and it's not the + + align:start position:0% +in the department right and it's not the + + + align:start position:0% +in the department right and it's not the +case that X has a supervisor who works + + align:start position:0% +case that X has a supervisor who works + + + align:start position:0% +case that X has a supervisor who works +in the department so this is our means + + align:start position:0% +in the department so this is our means + + + align:start position:0% +in the department so this is our means +of abstraction this is a rule and a rule + + align:start position:0% +of abstraction this is a rule and a rule + + + align:start position:0% +of abstraction this is a rule and a rule +has three parts + + align:start position:0% +has three parts + + + align:start position:0% +has three parts +they did the thing that says it's a rule + + align:start position:0% +they did the thing that says it's a rule + + + align:start position:0% +they did the thing that says it's a rule +and then there's the conclusion of the + + align:start position:0% +and then there's the conclusion of the + + + align:start position:0% +and then there's the conclusion of the +rule and then there's the body of the + + align:start position:0% +rule and then there's the body of the + + + align:start position:0% +rule and then there's the body of the +rule and you can read this as a piece of + + align:start position:0% +rule and you can read this as a piece of + + + align:start position:0% +rule and you can read this as a piece of +logic which says if you know that the + + align:start position:0% +logic which says if you know that the + + + align:start position:0% +logic which says if you know that the +body of the rule is true then you can + + align:start position:0% +body of the rule is true then you can + + + align:start position:0% +body of the rule is true then you can +conclude that the conclusion is true or + + align:start position:0% +conclude that the conclusion is true or + + + align:start position:0% +conclude that the conclusion is true or +in order to deduce that X is a big shot + + align:start position:0% +in order to deduce that X is a big shot + + + align:start position:0% +in order to deduce that X is a big shot +in some department it's enough to verify + + align:start position:0% +in some department it's enough to verify + + + align:start position:0% +in some department it's enough to verify +that and so that's what rules look like + + align:start position:0% + + + + align:start position:0% + +let's go back and look at the that merge + + align:start position:0% +let's go back and look at the that merge + + + align:start position:0% +let's go back and look at the that merge +example that I did before the break + + align:start position:0% +example that I did before the break + + + align:start position:0% +example that I did before the break +let's look how that would look in terms + + align:start position:0% +let's look how that would look in terms + + + align:start position:0% +let's look how that would look in terms +of rules I'm gonna take the logic I put + + align:start position:0% +of rules I'm gonna take the logic I put + + + align:start position:0% +of rules I'm gonna take the logic I put +up and just change it into a bunch of + + align:start position:0% +up and just change it into a bunch of + + + align:start position:0% +up and just change it into a bunch of +rules in this format okay + + align:start position:0% +rules in this format okay + + + align:start position:0% +rules in this format okay +we have a rule memory there was system + + align:start position:0% +we have a rule memory there was system + + + align:start position:0% +we have a rule memory there was system +merge to form there's a rule that says + + align:start position:0% + + + + align:start position:0% + +the empty list and Y merged to form Y + + align:start position:0% +the empty list and Y merged to form Y + + + align:start position:0% +the empty list and Y merged to form Y +this is the rural conclusion and notice + + align:start position:0% +this is the rural conclusion and notice + + + align:start position:0% +this is the rural conclusion and notice +that this particular rule has no body + + align:start position:0% +that this particular rule has no body + + + align:start position:0% +that this particular rule has no body +and in this language a rule with no body + + align:start position:0% +and in this language a rule with no body + + + align:start position:0% +and in this language a rule with no body +is something that is always true you can + + align:start position:0% +is something that is always true you can + + + align:start position:0% +is something that is always true you can +always assume that's true and there was + + align:start position:0% +always assume that's true and there was + + + align:start position:0% +always assume that's true and there was +another piece of logic that said + + align:start position:0% +another piece of logic that said + + + align:start position:0% +another piece of logic that said +anything in the empty list merged to + + align:start position:0% +anything in the empty list merged to + + + align:start position:0% +anything in the empty list merged to +form lis anything and that's this read a + + align:start position:0% +form lis anything and that's this read a + + + align:start position:0% +form lis anything and that's this read a +rule Y and the empty list merge to form + + align:start position:0% +rule Y and the empty list merge to form + + + align:start position:0% +rule Y and the empty list merge to form +why those correspond to the to end cases + + align:start position:0% +why those correspond to the to end cases + + + align:start position:0% +why those correspond to the to end cases +in our merge procedure but now we're + + align:start position:0% +in our merge procedure but now we're + + + align:start position:0% +in our merge procedure but now we're +talking about logic not a bad procedure + + align:start position:0% +talking about logic not a bad procedure + + + align:start position:0% +talking about logic not a bad procedure +and we had another rule which said if + + align:start position:0% +and we had another rule which said if + + + align:start position:0% +and we had another rule which said if +you know how how shorter things merge + + align:start position:0% +you know how how shorter things merge + + + align:start position:0% +you know how how shorter things merge +you can put them together so this says + + align:start position:0% +you can put them together so this says + + + align:start position:0% +you can put them together so this says +if you wanted if you have lists x and y + + align:start position:0% +if you wanted if you have lists x and y + + + align:start position:0% +if you wanted if you have lists x and y +and z and if you want to deduce that a + + align:start position:0% +and z and if you want to deduce that a + + + align:start position:0% +and z and if you want to deduce that a +dot X means constant a onto X or a list + + align:start position:0% +dot X means constant a onto X or a list + + + align:start position:0% +dot X means constant a onto X or a list +whose first thing is a and whose rest is + + align:start position:0% +whose first thing is a and whose rest is + + + align:start position:0% +whose first thing is a and whose rest is +X so if you wanted to do that a dot X + + align:start position:0% +X so if you wanted to do that a dot X + + + align:start position:0% +X so if you wanted to do that a dot X +and B dot Y merged to form B dot C right + + align:start position:0% +and B dot Y merged to form B dot C right + + + align:start position:0% +and B dot Y merged to form B dot C right +that would say you merge these two lists + + align:start position:0% +that would say you merge these two lists + + + align:start position:0% +that would say you merge these two lists +ax and B Y and you're going to get + + align:start position:0% +ax and B Y and you're going to get + + + align:start position:0% +ax and B Y and you're going to get +something that starts with B so in order + + align:start position:0% +something that starts with B so in order + + + align:start position:0% +something that starts with B so in order +to do it you can deduce that if you know + + align:start position:0% +to do it you can deduce that if you know + + + align:start position:0% +to do it you can deduce that if you know +that it's the case + + align:start position:0% +that it's the case + + + align:start position:0% +that it's the case +both that a dot X&Y merged to form Z and + + align:start position:0% +both that a dot X&Y merged to form Z and + + + align:start position:0% +both that a dot X&Y merged to form Z and +A's larger than B so when I merged them + + align:start position:0% +A's larger than B so when I merged them + + + align:start position:0% +A's larger than B so when I merged them +B will come first in the list in that + + align:start position:0% +B will come first in the list in that + + + align:start position:0% +B will come first in the list in that +car that's a little translation of the + + align:start position:0% +car that's a little translation of the + + + align:start position:0% +car that's a little translation of the +logic rule that I wrote in in pseudo + + align:start position:0% +logic rule that I wrote in in pseudo + + + align:start position:0% +logic rule that I wrote in in pseudo +English before and then just for for + + align:start position:0% +English before and then just for for + + + align:start position:0% +English before and then just for for +completeness here's the here's the other + + align:start position:0% +completeness here's the here's the other + + + align:start position:0% +completeness here's the here's the other +case write ax + B dot Y merged to form a + + align:start position:0% +case write ax + B dot Y merged to form a + + + align:start position:0% +case write ax + B dot Y merged to form a +dot C if X + B dot Y merged to form Z + + align:start position:0% +dot C if X + B dot Y merged to form Z + + + align:start position:0% +dot C if X + B dot Y merged to form Z +and B is larger than a and so that's a + + align:start position:0% +and B is larger than a and so that's a + + + align:start position:0% +and B is larger than a and so that's a +little program that I've typed in in + + align:start position:0% +little program that I've typed in in + + + align:start position:0% +little program that I've typed in in +this language and now let's look at it + + align:start position:0% +this language and now let's look at it + + + align:start position:0% +this language and now let's look at it +run so I I typed in the merge rules + + align:start position:0% +run so I I typed in the merge rules + + + align:start position:0% +run so I I typed in the merge rules +before and I could say I could use this + + align:start position:0% +before and I could say I could use this + + + align:start position:0% +before and I could say I could use this +like a procedure I could say merge to + + align:start position:0% +like a procedure I could say merge to + + + align:start position:0% +like a procedure I could say merge to +form 1 + 3 + 2 + 7 and so here I'm using + + align:start position:0% +form 1 + 3 + 2 + 7 and so here I'm using + + + align:start position:0% +form 1 + 3 + 2 + 7 and so here I'm using +it like the list procedure and now it's + + align:start position:0% +it like the list procedure and now it's + + + align:start position:0% +it like the list procedure and now it's +going to think about that for a while + + align:start position:0% +going to think about that for a while + + + align:start position:0% +going to think about that for a while +and apply these rules so it's found an + + align:start position:0% +and apply these rules so it's found an + + + align:start position:0% +and apply these rules so it's found an +answer now it's going to see if there + + align:start position:0% +answer now it's going to see if there + + + align:start position:0% +answer now it's going to see if there +any other answers because it doesn't + + align:start position:0% +any other answers because it doesn't + + + align:start position:0% +any other answers because it doesn't +know a priori there's only one answer so + + align:start position:0% +know a priori there's only one answer so + + + align:start position:0% +know a priori there's only one answer so +it's sitting here checking all + + align:start position:0% +it's sitting here checking all + + + align:start position:0% +it's sitting here checking all +possibilities and it says no more done + + align:start position:0% +possibilities and it says no more done + + + align:start position:0% +possibilities and it says no more done +so there I've used those rules like a + + align:start position:0% +so there I've used those rules like a + + + align:start position:0% +so there I've used those rules like a +procedure work remember the whole point + + align:start position:0% +procedure work remember the whole point + + + align:start position:0% +procedure work remember the whole point +is that I can ask different kinds of + + align:start position:0% +is that I can ask different kinds of + + + align:start position:0% +is that I can ask different kinds of +questions I could say + + align:start position:0% + + + + align:start position:0% + +merge to form let's see how about two + + align:start position:0% +merge to form let's see how about two + + + align:start position:0% +merge to form let's see how about two +and a some lists of two elements which I + + align:start position:0% +and a some lists of two elements which I + + + align:start position:0% +and a some lists of two elements which I +know starts with two and the other thing + + align:start position:0% +know starts with two and the other thing + + + align:start position:0% +know starts with two and the other thing +I don't know and X and some other lists + + align:start position:0% +I don't know and X and some other lists + + + align:start position:0% +I don't know and X and some other lists +merge to form one two three and four and + + align:start position:0% + + + + align:start position:0% + +so now it's gonna think about that right + + align:start position:0% +so now it's gonna think about that right + + + align:start position:0% +so now it's gonna think about that right +it's got to find all right so it's on + + align:start position:0% +it's got to find all right so it's on + + + align:start position:0% +it's got to find all right so it's on +one possibility said a could be three + + align:start position:0% +one possibility said a could be three + + + align:start position:0% +one possibility said a could be three +and X could be the list one four and now + + align:start position:0% +and X could be the list one four and now + + + align:start position:0% +and X could be the list one four and now +again it's got to check because it + + align:start position:0% +again it's got to check because it + + + align:start position:0% +again it's got to check because it +doesn't a priori know that there aren't + + align:start position:0% +doesn't a priori know that there aren't + + + align:start position:0% +doesn't a priori know that there aren't +any other possibilities going on okay or + + align:start position:0% +any other possibilities going on okay or + + + align:start position:0% +any other possibilities going on okay or +like I said I could say something like + + align:start position:0% +like I said I could say something like + + + align:start position:0% +like I said I could say something like +merge to form like what and what else + + align:start position:0% +merge to form like what and what else + + + align:start position:0% +merge to form like what and what else +merge to form one two three four five + + align:start position:0% + + + + align:start position:0% + +right now it's gonna think about that + + align:start position:0% +right now it's gonna think about that + + + align:start position:0% +right now it's gonna think about that +and there are a lot of answers that it + + align:start position:0% +and there are a lot of answers that it + + + align:start position:0% +and there are a lot of answers that it +might get and what you see is here + + align:start position:0% +might get and what you see is here + + + align:start position:0% +might get and what you see is here +you're you're really paying the price of + + align:start position:0% +you're you're really paying the price of + + + align:start position:0% +you're you're really paying the price of +slowness right and kind of for three + + align:start position:0% +slowness right and kind of for three + + + align:start position:0% +slowness right and kind of for three +reasons one is that this language is + + align:start position:0% +reasons one is that this language is + + + align:start position:0% +reasons one is that this language is +doubly interpreted whereas you know in a + + align:start position:0% +doubly interpreted whereas you know in a + + + align:start position:0% +doubly interpreted whereas you know in a +real implementation you would go compile + + align:start position:0% +real implementation you would go compile + + + align:start position:0% +real implementation you would go compile +this down to primitive operations the + + align:start position:0% +this down to primitive operations the + + + align:start position:0% +this down to primitive operations the +other reason is that this algorithm for + + align:start position:0% +other reason is that this algorithm for + + + align:start position:0% +other reason is that this algorithm for +this particular algorithm for merges is + + align:start position:0% +this particular algorithm for merges is + + + align:start position:0% +this particular algorithm for merges is +doubly recursive so it's going to take a + + align:start position:0% +doubly recursive so it's going to take a + + + align:start position:0% +doubly recursive so it's going to take a +very long time and eventually this is + + align:start position:0% +very long time and eventually this is + + + align:start position:0% +very long time and eventually this is +going to go through and find find wat 2 + + align:start position:0% +going to go through and find find wat 2 + + + align:start position:0% +going to go through and find find wat 2 +to the 5th possible answers and you see + + align:start position:0% +to the 5th possible answers and you see + + + align:start position:0% +to the 5th possible answers and you see +they come out in some some fairly + + align:start position:0% +they come out in some some fairly + + + align:start position:0% +they come out in some some fairly +arbitrary order depending on on which + + align:start position:0% +arbitrary order depending on on which + + + align:start position:0% +arbitrary order depending on on which +order it's going to be trying these + + align:start position:0% +order it's going to be trying these + + + align:start position:0% +order it's going to be trying these +rules in fact what we're going to do + + align:start position:0% +rules in fact what we're going to do + + + align:start position:0% +rules in fact what we're going to do +when they edit the videotape is speed + + align:start position:0% +when they edit the videotape is speed + + + align:start position:0% +when they edit the videotape is speed +all this up and don't you about taking + + align:start position:0% +all this up and don't you about taking + + + align:start position:0% +all this up and don't you about taking +out these weights and don't you which + + align:start position:0% +out these weights and don't you which + + + align:start position:0% +out these weights and don't you which +you could do that in your demos anyway + + align:start position:0% + + + + align:start position:0% + +anyway it's still grinding there + + align:start position:0% + + + + align:start position:0% + +anyway there are 32 possibilities we + + align:start position:0% +anyway there are 32 possibilities we + + + align:start position:0% +anyway there are 32 possibilities we +won't wait for it to print out all of + + align:start position:0% +won't wait for it to print out all of + + + align:start position:0% +won't wait for it to print out all of +them okay okay so the means of + + align:start position:0% +them okay okay so the means of + + + align:start position:0% +them okay okay so the means of +abstraction in this language are rules + + align:start position:0% + + + + align:start position:0% + +and so we take some bunch of things that + + align:start position:0% +and so we take some bunch of things that + + + align:start position:0% +and so we take some bunch of things that +are put together with logic and we name + + align:start position:0% +are put together with logic and we name + + + align:start position:0% +are put together with logic and we name +them and you can think of that as naming + + align:start position:0% +them and you can think of that as naming + + + align:start position:0% +them and you can think of that as naming +a particular pattern of logic or you can + + align:start position:0% +a particular pattern of logic or you can + + + align:start position:0% +a particular pattern of logic or you can +think of that of saying if you want to + + align:start position:0% +think of that of saying if you want to + + + align:start position:0% +think of that of saying if you want to +deduce some conclusion you can apply + + align:start position:0% +deduce some conclusion you can apply + + + align:start position:0% +deduce some conclusion you can apply +those rules of logic okay and those are + + align:start position:0% +those rules of logic okay and those are + + + align:start position:0% +those rules of logic okay and those are +the the three elements of this language + + align:start position:0% +the the three elements of this language + + + align:start position:0% +the the three elements of this language +let's break now and then we'll talk + + align:start position:0% +let's break now and then we'll talk + + + align:start position:0% +let's break now and then we'll talk +about how what's actually implemented + + align:start position:0% + + + + align:start position:0% + +Lisp value primitive or whatever + + align:start position:0% +Lisp value primitive or whatever + + + align:start position:0% +Lisp value primitive or whatever +interfere with your means to go both + + align:start position:0% +interfere with your means to go both + + + align:start position:0% +interfere with your means to go both +directions on a query okay that's it the + + align:start position:0% +directions on a query okay that's it the + + + align:start position:0% +directions on a query okay that's it the +question is just using this value + + align:start position:0% +question is just using this value + + + align:start position:0% +question is just using this value +interfere with the ability to go both + + align:start position:0% +interfere with the ability to go both + + + align:start position:0% +interfere with the ability to go both +directions on the query we haven't + + align:start position:0% +directions on the query we haven't + + + align:start position:0% +directions on the query we haven't +really talked about the implementation + + align:start position:0% +really talked about the implementation + + + align:start position:0% +really talked about the implementation +yet but the answer is yes it can in + + align:start position:0% +yet but the answer is yes it can in + + + align:start position:0% +yet but the answer is yes it can in +general as we'll see at the end although + + align:start position:0% +general as we'll see at the end although + + + align:start position:0% +general as we'll see at the end although +I really won't go into details it's + + align:start position:0% +I really won't go into details it's + + + align:start position:0% +I really won't go into details it's +fairly complicated especially when you + + align:start position:0% +fairly complicated especially when you + + + align:start position:0% +fairly complicated especially when you +use not when you use either not wirless + + align:start position:0% +use not when you use either not wirless + + + align:start position:0% +use not when you use either not wirless +value or or actually if you use anything + + align:start position:0% +value or or actually if you use anything + + + align:start position:0% +value or or actually if you use anything +besides only and it becomes very + + align:start position:0% +besides only and it becomes very + + + align:start position:0% +besides only and it becomes very +complicated to say whether when these + + align:start position:0% +complicated to say whether when these + + + align:start position:0% +complicated to say whether when these +things will work they they won't work + + align:start position:0% +things will work they they won't work + + + align:start position:0% +things will work they they won't work +quite in all situations I'll talk about + + align:start position:0% +quite in all situations I'll talk about + + + align:start position:0% +quite in all situations I'll talk about +that the end of the the second half + + align:start position:0% +that the end of the the second half + + + align:start position:0% +that the end of the the second half +today but the answer to your question is + + align:start position:0% +today but the answer to your question is + + + align:start position:0% +today but the answer to your question is +yes by dragging in a lot more power from + + align:start position:0% +yes by dragging in a lot more power from + + + align:start position:0% +yes by dragging in a lot more power from +this value you lose some of the some of + + align:start position:0% +this value you lose some of the some of + + + align:start position:0% +this value you lose some of the some of +the principle power of logic programming + + align:start position:0% +the principle power of logic programming + + + align:start position:0% +the principle power of logic programming +that's a trade-off that you have to make + + align:start position:0% + + + + align:start position:0% + +ok let's take a break + + align:start position:0% +ok let's take a break + + + align:start position:0% +ok let's take a break +[Music] \ No newline at end of file diff --git a/rIMCTzC1A3c.txt b/rIMCTzC1A3c.txt new file mode 100644 index 0000000000000000000000000000000000000000..97f50ae8b6da71a6d9783a8aacd22459c0d2436f --- /dev/null +++ b/rIMCTzC1A3c.txt @@ -0,0 +1,195 @@ +align:start position:0% + +why would MIT students bring their + + align:start position:0% +why would MIT students bring their + + + align:start position:0% +why would MIT students bring their +toenail clippings to class and how do + + align:start position:0% +toenail clippings to class and how do + + + align:start position:0% +toenail clippings to class and how do +100 people learn how to fly airplanes in + + align:start position:0% +100 people learn how to fly airplanes in + + + align:start position:0% +100 people learn how to fly airplanes in +three days could a film experience + + align:start position:0% +three days could a film experience + + + align:start position:0% +three days could a film experience +really be more important than learning + + align:start position:0% +really be more important than learning + + + align:start position:0% +really be more important than learning +quantum physics this is chalk radio a + + align:start position:0% +quantum physics this is chalk radio a + + + align:start position:0% +quantum physics this is chalk radio a +podcast about inspired teaching at MIT + + align:start position:0% +podcast about inspired teaching at MIT + + + align:start position:0% +podcast about inspired teaching at MIT +we have conversations with some of the + + align:start position:0% +we have conversations with some of the + + + align:start position:0% +we have conversations with some of the +professors that make some of the most + + align:start position:0% +professors that make some of the most + + + align:start position:0% +professors that make some of the most +interesting courses on campus come to + + align:start position:0% +interesting courses on campus come to + + + align:start position:0% +interesting courses on campus come to +life the conversations we have with our + + align:start position:0% +life the conversations we have with our + + + align:start position:0% +life the conversations we have with our +guests are candid quaniee serious and + + align:start position:0% +guests are candid quaniee serious and + + + align:start position:0% +guests are candid quaniee serious and +personal they're the kind of + + align:start position:0% +personal they're the kind of + + + align:start position:0% +personal they're the kind of +conversations you'd have if you bumped + + align:start position:0% +conversations you'd have if you bumped + + + align:start position:0% +conversations you'd have if you bumped +into your favorite professor in the + + align:start position:0% +into your favorite professor in the + + + align:start position:0% +into your favorite professor in the +infinite corridor and walk to them + + align:start position:0% +infinite corridor and walk to them + + + align:start position:0% +infinite corridor and walk to them +across campus and that's why we're doing + + align:start position:0% +across campus and that's why we're doing + + + align:start position:0% +across campus and that's why we're doing +this we want you to feel like you're + + align:start position:0% +this we want you to feel like you're + + + align:start position:0% +this we want you to feel like you're +right here with us walking underneath + + align:start position:0% +right here with us walking underneath + + + align:start position:0% +right here with us walking underneath +the dome experiencing the buzz that + + align:start position:0% +the dome experiencing the buzz that + + + align:start position:0% +the dome experiencing the buzz that +happens when people who love science + + align:start position:0% +happens when people who love science + + + align:start position:0% +happens when people who love science +learning and teaching all come together + + align:start position:0% +learning and teaching all come together + + + align:start position:0% +learning and teaching all come together +to think talk and dream I hope you + + align:start position:0% +to think talk and dream I hope you + + + align:start position:0% +to think talk and dream I hope you +listen to talk radio it's really the + + align:start position:0% +listen to talk radio it's really the + + + align:start position:0% +listen to talk radio it's really the +closest thing to being here \ No newline at end of file diff --git a/raTzkzML31w.txt b/raTzkzML31w.txt new file mode 100644 index 0000000000000000000000000000000000000000..d6dda8d65173e502d72b4f39793a7d41ca8d3d59 --- /dev/null +++ b/raTzkzML31w.txt @@ -0,0 +1,2041 @@ +OPERATOR:: The following content +is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: I want to pick +up exactly where I + +left off last time. + +When I was talking about various +sins one can commit + +with statistics. + +And I had been talking about the +sin of data enhancement, + +where the basic idea there is, +you take a piece of data, and + +you read much more into +it than it implies. + +In particular, a very common +thing people do with data is + +they extrapolate. + +I'd given you a couple +of examples. + +In the real world, it's often +not desirable to say that I + +have a point here, and a point +here, therefore the next point + +will surely be here. + +And we can just extrapolate +in a straight line. + +We before saw some examples +where I had an algorithm to + +generate points, and we fit a +curve to it, used the curve to + +predict future points, +and discovered + +it was nowhere close. + +Unfortunately, we often see +people do this sort of thing. + +One of my favorite stories is, +William Ruckelshaus, who was + +head of the Environmental +Protection Agency + +in the early 1970s. + +And he had a press conference, +spoke about the increased use + +of cars, and the decreased +amount of carpooling. + +He was trying to get people to +carpool, since at the time + +carpooling was on the way down, +and I now quote, "each + +car entering the central city, +sorry, in 1960," he said, + +"each car entering the central +city had 1.7 people in it. + +By 1970. this had dropped +to less than 1.2. + +If present trends continue, by +1980, more than 1 out of every + +10 cars entering the city will +have no driver." Amazingly + +enough, the press reported this +as a straight story, and + +talked about how we would be +dramatically dropping. + +Of course, as it happened, +it didn't occur. + +But it's just an example of, how +much trouble you can get + +into by extrapolating. + +The final sin I want to talk +about is probably the most + +common, and it's called the +Texas sharpshooter fallacy. + +Now before I get into +that, are any of + +you here from Texas? + +All right, you're going +to be offended. + +Let me think, OK, anybody +here from Oklahoma? + +You'll like it. + +I'll dump on Oklahoma, it will +be much better then. + +We'll talk about the Oklahoma +sharpshooter fallacy. + +We won't talk about the +BCS rankings, though. + +So the idea here is a +pretty simple one. + +This is a famous marksman who +fires his gun randomly at the + +side of a barn, has a bunch of +holes in it, then goes and + +takes a can of paint and draws +bullseyes around all the + +places his bullets +happened to hit. + +And people walk by the barn +and say, God, he is good. + +So obviously, not a good thing, +but amazingly easy to + +fall into this trap. + +So here's another example. + +In August of 2001, a paper which +people took seriously + +appeared in a moderately serious +journal called The New + +Scientist. And it announced that +researchers in Scotland + +had proven that anorexics +are likely to have + +been born in June. + +I'm sure you all knew that. + +How did how did they +prove this? + +Or demonstrate this? + +They studied 446 women. + +Each of whom had been +diagnosed anorexic. + +And they observed that about 30 +percent more than average + +were born in June. + +Now, since the monthly average +of births, if you divide this + +by 12, it's about 37, that +tells us that 48 + +were born in June. + +So at first sight, this seems +significant, and in fact if + +you run tests, and ask what's +the likelihood of that many + +more being born in 1 +month, you'll find + +that it's quite unlikely. + +In fact, you'll find the +probability of this happening + +is only about 3 percent, of it +happening just by accident. + +What's wrong with +the logic here? + +Yes? + +STUDENT: They only studied +diagnosed anorexics. + +PROFESSOR: No, because they were +only interested in the + +question of when are anorexics +born, so it made sense to only + +study those. + +Now maybe you're right, that we +could study that, in fact, + +more people are born +in June period. + +That could be true. + +This would be one of +the fallacies we + +looked at before, right? + +That there's a lurking variable +which is just that + +people are more likely +to be born in June. + +So that's certainly +a possibility. + +What else? + +What else is the flaw? + +Where's the flaw +in this logic? + +Well, what did they do? + +They participated in the +Oklahoma sharpshooter fallacy. + +What they did is, they looked +at 12 months, they took the + +months with the most births in +it, which happened to be June, + +and calculated the probability +of 3 percent. + +They didn't start with the +hypothesis that it was June. + +They started with 12 months, and +then they drew a bullseye + +around June. + +So the right question to ask +is, what's the probability, + +not that June had 48 babies, but +that at least one of the + +12 months had 48 babies. + +That probability is a lot to +higher than 3 percent, right? + +In fact, it's about +30 percent. + +So what we see is, again +perfectly reasonable + +statistical techniques, but +not looking at things + +in the right way. + +And answering the +wrong question. + +That make sense to everybody? + +And you can see why people can +fall into this trap, right? + +It was a perfectly sensible, +seemingly sensible argument. + +So the moral of this particular +thing is, be very + +careful about looking at your +data, drawing a conclusion, + +and then saying how probable +was that to have occurred? + +Because again, you're probably, +or maybe, drawing + +the bullseye around something +that's already there. + +Now if they had taken another +set of 446 anorexics, and + +again June was the month, +then there would be some + +credibility in it. + +Because they would have started +with the hypothesis, + +not that there existed a month, +but that June was + +particularly likely. + +But then they would have to also +check and make sure that + +June isn't just a popular +month to be born, as was + +suggested earlier. + +All right, I could go on and +on with this sort of thing, + +it's kind of fun. + +But I won't. + +Instead I'm going to torture +you with yet one more + +simulation. + +You may be tempted at this +point to just zone out. + +Try not to. + +And as an added incentive for +you to pay attention, I'm + +going to warn you that this +particular simulation will + +appear in the final, +or a variant of it. + +And what we'll be doing is, +early next week we'll be + +distributing code, which we'll +ask you to study, about two or + +three pages of code, and then +on the final we'll be asking + +you questions about the code. + +Not that you have to memorize +it, we'll give + +you a copy of it. + +But you should understand +it before you walk + +in to take the final. + +Because there will not be time +to look at that code for the + +first time during the +quiz, and figure + +out what it's doing. + +OK, so let's look at it. + +I should also warn you that this +code includes some Python + +concepts, at least one, that +you have not yet seen. + +We'll see it briefly today. + +This is on purpose, because one +of the things I hope you + +have learned to do this +semester, is look up things + +you don't know, and figure +out what they do. + +What they mean. + +Because we obviously can't, in +any course, or even any set of + +courses, tell you everything +you'll ever + +want to know in life. + +So intentionally, we've seeded +some things in this program + +that will be unfamiliar, so +during the time you're + +studying the program, get +online, look it up, figure out + +what they do. + +If you have trouble, we will be +having office hours, where + +you can go and get some help. + +But the TAs will expect you to +have at least tried to figure + +it out yourself. + +Yeah? + +STUDENT: Will the final +be open note? + +PROFESSOR: Final will be open +book, open notes, just like + +the quizzes. + +It will be the first two hours +of the allotted time, we won't + +go the whole 3 hours, OK? + +So it won't be hugely longer +than the quizzes. + +It would be a little +bit longer. + +And again, very much in the +same style of the quizzes. + +All right, let's look at this. + +Let's assume that you've won the +lottery, and have serious + +money that you foolishly wish to +invest in the stock market. + +There are two basic strategies +to choose from, in investing. + +You can either have what's +called an indexed portfolio, + +or a managed portfolio. + +Indexed portfolios, you +basically say, I want to own + +all of the stocks that there +are, and if the stock market + +goes up, I make money, if +the stock market goes + +down, I lose money. + +I'm not going to be thinking +I'm clever, and can pick + +winners and losers, I'm +just betting on + +the market as a whole. + +They're attractive, in +that a, they don't + +require a lot of thought. + +And b, they have what's called +a low expense ratio, since + +they're easy to implement, you +don't pay anyone to be + +brilliant to implement +if for you. + +So they're very low fees. + +A managed portfolio, you find +somebody you think is really + +smart, and you pay them a fair +amount of money, and in return + +they assert that they will pick +winners for you, and in + +fact, you will outperform +the stock market. + +And if it goes up 6 percent, +well you'll go up 10 percent + +or more, and if it goes down, +don't worry, I'm so smart your + +stocks won't go down. + +There's a lot of debate +about which is the + +better of these two. + +And so now we're going to try +and see if we can write a + +simulation that will give us +some insight as to which of + +these might be better +or worse. + +All right, so that's +the basic problem. + +Now, as we know, and by the way +we're not going to write a + +perfect simulation here, because +we're going to try and + +do it in 40 minutes, +or 30 minutes. + +And it would take at least an +hour do a perfect simulation + +of the stock market. + +All right. + +First thing we need to do is +have some sort of a theory. + +When we did the spring, we had +this theory of Hooke's Law + +that told us something, and we +built a simulation, or built + +some tools around that theory. + +Now we need to think about a +model of the stock market. + +And the model we're going to use +is based on what's called + +the Efficient Market +Hypothesis. + +So the moral here, again, is +whenever you're doing an + +implementation of a simulation, +you do need to + +have some underlying theory +about the model. + +What this model asserts +is that markets are + +informationally efficient. + +That is to say, current prices +reflect all publicly known + +information about each stock, +and therefore are unbiased. + +That if people thought that +the stock was underpriced, + +well people would buy more of +it in the price would have + +risen already. + +If people thought the stock was +overpriced, well, people + +would have tried to sell it, and +it would have come down. + +So this is a very popular +theory, believed by many + +famous economists today, and +in the past. And says, OK, + +that effectively means that +the market is memoryless. + +OK, that it doesn't matter what +the price of the stock + +was yesterday. + +Today, it's priced given the +best-known information, and so + +tomorrow it's equally likely +to go up or down. + +Relative to the whole +market, right? + +It's well known that over +periods of multiple decades, + +the market has a tendency +to go up. + +And so there's an upward bias to +the stock market, contrary + +to what you may have +seen recently. + +But that no particular stock +is more or less likely to + +outperform the market, because +all the information is + +incorporated in the price. + +And that leads to a notion of +being able to model the + +market, how? + +How would you model individual +stocks if you believe this + +hypothesis? + +Somebody? + +What's going to happen? + +STUDENT: Random walk. + +PROFESSOR: Yes, exactly right. + +So we would model it +as a random walk. + +In fact, there's a very famous +book called A Random Walk Down + +Wall Street, that was one of +the first to make this + +hypothesis. + +Now later, we may decide to +abandon this model, but for + +the moment let's accept that. + +And let's think about how +we're going to build the + +simulation. + +Whenever I think about how to +build an interesting program, + +and I hope whenever you think +about it, the first thing I + +think about is, what are the +classes I might want to have, + +what are the types? + +And it seems pretty obvious +that at least two of the + +things I'm going to want +are stock and market. + +After all, I'm going to try and +build a simulation of the + +stock market, so I might as +well have the notion of a + +market, and probably the +notion of a stock. + +Which should I implement +first? + +Well, my usual style of +programming would be to + +implement the one that's lowest +down in the hierarchy, + +near the bottom. + +I won't be able to show you what +a market does unless I + +have stocks, but I can look at +what an individual stock does + +without having a market. + +So why do I implement +this first? + +Because it will be easier to +unit test. I can build class + +stock, and I can test class +stock, before I + +have a class market. + +So now let's look at it. + +Clean up the desktop +a little bit. + +This is similar to, but not +identical to, what you have in + +your handout. + +All right, so there's +class stock. + +And I'm going to initialize +it, create them, with an + +opening price. + +When a stock is first listed in +the market, it comes with + +some price. + +I'm gonna keep as part of each +stock, it's history of prices, + +which we can initialize, well, +I've initialized it as empty, + +but that's probably the +wrong thing, right? + +I probably should have had it +being the, starting here, + +right, the opening price. + +Now comes an interesting part. + +Self dot distribution. + +Well, I lied to you a little bit +in my description of what + +it meant to have the Efficient +Market Hypothesis. + +I said that no stock is likely +to outperform the market or + +underperform the market. + +But it's not quite true, because +typically what they + +actually do that, is they say +it's adjusted for risk. + +It's clear that some stocks are +more volatile than others. + +If you will buy stock in an +electrical utility which has a + +guaranteed revenue stream, +because no matter how bad the + +economy gets, a lot of people +still use electricity, you + +don't expect it to +fluctuate a lot. + +If you buy stock in a high +tech company, that sells + +things on the internet, you +might expect it to fluctuate + +enormously. + +Or if you buy stock in a +retailer, you might expect it + +to go up or down more +dramatically with the economy, + +and so in fact there is a notion +of risk, and I'm not + +going to do this in this +simulation, but usually people + +have to be paid to take risk. + +And so it's usually the case +that you can get a higher + +return if you're willing +to take more risk. + +We might or might not have time +to come back to that. + +But more generally, the point +is, that each stock actually + +behaves a little bit +differently. + +There's a distribution +of how it would move. + +So even if, on average, the +stock is expected to not move + +at all from where it starts, +some stocks will be expected + +to just trundle along +without much + +change, not very volatile. + +And other stocks might jump up +and down a lot because they're + +very volatile. + +Even if the expected value +is the same, they'd + +move around a lot. + +So how can we model this +kind of thing? + +Well, we've already looked +at the basic notion. + +Last time we looked at the +notion, last lecture we looked + +at the idea of a distribution. + +And when we do a simulation, +we're pulling the samples from + +some distribution. + +It could be normal, everything, +that would be a + +Gaussian, where if you recall +there was a mean, and a + +standard deviation, and most +values were going to be close + +to the mean. + +Especially if there is a small +standard deviation. + +If there's a large standard +deviation it would be spread. + +Or it could be uniform, +where every + +value was equally probable. + +We also looked at exponential. + +So we're going to assign to each +stock, when we create it, + +a distribution. + +Some way of visualizing, or +thinking about, where we draw + +the price changes from. + +This gets us into a new +linguistic concept, which + +we'll see down here. + +You don't have this particular +code on your handout, you do + +have a code that uses +the same concept. + +So here's my unit +test procedure. + +And here's where I'm going +to create distributions. + +And I'm going to look at two. + +A random-- a uniform, +and a Gaussian. + +What lambda that does, it +creates on the fly a function, + +as the program runs. + +That I can then pass around. + +So here, I'm going to look at +the thing random dot uniform, + +for example, between minus +volatility and plus + +volatility. + +So ignoring the lambda, what +do we expect random dot + +uniform to do? + +It has equally likely, in the +range from minus volatility to + +plus volatility, it will return +any value in here. + +But notice the previous line, +where I am computing + +volatility. + +If I wanted every stock to have +the same volatility, I + +could just do that, if +you will, at the + +time I wrote my program. + +But here I want it +to be determined, + +chosen at run time. + +So first, I choose a volatility +randomly, from some + +distribution of possible +volatilities from 0 to, in + +this case, 0.2. + +Think of this as the percentage +move per day. + +So 2/10 of a percent, would +be the move here. + +And then I'll create this +function, this distribution d + +1, which will, whenever I call +it, give me a random, a + +uniformly selected value +between minus and plus + +volatility. + +Then when I create the stock, +here, I can pass it + +in, pass in d 1. + +OK, it's a new concept. + +I don't expect you'll all +immediately grab it, but you + +will need to understand it +before the quiz comes along. + +And then I could also do a +Gaussian one here, with the + +mean of 0 and the standard +deviation of volatility + +divided by 2. + +Where do these parameters +come from? + +I made them up out +of whole cloth. + +Later we'll talk about how 1 +could think about them more + +intelligently. + +Now what do I do with that? + +All right, we'll see +that in a minute. + +But people understand what +the basic idea here is. + +Now, I can set the +price of a stock. + +And when I do that, I'll +append it to history. + +I can, oh, these have got +some remnants which we + +really don't need. + +I'll get rid of this which is +just an uninteresting thing. + +And let's look at make move. + +Because this is the +interesting thing. + +Make move is what we call to +change the price of a stock, + +at the beginning or end +of a day if you will. + +So the first thing it does, is +it says, if self dot price is + +0, I'm just going to return. + +This is not the right thing +to do, by the way. + +Again, there are some +bugs in here. + +You won't find these bugs +in your handout, right? + +Code is different +in the handout. + +But I wanted to show these to +you so we could think about. + +What I'm more interested in here +than in the result of the + +simulation, is the process +of creating it. + +So why did I put this here? + +Why did I say if self dot +price equals 0 return? + +Because the first time I wrote +the program, I didn't have + +anything like that here, +and a stock could go + +to 0 and then recover. + +Or even go to negative values. + +Well we know stock prices +are never negative. + +And in fact we know if the price +goes to 0, it's delisted + +from the exchange. + +So I said, all right, we better +make a special case of + +that. it turns out, that this +will be a bug, and I want you + +to think about why it's wrong +for me to put this check here. + +The check needs to be somewhere +in the program, but + +this is not the right +place for it. + +So think about why I didn't +leave it here. + +OK, then we'll get the old +price, which we're going to + +try and remember, and now comes +the interesting part. + +We're going to try and +figure out how the + +price should change. + +So I'm first going to +compute something + +called the base move. + +Think of this as kind of the +basis from which we'll be + +computing the actual move. + +I'll draw something from the +distribution, so this is + +interesting, I'm now calling +self dot distribution, and + +remember this will be different +for each stock. + +It will return me some random +value from either the Gaussian + +or the normal distribution. + +With a different volatility for +the stocks because that + +was also selected randomly, +plus some market bias. + +Saying, well, the market on +average will go up a little + +bit, or go down a little bit. + +And then I'll set the new price, +if you will, self dot + +price, to self dot price times +1 plus the base move. + +So notice what this says. + +If the base move is 0, then +the price doesn't change. + +So that makes sense. + +Interesting question. + +Why do you think I said self +dot price times 1 plus the + +base move, rather than just +adding the base move to the + +stock, price of the stock? + +Again, the first time I coded +this, I had an addition there + +instead of a multiplication. + +What would the ramifications +of an addition there be? + +That would say, how much the +stock changed is independent + +of its current price. + +And when I ran that it, I got +weird results, because we know + +that a Google priced at, say, +300, is much more likely to + +move by 10 points in +a day than a stock + +that's priced at $0.50. + +So in fact, it is the case, if +you look at data, and by the + +way, that's the way I ended +up setting a lot of these + +parameters and playing with +it, was comparing what my + +simulation said to historical +stock data. + +And indeed it is the case that +the price of the stock, the + +move, the amount of move, tends +to be proportional to + +the price of the stock. + +Expensive stocks move more. + +Interestingly enough, the +percentage moves are not much + +different between cheap stocks +and expensive stocks. + +And that's why, I ended up using +a multiplicative factor, + +rather than an additive +factor. + +This is again a general +lesson. + +As you build these kinds of +simulations, or anything like + +this, you need to think through +whether things should + +be multiplicative or additive. + +Because you get very different +results, typically. + +Multiplicative is what you want +to do if the amount of + +change is proportional to the +current size, whether it's + +price or anything else, and +additive if the change is + +independent of the current +value, typically, is I think + +the general way to +think about it. + +Now, you'll see this other +kind of peculiar thing. + +So I've now set the price, and +then I've got this test here. + +If mo, mo stands for momentum. + +I'm now exploring the question +of whether or not stock prices + +are indeed memoryless, +or the stock changes. + +And the fancy word for +that is Poisson. + +People often model things as +Poisson processes, which is to + +say, processes in which past +behavior has no impact on + +future behavior, it's +memoryless. + +And in fact, that's what the +Efficient Market Hypothesis + +purports to say. + +It says that, since all the +information is in the current + +price, you don't have to worry +about whether it went up or + +down yesterday, to decide what +it's going to do today. + +There are people who don't +believe that, and instead + +argue that there is this +notion called momentum. + +These are called momentum +investors. + +And they say, what's most likely +to happen today, is + +what happened yesterday. + +Or more likely. + +If the stock went up yesterday, +it's more likely to + +go up today, than if it didn't +go up yesterday. + +So I wasn't sure which religion +I was willing to + +believe in, if either, so I +added a parameter called, if + +you believe in momentum, +then you should change + +the price by -- + +And here I just did something +taking a Gaussian times the + +last change, and, in +fact, added it in. + +So if it went up yesterday, it +will more likely go up today, + +because I'm throwing in a +positive number, otherwise a + +negative number. + +Notice that this is additive. + +Because it's dealing with +yesterday's price. + +Change, with the change. + +OK, so that's why we're +dealing with that. + +Now, here's where I should've +put in this test + +that I had up here. + +Get it out from there. + +Because what I want to do is, +say if self dot price is less + +than 0.01, I'm going to set it +to 0, just keep it there. + +That doesn't solve the problem +we had before though, right? + +Then I'm going to append it, and +keep the last change for + +future use. + +OK, people understand what's +going on here? + +And then show history is just +going to produce a plot. + +We've seen that a million +times before. + +Any questions about this? + +Well, I have a question? + +Does it make any sense? + +Is it going to work at all? + +So now let's test it. + +So, I now have this +unit test program + +called unit test stock. + +I originally did not make it a +function, I had it in-line, + +and I realized that was really +stupid, because I wanted to do + +it a lot of times. + +So it's got an internal +procedure, internal function, + +local to the unit test, that +runs the simulation. + +And it takes the set of stocks +to simulate, a fig, figure + +number, this is going to print +a bunch of graphs, and I want + +to say what graph it is, +and whether or not I + +believe in big mo. + +It sets the mean to 0, and then +for s in the stocks, it + +moves it, giving it the bias +and the momentum, then it + +shows the history. + +And then computes the mean of, +getting me the mean of all the + +stocks in it. + +We've seen this sort of thing +many times before. + +I've then got some constants. + +By the way, I want to emphasize +that I've named + +these constants to make +it easier to change. + +Starting with 20 stocks, +100 days. + +And then what I do is, I stock +sub 1, stocks 1 will be the + +empty list, stocks 2 is the +empty list. Why do you think + +I'm starting with bias of 0? + +Because, what do you think the +mean should be, if I simulate + +various things that +the bias of 0? + +I start $100 as the average +price of the stock, what + +should the average price +of the stock be? + +If my code is correct, what +should the average price be, + +after say, 100 days, +if there's no bias. + +Pardon? + +100, exactly. + +Since there's no upward +or downward bias. + +They may fluctuate wildly, but +if I look at enough stocks, + +the average should be +right around 100. + +I don't know what the average +would be if I chose a + +different bias. + +It's a little bit complicated, +so I chose the simplest bias. + +Important lesson, so that +there would be some + +predictability in the results, +and I would have some, if you + +will, smoke test for knowing +whether or not I was getting, + +my code seemed to be working. + +All right, and initially, well, +maybe initially, just to + +be simple I'm going to start +momentum equal to false. + +Because, again, it seems simpler +have a model where + +there's no momentum. + +I'm looking for the simplest +model possible for the first + +time I run it. + +And then we looked at this +little loop before, for i in + +range number of stocks, I'm +going to create two different + +lists of stocks, one where the +moves, or distributions, are + +chosen from a uniform, and the +other where they're Gaussian. + +Because I'm sort of curious as +to, again, which is the right + +way to think about +this, all right? + +And then, I'm going +to just call it. + +We'll see what we get. + +So let's do it. + +Let's hope that all the +changes I mad have not + +introduced a syntax error. + +All right, well at least +it did something. + +Let's see what it did. + +So the test on the left, you'll +remember, was the one + +with test one, I believe, was +the uniform distribution, and + +test two is the Gaussian. + +So, but let's, what should +we do first? + +Well, let's do the smoke test +number one: is the mean more + +or less what we expected? + +Well, it looks like it's dead on +100, which was our initial + +price in test two. + +And in test one it's a +little bit above 100. + +But, we didn't do that many +stocks, or that many days, so + +it's quite plausible +that it's correct. + +But, just to be sure, not to be +sure, but just to increase + +my confidence, I'm going +to just run it again. + +Well, here I'm a little bit +below 100 and in two, and test + +one a little bit below +100 as well. + +You remember last time was +a little bit above 100. + +I feel pretty good about this, +and in fact I ran it a lot of + +times in my office. + +And it just bounces around, +hovering around 100. + +Course, this is the wrong +way to do it. + +I should really just put it in +a nice test harness, where I + +run 100, 200, 1,000 trials, but +I didn't want to bore you + +with that here. + +So we'll see that, OK, we passed +the first smoke test. + +We seem to be where +we expect to be. + +Well, let's try smoke +test two. + +What else might we want to see, +to see if we got things + +working properly? + +Well, I kind of ignored the +notion of bias by making it 0, + +so let's give it a +big bias here. + +Assuming it will +let me edit it. + +We just gotta start it +up again, it's the + +safest thing to do. + +You wouldn't think I would +have, I don't have -- all + +right, be that way about it. + +Fortunately, we've been +through this before. + +We know if we relaunch +the Finder. + +Who says Mac OS is flawless? + +All right, we were down here, +and I was saying, let's try a + +larger, introduce a bias. + +Again, we're trying to see +if it does what we + +think it might do. + +So what do you think it +should do with a bias? + +Where should the mean be now? + +Still around 100? + +Or higher, right? + +Because we've now put in +a bias suggesting that + +it should go up. + +Oops. + +It wouldn't have hurt it. + +All right. + +So let's run it. + +Sure enough, for one, we see, +test two, it's a little bit + +over 100, and for test one +it's way over 100. + +Well, let's make sure +it's not a fluke. + +Try it again. + +So, sure enough, changing the +bias changed the price, and + +even changed it in the +right direction. + +So we can feel pretty +comfortable that it's doing + +something good with that. + +We could also feel pretty +comfortable that that's + +probably way too high +a bias, right? + +We would not expect that the +mean should be over 160, or in + +one case, 150, after only +100 days trading, right? + +Things don't typically go +up 50% in 100 days. + +They go down 50%, but -- + +All right, so that's good. + +Oh, let's look at something +else now. + +Let's go back to where, +a simpler bias here. + +We'll run it again. + +And think about, what's the +difference between the + +Gaussian and the normal? + +Can we deduce anything +about those? + +Not, well, let me ask you. + +What do you think, yes or no? + +Anybody see anything +interesting here? + +Yeah? + +STUDENT: The variance of the +Gaussian seems to be less than + +the variance of the uniform. + +PROFESSOR: The variance +of the Gaussian -- + +STUDENT: -- is less. + +PROFESSOR: So all right, that +appears to be the case here. + +But let's run it again, +as we've done with + +all the other tests. + +So we have a hypothesis. + +Let's not fall victim to the +Oklahoma sharpshooter. + +We'll test our hypothesis, or at +least examine it again, see + +if it's, in some sense, +repeatable. + +Well, now what do we see? + +Doesn't seem to be true +this time, right? + +Not obviously. + +So, we're not sure about this. + +So this is something +that we would need + +to investigate further. + +And we would need, to have to +look at it, and it's going to + +be very tricky, by the way, as +to what the right answer is. + +But if you think about it, it +would not be surprising if the + +Gaussians, at least, gave us +some surprising, more extreme, + +results, than the uniform. + +Because the uniform, as we've +set it up here, is bounded. + +The minimum and the maximum +is bounded. + +With the Gaussian, +there's a tail. + +And you might every once in a +while get this, at least as + +we've done it in this +case, this large + +move out at the end. + +You might not. + +There's nothing profound about +this, other than the + +understanding that the details +of how you set these things up + +can matter a lot. + +Well, the final thing I want +to look at is momentum. + +So let's go back, and let's +set mo to true here. + +Well, doesn't want us to +set mo to true here. + +Ah, there it does. + +So, and now let's run it +and see what happens. + +What do you think +should happen? + +Anybody? + +STUDENT: [INAUDIBLE] + +PROFESSOR: I think +you're right. + +These ones should curl, see +if I can -- oh, not bad. + +Let's run it. + +Well, it's a little hard +to see, but things + +tend to take off. + +Because once things started +moving, it tends to move in + +that direction. + +All right. + +How do we go about choosing +these parameters? + +How do we go about deciding +what to do? + +Well, we play with it, the way +I've been playing with it, and + +compare the results to some +set of real data. + +And then we try and get our +simulation to match the past, + +and hope that that will help +it predict the future. + +We're not enough time to +go through all the, + +to do that a lot. + +I will be posting code that +you can play with, and I + +suggest you go through exactly +this kind of exercise. + +Because this is really the way +that people do develop + +simulations. + +They don't, out of whole +cloth, get it + +right the first time. + +They build them, they do what if +games, they play with them, + +and then they try and adjust +them to get them right. + +The nice thing here is, you can +decide whether you believe + +momentum and see what it would +mean, or not mean, etc. + +All right, one more lecture. + +See you guys next week. \ No newline at end of file diff --git a/s-E5T3igntw.txt b/s-E5T3igntw.txt new file mode 100644 index 0000000000000000000000000000000000000000..e2df8af5a340c43bf91568bed1d5b2bb9222070b --- /dev/null +++ b/s-E5T3igntw.txt @@ -0,0 +1,1331 @@ +align:start position:0% + +equivalence relations are another kind + + align:start position:0% +equivalence relations are another kind + + + align:start position:0% +equivalence relations are another kind +of binary relation on a set which play a + + align:start position:0% +of binary relation on a set which play a + + + align:start position:0% +of binary relation on a set which play a +crucial role in mathematics and in + + align:start position:0% +crucial role in mathematics and in + + + align:start position:0% +crucial role in mathematics and in +computer science in particular and they + + align:start position:0% +computer science in particular and they + + + align:start position:0% +computer science in particular and they +can also be explained both in terms of + + align:start position:0% +can also be explained both in terms of + + + align:start position:0% +can also be explained both in terms of +digraphs and in terms of axioms so let's + + align:start position:0% +digraphs and in terms of axioms so let's + + + align:start position:0% +digraphs and in terms of axioms so let's +begin with a digraph explanation of an + + align:start position:0% +begin with a digraph explanation of an + + + align:start position:0% +begin with a digraph explanation of an +equivalence relation and the kind of + + align:start position:0% +equivalence relation and the kind of + + + align:start position:0% +equivalence relation and the kind of +relation that's an equivalence relation + + align:start position:0% +relation that's an equivalence relation + + + align:start position:0% +relation that's an equivalence relation +is the relation of there being a walk in + + align:start position:0% +is the relation of there being a walk in + + + align:start position:0% +is the relation of there being a walk in +both directions between two vertices so + + align:start position:0% +both directions between two vertices so + + + align:start position:0% +both directions between two vertices so +if there's a walk between vertex u and + + align:start position:0% +if there's a walk between vertex u and + + + align:start position:0% +if there's a walk between vertex u and +vertex V and conversely there's a walk + + align:start position:0% +vertex V and conversely there's a walk + + + align:start position:0% +vertex V and conversely there's a walk +from vertex V back to vertex u then U + + align:start position:0% +from vertex V back to vertex u then U + + + align:start position:0% +from vertex V back to vertex u then U +and V are said to be strongly connected + + align:start position:0% +and V are said to be strongly connected + + + align:start position:0% +and V are said to be strongly connected +and strongly connected is going to be an + + align:start position:0% +and strongly connected is going to be an + + + align:start position:0% +and strongly connected is going to be an +example of an equivalence relation so in + + align:start position:0% +example of an equivalence relation so in + + + align:start position:0% +example of an equivalence relation so in +terms of the walk relation including + + align:start position:0% +terms of the walk relation including + + + align:start position:0% +terms of the walk relation including +zero length walks the relation that + + align:start position:0% +zero length walks the relation that + + + align:start position:0% +zero length walks the relation that +we're talking about is u g star v and v + + align:start position:0% +we're talking about is u g star v and v + + + align:start position:0% +we're talking about is u g star v and v +g star u now as a property of relations + + align:start position:0% +g star u now as a property of relations + + + align:start position:0% +g star u now as a property of relations +this has a name it's called symmetry so + + align:start position:0% +this has a name it's called symmetry so + + + align:start position:0% +this has a name it's called symmetry so +a relation R on a set a is symmetric if + + align:start position:0% +a relation R on a set a is symmetric if + + + align:start position:0% +a relation R on a set a is symmetric if +and only if a are B implies B are a and + + align:start position:0% +and only if a are B implies B are a and + + + align:start position:0% +and only if a are B implies B are a and +the first remark is that the strongly + + align:start position:0% +the first remark is that the strongly + + + align:start position:0% +the first remark is that the strongly +connected relation is symmetric an + + align:start position:0% +connected relation is symmetric an + + + align:start position:0% +connected relation is symmetric an +equivalence relation is a symmetric + + align:start position:0% +equivalence relation is a symmetric + + + align:start position:0% +equivalence relation is a symmetric +relation that is transitive and + + align:start position:0% +relation that is transitive and + + + align:start position:0% +relation that is transitive and +reflexive and again we have immediately + + align:start position:0% +reflexive and again we have immediately + + + align:start position:0% +reflexive and again we have immediately +that the walk relation of the the mutual + + align:start position:0% +that the walk relation of the the mutual + + + align:start position:0% +that the walk relation of the the mutual +walk relation the two-way walk relation + + align:start position:0% +walk relation the two-way walk relation + + + align:start position:0% +walk relation the two-way walk relation +or strongly connected relation in a + + align:start position:0% +or strongly connected relation in a + + + align:start position:0% +or strongly connected relation in a +digraph is an equivalence relation + + align:start position:0% +digraph is an equivalence relation + + + align:start position:0% +digraph is an equivalence relation +because clearly if there's two way paths + + align:start position:0% +because clearly if there's two way paths + + + align:start position:0% +because clearly if there's two way paths +between U and V and between V and V and + + align:start position:0% +between U and V and between V and V and + + + align:start position:0% +between U and V and between V and V and +W then there's one between U and W by + + align:start position:0% +W then there's one between U and W by + + + align:start position:0% +W then there's one between U and W by +going from u to V to W and back likewise + + align:start position:0% +going from u to V to W and back likewise + + + align:start position:0% +going from u to V to W and back likewise +there is a length zero walk from any + + align:start position:0% +there is a length zero walk from any + + + align:start position:0% +there is a length zero walk from any +element to itself and by definition + + align:start position:0% +element to itself and by definition + + + align:start position:0% +element to itself and by definition +strong connectedness is symmetric so the + + align:start position:0% +strong connectedness is symmetric so the + + + align:start position:0% +strong connectedness is symmetric so the +strong connectedness relation in any + + align:start position:0% +strong connectedness relation in any + + + align:start position:0% +strong connectedness relation in any +digraph is an equivalence relation and + + align:start position:0% +digraph is an equivalence relation and + + + align:start position:0% +digraph is an equivalence relation and +the theorem is conversely that any + + align:start position:0% +the theorem is conversely that any + + + align:start position:0% +the theorem is conversely that any +equivalence relation anything that's an + + align:start position:0% +equivalence relation anything that's an + + + align:start position:0% +equivalence relation anything that's an +equivalence relation is the strongly + + align:start position:0% +equivalence relation is the strongly + + + align:start position:0% +equivalence relation is the strongly +connected relation of some digraph the + + align:start position:0% +connected relation of some digraph the + + + align:start position:0% +connected relation of some digraph the +proof is trivial it's the strongly + + align:start position:0% +proof is trivial it's the strongly + + + align:start position:0% +proof is trivial it's the strongly +connected relation of itself + + align:start position:0% +connected relation of itself + + + align:start position:0% +connected relation of itself +okay some examples of equivalence + + align:start position:0% +okay some examples of equivalence + + + align:start position:0% +okay some examples of equivalence +relations to see why they're so basic is + + align:start position:0% +relations to see why they're so basic is + + + align:start position:0% +relations to see why they're so basic is +that the most fundamental one is + + align:start position:0% +that the most fundamental one is + + + align:start position:0% +that the most fundamental one is +equality obviously equality is symmetric + + align:start position:0% +equality obviously equality is symmetric + + + align:start position:0% +equality obviously equality is symmetric +and reflexive and transitive + + align:start position:0% +and reflexive and transitive + + + align:start position:0% +and reflexive and transitive +and so it's an equivalence relation + + align:start position:0% +and so it's an equivalence relation + + + align:start position:0% +and so it's an equivalence relation +another one that we've seen is + + align:start position:0% +another one that we've seen is + + + align:start position:0% +another one that we've seen is +congruence mod in which you can also + + align:start position:0% +congruence mod in which you can also + + + align:start position:0% +congruence mod in which you can also +check is symmetric and transitive and + + align:start position:0% +check is symmetric and transitive and + + + align:start position:0% +check is symmetric and transitive and +reflexive and finally another relation + + align:start position:0% +reflexive and finally another relation + + + align:start position:0% +reflexive and finally another relation +would be that two sets are the same size + + align:start position:0% +would be that two sets are the same size + + + align:start position:0% +would be that two sets are the same size +providing they're finite sets and + + align:start position:0% +providing they're finite sets and + + + align:start position:0% +providing they're finite sets and +another example would be a bunch of + + align:start position:0% +another example would be a bunch of + + + align:start position:0% +another example would be a bunch of +objects having the same color two + + align:start position:0% +objects having the same color two + + + align:start position:0% +objects having the same color two +objects have the same color is a + + align:start position:0% +objects have the same color is a + + + align:start position:0% +objects have the same color is a +relation among objects that have color + + align:start position:0% +relation among objects that have color + + + align:start position:0% +relation among objects that have color +that is symmetric and transitive and + + align:start position:0% +that is symmetric and transitive and + + + align:start position:0% +that is symmetric and transitive and +reflexive so it's an equivalence + + align:start position:0% +reflexive so it's an equivalence + + + align:start position:0% +reflexive so it's an equivalence +relation let's illustrate some of these + + align:start position:0% +relation let's illustrate some of these + + + align:start position:0% +relation let's illustrate some of these +axioms that we have in terms of graphs + + align:start position:0% +axioms that we have in terms of graphs + + + align:start position:0% +axioms that we have in terms of graphs +it can be helpful to remember them so + + align:start position:0% +it can be helpful to remember them so + + + align:start position:0% +it can be helpful to remember them so +reflexive means that when you look at a + + align:start position:0% +reflexive means that when you look at a + + + align:start position:0% +reflexive means that when you look at a +digraph it's reflexive when there's a + + align:start position:0% +digraph it's reflexive when there's a + + + align:start position:0% +digraph it's reflexive when there's a +little self-loop from every vertex to + + align:start position:0% +little self-loop from every vertex to + + + align:start position:0% +little self-loop from every vertex to +itself so there's a length one path or + + align:start position:0% +itself so there's a length one path or + + + align:start position:0% +itself so there's a length one path or +an edge from the vertex to itself in + + align:start position:0% +an edge from the vertex to itself in + + + align:start position:0% +an edge from the vertex to itself in +reflexive graphs + + align:start position:0% +reflexive graphs + + + align:start position:0% +reflexive graphs +transitive means that whenever you have + + align:start position:0% +transitive means that whenever you have + + + align:start position:0% +transitive means that whenever you have +two edges connecting a one vertex to + + align:start position:0% +two edges connecting a one vertex to + + + align:start position:0% +two edges connecting a one vertex to +another there's a path of length two + + align:start position:0% +another there's a path of length two + + + align:start position:0% +another there's a path of length two +from one place to another then in fact + + align:start position:0% +from one place to another then in fact + + + align:start position:0% +from one place to another then in fact +there's an edge from that place to its + + align:start position:0% +there's an edge from that place to its + + + align:start position:0% +there's an edge from that place to its +target and of course as we said once + + align:start position:0% +target and of course as we said once + + + align:start position:0% +target and of course as we said once +that there's a an edge wherever there's + + align:start position:0% +that there's a an edge wherever there's + + + align:start position:0% +that there's a an edge wherever there's +a path of length two it follows by + + align:start position:0% +a path of length two it follows by + + + align:start position:0% +a path of length two it follows by +induction that there's an edge wherever + + align:start position:0% +induction that there's an edge wherever + + + align:start position:0% +induction that there's an edge wherever +there's a path of any length and that's + + align:start position:0% +there's a path of any length and that's + + + align:start position:0% +there's a path of any length and that's +what transitive means a symmetric means + + align:start position:0% +what transitive means a symmetric means + + + align:start position:0% +what transitive means a symmetric means +that whenever you have an edge from one + + align:start position:0% +that whenever you have an edge from one + + + align:start position:0% +that whenever you have an edge from one +vertex to another there is no edge back + + align:start position:0% +vertex to another there is no edge back + + + align:start position:0% +vertex to another there is no edge back +so in particular if I have an edge from + + align:start position:0% +so in particular if I have an edge from + + + align:start position:0% +so in particular if I have an edge from +this vertex to that vertex in blue there + + align:start position:0% +this vertex to that vertex in blue there + + + align:start position:0% +this vertex to that vertex in blue there +is no edge because it goes back in the + + align:start position:0% +is no edge because it goes back in the + + + align:start position:0% +is no edge because it goes back in the +other direction nor is there ever a + + align:start position:0% +other direction nor is there ever a + + + align:start position:0% +other direction nor is there ever a +self-loop in an asymmetric graph and + + align:start position:0% +self-loop in an asymmetric graph and + + + align:start position:0% +self-loop in an asymmetric graph and +finally in a symmetric graph wherever + + align:start position:0% +finally in a symmetric graph wherever + + + align:start position:0% +finally in a symmetric graph wherever +there's an edge there's an edge that + + align:start position:0% +there's an edge there's an edge that + + + align:start position:0% +there's an edge there's an edge that +goes back the other way so that can help + + align:start position:0% +goes back the other way so that can help + + + align:start position:0% +goes back the other way so that can help +you maybe remember what these properties + + align:start position:0% +you maybe remember what these properties + + + align:start position:0% +you maybe remember what these properties +mean now + + align:start position:0% +mean now + + + align:start position:0% +mean now +again equivalence relations besides + + align:start position:0% +again equivalence relations besides + + + align:start position:0% +again equivalence relations besides +being represented in terms of the + + align:start position:0% +being represented in terms of the + + + align:start position:0% +being represented in terms of the +strongly connected relation of a digraph + + align:start position:0% +strongly connected relation of a digraph + + + align:start position:0% +strongly connected relation of a digraph +can be represented in two other very + + align:start position:0% +can be represented in two other very + + + align:start position:0% +can be represented in two other very +natural ways that really explains where + + align:start position:0% +natural ways that really explains where + + + align:start position:0% +natural ways that really explains where +they come + + align:start position:0% +they come + + + align:start position:0% +they come +from what their properties are so + + align:start position:0% +from what their properties are so + + + align:start position:0% +from what their properties are so +whenever you have a total function f on + + align:start position:0% +whenever you have a total function f on + + + align:start position:0% +whenever you have a total function f on +a set a it defines an equivalence + + align:start position:0% +a set a it defines an equivalence + + + align:start position:0% +a set a it defines an equivalence +relation on the set a namely if f is a + + align:start position:0% +relation on the set a namely if f is a + + + align:start position:0% +relation on the set a namely if f is a +total function from domain a to co + + align:start position:0% +total function from domain a to co + + + align:start position:0% +total function from domain a to co +domain B then we can define an a + + align:start position:0% +domain B then we can define an a + + + align:start position:0% +domain B then we can define an a +relation we can call equivalence sub F + + align:start position:0% +relation we can call equivalence sub F + + + align:start position:0% +relation we can call equivalence sub F +on the set a by the rule that two + + align:start position:0% +on the set a by the rule that two + + + align:start position:0% +on the set a by the rule that two +elements are equivalence of F if and + + align:start position:0% +elements are equivalence of F if and + + + align:start position:0% +elements are equivalence of F if and +only if they have the same image under F + + align:start position:0% +only if they have the same image under F + + + align:start position:0% +only if they have the same image under F +they have the same thing that is a is + + align:start position:0% +they have the same thing that is a is + + + align:start position:0% +they have the same thing that is a is +equivalence of F to a prime if and only + + align:start position:0% +equivalence of F to a prime if and only + + + align:start position:0% +equivalence of F to a prime if and only +if F of a is equal to F of a prime and + + align:start position:0% +if F of a is equal to F of a prime and + + + align:start position:0% +if F of a is equal to F of a prime and +again equivalence of F immediately + + align:start position:0% +again equivalence of F immediately + + + align:start position:0% +again equivalence of F immediately +inherits the properties of equality + + align:start position:0% +inherits the properties of equality + + + align:start position:0% +inherits the properties of equality +which makes it an equivalence relation + + align:start position:0% +which makes it an equivalence relation + + + align:start position:0% +which makes it an equivalence relation +and the theorem that we have is that + + align:start position:0% +and the theorem that we have is that + + + align:start position:0% +and the theorem that we have is that +every relation are on a set a is an + + align:start position:0% +every relation are on a set a is an + + + align:start position:0% +every relation are on a set a is an +equivalence relation if and only if it + + align:start position:0% +equivalence relation if and only if it + + + align:start position:0% +equivalence relation if and only if it +in fact is equal to equivalence of F for + + align:start position:0% +in fact is equal to equivalence of F for + + + align:start position:0% +in fact is equal to equivalence of F for +some function f let's illustrate that we + + align:start position:0% +some function f let's illustrate that we + + + align:start position:0% +some function f let's illustrate that we +already remembered that congruence mod n + + align:start position:0% +already remembered that congruence mod n + + + align:start position:0% +already remembered that congruence mod n +can be understood as equivalent sub F + + align:start position:0% +can be understood as equivalent sub F + + + align:start position:0% +can be understood as equivalent sub F +where the mapping is just map things to + + align:start position:0% +where the mapping is just map things to + + + align:start position:0% +where the mapping is just map things to +remainders two numbers are congruent mod + + align:start position:0% +remainders two numbers are congruent mod + + + align:start position:0% +remainders two numbers are congruent mod +and if and only if they have the same + + align:start position:0% +and if and only if they have the same + + + align:start position:0% +and if and only if they have the same +remainder on division by M by n so map a + + align:start position:0% +remainder on division by M by n so map a + + + align:start position:0% +remainder on division by M by n so map a +number a to f of K equal its remainder + + align:start position:0% +number a to f of K equal its remainder + + + align:start position:0% +number a to f of K equal its remainder +and we have found the equivalence of F + + align:start position:0% +and we have found the equivalence of F + + + align:start position:0% +and we have found the equivalence of F +representation of congruence which is + + align:start position:0% +representation of congruence which is + + + align:start position:0% +representation of congruence which is +another way to verify that congruence is + + align:start position:0% +another way to verify that congruence is + + + align:start position:0% +another way to verify that congruence is +an equivalence relation finally whenever + + align:start position:0% +an equivalence relation finally whenever + + + align:start position:0% +an equivalence relation finally whenever +you have a partition of a set you can + + align:start position:0% +you have a partition of a set you can + + + align:start position:0% +you have a partition of a set you can +define an equivalence relation so a + + align:start position:0% +define an equivalence relation so a + + + align:start position:0% +define an equivalence relation so a +partition of a set it cuts up the set a + + align:start position:0% +partition of a set it cuts up the set a + + + align:start position:0% +partition of a set it cuts up the set a +into a bunch of blocks which are + + align:start position:0% +into a bunch of blocks which are + + + align:start position:0% +into a bunch of blocks which are +non-empty and every element is is a + + align:start position:0% +non-empty and every element is is a + + + align:start position:0% +non-empty and every element is is a +member of some block and the blocks + + align:start position:0% +member of some block and the blocks + + + align:start position:0% +member of some block and the blocks +don't overlap so in fact every element + + align:start position:0% +don't overlap so in fact every element + + + align:start position:0% +don't overlap so in fact every element +is a member of a unique block and that + + align:start position:0% +is a member of a unique block and that + + + align:start position:0% +is a member of a unique block and that +enables me to define an equivalence + + align:start position:0% +enables me to define an equivalence + + + align:start position:0% +enables me to define an equivalence +relation on a by the property that two + + align:start position:0% +relation on a by the property that two + + + align:start position:0% +relation on a by the property that two +elements are in the same block in fact + + align:start position:0% +elements are in the same block in fact + + + align:start position:0% +elements are in the same block in fact +that's the proof of the previous + + align:start position:0% +that's the proof of the previous + + + align:start position:0% +that's the proof of the previous +representation theorem in terms of of a + + align:start position:0% +representation theorem in terms of of a + + + align:start position:0% +representation theorem in terms of of a +function that you can map an element to + + align:start position:0% +function that you can map an element to + + + align:start position:0% +function that you can map an element to +the block that it's in in order to see + + align:start position:0% +the block that it's in in order to see + + + align:start position:0% +the block that it's in in order to see +that the block representation and the + + align:start position:0% +that the block representation and the + + + align:start position:0% +that the block representation and the +equivalence of F representation are the + + align:start position:0% +equivalence of F representation are the + + + align:start position:0% +equivalence of F representation are the +same the proof in the other direction + + align:start position:0% +same the proof in the other direction + + + align:start position:0% +same the proof in the other direction +that every equivalence relation + + align:start position:0% +that every equivalence relation + + + align:start position:0% +that every equivalence relation +can be represented in this way is an + + align:start position:0% +can be represented in this way is an + + + align:start position:0% +can be represented in this way is an +exercise in in axiomatic reasoning an + + align:start position:0% +exercise in in axiomatic reasoning an + + + align:start position:0% +exercise in in axiomatic reasoning an +elementary one that we're going to leave + + align:start position:0% +elementary one that we're going to leave + + + align:start position:0% +elementary one that we're going to leave +to a problem and not do in this + + align:start position:0% +to a problem and not do in this + + + align:start position:0% +to a problem and not do in this +presentation so the theorem finally is + + align:start position:0% +presentation so the theorem finally is + + + align:start position:0% +presentation so the theorem finally is +that again that a relation R in a set is + + align:start position:0% +that again that a relation R in a set is + + + align:start position:0% +that again that a relation R in a set is +an equivalence relation if and only if + + align:start position:0% +an equivalence relation if and only if + + + align:start position:0% +an equivalence relation if and only if +it is in fact the being in the same + + align:start position:0% +it is in fact the being in the same + + + align:start position:0% +it is in fact the being in the same +block relation for some partition and + + align:start position:0% +block relation for some partition and + + + align:start position:0% +block relation for some partition and +that is the story and multiple ways of + + align:start position:0% +that is the story and multiple ways of + + + align:start position:0% +that is the story and multiple ways of +understanding what equivalence relations + + align:start position:0% +understanding what equivalence relations + + + align:start position:0% +understanding what equivalence relations +are \ No newline at end of file diff --git a/s0gfi3OrtQk.txt b/s0gfi3OrtQk.txt new file mode 100644 index 0000000000000000000000000000000000000000..0e0246469999e902905d1ab1f19680f741fa64fb --- /dev/null +++ b/s0gfi3OrtQk.txt @@ -0,0 +1,12192 @@ +align:start position:0% + +well greetings everyone + + align:start position:0% +well greetings everyone + + + align:start position:0% +well greetings everyone +first of all in terms of the reading + + align:start position:0% +first of all in terms of the reading + + + align:start position:0% +first of all in terms of the reading +list + + align:start position:0% +list + + + align:start position:0% +list +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +today we're gonna finish + + align:start position:0% +today we're gonna finish + + + align:start position:0% +today we're gonna finish +which the two three things i + + align:start position:0% +which the two three things i + + + align:start position:0% +which the two three things i +deliberately didn't do + + align:start position:0% +deliberately didn't do + + + align:start position:0% +deliberately didn't do +at the end of the lecture on firms and + + align:start position:0% +at the end of the lecture on firms and + + + align:start position:0% +at the end of the lecture on firms and +production sets + + align:start position:0% +production sets + + + align:start position:0% +production sets +which was largely crept but with plenty + + align:start position:0% +which was largely crept but with plenty + + + align:start position:0% +which was largely crept but with plenty +of stuff added i should say the the + + align:start position:0% +of stuff added i should say the the + + + align:start position:0% +of stuff added i should say the the +stuff that's added is largely + + align:start position:0% +stuff that's added is largely + + + align:start position:0% +stuff that's added is largely +anticipating an application we got to at + + align:start position:0% +anticipating an application we got to at + + + align:start position:0% +anticipating an application we got to at +the end which is the impact of + + align:start position:0% +the end which is the impact of + + + align:start position:0% +the end which is the impact of +tariffs and so on on economic welfare + + align:start position:0% +tariffs and so on on economic welfare + + + align:start position:0% +tariffs and so on on economic welfare +so you'll have the tools + + align:start position:0% +so you'll have the tools + + + align:start position:0% +so you'll have the tools +at the time we get there although we + + align:start position:0% +at the time we get there although we + + + align:start position:0% +at the time we get there although we +will also provide some reminders the + + align:start position:0% +will also provide some reminders the + + + align:start position:0% +will also provide some reminders the +second thing is although it's not + + align:start position:0% +second thing is although it's not + + + align:start position:0% +second thing is although it's not +starred + + align:start position:0% +starred + + + align:start position:0% +starred +there are these things about uh other + + align:start position:0% +there are these things about uh other + + + align:start position:0% +there are these things about uh other +things on the reading list which are not + + align:start position:0% +things on the reading list which are not + + + align:start position:0% +things on the reading list which are not +starred in this case about the great + + align:start position:0% +starred in this case about the great + + + align:start position:0% +starred in this case about the great +japanese earthquake and that's i'm going + + align:start position:0% +japanese earthquake and that's i'm going + + + align:start position:0% +japanese earthquake and that's i'm going +to talk about that momentarily but you + + align:start position:0% +to talk about that momentarily but you + + + align:start position:0% +to talk about that momentarily but you +know i know everyone's quite busy + + align:start position:0% +know i know everyone's quite busy + + + align:start position:0% +know i know everyone's quite busy +and there's plenty of required things to + + align:start position:0% +and there's plenty of required things to + + + align:start position:0% +and there's plenty of required things to +do but if you get a chance i'm sure you + + align:start position:0% +do but if you get a chance i'm sure you + + + align:start position:0% +do but if you get a chance i'm sure you +actually would enjoy + + align:start position:0% +actually would enjoy + + + align:start position:0% +actually would enjoy +taking a look at that + + align:start position:0% +taking a look at that + + + align:start position:0% +taking a look at that +that article + + align:start position:0% +that article + + + align:start position:0% +that article +uh today + + align:start position:0% +uh today + + + align:start position:0% +uh today +the main thing i want to draw your + + align:start position:0% +the main thing i want to draw your + + + align:start position:0% +the main thing i want to draw your +attention to is + + align:start position:0% +attention to is + + + align:start position:0% +attention to is +decision making under uncertainty and + + align:start position:0% +decision making under uncertainty and + + + align:start position:0% +decision making under uncertainty and +also linear programs + + align:start position:0% +also linear programs + + + align:start position:0% +also linear programs +and that material is largely coming from + + align:start position:0% +and that material is largely coming from + + + align:start position:0% +and that material is largely coming from +nicholson and schneider although it does + + align:start position:0% +nicholson and schneider although it does + + + align:start position:0% +nicholson and schneider although it does +have some material that was moved + + align:start position:0% +have some material that was moved + + + align:start position:0% +have some material that was moved +relative to earlier years as you will + + align:start position:0% +relative to earlier years as you will + + + align:start position:0% +relative to earlier years as you will +see + + align:start position:0% +see + + + align:start position:0% +see +this medville which is short for the + + align:start position:0% +this medville which is short for the + + + align:start position:0% +this medville which is short for the +medieval village economy several of the + + align:start position:0% +medieval village economy several of the + + + align:start position:0% +medieval village economy several of the +slides today have material on that + + align:start position:0% +slides today have material on that + + + align:start position:0% +slides today have material on that +from that book which you therefore might + + align:start position:0% +from that book which you therefore might + + + align:start position:0% +from that book which you therefore might +find helpful in terms of the study guide + + align:start position:0% +find helpful in terms of the study guide + + + align:start position:0% +find helpful in terms of the study guide +we have some questions here + + align:start position:0% +we have some questions here + + + align:start position:0% +we have some questions here +and let me try + + align:start position:0% +and let me try + + + align:start position:0% +and let me try +something a bit new + + align:start position:0% +something a bit new + + + align:start position:0% +something a bit new +but nevertheless let me try armando + + align:start position:0% +but nevertheless let me try armando + + + align:start position:0% +but nevertheless let me try armando +could you take a crack at this one + + align:start position:0% +could you take a crack at this one + + + align:start position:0% +could you take a crack at this one +define increasing decreasing and + + align:start position:0% +define increasing decreasing and + + + align:start position:0% +define increasing decreasing and +constant returns to scale and production + + align:start position:0% +constant returns to scale and production + + + align:start position:0% +constant returns to scale and production +oh yeah so uh first constant returns to + + align:start position:0% +oh yeah so uh first constant returns to + + + align:start position:0% +oh yeah so uh first constant returns to +scale input means that if you double the + + align:start position:0% +scale input means that if you double the + + + align:start position:0% +scale input means that if you double the +inputs + + align:start position:0% +inputs + + + align:start position:0% +inputs +you get w outputs uh increasing means + + align:start position:0% +you get w outputs uh increasing means + + + align:start position:0% +you get w outputs uh increasing means +that + + align:start position:0% +that + + + align:start position:0% +that +efficiency increases as you scale it up + + align:start position:0% +efficiency increases as you scale it up + + + align:start position:0% +efficiency increases as you scale it up +so if you double the inputs you get more + + align:start position:0% +so if you double the inputs you get more + + + align:start position:0% +so if you double the inputs you get more +than double the outputs + + align:start position:0% +than double the outputs + + + align:start position:0% +than double the outputs +and decreasing is uh that if you double + + align:start position:0% +and decreasing is uh that if you double + + + align:start position:0% +and decreasing is uh that if you double +the inputs you would get less than + + align:start position:0% +the inputs you would get less than + + + align:start position:0% +the inputs you would get less than +double + + align:start position:0% +double + + + align:start position:0% +double +yeah that's fair + + align:start position:0% +yeah that's fair + + + align:start position:0% +yeah that's fair +that's a pretty good answer + + align:start position:0% +that's a pretty good answer + + + align:start position:0% +that's a pretty good answer +um + + align:start position:0% +um + + + align:start position:0% +um +yeah we can define these things in + + align:start position:0% +yeah we can define these things in + + + align:start position:0% +yeah we can define these things in +various ways they're all equivalent with + + align:start position:0% +various ways they're all equivalent with + + + align:start position:0% +various ways they're all equivalent with +one another the way you did it is fine + + align:start position:0% +one another the way you did it is fine + + + align:start position:0% +one another the way you did it is fine +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in + + align:start position:0% +in + + + align:start position:0% +in +in some respects the definitions are the + + align:start position:0% +in some respects the definitions are the + + + align:start position:0% +in some respects the definitions are the +reverse of what you would expect uh + + align:start position:0% +reverse of what you would expect uh + + + align:start position:0% +reverse of what you would expect uh +decreasing returns to scales means that + + align:start position:0% +decreasing returns to scales means that + + + align:start position:0% +decreasing returns to scales means that +if you pick + + align:start position:0% +if you pick + + + align:start position:0% +if you pick +any uh + + align:start position:0% +any uh + + + align:start position:0% +any uh +if you pick 0 and then the other point + + align:start position:0% +if you pick 0 and then the other point + + + align:start position:0% +if you pick 0 and then the other point +in the production possibility set + + align:start position:0% +in the production possibility set + + + align:start position:0% +in the production possibility set +and then pick alpha between 0 and 1 + + align:start position:0% +and then pick alpha between 0 and 1 + + + align:start position:0% +and then pick alpha between 0 and 1 +that that point is uh is also in the + + align:start position:0% +that that point is uh is also in the + + + align:start position:0% +that that point is uh is also in the +production set + + align:start position:0% +production set + + + align:start position:0% +production set +i say it's weird because decreasing + + align:start position:0% +i say it's weird because decreasing + + + align:start position:0% +i say it's weird because decreasing +imply you know you're actually scaling + + align:start position:0% +imply you know you're actually scaling + + + align:start position:0% +imply you know you're actually scaling +back + + align:start position:0% +back + + + align:start position:0% +back +as opposed to doubling and moving + + align:start position:0% +as opposed to doubling and moving + + + align:start position:0% +as opposed to doubling and moving +forward but it's the same definition + + align:start position:0% +forward but it's the same definition + + + align:start position:0% +forward but it's the same definition +because + + align:start position:0% +because + + + align:start position:0% +because +you do get that curvature in the uh + + align:start position:0% +you do get that curvature in the uh + + + align:start position:0% +you do get that curvature in the uh +in the production set + + align:start position:0% +in the production set + + + align:start position:0% +in the production set +um and likewise for increasing returns + + align:start position:0% +um and likewise for increasing returns + + + align:start position:0% +um and likewise for increasing returns +so thank you that's good + + align:start position:0% +so thank you that's good + + + align:start position:0% +so thank you that's good +all right uh + + align:start position:0% +all right uh + + + align:start position:0% +all right uh +i marked a few of these + + align:start position:0% +i marked a few of these + + + align:start position:0% +i marked a few of these +we don't have to do all of them + + align:start position:0% +we don't have to do all of them + + + align:start position:0% +we don't have to do all of them +how would you prove that maximized + + align:start position:0% +how would you prove that maximized + + + align:start position:0% +how would you prove that maximized +profits are homogeneous of degree one in + + align:start position:0% +profits are homogeneous of degree one in + + + align:start position:0% +profits are homogeneous of degree one in +prices p + + align:start position:0% +prices p + + + align:start position:0% +prices p +uh caleb + + align:start position:0% +uh caleb + + + align:start position:0% +uh caleb +if i'm saying your name correctly + + align:start position:0% +if i'm saying your name correctly + + + align:start position:0% +if i'm saying your name correctly +rollins + + align:start position:0% + + + + align:start position:0% + +uh yeah sorry what was the question + + align:start position:0% +uh yeah sorry what was the question + + + align:start position:0% +uh yeah sorry what was the question +prove that maximized profits are + + align:start position:0% +prove that maximized profits are + + + align:start position:0% +prove that maximized profits are +homogeneous of degree one and prices p + + align:start position:0% +homogeneous of degree one and prices p + + + align:start position:0% +homogeneous of degree one and prices p +how would you go about proving that + + align:start position:0% +how would you go about proving that + + + align:start position:0% +how would you go about proving that +um + + align:start position:0% +um + + + align:start position:0% +um +i'm not sure + + align:start position:0% +i'm not sure + + + align:start position:0% +i'm not sure +do you recall what homogeneous of degree + + align:start position:0% +do you recall what homogeneous of degree + + + align:start position:0% +do you recall what homogeneous of degree +one means + + align:start position:0% +one means + + + align:start position:0% +one means +uh no okay + + align:start position:0% +uh no okay + + + align:start position:0% +uh no okay +so homogeneous of degree one means that + + align:start position:0% +so homogeneous of degree one means that + + + align:start position:0% +so homogeneous of degree one means that +if you increase uh + + align:start position:0% +if you increase uh + + + align:start position:0% +if you increase uh +every element of the price vector + + align:start position:0% +every element of the price vector + + + align:start position:0% +every element of the price vector +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +by a constant + + align:start position:0% +by a constant + + + align:start position:0% +by a constant +that maximized profits increased by that + + align:start position:0% +that maximized profits increased by that + + + align:start position:0% +that maximized profits increased by that +same constant + + align:start position:0% +same constant + + + align:start position:0% +same constant +okay + + align:start position:0% + + + + align:start position:0% + +do you feel comfortable taking a crack + + align:start position:0% +do you feel comfortable taking a crack + + + align:start position:0% +do you feel comfortable taking a crack +at the rest of this + + align:start position:0% +at the rest of this + + + align:start position:0% +at the rest of this +oh i'm not sure + + align:start position:0% +oh i'm not sure + + + align:start position:0% +oh i'm not sure +what the answer is okay + + align:start position:0% +what the answer is okay + + + align:start position:0% +what the answer is okay +all right that's fine + + align:start position:0% +all right that's fine + + + align:start position:0% +all right that's fine +um + + align:start position:0% + + + + align:start position:0% + +and correct me if i'm saying your name's + + align:start position:0% +and correct me if i'm saying your name's + + + align:start position:0% +and correct me if i'm saying your name's +wrong i'm sure i am uh you can uh in the + + align:start position:0% +wrong i'm sure i am uh you can uh in the + + + align:start position:0% +wrong i'm sure i am uh you can uh in the +future you can just call me andy yeah + + align:start position:0% +future you can just call me andy yeah + + + align:start position:0% +future you can just call me andy yeah +andy okay + + align:start position:0% +andy okay + + + align:start position:0% +andy okay +that's the a in your middle initial fun + + align:start position:0% +that's the a in your middle initial fun + + + align:start position:0% +that's the a in your middle initial fun +okay + + align:start position:0% + + + + align:start position:0% + +so let's see do you want to try the same + + align:start position:0% +so let's see do you want to try the same + + + align:start position:0% +so let's see do you want to try the same +question + + align:start position:0% +question + + + align:start position:0% +question +uh sure yeah so um + + align:start position:0% +uh sure yeah so um + + + align:start position:0% +uh sure yeah so um +so i believe so homogeneity i believe + + align:start position:0% +so i believe so homogeneity i believe + + + align:start position:0% +so i believe so homogeneity i believe +means like um basically if we double the + + align:start position:0% +means like um basically if we double the + + + align:start position:0% +means like um basically if we double the +price if we double the prices um then we + + align:start position:0% +price if we double the prices um then we + + + align:start position:0% +price if we double the prices um then we +also double the profit right + + align:start position:0% +also double the profit right + + + align:start position:0% +also double the profit right +right so um um + + align:start position:0% +right so um um + + + align:start position:0% +right so um um +so i believe i believe the the product + + align:start position:0% +so i believe i believe the the product + + + align:start position:0% +so i believe i believe the the product +function is equal to the is equal to the + + align:start position:0% +function is equal to the is equal to the + + + align:start position:0% +function is equal to the is equal to the +price is p dot z where z is the + + align:start position:0% +price is p dot z where z is the + + + align:start position:0% +price is p dot z where z is the +production vector + + align:start position:0% +production vector + + + align:start position:0% +production vector +yes + + align:start position:0% +yes + + + align:start position:0% +yes +um and so if we so if we double the if + + align:start position:0% +um and so if we so if we double the if + + + align:start position:0% +um and so if we so if we double the if +we double the price uh p + + align:start position:0% +we double the price uh p + + + align:start position:0% +we double the price uh p +if we double the pr if we double the uh + + align:start position:0% +if we double the pr if we double the uh + + + align:start position:0% +if we double the pr if we double the uh +the production + + align:start position:0% +the production + + + align:start position:0% +the production +so if we maintain the same production + + align:start position:0% +so if we maintain the same production + + + align:start position:0% +so if we maintain the same production +vector z then we can we can guarantee + + align:start position:0% +vector z then we can we can guarantee + + + align:start position:0% +vector z then we can we can guarantee +that we at least double the profits + + align:start position:0% +that we at least double the profits + + + align:start position:0% +that we at least double the profits +um but if we were if we were able to do + + align:start position:0% +um but if we were if we were able to do + + + align:start position:0% +um but if we were if we were able to do +better then we could have the we could + + align:start position:0% +better then we could have the we could + + + align:start position:0% +better then we could have the we could +then have we could then have the prices + + align:start position:0% +then have we could then have the prices + + + align:start position:0% +then have we could then have the prices +again and obtain a better um + + align:start position:0% +again and obtain a better um + + + align:start position:0% +again and obtain a better um +basically a better production for the + + align:start position:0% +basically a better production for the + + + align:start position:0% +basically a better production for the +original on price level + + align:start position:0% +original on price level + + + align:start position:0% +original on price level +and so and so the so so basically the + + align:start position:0% +and so and so the so so basically the + + + align:start position:0% +and so and so the so so basically the +optimal um the optimal profits at the + + align:start position:0% +optimal um the optimal profits at the + + + align:start position:0% +optimal um the optimal profits at the +at the double prices must exactly equal + + align:start position:0% +at the double prices must exactly equal + + + align:start position:0% +at the double prices must exactly equal +twice the value at the regular prices + + align:start position:0% + + + + align:start position:0% + +right i + + align:start position:0% +right i + + + align:start position:0% +right i +i that's the correct answer + + align:start position:0% +i that's the correct answer + + + align:start position:0% +i that's the correct answer +um the way i like to think about it is + + align:start position:0% +um the way i like to think about it is + + + align:start position:0% +um the way i like to think about it is +if we + + align:start position:0% +if we + + + align:start position:0% +if we +graphically if we were + + align:start position:0% +graphically if we were + + + align:start position:0% +graphically if we were +doubling the price + + align:start position:0% +doubling the price + + + align:start position:0% +doubling the price +of every component of the price vector p + + align:start position:0% +of every component of the price vector p + + + align:start position:0% +of every component of the price vector p +then we're not changing the slope of + + align:start position:0% +then we're not changing the slope of + + + align:start position:0% +then we're not changing the slope of +that + + align:start position:0% +that + + + align:start position:0% +that +those um + + align:start position:0% +those um + + + align:start position:0% +those um +iso profit lines + + align:start position:0% +iso profit lines + + + align:start position:0% +iso profit lines +and so + + align:start position:0% +and so + + + align:start position:0% +and so +the tangency + + align:start position:0% +the tangency + + + align:start position:0% +the tangency +with the production possibilities + + align:start position:0% +with the production possibilities + + + align:start position:0% +with the production possibilities +frontier would be the same point + + align:start position:0% +frontier would be the same point + + + align:start position:0% +frontier would be the same point +and that's why + + align:start position:0% +and that's why + + + align:start position:0% +and that's why +the z says in p dot z is not moving + + align:start position:0% + + + + align:start position:0% + +great thank you + + align:start position:0% +great thank you + + + align:start position:0% +great thank you +and let's try just one more + + align:start position:0% +and let's try just one more + + + align:start position:0% +and let's try just one more +what is the definition of an isoquant + + align:start position:0% +what is the definition of an isoquant + + + align:start position:0% +what is the definition of an isoquant +so key + + align:start position:0% +so key + + + align:start position:0% +so key +q + + align:start position:0% + + + + align:start position:0% + +i think the definition of isoquant is + + align:start position:0% +i think the definition of isoquant is + + + align:start position:0% +i think the definition of isoquant is +like + + align:start position:0% +like + + + align:start position:0% +like +there was there was a set of input + + align:start position:0% +there was there was a set of input + + + align:start position:0% +there was there was a set of input +boundaries which + + align:start position:0% +boundaries which + + + align:start position:0% +boundaries which +given the + + align:start position:0% +given the + + + align:start position:0% +given the +um + + align:start position:0% +um + + + align:start position:0% +um +given the productivity + + align:start position:0% +given the productivity + + + align:start position:0% +given the productivity +uh they will output the same level of + + align:start position:0% +uh they will output the same level of + + + align:start position:0% +uh they will output the same level of +output + + align:start position:0% +output + + + align:start position:0% +output +and why + + align:start position:0% + + + + align:start position:0% + +all input bundles which + + align:start position:0% +all input bundles which + + + align:start position:0% +all input bundles which +produce the same level of output + + align:start position:0% +produce the same level of output + + + align:start position:0% +produce the same level of output +yes that's correct great thank you + + align:start position:0% +yes that's correct great thank you + + + align:start position:0% +yes that's correct great thank you +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um i was too ambitious and i marked off + + align:start position:0% +um i was too ambitious and i marked off + + + align:start position:0% +um i was too ambitious and i marked off +too many of these as i said i + + align:start position:0% +too many of these as i said i + + + align:start position:0% +too many of these as i said i +sort of choose at random in this case + + align:start position:0% +sort of choose at random in this case + + + align:start position:0% +sort of choose at random in this case +this morning i just marked + + align:start position:0% +this morning i just marked + + + align:start position:0% +this morning i just marked +a few of them take a look at the other + + align:start position:0% +a few of them take a look at the other + + + align:start position:0% +a few of them take a look at the other +ones + + align:start position:0% +ones + + + align:start position:0% +ones +as always these review questions are for + + align:start position:0% +as always these review questions are for + + + align:start position:0% +as always these review questions are for +your benefit for the class + + align:start position:0% +your benefit for the class + + + align:start position:0% +your benefit for the class +i'm only calling you be on + + align:start position:0% +i'm only calling you be on + + + align:start position:0% +i'm only calling you be on +on younow instead of just taking + + align:start position:0% +on younow instead of just taking + + + align:start position:0% +on younow instead of just taking +volunteers + + align:start position:0% +volunteers + + + align:start position:0% +volunteers +because i like class participation and + + align:start position:0% +because i like class participation and + + + align:start position:0% +because i like class participation and +it's just a reminder to try to + + align:start position:0% +it's just a reminder to try to + + + align:start position:0% +it's just a reminder to try to +try to keep up + + align:start position:0% +try to keep up + + + align:start position:0% +try to keep up +rather than having make up lost ground + + align:start position:0% +rather than having make up lost ground + + + align:start position:0% +rather than having make up lost ground +later when you're studying for the + + align:start position:0% +later when you're studying for the + + + align:start position:0% +later when you're studying for the +midterm or something if you keep up + + align:start position:0% +midterm or something if you keep up + + + align:start position:0% +midterm or something if you keep up +um with the class + + align:start position:0% +um with the class + + + align:start position:0% +um with the class +you'll be fine um okay so + + align:start position:0% +you'll be fine um okay so + + + align:start position:0% +you'll be fine um okay so +let me + + align:start position:0% +let me + + + align:start position:0% +let me +go + + align:start position:0% +go + + + align:start position:0% +go +to + + align:start position:0% +to + + + align:start position:0% +to +lecture four + + align:start position:0% +lecture four + + + align:start position:0% +lecture four +and + + align:start position:0% +and + + + align:start position:0% +and +and talk a little bit about uh three + + align:start position:0% +and talk a little bit about uh three + + + align:start position:0% +and talk a little bit about uh three +related examples of production i + + align:start position:0% +related examples of production i + + + align:start position:0% +related examples of production i +featured in the lecture + + align:start position:0% +featured in the lecture + + + align:start position:0% +featured in the lecture +the example of trade + + align:start position:0% +the example of trade + + + align:start position:0% +the example of trade +but here are some others that actually + + align:start position:0% +but here are some others that actually + + + align:start position:0% +but here are some others that actually +do relate to + + align:start position:0% +do relate to + + + align:start position:0% +do relate to +what we will get to at the end of + + align:start position:0% +what we will get to at the end of + + + align:start position:0% +what we will get to at the end of +lecture five as well + + align:start position:0% +lecture five as well + + + align:start position:0% +lecture five as well +first up i want to talk about leonty of + + align:start position:0% +first up i want to talk about leonty of + + + align:start position:0% +first up i want to talk about leonty of +input output matrices + + align:start position:0% +input output matrices + + + align:start position:0% +input output matrices +so + + align:start position:0% +so + + + align:start position:0% +so +leontes view + + align:start position:0% +leontes view + + + align:start position:0% +leontes view +of the economy + + align:start position:0% +of the economy + + + align:start position:0% +of the economy +production + + align:start position:0% +production + + + align:start position:0% +production +possibilities was interesting albeit a + + align:start position:0% +possibilities was interesting albeit a + + + align:start position:0% +possibilities was interesting albeit a +bit simple + + align:start position:0% +bit simple + + + align:start position:0% +bit simple +suppose there are three sectors for + + align:start position:0% +suppose there are three sectors for + + + align:start position:0% +suppose there are three sectors for +example as in this matrix + + align:start position:0% +example as in this matrix + + + align:start position:0% +example as in this matrix +you have a sector representing raw + + align:start position:0% +you have a sector representing raw + + + align:start position:0% +you have a sector representing raw +materials + + align:start position:0% +materials + + + align:start position:0% +materials +which could be agriculture mining and so + + align:start position:0% +which could be agriculture mining and so + + + align:start position:0% +which could be agriculture mining and so +on a sector representing services + + align:start position:0% +on a sector representing services + + + align:start position:0% +on a sector representing services +which would be retailing advertising + + align:start position:0% +which would be retailing advertising + + + align:start position:0% +which would be retailing advertising +transportation lawyers + + align:start position:0% +transportation lawyers + + + align:start position:0% +transportation lawyers +real estate agents and financial + + align:start position:0% +real estate agents and financial + + + align:start position:0% +real estate agents and financial +services + + align:start position:0% +services + + + align:start position:0% +services +to go on and on + + align:start position:0% +to go on and on + + + align:start position:0% +to go on and on +and manufacturing which i guess is + + align:start position:0% +and manufacturing which i guess is + + + align:start position:0% +and manufacturing which i guess is +pretty self-explanatory + + align:start position:0% +pretty self-explanatory + + + align:start position:0% +pretty self-explanatory +this entire page of the lecture + + align:start position:0% +this entire page of the lecture + + + align:start position:0% +this entire page of the lecture +is just meant to be representative + + align:start position:0% +is just meant to be representative + + + align:start position:0% +is just meant to be representative +obviously you can have + + align:start position:0% +obviously you can have + + + align:start position:0% +obviously you can have +many + + align:start position:0% +many + + + align:start position:0% +many +particular + + align:start position:0% +particular + + + align:start position:0% +particular +rows + + align:start position:0% +rows + + + align:start position:0% +rows +depending on your willingness to + + align:start position:0% +depending on your willingness to + + + align:start position:0% +depending on your willingness to +disaggregate further and further into + + align:start position:0% +disaggregate further and further into + + + align:start position:0% +disaggregate further and further into +more and more detail so this matrix + + align:start position:0% +more and more detail so this matrix + + + align:start position:0% +more and more detail so this matrix +what it's saying is + + align:start position:0% +what it's saying is + + + align:start position:0% +what it's saying is +the motivation for this is you have some + + align:start position:0% +the motivation for this is you have some + + + align:start position:0% +the motivation for this is you have some +final demand and how much would you need + + align:start position:0% +final demand and how much would you need + + + align:start position:0% +final demand and how much would you need +to produce + + align:start position:0% +to produce + + + align:start position:0% +to produce +to satisfy the final demand you could + + align:start position:0% +to satisfy the final demand you could + + + align:start position:0% +to satisfy the final demand you could +have final demand for services but the + + align:start position:0% +have final demand for services but the + + + align:start position:0% +have final demand for services but the +problem with that is that's the final + + align:start position:0% +problem with that is that's the final + + + align:start position:0% +problem with that is that's the final +demand not all the + + align:start position:0% +demand not all the + + + align:start position:0% +demand not all the +intermediaries services are in turn used + + align:start position:0% +intermediaries services are in turn used + + + align:start position:0% +intermediaries services are in turn used +in + + align:start position:0% +in + + + align:start position:0% +in +other sectors + + align:start position:0% +other sectors + + + align:start position:0% +other sectors +and in fact the column here represents + + align:start position:0% +and in fact the column here represents + + + align:start position:0% +and in fact the column here represents +that to produce one dollar worth of + + align:start position:0% +that to produce one dollar worth of + + + align:start position:0% +that to produce one dollar worth of +services + + align:start position:0% +services + + + align:start position:0% +services +services are used in other sectors as in + + align:start position:0% +services are used in other sectors as in + + + align:start position:0% +services are used in other sectors as in +this row + + align:start position:0% +this row + + + align:start position:0% +this row +services uh show up + + align:start position:0% +services uh show up + + + align:start position:0% +services uh show up +in producing raw materials services show + + align:start position:0% +in producing raw materials services show + + + align:start position:0% +in producing raw materials services show +up in producing services + + align:start position:0% +up in producing services + + + align:start position:0% +up in producing services +because of that aggregation problem and + + align:start position:0% +because of that aggregation problem and + + + align:start position:0% +because of that aggregation problem and +get used in manufacturing + + align:start position:0% +get used in manufacturing + + + align:start position:0% +get used in manufacturing +likewise if you go + + align:start position:0% +likewise if you go + + + align:start position:0% +likewise if you go +down the column + + align:start position:0% +down the column + + + align:start position:0% +down the column +to produce one dollar worth of services + + align:start position:0% +to produce one dollar worth of services + + + align:start position:0% +to produce one dollar worth of services +you need + + align:start position:0% +you need + + + align:start position:0% +you need +four cents worth of raw materials three + + align:start position:0% +four cents worth of raw materials three + + + align:start position:0% +four cents worth of raw materials three +cents worth of services + + align:start position:0% +cents worth of services + + + align:start position:0% +cents worth of services +and one cent worth of manufacturing + + align:start position:0% + + + + align:start position:0% + +so you can see its input output + + align:start position:0% +so you can see its input output + + + align:start position:0% +so you can see its input output +these are both in some sense direct + + align:start position:0% +these are both in some sense direct + + + align:start position:0% +these are both in some sense direct +outputs but also indirect inputs + + align:start position:0% +outputs but also indirect inputs + + + align:start position:0% +outputs but also indirect inputs +into + + align:start position:0% +into + + + align:start position:0% +into +other sectors this is a version by the + + align:start position:0% +other sectors this is a version by the + + + align:start position:0% +other sectors this is a version by the +way of the + + align:start position:0% +way of the + + + align:start position:0% +way of the +question having to do with aggregation + + align:start position:0% +question having to do with aggregation + + + align:start position:0% +question having to do with aggregation +last time we had a slide showing + + align:start position:0% +last time we had a slide showing + + + align:start position:0% +last time we had a slide showing +two goods x and y i think or was it y1 + + align:start position:0% +two goods x and y i think or was it y1 + + + align:start position:0% +two goods x and y i think or was it y1 +and y2 + + align:start position:0% +and y2 + + + align:start position:0% +and y2 +and + + align:start position:0% +and + + + align:start position:0% +and +one used y1 as an input and used y2 and + + align:start position:0% +one used y1 as an input and used y2 and + + + align:start position:0% +one used y1 as an input and used y2 and +the other industry used y2 as an input + + align:start position:0% +the other industry used y2 as an input + + + align:start position:0% +the other industry used y2 as an input +to produce y1 + + align:start position:0% +to produce y1 + + + align:start position:0% +to produce y1 +that was + + align:start position:0% +that was + + + align:start position:0% +that was +decreasing returns this is linear + + align:start position:0% +decreasing returns this is linear + + + align:start position:0% +decreasing returns this is linear +constant returns because everything here + + align:start position:0% +constant returns because everything here + + + align:start position:0% +constant returns because everything here +is linear but it is the same idea + + align:start position:0% +is linear but it is the same idea + + + align:start position:0% +is linear but it is the same idea +of inputs and outputs + + align:start position:0% +of inputs and outputs + + + align:start position:0% +of inputs and outputs +so we take this + + align:start position:0% +so we take this + + + align:start position:0% +so we take this +information in the input output matrix + + align:start position:0% +information in the input output matrix + + + align:start position:0% +information in the input output matrix +and summarize it in a matrix a and here + + align:start position:0% +and summarize it in a matrix a and here + + + align:start position:0% +and summarize it in a matrix a and here +we're just reproducing these row column + + align:start position:0% +we're just reproducing these row column + + + align:start position:0% +we're just reproducing these row column +elements + + align:start position:0% +elements + + + align:start position:0% +elements +exactly + + align:start position:0% + + + + align:start position:0% + +okay so the problem is we have final + + align:start position:0% +okay so the problem is we have final + + + align:start position:0% +okay so the problem is we have final +demands which are given + + align:start position:0% +demands which are given + + + align:start position:0% +demands which are given +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +three-dimensional column vector + + align:start position:0% + + + + align:start position:0% + +and it tells us + + align:start position:0% +and it tells us + + + align:start position:0% +and it tells us +uh how much we need we're going to need + + align:start position:0% +uh how much we need we're going to need + + + align:start position:0% +uh how much we need we're going to need +to end up delivering either to consumers + + align:start position:0% +to end up delivering either to consumers + + + align:start position:0% +to end up delivering either to consumers +or for exports + + align:start position:0% +or for exports + + + align:start position:0% +or for exports +of + + align:start position:0% +of + + + align:start position:0% +of +raw materials services and manufactured + + align:start position:0% +raw materials services and manufactured + + + align:start position:0% +raw materials services and manufactured +goods in that order + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +if we think about these equations here + + align:start position:0% +if we think about these equations here + + + align:start position:0% +if we think about these equations here +we want + + align:start position:0% +we want + + + align:start position:0% +we want +to produce x + + align:start position:0% +to produce x + + + align:start position:0% +to produce x +and then we + + align:start position:0% +and then we + + + align:start position:0% +and then we +want to figure out how much to produce + + align:start position:0% +want to figure out how much to produce + + + align:start position:0% +want to figure out how much to produce +if we want to meet meet the final + + align:start position:0% +if we want to meet meet the final + + + align:start position:0% +if we want to meet meet the final +demands of 400 200 600 but in addition + + align:start position:0% +demands of 400 200 600 but in addition + + + align:start position:0% +demands of 400 200 600 but in addition +to that + + align:start position:0% +to that + + + align:start position:0% +to that +some of that output + + align:start position:0% +some of that output + + + align:start position:0% +some of that output +gets used in turn as inputs and is not + + align:start position:0% +gets used in turn as inputs and is not + + + align:start position:0% +gets used in turn as inputs and is not +available + + align:start position:0% +available + + + align:start position:0% +available +for + + align:start position:0% +for + + + align:start position:0% +for +for uh consumer and export + + align:start position:0% +for uh consumer and export + + + align:start position:0% +for uh consumer and export +demands + + align:start position:0% +demands + + + align:start position:0% +demands +so + + align:start position:0% +so + + + align:start position:0% +so +the key equation here would be + + align:start position:0% +the key equation here would be + + + align:start position:0% +the key equation here would be +if we need to produce + + align:start position:0% +if we need to produce + + + align:start position:0% +if we need to produce +x + + align:start position:0% +x + + + align:start position:0% +x +but we lose a times x + + align:start position:0% +but we lose a times x + + + align:start position:0% +but we lose a times x +because some of that output gets used as + + align:start position:0% +because some of that output gets used as + + + align:start position:0% +because some of that output gets used as +inputs + + align:start position:0% +inputs + + + align:start position:0% +inputs +then + + align:start position:0% +then + + + align:start position:0% +then +we have to produce i minus a times x + + align:start position:0% +we have to produce i minus a times x + + + align:start position:0% +we have to produce i minus a times x +i is the identity matrix here + + align:start position:0% +i is the identity matrix here + + + align:start position:0% +i is the identity matrix here +so it just picks up the same + + align:start position:0% +so it just picks up the same + + + align:start position:0% +so it just picks up the same +it is + + align:start position:0% +it is + + + align:start position:0% +it is +one on the diagonal and zero on the off + + align:start position:0% +one on the diagonal and zero on the off + + + align:start position:0% +one on the diagonal and zero on the off +diagonal so + + align:start position:0% +diagonal so + + + align:start position:0% +diagonal so +for example + + align:start position:0% +for example + + + align:start position:0% +for example +i a would just give you + + align:start position:0% +i a would just give you + + + align:start position:0% +i a would just give you +x back + + align:start position:0% +x back + + + align:start position:0% +x back +as if you didn't have to use things as + + align:start position:0% +as if you didn't have to use things as + + + align:start position:0% +as if you didn't have to use things as +inputs + + align:start position:0% +inputs + + + align:start position:0% +inputs +ax that we've been going through here + + align:start position:0% +ax that we've been going through here + + + align:start position:0% +ax that we've been going through here +gives you if you're going to produce x + + align:start position:0% +gives you if you're going to produce x + + + align:start position:0% +gives you if you're going to produce x +how much of that x + + align:start position:0% +how much of that x + + + align:start position:0% +how much of that x +gets used up in + + align:start position:0% +gets used up in + + + align:start position:0% +gets used up in +producing services raw materials and + + align:start position:0% +producing services raw materials and + + + align:start position:0% +producing services raw materials and +manufacturing + + align:start position:0% +manufacturing + + + align:start position:0% +manufacturing +and what's left i minus a times x + + align:start position:0% +and what's left i minus a times x + + + align:start position:0% +and what's left i minus a times x +should just equal demand + + align:start position:0% +should just equal demand + + + align:start position:0% +should just equal demand +so this is a linear equation + + align:start position:0% +so this is a linear equation + + + align:start position:0% +so this is a linear equation +in the control variables namely x + + align:start position:0% +in the control variables namely x + + + align:start position:0% +in the control variables namely x +and also + + align:start position:0% +and also + + + align:start position:0% +and also +demands are given + + align:start position:0% +demands are given + + + align:start position:0% +demands are given +although to anticipate a bit + + align:start position:0% +although to anticipate a bit + + + align:start position:0% +although to anticipate a bit +you might think there's some trade-off + + align:start position:0% +you might think there's some trade-off + + + align:start position:0% +you might think there's some trade-off +in demands + + align:start position:0% +in demands + + + align:start position:0% +in demands +maybe some linear combination of demands + + align:start position:0% +maybe some linear combination of demands + + + align:start position:0% +maybe some linear combination of demands +is fine + + align:start position:0% +is fine + + + align:start position:0% +is fine +not just + + align:start position:0% +not just + + + align:start position:0% +not just +specific numbers + + align:start position:0% +specific numbers + + + align:start position:0% +specific numbers +and then you could imagine maximizing + + align:start position:0% +and then you could imagine maximizing + + + align:start position:0% +and then you could imagine maximizing +demand + + align:start position:0% +demand + + + align:start position:0% +demand +but in any event subject to this + + align:start position:0% +but in any event subject to this + + + align:start position:0% +but in any event subject to this +constraint + + align:start position:0% +constraint + + + align:start position:0% +constraint +here it's simpler we're just given the + + align:start position:0% +here it's simpler we're just given the + + + align:start position:0% +here it's simpler we're just given the +demands and we have to + + align:start position:0% +demands and we have to + + + align:start position:0% +demands and we have to +produce x in such a way as to meet the + + align:start position:0% +produce x in such a way as to meet the + + + align:start position:0% +produce x in such a way as to meet the +demand + + align:start position:0% +demand + + + align:start position:0% +demand +so this is a linear + + align:start position:0% +so this is a linear + + + align:start position:0% +so this is a linear +a system of + + align:start position:0% +a system of + + + align:start position:0% +a system of +linear equations + + align:start position:0% +linear equations + + + align:start position:0% +linear equations +and + + align:start position:0% + + + + align:start position:0% + +if you remember a little matrix algebra + + align:start position:0% +if you remember a little matrix algebra + + + align:start position:0% +if you remember a little matrix algebra +all we need to do is to invert um this + + align:start position:0% +all we need to do is to invert um this + + + align:start position:0% +all we need to do is to invert um this +matrix i minus a + + align:start position:0% +matrix i minus a + + + align:start position:0% +matrix i minus a +which eliminates it on both sides on the + + align:start position:0% +which eliminates it on both sides on the + + + align:start position:0% +which eliminates it on both sides on the +left-hand side and puts it on to the + + align:start position:0% +left-hand side and puts it on to the + + + align:start position:0% +left-hand side and puts it on to the +right-hand side + + align:start position:0% +right-hand side + + + align:start position:0% +right-hand side +so the x solution we want is i minus a + + align:start position:0% +so the x solution we want is i minus a + + + align:start position:0% +so the x solution we want is i minus a +times d + + align:start position:0% +times d + + + align:start position:0% +times d +so i'm minus a in this case you know you + + align:start position:0% +so i'm minus a in this case you know you + + + align:start position:0% +so i'm minus a in this case you know you +can go back up and realize that this was + + align:start position:0% +can go back up and realize that this was + + + align:start position:0% +can go back up and realize that this was +0.2 so i minus 1 minus 0.2 is 0.98 and + + align:start position:0% +0.2 so i minus 1 minus 0.2 is 0.98 and + + + align:start position:0% +0.2 so i minus 1 minus 0.2 is 0.98 and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +nothing gets subtracted on the off + + align:start position:0% +nothing gets subtracted on the off + + + align:start position:0% +nothing gets subtracted on the off +diagonal because i is 0 there + + align:start position:0% +diagonal because i is 0 there + + + align:start position:0% +diagonal because i is 0 there +so as long as this is what we would call + + align:start position:0% +so as long as this is what we would call + + + align:start position:0% +so as long as this is what we would call +a non-singular matrix that the rows and + + align:start position:0% +a non-singular matrix that the rows and + + + align:start position:0% +a non-singular matrix that the rows and +columns are independent of each other + + align:start position:0% +columns are independent of each other + + + align:start position:0% +columns are independent of each other +one is not a + + align:start position:0% +one is not a + + + align:start position:0% +one is not a +multiplicative factor of any of the + + align:start position:0% +multiplicative factor of any of the + + + align:start position:0% +multiplicative factor of any of the +other two + + align:start position:0% +other two + + + align:start position:0% +other two +then this inverse exists and we can + + align:start position:0% +then this inverse exists and we can + + + align:start position:0% +then this inverse exists and we can +solve the problem and you can see + + align:start position:0% +solve the problem and you can see + + + align:start position:0% +solve the problem and you can see +although it should be intuitive by now + + align:start position:0% +although it should be intuitive by now + + + align:start position:0% +although it should be intuitive by now +that they need to produce more than the + + align:start position:0% +that they need to produce more than the + + + align:start position:0% +that they need to produce more than the + + align:start position:0% + + + align:start position:0% +of raw materials they need to produce + + align:start position:0% +of raw materials they need to produce + + + align:start position:0% +of raw materials they need to produce +449. + + align:start position:0% +449. + + + align:start position:0% +449. +actually these were denoted in billions + + align:start position:0% +actually these were denoted in billions + + + align:start position:0% +actually these were denoted in billions +and and likewise + + align:start position:0% +and and likewise + + + align:start position:0% +and and likewise +how much more of each relative to the + + align:start position:0% +how much more of each relative to the + + + align:start position:0% +how much more of each relative to the +exogenously given demand + + align:start position:0% +exogenously given demand + + + align:start position:0% +exogenously given demand +actually depends + + align:start position:0% +actually depends + + + align:start position:0% +actually depends +you know in a pretty complicated way + + align:start position:0% +you know in a pretty complicated way + + + align:start position:0% +you know in a pretty complicated way +on + + align:start position:0% +on + + + align:start position:0% +on +that matrix a + + align:start position:0% +that matrix a + + + align:start position:0% +that matrix a +in the following sense to produce + + align:start position:0% +in the following sense to produce + + + align:start position:0% +in the following sense to produce +a unit of uh + + align:start position:0% +a unit of uh + + + align:start position:0% +a unit of uh +services + + align:start position:0% +services + + + align:start position:0% +services +one has to take into account + + align:start position:0% +one has to take into account + + + align:start position:0% +one has to take into account +the + + align:start position:0% +the + + + align:start position:0% +the +inputs of manufacturing and raw + + align:start position:0% +inputs of manufacturing and raw + + + align:start position:0% +inputs of manufacturing and raw +materials but to produce manufacturing + + align:start position:0% +materials but to produce manufacturing + + + align:start position:0% +materials but to produce manufacturing +and raw materials + + align:start position:0% +and raw materials + + + align:start position:0% +and raw materials +one has to take into account that they + + align:start position:0% +one has to take into account that they + + + align:start position:0% +one has to take into account that they +too use utilize services + + align:start position:0% + + + + align:start position:0% + +and so on and actually you can kind of + + align:start position:0% +and so on and actually you can kind of + + + align:start position:0% +and so on and actually you can kind of +keep going + + align:start position:0% +keep going + + + align:start position:0% +keep going +back into the matrix another way to + + align:start position:0% +back into the matrix another way to + + + align:start position:0% +back into the matrix another way to +write this system of equations actually + + align:start position:0% +write this system of equations actually + + + align:start position:0% +write this system of equations actually +is to get the inverse is to kind of + + align:start position:0% +is to get the inverse is to kind of + + + align:start position:0% +is to get the inverse is to kind of +successively + + align:start position:0% +successively + + + align:start position:0% +successively +plug in sort of first approximation + + align:start position:0% +plug in sort of first approximation + + + align:start position:0% +plug in sort of first approximation +second approximation third approximation + + align:start position:0% +second approximation third approximation + + + align:start position:0% +second approximation third approximation +as you take into account more and more + + align:start position:0% +as you take into account more and more + + + align:start position:0% +as you take into account more and more +of the layers + + align:start position:0% +of the layers + + + align:start position:0% +of the layers +uh + + align:start position:0% +uh + + + align:start position:0% +uh +of the interaction + + align:start position:0% +of the interaction + + + align:start position:0% +of the interaction +so you could have a sector + + align:start position:0% +so you could have a sector + + + align:start position:0% +so you could have a sector +which doesn't contribute much to final + + align:start position:0% +which doesn't contribute much to final + + + align:start position:0% +which doesn't contribute much to final +demand but is crucial as an input into + + align:start position:0% +demand but is crucial as an input into + + + align:start position:0% +demand but is crucial as an input into +the other two sectors so that sector + + align:start position:0% +the other two sectors so that sector + + + align:start position:0% +the other two sectors so that sector +could have a high importance even though + + align:start position:0% +could have a high importance even though + + + align:start position:0% +could have a high importance even though +it's not directly satisfying the demand + + align:start position:0% +it's not directly satisfying the demand + + + align:start position:0% +it's not directly satisfying the demand +of itself + + align:start position:0% +of itself + + + align:start position:0% +of itself +so then we come to + + align:start position:0% +so then we come to + + + align:start position:0% +so then we come to +google and in particular their algorithm + + align:start position:0% +google and in particular their algorithm + + + align:start position:0% +google and in particular their algorithm +when you type in a keyword it pops up in + + align:start position:0% +when you type in a keyword it pops up in + + + align:start position:0% +when you type in a keyword it pops up in +a rank order the most likely things that + + align:start position:0% +a rank order the most likely things that + + + align:start position:0% +a rank order the most likely things that +are related to what you just searched + + align:start position:0% +are related to what you just searched + + + align:start position:0% +are related to what you just searched +for this was invented by sergey brin and + + align:start position:0% +for this was invented by sergey brin and + + + align:start position:0% +for this was invented by sergey brin and +larry page + + align:start position:0% +larry page + + + align:start position:0% +larry page +i sometimes wonder if people's last + + align:start position:0% +i sometimes wonder if people's last + + + align:start position:0% +i sometimes wonder if people's last +names are not predictors of their + + align:start position:0% +names are not predictors of their + + + align:start position:0% +names are not predictors of their +eventual careers larry page being one of + + align:start position:0% +eventual careers larry page being one of + + + align:start position:0% +eventual careers larry page being one of +the fathers of paige rank but anyway + + align:start position:0% +the fathers of paige rank but anyway + + + align:start position:0% +the fathers of paige rank but anyway +that algorithm is really based on the + + align:start position:0% +that algorithm is really based on the + + + align:start position:0% +that algorithm is really based on the +same ideas that underlie leontya's + + align:start position:0% +same ideas that underlie leontya's + + + align:start position:0% +same ideas that underlie leontya's +ranking of industries which is + + align:start position:0% +ranking of industries which is + + + align:start position:0% +ranking of industries which is +you google up something + + align:start position:0% +you google up something + + + align:start position:0% +you google up something +and + + align:start position:0% +and + + + align:start position:0% +and +it it may be + + align:start position:0% +it it may be + + + align:start position:0% +it it may be +that + + align:start position:0% +that + + + align:start position:0% +that +there's an article that you might not + + align:start position:0% +there's an article that you might not + + + align:start position:0% +there's an article that you might not +have thought to be the + + align:start position:0% +have thought to be the + + + align:start position:0% +have thought to be the +most important one because it may not + + align:start position:0% +most important one because it may not + + + align:start position:0% +most important one because it may not +seem to answer the question directly but + + align:start position:0% +seem to answer the question directly but + + + align:start position:0% +seem to answer the question directly but +in fact it's the key article that + + align:start position:0% +in fact it's the key article that + + + align:start position:0% +in fact it's the key article that +started it all that has been cited and + + align:start position:0% +started it all that has been cited and + + + align:start position:0% +started it all that has been cited and +used by other things that are more + + align:start position:0% +used by other things that are more + + + align:start position:0% +used by other things that are more +directly linked to the google item that + + align:start position:0% +directly linked to the google item that + + + align:start position:0% +directly linked to the google item that +you're searching for + + align:start position:0% +you're searching for + + + align:start position:0% +you're searching for +and this display is you know not by + + align:start position:0% +and this display is you know not by + + + align:start position:0% +and this display is you know not by +sectors of industries but just by a + + align:start position:0% +sectors of industries but just by a + + + align:start position:0% +sectors of industries but just by a +network diagram + + align:start position:0% +network diagram + + + align:start position:0% +network diagram +you know you can see + + align:start position:0% +you know you can see + + + align:start position:0% +you know you can see +sort of these things directly related + + align:start position:0% +sort of these things directly related + + + align:start position:0% +sort of these things directly related +via pathways to things in the center + + align:start position:0% +via pathways to things in the center + + + align:start position:0% +via pathways to things in the center +these outliers or clusters and then it + + align:start position:0% +these outliers or clusters and then it + + + align:start position:0% +these outliers or clusters and then it +gets very thin but they could end up + + align:start position:0% +gets very thin but they could end up + + + align:start position:0% +gets very thin but they could end up +being important because they're related + + align:start position:0% +being important because they're related + + + align:start position:0% +being important because they're related +to things in the interior + + align:start position:0% +to things in the interior + + + align:start position:0% +to things in the interior +these things are ranked by distance + + align:start position:0% +these things are ranked by distance + + + align:start position:0% +these things are ranked by distance +actually re-ordered + + align:start position:0% +actually re-ordered + + + align:start position:0% +actually re-ordered +in order for the diagram to display the + + align:start position:0% +in order for the diagram to display the + + + align:start position:0% +in order for the diagram to display the +degree of closeness + + align:start position:0% +degree of closeness + + + align:start position:0% +degree of closeness +and they paige and those guys actually + + align:start position:0% +and they paige and those guys actually + + + align:start position:0% +and they paige and those guys actually +cited leontes but output matrix + + align:start position:0% +cited leontes but output matrix + + + align:start position:0% +cited leontes but output matrix +and then as a final example + + align:start position:0% +and then as a final example + + + align:start position:0% +and then as a final example +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +great east chap japanese earthquake + + align:start position:0% +great east chap japanese earthquake + + + align:start position:0% +great east chap japanese earthquake +to remind you + + align:start position:0% +to remind you + + + align:start position:0% +to remind you +there was an earthquake big one and then + + align:start position:0% +there was an earthquake big one and then + + + align:start position:0% +there was an earthquake big one and then +a subsequent tidal wave + + align:start position:0% +a subsequent tidal wave + + + align:start position:0% +a subsequent tidal wave +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +actually the coastline i think + + align:start position:0% +actually the coastline i think + + + align:start position:0% +actually the coastline i think +subsided by uh a meter or some + + align:start position:0% +subsided by uh a meter or some + + + align:start position:0% +subsided by uh a meter or some +outrageous amount and so + + align:start position:0% +outrageous amount and so + + + align:start position:0% +outrageous amount and so +in came the tidal wave doing + + align:start position:0% +in came the tidal wave doing + + + align:start position:0% +in came the tidal wave doing +a lot of damage and this is uh + + align:start position:0% +a lot of damage and this is uh + + + align:start position:0% +a lot of damage and this is uh +highlighting the damaged structures + + align:start position:0% +highlighting the damaged structures + + + align:start position:0% +highlighting the damaged structures +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +this is + + align:start position:0% +this is + + + align:start position:0% +this is +highlighting + + align:start position:0% +highlighting + + + align:start position:0% +highlighting +the headquarters of firms whose + + align:start position:0% +the headquarters of firms whose + + + align:start position:0% +the headquarters of firms whose +headquarters location was destroyed + + align:start position:0% +headquarters location was destroyed + + + align:start position:0% +headquarters location was destroyed +in the immediate aftermath of the + + align:start position:0% +in the immediate aftermath of the + + + align:start position:0% +in the immediate aftermath of the +earthquake and tsunami by the way the + + align:start position:0% +earthquake and tsunami by the way the + + + align:start position:0% +earthquake and tsunami by the way the +fukujima shima + + align:start position:0% +fukujima shima + + + align:start position:0% +fukujima shima +or nuclear power plant was right there + + align:start position:0% +or nuclear power plant was right there + + + align:start position:0% +or nuclear power plant was right there +adding to the mix + + align:start position:0% +adding to the mix + + + align:start position:0% +adding to the mix +so then we move over here this is all of + + align:start position:0% +so then we move over here this is all of + + + align:start position:0% +so then we move over here this is all of +the main island of japan and this is + + align:start position:0% +the main island of japan and this is + + + align:start position:0% +the main island of japan and this is +the area that's highlighted + + align:start position:0% +the area that's highlighted + + + align:start position:0% +the area that's highlighted +this small area here + + align:start position:0% +this small area here + + + align:start position:0% +this small area here +and then we ask as in an input output + + align:start position:0% +and then we ask as in an input output + + + align:start position:0% +and then we ask as in an input output +sense which industries had been + + align:start position:0% +sense which industries had been + + + align:start position:0% +sense which industries had been +supplying + + align:start position:0% +supplying + + + align:start position:0% +supplying +to + + align:start position:0% +to + + + align:start position:0% +to +headquarters + + align:start position:0% +headquarters + + + align:start position:0% +headquarters +which is not per se just where all the + + align:start position:0% +which is not per se just where all the + + + align:start position:0% +which is not per se just where all the +management is but like the primary + + align:start position:0% +management is but like the primary + + + align:start position:0% +management is but like the primary +production facility you have inputs + + align:start position:0% +production facility you have inputs + + + align:start position:0% +production facility you have inputs +applying to general motors for example + + align:start position:0% +applying to general motors for example + + + align:start position:0% +applying to general motors for example +in detroit you have tire manufacturers + + align:start position:0% +in detroit you have tire manufacturers + + + align:start position:0% +in detroit you have tire manufacturers +that are linked this is japan + + align:start position:0% +that are linked this is japan + + + align:start position:0% +that are linked this is japan +so we have input suppliers linked to + + align:start position:0% +so we have input suppliers linked to + + + align:start position:0% +so we have input suppliers linked to +headquarters or intermediate + + align:start position:0% +headquarters or intermediate + + + align:start position:0% +headquarters or intermediate +and likewise in principle it's not just + + align:start position:0% +and likewise in principle it's not just + + + align:start position:0% +and likewise in principle it's not just +inputs from + + align:start position:0% +inputs from + + + align:start position:0% +inputs from +upstream but outputs downstream the + + align:start position:0% +upstream but outputs downstream the + + + align:start position:0% +upstream but outputs downstream the +disruption here means you can't produce + + align:start position:0% +disruption here means you can't produce + + + align:start position:0% +disruption here means you can't produce +something which is in turn supplied + + align:start position:0% +something which is in turn supplied + + + align:start position:0% +something which is in turn supplied +downstream quote-unquote to others so + + align:start position:0% +downstream quote-unquote to others so + + + align:start position:0% +downstream quote-unquote to others so +the first-order connection as in the + + align:start position:0% +the first-order connection as in the + + + align:start position:0% +the first-order connection as in the +page rank are these areas in red and now + + align:start position:0% +page rank are these areas in red and now + + + align:start position:0% +page rank are these areas in red and now +we've covered all of japan because + + align:start position:0% +we've covered all of japan because + + + align:start position:0% +we've covered all of japan because +there's either an immediate input + + align:start position:0% +there's either an immediate input + + + align:start position:0% +there's either an immediate input +supplier or output purchaser indirectly + + align:start position:0% +supplier or output purchaser indirectly + + + align:start position:0% +supplier or output purchaser indirectly +damaged in in the sense of the first + + align:start position:0% +damaged in in the sense of the first + + + align:start position:0% +damaged in in the sense of the first +degree against the primary area of + + align:start position:0% +degree against the primary area of + + + align:start position:0% +degree against the primary area of +damage this is second degree damage + + align:start position:0% +damage this is second degree damage + + + align:start position:0% +damage this is second degree damage +a link to b who hit was hit with c and + + align:start position:0% +a link to b who hit was hit with c and + + + align:start position:0% +a link to b who hit was hit with c and +so on so eventually as you go in this + + align:start position:0% +so on so eventually as you go in this + + + align:start position:0% +so on so eventually as you go in this +case down to the fifth order most of + + align:start position:0% +case down to the fifth order most of + + + align:start position:0% +case down to the fifth order most of +japan was covered and in fact this + + align:start position:0% +japan was covered and in fact this + + + align:start position:0% +japan was covered and in fact this +japanese earthquake + + align:start position:0% +japanese earthquake + + + align:start position:0% +japanese earthquake +caused a drop in uh national level gdp + + align:start position:0% +caused a drop in uh national level gdp + + + align:start position:0% +caused a drop in uh national level gdp +of about one and a half percent + + align:start position:0% +of about one and a half percent + + + align:start position:0% +of about one and a half percent +it is quote just another + + align:start position:0% +it is quote just another + + + align:start position:0% +it is quote just another +illustration of the same mathematics so + + align:start position:0% +illustration of the same mathematics so + + + align:start position:0% +illustration of the same mathematics so +now with some trepidation let me go to + + align:start position:0% +now with some trepidation let me go to + + + align:start position:0% +now with some trepidation let me go to +lecture five and verify that you can see + + align:start position:0% +lecture five and verify that you can see + + + align:start position:0% +lecture five and verify that you can see +this on your screens + + align:start position:0% +this on your screens + + + align:start position:0% +this on your screens +as i move through it + + align:start position:0% +as i move through it + + + align:start position:0% +as i move through it +yes you can see it right + + align:start position:0% +yes you can see it right + + + align:start position:0% +yes you can see it right +so this is decision making under + + align:start position:0% +so this is decision making under + + + align:start position:0% +so this is decision making under +uncertainty and then we'll get back to + + align:start position:0% +uncertainty and then we'll get back to + + + align:start position:0% +uncertainty and then we'll get back to +some of our techniques in particular + + align:start position:0% +some of our techniques in particular + + + align:start position:0% +some of our techniques in particular +programming linear programming so + + align:start position:0% +programming linear programming so + + + align:start position:0% +programming linear programming so +let's suppose we have a lottery and + + align:start position:0% +let's suppose we have a lottery and + + + align:start position:0% +let's suppose we have a lottery and +there are little n distinct prizes + + align:start position:0% +there are little n distinct prizes + + + align:start position:0% +there are little n distinct prizes +possibly zero + + align:start position:0% +possibly zero + + + align:start position:0% +possibly zero +possibly negative if it + + align:start position:0% +possibly negative if it + + + align:start position:0% +possibly negative if it +takes money away so these uh x's are the + + align:start position:0% +takes money away so these uh x's are the + + + align:start position:0% +takes money away so these uh x's are the +amount of the winnings or losings + + align:start position:0% +amount of the winnings or losings + + + align:start position:0% +amount of the winnings or losings +if that event turns up in the lottery + + align:start position:0% +if that event turns up in the lottery + + + align:start position:0% +if that event turns up in the lottery +there are n possible things that could + + align:start position:0% +there are n possible things that could + + + align:start position:0% +there are n possible things that could +happen and they happen with these + + align:start position:0% +happen and they happen with these + + + align:start position:0% +happen and they happen with these +probabilities pi + + align:start position:0% +probabilities pi + + + align:start position:0% +probabilities pi +pi 1 being the probability that the + + align:start position:0% +pi 1 being the probability that the + + + align:start position:0% +pi 1 being the probability that the +gains or losses is in the order of x 1 + + align:start position:0% +gains or losses is in the order of x 1 + + + align:start position:0% +gains or losses is in the order of x 1 +pi 2 for x 2 and so on because it's a + + align:start position:0% +pi 2 for x 2 and so on because it's a + + + align:start position:0% +pi 2 for x 2 and so on because it's a +lottery + + align:start position:0% +lottery + + + align:start position:0% +lottery +the probabilities themselves are not + + align:start position:0% +the probabilities themselves are not + + + align:start position:0% +the probabilities themselves are not +negative they're zero or positive and + + align:start position:0% +negative they're zero or positive and + + + align:start position:0% +negative they're zero or positive and +it's a comprehensive lottery choosing + + align:start position:0% +it's a comprehensive lottery choosing + + + align:start position:0% +it's a comprehensive lottery choosing +over this vector of possible outcomes so + + align:start position:0% +over this vector of possible outcomes so + + + align:start position:0% +over this vector of possible outcomes so +the probabilities add up to one in other + + align:start position:0% +the probabilities add up to one in other + + + align:start position:0% +the probabilities add up to one in other +words the lottery is a well-defined + + align:start position:0% +words the lottery is a well-defined + + + align:start position:0% +words the lottery is a well-defined +random variable + + align:start position:0% +random variable + + + align:start position:0% +random variable +with these n distinct realizations + + align:start position:0% +with these n distinct realizations + + + align:start position:0% +with these n distinct realizations +and we can call the expectation of the + + align:start position:0% +and we can call the expectation of the + + + align:start position:0% +and we can call the expectation of the +lottery the expected outcome of the + + align:start position:0% +lottery the expected outcome of the + + + align:start position:0% +lottery the expected outcome of the +lottery or the rand variable capital x + + align:start position:0% +lottery or the rand variable capital x + + + align:start position:0% +lottery or the rand variable capital x +just to be the weighted average of the + + align:start position:0% +just to be the weighted average of the + + + align:start position:0% +just to be the weighted average of the +outcomes where the weights are these + + align:start position:0% +outcomes where the weights are these + + + align:start position:0% +outcomes where the weights are these +probabilities + + align:start position:0% +probabilities + + + align:start position:0% +probabilities +so part of this these next few slides + + align:start position:0% +so part of this these next few slides + + + align:start position:0% +so part of this these next few slides +have to do with the ideas of lotteries + + align:start position:0% +have to do with the ideas of lotteries + + + align:start position:0% +have to do with the ideas of lotteries +over discrete outcomes part of the next + + align:start position:0% +over discrete outcomes part of the next + + + align:start position:0% +over discrete outcomes part of the next +few slides + + align:start position:0% +few slides + + + align:start position:0% +few slides +are quick reviews of some basic ideas in + + align:start position:0% +are quick reviews of some basic ideas in + + + align:start position:0% +are quick reviews of some basic ideas in +statistics here's a basic idea from + + align:start position:0% +statistics here's a basic idea from + + + align:start position:0% +statistics here's a basic idea from +statistics if we have a random variable + + align:start position:0% +statistics if we have a random variable + + + align:start position:0% +statistics if we have a random variable +capital x + + align:start position:0% +capital x + + + align:start position:0% +capital x +we want to talk about its variability or + + align:start position:0% +we want to talk about its variability or + + + align:start position:0% +we want to talk about its variability or +its variance + + align:start position:0% +its variance + + + align:start position:0% +its variance +denoted sigma square x + + align:start position:0% +denoted sigma square x + + + align:start position:0% +denoted sigma square x +that is just the dispersion of x around + + align:start position:0% +that is just the dispersion of x around + + + align:start position:0% +that is just the dispersion of x around +the mean mu x u x was defined here as + + align:start position:0% +the mean mu x u x was defined here as + + + align:start position:0% +the mean mu x u x was defined here as +the previous slide as the mean + + align:start position:0% +the previous slide as the mean + + + align:start position:0% +the previous slide as the mean +squared so we square the differences if + + align:start position:0% +squared so we square the differences if + + + align:start position:0% +squared so we square the differences if +x were equal to its mean this would be + + align:start position:0% +x were equal to its mean this would be + + + align:start position:0% +x were equal to its mean this would be +zero + + align:start position:0% +zero + + + align:start position:0% +zero +the further away it is the higher the + + align:start position:0% +the further away it is the higher the + + + align:start position:0% +the further away it is the higher the +squared value would be expectation + + align:start position:0% +squared value would be expectation + + + align:start position:0% +squared value would be expectation +again means that we're just taking + + align:start position:0% +again means that we're just taking + + + align:start position:0% +again means that we're just taking +weighted averages + + align:start position:0% +weighted averages + + + align:start position:0% +weighted averages +with the weights being these pi i + + align:start position:0% +with the weights being these pi i + + + align:start position:0% +with the weights being these pi i +probabilities so this would be the + + align:start position:0% +probabilities so this would be the + + + align:start position:0% +probabilities so this would be the +formal expression + + align:start position:0% +formal expression + + + align:start position:0% +formal expression +the variance is a proxy for risk + + align:start position:0% +the variance is a proxy for risk + + + align:start position:0% +the variance is a proxy for risk +the square root of the variance is + + align:start position:0% +the square root of the variance is + + + align:start position:0% +the square root of the variance is +called the standard deviation + + align:start position:0% +called the standard deviation + + + align:start position:0% +called the standard deviation +and if we want to normalize it so we can + + align:start position:0% +and if we want to normalize it so we can + + + align:start position:0% +and if we want to normalize it so we can +interpret the units of it without + + align:start position:0% +interpret the units of it without + + + align:start position:0% +interpret the units of it without +knowing the magnitudes of the underlying + + align:start position:0% +knowing the magnitudes of the underlying + + + align:start position:0% +knowing the magnitudes of the underlying +variable + + align:start position:0% +variable + + + align:start position:0% +variable +we divide by its mean so the standard + + align:start position:0% +we divide by its mean so the standard + + + align:start position:0% +we divide by its mean so the standard +deviation divided by the mean + + align:start position:0% +deviation divided by the mean + + + align:start position:0% +deviation divided by the mean +is called the coefficient of variation + + align:start position:0% +is called the coefficient of variation + + + align:start position:0% +is called the coefficient of variation +what i mean by normalizing isn't just + + align:start position:0% +what i mean by normalizing isn't just + + + align:start position:0% +what i mean by normalizing isn't just +that we're dividing but the reason for + + align:start position:0% +that we're dividing but the reason for + + + align:start position:0% +that we're dividing but the reason for +dividing you could well imagine if we + + align:start position:0% +dividing you could well imagine if we + + + align:start position:0% +dividing you could well imagine if we +have two random variables and one is + + align:start position:0% +have two random variables and one is + + + align:start position:0% +have two random variables and one is +twice the other one + + align:start position:0% +twice the other one + + + align:start position:0% +twice the other one +then all the values are doubled and the + + align:start position:0% +then all the values are doubled and the + + + align:start position:0% +then all the values are doubled and the +measure of the dispersion will go up too + + align:start position:0% +measure of the dispersion will go up too + + + align:start position:0% +measure of the dispersion will go up too +so we wanted to measure a variability + + align:start position:0% +so we wanted to measure a variability + + + align:start position:0% +so we wanted to measure a variability +that's kind of independent of the scale + + align:start position:0% +that's kind of independent of the scale + + + align:start position:0% +that's kind of independent of the scale +of the underlying random variable itself + + align:start position:0% +of the underlying random variable itself + + + align:start position:0% +of the underlying random variable itself +one more slide on + + align:start position:0% +one more slide on + + + align:start position:0% +one more slide on +statistics + + align:start position:0% +statistics + + + align:start position:0% +statistics +so suppose + + align:start position:0% +so suppose + + + align:start position:0% +so suppose +the prize has two dimensions x and y + + align:start position:0% +the prize has two dimensions x and y + + + align:start position:0% +the prize has two dimensions x and y +not just the winnings and losings of + + align:start position:0% +not just the winnings and losings of + + + align:start position:0% +not just the winnings and losings of +dollars but maybe two different + + align:start position:0% +dollars but maybe two different + + + align:start position:0% +dollars but maybe two different +commodities + + align:start position:0% +commodities + + + align:start position:0% +commodities +so + + align:start position:0% +so + + + align:start position:0% +so +a particular realization + + align:start position:0% +a particular realization + + + align:start position:0% +a particular realization +or outcome would be a specification of + + align:start position:0% +or outcome would be a specification of + + + align:start position:0% +or outcome would be a specification of +both + + align:start position:0% +both + + + align:start position:0% +both +the value of x and the value of y x i y + + align:start position:0% +the value of x and the value of y x i y + + + align:start position:0% +the value of x and the value of y x i y +i for realization i + + align:start position:0% +i for realization i + + + align:start position:0% +i for realization i +realization i happens with probability + + align:start position:0% +realization i happens with probability + + + align:start position:0% +realization i happens with probability +pi i which is the same as before + + align:start position:0% +pi i which is the same as before + + + align:start position:0% +pi i which is the same as before +now though we can define the covariance + + align:start position:0% +now though we can define the covariance + + + align:start position:0% +now though we can define the covariance +between two random variables x and y + + align:start position:0% +between two random variables x and y + + + align:start position:0% +between two random variables x and y +to be + + align:start position:0% +to be + + + align:start position:0% +to be +the expectation + + align:start position:0% +the expectation + + + align:start position:0% +the expectation +of the product subtracting off the means + + align:start position:0% +of the product subtracting off the means + + + align:start position:0% +of the product subtracting off the means +so x less it's mean mu x times y minus + + align:start position:0% +so x less it's mean mu x times y minus + + + align:start position:0% +so x less it's mean mu x times y minus +its mean u y and i didn't write it out + + align:start position:0% +its mean u y and i didn't write it out + + + align:start position:0% +its mean u y and i didn't write it out +but you could just sum it up over the + + align:start position:0% +but you could just sum it up over the + + + align:start position:0% +but you could just sum it up over the +same pi i's instead of writing the + + align:start position:0% +same pi i's instead of writing the + + + align:start position:0% +same pi i's instead of writing the +expectation operator it tells you + + align:start position:0% +expectation operator it tells you + + + align:start position:0% +expectation operator it tells you +whether + + align:start position:0% +whether + + + align:start position:0% +whether +the variables x and y are moving + + align:start position:0% +the variables x and y are moving + + + align:start position:0% +the variables x and y are moving +together or moving in opposite + + align:start position:0% +together or moving in opposite + + + align:start position:0% +together or moving in opposite +directions + + align:start position:0% +directions + + + align:start position:0% +directions +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +when + + align:start position:0% +when + + + align:start position:0% +when +a high value of x + + align:start position:0% +a high value of x + + + align:start position:0% +a high value of x +corresponds with a high value of y + + align:start position:0% +corresponds with a high value of y + + + align:start position:0% +corresponds with a high value of y +thinking collectively about these + + align:start position:0% +thinking collectively about these + + + align:start position:0% +thinking collectively about these +realizations x i y i + + align:start position:0% +realizations x i y i + + + align:start position:0% +realizations x i y i +then this covariance is positive + + align:start position:0% +then this covariance is positive + + + align:start position:0% +then this covariance is positive +and likewise if a high x means a low y + + align:start position:0% +and likewise if a high x means a low y + + + align:start position:0% +and likewise if a high x means a low y +the covariance would be negative + + align:start position:0% +the covariance would be negative + + + align:start position:0% +the covariance would be negative +you could think about plotting + + align:start position:0% +you could think about plotting + + + align:start position:0% +you could think about plotting +the x i y i value variables as in a + + align:start position:0% +the x i y i value variables as in a + + + align:start position:0% +the x i y i value variables as in a +cloud + + align:start position:0% +cloud + + + align:start position:0% +cloud +and trying to figure out if the cloud is + + align:start position:0% +and trying to figure out if the cloud is + + + align:start position:0% +and trying to figure out if the cloud is +running + + align:start position:0% +running + + + align:start position:0% +running +on the 45 degree line or running in the + + align:start position:0% +on the 45 degree line or running in the + + + align:start position:0% +on the 45 degree line or running in the +reverse direction from northwest to + + align:start position:0% +reverse direction from northwest to + + + align:start position:0% +reverse direction from northwest to +southeast + + align:start position:0% +southeast + + + align:start position:0% +southeast +okay + + align:start position:0% +okay + + + align:start position:0% +okay +again it's useful to normalize + + align:start position:0% +again it's useful to normalize + + + align:start position:0% +again it's useful to normalize +so we take that covariance and just + + align:start position:0% +so we take that covariance and just + + + align:start position:0% +so we take that covariance and just +divide it by the + + align:start position:0% +divide it by the + + + align:start position:0% +divide it by the +product the variance called the + + align:start position:0% +product the variance called the + + + align:start position:0% +product the variance called the +correlation and correlations are by + + align:start position:0% +correlation and correlations are by + + + align:start position:0% +correlation and correlations are by +construction going to be between -1 and + + align:start position:0% +construction going to be between -1 and + + + align:start position:0% +construction going to be between -1 and +1 so again + + align:start position:0% +1 so again + + + align:start position:0% +1 so again +zero means no correlation one means + + align:start position:0% +zero means no correlation one means + + + align:start position:0% +zero means no correlation one means +perfect + + align:start position:0% +perfect + + + align:start position:0% +perfect +correlation + + align:start position:0% +correlation + + + align:start position:0% +correlation +positive direction and -1 means negative + + align:start position:0% +positive direction and -1 means negative + + + align:start position:0% +positive direction and -1 means negative +correlation + + align:start position:0% +correlation + + + align:start position:0% +correlation +so those are the three + + align:start position:0% +so those are the three + + + align:start position:0% +so those are the three +statistical review slides and we're + + align:start position:0% +statistical review slides and we're + + + align:start position:0% +statistical review slides and we're +going to come back to them momentarily + + align:start position:0% +going to come back to them momentarily + + + align:start position:0% +going to come back to them momentarily +they're all defined for random variables + + align:start position:0% +they're all defined for random variables + + + align:start position:0% +they're all defined for random variables +but we defined a random variable by + + align:start position:0% +but we defined a random variable by + + + align:start position:0% +but we defined a random variable by +first thinking about a lottery so let's + + align:start position:0% +first thinking about a lottery so let's + + + align:start position:0% +first thinking about a lottery so let's +come back to + + align:start position:0% +come back to + + + align:start position:0% +come back to +the lottery here in fact + + align:start position:0% +the lottery here in fact + + + align:start position:0% +the lottery here in fact +the underlying ingredients are x1 and x2 + + align:start position:0% +the underlying ingredients are x1 and x2 + + + align:start position:0% +the underlying ingredients are x1 and x2 +but they can only take on + + align:start position:0% +but they can only take on + + + align:start position:0% +but they can only take on +a finite number of values these dots + + align:start position:0% +a finite number of values these dots + + + align:start position:0% +a finite number of values these dots +represent a discrete point + + align:start position:0% +represent a discrete point + + + align:start position:0% +represent a discrete point +and this commodity space here the values + + align:start position:0% +and this commodity space here the values + + + align:start position:0% +and this commodity space here the values +of x and one and x two which are + + align:start position:0% +of x and one and x two which are + + + align:start position:0% +of x and one and x two which are +feasible + + align:start position:0% +feasible + + + align:start position:0% +feasible +this is not a convex space because you + + align:start position:0% +this is not a convex space because you + + + align:start position:0% +this is not a convex space because you +can easily find + + align:start position:0% +can easily find + + + align:start position:0% +can easily find +lines + + align:start position:0% +lines + + + align:start position:0% +lines +between any two of these dots + + align:start position:0% +between any two of these dots + + + align:start position:0% +between any two of these dots +and intermediate points on the line + + align:start position:0% +and intermediate points on the line + + + align:start position:0% +and intermediate points on the line +other than the end point are not + + align:start position:0% +other than the end point are not + + + align:start position:0% +other than the end point are not +in + + align:start position:0% +in + + + align:start position:0% +in +this + + align:start position:0% +this + + + align:start position:0% +this +consumption set + + align:start position:0% +consumption set + + + align:start position:0% +consumption set +so this is a non-convex set + + align:start position:0% +so this is a non-convex set + + + align:start position:0% +so this is a non-convex set +back to the lottery interpretation + + align:start position:0% +back to the lottery interpretation + + + align:start position:0% +back to the lottery interpretation +let's call say cs a particular + + align:start position:0% +let's call say cs a particular + + + align:start position:0% +let's call say cs a particular +realization or state or point in the + + align:start position:0% +realization or state or point in the + + + align:start position:0% +realization or state or point in the +commodity space in capital c + + align:start position:0% +commodity space in capital c + + + align:start position:0% +commodity space in capital c +s denotes the set of all possible states + + align:start position:0% +s denotes the set of all possible states + + + align:start position:0% +s denotes the set of all possible states +it's just counting up the number of dots + + align:start position:0% +it's just counting up the number of dots + + + align:start position:0% +it's just counting up the number of dots +you're seeing on this picture + + align:start position:0% +you're seeing on this picture + + + align:start position:0% +you're seeing on this picture +so for example if there are capital s + + align:start position:0% +so for example if there are capital s + + + align:start position:0% +so for example if there are capital s +dots or states each state corresponds to + + align:start position:0% +dots or states each state corresponds to + + + align:start position:0% +dots or states each state corresponds to +a particular consumption bundle in r2 + + align:start position:0% +a particular consumption bundle in r2 + + + align:start position:0% +a particular consumption bundle in r2 +and we can call pi s + + align:start position:0% +and we can call pi s + + + align:start position:0% +and we can call pi s +the probability of being in state s + + align:start position:0% +the probability of being in state s + + + align:start position:0% +the probability of being in state s +so we could have a lottery over this + + align:start position:0% +so we could have a lottery over this + + + align:start position:0% +so we could have a lottery over this +over this space + + align:start position:0% +over this space + + + align:start position:0% +over this space +if we define those lotteries + + align:start position:0% +if we define those lotteries + + + align:start position:0% +if we define those lotteries +a particular lottery + + align:start position:0% +a particular lottery + + + align:start position:0% +a particular lottery +would put a non-negative probability + + align:start position:0% +would put a non-negative probability + + + align:start position:0% +would put a non-negative probability +perhaps 0 + + align:start position:0% +perhaps 0 + + + align:start position:0% +perhaps 0 +on any particular state and the sum of + + align:start position:0% +on any particular state and the sum of + + + align:start position:0% +on any particular state and the sum of +the probabilities over all the states + + align:start position:0% +the probabilities over all the states + + + align:start position:0% +the probabilities over all the states +would have to add up to one + + align:start position:0% +would have to add up to one + + + align:start position:0% +would have to add up to one +so the that's a particular lottery + + align:start position:0% +so the that's a particular lottery + + + align:start position:0% +so the that's a particular lottery +the set of all possible lotteries is + + align:start position:0% +the set of all possible lotteries is + + + align:start position:0% +the set of all possible lotteries is +this set of all probabilities pi that + + align:start position:0% +this set of all probabilities pi that + + + align:start position:0% +this set of all probabilities pi that +satisfy these two characters call it + + align:start position:0% +satisfy these two characters call it + + + align:start position:0% +satisfy these two characters call it +capital pi + + align:start position:0% +capital pi + + + align:start position:0% +capital pi +it's also called a simplex by definition + + align:start position:0% +it's also called a simplex by definition + + + align:start position:0% +it's also called a simplex by definition +a simplex is a set where each element is + + align:start position:0% +a simplex is a set where each element is + + + align:start position:0% +a simplex is a set where each element is +non-negative and all the elements add up + + align:start position:0% +non-negative and all the elements add up + + + align:start position:0% +non-negative and all the elements add up +to one so a lottery satisfies the + + align:start position:0% +to one so a lottery satisfies the + + + align:start position:0% +to one so a lottery satisfies the +definition of a simplex other things do + + align:start position:0% +definition of a simplex other things do + + + align:start position:0% +definition of a simplex other things do +too + + align:start position:0% +too + + + align:start position:0% +too +okay so this becomes the new commodity + + align:start position:0% +okay so this becomes the new commodity + + + align:start position:0% +okay so this becomes the new commodity +space not the set of underlying points + + align:start position:0% +space not the set of underlying points + + + align:start position:0% +space not the set of underlying points +but the set of lotteries on those points + + align:start position:0% +but the set of lotteries on those points + + + align:start position:0% +but the set of lotteries on those points +and likewise we now can define + + align:start position:0% +and likewise we now can define + + + align:start position:0% +and likewise we now can define +preferences with this sort of squiggly + + align:start position:0% +preferences with this sort of squiggly + + + align:start position:0% +preferences with this sort of squiggly +script inequality over the set of + + align:start position:0% +script inequality over the set of + + + align:start position:0% +script inequality over the set of +possible lotteries and what we're going + + align:start position:0% +possible lotteries and what we're going + + + align:start position:0% +possible lotteries and what we're going +to use is von neumann morgenstern + + align:start position:0% +to use is von neumann morgenstern + + + align:start position:0% +to use is von neumann morgenstern +expected utility + + align:start position:0% +expected utility + + + align:start position:0% +expected utility +which is quite natural and it's saying + + align:start position:0% +which is quite natural and it's saying + + + align:start position:0% +which is quite natural and it's saying +take a particular point cs + + align:start position:0% +take a particular point cs + + + align:start position:0% +take a particular point cs +in that space take the underlying + + align:start position:0% +in that space take the underlying + + + align:start position:0% +in that space take the underlying +utility of it which we've been using + + align:start position:0% +utility of it which we've been using + + + align:start position:0% +utility of it which we've been using +before take the probability of that + + align:start position:0% +before take the probability of that + + + align:start position:0% +before take the probability of that +state and then sum up over all possible + + align:start position:0% +state and then sum up over all possible + + + align:start position:0% +state and then sum up over all possible +states and define this expected utility + + align:start position:0% +states and define this expected utility + + + align:start position:0% +states and define this expected utility +so these are the underlying real value + + align:start position:0% +so these are the underlying real value + + + align:start position:0% +so these are the underlying real value +numbers of deterministic utility this + + align:start position:0% +numbers of deterministic utility this + + + align:start position:0% +numbers of deterministic utility this +object over here on the left is the + + align:start position:0% +object over here on the left is the + + + align:start position:0% +object over here on the left is the +expected utility for a particular + + align:start position:0% +expected utility for a particular + + + align:start position:0% +expected utility for a particular +lottery pi + + align:start position:0% +lottery pi + + + align:start position:0% +lottery pi +and the idea now is that all possible + + align:start position:0% +and the idea now is that all possible + + + align:start position:0% +and the idea now is that all possible +lotteries can be ranked by this expected + + align:start position:0% +lotteries can be ranked by this expected + + + align:start position:0% +lotteries can be ranked by this expected +utility criterion + + align:start position:0% +utility criterion + + + align:start position:0% +utility criterion +let's just note in passing that this + + align:start position:0% +let's just note in passing that this + + + align:start position:0% +let's just note in passing that this +expected utility criterion is linear in + + align:start position:0% +expected utility criterion is linear in + + + align:start position:0% +expected utility criterion is linear in +the choice objects which are the + + align:start position:0% +the choice objects which are the + + + align:start position:0% +the choice objects which are the +lotteries + + align:start position:0% +lotteries + + + align:start position:0% +lotteries +these u of c s things become + + align:start position:0% +these u of c s things become + + + align:start position:0% +these u of c s things become +coefficients real numbers but we're not + + align:start position:0% +coefficients real numbers but we're not + + + align:start position:0% +coefficients real numbers but we're not +varying the underlying commodity points + + align:start position:0% +varying the underlying commodity points + + + align:start position:0% +varying the underlying commodity points +so these become fixed numbers and the + + align:start position:0% +so these become fixed numbers and the + + + align:start position:0% +so these become fixed numbers and the +thing that we're interested in varying + + align:start position:0% +thing that we're interested in varying + + + align:start position:0% +thing that we're interested in varying +would be the probabilities that + + align:start position:0% +would be the probabilities that + + + align:start position:0% +would be the probabilities that +constitute the lottery so the objective + + align:start position:0% +constitute the lottery so the objective + + + align:start position:0% +constitute the lottery so the objective +function is linear in the probabilities + + align:start position:0% +function is linear in the probabilities + + + align:start position:0% +function is linear in the probabilities +there are some criteria we need to + + align:start position:0% +there are some criteria we need to + + + align:start position:0% +there are some criteria we need to +satisfy in order to + + align:start position:0% +satisfy in order to + + + align:start position:0% +satisfy in order to +rank + + align:start position:0% +rank + + + align:start position:0% +rank +using expected utility + + align:start position:0% +using expected utility + + + align:start position:0% +using expected utility +what we want to get at the end of the + + align:start position:0% +what we want to get at the end of the + + + align:start position:0% +what we want to get at the end of the +day is that a + + align:start position:0% +day is that a + + + align:start position:0% +day is that a +long pie is strictly preferred to a + + align:start position:0% +long pie is strictly preferred to a + + + align:start position:0% +long pie is strictly preferred to a +lottery pi prime if the expected utility + + align:start position:0% +lottery pi prime if the expected utility + + + align:start position:0% +lottery pi prime if the expected utility +under pi is strictly greater than the + + align:start position:0% +under pi is strictly greater than the + + + align:start position:0% +under pi is strictly greater than the +expected utility under pi prime + + align:start position:0% +expected utility under pi prime + + + align:start position:0% +expected utility under pi prime +in order to do that we need three axioms + + align:start position:0% +in order to do that we need three axioms + + + align:start position:0% +in order to do that we need three axioms +these three + + align:start position:0% +these three + + + align:start position:0% +these three +the first combines two cheating a bit + + align:start position:0% +the first combines two cheating a bit + + + align:start position:0% +the first combines two cheating a bit +completeness + + align:start position:0% +completeness + + + align:start position:0% +completeness +says that all lotteries + + align:start position:0% +says that all lotteries + + + align:start position:0% +says that all lotteries +can be ranked and give us a number + + align:start position:0% +can be ranked and give us a number + + + align:start position:0% +can be ranked and give us a number +and transitivity + + align:start position:0% +and transitivity + + + align:start position:0% +and transitivity +i think you can see is going to be + + align:start position:0% +i think you can see is going to be + + + align:start position:0% +i think you can see is going to be +satisfied because + + align:start position:0% +satisfied because + + + align:start position:0% +satisfied because +if a is preferred to be lottery pi is + + align:start position:0% +if a is preferred to be lottery pi is + + + align:start position:0% +if a is preferred to be lottery pi is +preferred a lottery pi prime and pi + + align:start position:0% +preferred a lottery pi prime and pi + + + align:start position:0% +preferred a lottery pi prime and pi +prime is preferred to + + align:start position:0% +prime is preferred to + + + align:start position:0% +prime is preferred to +pi double prime + + align:start position:0% +pi double prime + + + align:start position:0% +pi double prime +under the preference ordering we can map + + align:start position:0% +under the preference ordering we can map + + + align:start position:0% +under the preference ordering we can map +those preference orderings into these + + align:start position:0% +those preference orderings into these + + + align:start position:0% +those preference orderings into these +expected + + align:start position:0% +expected + + + align:start position:0% +expected +utility + + align:start position:0% +utility + + + align:start position:0% +utility +objects which are just real numbers that + + align:start position:0% +objects which are just real numbers that + + + align:start position:0% +objects which are just real numbers that +satisfy + + align:start position:0% +satisfy + + + align:start position:0% +satisfy +transitivity + + align:start position:0% +transitivity + + + align:start position:0% +transitivity +so those are + + align:start position:0% +so those are + + + align:start position:0% +so those are +intuitive + + align:start position:0% +intuitive + + + align:start position:0% +intuitive +properties completeness and transitivity + + align:start position:0% +properties completeness and transitivity + + + align:start position:0% +properties completeness and transitivity +here's + + align:start position:0% +here's + + + align:start position:0% +here's +something called + + align:start position:0% +something called + + + align:start position:0% +something called +independence take two lotteries of focus + + align:start position:0% +independence take two lotteries of focus + + + align:start position:0% +independence take two lotteries of focus +denoted pi and pi prime and say that + + align:start position:0% +denoted pi and pi prime and say that + + + align:start position:0% +denoted pi and pi prime and say that +pi is weakly preferred under that + + align:start position:0% +pi is weakly preferred under that + + + align:start position:0% +pi is weakly preferred under that +expected utility ordering to pi prime + + align:start position:0% +expected utility ordering to pi prime + + + align:start position:0% +expected utility ordering to pi prime +then it has to be true + + align:start position:0% +then it has to be true + + + align:start position:0% +then it has to be true +that some alpha weighted uh lottery + + align:start position:0% +that some alpha weighted uh lottery + + + align:start position:0% +that some alpha weighted uh lottery +this is this is a lottery pi is a + + align:start position:0% +this is this is a lottery pi is a + + + align:start position:0% +this is this is a lottery pi is a +lottery + + align:start position:0% +lottery + + + align:start position:0% +lottery +and + + align:start position:0% +and + + + align:start position:0% +and +pi prime is a lottery and pi triple + + align:start position:0% +pi prime is a lottery and pi triple + + + align:start position:0% +pi prime is a lottery and pi triple +prime is also a lottery + + align:start position:0% +prime is also a lottery + + + align:start position:0% +prime is also a lottery +so now we're taking compound + + align:start position:0% +so now we're taking compound + + + align:start position:0% +so now we're taking compound +probabilities if you like + + align:start position:0% +probabilities if you like + + + align:start position:0% +probabilities if you like +when we take the alpha weighted sum + + align:start position:0% +when we take the alpha weighted sum + + + align:start position:0% +when we take the alpha weighted sum +of the lottery pi and pi prime + + align:start position:0% + + + + align:start position:0% + +if alpha were say equal to one + + align:start position:0% +if alpha were say equal to one + + + align:start position:0% +if alpha were say equal to one +then we're already given that pi is + + align:start position:0% +then we're already given that pi is + + + align:start position:0% +then we're already given that pi is +weakly preferred to pi prime and that + + align:start position:0% +weakly preferred to pi prime and that + + + align:start position:0% +weakly preferred to pi prime and that +would be an equivalent statement on the + + align:start position:0% +would be an equivalent statement on the + + + align:start position:0% +would be an equivalent statement on the +right hand side + + align:start position:0% +right hand side + + + align:start position:0% +right hand side +if alpha is less than one however then + + align:start position:0% +if alpha is less than one however then + + + align:start position:0% +if alpha is less than one however then +we're putting some weight on this + + align:start position:0% +we're putting some weight on this + + + align:start position:0% +we're putting some weight on this +extraneous third lottery pi double prime + + align:start position:0% +extraneous third lottery pi double prime + + + align:start position:0% +extraneous third lottery pi double prime +and then the notion of independence + + align:start position:0% +and then the notion of independence + + + align:start position:0% +and then the notion of independence +means + + align:start position:0% +means + + + align:start position:0% +means +that whatever this + + align:start position:0% +that whatever this + + + align:start position:0% +that whatever this +other lottery looks like it doesn't + + align:start position:0% +other lottery looks like it doesn't + + + align:start position:0% +other lottery looks like it doesn't +matter + + align:start position:0% +matter + + + align:start position:0% +matter +for fixed alpha when it comes to + + align:start position:0% +for fixed alpha when it comes to + + + align:start position:0% +for fixed alpha when it comes to +weighting + + align:start position:0% + + + + align:start position:0% + +pi and pi level + + align:start position:0% +pi and pi level + + + align:start position:0% +pi and pi level +awaiting the composite lottery because + + align:start position:0% +awaiting the composite lottery because + + + align:start position:0% +awaiting the composite lottery because +each one of these + + align:start position:0% +each one of these + + + align:start position:0% +each one of these +the second term in each one of these + + align:start position:0% +the second term in each one of these + + + align:start position:0% +the second term in each one of these +expressions is one minus alpha + + align:start position:0% +expressions is one minus alpha + + + align:start position:0% +expressions is one minus alpha +times pi double prime which isn't the + + align:start position:0% +times pi double prime which isn't the + + + align:start position:0% +times pi double prime which isn't the +same on the left hand side as it is on + + align:start position:0% +same on the left hand side as it is on + + + align:start position:0% +same on the left hand side as it is on +the right hand side + + align:start position:0% +the right hand side + + + align:start position:0% +the right hand side +so the ranking is independent of + + align:start position:0% +so the ranking is independent of + + + align:start position:0% +so the ranking is independent of +whatever that term is + + align:start position:0% + + + + align:start position:0% + +seems like it ought to be true but it's + + align:start position:0% +seems like it ought to be true but it's + + + align:start position:0% +seems like it ought to be true but it's +actually an axiom + + align:start position:0% +actually an axiom + + + align:start position:0% +actually an axiom +continuity is similar although + + align:start position:0% +continuity is similar although + + + align:start position:0% +continuity is similar although +not identical + + align:start position:0% +not identical + + + align:start position:0% +not identical +it says if we have three lotteries pi + + align:start position:0% +it says if we have three lotteries pi + + + align:start position:0% +it says if we have three lotteries pi +pi prime pi triple prime and they're + + align:start position:0% +pi prime pi triple prime and they're + + + align:start position:0% +pi prime pi triple prime and they're +rank ordered + + align:start position:0% +rank ordered + + + align:start position:0% +rank ordered +pi preferred to pi prime preferred to pi + + align:start position:0% +pi preferred to pi prime preferred to pi + + + align:start position:0% +pi preferred to pi prime preferred to pi +double prime + + align:start position:0% +double prime + + + align:start position:0% +double prime +then + + align:start position:0% + + + + align:start position:0% + +there exists numbers alpha and beta such + + align:start position:0% +there exists numbers alpha and beta such + + + align:start position:0% +there exists numbers alpha and beta such +that + + align:start position:0% +that + + + align:start position:0% +that +this weighted + + align:start position:0% +this weighted + + + align:start position:0% +this weighted +sum of pi + + align:start position:0% +sum of pi + + + align:start position:0% +sum of pi +and pi double prime + + align:start position:0% +and pi double prime + + + align:start position:0% +and pi double prime +weighted by alpha is strictly preferred + + align:start position:0% +weighted by alpha is strictly preferred + + + align:start position:0% +weighted by alpha is strictly preferred +to pi prime which is strictly preferred + + align:start position:0% +to pi prime which is strictly preferred + + + align:start position:0% +to pi prime which is strictly preferred +by the beta weighted sum of pi and pi + + align:start position:0% +by the beta weighted sum of pi and pi + + + align:start position:0% +by the beta weighted sum of pi and pi +double prime now the way to see this + + align:start position:0% +double prime now the way to see this + + + align:start position:0% +double prime now the way to see this +is + + align:start position:0% + + + + align:start position:0% + +that it's not required to be true for + + align:start position:0% +that it's not required to be true for + + + align:start position:0% +that it's not required to be true for +all alpha and beta it's only required to + + align:start position:0% +all alpha and beta it's only required to + + + align:start position:0% +all alpha and beta it's only required to +be true for some of them so if we were + + align:start position:0% +be true for some of them so if we were + + + align:start position:0% +be true for some of them so if we were +allowed to set alpha equal to one we + + align:start position:0% +allowed to set alpha equal to one we + + + align:start position:0% +allowed to set alpha equal to one we +would have + + align:start position:0% +would have + + + align:start position:0% +would have +alpha pi on the left hand side + + align:start position:0% +alpha pi on the left hand side + + + align:start position:0% +alpha pi on the left hand side +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +and pi prime would be over here + + align:start position:0% +and pi prime would be over here + + + align:start position:0% +and pi prime would be over here +we'd have pi preferred to pi prime but + + align:start position:0% +we'd have pi preferred to pi prime but + + + align:start position:0% +we'd have pi preferred to pi prime but +that was a given to begin with + + align:start position:0% +that was a given to begin with + + + align:start position:0% +that was a given to begin with +so no new information + + align:start position:0% +so no new information + + + align:start position:0% +so no new information +this is saying if alpha is arbitrarily + + align:start position:0% +this is saying if alpha is arbitrarily + + + align:start position:0% +this is saying if alpha is arbitrarily +close to one then that ought to be true + + align:start position:0% +close to one then that ought to be true + + + align:start position:0% +close to one then that ought to be true +and hence the notion of continuity + + align:start position:0% +and hence the notion of continuity + + + align:start position:0% +and hence the notion of continuity +likewise on the right hand side + + align:start position:0% +likewise on the right hand side + + + align:start position:0% +likewise on the right hand side +if beta were zero which it's not allowed + + align:start position:0% +if beta were zero which it's not allowed + + + align:start position:0% +if beta were zero which it's not allowed +to be + + align:start position:0% +to be + + + align:start position:0% +to be +then we'd be just getting pi double + + align:start position:0% +then we'd be just getting pi double + + + align:start position:0% +then we'd be just getting pi double +prime here and we're already given that + + align:start position:0% +prime here and we're already given that + + + align:start position:0% +prime here and we're already given that +pi + + align:start position:0% +pi + + + align:start position:0% +pi +prime is + + align:start position:0% +prime is + + + align:start position:0% +prime is +preferred to pi double prime + + align:start position:0% +preferred to pi double prime + + + align:start position:0% +preferred to pi double prime +the content of it is if theta is not + + align:start position:0% +the content of it is if theta is not + + + align:start position:0% +the content of it is if theta is not +zero but very close to zero + + align:start position:0% +zero but very close to zero + + + align:start position:0% +zero but very close to zero +then we should preserve the rank + + align:start position:0% +then we should preserve the rank + + + align:start position:0% +then we should preserve the rank +ordering + + align:start position:0% +ordering + + + align:start position:0% +ordering +these are intuitive properties + + align:start position:0% +these are intuitive properties + + + align:start position:0% +these are intuitive properties +they're here only to say that expected + + align:start position:0% +they're here only to say that expected + + + align:start position:0% +they're here only to say that expected +utility may not be quote unquote as + + align:start position:0% +utility may not be quote unquote as + + + align:start position:0% +utility may not be quote unquote as +general as you might think when facing + + align:start position:0% +general as you might think when facing + + + align:start position:0% +general as you might think when facing +problems of choice under uncertainty + + align:start position:0% +problems of choice under uncertainty + + + align:start position:0% +problems of choice under uncertainty +although it is very natural + + align:start position:0% +although it is very natural + + + align:start position:0% +although it is very natural +and these properties are similar + + align:start position:0% +and these properties are similar + + + align:start position:0% +and these properties are similar +in some respects to what we did before + + align:start position:0% +in some respects to what we did before + + + align:start position:0% +in some respects to what we did before +with ordinary preference orderings and + + align:start position:0% +with ordinary preference orderings and + + + align:start position:0% +with ordinary preference orderings and +with regard to what we did before + + align:start position:0% +with regard to what we did before + + + align:start position:0% +with regard to what we did before +there was already a question from one of + + align:start position:0% +there was already a question from one of + + + align:start position:0% +there was already a question from one of +you about this + + align:start position:0% +you about this + + + align:start position:0% +you about this +what about choice under uncertainty + + align:start position:0% +what about choice under uncertainty + + + align:start position:0% +what about choice under uncertainty +now our measure of utility becomes + + align:start position:0% +now our measure of utility becomes + + + align:start position:0% +now our measure of utility becomes +cardinal not just ordinal + + align:start position:0% +cardinal not just ordinal + + + align:start position:0% +cardinal not just ordinal +we're really going to care about the + + align:start position:0% +we're really going to care about the + + + align:start position:0% +we're really going to care about the +degree of curvature + + align:start position:0% +degree of curvature + + + align:start position:0% +degree of curvature +in this orange line + + align:start position:0% +in this orange line + + + align:start position:0% +in this orange line +which is mapping the expected utility + + align:start position:0% +which is mapping the expected utility + + + align:start position:0% +which is mapping the expected utility +outcome as we vary the input x + + align:start position:0% +outcome as we vary the input x + + + align:start position:0% +outcome as we vary the input x +so + + align:start position:0% +so + + + align:start position:0% +so +what's going on in this setup here we + + align:start position:0% +what's going on in this setup here we + + + align:start position:0% +what's going on in this setup here we +have income say moving around + + align:start position:0% +have income say moving around + + + align:start position:0% +have income say moving around +and it has a mean + + align:start position:0% +and it has a mean + + + align:start position:0% +and it has a mean +the expected value of x + + align:start position:0% +the expected value of x + + + align:start position:0% +the expected value of x +and it has a couple of endpoints the + + align:start position:0% +and it has a couple of endpoints the + + + align:start position:0% +and it has a couple of endpoints the +lowest + + align:start position:0% +lowest + + + align:start position:0% +lowest +value x0 the highest value x1 let's say + + align:start position:0% +value x0 the highest value x1 let's say + + + align:start position:0% +value x0 the highest value x1 let's say +for simplicity that's all that's going + + align:start position:0% +for simplicity that's all that's going + + + align:start position:0% +for simplicity that's all that's going +on + + align:start position:0% +on + + + align:start position:0% +on +that the lottery that creates the random + + align:start position:0% +that the lottery that creates the random + + + align:start position:0% +that the lottery that creates the random +variable is nothing other than some + + align:start position:0% +variable is nothing other than some + + + align:start position:0% +variable is nothing other than some +weighted average of x0 and x1 + + align:start position:0% +weighted average of x0 and x1 + + + align:start position:0% +weighted average of x0 and x1 +and those weights are such as to produce + + align:start position:0% +and those weights are such as to produce + + + align:start position:0% +and those weights are such as to produce +exactly this expected value + + align:start position:0% +exactly this expected value + + + align:start position:0% +exactly this expected value +and that's what's being drawn + + align:start position:0% +and that's what's being drawn + + + align:start position:0% +and that's what's being drawn +with this + + align:start position:0% +with this + + + align:start position:0% +with this +line + + align:start position:0% +line + + + align:start position:0% +line +namely + + align:start position:0% + + + + align:start position:0% + +expectation of x is a weighted + + align:start position:0% +expectation of x is a weighted + + + align:start position:0% +expectation of x is a weighted +combination of x0 and x1 + + align:start position:0% +combination of x0 and x1 + + + align:start position:0% +combination of x0 and x1 +given the expectation of x we could ask + + align:start position:0% +given the expectation of x we could ask + + + align:start position:0% +given the expectation of x we could ask +what the utility would be + + align:start position:0% +what the utility would be + + + align:start position:0% +what the utility would be +for that deterministic value and it + + align:start position:0% +for that deterministic value and it + + + align:start position:0% +for that deterministic value and it +would be + + align:start position:0% +would be + + + align:start position:0% +would be +we'd have to go up here if they were + + align:start position:0% +we'd have to go up here if they were + + + align:start position:0% +we'd have to go up here if they were +getting it for sure + + align:start position:0% +getting it for sure + + + align:start position:0% +getting it for sure +and over here and have the utility of + + align:start position:0% +and over here and have the utility of + + + align:start position:0% +and over here and have the utility of +the + + align:start position:0% +the + + + align:start position:0% +the +expectation of x + + align:start position:0% +expectation of x + + + align:start position:0% +expectation of x +that may be a funny place to start + + align:start position:0% +that may be a funny place to start + + + align:start position:0% +that may be a funny place to start +because there's a genuine lottery here + + align:start position:0% +because there's a genuine lottery here + + + align:start position:0% +because there's a genuine lottery here +and you can't get the mean for sure + + align:start position:0% +and you can't get the mean for sure + + + align:start position:0% +and you can't get the mean for sure +you have to engage in the lottery + + align:start position:0% +you have to engage in the lottery + + + align:start position:0% +you have to engage in the lottery +and sub for the randomness around the + + align:start position:0% +and sub for the randomness around the + + + align:start position:0% +and sub for the randomness around the +mean + + align:start position:0% +mean + + + align:start position:0% +mean +so + + align:start position:0% +so + + + align:start position:0% +so +what is the actual + + align:start position:0% +what is the actual + + + align:start position:0% +what is the actual +utility of the lottery well that can be + + align:start position:0% +utility of the lottery well that can be + + + align:start position:0% +utility of the lottery well that can be +achieved in this diagram + + align:start position:0% +achieved in this diagram + + + align:start position:0% +achieved in this diagram +by taking a weighted average of the + + align:start position:0% +by taking a weighted average of the + + + align:start position:0% +by taking a weighted average of the +utility of the extreme points here's the + + align:start position:0% +utility of the extreme points here's the + + + align:start position:0% +utility of the extreme points here's the +utility you would get for the high value + + align:start position:0% +utility you would get for the high value + + + align:start position:0% +utility you would get for the high value +x1 + + align:start position:0% +x1 + + + align:start position:0% +x1 +here's the utility you get for the low + + align:start position:0% +here's the utility you get for the low + + + align:start position:0% +here's the utility you get for the low +value x0 if you take a weighted average + + align:start position:0% +value x0 if you take a weighted average + + + align:start position:0% +value x0 if you take a weighted average +you'll be moving along this line you'll + + align:start position:0% +you'll be moving along this line you'll + + + align:start position:0% +you'll be moving along this line you'll +actually take this + + align:start position:0% +actually take this + + + align:start position:0% +actually take this +weighted average here + + align:start position:0% +weighted average here + + + align:start position:0% +weighted average here +that also determine the mean and go over + + align:start position:0% +that also determine the mean and go over + + + align:start position:0% +that also determine the mean and go over +here and plot the utility of the outcome + + align:start position:0% +here and plot the utility of the outcome + + + align:start position:0% +here and plot the utility of the outcome +so this is the expected utility under + + align:start position:0% +so this is the expected utility under + + + align:start position:0% +so this is the expected utility under +the actual lottery + + align:start position:0% +the actual lottery + + + align:start position:0% +the actual lottery +and it's just the appropriately weighted + + align:start position:0% +and it's just the appropriately weighted + + + align:start position:0% +and it's just the appropriately weighted +average of the utilities + + align:start position:0% +average of the utilities + + + align:start position:0% +average of the utilities +of the two extremes + + align:start position:0% +of the two extremes + + + align:start position:0% +of the two extremes +you're with me so far + + align:start position:0% +you're with me so far + + + align:start position:0% +you're with me so far +so + + align:start position:0% +so + + + align:start position:0% +so +as you can see + + align:start position:0% +as you can see + + + align:start position:0% +as you can see +if instead of suffering the lottery you + + align:start position:0% +if instead of suffering the lottery you + + + align:start position:0% +if instead of suffering the lottery you +gave this decision maker a deterministic + + align:start position:0% +gave this decision maker a deterministic + + + align:start position:0% +gave this decision maker a deterministic +value + + align:start position:0% +value + + + align:start position:0% +value +with the same utility level as the + + align:start position:0% +with the same utility level as the + + + align:start position:0% +with the same utility level as the +utility has under the lottery what would + + align:start position:0% +utility has under the lottery what would + + + align:start position:0% +utility has under the lottery what would +that value be that would be right here + + align:start position:0% +that value be that would be right here + + + align:start position:0% +that value be that would be right here +if you started with this value of x for + + align:start position:0% +if you started with this value of x for + + + align:start position:0% +if you started with this value of x for +sure + + align:start position:0% +sure + + + align:start position:0% +sure +and went up to the orange line + + align:start position:0% +and went up to the orange line + + + align:start position:0% +and went up to the orange line +you would get the utility uh there but + + align:start position:0% +you would get the utility uh there but + + + align:start position:0% +you would get the utility uh there but +that value of x is obviously a lot lower + + align:start position:0% +that value of x is obviously a lot lower + + + align:start position:0% +that value of x is obviously a lot lower +than the means this is called the + + align:start position:0% +than the means this is called the + + + align:start position:0% +than the means this is called the +certainty equivalent value of the + + align:start position:0% +certainty equivalent value of the + + + align:start position:0% +certainty equivalent value of the +lottery + + align:start position:0% +lottery + + + align:start position:0% +lottery +let me put it a bit differently + + align:start position:0% +let me put it a bit differently + + + align:start position:0% +let me put it a bit differently +if you + + align:start position:0% +if you + + + align:start position:0% +if you +told the household to choose between the + + align:start position:0% +told the household to choose between the + + + align:start position:0% +told the household to choose between the +lottery and a deterministic value with a + + align:start position:0% +lottery and a deterministic value with a + + + align:start position:0% +lottery and a deterministic value with a +mean less than the mean of the lottery + + align:start position:0% +mean less than the mean of the lottery + + + align:start position:0% +mean less than the mean of the lottery +they might choose the deterministic + + align:start position:0% +they might choose the deterministic + + + align:start position:0% +they might choose the deterministic +value as long as that value is not less + + align:start position:0% +value as long as that value is not less + + + align:start position:0% +value as long as that value is not less +than the risk premium + + align:start position:0% +than the risk premium + + + align:start position:0% +than the risk premium +anything here they would choose anything + + align:start position:0% +anything here they would choose anything + + + align:start position:0% +anything here they would choose anything +over here they would not right here they + + align:start position:0% +over here they would not right here they + + + align:start position:0% +over here they would not right here they +would be indifferent + + align:start position:0% +would be indifferent + + + align:start position:0% +would be indifferent +now as i think you can imagine + + align:start position:0% +now as i think you can imagine + + + align:start position:0% +now as i think you can imagine +if you + + align:start position:0% +if you + + + align:start position:0% +if you +increase the curvature of this function + + align:start position:0% +increase the curvature of this function + + + align:start position:0% +increase the curvature of this function +you're going to actually be lowering the + + align:start position:0% +you're going to actually be lowering the + + + align:start position:0% +you're going to actually be lowering the +expected utility of the lottery because + + align:start position:0% +expected utility of the lottery because + + + align:start position:0% +expected utility of the lottery because +there's more risk associated with it in + + align:start position:0% +there's more risk associated with it in + + + align:start position:0% +there's more risk associated with it in +the sense that you care more about the + + align:start position:0% +the sense that you care more about the + + + align:start position:0% +the sense that you care more about the +variance because your utility is more + + align:start position:0% +variance because your utility is more + + + align:start position:0% +variance because your utility is more +curved + + align:start position:0% +curved + + + align:start position:0% +curved +and that's going to change the certainty + + align:start position:0% +and that's going to change the certainty + + + align:start position:0% +and that's going to change the certainty +equivalent amount as well so from now on + + align:start position:0% +equivalent amount as well so from now on + + + align:start position:0% +equivalent amount as well so from now on +for much of the class we're going to be + + align:start position:0% +for much of the class we're going to be + + + align:start position:0% +for much of the class we're going to be +considering cardinal rather than ordinal + + align:start position:0% +considering cardinal rather than ordinal + + + align:start position:0% +considering cardinal rather than ordinal +utility + + align:start position:0% +utility + + + align:start position:0% +utility +what are standard measures of risk + + align:start position:0% +what are standard measures of risk + + + align:start position:0% +what are standard measures of risk +aversion + + align:start position:0% +aversion + + + align:start position:0% +aversion +there's something called absolute risk + + align:start position:0% +there's something called absolute risk + + + align:start position:0% +there's something called absolute risk +aversion + + align:start position:0% +aversion + + + align:start position:0% +aversion +and another thing called relative risk + + align:start position:0% +and another thing called relative risk + + + align:start position:0% +and another thing called relative risk +aversion + + align:start position:0% +aversion + + + align:start position:0% +aversion +absolute risk aversion has to do with + + align:start position:0% +absolute risk aversion has to do with + + + align:start position:0% +absolute risk aversion has to do with +how your marginal utility is changing + + align:start position:0% +how your marginal utility is changing + + + align:start position:0% +how your marginal utility is changing +as you change the reward + + align:start position:0% +as you change the reward + + + align:start position:0% +as you change the reward +the consumption + + align:start position:0% +the consumption + + + align:start position:0% +the consumption +and relative risk aversion has to do + + align:start position:0% +and relative risk aversion has to do + + + align:start position:0% +and relative risk aversion has to do +with how much utility is changing as you + + align:start position:0% +with how much utility is changing as you + + + align:start position:0% +with how much utility is changing as you +change the percentage of wealth that you + + align:start position:0% +change the percentage of wealth that you + + + align:start position:0% +change the percentage of wealth that you +have + + align:start position:0% +have + + + align:start position:0% +have +i'll spare you the derivations of all of + + align:start position:0% +i'll spare you the derivations of all of + + + align:start position:0% +i'll spare you the derivations of all of +this + + align:start position:0% +this + + + align:start position:0% +this +but i will show you some + + align:start position:0% +but i will show you some + + + align:start position:0% +but i will show you some +example utility functions that display + + align:start position:0% +example utility functions that display + + + align:start position:0% +example utility functions that display +either absolute risk aversion constant + + align:start position:0% +either absolute risk aversion constant + + + align:start position:0% +either absolute risk aversion constant +or + + align:start position:0% +or + + + align:start position:0% +or +uh relative risk conversion on the next + + align:start position:0% +uh relative risk conversion on the next + + + align:start position:0% +uh relative risk conversion on the next +slide + + align:start position:0% +slide + + + align:start position:0% +slide +so you know absolute risk aversion is + + align:start position:0% +so you know absolute risk aversion is + + + align:start position:0% +so you know absolute risk aversion is +sort of your willingness or not to take + + align:start position:0% +sort of your willingness or not to take + + + align:start position:0% +sort of your willingness or not to take +up gambles like starting with a hundred + + align:start position:0% +up gambles like starting with a hundred + + + align:start position:0% +up gambles like starting with a hundred +dollars and plus or minus 10 the lottery + + align:start position:0% +dollars and plus or minus 10 the lottery + + + align:start position:0% +dollars and plus or minus 10 the lottery +is from 110 to 90. + + align:start position:0% +is from 110 to 90. + + + align:start position:0% +is from 110 to 90. +the + + align:start position:0% +the + + + align:start position:0% +the +relative risk aversion has to do with + + align:start position:0% +relative risk aversion has to do with + + + align:start position:0% +relative risk aversion has to do with +proportional gambles you start with say + + align:start position:0% +proportional gambles you start with say + + + align:start position:0% +proportional gambles you start with say +a hundred + + align:start position:0% +a hundred + + + align:start position:0% +a hundred +and then have ten percent gains or + + align:start position:0% +and then have ten percent gains or + + + align:start position:0% +and then have ten percent gains or +losses that would be the same but you + + align:start position:0% +losses that would be the same but you + + + align:start position:0% +losses that would be the same but you +could start with a thousand and have ten + + align:start position:0% +could start with a thousand and have ten + + + align:start position:0% +could start with a thousand and have ten +percent gains and losses in which case + + align:start position:0% +percent gains and losses in which case + + + align:start position:0% +percent gains and losses in which case +you'd be facing a lottery that moves you + + align:start position:0% +you'd be facing a lottery that moves you + + + align:start position:0% +you'd be facing a lottery that moves you +from + + align:start position:0% +from + + + align:start position:0% +from +1100 to 900. + + align:start position:0% +1100 to 900. + + + align:start position:0% +1100 to 900. +under constant relative risk aversion + + align:start position:0% +under constant relative risk aversion + + + align:start position:0% +under constant relative risk aversion +all you care about are those percentage + + align:start position:0% +all you care about are those percentage + + + align:start position:0% +all you care about are those percentage +differences from your initial wealth + + align:start position:0% +differences from your initial wealth + + + align:start position:0% +differences from your initial wealth +under absolute risk aversion you + + align:start position:0% +under absolute risk aversion you + + + align:start position:0% +under absolute risk aversion you +actually don't like that new if you + + align:start position:0% +actually don't like that new if you + + + align:start position:0% +actually don't like that new if you +started with a thousand dollars as + + align:start position:0% +started with a thousand dollars as + + + align:start position:0% +started with a thousand dollars as +opposed to a hundred dollars your + + align:start position:0% +opposed to a hundred dollars your + + + align:start position:0% +opposed to a hundred dollars your +absolute risk aversion would actually be + + align:start position:0% +absolute risk aversion would actually be + + + align:start position:0% +absolute risk aversion would actually be +going down because of the curved utility + + align:start position:0% +going down because of the curved utility + + + align:start position:0% +going down because of the curved utility +you would be thinking about a lottery + + align:start position:0% +you would be thinking about a lottery + + + align:start position:0% +you would be thinking about a lottery +around the point that has less curvature + + align:start position:0% +around the point that has less curvature + + + align:start position:0% +around the point that has less curvature +attitudes toward risk do depend on these + + align:start position:0% +attitudes toward risk do depend on these + + + align:start position:0% +attitudes toward risk do depend on these +functions so here are the examples this + + align:start position:0% +functions so here are the examples this + + + align:start position:0% +functions so here are the examples this +one is constant absolute risk aversion + + align:start position:0% +one is constant absolute risk aversion + + + align:start position:0% +one is constant absolute risk aversion +constant absolute risk aversion + + align:start position:0% +constant absolute risk aversion + + + align:start position:0% +constant absolute risk aversion +and its exponential function + + align:start position:0% +and its exponential function + + + align:start position:0% +and its exponential function +look kind of weird at first because of + + align:start position:0% +look kind of weird at first because of + + + align:start position:0% +look kind of weird at first because of +all these negative signs + + align:start position:0% +all these negative signs + + + align:start position:0% +all these negative signs +say well exponential is positive yes so + + align:start position:0% +say well exponential is positive yes so + + + align:start position:0% +say well exponential is positive yes so +as c goes up utility's going down what + + align:start position:0% +as c goes up utility's going down what + + + align:start position:0% +as c goes up utility's going down what +the heck's going on here + + align:start position:0% +the heck's going on here + + + align:start position:0% +the heck's going on here +but the we put a negative sign in front + + align:start position:0% +but the we put a negative sign in front + + + align:start position:0% +but the we put a negative sign in front +of all of this to correct for that + + align:start position:0% +of all of this to correct for that + + + align:start position:0% +of all of this to correct for that +so you could take the derivative and the + + align:start position:0% +so you could take the derivative and the + + + align:start position:0% +so you could take the derivative and the +second derivative and verify that this + + align:start position:0% +second derivative and verify that this + + + align:start position:0% +second derivative and verify that this +function has constant absolute risk + + align:start position:0% +function has constant absolute risk + + + align:start position:0% +function has constant absolute risk +aversion and the order of magnitude is + + align:start position:0% +aversion and the order of magnitude is + + + align:start position:0% +aversion and the order of magnitude is +actually a + + align:start position:0% +actually a + + + align:start position:0% +actually a +or if you started down here we'd have + + align:start position:0% +or if you started down here we'd have + + + align:start position:0% +or if you started down here we'd have +constant relative risk aversion + + align:start position:0% +constant relative risk aversion + + + align:start position:0% +constant relative risk aversion +and you can verify if you did the math u + + align:start position:0% +and you can verify if you did the math u + + + align:start position:0% +and you can verify if you did the math u +prime over u double prime times c + + align:start position:0% +prime over u double prime times c + + + align:start position:0% +prime over u double prime times c +that you would get a number r so r is + + align:start position:0% +that you would get a number r so r is + + + align:start position:0% +that you would get a number r so r is +the constant + + align:start position:0% +the constant + + + align:start position:0% +the constant +level of of relative risk aversion under + + align:start position:0% +level of of relative risk aversion under + + + align:start position:0% +level of of relative risk aversion under +this function + + align:start position:0% +this function + + + align:start position:0% +this function +and we we often use these for different + + align:start position:0% +and we we often use these for different + + + align:start position:0% +and we we often use these for different +purposes + + align:start position:0% +purposes + + + align:start position:0% +purposes +they'll show up in in an application + + align:start position:0% +they'll show up in in an application + + + align:start position:0% +they'll show up in in an application +we'll get to in about i guess about four + + align:start position:0% +we'll get to in about i guess about four + + + align:start position:0% +we'll get to in about i guess about four +lectures + + align:start position:0% +lectures + + + align:start position:0% +lectures +let's talk some more about lotteries and + + align:start position:0% +let's talk some more about lotteries and + + + align:start position:0% +let's talk some more about lotteries and +uncertainty + + align:start position:0% +uncertainty + + + align:start position:0% +uncertainty +actually + + align:start position:0% +actually + + + align:start position:0% +actually +will now throw in not just uncertainty + + align:start position:0% +will now throw in not just uncertainty + + + align:start position:0% +will now throw in not just uncertainty +as in states of the world s but also + + align:start position:0% +as in states of the world s but also + + + align:start position:0% +as in states of the world s but also +time + + align:start position:0% +time + + + align:start position:0% +time +so time is evolving from day one to day + + align:start position:0% +so time is evolving from day one to day + + + align:start position:0% +so time is evolving from day one to day +two to day three so from the perspective + + align:start position:0% +two to day three so from the perspective + + + align:start position:0% +two to day three so from the perspective +of your initial starting point i zero + + align:start position:0% +of your initial starting point i zero + + + align:start position:0% +of your initial starting point i zero +you could experience a low or a high + + align:start position:0% +you could experience a low or a high + + + align:start position:0% +you could experience a low or a high +state at date one + + align:start position:0% +state at date one + + + align:start position:0% +state at date one +and if you're at date one + + align:start position:0% +and if you're at date one + + + align:start position:0% +and if you're at date one +you're still facing risk so you could go + + align:start position:0% +you're still facing risk so you could go + + + align:start position:0% +you're still facing risk so you could go +low or high from there + + align:start position:0% +low or high from there + + + align:start position:0% +low or high from there +if you went to medium + + align:start position:0% +if you went to medium + + + align:start position:0% +if you went to medium +then you could go and turn all over + + align:start position:0% +then you could go and turn all over + + + align:start position:0% +then you could go and turn all over +again from low medium to high + + align:start position:0% +again from low medium to high + + + align:start position:0% +again from low medium to high +these + + align:start position:0% +these + + + align:start position:0% +these +branches of the trees with the nodes + + align:start position:0% +branches of the trees with the nodes + + + align:start position:0% +branches of the trees with the nodes +reflect every possible realization and + + align:start position:0% +reflect every possible realization and + + + align:start position:0% +reflect every possible realization and +the path to get there + + align:start position:0% +the path to get there + + + align:start position:0% +the path to get there +from the standpoint of expected utility + + align:start position:0% +from the standpoint of expected utility + + + align:start position:0% +from the standpoint of expected utility +we would start here + + align:start position:0% +we would start here + + + align:start position:0% +we would start here +ex-ante + + align:start position:0% +ex-ante + + + align:start position:0% +ex-ante +before anything happens at all + + align:start position:0% +before anything happens at all + + + align:start position:0% +before anything happens at all +and trace the probabilities at date one + + align:start position:0% +and trace the probabilities at date one + + + align:start position:0% +and trace the probabilities at date one +you get this or this or this with + + align:start position:0% +you get this or this or this with + + + align:start position:0% +you get this or this or this with +certain probabilities pi of s1 given s0 + + align:start position:0% +certain probabilities pi of s1 given s0 + + + align:start position:0% +certain probabilities pi of s1 given s0 +but you'd also take into account day two + + align:start position:0% +but you'd also take into account day two + + + align:start position:0% +but you'd also take into account day two +so you take the expectation of being + + align:start position:0% +so you take the expectation of being + + + align:start position:0% +so you take the expectation of being +here or here + + align:start position:0% +here or here + + + align:start position:0% +here or here +or any of these intermediate branches + + align:start position:0% +or any of these intermediate branches + + + align:start position:0% +or any of these intermediate branches +and finally you'd have to add in the day + + align:start position:0% +and finally you'd have to add in the day + + + align:start position:0% +and finally you'd have to add in the day +three where the all these events at the + + align:start position:0% +three where the all these events at the + + + align:start position:0% +three where the all these events at the +thinnest branches of the tree could come + + align:start position:0% +thinnest branches of the tree could come + + + align:start position:0% +thinnest branches of the tree could come +to pass + + align:start position:0% +to pass + + + align:start position:0% +to pass +if there's anything counterintuitive + + align:start position:0% +if there's anything counterintuitive + + + align:start position:0% +if there's anything counterintuitive +about this diagram it is that when some + + align:start position:0% +about this diagram it is that when some + + + align:start position:0% +about this diagram it is that when some +things happen other things don't happen + + align:start position:0% +things happen other things don't happen + + + align:start position:0% +things happen other things don't happen +so when you're over here and move left + + align:start position:0% +so when you're over here and move left + + + align:start position:0% +so when you're over here and move left +you've eliminated you know the other two + + align:start position:0% +you've eliminated you know the other two + + + align:start position:0% +you've eliminated you know the other two +branches of the tree if you took + + align:start position:0% +branches of the tree if you took + + + align:start position:0% +branches of the tree if you took +expected utility from date one onward + + align:start position:0% +expected utility from date one onward + + + align:start position:0% +expected utility from date one onward +you would just be taking into account + + align:start position:0% +you would just be taking into account + + + align:start position:0% +you would just be taking into account +what's left that could potentially + + align:start position:0% +what's left that could potentially + + + align:start position:0% +what's left that could potentially +happen at random but this criterion down + + align:start position:0% +happen at random but this criterion down + + + align:start position:0% +happen at random but this criterion down +here is taking expected utility as if + + align:start position:0% +here is taking expected utility as if + + + align:start position:0% +here is taking expected utility as if +nothing yet has happened at all + + align:start position:0% +nothing yet has happened at all + + + align:start position:0% +nothing yet has happened at all +so so taking into account all the + + align:start position:0% +so so taking into account all the + + + align:start position:0% +so so taking into account all the +possible events at day one at day two + + align:start position:0% +possible events at day one at day two + + + align:start position:0% +possible events at day one at day two +and day three + + align:start position:0% +and day three + + + align:start position:0% +and day three +so + + align:start position:0% +so + + + align:start position:0% +so +we can kind of immediately get to a + + align:start position:0% +we can kind of immediately get to a + + + align:start position:0% +we can kind of immediately get to a +building block + + align:start position:0% +building block + + + align:start position:0% +building block +that's crucial to understand finance and + + align:start position:0% +that's crucial to understand finance and + + + align:start position:0% +that's crucial to understand finance and +financial markets and that's the notion + + align:start position:0% +financial markets and that's the notion + + + align:start position:0% +financial markets and that's the notion +of a state contingent commodity + + align:start position:0% +of a state contingent commodity + + + align:start position:0% +of a state contingent commodity +we've already been doing it a state + + align:start position:0% +we've already been doing it a state + + + align:start position:0% +we've already been doing it a state +contingent commodity with only one date + + align:start position:0% +contingent commodity with only one date + + + align:start position:0% +contingent commodity with only one date +would be the probability of getting a + + align:start position:0% +would be the probability of getting a + + + align:start position:0% +would be the probability of getting a +certain + + align:start position:0% +certain + + + align:start position:0% +certain +wealth payoff or a certain + + align:start position:0% +wealth payoff or a certain + + + align:start position:0% +wealth payoff or a certain +xy combination of goods and so on so we + + align:start position:0% +xy combination of goods and so on so we + + + align:start position:0% +xy combination of goods and so on so we +what you get depends on the state + + align:start position:0% +what you get depends on the state + + + align:start position:0% +what you get depends on the state +commodity bundle you get depends on the + + align:start position:0% +commodity bundle you get depends on the + + + align:start position:0% +commodity bundle you get depends on the +state we call it state contingent + + align:start position:0% +state we call it state contingent + + + align:start position:0% +state we call it state contingent +you get + + align:start position:0% +you get + + + align:start position:0% +you get +wheat tomorrow if it rains but nothing + + align:start position:0% +wheat tomorrow if it rains but nothing + + + align:start position:0% +wheat tomorrow if it rains but nothing +otherwise + + align:start position:0% +otherwise + + + align:start position:0% +otherwise +and we imagine you can actually buy + + align:start position:0% +and we imagine you can actually buy + + + align:start position:0% +and we imagine you can actually buy +these kinds of contingent payoff + + align:start position:0% +these kinds of contingent payoff + + + align:start position:0% +these kinds of contingent payoff +securities + + align:start position:0% +securities + + + align:start position:0% +securities +in the financial markets + + align:start position:0% +in the financial markets + + + align:start position:0% +in the financial markets +however a much better way to put that is + + align:start position:0% +however a much better way to put that is + + + align:start position:0% +however a much better way to put that is +any financial security is a weighted + + align:start position:0% +any financial security is a weighted + + + align:start position:0% +any financial security is a weighted +average probabilistic weighted average + + align:start position:0% +average probabilistic weighted average + + + align:start position:0% +average probabilistic weighted average +over all possible events + + align:start position:0% +over all possible events + + + align:start position:0% +over all possible events +for example + + align:start position:0% +for example + + + align:start position:0% +for example +you're an investor and you buy and + + align:start position:0% +you're an investor and you buy and + + + align:start position:0% +you're an investor and you buy and +someone's lending to you and let's + + align:start position:0% +someone's lending to you and let's + + + align:start position:0% +someone's lending to you and let's +imagine they're never going to default + + align:start position:0% +imagine they're never going to default + + + align:start position:0% +imagine they're never going to default +then you're going to get that money back + + align:start position:0% +then you're going to get that money back + + + align:start position:0% +then you're going to get that money back +for sure in which case it's not risky + + align:start position:0% +for sure in which case it's not risky + + + align:start position:0% +for sure in which case it's not risky +anymore but that's only because the + + align:start position:0% +anymore but that's only because the + + + align:start position:0% +anymore but that's only because the +event is the same + + align:start position:0% +event is the same + + + align:start position:0% +event is the same +or + + align:start position:0% +or + + + align:start position:0% +or +you could have something like a stock + + align:start position:0% +you could have something like a stock + + + align:start position:0% +you could have something like a stock +option so that it doesn't come in to + + align:start position:0% +option so that it doesn't come in to + + + align:start position:0% +option so that it doesn't come in to +play unless the stock prices are + + align:start position:0% +play unless the stock prices are + + + align:start position:0% +play unless the stock prices are +particularly high and you execute the + + align:start position:0% +particularly high and you execute the + + + align:start position:0% +particularly high and you execute the +option so all possible securities can be + + align:start position:0% +option so all possible securities can be + + + align:start position:0% +option so all possible securities can be +represented as linear combinations of + + align:start position:0% +represented as linear combinations of + + + align:start position:0% +represented as linear combinations of +these primitive aero debrew securities + + align:start position:0% +these primitive aero debrew securities + + + align:start position:0% +these primitive aero debrew securities +primitive in the sense that they + + align:start position:0% +primitive in the sense that they + + + align:start position:0% +primitive in the sense that they +building blocks only pay off in the + + align:start position:0% +building blocks only pay off in the + + + align:start position:0% +building blocks only pay off in the +event of one well-delineated event and + + align:start position:0% +event of one well-delineated event and + + + align:start position:0% +event of one well-delineated event and +zero otherwise so when we get to + + align:start position:0% +zero otherwise so when we get to + + + align:start position:0% +zero otherwise so when we get to +competitive markets and how to handle + + align:start position:0% +competitive markets and how to handle + + + align:start position:0% +competitive markets and how to handle +uncertainty will come back to these + + align:start position:0% +uncertainty will come back to these + + + align:start position:0% +uncertainty will come back to these +state contingent commodities + + align:start position:0% +state contingent commodities + + + align:start position:0% +state contingent commodities +okay so let's move + + align:start position:0% +okay so let's move + + + align:start position:0% +okay so let's move +to an application of various of these + + align:start position:0% +to an application of various of these + + + align:start position:0% +to an application of various of these +things + + align:start position:0% +things + + + align:start position:0% +things +one + + align:start position:0% +one + + + align:start position:0% +one +lotteries two random variables three uh + + align:start position:0% +lotteries two random variables three uh + + + align:start position:0% +lotteries two random variables three uh +diversification of portfolios except in + + align:start position:0% +diversification of portfolios except in + + + align:start position:0% +diversification of portfolios except in +this case they're not going to be + + align:start position:0% +this case they're not going to be + + + align:start position:0% +this case they're not going to be +trading financial assets they're going + + align:start position:0% +trading financial assets they're going + + + align:start position:0% +trading financial assets they're going +to be holding plots of land so the next + + align:start position:0% +to be holding plots of land so the next + + + align:start position:0% +to be holding plots of land so the next +map i'm going to show you is a village + + align:start position:0% +map i'm going to show you is a village + + + align:start position:0% +map i'm going to show you is a village +of elford in stratfordshire england in + + align:start position:0% +of elford in stratfordshire england in + + + align:start position:0% +of elford in stratfordshire england in +1719 before enclosures + + align:start position:0% +1719 before enclosures + + + align:start position:0% +1719 before enclosures +and + + align:start position:0% +and + + + align:start position:0% +and +shaded in black are the holdings of mr + + align:start position:0% +shaded in black are the holdings of mr + + + align:start position:0% +shaded in black are the holdings of mr +darlistan so here's that village alfred + + align:start position:0% +darlistan so here's that village alfred + + + align:start position:0% +darlistan so here's that village alfred +stratfordshire and you have to look a + + align:start position:0% +stratfordshire and you have to look a + + + align:start position:0% +stratfordshire and you have to look a +little close + + align:start position:0% +little close + + + align:start position:0% +little close +but you see these darker areas they are + + align:start position:0% +but you see these darker areas they are + + + align:start position:0% +but you see these darker areas they are +shaded in and represent the holdings of + + align:start position:0% +shaded in and represent the holdings of + + + align:start position:0% +shaded in and represent the holdings of +mr darlison + + align:start position:0% +mr darlison + + + align:start position:0% +mr darlison +mr darlistan has these long narrow + + align:start position:0% +mr darlistan has these long narrow + + + align:start position:0% +mr darlistan has these long narrow +strips of land all over the village in + + align:start position:0% +strips of land all over the village in + + + align:start position:0% +strips of land all over the village in +all the three fields and you could well + + align:start position:0% +all the three fields and you could well + + + align:start position:0% +all the three fields and you could well +think about that as a portfolio of land + + align:start position:0% +think about that as a portfolio of land + + + align:start position:0% +think about that as a portfolio of land +holdings and in some respects a + + align:start position:0% +holdings and in some respects a + + + align:start position:0% +holdings and in some respects a +portfolio of securities where in this + + align:start position:0% +portfolio of securities where in this + + + align:start position:0% +portfolio of securities where in this +case the holding of land + + align:start position:0% +case the holding of land + + + align:start position:0% +case the holding of land +yields a dividend which is the harvest + + align:start position:0% +yields a dividend which is the harvest + + + align:start position:0% +yields a dividend which is the harvest +and you may well surmise there's some + + align:start position:0% +and you may well surmise there's some + + + align:start position:0% +and you may well surmise there's some +risk here or they're weird people + + align:start position:0% +risk here or they're weird people + + + align:start position:0% +risk here or they're weird people +because why else would they be doing + + align:start position:0% +because why else would they be doing + + + align:start position:0% +because why else would they be doing +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +here's another view of + + align:start position:0% +here's another view of + + + align:start position:0% +here's another view of +the village of laxton i should at least + + align:start position:0% +the village of laxton i should at least + + + align:start position:0% +the village of laxton i should at least +tell you what enclosures are + + align:start position:0% +tell you what enclosures are + + + align:start position:0% +tell you what enclosures are +given the way this land was spread out + + align:start position:0% +given the way this land was spread out + + + align:start position:0% +given the way this land was spread out +it was + + align:start position:0% +it was + + + align:start position:0% +it was +impractical to put fences up that would + + align:start position:0% +impractical to put fences up that would + + + align:start position:0% +impractical to put fences up that would +mark the division of the boundary of all + + align:start position:0% +mark the division of the boundary of all + + + align:start position:0% +mark the division of the boundary of all +these various strips it would have been + + align:start position:0% +these various strips it would have been + + + align:start position:0% +these various strips it would have been +very costly to put up the fences and + + align:start position:0% +very costly to put up the fences and + + + align:start position:0% +very costly to put up the fences and +very difficult to plow see the little + + align:start position:0% +very difficult to plow see the little + + + align:start position:0% +very difficult to plow see the little +plows here + + align:start position:0% +plows here + + + align:start position:0% +plows here +eventual enclosures meant + + align:start position:0% +eventual enclosures meant + + + align:start position:0% +eventual enclosures meant +they put + + align:start position:0% +they put + + + align:start position:0% +they put +they divided it up they got rid of the + + align:start position:0% +they divided it up they got rid of the + + + align:start position:0% +they divided it up they got rid of the +air and divided up the land in a + + align:start position:0% +air and divided up the land in a + + + align:start position:0% +air and divided up the land in a +different way just put fences around the + + align:start position:0% +different way just put fences around the + + + align:start position:0% +different way just put fences around the +consolidated pieces of land but they + + align:start position:0% +consolidated pieces of land but they + + + align:start position:0% +consolidated pieces of land but they +didn't do that for hundreds of years + + align:start position:0% +didn't do that for hundreds of years + + + align:start position:0% +didn't do that for hundreds of years +they they kept the scrat the scattered + + align:start position:0% +they they kept the scrat the scattered + + + align:start position:0% +they they kept the scrat the scattered +strips for quite a long time + + align:start position:0% +strips for quite a long time + + + align:start position:0% +strips for quite a long time +okay so let's uh move to the data the + + align:start position:0% +okay so let's uh move to the data the + + + align:start position:0% +okay so let's uh move to the data the +data we have from this period of time + + align:start position:0% +data we have from this period of time + + + align:start position:0% +data we have from this period of time +is from the bishop of winchester + + align:start position:0% +is from the bishop of winchester + + + align:start position:0% +is from the bishop of winchester +the church was wealthy + + align:start position:0% +the church was wealthy + + + align:start position:0% +the church was wealthy +and they kept records so this is what + + align:start position:0% +and they kept records so this is what + + + align:start position:0% +and they kept records so this is what +survives + + align:start position:0% +survives + + + align:start position:0% +survives +the holdings of the bishop of winchester + + align:start position:0% +the holdings of the bishop of winchester + + + align:start position:0% +the holdings of the bishop of winchester +called domains + + align:start position:0% +called domains + + + align:start position:0% +called domains +the crops being wheat barley and oats + + align:start position:0% +the crops being wheat barley and oats + + + align:start position:0% +the crops being wheat barley and oats +various types of grains and these + + align:start position:0% +various types of grains and these + + + align:start position:0% +various types of grains and these +objects denote say + + align:start position:0% +objects denote say + + + align:start position:0% +objects denote say +the coefficient of variation which i've + + align:start position:0% +the coefficient of variation which i've + + + align:start position:0% +the coefficient of variation which i've +alerted you is the variance divided by + + align:start position:0% +alerted you is the variance divided by + + + align:start position:0% +alerted you is the variance divided by +the mean + + align:start position:0% +the mean + + + align:start position:0% +the mean +standard deviation divided by the mean + + align:start position:0% +standard deviation divided by the mean + + + align:start position:0% +standard deviation divided by the mean +so this number say 0.35 is in the middle + + align:start position:0% +so this number say 0.35 is in the middle + + + align:start position:0% +so this number say 0.35 is in the middle +of the two others actually it's a bit on + + align:start position:0% +of the two others actually it's a bit on + + + align:start position:0% +of the two others actually it's a bit on +the lower end even at 0.35 + + align:start position:0% +the lower end even at 0.35 + + + align:start position:0% +the lower end even at 0.35 +the coefficient of variation of that + + align:start position:0% +the coefficient of variation of that + + + align:start position:0% +the coefficient of variation of that +magnitude is a lot of risk so + + align:start position:0% +magnitude is a lot of risk so + + + align:start position:0% +magnitude is a lot of risk so +let's look at the picture + + align:start position:0% +let's look at the picture + + + align:start position:0% +let's look at the picture +if we have + + align:start position:0% +if we have + + + align:start position:0% +if we have +those scattered plots those strips + + align:start position:0% +those scattered plots those strips + + + align:start position:0% +those scattered plots those strips +we could plot the entire distribution of + + align:start position:0% +we could plot the entire distribution of + + + align:start position:0% +we could plot the entire distribution of +outcomes with their probabilities + + align:start position:0% +outcomes with their probabilities + + + align:start position:0% +outcomes with their probabilities +we could denote the mean mu sub s for + + align:start position:0% +we could denote the mean mu sub s for + + + align:start position:0% +we could denote the mean mu sub s for +scattered plots + + align:start position:0% +scattered plots + + + align:start position:0% +scattered plots +and then we have disastrous events so d + + align:start position:0% +and then we have disastrous events so d + + + align:start position:0% +and then we have disastrous events so d +represents sort of minimal subsistence + + align:start position:0% +represents sort of minimal subsistence + + + align:start position:0% +represents sort of minimal subsistence +consumption + + align:start position:0% +consumption + + + align:start position:0% +consumption +and if you have these scattered plots + + align:start position:0% +and if you have these scattered plots + + + align:start position:0% +and if you have these scattered plots +with that coefficient of variation of + + align:start position:0% +with that coefficient of variation of + + + align:start position:0% +with that coefficient of variation of +0.35 + + align:start position:0% +0.35 + + + align:start position:0% +0.35 +then roughly + + align:start position:0% +then roughly + + + align:start position:0% +then roughly +one in every 12 years you get a very low + + align:start position:0% +one in every 12 years you get a very low + + + align:start position:0% +one in every 12 years you get a very low +yield but less than two times uh two + + align:start position:0% +yield but less than two times uh two + + + align:start position:0% +yield but less than two times uh two +standard deviations below the mean and + + align:start position:0% +standard deviations below the mean and + + + align:start position:0% +standard deviations below the mean and +that's starvation and they were starving + + align:start position:0% +that's starvation and they were starving + + + align:start position:0% +that's starvation and they were starving +we know this periodically every 12 years + + align:start position:0% +we know this periodically every 12 years + + + align:start position:0% +we know this periodically every 12 years +or so not like clockwork but on average + + align:start position:0% +or so not like clockwork but on average + + + align:start position:0% +or so not like clockwork but on average +every 12 years now could they have done + + align:start position:0% +every 12 years now could they have done + + + align:start position:0% +every 12 years now could they have done +something different they could have + + align:start position:0% +something different they could have + + + align:start position:0% +something different they could have +consolidated the land + + align:start position:0% +consolidated the land + + + align:start position:0% +consolidated the land +and uh that would have gotten rid of + + align:start position:0% +and uh that would have gotten rid of + + + align:start position:0% +and uh that would have gotten rid of +certain costs and problems that would + + align:start position:0% +certain costs and problems that would + + + align:start position:0% +certain costs and problems that would +have + + align:start position:0% +have + + + align:start position:0% +have +moved up the mean + + align:start position:0% +moved up the mean + + + align:start position:0% +moved up the mean +but you'd be left with more mass in the + + align:start position:0% +but you'd be left with more mass in the + + + align:start position:0% +but you'd be left with more mass in the +tails + + align:start position:0% +tails + + + align:start position:0% +tails +and hence a higher probability of having + + align:start position:0% +and hence a higher probability of having + + + align:start position:0% +and hence a higher probability of having +a yield that was disastrous + + align:start position:0% +a yield that was disastrous + + + align:start position:0% +a yield that was disastrous +so the reason that they're spreading out + + align:start position:0% +so the reason that they're spreading out + + + align:start position:0% +so the reason that they're spreading out +the land like that despite costs has to + + align:start position:0% +the land like that despite costs has to + + + align:start position:0% +the land like that despite costs has to +do with trying to increase their + + align:start position:0% +do with trying to increase their + + + align:start position:0% +do with trying to increase their +expected utility by putting less mass in + + align:start position:0% +expected utility by putting less mass in + + + align:start position:0% +expected utility by putting less mass in +the tails + + align:start position:0% +the tails + + + align:start position:0% +the tails +also from the bishop of + + align:start position:0% +also from the bishop of + + + align:start position:0% +also from the bishop of +winchester estates + + align:start position:0% +winchester estates + + + align:start position:0% +winchester estates +which you can hardly see here this + + align:start position:0% +which you can hardly see here this + + + align:start position:0% +which you can hardly see here this +believe it or not is southern england + + align:start position:0% +believe it or not is southern england + + + align:start position:0% +believe it or not is southern england +this is the water down here + + align:start position:0% +this is the water down here + + + align:start position:0% +this is the water down here +and each one of these dots represents an + + align:start position:0% +and each one of these dots represents an + + + align:start position:0% +and each one of these dots represents an +ecclesiastical estate + + align:start position:0% +ecclesiastical estate + + + align:start position:0% +ecclesiastical estate +and we have the data of the yields the + + align:start position:0% +and we have the data of the yields the + + + align:start position:0% +and we have the data of the yields the +harvest yields + + align:start position:0% +harvest yields + + + align:start position:0% +harvest yields +in this case the cover the correlation + + align:start position:0% +in this case the cover the correlation + + + align:start position:0% +in this case the cover the correlation +the statistical concept we were chatting + + align:start position:0% +the statistical concept we were chatting + + + align:start position:0% +the statistical concept we were chatting +about earlier is what is being plotted + + align:start position:0% +about earlier is what is being plotted + + + align:start position:0% +about earlier is what is being plotted +here for + + align:start position:0% +here for + + + align:start position:0% +here for +villages that are relatively + + align:start position:0% +villages that are relatively + + + align:start position:0% +villages that are relatively +near to one another and villages that + + align:start position:0% +near to one another and villages that + + + align:start position:0% +near to one another and villages that +are relatively far away so b means near + + align:start position:0% +are relatively far away so b means near + + + align:start position:0% +are relatively far away so b means near +sorry it's hard to read the legend + + align:start position:0% +sorry it's hard to read the legend + + + align:start position:0% +sorry it's hard to read the legend +and so + + align:start position:0% +and so + + + align:start position:0% +and so +take two villages pairwise look at the + + align:start position:0% +take two villages pairwise look at the + + + align:start position:0% +take two villages pairwise look at the +correlation across the two villages it's + + align:start position:0% +correlation across the two villages it's + + + align:start position:0% +correlation across the two villages it's +0.68 on average picking villages that + + align:start position:0% +0.68 on average picking villages that + + + align:start position:0% +0.68 on average picking villages that +are near + + align:start position:0% +are near + + + align:start position:0% +are near +and if you have villages that are far + + align:start position:0% +and if you have villages that are far + + + align:start position:0% +and if you have villages that are far +away from other one another that + + align:start position:0% +away from other one another that + + + align:start position:0% +away from other one another that +correlation drops to something lower so + + align:start position:0% +correlation drops to something lower so + + + align:start position:0% +correlation drops to something lower so +the yields are not moving as much + + align:start position:0% +the yields are not moving as much + + + align:start position:0% +the yields are not moving as much +together so again if you were the bishop + + align:start position:0% +together so again if you were the bishop + + + align:start position:0% +together so again if you were the bishop +of winchester + + align:start position:0% +of winchester + + + align:start position:0% +of winchester +maybe you chose the location of your + + align:start position:0% +maybe you chose the location of your + + + align:start position:0% +maybe you chose the location of your +estates in order to try to ensure + + align:start position:0% +estates in order to try to ensure + + + align:start position:0% +estates in order to try to ensure +yourself of having somewhat regular + + align:start position:0% +yourself of having somewhat regular + + + align:start position:0% +yourself of having somewhat regular +grain for harvest for eating and to feed + + align:start position:0% +grain for harvest for eating and to feed + + + align:start position:0% +grain for harvest for eating and to feed +the horses and and so on + + align:start position:0% +the horses and and so on + + + align:start position:0% +the horses and and so on +horses are serious by the way that's the + + align:start position:0% +horses are serious by the way that's the + + + align:start position:0% +horses are serious by the way that's the +calvary that's the the main defense so + + align:start position:0% +calvary that's the the main defense so + + + align:start position:0% +calvary that's the the main defense so +they needed to keep them alive + + align:start position:0% +they needed to keep them alive + + + align:start position:0% +they needed to keep them alive +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then we come to + + align:start position:0% +then we come to + + + align:start position:0% +then we come to +a technique + + align:start position:0% +a technique + + + align:start position:0% +a technique +which we've kind of already been using + + align:start position:0% +which we've kind of already been using + + + align:start position:0% +which we've kind of already been using +but but let's do it from scratch + + align:start position:0% +but but let's do it from scratch + + + align:start position:0% +but but let's do it from scratch +and that's called uh linear programming + + align:start position:0% +and that's called uh linear programming + + + align:start position:0% +and that's called uh linear programming +so this is a linear programming problem + + align:start position:0% +so this is a linear programming problem + + + align:start position:0% +so this is a linear programming problem +x is the control variable a vector + + align:start position:0% +x is the control variable a vector + + + align:start position:0% +x is the control variable a vector +this + + align:start position:0% +this + + + align:start position:0% +this +say column vector these constants + + align:start position:0% +say column vector these constants + + + align:start position:0% +say column vector these constants +coefficients c + + align:start position:0% +coefficients c + + + align:start position:0% +coefficients c +uh represent a row vector + + align:start position:0% +uh represent a row vector + + + align:start position:0% +uh represent a row vector +so these are weights on the various x + + align:start position:0% +so these are weights on the various x + + + align:start position:0% +so these are weights on the various x +values + + align:start position:0% +values + + + align:start position:0% +values +this is a set of constraints + + align:start position:0% +this is a set of constraints + + + align:start position:0% +this is a set of constraints +which is this matrix a times x less than + + align:start position:0% +which is this matrix a times x less than + + + align:start position:0% +which is this matrix a times x less than +or equal to b and the x's are + + align:start position:0% +or equal to b and the x's are + + + align:start position:0% +or equal to b and the x's are +non-negative + + align:start position:0% +non-negative + + + align:start position:0% +non-negative +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +notation + + align:start position:0% +notation + + + align:start position:0% +notation +for a standard linear program + + align:start position:0% +for a standard linear program + + + align:start position:0% +for a standard linear program +namely + + align:start position:0% +namely + + + align:start position:0% +namely +the objective function + + align:start position:0% +the objective function + + + align:start position:0% +the objective function +and the constrained sets just represent + + align:start position:0% +and the constrained sets just represent + + + align:start position:0% +and the constrained sets just represent +linear combinations of the control + + align:start position:0% +linear combinations of the control + + + align:start position:0% +linear combinations of the control +variables x + + align:start position:0% +variables x + + + align:start position:0% +variables x +i had this in the back of my head when + + align:start position:0% +i had this in the back of my head when + + + align:start position:0% +i had this in the back of my head when +we were talking about the leonty of + + align:start position:0% +we were talking about the leonty of + + + align:start position:0% +we were talking about the leonty of +input output matrix and i said in words + + align:start position:0% +input output matrix and i said in words + + + align:start position:0% +input output matrix and i said in words +instead of taking final demand d as + + align:start position:0% +instead of taking final demand d as + + + align:start position:0% +instead of taking final demand d as +given + + align:start position:0% +given + + + align:start position:0% +given +maybe it's a weighted average of demands + + align:start position:0% +maybe it's a weighted average of demands + + + align:start position:0% +maybe it's a weighted average of demands +that you're trying to maximize and you + + align:start position:0% +that you're trying to maximize and you + + + align:start position:0% +that you're trying to maximize and you +actually have a choice of various + + align:start position:0% +actually have a choice of various + + + align:start position:0% +actually have a choice of various +production modes to maximize that + + align:start position:0% +production modes to maximize that + + + align:start position:0% +production modes to maximize that +weighted average so we actually saw an + + align:start position:0% +weighted average so we actually saw an + + + align:start position:0% +weighted average so we actually saw an +early version of a linear programming + + align:start position:0% +early version of a linear programming + + + align:start position:0% +early version of a linear programming +problem but the objective function was + + align:start position:0% +problem but the objective function was + + + align:start position:0% +problem but the objective function was +not made explicit + + align:start position:0% +not made explicit + + + align:start position:0% +not made explicit +this would be the consumer choice + + align:start position:0% +this would be the consumer choice + + + align:start position:0% +this would be the consumer choice +problem in a competitive environment so + + align:start position:0% +problem in a competitive environment so + + + align:start position:0% +problem in a competitive environment so +where there's a budget constraint so + + align:start position:0% +where there's a budget constraint so + + + align:start position:0% +where there's a budget constraint so +these discrete points commodity points c + + align:start position:0% +these discrete points commodity points c + + + align:start position:0% +these discrete points commodity points c +denote + + align:start position:0% +denote + + + align:start position:0% +denote +subscript s varying over + + align:start position:0% +subscript s varying over + + + align:start position:0% +subscript s varying over +capital s states of the world + + align:start position:0% +capital s states of the world + + + align:start position:0% +capital s states of the world +was the expected utility + + align:start position:0% +was the expected utility + + + align:start position:0% +was the expected utility +criterion + + align:start position:0% +criterion + + + align:start position:0% +criterion +so that's the objective function + + align:start position:0% +so that's the objective function + + + align:start position:0% +so that's the objective function +by choice of lotteries so the lotteries + + align:start position:0% +by choice of lotteries so the lotteries + + + align:start position:0% +by choice of lotteries so the lotteries +are non-negative and add up to one to + + align:start position:0% +are non-negative and add up to one to + + + align:start position:0% +are non-negative and add up to one to +qualify as a lottery any given lottery + + align:start position:0% +qualify as a lottery any given lottery + + + align:start position:0% +qualify as a lottery any given lottery +has to satisfy those two criteria + + align:start position:0% +has to satisfy those two criteria + + + align:start position:0% +has to satisfy those two criteria +the choice object as i said to belabor + + align:start position:0% +the choice object as i said to belabor + + + align:start position:0% +the choice object as i said to belabor +it is not c of s + + align:start position:0% +it is not c of s + + + align:start position:0% +it is not c of s +those are fixed commodity points the + + align:start position:0% +those are fixed commodity points the + + + align:start position:0% +those are fixed commodity points the +choice object are the pi's + + align:start position:0% +choice object are the pi's + + + align:start position:0% +choice object are the pi's +and we'll talk about a budget problem + + align:start position:0% +and we'll talk about a budget problem + + + align:start position:0% +and we'll talk about a budget problem +which is there are prices p depending on + + align:start position:0% +which is there are prices p depending on + + + align:start position:0% +which is there are prices p depending on +s that is to say depending on the + + align:start position:0% +s that is to say depending on the + + + align:start position:0% +s that is to say depending on the +underlying discrete bundle quite + + align:start position:0% +underlying discrete bundle quite + + + align:start position:0% +underlying discrete bundle quite +naturally + + align:start position:0% +naturally + + + align:start position:0% +naturally +and you've got a budget in dollars that + + align:start position:0% +and you've got a budget in dollars that + + + align:start position:0% +and you've got a budget in dollars that +you can use to buy a lottery + + align:start position:0% +you can use to buy a lottery + + + align:start position:0% +you can use to buy a lottery +but if the probability is non-trivial + + align:start position:0% +but if the probability is non-trivial + + + align:start position:0% +but if the probability is non-trivial +it's a number less than one and greater + + align:start position:0% +it's a number less than one and greater + + + align:start position:0% +it's a number less than one and greater +than zero + + align:start position:0% +than zero + + + align:start position:0% +than zero +then you scale the price of getting that + + align:start position:0% +then you scale the price of getting that + + + align:start position:0% +then you scale the price of getting that +bundle s back by pi in other words + + align:start position:0% +bundle s back by pi in other words + + + align:start position:0% +bundle s back by pi in other words +you're kind of paying the expected price + + align:start position:0% +you're kind of paying the expected price + + + align:start position:0% +you're kind of paying the expected price +if pi s were one then you're buying + + align:start position:0% +if pi s were one then you're buying + + + align:start position:0% +if pi s were one then you're buying +cs for sure + + align:start position:0% +cs for sure + + + align:start position:0% +cs for sure +and the price would be ps and that would + + align:start position:0% +and the price would be ps and that would + + + align:start position:0% +and the price would be ps and that would +look like you know the standard price + + align:start position:0% +look like you know the standard price + + + align:start position:0% +look like you know the standard price +times quantity cannot exceed the budget + + align:start position:0% +times quantity cannot exceed the budget + + + align:start position:0% +times quantity cannot exceed the budget +but here what you're buying is a lottery + + align:start position:0% +but here what you're buying is a lottery + + + align:start position:0% +but here what you're buying is a lottery +and the lottery can have non-degel + + align:start position:0% +and the lottery can have non-degel + + + align:start position:0% +and the lottery can have non-degel +degenerate elements we have to decide + + align:start position:0% +degenerate elements we have to decide + + + align:start position:0% +degenerate elements we have to decide +how you would be paying for what you + + align:start position:0% +how you would be paying for what you + + + align:start position:0% +how you would be paying for what you +would be paying if you were buying a + + align:start position:0% +would be paying if you were buying a + + + align:start position:0% +would be paying if you were buying a +lottery which were non-degenerate and + + align:start position:0% +lottery which were non-degenerate and + + + align:start position:0% +lottery which were non-degenerate and +here you kind of pay as per the + + align:start position:0% +here you kind of pay as per the + + + align:start position:0% +here you kind of pay as per the +actuarial value of the payoff + + align:start position:0% +actuarial value of the payoff + + + align:start position:0% +actuarial value of the payoff +well this is another linear program the + + align:start position:0% +well this is another linear program the + + + align:start position:0% +well this is another linear program the +objective function is linear in the pi's + + align:start position:0% +objective function is linear in the pi's + + + align:start position:0% +objective function is linear in the pi's +the constraint set is in the pi's + + align:start position:0% +the constraint set is in the pi's + + + align:start position:0% +the constraint set is in the pi's +including the budget set which is linear + + align:start position:0% +including the budget set which is linear + + + align:start position:0% +including the budget set which is linear +in the pi's so we can solve these things + + align:start position:0% +in the pi's so we can solve these things + + + align:start position:0% +in the pi's so we can solve these things +conceptually and numerically recognizing + + align:start position:0% +conceptually and numerically recognizing + + + align:start position:0% +conceptually and numerically recognizing +that it's just a version of the general + + align:start position:0% +that it's just a version of the general + + + align:start position:0% +that it's just a version of the general +notation + + align:start position:0% +notation + + + align:start position:0% +notation +and here's the third suppose we have a + + align:start position:0% +and here's the third suppose we have a + + + align:start position:0% +and here's the third suppose we have a +firm + + align:start position:0% +firm + + + align:start position:0% +firm +back to production again the firm can + + align:start position:0% +back to production again the firm can + + + align:start position:0% +back to production again the firm can +produce n possible goods the j good here + + align:start position:0% +produce n possible goods the j good here + + + align:start position:0% +produce n possible goods the j good here +has the price pj + + align:start position:0% +has the price pj + + + align:start position:0% +has the price pj +the firm has a fixed supply of inputs + + align:start position:0% +the firm has a fixed supply of inputs + + + align:start position:0% +the firm has a fixed supply of inputs +which makes the problem special they're + + align:start position:0% +which makes the problem special they're + + + align:start position:0% +which makes the problem special they're +not buying these they already have them + + align:start position:0% +not buying these they already have them + + + align:start position:0% +not buying these they already have them +in inventory + + align:start position:0% +in inventory + + + align:start position:0% +in inventory +and the technology tells us how much of + + align:start position:0% +and the technology tells us how much of + + + align:start position:0% +and the technology tells us how much of +input i is needed to produce good j + + align:start position:0% +input i is needed to produce good j + + + align:start position:0% +input i is needed to produce good j +those are the a i j's now here the + + align:start position:0% +those are the a i j's now here the + + + align:start position:0% +those are the a i j's now here the +natural objective function would be the + + align:start position:0% +natural objective function would be the + + + align:start position:0% +natural objective function would be the +revenue + + align:start position:0% +revenue + + + align:start position:0% +revenue +price times quantity uh summing over all + + align:start position:0% +price times quantity uh summing over all + + + align:start position:0% +price times quantity uh summing over all +the j goods and you're going to choose + + align:start position:0% +the j goods and you're going to choose + + + align:start position:0% +the j goods and you're going to choose +the qjs but you can't overutilize your + + align:start position:0% +the qjs but you can't overutilize your + + + align:start position:0% +the qjs but you can't overutilize your +inputs so + + align:start position:0% +inputs so + + + align:start position:0% +inputs so +if the firm is endowed with input i + + align:start position:0% +if the firm is endowed with input i + + + align:start position:0% +if the firm is endowed with input i +then you would say how much of input i + + align:start position:0% +then you would say how much of input i + + + align:start position:0% +then you would say how much of input i +is needed to produce good j times the + + align:start position:0% +is needed to produce good j times the + + + align:start position:0% +is needed to produce good j times the +proposed quantity of good j + + align:start position:0% +proposed quantity of good j + + + align:start position:0% +proposed quantity of good j +summing over all goods j this would be + + align:start position:0% +summing over all goods j this would be + + + align:start position:0% +summing over all goods j this would be +the total input requirement for good i + + align:start position:0% +the total input requirement for good i + + + align:start position:0% +the total input requirement for good i +input i associated with producing this + + align:start position:0% +input i associated with producing this + + + align:start position:0% +input i associated with producing this +vector of goods q indexed by j and so + + align:start position:0% +vector of goods q indexed by j and so + + + align:start position:0% +vector of goods q indexed by j and so +this is a linear constraint the queues + + align:start position:0% +this is a linear constraint the queues + + + align:start position:0% +this is a linear constraint the queues +are non-negative this is another linear + + align:start position:0% +are non-negative this is another linear + + + align:start position:0% +are non-negative this is another linear +program + + align:start position:0% +program + + + align:start position:0% +program +and the last one is what's called the + + align:start position:0% +and the last one is what's called the + + + align:start position:0% +and the last one is what's called the +transportation problem + + align:start position:0% +transportation problem + + + align:start position:0% +transportation problem +maybe just say it in words + + align:start position:0% +maybe just say it in words + + + align:start position:0% +maybe just say it in words +there are + + align:start position:0% +there are + + + align:start position:0% +there are +m warehouses which are stocked with + + align:start position:0% +m warehouses which are stocked with + + + align:start position:0% +m warehouses which are stocked with +goods + + align:start position:0% +goods + + + align:start position:0% +goods +and n retail outlets where goods are + + align:start position:0% +and n retail outlets where goods are + + + align:start position:0% +and n retail outlets where goods are +sold + + align:start position:0% +sold + + + align:start position:0% +sold +so here we have kind of geography and in + + align:start position:0% +so here we have kind of geography and in + + + align:start position:0% +so here we have kind of geography and in +particular + + align:start position:0% +particular + + + align:start position:0% +particular +in order to ship the product + + align:start position:0% +in order to ship the product + + + align:start position:0% +in order to ship the product +from a warehouse to an outlet you use up + + align:start position:0% +from a warehouse to an outlet you use up + + + align:start position:0% +from a warehouse to an outlet you use up +resources + + align:start position:0% +resources + + + align:start position:0% +resources +so this cost cij + + align:start position:0% +so this cost cij + + + align:start position:0% +so this cost cij +is the amount of resources you used up + + align:start position:0% +is the amount of resources you used up + + + align:start position:0% +is the amount of resources you used up +say in dollars to ship the good from + + align:start position:0% +say in dollars to ship the good from + + + align:start position:0% +say in dollars to ship the good from +warehouse i to outlet j + + align:start position:0% +warehouse i to outlet j + + + align:start position:0% +warehouse i to outlet j +and then the decision problem is + + align:start position:0% +and then the decision problem is + + + align:start position:0% +and then the decision problem is +you're given demands at all the outlets + + align:start position:0% +you're given demands at all the outlets + + + align:start position:0% +you're given demands at all the outlets +and you're given the amount initially in + + align:start position:0% +and you're given the amount initially in + + + align:start position:0% +and you're given the amount initially in +the warehouses and you want to then + + align:start position:0% +the warehouses and you want to then + + + align:start position:0% +the warehouses and you want to then +determine the shipments from all the + + align:start position:0% +determine the shipments from all the + + + align:start position:0% +determine the shipments from all the +different warehouses to all the + + align:start position:0% +different warehouses to all the + + + align:start position:0% +different warehouses to all the +different potential outlets to solve the + + align:start position:0% +different potential outlets to solve the + + + align:start position:0% +different potential outlets to solve the +problem which minimizes the total cost + + align:start position:0% +problem which minimizes the total cost + + + align:start position:0% +problem which minimizes the total cost +cost for mita j + + align:start position:0% +cost for mita j + + + align:start position:0% +cost for mita j +warehouses i to outlets j and these are + + align:start position:0% +warehouses i to outlets j and these are + + + align:start position:0% +warehouses i to outlets j and these are +the constraints the constraint says uh + + align:start position:0% +the constraints the constraint says uh + + + align:start position:0% +the constraints the constraint says uh +you've got so much in inventory + + align:start position:0% +you've got so much in inventory + + + align:start position:0% +you've got so much in inventory +at uh + + align:start position:0% +at uh + + + align:start position:0% +at uh +warehouse i + + align:start position:0% +warehouse i + + + align:start position:0% +warehouse i +so + + align:start position:0% +so + + + align:start position:0% +so +whatever you're shipping out of i to all + + align:start position:0% +whatever you're shipping out of i to all + + + align:start position:0% +whatever you're shipping out of i to all +these outlets j it cannot exceed the + + align:start position:0% +these outlets j it cannot exceed the + + + align:start position:0% +these outlets j it cannot exceed the +that level of inventory although it + + align:start position:0% +that level of inventory although it + + + align:start position:0% +that level of inventory although it +could be less and likewise you have to + + align:start position:0% +could be less and likewise you have to + + + align:start position:0% +could be less and likewise you have to +meet the demand at outlet j + + align:start position:0% +meet the demand at outlet j + + + align:start position:0% +meet the demand at outlet j +so the shipping that's coming from all + + align:start position:0% +so the shipping that's coming from all + + + align:start position:0% +so the shipping that's coming from all +possible outlets i to that particular j + + align:start position:0% +possible outlets i to that particular j + + + align:start position:0% +possible outlets i to that particular j +cannot be less than + + align:start position:0% +cannot be less than + + + align:start position:0% +cannot be less than +the demand + + align:start position:0% +the demand + + + align:start position:0% +the demand +so this is another geographic + + align:start position:0% +so this is another geographic + + + align:start position:0% +so this is another geographic +programming problem so we did ordinary + + align:start position:0% +programming problem so we did ordinary + + + align:start position:0% +programming problem so we did ordinary +production we did choice under + + align:start position:0% +production we did choice under + + + align:start position:0% +production we did choice under +uncertainty + + align:start position:0% +uncertainty + + + align:start position:0% +uncertainty +we did a spatial geographic problem + + align:start position:0% +we did a spatial geographic problem + + + align:start position:0% +we did a spatial geographic problem +they're they're all + + align:start position:0% +they're they're all + + + align:start position:0% +they're they're all +well-known prototypes in the literature + + align:start position:0% +well-known prototypes in the literature + + + align:start position:0% +well-known prototypes in the literature +and they all use this common tool which + + align:start position:0% +and they all use this common tool which + + + align:start position:0% +and they all use this common tool which +is a linear programming + + align:start position:0% +is a linear programming + + + align:start position:0% +is a linear programming +okay that's all i have for today \ No newline at end of file diff --git a/s7i_Dpz-DLU.txt b/s7i_Dpz-DLU.txt new file mode 100644 index 0000000000000000000000000000000000000000..56fd92adafda503bd024b289e9c17d6cf505fc0d --- /dev/null +++ b/s7i_Dpz-DLU.txt @@ -0,0 +1,531 @@ +align:start position:0% + +all right so on a scale of zero to ten + + align:start position:0% +all right so on a scale of zero to ten + + + align:start position:0% +all right so on a scale of zero to ten +how energetic is everyone feeling I'm + + align:start position:0% +how energetic is everyone feeling I'm + + + align:start position:0% +how energetic is everyone feeling I'm +going to count to three and then is that + + align:start position:0% +going to count to three and then is that + + + align:start position:0% +going to count to three and then is that +super familiar face hey Cody yeah + + align:start position:0% +super familiar face hey Cody yeah + + + align:start position:0% +super familiar face hey Cody yeah +so on the count of three I want everyone + + align:start position:0% +so on the count of three I want everyone + + + align:start position:0% +so on the count of three I want everyone +to say a number between zero and ten + + align:start position:0% +to say a number between zero and ten + + + align:start position:0% +to say a number between zero and ten +about how much energy you're feeling + + align:start position:0% +about how much energy you're feeling + + + align:start position:0% +about how much energy you're feeling +about being here today + + align:start position:0% +about being here today + + + align:start position:0% +about being here today +so I don't want to project I'm feeling a + + align:start position:0% +so I don't want to project I'm feeling a + + + align:start position:0% +so I don't want to project I'm feeling a +little bit low energy so I don't want to + + align:start position:0% +little bit low energy so I don't want to + + + align:start position:0% +little bit low energy so I don't want to +project so if you guys feel good tell me + + align:start position:0% +project so if you guys feel good tell me + + + align:start position:0% +project so if you guys feel good tell me +you feel good so that I know that it's + + align:start position:0% +you feel good so that I know that it's + + + align:start position:0% +you feel good so that I know that it's +not my internal state is not your state + + align:start position:0% +not my internal state is not your state + + + align:start position:0% +not my internal state is not your state +it's really important to gauge these + + align:start position:0% +it's really important to gauge these + + + align:start position:0% +it's really important to gauge these +things sometimes alright so one two + + align:start position:0% +things sometimes alright so one two + + + align:start position:0% +things sometimes alright so one two +three all right + + align:start position:0% +three all right + + + align:start position:0% +three all right +there's a gradient and mister but all + + align:start position:0% +there's a gradient and mister but all + + + align:start position:0% +there's a gradient and mister but all +right that's good nobody went down to + + align:start position:0% +right that's good nobody went down to + + + align:start position:0% +right that's good nobody went down to +three which is about where I am unless + + align:start position:0% +three which is about where I am unless + + + align:start position:0% +three which is about where I am unless +there was any 3s out there if there are + + align:start position:0% +there was any 3s out there if there are + + + align:start position:0% +there was any 3s out there if there are +come talk to me after there's support + + align:start position:0% +come talk to me after there's support + + + align:start position:0% +come talk to me after there's support +services and we can go like we can go + + align:start position:0% +services and we can go like we can go + + + align:start position:0% +services and we can go like we can go +together and get a little pumped up um + + align:start position:0% +together and get a little pumped up um + + + align:start position:0% +together and get a little pumped up um +but yes so again I want social + + align:start position:0% +but yes so again I want social + + + align:start position:0% +but yes so again I want social +interaction today so we're going to do + + align:start position:0% +interaction today so we're going to do + + + align:start position:0% +interaction today so we're going to do +something quicker than yesterday but I + + align:start position:0% +something quicker than yesterday but I + + + align:start position:0% +something quicker than yesterday but I +want people to introduce yourself and + + align:start position:0% +want people to introduce yourself and + + + align:start position:0% +want people to introduce yourself and +say random animal and make that animals + + align:start position:0% +say random animal and make that animals + + + align:start position:0% +say random animal and make that animals +noise if you can or attempt to so it's + + align:start position:0% +noise if you can or attempt to so it's + + + align:start position:0% +noise if you can or attempt to so it's +like if I am you know I'm Kyle and I it + + align:start position:0% +like if I am you know I'm Kyle and I it + + + align:start position:0% +like if I am you know I'm Kyle and I it +doesn't even have to I'm trying to make + + align:start position:0% +doesn't even have to I'm trying to make + + + align:start position:0% +doesn't even have to I'm trying to make +it rhyme or like have alliteration + + align:start position:0% +it rhyme or like have alliteration + + + align:start position:0% +it rhyme or like have alliteration +doesn't even have to be that I'm gonna + + align:start position:0% +doesn't even have to be that I'm gonna + + + align:start position:0% +doesn't even have to be that I'm gonna +say Kyle cat me out right that's most + + align:start position:0% +say Kyle cat me out right that's most + + + align:start position:0% +say Kyle cat me out right that's most +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you know that's more like what an actual + + align:start position:0% +you know that's more like what an actual + + + align:start position:0% +you know that's more like what an actual +cat says that's not what we represent + + align:start position:0% +cat says that's not what we represent + + + align:start position:0% +cat says that's not what we represent +cats saying yes so try to look around + + align:start position:0% +cats saying yes so try to look around + + + align:start position:0% +cats saying yes so try to look around +and figure out people's names and maybe + + align:start position:0% +and figure out people's names and maybe + + + align:start position:0% +and figure out people's names and maybe +one other thing something personal about + + align:start position:0% +one other thing something personal about + + + align:start position:0% +one other thing something personal about +us that we can get to know some type of + + align:start position:0% +us that we can get to know some type of + + + align:start position:0% +us that we can get to know some type of +thing what'swhat's it good great all + + align:start position:0% +thing what'swhat's it good great all + + + align:start position:0% +thing what'swhat's it good great all +right what you're hoping to have for + + align:start position:0% +right what you're hoping to have for + + + align:start position:0% +right what you're hoping to have for +dinner tonight thank you + + align:start position:0% +dinner tonight thank you + + + align:start position:0% +dinner tonight thank you +all right so Kyle + + align:start position:0% + + + + align:start position:0% + +probably Thai food but that's because + + align:start position:0% +probably Thai food but that's because + + + align:start position:0% +probably Thai food but that's because +it's my default and I never know what + + align:start position:0% +it's my default and I never know what + + + align:start position:0% +it's my default and I never know what +else to do + + align:start position:0% +else to do + + + align:start position:0% +else to do +so Thai food all right so anybody not + + align:start position:0% +so Thai food all right so anybody not + + + align:start position:0% +so Thai food all right so anybody not +know what Soylent is not Soylent Green + + align:start position:0% +know what Soylent is not Soylent Green + + + align:start position:0% +know what Soylent is not Soylent Green +know it right it has all the nutrients + + align:start position:0% +know it right it has all the nutrients + + + align:start position:0% +know it right it has all the nutrients +that a human needs to survive and you + + align:start position:0% +that a human needs to survive and you + + + align:start position:0% +that a human needs to survive and you +just drink it and you never have to + + align:start position:0% +just drink it and you never have to + + + align:start position:0% +just drink it and you never have to +worry about food that was so cool + + align:start position:0% +worry about food that was so cool + + + align:start position:0% +worry about food that was so cool +all right thank you so today at some + + align:start position:0% +all right thank you so today at some + + + align:start position:0% +all right thank you so today at some +point you're gonna break up into groups + + align:start position:0% +point you're gonna break up into groups + + + align:start position:0% +point you're gonna break up into groups +and at some point I'm gonna do a pop + + align:start position:0% +and at some point I'm gonna do a pop + + + align:start position:0% +and at some point I'm gonna do a pop +quiz and you're gonna have to tell me + + align:start position:0% +quiz and you're gonna have to tell me + + + align:start position:0% +quiz and you're gonna have to tell me +the names of the people in your group + + align:start position:0% +the names of the people in your group + + + align:start position:0% +the names of the people in your group +because I forgot to do that yesterday + + align:start position:0% +because I forgot to do that yesterday + + + align:start position:0% +because I forgot to do that yesterday +and I wonder how many of you know the + + align:start position:0% +and I wonder how many of you know the + + + align:start position:0% +and I wonder how many of you know the +names of the people that were in your + + align:start position:0% +names of the people that were in your + + + align:start position:0% +names of the people that were in your +group I'm not gonna ask you today I'm + + align:start position:0% +group I'm not gonna ask you today I'm + + + align:start position:0% +group I'm not gonna ask you today I'm +not gonna ask you about yesterday but + + align:start position:0% +not gonna ask you about yesterday but + + + align:start position:0% +not gonna ask you about yesterday but +today I will ask you about that so I + + align:start position:0% +today I will ask you about that so I + + + align:start position:0% +today I will ask you about that so I +mean some of you may have known the + + align:start position:0% +mean some of you may have known the + + + align:start position:0% +mean some of you may have known the +names thumbs up if you did \ No newline at end of file diff --git a/sZ2qulI6GEk.txt b/sZ2qulI6GEk.txt new file mode 100644 index 0000000000000000000000000000000000000000..c462eb1ba52c65d71c36bb9b0c0e97772765361e --- /dev/null +++ b/sZ2qulI6GEk.txt @@ -0,0 +1,2284 @@ +Today, and for the next two +weeks, we are going to be + +studying what, +for many engineers and a few + +scientists is the most popular +method of solving any + +differential equation of the +kind that they happen to be, + +and that is to use the popular +machine called the Laplace + +transform. +Now, you will get proficient in + +using it by the end of the two +weeks. + +But, there is always a certain +amount of mystery that hangs + +around it. +People scratch their heads and + +can't figure out where it comes +from. + +And, that bothers them a lot. +In the past, + +I've usually promised to tell +you, the students at the end of + +the two weeks, +but I almost never have time. + +So, I'm going to break that +glorious tradition and tell you + +up front at the beginning, +where it comes from, + +and then talk very fast for the +rest of the period. + +Okay, a good way of thinking of +where the Laplace transform + +comes from, and a way which I +think dispels some of its + +mystery is by thinking of power +series. + +I think virtually all of you +have studied power series except + +possibly a few students who just +had 18.01 here last semester, + +and probably shouldn't be +taking 18.03 anyway, + +now. +But anyway, a power series + +looks like this: +summation (a)n x to the n. + +And, you sum that from, + +let's say, zero to infinity. +And, the typical thing you want + +to do with it is add it up to +find out what its sum is. + +Now, the only way I will depart +from tradition, + +instead of calling the sum some +generic name like f of x, + +in order to identify +the sum with the coefficients, + +a, I'll call it a of x. + +Now, I want to make just one +slight change in that. + +I want to use computer +notation, which doesn't use the + +subscript (a)n. +Instead, this, + +it thinks of as a function of +the discreet variable, + +n. +In other words, + +it's a function which assigns +to n equals zero, + +one, two, three real numbers. +That's what this sequence of + +coefficients really is. +So, the computer notation will + +look almost the same. +It's just that I will write + +this in functional notation as a +of n instead of (a)n. + +But, it still means the real +number associated with the + +positive integer, +n, and everything else is the + +same. +See, what I'm thinking of this + +as doing is taking this discreet +function, which gives me the + +sequence of coefficients of the +power series, + +and associating that with the +sum of the power series. + +Let me give you some very +simple examples, + +two very simple examples, +which I think you know. + +Suppose this is a function one. +Now, what do I mean by that? + +I mean it's the constant +function, one. + +To every positive integer, +it assigns the number one. + +Okay, what's a of x? +What I'm saying is, + +in other words, +in this fancy, + +mystifying form, +is all of these guys are one, + +what's a of x? +One plus x plus x squared plus + +x cubed. +Look, you are supposed to be + +born knowing what that adds up +to. + +It adds up to one over one +minus x, + +except that's the wrong answer. +What's wrong about it? + +It's not true for every value +of x. + +That's only true when x is such +that that series converges, + +and that is only true when x +lies between negative one and + +one. +So, it's not this function. + +It's this function with its +domain restricted to be less + +than one in absolute value. +What does that converge to? + +If x is bigger than one, +the answer is it doesn't + +converge. +There's nothing else you can + +put here. +Okay, let's take another + +function. +Suppose this is, + +let's see, one over n +you probably won't know. + +Let's take one you will know, +one over n factorial. + +Suppose a of n is the function + +one over n factorial, + +what's a of x? +So, what I'm asking is, + +what does this add up to when +the coefficient here is one over + +n factorial? + +What's summation x to the n +over n factorial? + +It is e to the x. + +And, this doesn't have to be +qualified because this is true + +for all values of x. +So, in other words, + +from this peculiar point of +view, I think of a power as + +summing the operation, +of summing a power series as + +taking a discreet function +defined for positive integers, + +or nonnegative integers, +and doing this funny process. + +And, out of it comes a +continuous function of some + +sort. +And, notice what goes in is the + +variable, n. +But, what comes out is the + +variable, x. +Well, that's perfectly natural. + +That's the way a power series +is set up. + +So, the question I ask is, +this is a discreet situation, + +a discreet summation. +Suppose I made the summation + +continuous instead of discreet. +So, I want the continuous + +analog of what I did over there. +Okay, what would a continuous + +analog be? +Well, instead of, + +I'll replace n zero, +one, two, that will be replaced + +by a continued, +that's a discreet variable. + +I'll replace it by a continuous +variable, t, which runs from + +zero to infinity, +and is allowed to take every + +real value in between instead of +being only allowed to take the + +values of the positive +nonnegative integers. + +Okay, well, if I want to use t +instead of n, + +I clearly cannot sum in the +usual way over all real numbers. + +But, the way the procedure +which replaces summation over + +all real numbers is integration. +So, what I'm going to do is + +replace that sum by the integral +from zero to infinity. + +That's like the sum from zero +to infinity of what? + +Well, of some function, +but now n is being replaced by + +the continuous variable, +t. + +So, this is going to be a +function of t. + +And, how about the rest of it? +The rest I will just copy, + +x to the n'th. +Well, instead of n I have to + +write t and dt. +And, what's the sum? + +Well, I'll call the sum, +what's the sum a function of? + +I integrate out the t. +So, that doesn't appear in the + +answer. +All that appears is this + +number, x, this parameter, +x. + +For each value of x, +like one, two, + +or 26.3, this integral has a +certain value, + +and I can calculate it. +So, this is going to end up as + +a function of x, +just as it did before. + +Now, I could leave it in that +form, but no mathematician would + +like to do that, +and very few engineers either. + +The reason is, +in general, when you do + +integration and differentiation, +you do not want to have as the + +base of an exponential something +like x. + +The only convenient thing to +have is e, and the reason is + +because it's only e that people +really like to differentiate, + +e to the something. +The only thing is that people + +really like to differentiate or +integrate. + +So, I'm going to make this look +a little better by converting x + +to the t to the base e. +I remember how to do that. + +You write x equals e to the log +x and so x to + +the t will be e to the +log x times t, + +if you want. +Now, the only problem is I want + +to make one more little change. +After all, I want to be able to + +calculate this integral. +And, it's clear that if t is + +going to infinity, +if I have a number here, + +for example, +like x equals two, + +that integral is really quite +unlikely to converge. + +For example, +if a of t were just + +the constant function, +one, the integral certainly + +wouldn't converge. +It would be horrible. + +That integral only has a chance +of converging if x is a number + +less than one, +so that when I take bigger and + +bigger powers of it, +I get smaller and smaller + +numbers. +Don't forget, + +this is an improper integral +going all the way up to + +infinity. +Those need treatment, + +delicate handling. +All right, so I really want x + +to be less than one. +Otherwise, that integral is + +very unlikely to converge. +I'd better have it positive, + +because if I allow it to be +negative I'm going to get into + +trouble with negative powers, +see what's minus one, + +for example, +to the one half when t is one + +half. +That's already imaginary. + +I don't want that. +If you've got an exponential, + +the base has got to be a +positive number. + +So, I want x to be a positive +number. + +All right, if x in my actual +practices going to lie between + +zero and one in order to make +the integral converge, + +how about log x? +Well, log x, + +if x is less than one, +so log x is going to be + +less than zero, +and it's going to go all the + +way down to negative infinity. +So, this means log x is + +negative. +In this interesting range of x, + +the log x is always going to be +negative. + +And now, I don't like that. +The first place I'd like to + +call this by a new variable +since no one uses log x as a + +variable. +And, it would make sense to + +make it a negative, +to make it negative, + +that is, to write log x is +equal to negative s. + +Let's put it on the other side, +in order that since log x is + +always going to be less than +zero, then s will always be + +positive. +And it's always more convenient + +to work with positive numbers +instead of negative numbers. + +So, if I make those changes, +what happens to the integral? + +Well, I stress, +all these changes are just + +cosmetic to make things a little +easier to work with in terms of + +symbols. +First of all, + +the a I'm going to change. +I don't want to call it a of t + +because most people +don't call functions a of t. + +They call them f of t. +So, I'll call it f of t. + +x is e to the log x, +which is e to the minus s. + +So, x has its name changed to e + +to the minus s. +In other words, + +I'm using as the new variable +not x any longer but s in order + +that the base be e. +t, I now raise this to the t'th + +power, but by the laws of +exponents, that means I simply + +multiply the exponent by t, +and dt. + +And now, since I'm calling the +function f of t, + +the output ought to be called +capital F. + +But it's now a function, +since I've changed the + +variable, of s. +It's no longer a function of x. + +If you like, +you may think of this as a of, + +what's x? +x is e to the negative s, + +I guess. +I mean, no one would leave a + +function in that form. +It's simply a function of s. + +And, what is that? +So, what have we got, + +finally? +What we have, + +dear hearts, +is this thing, + +which I stress is nothing more +than the continuous analog of + +the summation of a power series. +This is the discrete version. + +This is by these perfectly +natural transformations the + +continuous version of the same +thing. + +It starts with a function +defined for positive values of + +t, and turns it into a function +of s. + +And, this is called the Laplace +transform. + +Now, if I've done my work +correctly, you should all be + +saying, oh, is that all? +But, I know you aren't. + +So, it's okay. +You'll get used to it. + +The first thing you have to get +used to is one thing some people + +never get used to, +which is you put in a function + +of t, and you get out a function +of s. + +How could that be? +You know, for an operator, + +you put in 3x, +and you get out three if it's a + +differentiation operator. +In other words, + +when you have an operator, +the things we've been talking + +about the last two or three +weeks in one form or another, + +at least the variable doesn't +get changed. + +Well, but for a transform it +does, and that's why it's called + +a transform. +So, the difference between a + +transform and an operator is +that for a transform a function + +of t comes in, +but a function of s comes out. + +The variable gets changed, +whereas for an operator, + +f of t goes in and +what comes out is g of t, + +a function using the +same variable like + +differentiation is a typical +example of an operator, + +or the linear differential +operators we've been talking + +about. +Well, but this doesn't behave + +that way. +The variable does get changed. + +That's, in fact, +extremely important in the + +applications. +In the applications, + +t usually means the time, +and s very often, + +not always, but very often is a +variable measuring frequency, + +for instance. +But, so that's a peculiar thing + +that's hard to get used to. +But, a good thing is the fact + +that it's a linear transform. +In other words, + +it obeys the laws we'd love and +like that the Laplace + +transform-- oh, +I never gave you any notation + +for the laplace transform. +Hey, I'd better do that. + +Okay, so, some notation: +there are two notations that + +are used. +Your book mostly uses the + +notation that the laplace +transform of f of t is capital F + +of s, +uses the same letter but with + +the same capital. +Now, as you will see, + +there are some places you +absolutely cannot use that + +notation. +It may seem strange, + +looks perfectly natural. +There are certain laws you + +cannot express using that +notation. + +It's baffling. +But, if you can't do it this + +way, you can do it using this +notation instead. + +One or the other will almost +always work. + +So, I'll use my little squiggly +notation, but that's what I use. + +I think it's a little more +vivid, and the trouble is that + +this piles up too many +parentheses. + +And, that's always hard to +read. + +So, I like this better. +So, these are two alternate + +ways of saying the same thing. +The Laplace transform of this + +function is that one. +Okay, well, let's use, + +for the linearity law, +it's definitely best. + +I really cannot express the +linearity law using the second + +notation, but using the first +notation, it's a breeze. + +The Laplace transform of the +sum of two functions is the sum + +of their Laplace transforms of +each of them separately. + +Or, better yet, +you could write it that way. + +Let's write it this way. +That way, it looks more like an + +operator, L of f plus L of g. + +And, of the same way, +if you take a function and + +multiply it by a constant and +take the laplace transform, + +you can pull the constant +outside. + +And, of course, +why are these true? + +These are true just because of +the form of the transform. + +If I add up f and g, +I simply add up the two + +corresponding integrals. +In other words, + +I'm using the fact that the +integral, this definite + +integral, is itself a linear +operator. + +Well, that's the general +setting. + +That's where it comes from, +and that's the notation for it. + +And, now we have to get to +work. + +The first thing to do to get +familiar with this is, + +obviously what we want to do is +say, okay, these were the + +transforms of some simple +discreet functions. + +Okay, suppose I put in some +familiar functions, + +f of t. +What do their Laplace + +transforms look like? +So, let's do that. + +So, one of the boards I should +keep stored. + +Why don't I store on this +board? + +I'll store on this board the +formulas as we get them. + +So, let's see, +what should we aim at, + +first? +Let's first find, + +and I'll do the calculations on +the sideboard, + +and we'll see how it works out. +I'm not very sure. + +In other words, +what's the Laplace transform of + +the function, +one? + +Well, there's an even easier +one. + +What's the Laplace transform of +the function zero? + +Answer: zero. +Very exciting. + +What's the Laplace transform of +one? + +Well, it doesn't turn out the +constant anymore than it turned + +out to be a constant up there. +Let's calculate it. + +Now, you can do these +calculations carefully, + +dotting all the i's, +or pretty carefully, + +or not carefully at all, +i.e. + +sloppily. +I'll let you be sloppy after, + +generally speaking, +you could be sloppy unless the + +directions tell you to be less +sloppy or to be careful, + +okay? +So, I'll do one carefully. + +Let's calculate the Laplace +transform of one carefully. + +Okay, in the beginning, +you've got nothing to use with + +the definition. +So, I have to calculate the + +integral from zero to infinity +of one, that's the f of t times + +e to the negative s t, +so I don't have to + +put in the one, +dt. + +All right, now, +let me remind you, + +this is an improper integral. +This is just about the first + +time in the course we've had an +improper integral. + +But, there are going to be a +lot of them over the next couple + +of weeks, nothing but. +All right, it's an improper + +integral. +That means we have to go back + +to the definition. +If you want to be careful, + +you have to go back to the +definition of improper integral. + +So, it's the limit, +as R goes to infinity, + +of what you get by integrating +only up as far as R. + +That's a definite integral. +That's a nice Riemann integral. + +So, this is what I have to +calculate. + +And, I have to take the limit +as R goes to infinity. + +Now, how do I calculate that? +Well, this integral is equal + +to, that's easy. +It's just integrating. + +Remember that you're +integrating with respect to t. + +So, s is a parameter. +It's like a constant, + +in other words. +So, it's e to the minus s t, + +and when I differentiated, + +the derivative of this would +have negative s. + +So, to get rid of that negative +s, so the derivative is e to the + +minus s t. +You have to put minus s + +in the denominator. +And now, I'll want to evaluate + +that between zero and R. +And, what do I get? + +Well it is at the upper limit. +So, it's e to the minus s times + +R minus, at the lower limit, +it's t is equal to zero, + +so whatever s is, +it's one. + +And that's divided by this +constant up front, + +negative s. So, + +the answer is, +it is equal to the limit of, + +as R goes to infinity, +of e to the negative s R minus + +one divided by minus s. + +Now, what's that? +Well, as R goes to infinity, + +e to the minus 2R, +or minus 5R goes to zero, + +and the answer is minus one +over minus s. + +So, that's one over s. +And so, that's our answer. + +Let's put it up here. +It's one over s, + +except it isn't. +I made a mistake. + +Well, not mistake, +a little oversight. + +What's the oversight? +This is okay. + +This is okay. +This is okay. + +This is not okay. +This is okay. + +But that's not okay. +What's wrong? + +I did slight a verbal hand. +Maybe some of you have picked + +it up and were too embarrassed +to correct me, + +but I said like e to the minus +2R obviously goes to + +zero, and e to the minus 5R +goes to zero. + +How about e to the minus minus +3 R? + +Does that go to zero? +No, that's e to the 3R, + +which goes to infinity. + +The only time this goes to zero +is if s is a positive number. + +Minus s looks like a negative +number, but it's not, + +if s is equal to minus two. +So, this is only true if s is + +positive because only if s is +positive is this exponent really + +negative and large, +and therefore going to + +infinity, going to zero as R +goes to infinity. + +So, the answer is not one over +s. + +It is one over s, +s must positive. + +Now, once again, +here, people don't worry about + +this sort of thing with power +series because it seems very + +obvious, you know, +one over x, + +absolute value of x is less +than one, + +when it gets to be the Laplace +transform, just because the + +Laplace transform is mysterious, +the question is, + +okay, the Laplace transform is +one over s of one, + +well, Laplace transform of one +I understand is one over s if s + +is positive. +What is it if s is negative? + +Okay, right down in your little +books, this, but that down, + +what is it if s is negative, +and write underneath that, + +this question is meaningless. +It doesn't mean anything. + +I'll draw you a picture. +This is a picture of the + +Laplace transform of one. +It is that. + +It's one branch of this curve. +It does not include the branch + +on the left. +It doesn't because I showed you + +it doesn't. +That's all there is to it. + +Okay, so I did that carefully. +Now I'm going to get a little + +less careful. +What's the Laplace transform of + +e to the a t? +First of all, + +in general, the kind of +functions for which people like + +to calculate the Laplace +transform, and basically the + +only ones there will be in the +tables are exactly the sort of + +functions that you used in +solving linear equations with + +constant coefficients. +What kinds of functions entered + +in there? +Exponentials, + +sines and cosines, +but they were really complex + +exponentials, +right? + +e to the t sine t, +but that was really a + +complex exponential, +too, just a little more + +complicated one, +polynomials, + +and that's about it. +t times e to the t, + +that was okay, +too. + +These are the functions for +which people calculate the + +Laplace transform, +and all the other functions + +they don't calculate the Laplace +transforms. + +So, I don't mean to disappoint +you here. + +You're going to say, +oh, what, that same old stuff? + +For two more weeks, +we've got that same, + +well, the Laplace transform +does a lot of things much better + +than the methods we've been +using. + +And, I won't. +I'll sell it when I get a + +chance to, for now, +let's just get familiar with + +it. +All right, so while I'm not + +going to calculate e to the a t +for you, + +because I'd like instead to +just prove a simple formula + +which will just give that, +and will also give us e to the + +a t sine t. +It will give us a lot more, + +instead. +I'm going to calculate a + +formula for the Laplace +transform of this guy if you + +already know the Laplace +transform of it. + +Now, see, this falls in that +category because this is really + +e to the a t times one. + +But, I already know the Laplace +transform of one. + +So that's, if I can get a +general formula for this, + +I'll be able to get the formula +for e to the a t as a + +consequence. +So, let's look for this Laplace + +transform. +Now, it's really easy. + +Let's see, where am I doing +calculations? + +Over here. +Okay, so we've got e. + +So, I want to calculate the +Laplace transform e to the a t f + +of t. +So I'm going to say that's the + +integral from zero to infinity +of e to the a t times f of t. + +And now, the rest I copy. + +That's the function part of it +that goes to the input, + +and then there's the other +part. + +This part is called the kernel, +by the way, but don't worry + +about that. +However, if you drop it in + +conversation, +people will look at you and + +say, gee, they know something I +don't. + +And you will. +You know that it's the kernel. + +Okay, well, now, +what kind of formula can I be + +looking for? +Clearly, I can only be looking + +for a formula which expresses it +in terms of the Laplace + +transform of f of t. +Let's calculate and see what we + +get. +Now, what would you do to that + +thing to make? +Well, obviously, + +the thing to do is to combine +the two exponentials. + +So, that's going to be the +integral from zero to infinity + +of f of t. +e, now, I'd like to put it, + +to combine the exponentials in +such a way that it has, + +still, that same form, +so, I'm going to begin with + +that negative sign, +and then see what the rest of + +it has to be. +What is it going to be? + +Well, minus s t and +plus a t, + +but I can make that minus a +here, and it will come out + +right. +So, it's minus s t plus a t, + +and there are the two parts, + +those two factors, +dt. + +So, what's that? +That's the Laplace transform. + +If the a weren't there, +this would be the Laplace + +transform of f of t. +What is it with the a there? + +It's the Laplace transform of f +of t, + +except that instead of the +variable, s has been replaced by + +the variable s minus a. + +I'll give you a second to +digest that. + +Well, you digest it while I'm +writing it because that's the + +answer. +And, the way this is most often + +used, I have to qualify it for +the value. + +So, if F of s is good +for s positive, + +the way it would be, +for example, + +if I used the function one +here, then to finish that off, + +then, F of s minus a will be, + +this will be good when s is +bigger than a. + +Why is that? +Well, because this is true. + +This is true. +If s minus a is + +positive, that's the condition. +That's what this Laplace + +transform is good. +But that simply says that s + +should be bigger than a. + +And, since this doesn't look +pretty, let me try to make it + +look a little bit prettier. +So, let's write it. + +So, this is assuming F of s is +for s greater than zero. + +Now, this is called something. + +This is called, +well, what would you call it? + +On the left side, +you multiply by an exponential. + +On the right, +you translate. + +You shift the argument over by +a. + +So, this is called, +gulp, the exponential shift. + +What? +Well, I'll call it the formula. + +The thing before, +when we talked about operators, + +we called it the exponential +shift rule or the exponential + +shift law. +But, in fact, + +this is, in a way, +a disguised form of the same + +law. +And, engineers who typically do + +all their work using the Laplace +transform and don't use + +operators, this is the form of +the exponential shift law that + +they would know. +What you can do with one, + +you can do with the other. +You can now use both. + +So, what's the answer to e to +the a t? + +Well, the answer is, +I'm supposed to, + +e to the a t times one, +the Laplace transform of one is + +one over s. +And, therefore, + +what I do is to multiply by e +to the a t, I change s to s + +minus a . +And so, that's the answer. + +Let's see, what else don't we +know? + +Well, how about sines and +cosines? + +Well, the way to do sines and +cosines is by making the + +observation that this formula +also works when a is a complex + +number. +So, can use also for a a + +complex number, for e to +the a plus b i times t. + +The Laplace transform of e to + +the a plus b i times t is one +over s minus a plus b i. + +And again, it will be for s +bigger than a. + +So, let's calculate the Laplace +transform of, + +let's say, well, +I've got to cover up something. + +Okay, so, that's the Laplace +transform. + +I've got to remember that. +So, let's calculate the Laplace + +transform of, +let's say, sine of a t + +and cosine a t. + +What do you get for that? +Well, just for a little + +variety, we could do it by using +that formula, + +and taking its real and +imaginary parts. + +Since some of you had so much +difficulty with the backwards + +Euler formula, +he is a good case where you + +could use it. +Suppose you want to calculate + +the Laplace transform of cosine +a t. + +Well, I'm going to write that +using, I want to calculate using + +complex exponentials. +The way I will do it is by + +using the backwards Euler +formula. + +So, this is e to the i a t plus +e to the minus i a t divided by + +two. + +Remember, the foreword Euler +formula would say e to the i a t + +equals cosine a t plus i sine a +t. + +That expresses the complex + +exponential in terms of sines +and cosines. + +This is the backward formula, +which just read it backwards, + +expressing cosines and sines in +terms of complex exponentials + +instead. +Both formulas are useful, + +almost equally useful, +in fact. + +And anyway, just remind you of +it, let's use this one. + +Okay, what's the Laplace +transform, then, + +of cosine a t? +Well, by linearity, + +it's equal to one half the +Laplace transform of this guy + +plus the Laplace transform of +that guy. + +And, what are those? +Well, the Laplace transform of + +e to the i a t is one over s +minus i a, + +and the Laplace +transform of the other guy is + +one divided by s plus i a. + +Now, of course, +this has become out to be a + +real function. +This is real. + +Every integral is real. +This must come out to be real. + +This looks kind of complex, +but it isn't. + +I know automatically that this +is going to be a real function. + +How I know that? +Well, mentally, + +you can combine the terms and +calculate. + +But, I know even before that. +Remember, there are two ways to + +see that something is real. +You can calculate it and see + +that its imaginary part is zero, +hack, or without any + +calculation, if you change i to +minus i, + +and you get the same thing, +it must be real. + +Now, if I change i to minus i +in this expression, + +what happens? +If I change i to minus i, + +this term turns into that one, +and this one turns into that + +one. +Conclusion: the sum of the two + +is unchanged. +And therefore, + +this is real. +Well, of course, + +in the time I took to make that +argument, I could have actually + +calculated it. +So, what the heck, + +let's calculate it? +So, you do the high school + +thing, and it's this guy plus +that guy on top, + +which makes 2s. +I on the bottom is the product + +of those, which by now you +should know the product of two + +complex numbers. +A product of a number and its + +complex conjugate is the sum of +the squares. + +So, what's the answer? +The twos cancel, + +and the answer is that the +Laplace transform of cosine a t + +is s over s squared plus a +squared. + +And, that will be true as, + +in general, it's true up there +for positive values of s only. + +And, the sine a t, +you can calculate that in + +recitation tomorrow. +The answer to that is a divided + +by s squared plus a squared. + +You would get the same answers +if you took the real and + +imaginary parts of that +expression. + +It's another way of getting at +the recitations tomorrow; + +we'll get practice in +calculating other functions + +related to these by using these +formulas, and also from scratch + +directly from the definition of +the Laplace transform. + +Well, there are two things +which we still should do. + +The first is I want to get you +started with calculating inverse + +Laplace transforms. +And, the reason for doing that + +is, in other words, +I've started with f of t, + +and we've been focusing +on what is capital F of s? + +But, you will find that when + +you go to solve differential +equations, by far, + +the hardest part of the +procedure is you get F of s. + +The Laplace transform of the +answer, and you have to convert + +that back into the answer in +terms of t that you were looking + +for. +In other words, + +the main step in the procedure +that you are going to be using + +for solving differential +equations is, + +and the hardest part of the +step will be to calculate + +inverse laplace transforms. +Now, you think that could be + +done by tables, +but, in fact, + +it can't unless the tables are +too long to be useful. + +You have to do a certain amount +of work yourself. + +And, the certain amount of work +that you have to do yourself + +involves partial fractions +decompositions. + +And, in case you were wondering +which you are not, + +the reason you learned partial +fractions in 18.01 was not to + +learn those silly integrals, +but he learned it so that when + +you got to 18.03 you would be +able to calculate, + +solve differential equations by +using Laplace transforms. + +Sorry. +That's life. + +Now, so a certain amount of the +recitation time tomorrow will be + +devoted to reminding you how to +do partial fractions since you + +haven't done it in a while, +and I assume, + +yeah, we had that, +I think. + +Okay, now, they also remind you +of the most efficient method, + +which about half of you have +had, and the rest think you + +might have had, +but really aren't sure. + +So, here's the answer. +We want to find out what it's + +inverse Laplace transform is. +What you have to do, + +it normally won't be in the +tables like this. + +You have to put it in a form in +which it will be in the tables. + +As you do that, +you have to make partial + +fractions decompositions, +which, to do it quickly, + +so if you don't know what I'm +doing now, or you think you once + +knew but don't quite remember, +go to recitation tomorrow. + +To get the coefficient here, +I cover up s, + +and I put s equals zero +because that's the law. + +To get this coefficient, +I cover up s plus three and I + +put s equals a negative three +because that's what you're + +supposed to do. +Put s equal negative three, + +you get minus one third. +This is equal to that. + +In this form, +I don't know what the inverse + +Laplace form is, +but in this form, + +I certainly do know with the +inverse Laplace transform + +because the inverse Laplace +transform is linear, + +and because each of these guys +especially occurs in those + +tables. +Well, what's this? + +Well, it's whatever the Laplace +transform of, + +inverse Laplace transform of +one over s is multiplied by one + +third. +Well, the inverse Laplace + +transform of one over s is one. +So, it's one third times one. + +How about the other guy? +Minus one third, + +the inverse Laplace transform +of one over s plus three, + +that's this formula. +a is negative three, + +and that makes e to the minus +3t. + +So, if this was the Laplace +transform of the solution to the + +differential equation, +then the solution in terms of t + +was this function. +Now, you'll get lots of + +practice in that. +All I'm doing now is signaling + +that that's the most important +and difficult step of the + +procedure, and that, +please, start getting practice. + +Get up to snuff doing that +procedure. + +Okay, in the time remaining, +I want to add one formula to + +this list, and that is going to +be the Laplace transform of, + +we still haven't done +polynomials. + +And now, to polynomials, +because the Laplace transform + +is linear, all I have to do is +know what the Laplace transform + +of, the individual term of a +polynomial. + +In other words, +what the Laplace transform of t + +to the n, +where n is some positive + +integer? +Well, let's bravely start + +trying to calculate it. +Integral from zero to infinity + +t to the n e to the negative st +dt. + +Now, I think you can see that + +the method you should use is +integration by part because this + +is a product of two things, +one of which you would like to + +differentiate a lot of times, +in fact, and the other won't + +hurt to integrate it because +it's very easy to integrate. + +So, this factor is going to be + +the one that's to be +differentiated, + +and this is the factor that +will be pleased to integrate it. + +Let's get started and see what +we can get out of it. + +Well, this time I'm going to +be, well, I'd better be a little + +careful because there's a point +here that's tricky. + +Okay, the first step of +integration by parts is you only + +do the integration. +You don't do the + +differentiation. +Remember, the variable is t. + +The s is just a parameter. +It's just a constant. + +It's hanging around, +not knowing what to do. + +Okay, so the first step is you +don't do the differentiation. + +You only do the integration. +Evaluate it between limits, + +and then you put a minus sign +before you forget to do it. + +And then, integral zero to +infinity. + +Now you do both operations. +So, it's n t to the n + +minus one, +and you also do the + +integration. +Okay, let's consider each of + +these pieces in turn. +Now, this piece, + +well, there's no problem with +the lower limit, + +zero, because when t is equal +to zero, this factor is zero, + +and the thing disappears as +long as n is one or higher. + +So, it's minus zero here at the +lower limit. + +The question is, +what is at the upper limit? + +So, what I have to do is find +out, what is the limit? + +The limit, as t goes to +infinity, that's what's + +happening up there, +of t to the n times e to the + +negative s t divided +by minus s. + +Well, as t goes to infinity, +this goes to infinity, + +of course. +This had better go to zero + +unless I want an answer, +infinity, which won't do me any + +good. +If this goes to zero, + +s had better be positive. +So, I'd better be restricting + +myself to that case. +Okay, so let's assume that s is + +positive so that this minus s +really is a negative number. + +Okay, then I have a chance. +So, this is going to be the + +limit. +Let's write it in a more + +familiar form with that down +below. + +So, it's t to the n. +That's going to infinity. + +But, the bottom is e to the +minus s t. + +But now, it's plus s t. +And, that's going to infinity, + +too, because s is positive. +So, the two guys are racing, + +and the question is, +oh, I lost a minus s here. + +So, oh... equals minus +one over s. + +How's that? +So, the question is only, + +which guy wins? +In the race to infinity, + +which one wins, +and how do you decide? + +And, the answer, +of course, is that's the bottom + +that wins. +The exponential always wins, + +and it's because of L'Hopital's +rule. + +You differentiate top and +bottom. + +Nothing much happens to the +bottom. + +It gets another factor of s, +but the top goes down to t to + +the n minus one. +L'Hopital it again, + +and again, and again, +and again, and again until + +finally you've reduced the top +to t to the zero where it's + +defenseless and just sitting +there, and nothing's happened to + +the bottom. +It's still got e to the s t. + +and that goes to infinity. + +So, the answer is, +this is zero by n applications + +of L'Hopital's rule. +Or, if you're very clever, + +you can do it in one, +but I won't tell you how. + +So, the answer is that this is +zero. + +At the upper limit, +it's also zero at least if s is + +positive, which is the case +we're considering. + +That leaves the rest of this. +All right, let's pull the + +constants out front. +That's plus. + +Two negatives make a plus. +n over s, + +now, what's left? +The integral from zero to + +infinity of t to the n minus +one, e to the minus s t dt. + +But, what on Earth is that? +That is n over s times + +the Laplace transform of t to +the n minus one. + +We got a reduction for it. +We don't get the answer in one + +step. +But, we get a reduction + +formula. +And, it says that the Laplace + +transform, let me write it this +way for once. + +The first way is now better, +is equal to n over s times the + +Laplace transform of n minus t +to the n minus one. + +Okay, the next step, + +this would be n over s times n +minus one over s times the + +Laplace transform of t to the n +minus two. + +If I can continue, + +I finally get in the top n +times n minus one times all the + +way down to one divided by the +same number of s's, + +n of them, times the Laplace +transform of t to the zero, + +finally. +See, one, zero, + +n minus one. +And so, what's the final + +answer? +It is n factorial over s to the + +what power? +Well, the Laplace transform of + +this is one over s. +So, the answer is it's s to the + +n plus one, +n of them here plus an extra + +one coming from the one over s +here. + +And, that's the answer. +The Laplace transform of t to + +the n, oddly enough, + +is more complicated, +and looks a little different + +from these. +It's n factorial over s to the + +n plus one. + +And, with that, +you can now calculate the + +Laplace transform of anything in +sight, and tomorrow you will. \ No newline at end of file diff --git a/urbZ8CTceu0.txt b/urbZ8CTceu0.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ca2a436ae3e022ba03391a0a937756f11a2f733 --- /dev/null +++ b/urbZ8CTceu0.txt @@ -0,0 +1,10083 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Just before the break, we were talking + + align:start position:0% +Just before the break, we were talking + + + align:start position:0% +Just before the break, we were talking +about the need for a light amplifier, an + + align:start position:0% +about the need for a light amplifier, an + + + align:start position:0% +about the need for a light amplifier, an +optical amplifier to make a lasing + + align:start position:0% +optical amplifier to make a lasing + + + align:start position:0% +optical amplifier to make a lasing +possible. All right. So, here we where + + align:start position:0% +possible. All right. So, here we where + + + align:start position:0% +possible. All right. So, here we where +we left off, we had the cavity or the + + align:start position:0% +we left off, we had the cavity or the + + + align:start position:0% +we left off, we had the cavity or the +resonator that gave us these modes + + align:start position:0% +resonator that gave us these modes + + + align:start position:0% +resonator that gave us these modes +and uh the spacing between them is C + + align:start position:0% +and uh the spacing between them is C + + + align:start position:0% +and uh the spacing between them is C +over2 L as we mentioned. And now we put + + align:start position:0% +over2 L as we mentioned. And now we put + + + align:start position:0% +over2 L as we mentioned. And now we put +the amplifier + + align:start position:0% +the amplifier + + + align:start position:0% +the amplifier +within this cavity to overcome the the + + align:start position:0% +within this cavity to overcome the the + + + align:start position:0% +within this cavity to overcome the the +losses. And let's say in general the the + + align:start position:0% +losses. And let's say in general the the + + + align:start position:0% +losses. And let's say in general the the +losses come from from uh the mirrors. + + align:start position:0% +losses come from from uh the mirrors. + + + align:start position:0% +losses come from from uh the mirrors. +And uh if there's enough gain here, + + align:start position:0% +And uh if there's enough gain here, + + + align:start position:0% +And uh if there's enough gain here, +let's say this is the the location of + + align:start position:0% +let's say this is the the location of + + + align:start position:0% +let's say this is the the location of +the gain in frequency. And if there is + + align:start position:0% +the gain in frequency. And if there is + + + align:start position:0% +the gain in frequency. And if there is +enough gain at this + + align:start position:0% +enough gain at this + + + align:start position:0% +enough gain at this +cavity resonance + + align:start position:0% +cavity resonance + + + align:start position:0% +cavity resonance +then we will get lasing and we'll get + + align:start position:0% +then we will get lasing and we'll get + + + align:start position:0% +then we will get lasing and we'll get +the light output by uh making this + + align:start position:0% +the light output by uh making this + + + align:start position:0% +the light output by uh making this +mirror not 100% reflective but uh little + + align:start position:0% +mirror not 100% reflective but uh little + + + align:start position:0% +mirror not 100% reflective but uh little +bit has a little transmission this + + align:start position:0% +bit has a little transmission this + + + align:start position:0% +bit has a little transmission this +mirror here so we can leak some of the + + align:start position:0% +mirror here so we can leak some of the + + + align:start position:0% +mirror here so we can leak some of the +light out. So the uh then the the + + align:start position:0% +light out. So the uh then the the + + + align:start position:0% +light out. So the uh then the the +spectral width of the laser then narrows + + align:start position:0% +spectral width of the laser then narrows + + + align:start position:0% +spectral width of the laser then narrows +down from initially this to to uh this + + align:start position:0% +down from initially this to to uh this + + + align:start position:0% +down from initially this to to uh this +uh essentially this delta function this + + align:start position:0% +uh essentially this delta function this + + + align:start position:0% +uh essentially this delta function this +delta f going close to zero and then in + + align:start position:0% +delta f going close to zero and then in + + + align:start position:0% +delta f going close to zero and then in +the time domain we get as a result of + + align:start position:0% +the time domain we get as a result of + + + align:start position:0% +the time domain we get as a result of +this narrowing we get a a wave that's a + + align:start position:0% +this narrowing we get a a wave that's a + + + align:start position:0% +this narrowing we get a a wave that's a +pure sinosoid constant in frequency and + + align:start position:0% +pure sinosoid constant in frequency and + + + align:start position:0% +pure sinosoid constant in frequency and +constant in amplitude and that's the + + align:start position:0% +constant in amplitude and that's the + + + align:start position:0% +constant in amplitude and that's the +sort of the output of a of a typical uh + + align:start position:0% +sort of the output of a of a typical uh + + + align:start position:0% +sort of the output of a of a typical uh +well shall we say an ideal an ideal + + align:start position:0% +well shall we say an ideal an ideal + + + align:start position:0% +well shall we say an ideal an ideal +laser. + + align:start position:0% +laser. + + + align:start position:0% +laser. +So now if uh if somebody then asks you + + align:start position:0% +So now if uh if somebody then asks you + + + align:start position:0% +So now if uh if somebody then asks you +where does uh where why does a laser + + align:start position:0% +where does uh where why does a laser + + + align:start position:0% +where does uh where why does a laser +have a very narrow spectral width then + + align:start position:0% +have a very narrow spectral width then + + + align:start position:0% +have a very narrow spectral width then +one can uh then say that it comes from + + align:start position:0% +one can uh then say that it comes from + + + align:start position:0% +one can uh then say that it comes from +the fact that we have an optical + + align:start position:0% +the fact that we have an optical + + + align:start position:0% +the fact that we have an optical +amplifier you know within a uh within a + + align:start position:0% +amplifier you know within a uh within a + + + align:start position:0% +amplifier you know within a uh within a +resonator with enough gain to overcome + + align:start position:0% +resonator with enough gain to overcome + + + align:start position:0% +resonator with enough gain to overcome +the losses to give us this extremely uh + + align:start position:0% +the losses to give us this extremely uh + + + align:start position:0% +the losses to give us this extremely uh +narrow line width. Now + + align:start position:0% +narrow line width. Now + + + align:start position:0% +narrow line width. Now +uh I'm going to then uh tell you about + + align:start position:0% +uh I'm going to then uh tell you about + + + align:start position:0% +uh I'm going to then uh tell you about +how the next property the one that that + + align:start position:0% +how the next property the one that that + + + align:start position:0% +how the next property the one that that +has to do with uh defraction limited + + align:start position:0% +has to do with uh defraction limited + + + align:start position:0% +has to do with uh defraction limited +columnation and focusing and so on. + + align:start position:0% +columnation and focusing and so on. + + + align:start position:0% +columnation and focusing and so on. +Where does this uh property uh come + + align:start position:0% +Where does this uh property uh come + + + align:start position:0% +Where does this uh property uh come +from? Again in a in a simple-minded way + + align:start position:0% +from? Again in a in a simple-minded way + + + align:start position:0% +from? Again in a in a simple-minded way +at this stage and later on we'll go into + + align:start position:0% +at this stage and later on we'll go into + + + align:start position:0% +at this stage and later on we'll go into +it in a little bit more more depth. + + align:start position:0% +it in a little bit more more depth. + + + align:start position:0% +it in a little bit more more depth. +Well, the the the this the spatial + + align:start position:0% +Well, the the the this the spatial + + + align:start position:0% +Well, the the the this the spatial +properties really come from the fact of + + align:start position:0% +properties really come from the fact of + + + align:start position:0% +properties really come from the fact of +course that we have an amplifier within + + align:start position:0% +course that we have an amplifier within + + + align:start position:0% +course that we have an amplifier within +within the resonator and we have these + + align:start position:0% +within the resonator and we have these + + + align:start position:0% +within the resonator and we have these +two mirrors. Let's take two plane + + align:start position:0% +two mirrors. Let's take two plane + + + align:start position:0% +two mirrors. Let's take two plane +mirrors for example. And we'll see later + + align:start position:0% +mirrors for example. And we'll see later + + + align:start position:0% +mirrors for example. And we'll see later +that that indeed the uh the mode that + + align:start position:0% +that that indeed the uh the mode that + + + align:start position:0% +that that indeed the uh the mode that +can be supported uh within that within + + align:start position:0% +can be supported uh within that within + + + align:start position:0% +can be supported uh within that within +that cavity is is uh essentially a + + align:start position:0% +that cavity is is uh essentially a + + + align:start position:0% +that cavity is is uh essentially a +parallel beam that gets reflected + + align:start position:0% +parallel beam that gets reflected + + + align:start position:0% +parallel beam that gets reflected +backwards and forwards between these uh + + align:start position:0% +backwards and forwards between these uh + + + align:start position:0% +backwards and forwards between these uh +two mirrors and and the amplifier then + + align:start position:0% +two mirrors and and the amplifier then + + + align:start position:0% +two mirrors and and the amplifier then +overcomes the losses in the cavity and + + align:start position:0% +overcomes the losses in the cavity and + + + align:start position:0% +overcomes the losses in the cavity and +this mirror has a little transmission. + + align:start position:0% +this mirror has a little transmission. + + + align:start position:0% +this mirror has a little transmission. +So the output here you would expect to + + align:start position:0% +So the output here you would expect to + + + align:start position:0% +So the output here you would expect to +be a uh a columnated beam a plane a + + align:start position:0% +be a uh a columnated beam a plane a + + + align:start position:0% +be a uh a columnated beam a plane a +plane wave with defraction limited uh uh + + align:start position:0% +plane wave with defraction limited uh uh + + + align:start position:0% +plane wave with defraction limited uh uh +columnation and if you put a lens will + + align:start position:0% +columnation and if you put a lens will + + + align:start position:0% +columnation and if you put a lens will +be diffraction limited focusing. Now not + + align:start position:0% +be diffraction limited focusing. Now not + + + align:start position:0% +be diffraction limited focusing. Now not +all laser cavities have plain mirrors. + + align:start position:0% +all laser cavities have plain mirrors. + + + align:start position:0% +all laser cavities have plain mirrors. +Some of them have curved mirrors like in + + align:start position:0% +Some of them have curved mirrors like in + + + align:start position:0% +Some of them have curved mirrors like in +this case two concave mirrors. Again the + + align:start position:0% +this case two concave mirrors. Again the + + + align:start position:0% +this case two concave mirrors. Again the +mode shape as we'll see later will be + + align:start position:0% +mode shape as we'll see later will be + + + align:start position:0% +mode shape as we'll see later will be +will be different from this will be + + align:start position:0% +will be different from this will be + + + align:start position:0% +will be different from this will be +something like that. And then if we let + + align:start position:0% +something like that. And then if we let + + + align:start position:0% +something like that. And then if we let +some of the light leak out through one + + align:start position:0% +some of the light leak out through one + + + align:start position:0% +some of the light leak out through one +of the curved mirrors, you'll see it + + align:start position:0% +of the curved mirrors, you'll see it + + + align:start position:0% +of the curved mirrors, you'll see it +will be diverging. Just because it's + + align:start position:0% +will be diverging. Just because it's + + + align:start position:0% +will be diverging. Just because it's +diverging, it doesn't mean that it's a + + align:start position:0% +diverging, it doesn't mean that it's a + + + align:start position:0% +diverging, it doesn't mean that it's a +bad beam. It it it just means that with + + align:start position:0% +bad beam. It it it just means that with + + + align:start position:0% +bad beam. It it it just means that with +lenses, we can convert it to any size + + align:start position:0% +lenses, we can convert it to any size + + + align:start position:0% +lenses, we can convert it to any size +beam we want and focus it and and so on. + + align:start position:0% +beam we want and focus it and and so on. + + + align:start position:0% +beam we want and focus it and and so on. +So it's really it's the cavity plus the + + align:start position:0% +So it's really it's the cavity plus the + + + align:start position:0% +So it's really it's the cavity plus the +amplifier uh that that gives us this + + align:start position:0% +amplifier uh that that gives us this + + + align:start position:0% +amplifier uh that that gives us this +very uniform uh wave that we uh we we + + align:start position:0% +very uniform uh wave that we uh we we + + + align:start position:0% +very uniform uh wave that we uh we we +talked about uh before. In fact, if uh + + align:start position:0% +talked about uh before. In fact, if uh + + + align:start position:0% +talked about uh before. In fact, if uh +we can shape the the output of uh of a + + align:start position:0% +we can shape the the output of uh of a + + + align:start position:0% +we can shape the the output of uh of a +laser beam is these two outputs, excuse + + align:start position:0% +laser beam is these two outputs, excuse + + + align:start position:0% +laser beam is these two outputs, excuse +me, with uh with lenses and then we can + + align:start position:0% +me, with uh with lenses and then we can + + + align:start position:0% +me, with uh with lenses and then we can +create here some small focus spot here + + align:start position:0% +create here some small focus spot here + + + align:start position:0% +create here some small focus spot here +maybe slightly bigger focus. We can then + + align:start position:0% +maybe slightly bigger focus. We can then + + + align:start position:0% +maybe slightly bigger focus. We can then +create a a narrower columnated beam from + + align:start position:0% +create a a narrower columnated beam from + + + align:start position:0% +create a a narrower columnated beam from +what we started with or a larger + + align:start position:0% +what we started with or a larger + + + align:start position:0% +what we started with or a larger +columnated beam and so on. It's all done + + align:start position:0% +columnated beam and so on. It's all done + + + align:start position:0% +columnated beam and so on. It's all done +with with the use of good optics outside + + align:start position:0% +with with the use of good optics outside + + + align:start position:0% +with with the use of good optics outside +the the laser cavity. So this uh all + + align:start position:0% +the the laser cavity. So this uh all + + + align:start position:0% +the the laser cavity. So this uh all +these properties to do with the with the + + align:start position:0% +these properties to do with the with the + + + align:start position:0% +these properties to do with the with the +spatial effects of of the laser beam + + align:start position:0% +spatial effects of of the laser beam + + + align:start position:0% +spatial effects of of the laser beam +then come from from the cavity plus the + + align:start position:0% +then come from from the cavity plus the + + + align:start position:0% +then come from from the cavity plus the +amplifier. All right. Now we want to + + align:start position:0% +amplifier. All right. Now we want to + + + align:start position:0% +amplifier. All right. Now we want to +talk about where where does high power + + align:start position:0% +talk about where where does high power + + + align:start position:0% +talk about where where does high power +uh uh come from? + + align:start position:0% +uh uh come from? + + + align:start position:0% +uh uh come from? +Excuse me. Well, the high power uh comes + + align:start position:0% +Excuse me. Well, the high power uh comes + + + align:start position:0% +Excuse me. Well, the high power uh comes +from uh obviously from the from the + + align:start position:0% +from uh obviously from the from the + + + align:start position:0% +from uh obviously from the from the +amplifier because it's the amplifier + + align:start position:0% +amplifier because it's the amplifier + + + align:start position:0% +amplifier because it's the amplifier +that that uh gives us gain to overcome + + align:start position:0% +that that uh gives us gain to overcome + + + align:start position:0% +that that uh gives us gain to overcome +the losses. And if we have more gain + + align:start position:0% +the losses. And if we have more gain + + + align:start position:0% +the losses. And if we have more gain +left, then that can be converted to uh + + align:start position:0% +left, then that can be converted to uh + + + align:start position:0% +left, then that can be converted to uh +to power out. So, so the the bigger the + + align:start position:0% +to power out. So, so the the bigger the + + + align:start position:0% +to power out. So, so the the bigger the +amplifier then the more power we'll get. + + align:start position:0% +amplifier then the more power we'll get. + + + align:start position:0% +amplifier then the more power we'll get. +As simple as that. So, sooner later we + + align:start position:0% +As simple as that. So, sooner later we + + + align:start position:0% +As simple as that. So, sooner later we +will find out about how an amplifier + + align:start position:0% +will find out about how an amplifier + + + align:start position:0% +will find out about how an amplifier +works. So, if we can come up with a + + align:start position:0% +works. So, if we can come up with a + + + align:start position:0% +works. So, if we can come up with a +bigger amplifier and how to make a + + align:start position:0% +bigger amplifier and how to make a + + + align:start position:0% +bigger amplifier and how to make a +bigger amplifier, then we'll really know + + align:start position:0% +bigger amplifier, then we'll really know + + + align:start position:0% +bigger amplifier, then we'll really know +the secret of making making high power + + align:start position:0% +the secret of making making high power + + + align:start position:0% +the secret of making making high power +uh lasers. So it's in the hands of the + + align:start position:0% +uh lasers. So it's in the hands of the + + + align:start position:0% +uh lasers. So it's in the hands of the +of the amplifier + + align:start position:0% +of the amplifier + + + align:start position:0% +of the amplifier +the the tuning the tuning range where + + align:start position:0% +the the tuning the tuning range where + + + align:start position:0% +the the tuning the tuning range where +does the tuning range come from? Well, + + align:start position:0% +does the tuning range come from? Well, + + + align:start position:0% +does the tuning range come from? Well, +let me give you again a very simple uh + + align:start position:0% +let me give you again a very simple uh + + + align:start position:0% +let me give you again a very simple uh +simple uh explanation. Let's go back to + + align:start position:0% +simple uh explanation. Let's go back to + + + align:start position:0% +simple uh explanation. Let's go back to +to the laser that we had two mirrors + + align:start position:0% +to the laser that we had two mirrors + + + align:start position:0% +to the laser that we had two mirrors +separated by distance L and a cavity. + + align:start position:0% +separated by distance L and a cavity. + + + align:start position:0% +separated by distance L and a cavity. +And then we had the cavity mode over + + align:start position:0% +And then we had the cavity mode over + + + align:start position:0% +And then we had the cavity mode over +here. And then this is the uh the + + align:start position:0% +here. And then this is the uh the + + + align:start position:0% +here. And then this is the uh the +amplifier bandwidth. This is where the + + align:start position:0% +amplifier bandwidth. This is where the + + + align:start position:0% +amplifier bandwidth. This is where the +amplifier likes to uh uh provide gain. + + align:start position:0% +amplifier likes to uh uh provide gain. + + + align:start position:0% +amplifier likes to uh uh provide gain. +And then we said that the output of the + + align:start position:0% +And then we said that the output of the + + + align:start position:0% +And then we said that the output of the +laser would be would be this delta + + align:start position:0% +laser would be would be this delta + + + align:start position:0% +laser would be would be this delta +function at the cavity resonance. Now + + align:start position:0% +function at the cavity resonance. Now + + + align:start position:0% +function at the cavity resonance. Now +these modes here are not fixed because + + align:start position:0% +these modes here are not fixed because + + + align:start position:0% +these modes here are not fixed because +they depend on on L. So if I change L + + align:start position:0% +they depend on on L. So if I change L + + + align:start position:0% +they depend on on L. So if I change L +the length of the cavity I can move + + align:start position:0% +the length of the cavity I can move + + + align:start position:0% +the length of the cavity I can move +these modes around. So if I move this + + align:start position:0% +these modes around. So if I move this + + + align:start position:0% +these modes around. So if I move this +cavity mode around if I moved it just a + + align:start position:0% +cavity mode around if I moved it just a + + + align:start position:0% +cavity mode around if I moved it just a +little bit here then this frequency here + + align:start position:0% +little bit here then this frequency here + + + align:start position:0% +little bit here then this frequency here +will be dragged. The laser frequency + + align:start position:0% +will be dragged. The laser frequency + + + align:start position:0% +will be dragged. The laser frequency +will be dragged with it. And the tuning + + align:start position:0% +will be dragged with it. And the tuning + + + align:start position:0% +will be dragged with it. And the tuning +range is really the width of the B of + + align:start position:0% +range is really the width of the B of + + + align:start position:0% +range is really the width of the B of +the bandwidth of the of the amplifier. + + align:start position:0% +the bandwidth of the of the amplifier. + + + align:start position:0% +the bandwidth of the of the amplifier. +because if I tune the cavity outside + + align:start position:0% +because if I tune the cavity outside + + + align:start position:0% +because if I tune the cavity outside +that I get no output output at all. Now + + align:start position:0% +that I get no output output at all. Now + + + align:start position:0% +that I get no output output at all. Now +here is a an amplifier that uh has a + + align:start position:0% +here is a an amplifier that uh has a + + + align:start position:0% +here is a an amplifier that uh has a +bandwidth that's bigger than what I + + align:start position:0% +bandwidth that's bigger than what I + + + align:start position:0% +bandwidth that's bigger than what I +showed you before which means now that + + align:start position:0% +showed you before which means now that + + + align:start position:0% +showed you before which means now that +the tuning range can be can be wider now + + align:start position:0% +the tuning range can be can be wider now + + + align:start position:0% +the tuning range can be can be wider now +okay depending again as I say on the + + align:start position:0% +okay depending again as I say on the + + + align:start position:0% +okay depending again as I say on the +width on the bandwidth of the of the + + align:start position:0% +width on the bandwidth of the of the + + + align:start position:0% +width on the bandwidth of the of the +amplifier and if I in this particular + + align:start position:0% +amplifier and if I in this particular + + + align:start position:0% +amplifier and if I in this particular +case if this mode leaves the amplifier + + align:start position:0% +case if this mode leaves the amplifier + + + align:start position:0% +case if this mode leaves the amplifier +at this end there's the other one that + + align:start position:0% +at this end there's the other one that + + + align:start position:0% +at this end there's the other one that +will come in so I will always get some + + align:start position:0% +will come in so I will always get some + + + align:start position:0% +will come in so I will always get some +output from the laser but uh the + + align:start position:0% +output from the laser but uh the + + + align:start position:0% +output from the laser but uh the +intensity can can vary depending on + + align:start position:0% +intensity can can vary depending on + + + align:start position:0% +intensity can can vary depending on +where I am with respect to gain curve. + + align:start position:0% +where I am with respect to gain curve. + + + align:start position:0% +where I am with respect to gain curve. +While over here in this previous one, if + + align:start position:0% +While over here in this previous one, if + + + align:start position:0% +While over here in this previous one, if +the mode is outside the amplifier + + align:start position:0% +the mode is outside the amplifier + + + align:start position:0% +the mode is outside the amplifier +bandwidth, I get no light output at all. + + align:start position:0% +bandwidth, I get no light output at all. + + + align:start position:0% +bandwidth, I get no light output at all. +So then so then the in summary then the + + align:start position:0% +So then so then the in summary then the + + + align:start position:0% +So then so then the in summary then the +tuning of a uh of a laser then depends + + align:start position:0% +tuning of a uh of a laser then depends + + + align:start position:0% +tuning of a uh of a laser then depends +on the bandwidth of the amplifier. The + + align:start position:0% +on the bandwidth of the amplifier. The + + + align:start position:0% +on the bandwidth of the amplifier. The +wider the bandwidth the the wider the + + align:start position:0% +wider the bandwidth the the wider the + + + align:start position:0% +wider the bandwidth the the wider the +tuning range. Okay. So now the the + + align:start position:0% +tuning range. Okay. So now the the + + + align:start position:0% +tuning range. Okay. So now the the +remaining property that we talked about + + align:start position:0% +remaining property that we talked about + + + align:start position:0% +remaining property that we talked about +before is the is the very short pulse + + align:start position:0% +before is the is the very short pulse + + + align:start position:0% +before is the is the very short pulse +width uh generation. So the question is + + align:start position:0% +width uh generation. So the question is + + + align:start position:0% +width uh generation. So the question is +where does where does this come from? + + align:start position:0% +where does where does this come from? + + + align:start position:0% +where does where does this come from? +Again in a simple simple-minded way + + align:start position:0% +Again in a simple simple-minded way + + + align:start position:0% +Again in a simple simple-minded way +again here to explain this I need to to + + align:start position:0% +again here to explain this I need to to + + + align:start position:0% +again here to explain this I need to to +uh uh give you a little bit of a + + align:start position:0% +uh uh give you a little bit of a + + + align:start position:0% +uh uh give you a little bit of a +background and then uh start with uh + + align:start position:0% +background and then uh start with uh + + + align:start position:0% +background and then uh start with uh +with what we've done before. So if you + + align:start position:0% +with what we've done before. So if you + + + align:start position:0% +with what we've done before. So if you +had a delta function in in frequency + + align:start position:0% +had a delta function in in frequency + + + align:start position:0% +had a delta function in in frequency +space uh the in the time domain you have + + align:start position:0% +space uh the in the time domain you have + + + align:start position:0% +space uh the in the time domain you have +essentially an oscillation a cinosodal + + align:start position:0% +essentially an oscillation a cinosodal + + + align:start position:0% +essentially an oscillation a cinosodal +oscillation with a constant amplitude + + align:start position:0% +oscillation with a constant amplitude + + + align:start position:0% +oscillation with a constant amplitude +and a constant frequency. This is what + + align:start position:0% +and a constant frequency. This is what + + + align:start position:0% +and a constant frequency. This is what +you know we've been talking about + + align:start position:0% +you know we've been talking about + + + align:start position:0% +you know we've been talking about +before. Now if I looked at the intensity + + align:start position:0% +before. Now if I looked at the intensity + + + align:start position:0% +before. Now if I looked at the intensity +remember this is now at optical + + align:start position:0% +remember this is now at optical + + + align:start position:0% +remember this is now at optical +frequency maybe 10^ the 15 hertz or so. + + align:start position:0% +frequency maybe 10^ the 15 hertz or so. + + + align:start position:0% +frequency maybe 10^ the 15 hertz or so. +So it's very high frequency. I cannot + + align:start position:0% +So it's very high frequency. I cannot + + + align:start position:0% +So it's very high frequency. I cannot +observe I don't have any way of + + align:start position:0% +observe I don't have any way of + + + align:start position:0% +observe I don't have any way of +observing it. But if I looked at the + + align:start position:0% +observing it. But if I looked at the + + + align:start position:0% +observing it. But if I looked at the +intensity associated with this using a + + align:start position:0% +intensity associated with this using a + + + align:start position:0% +intensity associated with this using a +uh square law detector, what I get is + + align:start position:0% +uh square law detector, what I get is + + + align:start position:0% +uh square law detector, what I get is +essentially a constant output constant + + align:start position:0% +essentially a constant output constant + + + align:start position:0% +essentially a constant output constant +intensity output associated with this + + align:start position:0% +intensity output associated with this + + + align:start position:0% +intensity output associated with this +wave. So if I have then a delta function + + align:start position:0% +wave. So if I have then a delta function + + + align:start position:0% +wave. So if I have then a delta function +in frequency, I have then intensity + + align:start position:0% +in frequency, I have then intensity + + + align:start position:0% +in frequency, I have then intensity +would be would be constant. So this is + + align:start position:0% +would be would be constant. So this is + + + align:start position:0% +would be would be constant. So this is +completely opposite to generation of + + align:start position:0% +completely opposite to generation of + + + align:start position:0% +completely opposite to generation of +short of short pulses. This is + + align:start position:0% +short of short pulses. This is + + + align:start position:0% +short of short pulses. This is +essentially you know a CW CW laser. But + + align:start position:0% +essentially you know a CW CW laser. But + + + align:start position:0% +essentially you know a CW CW laser. But +now let's let's see what happens to this + + align:start position:0% +now let's let's see what happens to this + + + align:start position:0% +now let's let's see what happens to this +constant output when I add when I add + + align:start position:0% +constant output when I add when I add + + + align:start position:0% +constant output when I add when I add +another frequency. If I have now two + + align:start position:0% +another frequency. If I have now two + + + align:start position:0% +another frequency. If I have now two +frequencies let's say that's that are + + align:start position:0% +frequencies let's say that's that are + + + align:start position:0% +frequencies let's say that's that are +oscillating one at f_sub_1 at f_sub_2 + + align:start position:0% +oscillating one at f_sub_1 at f_sub_2 + + + align:start position:0% +oscillating one at f_sub_1 at f_sub_2 +here they are difference in in + + align:start position:0% +here they are difference in in + + + align:start position:0% +here they are difference in in +wavelength a difference in the frequency + + align:start position:0% +wavelength a difference in the frequency + + + align:start position:0% +wavelength a difference in the frequency +separated let's say by f subs + + align:start position:0% +separated let's say by f subs + + + align:start position:0% +separated let's say by f subs +now in the when I look at them when I + + align:start position:0% +now in the when I look at them when I + + + align:start position:0% +now in the when I look at them when I +combine them and look at them in the + + align:start position:0% +combine them and look at them in the + + + align:start position:0% +combine them and look at them in the +time domain I get something like this + + align:start position:0% +time domain I get something like this + + + align:start position:0% +time domain I get something like this +which is like a beat frequency or is a + + align:start position:0% +which is like a beat frequency or is a + + + align:start position:0% +which is like a beat frequency or is a +beat frequency + + align:start position:0% +beat frequency + + + align:start position:0% +beat frequency +the the uh the period between these + + align:start position:0% +the the uh the period between these + + + align:start position:0% +the the uh the period between these +peaks t big t is just simply 1 over uh f + + align:start position:0% +peaks t big t is just simply 1 over uh f + + + align:start position:0% +peaks t big t is just simply 1 over uh f +subs the separation in frequency. But + + align:start position:0% +subs the separation in frequency. But + + + align:start position:0% +subs the separation in frequency. But +the if you look at the intensity + + align:start position:0% +the if you look at the intensity + + + align:start position:0% +the if you look at the intensity +associated with this wave looks + + align:start position:0% +associated with this wave looks + + + align:start position:0% +associated with this wave looks +something like this which is the + + align:start position:0% +something like this which is the + + + align:start position:0% +something like this which is the +envelope of of this beat. It's no longer + + align:start position:0% +envelope of of this beat. It's no longer + + + align:start position:0% +envelope of of this beat. It's no longer +constant just by simply adding uh two + + align:start position:0% +constant just by simply adding uh two + + + align:start position:0% +constant just by simply adding uh two +waves at different frequencies. And + + align:start position:0% +waves at different frequencies. And + + + align:start position:0% +waves at different frequencies. And +we're all familiar with beating effects + + align:start position:0% +we're all familiar with beating effects + + + align:start position:0% +we're all familiar with beating effects +of uh when two singers sing with two + + align:start position:0% +of uh when two singers sing with two + + + align:start position:0% +of uh when two singers sing with two +different two different frequencies then + + align:start position:0% +different two different frequencies then + + + align:start position:0% +different two different frequencies then +you'll hear the uh uh the beat. So + + align:start position:0% +you'll hear the uh uh the beat. So + + + align:start position:0% +you'll hear the uh uh the beat. So +basically now I've transformed a + + align:start position:0% +basically now I've transformed a + + + align:start position:0% +basically now I've transformed a +constant intensity to a to a sinosoidal + + align:start position:0% +constant intensity to a to a sinosoidal + + + align:start position:0% +constant intensity to a to a sinosoidal +uh intensity. It's not quite a short + + align:start position:0% +uh intensity. It's not quite a short + + + align:start position:0% +uh intensity. It's not quite a short +pulse yet, but it's it's sort of getting + + align:start position:0% +pulse yet, but it's it's sort of getting + + + align:start position:0% +pulse yet, but it's it's sort of getting +there. All right. So now let's look at + + align:start position:0% +there. All right. So now let's look at + + + align:start position:0% +there. All right. So now let's look at +let's look at what happens when we add + + align:start position:0% +let's look at what happens when we add + + + align:start position:0% +let's look at what happens when we add +another uh yet another frequency. All + + align:start position:0% +another uh yet another frequency. All + + + align:start position:0% +another uh yet another frequency. All +right. Here it is. Now we have three + + align:start position:0% +right. Here it is. Now we have three + + + align:start position:0% +right. Here it is. Now we have three +f_sub_1, f_sub_2, f3. Here they are in + + align:start position:0% +f_sub_1, f_sub_2, f3. Here they are in + + + align:start position:0% +f_sub_1, f_sub_2, f3. Here they are in +the time domain. I add them up and they + + align:start position:0% +the time domain. I add them up and they + + + align:start position:0% +the time domain. I add them up and they +give me some waveform like this. When I + + align:start position:0% +give me some waveform like this. When I + + + align:start position:0% +give me some waveform like this. When I +square this, I get the intensity to look + + align:start position:0% +square this, I get the intensity to look + + + align:start position:0% +square this, I get the intensity to look +like this. As you can see, now this + + align:start position:0% +like this. As you can see, now this + + + align:start position:0% +like this. As you can see, now this +width is beginning to look like a pulse. + + align:start position:0% +width is beginning to look like a pulse. + + + align:start position:0% +width is beginning to look like a pulse. +But again, not quite. Again, the the the + + align:start position:0% +But again, not quite. Again, the the the + + + align:start position:0% +But again, not quite. Again, the the the +repetition + + align:start position:0% +repetition + + + align:start position:0% +repetition +between these two peaks. The period + + align:start position:0% +between these two peaks. The period + + + align:start position:0% +between these two peaks. The period +between here and here, the time between + + align:start position:0% +between here and here, the time between + + + align:start position:0% +between here and here, the time between +the two peaks or the two sort of pulses + + align:start position:0% +the two peaks or the two sort of pulses + + + align:start position:0% +the two peaks or the two sort of pulses +at this stage is again one over fs where + + align:start position:0% +at this stage is again one over fs where + + + align:start position:0% +at this stage is again one over fs where +fs is the spacing between these modes. + + align:start position:0% +fs is the spacing between these modes. + + + align:start position:0% +fs is the spacing between these modes. +And we're assuming they are constant uh + + align:start position:0% +And we're assuming they are constant uh + + + align:start position:0% +And we're assuming they are constant uh +constant spacing between these + + align:start position:0% +constant spacing between these + + + align:start position:0% +constant spacing between these +frequencies. Now you can think you can + + align:start position:0% +frequencies. Now you can think you can + + + align:start position:0% +frequencies. Now you can think you can +add more and more frequencies and let's + + align:start position:0% +add more and more frequencies and let's + + + align:start position:0% +add more and more frequencies and let's +see and let's see what uh what happens. + + align:start position:0% +see and let's see what uh what happens. + + + align:start position:0% +see and let's see what uh what happens. +Uh now I've simplified the picture and I + + align:start position:0% +Uh now I've simplified the picture and I + + + align:start position:0% +Uh now I've simplified the picture and I +just put the intensity output that we've + + align:start position:0% +just put the intensity output that we've + + + align:start position:0% +just put the intensity output that we've +had before. Remember when we had only + + align:start position:0% +had before. Remember when we had only + + + align:start position:0% +had before. Remember when we had only +one it was constant intensity when we + + align:start position:0% +one it was constant intensity when we + + + align:start position:0% +one it was constant intensity when we +had two we we have this sinosoidal + + align:start position:0% +had two we we have this sinosoidal + + + align:start position:0% +had two we we have this sinosoidal +behavior. Three is like this. Four if + + align:start position:0% +behavior. Three is like this. Four if + + + align:start position:0% +behavior. Three is like this. Four if +you add four it begins like this. Eight + + align:start position:0% +you add four it begins like this. Eight + + + align:start position:0% +you add four it begins like this. Eight +if you eight then now it's beginning to + + align:start position:0% +if you eight then now it's beginning to + + + align:start position:0% +if you eight then now it's beginning to +look like a pulse. And then when you go + + align:start position:0% +look like a pulse. And then when you go + + + align:start position:0% +look like a pulse. And then when you go +to 16 frequencies that are constantly + + align:start position:0% +to 16 frequencies that are constantly + + + align:start position:0% +to 16 frequencies that are constantly +spaced, then indeed it begins to really + + align:start position:0% +spaced, then indeed it begins to really + + + align:start position:0% +spaced, then indeed it begins to really +look like a like a pulse. The period + + align:start position:0% +look like a like a pulse. The period + + + align:start position:0% +look like a like a pulse. The period +okay the separation between these pulse + + align:start position:0% +okay the separation between these pulse + + + align:start position:0% +okay the separation between these pulse +trains is again 1 / fs the uh frequency + + align:start position:0% +trains is again 1 / fs the uh frequency + + + align:start position:0% +trains is again 1 / fs the uh frequency +spacing between the modes and the pulse + + align:start position:0% +spacing between the modes and the pulse + + + align:start position:0% +spacing between the modes and the pulse +width which is the key thing here. The + + align:start position:0% +width which is the key thing here. The + + + align:start position:0% +width which is the key thing here. The +pulse width pulse width is given by one + + align:start position:0% +pulse width pulse width is given by one + + + align:start position:0% +pulse width pulse width is given by one +* n the number of of modes uh times + + align:start position:0% +* n the number of of modes uh times + + + align:start position:0% +* n the number of of modes uh times +fubs. + + align:start position:0% +fubs. + + + align:start position:0% +fubs. +So n * f subs is really the uh the total + + align:start position:0% +So n * f subs is really the uh the total + + + align:start position:0% +So n * f subs is really the uh the total +uh separation in frequency between the + + align:start position:0% +uh separation in frequency between the + + + align:start position:0% +uh separation in frequency between the +first and the last and the last uh + + align:start position:0% +first and the last and the last uh + + + align:start position:0% +first and the last and the last uh +frequencies or modes. All right. So then + + align:start position:0% +frequencies or modes. All right. So then + + + align:start position:0% +frequencies or modes. All right. So then +then you can see here that the shorter + + align:start position:0% +then you can see here that the shorter + + + align:start position:0% +then you can see here that the shorter +the pulse all right if you want a very + + align:start position:0% +the pulse all right if you want a very + + + align:start position:0% +the pulse all right if you want a very +short pulse then you want to make n + + align:start position:0% +short pulse then you want to make n + + + align:start position:0% +short pulse then you want to make n +times some fs very large which means + + align:start position:0% +times some fs very large which means + + + align:start position:0% +times some fs very large which means +either n is very large or f subs is is + + align:start position:0% +either n is very large or f subs is is + + + align:start position:0% +either n is very large or f subs is is +very large or certainly the product has + + align:start position:0% +very large or certainly the product has + + + align:start position:0% +very large or certainly the product has +to be very large. So when that's the + + align:start position:0% +to be very large. So when that's the + + + align:start position:0% +to be very large. So when that's the +bandwidth of the essentially the u of + + align:start position:0% +bandwidth of the essentially the u of + + + align:start position:0% +bandwidth of the essentially the u of +this of the spectrum of these uh of + + align:start position:0% +this of the spectrum of these uh of + + + align:start position:0% +this of the spectrum of these uh of +these modes. So the key thing then is to + + align:start position:0% +these modes. So the key thing then is to + + + align:start position:0% +these modes. So the key thing then is to +have let's say in this case lots of + + align:start position:0% +have let's say in this case lots of + + + align:start position:0% +have let's say in this case lots of +modes lots of modes extending over a + + align:start position:0% +modes lots of modes extending over a + + + align:start position:0% +modes lots of modes extending over a +wide frequency range and uh and then + + align:start position:0% +wide frequency range and uh and then + + + align:start position:0% +wide frequency range and uh and then +that would give us this u this uh short + + align:start position:0% +that would give us this u this uh short + + + align:start position:0% +that would give us this u this uh short +a short short pulse. All right, big + + align:start position:0% +a short short pulse. All right, big + + + align:start position:0% +a short short pulse. All right, big +question now is where can we find all + + align:start position:0% +question now is where can we find all + + + align:start position:0% +question now is where can we find all +these frequencies uh from in a laser. + + align:start position:0% +these frequencies uh from in a laser. + + + align:start position:0% +these frequencies uh from in a laser. +All right. So, so let's uh let's go back + + align:start position:0% +All right. So, so let's uh let's go back + + + align:start position:0% +All right. So, so let's uh let's go back +and remind ourselves what we just + + align:start position:0% +and remind ourselves what we just + + + align:start position:0% +and remind ourselves what we just +mentioned about lasers. We said that if + + align:start position:0% +mentioned about lasers. We said that if + + + align:start position:0% +mentioned about lasers. We said that if +we have a wide gain bandwidth gain + + align:start position:0% +we have a wide gain bandwidth gain + + + align:start position:0% +we have a wide gain bandwidth gain +medium amplifier and we have then lots + + align:start position:0% +medium amplifier and we have then lots + + + align:start position:0% +medium amplifier and we have then lots +of modes lots of cavity modes under the + + align:start position:0% +of modes lots of cavity modes under the + + + align:start position:0% +of modes lots of cavity modes under the +this this amplifier then and if there's + + align:start position:0% +this this amplifier then and if there's + + + align:start position:0% +this this amplifier then and if there's +enough gain to overcome the losses in + + align:start position:0% +enough gain to overcome the losses in + + + align:start position:0% +enough gain to overcome the losses in +all these modes and I would get + + align:start position:0% +all these modes and I would get + + + align:start position:0% +all these modes and I would get +essentially four four frequencies. Well, + + align:start position:0% +essentially four four frequencies. Well, + + + align:start position:0% +essentially four four frequencies. Well, +before we only talked about one but now + + align:start position:0% +before we only talked about one but now + + + align:start position:0% +before we only talked about one but now +I can generate four frequencies out of + + align:start position:0% +I can generate four frequencies out of + + + align:start position:0% +I can generate four frequencies out of +this amplifier + + align:start position:0% +this amplifier + + + align:start position:0% +this amplifier +if the amplifier allows me to oscillate + + align:start position:0% +if the amplifier allows me to oscillate + + + align:start position:0% +if the amplifier allows me to oscillate +at all these frequencies. That's all + + align:start position:0% +at all these frequencies. That's all + + + align:start position:0% +at all these frequencies. That's all +very nice. So we can see that this is + + align:start position:0% +very nice. So we can see that this is + + + align:start position:0% +very nice. So we can see that this is +the beginning of of having many modes. + + align:start position:0% +the beginning of of having many modes. + + + align:start position:0% +the beginning of of having many modes. +So if you can imagine an amplifier that + + align:start position:0% +So if you can imagine an amplifier that + + + align:start position:0% +So if you can imagine an amplifier that +has this has much bigger bandwidth than + + align:start position:0% +has this has much bigger bandwidth than + + + align:start position:0% +has this has much bigger bandwidth than +this then I can have more and more more + + align:start position:0% +this then I can have more and more more + + + align:start position:0% +this then I can have more and more more +of these uh modes oscillating. All + + align:start position:0% +of these uh modes oscillating. All + + + align:start position:0% +of these uh modes oscillating. All +right. And then so of course if I have + + align:start position:0% +right. And then so of course if I have + + + align:start position:0% +right. And then so of course if I have +just to remind you if I have uh you know + + align:start position:0% +just to remind you if I have uh you know + + + align:start position:0% +just to remind you if I have uh you know +16 of them then essentially and uh and a + + align:start position:0% +16 of them then essentially and uh and a + + + align:start position:0% +16 of them then essentially and uh and a +certain spacing uh between them but + + align:start position:0% +certain spacing uh between them but + + + align:start position:0% +certain spacing uh between them but +basically I can get a a uh a narrow + + align:start position:0% +basically I can get a a uh a narrow + + + align:start position:0% +basically I can get a a uh a narrow +pulse coming out of of the laser here + + align:start position:0% +pulse coming out of of the laser here + + + align:start position:0% +pulse coming out of of the laser here +without essentially uh doing anything. + + align:start position:0% +without essentially uh doing anything. + + + align:start position:0% +without essentially uh doing anything. +Now the uh + + align:start position:0% +Now the uh + + + align:start position:0% +Now the uh +I I didn't mention a certain key key + + align:start position:0% +I I didn't mention a certain key key + + + align:start position:0% +I I didn't mention a certain key key +issue here and that is when and and we + + align:start position:0% +issue here and that is when and and we + + + align:start position:0% +issue here and that is when and and we +can go back and and show you when we + + align:start position:0% +can go back and and show you when we + + + align:start position:0% +can go back and and show you when we +when I combine the sine waves let me let + + align:start position:0% +when I combine the sine waves let me let + + + align:start position:0% +when I combine the sine waves let me let +me go back to this uh uh to this + + align:start position:0% +me go back to this uh uh to this + + + align:start position:0% +me go back to this uh uh to this +viewraph here. when I combine these sine + + align:start position:0% +viewraph here. when I combine these sine + + + align:start position:0% +viewraph here. when I combine these sine +waves here, you know, the the the uh + + align:start position:0% +waves here, you know, the the the uh + + + align:start position:0% +waves here, you know, the the the uh +these waves had to be in phase + + align:start position:0% +these waves had to be in phase + + + align:start position:0% +these waves had to be in phase +somewhere, they had to start start + + align:start position:0% +somewhere, they had to start start + + + align:start position:0% +somewhere, they had to start start +together. And if they don't, then you + + align:start position:0% +together. And if they don't, then you + + + align:start position:0% +together. And if they don't, then you +wouldn't get uh this kind of behavior + + align:start position:0% +wouldn't get uh this kind of behavior + + + align:start position:0% +wouldn't get uh this kind of behavior +because if if if the relative phases are + + align:start position:0% +because if if if the relative phases are + + + align:start position:0% +because if if if the relative phases are +are way off and different, then then + + align:start position:0% +are way off and different, then then + + + align:start position:0% +are way off and different, then then +you're in real trouble. So So the uh let + + align:start position:0% +you're in real trouble. So So the uh let + + + align:start position:0% +you're in real trouble. So So the uh let +me see if I can find my uh view graph + + align:start position:0% +me see if I can find my uh view graph + + + align:start position:0% +me see if I can find my uh view graph +here. uh and this shows that what + + align:start position:0% +here. uh and this shows that what + + + align:start position:0% +here. uh and this shows that what +happens when uh when uh all the 16 modes + + align:start position:0% +happens when uh when uh all the 16 modes + + + align:start position:0% +happens when uh when uh all the 16 modes +in this case are all in phase or start + + align:start position:0% +in this case are all in phase or start + + + align:start position:0% +in this case are all in phase or start +together then indeed this is what I'll + + align:start position:0% +together then indeed this is what I'll + + + align:start position:0% +together then indeed this is what I'll +get. I get this pulse width as given by + + align:start position:0% +get. I get this pulse width as given by + + + align:start position:0% +get. I get this pulse width as given by +1 / nfs. So there's a special condition + + align:start position:0% +1 / nfs. So there's a special condition + + + align:start position:0% +1 / nfs. So there's a special condition +I have to satisfy in order to generate + + align:start position:0% +I have to satisfy in order to generate + + + align:start position:0% +I have to satisfy in order to generate +this narrow pulse width. And here's an + + align:start position:0% +this narrow pulse width. And here's an + + + align:start position:0% +this narrow pulse width. And here's an +example. What happens if only 10 of the + + align:start position:0% +example. What happens if only 10 of the + + + align:start position:0% +example. What happens if only 10 of the +16 start in phase and not all 16 of + + align:start position:0% +16 start in phase and not all 16 of + + + align:start position:0% +16 start in phase and not all 16 of +them? then I get a messy looking output + + align:start position:0% +them? then I get a messy looking output + + + align:start position:0% +them? then I get a messy looking output +like this and uh it's not like this at + + align:start position:0% +like this and uh it's not like this at + + + align:start position:0% +like this and uh it's not like this at +all. So in order to to generate very + + align:start position:0% +all. So in order to to generate very + + + align:start position:0% +all. So in order to to generate very +short pulses out of uh out of lasers + + align:start position:0% +short pulses out of uh out of lasers + + + align:start position:0% +short pulses out of uh out of lasers +then then I need to uh get all these + + align:start position:0% +then then I need to uh get all these + + + align:start position:0% +then then I need to uh get all these +modes under the gain curve to start + + align:start position:0% +modes under the gain curve to start + + + align:start position:0% +modes under the gain curve to start +together and that is the the topic of uh + + align:start position:0% +together and that is the the topic of uh + + + align:start position:0% +together and that is the the topic of uh +of phase locking or mode locking and we + + align:start position:0% +of phase locking or mode locking and we + + + align:start position:0% +of phase locking or mode locking and we +will talk about that later. So, so + + align:start position:0% +will talk about that later. So, so + + + align:start position:0% +will talk about that later. So, so +lasers can generate very very short + + align:start position:0% +lasers can generate very very short + + + align:start position:0% +lasers can generate very very short +pulses + + align:start position:0% +pulses + + + align:start position:0% +pulses +only if you can get all the modes all + + align:start position:0% +only if you can get all the modes all + + + align:start position:0% +only if you can get all the modes all +these modes to go and and they have to + + align:start position:0% +these modes to go and and they have to + + + align:start position:0% +these modes to go and and they have to +start together. They have to be phase + + align:start position:0% +start together. They have to be phase + + + align:start position:0% +start together. They have to be phase +locked or mode locked and and so on. And + + align:start position:0% +locked or mode locked and and so on. And + + + align:start position:0% +locked or mode locked and and so on. And +with that that's the output of the laser + + align:start position:0% +with that that's the output of the laser + + + align:start position:0% +with that that's the output of the laser +becomes the series of uh short pulses + + align:start position:0% +becomes the series of uh short pulses + + + align:start position:0% +becomes the series of uh short pulses +and if the bandwidth of the amplifier is + + align:start position:0% +and if the bandwidth of the amplifier is + + + align:start position:0% +and if the bandwidth of the amplifier is +very very broad then you can get these + + align:start position:0% +very very broad then you can get these + + + align:start position:0% +very very broad then you can get these +short pulses like picosconds and uh and + + align:start position:0% +short pulses like picosconds and uh and + + + align:start position:0% +short pulses like picosconds and uh and +shorter. All right. So now we've talked + + align:start position:0% +shorter. All right. So now we've talked + + + align:start position:0% +shorter. All right. So now we've talked +about uh so far we've talked about the + + align:start position:0% +about uh so far we've talked about the + + + align:start position:0% +about uh so far we've talked about the +unique properties of lasers. We talked + + align:start position:0% +unique properties of lasers. We talked + + + align:start position:0% +unique properties of lasers. We talked +about uh in a simple way how these + + align:start position:0% +about uh in a simple way how these + + + align:start position:0% +about uh in a simple way how these +properties uh come about. Now we're + + align:start position:0% +properties uh come about. Now we're + + + align:start position:0% +properties uh come about. Now we're +ready to to put all that stuff together + + align:start position:0% +ready to to put all that stuff together + + + align:start position:0% +ready to to put all that stuff together +and see how how a typical simple laser + + align:start position:0% +and see how how a typical simple laser + + + align:start position:0% +and see how how a typical simple laser +uh uh really works. All right. So now + + align:start position:0% +uh uh really works. All right. So now + + + align:start position:0% +uh uh really works. All right. So now +let's uh + + align:start position:0% +let's uh + + + align:start position:0% +let's uh +uh let's start talking about the the u + + align:start position:0% +uh let's start talking about the the u + + + align:start position:0% +uh let's start talking about the the u +simple laser. So here the title of this + + align:start position:0% +simple laser. So here the title of this + + + align:start position:0% +simple laser. So here the title of this +session as I had before is the operation + + align:start position:0% +session as I had before is the operation + + + align:start position:0% +session as I had before is the operation +of a of a simple laser and uh I have + + align:start position:0% +of a of a simple laser and uh I have + + + align:start position:0% +of a of a simple laser and uh I have +even a demonstration for you uh at at at + + align:start position:0% +even a demonstration for you uh at at at + + + align:start position:0% +even a demonstration for you uh at at at +this stage the uh the uh the lasers that + + align:start position:0% +this stage the uh the uh the lasers that + + + align:start position:0% +this stage the uh the uh the lasers that +that that we have simple ones called + + align:start position:0% +that that we have simple ones called + + + align:start position:0% +that that we have simple ones called +helium neon lasers and because the + + align:start position:0% +helium neon lasers and because the + + + align:start position:0% +helium neon lasers and because the +amplifier is a helium neon amplifier and + + align:start position:0% +amplifier is a helium neon amplifier and + + + align:start position:0% +amplifier is a helium neon amplifier and +we'll talk about how that works in a + + align:start position:0% +we'll talk about how that works in a + + + align:start position:0% +we'll talk about how that works in a +little while. Now here the the there + + align:start position:0% +little while. Now here the the there + + + align:start position:0% +little while. Now here the the there +have two kinds of lasers. one where the + + align:start position:0% +have two kinds of lasers. one where the + + + align:start position:0% +have two kinds of lasers. one where the +the amplifier tube uh is terminated by + + align:start position:0% +the amplifier tube uh is terminated by + + + align:start position:0% +the amplifier tube uh is terminated by +the two mirrors and uh and the uh called + + align:start position:0% +the two mirrors and uh and the uh called + + + align:start position:0% +the two mirrors and uh and the uh called +internal mirror uh laser and the other + + align:start position:0% +internal mirror uh laser and the other + + + align:start position:0% +internal mirror uh laser and the other +one uh and this is quite typical for a + + align:start position:0% +one uh and this is quite typical for a + + + align:start position:0% +one uh and this is quite typical for a +lot of lasers where the the uh the + + align:start position:0% +lot of lasers where the the uh the + + + align:start position:0% +lot of lasers where the the uh the +amplifier is terminated separately not + + align:start position:0% +amplifier is terminated separately not + + + align:start position:0% +amplifier is terminated separately not +at the mirrors and the mirrors are are + + align:start position:0% +at the mirrors and the mirrors are are + + + align:start position:0% +at the mirrors and the mirrors are are +again uh separated from from the from + + align:start position:0% +again uh separated from from the from + + + align:start position:0% +again uh separated from from the from +the amplifier and usually these are + + align:start position:0% +the amplifier and usually these are + + + align:start position:0% +the amplifier and usually these are +windows called uh there's a funny angle + + align:start position:0% +windows called uh there's a funny angle + + + align:start position:0% +windows called uh there's a funny angle +of rooster windows so at to minimize uh + + align:start position:0% +of rooster windows so at to minimize uh + + + align:start position:0% +of rooster windows so at to minimize uh +reflections. Again, we'll we'll mention + + align:start position:0% +reflections. Again, we'll we'll mention + + + align:start position:0% +reflections. Again, we'll we'll mention +that later. But basically here, what I + + align:start position:0% +that later. But basically here, what I + + + align:start position:0% +that later. But basically here, what I +would like to show you in in this + + align:start position:0% +would like to show you in in this + + + align:start position:0% +would like to show you in in this +demonstration + + align:start position:0% +demonstration + + + align:start position:0% +demonstration +is simple ampl uh simple uh uh lasers uh + + align:start position:0% +is simple ampl uh simple uh uh lasers uh + + + align:start position:0% +is simple ampl uh simple uh uh lasers uh +like these. Now, this one here, for + + align:start position:0% +like these. Now, this one here, for + + + align:start position:0% +like these. Now, this one here, for +example, it can't do very much because + + align:start position:0% +example, it can't do very much because + + + align:start position:0% +example, it can't do very much because +uh it can't adjust anything. It's all + + align:start position:0% +uh it can't adjust anything. It's all + + + align:start position:0% +uh it can't adjust anything. It's all +fixed. But this one here, if this mirror + + align:start position:0% +fixed. But this one here, if this mirror + + + align:start position:0% +fixed. But this one here, if this mirror +is is on an adjustable mount, then I can + + align:start position:0% +is is on an adjustable mount, then I can + + + align:start position:0% +is is on an adjustable mount, then I can +uh um adjust and move the mirror around, + + align:start position:0% +uh um adjust and move the mirror around, + + + align:start position:0% +uh um adjust and move the mirror around, +misalign, and so on. You can see how how + + align:start position:0% +misalign, and so on. You can see how how + + + align:start position:0% +misalign, and so on. You can see how how +easily it is to to stop the laser from + + align:start position:0% +easily it is to to stop the laser from + + + align:start position:0% +easily it is to to stop the laser from +lazing and also what happens as a + + align:start position:0% +lazing and also what happens as a + + + align:start position:0% +lazing and also what happens as a +function of u uh mirror adjustment. So + + align:start position:0% +function of u uh mirror adjustment. So + + + align:start position:0% +function of u uh mirror adjustment. So +let's uh let's now uh uh go to uh to the + + align:start position:0% +let's uh let's now uh uh go to uh to the + + + align:start position:0% +let's uh let's now uh uh go to uh to the +uh demonstration number one which is + + align:start position:0% +uh demonstration number one which is + + + align:start position:0% +uh demonstration number one which is +essentially on the uh on on on some + + align:start position:0% +essentially on the uh on on on some + + + align:start position:0% +essentially on the uh on on on some +simple-minded laser and show you how uh + + align:start position:0% +simple-minded laser and show you how uh + + + align:start position:0% +simple-minded laser and show you how uh +how it works from close. So now let's go + + align:start position:0% +how it works from close. So now let's go + + + align:start position:0% +how it works from close. So now let's go +look at this demonstration. + + align:start position:0% + + + + align:start position:0% + +Now we're ready to take a close look at + + align:start position:0% +Now we're ready to take a close look at + + + align:start position:0% +Now we're ready to take a close look at +a laser and see how it ticks and why it + + align:start position:0% +a laser and see how it ticks and why it + + + align:start position:0% +a laser and see how it ticks and why it +ticks. + + align:start position:0% +ticks. + + + align:start position:0% +ticks. +We've picked on a helium neon laser + + align:start position:0% +We've picked on a helium neon laser + + + align:start position:0% +We've picked on a helium neon laser +because a helium neon laser is a very + + align:start position:0% +because a helium neon laser is a very + + + align:start position:0% +because a helium neon laser is a very +simple one and also it's one of the + + align:start position:0% +simple one and also it's one of the + + + align:start position:0% +simple one and also it's one of the +first lasers. + + align:start position:0% +first lasers. + + + align:start position:0% +first lasers. +In fact, uh the first laser was the ruby + + align:start position:0% +In fact, uh the first laser was the ruby + + + align:start position:0% +In fact, uh the first laser was the ruby +laser and helium neon was uh was right + + align:start position:0% +laser and helium neon was uh was right + + + align:start position:0% +laser and helium neon was uh was right +after it. So it was the second laser + + align:start position:0% +after it. So it was the second laser + + + align:start position:0% +after it. So it was the second laser +action that uh that was observed. Also + + align:start position:0% +action that uh that was observed. Also + + + align:start position:0% +action that uh that was observed. Also +the red light from a helium neon laser + + align:start position:0% +the red light from a helium neon laser + + + align:start position:0% +the red light from a helium neon laser +is familiar to almost every one of you + + align:start position:0% +is familiar to almost every one of you + + + align:start position:0% +is familiar to almost every one of you +uh especially when you go to the + + align:start position:0% +uh especially when you go to the + + + align:start position:0% +uh especially when you go to the +supermarket and see it at the uh at the + + align:start position:0% +supermarket and see it at the uh at the + + + align:start position:0% +supermarket and see it at the uh at the +checkout counter. Usually a helium neon + + align:start position:0% +checkout counter. Usually a helium neon + + + align:start position:0% +checkout counter. Usually a helium neon +laser a red helium neon laser is used. + + align:start position:0% +laser a red helium neon laser is used. + + + align:start position:0% +laser a red helium neon laser is used. +So, let me start by showing you what a + + align:start position:0% +So, let me start by showing you what a + + + align:start position:0% +So, let me start by showing you what a +helium neon laser looks like. Here is a + + align:start position:0% +helium neon laser looks like. Here is a + + + align:start position:0% +helium neon laser looks like. Here is a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +helium neon laser, + + align:start position:0% +helium neon laser, + + + align:start position:0% +helium neon laser, +at least a helium neon laser. They all + + align:start position:0% +at least a helium neon laser. They all + + + align:start position:0% +at least a helium neon laser. They all +uh different. Uh now what I would like + + align:start position:0% +uh different. Uh now what I would like + + + align:start position:0% +uh different. Uh now what I would like +you to see here is that uh + + align:start position:0% +you to see here is that uh + + + align:start position:0% +you to see here is that uh +it's made up of a a discharge tube which + + align:start position:0% +it's made up of a a discharge tube which + + + align:start position:0% +it's made up of a a discharge tube which +is this which is the the amplifier + + align:start position:0% +is this which is the the amplifier + + + align:start position:0% +is this which is the the amplifier +that is necessary for laser action and + + align:start position:0% +that is necessary for laser action and + + + align:start position:0% +that is necessary for laser action and +then the discharge tube is terminated by + + align:start position:0% +then the discharge tube is terminated by + + + align:start position:0% +then the discharge tube is terminated by +by two mirrors. Here's a mirror on on + + align:start position:0% +by two mirrors. Here's a mirror on on + + + align:start position:0% +by two mirrors. Here's a mirror on on +this side. You can see it. Here's one + + align:start position:0% +this side. You can see it. Here's one + + + align:start position:0% +this side. You can see it. Here's one +mirror and and here is here is the other + + align:start position:0% +mirror and and here is here is the other + + + align:start position:0% +mirror and and here is here is the other +mirror. Okay. So, it's a it's a small + + align:start position:0% +mirror. Okay. So, it's a it's a small + + + align:start position:0% +mirror. Okay. So, it's a it's a small +this is a small laser and and the + + align:start position:0% +this is a small laser and and the + + + align:start position:0% +this is a small laser and and the +mirrors are sealed right onto onto the + + align:start position:0% +mirrors are sealed right onto onto the + + + align:start position:0% +mirrors are sealed right onto onto the +discharge tube. + + align:start position:0% +discharge tube. + + + align:start position:0% +discharge tube. +Now, let's see this laser uh in action. + + align:start position:0% +Now, let's see this laser uh in action. + + + align:start position:0% +Now, let's see this laser uh in action. +And we have it already set up for you + + align:start position:0% +And we have it already set up for you + + + align:start position:0% +And we have it already set up for you +over here. + + align:start position:0% +over here. + + + align:start position:0% +over here. +And then all I have to do is to uh turn + + align:start position:0% +And then all I have to do is to uh turn + + + align:start position:0% +And then all I have to do is to uh turn +the power supply on and count to five + + align:start position:0% +the power supply on and count to five + + + align:start position:0% +the power supply on and count to five +and the laser will come on. And here it + + align:start position:0% +and the laser will come on. And here it + + + align:start position:0% +and the laser will come on. And here it +is. Lasers on. + + align:start position:0% +is. Lasers on. + + + align:start position:0% +is. Lasers on. +You can see here is the the glow in the + + align:start position:0% +You can see here is the the glow in the + + + align:start position:0% +You can see here is the the glow in the +in the discharge. And you see a a a pink + + align:start position:0% +in the discharge. And you see a a a pink + + + align:start position:0% +in the discharge. And you see a a a pink +streak. And that's where the light goes + + align:start position:0% +streak. And that's where the light goes + + + align:start position:0% +streak. And that's where the light goes +backwards and forwards and gets + + align:start position:0% +backwards and forwards and gets + + + align:start position:0% +backwards and forwards and gets +amplified. And and here is uh the output + + align:start position:0% +amplified. And and here is uh the output + + + align:start position:0% +amplified. And and here is uh the output +mirror. Uh the other mirror is uh is + + align:start position:0% +mirror. Uh the other mirror is uh is + + + align:start position:0% +mirror. Uh the other mirror is uh is +sealed and the output from the mirror + + align:start position:0% +sealed and the output from the mirror + + + align:start position:0% +sealed and the output from the mirror +here then goes onto uh onto onto the + + align:start position:0% +here then goes onto uh onto onto the + + + align:start position:0% +here then goes onto uh onto onto the +screen + + align:start position:0% +screen + + + align:start position:0% +screen +and that's that's it. As long as we + + align:start position:0% +and that's that's it. As long as we + + + align:start position:0% +and that's that's it. As long as we +power the discharge and have enough gain + + align:start position:0% +power the discharge and have enough gain + + + align:start position:0% +power the discharge and have enough gain +to overcome the losses and we choose the + + align:start position:0% +to overcome the losses and we choose the + + + align:start position:0% +to overcome the losses and we choose the +mirror transmission appropriately + + align:start position:0% +mirror transmission appropriately + + + align:start position:0% +mirror transmission appropriately +the uh you'll get laser action. + + align:start position:0% +the uh you'll get laser action. + + + align:start position:0% +the uh you'll get laser action. +Now, with this kind of a laser, it's + + align:start position:0% +Now, with this kind of a laser, it's + + + align:start position:0% +Now, with this kind of a laser, it's +very difficult to uh to adjust anything + + align:start position:0% +very difficult to uh to adjust anything + + + align:start position:0% +very difficult to uh to adjust anything +and to play with it. So, what I'm going + + align:start position:0% +and to play with it. So, what I'm going + + + align:start position:0% +and to play with it. So, what I'm going +to do just so that you can see uh a + + align:start position:0% +to do just so that you can see uh a + + + align:start position:0% +to do just so that you can see uh a +little bit more uh of how a laser works, + + align:start position:0% +little bit more uh of how a laser works, + + + align:start position:0% +little bit more uh of how a laser works, +I'm going to go on and uh and and have a + + align:start position:0% +I'm going to go on and uh and and have a + + + align:start position:0% +I'm going to go on and uh and and have a +laser that that the mirrors in which the + + align:start position:0% +laser that that the mirrors in which the + + + align:start position:0% +laser that that the mirrors in which the +mirrors are external to the to the tube. + + align:start position:0% +mirrors are external to the to the tube. + + + align:start position:0% +mirrors are external to the to the tube. +Now in order to to have to separate the + + align:start position:0% +Now in order to to have to separate the + + + align:start position:0% +Now in order to to have to separate the +mirrors out from the from the amplifier + + align:start position:0% +mirrors out from the from the amplifier + + + align:start position:0% +mirrors out from the from the amplifier +from the discharge tube in this case we + + align:start position:0% +from the discharge tube in this case we + + + align:start position:0% +from the discharge tube in this case we +have to seal the we have to seal uh the + + align:start position:0% +have to seal the we have to seal uh the + + + align:start position:0% +have to seal the we have to seal uh the +the discharge tube. Now here is you can + + align:start position:0% +the discharge tube. Now here is you can + + + align:start position:0% +the discharge tube. Now here is you can +see here if we take a closeup at this + + align:start position:0% +see here if we take a closeup at this + + + align:start position:0% +see here if we take a closeup at this +here is a a sealed discharge tube + + align:start position:0% +here is a a sealed discharge tube + + + align:start position:0% +here is a a sealed discharge tube +doesn't have mirrors on it but has + + align:start position:0% +doesn't have mirrors on it but has + + + align:start position:0% +doesn't have mirrors on it but has +windows. Let's let me show it to you + + align:start position:0% +windows. Let's let me show it to you + + + align:start position:0% +windows. Let's let me show it to you +again. Here is here's the here's the + + align:start position:0% +again. Here is here's the here's the + + + align:start position:0% +again. Here is here's the here's the +amplifier section + + align:start position:0% +amplifier section + + + align:start position:0% +amplifier section +and here is the cathode and the anode is + + align:start position:0% +and here is the cathode and the anode is + + + align:start position:0% +and here is the cathode and the anode is +is over is over here. So the discharge + + align:start position:0% +is over is over here. So the discharge + + + align:start position:0% +is over is over here. So the discharge +then runs along uh this line over here. + + align:start position:0% +then runs along uh this line over here. + + + align:start position:0% +then runs along uh this line over here. +Okay, this capillary tube over here. Now + + align:start position:0% +Okay, this capillary tube over here. Now + + + align:start position:0% +Okay, this capillary tube over here. Now +let's focus at at the ends. + + align:start position:0% +let's focus at at the ends. + + + align:start position:0% +let's focus at at the ends. +We don't have as you can see we don't + + align:start position:0% +We don't have as you can see we don't + + + align:start position:0% +We don't have as you can see we don't +have square mirrors. You can see the the + + align:start position:0% +have square mirrors. You can see the the + + + align:start position:0% +have square mirrors. You can see the the +we don't have uh windows, I should say, + + align:start position:0% +we don't have uh windows, I should say, + + + align:start position:0% +we don't have uh windows, I should say, +not mirrors uh because we're going to + + align:start position:0% +not mirrors uh because we're going to + + + align:start position:0% +not mirrors uh because we're going to +have the mirrors external to to the + + align:start position:0% +have the mirrors external to to the + + + align:start position:0% +have the mirrors external to to the +discharge tube. But you can see that the + + align:start position:0% +discharge tube. But you can see that the + + + align:start position:0% +discharge tube. But you can see that the +windows are sealed, but they're not uh + + align:start position:0% +windows are sealed, but they're not uh + + + align:start position:0% +windows are sealed, but they're not uh +square to the to the tube. And uh the + + align:start position:0% +square to the to the tube. And uh the + + + align:start position:0% +square to the to the tube. And uh the +angle in fact is called the Brewster + + align:start position:0% +angle in fact is called the Brewster + + + align:start position:0% +angle in fact is called the Brewster +angle because at that angle there is no + + align:start position:0% +angle because at that angle there is no + + + align:start position:0% +angle because at that angle there is no +uh reflection from the glass surfaces + + align:start position:0% +uh reflection from the glass surfaces + + + align:start position:0% +uh reflection from the glass surfaces +for a certain polarization. + + align:start position:0% +for a certain polarization. + + + align:start position:0% +for a certain polarization. +So that's why one uses windows at a + + align:start position:0% +So that's why one uses windows at a + + + align:start position:0% +So that's why one uses windows at a +Brewster angle so that uh so that there + + align:start position:0% +Brewster angle so that uh so that there + + + align:start position:0% +Brewster angle so that uh so that there +is no uh no reflection at the windows + + align:start position:0% +is no uh no reflection at the windows + + + align:start position:0% +is no uh no reflection at the windows +and you can see both ends. Now if you + + align:start position:0% +and you can see both ends. Now if you + + + align:start position:0% +and you can see both ends. Now if you +take a look look at the other end over + + align:start position:0% +take a look look at the other end over + + + align:start position:0% +take a look look at the other end over +here close look at the other end you see + + align:start position:0% +here close look at the other end you see + + + align:start position:0% +here close look at the other end you see +that again both windows are are at uh at + + align:start position:0% +that again both windows are are at uh at + + + align:start position:0% +that again both windows are are at uh at +Brewster's angle. So here is then the uh + + align:start position:0% +Brewster's angle. So here is then the uh + + + align:start position:0% +Brewster's angle. So here is then the uh +the amplifier tube and now + + align:start position:0% +the amplifier tube and now + + + align:start position:0% +the amplifier tube and now +we have a another one a similar one that + + align:start position:0% +we have a another one a similar one that + + + align:start position:0% +we have a another one a similar one that +is placed and I'll position it in the + + align:start position:0% +is placed and I'll position it in the + + + align:start position:0% +is placed and I'll position it in the +same way that is placed uh over here + + align:start position:0% +same way that is placed uh over here + + + align:start position:0% +same way that is placed uh over here +that held held in place over here in + + align:start position:0% +that held held in place over here in + + + align:start position:0% +that held held in place over here in +this setup and uh and there's wires + + align:start position:0% +this setup and uh and there's wires + + + align:start position:0% +this setup and uh and there's wires +running to to run the discharge. So here + + align:start position:0% +running to to run the discharge. So here + + + align:start position:0% +running to to run the discharge. So here +is then the the uh the amplifier tube + + align:start position:0% +is then the the uh the amplifier tube + + + align:start position:0% +is then the the uh the amplifier tube +inside inside this laser + + align:start position:0% +inside inside this laser + + + align:start position:0% +inside inside this laser +and let me again point to the mirrors. + + align:start position:0% +and let me again point to the mirrors. + + + align:start position:0% +and let me again point to the mirrors. +Now here is here is one mirror and here + + align:start position:0% +Now here is here is one mirror and here + + + align:start position:0% +Now here is here is one mirror and here +is the other mirror and each mirror is + + align:start position:0% +is the other mirror and each mirror is + + + align:start position:0% +is the other mirror and each mirror is +held in a hefty mirror mount and the + + align:start position:0% +held in a hefty mirror mount and the + + + align:start position:0% +held in a hefty mirror mount and the +adjustments are over here. We have two + + align:start position:0% +adjustments are over here. We have two + + + align:start position:0% +adjustments are over here. We have two +adjustments over here and then we have + + align:start position:0% +adjustments over here and then we have + + + align:start position:0% +adjustments over here and then we have +similar adjustments over here. + + align:start position:0% +similar adjustments over here. + + + align:start position:0% +similar adjustments over here. +All right. So here is then the tube, the + + align:start position:0% +All right. So here is then the tube, the + + + align:start position:0% +All right. So here is then the tube, the +amplified tube. The windows are + + align:start position:0% +amplified tube. The windows are + + + align:start position:0% +amplified tube. The windows are +terminated with windows at Brewster's + + align:start position:0% +terminated with windows at Brewster's + + + align:start position:0% +terminated with windows at Brewster's +angle. And and then we have the two + + align:start position:0% +angle. And and then we have the two + + + align:start position:0% +angle. And and then we have the two +mirrors. + + align:start position:0% +mirrors. + + + align:start position:0% +mirrors. +So now I'm going to turn the discharge + + align:start position:0% +So now I'm going to turn the discharge + + + align:start position:0% +So now I'm going to turn the discharge +on. + + align:start position:0% +on. + + + align:start position:0% +on. +And here it is. And let's see if the + + align:start position:0% +And here it is. And let's see if the + + + align:start position:0% +And here it is. And let's see if the +laser is lazing. Right? So if I put a + + align:start position:0% +laser is lazing. Right? So if I put a + + + align:start position:0% +laser is lazing. Right? So if I put a +card here, you see that indeed laser is + + align:start position:0% +card here, you see that indeed laser is + + + align:start position:0% +card here, you see that indeed laser is +lazing. So what I'm doing here is + + align:start position:0% +lazing. So what I'm doing here is + + + align:start position:0% +lazing. So what I'm doing here is +reflecting it by this mirror here, then + + align:start position:0% +reflecting it by this mirror here, then + + + align:start position:0% +reflecting it by this mirror here, then +this mirror here. Here's the laser beam. + + align:start position:0% +this mirror here. Here's the laser beam. + + + align:start position:0% +this mirror here. Here's the laser beam. +and again onto onto the screen. So on + + align:start position:0% +and again onto onto the screen. So on + + + align:start position:0% +and again onto onto the screen. So on +the screen now we have essentially two + + align:start position:0% +the screen now we have essentially two + + + align:start position:0% +the screen now we have essentially two +spots. One is coming from the laser with + + align:start position:0% +spots. One is coming from the laser with + + + align:start position:0% +spots. One is coming from the laser with +the fixed mirrors. That's this one. And + + align:start position:0% +the fixed mirrors. That's this one. And + + + align:start position:0% +the fixed mirrors. That's this one. And +then the other one the other spot is + + align:start position:0% +then the other one the other spot is + + + align:start position:0% +then the other one the other spot is +coming from the laser with the + + align:start position:0% +coming from the laser with the + + + align:start position:0% +coming from the laser with the +adjustable mirrors + + align:start position:0% +adjustable mirrors + + + align:start position:0% +adjustable mirrors +uh here. So what I'm going to do is + + align:start position:0% +uh here. So what I'm going to do is + + + align:start position:0% +uh here. So what I'm going to do is +first block the laser with the fixed + + align:start position:0% +first block the laser with the fixed + + + align:start position:0% +first block the laser with the fixed +mirrors so that we don't have any + + align:start position:0% +mirrors so that we don't have any + + + align:start position:0% +mirrors so that we don't have any +confusion. And the only spot then is + + align:start position:0% +confusion. And the only spot then is + + + align:start position:0% +confusion. And the only spot then is +from the one from the laser with the + + align:start position:0% +from the one from the laser with the + + + align:start position:0% +from the one from the laser with the +adjustable mirrors. So now here we are. + + align:start position:0% +adjustable mirrors. So now here we are. + + + align:start position:0% +adjustable mirrors. So now here we are. +Here's the laser then all opened up. And + + align:start position:0% +Here's the laser then all opened up. And + + + align:start position:0% +Here's the laser then all opened up. And +now I'm going to show you how touchy the + + align:start position:0% +now I'm going to show you how touchy the + + + align:start position:0% +now I'm going to show you how touchy the +alignment is. So now if you watch the + + align:start position:0% +alignment is. So now if you watch the + + + align:start position:0% +alignment is. So now if you watch the +intensity on the screen as I as I + + align:start position:0% +intensity on the screen as I as I + + + align:start position:0% +intensity on the screen as I as I +slightly misalign you can see the light + + align:start position:0% +slightly misalign you can see the light + + + align:start position:0% +slightly misalign you can see the light +is out already just by very small very + + align:start position:0% +is out already just by very small very + + + align:start position:0% +is out already just by very small very +small misalignments. So here we are it's + + align:start position:0% +small misalignments. So here we are it's + + + align:start position:0% +small misalignments. So here we are it's +a peak value and then I go the other way + + align:start position:0% +a peak value and then I go the other way + + + align:start position:0% +a peak value and then I go the other way +and it's gone. So the alignment has to + + align:start position:0% +and it's gone. So the alignment has to + + + align:start position:0% +and it's gone. So the alignment has to +be has to be very very stable. + + align:start position:0% +be has to be very very stable. + + + align:start position:0% +be has to be very very stable. +All right. Now I can also adjust uh + + align:start position:0% +All right. Now I can also adjust uh + + + align:start position:0% +All right. Now I can also adjust uh +horizontal alignment again. + + align:start position:0% +horizontal alignment again. + + + align:start position:0% +horizontal alignment again. +Show you how how uh how touchy + + align:start position:0% +Show you how how uh how touchy + + + align:start position:0% +Show you how how uh how touchy +everything is. So here we are. Here is + + align:start position:0% +everything is. So here we are. Here is + + + align:start position:0% +everything is. So here we are. Here is +then uh in a nutshell. Here's the here's + + align:start position:0% +then uh in a nutshell. Here's the here's + + + align:start position:0% +then uh in a nutshell. Here's the here's +the amplifier section. The longer it is, + + align:start position:0% +the amplifier section. The longer it is, + + + align:start position:0% +the amplifier section. The longer it is, +of course, the more gain we have. And + + align:start position:0% +of course, the more gain we have. And + + + align:start position:0% +of course, the more gain we have. And +and the mirrors are placed this case + + align:start position:0% +and the mirrors are placed this case + + + align:start position:0% +and the mirrors are placed this case +about 50 cm apart. one uh this one is a + + align:start position:0% +about 50 cm apart. one uh this one is a + + + align:start position:0% +about 50 cm apart. one uh this one is a +flat mirror and this one is a spherical + + align:start position:0% +flat mirror and this one is a spherical + + + align:start position:0% +flat mirror and this one is a spherical +mirror and and the the alignment has to + + align:start position:0% +mirror and and the the alignment has to + + + align:start position:0% +mirror and and the the alignment has to +be has to be very stable because a small + + align:start position:0% +be has to be very stable because a small + + + align:start position:0% +be has to be very stable because a small +misalignment would uh would create a lot + + align:start position:0% +misalignment would uh would create a lot + + + align:start position:0% +misalignment would uh would create a lot +of loss and then we just don't have + + align:start position:0% +of loss and then we just don't have + + + align:start position:0% +of loss and then we just don't have +enough gain in the amplifier to overcome + + align:start position:0% +enough gain in the amplifier to overcome + + + align:start position:0% +enough gain in the amplifier to overcome +these losses and the laser quits. + + align:start position:0% +these losses and the laser quits. + + + align:start position:0% +these losses and the laser quits. +Now, + + align:start position:0% + + + + align:start position:0% + +I hope you've enjoyed + + align:start position:0% +I hope you've enjoyed + + + align:start position:0% +I hope you've enjoyed +watching this first demonstration on + + align:start position:0% +watching this first demonstration on + + + align:start position:0% +watching this first demonstration on +what goes on inside a laser. + + align:start position:0% +what goes on inside a laser. + + + align:start position:0% +what goes on inside a laser. +The the of course the key thing is the + + align:start position:0% +The the of course the key thing is the + + + align:start position:0% +The the of course the key thing is the +amplifier. And now I think we need to + + align:start position:0% +amplifier. And now I think we need to + + + align:start position:0% +amplifier. And now I think we need to +talk about how does a light amplifier + + align:start position:0% +talk about how does a light amplifier + + + align:start position:0% +talk about how does a light amplifier +work. So this is what I have now for + + align:start position:0% +work. So this is what I have now for + + + align:start position:0% +work. So this is what I have now for +this next topic is that how does really + + align:start position:0% +this next topic is that how does really + + + align:start position:0% +this next topic is that how does really +an optical amplifier really work. + + align:start position:0% +an optical amplifier really work. + + + align:start position:0% +an optical amplifier really work. +The so what what we mean by an optical + + align:start position:0% +The so what what we mean by an optical + + + align:start position:0% +The so what what we mean by an optical +amplifier, we need light going in to + + align:start position:0% +amplifier, we need light going in to + + + align:start position:0% +amplifier, we need light going in to +this magic box here and we need the + + align:start position:0% +this magic box here and we need the + + + align:start position:0% +this magic box here and we need the +light enhanced or increased or amplified + + align:start position:0% +light enhanced or increased or amplified + + + align:start position:0% +light enhanced or increased or amplified +at the at the other end. So the question + + align:start position:0% +at the at the other end. So the question + + + align:start position:0% +at the at the other end. So the question +is what is this magic box here that + + align:start position:0% +is what is this magic box here that + + + align:start position:0% +is what is this magic box here that +takes light from one end and actually + + align:start position:0% +takes light from one end and actually + + + align:start position:0% +takes light from one end and actually +amplifies it and sends it out at the + + align:start position:0% +amplifies it and sends it out at the + + + align:start position:0% +amplifies it and sends it out at the +other end. Right? That's that's the key + + align:start position:0% +other end. Right? That's that's the key + + + align:start position:0% +other end. Right? That's that's the key +question. The so in order to answer this + + align:start position:0% +question. The so in order to answer this + + + align:start position:0% +question. The so in order to answer this +we have to uh we have to uh see what we + + align:start position:0% +we have to uh we have to uh see what we + + + align:start position:0% +we have to uh we have to uh see what we +understand about the interaction of uh + + align:start position:0% +understand about the interaction of uh + + + align:start position:0% +understand about the interaction of uh +radiation or light with atoms or + + align:start position:0% +radiation or light with atoms or + + + align:start position:0% +radiation or light with atoms or +molecules. Right? So let's let's start + + align:start position:0% +molecules. Right? So let's let's start + + + align:start position:0% +molecules. Right? So let's let's start +with that. Now we're very familiar + + align:start position:0% +with that. Now we're very familiar + + + align:start position:0% +with that. Now we're very familiar +for example with light interacting with + + align:start position:0% +for example with light interacting with + + + align:start position:0% +for example with light interacting with +a material and getting absorbed that we + + align:start position:0% +a material and getting absorbed that we + + + align:start position:0% +a material and getting absorbed that we +we see that all the time. uh that + + align:start position:0% +we see that all the time. uh that + + + align:start position:0% +we see that all the time. uh that +sometimes completely absorbed and + + align:start position:0% +sometimes completely absorbed and + + + align:start position:0% +sometimes completely absorbed and +sometimes it's uh not completely + + align:start position:0% +sometimes it's uh not completely + + + align:start position:0% +sometimes it's uh not completely +absorbed like a piece of glass for + + align:start position:0% +absorbed like a piece of glass for + + + align:start position:0% +absorbed like a piece of glass for +example if you send light through a + + align:start position:0% +example if you send light through a + + + align:start position:0% +example if you send light through a +piece of glass if it's unccoated normal + + align:start position:0% +piece of glass if it's unccoated normal + + + align:start position:0% +piece of glass if it's unccoated normal +incidence and so on you lose about uh 8% + + align:start position:0% +incidence and so on you lose about uh 8% + + + align:start position:0% +incidence and so on you lose about uh 8% +or so for both both sides. So uh other + + align:start position:0% +or so for both both sides. So uh other + + + align:start position:0% +or so for both both sides. So uh other +materials will lose more and and we see + + align:start position:0% +materials will lose more and and we see + + + align:start position:0% +materials will lose more and and we see +that all the time. All right. So first + + align:start position:0% +that all the time. All right. So first + + + align:start position:0% +that all the time. All right. So first +let's understand what that is and once + + align:start position:0% +let's understand what that is and once + + + align:start position:0% +let's understand what that is and once +we understand what absorption is then + + align:start position:0% +we understand what absorption is then + + + align:start position:0% +we understand what absorption is then +then let's see how then we can + + align:start position:0% +then let's see how then we can + + + align:start position:0% +then let's see how then we can +understand uh amplification. So we'll + + align:start position:0% +understand uh amplification. So we'll + + + align:start position:0% +understand uh amplification. So we'll +start first by looking at absorption. + + align:start position:0% +start first by looking at absorption. + + + align:start position:0% +start first by looking at absorption. +All right. So here is the uh in order to + + align:start position:0% +All right. So here is the uh in order to + + + align:start position:0% +All right. So here is the uh in order to +understand absorption we need a model + + align:start position:0% +understand absorption we need a model + + + align:start position:0% +understand absorption we need a model +for for the atom. All right. And as I + + align:start position:0% +for for the atom. All right. And as I + + + align:start position:0% +for for the atom. All right. And as I +say in this course we keep everything + + align:start position:0% +say in this course we keep everything + + + align:start position:0% +say in this course we keep everything +very simple so that we can get a a a + + align:start position:0% +very simple so that we can get a a a + + + align:start position:0% +very simple so that we can get a a a +basic intuitive kind of understanding of + + align:start position:0% +basic intuitive kind of understanding of + + + align:start position:0% +basic intuitive kind of understanding of +what's going on rather than complicate + + align:start position:0% +what's going on rather than complicate + + + align:start position:0% +what's going on rather than complicate +things with a lot of math. Now, a model + + align:start position:0% +things with a lot of math. Now, a model + + + align:start position:0% +things with a lot of math. Now, a model +for for an atom, all right, is where + + align:start position:0% +for for an atom, all right, is where + + + align:start position:0% +for for an atom, all right, is where +let's say an atom has several uh energy + + align:start position:0% +let's say an atom has several uh energy + + + align:start position:0% +let's say an atom has several uh energy +levels or orbits or what have you. And + + align:start position:0% +levels or orbits or what have you. And + + + align:start position:0% +levels or orbits or what have you. And +the atom, here's the ball, here's the + + align:start position:0% +the atom, here's the ball, here's the + + + align:start position:0% +the atom, here's the ball, here's the +atom, uh is uh is in its ground state or + + align:start position:0% +atom, uh is uh is in its ground state or + + + align:start position:0% +atom, uh is uh is in its ground state or +lowest energy state at at the beginning. + + align:start position:0% +lowest energy state at at the beginning. + + + align:start position:0% +lowest energy state at at the beginning. +And all atoms essentially are at their + + align:start position:0% +And all atoms essentially are at their + + + align:start position:0% +And all atoms essentially are at their +lowest energy states at the beginning. + + align:start position:0% +lowest energy states at the beginning. + + + align:start position:0% +lowest energy states at the beginning. +Now when light comes in from over here + + align:start position:0% +Now when light comes in from over here + + + align:start position:0% +Now when light comes in from over here +let's say these are two photons coming + + align:start position:0% +let's say these are two photons coming + + + align:start position:0% +let's say these are two photons coming +in they will interact with the electrons + + align:start position:0% +in they will interact with the electrons + + + align:start position:0% +in they will interact with the electrons +let's say in this atom and will excite + + align:start position:0% +let's say in this atom and will excite + + + align:start position:0% +let's say in this atom and will excite +the electrons to to some higher state or + + align:start position:0% +the electrons to to some higher state or + + + align:start position:0% +the electrons to to some higher state or +even higher states in this case I'm only + + align:start position:0% +even higher states in this case I'm only + + + align:start position:0% +even higher states in this case I'm only +taking a very simple model just two-le + + align:start position:0% +taking a very simple model just two-le + + + align:start position:0% +taking a very simple model just two-le +system + + align:start position:0% +system + + + align:start position:0% +system +now if the if the light wavelength or + + align:start position:0% +now if the if the light wavelength or + + + align:start position:0% +now if the if the light wavelength or +light frequency is not correct the the + + align:start position:0% +light frequency is not correct the the + + + align:start position:0% +light frequency is not correct the the +atom will not be or the electrons here + + align:start position:0% +atom will not be or the electrons here + + + align:start position:0% +atom will not be or the electrons here +will not be excited at all. But if the + + align:start position:0% +will not be excited at all. But if the + + + align:start position:0% +will not be excited at all. But if the +light frequency or wavelength is + + align:start position:0% +light frequency or wavelength is + + + align:start position:0% +light frequency or wavelength is +a certain value of a certain value then + + align:start position:0% +a certain value of a certain value then + + + align:start position:0% +a certain value of a certain value then +the the electrons here can be excited + + align:start position:0% +the the electrons here can be excited + + + align:start position:0% +the the electrons here can be excited +and now on I'm going to call it the + + align:start position:0% +and now on I'm going to call it the + + + align:start position:0% +and now on I'm going to call it the +atoms can be can be excited from one + + align:start position:0% +atoms can be can be excited from one + + + align:start position:0% +atoms can be can be excited from one +level to another level. And when the + + align:start position:0% +level to another level. And when the + + + align:start position:0% +level to another level. And when the +atom is is excited from one level to + + align:start position:0% +atom is is excited from one level to + + + align:start position:0% +atom is is excited from one level to +another level, then essentially it takes + + align:start position:0% +another level, then essentially it takes + + + align:start position:0% +another level, then essentially it takes +it takes energy from the light or it + + align:start position:0% +it takes energy from the light or it + + + align:start position:0% +it takes energy from the light or it +takes photons from the light to to get + + align:start position:0% +takes photons from the light to to get + + + align:start position:0% +takes photons from the light to to get +excited because now the the the atom + + align:start position:0% +excited because now the the the atom + + + align:start position:0% +excited because now the the the atom +itself has now high energy than it + + align:start position:0% +itself has now high energy than it + + + align:start position:0% +itself has now high energy than it +started with. And the of course the + + align:start position:0% +started with. And the of course the + + + align:start position:0% +started with. And the of course the +light gave up its energy to to the atom. + + align:start position:0% +light gave up its energy to to the atom. + + + align:start position:0% +light gave up its energy to to the atom. +So it has less energy when when it + + align:start position:0% +So it has less energy when when it + + + align:start position:0% +So it has less energy when when it +leaves the atom and this is generally uh + + align:start position:0% +leaves the atom and this is generally uh + + + align:start position:0% +leaves the atom and this is generally uh +called uh absorption. And then let's say + + align:start position:0% +called uh absorption. And then let's say + + + align:start position:0% +called uh absorption. And then let's say +a few more words about that. Uh here + + align:start position:0% +a few more words about that. Uh here + + + align:start position:0% +a few more words about that. Uh here +again this picture that I had uh in + + align:start position:0% +again this picture that I had uh in + + + align:start position:0% +again this picture that I had uh in +terms of uh just straight waves here is + + align:start position:0% +terms of uh just straight waves here is + + + align:start position:0% +terms of uh just straight waves here is +a big wave coming in and a little wave + + align:start position:0% +a big wave coming in and a little wave + + + align:start position:0% +a big wave coming in and a little wave +coming out. And that essentially is is + + align:start position:0% +coming out. And that essentially is is + + + align:start position:0% +coming out. And that essentially is is +absorption. I've I've labeled here E1 + + align:start position:0% +absorption. I've I've labeled here E1 + + + align:start position:0% +absorption. I've I've labeled here E1 +and E2 for the energy levels. And it + + align:start position:0% +and E2 for the energy levels. And it + + + align:start position:0% +and E2 for the energy levels. And it +turns out that the frequency where you + + align:start position:0% +turns out that the frequency where you + + + align:start position:0% +turns out that the frequency where you +get maximum absorption or the wavelength + + align:start position:0% +get maximum absorption or the wavelength + + + align:start position:0% +get maximum absorption or the wavelength +of frequency you get maximum absorption + + align:start position:0% +of frequency you get maximum absorption + + + align:start position:0% +of frequency you get maximum absorption +is is given by uh the difference in + + align:start position:0% +is is given by uh the difference in + + + align:start position:0% +is is given by uh the difference in +energy E2 minus E1 divided by H which is + + align:start position:0% +energy E2 minus E1 divided by H which is + + + align:start position:0% +energy E2 minus E1 divided by H which is +plank's constant and that gives you the + + align:start position:0% +plank's constant and that gives you the + + + align:start position:0% +plank's constant and that gives you the +frequency uh that of at resonance and if + + align:start position:0% +frequency uh that of at resonance and if + + + align:start position:0% +frequency uh that of at resonance and if +you for example put put you put a + + align:start position:0% +you for example put put you put a + + + align:start position:0% +you for example put put you put a +detector out here and you can see that + + align:start position:0% +detector out here and you can see that + + + align:start position:0% +detector out here and you can see that +as you tune the frequency of the of this + + align:start position:0% +as you tune the frequency of the of this + + + align:start position:0% +as you tune the frequency of the of this +light source you have no absorption at + + align:start position:0% +light source you have no absorption at + + + align:start position:0% +light source you have no absorption at +the beginning all the intensity comes + + align:start position:0% +the beginning all the intensity comes + + + align:start position:0% +the beginning all the intensity comes +through and then when you're close to + + align:start position:0% +through and then when you're close to + + + align:start position:0% +through and then when you're close to +resonance what you will see a dip like + + align:start position:0% +resonance what you will see a dip like + + + align:start position:0% +resonance what you will see a dip like +this and back to no absorption. So over + + align:start position:0% +this and back to no absorption. So over + + + align:start position:0% +this and back to no absorption. So over +here there is some absorption and this + + align:start position:0% +here there is some absorption and this + + + align:start position:0% +here there is some absorption and this +absorption occurs at this resonance + + align:start position:0% +absorption occurs at this resonance + + + align:start position:0% +absorption occurs at this resonance +frequency determined by the energy level + + align:start position:0% +frequency determined by the energy level + + + align:start position:0% +frequency determined by the energy level +difference divided by plank's constant. + + align:start position:0% +difference divided by plank's constant. + + + align:start position:0% +difference divided by plank's constant. +Okay the wavelength of course is uh + + align:start position:0% +Okay the wavelength of course is uh + + + align:start position:0% +Okay the wavelength of course is uh +proportional uh uh to that as you know + + align:start position:0% +proportional uh uh to that as you know + + + align:start position:0% +proportional uh uh to that as you know +uh frequency times wavelength equals the + + align:start position:0% +uh frequency times wavelength equals the + + + align:start position:0% +uh frequency times wavelength equals the +speed of light. So that either you talk + + align:start position:0% +speed of light. So that either you talk + + + align:start position:0% +speed of light. So that either you talk +about frequencies or wavelength. In this + + align:start position:0% +about frequencies or wavelength. In this + + + align:start position:0% +about frequencies or wavelength. In this +course, I'd like to talk about frequency + + align:start position:0% +course, I'd like to talk about frequency + + + align:start position:0% +course, I'd like to talk about frequency +because it's easier to talk about + + align:start position:0% +because it's easier to talk about + + + align:start position:0% +because it's easier to talk about +frequencies than uh than wavelength. + + align:start position:0% +frequencies than uh than wavelength. + + + align:start position:0% +frequencies than uh than wavelength. +The uh now if again uh the the amount of + + align:start position:0% +The uh now if again uh the the amount of + + + align:start position:0% +The uh now if again uh the the amount of +absorption will depend on uh on the + + align:start position:0% +absorption will depend on uh on the + + + align:start position:0% +absorption will depend on uh on the +number of atoms or molecules that you + + align:start position:0% +number of atoms or molecules that you + + + align:start position:0% +number of atoms or molecules that you +have and the width for the absorption + + align:start position:0% +have and the width for the absorption + + + align:start position:0% +have and the width for the absorption +again depends on the particular + + align:start position:0% +again depends on the particular + + + align:start position:0% +again depends on the particular +transition in that particular atom. Now, + + align:start position:0% +transition in that particular atom. Now, + + + align:start position:0% +transition in that particular atom. Now, +if you don't believe me, you can do an + + align:start position:0% +if you don't believe me, you can do an + + + align:start position:0% +if you don't believe me, you can do an +experiment. And here is how you might do + + align:start position:0% +experiment. And here is how you might do + + + align:start position:0% +experiment. And here is how you might do +the the experiment. You take this uh + + align:start position:0% +the the experiment. You take this uh + + + align:start position:0% +the the experiment. You take this uh +variable wavelength light source and you + + align:start position:0% +variable wavelength light source and you + + + align:start position:0% +variable wavelength light source and you +send it into selected vapor, a vapor + + align:start position:0% +send it into selected vapor, a vapor + + + align:start position:0% +send it into selected vapor, a vapor +cell, and you put a detector at the + + align:start position:0% +cell, and you put a detector at the + + + align:start position:0% +cell, and you put a detector at the +other end. + + align:start position:0% +other end. + + + align:start position:0% +other end. +Again, you have now lots of atoms, let's + + align:start position:0% +Again, you have now lots of atoms, let's + + + align:start position:0% +Again, you have now lots of atoms, let's +say, or molecules. You send the light in + + align:start position:0% +say, or molecules. You send the light in + + + align:start position:0% +say, or molecules. You send the light in +and some of these going to be excited, + + align:start position:0% +and some of these going to be excited, + + + align:start position:0% +and some of these going to be excited, +going to go into this excited state, and + + align:start position:0% +going to go into this excited state, and + + + align:start position:0% +going to go into this excited state, and +the light is reduced. And that's what + + align:start position:0% +the light is reduced. And that's what + + + align:start position:0% +the light is reduced. And that's what +what we call as stimulated absorption. + + align:start position:0% +what we call as stimulated absorption. + + + align:start position:0% +what we call as stimulated absorption. +And then we generate the same curve as + + align:start position:0% +And then we generate the same curve as + + + align:start position:0% +And then we generate the same curve as +we had before. So if you look at the + + align:start position:0% +we had before. So if you look at the + + + align:start position:0% +we had before. So if you look at the +output of the detector as a function of + + align:start position:0% +output of the detector as a function of + + + align:start position:0% +output of the detector as a function of +frequency or wavelength, then you would + + align:start position:0% +frequency or wavelength, then you would + + + align:start position:0% +frequency or wavelength, then you would +see you'd see this dip occurring at this + + align:start position:0% +see you'd see this dip occurring at this + + + align:start position:0% +see you'd see this dip occurring at this +resonant frequency. + + align:start position:0% +resonant frequency. + + + align:start position:0% +resonant frequency. +And and this way you check out where + + align:start position:0% +And and this way you check out where + + + align:start position:0% +And and this way you check out where +this absorption occurs and and the width + + align:start position:0% +this absorption occurs and and the width + + + align:start position:0% +this absorption occurs and and the width +the width of it. Now the interesting + + align:start position:0% +the width of it. Now the interesting + + + align:start position:0% +the width of it. Now the interesting +thing here is that you note you'll + + align:start position:0% +thing here is that you note you'll + + + align:start position:0% +thing here is that you note you'll +notice that if this is a glass tube + + align:start position:0% +notice that if this is a glass tube + + + align:start position:0% +notice that if this is a glass tube +you'll notice some radiation coming out + + align:start position:0% +you'll notice some radiation coming out + + + align:start position:0% +you'll notice some radiation coming out +of the the side. Now that radiation is + + align:start position:0% +of the the side. Now that radiation is + + + align:start position:0% +of the the side. Now that radiation is +when you see before the the excitation + + align:start position:0% +when you see before the the excitation + + + align:start position:0% +when you see before the the excitation +all the atoms were in the ground state + + align:start position:0% +all the atoms were in the ground state + + + align:start position:0% +all the atoms were in the ground state +and that radiation there was no + + align:start position:0% +and that radiation there was no + + + align:start position:0% +and that radiation there was no +radiation coming out from the side. But + + align:start position:0% +radiation coming out from the side. But + + + align:start position:0% +radiation coming out from the side. But +when when you excite these atoms to an + + align:start position:0% +when when you excite these atoms to an + + + align:start position:0% +when when you excite these atoms to an +excited state, then another process + + align:start position:0% +excited state, then another process + + + align:start position:0% +excited state, then another process +comes in and that's called spontaneous + + align:start position:0% +comes in and that's called spontaneous + + + align:start position:0% +comes in and that's called spontaneous +emission. Cuz these atoms that are in + + align:start position:0% +emission. Cuz these atoms that are in + + + align:start position:0% +emission. Cuz these atoms that are in +the excited state, in lots of cases, + + align:start position:0% +the excited state, in lots of cases, + + + align:start position:0% +the excited state, in lots of cases, +they don't like to stay up there. They + + align:start position:0% +they don't like to stay up there. They + + + align:start position:0% +they don't like to stay up there. They +like to to come down. And when they + + align:start position:0% +like to to come down. And when they + + + align:start position:0% +like to to come down. And when they +decay, so-called decay, when they decay, + + align:start position:0% +decay, so-called decay, when they decay, + + + align:start position:0% +decay, so-called decay, when they decay, +they emit a photon in a in a random d + + align:start position:0% +they emit a photon in a in a random d + + + align:start position:0% +they emit a photon in a in a random d +direction. And the wavelength or + + align:start position:0% +direction. And the wavelength or + + + align:start position:0% +direction. And the wavelength or +frequency of this photon is is equal to + + align:start position:0% +frequency of this photon is is equal to + + + align:start position:0% +frequency of this photon is is equal to +to the one that brought it brought it + + align:start position:0% +to the one that brought it brought it + + + align:start position:0% +to the one that brought it brought it +up. So essentially the light that was + + align:start position:0% +up. So essentially the light that was + + + align:start position:0% +up. So essentially the light that was +absorbed from from the original beam is + + align:start position:0% +absorbed from from the original beam is + + + align:start position:0% +absorbed from from the original beam is +now sent into into all these directions. + + align:start position:0% +now sent into into all these directions. + + + align:start position:0% +now sent into into all these directions. +Okay. So now we've learned about what + + align:start position:0% +Okay. So now we've learned about what + + + align:start position:0% +Okay. So now we've learned about what +stimulated absorption is and what uh + + align:start position:0% +stimulated absorption is and what uh + + + align:start position:0% +stimulated absorption is and what uh +spontaneous uh what spontaneous emission + + align:start position:0% +spontaneous uh what spontaneous emission + + + align:start position:0% +spontaneous uh what spontaneous emission +is. Question is + + align:start position:0% +is. Question is + + + align:start position:0% +is. Question is +what about gain? What we're after is + + align:start position:0% +what about gain? What we're after is + + + align:start position:0% +what about gain? What we're after is +amplification. All right. So let's see + + align:start position:0% +amplification. All right. So let's see + + + align:start position:0% +amplification. All right. So let's see +how amplification then comes about. Now + + align:start position:0% +how amplification then comes about. Now + + + align:start position:0% +how amplification then comes about. Now +for amplification to understand + + align:start position:0% +for amplification to understand + + + align:start position:0% +for amplification to understand +amplification of light we reverse the + + align:start position:0% +amplification of light we reverse the + + + align:start position:0% +amplification of light we reverse the +picture. Instead of starting with the + + align:start position:0% +picture. Instead of starting with the + + + align:start position:0% +picture. Instead of starting with the +atom in the ground state which where it + + align:start position:0% +atom in the ground state which where it + + + align:start position:0% +atom in the ground state which where it +likes to be normally we're going to + + align:start position:0% +likes to be normally we're going to + + + align:start position:0% +likes to be normally we're going to +start with the atom in the excited + + align:start position:0% +start with the atom in the excited + + + align:start position:0% +start with the atom in the excited +state. So when when a photon comes in + + align:start position:0% +state. So when when a photon comes in + + + align:start position:0% +state. So when when a photon comes in +now there is no absorption that can take + + align:start position:0% +now there is no absorption that can take + + + align:start position:0% +now there is no absorption that can take +place but what can happen if the again + + align:start position:0% +place but what can happen if the again + + + align:start position:0% +place but what can happen if the again +if the frequency or wavelength of this + + align:start position:0% +if the frequency or wavelength of this + + + align:start position:0% +if the frequency or wavelength of this +photon is just right at the resonance + + align:start position:0% +photon is just right at the resonance + + + align:start position:0% +photon is just right at the resonance +frequency of this transition then what + + align:start position:0% +frequency of this transition then what + + + align:start position:0% +frequency of this transition then what +what can happen is that this light now + + align:start position:0% +what can happen is that this light now + + + align:start position:0% +what can happen is that this light now +will force this atom to come down + + align:start position:0% +will force this atom to come down + + + align:start position:0% +will force this atom to come down +because there's let's say there's no + + align:start position:0% +because there's let's say there's no + + + align:start position:0% +because there's let's say there's no +other energy levels to go up. It can + + align:start position:0% +other energy levels to go up. It can + + + align:start position:0% +other energy levels to go up. It can +even push it up. If there was an energy + + align:start position:0% +even push it up. If there was an energy + + + align:start position:0% +even push it up. If there was an energy +level here then it could kick it up. But + + align:start position:0% +level here then it could kick it up. But + + + align:start position:0% +level here then it could kick it up. But +in this particular case we say we only + + align:start position:0% +in this particular case we say we only + + + align:start position:0% +in this particular case we say we only +have two levels. So the only way for + + align:start position:0% +have two levels. So the only way for + + + align:start position:0% +have two levels. So the only way for +this atom to go is down. And then of + + align:start position:0% +this atom to go is down. And then of + + + align:start position:0% +this atom to go is down. And then of +course when it when an atom comes down + + align:start position:0% +course when it when an atom comes down + + + align:start position:0% +course when it when an atom comes down +remember atom had energy up here. When + + align:start position:0% +remember atom had energy up here. When + + + align:start position:0% +remember atom had energy up here. When +it comes down it will release a photon. + + align:start position:0% +it comes down it will release a photon. + + + align:start position:0% +it comes down it will release a photon. +Okay. So so this photon let's say is the + + align:start position:0% +Okay. So so this photon let's say is the + + + align:start position:0% +Okay. So so this photon let's say is the +original photon here. And this photon + + align:start position:0% +original photon here. And this photon + + + align:start position:0% +original photon here. And this photon +over here is due to the release of the + + align:start position:0% +over here is due to the release of the + + + align:start position:0% +over here is due to the release of the +photon from from this excited atom as it + + align:start position:0% +photon from from this excited atom as it + + + align:start position:0% +photon from from this excited atom as it +gets pushed by by this uh source here. + + align:start position:0% +gets pushed by by this uh source here. + + + align:start position:0% +gets pushed by by this uh source here. +So now what we're seeing we're seeing + + align:start position:0% +So now what we're seeing we're seeing + + + align:start position:0% +So now what we're seeing we're seeing +that we're getting two photons okay when + + align:start position:0% +that we're getting two photons okay when + + + align:start position:0% +that we're getting two photons okay when +coming out when we had only one going in + + align:start position:0% +coming out when we had only one going in + + + align:start position:0% +coming out when we had only one going in +and as a result of of the excited atom + + align:start position:0% +and as a result of of the excited atom + + + align:start position:0% +and as a result of of the excited atom +has been pushed down to the ground state + + align:start position:0% +has been pushed down to the ground state + + + align:start position:0% +has been pushed down to the ground state +and this is the the essentials or the + + align:start position:0% +and this is the the essentials or the + + + align:start position:0% +and this is the the essentials or the +basics of of stimulated stimulated + + align:start position:0% +basics of of stimulated stimulated + + + align:start position:0% +basics of of stimulated stimulated +emission or gain because now here you + + align:start position:0% +emission or gain because now here you + + + align:start position:0% +emission or gain because now here you +see that light light can be amplified. + + align:start position:0% +see that light light can be amplified. + + + align:start position:0% +see that light light can be amplified. +All right. So let's talk a little bit + + align:start position:0% +All right. So let's talk a little bit + + + align:start position:0% +All right. So let's talk a little bit +more more about this. + + align:start position:0% +more more about this. + + + align:start position:0% +more more about this. +Uh as I said before just like in + + align:start position:0% +Uh as I said before just like in + + + align:start position:0% +Uh as I said before just like in +absorption the resonance frequency is + + align:start position:0% +absorption the resonance frequency is + + + align:start position:0% +absorption the resonance frequency is +again determined by the energy level + + align:start position:0% +again determined by the energy level + + + align:start position:0% +again determined by the energy level +difference uh divided by plank's + + align:start position:0% +difference uh divided by plank's + + + align:start position:0% +difference uh divided by plank's +constant. All right. Now in this + + align:start position:0% +constant. All right. Now in this + + + align:start position:0% +constant. All right. Now in this +particular case if what you see when you + + align:start position:0% +particular case if what you see when you + + + align:start position:0% +particular case if what you see when you +watch at the output you see that indeed + + align:start position:0% +watch at the output you see that indeed + + + align:start position:0% +watch at the output you see that indeed +the light gets increases now instead of + + align:start position:0% +the light gets increases now instead of + + + align:start position:0% +the light gets increases now instead of +decreases as we had before when you hit + + align:start position:0% +decreases as we had before when you hit + + + align:start position:0% +decreases as we had before when you hit +when you hit resonance. Again the amount + + align:start position:0% +when you hit resonance. Again the amount + + + align:start position:0% +when you hit resonance. Again the amount +of increase will depend on again the + + align:start position:0% +of increase will depend on again the + + + align:start position:0% +of increase will depend on again the +number of atoms that you have and the + + align:start position:0% +number of atoms that you have and the + + + align:start position:0% +number of atoms that you have and the +width will also depend on the on the + + align:start position:0% +width will also depend on the on the + + + align:start position:0% +width will also depend on the on the +transition of that for that particular + + align:start position:0% +transition of that for that particular + + + align:start position:0% +transition of that for that particular +atom or molecule + + align:start position:0% +atom or molecule + + + align:start position:0% +atom or molecule +but it's the width is exactly the same + + align:start position:0% +but it's the width is exactly the same + + + align:start position:0% +but it's the width is exactly the same +as that in absorption that we had before + + align:start position:0% +as that in absorption that we had before + + + align:start position:0% +as that in absorption that we had before +and and in fact the the size of the of + + align:start position:0% +and and in fact the the size of the of + + + align:start position:0% +and and in fact the the size of the of +the gain is also uh as I said depends on + + align:start position:0% +the gain is also uh as I said depends on + + + align:start position:0% +the gain is also uh as I said depends on +the number of atoms in this case number + + align:start position:0% +the number of atoms in this case number + + + align:start position:0% +the number of atoms in this case number +of atoms in the excited state and uh + + align:start position:0% +of atoms in the excited state and uh + + + align:start position:0% +of atoms in the excited state and uh +would be exactly the same as if the + + align:start position:0% +would be exactly the same as if the + + + align:start position:0% +would be exactly the same as if the +process were reversed and all the atoms + + align:start position:0% +process were reversed and all the atoms + + + align:start position:0% +process were reversed and all the atoms +were in the ground state and the size of + + align:start position:0% +were in the ground state and the size of + + + align:start position:0% +were in the ground state and the size of +the absorption would be exactly the same + + align:start position:0% +the absorption would be exactly the same + + + align:start position:0% +the absorption would be exactly the same +as the size of the amplification. And + + align:start position:0% +as the size of the amplification. And + + + align:start position:0% +as the size of the amplification. And +certainly the widths uh are the same. + + align:start position:0% +certainly the widths uh are the same. + + + align:start position:0% +certainly the widths uh are the same. +And again, if you don't if you don't + + align:start position:0% +And again, if you don't if you don't + + + align:start position:0% +And again, if you don't if you don't +believe me, you do a little experiment. + + align:start position:0% +believe me, you do a little experiment. + + + align:start position:0% +believe me, you do a little experiment. +All right? And you do this little + + align:start position:0% +All right? And you do this little + + + align:start position:0% +All right? And you do this little +experiment here. You take a a light + + align:start position:0% +experiment here. You take a a light + + + align:start position:0% +experiment here. You take a a light +source and tunable uh light source and + + align:start position:0% +source and tunable uh light source and + + + align:start position:0% +source and tunable uh light source and +now you send it into into this + + align:start position:0% +now you send it into into this + + + align:start position:0% +now you send it into into this +amplifier. + + align:start position:0% +amplifier. + + + align:start position:0% +amplifier. +uh we we're not saying what kind of + + align:start position:0% +uh we we're not saying what kind of + + + align:start position:0% +uh we we're not saying what kind of +amplifier it is right now but basically + + align:start position:0% +amplifier it is right now but basically + + + align:start position:0% +amplifier it is right now but basically +it's a it's a way of amplifying light. + + align:start position:0% +it's a it's a way of amplifying light. + + + align:start position:0% +it's a it's a way of amplifying light. +It's an amplifier that can amplify + + align:start position:0% +It's an amplifier that can amplify + + + align:start position:0% +It's an amplifier that can amplify +light. So again you take this light + + align:start position:0% +light. So again you take this light + + + align:start position:0% +light. So again you take this light +source tunable you send it in and you + + align:start position:0% +source tunable you send it in and you + + + align:start position:0% +source tunable you send it in and you +measure the output on a detector. + + align:start position:0% +measure the output on a detector. + + + align:start position:0% +measure the output on a detector. +Basically this is the this is the + + align:start position:0% +Basically this is the this is the + + + align:start position:0% +Basically this is the this is the +amplifier has all the atoms let's say in + + align:start position:0% +amplifier has all the atoms let's say in + + + align:start position:0% +amplifier has all the atoms let's say in +the this excited state. you send the + + align:start position:0% +the this excited state. you send the + + + align:start position:0% +the this excited state. you send the +light coming in and if you hit the + + align:start position:0% +light coming in and if you hit the + + + align:start position:0% +light coming in and if you hit the +resonance, say we hit the resonance and + + align:start position:0% +resonance, say we hit the resonance and + + + align:start position:0% +resonance, say we hit the resonance and +you start driving some of these atoms + + align:start position:0% +you start driving some of these atoms + + + align:start position:0% +you start driving some of these atoms +down and the output is essentially uh uh + + align:start position:0% +down and the output is essentially uh uh + + + align:start position:0% +down and the output is essentially uh uh +going to be bigger than the than the + + align:start position:0% +going to be bigger than the than the + + + align:start position:0% +going to be bigger than the than the +input just like we said before at a + + align:start position:0% +input just like we said before at a + + + align:start position:0% +input just like we said before at a +certain frequency you're going to get + + align:start position:0% +certain frequency you're going to get + + + align:start position:0% +certain frequency you're going to get +you're going to get the amplification of + + align:start position:0% +you're going to get the amplification of + + + align:start position:0% +you're going to get the amplification of +this light. Now what about the while + + align:start position:0% +this light. Now what about the while + + + align:start position:0% +this light. Now what about the while +we're at this what about the spontaneous + + align:start position:0% +we're at this what about the spontaneous + + + align:start position:0% +we're at this what about the spontaneous +uh emission because before we said when + + align:start position:0% +uh emission because before we said when + + + align:start position:0% +uh emission because before we said when +all the atoms are in the excited state + + align:start position:0% +all the atoms are in the excited state + + + align:start position:0% +all the atoms are in the excited state +there will be spontaneous emission. Well + + align:start position:0% +there will be spontaneous emission. Well + + + align:start position:0% +there will be spontaneous emission. Well +that's true because if you wait long + + align:start position:0% +that's true because if you wait long + + + align:start position:0% +that's true because if you wait long +enough see if if you had a condition + + align:start position:0% +enough see if if you had a condition + + + align:start position:0% +enough see if if you had a condition +like this where there's no light coming + + align:start position:0% +like this where there's no light coming + + + align:start position:0% +like this where there's no light coming +in all the atoms are excited. If you + + align:start position:0% +in all the atoms are excited. If you + + + align:start position:0% +in all the atoms are excited. If you +wait long enough then all these atoms + + align:start position:0% +wait long enough then all these atoms + + + align:start position:0% +wait long enough then all these atoms +will decay spontaneously by themselves + + align:start position:0% +will decay spontaneously by themselves + + + align:start position:0% +will decay spontaneously by themselves +emitting light in all direction. And + + align:start position:0% +emitting light in all direction. And + + + align:start position:0% +emitting light in all direction. And +that's bad news because there's no more + + align:start position:0% +that's bad news because there's no more + + + align:start position:0% +that's bad news because there's no more +no more amplification. But when when uh + + align:start position:0% +no more amplification. But when when uh + + + align:start position:0% +no more amplification. But when when uh +when the light comes in, yes, it will + + align:start position:0% +when the light comes in, yes, it will + + + align:start position:0% +when the light comes in, yes, it will +interact with atoms and bring them down + + align:start position:0% +interact with atoms and bring them down + + + align:start position:0% +interact with atoms and bring them down +and and then the light will be + + align:start position:0% +and and then the light will be + + + align:start position:0% +and and then the light will be +amplified. But some of the other atoms + + align:start position:0% +amplified. But some of the other atoms + + + align:start position:0% +amplified. But some of the other atoms +here will also spontaneously decay and + + align:start position:0% +here will also spontaneously decay and + + + align:start position:0% +here will also spontaneously decay and +will emit radiation in all directions. + + align:start position:0% +will emit radiation in all directions. + + + align:start position:0% +will emit radiation in all directions. +And this is no good to you because these + + align:start position:0% +And this is no good to you because these + + + align:start position:0% +And this is no good to you because these +this light is lost and not available for + + align:start position:0% +this light is lost and not available for + + + align:start position:0% +this light is lost and not available for +for amplification. So the whole secret + + align:start position:0% +for amplification. So the whole secret + + + align:start position:0% +for amplification. So the whole secret +then of of amplification is to make sure + + align:start position:0% +then of of amplification is to make sure + + + align:start position:0% +then of of amplification is to make sure +that the the these atoms here are used + + align:start position:0% +that the the these atoms here are used + + + align:start position:0% +that the the these atoms here are used +up to generate amp gain to come down + + align:start position:0% +up to generate amp gain to come down + + + align:start position:0% +up to generate amp gain to come down +driven by this field here and not by and + + align:start position:0% +driven by this field here and not by and + + + align:start position:0% +driven by this field here and not by and +not drop down by themselves and and emit + + align:start position:0% +not drop down by themselves and and emit + + + align:start position:0% +not drop down by themselves and and emit +spontaneous emission. That's a tricky + + align:start position:0% +spontaneous emission. That's a tricky + + + align:start position:0% +spontaneous emission. That's a tricky +thing and you have to make sure you can + + align:start position:0% +thing and you have to make sure you can + + + align:start position:0% +thing and you have to make sure you can +handle that. Now to to summarize + + align:start position:0% +handle that. Now to to summarize + + + align:start position:0% +handle that. Now to to summarize +amplification + + align:start position:0% +amplification + + + align:start position:0% +amplification +uh is the following. we need for for + + align:start position:0% +uh is the following. we need for for + + + align:start position:0% +uh is the following. we need for for +well right let's look at loss first uh + + align:start position:0% +well right let's look at loss first uh + + + align:start position:0% +well right let's look at loss first uh +when when when we have a loss uh loss + + align:start position:0% +when when when we have a loss uh loss + + + align:start position:0% +when when when we have a loss uh loss +lossy device it means that we have uh + + align:start position:0% +lossy device it means that we have uh + + + align:start position:0% +lossy device it means that we have uh +before we only talked about one atom + + align:start position:0% +before we only talked about one atom + + + align:start position:0% +before we only talked about one atom +let's say in in a state here I can put + + align:start position:0% +let's say in in a state here I can put + + + align:start position:0% +let's say in in a state here I can put +lots of atoms or molecules in let's say + + align:start position:0% +lots of atoms or molecules in let's say + + + align:start position:0% +lots of atoms or molecules in let's say +in the ground state but fewer in the in + + align:start position:0% +in the ground state but fewer in the in + + + align:start position:0% +in the ground state but fewer in the in +the excited state so if there's more in + + align:start position:0% +the excited state so if there's more in + + + align:start position:0% +the excited state so if there's more in +the lower than the upper level then the + + align:start position:0% +the lower than the upper level then the + + + align:start position:0% +the lower than the upper level then the +net effect is absorption so if n1 which + + align:start position:0% +net effect is absorption so if n1 which + + + align:start position:0% +net effect is absorption so if n1 which +is the number in the lower level is + + align:start position:0% +is the number in the lower level is + + + align:start position:0% +is the number in the lower level is +bigger than n2 then the net effect is + + align:start position:0% +bigger than n2 then the net effect is + + + align:start position:0% +bigger than n2 then the net effect is +absorption + + align:start position:0% + + + + align:start position:0% + +Gain is when there is more in the upper + + align:start position:0% +Gain is when there is more in the upper + + + align:start position:0% +Gain is when there is more in the upper +than lower because if if if n_sub_2 is + + align:start position:0% +than lower because if if if n_sub_2 is + + + align:start position:0% +than lower because if if if n_sub_2 is +bigger than n1 then we have net gain and + + align:start position:0% +bigger than n1 then we have net gain and + + + align:start position:0% +bigger than n1 then we have net gain and +from now on I'll be referring to it as a + + align:start position:0% +from now on I'll be referring to it as a + + + align:start position:0% +from now on I'll be referring to it as a +population inversion because normally + + align:start position:0% +population inversion because normally + + + align:start position:0% +population inversion because normally +atoms like to be in the ground state to + + align:start position:0% +atoms like to be in the ground state to + + + align:start position:0% +atoms like to be in the ground state to +start with and not in the in the excited + + align:start position:0% +start with and not in the in the excited + + + align:start position:0% +start with and not in the in the excited +state. So I have to as we'll see later I + + align:start position:0% +state. So I have to as we'll see later I + + + align:start position:0% +state. So I have to as we'll see later I +have to do something to put the atoms up + + align:start position:0% +have to do something to put the atoms up + + + align:start position:0% +have to do something to put the atoms up +here and and the and it's the net + + align:start position:0% +here and and the and it's the net + + + align:start position:0% +here and and the and it's the net +difference that will give me that will + + align:start position:0% +difference that will give me that will + + + align:start position:0% +difference that will give me that will +give me uh the gain. + + align:start position:0% +give me uh the gain. + + + align:start position:0% +give me uh the gain. +Okay. So now uh it's only a matter of + + align:start position:0% +Okay. So now uh it's only a matter of + + + align:start position:0% +Okay. So now uh it's only a matter of +how to put more atoms in the upper state + + align:start position:0% +how to put more atoms in the upper state + + + align:start position:0% +how to put more atoms in the upper state +than in the lower state. That will give + + align:start position:0% +than in the lower state. That will give + + + align:start position:0% +than in the lower state. That will give +me that will give me the gain. All + + align:start position:0% +me that will give me the gain. All + + + align:start position:0% +me that will give me the gain. All +right. Question is how does a laser + + align:start position:0% +right. Question is how does a laser + + + align:start position:0% +right. Question is how does a laser +start? So I have gain so what? So, I'm + + align:start position:0% +start? So I have gain so what? So, I'm + + + align:start position:0% +start? So I have gain so what? So, I'm +going to sit around uh waiting for for + + align:start position:0% +going to sit around uh waiting for for + + + align:start position:0% +going to sit around uh waiting for for +the lasers. How does a laser start? All + + align:start position:0% +the lasers. How does a laser start? All + + + align:start position:0% +the lasers. How does a laser start? All +right. So, that's my my next question is + + align:start position:0% +right. So, that's my my next question is + + + align:start position:0% +right. So, that's my my next question is +that how does a laser uh uh sorry, no, I + + align:start position:0% +that how does a laser uh uh sorry, no, I + + + align:start position:0% +that how does a laser uh uh sorry, no, I +wasn't looking at my uh the question is + + align:start position:0% +wasn't looking at my uh the question is + + + align:start position:0% +wasn't looking at my uh the question is +now I should hold off a little bit, but + + align:start position:0% +now I should hold off a little bit, but + + + align:start position:0% +now I should hold off a little bit, but +how to make a an optical amplifier? And + + align:start position:0% +how to make a an optical amplifier? And + + + align:start position:0% +how to make a an optical amplifier? And +now uh let me just uh uh I got carried + + align:start position:0% +now uh let me just uh uh I got carried + + + align:start position:0% +now uh let me just uh uh I got carried +away not looking at my my visuals. Let + + align:start position:0% +away not looking at my my visuals. Let + + + align:start position:0% +away not looking at my my visuals. Let +me uh go back to fundamentals again. Uh + + align:start position:0% +me uh go back to fundamentals again. Uh + + + align:start position:0% +me uh go back to fundamentals again. Uh +I have all the atoms let's say to start + + align:start position:0% +I have all the atoms let's say to start + + + align:start position:0% +I have all the atoms let's say to start +with here in a typical atomic system, + + align:start position:0% +with here in a typical atomic system, + + + align:start position:0% +with here in a typical atomic system, +molecular system. But I need in order to + + align:start position:0% +molecular system. But I need in order to + + + align:start position:0% +molecular system. But I need in order to +get amplification I have to have more in + + align:start position:0% +get amplification I have to have more in + + + align:start position:0% +get amplification I have to have more in +the upper than than the lower. So I need + + align:start position:0% +the upper than than the lower. So I need + + + align:start position:0% +the upper than than the lower. So I need +a so-called pump. This pump could be as + + align:start position:0% +a so-called pump. This pump could be as + + + align:start position:0% +a so-called pump. This pump could be as +we'll see later could be optical field, + + align:start position:0% +we'll see later could be optical field, + + + align:start position:0% +we'll see later could be optical field, +could be a discharge lamp, could be a + + align:start position:0% +could be a discharge lamp, could be a + + + align:start position:0% +could be a discharge lamp, could be a +laser, could be collision, could be all + + align:start position:0% +laser, could be collision, could be all + + + align:start position:0% +laser, could be collision, could be all +kinds of things we'll talk about later. + + align:start position:0% +kinds of things we'll talk about later. + + + align:start position:0% +kinds of things we'll talk about later. +But basically for now let's call it a + + align:start position:0% +But basically for now let's call it a + + + align:start position:0% +But basically for now let's call it a +pump. And that's pump. The job of this + + align:start position:0% +pump. And that's pump. The job of this + + + align:start position:0% +pump. And that's pump. The job of this +pump is take some of these atoms and put + + align:start position:0% +pump is take some of these atoms and put + + + align:start position:0% +pump is take some of these atoms and put +them upstairs here. Otherwise, you know, + + align:start position:0% +them upstairs here. Otherwise, you know, + + + align:start position:0% +them upstairs here. Otherwise, you know, +right now it's like an absorber. This + + align:start position:0% +right now it's like an absorber. This + + + align:start position:0% +right now it's like an absorber. This +material acts like an absorber over + + align:start position:0% +material acts like an absorber over + + + align:start position:0% +material acts like an absorber over +here. It still looks like an absorber + + align:start position:0% +here. It still looks like an absorber + + + align:start position:0% +here. It still looks like an absorber +because you have more in the lower than + + align:start position:0% +because you have more in the lower than + + + align:start position:0% +because you have more in the lower than +in the upper. And as I keep transferring + + align:start position:0% +in the upper. And as I keep transferring + + + align:start position:0% +in the upper. And as I keep transferring +atoms from the lower level to the upper + + align:start position:0% +atoms from the lower level to the upper + + + align:start position:0% +atoms from the lower level to the upper +level, I get to a stage where let's say + + align:start position:0% +level, I get to a stage where let's say + + + align:start position:0% +level, I get to a stage where let's say +in this case I have four and four and uh + + align:start position:0% +in this case I have four and four and uh + + + align:start position:0% +in this case I have four and four and uh +it's no it's neither gain or absorption. + + align:start position:0% +it's no it's neither gain or absorption. + + + align:start position:0% +it's no it's neither gain or absorption. +In fact, the material becomes becomes + + align:start position:0% +In fact, the material becomes becomes + + + align:start position:0% +In fact, the material becomes becomes +transparent. And even if I increase the + + align:start position:0% +transparent. And even if I increase the + + + align:start position:0% +transparent. And even if I increase the +light doesn't matter because I the net + + align:start position:0% +light doesn't matter because I the net + + + align:start position:0% +light doesn't matter because I the net +effect is I have equal number in the + + align:start position:0% +effect is I have equal number in the + + + align:start position:0% +effect is I have equal number in the +upper and the lower and we call that + + align:start position:0% +upper and the lower and we call that + + + align:start position:0% +upper and the lower and we call that +saturation and there is no uh + + align:start position:0% +saturation and there is no uh + + + align:start position:0% +saturation and there is no uh +amplification or gain. So we started as + + align:start position:0% +amplification or gain. So we started as + + + align:start position:0% +amplification or gain. So we started as +an absorber and with this kind of a pump + + align:start position:0% +an absorber and with this kind of a pump + + + align:start position:0% +an absorber and with this kind of a pump +we we created less absorption but no no + + align:start position:0% +we we created less absorption but no no + + + align:start position:0% +we we created less absorption but no no +gain. So in order to to get gain I have + + align:start position:0% +gain. So in order to to get gain I have + + + align:start position:0% +gain. So in order to to get gain I have +to do a little trick. All right. So this + + align:start position:0% +to do a little trick. All right. So this + + + align:start position:0% +to do a little trick. All right. So this +this trick is is the following. I cannot + + align:start position:0% +this trick is is the following. I cannot + + + align:start position:0% +this trick is is the following. I cannot +use uh two-le system. I have to use one + + align:start position:0% +use uh two-le system. I have to use one + + + align:start position:0% +use uh two-le system. I have to use one +more. All right. So, we're going to + + align:start position:0% +more. All right. So, we're going to + + + align:start position:0% +more. All right. So, we're going to +complicate this by adding three levels + + align:start position:0% +complicate this by adding three levels + + + align:start position:0% +complicate this by adding three levels +to this particular atom or molecule. In + + align:start position:0% +to this particular atom or molecule. In + + + align:start position:0% +to this particular atom or molecule. In +this case, to start with, all the atoms + + align:start position:0% +this case, to start with, all the atoms + + + align:start position:0% +this case, to start with, all the atoms +are here in the in the lower level to to + + align:start position:0% +are here in the in the lower level to to + + + align:start position:0% +are here in the in the lower level to to +start with as as usual. Then, if I put + + align:start position:0% +start with as as usual. Then, if I put + + + align:start position:0% +start with as as usual. Then, if I put +this pump and this pump again could be + + align:start position:0% +this pump and this pump again could be + + + align:start position:0% +this pump and this pump again could be +optical pump or or whatever. This pump + + align:start position:0% +optical pump or or whatever. This pump + + + align:start position:0% +optical pump or or whatever. This pump +if it's uh if it resonates with a + + align:start position:0% +if it's uh if it resonates with a + + + align:start position:0% +if it's uh if it resonates with a +transition now from the first to the + + align:start position:0% +transition now from the first to the + + + align:start position:0% +transition now from the first to the +third level, it can take some of these + + align:start position:0% +third level, it can take some of these + + + align:start position:0% +third level, it can take some of these +atoms and put them and put them up here. + + align:start position:0% +atoms and put them and put them up here. + + + align:start position:0% +atoms and put them and put them up here. +Now if he puts them up here, as soon as + + align:start position:0% +Now if he puts them up here, as soon as + + + align:start position:0% +Now if he puts them up here, as soon as +you put some atoms up here, there is a + + align:start position:0% +you put some atoms up here, there is a + + + align:start position:0% +you put some atoms up here, there is a +population difference between level + + align:start position:0% +population difference between level + + + align:start position:0% +population difference between level +three and level two. So now you have + + align:start position:0% +three and level two. So now you have + + + align:start position:0% +three and level two. So now you have +amplification + + align:start position:0% +amplification + + + align:start position:0% +amplification +for for transitions for light at this at + + align:start position:0% +for for transitions for light at this at + + + align:start position:0% +for for transitions for light at this at +this frequency. But but if you look at + + align:start position:0% +this frequency. But but if you look at + + + align:start position:0% +this frequency. But but if you look at +level one and level three, that's still + + align:start position:0% +level one and level three, that's still + + + align:start position:0% +level one and level three, that's still +absorption or what have you, but + + align:start position:0% +absorption or what have you, but + + + align:start position:0% +absorption or what have you, but +certainly no amplification. So the + + align:start position:0% +certainly no amplification. So the + + + align:start position:0% +certainly no amplification. So the +amplification occurs as soon as you put + + align:start position:0% +amplification occurs as soon as you put + + + align:start position:0% +amplification occurs as soon as you put +one atom in in level three. uh because + + align:start position:0% +one atom in in level three. uh because + + + align:start position:0% +one atom in in level three. uh because +level two is is is empty. So you can + + align:start position:0% +level two is is is empty. So you can + + + align:start position:0% +level two is is is empty. So you can +create N3 bigger than N2 which is the + + align:start position:0% +create N3 bigger than N2 which is the + + + align:start position:0% +create N3 bigger than N2 which is the +condition for amplification as soon as + + align:start position:0% +condition for amplification as soon as + + + align:start position:0% +condition for amplification as soon as +you pump one atom into this into this + + align:start position:0% +you pump one atom into this into this + + + align:start position:0% +you pump one atom into this into this +level. So the amount of gain that you'll + + align:start position:0% +level. So the amount of gain that you'll + + + align:start position:0% +level. So the amount of gain that you'll +get will depend of course on N3 minus N2 + + align:start position:0% +get will depend of course on N3 minus N2 + + + align:start position:0% +get will depend of course on N3 minus N2 +on the population difference as we + + align:start position:0% +on the population difference as we + + + align:start position:0% +on the population difference as we +talked before and there will be a + + align:start position:0% +talked before and there will be a + + + align:start position:0% +talked before and there will be a +constant that multiplies it that depends + + align:start position:0% +constant that multiplies it that depends + + + align:start position:0% +constant that multiplies it that depends +on again the particular transition the + + align:start position:0% +on again the particular transition the + + + align:start position:0% +on again the particular transition the +particular atom and so on. But the key + + align:start position:0% +particular atom and so on. But the key + + + align:start position:0% +particular atom and so on. But the key +thing is that it's a population + + align:start position:0% +thing is that it's a population + + + align:start position:0% +thing is that it's a population +difference. If n3 is not bigger than n2 + + align:start position:0% +difference. If n3 is not bigger than n2 + + + align:start position:0% +difference. If n3 is not bigger than n2 +then forget it there is no gain. So the + + align:start position:0% +then forget it there is no gain. So the + + + align:start position:0% +then forget it there is no gain. So the +the frequency for the amplification for + + align:start position:0% +the frequency for the amplification for + + + align:start position:0% +the frequency for the amplification for +the amplified light will be at the at + + align:start position:0% +the amplified light will be at the at + + + align:start position:0% +the amplified light will be at the at +this transition frequency which is e3 + + align:start position:0% +this transition frequency which is e3 + + + align:start position:0% +this transition frequency which is e3 +minus e2 divided by by h which is + + align:start position:0% +minus e2 divided by by h which is + + + align:start position:0% +minus e2 divided by by h which is +blank's constant. Again if you want to + + align:start position:0% +blank's constant. Again if you want to + + + align:start position:0% +blank's constant. Again if you want to +do a uh an experiment then uh then you + + align:start position:0% +do a uh an experiment then uh then you + + + align:start position:0% +do a uh an experiment then uh then you +do the uh then this is the following + + align:start position:0% +do the uh then this is the following + + + align:start position:0% +do the uh then this is the following +experiment. You take again this + + align:start position:0% +experiment. You take again this + + + align:start position:0% +experiment. You take again this +amplifier. You take this uh tunable + + align:start position:0% +amplifier. You take this uh tunable + + + align:start position:0% +amplifier. You take this uh tunable +source uh and the amplifier now has a + + align:start position:0% +source uh and the amplifier now has a + + + align:start position:0% +source uh and the amplifier now has a +pump. The pump then takes atoms from + + align:start position:0% +pump. The pump then takes atoms from + + + align:start position:0% +pump. The pump then takes atoms from +here and puts them up here and creates a + + align:start position:0% +here and puts them up here and creates a + + + align:start position:0% +here and puts them up here and creates a +population inversion. And then you tune + + align:start position:0% +population inversion. And then you tune + + + align:start position:0% +population inversion. And then you tune +this you tune this light source here. + + align:start position:0% +this you tune this light source here. + + + align:start position:0% +this you tune this light source here. +And then you'll see that uh when you + + align:start position:0% +And then you'll see that uh when you + + + align:start position:0% +And then you'll see that uh when you +look at the output you see that again + + align:start position:0% +look at the output you see that again + + + align:start position:0% +look at the output you see that again +there will be amplification at this + + align:start position:0% +there will be amplification at this + + + align:start position:0% +there will be amplification at this +specific frequency that coincides to + + align:start position:0% +specific frequency that coincides to + + + align:start position:0% +specific frequency that coincides to +this this with this transition. + + align:start position:0% +this this with this transition. + + + align:start position:0% +this this with this transition. +All right. So, uh, I'm sure now that, + + align:start position:0% +All right. So, uh, I'm sure now that, + + + align:start position:0% +All right. So, uh, I'm sure now that, +uh, after hearing me talk about all + + align:start position:0% +uh, after hearing me talk about all + + + align:start position:0% +uh, after hearing me talk about all +this, I'm sure you'd like to see that, + + align:start position:0% +this, I'm sure you'd like to see that, + + + align:start position:0% +this, I'm sure you'd like to see that, +uh, indeed ampl optical amplification + + align:start position:0% +uh, indeed ampl optical amplification + + + align:start position:0% +uh, indeed ampl optical amplification +takes place or or the amplification of + + align:start position:0% +takes place or or the amplification of + + + align:start position:0% +takes place or or the amplification of +light takes place. And and and, uh, I we + + align:start position:0% +light takes place. And and and, uh, I we + + + align:start position:0% +light takes place. And and and, uh, I we +have a a demonstration for you again + + align:start position:0% +have a a demonstration for you again + + + align:start position:0% +have a a demonstration for you again +using a a helium neon uh, laser as as an + + align:start position:0% +using a a helium neon uh, laser as as an + + + align:start position:0% +using a a helium neon uh, laser as as an +amplifier, at least the helium neon part + + align:start position:0% +amplifier, at least the helium neon part + + + align:start position:0% +amplifier, at least the helium neon part +as the amplifier. and and uh and we do + + align:start position:0% +as the amplifier. and and uh and we do + + + align:start position:0% +as the amplifier. and and uh and we do +we will measure we'll actually measure + + align:start position:0% +we will measure we'll actually measure + + + align:start position:0% +we will measure we'll actually measure +uh ampl amplification uh of light we're + + align:start position:0% +uh ampl amplification uh of light we're + + + align:start position:0% +uh ampl amplification uh of light we're +all familiar with with absorption and + + align:start position:0% +all familiar with with absorption and + + + align:start position:0% +all familiar with with absorption and +attenuation of light but in this + + align:start position:0% +attenuation of light but in this + + + align:start position:0% +attenuation of light but in this +particular demonstration will be + + align:start position:0% +particular demonstration will be + + + align:start position:0% +particular demonstration will be +amplification of light so I think now + + align:start position:0% +amplification of light so I think now + + + align:start position:0% +amplification of light so I think now +we're ready to to enjoy this + + align:start position:0% +we're ready to to enjoy this + + + align:start position:0% +we're ready to to enjoy this +demonstration so let's go and uh and + + align:start position:0% +demonstration so let's go and uh and + + + align:start position:0% +demonstration so let's go and uh and +look at it + + align:start position:0% + + + + align:start position:0% + +as we have already learned the most + + align:start position:0% +as we have already learned the most + + + align:start position:0% +as we have already learned the most +important important component in a laser + + align:start position:0% +important important component in a laser + + + align:start position:0% +important important component in a laser +or the heart of the laser is the gain + + align:start position:0% +or the heart of the laser is the gain + + + align:start position:0% +or the heart of the laser is the gain +medium or the optical amplifier. + + align:start position:0% +medium or the optical amplifier. + + + align:start position:0% +medium or the optical amplifier. +This is no ordinary amplifier. This is + + align:start position:0% +This is no ordinary amplifier. This is + + + align:start position:0% +This is no ordinary amplifier. This is +an amplifier for light. + + align:start position:0% +an amplifier for light. + + + align:start position:0% +an amplifier for light. +And in this demonstration, we're going + + align:start position:0% +And in this demonstration, we're going + + + align:start position:0% +And in this demonstration, we're going +to show you and hopefully convince you + + align:start position:0% +to show you and hopefully convince you + + + align:start position:0% +to show you and hopefully convince you +that indeed light can be amplified. + + align:start position:0% +that indeed light can be amplified. + + + align:start position:0% +that indeed light can be amplified. +The amount of amplification is not so + + align:start position:0% +The amount of amplification is not so + + + align:start position:0% +The amount of amplification is not so +huge, but I'm sure will make it + + align:start position:0% +huge, but I'm sure will make it + + + align:start position:0% +huge, but I'm sure will make it +convincing enough so that you get the + + align:start position:0% +convincing enough so that you get the + + + align:start position:0% +convincing enough so that you get the +feel that indeed that light can be can + + align:start position:0% +feel that indeed that light can be can + + + align:start position:0% +feel that indeed that light can be can +be amplified. + + align:start position:0% +be amplified. + + + align:start position:0% +be amplified. +The setup we're going to use is is here + + align:start position:0% +The setup we're going to use is is here + + + align:start position:0% +The setup we're going to use is is here +going to have a + + align:start position:0% +going to have a + + + align:start position:0% +going to have a +a laser which is going to be our light + + align:start position:0% +a laser which is going to be our light + + + align:start position:0% +a laser which is going to be our light +source. Here's the here's the output of + + align:start position:0% +source. Here's the here's the output of + + + align:start position:0% +source. Here's the here's the output of +the of the laser. We're going to reflect + + align:start position:0% +the of the laser. We're going to reflect + + + align:start position:0% +the of the laser. We're going to reflect +it by this mirror here and then this + + align:start position:0% +it by this mirror here and then this + + + align:start position:0% +it by this mirror here and then this +mirror over here. Now the laser beam + + align:start position:0% +mirror over here. Now the laser beam + + + align:start position:0% +mirror over here. Now the laser beam +then enters this this optical amplifier. + + align:start position:0% +then enters this this optical amplifier. + + + align:start position:0% +then enters this this optical amplifier. +Now this optical amplifier + + align:start position:0% +Now this optical amplifier + + + align:start position:0% +Now this optical amplifier +is is essentially this is a is a + + align:start position:0% +is is essentially this is a is a + + + align:start position:0% +is is essentially this is a is a +discharge tube helium neon gas mixture + + align:start position:0% +discharge tube helium neon gas mixture + + + align:start position:0% +discharge tube helium neon gas mixture +uh that will give gain amplification or + + align:start position:0% +uh that will give gain amplification or + + + align:start position:0% +uh that will give gain amplification or +gain at 6328 anstroms. In fact, the + + align:start position:0% +gain at 6328 anstroms. In fact, the + + + align:start position:0% +gain at 6328 anstroms. In fact, the +light enters this window here and then + + align:start position:0% +light enters this window here and then + + + align:start position:0% +light enters this window here and then +comes out at the other end and that's + + align:start position:0% +comes out at the other end and that's + + + align:start position:0% +comes out at the other end and that's +what we have essentially uh uh mounted + + align:start position:0% +what we have essentially uh uh mounted + + + align:start position:0% +what we have essentially uh uh mounted +here right below. Okay. So + + align:start position:0% +here right below. Okay. So + + + align:start position:0% +here right below. Okay. So +the then the output + + align:start position:0% +the then the output + + + align:start position:0% +the then the output +uh through the through this amplifier + + align:start position:0% +uh through the through this amplifier + + + align:start position:0% +uh through the through this amplifier +and the amplifier right now is turned + + align:start position:0% +and the amplifier right now is turned + + + align:start position:0% +and the amplifier right now is turned +off. Then goes onto onto a detector over + + align:start position:0% +off. Then goes onto onto a detector over + + + align:start position:0% +off. Then goes onto onto a detector over +here and then the output of the detector + + align:start position:0% +here and then the output of the detector + + + align:start position:0% +here and then the output of the detector +then goes onto a scope onto oscilloscope + + align:start position:0% +then goes onto a scope onto oscilloscope + + + align:start position:0% +then goes onto a scope onto oscilloscope +over here and and also uh we look at the + + align:start position:0% +over here and and also uh we look at the + + + align:start position:0% +over here and and also uh we look at the +output on a on a digital uh on a digital + + align:start position:0% +output on a on a digital uh on a digital + + + align:start position:0% +output on a on a digital uh on a digital +digital meter. All right. So we have two + + align:start position:0% +digital meter. All right. So we have two + + + align:start position:0% +digital meter. All right. So we have two +ways of looking at the same at the same + + align:start position:0% +ways of looking at the same at the same + + + align:start position:0% +ways of looking at the same at the same +uh output. + + align:start position:0% +uh output. + + + align:start position:0% +uh output. +All right. Now we're ready to to set to + + align:start position:0% +All right. Now we're ready to to set to + + + align:start position:0% +All right. Now we're ready to to set to +set zero. Right. So first what I'm going + + align:start position:0% +set zero. Right. So first what I'm going + + + align:start position:0% +set zero. Right. So first what I'm going +to do is then block block the beam of + + align:start position:0% +to do is then block block the beam of + + + align:start position:0% +to do is then block block the beam of +light over here. And let's look at the + + align:start position:0% +light over here. And let's look at the + + + align:start position:0% +light over here. And let's look at the +zero on the scope and the zero on the on + + align:start position:0% +zero on the scope and the zero on the on + + + align:start position:0% +zero on the scope and the zero on the on +the meter. + + align:start position:0% +the meter. + + + align:start position:0% +the meter. +Now the meter says uh08 + + align:start position:0% +Now the meter says uh08 + + + align:start position:0% +Now the meter says uh08 +which is not quite zero. And the reason + + align:start position:0% +which is not quite zero. And the reason + + + align:start position:0% +which is not quite zero. And the reason +for that is because we have room light + + align:start position:0% +for that is because we have room light + + + align:start position:0% +for that is because we have room light +uh hitting the detector. So what I'm + + align:start position:0% +uh hitting the detector. So what I'm + + + align:start position:0% +uh hitting the detector. So what I'm +going to do to get rid of that, I'm + + align:start position:0% +going to do to get rid of that, I'm + + + align:start position:0% +going to do to get rid of that, I'm +going to put this little hood over the + + align:start position:0% +going to put this little hood over the + + + align:start position:0% +going to put this little hood over the +detector. + + align:start position:0% +detector. + + + align:start position:0% +detector. +Now we see that the output of the of the + + align:start position:0% +Now we see that the output of the of the + + + align:start position:0% +Now we see that the output of the of the +meter now is indeed is indeed zero. + + align:start position:0% +meter now is indeed is indeed zero. + + + align:start position:0% +meter now is indeed is indeed zero. +And also hopefully then the output of + + align:start position:0% +And also hopefully then the output of + + + align:start position:0% +And also hopefully then the output of +the scope here this is will be our zero + + align:start position:0% +the scope here this is will be our zero + + + align:start position:0% +the scope here this is will be our zero +on the on the oscilloscope. + + align:start position:0% +on the on the oscilloscope. + + + align:start position:0% +on the on the oscilloscope. +Now if I take this card away and let the + + align:start position:0% +Now if I take this card away and let the + + + align:start position:0% +Now if I take this card away and let the +light go through, you can see that now + + align:start position:0% +light go through, you can see that now + + + align:start position:0% +light go through, you can see that now +the output on the scope has changed and + + align:start position:0% +the output on the scope has changed and + + + align:start position:0% +the output on the scope has changed and +the meter reads around 364 + + align:start position:0% +the meter reads around 364 + + + align:start position:0% +the meter reads around 364 +or 63 or or thereabout which is the + + align:start position:0% +or 63 or or thereabout which is the + + + align:start position:0% +or 63 or or thereabout which is the +output of the laser. Now all I have to + + align:start position:0% +output of the laser. Now all I have to + + + align:start position:0% +output of the laser. Now all I have to +do is block block the laser beam + + align:start position:0% +do is block block the laser beam + + + align:start position:0% +do is block block the laser beam +and we go back to zero on the meter as + + align:start position:0% +and we go back to zero on the meter as + + + align:start position:0% +and we go back to zero on the meter as +well as zero on the scope. Here we are. + + align:start position:0% +well as zero on the scope. Here we are. + + + align:start position:0% +well as zero on the scope. Here we are. +laser beam is back again and then we get + + align:start position:0% +laser beam is back again and then we get + + + align:start position:0% +laser beam is back again and then we get +the that same value again. Now we're all + + align:start position:0% +the that same value again. Now we're all + + + align:start position:0% +the that same value again. Now we're all +familiar with absorption of light and uh + + align:start position:0% +familiar with absorption of light and uh + + + align:start position:0% +familiar with absorption of light and uh +I just want to just demonstrate it just + + align:start position:0% +I just want to just demonstrate it just + + + align:start position:0% +I just want to just demonstrate it just +for reference. I'm going to put a piece + + align:start position:0% +for reference. I'm going to put a piece + + + align:start position:0% +for reference. I'm going to put a piece +of glass in front of the of the laser + + align:start position:0% +of glass in front of the of the laser + + + align:start position:0% +of glass in front of the of the laser +beam and we know that glass at normal + + align:start position:0% +beam and we know that glass at normal + + + align:start position:0% +beam and we know that glass at normal +incidence has uh reflectivity of about + + align:start position:0% +incidence has uh reflectivity of about + + + align:start position:0% +incidence has uh reflectivity of about +4% per surface. So I should get an + + align:start position:0% +4% per surface. So I should get an + + + align:start position:0% +4% per surface. So I should get an +attenuation of about 8% or so uh when I + + align:start position:0% +attenuation of about 8% or so uh when I + + + align:start position:0% +attenuation of about 8% or so uh when I +put this piece of glass in in the in the + + align:start position:0% +put this piece of glass in in the in the + + + align:start position:0% +put this piece of glass in in the in the +beam of light. Now you can see the meter + + align:start position:0% +beam of light. Now you can see the meter + + + align:start position:0% +beam of light. Now you can see the meter +has dropped now to 330 + + align:start position:0% +has dropped now to 330 + + + align:start position:0% +has dropped now to 330 +uh + + align:start position:0% +uh + + + align:start position:0% +uh +300 and well if I can keep it still 320 + + align:start position:0% +300 and well if I can keep it still 320 + + + align:start position:0% +300 and well if I can keep it still 320 +something. Now if I take the piece of + + align:start position:0% +something. Now if I take the piece of + + + align:start position:0% +something. Now if I take the piece of +glass away you know we go up to the + + align:start position:0% +glass away you know we go up to the + + + align:start position:0% +glass away you know we go up to the +previous number of 360 something. So you + + align:start position:0% +previous number of 360 something. So you + + + align:start position:0% +previous number of 360 something. So you +can see we have about an attenuation of + + align:start position:0% +can see we have about an attenuation of + + + align:start position:0% +can see we have about an attenuation of +about uh 8 or so uh%. Now what I'm going + + align:start position:0% +about uh 8 or so uh%. Now what I'm going + + + align:start position:0% +about uh 8 or so uh%. Now what I'm going +to do now is put this piece of glass uh + + align:start position:0% +to do now is put this piece of glass uh + + + align:start position:0% +to do now is put this piece of glass uh +before the detector also. And indeed I'm + + align:start position:0% +before the detector also. And indeed I'm + + + align:start position:0% +before the detector also. And indeed I'm +going to hold it against the uh the the + + align:start position:0% +going to hold it against the uh the the + + + align:start position:0% +going to hold it against the uh the the +uh tube here so that I don't shake too + + align:start position:0% +uh tube here so that I don't shake too + + + align:start position:0% +uh tube here so that I don't shake too +much. And again you can see that the + + align:start position:0% +much. And again you can see that the + + + align:start position:0% +much. And again you can see that the +attenuation + + align:start position:0% +attenuation + + + align:start position:0% +attenuation +is is also about uh about 8% or so here. + + align:start position:0% +is is also about uh about 8% or so here. + + + align:start position:0% +is is also about uh about 8% or so here. +Let me put it in the front + + align:start position:0% + + + + align:start position:0% + +and and also then I'll put it in the + + align:start position:0% +and and also then I'll put it in the + + + align:start position:0% +and and also then I'll put it in the +back again and hopefully + + align:start position:0% +back again and hopefully + + + align:start position:0% +back again and hopefully +I'll put it in the same position. + + align:start position:0% +I'll put it in the same position. + + + align:start position:0% +I'll put it in the same position. +You can see this. + + align:start position:0% +You can see this. + + + align:start position:0% +You can see this. +I hold it still + + align:start position:0% + + + + align:start position:0% + +and then take it away + + align:start position:0% +and then take it away + + + align:start position:0% +and then take it away +and then roughly we get this 8% + + align:start position:0% +and then roughly we get this 8% + + + align:start position:0% +and then roughly we get this 8% +attenuation. So now we've demonstrated + + align:start position:0% +attenuation. So now we've demonstrated + + + align:start position:0% +attenuation. So now we've demonstrated +that indeed light can be can be easily + + align:start position:0% +that indeed light can be can be easily + + + align:start position:0% +that indeed light can be can be easily +uh easily attenuated. Now we come to + + align:start position:0% +uh easily attenuated. Now we come to + + + align:start position:0% +uh easily attenuated. Now we come to +this crucial uh demonstration of gain. + + align:start position:0% +this crucial uh demonstration of gain. + + + align:start position:0% +this crucial uh demonstration of gain. +So now I want you to then watch the both + + align:start position:0% +So now I want you to then watch the both + + + align:start position:0% +So now I want you to then watch the both +the scope and uh and the meter as I turn + + align:start position:0% +the scope and uh and the meter as I turn + + + align:start position:0% +the scope and uh and the meter as I turn +on the the amplifier. + + align:start position:0% +on the the amplifier. + + + align:start position:0% +on the the amplifier. +So here I'm going to now turn on the + + align:start position:0% +So here I'm going to now turn on the + + + align:start position:0% +So here I'm going to now turn on the +amplifier + + align:start position:0% +amplifier + + + align:start position:0% +amplifier +and remember this number is around 363 + + align:start position:0% +and remember this number is around 363 + + + align:start position:0% +and remember this number is around 363 +or so 364. + + align:start position:0% +or so 364. + + + align:start position:0% +or so 364. +Now you can see on the scope we jumped a + + align:start position:0% +Now you can see on the scope we jumped a + + + align:start position:0% +Now you can see on the scope we jumped a +little bit and and the meter has gone up + + align:start position:0% +little bit and and the meter has gone up + + + align:start position:0% +little bit and and the meter has gone up +to 380 something which is an increase of + + align:start position:0% +to 380 something which is an increase of + + + align:start position:0% +to 380 something which is an increase of +about 5%. Let me turn it off + + align:start position:0% +about 5%. Let me turn it off + + + align:start position:0% +about 5%. Let me turn it off +again. You can see on the scope went + + align:start position:0% +again. You can see on the scope went + + + align:start position:0% +again. You can see on the scope went +down. In fact, + + align:start position:0% +down. In fact, + + + align:start position:0% +down. In fact, +just watch the scope for a little while. + + align:start position:0% +just watch the scope for a little while. + + + align:start position:0% +just watch the scope for a little while. +I'm going to turn it on and off very + + align:start position:0% +I'm going to turn it on and off very + + + align:start position:0% +I'm going to turn it on and off very +fast so that you get a feel that here it + + align:start position:0% +fast so that you get a feel that here it + + + align:start position:0% +fast so that you get a feel that here it +goes up a little bit and down a little + + align:start position:0% +goes up a little bit and down a little + + + align:start position:0% +goes up a little bit and down a little +bit. Since it's only few% it's difficult + + align:start position:0% +bit. Since it's only few% it's difficult + + + align:start position:0% +bit. Since it's only few% it's difficult +to see it on the scope the way I have it + + align:start position:0% +to see it on the scope the way I have it + + + align:start position:0% +to see it on the scope the way I have it +set it up I have it set up but it's much + + align:start position:0% +set it up I have it set up but it's much + + + align:start position:0% +set it up I have it set up but it's much +easier to see it on the meter. So you + + align:start position:0% +easier to see it on the meter. So you + + + align:start position:0% +easier to see it on the meter. So you +can see that with amplification we have + + align:start position:0% +can see that with amplification we have + + + align:start position:0% +can see that with amplification we have +380 something with no amplification then + + align:start position:0% +380 something with no amplification then + + + align:start position:0% +380 something with no amplification then +we're back to 360 something again + + align:start position:0% +we're back to 360 something again + + + align:start position:0% +we're back to 360 something again +roughly it's about 5% uh amplification. + + align:start position:0% +roughly it's about 5% uh amplification. + + + align:start position:0% +roughly it's about 5% uh amplification. +Now you may wonder that uh maybe what + + align:start position:0% +Now you may wonder that uh maybe what + + + align:start position:0% +Now you may wonder that uh maybe what +we're getting is when I turn on the + + align:start position:0% +we're getting is when I turn on the + + + align:start position:0% +we're getting is when I turn on the +amplifier that we're getting light from + + align:start position:0% +amplifier that we're getting light from + + + align:start position:0% +amplifier that we're getting light from +the amplifier that hits hits the + + align:start position:0% +the amplifier that hits hits the + + + align:start position:0% +the amplifier that hits hits the +detector. It's not really amplification. + + align:start position:0% +detector. It's not really amplification. + + + align:start position:0% +detector. It's not really amplification. +So to prove this, what I'm going to do + + align:start position:0% +So to prove this, what I'm going to do + + + align:start position:0% +So to prove this, what I'm going to do +is block + + align:start position:0% +is block + + + align:start position:0% +is block +the beam of light going into the + + align:start position:0% +the beam of light going into the + + + align:start position:0% +the beam of light going into the +amplifier + + align:start position:0% +amplifier + + + align:start position:0% +amplifier +so that there's no light going on the + + align:start position:0% +so that there's no light going on the + + + align:start position:0% +so that there's no light going on the +detector. We back to our zero on the + + align:start position:0% +detector. We back to our zero on the + + + align:start position:0% +detector. We back to our zero on the +meter. And now what I'm going to do, I'm + + align:start position:0% +meter. And now what I'm going to do, I'm + + + align:start position:0% +meter. And now what I'm going to do, I'm +going to turn on the the amplifier just + + align:start position:0% +going to turn on the the amplifier just + + + align:start position:0% +going to turn on the the amplifier just +by itself just to see if there's any + + align:start position:0% +by itself just to see if there's any + + + align:start position:0% +by itself just to see if there's any +light from the amplifiers falling on the + + align:start position:0% +light from the amplifiers falling on the + + + align:start position:0% +light from the amplifiers falling on the +detector. So here we go. Watch the meter + + align:start position:0% +detector. So here we go. Watch the meter + + + align:start position:0% +detector. So here we go. Watch the meter +and the scope. And here is the amplifier + + align:start position:0% +and the scope. And here is the amplifier + + + align:start position:0% +and the scope. And here is the amplifier +on. Again, you can see that there's no + + align:start position:0% +on. Again, you can see that there's no + + + align:start position:0% +on. Again, you can see that there's no +change on the meter or the scope. Here's + + align:start position:0% +change on the meter or the scope. Here's + + + align:start position:0% +change on the meter or the scope. Here's +off. + + align:start position:0% +off. + + + align:start position:0% +off. +And do it again. On + + align:start position:0% +And do it again. On + + + align:start position:0% +And do it again. On +and and off. So indeed, we've shown that + + align:start position:0% +and and off. So indeed, we've shown that + + + align:start position:0% +and and off. So indeed, we've shown that +light from the amplifier or spontaneous + + align:start position:0% +light from the amplifier or spontaneous + + + align:start position:0% +light from the amplifier or spontaneous +emission from the amplifier is not + + align:start position:0% +emission from the amplifier is not + + + align:start position:0% +emission from the amplifier is not +hitting the detector and increasing uh + + align:start position:0% +hitting the detector and increasing uh + + + align:start position:0% +hitting the detector and increasing uh +the output. So again, let me just redo + + align:start position:0% +the output. So again, let me just redo + + + align:start position:0% +the output. So again, let me just redo +it again for you. Here is here is the + + align:start position:0% +it again for you. Here is here is the + + + align:start position:0% +it again for you. Here is here is the +light falling on the detector without + + align:start position:0% +light falling on the detector without + + + align:start position:0% +light falling on the detector without +amplification. + + align:start position:0% +amplification. + + + align:start position:0% +amplification. +Again, 360 something. And here comes the + + align:start position:0% +Again, 360 something. And here comes the + + + align:start position:0% +Again, 360 something. And here comes the +amplification + + align:start position:0% +amplification + + + align:start position:0% +amplification +again. + + align:start position:0% +again. + + + align:start position:0% +again. +It's a little Yeah, it's close to 380. A + + align:start position:0% +It's a little Yeah, it's close to 380. A + + + align:start position:0% +It's a little Yeah, it's close to 380. A +little bit less than we had before. + + align:start position:0% +little bit less than we had before. + + + align:start position:0% +little bit less than we had before. +Maybe the amplifier is getting a little + + align:start position:0% +Maybe the amplifier is getting a little + + + align:start position:0% +Maybe the amplifier is getting a little +old. Here we are without amplification. + + align:start position:0% +old. Here we are without amplification. + + + align:start position:0% +old. Here we are without amplification. +We have this value. + + align:start position:0% +We have this value. + + + align:start position:0% +We have this value. +Summary. + + align:start position:0% +Summary. + + + align:start position:0% +Summary. +Now I hope you've become a believer in + + align:start position:0% +Now I hope you've become a believer in + + + align:start position:0% +Now I hope you've become a believer in +that you've seen for yourself that light + + align:start position:0% +that you've seen for yourself that light + + + align:start position:0% +that you've seen for yourself that light +indeed can be can be amplified. + + align:start position:0% +indeed can be can be amplified. + + + align:start position:0% +indeed can be can be amplified. +The the uh last topic before we leave + + align:start position:0% +The the uh last topic before we leave + + + align:start position:0% +The the uh last topic before we leave +this session is on how does a laser + + align:start position:0% +this session is on how does a laser + + + align:start position:0% +this session is on how does a laser +start? You know just because + + align:start position:0% +start? You know just because + + + align:start position:0% +start? You know just because +we have inverted population we have + + align:start position:0% +we have inverted population we have + + + align:start position:0% +we have inverted population we have +between let's say level three and level + + align:start position:0% +between let's say level three and level + + + align:start position:0% +between let's say level three and level +two and but how does a laser really + + align:start position:0% +two and but how does a laser really + + + align:start position:0% +two and but how does a laser really +start? We have gain yes but how does it + + align:start position:0% +start? We have gain yes but how does it + + + align:start position:0% +start? We have gain yes but how does it +get started? because at the beginning + + align:start position:0% +get started? because at the beginning + + + align:start position:0% +get started? because at the beginning +there was no light uh at this at this + + align:start position:0% +there was no light uh at this at this + + + align:start position:0% +there was no light uh at this at this +frequency or wavelength. All right, + + align:start position:0% +frequency or wavelength. All right, + + + align:start position:0% +frequency or wavelength. All right, +there's plenty of pump light but there's + + align:start position:0% +there's plenty of pump light but there's + + + align:start position:0% +there's plenty of pump light but there's +no light to start the stimulated + + align:start position:0% +no light to start the stimulated + + + align:start position:0% +no light to start the stimulated +emission going. But it turns out that + + align:start position:0% +emission going. But it turns out that + + + align:start position:0% +emission going. But it turns out that +the light that uh that starts the laser + + align:start position:0% +the light that uh that starts the laser + + + align:start position:0% +the light that uh that starts the laser +going is spontaneous emission. Remember + + align:start position:0% +going is spontaneous emission. Remember + + + align:start position:0% +going is spontaneous emission. Remember +we talked before when atoms are left + + align:start position:0% +we talked before when atoms are left + + + align:start position:0% +we talked before when atoms are left +alone in the upper state they they decay + + align:start position:0% +alone in the upper state they they decay + + + align:start position:0% +alone in the upper state they they decay +to a lower level and they can emit + + align:start position:0% +to a lower level and they can emit + + + align:start position:0% +to a lower level and they can emit +photons all right in all directions. Now + + align:start position:0% +photons all right in all directions. Now + + + align:start position:0% +photons all right in all directions. Now +the spontaneous emission that the photon + + align:start position:0% +the spontaneous emission that the photon + + + align:start position:0% +the spontaneous emission that the photon +that is emitted along the axis of the + + align:start position:0% +that is emitted along the axis of the + + + align:start position:0% +that is emitted along the axis of the +cavity that's the one that gets the the + + align:start position:0% +cavity that's the one that gets the the + + + align:start position:0% +cavity that's the one that gets the the +stimulating emission going and I show it + + align:start position:0% +stimulating emission going and I show it + + + align:start position:0% +stimulating emission going and I show it +here. Uh here is the spontaneous + + align:start position:0% +here. Uh here is the spontaneous + + + align:start position:0% +here. Uh here is the spontaneous +emission along the axis. It hits another + + align:start position:0% +emission along the axis. It hits another + + + align:start position:0% +emission along the axis. It hits another +atom here that's in the excited state. + + align:start position:0% +atom here that's in the excited state. + + + align:start position:0% +atom here that's in the excited state. +So it gets amplified and then hits some + + align:start position:0% +So it gets amplified and then hits some + + + align:start position:0% +So it gets amplified and then hits some +more and gets even more amplified and so + + align:start position:0% +more and gets even more amplified and so + + + align:start position:0% +more and gets even more amplified and so +on. as he goes backwards and forwards + + align:start position:0% +on. as he goes backwards and forwards + + + align:start position:0% +on. as he goes backwards and forwards +then this builds up and and you uh get + + align:start position:0% +then this builds up and and you uh get + + + align:start position:0% +then this builds up and and you uh get +enough gain to overcome the losses and + + align:start position:0% +enough gain to overcome the losses and + + + align:start position:0% +enough gain to overcome the losses and +the laser will oscillate and if one of + + align:start position:0% +the laser will oscillate and if one of + + + align:start position:0% +the laser will oscillate and if one of +the mirrors has some transmission then + + align:start position:0% +the mirrors has some transmission then + + + align:start position:0% +the mirrors has some transmission then +you get you get the output. So indeed + + align:start position:0% +you get you get the output. So indeed + + + align:start position:0% +you get you get the output. So indeed +that's how an amplifier works and that's + + align:start position:0% +that's how an amplifier works and that's + + + align:start position:0% +that's how an amplifier works and that's +how a laser gets started. And then when + + align:start position:0% +how a laser gets started. And then when + + + align:start position:0% +how a laser gets started. And then when +we come back for our next session, we'll + + align:start position:0% +we come back for our next session, we'll + + + align:start position:0% +we come back for our next session, we'll +talk about the the laser beam properties + + align:start position:0% +talk about the the laser beam properties + + + align:start position:0% +talk about the the laser beam properties +and other properties and so \ No newline at end of file diff --git a/v9Xmajiraoc.txt b/v9Xmajiraoc.txt new file mode 100644 index 0000000000000000000000000000000000000000..c29f603028a935e826484807cdcf7d9bfe911bef --- /dev/null +++ b/v9Xmajiraoc.txt @@ -0,0 +1,8155 @@ +align:start position:0% + +Okay. So, we'll come to the last + + align:start position:0% +Okay. So, we'll come to the last + + + align:start position:0% +Okay. So, we'll come to the last +lecture. So, what I want to do is + + align:start position:0% +lecture. So, what I want to do is + + + align:start position:0% +lecture. So, what I want to do is +uh just do some overview of what we went + + align:start position:0% +uh just do some overview of what we went + + + align:start position:0% +uh just do some overview of what we went +through to uh uh make sure that + + align:start position:0% +through to uh uh make sure that + + + align:start position:0% +through to uh uh make sure that +everybody's uh remembers basically from + + align:start position:0% +everybody's uh remembers basically from + + + align:start position:0% +everybody's uh remembers basically from +the beginning. uh talk a little bit + + align:start position:0% +the beginning. uh talk a little bit + + + align:start position:0% +the beginning. uh talk a little bit +about the project + + align:start position:0% +about the project + + + align:start position:0% +about the project +and little bit about what what you can + + align:start position:0% +and little bit about what what you can + + + align:start position:0% +and little bit about what what you can +use this class material for. I mean this + + align:start position:0% +use this class material for. I mean this + + + align:start position:0% +use this class material for. I mean this +is at least my view after talking to few + + align:start position:0% +is at least my view after talking to few + + + align:start position:0% +is at least my view after talking to few +people who have been taking this class + + align:start position:0% +people who have been taking this class + + + align:start position:0% +people who have been taking this class +over the years where they have been + + align:start position:0% +over the years where they have been + + + align:start position:0% +over the years where they have been +using it and I think uh so you don't + + align:start position:0% +using it and I think uh so you don't + + + align:start position:0% +using it and I think uh so you don't +have to just completely the minute you + + align:start position:0% +have to just completely the minute you + + + align:start position:0% +have to just completely the minute you +finish the next quiz completely forget + + align:start position:0% +finish the next quiz completely forget + + + align:start position:0% +finish the next quiz completely forget +about this uh everything and just move + + align:start position:0% +about this uh everything and just move + + + align:start position:0% +about this uh everything and just move +on and if I have time I will go and talk + + align:start position:0% +on and if I have time I will go and talk + + + align:start position:0% +on and if I have time I will go and talk +about current research. So if you're + + align:start position:0% +about current research. So if you're + + + align:start position:0% +about current research. So if you're +interested in compiler stuff uh uh to + + align:start position:0% +interested in compiler stuff uh uh to + + + align:start position:0% +interested in compiler stuff uh uh to +give you a flavor of of this is great + + align:start position:0% +give you a flavor of of this is great + + + align:start position:0% +give you a flavor of of this is great +what you learned you actually did got a + + align:start position:0% +what you learned you actually did got a + + + align:start position:0% +what you learned you actually did got a +good sliver of what compilers are all + + align:start position:0% +good sliver of what compilers are all + + + align:start position:0% +good sliver of what compilers are all +about but what happens today in in in + + align:start position:0% +about but what happens today in in in + + + align:start position:0% +about but what happens today in in in +the research community just uh uh touch + + align:start position:0% +the research community just uh uh touch + + + align:start position:0% +the research community just uh uh touch +on some of that and hopefully we'll have + + align:start position:0% +on some of that and hopefully we'll have + + + align:start position:0% +on some of that and hopefully we'll have +some time for discussion and + + align:start position:0% +some time for discussion and + + + align:start position:0% +some time for discussion and +feedback so this is where I started uh + + align:start position:0% +feedback so this is where I started uh + + + align:start position:0% +feedback so this is where I started uh +we started saying we have these programs + + align:start position:0% +we started saying we have these programs + + + align:start position:0% +we started saying we have these programs +written in programming languages and + + align:start position:0% +written in programming languages and + + + align:start position:0% +written in programming languages and +then microp process understand uh + + align:start position:0% +then microp process understand uh + + + align:start position:0% +then microp process understand uh +assembly language or or uh uh object + + align:start position:0% +assembly language or or uh uh object + + + align:start position:0% +assembly language or or uh uh object +code and we want to build a compiler in + + align:start position:0% +code and we want to build a compiler in + + + align:start position:0% +code and we want to build a compiler in +there to do that and so here's a simple + + align:start position:0% +there to do that and so here's a simple + + + align:start position:0% +there to do that and so here's a simple +program I think we started with so the + + align:start position:0% +program I think we started with so the + + + align:start position:0% +program I think we started with so the +first thing you can do is you can + + align:start position:0% +first thing you can do is you can + + + align:start position:0% +first thing you can do is you can +generate this unoptimized piece of + + align:start position:0% +generate this unoptimized piece of + + + align:start position:0% +generate this unoptimized piece of +code uh uh that this actually came out + + align:start position:0% +code uh uh that this actually came out + + + align:start position:0% +code uh uh that this actually came out +of I had a CPC code that I came out of + + align:start position:0% +of I had a CPC code that I came out of + + + align:start position:0% +of I had a CPC code that I came out of +GCC minus0 and then the interesting + + align:start position:0% +GCC minus0 and then the interesting + + + align:start position:0% +GCC minus0 and then the interesting +thing is you can actually optimize and + + align:start position:0% +thing is you can actually optimize and + + + align:start position:0% +thing is you can actually optimize and +make get rid of lot of these redundant + + align:start position:0% +make get rid of lot of these redundant + + + align:start position:0% +make get rid of lot of these redundant +instructions and run it much faster. + + align:start position:0% +instructions and run it much faster. + + + align:start position:0% +instructions and run it much faster. +So uh and I think we went from doing + + align:start position:0% +So uh and I think we went from doing + + + align:start position:0% +So uh and I think we went from doing +left and now last uh uh project and this + + align:start position:0% +left and now last uh uh project and this + + + align:start position:0% +left and now last uh uh project and this +one what you're working on will end up + + align:start position:0% +one what you're working on will end up + + + align:start position:0% +one what you're working on will end up +more to the + + align:start position:0% +more to the + + + align:start position:0% +more to the +right. So in this thing you basically + + align:start position:0% +right. So in this thing you basically + + + align:start position:0% +right. So in this thing you basically +build one from scratch. This is very + + align:start position:0% +build one from scratch. This is very + + + align:start position:0% +build one from scratch. This is very +interesting because many places where + + align:start position:0% +interesting because many places where + + + align:start position:0% +interesting because many places where +you go take compiler course build a + + align:start position:0% +you go take compiler course build a + + + align:start position:0% +you go take compiler course build a +compiler from scr from scratch. But most + + align:start position:0% +compiler from scr from scratch. But most + + + align:start position:0% +compiler from scr from scratch. But most +of the time what you get since this is + + align:start position:0% +of the time what you get since this is + + + align:start position:0% +of the time what you get since this is +such a large project most places when + + align:start position:0% +such a large project most places when + + + align:start position:0% +such a large project most places when +you do teach a compiler course you get a + + align:start position:0% +you do teach a compiler course you get a + + + align:start position:0% +you do teach a compiler course you get a +template and saying here's a template + + align:start position:0% +template and saying here's a template + + + align:start position:0% +template and saying here's a template +you go fill out the things fill out the + + align:start position:0% +you go fill out the things fill out the + + + align:start position:0% +you go fill out the things fill out the +optimizations fill out passing and stuff + + align:start position:0% +optimizations fill out passing and stuff + + + align:start position:0% +optimizations fill out passing and stuff +like that and you you basically go end + + align:start position:0% +like that and you you basically go end + + + align:start position:0% +like that and you you basically go end +to end but what's missing there is most + + align:start position:0% +to end but what's missing there is most + + + align:start position:0% +to end but what's missing there is most +of the decisions are done for you okay + + align:start position:0% +of the decisions are done for you okay + + + align:start position:0% +of the decisions are done for you okay +you don't get to design the instruction + + align:start position:0% +you don't get to design the instruction + + + align:start position:0% +you don't get to design the instruction +set you don't get to design intermediate + + align:start position:0% +set you don't get to design intermediate + + + align:start position:0% +set you don't get to design intermediate +representation stuff like that so what + + align:start position:0% +representation stuff like that so what + + + align:start position:0% +representation stuff like that so what +that means is it's at end of the day you + + align:start position:0% +that means is it's at end of the day you + + + align:start position:0% +that means is it's at end of the day you +build a compiler but you don't have idea + + align:start position:0% +build a compiler but you don't have idea + + + align:start position:0% +build a compiler but you don't have idea +what the hard decisions are in this + + align:start position:0% +what the hard decisions are in this + + + align:start position:0% +what the hard decisions are in this +course we + + align:start position:0% +course we + + + align:start position:0% +course we +basically what I like to say is give you + + align:start position:0% +basically what I like to say is give you + + + align:start position:0% +basically what I like to say is give you +the rope to hang yourself with basically + + align:start position:0% +the rope to hang yourself with basically + + + align:start position:0% +the rope to hang yourself with basically +we said it's all open go do it and what + + align:start position:0% +we said it's all open go do it and what + + + align:start position:0% +we said it's all open go do it and what +that means is many times what happens is + + align:start position:0% +that means is many times what happens is + + + align:start position:0% +that means is many times what happens is +you do something you make a decision + + align:start position:0% +you do something you make a decision + + + align:start position:0% +you do something you make a decision +early on and then later you learn + + align:start position:0% +early on and then later you learn + + + align:start position:0% +early on and then later you learn +something and then you say that was a + + align:start position:0% +something and then you say that was a + + + align:start position:0% +something and then you say that was a +bad decision you had to go do undo + + align:start position:0% +bad decision you had to go do undo + + + align:start position:0% +bad decision you had to go do undo +things I mean I guess a lot of people + + align:start position:0% +things I mean I guess a lot of people + + + align:start position:0% +things I mean I guess a lot of people +had that feeling I think key thing is + + align:start position:0% +had that feeling I think key thing is + + + align:start position:0% +had that feeling I think key thing is +it's a much harder of course because of + + align:start position:0% +it's a much harder of course because of + + + align:start position:0% +it's a much harder of course because of +that. I mean if you talk to uh UPS in + + align:start position:0% +that. I mean if you talk to uh UPS in + + + align:start position:0% +that. I mean if you talk to uh UPS in +other institutions they might have done + + align:start position:0% +other institutions they might have done + + + align:start position:0% +other institutions they might have done +a compiler but you probably had to deal + + align:start position:0% +a compiler but you probably had to deal + + + align:start position:0% +a compiler but you probably had to deal +with lot of those decisions and and all + + align:start position:0% +with lot of those decisions and and all + + + align:start position:0% +with lot of those decisions and and all +the bad decisions and and and and + + align:start position:0% +the bad decisions and and and and + + + align:start position:0% +the bad decisions and and and and +recover from it and the nice thing about + + align:start position:0% +recover from it and the nice thing about + + + align:start position:0% +recover from it and the nice thing about +my students they managed to recover from + + align:start position:0% +my students they managed to recover from + + + align:start position:0% +my students they managed to recover from +those things and still doing keep going + + align:start position:0% +those things and still doing keep going + + + align:start position:0% +those things and still doing keep going +and that what that means is you + + align:start position:0% +and that what that means is you + + + align:start position:0% +and that what that means is you +understood some very basic stuff about + + align:start position:0% +understood some very basic stuff about + + + align:start position:0% +understood some very basic stuff about +building compile what are those hard + + align:start position:0% +building compile what are those hard + + + align:start position:0% +building compile what are those hard +decisions are this lot more important + + align:start position:0% +decisions are this lot more important + + + align:start position:0% +decisions are this lot more important +because next time when you decide the + + align:start position:0% +because next time when you decide the + + + align:start position:0% +because next time when you decide the +compile you actually have that knowledge + + align:start position:0% +compile you actually have that knowledge + + + align:start position:0% +compile you actually have that knowledge +because you actually had made decision + + align:start position:0% +because you actually had made decision + + + align:start position:0% +because you actually had made decision +yourself so I think that is key So if + + align:start position:0% +yourself so I think that is key So if + + + align:start position:0% +yourself so I think that is key So if +you look at a compiler, what's a + + align:start position:0% +you look at a compiler, what's a + + + align:start position:0% +you look at a compiler, what's a +compiler? So you have a program, you do + + align:start position:0% +compiler? So you have a program, you do + + + align:start position:0% +compiler? So you have a program, you do +lexical analysis, you get a token + + align:start position:0% +lexical analysis, you get a token + + + align:start position:0% +lexical analysis, you get a token +stream, uh you do syntax analysis, + + align:start position:0% +stream, uh you do syntax analysis, + + + align:start position:0% +stream, uh you do syntax analysis, +passer, get a pass tree, uh do some + + align:start position:0% +passer, get a pass tree, uh do some + + + align:start position:0% +passer, get a pass tree, uh do some +semantic analysis and have intermediate + + align:start position:0% +semantic analysis and have intermediate + + + align:start position:0% +semantic analysis and have intermediate +representation at the end, do code + + align:start position:0% +representation at the end, do code + + + align:start position:0% +representation at the end, do code +optimization, we did it in the different + + align:start position:0% +optimization, we did it in the different + + + align:start position:0% +optimization, we did it in the different +order, but normally the code + + align:start position:0% +order, but normally the code + + + align:start position:0% +order, but normally the code +optimization come you have optimized + + align:start position:0% +optimization come you have optimized + + + align:start position:0% +optimization come you have optimized +intermediate representation and finally + + align:start position:0% +intermediate representation and finally + + + align:start position:0% +intermediate representation and finally +a code generator that design assembly. + + align:start position:0% +a code generator that design assembly. + + + align:start position:0% +a code generator that design assembly. +So here's a question. Why do you need a + + align:start position:0% +So here's a question. Why do you need a + + + align:start position:0% +So here's a question. Why do you need a +lexical anal analyzer and a syntax + + align:start position:0% +lexical anal analyzer and a syntax + + + align:start position:0% +lexical anal analyzer and a syntax +analyzer? Why can't both be combined to + + align:start position:0% +analyzer? Why can't both be combined to + + + align:start position:0% +analyzer? Why can't both be combined to +one? Can you combine to one? + + align:start position:0% + + + + align:start position:0% + +Can't you just have a grammar that + + align:start position:0% + + + + align:start position:0% + +read just characters and and and then + + align:start position:0% +read just characters and and and then + + + align:start position:0% +read just characters and and and then +write your expressions and your tokens, + + align:start position:0% +write your expressions and your tokens, + + + align:start position:0% +write your expressions and your tokens, +your tokens also with the + + align:start position:0% +your tokens also with the + + + align:start position:0% +your tokens also with the +grammar. Why are naturally complex to + + align:start position:0% +grammar. Why are naturally complex to + + + align:start position:0% +grammar. Why are naturally complex to +have both of those? + + align:start position:0% +have both of those? + + + align:start position:0% +have both of those? +Okay, that's one answer. I think that's + + align:start position:0% +Okay, that's one answer. I think that's + + + align:start position:0% +Okay, that's one answer. I think that's +a good answer. What else like that? + + align:start position:0% +a good answer. What else like that? + + + align:start position:0% +a good answer. What else like that? +You need to actually see that time. + + align:start position:0% + + + + align:start position:0% + +Not really. I mean, one pass you have to + + align:start position:0% +Not really. I mean, one pass you have to + + + align:start position:0% +Not really. I mean, one pass you have to +only see little bit forward. You can + + align:start position:0% +only see little bit forward. You can + + + align:start position:0% +only see little bit forward. You can +still do + + align:start position:0% +still do + + + align:start position:0% +still do +that. What + + align:start position:0% + + + + align:start position:0% + +else? Everybody stopped. + + align:start position:0% +else? Everybody stopped. + + + align:start position:0% +else? Everybody stopped. +I guess you're asking Central + + align:start position:0% + + + + align:start position:0% + +different. + + align:start position:0% +different. + + + align:start position:0% +different. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Yeah. Okay. So, here's my take on it. I + + align:start position:0% +Yeah. Okay. So, here's my take on it. I + + + align:start position:0% +Yeah. Okay. So, here's my take on it. I +think there are a few things. First of + + align:start position:0% +think there are a few things. First of + + + align:start position:0% +think there are a few things. First of +all, it's doable. Okay. But then I + + align:start position:0% +all, it's doable. Okay. But then I + + + align:start position:0% +all, it's doable. Okay. But then I +probably have to I can't do just uh if I + + align:start position:0% +probably have to I can't do just uh if I + + + align:start position:0% +probably have to I can't do just uh if I +do LR one passing I I look ahead one uh + + align:start position:0% +do LR one passing I I look ahead one uh + + + align:start position:0% +do LR one passing I I look ahead one uh +token. But now if I if I actually build + + align:start position:0% +token. But now if I if I actually build + + + align:start position:0% +token. But now if I if I actually build +that gives me lot of expression + + align:start position:0% +that gives me lot of expression + + + align:start position:0% +that gives me lot of expression +expressiveness in my language. But on + + align:start position:0% +expressiveness in my language. But on + + + align:start position:0% +expressiveness in my language. But on +the other hand if now I actually have to + + align:start position:0% +the other hand if now I actually have to + + + align:start position:0% +the other hand if now I actually have to +build the token myself I probably have + + align:start position:0% +build the token myself I probably have + + + align:start position:0% +build the token myself I probably have +to look forward lot further. So in there + + align:start position:0% +to look forward lot further. So in there + + + align:start position:0% +to look forward lot further. So in there +so I might have issue about looking + + align:start position:0% +so I might have issue about looking + + + align:start position:0% +so I might have issue about looking +forward because the minute I I go there + + align:start position:0% +forward because the minute I I go there + + + align:start position:0% +forward because the minute I I go there +I probably cannot make that decision. So + + align:start position:0% +I probably cannot make that decision. So + + + align:start position:0% +I probably cannot make that decision. So +there might be look ahead issues in + + align:start position:0% +there might be look ahead issues in + + + align:start position:0% +there might be look ahead issues in +there. Second, I think it's little bit + + align:start position:0% +there. Second, I think it's little bit + + + align:start position:0% +there. Second, I think it's little bit +of historical research because at at a + + align:start position:0% +of historical research because at at a + + + align:start position:0% +of historical research because at at a +for a long time uh passing was a very + + align:start position:0% +for a long time uh passing was a very + + + align:start position:0% +for a long time uh passing was a very +computationheavy thing. I mean to build + + align:start position:0% +computationheavy thing. I mean to build + + + align:start position:0% +computationheavy thing. I mean to build +this uh past trees on large programs + + align:start position:0% +this uh past trees on large programs + + + align:start position:0% +this uh past trees on large programs +took lot of time, lot of effort, very + + align:start position:0% +took lot of time, lot of effort, very + + + align:start position:0% +took lot of time, lot of effort, very +large tables and stuff like that. It it + + align:start position:0% +large tables and stuff like that. It it + + + align:start position:0% +large tables and stuff like that. It it +was taxing programs. So by doing lexical + + align:start position:0% +was taxing programs. So by doing lexical + + + align:start position:0% +was taxing programs. So by doing lexical +analysis you really broke instead of + + align:start position:0% +analysis you really broke instead of + + + align:start position:0% +analysis you really broke instead of +having 100,000 characters you only have + + align:start position:0% +having 100,000 characters you only have + + + align:start position:0% +having 100,000 characters you only have +5,000 tokens. So it really reduces uh + + align:start position:0% +5,000 tokens. So it really reduces uh + + + align:start position:0% +5,000 tokens. So it really reduces uh +what you have to do. So in some sense + + align:start position:0% +what you have to do. So in some sense + + + align:start position:0% +what you have to do. So in some sense +when you're really doing that that that + + align:start position:0% +when you're really doing that that that + + + align:start position:0% +when you're really doing that that that +breakdown was a good logical breakdown + + align:start position:0% +breakdown was a good logical breakdown + + + align:start position:0% +breakdown was a good logical breakdown +but on the other hand I think you can do + + align:start position:0% +but on the other hand I think you can do + + + align:start position:0% +but on the other hand I think you can do +both together and there might be issues + + align:start position:0% +both together and there might be issues + + + align:start position:0% +both together and there might be issues +in there but but uh it's not I don't + + align:start position:0% +in there but but uh it's not I don't + + + align:start position:0% +in there but but uh it's not I don't +think it's fundamental. So in lexical + + align:start position:0% +think it's fundamental. So in lexical + + + align:start position:0% +think it's fundamental. So in lexical +analysis what do you do you have uh uh + + align:start position:0% +analysis what do you do you have uh uh + + + align:start position:0% +analysis what do you do you have uh uh +tokens out of uh character string and we + + align:start position:0% +tokens out of uh character string and we + + + align:start position:0% +tokens out of uh character string and we +deal with regular expressions and + + align:start position:0% +deal with regular expressions and + + + align:start position:0% +deal with regular expressions and +uh I'm just taking picking slides I mean + + align:start position:0% +uh I'm just taking picking slides I mean + + + align:start position:0% +uh I'm just taking picking slides I mean +you should know these things I don't + + align:start position:0% +you should know these things I don't + + + align:start position:0% +you should know these things I don't +have to go and explain what a regular + + align:start position:0% +have to go and explain what a regular + + + align:start position:0% +have to go and explain what a regular +expression works. So, so uh so this is + + align:start position:0% +expression works. So, so uh so this is + + + align:start position:0% +expression works. So, so uh so this is +just just to bring those things back to + + align:start position:0% +just just to bring those things back to + + + align:start position:0% +just just to bring those things back to +your + + align:start position:0% +your + + + align:start position:0% +your +mind and then we dealt with lexical + + align:start position:0% +mind and then we dealt with lexical + + + align:start position:0% +mind and then we dealt with lexical +analysis. So what we did was uh we + + align:start position:0% +analysis. So what we did was uh we + + + align:start position:0% +analysis. So what we did was uh we +define regular expressions and we built + + align:start position:0% +define regular expressions and we built + + + align:start position:0% +define regular expressions and we built +a a nondeterministic finite automaton + + align:start position:0% +a a nondeterministic finite automaton + + + align:start position:0% +a a nondeterministic finite automaton +out of that NFA and then we came up with + + align:start position:0% +out of that NFA and then we came up with + + + align:start position:0% +out of that NFA and then we came up with +algorithms actually go from NFA to DFA + + align:start position:0% +algorithms actually go from NFA to DFA + + + align:start position:0% +algorithms actually go from NFA to DFA +and then DFA you + + align:start position:0% +and then DFA you + + + align:start position:0% +and then DFA you +can go and build these tokens very + + align:start position:0% +can go and build these tokens very + + + align:start position:0% +can go and build these tokens very +nicely. So that was a really uh s nice + + align:start position:0% +nicely. So that was a really uh s nice + + + align:start position:0% +nicely. So that was a really uh s nice +set of theory that we really use in + + align:start position:0% +set of theory that we really use in + + + align:start position:0% +set of theory that we really use in +compilers. Then we went to syntax + + align:start position:0% +compilers. Then we went to syntax + + + align:start position:0% +compilers. Then we went to syntax +analysis. So that means we start + + align:start position:0% +analysis. So that means we start + + + align:start position:0% +analysis. So that means we start +defining language using contextual + + align:start position:0% +defining language using contextual + + + align:start position:0% +defining language using contextual +grammarss. Okay. So now we have a much + + align:start position:0% +grammarss. Okay. So now we have a much + + + align:start position:0% +grammarss. Okay. So now we have a much +more expressive thing. We can actually + + align:start position:0% +more expressive thing. We can actually + + + align:start position:0% +more expressive thing. We can actually +de uh create this grammarss for modern + + align:start position:0% +de uh create this grammarss for modern + + + align:start position:0% +de uh create this grammarss for modern +languages in there. And so here's a + + align:start position:0% +languages in there. And so here's a + + + align:start position:0% +languages in there. And so here's a +simple example where what you have is a + + align:start position:0% +simple example where what you have is a + + + align:start position:0% +simple example where what you have is a +a bunch of uh this expression recognizer + + align:start position:0% +a bunch of uh this expression recognizer + + + align:start position:0% +a bunch of uh this expression recognizer +with minus plus and multiply simple + + align:start position:0% +with minus plus and multiply simple + + + align:start position:0% +with minus plus and multiply simple +thing and then we basically build a + + align:start position:0% +thing and then we basically build a + + + align:start position:0% +thing and then we basically build a +pastry at then. So you give a token + + align:start position:0% +pastry at then. So you give a token + + + align:start position:0% +pastry at then. So you give a token +stream comes a pastry at then. So here's + + align:start position:0% +stream comes a pastry at then. So here's + + + align:start position:0% +stream comes a pastry at then. So here's +something a little bit new I'm adding in + + align:start position:0% +something a little bit new I'm adding in + + + align:start position:0% +something a little bit new I'm adding in +here that we didn't talk this time in + + align:start position:0% +here that we didn't talk this time in + + + align:start position:0% +here that we didn't talk this time in +the class. So if you look at different + + align:start position:0% +the class. So if you look at different + + + align:start position:0% +the class. So if you look at different +grammars the simplest grammar is a + + align:start position:0% +grammars the simplest grammar is a + + + align:start position:0% +grammars the simplest grammar is a +regular expression. It's a grammar. It's + + align:start position:0% +regular expression. It's a grammar. It's + + + align:start position:0% +regular expression. It's a grammar. It's +a very simple grammar and the biggest + + align:start position:0% +a very simple grammar and the biggest + + + align:start position:0% +a very simple grammar and the biggest +grammar is a context free grammar that + + align:start position:0% +grammar is a context free grammar that + + + align:start position:0% +grammar is a context free grammar that +basically says you can + + align:start position:0% +basically says you can + + + align:start position:0% +basically says you can +define from a context free language how + + align:start position:0% +define from a context free language how + + + align:start position:0% +define from a context free language how +big thing you can define. Uh something a + + align:start position:0% +big thing you can define. Uh something a + + + align:start position:0% +big thing you can define. Uh something a +little bit less is unambiguous grammar. + + align:start position:0% +little bit less is unambiguous grammar. + + + align:start position:0% +little bit less is unambiguous grammar. +So you can write context free grammar + + align:start position:0% +So you can write context free grammar + + + align:start position:0% +So you can write context free grammar +that's basically ambiguous. You you + + align:start position:0% +that's basically ambiguous. You you + + + align:start position:0% +that's basically ambiguous. You you +don't know ex you have multiple ways of + + align:start position:0% +don't know ex you have multiple ways of + + + align:start position:0% +don't know ex you have multiple ways of +going that and after that you can create + + align:start position:0% +going that and after that you can create + + + align:start position:0% +going that and after that you can create +more and more restrictive sets by + + align:start position:0% +more and more restrictive sets by + + + align:start position:0% +more and more restrictive sets by +defining the technique you can use to + + align:start position:0% +defining the technique you can use to + + + align:start position:0% +defining the technique you can use to +identify that. So for example if LR0 + + align:start position:0% +identify that. So for example if LR0 + + + align:start position:0% +identify that. So for example if LR0 +passer there's a certain type of + + align:start position:0% +passer there's a certain type of + + + align:start position:0% +passer there's a certain type of +grammars it can recognize beyond that it + + align:start position:0% +grammars it can recognize beyond that it + + + align:start position:0% +grammars it can recognize beyond that it +it's it cannot recognize that and and as + + align:start position:0% +it's it cannot recognize that and and as + + + align:start position:0% +it's it cannot recognize that and and as +we go key can keep building higher and + + align:start position:0% +we go key can keep building higher and + + + align:start position:0% +we go key can keep building higher and +higher things. So for example if you're + + align:start position:0% +higher things. So for example if you're + + + align:start position:0% +higher things. So for example if you're +doing doing a modern programming + + align:start position:0% +doing doing a modern programming + + + align:start position:0% +doing doing a modern programming +language you can come and say okay this + + align:start position:0% +language you can come and say okay this + + + align:start position:0% +language you can come and say okay this +language can be represented in a grammar + + align:start position:0% +language can be represented in a grammar + + + align:start position:0% +language can be represented in a grammar +that LR1 pass can pass. So so you can + + align:start position:0% +that LR1 pass can pass. So so you can + + + align:start position:0% +that LR1 pass can pass. So so you can +have this this multiple classes in there + + align:start position:0% +have this this multiple classes in there + + + align:start position:0% +have this this multiple classes in there +and this LRK K could be uh any number. + + align:start position:0% +and this LRK K could be uh any number. + + + align:start position:0% +and this LRK K could be uh any number. +So that's why I said if I actually start + + align:start position:0% +So that's why I said if I actually start + + + align:start position:0% +So that's why I said if I actually start +doing the entire tokens also uh uh uh uh + + align:start position:0% +doing the entire tokens also uh uh uh uh + + + align:start position:0% +doing the entire tokens also uh uh uh uh +using grammar so probably had to have a + + align:start position:0% +using grammar so probably had to have a + + + align:start position:0% +using grammar so probably had to have a +very high K in the K passer. + + align:start position:0% +very high K in the K passer. + + + align:start position:0% +very high K in the K passer. +So, so then basically we came up with + + align:start position:0% +So, so then basically we came up with + + + align:start position:0% +So, so then basically we came up with +this pass engine which you give this + + align:start position:0% +this pass engine which you give this + + + align:start position:0% +this pass engine which you give this +table and you have a state stack and a + + align:start position:0% +table and you have a state stack and a + + + align:start position:0% +table and you have a state stack and a +symbol stack and by and then we just + + align:start position:0% +symbol stack and by and then we just + + + align:start position:0% +symbol stack and by and then we just +basically go uh streaming through the + + align:start position:0% +basically go uh streaming through the + + + align:start position:0% +basically go uh streaming through the +input data and look at the current + + align:start position:0% +input data and look at the current + + + align:start position:0% +input data and look at the current +symbol and look at what's in this stack + + align:start position:0% +symbol and look at what's in this stack + + + align:start position:0% +symbol and look at what's in this stack +and we get a pass action given in the + + align:start position:0% +and we get a pass action given in the + + + align:start position:0% +and we get a pass action given in the +table. So, so this you can have a + + align:start position:0% +table. So, so this you can have a + + + align:start position:0% +table. So, so this you can have a +generic engine given a passer table and + + align:start position:0% +generic engine given a passer table and + + + align:start position:0% +generic engine given a passer table and +it will actually do the right thing and + + align:start position:0% +it will actually do the right thing and + + + align:start position:0% +it will actually do the right thing and +of course depending on a k you have to + + align:start position:0% +of course depending on a k you have to + + + align:start position:0% +of course depending on a k you have to +actually look ahead to a little bit and + + align:start position:0% +actually look ahead to a little bit and + + + align:start position:0% +actually look ahead to a little bit and +then we came up with a method to divide + + align:start position:0% +then we came up with a method to divide + + + align:start position:0% +then we came up with a method to divide +this passer table. Okay, lot of these + + align:start position:0% +this passer table. Okay, lot of these + + + align:start position:0% +this passer table. Okay, lot of these +things uh probably you can just + + align:start position:0% +things uh probably you can just + + + align:start position:0% +things uh probably you can just +completely forget about it after this + + align:start position:0% +completely forget about it after this + + + align:start position:0% +completely forget about it after this +class because you are not going to come + + align:start position:0% +class because you are not going to come + + + align:start position:0% +class because you are not going to come +up with and write uh a yak yourself to + + align:start position:0% +up with and write uh a yak yourself to + + + align:start position:0% +up with and write uh a yak yourself to +do a a pass generate. probably use a + + align:start position:0% +do a a pass generate. probably use a + + + align:start position:0% +do a a pass generate. probably use a +tool uh uh that actually do cop or + + align:start position:0% +tool uh uh that actually do cop or + + + align:start position:0% +tool uh uh that actually do cop or +something like that to do the generator. + + align:start position:0% +something like that to do the generator. + + + align:start position:0% +something like that to do the generator. +But the interesting thing to use that is + + align:start position:0% +But the interesting thing to use that is + + + align:start position:0% +But the interesting thing to use that is +mean it comes and say there's a shift + + align:start position:0% +mean it comes and say there's a shift + + + align:start position:0% +mean it comes and say there's a shift +reduce error you at least know what what + + align:start position:0% +reduce error you at least know what what + + + align:start position:0% +reduce error you at least know what what +it means instead of say done what this + + align:start position:0% +it means instead of say done what this + + + align:start position:0% +it means instead of say done what this +mean what do I have to do now you + + align:start position:0% +mean what do I have to do now you + + + align:start position:0% +mean what do I have to do now you +understand why it's saying there's a + + align:start position:0% +understand why it's saying there's a + + + align:start position:0% +understand why it's saying there's a +shift reduce error and shift conflict + + align:start position:0% +shift reduce error and shift conflict + + + align:start position:0% +shift reduce error and shift conflict +and then you actually can think through + + align:start position:0% +and then you actually can think through + + + align:start position:0% +and then you actually can think through +this and figure that out and that's why + + align:start position:0% +this and figure that out and that's why + + + align:start position:0% +this and figure that out and that's why +this learning this was + + align:start position:0% +this learning this was + + + align:start position:0% +this learning this was +interesting and then we move into uh + + align:start position:0% +interesting and then we move into uh + + + align:start position:0% +interesting and then we move into uh +semantic analysis did a a bunch of + + align:start position:0% +semantic analysis did a a bunch of + + + align:start position:0% +semantic analysis did a a bunch of +checks to understand uh the beyond + + align:start position:0% +checks to understand uh the beyond + + + align:start position:0% +checks to understand uh the beyond +context readiness. That means now you're + + align:start position:0% +context readiness. That means now you're + + + align:start position:0% +context readiness. That means now you're +actually putting context into these + + align:start position:0% +actually putting context into these + + + align:start position:0% +actually putting context into these +checks in there. Uh understand uh the + + align:start position:0% +checks in there. Uh understand uh the + + + align:start position:0% +checks in there. Uh understand uh the +types uh uh uh uh uniqueness of + + align:start position:0% +types uh uh uh uh uniqueness of + + + align:start position:0% +types uh uh uh uh uniqueness of +variables for control checks. You can do + + align:start position:0% +variables for control checks. You can do + + + align:start position:0% +variables for control checks. You can do +bunch of things statically and also + + align:start position:0% +bunch of things statically and also + + + align:start position:0% +bunch of things statically and also +dynamic things like array bound checks + + align:start position:0% +dynamic things like array bound checks + + + align:start position:0% +dynamic things like array bound checks +and null pointer checks that that can be + + align:start position:0% +and null pointer checks that that can be + + + align:start position:0% +and null pointer checks that that can be +done and by doing after doing that we + + align:start position:0% +done and by doing after doing that we + + + align:start position:0% +done and by doing after doing that we +translated into intermediate uh format + + align:start position:0% +translated into intermediate uh format + + + align:start position:0% +translated into intermediate uh format +that basically got rid of uh both the + + align:start position:0% +that basically got rid of uh both the + + + align:start position:0% +that basically got rid of uh both the +lot of language specific thing and also + + align:start position:0% +lot of language specific thing and also + + + align:start position:0% +lot of language specific thing and also +machine dependent part. So we came up + + align:start position:0% +machine dependent part. So we came up + + + align:start position:0% +machine dependent part. So we came up +with a very simple representation that + + align:start position:0% +with a very simple representation that + + + align:start position:0% +with a very simple representation that +just basically understand the program in + + align:start position:0% +just basically understand the program in + + + align:start position:0% +just basically understand the program in +there and we basically did multiple + + align:start position:0% +there and we basically did multiple + + + align:start position:0% +there and we basically did multiple +layers in the high level that has more + + align:start position:0% +layers in the high level that has more + + + align:start position:0% +layers in the high level that has more +and more language uh specific in high + + align:start position:0% +and more language uh specific in high + + + align:start position:0% +and more language uh specific in high +level and as we get to low level you you + + align:start position:0% +level and as we get to low level you you + + + align:start position:0% +level and as we get to low level you you +eliminate a lot of this language + + align:start position:0% +eliminate a lot of this language + + + align:start position:0% +eliminate a lot of this language +dependent stuff + + align:start position:0% +dependent stuff + + + align:start position:0% +dependent stuff +and and finally one before the last we + + align:start position:0% +and and finally one before the last we + + + align:start position:0% +and and finally one before the last we +did code optimization. So key thing is + + align:start position:0% +did code optimization. So key thing is + + + align:start position:0% +did code optimization. So key thing is +we want to get as close as possible to + + align:start position:0% +we want to get as close as possible to + + + align:start position:0% +we want to get as close as possible to +what somebody would write by hand in if + + align:start position:0% +what somebody would write by hand in if + + + align:start position:0% +what somebody would write by hand in if +we have good hand assembler and uh also + + align:start position:0% +we have good hand assembler and uh also + + + align:start position:0% +we have good hand assembler and uh also +we want to take start taking advantage + + align:start position:0% +we want to take start taking advantage + + + align:start position:0% +we want to take start taking advantage +of uh in this project uh exploiting uh + + align:start position:0% +of uh in this project uh exploiting uh + + + align:start position:0% +of uh in this project uh exploiting uh +ar architectural strengths and + + align:start position:0% +ar architectural strengths and + + + align:start position:0% +ar architectural strengths and +weaknesses uh strengths you take + + align:start position:0% +weaknesses uh strengths you take + + + align:start position:0% +weaknesses uh strengths you take +advantage of weaknesses you're trying to + + align:start position:0% +advantage of weaknesses you're trying to + + + align:start position:0% +advantage of weaknesses you're trying to +avoid uh uh in in there and we did bunch + + align:start position:0% +avoid uh uh in in there and we did bunch + + + align:start position:0% +avoid uh uh in in there and we did bunch +of things uh I guess we are doing + + align:start position:0% +of things uh I guess we are doing + + + align:start position:0% +of things uh I guess we are doing +register allocation and we are open to + + align:start position:0% +register allocation and we are open to + + + align:start position:0% +register allocation and we are open to +do other things in this thing + + align:start position:0% +do other things in this thing + + + align:start position:0% +do other things in this thing +So good. That's the entire semester and + + align:start position:0% +So good. That's the entire semester and + + + align:start position:0% +So good. That's the entire semester and +in in in in 10 + + align:start position:0% +in in in in 10 + + + align:start position:0% +in in in in 10 +minutes. + + align:start position:0% +minutes. + + + align:start position:0% +minutes. +So you guys have actually amazingly + + align:start position:0% +So you guys have actually amazingly + + + align:start position:0% +So you guys have actually amazingly +built a good compiler and and from all + + align:start position:0% +built a good compiler and and from all + + + align:start position:0% +built a good compiler and and from all +the indication every group managed to + + align:start position:0% +the indication every group managed to + + + align:start position:0% +the indication every group managed to +get a compiler working. This is amazing + + align:start position:0% +get a compiler working. This is amazing + + + align:start position:0% +get a compiler working. This is amazing +feed given how complex this project is + + align:start position:0% +feed given how complex this project is + + + align:start position:0% +feed given how complex this project is +and knowing this is not the only project + + align:start position:0% +and knowing this is not the only project + + + align:start position:0% +and knowing this is not the only project +you guys are also working on and and + + align:start position:0% +you guys are also working on and and + + + align:start position:0% +you guys are also working on and and +this is really cool. I think this is a + + align:start position:0% +this is really cool. I think this is a + + + align:start position:0% +this is really cool. I think this is a +great achievement to do uh get all those + + align:start position:0% +great achievement to do uh get all those + + + align:start position:0% +great achievement to do uh get all those +things done. And so now the fun part, + + align:start position:0% +things done. And so now the fun part, + + + align:start position:0% +things done. And so now the fun part, +this is optional, but I hope everybody + + align:start position:0% +this is optional, but I hope everybody + + + align:start position:0% +this is optional, but I hope everybody +participates. So what you want to do is + + align:start position:0% +participates. So what you want to do is + + + align:start position:0% +participates. So what you want to do is +figure out who has the fastest compiler + + align:start position:0% +figure out who has the fastest compiler + + + align:start position:0% +figure out who has the fastest compiler +or at least who produces the fastest + + align:start position:0% +or at least who produces the fastest + + + align:start position:0% +or at least who produces the fastest +code in in the compiler and uh uh and + + align:start position:0% +code in in the compiler and uh uh and + + + align:start position:0% +code in in the compiler and uh uh and +some years people have really surprised + + align:start position:0% +some years people have really surprised + + + align:start position:0% +some years people have really surprised +me and from how well they do and in fact + + align:start position:0% +me and from how well they do and in fact + + + align:start position:0% +me and from how well they do and in fact +one year they managed to beat GCC3 and I + + align:start position:0% +one year they managed to beat GCC3 and I + + + align:start position:0% +one year they managed to beat GCC3 and I +didn't believe them. them I said it + + align:start position:0% +didn't believe them. them I said it + + + align:start position:0% +didn't believe them. them I said it +can't be done but after looking at it + + align:start position:0% +can't be done but after looking at it + + + align:start position:0% +can't be done but after looking at it +they actually did it and so I'm like wow + + align:start position:0% +they actually did it and so I'm like wow + + + align:start position:0% +they actually did it and so I'm like wow +so uh people I mean I don't think they + + align:start position:0% +so uh people I mean I don't think they + + + align:start position:0% +so uh people I mean I don't think they +got any sleep for a few weeks but + + align:start position:0% +got any sleep for a few weeks but + + + align:start position:0% +got any sleep for a few weeks but +besides that I mean so there's a lot of + + align:start position:0% +besides that I mean so there's a lot of + + + align:start position:0% +besides that I mean so there's a lot of +history behind it so what I'm going to + + align:start position:0% +history behind it so what I'm going to + + + align:start position:0% +history behind it so what I'm going to +do is we it's for the first time we are + + align:start position:0% +do is we it's for the first time we are + + + align:start position:0% +do is we it's for the first time we are +going to give the program 12 hours in + + align:start position:0% +going to give the program 12 hours in + + + align:start position:0% +going to give the program 12 hours in +advance main reason is I want to make + + align:start position:0% +advance main reason is I want to make + + + align:start position:0% +advance main reason is I want to make +sure you get all your optimizations + + align:start position:0% +sure you get all your optimizations + + + align:start position:0% +sure you get all your optimizations +working on this program a lot of times + + align:start position:0% +working on this program a lot of times + + + align:start position:0% +working on this program a lot of times +it happen is I give it hour before + + align:start position:0% +it happen is I give it hour before + + + align:start position:0% +it happen is I give it hour before +within the hour beginning of the hour + + align:start position:0% +within the hour beginning of the hour + + + align:start position:0% +within the hour beginning of the hour +and for Most people some optimizations + + align:start position:0% +and for Most people some optimizations + + + align:start position:0% +and for Most people some optimizations +didn't work and actually there are some + + align:start position:0% +didn't work and actually there are some + + + align:start position:0% +didn't work and actually there are some +years that the most aggressive compilers + + align:start position:0% +years that the most aggressive compilers + + + align:start position:0% +years that the most aggressive compilers +didn't really win because they couldn't + + align:start position:0% +didn't really win because they couldn't + + + align:start position:0% +didn't really win because they couldn't +get the all the optimizations to work. + + align:start position:0% +get the all the optimizations to work. + + + align:start position:0% +get the all the optimizations to work. +They did a lot of things whereas uh the + + align:start position:0% +They did a lot of things whereas uh the + + + align:start position:0% +They did a lot of things whereas uh the +few compilers that did some things that + + align:start position:0% +few compilers that did some things that + + + align:start position:0% +few compilers that did some things that +managed to be more robust wins. And this + + align:start position:0% +managed to be more robust wins. And this + + + align:start position:0% +managed to be more robust wins. And this +year we give because of that I'm going + + align:start position:0% +year we give because of that I'm going + + + align:start position:0% +year we give because of that I'm going +to give two. + + align:start position:0% +to give two. + + + align:start position:0% +to give two. +But this has a huge temptation. You look + + align:start position:0% +But this has a huge temptation. You look + + + align:start position:0% +But this has a huge temptation. You look +at the code and say hm that statement + + align:start position:0% +at the code and say hm that statement + + + align:start position:0% +at the code and say hm that statement +there uh it's a random number. I know + + align:start position:0% +there uh it's a random number. I know + + + align:start position:0% +there uh it's a random number. I know +what it does. I can actually replace it + + align:start position:0% +what it does. I can actually replace it + + + align:start position:0% +what it does. I can actually replace it +with this this crazy thing and I can get + + align:start position:0% +with this this crazy thing and I can get + + + align:start position:0% +with this this crazy thing and I can get +uh this to run so much faster. I don't + + align:start position:0% +uh this to run so much faster. I don't + + + align:start position:0% +uh this to run so much faster. I don't +want to lo see that. I mean the thing is + + align:start position:0% +want to lo see that. I mean the thing is + + + align:start position:0% +want to lo see that. I mean the thing is +if you win then we will actually examine + + align:start position:0% +if you win then we will actually examine + + + align:start position:0% +if you win then we will actually examine +what you compiled it and you have to + + align:start position:0% +what you compiled it and you have to + + + align:start position:0% +what you compiled it and you have to +explain the code and tell us how you + + align:start position:0% +explain the code and tell us how you + + + align:start position:0% +explain the code and tell us how you +achieve that. Uh uh so so don't try to + + align:start position:0% +achieve that. Uh uh so so don't try to + + + align:start position:0% +achieve that. Uh uh so so don't try to +do crazy things to make everything you + + align:start position:0% +do crazy things to make everything you + + + align:start position:0% +do crazy things to make everything you +do should be correct. Okay, it's + + align:start position:0% +do should be correct. Okay, it's + + + align:start position:0% +do should be correct. Okay, it's +provably correct. I mean of course you + + align:start position:0% +provably correct. I mean of course you + + + align:start position:0% +provably correct. I mean of course you +have to do correct transformation but + + align:start position:0% +have to do correct transformation but + + + align:start position:0% +have to do correct transformation but +you should be able to prove that it's + + align:start position:0% +you should be able to prove that it's + + + align:start position:0% +you should be able to prove that it's +doable because there are a lot of times + + align:start position:0% +doable because there are a lot of times + + + align:start position:0% +doable because there are a lot of times +you look at the program and say ah this + + align:start position:0% +you look at the program and say ah this + + + align:start position:0% +you look at the program and say ah this +transformation is correct but but + + align:start position:0% +transformation is correct but but + + + align:start position:0% +transformation is correct but but +there's no way for you eyeball and you + + align:start position:0% +there's no way for you eyeball and you + + + align:start position:0% +there's no way for you eyeball and you +can do that but you should be able to + + align:start position:0% +can do that but you should be able to + + + align:start position:0% +can do that but you should be able to +the compiler should be able to prove + + align:start position:0% +the compiler should be able to prove + + + align:start position:0% +the compiler should be able to prove +everything it does in fact is correct so + + align:start position:0% +everything it does in fact is correct so + + + align:start position:0% +everything it does in fact is correct so +that's critical so you can't look at the + + align:start position:0% +that's critical so you can't look at the + + + align:start position:0% +that's critical so you can't look at the +function and say okay I can do this and + + align:start position:0% +function and say okay I can do this and + + + align:start position:0% +function and say okay I can do this and +it will work that doesn't work so you + + align:start position:0% +it will work that doesn't work so you + + + align:start position:0% +it will work that doesn't work so you +have actually say that I I go from A to + + align:start position:0% +have actually say that I I go from A to + + + align:start position:0% +have actually say that I I go from A to +B and I I in the compiling the code not + + align:start position:0% +B and I I in the compiling the code not + + + align:start position:0% +B and I I in the compiling the code not +in your head prove that going from A to + + align:start position:0% +in your head prove that going from A to + + + align:start position:0% +in your head prove that going from A to +B is correct so So, so I don't want that + + align:start position:0% +B is correct so So, so I don't want that + + + align:start position:0% +B is correct so So, so I don't want that +to people do that. So, uh this is on the + + align:start position:0% +to people do that. So, uh this is on the + + + align:start position:0% +to people do that. So, uh this is on the +14th at 11:00 a.m. and uh we'll announce + + align:start position:0% +14th at 11:00 a.m. and uh we'll announce + + + align:start position:0% +14th at 11:00 a.m. and uh we'll announce +a place where when we'll provide some + + align:start position:0% +a place where when we'll provide some + + + align:start position:0% +a place where when we'll provide some +refreshments so we can have fun and I + + align:start position:0% +refreshments so we can have fun and I + + + align:start position:0% +refreshments so we can have fun and I +think this is a fun time to celebrate + + align:start position:0% +think this is a fun time to celebrate + + + align:start position:0% +think this is a fun time to celebrate +everybody's what they have + + align:start position:0% +everybody's what they have + + + align:start position:0% +everybody's what they have +done. + + align:start position:0% +done. + + + align:start position:0% +done. +So little bit + + align:start position:0% +So little bit + + + align:start position:0% +So little bit +on so what's this all about? You had you + + align:start position:0% +on so what's this all about? You had you + + + align:start position:0% +on so what's this all about? You had you +spend a semester bunch of sleepless + + align:start position:0% +spend a semester bunch of sleepless + + + align:start position:0% +spend a semester bunch of sleepless +nights building a compiler. What did you + + align:start position:0% +nights building a compiler. What did you + + + align:start position:0% +nights building a compiler. What did you +gain? I think after you left this course + + align:start position:0% +gain? I think after you left this course + + + align:start position:0% +gain? I think after you left this course +at many different levels I think you + + align:start position:0% +at many different levels I think you + + + align:start position:0% +at many different levels I think you +have gained something. Uh most of you + + align:start position:0% +have gained something. Uh most of you + + + align:start position:0% +have gained something. Uh most of you +will become a pro will be programming + + align:start position:0% +will become a pro will be programming + + + align:start position:0% +will become a pro will be programming +for a long time in your careers and + + align:start position:0% +for a long time in your careers and + + + align:start position:0% +for a long time in your careers and +where you end up doing and I think this + + align:start position:0% +where you end up doing and I think this + + + align:start position:0% +where you end up doing and I think this +course you actually learn something in + + align:start position:0% +course you actually learn something in + + + align:start position:0% +course you actually learn something in +that and there are few things you might + + align:start position:0% +that and there are few things you might + + + align:start position:0% +that and there are few things you might +want to uh some direct things that we + + align:start position:0% +want to uh some direct things that we + + + align:start position:0% +want to uh some direct things that we +learn in this language you can use. + + align:start position:0% +learn in this language you can use. + + + align:start position:0% +learn in this language you can use. +uh some of this people you'll be working + + align:start position:0% +uh some of this people you'll be working + + + align:start position:0% +uh some of this people you'll be working +with uh things like new architectures + + align:start position:0% +with uh things like new architectures + + + align:start position:0% +with uh things like new architectures +either from designing architectures + + align:start position:0% +either from designing architectures + + + align:start position:0% +either from designing architectures +building compilers this large group of + + align:start position:0% +building compilers this large group of + + + align:start position:0% +building compilers this large group of +uh ECS type end up doing things like + + align:start position:0% +uh ECS type end up doing things like + + + align:start position:0% +uh ECS type end up doing things like +that and then I think that will be + + align:start position:0% +that and then I think that will be + + + align:start position:0% +that and then I think that will be +useful and very few of you probably one + + align:start position:0% +useful and very few of you probably one + + + align:start position:0% +useful and very few of you probably one +or two probably one in this class if I'm + + align:start position:0% +or two probably one in this class if I'm + + + align:start position:0% +or two probably one in this class if I'm +lucky we'll become a true compiler + + align:start position:0% +lucky we'll become a true compiler + + + align:start position:0% +lucky we'll become a true compiler +hacker and then and do a lot of it but + + align:start position:0% +hacker and then and do a lot of it but + + + align:start position:0% +hacker and then and do a lot of it but +even if you don't do that I think you'll + + align:start position:0% +even if you don't do that I think you'll + + + align:start position:0% +even if you don't do that I think you'll +learn a lot so from an informed + + align:start position:0% +learn a lot so from an informed + + + align:start position:0% +learn a lot so from an informed +programmer's point of view every + + align:start position:0% +programmer's point of view every + + + align:start position:0% +programmer's point of view every +programmer has to use a compiler and + + align:start position:0% +programmer has to use a compiler and + + + align:start position:0% +programmer has to use a compiler and +things like JIT compiler things are much + + align:start position:0% +things like JIT compiler things are much + + + align:start position:0% +things like JIT compiler things are much +even more complex more random lot of + + align:start position:0% +even more complex more random lot of + + + align:start position:0% +even more complex more random lot of +things happens and for most of you until + + align:start position:0% +things happens and for most of you until + + + align:start position:0% +things happens and for most of you until +now probably treated a compiler as a + + align:start position:0% +now probably treated a compiler as a + + + align:start position:0% +now probably treated a compiler as a +black box it's there you give a program + + align:start position:0% +black box it's there you give a program + + + align:start position:0% +black box it's there you give a program +something comes out and it runs + + align:start position:0% +something comes out and it runs + + + align:start position:0% +something comes out and it runs +and and you have to trust it to do the + + align:start position:0% +and and you have to trust it to do the + + + align:start position:0% +and and you have to trust it to do the +right thing and and of course compilers + + align:start position:0% +right thing and and of course compilers + + + align:start position:0% +right thing and and of course compilers +are programs they have bugs too and and + + align:start position:0% +are programs they have bugs too and and + + + align:start position:0% +are programs they have bugs too and and +they have many implications for + + align:start position:0% +they have many implications for + + + align:start position:0% +they have many implications for +performance debugging correctness that + + align:start position:0% +performance debugging correctness that + + + align:start position:0% +performance debugging correctness that +that from now you should be able to just + + align:start position:0% +that from now you should be able to just + + + align:start position:0% +that from now you should be able to just +not trust this black box to be working + + align:start position:0% +not trust this black box to be working + + + align:start position:0% +not trust this black box to be working +all the time and and and trusting it all + + align:start position:0% +all the time and and and trusting it all + + + align:start position:0% +all the time and and and trusting it all +the time. So what did you learn from + + align:start position:0% +the time. So what did you learn from + + + align:start position:0% +the time. So what did you learn from +6035? You learn how optimizations work + + align:start position:0% +6035? You learn how optimizations work + + + align:start position:0% +6035? You learn how optimizations work +and you also know why it didn't work. So + + align:start position:0% +and you also know why it didn't work. So + + + align:start position:0% +and you also know why it didn't work. So +assume you did something and you're + + align:start position:0% +assume you did something and you're + + + align:start position:0% +assume you did something and you're +expecting some result and if it doesn't + + align:start position:0% +expecting some result and if it doesn't + + + align:start position:0% +expecting some result and if it doesn't +happen of what you expected okay and you + + align:start position:0% +happen of what you expected okay and you + + + align:start position:0% +happen of what you expected okay and you +can look at that and say aha this is not + + align:start position:0% +can look at that and say aha this is not + + + align:start position:0% +can look at that and say aha this is not +my fault because I fooled the compiler + + align:start position:0% +my fault because I fooled the compiler + + + align:start position:0% +my fault because I fooled the compiler +compiler got fooled because of that it + + align:start position:0% +compiler got fooled because of that it + + + align:start position:0% +compiler got fooled because of that it +might be optimization problem it might + + align:start position:0% +might be optimization problem it might + + + align:start position:0% +might be optimization problem it might +be a correctness issue there might be + + align:start position:0% +be a correctness issue there might be + + + align:start position:0% +be a correctness issue there might be +issues in there that that you now + + align:start position:0% +issues in there that that you now + + + align:start position:0% +issues in there that that you now +because you understand what the + + align:start position:0% +because you understand what the + + + align:start position:0% +because you understand what the +compilers does can actually decipher + + align:start position:0% +compilers does can actually decipher + + + align:start position:0% +compilers does can actually decipher +that and another interesting thing is + + align:start position:0% +that and another interesting thing is + + + align:start position:0% +that and another interesting thing is +you should be able to read optimized + + align:start position:0% +you should be able to read optimized + + + align:start position:0% +you should be able to read optimized +code because you ran through the + + align:start position:0% +code because you ran through the + + + align:start position:0% +code because you ran through the +compiler and you're trying to debug and + + align:start position:0% +compiler and you're trying to debug and + + + align:start position:0% +compiler and you're trying to debug and +there's this this garbble group bunch of + + align:start position:0% +there's this this garbble group bunch of + + + align:start position:0% +there's this this garbble group bunch of +assembly instructions and you don't know + + align:start position:0% +assembly instructions and you don't know + + + align:start position:0% +assembly instructions and you don't know +what what's going on and if you know I + + align:start position:0% +what what's going on and if you know I + + + align:start position:0% +what what's going on and if you know I +say aha this is because it did common + + align:start position:0% +say aha this is because it did common + + + align:start position:0% +say aha this is because it did common +sub expression elimination I see that + + align:start position:0% +sub expression elimination I see that + + + align:start position:0% +sub expression elimination I see that +and that is why this code looks like + + align:start position:0% +and that is why this code looks like + + + align:start position:0% +and that is why this code looks like +this and I think for debugging purpose + + align:start position:0% +this and I think for debugging purpose + + + align:start position:0% +this and I think for debugging purpose +especially if you're doing lowle + + align:start position:0% +especially if you're doing lowle + + + align:start position:0% +especially if you're doing lowle +debugging this is very useful and and + + align:start position:0% +debugging this is very useful and and + + + align:start position:0% +debugging this is very useful and and +for + + align:start position:0% +for + + + align:start position:0% +for +example some of the stuff I have been uh + + align:start position:0% +example some of the stuff I have been uh + + + align:start position:0% +example some of the stuff I have been uh +uh involved recently is basically trying + + align:start position:0% +uh involved recently is basically trying + + + align:start position:0% +uh involved recently is basically trying +to uh reverse engineer production code + + align:start position:0% +to uh reverse engineer production code + + + align:start position:0% +to uh reverse engineer production code +so you don't have source you have you + + align:start position:0% +so you don't have source you have you + + + align:start position:0% +so you don't have source you have you +have a a binary and you need to figure + + align:start position:0% +have a a binary and you need to figure + + + align:start position:0% +have a a binary and you need to figure +out what what's happening in the binary + + align:start position:0% +out what what's happening in the binary + + + align:start position:0% +out what what's happening in the binary +and they optimize code and so you look + + align:start position:0% +and they optimize code and so you look + + + align:start position:0% +and they optimize code and so you look +at a piece of instructions and you say + + align:start position:0% +at a piece of instructions and you say + + + align:start position:0% +at a piece of instructions and you say +what kind of C code would have produced + + align:start position:0% +what kind of C code would have produced + + + align:start position:0% +what kind of C code would have produced +that and and and knowing optimization + + align:start position:0% +that and and and knowing optimization + + + align:start position:0% +that and and and knowing optimization +say aha this is probably what it + + align:start position:0% +say aha this is probably what it + + + align:start position:0% +say aha this is probably what it +produced and then after optimization + + align:start position:0% +produced and then after optimization + + + align:start position:0% +produced and then after optimization +this is how it looks like so knowing all + + align:start position:0% +this is how it looks like so knowing all + + + align:start position:0% +this is how it looks like so knowing all +this optimization what they do will be + + align:start position:0% +this optimization what they do will be + + + align:start position:0% +this optimization what they do will be +really useful when you're + + align:start position:0% + + + + align:start position:0% + +debugging second thing lot of people use + + align:start position:0% +debugging second thing lot of people use + + + align:start position:0% +debugging second thing lot of people use +uh this kind of knowledge is doing + + align:start position:0% +uh this kind of knowledge is doing + + + align:start position:0% +uh this kind of knowledge is doing +simple language + + align:start position:0% +simple language + + + align:start position:0% +simple language +extension Most of the time when you have + + align:start position:0% +extension Most of the time when you have + + + align:start position:0% +extension Most of the time when you have +a large programming project, one of the + + align:start position:0% +a large programming project, one of the + + + align:start position:0% +a large programming project, one of the +easiest abstraction you can do is do a + + align:start position:0% +easiest abstraction you can do is do a + + + align:start position:0% +easiest abstraction you can do is do a +very simple language abstraction. + + align:start position:0% +very simple language abstraction. + + + align:start position:0% +very simple language abstraction. +uh you are trying to some read some + + align:start position:0% +uh you are trying to some read some + + + align:start position:0% +uh you are trying to some read some +complex input out there XML file or some + + align:start position:0% +complex input out there XML file or some + + + align:start position:0% +complex input out there XML file or some +very comp you are trying to define some + + align:start position:0% +very comp you are trying to define some + + + align:start position:0% +very comp you are trying to define some +kind of interface uh you are + + align:start position:0% +kind of interface uh you are + + + align:start position:0% +kind of interface uh you are +doing you have bunch of uh very high + + align:start position:0% +doing you have bunch of uh very high + + + align:start position:0% +doing you have bunch of uh very high +level uh uh uh problem that that for + + align:start position:0% +level uh uh uh problem that that for + + + align:start position:0% +level uh uh uh problem that that for +example you're trying to build interface + + align:start position:0% +example you're trying to build interface + + + align:start position:0% +example you're trying to build interface +for people to use and you can say okay + + align:start position:0% +for people to use and you can say okay + + + align:start position:0% +for people to use and you can say okay +well I can build huge library or I can + + align:start position:0% +well I can build huge library or I can + + + align:start position:0% +well I can build huge library or I can +define a very simple language + + align:start position:0% +define a very simple language + + + align:start position:0% +define a very simple language +and nice thing about doing a language is + + align:start position:0% +and nice thing about doing a language is + + + align:start position:0% +and nice thing about doing a language is +you can easily add nice functionality in + + align:start position:0% +you can easily add nice functionality in + + + align:start position:0% +you can easily add nice functionality in +here. You can uh and and check for + + align:start position:0% +here. You can uh and and check for + + + align:start position:0% +here. You can uh and and check for +semantics and and and and you can you + + align:start position:0% +semantics and and and and you can you + + + align:start position:0% +semantics and and and and you can you +can instead of having a language type + + align:start position:0% +can instead of having a language type + + + align:start position:0% +can instead of having a language type +thing where if people make mistakes you + + align:start position:0% +thing where if people make mistakes you + + + align:start position:0% +thing where if people make mistakes you +do it's hard to understand building a + + align:start position:0% +do it's hard to understand building a + + + align:start position:0% +do it's hard to understand building a +simple language you can actually give + + align:start position:0% +simple language you can actually give + + + align:start position:0% +simple language you can actually give +people warnings and and and and and + + align:start position:0% +people warnings and and and and and + + + align:start position:0% +people warnings and and and and and +guide people within the domain you want + + align:start position:0% +guide people within the domain you want + + + align:start position:0% +guide people within the domain you want +to be and and you can also help with + + align:start position:0% +to be and and you can also help with + + + align:start position:0% +to be and and you can also help with +optimization. So so uh for example uh + + align:start position:0% +optimization. So so uh for example uh + + + align:start position:0% +optimization. So so uh for example uh +compilers show up in weird places. + + align:start position:0% +compilers show up in weird places. + + + align:start position:0% +compilers show up in weird places. +Postcript it's a printer but it's a + + align:start position:0% +Postcript it's a printer but it's a + + + align:start position:0% +Postcript it's a printer but it's a +language it has optimization openg for + + align:start position:0% +language it has optimization openg for + + + align:start position:0% +language it has optimization openg for +graphics XML okay all those things I + + align:start position:0% +graphics XML okay all those things I + + + align:start position:0% +graphics XML okay all those things I +mean they don't sound like a programming + + align:start position:0% +mean they don't sound like a programming + + + align:start position:0% +mean they don't sound like a programming +language but lot of this actually is a + + align:start position:0% +language but lot of this actually is a + + + align:start position:0% +language but lot of this actually is a +language that's a compiler and + + align:start position:0% +language that's a compiler and + + + align:start position:0% +language that's a compiler and +optimization all those tool chain comes + + align:start position:0% +optimization all those tool chain comes + + + align:start position:0% +optimization all those tool chain comes +comes into play and and a lot of times + + align:start position:0% +comes into play and and a lot of times + + + align:start position:0% +comes into play and and a lot of times +uh my feeling is as a programmer at + + align:start position:0% +uh my feeling is as a programmer at + + + align:start position:0% +uh my feeling is as a programmer at +least when I was doing a lot of + + align:start position:0% +least when I was doing a lot of + + + align:start position:0% +least when I was doing a lot of +programming every six months I came up + + align:start position:0% +programming every six months I came up + + + align:start position:0% +programming every six months I came up +with a problem I said the best solution + + align:start position:0% +with a problem I said the best solution + + + align:start position:0% +with a problem I said the best solution +is trying to come up with a simple + + align:start position:0% +is trying to come up with a simple + + + align:start position:0% +is trying to come up with a simple +language and I'll do the language and I + + align:start position:0% +language and I'll do the language and I + + + align:start position:0% +language and I'll do the language and I +I'll compile into that language and and + + align:start position:0% +I'll compile into that language and and + + + align:start position:0% +I'll compile into that language and and +and and and because of that I can have + + align:start position:0% +and and and because of that I can have + + + align:start position:0% +and and and because of that I can have +this interface that is that is lot + + align:start position:0% +this interface that is that is lot + + + align:start position:0% +this interface that is that is lot +tighter than anything you could do with + + align:start position:0% +tighter than anything you could do with + + + align:start position:0% +tighter than anything you could do with +uh uh providing a Java interface or + + align:start position:0% +uh uh providing a Java interface or + + + align:start position:0% +uh uh providing a Java interface or +something like that because when you + + align:start position:0% +something like that because when you + + + align:start position:0% +something like that because when you +need to do that a library people abuse + + align:start position:0% +need to do that a library people abuse + + + align:start position:0% +need to do that a library people abuse +it misuse it do things and in language + + align:start position:0% +it misuse it do things and in language + + + align:start position:0% +it misuse it do things and in language +you can actually have much more better + + align:start position:0% +you can actually have much more better + + + align:start position:0% +you can actually have much more better +control feedback uh even do nice + + align:start position:0% +control feedback uh even do nice + + + align:start position:0% +control feedback uh even do nice +optimizations and stuff like + + align:start position:0% +optimizations and stuff like + + + align:start position:0% +optimizations and stuff like +that and 6035 actually provided a lot of + + align:start position:0% +that and 6035 actually provided a lot of + + + align:start position:0% +that and 6035 actually provided a lot of +it I mean if you're doing language page + + align:start position:0% +it I mean if you're doing language page + + + align:start position:0% +it I mean if you're doing language page +you need uh lexa and a passer and we we + + align:start position:0% +you need uh lexa and a passer and we we + + + align:start position:0% +you need uh lexa and a passer and we we +actually gave you all those thing uh + + align:start position:0% +actually gave you all those thing uh + + + align:start position:0% +actually gave you all those thing uh +tools and you learn to do that and uh uh + + align:start position:0% +tools and you learn to do that and uh uh + + + align:start position:0% +tools and you learn to do that and uh uh +use intermediate representations how to + + align:start position:0% +use intermediate representations how to + + + align:start position:0% +use intermediate representations how to +build that you learned all those things + + align:start position:0% +build that you learned all those things + + + align:start position:0% +build that you learned all those things +next thing you might do + + align:start position:0% +next thing you might do + + + align:start position:0% +next thing you might do +is if you are involved in more aspect of + + align:start position:0% +is if you are involved in more aspect of + + + align:start position:0% +is if you are involved in more aspect of +e side or computer architecture side + + align:start position:0% +e side or computer architecture side + + + align:start position:0% +e side or computer architecture side +uh every processor there are many + + align:start position:0% +uh every processor there are many + + + align:start position:0% +uh every processor there are many +different processor out there it's not + + align:start position:0% +different processor out there it's not + + + align:start position:0% +different processor out there it's not +just Intel x86 out There are hundreds of + + align:start position:0% +just Intel x86 out There are hundreds of + + + align:start position:0% +just Intel x86 out There are hundreds of +different process. Your cell phone has + + align:start position:0% +different process. Your cell phone has + + + align:start position:0% +different process. Your cell phone has +one. Your watch has one. If need to + + align:start position:0% +one. Your watch has one. If need to + + + align:start position:0% +one. Your watch has one. If need to +build a process, you need to program it. + + align:start position:0% +build a process, you need to program it. + + + align:start position:0% +build a process, you need to program it. +And mean to you to program it, you need + + align:start position:0% +And mean to you to program it, you need + + + align:start position:0% +And mean to you to program it, you need +you need some kind of a tool chain + + align:start position:0% +you need some kind of a tool chain + + + align:start position:0% +you need some kind of a tool chain +probably C Java, some kind of a compiler + + align:start position:0% +probably C Java, some kind of a compiler + + + align:start position:0% +probably C Java, some kind of a compiler +or or a J that actually maps into that. + + align:start position:0% +or or a J that actually maps into that. + + + align:start position:0% +or or a J that actually maps into that. +And it has implication in many different + + align:start position:0% +And it has implication in many different + + + align:start position:0% +And it has implication in many different +directions. So for example, + + align:start position:0% +directions. So for example, + + + align:start position:0% +directions. So for example, +um if you are more from the architecture + + align:start position:0% +um if you are more from the architecture + + + align:start position:0% +um if you are more from the architecture +side, if you're designing architects, + + align:start position:0% +side, if you're designing architects, + + + align:start position:0% +side, if you're designing architects, +you really need to have understanding + + align:start position:0% +you really need to have understanding + + + align:start position:0% +you really need to have understanding +about the compile aspects. Also every + + align:start position:0% +about the compile aspects. Also every + + + align:start position:0% +about the compile aspects. Also every +architecture has to have coupled with + + align:start position:0% +architecture has to have coupled with + + + align:start position:0% +architecture has to have coupled with +the backend compiler that people targets + + align:start position:0% +the backend compiler that people targets + + + align:start position:0% +the backend compiler that people targets +that + + align:start position:0% +that + + + align:start position:0% +that +architecture. So I think that's from + + align:start position:0% +architecture. So I think that's from + + + align:start position:0% +architecture. So I think that's from +architect point of view there are a lot + + align:start position:0% +architect point of view there are a lot + + + align:start position:0% +architect point of view there are a lot +of cool things happening these days. I + + align:start position:0% +of cool things happening these days. I + + + align:start position:0% +of cool things happening these days. I +mean I don't know how many of you are + + align:start position:0% +mean I don't know how many of you are + + + align:start position:0% +mean I don't know how many of you are +interested in uh uh that area. Uh and + + align:start position:0% +interested in uh uh that area. Uh and + + + align:start position:0% +interested in uh uh that area. Uh and +people are looking at many different new + + align:start position:0% +people are looking at many different new + + + align:start position:0% +people are looking at many different new +architectures to build. How if you are + + align:start position:0% +architectures to build. How if you are + + + align:start position:0% +architectures to build. How if you are +building architect if you ever become + + align:start position:0% +building architect if you ever become + + + align:start position:0% +building architect if you ever become +architect you have to have a really good + + align:start position:0% +architect you have to have a really good + + + align:start position:0% +architect you have to have a really good +notion of what compilers can do and + + align:start position:0% +notion of what compilers can do and + + + align:start position:0% +notion of what compilers can do and +cannot do. So you can actually balance + + align:start position:0% +cannot do. So you can actually balance + + + align:start position:0% +cannot do. So you can actually balance +of what happens in hardware and what + + align:start position:0% +of what happens in hardware and what + + + align:start position:0% +of what happens in hardware and what +happens in software because compiler is + + align:start position:0% +happens in software because compiler is + + + align:start position:0% +happens in software because compiler is +the one come in the middle. So a very + + align:start position:0% +the one come in the middle. So a very + + + align:start position:0% +the one come in the middle. So a very +good architecture is somebody is done by + + align:start position:0% +good architecture is somebody is done by + + + align:start position:0% +good architecture is somebody is done by +people who really understand the + + align:start position:0% +people who really understand the + + + align:start position:0% +people who really understand the +capabilities and limitations of a + + align:start position:0% +capabilities and limitations of a + + + align:start position:0% +capabilities and limitations of a +compiler. They can say aha I can get the + + align:start position:0% +compiler. They can say aha I can get the + + + align:start position:0% +compiler. They can say aha I can get the +compiler to do this. I don't have to do + + align:start position:0% +compiler to do this. I don't have to do + + + align:start position:0% +compiler to do this. I don't have to do +it in hardware. This something that + + align:start position:0% +it in hardware. This something that + + + align:start position:0% +it in hardware. This something that +compilers can't do well. I will do it in + + align:start position:0% +compilers can't do well. I will do it in + + + align:start position:0% +compilers can't do well. I will do it in +hardware. So that limitation that people + + align:start position:0% +hardware. So that limitation that people + + + align:start position:0% +hardware. So that limitation that people +understand actually builds very good + + align:start position:0% +understand actually builds very good + + + align:start position:0% +understand actually builds very good +hardware. So knowing that is very + + align:start position:0% +hardware. So knowing that is very + + + align:start position:0% +hardware. So knowing that is very +important especially uh uh uh + + align:start position:0% +important especially uh uh uh + + + align:start position:0% +important especially uh uh uh +architects and this is what you + + align:start position:0% +architects and this is what you + + + align:start position:0% +architects and this is what you +learn. Excuse me. You need to you learn + + align:start position:0% +learn. Excuse me. You need to you learn + + + align:start position:0% +learn. Excuse me. You need to you learn +what the capabilities and limitations of + + align:start position:0% +what the capabilities and limitations of + + + align:start position:0% +what the capabilities and limitations of +compilers and you need to you learn how + + align:start position:0% +compilers and you need to you learn how + + + align:start position:0% +compilers and you need to you learn how +to think like a compiler + + align:start position:0% +to think like a compiler + + + align:start position:0% +to think like a compiler +writer and + + align:start position:0% +writer and + + + align:start position:0% +writer and +also every time you come up with a new + + align:start position:0% +also every time you come up with a new + + + align:start position:0% +also every time you come up with a new +architecture you actually had to have a + + align:start position:0% +architecture you actually had to have a + + + align:start position:0% +architecture you actually had to have a +compiler tool chain. So there will be + + align:start position:0% +compiler tool chain. So there will be + + + align:start position:0% +compiler tool chain. So there will be +even the same amount of people actually + + align:start position:0% +even the same amount of people actually + + + align:start position:0% +even the same amount of people actually +building the compiler tool chain and and + + align:start position:0% +building the compiler tool chain and and + + + align:start position:0% +building the compiler tool chain and and +and what that means is every + + align:start position:0% +and what that means is every + + + align:start position:0% +and what that means is every +architecture is a little bit different + + align:start position:0% +architecture is a little bit different + + + align:start position:0% +architecture is a little bit different +and how to take advantage of that + + align:start position:0% +and how to take advantage of that + + + align:start position:0% +and how to take advantage of that +differences generate the right code + + align:start position:0% +differences generate the right code + + + align:start position:0% +differences generate the right code +generate optimal code stuff like that + + align:start position:0% +generate optimal code stuff like that + + + align:start position:0% +generate optimal code stuff like that +and in here we learned a lot about that. + + align:start position:0% +and in here we learned a lot about that. + + + align:start position:0% +and in here we learned a lot about that. +uh uh we learned about intermediate + + align:start position:0% +uh uh we learned about intermediate + + + align:start position:0% +uh uh we learned about intermediate +representations + + align:start position:0% +representations + + + align:start position:0% +representations +uh doing lot of different optimizations + + align:start position:0% +uh doing lot of different optimizations + + + align:start position:0% +uh doing lot of different optimizations +uh things like issues like assembly + + align:start position:0% +uh things like issues like assembly + + + align:start position:0% +uh things like issues like assembly +interfaces register allocation issues + + align:start position:0% +interfaces register allocation issues + + + align:start position:0% +interfaces register allocation issues +code scheduling issues calling + + align:start position:0% +code scheduling issues calling + + + align:start position:0% +code scheduling issues calling +conventions stuff like that all those + + align:start position:0% +conventions stuff like that all those + + + align:start position:0% +conventions stuff like that all those +things come into play so this I I think + + align:start position:0% +things come into play so this I I think + + + align:start position:0% +things come into play so this I I think +interesting what do we have to do + + align:start position:0% + + + + align:start position:0% + +uh so all those interesting comes I I + + align:start position:0% +uh so all those interesting comes I I + + + align:start position:0% +uh so all those interesting comes I I +think there's a lot that you guys + + align:start position:0% +think there's a lot that you guys + + + align:start position:0% +think there's a lot that you guys +learned here and then finally + + align:start position:0% +learned here and then finally + + + align:start position:0% +learned here and then finally +If you are not sick of compilers by now, + + align:start position:0% +If you are not sick of compilers by now, + + + align:start position:0% +If you are not sick of compilers by now, +some of you might decided to actually + + align:start position:0% +some of you might decided to actually + + + align:start position:0% +some of you might decided to actually +become a true compiler hacker. Compiler + + align:start position:0% +become a true compiler hacker. Compiler + + + align:start position:0% +become a true compiler hacker. Compiler +is a very interesting field. It + + align:start position:0% +is a very interesting field. It + + + align:start position:0% +is a very interesting field. It +combines things like theory. lot of + + align:start position:0% +combines things like theory. lot of + + + align:start position:0% +combines things like theory. lot of +things you do things like uh if you look + + align:start position:0% +things you do things like uh if you look + + + align:start position:0% +things you do things like uh if you look +at lexical analysis passing uh uh data + + align:start position:0% +at lexical analysis passing uh uh data + + + align:start position:0% +at lexical analysis passing uh uh data +there's lot of very serious theory + + align:start position:0% +there's lot of very serious theory + + + align:start position:0% +there's lot of very serious theory +behind + + align:start position:0% +behind + + + align:start position:0% +behind +it and there's a lot of algorithms + + align:start position:0% +it and there's a lot of algorithms + + + align:start position:0% +it and there's a lot of algorithms +because everything in compiler is + + align:start position:0% +because everything in compiler is + + + align:start position:0% +because everything in compiler is +basically from algorithmic + + align:start position:0% +basically from algorithmic + + + align:start position:0% +basically from algorithmic +transformation and also the other aspect + + align:start position:0% +transformation and also the other aspect + + + align:start position:0% +transformation and also the other aspect +compilers is probably one of the most + + align:start position:0% +compilers is probably one of the most + + + align:start position:0% +compilers is probably one of the most +complex piece of code that you have to + + align:start position:0% +complex piece of code that you have to + + + align:start position:0% +complex piece of code that you have to +implement so there's a huge amount of + + align:start position:0% +implement so there's a huge amount of + + + align:start position:0% +implement so there's a huge amount of +implementation system aspect of it so it + + align:start position:0% +implementation system aspect of it so it + + + align:start position:0% +implementation system aspect of it so it +really spans the entire spectrum in + + align:start position:0% + + + + align:start position:0% + +Yeah, in theory what we do is basically + + align:start position:0% +Yeah, in theory what we do is basically + + + align:start position:0% +Yeah, in theory what we do is basically +we have to do develop these general + + align:start position:0% +we have to do develop these general + + + align:start position:0% +we have to do develop these general +abstract concepts uh and things like + + align:start position:0% +abstract concepts uh and things like + + + align:start position:0% +abstract concepts uh and things like +prove correctness, prove optimality. I + + align:start position:0% +prove correctness, prove optimality. I + + + align:start position:0% +prove correctness, prove optimality. I +mean for example uh uh interesting thing + + align:start position:0% +mean for example uh uh interesting thing + + + align:start position:0% +mean for example uh uh interesting thing +about something like Java these days. So + + align:start position:0% +about something like Java these days. So + + + align:start position:0% +about something like Java these days. So +when you get a Java piece of code and + + align:start position:0% +when you get a Java piece of code and + + + align:start position:0% +when you get a Java piece of code and +and and and you're running it, the + + align:start position:0% +and and and you're running it, the + + + align:start position:0% +and and and you're running it, the +people working on saying can you + + align:start position:0% +people working on saying can you + + + align:start position:0% +people working on saying can you +actually prove things about it. So + + align:start position:0% +actually prove things about it. So + + + align:start position:0% +actually prove things about it. So +instead of blindly run it, I I I you + + align:start position:0% +instead of blindly run it, I I I you + + + align:start position:0% +instead of blindly run it, I I I you +give me a proof that I can actually + + align:start position:0% +give me a proof that I can actually + + + align:start position:0% +give me a proof that I can actually +verify that in fact it's not going to do + + align:start position:0% +verify that in fact it's not going to do + + + align:start position:0% +verify that in fact it's not going to do +a bad thing. How do you do that? Okay, + + align:start position:0% +a bad thing. How do you do that? Okay, + + + align:start position:0% +a bad thing. How do you do that? Okay, +that thing called what's called proof + + align:start position:0% +that thing called what's called proof + + + align:start position:0% +that thing called what's called proof +carrying code. So code comes with a + + align:start position:0% +carrying code. So code comes with a + + + align:start position:0% +carrying code. So code comes with a +proof of its goodness. It says I will + + align:start position:0% +proof of its goodness. It says I will + + + align:start position:0% +proof of its goodness. It says I will +give you these guarantees and here's a + + align:start position:0% +give you these guarantees and here's a + + + align:start position:0% +give you these guarantees and here's a +proof and you can go and verify. So + + align:start position:0% +proof and you can go and verify. So + + + align:start position:0% +proof and you can go and verify. So +there are a lot of those kind of things + + align:start position:0% +there are a lot of those kind of things + + + align:start position:0% +there are a lot of those kind of things +very theoretical aspect for that. And + + align:start position:0% +very theoretical aspect for that. And + + + align:start position:0% +very theoretical aspect for that. And +also programming languages also people + + align:start position:0% +also programming languages also people + + + align:start position:0% +also programming languages also people +are exploring lot of different ways. I + + align:start position:0% +are exploring lot of different ways. I + + + align:start position:0% +are exploring lot of different ways. I +mean we are used to this imperative + + align:start position:0% +mean we are used to this imperative + + + align:start position:0% +mean we are used to this imperative +paradigm but there are object-oriented + + align:start position:0% +paradigm but there are object-oriented + + + align:start position:0% +paradigm but there are object-oriented +programming logic programming very + + align:start position:0% +programming logic programming very + + + align:start position:0% +programming logic programming very +different paradigms to think okay it's + + align:start position:0% +different paradigms to think okay it's + + + align:start position:0% +different paradigms to think okay it's +like I think one kind of touches some of + + align:start position:0% +like I think one kind of touches some of + + + align:start position:0% +like I think one kind of touches some of +it so what has it been like the very + + align:start position:0% +it so what has it been like the very + + + align:start position:0% +it so what has it been like the very +abstract concept of programming and lot + + align:start position:0% +abstract concept of programming and lot + + + align:start position:0% +abstract concept of programming and lot +of these come in this theory and here's + + align:start position:0% +of these come in this theory and here's + + + align:start position:0% +of these come in this theory and here's +some example past theory and we talked + + align:start position:0% +some example past theory and we talked + + + align:start position:0% +some example past theory and we talked +about latises in data flow there are a + + align:start position:0% +about latises in data flow there are a + + + align:start position:0% +about latises in data flow there are a +lot of theory behind it uh in + + align:start position:0% +lot of theory behind it uh in + + + align:start position:0% +lot of theory behind it uh in +programming language there are people + + align:start position:0% +programming language there are people + + + align:start position:0% +programming language there are people +doing languages just to evaluate this + + align:start position:0% +doing languages just to evaluate this + + + align:start position:0% +doing languages just to evaluate this +space in there. + + align:start position:0% + + + + align:start position:0% + +algorithms and most of the uh things + + align:start position:0% +algorithms and most of the uh things + + + align:start position:0% +algorithms and most of the uh things +we've learned has huge amount of + + align:start position:0% +we've learned has huge amount of + + + align:start position:0% +we've learned has huge amount of +algorithms and most transformation you + + align:start position:0% +algorithms and most transformation you + + + align:start position:0% +algorithms and most transformation you +have you want to do something and you + + align:start position:0% +have you want to do something and you + + + align:start position:0% +have you want to do something and you +need to have algorithmic solution do do + + align:start position:0% +need to have algorithmic solution do do + + + align:start position:0% +need to have algorithmic solution do do +that and think in we use things from all + + align:start position:0% +that and think in we use things from all + + + align:start position:0% +that and think in we use things from all +over the place graph theory number + + align:start position:0% +over the place graph theory number + + + align:start position:0% +over the place graph theory number +theory many different aspects come in + + align:start position:0% +theory many different aspects come in + + + align:start position:0% +theory many different aspects come in +optimization theory all those things + + align:start position:0% +optimization theory all those things + + + align:start position:0% +optimization theory all those things +come in in in doing lot of compile + + align:start position:0% +come in in in doing lot of compile + + + align:start position:0% +come in in in doing lot of compile +transformation and also there's another + + align:start position:0% +transformation and also there's another + + + align:start position:0% +transformation and also there's another +aspect of it lot of times lot of + + align:start position:0% +aspect of it lot of times lot of + + + align:start position:0% +aspect of it lot of times lot of +transformations her huristics because + + align:start position:0% +transformations her huristics because + + + align:start position:0% +transformations her huristics because +the the theoretical solution is too + + align:start position:0% +the the theoretical solution is too + + + align:start position:0% +the the theoretical solution is too +complicated. So people come up with + + align:start position:0% +complicated. So people come up with + + + align:start position:0% +complicated. So people come up with +huristics. So so there's a lot of + + align:start position:0% +huristics. So so there's a lot of + + + align:start position:0% +huristics. So so there's a lot of +algorithmic aspect and also lot of + + align:start position:0% +algorithmic aspect and also lot of + + + align:start position:0% +algorithmic aspect and also lot of +huristic development aspect. So there + + align:start position:0% +huristic development aspect. So there + + + align:start position:0% +huristic development aspect. So there +are there's huge range in here for + + align:start position:0% +are there's huge range in here for + + + align:start position:0% +are there's huge range in here for +people who are there are a lot of good + + align:start position:0% +people who are there are a lot of good + + + align:start position:0% +people who are there are a lot of good +compiler people who are really good + + align:start position:0% +compiler people who are really good + + + align:start position:0% +compiler people who are really good +algorithms + + align:start position:0% +algorithms + + + align:start position:0% +algorithms +people. Things like uh uh one recent + + align:start position:0% +people. Things like uh uh one recent + + + align:start position:0% +people. Things like uh uh one recent +optimization people have been working is + + align:start position:0% +optimization people have been working is + + + align:start position:0% +optimization people have been working is +called partial redundancy elimination. + + align:start position:0% +called partial redundancy elimination. + + + align:start position:0% +called partial redundancy elimination. +It's like combination of things like + + align:start position:0% +It's like combination of things like + + + align:start position:0% +It's like combination of things like +dead code elimination and and constant + + align:start position:0% +dead code elimination and and constant + + + align:start position:0% +dead code elimination and and constant +propagation and common sub expression + + align:start position:0% +propagation and common sub expression + + + align:start position:0% +propagation and common sub expression +elimination. Can you combine all those + + align:start position:0% +elimination. Can you combine all those + + + align:start position:0% +elimination. Can you combine all those +into one? Uh registation by graph + + align:start position:0% +into one? Uh registation by graph + + + align:start position:0% +into one? Uh registation by graph +coloring. So yes take abstract problem + + align:start position:0% +coloring. So yes take abstract problem + + + align:start position:0% +coloring. So yes take abstract problem +mapping to re really concrete + + align:start position:0% +mapping to re really concrete + + + align:start position:0% +mapping to re really concrete +algorithm things like most of the + + align:start position:0% +algorithm things like most of the + + + align:start position:0% +algorithm things like most of the +architectures have this multimedia + + align:start position:0% +architectures have this multimedia + + + align:start position:0% +architectures have this multimedia +instructions. How do you take advantage? + + align:start position:0% +instructions. How do you take advantage? + + + align:start position:0% +instructions. How do you take advantage? +How do you compile to that? There are a + + align:start position:0% +How do you compile to that? There are a + + + align:start position:0% +How do you compile to that? There are a +lot of algorithms behind doing things + + align:start position:0% +lot of algorithms behind doing things + + + align:start position:0% +lot of algorithms behind doing things +like that. Come up with a compiler to + + align:start position:0% +like that. Come up with a compiler to + + + align:start position:0% +like that. Come up with a compiler to +this + + align:start position:0% + + + + align:start position:0% + +automatically. And finally + + align:start position:0% +automatically. And finally + + + align:start position:0% +automatically. And finally +implementation compilers are probably + + align:start position:0% +implementation compilers are probably + + + align:start position:0% +implementation compilers are probably +one of the most complex pieces of + + align:start position:0% +one of the most complex pieces of + + + align:start position:0% +one of the most complex pieces of +software out there. I I was fond of + + align:start position:0% +software out there. I I was fond of + + + align:start position:0% +software out there. I I was fond of +saying for a long time one only saving + + align:start position:0% +saying for a long time one only saving + + + align:start position:0% +saying for a long time one only saving +grace for compilers is it's + + align:start position:0% +grace for compilers is it's + + + align:start position:0% +grace for compilers is it's +deterministic for example operating + + align:start position:0% +deterministic for example operating + + + align:start position:0% +deterministic for example operating +system deterministic but JIT compilers + + align:start position:0% +system deterministic but JIT compilers + + + align:start position:0% +system deterministic but JIT compilers +just completely threw that out + + align:start position:0% +just completely threw that out + + + align:start position:0% +just completely threw that out +basically. Now you compilers they are + + align:start position:0% +basically. Now you compilers they are + + + align:start position:0% +basically. Now you compilers they are +not even deterministic. So so so it's + + align:start position:0% +not even deterministic. So so so it's + + + align:start position:0% +not even deterministic. So so so it's +complex and it used to be deterministic. + + align:start position:0% +complex and it used to be deterministic. + + + align:start position:0% +complex and it used to be deterministic. +You can replay things and get the same + + align:start position:0% +You can replay things and get the same + + + align:start position:0% +You can replay things and get the same +results. But JIT compilers that entire + + align:start position:0% +results. But JIT compilers that entire + + + align:start position:0% +results. But JIT compilers that entire +concept is gone and and and so it's so + + align:start position:0% +concept is gone and and and so it's so + + + align:start position:0% +concept is gone and and and so it's so +we are + + align:start position:0% +we are + + + align:start position:0% +we are +basically every problem of developing a + + align:start position:0% +basically every problem of developing a + + + align:start position:0% +basically every problem of developing a +large piece of software is in here and + + align:start position:0% +large piece of software is in here and + + + align:start position:0% +large piece of software is in here and +and any reasonable compiler has probably + + align:start position:0% +and any reasonable compiler has probably + + + align:start position:0% +and any reasonable compiler has probably +millions of lines of code and the worst + + align:start position:0% +millions of lines of code and the worst + + + align:start position:0% +millions of lines of code and the worst +is most of other for operating system + + align:start position:0% +is most of other for operating system + + + align:start position:0% +is most of other for operating system +comes in nice modules. Compilers a lot + + align:start position:0% +comes in nice modules. Compilers a lot + + + align:start position:0% +comes in nice modules. Compilers a lot +of times one gigantic big beast. It just + + align:start position:0% +of times one gigantic big beast. It just + + + align:start position:0% +of times one gigantic big beast. It just +all has to work with a very much more + + align:start position:0% +all has to work with a very much more + + + align:start position:0% +all has to work with a very much more +closer approximation than because + + align:start position:0% +closer approximation than because + + + align:start position:0% +closer approximation than because +because in operating system there are + + align:start position:0% +because in operating system there are + + + align:start position:0% +because in operating system there are +very well definfined interfaces. + + align:start position:0% +very well definfined interfaces. + + + align:start position:0% +very well definfined interfaces. +Compilers very hard it's same piece of + + align:start position:0% +Compilers very hard it's same piece of + + + align:start position:0% +Compilers very hard it's same piece of +infra code that we have keep working on. + + align:start position:0% +infra code that we have keep working on. + + + align:start position:0% +infra code that we have keep working on. +So compilers in some sense uh has a huge + + align:start position:0% +So compilers in some sense uh has a huge + + + align:start position:0% +So compilers in some sense uh has a huge +systems problem in here. Git compilers + + align:start position:0% +systems problem in here. Git compilers + + + align:start position:0% +systems problem in here. Git compilers +uh + + align:start position:0% +uh + + + align:start position:0% +uh +compiler uh entire uh in I used to say + + align:start position:0% +compiler uh entire uh in I used to say + + + align:start position:0% +compiler uh entire uh in I used to say +one thing I I say is uh the most + + align:start position:0% +one thing I I say is uh the most + + + align:start position:0% +one thing I I say is uh the most +lucrative compiler uh uh business in + + align:start position:0% +lucrative compiler uh uh business in + + + align:start position:0% +lucrative compiler uh uh business in +industry is actually all the databases. + + align:start position:0% +industry is actually all the databases. + + + align:start position:0% +industry is actually all the databases. +What's a database? It's basically big + + align:start position:0% +What's a database? It's basically big + + + align:start position:0% +What's a database? It's basically big +query optimization engine and also + + align:start position:0% +query optimization engine and also + + + align:start position:0% +query optimization engine and also +there's some operating system aspect of + + align:start position:0% +there's some operating system aspect of + + + align:start position:0% +there's some operating system aspect of +it to get + + align:start position:0% +it to get + + + align:start position:0% +it to get +uh consistency persistency and and there + + align:start position:0% +uh consistency persistency and and there + + + align:start position:0% +uh consistency persistency and and there +are a lot of things you have to get but + + align:start position:0% +are a lot of things you have to get but + + + align:start position:0% +are a lot of things you have to get but +one large aspect is a query optimization + + align:start position:0% +one large aspect is a query optimization + + + align:start position:0% +one large aspect is a query optimization +so so there it's a compiler a lot of if + + align:start position:0% +so so there it's a compiler a lot of if + + + align:start position:0% +so so there it's a compiler a lot of if +you go to Oracle it's a large group of + + align:start position:0% +you go to Oracle it's a large group of + + + align:start position:0% +you go to Oracle it's a large group of +compiler type people working on on that + + align:start position:0% +compiler type people working on on that + + + align:start position:0% +compiler type people working on on that +uh postcript rasterizer it's a + + align:start position:0% +uh postcript rasterizer it's a + + + align:start position:0% +uh postcript rasterizer it's a +compiler I mean every HP printer + + align:start position:0% +compiler I mean every HP printer + + + align:start position:0% +compiler I mean every HP printer +division has bunch of compiler guys + + align:start position:0% +division has bunch of compiler guys + + + align:start position:0% +division has bunch of compiler guys +trying to figure out what's the best way + + align:start position:0% +trying to figure out what's the best way + + + align:start position:0% +trying to figure out what's the best way +to get from postcript raster right it's + + align:start position:0% +to get from postcript raster right it's + + + align:start position:0% +to get from postcript raster right it's +a compile file so there are a lot of + + align:start position:0% +a compile file so there are a lot of + + + align:start position:0% +a compile file so there are a lot of +places XML passing XML processing lot of + + align:start position:0% +places XML passing XML processing lot of + + + align:start position:0% +places XML passing XML processing lot of +things have very compile oriented things + + align:start position:0% +things have very compile oriented things + + + align:start position:0% +things have very compile oriented things +so if thinking like a compiler hacker is + + align:start position:0% +so if thinking like a compiler hacker is + + + align:start position:0% +so if thinking like a compiler hacker is +very interesting in these + + align:start position:0% +very interesting in these + + + align:start position:0% +very interesting in these +things + + align:start position:0% +things + + + align:start position:0% +things +so to be a compile hacker what do you + + align:start position:0% +so to be a compile hacker what do you + + + align:start position:0% +so to be a compile hacker what do you +learn in 6035 basically learn everything + + align:start position:0% +learn in 6035 basically learn everything + + + align:start position:0% +learn in 6035 basically learn everything +I everything we did is also like put in + + align:start position:0% +I everything we did is also like put in + + + align:start position:0% +I everything we did is also like put in +in this mind + + align:start position:0% +in this mind + + + align:start position:0% +in this mind +frame + + align:start position:0% + + + + align:start position:0% + +so Yeah, I have about 10 minutes before + + align:start position:0% +so Yeah, I have about 10 minutes before + + + align:start position:0% +so Yeah, I have about 10 minutes before +we do the HCAN review and in that 10 + + align:start position:0% +we do the HCAN review and in that 10 + + + align:start position:0% +we do the HCAN review and in that 10 +minutes I want to just switch gears a + + align:start position:0% +minutes I want to just switch gears a + + + align:start position:0% +minutes I want to just switch gears a +little bit and talk about current + + align:start position:0% +little bit and talk about current + + + align:start position:0% +little bit and talk about current +compiler research. So this is not going + + align:start position:0% +compiler research. So this is not going + + + align:start position:0% +compiler research. So this is not going +to be in the test. So don't worry about + + align:start position:0% +to be in the test. So don't worry about + + + align:start position:0% +to be in the test. So don't worry about +it and then don't have more. So I will + + align:start position:0% +it and then don't have more. So I will + + + align:start position:0% +it and then don't have more. So I will +go through something very far. So one + + align:start position:0% +go through something very far. So one + + + align:start position:0% +go through something very far. So one +thing I did was if you're interested I + + align:start position:0% +thing I did was if you're interested I + + + align:start position:0% +thing I did was if you're interested I +added a list of places where you find + + align:start position:0% +added a list of places where you find + + + align:start position:0% +added a list of places where you find +the most up-to-date compiler work. uh + + align:start position:0% +the most up-to-date compiler work. uh + + + align:start position:0% +the most up-to-date compiler work. uh +most of them are in conference + + align:start position:0% +most of them are in conference + + + align:start position:0% +most of them are in conference +proceedings because we most compiler + + align:start position:0% +proceedings because we most compiler + + + align:start position:0% +proceedings because we most compiler +people don't publish in journals with + + align:start position:0% +people don't publish in journals with + + + align:start position:0% +people don't publish in journals with +some areas it's all journals and I + + align:start position:0% +some areas it's all journals and I + + + align:start position:0% +some areas it's all journals and I +listed different proceedings so if you + + align:start position:0% +listed different proceedings so if you + + + align:start position:0% +listed different proceedings so if you +are really interested you can some of + + align:start position:0% +are really interested you can some of + + + align:start position:0% +are really interested you can some of +these journals are available on the web + + align:start position:0% +these journals are available on the web + + + align:start position:0% +these journals are available on the web +you can search for it I can look look it + + align:start position:0% +you can search for it I can look look it + + + align:start position:0% +you can search for it I can look look it +up uh this is not exhaustive list and + + align:start position:0% +up uh this is not exhaustive list and + + + align:start position:0% +up uh this is not exhaustive list and +this is some and and depending on where + + align:start position:0% +this is some and and depending on where + + + align:start position:0% +this is some and and depending on where +you emphasis there are it's a very broad + + align:start position:0% +you emphasis there are it's a very broad + + + align:start position:0% +you emphasis there are it's a very broad +field there are many many other + + align:start position:0% +field there are many many other + + + align:start position:0% +field there are many many other +conferences and and uh journals and and + + align:start position:0% +conferences and and uh journals and and + + + align:start position:0% +conferences and and uh journals and and +and places but but but here's a subset + + align:start position:0% +and places but but but here's a subset + + + align:start position:0% +and places but but but here's a subset +So what I want to do is switch from + + align:start position:0% + + + + align:start position:0% + +uh doing a class to give you a feel for + + align:start position:0% +uh doing a class to give you a feel for + + + align:start position:0% +uh doing a class to give you a feel for +what's happening at research. So I'm + + align:start position:0% +what's happening at research. So I'm + + + align:start position:0% +what's happening at research. So I'm +going to talk about a project that I'm + + align:start position:0% +going to talk about a project that I'm + + + align:start position:0% +going to talk about a project that I'm +doing in my group. There are a bunch of + + align:start position:0% +doing in my group. There are a bunch of + + + align:start position:0% +doing in my group. There are a bunch of +people out there uh sitting up there + + align:start position:0% +people out there uh sitting up there + + + align:start position:0% +people out there uh sitting up there +actually working on this project. So so + + align:start position:0% +actually working on this project. So so + + + align:start position:0% +actually working on this project. So so +I give you a very quick glimpse of what + + align:start position:0% +I give you a very quick glimpse of what + + + align:start position:0% +I give you a very quick glimpse of what +it's like. So one thing I'm building in + + align:start position:0% +it's like. So one thing I'm building in + + + align:start position:0% +it's like. So one thing I'm building in +my group that that's really exciting + + align:start position:0% +my group that that's really exciting + + + align:start position:0% +my group that that's really exciting +thing is this new uh language and + + align:start position:0% +thing is this new uh language and + + + align:start position:0% +thing is this new uh language and +compiler for streaming domain streaming + + align:start position:0% +compiler for streaming domain streaming + + + align:start position:0% +compiler for streaming domain streaming +means everything that from audio video + + align:start position:0% +means everything that from audio video + + + align:start position:0% +means everything that from audio video +everything in cell phone lot of + + align:start position:0% +everything in cell phone lot of + + + align:start position:0% +everything in cell phone lot of +applications today have data streaming + + align:start position:0% +applications today have data streaming + + + align:start position:0% +applications today have data streaming +through that and how do we actually + + align:start position:0% +through that and how do we actually + + + align:start position:0% +through that and how do we actually +program that so we have a language + + align:start position:0% +program that so we have a language + + + align:start position:0% +program that so we have a language +called stream it and it provides a very + + align:start position:0% +called stream it and it provides a very + + + align:start position:0% +called stream it and it provides a very +high level abstraction uh for streams. + + align:start position:0% +high level abstraction uh for streams. + + + align:start position:0% +high level abstraction uh for streams. +So lot of interesting thing that that + + align:start position:0% +So lot of interesting thing that that + + + align:start position:0% +So lot of interesting thing that that +draw drove us was most these streaming + + align:start position:0% +draw drove us was most these streaming + + + align:start position:0% +draw drove us was most these streaming +applications are written in nice blocks + + align:start position:0% +applications are written in nice blocks + + + align:start position:0% +applications are written in nice blocks +saying the block does something feed + + align:start position:0% +saying the block does something feed + + + align:start position:0% +saying the block does something feed +data to the next block and if you look + + align:start position:0% +data to the next block and if you look + + + align:start position:0% +data to the next block and if you look +at if you look at a DSP class it's all + + align:start position:0% +at if you look at a DSP class it's all + + + align:start position:0% +at if you look at a DSP class it's all +in block diagrams and the minute you + + align:start position:0% +in block diagrams and the minute you + + + align:start position:0% +in block diagrams and the minute you +write C the entire blocks vanishes all + + align:start position:0% +write C the entire blocks vanishes all + + + align:start position:0% +write C the entire blocks vanishes all +over the place and then it's a very ugly + + align:start position:0% +over the place and then it's a very ugly + + + align:start position:0% +over the place and then it's a very ugly +mess of C and so you figure out okay how + + align:start position:0% +mess of C and so you figure out okay how + + + align:start position:0% +mess of C and so you figure out okay how +can you actually have a language that + + align:start position:0% +can you actually have a language that + + + align:start position:0% +can you actually have a language that +you actually have that representation + + align:start position:0% +you actually have that representation + + + align:start position:0% +you actually have that representation +so another thing is minute you go into + + align:start position:0% +so another thing is minute you go into + + + align:start position:0% +so another thing is minute you go into +language like C + + align:start position:0% +language like C + + + align:start position:0% +language like C +uh those language is very hard to + + align:start position:0% +uh those language is very hard to + + + align:start position:0% +uh those language is very hard to +analyze because everything in single + + align:start position:0% +analyze because everything in single + + + align:start position:0% +analyze because everything in single +memory everything in single control flow + + align:start position:0% +memory everything in single control flow + + + align:start position:0% +memory everything in single control flow +all the nice representation is gone. So + + align:start position:0% +all the nice representation is gone. So + + + align:start position:0% +all the nice representation is gone. So +in this language what we have done is + + align:start position:0% +in this language what we have done is + + + align:start position:0% +in this language what we have done is +create a still maintain the that + + align:start position:0% +create a still maintain the that + + + align:start position:0% +create a still maintain the that +representation that gives us a nice uh + + align:start position:0% +representation that gives us a nice uh + + + align:start position:0% +representation that gives us a nice uh +ability to do a bunch of analysis and + + align:start position:0% +ability to do a bunch of analysis and + + + align:start position:0% +ability to do a bunch of analysis and +then we build a compiler that to + + align:start position:0% +then we build a compiler that to + + + align:start position:0% +then we build a compiler that to +understand all those uh things and + + align:start position:0% +understand all those uh things and + + + align:start position:0% +understand all those uh things and +actually can do really cool amount of + + align:start position:0% +actually can do really cool amount of + + + align:start position:0% +actually can do really cool amount of +transformation. So let me give you a + + align:start position:0% +transformation. So let me give you a + + + align:start position:0% +transformation. So let me give you a +little bit of a view of the language. + + align:start position:0% +little bit of a view of the language. + + + align:start position:0% +little bit of a view of the language. +It's kind of like Java. Uh so here's a + + align:start position:0% +It's kind of like Java. Uh so here's a + + + align:start position:0% +It's kind of like Java. Uh so here's a +filter. Here's a compute unit and it has + + align:start position:0% +filter. Here's a compute unit and it has + + + align:start position:0% +filter. Here's a compute unit and it has +uh what we call init function where when + + align:start position:0% +uh what we call init function where when + + + align:start position:0% +uh what we call init function where when +the filter starts it just calculates + + align:start position:0% +the filter starts it just calculates + + + align:start position:0% +the filter starts it just calculates +some local ones and then there's a thing + + align:start position:0% +some local ones and then there's a thing + + + align:start position:0% +some local ones and then there's a thing +called a work function that keep + + align:start position:0% +called a work function that keep + + + align:start position:0% +called a work function that keep +executing + + align:start position:0% +executing + + + align:start position:0% +executing +forever. So so what happens is there + + align:start position:0% +forever. So so what happens is there + + + align:start position:0% +forever. So so what happens is there +input data coming this work functions is + + align:start position:0% +input data coming this work functions is + + + align:start position:0% +input data coming this work functions is +I look at two peak two I take remove one + + align:start position:0% +I look at two peak two I take remove one + + + align:start position:0% +I look at two peak two I take remove one +from the input and put put produce one + + align:start position:0% +from the input and put put produce one + + + align:start position:0% +from the input and put put produce one +into the output. So every every + + align:start position:0% +into the output. So every every + + + align:start position:0% +into the output. So every every +invocation of that I look at two + + align:start position:0% +invocation of that I look at two + + + align:start position:0% +invocation of that I look at two +elements I produce one and consume one + + align:start position:0% +elements I produce one and consume one + + + align:start position:0% +elements I produce one and consume one +and the next invocation I will go up. So + + align:start position:0% +and the next invocation I will go up. So + + + align:start position:0% +and the next invocation I will go up. So +I keep doing this forever and so that's + + align:start position:0% +I keep doing this forever and so that's + + + align:start position:0% +I keep doing this forever and so that's +very representative of of of lot of + + align:start position:0% +very representative of of of lot of + + + align:start position:0% +very representative of of of lot of +stream calculation because same thing + + align:start position:0% +stream calculation because same thing + + + align:start position:0% +stream calculation because same thing +keep happening forever. So this is only + + align:start position:0% +keep happening forever. So this is only + + + align:start position:0% +keep happening forever. So this is only +one filter and then you can combine + + align:start position:0% +one filter and then you can combine + + + align:start position:0% +one filter and then you can combine +these filters from pipelines in parallel + + align:start position:0% +these filters from pipelines in parallel + + + align:start position:0% +these filters from pipelines in parallel +some for what what you call split joints + + align:start position:0% +some for what what you call split joints + + + align:start position:0% +some for what what you call split joints +and then there are a feedback loops and + + align:start position:0% +and then there are a feedback loops and + + + align:start position:0% +and then there are a feedback loops and +they have feedback. So by doing this you + + align:start position:0% +they have feedback. So by doing this you + + + align:start position:0% +they have feedback. So by doing this you +can build this very complex higher uh + + align:start position:0% +can build this very complex higher uh + + + align:start position:0% +can build this very complex higher uh +larger graphs. So here's a very simple + + align:start position:0% +larger graphs. So here's a very simple + + + align:start position:0% +larger graphs. So here's a very simple +uh uh streamit program. Uh the only + + align:start position:0% +uh uh streamit program. Uh the only + + + align:start position:0% +uh uh streamit program. Uh the only +thing to observe here the important + + align:start position:0% +thing to observe here the important + + + align:start position:0% +thing to observe here the important +thing is you have this graph + + align:start position:0% +thing is you have this graph + + + align:start position:0% +thing is you have this graph +representation and a text representation + + align:start position:0% +representation and a text representation + + + align:start position:0% +representation and a text representation +we almost one to one. You can look at a + + align:start position:0% +we almost one to one. You can look at a + + + align:start position:0% +we almost one to one. You can look at a +text and almost imagine what the graph + + align:start position:0% +text and almost imagine what the graph + + + align:start position:0% +text and almost imagine what the graph +is like. And what it says is is you + + align:start position:0% +is like. And what it says is is you + + + align:start position:0% +is like. And what it says is is you +build this graph and you instantiating + + align:start position:0% +build this graph and you instantiating + + + align:start position:0% +build this graph and you instantiating +these nodes into the graph and then then + + align:start position:0% +these nodes into the graph and then then + + + align:start position:0% +these nodes into the graph and then then +after this this program basically will + + align:start position:0% +after this this program basically will + + + align:start position:0% +after this this program basically will +build the graph and then when it say run + + align:start position:0% +build the graph and then when it say run + + + align:start position:0% +build the graph and then when it say run +it keep running forever. So it's not + + align:start position:0% +it keep running forever. So it's not + + + align:start position:0% +it keep running forever. So it's not +what what this program does is running + + align:start position:0% +what what this program does is running + + + align:start position:0% +what what this program does is running +of this program basically builds this + + align:start position:0% +of this program basically builds this + + + align:start position:0% +of this program basically builds this +entire graph and and you can build very + + align:start position:0% +entire graph and and you can build very + + + align:start position:0% +entire graph and and you can build very +large graph. So there are some examples + + align:start position:0% +large graph. So there are some examples + + + align:start position:0% +large graph. So there are some examples +of a graph of a FM + + align:start position:0% +of a graph of a FM + + + align:start position:0% +of a graph of a FM +radio that basically process a separate + + align:start position:0% +radio that basically process a separate + + + align:start position:0% +radio that basically process a separate +amplitude and frequency of voice and do + + align:start position:0% +amplitude and frequency of voice and do + + + align:start position:0% +amplitude and frequency of voice and do +different processing in there. Uh + + align:start position:0% +different processing in there. Uh + + + align:start position:0% +different processing in there. Uh +there's a GSM decoder in in a cell + + align:start position:0% +there's a GSM decoder in in a cell + + + align:start position:0% +there's a GSM decoder in in a cell +phone. So this complicated graphs each + + align:start position:0% +phone. So this complicated graphs each + + + align:start position:0% +phone. So this complicated graphs each +node is doing bunch of computation. + + align:start position:0% +node is doing bunch of computation. + + + align:start position:0% +node is doing bunch of computation. +uh this is 3G uh uh this next uh phone + + align:start position:0% +uh this is 3G uh uh this next uh phone + + + align:start position:0% +uh this is 3G uh uh this next uh phone +uh in there and so so we can build this + + align:start position:0% +uh in there and so so we can build this + + + align:start position:0% +uh in there and so so we can build this +graph. So the next thing I want to do is + + align:start position:0% +graph. So the next thing I want to do is + + + align:start position:0% +graph. So the next thing I want to do is +talk about some kind kind of + + align:start position:0% +talk about some kind kind of + + + align:start position:0% +talk about some kind kind of +optimization we can do that. So lot of + + align:start position:0% +optimization we can do that. So lot of + + + align:start position:0% +optimization we can do that. So lot of +these are for DSP applications. So one + + align:start position:0% +these are for DSP applications. So one + + + align:start position:0% +these are for DSP applications. So one +thing we compilers do is we basically + + align:start position:0% +thing we compilers do is we basically + + + align:start position:0% +thing we compilers do is we basically +look at what people do by hand and + + align:start position:0% +look at what people do by hand and + + + align:start position:0% +look at what people do by hand and +automate it. So what a good compiler did + + align:start position:0% +automate it. So what a good compiler did + + + align:start position:0% +automate it. So what a good compiler did +look at what assembly program is going + + align:start position:0% +look at what assembly program is going + + + align:start position:0% +look at what assembly program is going +to do by hand trying to abstract it out + + align:start position:0% +to do by hand trying to abstract it out + + + align:start position:0% +to do by hand trying to abstract it out +and automate it. So in here what we did + + align:start position:0% +and automate it. So in here what we did + + + align:start position:0% +and automate it. So in here what we did +was we looked at what DSP engineers do + + align:start position:0% +was we looked at what DSP engineers do + + + align:start position:0% +was we looked at what DSP engineers do +by hand and try to automate it. So one + + align:start position:0% +by hand and try to automate it. So one + + + align:start position:0% +by hand and try to automate it. So one +thing is DSP look at is what we call + + align:start position:0% +thing is DSP look at is what we call + + + align:start position:0% +thing is DSP look at is what we call +linear state space filters. These are + + align:start position:0% +linear state space filters. These are + + + align:start position:0% +linear state space filters. These are +the ones that are input are basically + + align:start position:0% +the ones that are input are basically + + + align:start position:0% +the ones that are input are basically +linear functions or outputs are linear + + align:start position:0% +linear functions or outputs are linear + + + align:start position:0% +linear functions or outputs are linear +function of inputs and some kind of + + align:start position:0% +function of inputs and some kind of + + + align:start position:0% +function of inputs and some kind of +internal state and the state also keeps + + align:start position:0% +internal state and the state also keeps + + + align:start position:0% +internal state and the state also keeps +changing from a linear function. So in + + align:start position:0% +changing from a linear function. So in + + + align:start position:0% +changing from a linear function. So in +in the DSP committee there's a lot of + + align:start position:0% +in the DSP committee there's a lot of + + + align:start position:0% +in the DSP committee there's a lot of +math around it and what we try to do is + + align:start position:0% +math around it and what we try to do is + + + align:start position:0% +math around it and what we try to do is +come up with a way to automate that. So + + align:start position:0% +come up with a way to automate that. So + + + align:start position:0% +come up with a way to automate that. So +uh many DSP filters programs fit into + + align:start position:0% +uh many DSP filters programs fit into + + + align:start position:0% +uh many DSP filters programs fit into +this + + align:start position:0% +this + + + align:start position:0% +this +category. So what that means is each + + align:start position:0% +category. So what that means is each + + + align:start position:0% +category. So what that means is each +block is represented by if you have + + align:start position:0% +block is represented by if you have + + + align:start position:0% +block is represented by if you have +input coming in and some local state and + + align:start position:0% +input coming in and some local state and + + + align:start position:0% +input coming in and some local state and +out uh local state is updated using the + + align:start position:0% +out uh local state is updated using the + + + align:start position:0% +out uh local state is updated using the +inputs and the previous state and output + + align:start position:0% +inputs and the previous state and output + + + align:start position:0% +inputs and the previous state and output +is also calculated using the inputs and + + align:start position:0% +is also calculated using the inputs and + + + align:start position:0% +is also calculated using the inputs and +the state and you have some matrices A B + + align:start position:0% +the state and you have some matrices A B + + + align:start position:0% +the state and you have some matrices A B +C D defining what's going on. + + align:start position:0% +C D defining what's going on. + + + align:start position:0% +C D defining what's going on. +So interesting thing here is assume you + + align:start position:0% +So interesting thing here is assume you + + + align:start position:0% +So interesting thing here is assume you +have a program uh in there uh we came up + + align:start position:0% +have a program uh in there uh we came up + + + align:start position:0% +have a program uh in there uh we came up +with uh uh here's a representation of + + align:start position:0% +with uh uh here's a representation of + + + align:start position:0% +with uh uh here's a representation of +that program in this space. So a b c d + + align:start position:0% +that program in this space. So a b c d + + + align:start position:0% +that program in this space. So a b c d +you have some concrete uh values in here + + align:start position:0% +you have some concrete uh values in here + + + align:start position:0% +you have some concrete uh values in here +and we came up with the linear data flow + + align:start position:0% +and we came up with the linear data flow + + + align:start position:0% +and we came up with the linear data flow +analysis to look at the program and get + + align:start position:0% +analysis to look at the program and get + + + align:start position:0% +analysis to look at the program and get +to the right. So you write somebody + + align:start position:0% +to the right. So you write somebody + + + align:start position:0% +to the right. So you write somebody +write this something looking like that + + align:start position:0% +write this something looking like that + + + align:start position:0% +write this something looking like that +left and we automatically do the data + + align:start position:0% +left and we automatically do the data + + + align:start position:0% +left and we automatically do the data +flow analysis and you can easily build + + align:start position:0% +flow analysis and you can easily build + + + align:start position:0% +flow analysis and you can easily build +the data flow equations and do that and + + align:start position:0% +the data flow equations and do that and + + + align:start position:0% +the data flow equations and do that and +we end up in the in this right. So the + + align:start position:0% +we end up in the in this right. So the + + + align:start position:0% +we end up in the in this right. So the +nice thing is now when we get to this + + align:start position:0% +nice thing is now when we get to this + + + align:start position:0% +nice thing is now when we get to this +representation so you you have learned + + align:start position:0% +representation so you you have learned + + + align:start position:0% +representation so you you have learned +different representation we learned one + + align:start position:0% +different representation we learned one + + + align:start position:0% +different representation we learned one +representation in this program in this + + align:start position:0% +representation in this program in this + + + align:start position:0% +representation in this program in this +class and here we have using a different + + align:start position:0% +class and here we have using a different + + + align:start position:0% +class and here we have using a different +intermediate representation it's + + align:start position:0% +intermediate representation it's + + + align:start position:0% +intermediate representation it's +basically four matrices representing + + align:start position:0% +basically four matrices representing + + + align:start position:0% +basically four matrices representing +each of these filters and the nice thing + + align:start position:0% +each of these filters and the nice thing + + + align:start position:0% +each of these filters and the nice thing +about that is when you have that you can + + align:start position:0% +about that is when you have that you can + + + align:start position:0% +about that is when you have that you can +do lot of interesting optimizations + + align:start position:0% +do lot of interesting optimizations + + + align:start position:0% +do lot of interesting optimizations +using those represent that + + align:start position:0% +using those represent that + + + align:start position:0% +using those represent that +representation I will show one and show + + align:start position:0% +representation I will show one and show + + + align:start position:0% +representation I will show one and show +results for uh two others so one thing + + align:start position:0% +results for uh two others so one thing + + + align:start position:0% +results for uh two others so one thing +you can do is combine adjacent filters + + align:start position:0% +you can do is combine adjacent filters + + + align:start position:0% +you can do is combine adjacent filters +so as Assume the filter one is to + + align:start position:0% +so as Assume the filter one is to + + + align:start position:0% +so as Assume the filter one is to +simplify only use D. So output for the + + align:start position:0% +simplify only use D. So output for the + + + align:start position:0% +simplify only use D. So output for the +first filter output is matrix multiplied + + align:start position:0% +first filter output is matrix multiplied + + + align:start position:0% +first filter output is matrix multiplied +by the input and the second filter has + + align:start position:0% +by the input and the second filter has + + + align:start position:0% +by the input and the second filter has +the same thing. One thing we can do is + + align:start position:0% +the same thing. One thing we can do is + + + align:start position:0% +the same thing. One thing we can do is +the so the output of both is D2 * D1* U + + align:start position:0% +the so the output of both is D2 * D1* U + + + align:start position:0% +the so the output of both is D2 * D1* U +and you can calculate this air priority + + align:start position:0% +and you can calculate this air priority + + + align:start position:0% +and you can calculate this air priority +at compile time and come up with a + + align:start position:0% +at compile time and come up with a + + + align:start position:0% +at compile time and come up with a +combined filter. Basically just do that. + + align:start position:0% +combined filter. Basically just do that. + + + align:start position:0% +combined filter. Basically just do that. +So instead of doing these two matrix + + align:start position:0% +So instead of doing these two matrix + + + align:start position:0% +So instead of doing these two matrix +separate things, I can just do a matrix + + align:start position:0% +separate things, I can just do a matrix + + + align:start position:0% +separate things, I can just do a matrix +multiplication because D1 and D2 are + + align:start position:0% +multiplication because D1 and D2 are + + + align:start position:0% +multiplication because D1 and D2 are +basically constants. It's in the program + + align:start position:0% +basically constants. It's in the program + + + align:start position:0% +basically constants. It's in the program +and I will do that matrix multiplication + + align:start position:0% +and I will do that matrix multiplication + + + align:start position:0% +and I will do that matrix multiplication +once and do that. So nice thing about + + align:start position:0% +once and do that. So nice thing about + + + align:start position:0% +once and do that. So nice thing about +here is so if you have these two filters + + align:start position:0% +here is so if you have these two filters + + + align:start position:0% +here is so if you have these two filters +like that and I can come up with this + + align:start position:0% +like that and I can come up with this + + + align:start position:0% +like that and I can come up with this +combined filter and in the first one uh + + align:start position:0% +combined filter and in the first one uh + + + align:start position:0% +combined filter and in the first one uh +for each output you can have to do eight + + align:start position:0% +for each output you can have to do eight + + + align:start position:0% +for each output you can have to do eight +floatingoint operations to get the + + align:start position:0% +floatingoint operations to get the + + + align:start position:0% +floatingoint operations to get the +output. In the second one you only need + + align:start position:0% +output. In the second one you only need + + + align:start position:0% +output. In the second one you only need +to do six operations because some of + + align:start position:0% +to do six operations because some of + + + align:start position:0% +to do six operations because some of +them are done once at the compile time. + + align:start position:0% +them are done once at the compile time. + + + align:start position:0% +them are done once at the compile time. +So I reduce the amount of operations you + + align:start position:0% +So I reduce the amount of operations you + + + align:start position:0% +So I reduce the amount of operations you +need to do. So by doing that I can + + align:start position:0% +need to do. So by doing that I can + + + align:start position:0% +need to do. So by doing that I can +really eliminate a lot of computation. + + align:start position:0% +really eliminate a lot of computation. + + + align:start position:0% +really eliminate a lot of computation. +So this is interesting + + align:start position:0% +So this is interesting + + + align:start position:0% +So this is interesting +optimization and the uh and actually if + + align:start position:0% +optimization and the uh and actually if + + + align:start position:0% +optimization and the uh and actually if +you do lot the the first decimator + + align:start position:0% +you do lot the the first decimator + + + align:start position:0% +you do lot the the first decimator +basically eliminates one value. So it's + + align:start position:0% +basically eliminates one value. So it's + + + align:start position:0% +basically eliminates one value. So it's +only looking at one result. If the + + align:start position:0% +only looking at one result. If the + + + align:start position:0% +only looking at one result. If the +decimate eliminate lot of values and + + align:start position:0% +decimate eliminate lot of values and + + + align:start position:0% +decimate eliminate lot of values and +only look at because lot of times in DSP + + align:start position:0% +only look at because lot of times in DSP + + + align:start position:0% +only look at because lot of times in DSP +that's what you do. You down sample you + + align:start position:0% +that's what you do. You down sample you + + + align:start position:0% +that's what you do. You down sample you +only look at every 100th value. If you + + align:start position:0% +only look at every 100th value. If you + + + align:start position:0% +only look at every 100th value. If you +go you can almost eliminate 75% of all + + align:start position:0% +go you can almost eliminate 75% of all + + + align:start position:0% +go you can almost eliminate 75% of all +the computation of them. So so need so + + align:start position:0% +the computation of them. So so need so + + + align:start position:0% +the computation of them. So so need so +you can do optimization you get rid of + + align:start position:0% +you can do optimization you get rid of + + + align:start position:0% +you can do optimization you get rid of +huge amount of computation. So in fact + + align:start position:0% +huge amount of computation. So in fact + + + align:start position:0% +huge amount of computation. So in fact +for bunch of programs we looked at so + + align:start position:0% +for bunch of programs we looked at so + + + align:start position:0% +for bunch of programs we looked at so +the first line is show uh the yellow uh + + align:start position:0% +the first line is show uh the yellow uh + + + align:start position:0% +the first line is show uh the yellow uh +the light uh uh blue line shows what we + + align:start position:0% +the light uh uh blue line shows what we + + + align:start position:0% +the light uh uh blue line shows what we +the results of the optimization I talk + + align:start position:0% +the results of the optimization I talk + + + align:start position:0% +the results of the optimization I talk +about. So most times you can eliminate + + align:start position:0% +about. So most times you can eliminate + + + align:start position:0% +about. So most times you can eliminate +80% of the computation. So 80% is huge + + align:start position:0% +80% of the computation. So 80% is huge + + + align:start position:0% +80% of the computation. So 80% is huge +basically at the end of the huge most of + + align:start position:0% +basically at the end of the huge most of + + + align:start position:0% +basically at the end of the huge most of +the computation is gone. So there are + + align:start position:0% +the computation is gone. So there are + + + align:start position:0% +the computation is gone. So there are +two other optimizations we did. The + + align:start position:0% +two other optimizations we did. The + + + align:start position:0% +two other optimizations we did. The +second one here is basically lot of in + + align:start position:0% +second one here is basically lot of in + + + align:start position:0% +second one here is basically lot of in +DSP people go from fre time time domain + + align:start position:0% +DSP people go from fre time time domain + + + align:start position:0% +DSP people go from fre time time domain +to frequency domain manually. We said + + align:start position:0% +to frequency domain manually. We said + + + align:start position:0% +to frequency domain manually. We said +why don't we do it auto why do you + + align:start position:0% +why don't we do it auto why do you + + + align:start position:0% +why don't we do it auto why do you +automate that? So we look at the program + + align:start position:0% +automate that? So we look at the program + + + align:start position:0% +automate that? So we look at the program +and said aha instead of doing all this + + align:start position:0% +and said aha instead of doing all this + + + align:start position:0% +and said aha instead of doing all this +thing in time domain we'll automatically + + align:start position:0% +thing in time domain we'll automatically + + + align:start position:0% +thing in time domain we'll automatically +go to frequency domain do a simplified + + align:start position:0% +go to frequency domain do a simplified + + + align:start position:0% +go to frequency domain do a simplified +calculation and come back to time domain + + align:start position:0% +calculation and come back to time domain + + + align:start position:0% +calculation and come back to time domain +and and it's a very very tedious process + + align:start position:0% +and and it's a very very tedious process + + + align:start position:0% +and and it's a very very tedious process +to do it manually because lot of these + + align:start position:0% +to do it manually because lot of these + + + align:start position:0% +to do it manually because lot of these +matrices has to be transformed lot of + + align:start position:0% +matrices has to be transformed lot of + + + align:start position:0% +matrices has to be transformed lot of +weird end conditions has to be met. It's + + align:start position:0% +weird end conditions has to be met. It's + + + align:start position:0% +weird end conditions has to be met. It's +all done automatically nicely in the + + align:start position:0% +all done automatically nicely in the + + + align:start position:0% +all done automatically nicely in the +compiler and and we get a huge amount of + + align:start position:0% +compiler and and we get a huge amount of + + + align:start position:0% +compiler and and we get a huge amount of +benefit and then we actually have a a + + align:start position:0% +benefit and then we actually have a a + + + align:start position:0% +benefit and then we actually have a a +programming we have algorithm to select + + align:start position:0% +programming we have algorithm to select + + + align:start position:0% +programming we have algorithm to select +what's the best transformations to do + + align:start position:0% +what's the best transformations to do + + + align:start position:0% +what's the best transformations to do +and get a good very good performance + + align:start position:0% +and get a good very good performance + + + align:start position:0% +and get a good very good performance +boost. So here are the kind of things we + + align:start position:0% +boost. So here are the kind of things we + + + align:start position:0% +boost. So here are the kind of things we +do today. So for this very high level + + align:start position:0% +do today. So for this very high level + + + align:start position:0% +do today. So for this very high level +new domain, we are building a compiler + + align:start position:0% +new domain, we are building a compiler + + + align:start position:0% +new domain, we are building a compiler +that basically trying to automate the + + align:start position:0% +that basically trying to automate the + + + align:start position:0% +that basically trying to automate the +DSP engineer because right now this is + + align:start position:0% +DSP engineer because right now this is + + + align:start position:0% +DSP engineer because right now this is +all done by some guy by hand uh uh + + align:start position:0% +all done by some guy by hand uh uh + + + align:start position:0% +all done by some guy by hand uh uh +basically for each algorithm. So we are + + align:start position:0% +basically for each algorithm. So we are + + + align:start position:0% +basically for each algorithm. So we are +trying to automate + + align:start position:0% +trying to automate + + + align:start position:0% +trying to automate +that. So this kind of gives you a feel + + align:start position:0% +that. So this kind of gives you a feel + + + align:start position:0% +that. So this kind of gives you a feel +for what goes uh few flows up here. Uh + + align:start position:0% +for what goes uh few flows up here. Uh + + + align:start position:0% +for what goes uh few flows up here. Uh +there are some people here who are uh + + align:start position:0% +there are some people here who are uh + + + align:start position:0% +there are some people here who are uh +basically working on these pro projects + + align:start position:0% +basically working on these pro projects + + + align:start position:0% +basically working on these pro projects +as Europs and if anybody else is + + align:start position:0% +as Europs and if anybody else is + + + align:start position:0% +as Europs and if anybody else is +interested in working in these kind of + + align:start position:0% +interested in working in these kind of + + + align:start position:0% +interested in working in these kind of +projects as Europs at some point uh + + align:start position:0% +projects as Europs at some point uh + + + align:start position:0% +projects as Europs at some point uh +uh send me mail. \ No newline at end of file diff --git a/wFP5VHGHFdk.txt b/wFP5VHGHFdk.txt new file mode 100644 index 0000000000000000000000000000000000000000..ba299687fad1d1b5e4de29be80b92cb0f7e4e1c7 --- /dev/null +++ b/wFP5VHGHFdk.txt @@ -0,0 +1,3521 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of +MIT courses, visit + +MIT OpenCourseWare +at ocw.mit.edu + +PROFESSOR: How about +I propose this? + +We go through +knapsack because it's + +on the Pset, not knapsack +but a variation of it. + +If we have time, we do +a couple variations. + +If not, maybe not. + +And if we have time, +we do at a distance. + +Let's see what happens +after knapsack. + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: How many +people got the difference + +between polynomial +and pseudo polynomial? + +OK, so we should +definitely do knapsack. + +AUDIENCE: Constant +factors, they don't matter. + +Oh wait. [INAUDIBLE]. + +Yeah, they do. + +PROFESSOR: So the thing is +it's not constant factors. + +That s there is not a constant. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So the +knapsack problem. + +So the way I look at it. + +You're a thief. + +You somehow made your +way into a vault. + +That vault has n items. + +AUDIENCE: Way +better than camping. + +PROFESSOR: Each item has +a weight of si pounds, + +and after you get +out of the vault, + +assuming you make it +alive and everything, + +you can sell it for vi +dollars on the market, + +so this is how much money +you get out of it, vi. + +Well, now the problem is the +only thing you have with you + +as you enter that vault +is one knapsack that + +can carry at most s pounds. + +If you try to put +more stuff in it, + +so if you try to load it +up with more than s pounds, + +it's going to break as you +try to escape from the vault + +and stuff is going +to fall on the floor, + +and then many laser beams +will shred you to pieces, + +so that's undesirable. + +So we can only load the +knapsack with s pounds. + +Now, given this +restriction, we want + +to make as much +money as possible + +out of the whole +thing, so we want + +to load up the +knapsack optimally. + +Does this make sense? + +Everyone remembers? + +Good. + +So two ways to solve it, +graphs and dynamic programming. + +We're going to do both. + +Who wants to go +for graphs first? + +Who wants-- OK, never mind. + +Majority has been achieved. + +How do we represent this? + +First off, let's +represent the solution. + +Our solution is which +items we chose, right? + +So we can phrase +this as n decisions. + +Each decision is a +true/false decision, + +and it indicates if you take +that item with you or not. + +So di says, do I take item i? + +So now this looks +more like a game. + +You are on a TV, +there's a game show, + +and you get asked n questions. + +Do you want to take this +item with you, yes or no? + +If you somehow +manage to get items + +that are more than s +pounds heavy, you get shot, + +you don't make it to +the end of the game. + +Otherwise, when +you leave the game, + +you make some +money and the money + +that you make depends on +what items you took with you. + +So now this looks +like the game problems + +that we used to solve with +graphs in that you have + +decisions, those +decisions are moves, + +and they get you through +a graph of states. + +Now, let's see +what's in the state. + +What do we need +to keep track of? + +First, we need to keep track of +what item we're thinking about, + +right? + +And then there's something else +that we need to keep track of. + +AUDIENCE: How much +capacity we have. + +PROFESSOR: Yep, very good. + +So the reason I +need that is when + +I'm deciding whether I'm +taking an item or not, + +I want to know if I'm +going to get shot or not. + +If I take too much stuff, +I'm not going to make it, + +so I need to know if this item +fits in my backpack or not. + +That's equivalent to knowing +how much weight I have left. + +So s pounds. + +Let's say this is +capacity, how much weight + +left in my backpack's capacity. + +This is equivalent to how much +weight I have accumulated, + +the total weight of my items. + +Weight of the items +I have taken so far. + +So the sum of the weights +of the taken items. + +AUDIENCE: [INAUDIBLE] left. + +Isn't it the total minus? + +PROFESSOR: Well, I'm +saying they're equivalent, + +so if you know one, you +can compute the other. + +They're not equal. + +Knowing one lets you +know the other one, + +but this is more useful in terms +of putting the graph together, + +I claim. + +We'll see if that +is true or not as we + +try to put the graph together. + +So what's a node? + +What's an edge? + +AUDIENCE: An edge is +putting in one more item, + +and a node is a state. + +PROFESSOR: So what the weight +going to be on an edge? + +If the edge means +I'm taking an item, + +then the weight is +going to be what? + +AUDIENCE: The weight of +the item you're adding. + +AUDIENCE: The earning +associated with that. + +PROFESSOR: Yeah. + +I like this better +because in the end, + +my goal is to maximize +earnings, right? + +And I'm going to feed my graph +to a shortest path algorithm. + +Maximize earnings, +minimize path weight. + +They're the same +issue, flip sign. + +So I'm going to say this is +the value of the item almost. + +Does this work or not? + +Negative value of the item. + +I have to flip the sign to turn +it from a maximization problem + +to a minimization problem. + +So shortest path will +give me the shortest path. + +That's going to correspond +to making the least + +amount of money if I +don't add this minus sign. + +So what's a node? + +AUDIENCE: Is it a +unique set of items? + +PROFESSOR: Sorry? + +AUDIENCE: A unique set of items. + +PROFESSOR: OK. + +So the state in a +node is going to have + +i, which is the item that I'm +looking at, because this way, + +I'm going to have one +node for each item. + +And what else did I say +I need to keep track of? + +AUDIENCE: The weight +of the taken items. + +PROFESSOR: Yep. + +Weight of taken. + +So this is sort of +like the gas problem + +where you have to keep track +of how much gas you have + +as well as where +you are on the map. + +Sorry if it brings bad memories. + +Let's talk about an example so +that we can draw a graph for it + +and see what things look like. + +So say we have three +items, and say our backpack + +has five pounds. + +And my three items +are a golden statue, + +value $10, weight, four pounds. + +These are 1800 dollars +when money actually + +used to be worth something. + +Crystal ball, you +can sell this for $4, + +and it weighs two pounds, and +someone in the previous section + +wanted a fountain +pen, so we're going + +to use a fountain +pen that's worth $7. + +Culture is worth a +lot of money, right? + +And weighs three pounds. + +Really ancient fountain pen. + +I don't know how +people wrote with it. + +So how do we draw +the graph for this? + +AUDIENCE: We'd make a tree +where each level the tree + +is take item i, or +don't take item i. + +Make a big binary tree. + +Does that make sense? + +PROFESSOR: So if each +level of the tree + +says whether I'm +taking an item or not, + +and then I have two +descendants, then that's + +going to be 2 to +the number of items. + +So that's going +to be exponential + +in the number of +items, whereas we're + +going to end up in a solution +where the running time is + +proportional to the +number of items. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I mean, it +makes sense in some cases, + +if you have fractional +costs or something. + +By the way, all these +weights are integers. + +Sorry I didn't mention that. + +My bad. + +But I like the idea of having +some sort of levels based + +on items, so let's say I'm +going to have a starting node, + +and then I'm going to have some +sort of layer for item one, + +some sort of layer for item +two, and some sort of layer + +for item three, some +sort of vertical layer. + +How many nodes do +I have in a layer? + +One node for each +possible weight + +because I promised that in a +node, I keep track of the item + +that I'm considering and +the weight of the items I've + +taken so far. + +How many possible +weights do I have here? + +AUDIENCE: Three weights. + +PROFESSOR: So my backpack +holds five pounds, so what + +are the possible sums I can get? + +How many? + +AUDIENCE: 4, 2, 3, 5. + +PROFESSOR: So far, I +heard 2 3, 4, 5, 6. + +Who wants to bid more? + +AUDIENCE: Not more than 6. + +PROFESSOR: So the +answer is 6, right? + +The possible weights are from +0, which is an empty knapsack, + +until weight 5, which +is a full knapsack. + +So weight 0, 1, 2, +3, 4, 5, 6, and I'm + +going to start +drawing the nodes. + +AUDIENCE: You could +have weight 10. + +PROFESSOR: We're +never going to fill up + +a knapsack with more than 5. + +Otherwise, we're going to die. + +AUDIENCE: Why do +we have 6, then? + +PROFESSOR: Because +I can't thank. + +Thank you. + +So this node, the first node. + +Weight in the backpack, 0. + +We're looking at item one. + +It's connected to +the starting node. + +What outgoing edges do I have? + +What do I do with item one? + +I can take it or not take it. + +AUDIENCE: You connect +the edges 4, 2, 3. + +Am I answering a +different question? + +AUDIENCE: If it's item one, +shouldn't it have a weight? + +PROFESSOR: So those have two +numbers in them, i and j. + +Sorry. + +They're in the wrong order here. + +1, 0. + +So I'm looking at item one. + +So far, I have zero +pounds in my backpack. + +Looking at item two with zero +pounds, looking at item three + +with zero pounds. + +Looking at item one with +one pound in my backpack, + +item two with one pound, +item three with one pound, + +so on and so forth. + +So if I'm looking +at item one, and I + +have zero pounds in my backpack +so far, what happens if I don't + +take item one? + +Where do I end up? + +AUDIENCE: 2, 0. + +PROFESSOR: Yeah. + +So I'm looking at item two +after I'm done deciding, + +what do I do with item one, +and if I don't take item one, + +then I'm not going to have +anything in my backpack. + +So this edge corresponds +to we don't just take one. + +What if I want to take item one? + +Where do I land? + +AUDIENCE: 2, 4. + +PROFESSOR: All right. + +2, 3. + +2, 4. + +So if I did take +item one, then I + +had zero pounds in +my backpack before. + +Now I have four pounds, and +I'm still considering item two. + +What about edge weights? + +What's the weight +of the edge that + +says I don't take item one? + +What's the weight of the edge +that says I do take item one? + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: Minus 10. + +PROFESSOR: All right. + +0 and minus 10. + +That minus lets us +get the shortest path. + +Now, suppose I'm in 2, 0. + +What are the outgoing edges? + +AUDIENCE: It's the same as +making a giant binary tree, + +right? + +PROFESSOR: It's not going +to be a tree because I + +can have multiple paths +from a root to some node. + +AUDIENCE: But this looks like +it's taking the same complexity + +as building a tree if you were +to carefully build the tree so + +that you don't have unfeasible +solutions on the tree. + +PROFESSOR: Then you're actually +doing dynamic programming. + +You're not building the +tree if you're doing that. + +You're still converging to this. + +You're probably thinking +this and you said binary + +decision tree, or at least +that's what I understood. + +You're probably thinking +of the right thing. + +We can see if we're thinking +the same thing when we end up + +looking at the running time. + +Yes? + +AUDIENCE: The goal here is to +have the most valuable items + +possible in the bag +in terms of money? + +PROFESSOR: Yeah. + +PROFESSOR: So the +negative 10 weight + +that you have there was +because that item was $10. + +PROFESSOR: Yep. + +And in the end, we're going to +give the graph to the shortest + +path algorithm. + +So yes, speaking of the +goal, what's the answer here, + +by the way? + +AUDIENCE: 11. + +PROFESSOR: 11. + +How do I get 11? + +AUDIENCE: By getting +the last two items. + +PROFESSOR: So I take +the ball and the pen + +and I get 11, right? + +Everyone on the same page? + +So I'm at item two. + +I have zero pounds +in my backpack. + +What are my outgoing edges? + +AUDIENCE: To 3, 0 and to 3, 2. + +Wait, sorry. + +That's the third item. + +PROFESSOR: No, second item. + +You're good. + +AUDIENCE: Shouldn't it be +3, 3 because the third item + +has three pounds? + +PROFESSOR: I said I'm +looking at the second item + +and then I'm deciding +where I'm going. + +So this graph has +a problem in that + +when I get to the third +item, what do I do? + +So I need one more layer here, +which means that I'm done. + +AUDIENCE: I was saying that it's +the outgoing edge from 2, 0, + +it's the weight +of the taken item, + +so if you decide to +take the third item, + +shouldn't the outgoing +edge go to 3, 3, not 3, 2? + +PROFESSOR: But when +I'm at layer two, + +I'm only looking at item two. + +So I'm looking at the +items in sequence. + +First I have to decide, +am I taking item one? + +Then I decide, am I taking item +two, and then I'm deciding, + +am I taking item three? + +While I'm here, I +don't see item three. + +I only see item two. + +AUDIENCE: Aren't those weights +on the left side, though? + +PROFESSOR: Yeah. + +These are backpack weights. + +So down here, these are +pounds and these are items. + +What are the weights +on the edges? + +0 and negative 1. + +PROFESSOR: OK. + +How about this other node, 2, 4? + +What are the edges +coming out of it. + +AUDIENCE: 2, 0. + +AUDIENCE: 3, 4. + +PROFESSOR: So if I decide I'm +not going to take item two, + +but I already have four +pounds in my backpack, + +I'm still going to end up with +four pounds in my backpack, + +and I don't get +anything out of it. + +And? + +AUDIENCE: That's it. + +PROFESSOR: And that's +it, because if I + +try to take the second item, +that would put me overweight, + +so the edge would +go out of the graph. + +Therefore, it doesn't exist. + +AUDIENCE: You can remove it, +and then you go back to 3, 0, + +right? + +Is that not allowed? + +PROFESSOR: No, +because when I'm here, + +I don't know how I got here. + +I don't know if I +had item one or not. + +The benefits of doing +it this way is here, + +I'm just looking at item two. + +I do not know how I got there. + +I do not care what +I'm going to do later. + +I'm just looking at +one item and making + +one decision based on that. + +Does this make sense? + +Where do I get my answer from? + +AUDIENCE: Can you put a +final node on the right side? + +PROFESSOR: OK, so +one way of doing + +it is that I'm going to have +a final note on the right side + +and connecting everything to it. + +AUDIENCE: Do you need the +done nodes right there, + +or could you have just skipped +done and connected 3 to that? + +PROFESSOR: So I can +do that, but then it's + +going to be hard to +reason about edges. + +This makes it easier +to reason about edges + +because when I'm +looking at this layer, + +I'm still going to +have edges deciding + +whether I take +item three or not. + +So it would be confusing to +have all the edges pointing + +to the same place. + +I can, it's just that the graph +would look more confusing. + +By the way, if I'm at 3, 2, +what are the outgoing edges + +from 3, 2? + +AUDIENCE: It's just +all horizontal. + +You can't take anymore. + +PROFESSOR: So I can be +done with two pounds, + +and that means I +get 0 or I can take + +item three, and then +where do I land? + +AUDIENCE: Negative 7. + +PROFESSOR: Does this +make sense now somewhat? + +AUDIENCE: So what about this +dynamic programming style? + +PROFESSOR: We'll +get there in a bit. + +Before, let's see what's +the running time for this. + +So one way of +finishing this up is + +we connect everything +to one destination node. + +Another way of doing it is that +we connect the source nodes + +to everything here with +edges of cost 0 and say, + +well, this is how much +weight we're going to waste. + +So if my solution path +goes here and then goes + +somewhere through +the graph, it means + +that I'm going to waste +one pound of capacity, + +so my backpack is going to +have four pounds when I'm done. + +AUDIENCE: Would it be +[INAUDIBLE] or infinity? + +PROFESSOR: What +should the weight be? + +Good question. + +AUDIENCE: This is +not possible, right? + +To get from s to 1, 1. + +PROFESSOR: So I'm saying +that if I get from s to 1, 1, + +this means that I'm +wasting a pound. + +My backpack will have +four pounds of stuff + +and then one pound of +capacity will go to waste. + +AUDIENCE: Isn't +there another way + +to waste it on the right +side if you end at the top? + +Or not at the bottom, basically. + +PROFESSOR: Yeah. + +AUDIENCE: So you're +not double counting + +in terms of losing stuff? + +You're representing +losing weight + +on the left side +and the right side. + +PROFESSOR: Well, if I represent +losing weight on the left side, + +then the advantage is that I +have a single destination node. + +What is it? + +AUDIENCE: That dot. + +PROFESSOR: So this +is the source. + +The destination is this guy. + +I can waste capacity +here, so that + +means I can say +that on this side, + +I don't need to waste stuff. + +On this side, I need +to arrive at done 5. + +That's the advantage of doing +it this way, aside from the fact + +that it's going to map +to dynamic programming. + +There are many ways of doing it. + +I can choose to connect +the source to 1, 0, + +and then look at all the paths +here and choose the best one. + +I can connect the +source to everything + +here with paths of some +weight, which you guys still + +need to tell me what it is, and +then I can look at the answer + +here. + +AUDIENCE: Cost 0. + +PROFESSOR: Thank you. + +So this is another way. + +And yet the third way +would be to only connect + +the source to the +first node, and then + +connect all these done nodes +to another node with cost 0, + +and this is equivalent to this. + +The reason we're +doing it this way + +is because this maps +to dynamic programming. + +AUDIENCE: Easier. + +PROFESSOR: Yeah. + +It maps closely to +how the DP runs. + +AUDIENCE: I mean is it +possible to do the DP such + +that you do it the +other way as well? + +PROFESSOR: Yeah. + +You can flip the DP around, too. + +How are we doing with this? + +So then I hope the running time +analysis will go really fast. + +How many vertices? + +AUDIENCE: v or three. + +PROFESSOR: OK, so v is? + +AUDIENCE: ns. + +PROFESSOR: n layers, right? + +n plus 1 layers, actually. + +AUDIENCE: n times weight mass. + +PROFESSOR: n times +capacity, right? + +So it's actually n plus +1 times capacity plus 1, + +but I don't want +to deal with that, + +so I'm going to use +order of so that I + +don't have to deal with that. + +How many edges going +out of a vertex? + +AUDIENCE: Two. + +PROFESSOR: Yep. + +So at most, two +edges per vertex. + +So how many edges total? + +AUDIENCE: ns. + +PROFESSOR: What shortest path +algorithm am I going to use? + +AUDIENCE: Bellman-Ford. + +AUDIENCE: Topological sort BFS. + +PROFESSOR: I'm going to +choose the second one + +because it runs faster. + +So Bellman-Ford's running +time is V times E. + +If I use the DAG algorithm, that +means topological sort and then + +a DFS. + +That's V plus E. +So please, whenever + +you have a dynamic programming +graph, this is the answer. + +It's never anything else. + +It's never Dijkstra. + +It's never Bellman-Ford. + +It's always this. + +And this means? + +AUDIENCE: ns. + +PROFESSOR: So this +is the running time + +of the graph solution. + +AUDIENCE: If you +use BFS, do you need + +to put in the dummy nodes +for the edge weights? + +PROFESSOR: If you use BFS. + +Yes. + +So then the running time +would be bigger than V plus E. + +AUDIENCE: Right. + +So then the running time +depends on [INAUDIBLE] + +multiply by s again? + +PROFESSOR: This isn't doing BFS. + +This is doing the +shortest path algorithm + +for direct acyclic graphs. + +It's the DAG shortest path. + +AUDIENCE: Right. + +PROFESSOR: Were you here +before Thanksgiving? + +AUDIENCE: No + +PROFESSOR: Right before? + +You missed the algorithm. + +It's in the Dijkstra +lecture notes. + +AUDIENCE: But +basically, you don't + +have to put in all +the dummy nodes? + +PROFESSOR: No. + +So you do a topological +sort, and then + +you only consider a +node once, and you + +look at all the edges +coming through it + +and make a decision +based on that. + +So this is the running +time, this is the algorithm, + +this is the solution. + +What if we do dynamic +programming instead? + +Instead of nodes, we +have sub-problems. + +A sub-problem maps to a node. + +The same things that we +decided about this data + +that we store in a +node, the same things + +are going to apply to the state +that we have in a sub-problem. + +So what are the sub-problems? + +First up, how many sub-problems +am I going to have? + +AUDIENCE: n. + +AUDIENCE: ns. + +PROFESSOR: I just said +that one sub-problem + +will map to a +vertex in the graph. + +ns vertices, ns +sub-problems, right? + +Come on, guys. + +Bear with me. + +Get more cookies. + +Are the cookies still there? + +Please pass them +around and eat them. + +Yes? + +AUDIENCE: One sub-problem would +be getting the most amount + +of money for that little weight. + +At one pound [INAUDIBLE], +how much [INAUDIBLE]. + +PROFESSOR: I like that, +so let's start writing. + +What is the maximum value that I +can get using a certain weight? + +If I label the nodes +indices i, j, I'm + +also going to label the +sub-problems using i, j. + +So I'm going to say +that sub-problem i, j + +is, what's the maximum +amount of money + +I can get by using a +weight of at most j, + +and you said +something about items, + +so we have to figure +out which items. + +Which items? + +Anyone else can help her. + +You already did the +hard work, so you + +have most of the +stuff filled in. + +Feel free to jump in. + +AUDIENCE: Greater +than or equal to i. + +PROFESSOR: OK. + +Sounds good. + +We're going to number the +items starting from 0 this time + +because we're going to have +a dynamic programming table, + +and that means we like +zero base indexing. + +So the items are going +to be 0, 1, and 2. + +0 is the statue, 1 is the +ball, and 2 is the pen. + +This means we're going to +look at suffixes of items. + +First, the empty set, +no item, then only + +the pen, then the ball +and the pen, and then + +the statue, the +ball, and the pen. + +And we're also going to +consider how much weight we + +have in our backpack. + +So let me write this again. + +0, 1, 2 here, and weights +0, 1, 2, 3, 4, 5, and this + +is going to be our DP table. + +Now, how are we going +to compute this? + +DP of i, j is? + +AUDIENCE: Maximum. + +PROFESSOR: All right, +a maximum of something. + +Good. + +Perfect way to start. + +How many decisions do we have? + +AUDIENCE: Two. + +PROFESSOR: Two. + +It's the same as in the +graph problem, right? + +Once we solve that, this +should be pretty easy + +because it's really +very similar. + +So the two decisions +are, do I take item i, + +do I not take item i? + +If I don't take item i, +what situation do I land in? + +So suppose I don't take item i. + +AUDIENCE: i plus 1. + +PROFESSOR: OK. + +i plus 1. + +So I have to make up my +answer using items i plus 1 + +all the way through n minus +1, and how much weight + +do they have to have? + +AUDIENCE: j. + +PROFESSOR: Yep. + +Now suppose I do take item i. + +What happens? + +AUDIENCE: i plus-- no, no, no. + +PROFESSOR: You're thinking +of the right thing. + +We're making some money, right? + +AUDIENCE: Value i. + +PROFESSOR: Value i. + +So this is how much +money we're making. + +Good. + +AUDIENCE: Plus dp i +plus 1 j minus weight i. + +PROFESSOR: Make sense? + +OK Now I only have to do +one more thing to make sure + +this code doesn't crash. + +AUDIENCE: I'm sorry. + +What's the third term for? + +PROFESSOR: This is I'm +making some money, right? + +This means I'm going to +have to look at the items + +starting from i plus +1 and i minus 1. + +And now I took item +i, so that means + +I have si pounds in my backpack. + +So the remaining items must +weigh j minus si pounds + +because I'm going to add +the si pounds for this item, + +and in total, I'm going +to have at most j pounds. + +Make some money, +lose some capacity. + +AUDIENCE: Did we [INAUDIBLE]? + +PROFESSOR: Yep. + +This is what happens when +you move from the graph + +to dynamic +programming, or you can + +draw the graph the +other way around. + +AUDIENCE: So could you +have also done plus si, + +and then done +something else as well? + +PROFESSOR: Sorry. + +Plus si-- + +AUDIENCE: If you did +plus si and then you + +did some other check +case that was different. + +PROFESSOR: Well, I do +need to make a check. + +AUDIENCE: Yes. + +So that's greater +than or equal to 0. + +PROFESSOR: This thing, right? + +Because otherwise, the +code is going to crash. + +So j minus si is +greater or equal to 0. + +I think this means j is greater +than or equal to si, right? + +AUDIENCE: Yes. + +PROFESSOR: OK. + +At least for me, the natural +order when I have the graph + +is to consider the moves +that by making in the game. + +I'm answering the +questions one by one. + +Do I take this item? + +Do I not take this item? + +When I'm in the DP, +when I make a decision, + +I want to have the full +information on that decision. + +Whether I take the +item or not depends + +on what would happen with +the items following it. + +Representing it +this way allows me + +to make the decision right here. + +AUDIENCE: If we'd done +prefixes rather than suffixes, + +we could have done it the same. + +PROFESSOR: It would have been +exactly the same as there. + +So we taught dynamic +programming over many years, + +and it turns out that +people understand suffixes + +better than prefixes, +and the graph format + +makes more sense +that way, so that's + +why we're doing it this way. + +It's for your own sake. + +Trust me. + +Or at least we think so. + +AUDIENCE: Where +does suffix come in? + +I know what it means. + +PROFESSOR: These guys. + +These are the sub-problems. + +Nothing, item two, items +one, two, zero, one, two, + +so it's a suffix of +the set of items. + +AUDIENCE: How come you're going +backwards rather than forwards? + +It doesn't actually matter if +you go backwards or forwards? + +PROFESSOR: Yep. + +In the end, we're going +to look at everything. + +So we need two things. + +We need to know where is +the answer going to be, + +and we need to know what +are the initial conditions. + +Actually, I lied. + +We also need a topological sort. + +So where do we want to start? + +AUDIENCE: First one. + +PROFESSOR: Where is the answer? + +Yes? + +AUDIENCE: The lower +right hand corner. + +I mean, if you have all +the [INAUDIBLE] nodes. + +Oh, we don't have a +Done column, do we? + +PROFESSOR: No. + +Well, so the answer will have +considered all the items, + +right? + +AUDIENCE: Top left. + +PROFESSOR: So which i? + +Almost. + +So the top left corner means +I looked at all the items + +and I have an empty knapsack. + +AUDIENCE: Oh, so the max +of all of the first column. + +PROFESSOR: So the +max of all columns + +would be the answer if the +weight here would be equal, + +but I said the weight has +to be smaller or equal, + +so the answer is easier. + +I don't have to do a max. + +AUDIENCE: Bottom left corner. + +PROFESSOR: I can only look here. + +So this means that I will +use a weight of at most s, + +because this is s, and I +will have considered items 0 + +and larger, so all the items. + +This is where the answer is. + +And in general terms, that +means DP of what and what? + +So what's the +bottom left corner? + +AUDIENCE: 0, s. + +PROFESSOR: Yep. + +AUDIENCE: Can you explain again +why it needs to be DP 0, s. + +PROFESSOR: I think it's +easier to look at 0, + +s and see how it maps +to the sub-problem, + +and then convince yourself +that this is the answer, + +so let's do that. + +DP of 0, s means i is 0, j is s. + +So this is going +to tell me what is + +the maximum amount +of dollars I can + +get by using a weight +of at most s-- agrees + +with the initial problem-- +and using items i or greater + +than i, or 0 or more, so +items 0 through n minus 1. + +These are all the items. + +This is the maximum +capacity, so this maps + +to the initial problem. + +And that's why I did this. + +That's why I don't have +an equal sign here. + +AUDIENCE: And if you +did have an equal sign, + +then you would be changing +your sub-problems? + +PROFESSOR: The recursion +stays the same, + +but I have to look at all +these to get the maximum. + +Someone suggested that. + +AUDIENCE: If you +put an equals there, + +you're going to have to do +something to the DP such + +that the equals +actually is captivated, + +because you can't +just arbitrarily-- + +PROFESSOR: What do +you think of this? + +AUDIENCE: Something there is +going to change, isn't it? + +PROFESSOR: No. + +I think this works. + +This stays the same no +matter what the sign is. + +The only thing that changes +is where is the answer + +and what are the +initial conditions. + +AUDIENCE: Oh. + +So there's something +else that changes. + +PROFESSOR: Yep. + +Initial conditions. + +Good. + +I like that you're +thinking about that + +because the next problem +changes pretty much that. + +The sign changes and +then these change. + +What's a good topological sort? + +This should be pretty easy. + +If I want to generate +a topological sort, + +what variables do I iterate +over, and in what order? + +AUDIENCE: i. + +PROFESSOR: OK. + +And you're pointing at n, right? + +AUDIENCE: n down to 0. + +PROFESSOR: Yep. + +And then the only one left +is j, so i in, and then j + +goes from where to where? + +AUDIENCE: j goes to s. + +AUDIENCE: It can go +either direction. + +PROFESSOR: Can it? + +What do the +dependencies look like? + +When I'm computing i, j, I +want i plus 1 and j minus-- + +so I'm looking at lower j's, +higher i's and lower j's. + +AUDIENCE: But it's +always higher i's. + +Doesn't that mean +in this for loop + +that you're already going to +have calculated the next right + +column, so it +doesn't matter where + +the column-- I may be wrong. + +PROFESSOR: You're right. + +Fine. + +OK, both orders work. + +I just looked at +this because I wanted + +to have a nice, simple-- +but fine, both work. + +AUDIENCE: Wait. + +You mean reversing j works? + +PROFESSOR: Yes, because +we're iterating over i + +before iterating over j. + +Of course, this +makes more sense. + +Just because they're +both good answers + +doesn't mean you should +choose the one that + +requires more thinking. + +I always like the answer +that requires the least + +amount of thinking to +prove that it's correct. + +AUDIENCE: Does that mean +you're starting with a full-- + +PROFESSOR: I start here. + +AUDIENCE: But if you're +going from s down to 0, + +then you're starting +down at the corner, which + +means you have a full knapsack, +so that doesn't make sense. + +PROFESSOR: So the argument +was when I compute this, + +I'm looking one +right, i plus 1j, + +and then I'm looking +somewhere here. + +And I've already +computed this column, + +so it doesn't matter +if I go up or down. + +And that argument is +correct because first I'm + +going to compute this column, +then this column, then + +this column, then this column. + +By the way, what's this column? + +This column is the +initial condition. + +Now that we figured out +the topological sort, + +let's try to compute +values here and see + +what the initial +condition should be. + +So if I want to +compute DP of 2, 0, + +that is the maximum of either +DP 3, 0 or something else. + +This is going to +evaluate to false, + +so it's going to be this. + +What should the answer be here? + +AUDIENCE: 0. + +PROFESSOR: 0. + +So we want DP of 3, 0 to +be 0 for this to work. + +So what's a reasonable +initial condition? + +AUDIENCE: Column +3 is of 0 height. + +PROFESSOR: DP of +nj is 0 for all j, + +pretty much what you +said in math mode. + +So I'm going to have +an extra column. + +This is like the Done +problem over there, + +and here I'm going +to say that whenever + +I'm looking at +the empty subset-- + +these are all suffixes. + +All three items, two items, +one item, empty suffix. + +Whenever I look at +the empty suffix, + +I can fill up a backpack with +any weight by using no items, + +and I'm going to make 0 money. + +So what are the values here? + +You guys nodded, +so you understood, + +so then you should +be able to dictate + +the values in the table. + +AUDIENCE: So is that one also +0 because you can't go up + +to anything, and then the next +one is 4 because you can go-- + +PROFESSOR: Sorry. + +Next one is-- so it's for +the fountain pen, right? + +Last item. + +AUDIENCE: Crystal ball. + +PROFESSOR: So we're +going statute, ball, pen. + +AUDIENCE: And this is weight +on the left side, right? + +PROFESSOR: So we're +filling them like this + +in the topological sort +order that we chose here. + +We said this is +the order, so this + +is what we're going to use +to calculate the table. + +AUDIENCE: Oh. + +So it's still 0, then. + +PROFESSOR: OK. + +AUDIENCE: 7. + +PROFESSOR: So here, +this condition + +is going to evaluate +to True finally, + +so this is going to be the +maximum of either DP i plus 1j, + +so DP of 3, 3, which is +0, or 7 plus DP of 3, 0. + +So 7 plus 0, which is 7. + +That's why it's 7. + +AUDIENCE: 7, 7. + +PROFESSOR: 7, 7. + +How about this? + +AUDIENCE: 0. + +0. + +4. + +PROFESSOR: The maximum +of 0 and 4 plus 0, right? + +AUDIENCE: 4. + +AUDIENCE: No. + +7. + +PROFESSOR: So it's the maximum +of 7 or 4 plus 0, so this is 7. + +AUDIENCE: 7. + +11. + +PROFESSOR: 7 or 4 plus 7. + +Does this make +sense for everyone? + +Last column. + +Let's do it. + +AUDIENCE: 0. + +Feels like 0. + +0 again. + +Why not? + +4. + +How much does this thing weigh? + +AUDIENCE: 4. + +AUDIENCE: 7. + +10. + +PROFESSOR: Sorry +for my handwriting. + +AUDIENCE: And it needs +to be 11 because you + +said that'd be the answer. + +PROFESSOR: All right. + +So it's 11 because it's either +this guy or 10 plus DP of 1, 1. + +The first item +weighs 4, so I need + +to look one right and +four up when adding. + +Does this make sense? + +Please say yes. + +AUDIENCE: What's the +[INAUDIBLE] again? + +I get how if you're +looking horizontally, + +the top thing is the max. + +It's saying DP of i plus 1 j. + +PROFESSOR: So this is +looking horizontally, + +and this means I +did not take item i. + +AUDIENCE: You +didn't take item i, + +but if you are going to take +item i, you add the value of i, + +and then you look back +for DP of i plus 1, + +which is the previous column, +and the row number is whatever + +capacity you have left +if you did take it? + +PROFESSOR: Yep. + +AUDIENCE: And so in +the case of cell 1, + +3, if you took item one, then +capacity you'd have left is 3. + +PROFESSOR: Right. + +So you said total +capacity three, right? + +So if I take item one, how +many pounds does it have? + +AUDIENCE: It has four. + +PROFESSOR: Statue is +0, ball is 1, pen is 2. + +AUDIENCE: Oh. + +You're not using-- + +PROFESSOR: So I'm +using those items, + +but I'm starting using +zero based indexing. + +AUDIENCE: Yeah, but we're +going from here to here. + +So I'm saying if you pick +the middle cell that's + +1, 3, that one-- + +PROFESSOR: So this has item +one, so the ball, weight three. + +If I take the ball, how +much weight do I have left? + +AUDIENCE: The ball +weighs two pounds, + +so you'd have three +pounds left, and that's + +why you're in the three column. + +PROFESSOR: I have a +backpack of three pounds, + +and then I put a ball +of two pounds in it, + +and I have three pounds left? + +AUDIENCE: No, no, no. + +You have three pounds left if +you put a ball and two pounds + +in, right? + +PROFESSOR: I have a +backpack of three pounds. + +I put a ball of two pounds. + +How many pounds do I +have left of capacity? + +So backpack, three pounds total. + +I put a ball in +that has two pounds. + +How many pounds? + +AUDIENCE: We have none left. + +Oh, it can hold +three total pounds? + +PROFESSOR: Yeah. + +AUDIENCE: Then you +have one pound left. + +But we have a five +pound backpack. + +PROFESSOR: Well, you said +we were looking at 3, 1. + +You said we were looking here. + +AUDIENCE: Yeah, +we're looking there. + +PROFESSOR: So this means +three pound backpack, + +because the sub-problem says +your weight is at most j. + +AUDIENCE: Got it, OK. + +Oh, I see. + +So j minus si is saying-- + +PROFESSOR: It means you used up, +so you put up something there, + +so you ate some capacity. + +AUDIENCE: Well, you ate +only two pounds, though, + +so why is it in row three? + +PROFESSOR: You told +me to start here. + +AUDIENCE: I know. + +I'm trying to remember +how we got there. + +PROFESSOR: You said, +let's start here. + +That's why this arrow +points here to one. + +You have two arrows, +2, 3, and 2, 1. + +AUDIENCE: Because +it's j minus si. + +AUDIENCE: Oh, I see. + +Minus 3. + +AUDIENCE: So j is the amount +of weight you have left, right? + +PROFESSOR: So j is +the amount of weight + +I can have for this sub-problem. + +AUDIENCE: Yeah, the +amount of capacity I + +have still in my backpack. + +PROFESSOR: Let's talk about +pseudo polynomial time + +very quickly and what +does it mean, OK? + +And you guys will promise to +look at the recitation notes + +and look at the other +problems, right? + +So incentive for that. + +Problem two is +easier than knapsack, + +so if you get that, that should +be a good confirmation that you + +got knapsack. + +Problem three is a bit +harder than problem two, + +but it shows up on +interviews, so you + +want to understand +problem three. + +I got problem two +twice in four years, + +so there's a decent +chance that you'll get it. + +So you want to get +to problem three, + +so you should go +through problem two. + +AUDIENCE: How many times +have you got problem three? + +PROFESSOR: Twice in +four years, so that's + +the problem that +you want to get to. + +Problem two is a stepping stone. + +So running time for +dynamic programming. + +How many sub-problems? + +AUDIENCE: Same, ns. + +PROFESSOR: Yep. + +Sub-problems. + +How many sub-problems +do I look at when + +I compute the answer +of a sub-problem? + +Two, right? + +So order one. + +So this is how +much time it takes + +to compute the answer +to a sub-problem, + +because I have the +max of two elements, + +so it's constant time. + +So the total running time is? + +AUDIENCE: Order ns. + +PROFESSOR: All right. + +Order of ns. + +This polynomial, is +this the same kind + +of algorithm as Dijkstra? + +AUDIENCE: Pseudo polynomial. + +PROFESSOR: Pseudo polynomial. + +AUDIENCE: Don't know why. + +PROFESSOR: So +intuitively, the problem + +is s shows up in +your running here, + +and s is the property +of your input numbers. + +It's not how many elements +you have in the input. + +It's what's inside +one of those elements. + +So let's see why that matters. + +Let's look at the +practical example. + +AUDIENCE: What about +measuring in cubic inches + +or cubic centimeters? + +Is that a problem? + +It would take a lot longer if +we do it in cubic centimeters. + +PROFESSOR: Yeah, +but then you could + +argue that if it's an integer +amount of cubic inches, + +you should divide +everything by that. + +Where this really +matters is suppose + +you have a 100 item +input, so 100 items. + +What's the worst case +input on a 32-bit machine? + +An input looks like +this, by the way. + +How many elements you have, +so 3, and then for each item, + +what's the weight +and what's the value? + +So then we're going to have +three weights, which I believe + +are 4, 2, 3. + +You guys have to +take my word for it. + +And then I have three +values, which are 10, 4, 7. + +Let's not worry +about the values. + +I claim that they're irrelevant. + +You can convince +yourselves afterwards + +that that's the case. + +Let's only look at this. + +The weights have to be between +0 and what for the problem + +to make sense? + +AUDIENCE: 5. + +PROFESSOR: If I have a +weight bigger than this, + +I know I'm not going +to take that item. + +How many bits do I need to +represent these weights? + +AUDIENCE: Log s. + +PROFESSOR: It's log +s plus 1 technically, + +but if I write order +of log s, I'm good. + +AUDIENCE: Times the +number of items. + +PROFESSOR: Yes. + +So if I want to +represent all of them, + +I have order of n times +log s, plus the number + +of bits required +to represent this. + +This is log n. + +So log n is smaller than n. + +I'm not going to add it here. + +So this is my input size. + +This is how many bits +I need for the input. + +So the worst case input +on a 32-bit machine + +is going to have +roughly 3,200 bits. + +What's the worst +case s that I can + +represent on a 32-bit machine? + +These are all 32-bit numbers. + +AUDIENCE: You mean each of the +weights are 32-bit numbers? + +PROFESSOR: Yeah. + +So what's the worst +case s I can represent? + +AUDIENCE: 2 to 31 minus 1. + +PROFESSOR: Which is roughly +4 times 10 to the ninth. + +So the worst case +running time is? + +Roughly ns, right? + +So n times s, which means +roughly 100 times 10 + +to the ninth, which means 4 +times 10 to the 11 operations. + +Now, suppose we're +looking at the worst case + +input on a 64-bit machine. + +Still 100 items. + +What's the input size? + +AUDIENCE: To the 21 +total at the end. + +PROFESSOR: That's +how many operations. + +Let's go through +it step by step. + +How many bits of input? + +AUDIENCE: 6,400. + +AUDIENCE: Where +does that come from? + +AUDIENCE: 100 items +times 32 bits. + +PROFESSOR: 100 items. + +Each item weight has 64 bits. + +What's the worst case s? + +AUDIENCE: 2 to the 64. + +PROFESSOR: 2 to the 64 minus 1. + +Doesn't matter too much. + +It's 1 times 10 to the 19th, +1.6 times 10 to the 19th. + +So the worst case +running time is? + +AUDIENCE: 10 to the 21. + +PROFESSOR: 10 to the 21. + +So what happened? + +I increased my word size. + +The running time +increased quadratically. + +This is not a +polynomial increase. + +What's the problem here? + +Why is this the case? + +If I write log s as +b, so log s becomes + +b, what's the input size? + +AUDIENCE: nb. + +PROFESSOR: Yep. n times +log s equals n times b, + +so this is the input size. + +Now, what is the running time? + +AUDIENCE: The number +of operations? + +PROFESSOR: Yep. + +AUDIENCE: n times 2 to the b. + +PROFESSOR: Yep. + +n times s, and s is 2 to the b. + +So this is the problem. + +This is a polynomial +in n and b, but here, + +if I write the input this +way, I have b as an exponent. + +So if I double +the number of bits + +by doubling the field +size, my running time + +increases quadratically, +so this is not polynomial. + +However, if I write it +as order of n times s, + +this looks like a polynomial. + +So it looks like a +polynomial, but it's not truly + +a polynomial, so that's why +it's pseudo, as in fake. + +AUDIENCE: So it's +actually exponential. + +PROFESSOR: It's not exponential. + +So an exponential +algorithm for this means + +try all the possible +subsets, and that's + +order of 2 to the n times +n to compute the sum. + +This is exponential, right? + +You have n here. + +It's clear. + +AUDIENCE: I know, but +if you have 2 to the b, + +that seems pretty clear as well. + +PROFESSOR: Well, you have +to look inside this s + +and see what it means. + +That's the difference. + +So by increasing +the number of items, + +if you double the +number of items + +but you don't do anything +to the word size, + +then your running time is +going to increase polynomially, + +but if you change +the field size, + +it's going to increase +exponentially. + +So pseudo polynomial means +watch out, there's a trap. + +It's not really polynomial. + +If you increase the input size +by increasing the number width, + +bad stuff is going to happen. + +So think of Dijkstra. + +What's the running +time of Dijkstra? + +You count the number of +vertices, the number of edges, + +and you have a polynomial +in that, right? + +You don't have to look +at the number size. + +You don't have to look at +any weird stuff like that. + +Here, you do. + +That's the difference. + +Does it make more sense? + +So whenever you have an +input number that shows up + +in your running time, instead +of how many numbers you have, + +that means there's a trap. + +That's pseudo polynomial. + +AUDIENCE: So it's just +like having some constant + +that depends on something? + +PROFESSOR: It's not a constant. + +AUDIENCE: I mean coefficient. + +AUDIENCE: Once you set it, +it's a constant, right? + +PROFESSOR: I mean, that's +true for everything, right? + +You can say that you have 10 to +the 80 atoms in the universe, + +so all the numbers that you work +with are at most 10 to the 80. + +Therefore, your running +time is order one + +no matter what you do, +and then running times + +are no longer useful. + +You have to draw +a line somewhere. + +AUDIENCE: I think it's just like +s, if it depends on your field + +size and you can scale +it, it's kind of like-- + +PROFESSOR: So +asymptotic running time. + +What's the point of that? + +How do our algorithms scale? + +As our data becomes +bigger and bigger, + +what happens to +the running time? + +This pseudo polynomial +thing tells you + +that if you're shifting +to a larger number size, + +to a larger word size, +then your running time + +is going to explode. + +It's not going to +scale linearly. + +Still don't buy it? + +AUDIENCE: I trust you, I just-- + +AUDIENCE: So it's only dependent +on the field in this case. + +PROFESSOR: Do you guys +want to look over Dijkstra + +and see what the input +to Dijkstra looks like + +and why that's different? + +Do you think that's +worth your time, + +given that this +is what's standing + +between you and the weekend? + +AUDIENCE: What time is it? + +PROFESSOR: If you guys want +to, I'm willing to do it. + +AUDIENCE: It's 4:07. + +I'll stay. + +PROFESSOR: Well, if you +guys want to go, you can go. + +I will draw this +for the people who + +still want to know +what it looks like. + +Dijkstra. + +What's the input to Dijkstra? + +It's a graph, right? + +AUDIENCE: Yeah, nodes and edges. + +PROFESSOR: What does +the graph look like? + +It's some number +of nodes, so it's + +a single number-- that's +the number of nodes-- + +that has log v bits in it. + +And then for each edge, we have +three numbers-- first vertex, + +second vertex, and the weight. + +What are the sizes +of these numbers? + +Log v, log v, and the last one? + +AUDIENCE: Log w? + +PROFESSOR: OK. + +And what's w? + +AUDIENCE: Maximum weight. + +PROFESSOR: Yeah. + +So this is a property of +the field size, right? + +Let's look at v, actually. + +So we have E edges here, right? + +So the input size is going to +be log v bits plus E times log v + +plus log w. + +AUDIENCE: How did you get that? + +PROFESSOR: Because I have the +edges, so I have E of these. + +I only have one vertex count, +but then I have E edges, + +and each edge has three +numbers, and these + +are the widths of the numbers. + +AUDIENCE: Is the +adjacent edges to v? + +Is that right? + +You say you have E edges. + +PROFESSOR: I'm +assuming it's a list, + +so the most compact +representation + +of edges, I think-- or +it might be a reasonably + +compact representation is that +you have the list of edges. + +So you have a graph +that has five nodes, + +and then you have an edge +that goes from 1 to 2, + +and then weight 3, an edge that +goes from 1 to 5, weight 4. + +AUDIENCE: If you use +a number, it's not a-- + +PROFESSOR: Well, do I need +anything else for vertices? + +Not really, right? + +AUDIENCE: So v1 and v2 are +neighbors of capital V? + +PROFESSOR: So v1, v2, w, +these are the first edge. + +Each edge has these fields. + +AUDIENCE: This is the +entire graph in one thing. + +PROFESSOR: This is the entire +graph as a list of numbers, + +and this is how +many bits it takes + +to represent the +graph in a reasonably + +compact representation. + +Now let's say little v is +log v, little w is log w. + +So then this is order of how +many bits do I have here? + +E times v plus w plus v. +I just replaced the logs + +with these variables. + +This is how many bits. + +Now, how many operations +does Dijkstra take? + +What's the running time? + +AUDIENCE: Well, it depends on-- + +AUDIENCE: E log v. + +AUDIENCE: Wouldn't +it be E plus v? + +That's the fastest one, right? + +But I think practically, +it's only going to be-- + +PROFESSOR: So this +is E plus v log + +v, the fastest +theoretical limit. + +This is still smaller +than E log v. This + +is going to make my life easier. + +So this is smaller than this. + +If this thing is polynomial, +this is polynomial for sure. + +E log v is E times little v. +So how many bits in the input? + +E times v plus w. + +How many operations? + +E times v. Any +exponential anywhere here? + +AUDIENCE: Wouldn't you +change the size of v? + +That looks fine. + +PROFESSOR: Well, so there is +a trick that v is 2 to the v, + +right? + +So you can say +that this is order + +of-- so this is +definitely bigger than 2 + +to the little v +times v, but then you + +have the same +thing in the input. + +So the input also has at least +2 to the little v times v bits. + +But don't worry about that. + +That's too much. + +The point is if you're worrying +about this, don't worry. + +The math still works out. + +So whatever you have +here as an input, + +the running time is +going to be a polynomial + +in the size of the input. + +What happens if you +double the word size? + +What happens if you +have bigger weights? + +AUDIENCE: Everything like +v is multiplied by 2, + +and w is multiplied by 2 and +everything in this problem, + +right? + +PROFESSOR: So if you're +doubling the word size, + +then this is going to double, +this is going to double. + +Everything's fine. + +What if you double the +size of the weights? + +AUDIENCE: That only +adds an extra bit. + +PROFESSOR: Sorry. + +So if you double the size +of the weight numbers? + +So if you move from 32-bit +weights to 64-bit weights? + +AUDIENCE: That's still a +constant factor, right? + +PROFESSOR: What happens +to the running time? + +AUDIENCE: Nothing. + +PROFESSOR: Nothing. + +w does not show up in Dijkstra. + +If it would, then +we'd be trouble. + +It wouldn't be +polynomial anymore. + +AUDIENCE: But +practically, you will + +be accessing that number, right? + +PROFESSOR: Yeah, +but that shows up + +in the cost of one operation. + +That's why I'm saying this +is how many operations + +you do, how many +arithmetic operations. + +Then the model of computation +that we use is RAM, + +and that says that +you can do any math + +operation in order one. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So here, my +number in the input, + +s, which is the +size of a weight, + +showed up in the running time. + +AUDIENCE: Oh, the +size of the input + +showed up in the running time. + +PROFESSOR: So the size +of the input is OK, + +but one number in +the input showed up, + +whereas here, +that's not the case. + +The weights do not show +up in the running time. + +AUDIENCE: So why don't we just +always run Dijkstra, then? + +PROFESSOR: Actually for this +problem, for the knapsack + +problem, you can't find an +algorithm that is polynomial. + +If you do, there's a +$1 million prize for it + +because you just proved +that p equals mp. + +This is the best we +can do for knapsack. + +AUDIENCE: Is counting +sort pseudo linear, + +because you need to +have a maximum, a range? + +Does that make sense? + +PROFESSOR: Counting sort. + +AUDIENCE: Depends on your range. + +PROFESSOR: Yeah, but the +range shows up under a log. + +You're allowed to have logs. + +You're allowed to have log w. + +You're not allowed to have w. + +It's dependent on the +size of the input. + +If you double the +number size, then you're + +going to have twice +as many rounds, + +but you don't have an +exponential number of rounds. + +Sorry. + +You're thinking +of counting sort. + +I thought radix sort. + +Radix sort doesn't +matter because you + +assume we can do +everything in-- never mind. + +You're right for counting sort. + +Sorry. + +You're right for counting sort. + +Sorry. + +I was confusing counting +sort with radix sort. + +So for counting sort, +yeah, it's not linear. + +It's linear in your +range size, which + +is not linear in the +input size, which + +is why we don't +do counting sort. + +We do radix sort. + +AUDIENCE: We do counting +sort in radix sort? + +PROFESSOR: Yeah. + +But radix sort limits the +size of the range, right? + +That's the point of radix sort. + +AUDIENCE: Oh. + +I see what you're thinking. + +So doing counting +sort with each number? + +AUDIENCE: Right, with +really big numbers, + +taking a really long time. + +AUDIENCE: Yeah, that +would take a long time. + +PROFESSOR: Yep. + +That is very true. + +If you try to do pure counting +sort on 64-bit numbers, + +you're going to run out of RAM. + +Does this make some sense? + +OK. + +Promise to look over the +other problems, and in return, + +given that I didn't have +time to cover them here, + +I promise to answer +any emails you + +guys might ask me +over the weekend. + +AUDIENCE: Oh. + +Awesome. \ No newline at end of file diff --git a/xCpg54xUzLE.txt b/xCpg54xUzLE.txt new file mode 100644 index 0000000000000000000000000000000000000000..b59f0a108522e9772184fb2b3c8eeab3db14f7d2 --- /dev/null +++ b/xCpg54xUzLE.txt @@ -0,0 +1,395 @@ +align:start position:0% + +so one of the major goals of the course + + align:start position:0% +so one of the major goals of the course + + + align:start position:0% +so one of the major goals of the course +is for because we all speak a language + + align:start position:0% +is for because we all speak a language + + + align:start position:0% +is for because we all speak a language +or sometimes many languages and while + + align:start position:0% +or sometimes many languages and while + + + align:start position:0% +or sometimes many languages and while +the students get to understand at the + + align:start position:0% +the students get to understand at the + + + align:start position:0% +the students get to understand at the +end of the course is that we all hold + + align:start position:0% +end of the course is that we all hold + + + align:start position:0% +end of the course is that we all hold +dear certain attitudes about language + + align:start position:0% +dear certain attitudes about language + + + align:start position:0% +dear certain attitudes about language +and some of it attitudes are positive + + align:start position:0% +and some of it attitudes are positive + + + align:start position:0% +and some of it attitudes are positive +for us doesn't for others but often + + align:start position:0% +for us doesn't for others but often + + + align:start position:0% +for us doesn't for others but often +times and this is actually one of the + + align:start position:0% +times and this is actually one of the + + + align:start position:0% +times and this is actually one of the +major issues that we discuss throughout + + align:start position:0% +major issues that we discuss throughout + + + align:start position:0% +major issues that we discuss throughout +the course is that sometimes we have + + align:start position:0% +the course is that sometimes we have + + + align:start position:0% +the course is that sometimes we have +attitudes that have a negative impact + + align:start position:0% +attitudes that have a negative impact + + + align:start position:0% +attitudes that have a negative impact +severe negative impact on the lives of + + align:start position:0% +severe negative impact on the lives of + + + align:start position:0% +severe negative impact on the lives of +other people the lives of sometimes + + align:start position:0% +other people the lives of sometimes + + + align:start position:0% +other people the lives of sometimes +entire communities and Nations so so I + + align:start position:0% +entire communities and Nations so so I + + + align:start position:0% +entire communities and Nations so so I +hope throughout that students can + + align:start position:0% +hope throughout that students can + + + align:start position:0% +hope throughout that students can +actually take the theory Dallas's in the + + align:start position:0% +actually take the theory Dallas's in the + + + align:start position:0% +actually take the theory Dallas's in the +course and see ways in which they can + + align:start position:0% +course and see ways in which they can + + + align:start position:0% +course and see ways in which they can +apply it to themselves to the + + align:start position:0% +apply it to themselves to the + + + align:start position:0% +apply it to themselves to the +communities to the countries so clearly + + align:start position:0% +communities to the countries so clearly + + + align:start position:0% +communities to the countries so clearly +the case that I that I have in mind the + + align:start position:0% +the case that I that I have in mind the + + + align:start position:0% +the case that I that I have in mind the +most is my own Haiti where attitudes + + align:start position:0% +most is my own Haiti where attitudes + + + align:start position:0% +most is my own Haiti where attitudes +about language I've been under one of + + align:start position:0% +about language I've been under one of + + + align:start position:0% +about language I've been under one of +the engines that have really gone + + align:start position:0% +the engines that have really gone + + + align:start position:0% +the engines that have really gone +against the interest of most Haitians + + align:start position:0% +against the interest of most Haitians + + + align:start position:0% +against the interest of most Haitians +that have allowed if you to keep the + + align:start position:0% +that have allowed if you to keep the + + + align:start position:0% +that have allowed if you to keep the +maturity and the oppression but then + + align:start position:0% +maturity and the oppression but then + + + align:start position:0% +maturity and the oppression but then +this is true also for the communities so + + align:start position:0% +this is true also for the communities so + + + align:start position:0% +this is true also for the communities so +I was very pleased to see that the + + align:start position:0% +I was very pleased to see that the + + + align:start position:0% +I was very pleased to see that the +students took that objectives very + + align:start position:0% +students took that objectives very + + + align:start position:0% +students took that objectives very +dearly and including some who in the + + align:start position:0% +dearly and including some who in the + + + align:start position:0% +dearly and including some who in the +course of this class I've applied + + align:start position:0% +course of this class I've applied + + + align:start position:0% +course of this class I've applied +whether what they've learned and taken + + align:start position:0% +whether what they've learned and taken + + + align:start position:0% +whether what they've learned and taken +it outside including volunteering in say + + align:start position:0% +it outside including volunteering in say + + + align:start position:0% +it outside including volunteering in say +this virtual English program that just + + align:start position:0% +this virtual English program that just + + + align:start position:0% +this virtual English program that just +started in in Boston is a Jewish program + + align:start position:0% +started in in Boston is a Jewish program + + + align:start position:0% +started in in Boston is a Jewish program +promoting the use of both in Creole in + + align:start position:0% +promoting the use of both in Creole in + + + align:start position:0% +promoting the use of both in Creole in +English and where students are immersed + + align:start position:0% +English and where students are immersed + + + align:start position:0% +English and where students are immersed +from kindergarten in both cruel in + + align:start position:0% +from kindergarten in both cruel in + + + align:start position:0% +from kindergarten in both cruel in +English and now this is related to that + + align:start position:0% +English and now this is related to that + + + align:start position:0% +English and now this is related to that +class + + align:start position:0% +class + + + align:start position:0% +class +my class and was volunteering in in that + + align:start position:0% +my class and was volunteering in in that + + + align:start position:0% +my class and was volunteering in in that +classroom for kindergarteners who are + + align:start position:0% +classroom for kindergarteners who are + + + align:start position:0% +classroom for kindergarteners who are +learning in Creole and in English and to + + align:start position:0% +learning in Creole and in English and to + + + align:start position:0% +learning in Creole and in English and to +me that's a dozen as a dream because + + align:start position:0% +me that's a dozen as a dream because + + + align:start position:0% +me that's a dozen as a dream because +it's one case where what you learn in + + align:start position:0% +it's one case where what you learn in + + + align:start position:0% +it's one case where what you learn in +the course can be directly applied in in + + align:start position:0% +the course can be directly applied in in + + + align:start position:0% +the course can be directly applied in in +the real-world contexts which can make + + align:start position:0% +the real-world contexts which can make + + + align:start position:0% +the real-world contexts which can make +actual positive change in the lives of + + align:start position:0% +actual positive change in the lives of + + + align:start position:0% +actual positive change in the lives of +these children \ No newline at end of file diff --git a/xwRn_lTA6JY.txt b/xwRn_lTA6JY.txt new file mode 100644 index 0000000000000000000000000000000000000000..34475fada021841123f8cba07a91752c1670061f --- /dev/null +++ b/xwRn_lTA6JY.txt @@ -0,0 +1,7387 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +In several of the previous lessons, + + align:start position:0% +In several of the previous lessons, + + + align:start position:0% +In several of the previous lessons, +we've focused primarily on the class of + + align:start position:0% +we've focused primarily on the class of + + + align:start position:0% +we've focused primarily on the class of +linear shift and variant systems that + + align:start position:0% +linear shift and variant systems that + + + align:start position:0% +linear shift and variant systems that +are representable by linear constant + + align:start position:0% +are representable by linear constant + + + align:start position:0% +are representable by linear constant +coefficient difference equations. And + + align:start position:0% +coefficient difference equations. And + + + align:start position:0% +coefficient difference equations. And +we've talked, for example, about methods + + align:start position:0% +we've talked, for example, about methods + + + align:start position:0% +we've talked, for example, about methods +for solving that class of equations. One + + align:start position:0% +for solving that class of equations. One + + + align:start position:0% +for solving that class of equations. One +of the reasons why linear constant + + align:start position:0% +of the reasons why linear constant + + + align:start position:0% +of the reasons why linear constant +coefficient difference equations + + align:start position:0% +coefficient difference equations + + + align:start position:0% +coefficient difference equations +represent a particularly important class + + align:start position:0% +represent a particularly important class + + + align:start position:0% +represent a particularly important class +of discrete time systems is because of + + align:start position:0% +of discrete time systems is because of + + + align:start position:0% +of discrete time systems is because of +the fact that they have a particularly + + align:start position:0% +the fact that they have a particularly + + + align:start position:0% +the fact that they have a particularly +straightforward implementation in terms + + align:start position:0% +straightforward implementation in terms + + + align:start position:0% +straightforward implementation in terms +of digital components. + + align:start position:0% +of digital components. + + + align:start position:0% +of digital components. +So in this lecture and actually over the + + align:start position:0% +So in this lecture and actually over the + + + align:start position:0% +So in this lecture and actually over the +next several lectures, what I'd like to + + align:start position:0% +next several lectures, what I'd like to + + + align:start position:0% +next several lectures, what I'd like to +focus on is that class of linear shift + + align:start position:0% +focus on is that class of linear shift + + + align:start position:0% +focus on is that class of linear shift +invariant systems and in particular the + + align:start position:0% +invariant systems and in particular the + + + align:start position:0% +invariant systems and in particular the +implementation of that class of systems. + + align:start position:0% +implementation of that class of systems. + + + align:start position:0% +implementation of that class of systems. +In other words, digital networks for the + + align:start position:0% +In other words, digital networks for the + + + align:start position:0% +In other words, digital networks for the +implementation of systems describable by + + align:start position:0% +implementation of systems describable by + + + align:start position:0% +implementation of systems describable by +linear constant coefficient difference + + align:start position:0% +linear constant coefficient difference + + + align:start position:0% +linear constant coefficient difference +equations. + + align:start position:0% +equations. + + + align:start position:0% +equations. +Well, as we have defined previously, + + align:start position:0% +Well, as we have defined previously, + + + align:start position:0% +Well, as we have defined previously, +an nth order linear constant coefficient + + align:start position:0% +an nth order linear constant coefficient + + + align:start position:0% +an nth order linear constant coefficient +difference equation + + align:start position:0% +difference equation + + + align:start position:0% +difference equation +essentially corresponds to a linear + + align:start position:0% +essentially corresponds to a linear + + + align:start position:0% +essentially corresponds to a linear +combination of delayed + + align:start position:0% +combination of delayed + + + align:start position:0% +combination of delayed +output sequences + + align:start position:0% +output sequences + + + align:start position:0% +output sequences +set equal to a linear combination of + + align:start position:0% +set equal to a linear combination of + + + align:start position:0% +set equal to a linear combination of +delayed input sequences. This is the + + align:start position:0% +delayed input sequences. This is the + + + align:start position:0% +delayed input sequences. This is the +general form for a linear constant + + align:start position:0% +general form for a linear constant + + + align:start position:0% +general form for a linear constant +coefficient difference equation which as + + align:start position:0% +coefficient difference equation which as + + + align:start position:0% +coefficient difference equation which as +we discussed + + align:start position:0% +we discussed + + + align:start position:0% +we discussed +in one of the early lectures actually + + align:start position:0% +in one of the early lectures actually + + + align:start position:0% +in one of the early lectures actually +lesson three + + align:start position:0% +lesson three + + + align:start position:0% +lesson three +corresponds to an explicit input output + + align:start position:0% +corresponds to an explicit input output + + + align:start position:0% +corresponds to an explicit input output +description for the system. In other + + align:start position:0% +description for the system. In other + + + align:start position:0% +description for the system. In other +words, we can solve this equation by + + align:start position:0% +words, we can solve this equation by + + + align:start position:0% +words, we can solve this equation by +taking this set of terms over to the + + align:start position:0% +taking this set of terms over to the + + + align:start position:0% +taking this set of terms over to the +right hand side of the equation. And the + + align:start position:0% +right hand side of the equation. And the + + + align:start position:0% +right hand side of the equation. And the +difference equation that results is a + + align:start position:0% +difference equation that results is a + + + align:start position:0% +difference equation that results is a +statement that says that y ofn the + + align:start position:0% +statement that says that y ofn the + + + align:start position:0% +statement that says that y ofn the +output sequence for the system + + align:start position:0% +output sequence for the system + + + align:start position:0% +output sequence for the system +is a linear combination of past outputs + + align:start position:0% +is a linear combination of past outputs + + + align:start position:0% +is a linear combination of past outputs +plus a linear combination of delayed + + align:start position:0% +plus a linear combination of delayed + + + align:start position:0% +plus a linear combination of delayed +inputs. + + align:start position:0% +inputs. + + + align:start position:0% +inputs. +Now we also discussed at that point in + + align:start position:0% +Now we also discussed at that point in + + + align:start position:0% +Now we also discussed at that point in +one of the early lectures the fact that + + align:start position:0% +one of the early lectures the fact that + + + align:start position:0% +one of the early lectures the fact that +a linear constant coefficient difference + + align:start position:0% +a linear constant coefficient difference + + + align:start position:0% +a linear constant coefficient difference +equation is not a unique description for + + align:start position:0% +equation is not a unique description for + + + align:start position:0% +equation is not a unique description for +a system. In other words, we saw that + + align:start position:0% +a system. In other words, we saw that + + + align:start position:0% +a system. In other words, we saw that +this system or a system that satisfies + + align:start position:0% +this system or a system that satisfies + + + align:start position:0% +this system or a system that satisfies +this equation could correspond to a + + align:start position:0% +this equation could correspond to a + + + align:start position:0% +this equation could correspond to a +causal system or in fact it could + + align:start position:0% +causal system or in fact it could + + + align:start position:0% +causal system or in fact it could +correspond to a non-causal system + + align:start position:0% +correspond to a non-causal system + + + align:start position:0% +correspond to a non-causal system +depending on the initial conditions or + + align:start position:0% +depending on the initial conditions or + + + align:start position:0% +depending on the initial conditions or +the boundary conditions that we impose + + align:start position:0% +the boundary conditions that we impose + + + align:start position:0% +the boundary conditions that we impose +on the equation. We could in particular + + align:start position:0% +on the equation. We could in particular + + + align:start position:0% +on the equation. We could in particular +impose the boundary condition the + + align:start position:0% +impose the boundary condition the + + + align:start position:0% +impose the boundary condition the +boundary conditions implied by the + + align:start position:0% +boundary conditions implied by the + + + align:start position:0% +boundary conditions implied by the +statement that the system is causal or + + align:start position:0% +statement that the system is causal or + + + align:start position:0% +statement that the system is causal or +we could impose boundary conditions + + align:start position:0% +we could impose boundary conditions + + + align:start position:0% +we could impose boundary conditions +implied by the statement that the system + + align:start position:0% +implied by the statement that the system + + + align:start position:0% +implied by the statement that the system +is non-causal. + + align:start position:0% +is non-causal. + + + align:start position:0% +is non-causal. +For this discussion for the discussion + + align:start position:0% +For this discussion for the discussion + + + align:start position:0% +For this discussion for the discussion +in this lecture and actually over the + + align:start position:0% +in this lecture and actually over the + + + align:start position:0% +in this lecture and actually over the +next several lectures the assumption + + align:start position:0% +next several lectures the assumption + + + align:start position:0% +next several lectures the assumption +will always be that we're talking about + + align:start position:0% +will always be that we're talking about + + + align:start position:0% +will always be that we're talking about +a causal system. In other words, the + + align:start position:0% +a causal system. In other words, the + + + align:start position:0% +a causal system. In other words, the +boundary conditions that we're imposing + + align:start position:0% +boundary conditions that we're imposing + + + align:start position:0% +boundary conditions that we're imposing +is that for the input zero for n less + + align:start position:0% +is that for the input zero for n less + + + align:start position:0% +is that for the input zero for n less +than say n1, the output will also be + + align:start position:0% +than say n1, the output will also be + + + align:start position:0% +than say n1, the output will also be +zero for n less than n1. So we're + + align:start position:0% +zero for n less than n1. So we're + + + align:start position:0% +zero for n less than n1. So we're +implying a set of boundary conditions by + + align:start position:0% +implying a set of boundary conditions by + + + align:start position:0% +implying a set of boundary conditions by +virtue of the fact that we're assuming + + align:start position:0% +virtue of the fact that we're assuming + + + align:start position:0% +virtue of the fact that we're assuming +that we're talking about causal systems. + + align:start position:0% +that we're talking about causal systems. + + + align:start position:0% +that we're talking about causal systems. +Now in implementing a system describable + + align:start position:0% +Now in implementing a system describable + + + align:start position:0% +Now in implementing a system describable +by a difference equation of this form + + align:start position:0% +by a difference equation of this form + + + align:start position:0% +by a difference equation of this form +what we see is that there are three + + align:start position:0% +what we see is that there are three + + + align:start position:0% +what we see is that there are three +basic operations that are involved. + + align:start position:0% +basic operations that are involved. + + + align:start position:0% +basic operations that are involved. +We have to somehow generate delayed + + align:start position:0% +We have to somehow generate delayed + + + align:start position:0% +We have to somehow generate delayed +sequences. We have to get y of n + + align:start position:0% +sequences. We have to get y of n + + + align:start position:0% +sequences. We have to get y of n +delayed. We have to get x of n delayed. + + align:start position:0% +delayed. We have to get x of n delayed. + + + align:start position:0% +delayed. We have to get x of n delayed. +So one of the basic operations is the + + align:start position:0% +So one of the basic operations is the + + + align:start position:0% +So one of the basic operations is the +operation of delay. + + align:start position:0% +operation of delay. + + + align:start position:0% +operation of delay. +Furthermore, we need to multiply these + + align:start position:0% +Furthermore, we need to multiply these + + + align:start position:0% +Furthermore, we need to multiply these +delayed sequences by scalers and these + + align:start position:0% +delayed sequences by scalers and these + + + align:start position:0% +delayed sequences by scalers and these +delayed sequences by scalers. So there + + align:start position:0% +delayed sequences by scalers. So there + + + align:start position:0% +delayed sequences by scalers. So there +is the additional operation of + + align:start position:0% +is the additional operation of + + + align:start position:0% +is the additional operation of +multiplication. + + align:start position:0% +multiplication. + + + align:start position:0% +multiplication. +And third, we have to accumulate these + + align:start position:0% +And third, we have to accumulate these + + + align:start position:0% +And third, we have to accumulate these +sums or accumulate these products. And + + align:start position:0% +sums or accumulate these products. And + + + align:start position:0% +sums or accumulate these products. And +so the third operation that is required + + align:start position:0% +so the third operation that is required + + + align:start position:0% +so the third operation that is required +in the implementation of a linear + + align:start position:0% +in the implementation of a linear + + + align:start position:0% +in the implementation of a linear +constant coefficient difference equation + + align:start position:0% +constant coefficient difference equation + + + align:start position:0% +constant coefficient difference equation +is the operation of addition. + + align:start position:0% +is the operation of addition. + + + align:start position:0% +is the operation of addition. +Consequently, if we were to think of + + align:start position:0% +Consequently, if we were to think of + + + align:start position:0% +Consequently, if we were to think of +basic digital network elements, we could + + align:start position:0% +basic digital network elements, we could + + + align:start position:0% +basic digital network elements, we could +choose as our basic elements the + + align:start position:0% +choose as our basic elements the + + + align:start position:0% +choose as our basic elements the +operations corresponding to delay, + + align:start position:0% +operations corresponding to delay, + + + align:start position:0% +operations corresponding to delay, +multiplication, and addition. + + align:start position:0% +multiplication, and addition. + + + align:start position:0% +multiplication, and addition. +In particular, what we'd like to develop + + align:start position:0% +In particular, what we'd like to develop + + + align:start position:0% +In particular, what we'd like to develop +or generate is a graphical + + align:start position:0% +or generate is a graphical + + + align:start position:0% +or generate is a graphical +representation of the difference + + align:start position:0% +representation of the difference + + + align:start position:0% +representation of the difference +equation, which is what we'll refer to + + align:start position:0% +equation, which is what we'll refer to + + + align:start position:0% +equation, which is what we'll refer to +as the digital network. So in essence, + + align:start position:0% +as the digital network. So in essence, + + + align:start position:0% +as the digital network. So in essence, +what we want is a graphical + + align:start position:0% +what we want is a graphical + + + align:start position:0% +what we want is a graphical +representation of these three operations + + align:start position:0% +representation of these three operations + + + align:start position:0% +representation of these three operations +which will combine together into a + + align:start position:0% +which will combine together into a + + + align:start position:0% +which will combine together into a +digital network. + + align:start position:0% +digital network. + + + align:start position:0% +digital network. +One type of notation which is + + align:start position:0% +One type of notation which is + + + align:start position:0% +One type of notation which is +essentially block diagram notation + + align:start position:0% +essentially block diagram notation + + + align:start position:0% +essentially block diagram notation +corresponds to representing the + + align:start position:0% +corresponds to representing the + + + align:start position:0% +corresponds to representing the +operation of delay + + align:start position:0% +operation of delay + + + align:start position:0% +operation of delay +as + + align:start position:0% +as + + + align:start position:0% +as +a box. + + align:start position:0% +a box. + + + align:start position:0% +a box. +The input of course is the sequence that + + align:start position:0% +The input of course is the sequence that + + + align:start position:0% +The input of course is the sequence that +we want to delay. Let's say x of n. + + align:start position:0% +we want to delay. Let's say x of n. + + + align:start position:0% +we want to delay. Let's say x of n. +And the output then is that sequence + + align:start position:0% +And the output then is that sequence + + + align:start position:0% +And the output then is that sequence +delayed by one sample x of n minus one. + + align:start position:0% +delayed by one sample x of n minus one. + + + align:start position:0% +delayed by one sample x of n minus one. +And typically in the block diagram type + + align:start position:0% +And typically in the block diagram type + + + align:start position:0% +And typically in the block diagram type +of representation, + + align:start position:0% +of representation, + + + align:start position:0% +of representation, +this element or block is denoted with a + + align:start position:0% +this element or block is denoted with a + + + align:start position:0% +this element or block is denoted with a +z to the minus1. + + align:start position:0% +z to the minus1. + + + align:start position:0% +z to the minus1. +Well, what does Z to the minus one have + + align:start position:0% +Well, what does Z to the minus one have + + + align:start position:0% +Well, what does Z to the minus one have +to do with the operation of delay? + + align:start position:0% +to do with the operation of delay? + + + align:start position:0% +to do with the operation of delay? +Simply that if we were to think of the Z + + align:start position:0% +Simply that if we were to think of the Z + + + align:start position:0% +Simply that if we were to think of the Z +transform of the input sequence and the + + align:start position:0% +transform of the input sequence and the + + + align:start position:0% +transform of the input sequence and the +Z transform of the output sequence, what + + align:start position:0% +Z transform of the output sequence, what + + + align:start position:0% +Z transform of the output sequence, what +we know is that those are related in + + align:start position:0% +we know is that those are related in + + + align:start position:0% +we know is that those are related in +fact by multiplication by Z to the + + align:start position:0% +fact by multiplication by Z to the + + + align:start position:0% +fact by multiplication by Z to the +minus1. So the implication in putting + + align:start position:0% +minus1. So the implication in putting + + + align:start position:0% +minus1. So the implication in putting +inside the box the notation Z to the + + align:start position:0% +inside the box the notation Z to the + + + align:start position:0% +inside the box the notation Z to the +minus1 the implication is that + + align:start position:0% +minus1 the implication is that + + + align:start position:0% +minus1 the implication is that +essentially what this block is doing is + + align:start position:0% +essentially what this block is doing is + + + align:start position:0% +essentially what this block is doing is +multiplying the input the Z transform of + + align:start position:0% +multiplying the input the Z transform of + + + align:start position:0% +multiplying the input the Z transform of +the input sequence by Z to the minus1. + + align:start position:0% +the input sequence by Z to the minus1. + + + align:start position:0% +the input sequence by Z to the minus1. +So that's one element. The second + + align:start position:0% +So that's one element. The second + + + align:start position:0% +So that's one element. The second +element that we need is the element for + + align:start position:0% +element that we need is the element for + + + align:start position:0% +element that we need is the element for +multiplication + + align:start position:0% +multiplication + + + align:start position:0% +multiplication +and typically that's denoted simply by a + + align:start position:0% +and typically that's denoted simply by a + + + align:start position:0% +and typically that's denoted simply by a +line with an arrow on it. The input to + + align:start position:0% +line with an arrow on it. The input to + + + align:start position:0% +line with an arrow on it. The input to +this branch is x of n. The output of the + + align:start position:0% +this branch is x of n. The output of the + + + align:start position:0% +this branch is x of n. The output of the +branch is or it could be of course y + + align:start position:0% +branch is or it could be of course y + + + align:start position:0% +branch is or it could be of course y +ofn. The output of the branch is that + + align:start position:0% +ofn. The output of the branch is that + + + align:start position:0% +ofn. The output of the branch is that +multiplied by a scalar. Let's say a the + + align:start position:0% +multiplied by a scalar. Let's say a the + + + align:start position:0% +multiplied by a scalar. Let's say a the +scaler a and this should be x of n. If + + align:start position:0% +scaler a and this should be x of n. If + + + align:start position:0% +scaler a and this should be x of n. If +we're talking about x of n in, we're + + align:start position:0% +we're talking about x of n in, we're + + + align:start position:0% +we're talking about x of n in, we're +talking about x of n out or a * x of n + + align:start position:0% +talking about x of n out or a * x of n + + + align:start position:0% +talking about x of n out or a * x of n +out. And the branch transmittance then + + align:start position:0% +out. And the branch transmittance then + + + align:start position:0% +out. And the branch transmittance then +is the coefficient a. So this branch + + align:start position:0% +is the coefficient a. So this branch + + + align:start position:0% +is the coefficient a. So this branch +allows for co coefficient + + align:start position:0% +allows for co coefficient + + + align:start position:0% +allows for co coefficient +multiplication. + + align:start position:0% +multiplication. + + + align:start position:0% +multiplication. +And finally, the third element that we + + align:start position:0% +And finally, the third element that we + + + align:start position:0% +And finally, the third element that we +want is an element that will perform + + align:start position:0% +want is an element that will perform + + + align:start position:0% +want is an element that will perform +addition. And that element is denoted in + + align:start position:0% +addition. And that element is denoted in + + + align:start position:0% +addition. And that element is denoted in +block diagram notation as a sum with two + + align:start position:0% +block diagram notation as a sum with two + + + align:start position:0% +block diagram notation as a sum with two +inputs + + align:start position:0% +inputs + + + align:start position:0% +inputs +and a single output. The input let's say + + align:start position:0% +and a single output. The input let's say + + + align:start position:0% +and a single output. The input let's say +x1 and x2. + + align:start position:0% +x1 and x2. + + + align:start position:0% +x1 and x2. +Then the output would be x1 plus x2 of n + + align:start position:0% +Then the output would be x1 plus x2 of n + + + align:start position:0% +Then the output would be x1 plus x2 of n +or of z depending on on how we choose to + + align:start position:0% +or of z depending on on how we choose to + + + align:start position:0% +or of z depending on on how we choose to +describe the sequence. + + align:start position:0% +describe the sequence. + + + align:start position:0% +describe the sequence. +Now in the difference equation of course + + align:start position:0% +Now in the difference equation of course + + + align:start position:0% +Now in the difference equation of course +we had to accumulate a number of terms. + + align:start position:0% +we had to accumulate a number of terms. + + + align:start position:0% +we had to accumulate a number of terms. +In other words there were more there was + + align:start position:0% +In other words there were more there was + + + align:start position:0% +In other words there were more there was +more than one term that we were adding + + align:start position:0% +more than one term that we were adding + + + align:start position:0% +more than one term that we were adding +up. + + align:start position:0% +up. + + + align:start position:0% +up. +Typically in either digital hardware or + + align:start position:0% +Typically in either digital hardware or + + + align:start position:0% +Typically in either digital hardware or +on a digital computer, when we're + + align:start position:0% +on a digital computer, when we're + + + align:start position:0% +on a digital computer, when we're +forming additions, the additions are + + align:start position:0% +forming additions, the additions are + + + align:start position:0% +forming additions, the additions are +formed in pairs. In other words, it's a + + align:start position:0% +formed in pairs. In other words, it's a + + + align:start position:0% +formed in pairs. In other words, it's a +it's we we form we accumulate a large + + align:start position:0% +it's we we form we accumulate a large + + + align:start position:0% +it's we we form we accumulate a large +number of terms by adding two terms + + align:start position:0% +number of terms by adding two terms + + + align:start position:0% +number of terms by adding two terms +together, then adding one to that, + + align:start position:0% +together, then adding one to that, + + + align:start position:0% +together, then adding one to that, +adding another one to that, etc. So, + + align:start position:0% +adding another one to that, etc. So, + + + align:start position:0% +adding another one to that, etc. So, +it's convenient in that sense to think + + align:start position:0% +it's convenient in that sense to think + + + align:start position:0% +it's convenient in that sense to think +of the addition as always being a + + align:start position:0% +of the addition as always being a + + + align:start position:0% +of the addition as always being a +twoinput one output addition. Of course, + + align:start position:0% +twoinput one output addition. Of course, + + + align:start position:0% +twoinput one output addition. Of course, +if we accumulate three terms, then it + + align:start position:0% +if we accumulate three terms, then it + + + align:start position:0% +if we accumulate three terms, then it +would require two adders to do that. + + align:start position:0% +would require two adders to do that. + + + align:start position:0% +would require two adders to do that. +So these then are the basic elements + + align:start position:0% +So these then are the basic elements + + + align:start position:0% +So these then are the basic elements +that correspond to a block diagram + + align:start position:0% +that correspond to a block diagram + + + align:start position:0% +that correspond to a block diagram +representation of a linear constant + + align:start position:0% +representation of a linear constant + + + align:start position:0% +representation of a linear constant +coefficient difference equation or + + align:start position:0% +coefficient difference equation or + + + align:start position:0% +coefficient difference equation or +equivalently correspond to a digital + + align:start position:0% +equivalently correspond to a digital + + + align:start position:0% +equivalently correspond to a digital +network. And for example, if we had a + + align:start position:0% +network. And for example, if we had a + + + align:start position:0% +network. And for example, if we had a +first order difference equation, let's + + align:start position:0% +first order difference equation, let's + + + align:start position:0% +first order difference equation, let's +say the equation y of n is equal to a * + + align:start position:0% +say the equation y of n is equal to a * + + + align:start position:0% +say the equation y of n is equal to a * +y of n -1 + x of n. We can represent + + align:start position:0% +y of n -1 + x of n. We can represent + + + align:start position:0% +y of n -1 + x of n. We can represent +that equation graphically in terms of + + align:start position:0% +that equation graphically in terms of + + + align:start position:0% +that equation graphically in terms of +these elements + + align:start position:0% +these elements + + + align:start position:0% +these elements +as I've indicated here. So what do we + + align:start position:0% +as I've indicated here. So what do we + + + align:start position:0% +as I've indicated here. So what do we +have? Well, we have as an input x of n + + align:start position:0% +have? Well, we have as an input x of n + + + align:start position:0% +have? Well, we have as an input x of n +as an output y of n. + + align:start position:0% +as an output y of n. + + + align:start position:0% +as an output y of n. +We need + + align:start position:0% +We need + + + align:start position:0% +We need +in implementing this difference equation + + align:start position:0% +in implementing this difference equation + + + align:start position:0% +in implementing this difference equation +to obtain y of n minus one and that's + + align:start position:0% +to obtain y of n minus one and that's + + + align:start position:0% +to obtain y of n minus one and that's +obtained with the delay element. + + align:start position:0% +obtained with the delay element. + + + align:start position:0% +obtained with the delay element. +y of n minus one is then multiplied by + + align:start position:0% +y of n minus one is then multiplied by + + + align:start position:0% +y of n minus one is then multiplied by +the coefficient a. So here we have a * y + + align:start position:0% +the coefficient a. So here we have a * y + + + align:start position:0% +the coefficient a. So here we have a * y +of n minus one. And then the difference + + align:start position:0% +of n minus one. And then the difference + + + align:start position:0% +of n minus one. And then the difference +equation states that y ofn is the sum of + + align:start position:0% +equation states that y ofn is the sum of + + + align:start position:0% +equation states that y ofn is the sum of +that with the input. And so that goes + + align:start position:0% +that with the input. And so that goes + + + align:start position:0% +that with the input. And so that goes +into the adder and out comes y ofn. So + + align:start position:0% +into the adder and out comes y ofn. So + + + align:start position:0% +into the adder and out comes y ofn. So +this then corresponds to a block diagram + + align:start position:0% +this then corresponds to a block diagram + + + align:start position:0% +this then corresponds to a block diagram +representation of the difference + + align:start position:0% +representation of the difference + + + align:start position:0% +representation of the difference +equation or equivalently a digital + + align:start position:0% +equation or equivalently a digital + + + align:start position:0% +equation or equivalently a digital +network in block diagram notation. + + align:start position:0% +network in block diagram notation. + + + align:start position:0% +network in block diagram notation. +This notation in fact is a very common + + align:start position:0% +This notation in fact is a very common + + + align:start position:0% +This notation in fact is a very common +type of notation for graphically + + align:start position:0% +type of notation for graphically + + + align:start position:0% +type of notation for graphically +representing a difference equation or + + align:start position:0% +representing a difference equation or + + + align:start position:0% +representing a difference equation or +digital network. There is an alternative + + align:start position:0% +digital network. There is an alternative + + + align:start position:0% +digital network. There is an alternative +notation which has a number of important + + align:start position:0% +notation which has a number of important + + + align:start position:0% +notation which has a number of important +advantages + + align:start position:0% +advantages + + + align:start position:0% +advantages +which is very much like the block + + align:start position:0% +which is very much like the block + + + align:start position:0% +which is very much like the block +diagram with just a few minor changes + + align:start position:0% +diagram with just a few minor changes + + + align:start position:0% +diagram with just a few minor changes +which turn out in some instances to be + + align:start position:0% +which turn out in some instances to be + + + align:start position:0% +which turn out in some instances to be +convenient. And that is the graphical + + align:start position:0% +convenient. And that is the graphical + + + align:start position:0% +convenient. And that is the graphical +representation of the difference + + align:start position:0% +representation of the difference + + + align:start position:0% +representation of the difference +equation or the digital network in terms + + align:start position:0% +equation or the digital network in terms + + + align:start position:0% +equation or the digital network in terms +of signal flow graphs. + + align:start position:0% +of signal flow graphs. + + + align:start position:0% +of signal flow graphs. +Well, let me introduce the notation of + + align:start position:0% +Well, let me introduce the notation of + + + align:start position:0% +Well, let me introduce the notation of +signal flow graphs first in general and + + align:start position:0% +signal flow graphs first in general and + + + align:start position:0% +signal flow graphs first in general and +then more specifically as it applies to + + align:start position:0% +then more specifically as it applies to + + + align:start position:0% +then more specifically as it applies to +linear constant coefficient difference + + align:start position:0% +linear constant coefficient difference + + + align:start position:0% +linear constant coefficient difference +equations. + + align:start position:0% +equations. + + + align:start position:0% +equations. +A signal flow graph is + + align:start position:0% +A signal flow graph is + + + align:start position:0% +A signal flow graph is +essentially by definition a network of + + align:start position:0% +essentially by definition a network of + + + align:start position:0% +essentially by definition a network of +directed branches which are connected at + + align:start position:0% +directed branches which are connected at + + + align:start position:0% +directed branches which are connected at +nodes. + + align:start position:0% +nodes. + + + align:start position:0% +nodes. +So what that says is that in a signal + + align:start position:0% +So what that says is that in a signal + + + align:start position:0% +So what that says is that in a signal +flow graph we have what we'll refer to + + align:start position:0% +flow graph we have what we'll refer to + + + align:start position:0% +flow graph we have what we'll refer to +as nodes + + align:start position:0% +as nodes + + + align:start position:0% +as nodes +and directed branches. In other words, + + align:start position:0% +and directed branches. In other words, + + + align:start position:0% +and directed branches. In other words, +branches with arrows on them. + + align:start position:0% +branches with arrows on them. + + + align:start position:0% +branches with arrows on them. +the nodes will be numbered + + align:start position:0% +the nodes will be numbered + + + align:start position:0% +the nodes will be numbered +and so for example we would have a node + + align:start position:0% +and so for example we would have a node + + + align:start position:0% +and so for example we would have a node +J and a node K. + + align:start position:0% +J and a node K. + + + align:start position:0% +J and a node K. +Furthermore each node in the network has + + align:start position:0% +Furthermore each node in the network has + + + align:start position:0% +Furthermore each node in the network has +a variable associated with it. So that + + align:start position:0% +a variable associated with it. So that + + + align:start position:0% +a variable associated with it. So that +for example the J node has the variable + + align:start position:0% +for example the J node has the variable + + + align:start position:0% +for example the J node has the variable +w subj. The kith node has the variable w + + align:start position:0% +w subj. The kith node has the variable w + + + align:start position:0% +w subj. The kith node has the variable w +subk + + align:start position:0% + + + + align:start position:0% + +and we have a branch going between the j + + align:start position:0% +and we have a branch going between the j + + + align:start position:0% +and we have a branch going between the j +node and the kith node which will be + + align:start position:0% +node and the kith node which will be + + + align:start position:0% +node and the kith node which will be +referred to as the jke kith branch. + + align:start position:0% +referred to as the jke kith branch. + + + align:start position:0% +referred to as the jke kith branch. +So essentially the numbering of the + + align:start position:0% +So essentially the numbering of the + + + align:start position:0% +So essentially the numbering of the +nodes allows us to refer to the nodes + + align:start position:0% +nodes allows us to refer to the nodes + + + align:start position:0% +nodes allows us to refer to the nodes +and also to refer to the branches + + align:start position:0% +and also to refer to the branches + + + align:start position:0% +and also to refer to the branches +referring to the branches by talking + + align:start position:0% +referring to the branches by talking + + + align:start position:0% +referring to the branches by talking +about which nodes the branches go + + align:start position:0% +about which nodes the branches go + + + align:start position:0% +about which nodes the branches go +between. + + align:start position:0% +between. + + + align:start position:0% +between. +The nodes that I've indicated here + + align:start position:0% +The nodes that I've indicated here + + + align:start position:0% +The nodes that I've indicated here +correspond to what we'll refer to as + + align:start position:0% +correspond to what we'll refer to as + + + align:start position:0% +correspond to what we'll refer to as +network nodes. There are also source + + align:start position:0% +network nodes. There are also source + + + align:start position:0% +network nodes. There are also source +nodes and I've indicated one here. A + + align:start position:0% +nodes and I've indicated one here. A + + + align:start position:0% +nodes and I've indicated one here. A +source node is a node that has no + + align:start position:0% +source node is a node that has no + + + align:start position:0% +source node is a node that has no +branches coming into it, only branches + + align:start position:0% +branches coming into it, only branches + + + align:start position:0% +branches coming into it, only branches +leaving it. + + align:start position:0% +leaving it. + + + align:start position:0% +leaving it. +And the opposite, namely a sync node, + + align:start position:0% +And the opposite, namely a sync node, + + + align:start position:0% +And the opposite, namely a sync node, +which is a node that has no branches + + align:start position:0% +which is a node that has no branches + + + align:start position:0% +which is a node that has no branches +going out of it and only branches coming + + align:start position:0% +going out of it and only branches coming + + + align:start position:0% +going out of it and only branches coming +into it. Basically, it's these type of + + align:start position:0% +into it. Basically, it's these type of + + + align:start position:0% +into it. Basically, it's these type of +nodes that allow us to get inputs into + + align:start position:0% +nodes that allow us to get inputs into + + + align:start position:0% +nodes that allow us to get inputs into +the network. It's this type of node that + + align:start position:0% +the network. It's this type of node that + + + align:start position:0% +the network. It's this type of node that +we use to represent outputs from the + + align:start position:0% +we use to represent outputs from the + + + align:start position:0% +we use to represent outputs from the +network. + + align:start position:0% +network. + + + align:start position:0% +network. +Now this defines essentially the + + align:start position:0% +Now this defines essentially the + + + align:start position:0% +Now this defines essentially the +notation. It doesn't yet specify what + + align:start position:0% +notation. It doesn't yet specify what + + + align:start position:0% +notation. It doesn't yet specify what +the algebraic construction of a signal + + align:start position:0% +the algebraic construction of a signal + + + align:start position:0% +the algebraic construction of a signal +flow graph is. So in particular there + + align:start position:0% +flow graph is. So in particular there + + + align:start position:0% +flow graph is. So in particular there +are some rules that tell us how the node + + align:start position:0% +are some rules that tell us how the node + + + align:start position:0% +are some rules that tell us how the node +variables are related to inputs and + + align:start position:0% +variables are related to inputs and + + + align:start position:0% +variables are related to inputs and +outputs of branches or equivalently the + + align:start position:0% +outputs of branches or equivalently the + + + align:start position:0% +outputs of branches or equivalently the +inputs and outputs of other nodes. + + align:start position:0% +inputs and outputs of other nodes. + + + align:start position:0% +inputs and outputs of other nodes. +A branch the JKith branch which + + align:start position:0% +A branch the JKith branch which + + + align:start position:0% +A branch the JKith branch which +originates at node J terminates at node + + align:start position:0% +originates at node J terminates at node + + + align:start position:0% +originates at node J terminates at node +K has as its input the variable of the + + align:start position:0% +K has as its input the variable of the + + + align:start position:0% +K has as its input the variable of the +node that it originates from. + + align:start position:0% +node that it originates from. + + + align:start position:0% +node that it originates from. +It also has an output. The output we + + align:start position:0% +It also has an output. The output we + + + align:start position:0% +It also has an output. The output we +will denote as V subj. That's the output + + align:start position:0% +will denote as V subj. That's the output + + + align:start position:0% +will denote as V subj. That's the output +of the JK branch. And what it is very + + align:start position:0% +of the JK branch. And what it is very + + + align:start position:0% +of the JK branch. And what it is very +simply in the most general sense in the + + align:start position:0% +simply in the most general sense in the + + + align:start position:0% +simply in the most general sense in the +most general context is some function of + + align:start position:0% +most general context is some function of + + + align:start position:0% +most general context is some function of +the input to the branch. So the output + + align:start position:0% +the input to the branch. So the output + + + align:start position:0% +the input to the branch. So the output +of a branch is some function of the + + align:start position:0% +of a branch is some function of the + + + align:start position:0% +of a branch is some function of the +input to the branch where this function + + align:start position:0% +input to the branch where this function + + + align:start position:0% +input to the branch where this function +is different of course for different + + align:start position:0% +is different of course for different + + + align:start position:0% +is different of course for different +branches. + + align:start position:0% +branches. + + + align:start position:0% +branches. +Finally to get the values of the node + + align:start position:0% +Finally to get the values of the node + + + align:start position:0% +Finally to get the values of the node +variables the node values are defined to + + align:start position:0% +variables the node values are defined to + + + align:start position:0% +variables the node values are defined to +be equal to the sum of the outputs of + + align:start position:0% +be equal to the sum of the outputs of + + + align:start position:0% +be equal to the sum of the outputs of +the branches entering the node. + + align:start position:0% +the branches entering the node. + + + align:start position:0% +the branches entering the node. +So that if we were to look up here for + + align:start position:0% +So that if we were to look up here for + + + align:start position:0% +So that if we were to look up here for +example, this node variable + + align:start position:0% +example, this node variable + + + align:start position:0% +example, this node variable +would be equal to the output of this + + align:start position:0% +would be equal to the output of this + + + align:start position:0% +would be equal to the output of this +branch plus the output of that branch. + + align:start position:0% +branch plus the output of that branch. + + + align:start position:0% +branch plus the output of that branch. +And that's essentially the algebraic + + align:start position:0% +And that's essentially the algebraic + + + align:start position:0% +And that's essentially the algebraic +construction of flow graphs. + + align:start position:0% +construction of flow graphs. + + + align:start position:0% +construction of flow graphs. +It's also convenient to separate + + align:start position:0% +It's also convenient to separate + + + align:start position:0% +It's also convenient to separate +notationally + + align:start position:0% +notationally + + + align:start position:0% +notationally +the output of the branches from an + + align:start position:0% +the output of the branches from an + + + align:start position:0% +the output of the branches from an +internal node to another internal node + + align:start position:0% +internal node to another internal node + + + align:start position:0% +internal node to another internal node +or from a network node to a network node + + align:start position:0% +or from a network node to a network node + + + align:start position:0% +or from a network node to a network node +from those that from those the output of + + align:start position:0% +from those that from those the output of + + + align:start position:0% +from those that from those the output of +those branches that originate at sources + + align:start position:0% +those branches that originate at sources + + + align:start position:0% +those branches that originate at sources +and go to network nodes. And the + + align:start position:0% +and go to network nodes. And the + + + align:start position:0% +and go to network nodes. And the +notation that we'll use is S subj K + + align:start position:0% +notation that we'll use is S subj K + + + align:start position:0% +notation that we'll use is S subj K +corresponding to the output of the + + align:start position:0% +corresponding to the output of the + + + align:start position:0% +corresponding to the output of the +branch that goes from the J source. The + + align:start position:0% +branch that goes from the J source. The + + + align:start position:0% +branch that goes from the J source. The +source is being numbered differently + + align:start position:0% +source is being numbered differently + + + align:start position:0% +source is being numbered differently +from the network nodes going from the J + + align:start position:0% +from the network nodes going from the J + + + align:start position:0% +from the network nodes going from the J +source to the kith network node. + + align:start position:0% +source to the kith network node. + + + align:start position:0% +source to the kith network node. +Okay. So what this says and this + + align:start position:0% +Okay. So what this says and this + + + align:start position:0% +Okay. So what this says and this +equation in particular says that + + align:start position:0% +equation in particular says that + + + align:start position:0% +equation in particular says that +algebraically + + align:start position:0% +algebraically + + + align:start position:0% +algebraically +the node variables + + align:start position:0% +the node variables + + + align:start position:0% +the node variables +are specified + + align:start position:0% +are specified + + + align:start position:0% +are specified +as the kith node variable + + align:start position:0% +as the kith node variable + + + align:start position:0% +as the kith node variable +being equal to the sum over the internal + + align:start position:0% +being equal to the sum over the internal + + + align:start position:0% +being equal to the sum over the internal +nodes + + align:start position:0% +nodes + + + align:start position:0% +nodes +of the output of the branches from the + + align:start position:0% +of the output of the branches from the + + + align:start position:0% +of the output of the branches from the +network nodes to the kith node plus the + + align:start position:0% +network nodes to the kith node plus the + + + align:start position:0% +network nodes to the kith node plus the +output of the branches from the J over + + align:start position:0% +output of the branches from the J over + + + align:start position:0% +output of the branches from the J over +all the source nodes from the J source + + align:start position:0% +all the source nodes from the J source + + + align:start position:0% +all the source nodes from the J source +no source node to the network node that + + align:start position:0% +no source node to the network node that + + + align:start position:0% +no source node to the network node that +we're focusing on. So this corresponds + + align:start position:0% +we're focusing on. So this corresponds + + + align:start position:0% +we're focusing on. So this corresponds +to the output of the branches from the + + align:start position:0% +to the output of the branches from the + + + align:start position:0% +to the output of the branches from the +network nodes and this corresponds to + + align:start position:0% +network nodes and this corresponds to + + + align:start position:0% +network nodes and this corresponds to +the output of the branches from the + + align:start position:0% +the output of the branches from the + + + align:start position:0% +the output of the branches from the +source nodes. + + align:start position:0% + + + + align:start position:0% + +Well, + + align:start position:0% +Well, + + + align:start position:0% +Well, +for linear constant coefficient + + align:start position:0% +for linear constant coefficient + + + align:start position:0% +for linear constant coefficient +difference equations, + + align:start position:0% +difference equations, + + + align:start position:0% +difference equations, +we don't need all of the generality that + + align:start position:0% +we don't need all of the generality that + + + align:start position:0% +we don't need all of the generality that +we've implied in the discussion so far. + + align:start position:0% +we've implied in the discussion so far. + + + align:start position:0% +we've implied in the discussion so far. +In particular, what we can concentrate + + align:start position:0% +In particular, what we can concentrate + + + align:start position:0% +In particular, what we can concentrate +on is a special set of signal flow + + align:start position:0% +on is a special set of signal flow + + + align:start position:0% +on is a special set of signal flow +graphs, namely signal flow graphs which + + align:start position:0% +graphs, namely signal flow graphs which + + + align:start position:0% +graphs, namely signal flow graphs which +are linear. + + align:start position:0% +are linear. + + + align:start position:0% +are linear. +And what we mean by linear is that the + + align:start position:0% +And what we mean by linear is that the + + + align:start position:0% +And what we mean by linear is that the +output of a branch + + align:start position:0% +output of a branch + + + align:start position:0% +output of a branch +is equal to the input to the branch + + align:start position:0% +is equal to the input to the branch + + + align:start position:0% +is equal to the input to the branch +multiplied by some function. Uh so that + + align:start position:0% +multiplied by some function. Uh so that + + + align:start position:0% +multiplied by some function. Uh so that +it's a linear relationship between the + + align:start position:0% +it's a linear relationship between the + + + align:start position:0% +it's a linear relationship between the +branch output and the branch input. In + + align:start position:0% +branch output and the branch input. In + + + align:start position:0% +branch output and the branch input. In +other words, v subj k the output of the + + align:start position:0% +other words, v subj k the output of the + + + align:start position:0% +other words, v subj k the output of the +branch from the j node to the kith node + + align:start position:0% +branch from the j node to the kith node + + + align:start position:0% +branch from the j node to the kith node +is equal to some function. This might be + + align:start position:0% +is equal to some function. This might be + + + align:start position:0% +is equal to some function. This might be +simply a scalar or it might be a + + align:start position:0% +simply a scalar or it might be a + + + align:start position:0% +simply a scalar or it might be a +function of z for example which will + + align:start position:0% +function of z for example which will + + + align:start position:0% +function of z for example which will +often turn out to be multiplied by the + + align:start position:0% +often turn out to be multiplied by the + + + align:start position:0% +often turn out to be multiplied by the +input to that branch. In other words, + + align:start position:0% +input to that branch. In other words, + + + align:start position:0% +input to that branch. In other words, +the value of the j node. + + align:start position:0% +the value of the j node. + + + align:start position:0% +the value of the j node. +So that is then the additional + + align:start position:0% +So that is then the additional + + + align:start position:0% +So that is then the additional +constraint that we impose if we're + + align:start position:0% +constraint that we impose if we're + + + align:start position:0% +constraint that we impose if we're +talking about linear signal flow graphs + + align:start position:0% +talking about linear signal flow graphs + + + align:start position:0% +talking about linear signal flow graphs +which we'll be concentrating on for the + + align:start position:0% +which we'll be concentrating on for the + + + align:start position:0% +which we'll be concentrating on for the +rest of the lecture. + + align:start position:0% +rest of the lecture. + + + align:start position:0% +rest of the lecture. +Okay. Well to see how a linear constant + + align:start position:0% +Okay. Well to see how a linear constant + + + align:start position:0% +Okay. Well to see how a linear constant +coefficient difference equation can be + + align:start position:0% +coefficient difference equation can be + + + align:start position:0% +coefficient difference equation can be +represented in terms of linear signal + + align:start position:0% +represented in terms of linear signal + + + align:start position:0% +represented in terms of linear signal +flow graphs. Let's take the same example + + align:start position:0% +flow graphs. Let's take the same example + + + align:start position:0% +flow graphs. Let's take the same example +that we had been that we worked with + + align:start position:0% +that we had been that we worked with + + + align:start position:0% +that we had been that we worked with +previously in terms of the block diagram + + align:start position:0% +previously in terms of the block diagram + + + align:start position:0% +previously in terms of the block diagram +notation. In other words, y of n is + + align:start position:0% +notation. In other words, y of n is + + + align:start position:0% +notation. In other words, y of n is +equal to a * y of n -1 + x of n. + + align:start position:0% +equal to a * y of n -1 + x of n. + + + align:start position:0% +equal to a * y of n -1 + x of n. +Well, we have a node that's a source + + align:start position:0% +Well, we have a node that's a source + + + align:start position:0% +Well, we have a node that's a source +node. That's x ofn. We have a node + + align:start position:0% +node. That's x ofn. We have a node + + + align:start position:0% +node. That's x ofn. We have a node +that's a sync node. That's y of n. + + align:start position:0% +that's a sync node. That's y of n. + + + align:start position:0% +that's a sync node. That's y of n. +That's what we'd like to get out of the + + align:start position:0% +That's what we'd like to get out of the + + + align:start position:0% +That's what we'd like to get out of the +network. And presumably somehow we've + + align:start position:0% +network. And presumably somehow we've + + + align:start position:0% +network. And presumably somehow we've +gotten a network node whose value will + + align:start position:0% +gotten a network node whose value will + + + align:start position:0% +gotten a network node whose value will +be y of n minus one. If we have that + + align:start position:0% +be y of n minus one. If we have that + + + align:start position:0% +be y of n minus one. If we have that +node then what we want to form to get y + + align:start position:0% +node then what we want to form to get y + + + align:start position:0% +node then what we want to form to get y +of n + + align:start position:0% +of n + + + align:start position:0% +of n +is a * y of n minus one. + + align:start position:0% +is a * y of n minus one. + + + align:start position:0% +is a * y of n minus one. +So we want y of n minus one multiplied + + align:start position:0% +So we want y of n minus one multiplied + + + align:start position:0% +So we want y of n minus one multiplied +by a which means that this branch has a + + align:start position:0% +by a which means that this branch has a + + + align:start position:0% +by a which means that this branch has a +transmittance + + align:start position:0% +transmittance + + + align:start position:0% +transmittance +which is or a gain which is a + + align:start position:0% +which is or a gain which is a + + + align:start position:0% +which is or a gain which is a +and then because of the algebraic + + align:start position:0% +and then because of the algebraic + + + align:start position:0% +and then because of the algebraic +definition at nodes the value of this + + align:start position:0% +definition at nodes the value of this + + + align:start position:0% +definition at nodes the value of this +node is the sum of this branch and the + + align:start position:0% +node is the sum of this branch and the + + + align:start position:0% +node is the sum of this branch and the +output of this branch. So if this branch + + align:start position:0% +output of this branch. So if this branch + + + align:start position:0% +output of this branch. So if this branch +has a gain of unity, + + align:start position:0% +has a gain of unity, + + + align:start position:0% +has a gain of unity, +then this node variable will have the + + align:start position:0% +then this node variable will have the + + + align:start position:0% +then this node variable will have the +value x of n + a * y of n minus one. + + align:start position:0% +value x of n + a * y of n minus one. + + + align:start position:0% +value x of n + a * y of n minus one. +Well, now we simply have to get from + + align:start position:0% +Well, now we simply have to get from + + + align:start position:0% +Well, now we simply have to get from +here all the way out to there. I've + + align:start position:0% +here all the way out to there. I've + + + align:start position:0% +here all the way out to there. I've +drawn it the network somewhat + + align:start position:0% +drawn it the network somewhat + + + align:start position:0% +drawn it the network somewhat +inefficiently. I can get from this node + + align:start position:0% +inefficiently. I can get from this node + + + align:start position:0% +inefficiently. I can get from this node +to this node simply with a unity gain. + + align:start position:0% +to this node simply with a unity gain. + + + align:start position:0% +to this node simply with a unity gain. +from this node to the output node again + + align:start position:0% +from this node to the output node again + + + align:start position:0% +from this node to the output node again +with a unity gain. + + align:start position:0% +with a unity gain. + + + align:start position:0% +with a unity gain. +And now the only question is of course + + align:start position:0% +And now the only question is of course + + + align:start position:0% +And now the only question is of course +if this is y of n then this node has + + align:start position:0% +if this is y of n then this node has + + + align:start position:0% +if this is y of n then this node has +value y of n also. How do I get from + + align:start position:0% +value y of n also. How do I get from + + + align:start position:0% +value y of n also. How do I get from +this node to this node if I'm talking + + align:start position:0% +this node to this node if I'm talking + + + align:start position:0% +this node to this node if I'm talking +about a linear signal flow graph? Well y + + align:start position:0% +about a linear signal flow graph? Well y + + + align:start position:0% +about a linear signal flow graph? Well y +of n minus one of course isn't a scalar + + align:start position:0% +of n minus one of course isn't a scalar + + + align:start position:0% +of n minus one of course isn't a scalar +multiplied by y of n. But y of z or the + + align:start position:0% +multiplied by y of n. But y of z or the + + + align:start position:0% +multiplied by y of n. But y of z or the +z transform rather of y of n minus one + + align:start position:0% +z transform rather of y of n minus one + + + align:start position:0% +z transform rather of y of n minus one +is actually a scalar or function + + align:start position:0% +is actually a scalar or function + + + align:start position:0% +is actually a scalar or function +multiplied by the z transform of y ofn. + + align:start position:0% +multiplied by the z transform of y ofn. + + + align:start position:0% +multiplied by the z transform of y ofn. +So if I were to think of this rather + + align:start position:0% +So if I were to think of this rather + + + align:start position:0% +So if I were to think of this rather +than in terms of the sequences, if I + + align:start position:0% +than in terms of the sequences, if I + + + align:start position:0% +than in terms of the sequences, if I +were to think of this in terms of the Z + + align:start position:0% +were to think of this in terms of the Z + + + align:start position:0% +were to think of this in terms of the Z +transform, + + align:start position:0% +transform, + + + align:start position:0% +transform, +then in fact the Z transform + + align:start position:0% +then in fact the Z transform + + + align:start position:0% +then in fact the Z transform +at this node would be Z to the minus1 + + align:start position:0% +at this node would be Z to the minus1 + + + align:start position:0% +at this node would be Z to the minus1 +times Y of Z. + + align:start position:0% +times Y of Z. + + + align:start position:0% +times Y of Z. +And consequently thinking of it in terms + + align:start position:0% +And consequently thinking of it in terms + + + align:start position:0% +And consequently thinking of it in terms +of Z transforms the gain of this branch + + align:start position:0% +of Z transforms the gain of this branch + + + align:start position:0% +of Z transforms the gain of this branch +then is + + align:start position:0% +then is + + + align:start position:0% +then is +Z to the minus1. + + align:start position:0% +Z to the minus1. + + + align:start position:0% +Z to the minus1. +So this in fact does correspond to + + align:start position:0% +So this in fact does correspond to + + + align:start position:0% +So this in fact does correspond to +multiplication by a function of Z as + + align:start position:0% +multiplication by a function of Z as + + + align:start position:0% +multiplication by a function of Z as +long as in the background what we + + align:start position:0% +long as in the background what we + + + align:start position:0% +long as in the background what we +remember is that we're essentially + + align:start position:0% +remember is that we're essentially + + + align:start position:0% +remember is that we're essentially +thinking of that as representing or the + + align:start position:0% +thinking of that as representing or the + + + align:start position:0% +thinking of that as representing or the +flow graph is representing relationships + + align:start position:0% +flow graph is representing relationships + + + align:start position:0% +flow graph is representing relationships +between the Z transform. Now obviously + + align:start position:0% +between the Z transform. Now obviously + + + align:start position:0% +between the Z transform. Now obviously +we wouldn't feel constraint to designate + + align:start position:0% +we wouldn't feel constraint to designate + + + align:start position:0% +we wouldn't feel constraint to designate +it that way all the time. In other + + align:start position:0% +it that way all the time. In other + + + align:start position:0% +it that way all the time. In other +words, I would I would feel very + + align:start position:0% +words, I would I would feel very + + + align:start position:0% +words, I would I would feel very +comfortable about drawing this flow + + align:start position:0% +comfortable about drawing this flow + + + align:start position:0% +comfortable about drawing this flow +graph and labeling this input as X ofn, + + align:start position:0% +graph and labeling this input as X ofn, + + + align:start position:0% +graph and labeling this input as X ofn, +labeling this node as Y of N and this is + + align:start position:0% +labeling this node as Y of N and this is + + + align:start position:0% +labeling this node as Y of N and this is +Y of N minus one and indicating that + + align:start position:0% +Y of N minus one and indicating that + + + align:start position:0% +Y of N minus one and indicating that +this branch has a transmittance of Z to + + align:start position:0% +this branch has a transmittance of Z to + + + align:start position:0% +this branch has a transmittance of Z to +the minus1. Just simply in the + + align:start position:0% +the minus1. Just simply in the + + + align:start position:0% +the minus1. Just simply in the +background, what we what we realize is + + align:start position:0% +background, what we what we realize is + + + align:start position:0% +background, what we what we realize is +it's not Y of N that's multiplied by Z + + align:start position:0% +it's not Y of N that's multiplied by Z + + + align:start position:0% +it's not Y of N that's multiplied by Z +to the minus1. It's Y of Z that's + + align:start position:0% +to the minus1. It's Y of Z that's + + + align:start position:0% +to the minus1. It's Y of Z that's +multiplied by Z to the minus1. + + align:start position:0% +multiplied by Z to the minus1. + + + align:start position:0% +multiplied by Z to the minus1. +Also, uh, notationally, it's usually + + align:start position:0% +Also, uh, notationally, it's usually + + + align:start position:0% +Also, uh, notationally, it's usually +convenient + + align:start position:0% +convenient + + + align:start position:0% +convenient +since very often we end up with branches + + align:start position:0% +since very often we end up with branches + + + align:start position:0% +since very often we end up with branches +that have unity gain + + align:start position:0% +that have unity gain + + + align:start position:0% +that have unity gain +to + + align:start position:0% +to + + + align:start position:0% +to +choose the convention that if a branch + + align:start position:0% +choose the convention that if a branch + + + align:start position:0% +choose the convention that if a branch +doesn't have the gain labeled on it, the + + align:start position:0% +doesn't have the gain labeled on it, the + + + align:start position:0% +doesn't have the gain labeled on it, the +implication is that what the gain is in + + align:start position:0% +implication is that what the gain is in + + + align:start position:0% +implication is that what the gain is in +fact is unity. So generally actually we + + align:start position:0% +fact is unity. So generally actually we + + + align:start position:0% +fact is unity. So generally actually we +won't + + align:start position:0% +won't + + + align:start position:0% +won't +specify explicitly unity gain. If there + + align:start position:0% +specify explicitly unity gain. If there + + + align:start position:0% +specify explicitly unity gain. If there +is a branch with unity gain, we simply + + align:start position:0% +is a branch with unity gain, we simply + + + align:start position:0% +is a branch with unity gain, we simply +won't label the gain. One final point + + align:start position:0% +won't label the gain. One final point + + + align:start position:0% +won't label the gain. One final point +and that is that you can I I think see + + align:start position:0% +and that is that you can I I think see + + + align:start position:0% +and that is that you can I I think see +uh you probably observed this for + + align:start position:0% +uh you probably observed this for + + + align:start position:0% +uh you probably observed this for +yourself already that actually this flow + + align:start position:0% +yourself already that actually this flow + + + align:start position:0% +yourself already that actually this flow +graph is drawn somewhat inefficiently as + + align:start position:0% +graph is drawn somewhat inefficiently as + + + align:start position:0% +graph is drawn somewhat inefficiently as +I've indicated it here. Basically, I can + + align:start position:0% +I've indicated it here. Basically, I can + + + align:start position:0% +I've indicated it here. Basically, I can +take these two nodes and collapse them + + align:start position:0% +take these two nodes and collapse them + + + align:start position:0% +take these two nodes and collapse them +together. + + align:start position:0% +together. + + + align:start position:0% +together. +I chose to draw this flow graph this way + + align:start position:0% +I chose to draw this flow graph this way + + + align:start position:0% +I chose to draw this flow graph this way +so that it looks as much like the block + + align:start position:0% +so that it looks as much like the block + + + align:start position:0% +so that it looks as much like the block +diagram representation as possible. And + + align:start position:0% +diagram representation as possible. And + + + align:start position:0% +diagram representation as possible. And +in fact, if you compare it back to the + + align:start position:0% +in fact, if you compare it back to the + + + align:start position:0% +in fact, if you compare it back to the +block diagram representation, it is + + align:start position:0% +block diagram representation, it is + + + align:start position:0% +block diagram representation, it is +basically the same except for the fact + + align:start position:0% +basically the same except for the fact + + + align:start position:0% +basically the same except for the fact +that we've chosen to represent this + + align:start position:0% +that we've chosen to represent this + + + align:start position:0% +that we've chosen to represent this +delay branch a little differently. And + + align:start position:0% +delay branch a little differently. And + + + align:start position:0% +delay branch a little differently. And +we've used the algebra of signal flow + + align:start position:0% +we've used the algebra of signal flow + + + align:start position:0% +we've used the algebra of signal flow +graphs to do the addition at nodes + + align:start position:0% +graphs to do the addition at nodes + + + align:start position:0% +graphs to do the addition at nodes +rather than explicitly putting in an + + align:start position:0% +rather than explicitly putting in an + + + align:start position:0% +rather than explicitly putting in an +adder. And that's really the only + + align:start position:0% +adder. And that's really the only + + + align:start position:0% +adder. And that's really the only +difference. + + align:start position:0% + + + + align:start position:0% + +Now + + align:start position:0% +Now + + + align:start position:0% +Now +what a flow graph or a block diagram is + + align:start position:0% +what a flow graph or a block diagram is + + + align:start position:0% +what a flow graph or a block diagram is +as I've stressed is a graphical + + align:start position:0% +as I've stressed is a graphical + + + align:start position:0% +as I've stressed is a graphical +representation of the difference + + align:start position:0% +representation of the difference + + + align:start position:0% +representation of the difference +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and what it in turn corresponds to is a + + align:start position:0% +and what it in turn corresponds to is a + + + align:start position:0% +and what it in turn corresponds to is a +graphical representation of a linear set + + align:start position:0% +graphical representation of a linear set + + + align:start position:0% +graphical representation of a linear set +of equations. is a set of equations + + align:start position:0% +of equations. is a set of equations + + + align:start position:0% +of equations. is a set of equations +which describe the relationships among + + align:start position:0% +which describe the relationships among + + + align:start position:0% +which describe the relationships among +the various variables or among the nodes + + align:start position:0% +the various variables or among the nodes + + + align:start position:0% +the various variables or among the nodes +in the digital network. + + align:start position:0% +in the digital network. + + + align:start position:0% +in the digital network. +If I were for example going to implement + + align:start position:0% +If I were for example going to implement + + + align:start position:0% +If I were for example going to implement +a difference equation or a signal flow + + align:start position:0% +a difference equation or a signal flow + + + align:start position:0% +a difference equation or a signal flow +graph on a digital computer, + + align:start position:0% +graph on a digital computer, + + + align:start position:0% +graph on a digital computer, +what I would implement in effect is not + + align:start position:0% +what I would implement in effect is not + + + align:start position:0% +what I would implement in effect is not +the graphics of the signal flow graph. I + + align:start position:0% +the graphics of the signal flow graph. I + + + align:start position:0% +the graphics of the signal flow graph. I +would implement the algebra of the + + align:start position:0% +would implement the algebra of the + + + align:start position:0% +would implement the algebra of the +signal flow graph. In other words, I + + align:start position:0% +signal flow graph. In other words, I + + + align:start position:0% +signal flow graph. In other words, I +would implement the linear set of + + align:start position:0% +would implement the linear set of + + + align:start position:0% +would implement the linear set of +equations that the flow graph + + align:start position:0% +equations that the flow graph + + + align:start position:0% +equations that the flow graph +corresponds to. + + align:start position:0% +corresponds to. + + + align:start position:0% +corresponds to. +Consequently, what I'd like to spend the + + align:start position:0% +Consequently, what I'd like to spend the + + + align:start position:0% +Consequently, what I'd like to spend the +remainder of the lecture on is focusing + + align:start position:0% +remainder of the lecture on is focusing + + + align:start position:0% +remainder of the lecture on is focusing +on the equivalent linear set of + + align:start position:0% +on the equivalent linear set of + + + align:start position:0% +on the equivalent linear set of +equations that the signal flow graph + + align:start position:0% +equations that the signal flow graph + + + align:start position:0% +equations that the signal flow graph +corresponds to. In other words, the + + align:start position:0% +corresponds to. In other words, the + + + align:start position:0% +corresponds to. In other words, the +matrix representation of a digital + + align:start position:0% +matrix representation of a digital + + + align:start position:0% +matrix representation of a digital +network. And the matrix representation + + align:start position:0% +network. And the matrix representation + + + align:start position:0% +network. And the matrix representation +is important from a number of points of + + align:start position:0% +is important from a number of points of + + + align:start position:0% +is important from a number of points of +view. One is of course that as I've just + + align:start position:0% +view. One is of course that as I've just + + + align:start position:0% +view. One is of course that as I've just +stressed it's important for the actual + + align:start position:0% +stressed it's important for the actual + + + align:start position:0% +stressed it's important for the actual +implementation of the digital network. + + align:start position:0% +implementation of the digital network. + + + align:start position:0% +implementation of the digital network. +It's also important in the sense that + + align:start position:0% +It's also important in the sense that + + + align:start position:0% +It's also important in the sense that +lots of properties of digital networks + + align:start position:0% +lots of properties of digital networks + + + align:start position:0% +lots of properties of digital networks +fall out from the properties of + + align:start position:0% +fall out from the properties of + + + align:start position:0% +fall out from the properties of +matrices. + + align:start position:0% +matrices. + + + align:start position:0% +matrices. +We won't in fact in this set of lectures + + align:start position:0% +We won't in fact in this set of lectures + + + align:start position:0% +We won't in fact in this set of lectures +be exploiting that particularly but it + + align:start position:0% +be exploiting that particularly but it + + + align:start position:0% +be exploiting that particularly but it +is one of the reasons why the matrix + + align:start position:0% +is one of the reasons why the matrix + + + align:start position:0% +is one of the reasons why the matrix +representation of digital networks is + + align:start position:0% +representation of digital networks is + + + align:start position:0% +representation of digital networks is +also important to be aware of. + + align:start position:0% +also important to be aware of. + + + align:start position:0% +also important to be aware of. +So let's then see what this graphical + + align:start position:0% +So let's then see what this graphical + + + align:start position:0% +So let's then see what this graphical +representation or the linear signal + + align:start position:0% +representation or the linear signal + + + align:start position:0% +representation or the linear signal +flowraph representation + + align:start position:0% +flowraph representation + + + align:start position:0% +flowraph representation +corresponds to in terms of a set of + + align:start position:0% +corresponds to in terms of a set of + + + align:start position:0% +corresponds to in terms of a set of +linear equations or in terms of a set of + + align:start position:0% +linear equations or in terms of a set of + + + align:start position:0% +linear equations or in terms of a set of +matrices. + + align:start position:0% +matrices. + + + align:start position:0% +matrices. +So we're considering then + + align:start position:0% +So we're considering then + + + align:start position:0% +So we're considering then +a general network. It has some internal + + align:start position:0% +a general network. It has some internal + + + align:start position:0% +a general network. It has some internal +nodes, branches coming into them. Uh + + align:start position:0% +nodes, branches coming into them. Uh + + + align:start position:0% +nodes, branches coming into them. Uh +I've indicated one source node and one + + align:start position:0% +I've indicated one source node and one + + + align:start position:0% +I've indicated one source node and one +sync node. More generally, there would + + align:start position:0% +sync node. More generally, there would + + + align:start position:0% +sync node. More generally, there would +be a set of source nodes and a set of + + align:start position:0% +be a set of source nodes and a set of + + + align:start position:0% +be a set of source nodes and a set of +sync nodes. + + align:start position:0% +sync nodes. + + + align:start position:0% +sync nodes. +The algebraic equations that the flow + + align:start position:0% +The algebraic equations that the flow + + + align:start position:0% +The algebraic equations that the flow +graph corresponds to is a statement + + align:start position:0% +graph corresponds to is a statement + + + align:start position:0% +graph corresponds to is a statement +between + + align:start position:0% +between + + + align:start position:0% +between +a statement of how the node variables + + align:start position:0% +a statement of how the node variables + + + align:start position:0% +a statement of how the node variables +are related to each other. And just to + + align:start position:0% +are related to each other. And just to + + + align:start position:0% +are related to each other. And just to +remind you of how that's generated the + + align:start position:0% +remind you of how that's generated the + + + align:start position:0% +remind you of how that's generated the +and I'm expressing this now in terms of + + align:start position:0% +and I'm expressing this now in terms of + + + align:start position:0% +and I'm expressing this now in terms of +the Z transforms of the node variables. + + align:start position:0% +the Z transforms of the node variables. + + + align:start position:0% +the Z transforms of the node variables. +The Z transform of the kith node + + align:start position:0% +The Z transform of the kith node + + + align:start position:0% +The Z transform of the kith node +variable is the sum over the network + + align:start position:0% +variable is the sum over the network + + + align:start position:0% +variable is the sum over the network +nodes + + align:start position:0% +nodes + + + align:start position:0% +nodes +of the branch outputs that's indicated + + align:start position:0% +of the branch outputs that's indicated + + + align:start position:0% +of the branch outputs that's indicated +here plus the sum over the source branch + + align:start position:0% +here plus the sum over the source branch + + + align:start position:0% +here plus the sum over the source branch +outputs. + + align:start position:0% +outputs. + + + align:start position:0% +outputs. +And incidentally I've assumed and it's + + align:start position:0% +And incidentally I've assumed and it's + + + align:start position:0% +And incidentally I've assumed and it's +just best to assume this because of + + align:start position:0% +just best to assume this because of + + + align:start position:0% +just best to assume this because of +notational convenience that there's a + + align:start position:0% +notational convenience that there's a + + + align:start position:0% +notational convenience that there's a +branch from every network node to every + + align:start position:0% +branch from every network node to every + + + align:start position:0% +branch from every network node to every +other network node. Obviously, I can + + align:start position:0% +other network node. Obviously, I can + + + align:start position:0% +other network node. Obviously, I can +always get away with that. If that + + align:start position:0% +always get away with that. If that + + + align:start position:0% +always get away with that. If that +branch doesn't really exist, I simply + + align:start position:0% +branch doesn't really exist, I simply + + + align:start position:0% +branch doesn't really exist, I simply +set the gain of that branch equal to + + align:start position:0% +set the gain of that branch equal to + + + align:start position:0% +set the gain of that branch equal to +zero. + + align:start position:0% +zero. + + + align:start position:0% +zero. +Now, furthermore, we have the + + align:start position:0% +Now, furthermore, we have the + + + align:start position:0% +Now, furthermore, we have the +relationship that defines what the + + align:start position:0% +relationship that defines what the + + + align:start position:0% +relationship that defines what the +branch output is in terms of the branch + + align:start position:0% +branch output is in terms of the branch + + + align:start position:0% +branch output is in terms of the branch +input or in terms of the node variables. + + align:start position:0% +input or in terms of the node variables. + + + align:start position:0% +input or in terms of the node variables. +So we have specifically the statement + + align:start position:0% +So we have specifically the statement + + + align:start position:0% +So we have specifically the statement +that V subj K the output of the JK + + align:start position:0% +that V subj K the output of the JK + + + align:start position:0% +that V subj K the output of the JK +branch is some function of Z + + align:start position:0% +branch is some function of Z + + + align:start position:0% +branch is some function of Z +multiplied by the branch input + + align:start position:0% +multiplied by the branch input + + + align:start position:0% +multiplied by the branch input +and furthermore the source branch output + + align:start position:0% +and furthermore the source branch output + + + align:start position:0% +and furthermore the source branch output +is some function or scalar multiplied by + + align:start position:0% +is some function or scalar multiplied by + + + align:start position:0% +is some function or scalar multiplied by +the source node value. + + align:start position:0% +the source node value. + + + align:start position:0% +the source node value. +Well, if we substitute these two + + align:start position:0% +Well, if we substitute these two + + + align:start position:0% +Well, if we substitute these two +equations into the previous equation + + align:start position:0% +equations into the previous equation + + + align:start position:0% +equations into the previous equation +which defined what the node values are, + + align:start position:0% +which defined what the node values are, + + + align:start position:0% +which defined what the node values are, +we end up with a statement that says + + align:start position:0% +we end up with a statement that says + + + align:start position:0% +we end up with a statement that says +that the node variables is equal to or + + align:start position:0% +that the node variables is equal to or + + + align:start position:0% +that the node variables is equal to or +equal to a linear combination of the + + align:start position:0% +equal to a linear combination of the + + + align:start position:0% +equal to a linear combination of the +node variables. the linear combination + + align:start position:0% +node variables. the linear combination + + + align:start position:0% +node variables. the linear combination +specified by the branch transmittances + + align:start position:0% +specified by the branch transmittances + + + align:start position:0% +specified by the branch transmittances +plus a linear combination of the source + + align:start position:0% +plus a linear combination of the source + + + align:start position:0% +plus a linear combination of the source +node values and this then is a set of + + align:start position:0% +node values and this then is a set of + + + align:start position:0% +node values and this then is a set of +linear equations that in essence defines + + align:start position:0% +linear equations that in essence defines + + + align:start position:0% +linear equations that in essence defines +the digital network. + + align:start position:0% +the digital network. + + + align:start position:0% +the digital network. +This is a set of equations of course + + align:start position:0% +This is a set of equations of course + + + align:start position:0% +This is a set of equations of course +because we have an equation like this + + align:start position:0% +because we have an equation like this + + + align:start position:0% +because we have an equation like this +for each value of K as K runs over all + + align:start position:0% +for each value of K as K runs over all + + + align:start position:0% +for each value of K as K runs over all +the network nodes. In other words, for K + + align:start position:0% +the network nodes. In other words, for K + + + align:start position:0% +the network nodes. In other words, for K +starting from one and running up to N, + + align:start position:0% +starting from one and running up to N, + + + align:start position:0% +starting from one and running up to N, +we can express this set of linear + + align:start position:0% +we can express this set of linear + + + align:start position:0% +we can express this set of linear +equations in matrix notation. + + align:start position:0% +equations in matrix notation. + + + align:start position:0% +equations in matrix notation. +If we think of a column vector + + align:start position:0% +If we think of a column vector + + + align:start position:0% +If we think of a column vector +corresponding to the node variables, + + align:start position:0% +corresponding to the node variables, + + + align:start position:0% +corresponding to the node variables, +then this equation says that the ve the + + align:start position:0% +then this equation says that the ve the + + + align:start position:0% +then this equation says that the ve the +vector or matrix column matrix of node + + align:start position:0% +vector or matrix column matrix of node + + + align:start position:0% +vector or matrix column matrix of node +variables is equal to a matrix of + + align:start position:0% +variables is equal to a matrix of + + + align:start position:0% +variables is equal to a matrix of +coefficients dictated by the branch + + align:start position:0% +coefficients dictated by the branch + + + align:start position:0% +coefficients dictated by the branch +transmittances + + align:start position:0% +transmittances + + + align:start position:0% +transmittances +multiplied again by the node variables + + align:start position:0% +multiplied again by the node variables + + + align:start position:0% +multiplied again by the node variables +plus a second matrix + + align:start position:0% +plus a second matrix + + + align:start position:0% +plus a second matrix +multiplied by the column of source node + + align:start position:0% +multiplied by the column of source node + + + align:start position:0% +multiplied by the column of source node +values. + + align:start position:0% +values. + + + align:start position:0% +values. +And there's one peculiar thing that + + align:start position:0% +And there's one peculiar thing that + + + align:start position:0% +And there's one peculiar thing that +happens notationally here which it's + + align:start position:0% +happens notationally here which it's + + + align:start position:0% +happens notationally here which it's +worthwhile to straighten out. + + align:start position:0% +worthwhile to straighten out. + + + align:start position:0% +worthwhile to straighten out. +It happens because of the way that we + + align:start position:0% +It happens because of the way that we + + + align:start position:0% +It happens because of the way that we +chose to write these equations that the + + align:start position:0% +chose to write these equations that the + + + align:start position:0% +chose to write these equations that the +branch transmittance values + + align:start position:0% +branch transmittance values + + + align:start position:0% +branch transmittance values +come into the matrix as I've indicated + + align:start position:0% +come into the matrix as I've indicated + + + align:start position:0% +come into the matrix as I've indicated +here. So the first row for example + + align:start position:0% +here. So the first row for example + + + align:start position:0% +here. So the first row for example +contains f11 f_sub_21 through fubn1. + + align:start position:0% +contains f11 f_sub_21 through fubn1. + + + align:start position:0% +contains f11 f_sub_21 through fubn1. +As you're well aware, typically in + + align:start position:0% +As you're well aware, typically in + + + align:start position:0% +As you're well aware, typically in +defining a matrix and matrix elements, + + align:start position:0% +defining a matrix and matrix elements, + + + align:start position:0% +defining a matrix and matrix elements, +the general convention is to refer to + + align:start position:0% +the general convention is to refer to + + + align:start position:0% +the general convention is to refer to +the matrix elements with the first index + + align:start position:0% +the matrix elements with the first index + + + align:start position:0% +the matrix elements with the first index +corresponding to the row, the second + + align:start position:0% +corresponding to the row, the second + + + align:start position:0% +corresponding to the row, the second +index corresponding to the column. So + + align:start position:0% +index corresponding to the column. So + + + align:start position:0% +index corresponding to the column. So +the the + + align:start position:0% +the the + + + align:start position:0% +the the +tendency is to refer to the matrix + + align:start position:0% +tendency is to refer to the matrix + + + align:start position:0% +tendency is to refer to the matrix +elements as a11 a12 through a1n etc. So + + align:start position:0% +elements as a11 a12 through a1n etc. So + + + align:start position:0% +elements as a11 a12 through a1n etc. So +that simply means that in writing this + + align:start position:0% +that simply means that in writing this + + + align:start position:0% +that simply means that in writing this +set of equations in compact matrix form, + + align:start position:0% +set of equations in compact matrix form, + + + align:start position:0% +set of equations in compact matrix form, +it's convenient to do that by referring + + align:start position:0% +it's convenient to do that by referring + + + align:start position:0% +it's convenient to do that by referring +to the transpose of a matrix of + + align:start position:0% +to the transpose of a matrix of + + + align:start position:0% +to the transpose of a matrix of +coefficients rather than directly to the + + align:start position:0% +coefficients rather than directly to the + + + align:start position:0% +coefficients rather than directly to the +matrix of coefficients itself. In other + + align:start position:0% +matrix of coefficients itself. In other + + + align:start position:0% +matrix of coefficients itself. In other +words, it's convenient when I write this + + align:start position:0% +words, it's convenient when I write this + + + align:start position:0% +words, it's convenient when I write this +set of equations or this set of + + align:start position:0% +set of equations or this set of + + + align:start position:0% +set of equations or this set of +equations in compact matrix notation + + align:start position:0% +equations in compact matrix notation + + + align:start position:0% +equations in compact matrix notation +to write it as I've indicated here. + + align:start position:0% +to write it as I've indicated here. + + + align:start position:0% +to write it as I've indicated here. +We have a column vector of node values, + + align:start position:0% +We have a column vector of node values, + + + align:start position:0% +We have a column vector of node values, +node variables equal to a transpose + + align:start position:0% +node variables equal to a transpose + + + align:start position:0% +node variables equal to a transpose +coefficient matrix multiplied by the + + align:start position:0% +coefficient matrix multiplied by the + + + align:start position:0% +coefficient matrix multiplied by the +column vector of node variables. And + + align:start position:0% +column vector of node variables. And + + + align:start position:0% +column vector of node variables. And +then the transpose of the transmittances + + align:start position:0% +then the transpose of the transmittances + + + align:start position:0% +then the transpose of the transmittances +that connect the sources to the internal + + align:start position:0% +that connect the sources to the internal + + + align:start position:0% +that connect the sources to the internal +network nodes multiplied by the source + + align:start position:0% +network nodes multiplied by the source + + + align:start position:0% +network nodes multiplied by the source +vector + + align:start position:0% +vector + + + align:start position:0% +vector +where the matrix f of z the kj element + + align:start position:0% +where the matrix f of z the kj element + + + align:start position:0% +where the matrix f of z the kj element +of the matrix f of z is f subkj of z. Uh + + align:start position:0% +of the matrix f of z is f subkj of z. Uh + + + align:start position:0% +of the matrix f of z is f subkj of z. Uh +I I think that it takes just a few + + align:start position:0% +I I think that it takes just a few + + + align:start position:0% +I I think that it takes just a few +minutes of private reflection to see + + align:start position:0% +minutes of private reflection to see + + + align:start position:0% +minutes of private reflection to see +that this works out notationally, but + + align:start position:0% +that this works out notationally, but + + + align:start position:0% +that this works out notationally, but +it's this reason it's it's to it's to + + align:start position:0% +it's this reason it's it's to it's to + + + align:start position:0% +it's this reason it's it's to it's to +interface the matrix notation and the + + align:start position:0% +interface the matrix notation and the + + + align:start position:0% +interface the matrix notation and the +flowraphph notation that makes it + + align:start position:0% +flowraphph notation that makes it + + + align:start position:0% +flowraphph notation that makes it +convenient to refer to the transpose to + + align:start position:0% +convenient to refer to the transpose to + + + align:start position:0% +convenient to refer to the transpose to +a transpose matrix here rather than uh + + align:start position:0% +a transpose matrix here rather than uh + + + align:start position:0% +a transpose matrix here rather than uh +omitting the transposition. + + align:start position:0% + + + + align:start position:0% + +It's typical and notationally what we'll + + align:start position:0% +It's typical and notationally what we'll + + + align:start position:0% +It's typical and notationally what we'll +also stick with in representing a + + align:start position:0% +also stick with in representing a + + + align:start position:0% +also stick with in representing a +digital network + + align:start position:0% +digital network + + + align:start position:0% +digital network +with flow graph notation to + + align:start position:0% +with flow graph notation to + + + align:start position:0% +with flow graph notation to +cons restrict ourselves always to + + align:start position:0% +cons restrict ourselves always to + + + align:start position:0% +cons restrict ourselves always to +branches that are either simply + + align:start position:0% +branches that are either simply + + + align:start position:0% +branches that are either simply +coefficient branches. In other words, + + align:start position:0% +coefficient branches. In other words, + + + align:start position:0% +coefficient branches. In other words, +they correspond to multiplication by a + + align:start position:0% +they correspond to multiplication by a + + + align:start position:0% +they correspond to multiplication by a +scalar or they're simply delay branches. + + align:start position:0% +scalar or they're simply delay branches. + + + align:start position:0% +scalar or they're simply delay branches. +In other words, they have a + + align:start position:0% +In other words, they have a + + + align:start position:0% +In other words, they have a +transmittance which is Z to the minus1. + + align:start position:0% +transmittance which is Z to the minus1. + + + align:start position:0% +transmittance which is Z to the minus1. +And with that restriction, it's + + align:start position:0% +And with that restriction, it's + + + align:start position:0% +And with that restriction, it's +convenient for a number of reasons and + + align:start position:0% +convenient for a number of reasons and + + + align:start position:0% +convenient for a number of reasons and +in particular for developing some + + align:start position:0% +in particular for developing some + + + align:start position:0% +in particular for developing some +network properties to consider + + align:start position:0% +network properties to consider + + + align:start position:0% +network properties to consider +decomposing + + align:start position:0% +decomposing + + + align:start position:0% +decomposing +this matrix equation in such a way that + + align:start position:0% +this matrix equation in such a way that + + + align:start position:0% +this matrix equation in such a way that +we separate out with the matrix + + align:start position:0% +we separate out with the matrix + + + align:start position:0% +we separate out with the matrix +franspose of Z the part of that matrix + + align:start position:0% +franspose of Z the part of that matrix + + + align:start position:0% +franspose of Z the part of that matrix +that corresponds to that that doesn't + + align:start position:0% +that corresponds to that that doesn't + + + align:start position:0% +that corresponds to that that doesn't +involve any delay terms and the part of + + align:start position:0% +involve any delay terms and the part of + + + align:start position:0% +involve any delay terms and the part of +that matrix mat that does involve delay + + align:start position:0% +that matrix mat that does involve delay + + + align:start position:0% +that matrix mat that does involve delay +terms. In particular, we can write the + + align:start position:0% +terms. In particular, we can write the + + + align:start position:0% +terms. In particular, we can write the +transposed matrix frposed of Z. We can + + align:start position:0% +transposed matrix frposed of Z. We can + + + align:start position:0% +transposed matrix frposed of Z. We can +separate it into the sum of two + + align:start position:0% +separate it into the sum of two + + + align:start position:0% +separate it into the sum of two +matrices. One matrix is simply a + + align:start position:0% +matrices. One matrix is simply a + + + align:start position:0% +matrices. One matrix is simply a +coefficient matrix. + + align:start position:0% +coefficient matrix. + + + align:start position:0% +coefficient matrix. +In other words, it involves no terms Z + + align:start position:0% +In other words, it involves no terms Z + + + align:start position:0% +In other words, it involves no terms Z +to the minus1. + + align:start position:0% +to the minus1. + + + align:start position:0% +to the minus1. +The second matrix contains only terms + + align:start position:0% +The second matrix contains only terms + + + align:start position:0% +The second matrix contains only terms +involving Z to the minus1. And of course + + align:start position:0% +involving Z to the minus1. And of course + + + align:start position:0% +involving Z to the minus1. And of course +we can pull the Z to the minus1 outside. + + align:start position:0% +we can pull the Z to the minus1 outside. + + + align:start position:0% +we can pull the Z to the minus1 outside. +And so we have the delay terms isolated. + + align:start position:0% +And so we have the delay terms isolated. + + + align:start position:0% +And so we have the delay terms isolated. +In other words, we have a matrix of + + align:start position:0% +In other words, we have a matrix of + + + align:start position:0% +In other words, we have a matrix of +coefficients here. M all of the terms + + align:start position:0% +coefficients here. M all of the terms + + + align:start position:0% +coefficients here. M all of the terms +multiplied by Z to the minus1. So the + + align:start position:0% +multiplied by Z to the minus1. So the + + + align:start position:0% +multiplied by Z to the minus1. So the +matrix F of Z can be separated into a + + align:start position:0% +matrix F of Z can be separated into a + + + align:start position:0% +matrix F of Z can be separated into a +coefficient matrix and a delay matrix. + + align:start position:0% +coefficient matrix and a delay matrix. + + + align:start position:0% +coefficient matrix and a delay matrix. +And if we now substitute that back into + + align:start position:0% +And if we now substitute that back into + + + align:start position:0% +And if we now substitute that back into +our original matrix equation, then we + + align:start position:0% +our original matrix equation, then we + + + align:start position:0% +our original matrix equation, then we +have the statement that says that the + + align:start position:0% +have the statement that says that the + + + align:start position:0% +have the statement that says that the +vector of node variables is a a + + align:start position:0% +vector of node variables is a a + + + align:start position:0% +vector of node variables is a a +coefficient matrix multiplied by that + + align:start position:0% +coefficient matrix multiplied by that + + + align:start position:0% +coefficient matrix multiplied by that +vector, a delay matrix multiplied by + + align:start position:0% +vector, a delay matrix multiplied by + + + align:start position:0% +vector, a delay matrix multiplied by +that vector. And then I'm assuming + + align:start position:0% +that vector. And then I'm assuming + + + align:start position:0% +that vector. And then I'm assuming +incidentally in this notation and of + + align:start position:0% +incidentally in this notation and of + + + align:start position:0% +incidentally in this notation and of +course it can be generalized quite + + align:start position:0% +course it can be generalized quite + + + align:start position:0% +course it can be generalized quite +easily that the sources are connected + + align:start position:0% +easily that the sources are connected + + + align:start position:0% +easily that the sources are connected +only with non-delay branches. + + align:start position:0% +only with non-delay branches. + + + align:start position:0% +only with non-delay branches. +I have suppressed incidentally in the + + align:start position:0% +I have suppressed incidentally in the + + + align:start position:0% +I have suppressed incidentally in the +discussion up to this point the + + align:start position:0% +discussion up to this point the + + + align:start position:0% +discussion up to this point the +additional statement that we need the + + align:start position:0% +additional statement that we need the + + + align:start position:0% +additional statement that we need the +additional set of equations that we need + + align:start position:0% +additional set of equations that we need + + + align:start position:0% +additional set of equations that we need +that tell us how finally we get from the + + align:start position:0% +that tell us how finally we get from the + + + align:start position:0% +that tell us how finally we get from the +set of internal network nodes to the + + align:start position:0% +set of internal network nodes to the + + + align:start position:0% +set of internal network nodes to the +network output. + + align:start position:0% +network output. + + + align:start position:0% +network output. +We have then + + align:start position:0% +We have then + + + align:start position:0% +We have then +an additional set of equations that + + align:start position:0% +an additional set of equations that + + + align:start position:0% +an additional set of equations that +specify what the sync node values are in + + align:start position:0% +specify what the sync node values are in + + + align:start position:0% +specify what the sync node values are in +terms of the internal network nodes. And + + align:start position:0% +terms of the internal network nodes. And + + + align:start position:0% +terms of the internal network nodes. And +often in referring to the matrix + + align:start position:0% +often in referring to the matrix + + + align:start position:0% +often in referring to the matrix +equations for a signal flow graph um + + align:start position:0% +equations for a signal flow graph um + + + align:start position:0% +equations for a signal flow graph um +sometimes we'll include this equation + + align:start position:0% +sometimes we'll include this equation + + + align:start position:0% +sometimes we'll include this equation +explicitly and sometimes we'll tend to + + align:start position:0% +explicitly and sometimes we'll tend to + + + align:start position:0% +explicitly and sometimes we'll tend to +suppress it. + + align:start position:0% +suppress it. + + + align:start position:0% +suppress it. +Now looking at this equation where we've + + align:start position:0% +Now looking at this equation where we've + + + align:start position:0% +Now looking at this equation where we've +separated out the coefficient and delay + + align:start position:0% +separated out the coefficient and delay + + + align:start position:0% +separated out the coefficient and delay +branches, we can alternatively + + align:start position:0% +branches, we can alternatively + + + align:start position:0% +branches, we can alternatively +reinterpret that equation in the time + + align:start position:0% +reinterpret that equation in the time + + + align:start position:0% +reinterpret that equation in the time +domain. It's expressed here in terms of + + align:start position:0% +domain. It's expressed here in terms of + + + align:start position:0% +domain. It's expressed here in terms of +Z transforms + + align:start position:0% +Z transforms + + + align:start position:0% +Z transforms +in the time domain. Then the this + + align:start position:0% +in the time domain. Then the this + + + align:start position:0% +in the time domain. Then the this +corresponds again to a matrix set of + + align:start position:0% +corresponds again to a matrix set of + + + align:start position:0% +corresponds again to a matrix set of +equations stating that the column vector + + align:start position:0% +equations stating that the column vector + + + align:start position:0% +equations stating that the column vector +W of N is equal to a coefficient matrix + + align:start position:0% +W of N is equal to a coefficient matrix + + + align:start position:0% +W of N is equal to a coefficient matrix +multiplied by the present state. In + + align:start position:0% +multiplied by the present state. In + + + align:start position:0% +multiplied by the present state. In +other words, the same column vector plus + + align:start position:0% +other words, the same column vector plus + + + align:start position:0% +other words, the same column vector plus +another matrix multiplied by that the + + align:start position:0% +another matrix multiplied by that the + + + align:start position:0% +another matrix multiplied by that the +the set of node variables one iteration + + align:start position:0% +the set of node variables one iteration + + + align:start position:0% +the set of node variables one iteration +previously. + + align:start position:0% +previously. + + + align:start position:0% +previously. +and then of course an equation coupling + + align:start position:0% +and then of course an equation coupling + + + align:start position:0% +and then of course an equation coupling +the sources into that and finally an + + align:start position:0% +the sources into that and finally an + + + align:start position:0% +the sources into that and finally an +equation that generates the sync node + + align:start position:0% +equation that generates the sync node + + + align:start position:0% +equation that generates the sync node +outputs from the node variables. But if + + align:start position:0% +outputs from the node variables. But if + + + align:start position:0% +outputs from the node variables. But if +you look at this what this says + + align:start position:0% +you look at this what this says + + + align:start position:0% +you look at this what this says +is what this corresponds to of course is + + align:start position:0% +is what this corresponds to of course is + + + align:start position:0% +is what this corresponds to of course is +a set of first order difference + + align:start position:0% +a set of first order difference + + + align:start position:0% +a set of first order difference +equations. So that essentially what + + align:start position:0% +equations. So that essentially what + + + align:start position:0% +equations. So that essentially what +we've done starting from our nth order + + align:start position:0% +we've done starting from our nth order + + + align:start position:0% +we've done starting from our nth order +linear constant coefficient difference + + align:start position:0% +linear constant coefficient difference + + + align:start position:0% +linear constant coefficient difference +equation through the signal flow graph + + align:start position:0% +equation through the signal flow graph + + + align:start position:0% +equation through the signal flow graph +representation + + align:start position:0% +representation + + + align:start position:0% +representation +we have in essence decomposed that into + + align:start position:0% +we have in essence decomposed that into + + + align:start position:0% +we have in essence decomposed that into +a set of first order linear constant + + align:start position:0% +a set of first order linear constant + + + align:start position:0% +a set of first order linear constant +coefficient difference equations of + + align:start position:0% +coefficient difference equations of + + + align:start position:0% +coefficient difference equations of +course all of them coupled + + align:start position:0% +course all of them coupled + + + align:start position:0% +course all of them coupled +and uh the + + align:start position:0% +and uh the + + + align:start position:0% +and uh the +discussion in the next several lectures + + align:start position:0% +discussion in the next several lectures + + + align:start position:0% +discussion in the next several lectures +will in fact involve what the various + + align:start position:0% +will in fact involve what the various + + + align:start position:0% +will in fact involve what the various +ious options are in terms of what + + align:start position:0% +ious options are in terms of what + + + align:start position:0% +ious options are in terms of what +various forms we can use or are commonly + + align:start position:0% +various forms we can use or are commonly + + + align:start position:0% +various forms we can use or are commonly +used in representing this large nth + + align:start position:0% +used in representing this large nth + + + align:start position:0% +used in representing this large nth +order equation. But what we see is that + + align:start position:0% +order equation. But what we see is that + + + align:start position:0% +order equation. But what we see is that +the signal flow graph in essence breaks + + align:start position:0% +the signal flow graph in essence breaks + + + align:start position:0% +the signal flow graph in essence breaks +down the nth order equation into a set + + align:start position:0% +down the nth order equation into a set + + + align:start position:0% +down the nth order equation into a set +of first order difference equations. + + align:start position:0% +of first order difference equations. + + + align:start position:0% +of first order difference equations. +Well, let's just finally look at an + + align:start position:0% +Well, let's just finally look at an + + + align:start position:0% +Well, let's just finally look at an +example of how the set of equations + + align:start position:0% +example of how the set of equations + + + align:start position:0% +example of how the set of equations +might look for a signal flow graph. A + + align:start position:0% +might look for a signal flow graph. A + + + align:start position:0% +might look for a signal flow graph. A +relatively simple uh example and + + align:start position:0% +relatively simple uh example and + + + align:start position:0% +relatively simple uh example and +incidentally somewhat meaningless in the + + align:start position:0% +incidentally somewhat meaningless in the + + + align:start position:0% +incidentally somewhat meaningless in the +sense that it's not a flow graph that is + + align:start position:0% +sense that it's not a flow graph that is + + + align:start position:0% +sense that it's not a flow graph that is +motivated by anything other than + + align:start position:0% +motivated by anything other than + + + align:start position:0% +motivated by anything other than +something to draw here for discussion. + + align:start position:0% +something to draw here for discussion. + + + align:start position:0% +something to draw here for discussion. +Well, all right. Here's a linear signal + + align:start position:0% +Well, all right. Here's a linear signal + + + align:start position:0% +Well, all right. Here's a linear signal +flow graph. It has these unity gain + + align:start position:0% +flow graph. It has these unity gain + + + align:start position:0% +flow graph. It has these unity gain +branches. It has a branch with gain B + + align:start position:0% +branches. It has a branch with gain B + + + align:start position:0% +branches. It has a branch with gain B +and a branch with gain A and the two + + align:start position:0% +and a branch with gain A and the two + + + align:start position:0% +and a branch with gain A and the two +delay branches. + + align:start position:0% +delay branches. + + + align:start position:0% +delay branches. +According to the algebra for the flow + + align:start position:0% +According to the algebra for the flow + + + align:start position:0% +According to the algebra for the flow +graph, this node variable is equal to B + + align:start position:0% +graph, this node variable is equal to B + + + align:start position:0% +graph, this node variable is equal to B +times this node variable. So that's this + + align:start position:0% +times this node variable. So that's this + + + align:start position:0% +times this node variable. So that's this +equation. This node variable is this one + + align:start position:0% +equation. This node variable is this one + + + align:start position:0% +equation. This node variable is this one +delayed plus this one delayed. That's + + align:start position:0% +delayed plus this one delayed. That's + + + align:start position:0% +delayed plus this one delayed. That's +this equation. and this node + + align:start position:0% +this equation. and this node + + + align:start position:0% +this equation. and this node +and I'm sorry this node is a * w2 of n + + align:start position:0% +and I'm sorry this node is a * w2 of n + + + align:start position:0% +and I'm sorry this node is a * w2 of n +plus the source. So those are the linear + + align:start position:0% +plus the source. So those are the linear + + + align:start position:0% +plus the source. So those are the linear +equations defining the internal network + + align:start position:0% +equations defining the internal network + + + align:start position:0% +equations defining the internal network +nodes. + + align:start position:0% +nodes. + + + align:start position:0% +nodes. +And this corresponds then to a um a + + align:start position:0% +And this corresponds then to a um a + + + align:start position:0% +And this corresponds then to a um a +matrix equation. Let me draw your + + align:start position:0% +matrix equation. Let me draw your + + + align:start position:0% +matrix equation. Let me draw your +attention to the fact incidentally that + + align:start position:0% +attention to the fact incidentally that + + + align:start position:0% +attention to the fact incidentally that +the way that I've numbered these nodes + + align:start position:0% +the way that I've numbered these nodes + + + align:start position:0% +the way that I've numbered these nodes +in fact is not the order in which I can + + align:start position:0% +in fact is not the order in which I can + + + align:start position:0% +in fact is not the order in which I can +compute them if I were to compute them + + align:start position:0% +compute them if I were to compute them + + + align:start position:0% +compute them if I were to compute them +successively. Now what I mean by that is + + align:start position:0% +successively. Now what I mean by that is + + + align:start position:0% +successively. Now what I mean by that is +suppose that in my numbering what I + + align:start position:0% +suppose that in my numbering what I + + + align:start position:0% +suppose that in my numbering what I +decide is that what the numbering means + + align:start position:0% +decide is that what the numbering means + + + align:start position:0% +decide is that what the numbering means +is that node one I'll compute first, + + align:start position:0% +is that node one I'll compute first, + + + align:start position:0% +is that node one I'll compute first, +node two I'll compute second, node three + + align:start position:0% +node two I'll compute second, node three + + + align:start position:0% +node two I'll compute second, node three +I'll compute third. + + align:start position:0% +I'll compute third. + + + align:start position:0% +I'll compute third. +to compute node one I need node three + + align:start position:0% +to compute node one I need node three + + + align:start position:0% +to compute node one I need node three +and I can't I don't have node three if + + align:start position:0% +and I can't I don't have node three if + + + align:start position:0% +and I can't I don't have node three if +I'm going to compute that after node one + + align:start position:0% +I'm going to compute that after node one + + + align:start position:0% +I'm going to compute that after node one +so actually the order that I've + + align:start position:0% +so actually the order that I've + + + align:start position:0% +so actually the order that I've +specified here for the nodes is not an + + align:start position:0% +specified here for the nodes is not an + + + align:start position:0% +specified here for the nodes is not an +order in which I can compute the network + + align:start position:0% +order in which I can compute the network + + + align:start position:0% +order in which I can compute the network +or another way to say that is that this + + align:start position:0% +or another way to say that is that this + + + align:start position:0% +or another way to say that is that this +network as I've numbered the nodes is + + align:start position:0% +network as I've numbered the nodes is + + + align:start position:0% +network as I've numbered the nodes is +not computable + + align:start position:0% +not computable + + + align:start position:0% +not computable +but let's go on + + align:start position:0% +but let's go on + + + align:start position:0% +but let's go on +and we'll Look in fact at a + + align:start position:0% +and we'll Look in fact at a + + + align:start position:0% +and we'll Look in fact at a +rearrangement of the nodes that is + + align:start position:0% +rearrangement of the nodes that is + + + align:start position:0% +rearrangement of the nodes that is +computable. But let's see how the matrix + + align:start position:0% +computable. But let's see how the matrix + + + align:start position:0% +computable. But let's see how the matrix +equation looks. Simply this equation + + align:start position:0% +equation looks. Simply this equation + + + align:start position:0% +equation looks. Simply this equation +rewritten in terms of a set of matrices. + + align:start position:0% +rewritten in terms of a set of matrices. + + + align:start position:0% +rewritten in terms of a set of matrices. +Then it comes out as I've indicated + + align:start position:0% +Then it comes out as I've indicated + + + align:start position:0% +Then it comes out as I've indicated +here. We have the matrix F subc. This is + + align:start position:0% +here. We have the matrix F subc. This is + + + align:start position:0% +here. We have the matrix F subc. This is +the coefficient matrix. This is the + + align:start position:0% +the coefficient matrix. This is the + + + align:start position:0% +the coefficient matrix. This is the +delay matrix. So it involves a vector of + + align:start position:0% +delay matrix. So it involves a vector of + + + align:start position:0% +delay matrix. So it involves a vector of +only the laid sequences and then the + + align:start position:0% +only the laid sequences and then the + + + align:start position:0% +only the laid sequences and then the +input coupled in. + + align:start position:0% +input coupled in. + + + align:start position:0% +input coupled in. +Let me point out incidentally just keep + + align:start position:0% +Let me point out incidentally just keep + + + align:start position:0% +Let me point out incidentally just keep +track of the fact that this matrix the + + align:start position:0% +track of the fact that this matrix the + + + align:start position:0% +track of the fact that this matrix the +coefficient matrix happens to have an + + align:start position:0% +coefficient matrix happens to have an + + + align:start position:0% +coefficient matrix happens to have an +element on or above the major diagonal. + + align:start position:0% +element on or above the major diagonal. + + + align:start position:0% +element on or above the major diagonal. +And uh that shouldn't have any + + align:start position:0% +And uh that shouldn't have any + + + align:start position:0% +And uh that shouldn't have any +particular meaning right now but it will + + align:start position:0% +particular meaning right now but it will + + + align:start position:0% +particular meaning right now but it will +in a couple of minutes. + + align:start position:0% +in a couple of minutes. + + + align:start position:0% +in a couple of minutes. +All right, let's consider a slightly + + align:start position:0% +All right, let's consider a slightly + + + align:start position:0% +All right, let's consider a slightly +different ordering for the network + + align:start position:0% +different ordering for the network + + + align:start position:0% +different ordering for the network +nodes. This is the same network. + + align:start position:0% +nodes. This is the same network. + + + align:start position:0% +nodes. This is the same network. +I now have ordered the nodes slightly + + align:start position:0% +I now have ordered the nodes slightly + + + align:start position:0% +I now have ordered the nodes slightly +differently. I'm calling this node one, + + align:start position:0% +differently. I'm calling this node one, + + + align:start position:0% +differently. I'm calling this node one, +this node two, and this node three. And + + align:start position:0% +this node two, and this node three. And + + + align:start position:0% +this node two, and this node three. And +let's just inquire as to whether + + align:start position:0% +let's just inquire as to whether + + + align:start position:0% +let's just inquire as to whether +the nodes ordered as I've indicated here + + align:start position:0% +the nodes ordered as I've indicated here + + + align:start position:0% +the nodes ordered as I've indicated here +are now computable. + + align:start position:0% +are now computable. + + + align:start position:0% +are now computable. +Well, to get node one, I need w of n + + align:start position:0% +Well, to get node one, I need w of n + + + align:start position:0% +Well, to get node one, I need w of n +minus one, which of course I've got + + align:start position:0% +minus one, which of course I've got + + + align:start position:0% +minus one, which of course I've got +because that's from the previous + + align:start position:0% +because that's from the previous + + + align:start position:0% +because that's from the previous +iteration. I need w3 of n minus one and + + align:start position:0% +iteration. I need w3 of n minus one and + + + align:start position:0% +iteration. I need w3 of n minus one and +that I've got from the previous + + align:start position:0% +that I've got from the previous + + + align:start position:0% +that I've got from the previous +iteration. So this node can be computed. + + align:start position:0% +iteration. So this node can be computed. + + + align:start position:0% +iteration. So this node can be computed. +To compute this node, I need the source + + align:start position:0% +To compute this node, I need the source + + + align:start position:0% +To compute this node, I need the source +which I have and I need w1 of n which I + + align:start position:0% +which I have and I need w1 of n which I + + + align:start position:0% +which I have and I need w1 of n which I +just got. So this can be computed. And + + align:start position:0% +just got. So this can be computed. And + + + align:start position:0% +just got. So this can be computed. And +then to compute w3 of n I need w2 of n + + align:start position:0% +then to compute w3 of n I need w2 of n + + + align:start position:0% +then to compute w3 of n I need w2 of n +which I've just computed. And so in fact + + align:start position:0% +which I've just computed. And so in fact + + + align:start position:0% +which I've just computed. And so in fact +the nodes numbered in this order are + + align:start position:0% +the nodes numbered in this order are + + + align:start position:0% +the nodes numbered in this order are +computable whereas the nodes numbered in + + align:start position:0% +computable whereas the nodes numbered in + + + align:start position:0% +computable whereas the nodes numbered in +the previous order are not computable. + + align:start position:0% +the previous order are not computable. + + + align:start position:0% +the previous order are not computable. +If I look at the equations for this + + align:start position:0% +If I look at the equations for this + + + align:start position:0% +If I look at the equations for this +they're of course the same equations as + + align:start position:0% +they're of course the same equations as + + + align:start position:0% +they're of course the same equations as +I had previously except that some of the + + align:start position:0% +I had previously except that some of the + + + align:start position:0% +I had previously except that some of the +indices are changed. And so it simply + + align:start position:0% +indices are changed. And so it simply + + + align:start position:0% +indices are changed. And so it simply +involves changing some of the rows and + + align:start position:0% +involves changing some of the rows and + + + align:start position:0% +involves changing some of the rows and +columns. And what it comes out to look + + align:start position:0% +columns. And what it comes out to look + + + align:start position:0% +columns. And what it comes out to look +like in fact is what I've indicated + + align:start position:0% +like in fact is what I've indicated + + + align:start position:0% +like in fact is what I've indicated +here. + + align:start position:0% +here. + + + align:start position:0% +here. +Again, the coefficient matrix the + + align:start position:0% +Again, the coefficient matrix the + + + align:start position:0% +Again, the coefficient matrix the +elements are the the same elements + + align:start position:0% +elements are the the same elements + + + align:start position:0% +elements are the the same elements +appear but the order is swapped around + + align:start position:0% +appear but the order is swapped around + + + align:start position:0% +appear but the order is swapped around +multiplied by the vector of current node + + align:start position:0% +multiplied by the vector of current node + + + align:start position:0% +multiplied by the vector of current node +states. and then a delay matrix + + align:start position:0% +states. and then a delay matrix + + + align:start position:0% +states. and then a delay matrix +uh multiplied by the vector of delayed + + align:start position:0% +uh multiplied by the vector of delayed + + + align:start position:0% +uh multiplied by the vector of delayed +states and then the input coupled in. + + align:start position:0% +states and then the input coupled in. + + + align:start position:0% +states and then the input coupled in. +And notice that in this case we don't + + align:start position:0% +And notice that in this case we don't + + + align:start position:0% +And notice that in this case we don't +have any nonzero values on or above the + + align:start position:0% +have any nonzero values on or above the + + + align:start position:0% +have any nonzero values on or above the +main diagonal. + + align:start position:0% +main diagonal. + + + align:start position:0% +main diagonal. +It turns out that you can show and and + + align:start position:0% +It turns out that you can show and and + + + align:start position:0% +It turns out that you can show and and +it's not uh that it's not too difficult + + align:start position:0% +it's not uh that it's not too difficult + + + align:start position:0% +it's not uh that it's not too difficult +to do. You can show that a necessary and + + align:start position:0% +to do. You can show that a necessary and + + + align:start position:0% +to do. You can show that a necessary and +sufficient condition for the node + + align:start position:0% +sufficient condition for the node + + + align:start position:0% +sufficient condition for the node +numbering to correspond to a computable + + align:start position:0% +numbering to correspond to a computable + + + align:start position:0% +numbering to correspond to a computable +network or to be a computable numbering + + align:start position:0% +network or to be a computable numbering + + + align:start position:0% +network or to be a computable numbering +is that this coefficient matrix has to + + align:start position:0% +is that this coefficient matrix has to + + + align:start position:0% +is that this coefficient matrix has to +have the form that there are no nonzero + + align:start position:0% +have the form that there are no nonzero + + + align:start position:0% +have the form that there are no nonzero +elements on or above the major diagonal. + + align:start position:0% +elements on or above the major diagonal. + + + align:start position:0% +elements on or above the major diagonal. +So uh often if the nodes are numbered in + + align:start position:0% +So uh often if the nodes are numbered in + + + align:start position:0% +So uh often if the nodes are numbered in +a non-computable order the order can + + align:start position:0% +a non-computable order the order can + + + align:start position:0% +a non-computable order the order can +simply be rearranged so that it is + + align:start position:0% +simply be rearranged so that it is + + + align:start position:0% +simply be rearranged so that it is +computable. + + align:start position:0% +computable. + + + align:start position:0% +computable. +It does turn out incidentally that there + + align:start position:0% +It does turn out incidentally that there + + + align:start position:0% +It does turn out incidentally that there +are some networks for which no matter + + align:start position:0% +are some networks for which no matter + + + align:start position:0% +are some networks for which no matter +how you number the nodes you can't + + align:start position:0% +how you number the nodes you can't + + + align:start position:0% +how you number the nodes you can't +number them in an order that makes the + + align:start position:0% +number them in an order that makes the + + + align:start position:0% +number them in an order that makes the +network computable. + + align:start position:0% +network computable. + + + align:start position:0% +network computable. +Computability, as I've just said, is the + + align:start position:0% +Computability, as I've just said, is the + + + align:start position:0% +Computability, as I've just said, is the +statement that the nodes can be numbered + + align:start position:0% +statement that the nodes can be numbered + + + align:start position:0% +statement that the nodes can be numbered +in such a way that it's zero above or on + + align:start position:0% +in such a way that it's zero above or on + + + align:start position:0% +in such a way that it's zero above or on +the main diagonal. + + align:start position:0% +the main diagonal. + + + align:start position:0% +the main diagonal. +As you'll see as you work some problems + + align:start position:0% +As you'll see as you work some problems + + + align:start position:0% +As you'll see as you work some problems +in the study guide, a non-computable + + align:start position:0% +in the study guide, a non-computable + + + align:start position:0% +in the study guide, a non-computable +network. In essence, what happens is + + align:start position:0% +network. In essence, what happens is + + + align:start position:0% +network. In essence, what happens is +that we have a set of nodes in the + + align:start position:0% +that we have a set of nodes in the + + + align:start position:0% +that we have a set of nodes in the +network, all of which are connected + + align:start position:0% +network, all of which are connected + + + align:start position:0% +network, all of which are connected +together by + + align:start position:0% +together by + + + align:start position:0% +together by +nondlay branches. And so you can see + + align:start position:0% +nondlay branches. And so you can see + + + align:start position:0% +nondlay branches. And so you can see +that what happens is to compute this one + + align:start position:0% +that what happens is to compute this one + + + align:start position:0% +that what happens is to compute this one +I need that one but to compute that one + + align:start position:0% +I need that one but to compute that one + + + align:start position:0% +I need that one but to compute that one +I need this one but to compute this one + + align:start position:0% +I need this one but to compute this one + + + align:start position:0% +I need this one but to compute this one +I need this but to compute that I need + + align:start position:0% +I need this but to compute that I need + + + align:start position:0% +I need this but to compute that I need +that. There's no way to get out of that + + align:start position:0% +that. There's no way to get out of that + + + align:start position:0% +that. There's no way to get out of that +loop. So if there's a delayfree loop in + + align:start position:0% +loop. So if there's a delayfree loop in + + + align:start position:0% +loop. So if there's a delayfree loop in +the network it turns out that that + + align:start position:0% +the network it turns out that that + + + align:start position:0% +the network it turns out that that +corresponds to a non-computable network. + + align:start position:0% +corresponds to a non-computable network. + + + align:start position:0% +corresponds to a non-computable network. +Although it's important to stress that + + align:start position:0% +Although it's important to stress that + + + align:start position:0% +Although it's important to stress that +the non-computability doesn't mean that + + align:start position:0% +the non-computability doesn't mean that + + + align:start position:0% +the non-computability doesn't mean that +the set of equations can't be solved. + + align:start position:0% +the set of equations can't be solved. + + + align:start position:0% +the set of equations can't be solved. +The set of equations can still be solved + + align:start position:0% +The set of equations can still be solved + + + align:start position:0% +The set of equations can still be solved +or the network can be rearranged. What + + align:start position:0% +or the network can be rearranged. What + + + align:start position:0% +or the network can be rearranged. What +it simply means is that + + align:start position:0% +it simply means is that + + + align:start position:0% +it simply means is that +non-computability means that we can't + + align:start position:0% +non-computability means that we can't + + + align:start position:0% +non-computability means that we can't +compute the node variables in sequence. + + align:start position:0% +compute the node variables in sequence. + + + align:start position:0% +compute the node variables in sequence. +We can't start with W1 event and then go + + align:start position:0% +We can't start with W1 event and then go + + + align:start position:0% +We can't start with W1 event and then go +on to W2 event and then W3 event etc. + + align:start position:0% +on to W2 event and then W3 event etc. + + + align:start position:0% +on to W2 event and then W3 event etc. +Well, this issue of non-compu + + align:start position:0% +Well, this issue of non-compu + + + align:start position:0% +Well, this issue of non-compu +computability is just one brief glimpse + + align:start position:0% +computability is just one brief glimpse + + + align:start position:0% +computability is just one brief glimpse +in fact into the kinds of network + + align:start position:0% +in fact into the kinds of network + + + align:start position:0% +in fact into the kinds of network +properties that can be pulled out of + + align:start position:0% +properties that can be pulled out of + + + align:start position:0% +properties that can be pulled out of +either the signal flowraph + + align:start position:0% +either the signal flowraph + + + align:start position:0% +either the signal flowraph +representation and properties of signal + + align:start position:0% +representation and properties of signal + + + align:start position:0% +representation and properties of signal +flow graphs or out of the matrix + + align:start position:0% +flow graphs or out of the matrix + + + align:start position:0% +flow graphs or out of the matrix +representation. + + align:start position:0% +representation. + + + align:start position:0% +representation. +As I indicated at the beginning of the + + align:start position:0% +As I indicated at the beginning of the + + + align:start position:0% +As I indicated at the beginning of the +lecture, we won't be exploiting these + + align:start position:0% +lecture, we won't be exploiting these + + + align:start position:0% +lecture, we won't be exploiting these +kinds of properties. There is in fact a + + align:start position:0% +kinds of properties. There is in fact a + + + align:start position:0% +kinds of properties. There is in fact a +rather lengthy discussion of properties + + align:start position:0% +rather lengthy discussion of properties + + + align:start position:0% +rather lengthy discussion of properties +of digital networks in the text which we + + align:start position:0% +of digital networks in the text which we + + + align:start position:0% +of digital networks in the text which we +won't be going into further in the next + + align:start position:0% +won't be going into further in the next + + + align:start position:0% +won't be going into further in the next +several lectures. What we'll concentrate + + align:start position:0% +several lectures. What we'll concentrate + + + align:start position:0% +several lectures. What we'll concentrate +on are the more common digital network + + align:start position:0% +on are the more common digital network + + + align:start position:0% +on are the more common digital network +structures for implementing both finite + + align:start position:0% +structures for implementing both finite + + + align:start position:0% +structures for implementing both finite +impulse response or recursive digital + + align:start position:0% +impulse response or recursive digital + + + align:start position:0% +impulse response or recursive digital +filters and finite impulse response or + + align:start position:0% +filters and finite impulse response or + + + align:start position:0% +filters and finite impulse response or +non-recursive digital filters. Thank + + align:start position:0% +non-recursive digital filters. Thank + + + align:start position:0% +non-recursive digital filters. Thank +you. + + align:start position:0% +you. + + + align:start position:0% +you. +[Music] \ No newline at end of file diff --git a/zDHhHPZm2rc.txt b/zDHhHPZm2rc.txt new file mode 100644 index 0000000000000000000000000000000000000000..ca80022bace33d665a5db5dd4475c137447a5293 --- /dev/null +++ b/zDHhHPZm2rc.txt @@ -0,0 +1,7683 @@ +align:start position:0% + +all right good morning everyone oh do we + + align:start position:0% +all right good morning everyone oh do we + + + align:start position:0% +all right good morning everyone oh do we +have a treat for you today I'm going to + + align:start position:0% +have a treat for you today I'm going to + + + align:start position:0% +have a treat for you today I'm going to +publicise for the first time my my + + align:start position:0% +publicise for the first time my my + + + align:start position:0% +publicise for the first time my my +hidden talent of mind-reading and since + + align:start position:0% +hidden talent of mind-reading and since + + + align:start position:0% +hidden talent of mind-reading and since +this is a magic trick every every + + align:start position:0% +this is a magic trick every every + + + align:start position:0% +this is a magic trick every every +magician needs an assistant and I want + + align:start position:0% +magician needs an assistant and I want + + + align:start position:0% +magician needs an assistant and I want +to introduce Billy Moses to you Billy is + + align:start position:0% +to introduce Billy Moses to you Billy is + + + align:start position:0% +to introduce Billy Moses to you Billy is +a PhD student he already has three + + align:start position:0% +a PhD student he already has three + + + align:start position:0% +a PhD student he already has three +degrees from MIT but he wants a fourth I + + align:start position:0% +degrees from MIT but he wants a fourth I + + + align:start position:0% +degrees from MIT but he wants a fourth I +guess and so so I'm gonna turn it over + + align:start position:0% +guess and so so I'm gonna turn it over + + + align:start position:0% +guess and so so I'm gonna turn it over +to Billy here and and Billy's going to + + align:start position:0% +to Billy here and and Billy's going to + + + align:start position:0% +to Billy here and and Billy's going to +sort of set things up I'm just going to + + align:start position:0% +sort of set things up I'm just going to + + + align:start position:0% +sort of set things up I'm just going to +do my thing which is read your minds + + align:start position:0% +do my thing which is read your minds + + + align:start position:0% +do my thing which is read your minds +okay so go ahead Billy so what's gonna + + align:start position:0% +okay so go ahead Billy so what's gonna + + + align:start position:0% +okay so go ahead Billy so what's gonna +happen is I'm gonna I have this card + + align:start position:0% +happen is I'm gonna I have this card + + + align:start position:0% +happen is I'm gonna I have this card +back right here normal card deck + + align:start position:0% +back right here normal card deck + + + align:start position:0% +back right here normal card deck +perfectly normal cards they're not in + + align:start position:0% +perfectly normal cards they're not in + + + align:start position:0% +perfectly normal cards they're not in +any weird order you can see them I'm + + align:start position:0% +any weird order you can see them I'm + + + align:start position:0% +any weird order you can see them I'm +gonna give five people the opportunity + + align:start position:0% +gonna give five people the opportunity + + + align:start position:0% +gonna give five people the opportunity +to pull a card and then give it back to + + align:start position:0% +to pull a card and then give it back to + + + align:start position:0% +to pull a card and then give it back to +me they can look at the card then what's + + align:start position:0% +me they can look at the card then what's + + + align:start position:0% +me they can look at the card then what's +going to happen is I'm going to turn + + align:start position:0% +going to happen is I'm going to turn + + + align:start position:0% +going to happen is I'm going to turn +over four of these cards show you the + + align:start position:0% +over four of these cards show you the + + + align:start position:0% +over four of these cards show you the +final card and then trainees trying and + + align:start position:0% +final card and then trainees trying and + + + align:start position:0% +final card and then trainees trying and +they try to guess the fifth card well + + align:start position:0% +they try to guess the fifth card well + + + align:start position:0% +they try to guess the fifth card well +but what I need you to do is when I'm + + align:start position:0% +but what I need you to do is when I'm + + + align:start position:0% +but what I need you to do is when I'm +gonna guess I need all of you to really + + align:start position:0% +gonna guess I need all of you to really + + + align:start position:0% +gonna guess I need all of you to really +focus on that hidden card I mean in your + + align:start position:0% +focus on that hidden card I mean in your + + + align:start position:0% +focus on that hidden card I mean in your +heads right + + align:start position:0% +heads right + + + align:start position:0% +heads right +so I can't do individual mind-reading + + align:start position:0% +so I can't do individual mind-reading + + + align:start position:0% +so I can't do individual mind-reading +just in case you guys were worried you + + align:start position:0% +just in case you guys were worried you + + + align:start position:0% +just in case you guys were worried you +know so if you think I'm running a + + align:start position:0% +know so if you think I'm running a + + + align:start position:0% +know so if you think I'm running a +terrible colored shirt I'm not gonna + + align:start position:0% +terrible colored shirt I'm not gonna + + + align:start position:0% +terrible colored shirt I'm not gonna +know okay but if you all think of this + + align:start position:0% +know okay but if you all think of this + + + align:start position:0% +know okay but if you all think of this +this hidden card I'm gonna be able to + + align:start position:0% +this hidden card I'm gonna be able to + + + align:start position:0% +this hidden card I'm gonna be able to +guess it but so I need some help + + align:start position:0% +guess it but so I need some help + + + align:start position:0% +guess it but so I need some help +all right okay you're gonna wants to try + + align:start position:0% +all right okay you're gonna wants to try + + + align:start position:0% +all right okay you're gonna wants to try +pulling some of the cards okay and your + + align:start position:0% +pulling some of the cards okay and your + + + align:start position:0% +pulling some of the cards okay and your +favorite body right yeah all right you + + align:start position:0% +favorite body right yeah all right you + + + align:start position:0% +favorite body right yeah all right you +can look at it give it back to me once + + align:start position:0% +can look at it give it back to me once + + + align:start position:0% +can look at it give it back to me once +you cool anyone else want to pick a card + + align:start position:0% +you cool anyone else want to pick a card + + + align:start position:0% +you cool anyone else want to pick a card +pick a card there you go and look at the + + align:start position:0% +pick a card there you go and look at the + + + align:start position:0% +pick a card there you go and look at the +full deck look at whatever card you want + + align:start position:0% +full deck look at whatever card you want + + + align:start position:0% +full deck look at whatever card you want +take it cool + + align:start position:0% + + + + align:start position:0% + +okay anyone else wanna pick a card cool + + align:start position:0% +okay anyone else wanna pick a card cool + + + align:start position:0% +okay anyone else wanna pick a card cool +and pick a card + + align:start position:0% + + + + align:start position:0% + +cool okay get my cards all nice together + + align:start position:0% + + + + align:start position:0% + +okay so five cards I'm going to show you + + align:start position:0% +okay so five cards I'm going to show you + + + align:start position:0% +okay so five cards I'm going to show you +first and then we're gonna present them + + align:start position:0% +first and then we're gonna present them + + + align:start position:0% +first and then we're gonna present them +in a fun way for sure you need to see so + + align:start position:0% +in a fun way for sure you need to see so + + + align:start position:0% +in a fun way for sure you need to see so +the five cards are as follows + + align:start position:0% +the five cards are as follows + + + align:start position:0% +the five cards are as follows +we have this wonderful seven of clubs we + + align:start position:0% +we have this wonderful seven of clubs we + + + align:start position:0% +we have this wonderful seven of clubs we +have a Jack of Hearts we have seven of + + align:start position:0% +have a Jack of Hearts we have seven of + + + align:start position:0% +have a Jack of Hearts we have seven of +Hearts we have Queen of Spades we have + + align:start position:0% +Hearts we have Queen of Spades we have + + + align:start position:0% +Hearts we have Queen of Spades we have +ten of clubs now for the people who + + align:start position:0% +ten of clubs now for the people who + + + align:start position:0% +ten of clubs now for the people who +pulled the carts these are indeed the + + align:start position:0% +pulled the carts these are indeed the + + + align:start position:0% +pulled the carts these are indeed the +cards that you gave me right no one + + align:start position:0% +cards that you gave me right no one + + + align:start position:0% +cards that you gave me right no one +missed their card in the deck okay I'll + + align:start position:0% +missed their card in the deck okay I'll + + + align:start position:0% +missed their card in the deck okay I'll +go get Trini alright yep okay the first + + align:start position:0% +go get Trini alright yep okay the first + + + align:start position:0% +go get Trini alright yep okay the first +card is the seven of clubs the second + + align:start position:0% +card is the seven of clubs the second + + + align:start position:0% +card is the seven of clubs the second +card is the Jack of Hearts the third + + align:start position:0% +card is the Jack of Hearts the third + + + align:start position:0% +card is the Jack of Hearts the third +card is the seven of Hearts the fourth + + align:start position:0% +card is the seven of Hearts the fourth + + + align:start position:0% +card is the seven of Hearts the fourth +card is and this is the final card that + + align:start position:0% +card is and this is the final card that + + + align:start position:0% +card is and this is the final card that +Trini will be able to see the Queen of + + align:start position:0% +Trini will be able to see the Queen of + + + align:start position:0% +Trini will be able to see the Queen of +Spades + + align:start position:0% +Spades + + + align:start position:0% +Spades +now everyone think to yourself you've + + align:start position:0% +now everyone think to yourself you've + + + align:start position:0% +now everyone think to yourself you've +got to see the cards the fifth card that + + align:start position:0% +got to see the cards the fifth card that + + + align:start position:0% +got to see the cards the fifth card that +Trini is gonna have think it very + + align:start position:0% +Trini is gonna have think it very + + + align:start position:0% +Trini is gonna have think it very +closely in your mind thinks right + + align:start position:0% +closely in your mind thinks right + + + align:start position:0% +closely in your mind thinks right +definitely a clubs definitely a clubs + + align:start position:0% +definitely a clubs definitely a clubs + + + align:start position:0% +definitely a clubs definitely a clubs +okay see and I'm getting I'm getting a + + align:start position:0% +okay see and I'm getting I'm getting a + + + align:start position:0% +okay see and I'm getting I'm getting a +ten of clubs and it is a ten of clubs + + align:start position:0% +ten of clubs and it is a ten of clubs + + + align:start position:0% +ten of clubs and it is a ten of clubs +alright thank you + + align:start position:0% +alright thank you + + + align:start position:0% +alright thank you +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +all right so I guess I'll have to + + align:start position:0% +all right so I guess I'll have to + + + align:start position:0% +all right so I guess I'll have to +confess I'm not a mind-reader but I also + + align:start position:0% +confess I'm not a mind-reader but I also + + + align:start position:0% +confess I'm not a mind-reader but I also +did not cheat okay so this there's an + + align:start position:0% +did not cheat okay so this there's an + + + align:start position:0% +did not cheat okay so this there's an +algorithm here and that you guys want to + + align:start position:0% +algorithm here and that you guys want to + + + align:start position:0% +algorithm here and that you guys want to +know what the algorithm is so you can go + + align:start position:0% +know what the algorithm is so you can go + + + align:start position:0% +know what the algorithm is so you can go +try this out I guess when you go back + + align:start position:0% +try this out I guess when you go back + + + align:start position:0% +try this out I guess when you go back +home next or whatever at your at your + + align:start position:0% +home next or whatever at your at your + + + align:start position:0% +home next or whatever at your at your +dorms or with your with your classmates + + align:start position:0% +dorms or with your with your classmates + + + align:start position:0% +dorms or with your with your classmates +so it's not as easy as it might seem + + align:start position:0% +so it's not as easy as it might seem + + + align:start position:0% +so it's not as easy as it might seem +simply because the combinations aren't + + align:start position:0% +simply because the combinations aren't + + + align:start position:0% +simply because the combinations aren't +really in our favor right so if you + + align:start position:0% +really in our favor right so if you + + + align:start position:0% +really in our favor right so if you +think about it there's 52 cards so this + + align:start position:0% +think about it there's 52 cards so this + + + align:start position:0% +think about it there's 52 cards so this +is a regular deck of cards you know it's + + align:start position:0% +is a regular deck of cards you know it's + + + align:start position:0% +is a regular deck of cards you know it's +as I said there's no cheating here Billy + + align:start position:0% +as I said there's no cheating here Billy + + + align:start position:0% +as I said there's no cheating here Billy +showed me four cards so which means the + + align:start position:0% +showed me four cards so which means the + + + align:start position:0% +showed me four cards so which means the +fifth car I could be you know one of 48 + + align:start position:0% +fifth car I could be you know one of 48 + + + align:start position:0% +fifth car I could be you know one of 48 +right I mean it's completely random you + + align:start position:0% +right I mean it's completely random you + + + align:start position:0% +right I mean it's completely random you +guys picked these five cards completely + + align:start position:0% +guys picked these five cards completely + + + align:start position:0% +guys picked these five cards completely +at random so there's there's no way that + + align:start position:0% +at random so there's there's no way that + + + align:start position:0% +at random so there's there's no way that +that fifth card could be anything + + align:start position:0% +that fifth card could be anything + + + align:start position:0% +that fifth card could be anything +specific okay so what Billy had to do + + align:start position:0% +specific okay so what Billy had to do + + + align:start position:0% +specific okay so what Billy had to do +was in the four cards that he showed me + + align:start position:0% +was in the four cards that he showed me + + + align:start position:0% +was in the four cards that he showed me +he really had to communicate one of + + align:start position:0% +he really had to communicate one of + + + align:start position:0% +he really had to communicate one of +specifically you know one of 48 + + align:start position:0% +specifically you know one of 48 + + + align:start position:0% +specifically you know one of 48 +possibilities which is kind of you know + + align:start position:0% +possibilities which is kind of you know + + + align:start position:0% +possibilities which is kind of you know +if you look if you think about it the + + align:start position:0% +if you look if you think about it the + + + align:start position:0% +if you look if you think about it the +map doesn't quite work out right and so + + align:start position:0% +map doesn't quite work out right and so + + + align:start position:0% +map doesn't quite work out right and so +if you just say so what what are the + + align:start position:0% +if you just say so what what are the + + + align:start position:0% +if you just say so what what are the +ways how much information could you + + align:start position:0% +ways how much information could you + + + align:start position:0% +ways how much information could you +imagine communicating in terms of bits + + align:start position:0% +imagine communicating in terms of bits + + + align:start position:0% +imagine communicating in terms of bits +of information right you know in terms + + align:start position:0% +of information right you know in terms + + + align:start position:0% +of information right you know in terms +of possibilities or bits how much + + align:start position:0% +of possibilities or bits how much + + + align:start position:0% +of possibilities or bits how much +information do you think that that Billy + + align:start position:0% +information do you think that that Billy + + + align:start position:0% +information do you think that that Billy +could communicate in these four cards + + align:start position:0% +could communicate in these four cards + + + align:start position:0% +could communicate in these four cards +who's were also picked at random + + align:start position:0% +who's were also picked at random + + + align:start position:0% +who's were also picked at random +obviously they have to be specific cards + + align:start position:0% +obviously they have to be specific cards + + + align:start position:0% +obviously they have to be specific cards +right he just put them up there right so + + align:start position:0% +right he just put them up there right so + + + align:start position:0% +right he just put them up there right so +so if I have four cards what are the + + align:start position:0% +so if I have four cards what are the + + + align:start position:0% +so if I have four cards what are the +ways that Billy could communicate + + align:start position:0% +ways that Billy could communicate + + + align:start position:0% +ways that Billy could communicate +information when you saw what he did any + + align:start position:0% +information when you saw what he did any + + + align:start position:0% +information when you saw what he did any +any ideas + + align:start position:0% + + + + align:start position:0% + +yeah the order the class are plates so + + align:start position:0% +yeah the order the class are plates so + + + align:start position:0% +yeah the order the class are plates so +that's that's a great answer but if you + + align:start position:0% +that's that's a great answer but if you + + + align:start position:0% +that's that's a great answer but if you +look at the order in which the cards are + + align:start position:0% +look at the order in which the cards are + + + align:start position:0% +look at the order in which the cards are +placed how many different orderings are + + align:start position:0% +placed how many different orderings are + + + align:start position:0% +placed how many different orderings are +there four cards how many different + + align:start position:0% +there four cards how many different + + + align:start position:0% +there four cards how many different +orderings four factorial right and that + + align:start position:0% +orderings four factorial right and that + + + align:start position:0% +orderings four factorial right and that +is 24 right so I'm not quite at 48 yet + + align:start position:0% +is 24 right so I'm not quite at 48 yet + + + align:start position:0% +is 24 right so I'm not quite at 48 yet +right so that's that's a bit of a + + align:start position:0% +right so that's that's a bit of a + + + align:start position:0% +right so that's that's a bit of a +problem right so is there something else + + align:start position:0% +problem right so is there something else + + + align:start position:0% +problem right so is there something else +going on other than the ordering yeah so + + align:start position:0% +going on other than the ordering yeah so + + + align:start position:0% +going on other than the ordering yeah so +you mean the way he put them up you know + + align:start position:0% +you mean the way he put them up you know + + + align:start position:0% +you mean the way he put them up you know +slowed its you know slowly versus + + align:start position:0% +slowed its you know slowly versus + + + align:start position:0% +slowed its you know slowly versus +quickly or do you mean something which + + align:start position:0% +quickly or do you mean something which + + + align:start position:0% +quickly or do you mean something which +was the time in terms of the exposure of + + align:start position:0% +was the time in terms of the exposure of + + + align:start position:0% +was the time in terms of the exposure of +the car sir + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +well that's all part of the ordering I + + align:start position:0% +well that's all part of the ordering I + + + align:start position:0% +well that's all part of the ordering I +mean you have to be a little careful + + align:start position:0% +mean you have to be a little careful + + + align:start position:0% +mean you have to be a little careful +here in that I mean the you can't do + + align:start position:0% +here in that I mean the you can't do + + + align:start position:0% +here in that I mean the you can't do +both right I mean you can't constrain + + align:start position:0% +both right I mean you can't constrain + + + align:start position:0% +both right I mean you can't constrain +the ordering and then say that there's + + align:start position:0% +the ordering and then say that there's + + + align:start position:0% +the ordering and then say that there's +24 different orderings the moment you + + align:start position:0% +24 different orderings the moment you + + + align:start position:0% +24 different orderings the moment you +constrain orderings the number of + + align:start position:0% +constrain orderings the number of + + + align:start position:0% +constrain orderings the number of +ordering strengths right + + align:start position:0% +ordering strengths right + + + align:start position:0% +ordering strengths right +so I will say that as I said this is a + + align:start position:0% +so I will say that as I said this is a + + + align:start position:0% +so I will say that as I said this is a +very legit Rick it's completely + + align:start position:0% +very legit Rick it's completely + + + align:start position:0% +very legit Rick it's completely +algorithmic we're gonna write code for + + align:start position:0% +algorithmic we're gonna write code for + + + align:start position:0% +algorithmic we're gonna write code for +it or I'm gonna show you code for it but + + align:start position:0% +it or I'm gonna show you code for it but + + + align:start position:0% +it or I'm gonna show you code for it but +there's nothing else other than the + + align:start position:0% +there's nothing else other than the + + + align:start position:0% +there's nothing else other than the +ordering okay he is there's no sleight + + align:start position:0% +ordering okay he is there's no sleight + + + align:start position:0% +ordering okay he is there's no sleight +of hand there's no hidden communication + + align:start position:0% +of hand there's no hidden communication + + + align:start position:0% +of hand there's no hidden communication +you know he didn't stress words you know + + align:start position:0% +you know he didn't stress words you know + + + align:start position:0% +you know he didn't stress words you know +clubs meant something or you know spades + + align:start position:0% +clubs meant something or you know spades + + + align:start position:0% +clubs meant something or you know spades +meant something else it was just the + + align:start position:0% +meant something else it was just the + + + align:start position:0% +meant something else it was just the +ordering okay and so so there's a gap + + align:start position:0% +ordering okay and so so there's a gap + + + align:start position:0% +ordering okay and so so there's a gap +here in terms of 24 and 48 right and so + + align:start position:0% +here in terms of 24 and 48 right and so + + + align:start position:0% +here in terms of 24 and 48 right and so +what's cool about this trick is we're + + align:start position:0% +what's cool about this trick is we're + + + align:start position:0% +what's cool about this trick is we're +actually going to be able to do this + + align:start position:0% +actually going to be able to do this + + + align:start position:0% +actually going to be able to do this +original trick where the fifth card + + align:start position:0% +original trick where the fifth card + + + align:start position:0% +original trick where the fifth card +could be one or 48 because we're going + + align:start position:0% +could be one or 48 because we're going + + + align:start position:0% +could be one or 48 because we're going +to do one thing that you probably didn't + + align:start position:0% +to do one thing that you probably didn't + + + align:start position:0% +to do one thing that you probably didn't +notice because we only did the trick + + align:start position:0% +notice because we only did the trick + + + align:start position:0% +notice because we only did the trick +once all right and so let me explain how + + align:start position:0% +once all right and so let me explain how + + + align:start position:0% +once all right and so let me explain how +this is gonna work with just sort of + + align:start position:0% +this is gonna work with just sort of + + + align:start position:0% +this is gonna work with just sort of +randomly picking I'm just gonna pick the + + align:start position:0% +randomly picking I'm just gonna pick the + + + align:start position:0% +randomly picking I'm just gonna pick the +top five cards assuming these are these + + align:start position:0% +top five cards assuming these are these + + + align:start position:0% +top five cards assuming these are these +are shuffled and you can assume these + + align:start position:0% +are shuffled and you can assume these + + + align:start position:0% +are shuffled and you can assume these +things that are at random right so so I + + align:start position:0% +things that are at random right so so I + + + align:start position:0% +things that are at random right so so I +have five cards that I've picked here + + align:start position:0% +have five cards that I've picked here + + + align:start position:0% +have five cards that I've picked here +and I can you all see them right okay + + align:start position:0% +and I can you all see them right okay + + + align:start position:0% +and I can you all see them right okay +what what do you what do you notice + + align:start position:0% +what what do you what do you notice + + + align:start position:0% +what what do you what do you notice +about these five cards anything yeah + + align:start position:0% +about these five cards anything yeah + + + align:start position:0% +about these five cards anything yeah +buddy + + align:start position:0% + + + + align:start position:0% + +right so you're saying the suit right so + + align:start position:0% +right so you're saying the suit right so + + + align:start position:0% +right so you're saying the suit right so +it is clear I mean this is true here you + + align:start position:0% +it is clear I mean this is true here you + + + align:start position:0% +it is clear I mean this is true here you +have the seven of clubs and the ten of + + align:start position:0% +have the seven of clubs and the ten of + + + align:start position:0% +have the seven of clubs and the ten of +clubs right over these the cards that + + align:start position:0% +clubs right over these the cards that + + + align:start position:0% +clubs right over these the cards that +you pulled out or closed anyway so so + + align:start position:0% +you pulled out or closed anyway so so + + + align:start position:0% +you pulled out or closed anyway so so +they look pretty similar to the ones we + + align:start position:0% +they look pretty similar to the ones we + + + align:start position:0% +they look pretty similar to the ones we +used but this probably just because I've + + align:start position:0% +used but this probably just because I've + + + align:start position:0% +used but this probably just because I've +been in shuffled the deck but obviously + + align:start position:0% +been in shuffled the deck but obviously + + + align:start position:0% +been in shuffled the deck but obviously +if you have five cards and you only have + + align:start position:0% +if you have five cards and you only have + + + align:start position:0% +if you have five cards and you only have +four suits I guess you could call it the + + align:start position:0% +four suits I guess you could call it the + + + align:start position:0% +four suits I guess you could call it the +pigeonhole principle from 604 to but + + align:start position:0% +pigeonhole principle from 604 to but + + + align:start position:0% +pigeonhole principle from 604 to but +you're definitely going to have a pair + + align:start position:0% +you're definitely going to have a pair + + + align:start position:0% +you're definitely going to have a pair +of cards that are going to be of the + + align:start position:0% +of cards that are going to be of the + + + align:start position:0% +of cards that are going to be of the +same suit right I mean they baby more + + align:start position:0% +same suit right I mean they baby more + + + align:start position:0% +same suit right I mean they baby more +than two cards of the same suit but you + + align:start position:0% +than two cards of the same suit but you + + + align:start position:0% +than two cards of the same suit but you +guaranteed for any five cards let me + + align:start position:0% +guaranteed for any five cards let me + + + align:start position:0% +guaranteed for any five cards let me +just pick another five that two of them + + align:start position:0% +just pick another five that two of them + + + align:start position:0% +just pick another five that two of them +are going to be of the same suit right + + align:start position:0% +are going to be of the same suit right + + + align:start position:0% +are going to be of the same suit right +that's pretty much guaranteed and so we + + align:start position:0% +that's pretty much guaranteed and so we + + + align:start position:0% +that's pretty much guaranteed and so we +ended up ended up getting clubs again + + align:start position:0% +ended up ended up getting clubs again + + + align:start position:0% +ended up ended up getting clubs again +here and so you have two and four of the + + align:start position:0% +here and so you have two and four of the + + + align:start position:0% +here and so you have two and four of the +same same suit so so the first thing + + align:start position:0% +same same suit so so the first thing + + + align:start position:0% +same same suit so so the first thing +that happens in this trick is we use the + + align:start position:0% +that happens in this trick is we use the + + + align:start position:0% +that happens in this trick is we use the +first card to give away the suit right + + align:start position:0% +first card to give away the suit right + + + align:start position:0% +first card to give away the suit right +or Billy use the first card to give away + + align:start position:0% +or Billy use the first card to give away + + + align:start position:0% +or Billy use the first card to give away +the soup all right doesn't quite I + + align:start position:0% +the soup all right doesn't quite I + + + align:start position:0% +the soup all right doesn't quite I +finished the story here because let's + + align:start position:0% +finished the story here because let's + + + align:start position:0% +finished the story here because let's +just say that I'm gonna use the first + + align:start position:0% +just say that I'm gonna use the first + + + align:start position:0% +just say that I'm gonna use the first +car to signify the suit so in this in + + align:start position:0% +car to signify the suit so in this in + + + align:start position:0% +car to signify the suit so in this in +this case let's just say I gonna do + + align:start position:0% +this case let's just say I gonna do + + + align:start position:0% +this case let's just say I gonna do +clubs now I have a choice here I could a + + align:start position:0% +clubs now I have a choice here I could a + + + align:start position:0% +clubs now I have a choice here I could a +Billy I could have hidden to and showed + + align:start position:0% +Billy I could have hidden to and showed + + + align:start position:0% +Billy I could have hidden to and showed +me the four of clubs as the first card + + align:start position:0% +me the four of clubs as the first card + + + align:start position:0% +me the four of clubs as the first card +right or vice versa right and keep that + + align:start position:0% +right or vice versa right and keep that + + + align:start position:0% +right or vice versa right and keep that +in mind because that's actually + + align:start position:0% +in mind because that's actually + + + align:start position:0% +in mind because that's actually +incredibly important right but if you + + align:start position:0% +incredibly important right but if you + + + align:start position:0% +incredibly important right but if you +just say that the first card is going to + + align:start position:0% +just say that the first card is going to + + + align:start position:0% +just say that the first card is going to +signify the suit then let's say the suit + + align:start position:0% +signify the suit then let's say the suit + + + align:start position:0% +signify the suit then let's say the suit +is now out of the picture right so I + + align:start position:0% +is now out of the picture right so I + + + align:start position:0% +is now out of the picture right so I +know the suit of the card + + align:start position:0% + + + + align:start position:0% + +hominid so I have three cards left + + align:start position:0% +hominid so I have three cards left + + + align:start position:0% +hominid so I have three cards left +alright and um I got a hidden card I + + align:start position:0% +alright and um I got a hidden card I + + + align:start position:0% +alright and um I got a hidden card I +know the suit of the hidden card but + + align:start position:0% +know the suit of the hidden card but + + + align:start position:0% +know the suit of the hidden card but +that card could be the hidden card how + + align:start position:0% +that card could be the hidden card how + + + align:start position:0% +that card could be the hidden card how +many possibilities are there for the + + align:start position:0% +many possibilities are there for the + + + align:start position:0% +many possibilities are there for the +hidden card now how many possibilities I + + align:start position:0% +hidden card now how many possibilities I + + + align:start position:0% +hidden card now how many possibilities I +mean this is all a random well 13 oh + + align:start position:0% +mean this is all a random well 13 oh + + + align:start position:0% +mean this is all a random well 13 oh +good point + + align:start position:0% +good point + + + align:start position:0% +good point +yeah oh good good good so this is + + align:start position:0% +yeah oh good good good so this is + + + align:start position:0% +yeah oh good good good so this is +exactly why I need a tenth of students + + align:start position:0% +exactly why I need a tenth of students + + + align:start position:0% +exactly why I need a tenth of students +okay good so there's 12 possibilities + + align:start position:0% +okay good so there's 12 possibilities + + + align:start position:0% +okay good so there's 12 possibilities +since one of them was one of them was + + align:start position:0% +since one of them was one of them was + + + align:start position:0% +since one of them was one of them was +shown right so ah + + align:start position:0% +shown right so ah + + + align:start position:0% +shown right so ah +did that help us there are three cards + + align:start position:0% +did that help us there are three cards + + + align:start position:0% +did that help us there are three cards +left and so how many different I mean + + align:start position:0% +left and so how many different I mean + + + align:start position:0% +left and so how many different I mean +the first card is the first card right + + align:start position:0% +the first card is the first card right + + + align:start position:0% +the first card is the first card right +so it's no longer part of this + + align:start position:0% +so it's no longer part of this + + + align:start position:0% +so it's no longer part of this +permutations + + align:start position:0% +permutations + + + align:start position:0% +permutations +I can't count it in terms of the + + align:start position:0% +I can't count it in terms of the + + + align:start position:0% +I can't count it in terms of the +permutations there's only three cards + + align:start position:0% +permutations there's only three cards + + + align:start position:0% +permutations there's only three cards +left and those certainly those three + + align:start position:0% +left and those certainly those three + + + align:start position:0% +left and those certainly those three +cards could be ordered in a certain way + + align:start position:0% +cards could be ordered in a certain way + + + align:start position:0% +cards could be ordered in a certain way +but how many combinations or + + align:start position:0% +but how many combinations or + + + align:start position:0% +but how many combinations or +permutations are there of three cards + + align:start position:0% +permutations are there of three cards + + + align:start position:0% +permutations are there of three cards +only six permutations so again I seem to + + align:start position:0% +only six permutations so again I seem to + + + align:start position:0% +only six permutations so again I seem to +have a problem here I don't seem to have + + align:start position:0% +have a problem here I don't seem to have + + + align:start position:0% +have a problem here I don't seem to have +solved the original problem of the 24 to + + align:start position:0% +solved the original problem of the 24 to + + + align:start position:0% +solved the original problem of the 24 to +48 I still have a 6 to 12 gap right so + + align:start position:0% +48 I still have a 6 to 12 gap right so + + + align:start position:0% +48 I still have a 6 to 12 gap right so +we're gonna have to somehow cover that + + align:start position:0% +we're gonna have to somehow cover that + + + align:start position:0% +we're gonna have to somehow cover that +gap all right + + align:start position:0% +gap all right + + + align:start position:0% +gap all right +and any thoughts give you a little bit + + align:start position:0% +and any thoughts give you a little bit + + + align:start position:0% +and any thoughts give you a little bit +of a hint as to how this gap is going to + + align:start position:0% +of a hint as to how this gap is going to + + + align:start position:0% +of a hint as to how this gap is going to +be covered when I talked about the 2 and + + align:start position:0% +be covered when I talked about the 2 and + + + align:start position:0% +be covered when I talked about the 2 and +the 4 + + align:start position:0% +the 4 + + + align:start position:0% +the 4 +how am I going to cover this gap the 6 + + align:start position:0% +how am I going to cover this gap the 6 + + + align:start position:0% +how am I going to cover this gap the 6 +to 12 gap right + + align:start position:0% + + + + align:start position:0% + +yeah say you mean Billy is gonna say + + align:start position:0% +yeah say you mean Billy is gonna say + + + align:start position:0% +yeah say you mean Billy is gonna say +something yeah so I mean he the only + + align:start position:0% +something yeah so I mean he the only + + + align:start position:0% +something yeah so I mean he the only +thing he can do is is give me give me an + + align:start position:0% +thing he can do is is give me give me an + + + align:start position:0% +thing he can do is is give me give me an +ordering of the remaining three cards + + align:start position:0% +ordering of the remaining three cards + + + align:start position:0% +ordering of the remaining three cards +right yeah go ahead Kevin right that's + + align:start position:0% +right yeah go ahead Kevin right that's + + + align:start position:0% +right yeah go ahead Kevin right that's +good that's good + + align:start position:0% +good that's good + + + align:start position:0% +good that's good +a little high limit on the range exactly + + align:start position:0% +a little high limit on the range exactly + + + align:start position:0% +a little high limit on the range exactly +right exactly right so what's happening + + align:start position:0% +right exactly right so what's happening + + + align:start position:0% +right exactly right so what's happening +here is not only do I have the first + + align:start position:0% +here is not only do I have the first + + + align:start position:0% +here is not only do I have the first +card and it's not that the first card is + + align:start position:0% +card and it's not that the first card is + + + align:start position:0% +card and it's not that the first card is +just giving me the suit I mean that's + + align:start position:0% +just giving me the suit I mean that's + + + align:start position:0% +just giving me the suit I mean that's +the way I said it right but the first + + align:start position:0% +the way I said it right but the first + + + align:start position:0% +the way I said it right but the first +card also has a number on it right the + + align:start position:0% +card also has a number on it right the + + + align:start position:0% +card also has a number on it right the +first card has a number on it so that + + align:start position:0% +first card has a number on it so that + + + align:start position:0% +first card has a number on it so that +number could be an anchor that is going + + align:start position:0% +number could be an anchor that is going + + + align:start position:0% +number could be an anchor that is going +to help me figure out what the hidden + + align:start position:0% +to help me figure out what the hidden + + + align:start position:0% +to help me figure out what the hidden +card is right and what's important to + + align:start position:0% +card is right and what's important to + + + align:start position:0% +card is right and what's important to +understand and this is really the last + + align:start position:0% +understand and this is really the last + + + align:start position:0% +understand and this is really the last +interesting point with respect to + + align:start position:0% +interesting point with respect to + + + align:start position:0% +interesting point with respect to +shrinking these possibilities are these + + align:start position:0% +shrinking these possibilities are these + + + align:start position:0% +shrinking these possibilities are these +permutations down is you want to think + + align:start position:0% +permutations down is you want to think + + + align:start position:0% +permutations down is you want to think +about your let me draw this out properly + + align:start position:0% +about your let me draw this out properly + + + align:start position:0% +about your let me draw this out properly +in nice little circle you don't want to + + align:start position:0% +in nice little circle you don't want to + + + align:start position:0% +in nice little circle you don't want to +think about just ascending sequence of + + align:start position:0% +think about just ascending sequence of + + + align:start position:0% +think about just ascending sequence of +of cards or numbers you want to think + + align:start position:0% +of cards or numbers you want to think + + + align:start position:0% +of cards or numbers you want to think +about this as being circular as you'll + + align:start position:0% +about this as being circular as you'll + + + align:start position:0% +about this as being circular as you'll +see for the following reason + + align:start position:0% + + + + align:start position:0% + +all right so let's just say the ACE is a + + align:start position:0% +all right so let's just say the ACE is a + + + align:start position:0% +all right so let's just say the ACE is a +1 and so we're gonna think of that as + + align:start position:0% +1 and so we're gonna think of that as + + + align:start position:0% +1 and so we're gonna think of that as +being the the smallest number so you go + + align:start position:0% +being the the smallest number so you go + + + align:start position:0% +being the the smallest number so you go +1 through 13 in this case the king is + + align:start position:0% +1 through 13 in this case the king is + + + align:start position:0% +1 through 13 in this case the king is +the 13 all right so that's your number + + align:start position:0% +the 13 all right so that's your number + + + align:start position:0% +the 13 all right so that's your number +and so you could you could imagine you + + align:start position:0% +and so you could you could imagine you + + + align:start position:0% +and so you could you could imagine you +go 1 through 13 so let's just do that + + align:start position:0% +go 1 through 13 so let's just do that + + + align:start position:0% +go 1 through 13 so let's just do that +first and then I'll explain to you why I + + align:start position:0% +first and then I'll explain to you why I + + + align:start position:0% +first and then I'll explain to you why I +drew it in a circle + + align:start position:0% +drew it in a circle + + + align:start position:0% +drew it in a circle +and the first thing that happens is I'm + + align:start position:0% +and the first thing that happens is I'm + + + align:start position:0% +and the first thing that happens is I'm +going to take some card here and I'm + + align:start position:0% +going to take some card here and I'm + + + align:start position:0% +going to take some card here and I'm +gonna make that the first card right so + + align:start position:0% +gonna make that the first card right so + + + align:start position:0% +gonna make that the first card right so +I don't care about suits anymore and if + + align:start position:0% +I don't care about suits anymore and if + + + align:start position:0% +I don't care about suits anymore and if +I just picked this another five cards + + align:start position:0% +I just picked this another five cards + + + align:start position:0% +I just picked this another five cards +let's just do this again but there's + + align:start position:0% +let's just do this again but there's + + + align:start position:0% +let's just do this again but there's +another set of five cards and what do I + + align:start position:0% +another set of five cards and what do I + + + align:start position:0% +another set of five cards and what do I +have here oh I got a I got all hot + + align:start position:0% +have here oh I got a I got all hot + + + align:start position:0% +have here oh I got a I got all hot +mostly hearts okay so let me do + + align:start position:0% +mostly hearts okay so let me do + + + align:start position:0% +mostly hearts okay so let me do +something more interesting this is too + + align:start position:0% +something more interesting this is too + + + align:start position:0% +something more interesting this is too +many hearts there right let's do this so + + align:start position:0% +many hearts there right let's do this so + + + align:start position:0% +many hearts there right let's do this so +so now I got a 2 and a Jack and I got a + + align:start position:0% +so now I got a 2 and a Jack and I got a + + + align:start position:0% +so now I got a 2 and a Jack and I got a +10 and an 8 + + align:start position:0% +10 and an 8 + + + align:start position:0% +10 and an 8 +ok now I'll make this even more + + align:start position:0% +ok now I'll make this even more + + + align:start position:0% +ok now I'll make this even more +interesting by picking I want to pick I + + align:start position:0% +interesting by picking I want to pick I + + + align:start position:0% +interesting by picking I want to pick I +want to get a hearts card and let's see + + align:start position:0% +want to get a hearts card and let's see + + + align:start position:0% +want to get a hearts card and let's see +how this works + + align:start position:0% + + + + align:start position:0% + +finally all right so so this is what I + + align:start position:0% +finally all right so so this is what I + + + align:start position:0% +finally all right so so this is what I +have King of Hearts 8 Oh spades etc so + + align:start position:0% +have King of Hearts 8 Oh spades etc so + + + align:start position:0% +have King of Hearts 8 Oh spades etc so +the two cards were the same suit of the + + align:start position:0% +the two cards were the same suit of the + + + align:start position:0% +the two cards were the same suit of the +the 2 and the Jack right and so here's + + align:start position:0% +the 2 and the Jack right and so here's + + + align:start position:0% +the 2 and the Jack right and so here's +the important thing one of the things + + align:start position:0% +the important thing one of the things + + + align:start position:0% +the important thing one of the things +that Billy did kind of in a subtle way + + align:start position:0% +that Billy did kind of in a subtle way + + + align:start position:0% +that Billy did kind of in a subtle way +I'm assuming and some of you may have + + align:start position:0% +I'm assuming and some of you may have + + + align:start position:0% +I'm assuming and some of you may have +picked up on it + + align:start position:0% +picked up on it + + + align:start position:0% +picked up on it +the very first card that he asked one of + + align:start position:0% +the very first card that he asked one of + + + align:start position:0% +the very first card that he asked one of +you to pick it certainly wasn't the + + align:start position:0% +you to pick it certainly wasn't the + + + align:start position:0% +you to pick it certainly wasn't the +hidden card right I mean he got all 5 + + align:start position:0% +hidden card right I mean he got all 5 + + + align:start position:0% +hidden card right I mean he got all 5 +cards and then he decided which of the + + align:start position:0% +cards and then he decided which of the + + + align:start position:0% +cards and then he decided which of the +cards was going to be the hidden card + + align:start position:0% +cards was going to be the hidden card + + + align:start position:0% +cards was going to be the hidden card +and then took the remaining four cards + + align:start position:0% +and then took the remaining four cards + + + align:start position:0% +and then took the remaining four cards +and encoded them right and if you don't + + align:start position:0% +and encoded them right and if you don't + + + align:start position:0% +and encoded them right and if you don't +do that if you just say this if you if + + align:start position:0% +do that if you just say this if you if + + + align:start position:0% +do that if you just say this if you if +you this trick won't work if this is the + + align:start position:0% +you this trick won't work if this is the + + + align:start position:0% +you this trick won't work if this is the +hidden card okay this trick is only + + align:start position:0% +hidden card okay this trick is only + + + align:start position:0% +hidden card okay this trick is only +going to work + + align:start position:0% +going to work + + + align:start position:0% +going to work +as it turns out on if the the hidden + + align:start position:0% +as it turns out on if the the hidden + + + align:start position:0% +as it turns out on if the the hidden +card is a - it won't even work if the + + align:start position:0% +card is a - it won't even work if the + + + align:start position:0% +card is a - it won't even work if the +hidden card is a jack okay um and + + align:start position:0% +hidden card is a jack okay um and + + + align:start position:0% +hidden card is a jack okay um and +there's a reason for that + + align:start position:0% +there's a reason for that + + + align:start position:0% +there's a reason for that +alright and can you can you think of the + + align:start position:0% +alright and can you can you think of the + + + align:start position:0% +alright and can you can you think of the +reason for that um if you look at the + + align:start position:0% +reason for that um if you look at the + + + align:start position:0% +reason for that um if you look at the +board can you think of the reason for + + align:start position:0% +board can you think of the reason for + + + align:start position:0% +board can you think of the reason for +that someone other than buddy someone + + align:start position:0% +that someone other than buddy someone + + + align:start position:0% +that someone other than buddy someone +else what do you see up here so what am + + align:start position:0% +else what do you see up here so what am + + + align:start position:0% +else what do you see up here so what am +I trying to do in terms of what what + + align:start position:0% +I trying to do in terms of what what + + + align:start position:0% +I trying to do in terms of what what +would happen I you guys talked about + + align:start position:0% +would happen I you guys talked about + + + align:start position:0% +would happen I you guys talked about +Kevin mentioned the distance and things + + align:start position:0% +Kevin mentioned the distance and things + + + align:start position:0% +Kevin mentioned the distance and things +like that right you know you can call it + + align:start position:0% +like that right you know you can call it + + + align:start position:0% +like that right you know you can call it +the offset so what would happen if I hit + + align:start position:0% +the offset so what would happen if I hit + + + align:start position:0% +the offset so what would happen if I hit +the jack and I did this I did something + + align:start position:0% +the jack and I did this I did something + + + align:start position:0% +the jack and I did this I did something +like this where I the two of diamonds + + align:start position:0% +like this where I the two of diamonds + + + align:start position:0% +like this where I the two of diamonds +was the first card that was put out and + + align:start position:0% +was the first card that was put out and + + + align:start position:0% +was the first card that was put out and +then I tried to encode a number using + + align:start position:0% +then I tried to encode a number using + + + align:start position:0% +then I tried to encode a number using +these remaining three cards what's the + + align:start position:0% +these remaining three cards what's the + + + align:start position:0% +these remaining three cards what's the +what's the biggest number that I could + + align:start position:0% +what's the biggest number that I could + + + align:start position:0% +what's the biggest number that I could +encode I mean in in III I need to encode + + align:start position:0% +encode I mean in in III I need to encode + + + align:start position:0% +encode I mean in in III I need to encode +lots of numbers right alright so what's + + align:start position:0% +lots of numbers right alright so what's + + + align:start position:0% +lots of numbers right alright so what's +the what's the biggest number that I + + align:start position:0% +the what's the biggest number that I + + + align:start position:0% +the what's the biggest number that I +could encode here if I had six + + align:start position:0% +could encode here if I had six + + + align:start position:0% +could encode here if I had six +permutations and I start with one the + + align:start position:0% +permutations and I start with one the + + + align:start position:0% +permutations and I start with one the +biggest number that could encode is a + + align:start position:0% +biggest number that could encode is a + + + align:start position:0% +biggest number that could encode is a +six right + + align:start position:0% +six right + + + align:start position:0% +six right +sadly the jack is too far away from the + + align:start position:0% +sadly the jack is too far away from the + + + align:start position:0% +sadly the jack is too far away from the +two right if I think of the jack is + + align:start position:0% +two right if I think of the jack is + + + align:start position:0% +two right if I think of the jack is +being an 11 it's 9 away from the two + + align:start position:0% +being an 11 it's 9 away from the two + + + align:start position:0% +being an 11 it's 9 away from the two +right but help me out here what could I + + align:start position:0% +right but help me out here what could I + + + align:start position:0% +right but help me out here what could I +do if I if I flipped it what happens you + + align:start position:0% +do if I if I flipped it what happens you + + + align:start position:0% +do if I if I flipped it what happens you +can count backwards or what do I have up + + align:start position:0% +can count backwards or what do I have up + + + align:start position:0% +can count backwards or what do I have up +there and on the board what do you see + + align:start position:0% +there and on the board what do you see + + + align:start position:0% +there and on the board what do you see +up there on the board I wrote something + + align:start position:0% +up there on the board I wrote something + + + align:start position:0% +up there on the board I wrote something +that was linear but what what what do I + + align:start position:0% +that was linear but what what what do I + + + align:start position:0% +that was linear but what what what do I +have up there on the left circular so + + align:start position:0% +have up there on the left circular so + + + align:start position:0% +have up there on the left circular so +you think more moderate Marik + + align:start position:0% +you think more moderate Marik + + + align:start position:0% +you think more moderate Marik +you know think think of this is being + + align:start position:0% +you know think think of this is being + + + align:start position:0% +you know think think of this is being +circular okay so what happens is that if + + align:start position:0% +circular okay so what happens is that if + + + align:start position:0% +circular okay so what happens is that if +I picked a two energy and a jack and if + + align:start position:0% +I picked a two energy and a jack and if + + + align:start position:0% +I picked a two energy and a jack and if +I I what I want to do is to go clockwise + + align:start position:0% +I I what I want to do is to go clockwise + + + align:start position:0% +I I what I want to do is to go clockwise +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +because they're only 13 cards for any + + align:start position:0% +because they're only 13 cards for any + + + align:start position:0% +because they're only 13 cards for any +pair of cards it's always the case that + + align:start position:0% +pair of cards it's always the case that + + + align:start position:0% +pair of cards it's always the case that +I can choose the first car in such a way + + align:start position:0% +I can choose the first car in such a way + + + align:start position:0% +I can choose the first car in such a way +that the hidden card is at most six away + + align:start position:0% +that the hidden card is at most six away + + + align:start position:0% +that the hidden card is at most six away +from the first card okay + + align:start position:0% +from the first card okay + + + align:start position:0% +from the first card okay +because you you you could get into a + + align:start position:0% +because you you you could get into a + + + align:start position:0% +because you you you could get into a +situation where obviously if I ended up + + align:start position:0% +situation where obviously if I ended up + + + align:start position:0% +situation where obviously if I ended up +hiding the jack and exposing the two inw + + align:start position:0% +hiding the jack and exposing the two inw + + + align:start position:0% +hiding the jack and exposing the two inw +in code but if I unhide the two and + + align:start position:0% +in code but if I unhide the two and + + + align:start position:0% +in code but if I unhide the two and +expose the jack + + align:start position:0% +expose the jack + + + align:start position:0% +expose the jack +then I go one two three four and I'm at + + align:start position:0% +then I go one two three four and I'm at + + + align:start position:0% +then I go one two three four and I'm at +basically four okay so so that's the + + align:start position:0% +basically four okay so so that's the + + + align:start position:0% +basically four okay so so that's the +last thing all right so let's just do + + align:start position:0% +last thing all right so let's just do + + + align:start position:0% +last thing all right so let's just do +this really quickly with yet another set + + align:start position:0% +this really quickly with yet another set + + + align:start position:0% +this really quickly with yet another set +of five cards right now obviously we + + align:start position:0% +of five cards right now obviously we + + + align:start position:0% +of five cards right now obviously we +practice so we could do this fairly + + align:start position:0% +practice so we could do this fairly + + + align:start position:0% +practice so we could do this fairly +quickly right but and you can practice + + align:start position:0% +quickly right but and you can practice + + + align:start position:0% +quickly right but and you can practice +too but sometimes it thinks you get + + align:start position:0% +too but sometimes it thinks you get + + + align:start position:0% +too but sometimes it thinks you get +lucky you know and you get easy easy + + align:start position:0% +lucky you know and you get easy easy + + + align:start position:0% +lucky you know and you get easy easy +things to encode right so what happens + + align:start position:0% +things to encode right so what happens + + + align:start position:0% +things to encode right so what happens +here someone wants so now that you know + + align:start position:0% +here someone wants so now that you know + + + align:start position:0% +here someone wants so now that you know +the algorithm you have some choices here + + align:start position:0% +the algorithm you have some choices here + + + align:start position:0% +the algorithm you have some choices here +but obviously you have that not all + + align:start position:0% +but obviously you have that not all + + + align:start position:0% +but obviously you have that not all +choices will work you got to be a little + + align:start position:0% +choices will work you got to be a little + + + align:start position:0% +choices will work you got to be a little +bit careful what would you what would + + align:start position:0% +bit careful what would you what would + + + align:start position:0% +bit careful what would you what would +you hide so so you need to make sure + + align:start position:0% +you hide so so you need to make sure + + + align:start position:0% +you hide so so you need to make sure +that you you get you can choose a pair + + align:start position:0% +that you you get you can choose a pair + + + align:start position:0% +that you you get you can choose a pair +of I'll make this a little bit easier + + align:start position:0% + + + + align:start position:0% + +sometimes choices make things more + + align:start position:0% +sometimes choices make things more + + + align:start position:0% +sometimes choices make things more +difficult right perfect + + align:start position:0% +difficult right perfect + + + align:start position:0% +difficult right perfect +all right so so what you see here is + + align:start position:0% +all right so so what you see here is + + + align:start position:0% +all right so so what you see here is +your you know that you have to do the + + align:start position:0% +your you know that you have to do the + + + align:start position:0% +your you know that you have to do the +clubs now right because you have the the + + align:start position:0% +clubs now right because you have the the + + + align:start position:0% +clubs now right because you have the the +clubs as being the the suit that's + + align:start position:0% +clubs as being the the suit that's + + + align:start position:0% +clubs as being the the suit that's +repeated no other suits are repeated + + align:start position:0% +repeated no other suits are repeated + + + align:start position:0% +repeated no other suits are repeated +right so what am I going to expose and + + align:start position:0% +right so what am I going to expose and + + + align:start position:0% +right so what am I going to expose and +what am I going to hide that's your + + align:start position:0% +what am I going to hide that's your + + + align:start position:0% +what am I going to hide that's your +first question right someone else you + + align:start position:0% +first question right someone else you + + + align:start position:0% +first question right someone else you +guys could all gonna have to do this + + align:start position:0% +guys could all gonna have to do this + + + align:start position:0% +guys could all gonna have to do this +trick that's the final exam for this + + align:start position:0% +trick that's the final exam for this + + + align:start position:0% +trick that's the final exam for this +class + + align:start position:0% +class + + + align:start position:0% +class +okay on Friday next week you're all + + align:start position:0% +okay on Friday next week you're all + + + align:start position:0% +okay on Friday next week you're all +doing the trick no all right so what am + + align:start position:0% +doing the trick no all right so what am + + + align:start position:0% +doing the trick no all right so what am +I going to what am I going to yeah go + + align:start position:0% +I going to what am I going to yeah go + + + align:start position:0% +I going to what am I going to yeah go +ahead Josh + + align:start position:0% + + + + align:start position:0% + +you're gonna hide the ace exactly right + + align:start position:0% +you're gonna hide the ace exactly right + + + align:start position:0% +you're gonna hide the ace exactly right +you you want to hide the ace because you + + align:start position:0% +you you want to hide the ace because you + + + align:start position:0% +you you want to hide the ace because you +want to go this way and if you do it the + + align:start position:0% +want to go this way and if you do it the + + + align:start position:0% +want to go this way and if you do it the +other way around it's not going to work + + align:start position:0% +other way around it's not going to work + + + align:start position:0% +other way around it's not going to work +you're gonna hide the ace and you're + + align:start position:0% +you're gonna hide the ace and you're + + + align:start position:0% +you're gonna hide the ace and you're +going to make the king the first card + + align:start position:0% +going to make the king the first card + + + align:start position:0% +going to make the king the first card +and and now what you need to do is this + + align:start position:0% +and and now what you need to do is this + + + align:start position:0% +and and now what you need to do is this +is this is gone right and now what I + + align:start position:0% +is this is gone right and now what I + + + align:start position:0% +is this is gone right and now what I +need to do is I need to encode a number + + align:start position:0% +need to do is I need to encode a number + + + align:start position:0% +need to do is I need to encode a number +between one and six in general in this + + align:start position:0% +between one and six in general in this + + + align:start position:0% +between one and six in general in this +case I need to encode the number one + + align:start position:0% +case I need to encode the number one + + + align:start position:0% +case I need to encode the number one +okay in order to give away the fact that + + align:start position:0% +okay in order to give away the fact that + + + align:start position:0% +okay in order to give away the fact that +the hidden card is an ace and now I can + + align:start position:0% +the hidden card is an ace and now I can + + + align:start position:0% +the hidden card is an ace and now I can +do what was suggested before we just + + align:start position:0% +do what was suggested before we just + + + align:start position:0% +do what was suggested before we just +have some sort of I mean there's + + align:start position:0% +have some sort of I mean there's + + + align:start position:0% +have some sort of I mean there's +obviously an ordering associated with + + align:start position:0% +obviously an ordering associated with + + + align:start position:0% +obviously an ordering associated with +with these cards that you see up here if + + align:start position:0% +with these cards that you see up here if + + + align:start position:0% +with these cards that you see up here if +I call this a1 and I call this the 13 + + align:start position:0% +I call this a1 and I call this the 13 + + + align:start position:0% +I call this a1 and I call this the 13 +then that let's do the logical thing + + align:start position:0% +then that let's do the logical thing + + + align:start position:0% +then that let's do the logical thing +which is 1 is smaller than 2 which is + + align:start position:0% +which is 1 is smaller than 2 which is + + + align:start position:0% +which is 1 is smaller than 2 which is +smaller than 13 but I might end up you + + align:start position:0% +smaller than 13 but I might end up you + + + align:start position:0% +smaller than 13 but I might end up you +know I might have a and nine of Hearts + + align:start position:0% +know I might have a and nine of Hearts + + + align:start position:0% +know I might have a and nine of Hearts +here rather than a 5 of Hearts and I got + + align:start position:0% +here rather than a 5 of Hearts and I got + + + align:start position:0% +here rather than a 5 of Hearts and I got +to obviously be able to order the nine + + align:start position:0% +to obviously be able to order the nine + + + align:start position:0% +to obviously be able to order the nine +of Hearts in relation to the 5 of Hearts + + align:start position:0% +of Hearts in relation to the 5 of Hearts + + + align:start position:0% +of Hearts in relation to the 5 of Hearts +as well right so because I that all of + + align:start position:0% +as well right so because I that all of + + + align:start position:0% +as well right so because I that all of +these could be nines actually right and + + align:start position:0% +these could be nines actually right and + + + align:start position:0% +these could be nines actually right and +and so so I can't just rely on the + + align:start position:0% +and so so I can't just rely on the + + + align:start position:0% +and so so I can't just rely on the +number to do the ordering so I could + + align:start position:0% +number to do the ordering so I could + + + align:start position:0% +number to do the ordering so I could +just choose an arbitrary clubs is small + + align:start position:0% +just choose an arbitrary clubs is small + + + align:start position:0% +just choose an arbitrary clubs is small +the smallest diamonds is the next and + + align:start position:0% +the smallest diamonds is the next and + + + align:start position:0% +the smallest diamonds is the next and +then I got hearts I just did this + + align:start position:0% +then I got hearts I just did this + + + align:start position:0% +then I got hearts I just did this +because this is a little bit easy to + + align:start position:0% +because this is a little bit easy to + + + align:start position:0% +because this is a little bit easy to +remember for me you can do this in many + + align:start position:0% +remember for me you can do this in many + + + align:start position:0% +remember for me you can do this in many +different ways in alphabetical order you + + align:start position:0% +different ways in alphabetical order you + + + align:start position:0% +different ways in alphabetical order you +know see DHS and so so this that's + + align:start position:0% +know see DHS and so so this that's + + + align:start position:0% +know see DHS and so so this that's +that's moot here what I need to do is to + + align:start position:0% +that's moot here what I need to do is to + + + align:start position:0% +that's moot here what I need to do is to +encode the number one okay and then I + + align:start position:0% +encode the number one okay and then I + + + align:start position:0% +encode the number one okay and then I +encode that in order to encode the + + align:start position:0% +encode that in order to encode the + + + align:start position:0% +encode that in order to encode the +number one I have to have some sort of + + align:start position:0% +number one I have to have some sort of + + + align:start position:0% +number one I have to have some sort of +way of ordering this and so what I'm + + align:start position:0% +way of ordering this and so what I'm + + + align:start position:0% +way of ordering this and so what I'm +going to do is I'm going to say SLM is + + align:start position:0% +going to do is I'm going to say SLM is + + + align:start position:0% +going to do is I'm going to say SLM is +one so what do I mean by SLM the + + align:start position:0% +one so what do I mean by SLM the + + + align:start position:0% +one so what do I mean by SLM the +smallest card is is first the I'm sorry + + align:start position:0% +smallest card is is first the I'm sorry + + + align:start position:0% +smallest card is is first the I'm sorry +SML is + + align:start position:0% +SML is + + + align:start position:0% +SML is +increasing this the smallest card is is + + align:start position:0% +increasing this the smallest card is is + + + align:start position:0% +increasing this the smallest card is is +the first one the medium card is the + + align:start position:0% +the first one the medium card is the + + + align:start position:0% +the first one the medium card is the +second one and the largest card is the + + align:start position:0% +second one and the largest card is the + + + align:start position:0% +second one and the largest card is the +third one okay and I'll write this out + + align:start position:0% +third one okay and I'll write this out + + + align:start position:0% +third one okay and I'll write this out +and you can see the code for it but when + + align:start position:0% +and you can see the code for it but when + + + align:start position:0% +and you can see the code for it but when +you see something like L LM s you're + + align:start position:0% +you see something like L LM s you're + + + align:start position:0% +you see something like L LM s you're +going to get a six and there's obviously + + align:start position:0% +going to get a six and there's obviously + + + align:start position:0% +going to get a six and there's obviously +six of these different combinations + + align:start position:0% +six of these different combinations + + + align:start position:0% +six of these different combinations +right + + align:start position:0% +right + + + align:start position:0% +right +the details are actually entirely up to + + align:start position:0% +the details are actually entirely up to + + + align:start position:0% +the details are actually entirely up to +you I mean the most important thing here + + align:start position:0% +you I mean the most important thing here + + + align:start position:0% +you I mean the most important thing here +is the ordering that Billy had had to be + + align:start position:0% +is the ordering that Billy had had to be + + + align:start position:0% +is the ordering that Billy had had to be +the ordering that I had alright and so + + align:start position:0% +the ordering that I had alright and so + + + align:start position:0% +the ordering that I had alright and so +yesterday when we practiced one time + + align:start position:0% +yesterday when we practiced one time + + + align:start position:0% +yesterday when we practiced one time +there was a mismatch and we got it wrong + + align:start position:0% +there was a mismatch and we got it wrong + + + align:start position:0% +there was a mismatch and we got it wrong +but that's the only way the trick would + + align:start position:0% +but that's the only way the trick would + + + align:start position:0% +but that's the only way the trick would +would fail I really I mean other than + + align:start position:0% +would fail I really I mean other than + + + align:start position:0% +would fail I really I mean other than +human error is if the is the encoding + + align:start position:0% +human error is if the is the encoding + + + align:start position:0% +human error is if the is the encoding +this is really encoding followed by + + align:start position:0% +this is really encoding followed by + + + align:start position:0% +this is really encoding followed by +decoding and obviously you need the same + + align:start position:0% +decoding and obviously you need the same + + + align:start position:0% +decoding and obviously you need the same +algorithm if you will which requires + + align:start position:0% +algorithm if you will which requires + + + align:start position:0% +algorithm if you will which requires +that you need the same ordering in this + + align:start position:0% +that you need the same ordering in this + + + align:start position:0% +that you need the same ordering in this +case for the for the cards right so so + + align:start position:0% +case for the for the cards right so so + + + align:start position:0% +case for the for the cards right so so +that's it that's that's the trick um it + + align:start position:0% +that's it that's that's the trick um it + + + align:start position:0% +that's it that's that's the trick um it +doesn't seem that interesting anymore + + align:start position:0% +doesn't seem that interesting anymore + + + align:start position:0% +doesn't seem that interesting anymore +huh but no it is interesting if you show + + align:start position:0% +huh but no it is interesting if you show + + + align:start position:0% +huh but no it is interesting if you show +it to people and and the fun part is + + align:start position:0% +it to people and and the fun part is + + + align:start position:0% +it to people and and the fun part is +didn't and actually doing it so I + + align:start position:0% +didn't and actually doing it so I + + + align:start position:0% +didn't and actually doing it so I +encourage you all to do it any questions + + align:start position:0% +encourage you all to do it any questions + + + align:start position:0% +encourage you all to do it any questions +about how this trick works so what I + + align:start position:0% +about how this trick works so what I + + + align:start position:0% +about how this trick works so what I +like to do is show you some code for for + + align:start position:0% +like to do is show you some code for for + + + align:start position:0% +like to do is show you some code for for +this trick and there's also a code that + + align:start position:0% +this trick and there's also a code that + + + align:start position:0% +this trick and there's also a code that +was useful to both of us because we + + align:start position:0% +was useful to both of us because we + + + align:start position:0% +was useful to both of us because we +could practice by ourselves we didn't + + align:start position:0% +could practice by ourselves we didn't + + + align:start position:0% +could practice by ourselves we didn't +have to be in the same room to practice + + align:start position:0% +have to be in the same room to practice + + + align:start position:0% +have to be in the same room to practice +because I could sort of randomly + + align:start position:0% +because I could sort of randomly + + + align:start position:0% +because I could sort of randomly +generate a bunch of these four cards and + + align:start position:0% +generate a bunch of these four cards and + + + align:start position:0% +generate a bunch of these four cards and +obviously the program knew what the + + align:start position:0% +obviously the program knew what the + + + align:start position:0% +obviously the program knew what the +hidden card was and I could you know + + align:start position:0% +hidden card was and I could you know + + + align:start position:0% +hidden card was and I could you know +I'll show you the code I could type in + + align:start position:0% +I'll show you the code I could type in + + + align:start position:0% +I'll show you the code I could type in +what the hidden card was and we it would + + align:start position:0% +what the hidden card was and we it would + + + align:start position:0% +what the hidden card was and we it would +say you know I guess I'd say you're a + + align:start position:0% +say you know I guess I'd say you're a + + + align:start position:0% +say you know I guess I'd say you're a +mind-reader extraordinaire or sorry not + + align:start position:0% +mind-reader extraordinaire or sorry not + + + align:start position:0% +mind-reader extraordinaire or sorry not +impressed and then Billy could do the + + align:start position:0% +impressed and then Billy could do the + + + align:start position:0% +impressed and then Billy could do the +same thing in terms of checking is n + + align:start position:0% +same thing in terms of checking is n + + + align:start position:0% +same thing in terms of checking is n +coding + + align:start position:0% +coding + + + align:start position:0% +coding +alright and then after we're done here + + align:start position:0% +alright and then after we're done here + + + align:start position:0% +alright and then after we're done here +talking about the code and there's some + + align:start position:0% +talking about the code and there's some + + + align:start position:0% +talking about the code and there's some +interesting things with the code it + + align:start position:0% +interesting things with the code it + + + align:start position:0% +interesting things with the code it +let's talk about whether you could talk + + align:start position:0% +let's talk about whether you could talk + + + align:start position:0% +let's talk about whether you could talk +about different kinds of tricks and in + + align:start position:0% +about different kinds of tricks and in + + + align:start position:0% +about different kinds of tricks and in +particular I want to talk about whether + + align:start position:0% +particular I want to talk about whether + + + align:start position:0% +particular I want to talk about whether +we could go from five cards to four + + align:start position:0% +we could go from five cards to four + + + align:start position:0% +we could go from five cards to four +cards + + align:start position:0% +cards + + + align:start position:0% +cards +using a different encoding scheme right + + align:start position:0% +using a different encoding scheme right + + + align:start position:0% +using a different encoding scheme right +so cool so I wrote this code about a + + align:start position:0% +so cool so I wrote this code about a + + + align:start position:0% +so cool so I wrote this code about a +year ago and I think I'd probably write + + align:start position:0% +year ago and I think I'd probably write + + + align:start position:0% +year ago and I think I'd probably write +it differently now + + align:start position:0% +it differently now + + + align:start position:0% +it differently now +but we have what we have so the first + + align:start position:0% +but we have what we have so the first + + + align:start position:0% +but we have what we have so the first +thing is you have to decide on an order + + align:start position:0% +thing is you have to decide on an order + + + align:start position:0% +thing is you have to decide on an order +right you absolutely have to decide in + + align:start position:0% +right you absolutely have to decide in + + + align:start position:0% +right you absolutely have to decide in +an order and the cards themselves as I + + align:start position:0% +an order and the cards themselves as I + + + align:start position:0% +an order and the cards themselves as I +mentioned I'm this natural order + + align:start position:0% +mentioned I'm this natural order + + + align:start position:0% +mentioned I'm this natural order +associated with the numbers and of + + align:start position:0% +associated with the numbers and of + + + align:start position:0% +associated with the numbers and of +course you can decide if you want to + + align:start position:0% +course you can decide if you want to + + + align:start position:0% +course you can decide if you want to +start with the with the two and then + + align:start position:0% +start with the with the two and then + + + align:start position:0% +start with the with the two and then +yeah and the ace could be 14 I mean kind + + align:start position:0% +yeah and the ace could be 14 I mean kind + + + align:start position:0% +yeah and the ace could be 14 I mean kind +of makes sense to for you to go 1 + + align:start position:0% +of makes sense to for you to go 1 + + + align:start position:0% +of makes sense to for you to go 1 +through 13 so that's really what we have + + align:start position:0% +through 13 so that's really what we have + + + align:start position:0% +through 13 so that's really what we have +here the ace is the smallest card and + + align:start position:0% +here the ace is the smallest card and + + + align:start position:0% +here the ace is the smallest card and +the King is the biggest card and as I + + align:start position:0% +the King is the biggest card and as I + + + align:start position:0% +the King is the biggest card and as I +mentioned I the clubs are smaller than + + align:start position:0% +mentioned I the clubs are smaller than + + + align:start position:0% +mentioned I the clubs are smaller than +the diamonds etc so I just have a deck + + align:start position:0% +the diamonds etc so I just have a deck + + + align:start position:0% +the diamonds etc so I just have a deck +of cards that is ordered as you see up + + align:start position:0% +of cards that is ordered as you see up + + + align:start position:0% +of cards that is ordered as you see up +there and that's just a Python list that + + align:start position:0% +there and that's just a Python list that + + + align:start position:0% +there and that's just a Python list that +tells you what the ordering of these 52 + + align:start position:0% +tells you what the ordering of these 52 + + + align:start position:0% +tells you what the ordering of these 52 +cards are right that makes sense so the + + align:start position:0% +cards are right that makes sense so the + + + align:start position:0% +cards are right that makes sense so the +so the there's many procedures here many + + align:start position:0% +so the there's many procedures here many + + + align:start position:0% +so the there's many procedures here many +routines that do different things and a + + align:start position:0% +routines that do different things and a + + + align:start position:0% +routines that do different things and a +lot of them use the same code so I'm not + + align:start position:0% +lot of them use the same code so I'm not + + + align:start position:0% +lot of them use the same code so I'm not +gonna explain each each one of them but + + align:start position:0% +gonna explain each each one of them but + + + align:start position:0% +gonna explain each each one of them but +this one is the is a good one and I'll + + align:start position:0% +this one is the is a good one and I'll + + + align:start position:0% +this one is the is a good one and I'll +also show you the computer assistant one + + align:start position:0% +also show you the computer assistant one + + + align:start position:0% +also show you the computer assistant one +which is essentially this procedure + + align:start position:0% +which is essentially this procedure + + + align:start position:0% +which is essentially this procedure +except that it allows it allowed me to + + align:start position:0% +except that it allows it allowed me to + + + align:start position:0% +except that it allows it allowed me to +practice by myself and I generated cards + + align:start position:0% +practice by myself and I generated cards + + + align:start position:0% +practice by myself and I generated cards +randomly in this case what happens is + + align:start position:0% +randomly in this case what happens is + + + align:start position:0% +randomly in this case what happens is +you input five cards and what this does + + align:start position:0% +you input five cards and what this does + + + align:start position:0% +you input five cards and what this does +is so you could sort of take five cards + + align:start position:0% +is so you could sort of take five cards + + + align:start position:0% +is so you could sort of take five cards +out from the deck and then manually you + + align:start position:0% +out from the deck and then manually you + + + align:start position:0% +out from the deck and then manually you +can you can choose the hidden card order + + align:start position:0% +can you can choose the hidden card order + + + align:start position:0% +can you can choose the hidden card order +the remaining four and if you typed in + + align:start position:0% +the remaining four and if you typed in + + + align:start position:0% +the remaining four and if you typed in +those five cards into this particular + + align:start position:0% +those five cards into this particular + + + align:start position:0% +those five cards into this particular +procedure it would give you the first + + align:start position:0% +procedure it would give you the first + + + align:start position:0% +procedure it would give you the first +four cards okay and so you can then + + align:start position:0% +four cards okay and so you can then + + + align:start position:0% +four cards okay and so you can then +verify that you've done the ordering so + + align:start position:0% +verify that you've done the ordering so + + + align:start position:0% +verify that you've done the ordering so +this would be something that I don't + + align:start position:0% +this would be something that I don't + + + align:start position:0% +this would be something that I don't +have Billy used this to practice but he + + align:start position:0% +have Billy used this to practice but he + + + align:start position:0% +have Billy used this to practice but he +could have so what do I have here well + + align:start position:0% +could have so what do I have here well + + + align:start position:0% +could have so what do I have here well +the first thing is just printing out + + align:start position:0% +the first thing is just printing out + + + align:start position:0% +the first thing is just printing out +what the order is + + align:start position:0% +what the order is + + + align:start position:0% +what the order is +there's a bunch of things that need to + + align:start position:0% +there's a bunch of things that need to + + + align:start position:0% +there's a bunch of things that need to +get initialized cards is simply a list + + align:start position:0% +get initialized cards is simply a list + + + align:start position:0% +get initialized cards is simply a list +of five cards and and then you have C in + + align:start position:0% +of five cards and and then you have C in + + + align:start position:0% +of five cards and and then you have C in +index or CN which is the indices in that + + align:start position:0% +index or CN which is the indices in that + + + align:start position:0% +index or CN which is the indices in that +in that giant list that we have that had + + align:start position:0% +in that giant list that we have that had + + + align:start position:0% +in that giant list that we have that had +52 cards in it it's there just the + + align:start position:0% +52 cards in it it's there just the + + + align:start position:0% +52 cards in it it's there just the +indices of the various cards you can you + + align:start position:0% +indices of the various cards you can you + + + align:start position:0% +indices of the various cards you can you +can use dot index which is a method to + + align:start position:0% +can use dot index which is a method to + + + align:start position:0% +can use dot index which is a method to +go from a card which is like a + + align:start position:0% +go from a card which is like a + + + align:start position:0% +go from a card which is like a +underscore see for example to the to the + + align:start position:0% +underscore see for example to the to the + + + align:start position:0% +underscore see for example to the to the +index and and then card suits are what + + align:start position:0% +index and and then card suits are what + + + align:start position:0% +index and and then card suits are what +the suits are for the cards and it's 0 1 + + align:start position:0% +the suits are for the cards and it's 0 1 + + + align:start position:0% +the suits are for the cards and it's 0 1 +2 & 3 for clubs diamonds etc and then + + align:start position:0% +2 & 3 for clubs diamonds etc and then + + + align:start position:0% +2 & 3 for clubs diamonds etc and then +the numbers are what the numbers of the + + align:start position:0% +the numbers are what the numbers of the + + + align:start position:0% +the numbers are what the numbers of the +cards are 1 through 13 okay I kind of + + align:start position:0% +cards are 1 through 13 okay I kind of + + + align:start position:0% +cards are 1 through 13 okay I kind of +need this there's a bunch of bookkeeping + + align:start position:0% +need this there's a bunch of bookkeeping + + + align:start position:0% +need this there's a bunch of bookkeeping +as you can imagine you know if you're + + align:start position:0% +as you can imagine you know if you're + + + align:start position:0% +as you can imagine you know if you're +doing things in our in our head here but + + align:start position:0% +doing things in our in our head here but + + + align:start position:0% +doing things in our in our head here but +if you want to get a computer program to + + align:start position:0% +if you want to get a computer program to + + + align:start position:0% +if you want to get a computer program to +actually do all of these computations + + align:start position:0% +actually do all of these computations + + + align:start position:0% +actually do all of these computations +it's not complicated but you have to + + align:start position:0% +it's not complicated but you have to + + + align:start position:0% +it's not complicated but you have to +worry about the four suits and you got + + align:start position:0% +worry about the four suits and you got + + + align:start position:0% +worry about the four suits and you got +to worry about the 13 cards and you have + + align:start position:0% +to worry about the 13 cards and you have + + + align:start position:0% +to worry about the 13 cards and you have +to go ahead and encode SML or produce + + align:start position:0% +to go ahead and encode SML or produce + + + align:start position:0% +to go ahead and encode SML or produce +this encoding right so you can imagine + + align:start position:0% +this encoding right so you can imagine + + + align:start position:0% +this encoding right so you can imagine +there's a bunch of code it's not + + align:start position:0% +there's a bunch of code it's not + + + align:start position:0% +there's a bunch of code it's not +complicated code but there's a bunch of + + align:start position:0% +complicated code but there's a bunch of + + + align:start position:0% +complicated code but there's a bunch of +code right so the first thing that + + align:start position:0% +code right so the first thing that + + + align:start position:0% +code right so the first thing that +happens here is in this particular + + align:start position:0% +happens here is in this particular + + + align:start position:0% +happens here is in this particular +procedure you want to input these cards + + align:start position:0% +procedure you want to input these cards + + + align:start position:0% +procedure you want to input these cards +in and so let me just run it and and so + + align:start position:0% +in and so let me just run it and and so + + + align:start position:0% +in and so let me just run it and and so +you get a sense of what this procedure + + align:start position:0% +you get a sense of what this procedure + + + align:start position:0% +you get a sense of what this procedure +does alright beautiful so let's just say + + align:start position:0% +does alright beautiful so let's just say + + + align:start position:0% +does alright beautiful so let's just say +let me just pick five of these here so + + align:start position:0% +let me just pick five of these here so + + + align:start position:0% +let me just pick five of these here so +first one is five hearts I'm sorry five + + align:start position:0% +first one is five hearts I'm sorry five + + + align:start position:0% +first one is five hearts I'm sorry five +of five of Hearts yep five hearts nine + + align:start position:0% +of five of Hearts yep five hearts nine + + + align:start position:0% +of five of Hearts yep five hearts nine +of diamonds jack of spades ten of Hearts + + align:start position:0% + + + + align:start position:0% + +and so it essentially says the first so + + align:start position:0% +and so it essentially says the first so + + + align:start position:0% +and so it essentially says the first so +if I have something like this it ended + + align:start position:0% +if I have something like this it ended + + + align:start position:0% +if I have something like this it ended +up choosing you'd end up choosing the + + align:start position:0% +up choosing you'd end up choosing the + + + align:start position:0% +up choosing you'd end up choosing the +ten as the hidden card and decided to + + align:start position:0% +ten as the hidden card and decided to + + + align:start position:0% +ten as the hidden card and decided to +choose five as the first one and then + + align:start position:0% +choose five as the first one and then + + + align:start position:0% +choose five as the first one and then +because ten was the hidden card you + + align:start position:0% +because ten was the hidden card you + + + align:start position:0% +because ten was the hidden card you +needed to encode five right and + + align:start position:0% +needed to encode five right and + + + align:start position:0% +needed to encode five right and +so so the way you encode five is is by + + align:start position:0% +so so the way you encode five is is by + + + align:start position:0% +so so the way you encode five is is by +encoding L s and M so the first card + + align:start position:0% +encoding L s and M so the first card + + + align:start position:0% +encoding L s and M so the first card +that should should be up is a jack + + align:start position:0% +that should should be up is a jack + + + align:start position:0% +that should should be up is a jack +followed by the the smallest card which + + align:start position:0% +followed by the the smallest card which + + + align:start position:0% +followed by the the smallest card which +is an 8 followed by a 9 okay that's + + align:start position:0% +is an 8 followed by a 9 okay that's + + + align:start position:0% +is an 8 followed by a 9 okay that's +essentially it so now that you've seen + + align:start position:0% +essentially it so now that you've seen + + + align:start position:0% +essentially it so now that you've seen +that let's let's take a look I'm not + + align:start position:0% +that let's let's take a look I'm not + + + align:start position:0% +that let's let's take a look I'm not +going to go through every line of code + + align:start position:0% +going to go through every line of code + + + align:start position:0% +going to go through every line of code +here I want to point out if a couple of + + align:start position:0% +here I want to point out if a couple of + + + align:start position:0% +here I want to point out if a couple of +things that that are interesting this is + + align:start position:0% +things that that are interesting this is + + + align:start position:0% +things that that are interesting this is +simply I filling in that data structures + + align:start position:0% +simply I filling in that data structures + + + align:start position:0% +simply I filling in that data structures +the only thing that's interesting here + + align:start position:0% +the only thing that's interesting here + + + align:start position:0% +the only thing that's interesting here +or the thing that's probably the most + + align:start position:0% +or the thing that's probably the most + + + align:start position:0% +or the thing that's probably the most +interesting here is what I've + + align:start position:0% +interesting here is what I've + + + align:start position:0% +interesting here is what I've +highlighted this is a way of taking an + + align:start position:0% +highlighted this is a way of taking an + + + align:start position:0% +highlighted this is a way of taking an +element in a Python list and getting the + + align:start position:0% +element in a Python list and getting the + + + align:start position:0% +element in a Python list and getting the +index for it and so that's essentially + + align:start position:0% +index for it and so that's essentially + + + align:start position:0% +index for it and so that's essentially +something that it's object-oriented + + align:start position:0% +something that it's object-oriented + + + align:start position:0% +something that it's object-oriented +programming we probably won't get into + + align:start position:0% +programming we probably won't get into + + + align:start position:0% +programming we probably won't get into +that in in this class but you'll + + align:start position:0% +that in in this class but you'll + + + align:start position:0% +that in in this class but you'll +definitely see that in Dublin EIN and + + align:start position:0% +definitely see that in Dublin EIN and + + + align:start position:0% +definitely see that in Dublin EIN and +other classes and essentially what we + + align:start position:0% +other classes and essentially what we + + + align:start position:0% +other classes and essentially what we +have here given the ordering is the the + + align:start position:0% +have here given the ordering is the the + + + align:start position:0% +have here given the ordering is the the +the suits simply correspond to whatever + + align:start position:0% +the suits simply correspond to whatever + + + align:start position:0% +the suits simply correspond to whatever +the indexes mod four because as you can + + align:start position:0% +the indexes mod four because as you can + + + align:start position:0% +the indexes mod four because as you can +see from this clip clubs are this is 0 + + align:start position:0% +see from this clip clubs are this is 0 + + + align:start position:0% +see from this clip clubs are this is 0 +the index 0 and the next the next Club + + align:start position:0% +the index 0 and the next the next Club + + + align:start position:0% +the index 0 and the next the next Club +is it is index 0 1 2 3 4 so you're going + + align:start position:0% +is it is index 0 1 2 3 4 so you're going + + + align:start position:0% +is it is index 0 1 2 3 4 so you're going +to get mod of clubs is always going to + + align:start position:0% +to get mod of clubs is always going to + + + align:start position:0% +to get mod of clubs is always going to +be mod 4 of clubs is always going to be + + align:start position:0% +be mod 4 of clubs is always going to be + + + align:start position:0% +be mod 4 of clubs is always going to be +a 0 mod 4 of diamonds is always going to + + align:start position:0% +a 0 mod 4 of diamonds is always going to + + + align:start position:0% +a 0 mod 4 of diamonds is always going to +be a 1 etc right so that's essentially + + align:start position:0% +be a 1 etc right so that's essentially + + + align:start position:0% +be a 1 etc right so that's essentially +what happens here and the first thing I + + align:start position:0% +what happens here and the first thing I + + + align:start position:0% +what happens here and the first thing I +need to do is figure out two cards that + + align:start position:0% +need to do is figure out two cards that + + + align:start position:0% +need to do is figure out two cards that +have the same suit because that's + + align:start position:0% +have the same suit because that's + + + align:start position:0% +have the same suit because that's +important because that's going to + + align:start position:0% +important because that's going to + + + align:start position:0% +important because that's going to +determine what my first card is and what + + align:start position:0% +determine what my first card is and what + + + align:start position:0% +determine what my first card is and what +my hidden cards are and that's what + + align:start position:0% +my hidden cards are and that's what + + + align:start position:0% +my hidden cards are and that's what +happens over here and then once I have + + align:start position:0% +happens over here and then once I have + + + align:start position:0% +happens over here and then once I have +that I need I've sort of split these + + align:start position:0% +that I need I've sort of split these + + + align:start position:0% +that I need I've sort of split these +five cards into two piles one of which + + align:start position:0% +five cards into two piles one of which + + + align:start position:0% +five cards into two piles one of which +has the the hidden and the first card in + + align:start position:0% +has the the hidden and the first card in + + + align:start position:0% +has the the hidden and the first card in +it and I'll the other pile has the three + + align:start position:0% +it and I'll the other pile has the three + + + align:start position:0% +it and I'll the other pile has the three +cards that correspond to the ordering in + + align:start position:0% +cards that correspond to the ordering in + + + align:start position:0% +cards that correspond to the ordering in +it obviously the computations that I + + align:start position:0% +it obviously the computations that I + + + align:start position:0% +it obviously the computations that I +have to do for the first couple are + + align:start position:0% +have to do for the first couple are + + + align:start position:0% +have to do for the first couple are +quite different from the ones for the + + align:start position:0% +quite different from the ones for the + + + align:start position:0% +quite different from the ones for the +the remaining three cards in one case + + align:start position:0% +the remaining three cards in one case + + + align:start position:0% +the remaining three cards in one case +it's ordering in the other case is the + + align:start position:0% +it's ordering in the other case is the + + + align:start position:0% +it's ordering in the other case is the +comparison and I do have two the most + + align:start position:0% +comparison and I do have two the most + + + align:start position:0% +comparison and I do have two the most +interesting remaining part of the code + + align:start position:0% +interesting remaining part of the code + + + align:start position:0% +interesting remaining part of the code +that I'm going to show you is the + + align:start position:0% +that I'm going to show you is the + + + align:start position:0% +that I'm going to show you is the +determination of what the hidden card is + + align:start position:0% +determination of what the hidden card is + + + align:start position:0% +determination of what the hidden card is +and what the first card is and that's + + align:start position:0% +and what the first card is and that's + + + align:start position:0% +and what the first card is and that's +going to require this is the part that + + align:start position:0% +going to require this is the part that + + + align:start position:0% +going to require this is the part that +actually took me the longest to code I + + align:start position:0% +actually took me the longest to code I + + + align:start position:0% +actually took me the longest to code I +got it wrong a couple of times it's + + align:start position:0% +got it wrong a couple of times it's + + + align:start position:0% +got it wrong a couple of times it's +going to require me it's five lines of + + align:start position:0% +going to require me it's five lines of + + + align:start position:0% +going to require me it's five lines of +code but it's subtle he's gonna require + + align:start position:0% +code but it's subtle he's gonna require + + + align:start position:0% +code but it's subtle he's gonna require +me to kind of figure out whether it's + + align:start position:0% +me to kind of figure out whether it's + + + align:start position:0% +me to kind of figure out whether it's +the jack where's the two you know or + + align:start position:0% +the jack where's the two you know or + + + align:start position:0% +the jack where's the two you know or +weisswurst + + align:start position:0% +weisswurst + + + align:start position:0% +weisswurst +right and and things get a little bit + + align:start position:0% +right and and things get a little bit + + + align:start position:0% +right and and things get a little bit +interesting for example if you had if it + + align:start position:0% +interesting for example if you had if it + + + align:start position:0% +interesting for example if you had if it +wasn't the jack in the two the example I + + align:start position:0% +wasn't the jack in the two the example I + + + align:start position:0% +wasn't the jack in the two the example I +had here it's illicit let's put the jack + + align:start position:0% +had here it's illicit let's put the jack + + + align:start position:0% +had here it's illicit let's put the jack +into let's say I had a three and a ten + + align:start position:0% +into let's say I had a three and a ten + + + align:start position:0% +into let's say I had a three and a ten +right um they're kind of the furthest + + align:start position:0% +right um they're kind of the furthest + + + align:start position:0% +right um they're kind of the furthest +apart and you have to be kind of super + + align:start position:0% +apart and you have to be kind of super + + + align:start position:0% +apart and you have to be kind of super +careful here because you know three to + + align:start position:0% +careful here because you know three to + + + align:start position:0% +careful here because you know three to +ten is obviously seven which is too + + align:start position:0% +ten is obviously seven which is too + + + align:start position:0% +ten is obviously seven which is too +large but you need to go ten to three + + align:start position:0% +large but you need to go ten to three + + + align:start position:0% +large but you need to go ten to three +which is six right so the things that + + align:start position:0% +which is six right so the things that + + + align:start position:0% +which is six right so the things that +are diametrically opposite to each other + + align:start position:0% +are diametrically opposite to each other + + + align:start position:0% +are diametrically opposite to each other +are usually the hardest when it comes to + + align:start position:0% +are usually the hardest when it comes to + + + align:start position:0% +are usually the hardest when it comes to +actually doing the trick but it's all + + align:start position:0% +actually doing the trick but it's all + + + align:start position:0% +actually doing the trick but it's all +there was off it was also hard from a + + align:start position:0% +there was off it was also hard from a + + + align:start position:0% +there was off it was also hard from a +standpoint of coding I had to get the + + align:start position:0% +standpoint of coding I had to get the + + + align:start position:0% +standpoint of coding I had to get the +mods right and and the subtraction the + + align:start position:0% +mods right and and the subtraction the + + + align:start position:0% +mods right and and the subtraction the +and and in in terms of what got + + align:start position:0% +and and in in terms of what got + + + align:start position:0% +and and in in terms of what got +subtracted from the other so so the rest + + align:start position:0% +subtracted from the other so so the rest + + + align:start position:0% +subtracted from the other so so the rest +of it is I just have a high level + + align:start position:0% +of it is I just have a high level + + + align:start position:0% +of it is I just have a high level +descriptions obviously the code for + + align:start position:0% +descriptions obviously the code for + + + align:start position:0% +descriptions obviously the code for +these individual subroutines is is in + + align:start position:0% +these individual subroutines is is in + + + align:start position:0% +these individual subroutines is is in +the file as well but this one determines + + align:start position:0% +the file as well but this one determines + + + align:start position:0% +the file as well but this one determines +what's hidden what the other card is and + + align:start position:0% +what's hidden what the other card is and + + + align:start position:0% +what's hidden what the other card is and +what the number that you need to encode + + align:start position:0% +what the number that you need to encode + + + align:start position:0% +what the number that you need to encode +is so when you go do the split and you + + align:start position:0% +is so when you go do the split and you + + + align:start position:0% +is so when you go do the split and you +have the two cards you obviously need to + + align:start position:0% +have the two cards you obviously need to + + + align:start position:0% +have the two cards you obviously need to +decide which one goes first which one is + + align:start position:0% +decide which one goes first which one is + + + align:start position:0% +decide which one goes first which one is +hidden and you also get the number right + + align:start position:0% +hidden and you also get the number right + + + align:start position:0% +hidden and you also get the number right +and that number had better be between + + align:start position:0% +and that number had better be between + + + align:start position:0% +and that number had better be between +one and six otherwise this is not going + + align:start position:0% +one and six otherwise this is not going + + + align:start position:0% +one and six otherwise this is not going +to work and then you remove the other + + align:start position:0% +to work and then you remove the other + + + align:start position:0% +to work and then you remove the other +the two cards hidden and other from from + + align:start position:0% +the two cards hidden and other from from + + + align:start position:0% +the two cards hidden and other from from +the set of five cards in order to + + align:start position:0% +the set of five cards in order to + + + align:start position:0% +the set of five cards in order to +actually do this SML it was a little + + align:start position:0% +actually do this SML it was a little + + + align:start position:0% +actually do this SML it was a little +easier for me to sort these cards and + + align:start position:0% +easier for me to sort these cards and + + + align:start position:0% +easier for me to sort these cards and +then depending on the number and code I + + align:start position:0% +then depending on the number and code I + + + align:start position:0% +then depending on the number and code I +changed the order obviously if I sort + + align:start position:0% +changed the order obviously if I sort + + + align:start position:0% +changed the order obviously if I sort +the cards I'm going to get SML and that + + align:start position:0% +the cards I'm going to get SML and that + + + align:start position:0% +the cards I'm going to get SML and that +may not be what I want but it's it's + + align:start position:0% +may not be what I want but it's it's + + + align:start position:0% +may not be what I want but it's it's +easier to start with SML saying this is + + align:start position:0% +easier to start with SML saying this is + + + align:start position:0% +easier to start with SML saying this is +the order that gave me the number one as + + align:start position:0% +the order that gave me the number one as + + + align:start position:0% +the order that gave me the number one as +an encoding what do I need to do in + + align:start position:0% +an encoding what do I need to do in + + + align:start position:0% +an encoding what do I need to do in +order to change that encoding to a 2 or + + align:start position:0% +order to change that encoding to a 2 or + + + align:start position:0% +order to change that encoding to a 2 or +a 5 or a 6 or what-have-you + + align:start position:0% +a 5 or a 6 or what-have-you + + + align:start position:0% +a 5 or a 6 or what-have-you +okay and so that's what this this output + + align:start position:0% +okay and so that's what this this output + + + align:start position:0% +okay and so that's what this this output +next three cards does so said this this + + align:start position:0% +next three cards does so said this this + + + align:start position:0% +next three cards does so said this this +is what took me the longest to code + + align:start position:0% +is what took me the longest to code + + + align:start position:0% +is what took me the longest to code +right I mean it was a few minutes but + + align:start position:0% +right I mean it was a few minutes but + + + align:start position:0% +right I mean it was a few minutes but +the rest of it was was pretty much busy + + align:start position:0% +the rest of it was was pretty much busy + + + align:start position:0% +the rest of it was was pretty much busy +work it wasn't too much thinking so this + + align:start position:0% +work it wasn't too much thinking so this + + + align:start position:0% +work it wasn't too much thinking so this +thing here as you can see that encode is + + align:start position:0% +thing here as you can see that encode is + + + align:start position:0% +thing here as you can see that encode is +don't you need only to worry too much + + align:start position:0% +don't you need only to worry too much + + + align:start position:0% +don't you need only to worry too much +about the list itself and the indexing + + align:start position:0% +about the list itself and the indexing + + + align:start position:0% +about the list itself and the indexing +into it the bottom line is I need to + + align:start position:0% +into it the bottom line is I need to + + + align:start position:0% +into it the bottom line is I need to +figure out this situation and I need to + + align:start position:0% +figure out this situation and I need to + + + align:start position:0% +figure out this situation and I need to +subtract and so when I when I see + + align:start position:0% +subtract and so when I when I see + + + align:start position:0% +subtract and so when I when I see +something that says ten and a three I + + align:start position:0% +something that says ten and a three I + + + align:start position:0% +something that says ten and a three I +end up getting a seven and then I know + + align:start position:0% +end up getting a seven and then I know + + + align:start position:0% +end up getting a seven and then I know +that I have to do a flip okay but it + + align:start position:0% +that I have to do a flip okay but it + + + align:start position:0% +that I have to do a flip okay but it +also may be the case that I might get + + align:start position:0% +also may be the case that I might get + + + align:start position:0% +also may be the case that I might get +something that I the reason I need the + + align:start position:0% +something that I the reason I need the + + + align:start position:0% +something that I the reason I need the +the the Mod 13 is partly because I might + + align:start position:0% +the the Mod 13 is partly because I might + + + align:start position:0% +the the Mod 13 is partly because I might +end up getting a negative number right + + align:start position:0% +end up getting a negative number right + + + align:start position:0% +end up getting a negative number right +so it's not clear that encode take away + + align:start position:0% +so it's not clear that encode take away + + + align:start position:0% +so it's not clear that encode take away +the Mod 13 is going to give me a + + align:start position:0% +the Mod 13 is going to give me a + + + align:start position:0% +the Mod 13 is going to give me a +positive number right you know I might + + align:start position:0% +positive number right you know I might + + + align:start position:0% +positive number right you know I might +be subtracting 9 from two right so I end + + align:start position:0% +be subtracting 9 from two right so I end + + + align:start position:0% +be subtracting 9 from two right so I end +up getting a minus seven right so so you + + align:start position:0% +up getting a minus seven right so so you + + + align:start position:0% +up getting a minus seven right so so you +don't know this I mean the program + + align:start position:0% +don't know this I mean the program + + + align:start position:0% +don't know this I mean the program +doesn't know which one is which and it + + align:start position:0% +doesn't know which one is which and it + + + align:start position:0% +doesn't know which one is which and it +has to figure out which one is which and + + align:start position:0% +has to figure out which one is which and + + + align:start position:0% +has to figure out which one is which and +flip them together so I if there's any + + align:start position:0% +flip them together so I if there's any + + + align:start position:0% +flip them together so I if there's any +code that you want to look at carefully + + align:start position:0% +code that you want to look at carefully + + + align:start position:0% +code that you want to look at carefully +it's it's this is this code and it's + + align:start position:0% +it's it's this is this code and it's + + + align:start position:0% +it's it's this is this code and it's +just a matter of sort of going through + + align:start position:0% +just a matter of sort of going through + + + align:start position:0% +just a matter of sort of going through +the combinations and making sure I know + + align:start position:0% +the combinations and making sure I know + + + align:start position:0% +the combinations and making sure I know +it works but you need to convince + + align:start position:0% +it works but you need to convince + + + align:start position:0% +it works but you need to convince +yourself it works all right so that's + + align:start position:0% +yourself it works all right so that's + + + align:start position:0% +yourself it works all right so that's +pretty much it it's there's not much + + align:start position:0% +pretty much it it's there's not much + + + align:start position:0% +pretty much it it's there's not much +more to say here that wouldn't be kind + + align:start position:0% +more to say here that wouldn't be kind + + + align:start position:0% +more to say here that wouldn't be kind +of obvious to you looking at it + + align:start position:0% +of obvious to you looking at it + + + align:start position:0% +of obvious to you looking at it +carefully so I don't want to belabor the + + align:start position:0% +carefully so I don't want to belabor the + + + align:start position:0% +carefully so I don't want to belabor the +obvious and I'll put next three cards is + + align:start position:0% +obvious and I'll put next three cards is + + + align:start position:0% +obvious and I'll put next three cards is +the part that I just described you start + + align:start position:0% +the part that I just described you start + + + align:start position:0% +the part that I just described you start +with sort of the default ordering which + + align:start position:0% +with sort of the default ordering which + + + align:start position:0% +with sort of the default ordering which +encodes a 1 and then you need to do a + + align:start position:0% +encodes a 1 and then you need to do a + + + align:start position:0% +encodes a 1 and then you need to do a +little bit of flipping if you want to + + align:start position:0% +little bit of flipping if you want to + + + align:start position:0% +little bit of flipping if you want to +encode a at 3 for example and if you + + align:start position:0% +encode a at 3 for example and if you + + + align:start position:0% +encode a at 3 for example and if you +want to encode a 3 then you change + + align:start position:0% +want to encode a 3 then you change + + + align:start position:0% +want to encode a 3 then you change +things around + + align:start position:0% +things around + + + align:start position:0% +things around +and this is exactly what I described to + + align:start position:0% +and this is exactly what I described to + + + align:start position:0% +and this is exactly what I described to +you before right so this is actually + + align:start position:0% +you before right so this is actually + + + align:start position:0% +you before right so this is actually +fairly straightforward if you have that + + align:start position:0% +fairly straightforward if you have that + + + align:start position:0% +fairly straightforward if you have that +table written in front of you you just + + align:start position:0% +table written in front of you you just + + + align:start position:0% +table written in front of you you just +go off and write that okay + + align:start position:0% +go off and write that okay + + + align:start position:0% +go off and write that okay +certainly if you change the algorithm + + align:start position:0% +certainly if you change the algorithm + + + align:start position:0% +certainly if you change the algorithm +you know all of this would change quite + + align:start position:0% +you know all of this would change quite + + + align:start position:0% +you know all of this would change quite +dramatically and that this there's an + + align:start position:0% +dramatically and that this there's an + + + align:start position:0% +dramatically and that this there's an +exercise which asks you to do that which + + align:start position:0% +exercise which asks you to do that which + + + align:start position:0% +exercise which asks you to do that which +you could certainly try to do I want to + + align:start position:0% +you could certainly try to do I want to + + + align:start position:0% +you could certainly try to do I want to +show you one other thing which is which + + align:start position:0% +show you one other thing which is which + + + align:start position:0% +show you one other thing which is which +is interesting and and then I want to + + align:start position:0% +is interesting and and then I want to + + + align:start position:0% +is interesting and and then I want to +run this new subroutine so what I have + + align:start position:0% +run this new subroutine so what I have + + + align:start position:0% +run this new subroutine so what I have +here is I'm gonna run I've already run + + align:start position:0% +here is I'm gonna run I've already run + + + align:start position:0% +here is I'm gonna run I've already run +it so I want to show you + + align:start position:0% +it so I want to show you + + + align:start position:0% +it so I want to show you +computer assistant which was very useful + + align:start position:0% +computer assistant which was very useful + + + align:start position:0% +computer assistant which was very useful +to me um and this says please give me a + + align:start position:0% +to me um and this says please give me a + + + align:start position:0% +to me um and this says please give me a +random number of at least six digits + + align:start position:0% +random number of at least six digits + + + align:start position:0% +random number of at least six digits +right so obviously I don't want to know + + align:start position:0% +right so obviously I don't want to know + + + align:start position:0% +right so obviously I don't want to know +what the hidden card is if I want to + + align:start position:0% +what the hidden card is if I want to + + + align:start position:0% +what the hidden card is if I want to +practice in a legitimate way right so um + + align:start position:0% +practice in a legitimate way right so um + + + align:start position:0% +practice in a legitimate way right so um +so what I did was I said I'm gonna have + + align:start position:0% +so what I did was I said I'm gonna have + + + align:start position:0% +so what I did was I said I'm gonna have +this sort of hokey I'm just really hokey + + align:start position:0% +this sort of hokey I'm just really hokey + + + align:start position:0% +this sort of hokey I'm just really hokey +I'm gonna have this hokey algorithm + + align:start position:0% +I'm gonna have this hokey algorithm + + + align:start position:0% +I'm gonna have this hokey algorithm +that's gonna take this giant number that + + align:start position:0% +that's gonna take this giant number that + + + align:start position:0% +that's gonna take this giant number that +I'm gonna type in and somehow I'm going + + align:start position:0% +I'm gonna type in and somehow I'm going + + + align:start position:0% +I'm gonna type in and somehow I'm going +to take this giant number and it it's + + align:start position:0% +to take this giant number and it it's + + + align:start position:0% +to take this giant number and it it's +going to deterministically generate five + + align:start position:0% +going to deterministically generate five + + + align:start position:0% +going to deterministically generate five +cards based on this giant number okay + + align:start position:0% +cards based on this giant number okay + + + align:start position:0% +cards based on this giant number okay +but I didn't want to have an obvious way + + align:start position:0% +but I didn't want to have an obvious way + + + align:start position:0% +but I didn't want to have an obvious way +I mean I don't want to say I'm the + + align:start position:0% +I mean I don't want to say I'm the + + + align:start position:0% +I mean I don't want to say I'm the +number one two three four five and then + + align:start position:0% +number one two three four five and then + + + align:start position:0% +number one two three four five and then +end up getting the first five cards in + + align:start position:0% +end up getting the first five cards in + + + align:start position:0% +end up getting the first five cards in +the deck or something like that because + + align:start position:0% +the deck or something like that because + + + align:start position:0% +the deck or something like that because +that was sort of give it away right so I + + align:start position:0% +that was sort of give it away right so I + + + align:start position:0% +that was sort of give it away right so I +want to have some sort of some sort of + + align:start position:0% +want to have some sort of some sort of + + + align:start position:0% +want to have some sort of some sort of +obfuscated way of taking a giant number + + align:start position:0% +obfuscated way of taking a giant number + + + align:start position:0% +obfuscated way of taking a giant number +and generating something that was at + + align:start position:0% +and generating something that was at + + + align:start position:0% +and generating something that was at +least unpredictable to me in terms of + + align:start position:0% +least unpredictable to me in terms of + + + align:start position:0% +least unpredictable to me in terms of +the five cards that are generated okay + + align:start position:0% +the five cards that are generated okay + + + align:start position:0% +the five cards that are generated okay +and so what I do is if I type in if I + + align:start position:0% +and so what I do is if I type in if I + + + align:start position:0% +and so what I do is if I type in if I +type in a number you know some some + + align:start position:0% +type in a number you know some some + + + align:start position:0% +type in a number you know some some +random number and at this point I have + + align:start position:0% +random number and at this point I have + + + align:start position:0% +random number and at this point I have +no idea what the what the five cards are + + align:start position:0% +no idea what the what the five cards are + + + align:start position:0% +no idea what the what the five cards are +going to be generated are okay and this + + align:start position:0% +going to be generated are okay and this + + + align:start position:0% +going to be generated are okay and this +just tell me it does do the assistant + + align:start position:0% +just tell me it does do the assistant + + + align:start position:0% +just tell me it does do the assistant +order its cards functionality so it does + + align:start position:0% +order its cards functionality so it does + + + align:start position:0% +order its cards functionality so it does +take those five cards hides a car right + + align:start position:0% +take those five cards hides a car right + + + align:start position:0% +take those five cards hides a car right +and then exposes the four cards to me + + align:start position:0% +and then exposes the four cards to me + + + align:start position:0% +and then exposes the four cards to me +right and so I'd get different depending + + align:start position:0% +right and so I'd get different depending + + + align:start position:0% +right and so I'd get different depending +on what numbers I types of + + align:start position:0% +on what numbers I types of + + + align:start position:0% +on what numbers I types of +the way I practiced is I just sort of + + align:start position:0% +the way I practiced is I just sort of + + + align:start position:0% +the way I practiced is I just sort of +you know close my eyes and just type + + align:start position:0% +you know close my eyes and just type + + + align:start position:0% +you know close my eyes and just type +some random number and then it would + + align:start position:0% +some random number and then it would + + + align:start position:0% +some random number and then it would +produce four cards for me and notice + + align:start position:0% +produce four cards for me and notice + + + align:start position:0% +produce four cards for me and notice +that this is wonderful + + align:start position:0% +that this is wonderful + + + align:start position:0% +that this is wonderful +notice that there's a buck right this is + + align:start position:0% +notice that there's a buck right this is + + + align:start position:0% +notice that there's a buck right this is +exactly why I put this up and wow what + + align:start position:0% +exactly why I put this up and wow what + + + align:start position:0% +exactly why I put this up and wow what +luck right so so notice that this this + + align:start position:0% +luck right so so notice that this this + + + align:start position:0% +luck right so so notice that this this +didn't work right you know and that's + + align:start position:0% +didn't work right you know and that's + + + align:start position:0% +didn't work right you know and that's +the fix that's the next exercise I'm not + + align:start position:0% +the fix that's the next exercise I'm not + + + align:start position:0% +the fix that's the next exercise I'm not +I can't do not it's an exercise in that + + align:start position:0% +I can't do not it's an exercise in that + + + align:start position:0% +I can't do not it's an exercise in that +that's going to be up there which is you + + align:start position:0% +that's going to be up there which is you + + + align:start position:0% +that's going to be up there which is you +know fix my hokey algorithm so it + + align:start position:0% +know fix my hokey algorithm so it + + + align:start position:0% +know fix my hokey algorithm so it +doesn't do this okay and so what + + align:start position:0% +doesn't do this okay and so what + + + align:start position:0% +doesn't do this okay and so what +happened here was I had a deterministic + + align:start position:0% +happened here was I had a deterministic + + + align:start position:0% +happened here was I had a deterministic +way this wasn't a random number + + align:start position:0% +way this wasn't a random number + + + align:start position:0% +way this wasn't a random number +generator that the good way of doing + + align:start position:0% +generator that the good way of doing + + + align:start position:0% +generator that the good way of doing +this would have been to use pythons + + align:start position:0% +this would have been to use pythons + + + align:start position:0% +this would have been to use pythons +random random number generator facility + + align:start position:0% +random random number generator facility + + + align:start position:0% +random random number generator facility +and not have me do anything not because + + align:start position:0% +and not have me do anything not because + + + align:start position:0% +and not have me do anything not because +obviously I typed something that turned + + align:start position:0% +obviously I typed something that turned + + + align:start position:0% +obviously I typed something that turned +into into that which is a deck that has + + align:start position:0% +into into that which is a deck that has + + + align:start position:0% +into into that which is a deck that has +you know - King of Hearts in it and so + + align:start position:0% +you know - King of Hearts in it and so + + + align:start position:0% +you know - King of Hearts in it and so +so my deterministic way which was a + + align:start position:0% +so my deterministic way which was a + + + align:start position:0% +so my deterministic way which was a +convenient way because only four lines + + align:start position:0% +convenient way because only four lines + + + align:start position:0% +convenient way because only four lines +of code didn't need me to to include the + + align:start position:0% +of code didn't need me to to include the + + + align:start position:0% +of code didn't need me to to include the +Python random Lib library etc causes + + align:start position:0% +Python random Lib library etc causes + + + align:start position:0% +Python random Lib library etc causes +trouble right so this obviously won't + + align:start position:0% +trouble right so this obviously won't + + + align:start position:0% +trouble right so this obviously won't +work right so I'll just type something + + align:start position:0% +work right so I'll just type something + + + align:start position:0% +work right so I'll just type something +and it's gonna say sorry not impressed + + align:start position:0% +and it's gonna say sorry not impressed + + + align:start position:0% +and it's gonna say sorry not impressed +okay I'm not impressed with my guests + + align:start position:0% +okay I'm not impressed with my guests + + + align:start position:0% +okay I'm not impressed with my guests +and not impressed with my code okay so + + align:start position:0% +and not impressed with my code okay so + + + align:start position:0% +and not impressed with my code okay so +let me do this again and so let me just + + align:start position:0% +let me do this again and so let me just + + + align:start position:0% +let me do this again and so let me just +do that and now what + + align:start position:0% + + + + align:start position:0% + +is this this is ridiculous I mean does + + align:start position:0% +is this this is ridiculous I mean does + + + align:start position:0% +is this this is ridiculous I mean does +my code even work I'm gonna blame it on + + align:start position:0% +my code even work I'm gonna blame it on + + + align:start position:0% +my code even work I'm gonna blame it on +my computer I told you my my laptop was + + align:start position:0% +my computer I told you my my laptop was + + + align:start position:0% +my computer I told you my my laptop was +acting up okay okay one one one two two + + align:start position:0% +acting up okay okay one one one two two + + + align:start position:0% +acting up okay okay one one one two two +two oh thank you all right so so now I I + + align:start position:0% +two oh thank you all right so so now I I + + + align:start position:0% +two oh thank you all right so so now I I +see this and I say seven of seven of + + align:start position:0% +see this and I say seven of seven of + + + align:start position:0% +see this and I say seven of seven of +clubs so that's the first card so + + align:start position:0% +clubs so that's the first card so + + + align:start position:0% +clubs so that's the first card so +clearly it's the clubs and then ten King + + align:start position:0% +clearly it's the clubs and then ten King + + + align:start position:0% +clearly it's the clubs and then ten King +and six right so 10 is the medium so I + + align:start position:0% +and six right so 10 is the medium so I + + + align:start position:0% +and six right so 10 is the medium so I +got medium/large MLS right so MLS is MLS + + align:start position:0% +got medium/large MLS right so MLS is MLS + + + align:start position:0% +got medium/large MLS right so MLS is MLS +would be four right so so four would + + align:start position:0% +would be four right so so four would + + + align:start position:0% +would be four right so so four would +give me the Jack of Clubs right there + + align:start position:0% +give me the Jack of Clubs right there + + + align:start position:0% +give me the Jack of Clubs right there +you go + + align:start position:0% +you go + + + align:start position:0% +you go +right so so this worked okay but I'd not + + align:start position:0% +right so so this worked okay but I'd not + + + align:start position:0% +right so so this worked okay but I'd not +want to show you the last thing I'll do + + align:start position:0% +want to show you the last thing I'll do + + + align:start position:0% +want to show you the last thing I'll do +is show you this code and you guys + + align:start position:0% +is show you this code and you guys + + + align:start position:0% +is show you this code and you guys +should absolutely fix this code it is + + align:start position:0% +should absolutely fix this code it is + + + align:start position:0% +should absolutely fix this code it is +clear what your exercises or you could + + align:start position:0% +clear what your exercises or you could + + + align:start position:0% +clear what your exercises or you could +be I do want to talk about doing this + + align:start position:0% +be I do want to talk about doing this + + + align:start position:0% +be I do want to talk about doing this +with four cards so so notice that this + + align:start position:0% +with four cards so so notice that this + + + align:start position:0% +with four cards so so notice that this +this is the offending line of code okay + + align:start position:0% +this is the offending line of code okay + + + align:start position:0% +this is the offending line of code okay +so what I did was I wanted to generate + + align:start position:0% +so what I did was I wanted to generate + + + align:start position:0% +so what I did was I wanted to generate +five kind of random looking numbers out + + align:start position:0% +five kind of random looking numbers out + + + align:start position:0% +five kind of random looking numbers out +of this giant number that I typed in + + align:start position:0% +of this giant number that I typed in + + + align:start position:0% +of this giant number that I typed in +right and and I got lazy and I was tired + + align:start position:0% +right and and I got lazy and I was tired + + + align:start position:0% +right and and I got lazy and I was tired +of this puzzle by the time I ended up + + align:start position:0% +of this puzzle by the time I ended up + + + align:start position:0% +of this puzzle by the time I ended up +coding it so I just said you know I want + + align:start position:0% +coding it so I just said you know I want + + + align:start position:0% +coding it so I just said you know I want +I don't want to include random dot Lib + + align:start position:0% +I don't want to include random dot Lib + + + align:start position:0% +I don't want to include random dot Lib +from Python I'm just going to take this + + align:start position:0% +from Python I'm just going to take this + + + align:start position:0% +from Python I'm just going to take this +and I'm going to do some sort of + + align:start position:0% +and I'm going to do some sort of + + + align:start position:0% +and I'm going to do some sort of +iterative computation where I'm + + align:start position:0% +iterative computation where I'm + + + align:start position:0% +iterative computation where I'm +generating what I think are our random + + align:start position:0% +generating what I think are our random + + + align:start position:0% +generating what I think are our random +numbers between 1 and 52 from this giant + + align:start position:0% +numbers between 1 and 52 from this giant + + + align:start position:0% +numbers between 1 and 52 from this giant +number that I typed in I'm going to do + + align:start position:0% +number that I typed in I'm going to do + + + align:start position:0% +number that I typed in I'm going to do +this 5 times and what happened as you + + align:start position:0% +this 5 times and what happened as you + + + align:start position:0% +this 5 times and what happened as you +saw is that I generated the same number + + align:start position:0% +saw is that I generated the same number + + + align:start position:0% +saw is that I generated the same number +twice a couple of times right and that's + + align:start position:0% +twice a couple of times right and that's + + + align:start position:0% +twice a couple of times right and that's +why obviously the trick doesn't work in + + align:start position:0% +why obviously the trick doesn't work in + + + align:start position:0% +why obviously the trick doesn't work in +that case right what was interesting was + + align:start position:0% +that case right what was interesting was + + + align:start position:0% +that case right what was interesting was +the way I found this bug was not the + + align:start position:0% +the way I found this bug was not the + + + align:start position:0% +the way I found this bug was not the +obvious way that we just saw here was it + + align:start position:0% +obvious way that we just saw here was it + + + align:start position:0% +obvious way that we just saw here was it +was actually something where it the the + + align:start position:0% +was actually something where it the the + + + align:start position:0% +was actually something where it the the +hidden card was the same as one of the + + align:start position:0% +hidden card was the same as one of the + + + align:start position:0% +hidden card was the same as one of the +four carbs okay that was exposed so I + + align:start position:0% +four carbs okay that was exposed so I + + + align:start position:0% +four carbs okay that was exposed so I +didn't know that right so I'm like what + + align:start position:0% +didn't know that right so I'm like what + + + align:start position:0% +didn't know that right so I'm like what +you know + + align:start position:0% +you know + + + align:start position:0% +you know +not getting this right right it kept + + align:start position:0% +not getting this right right it kept + + + align:start position:0% +not getting this right right it kept +saying sorry not impressed right and + + align:start position:0% +saying sorry not impressed right and + + + align:start position:0% +saying sorry not impressed right and +what it meant was it wasn't impressed + + align:start position:0% +what it meant was it wasn't impressed + + + align:start position:0% +what it meant was it wasn't impressed +with my coding not with my deductive + + align:start position:0% +with my coding not with my deductive + + + align:start position:0% +with my coding not with my deductive +skills okay so it took me a while to + + align:start position:0% +skills okay so it took me a while to + + + align:start position:0% +skills okay so it took me a while to +figure this out + + align:start position:0% +figure this out + + + align:start position:0% +figure this out +all right and you can fix it okay so so + + align:start position:0% +all right and you can fix it okay so so + + + align:start position:0% +all right and you can fix it okay so so +that's it any any questions about the + + align:start position:0% +that's it any any questions about the + + + align:start position:0% +that's it any any questions about the +what we've talked about the puzzle or + + align:start position:0% +what we've talked about the puzzle or + + + align:start position:0% +what we've talked about the puzzle or +the code right okay so in the five + + align:start position:0% +the code right okay so in the five + + + align:start position:0% +the code right okay so in the five +minutes that we have left let's talk + + align:start position:0% +minutes that we have left let's talk + + + align:start position:0% +minutes that we have left let's talk +about whether they would be a trick + + align:start position:0% +about whether they would be a trick + + + align:start position:0% +about whether they would be a trick +which would be perhaps even more + + align:start position:0% +which would be perhaps even more + + + align:start position:0% +which would be perhaps even more +impressive where we would only use four + + align:start position:0% +impressive where we would only use four + + + align:start position:0% +impressive where we would only use four +cards right so it'd only be four cards I + + align:start position:0% +cards right so it'd only be four cards I + + + align:start position:0% +cards right so it'd only be four cards I +that the audience selects and we would + + align:start position:0% +that the audience selects and we would + + + align:start position:0% +that the audience selects and we would +Billy I guess would show me three cards + + align:start position:0% +Billy I guess would show me three cards + + + align:start position:0% +Billy I guess would show me three cards +and I'd have to guess the fourth okay I + + align:start position:0% +and I'd have to guess the fourth okay I + + + align:start position:0% +and I'd have to guess the fourth okay I +would that would that be possible + + align:start position:0% +would that would that be possible + + + align:start position:0% +would that would that be possible +I mean the numbers really you know don't + + align:start position:0% +I mean the numbers really you know don't + + + align:start position:0% +I mean the numbers really you know don't +work right because that that fourth card + + align:start position:0% +work right because that that fourth card + + + align:start position:0% +work right because that that fourth card +I could be one out of I guess if you + + align:start position:0% +I could be one out of I guess if you + + + align:start position:0% +I could be one out of I guess if you +show three cards one or 49 different + + align:start position:0% +show three cards one or 49 different + + + align:start position:0% +show three cards one or 49 different +possibilities and it would be it would + + align:start position:0% +possibilities and it would be it would + + + align:start position:0% +possibilities and it would be it would +be pretty difficult right I'm you could + + align:start position:0% +be pretty difficult right I'm you could + + + align:start position:0% +be pretty difficult right I'm you could +you know think about something where the + + align:start position:0% +you know think about something where the + + + align:start position:0% +you know think about something where the +only way I could come up with + + align:start position:0% +only way I could come up with + + + align:start position:0% +only way I could come up with +it was required much more encoding but I + + align:start position:0% +it was required much more encoding but I + + + align:start position:0% +it was required much more encoding but I +was thinking about something like this + + align:start position:0% +was thinking about something like this + + + align:start position:0% +was thinking about something like this +right where let's say I have these four + + align:start position:0% +right where let's say I have these four + + + align:start position:0% +right where let's say I have these four +cards right and let's even take let's + + align:start position:0% +cards right and let's even take let's + + + align:start position:0% +cards right and let's even take let's +let's say that they're all of different + + align:start position:0% +let's say that they're all of different + + + align:start position:0% +let's say that they're all of different +suits right because that's possible what + + align:start position:0% +suits right because that's possible what + + + align:start position:0% +suits right because that's possible what +the other thing that happens when you + + align:start position:0% +the other thing that happens when you + + + align:start position:0% +the other thing that happens when you +have when you only have four cards is + + align:start position:0% +have when you only have four cards is + + + align:start position:0% +have when you only have four cards is +they're all four could be of different + + align:start position:0% +they're all four could be of different + + + align:start position:0% +they're all four could be of different +suits right that's certainly possible I + + align:start position:0% +suits right that's certainly possible I + + + align:start position:0% +suits right that's certainly possible I +keep + + align:start position:0% + + + + align:start position:0% + +whatever I want I want to heart okay + + align:start position:0% +whatever I want I want to heart okay + + + align:start position:0% +whatever I want I want to heart okay +good so I have something like this and + + align:start position:0% +good so I have something like this and + + + align:start position:0% +good so I have something like this and +now I'm in real trouble + + align:start position:0% +now I'm in real trouble + + + align:start position:0% +now I'm in real trouble +right I mean clearly anything that we + + align:start position:0% +right I mean clearly anything that we + + + align:start position:0% +right I mean clearly anything that we +talked about isn't going to work right + + align:start position:0% +talked about isn't going to work right + + + align:start position:0% +talked about isn't going to work right +so let's just say that I that I end up + + align:start position:0% +so let's just say that I that I end up + + + align:start position:0% +so let's just say that I that I end up +choosing one of these cards you know to + + align:start position:0% +choosing one of these cards you know to + + + align:start position:0% +choosing one of these cards you know to +hide right so there's this ace is hidden + + align:start position:0% +hide right so there's this ace is hidden + + + align:start position:0% +hide right so there's this ace is hidden +okay because it's not quite clear what + + align:start position:0% +okay because it's not quite clear what + + + align:start position:0% +okay because it's not quite clear what +I'm what I can do here but bear with me + + align:start position:0% +I'm what I can do here but bear with me + + + align:start position:0% +I'm what I can do here but bear with me +for just a minute so for argument's sake + + align:start position:0% +for just a minute so for argument's sake + + + align:start position:0% +for just a minute so for argument's sake +let's say that that now at this point + + align:start position:0% +let's say that that now at this point + + + align:start position:0% +let's say that that now at this point +I'm trying to get more information out + + align:start position:0% +I'm trying to get more information out + + + align:start position:0% +I'm trying to get more information out +of this the ordering isn't going to help + + align:start position:0% +of this the ordering isn't going to help + + + align:start position:0% +of this the ordering isn't going to help +me I mean the ordering is in is going to + + align:start position:0% +me I mean the ordering is in is going to + + + align:start position:0% +me I mean the ordering is in is going to +help me a little bit but what am I gonna + + align:start position:0% +help me a little bit but what am I gonna + + + align:start position:0% +help me a little bit but what am I gonna +get like six you know one through six + + align:start position:0% +get like six you know one through six + + + align:start position:0% +get like six you know one through six +from this so I could say the first card + + align:start position:0% +from this so I could say the first card + + + align:start position:0% +from this so I could say the first card +is is an anchor okay and so I'm gonna + + align:start position:0% +is is an anchor okay and so I'm gonna + + + align:start position:0% +is is an anchor okay and so I'm gonna +expose this so the only thing I could + + align:start position:0% +expose this so the only thing I could + + + align:start position:0% +expose this so the only thing I could +think of was you could sort of do this + + align:start position:0% +think of was you could sort of do this + + + align:start position:0% +think of was you could sort of do this +is a little bit obvious and maybe giving + + align:start position:0% +is a little bit obvious and maybe giving + + + align:start position:0% +is a little bit obvious and maybe giving +things away but depending on where you + + align:start position:0% +things away but depending on where you + + + align:start position:0% +things away but depending on where you +have the hidden card and you can get + + align:start position:0% +have the hidden card and you can get + + + align:start position:0% +have the hidden card and you can get +more information based on the order in + + align:start position:0% +more information based on the order in + + + align:start position:0% +more information based on the order in +which you put these cards out and + + align:start position:0% +which you put these cards out and + + + align:start position:0% +which you put these cards out and +whether they're to the left or the right + + align:start position:0% +whether they're to the left or the right + + + align:start position:0% +whether they're to the left or the right +of this of this hidden card okay so you + + align:start position:0% +of this of this hidden card okay so you + + + align:start position:0% +of this of this hidden card okay so you +need to do something like that I mean I + + align:start position:0% +need to do something like that I mean I + + + align:start position:0% +need to do something like that I mean I +haven't figured this out at least I + + align:start position:0% +haven't figured this out at least I + + + align:start position:0% +haven't figured this out at least I +can't think of think of a a complete + + align:start position:0% +can't think of think of a a complete + + + align:start position:0% +can't think of think of a a complete +solution to this puzzle but I do feel + + align:start position:0% +solution to this puzzle but I do feel + + + align:start position:0% +solution to this puzzle but I do feel +like that you can get some information + + align:start position:0% +like that you can get some information + + + align:start position:0% +like that you can get some information +additional information based on whether + + align:start position:0% +additional information based on whether + + + align:start position:0% +additional information based on whether +you put things to the left or the right + + align:start position:0% +you put things to the left or the right + + + align:start position:0% +you put things to the left or the right +and that's clearly a bit of information + + align:start position:0% +and that's clearly a bit of information + + + align:start position:0% +and that's clearly a bit of information +that you get and maybe you could add to + + align:start position:0% +that you get and maybe you could add to + + + align:start position:0% +that you get and maybe you could add to +that and you know think about it right + + align:start position:0% +that and you know think about it right + + + align:start position:0% +that and you know think about it right +it's I think it makes for an interesting + + align:start position:0% +it's I think it makes for an interesting + + + align:start position:0% +it's I think it makes for an interesting +exercise and obviously there's other + + align:start position:0% +exercise and obviously there's other + + + align:start position:0% +exercise and obviously there's other +ways of doing the five card trick as + + align:start position:0% +ways of doing the five card trick as + + + align:start position:0% +ways of doing the five card trick as +well all right cool all right that's all + + align:start position:0% +well all right cool all right that's all + + + align:start position:0% +well all right cool all right that's all +I had for today if there are no + + align:start position:0% +I had for today if there are no + + + align:start position:0% +I had for today if there are no +questions we can close this pretty first + + align:start position:0% +questions we can close this pretty first + + + align:start position:0% +questions we can close this pretty first +session \ No newline at end of file diff --git a/zOZw3zCLzyE.txt b/zOZw3zCLzyE.txt new file mode 100644 index 0000000000000000000000000000000000000000..335685b1c4e6c3e7e11b3b322efcf13937feca9f --- /dev/null +++ b/zOZw3zCLzyE.txt @@ -0,0 +1,2857 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK, so let me go +back to what we were doing. + +The plan for today +is as follows. + +We're going to look at +this unitary time evolution + +and calculate this operator +u, given the Hamiltonian. + +That will be the first +order of business today. + +Then we will look +at the Heisenberg + +picture of quantum mechanics. + +And the Heisenberg picture +of quantum mechanics + +is one where the operators, +the Schrodinger operators, + +acquire time dependence. + +And it's a pretty useful way of +seeing things, a pretty useful + +way of calculating +things as well, + +and makes the relation between +classical mechanics and quantum + +mechanics more obvious. + +So it's a very important tool. + +So we'll discuss that. + +We'll find the Heisenberg +equations of motion + +and solve them for a +particular case today. + +All this material is not so +to be covered in the test. + +The only part-- of course, +the first few things + +I will say today about solving +for the unitary operator + +you've done in other ways, and +I will do it again this time. + +So going back to what we +were saying last time, + +we postulated unitary +time evolution. + +We said that psi at t was given +by some operator U of t t0 psi + +t0. + +And then we found +that this equation + +implied the Schrodinger +equation with a Hamiltonian + +given by the +following expression. + +ih dU dt of t t0 +u dagger of t t0. + +So that was our derivation +of the Schrodinger equation. + +We start with the +time evolution. + +We found that, whenever we +declare that states evolve + +in time in that way, they +satisfy a first order time + +differential equation +of the Schrodinger form + +in which the Hamiltonian +is given in terms of U + +by this equation. + +And we talked about +this operator. + +First we showed that it +doesn't depend really on t0. + +Then we showed that +it's Hermitian. + +It has units of energy. + +And as you may have seen +already in the notes, + +there is a very +clear correspondence + +between this +operator and the way + +the dynamics follows with +the ideas of Poisson brackets + +that are the precursors +of commutators + +from classical mechanics. + +So that's in the notes. + +I will not go in detail in this. + +Many of you may have not +heard of Poisson brackets. + +It's an interesting +thing, and really that + +will be good enough. + +So our goal today +is to find U given + +H, because as we mentioned +last time, for physics + +it is typically more +easy to invent a quantum + +system by postulating +a Hamiltonian + +and then solving it than +postulating a time evolution + +operator. + +So our goal in general is to +find U of t t0 given H of t. + +That's what we're +supposed to do. + +So the first thing +I'm going to do + +is multiply this equation by u. + +By multiplying this equation +by a u from the right, + +I will write first this +term. ih dU dt of t t0 + +is equal to H of t U of t t0. + +So I multiplied this +equation by u from the right. + +This operator is unitary, +so u dagger u is one. + +That's why this equation +cleaned up to this. + +Now there's no confusion +really here with derivatives, + +so I might this well write +them with normal derivatives. + +So I'll write this +equation as d dt of U t t0 + +is equal to H of t U of t t0. + +You should be able to +look at that equation + +and say I see the +Schrodinger equation there. + +How? + +Imagine that you have a psi +of t0 here, and you put it in. + +Then the right hand side becomes +h and t acting on psi of t. + +And on the left hand +side, this psi of t0 + +can be put inside the derivative +because it doesn't depend on t. + +Therefore this becomes +ih bar d dt of psi of t. + +So the Schrodinger +equation is there. + +OK so now let's solve this. + +We'll go through three cases. + +Case one, h is time independent. + +So we're doing this +sort of quickly. + +So H of t is really H like that. + +No explicit time +dependence there. + +So what do we have? + +ih bar. + +Let's write dU dt +is equal H times U. + +And we tried to write a +solution of the form U + +use equal to e to the minus +iHt over h bar times U0. + +Does that work? + +Well, we can think du dt and ih. + +So we get ih. + +When I take dU dt, I have to +differentiate this exponential. + +And now in this exponential, +this full operator H is there. + +But we are differentiating +with respect to time. + +And H doesn't depend +on time, so this is not + +a very difficult situation. + +You could imagine the +power series expansion. + +And H, as far as +this derivative goes, + +is like if it would +be even a number. + +It wouldn't make any +difference if it's an operator. + +So the derivative with +respect to time of this thing + +is minus iH over h times +the same exponential. + +Moreover, the position +of this h could be here, + +or it could be to the right. + +It cannot be to the +right of U0 though, + +because this is a matrix, a +constant matrix that we've put + +in here as a possible thing +for boundary condition. + +So so far we've taken +this derivative, + +and then i's cancel, the h +bar cancels, and you get H. + +But this whole +thing is, again, U. + +So the equation has been solved. + +So try this. + +And it works. + +So having this solution +we can write, for example, + +that U of t t0 is going +to be e to the minus + +iHt over h bar, some +constant matrix. + +When t is equal to t0, this +matrix becomes the unit matrix. + +So this is e to the minus +iHt0 over h bar times U0. + +And therefore from +here, U0 is the inverse + +of this matrix, which is nothing +else but e to the iHt0 over h + +bar. + +So I can substitute back +here what U0 is and finally + +obtain U of t t0 is e to the +minus iH over h bar t minus t0. + +And this is for h +time independent. + +And that's our solution. + +There's very little +to add to this. + +We discussed that in +recitation on Thursday. + +This unitary operator +you've been seeing that + +from the beginning of +the course in some sense, + +that you evolve +energy eigenstate. + +If this acts on any +energy eigenstate, + +h is an energy-- if you act +here on an energy eigenstate, + +the energy eigenstate is an +eigenstate precisely for H, + +you can put just +the number here. + +That is e to the, say, +alpha h on a state psi + +n is equal to e to the +alpha en psi n if h on psi n + +is equal to en on psi n. + +So the function of an operator +acting on an eigenstate + +is just the function +evaluated at the eigenvalue. + +So this is a rule that you've +been using a really long time. + +OK, so when h is time +independent, that's what it is. + +How about when h has a +little time dependence? + +What do I call a +little time dependence? + +A little time dependence +is an idea, the sign + +to make it possible for +you to solve the equation, + +even though it has +some time dependence. + +So you could have Hamiltonians +that are time dependent, + +but still have a +simplifying virtue. + +So H of t is time dependent. + +But assume that H at t1 and h +at t2 commute for all t1 and t2. + +So what could that be? + +For example, you know that the +particle in a magnetic field, + +the spin in a magnetic field +is minus gamma B dot the spin. + +And you could have a time +dependent magnetic field, B + +of t times the spin. + +I'm not sure this is the +constant gamma that they + +usually call gamma, +but it may be. + +Now then if the magnetic field +is time dependent, but imagine + +its direction is +not time dependent. + +So if its direction is not time +dependent, then, for example, + +you would have here minus +gamma Bz of t times Sz. + +And the Hamiltonian at +different times commute + +because Sz commutes with itself, +and the fact that it's time + +independent doesn't +make it fail to commute. + +So if you have a magnetic field +that is fixed in one direction + +but change in time, you +can have a situation where + +your Hamiltonian +is time dependent, + +but still at different +times it commutes. + +And you will discuss such +case because it's interesting. + +But later on as we do +nuclear magnetic resonance, + +we will have the +more interesting case + +in which a magnetic field +rotates and therefore it's + +not that simple. + +So what happens if you have a +time dependent Hamiltonian that + +actually commutes? + +Well, the claim +is that U of t t0 + +is given by a natural extension +of what we had before. + +You would want to put +exponential of minus iHt, + +but the reason this worked +was because the derivative + +with respect to time brought +down an iH over h bar. + +So one way to fix this is to +put t t0 H of t prime dt prime. + +So this is an +answer to try this. + +Look at this. + +If the Hamiltonian were +to be time independent, + +you could take it out. + +And then you would +get t minus t0. + +That brings you back to this +case, so this looks reasonable. + +So let me call this +quantity R of t. + +And then you notice +that R dot of t, + +the derivative of this +quantity with respect to time. + +Well, when you differentiate +an integral the upper argument, + +you get just the +integrand evaluated + +at the time represented +by the upper argument + +of the upper limit +of integration. + +So this is H of t. + +And now here comes +a crucial point. + +You're trying to differentiate. + +This U is really e +to the R. And you're + +trying to differentiate to see +if the equation holds dU dt. + +So what is the dU dt? + +Would be d dt of 1 plus R +plus RR plus 1 3 factor RRR. + +And now what happens? + +You differentiate here, and +the first term is R dot. + +Here You, would have one +half R dot R plus R R dot. + +And then 1 over 3 factorial, +but three factors. + +R dot RR plus R R +dot R plus RR R dot. + +But here is the +claim R dot commutes + +with R. Claim R +dot and R commute. + +Why is that? + +Well, R dot depends on +H. And R is an integral + +of H as well, but the H +at different times commute + +anyway, so this must be true. + +There's no place where you +can get a contribution, + +because R dot is like an H, +and here's an integral of H. + +So since the Hamiltonians +are assumed to commute, + +R dot commutes with +R. And this becomes + +like a normal derivative of +an exponential in which you + +can move the R dot to +the left everywhere. + +And you're differentiating +the usual thing. + +So this is R dot and times +the exponential of R. + +So actually that +means that we've + +got pretty much our answer, +because R dot is minus + +i over h bar H of t. + +And e to the R is U, +so we got dU dt equals + +this, which is the +same as this equation. + +The only reason a derivative +with respect to time will not + +give the usual thing is if +R and R dot fail to commute, + +and they don't. + +So you could put the R dot here. + +You can put R dot +on the other side, + +because it commutes with +R, but it's better here. + +And therefore you've got +this very nice solution. + +So the solution is not that bad. + +Now finally, I want to discuss +for a second the general case. + +So that's case-- there was a +1, a 2, a 3 H of t general. + +What can you do? + +Well, if H of t is +general, there's + +not too much you can do. + +You can write +something that will + +get you started doing +things, but it's not + +obviously terribly useful. + +But it's interesting +anyway that there's + +a way to write something +that makes sense. + +So here it is. + +U of t and t0. + +I'll write the answer +and explain how it looks, + +and then you will +see that it's OK. + +It's interesting. + +But it probably is not +the most practical way + +you can solve this problem. + +So here it is. + +There's an acronym +for this thing. + +T it's called the time +ordered exponential. + +This operator does something +to the exponential function. + +So it's a definition. + +So I have to say what +this time ordered + +exponential is, and +it's the following. + +You take the exponential +and just begin to expand. + +So 1 minus i over +h bar-- or I'll + +put like this, plus minus +i over h bar integral + +from t0 to t of dt1 H of t1. + +So far, so good. + +I've just expanded this. + +Now if I would +continue expanding, + +I would get something that +doesn't provide the solution. + +You see, this thing +is the solution + +when the Hamiltonian at +different times commute. + +So it's unlikely to +be the solution when + +they don't commute. + +In fact, it's not the solution. + +So what is the next term here? + +The next term is you +think of the exponential + +as you would expand as usual. + +So you will have here plus one +half of this thing squared. + +So I will put something and then +erase it, so maybe don't copy. + +One half minus i +over h bar squared. + +And you would say, well, t0 +to t dt prime H of t prime. + +t0 to t dt double prime +H of double prime. + +Well, that would be +just an exponential. + +So what is a time +ordered exponential? + +You erase the one half. + +And then for notation +call this t1 and t1. + +And then the next integral +do it only up to time t1, + +and call this t2. + +So t1 will always +be greater than t2, + +because t2 is integrated +from t0 to t1. + +And as you integrate here over +the various t1's, you just + +integrate up to that value. + +So you're doing less +of the full integral + +then you should be +doing, and that's + +why the factor of one +half has disappeared. + +This can be continued. + +I can write the next one would +be minus i over h bar cubed + +integral t0 to t H of t1 +integral t0 to t1 dt2 H of t2. + +And then they next +integral goes up to t2. + +So t0 to t2 dt3 H of t3. + +Anyway, that's a time +ordered exponential. + +And I leave it to you to +take the time derivative, + +at least to see that the first +few terms are working exactly + +the way they should. + +That is, if you take a +time derivative of this, + +you will get H times that thing. + +So since it's a +power series, you + +will differentiate +the first term, + +and you will get +the right thing. + +Then the second term and you +will start getting everything + +that you need. + +So it's a funny object. + +It's reassuring that +something like this success, + +but in general, you +would want to be + +able to do all these +integrals and to sum them up. + +And in general, +it's not that easy. + +So it's of limited usefulness. + +It's a nice thing +that you can write it, + +and you can prove things +about it and manipulate it. + +But when you have a +practical problem, + +generally that's not +the way you solve it. + +In fact, when we will discuss +the rotating magnetic fields + +for magnetic resonance, we +will not solve it in this way. + +We will try to figure out +the solution some other way. + +But in terms of +completeness, it's + +kind of pretty in +that you go from + +the exponential to the +time ordered exponential. + +And I think you'll see +more of this in 806. + +So that's basically +our solution for H + +and for the unitary +operator U in terms of H. + +And what we're +going to do now is + +turn to the Heisenberg +picture of quantum mechanics. + +Yes, questions? + +AUDIENCE: Why does +R dot [INAUDIBLE]? + +PROFESSOR: Because that's +really a property of integrals. + +d dx integral up +to x from x0 g of x + +prime dx prime is +just equal to g of x. + +This is a constant +here, so you're not + +varying the integral +over in this limit. + +So if this limit would +also be x dependent, + +you would get +another contribution, + +but we only get the +contribution from here. + +What's really happening +is you're integrating up + +to x, then up to x plus +epsilon subtracting, + +so you pick up the value of the +function of the upper limit. + +Yes? + +AUDIENCE: So what happens to +the T that was pre factor? + +PROFESSOR: What +happens to this T? + +AUDIENCE: Yeah, what happens? + +PROFESSOR: That's just a symbol. + +It says time order the +following exponential. + +So at this stage, +this is a definition + +of what t on an +exponential means. + +AUDIENCE: OK. + +PROFESSOR: It's not-- +let me say T is not + +an operator in the usual +sense of quantum mechanics + +or anything like that. + +It's an instruction. + +Whenever you have an +exponential of this form, + +the time ordered +exponential is this series + +that we've written down. + +It's just a definition. + +Yes? + +AUDIENCE: So when we have +operators in differential + +equations, do we +still get [INAUDIBLE]? + +PROFESSOR: If we have what? + +AUDIENCE: If we have operators +in differential equations + +do we still get unique +[INAUDIBLE] solutions? + +PROFESSOR: Yes, pretty much. + +Because at the end +of the day, this + +is a first order matrix +differential equation. + +So it's a collection of first +order differential equations + +for every element of a matrix. + +It's pretty much the +same as you have before. + +If you know the operator +at any time, initial time, + +with the differential +equation you know the operator + +at a little bit time later. + +So the operator is +completely determined + +if you know it initially and +the differential equation. + +So I think it's +completely analogous. + +It's just that it's +harder to solve. + +Nothing else. + +One last question. + +AUDIENCE: So let's say +that we can somehow + +fly in this unitary operator, +and then we have a differential + +equation, and we +somehow, let's say, get + +a wave function out of it. + +What is the interpretation +of that wave function? + +PROFESSOR: Well, +it's not that we + +get the wave +function out of this. + +What really is +happening is that you + +have learned how to calculate +this operator given H. + +And therefore now you're able +to evolve any wave function. + +So you have solved +the dynamical system. + +If somebody tells you a time +equals 0, your system is here, + +you can now calculate where it's +going to be at the later time. + +So that's really all +you have achieved. + +You now know the solution. + +When you're doing +mechanics and they ask you + +for an orbit problem, +they say at this time + +the planet is here. + +What are you supposed to find? + +x is a function of time. + +You now know how it's +going to develop. + +You've solved +equations of motion. + +Here it's the same. + +You know the wave +function of time equals. + +If you know it at any time, +you've solved problem. + +OK, so Heisenberg picture +of quantum mechanics. + +Heisenberg picture. + +So basically the +Heisenberg picture + +exists thanks to the existence +of the Schrodinger picture. + +Heisenberg picture +of quantum mechanics + +is not something +that you necessarily + +invent from the beginning. + +The way we think of it is we +assume there is a Schrodinger + +picture that we've developed in +which we have operators like x, + +p, spin, Hamiltonians, +and wave functions. + +And then we are going to +define a new way of thinking + +about this, which is +called the Heisenberg + +picture of the +quantum mechanics. + +So it all begins by considering +a Schrodinger operator + +As hat, which is s +is for Schrodinger. + +And the motivation comes +from expectation values. + +Suppose you have time +dependent states, + +in fact, matrix elements. + +One time dependent state alpha +of t, one time dependent state + +beta of t. + +Two independent time +dependent states. + +So you could ask what is +the matrix element of A + +between these two time dependent +states, a matrix element. + +But then, armed with +our unitary operator, + +we know that As is here, and +this state beta at time t + +is equal to U of t +comma 0 beta at time 0. + +And alpha t is equal to +alpha at 0 U dagger of t0. + +So the states have +time dependence. + +But the time +dependence has already + +been found, say, in principle, +if you know U dagger. + +And then you can speak about the +time dependent matrix elements + +of the operator As +or the matrix element + +of this time dependent +operator between the time + +equals 0 states. + +And this operator is +sufficiently important + +that this operator is +called the Heisenberg + +version of the operator s. + +Has time dependence, and it's +defined by this equation. + +So whenever you have +Schrodinger operator, + +whether it be time dependent +or time independent, + +whatever the +Schrodinger operator is, + +I have now a +definition of what I + +will call the +Heisenberg operator. + +And it is obtained by acting +with a unitary operator, U. + +And operators always act +on operators from the left + +and from the right. + +That's something that operators +act on states from the left. + +They act on the state. + +But operators act on +operator from the left + +and from the right, +as you see them here, + +is the natural, ideal +thing to happen. + +If you have an operator that's +on another from the right only + +or from the left +only, I think you + +have grounds to be +suspicious that maybe you're + +not doing things right. + +So this is the +Heisenberg operator. + +And as you can +imagine, there's a lot + +of things to be said +about this operator. + +So let's begin with a remark. + +Are there questions about +this Heisenberg operator. + +Yes? + +AUDIENCE: Do we know anything +about the Schrodinger operator? + +PROFESSOR: You have +to speak louder. + +AUDIENCE: Is the +Schrodinger operator + +related to the +Hamiltonian [INAUDIBLE]? + +PROFESSOR: Any +Schrodinger operator, + +this could be the +Hamiltonian, this + +could be x hat, it +could be Sz, could + +be any of the +operators you know. + +All the operators you know +are Schrodinger operators. + +So remarks, comments. + +OK, comments. + +One, at t equals 0 +A Heisenberg becomes + +identical to A +Schrodinger at t equals 0. + +So look why. + +Because when t is equal to 0, +U of t-- of 0 0 is the operator + +propagates no state, so +it's equal to the identity. + +So this is a wonderful +relation that + +tell us you that time equals +0 the two operators are really + +the same. + +And another simple remark. + +If you have the unit operator +in the Schrodinger picture, + +what is the unit operator +in the Heisenberg picture? + +Well, it would be U +t 0 dagger 1 U t 0. + +But 1 doesn't matter. + +U dagger with U is 1. + +This is a 1 Schrodinger, +and therefore it's + +the same operator. + +So the unit operator +is the same. + +It just doesn't +change whatsoever. + +OK, so that's good. + +But now this is something +interesting also happens. + +Suppose you have +Schrodinger operator + +C that is equal to the product +of A with B, two Schrodingers. + +If I try to figure +out what is CH, + +I would put U dagger-- avoid +all the letters, the t 0. + +It's supposed to be t 0. + +Cs U. But that's equal +U dagger As Bs U. + +But now, in between +the two operators, + +you can put a U U dagger, +which is equal to 1. + +So As U U dagger +Bs U. And then you + +see why this is really nice. + +Because what do you get is +that C Heisenberg is just + +A Heisenberg times B Heisenberg. + +So if you have C Schrodinger +equals A Schrodinger, B + +Schrodinger, C Heisenberg is +A Heisenberg B Heisenberg. + +So there's a nice correspondence +between those operators. + +Also you can do is +for commutators. + +So you don't have to +worry about this thing. + +So for example, if A +Schrodinger with B Schrodinger + +is equal to C Schrodinger, +then by doing exactly + +the same things, you see that +A Heisenberg with B Heisenberg + +would be the commutator +equal to C Heisenberg. + +Yes? + +AUDIENCE: That argument +for the identity operators + +being the same in both pictures. + +If the Hamiltonian +is time independent, + +does that work for any +operator that commutes + +with the Hamiltonian? + +PROFESSOR: Hamiltonian +is [INAUDIBLE]. + +AUDIENCE: Because then you +can push the operator just + +through the exponential +of the Hamiltonian. + +PROFESSOR: Yeah, we'll +see things like that. + +We could discuss that +maybe a little later. + +But there are some cases, +as we will see immediately, + +in which some operators are +the same in the two pictures. + +So basically operators that +commute with the Hamiltonian + +as you say, since U +involves the Hamiltonian, + +and this is the +Hamiltonian, if the operator + +commutes with the Hamiltonian +and you can move them across, + +then they are the same. + +So I think it's definitely true. + +So we will have an +interesting question, + +in fact, whether the +Heisenberg Hamiltonian is + +equal to the +Schrodinger Hamiltonian, + +and we'll answer that very soon. + +So the one example that here I +think you should keep in mind + +is this one. + +You know this is true. + +So what do you knowing +the Heisenberg picture? + +That X Heisenberg of t times +P Heisenberg of t commutator + +is equal to the Heisenberg +version of this. + +But here was the unit operator. + +And therefore this is just ih +bar times the unit operator + +again, because +the units operator + +is the same in all pictures. + +So these commutation relation +is true for any Heisenberg + +operator. + +Whatever commutation relation +you have of Schrodinger, + +it's true for +Heisenberg as well. + +OK, so then let's talk +about Hamiltonians. + +Three, Hamiltonians. + +So Heisenberg +Hamiltonian by definition + +would be equal to U dagger +t 0 Schrodinger Hamiltonian + +times U of t 0. + +So if the Schrodinger +Hamiltonian-- actually, + +if Hs at t1 commutes +units with Hs at t2, + +the Schrodinger Hamiltonian +is such that for all t1 and t2 + +they commute with each other. + +Remember, if that is the +case, the unitary operator + +is any way built +by an exponential. + +It's this one. + +And the Schrodinger +Hamiltonians commute. + +So as was asked in +the question before, + +this thing commutes +with that, and you + +get that they are the same. + +So if this is happening, the +two Hamiltonians are identical. + +And we'll have the +chance to check + +this today in a nice example. + +So I will write in this +as saying the Heisenberg + +Hamiltonian as a +function of time + +then is equal to the +Schrodinger Hamiltonian + +as a function of time. + +And this goes Hs of t1 +and Hs of t2 commute. + +OK, now I want you +to notice this thing. + +Suppose the Hs of t is some +Hs of x,p, and t, for example. + +OK, now you come and +turn it into Heisenberg + +by putting a U dagger from the +left and a U from the right. + +What will that do? + +It will put U dagger from the +left, U dagger on the right. + +And then it will start +working it's way inside, + +and any x that it will find +will turn into a Heisenberg x. + +Any p will turn +into Heisenberg p. + +Imagine, for example, +any Hamiltonian + +is some function of x. + +It has an x squared. + +Well the U dagger +and U come and turn + +this into x Heisenberg squared. + +So what I claim here happens +is that H Heisenberg of t + +is equal to U dagger H +Schrodinger of x, p, t, U. + +And therefore this +becomes H Schrodinger of x + +Heisenberg of t, P +Heisenberg of t, and t. + +So here is what the +Heisenberg Hamiltonian is. + +It's the Schrodinger Hamiltonian +where X's, and P's, or spins + +and everything has +become Heisenberg. + +So the equality of +the two Hamiltonians + +is a very funny condition on +the Schrodinger Hamiltonian, + +because this is supposed to +be equal to the Schrodinger + +Hamiltonian, which +is of x, p, and t. + +So you have a function +of x, p, and t. + +And you put X +Heisenberg P Heisenberg, + +and somehow the whole +thing is the same. + +So this is something very +useful and we'll need it. + +One more comment, +expectation values. + +So this is three. + +Comment number four on +expectation values, which + +is something you've already-- +it's sort of the way + +we began the discussion and +wanted to make sure it's clear. + +So four, expectation values. + +So we started with this +with alpha and beta, + +two arbitrary states, +matrix elements. + +Take them equal and to +be equal to psi of t. + +So you would have psi +t As psi t is, in fact, + +equal to psi 0 A +Heisenberg psi 0. + +Now that is a key equation. + +You know you're doing +expectation value at any given + +time of a Schrodinger operator, +turn it into Heisenberg + +and work at time equals 0. + +It simplifies life tremendously. + +Now this is the key identity. + +It's the way we motivated +everything in a way. + +And it's written in +a way that maybe it's + +a little too schematic, +but we write it this way. + +We just say the +expectation value + +of As is equal to the +expectation value of AH. + +And this, well, we +save time like that, + +but you have to +know what you mean. + +When you're computing +the expectation + +value for a +Schrodinger operator, + +you're using time +dependent states. + +When you're computing +the expectation + +value of the +Heisenberg operator, + +you're using the time equals +0 version of the states, + +but they are the same. + +So we say that the +Schrodinger expectation value + +is equal to the Heisenberg +expectation value. + +We right it in the bottom, +but we mean the top equation. + +And we use it that way. + +So the Heisenberg +operators, at this moment, + +are a little mysterious. + +They're supposed to be +given by this formula, + +but we've seen that +calculating U can be difficult. + +So calculating the +Heisenberg operator + +can be difficult sometimes. + +So what we try to do +in order to simplify + +that is find an equation that +is satisfied by the Heisenberg + +operator, a time +derivative equation. + +So let's try to find +an equation that + +is satisfied by the Heisenberg +operator rather than a formula. + +You'll say, well, +this is better. + +But the fact is that seldom you +know U. And even if you know U, + +you have to do this +simplification, which is hard. + +So finding a differential +equation for the operator + +is useful. + +So differential equation +for Heisenberg operators. + +So what do we want to do? + +We want to calculate ih bar d +dt of the Heisenberg operator. + +And so what do we get? + +Well, we have several things. + +Remember, the +Schrodinger operator + +can have a bit of +time dependence. + +The time dependence would be +an explicit time dependence. + +So let's take the time +derivative of all this. + +So you would have three terms. + +ih bar dU dagger dt +As U plus U dagger + +As dU dt plus-- with an ih bar-- +U dagger ih bar dAs minus dt. + +dAs dt and U. + +Well, you have these equations. + +Those were the +Schrodinger equations + +we started with today. + +The derivatives of U, or +the derivatives of U dagger. + +so what did we have? + +Well, we have that ih bar dU dt +was HU-- H Schrodinger times U. + +And therefore ih +bar dU dagger dt. + +I take the dagger of this. + +I would get a minus sign. + +I would put it on +the other side. + +Is equal to U dagger +Hs with a minus here. + +And all the U's are +U's of t and t0. + +I ran out of this thick chalk. + +So we'll continue +with thin chalk. + +All right, so we are here. + +We wrote the time +derivative, and we + +have three terms to work out. + +So what are they? + +Well we have this +thing, ih bar this. + +So let's write it. ih bar d +d dt of As-- of A Heisenberg, + +I'm sorry-- Is equal to that +term is minus U dagger Hs A + +Schrodinger U. + +The next term plus ih +bar dU dt on the right. + +So we have plus U dagger +As Hs dU dt, so U. Well, + +that's not bad. + +It's actually quite nice. + +And then the last term, which +I have very little to say, + +because in general, this +is a derivative of a time + +dependent operator. + +Partial with respect to time, +it would be 0 if As depends, + +just say, on X, on P, on +Sx, or any of those things, + +has to have a particular t. + +So I will just leave this as +plus ih bar dAs dt Heisenberg. + +The Heisenberg version +of this operator using + +the definition that anything, +any operator that we have + +a U dagger in front, +a U to the right, + +is the Heisenberg +version of the operator. + +So I think I'm doing all +right with this equation. + +So what did we have? + +Here it is. ih bar d dt +of A Heisenberg of t. + +And now comes the +nice thing, of course. + +This thing, look at it. + +U dagger U. This +turns everything here + +into Heisenberg. + +H Heisenberg, A Heisenberg. + +Here you have A Heisenberg H +Heisenberg, and what you got + +is the commutator between them. + +So this thing is A Heisenberg +commutator with H Heisenberg. + +That whole thing. + +And then you have plus +ih bar dAs dt Heisenberg. + +So that is the Heisenberg +equation of motion. + +That is how you can calculate +a Heisenberg operator + +if you want. + +You tried to solve this +differential equation, + +and many times +that's the simplest + +way to calculate the +Heisenberg operator. + +So there you go. + +It's a pretty +important equation. + +So let's consider +particular cases immediately + +to just get some intuition. + +So remarks. + +Suppose As has no +explicit time dependence. + +So basically, there's +no explicit t, + +and therefore this +derivative goes away. + +So the equation becomes +ih bar dAh, of course, + +dt is equal to Ah +Heisenberg sub h of t. + +And you know the +Heisenberg operator + +is supposed to be simpler. + +Simple. + +If the Schrodinger operator +is time independent, + +it's identical to the +Schrodinger Hamiltonian. + +Even if the Schrodinger +operator has time dependence, + +but they commute, this +will become the Schrodinger + +Hamiltonian. + +But we can leave it like that. + +It's a nice thing anyway. + +Time dependence of +expectation value. + +So let me do a little remark on +time dependence of expectation + +values. + +So suppose you have the usual +thing that you want to compute. + +How does the expectation value +of a Schrodinger operator + +depend on time? + +You're faced with that +expectation value of As, + +and it changes in +time, and you want + +to know how you +can compute that. + +Well, you first say, +OK, ih bar d dt. + +But this thing is nothing but +psi 0 A Heisenberg of t psi 0. + +Now I can let the +derivative go in. + +So this becomes psi 0 +ih bar dAh dt psi 0. + +And using this, assuming that +A is still no time dependence, + +A has no explicit +time dependence, + +then you can use +just this equation, + +which give you +psi 0 Ah Hh psi 0. + +So all in all, what +have you gotten? + +You've gotten a rather simple +thing, the time derivative + +of the expectation values. + +So ih bar d dt. + +And now I write +the left hand side + +as just expectation value +of H Heisenberg of t. + +And on the left hand side has +to the A Schrodinger expectation + +value, but we call +those expectation values + +the same thing as a +Heisenberg expectation value. + +So this thing becomes the right +hand side is the expectation + +value of A Heisenberg +H Heisenberg like that. + +And just the way we say +that Heisenberg expectation + +values are the same as +Schrodinger expectation values, + +you could as well +write, if you prefer, + +as d dt of A Schrodinger +is equal to the expectation + +value of A Schrodinger +with H Schrodinger. + +It's really the same equation. + +This equation we derived +a couple of lectures ago. + +And now we know that +the expectation values + +of Schrodinger operators are +the same as the expectation + +value of their +Heisenberg counterparts, + +except that the states are +taking up time equals 0. + +So you can use either +form of this equation. + +The bottom one is one +that you've already seen. + +The top one now looks almost +obvious from the bottom one, + +but it really took +quite a bit to get it. + +One last comment +on these operators. + +How about conserved operators? + +What are those things? + +A time independent As +is set to be conserved + +if it commutes with a +Schrodinger Hamiltonian. + +If As commutes with As equals 0. + +Now you know that if As with +Hs is 0, Ah with Hh is 0, + +because the map between +Heisenberg and Schrodinger + +pictures is a commutator that +is valued at the Schrodinger + +picture is valued in the +Heisenberg picture by putting + +H's. + +So what you realize from +this is that this thing, + +this implies Ah +commutes with Hh. + +And therefore by +point 1, by 1, you + +have to dAh dt is equal to 0. + +And this is nice, actually. + +The Heisenberg operator is +actually time independent. + +It just doesn't depend on time. + +So a Schrodinger operator, +it's a funny operator. + +It doesn't have time in there. + +It has X's, P's, spins, and +you don't know in general, + +if it's time independent +in the sense of conserve + +of expectation values. + +But whenever As +commutes with Hs, + +well, the expectation +values don't change in time. + +But as you know, this +d dt can be brought in, + +because the states are +not time dependent. + +So the fact that this +is 0 means the operator, + +Heisenberg operator, is +really time independent. + +Whenever you have a +Schrodinger operator, has no t, + +the Heisenberg one +can have a lot of t. + +But if the operator +is conserved, + +then the Heisenberg operator +will have no t's after all. + +It will really be conserved. + +So let's use our last 10 +minutes to do an example + +and illustrate much of this. + +In the notes, there +will be three examples. + +I will do just one in lecture. + +You can do the other ones +in recitation next week. + +There's no need really +that you study these things + +at this moment. + +Just try to get whatever you +can now from the lecture, + +and next week you'll +go back to this. + +So the example is the +harmonic oscillator. + +And it will illustrate the +ideas very nicely, I think. + +The Schrodinger +Hamiltonian is p squared + +over 2m plus 1/2 m omega +squared x hat squared. + +OK, I could put x Schrodinger +and p Schrodinger, but that + +would be just far +too much. x and p + +are the operators +you've always known. + +They are Schrodinger operators. + +So we leave them like that. + +Now I have to write the +Heisenberg Hamiltonian. + +Well, what is the +Heisenberg Hamiltonian? + +yes? + +AUDIENCE: It's identical. + +PROFESSOR: Sorry? + +AUDIENCE: It's identical. + +PROFESSOR: Identical, yes. + +But I will leave that +for a little later. + +I will just assume, +well, I'm supposed + +to do U dagger U. +As you said, this + +is a time independent +Hamiltonian. + +It better be the +same, but it will + +be clearer if we now write +what it should be in general. + +Have a U dagger and +a U from the right. + +They come here, and they turn +this into P Heisenberg over 2m + +plus 1/2 m omega +squared x Heisenberg. + +OK, that's your +Heisenberg Hamiltonian. + +And we will check, in fact, +that it's time independent. + +So how about the operators X +Heisenberg and P Heisenberg. + +What are they? + +Well, I don't know +how to get them, + +unless I do this +sort of U thing. + +That doesn't look too bad +but certainly would be messy. + +You would have to do +an exponential of e + +to the minus iHt over +t with the x operator + +and another exponential. + +Sounds a little complicated. + +So let's do it the way the +equations of the Heisenberg + +operators tell you. + +Well, X and P are time +independent Schrodinger + +operators, so that equation +that I boxed holds. + +So ih dx Heisenberg +dt is nothing else + +than X Heisenberg commuted +with H Heisenberg. + +OK, can we do that commutator? + +Yes. + +Because X Heisenberg, +as you remember, + +just commutes with P Heisenberg. + +So instead of the +Hamiltonian, you can put this. + +This is X Heisenberg P +Heisenberg squared over 2m. + +OK well, X Heisenberg +P Heisenberg + +is like you had X and P. +So what is this commutator? + +You probably know it by now. + +You act with this +and these two p. + +So it acts on one, acts on the +other, gives the same on each. + +So you get P Heisenberg times +the commutator of X and P, + +which is ih bar +times a factor of 2. + +So we could put hats. + +Better maybe. + +And then what do we get? + +The ih there and ih cancels. + +And we get some +nice equation that + +says dX Heisenberg dt is +1 over m P Heisenberg. + +Well, it actually +looks like an equation + +in classical mechanics. + +dx dt is P over m. + +So that's a good thing about the +Heisenberg equations of motion. + +They look like +ordinary equations + +for dynamical variables. + +Well, we've got this one. + +Let's get P. Well, we didn't +get the operator still, + +but we got an equation. + +So how about P dP dt. + +So ih dP Heisenberg dt would be +P Heisenberg with H Heisenberg. + +And this time only the +potential term in here matters. + +So it's P Heisenberg +with 1/2 m omega + +squared X Heisenberg squared. + +So what do we? + +We get 1/2 m omega squared. + +Then we get again a factor of 2. + +Then we get one left over Xh. + +And then a P with Xh, +which is a minus ih bar. + +So the ih bars cancel, and we +get dPh dt is equal to-- the h + +bar cancelled-- m +omega squared Xh. + +Minus m. + +All right, so these are our +Heisenberg equations of motion. + +So how do we solve for them now? + +Well, you sort of have +to try the kind of things + +that you would do classically. + +Take a second derivative +of this equation. + +d second Xh dt squared +would be 1 over m dPh dt. + +And the dPh dt +would be [INAUDIBLE] + +1 over m times minus +m omega squared Xh. + +So d second Xh dt squared is +equal to minus omega squared + +Xh, exactly the +equation of motion + +of a harmonic oscillator. + +It's really absolutely +nice that you + +recover those equations +that you had before, + +except that now you're +talking operators. + +And it's going to simplify your +life quite dramatically when + +you try to use these +operators, because, in a sense, + +solving for the time +dependent Heisenberg operators + +is the same as finding the +time evolution of all states. + +This time the operators +change, and you + +will know what they change like. + +So you have this. + +And then you write Xh is equal +to A cosine omega t plus B + +sine omega t where A +and B are some time + +independent operators. + +So Xh of t, well, +that's a solution. + +How about what is P? + +Ph of t would be m dX m dx dt. + +So you get minus m omega +sine omega tA plus m omega + +cosine omega tB. + +OK, so that's it. + +That is the most +general solution. + +But it still doesn't look like +what you would want, does it? + +No, because you haven't used +the time equals 0 conditions. + +At time equals 0, the +Heisenberg operators + +are identical they to the +Schrodinger operators. + +So at t equals 0, +Xh of t becomes A, + +but that must be X hat, +the Schrodinger operator. + +And at t equals +0, Ph of t becomes + +equal to this is 0 +m omega B. And that + +must be equal to +the P hat operator. + +So actually we have already +now A and B. So B from here + +is P hat over m omega. + +And therefore Xh +of t is equal to A, + +which is X hat cosine +omega t plus B, which + +is P hat over m +omega sine omega t. + +An Ph of t is here. + +A is-- Ph of t is m omega +B, which is [INAUDIBLE] P. + +So it's P hat cosine +omega t minus m omega X + +hat sine omega t. + +So let's see. + +I hope I didn't make mistakes. + +P hat minus m omega +X hat sine omega t. + +Yep, this is correct. + +This is your whole solution +for the Heisenberg operators. + +So any expectation value +of any power of X and P + +that you will want to +find its time dependence, + +just put those +Heisenberg operators, + +and you will calculate things +with states at time equals 0. + +It will become very easy. + +So the last thing +I want to do is + +complete the promise +that we had about what + +is the Heisenberg Hamiltonian. + +Well, we had the Heisenberg +Hamiltonian there. + +And now we know the +Heisenberg operators + +in terms of the Schrodinger one. + +So Hh of t is equal to +Ph-- 1/2m Ph squared. + +So I have P hat cosine omega t +minus m omega X hat sine omega + +t squared plus 1/2 m +omega squared Xh squared. + +So X hat cosine +omega t plus P hat + +over m omega sine +omega t squared. + +So that's what the +Heisenberg Hamiltonian is. + +So let's simplify this. + +Well, let's square these things. + +You have 1/2m cosine squared +omega t P hat squared. + +Let's do the square of this one. + +You would have +plus 1/2m m squared + +omega squared sine +squared omega t X squared. + +And then we have +the cross product, + +which would be plus-- +or actually minus 1/2m. + +The product of these two things. + +m omega sine omega +t cosine omega t. + +And you have Px plus XP. + +OK, I squared the first terms. + +Now the second one. + +Well, let's square +the P squared here. + +What do we have? + +1/2 m omega squared +over m squared + +omega squared sine squared +of omega t P squared. + +The x plus 1/2 m +omega squared cosine + +squared omega t X squared. + +And the cross term. + +Plus 1/2 m omega squared over +m omega times cosine omega t + +sine omega t XP plus PX. + +A little bit of work, +but what do we get? + +Well, 1/2 m. + +And here we must +have 1/2 m, correct. + +1/2 m. + +Sine squared omega t P squared. + +So this is equal +1/2 m P squared. + +These one's, hall here you +have 1/2 m omega squared. + +So it's 1/2 m omega +squared cosine and sine + +squared is X hat squared. + +And then here we have +all being over 2. + +And here omega over 2, +same factors, same factors, + +opposite signs. + +Very good. + +Schrodinger Hamiltonian. + +So you confirm that this +theoretical expectation + +is absolutely correct. + +And what's the meaning? + +You have the +Heisenberg Hamiltonian + +written in terms of the +Heisenberg variables. + +But by the time you substitute +these Heisenberg variables in, + +it just becomes identical to +the Schrodinger Hamiltonian. + +All right, so that's +all for today. + +I hope to see in office +hours in the coming days. + +Be here Wednesday 12:30, +maybe 12:25 would be better, + +and we'll see you then. + +[APPLAUSE] \ No newline at end of file